𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, April 18, 2025
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Sat 19 Apr 02:49:29 BST 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/2025/04/18/


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

QmbHjgPAAcGNUG9Sej4vSKhK8DfUYokfFkXLdKwr1JtGJG
QmdLsuRLzrwb58dZaSmJah6oCmNNZ6cW4ick4chqJmHjmY
QmTNR3uqcbMYjPAbbHjBqyNJb3ib8kytQvdFnATzkBFVvo
QmfCHrqMLfMsHXYnQeAvVuNYt91Zw2AmMJ5mx4RqsrWy3b
QmR2rr1yXDANjQBEz2oGtd2UMgy9U37FHdjpUhPfAk7h5z
QmWE6ucdKk9Q1pi6ce3ko9xPWd9Y4BjpLij3W7tJ5TMjG3
QmaoEDiALTYYZdaq3SQ86aQpMwUji1nqCeLbXAoszFRYvJ
QmSTkZUY74BcgbgqS6JKwwNbVnbzY5uqwpgWtYonGJua8s
QmXZcp3rXLYa24pYd7jUu6sPDrhziRCNCok875WLJTLysP
QmUE7nd24kx2soZFbSYKDsb1ik1wpirFTRTBhDTj6w9sjh
QmdKeWBhfnjgQLYU48wto7DdStpXsB5mE1yEEnWcxQ53vu
QmfSnnTnjcAe3YvtRsVgAwUJfpcEk1dM5J5yjJLyv7MxqM
QmQ16CkpxBbMzPZ6wZcuKBUcxH1RZ8uAEhcvdBsPRpVZe9
QmT3gTQRv33wEDtJveL8DiqiacGeRaxEbRFDUyVSJEAvDL
QmTs9qcwghZPs5oBh9qzsu8a11T4s6xHrJjVNyk5miFy3X
Qmdqd6mb8mj27qVvQZRR7sjshrXYYirWm9vRttLkNB5rW6
QmSjY85vxbu9nNFHUMmuK7CxRame2VYuhb523CJaK5zRkj
QmZwah9nZHVvSzbJWEAMxumYDpanFPqTahnqoNP83tuZbx
QmQWSrGfeYwgf6HE9N3742DJrJwq8uNSCUAz469CnuUFGe
QmcgTTyseF5zFd4MLquM4PtJZzkFcBEqaUbqDe4eaUx6Na
QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu


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

⦿ Techrights  -  All Your "Github Projects" Will be Gone One Day (Just Like Skype)

⦿ Techrights  -  Fedora Already Lost Its Soul Under IBM

⦿ Techrights  -  Google News is Dying

⦿ Techrights  -  IRC Proceedings: Thursday, April 17, 2025

⦿ Techrights  -  Microsoft is Still Attacking GNU/Linux and the Net

⦿ Techrights  -  Microsoft's Attack Dogs Have Failed. Now What?

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  "Sayonara" (さよなら), Microsoft

⦿ Techrights  -  Sounds Like IBM is Preparing for Mass Layoffs/Redundancies in Red Hat, Albeit in "PIP" (Performance Improvement Plan) or "Relocation" Clothing

⦿ Techrights  -  To Understand Who's Truly Controlling You Follow the Trail of Censorship (or Self-Censorship)

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2025/04/18/All_Your_Github_Projects_Will_be_Gone_One_Day_Just_Like_Skype.shtml
https://techrights.org/n/2025/04/18/Fedora_Already_Lost_Its_Soul_Under_IBM.shtml
https://techrights.org/n/2025/04/18/Google_News_is_Dying.shtml
https://techrights.org/n/2025/04/18/IRC_Proceedings_Thursday_April_17_2025.shtml
https://techrights.org/n/2025/04/18/Microsoft_is_Still_Attacking_GNU_Linux_and_the_Net.shtml
https://techrights.org/n/2025/04/18/Microsoft_s_Attack_Dogs_Have_Failed_Now_What.shtml
https://techrights.org/n/2025/04/18/Over_at_Tux_Machines.shtml
https://techrights.org/n/2025/04/18/Sayonara_さよなら_Microsoft.shtml
https://techrights.org/n/2025/04/18/Sounds_Like_IBM_is_Preparing_for_Mass_Layoffs_Redundancies_in_R.shtml
https://techrights.org/n/2025/04/18/To_Understand_Who_s_Truly_Controlling_You_Follow_the_Trail_of_C.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2025/04/18/Gemini_Links_18_04_2025_Pinephone_Pro_and_Linux_is_too_Easy.shtml
https://techrights.org/n/2025/04/18/Gemini_Links_18_04_2025_Price_of_Games_and_State_of_Tinylog.shtml
https://techrights.org/n/2025/04/18/Links_18_04_2025_Fentanylware_TikTok_Exodus_Continues_Chinese_W.shtml
https://techrights.org/n/2025/04/18/Links_18_04_2025_Layoffs_at_Microsoft_Infosys_and_Qt_Becoming_I.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 77

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/All_Your_Github_Projects_Will_be_Gone_One_Day_Just_Like_Skype.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/All_Your_Github_Projects_Will_be_Gone_One_Day_Just_Like_Skype.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ All Your "Github Projects" Will be Gone One
Day (Just Like Skype)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025,
updated Apr 18, 2025


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


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


Skype is about_to_be_turned_off_permanently (neither you nor any other company
can host it; Skype is centralised and proprietary) and many people fume because
they had bought Skype "credits" (for international calls) and lost them all.


Skype is an example of what happens when one relies on Microsoft. Never ever
rely on Microsoft. Pay close attention to Microsoft's history and why there's
disdain if not hate.


But there's a bigger lesson somewhere in all this. Why are so many projects/
people/companies eager to outsource their code to Skype's bad_steward, which
brought down Skype from a "market leader" to "something nobody uses anymore"?
Now, do not say "Teams"; that's nonsense, it's not even a comparable thing.
That's like comparing MSN to Skype or comparing MSN to Facebook.


Now, regarding GitHub, it's just a loss leader (losing a ton of money) acquired
by Microsoft because CodePlex failed and forever shut down (most people cannot
even remember it ever existed). Just like Skype, GitHub will go offline one
day. Microsoft can never find a way to make GitHub profitable (nor did the
original owners), hence the mass layoffs and office shutdowns. In terms of
traffic, GitHub has declined, as did LinkedIn (also mass layoffs and office
shutdowns).


GitHub is NOT free. It never was.


If you have code you wish to share and keep, then start learning how to do so
on your own (or find people who can help make it happen). Git isn't difficult
and GitHub_is_an_attack_on_Git,_it's_not_Git. █


    * To_Understand_Who's_Truly_Controlling_You_Follow_the_Trail_of_Censorship_
      (or_Self-Censorship)
    * Microsoft's_Attack_Dogs_Have_Failed._Now_What?


⣿⣿⣿⣿⠟⣋⣭⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠻⢿⣿⣿⣿⣿⣏⣉⡉⣭⠭⣭⣿⣾⣿⣿⣭⣽⣽⣯⣿⣿⣫⣿⣿⣿⣿⣿⣯⣿⣽⣯⣿⣿⣽⣿⣛⣿⣾⣾⣿⠿⣿⣿⣿⣿
⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠀⠀⠀⠀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣯⣯⣁⣭⣭⣭⣭⣤⣬⡩⣭⡌⣽⣿⣯⣽⠉⡽⠿⢽⣿⣿⣿⢩⣩⣭⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⣛⡚⢪⡫⣃⠀⢹⣿⣿⣿⣿⣿⣥⣭⣼⣿⣿⣿⣿⣿⣿⣯⣭⣤⣭⡉⣽⣿⣿⣿⣿⡄⣀⣀⣀⣀⣶⣒⣛⣛⣿⡿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣇⠀⠸⣝⣿⣽⡳⠍⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠹⣛⣿⣿⠿⣿⡷⠰⠶⣿⣿⡿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣫⢶⣮⢹⣽⣿⣻⣿⣿⣿⣿⣦⡐⠤⢼⣷⡄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢉⣳⠞⡉⠀⠀⠀⠀⠀⢠⣨⣶⣥⡘⠇⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣼⣶⡿⠿⠟⢿⣿⠛⠉⠉⠐⠚⠟⠑⠋⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⣰⣿⣿⣿⣿⣿⣿⣦⣠⡅⠁⠉⢿⣿⣿⣿⣷⣾⣶⣴⣂⣾⡿⠃⠀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀
⠀⠉⠀⢸⣯⡿⣛⣭⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣤⣤⣤⢉⣿⣽⣿⡿⠛⣟⣿⣿⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣦⣴⡿⡻⣿⣿⣥⣤⣶⢠⣤⣀
⠀⠀⠀⢸⡧⠙⠋⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠸⣿⣿⣿⢸⣿⢿⣯⣗⣖⣃⣀⠚⣭⣭⣽⠿⣿⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡇⠀⠀⠀⢨⠒⠚⠹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⡝⠀⠀⠀⡇⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⢨⣠⠄⠀⠈⠙⢿⣿⡿⣿⣿⣿⣵⣿⡿⠟⠀⡇⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠛⠋⠹⠌⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣻⡿⠿⠟⠃⠀⠀⠙⠀⠀⠀
⣿⣿⣿⣀⣀⡀⠀⢀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣷⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣿⣿⣿⣿⠿⠿⠭⠭⣿⣿⣟⣛⣿⣻⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⡟⣁⣤⣤⣴⣶⣄⠈⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣛⣛⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡩⣭⣭⣭⣭⣭⣿⣭⣭⣭⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣷⣽⣿⣿⣿⣿⡇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣛⣻⣟⣎⠿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⣻⣿⣿⣿⣿⡿⣫⣭⡻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⠟⠛⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣏⣠⣼⣿⣿⣷⣝⣿⣿⡿⠜⢻⣿⣿⠽⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠛⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⡎⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⠉⠉⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣤⢸⣬⡫⣴⣿⣿⢸⣿⣿⣿⣿⣿⣀⡀⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠘⣿⣿⣿⡟⠉⣿⣿⡿⣿⣿⣯⣷⣿⡿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡻⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤
⣿⡿⠁⠀⠀⠈⠛⠻⠿⡾⠿⠛⠁⠹⣏⣝⣫⡿⣿⡋⠋⢉⠀⣿⣿⣿⣿⣿⡯⢹⡿⣕⡿⡿⣮⢛⣓⣒⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢸⣬⣿⣿⣿⡿⠿⠿⠿⠿⡶⣶⡶
⠛⣥⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠃⢂⣾⣾⣿⣾⡿⠄⣿⣿⣿⣿⣿⠿⣵⢱⣽⣿⣺⣿⣧⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⠙⣿⡿⠩⠍⠥⣠⠀⡄⡈⢫⡅⡒⣴⠰⢸⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⠙⢠⣟⣿⣿⣿⣿⣹⣤⢿⠈⢿⣿⣿⡆⠿⣻⣟⣿⢷⡜⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣤⠛⠋⠁⡆⠇⠟⠄⠧⠃⠀⠂⠃⠃⠒⠀⠈⢉⠉⣉⢙⡛
⠀⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣿⣿⣿⣿⠿⣲⣧⡀⣽⣿⣿⡖⢻⣻⣻⣯⣾⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡫⢩⢠⢠⢀⢲⢢⢲⠀⡆⡆⡀⡎⡇⠯⢸⢹⠀⢀⡇⡻⠈⢸⠂
⠀⠀⠙⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⣹⣿⣿⣤⣿⣿⣿⣿⠿⣿⣛⣬⣿⡿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇⠉⠉⠉⠉⠁⠀⠀⠀⠑⠸⠸⠸⠈⠘⠈⠄⠀⠁⠂⠓⠁⢃⠑⣉⢈⣈⠁⠁⠁⠉⠀⠀
⠀⠀⠀⠀⠈⠙⠿⣏⡇⠃⠀⠀⠀⠀⠘⣿⣿⠏⠀⠙⣿⣿⣿⣿⢧⣵⠫⢿⢿⣟⣣⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢒⡴⢲⡶⣶⣖⣀⣂⣐⣒⣀⣀⠀⢲⢰⢰⠀⣇⠇⡇⡏⣸⢜⠃⠀⡃⣸⢸⢰⠀⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣼⣿⣿⣵⡡⣅⡋⡝⠵⢾⡏⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠉⠚⠫⠿⣻⠿⣿⣿⣿⣘⣘⣚⣤⣋⣼⣡⣥⣭⣬⣬⣵⣮⣶⣦⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠭⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣎⣘⣅⣨⣸⣿⣿⣿⣿⣃⣿⢹⣹⣋⣍⣈⣩⣉⣉⣥⣉⣉⣋⣉⣩⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⢸⣿⣿⣿⢿⢿⡿⢿⢿⣿⣿⣿⣿⣿⣿⢿⠿⢿⠿⡿⠿⢿⡿⣿⣿⣿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡭⢻⠟⢹⢛⡛⡿⢻⣛⣏⠛⠙⡏⡩⡉⡋⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣷⣿⣾⣦⣴⣼⣿⣿⣿⣿⣶⡿⢸⣤⣴⣤⣥⣿⣵⣧⣦⣤⣮⣬⣵⣧⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣛⣿⡿⠿⠿⡿⠿⠿⠿⢿⣿⣿⠿⠿⡿⠿⢿⣿⡿⡿⠿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣳⣧⣶⣷⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣾⣿⣷⣷⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⢛⠟⠛⢿⣿⣿⣿⣿⣿⠛⣿⢻⠻⡛⠟⠛⠛⠛⠛⠛⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⢛⣸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣘⣀⣈⣿⣿⣿⣿⣿⣏⣹⣿⢹⢉⢋⣉⣋⣩⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡻⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⣥⣧⣤⣥⣿⣼⣬⣶⣼⣤⣬⣽⣥⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 187

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/Fedora_Already_Lost_Its_Soul_Under_IBM.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/Fedora_Already_Lost_Its_Soul_Under_IBM.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Fedora Already Lost Its Soul Under
IBM⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025,
updated Apr 18, 2025


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


I am not a stranger to Fedora. I used the first two versions of Fedora. I later
used some more versions of it, but not after 2010. It just gave me too many
problems/trouble (I wrote a lot about it in my personal site back then*).


Fedora used to be very strict compared to many other distros and it had
attracted very bright volunteers.


Now that Fedora has a_new_lead and a_buzzword_direction (Microsoft/IBM hype)
there is also a new release [1, 2, 3], less than two weeks after the
appointment of the new leader, who swims_in_buzzwords.


Fedora is (of course) used to test things before they go to proprietary_RHEL.
More people can see that and since IBM started hiding source code many Fedora
volunteers have jumped ship.


From what we can gather, based on the wiki, the chats and the planet (of
Fedora), not many people are still involved in the project. IBM made cuts. Many
non-staff left over time (or became a lot less involved).


"I used to work at Red Hat and most of the US engineering base is in MA, not in
Raleigh, NC. Raleigh is the HQ so has all of the back office functions and
people from all functions as well but most US based engineers are in the MA
office outside of Boston," somebody wrote hours_ago about this_report_about_IBM
convergence_or_bluewashing ("IBM to combine key division with Red Hat unit").
"The CEO now is Matt Hicks (not Jim Whitehurst who sadly left after the IBM
acquisition) and Matt was the Red Hat engineering leader so was based in MA as
well. I do not know if there will be lay offs, however they are different
product areas of middleware. I am assuming they will integrate where they can.
Many middleware engineers are around the globe."


Critics of the company and of DEI showed_a_recent_message_from_Matt_Hicks: "In
an email to Red Hat (IBM) employees, leaked to The Lunduke Journal, CEO Matt
Hicks outlines where DEl [sic] is to be removed within the company." (Well, the
Fedora_DEI_room_became_more_private and less active about 10 days ago)


Perhaps, like in_Automattic, the threat will be seen ....... or described
...... as whistleblowers, not Microsoft and Windows. █


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Following_Layoffs,_Automattic_Employees_Discover_Leak-
                             Catching_Watermarks⦈_


___


* Ryan, who also used to use Fedora (and wrote a lot about it over the years,
even decades), says in IRC: "I no longer use Fedora on anything and haven't for
a while. It seems that maybe the only distribution actually committed to its
native package manager is Debian, or Arch, and since I already know how to use
Debian and have for over 25 years, it's easier to stick to that, including in
Crostini on my Chromebook, where I could theoretically have as many
distributions as there are space for. Google lets you go off the rails with
Crostini and install whatever you want, but the default and supported
distribution is the Stable release of Debian, where of course backports
functions. I thought that I hated Flatpak when I was only using "native Linux"
(that is on a PC), but I really hate it on Crostini. Crostini has a proxy from
wayland or X called Sommelier. It functions well with applications from Debian
or even AppImages, but not Flatpaks. The titlebars are all messed up on
Flatpaks. I don't know why and sometimes I don't care. But the Debian packages
always work better so unless they're just not packaging something for Debian, I
never use a Flatpak on my Chromebook. It's even more jarring than trying to use
Windows programs in Wine on Crostini in a Chromebook, and that's saying a lot.
The push for Flatpaks came from Red Hat, and in a lot of ways they really just
encourage distributions to give a non-native approach to package management,
which is how a lot of bad things can happen. Like security threats (untrusted
builds, proprietary software, libraries not getting patched), the titlebar
glitching on Chromebooks, and just overall bloat and the sandbox messing with
the user if they need to change something, or sometimes even bricking the
application. I think the idea of pushing non-native builds is just making
everything worse, because software needs to work well with whatever system it
finds itself and you don't get that really when the person who built it doesn't
even run the same OS, or version of the OS, as you do. Fedora wants to move to
Flatpaks because they have IBM pushing it hard, they want a system where the
main file system is mounted read-only because they saw a Mac do it. It's just
insane and I think users don't like that when your target is power users who
like to mess with stuff and you tell them "No messing with that!" Whoever
designed this maybe didn't set out to create something even worse than Windows,
but it's what it is. it doesn't just have versioning hell, it's really full of
bugs, or in some cases design goals that get in the way of the program running
right. One of the things Chrome OS does do well is I really don't have to care
much about what the system is doing because it tends to itself. Even the Linux
container (Crostini) hasn't given me any real trouble. The firmware doesn't
glitch out and cause problems with the OS, because it's designed to work
together, unlike UEFI and Linux. The main reason I no longer use a PC is the
firmware. You may eventually get it working with some OS other than Windows,
but they deliberately make it hard. They do no testing. And it's such a
ramshackle development that it's amazing when it even mostly works. It's not
surprising to me that people are buying Chromebooks then rigging them to run
Linux or even Windows (replacing ChromeOS) after the fact. It's really hard to
get away from UEFI and get an x86 system otherwise. Of course UEFI causes
problems with Windows. They just special case everything and hide the errors
better. Including covering them up with the bootsplash. They disable power
management features that don't work due to firmware and chip bugs. They hide
error messages. A modern PC really has three problems. Windows, UEFI firmware,
and the Intel processor. You rig up a Chromebook to run Linux, you get rid of
2/3 of those pain points, and can still run Windows programs in Wine. It's
easier to buy a Raspberry Pi if you don't care about x86 binaries at all. That
may be my next stop years from now."


    * Microsoft_is_Still_Attacking_GNU/Linux_and_the_Net
    * To_Understand_Who's_Truly_Controlling_You_Follow_the_Trail_of_Censorship_
      (or_Self-Censorship)


⠀⠀⡂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣌⡛⠻⠿⢻⣿⣿⠀⡃⡌⢉⣹⢩⡅⣿⢈⣉⠸⢉⢹⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⣾⣶⣿⣷⣶⣿⣾⣿⣾⣶⣾⡷⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡏⣯⣿⣼⢙⣙⣯⡏⣽⢹⢹⡏⣝⣿⢻⣟⣿⢸⣿⡏⣯⡏⡏⣿⣿⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣾⣷⣾⣿⣧⣷⣿⣾⣿⣷⣾⣷⣾⣿⣷⣶⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢩⣻⣿⣭⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢉⢀⣠⣴⣆⠀⠚⢿⣿⣿⣿⡟⠁⠀⢀⣿⣿⠛⠀⠘⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⢿⣟⡩⣽⣀⣤⠀⠙⠋⠁⠁⠀⠀⢀⠉⠟⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠰⡆⠿⠃⠐⠆⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⡟⠋⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠀⠈⠹⣿⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣵⣽⡇⠀⠀⠀⢀⠀⢀⢀⣿⢿⣿⣿⡛⡛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⢀⣠⣤⠽⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠐⠛⠋⠀⢠⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⡴⢼⠿⠿⡇⠀⠀⠀⠀⠐⠶⠖⠶⣸⡏⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢯⡉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⢷⢀⣤⣼⣟⣻⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢀⣤⡴⠈⠂⠑⢱⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠯⠿⣿⣄⠀⢀⡀⠀⠀⢀⣠⣾⣿⡶⠾⠿⠟⠛⠿⠿⢿⣿⣿⣿⣟⣻⣯⣭⣿⣿⣿⣿⣿⣷⡆⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡆⡤⠟⠙⠟⠙⠀⠀⢤⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⣀⣙⣷⣶⣾⣿⡿⠛⠉⠀⠀⠀⠀⠤⠶⠚⠛⠛⠛⠛⠉⠉⠉⠉⠍⠉⠉⠉⢩⠉⠖⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠀⣧⡏⡁⣀⣀⡉⡉⣉⣀⣿⣄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠏⢀⣠⣼⣶⣾⡯⠠⣀⣀⢀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⢉⣴⠷⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠁⠠⠁⠒⠋⠇⠗⠻⢻⣿⡟⠃⣤⠀⣀⣾⣿⣿⣿⣿⣿⣿⣁⢱⢶⡶⠾⡷⠀⠈⢱⣖⠛⠋⢱⣤⠀⠀⠀⠀⢿⡿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⡄⠰⠀⠀⠀⠀⠀⠀⠬⣿⠇⠀⣈⣀⠀⠐⡲⣿⣿⣿⣿⡿⠿⠐⣚⣓⣛⡗⠾⠆⠀⠐⣶⡆⠂⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢂⣧⣼⠀⠀⠀⠀⠀⠀⢸⣿⠐⣼⣿⣿⣷⡇⢴⣿⣿⣿⣹⠛⠻⠿⠿⠿⠿⠇⠀⠀⠀⣸⣿⣯⣴⠃⠀⠀⠀⠀⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢁⣴⣾⣿⣶⣶⣶⣤⣤⣤⣼⣿⣾⣿⣯⣛⣫⣤⣼⣿⣿⢿⡷⡱⡇⡆⣞⣿⠂⠒⢰⢴⣒⢔⡊⣦⡮⡶⠠⢸⢰⡠⡎⣦⡮⢾⢀⠀⢰⢰⢔⡂⣧⢒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣖⣠⣼⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⠛⠁⢘⢿⣿⣿⣶⣿⡞⣾⣿⣶⠈⣿⠒⠻⢷⣾⣾⡞⠠⠀⠀⠀⠒⠒⠚⠚⠒⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣭⣻⣷⣿⣿⣿⣿⣷⡈⠘⠛⠷⠶⠶⠾⠟⣻⡻⢻⢿⣯⣽⣿⣶⣿⣿⣇⣿⣿⣆⣼⣯⣭⡅⠀⠀⠀⠀⣾⣿⠟⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣭⠉⠉⠁⠉⠉⠉⠀⠈⠉⠈⠁⠉⠀⠀⠀⠉⠉⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⠤⡀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⠀⠀⢀⡀⢀⡀⠀⠀⣀⠀⠀⠀⢀⣤⣤⡀⠀⣀⠀⠀⠀⣀⠀⣀⣈⣁⡀⠃⣀⣀⣀⡀⠀⢀⣠⣤⣀⠀⠀⣀⣀⣀⣀⠀⣀⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⡿⠀⣿⠀⠀⢸⡇⠈⢷⡄⣼⠋⠀⠀⠀⣿⣀⡀⠙⠀⣿⠀⠰⠀⣿⠀⣿⠀⠀⣿⠀⡿⠀⠈⣿⢠⡟⠁⠀⠈⢷⠀⣿⠀⠀⣸⡇⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣖⠋⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⢳⠀⣿⠀⠀⢸⡇⠀⠀⣿⠁⠀⠀⠀⠠⡄⠉⠙⢳⡄⢿⠀⠀⠀⡿⠀⣿⠉⠉⠁⠀⣿⠉⠉⠁⠸⣇⠀⠀⠀⣼⠀⣿⠉⠉⢻⡆⠀⠀⡇⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠚⠋⠀⠘⠓⠒⠛⠁⠀⠀⠛⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⡈⠓⠒⠚⠁⠀⠛⠀⠄⠀⠀⠛⠀⠀⠰⠀⠙⠓⠒⠛⠁⠀⠛⠀⠀⠘⠓⠀⠀⠓⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠏⠀⠒⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠄⠀⠀⠀⠀⠈⠀⠤⠀⡔⢠⣶⠿⠂⠀⠂⠀⠀⠀⠀⠂⠌⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡈⠀⠀⠀⢠⡤⣤⣴⣷⠃⣆⢶⡦⠂⠀⣀⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⢛⣶⡼⠛⠙⠛⢷⣿⡏⠀⠈⡐⠀⠀⠀⠠⠤⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠁⢀⣀⠀⠀⠐⠛⠀⠀⢠⠇⠀⠀⡄⠀⠀⠀⣀⣝⠁⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣾⡛⢿⣦⣤⡀⢀⣀⢸⠀⠀⠀⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠠⣮⡠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⡦⣼⣿⣳⣌⣟⡻⠇⢨⡆⡏⠀⠀⠀⣇⢑⣶⡿⢛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⠛⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⣿⣿⣿⣿⣶⡇⠀⠸⠷⠂⡠⢤⣤⣾⣿⠟⠀⣿⠇⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⣿⠟⠁⠀⠀⠀⠀⣴⣿⣿⡿⠃⢀⣀⡌⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠁⠀⠀⠀⠀⠀⠀⣼⡿⠏⣆⡾⣯⣭⣼⣭⣴⡶⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⣋⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⡇⠒⡄⢸⡂⢲⢰⣶⡄⣖⡂⡇⡗⡯⣶⢱⡮⡇⠒⢱⣲⡖⠂⣖⡇⡀⠀⣒⢰⣲⠀⡖⡆⠃⣀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢶⠶⠞⠺⠖⠱⠿⠷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⣨⡼⣳⠅⠗⠿⠰⠅⢇⣀⢸⡼⠀⠈⠠⠅⠇⠸⠼⠈⠸⠬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠤⠀⠀⠀⠁⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⣴⣄⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⢰⣶⣶⣶⣶⣶⣶⠀⠀⠀
⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠸⠿⠿⠿⠿⠿⠿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣤⣤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣖⣒⢠⢤⡀⡆⡆⡠⢄⢠⢠⡀⡔⡆⡤⢄⢀⠤⡄⠀⡆⠀⢀⢤⡀⡀⢠⢀⠤⡠⢴⢴⠆⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠇⠀⠳⠤⠃⠇⠇⠧⠜⠸⠆⠿⠀⠇⠇⠸⠸⠤⡇⠀⠧⠤⠸⠽⠇⠧⢾⠹⠤⠃⠸⠸⠀⠯⠕⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⢆⢀⠀⡀⣰⣀⣀⣀⢀⣀⣀⡀⢀⣀⢀⣎⣹⡁⡂⣀⣀⠀⢰⠒⠋⣁⣀⣀⢀⣀⡀⡆⢀⣀⠀⡀⢀⢀⣀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠗⠺⠼⢄⠇⠸⠄⠧⡼⠸⠀⠇⠸⠶⠼⠄⠧⠸⠄⠇⢧⡼⠀⠸⠭⠅⠇⠇⠸⢸⢄⠟⠇⠣⡠⠇⢇⢼⠸⡤⠕⢧⠬⠨⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢤⠤⡠⡄⢀⠀⠀⡀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⢀⠀⢀⡀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⢀⢀⣀⣀⣀⣀⠀⠀⠀⠀
⠀⣸⣀⠇⡧⣓⡅⣏⣸⢸⣁⡇⢣⡎⢞⣚⢺⠉⠀⢸⣀⡸⣓⡇⣝⣻⢸⢮⡐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢈⣁⣉⡉⣉⣀⣈⣁⢉⣁⣁⣈⣉⣁⣉⡉⣈⢈⡉⡉⠉⠁⠀⠀⠀⠀
⠀⣠⢄⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣈⣉⡉⢁⣉⣉⡉⣉⢈⢉⣈⣉⣉⣉⣉⣁⡉⣈⠁⠁⠀⠀⠀⠀⠀⠀
⠀⡇⢀⣵⠭⡆⢹⠡⡋⢑⢸⠉⡆⡇⡏⢱⢰⠉⡇⠀⢹⡎⣇⢇⡯⡇⢹⠁⡮⢵⢸⠁⡏⢱⢹⢰⠭⡆⡏⢹⢔⢁⡯⡇⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⣁⣈⢉⣉⣁⣉⢈⣈⣉⣉⣉⣉⢉⣈⣁⣉⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠈⠉⠀⠉⠉⠈⠁⠉⠁⠈⠀⠁⠁⠁⠈⠀⠭⠇⠀⠈⠁⠈⠀⠉⠈⠈⠁⠈⠁⠈⠀⠁⠈⠈⠈⠉⠉⠁⠈⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀
⢀⣤⢀⣀⣀⣀⡀⠀⣀⠀⢀⣀⢀⡀⢀⣀⡀⣀⢀⡀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀
⠐⣿⣿⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⣿⡿⠛⠛⠙⠛⠻⣿⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⠐⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⡘⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣼⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡄⠀⢀⡙⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⡇⡿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢠⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 391

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/Google_News_is_Dying.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/Google_News_is_Dying.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Google News is
Dying⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025


Google News had many_layoffs in recent years. That was in "the news", even in
Google News. Recently we've repeatedly complained about 1) lack of source
diversity in Google News; 2) slopfarm takeover in Google News.


Google lessens the incentive to do real journalism and rewards Serial Sloppers.
Plagiarism in other words...


Now, get a load of this:


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


Yes, that's a tweet right there as a "news source", not even naming the
messenger (a Republican bigot) and treating MElon's algorithmic/biased site as
a source of verified news.


Thanks, Google News.


We now understand so much more about that incident: "thoughts and prayers".


What might come next: spewing out LLM slop (which they call "Gemini")? Remember
what happened to Apple when it tried it.


Shame on Google. Given its budget, it could do so much better. But without much
competition in this particular area is lacks an incentive to improve. Over the
past 15 years Google News only got worse and worse each year, partly because of
copyright lawsuits. █


    * Microsoft's_Attack_Dogs_Have_Failed._Now_What?
    * Links_18/04/2025:_Layoffs_at_Microsoft_Infosys_and_Qt_Becoming
      Increasingly_Proprietary_(Plus_Slop)


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀
⠀⢰⡥⡦⣦⣶⣷⢴⢶⡦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⢀⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀
⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⡀⠀⠀⡀⣀⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⡀⠀
⢀⣀⣀⣀⣀⣀⣀⣈⣙⣻⣿⣷⣦⣀⣀⣨⠭⠭⠥⠀⠀⠁⠉⠈⠉⠀⠀⠈⠈⠉⠈⠉⠁⠀⠀⠈⠉⠉⠈⠉⠉⢈⡉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠉⠉⠁⠉⡁⠀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠮⠖⠖⠶⠱⠷⠶⠐⠷⠾⠶⠲⠷⠷⠶⠶⠆⠟⠿⠖⠆⠀⠀⠀⠐⠐⠶⠶⠶⠶⠆⠴⠴⠶⠶⠶⠲⠖⠶⠶⠆⠆⠰⠶⠖⠆⠲⠶⠶⠴⠐⠶⠴⠲⠶⠲⠶⠄⠀⡇⠀
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢶⡶⠆⠤⠶⠶⠶⠆⠖⠰⠰⠦⠶⠲⠶⠲⠲⠂⠀⠀⠀⠘⡚⠒⠛⠘⠃⠛⠋⢙⠛⠚⠚⠓⠛⠓⠚⠛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠏⠿⢿⣿⣶⣤⣦⠰⠴⠤⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠙⠁⠈⠃⠉⠉⠉⠉⠁⠁⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠻⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⡇⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⡇⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣤⣤⡄⣤⣤⣤⣤⣹⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣠⡀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⣿⣿⣿⡏⠉⠁⣩⣿⣿⣿⣿⣿⠋⠈⠛⠋⠉⠆⠀⢘⣃⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⡀⡀⣀⣀⢀⡀⠀⠀⠀⡇⠀
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⢷⡛⠓⠒⡗⠒⠒⠓⠒⠂⣿⣿⡇⠛⠿⣿⣷⣄⠀⠀⢀⠀⠀⢨⣭⣥⣍⣭⣩⣍⣭⣬⣉⣍⡍⠉⠈⠁⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣦⣯⣿⣷⣶⣶⣾⣿⣿⣿⣾⣿⡆⠀⠠⠴⠤⠤⠠⡤⠀⢤⠠⠤⢦⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣯⣿⣯⣿⣯⣽⣿⣿⣾⣿⣯⣷⣿⣿⣿⣿⣿⣧⠀⢀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣟⣟⣿⣿⣿⣿⣿⡏⠁⢨⣥⢤⣠⣤⣤⣄⣤⣤⣠⣄⣤⡤⣤⣄⢠⣤⣤⣄⣤⡄⣤⣤⡄⣤⣀⣤⣤⣤⣤⣤⣤⣤⡄⠀⡇⠀
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣿⣿⣿⣿⣛⣟⣍⣭⣉⣩⣩⣭⣝⣿⣿⣿⣿⣭⣭⣿⡄⠀⠰⠴⠦⢴⠤⠤⡤⠤⠴⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢬⢩⣭⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠐⠒⠒⠒⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⢠⣦⣤⣴⣀⡄⡦⣤⣤⣤⣴⢠⣤⡶⣦⡤⣤⣤⠀⠀⠀⠀⠀⢰⡆⠤⠤⠤⠤⠤⠄⠤⠤⠤⢤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣍⣭⣭⣭⡍⣭⣭⡭⣭⣭⣍⢭⡭⡭⡩⠭⣭⣭⡍⠀⠀⠀⠀⠀⠰⠶⠶⠴⠦⠄⠶⠴⠴⠢⠤⠴⠔⠶⠤⠴⠴⠤⢴⠦⠶⠐⠶⠦⠴⠲⠦⠴⢖⠄⠀⠀⠀⠀⠀⡇⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣭⣭⣭⠭⣭⣭⢉⢭⢭⣭⣭⡭⡩⢩⣭⢩⡭⡭⢡⣤⠀⠀⠀⠀⠐⠐⠒⠒⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡉⣉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⡇⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⡇⠀

                    ䷩ 𝚕𝚒𝚗𝚎 470

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/IRC_Proceedings_Thursday_April_17_2025.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/IRC_Proceedings_Thursday_April_17_2025.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Thursday, April 17,
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now


    * Gemini_Links_18/04/2025:_Pinephone_Pro_and_Linux_is_too_Easy
    * Over_at_Tux_Machines...


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣧⡼⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠿⢛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡆⡻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣀⢠⢥⣐⡀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⣏⠱⠩⠁⣿⣯⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢿⣿⣿⣿⣿⡇⢻⣿⣿⣿⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠂⠀⠐⢾⣿⣿⣷⣲⣤⣪⡷⠿⣿⣿⣿⣿⣿⣿⣿⣤⡸⢲⡆⣼⣿⣿⣟⣷⣦⣈⣍⣉⡛⠻⠁⠉⣿⣿⠿⠿⠿⠿⢿⡿⠿⠿⠿
⠐⢤⣼⠟⣿⣻⡇⢸⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣎⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣭⣿⣶⣤⣤⣴⣞⣿⣰
⠀⠘⣿⠀⣿⣿⣧⢐⣿⣻⣿⡏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠸⣿⣿⣿⣿⣿⣯⣈⣦⡠⣤⡀⠈⢻⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣧⢹⡟⢃
⠀⠀⠁⠀⢺⣿⣿⡆⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣭⠷⢡⡁⠀⠈⣿⣿⣿⣿⣿⣿⡀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣿⢹⣟⣽⣿⣿⡻⠄⣾⣿
⠀⠀⠀⠀⠈⣻⣿⠀⣼⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠳⡂⣼⣿⣦⣶⣿⣿⣿⣿⣿⣿⡗⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⣿⢻⣿
⠀⠀⠀⠛⡇⣿⡟⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠁⠀⢸⣿⡀⠉⠁⠙⢿⣿⣿⣿⣿⣿⣦⣠⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠄⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣆⠁⠀⢠⣿⣿⣦⣾⣷⡆⠙⠻⣿⣿⣻⣿⡟⠁⠇⣿⣿⣯⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⢰⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⣿⣿⣟⣾⣿⡯⣹⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⣶⠀⢹⣿⣿⡟⠁⠀⠀⢿⣯⣿⣿⣯⡛⣻⣿⣿⣿⣿⣿⡟⠛⣯⠻⠟⠻⣿
⠀⠀⠀⠀⠀⢠⣽⣎⢘⣿⣿⣿⣿⣷⡌⣻⣿⣿⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⠟⢿⣿⣿⠟⢋⣭⣷⡿⢿⣾⣿⣿⣧⠀⠀⠻⡇⠀⠀⠀⠀⠈⠩⢿⡿⡿⡅⣨⣿⣿⣿⣿⡧⣷⣶⣿⡖⢻⣦⡙
⠀⠀⠀⠀⠀⣸⣿⣯⣀⣹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣴⣶⣿⣿⣿⡟⣿⣿⣿⠃⠀⠙⠉⢠⣿⣿⣿⣧⢸⣿⣿⣿⣿⣤⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠁⠁⠛⠛⠃⠛⠛⠟⠀⢽⣿⣧
⠀⠀⠀⠀⠀⠁⠹⣿⣿⠿⠟⠛⠛⠛⠻⠟⠛⠛⠉⠀⠁⠈⠉⠳⡀⠀⠀⣈⡉⠉⠉⠙⠁⠀⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣿⣿⡆⣿⣷⣌⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⠿⢁⣀⡀⠀⠀⠰⢿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠵⠀⠦⣧⠄⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣷⣤⣴⣶⣾⡟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⢿⣿⡄⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⡊⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⢷⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣶⣶⡰⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠈⠉⠀⠀⠉⠉⠙⠛⠛⠛⢛⣟⣛⣛⣯⣿⣿⣿⣀⣀⠀⠀⠈⠉⡿⠿⠿⠿⠧⢤⣤⣄⣾⠀⠈⠛⠿⢦⣤⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣦⢈⢹⣿⣿⣽⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣯⡀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⡐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 698

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/Microsoft_is_Still_Attacking_GNU_Linux_and_the_Net.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/Microsoft_is_Still_Attacking_GNU_Linux_and_the_Net.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft is Still Attacking GNU/Linux and
the Net⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇children_of_UEFI⦈_


Last year: Microsoft_Saturated_E-mail_with_Junk_(Windows_Botnets_Spew_Out_Lots
of_These)_and_Now_It_Does_the_Same_to_the_World_Wide_Web


The Web has become infested or plagued or littered with slopfarms*. A lot of
articles about... well, just about anything... aren't really articles but LLM
slop. It's not always obvious, but people learn to discern or to "feel" when
they read slop. Then they can run some scanners to affirm this feeling.


The examples at the bottom are almost entirely FUD, they all touch "Linux", and
they're LLM slop. We can imagine that a Microsoft LLM was leveraged to spew
those out this week. That's what typically happens.


Those who got conned into thinking Microsoft is no longer an enemy of Linux
(Torvalds_may_be_among_them) ought to read this_new_article (the old headline
said, "Google and AWS: Linux too hard, so customers move to Azure", now it says
"Google, AWS say it's too hard for customers to use Linux to swerve Azure"). To
quote: "When moving to the cloud, companies with significant investments in
Microsoft infrastructure wares simply can't afford to rewrite everything for
Linux, so they end up migrating to Azure to dodge the markups Redmond charges
for running its server software in competitors' clouds. [...] The issue stems
from changes to Microsoft's cloud licensing practices some years back.
Customers used to be able to use regular software licenses to host Microsoft
server software on outsourced hardware. But in 2019, Microsoft began requiring
new, separate licenses to host virtualized versions of these servers within
Amazon, Google, and Alibaba's clouds – three businesses Microsoft classified as
"listed providers." As a result, customers must pay up to four times more to
run Windows Server VMs on Google Cloud Platform or AWS, making GCP “less
competitive than on Azure,” Google told the CMA. [...] The pricing issue means
customers that went all in with Windows Server on-prem are “denied effective
competitive choice or innovative alternatives” when going into the cloud,
according to Google's submission to the CMA."


Last year when a complaint to this effect was brought up Microsoft_bribed_the
government_using_money_that_did_not_even_exist.


Never underestimate how evil Microsoft is. It's hiring stabbers and stranglers.
It's a sociopathic cult. If the Web is critical of Microsoft, then Microsoft
will attack the Web with chaff. █


________


* New example #1:


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


LLM slop.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Tails,_the_secure_operating_system_designed_to_protect_your
                            privacy_and_anonymity⦈_


New example #2:


         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇UNC5174_Reemerges_with_SNOWLIGHT_Malware⦈_


LLM slop.


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Recently,_the_infamous_China-linked_threat_actor_UNC5174⦈_


New example #3:


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


LLM slop.


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


New example #4:


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇BPFDoor:_Understanding_Malware_Threats_and_Mitigation
                                   Tactics⦈_


LLM slop.


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


    * Over_at_Tux_Machines...
    * Fedora_Already_Lost_Its_Soul_Under_IBM


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⡴⡐⢐⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⣿⢫⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⡙⢿⣿⣿⣿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠽⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⡿⣫⣿⣿⣿⣶⣿⣿⣿⢏⣾⣿⣿⠛⡄⣍⡻⢿⣧⡻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⢋⣾⣿⣿⣿⣿⣿⣿⡿⢣⣾⣿⢟⣵⣷⢁⣿⣿⣦⡹⣧⣻⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡿⣱⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⢟⣵⣿⣿⣿⠀⢹⣿⣿⡷⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⡿⣫⣶⡿⢋⣵⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⡌⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢏⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣫⣾⣿⢏⣴⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⣡⣭⣭⣶⣶⣭⢻⣿⣿⡟⣼⣿⡿⠿⠿⠷⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣑⡭⢡⡆⢰⣶⠐⣶⣬⣼⣿⣿⣿⣿⣿⣘⢛⡝⡓⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⡏⣾⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠟⠁⡉⠉⠉⠉⣁⠻⣿⣿⣿⣿⣿⡟⡿⠟⠂⠀⢁⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⢳⡟⣼⣿⣿⣿⣿⠿⠿⢶⠮⠍⢉⣵⣶⡀⠈⠀⠀⢀⣼⣿⣮⠙⣿⣿⣿⡇⠡⣆⠀⠀⣸⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢿⣿⢘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡎⣭⣷⣒⣚⡛⠛⢋⣡⢀⣿⣿⣿⣿⢰⣤⣈⣭⡍⣵⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⠇⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⢱⣿⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣯⣥⣶⣿⣿⡏⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢏⣾⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡻⠿⢟⢿⣿⡟⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⡿⣸⡌⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣛⢛⣿⣾⢏⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣎⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣿⣿⣷⣶⣾⠀⠀⠀⠀⠀⠀⣄⣾⡈⣷⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⡘⢰⢌⡍⡉⠛⣛⣛⣋⣵⣿⣿⢹⣇⣿⣿⠿⠄⠀⠀⠀⢀⡀⠀⢚⠻⢿⢀⣿⣿⣿⣶⡄⠀⠀⠒⠛⠿⣷⣦⣾⣿⣿⣿⣁⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣆⢬⣅⡛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⢧⡀⠀⠰⢃⢸⣿⣿⡇⢲⣿⣿⡁⠀⠀⠂⢨⡛⠛⣻⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠞⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⡹⣿⣧⡻⠅⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣶⣦⣶⠇⣿⣿⣿⣇⣄⢍⣻⠷⠤⠀⠀⢫⣾⣶⣶⣶⣊⣀⣴⡒⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⢟⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣛⢿⣿⣿⣿⣿⣷⢹⣿⣷⡀⠻⠿⣿⣿⣿⣷⢻⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⣿⣿⣯⣝⣛⣛⣿⣿⣦⣙⠿⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣘⣡⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣡⣿⣿⠟⠛⠛⠛⠿⢭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣧⣿⣿⣷⡀⠀⢿⣿⡜⣿⣾⣾⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⣷⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠉⢿⢸⣿⣿⣿⣯⢻⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⢿⣿⣿⣿⣿⡼⣟⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⠿⠿⠟⠛⣭⡀⠦⣩⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠿⠸⠇⣛⣥⣾⣿⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣠⡘⣿⣿⣿⣿⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠙⣿⣿⣿⣿⣿⣿⢡⡇⠀⠘⢛⡃⢿⣿⠟⠁⢸⠃⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠻⢿⣿⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢀⣿⠀⠈⣼⠇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢰⣿⠀⠀⠀⢸⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⠎⠀⢤⣄⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠧⠀⣿⠿⢿⡄⢺⣿⣧⡀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠘⠃⠀⠙⠋⠋⠛⠛⠋⠉⠛⠛⠛⠙⠛⣿⣿⣿⣉⣉⣉⣟⣿⣿⣯⣉⣉⣉⣉⣹⣿⣿⣿⣍⣉⣩⣍⣉⣟⣿⣿⣯⣉⣉⣉⣙⣟⣿⣿⣉⣉⣉⣉⣉⣉⣿⣿⣿⣯⣉⣉⣿⣿⣉⣉⣉⣟⣿⣿⣏⣉⣉⣍⣹⣉⣉
⣿⣿⣯⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⣩⣝⠛⡉⡋⡋⡟⡛⠛⢫⢹⣯⠉⡙⠛⡉⡍⡟⢻⡏⣭⢙⠉⢹⡏⠉⠟⠻⢛⠛⡟⡛⠛⢹⢛⠛⢛⣯⢹⠉⡛⡻⢛⢹⠛⢛⢙⠛⢻⡏⠍⡋⡟⢛⠛⠻⠛⣿⠉⢫⡟⠛⡛⢛⡛⠟⠛⡍⣿⠏⠹⢿⣿⣿⡇
⣿⣿⣷⣬⣥⣼⣥⣧⣥⣥⣵⣤⣬⣼⣿⣤⣧⣤⣥⣥⣥⣼⣷⣭⣼⣭⣼⣯⣥⣦⣵⣬⣤⣤⣥⣽⣬⣬⣁⣾⣿⣬⣴⣃⣵⣬⣬⣤⣬⣬⣬⣼⣧⣽⣥⣥⣬⣬⣤⣤⣿⣤⣤⣥⣥⣥⣯⣥⣤⣥⣥⣿⣬⣤⣽⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠛⠛⠛⢸⣿⠹⢱⢘⠛⡟⠟⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣬⣦⣽⣬⣯⣬⣯⣤⣤⣵⣴⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⡿⠉⠉⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⠃⠀⠀⠀⠈⢹⣿⠉⢛⠉⠛⠛⢛⡯⠛⠛⣿⣿⣿⣿⣿⣿⠍⡋⢙⡏⡛⠛⠛⠛⠛⢻⣿⣿⡯⢙⢋⠛⡯⠏⢿⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⡆⠀⠀⠀⠐⠘⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡙⠋⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡈⠡⠀⠉⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠀⠁⢀⣀⣀⣄⣀⣀⣁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠤⠤⠤⠀⢰⣤⣦⣤⣦⣶⣶⣤⣦⣴⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠉⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣼⣧⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡏⣿⣭⠻⢻⠹⠻⢟⢻⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣶⣷⣾⣶⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣙⣛⣻⣉⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣙⢟⣛⣟⣛⣛⣻⣛⣛⣛⡛⢛⢛⣛⣛⣋⣛⠛⣛⣙⣛⣛⣛⣛⡛⣛⣻⣛⣛⡛⣛⣛⣙⣛⣛⢛⣛⠻⣙⣛⢙⣻⣛⣙⣻⣛⣛⣛⣛⢛⣛⣟⢛⣛⣛⣋⣙⣛⣛⣙⣻⣻⣛⣟⣟⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣥⣭⣭⣥⣭⣬⣭⣬⣍⣭⣭⣨⣭⣤⣭⣉⣭⣭⣭⣯⣭⣭⣍⣭⣥⣭⣭⣥⣭⣭⣬⣬⣥⣭⣭⣿⣭⣭⣬⣭⣭⣯⣭⣧⣭⣭⣭⣯⣭⣩⣭⣭⣬⣹⣭⣍⣭⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡻⢿⠿⠿⠻⢿⠿⠿⠟⡿⠿⠿⢿⢻⣿⡟⢻⠿⠻⠻⠿⠿⠟⠻⠿⠻⠿⠟⠻⠻⠿⠟⠛⠿⢿⠿⠿⠿⠿⠿⠿⠿⠻⠟⠿⠿⠻⠿⡿⠿⠻⠿⡿⠿⠻⠿⠿⠿⠿⠿⠻⠿⠿⢻⠟⠿⠿⠟⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⣙⡛⣻⣉⣛⣛⣻⣙⢏⣙⣋⣛⣙⢛⣙⣙⣚⣉⣛⣛⣛⣟⣘⣛⢛⣛⣛⣋⣙⣋⣛⣛⣛⣉⣛⣏⣛⣟⣛⣉⣛⣓⣛⣛⢛⣛⣟⢛⣙⣛⣋⣛⣙⣋⣒⣋⣛⣛⣙⣻⣋⣛⣙⣟⣛⣛⣻⣏⣛⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣭⣧⣭⣭⣬⣥⣤⣭⣹⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠻⠟⠿⠿⠿⠻⠿⠻⠿⠿⠿⠛⠟⠟⠟⣿⠟⠟⢿⡟⠿⠿⠿⠻⠿⠿⠟⠟⠿⠛⡿⣿⠿⠿⠟⠿⠿⠿⠿⠟⠿⠿⠿⠟⡿⠿⠻⠿⠟⠿⠿⠿⠿⠿⠿⠿⠛⠿⠻⡿⠿⠿⠻⢿⠿⢿⠻⢟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣋⣛⣛⣻⣟⣏⣛⣓⣟⣙⣑⣛⣛⡙⣟⣋⣛⣛⣛⣛⣋⣺⣩⣛⣙⣛⣋⣻⣛⣛⣙⣻⣒⣻⣹⣑⣛⣉⣻⣻⣟⣻⣛⣙⣛⢛⣋⣻⣛⣉⢛⢙⣛⣛⣛⣛⣛⣛⣋⣙⣟⣛⢻⣚⣛⡛⣛⣛⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⣭⡯⢧⣬⡽⢭⣬⣬⣤⣭⡭⣭⡽⣭⣭⡭⢬⣬⣭⣬⡭⣤⠭⣥⣥⣭⣼⣭⢬⣭⡧⢽⡭⣥⣭⢭⣭⢭⣥⣏⡯⢭⡬⡭⣽⡭⣬⣭⡭⢭⡬⡽⢬⢽⣭⣭⣬⣤⡍⣦⣥⡽⡥⣬⣭⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠶⢰⠲⠖⠶⣶⠶⠶⠲⠗⠶⠷⡶⠶⠖⠶⠳⢶⣶⣴⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣾⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣥⣤⣥⣤⣤⣤⣥⣤⣦⣤⣬⣤⣼⣤⣤⣬⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣥⣼⣤⣤⣤⣤⣦⣤⣥⣤⣥⣤⣤⣤⣧⣤⣤⣼⣤⣤⣤⣤⣤⣤⣧⣤⣤⣥⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⣭⣭⣥⣬⣿⣭⣧⣭⣥⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⠿⡟⠟⠻⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣴⢧⡁⣿⣧⣧⢬⣿⣥⡯⠶⣿⣵⣼⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⣿⣿⣿⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⣻⢻⠛⣟⢟⣟⣟⣻⡟⣟⣛⣿⢻⣿⢻⢻⠿⣿⢿⠿⢿⢿⡿⣿⠿⡿⢿⠿⡿⢿⡿⡿⣿⢻⢿⠻⢿⡿⢟⡟⢿⡻⣻⢻⢻⢻⢻⢻⣿⢻⢻⣻⢛⡟⣟⢻⣻⡟⣿⢻⠿⣿⠻⡿⡿⡿⡿⠿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣽⣼⣼⣬⣮⣿⣿⣼⣧⣿⣼⣿⣼⣿⣴⣼⣴⣦⣶⣧⣿⣼⣴⣾⣼⣸⣺⣴⣷⣼⣷⣵⣽⣼⣼⣼⣼⣯⣶⣧⣧⣷⣽⣼⣮⣧⣿⣼⣿⣴⣼⣼⣴⣧⣿⣼⣿⣿⣼⣼⣽⣼⣼⣴⣽⣽⣼⣼⣴⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣻⣿⡻⣿⠻⢿⢹⢿⠿⡏⡏⣿⡟⣟⢿⠿⡿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣬⣿⣧⣾⣽⣼⣼⣴⣭⣧⣧⣿⣧⣽⣼⣴⣭⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⣐⡀⢉⣿⣿⣩⣻⣉⣛⣽⣻⣉⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣫⣻⣏⣿⣟⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣖⣿⣗⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢤⡤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣭⣭⣽⣭⣯⣭⣯⣭⣭⣯⣭⣭⣭⣽⣭⣭⣽⣭⣭⣯⣭⣿⡿⣛⣛⣛⣓⣀⣀⠀⠀⠀⠘⣇⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⢀⡆⢻⠆⠀⠂⠂⠛⠁⠐⢁⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⢛⡻⠿⠟⡿⣿⠿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⣿⣬⣵⣤⣧⣤⣤⣽⣥⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
⡷⠤⠠⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠠⠄⠤⠀⠤⠤⠤⠤⠠⠤⠤⠤⠤⠠⠠⠤⠤⠄⠤⠄⠤⠤⠤⠤⠤⠠⠄⠤⠤⠤⠠⠤⠠⠤⠤⠤⠤⠤⠠⠤⠤⠼⠿⣿⣿⣿⣿
⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣿⣿⣿⣿⣿⣿
⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠂⠒⠒⠀⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠐⠂⠐⠒⠂⠒⠂⠐⠒⠒⠐⠒⠒⠐⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠐⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠿⢿⣿⢿⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣶⣾⣷⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣛⣻⣽⣉⣏⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿
⣿⣿⣿⣿⣦⠍⠀⠀⠁⠃⠉⠉⠁⠈⠑⣉⡁⢈⣽⣿⣿⣷⣶⣶⣷⣿⣿⣶⣶⣶⣶⣶⣷⣿⣿⣷⣶⣶⣷⣶⣷⣿⣿⣶⣶⣶⣶⣷⣾⣿⣶⣶⣶⣶⣶⣶⣷⣿⣿⣶⣶⣾⣿⣷⣶⣶⣷⣿⣿⣶⣾⣶⣦⣿⣶⣶⣶⣦
⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⢿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⠿⢿⢿⣿⡿⠿⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉
⣿⣿⣿⣿⣿⣿⣆⣹⣀⣦⣰⣸⢐⢸⣀⣆⣆⣇⣆⠅⢰⣿⣸⣢⠰⣈⣠⣀⣆⣿⣢⣉⣀⣁⣇⣇⣄⣂⣁⣸⣇⣌⣀⣈⣂⣆⣂⣀⣄⣆⡦⢰⣷⣠⣰⣀⣐⣰⣸⣿⣇⣇⣆⣆⣸⣘⣟⣠⣰⣠⣠⣸⣿⣿⣿⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣾⣿⣟⢻⠶⣿⢿⢻⠿⠟⠻⡿⢿⢿⣿⢿⡿⢿⡿⢻⡿⡛⠟⡿⢿⠿⠟⣿⢿⡿⢷⢻⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣘⣘⣀⣈⣘⠈⢂⣀⣃⣃⣠⣇⣀⣃⣂⣜⣘⣇⣂⣇⣃⣎⣀⣃⣃⣳⠈⢚⣠⣐⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠇⠀⠀⠛⢻⣿⠉⠋⠉⠛⡛⣻⠝⠛⣻⣿⣿⣿⣿⣿⠭⡟⣿⡟⡟⠛⠛⠛⠛⣿⣿⡟⢝⢟⠛⡟⠻⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠛⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠻
⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣟⣛⣙⣘⣛⣛⣛⣻⣙⣙⣙⣛⣛⣙⣙⣋⣊⣋⣛⣛⣋⣘⣻⡿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡱⣿⣿⢾⣉⣉⣉⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⢻⢸⣧⡌⠛⠋⡛⠻⣛⢙⢛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣷⣶⣷⣾⣶⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣛⣛⣛⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⢻⠟⠻⢻⠛⠛⠛⠛⠻⠛⠛⠟⠻⠻⠛⠛⠻⢻⠛⠛⠛⠛⠟⠛⢻⠻⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⢻⠻⠛⠛⠛⡟⠛⠛⠛⡟⠟⠛⠛⠟⠛⡟⠛⠛⠛⡛⠟⠛⠛⠛⠿⠛⠻⠟⠛⣿⣿⣿
⣿⣙⣛⣝⣛⣛⡛⣛⣹⣚⣿⢛⣛⣛⣟⣛⣛⣛⣓⣛⡙⣏⣋⣛⣓⣋⣙⣛⣋⣛⣙⣛⣛⣗⣛⣛⣟⣛⣃⣋⣙⣋⢋⣙⣏⣛⣟⢓⣛⣛⣛⣛⣚⣛⣛⣛⣛⣋⢻⣛⣛⣋⣛⣻⣚⣃⣹⣛⣛⣛⣛⣛⡙⣿⣿⣿⣿⣿
⣿⣉⣉⣈⣹⣩⣉⣉⣀⣉⣉⣉⣉⣍⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⢿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⡿⠿⠿⡿⠿⢿⠿⢿⣿⣿
⣿⠶⡖⠶⡶⠲⠶⠶⠶⠖⠶⡶⠶⠶⠶⠶⠶⠖⠶⠶⡶⠗⠶⠶⠲⠚⠷⠶⠾⠾⠶⠶⠞⠖⢶⠶⢶⠶⠖⠲⠖⡖⠶⣶⠾⠶⡾⠖⠶⠖⠶⠲⠶⠶⠶⠲⢶⠲⠶⠖⢶⠲⠖⠲⠒⠶⠷⡖⠷⠶⠒⠲⠶⠶⠶⢾⣿⣿
⣿⣛⣛⣛⣛⣓⡛⡙⣚⣛⣙⣛⣉⣻⣺⣙⣋⣛⣙⣟⣛⣛⣛⣛⣛⣛⣟⣟⣋⣛⣉⣻⣛⣛⣹⡛⣛⣏⣟⣋⣛⣛⣉⣉⣛⣋⣙⣋⣛⣏⣍⣙⣛⣙⣑⣛⣚⣛⣋⣟⣛⠛⣋⣙⣋⣛⣋⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠤⠤⠤⠤⢼⠤⠤⠤⠬⡤⠤⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠥⠤⠼⡤⠤⠼⡤⡤⡤⠼⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⢧⠧⠤⠤⠤⠤⡤⠤⠬⠤⠤⠤⠬⠤⡤⠤⠤⠬⠤⠤⢤⠤⠼⠤⠤⠤⠤⠤⣤⣼⣿⣿
⣿⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⠲⣖⠺⠲⠖⠶⠶⠶⠞⠶⢶⠳⠶⠶⠶⠶⠖⠿⠲⠶⠷⠷⠶⢶⠶⠖⠖⠷⡖⠖⠶⠾⠖⠶⡚⠶⡖⠶⠶⡖⠷⠶⢶⡶⠓⠶⠶⠶⠷⠶⠒⠶⠲⠶⠚⠖⠲⠶⡶⠶⢲⣶⣿⣿⣿⣿
⣿⣓⣛⣛⣛⢛⣛⣹⣙⣻⣛⣛⣓⣟⡛⣛⣑⣓⣻⣋⣛⣓⣛⢛⣛⣋⣚⣻⢛⣛⣛⣛⣛⡛⡛⢛⣟⣋⣛⣓⣛⣛⣛⣛⣹⣛⣛⣛⣛⣛⡙⣟⣙⣉⣻⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⡿⠿⠛⢿⡿⠿⡿⢿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣏⣉⣉⣟⣋⣽⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣻⢧⢾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⡏⡏⣯⡏⣿⡏⣿⠻⣟⡿⡟⡟⣿⣻⣿⢹⣿⢻⢻⢿⢹⢻⣿⢛⡿⣻⣿⡟⡟⣟⡿⡏⡟⡟⡟⡟⡟⣿⣏⢿⢹⣿⢿⢹⢻⢟⣿⢻⢻⡟⣿⣿⡏⣿⢹⢻⢻⡟⣿⣿⢻⢹⠻⣿⣿⢻⢻⢻⢻⢹⣿⣿⣿⣿
⣿⣿⣿⣷⣷⣷⣿⣷⣿⣷⣿⣿⣿⣷⣷⣷⣿⣾⣿⣾⣾⣾⣾⣾⣾⣾⣿⣿⣿⣾⣿⣷⣷⣿⣷⣷⣷⣷⣷⣧⣯⣿⣿⣾⣾⣾⣾⣾⣾⣾⣿⣾⣾⣷⣿⣿⣷⣿⣾⣾⣾⣷⣿⣾⣾⣾⣿⣿⣾⣾⣾⣾⣾⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⢹⢻⢹⣻⣻⣻⣻⢻⢹⢻⢻⢻⢻⢻⣿⣿⣟⡿⣿⣻⢹⢻⢻⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣾⣿⣴⣾⣾⣾⣾⣾⣾⣾⣾⣾⣿⣿⣷⣷⣷⣿⣾⣾⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠁⣉⠈⣉⣿⣿⣉⣹⣭⣛⣽⣻⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠡⣀⠀⠀⣰⡖⠀⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢛⠉⡀⣦⣾⣿⢻⣿⣝⠛⠛⠛⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⠀⠀⢠⠀⣬⠠⠋⢻⣾⡿⠛⠛⠻⠿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣥⣃⣿⣋⣄⣰⣀⣨⣐⣖⣐⣅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣾⣾⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠐⠒⠂⠐⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⢻⣿⣿⣿⣿⣿
⣿⣉⡉⣉⣉⣉⣉⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠒⠒⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠂⠐⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠁⠉⠉⠁⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠈⠉⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣹⣦⣧⣤⣤⣥⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠛⢻⡟⠟⠻⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1038

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/Microsoft_s_Attack_Dogs_Have_Failed_Now_What.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/Microsoft_s_Attack_Dogs_Have_Failed_Now_What.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft's Attack Dogs Have Failed. Now
What?⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025,
updated Apr 18, 2025


             🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Dog_fail:_I_got_it!_..._reality⦈_


As pointed_out_earlier_today, Microsoft is "hiring stabbers and stranglers.
It's a sociopathic cult."


It would be utterly foolish to assume that Microsoft has any intention of
changing. It never changed and it's trying to silence critics instead of
improving its behaviour.


Does it work? Not really. Sometimes it does. Sometimes it can become a mere
nuisance to critics. Sometimes - like in our case - it backfires_on_Microsoft
and it panics when belatedly held accountable [1, 2], even if that means
travelling across the ocean to face_justice_here. That's what happens when
aiming_for_low and cheap. At the end we expect to publish hundreds of articles
under the banner "Microsofters' SLAPP Censorship" and there will be several
other mini-series (as we don't write books; the topic may well be covered in
over 1,000 parts). Then_we'll_start_campaigning_with_MPs,_regulators_and_NGOs.
We'll work to ensure Microsoft can never do this again. Ever. To anybody. █


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇We'll_attack_wives,_mothers_and_girlfriends;_Oh,_not_a_good
                               plan_after_all⦈_


    * All_Your_"Github_Projects"_Will_be_Gone_One_Day_(Just_Like_Skype)
    * Google_News_is_Dying


⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣻⣿⢧⠔⠋⢚⣿⣭⣚⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⢱⣿⠏⠀⠀⠀⠩⢻⡷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣇⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⠈⠀⢀⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠂⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃
⠀⠀⢠⣌⠻⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⡿⠟⠋⠁⠄⠀⠀
⠀⠀⠀⠛⢦⠠⠊⠪⠻⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⢒⢒⣒⡦⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠈⣿⣿⣿⣿⣿⣿⣿⡧⠀⠘⠋⠁⠀⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣭⡝⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⢟⣉⡉⠛⣿⢧⣤⣤⠀⣀⣀⠀⣤⣤⡌⢸⠀⢨⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠕⠈⣭⢿⣿⡿⣞⠋⢉⣭⣭⠅⢸⣿⡇⠘⠋⢩⣶⣦⣴⣶⠀⣠⣶⣶⣦⡀⣾⣿⣷⠄⢿⢡⣶⣶⢸⣿⣿⡆⣿⣿⠀⢸⠀⠈⢻⣿⣿⣿⣿⣿⡟⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣿⣇⣿⣴⣭⣭⣭⠀⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⣿⢸⣿⣿⢰⣿⣿⠀⣿⣿⠀⠘⠀⠀⠀⠀⠈⠉⠉⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣤⠤⢶⡆⠀⡀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⢀⣿⢸⣿⣿⢸⣿⣿⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⡇
⠀⠀⢸⡏⠀⢸⠇⠀⠀⠀⠀⠀⠁⠤⢬⣭⣿⣿⣛⠃⠀⠀⠀⠂⠀⠸⠿⠇⠀⠀⢨⣿⣋⣿⣿⠀⠻⠿⡾⠿⠃⠘⠿⠷⠎⠛⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢘⠀⣸⣃⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣴⠀⠀⢰⣾⣿⣿⣶⡆⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠈⢀⠋⠛⠙⠋⠀⠀⠀⠀⠀⢸⠀⡖⢲⢺⣿⢫⡛⠢⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⣶⣷⣥⣀⠀⠀⠀⠀⠀⠀⠈⠀⡇⣸⢨⣛⠼⠇⣀⠀⣿⣷⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⢸⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⢀⠯⣾⢋⡃⠶⠀⠀⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡠⠤⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣾⡁⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⡄⠀⠀⠀⠀⠀⢰⣶⣶⣶⠀⠀⠀⠀⠀⠁⠀⣬⣤⣬⡍⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠨⠇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣯⣗⠢⠶⣤⣤⡤⠦⠤⠤⣯⣿⣿⡇⢀⠀⠀⠀⠀⣺⡛⠛⣿⠀⠀⠀⠀⠀⠀⣄⣿⣻⣿⡏⢀⣀⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣦⢉⡛⠐⠥⣵⢿⣿⣿⠀⢸⠀⠀⠀⠀⡏⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⡿⠶⠾⡇⠀⢀⠀⡶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⣿⣿⣿⣿⣿⠙⠏⠀⠀⠀⠉⠛⢿⠀⠸⠀⠀⠁⠀⡧⠆⣀⠀⠘⢿⠷⠀⠀⠘⢹⠇⠀⠀⡇⠀⣀⠀⠃⠹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⣾⠟⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⡐⣻⣦⣤⣷⣀⡀⡄⠒⠼⠶⠶⢶⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⡇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⢸⣿⣿⣿⣿⣯⣿⣿⣿⡗⣾⣿⣿⣿⣿⠓⠛⢳⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢉⡏⠉⠙⠛⠛⠛⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠈⠀⠀
⢸⣿⣿⣿⣿⣿⢿⣿⡿⠇⠿⢿⡛⡛⣿⢀⣀⣾⣐⡢⢂⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⡖⠚⢛⣿⣿⣿⣿⣿⣿⣄⠀⠒⠂⠀⠀⠀⠄⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⠘⡛⠻⠛⠛⠛⣛⣟⣅⣠⣀⣨⣧⣶⣿⣰⣿⣭⣥⣴⣦⣤⣤⣤⣤⣤⣠⣤⣄⣄⣄⣤⣭⣤⣭⡅⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢄⡀⠀⠐⠀⠀⡀⠀⢀⠀
⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⣿⣷⣶⣶⣟⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣠⣀⣀⡀⠄⠀⣀⠀⠀⠀⠀⠀⠐⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣆⣀⠀⠀⡠⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣼⣿⠙⢿⠿⠏⠀⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣊⣿⠛⢛⣂⣠⣵⡃
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆⠀⠀⠀⢠⣆⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⣿⡇⠀⣀⣸⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣦⣿⣿⡿⢻⣿⣧⢸⣿⣿⡽⣩⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣮⣿⣿⣿⣿⣿⣿⣃⠘⡿⠟⠀⠻⠏⢢⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣧⣴⣿⡄⠀⠀⠀⣿⣆⢺⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣛⠚⡂⠀⡀⠛⣿⣆⣶⣦⣸⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣷⢾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣏⢳⣿⣉⣉⡿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣅⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣭⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢤⠾⠻⠿⠧⠿⠿⠷⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡴⠋⢛⣿⣽⣺⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⣿⣿⠀⠀⠀⠹⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠠⠤⠐⠋⠁⠀⠀⠀⠀⠈⠉⡤⣄⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠉⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⣌⠻⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀
⠀⠀⠀⠙⢥⡀⡡⠢⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠀⠀⣤⣄⠠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡞⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃⠈⠹⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⡀⠀⠁⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣭⡝⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢟⣋⡉⠙⢿⢩⣤⣤⠀⣀⣀⠀⣤⣤⠀⡿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⢻⠝⠛⣻⣿⣷⣞⠿⠛⢛⣛⡃⢸⣿⡇⢙⠛⢩⣶⣦⣶⣶⠀⣠⣶⣶⣦⡀⣾⣿⣷⡄⣸⢰⣶⣶⢸⣿⣿⡆⣿⣿⠀⢷⡇⠀⠸⣿⣿⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣽⣿⣸⣇⣀⣛⣛⡁⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⢰⢸⣿⣿⢰⣿⣿⠀⣿⣿⠐⠐⠃⠀⠀⠉⠉⠛⠛⠛⠋⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⠿⠉⠀⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⢿⢸⣿⣿⢸⣿⣿⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀
⠀⠀⠀⣾⠃⠄⣾⠀⠈⠀⠀⠀⠐⢀⣀⣘⣻⣿⡿⠿⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⢬⣿⣋⣿⣿⠀⠻⠿⡾⠿⠃⠘⠿⠷⠆⠿⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠆⠀⣿⡀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣏⡥⠀⠀⣴⣶⣶⣶⣦⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡁⠐⠛⠛⠻⠁⠀⠀⠀⠀⠀⡆⠠⠤⡍⣿⡿⠻⠧⠄⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣬⣄⡀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⡇⡻⢧⣿⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣶⣤⣄⡀⢀⠀⠀⠈⢸⠁⡿⠢⠤⡌⠁⠸⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣠⣗⢰⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣄⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⣃⣀⣻⠇⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡇⡂
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⠯⣭⣭⣍⣩⣉⣉⣉⣹⣿⣿⣿⠀⠀⠀⠀⠀⢀⡿⠿⠻⠇⠀⠀⠀⠀⠀⠐⣸⡿⣽⣿⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠂
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣶⣬⡉⠻⠄⠄⣰⣽⣿⣿⡇⠀⡇⠀⠀⠀⢸⣻⠟⠀⠄⣠⣤⡄⠀⢀⠈⢹⣯⣭⣿⠈⢃⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⣿⣿⣿⣿⡿⣟⠀⠀⠈⠉⠻⢿⡇⠀⠁⠀⠀⠀⢸⠀⣴⣦⠀⢨⡍⠁⢀⢠⠆⡾⠀⠀⢸⠀⠀⠀⠸⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠾⠴⣶⣿⣿⣿⣷⣶⠘⠀⣄⣧⣤⣤⣜⡀⠈⠀⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣻⣿⣿⣿⣿⣿⠁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣀⣸⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⢦⣿⣿⣿⣿⡿⠽⠛⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠶⠶⠶⠶⠦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀
⢸⣿⣿⣿⣿⣿⡿⠿⢿⣿⢼⠿⣿⠿⢿⡇⠄⢼⣇⠤⡤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⠿⠿⠟⠻⠿⢿⣋⢁⣀⣀⣩⣁⣾⡏⣿⣭⣽⣮⣄⣉⣉⣉⣁⣀⣀⡀⢀⡀⢀⢨⣽⣾⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⠋⠁⠀⢰⣶⣶⣶⣴⣶⣦⣤⣤⣬⣅⣀⣀⣀⣀⡀⡈⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣸⣿⢻⣿⣿⣿⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣶⣶⣦⠀⠀⠀⠀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⠿⠟⢸⣇⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢿⣿⡿⠧⠀⡆⠇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣷⡀⠀⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⡇⢈⣿⣿⡧⠀⠘⠿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣙⣿⣿⠿⣯⣥⠈⠀⠙⢋⠒⠂⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣍⣿⣿⣿⣿⣶⣿⡎⠁⣄⠀⠀⢺⡿⠆⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣯⣀⣿⡇⠀⠀⠀⢾⣇⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠷⠇⢀⡀⠾⢿⡦⣹⣅⢀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣷⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣴⣦⣭⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣟⠻⣽⡋⡉⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⣟⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣻⣿⣿⣿⣿⢿⣟⠟⣿⣿⣿⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢘⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠴⠾⠫⠽⠧⠿⠷⠴⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡸⠛⢻⣿⣿⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠹⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⠒⢮⣇⠀⠀⠀⠀⠈⣿⣤⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢘⠛⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⡏⠀⢓⠀⠀⠀⠀⠀⠀⠀⠛⠃⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡋⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡙⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁
⠀⠀⠀⠘⠿⡂⠉⠴⢝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠛⠃⠀⢀⡀⠠⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠃⠸⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⡿⠿⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠊⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣭⡝⣿⣿⣿⣿⣿⡷⠀⠀⠈⠈⠀⠀⠀⢸⣛⡉⠒⠃⢡⣥⣤⠀⣀⣀⠀⣤⣤⠄⣸⣽⠀⠠⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣻⠟⣻⣿⣿⣭⠻⡟⠛⣛⡃⢸⣿⡇⠻⡛⢩⣶⣦⣶⣶⠀⣠⣶⣶⣦⡀⣾⣿⣷⠄⠀⢰⣶⣦⢸⣿⣿⡆⣿⣿⠀⣿⢸⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣭⣿⡏⣿⣐⣚⣛⡃⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠈⠉⢸⣿⣿⢰⣿⣿⠀⣿⣿⠀⡇⠸⠀⠀⠘⠛⠻⠿⠿⠿⠃⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⠟⠁⢸⣿⡇⠀⠀⣿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⢸⣿⣿⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡿⠤⢰⡇⠀⠀⠀⠀⠀⠀⢀⢀⡟⣿⣿⢿⠯⠭⠤⠤⠄⠸⠿⠇⠤⠤⢬⣿⣋⣿⣿⠀⠻⠿⡾⠿⠃⠘⠿⠷⠆⠶⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠶⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡿⣒⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠀⠿⠿⠻⠏⠀⠀⠀⠀⠀⢸⠀⡤⣌⢸⣿⡿⠧⣀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⢸⣶⣬⣆⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠹⠸⢿⣸⣆⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣶⣤⣀⡀⢀⠀⠀⠀⠁⡓⣾⠷⣄⣠⠓⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣄⣀⣼⡀⣿⣷⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣠⡀⠀⠀⠀⠒⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠄⠐⠈⠲⠶⠉⠒⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢺⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⡿⡯⣉⣉⣙⣛⣛⣛⣛⣛⣻⣿⣿⠁⠀⠀⠀⠀⠀⣿⣸⠋⢁⠀⣀⡀⠉⠀⠁⠀⣿⣟⣿⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣭⣙⠻⠇⢀⣍⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠉⣤⡄⠈⢻⠛⠀⠈⡍⢩⣯⣍⣸⡇⠲⢒⠀⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣧⠾⠂⠀⠈⠙⠻⢿⣿⠀⠀⠀⠀⠀⠠⡇⣬⣽⣷⣶⣿⣄⡄⡆⢡⢼⠁⠀⢀⡇⠀⠐⠀⡏⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⡗⠚⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠴⡷⣾⠛⠋⠛⠛⠛⠃⠀⠄⢸⣀⣀⣸⠀⠐⠂⠀⠄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠰⢶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀
⢸⣿⣿⣿⣿⣿⣟⣿⣿⡗⣧⣽⣿⣿⣿⣿⢯⠷⢽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠤⢤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿⣿⡿⣿⣿⠠⠐⣯⠠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⠀⠀⠀⠀⠉⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀
⢸⡿⠿⡿⠟⠿⡿⠶⠟⠃⠀⢀⣘⣃⢸⣿⢹⣟⣛⣃⣩⣉⣉⣉⣉⣀⠀⠀⠀⠀⠀⢠⣳⣾⣵⡄⠀⢹⣿⣿⣿⣿⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣼⣿⣿⣿⣿⣿⣇⠀⠀⢠⣴⣤⣤⣤⣴⣦⡀⣀⣀⣛⣀⢀⣀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠘⠀⠀⠂
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣦⠈⣤⣶⣄⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠙⠹⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢟⢻⣿⣶⡆⠀⢠⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣆⠀⢿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣤⣴⣶⣾⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⠿⠀⠈⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡛⢻⣿⡿⢿⢋⠈⠃⠀⢀⡀⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣜⣿⣿⣷⣿⣶⣿⡏⠁⢀⡀⠈⢹⣿⠇⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⡀⣸⡧⠀⠀⠁⢰⣧⠨⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣮⡀⠀⢼⣿⣇⢘⣯⠁⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢣⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣰⣯⣙⣷⣼⣿⣾⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠋⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣁⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣟⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣿⣿⣿⣿⠿⡿⠛⣻⡿⣿⣿⣿⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢘⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡅
⠸⠴⠾⠫⠽⠧⠿⠷⠤⠷⠾⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⠀⠀⢻⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣟⠻⣿⣼⡄⠀⠀⢹⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠛⠋⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⡖⣫⠍⠀⠀⠀⠰⠛⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠏⣽⠯⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣉⠪⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠹⢇⠈⢣⠮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⠋⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡽⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣻⡿⠟⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠂⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣭⡝⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣛⡃⠉⠅⢠⣬⣤⠀⣀⣀⠀⣤⣤⠀⢠⣿⡇⠀⢼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢟⡝⢛⢿⣿⣯⡍⣿⠛⢛⠃⢸⣿⡇⠛⠛⢩⣶⣦⣶⣶⠀⣠⣶⣶⣦⡀⣾⣿⣷⠄⠀⢰⣶⣦⢸⣿⣿⡆⣿⣿⠀⣼⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣽⣿⢹⣇⣐⣛⡃⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠉⢸⣿⣿⢸⣿⣿⠀⣿⣿⠀⣿⢼⡇⠀⠈⠛⠿⠿⠿⠿⠟⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠂⢸⣿⣿⢸⣿⣿⠀⠻⠿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠲⠄⡞⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡧⡯⠭⠥⠤⠄⠸⠿⠇⠤⠄⢬⣿⣋⣿⣿⠀⠻⠿⡾⠿⠃⠘⠿⠷⠆⠶⠸⠿⠿⠀⠿⠿⠆⠿⠿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀
⠀⠤⡆⢠⡟⠀⢀⠃⠀⠀⠀⠀⠀⡀⠀⠀⡿⢻⣿⢓⠂⠀⠀⣤⣤⣤⣤⡄⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠀⠁⠸⠿⠛⠿⠀⠀⠀⠀⠀⠀⠇⢀⢤⡁⣿⡿⠾⢀⡀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⢸⣷⣦⣥⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢸⠃⠿⣆⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⡀⠀⠀⠀⢘⢰⡷⢦⣀⡘⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣠⡇⣸⣷⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠐⠀⢀⣀⣄⠀⢀⠀⠀⠀⠀⠄⡀⠀⠆⠰⠲⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣯⣿⠿⢉⣉⣉⣛⣛⣛⣛⣛⣛⣿⣿⡇⠀⠀⠀⠀⠀⢸⡟⢁⡤⠁⠺⠿⠆⠀⠄⠀⣸⣿⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣶⣬⣍⡛⠯⢀⢀⠌⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⢁⣙⣿⣤⣴⣇⠀⢰⠈⡈⣿⣈⣈⡿⠐⠒⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢿⢿⢿⣿⣿⣿⣯⡶⠂⠀⠀⠉⠛⠿⣿⠃⢠⠀⠀⠀⠈⡟⠈⠻⠿⠻⠻⠿⠟⠀⠠⠀⡇⠁⠀⡇⠀⠀⠀⠘⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⡿⠐⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢤⢷⣶⣤⣤⣤⣄⠀⠀⠀⢀⢀⣇⣀⣀⡇⠀⠂⠀⠠⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⡿⣿⣿⣿⣿⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣟⣿⣿⣿⡯⣼⣿⣿⡿⣿⠯⡹⠯⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠠⡤⠤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⢿⡿⠿⣿⠀⠤⣸⡀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠁⠀⠀⡀⠀⠀⠀⠀⠈⠉⠀⠀⣰⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁
⢸⠿⠿⠿⠟⠻⠿⠶⠿⠛⠀⠀⢀⢋⠀⣿⢉⣿⢋⣛⣈⣌⣉⡉⣉⡀⠀⠀⠀⠀⠀⢀⣖⣾⣯⣤⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣷⠄⢠⣤⣦⣤⣤⣤⣤⣄⢀⣀⣙⣃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣇⢻⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⡀⣠⣤⣤⡀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⢿⡿⠀⠿⠏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⠻⣿⣷⣶⠀⢀⠂
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⣤⣶⣾⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢏⡛⣻⣿⣿⣿⣛⡀⠃⠀⢀⡀⡒⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣤⡻⣿⣿⣿⣷⣼⣯⠑⢀⣀⠀⠩⣿⣷⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⡇⣨⣿⠀⠀⠉⢰⣿⡐⢳⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣁⠀⢰⣿⣧⢈⡛⡁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⣬⠹⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣟⣳⣶⣿⣾⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣿⠋⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣿⣻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣞⣿⣿⣿⣿⡿⣿⠛⢻⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣻⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣟⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠸⠤⠿⠻⠽⠷⠿⠷⠤⠾⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⠀⠈⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⡹⣿⣽⡆⠀⠘⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣟⠛⠁⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⠿⠾⠥⠄⠀⠾⠛⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⡟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡟⣹⡯⠍⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠩⠭⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢦⡑⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠈⠻⣀⢉⠖⢝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠛⠀⠀⢀⠀⠤⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣼⠃⢾⣿⣿⣿⣿⣿⣿⣿⠏⠉⢻⡿⠟⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠉⠀⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣭⡝⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣘⡛⠀⠀⢠⣤⣥⠀⣀⣀⠀⣤⣤⠄⠇⡾⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⡯⠛⣛⣿⣿⡗⠻⠛⢛⡃⢸⣿⡇⠙⠛⢩⣶⣦⣶⣶⠀⣠⣶⣶⣦⡀⣾⣿⣷⡄⠀⢰⣶⣦⢸⣿⣿⡆⣿⣿⠀⣷⡏⡇⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣽⣿⣇⣿⣐⣚⡃⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠉⢸⣿⣿⢠⣿⣿⠀⣿⣿⠀⡿⡇⠧⠀⠀⠙⠛⠿⠿⠿⠿⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⣤⢤⡀⠀⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣽⣯⣿⠿⠃⢸⣿⡇⠀⠀⣿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠂⢸⣿⣿⢨⣿⣿⠀⠹⠿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠁⠀⠀⠐⢀⣀⣘⢛⣿⣿⠿⠉⠩⠤⠄⠸⠿⠇⠠⠄⢬⣿⣋⣿⣿⠀⠻⠿⡾⠿⠃⠘⠿⠷⠆⠶⠸⠿⠿⠈⠿⠿⠆⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠐⢲⠀⣿⡀⠀⡜⠀⠀⠀⠀⠀⠸⠀⠀⣼⢿⣿⣏⡩⠀⠀⣤⣴⣶⣦⣤⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠁⠀⠀⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠤⡍⢺⡿⠟⠧⡀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀
⢸⣿⣷⣮⣄⣀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⡇⡺⢧⣾⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⢀⠀⠀⠈⠸⢃⣿⠣⠤⡰⠁⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣠⣟⢠⣷⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣤⠛⣀⡈⠰⣷⡶⠀⠠⡀⠈⠇⢀⠖⠆⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡟⣿⣾⣿⣽⣹⠯⣭⣍⣉⣩⣉⣉⣛⣙⣻⣿⣿⠀⠀⠀⠀⠀⠀⡇⢐⢻⣦⣠⣦⠀⠀⡆⠃⢸⡯⣽⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣶⣬⡙⠻⠄⢀⡀⢸⣿⣿⡟⠀⡇⠀⠀⠀⢠⠗⢾⣿⠿⠻⠿⠿⠅⠁⠈⢹⣧⣅⣿⠀⠒⠂⢀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⣿⣿⣿⣿⠿⠌⠀⠀⠀⠙⠻⢿⡇⠀⡇⠀⠀⠀⢸⣶⣮⣤⣄⣀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠂⠸⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣇⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⠯⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣀⣠⣀⣀⣸⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣻⣿⢽⣿⣿⣿⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣹⣿⣿⣽⢦⣿⣿⣿⢿⡿⠭⠛⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⠤⢤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠸⣿⡿⣿⡿⠿⣿⠿⠿⣿⡿⠴⠿⢿⠽⢿⡇⠤⢬⠥⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⢸⠿⠛⠿⠟⠛⠛⠿⠟⡉⠁⠀⣀⣉⡀⣾⡏⣿⣍⣙⡀⣀⣉⣉⡉⡁⡀⠀⠀⠀⠀⢀⣐⣒⣒⣲⣆⠈⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢿⣿⣿⣿⣿⡇⠀⢠⣦⣴⣤⣤⣤⣤⢄⢀⣀⣈⣃⣀⣀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⢸⠀⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣄⢀⣴⣤⡄⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣶⡀⠀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣥⣤⣶⣶⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⠀⠀⣠⣄⠀⠀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣴⣙⣿⣿⣿⣿⠀⣿⠛⠁⠀⠀⠘⠷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡏⣉⡙⣻⣿⠿⣇⡀⠹⠀⢀⡖⣚⡆⠸⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣶⣍⣿⡿⣵⣷⣾⡗⠈⠀⣄⠄⠁⢿⡿⢡⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣖⣤⣠⣿⠆⡀⠈⠀⣿⡄⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣷⣿⣿⢴⣅⠄⣀⣿⢷⡬⣿⣏⢨⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣯⢹⣉⣠⣏⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢽⣧⣼⣷⣹⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣟⠫⣿⣈⣀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⣿⣏⣿⣯⣯⣠⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣟⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⣼⣿⣿⣿⣿⡟⣋⣿⢿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣝⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣡⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠸⠤⠿⠳⠼⠧⠽⠬⠤⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⡹⣿⣽⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⠉⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⡿⠿⠧⠤⠠⠿⠛⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢫⣿⣿⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠭⠠⠤⠤⠄⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠠⣌⠺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠙⢅⠀⠔⠪⡻⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠁⠀⢀⡤⠤⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠸⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⠿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣭⡝⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣘⣻⠋⠂⢠⣤⣤⠀⣀⣀⠀⣤⣤⠄⠘⣸⣿⠠⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠛⠯⠋⢝⣻⣿⣾⢘⠟⠉⡁⢸⣿⡇⠙⠛⢩⣶⣦⣶⣶⠀⣠⣶⣶⣤⡀⣾⣿⣷⡄⠀⢠⣶⣶⢸⣿⣿⡆⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣿⡟⣾⣥⣉⡁⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⢰⣿⣿⠀⣿⣿⠀⢸⠿⠺⠀⠀⠉⠛⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⠤⠤⡄⠀⠠⠈⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⠁⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⢰⣿⣿⠀⠹⠿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⡏⠄⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⣛⣽⣿⠿⠗⠒⠒⠀⠸⠿⠇⠀⠀⢬⣿⣋⣿⣿⠀⠻⠿⡾⠿⠃⠘⠿⠷⠆⠛⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠒⠀⢸⣇⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣿⡟⣩⠀⠀⢰⣶⣶⣶⣲⡄⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣂⠈⠀⠛⠛⠙⠃⠀⠀⠀⠀⠀⢰⠀⡀⢤⢸⣿⢗⠓⠤⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀
⢸⣿⣿⣶⣮⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⢘⠻⠼⡇⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⡀⠀⠀⠁⠍⣼⠛⠤⠠⠉⠀⠿⠿⡿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⢀⠂⣴⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣼⡅⣿⣿⣧⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢠⠀⠾⣧⣀⣠⠉⠀⢠⠘⠧⢸⣉⡠⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣼⣟⡧⢬⣭⣭⣭⡭⢍⣉⣉⣽⣿⣿⠁⠀⠀⠀⠀⠀⣼⠸⣿⣿⠿⣿⣷⡖⠘⠀⠀⣿⣭⣽⡗⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣷⣦⡌⠙⠃⠄⢀⠨⣿⣿⣿⠀⠈⠀⠀⠀⢠⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠉⣧⣥⣼⡇⠐⠂⠀⡄⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⠿⣟⣿⣿⣿⣿⡟⠂⠀⠀⠀⠈⠛⠿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣦⡄⠀⠠⢰⠀⠀⠈⠇⠀⠀⠀⠇⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⡿⢺⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⣄⣸⣤⣀⣸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⣍⣿⣉⠿⣿⢷⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡟⣿⣿⣿⣏⣯⣏⣿⣿⡇⠲⣼⣿⣿⣻⣿⠢⠙⢛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢴⠶⠤⠤⠤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢸⣿⣿⣿⣿⠿⢿⡿⢿⣿⡷⠸⠞⢿⡒⢻⡟⣀⣀⣧⡤⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠸⠿⠋⠛⠛⠉⠙⠛⡛⠋⠀⠀⣀⣈⣀⣸⡇⣸⣇⣉⣁⣀⣀⣉⣉⣁⠀⠀⠀⠀⠀⢀⣤⣙⣲⣖⣶⠀⠈⠉⠩⣭⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣷⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⠀⠀⠀⠀⢠⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⣉⣀⣀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣦⢀⣤⣦⣄⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⢟⢿⣿⣶⡆⠀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣴⣤⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢹⠛⣿⣿⣻⣿⣯⠀⣀⣾⡦⠀⠀⢶⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢤⣌⣹⡞⣿⣿⠀⣟⠉⠀⣀⣀⠈⢻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⠻⠟⢋⣀⣉⢫⣿⠿⣿⠄⠘⠀⠸⣿⣛⣃⠘⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣿⣤⣶⣎⣸⡿⡗⣷⣶⡿⢀⠀⣤⠂⠀⢻⡿⢠⠀⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣁⣿⣿⣷⣨⣠⣿⡇⢀⠀⠀⣿⡇⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡯⣽⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣯⣿⣿⡿⣴⣧⡀⣀⢿⡿⡕⣿⣟⢡⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⢻⣿⣿⣿⣿⣿⣿⡿⣷⣶⡿⢿⣿⣿⣿⣿⣾⣿⣿⣩⣈⣠⣤⣻⣾⣿⣯⣿⣿⣿⣿⣿⢿⣿⣾⡿⠟⠎⣡⣵⣯⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣾⣿⡟⣿⣿⣿⢯⠙⢾⠅⣀⠹⠏⣿⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⣿⠻⣿⣿⣟⣿⣧⣦⣠⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣟⢽⢬⣿⣽⡯⡟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⣵⣻⣿⣿⣻⣟⡋⣽⣿⣿⣿⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢭⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⡛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⡫⢛⣽⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡅
⠸⠤⠿⠳⠦⠦⠼⠤⢤⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⢻⣿⣿⡆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡍⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢧⡄⢨⣿⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠻⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢿⣿⣿⡟⣛⠁⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠸⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠭⠥⠤⠤⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣤⡑⢝⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠙⠣⡀⡱⠒⢝⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠀⠀⡤⠤⠤⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠀⢿⣿⣿⣿⣿⣿⣿⣿⠋⠈⣿⠿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣭⡝⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⡛⡏⠀⢠⣤⣬⠀⣀⣀⠀⣤⣤⠄⠀⢠⣿⡗⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⠫⠏⢩⣻⣿⣷⠎⠿⠍⡁⢸⣿⡇⠙⠛⢩⣶⣦⣶⣶⠀⣠⣶⣶⣤⡀⣾⣿⣷⡄⡀⢠⣶⣶⢸⣿⣿⡆⣿⣿⠀⢈⣾⢸⡇⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣽⣿⣸⣧⣬⡁⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⠰⣿⣿⠀⣿⣿⠀⢸⠿⠸⠇⠀⠈⠛⠛⠻⠿⠿⠏⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⣿⣿⠃⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠄⢸⣿⣿⢸⣿⣿⠀⠹⠿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⣟⣿⣿⡷⠟⠒⠒⠀⠸⠿⠇⠀⠀⢬⣿⣋⣿⣿⠀⠻⠿⠾⠿⠃⠘⠿⠷⠆⠛⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠂⡇⢰⣏⣀⣠⠃⠀⠀⠀⠀⠀⡆⠀⠀⡿⣹⣿⢩⠅⠀⠀⣶⣶⣖⣒⡦⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣄⠀⠀⠘⠛⠙⠛⠀⠀⠀⠀⠀⠀⠂⢠⢰⡀⣿⠟⡛⠠⠄⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⢸⣿⣿⣷⣾⣥⣀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢸⠁⡛⠤⠇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⢀⠀⠀⠁⠬⢸⠛⠠⠄⠍⠀⠸⠿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠙⠻⠓⠀⠰⡖⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⡇⢼⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⡄⠀⠀⠀⠀⠀⢠⣄⣤⣼⣷⣾⣧⡀⠀⠆⠀⢠⣁⠰⠴⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣧⣇⡻⠤⣭⣭⣭⣭⢍⣉⣉⣍⣿⣿⡇⠀⠀⠀⠀⠀⣸⣯⡿⠛⠉⠉⠉⠁⠀⠀⠀⣽⢭⣍⡗⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣻⣿⣶⣬⠙⠓⠀⠀⡀⣿⣿⣿⠇⠈⠀⠀⠀⣰⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠉⣽⣬⣤⡇⠀⠒⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣻⣿⣿⢻⡿⠓⠀⠀⠀⠈⠙⠻⢿⠀⢰⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣇⠀⠠⠀⡇⠀⠀⡇⠀⠀⠀⠁⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⡇⣾⣯⣿⡿⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⢠⣐⣥⣀⣀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣿⣇⡭⢿⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⡗⢾⣿⡿⡟⣿⠓⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡦⠤⠤⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣻⣿⡿⣿⡿⠿⣿⡿⠃⠞⢻⡗⠻⣿⠀⣀⡘⡠⢀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠿⣿⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠸⠻⠋⠋⠛⠋⠉⠛⠛⠋⠁⠀⢀⣀⣀⣠⣿⣰⣯⣁⣁⡀⣈⣈⣉⣉⠀⠀⠀⠀⠀⢀⣄⣙⣓⣐⣲⡀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⡀⠀⠀⠀⢠⣦⣴⣦⣤⣤⣤⣤⡄⣀⣀⣙⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠂⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣤⠀⣠⣤⣄⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢟⢻⣿⣷⣆⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⣀⡀⠀⠀⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣥⣤⣴⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠛⠻⣿⣿⣿⣿⠀⣴⣿⠃⠀⠀⢻⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢧⣤⢹⡾⣿⣿⠀⢻⠀⠀⣤⣄⠀⢡⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣟⠛⢑⣀⣈⢉⣽⠿⢿⡄⠈⢀⠨⣿⢙⣃⠈⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⣽⣆⣴⢦⣘⣿⠟⣾⣶⣿⠃⠀⣾⠓⠀⢸⡿⢷⡄⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣿⣿⣷⣤⢠⣿⡏⠀⠀⠀⢿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠯⣭⣿⣿⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣯⣿⣿⣿⣥⣇⣀⢀⣾⣿⣯⣿⣽⡡⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⡿⢻⣿⣿⣿⣿⣶⣿⣿⣍⣅⢀⣤⣹⣾⣿⣿⣽⣿⣿⣿⣿⡿⣿⣾⣿⠟⠅⣡⣽⣾⢼⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣷⣷⣿⣻⣿⣿⡿⡉⠺⡅⠠⡸⠏⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡏⢿⣿⣷⣸⣿⣶⣤⣾⣯⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣩⢽⣫⣽⣯⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣧⣹⣿⣿⣟⣟⡉⣽⣟⣿⣿⣯⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣯⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⠛⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡻⢛⣼⣿⣿⣿⣿⣿⡟⣿⣿⣿⣯⣿⡅
⠸⠤⠾⠳⠦⠦⠼⠤⠤⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡏⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠻⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠙⠉⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⢱⡶⠶⠒⢃⠀⠀⠀⠀⠐⠄⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠩⠭⠍⠅⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢤⡑⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠈⠫⣀⠠⠒⢝⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡼⠃⢿⣿⣿⣿⣿⣿⣿⣿⠏⠙⢻⣿⠿⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣭⡝⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⡸⢷⠀⢠⣤⣤⠁⣀⣀⠀⣤⣤⠀⠀⡇⡞⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠽⠁⣛⣿⣷⡗⠻⠛⠃⢸⣿⡇⠙⠛⢩⣶⣦⣶⣶⠀⣠⣴⣶⣦⡀⣼⣿⣷⡄⠀⢠⣶⣶⢸⣿⣿⡆⣿⣿⠀⠀⣿⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣽⣿⢧⣟⣐⡃⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠁⢸⣿⣿⠐⣿⣿⠀⣿⣿⠀⠀⣿⡇⠇⠀⠀⠙⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡤⠤⢤⠀⠀⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⣿⣿⠇⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⠀⣿⣿⠀⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠃⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⣘⣻⣿⡟⠿⠀⠁⠀⠸⠿⠇⠠⠀⢬⣿⣋⣿⣿⠀⠻⠿⠾⠿⠃⠘⠿⠷⠆⠶⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠂⠀⣿⡀⣀⡇⠀⠀⠀⠀⠀⠈⠀⠀⣾⢿⣿⢏⡍⠀⠀⣴⣶⣶⣶⣤⠀⠈⠙⠛⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣐⡀⠁⠘⠛⠋⠛⠁⠀⠀⠀⠀⠀⡆⢀⠤⡅⣿⡿⠛⠧⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣶⣥⣀⠀⠀⠀⠀⠀⠀⠀⠁⢸⢀⡇⡛⢧⣿⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⢠⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⢀⠀⠀⠈⠨⢡⡟⠢⠨⡌⠁⠸⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⣅⠉⠀⡄⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣦⣤⡠⣏⢰⣷⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣿⢿⡿⠿⣼⣒⠂⠁⠀⠀⠂⠀⠖⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣾⣧⣿⡺⠭⣭⣭⣍⣉⡉⣙⣋⣙⣻⣿⡏⠀⠀⠀⠀⢀⣼⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣷⣦⣌⠙⠻⠀⢀⠀⣼⣿⣿⡇⠀⠁⠀⣠⣼⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⣼⣌⣀⣿⠀⠒⠀⢀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠻⢿⠏⣿⣿⢷⡿⠂⠂⠀⠀⠈⠙⠻⢿⡇⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣟⡉⠉⠀⠀⠄⡇⠀⠀⡿⠀⠀⠀⢸⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⣧⣿⡻⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⣿⣿⠇⣾⣿⣿⣿⣿⣷⡀⠀⢀⣀⣇⣀⣀⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣯⣍⣹⣏⡔⠟⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢿⣿⣿⣧⣿⣯⢹⣿⣿⡶⠆⣿⡿⡟⣿⠇⠝⠃⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⢿⡿⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⡤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢸⣿⣚⣿⣿⡿⠿⣿⠿⡿⣿⠇⠧⠻⡇⠛⣿⠁⠀⡈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⢰⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠛⠙⠛⠛⠙⠛⠛⠛⠉⠀⢀⢀⢁⡀⣿⢀⣿⠈⣉⠀⢈⣈⡉⠉⠀⠀⠀⠀⠀⠀⡀⢐⡒⠂⡰⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠆⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⡄⣀⢀⢀⡛⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣠⠀⢀⣤⣄⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠤⠀⠀⠠⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡿⢿⣿⣧⣦⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡇⠀⣠⣿⡆⠀⠀⣄⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣭⣍⣩⣤⡄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠈⠛⠛⢿⡿⣿⣷⠀⣿⠋⠀⠀⠀⢻⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⠀⠁⣀⠐⣵⢽⣿⠄⢘⠀⠀⣴⣦⠀⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣽⠿⡟⠀⢀⠀⢉⣩⡟⠇⢀⠀⣠⡠⣿⡛⢓⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣅⣽⣇⣠⢄⡈⡿⠇⢰⣶⣾⠀⠀⣶⡑⠈⠸⡿⢻⡇⢹⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣺⣿⣿⣤⢠⣿⡏⠀⠀⠀⢻⣧⡘⣶⢿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⠿⣭⣿⣿⡇⣼⣿⡿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣮⣿⡞⣟⡃⣆⣀⢀⣹⣿⣧⢿⣿⡁⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⣿⡟⣿⣿⣿⣽⣿⣿⣿⢿⡶⡿⠷⣿⣿⣿⣿⣷⣿⣿⡍⣅⠀⣤⣘⣦⣿⣿⣻⣿⣿⣿⣿⣿⣟⣽⣿⡟⠉⢁⣉⣿⢼⡇⢼⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣷⣿⣷⢻⣿⣿⡿⡉⢡⡏⠀⡨⠟⢹⢯⣻⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠿⣿⡟⣻⣿⣷⢹⡿⣴⣀⣤⣾⠹⣿⣿⣿⣾⣿⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣿⣿⣿⣿⣷⣿⣯⠫⣣⣿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣜⣇⣘⣿⣿⣟⣿⠛⢹⡟⣟⣿⣿⡉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣯⣹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢘⣯⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⠟⢫⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣏⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣞⡛⣹⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡿⡇
⠸⠤⠾⠳⠦⠤⠼⠤⢤⠦⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣾⠿⠿⠿⠿⠿⠿⠧⠟⠿⠻⠿⠿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣟⠛⠉⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠻⣟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠷⠦⡾⢿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⢿⣿⣿⣿⡿⠀⠀⠀⠀⢠⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠉⠉⠉⠀⢻⠟⠸⡏⠁⠉⠉⠀⠀⠠⠤⠉⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⡑⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠃⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠫⡀⠈⠖⢝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠛⠂⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣪⠇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣭⡝⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⡸⢿⠁⢠⣤⣤⠀⣀⣀⠀⣤⣤⠀⠀⡆⣼⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡯⠛⣻⣿⣿⣯⠹⡟⠃⢸⣿⡇⠙⠛⢩⣶⣦⣶⣶⠁⣠⣴⣶⣤⡀⣼⣿⣷⡌⠀⢠⣦⣦⢸⣿⣿⡆⣿⣿⠀⠀⣧⡏⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⣿⡇⣿⣐⡂⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠉⢸⣿⣿⠀⣿⣿⠀⣿⣿⠀⠀⣿⡇⣧⠀⠀⠹⠿⠿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣤⢤⡄⠀⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⢹⣯⣿⡇⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⠀⣿⣿⠀⠹⠿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣘⠛⣿⣿⢼⠭⠭⠄⠸⠿⠇⠠⠄⢬⣿⣋⣿⣿⠀⠻⠿⠾⠿⠃⠘⠿⠷⠆⠦⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢲⠀⣼⡁⠀⡘⠀⠀⠀⠀⠀⢰⠀⠀⢸⢣⣿⡟⡊⠀⠀⢠⣤⣤⣤⣤⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣐⠀⠀⠀⠛⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠤⡍⢺⣿⠟⠇⡀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣶⣤⣅⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇⠺⢇⣼⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠠⡦⣠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⢀⠀⠀⠈⠀⠃⡿⠆⠄⢐⠃⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣷⣤⡄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣄⣀⣷⢀⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣾⣿⡋⠛⠛⠛⠋⠀⠀⠀⠀⠖⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡿⣿⣶⣯⣽⠹⠏⣉⣉⣉⣉⣛⣛⣛⣛⣻⣿⣿⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣤⣀⣀⠀⠀⠀⢸⣟⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣼⡏⣷⡦⣍⡙⠻⠄⠀⠈⢸⣿⣿⡏⠀⡂⢠⣿⣿⡿⣿⣿⣿⣿⣿⠛⠻⠀⠀⠀⢸⣇⣀⣸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⣿⣿⡗⣿⠒⠀⠀⠀⠀⠘⠿⣿⡇⠀⠀⣿⣿⠏⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⡼⠉⠉⢹⠀⠀⠀⢸⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡟⣿⣿⣿⣿⣿⣿⢿⣿⣇⣿⣿⣿⣿⣿⣇⠠⣶⣾⢻⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⣿⠉⠀⠀⠀⡀⣇⣀⡀⡘⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣉⣹⣿⠈⢹⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣟⣿⣿⣷⣻⣻⢹⣿⣿⠸⠄⣿⡟⡿⢿⡇⠍⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠿⢿⡿⠧⠿⢿⠿⠿⢯⠅⠤⠿⠧⠼⣾⠇⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠟⠙⠹⠛⠛⠛⠛⠛⠉⠀⠀⠀⠁⠀⣿⠀⣿⠉⢙⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⠒⠂⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣤⣴⣴⣴⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠸⣿⣷⣿⣷⣾⣿⣿⣶⣤⣦⣦⣴⣶⣴⣷⣾⣿⣿⣿⡀⠀⠀⢀⣀⠀⠀⠀⠀⢤⣤⣄⣠⣀⣀⢀⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣄⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣤⣮⣶⣿⣿⣾⣶⣾⣶⣴⣶⣶⣄⣀⣀⣀⣀⠀⢀⣀⣀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣟⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⡆⠈⠇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⢿⣿⣧⣤⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡿⣿⣅⣹⣿⣿⡆⠀⣾⡟⠀⠀⠸⣦⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣅⣉⣉⣉⣠⡀
⢸⣿⣷⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠃⠀⠘⠚⠾⡿⢿⣥⠀⠋⠀⠀⠀⠀⠙⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣤⣂⠀⠀⢀⠀⣤⢰⣞⠀⠀⠀⠰⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣤⣿⣿⣿⣿⢿⣿⣿⣿⣿⣍⠉⠩⠿⠛⠀⠀⠀⠀⠈⠚⠅⠀⢰⣶⡈⣿⡿⢾⣷⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣏⡀⢈⣄⢀⡄⡀⣻⡇⢰⣤⣼⠂⠘⣿⡃⠈⠹⡽⣿⡇⢿⢿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⠡⣯⣽⣿⢿⣿⣿⣶⣿⣿⣷⣿⣿⣄⣸⣻⣿⣄⢰⣿⣧⠀⠀⠀⣻⣷⡸⣶⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⣿⣿⣷⣯⠛⢉⡛⣿⠃⠀⠘⣿⣿⣿⣿⣿⣿⣶⣮⣿⣷⡜⣻⠾⣟⠃⠀⠀⠀⢻⣿⣇⢿⣟⡉⠁⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⢽⡟⢻⣟⣿⣭⣥⡤⣹⢈⡥⠼⠗⣿⣿⣿⣿⣥⣴⣾⡍⠉⠀⣀⠀⣤⣸⣿⣻⣿⣿⣽⢿⣯⡟⢩⣼⡊⠉⠓⣛⣹⢪⠁⢼⣾⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣷⣿⣷⣾⣶⠿⣯⣿⡿⠉⠂⡏⢀⠀⠝⠙⢇⣹⣿⣿⣿⣧⣮⣤⣿⣿⣧⣿⣿⠟⢿⡟⢻⣶⠃⠈⣷⣠⣀⣀⡴⠹⣾⣷⣿⣴⣿⣋⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇
⠠⣿⣾⠿⣿⣷⣾⣏⠨⣇⣻⣶⣖⣲⠿⣗⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣘⣇⡈⣛⣙⠛⠿⠙⢛⡟⣻⣷⢻⠈⡽⣿⣿⣟⣽⣶⣿⣿⣿⣿⣿⠟⠉⣍⣙⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣏⣿⣏⣿⣿⡃
⢘⡯⣽⣿⠿⣿⣿⣿⣷⣵⣿⣿⣽⣎⣨⠗⢋⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣤⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣿⣿⣿⣟⢾⠻⢉⣷⣿⣿⣷⣿⡟⢿⣿⣿⣿⣿⡇
⠨⠤⠼⠳⠦⠤⠼⠤⠤⡶⠿⠿⠿⠷⠿⠿⠿⠿⠿⠙⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠩⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠾⠧⠝⠷⠾⠿⠿⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠛⠉⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠻⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠉⠙⡻⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠉⠉⣯⣿⣿⡿⣿⡿⢿⠀⠐⠁⣴⡷⠆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡙⠯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢻⠁⠈⠛⠛⠉⠀⠀⠀⠉⠀⠀⠀⠠⣿⠃⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠫⣀⠈⠔⢝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣎⠏⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣭⡝⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢀⣀⡘⢦⠄⢠⣤⣤⠀⣀⣀⠀⣤⣤⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡫⠛⠻⢿⣿⣭⠹⡟⠃⢸⣿⡇⠚⠛⢡⣶⣦⣶⣶⠁⣠⣴⣶⣤⡀⣼⣿⣷⠌⠀⢠⣦⣤⢰⣿⣿⡄⣿⣿⠀⠀⣠⡿⣻⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣭⣿⡇⣾⣀⡂⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠈⠉⢸⣿⣿⠀⣿⣿⠀⣿⣿⠀⠀⣿⡏⣸⠀⠀⠙⠿⠿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢧⣿⣿⡇⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠰⠀⢸⣿⣿⠀⣿⣿⠀⠹⠿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢐⠿⣿⣿⢼⠭⠭⠄⠸⠿⠇⠠⠄⢨⣿⣋⣿⣿⠀⠻⠿⠾⠿⠃⠘⠿⠷⠆⠶⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢲⠀⣸⡃⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⢸⠇⣿⡟⡒⠀⠀⢠⣤⣤⣤⣤⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⠀⠈⠀⠛⠛⠻⠇⠀⠀⠀⠀⠀⠸⠀⡄⡌⢺⣿⠷⠇⣀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣤⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⢇⣸⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡆⠐⠷⠤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣟⣿⣿⣿⣿⣶⣤⣄⠀⢀⠀⠀⠀⠀⡃⡾⠆⡄⢀⠂⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡶⣿⣶⣆⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣴⢀⣷⣶⣦⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⣀⣤⣴⣿⣿⣧⣄⠀⠉⠁⠀⠀⠀⠀⠐⠀⠠⠄⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡿⣿⣶⣿⣹⠹⢏⣉⣉⣉⣛⣛⣛⢛⣛⢻⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⢠⡞⣖⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣏⣿⣿⣿⣼⣟⣷⢦⠉⠙⠫⠅⠀⠀⢸⣿⣿⣿⠀⣰⣿⠿⠃⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣇⣁⣸⠀⠠⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⡿⣿⣿⡗⠞⠒⠀⠀⠀⠀⠈⠹⣿⡇⠀⠉⠀⠀⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣾⡇⣿⣿⣿⣿⣿⣿⢿⣿⡏⣿⣿⣿⣿⣿⣇⠀⣶⣾⠫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣉⣛⣿⠀⠹⠗⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡿⠉⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢂⣿⣿⣯⣻⣹⢙⣿⣿⢹⠄⠿⡟⣿⢿⡏⠍⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠿⠴⠿⠷⠯⠽⠿⠯⠽⢭⠜⠠⠼⠇⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⡼⠀⠀⠀⠈⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⠸⠿⠿⠙⠹⠛⠛⠛⠛⠟⠉⠀⠀⠀⠈⠀⣼⠃⣽⠉⠉⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡄⢠⣄⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣇⡿⠠⡶⣶⣾⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⡆⠀⠀⢈⡟⠉⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⢀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀
⢰⣷⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⢻⡀⠀⠀⢺⣿⣿⣿⣿⣿⣧⣀⣠⣶⣦⣤⣤⡴⣶⣦⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣻⣟⠙⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⠿⢻⣿⣿⡟⠀⢀⣿⡿⠀⠸⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣥⡄⣾⣿⣿⣇⣤⠀⠀
⠸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⢄⡠⠾⠢⣅⣹⡃⢀⠀⠸⡟⠁⠀⠀⠘⡏⠀⢸⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣄⣉⣉⠉⣠⡀
⢸⣿⣷⣾⣡⡬⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣯⣿⣿⣿⣥⠻⠀⠀⠈⠘⠿⡿⠖⠠⠀⡇⠀⢀⣠⡀⢠⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣿⣿⡇
⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⢿⠻⣿⣶⣿⣧⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⢠⢰⡆⠀⣤⡀⢸⣿⣷⣺⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣗⣻⣤⣼⣯⣿⣿⢿⣿⡿⣿⣿⠉⠈⠨⠛⠑⠀⠀⠀⠀⠈⡘⠀⠀⣿⣷⠘⣿⠿⢽⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣟⣸⣿⣿⣯⣿⣭⣩⣿⣿⣿⡁⣒⣿⣿⣿⣿⠾⣾⣿⣿⣿⣇⡀⢀⣄⢀⡄⡀⢲⡆⠀⢤⣄⡀⣸⣿⠀⠈⠣⠼⣿⡄⠙⣿⠿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣹⣿⣿⣿⢿⢿⣿⣿⡇
⠀⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⣿⣿⣟⣿⣿⢿⠠⣍⣽⡿⠿⣿⣷⣴⣿⣿⣶⣿⣇⡀⢐⣨⣬⡀⣹⣿⡆⠀⠀⠰⣿⣿⠈⣤⣾⣮⣾⡝⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⣹⣿⣿⣿⡭⡿⣿⠾⢭⡿⣿⡻⣿⣿⣷⡭⠉⢈⠉⣿⠁⠀⠈⢻⣿⣿⣿⣿⣿⣶⣄⣿⣷⡎⣳⠿⡟⠃⠀⠀⠀⠻⢿⣆⢿⡟⠉⠈⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢨⡋⢺⡇⢹⡛⣿⣭⣤⡄⢙⠉⡄⠼⠒⢿⣿⡟⣻⡥⢴⣮⡀⠀⠀⢀⠀⢀⠸⣻⣻⣿⣯⣩⠹⣯⡍⢡⡴⠂⠉⠒⣚⣹⣈⡕⢲⣾⣼⣧⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣗⢿⣷⣶⣼⠟⣯⣿⡿⠉⠀⡇⠀⠀⠌⠹⢆⡙⣷⣞⣿⣧⣬⣤⣾⣿⣥⣟⡿⠛⢿⡏⠛⡖⠃⠈⣶⢠⡀⣀⠤⠁⣼⣷⣆⣰⣿⢛⡹⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⣿⡇
⠠⣿⣦⠾⣿⣧⢾⣇⠀⣃⣺⣶⣖⣰⠿⡗⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣤⣐⡇⡀⢉⡈⠛⠻⠛⢻⡞⣳⣷⢻⠈⡼⣿⣿⣏⣰⡦⣾⣿⣿⣿⣿⠿⠉⣌⠉⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⢋⣿⣏⣿⣿⠃
⢐⡯⣽⣿⠿⣿⣿⣿⣷⣵⣿⣮⢽⣎⣠⠖⠊⣛⡿⣽⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡏⣹⡿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣿⣥⣿⣿⣯⣽⣿⣿⣿⣿⣿⣯⣿⣬⣿⣿⣿⣿⣟⠼⠫⢉⣵⣾⣿⣷⣿⡟⢿⣿⣟⣛⣿⡃
⠨⠤⠼⠣⠦⠤⠼⠤⠤⠤⠿⠿⠿⠷⠿⠿⠿⠿⠿⠘⠋⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠾⠩⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠦⠧⠌⠱⠾⠽⠷⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠛⠉⠉⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠻⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠉⢁⡿⣿⣿⣿⣿⣿⣇⠸⣾⢧⣸⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡙⠮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⡿⢿⣿⣿⠧⠿⠀⠹⠞⠛⠫⠀⣠⡿⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠫⣀⠈⠔⢍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠒⠂⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⠇⠀⠀⣎⠏⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣭⡝⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢠⣤⣤⠀⣀⣀⠀⣤⣤⠄⠀⠀⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡫⠛⠻⢿⣿⣭⠹⡟⠃⢸⣿⡇⠘⠛⢡⣶⣦⣶⣶⠁⣠⣴⣶⣤⡀⣼⣿⣷⠄⠀⢠⣤⣤⢰⣿⣿⡄⣿⣿⠀⠀⢠⡟⢻⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣍⣿⡇⣾⣀⡀⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠈⠉⢸⣿⣿⠀⣿⣿⠀⣿⣿⠀⠀⣼⡏⣻⠀⠀⠙⠿⠿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢧⣿⣿⡇⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠐⠀⢸⣿⣿⠀⣿⣿⠀⠹⠿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⣿⢼⠭⠭⠄⠸⠿⠇⠠⠄⢨⣿⣋⣿⣿⠀⠻⠿⠾⠿⠃⠘⠿⠷⠆⠆⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢲⠀⣸⡃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⡟⡒⠀⠀⢠⣤⣤⣤⣤⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⠀⠈⠀⠛⠛⠻⠇⠀⠀⠀⠀⠀⠸⠀⡄⡌⢸⣿⠷⠇⣀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⢇⣸⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣩⣧⣘⡃⠒⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣟⣿⣿⣿⣿⣶⣤⣄⠀⢀⠀⠀⠀⠀⡃⡿⠆⡄⢀⠂⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣿⡟⠛⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣴⢀⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⠄⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡿⣿⣶⣿⣹⠹⢏⣉⣉⣉⣛⣛⣛⢛⢛⢻⣿⣿⠀⣸⣿⡟⠙⠛⢿⣿⣿⣿⣟⠙⠋⠀⠀⠀⠀⣖⣖⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣯⣿⣿⣿⣼⣟⣷⠤⠉⠙⠻⠅⠀⠀⢸⣿⣿⣿⠀⠁⠀⠃⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣏⣉⣸⠀⠠⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⠿⠿⡿⣿⣷⡇⠐⠀⠀⠀⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣾⡇⣾⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣇⠀⣰⣼⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣣⣿⣿⡿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣉⣋⣿⠀⠑⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⢈⣿⣿⣇⢻⣹⢙⣿⣿⢹⠤⢷⡟⣿⢻⡏⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠯⠼⠿⠿⠯⠵⠯⠤⠽⢯⠼⠠⠼⠧⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⡼⠀⠀⠀⠈⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⠸⠿⠿⠙⠹⠛⠚⠚⠓⠛⠁⠀⠀⠀⠁⠀⣼⠁⣽⠈⠉⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢄⣠⣄⣤⣤⣤⣤⣤⣶⣶⣦⣶⣶⣶⣄⡿⠀⡶⣶⣾⣶⣶⣶⣦⣄⣤⣄⣄⣠⣤⣠⠀⢴⣐⡀⠀⠀⢰⣾⡄⢶⡄⠀⠀⠀⣄⡠⣀⣀⣀⡀⢀⡀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀
⢰⣷⣿⣿⣿⣿⣿⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣹⣼⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣟⣵⢿⣿⣿⡆⠀⢸⣿⡇⠈⣿⣄⠀⠀⣻⣿⣾⣿⣿⣿⣥⣀⣢⣤⣦⣤⣠⠴⢶⣦⣤⡄⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⡛⣟⠙⣿⣿⣿⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⠿⢶⣿⣿⠃⠀⣿⡿⠁⠀⠻⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⡟⢣⣌⣄⠄⣾⣿⣿⣇⣤⠀⠀
⢘⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⡻⢇⢀⠠⠾⠱⢀⠙⡉⠀⠀⢸⠀⠀⠀⡀⠸⡀⠀⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⢶⣀⣉⣉⢉⣠⡀
⢠⣿⣷⣾⣡⡄⣾⣿⣻⡿⢻⣿⣿⣿⣿⣶⣿⣿⡿⣷⡧⣿⣿⣿⣯⣽⣿⣿⣠⠚⠀⠀⠀⠀⠮⡷⠆⠀⢸⣀⠀⣺⣿⣤⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢧⣿⢯⠙⢿⣦⣿⣧⣿⣿⣿⣿⣿⣿⣻⢻⡀⢀⠀⠀⠀⠀⢠⢠⡆⢘⣿⡈⣻⣿⣿⣿⡆⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣟⠲⣤⣼⣟⣿⣿⢿⣿⣟⣿⣟⠉⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠠⠈⢿⣟⠘⠷⡞⣿⣇⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠰⣿⣿⣿⣏⢸⣿⣿⣿⣿⣍⢩⣿⣿⣿⡑⣒⣿⣿⣿⣿⠾⣿⣿⣿⣿⣅⡀⢐⣄⠀⠄⡀⢰⠀⠀⢤⢄⠀⣽⣿⠀⠀⠁⣿⣿⡆⣽⣿⠿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡈⣹⣿⣿⣿⡻⢿⣿⣿⡇
⠀⣅⣹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣻⣤⡯⣿⣟⣟⣿⡛⢿⠠⢏⣽⡿⠿⣿⣷⣴⣿⣼⣶⠧⣧⡀⢀⣨⣌⡀⢻⡿⡆⠀⠀⢻⣿⡇⣠⣶⢾⡮⠝⠝⢿⣿⣿⣿⣇⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇
⠠⣥⣿⡏⢹⣿⣿⣿⠍⠟⣿⢾⢯⡿⣿⡻⣿⣿⣷⡭⠉⠈⡙⢿⠁⠀⠈⢿⣿⣿⣿⣿⣷⣶⣄⣿⣷⡌⣳⠀⠀⠀⠈⠀⠈⡛⠻⢗⣿⣿⠁⠁⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⡕⢀⡒⢪⡙⣿⣥⣤⡄⣘⠈⡄⠼⠒⢷⣿⡋⣻⡤⢴⣆⡀⠀⠀⢀⠀⣀⠘⣻⣻⣿⡏⣩⠙⣯⡏⠡⠴⠂⠈⠑⣒⣽⠈⠁⢾⣿⡾⣷⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⢗⢿⣷⣶⣼⠟⢯⣽⡟⠉⠀⡇⠀⠀⠌⠙⠂⣐⣷⣎⣍⣧⣬⣤⣾⣿⣦⣛⡿⠋⢟⡏⠉⣄⡃⠈⣆⣠⡀⣀⡠⠁⢸⣶⠆⣰⣿⣓⣫⠝⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠘⢿⣿⣿⣿⣿⡇
⠀⣾⣦⠺⣿⣧⢾⣇⠠⢃⣺⣦⣖⠰⠻⠇⢯⣟⣿⣿⣿⣿⣿⣿⣿⣾⠿⢯⣿⣤⣤⡀⡃⡀⣁⡈⠒⠻⠉⢙⠞⢱⣴⠻⠈⠘⢿⣿⣇⣰⡤⣾⣿⣿⣿⡿⠿⠉⣈⠉⣏⣿⣿⢿⣻⣿⡿⣿⣿⣿⣿⣶⢋⣿⣇⣽⣻⠃
⠀⠧⣨⣯⠿⣿⣿⣿⣷⣵⣿⣮⢽⣌⣨⠔⠊⣛⡟⣽⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⠏⣹⡟⣿⣿⣿⣿⣿⣽⣿⣶⣿⣿⣄⣾⣿⣯⣯⣿⣿⢿⣿⣿⣧⣿⣬⣿⣿⣿⣼⣟⠬⠋⢉⣡⣼⣿⣷⣿⡇⢿⣻⢟⣛⣿⡁
⠠⠤⠼⠣⠦⠤⠼⠤⠤⠤⠿⠿⠿⠷⠿⠿⠿⠾⠿⠘⠃⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠗⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠾⠩⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠦⠧⠈⠰⠦⠽⠷⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠛⠉⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠻⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠉⠉⠁⢀⣿⣿⣿⣿⣿⣿⡋⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡙⠮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⣖⠻⣿⣿⣿⡟⠀⣿⠀⠂⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠫⣄⠈⠔⠬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠛⢻⡟⢍⠹⠿⠛⠛⠋⠈⠀⠀⠈⠁⢴⣿⠀⠀⠀⣮⠇⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠀⢹⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢩⣭⡍⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢈⣃⡀⠀⠀⢠⣤⣤⠀⣀⣀⠀⣤⣤⠌⠀⠀⣸⣾⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡫⠛⢛⣿⣿⣭⠹⡟⠃⢸⣿⡇⠘⠛⢡⣶⣦⣶⣶⠁⣠⣴⣶⣤⡀⣾⣿⣷⠄⠀⢠⣤⣤⢰⣿⣿⡄⣿⣿⠀⠀⣴⡏⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣤⣿⡇⣿⣀⡂⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⠀⣿⣿⠀⣿⣿⠀⠀⣿⡇⢸⠀⠀⠙⠿⠿⠿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣿⣿⡇⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⠀⣿⣿⠀⠹⠿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⢸⠃⠀⠁⠀⠀⠀⠀⢀⢐⡛⣿⣿⠼⠍⠭⠀⠸⠿⠇⠠⠄⢬⣿⣋⣿⣿⠀⠻⠿⠾⠿⠃⠘⠿⠷⠆⠀⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⠀⣼⡀⠀⡘⠀⠀⠀⠀⠀⢠⠀⠀⢸⢗⣿⡟⡈⠀⠀⢠⣤⣤⣤⣤⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⠀⠀⠀⠛⠛⠛⠇⠀⠀⠀⠀⠀⠈⠀⠤⡌⢸⡿⠟⠇⣀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⣠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣦⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⢧⣸⠀⠀⠀⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⣷⡬⠀⠁⡀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣟⣿⣿⣿⣿⣶⣤⣄⡀⢀⠀⠀⠈⠀⠃⡿⠃⠄⢠⠁⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣄⢠⣾⣿⣇⡈⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣾⠀⣷⣾⣦⣤⣤⣄⣄⣄⣀⣄⣀⣀⣀⣀⣀⠀⣼⣿⡿⢿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⢀⡀⠒⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣽⣶⣿⣼⠹⠏⣉⣉⣉⣉⣙⡛⡛⣛⣻⣿⣿⠀⠋⢉⡆⠀⠉⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⢰⡟⡛⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣼⣏⣷⡦⡈⠙⠻⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢸⣇⣀⣸⠀⠂⠀⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣻⡿⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣏⠟⢿⡿⣽⣗⠇⠤⠂⠀⠀⠀⠀⠘⠻⢿⡇⠀⠀⠀⠀⢠⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠸⠈⠉⢹⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⡇⣾⣿⣿⣿⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣇⠀⣨⣺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢻⡷⠂⠀⠀⠀⠀⠀⠀⡀⣄⣀⢀⡸⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⢑⣿⣿⡿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣉⣉⡿⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠈⣿⣿⣧⠹⣹⡙⣿⣿⢸⠆⣿⡟⢿⢻⡇⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢚⡟⠷⠷⠿⠷⠿⠽⢯⠼⠤⠼⠇⠘⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠟⠉⠙⠋⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⣼⠁⣽⠈⠉⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⢠⡄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣄⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣿⣶⣶⣿⠀⡶⣶⢾⣶⣶⣦⣶⣤⣤⣤⣤⣤⣤⣤⡀⣄⣴⠀⠀⠀⣿⣧⠘⣷⣀⠀⠀⠀⠠⡤⢄⣀⣀⡄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣻⣯⣾⢿⣿⡇⠀⢸⣿⠇⠀⢻⣿⡇⠀⠸⠻⣿⣾⣿⣿⣿⣥⣤⣶⣶⣧⣧⣠⠚⣿⣶⡦⢤⣠⣀⣀⡀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣷⣿⡛⣏⠉⣿⣿⣿⣽⣷⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠿⠻⡿⠗⠀⠈⡋⠀⠀⠀⠹⡇⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣁⣾⣇⠆⣿⠿⣿⣧⣤⠀⠀
⢸⣿⡿⢛⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣻⣆⢀⠀⠟⠀⣀⠹⠂⠀⢠⣇⠀⣴⣶⣄⣿⡀⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣷⣀⣉⣉⣉⣠⡄
⢨⣿⣿⣭⣤⣀⣽⣾⣻⣟⢻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠗⣾⣿⣿⣯⣽⣿⣿⣥⠛⠀⠀⠀⠀⠶⠔⠄⠈⣿⣆⢿⣿⣿⣿⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣻⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢣⡮⠎⠉⠿⣶⣿⣧⣿⣿⣿⣿⣿⣿⢛⢻⡀⡀⠀⠀⡀⠀⢠⢰⠂⠻⣿⡊⣿⣧⣿⣇⠸⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⣿⣿⢕⣿⣿⣿⡿⣟⡳⢤⣾⣏⣿⣿⢿⣿⣛⣻⣇⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡐⠄⠀⣿⣇⢻⣿⢸⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⡿⣿⣿⣏⣸⣿⣿⣏⣿⣤⣩⣿⣿⣿⡉⣒⣿⣿⣿⣿⠺⣿⣿⣿⣟⣀⡀⠐⣄⠀⠄⡀⣱⠆⠀⢠⢼⠆⣿⣿⡆⠈⢸⣿⣿⠈⡛⢿⠿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡌⣹⣿⣿⣿⠻⢿⣿⣿⡇
⢀⣤⣴⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⣯⢿⣿⣿⣿⡻⢻⠀⠏⣴⡟⠻⣿⣷⣴⣻⡼⣶⠯⠧⡀⢈⣤⣼⡀⢹⣿⠧⢀⠀⠉⢉⣤⡰⣶⣾⡦⠞⢝⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣶⣿⠏⢼⣿⣿⣿⠜⠯⡇⢞⠭⡝⡿⡛⣿⣿⣷⠭⠉⠈⠉⢹⠀⠀⠀⠹⢿⣿⣿⣿⣿⣶⣤⣿⡷⡆⣷⠖⠁⠀⠘⢙⣈⡹⠻⢿⣿⣿⡁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⡅⣩⡒⠪⣉⣽⣤⣤⡄⣠⠀⡆⠾⠐⢷⡿⡍⣫⡒⢲⣎⡄⠀⠀⢀⡀⠀⠘⣛⣹⣿⣏⣽⠙⡶⡌⠡⡞⠒⠈⠉⣑⢽⠢⠽⢽⣿⡟⣿⣿⣾⣶⡿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣿⣿⣿⡇
⠀⢶⢿⡷⣾⠳⠛⡯⣽⠝⠉⠀⡅⠀⠀⠈⢘⠀⣐⣾⣬⣭⣦⣶⣤⢿⣿⣤⣭⡿⠋⠏⡏⠁⡄⠁⠀⠇⢠⣀⣀⢄⠁⣾⠷⡊⣴⣓⣉⠽⠷⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣞⡼⣿⣿⣿⣿⣿⡇
⠠⣾⣶⠒⡿⣷⢜⣧⠠⡣⡹⢦⣯⢨⠻⢍⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣿⣦⣤⣀⣃⣀⣀⡀⠙⠛⠉⢹⡟⣑⣾⠢⠀⠘⣿⣿⣃⡴⡶⣿⣿⣿⣿⡿⢛⢀⡄⣘⣯⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⡟⢥⣿⣃⣽⣻⡇
⠀⡧⣬⣧⠿⣿⣿⣿⣿⣽⣿⣮⢼⣥⣤⠖⠁⣙⡿⣽⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⣿⣽⠇⣻⠿⣿⣿⣿⣿⣿⣿⡿⣶⣿⣷⣄⣿⣻⣮⣿⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣯⣚⠉⢙⣤⣿⣿⣶⠿⠆⢻⡻⠟⣛⡟⠅
⠨⠤⠼⠣⠤⠤⠼⠤⠤⠤⠾⠿⠿⠿⠿⠿⠿⠿⠍⠸⠅⠾⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠦⠹⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠿⠿⠿⠿⠷⠦⠇⠈⠰⠶⠾⠿⠁
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣟⠉⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠻⣟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠭⠍⠉⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⡙⠮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣷⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠫⡀⠈⠒⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠛⣿⣾⠿⣿⣿⣿⣿⠏⠝⠛⠛⠿⠀⣸⡆⠀⠀⢠⣬⠃⢺⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⠿⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣭⡝⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢛⣁⡀⠉⠁⢠⣤⣤⠀⣀⣀⠀⣤⣤⠀⠀⡇⣾⡯⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠯⠃⣛⣗⣷⡖⠹⠛⠃⢸⣿⡇⠙⠛⢡⣶⣦⣶⣶⠁⣠⣴⣶⣤⡀⣼⣿⣷⠄⠀⢠⣤⣤⢸⣿⣿⡄⣿⣿⠀⠀⣧⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣽⣿⣇⣿⣀⡂⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⠀⣿⣿⠀⣿⣿⠀⠀⣿⠇⠧⠀⠀⠙⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡤⠤⢤⡄⠀⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⢸⣿⣿⠇⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⠀⣿⣿⠀⠹⠿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⢘⢛⣿⡿⠾⠈⠀⠀⠸⠿⠇⠠⠀⢬⣿⣋⣿⣿⠀⠻⠿⠾⠿⠃⠘⠿⠷⠆⠀⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠐⠀⣾⡀⠀⡈⠀⠀⠀⠀⠀⠰⠀⠀⣸⢰⣿⣏⡩⠀⠀⣠⣶⣶⣦⣤⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⠀⠁⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠄⡅⢹⡿⠛⠧⡀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡆⢆⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣦⣥⣀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⡇⡚⢧⣾⠀⠀⠀⣿⣿⣿⣯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠿⠿⣂⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣟⣿⣿⣿⣿⣶⣤⣄⡀⢀⠀⠀⠀⠨⠁⡟⠠⠄⠀⠁⠰⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣶⣶⣄⣴⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣤⣤⡠⡏⢠⣷⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⢸⣿⣟⠹⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣸⣿⣿⡓⣿⣾⣇⣿⠸⠭⣍⣍⣉⣉⡉⢉⠉⣙⣻⣿⡿⠀⠀⠸⠀⠀⣰⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢸⡏⡛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣼⣻⡗⡄⠈⠉⠻⠀⠀⠀⢸⣿⣿⡇⠀⠂⠀⠀⢠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⢹⣇⣀⣿⠀⠒⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠛⢿⠏⣿⡕⠃⠀⠀⠀⠀⠀⠀⠀⠻⢿⡇⠀⠀⠀⠀⠘⠻⣋⣉⠀⠀⠀⠀⠀⠀⠀⠄⠜⠀⠀⢸⠀⠀⠀⠸⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠇⣿⣿⣿⣷⣿⡿⢻⣿⣇⣿⣿⣿⢿⣿⣇⠀⠄⢈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣇⣀⣀⡈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⠀⣿⣿⡟⣿⣿⣿⣿⣿⢸⣿⣿⢏⣈⣹⡏⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡀⣿⣿⡇⠹⠁⠙⣿⡿⠸⠆⢺⠊⢟⣻⡇⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠿⠴⠿⠷⠦⠟⠶⠷⠿⠧⠆⠀⠤⠅⠈⣿⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠟⠛⠙⠙⠋⠙⠛⠚⠛⠁⠀⠀⠀⠀⠀⣿⠀⣿⠀⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢰⣧⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣄⣀⣄⣤⣤⣤⣴⣶⣶⣶⣶⣴⣶⣦⣶⣿⣀⢶⣿⣿⣶⣴⣶⣤⣤⣀⣤⣤⣤⣀⡀⡀⣤⡆⠀⢀⣿⡿⠀⢸⣿⡃⠀⡃⠀⠠⡤⢄⣠⢀⠄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣡⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡿⣿⣿⡇⠀⠀⡃⠀⠀⠀⢻⣇⠀⡧⡘⠛⣿⣿⣿⣿⣿⣤⣤⣴⣶⣶⣶⣶⡙⣿⣶⡦⢤⣠⣠⣀⠄⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣷⣿⡋⣏⠈⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠼⠶⢓⠛⠃⡁⠀⢀⣇⠀⢲⣶⣾⣿⡆⢏⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣧⡆⠆⠿⠿⣿⣧⡶⠀⠀
⠘⣿⠿⢻⡟⠛⠟⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⢿⡿⣿⣾⣿⣿⣿⣿⣦⡐⡂⢀⠀⠀⠀⠀⠀⠀⠈⢿⣆⢿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣟⣲⣀⣉⣉⣀⣤⡄
⢠⣿⣿⠭⣤⣔⣾⣿⣻⣟⢘⣿⣿⣿⣿⣿⣿⣿⢾⣿⠇⢩⣴⣿⣧⡾⣿⣷⡄⠋⠀⠀⠀⠐⠒⡀⠆⠹⣿⣯⣿⡏⣿⣇⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣻⣿⡇
⢸⣟⣷⣶⣾⣿⣿⣿⣿⣿⣾⡟⠻⣁⡖⠀⠙⠻⢦⣾⣭⣿⣿⣿⣿⣿⣽⠿⠄⠀⠀⠀⠀⠀⠀⠠⢐⠄⣿⣷⡈⢿⣽⣿⣆⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⢞⣿⣿⣟⡟⢏⢓⢤⣿⣧⣿⡿⢿⣿⣛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣿⣷⠀⠹⡿⠿⣠⡏⢻⣿⣿⡿⣻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⣿⡿⣯⣏⢸⣿⣿⣆⡿⣄⣹⣿⢿⣿⡁⣸⣿⣿⣿⡟⠾⣿⣿⣽⣟⠁⠀⠨⣄⠠⠆⡀⠲⠁⠐⢲⠬⢨⠛⠉⠀⠀⠉⠾⣛⢿⢿⠻⡛⢾⣷⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣼⣿⣿⣿⡹⢻⣿⣿⡇
⠀⣤⣠⣿⣿⣿⣿⣿⣿⣿⣯⣶⣧⣾⣭⣿⣿⣯⡿⠏⣻⠀⡀⣌⠘⠻⢿⣷⣶⢣⡼⣿⠳⠅⠀⣜⡬⢴⢋⠀⣬⣶⢀⣀⢀⢨⣥⣺⣶⣿⡖⣟⣙⣿⣿⡿⣿⣡⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡇
⢸⣶⢿⠟⢸⣿⣿⠿⠀⠝⡇⠶⠨⠻⠿⡛⣿⣾⡷⠥⠉⠈⠉⠍⠀⠀⠀⠹⢯⣿⣿⣿⣻⣶⣤⢿⢗⡮⡽⠚⣙⠋⢋⣹⣩⡙⢻⢽⣿⣿⡀⠀⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠨⠅⣨⡂⠨⣽⣿⣤⣦⣀⡠⠀⡖⠞⠀⢛⡏⢎⣅⡒⢂⣠⠄⠀⠀⢀⡀⠀⠈⣙⣹⡟⡇⡍⠸⡴⠈⡀⠘⠀⠀⠈⡍⢿⠡⢾⢯⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣻⣿⣿⡿⢻⣽⢿⣿⣿⣿⡇
⠀⢇⢿⣷⣾⠰⠚⠯⣿⠙⠁⠀⠅⠀⠀⠈⢈⠀⣐⣺⣮⣭⣤⣶⣴⢿⡟⣠⣬⠿⠉⢉⠀⢀⠀⢁⠀⡅⢀⣀⢄⡀⠀⣼⠖⠉⣼⣒⣩⠞⠛⢹⣿⡿⣿⣿⣿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⢫⢻⣿⡿⣿⣿⡇
⠠⢼⣦⠙⠼⡷⢺⣅⠠⡃⢙⢯⣧⢈⢻⢁⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣬⣵⢦⣖⣀⣀⣀⣀⡀⠉⣋⡁⣨⠋⣀⣾⣀⡀⠈⣸⣿⣁⡴⢄⣿⣿⣿⣿⡟⣁⢀⡄⡨⣯⣿⣾⢿⣿⣿⠟⣿⣿⠿⣿⡎⢤⣿⣧⣿⣽⠁
⢀⡢⣬⣧⠿⣿⣿⣿⣿⣽⣷⣦⢼⣤⣤⠖⠁⣛⣿⢼⠿⣿⣿⣺⣷⣿⣿⣿⣏⣿⣿⣽⡃⣻⠿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣷⣤⣾⣽⣮⣷⢼⣿⢻⣿⣿⣶⣿⣾⣿⣿⣷⣷⣷⡒⠐⣀⣴⣿⣿⡾⠟⡀⢹⠙⠃⢍⠟⠄
⠠⠤⠴⠃⠤⠤⠼⠤⠤⠤⠾⠿⠿⠾⠿⠷⠯⠯⠍⠸⠈⠯⠽⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠻⠲⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂⠤⠸⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠻⠗⠧⠀⠘⠒⠺⠗⠂
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠉⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠻⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠩⠭⠍⠁⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣦⣌⡉⠉⠛⢛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⡑⢝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢻⣿⣧⡀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠈⠫⡀⠀⠒⢝⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡄⠀⠀⡀⢰⡼⠁⢿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢻⡿⠟⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣭⡝⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⢟⣋⡛⠿⠟⢡⣤⣤⠉⣀⣉⠁⣤⣤⠀⠀⠇⡏⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠭⠃⣛⣿⣷⡖⠻⠛⠃⢸⣿⡇⠙⠛⢡⣶⣦⣶⣶⠀⣠⣴⣶⣤⡀⣾⣿⣷⠄⠀⢠⣤⣤⢰⣿⣿⡄⣿⣿⠀⠀⣿⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣽⣿⢡⣇⣐⡂⢸⣿⡇⠀⠀⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⠀⣿⣿⠀⣿⣿⠀⠀⣿⠇⠇⠀⠀⠙⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡤⠤⢤⠀⠀⠄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣸⣿⣿⠇⢸⣿⡇⠀⠀⢿⣿⣇⣿⣿⠀⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⠀⣿⣿⠀⠹⠿⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠅⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⣘⢛⣿⡟⠿⠈⠀⠀⠸⠿⠇⠠⠀⢬⣿⣋⣿⣿⠀⠻⠿⠾⠿⠃⠘⠿⠷⠆⠀⠸⠿⠿⠀⠿⠿⠆⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠒⠀⣿⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⢋⡥⠀⠀⣤⣶⣶⣦⣤⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⠁⠐⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁⣺⠿⠛⠠⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⡔⠇⠠⠀⠀⣄⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡛⢇⣿⠀⠀⢀⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣮⠙⠋⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣯⣿⣻⣿⣿⣿⣿⣶⣤⣄⡀⢀⠀⠀⠀⠨⢁⠟⠠⠀⡈⠁⠸⠿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⣿⣦⣰⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣤⣤⡠⡇⢰⣶⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣰⣿⢿⡉⠿⠿⢿⣿⣿⣿⡟⠻⠏⠀⠀⠀⠀⠀⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣼⣿⣿⡓⣿⣾⡇⣿⡺⠩⣩⣉⣉⣉⡉⢉⠉⣙⣻⣿⡏⠀⠀⠇⠀⢀⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢸⡏⡙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣼⣹⠳⡆⡈⠉⠻⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣼⣿⡿⡟⠁⠀⠀⠀⠀⠀⠠⠉⢹⣥⣀⣿⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⡇⣽⣿⣿⡿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡻⠻⢿⠏⣟⣅⠇⠀⠀⠀⠀⠀⠀⠀⠻⢿⡇⠀⠀⠀⠀⠉⢳⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠸⠀⠀⠀⠸⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣿⡧⣿⣿⣿⣷⣿⡿⢿⣿⣇⣿⣿⣿⢿⣿⡇⠀⢄⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇⣀⣀⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠀⣿⣿⡟⣿⣿⣿⣿⣿⢸⣿⣿⣏⣈⣹⡏⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠀⣿⣿⡇⢹⠁⠙⣿⣻⠸⠆⠺⠋⠟⣿⡇⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⢤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠿⠶⠿⠷⠦⠟⠶⠲⠿⠯⠆⠂⠤⠅⠈⣿⠃⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠀⠀⢰⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠿⠛⠙⠙⠋⠙⠛⠚⠛⠁⠀⠀⠀⠁⠀⣿⠀⣯⠀⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣴⣿⡆⢨⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⡟⢀⠾⣷⢿⣷⣴⣶⣦⣄⣀⣠⣤⣤⣤⡄⠀⡀⠀⠀⡏⠉⠁⠈⠻⣇⠀⢰⡇⠀⢠⡤⢠⣤⣀⡄⠀⠀⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣡⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠇⠀⠈⠀⢠⣇⠀⢀⣀⣀⣿⡆⢸⣷⡛⢿⣿⣿⣿⣿⣿⣤⣤⣶⣶⣾⢷⣶⠘⣿⣷⡦⢤⣤⣤⣤⡀⡀⠀⠀⣠⣤⣤⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣷⣿⡛⣏⢙⣿⣿⣿⣽⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠿⢆⠄⠀⡀⠈⣿⣆⢸⣿⣿⣿⡇⢿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣶⡤⣂⠿⠻⣿⣧⡶⠀⠀
⠘⣿⠿⢻⡟⠛⢟⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣦⡳⡆⢀⠀⠀⠀⠀⠈⠂⠻⣿⡯⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⣶⣤⣅⣀⣠⣴⡄
⢀⣿⣾⢍⣤⣬⣾⣿⣻⣟⢙⣿⣿⣿⣿⣿⣿⣿⢶⣿⠇⢨⣴⣿⣧⣾⣿⣿⡄⠋⠀⠀⠀⠀⠒⠆⢀⣿⣧⢹⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣟⡇
⢸⣿⣷⣿⣶⣿⣿⣿⣿⣿⣾⡟⠹⡁⡆⢈⠈⢛⢦⣿⣥⣿⣿⣿⣿⣿⣽⠻⠀⠀⠀⠀⠀⠀⠀⡴⠘⣿⣿⠇⠋⣿⣿⣧⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣟⣿⣿⣿⣿⢚⣿⣿⣿⡝⣏⠓⢠⣿⣃⣿⡿⢿⣿⣛⣿⣅⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠈⣀⡠⠂⠹⣿⣋⠲⣠⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⡿⣯⣎⢸⣿⣿⣄⡾⣤⣭⣿⣿⣿⡁⢸⣿⣿⣿⣿⠾⣿⣿⢽⢟⠁⠀⠠⣄⠠⠆⡀⡲⠀⠐⣶⠼⠀⠃⠀⠀⠀⠈⠾⣛⡿⣿⠻⡓⠿⣿⡿⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣼⣿⣿⣿⡙⢻⣿⣿⡇
⠀⣤⣠⣿⣿⣿⣿⣿⣿⣿⣯⣶⣧⣾⣭⢿⣿⣯⣿⠏⣯⠀⡀⢌⠚⠿⢿⣷⣶⣳⠾⣳⠳⠅⠀⣘⡭⢤⣂⠀⣬⣼⢀⣀⢀⣨⣡⣺⣶⣿⡖⣟⣛⣿⣿⡿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇
⢰⣾⢿⠟⢽⣿⣿⡿⠈⠟⡇⠲⠢⠻⠿⡛⣿⣾⡷⠅⠉⠀⠁⢍⠀⠀⠀⠙⢿⣿⣿⣾⣻⣶⣤⢿⠷⡮⡽⡞⣙⠋⢋⣻⣩⡝⢻⣽⣿⣿⡀⠀⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠅⣩⡂⠨⣹⣿⣤⣤⡀⡠⢀⡖⠞⠀⢓⡟⣌⣌⡒⢒⣀⡄⠀⠀⢀⡀⠀⠈⣙⣹⣟⡇⡉⠸⡴⠀⡀⠚⠁⠀⠈⡭⢽⠫⢟⢿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⢿⣿⣿⣿⡇
⠀⢧⢿⣷⣾⠰⠚⠯⣿⡙⠁⠀⠅⠀⡀⠀⢈⠀⣐⣾⣮⣭⣤⣶⣴⣿⣟⢠⣭⡿⠉⢋⠀⠀⠀⠁⠀⠇⢀⣀⢀⡀⠀⣺⠖⠈⡼⣖⡩⠺⠝⢝⣿⡿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⡧⠫⢻⣿⡿⣿⣿⡇
⠠⠾⣦⠒⡙⡷⢺⣧⠠⡃⠙⢯⣯⢈⢻⢉⢿⣽⣿⣿⣿⣿⣿⣿⣿⣻⡿⣼⣵⣦⣆⣀⣀⣀⡀⡀⠈⡋⡀⣨⠋⣀⣶⣂⡀⠈⣹⣻⣁⡴⢆⣽⣿⣿⣿⡏⣂⢀⡄⡠⣧⣿⣟⢻⣿⣿⠿⡿⣿⠿⣿⣞⢠⣿⣇⣿⣽⡀
⠀⡦⣼⣷⠿⣿⣿⣿⣿⣽⣷⣦⢼⣄⣤⠖⢁⣟⡿⣼⠿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣭⡃⣻⠿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣷⣤⣾⣽⣮⣷⢬⣿⢻⣿⣿⣶⣿⣾⣿⣿⣷⣷⣷⡚⠀⣀⣴⣿⣿⡾⠛⡀⢹⠛⠃⢍⢏⠄
⠠⠤⠔⠃⠤⠄⠼⠤⠤⠤⠿⠿⠿⠾⠿⠷⠿⠯⠭⠸⠄⠮⠭⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠳⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠈⠤⠸⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠻⠗⠧⠀⠐⠒⠺⠇⠂
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠋⠉⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢌⡑⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠘⠯⡀⠁⠢⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⢀⣴⣿⣿⣿⣿⣿⣿⣏⣿⣷⣄⠀⠀⠀⠀⠀⢰⡼⠀⢿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢻⡿⠟⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠉⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⠀⠀⠀⠅⡏⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠍⠋⡛⣿⣧⡏⠿⠛⢛⣛⣛⠛⠛⠛⣛⠛⣿⠛⢛⡁⠀⠀⠀⠀⣾⡿⣋⠿⢿⣿⡿⠭⠁⠐⠋⠉⢾⣿⠀⠀⠀⣿⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣽⣿⢠⣇⣐⣛⣛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⢹⠃⠈⠁⠀⠀⠐⠂⠀⠀⠀⢀⢻⣿⠀⠀⠀⣿⠇⠇⠀⠀⠙⠻⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⡀⣘⢻⣿⡏⠿⠉⠁⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠂⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⢏⡁⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣀⠀⠀⠐⠛⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠤⡁⣺⡿⠺⠤⡀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡐⡅⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣶⣬⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠻⢄⣿⠀⠀⢀⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡙⠻⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣻⣿⣿⣿⣿⣦⣤⣀⠀⢀⠀⠀⠈⢸⢠⠿⠠⠀⡈⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢀⣶⣿⣷⣄⣴⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣤⣀⣠⡇⢠⣶⣶⣤⣤⣤⣄⣄⣤⣄⣀⣀⣀⣀⣀⣾⣿⢏⠹⠿⠿⣿⣿⣿⣿⠛⠿⠁⠀⠀⠀⠀⠀⠂⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡗⣿⣾⡇⣿⠻⢍⣉⣉⣉⣉⣉⡛⠛⣛⣿⣿⡏⠉⠈⠂⠀⣼⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢸⣏⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣽⣻⠒⡀⠈⠙⠻⠀⠀⠀⢸⣿⣿⡇⠀⠂⠀⠰⢿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⢸⣅⣀⣿⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡿⠿⢿⠏⣟⠜⠁⠀⠀⠀⠀⠀⠀⠀⠻⢿⡇⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠸⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣇⣿⣿⣿⣷⣿⡟⢿⣿⣇⣿⣿⣿⢿⣿⡇⠀⡀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⣀⣀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠹⣿⣿⡿⣿⣿⣿⣿⣿⢸⣿⣿⣟⣈⣹⡏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣀⣿⣿⡧⠹⢉⠙⣿⣿⠰⠄⢺⠟⠟⣿⡇⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠿⠤⠿⠧⠤⠯⠶⠧⠿⠽⠆⠄⠤⠅⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠐⣶⣤⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⢰⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠟⠙⠙⠛⠛⠺⠚⠛⠀⠀⠀⠀⠁⠀⣿⠀⣯⠀⠁⠀⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠃⠀⢼⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣶⣦⣴⣴⣤⣤⣟⠠⣶⣶⣿⣶⣶⣶⣦⣄⣀⣀⣀⣄⣄⡀⠀⠀⢰⡇⠀⠀⠀⠀⣹⡆⢀⣶⡆⠀⠠⡤⣄⣠⢀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣿⣿⣿⣿⡿⢃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣼⣿⣿⣿⣿⣟⣿⣿⣿⡿⡿⠇⢀⠀⠘⣿⡄⠀⠀⠀⣿⡇⣸⣿⡿⡛⢻⣿⣿⣿⣿⣿⣤⣤⣶⣶⣾⣶⣤⣌⣿⣷⡦⣠⣤⣄⣀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣷⣿⡛⠏⠘⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⠾⢇⠚⠂⡀⢿⣷⢀⣸⣿⣿⠇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢠⣤⡤⡆⠿⠻⣿⣧⡶⠀⠀
⢘⣿⡿⢻⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣮⡫⡆⢀⠀⠞⠀⠀⢁⣾⣿⢺⣿⣻⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣲⣄⣩⣁⣀⣴⡄
⢀⣿⣶⢍⣠⡀⣴⣿⣻⡟⢸⣿⣿⣿⣿⣿⣿⣿⢾⣷⠇⢉⣵⣿⣇⡽⣿⣟⡄⠛⠀⠀⠀⠀⠸⡿⠟⠀⠫⢿⠿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣿⡇
⢸⣿⣧⣿⣷⣿⣿⣿⣿⣿⣾⡛⠹⠁⡦⢈⠉⢿⢦⣾⣡⣿⣿⣿⣿⣿⣽⠻⠸⠀⠀⠀⠀⠀⠀⠀⠄⠀⣤⢨⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⡛⢇⠓⢤⣟⣋⣿⡿⢿⣿⣛⣻⣇⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⣃⡄⢸⣿⣛⡰⣠⡇⢻⣿⣿⡿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⣿⣿⣯⣏⢹⣿⣿⣄⣼⣈⣩⣿⣿⣿⣁⢺⣿⣿⣿⡿⠾⣿⣿⣿⣟⢀⠀⠈⣄⠠⢄⠀⡱⠠⠐⣤⢼⠆⠍⠀⠀⠈⠉⠾⢻⠿⣿⢿⠻⢿⣿⣿⣻⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣼⣿⣿⣿⡹⢻⣿⣿⡇
⠀⣄⣰⣿⣿⣿⣿⣿⣿⣷⣿⣦⣯⣶⡯⣿⣛⣟⣿⠟⢧⠀⠀⣈⠙⠿⣿⣷⣴⣫⡼⣾⠪⠅⠀⣘⣭⣾⢂⢀⣬⣦⢀⢀⠀⣨⣡⡸⣶⣿⡖⣿⣙⢿⣿⡿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡇
⢰⣾⣿⡏⣽⢿⣿⠝⠈⠙⡇⠶⢩⡻⣿⡻⣿⣽⣷⠭⠉⠈⠉⣘⠀⠀⠀⠻⢯⣾⣿⣿⣻⣶⣤⣽⠷⡮⣿⢝⠙⠋⢟⣿⢊⣝⢻⣿⣿⣿⡁⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠉⢈⠂⢩⣹⣿⣤⣤⠀⣀⠀⡄⠜⠀⠷⡏⣉⣁⡀⢂⣂⡄⠀⠀⢀⠀⠀⠈⣙⢹⡟⡏⠉⠹⡼⠈⠀⠐⠃⠀⠈⣉⢿⠸⠿⢽⡿⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⢻⣿⢿⣿⣿⣿⡇
⠀⡖⣿⣷⣶⠴⠊⠭⣿⡙⠁⠠⡁⠀⠀⠈⠘⠀⣐⣶⣾⣭⣠⣦⣤⢿⡿⢀⣽⡿⠉⢋⠁⠀⠀⠁⠀⠃⢀⣀⣀⡄⠀⣺⠖⠈⣰⣒⣩⠽⠘⢩⣿⡿⣿⣿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣽⡇⠻⢻⣿⡷⣿⣿⡇
⠠⣼⣤⠍⠻⡧⢾⣃⠠⢃⠘⣶⣗⠐⠻⠀⢯⣝⢾⣿⣿⣿⣿⣿⣿⣿⡿⢼⣽⣤⣄⣀⡀⣀⣀⡀⠀⠛⠁⢩⠛⣄⣶⡀⠀⠀⣸⣿⣁⡴⠄⣻⣿⣿⣿⡿⣁⢀⡄⡨⣧⣿⣞⢻⣿⣿⠿⡿⣿⠿⣿⡞⢤⣿⣇⣷⣼⡀
⠀⡄⣘⣯⠿⣿⣿⣿⣮⣷⣷⠮⢽⣄⣨⠔⢉⣳⡿⣽⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⣿⣽⡃⣻⠿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣷⣤⣿⣽⣮⣷⢼⣿⢻⣿⣿⣷⣿⣾⣿⣿⣷⣷⣧⡚⠁⣀⣤⣿⣿⡾⠛⡀⠻⠙⠁⢍⢾⠄
⠠⠤⠼⠁⠤⠤⠼⠤⠤⠤⠿⠿⠿⠴⠿⠷⠿⠿⠍⠸⠔⠮⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠲⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠴⠸⠯⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠻⠗⠧⠀⠘⠒⠺⠏⠂
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡟⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⢿⡏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢈⠻⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⢕⡀⠑⠬⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡹⠃⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢻⣿⠿⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡇⡎⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡫⠃⠻⣿⣯⡍⢿⠛⠛⠛⠛⡛⡛⡿⣿⡿⠿⠿⠟⠃⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣵⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⣿⢁⣗⣀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⣿⡿⣯⠻⣿⣿⢿⠏⠀⠙⠩⠙⣿⡇⠀⠀⠀⣿⠇⡇⠀⠀⠻⠿⠿⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣸⣿⣿⡿⠋⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⠉⠀⠈⠹⠄⠀⠀⢸⣿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣿⡟⣿⠭⠭⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠠⠀⣿⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⠗⡂⠀⠀⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠂⠀⠿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠁⣾⣿⠾⢁⡀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠠⡂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠿⣆⣶⠀⠀⢀⣿⣿⣟⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⠻⠷⣇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠈⢘⢂⡷⢀⢀⡐⠂⢸⣿⣿⣿⣿⡇⠀⠀⠀⢠⣴⣦⣄⣀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⣤⣀⢀⡖⢨⣧⣶⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⠀⢠⣿⣿⡛⠿⡿⢿⣿⣿⣿⠛⠻⠟⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠷⣷⣼⡏⣽⠹⢉⣉⣛⣛⣛⣛⠛⠛⢛⣿⣿⠟⠀⠑⠀⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡛⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣹⢿⠦⡌⠉⠙⠯⠀⠀⠀⢸⣿⣷⡇⠀⠆⠀⠸⣶⣭⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣃⣁⣿⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠯⠿⢿⡟⡟⡧⠇⠀⠀⠀⠀⠀⠀⠈⠿⣿⡇⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠉⢹⠀⠀⠀⢸⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡇⣿⣿⣿⣷⣿⡿⢿⣿⡇⣿⣿⣿⣿⣷⡆⠈⠀⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡈⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⢩⣿⣿⣿⣿⣿⣷⣾⣿⢸⣿⣿⣟⡘⢻⡏⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠀⣿⣿⡇⠻⢋⢹⣿⣿⢸⡍⢾⡟⡿⣿⡏⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⠤⠿⢯⣅⣦⣭⢥⣿⣽⠄⠄⠈⠁⠘⣿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡇⠘⣿⣶⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠿⠛⠲⠒⠒⠶⠴⠶⠈⠀⠀⠀⠀⠀⣿⠀⣶⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠀⠀⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣦⣶⣤⡀⡿⠀⣤⣦⣴⣦⣴⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⢸⣧⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣠⢀⣀⣀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣿⣿⣿⣿⣿⣋⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⢋⣼⣿⣿⣿⣿⠟⣿⣿⣿⣿⠻⢳⠄⢨⣿⡀⠀⠀⠀⣸⡇⠠⣠⣀⡼⠒⠾⣷⣾⣿⣟⣷⣄⣀⣤⣤⣤⣥⡀⡄⢶⣦⣤⣄⣀⡀⣀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣯⣿⠿⡟⠙⣧⣿⣿⣿⣹⣿⣿⣟⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣵⡴⠐⢒⣼⡿⠉⠀⠀⢠⣿⠃⣬⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢏⣲⣀⣀⠄⣿⠿⣿⣧⣤⠀⠀
⠸⣿⣿⢿⡿⠿⢿⣿⣷⣿⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣭⣾⣿⣿⣿⣷⣮⣽⡕⠀⠀⠰⠿⠛⠃⠀⠸⠃⣼⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣴⣄⣉⣉⣁⣠⡀
⠀⣟⣧⣚⢁⠀⣬⣽⢿⡿⠹⣿⣿⢿⣷⣾⣿⣿⣴⣷⡇⢙⣩⣿⣏⣽⣿⣷⡍⠾⠀⠀⠀⠈⠤⠄⠀⠘⡛⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⠿⡇
⢸⣿⣭⣼⣯⣿⣿⣿⣿⣿⣾⠟⠿⠋⡉⠉⠛⢿⣤⣿⣂⣾⣿⣟⣿⣿⣿⢿⣵⠀⠀⠀⠀⠀⠀⣤⠀⠔⣡⢚⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣧⣶⡲⣇⠠⣀⣾⡞⣿⣿⢿⣿⠻⢿⡇⠁⠀⠈⠛⠂⠀⠀⠀⠀⠈⠐⠀⠈⠠⡈⢹⣿⡟⢼⢩⣟⢿⣿⣿⣿⢿⣿⣿⣿⣿⡟⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⣿⣿⣿⠏⢹⣿⣿⡯⣿⡋⢉⣿⣷⣞⠂⢸⣿⣿⣿⣷⢼⣿⣽⣿⡿⠀⠀⢀⡀⢀⡄⠀⢠⠀⠠⣤⣰⠏⠟⠂⠀⠙⠛⣵⣻⡷⣾⣿⠿⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⡈⣸⣿⣿⣿⡻⢿⣿⣿⡇
⠀⡈⢁⡿⣿⣾⣿⣿⣿⣿⣟⣍⣉⣌⡛⣿⢟⣛⣿⠛⢶⠀⠉⡙⡿⢿⣾⣷⣤⣿⣼⣶⣗⣅⠀⠠⣩⣾⠤⡂⣐⣦⢀⠀⠀⢑⣃⣼⣥⣶⡦⣿⠟⢿⣿⣿⣿⣏⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⡇
⢰⣯⣿⡯⢻⣿⣿⡻⠉⠛⡏⠭⢙⣿⣿⠾⣿⣽⣟⡓⠚⠀⠂⠹⠁⠀⠈⢻⣓⣽⣿⣿⣷⣤⣄⣿⣧⣜⣻⡕⠻⠛⡟⢿⢞⣻⢿⣿⣿⣿⠋⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇
⠘⠉⢋⠄⢘⡻⣿⣁⣀⠀⢁⠀⡄⡵⠀⠧⡟⣙⡓⠤⢤⠄⡀⠁⠀⠀⠀⠀⠘⠻⢻⣿⡏⠙⠹⣩⡙⠉⡱⠚⠉⠓⣚⣿⣹⡿⢿⡿⡿⡿⣷⣷⣶⡿⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⡅
⠀⡦⣿⣧⣴⢬⢮⣿⣿⡳⠃⠈⡃⠀⠀⠀⠐⠈⢫⢵⣼⣯⣄⣤⣀⣾⣧⢀⣒⣿⠛⡟⠁⢁⠀⠃⠀⡃⣀⠀⣀⠄⠋⢾⡤⠋⢲⡿⢓⣽⡿⢛⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⡖⠸⢾⣷⡯⣿⣿⡇
⢠⣸⣠⠝⣹⣦⣴⡆⢉⠇⠲⣄⣗⠐⢲⡂⣾⣲⣿⣿⣿⣿⣿⣿⣿⣾⣷⢾⣹⣄⣄⠈⡀⠈⡁⠀⠒⠏⠋⢙⠾⠁⣤⠻⠈⠐⢻⣿⢃⣠⠄⣺⣿⣿⣿⡿⠏⠀⡉⢙⣏⣿⡿⢟⣿⣿⡿⣿⣿⣿⣷⡞⢠⣫⣇⣯⣹⡁
⠀⢅⣘⣖⠶⣿⣾⣿⣶⣳⣶⣼⣹⣊⣈⡬⠊⢽⣿⣹⣿⣿⣿⣿⣯⣿⣿⣾⡿⣿⣿⣹⠏⣿⢿⣷⣶⣿⣶⣿⣵⣿⣿⣻⣧⣀⣼⣛⣏⣷⣴⣿⢿⣿⣿⣧⣷⡼⣿⣿⣿⣷⣏⠼⠫⢙⣠⣽⣿⣶⠏⠀⢹⠻⠛⡛⡽⠀
⠠⠤⠬⠢⠤⠤⠼⠤⠤⠦⠿⠿⠾⠿⠿⠷⠾⠿⠒⠚⠍⠯⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠻⠦⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠭⠹⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠿⠿⠿⠿⠳⠆⠇⠀⠰⠲⠼⠦⠂
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠛⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢈⠪⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢷⠈⠑⡭⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠏⢽⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⠿⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠊⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣴⠀⠀⢈⣭⡇⠀⠀⠀⠀⠀⠀⠀⡆⣼⡏⠀⢨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣟⠏⢿⣿⣟⣟⢿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣇⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣏⣻⣿⡇⡦⠀⠴⠿⠟⠁⠁⠁⠈⠁⠁⠀⠸⠇⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⡇⣇⠀⠈⠻⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢸⣟⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⢿⣿⣿⣿⠏⠉⠋⠍⢹⣿⠀⠀⠀⠀⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣾⠛⣋⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠉⠉⢡⣲⠉⠻⠤⠀⡀⣼⣿⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⢠⠀⣼⠀⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⢸⢶⣿⡗⠄⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⣀⡛⢼⣿⣷⡇⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⢼⡇⣰⠀⠁⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢿⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠐⠐⠇⣶⠌⠉⠠⠆⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⡀⠀⠀⣠⣾⣿⣿⣦⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⡦⠀⣧⣤⣀⣀⣀⣀⡉⠉⠉⠉⠁⠀⠀⣠⣿⡿⢿⣷⣾⠿⣿⣿⡟⠛⠿⠶⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡿⣵⣬⡟⣻⢻⡛⠛⠛⠛⠛⠻⠿⠿⠿⠿⢟⣹⠈⢪⠉⢹⣄⣸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⡶⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣧⣿⣿⣯⣹⡶⠦⡉⠛⠻⢿⡉⠈⠁⢹⣿⣿⡇⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠂⠄⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⢸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠙⠛⢹⠀⠀⠀⠘⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡇⣾⣿⣿⣯⣿⣿⣿⣿⡇⣿⣽⣿⣿⣶⡆⠈⠁⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⠣⣿⣿⣿⣿⣿⣷⣾⣿⢳⣿⣿⡿⠙⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠛⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠀⣿⣿⡇⢹⠛⠻⣿⣿⢨⡁⢭⡟⣿⣿⡇⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⠀⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣟⣀⣿⣿⣁⣄⣀⣀⣻⣛⡀⠀⠈⡀⠐⣼⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠻⣿⡿⠀⢸⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡞⠀⠉⠉⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⡶⠲⠲⠖⠢⠴⠤⠶⠊⠀⠀⠀⠀⠀⣿⠀⣰⠒⠒⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⢀⠀⢀⣀⣀⣠⣤⣤⣠⣄⣀⠀⡿⢀⣭⣤⣤⣤⣠⣀⣄⡀⢀⡀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣴⣾⣿⣿⡿⠏⢿⣿⣿⣿⣿⡿⣿⣷⣶⣴⢐⢝⠨⡿⣿⣿⣿⠿⢿⢿⣿⡶⠀⢠⣿⣇⠀⠀⠀⠀⣸⠇⠀⡄⣄⣀⢀⠲⢶⣷⣾⣾⣷⣶⡀⢀⢀⣠⣀⣀⢀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣷⣼⠟⡟⠹⣧⣽⣿⣩⠉⣹⣕⣓⢎⣽⢿⣿⣻⣿⣿⣿⣿⣿⡴⣶⣿⠟⠁⠁⠄⡀⢠⣿⢀⣾⣿⣿⣿⣷⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣷⣿⣿⣯⣾⣿⣿⣟⢀⢀⠀⡀⣾⣿⣿⣇⣤⠀⠀
⠸⣿⣿⢿⡿⢿⡿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⡗⣸⣿⣿⣿⣯⣝⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⠅⣶⢠⡀⠛⠛⠃⢀⡀
⠀⣟⣤⠒⠃⠀⣔⣿⢿⡿⢻⣿⣿⢿⣷⣼⣿⣿⣵⣥⡏⠙⣛⢟⡟⣻⣿⢇⡀⠴⠀⠀⠀⠀⢀⣴⡞⣙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠓⠻⣿⡇
⢸⡿⣉⣼⣿⣶⣿⣿⣾⣷⣼⡿⢻⠊⡛⠙⠳⢿⣈⣹⡄⣼⣿⣿⣿⣿⣿⣿⢓⠀⠀⠀⠀⠀⠈⢉⠠⡄⡒⣻⢿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣿⣽⣿⡿⣿⣿⣿⣿⢹⣿⣦⣤⢲⡇⠤⢀⡤⠜⣿⣿⣿⣿⠿⢿⠇⠉⠀⠈⠐⠀⠀⠀⠀⠀⠈⠀⠉⠉⠈⠉⢻⣿⡿⢹⢙⡟⣿⣿⣿⣿⢿⣿⣿⣿⣿⡟⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢻⣿⡟⡕⢻⣿⣿⡙⣼⠛⠛⣯⣧⣽⠀⠼⣷⣿⣷⣷⢸⣿⣲⣼⢿⠀⠀⠀⡀⠀⡀⠀⢀⠀⠀⣀⣰⡖⡗⠅⠈⠙⠳⣶⠾⣿⣾⣿⣿⣳⣾⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⡉⢘⣿⣿⣿⠿⢿⣿⣿⡇
⠀⠀⢋⣿⣾⣾⣿⣿⣿⣟⣿⣌⠋⣉⠛⣶⡜⠿⣿⠿⣤⠀⠙⠑⠽⣷⣬⣦⣠⡟⣨⡬⢄⡄⠀⢐⢛⣘⠄⠂⢰⣄⠀⠀⠈⠈⡒⢸⣭⣴⣄⣽⡻⣾⣿⣿⣿⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣿⡇
⠠⣑⣾⡗⢻⣿⣿⣻⠉⠛⡋⣙⠛⢿⣷⢽⣿⣫⡏⡒⠚⠀⠂⠹⠁⠀⠉⢻⢛⣬⣧⣽⢧⣬⢀⣿⣯⡙⢶⠣⠿⠟⡾⣶⠔⢿⣿⣿⣿⣿⠃⠘⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠉⠉⡀⠘⢺⣿⠀⡀⠀⠁⠀⡈⣱⠉⣢⡿⠛⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠻⢻⡿⡟⠛⢻⣙⠒⠉⡫⠄⠒⠲⠨⢾⢚⣿⣺⣿⠿⣿⣧⣧⣬⣿⣽⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⢻⣿⣿⣿⣿⣿⡇
⠀⡄⣾⣆⡬⣡⣝⣓⣿⠶⠂⠀⠃⠀⠀⠐⠡⠉⠣⣢⣐⣛⡁⣀⣀⣶⣶⠀⠴⣶⠞⡷⠃⠀⠀⠋⠀⠀⠀⠀⠀⡀⠋⣹⣩⠔⠨⠭⠟⣳⡿⠿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢟⣿⢟⡭⠈⢽⣳⢿⣿⣿⡇
⢀⣱⣉⠁⢹⡄⣠⠏⠉⠆⢴⡤⠧⠠⢴⠄⣔⡰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣽⢻⡁⡀⠀⠀⠈⠀⠀⠠⠗⠚⠲⡿⠂⣀⠨⠀⠀⢹⣯⠊⢀⡀⢾⣿⣿⣿⣿⠇⠉⡀⠹⠟⣿⣽⡿⣿⣿⣿⣿⣿⣿⣧⡴⢈⢏⡁⣟⢻⠃
⠀⠋⠑⣆⠴⣻⣾⣿⣤⣢⣤⣙⣻⠀⢘⡠⠚⢩⣿⢻⣿⣿⣿⣿⣟⣿⣶⣼⡿⣿⣿⢻⡇⢶⣾⣦⣶⣶⣶⣞⣲⣿⣭⣶⣤⠀⣸⠿⡘⣯⣠⣿⠿⣿⣯⣥⣦⣰⣷⣷⣯⣯⡗⡬⠋⠋⣀⣢⣿⣭⡯⠀⢺⠿⠋⠟⣸⠁
⠠⠤⠼⠢⠤⠄⠼⠤⠤⠤⠿⠶⠾⠽⠿⠦⠠⠽⠂⠹⠋⠻⠟⠿⠿⠿⠿⠿⠷⠿⠿⠿⠶⠽⠌⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠉⠍⠻⠾⠿⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠤⠿⠿⠿⠿⠓⠀⠆⠀⠀⠀⠿⠗⠂
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠪⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢷⠈⠓⡩⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡏⢹⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⡿⠟⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠂⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣭⠍⠉⠉⣀⡆⠀⠀⠀⠀⠀⠀⠀⠄⢰⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⠿⢿⣿⣟⣛⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⡅⣟⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢖⣳⣿⡏⣬⠁⠴⠶⠶⠂⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣾⣿⣇⡀⠀⠀⠀⠀⠀⠀⣿⡇⣇⠀⠨⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢳⣿⢾⣿⠿⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡏⠁⠈⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣸⣛⣛⣁⣀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠋⣏⠫⡟⣿⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⢸⠁⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⢸⢦⣿⡿⠭⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠉⠩⣽⣿⠉⠿⡥⣀⢡⣿⣗⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠶⢶⡆⠀⠀⠀⠀⠀⠘⠀⡀⡚⢼⣿⣷⡇⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⢸⡏⢰⠈⠁⠀⣿⣿⣿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠁⠐⠀⠇⣶⡌⠉⠠⠄⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣶⣶⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⡤⠀⣇⣤⢀⠀⠀⠀⠉⠉⠉⠉⠁⠀⣀⣠⣴⣶⣦⣤⣬⡁⢼⣿⠟⠛⢷⡤⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣧⣷⣬⡟⣻⢻⡛⠛⠻⠿⠿⠿⠿⠿⠏⢋⣋⣽⢩⡻⠿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣇⣿⣿⣟⣻⡴⠌⡙⠛⠻⣟⡉⠀⠀⢱⣾⣿⡿⠀⠀⠐⢻⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⡇⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⠧⡆⠄⠀⠀⠀⠀⠀⠈⣻⣿⡇⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⢻⠀⠀⠀⠀⢰⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣾⡇⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣼⣿⣿⣾⡄⠘⠁⠹⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⠀⠀⢸⠀⠀⠀⠀⠀⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⢣⣿⣿⣿⣿⣿⣷⣼⣿⣇⣿⣿⣿⠙⠿⡿⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠿⠶⠶⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⠐⣿⣿⡇⢿⢻⠻⣿⣿⢸⡁⣯⠿⣿⣾⡇⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣤⡟⠘⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣟⣀⣿⣟⣃⣜⣚⣂⣻⡟⡈⠀⢈⡄⢱⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⢿⣿⠃⠀⣿⡶⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠉⠉⠉⠉⠛⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⠶⢠⠦⠤⢴⣤⠤⠈⠁⠀⠀⠀⠀⣿⠀⣴⠂⠢⠐⠀⠀⠐⠒⠂⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣠⣀⣠⣿⠀⣹⣄⣰⣤⣀⣤⣄⠀⣀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀
⢰⣤⣾⣦⣶⣿⡿⠟⢿⣿⣿⣿⣿⣿⡿⣷⢤⡤⠁⠙⢘⣿⣿⣿⣿⢿⡿⡿⠿⠏⣼⣿⠀⠀⠀⡀⠀⣸⠇⠀⣤⣄⣀⡀⣰⣤⣶⣯⣽⣶⣿⣤⡀⠀⣀⣠⣠⣀⢀⠀⣤⣄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣷⣺⠴⡯⠿⢶⣿⣿⢱⠉⢸⣟⣀⢾⣽⣳⣿⢿⣷⣶⣶⠚⠷⡿⠟⠁⠀⠀⠠⠀⣰⡿⠀⢠⣿⣿⣿⣿⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣷⣿⣿⣄⣠⣿⣷⣆⠠⠀⠀⠀⣼⣿⣿⡆⣀⠀⠀
⢸⣿⣿⣿⡿⣿⣿⡿⣷⣴⣤⣿⣿⣿⣿⢿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣝⢳⡀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⣿⠄⣶⣉⠊⠿⠟⠛⠂⠀
⠈⡿⣬⠴⠃⠀⣡⢻⢿⣿⢻⣿⣿⣿⣯⣼⣿⣿⣹⣧⡓⠙⣛⣿⡟⣻⣿⠎⠀⠴⠀⠀⠀⠀⠀⢛⠛⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇
⢰⣿⣹⣹⣯⣷⣿⣿⣾⣷⣼⣿⣿⠈⡛⠛⠳⣿⠈⣻⡅⣴⣿⣿⣿⣿⣿⣿⣣⠀⠀⠀⠀⢠⠾⠿⢦⠀⣤⣙⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⡇
⠸⣷⣿⣿⣿⣿⣿⣿⣿⠻⣻⣦⣤⢶⡅⠀⠀⣠⡼⣿⣿⣿⣏⠿⣿⠏⠋⠀⠐⠶⠀⠀⠀⠐⠀⠈⠀⠉⠻⠹⠩⢻⣿⣿⣻⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢿⣿⡟⡕⢻⣿⢿⡋⣶⠙⠛⣿⣧⣽⠀⠼⣷⣿⣶⡯⣹⣺⣲⢾⣷⠀⠀⠐⠀⠀⡀⠀⠀⠀⢀⣀⣠⡖⠦⠃⠈⠻⢶⣮⣿⣯⣼⣿⣿⣻⣾⣯⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠙⣿⣿⣿⢿⣿⣿⣿⡇
⠀⠈⠫⣽⣷⣼⣿⣿⣿⣟⡶⡚⠝⠉⠛⣦⠰⡿⣿⣿⣅⢈⠘⠑⣿⣗⣬⣦⣈⡗⣨⣭⣤⡎⠈⢸⢿⣹⣀⠄⠠⡀⠀⠈⠉⠡⡝⢘⣋⣤⣟⣿⢻⣾⣿⣿⣾⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣮⢽⣿⣿⡇
⢠⡓⣾⡗⢻⣿⣽⣓⠛⠻⡏⣙⠟⣾⣷⢵⣶⣿⣏⠇⠼⠀⠔⠳⠀⠈⠛⣿⠏⣱⣭⣿⣯⣉⠀⣾⣏⡿⣖⠰⢿⡟⡼⣴⡦⣾⣿⣿⣿⣿⠓⠣⣶⣽⣿⣯⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⣿⡇
⠸⠛⠍⠁⠺⠻⡿⠃⠀⠀⠁⠀⡈⣩⠉⢆⡿⠻⠋⣁⡀⠀⠀⠁⠀⠀⠀⠀⠘⢿⢿⣿⡟⠿⢻⢙⠻⠓⢫⠁⠖⠤⠭⢝⢺⣟⢿⣿⣿⣿⣯⣧⣼⣿⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⠇
⠀⡅⣾⣆⡨⣈⣝⡋⡿⢤⠎⠀⠇⠁⠀⠘⠡⠉⢒⣢⠒⠚⠁⡀⢀⣴⣶⠀⠠⣶⠾⡧⠇⠃⠈⢏⠀⡄⠀⠀⠀⠀⠚⣹⣀⠑⢸⣟⠦⢯⣿⣿⣿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⡙⣽⢭⣿⣿⣿⡇
⠀⢱⢉⡓⢽⡄⣨⠍⠫⠄⢦⡤⡥⠤⢤⠤⣤⢤⣶⣾⣿⣿⣿⣿⣿⣽⣧⡸⣿⠉⣀⠱⠀⠐⠂⠀⠀⣇⠘⠶⡵⠗⡀⠜⠁⠀⠾⣶⠈⢋⠀⢴⣿⣯⣿⣿⡯⠙⡁⠹⡿⣿⣻⣿⣿⣿⣿⣾⣿⣾⣯⡠⠘⣟⡋⠿⢿⠃
⠈⠛⠹⡤⠾⣯⣼⣿⣬⢮⣃⡽⣯⠄⠈⣀⠝⣣⣿⢻⣿⣿⣿⣻⣟⣿⣶⣬⡿⣿⣿⢶⡗⣶⣷⣦⣤⣴⣤⣾⣥⣖⣳⣦⣀⠀⣾⠾⠲⣟⢡⣾⣿⣿⣷⣢⣦⣰⣧⣮⣟⣟⡗⣙⢓⠛⠉⢯⣿⣩⡟⠁⢼⣿⡗⢿⢻⠂
⠀⠤⠤⠠⠤⠤⠼⠶⠤⠤⠿⠿⠽⠳⠿⠤⠤⠼⠂⠽⠉⠻⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠧⠿⠝⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠚⠷⠻⠽⠿⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠖⠤⠾⠿⠿⠿⠯⠀⠀⠀⠁⠠⠲⠧⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠪⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢷⠈⠓⡩⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠂⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣭⠍⠉⢁⣒⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠋⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⠿⢿⣿⣟⣛⢿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄⡿⡿⠀⢨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⣛⣿⡇⣬⠁⠴⠶⠶⠂⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⣾⣛⠲⠶⠴⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣇⠀⠨⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢗⡿⢾⣶⠖⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⡏⠁⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠉⢩⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣸⢛⣛⣉⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⢸⠁⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⢰⢆⣿⡿⠭⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⡝⢹⢻⣷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠶⢶⡆⠀⠀⠀⠀⠀⠘⠀⠀⡚⢼⣿⣷⡆⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠈⠉⠭⣿⣏⠹⢿⢆⣀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⡆⢸⡇⢠⠈⠁⠀⣿⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⠸⢧⡀⠀⠙⠉⠁⠀⠀⠀⠀⠘⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠐⠀⠇⣶⠍⠉⠠⠄⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⡁⢠⣴⣎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣏⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⣤⠀⣇⣤⠁⠀⠀⠀⠉⠉⠉⠉⠁⣀⣀⣀⣀⣀⣀⣀⣼⣧⡉⠁⠙⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣦⣷⣨⡟⢻⢻⡛⠛⠿⠿⠿⠿⠿⠿⠦⢈⣉⣛⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣇⣿⣿⣇⣻⡤⠌⡙⠛⠿⣟⠁⠀⠀⢰⣾⣿⡿⠈⠀⠘⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢸⡇⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⡇⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠓⢻⠀⠀⠀⠀⠰⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣸⡇⣹⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⣿⣿⣾⡄⠘⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠃⣿⣿⣿⣿⣿⣧⣼⣿⢇⣿⣼⡿⠙⠿⡷⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣼⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠲⠷⠶⠶⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⠈⣿⣿⡇⢻⠻⠻⣿⣿⢸⡁⢏⠁⡿⣾⡗⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⣼⠁⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣗⣀⣿⣟⣁⣘⣀⣀⣺⡛⡈⠀⢈⡀⠱⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠿⣿⠟⠀⣿⡦⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢈⡽⠉⠉⠉⠛⠛⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⠶⢠⠦⠤⢤⣤⠤⠉⠁⠀⠀⠀⠀⣽⠀⣤⠂⠠⠐⠀⠀⠐⠒⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡄⠀⠀⣿⠀⣉⣄⣰⢄⡀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀
⢠⣤⣴⣦⣴⣿⡟⠛⢻⣿⣿⣿⣿⣻⣾⣷⣤⣤⢀⠙⠹⣿⣻⣿⣿⠻⠿⡟⠀⣼⣿⠀⠀⢀⠀⠀⣼⠇⢀⢀⣠⣦⣀⡀⢠⣤⣤⣯⣽⣦⡦⢤⠀⠀⢀⣀⣀⣄⣀⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣇⣰⠐⡟⠫⢭⣿⣧⠑⠉⢹⣧⣁⢨⡽⢿⣿⡯⣵⣤⢶⣴⣾⠟⠃⠀⠀⠐⠀⣾⡟⠀⠀⢺⣿⣿⣿⣿⣿⣥⣬⣿⣿⣿⣿⣿⣿⣷⣾⣿⣋⢹⣾⣤⣾⣿⣅⣠⣶⣗⠴⠀⠀⠀⠀⣴⣿⣿⡆⣀⠀⠀
⠸⣿⣿⣿⡿⢿⣿⡿⣶⣶⣤⣿⣿⣿⣿⢿⣿⣿⣿⣯⡟⣸⣻⣿⣿⡿⢄⠉⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⡷⠀⢴⢉⠊⠿⠿⠋⠀⠀
⠀⡿⣬⠴⠃⠀⠀⠒⢿⣿⢻⣿⣿⢿⣧⣌⣿⣿⣹⣧⡋⠙⣛⣿⡟⣻⣿⡟⠀⠴⠀⠀⢀⠾⠿⠿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⡿⠒⢶⣿⡇
⢰⣿⣉⣹⣯⣦⣿⣾⣾⣶⣸⡿⠿⠘⠛⠛⠻⣿⡈⣻⡄⢼⣻⠿⣿⣿⣿⡿⡂⠀⠀⠀⢠⣾⣿⣦⠀⠀⣀⡙⠿⢿⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣿⡇
⠸⣷⣿⣿⣿⣿⣿⣿⣿⠻⣿⡦⣤⢤⡅⠀⠀⡨⠜⣿⣿⣿⣏⠻⢿⠋⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠜⠛⢳⣿⣿⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⡟⡕⢻⣿⢿⠋⣴⠙⠓⣿⣦⡵⠀⠬⣶⣶⣦⡧⡹⢲⣢⢼⣧⠀⠀⠠⠀⠀⠀⠀⡄⠀⢀⣀⢠⡐⡮⠃⠈⠻⢦⢢⣿⣿⣽⣿⣟⣫⣾⣯⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⠉⠙⣿⣿⣿⢿⣿⣿⣿⡇
⠀⠈⠃⡽⣶⣼⣿⣿⣿⣟⡲⡒⠍⠉⠛⣤⠐⠿⣿⠿⡄⠈⠘⠁⢽⣗⣤⣄⣈⡗⢈⣥⣤⡆⠀⠈⠻⡱⡀⠄⠠⡀⠀⠈⠙⠁⡽⠘⣋⣤⡻⣿⢻⣾⣿⣿⣾⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣾⣿⣮⣭⣿⣿⠇
⠀⡓⣾⡟⢻⣿⣽⣋⠙⠛⡏⢁⠋⣾⣷⢵⣶⣿⣍⠅⠼⠀⠀⠲⠀⠈⠙⢿⠯⣲⣥⣳⣤⣉⠀⣶⣏⡛⣖⢠⢿⡿⡴⣴⡤⣾⣾⣿⣿⣿⡃⠓⣶⣽⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⡇
⠠⠙⠉⠀⠘⠸⣿⠃⠀⠀⠁⠀⠈⣩⠉⢆⡟⠛⠯⠁⠀⠀⠀⠁⠀⠀⠀⠀⠘⠿⢿⣿⠞⠻⢲⢛⠁⠃⢩⠀⠖⠤⠥⢟⠶⣟⢿⣿⣿⣿⣦⣦⣘⣿⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⠿⣻⣿⣿⣿⣿⠃
⠀⡄⣾⣆⡨⣀⣍⡛⡽⢤⠎⠐⠇⠁⠀⠐⢡⠉⢒⣢⠐⠐⠁⡀⠀⣴⣄⠀⠤⣶⠾⡂⠇⠀⠈⠋⠀⡀⠀⠀⠀⠀⠚⣹⢀⠩⢘⣉⠢⢧⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣻⣿⢾⣿⢾⡉⠘⣽⢭⣿⣿⣿⡇
⢀⢡⢉⡃⢰⡀⣠⠋⠫⠄⢤⡤⡥⠠⠤⠤⣤⠤⣶⣾⣿⣿⣿⣿⣯⡽⣧⢰⣿⠉⡀⠐⠀⠀⠀⠀⠀⡅⠘⠲⡵⠐⠀⠘⠁⠀⢿⣷⠈⠉⠀⢴⣿⣯⣿⣿⡯⠙⠁⠹⡿⣿⣻⣿⣿⣿⣿⣾⣿⣾⣏⡠⠘⣟⠃⠿⢿⠃
⠀⠛⠱⡤⠦⣦⣼⣽⣬⣮⣄⡽⠏⠈⠀⡀⠝⢣⡟⢻⣿⣿⣿⣻⣟⣶⣴⣬⡿⣿⣷⢲⡂⢶⣶⣦⣤⣤⣤⣮⣤⣖⡣⢤⣀⠀⣼⠾⠲⡾⢠⣾⣿⣿⣷⣠⣔⢰⣧⣶⣞⣟⡇⡈⠟⠛⠉⢍⣻⣩⡟⠁⢼⣿⠶⠿⠹⠂
⠀⠤⠤⠀⠤⠤⠼⠦⠤⠤⠿⠧⠵⠳⠿⠤⠤⠽⠂⠹⠉⠻⠿⠿⠿⠾⠿⠿⠷⠿⠿⠯⠦⠽⠍⠿⠿⠿⠿⠿⠷⠯⠿⠿⠿⠾⠿⠚⠷⠺⠽⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠖⠠⠾⠿⠿⠿⠋⠀⠀⠀⠀⠁⠲⠇⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠪⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢷⠈⠓⡉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⣹⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠊⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣭⠍⠉⢑⣖⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠋⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⠿⢿⣿⣟⣛⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄⡿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢖⣓⣿⡇⣬⠁⠴⠶⠶⠂⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⣿⣛⠒⠶⠼⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⣇⠀⠨⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢱⡿⢾⣿⠗⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⡏⠃⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠉⢩⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣸⢛⣛⣉⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⣤⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⣸⠁⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⢰⢦⣿⡿⠭⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠿⠶⢶⡆⠀⠀⠀⠀⠀⠘⠀⠀⡚⢼⣿⣷⡇⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣤⣿⣿⣿⣿⣿⣿⣟⣻⡛⡟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⡆⢸⡏⢠⠈⠁⠀⣿⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⢰⡍⢠⣿⠋⢈⣽⣷⣿⣧⡟⣿⣇⡼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠁⠐⠀⠇⣶⠍⠉⠠⠄⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣧⠛⢿⣇⡛⠛⠋⠉⠏⠁⠀⠀⠀⠛⡟⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣏⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⣤⠀⣇⣤⠁⠀⠀⠀⠉⠉⠉⠉⠡⠤⣄⣀⣀⣀⠀⢀⣠⣿⠀⠈⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⢻⣿⣿⣦⣷⣨⡟⢻⢻⡛⠛⠿⠿⠿⠿⠿⠿⠤⢈⣙⣛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣇⣿⣿⣏⣻⡤⠌⡙⠛⠿⣟⠃⠀⠀⢰⣾⣿⡯⠐⠀⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⡇⠉⢸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⡆⠀⠈⠀⠀⠀⠀⠀⠘⣻⣿⡇⠀⠀⠀⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠓⢻⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣸⡇⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣻⣿⣿⣾⡄⠘⢃⠹⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⢣⣿⣿⣿⣿⣿⣷⣼⣿⣇⣿⣾⣿⠛⢿⡷⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣼⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠲⠷⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣟⠀⣿⣿⡇⢻⢻⠻⣿⣿⢸⡁⢯⠛⡿⣾⡗⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣼⠃⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣀⣿⣿⣉⣘⣘⣂⣻⡿⡈⠀⢘⣆⠑⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⣿⠟⠀⣿⡄⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⡽⠉⠉⠉⠙⠛⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⠶⢠⠦⠤⢴⣤⠤⠉⠁⠀⠀⠀⠀⣼⠀⣤⠂⠠⠀⠀⠂⠐⠒⠀⠀⠀⢠⠇⠀⠀⠈⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣿⠀⣙⣀⣠⣤⣀⡤⡀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀
⢀⣤⣴⣦⣶⣾⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣤⣴⠘⠹⣹⣿⣿⣻⣿⣿⣿⠷⢸⣿⠃⠀⠀⠀⣠⡿⠀⠀⢀⣀⣄⣦⣀⣀⢴⣤⣤⣯⣭⣦⣦⣄⠀⠀⢀⣀⢀⣀⣀⣀⣤⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣇⣺⠼⡟⠿⣿⣿⣟⠙⠋⢹⣿⣔⢺⣷⣿⣿⣿⡇⢀⠀⣠⣾⡏⠀⠀⠀⢲⣿⠇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣷⣾⣿⣋⢹⣿⣷⣽⣿⣅⣴⣾⣷⣶⠀⠀⠀⠀⣼⣿⣿⡆⣀⠀⠀
⢸⣿⣿⣿⡿⢿⣿⣿⣶⣶⣤⣿⣿⣿⣷⢿⣿⣿⣿⣿⣯⣸⣿⣿⣿⡛⠿⠟⠁⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣿⠇⢴⡉⠊⠻⠟⠛⠀⠀
⠀⡿⣭⠴⠃⠀⣀⠁⣿⣿⢻⢿⣿⢿⣯⣜⠿⣿⣻⣧⡗⠛⣛⠿⡟⢻⣶⡆⠀⠄⠁⠾⠿⢿⣅⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⢳⣿⡇
⢰⣿⣙⣹⣯⣦⣿⣿⣾⣶⣾⢿⠺⠘⠛⠙⠓⣿⡈⣻⡃⢴⣿⠟⢿⣿⣿⡟⡧⠀⠀⠘⠛⠿⠷⠀⠀⣀⣈⣛⠿⢿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⡄
⠸⣷⣽⣿⣿⣿⣿⣿⣿⠫⣶⠆⣤⢤⡃⠀⠀⡠⡘⣿⣟⣿⣏⠻⢿⠃⠋⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠛⠻⠼⠻⢻⣿⣿⣿⣻⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢿⣿⠙⡕⢻⣿⣷⠉⣤⠉⠫⢻⣦⡵⠀⠸⣶⣶⣦⡧⡹⣳⣢⢼⣷⠀⠀⠠⠀⠀⠀⠀⢀⠀⢀⣀⢠⡒⡢⠃⠈⠻⢦⣮⣿⣿⣽⣿⣟⣻⣾⣯⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠙⢿⡽⣿⢿⢿⣿⣿⡇
⠀⠈⠋⣼⣶⣼⣿⣿⣾⣟⡶⡞⠍⠉⠛⣄⠔⡿⣿⣿⡤⠈⠙⠃⢿⣗⣤⣆⢈⡇⢨⣥⢠⠂⠀⠀⠛⡉⡀⠌⠠⡀⠀⢨⠙⠡⡝⠘⣙⣤⣿⣻⢫⣶⣿⣿⣾⣏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣯⣮⢼⣿⣿⡇
⠀⡑⣾⡿⢻⢿⣽⣋⠉⠛⡛⡃⠋⣾⣷⣵⣶⣾⣍⠦⠾⠀⠀⠰⠀⠈⠛⢿⠏⣰⣥⣻⣮⣉⠂⡶⣏⡛⣔⢲⢿⡿⡶⣴⡤⣾⣾⣿⣿⣿⡗⠗⣶⣽⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣫⣿⣿⣿⡇
⠰⠙⠉⡁⠘⠾⡿⠓⠂⠀⠃⠀⡈⣩⠉⣦⣿⠛⠯⢁⣀⠀⠀⠁⠀⠀⠀⠈⠸⠿⠿⣿⠖⠋⢲⠙⠀⠁⢉⠀⠞⠤⠵⢟⠶⣟⢿⣿⣿⣿⣮⣦⣸⣿⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⠇
⠀⡄⣾⣄⡬⣈⣜⡁⡷⠤⠊⠀⠁⠀⠀⠀⢣⠀⢓⡀⠐⠒⠁⡀⠀⣴⣤⠀⠠⣖⠼⡆⠆⠀⠈⠏⠀⡀⠀⠀⠀⠀⠊⠛⢀⠭⢙⣃⠦⢋⡻⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢷⣿⢿⡃⠈⣹⢬⣿⣿⣿⡇
⠀⢡⢉⡃⢴⡀⣠⠍⠫⠄⢤⡠⡄⠠⠤⠀⡤⢤⣶⣾⣿⣿⣿⣿⣷⣿⣧⢀⢟⠉⠀⠑⠀⠀⠀⠀⠀⡄⠐⠲⡷⢀⠀⠘⠁⠀⢷⣖⠀⠀⠀⢴⣿⣯⣷⣾⠏⠉⠁⠩⡿⣿⣻⣿⣿⣿⣿⣾⣿⣾⣇⡠⠙⣟⡋⠿⢿⠇
⠀⠛⠱⡄⠦⣮⣼⣽⡬⣌⣆⡿⠯⠈⠘⡀⠝⢳⡻⢻⣿⣿⣿⣿⣟⣷⣾⣴⣿⣿⣶⢲⡒⢶⣶⣦⣤⣤⣤⡤⣤⣖⡃⢤⣄⠀⣸⠾⠰⣏⠁⣾⣿⣿⣿⣢⣔⢰⣧⣶⣞⣟⡗⡘⠓⠛⠉⢯⣿⣉⡟⠁⢽⣿⡶⠟⠹⠂
⠀⠤⠤⠀⠤⠤⠼⠦⠤⠤⠿⠧⠵⠳⠿⠤⠤⠽⠢⠽⠉⠻⠿⠿⠿⠿⠿⠿⠷⠿⠿⠯⠆⠿⠈⠿⠿⠿⠿⠿⠷⠯⠿⠿⠿⠿⠿⠚⠷⠺⠬⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠖⠠⠾⠷⠿⠿⠯⠐⠀⠂⠀⠀⠰⠧⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⡿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠪⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣳⠈⠊⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡏⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠊⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣭⠉⠉⢁⣤⡆⠀⠀⠀⠀⠀⠀⠀⡆⣸⡿⠀⢈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⠿⢿⣿⣟⡛⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣧⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣖⣻⣿⡇⣬⠀⠴⠶⠶⠂⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⣿⡓⠒⠒⢾⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠈⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⢸⡷⢶⡿⠗⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣾⢛⣛⣁⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣧⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⣼⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡧⠍⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⢼⣿⣷⡇⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⡭⣎⠀⢀⣤⣶⣾⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡆⣿⡅⣤⠈⠁⠀⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⣴⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠐⠠⠇⣦⠍⠉⠠⠄⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢑⣿⠋⣭⣿⣿⣿⣼⣻⣿⣬⢽⣿⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣰⣀⠀⠀⡬⠀⣇⣤⢁⠁⠀⠈⠉⠉⠉⠉⠗⠢⣄⣀⣀⡀⠀⢀⣠⣮⠘⣿⣀⠛⠟⠻⡿⠃⠐⠀⠀⠘⢻⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⢹⣿⣿⣮⣷⣸⡟⣿⢻⡛⠛⠿⠿⠿⠿⠿⠧⠄⢈⣉⡻⣿⣿⣿⣿⡇⠀⠻⠁⠉⠀⠀⠁⠀⠀⠀⠀⠀⠳⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡆⣿⣿⣇⢻⢤⡌⡙⠛⠿⣟⠁⠀⠀⢰⣾⣿⡟⠀⠸⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣿⡿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡇⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠛⢻⠀⠀⠀⠰⠰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡇⣿⣿⣿⣯⣿⣿⣿⣿⡇⣿⣸⣿⣿⣾⡄⠘⠣⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⢸⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⢰⣿⣿⡿⣿⣿⣷⣼⣿⢃⣿⣿⡿⠛⢿⡗⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠒⠛⠷⠶⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⠀⣿⣿⡇⢻⠛⠛⢿⣿⢸⡁⠯⠩⡿⣾⡗⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣀⣿⣟⣁⣘⣡⣀⣽⡻⡈⠁⢀⡀⠑⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⡿⠀⣿⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⠉⠉⠉⠉⠉⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⠶⢠⠶⠤⢭⢤⠤⠈⠀⠀⠀⠀⠀⣾⠀⣤⠂⠀⠐⠐⠀⠒⠀⠀⠀⠀⡌⠀⠉⠉⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣄⣀⡀⣿⠀⣩⣄⣠⣤⣀⣀⡄⠀⠀⢀⣾⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣄⣴⣶⣶⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣴⠅⠛⡹⣿⣿⣿⣿⣿⣷⠘⣿⡇⠀⠀⠀⣼⠇⠀⠀⢴⣾⣶⣤⣄⣀⣀⣰⣤⣴⣧⣽⣶⣿⣤⡀⠀⢀⣠⣀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣇⣲⠼⡿⠿⣯⣿⣛⢻⠋⢹⣿⣃⢾⣿⣿⣿⣿⣿⣿⠞⣰⣿⠇⠀⠰⣾⡿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣹⣿⣷⣿⣿⣥⣤⣾⣷⣾⣢⣄⠀⠀⣾⣿⣿⣆⣀⠀⠀
⢸⣿⣿⣿⡿⢿⣿⣿⣶⣶⣤⣿⣿⣿⣿⢿⣶⣿⣿⣿⣿⣹⣿⣿⣛⣁⣴⡿⠋⠀⢀⣼⡟⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢶⣉⠀⠛⠛⠋⢀⡀
⠀⡿⣬⠰⠃⠀⣀⠟⣿⣿⢻⣿⣿⠿⣯⣌⣿⣿⣹⣧⡟⠻⣛⣿⣏⡙⣛⠀⠀⠾⠿⢿⣷⣶⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠛⠻⡿⡇
⢰⣿⣉⣼⣯⣤⣿⣿⣼⣦⢲⡾⠺⠈⠛⠛⠓⡿⣉⢻⡁⣽⣿⠟⢿⣿⢏⡦⠊⠀⠀⠀⠀⠉⠁⠀⠀⣔⣬⣹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡇
⠸⣻⣽⣿⣿⣿⣿⣿⣿⠉⣾⡀⣤⢤⡁⠀⠀⣠⡘⣿⣟⣿⣏⠻⣿⠋⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠺⠛⢳⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⣿⣿⡘⡇⢻⣿⣷⠋⣴⠉⠃⣋⣦⡵⠀⠼⣷⣿⣶⠧⡹⣲⣦⠼⢦⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⢠⡀⠂⠃⠈⠻⢦⣦⣿⣿⣿⣿⣟⣻⣾⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠁⠙⣿⣼⣿⢿⢿⣿⣿⡇
⠀⠀⠋⡴⣶⣼⣿⣿⣶⣟⡲⡒⠙⠉⠉⣄⠔⡿⣿⠿⡀⠈⠙⠃⢻⣃⣤⣄⢈⡇⣈⣤⣤⠀⠀⠀⢙⡁⠀⠄⠠⡀⠀⠈⠉⠡⠝⣸⣉⣨⣿⣿⣻⣿⣿⣿⣾⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣦⢼⣿⣿⡇
⢠⢑⣾⡷⠻⣿⣽⣋⠉⠛⡛⢡⠣⣾⣦⣵⣶⣬⣉⠧⠼⠀⠀⠲⠀⠈⠉⢿⠏⣠⣄⡳⢄⣉⠂⡶⣏⡻⣖⠲⢿⡿⡶⣴⡠⣾⣿⣿⣿⣿⡆⠱⣶⣾⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇
⠸⠙⠉⠁⠘⠾⡿⠃⠀⠀⠁⠈⡈⣩⠉⣎⣿⠚⠯⢁⣀⠀⠀⠁⠀⠀⠀⠀⠘⠻⢯⣧⠐⠋⢒⠙⠀⠁⢩⠀⠖⠤⠽⢝⢾⣟⣿⣿⣿⣿⣮⣦⣸⣿⣹⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⣿⣟⣿⡇
⠈⡄⣾⣆⡨⣀⣌⡉⠽⠤⠊⠀⠃⠁⠀⠈⠫⠁⢒⡂⠐⠒⠃⡀⠀⣴⣤⡀⠠⣶⠴⡂⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠊⠑⢀⠭⢽⡋⠂⢃⢿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢿⡅⠈⣽⢭⣟⣿⣿⡇
⠀⢡⢈⠉⢵⡁⣀⠏⠫⠀⢤⡠⡄⠠⠤⠀⣤⢤⣶⣿⣿⣿⣿⣿⣿⡿⣦⠠⣿⠁⠀⠐⠀⠀⠀⠀⠀⡄⠐⠲⡵⠀⠀⠈⠁⠀⠱⣖⠈⠀⠀⢴⣿⣯⣷⡾⠏⠙⠀⠫⠟⣿⣻⡿⣿⣿⣿⣿⣿⣿⣃⡠⠘⡞⠁⠻⢻⠃
⠀⠟⠻⠄⠦⣮⣼⣶⡬⣮⣆⡿⢧⠈⠈⡀⠝⢳⡻⢻⣿⣿⣿⣻⣟⣷⣿⣤⡿⣿⣷⢲⡒⣶⣶⣦⣤⣤⣤⣦⣤⣖⡣⢤⣄⠀⣰⠞⠲⡾⠠⣾⣿⣿⣯⣠⣦⣰⣧⣶⣟⣛⡇⡘⢓⠛⠁⢏⣿⣩⠏⠁⢬⣿⠷⠟⠙⠂
⠠⠤⠤⠀⠤⠤⠼⠤⠤⠤⠿⠧⠵⠳⠿⠤⠤⠽⠈⠽⠉⠩⠿⠾⠿⠿⠿⠿⠶⠿⠿⠯⠄⠿⠈⠿⠿⠿⠿⠿⠿⠯⠿⠿⠿⠶⠿⠚⠷⠻⠬⠿⠰⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠖⠠⠾⠿⠿⠿⠃⠀⠄⠀⠀⠀⠸⠥⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣿⡗⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⡢⠈⠊⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⠿⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠊⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣸⣭⠉⠉⢩⣵⡆⠀⠀⠀⠀⠀⠀⠀⡆⡜⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⢟⠟⢿⣿⣟⡛⣿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣢⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣖⣻⣿⠇⡬⠀⠴⠶⠖⠂⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⡓⠒⠒⢚⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠈⠻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⣿⢸⡷⣶⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡿⣿⣛⣛⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢘⣿⣧⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠀⠀⣼⠀⠀⠸⠀⠀⠀⠀⠀⢠⠀⠀⣰⣶⣿⡧⠍⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣻⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠿⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⣀⠛⢼⣿⣶⠃⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢺⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡆⣿⡅⣤⠈⠁⠀⣿⣿⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠀⠀⣤⣶⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⣿⡿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠘⠰⠇⣦⠍⠉⠠⠄⢰⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣿⣿⣿⣿⣿⣿⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣰⣀⠀⠀⡬⢘⣅⣤⢁⠁⠀⠈⠉⠉⠉⠙⠑⠲⣤⣀⣀⠀⠀⠀⣠⡿⢰⡟⢻⣽⣿⣿⣯⣟⣿⣧⣽⣿⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢸⣿⣿⣮⣧⣼⡟⣻⣻⡛⠛⠿⠿⠿⠿⠿⠶⠤⣄⣙⢿⣷⣶⣿⣿⡇⢸⣷⣘⢿⢟⣿⠿⢁⠊⠀⠀⠛⡷⠶⢤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡆⣿⣿⣗⢻⢤⡌⠙⠛⠿⣟⠉⠀⠀⢰⣿⣿⡗⠈⢻⣿⣿⡇⠘⡝⠈⠁⠈⠉⠀⠐⠀⠢⠀⠘⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣻⡿⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣿⡿⡾⡦⠃⠐⠀⠀⠀⠀⠀⠈⣻⣿⡇⠀⠀⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠙⢻⠀⠀⠀⢸⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡇⣿⣿⣿⣯⣿⣿⣿⣿⡇⣿⣿⣿⣿⣾⡌⠸⠃⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠘⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠰⣿⣿⡿⣿⣿⣷⣼⣿⢣⣿⣿⡟⠙⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠒⠛⠻⠷⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣟⠀⣿⣿⡇⢻⠻⠻⣿⣿⢘⡁⣯⠋⡿⣾⡇⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣛⣀⣿⣿⣁⣘⣛⣒⣿⣛⡈⠁⢘⡁⢑⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠀⣏⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠉⠉⠉⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⠶⢠⡦⠤⢭⣤⠤⠉⠀⠀⠀⠀⠀⣿⠀⣴⠂⠆⠐⠐⠀⠒⠒⠀⠀⢘⠛⠿⠟⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣄⡀⠀⡿⠀⣝⣄⣠⣄⣀⣀⡀⠀⠀⢠⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⣴⣶⣶⣾⡿⠛⢻⣿⣿⣿⣿⣷⡿⣷⣄⡤⠀⠙⠙⡿⡛⣿⣟⣶⠀⣿⣄⠀⠀⢀⣿⠀⠀⠀⠠⣾⣷⣶⣠⣄⣀⡀⣰⣤⣶⣧⣽⣶⢾⣠⡀⠀⢀⣠⠀⣤⠠⡄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣣⣲⠸⡿⠻⣯⣿⣟⠫⠉⢹⣗⡀⢪⣿⣿⣿⣟⣿⡈⠇⣿⡏⠀⢠⣼⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣾⣿⠁⡹⣢⣷⣾⣿⣄⣤⣾⣦⢦⢀⡀⠀⠀⣾⣿⣿⣆⣀⠀⠀
⠸⣿⣿⢿⡿⣿⣿⣿⣦⣶⣤⣾⣿⣿⣿⢿⣷⣿⣿⣿⣟⣸⣿⣿⡿⠐⣸⡿⠁⣀⣾⠋⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣿⠂⡴⣀⠀⠛⠛⠃⢀⡀
⠀⡿⣭⠰⠃⠀⡀⠊⣿⣿⢹⢿⣿⠿⣧⣜⣿⣿⣿⣮⡋⠽⡛⣥⣶⣾⠿⠷⠿⣿⡏⠀⠹⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠝⠻⣿⡇
⢰⣿⡉⣝⣋⣶⣿⣿⣼⣦⢶⠿⠺⠈⠛⠛⠷⣯⠈⢿⠀⢼⣿⡿⢦⡤⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡆
⠸⣿⣹⣿⣿⣿⣿⣿⣿⠨⣴⠂⣤⢤⡅⠀⠀⡠⡘⣿⣽⣿⣯⠻⣿⠃⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠜⠉⢳⣿⣿⣻⢻⣹⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⣿⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣷⡹⡗⢻⣿⣿⠉⠰⠋⠑⣛⣦⡵⠀⠸⣶⣾⣶⡥⡹⢴⣢⢼⢦⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⠠⡀⠂⠃⠈⠻⢶⣶⣿⣷⣼⣿⣟⣩⣾⣯⡿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠙⢿⣽⣿⢿⢿⣿⣿⡇
⠀⠈⠋⣾⢶⣼⣿⣿⣶⣟⡲⡒⠟⠉⠝⣄⡔⡿⣿⣿⡠⢈⡛⠃⢻⣃⣤⣄⢈⡇⢈⣄⣄⠀⠀⠀⠩⠃⠀⠆⠠⡀⠀⠈⠋⠡⠍⣘⣈⣠⣝⡿⠻⣶⣿⣿⢾⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣦⢼⣿⣿⡇
⠀⡓⣼⡗⠻⣿⣽⡋⠋⠛⡛⡡⠋⣾⣶⣵⣶⣾⣍⠥⠼⠀⠄⠲⠀⠈⠙⢟⠏⣠⣁⡡⢄⣁⠂⡶⣏⡛⣖⠰⢿⡿⡴⣴⠢⢷⣾⣿⣿⣿⠀⠑⣶⣾⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣋⣷⣿⣿⡇
⠠⠛⠉⠁⠐⠎⡿⠓⠀⠀⠃⠈⡈⣩⠉⣆⡿⠺⠭⢁⡀⠐⠀⠁⠀⠀⠀⠀⠘⠻⠃⡷⠐⠃⢢⠙⠁⠃⢩⠀⠖⠤⠥⢝⢴⡟⢿⣿⣿⡽⣦⣦⣼⣿⣽⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⡿⣿⡻⡿⢻⢻⣿⣿⣏⣿⡇
⠀⡀⣴⣀⡐⣀⣍⡁⣝⢤⠊⠐⠅⠀⠀⠀⠠⠀⢓⡀⠰⠒⠁⡀⠀⣴⣄⡀⠠⣖⠼⡀⠁⠀⠈⠋⠀⡀⠀⠀⠀⠀⠂⠑⢀⠨⠹⡉⠊⢣⠻⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⠿⢿⢿⡅⡀⣽⣼⡟⣿⣿⡇
⠀⢡⠉⡃⢷⡃⣐⠏⠩⠀⢄⡀⡄⠠⠤⠀⣤⢤⣶⣿⣿⣿⣿⣿⣏⡿⣧⢴⢟⠁⠀⠐⠀⠀⠀⠀⠀⡄⠀⠲⣵⠀⠀⠍⠁⠀⠑⣆⠈⠀⠀⢴⣿⣯⣿⠿⠟⠙⠀⠩⠟⣯⡻⡿⣿⣿⣿⣾⣿⣿⣇⡠⠈⣟⠁⣟⢻⠃
⠀⠝⠩⠄⠢⣦⣼⣶⡬⣌⣆⡿⡇⠀⠀⡀⠛⢳⡻⢻⣿⣿⣿⣻⢟⣷⢵⣼⣿⣿⣶⢲⡒⢶⣶⣦⣠⣴⣤⣦⣤⣖⡃⢤⣀⠀⣴⠞⠰⣎⢡⣾⣿⣿⣦⣢⣦⣰⣧⣦⣟⣛⡗⡈⢑⠛⠀⢣⣼⣩⠏⠁⢸⣿⠿⠟⡹⠃
⠠⠤⠤⠀⠤⠤⠼⠴⠤⠤⠿⠧⠽⠳⠿⠤⠤⠽⠂⠽⠋⠩⠿⠾⠿⠿⠿⠿⠷⠿⠿⠯⠆⠿⠈⠿⠿⠿⠿⠿⠽⠯⠯⠷⠿⠾⠿⠚⠷⠻⠬⠿⠸⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠦⠠⠾⠷⠿⠿⠧⠀⠀⠀⠀⠀⠺⠧⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣿⡗⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⡢⠈⠊⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⠏⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠉⠊⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣼⣬⠉⠉⢩⣥⡆⠀⠀⠀⠀⠀⠀⠀⡆⡜⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⢟⠿⣿⣿⣟⡛⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣧⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣖⢻⣿⡇⣬⠀⠴⠶⠖⠂⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⡓⠒⠒⢚⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠈⠻⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢸⡷⣶⣾⠟⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⡿⣿⣛⣛⣁⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢘⣿⣧⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢠⠀⣼⠀⠀⡸⠀⠀⠀⠀⠀⠠⠀⠀⣰⣶⣿⡧⠍⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠿⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⣀⠛⢼⣿⣶⠃⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣬⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡆⣿⠅⣤⠈⠁⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠘⠰⠇⣦⠍⠉⠠⠄⢰⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⣾⣿⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣰⣀⠀⠀⡬⢘⣅⣬⢁⠁⠀⠈⠉⠉⠉⠉⠉⠲⣤⣀⠀⠀⠀⠀⣠⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢹⣿⣿⣮⣧⣼⡟⣿⣻⡛⠛⠿⠿⠿⠿⠿⠶⠤⣌⠿⣿⣦⣤⣾⣿⠃⣰⡿⣿⣿⣿⣿⣯⣿⣿⣼⢿⣷⡶⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣆⣿⣿⣗⢻⢄⠬⠙⠛⠿⣟⠉⠀⠀⢰⣿⣷⡮⡛⣿⣿⣿⠀⣿⣇⡿⣿⢿⣿⠿⡱⠃⠀⡸⢿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣿⡿⡾⡦⠂⠌⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⢹⡿⠟⠀⢻⡿⠉⠁⠍⠉⠠⠶⠶⠦⢁⠞⠉⠙⢻⠀⠀⠀⢸⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡇⣿⣿⣿⣯⣿⣿⣿⣿⡇⣿⣽⣿⣿⣾⡌⠘⠃⠑⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠰⣿⣿⡿⣿⣿⣷⣼⣿⢣⣿⣿⡟⠛⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠷⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣟⠀⣿⡿⡇⢻⠟⠻⣿⣿⢘⡁⣯⡋⡿⣾⡇⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣻⣀⣿⣿⣁⣜⣺⣐⣻⣛⡌⠁⣘⡁⢑⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠉⠉⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣶⠶⢠⠦⠬⢭⣤⠤⠉⠀⠀⠀⠀⠀⣿⠀⣴⠂⠤⠐⠐⠀⠒⠒⠀⢠⣾⣿⡿⢋⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡀⠀⠠⡿⠀⣽⣤⣤⢤⣀⣀⡀⠀⠀⡼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣠⣤⣦⣶⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣷⣤⡤⠀⠛⠘⣿⠻⣿⣿⡤⣼⣧⠀⠀⢠⡇⠀⠀⠀⠀⢠⣾⣿⣶⣄⣤⣄⡀⣰⣤⣴⣧⣽⣶⣿⣧⡀⠀⢀⣠⣠⣤⢠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣇⣲⠼⡟⠽⢏⣽⣫⠳⠋⢹⣪⣂⢪⡿⢿⣿⣯⣿⡗⢹⣿⠀⠀⣼⠃⠀⠀⠀⠀⠉⠁⠈⣿⣿⣿⣿⣿⣯⣤⣤⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆⣹⣿⣷⣾⣿⣥⣴⣿⣇⣃⠀⠀⠀⠀⣾⣿⣿⣆⣀⠀⠀
⠸⣿⣿⣿⡿⣿⣿⣿⣶⣴⣤⣾⣿⣿⣿⢿⣶⣿⣿⣿⣯⣸⣿⣿⣯⠁⣿⡿⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⠇⡴⡀⠀⠛⠛⠃⢀⡀
⠀⡿⣭⠼⠃⠀⢀⠗⣿⣿⢹⢿⣿⣿⣧⣌⠿⣿⣻⣥⡗⠟⢛⣋⣡⣾⣿⣵⣾⡏⠀⠀⢀⣀⣀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠛⠻⣿⡇
⢰⣿⡙⣽⣏⣦⣿⣷⣾⣦⣶⠶⢻⠀⠛⠁⠁⣯⢈⢩⡀⣴⣻⠍⢋⡁⢬⡉⠉⠀⠀⠀⠀⠙⠛⠃⢀⣤⣖⣉⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡆
⠸⣿⣿⣿⣿⣿⣿⣿⣿⠩⣾⡂⣤⣤⡅⠀⠀⣀⡘⣿⣿⣿⣍⠛⣿⠋⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠹⢳⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣿⣾⡹⡗⢻⣿⣿⠋⡠⠛⠓⣻⣦⡶⠀⣘⣶⣾⣶⡧⣹⣴⣦⢼⣷⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⢀⠠⡀⠂⠃⠈⠻⢶⣦⣿⣿⣼⣿⣟⣹⣾⣯⡿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⠉⠙⣿⣿⣿⢿⣿⣿⣿⡇
⠀⠈⠀⣿⣷⣼⣿⣿⣶⡟⣢⡐⠟⠛⠛⣄⣴⡿⣿⣿⡤⢈⠛⠃⢿⣇⣤⣄⢈⡇⢨⣤⣤⡆⠀⠀⢹⢃⠀⠄⠠⡀⠀⠈⠉⠥⠍⢐⣊⣴⣭⣿⢻⣾⣿⣿⢾⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣦⢼⣿⣿⡇
⢠⡒⣸⡧⠻⣿⣹⡏⠛⠿⡛⠥⠢⣾⣧⣵⣶⣖⣻⠧⠼⠀⠄⠰⠀⠈⠛⢿⠏⣠⡀⣱⢄⣉⠂⡶⣏⡻⣖⢰⢿⡿⡶⣴⠢⢶⣾⣿⣿⣿⡖⠣⣶⣾⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣿⡇
⠰⠟⠉⠀⠘⠾⡿⠑⠀⠀⠃⠉⠘⢪⠋⢎⣿⠿⢯⢁⡀⡀⠀⠁⠀⠀⠀⠀⠘⠻⠇⣧⠐⠃⢲⠛⠁⠁⢉⠀⠞⠤⠽⢽⢲⡟⢿⣿⣿⡽⣮⣦⣼⣿⣽⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢻⣻⣿⣿⣿⣿⡃
⠀⡀⣴⡀⣐⢀⡛⠒⣛⢠⠆⠀⠇⠈⠀⠈⢣⠈⢓⡂⠰⠒⡂⠀⠀⣴⣤⠀⠠⣖⠼⡆⠁⠀⠈⠋⠀⠀⠀⠀⠀⠀⠊⠛⣀⠠⢘⣋⠂⢃⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⢻⡍⡈⣽⣼⣟⣿⣿⡇
⠀⢣⠉⠏⣷⡋⣈⡏⠿⠀⣀⡀⣄⠠⢤⠄⣤⢤⣰⣾⣿⣿⣿⣿⣿⣿⣥⠴⣟⠁⠀⠐⠀⠀⠀⠀⠀⡄⠘⠲⣵⢀⠀⠌⠁⠀⠰⣖⠀⠀⠀⢴⣿⣯⣷⡿⠟⠉⠄⠩⡟⣿⡻⡿⣿⣿⣿⣿⣿⣿⣇⡠⠈⣟⠁⣿⢻⠃
⠈⠟⠫⡄⠢⢧⣼⣲⡨⣄⣄⡿⠗⠐⠈⣀⠝⢳⡻⢿⣿⣿⣿⣻⣟⣵⢿⣭⣿⣿⣷⢲⡒⣶⣖⣦⣤⣴⣤⣦⣤⣖⡓⢤⣀⠀⣸⠾⠰⣞⢁⣾⣿⣿⣿⣂⣦⣰⣷⣶⣟⣛⡗⡈⢑⠛⠁⢠⣿⣩⠏⠁⢸⣿⠿⠿⠻⠂
⠀⠤⠤⠀⠤⠤⠼⠤⠤⠤⠿⠯⠽⠳⠾⠥⠤⠾⠏⠹⠙⠻⠿⠾⠿⠿⠿⠿⠷⠿⠿⠯⠆⠿⠍⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠚⠷⠻⠭⠿⠸⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠦⠀⠾⠷⠿⠿⠇⠀⠄⠀⠄⠀⠲⠧⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⢝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⡦⠉⠪⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⠏⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠁⠊⠻⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣼⣬⠉⠉⢩⣥⡆⠀⠀⠀⠀⠀⠀⠀⡆⡜⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠿⣿⣿⣟⡛⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣧⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡖⢿⣿⠇⣬⠀⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⡓⠒⠒⢚⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠈⠻⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢸⡷⢶⣶⠖⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠉⢹⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⢛⣛⣉⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢘⣿⣧⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢀⠀⣼⠀⠀⠸⠀⠀⠀⠀⠀⠠⠀⠀⣲⣴⣿⡧⠍⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⣿⡶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠏⣽⣿⣴⠂⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⡆⣿⠋⣤⠈⠁⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠘⠠⠇⣦⠙⠋⠠⠄⢠⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⣀⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣯⣿⣷⣿⣿⣿⣿⣿⣿⣷⣦⣐⡀⠀⠀⡌⠐⣅⣬⠀⠁⠀⠈⠉⠉⠙⠁⠱⢤⣀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣮⣧⣸⡟⣻⢻⠛⠛⠿⠿⠿⠿⠷⠦⢌⡻⣿⣶⡀⢀⣴⣿⠀⠀⠀⣠⣷⣿⣿⣷⣶⣦⣀⠂⢠⡶⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡆⣿⣿⣇⢻⢸⠌⠙⠚⠿⣟⠁⠀⠀⢰⣷⣾⡿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣯⣿⣶⣸⡇⠈⢿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡂⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠸⣿⣿⠇⠀⣿⡎⣿⣿⣿⣿⣟⡹⠋⠉⣿⡟⠋⠛⢻⠀⠀⠀⠨⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣽⡇⣾⣿⣿⣟⣿⣿⣿⣿⡇⣿⢻⣿⣿⣶⡌⠹⠁⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⡏⠀⠀⠀⡿⣿⢗⠣⠛⠁⣤⣷⣦⡌⢠⡇⠀⠀⠸⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⢃⣿⣿⣿⣿⣿⣧⣼⣿⢣⣿⣿⡟⠛⢿⡗⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠁⠀⠁⠀⠀⠈⠉⠁⠀⠀⠛⠻⠷⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⠀⣿⣯⡇⢻⠿⠻⣿⣿⢸⡃⡏⠁⣶⣾⡇⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣗⢀⣿⣿⣃⣜⣪⣀⣻⡛⠈⠁⢈⡀⠱⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡸⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣭⣭⠤⢨⡥⠬⢭⣤⡤⠍⠁⠀⠀⠀⠀⣼⠁⣤⠀⠤⠁⠀⠀⠀⠀⢀⣀⣀⣼⢛⣡⣤⣀⡀⠀⣀⣠⣤⣀⠀⣿⣿⡇⣉⣉⡁⣰⣶⣆⢀⣀⠀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⡀⠀⠀⣿⠀⣹⣄⣠⣄⢀⠀⣀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠸⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣠⣤⣤⣶⡟⠛⢻⣿⣿⣿⣿⣷⡺⣦⣤⡄⠁⠙⠘⡿⠿⣿⣟⠀⣼⣿⡇⠀⣿⣿⠋⣍⣽⢀⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡏⠀⢀⣤⠀⡀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⡆⣰⠸⡿⠟⢯⣽⠻⢻⠋⢹⡒⠀⠌⡗⢟⣿⢟⣏⠀⣿⣿⡇⢠⠻⣿⣤⣿⠟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⡆⡸⣯⣧⣾⣿⣇⣴⣶⣧⠢⠀⡀⠀⠀⣼⣿⣿⣇⣀⠀⠀
⢸⣿⣿⣿⡿⣿⣿⣿⣦⣵⣤⣾⣿⣿⣶⢿⣶⣿⣟⣚⣇⣰⣿⣯⡍⢰⣧⠀⢠⡿⠀⠀⠉⠀⠀⠀⠈⠁⢀⣀⣄⣤⣄⣤⣀⣠⣤⣤⣄⡄⠘⠟⠛⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⠀⣰⢀⠀⠛⠛⠃⣀⡀
⠀⡿⣉⠤⠃⠀⡀⠐⣼⣿⢻⣿⣿⣿⢯⣌⠿⣟⣙⣤⣗⠿⠛⠃⣠⡿⠋⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠙⠻⣿⡇
⢰⣷⠙⡔⣎⣤⣷⣶⣼⣧⢶⣾⢺⠂⠛⠉⠁⣿⠈⢡⡁⣴⠺⠿⠿⠿⢿⠿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠉⠿⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡬⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡆
⢸⣷⣻⣿⣿⣿⣿⣿⣯⠃⣿⠆⣠⢄⡃⠀⠀⢀⡘⣾⣟⣿⣏⡰⠞⠃⠂⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠀⠐⠋⠒⣾⣿⣻⣓⣹⢿⣿⣿⡿⢿⣿⣿⣿⣿⡟⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⠚⡓⠛⣿⣿⠉⠠⠋⠓⢛⣆⡳⠀⢐⣷⡦⣦⡏⠸⢩⢄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠⡄⠰⠃⠈⠻⢦⣦⣾⣯⣼⣿⣟⣩⣾⣯⢿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠋⠉⠉⢿⠿⣿⢿⢿⣿⣿⡇
⠀⠉⠉⣴⣥⣾⣿⣾⣶⡟⡢⠐⠛⠓⠖⣄⡤⡿⣗⢿⠀⠀⠁⠉⢸⢀⣄⡄⠀⠂⠀⣁⠀⠀⠀⠀⠸⡁⠀⠀⠠⡀⠀⠀⠃⠁⠄⢐⣈⣰⣔⣹⢫⣴⣾⣿⢶⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣶⢼⣿⣿⡃
⠀⡒⣸⡧⢟⣿⣹⡟⠛⠳⠟⠃⠶⣶⣤⣡⣦⣖⣞⠦⠴⠀⠀⠠⠀⠀⠉⠛⠣⠀⡀⠀⠀⠀⠒⠤⢖⠑⣖⠠⢲⡿⣴⣤⠠⠲⣾⣷⣿⣿⡀⠑⣶⣾⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣷⣿⣿⡇
⠰⠛⠉⠁⠰⠼⣿⠓⠀⠀⠂⠐⠘⢢⠛⢆⡽⠾⠯⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠙⠀⠁⢋⠀⠖⠠⠥⢝⢳⠟⢻⣽⣿⡿⣦⣤⣬⣿⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠻⢻⣿⣿⣟⣾⠃
⠀⡀⣴⡄⢐⢀⡙⠂⢓⣀⠔⠀⠇⠉⠀⠀⢀⠀⢂⡠⠠⠰⠂⠀⠀⣠⣄⠀⠀⡄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠒⢙⢀⠀⢩⣃⠆⠋⠿⠿⣿⣿⣿⢿⡿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣷⣒⢾⢻⣍⠀⣹⣡⣟⣿⣿⡇
⠀⢀⠙⠉⢹⡘⣉⡏⠙⠈⣀⡀⣀⢀⣠⠀⣠⣀⣠⣿⣷⣷⣾⣿⣷⣹⣯⠠⢖⠃⠀⠀⠀⠀⠀⠀⠀⣤⠐⠰⣴⠀⡀⠈⠁⠀⠘⣖⡀⠀⠀⠰⣿⣯⣿⠞⠋⠉⠀⠈⡿⣿⣹⠟⢿⣾⣿⣿⣿⣿⣇⡠⠌⢛⡁⢝⢻⠃
⠀⠛⠻⠄⢀⢕⣨⣦⣄⣔⣀⡛⠖⠐⠨⢀⡹⢗⡿⠿⣿⣿⣿⢻⡟⣲⣭⣤⣿⣿⣶⠆⡆⢦⣤⣢⣠⣤⣤⣴⢥⣆⣛⢤⣄⠀⢠⠒⠒⣎⠁⣶⣿⣿⣟⣂⣴⣰⣷⣦⣞⣙⣷⡒⠃⠓⠁⢠⣽⣩⡵⠉⠨⢾⠟⠿⠹⠀
⠠⠄⠴⠠⠤⠤⠼⠤⠤⠤⠿⠭⠍⠒⠾⠥⠀⠲⠏⠩⠉⠿⠿⠾⠿⠿⠿⠿⠦⠿⠿⠾⠧⠪⠍⠿⠿⠿⠿⠿⠿⠯⠿⠽⠿⠾⠻⠒⠳⠺⠧⠿⠴⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠶⠀⠾⠷⠿⠿⠋⠄⠆⠀⠀⠀⠰⠅⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣷⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⢝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⡦⠉⠪⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢛⡏⣽⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⠿⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠁⠊⠻⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣭⠉⠉⢡⣤⡆⠀⠀⠀⠀⠀⠀⠀⡆⣸⡟⠀⢈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡿⢿⣟⡿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣇⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡎⢿⣿⡇⣬⠀⣴⣶⡶⠂⠀⠀⠈⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⣿⡛⠒⠲⢼⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣇⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢱⣿⣶⣶⡖⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡏⠉⢹⠃⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢀⠀⣸⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⢲⣤⣿⡯⠭⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⣿⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠾⣸⣿⣧⡆⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣬⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⣸⡏⢨⠁⠂⠀⡿⠿⠿⠿⢿⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣬⡑⠛⠀⠄⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣀⠀⣇⣀⠀⠀⠀⠀⠉⠙⠛⠉⣧⡀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⢠⣼⠷⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣦⣧⣀⡿⢿⢿⡟⠿⠿⠿⠿⠿⠷⠜⢿⣷⣶⣶⠀⠀⣸⠀⠀⠀⠙⠻⡿⢿⣄⡀⠀⠀⠀⠀⠀⡴⠦⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢸⣿⣿⡇⣿⣿⣏⢻⡬⣍⠛⠓⠶⣞⠂⠀⠀⢻⣟⢿⣿⣤⣾⣿⠀⠀⠀⠀⠀⣈⣀⣈⣁⣀⠀⠀⠈⢸⡇⠀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⢧⡇⡆⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣿⣿⣿⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡿⣦⡀⢸⠛⠛⢻⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢸⡟⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣿⣿⡌⠉⠫⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣸⠛⠁⠀⠀⣾⣹⣿⣿⣿⣿⡟⣿⠟⠻⣷⡸⠀⠀⢸⠀⠀⠀⠀⠀⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⡇⣾⣿⣿⣿⣿⣯⣼⣿⡇⣿⣿⣿⠿⠟⣷⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⣿⣷⣿⣿⠟⣋⣭⣷⣆⡙⢹⠿⠶⠶⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⠁⣿⣿⡇⠻⠻⠻⣿⣿⢗⡃⡈⡛⢶⢶⡇⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠻⠋⠙⠊⠀⠈⠛⠛⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⡿⠀⣿⣿⡇⣆⣄⣀⣾⡟⠘⠁⠀⡃⠹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠉⠉⠉⠉⠉⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣭⢤⢭⡭⠭⣭⣅⣭⠕⠁⠈⠀⠀⠀⢸⠇⢠⠄⠠⠁⠀⠀⠤⠀⢀⣀⣀⣴⢞⣁⣤⣀⡀⠀⣀⣠⣤⣀⠀⣿⣿⡇⣉⣉⡁⣰⣶⣆⢀⣀⠀⣀⣀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠀⣘⣂⣠⣄⡀⢀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠸⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⣀⣄⣀⣰⡶⠟⢻⣿⣿⣿⣿⣿⣶⣷⣤⡄⠉⠹⠹⢿⡟⣿⡿⢀⣾⣿⡇⠀⣿⣿⠋⣩⣽⢠⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡏⠀⠀⣀⡀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⢸⣯⣿⣿⣿⣿⡅⢰⠨⣿⠛⡏⣽⠟⠱⠉⢹⢄⡂⠘⠃⠍⣶⣟⡃⣿⣸⣿⡇⡇⠻⣿⣤⣿⠟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⡏⠹⣯⣥⣼⣿⣅⣤⣼⣧⡒⢀⠀⠀⠀⣴⣿⣿⣧⣀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣦⣵⣄⣼⢿⣿⣾⣿⣷⣿⣿⠘⡃⢸⣿⡷⢃⣿⡆⠀⣰⠁⠀⠀⠉⠀⠀⠀⠈⠁⠀⢀⣀⣠⣄⣀⣀⣠⣤⣤⣤⡀⠘⠟⠛⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⠇⢰⠌⠀⠛⠛⠋⢀⡀
⠀⡿⣍⡀⠃⠀⠀⢧⣺⣿⠻⣿⢿⣿⣯⣘⢿⡟⢻⣉⠿⠿⠟⢁⣾⡟⠁⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⡿⠛⠛⣿⡇
⢠⣷⡛⠂⣂⣤⢲⣷⣼⣧⣠⣼⢴⠄⠿⠋⠀⣽⠉⢋⣤⣴⣶⣿⣋⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠻⢿⢟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣧⡄
⠘⣟⣟⣿⣿⣿⣾⣿⣿⠋⢸⡄⣀⣀⡊⠀⠀⠀⠀⠞⢳⣆⣤⠼⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠿⠋⠒⠛⣾⣿⣻⡍⣍⢿⣿⣿⣿⢿⣿⣿⣿⣯⡟⣿⣯⣭⣤⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢻⣿⣙⣟⠝⣿⣿⠙⢠⠞⠑⠻⣌⢱⠄⢐⢬⠄⡤⡍⠈⢠⢤⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⢤⣼⣏⣨⣿⣟⢻⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠈⠙⢿⣾⣿⢿⣿⣿⣿⡇
⠀⠘⠙⢙⣧⣤⣿⣾⣷⣞⠢⠀⠚⠛⠒⣄⡀⣾⣟⠾⠃⠀⠀⠈⠘⠀⢀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠃⠀⠨⠈⣚⣡⡘⠻⢿⣥⣾⣿⣷⡿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣿⣿⣿⣴⣤⣿⣿⡇
⢀⡐⢐⣿⢻⣿⣻⡿⠛⠳⠿⠋⠲⣰⣤⣨⣤⢄⡚⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠑⣢⠀⢰⡾⢰⣠⠀⢶⣶⣾⣿⣿⠀⠀⢴⢮⣿⣿⣼⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣾⣿⡇
⠘⠰⠊⠁⠀⠾⢿⠅⠀⠀⠀⠀⠀⢊⠛⢄⢹⠎⢭⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢘⠁⠠⠁⠠⢔⠲⡾⢿⣿⡿⣯⣠⣠⣈⣽⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⢻⢻⣿⣿⣿⢿⡇
⠀⠀⣠⡄⢀⠄⠸⠂⠘⢀⠀⠀⠇⠀⠀⠀⢀⡀⠲⠉⠀⠤⠂⠀⠀⢠⡄⡀⢀⡠⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⢘⠀⠀⢉⣋⠀⠋⠞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⢿⣿⣿⣿⣏⣗⣾⠻⣻⠈⢡⡩⡟⢿⣿⡇
⠀⢠⠙⠉⢸⡜⠁⡟⠚⠎⢀⠀⣀⠀⣀⠀⣀⣀⣤⣵⣷⣶⣶⣾⣾⢸⣏⡀⠶⠊⠀⠀⠄⠀⠀⠀⠀⠤⠴⠠⣰⠆⠀⠘⠉⠀⠘⣂⠀⠀⠀⠠⣿⣯⣿⡾⠟⠉⠁⠘⡵⣿⣻⡿⢿⣿⣿⣶⣿⣾⣇⡠⠜⠋⠋⠹⢻⠇
⠀⠛⠓⣁⠀⣭⣨⣧⣄⣄⢀⡓⢶⠀⠈⠂⡹⢶⡽⠿⣿⣿⣿⣻⡗⣠⣬⣁⣼⣳⣦⡄⡆⢤⡤⣤⣀⣬⣤⣰⠢⡤⡘⢤⣄⠀⢀⡴⠆⠆⠁⣴⣿⣿⣟⠄⣤⠀⣦⣤⣶⣙⣿⣂⠓⠚⠁⢁⣹⣋⡽⠉⢪⢶⡾⠾⠙⠂
⠀⠄⠲⠀⠬⠤⠴⠤⠤⠤⠿⠽⠤⠶⠴⠏⠀⠰⠍⠰⠙⠟⠻⠿⠿⠿⠿⠿⠦⠼⠿⠷⠧⠼⠟⠹⠿⠿⠿⠿⠿⠾⠿⠾⠿⠶⠾⠒⠷⠾⠆⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠖⠀⠶⠷⠿⠿⠿⠄⠆⠀⠀⠀⠰⠭⠄
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠟⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣷⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⢝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⡦⠉⠪⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⣹⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⠟⠋⠀
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠑⠈⠻⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⣠⠀⠀⢀⣄⡆⠀⠀⠀⠀⠀⠀⠀⡄⢰⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄⡿⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣨⠇⣿⡏⣬⠁⣠⣶⣶⠂⠀⠀⠀⠂⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⣼⡿⠦⠤⠬⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣻⠀⠈⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⣿⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⡏⠃⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡟⠉⢛⡇⠀⠄⠀⠀⠀⠀⠀⢐⣿⣿⣿⢸⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⢲⡆⣿⣿⡙⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣥⣤⡄⠀⠀⠀⠀⠀⢠⠀⠀⠸⢱⣿⣇⡆⠀⠀⢸⣿⣿⣿⣷⠃⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣤⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠏⣇⢸⡏⢩⠁⠒⠀⣸⠿⢿⣿⣿⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣨⡑⠚⠀⡀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡄⠀⠀⢀⠂⡏⢁⡀⠐⠀⠀⠉⠛⠛⣛⡋⠀⠀⠀⠀⠘⣯⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⢻⣀⣿⢿⢿⡿⠿⠿⠿⠿⠿⣽⣿⣶⣶⣶⣶⠀⠹⠀⠀⠀⠀⣾⡛⢳⣾⠟⠀⠀⠀⠀⠀⠀⡤⠤⢤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⣻⢿⣿⠺⡌⢍⠒⠒⢶⣶⠂⠈⢻⣿⣿⣿⣿⠀⣴⡇⠀⠀⠀⠀⠙⠾⠻⢶⡄⠀⠀⠀⠀⢠⡇⠀⢸⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢧⣯⡂⠀⠀⠈⠁⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⠒⢺⠀⠀⠀⠀⠐⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢽⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣷⣯⠉⠏⠟⣋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⠿⠃⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣼⣯⢸⣿⣿⣿⣿⣿⣹⣿⡏⣿⣿⣿⠿⢿⣿⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⣿⠿⢿⡄⠾⠶⠶⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣹⠇⣿⣿⣿⠘⠿⠽⣿⣿⡇⠛⢘⠻⣶⢶⣿⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢰⣿⣾⣿⣿⡿⢏⣳⣧⡐⠜⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡿⠀⡟⣿⡞⠆⠀⠠⢸⡿⠇⠉⠈⠂⠹⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠇⠀⠀⠀⠀⠘⣿⠿⠛⣉⣀⡙⣛⣋⡛⠷⠏⠀⠀⠀⠀⠀⠠⠀⠀⠀⣹⠉⠉⠉⠉⠛⠓⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⣭⣥⣭⢍⣩⢭⣍⣍⣬⡽⠁⠈⠀⠡⠀⢸⡇⢠⡄⠠⠀⠀⠀⠠⠄⣀⣀⣀⣠⢀⣈⣤⣀⡀⠀⣀⣠⣄⣀⠀⣿⣿⡇⣉⣉⡁⣴⣶⣆⢀⣀⠀⣀⣀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⢸⠇⢘⣇⣀⣄⡀⢀⠀⠀⣸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡆⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⢀⣀⣀⣴⡦⠟⢻⣿⣿⣿⣿⣿⣶⣷⣤⡄⠈⠹⠛⣿⡟⢿⡿⣀⢻⣿⡇⠀⣿⣿⠋⣭⣽⢠⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡏⠀⣀⣀⣀⣄⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⡅⢠⢄⣿⠟⠿⢻⠟⠲⠉⢹⡁⠀⠐⠓⡟⣵⡟⣵⡇⣸⣿⡇⠀⠻⣿⣤⣿⠟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⡟⠻⢧⣯⣼⣿⣃⣠⣶⣦⡒⠀⠀⠀⠀⢰⣿⣿⣷⢀⡀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣨⣄⣴⣟⣿⣾⣷⣯⣿⣿⣺⣿⣠⣿⠏⣿⣷⠀⠀⡖⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⢠⣠⣤⣠⣀⣀⣤⣤⣤⣀⠸⠟⠛⠛⣠⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⡗⢠⡎⠁⠙⠟⠛⠀⠀
⠀⡿⡏⣉⠏⠀⠉⠻⣼⣿⠿⣿⣿⣿⣿⣙⣿⡿⢛⣫⢿⢚⠓⣸⡿⠃⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣾⣿⠟⠳⣿⡇
⢠⣷⠚⣀⡆⣀⣰⣴⣬⣯⣠⣽⡟⡇⠹⠟⠁⣿⠋⣩⣤⣤⣾⠟⠁⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣝⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄
⠘⡏⡇⣿⣿⣿⣾⣿⣿⡿⢩⡥⢀⣀⡐⠀⠀⠀⠈⠧⠈⡉⢡⠶⢾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠓⣾⣿⢿⡍⣝⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⢿⣿⠻⡿⢽⣿⣿⠛⢡⡜⠃⠿⣽⢁⡄⠀⢎⠤⣤⣙⠉⢁⠠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠛⠅⣬⣴⣟⣘⣿⣿⢛⣾⣿⢿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠙⢿⣟⣻⢿⣿⣿⣿⡇
⠈⠘⠛⣸⣯⣄⣿⣿⣧⣾⠦⡀⠻⠛⠐⣀⠀⣼⣟⢼⠃⠀⠀⠈⠘⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠇⠈⠀⠀⡀⠀⠀⠓⠁⢨⠉⢍⣫⡉⠹⠿⣤⣾⣿⣧⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⣿⣴⡥⣿⣿⡇
⢀⡠⢴⣿⢹⣿⣿⡿⠟⠷⠻⠞⠴⣤⣦⣨⣤⣔⡚⡃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠒⢄⠄⠰⣼⢤⢤⡄⡰⣶⣆⣿⣿⡇⠁⢤⢮⣿⣿⣸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣟⣳⣾⣽⠁
⠘⠐⠚⠛⠨⠿⣿⡃⠀⠀⠐⠀⠀⠊⡙⢋⢹⠮⢏⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠐⠁⠀⠁⣈⣂⠳⡶⢻⣗⡿⣿⢠⣠⣈⣿⣏⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⠿⣻⣿⣿⣿⣷⡇
⠀⠀⢠⡄⢀⠄⠘⠦⠰⢀⠠⠀⢇⠈⠀⠈⠉⠀⢠⠌⠁⠤⠄⠀⠀⢀⣄⠀⠀⡠⠄⠄⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠠⠐⠂⠉⢕⣃⠥⠻⠼⢿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣗⡗⣾⠻⣻⠀⢱⡭⡽⣿⣿⡆
⠀⢨⠙⠻⢸⡜⠋⣛⠚⠎⠀⠀⢀⠀⣀⡀⢀⣀⣠⣽⣶⣶⣶⣶⣶⢽⣯⡀⡲⠖⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⣐⠄⠂⠘⠛⠁⠰⢒⠀⠂⠀⠠⣿⣿⣿⡶⠟⠛⠁⠉⢻⣿⣻⡿⣿⣯⣿⣶⣾⣶⣿⠠⡜⢛⢟⠹⢿⠇
⠀⠟⠳⡁⠄⣩⣀⡧⣀⣂⠀⢓⢾⠂⠈⠆⢹⣶⠽⣿⣿⣿⣿⡿⣿⢠⣬⣁⣸⣷⣦⡤⡤⢤⡤⢄⣀⣨⣀⣠⠪⣠⠸⢤⣀⠀⢀⣤⠄⠶⠂⣴⣾⣿⣯⡇⣠⡀⣶⣤⣶⠛⣫⠅⠲⠿⠏⠩⣹⣛⣫⠉⠠⣷⡶⢾⠛⠂
⠀⠄⠂⠀⠬⠤⠼⠤⠤⠤⠾⠿⠲⠶⠴⠎⠀⠬⠝⠒⠝⠻⠛⠧⠷⠿⠿⠿⠧⠼⠿⠷⠦⠐⠗⠻⠿⠿⠿⠿⠿⠾⠛⠶⠿⠧⠾⠗⠲⠶⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠯⠀⠤⠶⠾⠿⠿⠁⠄⠀⠈⠁⠠⠾⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠟⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠛⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠝⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡦⠈⠪⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠒⠄⠁⠉⠪⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢰⣆⡈⠀⠀⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⢨⠽⣿⡿⣨⠃⣠⣶⣶⠆⠀⠀⠀⠂⠀⠀⠰⢦⠀⠀⠀⠀⠀⠀⠀⢸⡿⠦⠤⠤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣟⢸⠀⠀⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⡇⣿⣶⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠋⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢳⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⢸⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠐⢲⡎⣿⣿⣘⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⣧⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣿⡏⡄⠀⠀⢸⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣶⣤⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⡉⢡⢸⡏⢩⠁⠒⠀⢸⠿⣿⣿⣿⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠄⡌⢨⡙⠚⠀⡀⠀⣾⣿⣿⣿⣾⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡄⠀⠀⢠⠃⣮⢁⡀⠐⠀⠀⠋⠛⠛⠛⠛⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢻⣄⣿⢿⣷⡿⠿⠿⠿⠿⠿⣷⣶⣶⣶⣶⣾⢿⠀⠀⠀⠀⠀⢰⠛⠓⣶⡆⠀⠀⠀⠀⠀⠀⣤⠤⢬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣯⢸⣿⣿⠺⣯⣍⠒⠒⠶⣶⡒⢻⣿⣦⣴⣿⣿⠀⢃⠀⠀⠀⠀⠾⣄⣰⣿⠉⠀⠀⠀⠀⠀⠄⡟⠀⢸⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣿⣿⣧⠿⠐⠠⠀⠈⠁⠀⠹⢿⣿⣿⣿⣰⣿⠀⠀⠀⠀⠀⠀⠛⠙⠓⠂⠀⠀⠀⠀⢠⠟⠒⠚⡇⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣷⣯⣯⠉⠏⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢸⣿⣿⣿⣿⣿⣭⣿⡟⣿⣿⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠒⠶⠶⠶⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣹⡏⢸⣿⣿⠹⡿⠿⣿⣿⡇⠛⢘⠛⢲⣦⣿⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⡇⣼⣿⡿⠀⠀⠠⢸⡿⠇⠉⠈⠀⠘⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⢠⣿⣿⡿⣛⣛⡛⣙⣉⡀⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠉⠉⠉⠙⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⣭⣭⣬⡭⣩⣠⣍⣍⣭⡽⠁⠀⠀⠉⠀⢸⡇⢀⡄⠠⠀⠀⠀⠠⠄⢀⣀⣀⡀⢀⣉⣤⣀⡀⠀⣀⣨⣭⣙⠃⣿⣿⡇⣉⣉⡁⣴⣷⣆⢀⣀⠀⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠀⠀⠁⠀⠀⠈⠁⢀⠀⠀⣀⠀⠀⢸⡇⢘⣇⣀⣀⠀⠀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⢀⡀⢀⣀⣄⣴⣶⠿⠻⣿⣿⣿⣻⢻⣄⣦⣄⣀⠈⠈⠛⢿⡿⣿⡷⡰⢻⣿⡇⠀⣿⣿⠋⣩⣽⢀⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⡀⢀⣀⣤⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⡇⢠⡄⡿⠏⢯⣉⡾⠑⠉⠙⠅⠀⠀⠢⠵⣀⠟⣼⡇⢸⣿⡇⠀⠻⣿⣤⣿⠟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⡎⠉⢷⣦⣼⣿⣅⣠⣴⣦⡐⠀⠀⠀⠀⢰⣿⣿⣷⢀⡀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣨⣄⣠⣞⣶⣶⡶⣦⣴⣶⣤⢄⠀⡭⢸⣿⠇⠀⢠⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⢀⢀⣠⣤⣀⣄⣀⣤⣤⣄⣀⠸⠿⠛⠛⣠⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⣄⣾⠗⠠⣎⠁⠹⠟⠛⠁⠀
⠀⢾⡛⣃⠋⠀⠉⠁⢕⣿⡿⣿⣿⣿⣿⡁⢸⡿⢟⢀⠙⠈⢠⣿⡟⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣷⣾⠗⠲⣾⡇
⢈⣾⠲⢃⡄⢀⠀⣤⣤⣯⣀⣬⡿⡇⠹⠎⠀⢈⢇⣋⣁⣴⡿⠋⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⡄
⠸⡏⡗⣶⣿⣿⣾⣿⣿⠻⢁⣧⢀⣀⡀⠀⠀⠀⠋⠙⠛⢋⣠⣤⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠐⠘⢳⣿⣟⡟⣝⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢯⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇
⠀⢻⣿⠝⠿⠹⣿⣿⡝⠃⡸⠋⠾⢝⠑⡄⠀⠀⠄⠀⡐⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠅⠬⣥⣟⣈⣿⣿⠛⣴⣿⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠙⢿⣿⣿⡿⣿⣿⣿⡇
⠀⠸⠙⢁⢬⣀⣿⣷⣧⣴⢦⠄⠘⠛⠀⢀⠀⢸⡟⠸⠇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠍⢋⣀⠹⠿⣥⣴⣿⣧⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣿⣿⣥⣤⣾⣿⡇
⠀⠀⠀⣺⢸⣿⣟⣿⠿⠻⠶⠞⠠⢤⣦⣈⣤⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠄⠐⣼⠄⣄⡀⠠⣶⣔⣹⣯⡅⠀⢤⢮⣿⣿⣱⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣷⣮⣿⡄
⠘⠴⠈⠉⠀⢥⢿⡟⠀⠀⠐⠀⠀⠊⡙⢫⢹⢯⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⣀⣀⠢⣶⢼⣟⡿⣿⢡⣀⣈⣹⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣲⡇
⠀⠁⢀⡄⠀⠀⠘⡶⠐⠀⡀⠀⢀⠈⠀⠈⠉⠂⠠⠄⠀⣅⠄⠀⠀⠀⣤⠀⠀⣀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠠⠐⡆⠉⣅⡓⠡⠛⢴⠻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣷⢺⠿⢟⠀⢉⣭⣽⢿⣾⡇
⠀⠨⠘⠛⢙⡭⠋⣙⠒⠎⠁⠀⢀⠀⣀⡀⢀⣀⣀⣩⣶⣶⣴⣶⣶⣟⣏⡁⡰⠖⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⣀⡄⠀⠀⠛⠁⠐⢖⠄⠂⠀⠠⣽⣿⣽⣷⠿⠋⠉⠘⢫⢿⣟⣿⢿⣯⣿⣷⣿⣷⣿⠀⡌⢛⠟⠹⢿⠇
⠀⠒⠳⣃⠀⣩⣈⡯⣀⣂⠀⠙⣾⠄⠀⠃⢘⣿⠽⣿⣿⣿⣿⡟⡿⢀⣜⣁⣸⣷⣦⡤⡤⢤⣤⢤⣀⣈⣄⣀⢮⣠⠼⣀⣀⠀⢀⣤⠅⢴⠂⢠⣾⣿⣯⡧⢠⡄⣴⣤⣴⡚⢻⠍⠔⠾⠏⠩⣘⣟⣻⠋⠀⣧⣶⢾⠗⠂
⠀⠄⠂⢀⠤⠤⠼⠤⠤⠤⠾⠷⠲⠶⠴⠖⠁⠨⠭⠒⠌⠻⠿⠯⠿⠯⠿⠿⠿⠼⠿⠷⠦⠐⠏⠛⠿⠿⠿⠿⠿⠿⠻⠶⠿⠧⠾⠷⠲⠶⠆⠿⠏⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠯⠄⠠⠶⠾⠿⠿⠁⠠⠀⠀⠁⠀⠾⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⠄⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠍⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣶⡌⠪⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠈⠪⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣆⡍⠀⠀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⢿⣻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣼⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⢰⠽⣿⡿⢨⡃⣠⣶⣶⠖⠀⠀⠀⠂⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⢸⣿⠧⠤⠤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠽⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⡇⣿⣴⣶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢘⠃⠈⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠋⠋⡇⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⢷⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⡀⢠⡏⠀⠠⠇⠀⠀⠀⠀⠀⠀⠐⠒⣧⣿⣿⣘⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣧⢤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⣿⣏⡤⠀⠀⢸⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣦⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠈⢩⢰⡟⢉⡉⠐⠀⢸⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠆⣼⢨⣙⠚⠁⣀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡆⠀⠀⢀⡂⢸⢁⡀⠐⠀⠀⠉⠛⠛⠛⠛⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣶⣻⣄⣿⢻⡷⡿⠿⠿⠿⠿⠿⠷⣶⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⢰⠛⠓⣶⠀⢀⡀⠀⠀⠀⠀⣤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣷⢸⣿⣿⠺⣧⠉⠒⠒⠶⣶⡖⣠⣀⠀⢦⣿⣿⣷⠀⠀⠀⠀⠀⣸⣀⣀⣿⡏⠀⠀⠀⠀⠀⠤⡿⠀⢠⡇⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⢳⣾⣿⣿⣿⣿⣿⣿⣷⠄⠐⠠⠄⠀⠉⠿⣿⣷⣾⣿⣿⢈⡆⠀⠀⠀⠉⠛⢭⣽⣿⡀⠀⠀⠀⠀⠀⠀⡟⠒⠚⡇⠀⠀⠀⡄⢾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢸⣿⢣⣿⣿⣿⢻⣿⣿⣿⣿⢸⣿⣿⣿⡯⣯⠉⠻⡘⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠉⠉⠛⠂⢀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣾⣿⢸⣿⣿⣿⣿⣿⣭⣿⡟⣾⣯⣿⡿⠯⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡿⢸⣿⣿⠸⡿⠿⢿⣿⡇⡟⢘⠛⢒⣦⣿⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡇⢸⣻⡟⢸⠄⠀⠼⣿⠇⠉⠀⠀⠘⢌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⣤⣶⣞⣻⡻⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣩⡏⠉⠉⠙⠛⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢈⣭⣭⣬⡭⣭⣤⣩⣍⣉⡭⠀⠀⠀⠩⠄⢨⡏⠀⡤⠀⠌⠄⠀⠠⠄⢀⣀⣀⡀⢒⣋⣤⣀⡀⠀⣀⣠⣬⣙⠏⣿⣿⡇⣉⣉⡁⣶⣶⣆⢀⣀⠀⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⣀⢀⠀⣸⡇⠘⣇⣀⣤⡀⠀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⠀⣀⣤⣰⣴⡼⢾⣿⣿⣿⣿⣿⣦⣶⣤⣀⠈⠉⠋⢿⣿⣿⡇⡤⣾⣿⡇⠄⣿⣿⠋⣭⣽⢠⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⢀⢀⣠⣤⢠⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⢀⡤⡻⡿⣿⣻⡿⠻⠍⠹⡿⠀⠠⠛⣞⢿⢟⣾⠃⢸⣿⡇⠀⠻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⡞⠈⢷⣾⣦⣿⣧⣀⣤⣶⡴⠂⠀⠀⠀⢠⣾⣿⣷⢀⡀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣧⣌⣄⣠⣿⣿⣶⣶⣶⣿⣿⡶⢾⡆⠎⣿⣿⠀⠀⡆⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⣀⣀⣀⣀⡀⠀⣀⣤⣠⣀⣀⠘⠿⠛⠛⣠⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣽⣿⠠⡎⠉⠙⠿⠛⠑⠀
⠀⢾⡛⣁⠏⠀⠉⠛⣹⣿⡿⣿⣿⣿⣿⣁⢹⣿⠟⠁⠹⠈⣴⣿⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣦⣷⣾⡷⠲⢿⡇
⢈⣾⡷⢃⣄⢠⣤⣤⣤⣿⣄⣤⡧⡇⠘⠏⠡⠠⠇⠙⣀⣼⠟⠁⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣹⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄
⠸⡏⡷⣾⣿⣿⣾⣿⣿⠻⢩⣠⢀⣀⡀⠀⠀⠛⠛⠿⠛⢁⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠐⠂⢲⣿⣿⡟⢹⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇
⢀⢿⣿⡟⠿⠻⣿⣿⡝⠃⡸⠃⠸⢁⡙⡄⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠭⠠⡱⢛⣀⣿⣿⠛⣵⣿⡻⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠙⢻⣷⣻⣿⣿⣿⣿⡇
⠀⠘⠻⢉⣯⣄⣿⣿⣷⣴⢦⡄⠈⠛⠋⢂⠀⢠⡟⠠⠂⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠋⣍⠉⠿⣅⣤⣿⣧⡼⠉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣿⣾⣥⣤⣾⣿⡇
⠀⠠⢄⣾⢹⣿⡟⣿⠿⠻⠼⠞⠠⣦⣦⣘⣄⡀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢠⠄⡄⡀⠠⣴⣆⣸⣯⡍⠀⢠⣬⣿⣿⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣾⣿⡄
⠘⠴⠘⠛⠠⣷⣿⡇⠀⠀⠀⠀⠀⠊⡙⢫⡹⠧⠛⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⢀⣀⠀⢶⢌⣗⡿⣿⢠⣀⣀⣛⣏⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⢷⡇
⠀⠀⢀⡄⠀⠠⠈⡦⠀⢀⡀⠀⢐⠈⠀⠈⠉⡂⠠⠤⠀⠄⠀⠀⠀⠀⣀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⡆⠀⢀⣛⠠⠹⢸⢻⣾⣿⣽⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣯⣼⣿⣗⡁⢏⣏⣽⢿⣿⡇
⠀⠨⠘⠛⠙⡅⠋⠛⠒⠆⠁⡀⢀⠀⢀⣀⠀⣁⣀⣭⣶⣴⣶⣶⣶⡎⣏⡁⢰⠖⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⣄⡆⠀⠀⠛⠅⠐⢆⡠⠒⠂⠀⣼⣿⣿⣷⡿⠉⠋⠘⢻⢿⣿⣿⣿⣯⢿⣷⣿⣷⣿⡁⠄⢛⠟⠙⠿⡇
⠀⠒⠳⣁⠀⣩⣂⣯⣄⣂⠀⠙⢾⠄⠀⠃⢘⡷⠭⣿⣿⣿⣿⡟⣿⠢⣜⣁⣸⣷⣶⣤⣤⢤⣤⢤⡀⣈⣄⣀⡮⣠⠼⢠⣀⠀⠀⣥⡅⢤⠛⣠⣾⣿⣿⡧⢠⡀⣴⣤⣤⡚⢻⡅⠸⠿⠟⠩⣙⣟⣻⠋⠀⣷⣷⢶⡷⠇
⠀⠄⠂⢀⠬⠄⠼⠤⠤⠤⠼⠷⠲⠷⠦⠖⠁⠠⠭⠒⠎⠻⠟⠿⠿⠾⠿⠿⠿⠽⠿⠷⠮⠀⠋⠚⠻⠿⠿⠿⠿⠿⠻⠴⠿⠧⠾⠷⠲⠶⠇⠾⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠭⠄⠠⠶⠾⠿⠟⠍⠠⠀⠀⠁⠀⠶⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡆⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠻⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠨⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢳⠌⠲⢝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⠊⠙⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣆⡈⠁⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠠⢀⢻⡆⠁⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠛⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⢰⠹⣿⣿⢨⡃⢠⣶⣶⠖⠀⠐⠀⠒⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠦⠤⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠽⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣾⣴⣶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠑⠈⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠋⠉⡇⠀⠨⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⡀⢀⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⣧⢻⣿⠌⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢸⣧⢤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⣿⣿⣤⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢹⢠⣟⢁⡍⠐⠀⢸⠿⠽⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠐⠀⠄⣼⢠⣉⠚⠃⣀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⠀⠀⢀⡀⢸⢁⡀⠐⠀⠀⠉⠙⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣶⣺⣄⣿⠿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣶⣶⡆⠀⠀⠀⠀⠀⢰⡟⠛⣷⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⢸⣿⣿⡛⡇⠍⠐⠒⠲⣶⡖⠀⠀⠀⢻⣿⣿⡧⠀⠀⠀⠀⠀⢸⣀⣀⡿⣀⠀⠄⠀⠀⠀⠤⣿⠀⢠⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⡿⡌⢰⠠⠄⠀⠉⣠⡄⠀⢸⣿⣿⣇⠀⠀⠀⠀⣀⡇⠀⠉⣹⠇⠀⠀⠀⠀⠀⠀⡟⠛⠚⡇⠀⠀⠀⡄⢾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢸⣿⢫⣿⣿⣿⣻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⠉⠻⡙⢛⠄⠀⠀⠀⠀⠻⢿⣷⣦⡉⠙⣼⡇⠀⠀⠀⠀⠙⠢⣾⣧⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣼⣿⢸⣿⣿⣿⣿⣿⣭⣿⡟⣸⢗⣿⡿⠷⢿⡆⠘⠄⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠐⠶⠶⠶⠶⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢸⣿⣿⠸⡿⠿⢿⣿⡗⡟⢘⡙⢓⡶⣾⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢿⡇⢸⢿⠟⢘⠀⠂⠸⣿⠇⠉⠀⠠⠘⢍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢩⡏⠉⠉⠉⠙⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣭⣬⡭⣩⣭⣭⣉⣬⡭⠉⠀⠀⠈⠅⠀⡿⠀⡤⠀⠈⠀⠀⠠⠀⣀⣀⣀⡀⢀⣋⣤⣀⡀⠀⣀⣠⣤⣀⠀⣿⣿⡇⣉⣉⡁⣰⣶⣆⢀⣀⠀⣀⣀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠉⠁⠀⠁⠀⠀⠀⠁⠀⠀⠀⣀⣀⢀⠸⡇⠐⣇⣀⣤⢀⠀⡀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⣠⣄⣰⣶⡾⢿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡈⠉⠟⢿⣿⣿⡅⣀⣼⣿⡇⠀⣿⣿⠋⣭⣿⢠⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡇⠀⣿⣇⣿⡟⠀⢀⢠⣠⢠⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⢠⣤⣿⡿⣿⣿⣿⠿⡟⠛⣿⠉⠀⠫⠝⡯⢏⣿⠋⢽⣿⡇⠀⠻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢠⣿⡉⠷⣾⣦⣿⣯⣤⣤⣶⣴⠂⠀⠀⠀⢠⣾⣿⣷⢀⡀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣯⣬⣤⣈⣿⣿⣷⣶⣷⣿⣿⡶⠊⠪⢱⣿⡇⠀⣴⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠸⠿⠟⠛⣠⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⠂⣮⠉⠘⠛⠛⠁⡀
⠀⢺⡟⣉⠟⠀⠉⠙⢹⣿⡿⣿⣿⣿⣿⣅⡹⣿⡟⣃⡐⢀⣾⡿⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡠⣾⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⡿⠻⣿⡇
⢨⣼⡞⠃⡆⣠⣠⣴⣦⣿⣤⣤⡦⡇⠘⢟⠁⠺⠃⠑⣠⡾⠟⠁⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡹⣿⣿⣶⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡄
⢸⣿⣿⣾⣿⣿⣾⣿⣿⡻⢩⣷⢀⡁⡀⠀⠖⠷⠶⠿⠋⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠀⢲⣿⣿⡋⢩⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⣭⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢹⣿⣟⡿⠻⣿⣿⡟⠃⡸⠋⠸⣭⡑⡄⠀⠀⢀⠐⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠠⠨⣟⣀⣿⣿⠛⣵⣿⡻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠉⠉⠻⣷⣿⡿⣿⣿⣿⡇
⠀⠈⠙⢛⣼⣄⣿⣿⣷⣴⠧⡄⠈⠟⠋⢂⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠋⣅⠁⠿⣃⣴⣷⣿⡞⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣾⣧⣭⣼⣿⡇
⢀⠀⠀⣼⣿⣿⣟⣿⠿⠿⠶⠞⠳⢦⣦⣀⣤⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠆⠀⠀⣶⣦⣸⣯⡍⠈⢠⣤⣝⣿⣧⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣾⣿⡇
⠘⠞⠚⠛⢀⣿⣿⡟⠁⠀⠐⠀⠀⠚⡙⠫⡹⡧⢝⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⣿⣺⢿⣤⣀⣀⣙⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⡿⣿⣿⣿⢿⡇
⠀⠁⢀⣤⠀⠠⠉⡷⠀⣆⡀⠄⢰⠈⠁⠀⠉⡀⠠⠤⠈⠬⠔⠀⠀⠀⣠⠀⢀⣀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⠀⠀⠂⡂⠀⠈⣚⠠⠸⣹⡻⣾⣿⣯⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣻⣾⣿⣟⣃⢟⣿⣽⣿⣿⡇
⠀⠀⡜⠛⠏⣇⠋⢸⠒⠇⠁⡀⢀⡀⣀⣀⠀⣀⣀⣩⣷⣶⣶⣾⣷⣎⣏⡁⣰⠖⠀⠀⠠⠀⠀⠀⠀⢀⠤⠤⢄⡢⠀⠀⡛⠁⠀⢆⡰⠂⠀⢀⣼⣿⣿⣷⠿⠋⠙⠘⢻⢿⣿⣿⣿⣿⢿⣿⣾⣷⣿⣇⠤⢻⣿⠙⡿⡇
⠀⠒⠓⣍⠠⣉⣆⣽⣄⣂⡀⡘⣺⡄⠀⠛⢘⡷⠿⡿⣿⣿⣿⣿⣿⢱⣝⣅⣺⣿⣶⣤⣤⢤⣤⣤⣄⣈⣅⣀⡾⣠⡜⢧⣄⠀⠀⣤⡤⢦⡚⢰⣾⣿⣿⣭⢠⡄⢴⣤⣤⡚⣻⡝⠑⠿⠏⠉⣘⣟⣛⣿⠡⣿⣿⢾⡟⠇
⠀⠤⠂⢀⠤⠄⠼⠤⠤⠤⠼⠿⡲⠷⠦⠖⠁⠠⠽⠒⠞⠻⠿⠿⠿⠿⠿⠿⠿⠴⠿⠷⠾⠀⠿⠚⠿⠿⠿⠿⠿⠷⠛⠷⠿⠧⠾⠷⠺⠶⠿⠺⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠅⠠⠶⠾⠿⠿⠏⠡⠀⠉⠁⠀⠾⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡆⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠈⠉⠙⠛⠻⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠪⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢷⡌⠑⢝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⢩⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⡿⠟⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⠙⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣏⡍⠉⠉⣅⣴⠀⠀⠀⠀⠀⠀⠀⢐⢠⢿⡇⠀⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⢹⣿⣿⢽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢨⣼⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⠹⣿⣿⢠⡅⢠⣶⣶⠖⠀⠀⠀⠈⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⢸⣟⠓⠒⠒⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠙⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣾⣵⣶⣶⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠋⠉⡟⠀⠨⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣤⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⢀⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⣦⢻⣿⠭⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢸⣷⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠠⢏⣾⣿⣴⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢹⢀⡿⠁⡌⠑⠀⢸⢿⠽⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠐⠀⠀⢸⢠⣉⠚⠃⠠⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⢀⡀⢸⢠⡄⠐⠀⠀⠈⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⡾⣄⣸⡟⡿⣿⠛⠿⠿⠿⠿⠿⠿⠿⠿⣶⣶⡆⠀⠀⠀⠀⠀⢸⡏⠛⣿⠀⠀⠀⠀⠀⠀⠀⣴⠶⠦⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⢸⣿⣿⡟⣇⢍⠉⠚⠲⢶⣒⠀⠺⠟⣶⣿⣿⡇⠀⠀⠀⠀⠀⢸⣁⣀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⡿⡬⠰⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠠⠀⠀⠀⠀⡆⠀⠀⢹⡠⠠⠄⠀⠀⠀⠀⡏⠙⠛⡇⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢡⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣭⠈⠙⡘⢋⠄⠀⠀⠀⠀⣤⣄⠀⠀⠈⠙⣇⠀⠀⠀⠠⢄⣇⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢸⡏⢨⣿⣿⣿⣿⣿⣁⣿⣿⢸⣇⣿⡿⠡⢹⡆⠃⡆⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⡀⣠⣿⡄⠀⠀⠀⠀⠈⠳⠿⢧⡄⠀⠀⠀⠀⠀⠒⠻⠷⠶⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢸⣿⣯⠙⡿⡟⢿⣿⡇⣟⠚⣙⠑⡶⣾⠃⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢿⠋⢸⢿⠟⠰⠀⢢⠄⡟⠇⡏⠀⠀⠈⠧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣭⡬⡭⣩⠭⢭⣩⣩⡭⠋⠀⠁⠀⠄⠀⣿⠀⡤⠀⠌⠀⠀⠀⠀⣀⣀⣀⡀⢀⣃⣤⣀⡀⠀⣀⣠⣄⣀⠀⣿⣿⡇⣉⣉⡁⣰⣶⣆⢀⣀⠀⣀⣀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠁⠀⡀⠀⠀⠀⠀⡀⣀⢀⣀⡀⠀⢠⡇⠈⣃⣀⣠⡀⡀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⠀⣠⣤⣤⣶⣾⠾⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠈⠉⠿⣿⣿⡇⠀⢸⣿⡇⠀⣿⣿⠋⣭⣿⢀⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⢀⣠⡄⠠⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⡆⣦⣿⡿⢿⣿⣿⠟⠏⠉⠾⠂⠀⠺⠝⣿⢭⣴⠾⣿⣿⡇⠀⠻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢠⣷⣀⢿⣾⣦⣾⣧⣤⣤⣾⣴⡇⡀⠀⠀⠀⣿⣿⣿⣆⡀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣬⣤⣠⣿⣿⣷⣶⣶⣿⣿⡗⠖⠰⣠⣾⠉⢰⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⣄⢂⣠⣤⣶⢢⣤⡶⠇⣤⣀⠸⠿⠛⠛⣠⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠀⠶⠁⠘⠛⠛⠂⡀
⠀⢸⠏⣁⠝⠀⠀⠙⢡⣿⡿⢿⣿⣿⢿⣅⡹⣿⣋⡓⠀⢢⣿⡗⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠝⠋⠟⡋⠛⠀⢸⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠛⣿⡇
⢨⣼⡞⠳⣀⣠⡄⣴⣶⣼⣤⣤⡧⠇⠘⠟⠉⠨⠏⠘⣰⣿⠏⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡆
⢸⢿⣸⣻⣿⣿⣾⣿⣿⡟⢉⣥⠄⡀⡀⠴⢶⣤⡶⠟⠋⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣋⢩⡥⣿⣿⣿⡿⣿⣿⣿⣿⣿⢻⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⣸⣿⣿⢻⠓⢿⣿⡏⠃⡬⠛⠨⢁⡁⠀⢀⠀⠘⠛⠻⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢈⣁⣿⣿⠋⣱⣿⡯⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠃⠉⠹⠿⣿⡿⣿⣿⣿⡇
⠀⠈⠙⢋⣽⣥⣼⣿⣿⣶⡗⡄⠀⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠉⢄⠀⠺⢧⣴⣿⡿⣾⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣦⣼⣿⡇
⢀⠀⠀⣾⣿⣿⣟⣿⠟⠻⠿⠞⠡⠦⣤⣀⣠⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢈⣭⣄⠀⠐⡦⣜⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣿⡇
⠘⣖⠒⠋⠀⡿⣿⡟⠀⠀⠀⠀⠀⠒⡉⠛⡝⡧⠝⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⢴⣺⢩⣴⣤⣄⣉⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣻⡅
⠀⠀⢀⣤⠀⡀⠀⠳⠂⠀⡀⠄⠰⠈⠁⠀⠘⡀⠀⠦⠈⠠⠔⠀⠀⠀⣤⠀⠀⣀⠤⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠂⡓⠀⠨⣘⠀⠈⠽⠚⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⢺⢿⢟⡇⡛⣿⢭⣿⣿⡇
⠀⠀⠈⠛⠃⣧⠋⢹⠓⠓⠁⡀⢀⡀⣀⣀⢀⣀⣀⣬⣽⣶⣶⣾⣷⡎⡯⣁⢰⠖⠃⠀⠠⠀⠀⠀⠀⠠⡤⠤⢄⡢⠀⠀⡋⠁⠀⠇⡤⠀⠀⠀⢼⣿⣽⣷⡿⠯⠉⠈⢫⡿⣟⣻⣿⣿⣿⣿⣾⣿⣿⣇⡤⢚⣿⡃⡿⠇
⠀⠘⠛⢏⠀⣉⣗⣽⣤⣀⡀⣘⠲⠆⠀⠙⢈⠷⡾⠿⣿⣿⣿⣿⢿⠇⣦⣭⣨⣾⣶⣦⢤⠤⣤⢀⣄⢠⣥⣤⡬⣀⡎⡣⣄⡀⠀⣹⡿⠲⠟⢢⣾⣿⣿⣱⢠⣄⣰⣶⣴⣞⣛⡝⡚⠚⠋⠉⣜⣿⣹⡿⠁⣽⣿⢷⠿⠃
⠀⠤⠐⠠⠤⠄⠼⠤⠤⠤⠼⠿⠷⠳⠶⠞⠁⠐⠼⠒⠸⠻⠿⠿⠽⠾⠿⠿⠿⠤⠿⠿⠾⠄⠾⠹⠿⠿⠿⠿⠿⠷⠟⠥⠽⠷⠴⠷⠚⠖⠿⠼⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠖⠠⠶⠿⠿⠿⠏⠠⠀⠀⠃⠀⠾⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡆⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠪⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢷⠌⠑⢝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⠩⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⣿⣿⠿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⠀⠙⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣯⡍⠉⠉⣩⣴⠀⠀⠀⠀⠀⠀⠀⢠⢠⢻⡇⠀⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠻⠹⣿⣻⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢈⣼⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⠺⣿⣿⢠⡅⢠⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⢸⣟⠓⠒⠒⣚⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡀⠀⠙⠿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣾⢵⣶⣶⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠉⠉⡝⠀⠨⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡟⠛⠋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⢀⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⣦⢿⣿⠭⠅⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⢸⣷⢦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⣾⣿⣴⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢀⡿⠁⡌⠁⠀⢸⣿⠽⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣷⣿⣷⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⢸⢠⣍⠛⠃⠠⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣹⣿⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⢀⡄⢸⣀⣄⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⡾⣅⣸⡟⡿⣟⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣶⡆⠀⠀⠀⠀⠀⢸⡏⠙⣻⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⢸⣿⣿⡟⢇⣭⠈⠚⠳⢶⣓⠀⢀⠀⢲⣿⣿⡇⠀⠀⠀⠀⠀⢸⣅⣀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣹⣿⣿⣿⢿⣿⣿⡿⡬⢠⠀⠀⠀⠀⠀⠹⠻⣦⣿⣿⠇⢀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⡇⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣇⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣧⠈⠙⡙⠃⠆⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⡀⠀⠀⠀⠀⢀⣇⣀⣀⣈⡄⠤⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢸⡟⣸⣿⣿⣿⣿⣿⣄⣿⣿⢸⣇⣿⡿⠥⢸⡆⠀⠂⠀⠀⠀⠀⠀⢀⣦⣄⠀⠀⠀⠻⡄⠀⠀⠀⠀⢌⡉⠉⣉⡟⠂⠀⠀⠀⠀⠈⠒⠛⠻⠷⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣾⣷⢸⣿⣏⠜⡟⡟⢿⣿⡟⣞⠚⣙⠁⡶⣾⠃⢤⡀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣀⣼⣿⠀⠀⠀⠀⠀⠈⠚⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢣⢸⢿⠟⢰⠀⠤⠤⢿⠃⡏⠀⠁⠀⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣭⡤⡬⣭⠭⢭⣩⣭⡭⠉⠀⠀⠀⠄⠀⣿⠀⡤⠀⠌⠀⠀⠀⠀⢀⣀⣀⡀⢀⣃⣤⣀⡀⠀⣀⣠⣄⣀⠀⣿⣿⡇⣉⣉⡁⣸⣶⣆⢀⣀⠀⣀⣀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⡇⢠⣃⣀⣠⡀⢀⢀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡆⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣄⢀⣠⣴⣤⣶⡾⠾⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠉⠋⠹⣿⣿⡏⠀⢸⣿⡇⠀⣿⣿⠋⣿⣿⢀⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⣀⣀⣀⠠⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⡄⣦⣽⡿⢿⣿⣿⠟⡏⠉⠿⠁⠀⣄⡸⣯⠟⣃⣀⣼⣿⡇⠀⠻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⣨⠻⣾⣶⣾⣧⣤⣤⣾⣷⠦⢀⡀⠀⠀⣿⣿⣿⣆⣀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣠⣿⣿⣷⣷⣷⣽⣿⡷⠯⡧⢨⡾⠯⡟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⣠⣶⣶⣷⣄⣶⣥⣴⡄⢀⣠⣀⠸⠿⠟⠛⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⡷⠅⠈⠛⠛⢀⡀
⠀⢺⢟⣉⠝⠀⠀⠙⣫⣿⡿⣿⣿⣿⣿⣅⣹⣿⢏⡉⠐⣰⣿⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣿⡿⢟⣲⣿⣿⣿⣿⣾⢸⣿⣿⣻⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠟⠛⣿⡇
⢨⣼⡞⠳⢂⢰⣤⣤⣶⣽⣤⣤⡷⡧⠘⠟⠙⡬⠏⠈⣰⡿⠏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠋⡿⢿⡟⠁⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⢸⢿⢸⣶⣿⣿⣾⣿⣿⡟⢉⣄⠀⣀⣠⣤⣀⣁⣴⠾⢋⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⢻⣿⣯⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⣸⣾⣟⢻⠓⢿⣿⡟⠃⡼⠃⠈⢁⡀⠈⠉⠉⠙⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⠋⣱⣿⡏⠿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠈⠙⠿⣿⡿⢿⣿⣿⡇
⠈⠈⠙⢙⣹⣥⣼⣿⣿⣶⡷⡤⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠺⠧⣴⣾⣿⣦⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣷⣤⣼⣿⡇
⢀⠀⠄⣾⡿⣿⣟⣿⠿⠻⠿⠞⠱⠦⣤⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣁⣄⠀⠀⡶⣞⣿⣧⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⡇
⠈⡟⠒⠛⠀⡾⣿⡿⠀⠀⠀⠀⠁⠐⣉⠛⡍⡧⠭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢴⣲⢡⣴⣤⣄⣨⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣻⡇
⠀⠀⢀⣤⠀⡀⠀⠳⠂⡆⡀⠄⠰⠈⠁⠀⠈⠁⠀⠦⠈⠠⠔⠀⠀⠀⣤⠀⠀⣀⠤⠠⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠂⡓⠀⠨⣘⡀⠀⢭⠟⢿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣲⣿⢞⣏⠜⣿⣽⣟⣿⡇
⠀⠀⠈⠛⠋⣣⠋⢙⠓⠳⢁⡄⢐⡀⣀⣀⣀⣀⣀⣬⣵⣶⣶⣾⣷⣏⣿⣁⢰⠖⠁⠀⠠⠀⠀⠀⠀⢠⡤⠤⢄⡲⠀⠀⡛⠁⠀⣗⣆⠀⠀⠀⣼⣿⣯⣷⡻⠏⠉⠁⢻⡟⣟⣻⣿⣿⣿⣿⣾⣿⣿⣇⡤⢚⣿⡇⡿⠇
⠀⠘⠛⢎⠀⣈⣗⣽⣤⣀⡀⢘⡲⠇⠀⠙⢀⠷⡾⠿⢿⣿⣿⣻⢿⠻⣶⣭⣪⣾⣶⣶⢤⠤⣤⣄⣄⢠⣥⣤⡬⣄⣎⣣⣤⡀⠀⣹⡿⠲⠟⢠⣾⣿⣿⣯⢤⣄⣰⣶⣶⣖⣛⡟⡚⠛⠛⠉⣌⣿⣻⣿⠁⣽⣿⠷⠿⠁
⠀⠤⠐⠠⠤⠥⠼⠤⠤⠤⠼⠿⠷⠲⠶⠖⠁⠐⠼⠒⠾⠻⠿⠿⠽⠾⠿⠿⠿⠧⠿⠿⠾⠄⠿⠹⠿⠿⠿⠿⠿⠷⠿⠥⠽⠿⠾⠿⠚⠒⠿⠼⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠖⠠⠾⠿⠿⠿⠯⠠⠀⠄⠏⠀⠾⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡆⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠪⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢗⠌⠑⢝⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⠉⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⠿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠐⠝⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣯⡍⠉⠉⣉⣴⠀⠀⠀⠀⠀⠀⠀⢀⢠⢿⡇⠀⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠻⠹⣿⣻⣻⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⠺⣿⣿⢠⡅⠠⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⢸⣟⠓⠒⠒⣚⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡀⠀⠙⠿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣾⢷⣶⣶⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠉⠉⡝⠀⠨⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡟⠛⠋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⣿⠭⠁⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⢸⣷⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⣾⣿⣴⠀⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢀⡿⠁⡌⠉⠀⢸⣿⠭⠽⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣷⣿⣷⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⢸⢠⡈⠓⠃⠠⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢻⣿⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⢀⡄⢸⣀⣄⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣾⣅⣸⡟⡿⣿⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣶⡆⠀⠀⠀⠀⠀⢸⡏⠝⣻⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⢸⣿⣿⡛⢇⢭⠈⠚⠳⠶⣛⠀⠀⠀⢲⣿⣿⡇⠀⠀⠀⠀⠀⢸⣥⣀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⢿⣿⣿⡿⡼⢠⠁⠀⠀⠀⠀⣀⡀⠘⣿⣿⠇⠀⠀⠀⠀⠀⡈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⡇⠀⠀⠀⠈⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣯⣥⠈⠙⠘⠓⠖⠀⠀⠀⠀⠀⠑⢹⣦⡈⠙⠀⠈⠀⠀⠀⢀⣇⣀⣀⡘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢸⣿⣰⣿⣿⣿⣿⣿⣍⣿⣿⢸⣏⣿⡿⠧⢹⡆⠀⠅⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣖⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⠀⠄⠀⠀⠀⠈⠒⠛⠿⠷⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣾⣷⢸⣿⣯⠌⡿⡟⢿⣿⡟⣚⢛⣙⠳⡶⣾⠃⢤⡀⠀⠀⠀⠀⠀⣰⣦⣄⠀⠀⠈⢻⡀⠀⠀⠀⠠⢄⡀⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢳⢸⣿⡟⠶⠀⠤⠎⠿⠓⡏⠀⠙⠈⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⣦⣤⣿⡇⠀⠀⠀⠀⠀⠑⠚⣟⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣭⡦⡤⣭⡭⢭⢭⣩⡭⠉⠀⠀⠀⠀⠀⣿⠀⡄⠀⠌⠀⠀⠀⠀⢀⣀⣀⡉⢛⣛⣭⣀⡀⠀⣀⣠⣄⣀⠀⣿⣿⡇⣉⣉⡁⣸⣶⣆⢀⣀⠀⣀⣀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⡀⠀⠀⡇⢀⣃⣀⣤⣀⣀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡆⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣀⢀⢠⣤⣴⣶⡾⠛⣿⣿⣿⣿⣿⣷⣶⣤⣤⡀⠉⠉⠹⣿⠿⣿⠀⢸⣿⡇⡀⣿⣿⠛⣯⣿⢀⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⡀⣀⡀⠀⠀⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⡆⣤⣼⠿⢿⣯⣿⠏⡏⠉⡩⠇⠀⠄⠐⡹⢸⠀⠀⣸⣿⡇⠀⠻⣿⣤⣿⠟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣶⣨⠹⣾⣶⣾⣯⣤⣤⣾⣧⠆⠀⡀⠀⠀⣿⣿⣿⣆⣀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣧⣠⣿⣿⣷⣶⣿⣿⣿⡷⠪⣢⢈⣤⣴⠖⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣄⣀⠸⠿⠟⠛⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⡿⠀⡖⠡⠈⠛⠛⠀⡀
⠀⢸⠟⣁⠝⠀⠀⠙⢈⣿⡿⣿⣿⣿⣿⣅⡹⣿⣿⣁⠀⣡⣾⢋⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣯⣿⣿⣿⣿⣿⣶⣜⢿⣿⣿⣿⣻⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠿⠛⣿⡇
⢠⣽⡞⠣⢲⢀⣨⣴⣶⣾⣤⣧⡷⢇⠘⠛⠙⠨⠟⠈⣰⣿⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⣿⣿⡿⣹⣿⣿⣿⣯⡆⠿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⢸⢿⢸⣲⣿⣿⣾⣿⣿⡟⠉⣤⢀⠀⠀⢀⣀⣀⣠⣾⣫⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠷⣿⡿⢻⣿⣿⡟⠁⠈⣿⣿⣿⡿⣿⣿⣿⣿⣿⢻⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⢸⣾⣿⢻⠛⢿⣿⡟⠃⡴⠋⠄⠛⠛⠛⠉⠙⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⣿⠋⣱⣿⡏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠉⠙⡿⣿⡿⢿⣿⣿⡇
⠀⠀⠙⢋⣮⣥⣼⣷⣿⣶⠗⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠺⠧⣴⣿⣿⢦⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣷⣤⢼⣿⡇
⠀⡀⠀⣺⡿⣿⣟⣿⠟⠛⠷⠟⠡⠠⣤⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣀⡄⠀⠀⡦⣴⣿⣧⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇
⠐⡗⠒⠛⠀⠼⣿⡟⠀⠀⠐⠀⠁⠐⡈⠓⡍⡥⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢴⣲⢡⡴⣤⣤⣨⣷⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣻⡇
⠀⠀⢀⣤⠀⡀⠀⠳⠂⠂⡀⠄⠰⡈⠁⠀⠈⠁⠀⡦⠀⠠⠔⠀⠀⠀⣤⠀⠀⣀⠤⠠⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠂⡓⠀⠨⣘⡀⠀⢽⠞⢿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣲⡿⢞⡏⠘⣿⣽⡿⣿⡇
⠀⠀⠌⠋⢋⣷⠋⢙⠓⠳⠁⡄⢐⡀⢀⣀⣀⣀⣀⣬⣵⣶⣶⣶⣷⡇⣿⣁⢰⠖⠁⠀⠠⠀⠀⠀⠀⠠⡤⠦⢄⡲⠁⠀⡛⠁⠀⢗⡂⠒⠀⠀⣼⣿⣯⣷⡛⠟⠙⠀⢫⡟⣟⡻⣿⣿⣿⣿⣾⣿⣿⣇⡤⢚⣿⡏⡿⠇
⠀⠘⠚⢇⠀⣨⣗⣼⣤⡂⡀⢘⡲⠇⠀⠙⢈⡷⣾⠿⢿⣿⣿⣻⢿⠛⣤⣭⣸⣾⣶⣶⢤⠤⣤⣄⣄⢠⣥⣤⡬⣄⡎⣣⣤⡀⠀⣹⡿⠲⡟⢢⣾⣿⣿⣯⢤⣄⣰⣶⣾⣖⣛⡕⡛⠛⠛⠉⣌⣿⣹⣿⠁⣽⣿⠷⠿⠁
⠀⠤⠐⠠⠤⠅⠼⠤⠤⠤⠾⠿⠷⠲⠦⠞⠅⠐⠽⠓⠮⠻⠿⠿⠽⠿⠿⠿⠿⠥⠿⠿⠾⠄⠾⠹⠿⠿⠿⠿⠿⠷⠿⠥⠽⠿⠾⠟⠚⠒⠿⠼⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠖⠠⠾⠿⠿⠿⠯⠠⠀⠀⠏⠀⠾⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡆⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⠀⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠪⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢗⡌⠑⢝⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡻⠉⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⠿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠈⠑⠝⠏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⡍⠉⠉⣭⣴⠀⠀⠀⠀⠀⠀⠀⢀⢀⢿⡇⠀⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠻⠹⣿⣻⢻⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣸⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⠺⣿⣿⢠⡅⠠⢶⣶⠖⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⣟⠓⠒⠒⣚⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡀⠀⠙⠿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣾⢷⣶⣾⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠉⠉⡝⠀⠨⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡟⠛⠋⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⣿⠭⠅⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⢸⣷⡦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⣿⣴⠀⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢀⣿⠁⡌⠉⠀⢸⣿⢭⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢷⣿⣷⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⢸⢠⡨⠛⠃⠠⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢻⣿⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⢀⡄⢸⣠⣌⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣾⣅⣸⡟⡟⣿⠛⠻⠿⠿⠿⠿⠿⠿⠿⣾⣶⡆⠀⠀⠀⠀⠀⢰⡏⠍⣻⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀
⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣷⢸⣿⣿⡙⢇⢬⠉⠚⠓⠶⣟⠁⠀⠀⢲⣿⣿⡇⠀⠀⠀⠀⠀⢸⣧⣀⣽⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⢿⣿⣿⡿⡾⠢⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⡈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣿⠀⣿⣿⣿⣏⣟⣿⣿⣿⢡⣿⣿⣿⣿⣥⠈⠙⠘⠃⠂⠀⠀⠀⠀⠀⢠⣄⠀⠀⠉⠀⠈⠀⠀⠀⢀⣇⣀⣀⡘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡟⣰⣿⣿⣿⢿⣿⣦⣿⣿⢸⠇⣿⡿⠧⢹⡆⠈⠄⠀⠀⠀⠀⠀⠀⠀⠈⣸⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠒⠛⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣼⣷⢹⣿⡟⡜⠿⡟⠻⣿⡿⣘⠂⣙⠠⡖⣾⠃⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢁⢘⣿⡟⠐⠀⣀⠀⠿⠃⡏⠀⠀⠀⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⡀⠀⠘⢏⠀⠀⠀⠠⠤⣀⠀⢀⣘⣃⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠉⠉⠉⠉⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣭⡤⠤⣭⡭⢭⢭⣬⡭⠈⠀⠀⠀⠀⠀⣿⠀⡤⠀⠄⠀⠀⠀⠀⢈⣉⣛⣿⢆⣰⣯⣀⡀⠀⣀⣠⣌⣑⠋⣿⣿⡇⣉⣉⡁⣸⣶⣆⢀⣀⠀⣀⣀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⡏⠀⣃⣄⣠⣀⣀⣀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⢀⣠⣤⣄⣶⡜⠘⣿⣿⣿⣿⣿⠷⣶⣦⢤⡀⠈⠋⠘⢟⠝⣥⠀⢸⣿⡇⠀⣿⣿⠛⣯⣿⢀⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⠀⣀⣠⢠⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀
⢸⣿⣷⣿⣿⣿⣿⠆⣤⢸⠿⠿⠿⣿⠇⠋⠉⡄⠀⠀⠀⠀⠠⠾⢙⠀⣸⣿⡇⠃⠻⣿⣤⣿⠟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⣈⣹⢾⣦⣮⣽⣤⣤⣾⣴⡆⠀⡀⠀⠀⣿⣿⣿⣆⣤⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣠⣟⣿⣷⣶⣷⣼⣿⡷⠀⡠⢑⠒⢀⣠⠤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⣠⣄⣤⣤⣀⢀⣠⣤⣠⣀⠸⠿⠟⠛⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⠀⡔⠁⠈⠛⠛⢀⡀
⠀⢸⢻⣁⢜⠁⠀⠉⠰⣽⣿⣿⣿⣿⣿⣄⡹⣿⢏⠉⠀⢁⣴⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣭⣭⣽⣛⠋⢺⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠿⠛⣿⠇
⢠⣽⡾⠓⢲⣀⢀⣦⣦⣼⣅⣤⠷⠂⠘⠟⠉⠈⡋⠈⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣾⣿⣟⣿⣿⣿⣿⣎⢿⡿⣿⣯⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀
⢸⣿⢺⣸⣿⣶⣶⣿⣻⡏⢹⣭⠁⡀⣀⣀⣀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⢻⣍⣶⣿⣿⣿⣿⡿⠄⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⢻⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇
⠐⣸⣯⣿⢻⠗⢻⣿⣟⠃⡤⠋⠰⠶⠮⣌⠙⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠈⠙⠁⠺⠛⠛⠀⠀⠀⣼⣿⠏⢡⢿⡮⠿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠁⢙⣿⣾⡿⢿⣿⣿⡇
⠀⠀⠹⢋⣪⣥⣼⣿⣿⣶⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠘⠧⣶⣾⡿⣦⠁⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣦⢾⣿⡇
⢀⠀⠆⣸⡿⣿⣟⣿⠟⠛⠾⠞⠁⠀⢀⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣅⢄⠀⠀⣶⣾⣷⣧⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⡵⠓⠛⠁⠾⠿⡿⠁⠀⠀⠀⠁⠐⡀⠛⡌⡥⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⢴⣸⣡⣴⣤⣤⣨⣷⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⡿⣿⡿⣿⣿⣿⣿⣻⡇
⠀⠀⢀⣤⠀⡀⠀⠳⠂⠂⣀⠄⠸⠈⠁⠀⠈⢀⠀⡆⠈⠠⠔⠀⠀⠀⣠⡄⠀⢀⠤⠠⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠂⡓⠀⠨⣙⡢⠈⢿⠟⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⣺⡿⢿⡏⠘⣾⣮⡿⣿⡇
⠀⠀⠆⠋⠉⣧⠋⢉⠓⠒⠀⡀⢐⡀⣀⣠⣀⣀⣀⣬⣽⣶⣶⣾⣿⣇⣿⣁⢰⠖⠁⠀⠠⠀⠀⠀⠀⠠⡤⠆⢄⡶⠀⠀⡏⠁⠀⠖⣒⠀⠂⠀⢼⣿⣿⣷⡿⠟⠉⠈⢻⡟⣟⡻⣿⣿⣿⣿⣾⣿⣿⣇⡤⠛⣿⠁⢟⠇
⠈⠘⠚⢋⠠⣨⣗⣼⢦⡀⡐⣈⡲⢗⠀⠑⢈⡿⣾⠿⢿⣿⣿⣻⢿⠋⣮⣭⣸⣻⣶⣦⢴⠦⣤⣄⣄⣠⣥⣤⡬⣄⣖⡣⣤⡀⠀⣽⡿⠲⢟⢂⣾⣿⣿⣷⣠⣆⣰⣶⣶⣎⣝⡗⡛⠛⠛⢡⣼⣿⣹⡿⠁⠽⣿⠿⠿⠄
⠀⠠⠐⠠⠤⠅⠼⠤⠤⠤⠾⠿⠷⠸⠦⠖⠅⠐⠹⠚⠫⠻⠿⠽⠽⠾⠿⠿⠿⠤⠿⠷⠾⠄⠿⠹⠿⠿⠿⠿⠿⠷⠿⠡⠽⠿⠾⠟⠚⠗⠿⠼⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠖⠠⠾⠿⠿⠿⠯⠠⠀⠀⠫⠀⠿⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⡆⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠺⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢗⡌⠑⢝⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⠿⠋⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠈⠑⠝⠏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠈⣭⣽⠀⠀⠀⠀⠀⠀⠀⢀⢠⢿⡇⠀⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡻⠽⣿⣻⣛⠻⣿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣸⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡚⣿⣿⢠⡍⠠⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠗⠒⠒⣚⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡄⠀⠘⠿⠿⢿⣿⣿⡟⠁⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣾⢷⣾⡿⠗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠉⠉⡝⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡟⣛⣋⣁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⠯⠅⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⢸⣷⡆⣶⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⣾⣿⣶⠀⠀⢀⣿⣿⣷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠄⣿⠁⡌⠉⠀⢸⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢷⣿⣷⣦⣄⣀⠀⠀⠀⠀⠈⠀⠀⢸⢰⣨⠙⠃⠠⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢹⣿⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⢀⡌⢸⣠⣌⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣾⣥⣸⡟⡟⣿⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡏⠍⣿⠀⠀⠀⠀⠀⠀⠀⢰⢶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣷⢸⣿⣿⡛⣇⢤⠉⠙⠛⠿⣟⠁⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⢸⣥⣤⣽⠀⠀⠀⠀⠀⢀⠐⣾⠀⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⢿⣿⣿⡿⡾⢢⠐⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⢀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⢐⠀⡏⠉⠉⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣿⠃⣿⣿⣿⣏⣟⣿⣿⣿⢣⣿⣿⣿⣿⣭⠌⢙⡘⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣧⣄⣀⣜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡿⣰⣿⣿⣿⢿⣿⣧⣿⣿⢸⠏⣿⡿⠭⢽⡇⠀⠃⠄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣟⣷⢹⣿⡿⡜⡿⡟⠻⣿⡿⢘⠒⣙⢠⡖⣾⠇⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣳⣘⣿⣟⡑⣀⣀⡀⣿⢇⡏⠁⠁⠈⠧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠉⠉⠉⠉⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣭⣤⡤⢭⡭⢬⣭⣤⠭⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⠀⠀⠀⠀⠀⣠⣶⣀⡀⢀⣸⣥⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣸⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⣀⡟⠀⣛⣀⣴⣄⣀⡀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⢹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣄⣀⣠⣤⣤⣶⢶⠛⣿⣿⣿⣿⣿⣏⣶⣦⣥⡀⠈⠋⢘⡿⠿⣿⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢀⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⡀⣀⣀⢀⠐⣤⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⡇⣶⡼⡿⠻⣯⣿⡟⡎⠁⣴⡀⠀⠤⠀⣠⡾⢢⠀⣸⣿⡇⡔⠻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⣥⣿⣻⣶⣾⣿⣦⣶⣿⣶⠂⠀⡀⠀⠀⣿⢿⣿⣇⣤⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣧⣠⣿⣻⣷⣿⣿⣷⣿⣟⢊⡀⢵⢓⠛⡂⠀⠐⠊⠀⠀⠀⠉⠀⠀⠀⠈⡁⠀⢀⣠⣤⣀⡀⠀⢀⣠⣤⣤⣄⠸⠿⠟⠛⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⢁⡗⢠⠀⠛⡉⢁⡀
⠀⢸⢻⣁⠝⠁⠈⠜⢶⣿⣿⢿⣿⢿⣿⣟⡹⣿⣆⣙⡏⠛⢙⣩⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠙⣿⠇
⢠⣽⡾⢳⣶⣠⣰⣶⣾⣾⣤⣤⠿⠓⠘⠛⠙⠸⡏⠉⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠿⣿⣿⣿⠿⠄⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⢸⣿⢻⣻⣿⣿⣾⣿⣿⡟⢫⣷⠄⣀⣠⣀⠀⠀⢀⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠿⠉⠉⠄⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣱⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢰⣸⣿⣿⣻⡗⢿⣿⣟⠃⡜⠉⢤⣬⣇⡉⢳⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⣱⢿⡯⠟⣿⢿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠃⠉⢹⠿⣿⡿⢿⣿⣿⡇
⠀⠁⠻⢋⣿⣵⣾⣿⣿⣶⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⡛⢳⣶⣿⡿⣾⠇⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣿⡇
⢀⡀⠤⣾⣿⢿⣿⣿⠟⠛⠿⠟⠁⠀⢤⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⣦⢀⣩⠄⠀⠀⣶⣾⣷⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⡽⡛⠟⠁⡾⡿⡿⠇⠀⠀⠀⠁⠐⡀⠛⣌⡧⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠠⠤⢈⢴⡦⢤⣽⣯⣴⣤⣤⣬⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣯⣿⣿⣿⣿⡇
⠀⠀⢀⣤⠀⡀⠘⡳⠆⠦⣀⠄⠸⠀⠁⠀⠽⣃⠀⣂⡀⠠⠴⠀⠀⠀⣠⡄⠀⢀⠤⠨⠄⠀⠀⠘⠉⠀⠀⠀⠀⠀⡀⠞⣓⢀⠬⣙⡳⠾⢽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⡿⢿⣏⠚⣾⣾⣟⣿⡇
⠀⠀⠆⠛⢋⣧⠋⢉⠓⠒⠀⡀⢐⡀⣀⣨⢀⣀⣀⣬⣽⣷⣶⣾⣿⣏⡿⣍⢼⢞⠉⠀⠠⠀⠀⠀⠀⠠⡄⠖⢶⡗⢀⡀⡟⠁⢀⠷⣖⠂⠀⠁⢾⣿⣿⣿⡟⡟⠙⠁⢫⠟⣿⡻⡿⣿⣿⣿⣿⣿⣿⣟⡤⠙⣿⣏⣿⠇
⠨⠘⠚⢋⠀⣸⣗⣼⣦⡠⡔⣈⡳⢗⠀⠙⢈⡿⣾⡿⢿⣿⣿⣻⢿⢻⣯⣭⣹⣿⣾⣷⢴⠦⣤⣔⣤⣤⣥⣤⣾⣤⣖⡳⣦⡄⠀⣽⣿⣲⣿⢃⣿⣿⣿⣷⣮⣆⣰⣷⣾⣿⣝⣟⡟⢛⠻⣩⣾⣿⣭⣯⠱⣿⣿⠿⠿⠅
⠀⠠⠔⠠⠤⠥⠼⠤⠤⠤⠮⠿⠿⠾⠦⠞⠅⠐⠽⠚⠯⠻⠿⠽⠽⠿⠿⠿⠯⠧⠿⠿⠾⠤⠿⠹⠿⠿⠿⠿⠿⠷⠿⠽⠿⠿⠾⠟⠚⠷⠿⠼⠿⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠠⠾⠿⠿⠿⠯⠰⠀⠄⠣⠐⠿⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⡆⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠺⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢓⡄⠑⢝⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡽⠈⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣿⣿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠑⠝⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆⠀⠀⣤⣼⠀⠀⠀⠀⠀⠀⠀⢰⢠⢿⡇⠀⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡻⠿⣿⣻⣛⠻⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣸⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡺⣿⣿⢠⡅⠠⠶⠶⠖⠀⠀⠀⠈⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠗⠒⠒⣛⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡄⠀⠘⠿⠿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣾⢳⣿⡿⠗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠉⠉⡝⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡟⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⢤⣤⣽⡇⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⠮⠅⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⢸⣷⡦⣶⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⣾⣿⣶⠀⠀⢀⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⣿⠁⡄⠉⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢷⣿⣷⣦⣤⣀⠀⠀⠀⠀⠈⠀⠀⠸⢰⡨⠙⠃⠠⠀⢸⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢹⣿⣼⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⢀⡌⢸⣠⣌⢀⣁⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣞⣥⣼⡟⡟⣿⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡏⠉⣹⠀⠀⠀⠀⠀⠀⠀⢰⢒⠖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⣼⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣷⣸⣿⣿⡛⣇⢄⡉⠙⠛⠿⣟⠁⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⢸⣥⣤⣽⠀⠀⠀⠀⠀⠀⠐⣾⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣹⣿⣿⣿⣿⣿⣿⡿⡾⠠⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⠇⢀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⡏⠉⠉⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣿⠁⣿⣿⣿⣏⣟⣿⣿⣿⢣⣿⣿⣿⡿⣦⠌⠙⠘⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠀⢀⣧⣤⣄⣜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡟⢀⣿⣿⣿⢿⣿⢦⣿⣿⢸⡇⣿⠿⠣⢹⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠒⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣷⢻⣿⣟⡜⠿⠛⠟⣿⡿⢘⠒⡉⢀⡗⣾⠗⢢⡀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣻⣸⣿⣟⡁⣀⣢⡀⣿⢃⡇⠀⣀⠀⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⠉⠉⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣭⡤⠤⢤⠥⠤⢭⣠⠥⠀⠀⠀⠀⠀⠀⣿⠀⡤⠀⠀⠐⠐⠀⠀⢀⣀⣀⡌⢛⣳⣤⣀⡀⠀⣀⣠⣤⣀⠀⣿⣿⡇⣉⣉⡁⣸⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠈⠈⠁⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⠀⠀⢀⡟⠀⣋⣀⣤⣀⣀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣠⠀⣤⣤⣤⣶⠾⠛⢿⣿⣿⣿⣛⣷⢶⣦⣤⠀⠈⠋⢙⡿⡿⣤⠀⢸⣿⡇⡆⣿⣿⠛⣯⣿⢀⣴⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⣤⣤⣄⢠⠰⢤⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⢂⣶⡼⡟⠳⣫⣿⡇⠄⠁⡸⣀⠀⢈⡄⠔⡶⣧⠀⣼⣿⡇⢳⠻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⣤⣿⢻⣧⣾⣷⣥⣴⣿⣖⢄⣀⡀⠀⠀⣿⢿⣿⣇⣤⠀
⢸⣿⣿⣿⣿⡿⣿⣿⣿⣦⣦⣤⣯⣯⣷⣷⣧⣷⣿⠗⠀⣀⣋⢘⠻⠄⢀⠀⣠⠏⠀⠀⠉⠀⠀⠀⠀⠁⣤⣴⣷⣷⣶⣶⣄⡀⣠⣤⣤⣄⠸⠿⠟⠛⣠⣿⣷⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡗⢁⡔⣠⠀⢙⠉⢁⡀
⠀⢸⢿⣁⠌⠀⠀⠘⢻⣿⣿⢿⣿⣿⣿⣅⣹⣿⠒⣅⡼⢿⢺⠋⣀⣀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⠛⣽⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣷⣿⠿⠉⢿⠇
⢠⣽⡾⠓⢲⢠⣠⣶⣶⣾⣤⠼⠿⠛⠘⠛⠙⠈⠏⠙⠄⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠞⠿⠟⠀⠀⠦⠪⠿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆
⢸⣿⢻⣲⣿⣿⣿⣿⣿⡟⢩⣷⢀⣢⣄⡀⠀⠀⠀⣰⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣹⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⡼⣿⣿⣻⡓⢻⣿⡟⠓⡍⠥⣥⣝⡈⠹⣶⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⢰⢿⡇⠿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠈⢹⠿⢿⡿⠿⢿⣿⡇
⠀⠀⠙⢋⣽⣵⣼⣿⣿⣶⠇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡛⠧⣶⣾⡿⣶⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣿⡇
⢀⡀⠒⣾⡏⢿⣟⣻⠟⠋⠦⠚⠁⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠄⢄⠀⢀⣦⢀⣬⠤⠀⠐⣶⣾⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇
⠐⡗⡛⠙⠁⡞⡻⡿⠅⠀⠀⠀⠀⠐⡀⠓⣌⡵⠄⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠚⠰⢆⠀⠀⠐⢶⠀⠀⠈⠁⠀⠀⠤⠤⢬⢿⣿⢿⣽⣯⣽⣦⣤⣬⣷⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣤⠀⡐⢈⡳⠆⠦⣠⠄⠰⠀⠁⠀⠙⢉⠀⣆⠀⠠⠴⠀⠀⢀⣤⡤⠀⢤⣴⢨⡄⠀⠀⠘⠋⠀⠀⠀⠀⠀⡀⠋⣟⣁⢰⣽⡿⠚⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⢿⡏⢀⣿⣾⡟⣿⡇
⠀⠀⠂⠛⢉⣧⠋⢈⠃⠓⠀⡀⢀⡀⣀⡠⢀⣠⣄⣬⣽⣷⣶⣾⣿⣏⡿⣥⢼⣟⠁⠀⠰⠀⠀⠀⠀⠠⡇⠖⢦⡗⠀⡀⡏⠑⠀⠿⣞⠈⢉⣈⣾⣿⣿⣿⣿⡟⠙⠙⢫⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠉⣟⡅⣛⠇
⠨⠘⠚⢃⠄⣸⣗⣽⣢⡠⣔⣈⡳⢗⠀⠁⢀⠿⣶⠿⢿⣿⣿⣿⢿⣻⣭⣭⣽⣿⣾⣷⢶⠲⣶⣖⣦⣤⣦⣤⣶⣤⣞⡳⣤⡄⠀⣿⣿⣲⣿⢷⣿⣿⣿⣧⣧⣞⣲⣷⣾⣿⣫⣟⡛⢛⠿⣹⣯⣿⣭⣏⠑⡽⣿⠿⠿⡇
⠀⠠⠔⠢⠤⠥⠼⠤⠤⠤⠮⠿⠿⠚⠦⠞⠅⠐⠺⠝⠯⠙⠛⠿⠽⠿⠿⠿⠿⠷⠿⠿⠾⠤⠿⠩⠿⠿⠿⠿⠿⠿⠿⠥⠿⠿⠾⠿⠚⠷⠻⠼⠿⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢮⠰⠾⠿⠿⠿⠯⠸⠀⠂⠇⠐⠿⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢿⣿⡆⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠺⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢑⡆⠑⢝⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡽⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠑⠍⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆⠀⠀⣦⣼⠀⠀⠀⠀⠀⠀⠀⢸⢠⢻⡇⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡻⠿⣿⣻⣛⠻⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣸⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣚⣿⣿⢠⡅⠠⠶⠶⠖⠀⠀⠀⠉⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠗⠒⠒⣛⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡄⠀⠊⠿⠿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣾⢿⣿⡿⠗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠉⠉⡝⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣗⣛⣛⣀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⡤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠬⠅⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠃⢸⣷⠦⣶⠀⠀⠀⠀⠀⠀⡀⠀⠐⠃⣾⣿⣶⠀⠀⢠⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⣿⠁⡄⠉⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢷⣿⣷⣦⣤⣀⠀⠀⠀⠀⠈⠀⠀⠸⢰⡨⠉⠁⠠⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢹⣿⣼⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⢀⡌⢸⣠⣌⢀⣁⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣯⣿⣿⣎⣥⣼⡟⡟⣿⠛⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡏⠉⣽⠀⠀⠀⠀⠀⠀⠀⢰⢒⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⣽⣿⣿⣾⣿⣾⣾⣿⡇⣿⣿⣷⢸⣿⣿⡛⣇⢤⠈⠙⠛⠿⣟⠁⠀⠈⢹⣿⣿⡇⠀⠀⠀⠀⠀⢸⣥⣤⣽⠀⠀⠀⠀⠀⠀⠐⣾⡀⠀⡟⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⡮⢠⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⢀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⡏⠉⠉⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣿⠀⣿⣿⣿⣏⣟⣿⣿⣿⠁⣿⣿⣿⡟⣦⠌⠙⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⢀⣤⣤⣤⣜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢿⡟⢀⣿⣿⣿⢿⣿⣦⣿⣿⢸⣏⣿⡿⠣⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣷⠈⣿⣿⡘⠟⡟⠻⣿⡿⢘⠒⡉⢁⡗⣾⠓⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣻⣡⢐⣿⣟⡁⣀⣀⣀⣟⣁⡇⠀⣈⠀⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠉⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣥⣥⡤⠤⢤⠥⠬⢬⣠⠤⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⠀⠐⠐⠀⠀⣀⣀⣈⣹⢆⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣼⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⢀⡟⠀⣛⣀⣠⣄⢀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣄⡀⣠⣤⣤⣴⠾⠛⣿⣿⣿⣿⡿⢦⢴⣤⣤⡄⠀⠉⠙⢟⠛⢃⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⡄⣀⣀⠠⠀⢴⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀
⢸⣿⣷⣿⣿⣿⣿⢆⣴⡸⡟⠻⢋⣿⠏⠌⠁⣜⠀⠀⠀⠀⡠⡾⣏⠀⣼⣿⣇⣦⣻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⣠⡙⣿⣧⣶⣷⣦⣶⣿⣖⠆⢀⡀⠀⠀⣿⢿⣿⣇⡤⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣠⣿⣿⣷⣷⣷⣼⣿⡗⠀⠀⡀⣱⡮⣄⠀⠀⠸⡿⠛⠀⠉⠀⠀⠀⠀⠁⣠⣴⣶⣶⣶⣦⣄⡀⣀⣤⣤⣄⠸⠿⠟⠛⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⢁⡆⢠⠀⠉⠉⢁⠀
⠀⢸⢿⢁⠜⠁⠀⠈⢲⣿⣿⢻⣿⢿⢿⣄⣩⣿⣋⣅⣀⠀⡃⠍⢀⠏⣄⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣸⠻⣿⣿⣿⣿⡿⡿⡟⢹⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣾⡟⠉⣿⠃
⢠⣽⡾⠓⢲⢀⣤⣷⣦⣼⣥⣴⠿⠚⠈⠟⠉⠈⠟⠙⠊⠀⣈⡠⠄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⡛⠛⠛⣭⠈⣰⠆⠟⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⢸⣻⢻⣲⣿⣿⣿⣿⣿⡏⢹⣾⠀⣤⣤⡀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠒⠊⠁⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣳⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⣼⣿⣿⣻⠓⢻⣿⣟⠓⢱⠶⢤⣙⠀⠹⣶⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠇⢸⢿⡆⠟⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠈⢙⠿⣿⣿⢿⢿⣿⡇
⠀⠀⠙⢋⣬⣵⣼⣿⣿⣶⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡛⠧⣴⣿⡿⣾⠂⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⢾⣿⡇
⢀⠀⠀⣸⡏⢿⣟⣹⠟⠋⠢⠞⠁⠀⣠⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡄⠀⠀⠄⡔⢄⠀⢀⣦⢀⣬⠤⠀⠐⣶⣾⣷⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⡕⡓⠙⠁⠜⠻⡯⠅⠀⠀⠀⠀⠘⡀⠛⣌⡷⠎⠇⠁⣀⠀⠀⠀⠀⠀⠀⠀⠸⠲⢦⠀⠀⠈⢲⠈⠀⠑⠩⠀⠀⠤⠤⣭⣿⣿⣿⣽⣿⣵⣦⣤⣬⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⡇
⠀⠀⢀⣤⠀⡀⢀⡳⠆⠶⣀⠄⠸⠀⠁⠀⠘⢡⠐⣂⠀⠠⠴⠀⠀⢀⣤⡄⠀⢤⣴⡸⢄⠀⠀⠘⠏⠀⠀⠈⠀⠀⠀⠛⣽⣁⠶⣽⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⢿⣏⣈⣿⣿⣟⣿⡇
⠀⠀⢂⠛⠯⣧⠋⢈⠛⠛⠀⣄⢀⡀⣀⣠⢀⣠⣀⣬⣽⣷⣿⣾⣿⣏⣟⣥⢾⢞⢉⠀⠐⠀⠐⠀⠀⠠⡵⠒⠦⡇⢀⡀⡏⠁⢈⡷⣾⠋⢉⡁⣾⣿⣿⣿⣿⠟⠙⠑⢫⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠉⣟⣏⣛⠇
⠈⠘⠚⢃⠀⣨⣗⣽⣦⡠⣔⣈⡳⢗⠀⠁⢀⡿⣶⠿⢿⣿⣿⣿⢿⣫⣯⣭⣽⣿⣾⣷⢴⠶⣴⣆⣦⣤⣧⣤⣶⣤⣖⡳⣦⣂⢀⣿⣿⣲⣟⣷⣿⣿⣿⣿⣣⣎⣰⣷⣶⣏⣯⣗⡛⢛⠿⢹⣭⣿⣭⣿⠑⡿⣿⠿⠿⡆
⠀⠠⠔⠠⠤⠥⠼⠤⠤⠤⠮⠿⠯⠖⠦⠞⠅⠐⠺⠍⠫⠙⠻⠿⠽⠿⠿⠿⠿⠷⠿⠿⠾⠤⠿⠭⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠾⠟⠛⠷⠻⠼⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠮⠠⠾⠿⠿⠿⠯⠸⠀⠂⠭⠀⠿⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⣿⡆⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⡛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢹⡆⠑⢝⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣿⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠉⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆⠀⠀⣶⣼⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡻⠿⣿⣻⣛⠻⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⢘⣸⠸⠁⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣚⣿⣿⢠⡅⠠⠶⠷⠖⠀⠀⠀⠉⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠒⠒⢺⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⡄⠀⠈⠻⠿⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣾⣿⣿⡿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣼⡯⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⠉⠉⡽⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣟⣛⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡦⣤⣽⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⠯⠅⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣷⠦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣿⣶⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⣿⠁⡄⠉⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢷⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⢠⣨⠉⠁⠠⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢻⣿⣼⣿⣿⣿⣿⣿⣿⣷⣦⣐⡀⠀⢀⡌⢸⣀⣬⢀⣁⡀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡎⣥⣼⡟⡟⣿⠛⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⢠⡏⠍⢹⠀⠀⠀⠀⠀⠀⠀⢰⡖⡒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣹⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⢴⣿⣿⡛⣣⠀⠈⠙⠛⠻⣿⠁⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⢸⣧⣤⣼⠀⠀⠀⠀⠀⠀⠐⣺⡀⠀⣿⠀⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡾⠠⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠃⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣿⠇⣿⣿⣿⣏⣟⣿⣿⣿⡇⣿⣿⣿⣟⣮⠌⠙⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⣤⣄⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⣿⠂⣿⣿⣿⣿⣿⣢⣼⣿⢸⣇⣾⡟⠫⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣟⠁⣿⣟⡇⠹⠟⠛⣿⣿⢘⡀⡈⠁⡓⣾⡇⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣻⣇⣀⣿⣟⡁⣀⣀⣀⣋⡁⡀⠀⣀⡀⠡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠉⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣥⣦⠤⢤⠤⠤⢤⣤⠤⠀⠀⠀⠀⠂⠀⣿⠀⡤⠂⠂⠐⠀⠀⠀⢀⣀⣀⡀⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣸⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠁⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⢀⡀⠀⠀⡿⠀⣙⣀⣤⣀⢀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣄⠀⢠⣤⣤⣖⠴⠛⣻⣿⣿⣿⣿⡃⣶⣤⣠⠄⠀⠉⠙⠿⠛⡿⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣧⣿⡟⠀⠄⡠⣤⣀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⠀⣴⡼⡟⠻⢻⣿⠏⠀⠁⠲⠀⡀⠀⠈⠠⠾⢛⠀⣸⣿⡇⠀⢻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⣆⣘⣣⣄⣦⣷⣴⣶⣾⣦⠀⠀⡀⠀⠀⣿⢿⣿⣇⣤⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣼⣻⣿⣿⢿⣿⣿⠿⠀⠀⢠⣴⣮⣄⡀⢶⣿⣦⣴⡆⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠘⠿⠿⠛⣠⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣽⣿⣶⣾⣟⢀⡁⠠⠀⠉⢉⢁⠀
⠀⢸⢿⢁⠌⠁⠀⡈⢒⣿⣿⢿⣿⢿⠿⢧⡈⣿⣏⣓⣀⠀⠘⠛⠙⣗⠁⠈⢿⡟⠛⠁⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣷⣶⣟⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣶⣾⣟⡉⡻⠃
⢠⣽⣷⠛⢼⣠⣰⣶⣶⣼⣥⣥⣿⠘⠀⠛⠀⠈⣏⠉⠉⠀⠘⠫⠀⠹⡄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣿⣿⣿⣿⣿⡟⠳⣅⠟⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⣻⣻⣻⣾⣿⣿⣿⣿⡏⠹⣿⠀⣴⢦⣄⠀⠀⠀⠁⢀⣰⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⣿⣿⡇⠀⣼⢿⠟⠛⠀⢿⣿⣿⡿⢿⣿⣿⣿⣿⣷⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣜⣿⣟⡻⡗⢿⣿⣏⠓⢾⠳⠲⣝⡉⠸⢷⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⠁⠙⠛⠃⠈⠃⠲⠲⠀⠀⢼⣿⠏⢸⢿⡯⡿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢁⠈⢹⡿⣿⣿⠻⢿⣿⡇
⠀⠀⠙⠋⣵⣵⣼⣿⣿⣶⠆⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠀⡘⠻⣶⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⡇
⠀⠄⠀⣸⣯⢿⣟⣻⠟⠋⠤⠔⠀⠀⢠⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⣠⣀⣀⠀⠄⢀⡀⢄⠀⠠⡖⡔⢤⡀⢀⣦⣤⣼⣶⠀⠀⣾⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⡏⠓⠉⠁⠞⠿⡯⠁⠀⠀⠀⠀⠘⣢⠛⣄⡿⠎⠄⠁⠀⡀⠀⠀⠀⠀⠀⠀⠘⢳⢪⣥⠆⠺⢲⢉⠀⠙⣫⠀⠚⠤⠽⣽⣿⣿⣿⣿⣿⣷⣯⣦⣬⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢀⣴⡀⡐⢀⡴⠆⣴⡄⠄⠠⠄⠃⠀⠈⢊⠐⢒⠀⠰⠠⠀⠀⢀⣠⣤⠀⢤⣶⡼⣗⡇⠀⠘⠏⠁⠌⠀⠀⠀⡀⠏⣿⣋⠷⡽⣿⠾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣯⡚⣿⣿⡟⣿⡇
⠀⠀⢂⠻⢋⣗⡋⢨⡛⠞⠄⣀⡀⡂⣀⡠⢀⣠⣄⣤⣽⣷⣿⣾⣿⣧⡟⣍⢾⣞⠁⠀⠑⠀⠀⠂⠀⠠⡕⠖⠶⣿⢀⡀⡟⠑⠊⣿⣷⠋⢙⣈⣾⣿⣿⣿⣿⡟⠙⠛⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡤⠈⣿⡋⣟⠃
⠈⠐⠚⢋⠀⣪⣗⣽⣢⡀⣔⣊⡓⢖⠐⠈⢀⠝⢒⡿⢿⣿⣿⣿⢷⣿⣧⣭⣩⣿⣽⣷⢶⠆⣶⣆⣦⣤⣶⣤⣼⣤⣖⣻⣶⣆⠀⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣮⣰⣿⣾⣯⣯⣟⡛⢻⢻⢀⣺⣿⣭⡏⠑⣾⣿⠿⠿⡂
⠠⠠⠔⠢⠤⠄⠼⠤⠤⠤⠾⠿⠯⠕⠒⠞⠅⠐⠺⠍⠩⠙⠻⠿⠼⠿⠿⠿⠿⠶⠿⠿⠾⠖⠯⠩⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠚⠷⠻⠮⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠮⠤⠾⠿⠿⠿⠯⠐⠄⠂⠌⠄⠻⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⣿⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⡛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠻⡆⠙⠊⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢻⡿⠟⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠉⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣧⡆⠀⠀⢢⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡻⠿⡿⣻⣛⡻⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡇⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣖⣿⣿⢠⡍⠠⠾⠿⠟⠀⠀⠀⠉⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⠀⢠⣿⡇⠒⠒⢺⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡇⠀⠈⠻⠿⠿⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣸⣷⣿⡿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣿⡇⣟⣛⣓⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣦⣤⣼⣟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⣿⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣶⣼⣿⠧⠅⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠿⠦⣶⠃⠀⠀⠀⠀⠀⠀⠀⢀⠃⣼⣿⣶⠀⠀⠀⣿⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣶⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡆⣿⠁⡄⠈⠁⢀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣷⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠘⠰⢀⣦⠉⠁⠠⠄⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡀⠀⢀⡌⢸⣀⣬⢀⣁⣀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣼⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⢹⣿⣿⡎⣧⣸⡟⣿⣻⠛⠛⠛⠿⠿⠿⠿⠿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⡏⠉⢹⠃⠀⠀⠀⠀⠀⠀⢰⡖⡒⣶⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣦⣿⣿⣋⢳⠀⠌⠉⠛⠻⢿⠁⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⢰⣧⣤⣼⠀⠀⠀⠀⠀⠀⠐⢸⣁⡀⣿⠀⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣿⣿⡿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⡈⠉⠉⢹⠀⠀⠀⠀⢨⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣽⡏⣿⣿⣿⣏⣟⣿⣿⣿⡇⣿⣿⣿⣿⣮⡌⠙⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣨⣤⣤⣼⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣇⣿⠇⣿⣿⣿⣿⣿⣦⣼⣿⢃⡏⣝⡿⠫⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣷⡿⠂⣿⡗⡇⠹⠟⠻⢿⢿⢘⡁⡍⡁⡗⣾⡇⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣻⣇⣀⣿⣟⡃⢀⢀⣀⣘⡀⡀⡀⢀⡀⠡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠁⠉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣥⣦⠤⢠⡤⠤⢤⣤⡤⠁⠀⠀⠀⠀⠀⣾⠀⣤⠂⠒⠐⠀⠀⠀⣀⣀⣀⡀⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣼⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⠀⠀⠀⡿⠀⢙⣀⣠⣀⣀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⣀⣤⣤⣰⠲⠛⣿⣿⣿⣿⣿⡇⣶⣶⢤⠀⠀⠉⠙⢿⢽⣽⠀⢸⣿⡇⡂⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⢤⢠⣠⡀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⢀⣴⡼⡿⠩⢻⣿⡏⠀⠀⠰⠅⠀⠀⠀⠰⣿⢷⠀⣸⣿⡇⣣⣻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⣂⣘⣏⣦⢴⣶⣦⣦⣶⣦⢢⢀⠀⠀⠀⣾⠿⣿⣇⣤⠀
⠸⣿⣿⣿⣿⣿⡿⣿⡿⣦⣷⣤⣼⣽⣿⣿⢿⣿⣿⠿⠃⠁⢰⣰⡏⡄⠀⣀⡀⠰⣿⠀⠉⠁⠀⠀⠈⠡⣶⠀⠀⠀⠀⢀⠀⢀⣠⣤⣤⣄⠘⠿⠿⠛⣠⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿⣟⢑⡱⠀⢀⢉⡉⢁⡀
⠀⠸⣿⢁⠌⠀⠀⠀⢱⣿⣿⢿⣿⢿⡿⣧⣈⢿⡯⣧⣀⠂⠘⠛⠹⣗⠰⣿⣷⣄⣿⠀⠀⠈⠉⠉⠛⠀⠛⣧⣤⣶⣶⣦⣤⣎⠿⣿⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣶⣿⡟⠉⠹⠃
⢠⣶⣧⠛⢸⣀⣀⣷⣷⣼⣧⣴⠾⠘⠀⠛⠉⠈⠟⠉⠉⠀⢼⢿⠏⢘⠁⢹⣿⠿⠃⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⣿⡿⢿⣦⠟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⢻⣿⣻⣾⣿⣿⣿⣿⡏⢙⣙⠄⢸⡛⢦⡀⠀⠀⠀⠀⣠⡤⠖⠒⠒⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⠗⣿⣿⣯⠁⣙⣿⣷⠟⠇⢘⣿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⡀⣿⣿⡻⡗⢻⣿⣯⠛⠸⠉⠙⠮⣀⡘⠿⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠻⠷⠠⠿⠠⠶⠄⠀⠸⣿⢏⢰⣾⡭⡿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢁⡀⠘⠿⢿⣿⠻⢿⣿⡇
⠀⠀⠘⠋⣱⣥⣼⣿⣿⣶⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⡙⠳⣶⣿⣿⣿⠃⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⡾⣿⡇
⠀⠀⠀⣸⡏⢿⣟⣹⠟⠋⠀⠔⠀⠀⢠⣤⣠⣄⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⣠⣀⢠⣄⣀⠂⠴⢈⡁⣄⠀⢠⡶⡰⢄⡀⢀⣶⡄⣴⣶⠂⠀⢾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠐⡇⠓⠍⠁⠌⠿⡯⠗⠀⠀⠀⠀⠘⣢⠉⣆⡿⠎⠇⠁⢀⡀⠀⠀⠀⠀⠀⠀⠘⢿⢎⣭⠟⠹⢲⠉⠀⠉⣫⠵⠾⠧⠽⣽⣿⣿⣿⣿⣿⣿⣯⣧⣴⣿⣽⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡇
⠀⠀⣀⣴⡅⣐⢀⡰⠆⠴⣄⠄⠠⠆⠉⠀⠘⢊⠀⢒⠀⠰⠤⠀⠀⢀⣰⣤⡀⢤⣴⣼⣟⡇⠂⠈⠏⠃⡌⠉⠀⠀⠠⠛⣿⣛⣿⣽⢿⠿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣭⣨⣿⣿⡟⣿⡇
⠀⠀⢂⠛⣏⣿⡋⢨⡛⠞⠈⣀⡀⡂⣀⡠⢀⣠⣄⣬⣽⣷⣷⣿⣿⣷⣟⣍⢾⣞⠁⠀⠑⠀⠐⠀⠀⠤⣥⠞⠶⣼⠆⡀⠹⠑⠢⣿⣶⠏⢉⣈⣾⣿⣿⣿⣿⡟⠉⠒⠻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡥⢈⢿⡇⣛⠃
⠈⠐⠚⠫⠀⣊⣗⣼⣲⡀⣔⣎⡓⢖⠐⠈⢀⠹⢗⠿⢿⣿⣿⣿⢿⡏⣥⣭⣽⣿⣽⣷⢶⠆⣶⣔⣦⣤⣶⣤⣼⣥⣶⣻⣶⣄⠀⣾⣿⣻⣿⣷⣿⣿⣿⣿⣟⣾⣲⣿⣾⣾⣋⣗⣚⢟⢻⢃⣻⣿⣭⣿⠙⣾⣿⠿⠿⡆
⠠⠠⠄⠢⠤⠤⠼⠤⠤⠤⠾⠿⠯⠕⠒⠞⠅⠐⠺⠌⠩⠙⠛⠿⠽⠿⠿⠿⠿⠦⠿⠿⠟⠖⠿⠏⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠺⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠤⠾⠿⠿⠿⠿⠅⠆⠒⠭⠄⠻⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⡛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠹⡦⠉⠊⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠁⢿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢻⣿⠿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠈⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣴⠀⠀⢠⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⢿⠟⣿⣿⣟⡛⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣰⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣖⢻⣿⢁⡌⠀⠴⠷⠖⠀⠀⠀⠈⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⣿⡏⠒⠒⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡇⠀⠈⠻⠿⠿⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡏⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⡟⣿⣚⣓⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⣾⠀⠀⠸⠀⠀⠀⠀⠀⠠⠀⠀⣶⣸⣿⡧⠅⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⡦⢶⡆⠀⠀⠀⠀⠀⠀⠀⢀⠃⣼⣿⢰⠂⠀⠀⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠇⣤⠈⠁⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠐⠰⠇⣦⠉⠉⠠⠄⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⡌⢘⣁⣠⢀⣀⣀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢹⣯⣿⡎⣧⣸⡟⣻⣻⡛⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⡏⠍⢹⡇⠀⠀⠀⠀⠀⠀⢰⡖⡒⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣸⣿⣿⡆⣿⣿⣇⢻⠀⡈⠉⠛⠻⢿⠁⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⠀⢀⣧⣤⣼⠃⠀⠀⠀⠀⠀⠀⢺⡇⠀⢹⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣿⣿⡿⡶⠀⠄⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⣸⠉⠉⢹⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡯⣻⡇⢸⣿⣿⣏⣿⢿⣿⣿⡇⣿⣿⣿⣿⢦⡄⠘⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣸⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣿⠇⣿⣿⣿⣿⣿⢢⣼⣿⡇⡜⣎⡏⠩⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡧⣿⠂⣿⣿⡇⠑⠛⠛⢿⢿⢘⡁⣉⡁⡖⢺⡇⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣻⣏⣀⣿⣟⡃⣁⣐⣀⣘⡀⠀⠀⢀⡀⠁⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠈⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣥⣶⠴⢠⡤⠤⠤⣤⡤⠀⠀⠀⠀⠀⠀⣸⠀⣤⠂⠐⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣸⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⠀⠀⠀⡿⠀⢙⣀⢀⡀⠀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⢀⣤⣤⡰⠐⠃⢹⣿⣿⣿⣿⠃⢰⣶⣤⠄⠀⠈⠉⠿⠖⡢⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⠤⠄⣄⡀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⢸⣿⣿⣾⣿⣿⣿⠂⣰⡼⡿⠛⢯⣽⠟⠀⠀⠠⠀⠀⠀⠀⠀⠼⠤⠀⣼⣿⣇⠀⠻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣗⢂⡈⡆⣦⣴⣵⣦⣦⣶⣦⠀⠀⠀⠀⠀⢾⡿⣿⣧⣤⠀
⠸⣿⣿⣿⣿⣿⣿⣿⡿⣦⣵⣤⣬⣻⣿⣶⣿⣶⣾⡿⠀⡀⢰⣠⡬⠀⠀⢰⣾⣧⠀⠀⠉⠁⠀⠀⠈⠁⣴⠀⠀⢀⣀⣀⠀⠀⢠⣤⣠⣄⠘⠿⠿⠛⣀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣴⣟⠂⣐⠠⢀⠙⠋⠁⠀
⠀⠐⡿⢉⡠⠁⠀⠀⠁⣾⣿⠿⣿⣿⡿⣧⣈⢿⣏⣅⣀⡀⠘⠛⢡⡇⠀⢀⠹⣿⡛⠀⠀⠀⠀⠀⢠⣾⣯⣶⣿⣿⣿⣿⣿⣶⣝⣿⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⡿⠋⢹⠂
⢠⣷⣧⠛⠐⣂⣤⣦⣼⣶⣧⢤⡸⣈⠄⠛⠉⠀⢟⠉⠋⠀⠐⡻⠏⠂⠰⣿⣇⣹⡃⠀⠀⠘⠛⠒⠒⢻⡟⢻⣿⣿⣿⣿⣟⠛⢧⡛⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤⣽⣿⣷⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⣿⣿⣻⣾⣿⣿⣟⣿⣯⢁⣺⡀⡯⠿⣆⠀⠀⠀⠀⣀⡶⠶⠚⠉⠙⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠸⡁⣿⣿⣿⠀⢨⠯⠾⠋⠃⢈⣿⣿⡿⢿⣿⣿⣿⣿⡏⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⡀⣿⣾⡙⡓⠻⣿⣯⠑⠹⠈⠙⠢⣬⡛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠛⠃⠚⠀⠀⠀⢿⡟⢠⣾⣏⠿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠋⠀⠈⡿⢿⣿⠿⢿⣿⡇
⠀⠁⠘⠋⣑⣥⣮⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⡘⠻⣴⣿⣿⣿⡇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠾⣿⡇
⠀⡀⠐⣐⣯⢿⣟⣻⠿⠛⠀⠚⠀⠀⢠⣄⢀⣄⠀⡀⠀⠠⠀⠀⢀⠀⠀⠀⢠⠄⣀⣄⡠⣄⣀⠂⠴⢊⡑⣄⠀⢠⡶⡰⢄⡀⠀⢠⣤⣬⡶⠀⠐⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣷⣿⠃
⠐⢏⠓⠙⠃⠼⠽⠯⠝⠀⠀⠀⠀⠘⢢⠙⣤⣿⠖⠷⠁⠀⡀⠀⠀⠀⠀⠀⠀⠘⢻⢾⣽⡜⠹⢷⠛⠈⠉⣯⠵⠶⠣⠭⣿⣿⣿⣿⣽⣿⣿⣮⣧⣬⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⡆
⠀⠀⡀⣴⣅⣀⢀⡹⢖⢰⣄⠄⠀⠄⠉⠀⠈⢊⠀⢒⡀⠰⠤⠁⠀⠀⣠⣤⡀⠤⣴⣾⣿⡇⠂⠈⠏⠁⠈⠉⠀⠀⠀⠟⣿⣟⡿⣽⣿⡿⢿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⠿⣻⡈⣿⣷⣞⣿⡇
⠀⠀⠂⠙⠉⣽⡘⢀⡛⠚⠋⣀⡀⣂⢀⡠⠄⣠⣄⣤⣽⣷⣷⣿⣿⣿⡿⣍⠴⣖⠋⠀⠐⠀⠀⠂⠀⠠⣥⠼⠶⣼⠆⡀⠹⠋⢘⣿⣗⡟⢙⣙⢾⣿⣿⣿⣾⡟⠛⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠌⣻⡋⢙⠇
⠈⠀⠚⠃⠀⣈⣗⣸⣲⡄⣔⣊⡓⢖⠐⠈⢀⡹⢓⡿⠿⣿⣿⣿⢿⡯⣩⣭⣬⣿⣿⣷⢶⡆⣴⣄⣦⣤⣶⣤⣼⣥⣶⣻⣦⣄⠀⣼⣿⣛⣿⣹⣿⣿⣿⣿⣟⣾⣲⣿⣶⣿⣯⣷⣘⢛⢻⢡⣩⣿⣯⡟⠉⢼⢿⡿⠿⠄
⠠⠠⠄⠢⠤⠄⠼⠤⠤⠤⠾⠿⠭⠕⠒⠶⠅⠀⠲⠏⠡⠙⠛⠿⠾⠿⠿⠿⠿⠶⠿⠿⠞⠗⠮⠍⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠻⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠤⠾⠿⠿⠿⠿⠌⠆⠐⠉⠁⠾⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⡦⠈⠪⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠃⢿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⠿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠪⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣴⠀⠀⢠⣼⡇⠀⠀⠀⠀⠀⠀⠀⡇⡼⡇⠀⢨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⢟⠟⣿⣟⣟⡛⢿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷⡇⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡖⢻⣿⠇⡬⠀⠴⠷⠖⠀⠀⠀⠈⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⣿⡏⠒⠒⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣇⠀⠀⠻⠿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡏⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣾⣚⣛⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠀⣼⠁⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⢰⢠⣿⡧⠍⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠿⡦⢶⡆⠀⠀⠀⠀⠀⠀⠀⡀⠛⢼⣿⢰⡆⠀⠀⣸⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣾⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⡏⣠⠈⠁⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣾⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠠⠇⣦⠍⠉⠠⠄⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⡬⠀⣇⣤⢁⣀⣀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣾⣿⡯⣷⣨⡟⣻⢻⡛⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⡿⠉⢹⡇⠀⠀⠀⠀⠀⠀⢀⡖⡒⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣿⣿⢸⣿⣿⡇⣿⣿⣇⢻⡆⡈⠉⠛⠻⢿⠁⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⣧⣤⣼⡇⠀⠀⠀⠀⠀⠀⢺⡇⠀⢸⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣷⡿⣿⣿⣿⡷⠃⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⢠⠀⠀⢀⠃⠀⠀⠀⠀⠀⡀⢸⠉⠉⢹⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⢸⣿⣿⣏⣿⣿⣿⣿⡇⣿⣿⣿⣿⢪⡤⠈⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣸⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢸⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡿⣿⡇⣾⣿⣿⣿⣿⣢⣼⣿⡃⣿⣈⡿⠩⢺⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⣾⠁⣿⣿⡇⠑⠻⠻⣿⣿⢀⡁⢉⡁⠐⢸⡇⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣇⣟⣀⣟⣟⡃⢇⣐⣀⣸⡑⠠⠀⢈⡁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣤⣶⠴⢠⡤⠤⠤⣤⡤⠀⠀⠀⠀⠀⠀⢸⠃⢠⠂⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣸⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢀⡀⠀⠀⡼⠀⢙⣀⢠⡀⠀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⠀⢀⣤⣄⡄⠲⠃⢻⣿⣿⣷⣿⣃⡸⣶⢤⠄⠀⠉⠉⠿⠅⢺⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣇⣿⡟⠀⠀⢠⣤⠤⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⡂⣰⠶⡿⠛⣉⣾⠽⠀⠀⢠⣄⠀⠀⠀⠀⠶⠇⠀⣸⣿⡇⠀⢻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢐⣟⢆⡈⠗⣤⣦⣭⣤⣤⣴⣶⡀⠀⠀⠀⠀⢼⡿⣿⣷⣤⠄
⢸⣿⣿⣿⣿⣿⡿⣿⡿⣦⣴⣤⣼⣿⣿⣿⢿⣶⣾⠿⠁⡀⢰⣀⣸⡿⣦⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⢀⣠⣤⣤⣤⣤⣀⠀⣤⣤⣄⠘⠿⠿⠛⣀⣾⣿⣾⣿⣿⣿⣷⣿⣿⣽⣽⣷⣴⡤⣞⠁⣰⢠⢀⠙⠉⠁⠀
⠀⠸⡟⢉⠠⠁⠀⢀⠁⢾⣿⠿⣿⣿⣿⣿⣈⠿⡏⣃⣇⡀⠸⠛⠑⠆⢿⣿⣶⣤⠄⠀⠀⠀⠀⠀⠐⢶⣾⣿⣿⣿⣿⣿⣿⡿⡷⣿⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣶⣷⡟⠋⠻⠇
⢠⣷⣧⠛⢘⣆⣤⣴⣼⣾⣧⣴⢺⣌⡀⠛⠉⠰⢟⠉⢉⢁⣈⡻⠍⣓⠐⣩⡋⠿⠷⠀⠀⠈⠓⢢⣴⣿⡟⣸⣿⣿⠿⠿⣭⡉⢹⣯⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢨⣿⣷⣟⣾⣿⣿⣿⣿⣯⢹⢬⣽⠈⢿⣦⣀⣀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⣼⣿⣿⠀⣠⠟⠾⠏⠁⢈⣿⣿⣿⢿⣿⣿⣿⣿⡏⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⡄⣿⣷⡛⡓⠻⣿⣿⠛⠈⠂⠈⠑⠶⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢿⡟⢠⣾⡯⠽⢿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠋⠀⠉⠻⢿⣿⠿⢿⣿⡅
⠀⠀⠘⠋⣱⣥⣮⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡘⠫⣴⣾⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣾⣿⡇
⠀⣀⠐⣲⡏⢻⣟⣻⠏⠛⠀⠐⠁⠀⢀⣄⢀⣀⢀⡈⠄⠠⠀⠀⢠⠀⠀⠀⢀⠄⣀⣄⠠⣄⣀⠒⠴⢒⡑⢄⠀⣠⡴⡰⢠⡀⢀⢠⣤⣤⣷⡄⠐⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⡇
⠐⢏⠓⠉⠁⠬⠽⠯⠏⠀⠀⠀⠀⠈⢢⠙⡦⣻⠆⠼⠁⢀⡀⠀⠀⠀⠀⠀⠀⠘⢻⢞⣵⡟⠻⢷⢚⠀⠉⢫⠝⠳⠦⠵⣿⣿⣿⣿⣽⣿⣿⣮⣧⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣀⣤⡅⣐⢀⡸⠖⢰⣄⠔⠀⠄⠉⠀⠈⢈⠀⢒⡀⠠⠤⠁⠀⠀⣠⣤⡀⢤⣤⣼⣿⡇⠖⠈⠟⠃⡈⠉⠀⠀⠀⠞⣿⣟⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⣫⣘⣿⣿⣞⣿⡇
⠀⠀⢂⠙⢫⣹⡈⢀⡙⠙⠊⢀⡀⣂⢀⡠⠄⣠⣀⣬⣽⣷⣷⣷⣿⣿⡹⣥⠴⣗⠋⠀⠀⠀⠐⠂⠀⠤⣵⠜⠶⣼⡄⡄⢹⠩⠐⣿⣷⡟⢙⣉⣾⣿⣿⣿⡾⡿⠛⠻⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⢌⢿⡉⢹⠇
⠈⠀⠚⠃⠀⣘⢵⣸⣲⣄⣔⣊⡓⠖⠐⠈⢁⡹⢷⡿⠿⣿⣿⣿⢿⡯⣯⣭⣽⣿⣽⣷⢶⡆⢦⣦⣢⣤⣤⣤⣼⣧⣶⣛⣤⣆⠀⣾⣿⡛⣿⢻⣿⣿⣿⣿⣟⣾⣲⣿⣶⣾⣋⣿⣉⢟⢿⠃⣿⣽⣯⣟⠉⢼⢿⡿⠿⠂
⠠⠠⠄⠢⠤⠤⠼⠤⠤⠤⠾⠿⠯⠅⠒⠶⠅⠀⠺⠎⠹⠙⠛⠿⠾⠿⠿⠿⠿⠧⠾⠿⠞⠷⠮⠍⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠻⠺⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠠⠾⠿⠿⠿⠿⠄⠆⠀⠉⠁⠺⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⡲⠈⠪⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠇⢽⣿⣿⣿⣿⣿⣿⣿⡟⠙⢻⣿⡿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠊⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⡇⣼⡿⠀⢨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⠿⢿⡟⣟⡛⢿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣇⡏⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣖⢻⣿⡇⣬⠀⠴⠷⠶⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⣿⡏⠒⠒⢚⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣇⠀⠀⠹⠿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⠿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡏⠉⢩⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣚⣓⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠀⣸⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⣿⡯⠭⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠈⠀⠿⠶⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠚⢸⣿⣧⡆⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣾⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⢸⡏⢠⠈⠁⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⡿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠠⠇⣦⠍⠉⠠⠄⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⡠⠀⡇⣤⢁⣀⣀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣼⣿⣧⢧⣨⣿⢻⢻⡛⠛⠛⠻⠻⠿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠉⢩⡇⠀⠀⠀⠀⠀⠀⠀⡖⠒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢻⣿⣿⣷⣿⣿⣷⣿⣿⢸⣿⣿⡆⣾⣿⣏⢻⡆⡠⠉⠛⠻⢿⡉⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⣯⣤⣼⡇⠀⠀⠀⠀⠀⠀⢲⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣿⣿⣿⣿⡷⠇⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⢀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣸⡿⢹⣿⣿⣟⣟⢻⣿⣿⡏⣾⣿⣿⣿⢶⡤⠈⠃⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣸⣤⣤⣤⡁⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⣸⣿⣿⣿⣿⢣⣼⣿⡃⣯⣬⡿⠩⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡏⣼⠇⣼⣿⡟⠐⠛⠙⢿⡿⡇⣁⢈⡁⠐⢰⡟⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⡟⣂⣏⣟⣃⣇⣐⣀⣸⡐⠀⠀⢀⣁⠐⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠉⠉⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣥⣴⠤⢠⡤⠤⠤⣤⡤⠄⠀⠀⠀⠀⠀⢸⡇⢠⠀⠐⠀⠂⠀⠀⣀⣀⣀⡀⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣼⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣼⠁⢙⡁⢀⣀⠀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⡀⢀⣤⣄⡴⠖⠏⢻⣿⣿⣟⡛⠓⠰⣶⣄⡄⠀⠈⠁⢻⠓⢾⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣧⣿⡟⠀⠄⠤⢤⡄⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⢸⣿⣿⣾⣿⣿⣿⠀⣰⠦⡿⠊⠉⠄⡻⠑⠀⢰⡄⠀⠀⠀⠇⡰⠆⠀⣸⣿⡇⠀⢻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣷⣀⠀⠀⣄⣢⣶⣤⣤⣴⣶⠀⠀⠀⠀⠀⢸⡿⣿⣷⣤⠄
⠸⣿⣿⣿⣿⣿⡿⢿⡿⣦⣼⣤⣴⣷⣿⣿⢾⣴⣿⠿⠂⡀⢀⣘⣾⢀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⣀⣠⣴⣶⣶⣶⣶⣤⣀⢤⣤⣄⠸⠿⠿⠛⣀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣯⣿⣷⣦⣴⣿⠃⣐⠀⠀⢉⠋⠁⠀
⠀⠀⠟⠋⡠⠅⠀⠀⢒⢼⡿⡿⣿⠿⣿⣿⣌⢿⣏⣭⣄⠂⠸⢏⣡⠤⣴⣶⢶⣶⡄⠀⠀⠀⣀⠀⠀⢀⣿⠿⣿⣿⣿⣿⣿⣟⣏⠾⣿⣿⣟⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣽⣶⣿⡿⠋⠛⠂
⢠⣷⣾⡜⠂⣂⣠⣰⣶⣴⡷⣚⡽⡦⣄⠙⠉⠁⠝⠉⡫⠄⠐⠛⠉⠀⠒⠶⠍⠉⠁⠀⠀⠀⠀⠀⢠⡼⡟⢠⣿⣿⠛⠛⣷⠄⣸⣶⢺⣿⣭⣿⣿⣯⣽⣿⣿⣿⣿⣿⣷⣠⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⢸⡟⡟⣟⣷⣿⣿⣿⣿⣯⠉⠏⠙⢀⣙⠛⠋⠁⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⠿⠟⠀⢰⡒⢒⠃⠀⢘⣽⣿⣿⢿⣿⣿⣿⣿⣏⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠂⣻⣿⡟⡛⠛⣿⣿⠓⠀⠀⠀⠀⠈⠉⠑⠒⠂⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢡⣾⣯⡽⢿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡋⠀⠈⠻⠿⣿⠿⢿⣿⡇
⠀⠀⠘⠉⣱⣥⣮⡿⣿⣶⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣘⠻⣴⣾⣿⣷⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⡇
⢀⣀⡰⢒⣯⠹⣟⣻⠯⠛⠀⠐⠃⠀⢀⣄⣀⣠⢀⡈⠄⠠⠀⠀⢀⠄⠀⠀⠀⠤⢀⣀⣠⣄⣀⠐⢴⢖⡙⢦⠀⠠⡶⢰⢀⣀⠀⣠⡤⣤⣤⡄⠐⢶⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⠇
⠐⢯⠓⠉⠁⠰⢹⠯⠕⠀⠀⠀⠀⠈⢃⠙⣢⣹⠖⣼⡉⢀⡀⠀⠀⠀⠀⠀⠀⠐⢿⠟⣽⡖⢻⠷⡞⠉⠉⣫⡵⠷⢢⢬⢿⣿⣿⣿⣿⣿⣿⣮⣧⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆
⠀⠀⢀⣴⣄⢀⢈⡸⠲⢸⣄⠔⠀⠄⠈⠀⠈⢊⠁⢒⡀⠠⠄⠁⠀⠀⢠⣤⠀⠠⣤⣦⣿⡗⠜⠀⠟⠃⠨⠉⠀⠀⢀⠞⢿⣟⡿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣘⣻⣿⣾⣿⡇
⠀⠀⠓⠙⠉⢹⡌⠀⡙⠘⠊⢀⡀⣂⢀⣠⠄⣠⣤⣨⣽⣿⣾⣷⣿⣿⣸⣫⡰⢶⡋⡀⠀⠆⠀⠒⠀⠄⣶⡘⠶⣾⡎⣀⢸⠛⠚⢽⣷⡟⢙⣍⣿⣿⣿⣿⣿⣿⠛⠛⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠌⣽⡋⢻⠇
⠈⠀⠛⠓⠄⢐⣽⣪⣷⣄⣔⣊⡛⠶⠐⠈⢁⡹⢷⡿⠿⣿⣿⣿⣿⡿⢯⣭⣭⣿⣿⣷⠶⡆⢤⣤⣲⣤⣴⣤⣴⣧⣴⣛⢤⣤⠀⣼⣿⣛⣿⣻⣿⣿⣿⣿⣟⣷⣐⣿⣶⣿⣯⣽⣋⠿⠟⠋⣩⣿⣫⣿⠉⢸⢿⡿⠿⠆
⠠⠠⠄⠂⠤⠤⠼⠤⠤⠤⠾⠿⠯⠭⠒⠶⠍⠀⠚⠏⠹⠈⠛⠿⠯⠿⠿⠿⠿⠷⠾⠿⠿⠷⠾⠏⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠻⠺⠯⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄⠶⠾⠿⠿⠿⠁⠆⠐⠙⠁⠻⠇
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⣿⡷⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣛⡛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⡲⠈⠪⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠇⢼⣿⣿⣿⣿⣿⣿⣿⡟⠙⢻⣿⠿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠊⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⢠⣬⡇⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⠿⢿⡟⣟⡛⢿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣇⡏⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣖⢻⣿⡇⣬⠀⠴⠷⠶⠂⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⣿⡏⠒⠒⢚⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⠀⠐⠙⠿⠿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⠿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡏⠉⢩⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣚⣛⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡤⣤⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⢸⠇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⣿⡯⠭⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠿⠶⢴⡆⠀⠀⠀⠀⠀⢀⠀⠀⡚⢸⣿⣧⡆⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣾⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡆⢸⡏⢠⠈⠁⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⡿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠇⣦⠍⠉⠀⠄⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⡠⠀⣇⣠⣁⣀⣀⡀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣼⣿⣷⢧⣨⣟⢻⢻⡛⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠉⢩⡇⠀⠀⠀⠀⠀⠀⠀⡖⠒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢻⣿⣿⣷⣿⣿⣷⣿⣿⢸⣿⣿⡇⣾⣿⣟⣻⡄⡤⠉⠛⠻⢿⡉⠀⠈⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⣯⣤⣬⡇⠀⠀⠀⠀⠀⠀⢲⡇⠀⢸⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣿⣾⣿⣿⢷⠇⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡿⢹⣿⣿⣟⣟⠹⣿⣿⡏⣾⣿⣿⣿⣤⡤⠉⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣸⣤⣤⣤⡃⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡗⢸⣿⣿⢿⡿⢣⣼⣿⡇⣿⢸⡿⠩⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣸⠇⣼⣿⢼⠸⠻⠻⢿⡿⡇⣁⢨⠁⠰⢰⡟⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⡟⣂⡏⣟⣃⣄⣄⣀⣸⡓⠀⠀⢀⣁⠐⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣼⠀⠀⠀⠉⠉⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣥⣴⠴⠤⡤⠤⠤⡤⡤⠄⠀⠀⠀⠀⠀⢸⡇⢠⠀⠐⠀⠂⠀⠀⣀⣀⣀⡀⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣸⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⢸⠃⢈⠁⠀⠀⢀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⠀⣀⣤⣄⣒⠙⠫⣿⣿⣷⣚⡇⠲⣶⢤⡤⠀⠈⠁⠻⠶⢿⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣧⣿⡟⠀⠤⠀⠀⡄⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀
⢸⣿⣿⣾⣿⣿⣟⡀⣠⠦⠿⠉⠉⣝⡛⠁⠀⠨⣆⢀⠀⠀⡴⡐⠖⠀⣼⣿⡇⠀⢻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⡷⠂⡀⠁⣄⣠⣷⣦⣤⣴⣶⠌⠀⠀⠀⠀⢸⡿⣿⣿⣠⡄
⠸⣿⣿⣿⣿⣿⡿⣿⣿⣶⣼⣤⣤⣵⣿⣿⣾⣷⣿⡿⠐⡀⢠⣰⣮⡤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⣠⣴⣶⣷⣾⣿⣷⣶⣤⣀⣤⣤⠸⠿⠿⠛⣀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣽⣯⣵⣦⡴⣖⠋⣸⠢⠄⠈⠉⠉⠀
⠀⠀⠟⢋⡠⠅⠀⠐⢒⣾⣿⡟⣟⣛⠛⢿⣈⢿⣇⣸⣤⠃⢸⣹⡁⢀⣁⣴⡿⣷⡀⠀⠀⠀⠠⠀⠀⢠⣿⠟⣿⣿⣿⣿⣿⣿⣻⠹⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣽⣶⣾⡿⠋⠛⠇
⢰⣷⣿⡜⠂⣂⣤⢴⣽⣤⣯⠴⠿⠋⠻⡶⠬⠠⠽⠗⠋⠀⠀⠀⠀⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠤⣾⡟⢰⣿⣟⠋⠛⢷⠄⣠⢷⢻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⢤⣼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⢸⣟⣟⣟⣷⣿⣿⣟⣿⣿⠋⠉⠀⠈⠲⠤⣀⣀⢀⣀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠘⠋⠃⠀⠀⠈⢙⠂⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣏⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇
⠀⠂⣻⣿⡿⡗⠚⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢩⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠈⠉⣿⣿⣿⠿⢿⣿⡁
⠀⠀⠘⠋⣱⣧⣦⡿⣿⣶⡦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠌⣈⡻⢿⣿⣿⣷⡟⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣦⣿⡇
⢀⣠⡀⢂⡧⠼⣿⣻⡿⠛⠁⠐⠃⠀⠀⣄⢀⢠⠀⡈⠄⠀⠀⠠⢀⠄⠀⠀⠂⡦⢠⣄⣄⣄⣄⡐⢤⣶⡙⢦⡀⢤⣶⢶⢠⣄⠀⣠⡤⣤⣤⡄⠘⢶⣾⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠇
⠐⢯⠘⠪⠁⠰⢻⢯⠅⠀⠀⠀⠀⠈⢃⠘⣢⣸⠶⡹⠍⢀⡀⠀⠐⠀⠀⠀⠀⠐⢿⡿⣹⡿⢻⠷⡞⠋⠉⣹⣵⠷⢶⢼⣿⣿⣾⣿⣿⣿⣿⣾⣵⣤⣿⣯⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢀⣠⣄⢀⠀⡸⠶⠸⣄⠠⠀⠤⠈⠀⠠⢈⠃⢲⣄⠠⠄⠂⠀⠀⢠⣦⠄⠤⣤⣦⣿⡗⠜⠀⡟⠃⠈⠉⠁⠀⢃⠞⢿⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣙⣯⣿⣿⣿⡇
⠀⠀⠒⠙⠉⢹⡜⠁⡙⠙⠋⢀⡀⣂⢀⣠⠄⣀⣀⣤⣽⣷⣶⣿⣿⣿⣹⣯⡰⠶⡋⡀⠀⠇⠀⠓⠀⠤⣾⡺⠶⣾⡟⣂⢸⠙⠜⣽⣿⣏⢙⣉⣹⣿⣿⣿⣿⣿⠟⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠌⢽⡏⣹⠇
⠀⠄⠓⠃⠅⢐⣽⣪⣷⣄⣄⣢⣛⠾⡀⠈⠃⡹⢳⡿⠿⣿⣿⣿⡿⡿⢿⣭⣟⣿⣿⣿⠶⡆⣤⣶⣲⣤⣴⣤⣴⣥⣴⣚⢦⣤⠀⣼⣿⣛⣿⣟⣿⣿⣿⣿⣟⣷⣐⣾⣶⣿⣯⣽⣫⡛⠛⠋⣩⣽⣯⣿⠉⢸⢿⡿⠿⠇
⠠⠤⠄⠂⠤⠤⠼⠤⠤⠤⠶⠿⠿⠬⠒⠴⠫⠀⠒⠏⠹⠌⠿⠿⠯⠿⠿⠿⠿⠷⠾⠿⠿⠷⠾⠏⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠻⠺⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠄⠶⠾⠿⠿⠿⠁⠆⠀⠉⠁⠺⠅
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⣿⡷⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣛⡛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⡲⠈⠪⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠇⢼⣿⣿⣿⣿⣿⣿⣿⡟⠙⢻⣿⠿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠈⠊⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣤⠀⠂⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⠿⢿⣟⣟⡛⢿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣇⡏⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣖⢳⣿⡇⣬⠀⠴⠷⠶⠂⠀⠀⠀⠁⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⣿⡏⠒⠒⠒⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣷⠀⠀⠙⠿⠿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⣿⠿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢠⣿⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡏⠉⢩⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⣚⣛⣁⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣤⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⢸⠇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⣿⡯⠭⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠈⠀⡿⡶⢴⡆⠀⠀⠀⠀⠀⢀⠀⡀⡘⢸⣿⣧⡆⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡆⢸⡏⢠⠀⠁⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⡿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠇⣦⠍⠉⠀⠄⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣤⣂⠀⠀⣠⠁⣇⣠⣁⣀⣀⡀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⢿⣠⣿⢻⢻⡟⠛⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⣼⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⡖⠒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢻⣿⣿⣷⢿⣿⣷⣿⣿⢸⣿⣿⡆⣾⣿⣟⡛⡦⠠⠉⠛⠻⢿⡉⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣤⣤⡇⠀⠀⠀⠀⠀⠀⢒⡇⠀⢸⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢷⠅⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠉⠉⢙⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣸⡿⢺⣿⣿⣿⣹⡿⣿⣿⡏⣼⣿⣿⣿⢷⡤⠉⠃⠙⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣤⣤⣤⡃⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⢸⣿⣿⢿⣿⣧⣼⣿⡇⣯⣸⣿⠫⠄⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣿⣻⡇⣸⣿⣸⠘⠻⠻⢿⣿⡇⣃⢨⠁⠘⢰⡟⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣟⣟⡇⣞⣿⣃⠀⣐⣀⣸⡃⢀⢀⢀⣀⠐⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣼⠀⠀⠀⠈⠉⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣭⣴⠶⠤⣤⠤⠤⣄⡤⠄⠀⠀⠀⠀⠀⢸⡇⢠⠀⠐⠀⠂⠂⠀⣀⣀⣀⡀⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣼⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⢸⠃⠘⠃⢀⣀⠀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣀⢀⣠⣄⣀⡰⠘⠙⣿⣿⣿⡚⣟⠰⣶⣤⡀⠀⠈⠁⢻⠶⢷⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣧⣿⡟⠀⠀⢀⣠⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⡁⣠⡆⢿⠛⠭⢍⡿⠓⠀⢠⡅⡀⠀⠀⢶⡄⠎⠀⣼⣿⡇⠀⢻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢐⣿⠂⡀⠃⣄⢠⣼⣦⣤⣦⣷⡈⠀⠀⠀⠀⢸⡿⣿⣿⣠⡄
⠸⣿⣿⣿⣿⣿⣿⣿⡿⣶⣌⠀⠀⡩⢱⣶⢶⣶⣿⠿⠶⡔⢀⣤⣤⡀⠀⠀⣀⡤⠄⠀⠉⠁⠀⠀⠈⠁⢰⣶⣿⣿⣾⣿⣿⣶⣶⣄⣤⣄⠸⠿⠿⠛⣀⣾⣷⣶⣿⣿⣿⣿⣽⣿⣿⣟⣿⣶⣤⡞⡃⣑⠀⢀⣈⠋⠉⠀
⠀⠀⠿⡏⡠⠅⠀⠀⢒⢾⣿⣿⢿⠻⢷⣥⣀⣻⠻⣟⡣⠥⠐⠛⠃⠀⣤⣶⣿⣧⠀⠀⠀⠀⠠⢀⠀⢠⣿⠟⣿⣿⣿⣿⣿⣻⡻⠙⢿⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣶⣷⡿⠋⢛⠇
⢠⣧⣶⡟⠂⣆⣤⣸⣼⣦⣿⠔⡛⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠈⠀⠸⢏⢰⣿⣟⠋⠉⢣⠄⣠⢿⢻⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⡦⣼⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⢸⡏⣟⣟⣷⣿⣿⣟⣿⣿⠋⠀⠀⠀⠀⠙⠒⠄⣀⣠⡴⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠉⠀⠀⠈⠘⠀⠀⠸⣿⣿⣿⢿⣿⣿⣿⣿⣟⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⠃⣻⣿⣟⡟⠺⢿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡋⠀⠉⡿⠷⣿⡿⢿⣿⡇
⠀⠈⠘⠉⣱⣧⣦⡿⣿⣶⣦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⣈⡛⢽⣿⣿⣿⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡇
⠀⢠⡀⢒⣯⠝⣿⣻⡿⠛⠁⠐⠋⠀⠀⣄⣀⣤⠀⡈⠀⠀⠀⠠⢀⠄⠀⠀⢰⡤⢀⣄⣠⣄⣀⡐⢠⢶⣉⢦⡀⢤⣶⢲⠠⣀⠀⣠⡤⣠⣤⡄⠀⢶⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠐⢫⡓⠉⠋⠸⠻⢫⠗⠀⠀⠀⠈⠉⢓⠜⣣⣹⠷⠹⠏⣀⡀⠄⠐⠀⠀⠀⠈⠱⢿⡿⣻⡿⢻⡷⡟⡋⠉⣹⡽⠷⢦⢬⣿⣿⣿⣿⣿⣿⣿⣶⣵⣤⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢀⣠⣄⢀⠀⣙⠶⠸⣤⡠⠀⠤⠈⠀⠠⠈⡃⢲⣠⠀⠆⠂⠀⠀⣠⣦⡄⠀⣴⣦⣿⡟⠖⠉⡿⠓⢨⠉⠀⠈⢚⠞⢿⣟⣿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣸⣿⣿⣿⣿⡇
⠀⠀⠐⠘⠉⠽⡞⠁⡙⠙⠊⢀⡀⣀⢀⣠⠄⣀⣀⣤⣽⣿⣶⣿⣿⣿⣹⣯⡴⠶⡋⡀⠀⠇⠀⠟⠂⠤⣿⡖⠷⣾⡏⣂⢺⠉⠊⣽⣿⣏⠙⣙⣽⣿⣿⣿⣾⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠎⣹⡯⢹⠇
⠈⠄⠓⠛⠄⢐⣽⣪⣷⣄⢄⣢⣛⠾⡐⠈⠃⡸⢳⡿⠿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⡶⡖⢶⣶⣲⣤⣼⣤⣴⣧⣴⣚⢶⣴⡀⣼⣿⣛⣾⣿⣿⣿⣿⣿⣟⣷⣐⣿⣶⣿⣿⣹⣻⠟⠟⠋⣰⣽⣫⣽⠙⢮⠿⡿⠿⠇
⠠⠤⠄⠀⠤⠤⠼⠤⠤⠤⠶⠿⠿⠬⠒⠴⠫⠀⠒⠯⠹⠍⠿⠿⠯⠿⠿⠿⠿⠷⠾⠿⠿⠷⠺⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠺⠯⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠶⠾⠿⠿⠿⠍⠆⠐⠩⠅⠸⠄
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡿⣿⡷⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣛⡛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⡲⠈⠪⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⠿⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠊⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠀⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢟⠿⢿⡟⣟⡛⢿⠿⠿⠿⠿⠿⡿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣄⡏⣽⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣖⢳⣿⡇⣬⠀⠴⠷⠶⠂⠀⠀⠀⠉⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⣾⡏⠒⠒⠒⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣽⠀⠀⠙⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢳⡿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡏⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣸⣚⣛⣃⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣦⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⡿⠭⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⢾⡶⢴⡆⠀⠀⠀⠀⠀⢀⠀⡀⡘⢰⣿⣇⡆⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠆⢸⡎⢠⠀⠁⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⡿⣾⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠂⠆⣠⡌⠉⠀⠄⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣶⡄⣆⠀⠀⣠⠁⣇⣠⡅⣈⣀⡀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣷⢹⣄⣿⢻⢻⡟⠛⠛⠻⠻⠿⠿⠿⠿⠿⣿⣿⠂⠀⠀⠀⠀⠀⢸⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⣶⠒⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣿⢫⣿⣿⣷⢿⣿⣷⣿⣿⢸⡿⣿⡧⣼⣿⡿⡙⡶⢠⠉⠛⠛⠿⡏⠁⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣤⣤⡇⠀⠀⠀⠀⠀⠀⠒⣇⠀⢸⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢿⣿⢼⣿⣿⣿⢹⣿⣿⣿⣿⢸⣫⣿⣿⣿⣿⣿⣿⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠉⠉⠙⡇⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢸⣿⢸⣿⣿⣿⣸⠿⣿⣿⡟⣼⣟⣿⣷⠷⣤⠉⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⣀⣥⣤⣤⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣾⣿⢸⣿⣿⢻⡿⢃⣼⣿⡇⡏⢥⣿⠃⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡇⢸⣿⣸⠘⠓⠓⢿⣿⠇⣃⠈⠉⠸⢲⣿⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠨⡟⣛⡇⣸⣿⣋⢀⢀⣀⣠⡃⢀⠀⢀⣀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠈⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣬⣦⣤⠤⠤⣤⠤⠤⣤⡤⠄⠀⠀⠀⠀⠀⢸⡇⢠⠄⠐⠀⠀⠂⠐⣀⣀⣀⡄⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣼⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⢸⠃⠉⠃⠀⠄⠀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⢀⣠⡀⣠⡴⠚⠹⣿⡿⣿⣚⠃⠰⣶⠤⡄⠀⠈⠉⠾⠖⢱⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣧⣿⡟⠀⠀⡀⣠⡄⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀
⢸⣿⣯⣿⣿⣯⣛⡃⣀⡆⢾⠂⠂⠄⠏⠑⠀⠠⡄⠀⠀⠀⠁⡀⠞⠀⣸⣿⡇⠀⢻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢠⣷⣂⡀⠀⣠⠤⣺⣤⠤⣤⣧⠀⠀⠀⠀⠀⢰⡿⢿⣿⣠⡄
⠸⣿⣿⣿⣿⣿⡿⢿⡿⢦⣌⣠⡀⣴⣷⣔⡰⣦⣴⡿⣀⡐⠀⣵⣴⡀⢀⡀⣀⣤⠖⠀⠉⠁⠀⠀⠈⠁⣠⣶⣿⣷⣾⣿⣿⣾⣷⣦⣀⣄⠸⠿⠿⠛⣀⣾⣷⣾⣿⣿⣯⣿⣯⣭⣤⣬⣽⣦⡤⡦⠁⢀⠀⢀⣈⠉⠉⠀
⠀⠀⠻⡏⡠⠏⠀⠀⠁⢺⣿⣿⡿⠧⠺⠍⠈⠁⠁⠈⠒⠀⠈⠁⠀⠁⠾⣿⣋⡃⠀⠀⠀⠀⠀⠄⡀⢀⣿⠏⣻⣿⣿⣿⣿⣻⡛⠈⢻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣶⣾⣿⠋⠉⠂
⢠⣧⣾⡟⠂⡆⡠⢰⠶⣤⣧⢠⣧⠏⠙⠶⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢠⣿⡟⠁⠁⠣⠄⠀⠿⢻⣿⣯⣿⣿⣯⣽⣿⣿⣿⣿⣿⣖⡦⣴⣿⣶⣶⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⡏⣟⣟⣷⣿⣯⣜⣿⣿⠋⠀⠀⠀⠀⠀⠈⠑⠢⠤⣶⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠨⣿⣿⣿⠿⣿⣿⣿⣿⣯⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡇
⠀⠂⣱⣾⣛⡗⠘⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡿⠁⡵⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠀⢉⣿⠷⣿⡟⠿⣿⡇
⠀⠈⠘⠙⢙⢯⣦⡿⣿⣶⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢈⡙⢿⣿⣿⣿⡏⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣖⣿⡇
⢀⣠⡀⢂⣏⠼⡿⣫⡿⠛⠃⠴⠋⠀⢠⣄⣀⣠⣄⣈⠠⠀⠂⠠⠀⠄⠀⠀⢂⣤⢀⣄⣀⣄⣀⡐⢰⢖⣉⢦⡀⣆⣶⢲⡦⣄⠀⡠⡄⢄⣠⡆⠀⢶⣶⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠐⢚⠑⠈⠉⠰⢨⢫⠅⠂⠀⠀⠀⠀⠓⡜⢣⣸⠷⠹⠎⢀⡀⠀⠐⠀⠀⠀⠀⠰⢿⡿⣻⡿⢻⡿⡟⡛⠉⢹⡽⠷⠶⠬⢿⣿⣿⣿⣿⣿⣿⣷⣽⣤⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆
⠀⠀⢀⣠⣄⢀⠀⣈⠆⣘⣤⡠⠀⠠⠈⠀⠀⠁⡃⠺⣥⠀⠆⠀⠀⠀⢀⣦⠀⠠⣴⡦⣿⠛⠐⠁⢹⠓⢨⠁⠀⠈⢘⠝⣿⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣡⣿⣿⣿⣻⡇
⠀⠀⠐⠘⠉⠘⡞⠁⡙⠉⠊⢀⡀⢐⠀⣀⠤⣀⣄⣠⣽⣿⣶⣾⣿⣿⣹⣻⡥⠶⡋⡀⠀⠂⠀⠂⠀⠄⢼⡒⠶⣦⡷⣃⢸⠋⠊⣽⣿⡟⠉⣉⢳⣿⣿⣿⣿⣿⠟⢛⠟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠎⣹⡟⢘⡃
⠈⠄⠓⠛⠄⢐⣽⣪⣷⣄⢤⡐⡙⠾⡀⠈⠉⡨⠳⡘⠿⣿⣿⣿⡿⡾⢸⣭⣭⣿⣿⣿⡶⣖⢶⣤⣲⣤⣼⣤⣴⣿⣼⣚⢶⣴⡀⣸⣿⣛⢾⣛⣷⣿⣿⣿⣿⣴⣐⣾⣶⣿⣽⣹⢪⢛⡛⠃⢰⣹⣫⣿⠉⠒⠿⡿⠻⠃
⠠⠤⠄⠀⠤⠤⠼⠤⠤⠤⠶⠿⠯⠬⠒⠴⠫⠀⠒⠦⠩⠍⠻⠿⠧⠷⠷⠿⠿⠿⠾⠾⠿⠡⠺⠏⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠺⠟⠷⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠅⠶⠿⠿⠿⠿⠁⠦⠐⠀⠀⠼⠆
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⣿⣷⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠪⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣳⠈⠓⢙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠲⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⠿⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠂⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⢟⠿⢻⣟⣟⣛⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏⢹⠀⠰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⢛⣿⡇⣬⠁⠴⠿⠿⠃⠀⠀⠀⠁⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⣼⣯⠁⠒⠒⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⠀⠀⠘⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢃⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡿⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⢸⠛⢛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⢶⣶⣿⡃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⡿⠬⠀⠀⢀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠼⠷⢰⡎⠀⠀⠀⠀⠀⠀⠀⢀⡘⢠⣿⡇⡆⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⢰⢸⡇⢰⠀⠉⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠂⠆⢠⡌⠉⠀⠤⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣶⣄⣆⠀⠀⣠⠁⣇⣠⡅⣈⣀⣀⣈⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣿⣷⢹⣤⣿⢻⣟⣟⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⣶⠒⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣇⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣷⢸⣿⣿⣙⡇⡀⠉⠙⠛⠿⡏⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⡼⣤⣤⡇⠀⠀⠀⠀⠀⠀⠒⣇⣀⣸⡇⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣸⣿⣿⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠉⠉⠉⡇⠀⠀⠀⠄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢸⣿⢺⣿⣿⣿⢸⡟⣿⣿⣿⢸⡟⣿⣿⠧⣤⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣥⣤⣤⣇⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣼⢿⢸⣿⣿⢿⣿⣗⣤⣿⡇⣾⢢⣿⠃⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⡿⡇⢸⣿⣸⠈⠇⠛⠿⣿⡇⣃⠈⠉⢈⠐⣿⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡿⣷⡃⣸⣿⣋⡀⣀⣀⣀⣇⢀⠀⢀⠀⠀⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣭⣬⣴⡦⠄⡤⠤⠤⢤⡤⠄⠀⠀⠀⠀⠀⢰⡇⢰⡆⠀⠀⠀⠀⠀⣀⣀⣀⡄⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣼⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠇⠈⠁⢀⣄⡀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣹⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⠀⣠⣄⡀⠤⠂⠙⢿⣿⣿⣘⠛⠰⣶⡆⠀⠀⠈⠉⠿⡖⠩⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣧⣿⡟⠀⠠⢀⡀⡤⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀
⢸⣿⣿⣿⣿⣯⣿⡁⢀⡆⢺⠀⠡⠄⣭⣬⡀⠀⣖⠀⠀⠀⠀⠀⠖⠀⣸⣿⡇⠀⠻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢠⣿⢧⣀⢁⣤⣀⣶⣦⣴⣶⣷⠀⠀⠀⠀⠀⢰⡿⢿⣿⣤⡄
⠸⠿⣿⣿⣿⣿⠿⢿⣿⢷⣴⣤⣤⣤⣫⣟⠙⠒⠋⠉⠀⠀⣀⣶⠧⣤⣄⢀⣔⠒⡶⠂⠉⠁⠀⠀⠈⠁⣠⣶⣿⣷⣶⣿⣿⣾⣿⣦⢀⣄⠸⠿⠿⠛⣀⣼⣿⣿⣿⣿⣿⣶⣼⣿⣽⣿⣿⣤⣤⡂⠀⢀⠀⠀⣈⠉⠉⠀
⠀⠀⠛⡏⡠⠌⠀⠀⠀⠼⣿⠿⠛⡛⢉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣌⡄⠀⠀⠀⠀⠐⠤⠀⢀⣿⠏⢻⡿⢿⣽⣿⣟⡛⠈⢻⣿⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠻⣿⣿⣿⣷⣿⣶⣶⣿⢂⠉⠃
⢠⣧⣾⣟⠃⠂⣀⣰⡾⣶⣷⡤⡾⠃⠀⠃⠘⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢿⡟⠋⠉⠃⠄⠀⠼⢻⣿⣦⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⡲⣶⣿⣷⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⣿⢿⢺⣻⣿⣿⣮⣳⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠾⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠿⣿⣿⣿⣿⣿⢿⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⣿⣿⣿⣿⡇
⠀⢀⠠⡘⠌⢛⠘⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡿⠁⡶⣽⡿⢿⣿⣿⣸⢿⣿⣿⣿⣿⣿⣿⣿⣎⠉⠀⠀⣉⠯⣿⡟⠿⣿⡇
⠀⠀⠈⠁⢁⣯⣦⣽⣿⣷⣦⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠵⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡖⢿⡇
⢀⢀⡀⢀⣞⠈⢼⣋⡿⠛⠃⠀⠋⠀⠀⣤⣀⣠⡄⣈⠡⠀⠂⠀⠀⡄⠀⠀⠀⡠⢀⣠⡀⢤⣀⡀⢰⣞⡉⠣⡂⠠⣶⢂⢂⢀⠀⠠⡄⢠⣴⠆⠀⠰⣶⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠇
⠈⠪⡝⠀⠉⠀⠒⢿⡍⠀⠀⠀⠀⠀⠑⡌⢱⣸⠟⠫⠈⣀⣀⠀⠐⠀⠀⠀⠀⠀⠻⠷⣩⡟⢻⡿⡟⡋⠉⢹⡭⠷⠲⠤⣼⣿⣿⣿⣯⣿⣿⢷⣬⣤⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡀
⠀⠀⢀⣠⣦⢀⡀⣀⠷⠠⣧⡠⠀⠠⠈⠀⠀⠀⠁⠙⡀⠀⠆⠈⠀⠀⢀⣦⡀⠠⢴⡦⢿⡯⠒⠀⠹⠉⠠⠁⡀⠀⠀⠙⢯⣟⣻⣯⣿⣿⢾⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⡿⣫⢅⣳⣿⣾⢻⡇
⠀⠀⠐⡈⠋⠟⣖⠃⣈⠙⠃⢀⡀⢐⠀⢠⡤⢀⣤⣠⣶⣿⣿⣿⣿⣿⣽⣿⡄⠶⡋⡀⠀⠂⠀⠀⠀⠀⢸⡹⠓⢮⠖⢁⠨⠉⠂⢸⣿⣟⢙⣗⢹⣿⣿⣿⣿⣿⠛⢛⠋⡿⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⡖⣩⣛⣘⡃
⠈⠁⠐⠛⠤⢀⣨⣢⣷⣆⢤⡐⡙⠿⠀⠂⠁⡈⠛⠞⠿⢿⣿⣿⡟⣿⢡⣮⣭⣽⣯⣿⡖⣶⠲⣶⣖⣤⣴⣦⣴⣷⣴⣺⣷⣶⡀⢠⣿⢟⢿⣽⣿⣿⣿⣿⣿⣰⣄⣾⣶⣿⣩⣹⢢⠟⠛⠃⣐⣼⣯⡽⠛⠑⠿⠿⠻⠃
⠠⠤⠤⠀⠤⠄⠼⠤⠤⠤⠶⠿⠯⠬⠖⠶⠫⠀⠰⠦⠨⠏⠙⠯⠷⠿⠿⠿⠿⠷⠾⠿⠿⠷⠼⠿⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠪⠟⠷⠽⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠥⠶⠾⠿⠿⠟⠡⠰⠐⠀⠀⠸⠆
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⢿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠪⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢗⠌⠑⢉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠒⠂⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠇⠸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠛⣿⠿⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠁⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⣶⣎⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢟⡻⢻⣿⣿⣛⢻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⡚⣿⡏⣰⠁⠴⠿⠶⠋⠀⠀⠀⠁⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠓⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⠀⠀⠈⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣿⣿⣿⡟⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⢸⡟⠋⠉⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣶⢶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⠀⢸⡇⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⢨⣶⣿⡿⠬⠀⠀⢀⠀⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠸⠷⠲⡾⠀⠀⠀⠀⠀⠀⠀⢀⡘⢡⣿⡧⡖⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣦⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⢸⣏⢠⠄⠉⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠂⠎⢰⡌⠉⠀⠦⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣾⣏⣿⣿⣿⣿⣿⣿⣿⣷⣤⣅⠀⠀⢰⠁⣬⣠⡄⣀⣀⣀⣈⣉⣉⣉⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⡇⣯⣿⡷⢹⣦⣿⢹⣟⣟⢛⠛⠛⠛⠛⠛⠿⠟⠻⣿⣿⡇⠀⠀⠀⠀⠀⢸⠋⠋⣿⠀⠀⠀⠀⠀⠀⠀⣶⠛⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⢸⢿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣾⣿⣇⣿⣿⣷⢸⣿⣿⣘⡗⠆⠈⠉⠛⠿⡏⠀⠀⠉⣽⣿⣿⠃⠀⠀⠀⠀⠀⡸⠤⢤⡿⠀⠀⠀⠀⠀⠀⠂⣿⣀⣀⡇⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣾⣻⣿⣿⢿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠏⠉⠉⡇⠀⠀⠀⠇⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢰⣿⢸⣿⣿⣿⢹⣿⢿⣿⣿⢸⣿⢿⣿⡇⣤⠀⠑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣧⣤⣤⣇⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣼⡿⢸⣿⣿⢿⡻⡿⣦⣿⡏⣸⢣⣿⠃⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⢸⣿⣙⠀⠏⠙⠻⢿⡇⣏⠀⠉⠈⠑⣿⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⡀⣸⣻⣋⣀⣀⣀⣀⣗⠂⠃⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣥⣮⣶⡶⠆⠴⠤⠤⠤⡤⠄⠀⠀⠀⠀⠂⠀⡏⢠⡆⠀⠂⠀⠀⠀⣀⣀⣀⡄⢀⣠⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣼⣿⣇⢀⣀⠀⣀⣀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⡀⠀⠀⠰⠇⠈⢁⣀⢀⠀⠀⠀⢸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣻⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⠀⣤⣄⣀⢐⠀⠉⢿⣿⣿⡝⠁⠐⡒⠀⠀⠀⠀⠁⠈⠂⠈⠀⢺⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣧⣿⡟⠀⠠⠀⢠⣀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀
⢸⣿⣿⣿⣿⣧⣿⡷⢀⡆⠸⠃⠑⢀⠀⢼⡿⠦⡀⠀⠀⠀⠀⠀⠚⠀⣼⣿⡇⠀⢻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⣏⣀⢀⣠⣠⣤⣥⢴⣶⣶⠀⠁⠀⠀⠀⠰⡿⢿⣿⣤⡄
⠸⠿⣿⣿⡿⣿⠿⢿⣿⠷⣤⣦⣤⣤⣤⡾⠁⠀⠀⠈⠀⠄⠀⠢⣾⣶⣄⠀⠀⠀⢀⠾⠛⠁⠀⠀⠈⠁⢠⣶⣿⣿⣶⣿⣷⣾⣿⣶⡀⣄⠸⠿⠿⠛⣀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣷⣶⣤⣞⡋⢀⡃⠀⣈⣉⠉⠀
⠀⠀⠸⡋⠠⠌⠀⠀⠠⢚⣿⠿⡛⡛⠻⠧⠗⢰⢤⡀⠀⠀⠀⠀⠀⠉⠛⠷⢠⣀⠁⠀⠀⠀⠀⠂⠄⢠⣿⠏⢹⡿⠿⣹⡿⠿⠿⠋⠛⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣽⡿⢿⣿⣿⣿⣿⣿⣷⣶⣿⠉⠈⠂
⢰⣧⣾⣟⠃⢂⣠⣰⡶⣧⣾⡄⡾⠗⠀⠀⠀⠀⠀⠳⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⠚⠛⠋⠀⠀⠔⢛⣿⣧⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⡰⢶⣿⣷⣶⣾⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡀
⢸⡿⢿⢻⣻⣿⢿⣿⣛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⢹⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢁⠬⡬⢉⢛⠘⢻⣿⡉⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡿⣿⠉⡼⣿⣿⠿⣿⡿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣀⠀⣽⠛⣿⡟⠻⣿⡇
⠀⠀⠈⠁⢡⡶⣤⣿⣿⣿⣶⠴⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢷⣿⣿⡿⡟⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⡇
⠀⢀⡀⢀⣿⠬⢽⣏⡿⠛⠋⠒⠋⠀⠠⣤⣤⣴⡤⣠⡡⠀⠃⠀⠄⠆⠀⠀⠀⡤⢄⣤⣀⠤⢀⣀⢰⣎⣉⠡⣀⠐⢴⢦⣂⢄⠀⠀⡤⢠⣴⡆⠀⠰⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠈⠫⠜⠀⠉⠀⠐⢻⡍⠀⠀⠀⠀⠀⠁⡌⢱⣼⡿⠫⠎⢀⣀⠂⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⠋⠿⣿⡛⠋⣹⡿⠚⠓⠬⢽⣿⣿⣿⣯⣿⣿⣿⣮⣦⣿⣯⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢠⣦⣀⡀⣀⠗⠊⢧⡄⠀⠰⠀⠀⠀⠁⠀⠛⣃⠀⠂⢈⠀⠀⢀⣶⣂⠀⢴⣲⢿⣋⠐⠀⠹⠉⠀⠀⠉⠈⢀⠙⢯⣿⣿⣦⡽⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡅⢻⣿⣾⣿⡇
⢀⠀⠈⡈⠉⢐⣶⠁⣈⠉⠡⠀⣀⢰⡀⠠⡤⢠⣤⣤⣶⣿⣿⣿⣿⣿⣧⣷⡄⠺⡋⠀⠀⠐⠀⠀⠀⠀⢸⡚⠓⢮⠷⢁⠨⠋⠂⢽⣿⣿⠉⣭⣹⣿⣿⣿⣿⣿⡟⠛⠛⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⡖⣹⣏⢈⡃
⠀⠁⠘⠛⠡⢀⣨⣗⣵⣆⡠⣐⣉⠿⡂⠂⢉⡈⠛⣾⠛⢿⣿⣿⡟⣿⣉⣿⣥⣿⣯⣿⡖⣾⠰⣶⣖⣤⣴⣶⣴⣗⣴⣺⣷⣴⡀⣰⣿⢟⢻⣿⣿⣿⣿⣿⣿⣲⣆⣾⣿⣿⣽⣹⢦⠟⡛⠇⣐⣽⣯⣽⠍⠃⠿⡿⠻⠃
⠠⠤⠤⠀⠤⠄⠼⠤⠤⠤⠾⠾⡯⠭⠗⠶⠏⠠⠴⠮⠈⠅⠹⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠷⠴⠯⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠟⠿⠽⠏⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢥⠶⠿⠿⠿⠟⠥⠰⠐⠈⠀⠸⠆
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⠛⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠿⢿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠲⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢗⠆⠑⠩⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠒⠂⠀⠀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠙⣿⠿⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠉⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣷⡆⠀⠀⣦⣾⠀⠀⠀⠀⠀⠀⠀⠰⢰⢹⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢟⡛⠹⣿⣿⣺⢻⡟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣾⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣘⣿⡟⣰⠀⠰⠿⠿⠋⠀⠀⠀⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢸⣯⠉⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠸⠀⠀⠈⠻⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⣻⣿⠟⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⢻⡏⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠶⠶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡄⢠⡏⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢈⣷⣿⣿⠢⠀⠀⠀⡀⢤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠀⠸⠷⠶⣾⠀⠀⠀⠀⠀⠀⠀⢀⠘⠣⣿⡷⣶⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⢸⣏⠀⡆⠈⠀⢸⣿⣚⣻⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢿⣿⢻⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠞⢰⡠⠉⠁⠶⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢘⣿⣿⣹⣿⣾⣿⣿⣿⣿⣿⣿⣷⣦⣧⣀⠀⢰⠅⢸⣠⣄⣀⣀⣀⣀⣈⣉⣉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⢻⣿⡏⣧⣿⡿⢩⣆⣽⢙⡟⣟⣛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⡇⠀⠀⠀⠀⠀⢸⠏⠋⣿⠀⠀⠀⠀⠀⠀⠀⢼⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⢸⣿⣿⣉⣇⢔⠀⠉⠙⠻⢏⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠸⠤⠤⣿⠀⠁⠀⠀⠀⠀⠂⣿⣀⣀⡇⠀⠀⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣹⡿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⢣⣼⣿⣿⣾⣻⣿⣿⢟⠎⠐⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⠀⠀⠀⡂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡇⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢇⣿⠀⣿⣿⣿⣫⣏⠿⣿⣿⢸⡿⣿⣿⡗⣴⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣃⡀⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢸⣿⢨⣿⣿⢿⣻⣟⣦⣿⣿⢸⠧⣿⠇⠂⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢸⠏⢸⣿⣡⠀⠋⠋⠻⣿⡇⢈⡁⠌⠁⠃⣿⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢿⣻⣁⣸⣻⣉⣐⣀⣀⣀⣚⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣴⣶⣶⠶⠖⠤⠦⠴⠠⠴⠆⠀⠀⠀⠀⠀⠀⣿⢐⡆⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⣠⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣴⣶⣇⢀⣀⠀⣀⣀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠇⠀⠁⠀⢄⠀⠀⠀⢿⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣻⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣀⢀⣄⣄⣀⠀⠂⠉⢿⣿⣿⣞⠉⠀⢀⣤⣄⠀⠀⠁⠀⠀⠀⠀⣺⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣧⣿⡟⠀⠀⠄⠠⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀
⢸⣿⣿⣿⣿⣯⣽⣇⢀⡆⠸⠃⠉⠀⠀⠀⣈⠿⠉⠂⠀⠀⠀⠉⠘⠀⣾⣿⡇⠀⢻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⢧⣄⣀⣠⡀⣤⣦⣤⣶⣶⡄⠀⠀⠀⠀⠠⡿⢿⣿⣧⠆
⠸⠿⣿⣿⡿⣿⠿⠿⣿⠷⣦⣦⣤⣤⣴⣿⡿⠅⠀⠀⠀⠈⠀⠛⠻⢦⣀⠀⠀⠀⠀⢀⠽⠷⠄⠀⠈⠁⢠⣾⣿⣿⣤⣿⣿⣾⣿⣧⡄⣀⠸⠿⠿⠛⣀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣵⣦⣤⣠⡀⢀⡀⠀⣈⣉⠉⠀
⠀⠀⠘⣋⠤⠂⠀⠀⠀⠲⣿⠿⢙⡿⠿⠿⡣⡀⠀⣀⡴⣤⠀⠀⠀⠀⠉⠓⠤⠀⠀⠀⠀⠀⠈⠒⠂⠠⢿⡟⢹⣿⣿⢻⣿⣿⣿⡏⠳⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⣷⣶⣿⠃⠀⠇
⢰⣿⣾⣟⠃⢃⣠⡐⡶⣷⣾⣤⣾⠯⠀⠀⠁⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢾⠓⠄⠚⠛⠒⠀⠀⠚⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⢴⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⢿⢻⣻⣿⣿⣿⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡟⣿⣿⣿⣿⣿⢹⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⡇
⠀⢅⢴⣼⣊⢛⡈⢻⣿⡍⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⡿⠁⡴⣯⣿⠿⣿⡿⢸⠿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣁⠀⣸⠛⣼⡟⠙⢿⡇
⠀⠀⠈⠀⢠⡾⣶⣿⣻⣿⣷⠵⠂⡀⠈⠀⠀⠀⠀⠄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⡿⣟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇
⢀⢄⢀⠀⣼⠕⠹⣯⣿⠋⠋⠐⠋⠀⠠⣤⣤⣶⡄⣠⡱⠀⠃⠀⠀⠆⠀⠀⠀⡄⢀⣤⣄⠤⡀⣀⢀⣞⣍⠡⣔⠀⢰⠦⣇⣠⠀⠀⣤⢀⣴⡆⠀⠰⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠈⠉⠜⠀⠁⠀⠁⠟⡍⠀⠀⠀⠀⠀⠉⡌⠑⣼⡿⠻⠏⢀⣀⠀⠀⠀⠀⠀⠀⠀⠟⠿⢿⣿⠊⡿⢿⣛⠋⡙⡽⠘⠓⠤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡄
⠀⠀⠠⢠⣶⣀⡄⣀⢟⠩⠷⡤⠂⠰⠀⠀⠀⠀⠚⠙⣗⡀⠒⢈⠀⡀⢀⣶⣦⠀⢴⣶⢻⢯⠐⠁⠘⠉⠐⠄⠉⠈⠀⠙⢻⣿⣽⣶⠭⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣯⡵⢿⣿⣾⣿⡇
⢀⠀⠈⢂⠉⠑⣷⠀⣈⠁⠁⠀⣀⠨⡄⠠⣤⢤⣤⣤⣴⣿⣿⣿⣿⣿⣧⣿⡄⠘⣋⢀⠀⠐⠀⠀⠀⠀⠸⡒⠛⢫⠿⢨⡈⠉⠀⢸⣿⣿⠉⣫⣻⣿⣿⣿⣿⣿⠛⢛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣹⣏⢘⡃
⠀⠉⠘⠋⠡⢄⣬⣧⣾⣦⡠⣔⣨⡿⠃⠀⠈⡀⠛⣾⠛⢿⣿⣿⣟⣿⣁⣴⣧⣬⠯⣿⡗⣺⠐⣶⣶⣦⣴⣶⣶⣗⣶⣯⣵⣦⡀⣠⣿⣟⢻⣿⣿⣿⣿⣿⣿⣳⣆⣾⣷⣿⣯⣹⠦⠿⠛⠋⣐⣭⣯⣽⡏⠑⡿⠿⠛⠃
⠠⠤⠤⠀⠤⠄⠼⠦⠤⠴⠾⠾⡿⠭⠗⠷⠏⠤⠬⠾⠈⠅⠨⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠧⠬⠿⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢭⠴⠿⠿⠿⠿⠡⠰⠀⠢⠀⠀⠆
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⠿⠛⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⡿⢿⣿⠆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠉⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⡆⠙⠪⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠘⠂⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠐⣿⣿⣿⣿⣿⣿⣿⡿⠉⠘⣿⠿⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠁⠈⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆⠀⠀⣶⣾⠀⠀⠀⠀⠀⠀⠀⢸⢰⢹⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢟⡛⠹⣿⣿⣻⠻⡿⠛⠛⠛⠟⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣾⢸⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣘⣿⣿⣰⡄⠰⠿⠿⠋⠀⠀⠀⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢸⣯⠉⠉⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⡿⠸⡄⠀⠈⠛⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⡿⣺⣿⠿⠛⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣷⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠷⠶⢶⣾⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡄⠀⡟⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣿⠂⠂⠀⠀⣀⣤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⡀⠀⠀⠀⠀⠸⠿⠖⢶⠀⠀⠀⠀⠀⠀⠄⢀⢐⠃⣿⡿⢾⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⣿⠀⡆⠈⠀⢸⣗⣚⣒⡚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⢏⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠸⢰⠢⠉⠁⠐⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⢹⣿⣸⣿⣿⣿⣿⣿⣿⣿⣦⠠⣀⠀⢀⠄⢸⣠⣤⣀⣀⣀⣀⣀⣀⣀⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⢿⣿⡟⣭⣿⡿⠍⣦⣼⣏⡟⣿⣙⣛⣛⡛⢛⠛⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣿⣍⣳⢐⠀⠉⠉⠻⠯⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⠧⠤⢾⠀⠀⠀⠀⠀⠀⠐⣾⣀⣀⡏⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣾⣿⢿⣿⣟⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⡇⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣾⡇⣿⠀⣿⣿⣿⣧⣿⠿⣿⣿⢠⡏⣻⣿⡏⣶⡂⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣦⣤⣤⣌⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⢧⣿⠀⣿⣿⡟⣟⢛⠱⣾⣿⢸⠧⣿⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⢸⡏⠈⣿⣇⠅⠘⠈⠛⣿⠿⢨⡁⠌⠁⡁⣿⠓⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢻⣸⣁⠰⠹⢅⣀⣀⡄⣀⢚⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣴⣴⣶⠶⠖⠤⠦⠲⠴⠴⠶⠀⠀⠀⠀⠀⠀⣿⠀⡆⠀⠂⠀⠀⠀⣀⣀⣀⡄⢀⣀⣤⣀⡀⠀⣀⣤⣤⣀⠀⣿⣿⡇⣉⣉⡁⣴⣶⣇⢀⣀⠀⣀⣀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢠⠀⠀⠀⠟⠀⠁⠀⠀⠀⠀⠀⣸⣿⣿⠇⣾⣿⣉⣿⣷⢰⣿⡏⣻⣿⡇⣿⣿⡇⣿⣿⡇⢹⣿⡏⢸⣿⡇⣿⣿⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⢀⣤⣦⠠⠔⠊⠁⢹⡿⢿⡆⠘⠌⠀⢀⣲⣶⡄⠀⠀⠀⠁⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⢠⣶⡾⢻⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⡇⠀⣿⣧⣿⡟⠀⠀⠀⠀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀
⢸⣿⣿⣿⣿⣯⣮⣅⣀⣶⠘⠃⠀⠂⠀⠀⠀⢀⠙⠃⠈⠀⠀⠀⠄⠀⣼⣿⡇⠀⢻⣿⣤⣿⡟⠸⣿⣧⣼⣿⡇⣿⣿⡇⣿⣿⡇⢸⣿⣧⠀⢹⣿⣿⡇⢰⣿⠿⣄⣀⢰⡄⣦⣶⡤⢴⣾⠆⠀⠀⠀⠀⠀⡿⠿⣿⣧⠆
⠸⠿⢿⣿⡿⢿⠿⠿⠿⠟⢦⣶⣤⣦⣴⣿⡿⠟⢃⢀⡠⠀⠀⠈⠉⠢⠄⠀⠀⠀⠀⠀⠉⠥⠶⣷⠈⠁⢠⣶⣿⡿⣆⣾⣿⣾⣿⣷⡄⣀⠸⠿⠿⠛⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣤⠠⡁⢀⡀⠐⢀⣉⠉⠁
⠀⠀⠘⣣⠠⠆⠀⠀⠀⠁⢾⠿⢹⣿⠛⠛⣂⠀⠘⠀⢈⡂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠰⢺⡿⠻⣿⣿⡿⣿⣿⣿⡟⠻⣽⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⡖⠻⠛⣿⣿⣿⣿⣶⣷⣾⣿⢉⢀⠀
⢰⣿⣿⣕⠃⠌⡠⠀⡄⢴⣾⣤⢾⠟⠀⠀⠁⠀⠀⠀⠀⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⠯⠅⠰⠻⠩⠉⠡⠄⣿⣷⣽⣿⣿⣷⣿⣿⣿⣿⣿⠿⠷⢶⣿⣿⣿⣾⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⡄
⠸⣿⢻⢻⣻⣿⠿⣿⣝⣻⡏⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠝⣿⣿⣿⣿⣿⢽⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣮⢽⣿⣿⣿⡇
⠀⠈⢤⣴⣍⢙⡉⢙⣿⡏⠀⠀⠀⠀⢠⠀⡘⠀⠀⠀⠀⢀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢿⠇⠴⣯⡾⡿⣿⣿⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⣸⡛⣺⡿⠛⢻⡇
⠀⠀⠀⠁⢀⠵⣶⣾⣻⣿⣿⠽⠂⡀⠀⠀⠀⠄⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠈⠱⢿⣿⡿⣿⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⡇
⢀⢤⢠⠀⣼⡁⢪⣯⣿⠋⠋⠐⠋⠀⠁⢶⣦⢶⡦⣲⣱⠀⠃⠀⠀⠔⠀⠀⠀⠤⢄⣤⣄⠤⠀⣈⠀⣞⣩⡙⣆⠀⢠⠆⣂⣀⠀⠀⣠⣀⣤⡆⢀⠀⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇
⠈⠉⠝⠀⠀⠀⠂⠟⡏⠀⠀⠀⠀⠀⠈⡀⠉⣪⡟⠣⠆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠟⠟⢫⣷⠐⠛⢻⣉⠉⠉⡭⠒⠛⢤⣿⡿⣿⣿⣿⣿⢿⣿⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⡅
⠀⠀⠀⠠⣶⣀⡄⣀⣊⡁⠵⠤⠂⠐⠀⠀⠀⠀⠘⠘⢷⣀⠐⠀⠀⣀⡀⣴⣂⠀⠰⡲⠺⣯⠀⠃⠈⠋⠀⠆⠀⠀⠁⠐⢻⣽⣭⠶⡬⢿⣟⣿⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣻⡧⠣⣿⣿⡿⡇
⠀⡀⠀⢀⠉⠑⢷⡀⣀⠁⠉⠀⢄⠠⡄⠤⣤⠠⣤⢤⣶⣾⣿⣿⣿⡿⣧⢿⣦⠘⣋⢁⡀⠘⠀⠈⠀⠀⠰⡖⠛⠻⠿⢈⡄⠍⠁⠠⣿⣿⠊⣩⣠⢿⣿⣿⣿⣿⠛⠋⡛⢳⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡔⣈⣋⠀⡁
⠀⠙⠈⠉⠡⠄⣤⣧⣾⣶⡬⣄⣨⡽⠃⠀⠈⡀⠛⣳⡛⢻⣿⣿⣿⣻⣑⣴⣶⣴⠿⣿⡗⢺⠐⣶⣦⣦⣴⣶⣶⣗⡶⣧⡵⣶⣆⢀⣿⢿⡙⣯⣿⣿⢿⣿⣿⣱⣮⣽⣿⣿⣯⣽⡯⠭⠛⠉⣀⣦⣯⣼⠂⠱⠾⠿⠛⠃
⠠⠤⠤⠀⠠⠤⠼⠤⠴⠶⠮⠿⠿⠥⠵⠳⠏⠠⠬⠽⠀⠍⠈⠿⠿⠾⠿⠿⠿⠿⠷⠷⠿⠯⠬⠿⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠛⠝⠻⠮⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠴⠾⠿⠿⠿⠣⠸⠀⠂⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣶⣶⣴⣶⣦⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣖⣿⢿⣽⣇⡹⠿⠶⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣶⣶⣶⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣦⣶⣿⣿⣿⣿⣿⣶⣦⡄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⡀⠀⠀⠈⡿⢠⡶⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠙⠻⠿⠟⠋⠉⠓⠻⢼⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣾⠃⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⢠⣤⣤⣬⣤⣤⣶⣤⡄⠀⠀
⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⢿⡿⠋⠟⠀⠀⠀⢸⡏⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣦⡀⠀⠀⠀⠘⢣⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀
⣿⣿⣿⣁⡀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣅⠀⡆⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣫⣿⣧⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢀⡿⠁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⡾⠛⠻⢿⠗⠀⠀⠘⠻⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⣿⣿⠉⠀⠀⠐⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠈⣿⡇⢠⣌⣀⣠⠄⠀⠀⠀⣿⣷⣴⣴⣤⣧⡄⡤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣝⠓⠀⠀⠀⡴⠀⢰⣿⣿⣷⣄⠀⣿⡏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠀⠀⠀⢹⣧⡈⠻⠛⠛⠀⠀⠀⢀⣿⣿⡿⣿⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣏⣿⠀⠀⠀⠀⠀⠀⠉⢱⣶⣿⡟⣛⠃⠀⠀⠀⠀
⠏⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⣠⣼⣿⣿⣿⠻⡆⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⠇⠀⠀⠀⠀
⡶⠀⣴⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⢀⠀⠀⠀⢻⣿⢿⣿⠉⠀⠈⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡼⠃⠀⠘⢁⠉⡿⠿⢻⣿⣿⣿⣿⣶⣟⣴⣿⠀⠀⠀⠘⠻⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣾⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡴⠁⠠⠀⠀⠀⠐⠁⠀⠛⢹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣆⣀⠩⣿⣟⢿⣟⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠙⠀⠀⠝⠋⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣯⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡄⣤⣤⣤⣤⣤⣤⢠⣤⢠⣤⠀⠀⣤⣤⣤⣤⣤⣤⣤⣠⣤⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⡿⣿⣧⠈⢸⣿⢸⣿⠀⢰⣿⣿⢸⣿⠀⣿⡇⣾⣿⡇⣿⣟⣿⣿⣿⡟⠿⣿⣿⣿⣿⢿⣿⢿⣿⡿⣿⣧⠸⢷⣭⠀⢀⣠⣴⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠿⠇⠿⠷⠀⠸⠿⠾⠿⠆⠸⠿⠿⠿⠿⠀⠿⠇⠿⠻⠷⠿⡾⠟⠿⠿⠷⠀⠻⠿⠹⠿⠸⠿⠸⠿⠇⠿⠷⠼⢧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣶⣶⣶⣶⣶⣶⣶⣠⣴⣶⣶⣦⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢠⣴⣦⠀⢠⣤⡄⣤⡄⣤⢠⣤⣤⠀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣦⣦⢠⡄⣤⣤⢠⡄⣤⢠⣤⣤⢠⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⡷⢼⣿⣿⣙⣿⣯⠀⢸⣿⣿⣿⣿⣿⣸⡇⣿⠀⣿⣿⣭⢻⡿⣿⣿⣏⣿⡗⣿⣷⢼⣿⣿⢸⡇⣿⡷⢸⣿⣿⢸⣧⣿⢘⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠇⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠁⠿⠿⠿⠿⠿⠿⠼⠷⠿⠀⠸⠷⠿⠸⠇⠿⠿⠏⠿⠷⠿⠇⠸⠟⠿⠸⠇⠿⠷⠾⠟⠿⠸⠿⠿⠸⠷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃⣾⠇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢸⣿⣿⣿⣿⣿⡏⣸⡟⠀⠀⠀⣸⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣀⣤⣥⣷⣶⣶⣶⣶⣦⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠋⠀⠀⠈⢿⣿⣿⣿⣿⢃⣿⠃⠀⠀⠀⣿⡇⠀⠀⠀⠉⠀⠚⢉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣏⢩⣭⣭⠙⠛⠻⠟⠋⠉⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⡟⣼⡟⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⡀⠀⠀⠀⣸⣷⡄⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢁⣿⠁⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣟⠛⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣿⣿⣿⡆⠀⠀⠻⣿⣧⠀⠀⢰⡄⠀⠈⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⠀⣀⣿⣿⣿⣿⣿⣽⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⠃⠀⠀⠀⠈⠀⡀⠀⠀⠻⠀⠀⢿⣿⣿⣭⣿⡦⣤⣶⣶⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠐⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠘⠛⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⣿⣿⣿⣿⡉⠙⠛⠿⣿⣿⣿⠁⠀⠀⠀⠀⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣛⣩⣿⣿⣿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣀⣤⣿⣿⣿⡏⠁⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠙⠛⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣶⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣟⣿⣾⣿⣿⣿⢻⠀⢸⣷⣿⣷⣿⢻⣧⢿⣿⠟⠀⣼⣿⡇⠀⣼⡟⣿⣶⣿⢻⣧⣾⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢸⣿⣼⡇⠀⢸⣿⣇⢸⣿⠿⢿⣿⢿⣿⠿⣿⡟⣷⠀⢀⣿⣿⢸⣿⡇⣿⡇⠀⠀
⠀⢸⣟⣿⣿⣿⣻⣿⠀⠀⢸⣿⣿⣿⣿⢸⣿⢸⣿⠀⠀⣿⣿⣷⠀⣿⡟⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⡿⣿⣿⡟⠋⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⢸⣿⠃⢸⣿⢸⣿⠛⣿⡟⣿⡀⢸⣿⣿⣿⣿⡇⣿⡇⠀⠀
⠀⠘⠛⠛⠙⠛⠚⠛⠿⠀⠘⠃⠛⠋⠛⠛⠃⠘⠛⠀⠀⠛⠛⠛⠀⠘⠛⠛⠋⠛⢛⠃⠝⠛⠋⠘⠛⠛⠃⠀⠛⠛⠃⠛⠛⠛⠛⠛⠛⠛⠙⠓⠀⠛⠋⠛⠚⠛⠀⠘⠛⠘⢛⣛⣿⣷⣿⣷⣾⣻⣟⣛⠛⠛⠛⠛⠃⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3233

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/Over_at_Tux_Machines.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Apr 18, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇School_Scooters⦈_


⚓  Updated This Past Day⠀⇛


   1. ⚓ Ubuntu_25.04_“Plucky_Puffin”_Is_Now_Available_for_Download,_This_Is
      What’s_New⠀⇛


           Canonical published today the Ubuntu 25.04 (Plucky Puffin)
           release, the latest stable version of their popular GNU/Linux
           distribution, featuring up-to-date components and new features.


   2. ⚓ LXQt_2.2_Desktop_Environment_Released_with_Many_Wayland_Improvements⠀⇛


           LXQt 2.2 has been released today as the latest stable version
           of the lightweight desktop environment for Linux-based
           operating systems, featuring many improvements to Wayland
           support and updated components.


   3. ⚓ KDE_Gear_25.04_Applications_Suite_Officially_Released,_Here’s_What’s
      New⠀⇛


           The KDE Project released today KDE Gear 25.04 as the latest
           version to this collection of apps for the KDE Plasma desktop
           environment and the Linux ecosystem, adding new features and
           enhancements to your favorite KDE applications.


   4. ⚓ TrueNAS_25.04_(Fangtooth)_Open-Source_NAS_Released⠀⇛


           TrueNAS 25.04 open-source NAS launches with ZFS fast
           deduplication


   5. ⚓ Deepin_23.1_Launches_with_Smarter_AI,_Enhanced_Hardware_Support⠀⇛


           Debian-based Deepin 23.1 is out now with Linux kernels 6.6/6.12


   6. ⚓ Tor_Browser_14.5_Introduces_Android_Connection_Assist⠀⇛


           The latest Tor Browser adds Connection Assist to Android


   7. ⚓ Free,_Libre,_and_Open_Source_Software_Leftovers⠀⇛


           FOSS picks


      ⚓  New⠀⇛


   8. ⚓ Elive_3.8.48_released⠀⇛


           The Elive Team is pleased to announce the release of 3.8.48


   9. ⚓ GNU/Linux_Leftovers⠀⇛


           mostly GNU/Linux links


  10. ⚓ Kernel:_Asahi,_Hammerspace,_and_Zephyr⠀⇛


           kernel news


  11. ⚓ Open_Hardware/Modding:_STM32,_Arduino,_and_More⠀⇛


           Hardware leftovers


  12. ⚓ Free,_Libre,_and_Open_Source_Software_Leftovers⠀⇛


           FOSS picks


  13. ⚓ Programming_Leftovers⠀⇛


           Development related stories


  14. ⚓ Security_Leftovers⠀⇛


           Security picks


  15. ⚓ Free_and_Open_Source_Software⠀⇛


           This is free and open source software


  16. ⚓ FreedomBox_–_Debian-based_distribution⠀⇛


           FreedomBox is made up of two things: a free and open source
           software system and inexpensive hardware


  17. ⚓ These_6_Linux_apps_are_the_secret_sauce_to_my_creative_process⠀⇛


           As a creator, I know having the right tools can make all the
           difference


  18. ⚓ My_experience_in_the_Debian_LTS_and_ELTS_projects⠀⇛


           Last year, I decided to start participating in the Debian LTS
           and ELTS projects


  19. ⚓ GNOME_48.1_Desktop_Is_Out_to_Improve_HDR_Support_and_Fix_Various
      Issues⠀⇛


           The GNOME project released today GNOME 48.1 as the first
           maintenance update to the latest GNOME 48 “Bengaluru” desktop
           environment series to fix bugs and improve existing
           functionality.


  20. ⚓ Android_Leftovers⠀⇛


           You're Missing Out on Hidden Android Updates


  21. ⚓ Meet_PorteuX,_the_Slackware-Based_Lightweight_Live_Linux_Distro⠀⇛


           It seems like no matter what happens, the Linux community comes
           out with new live distros


  22. ⚓ My_portrait_of_Charles_Darwin_in_a_museum⠀⇛


           I'm super excited to share this with you: my artwork is now on
           display in a museum


  23. ⚓ Best_Free_and_Open_Source_Software,_howtos_and_Installations⠀⇛


           This is free and open source software


  24. ⚓ Guix_System_–_Linux_distribution_built_around_Guix⠀⇛


           Guix System is a rolling release, free and open source Linux
           distribution built around Guix


  25. ⚓ Tax_Reduction⠀⇛


           While I was working at Digital Equipment Corporation (DEC) in
           the early 1980s


  26. ⚓ Zorin_OS_17.3_review_-_Would_you_pay_for_your_Linux_desktop?⠀⇛


           For reasons many and varied, the commercial Linux desktop has
           never quite caught on


  27. ⚓ Linux_laptop_lagging?_5_simple_ways_to_speed_it_up_fast⠀⇛


           If your computer is running Linux and it seems a bit slow


  28. ⚓ GNU/Linux_Leftovers⠀⇛


           some more links pertaining to GNU/Linux news


  29. ⚓ Wayland's_Future_and_NVIDIA_575.51.02_Beta_Driver⠀⇛


           Graphics news


  30. ⚓ Devices/Open_Hardware:_Raspberry_Pi_and_OpenWRT⠀⇛


           a handful of leftovers


  31. ⚓ Red_Hat_Leftovers⠀⇛


           corporate stuff mostly


  32. ⚓ today's_howtos⠀⇛


           first batch for today


  33. ⚓ Security_and_Windows_TCO_Leftovers⠀⇛


           many Windows TCO examples


  34. ⚓ Games:_Valve_and_Linux,_One_Year_of_Mahjong_Solitaire,_and_More⠀⇛


           a handful of stories for today


  35. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


  36. ⚓ Kernel_Articles,_Mostly_LWN⠀⇛


           now outside the paywall


  37. ⚓ Taking_notes_with_Joplin⠀⇛


           Joplin is an open-source note-taking application designed to
           handle taking many kinds of notes, whether it is managing code
           snippets, writing documentation, jotting down lecture notes, or
           drafting a novel


  38. ⚓ Debian_Project_Leader_election_2025_edition⠀⇛


           Four candidates have stepped up


      =========================================================================
      The corresponding text-only bulletin for Thursday contains all the text.
    * IRC_Proceedings:_Thursday,_April_17,_2025
    * Microsoft_is_Still_Attacking_GNU/Linux_and_the_Net


⣿⣿⣿⣿⣿⣿⣽⣿⡟⣿⣿⢹⣿⣾⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⢠⣽⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠥⠀
⣿⣿⣿⣿⣿⣿⣽⣿⣷⣿⣿⡞⣿⣯⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠟⠀
⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠔⠀⠀
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠂⠀⠀
⣿⣿⣿⣿⣿⣿⣸⣿⢿⣿⣿⣿⣹⣿⣿⣿⢿⣿⠛⡿⠿⠿⠿⣿⣿⣿⣿⣿⣏⣉⣛⣛⠙⠛⢿⣿⣿⣿⣿⠉⢹⣿⣏⣉⡻⣿⣿⣟⡛⠛⢫⣯⣿⣿⣿⣿⡟⠋⣉⣿⠿⠿⢷⣶⡀⠻⠿⠿⠋⣠⣄⣿⣛⣛⠻⠇⠀⠀
⣿⣿⣿⣿⣭⣭⣨⣄⣨⣉⡙⢿⡏⣿⠋⣭⣠⣤⣤⣴⣶⣶⣶⣦⡙⣿⣿⡟⠉⣤⣭⣍⣙⣻⡆⢩⣭⡏⢠⣶⣷⣶⣶⣶⡇⢨⣭⣭⠀⣿⣿⣿⣷⠀⣦⣦⠀⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⡇⢸⣿⣿⣿⣷⡾⠈⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢳⢿⡆⢹⣻⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⡇⢰⣿⣿⣿⣿⣿⣧⠸⣿⣇⠘⣿⣿⣿⣿⣿⣇⢸⣿⡏⠀⣿⣿⣿⣿⠀⠟⠿⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⣿⣿⣿⠧⢰⠀⠂⠀
⣿⣿⣼⣿⣿⡟⣿⣿⣿⡝⣿⣿⡀⢸⣿⡀⢧⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣷⠈⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⢸⣿⣧⢰⣿⣿⣿⣿⠀⢰⣶⠀⣿⣿⣿⣿⣿⣿⡏⢠⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⠂⠀⢀
⣿⡿⣿⣿⣿⡇⣿⣿⣿⡗⣿⣿⣷⠘⣿⣷⠘⣽⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⠀⢠⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾
⣿⢿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⠸⣿⣇⠙⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⡇⢻⣿⣿⣿⣿⣿⡆⢿⣿⡀⣿⣿⣿⣿⣿⣿⠀⢿⠿⢸⣿⣿⣿⣿⠀⠘⠛⠀⣿⣿⣿⣿⣿⣿⠃⠈⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⠛⣻⣿
⣿⣼⣿⣿⣿⣧⣿⣿⣿⡇⣿⣿⣿⣿⢀⢹⣿⠄⢻⣿⣿⣿⣿⣿⣿⣿⠈⠛⠃⢸⣿⣿⣿⣿⣿⡇⠀⠁⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿
⡟⣿⣿⣿⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⣸⡍⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡀⠄⠀⠸⣿⣿⣿⣿⣿⡇⠠⡀⠀⢸⣿⣿⣿⣿⣿⠀⢰⠀⢸⣿⣿⣿⡏⠀⠀⢰⠀⠈⠉⠉⠉⠉⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢷⣿⣿⣿⣿⢸⣿⣿⣿⣷⣿⣿⣿⣿⡏⣿⢀⠀⣀⠘⠛⠿⠿⠿⠿⠛⠃⠰⡠⠀⠙⣿⣿⣿⣿⣿⠀⠀⠀⠈⠟⣿⣿⣿⣿⠀⠀⠀⠈⢸⣿⣿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⠟⠛⠛⠘⠛⠛⢛⣉⣬⣭⣭⠭⠄⠀⠀⠀⠁⠀⠀⠀⠁⠟⠛⠁⠀⠀⠀⠀⠀⠁⣿⣿⣿⡟⡄⠀⠀⠀⠀⣿⣿⣿⠁⠀⣶⠀⠀⢸⢿⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠠⣤⣤⣀⠀⠀⠀⠀
⠒⠀⠁⠀⠀⠀⠀⣀⣀⣉⣉⣁⣀⡀⠀⠀⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢀⡀⠁⠈⠋⠁⠀⠀⠀⢀⠀⠀⠉⠉⠀⢀⠀⠛⢀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⡄⠀⠀⠀⣸⣶⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠗⠚⠓⠿⠿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠘⠇⢀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⡼⠁⠀⠀⠀⠀⠣⠴⠤⡏⠀⠀⠀⠀⠀⣸⠷⠿⢿⡀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢁⠀⠀⠀⠋⢲⣶⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠉⠀⠀⠘⣄⣀⠴⢶⣀⡀⠀⠀⠈⠈⠙⠒⣀⣀⣀⣀⣀⣀⣀⡸⠤⠤⠤⠖⠲⣿⣷⣿⣿⠗⠉⠉⠉⠉⠁⠀⠘⠓⠒⢃⣤⡀⠀⣶⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣤⠝⠓⠒⠒⠉⠉⢱⣶⣶⣶⡖⢀⡀⠀⣴⡾⢻⣿⡿⠁⣶⣤⣄⡀⢰⣿⣿⣿⣿⠀⣀⣤⣤⣦⠀⠀⠀⠈⢿⠐⢿⣷⠈⠛⠛⠛⠻⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⣿⣿⣿⣿⠏⣼⣿⣶⣤⡀⢠⣿⠋⢹⣿⡇⣾⣿⣿⣿⣯⡿⣿⡏⠈⠛⠛⠋⠃⠞⠛⠛⠻⠿⠷⣤⣬⣽⣦⡀⠀⠀⠘⠋⠉⡉⠉⠉⠁⠀⠀⠐⠀⠀⠀⠔⢠⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⣿⣿⣿⠇⠸⠛⠿⠿⡿⠟⠛⠻⠾⠘⠻⠃⠀⠀⠀⠀⢸⢃⠀⠁⠀⣁⠀⠀⡀⠀⠀⠀⠀⠐⡐⡙⠉⢿⣿⡷⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣷⣼⣦⣴⡶⣼⣴⣤⠀⠀⠀⢐
⣿⣿⣿⣿⣿⣿⣿⣥⣀⡀⠀⠀⠀⠀⢀⠉⠀⠠⠛⠃⢀⣀⣠⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣤⣶⣦⡀⠀⠀⠜⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢀⣾⠻⠬⣬⢩⣿⡿⣿⣻⢿⣧⣴⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠀⠀⠉⠈⠀⣿⣿⣿⣿⡅⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣓⡀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠐⠃⠀⠀⠀⠁⠀⢠⣅⢁⣄⣋⣙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣷⣶⡄⣰⣽⣿⣿⣿⣧⠀⠀⢀⣄⠀⠀⠀⠀⢀⣀⢠⣶⣷⣤⣤⣤⣤⣤⣤⣴⣶⣾⣭⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠙⠿⣹⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠠⠀⠙⣀⣺⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣶⣶⣿⣿⣿⣿⣟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⡿⠞⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⡀⠀⠀⡀⢁⢤⣽⣯⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠉⠀⠀⠙⢻⣿⣷⢶⣖⣛⡿⣉⢉⣹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣀⣀⣀⣠⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣋
⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⡐⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⢀⣼⣾⣜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3543

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/Sayonara_さよなら_Microsoft.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/Sayonara_さよなら_Microsoft.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ "Sayonara" (さよなら),
Microsoft⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025


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


11 days ago we mentioned_how_Windows_had_fallen_below_iOS_in_some_countries.
We're seeing it in Japan and based on recent_trends, or perhaps extrapolating a
little, as early as this summer statCounter may see more Web requests in Japan
coming from iPhone than all Windows-running PCs combined. It looks_like_this at
the moment:


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


A few months ago we saw GNU/Linux_gaining_a_lot and we revisited the matter
earlier this month.


Japan has several of its own BSD and GNU/Linux distros. With tariffs from a so-
called (former) "ally", will influential politicians run into Free software's
arms? Or ARM? Engineering and Windows are sort of paradoxical irrespective of
the context. █


    * Links_18/04/2025:_Layoffs_at_Microsoft_Infosys_and_Qt_Becoming
      Increasingly_Proprietary_(Plus_Slop)
    * Sounds_Like_IBM_is_Preparing_for_Mass_Layoffs/Redundancies_in_Red_Hat,
      Albeit_in_"PIP"_(Performance_Improvement_Plan)_or_"Relocation"_Clothing


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⠿⢿⢿⠿⠿⣿⢿⠿⣿⣿⠿⠿⠿⠿⢿⡿⡿⠿⠿⡿⢿⢿⢿⠻⡿⡿⠿⣿⡿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿
⣿⢬⣆⡵⠼⠧⢤⣽⣿⣨⣯⣄⣧⣯⣤⣼⣿⣿⣤⣤⣼⣮⣼⣽⣥⣼⣧⣿⣤⣟⣤⣯⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣦⣷⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿
⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿
⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⠭⠭⠭⠭⠭⠭⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣟⠛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⢛⣛⣛⣛⣛⣛⣛⡛⣛⢛⢛⡛⡛⡇⢽⠩⣿⢩⡍⡏⡏⡏⣭⢹⢸⡏⣋⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⠿⠿⠿⢿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⡄⠀⠀⠙⠋⢿⣿⣿⣿⡇⣷⣿⣷⣷⣾⣿⣾⣷⣾⣷⣾⣷⣶⣷⣿⣾⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣦⣄⣀⣀⣨⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣷⣶⣾⠿⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣭⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣯⣤⣤⣼⣿⠀⠀⠀⢠⣥⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⣿⠒⠒⢲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣯⣭⣽⠀⠀⢸⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⣿⣿⣿⣿⡿⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3629

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/Sounds_Like_IBM_is_Preparing_for_Mass_Layoffs_Redundancies_in_R.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/Sounds_Like_IBM_is_Preparing_for_Mass_Layoffs_Redundancies_in_R.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Sounds Like IBM is Preparing for Mass
Layoffs/Redundancies in Red Hat, Albeit in "PIP" (Performance Improvement Plan)
or "Relocation" Clothing⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025,
updated Apr 18, 2025


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


This isn't the "old" IBM; they're applying pressure by confusion and
humiliation


Related: PIP_(Performance_Improvement_Plan)_as_an_Instrumental_But_Largely
Hidden_(From_the_Public)_Extra_Layer_of_IBM's_Workforce_Reductions


It's Friday. In Europe people already cleared their desk and went home
(Easter). In the US they're about to or did so yesterday, Maundy_Thursday. 3
hours ago (around the time I published "Red_Hat_and_IBM,_Layoffs_and_Shutdowns"
in the sister site) somebody posted_the_following_"gossip":


     § Red Hat / IBM Dallas office complete S Show


     The IBM employees working on the Red Hat team are experiencing a
     complete S Show right now. First, they’re told there’s no way the
     center is closing. Then, told the center is closing and the must move
     to Austin. Being told Red Hat will never cancel the contract but they
     may cancel the contract. The same day they announced the move, they
     announced PIPs. It’s an unorganized mess. Can’t believe Red Hat or
     IBM is allowing this. Crazy times!


Contradictory stories from management_figures always imply that someone is
lying. I know this from personal_experience. IBM does_not_seem_to_value_Red
Hat's_community_assets or its spirit/principles. The current IBM management
aims only for one thing: money. See these_latest_comments. They're burning
things just to meet the next quarterly targets and use the profits (or debt) to
buy the revenue of other companies (via acquisitions). They're gaming the
system.


"Expensive" staff is perhaps most "vulnerable" or "at-risk" right now. IBM does
not fancy outright laying off people, at least not before trying PIPs,
relocations, RTO etc. Do not delay or wait for an inevitable "conclusion". IBM
is notorious right now for lousy severance terms. █


    * "Sayonara"_(さよなら),_Microsoft
    * Gemini_Links_18/04/2025:_Price_of_Games_and_State_of_Tinylog


⠀⠘⠋⢀⠈⠀⠧⡁⢫⣐⣸⠿⣿⣿⡩⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⢭⣿⣿⣿⡿⡷⣶⠶⠿⢿⠿⣿⣿⣿⣿⡏⣿⣿⡿⠿⢿⣿⡿⢿⣿⣿⡿⣿⣿⢽⣿⣿⣤⣀⣮⠓⠩⣅⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⡋⠄⠆⢰⣷⡬⠿⠿⠿⠿⠿⢿⣿⣯⣤⣄⣠⣽⣧⣆⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣿⣿⣿⣿⣇⣰⢿⣿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡉⠴⠈⡆⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠐⢺⠋⠭⣿⣿⣿⣾⣿⡿⢿⣿⣿⡿⣿⣾⣿⣿⣷⣾⣶⣩⣼⡿⣿⣿⣿⣰⣶⣶⣾⣿⣷⣾⣶⣶⢶⣿⣿⢿⣿⣶⣶⣾⣿⣷⣶⣶⣔⣲⣛⣿⣿⠛⣿⣿⣿⣿⡿⢿⡿⣟⡿⣟⡏⠉⠉⠁⠁⣲⣒⡏⠈⠉⠉⠉⠉⠉
⢀⣤⢰⣗⣭⣭⣭⣿⣿⢷⣾⣿⣿⣷⣿⣿⠿⣿⣷⣿⣿⣿⣷⣳⣛⡿⡿⣿⣿⣿⣿⣿⣿⢹⣏⣩⣼⡟⡿⠿⣟⣿⣿⣿⣿⣿⣿⣺⡽⢙⣾⣿⣵⣾⡟⠛⣿⠉⠛⠝⣋⣵⣾⣭⠀⠀⠀⠀⠀⠠⣼⠀⠀⠀⠀⠀⠀⠀
⢰⣽⢸⡿⣿⣎⣻⣿⣻⣾⡧⢈⡛⠋⠉⠁⠀⠉⠉⢹⠉⡇⢁⡆⠛⠃⠢⠃⠉⠉⠓⠉⠁⠀⠀⠛⠋⠀⠀⠀⠂⠛⠑⠁⠠⠀⠋⠈⠃⢰⢙⠀⠀⠒⠀⠀⠀⠠⠐⡺⠗⣻⣗⢿⠀⠀⠀⠀⠀⢠⣽⠀⠀⠀⠀⠀⠀⠀
⢨⣷⢼⢿⡮⠫⡫⣙⢻⣟⡾⠄⠀⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⠹⠉⡽⢩⠯⣭⣉⡍⡁⡏⠉⠉⠉⠉⢉⡍⣩⠭⠩⠉⠉⠉⠉⢉⠋⣼⡏⠉⠉⠉⠉⡍⠀⠀⠐⠞⣻⣿⡿⠛⡏⠙⠉⠉⠙⢈⣟⢼⣿⣾⣿⡟⠓⠒
⢸⣿⢴⣿⣿⣅⠘⢇⠈⠁⠈⠈⠀⠀⢸⣿⣗⣲⣒⣺⡷⣻⢻⣒⣒⣒⡒⠆⠉⢲⢻⡃⠀⡇⠛⡙⠉⠀⣺⣿⣷⠋⣛⣀⡀⣀⡈⣻⣻⣿⣁⠀⠀⠒⢒⠂⣀⣠⣶⢻⣧⣿⣟⠁⠂⠘⠛⠿⠿⠸⠯⠸⢿⣿⣿⣿⠿⠟
⢸⣿⠘⣿⣿⣿⣄⠰⠑⠀⠀⠀⠀⠀⠈⡷⣻⣿⣿⣿⣿⢭⣿⣿⣿⣿⣿⣿⣿⣯⢹⠀⢥⡏⣹⡉⢫⡅⠙⢰⠿⠯⡍⣽⣽⢩⣿⣿⢨⣭⣭⡍⣩⣭⣡⠙⢠⣴⣿⡿⡗⠐⠤⠖⢒⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣇⣨⣥
⢘⡟⢸⢹⣿⣿⠉⠷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣹⣿⢸⠀⣿⠇⢿⠇⢾⡗⢸⠸⣿⣿⡻⣻⢏⠘⣿⣿⢰⣾⣿⣿⣿⡿⠿⢸⢸⣻⣺⣷⣤⣤⣖⡻⣯⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⢰⡧⠬⢸⣿⡿⠀⣿⢮⠡⢰⡒⡒⢖⣲⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠟⣿⣿⣿⢻⢿⢻⣛⣻⡟⢻⡟⢺⢛⣿⡛⢻⣿⣿⠻⣿⣿⢻⣿⠿⠻⣟⣩⣭⣾⣼⣿⣿⣿⢿⣩⣶⢥⣽⣷⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⢘⡁⠀⠈⣛⣷⠀⣿⢸⢸⡘⢊⠲⣂⠃⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣿⣿⡟⢸⠾⢾⣿⢹⡇⣿⡯⢸⢸⣿⡇⢣⣭⣽⣶⡿⠓⢹⣿⣯⢽⣿⢽⣵⢸⢠⣿⣿⣿⣸⢳⣟⣟⣿⣯⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⢸⡁⣰⣾⣿⣿⡄⣿⣿⢻⣿⣦⡀⢈⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⢾⢰⢾⠿⠿⠷⡿⠧⢸⢼⣿⢿⡿⡿⢿⡤⠬⠶⠾⠿⠿⠬⣿⣾⠧⢸⠸⠿⢟⠻⢛⣬⢟⡞⢿⡏⡇⠀⠀⠀⠀⢸⡿⢿⡟⡛⢿⣿
⢸⣷⢻⣿⣿⣿⡆⣿⣿⢿⣿⣿⡇⣿⣿⣿⣾⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⡟⣸⣯⣿⢟⣇⢸⣸⡖⠀⡿⠓⢹⣿⣽⡄⣀⣤⡠⠀⣭⣭⣤⢸⠀⣶⣿⢸⣿⢾⡿⠽⢭⠿⡇⠀⠀⠀⠀⠘⠋⠫⠎⠈⠀⠻
⢸⣿⢸⡿⣿⣿⢱⣯⣭⢹⣿⣿⡇⣿⣿⣿⣿⣻⣿⣿⣯⣚⣛⣻⣿⣩⣥⣿⣼⣿⣸⣽⣁⣙⣉⣿⣸⣟⣸⢹⣀⣀⣯⣽⣼⣟⣿⣥⣾⣿⣆⣀⣿⣋⣹⢸⢀⣛⣻⣘⣻⣾⣷⣲⣿⣷⡅⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀
⢸⣿⢸⣟⣿⡇⣼⣿⠿⢾⣿⣿⡇⣿⣿⣿⣿⢓⣿⣿⣟⡻⢯⣿⣾⣿⢹⣷⣷⣾⢸⣼⡿⠇⡂⢠⣼⡇⢸⢀⢀⠀⣖⣶⣆⣀⣀⣀⢈⡈⢠⣤⣤⡄⠀⢸⢸⡅⣿⣶⣨⣼⣵⢧⣽⣤⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄
⢸⣿⢸⡏⣿⡿⢸⣿⣿⢸⠶⠖⠒⠉⣡⣿⢩⣝⢸⡇⢻⣿⣶⢻⣿⣿⢺⣿⣯⣿⢸⣿⣧⢾⣿⢸⡿⠇⢸⠐⣿⡀⣿⣿⣿⣾⣶⣶⣾⣿⢶⣿⣿⣿⡄⢸⢸⡷⣿⣭⣹⣹⣉⣏⣽⣩⡇⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣇
⠈⣯⣼⣟⣿⣂⣘⣻⣿⠬⢶⣷⠇⠠⢹⢓⣌⣽⣋⡗⣯⣽⣿⣿⣿⣿⣈⣯⣘⣙⣸⣻⣧⣿⣏⣬⣿⣆⣸⠀⣘⣂⣿⣯⣿⣽⣿⣿⣿⣿⣂⣿⣿⣯⡇⣘⠸⣃⣿⡿⣼⢳⠛⡞⢿⠿⡇⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿
⢠⣿⢸⣟⣛⣉⡙⢘⠛⣷⡎⠁⠀⠀⠘⣶⠤⣿⢷⡿⢿⠈⢒⠃⣚⢙⣟⣻⣟⣍⣉⣁⣿⣿⣻⣿⡝⢋⢙⣻⣿⣿⣝⢿⣿⣿⣿⡿⠟⢫⡭⣛⣯⣭⡍⠉⠀⡀⣫⡙⣿⢾⠟⡽⣿⡿⡇⠀⠀⠀⡀⣨⣿⣿⣿⣿⣿⣿
⢸⣿⢼⣿⣷⢻⡟⢸⠀⣿⣧⠀⠀⠀⠈⣿⣶⣵⣿⣿⣦⡴⡃⢨⡍⢀⡭⣭⡭⣿⣿⣿⣿⣿⣿⣿⣛⣿⠨⣹⣿⣿⣿⣷⡿⠿⢷⣷⠖⢾⡷⣿⣿⣿⣶⡉⢠⣿⣛⣱⣿⣿⣗⣳⣿⣥⡇⠒⠒⠶⠓⠚⠛⠻⠿⠿⠟⠻
⢸⣿⣼⣿⣿⢸⣿⣼⣄⡿⠟⠪⢿⣳⠈⠈⣉⣙⠿⠿⢉⢁⣄⠀⠀⢘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣯⣭⣤⣝⣷⣳⣿⣟⣉⣙⣿⣹⣥⣼⣿⣿⣿⣿⣾⣼⢣⣿⣡⡆⠀⠀⢠⠀⠀⠀⠀⠀⠠⠀⠀
⢸⣿⢼⣿⣿⢸⣿⠟⠋⠀⠀⠀⠘⣿⡸⣿⣿⡯⣼⣭⣿⣿⣿⣏⣁⢀⣿⢸⠛⣟⣻⣿⣿⣿⣿⣟⢿⣟⣿⣿⣿⣿⣿⣟⣿⣿⠛⢟⡛⠿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⠟⢿⢿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀
⣺⣿⢸⣿⡿⠏⠻⠷⠂⠀⠀⠀⠀⠈⢁⣁⡀⢰⣿⣯⣜⠋⡈⣿⣿⣿⣿⢸⣿⣽⡏⣻⣿⣿⣿⣩⡾⣿⣏⣛⠛⠓⠒⠐⢾⣯⣄⣼⣷⡐⢾⣷⣸⣏⣿⢀⠠⠾⡍⠓⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⡟⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠁⠠⠀⠀⢨⠟⠏⠛⠎⣹⣿⡇⣿⣿⣿⣿⣿⣅⡘⣿⣿⣿⣗⣦⠀⢻⣿⣿⣟⣯⣄⠨⣽⣿⣿⣿⡆⢀⢀⠄⠠⣿⢺⣶⣯⠽⢛⣇⠀⠀⠀⠀⠐⠂⠀⠐⠂⠀⠀
⠀⠿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠦⠐⡖⠒⠀⣀⠀⠀⠀⠀⠈⣿⣿⡇⣿⣿⣛⣟⣛⡿⠃⣿⣿⣿⢧⠉⠸⡇⣿⡟⢉⠉⠉⢡⣅⣀⣋⣛⡇⠀⠐⠆⠀⣿⢸⣿⣿⣾⣯⣿⠀⠀⠀⠀⠀⢀⣛⣛⣛⡀⠀
⡀⣀⣀⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠖⠀⠬⠁⠂⣀⢨⣧⢲⠐⠀⠀⢾⣿⠿⣿⣿⣿⣿⣿⠇⡖⣿⣿⣾⣷⡇⠠⠀⣿⣿⣿⣧⠀⣼⣿⣿⣿⣷⣧⣤⣤⣤⡀⢿⢸⣿⣿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀
⣿⢻⣿⡾⠻⡿⠛⠁⠁⠀⠀⠠⠠⢈⢴⡶⢻⢼⣲⠍⡍⠀⠀⠁⠠⠫⠻⢛⣗⣤⡀⢻⣿⣿⣿⣏⠀⠉⣿⣿⣿⠿⠃⠀⠉⣿⣿⣿⡿⠶⣿⣿⣿⣿⣿⡇⠈⣹⣯⣶⣾⣿⣿⡞⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢑⣦⡤⣀⡀⠀⢀⣀⣌⣸⣿⣆⣛⣿⣧⡗⣴⢆⣀⢠⣠⣴⣿⣿⣿⣿⡿⣿⣿⣝⣿⣷⣄⢭⣯⣯⣿⣿⣶⣔⠩⡉⢌⣠⡀⢰⣽⢽⣿⣯⡟⠠⣿⠛⠽⡟⠿⠿⠿⠷⠮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⣤⠘⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⠸⠇⢹⣤⣺⣿⣿⣿⣿⣿⣿⣸⡿⣿⣿⣿⣿⣷⣿⣿⣌⢟⢿⣿⣣⣬⣵⣽⢯⡦⡉⠛⠻⠇⠁⠀⠉⠁⠀⠈⠱⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠁⠀⠀⠀⠐⠒⢸⠉⠍⠉⠉⠉⠉⡇⠈⠀⠀⠀⠀⠘⠿⠿⡿⢹⣿⣿⣿⣿⣿⡟⣿⣷⠙⠻⣷⢳⡹⣿⢿⣾⣧⠿⢮⡻⠿⠟⠈⠋⠀⠀⠀⠀⢓⠒⠀⠀⠀⢐⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⣌⠀⠀⣾⣦⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠏⢻⣿⠚⣧⠀⠀⠈⠃⠙⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠙⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3725

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/04/18/To_Understand_Who_s_Truly_Controlling_You_Follow_the_Trail_of_C.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/04/18/To_Understand_Who_s_Truly_Controlling_You_Follow_the_Trail_of_C.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ To Understand Who's Truly Controlling You
Follow the Trail of Censorship (or Self-
Censorship)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025


5+ years ago: The_Linux_Foundation's_Linux_Kernel_Code_of_Conduct_(CoC)
Committee_is_Now_Officially_Corporate


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Tom_backfire:_Code_of_conduct,_Enforcement,_and_you⦈_


THIS past week we published a number of articles about the Linux_Foundation,
which keeps_trolling_the_community while deleting or misusing the word
"community". Over 5 years ago we compared the old Linux Foundation site to the
current (back then) site. All mentions of community got removed. That word used
to be everywhere in the site; they systematically replaced community with
Microsoft et al. and Torvalds has been rendered a Wintel mascot [1, 2], forced
to embrace things he disagrees with and dislikes (Rust is one of those things).


Censorship is a powerful thing, and not merely a concept. I worked in a company
called "Open Source" long enough to realise dissent is not really allowed,
except as a "token" or mere "discussion" gesture.


When people say they oppose a Code of Conduct (CoC) the immediate, reflexive
assumption is that they're bigots or something. Surely, they just want to cause
trouble, right? They worry a CoC would "get them".


I learned the hard way that disciplinary processes such as Code of Conduct
enforcements aren't about manners. I saw this in EPO, I_see_this_in_Python, and
we'll probably see this in WINE some time soon (it adopted a CoC when Mono was
dumped_into_it to distract from what_Microsoft_had_done_to_GNU/Linux_users).


If you believe that CoCs are about combating right-wing bigotry, then congrats!
You have been conned.


Opposing CoCs is mostly about freedom of expression and the right of dissent.
Democracies are in some sense not compatible with (in_practice) CoCs. Do not
let media steal and steer the narrative; CoCs are not about "social justice",
they're about corporate domination. Those two things are almost always
opposites. █


    * Fedora_Already_Lost_Its_Soul_Under_IBM
    * All_Your_"Github_Projects"_Will_be_Gone_One_Day_(Just_Like_Skype)


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠒⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡻⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠐⡖⠂⣦⢰⡆⡖⠂⡴⠒⡄⣶⠒⡄⡔⢲⡄⡖⠒⢰⠀⣰⠀⡖⠂⣶⠀⡆⢲⡖⠈⠀⠀⠀⠀⠀⠀⢀⠀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⡗⠂⡏⢾⡇⡗⠂⡇⠀⡇⣿⢺⠁⡇⢀⡀⡗⠂⡞⢇⢿⠀⡗⠂⣏⢣⡇⢸⡇⢰⠀⠀⠀⠀⠀⣰⡿⡄⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣔⣓⡂⠃⠘⠃⠃⠀⠙⠒⠁⠛⠈⠃⠙⠚⠁⠓⠒⠃⠘⠘⠀⠓⡂⠛⠈⠃⠘⣃⡜⡀⠀⣾⣦⡀⢹⣿⣇⠉⠙⢻⣿⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⢀⣀⣉⢛⡉⠉⣉⣁⣉⡁⢉⣉⢉⣁⣉⣉⣉⣋⣉⣂⡘⢒⣢⣶⣶⣶⣾⡇⠀⢿⣿⣷⡘⣿⣿⠀⣤⠀⢩⡍⢠⡤⣤⡀⢨⠅⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠿⣧⠰⠟⣠⠸⡆⡾⠀⣿⢠⢸⡇⢸⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⡷⠀⠀⢠⣶⠚⠀⠀⠀⢻⠃⡆⣿⠸⢸⡇⢸⡀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣦⣤⣽⣿⣶⣦⣤⣤⡸⣠⣧⠙⠶⠞⠁⠘⠳⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠋⠉⠋⠉⠀⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡳⣿⣿⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣴⠒⢦⠀⣴⠒⢶⡉⢰⠒⢲⡄⢰⡖⠒⠀⠀⢠⡖⠲⣆⠀⡖⠒⠊⠟⢀⡶⠒⣮⢉⡴⠒⣦⠁⣶⠙⢰⠂⣶⠒⢲⡄⢰⠀⠀⣶⢀⡶⠒⣦⠐⢲⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⣿⠰⢸⡇⢸⠀⢸⡇⢸⣧⡄⠀⠀⢸⡇⠀⣿⠀⣧⣤⠀⢀⢸⡇⣦⣟⢸⡇⠆⢸⠀⣿⢧⢸⠀⣿⠀⢸⡇⢸⠀⠀⣿⢸⡇⠀⠙⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⣰⠀⣿⠀⢸⡇⢸⠀⢸⡇⢸⡇⠀⠘⠀⢸⡇⠀⣿⠀⡇⠀⠀⣾⢸⡇⠃⣶⠸⡇⠁⣼⠀⣿⠈⣿⠀⣿⠀⢸⡇⢸⡄⢀⡟⠸⡇⠀⣶⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠈⠛⠋⠀⠘⠛⠋⠀⠘⠛⠛⠀⡀⠀⠙⠋⠁⠀⠃⣠⣧⡘⠃⠙⠛⠁⠀⠉⠛⠉⠀⣛⣴⣼⣤⡙⠛⠋⠀⠈⠙⠋⠁⠀⠉⠛⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣉⠰⠁⢀⡀⢼⡇⠈⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣶⣶⣦⣤⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⠀⠙⠿⠟⣡⣶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⠟⠻⠛⠛⠛⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠲⣶⡀⢐⣿⠃⠀⠀⢀⣦⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣦⣄⡈⠉⠉⠁⢀⣠⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣀⠀⠀⠀⠠⢤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3826

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 18/04/2025: Pinephone Pro and
Linux is too Easy⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇voodoo⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Politics and World Events⠀➾


                # ⚓ Israel⠀⇛


                       There are no words. I carry the boycott in my heart
                       even if the governments of the West stand complicit
                       in the genocide.


          o § Technology and Free Software⠀➾


                # ⚓ Pointless_auditing_😵⠀⇛


                       A while ago at work I fixed some things and
                       released to prod. As usual, this involved tickets,
                       code reviews, pull requests, test evidence, change
                       request approvals, post implementation checks, and
                       I've probably missed a few things off that list.
                       It's a bit tedious but normal. Time passed and I
                       now remember very little about it, but there's lots
                       of audit trail.


                       Today at 4:20pm I was asked to supply some evidence
                       for an audit of the change request, and could I do
                       so by 4:30, please. I was puzzled. The audit ticket
                       is in the same ticketing system, so the change
                       number automagically links to the ticket, which in
                       turn links to the other information. What more do
                       you need?


                # ⚓ Pinephone_Pro⠀⇛


                       I got #X11 running on the #PinephonePro under
                       #FreeBSD ! Shown here running my favourite #icewm
                       window manager. Super exciting! Now to get the
                       touch screen working 😬


                # ⚓ Recent_Read_and_Linux_is_too_Easy,_Redux⠀⇛


                       I found an old book written by Isaac Asimov while
                       perusing the stacks at my local library, it is "Buy
                       Jupiter" [0], a collection of his older short
                       stories. It is different from most, however, in
                       that the author follows each story with some auto-
                       biographical notes on what he was doing at the time
                       and how the story came to be published. It's a
                       great look into Asimov's mid-life and career, and I
                       found these notes very interesting.


                       ~ A recent republic bbs comment about how Linux had
                       become too easy reminded me of the very first
                       gopher post I wrote back in 2009 titled "Linux is
                       Boring, or Saved by the Slack" [1], followed up in
                       2020 by some similar sentiment [2] when sparcipx
                       mentioned wanting to ditch linux (sadly, his phlog
                       post is no longer online for me to reference).
                       There were more replies on the latter by ratfactor
                       [3], logout [4], and 1436.ninja [5].


                # ⚓ A_tipsy_girl's_thoughts_about_roguelikes/lites⠀⇛


                       Let me preface this by saying that — like the title
                       says — I'm not in the most sober of states while
                       writing this, but the thoughts running through my
                       head are plenty and I can't keep them all to
                       myself, can I? So excuse any grammatical errors I
                       might unknowingly make while writing this


                       Games are fun, REALLY fun, I mean most of you
                       reading this must've played at least *A* game
                       before in your life and it was definitely fun,
                       wasn't it? Recently I've been starting to play more
                       indie games, and more specifically, 𝓻𝓸𝓰𝓾𝓮𝓵𝓲𝓴𝓮𝓼 (and
                       roguelites as well, but it doesn't sound as
                       catchy). Now I've been a big fun of roguelikes for
                       as long as I can remember, pretty sure my first
                       PROPER roguelike was Enter the Gungeon, fun game, I
                       need to play it again sometimes, but as time went
                       on I had an itch, an insatiable itch which I
                       couldn't get rid of, yet I knew exactly what I
                       needed. More roguelikes


                # ⚓ Analog:_Comparator_Part_II_(publ._2025-04-17)⠀⇛


                       I've had some trouble implementing my comparator
                       using just op amps and the DG212B analog switches.
                       In my tests, something strange is happening where
                       the analog switches lock up after about a minute or
                       so of use, i.e., they stop responding to the
                       signals from the op amps. It is not quite the same
                       thing as latching up, since voltage supply is not
                       removed. However, if I cycle my +/- 15V power
                       supply, then the problem does go away, at least for
                       another minute or so. I think it is something
                       related to capacitance, as I can sometimes unlock
                       the analog switches by touching on the board with
                       my finger. I wondered if maybe there was a loose
                       connection somewhere but after further
                       investigation I don't think so. I'm planning to
                       build a simpler version of the circuit and do some
                       more testing.


                # § Internet/Gemini⠀➾


                      # ⚓ Tinylog_aggregator_update⠀⇛


                             This entry started as en email to
                             @fab@redterminal.org (for the second part of
                             this entry) but I thought it was a good idea
                             to actually publish it here, so here we are :
                             ).


                             Today (well, technically it is now
                             yesterday), I updated the tinylog aggregator,
                             both the codebase of GTL (the tool used to
                             generate the aggregator page) and the
                             subscription list.


                             Regarding the codebase of GTL, I didn’t
                             change anything related to the spec yet,
                             except the way the date format. But that
                             isn’t a change in the codebase per say,
                             because that display format was a
                             configuration, so I updated the config, not
                             the code.


                             What changed with GTL code is its robustness
                             to ensure links were aggregated correctly.
                             What I found was that firing go routine to
                             retrieve all entries in a loop was causing
                             issues apparently. I simply added a timer to
                             wait 200 milliseconds between each requests.
                             Doing so made GTL timeline calculation a bit
                             slower, it is true, but made it a lot more
                             robust. So at least for the aggregator I’m
                             going to keep it like that. Maybe I’ll make
                             that parameter configurable so people with
                             stronger computers and/or network may want to
                             reduce that waiting time? I don’t know, but
                             at least the aggregator page has been stable
                             the full afternoon without tinylog entries
                             disappearing and reappearing during each
                             update.


                      # ⚓ Freezr_"P.E.B.C.A.K."_⌨️⠀⇛


                             Indeed… I am finally here again! 💪 I am going
                             to dedicate more time to this capsule even
                             though my spare time has shrunk to almost
                             nothing, but I still love the idea to have
                             Gemini to succeed so I won't give up just for
                             the laziness!


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


    * Links_17/04/2025:_Russian_Bot_Farms_Infect_TikTok_(Which_US_Government
      and_SCOTUS_Decided_to_Block_January_19),_US_Hardware_Stocks_Crash_Due_to
      Tariffs
    * IRC_Proceedings:_Thursday,_April_17,_2025



                    ䷩ 𝚕𝚒𝚗𝚎 4042

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 18/04/2025: Price of Games and
State of Tinylog⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ 🔤SpellBinding_—_ACEIURQ_Wordo:_DIVAN⠀⇛


                # ⚓ Narc_Jarvis_is_no_milkshake_duck⠀⇛


                       Yesterday I noted I was having some kind of
                       Thought. I have now read so many articles on
                       identity and technofeudalism that I'm losing my own
                       plot. Here's a first shot at an abstract slash
                       summary of whatever point I'm attempting.


          o § Technology and Free Software⠀➾


                # ⚓ $80_for_a_Nintendo_game_is_pretty_cheap_by_my_personal
                  early-to-mid_’90s_standards⠀⇛


                       I’ll put this link up front not because it’s likely
                       that you’ll need to refer to it to understand what
                       I’m writing here — you won’t — but more on general
                       principle:


                       [...]


                       Now then.


                       Recently, many people have been discussing the
                       prices of first-party Nintendo Switch 2 games.
                       Current estimates are that digital games will cost
                       $80 (the price of Mario Kart World). As I write
                       this, most of us are used to paying $60 for first-
                       party Nintendo games, with The Legend of Zelda:
                       Tears of the Kingdom being a noticeable (and
                       alarming) break from tradition at $70 at the time
                       of its release in May 2023. In contrast to games
                       sold on Steam, first-party Switch games sold in the
                       Nintendo eShop rarely go on sale and when they do,
                       it’s usually for only $10 off the unchanging
                       sticker price.


                       While $80 gives me sticker shock just like everyone
                       else, I thought that this would mostly be in line
                       with inflation. Kyle Orland, writing at Ars
                       Technica, has a nice chart showing “Average
                       inflation-adjusted prices for top-end video games”
                       (in 2/2025 dollars). Long story short, games were
                       significantly more expensive than $80-in-February-
                       2025 back in the 80s and mid-90s:


                       => https://arstechnica.com/gaming/2025/04/will-
                       mario-kart-worlds-80-price-become-gamings-new-
                       normal/ Kyle Orland at Ars Technica, “Mario Kart
                       World’s $80 price isn’t that high, historically”


                       However, even after seeing this article, I didn’t
                       really have an idea of what I actually paid for
                       games back in the day. Sure, one could look at
                       scans of 30-year-old advertisements passed around
                       on the Internet, but those are sales and it’s not
                       really obvious how representative those numbers
                       would be. Plus, I generally didn’t buy games at the
                       more expensive toy store — I bought them at a
                       decent discount later on at the local boring
                       department store.


                # ⚓ Tinylog⠀⇛


                       I agree with the all things described in last
                       commit. The tinylog format should be easy (as the
                       Gemini protocol is) and human manageable. So the
                       simplification of date format and in the same
                       manner simplification of response format will help
                       us to use tinylogs.


                       The only open issue for me is how people who use
                       more complicated date format should behave. I'm
                       using the linux date command in vi to add date
                       heading of every entry. And it's easy to do that in
                       the new manner for new entries. Should I have to
                       correct the older entries?


                       P.S I've announced RFC update call on
                       comp.infosystems.gemini so more people will be able
                       to remember about tinylogs.


                # ⚓ Digital_housekeeping:_~/.alias⠀⇛


                       Today, alongside clearing out about an inch-high
                       stack of physical paperwork, I hacked back the
                       hypertrophy in my ~/.alias file. This is the file
                       that sets up the abbreviations and utilities that
                       are available on the commandline for me, beyond the
                       system defaults.


                       This file is part of a small set of material which
                       gets hodded from laptop to laptop and from one
                       shell account to another; those dotfiles go back to
                       1995 in my lamentable case, and represent a series
                       of nine personal machines such as laptops, and a
                       bunch of work/social UNIX and Linux accounts.
                       Continuity is good; clutter is bad.


                       Getting the most out of muscle memory means having
                       roughly the same shortcuts and commands everywhere,
                       so some means must be found for keeping my personal
                       day-to-day machine in sync with the three or four
                       others I must use for work or social matters.
                       Nowadays there is no longer NFS to centralise all
                       this.


                       Ultimately this material is pretty valuable. It
                       saves huge amounts of repeated effort, and is how
                       Ken Thompson and Doug McIlroy wanted us to use
                       UNIX: gradually building up tools based on other
                       tools. I have a tool just for finding out what
                       commands I am overusing, so I can save them as
                       aliases or scripts. That is of course upstream of
                       the problem of having so many saved scripts that
                       the system starts to become cluttered and
                       unmanagable.


                # § Internet/Gemini⠀➾


                      # ⚓ Why_I_do_not_use_social_media⠀⇛


                             As common as this type of post or blog entry
                             may be, I really wish to speak out on this.


                             For years and months long before, I thought I
                             would not be able to live without some sort
                             of social platform. In most cases, I spent
                             time and time again, looking at varying posts
                             on various apps.


                             I probably spent most of it on YouTube.
                             Considering how easy it is to find content on
                             there, with sheer amounts of videos, it is no
                             wonder why that is the case. Though, all of
                             this is still pretty much served by the
                             algorithm and not my own sound reasoning.


                             Now, algorithms are various - today this is
                             pretty much a blanket term. Either way almost
                             all, if not all, social media use some sort
                             of algorithm for finding and choosing the
                             content you are most likely to consume and,
                             thus, spend more time on the platform. As a
                             result, however, it ends up destroying the
                             human brain, with endless stream of mindless
                             content.


                             This is not how it used to be: without enough
                             computational power or the modern
                             technologies we use, there was no way of
                             serving such an algorithm en masse. Somehow,
                             people still found entertainment in the BASIC
                             programs from magazines or their own
                             discovery and learning. People spent time
                             finding good sites and reading blogs or, at
                             the time, just reading the personal sites of
                             others.


                             Now, though, we are served a mindless and ad-
                             filled web. We are served filtered content
                             and censored news. Sites are heavy and
                             riddled with useless features or tons of
                             spying javascript. That is not how it should
                             be.


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


    * Sounds_Like_IBM_is_Preparing_for_Mass_Layoffs/Redundancies_in_Red_Hat,
      Albeit_in_"PIP"_(Performance_Improvement_Plan)_or_"Relocation"_Clothing
    * Links_18/04/2025:_"Fentanylware_(TikTok)_Exodus_Continues",_Chinese
      Weapons_Allegedly_in_Russia_Already



                    ䷩ 𝚕𝚒𝚗𝚎 4280

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 18/04/2025: "Fentanylware (TikTok)
Exodus Continues", Chinese Weapons Allegedly in Russia
Already⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Signpost_indicating_the_distance_between_different_cities
and_Natashquan,_Minganie,_Quebec,_Canada⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Privatisation/Privateering
          o Security
                # Privacy/Surveillance
                # Confidentiality
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # Overpopulation
          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
                # Patents
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ NYPost ☛ Spain’s_Sagrada_Familia creating_space_to_curb_tourist
            crowds_as_public_area_reaches_‘saturation_point’⠀⇛


                 Many travelers to Barcelona, Spain, may find themselves
                 at one of the most beautiful sacred places in the world:
                 the Sagrada Familia.


          o ⚓ France24 ☛ 'Paris_Noir':_A_cultural_crossroads_for_Black
            artists⠀⇛


                 Paris's status as a cosmopolitan hub for artists from all
                 over the world was forged in the 20th century,
                 particularly in the postwar period, when it was seen as a
                 beacon for Black artists and intellectuals fleeing
                 colonisation, racism and segregation in their countries
                 of origin. The "Paris Noir" exhibition at Paris's
                 Pompidou Centre is now exploring that pivotal moment when
                 the French capital served as a crossroads for the major
                 Black figures who were debating and designing a post-
                 colonial future. The show features 350 works by 150
                 artists of African heritage – many of whom have been
                 historically sidelined or forgotten – in an attempt to
                 re-write these "unrecognised and fundamental"
                 contributions into a more complete history of art.


          o ⚓ Hackaday ☛ A_Blacksmith_Shows_Us_How_To_Choose_An_Anvil⠀⇛


                 No doubt many readers have at times wished to try their
                 hand at blacksmithing, but it’s fair to say that
                 acquiring an anvil represents quite the hurdle. For
                 anyone not knowing where to turn there’s a video from
                 [Black Bear Forge], in which he takes us through a range
                 of budget options.


          o ⚓ Chris_H-C:_Perfect_is_the_Enemy_of_Good_Enough⠀⇛


                 My Papa, my mother’s father, C. J. Mortimer died in Saint
                 John, New Brunswick in 2020. Flying through the Toronto
                 and Montreal airports in September to his funeral was one
                 of the surreal experiences of my life, with misting
                 tunnels of aerosolized alcohol to kill any microbe on
                 your skin, hair, clothes, and luggage; airport terminals
                 with more rodent traps than people; and a
                 hypersensitivity to everyone’s cough and sniffle that I
                 haven’t been able to shake.


                 I was angry, then. I’m still angry. Angry that I couldn’t
                 hug my grandmother. Angry that weeping itself was
                 complicated and contagious. Angry that I couldn’t be
                 together or near or held. Angry that I was putting my
                 family at home at risk by even going. Angry that we
                 didn’t hold the line on the lockdowns long enough to
                 manage the disease properly. Angry at the whiners.


          o § Science⠀➾


                # ⚓ Tom's Hardware ☛ Chinese_brain_computer_interface_user
                  reportedly_plays_'Black_Myth:_Wukong,'_other_games⠀⇛


                       Chinese researchers claim their high-precision
                       real-time BCI is good enough for Black Myth: Wukong
                       gaming.


                # ⚓ Science Alert ☛ Meet_Zhúlóng,_The_Milky_Way_'Twin'_That
                  Shakes_Up_Our_Cosmic_Timeline⠀⇛


                       It's truly incredible.


                # ⚓ Science Alert ☛ Study_on_Mice_Suggests_Surprising_Link
                  Between_Nose-Picking_And_Alzheimer's⠀⇛


                       Do you really need to pick it?


                # ⚓ Science Alert ☛ There's_A_Sky_Full_of_Meteors_in_April!
                  Here's_What's_on_This_Easter_Weekend⠀⇛


                       The first good shower of the season.


                # ⚓ Science Alert ☛ Curiosity_Finds_First_In_Situ_Evidence_of
                  Carbon_Cycle_on_Ancient_Mars⠀⇛


                       "It tells us that the planet was habitable."


                # ⚓ Science Alert ☛ Half_The_Universe's_Matter_Was_Missing.
                  Astronomers_Just_Found_It.⠀⇛


                       "Opens the door for an exciting new line of
                       research."


          o § Career/Education⠀➾


                # ⚓ Stanford University ☛ Strawser_|_Stanford_must_never
                  surrender⠀⇛


                       Dihydroxyacetone Man’s repeated attacks on every
                       aspect of our community demand bold action from
                       Stanford leadership, writes Strawser.


                # ⚓ New York Times ☛ School_Vouchers_Won_in_Texas._Next_Up,_the
                  Nation.⠀⇛


                       Choice laws have now passed in every major
                       Republican state. Congress and Hell Toupée are now
                       aiming at blue states that have resisted vouchers
                       for decades.


                # ⚓ University of Michigan ☛ GEO_holds_rally_in_support_of
                  international_graduate_workers⠀⇛


                       More than 200 protesters with the Graduate
                       Employees’ Organization gathered outside Rackham
                       Auditorium Thursday afternoon for an Immigration
                       Rights Solidarity Rally. The protest was a response
                       to 12 recent University of Michigan student visa
                       terminations by the Department of Homeland
                       Security, amongst fears of further visa revocations
                       for international graduate workers. 


                # ⚓ Chronicle Of Higher Education ☛ A_Professor_Reflects_on_a
                  Decades-Long_Effort_to_Deport_Pro-Palestinian_Protesters⠀⇛


                       The Reagan administration detained the “Los Angeles
                       Eight,” mostly students and recent graduates. Hell
                       Toupée is now citing similar national-security
                       arguments in his immigration crackdown.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Modernizing_An_Enigma_Machine⠀⇛


                       This project by [Miro] is awesome, not only did he
                       build a replica Enigma machine using modern
                       technologies, but after completing it, he went back
                       and revised several components to make it more
                       usable. We’ve featured Enigma machines here before;
                       they are complex combinations of mechanical and
                       electrical components that form one of the most
                       recognizable encryption methods in history.


                # ⚓ Hackaday ☛ Bicycle_Gearbox_Does_It_By_Folding⠀⇛


                       If you’ve spent any time on two wheels, you’ve
                       certainly experienced the woes of poor bicycle
                       shifting. You hit the button or twist the knob
                       expecting a smooth transition into the next gear,
                       only to be met with angry metallic clanking that
                       you try to push though but ultimately can’t.
                       Bicycle manufacturers collectively spent millions
                       attempting to remedy this issue with the likes of
                       gearboxes, electronic shifting, and even belt-
                       driven bikes. But Praxis believes to have a better
                       solution in their prototype HiT system.


                # ⚓ Hackaday ☛ Designing_An_FM_Drum_Synth_From_Scratch⠀⇛


                       How it started: a simple repair job on a Roland
                       drum machine. How it ended: a scratch-built FM drum
                       synth module that’s completely analog, and
                       completely cool.


                # ⚓ Hackaday ☛ Rise_Of_The_Robots:_How_Robots_Are_Changing
                  Dairy_Farms⠀⇛


                       Running a dairy farm used to be a rather hands-on
                       experience, with the farmer required to be around
                       every few hours to milk the cows, feed them, do all
                       the veterinarian tasks that the farmer can do
                       themselves, and so on. The introduction of milking
                       machines in the early 20th century however began a
                       trend of increased automation whereby a single
                       farmer could handle a hundred cows by the end of
                       the century instead of only a couple. In a recent
                       article in IEEE Spectrum covers the continued
                       progress here is covered, including cows milking
                       themselves, on-demand style as shown in the top
                       image.


                # ⚓ Hackaday ☛ Budget_Schlieren_Imaging_Setup_Uses_3D_Printing
                  To_Reveal_The_Unseen⠀⇛


                       We’re suckers here for projects that let you see
                       the unseeable, and [Ayden Wardell Aerospace]
                       provides that on a budget with their $30 Schlieren
                       Imaging Setup. The unseeable in question is
                       differences in air density– or, more precisely,
                       differences in the refractive index of the fluid
                       the imaging set up makes use of, in this case air.
                       Think of how you can see waves of “heat” on a warm
                       day– that’s lower-density hot air refracting light
                       as it rises. Schlieren photography takes advantage
                       of this, allowing to analyze fluid flows– for
                       example, the mach cones in a DIY rocket nozzle,
                       which is what got [Ayden Wardell Aerospace]
                       interested in the technique.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ Measles_Outbreaks_in_Canada_and_Mexico
                  Bring_Grim_Prognosis⠀⇛


                       Surges in Mennonite communities near the U.S.
                       border may complicate containment efforts, experts
                       say.


                # ⚓ New York Times ☛ The_Firefighter_With_O.C.D._and_the
                  Vaccine_He_Believed_Would_Kill_Him⠀⇛


                       For years, Timmy Reen tried to hide his compulsions
                       and rituals from everyone at his New York City
                       firehouse — until his secret was forced out in the
                       open.


                # ⚓ PHR ☛ Dihydroxyacetone_Man_Administration’s_Immigration
                  Policies_and_Rhetoric_Block_Access_to_Health_Care:_PHR
                  Research_Brief⠀⇛


                       The Forrest Dump administration’s immigration
                       policies are resulting in decreased access to
                       health care among undocumented immigrants,
                       individuals with other immigration statuses, and
                       U.S. citizens, according to a new survey of 173
                       health care professionals across the United States,
                       published today by Physicians for Human Rights
                       (PHR).


                # ⚓ The Straits Times ☛ China's_former_agriculture_minister
                  faces_graft_charges⠀⇛


                       China's former agriculture minister, Tang Renjian,
                       is facing bribery charges, the nation's top
                       prosecutor said on Thursday, after his high-profile
                       arrest last year in President Pooh-tin Jinping's
                       sweeping anti-graft campaign.


                # ⚓ The Straits Times ☛ Little_bites,_big_returns:_India’s
                  snacks_industry_draws_foreign_investors⠀⇛


                       The industry is projected to grow at a rate of
                       around 10.5 per cent each year for the next five
                       years.


          o § Proprietary⠀➾


                # ⚓ Microsoft_Infosys_Layoffs:_IT_Giant_Lays_Off_More_240
                  Trainees_Who_Failed_Internal_Assessments,_Offers_Free
                  Upskilling⠀⇛


                       Infosys has reportedly laid off around 240 trainees
                       after they failed to pass internal assessments. The
                       development follows a previous round of layoffs in
                       February for similar reasons. The Infosys layoffs
                       came as the company announced its fiscal fourth-
                       quarter earnings results. Infosys on Thursday
                       reported that its consolidated net profit for the
                       fourth quarter of the financial year 2024-25
                       dropped by 11.7% to INR 7,033 crore compared to the
                       same quarter last year.


                # ⚓ Amazon Inc ☛ Port_.NET_Framework_workloads_to_Linux_with
                  Amazon_Q_Developer,_Part_3:_Web_APIs⠀⇛


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ Scoop News Group ☛ House_investigation_into_DeepSeek
                        teases_out_funding,_security_realities_around_Chinese
                        Hey_Hi_(AI)_tool [Ed: Hype and hysteria over a passing
                        fad that makes FUD]⠀⇛


                             A new report fleshes out the resources that
                             went into building DeepSeek’s R1 reasoning
                             model and potential risks to U.S. economic
                             and national security.


                      # ⚓ Press Gazette ☛ AI_scraper_violations_and_what_we_can
                        do_about_them:_New_research_reveals_scale_of_problem⠀⇛


                             Paul Hood reveals data from new Miso.AI
                             research into Hey Hi (AI) scrapers and
                             suggests some tech solutions.


                # § Social Control Media⠀➾


                      # ⚓ The Straits Times ☛ Dihydroxyacetone_Man_signals_tit-
                        for-tat_China_tariffs_may_be_near_end;_Fentanylware_
                        (TikTok)_deal_on_ice⠀⇛


                             The Insurrectionist on Thursday signaled a
                             potential end to the tit-for-tat tariff hikes
                             between the U.S. and China that shocked
                             markets, and that a deal over the fate of
                             social control media platform Fentanylware
                             (TikTok) may have to wait.


                      # ⚓ Digital Music News ☛ Fentanylware_(TikTok)_Exodus
                        Continues:_US_Head_of_Policy_Steps_Down_Amid_Ongoing
                        Negotiations⠀⇛


                             TikTok’s U.S. Public Policy Chief Michael
                             Beckerman is stepping down from his role to
                             transition to a global advisory position. The
                             departure comes amid the second extension of
                             the U.S. deadline for ByteDance to divest
                             from Fentanylware (TikTok) — and follows a
                             number of high-profile departures at the app.


                      # ⚓ New York Times ☛ At_Meta_Antitrust_Trial,_Sheryl
                        Sandberg_Testifies_About_Competition_and_Instagram
                        Deal⠀⇛


                             In her second day on the stand of a landmark
                             antitrust trial over Meta’s power, Ms.
                             Sandberg, the former chief operating officer,
                             also said the company faced plenty of
                             competition from TikTok.


                      # ⚓ France24 ☛ TikTok_trials_it’s_own_take_on_X-style
                        “community_notes”_against_misinformation⠀⇛


                             To add context to videos, social control
                             media behemoth Fentanylware (TikTok) has
                             launched Footnotes: a crowd-sourced fact-
                             checking feature similar to the "community
                             notes" used by X and Meta. TikTok's version
                             though, takes a different approach -
                             - complementing it's professional fact-
                             checking, and not replacing it. It is
                             trialling first in the US, where it's future
                             currently hangs in the balance, as the
                             deadline for its US divestiture is just
                             months away. Vedika Bahl tells us what we
                             know, in Truth or Fake.


          o § Privatisation/Privateering⠀➾


                # ⚓ Pro Publica ☛ Trump_Team_Eyes_Thiel-Backed_Firm_Ramp_for
                  $700B_Payments_Program⠀⇛


                       Four days before Donald Trump’s inauguration,
                       financial technology startup Ramp published a pitch
                       for how to tackle wasteful government spending. In
                       a 4,000-word blog post titled “The Efficiency
                       Formula,” Ramp’s CEO and one of its investors
                       echoed ideas similar to those promoted by Trump and
                       his billionaire ally Elon Musk: Federal programs
                       were overrun by fraud, and commonsense business
                       techniques could provide a quick fix.


                       Ramp sells corporate credit cards and artificial
                       intelligence software for businesses to analyze
                       spending. And while the firm appears to have no
                       existing federal contracts, the post implied the
                       government should consider hiring it. Just as Ramp
                       helped businesses manage their budgets, the company
                       “could do the same for a variety of government
                       agencies,” according to the blog and company social
                       media posts.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Security Week ☛ Man_Helped_Chinese_Nationals_Get_Jobs
                        Involving_Sensitive_US_Government_Projects⠀⇛


                             Minh Phuong Ngoc Vong pleaded guilty to
                             defrauding US companies of roughly $1 million
                             in a fake IT worker scheme.


                      # ⚓ EDRI ☛ Civil_society_to_European_Commission:_Act_now
                        to_defend_fundamental_rights_from_Hungary’s_Pride_ban
                        and_the_use_of_facial_recognition_against_protesters⠀⇛


                             EDRi, along with a broad coalition of civil
                             society organisations, demands urgent action
                             from the European Commission on Hungary’s new
                             law banning Pride marches and permitting the
                             use of live facial recognition technology
                             targeting protesters.


                      # ⚓ OpenRightsGroup ☛ New_report:_How_Meta_is_monetising
                        the_migrant_crisis⠀⇛


                             How Meta monetises the migrant crisis Social
                             media giant Meta is profiting from the global
                             migrant crisis – enabling both criminals and
                             the UK Home Office to target vulnerable
                             migrants with adverts. Research by ORG found
                             that fraudulent adverts offering fake
                             identity documents are still being run on
                             Facebook.


                # § Confidentiality⠀➾


                      # ⚓ Dhole Moments ☛ Retrospective:_Five_Years_Blogging
                        About_Cryptography_as_a_Gay_Furry_Online⠀⇛


                             The history of this blog might very well be a
                             cautionary tail (sic) about scope creep. The
                             Original Vision For Dhole Moments Originally,
                             I just wanted a place to write about things
                             too long for Ex-Twitter (back when I was an
                             avid Ex-Twitter poster).


          o § Defence/Aggression⠀➾


                # ⚓ JURIST ☛ UN_Security_Council_urged_to_take_united_action_in
                  DR_Congo_as_conflict_deepens⠀⇛


                       UN Special Envoy Huang Xia called for greater
                       coordination of efforts to resolve the conflict in
                       the Democratic Republic of the Congo on Wednesday
                       amid escalating violence by the M23 rebel group and
                       a deepening humanitarian crisis in the region.


                # ⚓ Hong Kong Free Press ☛ Nat._sec_amendments_to_Hong_Kong
                  union_laws_to_be_submitted_to_‘patriots_only’_legislature_at
                  end_of_month⠀⇛


                       Amendments to Hong Kong’s trade union laws
                       proposing jail terms of up to three years for
                       national security infractions will go to the city’s
                       legislature later this month.


                # ⚓ Defence Web ☛ Amnesty_calls_for_justice_over_reckless
                  security_force_violence_in_Mozambique⠀⇛


                       Mozambican security forces used reckless and
                       unnecessary force in a widespread crackdown on
                       protests following last October’s election,
                       resulting in unlawful killings and devastating
                       injuries, Amnesty International has said in a new
                       report.


                # ⚓ Atlantic Council ☛ The_US_must_sustain_counterterrorism
                  operations_in_Somalia—the_costs_of_retreat_are_too_high⠀⇛


                       To maintain a foothold in East Africa’s security
                       architecture, the US must prioritize continuity,
                       including keeping the US embassy in Mogadishu open.


                # ⚓ JURIST ☛ Gambia_former_paramilitary_soldier_convicted_under
                  US_Torture_Act⠀⇛


                       Gambian national Michael Sang Correa was convicted
                       by a Colorado jury for participating in the torture
                       of victims in 2006, the US Department of Justice
                       (DOJ) said Tuesday. Correa was a part of a
                       paramilitary unit known as the “Junglers,” run by
                       Yahya Jammeh, dictator and former Gambian
                       president.


                # ⚓ RFERL ☛ US_Air_Strikes_Targeting_Yemeni_Oil_Port;_Huthis
                  Say_Attack_Killed_20_People⠀⇛


                       The US military said it destroyed a key Yemeni fuel
                       port held by Huthi rebels, who said the air strikes
                       also killed 20 people and wounded 50 others.


                # ⚓ France24 ☛ Hamas_rejects_Israel's_latest_ceasefire
                  proposal,_calls_for_comprehensive_deal⠀⇛


                       Hamas on Thursday rejected Israel's latest truce
                       offer, demanding a "comprehensive" deal to end the
                       18-month war. The group's chief negotiator spoke
                       after Gaza rescuers said Israeli strikes killed at
                       least 40, mostly women and children, in renewed
                       attacks


                # ⚓ New York Times ☛ Dihydroxyacetone_Man_Waved_Off_Planned
                  Israeli_Strike_on_Iranian_Nuclear_Sites⠀⇛


                       Israel developed plans for attacking Iranian
                       nuclear facilities that would have required U.S.
                       assistance. But some administration officials had
                       doubts.


                # ⚓ New York Times ☛ Israel_Strikes_Area_With_Tent_Camps_for
                  Displaced_Gazans⠀⇛


                       The attack on the Mawasi area of southern Gaza
                       killed at least a dozen people, according to the
                       emergency rescue service in the territory. Israel
                       did not confirm the location of the attack.


                # ⚓ France24 ☛ Israel_continues_pounding_on_Gaza,_at_least_40
                  killed_in_strikes⠀⇛


                       Gaza's civil defence agency said Thursday that a
                       rash of Israeli air strikes killed at least 40
                       people, most of them in encampments for displaced
                       civilians, as Israel pressed its offensive in the
                       Palestinian territory. The Israeli military said it
                       was looking into reports of the strikes, which came
                       as Hamas officials reported that internal
                       deliberations on the latest Israeli truce offer
                       were nearly complete.


                # ⚓ Defence Web ☛ G7_and_EU_denounce_two-year-old_Sudan_war⠀⇛


                       The war in Sudan, dubbed by some the one the world
                       forgot, this week marked the second year of ongoing
                       hostilities between the Sudanese Armed Forces (SAF)
                       and the opposition Rapid Support Forces (RSF),
                       Events in the east African country led to what are
                       currently the world’s largest humanitarian and
                       displacement crises.


                # ⚓ Pro Publica ☛ After_Downfall,_Terrorgram_Still_Inspires
                  Violence⠀⇛


                # ⚓ The Express Tribune ☛ Hacking_group_Anonymous_targets
                  Russia,_releases_Trump_files⠀⇛


                       Hacking group Anonymous has claimed responsibility
                       for a large-scale cyberattack on Russian networks,
                       releasing what it says is 10 terabytes of leaked
                       data containing sensitive information on political
                       figures, state-affiliated businesses, Kremlin
                       assets abroad, and even files allegedly linked to
                       US President Donald Trump.


                       The data was released on 15 April and announced
                       publicly via the group’s official account on X,
                       formerly known as Twitter. In the post, Anonymous
                       stated: “In defence of Ukraine Anonymous has
                       released 10TB of leaked data on all businesses
                       operating in Russia, all Kremlin assets in the
                       West, pro-Russian officials, Donald Trump, and
                       more.”


                       Accompanying the post was a photo of file folders,
                       one of which was labelled “Leaked Data of Donald
                       Trump.”


                # ⚓ The Straits Times ☛ Malaysia_PM_to_hold_talks_with_Myanmar
                  opposition_after_meeting_junta_chief⠀⇛


                       BANGKOK - Malaysian Prime Minister Anwar Ibrahim
                       will hold talks with a key Myanmar opposition group
                       on Friday, a day after he met the leader of the
                       war-torn country's ruling junta in Bangkok to
                       discuss humanitarian needs after a devastating
                       earthquake.


                # ⚓ The Straits Times ☛ Malaysia_PM_met_Myanmar_junta_chief
                  amid_opposition_to_talks⠀⇛


                       PM Anwar said he will meet Myanmar’s Senior General
                       Min Aung Hlaing on humanitarian grounds.


                # ⚓ The Straits Times ☛ Malaysia_trade_minister_to_head_to_U.S.
                  next_week_for_tariff_talks⠀⇛


                       KUALA LUMPUR - Malaysia's trade minister will
                       travel to the United States on April 24 to meet the
                       U.S. Trade Representative and other officials for
                       talks about the U.S. tariffs imposed on the
                       country, state media agency Bernama reported on
                       Thursday.


                # ⚓ Xi_Jinping_talks_of_former_fights_and_future_shocks_on
                  Southeast_Asian_tour⠀⇛


                       The Chinese president is in Cambodia after visiting
                       Vietnam, Malaysia amid a trade battle with the U.S.


                # ⚓ The Straits Times ☛ China_commends_Cambodia_when_asked
                  about_Taiwanese_deportation⠀⇛


                       China on Thursday commended the Cambodian
                       government for following the "one China principle"
                       when asked to comment on their deportation of
                       Taiwanese citizens to China earlier this week.


                # ⚓ Myanmar_junta_chief_meets_Malaysian_PM_in_Bangkok,_frees
                  5,000_in_prisoner_amnesty⠀⇛


                       High-profile figures, such as Aung San Suu Kyi,
                       were not included in Thursday’s release.


                # ⚓ New York Times ☛ Here’s_What_to_Know_About_Rare_Earth
                  Minerals_and_Renewable_Energy⠀⇛


                       The shift to cleaner power needs resources from
                       China. An export ban just cut off some supplies.


                # ⚓ CS Monitor ☛ Slapped_with_tariffs,_some_US_trade_partners
                  lean_toward_Beijing⠀⇛


                       To maximize the impact of tariffs, Washington wants
                       to ensure China cannot trade more with other
                       countries. But Beijing is a tempting trade partner.


                # ⚓ New York Times ☛ China_Wants_Countries_to_Unite_Against
                  Convicted_Felon,_but_Is_Met_With_Wariness⠀⇛


                       Beijing is using a mix of carrots and sticks to try
                       to prevent other countries from siding with the
                       United States in isolating China.


                # ⚓ Hong Kong Free Press ☛ Nvidia_CEO_visits_China_as_US_tech
                  curbs,_trade_war_threaten_sales⠀⇛


                       Nvidia CEO Jensen Huang arrived in Beijing on
                       Thursday, state media said, days after the United
                       States curbed sales of its H20 artificial
                       intelligence chips to China.


                # ⚓ New York Times ☛ Nvidia_C.E.O._Meets_With_Chinese_Trade
                  Officials_in_Beijing⠀⇛


                       The day before the visit by Jensen Huang, lawmakers
                       in Washington said they were investigating whether
                       the chipmaker’s sales in China violated U.S. rules.


                # ⚓ Silicon Angle ☛ Nvidia_CEO_Jensen_Huang_visits_Beijing
                  following_US_chip_export_restrictions⠀⇛


                       Nvidia Corp. Chief Executive Officer Jensen Huang
                       visited Beijing today to meet with Chinese
                       officials and the chipmaker’s local customers.
                       According to the Financial Times, DeepSeek founder
                       Liang Wenfeng was among the clients who
                       participated in the discussions. DeepSeek rose to
                       prominence earlier this year after it released a
                       reasoning model called R1.


                # ⚓ CS Monitor ☛ California_designs_a_trade_plan_to_blunt
                  tariffs._Be_careful,_China_expert_says.⠀⇛


                       California Gov. Gavin Newsom says that to protect
                       its economy from tariffs, the state can make its
                       own trade deals with China. Orville Schell,
                       director of the Center on U.S.-China Relations at
                       the Asia Society, says California has to step
                       carefully to avoid working against federal
                       government interests.


                # ⚓ The Straits Times ☛ China,_US_at_impasse_over_who_should
                  start_trade_talks⠀⇛


                       China's commerce ministry on Thursday urged the
                       United States to stop putting \"extreme pressure\"
                       on the world's second-largest economy and demanded
                       respect in any trade talks, but the two sides
                       remained at an impasse over who should start those
                       talks.


                # ⚓ China_appoints_new_trade_negotiator_as_US_tariff_tensions
                  mount⠀⇛


                       Li Chenggang, a legal expert and former WTO envoy,
                       takes post at a challenging time for US-China
                       relations.


                # ⚓ The Straits Times ☛ China’s_Pooh-tin_Jinping_arrives_in
                  Cambodia_for_state_visit⠀⇛


                       Beijing is seeking to strengthen regional trade
                       ties and offset the impact of US tariffs.


                # ⚓ New Yorker ☛ China’s_Plan_to_Fight_Convicted_Felon’s_Trade
                  War⠀⇛


                       A professor at M.I.T. on how Pooh-tin Jinping is
                       likely to respond to U.S. tariffs and why the
                       standoff won’t weaken the Chinese Communist Party’s
                       grip on power.


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


                      # ⚓ Meduza ☛ Russia_drafts_legal_framework_for_return_of
                        Western_firms,_including_local_production_and
                        technology_transfer_requirements_—_Bloomberg_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Journalists_identify_Russian_teen_arrested
                        for_arson_attacks_as_son_of_regular_participant_in
                        State_Duma_events_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ My_house_is_your_house_A_new_investigation
                        suggests_that_Moscow’s_political_and_economic_favors
                        fuel_Serbia’s_fast-tracked_citizenship_for_well-
                        connected_Russians_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russia_has_arrested_the_Kursk_region's_ex-
                        governor._He_oversaw_the_construction_of_anti-tank
                        barriers_—_which_later_crumbled_from_rain_and_snow._—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Moscow_planning_to_use_seized_American
                        company_to_supply_food_to_Russian_army_—_Reuters_—
                        Meduza⠀⇛


                      # ⚓ RFERL ☛ Russia_Removes_Afghanistan's_Taliban_From
                        Terror_List_In_Step_Toward_Recognition⠀⇛


                             Russia’s Supreme Court removed Afghanistan's
                             militant Taliban rulers from its list of
                             banned terrorist groups in a step toward
                             recognizing the group that seized power in
                             2021 as international forces withdrew from
                             the war-torn country.


                      # ⚓ Meduza ☛ Russia_says_the_Taliban_is_no_longer_a
                        terrorist_group_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Czech_Republic_declares_oil_independence
                        from_Russia_—_Meduza⠀⇛


                      # ⚓ RFERL ☛ Moldova_Sets_Elections_For_September_28_In
                        Battle_Between_EU_and_Russian_Camps⠀⇛


                             Moldova's lawmakers voted to set the next
                             parliamentary elections for September 28 in a
                             test for the country's fragile democracy
                             caught between pro-European and pro-Russian
                             forces.


                      # ⚓ LRT ☛ Russian_nationals_in_Lithuania_to_lose_visas
                        for_frequent_trips_home⠀⇛


                             On Thursday, the Lithuanian parliament
                             tightened and extended sanctions against
                             Russian and Belarusian citizens for another
                             year. Under the new measures, Russian
                             nationals who travel to Belarus or Russia
                             more than once every three months will lose
                             their right to stay in Lithuania.


                      # ⚓ LRT ☛ Russian_media_identifies_embassy_worker_in
                        Vilnius_as_FSB_officer⠀⇛


                             A member of staff at the Russian Embassy in
                             Vilnius is also an officer at the Russian
                             intelligence service, the FSB, according to
                             information published by RuPEP, an online
                             database of public officials compiled by
                             independent Russian media.


                      # ⚓ JURIST ☛ Former_governor_of_Russia’s_Kursk_region
                        detained_over_alleged_fraud_tied_to_border
                        fortifications⠀⇛


                             A Moscow court on Wednesday ordered former
                             Kursk region governor Alexei Smirnov held in
                             custody as authorities investigate “major
                             fraud” allegations ahead of his June 15
                             trial, according to state news agency TASS.


                      # ⚓ Atlantic Council ☛ Russia_Sanctions_Database:
                        November_2024⠀⇛


                             The Atlantic Council’s Russia Sanctions
                             Database tracks the restrictive economic
                             measures Western allies have placed on Russia
                             and evaluates whether these measures are
                             successful in achieving the stated
                             objectives.


                      # ⚓ Meduza ☛ 'I've_done_my_job_no_worse_than_other
                        deputies'_This_Russian_municipal_lawmaker_has_been
                        working_remotely_for_four_years_—_from_Dnipro,_Ukraine
                        —_Meduza⠀⇛


                      # ⚓ Meduza ☛ Zelensky_says_Ukraine_will_present_evidence
                        that_China_is_supplying_weapons_to_Russia_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ U.S._and_Ukraine_sign_memorandum_on_intent
                        to_reach_mineral_resources_deal_—_Meduza⠀⇛


                      # ⚓ New York Times ☛ Ukraine_and_U.S._Sign_Agreement_in
                        Lead-Up_to_Full_Minerals_Deal⠀⇛


                             The signed memorandum of understanding was
                             thin on details, and the White House did not
                             comment. But Hell Toupée has said he expects
                             to sign a minerals deal with Kyiv soon.


                      # ⚓ France24 ☛ Ukrainians_see_minerals_deal_as_'typical
                        of_Convicted_Felon's_gangster-style_diplomacy',
                        observer_says⠀⇛


                             Dihydroxyacetone Man on Thursday said he
                             doesn't hold Zelenskyy "responsible" for
                             Russia's invasion of his country but
                             continued to criticize the Ukrainian leader.
                             Convicted Felon added Thursday that a deal
                             with Ukraine on extracting the war-wracked
                             country's strategic minerals could be reached
                             next week. We speak to Kyiv Independent
                             reporter Francis Farrell. He says that
                             Ukrainians see the deal as 'exploitative and
                             typical of Convicted Felon's gangster-like
                             diplomacy.


                      # ⚓ France24 ☛ 🔴_Ukraine,_US_sign_'memorandum_of_intent'
                        on_resources_deal⠀⇛


                      # ⚓ France24 ☛ Ukraine,_US_sign_'memorandum_of_intent'_on
                        critical_minerals_deal⠀⇛


                             Ukraine and the US signed a "memorandum of
                             intent" on Thursday to advance a deal
                             granting Washington access to Kyiv’s natural
                             resources and critical minerals, Ukraine
                             said. The pact aims to foster an economic
                             partnership and create a reconstruction fund,
                             Deputy PM Yulia Svyrydenko said.


                      # ⚓ New York Times ☛ Europe_and_America,_at_Odds_Over
                        Ukraine,_Try_Talking_to_Each_Other⠀⇛


                             President Emmanuel Macron of France hosted a
                             lunch with Secretary of State Marco Rubio and
                             Steve Witkoff, Hell Toupée’s envoy, as
                             European delegations converged on Paris.


                      # ⚓ New York Times ☛ The_Ukrainian_Schoolmaster_Teaching
                        History_to_His_Invaders⠀⇛


                             Vitalii Dribnytsia engages with Russians
                             online to correct Kremlin propaganda about
                             Ukraine. Over time, he has come to realize
                             his more important audience is Ukrainians
                             themselves.


                      # ⚓ RFERL ☛ Russian_Attack_On_Dnipropetrovsk_Kills_At
                        Least_5,_Including_Child,_Injures_Dozens⠀⇛


                             A Russian drone attack killed at least three
                             people, including a child and an elderly
                             woman, and injured dozens of others late on
                             April 16 in the southeastern Ukrainian city
                             of Dnipro, the regional governor said.


                      # ⚓ RFERL ☛ France_Says_Europe_Now_'At_The_Table'_As
                        Paris_Peace_Talks_End⠀⇛


                             French officials have praised talks held
                             between key European countries, Ukraine, and
                             the United States, the first involving the
                             three sides since US President The
                             Insurrectionist took power, as they look to
                             end Europe's largest conflict since the end
                             of World War II.


                      # ⚓ France24 ☛ Macron_hosts_talks_on_Ukraine,_Middle_East
                        and_Iran_with_US_in_Paris⠀⇛


                             France's President Emmanuel Macron, US
                             Secretary of State Marco Rubio, and US envoy
                             Steve Witkoff held a meeting in Paris on
                             Thursday focused on crafting a Ukraine
                             ceasefire, addressing tensions in the Middle
                             East, and discussing Iran's nuclear
                             programme. Here's FRANCE 24 Kethevane
                             Gorestani's analysis on this meeting.


                      # ⚓ RFERL ☛ Ukraine,_US_Sign_Memorandum_On_Economic
                        Partnership,_Ukrainian_Official_Says⠀⇛


                             Ukraine and the United States have "taken a
                             step" toward a joint economic partnership
                             agreement, Economy Minister Yulia Svyrydenko
                             said on April 17.


                      # ⚓ North_Korean_troops_may_enter_Ukraine_soon,_Kyiv
                        warns⠀⇛


                             North Korean troop operations have so far
                             been concentrated in Russia’s Kursk region.


                      # ⚓ France24 ☛ Who_is_Steve_Witkoff,_Convicted_Felon's
                        longtime_envoy_and_friend_?⠀⇛


                             As discussions on Ukraine took place in Paris
                             between Emmanuel Macron and several US
                             envoys, Steve Witkoff's presence drew
                             attention. Not a career diplomat, he is a
                             long-time friend of The Insurrectionist and
                             officially his envoy for the Middle East,
                             though his influence extends far beyond that.


                      # ⚓ France24 ☛ Steve_Witkoff_in_Paris:_Who’s_Convicted
                        Felon’s_Mr_Fix_It?⠀⇛


                             The Insurrectionist’s Mr Fix it on Gaza,
                             Ukraine and now Iran in Paris alongside Marco
                             Rubio. Sticklers for protocol would normally
                             insist that the US Secretary of State’s the
                             bill topper of diplo tour… but these aren’t
                             normal times. Does the 67-year New York real
                             estate mogul hold sway?


                      # ⚓ Atlantic Council ☛ The_Ukrainian_army_is_now_Europe’s
                        most_credible_security_guarantee⠀⇛


                             As Europe confronts the new geopolitical
                             realities of an expansionist Russia and an
                             isolationist United States, the continent's
                             most credible security guarantee is now the
                             Ukrainian Armed Forces, writes Pavlo
                             Verkhniatskyi.


                      # ⚓ Latvia ☛ Latvian_'Atlas_Aerospace'_produces
                        reconnaissance_drones_for_Ukraine⠀⇛


                             Atlas Aerospace went from the idea of
                             manufacturing drones for commercial use in
                             2015 to manufacturing reconnaissance drones
                             for military use. From having to doubt itself
                             and convince investors, the company is now a
                             supplier to NATO and Ukraine. LSM.lv visited
                             the company as part of its article series
                             "Forge of Military Power".


                      # ⚓ Atlantic Council ☛ Putin_is_attempting_to_intimidate
                        Merz_with_yet_more_Russian_red_lines⠀⇛


                             As Germany’s next chancellor Friedrich Merz
                             prepares to boost support for Ukraine, the
                             Kremlin is already seeking to deter him with
                             intimidation tactics, writes Peter Dickinson.
                             Merz's response will help define whether he
                             is capable of leading Europe.


                      # ⚓ Latvia ☛ Fifth_failed_auction_of_'Moscow_House'_in
                        Rīga⠀⇛


                             The State Enterprise "Valsts nekustamie
                             īpašumi" (VNĪ) has failed to sell the so-
                             called Moscow House on Marijas Street, Rīga,
                             in the fifth auction, according to
                             information on the electronic auction
                             website, LETA reports on 17 April.


          o § Environment⠀➾


                # ⚓ The Straits Times ☛ Heavy_rain,_flash_floods_to_continue_in
                  Penang_amid_monsoon_transition⠀⇛


                       In several low-lying areas, water was surging into
                       homes. Overflowing drains caused streets to become
                       submerged.


                # § Energy/Transportation⠀➾


                      # ⚓ New York Times ☛ South_Korea_Shipbuilding_Strength
                        Could_Help_in_Tariff_Talks_With_U.S.⠀⇛


                             As it faces the possibility of a 25 percent
                             tariff on its exports, South Korea has taken
                             notice of Hell Toupée’s stated goal to revive
                             U.S. shipbuilding.


                      # ⚓ The Straits Times ☛ Dihydroxyacetone_Man_includes_US
                        troop_costs_in_tariff_talks_with_Asian_allies⠀⇛


                             Japan and South Korea both view the issue of
                             defence spending as separate from trade.


                      # ⚓ Atlantic Council ☛ How_the_National_Energy_Dominance
                        Council_can_set_the_US_on_the_path_to_energy_security⠀⇛


                             The National Energy Dominance Council must
                             act quickly to restore stability to the
                             energy industry amid geopolitical
                             uncertainty.


                      # ⚓ Hong Kong Free Press ☛ Hong_Kong’s_CK_Hutchison
                        should_‘take_responsibility_for_own_mistake’_over_ports
                        deal,_says_pro-Beijing_politician⠀⇛


                             Hong Kong conglomerate CK Hutchison should
                             “take responsibility for its own mistake”
                             over a deal to offload its overseas ports –
                             including two at the Panama Canal – to a US-
                             led consortium, a pro-Beijing politician has
                             said.


                # § Wildlife/Nature⠀➾


                      # ⚓ Science Alert ☛ Mysterious_3-Toed_Footprints_in
                        Canada_Reveal_New_Ankylosaur_Species⠀⇛


                             Check out these feet!


                      # ⚓ Defence Web ☛ Rhino_poaching_crackdown:_Kruger
                        staff’s_efforts_lead_to_major_sentences⠀⇛


                             The value of proper training added to on-the-
                             job gut feel paid off for two Kruger National
                             Park (KNP) staffers with an 11-year sentence
                             handed to a suspected rhino poacher this
                             month, five years after the suspect was
                             apprehended.


                # § Overpopulation⠀➾


                      # ⚓ France24 ☛ One_million_Haitian_children_face
                        'critical'_food_shortage,_says_UN⠀⇛


                             More than one million children in Haiti are
                             suffering critical food shortages due to
                             violence, displacement, and limited aid
                             access, UNICEF said Thursday. Nearly 2.9
                             million children—one in four—face severe food
                             insecurity, per the IPC, a global hunger
                             monitoring system.


          o § Finance⠀➾


                # ⚓ Hong Kong Free Press ☛ 5_mainland_Chinese_visitors_jailed
                  for_3_weeks_after_Coldplay_ticket_scalping_arrests⠀⇛


                       Five mainland Chinese visitors have been jailed for
                       three weeks for breaching their conditions of stay
                       in Hong Kong after they were arrested on suspicion
                       of ticket scalping last week outside a concert by
                       the British band Coldplay.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_Originals:_Two_Moons
                  Distillery_infuses_city’s_heritage_into_handcrafted_gin⠀⇛


                       As Hong Kong’s economic boom faded and
                       manufacturing moved to China, some long-
                       established, family-run companies preserved their
                       traditions as others innovated to survive. In our
                       new series, HKFP documents the craftmanship and
                       spirit behind the goods that are still proudly
                       “Made in Hong Kong,” as local firms navigate the
                       US-China trade war.


                # ⚓ France24 ☛ Dihydroxyacetone_Man_says_Fed_Chair_Jerome
                  Powell's_termination_"cannot_come_fast_enough"⠀⇛


                       US President The Insurrectionist has called for
                       Federal Reserve Chair Jerome Powell to be fired, a
                       day after the central bank chief delivered a stark
                       warning about the effects of tariffs. Meanwhile,
                       Chinese President Pooh-tin Jinping is ending his
                       Asian tour with a visit to Cambodia, portraying
                       China as a stable trading partner. Plus, the Hermès
                       Birkin handbag is about to get a lot more
                       expensive, at least in the US.


                # ⚓ JURIST ☛ Texas_judge_blocks_federal_rule_intended_to_reduce
                  credit_card_late_fees⠀⇛


                       A federal judge in Texas vacated a Consumer
                       Financial Protection Bureau (CFPB) regulation on
                       Tuesday. The ruling by Judge Mark Pittman, a
                       federal district court judge for the Northern
                       District of Texas, removes many previous caps from
                       credit card late fees.


                # ⚓ Federal News Network ☛ Benefits_worries_nag_at_federal
                  employees⠀⇛


                       With threats coming to health care plan costs,
                       retirement contributions, and basic job security
                       itself, no wonder feds feeling hightened anxiety!


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Ruben Schade ☛ Postal_voting_in_the_2025_Australian
                  election⠀⇛


                       The 2025 Australian Federal election will be taking
                       place when Clara and I are outside our electorate,
                       so we opted for a postal vote. This means no
                       democracy_sausage on polling day, but we’re still
                       able to perform our civic duty. Well, that and the
                       fact voting is comulspry in Australia (as it should
                       be, you have a responsibility in a democracy), so
                       we don’t want to cop a fine.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Science Alert ☛ Can_We_Trust_Our_Eyes_Anymore?_The
                        Dark_Side_of_Apple's_New_Hey_Hi_(AI)_Clean_Up_Tool⠀⇛


                             Photo or it didn't happen.


                      # ⚓ OpenRightsGroup ☛ Bad_Ads:_Targeted_Disinformation,
                        Division_and_Fraud_on_Meta’s_Platforms⠀⇛


                             This report lays out clear evidence of how
                             Meta enables bad actors to use its targeted
                             advertising system to manipulate elections,
                             spread disinformation, fuel division, and
                             facilitate fraud. Executive Summary Meta’s
                             social control media platforms, Facebook
                             (Farcebook) and Instagram, sit at the
                             intersection of the attention economy and
                             surveillance capitalism.


          o § Censorship/Free Speech⠀➾


                # ⚓ The Straits Times ☛ Kudos_for_Xi’s_visit_to_Malaysia
                  eclipsed_by_flag_furore⠀⇛


                       The missing crescent moon on Malaysian flags
                       featured in Chinese-language media marred euphoria
                       over the visit.


                # ⚓ Chinese_artist_fined_for_filming_Uyghur_folk_music_in
                  Xinjiang⠀⇛


                       While Guo Zhenming is punished, performances by a
                       state-backed Uyghur dance troupe in Europe are
                       promoted.


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


                # ⚓ Stanford University ☛ GSC_questions_The_Daily_on_free
                  speech_policies_and_source_anonymity⠀⇛


                       The GSC questioned The Daily’s executive editing
                       team on student requests for anonymity and other
                       concerns related to free speech.


          o § Civil Rights/Policing⠀➾


                # ⚓ New York Times ☛ Judge_Delays_a_Resentencing_Hearing_for
                  the_Menendez_Brothers⠀⇛


                       The proceedings were pushed back for three weeks
                       over the issue of whether a key report on Erik and
                       Lyle Menendez was admissible.


                # ⚓ New York Times ☛ Costa_Rica_Violated_Rights_of_81_Migrant
                  Children_Deported_by_U.S.,_Lawsuit_Says⠀⇛


                       A legal challenge filed Thursday aims to encourage
                       Central American countries to push back against the
                       Convicted Felon administration’s immigration
                       policies.


                # ⚓ Press Gazette ☛ Why_UK’s_contempt_of_court_laws_need_reform
                  for_digital_age⠀⇛


                       Disorder after the Southport stabbings last summer
                       has been called an "indirect result of contempt of
                       court laws".


                # ⚓ Pro Publica ☛ Wisconsin’s_Name-Change_Law_Raises_Safety
                  Risks_for_Transgender_People⠀⇛


                       In 2022, after living as a boy and going by a new
                       name for several years, a 15-year-old from Madison,
                       Wisconsin, wanted to make it official. Like most
                       teenagers, he dreamed of getting his driver’s
                       license, and his family wanted his government
                       identification to reflect who he really was.


                       But Wisconsin law has a caveat: He would have to
                       publish his old, feminine name and new name in the
                       local newspaper for three weeks — essentially
                       announcing to the world that he is transgender.


                # ⚓ JURIST ☛ Canada_Federal_Court_of_Appeal_upholds_assault-
                  style_firearms_ban⠀⇛


                       Canada’s Federal Court of Appeal dismissed a
                       prominent challenge to the federal government’s
                       2020 ban on assault-style firearms on Tuesday. The
                       ruling upheld the legality of the government’s
                       decision to prohibit over 1,500 models of firearms
                       deemed by Ottawa to be “assault-style” and
                       unsuitable for civilian ownership.


                # ⚓ JURIST ☛ IOM_reports_Pakistan_forcibly_deported_nearly
                  60,000_Afghan_refugees_since_start_of_April⠀⇛


                       The International Organization for Migration (IOM)
                       on Tuesday reported that nearly 60,000 Afghan
                       refugees have been forcibly deported from Pakistan
                       so far this month.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ MWL ☛ 85:_George_is_Asleep⠀⇛


                       Here’s some of the new Networking for System
                       Administrators, because while the Laserblasted
                       Kickstarter ends today I am utterly sick of
                       shilling it. Think of the network as a conference
                       room. At the physical layer you have a table and
                       chairs. The room is a broadcast domain.


                # ⚓ Stuart_Langridge:_Serving_streaming_video_that_adapts_to
                  bandwidth_from_your_own_website⠀⇛


                       Recently, I was involved in an event where a video
                       was shown, and the event was filmed. It would be
                       nice to put the video of the event up somewhere so
                       other people who weren't there could watch it.
                       Obvious answer: upload it to YouTube. However, the
                       video that was shown at the event is Copyrighted
                       Media Content and therefore is disallowed by
                       YouTube and the copyright monopoly holder; it's not
                       demonetised (which wouldn't be a problem), it's
                       flat-out blocked. So YouTube is out.


                # ⚓ Internet Society ☛ Internet_Trust:_Why_We_Need_It_and_How
                  to_Achieve_It⠀⇛


                       Trust in the Internet is crucial, but it has
                       fluctuated. Let’s dive into Internet trust, what
                       makes a trustworthy Internet, and why people should
                       care.  


      § Monopolies/Monopsonies⠀➾


          o ⚓ New York Times ☛ What_to_Know_About_Convicted_Felon’s_Antitrust
            Efforts_Against_Google,_Meta_and_Other_Tech_Giants⠀⇛


                 The Forrest Dump administration is continuing an
                 aggressive effort to rein in the power of the biggest
                 tech companies. Here’s what to know.


          o ⚓ New York Times ☛ Google_Is_Illegally_Monopolizing_Online
            Advertising_Tech,_Judge_Rules⠀⇛


                 It was the second time in a year that a U.S. court found
                 that the company had acted illegally to remain dominant.


          o ⚓ New York Times ☛ A_Judge_Ruled_That_Surveillance_Giant_Google
            Acted_Illegally_to_Dominate_Ad_Tech⠀⇛


                 Also, a daily pill may work as well as Ozempic. Here’s
                 the latest at the end of Thursday.


          o ⚓ France24 ☛ Google_holds_illegal_monopolies_in_online_ad_tech,_US
            judge_rules⠀⇛


                 Google illegally wielded monopoly power in the online ad
                 technology market, a US judge ruled on Thursday, in a
                 legal blow that could rattle the tech giant's revenue
                 engine. It is one of two federal suits targeting
                 Surveillance Giant Google that could ultimately see the
                 company split up and curb its influence – and part of a
                 wider government push to rein in Big Tech.


          o ⚓ Silicon Angle ☛ Court_rules_against_Surveillance_Giant_Google_in
            advertising_technology_antitrust_case⠀⇛


                 A federal court today found that Surveillance Giant
                 Google LLC maintains an illegal monopoly in the
                 advertising technology market. The decision comes less
                 than a year after a similar antitrust ruling against the
                 Alphabet Inc. unit’s search business.


          o ⚓ Public Knowledge ☛ Public_Knowledge_Urges_Federal_Court_To_Adopt
            Strong_Remedies_in_Surveillance_Giant_Google_Ad_Tech_Monopoly
            Decision [Ed: Public Knowledge does not disclose Microsoft_is
            inside_its_Board]⠀⇛


                 Judge rules that Surveillance Giant Google violated
                 antitrust law by monopolizing two markets of the digital
                 advertising ecosystem.


          o § Patents⠀➾


                # ⚓ JUVE ☛ Ones_to_Watch_UK_2025:_Edmund_Eustace [Ed: Classic
                  spam from JUVE, albeit disguised as journalism]⠀⇛


                       Every year, JUVE Patent carries out extensive
                       research in the UK patent monopoly market,
                       culminating in the publication of the UK patent
                       monopoly ranking. Our latest research highlighted
                       Edmund Eustace, a barrister from 8 New Square as
                       one of the current ‘Ones to Watch’ in the UK patent
                       monopoly market.


                # ⚓ Unified Patents ☛ $32,000_for_AutoConnect_Holdings
                  automotive_patents_prior_art⠀⇛


                       Unified Patents added sixteen new PATROLL contests,
                       each with a $2,000 cash prize, seeking prior art on
                       the list below. The patents are owned by
                       AutoConnect Holdings LLC, an NPE. The patents
                       generally relate to vehicle ecosystems.


                       The contests will expire on June 2, 2025. Please
                       visit PATROLL for more information and to submit an
                       entry for these contests. PATROLL researchers are
                       required to use Pearl to generate claim charts.
                       Submitted invalidity charts must address every
                       limitation of the challenged claim.


                # ⚓ Dennis Crouch/Patently-O ☛ I_Know_I’m_Going_to_Love_a_Brief
                  That_Repeatedly_Cites_Marbury_v._Madison⠀⇛


                       Back when he was a law professor here at Mizzou, I
                       recall taking with Sen. Josh Hawley about his
                       favorite Supreme Court case - Marbury v. Madison, 5
                       U.S. (1 Cranch) 137 (1803).  The case has come to
                       stand for the principle of judicial review,
                       establishing the Supreme Court's authority to
                       determine the constitutionality of laws and
                       executive actions.


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ Novartis_and_Accord_settle_UPC_dispute_over
                        drug_administration_with_apple_sauce [Ed: UPC itself is
                        not legal; this case and the unconstitutional kangaroo
                        court should be dissolved]⠀⇛


                             The dispute centred on Novartis’ patent
                             monopoly EP 2 501 384, which protects a
                             method of treating proliferative disorders
                             and other pathological conditions mediated by
                             BCR-ABL, C-KIT, DDR1, DDR2 or PDGF-R kinase
                             activity. In simpler terms, it protects the
                             administration of nilotinib together with
                             apple sauce.


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ Professor_J._Thomas_McCarthy:_"What_is_the
                  'Zone_of_Natural_Expansion'_Doctrine?"⠀⇛


                       Professor McCarty, renowned author of McCarthy on
                       Trademarks and Unfair Competition, cast a critical
                       eye on two recent decisions (one from the CAFC, one
                       from the TTAB) discussing the zone-of-natural-
                       expansion "doctrine." He asks, "what is it?" "How
                       does it fit with the familiar 'related goods and
                       services' rule and the test of likelihood of
                       confusion?" The professor concludes that it is not
                       a "doctrine" at all. "Neither the Federal Circuit
                       nor the T.T.A.B. has the authority to replace the
                       statutory likelihood of confusion test with a
                       'doctrine' of 'zone of natural expansion' to decide
                       issues of priority and entitlement to
                       registration."


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Drake_Elevates_the_Heat_on_Universal
                  Music_With_Amended_‘Not_Like_Us’_Defamation_Suit:_‘UMG_Will
                  Be_Held_Accountable’⠀⇛


                       Right on cue, Drake and his legal team have fired
                       off an amended “Not Like Us” defamation lawsuit
                       against Universal Music Group (UMG). The “Nokia”
                       act and his counsel submitted the bolstered
                       complaint yesterday, just a couple weeks removed
                       from a major discovery win.


                # ⚓ Press Gazette ☛ ‘Unsustainable_status_quo’:_Hey_Hi_(AI)
                  companies_and_publishers_respond_to_Govt_copyright_monopoly
                  consultation⠀⇛


                       Opt-out proposal like burglars being allowed unless
                       banned by sign on front door, one response says.


    * Gemini_Links_18/04/2025:_Price_of_Games_and_State_of_Tinylog
    * next



                    ䷩ 𝚕𝚒𝚗𝚎 5999

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 18/04/2025: Layoffs at Microsoft
Infosys and Qt Becoming Increasingly Proprietary (Plus
Slop)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Apr 18, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_so-called_Mon_Village_is_a_village_built_on_the_edge_of
an_artificial_lake_in_Sangkhaburi_or_Sangkhla_Buri,_Thailand,_by_Mon_people,
originally_refugees_from_Myanmar⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇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
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Stefano Marinelli ☛ Why_I'm_Expanding_My_Blogging_Presence⠀⇛


                 I've decided to start writing on a personal blog again.
                 Not just on IT Notes, where I'll continue to publish
                 technical content as I've been doing, but also on a more
                 personal and general blog. And this for a number of
                 reasons.


                 One above all: too many things I've written on social
                 media have disappeared into nothingness after a few days.
                 Content there is meant to be momentary, ephemeral. It's
                 not for nothing that we talk about microblogging: posts
                 appear in timelines and then vanish in the continuous
                 flow of new content. After six days, six months, six
                 years... it's as if they never existed.


          o ⚓ Ruben Schade ☛ Stefano_Marinelli_is_expanding_his_blogging
            presence⠀⇛


                 I’ve got another post coming up soon comparing a few
                 different blogging tools for people who want to dip their
                 toes into this wonderful form of self-expression (present
                 writer notwithstanding), but in the meantime I’m so happy
                 to add Stefano’s blog to Clara’s and my RSS reader.


                 And yes, that was a not-so-thinly-veiled push for you to
                 start one as well, dear reader, if you haven’t already.


          o ⚓ Justin Vollmer ☛ Operating_Rules_for_Email_Collaboration⠀⇛


                 I’ve slowly been improving my email usage over time,
                 since my tendency left unchecked is to be verbose.
                 However, I’ve learned that verboseness should not be the
                 norm when communicating via email, as it can cause your
                 thoughts to be lost in the weeds. And now that I am using
                 email much more than earlier in my career, learning to
                 use it well is important.


          o ⚓ [Repeat] Ruben Schade ☛ Brolific⠀⇛


                 R.L. Dane enquired about how one maintains a regular
                 blogging habit, and counted my number of posts with a
                 simple bash script.


                 I wouldn’t say I have a specific recipe for a successful
                 blog, though there are always a few points to keep in
                 mind: [...]


          o ⚓ Elliot C Smith ☛ Is_retention_is_the_only_real_measure_of_product
            market_fit?⠀⇛


                 So, is retention the only measure of PMF? Strictly
                 speaking, no, but it is probably the most telling. If you
                 can’t keep your customers happy and around for the long
                 term you can’t really claim to have a strong fit.


          o § Standards/Consortia⠀➾


                # ⚓ ARRL ☛ World_Amateur_Radio_Day_–_International_Amateur
                  Radio_Union_Formed_100_Years_Ago⠀⇛


                       April 18th is honored as World Amateur Radio Day,
                       when we celebrate the founding of the International
                       Amateur Radio Union (IARU). The organization was
                       born out of a meeting in Paris on April 17, 1925.
                       ARRL took a leadership role in its founding, with
                       ARRL Founder Hiram Percy Maxim, then 1AW, serving
                       as the first President of IARU.


                       As reported by Kenneth B. Warner, 1BHW, in the June
                       1925 edition of QST: [...]


                # ⚓ [Repeat] Silicon Angle ☛ US_extends_contract_to_fund_the
                  CVE_vulnerability_database⠀⇛


                       Launched in 1999, CVE provides information about
                       cybersecurity vulnerabilities in software products.
                       The database has more than 170,000 entries and
                       counting. By storing vulnerability details in one
                       place, it removes the need for cybersecurity
                       professionals to piece together information about
                       an exploit from multiple sources.


                # ⚓ Techdirt ☛ US_Government_Almost_Kills_Critical
                  Cybersecurity_Database⠀⇛


                       In what appears to be the latest move in this
                       administration’s total incompetence with regards to
                       critical government tech infrastructure, MITRE
                       announced yesterday that funding had run out for
                       the Common Vulnerabilities and Exposures (CVE)
                       system, the fundamental framework that basically
                       everyone in cybersecurity relies on to keep
                       computer systems safe. After the entire
                       cybersecurity world freaked the fuck out, one of
                       the remaining unfired people at the the U.S.
                       Cybersecurity and Infrastructure Security Agency
                       (CISA) announced that they had extended the funding
                       for another 11 months.


          o § Science⠀➾


                # ⚓ The Local SE ☛ 'Never_waste_a_good_crisis':_How_Sweden
                  wants_to_attract_US_talent_fleeing_Trump⠀⇛


                       “We say you should never waste a good crisis,” he
                       tells The Local. “With the Trump administration
                       withdrawing funding to research and development and
                       also changing the agenda in the US, we think that
                       many people are now rethinking where they should be
                       situated to have the best possibility for their
                       businesses to try and thrive and grow.”


                # ⚓ Futurism ☛ Oops!_It_Appears_There's_a_Striking_Flaw_in_That
                  Claim_About_Detecting_Alien_Life⠀⇛


                       But the situation may not be so clear cut. While
                       dimethyl sulfide is an organic material on our
                       planet, there's a body of evidence suggesting that
                       nonbiological processes elsewhere in the cosmos
                       could produce the compound, notes science writer
                       Corey S. Powell in a Bluesky thread.


                # ⚓ Wired ☛ Thousands_of_Urine_and_Tissue_Samples_Are_in_Danger
                  of_Rotting_After_Staff_Cuts_at_a_CDC_Laboratory⠀⇛


                       The NIOSH researchers collected the tissue samples
                       as part of experiments to determine how Americans
                       may be impacted by chemicals and other substances
                       they are exposed to at their jobs. Some of the
                       samples are stored in a refrigerator that needs to
                       be kept at -112 Farenheit at all times, while
                       others are stored in liquid nitrogen. Unless
                       someone inside the federal government continues to
                       ensure the liquid nitrogen doesn’t totally
                       evaporate, the samples will eventually defrost and
                       begin to rot, according to three staff researchers
                       who work with such materials.


                # ⚓ Bob Monsour ☛ The_personal_effects_of_NIH_funding_cuts⠀⇛


                       It's difficult to overstate the importance of the
                       NIH to the development of scientific breakthroughs
                       that affect our health and that of our loved ones.


                       Here are just a few recent articles (all are 'gift
                       links') from the Washington Post and the New York
                       Times about the funding cuts to the NIH that are
                       being proposed and already underway by the current
                       administration: [...]


                # ⚓ Society for Scholarly Publishing ☛ Guest_Post:_Preprints
                  Serve_the_Anti-science_Agenda_–_This_Is_Why_We_Need_Peer
                  Review⠀⇛


                       Yes – there are benefits to more freely and quickly
                       sharing science. But preprints join predatory
                       publishers and paper mills to fuel a growing
                       challenge for our society: distinguishing credible
                       science from inaccurate, biased, and misleading
                       work. This is encouraging a race to the bottom,
                       where good science can carry the same weight as bad
                       science, ‘alternative facts,’ and ‘truthiness’ –
                       which is actually no weight at all.


                       So it should be alarming when preprints are cited
                       like fully-reviewed articles and used in the news
                       media when their lack of legitimacy is often buried
                       in fine print easily missed or misunderstood by the
                       average reader. (As well as the informed reader —
                       I’ve interviewed dozens of scientists who don’t
                       know how to evaluate preprints, what they can
                       trust, or what they can use in their own research.)


          o § Career/Education⠀➾


                # ⚓ University of Michigan ☛ On_keeping_a_college_notebook⠀⇛


                       My most prized possession is probably one of my
                       most beat-up, but I’ve never believed in saving the
                       things you love. It’s an olive-green Leuchtturm1917
                       with dotted note paper because I had a bullet
                       journal for a few months in high school and
                       realized I could never go back to line-ruled paper.


                # ⚓ Alex Ewerlöf ☛ Staff+_self-onboarding_questions⠀⇛


                       In a previous post we have covered what your
                       manager can do to facilitate your onboarding:


                       This post is about what YOU can do as a senior IC
                       to self-onboard. More specifically: how to ask
                       questions as a senior technical leader.


                # ⚓ Yilei Yang ☛ On_What_Drives_Me⠀⇛


                       I’m starting a new career chapter soon, a once-in-
                       a-lifetime opportunity. I’m sure the company
                       mission alone will motivate me for a long time,
                       even leave me little to no time for Mango. Still, I
                       hope to find old and new interactions, in or
                       outside of the company, to have a sustained impact
                       in me.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ Cervoz_M.2_SFP_Ethernet_expansion_modules
                  support_long_cables_(up_to_several_kilometers)_for_robotics⠀⇛


                       Cervoz M.2 MEC-LAN-2001-SFP and MEC-LAN-2002-SFP
                       are M.2 SFP Ethernet expansion modules delivering
                       gigabit Ethernet speed over long distances for
                       robotics using an defective chip maker Intel i210-
                       IS controller compliant with IEEE 802.3x and 802.3z
                       standards.


                # ⚓ CNX Software ☛ LaserPecker_LP5_Review_–_A_20W_diode_&_fiber
                  laser_engraver_tested_with_LDS_software,_rotary_extension,
                  safety_enclosure⠀⇛


                       We have already checked the specifications, done an
                       unboxing, and shown how to assemble the LaserPecker
                       LP5 2-in-1 fiber & diode laser engraver along with
                       its safety enclosure and rotary extension in the
                       first part of the review.


                # ⚓ CNX Software ☛ Radxa_Dragon_Q6A_–_A_Qualcomm_QCS6490_Edge
                  Hey_Hi_(AI)_SBC_with_GbE,_WiFi_6,_three_camera_connectors⠀⇛


                       Radxa Dragon Q6A is an upcoming credit card-sized
                       SBC powered by a Qualcomm QCS6490 octa-core SoC
                       with a 12 TOPS Hey Hi (AI) accelerator, up to 16GB
                       LPDDR5 memory, and the usual ports found on
                       Raspberry Pi-like single board computers such as
                       gigabit Ethernet, four USB ports, HDMI video
                       output, and a 40-pin GPIO header.


                # ⚓ CNX Software ☛ LaserPecker_LP5_Review_–_Part_2:_A_20W_diode
                  &_fiber_laser_engraver_tested_with_LDS_software,_rotary
                  extension,_safety_enclosure⠀⇛


                # ⚓ CNX Software ☛ Axelera_Metis_Compute_Board_pairs_Rockchip
                  RK3588_SoC_with_214_TOPS_Metis_Hey_Hi_(AI)_accelerator⠀⇛


                       Axelera Metis Computer Board is a Rockchip RK3588
                       mini-ITX motherboard equipped with a Metis AIPU (AI
                       Processing Unit) capable of delivering up to 214
                       TOPS, 16GB LPDDR4 memory for the CPU, and 4GB
                       LPDDR4x RAM for the Hey Hi (AI) accelerator.


                # ⚓ Axios ☛ TSMC_to_make_30%_of_top_chips_in_U.S.⠀⇛


                       Why it matters: Chairman and CEO CC Wei told
                       investors the scope of the company's Phoenix
                       investment will create "an independent leading-edge
                       semiconductor manufacturing cluster in the U.S."


                # ⚓ Tom's Hardware ☛ Lawmakers_demand_answers_from_Nvidia_over
                  suspected_GPU_diversions_to_China,_company_denies_any
                  wrongdoing⠀⇛


                       A U.S. congressional investigation suspects that
                       Chinese AI company DeepSeek has trained its large
                       language model using tens of thousands of Nvidia
                       GPUs, many covered by U.S. export controls. As
                       Nvidia's hardware was central to China's AI
                       progress, the House Select Committee on the CCP
                       this week sent a formal letter to Nvidia asking to
                       provide extensive records amid suspicions that its
                       GPUs ended up at DeepSeek through Singapore despite
                       export restrictions.


                       Nvidia denies any wrongdoing and says its clients
                       use billing addresses in Singapore, but want their
                       GPUs developed elsewhere.


                # ⚓ India Times ☛ Chip_giant_TSMC_sees_net_profit_rise_60.3%_in
                  March_quarter⠀⇛


                       TSMC chairman and chief executive C.C. Wei said the
                       company had not detected "any change in customer
                       behaviour" so far. Demand for chips has soared in
                       recent years on demand for AI technology, but there
                       are fears US President Donald Trump's far-reaching
                       tariffs could drive up consumer prices and hurt
                       chipmakers.


                # ⚓ Tedium ☛ Tech-Buying_In_A_Time_Of_Tariffs:_The_Case_For
                  Buying_Used⠀⇛


                       Here’s the thing about tariffs that may not be
                       clear to folks just hearing numbers: They have a
                       cascading effect.


                       Depending on how a good gets manufactured, it could
                       be getting hit by tariffs multiple times over—as
                       raw materials, components, and finished products
                       may all get hit with tariffs at different parts of
                       the manufacturing process.


                # ⚓ The Register UK ☛ TSMC_prepping_for_tariff_turmoil,_denies
                  JV_talks_with_Intel⠀⇛


                       TSMC's top brass insist it is not entertaining a
                       joint venture with beleaguered chip biz Intel,
                       though it is steeling itself for potential effects
                       from the Trump administration's ever-changing
                       tariff schemes.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ NYPost ☛ They’re_sick_of_‘SkinnyTok’_—_dangerous
                  Fentanylware_(TikTok)_trend_glorifies_starvation,_experts
                  warn⠀⇛


                       It’s sending vulnerable users down a dangerous
                       spiral.


                # ⚓ Axios ☛ Luigi_Mangione_indicted_in_NY_as_death_penalty
                  sought_in_health_CEO_killing⠀⇛


                       A federal complaint against Mangione was unsealed
                       in December but he had not been indicted on those
                       charges until Thursday.


                # ⚓ The Independent UK ☛ UnitedHealthcare_killing_suspect_Luigi
                  Mangione_indicted_as_prosecutors_push_for_death_penalty⠀⇛


                       Mangione’s lawyers have argued that U.S. Attorney
                       General Pam Bondi's announcement this month
                       ordering prosecutors to seek the death penalty was
                       a “political stunt” that corrupted the grand jury
                       process and deprived him of his constitutional
                       right to due process.


                # ⚓ Futurism ☛ You_Might_Not_Want_to_Touch_Receipts_After
                  Seeing_This_Horrifying_Research⠀⇛


                       According to new research from the Center for
                       Environmental Health, the tiny paper documents used
                       by major US retailers contain alarmingly high
                       levels of Bisphenol S (BPS), an industrial chemical
                       used in plastics manufacturing — high enough to be
                       dangerous even in the brief period it takes you to
                       stuff one into your pocket.


                # ⚓ Center for Environmental Health ☛ ‘Touching_1_Receipt_for
                  10_Seconds’_Results_in_Exposure_to_the_Chemical_BPS_Above_the
                  Safe_Limit_-_Center_for_Environmental_Health⠀⇛


                       BPS, like BPA, is a hormone-disrupting chemical
                       that mimics estrogen and can disrupt the normal
                       functioning of the body, including metabolism,
                       growth and development, and reproduction. Studies
                       show that BPS can be absorbed through skin when
                       handling receipt paper–even for short periods.


                       “Based on these studies and testing by an
                       independent lab, the concentrations were so high
                       that touching only 1 receipt with BPS for 10
                       seconds resulted in exposure above the safe harbor
                       level which requires a clear and reasonable warning
                       to consumers,” said Mihir Vohra, Science Lead at
                       CEH.


                # ⚓ Air Force Times ☛ Nurses_rally_outside_VA_hospitals_to
                  highlight_staff_cuts,_vacancies⠀⇛


                       “All of those things affect our time and our
                       ability to care for our veterans.”


                       Johnson, a seven-year employee of VA, was one of
                       dozens of department nurses rallying outside the
                       California hospital Wednesday to protest an array
                       of moves by President Donald Trump’s administration
                       that they say unnecessarily threatens the health of
                       veterans and federal workers.


                # ⚓ Carlo Zottmann ☛ Carlo_Zottmann_-_Sarcasm_is_poison⠀⇛


                       When life gets rough, it’s easy to become sarcastic
                       or cynical, but I long ago I came to realize that’s
                       not healthy at all. In a way it’s like really
                       having to pee while being in a swimming pool with
                       others (bear with me). You could be blasé about it,
                       and every time there’s a bitter laugh about the
                       situation, you pee a tiny bit. It’s a big pool,
                       right? No harm done. And the others do it, too!
                       Easy.


                       Yet do it often enough, and you’re submerged in
                       piss.


                # ⚓ Matan Abudy ☛ My_iPhone’s_Screen_Time_is_gaslighting_me_|
                  Matan_Abudy⠀⇛


                       Then the results came in. Although I managed to cut
                       my screen time by about 10-20%, it was nothing
                       compared to my friends. While I was still around 4-
                       5 hours a day, they were usually in 3-4 hour range,
                       some even reached 2.


                       But here is the strange part: when I looked at the
                       breakdown Screen Time gave me, the numbers didn’t
                       add up.


          o § Proprietary⠀➾


                # ⚓ Qt ☛ QML_Debugging_in_Visual_Studio_Code [Ed: Why does Qt
                  shill proprietary spyware of Microsoft again?]⠀⇛


                       We’re excited to announce a major step forward for
                       QML development workflows...


                # ⚓ Tom's Hardware ☛ Microsoft_warns_of_Outlook_Classic_bug
                  that_can_crank_CPU_use_up_to_50%_when_typing⠀⇛


                       Microsoft has confirmed that Outlook Classic is
                       plagued by a bug causing high CPU usage spikes,
                       triggered whenever you're typing a message.


                # ⚓ WhichUK ☛ How_to_stop_scam_pop-ups_on_backdoored_Windows_–
                  according_to_a_tech_expert [Ed: Delete Windows? Use something
                  better?]⠀⇛


                       Scammers desperate to make a quick profit are
                       tricking unsuspecting users into calling fake
                       support numbers


                # ⚓ Medium ☛ Restore_MSSQL_Database_file_.bak_on_a_Linux_Server
                  [Ed: MSSQL does not really run on Linux. It's a lie.]⠀⇛


                # ⚓ The Register UK ☛ Google,_AWS_say_it's_too_hard_for
                  customers_to_use_Linux_to_swerve_Azure⠀⇛


                       The issue stems from changes to Microsoft's cloud
                       licensing practices some years back. Customers used
                       to be able to use regular software licenses to host
                       Microsoft server software on outsourced hardware.
                       But in 2019, Microsoft began requiring new,
                       separate licenses to host virtualized versions of
                       these servers within Amazon, Google, and Alibaba's
                       clouds – three businesses Microsoft classified as
                       "listed providers."


                # ⚓ India News ☛ Amid_layoffs_at_Infosys,_Google,_Microsoft,
                  bad_news_for_Flipkart_employees_as_it_asks_them_to_work..⠀⇛


                       Flipkart is among the last new-age firms,
                       especially in the e-commerce space, to end its WFH
                       policy. Most of the employees at rival firms such
                       as Meesho, Amazon, Blinkit and Zepto have been
                       working from the office for five days a week.


                # ⚓ Macworld ☛ Tariffs_aren't_the_only_reason_why_your_next
                  Apple_device_might_be_more_expensive⠀⇛


                       According to a report by Digital Chat Station on
                       Weibo, Apple will “definitely use TSMC’s 2nm
                       process” in its chips next year. That’s exciting
                       for buyers who want the latest and greatest tech,
                       but not for the price tag. The 2nm process is
                       reportedly a lot more expensive than 3nm, which
                       means prices might be going up.


                       It’s been reported that the cost of a 2nm wafer is
                       $30,000, versus $18,000 for 3nm chips.


                # ⚓ Tedium ☛ Windows_10_End-Of-Life:_Are_Non-Techies_Screwed?⠀⇛


                       The mom spoke for a certain population segment that
                       often gets neglected in society: The person who
                       thinks that what we have is already good enough,
                       who isn’t convinced by things like whiz-bang
                       graphics or cool accessories.


                       “I’m going to say no, and I’m going to explain to
                       him how people market things to make you spend more
                       money,” she said at the time.


                # ⚓ The Register UK ☛ GoDaddy_mistake_took_Zoom_offline_for
                  about_90_minutes⠀⇛


                       Cisco’s ThousandEyes observability outfit analyzed
                       the incident and picked it as a DNS problem that
                       meant top-level domain nameservers did not have the
                       records for zoom.us.


                       “The issue had a cascading effect that impacted
                       Zoom's services, particularly their main webpage,
                       zoom.com,” ThousandEyes added. “This indicates that
                       the content delivery network (CDN) serving Zoom was
                       unable to connect to the backend services hosted on
                       zoom.us.


                       That assessment was correct, but we’ll get to that
                       in a bit.


                # ⚓ Silicon Angle ☛ Amazon_partners_with_GitLab_to_bring_Q
                  Developer_to_DevSecOps_workflows⠀⇛


                       Amazon Web Services Inc. today announced a
                       partnership with DevSecOps tooling provider GitLab
                       Inc. that will integrate it with agentic artificial
                       intelligence development assistant Q Developer.


                # ⚓ Idiomdrottning ☛ I_stopped_sticking_to_FOSS_but_immediately
                  regretted_that_decision⠀⇛


                       After getting the iPad I immediately regretted
                       that. It was so much worse than I could’ve ever
                       imagined.


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ Futurism ☛ Elon_Musk_Lost_It_on_a_Call_With_the
                        Government_After_Autopilot_Killed_a_Tesla_Driver⠀⇛


                             The entire front of the vehicle was ripped
                             off, sending the SUV spinning. Huan was
                             pronounced dead hours after being taken to
                             the hospital.


                             According to details released years later,
                             the National Transportation Safety Board
                             (NTSB) confirmed that the software Huang had
                             been using Autopilot, and had informed both
                             his brother and his wife that it had
                             previously swerved toward the exact road
                             barrier into which he ultimately crashed.


                      # ⚓ Los Angeles Times ☛ Why_Brazilian_DJ_Alok_wants_to
                        ‘keep_art_human’⠀⇛


                             The 33-year-old electronic artist
                             acknowledged that certain software tools have
                             helped him extract vocals, samples and
                             instruments necessary to form creative beats.
                             Yet he doesn’t believe AI should replace
                             artistic sensibility, “because to create art,
                             you need to touch the soul.”


                      # ⚓ 404 Media ☛ This_‘College_Protester’_Isn’t_Real._It’s
                        an_AI-Powered_Undercover_Bot_for_Cops⠀⇛


                             Massive Blue is helping cops deploy AI-
                             powered social media bots to talk to people
                             they suspect are anything from violent sex
                             criminals all the way to vaguely defined
                             “protesters.”


                      # ⚓ Jamie Zawinski ☛ Hello_fellow_kids!_Doing_crimes_is
                        TIGHT!⠀⇛


                      # ⚓ The Independent UK ☛ Seattle_crosswalk_audio_buttons
                        hacked_to_imitate_Jeff_Bezos’_voice_pleading_not_to_tax
                        the_rich⠀⇛


                             It wasn’t immediately clear how many
                             crosswalk buttons were impacted.


                             The Seattle Department of Transportation said
                             it was responding to “several locations which
                             have been altered to play fake audio
                             messages.” The department said in a statement
                             on Wednesday evening: “We have corrected walk
                             signal messages in multiple locations, and
                             will continue to respond to tampered push
                             buttons if we learn of them.”


                      # ⚓ Michael Burkhardt ☛ Chats_with_Claude:_On_Fascism_-
                        Michael_Burkhardt's_Whirled_Wide_Web⠀⇛


                             In light of the recent news that the Trump
                             administration is using the IRS to target a
                             private university, I wondered: what has to
                             happen before we can legitimately use the
                             term fascism? So I had a short chat with
                             Claude. Here’s the transcript: [...]


                # § Social Control Media⠀➾


                      # ⚓ Thibault_Martin:_Social_media_affect_me_more_than_I
                        thought⠀⇛


                             I've struggled with focus earlier this year.
                             I felt pulled in all directions, overwhelmed
                             by the world, and generally miserable. I
                             decided_to_abstain_from_using_social_control
                             media for a week to see if anything would
                             change.


                             The Joy of Missing Out was so strong that I
                             ended up staying_off_social_control_media_for
                             3_whole_weeks. I realized that engaging with
                             social control media harmed my mental health,
                             and I could develop strategies to improve my
                             relationship with it.


                      # ⚓ Futurism ☛ OpenAI_Is_Secretly_Building_a_Social
                        Network⠀⇛


                             If it goes ahead, it sounds reminiscent of
                             how X directly integrates Musk's Grok AI
                             model into the website, where it operates
                             both as a standalone chatbot, while also
                             being capable of responding directly to
                             users' posts at their request.


                      # ⚓ The Nation ☛ A_Disgraced_Hunter_Biden_Informant_Had
                        Ties_to_Trump_Social_Media_Bid⠀⇛


                             Last year, Smirnov pleaded guilty to multiple
                             federal charges—including making a false
                             statement about the Bidens—and was sentenced
                             to six years in prison, so it’s difficult to
                             discern, based on the new DOJ filing, what
                             might cast fresh doubt on his conviction.
                             (The Justice Department did not respond to
                             requests for comment on this piece; Smirnov’s
                             lawyer declined to comment.)


                             The intrigue here deepens in view of
                             continued revelations about Smirnov’s
                             dealings with Trump’s business empire.
                             Trump’s own personal business associates paid
                             Smirnov under unclear circumstances via a
                             mysterious American firm in 2020—the same
                             year he was providing false statements about
                             the Bidens to the FBI. But Smirnov had other,
                             unreported ties to Donald Trump and his
                             businesses, via a convoluted group of linked
                             companies, one of which came close to
                             building a Trump-branded social media
                             platform, like the firm that later became
                             known as Truth Social, even though Smirnov
                             reportedly had little direct involvement in
                             the plan.


          o § Pseudo-Open Source⠀➾


                # § Openwashing⠀➾


                      # ⚓ The New Stack ☛ Kelsey_Hightower,_AWS's_Eswar_Bala_on
                        Open_Source's_Evolution⠀⇛


                             “The origins of open source came from
                             fighting against the big vendors,” said
                             Hightower. “So, when you see a big vendor do
                             something in open source, you naturally
                             question the motives. Like, you can’t ignore
                             that particular truth.”


                             So what does it mean when we use “AWS” and
                             “open source” in the same sentence?


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Simon Josefsson ☛ Verified_Reproducible_Tarballs⠀⇛


                             How do you know that the XZ release tarballs
                             was actually derived from its version control
                             sources? The same for Gzip? Coreutils? Tar?
                             Sed? Bash? GCC? We don’t know this! I am not
                             aware of any automated or collaborative
                             effort to perform this independent
                             confirmation. Nor am I aware of anyone
                             attempting to do this on a regular basis. We
                             would want to be able to do this in the year
                             2042 too. I think the best way to reach that
                             is to do the verification continuously in a
                             pipeline, fixing bugs as time passes. The
                             current state of the art seems to be that
                             people audit the differences manually and
                             hope to find something. I suspect many
                             package maintainers ignore the problem and
                             take the release source tarballs and trust
                             upstream about this.


                             We can do better.


                      # ⚓ The Register UK ☛ Tesla_fudged_odometer_to_defraud
                        me,_owner_claims⠀⇛


                             After the last visit to the shop, he claimed
                             he noticed something odd: He was burning
                             through a lot more miles for the same trips.
                             A normal commute for him averaged 55.54 miles
                             a day between December and February, but by
                             March the odometer was registering 72.35
                             miles a day for the same journey, he reckons.


                             By July he'd passed the 50,000-mile limit. He
                             then discovered that Tesla had issued a
                             recall for faulty suspension systems, so in
                             January 2024 he went to store for a sixth
                             time to fix his suspension again, and was
                             told he had to pay because the warranty had
                             expired and the recall didn't apply to him.


                      # ⚓ Terence Eden ☛ That’s_Not_How_A_SIM_Swap_Attack
                        Works⠀⇛


                             I realise it is in the consumer rights
                             section of the newspaper, not the technology
                             section, and I dare-say some editorialising
                             has gone on, but that's nonsense.


                             Here's how a SIM swap works.


                # § Privacy/Surveillance⠀➾


                      # ⚓ EDRI ☛ Civil_society_files_DSA_complaint_against_Meta
                        for_toxic,_profiling-fueled_feeds⠀⇛


                             Civil society organisations Bits of Freedom,
                             Convocation Design + Research, European
                             Digital Rights (EDRi), and Gesellschaft für
                             Freiheitsrechte (GFF) are filing a complaint
                             against Meta for violating the Digital
                             Services Act (DSA).


                      # ⚓ JURIST ☛ Europe_rights_court_rules_Netherlands
                        violated_privacy_right_for_long-term_maternal
                        separation⠀⇛


                             The European Court of Human Rights ruled on
                             Tuesday that the Netherlands violated Article
                             8 of the European Convention on Human Rights,
                             which guarantees the right to respect for
                             private and family life, in a case involving
                             the long-term separation of a mother from her
                             daughter following the mother’s loss of
                             parental authority.


                      # ⚓ Los Angeles Times ☛ Congressmen_sound_alarm_over_data
                        privacy_following_23andMe_bankruptcy⠀⇛


                             The Republican representatives — Brett
                             Guthrie from Kentucky, Gus Bilirakis from
                             Florida and Gary Palmer from Alaska — sent a
                             letter to 23andMe interim Chief Executive Joe
                             Selsavage on Thursday requesting answers to
                             several questions by May 1.


                             The questions revolve around the fate of
                             23andMe’s genetic database, which includes
                             DNA information from more than 15 million
                             people. The congressmen asked the company how
                             it would protect the data in an event of a
                             sale and how it would vet potential buyers.


                      # ⚓ Wired ☛ How_Americans_Are_Surveilled_During
                        Protests⠀⇛


                             There have been a number of protests in the
                             past few months pushing back against
                             President Trump’s most recent policy changes,
                             and we're likely to see more. Today on the
                             show, WIRED’s senior editor of security and
                             investigations, Andrew Couts, talks us
                             through the technology being used by law
                             enforcement to surveil protests, how
                             surveillance tech has evolved over the years,
                             and what it means for anyone taking to the
                             streets or posting to social media to voice
                             their concerns. Plus, we share WIRED tips on
                             how to stay safe, should you choose to
                             protest.


                      # ⚓ Wired ☛ New_Jersey_Sues_Discord_for_Allegedly_Failing
                        to_Protect_Children⠀⇛


                             The lawsuit, filed on Thursday, comes after a
                             multiyear investigation by the New Jersey
                             Office of Attorney General. The AG’s office
                             claims it has uncovered evidence that,
                             despite Discord’s policies to protect
                             children and teens, the popular messaging app
                             is putting youth “at risk.”


                             “We’re the first state in the country to sue
                             Discord,” Attorney General Matthew Platkin
                             tells WIRED.


                      # ⚓ Bruce Schneier ☛ Age_Verification_Using_Facial
                        Scans⠀⇛


                             I look forward to all the videos of people
                             hacking this system using various disguises.


                      # ⚓ The Telegraph UK ☛ Electric_cars_threaten_national
                        security,_defence_chiefs_warn⠀⇛


                             A report by the Defence Science and
                             Technology Laboratory (DSTL) found that there
                             were concerns Beijing – which dominates the
                             market – could effectively eavesdrop on
                             conversations using the vehicles, which are
                             to be introduced for all ministers and
                             officials by the end of 2027.


                             The warning in the report, which was
                             delivered to the previous Tory government,
                             contributed to fears at senior levels in
                             Rishi Sunak’s administration that electric
                             cars were “basically mobile spying platforms”
                             and even those made in the West using Chinese
                             parts were susceptible.


                      # ⚓ Scoop News Group ☛ Palantir,_Anthropic,_Google_deepen
                        ties_on_government_AI_use_with_Claude_partnership⠀⇛


                             In a press release announcing the
                             collaboration Thursday, the companies
                             revealed that they are now working together
                             through FedStart, a Palantir program meant to
                             aid compliance with FedRAMP. Google Cloud is
                             also a major partner.


                             As they increasingly attempt to sell their
                             technology to the federal government, AI
                             companies are currently figuring out how best
                             to approach FedRAMP, FedScoop previously
                             reported. The General Services
                             Administration-housed program oversees
                             security standards and benchmarks, and is
                             focused on reducing the need for multiple
                             agencies to conduct redundant reviews of
                             cloud technology.


                      # ⚓ NYOB ☛ EU_pledged_to_improve_GDPR_cooperation_-_and
                        made_it_worse⠀⇛


                             As of 2018, the GDPR is supposed to ensure
                             that Europeans enjoy privacy rights
                             throughout the entire EU. However, when
                             people's rights are violated by companies
                             based in another EU/EEA Member State,
                             complaints are dealt with through a complex
                             "cooperation mechanism" between the Data
                             Protection Authority (DPA) in the users'
                             Member State and the DPA in the company's
                             Member State. This enforcement mechanism is
                             at the core of the generally acknowledged
                             enforcement failure of the GDPR. Complaints
                             get lost, decisions take years and there is
                             virtually no possibility to act against
                             inactive DPAs. The EU has ventured to solve
                             this through a "GDPR Procedural Regulation".
                             But it becomes clear now, that it is about to
                             fail miserably. The final so-called
                             “trilogue” negotiations between the European
                             Parliament, the Member States and the
                             European Commission has led to a legislative
                             mess that will likely make procedures more
                             complex, slower and prone to legal
                             challenges. noyb has been closely following
                             the dossier and is now issuing a public
                             warning. The file needs intensive additional
                             work. The current approach seems to make
                             things worse overall.


                      # ⚓ The Verge ☛ Discord_is_verifying_some_users’_age_with
                        ID_and_facial_scans⠀⇛


                             The new face and ID scanning requirements
                             only apply to Discord users who haven’t
                             previously verified their age on the
                             platform. Discord says this is a “one-time
                             process” that will be triggered in two
                             situations: when users are exposed to nude or
                             sexually explicit content that’s been flagged
                             by Discord’s sensitive media filter, or when
                             users attempt to change filter control
                             settings to prevent such content from being
                             blurred or blocked.


          o § Defence/Aggression⠀➾


                # ⚓ New York Times ☛ Assad_Defaced:_Syrians_Destroy_a
                  Dictator’s_Icons⠀⇛


                       Images of Bashar al-Assad and his family were
                       emblematic of the dynasty’s grip on Syria. Though
                       remnants linger after the regime’s ouster, the
                       removal of the once ubiquitous relics has offered
                       catharsis.


                # ⚓ France24 ☛ Two_years_of_war_in_Sudan_triggered_the_“world's
                  worst_humanitarian_crisis”⠀⇛


                       Once allies, they're now enemies. In 2019, the
                       Sudanese army and the Rapid Support Forces worked
                       together to oust former strongman Omar al-Bashir
                       from power. But after a failed transition to
                       civilian rule, the Sudanese army chief, General
                       Abdel Fattah al-Burhan, and the Rapid Support
                       Forces commander, General Mohamed Hamdan Daglo,
                       worked together again in 2021 to overthrow the
                       government. For a time, Sudanese expected a
                       peaceful return to civilian rule. Then came April
                       2023 and two years of civil war. Tens of thousands
                       of people have been killed and more than 13 million
                       uprooted, with reports of rape being used as a
                       weapon of war across the country. The UN also says
                       it's the world's biggest crisis of hunger and
                       displacement. And the effects of the war are
                       spreading beyond Sudan's borders.


                # ⚓ Los Angeles Times ☛ Contributor:_The_constitutional_crisis
                  is_real⠀⇛


                       Is the U.S. facing a constitutional crisis? The
                       answer, unequivocally and emphatically, is yes. But
                       it also could get much worse.


                # ⚓ RFA ☛ Beijing,_Manila_at_odds_over_Google_Maps_update_on
                  South_China_Sea⠀⇛


                       It’s unclear why Google made the change, but a
                       spokesperson told Agence France-Presse: “The West
                       Philippine Sea has always been labeled on Google
                       Maps. We recently made this label easier to see at
                       additional zoom levels.”


                # ⚓ Energy Mix Productions Inc ☛ Big_Banks_Look_for_Profits
                  Amid_Global_Temperature_Rise⠀⇛


                       “We now expect a 3°C world” amid setbacks to global
                       decarbonization efforts, Morgan Stanley told
                       clients, in a forecast that SciAm says was “tucked
                       into a mundane research report” on the bright
                       future of air conditioning stocks. JPMorgan told
                       investors it evaluates climate risks against
                       “baseline” scenarios that assume global warming of
                       2.7°C to over 3°C by 2100.


                # ⚓ The Register UK ☛ Whistleblower_describes_how_DOGE_[sic]
                  tore_through_NLRB_IT_system⠀⇛


                       Democratic lawmakers are calling for an
                       investigation after a tech staffer at the US
                       National Labor Relations Board (NLRB) blew the
                       whistle on the cost-trimming DOGE [sic]'s
                       activities at the employment watchdog – which the
                       staffer claims included being granted superuser
                       status in contravention of standard operating
                       procedures, exfiltrating data, and seemingly
                       leaking credentials to someone with a Russian IP
                       address.


                # ⚓ Scoop News Group ☛ 35_countries_use_Chinese_networks_for
                  transporting_mobile_user_traffic,_posing_cyber_risks⠀⇛


                       “A major issue lies in the fact that these
                       providers operate under the direction of the
                       Chinese government, raising the risk of global
                       surveillance, data interception, and exploitation
                       for state-sponsored cyber espionage,” the analysis
                       reads. “Their role in the mobile interconnect
                       system grants them access to critical functions,
                       including device authentication, call setup, SMS
                       delivery, location updates, and data session
                       management — making them prime channels for
                       exploiting network vulnerabilities.”


                # ⚓ Crooked Timber ☛ The_point_of_no_return:Only_days_left_to
                  stop_a_totalitarian_state_in_the_US_—_Crooked_Timber⠀⇛


                       Back in November, when I concluded that Trump’s
                       dictatorship was a fait accompli lots of readers
                       thought I was going over the top. In retrospect,
                       and with one exception, I was hopelessly over-
                       optimistic. I imagined a trajectory similar to
                       Orban’s Hungary, with a gradual squeeze on
                       political opposition and civil society, playing out
                       over years and multiple terms in office,.


                       The reality has been massively worse, both in terms
                       of speed and scope. Threats of conquest against
                       friendly countries, masked thugs abducting people
                       from the street, shakedowns of property from
                       enemies of the state, concentration camps outside
                       the reach of the legal system, all happening at a
                       pace more comparable to Germany in 1933 than to the
                       examples I had in mind.


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


                      # ⚓ Meduza ☛ Russia_jails_four_journalists_for_5.5_years
                        over_alleged_ties_to_Navalny's_team,_including_past
                        Reuters_and_AP_contributors_—_Meduza⠀⇛


                      # ⚓ RFERL ☛ Russian_Journalists_Handed_Prison_Terms_For
                        Alleged_Ties_To_Navalny⠀⇛


                             Four Russian journalists have been sentenced
                             by a Moscow court to 5 1/2 years in prison
                             each for their activities linked to the late
                             opposition leader Aleksei Navalny’s Anti-
                             Corruption Foundation (FBK), which Russian
                             authorities have designated as an "extremist
                             organization."


          o § Environment⠀➾


                # ⚓ EcoWatch ☛ Climate_Change_Will_Increase_Arsenic_Levels_in
                  Rice,_Study_Finds⠀⇛


                       The researchers found that temperatures above two
                       degrees Celsius and rising levels of carbon dioxide
                       in the atmosphere lead to higher inorganic arsenic
                       (iAs) concentrations in rice, which could increase
                       the lifetime health risks of populations across
                       Asia by 2050, a press release from Columbia’s
                       Mailman School of Public Health said.


                # ⚓ Michigan News ☛ US_Army_engineers_decide_to_fast-track
                  Great_Lakes_tunnel_permits_under_Trump_energy_emergency
                  order⠀⇛


                       “The only energy ‘emergency’ the American people
                       face is Trump’s efforts to disregard clean air and
                       water safeguards in order to rush through dirty,
                       dangerous fossil fuel projects,” said Mahyar
                       Sorour, director of the Sierra Club’s Beyond Fossil
                       Fuels Policy.


                # ⚓ Bridge Michigan ☛ Earth_Day_events_planned_across_Michigan;
                  find_one_in_your_area⠀⇛


                       Earth Day is coming up on Tuesday.


                       While plenty of events are happening on the day
                       itself, many are also scheduled for the weekends
                       before and after.


                       The holiday can be a good excuse to get out and
                       enjoy the Michigan outdoors. Whether you live in
                       Augusta or Alpena, there’s probably something Earth
                       Day-related happening near you.


                # § Energy/Transportation⠀➾


                      # ⚓ Vintage Everyday ☛ Inside_the_Cockpit_of_a_Concorde⠀⇛


                             Although Concorde’s small dimensions
                             effectively created the sense of a packed-in
                             bank of instruments, there wasn’t much more
                             on this busy flight deck than you’d find on
                             any other airliner at the time.


                      # ⚓ Energy Mix Productions Inc ☛ AI_Electricity_Demand
                        Could_Mean_Grid_Strain_or_Gain⠀⇛


                             A new report this week from the International
                             Energy Agency (IEA) confirms that the rapid
                             spread of data centres, driven by soaring
                             demand for artificial intelligence
                             technologies, is one of several factors
                             putting pressure on electricity systems
                             around the world.


                             “A typical AI-focused data centre consumes as
                             much electricity as 100,000 households, but
                             the largest ones under construction today
                             will consume 20 times as much,” the IEA
                             writes. Poor planning could worsen their
                             impact, but AI also has the potential to
                             improve how power grids function.


                # § Wildlife/Nature⠀➾


                      # ⚓ New York Times ☛ The_‘Great_Moose_Migration’
                        Livestream_Captivates_Sweden⠀⇛


                             Moose fans are following the weekslong moose
                             migration, which airs live on the national
                             broadcaster. “This is reality TV at its
                             finest,” a moderator of a zealous Facebook
                             (Farcebook) group said.


                      # ⚓ Science Alert ☛ When_The_Pandemic_Came,_Zoos_Closed,
                        And_The_Animals_Started_to_Act_Differently⠀⇛


                             When the humans go away...


                      # ⚓ LRT ☛ Cherry_blossoms_draw_crowds_in_Vilnius_–
                        photos⠀⇛


                             The 200 cherry trees were planted in 2001 to
                             mark the 100th anniversary of the birth of
                             Chiune Sugihara, a Japanese diplomat who
                             saved about 6,000 Jews from Lithuania, Poland
                             and Germany during World War Two. A monument
                             at the park’s entrance notes that the trees
                             were a gift from the people of Japan to
                             Lithuania.


                # § Overpopulation⠀➾


                      # ⚓ European Commission ☛ Commission_invests_€86_million
                        to_improve_climate_resilience_and_water_security⠀⇛


          o § Finance⠀➾


                # ⚓ The Straits Times ☛ Chinese_official_says_US_tariff_aims_to
                  ‘take_away_Hong_Kong’s_life’⠀⇛


                       Mr Xia Baolong made the comments in a televised
                       speech on Hong Kong’s National Security Education
                       day.


                # ⚓ New York Times ☛ Biden_Condemns_Convicted_Felon_Over_Social
                  Security_in_First_Speech_Since_Leaving_Office⠀⇛


                       In Joseph R. Biden Jr.’s first extensive speech
                       since he left office, he accused the Convicted
                       Felon administration of “taking a hatchet” to the
                       Social Security Administration.


                # ⚓ New York Times ☛ Amazon_Sellers_Struggle_with_Convicted
                  Felon’s_Tariff_Plans⠀⇛


                       An Illinois couple who sell party supplies on
                       Amazon have been frantically trying to understand
                       and adapt to new costs caused by Hell Toupée’s
                       tariffs.


                # ⚓ France24 ☛ Viral_TikTok’s_from_Chinese_manufacturers
                  falsely_claim_that_luxury_handbags_are_made_in_China⠀⇛


                       In response to The Insurrectionist’s trade war,
                       Chinese factories are flooding Fentanylware
                       (TikTok) with viral videos claiming to ‘expose’ the
                       truth behind the manufacturing process of luxury
                       handbags, including Hermes, Louis Vuitton, Gucci,
                       Prada…allegedly, they’re all ‘made in China!’ We
                       debunk these claims in this edition of Truth or
                       Fake.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Press Gazette ☛ Global_ad_spend_against_news_down_by_a
                  third_since_pre-Covid⠀⇛


                       Professionally-produced content being overtaken for
                       ad spend by creators and influencers.


                # ⚓ Deccan Chronicle ☛ OpenAI_in_Talks_to_Acquire_AI_Coding
                  Tool_Windsurf_for_$3_Billion:_Report⠀⇛


                       This acquisition would position OpenAI to better
                       compete with companies offering AI coding services,
                       including Anthropic, Microsoft’s GitHub, and
                       Anysphere. Windsurf, founded in 2021, would join
                       the list of startups acquired by OpenAI, which
                       currently includes vector database company Rockset
                       and Multi.


                # ⚓ Techdirt ☛ The_“De”_In_“Decentralization”_Stands_For
                  “Democracy”⠀⇛


                       There’s a certain dark irony in watching tech
                       billionaires who built their empires on the
                       “democratizing power of technology” now actively
                       working to dismantle democratic institutions. The
                       same figures who once championed connection and
                       openness are now the architects of the most
                       dangerous centralization of power in modern
                       history.


                # ⚓ Semafor Inc ☛ Activist_seeks_CEO_change_at_Hewlett_Packard
                  Enterprise⠀⇛


                       HPE’s board is expected to meet in coming days to
                       discuss whether to replace CEO Antonio Neri, a
                       Hewlett Packard lifer who has run the company since
                       2018, following a proposal from activist investor
                       Elliott Management to do that, according to people
                       close to the company.


                # ⚓ Molly White ☛ Trump’s_newest_grift:_Building_a
                  cryptocurrency_empire_while_destroying_its_regulators⠀⇛


                       The benefits to these companies have been
                       substantial: at least eight SEC enforcement cases
                       against cryptocurrency firms have been dropped with
                       prejudice or stayed pending resolution. Many have
                       also been invited to shape the new rules for their
                       industry, giving them a priceless opportunity to
                       establish a profitable environment without
                       burdensome financial oversight, legal compliance,
                       and consumer protection requirements.


                # ⚓ Carl Svensson ☛ Honest_and_Elitist_Thoughts_on_Why
                  Computers_Were_More_Fun_Before⠀⇛


                       Built-in gatekeeping for nerds is now long gone,
                       usurped by the lowest common denominator in
                       economies of scale. Consumerist convenience, walled
                       gardens, corporate risk-adversity and shallow
                       aesthetical homogenization have replaced the
                       sprawling hobbyist collective that once made up the
                       bulk of personal computers and their users.


                       I have a hard time blaming the users upon which all
                       of this was forced. They probably, in their heart
                       of hearts, wanted this development every bit as
                       little as I did. But the genie is out of its
                       bottle, and the good old days aren't coming back.


                       It's not that there aren't computer nerds anymore.
                       They're just much harder to spot, since most people
                       who own a computer nowadays care very little about
                       their machines. This, I think, is a rarely
                       discussed reason for why so many of us old geeks
                       seek refuge in retro computing. Nobody in their
                       right mind would buy a second hand Amiga today -
                       unless they have aficion for using computers for
                       the sake of using computers.


                # ⚓ Futurism ☛ Zillionaire_Girlbosses_Astonished_by_Backlash_to
                  Their_Frivolous_Trip_to_Space⠀⇛


                       The vacuous publicity stunt — which claimed to make
                       the crew [sic] of mostly uber-wealthy media
                       personalities "astronauts" after a mere two days of
                       basic safety training — drew plenty of criticism.


                       After all, apart from spending an obscene amount of
                       money and rattling off cringeworthy statements
                       about "making space for future women," the crew
                       [sic] had little to contribute to science,
                       discourse, or meaningful feminism.


                # ⚓ The Cyber Show ☛ Freedom_Fighters_(Part_3)⠀⇛


                       As we've been saying here for a while cybersecurity
                       is a political struggle. If the US is growing
                       hostile to cybersecurity, what does this mean?


                       It is hard not to be in a state of denial around
                       recent events. What's happening in the USA is
                       simply bizarre. One expects to wake up any moment
                       and find it was all a bad dream or test of public
                       credulity?


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Axios ☛ Trump_tariffs_inspire_Chinese_manufacturer
                        TikTok_trend⠀⇛


                             Even if the products are real, it's often
                             unclear from the videos how to make a
                             purchase.


                             Reality check: As attractive as it might
                             sound to avoid markups, it's often not
                             advisable or not possible to buy directly
                             from Chinese factories.


                      # ⚓ Tracy Durnell ☛ Ceding_the_work_of_interpretation⠀⇛


                             All together, I see these pieces adding up to
                             an avoidance of making our own decisions,
                             exercising our own judgment, trusting our own
                             interpretations. And, fair — we’re all
                             overwhelmed, drowning in content.


                      # ⚓ Axios ☛ MAGA-friendly_outlets_reshape_White_House
                        press_briefings⠀⇛


                             The increased access comes as part of the
                             Trump administration's push to elevate "new
                             media," which includes nonpartisan digital
                             outlets like Axios and Semafor but also
                             Trump-aligned outlets.


                             The new approach yields more supportive
                             questions, fortifying the MAGA media
                             ecosystem from the inside out.


                      # ⚓ The Washington Post ☛ Russia_seeds_chatbots_with
                        lies._Any_bad_actor_can_game_AI_the_same_way.⠀⇛


                             Russia is automating the spread of false
                             information to fool artificial intelligence
                             chatbots on key topics, offering a playbook
                             to other bad actors on how to game AI to push
                             content meant to inflame, influence and
                             obfuscate instead of inform.


                             Experts warn the problem is worsening as more
                             people rely on chatbots rushed to market,
                             social media companies cut back on moderation
                             and the Trump administration disbands
                             government teams fighting disinformation.


          o § Censorship/Free Speech⠀➾


                # ⚓ China_detains_Tibetans_for_sharing_photos_of_late_Buddhist
                  leader⠀⇛


                       Officials place monastery of Tulku Hungkar Dorje
                       under strict surveillance, forbid public memorials.


                # ⚓ Citizen Lab ☛ JUICYJAM:_How_Thai_Authorities_Use_Online
                  Doxxing_to_Suppress_Dissent⠀⇛


                       A sustained, coordinated social control media
                       harassment and doxxing campaign – which we
                       codenamed JUICYJAM – targeting the pro-democracy
                       movement in Thailand has run uninterrupted, and
                       unchallenged, since at least August 2020. Through
                       our analysis of public social control media posts
                       we determined that the campaign was not only
                       inauthentic, but the information revealed could not
                       have been reasonably sourced from a private
                       individual.


                # ⚓ FAIR ☛ Fox_News_Can’t_Admit_Jewish_Identity_of_Anti-Israel
                  Protesters⠀⇛


                       AP (3/13/25): “Demonstrators from [Jewish Voice for
                       Peace] filled the lobby of Trump Tower…to denounce
                       the immigration arrest of Mahmoud Khalil, a pro-
                       Palestinian activist who helped lead protests
                       against Israel at Columbia University.” In its
                       coverage of Jewish Voice for Peace’s Trump Tower
                       protest, Fox News obscured the Jewish identity of
                       protesters—while echoing antisemitic conspiracy
                       theories and racist tropes.


                # ⚓ Deccan Chronicle ☛ All_India_Muslim_Jamaat_Issues_Fatwa
                  Against_Vijay_Over_Iftar_Party⠀⇛


                # ⚓ Techdirt ☛ Library_Study_Shows_It’s_Just_Politicians_And
                  Activist_Groups_Trying_To_Get_Books_Banned⠀⇛


                       The latest report [PDF] on censorship efforts
                       compiled by the American Library Association makes
                       it clear this isn’t a groundswell movement by
                       personally offended parents to protect their kids
                       from certain content. This is an activist movement
                       that is determined to eliminate access to this
                       content by whatever means necessary. Unfortunately,
                       these groups are being helped along by legislators
                       who believe their personal beliefs should be the
                       only ones protected by the Constitution.


                # ⚓ The Record ☛ Chris_Krebs_leaves_SentinelOne_after_Trump
                  memo,_saying_‘this_is_my_fight’_|_The_Record_from_Recorded
                  Future_News⠀⇛


                       “It’s about the government pulling its levers to
                       punish dissent, to go after corporate interests and
                       corporate relationships,” Krebs told the Wall
                       Street Journal in his first interview since Trump’s
                       move. Reuters noted last week that other large
                       cybersecurity companies have been largely silent
                       about Trump’s memo.


                # ⚓ Scoop News Group ☛ Chris_Krebs_resigns_from_SentinelOne_to
                  focus_on_fighting_Trump’s_executive_order⠀⇛


                       The executive order targeting Krebs and another
                       former Department of Homeland Security official,
                       Miles Taylor, have come under scathing criticism
                       from both the left and the right.


                       Conservative legal scholar J. Michael Luttig
                       described them as “constitutionally corrupt,” “a
                       travesty of justice” and “shameful.”


                # ⚓ The Register UK ☛ Krebs_resigns_from_SentinelOne_after
                  Trump_memo_targets_him⠀⇛


                       Krebs, a Republican who Trump appointed to lead US
                       cybersecurity operations in 2017, was famously
                       fired via tweet five years ago after he publicly
                       contradicted Trump's false claims of election
                       fraud. Krebs declared the 2020 US presidential
                       election "the most secure in American history."


                # ⚓ Reuters ☛ Ex-CISA_chief_Chris_Krebs_leaving_SentinelOne
                  following_Trump_pressure⠀⇛


                       Trump fired Krebs from CISA in November 2020
                       following his refusal to endorse the president's
                       false claim that the election had been rigged by
                       his then-opponent, former President Joe Biden. Last
                       week, Trump signed an order that stripped Krebs and
                       employees of the firm of their security clearances.
                       The rationale for targeting SentinelOne, whose
                       products are used to fight hackers and
                       cybercriminals, was never publicly explained, but
                       the move fits within Trump's wider campaign to use
                       the might of the U.S. government to crush his
                       political opponents.


                # ⚓ The Fediverse Report ☛ Bluesky,_censorship_and_country-
                  based_moderation⠀⇛


                       In response to the censorship requests, users on X
                       started to move towards Bluesky, to avoid the
                       restrictions. The censorship requests from the
                       Turkish government quickly extended to Bluesky, and
                       Bianet reported on April 5th that 44 Bluesky
                       accounts had been ordered to be blocked by the
                       Turkish judicial system, citing concerns over
                       national security and public order. Bianet noted
                       that at that time, Bluesky PBC (the company behind
                       Bluesky) had not yet blocked any of these accounts,
                       and that they remained accessible from Turkey.


                # ⚓ Axios ☛ Trump_wants_to_assert_control_at_Harvard,_other
                  elite_colleges⠀⇛


                       Why it matters: The administration's recent demands
                       of Harvard and other elite institutions show the
                       government's playbook to influence and reorient the
                       priorities of universities through federal funds.


                       While the demands revolve around institutional
                       policies, the freezes and cuts largely threaten
                       scientific research.


                # ⚓ Techdirt ☛ Otherwise_Objectionable:_How_230_Let_US_Internet
                  Companies_Win⠀⇛


                       We discuss how other places regulate the internet,
                       including Europe, Japan, Australia, South Korea,
                       Brazil and more. And how each of their approaches
                       created real burdens — the exact kinds of burdens
                       that Chris Cox and Ron Wyden were trying to avoid
                       while drafting Section 230.


                       What’s particularly striking is how Section 230
                       functioned as a kind of incubator. The early
                       freedom from crushing legal uncertainty allowed
                       companies to build services compelling enough that
                       international users demanded access to them,
                       creating pressure on foreign regulators to
                       accommodate these platforms rather than block them
                       entirely. This explains what seems like a
                       contradiction: how platforms built under Section
                       230’s protection can operate in jurisdictions with
                       much stricter liability regimes. They succeeded not
                       despite Section 230, but because of the head start
                       it provided, reinforcing the idea that Section
                       230’s biggest value is in protecting smaller, newer
                       platforms.


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


                # ⚓ CPJ ☛ Trial_of_5_journalists_who_covered_Turkish_protests
                  set_to_open⠀⇛


                       “This trial has been invented as a scare tactic to
                       intimidate and deter all journalists in Turkey from
                       reporting from the field. Experienced journalists
                       should not be forced to explain in court why they
                       were photographing Turkey’s biggest protests in a
                       decade, in its biggest city,” said Özgür Öğret,
                       CPJ’s Turkey representative. “Authorities should
                       drop the charges against the five photojournalists
                       who already suffer enough in trying to capture
                       images of historic events while repeatedly being
                       beaten, tear gassed and shot with rubber bullets.”


                # ⚓ CPJ ☛ Kazakh_journalist_Temirlan_Yensebek_sentenced_to_5
                  years_of_restricted_freedom⠀⇛


                       “Yensebek’s conviction is a clear example of how
                       Kazakh authorities use such measures to intimidate
                       and silence critical journalists,” said CPJ Chief
                       of Programs Carlos Martinez de la Serna. “We call
                       on the authorities in Kazakhstan not to contest any
                       potential appeal of his conviction and to ensure
                       that journalists in the country can carry out their
                       work without fear of criminal prosecution.”


                # ⚓ Tech Central (South Africa) ☛ TechCentral_acquired_in
                  significant_boost_for_ICT_publishing⠀⇛


                       TechCentral, South Africa’s most powerful B2B
                       technology news and information platform, has a new
                       owner.


                       TechCentral’s long-serving business partner,
                       Publishared – founded by digital publishing
                       industry veteran Michelle Losco – has acquired
                       NewsCentral Media, TechCentral’s publisher, for an
                       undisclosed sum.


                # ⚓ CPJ ☛ 4_Russian_journalists_sentenced_to_5_½_years_in
                  prison⠀⇛


                       “The sentencing of four journalists at once to 5 ½
                       years in prison is blatant testimony to Russian
                       authorities’ profound contempt for press freedom,”
                       said CPJ Chief Programs Officer Carlos Martinez de
                       la Serna. “Russian authorities should immediately
                       release Antonina Favorskaya, Artyom Krieger,
                       Konstantin Gabov and Sergey Karelin, drop all
                       charges against them, and stop jailing journalists
                       in retaliation for their work.”


                       The court also banned them from publishing any
                       content on the [Internet] for three years after
                       they complete their prison sentences.


                # ⚓ CPJ ☛ Upholding_and_Expanding_the_Rule_of_Law_in_the_EU:
                  Joint_Recommendations_Towards_a_Strongera_and_More_Effective
                  2025_Rule_of_Law_Report [PDF]⠀⇛


                       The profound political shifts witnessed in 2024, a
                       year marked by electoral upheavals and changing
                       political landscapes across Europe and the world,
                       are testing the resilience of democratic
                       institutions, highlighting the need for continued
                       and coordinated action in protecting the rule of
                       law, democracy and fundamental rights in the EU.
                       Upholding the rule of law is a top priority, and
                       strengthening the Rule of Law Report is essential
                       to this effort. Making it more effective requires
                       closer collaboration with all key actors committed
                       to the rule of law in the EU, including civil
                       society organisations (CSOs), journalists, and
                       academics.


                # ⚓ [Old] Buttondown LLC ☛ What_is_"media"?_A_primer_for
                  Americans.⠀⇛


                       Just in time for a massive transformation in the
                       way we use and consume media in the United States,
                       I’ll be sending you a lot of letters. They’re based
                       on an introductory media studies course I taught in
                       the spring of 2024 at the University of San
                       Francisco.


                       I owe a lot to my USF colleagues and students, who
                       taught me how to teach media in the twenty-first
                       century. My students asked unexpected questions and
                       spurred me to rethink my approach and the topics I
                       covered. They also introduced me to pop culture and
                       perspectives I never would have discovered on my
                       own, outside the classroom. With these letters, I
                       hope to extend that classroom experience to you, my
                       reader.


                # ⚓ YLE ☛ Finnish_Broadcasting_Company_Yle_to_begin_second
                  phase_of_restructuring_talks⠀⇛


                       These cuts — the biggest in Yle's nearly 100-year
                       history — are as a result of initial plans by the
                       two main government parties, the National Coalition
                       Party and the Finns Party, to reduce Yle's annual
                       funding by more than 100 million euros.


                       Instead, an all-party parliamentary working group
                       agreed in September last year to cut Yle's budget
                       by 66 million euros over a three-year period.


          o § Civil Rights/Policing⠀➾


                # ⚓ Bryan Lunduke ☛ Adobe_Scaling_Back_DEI,_Dropping_Diversity
                  Quotas⠀⇛


                       The Photoshop maker appears to be dramatically
                       reducing their focus on Diversity, Equity, &
                       Inclusion - which is making some Adobe employees
                       very grumpy.


                # ⚓ Advance Local Media LLC ☛ Texas_sex_toy_law_could_lead_to
                  more_civil_rights_restrictions,_advocates_warn⠀⇛


                       To explore the potential impacts of these laws,
                       LoneStarLive.com spoke to Ricci Levy, president and
                       CEO of the Woodhull Freedom Foundation, a human
                       rights organization that advocates for sexual
                       freedom.


                       This conversation has been edited for length and
                       clarity.


                # ⚓ Los Angeles Times ☛ What_is_stopping_Trump_from_exiling_you
                  to_a_foreign_prison?⠀⇛


                       The legal world has been on notice for a
                       constitutional clash ever since Trump resumed
                       office in January, meticulously analyzing a series
                       of court rulings that challenge the White House and
                       following the administration’s reluctant, often
                       defiant, response.


                       But constitutional scholars see no ambiguity in the
                       consequences of the president’s latest threat.
                       Trump’s plans to forcibly remove U.S. citizens
                       abroad — under any circumstances — is the bright
                       red line they have been waiting for.


                # ⚓ 404 Media ☛ Leaked:_Palantir’s_Plan_to_Help_ICE_Deport
                  People⠀⇛


                       Internal Palantir Slack chats and message boards
                       obtained by 404 Media show the contracting giant is
                       helping find the location of people flagged for
                       deportation, that Palantir is now a “more mature
                       partner to ICE,” and how Palantir is addressing
                       employee concerns with discussion groups on ethics.


                # ⚓ El País ☛ Sly_Stone,_the_artist_who_changed_music_history
                  and_disappeared:_‘He_had_everything_and_almost_deliberately
                  threw_it_away’⠀⇛


                       The documentary ‘Sly Lives! (aka The Burden of
                       Black Genius)’ explores the meteoric rise and
                       dramatic fall of Sly & The Family Stone — a band
                       that defined a new era in the 1960s, led by a
                       frontman as brilliant as he was erratic


                # ⚓ Wired ☛ This_‘College_Protester’_Isn’t_Real._It’s_an_AI-
                  Powered_Undercover_Bot_for_Cops⠀⇛


                       American police departments near the United States-
                       Mexico border are paying hundreds of thousands of
                       dollars for an unproven and secretive technology
                       that uses AI-generated online personas designed to
                       interact with and collect intelligence on “college
                       protesters,” “radicalized” political activists, and
                       suspected drug and human traffickers, according to
                       internal documents, contracts, and communications
                       that 404 Media obtained via public records
                       requests.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ RTL ☛ Netflix_earnings_top_forecasts_despite_economic
                  turmoil⠀⇛


                       The streaming television service declared itself
                       "off to a good start in 2025" with a profit of $2.9
                       billion on revenue of $10.5 billion in the first
                       quarter of the year.


      § Monopolies/Monopsonies⠀➾


          o ⚓ New York Times ☛ Why_Antitrust_Breakups_of_Surveillance_Giant
            Google_and_Meta_Could_Be_Difficult⠀⇛


                 For the first time since the late 1990s Abusive
                 Monopolist Microsoft case, federal trials are weighing
                 antitrust breakups, a tactic that harks back to Standard
                 Oil.


          o ⚓ KOL459_|_Ex-Twitter_Spaces:_Jack_Dorsey,_MElon,_Libertarian
            Property_Rights,_and_the_Case_for_Abolishing_Intellectual_[sic]
            Property_[sic]⠀⇛


                 Kinsella on Liberty Podcast: Episode 459.


                 In response to lots of froth on Ex-Twitter related to
                 Jack Dorsey's call to "delete all IP law," which was
                 echoed by MElon (Musk and Dorsey: “delete all IP law”) I
                 decided to attempt to host an impromptu Ex-Twitter Spaces
                 about this. After overcoming some technical glitches,
                 here is the result (and thanks to @Brunopbch,
                 @NotGovernor (Patrick Smith), and @TrueAmPatriot86 for
                 assists).


          o ⚓ RTL ☛ Antitrust_suit:_Google_has_illegal_monopoly_in_ad_tech,_US
            judge_rules⠀⇛


                 The federal government and more than a dozen US states
                 filed the antitrust suit against Alphabet-owned Google,
                 accusing it of acting illegally to dominate three sectors
                 of digital advertising -- publisher ad servers,
                 advertiser tools, and ad exchanges.


          o ⚓ CBC ☛ Google_has_illegal_monopoly_in_online_ad_tech,_U.S._judge
            rules⠀⇛


                 Although antitrust regulators prevailed both times, the
                 battle is likely to continue for several more years as
                 Google tries to overturn the two monopoly decisions in
                 appeals while forging ahead in the new and highly
                 lucrative technological frontier of artificial
                 intelligence.


                 The next step in the latest case is a penalty phase that
                 will likely begin late this year or early next year.


          o ⚓ Los Angeles Times ☛ 'The_anti-trust_tides_have_turned.'_What_a
            judge's_ruling_over_Google's_'monopoly'_on_ad-tech_means⠀⇛


                 Judge Leonie Brinkema of the U.S. District Court for the
                 Eastern District of Virginia said in a decision that
                 Google illegally maintained and acquired a monopoly in
                 two markets for advertising technology — publisher ad
                 servers and the market for ad exchanges.


                 But in a partial win for Google, antitrust enforcers
                 failed to prove that the company held a monopoly in
                 advertiser ad networks, the judge found.


          o ⚓ Deseret Media ☛ Google_holds_illegal_monopolies_in_ad_tech,_US
            judge_finds⠀⇛


                 A U.S. judge ruled Google illegally monopolized two
                 online ad tech markets.


                 Judge Brinkema found Google maintained monopoly power in
                 publisher ad servers and exchanges.


          o ⚓ Vox ☛ Will_the_courts_break_up_Google?_The_company’s_anti-trust
            problems,_briefly_explained⠀⇛


                 Google just lost a huge antitrust case. A federal judge
                 in Virginia ruled on Thursday that the search giant
                 illegally maintained a monopoly in the online advertising
                 market, leveraging its position to make more money and
                 squash competition. The Justice Department, which
                 initiated the case along with several states, has called
                 for Google to be broken up.


          o ⚓ Common Dreams ☛ Google’s_Illegal_Internet_Ad_Monopoly_Blunts
            America’s_Competitive_Edge_in_Tech⠀⇛


                 “Our nation has grown prosperous and powerful because of
                 competition and Google’s illegal monopolies are blunting
                 our competitive edge in the tech industry. The company’s
                 near-total dominance of the online advertising market
                 hurts media companies, rival search engines, social media
                 companies and anyone who consumes media on the internet.
                 As one of the richest, most powerful companies in the
                 history of humanity, a mere fine or slap on the wrist
                 won’t cut it. For the good of our nation and the health
                 of our tech and media industries the government must
                 force Google to sell its advertising technology
                 division.”


          o ⚓ Wired ☛ Google_Is_Once_Again_Deemed_a_Monopoly,_This_Time_in_Ad
            Tech⠀⇛


                 Judge Leonie Brinkema of the US District Court for the
                 Eastern District of Virginia determined that Google
                 illegally monopolized parts of its advertising technology
                 business to dominate the programmatic ad market, a major
                 source of revenue for the company. Google generated
                 nearly $30.4 billion in worldwide revenue last year from
                 placing ads on other apps and websites. Now, a
                 substantial portion of those sales are threatened by
                 penalties that may follow Brinkema’s ruling. A best-case
                 scenario for US consumers is a browsing experience filled
                 with fewer ads and paywalls and more content choices.


          o ⚓ Axios ☛ Google_loses_online_advertising_monopoly_case⠀⇛


                 How it works: The federal government and 17 states who
                 brought the suit seek to force Google to sell off part of
                 its "network" ad business, which sells ads on other
                 publishers' inventory.


                 That accounts for roughly 12% of Alphabet's overall
                 business. Google argues spinning it out would actually
                 hurt publishers, because it would force them to buy ads
                 through more expensive rival networks.


          o ⚓ The Verge ☛ Google_loses_ad_tech_monopoly_case⠀⇛


                 The US Department of Justice has won its antitrust case
                 against Google, which accused the company of operating a
                 monopoly in the advertising technology industry. The
                 ruling, which marks Google’s most recent antitrust loss
                 following its Search case, says the tech giant’s
                 anticompetitive practices in two key markets
                 “substantially harmed” publishers and users on the web.


          o § Patents⠀➾


                # ⚓ Unified Patents ☛ $4,000_for_Polaris_PowerLED_memory
                  controller_patents_prior_art⠀⇛


                       Unified Patents added two new PATROLL contests,
                       each with a $2,000 cash prize, seeking prior art on
                       the list below. The patents are owned by Polaris
                       PowerLED Technologies, LLC, an NPE. The patents
                       generally relate to various nonvolatile memory
                       technologies. The ‘085 patent monopoly has been
                       asserted against Western_Digital and is involved in
                       a declaratory judgement action with Micron.


                       The contests will expire on May 1, 2025. Please
                       visit PATROLL for more information and to submit an
                       entry for these contests. PATROLL researchers are
                       required to use Pearl to generate claim charts.


                # ⚓ MIT Technology Review ☛ Jurassic_Patent:_How_Colossal
                  Biosciences_is_attempting_to_own_the_“woolly_mammoth”⠀⇛


                       Colossal Biosciences not only wants to bring back
                       the woolly mammoth—it wants to patent monopoly it,
                       too. MIT Technology Review has learned the Texas
                       startup is seeking a patent monopoly that would
                       give it exclusive legal rights to create and sell
                       gene-edited elephants containing ancient mammoth
                       DNA.


                # ⚓ Unified Patents ☛ $8,000_awarded_for_Dominion_Harbor
                  entity,_Arlington_Technologies,_networking_patents_prior
                  art⠀⇛


                       Unified is pleased to announce PATROLL
                       crowdsourcing contest winners below totaling $8,000
                       in cash prizes. The patents are owned by Arlington
                       Technologies LLC, an NPE and entity of Dominion
                       Harbor_Group. The patents relate to various
                       technologies and two of the patents have been
                       asserted against Comcast.


                # ⚓ Unified Patents ☛ Ascend_Innovation_entity,_Accessify,
                  communications_patent_monopoly_prior_art_found⠀⇛


                       Unified is pleased to announce prior art has been
                       found on U.S._Patent_7,197,640, owned by Accessify
                       LLC, an NPE and entity of Ascend Innovation
                       Management, LLC. The '640 patent monopoly relates
                       generally to the use of identification codes in the
                       handling and management of communications.


                       We would also like to thank the dozens of other
                       high-quality submissions that were made on this
                       patent.


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ UPC_rules_on_product-by-process_claims_in
                        Knaus_Tabbert_campervan_dispute [Ed: UPC is illegal, so
                        any "rules" are just abuse on top of existing abuses]⠀⇛


                             The proceedings between Yellow Sphere and
                             Knaus Tabbert related to EP 3 356 109 B1.
                             They centred on the interpretation of
                             product-by-process claims. EP 109 covers a
                             new type of frame for campervans that is
                             particularly light yet strong. Erwin Härtwich
                             and Alexander Christ are listed as inventors
                             in the EPO register.


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ TTAB_Partially_Grants_GUIDEON_Cancellation
                  Petition_but_Rejects_Zone-of-Natural-Expansion_Claim⠀⇛


                       The Board granted in part this petition for
                       cancellation of a registration for the mark GUIDEON
                       for, inter alia, providing online employment
                       information (class 35) and educational services
                       (class 41) to veterans and military families,
                       finding confusion likely as to the class 35
                       services with the identical mark registered for
                       "Computer application software for smartphone
                       operating systems, namely, software for a directory
                       of listings with corresponding location primarily
                       on military installations." Registrant's class 41
                       services, however, were deemed not related to
                       Petitioner Streeter's services, nor did the zone-
                       of-natural-expansion apply. Katharine_Lee_Streeter
                       v._GuideOn_Education_Consulting_LLC, Cancellation
                       No. 92077751 (April 11, 2025) [not precedential]
                       (Opinion by Judge David K. Heasley).


                # ⚓ TTAB Blog ☛ CAFC_Upholds_TTAB_Dismissal_of_"fleur-de-lis"
                  Cancellation_Petition_Due_to_Lack_of_Standing⠀⇛


                       Michel J. Messier of Rutland, Vermont, petitioned
                       to cancel a registration for the mark shown below,
                       owned by the New Orleans Saints football team, for
                       "entertainment services in the form of professional
                       football games and exhibitions." Mr. Messier
                       alleged that he is a "direct descendant of the
                       Kings of France (Scotland, Aragon, and Castille)”
                       and that he and his family own “intellectual
                       property rights to the Fleur de Lys, Orleans and
                       Saints marks." Not good enough, said the CAFC.
                       Michel_J._Messier_v._New_Orleans_Louisiana_Saints,
                       LLC, Appeal No. 2024-2271 (April 14, 2025) [not
                       precedential].


          o § Copyrights⠀➾


                # ⚓ Public Domain Review ☛ Sea_Monsters_Unmasked_and_Sea_Fables
                  Explained_by_Henry_Lee_(1883)⠀⇛


                       Pamphlets on sea beasts produced for the
                       International Fisheries Exhibition of 1883.


                # ⚓ Torrent Freak ☛ Alleged_Anna's_Archive_Operator_Dropped
                  from_U.S._'Scraping'_Lawsuit⠀⇛


                       Anna’s Archive is a meta-search engine for shadow
                       libraries that allows users to find pirated books
                       and other related resources.


                       In late 2023, the search engine Anna’s Archive
                       expanded its offering by making data from OCLC’s
                       proprietary WorldCat database available online.


                       Anna’s Archive scraped several terabytes of data
                       over the course of a year and published roughly 700
                       million unique records online, for free.


                       These records contain no copyrighted books or
                       articles. However, they can help to create a to-do
                       list of all missing shadow library content on the
                       web, with the ultimate goal of making as much
                       content publicly available as possible.


                # ⚓ The Verge ☛ Wikipedia_is_giving_AI_developers_its_data_to
                  fend_off_bot_scrapers⠀⇛


                       Wikimedia says the dataset hosted by Kaggle has
                       been “designed with machine learning workflows in
                       mind,” making it easier for AI developers to access
                       machine-readable article data for modeling, fine-
                       tuning, benchmarking, alignment, and analysis. The
                       content within the dataset is openly licensed, and
                       as of April 15th, includes research summaries,
                       short descriptions, image links, infobox data, and
                       article sections — minus references or non-written
                       elements like audio files.


    * Google_News_is_Dying
    * "Sayonara"_(さよなら),_Microsoft


╘══════════════════════════════════════════════════════════════════════════════╛
                       ¶ Lines in total: 8378
    ➮ Generation completed at 02:49, i.e. 16 seconds to (re)generate ⟲