𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, March 14, 2025
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Generated Sat 15 Mar 02:49:23 GMT 2025
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2025/03/14/


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

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

⦿ Techrights  -  Antisemitic Attacks on Richard Matthew Stallman (RMS) in Wikipedia This Week

⦿ Techrights  -  Bluewashing Ends DEI at IBM and at Red Hat (HR or Hiring Become Gender- and Race-Neutral)

⦿ Techrights  -  'India Today' is a Slopfarm, Sometimes 'Covering' "Linux" With Slop Images

⦿ Techrights  -  IRC Proceedings: Thursday, March 13, 2025

⦿ Techrights  -  Meanwhile at Microsoft Canonical...

⦿ Techrights  -  Microsoft Money Used for Abuse of Women and Against Journalism in Support of Women (the Victims)

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Rumours of IBM Layoffs Again, This Time Marketing

⦿ Techrights  -  Slopwatch: linuxsecurity.com and hamradio.my (in Planet Ubuntu) Are at It Again With LLM Slop About "Linux"

⦿ Techrights  -  The Fall of the Open Source Initiative (OSI): The OSI Does Not Speak For You, OSI Staff Speaks for GAFAM/Microsoft (the Paymasters)

⦿ Techrights  -  Windows is Fast Becoming Insignificant to Zimbabweans

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2025/03/14/Antisemitic_Attacks_on_Richard_Matthew_Stallman_RMS_in_Wikipedi.shtml
https://techrights.org/n/2025/03/14/Bluewashing_Ends_DEI_at_IBM_and_at_Red_Hat_HR_or_Hiring_Become_.shtml
https://techrights.org/n/2025/03/14/India_Today_is_a_Slopfarm_Sometimes_Covering_Linux_With_Slop_Im.shtml
https://techrights.org/n/2025/03/14/IRC_Proceedings_Thursday_March_13_2025.shtml
https://techrights.org/n/2025/03/14/Meanwhile_at_Microsoft_Canonical.shtml
https://techrights.org/n/2025/03/14/Microsoft_Money_Used_for_Abuse_of_Women_and_Against_Journalism_.shtml
https://techrights.org/n/2025/03/14/Over_at_Tux_Machines.shtml
https://techrights.org/n/2025/03/14/Rumours_of_IBM_Layoffs_Again_This_Time_Marketing.shtml
https://techrights.org/n/2025/03/14/Slopwatch_linuxsecurity_com_and_hamradio_my_in_Planet_Ubuntu_Ar.shtml
https://techrights.org/n/2025/03/14/The_Fall_of_the_Open_Source_Initiative_OSI_The_OSI_Does_Not_Spe.shtml
https://techrights.org/n/2025/03/14/Windows_is_Fast_Becoming_Insignificant_to_Zimbabweans.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2025/03/14/Gemini_Links_14_03_2025_Grizzy_Bear_and_Prime_Beats.shtml
https://techrights.org/n/2025/03/14/Gemini_Links_14_03_2025_Lojl_and_Docker_Context_Stuff.shtml
https://techrights.org/n/2025/03/14/Links_13_03_2025_Intel_Rotates_Figurehead_and_South_Korea_Impor.shtml
https://techrights.org/n/2025/03/14/Links_14_03_2025_Chinese_Tensions_With_Australia_Putin_Turns_Do.shtml
https://techrights.org/n/2025/03/14/Links_14_03_2025_ProPublica_Admitting_That_It_Uses_Slop_Foolish.shtml
https://techrights.org/n/2025/03/14/Links_14_03_2025_Scam_Currencies_in_the_US_and_Oligarchs_Includ.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 82

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/Antisemitic_Attacks_on_Richard_Matthew_Stallman_RMS_in_Wikipedi.shtml
    Gemini version at https://techrights.org/n/2025/03/14/Antisemitic_Attacks_on_Richard_Matthew_Stallman_RMS_in_Wikipedi.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Antisemitic Attacks on Richard Matthew
Stallman (RMS) in Wikipedia This Week⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


Vandalism:


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


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


Did the man strike a nerve or what?


Related:


    * Microsoft_and_Bill_Gates_Both_Bribe_Wikipedia_(and_It'll_Protect_Their
      Online_'Reputation'_in_Return)
    * Wikipedia,_Which_is_Sponsored_by_Microsoft_and_Bill_Gates,_Wants_to_Add_a
      Code_of_Conduct_(Code_of_Censorship)
    * Wikipedia_is_Vandalism,_Brought_to_You_by_Microsoft_and_Bill_Gates
    * The_Web,_Including_Wikipedia,_Gets_Filled_With_Lies_About_Bill_Gates,
      Added_by_Bill_Gates_and_His_PR_Team
    * Bluewashing_Ends_DEI_at_IBM_and_at_Red_Hat_(HR_or_Hiring_Become_Gender-
      and_Race-Neutral)
    * Links_14/03/2025:_Scam_Currencies_in_the_US_and_Oligarchs_(Including
      GAFAM)_Controlling_All_the_Major_Policies


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                    ䷩ 𝚕𝚒𝚗𝚎 164

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/Bluewashing_Ends_DEI_at_IBM_and_at_Red_Hat_HR_or_Hiring_Become_.shtml
    Gemini version at https://techrights.org/n/2025/03/14/Bluewashing_Ends_DEI_at_IBM_and_at_Red_Hat_HR_or_Hiring_Become_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Bluewashing Ends DEI at IBM and at Red Hat
(HR or Hiring Become Gender- and Race-Neutral)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Mar 14, 2025,
updated Mar 14, 2025


IBM is adjusting itself to the new administration in the US, just like GAFAM.
What does this mean to Red Hat? Probably a lot. All that "whitelist_is_racist"
stuff is likely a thing of the past, with the same applying to diversity
quotas. This news report from a Red Hat-connected publisher has just said:


     Facing legal challenges and White House pressure, IBM has ditched a
     corporate policy which considered diversity hiring when calculating
     executive pay.


     In its latest annual report, released this week, the large Triangle
     employer and owner of the Raleigh software giant Red Hat also stopped
     using the word “diversity” after including the word multiple times in
     recent yearly reports.


     “It’s important to underscore that diversity is not a metric for
     compensation,” IBM spokesperson Sarah Minkel told The News & Observer
     in an email Tuesday.


     In early 2021, months removed from the murder of George Floyd and a
     summer of social justice protests, IBM began sharing overviews of its
     “diversity, equity and inclusion efforts.” That year, the global
     technology company also added “a diversity modifier” which influenced
     executive compensation, crediting managers whose hiring efforts
     better reflected the diversity of their communities.


This has not yet been brought up at #dei:fedoraproject.org, but that room is
more or less dead already. This is all the activity this past week:


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


Red Hat has long used the "diversity" stick to hit the FSF and other
'ideological rivals', more so after IBM took over. Even if Red_Hat_itself_was
merely_projecting.


Race aside, when it comes to nationality IBM remains biased (towards_low
salaries). See below this_new_thread. █


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇From_Amazon_to_Pinterest:_The_40_tech_companies_that_file
                    the_most_H-1B_immigrant_work_visas_!⦈_


    * Links_13/03/2025:_Intel_Rotates_Figurehead_and_South_Korea_Imports_Karen
      People_From_Myanmar
    * Antisemitic_Attacks_on_Richard_Matthew_Stallman_(RMS)_in_Wikipedia_This
      Week


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⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡇⣷⢨⣹⣭⡝⣉⡩⡉⡟⣭⢸⣯⢩⠋⣉⡋⢅⠯⡉⡍⣽⢩⢸⢸⢩⡝⠫⢅⣾⡇⡇⣃⢺⡌⢏⢸⣿⢸⢍⢹⡹⣹⢩⢹⢨⡅⣏⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣾⣶⣶⣿⣶⣷⣶⣾⣶⣾⣷⣾⣷⣶⣕⣢⣶⣶⣶⣿⣶⣶⣶⣶⣶⣔⣢⣿⣷⣷⣶⣶⣾⣾⣶⣿⣶⣶⣶⣣⣿⣶⣾⣾⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⣟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣧⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢩⠻⣿⡇⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⠿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⡿⡿⣿⣿⣿⡿⡿⡿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣉⢙⣾⣿⣿⣿⣿
⣿⣿⣿⣬⣿⣿⡇⣿⣴⣧⣧⣿⣤⣧⣿⣦⣧⣼⣤⣾⣵⣼⣼⣧⣿⣬⣧⣿⣴⣦⣿⣼⣧⣦⣼⣴⣤⣼⣷⣿⣧⣧⣧⣴⣼⣬⣥⣧⣿⣬⣴⣼⣤⣿⣧⣧⣼⣤⣾⡼⢧⣽⣤⣧⣤⣶⣤⣿⣿⣿⣛⣒⣚⣻⣿⣿⣿⣿
⣿⣿⣯⣄⣸⣿⡇⣿⢻⠻⡿⢿⣿⡟⣿⠻⡿⡟⡟⡿⢿⢿⣿⠿⡿⢿⠿⢻⣿⢻⠻⢿⢻⠛⣿⢻⡿⢿⠿⡿⣿⠿⡻⠿⢿⠿⣿⣿⠿⡿⠿⡿⠟⢿⡿⢿⡿⠿⣿⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣹⡿⣿⡇⣿⣬⣬⣥⣼⣽⣧⣭⣴⣽⣷⣥⣧⣮⣿⣭⣬⣥⣵⣤⣮⣯⣼⣼⣿⣬⣬⣿⣬⣥⣭⣬⣥⣭⣀⣥⣧⣬⣥⣯⣿⣼⣼⣬⣦⣧⣬⣷⣮⣥⣤⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣮⣾⣿⡇⣿⢿⣿⡿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⠿⠿⡿⡿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣮⣦⣤⣷⣦⣶⣤⣦⣤⣷⣴⣧⣤⣶⣬⣤⣴⣬⣭⣤⣤⣥⣧⣼⣧⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣯⣍⣉⠉⣍⣩⣉⣉⣩⣫⣫⣋⣟⣉⣩⣭⣫⣟⣉⣉⣹⣉⣭⣉⣍⣉⣉⣻⠋⣭⣟⣍⣽⠉⣩⣍⣉⡉⢹⣉⣉⣋⣏⣙⣯⣉⣹⣭⣝⣝⣍⣉⣿⣩⣉⣏⣏⣉⣩⣫⣏⣉⣭⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⡟⠿⢿⡟⠟⢿⠿⠟⡿⢿⢻⡟⡿⢿⠟⠟⣿⠿⠿⣻⡿⠿⡟⠛⠛⠛⣿⣿⠟⡿⡿⣿⠻⠿⠿⠿⢿⠻⡿⣿⠛⣟⢛⢿⢿⡿⣿⣟⡿⢿⡿⡿⡿⡟⠟⠿⠿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣶⣶⣶⣿⣶⣶⣶⣶⣿⣿⣶⣷⣶⣾⣶⣾⣶⠶⡶⢾⣶⡶⣷⣷⣾⢶⣷⣶⣶⣾⣶⣾⣶⣶⣶⣶⣾⣾⣶⣿⣾⣾⣶⣾⣶⣶⣾⣾⣶⣾⣾⣶⣶⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣭⣭⣥⣤⣤⣤⣾⣥⣯⣮⣤⣤⣯⣤⣶⣤⣧⣤⣧⣤⣤⣧⣤⣥⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⢿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣭⣽⣤⣧⣤⣤⣤⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣍⣉⢉⣉⢟⣢⣉⣍⣩⣩⣯⣍⣉⣙⣉⣍⣭⢟⣌⣩⣿⣉⡹⣳⣭⣩⣩⣩⢩⣣⣍⣁⣉⣉⢯⣠⣭⣩⣽⣏⣉⣉⣉⣉⣉⣹⣏⣉⡯⣍⣭⣉⣉⣍⣉⣙⣏⣈⣉⣿⣭⣪⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⠛⠛⢙⣿⠛⠛⣛⠛⠛⠛⠙⠛⢿⠋⡛⠛⣿⠉⠙⣿⠋⡛⣻⡟⠛⠛⠛⢻⠙⣿⣝⢻⣛⣛⠛⠋⢛⠛⠛⠛⣿⠛⡛⢛⢙⡟⡋⠛⠛⡟⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⢻⠿⢻⢟⢛⠻⠿⠟⠿⠿⠻⠻⠿⠿⠿⠿⠻⠿⠿⠿⠻⠿⠿⠿⠿⠟⠛⠛⠛⢿⠻⠿⠿⠿⠿⡻⢶⠿⠟⠟⠿⠟⠛⠿⠿⢛⠛⠟⠿⠾⠟⠟⡛⠿⠻⠿⠻⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣷⣷⣶⣿⣾⣷⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣦⣽⣷⣴⣷⣾⣾⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣾⣷⣶⣶⣶⣾⣷⣶⣶⣶⣾⣾⣶⣶⣶⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣇⣨⣧⣉⣀⣉⣉⣿⣿⣀⣸⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⡛⣿⣿⣿⣿⣿⣿⡟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣗⣅⣿⣇⣏⣠⡁⣇⣇⣇⣇⣅⣨⣸⡇⣿⣩⣋⣍⣍⣸⣿⣽⣩⣹⣉⣽⣉⣟⣿⣹⣉⣏⣷⣏⣏⢹⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣻⡻⣿⡇⣿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⢿⣿⣿⣿⢿⡿⣿⣿⣿⢿⣿⣿⢿⣿⣿⢿⣿⢿⣿⣿⣾⡩⢻⣾⣿⣿⣿⣿
⣿⣿⣷⣘⣶⣿⡇⣿⣯⣵⣮⣧⣴⣤⣼⣤⣦⣶⣠⣤⣤⣰⣣⣤⣤⣧⣤⣤⣤⣤⣧⣤⣧⣤⣰⣤⣤⣼⣤⣖⣼⣠⣤⣄⣦⣴⣧⣤⣴⣥⣤⣤⣄⣾⣤⣤⣤⣴⣧⣤⣤⣰⣴⣴⣧⣴⣴⣤⣾⣿⣻⣬⣼⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣉⣉⣉⡩⣹⣉⣹⠉⣉⣩⣏⣉⣹⣭⣫⣩⣽⣭⣝⣍⣉⡍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢩⠿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣬⣾⣿⡇⣿⠟⣿⡍⠹⠙⢻⢟⠟⠛⠛⠛⠟⢻⡻⠛⠛⠻⠻⠛⢻⢻⠛⠛⢻⠟⠻⡿⡟⡋⡟⡏⠻⣛⡛⢻⡿⠛⠛⠟⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⠿⠿⢻⠛⠻⢿⢛⠿⢿⠻⠟⢻⢿⠻⢿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣯⣶⣶⢾⠶⢶⣾⠶⣶⣾⢶⡶⢶⣾⢶⣾⠶⣶⡶⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣟⣤⣤⣼⣤⣤⣼⣬⣤⣼⣤⣤⣤⣼⣤⣼⣤⣤⣤⣬⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣉⣈⣊⣁⣹⣈⣇⣩⣉⣛⣏⣹⣉⣫⣋⣉⣋⢭⣟⣈⣙⣸⣈⣉⣹⣉⣉⣉⣋⣁⣏⡉⣹⣀⣸⣘⣕⣀⣉⣉⣇⣉⣏⣉⣙⣈⣉⣉⣸⣁⣉⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡯⠭⠭⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿
⣿⣿⡿⣛⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡛⠻⣽⣿⣿⣿⣿
⣿⣿⣷⣘⣶⣿⡇⣿⣓⣗⣂⣅⣂⣯⣩⣉⣏⣷⣛⣽⣛⣙⣭⣉⣛⣈⣟⣝⣉⣘⣩⣽⣉⣝⣙⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣿⣿⣿⣿⣿
⣿⣿⣿⡩⢹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢩⠿⣿⡇⣿⣬⣍⡙⢡⣩⣉⣇⣊⣉⣈⣉⣍⣉⡉⢡⣽⣁⣍⣍⣍⣷⣼⣀⣉⣠⣇⣉⣉⣩⣏⣉⣇⣉⣉⣩⣩⣝⣽⣉⣍⣉⠉⣉⣉⣩⣈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣽⣵⣿⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⣿⣿⣿
⣿⣿⣿⢛⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⣽⣿⣿⣿⣿
⣿⣿⣷⣘⣶⣿⡇⣿⣘⣍⣛⣉⡨⣽⣸⣋⣉⣑⣸⣉⣁⣉⣁⣏⣩⣉⣅⣉⣩⣹⣓⣍⣙⣛⣚⣉⣃⣉⣇⣉⣁⣇⣸⣉⣉⣉⣃⣑⣇⣉⣹⣉⣉⣉⣁⣁⣉⣍⣉⣸⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⠼⢿⣿⣿⣿⣿
⣿⣿⣟⡩⢹⣿⡇⣿⠛⠛⠛⠛⠛⠛⠛⢻⠛⢹⠙⠛⠛⠝⠟⠛⠛⠋⡟⠛⠉⠛⠛⣻⠟⠛⠻⡟⡛⠻⠙⠛⠛⠛⠛⠛⠋⠟⠋⡍⠛⠛⠛⠙⠻⡻⠟⠻⡏⢩⢹⠏⢟⠟⠛⢹⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢩⢿⣿⡇⣿⡟⠷⢿⡿⡟⠿⠿⠿⢿⠿⢿⢻⡟⠟⠟⠛⠻⠿⢿⡿⡟⠻⠿⠿⡿⠿⠿⠿⠿⠾⢿⠻⠻⠿⠟⡿⠿⠿⡻⠿⠿⠿⠿⠿⢿⢻⠿⠿⠿⢿⠻⠿⠿⠿⠿⢿⡿⢿⠻⡻⠿⣿⡻⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣝⣵⣿⡇⡿⣶⣶⣶⣷⣷⣶⣦⣵⡾⣿⣶⣾⣶⣷⣶⣶⡶⣾⣾⡶⣶⢶⣶⣷⣷⡶⡶⡴⣶⣯⣾⢾⣶⣷⣶⣷⣶⣶⣷⣶⢾⣶⣶⣶⣿⣾⣶⣶⣶⣶⣾⣾⣶⣴⣶⣿⣶⣾⣶⣿⣾⣼⡷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣤⣾⣴⣤⣤⣴⣤⣤⣤⣱⣤⣤⣄⣦⣬⣦⣤⣧⣴⣴⣧⣴⣶⣦⣌⣿⣼⣤⣼⣦⣶⣤⣧⣤⣴⣶⣢⣤⣖⣜⣼⣤⣬⣦⣦⣶⣤⣼⣤⣾⣴⣤⣠⣴⣦⣼⣶⣦⣇⣤⣤⣄⣤⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣨⣩⣏⣩⣋⣉⢉⣇⣁⣍⣭⣽⣁⣉⡉⣁⣉⣹⣁⣉⣡⣹⣉⣉⣆⣍⢩⣍⣹⠉⣨⣉⣹⣉⣹⣉⣉⣩⣉⣯⣍⣉⣍⣩⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣏⣉⣩⣉⣭⣹⣉⣉⣉⣏⣩⣋⣉⣩⣹⣉⣉⢩⣿⣝⣽⣏⣉⣉⣹⣍⣹⣍⣉⣉⣉⡝⢿⣯⣭⣟⣍⣩⣙⣉⣉⣻⣭⣻⣩⣝⣍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿
⣿⣿⣿⢿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠭⢭⣽⣿⣿⣿⣿
⣿⣿⣧⠹⣥⣿⡇⣿⣋⣍⣉⣍⣹⣝⣝⣍⣹⣹⣉⣩⣝⣹⣉⣉⣉⣭⣏⣏⣏⡹⢹⣫⣭⣩⣽⣏⣩⣉⣫⣉⣉⣭⣭⣻⣭⣫⣉⣹⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣓⣰⢿⣿⣿⣿⣿
⣿⣿⣟⠫⢹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣧⣘⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿
⣿⣿⣿⢟⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠍⢭⣽⣿⣿⣿⣿
⣿⣿⣷⣹⣷⣿⡇⣿⣈⣊⣮⣀⣏⣉⣩⣡⣼⣉⣽⣦⣍⣥⣉⣉⣏⣉⢩⣩⣩⣉⣹⣉⣬⣉⣩⣈⣏⣩⣉⣅⣉⣩⣉⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠑⠸⢿⣿⣿⣿⣿
⣿⣿⣟⡉⢹⣿⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣷⣙⣵⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡯⠭⠭⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿
⣿⣿⣿⢛⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡛⠻⣽⣿⣿⣿⣿
⣿⣿⣷⣘⣶⣿⡇⣿⣂⣂⣁⣯⣗⣛⣑⣈⣉⣹⣘⣋⣉⣋⣉⣉⣹⣈⣘⣑⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⠼⢿⣿⣿⣿⣿
⣿⣿⣟⡉⢹⣿⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣷⣝⣵⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⣿⣿⣿
⣿⣿⡿⣛⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡒⠲⣾⣿⣿⣿⣿
⣿⣿⣷⣘⣶⣿⡇⣿⣋⣁⣁⣇⣉⣩⣹⣏⣈⣉⣇⣁⣝⣹⣹⣈⣉⣉⣁⣩⣩⣉⣉⣹⣙⣟⣛⣙⣈⣹⣰⣈⣉⣛⣟⣻⣜⣋⣹⣜⣓⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣉⢹⣿⡇⣿⠟⠏⠋⡟⠻⠛⡟⠙⠉⠙⠛⢹⠉⠛⡟⠛⠛⠹⠛⣿⠟⢽⠛⡟⠛⠉⡛⡏⠛⠻⡝⠛⢛⣻⠛⡻⡻⠛⠻⡏⠿⠛⣟⢛⠛⠋⠋⡏⠛⡏⠛⠋⠙⢻⠟⠛⠋⠿⠛⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢩⠿⣿⡇⣿⢿⠻⠻⠟⠿⣿⠿⡟⢿⠿⠿⡿⣿⣿⠻⢿⠿⢻⡟⠿⢿⣿⢾⢻⠿⠛⠾⠟⡿⠿⢿⢿⠷⢿⢿⠿⡟⠻⠿⢻⠛⠿⢿⣛⠿⣿⠿⠿⡿⢿⡿⠿⠻⠿⠟⡿⠿⡿⡿⣾⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣽⣵⣿⡇⣿⣾⡶⣦⡴⣾⣷⣶⢶⣾⣶⣶⣶⣶⣴⣶⣾⣶⣾⣶⣶⣾⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣾⣶⣶⣾⣶⣾⣶⣶⣴⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣦⣥⣤⣬⣧⣄⣠⣥⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣉⣗⣀⣒⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⡛⠛⠛⠛⡿⢍⠛⡛⢛⢛⣟⡻⡻⣙⡛⡛⠻⡛⠛⠛⣟⢍⠫⣫⠹⡉⠉⠹⡩⢋⡿⡝⠛⠛⡛⡛⠋⠛⠛⢛⢏⠉⠛⠛⣟⣛⠋⡙⠻⣛⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⠟⠟⡟⠛⠛⠛⠛⢻⣛⢟⠻⢛⡟⠛⢻⡻⡛⠛⠛⢻⠛⣛⠛⡛⠛⡟⠛⢛⡛⣻⠛⡻⣻⡟⠛⡛⢻⢛⡻⡻⠛⠛⠛⠛⠛⢻⡟⠛⡟⢛⠛⡛⡛⡛⣛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⣛⣻⣿⣿⣿⣿
⣿⣿⣯⢺⣮⣿⡇⣿⠍⠛⡛⡛⣛⢛⠛⢹⢙⣫⢻⢉⡛⢛⣻⡛⡛⣻⢫⠋⣹⣿⣿⠙⠛⠛⠛⡿⢍⠛⡛⢛⠛⠏⠻⠛⠙⠛⠛⠛⠙⠛⠻⡙⡛⠛⠛⠛⠛⢏⣻⠝⣟⢛⢛⠙⣿⣿⣿⣿⣿⣿⣿⠢⢸⣿⣿⣿⣿⣿
⣿⣿⡿⢗⢻⣿⡇⣿⠿⠿⠿⠿⠿⠿⠻⠿⣿⠿⠿⠿⠿⠿⠿⣿⠿⡿⠿⢿⡿⢿⡿⢿⡟⠾⠿⠿⠺⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⣿⠻⣻⠛⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⠷⣾⣿⡇⣿⣷⣷⣿⣼⣶⣶⣾⣷⣿⣦⣶⣶⣷⣾⣾⣿⣿⣾⣶⣾⣿⣾⣷⣿⣷⣶⣶⣶⣦⣽⣾⣶⣾⣷⣶⣶⣷⣾⣶⣾⣷⣷⣶⣶⣿⣶⣷⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⠸⣩⣿⡇⣿⣿⣿⢿⣿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⣴⣽⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⠿⣿⣿⣿⣿⣿⡿⣿⢿⣿⢿⢿⢿⠿⢿⠿⠿⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣴⣽⣭⣼⣤⣤⣤⣥⣤⣤⣼⣴⣴⣭⣼⣤⣤⣤⣀⣤⣯⣬⣴⣵⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣐⣽⣉⣹⣉⣉⡉⣁⣉⢉⣍⣉⣫⣉⣉⣁⣁⣉⣍⣍⣍⣗⣁⣉⣩⣹⣁⣍⣉⣹⣊⣌⣜⣅⣀⣁⣏⣉⣏⣁⣏⣨⣩⣏⣩⣩⣟⣍⣖⣀⣐⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣯⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿
⣿⣿⣿⢛⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⠻⣽⣿⣿⣿⣿
⣿⣿⣷⣘⣶⣿⡇⣟⣜⣍⣊⣉⣸⣉⣉⣛⣊⣋⣹⣒⡉⣁⣁⣉⣉⣈⣹⣈⣉⣍⣑⣋⣑⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠭⠼⢿⣿⣿⣿⣿
⣿⣿⣋⡍⡉⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢩⠿⣿⡇⣿⣜⣾⣝⣈⣉⡉⣍⣇⣉⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 385

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/India_Today_is_a_Slopfarm_Sometimes_Covering_Linux_With_Slop_Im.shtml
    Gemini version at https://techrights.org/n/2025/03/14/India_Today_is_a_Slopfarm_Sometimes_Covering_Linux_With_Slop_Im.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 'India Today' is a Slopfarm, Sometimes
'Covering' "Linux" With Slop Images⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025,
updated Mar 14, 2025


What proportion of today's remaining (still online) Web is pure garbage?


New example of pure BS (it smells like slop from a distance):


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Anthropic_CEO_says_AI_to_generate_all_code_by_year-end,
                   Linux_creator_calls_it_90_per_cent_hype⦈_


The "smell test" was good enough, scanners say the same:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇As_artificial_intelligence_(AI)_is_rapidly_evolving,_tech
                      leaders_are_split_on_its_impact.⦈_


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Despite_these_concerns,_major_tech_companies_continue
  integrating_AI_into_software_development._Google_CEO_Sundar_Pichai_revealed
  that_over_25_per_cent_of_Google’s_new_code_is_already_generated_by_AI,_with
                 human_engineers_reviewing_and_refining_it.⦈_


Garbage like the above makes the Web in_general a worse place to find
information.


Suffice to say, some LLM scrapers will "swallow" their own "poo" (above) and
progressively get worse.


This also might contribute to Indians getting stigmatised as slopfarmers. It
wouldn't be false to assert many "news" sites out there, in_English_too, are
based in India and have unoriginal content or LLM slop.


If quality only ever goes down, it'll feed back into future "content". Imagine
planning a NASA moon landing using nothing but Medieval books and the Bible. █


    * Gemini_Links_14/03/2025:_Grizzy_Bear_and_Prime_Beats
    * next


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⣿⣿⣓⣻⣿⣴⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢟⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣞⣽⣷⣷⣶⣷⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶
⣿⣿⣤⣿⣿⣦⣼⣤⣷⣷⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⢛⠛⢛⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⠿⢿⣿⣿⢿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀
⣿⣿⣿⣿⣿⣷⣶⣷⣷⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣄⣼⣿⣿⣿⣋⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⣿⣿⣿⣿⣿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢻⡿⠋⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠁⠈⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⣀⣤⡄⠐⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠂⠁⣀⠄⠢⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠠⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠺⡿⠀⠀⠀⠀⠀⠀⠈⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢠⣤⠀⢠⡌⢲⠀⠨⠀⠀⠀⠀⠀⢀⡄⠀⠐⠑⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⢛⢻⢻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⡠⡌⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⣆⣸⡇⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⣘⠑⢺⣿⣿⣷⡾⠒⢺⠀⠀⠄⠀⠀⣠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣽⣿⣟⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠆⣾⣿⣿⣿⣿⣿⡧⠑⠈⠀⢀⣤⠖⠈⠝⠁⠀⠰⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⢀⣠⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣝⣹⣋⣉⣯⣟⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣽⣿⣿⣿⣿⣿⠿⠏⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⣠⠌⠀⠀⠀⢀⡠⠤⠄⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣟⣿⣿⠛⡟⡻⣿⢻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠠⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣷⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣷⣼⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣷⣌⣉⣉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⣿⣿⣿⣿⣿⣿⣶⣷⣾⣤⣤⣤⣤⣦⣤⣤⣤⣼⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⣭⣭⣭⣭⣭⣭⣭⣭⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⡿⠿⡿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣟⣟⣿⣛⣿⣿⣻⣻⣿⣟⣛⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣷⣶⣶⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⡏⣴⣾⣿⣶⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡄⣿⣿⣦⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣉⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⢤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣒⣒⣒⣖⣖⣒⣒⢲⣒⣖⣒⣚⣒⣓⣒⣒⣓⣛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⡿⡿⠿⠿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 501

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/IRC_Proceedings_Thursday_March_13_2025.shtml
    Gemini version at https://techrights.org/n/2025/03/14/IRC_Proceedings_Thursday_March_13_2025.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Thursday, March 13,
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Variant_Yellow⦈_


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


===============================================================================
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contain all the text.


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⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠰⣾⣿⣿⡿⠿⣟⣻⣭⣭⣷⣶⣶⣶⣾⣿⣿⣷⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠻⣇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠳⣙⠿⠿⣛⣋⣭⣵⣶⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠤⠉⡙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣋⣥⣌⠀⠀⠀⠀⡟⣿⡗⣯⡛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠉⠐⠆⠈⠙⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣉⣥⣶⣿⣿⣿⣿⣿⡃⠀⠀⠀⣿⡟⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠿⢛⣫⣥⣶⣿⡿⣿⡿⠿⠛⢟⢻⠛⠻⣇⠀⠀⠀⡻⡷⡿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠘⢏⠹⠿⢿⣶⣤⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⣴⣿⡿⢿⣿⠟⠛⠁⠀⠈⠐⠀⠀⠂⢐⣄⣈⣥⣤⣤⣤⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠾⣷⣮⣈⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣟⣵⣿⣿⣿⣶⣤⣄⣀⠀⣤⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⣽⣿⡯⠿⠿⢿⣿⣿⣿⣿⣶⡾⠛⠒⠢⡀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⢟⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠈⠻⣿⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⡿⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣈⢙⡻⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣆⢀⣤⣾⣿⡿⢟⣫⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⠀⠀
⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⣄⠀⠀⠹⣷⣬⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠒⠒⠀⢀⣀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⣶⣄⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠿⢗⣟⡳⢦⣀⡿⠟⠋⢐⣶⠉⢹⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠰⠿⢟⣃⢄⣈⣡⡤⠤⠶⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠐⠂⠉⠤⢷⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⡿⠁⠀
⣴⠖⠀⠀⠀⠴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⠀⢠⡟⠀⠀⠀
⠀⠀⠀⠀⠂⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⢿⡑⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⢠⡿⠁⠀⠀⠀
⠀⠀⠀⠀⢀⣤⠚⠛⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠊⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀
⣀⠀⠐⠋⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⠴⠃⠀⠀⠀⠀⠀⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⢿⡿⢤⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠷⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 733

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/Meanwhile_at_Microsoft_Canonical.shtml
    Gemini version at https://techrights.org/n/2025/03/14/Meanwhile_at_Microsoft_Canonical.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Meanwhile at Microsoft
Canonical...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


Promoting proprietary surveillance by a company that actively attacks Linux in
a lot of ways:


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


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


If you are hoping to see Microsoft and Windows replaced by GNU/Linux, then
don't rely on Canonical and Ubuntu. They actively_promote_Microsoft and
habitually_Windows, too. █


    * Over_at_Tux_Machines...
    * Links_13/03/2025:_Intel_Rotates_Figurehead_and_South_Korea_Imports_Karen
      People_From_Myanmar


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                    ䷩ 𝚕𝚒𝚗𝚎 793

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/Microsoft_Money_Used_for_Abuse_of_Women_and_Against_Journalism_.shtml
    Gemini version at https://techrights.org/n/2025/03/14/Microsoft_Money_Used_for_Abuse_of_Women_and_Against_Journalism_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Money Used for Abuse of Women and
Against Journalism in Support of Women (the
Victims)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


"Never interrupt your opponent while he is in the middle of making_a_mistake."


What has Microsoft become a "money_supplier" of? That does get worse than the
Gates_Foundation offering backing to the activity of trafficking_underage_girls
for_sex, or does it? Whose terrible idea was this???


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


We typically know (and have said several times before) that we're effective -
or a thorn_in_the_side of bad people - when they attempt to silence us, defame
us, waste our time, or engage in digital crimes against us (not limited to DDoS
attacks, identity theft, social engineering attacks, doxing and so on).


Suffice to say, a lot of the libel lawsuits out there are pure SLAPP (more so
in London where many "Guns for Hire" lurk) or boil down to "you said something
about me (or my company) that made me unhappy" (not all lawsuits are lawsuits
that boil down to this, but many are). A variant of it is, "I have more money
than you, so I will sue you until you censor yourself or I shall seek "Revenge"
financially" (by frivolous suits). Rich companies can use people who are not
rich as proxies with the same aim. This is an alluring tactic that gives those
companies protection from bad publicity or risk of counterclaims, recovery of
legal fees etc. There are protections against such tactics though.


In my case, I became more vocal because it's really quite trivial and immoral
on many levels; you see, sometimes a person might jump to the rescue of women
battered to death by a boyfriend or spouse, only to be killed for trying to do
the right thing and help (preventing a death). In this case, when dealing with
serial stranglers of women, the effort to 'kill' that who does the moral thing
(Good Samaritan) is in "slow motion" and is backed by Microsoft money via "Guns
for Hire" working with a 5-digit_bank_account (less than 100,000 left) on
behalf_of_foreigners, one of whom has harassed me since 2012 [1, 2]. The other
seems embroiled in a_class_action_lawsuit_that_may_cost_Microsoft_$9_billion_in
damages.


As I stated yesterday, the deeper they go and the longer it goes on for, the
more embarrassing it'll get for Microsoft and other parties. People must_see
how_absurd_and_perverse_this_is. █


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


“If you know the enemy and know yourself, you need not fear the result of a
hundred battles. If you know yourself but not the enemy, for every victory
gained you will also suffer a defeat. If you know neither the enemy nor
yourself, you will succumb in every battle.” - Sun Tzu, The Art of War


    * Slopwatch:_linuxsecurity.com_and_hamradio.my_(in_Planet_Ubuntu)_Are_at_It
      Again_With_LLM_Slop_About_"Linux"
    * The_Fall_of_the_Open_Source_Initiative_(OSI):_The_OSI_Does_Not_Speak_For
      You,_OSI_Staff_Speaks_for_GAFAM/Microsoft_(the_Paymasters)


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⣿⣿⣿⣿⣿⣿⣿⠀⣧⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⠟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣤⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣯⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⣿⣿⣽⣿⠂⠀⠀⠀⠀⢀⣀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⠛⠻⠿⢿⠀⢠⣴⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⡀⠀⠠⣤⣐⣒⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣄⠀⠉⠛⠻⣿⠃⠀⣠⣔⠂⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢳⣶⣶⣾⣿⡀⠀⠴⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣛⠀⢀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⠭⠍⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣿⡟⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⠁⣿⣿⣿⠀⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡇⣿⣇⠀⣿⣿⣀⣿⣿⠀⢻⣷⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣸⡿⣿⣿⡇⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣶⣿⣿⠙⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⡆⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣧⢸⣿⣿⣿⣯⣭⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠁⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⣽⣿⣿⣿⣾⣭⣭⣿⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣠⣤⣄⣼⣤⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣴⣤⣤⣤⡀⠀⠀⠀⣀⠀⣀⠀⠠⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⢀⣼⣿⣿⣿⢿⡸⠐⠢⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡻⣿⣿⣿⣿⣿⣿⠂⢐⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣮⣯⣿⣽⣿⣿⣭⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⡶⠀⠆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣣⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡀
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⠀⢸⠇⠀⠀⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⢩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⠟⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⡿⠋⠁⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠹⢿⣿⣿⣿⣷⡿⠒
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠈⠛⠻⠏⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⢹⣿⡇⡅⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⣾⣿⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⣀⣀⣠⣴⡾⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⣄⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⣧⣾⣿⣿⣿⣿⣿⣿⠿⠯⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣶⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⣶⣶⣿⣿⣿⠃⠀⠀⠀⠀⣀⡤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠋⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡙⠛⠿⠿⠂⠠⣶⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣄⠀⠀⣤⣬⣵⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣦⠀⠈⠉⠛⡿⠇⠀⢤⣖⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢹⣷⣶⣾⣿⡀⠀⠐⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣭⣍⣩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣛⡀⢀⣀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣭⠭⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⡆⠀⣿⣿⢿⣿⣿⠛⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⠁⣿⣿⣿⠀⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢠⣿⡇⣿⣇⠀⣿⣿⣈⣿⡿⠀⢻⣷⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣸⡿⣿⣿⣇⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢦⣿⣿⠙⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⢀⣿⣿⢹⣿⡇⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣶⣿⣿⡶⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⣿⣿⣿⣿⣿⣾⣭⣭⣿⣯⣯⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣠⣤⣄⣼⣤⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣭⣭⣭⣭⣭⣭⠉⢉⡁⢠⣄⣀⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⣶⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠁⠐⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣽⠀⠀⠀⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡅⡂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣄⠀⠀
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣗⠀
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠁⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⡀⠀⡇⠀⠀⣠⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠿⣋⣁⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠋⢍⣽⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠀⡀⡀⢀⢂⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠠⠀⡨⡨⡴⣜⣼⠭⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣥⣶⣶⣤⣤⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⣿⣿⣿⣿⣟⣿⡒⠝⠚⠒
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣀⣀⣀⠀⠀⠀⠈⠙⡛⠛⠏⠉⠉⠀⠀⠀⠀⠀
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢀⡀⠀⣶⣿⣾⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣛⣛⣛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠁⣯⠙⠛⠻⠗⠀⠶⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣛⣛⣛⡛⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⡄⠀⠰⣶⣭⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣠⣾⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣦⠀⠈⠉⢻⡯⠀⠠⢴⡮⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣶⣶⣶⣶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⣄⠀⢈⣿⣿⣷⣿⣧⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣛⣛⣛⣛⣛⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠏⣛⠛⠛⠋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⣿⣿⣿⡆⠙⣿⣿⣿⣿⣟⠙⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⠁⣿⣿⣿⠇⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣻⣿⡿⠀⢻⣷⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣤⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⢩⣿⣿⣿⣯⣯⣭⣾⣽⣭⣇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣠⣤⣄⣼⣤⣤⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣛⣛⣻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣍⣉⣉⣍⣛⣛⣛⣛⣛⢛⠛⠛⠃⠀⠀⠀⢘⣿⣿⡿⣛⠿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣅⣼⣤⣧⣽⣿⣿⣟⣖⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠋⠁⢀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⢶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠀⠀⡆⠀⠀⠀⠀⠈⠃⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⣡⣤⣤⣤⣤⣴⣴⣶⠖⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⢿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠁⠀⠀⠼⠿⠿⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡛⠛⣋⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣟⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⡿⡿⡟⠋⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡷⠶⠖⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣶⣶⣶⣤⣀⣠⣤⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⣤⡀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢿⣆⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠙⢷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣆⠀⣼⣿⣿⣿⣿⣷⣾⣿⣿⡟⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⢹⣿⣿⣿⣟⣻⣿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⢀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣭⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⡀⢀⣤⣬⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢭⣀⣨⣿⠥⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⢀⣵⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠙⠛⢿⣿⣯⠀⢀⣤⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⣭⣭⣭⣭⣭⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣦⡀⠀⢀⣼⣷⣶⣤⣤⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣭⣩⣭⣭⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣿⣿⠀⠀⠀⣿⡿⣿⡎⠻⣿⣿⢿⣿⣿⡞⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⢁⣿⣿⣿⡆⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⢀⣿⡇⣿⣇⠀⣿⣿⣻⣿⡿⠀⢻⣧⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣧⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⢸⣿⣿⢻⣿⡇⣿⣿⠃⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠆⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⢹⣿⣯⣭⣧⣭⣾⣭⣭⡆⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣣⣤⣄⣼⣤⣤⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣬⣭⣭⣭⣭⣭⣭⣭⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠃⠀⠀⣲⣹⠻⣷⢿⡿
⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⠀⣀⣠⣻⣿⣿⣿⣿⠻
⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣥⣿⣿⣿⣟⣟⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣯⣿⣽⣿⣿⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⡿⢿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣤⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⠇⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡆⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠄⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠙⣽⣿⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣍⡀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣀⣸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠁⠈⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⠓⢼⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣄⣠⣄⠀⠀⠀⢀⣽⣿⣿⣿⢰⣿⣿⣿⣿⣿⢿⡿⢵⠓⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣤⠹⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠸⠉⠙⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠀⠀⠐⢶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢦⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣴⣾⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠏⢿⡿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡀⠘⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣄⠘⢿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠄⣪⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⡀⠀⠈⠉⠛⠛⠻⠃⠐⣿⣿⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄⠛⠁⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠻⠷⣶⣿⣷⣶⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣩⣉⣉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣯⣭⣍⣀⣀⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣍⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⠀⠀⠀⣿⡿⣿⡆⠉⣿⣿⢿⣿⣿⣿⣿⣿⣻⣿⠃⠀⠸⠿⣿⣿⠿⠆⣿⣿⠀⣿⣿⣿⠃⣿⣿⣿⡆⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣥⣿⣿⠀⠀⢀⣿⡇⣿⣇⠀⣿⣿⣸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣸⡿⣿⣿⠀⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣧⣿⣿⠀⣿⣿⠙⣿⣾⠟⠉⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢻⣿⡇⣿⣿⠃⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣿⠇⣿⣿⠆⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠉⠩⣧⣭⣦⣭⣭⣦⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣣⣤⣄⣼⣤⣤⣤⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⣛⣛⣛⣛⠛⣛⡛⣛⠛⠛⠛⠛⠛⠀⠀⢀⠀⣘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣛⣎⡶⣼⢿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣾⣿⣿⣿⣿⣿⣷⣫⣳
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠁⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡄⣀⣤⣶⣿⣧⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⢿⣿⣿⣿⣿⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠙⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⡟⠛⠀⢀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢼⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠤⢸⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣶⣶⣤⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠋⠏⠃⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠉⢩⣥⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠋⠛⠋⠛⠛⠁⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢅⠀⠀⠀⠀⠈⠹⣯⣽⣯⣭⣭⣭⣿⣭⣭⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠋⠀⠈⠙⠢⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣭⣉⣉⣭⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⠤⣲⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⡇⢀⣴⣥⡞⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⠀⠀⠀⠀⠀⠀⠉⣉⣉⣁⢨⣿⠯⠄⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣠⣾⣦⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣩⣩⣩⣩⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠉⠛⣛⠿⠿⣿⣿⡄⠀⣴⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣤⡀⠀⢀⣠⣾⣿⣿⣿⣷⣶⣤⣴⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⣠⠄⠀⠀⡄⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣭⣩⣍⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⡿⣿⡆⠀⣿⣿⠿⣿⣿⣿⣿⣿⣻⣿⣻⣇⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⠀⣿⣿⣷⡇⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣧⣿⣯⣿⣷⡄⣿⣿⠀⠀⢀⣿⡇⣿⡇⠀⣿⣿⣀⣿⡿⣿⣿⣿⣿⣯⣿⠿⠂⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣸⡿⣿⣿⠀⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣴⣶⣼⣿⣇⣿⣿⠀⣿⣿⠙⣷⣾⣿⣿⣿⣿⠛⠁⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢹⣿⡇⣿⣟⠂⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⡀⣿⣿⠀⠀⣿⣿⠀⣿⣿⠸⣿⠇⣿⣿⡄⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠉⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠀⢩⣭⣧⣭⣭⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣣⣤⣄⣼⣤⣤⣤⣾⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣙⣛⡛⡛⠛⠛⡛⣛⠛⠛⠛⠛⠛⠀⠀⠀⣾⡿⡻⣿⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠠⣠⢀⣆⣔⡺⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣤⣿⣿⣿⣿⣿⠶⡐⡀
⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣟⣃⠴⠵
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⡉
⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⠯⠁⠀⢿⣿⣿⣿⡿⣛⣿⣿⣿⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⣤⣶⣾⣿⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡥⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣾⡀⢸⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡈⢸⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⢿⠋⠉⠀⠊⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠛⠋⣁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠟⠻⠏⠻⠟⠙⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣰⣈⣟⠳⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠈⠗⠒⠀⠀⠀⠀⠀⠈⠹⣯⣿⣿⣽⣯⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣿⣿⣿⡟⣛⣻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⢞⣽⠟⠁⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣴⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⠿⠿⠿⣿⣿⣿⣿⣿⣿⠀⣴⣷⣿⠃⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⣴⣿⣿⣿⣴⣿⣿⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣭⣭⣀⣐⣛⣒⣀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣄⠀⠀⠀⠀⠀⠀⠀⢉⣽⣟⣛⡻⠿⠿⠿⠄⠐⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣦⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⡄⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣶⣶⠚⠀⠀⠀⢿⣿⠿⠁⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⣿⠀⠀⠀⣿⡿⣿⡆⠀⣿⣿⠿⣿⣿⠟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⠀⣿⣿⡇⠀⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⣿⣿⣿⣿⣷⣿⣿⣟⣿⣷⠗⣿⣿⠀⠀⢀⣿⡇⣿⡇⠀⣿⣿⣀⣿⡿⠙⢻⣿⣿⣯⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣰⡟⣿⡇⠀⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠀⢀⣼⣿⣃⣿⣿⠀⣿⣿⠙⣷⣦⠀⠈⣿⣿⣿⣿⣿⠋⠁⣿⣿⢸⡆⣿⣿⠀⣿⣿⢹⣿⡇⣿⡇⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣻⣿⣦⣿⣿⠀⣿⣿⣴⣶⣿⣿⣿⣿⣿⣷⡄⣿⣿⣽⡇⣿⣿⠀⣿⣿⢸⣿⠃⣿⡇⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣧⣩⠉⠀⠉⠉⠀⠉⠀⠉⠁⠀⠉⠉⠩⣥⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣠⣤⣄⣼⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣙⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠀⡀⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣷⣞⣈⣽⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠄⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠈⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠙⢿⣿⣿⣿⣿⣟⣩⣿⣿⣿⠀⠀⠀⠀⠰⣧⡀⠀⠀⠀⠀⠀⠀⠀⢪⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣶⣷⣿⣮⣿⣿⣿⣿⣿⣿⣿⠀⠀⢄⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄⠄⠈⢣⣧⢀⠀⠀⠀⢀⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡆⠀⠐⠄⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣗⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣷⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣀⣰⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣌⢙⣿⣿⣿⣿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢐⣿⣿⣿⣿⢿⠿⠟⠇⠀⠈⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣀⠏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⣿⣏⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⡟⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⡀⢴⣀⣀⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣾⣿⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⢀⣴⣿⡃⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⠀⠀⣜⣠⡿⠃⠀⠀⠀⢀⠆⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢻⣿⠆⠀⠀⠀⢠⣾⣿⣿⣿⣴⣾⣿⣿⣤⣿⡖⠚⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠀⢾⣿⡿⠁⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣬⣯⣭⣥⡀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣭⣝⣛⣛⣛⠛⠛⠃⢈⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣄⡀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⢠⠀⠀⠀⠀⣤⣤⣤⣤⠄⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡟⠋⣿⣿⠿⣿⣆⠙⣿⣿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣧⣿⣿⠾⣿⣿⣿⠀⣿⣿⡇⠀⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⡿⣯⣿⣏⣿⣷⣿⣿⣿⠀⠀⢀⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠠⣿⣿⣿⣸⡿⣿⣷⠀⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣹⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠙⣷⣦⠀⠈⣿⣿⠈⠻⣿⣿⣿⣿⣿⠉⠀⣿⣿⢰⣿⣿⢹⣿⡇⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣤⡄⣸⣿⣿⣻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⣤⣴⣾⣿⣿⣿⣿⢠⡄⣿⣿⠈⣿⣿⢸⣿⠃⣿⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣯⣤⣭⣭⣤⣴⣭⣿⣿⣿⣿⣿⣷⣭⣽⣿⣷⣭⣭⣤⡉⠉⠀⠉⠀⠉⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣠⣤⣄⣼⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⣉⣁⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠈⠛⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠈⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠃⠀⡜⣆⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠀⠠⠈⣾⣆⡀⠀⠀⠀⠀⠈⢦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣪⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠱⣀⠀⠘⣾⣷⠀⠀⠀⠀⠀⠀⠱⣞⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠀⠀⢱⡔⣤⡙⣿⣦⡄⠀⠀⠠⣄⠠⠘⠅⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⡄⠐⠹⡏⠣⠘⠋⠉⠀⠀⠰⠛⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢒⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠟⠛⠛⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣧⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣗⣼⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣿⣿⣿⣿⣟⡉⠉⠛⠻⢿⣿⣿⣿⡇⠼⣿⢿⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣝⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠐⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⠈⣽⣄⡀⡉⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⠈⠍⠋⠈⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⡀⠈⢙⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠊⠉⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠠⠤⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣤⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣌⣀⣼⣿⣯⡀⢀⡀⠘⠯⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⠃⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣘⣿⣷⣀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠿⠿⠿⠿⠿⠿⠿⠆⠘⢫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⣾⣿⣿⣿⣶⣶⣾⣿⣿⣧⣾⣿⣿⠀⠀⠀⣿⣿⣿⡆⣀⣿⣿⠿⣿⣆⠘⣿⡿⣻⣿⣻⣿⣿⣿⣿⣿⢿⢇⣿⣿⣿⣿⣿⣿⠏⣿⣿⣷⠀⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣤⣠⣠⣤⣴⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠃⢠⣿⡇⣿⣇⣿⣿⣿⣸⣿⡿⠀⢻⣧⣿⡏⠻⠿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣻⣿⣻⣿⣿⠁⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠀⠀⠈⠻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢻⣿⡇⣿⣿⡄⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣼⣿⣟⣻⣿⣿⣿⣿⣤⡄⣸⣿⠟⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⢸⣿⣿⣾⣿⠇⣿⣿⠇⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣽⣿⣿⣿⣭⣽⣯⣯⣿⣿⣭⣭⠅⠉⠉⠀⣬⣿⣅⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⣠⣭⣭⣾⣧⣭⣭⣾⣭⣭⡇⠉⠀⠉⢉⣤⣭⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣣⣤⣄⣼⣤⣤⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣴⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣾⣷⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣤⠀⢨⣥⣾⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠂⠀⠀⠀⠀⢀⣀⢀⠀⠀⢀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡠⡄⢲⡈⣿⢿⡄⠀⠐⠀⠀⠘⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣖⢷⡌⢿⣿⣄⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⠟⡋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠜⣮⣿⣼⣿⣿⣆⠀⠀⠀⢀⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢺⢟⠝⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣜⢿⣻⣿⣿⣿⣦⡀⠀⢹⣦⣐⠾⠻⢋⣾⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠋⠻⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⢯⢻⣿⢏⠹⠋⠁⠀⠈⠿⠛⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠛⠛⠁⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⡦⣰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⠋⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣟⣾⡿⡏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⠉⠉⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⡮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣯⣯⡉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡛⢿⡿⣿⣿⣟⠋⠙⠃⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣟⠉⠈⠁⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣇⠈⠛⠿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠟⠏⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣟⢷⣦⣈⡻⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠀⡠⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡙⠿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢀⣀⣀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠘⠉⢁⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⡀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠛⠿⠆⣠⣾⡇⠀⠀⠀⠠⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣦⡀⠀⠀⢉⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⡏⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠘⢿⣿⢅⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡆⣤⣾⣿⣿⡿⣇⣿⣿⡀⠀⠀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⢃⣼⣿⣿⣿⣿⣿⠇⣿⣿⢻⣿⣿⣿⣏⣿⣿⣿⣷⣿⣿⠿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣿⣿⣍⡉⣁⣁⣿⡏⣿⣷⢀⣿⣿⣷⡀⢀⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⢀⢻⣧⣿⡏⠙⠻⢿⡿⣿⣿⣿⡇⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣙⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣿⣽⣿⣿⣾⣿⣿⣷⣿⣿⣽⣿⣿⣭⣥⣸⣿⣇⣿⣿⠀⣿⣿⢛⣷⣮⣿⣿⣿⣿⠀⠀⠀⠀⠁⣿⣿⢻⡇⣿⣿⣸⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣤⣤⣤⣤⣴⣾⣿⣿⣿⣷⣿⣿⣻⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡄⣿⣿⠈⣿⣿⠛⠋⣿⣿⠀⠀⠀⠀⠀⣿⣿⠻⡇⣿⣿⢿⣿⣿⣿⣿⠇⣿⣿⡟⣿⣿⣤⡄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠿⣿⣿⣿⣿⣽⣽⣿⣭⣩⠀⠈⠉⢁⣉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠭⠾⠭⣯⣧⣭⣶⣭⠍⠃⠩⠩⣭⣥⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⣾⣢⣤⣤⣼⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣁⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⣤⣾⣿⣿⣿⣿⣅⠀⠀⠀⣸⣿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣶⣶⡆⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⣀⣄⡀⠀⠀⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⢀⢤⡺⣧⣹⣿⣷⡀⠀⠀⠈⢟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣫⣷⣿⣿⣟⣿⣷⡄⠀⠀⣠⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣗⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⣿⣿⣿⣿⣿⣆⠀⠘⢿⣾⠣⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⣿⣦⡜⠟⠛⣳⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠋⠁⠀⠈⠟⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠛⠁⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⠿⠃⠉⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡏⠛⠋⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣭⡁⠈⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⢿⠿⣿⣿⣿⣿⣅⡉⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣻⢿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣍⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣧⠀⠙⠛⠿⠟⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠻⠉⠕⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣵⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠂⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣻⣧⣶⣄⠉⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡍⣛⠳⢲⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡧⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⣾⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠛⠋⢁⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⣿⠿⠀⣠⣶⠀⠀⠀⠀⠠⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠲⣦⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣶⣦⣤⣾⣿⣿⣷⣄⠀⠀⠀⢩⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⢸⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠿⣿⣿⣿⣯⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⠀⠀⠘⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⡇⣿⣿⡿⠿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠁⢿⣿⣌⡉⠁⠀⣿⡏⣿⣷⢰⣿⣿⣆⠀⢷⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣧⣿⡏⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⢻⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣦⣌⡉⠋⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣝⢿⣿⡆⢸⣿⣇⣻⣿⠈⣿⣿⠈⠀⢸⣿⣇⣿⣿⠀⣿⣿⠙⣷⣦⠀⡈⣿⣿⣠⣴⣶⠀⠀⣿⣿⠘⠇⣿⣿⠈⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣫⣿⡟⢸⣿⣟⣻⣿⣧⣿⣿⣬⣝⣼⣿⣟⢻⣿⡄⣿⣿⠀⣿⣿⠻⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣾⣿⣇⣿⣿⡟⣿⣿⣭⡍⣀⣀⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣭⣭⣽⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠉⠁⠉⠉⠀⠉⠉⠀⢤⣭⠭⠩⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠉⢭⣧⣭⣴⣭⣭⣿⣭⡉⠍⠁⠻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⣿⣤⣤⣠⣤⣤⣴⣶⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠁⠀⠀⠀⣰⣿⠋⠉⠉⠙⠻⠿⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⢀⣀⣄⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣀⢤⣶⣾⣿⣿⣧⡐⠂⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠗⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠉⣿⣷⡌⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠈⠛⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠡⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠁⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦⣌⠙⠏⠙⠻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡈⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠉⠛⠻⣿⠿⠛⢁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣟⢿⡄⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣶⡤⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⢭⣓⠁⠀⠀⠀⠈⠙⢿⣿⣷⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣝⡣⣈⢀⡠⣑⠦⢄⠀⠀⠈⠙⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣄⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠻⢶⡋⠀⡉⠃⠀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡟⠁⠾⠛⠉⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⣘⡮⠁⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⢀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣾⡆⢀⣰⣶⠀⠀⠀⠀⠲⣶⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣤⣬⣅⣴⣿⣿⣿⣦⡀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣽⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠸⣿⣿⣃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣿⣿⣿⣿⡆⠀⢹⣿⣿⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⢸⣿⡀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⢿⢿⣿⣿⣿⣿⣷⢦⣸⣿⣿⣷⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡧⣿⣿⣍⡉⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣷⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣛⣻⣿⣿⣿⣦⣄⠀⠉⠉⠉⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣿⣿⣿⣿⣟⢿⣿⣟⣻⣿⠙⣿⣿⠀⠛⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠙⣿⣿⢻⣿⡇⣿⣿⠃⣿⣿⣻⣿⣿⣿⣿⣿⡻⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣿⣿⣠⣿⡏⢸⣿⡟⢻⣿⡇⣿⣿⣤⡌⣽⣿⠟⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⣤⣤⣤⣶⣷⣿⣿⠀⠀⣿⣿⠀⣿⣿⢸⣿⠇⣿⣿⣦⣿⣿⣭⡍⣿⡿⠿⠋⣁⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠭⠉⠀⠉⠉⠁⠈⠉⠁⠉⠉⠉⠁⠉⠉⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠻⠿⠿⠟⠋⠉⠉⠀⠀⠉⠉⠀⠉⠉⠁⢭⣤⣭⣭⣯⣭⣭⣭⣥⣿⠿⠿⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣡⣰⣿⣿⣿⣶⣶⣦⣤⣤⣴⣶⣾⣿⣶⣶⣶⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⠋⠁⠀⠀⣠⣿⠏⠉⠉⣙⠿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠀⠀⢀⣤⣦⡄⠀⢠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣞⠛⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣷⣿⣽⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠅⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠁⠀⠉⠛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠂⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠐⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⠁⠈⠀⠀⠀⠀⣴⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠉⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣭⠀⠀⠀⠀⠀⠀⢀⣻⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣭⣉⣛⣿⠟⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠟⠋⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿
⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠛⠿⣿⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣄⡀⠈⠋⣁⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣝⠷⠀⠀⠈⠙⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣏⡆⠈⠑⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⣐⣀⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠁⣶⡿⠛⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣿⠁⠀⠀⠀⠀⣾⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣥⢀⣤⣄⠀⠀⣠⠀⠀⠀⠀⢀⣀⣤⡄⠀
⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⢹⠛⢋⣠⣾⣿⡆⠀⠀⠀⠀⠙⣛⣛⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣤
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠁⣸⣿⣿⣿⣿⣿⡿⡀⡀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⣠⣿⣿⣿⣿⣿⡏⠀⠈⠃⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⣸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣷⡘⢦⣰⡶⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⣿⣿⣿⣯⣭⣧⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣷⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣀⡀⠹⣿⡏⢀⣶⣎⠃⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣿⣿⡟⢻⣿⣏⣻⣿⣴⣿⣿⠀⣼⣿⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣴⣿⣿⣻⣿⡇⣿⣿⡇⣿⣿⠛⠃⠀⢀⣼⣿⣿⣿⣷⣂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠟⣋⣿⣿⣠⣿⣿⣾⣿⣟⣻⣿⡿⣿⣿⣤⡄⣼⣿⡟⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢸⣿⠇⣿⣿⠃⣿⣿⣤⡄⣴⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠋⠉⠉⠈⠉⠉⠁⠈⠉⠁⠉⠉⠉⠁⠉⠉⠁⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⢀⣴⣶⣶⣶⣭⡿⠀⠀⠉⠉⠀⠉⠉⠀⠉⠀⠉⠉⠀⠉⣭⣭⣥⡟⣛⣫⣽⣽⣿⣿⣦⣄⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡛⢛⣛⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⡀⣀⣿⣿⣿⣿⡾⠻⣿⣿⠟⠛⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠉⠉⠛⠛⠛⠛⠛⠻⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⢛⣠⣶⣿⣶⣀⣤⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣟⣥⣤⣤⣤⣤⠀⠠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠋⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⣿⣿⡾⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠁⠀⠈⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢈⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠀⢸⠟⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⣿⣿⣿⣯⣉⠻⢿⣿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠉⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⠀⠉⠉⢻⡿⠟⢋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣥⡀⠉⠉⠙⠻⢿⣿⣿⣝⠻⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡶⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠦⠀⠀⠀⠀⠀⠀⠉⠻⣶⣦⣀⠝⠻⣿⣽⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⡈⢈⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⠄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠏⠀⠜⠛⠋⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠛⠻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠰⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡶⢠⣴⣦⠀⠀⢀⣤⠀⠀⠀⠀⢤⣥⣴⡆
⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣏⠁⣸⡟⢉⣠⣾⣿⣿⡄⠀⠀⠀⠀⣩⣭⣭
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢹⣿⣯
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡏⢹⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣧⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠏⠀⠠⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⢻⣿⣧⣿⣿⣺⣿⣿⠀⣤⣼⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⢹⣿⡿⣟⣛⣁⣿⣿⣺⣿⣿⣿⣿⡟⢻⣿⡏⣿⣿⣤⡌⣿⣿⠟⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⢠⣿⣿⣾⣿⣷⣿⣿⡏⣿⣿⣤⡄⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣟⣋⣭⡽⠾⠋⠉⠉⠀⣉⣩⣵⣮⣿⣿⣭⠉⠉⠁⠉⠉⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠈⠉⠍⠁⠉⠀⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠴⠾⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⢀⢠⣾⣿⣿⣶⣦⣤
⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢵
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋⢋⣿⣿⣿⣿⣿⣦⣾⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⢠⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⠻⠟⠋⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⡿⠿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⢰⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠽⣿⡷⠏⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣟⣛⠍⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⠃⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣽⣯⣉⡙⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣆⠉⠛⠛⠿⣿⣿⣿⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⡿⠃⠊⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣤⣤⣀⠝⠉⢠⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠂⢀⣴⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣻⠃⠀⠈⠀⠀⠀⣠⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣄⠀⠀⠀⡀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡏⠀⣾⣿⡆⠀⣀⣴⣧⠀⠀⠀⠀⠚⠿⣿⠤
⠀⢀⣰⣿⣿⣿⣿⣍⠉⢻⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⣤⣠⣏⣀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⣶⣶⡖
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⡿⠟⠁⠹⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠹⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⡎⡿⣿⣿⣿⡇⠂⣿⣿⠀⠀⠀⣿⡿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⡟⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣭⣯⣥⣇⣿⡏⣿⣧⠀⣿⣿⠀⠀⢀⣿⡇⣿⡇⠀⣿⣿⣀⣿⡿⠀⢻⣿⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣿⡿⣿⣿⡄⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠙⣷⣦⠀⠈⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⢰⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟⢻⣿⣟⣻⣿⡇⣿⣿⣤⡄⣸⣿⠛⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣼⣿⣿⢸⣿⢇⣿⣿⣿⣿⣿⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠙⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⣉⣩⣭⣶⣿⣏⣭⣬⠉⠁⠩⣭⣍⠁⠉⠉⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⣭⣿⣭⣭⣧⣭⣾⡿⠍⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⠇⠈⣀⣠⣤⣴⢶⣿⣿⠿⠟⠛⠉⠉⢀⣀⡀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣭⣿⣿⣟⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⠈⠽⢿⣿⣿⣿⣿⣿⢋⣰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠿⠿⣿⣿⡿⠻⠿⠛⠛⠛⠛⠛⠛⠛⢂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠉⣤⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠠⢤⡬⣭⠀⢠⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⠉⠀⠀⣿⣿⢿⢋⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣬⡉⠁⠀⠀⠀⣭⣇⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⢿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢻⣿⡾⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⢻⣿⣿⠿⠟⠙⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠸⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣦⣤⣶⣿⣿⣿⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⣉⡉⠉⠛⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣄⠀⠈⠉⢹⣿⠿⠛⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠙⠿⠟⠉⠀⠀⠈⠛⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⠚⠁⠠⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⠇⢠⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⡏⠀⠀⠀⠀⠀⢀⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⠀⠀⢀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠛⠛⢿⣿⡿⠀⢰⣿⡦⠀⠀⣠⣶⡆⠀⠀⠀⠀⠲⣾⣿⣀⠀⠀
⣯⣄⠀⠀⠛⣿⣿⣿⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠧⠀⣴⣿⣯⡀⠀⡼⠁⢠⣤⣾⣿⣿⡿⠀⠀⠀⠀⠀⣤⣴⣶⠀⠀
⣿⣿⣿⣶⣄⡀⠀⠀⢁⠁⠁⠉⣾⣿⢿⣷⡆⠀⣾⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⡿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠆⣿⣿⠀⣿⣿⣿⠋⣿⣿⣷⣧⣿⣿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀
⣿⣿⣿⣿⣿⣿⣶⣶⣷⣵⡾⡇⣿⣿⣌⡩⡥⠂⣿⡏⣿⣧⠀⣿⣿⠀⠀⢀⣿⡇⣿⡇⠀⣿⣿⣀⣿⡿⠀⢻⣧⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⢸⣿⣿⣿⣸⡟⣿⣿⣇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠿⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣬⣝⢿⣿⡆⢰⣿⣇⣸⣿⠀⣿⣿⠀⠀⢸⣿⣃⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⢾⣿⣿⢹⣿⡇⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡏⢸⣿⡟⢻⣿⡆⣿⣿⣤⡄⣸⣿⠛⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠙⣿⣿⣸⣿⠇⣿⣿⣿⣿⣿⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠉⠀⠈⠉⠁⠈⠉⠁⠉⠉⠉⠁⠉⠉⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⢠⣭⡭⠀⢩⣭⣧⣭⣾⣭⣭⣿⠍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛
⣿⣶⣿⣻⣿⠏⠽⠄⠀⠀⣀⣠⣤⠶⠞⠁⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣶⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠘⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠿⠛⠛⠛⠛⠛⠛⠀⠈⠛⠻⠿⠻⠿⠿⠿⠛⠀⠀⠋⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣯⡀⣀⣀⣄⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠋⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠘⢿⣽⢿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠃⠀⠈⠛⢉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⡍⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠾⠍⢀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⠈⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠿⠛⠉⠑⠙⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡉⠛⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠄⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠛⠛⠿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠈⠛⢾⣤⣄⠂⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢸⣿⣿⣿⣛⠻⢿⣿⣿⣿⣿⣿⣿⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠁⠙⠛⠋⠁⠀⠀⠀⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣆⠀⠈⠉⠹⣿⡿⠟⢋⣉⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣦⠘⠁⣴⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿
⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⡿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡿⠂⣠⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣛⠁⠐⠛⠉⠁⠀⣠⣤⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇⠀⠀⠀⠀⠀⠰⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⠻⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⣾⣿⣆⠠⠀⣴⡄⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⣒⣀⣀⡄⠀⠀⠀⠀
⠀⠁⠢⠌⡙⠺⢕⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠀⠄⣽⡟⠋⠀⢸⠟⠛⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠛⠿⠿⠤⠄⠀⠀⠀
⣤⣀⡀⠒⠬⣛⠲⣌⡐⠽⢲⡄⣾⣿⢿⣷⡄⠀⣾⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⡿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⢾⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⣶⣶⡶⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣦⡉⠒⢝⡢⠀⠀⢿⣿⣌⡉⠁⠀⣿⡇⣿⣧⠀⣿⣿⠀⠀⢀⣿⡇⣿⣇⡀⣿⣿⣀⣿⡿⠀⢻⣧⣿⡏⠀⠀⠀⠀⣿⣿⢈⡆⣿⣿⠘⣿⣿⣿⣸⡿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⢿⣿⣷⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⣀⣙⢻⣿⡆⢰⣿⣇⣹⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠁⣿⣿⠙⣷⣦⠀⠈⣿⣿⠀⠀⠀⠀⠀⣿⣿⣾⣇⣿⣿⠀⣿⣿⢹⣿⡇⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⢿⣿⣠⣿⡇⢸⣿⡟⢻⣿⡆⣿⣿⣤⡄⣸⣿⠛⢻⣿⡀⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⠀⣿⣿⣾⣿⢿⣿⣿⡟⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⢿⣿⣷⡆⠀⠀
⣿⣿⣿⠿⠿⠛⠛⢋⣉⣀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠁⠈⠉⠁⠉⠉⠉⠁⠉⠉⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⢩⣭⣿⠇⣭⣭⣴⣭⣭⣿⣯⣾⣽⡭⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀
⠉⢀⣀⣠⣤⣤⣼⣤⣀⣀⡀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢁⣴⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿
⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿
⠄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣵⣶⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⠿⠛⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⣿⠋⠃⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⡿⠿⠛⠀⠀⠉⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣟⠛⠋⠉⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢻⣿⡿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠁⠀⠀⠙⠛⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⢆⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿
⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⡅⠴⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠿⢿⣟⣠⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣄⠀⠀⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⣿⣿⣿⣿⠆⠈⠛⢿⣶⣄⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿
⣿⣄⡁⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠂⠈⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⣿⣿⣷⠈⠛⠻⠿⣿⣿⣿⣿⡿⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠉⠻⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⠀⠼⠛⣩⣴⣶⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⣿⣿⣿⠁⣴⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡟⠀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⣿⣿⣿⡿⠋⣰⣿⡿⠟⠋⠁⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠁⠀⠉⠀⠀⠀⣴⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡄⡀⠀⠀⠀⠀⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡶⣭⡻⢕⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠏⠀⣼⣷⣦⠀⠀⣠⣴⠀⠀⠀⠀⠀⢐⣚⣁⣀⡄⠀⠀⠀⠀⠀
⡓⠬⣛⢶⣍⡟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⣿⣿⣿⡉⠀⢸⡟⠉⢁⣠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠻⢿⣿⣧⡄⠀⠀⠀⠀
⣿⣷⣄⡙⠚⠁⠀⠀⠀⠀⠀⠀⣶⣿⢻⣷⡆⠀⣾⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⣿⢷⣿⣿⠿⣿⣿⣿⣖⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⣶⣶⣶⠆⠀⠀⠀⠀
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣌⡉⠁⠀⣿⡇⣿⣧⠀⣿⣿⠀⠀⢰⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣧⣿⡏⠀⠀⢰⡿⣿⣿⣿⡟⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⣿⣿⣿⡤⠂⠀⠀⠀
⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣙⢻⣿⡆⢰⣿⣇⣹⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠙⣷⣦⠀⠈⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⠀⣿⣿⣻⣿⡇⣿⣿⠇⣿⣿⠛⠃⠀⠀⠀⠀⢹⣿⣿⣿⠇⠀⠀⠀
⣀⣤⣴⣶⡤⠀⠀⠀⠀⠀⠀⠀⢿⣿⣠⣿⡇⢸⣿⡟⢻⣿⡇⣿⣿⣤⡄⣸⣿⠟⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⢿⡇⣿⣿⣰⣿⣿⣿⣿⡟⣿⣷⠀⣿⣿⣤⡄⠀⠀⠀⠀⠸⣿⣿⣧⣤⠀⠀⠀
⣿⢿⡿⠶⠶⠄⠀⠀⠀⣤⣦⡀⠀⠉⠉⠉⠀⠈⠉⠁⠈⠉⠁⠉⠉⠉⠁⠉⠉⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⣿⣿⡭⣭⣾⣷⣭⣽⣿⣿⣽⣿⣭⠀⠉⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠰⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢟⣴⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿
⠛⢻⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿
⠀⢸⣿⣿⡟⠟⠉⠀⢀⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡿⠛⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠙⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣥⣶⣴⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠻⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠋⠀⠀⠀⠹⠟⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿
⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠩⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠉⠻⣿⣿⣿⣿⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⡐⠦⣇⡹⣝⠺⣤⣒⠐⠀⠀⠀⠉⠻⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⣤⣶⣭⣻⣿⣿⢛⢻⣚⡊⠙⠅⠀⠠⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⡦⣕⠶⡄⣀⠤⡠⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿
⠛⢿⣿⣿⣻⢿⠅⠈⠛⣿⣷⣍⠻⢿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠙⢿⣯⡀⠀⣬⡙⢿⣷⣤⡉⠀⣀⠀⡀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠉⠀⠉⠻⣿⣦⡀⠊⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠐⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏⣾⣿⣿⣿⣿⣿
⠉⠂⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡍⠻⠿⣿⣿⣿⣿⣿⣿⣧⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠹⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣄⡀⠀⢨⢿⣛⣯⣭⣶⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣄⡀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠓⣤⣾⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⢼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣰⣾⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⢿⣿⣿⣿⡟⢋⣿⣿⣿⡿⠟⢋⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⠺⠛⠉⠁⢠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡁⢠⡄⠀⠀⠠⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⣰⣦⣼⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠟⠃⢠⣿⠿⠿⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⢶⣶⣶⣶⡇⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣤⣶⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠃⠀⠀⠀⠀
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢻⣷⡄⠀⣾⣿⣿⡇⠀⣿⣿⠛⠿⠃⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⢀⣿⣿⣿⣿⣿⡿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⠿⠇⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀
⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠀⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣧⣿⡏⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⡁⠀⠀⠀
⣤⡄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣙⢻⣿⡆⢰⣿⣇⣹⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠙⣷⣦⠀⠈⣿⣿⠀⠀⣸⣿⣿⣿⣿⠟⠀⣿⣿⣾⣿⣿⣻⣿⡇⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀
⣀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⢿⣿⣠⣿⡏⢸⣿⡟⢻⣿⡇⣿⣿⣤⡄⣼⣿⡟⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⢀⣿⣿⣿⣿⣿⣰⣷⣿⣿⣿⣿⣿⣿⣿⠇⣿⡿⠀⣿⣿⣤⡄⠀⠀⠀⠀⢿⣿⣿⣧⣄⠀⠀⠀
⣿⡟⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠁⠈⠉⠁⠉⠉⠉⢥⣭⡭⠄⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⢀⣼⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⡿⠍⠀⠉⠀⠉⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼
⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹
⠀⢸⣿⣿⣿⣿⣿⠫⣉⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⡿⢯⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠀⠀⠉⠈⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⣿⠟⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠹⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠛⠃⠀⠀⠀⠘⠿⠟⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⠟⣛⢿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠵⢹⣱⢭⣷⣶⣿⣿⣽⣧⢭⣿⣿⣟⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢢⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⣿⣿⣿
⠀⠀⠀⠀⠙⢿⣿⣿⡉⠁⠉⠿⣿⣿⣝⢿⣿⣿⣿⡀⠸⣿⣿⣿⣿⣏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⢦⡀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠈⠻⢿⣷⣌⠻⣯⡉⠠⠈⢙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⢸⣿⣿⣿
⠀⠙⠳⣄⠀⠀⠀⠀⠀⠻⢿⣷⣄⠀⠈⠻⣿⣷⣄⠙⡄⠀⠀⠟⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣿⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣿⣿⣿
⠀⣀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠙⢿⣷⣤⣼⣮⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡄⠈⠉⢹⣿⣿⣯⣽⣷⣾⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠉⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⢆⣴⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠏⣼⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣇⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣦⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⢿⣿⣥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣉⠻⢷⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠿⠿⠃⠰⠟⠋⠉⢠⣾⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣎⢠⣷⡄⠀⠀⣾⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢣⣾⣾⣿⠃⠀⢀⣄⠀⠀⠀⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠛⠁⣾⡿⠿⠏⢀⣶⣿⣿⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣤⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⢻⣷⡆⠀⣾⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⣸⣿⣿⣿⣿⣿⠟⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠿⠇⠀⠀⠀⠀⣾⣿⣿⣿⣷⡶⠀⠀
⠀⠀⠀⢰⣾⣾⡆⠀⠀⠀⠀⠀⢿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠀⣿⣿⢀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣧⣿⡏⠀⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣀⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠂⠀
⠀⠀⠀⠘⢿⣿⠃⠀⠀⠀⠀⠀⣀⣙⢿⣿⡆⢸⣿⣇⣻⣿⡀⣿⣿⠻⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠀⣸⣿⣿⣿⣿⣿⣴⣶⣿⣿⣿⣿⣿⢻⣿⡇⣿⡿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣠⣿⡏⢸⣿⡟⢻⣿⡇⣿⣿⣦⡔⣼⣿⡟⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⢸⣿⠇⣿⣿⠀⣿⣿⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠁⠈⠉⠁⠉⠉⠉⠁⠉⠉⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠀⠉⠉⠀⠉⡠⡉⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⡿⢿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡔⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⡉⠉⠛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⢹⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⣟⡛⠛⢛⣋⣨⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢻⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⠁⠀⠀⠀⠀⢻⣿⠿⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⣿⣯⣟⣿⣫⣿⣿⣿⣷⣿⣿⣾⣟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠯⣱⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣸
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠈⠙⠻⣿⣿⡏⣿
⣤⣬⡛⣿⣯⡀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠉⠙⢿⣿⣿⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⣿
⣿⣿⣷⣧⠉⠻⠆⠀⠀⠀⠀⠙⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠙⠛⢿⣿⣿⣿⣿⣿⣷⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣶⣠⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣡⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⣄⣿⡷⠈⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣿⣿⢀⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡆⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠿⣿⣦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠏⣾⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⢠⣿⡄⠀⢰⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣿⣿⣧⣦⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⠟⢀⣴⣾⡇⠀⠀⠀⠀⠀⢰⣿⣟⣋⣤⣤⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣧⣀⣸⣿⢉⣡⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣯⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⡭⠀⠀
⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀
⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣤⠤⣴⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⣵⣿⣿⣿⣿⣿⡿⡿⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⣶⣿⢻⣷⡆⠀⣿⣿⣿⡟⣿⣿⣿⡟⢿⡏⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⢳⣿⣿⣿⣿⣿⢿⣧⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⠀⣿⣿⠿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠿⣿⣿⠿⠿⢳⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⣿⣿⠀⣿⣿⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⣙⢿⣿⡆⢸⣿⣇⣻⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⢻⣿⡇⣿⣿⠀⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣠⣿⡏⢸⣿⡟⢻⣿⡇⣿⣿⣤⡄⣼⣿⡟⢻⣿⡄⣿⣿⠀⣿⣿⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⣿⣿⠀⣿⣿⢸⣿⠇⣿⣿⠀⣿⣿⣬⡅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠁⠈⠉⠁⢉⣉⣭⣥⣭⣭⣽⣬⣍⠁⠉⠉⠀⠉⠉⠘⠻⢿⢿⣿⢿⣿⡟⢩⣭⣭⡴⠦⣭⣭⡄⠍⠉⠀⠉⠀⠉⣉⣤⣭⣭⣭⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣇⡳⠟⠁⠁⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⢦⡄⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠋⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣛⣛⣿⣽⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠹⣿⣿⣿⣿⠛⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠈⠀⠀⠀⠀⠀⠙⠿⠟⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠻⢿⣿⣿⡿⠿⠿⠿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⡤⣤⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣯⣻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⠿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿
⣲⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣍⠉⠛⠉⠁⠀⠈⠉⠛⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠉⢙⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⣲⣾⣿⣿⡿⡟⠛⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⣻⣻⣿⣿⢿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⣱⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⣿⣿⣤⣤⣤⣤⣦⣄⡀⠠⠤⠀⢀⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣄⢸⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀
⣿⣿⠟⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢿⣿⠏⣼⡿⠛⠋⣻⣿⣿⣿⣿⣿⣿⠿⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣰⣿⣷⠀⣸⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⠃⠀⢀⡄⠀⠀⠀⠀⠀⠀⣀⣤⣶⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⢻⣿⣿⣿⠟⢠⣶⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⣬⣿⣇⣤⣾⣿⣿⣿⢁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⠀
⠀⠀⠀⣠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⣶⣾⣷⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣿⣿⣿⠟⠻⠯⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠿⣿⣿⣏⣻⢿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⢿⣷⡆⠀⣿⣿⣿⡇⠻⣿⣿⠿⠿⠟⣿⣿⣿⡇⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⡀⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠀⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣷⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣾⣿⣿⣿⠃⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⢿⣿⡆⢸⣿⣇⣻⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⠀⣿⣿⢻⣿⡇⣿⣿⠂⣿⣿⢛⡃⢿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣠⣿⡏⢸⣿⡟⢻⣿⡇⣿⣿⣤⣾⣿⣿⣿⣿⣿⡾⣿⣿⠀⣿⣿⠀⠀⣿⣿⢿⣿⣿⣿⡏⣿⣿⣿⡇⣿⣿⠀⣿⣿⢸⣿⠇⣿⣿⡠⣿⣿⣬⡍⣦⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠁⠈⠉⠁⠉⣭⣽⣵⣭⣭⣽⣿⣿⠅⠉⠉⠀⠉⠉⠀⠀⠉⠉⠈⠛⣿⣿⣧⣭⣭⣼⣧⣭⣭⣤⡩⡭⠈⠉⢀⣭⣭⣯⣭⣭⣭⣥⣿⣿⣦⡀⠀⢀⣴⣿⢿⣿⣿⣿
⣷⣤⣾⣳⣾⣧⣾⣶⣤⣦⣶⣶⣦⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⡿⠿⠿⢛⣋⣁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⡟⠐⠙⠉⠉
⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⠛⠀⠀⠈⣿⣿⣿⡿⠁⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣟⢛⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣫⢛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡓⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⠟⠿⠟⠿⡿⠟⠻⠋⠉⠃⠈⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠙⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣼⣿⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⡀⠉⣽⣿⣿⣿⣿⡿⠿⠛⠛⠋⠺⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢻⣿⣿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣾⣿⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠛
⣿⣿⣿⣿⣿⣿⣿⣿⡁⠉⢻⣿⡏⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⠛⠉⠀⠐⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⡀⠀
⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⣿⣿⠟⠉⢸⣿⣿⣿⣿⡿⠟⠛⠉⠙⠋⠻⡿⠂
⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⣿⣧⣤⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣴⣿⠀⠀⠀⠀⠀⠀⣴⣿
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠛⢽⣿⡿⠟⣁⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿
⣵⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣾⣿⣿⣿⡿⢿⠁⠀⠀⠀⠀⠀⠀⠈
⣷⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠁⠀⠄⠀⠀⠀⠀⠀⠀
⣉⣉⣉⠀⠀⠀⠀⢀⣤⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⡿⠆⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣿⣷⣶⣦⣶⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⢿⠿⠿⠃⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢴⡎⠀⢠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠀⠁⠙⠿⠿⠿⢿⣿⠿⠋⠁⣦⣴⣇⡤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⡆⠀⣾⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⢀⣸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢁⣿⣿⣿⡄⣿⣿⢿⠇⠏⢁⣦⣶⣿⣿⢎⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠀⣿⣿⠀⠀⢠⣿⡇⣿⣧⣷⣿⣿⣠⣿⣿⣶⢻⣷⣿⡏⠀⠘⠻⠟⣿⣿⢻⡏⣿⣿⠙⣿⣿⣿⣾⣿⣿⣿⡇⣿⣿⣈⣡⣶⣿⣿⣿⣿⣿⣇⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⢿⣿⡆⢸⣿⣇⣹⣿⠀⣿⣿⠀⠀⢸⣿⣷⣿⣿⢿⣿⣿⢛⣿⣯⠟⠘⣿⣿⠁⠀⠀⠀⠀⣿⣿⢸⡇⣿⣿⠀⣿⣿⢻⣿⡇⣿⣿⠃⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⢐
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣺⣿⣟⣸⣿⡟⢻⣿⡇⣿⣿⣤⡄⣼⣿⡟⢿⣿⡿⣿⣿⠻⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠁⣿⣿⠀⣿⣿⢺⣿⡇⣿⣿⡆⣿⣿⣭⡍⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⣾⣾
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣭⣭⣅⠈⠉⠁⠉⠉⠉⠁⠉⠉⠁⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠩⣴⣭⣭⣮⣭⣤⣭⣭⣧⣭⣭⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣦⣦⣠⣤⣄⣄⣀⣀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠂⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣼⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⣿⣿⣿⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠙⠁⠀⠀⠀⠀⠙⠿⠟⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⢿⡿⣿⡟⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⠿⠿⠟⠛⠛⠛⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⠟⠺⢍⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠛⠛⠛⠋⠓⢺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⢀⣾⣿⣿⣿⣿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⣿⣿⣿⣿⣿⣿⣿⢛⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣤⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣧⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠙⠻⣿⡏⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣏⠁⢀⣾⣿⣿⣿⡿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣤⣾⣿⣿⠇⠀⢀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣴⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠋⠙⢿⣿⠛⣁⣶⣿⣿⣿⡗⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀
⡿⠿⠟⠛⣛⣛⣛⣛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠐⠀⠀
⠛⠛⠛⠛⠛⠛⠉⠉⠉⣉⡙⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣶⣶⣾⣿⣶⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣆⣰⡤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠻⠿⠻⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⣺⣿⣿⣿⣿⡏⠁⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⡯⣙⣿⡿⠃⣀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⡆⠀⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣦⣼⣿⣇⣸⣿⣣⣤⡼⠿⣿⣿⠿⠇⣿⣿⠛⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⡿⠉⠀⣤⣾⣿⣿⣿⣿
⣠⣾⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠀⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⣿⢿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣻⡟⠛⠉⣠⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⣈⣙⢿⣿⣆⢸⣿⣇⣻⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣿⣾⣿⣿⣿⣿⣿⡿⠛⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢹⣿⡇⣿⣿⠏⣿⣿⢛⣣⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣺⣿⣿⣾⣿⣟⣿⣿⣷⣿⣿⣤⡄⣼⣿⠟⢻⣿⡆⣿⣿⠀⣿⣿⠉⠁⣿⣿⠈⠁⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢸⣿⠇⣿⣿⣷⣿⣿⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣟
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠽⠿⠿⠿⠿⢿⣯⣭⣥⣭⣭⣭⡥⠍⠉⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠀⠉⠉⢯⣭⣭⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣾⣣⣤⣤⣼⣾⣿⣶⣶⣤⣤⣤⣤⣤⣤⡀⠀⠠⢝⣛⣛⠿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠻⣿⣿⣿⡿⠉⢙⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠙⠁⠀⠀⠀⠀⠙⠟⠛⢁⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣋⣑⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⢿⣿⣿⣿⠿⠿⠟⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠑⠉⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢩⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⡟⠊⠈⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⣿⣿⠟⠛⠙⠫⠃⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣷⢁⠔⠐⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢉⠛⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣀⠀⠈⢉⣿
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣯⠙⠻⣿⡉⠉⠉⠉⠉⠙⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣻⣿⡻⣿⣷⣍⡻⣦⣀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣛⢿⣯⡻⢿⣝⢮⣗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣷⠀⠉⢾⣮⡅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡟⠛⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣧⡀⢠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠻⣿⣿⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⣉⣉⣭⣭⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠋⠉⢉⣉⣉⣉⣉⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣾⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⣀⣤⣴⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠋⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⡆⠀⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠀⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣧⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠾
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⣈⣙⢿⣿⡆⢸⣿⣇⣻⣿⡀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠀⠀⣤⣤⣤⣿⣿⣀⡀⣿⣿⠀⣿⣿⢹⣿⡇⣿⣿⠟⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣾⠻⠟⠛⢁⣤
⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣇⣿⣿⣠⣿⡟⢸⣿⡟⢻⣿⡇⣿⣿⣤⡄⣼⣿⡟⢻⣿⡆⣿⣿⠀⣿⣿⠀⠀⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢸⣿⠇⣿⣿⠀⣿⣿⣭⡍⠿⠿⠻⠻⠟⢛⣛⣀⣤⣴⣿⣿
⠀⠀⠀⣀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣤⣭⣭⣁⣬⣭⣥⣭⣭⣭⣥⣭⣭⣤⣬⣍⣁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠅⠉⠉⠀⠉⠀⠉⠉⠀⠉⠉⠉⠁⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣾⣻⣾⣥⣼⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠈⢿⣿⣿⡏⢀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠈⠉⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠣⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠛⠓⠃⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠛⢿⣿⠿⠟⠛⠛⠉⠉⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⠠⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⡿⢛⠉⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⢻⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡏⠛⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⢿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⣀⠀⢰⣿
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡙⢿⣿⣉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡌⠛⠷⡆⠀⠀⠀⠀⠛⠻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⡿⣿⣿⣿⣿⣮⣵⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⢿⣿⡳⢯⡕⢾⣗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣷⡄⠙⢿⣿⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⢿⠿⣿⠿⠛⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡒⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣾⣿⣆⠀⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⣿⣿⠿⠿⠿⠛⠛⣉⣉⣉⣭⣭⣴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿
⣾⣴⣦⣥⣤⣴⣶⣶⣾⣿⣿⣿⣿⣛⣿⣿⣿⣶⣿⣆⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣴⠶⠾⠓⠛⠛⠋⠉⠉⠉⠀⢀⣀⣠⣤⣤⡤⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣀⡀⠀⣀⣀⣠⣤⣶⣶⣶⣶⣿⠿⠿⢿⣿⣿⣟⣫⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⡿⠟⠿⠿⠛⠛⠛⠛⠛⠛⠛⣿⣿⢿⣿⡏⠉⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⣸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠀⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣷⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢛⣡⣤⣤⣀⡀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣈⣙⢿⣿⣆⢸⣿⣇⣻⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢹⣿⡇⣿⣿⠿⣿⣿⢻⣿⣿⣿⣿⣿⠷⡟⢻⠻⣿⠃⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⣿⣿⣨⣿⡟⢸⣿⡟⢻⣿⡇⣿⣿⣤⡄⣼⣿⡟⢻⣿⡆⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⢠⣼⣷⣿⣿⣴⡆⣿⣿⣶⣿⣿⢸⣿⠃⣿⣿⠀⣿⣿⣬⡍⣿⣫⣝⡛⢿⣧⡄⠒⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣾⣭⣭⣽⣆⠉⠉⠁⠈⠉⠁⠉⣉⣉⣁⣉⣉⣀⣈⣉⡁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠀⠉⠀⠉⠉⠀⠉⠉⠉⠁⣉⡋⠈⠀⠊⣁⣤⣤⣴⣶⣿⣿
⠀⠀⠀⢀⣠⣤⣼⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠻⣿⣿⡿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⠉⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠻⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⣿⠿⠟⠛⠛⠋⠉⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢡⣤⣤⣤⣤⣤⣤⣤⠄⠀⠄⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠷⠄⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠟⠍⠅⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣶⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠉⠀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠉⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⡿⠛⠉⠀
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⣍⡙⢿⣦⣌⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠈⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠻⠷⣦⡄⠀⠀⠈⠛⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣤⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⡿⢿⣾⣽⡶⣤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠻⣿⣿⣿⣯⡲⣽⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣧⡈⠹⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣽⣿⡄⠀⠀⣼⣿⣿⣿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣤⣴⣿⡏⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⡿⠃⣠⣾⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣯⣀⣸⣿⣉⣠⣾⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⡿⣶
⠿⠿⣿⣿⣿⠿⠿⠛⣉⣉⣉⣭⣭⣥⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣽⣿
⣵⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡯⠿⠷⠶⠿⠧⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣤⣴⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣵
⠶⠶⠞⠛⠛⠉⠉⠉⠉⠁⣀⣀⣠⣤⣶⣶⣶⡀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠻
⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠄⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⣿⣿⣿⣏⡛⠀
⠽⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⣾⣿⢿⣿⡆⠀⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⡆⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢟⣿⣛⣱⣄⣀⢀⢨⠛⠉⠃⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠀⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣷⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣛⣻⢿⢻⣑⣛⡟⠿⠟⠀⠀⠀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⣈⣙⢿⣿⣆⢸⣿⣇⣹⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⣡⣴⣶⣶⣦⣿⣿⣴⡆⣿⣿⠀⣿⣿⢹⣿⡇⣿⣿⡇⣿⣿⠛⡛⣿⣯⡌⠁⠀⠀⠀⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣆⣿⣿⣠⣿⡟⢸⣿⡟⢻⣿⡇⣿⣿⣤⡄⣼⣿⡟⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⠻⠁⣿⣿⠀⣿⣿⢸⣿⠃⣿⣿⠀⣿⣿⣤⡄⣈⣀⣠⣶⣶⣶⡉⠿⡿⠿⠟⠛
⠀⠀⠀⣀⢴⣿⣿⣿⣿⣿⣿⣿⣾⣭⣭⣭⣤⣭⣍⣡⣬⣭⣥⣭⣽⣯⣵⣭⣭⣵⣬⣭⡁⠉⠉⠀⠉⠉⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⡭⠀⠀⠉⠉⠀⠉⠉⠀⠉⠀⠉⠉⠀⠉⠉⠉⢥⣿⣷⣿⣿⣿⣿⣿⣽⡱⠀⠀⣀
⣤⣴⣾⣻⣾⣧⣼⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣷⣦⠛⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠻⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠹⣿⠿⠿⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣤⣤⣤⡄⠄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠟⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠙⠻⠿
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⣀⣐⣿⣿⣿⣿⠿⠛⠉⠀⠉⠙⠅⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⢀⡀⣀⣠⣄⣤⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠛⢿⡉⠀⠈⠉⠙⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡍⠀⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡮⣟⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⢿⣿⡷⢾⣿⡿⣕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⡟⠛⠛⣿⣿⣿⣿⡿⠋⠉⠉⠉⠈⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡀⢙⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣧⣀⣠⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣶⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡛⠙⣿⡟⢋⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠃⠀⠀⠀
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠙⢿⣿⣳⡀⢀⠀⠀
⣿⡿⠿⠿⠿⠿⠿⢛⣛⣛⣛⡋⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠸⣿⣷⣴⣿⣷⣤
⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⠆⠀⠀⠘⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣦⣎⣻⢿⣿⣿⣿
⠿⠿⠿⠿⠟⠻⠿⠿⠛⠟⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⡅⣀⠀⢻⣿⣿⣻⣿⣽⣿⣿⣷⣮⡋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⠿⡿⠿⡾⠿⠿⠿⢿⣿⠁⠁⢹⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⡆⠀⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⠿⣿⣦⣼⣿⣧⣸⣿⣷⣷⡼⠿⣿⣿⠿⠇⣿⣿⠈⣿⣿⣿⢁⣿⣿⣿⣆⣿⣿⠿⠇⠀⢠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣾⣿⣿⣶⣄⣀⠀⠀⠀⣿⣿⣌⡉⠁⠀⣿⡏⣿⣷⠀⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣾⣿⣿⣿⠁⣿⣿⣐⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣾⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⣈⣙⢿⣿⣆⣸⣿⣧⣿⣿⣠⣿⣿⣤⣄⢸⣿⣇⣿⣿⠀⣿⣿⠛⣿⣾⣿⡟⣿⣿⢿⠃⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢹⣿⡇⣿⣿⡇⣿⣿⣛⣻⣿⣿⣿⡼⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣯⣽⣿⣿⡟⢻⣿⡄⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢸⣿⠇⣿⣿⠁⣿⣿⣭⡍⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⣈⣉⣉⣁⣈⣩⣭⣭⣭⣭⣽⡭⠉⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠀⠉⠉⠀⠉⠉⣭⣥⣿⣿⣿⠿⠁⠀⠁⢻⣿⣿⣿⣿
⣿⣤⣿⣻⣾⣧⣼⣤⣤⣶⣿⣿⣿⣿⣿⡿⠛⠻⠻⠿⠿⣿⣿⣿⣿⣶⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⢀⣴⣾⣿⣿⣿⡯
⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⣶⣤⡀⠀⠀⠸⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⢻⣿⣿⣿⡟⠛⢻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠻⡿⠟⠃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠋⠙⠙⠋⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠁⠀⠀⠅⠁⡁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠀⠀⠀⠀⠘⠛⠛⠚⠒⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣤⣽⠁⢻⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡍⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⣀⣴⣿⣿⣿⡿⠛⠋⠉⠈⠉⠭⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⠀⠈⠉⠉⠙⠛⠛⠳⠂⠀⠀
⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣽⣿⣿⣭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢙⣻⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣻⣿⠉⠙⣿⣿⣿⣿⠿⠉⠁⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⣴⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣾⣷⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡄⠀
⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣍⣉⣿⣏⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⠁⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢂⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤
⣿⣿⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡘⠂⠀⠀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⢉⣉⣩⣭⣭⣍⡀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⢹⣿⣿⢟⣰⣂⠀⠀⠀⠈⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡌⢿⣿⣷⣿⣿⣶⡄⠀⠀⢻⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⣿⣿⣿⣿⣿⣿⣿⣮⣟⢿⣿⣿⡿⠷⠄⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣮⡁⠀⠀⢱⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣶⣶⣶⣶⣿⡆⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿
⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⣿⠿⠿⠾⡀⠀⠀⠰⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⡄⣾⣿⣿⣿⣦⣤⣿⣿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⣿⡿⡿⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⠿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⢁⣿⣿⣿⡇⣿⣿⢿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣯⣿⣿⣿⣷⡆⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣷⣿⡏⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣩⣄⣀⡀⣈⣙⣿⣿⣞⢻⣿⣿⣿⣿⡀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣻⡻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⣿⣿⣻⣿⣿⣾⣿⣿⣿⣿⡇⣿⣿⣤⡄⣼⣿⡟⢻⣿⡆⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⢠⠄⣿⣿⠀⣿⣿⢸⣿⠇⣿⣿⡿⣿⣿⣭⡄⠀⣀⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣤⣌⣉⠉⠉⠠⠭⢭⣉⣉⡉⠁⠉⠉⠉⠁⠉⠉⠁⢨⣭⣵⣿⣿⣶⣿⣭⣤⣀⠉⠉⠀⠀⢀⣠⣤⣭⣭⣴⠀⠉⠉⠀⠉⢉⣀⣭⣤⣭⡭⡧⠉⠉⠉⢁⣾⣿⣿⣿⣿⣿⡟⠰⣾⣯⠙⠛
⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣐⣒⣤⣬⣁⡉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣶⣿⣿⣿⣿⠍⢠⠤⣤⡀⠀⣾⣿⣿⣿⣿⣿⣿⣤⢨⣿⡿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠹⣿⣿⣿⣿⠛⠻⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀⠀⠀⠹⣿⡿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⠻⠏⠛⠋⠁⠀⠀⠀⠀⠐⢿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠉⠛⢻⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⠿⠋⠉⠁⠀⠉⠋⠂⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣤⣤⣤⣤⡄⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢦⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣇⠀⣸⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⢀⣠⠀⠀⠀⠀⠀⠀⣶⣿⣥⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⢿⣿⠿⢋⣴⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣴⣿⣶⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⣭⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀
⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠤⡀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀
⠿⠆⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣶⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣶⣾⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠻⣿⣿⣿⡏⢀⣀⡀⠀⠀⢿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀
⡿⠷⠀⠀⠀⠸⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢼⣿⣻⣿⣽⣿⣷⡄⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣞⣟⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠓⠄⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⠉⠐⣻⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡿⠿⠿⠿⢿⠏⠈⠁⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀
⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡦⡄⣿⣿⣿⡇⠀⣿⣿⠟⠛⠛⣿⣿⣿⡇⠀⣿⣿⠿⣿⣆⠘⣿⡇⢸⣿⠃⠀⠸⢿⣿⣿⠿⠇⣿⣿⠀⣿⣿⣿⢁⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀
⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⢿⣷⣿⣿⣿⣿⣿⣇⣿⡏⣿⣷⠀⣿⣿⠀⠀⢠⣿⡇⣿⣇⠀⣿⣿⣀⣿⡿⠀⢻⣷⣿⡏⠀⠀⠀⠀⣿⣿⢸⡇⣿⣿⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣛⣛⣙⢿⣿⣟⢻⣿⣇⣻⣿⠀⣿⣿⠀⠀⢸⣿⣇⣿⣿⠀⣿⣿⠛⣷⣦⠀⠈⣿⣿⠁⠀⠀⠀⠀⣿⣿⠘⠃⣿⣿⠀⣿⣿⢻⣿⡇⣿⣿⡿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣶⣄⠀⠉⠉⠙⠛⣿⣿⣻⣿⡟⢸⣿⡟⢻⣿⡇⣿⣿⣦⡄⣼⣿⡟⢻⣿⡆⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⣀⣀⠀⣿⣿⠀⠀⣿⣿⠀⣿⣿⣿⣿⠇⣿⣿⠁⣿⣿⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠈⠘⠋⠩⠭⠤⠭⠍⠁⠈⠉⠁⠉⠉⢩⣵⣿⣿⣿⣿⣿⣧⣭⣉⠀⠉⠉⠀⣀⣉⣭⣤⣿⡏⠁⠀⠉⠉⠀⠀⠉⣩⣴⣭⣭⣯⣭⣤⠉⢉⣀⣭⣭⣭⣽⣿⡿⠿⢻⣿⢿⣿⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣷⣶⣾⣽⣖⣒⣆⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣧⣧⣤⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿⣿⣿⠁⢀⣾⡏⠚⠹⠝⠛⣿⣿⡇
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠈⠉⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠿⠿⠛⠟⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣀⡀⠀⠨⢿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⠿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣋⣙⢙⣉⣯⣭⡤⡤⣅⡠⢤⠀⢩⣍⠋⠣⣈⣄⣉⣡⣼⡆⠀⠀⠀⠀⣿⣿⣿⡄⣠⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⡮⠯
⠀⣖⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣿⣿⣿⠿⠿⠟⣻⣿⠿⢿⣿⣿⣿⣿⠀⣾⣿⠀⣸⣿⣿⣿⣷⠋⠀⠞⠀⠀⠀⣘⠋⣩⡇⠄⠈⢾⣿⣍⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⡉⠉⠉⣧⣴⡄⢀⠭⣿
⠀⢈⠀⠀⠀⠀⠘⣿⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡯⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⢿⡦⢒⣳⡀⠀⠀⠀⣼⣿⣿⣷⡀⠀⢸⣿⡨⠁⠀⠁⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⡇⣼⡟⠡⣀⣀⣀⣿⣿⣋⣄⠩⠓
⠀⠈⠅⠀⠀⠀⢰⡇⣀⠀⡔⣦⡀⠀⠙⣿⣿⣿⠿⢽⠯⣤⣿⡿⠀⠀⢴⠂⠁⠀⠀⣀⣼⡇⢸⠁⢸⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣷⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢿⣻⣿⣛⣿⣷⣞⣯⡋⠙⠀
⠀⠀⢂⠀⠀⠀⠀⢁⢻⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃⠀⢀⣴⣟⣻⣿⡇⢸⡇⣼⣶⣇⠀⠀⠀⠠⠟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠉⠙⠋⠹⣿⣿⣿⣿⣶⣄⣰⣶⡤⠘⠛⠛⠛⠛⢛⣻⣛⣧⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⣿⣿⣿⠟⣿⠟⠀⣿⣿⠿⡓⠄⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠤⠤⢀⣽⡋⠀⠈⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⣾⣿⡿⣶⣿⡶⠋⢀⣾⣿⣿⣿⡀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠻⢿⣶⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣴
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡖⢉⠕⠁⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⢹⡿⡟⠿⠙⠛⠙⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⡿⠀⠀⠁⠀⠀⠀⢰⣿⡟⢿⣿⡇⠀⠀⠀⠟⠀⠀⠀⠀⠀⠄⠀⠰⢛⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠛⠛⢛⣻⢃⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣿⠀⠀⠀⠀⠀⢰⣿⠹⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⢻⣧⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⢻⡆⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠰⠣⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠳⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⠃⣀⠡⢝⣒⣾⣁⣠⣤⣤⣶⣶⣾⣿⡟⠁⠀⠀⠀⡀⠀⠀⠉⠀⠄⢸⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣾⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⠸⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡎⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠀⢸⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢹⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣤⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣹⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣿⣾⠛⠃⠛⠃⠸⣿⠿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠂⠈⠉⠉⠀⠿⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣭⢭⠭⢽⣿⣿⣿⣿⡯
⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠿⠟⠛⠟⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣀⡀⠀⠸⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢿⡇⠀⠀⠀⠀⠀⠟⠿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡷
⠸⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣋⣙⢙⣙⣯⣽⡤⡤⡅⠀⢤⠀⢨⣝⠋⠣⣌⣀⣍⣡⣼⡆⠀⠀⠀⠀⣿⣿⣿⡄⣠⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣼⣻⣀⣸⣶⣷⣆⣶⡖⢶⡮⠯
⠀⣖⠀⠀⠀⠀⢰⠾⣯⠽⢿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠿⢿⣿⣿⣿⣿⠀⣾⣿⠀⣸⣿⣿⣿⣷⠋⠀⠞⠀⠀⠀⣘⠋⣩⡇⠄⠈⢾⣿⣍⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⡉⠉⠉⣧⣴⡄⢀⠭⣿
⠀⢨⠀⠀⠀⠀⠘⣾⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡏⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⢿⡆⢒⣳⡀⠀⠀⠀⣸⣿⣿⣷⡀⠀⢸⣿⡩⠁⠀⠀⣿⣿⣛⢻⣿⣿⣿⣿⣿⣿⣿⡇⣼⡟⠡⣀⣀⣀⣿⣿⣋⣄⠩⠓
⠀⠈⠁⠀⠀⠀⢰⡇⣀⠀⡔⣦⡀⠀⠙⣿⣿⣿⠿⣽⠯⣤⣿⡿⠀⠀⢴⠂⠁⠀⠀⣀⣼⡇⢰⠁⢸⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣷⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢿⣻⣿⣻⣿⣷⣾⣍⡋⠙⠀
⠀⠀⢇⠀⠀⠀⠀⢁⢻⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃⠀⢀⣴⣟⣻⣿⡇⢸⡇⣼⣶⣇⠀⠀⠀⠰⠟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠉⠙⠋⠹⣿⣿⣿⣿⣶⣄⣰⣶⡤⠘⠛⠛⠛⠛⣛⣛⣟⣧⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⣿⣿⣿⠟⣿⠟⠀⣿⣿⠿⡓⠄⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠤⠤⢀⣽⡋⠀⠈⢭⣭⣭⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⣾⣿⡿⣶⣿⡶⠋⢀⣼⣿⣿⣿⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠻⢿⣦⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣴
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡖⢉⠕⠁⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⢹⡿⡟⠿⠙⠛⠙⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡿⠀⠀⠁⠀⠀⠀⢰⣿⡟⢿⣿⡇⠀⠀⠀⠟⠀⠀⠀⠀⠀⠄⠀⠰⢛⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠛⠛⢛⣻⢇⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣿⠀⠀⠀⠀⠀⢰⣿⠙⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⢻⣧⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⢻⡆⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢰⠣⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠷⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⠃⣀⠡⢍⣒⣾⣁⣠⣤⣤⣶⣶⣾⣿⡟⠁⠀⠀⠀⡀⠀⠀⠉⠀⡄⢸⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠈⠀⠀⠀⢻⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⠸⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠀⢸⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢹⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣤⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣹⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣿⣛⣿⣾⠛⠃⠛⠃⠸⣿⠿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠂⠈⠉⠉⠀⠿⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠭⠭⢽⣿⣿⣿⣿⡯
⠁⠁⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠘⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠿⠿⠿⠟⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣀⣀⠀⠸⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⠿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠘⠀⠀⠀⠀⠀⠏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣋⣙⢙⣙⣯⣭⡤⡤⣅⡀⢤⠀⢨⣍⡋⠣⣤⣄⣭⣥⣼⡇⠀⠀⠀⠀⠿⣿⣿⡆⣠⣄⢸⣿⡛⠒⠉⠀⣇⣈⣴⣤⣧⣤⣤⣤⣤⣤⣤⣤⣼⣻⣀⣸⣷⣿⡆⣶⡖⢶⡶⠯
⠀⢥⠀⠀⠀⠀⢰⠾⣿⡽⢿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠻⢿⣿⣿⣿⣿⠀⢸⣿⠁⣸⣿⣿⣿⡷⠋⠀⠚⠀⠀⠈⢈⠉⣉⡇⠄⠈⢻⣿⣭⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣛⣉⡉⠉⠉⣧⣴⡄⢀⠭⢽
⠀⢨⠀⠀⠀⠀⠘⣞⠛⠛⠋⠙⠋⠚⢻⣿⣿⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⠸⡿⣿⣿⢿⡆⢚⡭⡀⠀⠀⠀⢼⣿⣿⣷⡀⠀⢸⣿⡨⠁⠀⠀⣿⣿⣋⢿⣿⣿⣽⣿⣷⣿⣿⡇⣰⡟⠁⣀⣀⣀⣿⣿⣋⣄⠩⠓
⠀⠀⠇⠀⠀⠀⢰⡇⣀⠀⣔⣶⡀⠁⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠂⠁⠀⠀⣀⣼⡇⢸⠃⢸⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣼⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⢿⢟⣻⣟⣻⣿⣷⣾⣯⣋⠙⠂
⠀⠀⢇⠀⠀⠀⠀⠙⢻⡇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠊⠀⢀⣴⣟⣻⣿⡇⢸⡇⣼⣷⣧⠀⠀⠀⠰⠏⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣶⡤⠘⠛⠛⢛⠛⣛⣛⣛⣫⣤⠀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⣿⠟⠀⣽⣿⡿⡑⢄⠀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠤⠤⢀⣼⡋⠀⠈⢭⣭⣭⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⣾⣿⡿⢷⣿⠷⠋⢀⣾⣿⣿⣿⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠸⠿⣧⣄⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣴
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡖⣈⠝⠁⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⢹⡿⡟⠿⠙⠋⠈⠛⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣿⠀⠀⠁⠀⠀⠀⢐⣿⡟⢿⣿⡇⠀⠀⠀⠝⠀⠀⠀⠀⠀⠀⠀⠘⢋⣿⣿⣿⣷⡧⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⣛⣻⢏⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣿⠀⠀⠀⠀⠀⢰⣿⠙⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠉⢻⣧⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⢛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡟⠻⡆⠀⠀⠀⡀⠁⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠠⢪⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⠁⣀⠈⢍⣁⣹⣁⣠⣤⣤⣶⣶⣾⣿⡟⠁⠀⠀⠀⣠⢤⡄⠉⠀⠂⠰⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠂⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⣷⠀⣿⡏⠀⢰⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠀⢸⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⡇⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⡀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣻⣼⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠂⠈⠉⠉⠀⠿⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠘⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠿⠿⠻⠟⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⠄⠀⠀⠀⠀⢀⣀⣀⠀⠸⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣛⣉⣉⣟⣋⣙⢙⣉⣯⣭⣤⡤⣅⡀⢤⠀⢨⣝⡋⢣⣄⣄⣍⣡⣸⡆⠀⠀⠀⠀⢿⣿⣿⡀⣠⣄⢸⣿⡛⠒⠉⠀⣇⣈⣴⣤⣧⣤⣤⣤⣤⣤⣤⣤⣼⣻⣀⣸⣶⣷⡆⣶⡖⢶⡾⠭
⠀⢆⠀⠀⠀⠀⢰⠾⣯⡽⢿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠀⣸⣿⣿⣿⡷⠁⠀⠛⠀⠀⠈⣌⠉⣩⡇⠄⠈⢻⣿⣭⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⣉⠉⠉⣧⣤⡄⢀⠭⢽
⠀⢈⠀⠀⠀⠀⠈⣟⠛⠛⠋⠙⠋⠚⢻⣿⣿⣿⣿⣿⣿⡟⣻⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⢿⡆⢛⠭⡀⠀⠀⠀⣾⣿⣿⣷⡀⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣿⣿⣷⣿⣿⡇⣴⡟⠁⣀⣀⣀⣿⣿⣋⣄⠩⠓
⠀⠀⠅⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠁⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠂⠁⠀⢀⣠⣼⡇⢸⠀⢸⠀⠂⠀⠀⠀⠘⢿⣿⣿⣿⣷⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣛⣿⣻⣿⣷⣞⣏⣋⠙⠂
⠀⠀⢂⠀⠀⠀⠀⠙⢻⡇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠊⠀⢀⣴⣟⣻⣿⡇⢸⠇⣾⣷⣇⠀⠀⠀⠰⢋⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠛⠛⠛⠛⢛⢛⣛⣣⣤⠀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⣿⠟⠀⣿⣿⢿⠑⠄⠀⢄⢁⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠤⠤⢀⣼⡋⠀⠈⢭⣭⣭⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⣾⣿⣿⠷⣿⠗⠃⢠⣾⣿⣿⣿⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠸⢿⣧⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡖⣈⠝⠁⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⢻⡿⡏⠿⠙⠏⠈⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣿⠀⠀⠀⠀⠀⠀⢐⣿⠟⢿⣿⡇⠀⠀⠀⠋⠀⠀⠀⠀⠀⠆⠀⠘⢋⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣿⠀⠀⠀⠀⠀⢰⣿⠙⠀⠈⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⢻⣧⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡟⠻⡆⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⢫⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⠃⣀⠈⢍⣉⣽⣁⣀⣤⣤⣴⣶⣾⣿⡟⠁⠀⠀⠀⣠⢦⡄⠉⡀⠀⠸⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⠀⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣼⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠀⢸⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⡀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠙⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⢛⣟⣼⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠂⠈⠉⠉⠀⠿⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠘⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠿⠛⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⢀⣀⡀⠀⠸⢿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠘⠀⠀⠀⠀⠀⠏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣋⣙⢉⣉⣯⣭⡤⠤⢅⡀⠤⠀⢨⣝⡋⠣⣈⣀⣉⣁⣸⡄⠀⠀⠀⢀⢿⣿⣿⠀⣤⣄⢸⣿⡓⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣛⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⠥⠀⠀⠀⠀⢰⠾⣯⠽⢿⣿⣿⣿⣿⣿⠿⠿⠿⣻⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠁⣸⣿⣿⣿⣷⠁⠀⠋⠀⠀⠈⡌⠉⣭⡜⠀⠈⢾⣿⣍⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣋⡉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠨⠀⠀⠀⠀⠘⣟⠛⠛⠋⠙⠋⠚⢻⣿⣿⣿⣿⣿⣿⡟⣻⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡧⠒⢻⠥⡀⠀⠀⠀⣿⣿⣿⣟⠀⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣷⣿⣿⡇⣰⡟⠁⢀⢀⣀⣿⣿⣋⡀⢩⠓
⠀⠀⡇⠀⠀⠀⢰⡃⣀⠀⡔⣦⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣽⣿⠀⠀⢰⠂⠁⠀⠀⣀⣼⡃⣿⠀⣯⢀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣶⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣻⣿⣟⣿⣷⣚⣏⣋⠙⠂
⠀⠀⢢⠀⠀⠀⠀⠁⢻⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠊⠀⢀⣴⣿⣿⣿⡇⣿⠇⣿⣶⣆⠀⠀⠀⠰⢋⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠉⠙⠛⠙⢿⣿⣿⣿⣶⣄⣰⣶⡤⠘⠛⠛⠛⠛⢛⣟⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⣿⠟⢀⢿⣿⢿⠣⡄⠀⣀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠤⠤⢀⣜⡋⠀⠉⢭⣍⣩⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣷⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⣾⣾⣿⢶⣿⠖⠁⢠⣿⣿⣿⣿⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠺⢿⣦⣄⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡖⣉⠝⠁⠀⠀⣼⣿⣿⣿⡏⠀⠀⠀⣿⣿⡟⠿⠙⠏⠙⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠟⡿⠀⠀⠁⠀⠀⠀⢰⣿⠛⢿⣿⡇⠀⠀⠀⠋⠀⠀⠀⠀⠀⠆⠀⠘⢋⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢇⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣿⠀⠀⠀⠀⠀⠠⣿⢻⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠉⢻⣧⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡟⠻⡆⠀⠀⠀⡀⠀⠙⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⢫⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠀⠃⣀⡈⢍⣁⣜⣁⣀⣤⣤⣴⣶⣾⣿⡟⠁⠀⠀⠀⣠⢤⡤⠔⠀⡀⠰⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣾⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣧⣿⣿⡧⠀⣿⡇⠈⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣼⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠠⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠀⢸⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡇⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣛⣼⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠿⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠈⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣋⣹⢙⣙⣯⣭⡠⡤⠅⠀⠤⠀⢨⣍⡋⢃⣈⣀⣉⣁⣿⠀⠀⠀⠀⢸⣿⣿⣷⠀⣤⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣛⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⡠⠀⠀⠀⠀⢰⡾⣯⠽⢿⡿⣿⣻⣿⣿⠿⠿⠿⣻⣿⠛⢿⣿⣿⣿⣿⠀⢼⣿⠁⣸⣿⣿⣿⠷⠁⠰⠇⠀⠀⢋⡛⠋⣽⢰⠀⠈⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣋⡉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠈⠀⠀⠀⠀⠘⣾⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣻⡯⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡷⠒⡫⢅⠀⠀⠀⢰⣷⣾⣿⣞⠀⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢿⣿⣿⣽⣿⣾⣿⣿⡇⣰⡟⠁⢀⢀⣀⣿⣿⣊⡀⢩⠓
⠀⠐⠀⠀⠀⠀⢰⡇⣀⠀⡔⣦⡀⠀⠉⣿⣿⣿⠯⢽⠯⣤⣿⣿⠀⠀⢰⠆⠁⠀⠀⢀⣼⠋⣿⠀⡇⢐⠀⡀⠀⠀⠿⣿⣿⣿⣷⣦⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣻⣿⣿⣿⣷⣞⣋⣋⠑⠂
⠀⠀⢃⠀⠀⠀⠀⠁⢻⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠊⠀⠀⣠⣾⣿⣿⡆⣿⠀⣿⣾⡀⠁⠀⠀⠴⢏⣿⣿⣿⣿⣿⣿⣶⡄⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠛⠛⠛⢛⣛⢻⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣷⠃⢠⣿⣿⣟⢦⡀⠀⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠤⠤⢀⣟⡋⠀⠉⢭⣍⣩⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⣴⣿⣿⣿⣿⠶⠁⢰⣾⣿⣿⣯⠀⠁⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠺⢿⣦⣄⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡍⢁⠖⠁⠀⠀⣽⣿⣿⣿⡏⠀⠀⠀⣿⣿⡯⡿⠛⠏⠑⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡟⠁⠁⠁⠀⠀⠀⢸⣿⠛⣿⣿⠁⠀⠀⠀⠏⠀⠀⠀⠀⠀⡆⠀⠸⢛⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣷⠀⠀⠀⠀⠀⢠⣿⢿⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠋⠉⠛⢻⣇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⢯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡟⢿⡄⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠰⠫⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠳⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⠃⣀⠩⠝⣒⣒⣋⣀⣤⣤⣴⣶⣾⣿⡟⠁⠀⠀⠀⢀⢤⣤⢖⠐⠀⠸⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠈⣿⡇⠀⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣼⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠀⢸⣿⢽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡇⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣛⣛⣻⣼⠛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠐⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠿⠛⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣋⣉⣉⣟⣋⣙⢙⣉⣯⣭⡥⡤⢅⠀⢤⠀⢨⣍⡋⢣⣈⣀⣉⣁⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⣤⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⢀⠀⠀⠀⠀⢰⠾⣯⠽⢿⠿⣿⣿⣿⣿⠿⠿⠟⢻⣿⠛⢿⣿⣿⣿⣿⠀⢾⣿⠀⣸⣿⣿⣿⡟⠋⢰⠃⠀⠀⢀⠛⣛⣹⢰⠂⠈⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⡉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠀⠀⠀⠀⠀⠘⣾⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣻⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡇⠒⣠⣀⠀⠀⠀⢸⣶⣾⣿⡴⠀⠀⢸⣿⡨⠁⠀⠀⣿⣿⡛⢿⣿⣿⣽⣿⣶⣿⣿⡇⣰⡟⠡⢀⢀⣀⣿⣿⣊⡀⢩⠓
⠀⠈⠂⠀⠀⠀⢰⡇⣀⠀⡔⣦⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣻⣿⠀⠀⢰⠖⠈⠀⠀⠀⣨⡝⡧⢻⡅⠠⠀⠀⠀⠘⢿⣿⣿⣿⣶⣦⣸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣿⣿⣟⣻⣷⣚⣋⣋⠑⠂
⠀⠀⠂⠀⠀⠀⠀⢉⢻⠇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⢀⣴⣾⣿⡀⣿⢰⣧⣼⡀⠇⠀⠀⢸⠟⣿⣿⣿⣿⣿⣿⣦⡄⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠛⠛⠛⠛⡛⣻⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣰⣿⣷⣾⠿⣷⠇⢸⣿⣿⣷⢄⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠤⠤⠀⣞⡋⠈⠉⢩⣍⣩⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣧⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⣠⣿⣾⣿⣷⡴⠃⢀⣾⣿⣿⣟⠀⠁⠀⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠺⢿⣦⣄⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣛⠛⡭⠋⠀⠀⣺⣿⣿⣿⡏⠀⠀⠀⣿⣿⡟⣿⠿⠟⠫⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠋⠊⠀⠀⠀⢠⣿⠟⣿⣿⠁⠀⠀⠀⡟⠈⠀⠀⠀⠀⡄⠀⠩⠛⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⣧⠀⠀⠀⠀⠀⢀⣾⢿⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠜⠛⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡀⠀⠀⠀⠀⠀⠻⠈⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⢿⠂⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠰⢪⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡙⠲⠴⣿⡿⠛⠳⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠪⣀⠓⢲⣤⣤⣾⣀⣤⣤⣴⣶⣾⣿⡿⠁⠀⠀⠀⢀⣀⣠⣔⠁⠀⠰⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡷⠘⣿⡇⠘⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠠⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠀⢸⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣷⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡇⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠉⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠓⠛⠃⠈⠛⠟⠋⠀⢙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣻⣼⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠐⠁⠀⠀⠀⠙⢻⣿⣿⣿⡿⠿⠛⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠐⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠀⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣋⣹⢙⣉⣯⣽⡤⡤⢅⠀⢠⠀⢈⣍⡋⢣⣈⣀⣉⣁⣿⠀⠀⠀⠀⠰⣿⣿⣇⠀⣠⣄⢸⣿⡓⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⡆⣶⡖⢶⡮⠭
⠀⠔⠀⠀⠀⠀⢰⠾⣯⡽⢿⠿⣿⣿⣿⡿⠿⠿⠟⢛⣿⠛⢿⣿⣿⣿⣿⠀⢼⣿⠁⣸⣿⣿⣿⣷⠏⢠⠆⠀⠀⢂⠛⢛⣹⢠⠂⠈⢾⣿⣍⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⠉⠉⠉⣧⣤⡄⢀⠭⢽
⠀⠈⠀⠀⠀⠀⠘⣾⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⣯⠡⢀⠈⠀⠀⠀⢸⣷⣶⣿⣨⠀⠀⢸⣿⡨⠀⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣶⣿⣿⡇⣰⡟⠡⢀⢀⣀⣿⣿⣋⡄⠩⠓
⠀⠀⠆⠀⠀⠀⢰⡇⣀⠀⡔⣦⡀⠀⠉⣿⣿⣿⠯⢽⠯⣤⣻⣿⠀⠀⢰⠖⠈⠀⠀⠀⢈⡩⣇⡆⡏⠉⠀⠀⠀⠀⢿⣿⣿⣿⣶⣦⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣻⣿⣛⣻⣳⣚⣋⣋⠙⠀
⠀⠀⠂⠀⠀⠀⠀⠑⢻⡇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠌⠀⠀⠀⣠⣴⣿⡇⣿⠀⣧⣀⡀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠛⠛⠛⠛⣛⢛⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⣾⣯⣭⣿⣇⡿⠀⣿⣿⣧⡀⠀⠀⠊⡡⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠤⠤⢀⣞⡋⠀⠉⢭⣭⣭⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣧⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡾⣽⣿⣿⣁⡟⠁⣠⣿⣿⣝⠈⠃⠀⢂⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣾⠿⠿⣛⡿⠋⠀⢀⣿⣿⣿⡟⠀⠀⠀⣹⣿⠟⢹⢿⡿⠟⠽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢧⣾⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⠿⠿⡤⠊⠀⠀⠀⣼⡟⣿⣿⡇⠀⠀⠀⡼⠁⠀⠀⠀⠀⡀⠀⢫⠟⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⢛⣻⢏⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢹⠀⠀⠀⠀⠀⠀⣰⣿⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠬⠛⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⣼⡇⠀⠀⠀⠀⠀⠹⡏⠀⠀⠈⠃⢀⡀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠈⢿⠆⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠠⢪⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠳⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣉⠳⢄⣀⣀⣠⣦⣤⣥⣴⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⣀⡬⡄⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡷⠐⣿⡇⠀⢰⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣼⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠀⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣷⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠓⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣛⣼⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠑⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢹⠉⠀⠀⠀⠙⢻⣿⣿⣿⡿⠿⠟⠻⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠈⠀⠀⠀⠀⠀⠏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣋⣩⢉⣉⣯⣭⡤⡤⢅⠀⠤⠀⢨⣍⡋⠣⣈⣀⣉⣡⣸⡀⠀⠀⠀⠀⣿⣿⣷⠀⢠⣄⢸⣿⡛⠒⠉⠀⣇⣈⣴⣤⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣷⣷⡆⣶⡖⢶⡾⠭
⠀⢠⠀⠀⠀⠀⢰⠾⣯⠽⢿⠿⣿⣿⣿⠿⠿⠿⠟⣻⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠁⣸⣿⣿⣿⣿⡿⠁⡴⠀⠀⠐⡚⢛⣛⡆⡄⠈⢻⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⠉⠉⠉⣧⣤⡄⢀⠭⢽
⠀⠈⠀⠀⠀⠀⠈⣾⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⣿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⣿⠙⡀⠀⠁⠀⠀⠀⣷⣶⣿⣇⠇⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠁⢀⢀⣀⣿⣿⣋⣄⠩⠓
⠀⠈⠀⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣹⣿⠀⠀⢰⠖⠈⠀⠀⠀⠈⣉⢽⢨⣼⠒⠀⠀⠀⠀⠹⣿⣿⣿⣶⣦⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣻⣿⣿⣻⣷⣚⣋⣋⠙⠂
⠀⠀⠃⠀⠀⠀⠀⠑⢻⠇⠑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌⠀⠀⠀⢀⣠⣾⣇⢸⡏⢸⡀⡄⠠⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣤⡀⠀⠈⠉⠙⠛⠑⢿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠛⠛⢛⠛⠛⢛⣛⣫⣤⠀
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣰⣿⡛⣿⣿⢸⡇⢸⣿⣷⡀⠀⠀⠀⠋⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠤⠤⠀⣜⡋⠀⠉⢭⣭⣭⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⢰⣯⣿⣿⡟⢱⡞⠀⣸⣿⣮⠌⠢⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⣿⣾⡿⠾⡿⠋⠀⢰⣿⣿⣿⠂⠀⠀⢸⣿⠿⢻⣿⣿⠛⡻⣟⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⢰⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⣧⣆⣠⠟⠀⠀⢀⣾⢿⣿⡟⠀⠀⠀⢸⠃⠀⠈⠀⠀⢀⠀⠘⠽⢿⣿⣷⣦⣦⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⢛⣻⢇⣿⣿⣿⣷⣶⣿
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠷⡏⠀⠈⠁⠀⠀⠀⣼⡇⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢛⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⣄⣷⠀⠀⠀⠀⠀⠰⡏⠃⠀⠘⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠁⠻⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⢪⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠳⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣹⠻⢄⣀⣀⣀⣠⣤⣥⣴⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⢀⣬⢅⠀⠀⡄⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠈⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡷⠨⣿⡿⠀⢰⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠚⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣷⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣿⣼⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠉⠿⠀⠀⠀⠙⠻⣿⣿⣿⡿⠿⠿⠿⠟⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣛⣉⣉⣟⣋⣹⢉⣙⣯⣽⣥⡤⢅⠀⠠⠀⢨⣍⡋⠣⣈⣀⣉⣁⣼⡇⠀⠀⠀⠀⢾⣿⣷⡀⢀⣄⢸⣿⡛⠒⠉⠀⣇⣈⣴⣤⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣷⣷⣆⣶⡖⢶⡾⠭
⠀⢄⠀⠀⠀⠀⢰⠾⣯⡽⢿⣿⣿⣿⣿⡿⠿⠿⠟⣻⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠁⣸⣿⣿⣿⣿⣿⠃⣠⠀⠀⠀⢑⠛⣛⡃⡀⠈⢿⣿⣍⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⠉⠉⠉⣧⣤⡄⢀⠭⢿
⠀⢀⡀⠀⠀⠀⠘⣿⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⣟⠝⢃⣀⠉⠀⠀⠀⢸⣦⣾⣟⡅⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠡⢀⢀⣀⣿⣿⣋⡄⠩⠓
⠀⠈⠀⠀⠀⠀⢰⡇⣀⠀⣔⣶⡀⠁⠉⣿⣿⣿⠯⢽⠯⣤⣿⣿⠀⠀⢰⠖⠈⠀⠀⠀⠈⢉⠝⡇⢩⠒⠂⠀⠀⠀⠸⣿⣿⣿⣷⣦⣸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣛⣿⣿⣻⣷⣚⣋⣋⠙⠂
⠀⠀⢇⠀⠀⠀⠀⢙⢻⡇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌⠀⠀⠀⠀⣠⣾⣯⠀⣗⠘⡆⠀⠀⡀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣤⣄⠀⠈⠉⠙⠛⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠛⠛⠛⠛⡛⢟⣛⣫⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⣾⡛⣿⣿⡄⣿⠀⣿⣿⡀⠀⠀⠀⠘⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠤⠤⠀⣝⡋⠀⠉⢭⣭⣭⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣷⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠⠀⢠⣏⣿⣿⡟⠛⣿⠃⢀⣿⣏⡋⠲⠀⠐⢄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠸⠿⣦⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣾⣾⡿⠾⣿⠞⠁⠀⣿⣿⣿⠇⠀⠀⢰⣿⠿⠻⣿⣿⠿⡻⢟⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⣧⣤⢈⡹⠋⠀⠀⣰⢿⣿⣿⠀⠀⠀⠈⠏⠀⠈⠀⠀⢀⠀⠘⡽⢿⣿⣿⣦⣴⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⢛⣻⢫⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣡⢾⠉⠁⠉⠀⠀⠀⢀⡏⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠛⠛⠻⣿⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢄⢸⡆⠀⠀⠀⠀⠀⡎⠃⠀⠈⠛⢀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⠃⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣘⠟⢇⣀⣀⣀⣠⣤⣥⣶⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⢀⣠⢍⢀⠀⡄⠉⢂⠀⠀⠀⠁⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣾⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡷⠀⣿⣿⠀⢰⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠠⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣛⣾⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⢭⡭⢽⣿⣿⣿⣿⡯
⠀⠈⠉⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⠹⠀⠀⠀⠈⠛⣿⣿⣿⡿⠿⠿⠿⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠘⠁⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣛⣉⣉⣟⣋⣹⢉⣉⣯⣽⡥⡤⢅⠀⠤⠀⢨⣝⡋⢣⣈⣀⣉⣡⣸⡇⠀⠀⠀⠀⢸⣿⣿⡆⠀⣄⢸⣿⡛⠒⠉⠀⣇⣈⣴⣤⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⡯⠭
⠀⢴⠀⠀⠀⠀⢰⠾⣯⡽⢿⣿⣿⣿⣿⣿⠿⠿⠿⣻⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠀⣸⣿⣿⣿⣿⣿⠃⢀⠄⠀⠀⢂⠛⢛⣹⠀⠈⢻⣿⣍⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⡉⠉⠉⣧⣴⡄⢀⠭⣿
⠀⢈⠀⠀⠀⠀⠘⣿⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣻⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡿⡩⠃⣀⡈⠀⠀⠀⠀⣷⣶⣿⡈⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠡⣀⢀⣀⣿⣿⣋⡄⢩⠓
⠀⠈⠁⠀⠀⠀⢰⡇⣀⠀⣔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠖⠈⠀⠀⠀⠈⢉⠍⡟⠉⡕⠒⠀⠀⠀⠀⣿⣿⣿⣷⣦⣸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣻⣟⣿⣻⣷⣞⣏⣋⠙⠂
⠀⠀⢣⠀⠀⠀⠀⢑⢻⡇⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌⠀⠀⠀⠀⣠⣶⣿⡀⢿⠂⣷⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠛⠛⢛⠛⡛⢛⣛⣫⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⣾⣛⣻⣿⡇⢸⠇⣿⣿⣄⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠤⠤⠀⣽⡋⠀⠉⢭⣭⣭⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⠀⣾⣹⣿⣿⠛⣷⠟⠀⣿⣧⡫⠑⠄⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣴⣿⡿⠷⢿⡶⠋⠀⣾⣿⣿⡷⠀⠀⠀⣿⡿⠟⣿⣿⡿⢻⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⣯⣤⠈⣩⠏⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⡟⠀⠀⠁⠀⢀⠀⠈⡻⢿⣻⣿⣶⣤⡄⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣁⢼⡉⠉⠈⠁⠀⠀⠀⣾⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠛⠛⠿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢥⡈⣧⠀⠀⠀⠀⠀⣰⠋⠀⠀⠛⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢰⢯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⠷⢿⣀⣀⣀⣠⣤⣼⣴⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⢀⣀⢍⢀⠀⡄⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⣿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡷⠀⣿⣿⠀⢴⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣟⣼⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⢁⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁⠇⠀⠀⠀⠉⠻⣿⣿⡿⠿⠛⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠉⠉⠛⣒⡶
⠘⠀⠀⠀⠀⠀⠏⠉⢉⣉⣉⣙⣛⣉⣉⣟⣋⣹⢙⣙⣯⣭⡡⠤⢅⠀⠤⠀⢨⣝⠋⠣⣈⣄⣉⣡⣀⣽⠀⠀⠀⠀⠀⠾⣿⣿⡀⢀⢸⣿⡓⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⡮⠭
⠀⣖⠀⠀⠀⠀⢰⡾⣯⡽⢿⢿⣿⣿⣿⣿⠿⠿⠟⢻⣿⠛⢿⣿⣿⣿⣿⠀⢼⣿⠀⣸⣿⣿⣿⣿⣿⡟⠀⡴⠀⠀⠐⡘⠛⣉⡇⡌⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⡉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⢨⠀⠀⠀⠀⠈⣿⠛⠛⠛⠙⠋⠚⢻⣿⣿⣿⣿⣿⣿⡟⣻⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡿⢩⣉⣠⠄⠁⠀⠀⠀⣸⣶⣾⣧⠁⢸⣿⡨⠁⠀⠀⣿⣿⡋⢿⣿⣿⣽⣿⣷⣿⣿⡇⣰⡟⠁⣀⢀⣀⣿⣿⣋⡄⢩⠓
⠀⠈⡆⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠖⠉⠀⠀⠀⠈⢉⡩⢺⢠⢰⠉⠁⠀⠀⠀⢰⣿⣿⣿⣶⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⡛⠛⠯⠽⠿⣿⢟⣻⣿⣟⣻⣷⣞⣏⣋⠙⠂
⠀⠀⢇⠀⠀⠀⠀⢑⢻⡇⠙⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌⠀⠀⠀⠀⣀⣴⣿⣇⢸⡏⢸⡄⡀⠀⡄⠀⢀⣾⣿⣿⣿⣿⣿⣦⣤⡀⠈⠉⠙⠛⠙⢿⣿⣿⣿⣶⣄⣰⣶⡤⠈⠙⠛⠛⣛⡻⢻⣛⣧⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⣴⣟⣻⣿⣿⢸⡇⢸⣿⣧⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠤⠤⠀⣜⡋⠀⠉⢭⣭⣩⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣷⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⠀⢾⣭⡿⣿⡟⢻⠟⠀⣸⣿⣙⠌⠂⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣴⣷⣾⡿⠿⡷⠋⠀⣼⣿⣿⣿⠆⠀⠀⢸⣿⡿⢻⣿⡿⢟⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿⣶⣀⣨⠋⠀⠀⢀⣾⣿⣿⡟⠀⠀⠀⢸⠃⠀⠈⠀⠀⡄⠀⢙⠿⣟⣿⣷⣤⣄⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣡⠾⡇⠀⠈⠁⠀⠀⠀⣸⠇⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⢿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠳⡄⣷⠀⠀⠀⠀⠀⢸⠙⠀⠀⠙⢃⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⠪⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⡟⢻⣀⣀⣀⣠⣤⣼⣶⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡄⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣾⣿⡷⠀⣿⡇⠀⢱⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠉⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣻⣛⣿⣾⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠈⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠍⢽⣿⣿⣿⣿⡯
⠀⠩⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣻⣟
⢀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠉⠻⠀⠀⠀⠈⠙⣿⣿⡿⠻⠟⠟⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠐⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠈⠁⠀⠀⠀⠀⠏⠉⢉⣉⣉⣙⣛⣉⣉⣟⣋⣹⢛⣙⣯⣭⡡⡤⡅⠀⠤⠀⢨⣍⠋⠣⣈⣀⣉⣁⣀⣨⡇⠀⠀⠀⠀⠰⢿⣿⡆⠀⢸⣿⡓⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⣼⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣿⣿⣿⠿⠿⠿⣿⣿⠻⢿⣿⣿⣿⣿⠀⢼⣿⠀⣸⣿⣿⣿⣷⣿⣿⠃⢠⠆⠀⠀⢂⠛⢋⣽⠀⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⡉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠸⠀⠀⠀⠀⠈⣿⠛⠛⠛⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣻⡯⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡿⠉⡝⣡⠤⠈⠀⠀⠀⢸⣷⣶⣿⡈⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣷⣿⣿⡇⣰⡟⠡⣀⢀⣀⣿⣿⣋⡄⢩⠓
⠀⠈⠄⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠖⠉⠀⠀⠀⠈⠉⣩⠜⡇⢶⠊⠁⠀⠀⠀⠠⣿⣿⣿⣶⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⡛⠛⠯⠽⠿⣿⢟⣛⣿⣟⣻⣷⣞⣏⣋⠑⠂
⠀⠀⢂⠀⠀⠀⠀⢙⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⢀⣴⣾⣿⠈⣏⢸⡆⠃⠀⢀⠀⠀⣴⣿⣿⣿⣿⣿⣤⣄⡀⠈⠉⠙⠛⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠈⠛⠛⠛⠛⣛⢻⣛⣧⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣴⣿⣻⣿⣿⢰⡟⢸⣿⣿⣄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠤⠤⠠⣜⡋⠀⠉⢩⣍⣩⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠀⢸⣯⣿⢿⡟⢹⠟⠁⣘⣿⣉⡏⠢⠀⠀⢄⣼⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠺⢿⣦⣄⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣰⣷⢶⡿⠿⡿⠋⠀⣸⣿⣿⣿⠇⠀⠀⢰⣿⣿⠿⣿⣿⠿⣻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⣶⣂⡠⠋⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⢸⠏⠁⠈⠉⠉⠀⠀⠙⣻⢿⣻⣷⣤⣤⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡥⠞⡇⠀⠀⠀⠀⠀⠀⣼⡇⠘⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠱⡄⣷⠀⠀⠀⠀⠀⣸⠛⠁⠀⠘⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢹⡷⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⠮⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠿⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠟⢻⣀⣀⣀⣠⣤⣼⣶⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠈⢂⡀⠀⠀⠀⠁⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠈⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣾⣿⡧⠈⣿⡇⠀⢰⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣷⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠉⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣿⣛⣟⣾⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠓⠂⠈⠉⠉⠈⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠍⢽⣿⣿⣿⣿⡯
⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⠟⠋⠿⠀⠀⠀⠙⢻⣿⡟⠿⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⡿⣿⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠈⠀⠀⠀⠀⠀⠏⠉⢉⣉⣉⣙⣛⣉⣉⣟⣋⣹⢙⣙⣯⣭⡡⠤⢅⠠⠤⠀⢨⣍⡋⠃⣈⣀⣉⣁⣀⣀⣸⡇⠀⠀⠀⠀⣾⣿⣷⡀⢈⣿⡓⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣘⣛⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⢴⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣿⣿⣿⠿⠿⠟⢛⣻⠛⢿⣿⣿⣿⣿⠀⢼⣿⠀⣸⣿⣿⣿⣷⣿⣿⣿⠃⣠⠀⠀⠀⢐⠛⣋⡃⢸⣿⣄⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣋⡉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⢈⠀⠀⠀⠀⠈⣿⠛⠛⠛⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡟⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡿⠉⡩⠙⣁⡀⠋⠀⠀⠀⢸⣦⣾⣗⣻⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣷⣿⣿⡇⣰⡟⠁⡀⢀⣀⣿⣿⣋⡄⢩⠓
⠀⠈⠄⠀⠀⠀⢰⡇⣀⠀⡔⣦⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣻⣿⠀⠀⢰⠖⠉⠀⠀⠀⠈⠉⢉⡠⣽⡉⡔⠒⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⡛⠛⠯⠽⠿⣿⢟⣻⣻⣟⣿⣷⣞⣏⣛⠙⠂
⠀⠀⢆⠀⠀⠀⠀⢙⢻⡇⠑⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌⠀⠀⠀⠀⠀⣠⣶⣿⡀⣿⠁⣇⢠⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣤⣀⡀⠈⠉⠙⠛⠙⢿⣿⣿⣿⣶⣄⣰⣶⡤⠈⠙⠛⠛⡛⠻⢛⣛⣫⣤⠀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣠⣾⣛⣻⣿⠇⣿⠁⣿⣶⢆⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⡄⠀⠤⠤⢀⣜⡋⠀⠉⢩⣍⣩⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣷⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠀⠰⣯⣽⢿⣟⠋⡾⠃⠀⣿⡇⢻⠑⠄⠀⢄⢀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠺⢿⣦⣄⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⣾⣶⡿⠶⣿⠞⠁⢰⣿⣿⣿⡷⠀⠀⠀⣶⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⣦⣂⣈⠝⠁⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⡿⠛⠀⠋⠋⠁⠈⠙⢿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡥⠞⡇⠀⠀⠁⠀⠀⠀⣸⡟⠘⢿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠿⠿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⢯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠱⡄⣷⠀⠀⠀⠀⠀⢰⡇⠇⠀⠘⢿⡂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣱⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⠮⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠿⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠟⢻⣀⣀⣀⣠⣤⣼⣷⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⡀⠈⢀⡀⠀⠀⠀⠙⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣾⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣾⣿⡶⠉⣿⡇⠀⢰⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠉⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣿⣾⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠓⠂⠈⠉⠉⠈⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠉⠩⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠿⠻⣏⠉⠉⠙⠿⣿⡿⠿⠟⠻⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⠈⣻⠃⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠉⠉⠛⣒⡶
⠈⠀⠀⠀⠀⠀⠏⠉⢉⣉⣉⣙⣛⣉⣉⣟⣋⣹⢙⣙⣯⣭⣡⣤⢅⠀⢤⠀⢨⣍⠋⠣⣨⣤⣭⣥⣤⣤⣤⣿⠀⠀⠀⠀⠀⣶⣶⣦⠀⢸⡛⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣷⣷⡆⣶⡖⢶⡾⠭
⠀⡦⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣿⣿⡿⠿⠿⠻⣻⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠀⣹⣿⣿⣿⣷⣿⣿⣿⡿⠀⣠⠀⠀⠠⠹⠿⠛⠄⣾⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⡉⠉⠉⣧⣴⡄⢀⠭⢿
⠀⢀⠀⠀⠀⠀⠈⣟⠛⠛⠛⠙⠋⠚⢻⣿⣿⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⠸⡿⣿⣿⡿⠉⠉⢋⠿⠁⠘⠇⠀⠀⠀⢹⣤⣽⡇⣿⡨⠁⠀⠀⣿⣿⡋⢿⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠁⣀⣀⣀⣿⣿⣋⣄⠩⠓
⠀⠈⠆⠀⠀⠀⢰⡃⣀⠀⣔⣶⡄⠁⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠖⠉⠀⠀⠀⠈⠉⠉⣀⠨⡗⡚⡭⢄⠀⠀⠀⠀⢨⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣻⣛⣛⣻⣷⣞⣯⣋⠙⠀
⠀⠀⢂⠀⠀⠀⠀⢁⢻⡇⠙⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌⠀⠀⠀⠀⠀⢀⣶⣿⡇⢰⡧⢻⡄⡀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣤⣀⡀⠈⠉⠙⠋⠉⢿⣿⣿⣿⣶⣄⣰⣶⡤⠈⠙⠛⢛⠛⡛⢛⣛⣧⣤⠀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⣼⣟⣳⣿⣿⢸⡷⢸⣷⣧⠀⠀⠀⠀⠰⢻⣿⣿⣿⣿⣿⣿⡄⠀⠤⠤⢀⣜⡋⠀⠈⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠⠀⠀⠀⣾⣸⡿⡿⠟⢫⡾⠃⢸⣿⠫⡗⢄⠀⢀⠐⣹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⢿⣦⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣴⣯⠽⢧⣼⣦⠞⠀⣠⣿⣿⣷⡀⠀⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⣭⡄⠈⣱⠞⠁⠀⢀⣿⣿⣿⡇⠀⠀⠀⢸⢿⠏⠜⠛⠃⠘⠙⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣁⡴⣿⠉⠁⠈⠁⠀⠀⠀⣾⠉⢿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⣧⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠻⣄⣿⠀⠀⠀⠀⠀⢀⡞⠋⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣣⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⢪⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠿⢻⣀⣀⣀⣤⣤⣼⣷⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠈⢂⠀⠀⠀⠀⠙⠀⠀⠀⢀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠈⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣾⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣾⣿⡾⠁⣿⡇⢀⢰⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣛⣛⣟⣾⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡿⠿⢿⠉⠛⠛⠿⣿⡿⠿⠿⠻⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⣿⠈⢛⡏⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠉⠉⠛⣒⡶
⠈⠀⠀⠀⠀⠀⠏⠉⢉⣉⣉⣙⣛⣉⣙⣟⣋⣹⢛⣙⣯⣽⡡⡤⢅⠀⠤⠀⢨⣍⠋⠣⣈⣀⣍⣡⣠⣄⣤⣾⡇⠀⠀⠀⠀⢠⣤⣤⡀⠈⡛⠒⠉⠀⣇⣈⣴⣤⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⡆⣶⡖⢶⡾⠭
⠀⢦⠀⠀⠀⠀⢰⠾⣯⡽⢿⢿⣿⣿⣿⣿⠿⠿⠿⢻⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠀⣸⣿⣿⣿⣷⣿⣿⣿⣿⠇⠀⡀⠀⠀⠸⣿⡿⠇⢸⣭⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⡉⠉⠉⣧⣴⡄⢀⠭⢽
⠀⢐⠀⠀⠀⠀⠀⣿⠛⠛⠛⠙⠋⠚⢻⣿⣿⣿⣿⣿⣿⡟⣿⣿⠉⠀⠉⠀⠈⠀⠸⡿⣿⣿⡿⠉⠉⢋⣿⣋⡀⠚⠀⠀⠀⠀⣄⣐⣆⣿⡨⠁⠀⠀⣿⣿⡋⢿⣿⣿⣽⣿⣷⣿⣿⡇⣰⡟⠡⢀⢀⣀⣿⣿⣋⣄⠩⠓
⠀⠈⠄⠀⠀⠀⢰⡇⣀⠀⣔⣶⡄⠁⠉⣿⣿⣿⠿⢽⠯⣤⣹⣿⠀⠀⢠⠖⠈⠀⠀⠀⠈⠉⠉⣀⠤⢹⡤⠶⣓⡀⠀⠀⠀⠀⣻⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣛⣛⣛⣿⣳⣞⣏⣋⠙⠀
⠀⠀⢎⠀⠀⠀⠀⠙⢻⡇⠑⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌⠀⠀⠀⠀⠀⣠⣶⣿⣿⠀⣼⡀⢸⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣦⣄⡀⠈⠉⠙⠋⠁⢿⣿⣿⣿⣶⣄⣰⣶⡤⠈⠛⠛⠛⠛⡛⢻⣛⣯⣤⠀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⣴⠟⠷⣿⣿⠀⣿⡆⣸⣦⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠤⠤⢀⣜⡋⠀⠈⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠⠀⠀⠀⣾⠙⠿⡿⣿⣿⣀⡿⠀⣿⠟⡗⢄⠀⢀⠐⣹⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠈⠀⢀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣠⣯⡉⢄⣸⣆⣸⠏⠀⣠⣿⣷⡄⠀⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿
⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⣋⡁⠀⠐⠞⠉⠀⠀⢸⣿⣿⣷⠁⠀⠀⢸⢿⠃⠟⠛⠃⠉⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣿⣿⣿⣷⣶⣿
⠀⠀⢿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠁⣀⢼⡟⠉⠀⠊⠀⠀⠀⢠⠟⢿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠸⠿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢛⢯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠘⢅⠸⡧⠀⠀⠀⠀⠀⠀⠚⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⡸⢿⣗⣀⣀⣀⣤⣤⣶⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⡄⡀⢀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣾⣿⣿⠉⣿⡇⢸⢰⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠠⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠉⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣿⣛⣿⣾⡛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⢉⠉⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⠋⠉⠋⠀⠀⠀⠙⢻⣿⡿⠿⠿⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⢀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣟⠿⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠟⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠈⠂⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣋⣉⣉⣟⣋⣙⢙⣙⣯⣭⡠⡤⢅⠀⠤⠀⢨⣍⠋⠣⣌⣄⣍⣡⣀⣨⣿⠇⠀⠀⠀⠀⣼⣿⣷⠀⢨⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⡮⠭
⠀⢤⠀⠀⠀⠀⢰⠾⣯⠽⢿⢾⣿⣿⣿⣿⠿⠿⠿⢻⣿⠛⢿⣿⣿⣿⣿⠀⢼⣿⠀⣸⣿⣿⣿⣷⣿⣿⡟⠀⣠⠀⠀⠀⢃⠛⢛⡁⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⡉⠉⠉⣧⣴⡄⢀⠭⣿
⠀⢈⡀⠀⠀⠀⠘⣿⠛⠛⠛⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡟⠉⢉⠟⢀⣀⠁⠀⠀⠀⢸⣶⣶⣇⢸⣿⡨⠀⠀⠀⣿⣿⡋⢿⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠁⢀⢀⣀⣿⣿⣋⣄⢩⠓
⠀⠈⠀⠀⠀⠀⢰⡇⣀⠀⣔⣶⡀⠁⠉⣿⣿⣿⠿⢽⠯⣤⣽⡿⠀⠀⢰⠖⠉⠀⠀⠀⠀⠉⣩⠔⢻⠃⢹⠖⠂⠀⠀⠀⢨⣿⣿⣷⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣛⣻⣛⣻⣳⣞⣏⣋⠙⠀
⠀⠀⢆⠀⠀⠀⠀⢙⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌⠀⠀⠀⠀⢀⣶⣿⣷⡂⣾⡆⢸⡀⠁⠀⠀⠀⠀⣤⣿⣿⣿⣿⣶⣤⡀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣶⡤⠈⠛⠛⠛⢛⡛⢛⣛⣧⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⣴⣟⣛⣿⣿⡇⣸⡇⢸⣷⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠤⠤⢀⣝⡋⠀⠈⢩⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢼⣇⠿⢿⡿⠿⣿⠟⠀⢸⡏⡏⠢⠀⠠⢄⣸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠺⢿⣦⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⣾⡭⠱⢶⣿⡴⠋⠀⣴⣿⣿⠇⠀⠀⢰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿
⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⣅⡄⠉⡹⠋⠀⠀⢠⣿⣿⣿⠂⠀⠀⢈⠏⠇⠘⠀⠀⠀⠀⢻⠿⣟⣿⣷⣤⣄⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⢛⣻⢏⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢃⡴⣿⠉⠁⠈⠀⠀⠀⢀⡏⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⢿⣿⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⢛⢧⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠻⣄⢻⡆⠀⠀⠀⠀⠀⠘⠁⠀⠘⢛⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⢯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠹⢿⣇⣀⣀⣤⣤⣤⣶⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⣀⣴⠃⠀⢠⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠂⠒⠂⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣾⣿⡿⠸⣿⡇⠀⢸⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡇⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣟⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣹⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣻⣛⣿⣾⠛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠁⠀⠛⠀⠀⠀⠈⠹⣿⣿⡿⠿⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⢀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⢿⣿⡇⠀⠀⠀⠀⢀⣀⡀⠀⠸⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠈⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣛⣉⣉⣟⣋⣹⢙⣙⣯⣽⡡⠤⢅⠀⢤⠀⢨⣍⠋⠣⣬⣄⣍⣡⣠⣿⡇⠀⠀⠀⠀⠻⣿⣿⡆⣀⢸⣿⡛⠘⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣼⣻⣀⣸⣷⣷⡆⣶⡖⢶⡾⠯
⠀⢤⠀⠀⠀⠀⢰⠾⣿⠽⢿⣾⣿⣿⣿⡿⠿⠿⠿⢻⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠀⣸⣿⣿⣿⣷⣿⡿⠀⡴⠀⠀⠀⠡⠉⢁⡄⠈⢿⣿⣍⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢛⣉⠉⠉⠉⣧⣴⡄⢀⠭⢿
⠀⢀⠀⠀⠀⠀⠘⣾⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⠸⡿⣿⣿⡟⢡⣋⣨⠤⠄⠀⠀⠀⠰⢿⣿⣿⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣷⣿⣿⡇⣸⡟⠁⣀⣀⣀⣿⣿⣋⣄⠩⠓
⠀⠘⠄⠀⠀⠀⢰⡃⣀⠀⣔⣶⡀⠀⠉⣿⣿⣿⠯⢽⠯⣤⣻⡿⠀⠀⢰⠖⠉⠀⠀⠀⠀⣩⠝⢹⡇⢰⠋⠉⠀⠀⠀⠐⠻⢿⣿⣶⣼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⢿⢟⣛⣛⣛⣻⣷⣞⣏⣋⠙⠂
⠀⠀⢆⠀⠀⠀⠀⢙⢻⡇⠙⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⢀⣴⣿⣿⡆⢸⡇⢸⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣦⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠈⠙⠛⢛⠛⠛⢛⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣰⢿⣉⣻⣿⣷⣸⡏⢸⣿⣧⡀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠤⠤⢀⣼⡋⠀⠈⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠰⣯⣸⠿⣿⠛⣿⠏⠀⣸⣯⡙⠈⠂⠀⢒⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⣾⠶⢜⣷⣿⠿⠋⠀⣼⣿⣿⡿⠀⠀⠀⣿⣿⡿⣿⣿⡟⠻⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⣷⣆⢀⡼⠃⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠼⠛⠀⠁⠀⠀⠀⠈⡿⠿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⢛⣻⢇⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡷⢻⠅⠀⠈⠀⠀⠀⢀⣿⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠛⠛⠿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⢛⢯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⢳⣸⡇⠀⠀⠀⠀⠀⣾⠈⠀⠀⠙⢁⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠘⢶⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⢯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠿⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⠛⢷⣀⣀⣀⣠⣤⣯⣶⣶⣾⣿⡟⠁⠀⠀⠀⠀⢀⣠⡶⠃⠀⢠⢈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠂⠒⠂⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣾⣿⡯⠀⣿⡇⠈⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣴⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠠⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣤⣄
⡀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣛⣛⣟⣾⡛⠃⠛⠃⠺⣿⠿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠉⠀⠀⠀⠀⠈⢿⣿⣿⡿⠿⠟⠻⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⢀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⢠⣤⣤⠀⠀⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠈⠁⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣛⣉⣉⣟⣋⣹⢛⣙⣯⣭⣡⡤⢅⠀⢤⠀⢨⣍⡋⢣⣈⣀⣍⣡⣸⡇⠀⠀⠀⠀⠈⠿⠿⠇⢠⣄⢸⣿⡓⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⡆⣶⡖⢶⡮⠭
⠀⢤⠀⠀⠀⠀⢰⠾⣿⠽⢿⢾⣿⣿⣿⣿⠿⠿⠿⢻⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠀⣸⣿⣿⣿⣿⣿⠁⢾⠁⠀⠀⠐⣄⣨⣧⠀⠈⢿⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⣉⠉⠉⣧⣴⡄⢀⠭⢽
⠀⢐⠀⠀⠀⠀⠘⣿⠛⠛⠛⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⣿⡧⠴⣢⣄⠀⠀⠀⠀⣻⣿⣿⠆⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠁⣀⢀⣀⣿⣿⣋⣄⠩⠓
⠀⠈⠀⠀⠀⠀⢰⡇⣀⠀⣔⣶⡄⠀⠉⣿⣿⣿⠿⢽⠯⣤⣹⣿⠀⠀⢰⠖⠉⠀⠀⠀⢈⡍⢹⣇⢻⡀⠀⠀⠀⠀⠈⠙⣻⣿⣷⣦⣸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢿⣻⣻⣛⣻⣷⣞⣯⣋⠙⠀
⠀⠀⢖⠀⠀⠀⠀⢙⢻⡇⠑⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⣠⣾⣿⣷⢸⣧⢠⣧⣄⠀⠀⠀⠀⠸⢻⣿⣿⣿⣿⣿⣶⣄⠀⠈⠉⠙⠛⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠈⠙⠛⠛⠛⣛⢛⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡾⣯⣽⣿⣿⣼⡏⢸⣿⣿⣦⠀⠀⠀⠠⢺⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠤⠤⢀⣜⡋⠀⠈⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⡺⢧⣿⢿⡏⣽⠏⢀⣼⣿⣯⡃⠙⠀⢈⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠈⠀⢀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣼⡿⠿⢟⣻⠟⠁⠀⣼⣿⣿⣿⠃⠀⠀⢸⣿⣿⢿⡿⣿⠛⠽⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢑⡾⠶⢤⡔⠁⠀⠀⢰⣿⢿⣿⡟⠀⠀⠀⠠⠏⠙⠈⠀⠀⠀⠀⠘⠽⢻⣿⣿⣶⣴⡄⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢇⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⡇⠀⠀⠀⠀⠀⢀⣾⡇⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⡄⣿⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠘⠾⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⠺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣏⠙⢄⣀⣀⣀⣤⣤⣥⣴⣶⣾⣿⡿⠁⠀⠀⠀⠀⢀⣠⡾⠃⠀⢀⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣾⣿⡿⠀⣿⡇⠈⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣤⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⡟⢛⣛⣾⡛⠃⠛⠃⠺⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠉⠍⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠉⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠉⠁⠀⠀⠀⠀⠻⣿⣿⣿⡿⠿⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⢠⣶⣶⡄⠀⠿⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡷
⠘⠃⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣛⣉⣙⣟⣋⣹⢙⣙⣯⣭⡠⡤⢅⠠⢤⠀⢨⣍⡋⠣⢈⣄⣍⣩⡧⠀⠀⠀⠀⠀⠹⠿⠳⢀⣤⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⡦⠀⠀⠀⠀⢰⠾⣿⠽⢿⢾⣿⣻⣿⣿⠿⠿⠿⢻⣿⠛⢿⣿⣿⣿⣿⠀⢺⣿⠀⣸⣿⣿⣿⡿⠃⠰⠃⠀⠀⠀⣧⣬⣽⢤⠂⠈⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⡉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⢘⠀⠀⠀⠀⠘⣿⠛⠛⠋⠙⠋⠚⢻⣿⣿⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⣿⢐⢋⠥⠀⠀⠀⠀⣿⣿⣿⡷⠀⠀⢸⣿⡨⠀⠀⠀⣿⣿⡋⢻⣿⣿⣿⣿⣷⣿⣿⡇⣰⡟⠁⢀⢀⣀⣿⣿⣋⡀⢩⠓
⠀⠘⠀⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣹⡿⠀⠀⢰⠖⠉⠀⠀⠀⣨⠝⣿⠌⣇⠐⠀⠀⠀⠀⢉⣽⣿⣿⣶⣄⣸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣻⣻⣿⣻⣓⣚⣏⣛⠑⠂
⠀⠀⢢⠀⠀⠀⠀⢁⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⢀⣤⣾⣿⡆⣿⠄⣿⣴⡀⠀⠂⠀⠘⠟⣿⣿⣿⣿⣿⣿⣶⡄⠀⠈⠉⠙⠛⠙⢿⣿⣿⣿⣶⣄⣰⣶⡤⠈⠛⠛⠛⠛⡛⢿⣛⣧⣄⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣰⢿⣭⣽⣿⣧⡟⠀⣿⣿⣷⢄⠀⠀⠀⠔⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠤⠤⢀⣜⡋⠀⠉⢩⣍⣩⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⢐⡿⣼⣿⣿⣩⠏⠀⣼⣿⣿⣟⠈⠁⠀⣙⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣿⠿⠿⣟⠟⠁⠀⢨⣿⣿⣿⡟⠀⠀⠀⢻⣿⡿⣻⠿⡿⠛⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⠿⠟⡴⠋⠀⠀⠀⣿⡿⣿⣿⠁⠀⠀⠀⢸⠋⠃⠈⠀⠀⠀⠀⠉⠟⣻⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢃⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⢷⠀⠀⠀⠀⠀⠀⣰⣿⠁⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠛⠛⠻⣿⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⣼⡇⠀⠀⠀⠀⠐⣿⠈⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠙⡟⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠠⠪⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣉⠳⢀⣀⣀⣠⣦⣤⣤⣶⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⣠⠼⠀⠀⢀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⠈⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠀⢹⣿⢽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡇⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠉⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣀
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣟⣾⠛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⢭⠭⢽⣿⣿⣿⣿⡯
⠀⠙⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠘⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠻⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠐⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⡄⠀⠸⠿⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡶
⠘⠁⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣋⣉⣙⣟⣋⣹⢙⣙⣯⣭⡡⣤⣅⡀⢤⠀⢨⣍⡋⠣⣌⣀⣍⣿⠀⠀⠀⠀⠀⠩⠿⠿⠀⣴⣤⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⡮⠭
⠀⠤⠀⠀⠀⠀⢰⠾⣯⠽⢿⢾⣿⣻⣿⣿⠿⠿⠻⢻⣿⠻⢿⣿⣿⣿⣿⠀⢸⣿⠀⣸⣿⣿⣿⡏⠀⡌⠀⠀⠀⢱⣀⣭⡇⡴⠂⠈⢾⣿⣍⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⠉⠉⠉⣧⣤⡄⢀⠭⢿
⠀⠈⠀⠀⠀⠀⠘⣿⠛⠛⠋⠙⠋⠛⢻⣿⣻⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡅⠴⢒⣀⠀⠀⠀⢘⣿⣿⡷⠂⠀⠀⢸⣿⡨⠀⠀⠀⣿⣿⡋⢻⣿⣿⣿⣿⣷⣿⣿⡇⣸⡟⠡⣀⢀⣀⣿⣿⣋⣄⢩⠓
⠀⠘⠄⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⡿⠀⠀⢰⠂⠁⠀⠀⠀⡨⢹⣅⢦⠁⠀⠀⠀⠀⠈⠛⣿⣿⣷⣶⠂⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⡛⠛⠯⠽⠿⣿⢟⣛⣻⣛⣻⣷⣞⣏⣋⠙⠀
⠀⠀⠇⠀⠀⠀⠀⢉⢻⡇⠙⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠊⠀⠀⢀⣴⣾⣇⠸⣏⢨⣧⡄⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠈⠙⠛⡛⠛⠛⢛⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣛⣿⣿⣰⡇⢸⣿⣿⣄⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠤⠤⢀⣝⡋⠀⠈⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢰⣏⣿⢿⡟⢹⠏⢀⣼⣿⣿⠇⠑⠀⠐⣢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣾⣶⣿⢿⡿⠁⠀⢸⣿⣿⣿⠃⠀⠀⠈⣿⣿⢟⡿⣿⠟⡻⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣆⡤⠋⠀⠀⠀⣿⢿⣿⡟⠀⠀⠀⠠⡟⠙⠀⠁⠀⠀⠀⠀⡽⢻⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⢛⣻⢇⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⡇⠀⠈⠀⠀⠀⠀⣼⣿⠈⢻⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢛⢯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣄⣷⠀⠀⠀⠀⠀⠠⣿⠃⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠠⢫⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠷⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⢸⣛⠶⢀⣀⣀⣠⣤⣥⣤⣶⣶⣾⣿⡟⠁⠀⠀⠀⠀⢀⣠⠎⠀⠀⢁⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⠈⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠠⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣤⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣹⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣿⣛⣿⣼⠛⠃⠛⠃⠸⣿⠿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠂⠈⠉⠉⠀⠿⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⢭⠭⠍⢽⣿⣿⣿⣿⡯
⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠙⠓⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠻⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⡀⠀⠽⠿⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠉⠉⠛⣒⡶
⠀⠀⠀⠀⠀⠀⠏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣛⣹⢛⣙⣯⣭⣡⢤⠅⠠⢤⠀⢨⣉⠋⠣⣌⣄⣝⣿⠀⠀⠀⠀⢀⠩⠿⠿⠀⣴⣤⣄⢸⣿⡛⠐⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⡆⣶⡖⢶⡮⠭
⠀⠀⠀⠀⠀⠀⢰⠾⣿⡽⢿⠿⣿⣿⣿⣿⠿⠿⠿⢻⣿⠛⢿⣿⣿⣿⣿⠀⢸⣿⠀⣸⣿⣿⣿⡟⠀⡌⠀⠀⠀⢠⣀⣭⡇⠁⠆⠈⢿⣿⣍⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⡉⠉⠉⣧⣤⡄⢀⠭⢽
⠀⢀⠀⠀⠀⠀⠀⣟⠛⠛⠋⠙⠋⠚⢻⣿⣿⣿⣿⣿⣿⡟⣻⡿⠉⠀⠉⠀⠈⠀⠸⡿⣿⣿⡋⣡⠂⠁⠀⠀⠀⢘⣿⣿⡷⠂⠁⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣿⣿⣾⣿⣿⡇⣰⡟⠡⡀⢀⣀⣿⣿⣋⣄⠩⠓
⠀⠈⡀⠀⠀⠀⢰⡇⣀⠀⡔⣶⡄⠀⠉⣿⣿⣿⠿⢽⠯⣤⣻⣿⠀⠀⢰⠆⠉⠀⠀⠀⣈⢭⡇⠀⡔⠋⠁⠀⠀⠈⠛⣿⣿⣶⣖⠂⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣛⣻⣛⣿⣷⣚⣏⣋⠙⠀
⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠑⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠊⠀⠀⠀⣠⣾⣇⠈⣗⠀⣇⡀⠀⠀⠀⠀⣰⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠉⠙⠋⠉⢿⣿⣿⣿⣶⣄⣰⣶⡤⠈⠙⠛⠛⠛⢛⢛⣛⣯⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⡾⢻⣿⣿⢀⡟⠠⣿⣷⣄⠀⠀⠀⢁⢼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠤⠤⢀⣼⡋⠀⠈⢩⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢰⣇⣻⣿⡟⢻⡟⠁⣀⣿⣟⠏⠳⠀⠐⢄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣾⣯⠿⢾⣿⠊⠀⢰⣿⣿⣿⠇⠀⠀⠈⣿⣿⢻⡿⣿⠛⡿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣭⣄⣉⠝⠁⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⡟⠙⠀⠀⠀⠀⠀⠈⠽⢻⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⡏⠁⠁⠁⠀⠀⠀⢰⣿⠈⢻⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠝⠛⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢛⢯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⡄⢳⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⠪⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠿⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⢸⣺⠇⢀⣀⣀⣀⣄⣥⣤⣴⣶⣾⣿⡿⠁⠀⠀⠀⠀⢀⣠⠆⠀⠀⢨⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣾⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⢸⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣴⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢹⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡇⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠓⠛⠃⠈⠛⠟⠋⠀⢙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣛⣛⣻⣾⠛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠐⠈⠋⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠛⠂⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠻⠟⠛⠟⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣤⣤⡀⠀⠿⠿⢿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠘⠁⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣋⣉⣉⣟⣛⣹⢙⣙⣯⣽⣡⢤⣅⠤⢤⠀⢨⣝⡋⠣⣌⣄⣽⣿⠀⠀⠀⠀⠈⠩⠿⠷⠀⣴⣤⣄⢸⣿⡛⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⡯⠭
⠀⢠⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣿⣿⣿⠿⠿⠿⣛⣿⠻⢿⣿⣿⣿⣿⠀⢾⣿⠀⣸⣿⣿⣿⡏⢀⡆⠀⠀⠀⣇⣀⣽⡄⠐⠂⠈⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⠉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡋⣠⠬⠁⠀⠀⠀⢛⣿⣿⡷⠂⠀⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣿⣿⣿⣿⣿⡇⣰⡟⠡⢀⣀⣀⣿⣿⣋⡄⢩⠓
⠀⠘⡀⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠀⠩⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠂⠉⠀⠀⠀⢉⢭⡋⠈⡴⠒⠀⠀⠀⠈⠛⣿⣿⣶⣖⠂⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣛⣛⣛⣻⣳⣞⣏⣋⠙⠀
⠀⠀⢆⠀⠀⠀⠀⢉⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠊⠀⠀⠀⣠⣾⣇⢸⣗⠀⣇⡀⠀⠀⠀⠀⣰⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠉⠙⠛⠹⢿⣿⣿⣿⣶⣄⣰⣦⡤⠈⠙⠛⠛⠛⣛⢛⣛⣧⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⣿⣿⢀⡏⢰⣿⣷⡀⠀⠀⠀⢉⢼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠤⠤⢀⣽⡋⠀⠈⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢰⣏⣿⣿⡟⢻⡟⠁⣰⣿⣟⠏⠲⠀⠐⢄⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠺⢿⣦⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⣼⣭⣿⣿⣿⠞⠀⢰⣿⣿⣿⠇⠀⠀⠀⣿⣿⢻⣿⣿⠛⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡍⢉⠟⠁⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⡟⠘⠈⠀⠀⠀⠀⠈⠿⢻⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠛⠛⠛⣻⢇⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡏⠉⠉⠁⠀⠀⠀⢰⣿⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⠛⠻⣿⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⡀⢳⠀⠀⠀⠀⠀⢀⡟⠏⠀⠈⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢰⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠳⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⢸⣺⠇⢀⣀⣀⣀⣬⣥⣤⣴⣶⣾⣿⡟⠁⠀⠀⠀⠀⢀⡴⠂⠀⠀⢩⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠈⠛⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣾⣿⢻⣿⡿⣿⡗⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⢸⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⢙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣛⣛⣻⣾⠛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⡉⠙⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠀⠀⢸⣿⣿⣿⣻⣟
⡠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠳⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⢀⣤⣤⠀⠈⠿⠿⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢿⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣋⣉⣙⣟⣛⣹⢛⣙⣯⣭⣡⡤⣅⡠⣤⠀⢨⣝⡋⠣⣈⣀⣩⡇⠀⠀⠀⠀⡈⠽⠿⠃⢀⣴⣤⣄⢸⣿⡓⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣛⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⣧⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠻⢿⣿⣿⣿⣿⠀⢾⣿⠀⣸⣿⣿⣿⡇⢠⠂⠀⠀⠈⣄⣨⣽⡄⠑⠂⠈⢾⣿⣍⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⡉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠠⡀⠀⠀⠀⠘⣿⠛⠛⠛⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡟⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡋⡠⠈⠀⠀⠀⠀⣻⣿⣿⡷⠂⠀⠀⢸⣿⡨⠀⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠡⠀⣀⣀⣿⣿⣋⡄⢩⠓
⠀⠘⡀⠀⠀⠀⢰⡇⣀⠀⣔⣦⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⡿⠀⠀⢰⠂⠉⠀⠀⠀⢉⢹⠋⠈⡖⠒⠀⠀⠀⠈⠙⣿⣿⣶⣖⠂⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢿⣛⣛⣻⣻⣷⣚⣏⣋⠙⠀
⠀⠀⠂⠀⠀⠀⠀⢉⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠊⠀⠀⠀⣠⣶⣇⢸⡟⢘⣆⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠉⠙⠋⠹⢿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠙⠛⠛⠛⢛⢛⣛⣫⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⣿⣿⢠⡇⢸⣿⣷⣄⠀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠤⠤⢀⣝⡋⠀⠉⢩⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡧⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢠⡟⣿⣿⡟⢻⡟⠁⣸⣿⣟⠏⠓⠀⠀⢂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠺⢿⣦⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⣼⣭⣿⣿⣿⠞⠀⢰⣿⣿⣿⡧⠀⠀⠀⣿⣿⠻⡿⣿⠛⡿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣫⡍⢉⠟⠁⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⡟⠙⠀⠁⠀⠀⠀⠈⠟⢻⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢇⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡏⠉⠙⠁⠀⠀⠀⢰⣿⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠛⠻⣿⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⣧⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⡀⢳⠀⠀⠀⠀⠀⢀⣿⠻⠀⠀⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠈⠙⡟⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢰⢫⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠲⠴⣿⡿⠛⠳⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⢸⣾⠇⢀⣀⣀⣀⣄⣥⣤⣴⣶⣾⣿⡿⠁⠀⠀⠀⠀⢀⡴⠂⠀⡄⢨⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣾⣿⢻⣿⡿⣿⡗⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⢸⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠠⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠀⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣿⣼⠛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⢭⠭⢽⣿⣿⣿⣿⡯
⠀⡈⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡟⠋⠿⠆⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⢀⣤⣄⠀⠸⠿⠿⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢿⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣋⣉⣙⣟⣋⣹⢛⣙⣯⣭⣡⡤⣥⠀⢠⠀⢨⣝⡋⠣⣈⣀⣽⡀⠀⠀⠀⠀⠀⠿⠛⡆⢀⣶⣤⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣘⣛⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⣢⠀⠀⠀⠀⢰⠾⣯⠽⢿⠿⣿⣿⣿⣿⠿⠿⠿⢻⣿⠻⢿⣿⣿⣿⣿⠀⢾⣿⠀⣸⣿⣿⣿⡇⢰⠀⠀⠀⢰⣀⣭⣿⠰⠰⠂⠈⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⠉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⢠⠀⠀⠀⠀⠘⣟⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡟⠉⠀⠉⠀⠈⠀⢸⡿⣿⡿⣫⡤⠈⠀⠀⠀⠈⣿⣿⣿⡗⠁⠀⠀⢸⣿⡨⠀⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠡⠀⢀⣀⣿⣿⣋⡄⠩⠓
⠀⠘⡀⠀⠀⠀⢰⡇⣀⠀⡔⣦⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠂⠉⠀⠀⠀⢉⢱⠉⢠⠚⠂⠀⠀⠀⠈⠉⣿⣿⣷⣶⠂⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣛⣻⣿⣻⣷⣚⣏⣋⠑⠂
⠀⠀⣆⠀⠀⠀⠀⢉⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠊⠀⠀⠀⣠⣶⣟⢸⡎⢸⣄⡄⠀⠀⠀⠈⣼⠿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠉⠙⠋⠹⣿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠛⠛⠛⠛⠛⢛⣛⣧⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⢿⣿⢸⡇⢸⣿⣿⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠤⠤⢀⣜⡋⠀⠉⢩⣍⣩⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢠⣟⢻⣿⡟⢻⡟⠀⣸⣿⣿⡣⠑⠆⠀⢂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⣼⣯⡿⣾⣿⠊⠀⢰⣿⣿⣿⡷⠀⠀⠀⣿⣿⠛⡿⣿⠟⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣞⣯⡭⣉⠟⠁⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⡝⠉⠀⠁⠀⠀⠀⠈⠟⢻⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠛⠛⠛⣻⢏⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡏⠉⠑⠁⠀⠀⠀⢰⣿⠁⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⢧⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⡄⢳⠀⠀⠀⠀⠀⢀⣿⠹⠀⠀⠙⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠘⡟⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠰⠫⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠳⣦⢄⡀⠀⠀⠀⠀⠀⠀⠠⠐⢸⣾⠇⢀⣀⣀⣀⣤⣭⣤⣶⣶⣾⣿⡟⠁⠀⠀⠀⠀⢀⣤⠂⠀⡄⢠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣾⣿⢻⣿⡿⣿⡗⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⢸⢸⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠻
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠠⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠐⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠓⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣿⣾⠛⠃⠛⠃⠺⣿⠿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠆⠀⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠟⠻⠗⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠟⠛⠟⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⣠⣤⡄⠀⠹⠿⠿⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣛⣉⣉⣟⣋⣹⢛⣙⣯⣭⣤⡤⢅⡠⢤⠀⢨⣍⠋⠣⣌⣤⣿⡀⠀⠀⠀⠀⠠⠟⣛⡄⢀⣶⣤⣄⢸⣿⡓⠘⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⡮⠭
⠀⣄⠀⠀⠀⠀⢰⠾⣿⠽⢿⢿⣿⣻⣿⣿⠿⠿⠟⣻⣿⠻⢿⣿⣿⣿⣿⠀⢾⣿⠀⣸⣿⣿⣿⡄⣰⠀⠀⠀⣧⣀⣽⣷⠘⠀⠂⠈⢾⣿⣍⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⠉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠀⠀⠀⠀⠀⠘⣟⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡟⠉⠀⠉⠀⠈⠀⢸⡿⣿⡿⢫⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠁⠀⠀⢸⣿⡩⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣿⣿⣿⡇⣸⡟⠁⢀⣀⣀⣿⣿⣋⣄⠩⠓
⠀⠘⡁⠀⠀⠀⢰⡃⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠯⢽⠯⣤⣿⡿⠀⠀⢰⠆⠉⠀⠀⠀⢈⣱⢠⢸⠉⠀⠀⠀⠀⠈⢅⣹⣿⣿⣶⡆⢼⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣛⣛⣛⣿⣷⣚⣫⣋⠙⠀
⠀⠀⡆⠀⠀⠀⠀⢉⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠊⠀⠀⠀⢀⣴⣿⢸⣇⢸⣄⢠⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣶⡤⠘⠛⠛⠛⠛⠛⢟⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣴⠟⣿⣿⣦⡏⢸⣿⣿⣧⡀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠤⠤⢀⣝⡋⠀⠈⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⣾⡻⣿⣿⠋⡟⠁⣸⣿⣿⣿⠌⠃⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠺⢿⣦⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣰⣯⣽⠷⣿⠏⠀⢰⣿⣿⣿⣿⠆⠀⠀⢸⣿⡿⢻⣿⡿⢻⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣥⣉⠝⠁⠀⠀⣸⣿⣿⣿⠛⠀⠀⠀⢼⠋⠃⠈⠀⠀⠀⠀⠩⠟⣿⣿⣷⣴⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⢛⣻⢇⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢾⠉⠘⠋⠀⠀⠀⢠⣿⡇⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢄⢸⡄⠀⠀⠀⠀⠀⣾⠛⠇⠀⠘⠁⢀⡀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⢿⠂⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⠯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣞⠇⢀⣀⣀⣀⣤⣭⣤⣶⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⣠⠄⠀⡄⢠⠈⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠛⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡧⠀⣿⡇⢈⢰⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠐⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠓⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣛⣛⣻⣾⠛⠃⠛⠃⠺⣿⠿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠈⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠁⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠛⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢠⣤⣄⠀⠸⠿⠿⢿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣋⣉⣉⣟⣋⣹⢙⣙⣯⣭⡡⠤⣄⠀⢄⠀⢨⣍⠋⠣⣈⣈⣹⠀⠀⠀⠀⠀⠠⠿⠛⣄⠀⣴⣤⣄⢸⣿⡓⠒⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⡀⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣻⣿⣿⠿⠿⠿⣻⣿⠛⢿⣿⣿⣿⣿⠀⢾⣿⠀⣸⣿⣿⣿⡇⢰⠁⠀⠀⢢⡀⢭⣿⡔⠶⠂⠈⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⠉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠐⠀⠀⠀⠀⠘⣞⠛⠛⠋⠙⠋⠛⢻⣿⣿⣿⣿⣿⣿⡟⣿⡟⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡛⡁⠈⠀⠀⠀⠘⣻⣿⣿⡷⠋⠀⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⠻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠁⠀⢀⣀⣿⣿⣋⡄⠩⠓
⠀⠈⡀⠀⠀⠀⢰⡇⣀⠀⡔⣦⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⣯⠀⠀⢰⠖⠉⠀⠀⠀⠈⣙⡀⢲⠋⠂⠀⠀⠀⠈⠉⢻⣿⣷⣶⡆⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢿⣛⣟⣟⣿⣳⣚⣏⣋⠙⠀
⠀⠀⠂⠀⠀⠀⠀⢉⢻⠇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⢀⣴⣾⡛⣿⠈⡆⢠⠀⠀⠀⠀⠱⣷⢿⣿⣿⣿⣿⣿⣤⡀⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣶⡄⠈⠛⠛⠛⠛⢛⢛⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣴⠿⠿⣿⣇⡿⠘⣿⣷⣧⡀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠤⠤⢀⣜⡋⠀⠉⢩⣍⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣧⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⣼⠋⣿⣿⠋⡿⠃⢠⣻⣿⣿⠍⠢⠀⠐⢄⣾⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣠⣮⣽⣷⣿⠟⠁⠀⣿⣿⣿⣿⠆⠀⠀⢸⣿⣿⢿⣿⣿⠟⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⣻⣩⠉⡹⠋⠀⠀⢰⣿⣿⣿⡻⠀⠀⠀⢸⡟⠛⠈⠀⠀⠀⠀⢛⠿⣟⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢇⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣫⢾⠉⠙⠋⠀⠀⠀⢀⣾⡏⠘⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⠿⢿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢅⢸⡄⠀⠀⠀⠀⠀⣸⡟⠇⠀⠘⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⠮⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠳⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣟⠧⢀⣀⣀⣀⣠⣬⣤⣴⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⢀⡜⠀⡄⢠⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠁⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡯⠀⣿⡇⢈⢰⣿⣿⣇⣸⣿⣴⣿⣿⢸⣿⣻⣿⣴⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠠⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠐⣿⡇⠈⢹⣿⢽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠉⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠓⠛⠃⠈⠛⠟⠋⠀⢙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠐⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣛⣛⣻⣾⠛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣤⣀⠀⠘⠿⠿⢿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢿⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣛⣹⢙⣙⣯⣭⡡⡤⣅⠠⢄⠀⢨⣍⠋⠣⣌⣄⣽⡃⠀⠀⠀⠀⠀⠽⠿⢆⠀⣴⣤⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⠯⠯
⠀⠀⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣻⣿⣿⠿⠿⠿⣻⣿⠛⢿⣿⣿⣿⣿⠀⢼⣿⠀⣸⣿⣿⣿⡟⢀⠂⠀⠀⢰⡀⢨⣿⡄⠖⠂⠈⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⠉⠉⠉⣧⣴⡄⢀⠭⣿
⠀⠐⠀⠀⠀⠀⠘⣞⠛⠛⠋⠙⠋⠛⢻⣿⣻⣿⣿⣿⣿⡟⣿⡟⠉⠀⠉⠀⠈⠀⠸⡿⣿⣿⢟⠉⠘⠀⠀⠀⠸⣻⣿⣿⣷⠖⠀⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠁⠀⢀⣀⣿⣿⣋⣄⢩⠓
⠀⠘⡀⠀⠀⠀⢰⡃⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠆⠉⠀⠀⠀⠈⢉⡋⢶⠚⠂⠀⠀⠀⠘⠛⢿⣿⣷⣶⣆⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢿⣛⣛⣟⣿⣷⣚⣯⣋⠙⠂
⠀⠀⠇⠀⠀⠀⠀⢉⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⣤⣾⠇⣿⠈⡆⠀⠀⠀⠀⠀⠂⣦⣿⣿⣿⣿⣿⣿⣤⡀⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠈⠙⠛⠛⠛⠛⢟⣛⣧⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣠⡾⠿⣿⡇⣿⠀⣿⣷⣧⡀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠤⠤⢀⣜⡋⠀⠉⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⣧⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⣰⠏⣿⣿⠟⢻⠋⢀⣿⣿⣿⠏⠢⠀⠠⢄⣼⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠸⢿⣦⡄⠀⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣼⣿⣿⣽⡷⠃⠀⣾⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⠿⣻⢿⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣟⣋⠍⣰⠊⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⢘⡿⠹⠈⠁⠉⠀⠀⠛⡿⢿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢏⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣵⠋⠙⠛⠁⠀⠀⠀⣾⡿⠘⣿⡇⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢅⢸⡄⠀⠀⠀⠀⠀⣸⡟⡇⠀⠘⠇⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠻⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⠯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣷⠧⢀⣀⣀⣀⣤⣼⣥⣶⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⢀⡤⠁⡄⢠⡀⡁⠠⠀⠀⠀⠁⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡯⠀⣿⡇⢘⢰⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠐⣿⡇⠈⢹⣿⢽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡏⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠃⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣻⣾⠛⠃⠛⠃⠸⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠄⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡛⠀⠀⠉⠀⠀⣀⡀⠀⠈⠿⠿⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣲⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣋⣉⣉⣟⣋⣹⢛⣙⣯⣭⡡⢤⢅⠀⠤⠀⢨⣍⠋⠣⣌⣄⣙⣇⠀⠀⠀⠀⠀⣻⠿⢆⠀⢰⣤⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⡣⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣻⣿⠿⠿⠿⠿⢻⣿⠻⢿⣿⣿⣿⣿⠀⢾⣿⠀⣸⣿⣿⣿⣿⠀⡆⠀⠀⢠⠀⢐⣺⡆⢴⠂⠈⢾⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⠉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠐⠀⠀⠀⠀⠘⣞⠛⠛⠋⠙⠋⠛⢻⣿⣻⣿⣿⣿⣿⡟⣿⡿⠉⠀⠉⠀⠈⠀⠸⡿⣿⣿⡿⠙⠐⠃⠀⠀⠸⢷⣾⣿⣷⣤⠀⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⢻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠡⠀⣀⣀⣿⣿⣋⣄⢩⠓
⠀⠈⡀⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠖⠉⠀⠀⠀⠈⠉⡆⣥⠖⠀⠀⠀⠀⠙⠿⢿⣿⣶⣶⣆⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⣿⢟⣛⣻⣟⣿⣷⣞⣏⣋⠙⠂
⠀⠀⠆⠀⠀⠀⠀⢉⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⣠⣴⡏⣷⠈⡆⠀⡀⠀⠀⠀⠄⣌⣿⣿⣿⣿⣿⣿⣄⡀⠀⠈⠉⠙⠋⠙⢿⣿⣿⣿⣶⣄⣰⣦⡤⠘⠛⠛⠛⠛⣛⢟⣛⣧⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡴⢿⣿⡇⣿⠀⣿⣶⣵⡀⠀⠀⠀⠛⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠤⠤⢀⣜⡋⠀⠉⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⢠⠏⢷⣿⡿⢳⠟⠀⣿⣿⡿⣟⠢⠀⠀⠄⢨⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠸⢿⣦⣄⠀⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣼⣛⣿⣽⣷⠎⠀⣸⣿⣿⣿⣇⠀⠀⢀⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣾⣛⡛⢒⠟⠁⠀⢀⣾⣿⣿⡿⡆⠀⠀⠀⣿⠻⠁⠋⠉⠁⠁⠙⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⠛⣻⢇⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣡⠛⠛⠽⠃⠀⠀⠀⣸⣿⠘⣿⣇⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠁⠸⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢻⢯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢏⠈⡄⠀⠀⠀⠀⠀⢰⡟⡇⠀⠘⠿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⣷⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⢯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣆⠿⢀⣀⣀⣀⣠⣼⣥⣶⣶⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⡠⠁⡄⢠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡿⠀⣿⡇⢸⢰⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠐⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣠⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠓⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣿⣾⠛⠃⠛⠃⠺⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠈⠉⠛⢿⣿⣿⣿⣿⡿⠻⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣚⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡻⠋⠀⠉⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢻⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠉⠉⠛⣒⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣙⣛⣉⣙⣟⣛⣹⢛⣙⣯⣽⡡⠤⢅⠀⢤⠀⢨⣍⠋⠣⣌⣀⣩⣿⠀⠀⠀⠀⠀⠐⣿⣷⠀⠀⣤⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣸⣻⣀⣸⣶⣷⣆⣶⡖⢶⡮⠭
⠀⡀⠀⠀⠀⠀⢰⠾⣯⠽⢿⢿⣿⣻⣿⣿⠿⠿⠿⣻⣿⠛⢿⣿⣿⣿⣿⠀⢼⣿⠀⣸⣿⣿⣿⣿⡇⢠⠆⠀⠀⡈⠁⠬⣷⢀⡂⠈⢻⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⡉⠉⠉⣧⣴⡄⢀⠭⣿
⠀⠀⠀⠀⠀⠀⠘⣞⠛⠛⠋⠙⠋⠛⢻⣿⣻⣿⣿⣿⣿⡟⣿⡟⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡿⠩⠇⠸⡀⠀⠀⢷⣤⣿⣿⣄⡁⠀⢸⣿⡨⠁⠀⠀⣿⣿⡋⠻⣿⣿⣽⣿⣿⣿⣿⡇⣰⡟⠡⡀⢀⣀⣿⣿⣋⣄⠩⠓
⠀⠐⡀⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⣿⠀⠀⢰⠆⠉⠀⠀⠀⠈⠉⢹⢐⣠⢄⠀⠀⠀⠐⢿⣿⣿⣧⣶⣆⢸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡛⠛⠯⠽⠿⢿⢟⣛⣛⣛⣿⣷⣞⣏⣋⠙⠂
⠀⠀⠆⠀⠀⠀⠀⢉⢻⠇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⢀⣤⣾⢹⡌⢧⠀⠀⠀⠀⠀⢀⢈⣿⣿⣿⣿⣿⣿⣄⡀⠀⠈⠉⠙⠋⠹⢿⣿⣿⣿⣶⣄⣰⣶⡤⠘⠙⠛⠛⠛⣛⢟⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣰⣿⣿⣷⢸⡇⢸⣆⣜⡀⠀⠀⠀⠸⠟⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠤⠤⢀⣜⡋⠀⠈⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⡾⢳⣶⣾⠿⣸⠇⢸⣿⣟⢿⠢⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠺⢿⣦⣄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣈⡛⢾⣍⣧⣤⠃⠀⣾⣿⣿⣦⠀⠀⠀⣴⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢰⠿⠛⠩⢭⠟⠁⠀⢨⣿⣿⣿⡏⠀⠀⠀⢿⠟⠇⠙⠛⠃⠈⠱⢿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠛⢛⣻⢇⣾⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢁⡽⠟⠗⠖⠁⠀⠀⠀⣿⠋⢿⣷⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠠⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⢛⣧⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢟⠉⣇⠀⠀⠀⠀⠀⠀⣾⠿⠀⠈⢿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢰⠫⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢀⡉⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣣⠼⢀⣀⣀⣀⣤⣴⣧⣶⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⡀⠁⡄⢀⡁⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡿⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣾⣿⡿⠀⣿⡇⢸⢰⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣵⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠐⣿⡇⠈⢹⣿⢽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢻⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⡧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣤⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠓⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣻⣾⠛⠃⠛⠃⠺⣿⡿
⠁⠛⠁⠞⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢭⠭⠭⢽⣿⣿⣿⣿⡯
⠀⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣻⣟
⠀⠀⠂⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠉⠛⢿⣿⣿⣿⣿⡿⠟⠟⠛⠛⡇⢸⣿⣿⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣒⣓
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠉⠁⠀⠀⠀⠀⠀⠹⠿⠿⣿⣧⠀⠀⠀⠀⡇⠘⠛⢿⡇⠀⠀⠀⠀⠀⠿⢿⢿⣿⠀⠀⠀⠀⠀⠈⠉⠛⣒⡷
⠘⠀⠀⠀⠀⠀⡏⠉⢉⣉⣉⣉⣋⣉⣉⣟⣋⣹⢙⣙⣯⣭⡡⠤⢅⠀⢄⠀⢨⣍⠋⠣⣌⣀⣍⣿⡇⠀⠀⠀⠀⠠⢿⣷⡀⠀⣠⣄⢸⣿⡓⠚⠉⠀⣇⣈⣴⣴⣧⣤⣤⣤⣤⣤⣤⣤⣘⣻⣀⣸⣶⣷⣆⣶⡖⢶⠯⠭
⠀⢠⠀⠀⠀⠀⢰⠾⣯⠽⢿⠿⣿⣻⣿⣿⠿⠿⠿⣻⣿⠛⢿⣿⣿⣿⣿⠀⢾⣿⠀⣸⣿⣿⣿⣿⡷⠀⠄⠀⠀⣀⠉⠩⣵⠀⡀⠈⢿⣿⣍⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣉⡉⠉⠉⣧⣤⡄⢀⠭⣿
⠀⠨⠀⠀⠀⠀⠘⣞⠛⠛⠋⠙⠋⠛⢻⣿⣻⣿⣿⣿⣿⡟⣿⡟⠉⠀⠉⠀⠈⠀⢸⡿⣿⣿⡿⠈⠏⢸⡀⠀⢀⢸⣤⣼⣿⣇⡁⠀⢸⣿⡬⠁⠀⠀⣿⣿⡋⠻⣿⣿⣽⣿⣷⣿⣿⡇⣸⡟⠁⢀⢀⣀⣿⣿⣋⡄⢩⠓
⠀⠘⡀⠀⠀⠀⢰⡇⣀⠀⡔⣶⡀⠀⠉⣿⣿⣿⠿⢽⠯⣤⣿⡿⠀⠀⢰⠖⠉⠀⠀⠀⠈⠉⢩⢀⢀⢄⠀⠀⠀⠘⢿⣿⣿⣿⣶⣆⣸⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⡛⠛⠯⠽⠿⣿⢟⣛⣛⣛⣿⣷⣞⣋⣋⠑⠂
⠀⠀⠇⠀⠀⠀⠀⢁⢻⡇⠙⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⢀⣤⣶⢹⡼⢸⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣄⡀⠀⠈⠉⠙⠋⠹⢿⣿⣿⣿⣶⣄⣰⣦⡤⠈⠙⠛⠛⠛⣛⢿⣛⣣⣤⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⣾⣿⣿⡌⣷⢸⣦⣜⡄⠀⠀⠈⠸⠻⣹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠤⠤⢀⣜⡋⠀⠉⢭⣭⣭⠿⠇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⣼⠻⣤⣾⡟⣃⡏⠘⣿⣿⢻⠢⠀⠀⢀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠺⢿⣦⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤
⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡟⢶⣍⣻⣤⠎⠀⣴⣾⣿⣶⠁⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⢸⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡿⠛⠨⢭⡝⠁⠀⢀⣿⣿⣿⣯⠀⠀⠀⢹⡿⡇⠘⠛⠋⠈⠉⢻⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠛⠛⠛⣻⢇⣿⣿⣿⣷⣶⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠀⣸⠿⠓⡰⠊⠀⠀⠀⣼⡏⢻⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⢛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢷⠊⢹⠀⠀⠀⠀⠀⠀⣰⢿⠀⠈⢿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⢰⠫⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⠀⠀⠀⢀⡙⠒⠴⣿⡿⠛⠻⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣱⠸⢇⣀⣀⣀⣠⣤⣯⣶⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⡀⠀⡄⢠⡁⡉⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⡘⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠉⣾⡟⣿⣧⢸⣿⡟⣿⡟⣶⣿⢻⣿⡟⣿⡇⣿⣿⣄⣿⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⣿⡏⣿⣿⡗⣿⣷⣿⣿⡿⠀⣿⡇⢸⢰⣿⣿⣇⣹⣿⣴⣿⣿⢸⣿⣻⣿⣽⣿⡿⣿⣿⠿⢸⣿⡿⣿⡆⠛⠛⠿
⠀⠀⢿⣿⣦⡀⢸⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣷⣿⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⠀⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⠃⠀⠐⣿⡇⠈⢹⣿⢽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣶⢸⣿⣿⣿⡃⠀⠀⠀
⠀⠀⣾⣾⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⢹⣿⣿⠃⠀⢸⣿⢸⣿⢹⣿⠀⣿⣇⣀⠀⠀⣿⡏⣿⡇⣿⡇⠀⣿⡏⠀⠀⠀⣿⣇⡀⣾⣿⣾⣿⡘⣿⣿⡟⣿⣿⣿⠍⢹⣿⣧⣼⣿⣿⣶⣾⣿⡏⣿⡇⢀⣤⣄
⠀⠀⠙⠛⣛⠋⠘⠛⠓⠛⠃⠈⠛⠟⠋⠀⣙⡛⠛⠘⠛⠛⠀⠀⠘⠛⠘⠛⠘⠛⠘⠛⠛⠛⠀⠀⠛⠃⠛⠃⠛⠃⠀⠛⠃⠀⠀⠀⠛⠛⠃⠛⠛⠘⠛⠃⠛⠛⠃⠛⠛⠃⠀⠘⠛⠃⡟⣟⣛⣻⣾⠛⠃⠛⠃⠺⣿⡿
⠁⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠓⠂⠈⠉⠉⠀⠷⠂⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2721

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2025/03/14/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Mar 14, 2025


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Ubuntu_25.04_Default_Wallpaper_&_Mascot_Unveiled⠀⇛


           The default wallpaper for Ubuntu 25.04 ‘Plucky Puffin’ has been
           unveiled


      ⚓  New⠀⇛


   2. ⚓ today's_leftovers⠀⇛


           GNU/Linux and more


   3. ⚓ Security_Leftovers⠀⇛


           and Windows aspects


   4. ⚓ Programming_Leftovers⠀⇛


           Development news


   5. ⚓ Games:_Max_Payne_and_Sudoku⠀⇛


           gaming news


   6. ⚓ Gnome’s_Dash_to_Panel_Extension_Gets_a_Massive_Update⠀⇛


           GNOME update


   7. ⚓ today's_howtos⠀⇛


           only 3 more for now


   8. ⚓ ZFS_Orchestration_Tools_and_Wheatstone_Adds_Linux_Audio_Driver⠀⇛


           kernel news


   9. ⚓ EPEL,_IBM,_and_RHEL_Clones⠀⇛


           Red Hat leftovers


  10. ⚓ Open_Infrastructure_Foundation_(OpenInfra):_Openwashing_or_Community-
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           the usual from LF


  11. ⚓ KDE’s_X11_Support_to_Continue_Until_Plasma_7⠀⇛


           KDE has separated KWin X11 and KWin Wayland. Wayland takes
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  12. ⚓ Stable_kernels:_Linux_6.13.7,_Linux_6.12.19,_Linux_6.6.83,_Linux
      6.1.131,_Linux_5.15.179,_Linux_5.10.235,_and_Linux_5.4.291⠀⇛


           I'm announcing the release of the 6.13.7 kernel


  13. ⚓ DXVK_2.6_Adds_NVIDIA_Reflex_Support,_Improvements_for_Many_Games⠀⇛


           DXVK 2.6 Vulkan-based implementation of D3D9, D3D10, and D3D11
           for Linux / Wine is now available for download as a significant
           update that improves support for multiple games.


  14. ⚓ Programming_Leftovers⠀⇛


           Development and more


  15. ⚓ Security_Leftovers_and_Windows_TCO⠀⇛


           Windows TCO examples included


  16. ⚓ Free,_Libre,_and_Open_Source_Software_and_Programming_Leftovers⠀⇛


           3 more stories/links


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           GNU/Linux focused stories


  18. ⚓ Mozilla_and_Tor_Leftovers⠀⇛


           also forks and rust


  19. ⚓ Software:_Zotero,_Kdenlive_24.12.3,_and_Strawberry_Music_Player⠀⇛


           Applications and releases


  20. ⚓ Open_Hardware_and_Linux_Devices⠀⇛


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  21. ⚓ Fedora_discusses_Flatpak_priorities_and_latest_from_Red_Hat's_Site⠀⇛


           redhat.com mostly


  22. ⚓ Android_Leftovers⠀⇛


           Google teases Android 16 Beta 3 update tomorrow


  23. ⚓ 6_Linux_window_managers_that_will_change_how_you_use_your_PC⠀⇛


           Many Linux distros will ship with a WM, depending on the
           Desktop Environment (DE)


  24. ⚓ Best_Free_and_Open_Source_Software,_howtos_and_Installations⠀⇛


           Only free and open source software is eligible for inclusion
           here


  25. ⚓ Games:_Machine_Mind,_Old_Skies,_and_More⠀⇛


           new from GamingOnLinux


  26. ⚓ Maps_and_GNOME_48⠀⇛


           In a few days it's time for the GNOME 48 release


  27. ⚓ Max_Payne_running_seamlessly_on_Linux_4K⠀⇛


           So I wondered, can it run in Linux


  28. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


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


                         Span from 2025-03-07 to 2025-03-13
      908 /n/2025/03/08/New_WINE_and_Games_News.shtml


      663 /n/2025/03/08/
          Garuda_Linux_Broadwing_Released_with_New_Mokka_Edition_New_Welc.shtml


    * IRC_Proceedings:_Thursday,_March_13,_2025
    * Meanwhile_at_Microsoft_Canonical...


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠫⠇⠉⡛⠁⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣴⣶⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣌⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠛⠻⠿⠛⠒⠂⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠆⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⢿⣿⣿⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠸⢟⠁⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠏⣿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠑⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢳⣿⢻⣿⣿⣿⣿⡄⢻⣇⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⠈⢟⣿⣿⣿⡏⢹⡿⣿⣿⣿⣿
⡟⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣛⣿⣿⣿⣿⠛⣹⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡣⡐⣿⢻⣦⣍⢐⣻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⢀⡾⣿⣿⣿⣿⢎⡋⠻⣿⣿⣿
⣷⣹⡿⣙⣿⣼⣇⡾⣹⣛⡏⢱⣯⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⠷⣿⣿⣿⣿⣎⠓⠌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠛⡇⢨⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣇⠙⡛⢿⢸⡆⣹⣷⣿⣿⣿
⣿⣿⣧⣿⣿⣟⡿⣼⣿⣂⡦⠿⠗⣿⣿⣻⣿⣶⣿⣟⢸⣯⣿⡏⠠⠠⣿⣿⣿⣯⡟⠁⠠⠀⠙⡂⠐⡀⠀⠀⣷⡊⠀⣀⡤⠂⠀⠀⣼⣏⡻⣌⣾⣷⣿⡿⣿⣿⣿⣿⠽⣯⣽⣿⣷⡏⣹⢿⣄⢹⡞⠹⡗⢻⣿⣿⣿⣿
⣿⣿⣿⣯⣿⣿⣀⣿⡿⢿⡆⠠⠀⢈⢻⣿⣿⣧⣿⣻⡼⠛⡿⡛⠛⢺⣿⢸⣿⣿⣾⢀⣀⡀⠀⠈⠿⠆⠤⢠⡟⠓⠈⠀⠀⠀⠀⠀⢻⣿⣇⢉⣬⣿⣯⣟⢿⣿⣿⣿⠀⣿⣿⣿⣿⡇⣿⣦⣽⠣⡀⢠⠃⠈⣏⣿⢩⣿
⣿⣿⣿⡟⠋⠉⢠⡏⠠⡜⢧⠀⣿⢿⢟⠛⡟⣿⣿⡿⡒⠄⡟⠃⢰⠸⣿⣰⡏⢿⣿⣿⣿⡇⠀⠀⠀⠀⢀⢈⠃⠀⠀⢀⣏⣀⠰⡞⠀⢧⣟⢸⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣽⣧⣀⢬⣧⡀⢿⡌⣌⣹
⣿⡿⠃⠀⠀⢀⣿⠐⢰⣿⣿⡶⣻⣿⠛⠙⢩⡿⠁⠀⠄⠁⡇⠀⢸⡇⡿⣿⣤⠔⣿⣿⣿⠇⠀⠀⠀⠀⠸⠁⠀⠀⠀⢸⣿⣿⣿⢅⣲⢸⣿⡜⣿⣿⣫⣼⣿⣾⢿⣿⣿⣿⣿⣟⣿⠏⣸⣯⣃⣽⣇⣨⣭⣁⡸⢻⣯⢿
⣿⣡⠴⠖⢒⣏⠀⠐⢼⣿⣿⣰⣿⣛⡈⠠⢸⡟⠁⠄⡀⠀⣄⡠⠀⡇⣿⣿⣿⡿⢿⠛⢈⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⣸⣿⣿⣿⠈⡁⣿⣿⣗⣿⣿⡿⢉⣿⣿⣾⣿⣛⡿⠏⣿⡯⣶⣼⣿⣿⣴⢧⣽⡻⠐⠃⣹⠋⣿
⣿⡀⠀⢀⡎⡋⣶⣴⢖⣻⣿⣿⣿⣿⣿⢶⣿⣳⣴⣶⣶⢶⡏⢀⣀⣳⠘⣿⣿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣿⡟⢟⢁⡟⠹⣧⣿⣿⣶⣻⢿⠇⢺⡙⣾⣧⢈⣸⣀⢁⣰⠉⢉⡹⠻⡾⣿⠗⠒⢿⠋⣹
⠉⢿⣤⣾⣿⣧⠼⣿⣾⣿⣿⠿⢿⣿⢾⣿⣿⣿⠝⢻⢽⣀⢻⣿⡯⣽⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠋⠉⠙⠛⠛⠛⣛⢿⣿⣿⢃⡿⣿⣽⢼⣌⢻⣿⣾⠇⣫⢆⣏⠀⣨⢰⡀⠓⠇⡧⠀⠘⢴⡯
⣾⣾⣿⠁⢠⣈⣿⣿⣿⣿⣷⣀⣈⣿⣼⣤⣟⡿⢿⣿⣿⣿⡿⢶⣿⡷⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠒⠉⢀⢳⣿⣿⣧⡢⢻⣿⣿⣎⣨⣿⡿⣆⢼⣾⠃⠀⢅⡠⣇⢰⢢⡷⠀⢾⣋⣃
⣿⣿⣿⣿⣟⣿⣿⣿⣏⠉⢙⣿⣦⣿⣽⣿⣿⣷⣾⡿⠿⡿⠿⢛⢷⣿⣼⣿⢾⢳⡁⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⢠⢀⡠⠀⡎⠁⠀⢹⣿⡤⢸⣿⣿⣿⣻⣿⣧⣿⣿⣿⣆⠀⠀⠀⢺⠿⠈⡶⢷⣼⣿⠷
⣯⣄⣈⣿⣿⣿⣽⣮⣿⣿⠿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿⢳⣶⣷⣧⣶⢿⣿⣿⣼⣀⣀⠀⢞⣧⡀⣰⣤⠀⢐⣮⠀⠀⠁⠀⢀⠞⠁⠀⢸⡏⣳⣶⣟⣿⣧⣮⣿⡿⣟⡲⢮⣬⣿⣿⣚⠙⢍⠓⢿⡍⠔⣾⡛⢯⠴⣡⠉
⣻⣻⣿⣿⣿⣿⣿⣿⣾⣝⣷⣿⣬⡻⣿⣯⣿⣯⣽⢿⣿⣷⣿⣿⣼⣷⢧⣿⣿⣿⡟⣻⠛⢲⣿⣿⣷⣾⣿⣿⣇⡉⠀⠀⠀⣎⡠⠀⣀⣠⡏⠌⢙⣼⣵⣿⢯⣿⣿⣿⡤⣖⣿⣧⢀⣺⣗⣬⣤⣼⣿⣓⠟⠁⢻⠱⡄⠲
⣿⣿⣿⣿⡿⠿⣻⣿⡯⣿⣿⣿⣿⣿⣿⣟⡻⣿⡿⣾⣿⣟⢽⣿⣿⡟⠟⣻⣧⢿⡿⡽⣶⣾⣿⣿⣿⡿⣿⣿⢠⣿⣆⢀⣀⣗⣿⡅⢻⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣴⣿⡿⡕⠯⠠⡌⢻⣏⢁⣾⣿⣿⣤⡠⠸⠦⣌⣦
⡿⣿⢿⣇⣀⠤⣿⡯⢟⣽⣿⣿⡿⢳⢁⣿⣿⣿⣿⣿⠻⢮⣎⣼⣿⣾⣿⣦⣿⢃⠇⣽⣿⢿⣿⡾⠟⡀⢸⣯⢼⠟⠻⡆⠀⣿⣽⣻⢿⣿⣿⢿⣟⣙⣫⠝⢉⠻⣦⣝⠻⣿⣶⡄⠦⡟⢚⢛⣿⣿⣿⡇⠠⢝⢁⢀⠟⠙

                    ䷩ 𝚕𝚒𝚗𝚎 2964

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

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    Gemini version at https://techrights.org/n/2025/03/14/Rumours_of_IBM_Layoffs_Again_This_Time_Marketing.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Rumours of IBM Layoffs Again, This Time
Marketing⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025,
updated Mar 14, 2025


IBM does not deny that there_are_mass_layoffs_this_year (worldwide, not only
"expensive"_countries), it just batches and keeps numbers low enough to evade
disclosure/transparency rules (for instance, lay off no more than 20 people per
site per time period).


Here's a clue as to where_cuts_are_happening_this_week:


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


They_typically_keep_quiet_when_that_happens_in_marketing. It's "bad marketing"
to talk about layoffs. █


    * The_Fall_of_the_Open_Source_Initiative_(OSI):_The_OSI_Does_Not_Speak_For
      You,_OSI_Staff_Speaks_for_GAFAM/Microsoft_(the_Paymasters)
    * Windows_is_Fast_Becoming_Insignificant_to_Zimbabweans


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⣿⣿⣿⣿⣷⢰⡄⣍⢯⢩⢋⣹⢩⠙⣡⢸⣯⣩⢋⣹⠩⠩⠩⡏⣉⢫⣼⢸⢩⣹⠫⢩⣿⢰⣖⡸⢆⠻⣴⣿⢸⢩⢩⠹⡝⣍⠇⣥⣴⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣯⣭⣭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣉⢉⣉⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡅⢧⣽⣿⣿⣿⢙⠉⠛⢿⣯⠟⢻⢟⢻⠏⣭⡿⡹⠹⢿⢛⢛⣟⢻⡍⢹⢹⣽⢻⢻⣽⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⡟⡛⢛⢻⡟⠛⠛⡛⡟⠛⠛⡟⢛⣻⡛⡛⣛⡛⠛⡟⠛⠛⠛⣿⠛⠟⡟⠟⢛⠛⠛⠛⣻⠻⠛⣛⡛⢻⠛⢻⣛⢟⡿⣿⡻⠛⠻⠛⢿⠛⠟⣛⢻⠻⣛⠻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣣⣾⣿⣿⠿⠷⡿⠿⠿⠿⡿⠿⠿⠿⣿⠿⠿⢻⠛⠿⠿⠻⠿⡿⠿⠿⡿⠿⠿⠿⡿⠿⠿⢿⠿⢻⠟⠿⢿⠿⠿⠿⠿⠿⠿⠿⡿⠾⠾⠿⠿⠿⡿⠻⠿⠟⠻⡿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⣶⣾⢼⢷⣶⣶⣶⡷⣶⣶⣾⡶⢿⣶⣶⣶⣮⣶⢶⣾⢾⣶⣷⣧⣶⣾⣾⣶⠾⣶⣶⣾⣶⢶⣶⣶⣶⢶⣶⣷⣶⣶⣶⣦⣴⣷⢶⣶⣶⢶⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣠⣠⣤⣤⣤⣤⣤⣧⣤⣤⣷⣴⣤⣤⣤⣤⣼⣠⣤⣼⣤⣤⣼⣠⣤⣼⣤⣤⣤⣼⣤⣤⣤⣦⣤⣤⣤⣤⣤⣼⣄⣠⣤⣤⣤⣧⣤⣴⣤⣀⣧⣤⣼⣠⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡗⢍⣿⢰⡁⢼⠰⠸⠇⠇⠬⠄⣻⢱⠉⠽⠩⡋⠁⢿⢩⠩⡫⠍⠭⠍⡭⣏⢍⢩⢿⠩⠩⡍⢱⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣧⣦⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣷⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⡶⠶⣖⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡅⢧⣽⣿⣿⢽⠙⠛⠛⡫⠟⠛⢿⠿⡽⠟⠛⡛⡟⠫⠉⡽⡛⡟⠛⠛⡟⠛⠏⠿⢻⠙⠟⠛⠍⢻⠛⢻⠹⠻⢿⠛⠻⡛⠛⡿⢟⣛⠻⡿⠛⡟⠻⠛⠛⠛⠛⢻⣿⣿⣿⣿⡇⣇⣂⡾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⡋⣿⣿⣿⡟⠛⠛⡛⡛⡛⠛⠛⠛⣟⡛⡛⠛⢻⡟⢻⠛⡛⢻⠛⡛⣛⢻⠛⠻⢟⠛⡟⠛⣻⠛⠛⠛⠛⢛⠛⡛⠛⢿⠛⠛⢻⠛⡟⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣮⣭⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡯⠭⠭⠭⠭⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢟⡛⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡏⡖⠐⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣳⣾⣿⣿⣿⣤⣤⣤⣴⣦⣤⣧⣤⣤⣤⣾⣤⣼⣤⣆⣾⣽⣮⣤⣤⣤⣴⣧⣤⣴⣤⣤⣤⣤⣇⣤⣼⣶⣧⣬⣼⣤⣦⣦⣤⣤⣴⣽⣤⣥⣤⣤⣧⣤⣶⣦⣽⣶⣶⣿⣿⣇⣃⣀⣛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣅⣿⣿⣿⣉⣉⣉⣏⣹⣍⣅⣸⣉⣉⣉⣉⣍⣁⣁⣁⣙⣅⣉⣹⣉⣉⣁⣏⣉⣉⣉⣈⣏⣉⣇⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⡞⣻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3050

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/Slopwatch_linuxsecurity_com_and_hamradio_my_in_Planet_Ubuntu_Ar.shtml
    Gemini version at https://techrights.org/n/2025/03/14/Slopwatch_linuxsecurity_com_and_hamradio_my_in_Planet_Ubuntu_Ar.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Slopwatch: linuxsecurity.com and
hamradio.my (in Planet Ubuntu) Are at It Again With LLM Slop About
"Linux"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025,
updated Mar 14, 2025


"Slopwatch" is a never-ending and much-needed (due to growing urgency) series
that aggregates several new examples of LLM slop (i.e. paragraphs stuck
together with other paragraphs whose words are strung together by a statistic
model built by scanning "tokens", not learning anything at all about meanings
and barely grasping grammar, either). We focus on that which impacts "Linux" or
related topics because otherwise the scope of the job would be endless. We
informally made it our 'job' to identify which sites became slopfarm and then
watch them closely, giving them "another chance" (to correct their ways after
'experimenting'_in_LLMs_like_LinuxInsider_did).


Let's start with hamradio.my (aggregated in Planet Ubuntu) because some of its
output seems legitimate, some is evidently a mixture, and some is very
obviously LLM slop. Consider this latest one:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇RT_Kernels_for_Audiophiles:_Enhanced_Audio_Performance_on
                                    Linux⦈_


Even before feeding that into a scanner it seemed rather obvious that this was
LLM slop. And it was:


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇A_real-time_kernel_is_a_modified_version_of_the_standard
Linux_kernel_designed_to_handle_time-sensitive_tasks_with_greater_precision_and
consistency._Unlike_standard_kernels_that_prioritize_overall_system_throughput,
   RT_kernels_focus_on_minimizing_latency_and_providing_predictable_response
                                   times.⦈_


linuxsecurity.com has long been a slopfarm and its latest output seems like
plagiarism of many_pieces from or about the Linux_Foundation.


Here is the machine-generated puff piece:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Strength_in_Unity:_OpenInfra_and_Linux_Foundation_Join_to
                     Revolutionize_Open-source_Security_⦈_


No room for doubt.


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Exciting_news_has_just_reached_the_open-source_community:
OpenStack,_now_known_as_OpenInfra_Foundation,_is_joining_forces_with_the_Linux
                                 Foundation⦈_


That's just a sample of examples of fake 'articles' about "Linux". Surely many
more will come and we'll report on what we find.


LLM slop does not save time; it does not have intelligence either. It does not
make anyone smarter and it mostly wastes people's time by distracting them from
real articles, composed by people who actually comprehend what they write about
(paragraphs that organise thoughts and articulate them clearly).


We should also revisit the difference between shorten and summarise, as many
sites out there falsely claim that LLMs can save time not just for fake writers
but also real readers. Without actually understanding the message, a machine
cannot summarise that message, it can just cull ("shorten") parts of it, so
there's no real, viable use case for LLMs. Over 99% of the alleged "use cases"
are lies or false marketing; it's effective at misleading shareholders though,
using the veneer of "novelty" or "future promise". They don't tell those
investors about legal risks and bad reputation associated with plagiarism. █


    * Links_14/03/2025:_Chinese_Tensions_With_Australia,_Putin_Turns_Down
      Ceasefire
    * Microsoft_Money_Used_for_Abuse_of_Women_and_Against_Journalism_in_Support
      of_Women_(the_Victims)


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣷⣷⣶⣷⣷⣶⣾⣶⣾⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⣾⣶⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⠿⠿⠿⠿⡿⠿⠿⢿⠿⠿⠿⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣤⣤⣤⣧⣤⣤⣤⣤⣧⣤⣤⣼⣤⣤⣤⣧⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣼⣤⣤⣤⣧⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠿⠿⣿⠯⠿⠿⠽⠽⠽⠿⡿⠽⠯⠿⠽⠿⠿⠿⠿⠿⡿⣿⠿⢿⠿⠿⠿⠿⢿⡿⢿⠿⢿⠯⠿⠽⠿⠯⡿⠿⠽⠿⡿⠿⠽⠿⠽⠯⡽⠽⠿⢿⡿⠿⠿⠿⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣯⣭⣽⣿⣽⣽⣯⣽⣯⣭⣯⣽⣯⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠛⢛⣿⢟⠿⠿⠿⡿⠟⠿⡟⠻⠿⢿⠟⡿⠿⠟⠻⠿⠿⠻⠛⡿⠿⠿⡟⢛⠿⠻⡿⡿⠿⠿⢿⠟⣿⠻⢿⠿⠛⠿⣿⠛⠿⡿⠟⠿⠿⠿⢿⢿⠿⠿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣾⣿⣶⣶⣾⣾⣶⣶⣶⣷⣶⣶⣿⣶⣶⣶⣷⣶⣦⣶⣶⣶⣶⣶⣶⣷⣾⣶⣾⣶⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣾⣶⣶⣿⣶⣾⣶⣶⣾⣷⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣃⣯⣏⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣭⣭⣭⣽⣽⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣭⣯⣭⣭⣭⣽⣭⣍⣭⣭⣯⣭⣭⣭⣯⣭⣿⣭⣯⣭⣭⣭⣯⣭⣯⣯⣭⣭⣿⣭⣽⣯⣭⣭⣭⣽⣯⣽⣭⣭⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣷⣾⣶⣶⣷⣶⣶⣷⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⢿⣏⡉⠙⠛⡏⢻⠛⠛⠏⡭⡏⠝⢛⠛⠋⢍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣯⣽⣭⣭⣭⣭⣯⣽⣭⡭⣭⣯⣭⢭⣯⣯⣽⡭⢭⣭⣭⡭⣯⣽⣽⣭⣭⣭⣭⣥⣽⣭⣯⣭⣭⣯⣭⣭⣭⣭⣥⣯⣭⣭⣯⣭⣭⣽⣭⣭⣭⣭⣭⣭⣯⣭⣽⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣾⣷⣾⣾⣾⣶⣷⣿⣷⣷⣶⣿⣾⣶⣾⣷⣿⣿⣾⣿⣾⣿⣿⣾⣶⣿⣷⣶⣷⣿⣶⣷⣿⣾⣿⣾⣾⣿⣿⣷⣶⣷⣶⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣽⣽⣭⣭⣯⣭⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡛⢛⢟⣻⣿⣻⣿⣿⣻⣿⣿⣻⣿⣿⢿⣿⡿⣻⣛⣿⢻⣿⣿⣿⣻⣻⣟⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣛⢻⣛⣛⣛⣛⣻⣛⣛⣛⣟⣛⡛⣟⣛⣛⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣟⣛⣟⣛⣻⡛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣛⣻⣛⣟⣛⣛⣛⣻⣛⣻⣛⣟⣛⣟⣛⣛⣻⣛⣟⣻⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⢿⡿⠿⢿⣿⠿⠿⡿⢿⣿⣿⡿⣿⢿⣿⠿⣿⣿⢿⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣧⣤⣼⣤⣬⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣬⣷⣶⣶⣶⣶
⣿⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡶⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒
⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⡿⠛⣉⡛⢿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⠀⣿⣋⣿⠄⣿⣷⣶⣶⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⣦⣈⣛⣉⣴⣿⣷⣶⣷⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⠛⠻⠿⠿⠟⠛⠿⠿⠿⠿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣿⣷⣶⣆⢸⣿⣯⣥⣦⣤⣴⣷⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⢀⣍⠈⣉⣿⣿⣈⣉⣉⣋⣽⣻⣙⣯⣭⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠒⠰⠐⣢⣲⣿⣿⡏⢁⣠⣤⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣉⣽⣶⣿⣿⡅⢺⣿⣿⣿⡀⣿⣿⣙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⢯⡭⣿⡿⣿⣭⢿⡯⣭⡿⣽⣯⣽⠿⢭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⢀⣾⣿⣿⣿⠟⣿⣧⣈⡿⠿⠛⠋⠉⢻⣷⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣯⣴⣿⣿⣯⣶⣿⣿⣤⣤⣤⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠀⠀⢀⢢⣤⢰⣀⡤⣄⣤⡴⢦⢠⢠⠀⠠⠠⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠀⠀⠛⠀⠋⠀⠀⠒⠀⠒⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠠⢄⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⣿⠖⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠓⣻⣿⣿⣿⣿⣿⠀⢠⣤⣤⣾⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⣿⣿⣿⣷⠿⠋⣩⣟⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢀⠁⠚⣿⣿⣿⣶⣾⣿⣿⣷⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠈⠈⠀⣿⣿⣿⣿⠟⠿⣿⢿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡠⣴⣶⠐⠛⢻⠽⠟⠀⠀⠸⢷⠹⠟⠛⠍⠉⠁⣋⢯⣫⣳⢑⣀⠀⣀⣀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠀⠟⣁⣴⡦⠁⠠⠄⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⡿⠁⠀⠈⠑⠀⠀⠀⠒⠾⣿⣷⣄⡀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠹⠃⠾⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⣿⣿
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⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠒⠒⠒⠒⢻⣿⣿⣿⣿⣿⣿⠸⣿⣯⣽⣿⢸⣿⣿⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

                    ䷩ 𝚕𝚒𝚗𝚎 3224

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/The_Fall_of_the_Open_Source_Initiative_OSI_The_OSI_Does_Not_Spe.shtml
    Gemini version at https://techrights.org/n/2025/03/14/The_Fall_of_the_Open_Source_Initiative_OSI_The_OSI_Does_Not_Spe.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Fall of the Open Source Initiative
(OSI): The OSI Does Not Speak For You, OSI Staff Speaks for GAFAM/Microsoft
(the Paymasters)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Open_Source_Initiative_(OSI)_ENTRYISM,_a_Lobbyist_of
                                  Microsoft⦈_


The OSI is panicking. This is very encouraging to us. This series is fast
becoming longer than we initially expected because the OSI seems to have kicked
into "damage control" mode (catastrophe mitigation), seeing that more leakers
or whistleblowers are eager to say or do things. They try ban people. It
doesn't make things any better. Instead of OS (Open Source) it's becoming
MarcOS. The OSI became an evil dictatorship with its_own_Mussolini_in_charge.
It cannot end well...


For the first time in ages, opensource.org and opensource.net became a little
active again (not much, but they try to change the subject or "prove wrong" the
critics). Those are OSI-run but hardly running during recent blunders.
Misdirecting outrage/energy? Rerouting people?


What's noteworthy is that many people read the past 2 parts, which deal with
bylaws and who actually controls the Open Source Definition. People start
realising that the OSI is a poser more than anything. It violates_members'
privacy and over 97% of its income does_not_come_from_members but from
companies, notably Microsoft.


"Excellent!" one person said about revelations. "Great work, keep their feet to
the fire! In the best outcome, there can be some kind of reform either of the
OSI or through creation of a new steward for FOSS licensing, one that will take
its responsibilities seriously."


The FSF predates all this; OSI was an attempt to marginalise it, if not
initially than soon afterwards. Bruce Perens, who had cofounded OSI, spoke
about it publicly more than 2 decades ago.


We hope that more people will understand what the OSI really is, especially
people who joined based on false pretences. We need transparency.


Speaking of transparency, the EU has this_new_initiative with a four-week
feedback period open until 15 April 2025 CET:


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


"Important for FOSS," says an associate, but a recent talk in Germany (CCC)
showed that it is stacked and "Sompi" (in IRC) noticed the same firsthand. They
don't really listen to those who aren't rich or don't run large companies. It
is a like EPO consultations, where anyone can send something but input will
only be taken seriously if it's some large (money) stakeholder, not some
"pesky" citizen or university professor.


"Decisions are being made while cutting out the public input," said an
associate. It's possible that OSI will participate in the above (Jordan Maris,
Simon Phipps et al), but we must remember that they work for a front group
controlled and funded by GAFAM going under "open source". Put another way, they
don't represent us; they speak for proprietary software companies, but they
wear "open" on their sleeve. █


    * Microsoft_Money_Used_for_Abuse_of_Women_and_Against_Journalism_in_Support
      of_Women_(the_Victims)
    * Rumours_of_IBM_Layoffs_Again,_This_Time_Marketing


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣹⣝⣿⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣖⡆⣖⡂⣴⣶⣦⣰⣶⡆⣴⣶⢀⣶⣠⣶⣶⡄⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣶⣦⣴⡶⠂⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣋⣃⣓⣂⡿⠿⠟⠹⢿⠇⠻⠟⠈⠿⠹⠿⠿⠏⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠟⠿⠿⠟⠻⠷⠆⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠇⠹⠀⠋⠐⠝⠘⠇⠸⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣯⣯⣯⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⠉⠁⠘⡇⠙⢻⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡿⠛⡟⣿⣿⡟⢻⠿⢿⣿⣿⣿⠛⠛⢛⡟⣻⠿⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡟⠛⠛⠻⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣤⣤⣤⣧⣤⣼⣤⣤⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡏⣻⡛⢻⠛⣿⠋⡛⠙⢻⡏⢛⣿⢻⡟⠛⣛⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣿⣽⣯⣭⣽⣭⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣶⣶⣶⣿⣶⣷⣶⣾⣷⣾⣿⣾⣷⣶⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡻⠿⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠾⠧⠶⢾⢷⡶⠶⠶⠶⠿⠶⡿⢶⠴⡶⠾⠶⡾⠿⡶⢶⠶⡶⠾⢷⠿⢶⠶⢦⠿⠶⢿⠶⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢾⣷⢶⣶⣶⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣟⣟⣛⣛⣟⣻⣛⣳⣻⣛⣟⣻⣛⣛⣛⣛⣻⣟⣛⣻⣛⣻⣟⣛⣛⡛⣟⣻⣳⣛⣛⣟⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠷⣶⣶⡶⡶⠶⢶⡾⢿⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣝⣭⣬⣭⣭⣭⣭⣯⣭⣭⣭⣯⣥⣩⣭⣭⣭⣭⣯⣽⣭⣬⣭⣿⣧⣥⣭⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣷⣶⣾⣷⣶⣾⣷⣾⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣙⣙⣛⣛⣻⣛⣟⣛⣛⣛⢛⣻⣙⣟⣛⣛⣏⣟⣻⣙⣋⣛⣛⣟⣏⣛⣟⣛⣛⣙⣙⣻⡛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣯⣬⣽⣭⣯⣭⣭⣭⣽⣽⣭⣭⣯⣧⣭⣬⣭⣯⣭⣬⣭⣽⣭⣭⣥⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣤⣤⣶⣤⣤⣼⣤⣼⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢛⣿⠿⠿⢿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⣿⣿⣯⣍⣉⣋⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣉⣍⣩⣉⣹⣙⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⢾⣶⣾⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠶⠾⡷⡾⠶⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣶⣷⣶⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⡿⢿⡟⣿⡿⢿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣦⣯⣾⣧⣿⣵⣮⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3351

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/03/14/Windows_is_Fast_Becoming_Insignificant_to_Zimbabweans.shtml
    Gemini version at https://techrights.org/n/2025/03/14/Windows_is_Fast_Becoming_Insignificant_to_Zimbabweans.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Windows is Fast Becoming Insignificant to
Zimbabweans⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


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


In 2023 we already_saw_Microsoft's_pains_in_Zimbabwe - not that Microsoft
really minds these poor countries, it_views_them_as_"drug_addicts" and tries to
flood them with Windows "drugs".


We've only just noticed Windows_taking_a_big_tumble:


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


So based on this survey, less than 1 in 6 Web requests may originate from
Windows. Almost_3/4_use_mobile.


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


Windows - like_Skype_and_XBox - is not really financially viable when its
number of users (or income) falls below some level/soft threshold. That's when
the quality of Windows and its patches go down the drain; then Windows circles
down the drain. █


    * Rumours_of_IBM_Layoffs_Again,_This_Time_Marketing
    * Links_14/03/2025:_ProPublica_Admitting_That_It_Uses_Slop_(Foolish_Move),
      RIP_Mark_Klein


⠀⠀⠖⢀⣋⣭⣽⣫⡀⠀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠋⠉⠋⠀⠀⠀⠉⠀⠀⣹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠾⣿⣷⢩⣍⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣶⡆⣠⣼⠄⠉⢃⠀⢀⡀⠀⠀⠀⠀⠉⠀⠐⠃⣴⣶⣿⠿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠐⠁⣀⡀⠀⠉⠑⠀⠀⠀⠀⠀⠐⠶⢿⣿⣿⣿⠓⠛⣤⡄⣛⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠁⠙⠆⠀⠀⠀⠀⠙⠋⣶⡖⠂⠀⠈⠉⠁⠀⣀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠛⠖⠀⢀⠘⠂⠀⢒⢨⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡳⢲⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⠀⠈⣀⠀⠀⣀⠀⠄⠄⠀⠐⠀⠀⠀⠐⠛⠷⠺⢿⠟⠛⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠈⠂⠀⡀⠀⠁⠶⠌⢠⣤⣄⡀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣶⣶⣶⣤⣄⡀⢹⣿⣿⣿⣿⣇⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠁⠈⣅⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⡆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⠋⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣹⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⣿⣿⡿⢟⣛⠁⢂⡵⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣤⣶⣶⣄⠀⠀⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣷⣤⣀⡘⣿⡅⠘⣧⣤⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣄⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⠿⣿⣿⣦⡁⡴⣣⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⢉⣴⣿⣿⣿⣶⣶⣶⣶⣦⡀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⣿⣿⡆⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⡛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣷⡄⠹⣿⣿⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣧⡌⢀⣾⣿⣿⣿⣿⡿⣿⠿⠟⢡⣴⣿⣿⣯⠀⠈⢻⣿⡿⠁⠀⣼⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡿⠋⠀⢾⣿⣿⣿⣿⣿⠁⠀⠀⣰⣿⣿⣿⣿⣿⠃⠀⠀⠙⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣾⣿⣿⣿⣿⣿⣿⡟⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⢠⣶⣿⡙⢿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠈⠁⣿⣿⣌⠻⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡟⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠃⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣾⣿⡇⠙⠿⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢀⡄⠀⣿⣿⣿⣿⢿⣿⣿⣿⣧⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣤⣀⠀⠙⠃⠀⣀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢻⣿⣿⣿⣷⣶⡇⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸⠀⠙⠛⠉⣠⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⡗⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡀⢿⣿⡇⢸⡉⠁⠩⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⣴⡆⠘⣶⣶⣶⣿⣿⡇⠰⢄⣀⣼⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⡁⢨⡟⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⠟⠿⠿⠁⠀⠃⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠛⠛⣛⡛⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠟⠀⣾⣿⣿⣿⣿⣿⡇⣠⣼⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠋⠛⣿⣿⠀⠀⠀⣤⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠸⣿⡁⡿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣰⣿⣿⣿⢻⣿⠏⠓⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡿⠀⣾⣦⣼⣧⣤⣾⣧⣼⣧⣆⡄⠀⠀⠀⠀⠀⠀
⠀⠐⠛⠀⠃⠀⠀⢠⠀⢰⣿⣿⣿⠀⠀⠀⠰⣿⣿⣿⣿⢸⣿⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣸⣿⠇⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⣾⣶⣿
⠀⣿⠀⡆⠀⠀⠀⠸⠀⢸⣿⣿⣿⠀⠀⠀⠀⢸⠟⢙⣿⢸⣿⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣉⠶⠁⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⢠⣿⣿⣿
⣀⠉⠀⢀⣐⣦⣤⣾⣶⣾⣿⣿⣿⠀⠀⠀⠀⣸⣤⣼⣿⢸⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢿⣷⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⡿⣿⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠠⡤⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⢰⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣷⣶⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣠⣀⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡥⠀⠉⠉⠉⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣿⣿⣁⣸⣿⣿⣿⣿⠋⠙⠛⠻⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⡏⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⡀⢰⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠛⢻⣿⡛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠷⣿⣿⣿⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⣠⣾⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢠⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⡟⠛⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣼⣿⡇⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣠⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⡋⠙⠲⢤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⠛⠉⠺⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣤⣤⣤⣰⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣉⣉⣉⣉⣹⣿⣿⣧⣶⣴⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣛⢻⡿⠿⢿⠹⢿⠿⡿⠿⢿⢷⡶⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣵⣿⣧⣧⣿⣼⣽⣦⣯⣧⣦⣦⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⢉⣻⡋⡟⡯⢹⠭⣯⢉⣹⣿⣿⠹⣻⡿⣿⣿⢍⢩⠫⣹⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣾⣷⣶⣾⣷⣾⣶⣷⣿⣾⣿⣿⣾⣿⣾⣿⣿⣶⣷⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢠⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢸⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⡿⠛⡛⢿⠿⠿⠀⠸⠿⠿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⡟⣿⣿⣿⣿⣿⡟⣿⣿⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢻⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣤⣾⣿⣿⡄⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⣸⠀⢿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠁⠹⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⡉⠋⠁⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣟⠉⣉⠃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⠀⣛⣛⣛⠁⠀⠀⣚⣛⠀⠀⠀⣛⡃⠘⠀⠃⠀⠀⠈⠀⠋⠈⡃⠃⡃⡀⡁⠈⠀⠁⣐⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢀⣒⣛⣛⣀⡀⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠟⣿⣿⣇⠀⠀⠈⠁⠀⢠⣶⣿⣿⠀⠙⠁⣾⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢹⠃⣾⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡏⠛⢿⣷⣦⣤⣤⣴⣿⣿⣿⡿⢰⣴⣼⣿⠀⠀⣿⣿⡟⠛⠉⠝⣿⣿⣿⡟⢻⣿⣿⡏⠙⠿⠿⠻⡟⠋⢠⣴⠀⢰⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⠸⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⠀⠛⠃⣀⣶⣿⡄⠉⠹⠹⠁⠈⣿⣿⡇⢠⣶⣦⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣷⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡆⢀⣿⣿⣿⣿⣿⣥⡀⠀⢠⡀⠀⢹⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣟⣉⣉⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣶⡇⢸⣿⣿⣿⣿⡟⠻⠇⢸⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⣿⣿⠃⠀⠸⠿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢸⣿⣿⣿⠈⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⡿⠇⠈⠛⠿⣿⣿⡟⠉⠀⢠⠀⢀⣄⣾⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡆⢹⠟⠉⠃⠀⢰⡆⢸⣿⣿⣿⠁⠀⣠⣆⡀⠀⠛⠀⣧⣼⣿⣇⣸⣿⣿⡇⠈⠙⠟⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠇⠀⢰⣿⡆⢰⣾⡇⢸⠻⢻⡿⠀⠀⣿⣿⡇⢸⣾⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣤⣤⡀⠉⠘⠙⠙⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡿⢀⠀⣈⠉⠀⢸⣿⣷⠀⣀⡀⠃⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠴⠀⠰⠆⠙⠻⠿⠟⠻⠇⠿⠿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣷⣤⣤⡅⣭⣭⣭⣭⣭⣭⡍⢩⡍⢉⡀⠀⠨⠉⢀⣡⣬⡀⢁⣤⣤⠈⢭⣭⣬⣭⣥⣄⣬⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣯⣽⣉⣉⣩⣹⣿⣋⣋⣏⣍⣿⣯⣉⣹⣛⣙⣋⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⠉⢹⣿⣿⠁⠘⢀⣾⠩⠁⠀⣰⣾⣿⡿⢀⣸⣿⣿⡀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡂⣶⣶⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⡟⠀⢸⣿⣿⠀⠟⢛⣩⡴⠟⠀⠙⠛⠟⠃⠀⢿⣿⣿⣿⣿⠀⠿⠿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⣿⣿⡿⢿⡿⠿⠛⠟⢹⢿⣿⣿⣿⣿⡍⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⠇⠀⢸⡿⠛⢀⣿⣿⣿⠃⠀⠘⢂⠠⢀⣤⣦⣄⠈⠉⠛⠻⢂⠰⠒⠈⠻⢛⠛⠉⠉⠁⠀⠉⠉⠙⠉⡍⢩⡁⠈⠀⠉⠀⢉⡁⣀⣀⣠⡄⢀⣠⠀⠈⠉⠉⠉⠀⠀⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⡇⠉⠀⠀⠄⠤⠰⠟⠛⠉⠤⠤⠇⠈⠉⠐⠛⠛⠛⠛⠛⠃⠀⠈⠉⠒⠂⠀⠀⠉⠀⠈⠙⠓⠑⠊⠁⠤⠠⠠⠄⠀⣈⣤⡶⢦⠤⡤⣬⣬⣉⣉⣉⣋⣹⣑⠀⢓⢒⣀⡀⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣧⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣶⣶⣶⣶⣶⣶⣴⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠿⠛⡛⠛⠛⢛⢻⣿⣿⣿⣿⣿⡿⣛⢿⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⡿⢛⢻⡛⠻⡻⠛⠻⠛⢻⣿⣿⣿⣿⣿⢛⠻⢻⢛⠛⠛⡛⠛⡻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⡺⠷⠳⠷⠶⠖⠶⠾⡻⢻⣿⣿⣿⡿⢷⢿⢞⠗⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠷⢿⢖⠶⠿⠶⠞⠖⠾⠿⠿⠛⣿⣿⣷⣿⣷⣿⣶⣶⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣾⣷⣶⣶⣷⣷⣿⣿⣿⣿⣿⣶⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣶⣧⣶⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⡟⣿⢻⣿⡿⣿⠹⡟⡿⡿⡿⡿⣿⢿⢿⣿⣿⢻⡟⡿⡿⡿⡿⢿⠹⡿⣿⢿⠿⣿⣿⣿⣿⢿⢿⢿⡿⡿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣧⣯⣴⣴⣷⣼⣤⣧⣧⣯⣯⣧⣿⣦⣷⣼⣿⣧⣼⣧⣯⣯⣧⣼⣤⣦⣿⣮⣯⣮⣿⣿⣵⣼⣽⣽⣧⣦⣿⣿⣮⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿
⣿⣿⡏⣴⣟⣟⣟⡟⡻⠟⣟⡇⡟⢻⣿⡼⢇⡟⢿⢻⡿⣻⠛⡏⣿⣇⡺⢸⣻⠻⡟⣿⠻⣿⡷⣢⢸⣻⣻⠃⣟⡟⠟⣿⣻⠟⠛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣷⣶⣿⣷⣶⣶⣶⣷⣷⣾⣿⣷⣿⣷⣾⣾⣿⣾⣶⣷⣾⣷⣶⣾⣿⣶⣷⣿⣶⣿⣶⣶⣾⣿⣿⣶⣶⣷⣶⣷⣾⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⣚⠉⠨⢹⡷⢈⠆⡱⠀⢊⣟⣻⣏⢣⡏⢹⣽⡗⢌⠆⠖⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠛⢙⠛⣟⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢠⡀⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣤⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⢸⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⡇⠿⠇⠀⠸⠿⠿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⡇⣿⣇⢀⣼⣿⣿⡄⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⢠⡀⢿⣿⠀⣿⣿⣿⣿⣿⡇⠀⠿⠿⣿⣿⣿⣿⠈⠃⠉⢠⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣾⣧⠘⣿⠀⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠙⣿⣿⠀⣀⣀⣾⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣀⠙⠀⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⣿⣿⣿⠁⠀⠀⢠⣄⠀⠀⠀⠸⡿⠀⠟⢿⠟⠇⠀⠸⠻⠿⠏⠻⡿⡿⠿⠟⠿⠟⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡏⢀⣾⣿⣿⣿⣷⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⠿⠟⠁⠀⢀⠀⠇⠀⣇⣉⣀⣠⣀⠀⠉⠌⠀⠀⡀⠀⣇⣇⣁⣀⠈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠁⣾⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⣴⣿⡄⡀⢸⣿⣿⣿⣿⣿⠀⢀⣠⣤⣶⣿⠀⣿⣿⢿⡏⠀⣿⣿⣿⠁⠙⠻⠟⠟⡏⠀⣰⣾⣦⣴⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠻⠀⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡇⠈⠘⠀⠁⡀⠀⢿⣿⠀⣤⣤⣦⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⣷⡆⠈⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⣿⡇⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣠⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠏⠁⢰⣶⠀⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣉⣉⣉⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⡇⢠⣰⣀⡄⠀⣤⣿⣿⠀⠀⢀⣀⣄⡄⠈⢻⣿⡟⠻⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣿⣿⣿⣷⠈⣿⣿⣿⡿⣿⠃⠀⢸⣿⣿⣿⣿⣿⠀⠈⠉⠙⠛⡿⠀⣿⣿⣿⣷⣀⣿⣿⣿⣦⣼⣿⣿⣿⣿⣶⣄⠈⠀⠀⢿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡁⠀⣿⣿⣿⣿⣿⠀⠹⠟⠙⠃⠘⠀⣆⠀⣿⣿⣿⡟⠀⢀⣠⣧⠀⢀⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⡇⠈⢿⣿⣿⣿⡿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⢿⡏⢰⣷⠀⣿⣿⣿⣿⣿⡆⠀⣰⣿⣶⣆⣸⣿⠀⣿⣿⣿⠇⠀⢸⣿⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠛⢀⠀⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠈⠀⣿⣿⣀⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣷⣾⣿⣶⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⠛⠛⠛⡇⠿⠇⠀⠹⠿⠿⠁⠦⠰⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠿⠿⠿⠿⠿⠿⠄⠦⠄⠈⠀⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⢸⣿⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⢿⡇⢀⠘⠉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠿⠿⠿⠿⠻⠿⠿⠿⠿⠛⠻⠿⠿⢿⢿⠿⢿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⡇⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠛⠛⠛⠉⠋⣉⣉⣉⣠⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣴⣶⣦⣤⣤⣤⣤⣤⣀⣁⣤⣤⣄⣄⣉⣉⠉⡉⠉⠙⠉⠛⠛⠛⠛⠋⠙⠛⠛⢸⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⢙⡏⠋⠋⠋⠙⢻⣿⡟⠍⣻⠉⠛⠋⠋⠛⠛⣿⣿⡫⢝⡏⠙⠙⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3531

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 14/03/2025: Grizzy Bear and
Prime Beats⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Dangers_-_Grizzy_Bear⠀⇛


                       This is the next part of the chapter 'Dangers',
                       continuing on from the discussions between Lantashi
                       and Lee. This scene is called 'Grizzly Bear'. This
                       is the start of where things will get very exciting
                       for two the friends going forward in the story!


                # ⚓ Fixed_points_in_arguments⠀⇛


                       By coincidence, this is broadly in my policy area
                       of UK housing.


                       What he's identified here is a tactic of
                       maintaining a particular assertion at all costs.
                       The costs in particular include credibility with
                       outsiders. And this assertion is being maintained
                       rhetorically to avoid undermining some ulterior
                       proposition. Per his example, the actual position
                       being defended is a sacred value that is two or
                       three logical steps away from the "fixed point"
                       argument. It's a sort of rhetorical "Defence In
                       Depth".


                       So the point of repeating the lie is to avoid
                       exposing a different lie that would be more painful
                       to abjure. Implicitly, in-group cohesion is more
                       important than credibility and fidelity to truth.


                # ⚓ More_translations⠀⇛


                       On the horizon of torrents, the English GOG version
                       of the first part of "Space Rangers" (v1.7.2)
                       appeared. It was immediately boarded and gutted.


                # ⚓ [01]_after_2_years..._hello_smol.pub!!⠀⇛


                       it's funny how i've had an account here for a good
                       2 or so years already, but only decided that now's
                       the time to actually do something on it. well...
                       these things are better late than never, i guess!


                       who i am in specific isn't so important. maybe one
                       day i'll dedicate a blog to properly introduce
                       myself—but you have to understand that
                       introductions, in general, are a bit hard for me!
                       i'm a 20-something year old person from the
                       philippines. on the younger side, maybe? just in
                       time to be barely within the target demographic for
                       algorithm-driven "brainrot" platforms, for sure
                       haha.


                       that said, identity is so hard for me to pin down.
                       i was barely given the privilege to form one of my
                       own when i was younger, so i'm in the process to
                       try and figure out the things i like and don't
                       like. if you make any references to any widely
                       popular media around me, please understand that
                       i'll sometimes give a polite laugh and go "haha, i
                       haven't seen that yet. sorry! please tell me more!"
                       i guess which is one of the reasons why i'm here
                       now.


                # ⚓ Steven_universe:_vCJD_edition_chapter_4/_Enrtry_for_side_D
                  of_vCJD⠀⇛


                # ⚓ Prime_Beats⠀⇛


                       Music generally repeats itself, though something in
                       4/4 time (like nearly all pop music) repeats with
                       more regularity than anything that uses prime
                       numbers of any notable size. The following (which
                       stops mercifully short of the full least common
                       multiple) plays 3 against 5, 7, 11, and 13, with
                       pitches picked somewhat at random resulting in a 5-
                       20 pitch set or here D Eb A Bb G.


          o § Politics and World Events⠀➾


                # ⚓ Category_III:_The_Untold_Story_of_Hong_Kong_Exploitation
                  Cinema⠀⇛


          o § Technology and Free Software⠀➾


                # ⚓ smol.pub⠀⇛


                       I have no real idea what to do with this space, but
                       I do love the ideas behind smol.pub, so here we
                       are. This space is currently so small there is a
                       feed of every single person's posts. Twitter was
                       like this at the very start, when it was still
                       called Twttr and no one really knew it existed. I
                       would post via SMS. This feels less archaic in some
                       ways, more archaic in others. I like the idea of
                       posting small thoughts into the void: no likes, no
                       replies. Just posts and links, like God intended.


                # ⚓ i_got_mail⠀⇛


                       today I wrote myself an email that contained some
                       files I needed


                       back in the day, before google drive and cloud
                       storage, the way my sister taught me to put a file
                       up on the internet so i could access it from
                       different places and devices was to attach it to an
                       email and send it to myself


                       i am no expert but i am sure this is not the oldest
                       tactic that achieves this particular utility, and
                       it is demonstrably not the youngest


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


    * Links_14/03/2025:_ProPublica_Admitting_That_It_Uses_Slop_(Foolish_Move),
      RIP_Mark_Klein
    * 'India_Today'_is_a_Slopfarm,_Sometimes_'Covering'_"Linux"_With_Slop
      Images



                    ䷩ 𝚕𝚒𝚗𝚎 3709

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 14/03/2025: Löjl and Docker
Context Stuff⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Löjl⠀⇛


                       “Löje” is a bit archaic (outside of several
                       fossilizing specific expressions that are still in
                       use, like “göra till åtlöje”). When wanting to use
                       a noun form of “löjlig”, instead of repurposing
                       “löje”, which doesn’t have the same disparaging
                       weight, people went two directions.


                       One is “löjligheter”. "Vad är det här för
                       löjligheter?" a rich CEO might exclaim.


                       The other is “löjl”, which is more slangy, more
                       something Buffy or Willow would say, "Vad är det
                       här för löjl?"


                # ⚓ Testing⠀⇛


                       I saw the best minds of my generation destroyed by
                       madness. Now is the time for all good men to come
                       to the aid of their country. What do we say to the
                       God of Death? Not today.


                # ⚓ 🔤SpellBinding_—_ASHIPRD_Wordo:_BRAVO⠀⇛


          o § Technology and Free Software⠀➾


                # ⚓ TIL:_Docker_Context_Stuff⠀⇛


                       TIL: Some things about docker I really should have
                       known by now but didn't.


                       If you have a slow docker build due to loading the
                       build context, you should setup a .dockerignore
                       file.


                       To make it as fast as possible, your .dockerignore
                       could look like this:


                       *
                       !./pyproject.toml
                       !uv.lock
                       !./src/**/*.py
                       The top line `*` ignores all files, then use `!` to
                       include certain files or file paths. It uses a
                       globbing syntaxt similar to gitignore files.


                # § Programming⠀➾


                      # ⚓ [Old] smol-cli⠀⇛


                             I have almost got this CLI working, written
                             in the most vanilla of Rust code. Writing a
                             tool like this in Rust probably doesn't make
                             much sense, but i'm trying to learn the
                             language, and writing CLIs seems to be the
                             thing to do. Let's see if I can post this
                             message, and if I can, I'll try and update to
                             point to a github repo.


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


    * Links_14/03/2025:_Scam_Currencies_in_the_US_and_Oligarchs_(Including
      GAFAM)_Controlling_All_the_Major_Policies
    * Links_14/03/2025:_Chinese_Tensions_With_Australia,_Putin_Turns_Down
      Ceasefire



                    ䷩ 𝚕𝚒𝚗𝚎 3827

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 13/03/2025: Intel Rotates Figurehead
and South Korea Imports Karen People From
Myanmar⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Integrity/Availability/Authenticity
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # 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 ⚓ The Straits Times ☛ China’s_Haidilao_to_compensate_thousands_of
            customers_over_hotpot_pee_incident⠀⇛


                 Video showing two men urinating into the broth of their
                 hotpot started circulating online late in February.


          o ⚓ Hackaday ☛ A_Fast_Rewind_To_The_Era_Of_Tapesponding⠀⇛


                 Imagine a time before Discord servers and cheap long-
                 distance calls. Back in the 1950s, a curious and crafty
                 group of enthusiasts invented their own global social
                 network: on reels of magnetic tape. They called it
                 tapesponding (short for tape corresponding), and it was a
                 booming hobby for thousands of radio hams, tinkerers, and
                 audio geeks. Here’s the original video on this analog
                 marvel.


          o § Science⠀➾


                # ⚓ Science Alert ☛ Violent_Supernovae_Could_Have_Triggered_at
                  Least_2_Extinction_Events⠀⇛


                       A major impact on Earth's history.


                # ⚓ Science Alert ☛ Source_of_Mystery_Radio_Signal_Traced_to
                  Clash_of_Magnetic_Titans⠀⇛


                       Boom! Boom! Boom!


                # ⚓ Science Alert ☛ Face_of_Overlooked_Human_Ancestor_Could_Set
                  Record_in_Western_Europe⠀⇛


                       But who does it belong to?


          o § Career/Education⠀➾


                # ⚓ JURIST ☛ Philippines_human_rights_watchdog_expresses
                  support_for_proposed_internet_safety_education_bill⠀⇛


                       A human rights watchdog in the Philippines on
                       Monday declared its “full support” for the passage
                       of a proposed internet safety education bill
                       protecting children from online sexual abuse and
                       exploitation. The Commission on Human Rights (CHR),
                       an independent National Human Rights Institution,
                       expressed its approval of the newly introduced
                       Senate Bill (SB) 2934.


          o § Hardware⠀➾


                # ⚓ New York Times ☛ Intel_Names_Lip-Bu_Tan_as_New_CEO_Amid
                  Turnaround_Efforts⠀⇛


                       The semiconductor pioneer appointed Lip-Bu Tan, a
                       well-known tech investor and executive, as its new
                       leader.


                # ⚓ Silicon Angle ☛ Intel_finally_gets_a_new_CEO:_industry
                  veteran_Lip-Bu_Tan⠀⇛


                       Embattled chipmaker defective chip maker Intel
                       Corp. is hopeful of better days ahead after hiring
                       Lip-Bu Tan as its new chief executive, ending a
                       months-long search for a new leader that followed
                       the ouster of its previous CEO Pat Gelsinger in
                       December.


                # ⚓ Tom's Hardware ☛ Intel_appoints_Lip-Bu_Tan_as_permanent
                  CEO⠀⇛


                       Industry veteran Lip-Bu Tan becomes Intel's
                       permanent CEO, rejoins the company's board-of-
                       directors.


                # ⚓ Silicon Angle ☛ Report:_TSMC_could_launch_joint_venture
                  with_partners_to_run_Intel’s_fabs⠀⇛


                       Taiwan Semiconductor Manufacturing Co. could form a
                       joint venture with several chipmakers to operate
                       defective chip maker Intel Corp.’s fabs, Reuters
                       reported today. The company is said to have pitched
                       the idea to Nvidia Corp., Advanced Micro Devices
                       Inc., Broadcom Inc. and Qualcomm Inc.


                # ⚓ Tom's Hardware ☛ TSMC_and_defective_chip_maker_Intel
                  foundry_joint_venture_reportedly_still_in_the_works_—_AMD,
                  Broadcom,_and_Nvidia_approached⠀⇛


                       TSMC reportedly asked its biggest customers to
                       invest in joint venture that would operate Intel's
                       production facilities.


                # ⚓ Tom's Hardware ☛ Asus_anticipates_price_increases_as_it
                  shifts_production_from_China⠀⇛


                       Asus vows to avoid price hikes due to incoming
                       tariffs, but it warns that it will not be able to
                       offset all the extra costs.


                # ⚓ Hackaday ☛ Some_Useful_Notes_On_The_6805-EC10_Addressable
                  RGB_LED⠀⇛


                       LEDs are getting smaller and smaller, and the
                       newest generations of indexable RGB LEDs are even
                       fiddlier to use than their already diminutive
                       predecessors. [Alex Lorman] has written some notes
                       about the minuscule SK6805-EC10 series of LEDs,
                       which may be helpful to those wanting to learn how
                       to deal with these in a more controlled manner.


                # ⚓ Hackaday ☛ Pixel_Watch_3’s_Loss_Of_Pulse_Detection:_The
                  Algorithms_That_Tell_Someone_Is_Dying⠀⇛


                       More and more of the ‘smart’ gadgets like watches
                       and phones that we carry around with us these days
                       come with features that we’d not care to ever need.
                       Since these are devices that we strap onto our
                       wrists and generally carry in close proximity to
                       our bodies, they can use their sensors to make an
                       estimation of whether said body is possibly in the
                       process of expiring. This can be due to a severe
                       kinetic event like a car crash, or something more
                       subtle like the cessation of the beating of one’s
                       heart.


                # ⚓ Hackaday ☛ FlyingCam_Is_A_Sweet_DIY_Webcam_On_A_Stick⠀⇛


                       Imagine you want to monitor a pot on the stove to
                       see if it’s boiling over for just a few minutes,
                       but you don’t want to have a dedicated permanent IP
                       webcam solution in your kitchen. [Sebastian
                       Duell]’s FlyingCam hijacks an IKEA lamp gooseneck
                       to become something you never knew you needed: a
                       wireless camera for short-term random remote
                       observation. It’s a beautiful combination of 3D
                       printing and commercial device re-use, and when
                       paired with his DIY wireless screen, it’s a
                       complete solution.


                # ⚓ Hackaday ☛ Meshtastic_Adds_Wireless_Connectivity_To_Possum
                  Trap⠀⇛


                       Perhaps every gardener to attempt to grow a tomato,
                       lettuce, or bean has had to contend with animals
                       trying to enjoy the food before the gardener
                       themselves can, whether it’s a groundhog, rabbit,
                       mouse, crow, or even iguana. There are numerous
                       ways to discourage these mischievous animals from
                       foraging the garden beds including traps, but these
                       devices have their downsides as well. False alarms
                       can be a problem as well as trapping animals that
                       will be overly aggravated to be inside the trap
                       (like skunks) and while the latter problem can’t
                       easily be solved by technology, the former can with
                       the help of Meshtastic.


                # ⚓ CNX Software ☛ Texas_Instruments_MSPM0C1104_is_the_world’s
                  smallest_microcontroller_with_a_size_of_1.38mm2⠀⇛


                       Texas Instruments (TI) has expanded the MSPM0 Arm
                       Cortex-M0+ MCU family with the MSPM0C1104 which is
                       the world’s smallest microcontroller measuring just
                       1.38mm2 in its WCSP package, or about the size of a
                       black pepper flake. Equipped with up to 16KB flash,
                       1KB SRAM, I/Os such as GPIO, I2C, UART, SPI, and a
                       12-bit analog-to-digital converter (ADC), the
                       MSPM0C1104 is optimized for space-constrained
                       applications such as medical wearables and personal
                       electronics.


                # ⚓ CNX Software ☛ 5th_Gen_AMD_EPYC_Embedded_9005_Series_Zen_5
                  processors_supports_up_to_6TB_DDR5_memory,_up_to_160_PCIe_Gen
                  5_lanes⠀⇛


                       AMD has just introduced the 5th Gen AMD EPYC
                       Embedded 9005 Series “Zen 5” processors designed
                       for embedded systems with a focus on longevity (7
                       years), reliability, and system resiliency, and
                       targeting networking, storage, and industrial edge
                       systems with support for up to 6TB of DDR5 memory,
                       up to 160 PCIe Gen5 lanes with CXL 2.0. The EPYC
                       Embedded 9005 Series processors are offered with 8
                       to 192 cores in a single socket and deliver up to a
                       1.3x faster networking process and 1.6x faster
                       storage.


                # ⚓ CNX Software ☛ Geehy_G32R501_dual-core_Cortex-M52
                  industrial_Hey_Hi_(AI)_MCU_targets_industrial_and_automotive
                  applications⠀⇛


                       Geehy Semiconductor has introduced the G32R501
                       Cortex-M52 industrial Hey Hi (AI) MCU, the
                       industry’s first real-time MCU based on a dual-core
                       Arm Cortex-M52 architecture. Designed for
                       industrial automation, commercial power supplies,
                       and electric vehicles.


                # ⚓ CNX Software ☛ Microchip_PIC32A_is_a_32-bit_MCU_family_with
                  high-performance_analog_peripherals_supporting_up_to_40
                  Msps⠀⇛


                       Microchip Technology PIC32A is a new family of 32-
                       bit microcontrollers clocked at up to 200 MHz with
                       high-speed analog peripherals that include up to 40
                       Msps 12-bit ADCs, high-speed 5 ns comparators and
                       100 MHz operational amplifiers for smart edge
                       sensing.


                # ⚓ CNX Software ☛ Tiny_Silicon_Labs_BG29_Bluetooth_LE_SoC
                  measures_just_2.8_x_2.6mm_for_wearables_and_sensors⠀⇛


                       Yesterday, we wrote about the world’s smallest
                       microcontroller (TI MSPM0C1104), which measures
                       just 1.38mm2 in its smallest package. However, it
                       is designed for general-purpose applications
                       without built-in wireless connectivity. If you need
                       Bluetooth LE in a tiny form factor, Silicon Labs
                       BG29 wireless SoC, with a 2.8x 2.6mm package, is
                       worth a look.


                # ⚓ CNX Software ☛ Semtech_LR2021_“LoRa_Plus”_transceiver
                  supports_LoRa_Gen_4,_Amazon_Sidewalk,_Meshtastic,_wM-BUS,_Wi-
                  SUN_FSK,_and_Z-Wave⠀⇛


                       Semtech LR2021, the first chip in the LoRa Plus
                       family, supports LoRa Gen 4 technology with both
                       terrestrial and satellite networks in the Sub-GHz,
                       2.4 GHz ISM bands, and licensed S-band, while
                       keeping backward compatibility with previous-
                       generation LoRa devices.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New Yorker ☛ The_Maddening_Disconnect_of_Phone_Therapy_in
                  “Happy_to_Help_You,”_featuring_Amy_Sedaris⠀⇛


                       Jeremy Beiler’s short film follows a mental-health
                       volunteer’s unravelling after a caller gets under
                       his skin.


                # ⚓ [Repeat] Overpopulation ☛ Canceling_the_Demographic_and
                  Health_Surveys_and_Ending_USAID’s_role_in_Family_Planning_and
                  Reproductive_Health_Programs:_Why_it_Matters⠀⇛


                       In a world with changing demographic trends, does
                       the retreat by the U.S. government from
                       international population and family planning
                       programs matter? Our answer is a resounding yes. by
                       Win Brown and Karen Hardee We are demographers who
                       earned our graduate degrees in the 1980s, when
                       academic programs in population and family planning
                       were booming.


                # ⚓ Latvia ☛ Flu_still_raging_across_Latvia⠀⇛


                       Influenza remains widespread across Latvia. Last
                       week, 477 cases (previously 440) were clinically
                       diagnosed with influenza, the Disease Prevention
                       and Control Center (SPKC) said March 12.


                # ⚓ New York Times ☛ ‘Let’s_Not_Talk_About_It’:_5_Years_Later,
                  China’s_Covid_Shadow_Lingers⠀⇛


                       People who endured the longest Covid restrictions
                       in the world are still grappling with what they
                       lost: their loved ones, their livelihoods, their
                       dignity.


                # ⚓ France24 ☛ Pope_Francis_marks_12_years_in_papacy_from
                  hospital_amid_uncertain_future⠀⇛


                       Pope Francis marks 12 years as head of the Catholic
                       Church on Thursday after recovering from a serious
                       case of pneumonia at Rome's Gemelli hospital where
                       he was admitted on February 14.. His extended
                       hospital stay has sparked concerns about his
                       ability to lead the 1.4 billion Catholics
                       worldwide.


                # ⚓ The Straits Times ☛ China_says_US_owes_‘big_thank_you’_on
                  fentanyl,_calls_for_talks⠀⇛


                       Chinese officials said the country has achieved
                       success in controlling the drugs and done all it
                       can.


                # ⚓ The Straits Times ☛ What’s_in_it_for_Beijing_to_crack_down
                  harder_on_fentanyl?⠀⇛


                       Dihydroxyacetone Man has linked the fentanyl issue
                       to tariffs but China seems to be taking a wait-and-
                       see approach.


                # ⚓ Hong Kong Free Press ☛ Over_50_Hong_Kong_students_and
                  teachers_contract_gastroenteritis_after_trip_to_mainland
                  China,_gov’t_says⠀⇛


                       More than 50 students and teachers from three Hong
                       Kong schools have contracted gastroenteritis after
                       dining at the same restaurants during an exchange
                       trip to mainland China, according to the city’s
                       health authorities.


                # ⚓ Science Alert ☛ A_Cheap_Daily_Supplement_Appears_to_Boost
                  Brain_Function_in_Older_People⠀⇛


                       The effect can be seen within weeks.


                # ⚓ Science Alert ☛ 66_Dinosaur_Footprints_Found_Hiding_in
                  Plain_Sight_at_Australian_School⠀⇛


                       "My jaw dropped."


                # ⚓ Science Alert ☛ 4_Rocky_Worlds_Found_Orbiting_Earth's
                  Closest_Single_Star,_And_They're_Tiny⠀⇛


                       "It's a really exciting find."


                # ⚓ Science Alert ☛ Why_Does_Ranch_Dressing_Act_So_Weird?_A
                  Physicist_Explains.⠀⇛


                       Soft matter is bizarre.


                # ⚓ Science Alert ☛ Experts_Warn_Against_Slushies_For_Kids,
                  After_UK_Hospitalizations⠀⇛


                       The sweet treat comes with serious risk.


                # ⚓ Stanford University ☛ From_the_periodic_table_to_the_food
                  we_eat:_Chemistry_in_the_Kitchen_draws_students_in⠀⇛


                       In the Introductory Seminar CHEM 29N: Chemistry in
                       the Kitchen. students learn about the chemical
                       makeup of food.


                # ⚓ Latvia ☛ Food_security_in_focus_of_agricultural_research_in
                  Latvia⠀⇛


                       This year, €9 million from the national budget is
                       earmarked for agricultural research. A significant
                       part of the funding is intended for renovating
                       laboratories and replacing equipment, but among
                       research priorities are plant health, productivity,
                       environmental protection and food quality and
                       safety, Latvian Radio reports on March 12.


                # ⚓ New York Times ☛ Gerald_Stratford_Is_Still_Growing_Very_Big
                  Vegetables⠀⇛


                       A photo he shared on social control media of
                       himself holding a giant bundle of arugula propelled
                       him to an unusual kind of internet fame.


                # ⚓ MIT Technology Review ☛ This_artificial_leaf_makes
                  hydrocarbons_out_of_carbon_dioxide⠀⇛


                       For many years, researchers have been working to
                       build devices that can mimic photosynthesis—the
                       process by which plants use sunlight and carbon
                       dioxide to make their fuel. These artificial leaves
                       use sunlight to separate water into oxygen and
                       hydrogen, which could then be used to fuel cars or
                       generate electricity.


                # ⚓ Photos:_Colorful_harvest_festival_in_Myanmar_bustles_with
                  visitors⠀⇛


                       The Shwe Saryan Pagoda Festival in Myanmar's Shwe
                       Saryan village is already busy with visitors.


          o § Proprietary⠀➾


                # ⚓ Beta News ☛ Microsoft_is_killing_off_the_Remote_Desktop_app
                  and_replacing_it_with_something_with_known_limitations⠀⇛


                       Microsoft has announced that it is pulling the plug
                       on the Remote Desktop app. In just 6 weeks, the app
                       will not only no longer be supported, it will also
                       not be available to download from the Microsoft
                       Store. But Microsoft is not completely abandoning
                       people who need to be able to remotely access
                       systems — it is replacing the Remote Desktop app
                       with the Windows App.>


                # ⚓ Silicon Angle ☛ Adobe_stock_drops_as_Hey_Hi_(AI)
                  monetization_concerns_weigh_on_investors⠀⇛


                       Shares in Adobe Inc. fell over 4% in late trading
                       today on concerns about the creative, marketing and
                       document management solutions company’s efforts to
                       make money from its artificial intelligence
                       offerings, despite Adobe reporting otherwise solid
                       fiscal 2025 first-quarter results.


                # ⚓ PC World ☛ Giant,_Hey_Hi_(AI)_ads_are_coming_to_backdoored
                  Windows_Copilot._Thanks,_Microsoft⠀⇛


                       For years, backdoored Windows users have complained
                       about “ads” touting Abusive Monopolist Microsoft
                       services, showing up in various places.


                # § Social Control Media⠀➾


                      # ⚓ New York Times ☛ NBA_Stars_Like_Jalen_Brunson_Enlist
                        Social_Media_Surrogates_to_Expand_Reach_in_China⠀⇛


                             Companies like East Goes Global manage
                             accounts for N.B.A. players, expanding their
                             reach, creating business opportunities and
                             pushing for All-Star votes.


                      # ⚓ New York Times ☛ How_to_Spend_Less_Time_on_Social
                        Media_(or_Leave_It_Altogether)⠀⇛


                             If you’re feeling overwhelmed but don’t quite
                             have the willpower to curb your online habit,
                             your phone can help you manage your time
                             online.


                      # ⚓ CS Monitor ☛ This_Haitian_shot_to_fame_on_TikTok,_but
                        others_profited_from_his_clips⠀⇛


                             Social media may democratize knowledge, but
                             they can also perpetuate perceptions that
                             ideas from some countries are worth more than
                             those from others.


                      # ⚓ France24 ☛ The_‘Kung_Fu_Girls’_bringing_ancient
                        Chinese_martial_arts_to_new_audience⠀⇛


                             Mixing deft martial arts and social control
                             media savvy, an all-female group in China are
                             helping to breathe new life into the ancient
                             practice of kung fu. Known as the Emei Kung
                             Fu Girls, their slick online videos have
                             proved a massive hit on China’s version of
                             Fentanylware (TikTok) and are helping to
                             encourage girls to get involved in what has
                             traditionally been a male-dominated sphere.


                      # ⚓ The Straits Times ☛ Indonesia_court_jails_transgender
                        woman_for_‘hate_speech’_about_Jesus’_hair⠀⇛


                             The woman, who sold beauty products online,
                             made the remark during a Fentanylware
                             (TikTok) live streaming.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Security Week ☛ Beware_of_DeepSeek_Hype:_It’s_a
                        Breeding_Ground_for_Scammers⠀⇛


                             Exploiting trust in the DeepSeek brand,
                             scammers attempt to harvest personal
                             information or steal user credentials.


                      # ⚓ Security Week ☛ Fraud_Losses_Reached_$12.5_Billion_in
                        2024:_FTC⠀⇛


                             FTC says reported losses to fraud exceeded
                             $12.5 billion in 2024, with $5.7 billion lost
                             to investment scams.


          o § Defence/Aggression⠀➾


                # ⚓ The Straits Times ☛ South_Korean_pastor_vows_revolt_against
                  Yoon’s_impeachment⠀⇛


                       The authorities are worried about the potential for
                       violence when the ruling is issued.


                # ⚓ The Straits Times ☛ South_Korea_bans_drones_around_top
                  court_ahead_of_Yoon_impeachment_ruling⠀⇛


                       South Korea's air traffic authorities will ban
                       drones from flying around the Constitutional Court
                       in Seoul from Thursday ahead of the ruling on the
                       impeachment of President Yoon Suk Yeol.


                # ⚓ The Straits Times ☛ South_Korea_charges_air_force_pilots
                  with_criminal_negligence_in_accidental_bombing_of_village⠀⇛


                       The pilots made errors when they entered
                       coordinates into the aircraft systems.


                # ⚓ New York Times ☛ Chinese_Warships_Circle_Australia_and
                  Leave_It_Feeling_‘Near_Naked’⠀⇛


                       The unusual deployment by three navy ships over the
                       past month has prompted a debate in Australia about
                       its aging fleet and reliance on the United States.


                # ⚓ New York Times ☛ Plans_for_a_Chinese_Port_in_the_Black_Sea
                  Roil_Georgia_Politics⠀⇛


                       Georgia’s government sparked an uproar by
                       announcing that a port project on the Black Sea
                       will be awarded to a company from China after
                       canceling a contract with a consortium that
                       included Western firms.


                # ⚓ The Straits Times ☛ China_accuses_New_Zealand’s_top_spy_of
                  spreading_‘false_information’⠀⇛


                       The Cook Islands is at the heart of recent tensions
                       between China and New Zealand.


                # ⚓ Indonesia_to_ratify_South_China_Sea_deal_with_Vietnam_in
                  April⠀⇛


                       The two countries concluded 12 years of
                       negotiations on exclusive economic zones in 2022.


                # ⚓ Chinese_envoy_discusses_election_with_Myanmar_junta_chief⠀⇛


                       Myanmar and China hope the election can help end
                       the civil war but critics say it will be a “sham”.


                # ⚓ JURIST ☛ UN_called_to_investigate_possible_affiliation_of
                  Special_Envoy_to_Myanmar_with_China_companies⠀⇛


                       Justice for Myanmar (JFM) released a statement
                       calling on the United Nations to investigate
                       possible conflicts of interest with its Special
                       Envoy to Myanmar due to her possible links with
                       Chinese state-owned entities.


                # ⚓ New York Times ☛ Separatists_Are_Still_Holding_Hundreds_of
                  Hostages_in_Pakistan_Train_Standoff⠀⇛


                       Pakistani security forces declared an end to ethnic
                       separatists’ seizure of a train carrying more than
                       400 people.


                # ⚓ The Straits Times ☛ How_separatist_militants_hijacked_a
                  train_in_Pakistan⠀⇛


                       Pakistani security forces are carrying out a rescue
                       operation to free dozens of passengers taken
                       hostage by separatist militants who hijacked their
                       train in the southwest of the country on Tuesday.


                # ⚓ The Straits Times ☛ Pakistan_security_forces_free_190
                  hostages_in_train_siege⠀⇛


                       More than 450 passengers were on board when a
                       separatist militant group captured the train.


                # ⚓ The Straits Times ☛ Pakistan_train_hijack_hostages_end
                  ordeal_with_arrival_in_Quetta⠀⇛


                       Dozens of people rescued from a train hijacked by
                       separatist militants in southwest Pakistan arrived
                       on Thursday in the city of Quetta, hours after
                       security forces killed all 33 attackers to end a
                       day-long standoff.


                # ⚓ New York Times ☛ Mahmoud_Khalil_Has_Not_Been_Allowed_to
                  Speak_Privately_With_Lawyers⠀⇛


                       Mahmoud Khalil, a legal permanent resident who the
                       Convicted Felon administration has claimed is a
                       national security threat, is in immigration
                       detention in Louisiana.


                # ⚓ CS Monitor ☛ How_Israel_failed_to_anticipate_Hamas:
                  defective_chip_maker_Intel_trusted_tech_over_people⠀⇛


                       On Oct. 7, Hamas forces penetrated a $1.1 billion,
                       high-tech Israeli barrier on the Gaza border.
                       Israel’s army and Shin Bet security force say their
                       intelligence failed by relying on technology at the
                       expense of humans.


                # ⚓ Pacific_governments_warned_of_‘threat’_from_Cambodia’s
                  Prince_Group⠀⇛


                       A US-based think tank says the company could help
                       China expand its influence.


                # ⚓ Defence Web ☛ Non-conventional_but_increasingly
                  sophisticated_maritime_threats_will_persist_in_Africa⠀⇛


                       A naval war between African states is unlikely.
                       Rather, the primary maritime security threat is
                       from non-state actors using increasingly
                       sophisticated technology like unmanned vessels.
                       This is according to Denys Reva, Maritime Security
                       Researcher at the Institute for Security Studies
                       (ISS).


                # ⚓ France24 ☛ Syria's_interim_president_announces_formation_of
                  national_security_council⠀⇛


                       Syria's interim President Ahmed al-Sharaa issued a
                       decree on Wednesday to form the country's national
                       security council, according to a statement from
                       the Syrian president's office. The council will
                       take decisions related to the country's national
                       security and challenges facing the state.


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


                      # ⚓ New York Times ☛ Europe_Expected_a_Transactional
                        Convicted_Felon._It_Got_Something_Else.⠀⇛


                             Europe had been banking on a United States
                             that wanted to make a deal on tariffs and
                             trade. With little progress in that
                             direction, it’s reluctantly starting to hit
                             back.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ American Oversight ☛ American_Oversight_Sues_Convicted
                  Felon_Administration_for_Directing_Agency_Staff_to_Shred_and
                  Burn_Government_Records⠀⇛


                       American Oversight filed suit against government
                       for violating the Federal Records Act and other
                       transparency laws following reports staff were
                       instructed to destroy documents.


                # ⚓ American Oversight ☛ Where_Are_Convicted_Felon_Border
                  Patrol_Chief_Mike_Banks’_Communications_from_His_Time_as
                  Texas_Border_Czar?⠀⇛


                       The lack of records in response to American
                       Oversight’s requests from its two-year
                       investigation of Banks raises questions about
                       public accountability and transparency.


          o § Environment⠀➾


                # ⚓ Science Alert ☛ Climate_Change_Could_Put_Us_at_Greater_Risk
                  of_Sewage_Diseases⠀⇛


                       Forget swimming.


                # § Energy/Transportation⠀➾


                      # ⚓ New York Times ☛ China_Cools_on_MElon:_‘Two_Cars_for
                        the_Price_of_One_Tesla’⠀⇛


                             MElon, the company’s chief executive, is fast
                             losing out to Chinese electric carmakers in
                             Tesla’s second-most-important market.


                      # ⚓ Breach Media ☛ Liberals’_high-speed_rail:_a_fast
                        track_to_privatization⠀⇛


                             Experts say Trudeau’s plan will sideline VIA
                             Rail—and passengers will pay the price


                      # ⚓ France24 ☛ Dihydroxyacetone_Man_vows_further_action
                        as_US_trading_partners_hit_back_at_25%_steel_and
                        aluminium_tariffs⠀⇛


                             A new, 25% import tax on all steel and
                             aluminium coming into the United States has
                             taken effect, drawing swift retaliatory
                             measures from Canada and the European Union. 
                             The Insurrectionist warned of a further
                             response. Sweeping metal tariffs imposed
                             during Convicted Felon's first term did have
                             some positive impact on the US steel and
                             aluminium industries but negatively affected
                             other sectors downstream. Plus, US inflation
                             in February cooled slighly.


                      # ⚓ Atlantic Council ☛ Carole_House_testifies_to_House
                        Committee_on_Financial_Services_on_regulation_and
                        security_in_stablecoins_and_digital_payments⠀⇛


                             On March 11, Senior Fellow Carole House
                             testified to the House Committee on Financial
                             Services at a hearing titled, "Examining a
                             Federal Framework for Payment Stablecoins and
                             Consequences of a US Central Bank Digital
                             Currency."


                      # ⚓ Tom's Hardware ☛ YouTubers_Give_New_Meaning_to_“Air
                        Printing”⠀⇛


                             YouTubers mount an Elegoo Centauri Carbon on
                             an RC plane and print while flying.


                      # ⚓ Hong Kong Free Press ☛ Hong_Kong_Tramways_‘facing
                        fierce_competition’_as_patronage_remains_below_pre-
                        pandemic_levels⠀⇛


                             Hong Kong Tramways “is facing fierce
                             competition” from other modes of public
                             transport as the number of passengers remains
                             below pre-pandemic levels, the city’s
                             transport advisory body has said.


                      # ⚓ Hong Kong Free Press ☛ Cathay_Pacific_says_profit
                        edged_up_in_2024⠀⇛


                             Hong Kong carrier Cathay Pacific said on
                             Wednesday that its attributable profit rose
                             slightly in 2024 to US$1.27 billion, after
                             announcing earlier this year that its flights
                             were finally back to pre-pandemic levels.


                # § Overpopulation⠀➾


                      # ⚓ South_Korean_county_to_accept_Myanmar_refugees_amid
                        population_decline⠀⇛


                             Yeongyang said it would initially accept some
                             of Myanmar’s Karen people.


                      # ⚓ The Straits Times ☛ South_Korean_county,_fearing
                        extinction,_looking_to_attract_Myanmar_refugees [Ed:
                        Not accepting "refugees" amid overpopulation does not
                        mean "extinction"]⠀⇛


                             They are looking to attract about 40 Myanmar
                             refugees.


          o § Finance⠀➾


                # ⚓ The Straits Times ☛ Private_clinics_in_Malaysia_push_for
                  fee_hikes_amid_soaring_healthcare_costs⠀⇛


                       Consumers are worried hikes by GPs would impact
                       affordability and accessibility.


                # ⚓ Atlantic Council ☛ China’s_economic_plans_prioritize
                  consumption—but_only_on_paper⠀⇛


                       At last week's meeting of the National People's
                       Congress, China declared consumption as the number
                       one priority. But will the spending plans actually
                       support consumers and businesses?


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The Straits Times ☛ China’s_top_lawmaker_meets_journalists
                  after_missing_key_Parliament_session⠀⇛


                       Mr Zhao Leji thanked the journalists for their
                       coverage.


                # ⚓ Hong Kong Free Press ☛ Dalai_Lama_book_offers_‘framework’
                  for_Tibet’s_future_after_his_death⠀⇛


                       The Dalai Lama published a book Tuesday that he
                       says is a “framework for the future of Tibet”, to
                       guide compatriots in relations with Beijing after
                       his death.


                # ⚓ France24 ☛ Yes,_Hell_Toupée_reposted_an_anti-LGBT_‘Pink
                  Triangle'_from_the_Nazi_era⠀⇛


                       Internet users around the world have been reacting
                       to a post by President The Insurrectionist on his
                       Truth Social platform, where he shared a link that
                       displayed a “no” sign over a downward-facing pink
                       triangle. The pink triangle symbol was used by Nazi
                       Germany to identify LGBTQ+ people in concentration
                       camps. It’s unclear whether Convicted Felon had
                       read the opinion piece or is aware of the
                       historical significance. Vedika Bahl goes through
                       it in Truth or Fake.


                # ⚓ New York Times ☛ Inside_Convicted_Felon’s_Crackdown_on
                  Dissent:_Obscure_Laws,_ICE_Agents_and_Fear⠀⇛


                       Hell Toupée is clamping down broadly on dissent
                       using the tools of the federal government.


                # ⚓ JURIST ☛ US_government_workers_file_lawsuit_against
                  Convicted_Felon_following_mass_firings⠀⇛


                       A group of US probationary government employees who
                       lost their jobs as part of President The
                       Insurrectionist’s purge of the federal workforce
                       filed a lawsuit Tuesday, claiming the mass firings
                       were illegal and should be reversed.


                # ⚓ Hong Kong Free Press ☛ Nearly_half_of_Hongkongers
                  dissatisfied_with_opposition-free_legislature_–_survey⠀⇛


                       Almost half of Hongkongers have expressed
                       dissatisfaction with the performance of the city’s
                       opposition-free legislature, according to a survey
                       by local think tank Path of Democracy. The poll
                       surveyed around 1,000 people between January and
                       February to ask whether they were satisfied with
                       the city’s government and legislature.


          o § Censorship/Free Speech⠀➾


                # ⚓ Hong_Kong_media_urged_to_back_up_Facebook_(Farcebook)
                  protest_videos⠀⇛


                       Meta says it will start deleted archived videos
                       from servers.


                # ⚓ Press Gazette ☛ Douglas_Murray_wins_‘substantial’_damages
                  after_Observer_column_error⠀⇛


                       An Observer writer inaccurately claimed comments
                       made by Murray in 2023 had referred to the 2024
                       riots.


                # ⚓ CS Monitor ☛ Columbia_protester_arrest_ignites_free_speech
                  tug-of-war⠀⇛


                       The Forrest Dump administration says deportation
                       can be a tool to combat antisemitism and terrorism.
                       Critics see violations of free speech and immigrant
                       rights.


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


                # ⚓ Press Gazette ☛ Deliveries_of_China_Daily_newspaper_to_MPs
                  could_be_stopped⠀⇛


                       One MP said the CCP-funded newspaper is "the only
                       thing which arrives every day, without fail".


                # ⚓ BIA Net ☛ Independent_news_outlet_Gazete_Duvar_shutting
                  down_due_to_financial_difficulties⠀⇛


                       The outlet's executives say sharply reduced website
                       traffic due to Google's algorithm changes was the
                       primary reason behind their decision.


          o § Civil Rights/Policing⠀➾


                # ⚓ NYPost ☛ FEMA_launches_review_of_migrant_shelter_aid,
                  suggesting_smuggling_laws_were_violated⠀⇛


                       The Forrest Dump administration has launched a
                       review of organizations that provide temporary
                       housing and other aid to migrants, suggesting they
                       may have violated a law used to prosecute
                       smugglers.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Internet Society ☛ Community_Snapshot—February⠀⇛


                       Here's a look at everything the Internet Society
                       chapters accomplished in the month of February
                       2025.


      § Monopolies/Monopsonies⠀➾


          o ⚓ Silicon Angle ☛ After_confusion,_FTC_says_it_will_go_ahead_with
            Amazon_deceptive_practices_case⠀⇛


                 Following a short delay over what may or may not have
                 been staffing shortages, the Federal Trade Commission now
                 says it will now continue with its consumer protection
                 trial against Amazon.com Inc.


          o § Patents⠀➾


                # ⚓ Dennis Crouch/Patently-O ☛ Convergence:_Island_IP_Points_to
                  Wave_of_Rule_36_Petitions⠀⇛


                       Island Intellectual Property has filed a rare
                       supplemental brief in its pending Supreme Court
                       case, drawing the Court's attention to the growing
                       body of certiorari petitions challenging Federal
                       Circuit practices.  The brief, submitted under
                       Supreme Court Rule 15.8, highlights several new
                       petitions that address the same questions Island IP
                       raised about summary judgment standards and the
                       Federal Circuit's use of Rule 36 affirmances.


                # ⚓ Kluwer Patent Blog ☛ Navigating_the_intersection_between_IP
                  and_competition_law:_some_clarity_from_the_Belgian_Supreme
                  Court⠀⇛


                       The refusal to grant a licence for intellectual
                       property (IP) rights can sometimes conflict with
                       competition law. This topic has already been
                       explored in the case law of national courts and the
                       Court of Justice of the European Union, most
                       notably in the landmark case IMS Health (C418/01)
                       of 29 April 2004.


                # ⚓ Dennis Crouch/Patently-O ☛ Federal_Circuit_Rejects_“Once
                  Generic,_Always_Generic”_Rule_in_Trademark_Dispute_Between
                  Whiskey_Makers⠀⇛


                       Bullshine Distillery LLC v. Sazerac Brands, LLC,
                       2023-1682 (Fed. Cir. March 12, 2025)


                       In an interesting trademark decision, the Federal
                       Circuit has clarified that terms once considered
                       generic do not necessarily remain permanently
                       unregistrable.  provides important guidance on
                       genericness timing and addresses a question of
                       first impression in trademark law.


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ French_law_firms_race_to_adapt_as_UPC_reshapes
                        patent_monopoly_litigation_landscape [Ed: UPC is
                        illegal and unconstitutional, yet this site is being
                        paid to promote and celebrate illegality]⠀⇛


                             Paris ranks among the most active non-German
                             UPC locations. According to late February
                             statistics, the Paris local division has 17
                             infringement actions, while the central
                             division has one. The central division in
                             Paris currently has 41 revocation actions
                             pending, as well as two counterclaims for
                             infringement.


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ CAFC_Hears_Oral_Arguments_in_FUCK_and_RAPUNZEL
                  Appeals⠀⇛


                       The CAFC recently heard oral argument in two
                       appeals from the TTAB. In In re Brunetti, the Board
                       refused registration of the mark FUCK for phone
                       cases, jewelry, bags, and retail store services on
                       the ground of failure-to-function, concluding that
                       the word "fuck" is in such widespread use that it
                       does not create the commercial impression of a
                       source indicator, but rather expresses well-
                       recognized, familiar sentiments. [TTABlogged here].


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Hip-Hop_Super-Producer_Turbo_Beats_$10
                  Million_Infringement_Claim_Surrounding_Now-Famous_‘Run_That
                  Back,_Turbo’_Producer_Tag⠀⇛


                       Producer Turbo wins the $10 million infringement
                       claim filed against him by the vocalist of his now-
                       famous ‘Run that back, Turbo’ producer tag. The
                       suit was initially filed in January 2024 by
                       musician Jamal Britt, whose voice is heard in
                       Turbo’s now-iconic “Run that back, Turbo” producer
                       tag.


                # ⚓ Public Domain Review ☛ Ostrich_Egg-Shell_Cups_of
                  Mesopotamia_and_the_Ostrich_in_Ancient_and_Modern_Times_
                  (1926)⠀⇛


                       A cultural history of ostrich eggs and the birds
                       that lay them.


                # ⚓ Public Domain Review ☛ A_Princely_Ploy:_Inside_the_Ruse_of
                  a_French-Armenian_Scammer⠀⇛


                       After proclaiming himself the direct descendant of
                       a 12th-century Crusader king, the Armenian priest
                       and educator Ambroise Calfa hit upon an ignoble
                       scheme: grant knighthood to anyone willing to pay.
                       Jennifer Manoukian recovers the cunning exploits of
                       this forgotten 19th-century conman, whose initially
                       honorable intentions quickly escalated into all-out
                       fraud.


                # ⚓ Public Domain Review ☛ Con_Heir:_Tiny_Cryptic_#4⠀⇛


                       Fourth instalment in our new series of extremely
                       small and free-form cryptic crossword puzzles,
                       themed on our latest essay.


    * Meanwhile_at_Microsoft_Canonical...
    * Bluewashing_Ends_DEI_at_IBM_and_at_Red_Hat_(HR_or_Hiring_Become_Gender-
      and_Race-Neutral)



                    ䷩ 𝚕𝚒𝚗𝚎 5092

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 14/03/2025: Chinese Tensions With
Australia, Putin Turns Down Ceasefire⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Standards/Consortia
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # 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
                # Mobile_Systems/Mobile_Applications
          o Monopolies/Monopsonies
                # Trademarks
    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Got_Junk?_Then_Build_This_Scrappy_TEA_Laser⠀⇛


                 A piece of glass, some bits of tinfoil, a sheet of
                 plastic, a couple of razor blades, and a few assorted
                 bits and bobs are all it takes to build this TEA nitrogen
                 laser. Oh, and a 5,000-volt flyback supply with enough
                 amperage to stop your heart. You’ll need that too.


          o § Standards/Consortia⠀➾


                # ⚓ Latvia ☛ People_with_a_disability_less_likely_to_use_the
                  internet⠀⇛


                       In 2024, the share of people in the European Union
                       who had used the internet in the previous 12 months
                       was 87.2% among people with a disability and 95.2%
                       among those without.


          o § Science⠀➾


                # ⚓ New York Times ☛ Video:_Blood_Moon_Total_Lunar_Eclipse:
                  When_and_How_to_Watch⠀⇛


                       Earth’s shadow will block most of the light that
                       illuminates the lunar surface, creating what is
                       known as a blood moon.


                # ⚓ Science Alert ☛ Squids'_Amazing_Color_Shifting_Could_Be_Key
                  to_Hyper-Efficient_Solar_Tech⠀⇛


                       "Really insane."


                # ⚓ Science Alert ☛ World_First:_Physicists_Create_a_Supersolid
                  Out_of_Light⠀⇛


                       A super solid achievement!


                # ⚓ Science Alert ☛ NASA_Reports_Sea_Levels_Rose_by
                  'Unexpected'_Amount_in_Earth's_Hottest_Year⠀⇛


                       Caused primarily by two factors.


                # ⚓ Science Alert ☛ En_Route_to_Asteroid_Collision,_HERA_Snaps
                  Rare_Images_of_Martian_Moon⠀⇛


                       It's tiny and mysterious.


                # ⚓ Science Alert ☛ It's_Pi_Day._Here's_Why_This_Special_Number
                  Gets_a_Global_Celebration.⠀⇛


                       We love pi.


          o § Career/Education⠀➾


                # ⚓ The Straits Times ☛ Private_education_spending_in_South
                  Korea_hits_record_$26.8b_despite_fall_in_student_numbers⠀⇛


                       A notable trend in the data is the steep rise in
                       private education spending in rural areas.


                # ⚓ Hong_Kong_teen’s_death_sparks_concerns_over_mainland_China
                  study_trips⠀⇛


                       The government is tight-lipped, as students are
                       increasingly pressured to take part in such trips.


                # ⚓ Stanford University ☛ Strawser_|_Dear_ASSU:_Be_the_leaders
                  the_Convicted_Felon_era_calls_for⠀⇛


                       Strawser argues that the ASSU, more than ever, must
                       take its kiddy gloves off to be the leaders that
                       students need in the Convicted Felon era.


                # ⚓ Stanford University ☛ Stanford_in_the_Media:_‘To_All_the
                  Boys:_Always_and_Forever’_depicts_realistic_college
                  admissions⠀⇛


                       Muller reflects on the 2021 rom-com, “To All the
                       Boys: Always and Forever,” in which protagonist
                       Lara Jean grapples with her Stanford rejection.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ Thundercomm_TurboX_C6690_SoM_runs_Android_15
                  on_Qualcomm_DragonWing_QCS6690_SoC_for_terminal_equipment⠀⇛


                       Unveiled at Embedded World 2025, Thundercomm’s
                       TurboX C6690 is a SoM (System-on-Module) powered by
                       a 4nm Qualcomm Dragonwing QCS6690 octa-core SoC,
                       and designed for Android 15-based terminal
                       equipment such as industrial handheld devices,
                       industrial tablets, edge computing, and smart
                       retail applications.


                # ⚓ CNX Software ☛ Variscite_VAR-SOM-AM62P_SoM_features_Texas
                  Instruments_Sitara_AM62P5_SoC_for_cost-effective_multimedia
                  applications⠀⇛


                       Variscite VAR-SOM-AM62P is a system-on-module
                       powered by Texas Instruments Sitara AM62P5 quad-
                       core Cortex-A53 + Cortex-R5F SoC coupled with up to
                       8GB LPDDR4 RAM and 128GB eMMC flash, and designed
                       for cost-effective multimedia applications.


                # ⚓ Hackaday ☛ The_Mysterious_And_Important_Work_Of_Prop_Design
                  On_Severance⠀⇛


                       Have you seen Severance? Chances are good that you
                       have; the TV series has become wildly popular in
                       its second season, to the point where the fandom’s
                       dedication is difficult to distinguish from the in-
                       universe cult of [Kier]. Part of the show’s appeal
                       comes from its overall aesthetic, which is captured
                       in this description of the building of one of the
                       show’s props.


                # ⚓ Hackaday ☛ Hacking_A_Rotary_Phone⠀⇛


                       [Yaymukund] made an interesting observation. Old-
                       style rotary phones were made to last and made for
                       service. Why? Because you didn’t own them, the
                       phone company did. There was no advantage for them
                       for you to need a service call or a new phone. Of
                       course, many of these old phones are still hanging
                       around like the GPO 746 that appears in the post.


                # ⚓ The Next Platform ☛ Lip-Bu_Tan:_Intel’s_New_–_And_Maybe
                  Last_–_CEO⠀⇛


                       In_his_letter_to_defective_chip_maker_Intel
                       employees, new chief executive officer Lip-Bu Tan,
                       who starts his new job next Tuesday, tells them
                       that he is “never deterred by challenges.”


                # ⚓ The New Stack ☛ Intel’s_New_CEO_Will_Make_Changes_to
                  Reshape_Software_Strategy⠀⇛


                       Software was a priority for the previous CEO Pat
                       Gelsinger.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ Keir_Starmer_Wants_to_Abolish_NHS_England:
                  What_to_Know_About_His_Plan⠀⇛


                       The British prime minister said he would scrap an
                       agency that was created in 2013 to help run the
                       health service. He said the move would save money
                       by avoiding duplication.


                # ⚓ New York Times ☛ Dr._Oz’s_Journey_From_Heart_Doctor_to
                  Celebrity_to_Iconoclast⠀⇛


                       A once-respected surgeon found fame and fortune as
                       medicine’s biggest iconoclast. Now he’s on the cusp
                       of power to help shape American public health.


                # ⚓ PHR ☛ New_Guide_Helps_U.S._Health_Professionals_Protect
                  Patients_from_Immigration_Enforcement⠀⇛


                       Following the Convicted Felon administration’s
                       decision to end guidance protecting “sensitive
                       locations” such as health care facilities from
                       immigration enforcement actions, a new guide
                       published today provides information to health care
                       workers about how to navigate the new enforcement
                       landscape while upholding ethical duties. 


                # ⚓ Latvia ☛ Hospitals_outside_Rīga_say_patient_flow_is_too
                  high⠀⇛


                       Rīga's largest hospitals sometimes direct patients
                       to hospitals outside Rīga to manage their patient
                       flow. However, hospitals in cities close to Rīga
                       also face high patient flows and are therefore not
                       ready to take on many more patients, Latvian Radio
                       reported on March 13.


                # ⚓ The Straits Times ☛ Polam_Kopitiam_food_poisoning_deaths_in
                  Taiwan:_Victims’_families_to_receive_record_govt_payout⠀⇛


                       Six people died after eating at the Malaysian
                       restaurant in Taipei in 2024.


                # ⚓ The Straits Times ☛ Malaysia_gives_green_light_to_higher_GP
                  fees⠀⇛


                       GPs said that costs had gone up over the years.


                # ⚓ Hong Kong Free Press ☛ China_restaurant_chain_Haidilao
                  refunds_thousands_after_diner_urinates_in_hotpot [Ed: Social
                  control media in action]⠀⇛


                       One of China’s biggest restaurant chains has
                       promised to refund thousands of customers after
                       footage of a patron urinating into a simmering
                       hotpot went viral online, triggering a public
                       outcry.


                # ⚓ Science Alert ☛ World-First:_Man_Leaves_Hospital_With_Life-
                  Saving_Titanium_Heart⠀⇛


                       Enough to give a surgeon goosebumps.


                # ⚓ Science Alert ☛ Just_5_Days_of_Junk_Food_Can_Trigger
                  Obesity's_Hold_on_Your_Brain⠀⇛


                       Short-term diet has lasting effects.


                # ⚓ Science Alert ☛ Energy_Signals_From_Milky_Way's_Core_Hint
                  at_New_Type_of_Dark_Matter⠀⇛


                       This could explain other physics mysteries too.


                # ⚓ New York Times ☛ Bumble_Bee_Foods_Is_Accused_of_Tolerating
                  Forced_Labor_in_Supply_Chain⠀⇛


                       In a lawsuit filed in California, the plaintiffs
                       said that Bumble Bee Foods was aware of and
                       benefited from abuse by suppliers. The company
                       declined to comment.


                # ⚓ Federal News Network ☛ Dihydroxyacetone_Man_administration
                  withdraws_CDC_director_nomination_just_before_Senate
                  hearing⠀⇛


                       The White House has withdrawn the nomination of
                       David Weldon, a former Florida congressman, to lead
                       the Centers for Disease Control and Prevention.


          o § Proprietary⠀➾


                # ⚓ New York Times ☛ How_Generative_Hey_Hi_(AI)_Complements_the
                  MAGA_Style⠀⇛


                       Online Convicted Felon supporters have embraced a
                       unique form of irony that is hard to parse — and
                       easy to deploy with new technologies.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ The Straits Times ☛ North_Korean_IT_workers_forced
                        into_brutal_workloads,_surveilled_24/7:_Report⠀⇛


                             The workers typically work over 10 hours
                             daily and live in cramped accommodations, the
                             report said.


          o § Defence/Aggression⠀➾


                # ⚓ The Straits Times ☛ Malaysian_police_gun_down_3_robbers
                  behind_spate_of_house_break-ins⠀⇛


                       The suspects attacked the police using machetes
                       before they were shot.


                # ⚓ The Straits Times ☛ Ahead_of_Yoon_impeachment_ruling,_South
                  Korea_acting_president_says_must_accept_any_decision⠀⇛


                       The court ruling is due to come within days.


                # ⚓ Meduza ☛ Armenia_and_Azerbaijan_agree_on_draft_peace
                  agreement_—_Meduza⠀⇛


                # ⚓ New York Times ☛ Inside_the_Pakistan_Train_Hijacking
                  Standoff⠀⇛


                       Pakistani security forces declared an end to ethnic
                       separatists’ seizure of a train carrying more than
                       400 people.


                # ⚓ The Straits Times ☛ At_least_25_bodies_retrieved_from
                  Pakistan_train_siege⠀⇛


                       Security forces freed more than 340 train
                       passengers in a two-day rescue operation.


                # ⚓ The Straits Times ☛ Pakistan_train_hijack_hostages_end
                  ordeal_with_arrival_in_Quetta,_given_first-aid⠀⇛


                       Security forces killed all 33 attackers to end a
                       day-long stand-off.


                # ⚓ New York Times ☛ U.N._Accuses_Israel_of_Targeting
                  Reproductive_Health_Facilities_in_Gaza⠀⇛


                       A report by a U.N. committee found that Israel has
                       committed “genocidal acts” intended to prevent
                       births. Israel quickly rejected the findings as
                       biased.


                # ⚓ France24 ☛ UN_report_denounces_Israel's_'genocidal'
                  targeting_of_reproductive_facilities_in_Gaza⠀⇛


                       A new report by the United Nation's Human Rights
                       Commission found that Israel's "systematic
                       destruction of sexual and reproductive healthcare,"
                       including its targeting of fertility clinics, in
                       Gaza amounts to "genocidal acts". Israeli Prime
                       Minister Benjamin Netanyahu blasted the report,
                       which also cites the Israeli military's pervasive
                       use of sexual violence against Palestinian women,
                       men, girls, and boys, as "anti-Semitic" and
                       "absurd".


                # ⚓ New York Times ☛ In_a_Europe_Adrift,_Macron_Seizes_the
                  Moment⠀⇛


                       The French president’s prescriptions for “strategic
                       autonomy” and a European force for Ukraine are
                       suddenly timely in a world with a less dependable
                       America.


                # ⚓ New York Times ☛ Israel-Hamas_Talks_Deadlocked_as_Convicted
                  Felon_Envoy_Turns_to_Ukraine⠀⇛


                       The two sides are supposed to negotiate a second
                       phase of the cease-fire agreement that would end
                       the war, but they remain far apart on how to move
                       forward.


                # ⚓ Beijing_tight-lipped_on_reports_of_collision_between
                  Chinese,_North_Korean_ships⠀⇛


                       The North Korean vessel was suspected of smuggling
                       coal, a violation of UN sanctions.


                # ⚓ New York Times ☛ Why_China_Is_Worried_About_Convicted
                  Felon’s_Tariffs_on_Mexico⠀⇛


                       China’s exports to developing markets have soared,
                       opening indirect routes to the U.S. market that
                       officials in Beijing worry may be closed under
                       pressure from Hell Toupée.


                # ⚓ The Straits Times ☛ China_cools_on_MElon:_‘Two_cars_for_the
                  price_of_one_Tesla’⠀⇛


                       Chinese drivers who once flocked to Tesla are
                       turning more and more to local brands.


                # ⚓ The Straits Times ☛ Taiwan_president_warns_of_China’s
                  ‘infiltration’_effort,_vows_countermeasures⠀⇛


                       Taiwan has accused China of stepping up military
                       drills.


                # ⚓ Taiwan_president_slams_China_as_‘foreign_hostile_force’_in
                  toughest_rhetoric_yet⠀⇛


                       Beijing is carrying out activities such as
                       division, destruction, and subversion, Lai Ching-te
                       says.


                # ⚓ The Straits Times ☛ Australia_moves_to_arm_troops_with
                  anti-ship_missiles_as_China_threat_looms⠀⇛


                       Australia is scrambling to deploy new long-range
                       missiles as Chinese warships arrive off their
                       coast.


                # ⚓ European_Parliament_resolution_condemns_deporting_40
                  Uyghurs_from_Thailand_to_China⠀⇛


                       Meanwhile, 2 Uyghurs who traveled south, but
                       abandoned plans to escape in 2014 were sentenced to
                       9 years.


                # ⚓ France24 ☛ Many_European_leaders_'_desperately_hoping_US
                  remains_committed_to_NATO'⠀⇛


                       FRANCE 24's Yinka Oyetade speaks to Dafydd Townley,
                       from the University of Portsmouth's Professional
                       Military Education Team, about the meeting between
                       The Insurrectionist and NATO chief Mark Rutte. He
                       says that for all the bluster coming from the White
                       House, many European security experts, ministers
                       and prime ministers 'are desperately hoping that
                       the United States remains committed to NATO and the
                       security of Europe'.


                # ⚓ Defence Web ☛ Criminality_will_be_‘dealt_with_decisively’
                  says_Eskom⠀⇛


                       Eskom, in collaboration with the National Joint
                       Operational and Intelligence Structure (NATJOINTS)
                       Energy Safety and Security Priority Committee, is
                       continuing its crackdown on criminality within the
                       organisation. This after the power utility and law
                       enforcement executed several arrests related to
                       theft and corruption over the past few months.


                # ⚓ Scoop News Group ☛ US_must_prioritize_cybersecurity
                  training_for_the_military’s_engineers⠀⇛


                       The Defense Department faces a startling capability
                       gap.


                # ⚓ Atlantic Council ☛ Present_without_impact?_How_the_Middle
                  East_perceives_China’s_diplomatic_engagement⠀⇛


                       In a new Scowcroft Middle East Security Initiative
                       issue brief, “Present without impact? How the
                       Middle East perceives China’s diplomatic
                       engagement,” Jonathan Fulton argues that despite
                       economic advancements and high-profile diplomatic
                       engagements, China’s influence remains largely
                       economic rather than political.


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


                      # ⚓ New York Times ☛ As_Russia_Tries_to_Push_Ukraine_Out
                        of_Kursk,_Here’s_What_to_Know⠀⇛


                             Russia claimed to retake a key town in the
                             area from Ukrainian forces. Ukraine’s top
                             military commander has said that its forces
                             would continue to “hold the line.”


                      # ⚓ France24 ☛ Putin_agrees_in_principle_to_Ukraine
                        ceasefire_proposal⠀⇛


                             Russian President Vladimir Putin said he
                             agreed in principle to the US-drafted
                             proposal for a 30-day ceasefire in Ukraine,
                             but noted that the potential agreement in its
                             current format needed revisions. Putin
                             notably highlighted his objective to reclaim
                             the Kursk region in southeastern Russia,
                             which Ukrainian troops captured last summer,
                             before agreeing to a truce. The Russian
                             leader posited that Ukraine could use the
                             pause as an opportunity to regroup.


                      # ⚓ France24 ☛ 'Putin_is_clearly_not_interested_in
                        stopping_the_war_on_any_terms_other_than_Ukraine's
                        capitulation'⠀⇛


                             Russian President Vladimir Putin expresses
                             "serious" reservations about Washington's
                             plan for a 30-day ceasefire in Ukraine but
                             Moscow was ready to discuss it with US
                             President The Insurrectionist. For in-depth
                             analysis and a deeper perspective, FRANCE
                             24's Erin Ogunkeye welcomes Peter Zalmayev,
                             Director of the Eurasian Democracy
                             Initiative.


                      # ⚓ France24 ☛ Putin_says_he_supports_‘idea’_of_Ukraine
                        ceasefire,_but_that_it_needs_‘detailed_work’⠀⇛


                             President Vladimir Putin on Thursday made his
                             first public comments on a Washington-
                             proposed 30-day ceasefire between Russia and
                             Ukraine, saying he supported the “idea” of a
                             truce, but that the plan in its present form
                             needed “more detailed work”. He also said the
                             “root causes” of the conflict needed to be
                             removed, but without mentioning what those
                             might be.


                      # ⚓ France24 ☛ 🔴_Follow_live:_Putin_'in_favour'_of_a_30-
                        day_ceasefire_in_Ukraine_but_says_it_must_lead_to
                        'long-term_peace'⠀⇛


                      # ⚓ RFERL ☛ ANALYSIS:_Pressed_On_Cease-Fire,_Putin
                        Insists_On_Discussion_Of_‘Root_Causes’_Of_Ukraine_War⠀⇛


                             Russian President Vladimir Putin buried the
                             lead about whether he would agree to a US-
                             brokered proposal for a 30-day cease-fire in
                             Ukraine.


                      # ⚓ RFERL ☛ Putin_Says_Russia_Agrees_With_US_Cease-Fire
                        Proposal_But_'With_Nuances'⠀⇛


                             President Vladimir Putin says Russia agrees
                             with a US proposal for a cease-fire with
                             Ukraine, but that "there are nuances" and any
                             agreement should lead to long-term peace.


                      # ⚓ RFERL ☛ Kremlin_Aide_Rejects_Any_Temporary_Cease-Fire
                        As_US_Negotiators_Arrive_In_Moscow⠀⇛


                             A senior aide to President Vladimir Putin has
                             rejected any temporary cease-fire with
                             Ukraine just hours before a US delegation
                             arrived in Russia for talks with Moscow where
                             they will urge the Kremlin to agree to a 30-
                             day cease-fire proposal or face sanctions.


                      # ⚓ New York Times ☛ Putin,_in_No_Hurry_for_30-Day_Truce,
                        Seeks_Ukrainian_Concessions⠀⇛


                             The remarks by the Russian leader suggested
                             he wanted to draw out negotiations or make a
                             truce impossible. Ukraine’s leader called the
                             response to a cease-fire plan “manipulative.”


                      # ⚓ New York Times ☛ Putin_Stops_Far_Short_of_Agreeing_to
                        a_Cease-Fire,_and_Adds_Tough_Conditions⠀⇛


                             President Volodymyr Zelensky of Ukraine said
                             the Russian leader had no desire to end the
                             war, proposing conditions that made a truce
                             unattainable.


                      # ⚓ New York Times ☛ Friday_Briefing:_Putin_Speaks_on
                        Ukraine_Cease-Fire⠀⇛


                             Plus, Siberia’s bone hunters.


                      # ⚓ New York Times ☛ U.S._Negotiators_Are_en_Route_to
                        Moscow,_Kremlin_Says⠀⇛


                             President Vladimir V. Putin of Russia is
                             weighing a 30-day cease-fire proposal from
                             the United States and Ukraine.


                      # ⚓ Meduza ☛ Putin_says_Russia_supports_a_ceasefire,_but
                        there_are_‘issues_to_discuss’_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Putin_endorses_idea_of_a_ceasefire_—_with
                        ‘nuances’⠀⇛


                      # ⚓ RFERL ☛ Pressed_On_Cease-Fire,_Putin_Insists_On
                        Discussion_Of_‘Root_Causes’_Of_Ukraine_War⠀⇛


                             Russian President Vladimir Putin buried the
                             lead about whether he would agree to a US-
                             brokered proposal for a 30-day cease-fire in
                             Ukraine.


                      # ⚓ Latvia ☛ Nordics_and_Baltics_say_U.S._meeting_with
                        Ukraine_in_Saudi_Arabia_is_"a_step_in_the_right
                        direction"⠀⇛


                             The Ministers for Foreign Affairs of the
                             Nordic and Baltic countries (NB8) have issued
                             a brief joint statement commenting on the
                             meeting March 12 between American and
                             Ukrainian officials in Riyadh, the capital of
                             Saudi Arabia.


                      # ⚓ Atlantic Council ☛ Ukraine’s_innovative_defense_tech
                        sector_is_the_country’s_trump_card⠀⇛


                             From the Black Sea to deep inside Russia,
                             Ukraine's innovative and rapidly expanding
                             defense tech sector is proving to be the
                             country's secret weapon as it fights for
                             survival against one of the world's strongest
                             military superpowers, writes David
                             Kirichenko.


                      # ⚓ France24 ☛ NATO's_'Dihydroxyacetone_Man_whisperer'
                        treads_carefully_on_Greenland_and_defense⠀⇛


                             He's been dubbed the "Dihydroxyacetone Man
                             whisperer," but NATO chief Mark Rutte
                             struggled to get a word in Thursday as the US
                             president mused about annexing Greenland and
                             criticized allies over defense spending. The
                             former Dutch prime minister visited the White
                             House seeking to convince a skeptical The
                             Insurrectionist to maintain US commitment to
                             the transatlantic alliance and to Ukraine.
                             The Guardian Washington bureau chief David
                             Smith reports from Washington.


                      # ⚓ JURIST ☛ Russia_Supreme_Court_upholds_12-year
                        imprisonment_of_transgender_anti-war_activist⠀⇛


                             Russian Supreme Court upheld the 12-year
                             imprisonment of a transgender anti-war
                             activist Mark Kislitsyn, stated Amnesty
                             International on Wednesday. The group said
                             convicting the activist of high treason for
                             sending US $10 to a Ukrainian bank account
                             “defied common sense,” urging his immediate
                             release.


                      # ⚓ LRT ☛ Western,_Ukrainian_defence_companies_show
                        interest_in_Lithuania_–_PM⠀⇛


                             At least four defence industry companies from
                             Germany and Ukraine want to cooperate with
                             Lithuania, Prime Minister Gintautas Paluckas
                             said on Thursday.


                      # ⚓ LRT ☛ Lithuanian_injured_in_Kursk:_Russians_focus_all
                        their_effort_here⠀⇛


                             A Lithuanian volunteer, Osvaldas, was injured
                             on March 10 while fighting on the Ukrainian
                             side in Kursk. He tells LRT that his injuries
                             are not life-threatening and shares what the
                             moods are among Ukrainians occupying a piece
                             of Russian land that has lately seen the most
                             intense fighting.


                      # ⚓ New York Times ☛ Dihydroxyacetone_Man_Sees_‘Good
                        Signals’_on_Russia-Ukraine_Cease-Fire._Zelensky_Does
                        Not.⠀⇛


                             U.S. officials were in Moscow for talks, and
                             the Russian leader said he was open to a
                             cease-fire, but President Volodymyr Zelensky
                             of Ukraine expressed skepticism.


                      # ⚓ New York Times ☛ How_Zelensky_Can_Help_Ukraine⠀⇛


                             Different sides of the war in Ukraine reach
                             for different, simple narratives about Mr.
                             Zelensky. The truth has always been more
                             complicated.


                      # ⚓ New York Times ☛ Russia_Says_It_Has_Retaken_Key_Kursk
                        Town_From_Ukraine⠀⇛


                             Ukrainian officials have not confirmed a
                             retreat from the town in Russia’s Kursk
                             region, parts of which were captured by
                             Kyiv’s forces last summer.


                      # ⚓ Meduza ☛ Ukraine_to_hold_Kursk_defense_‘as_long_as
                        necessary,’_top_commander_says⠀⇛


                      # ⚓ Meduza ☛ Ukraine_has_run_out_of_ATACMS_missiles⠀⇛


                      # ⚓ Meduza ☛ Ukraine_tells_U.S._that_it_will_never_agree
                        to_limit_its_armed_forces_or_renounce_NATO
                        aspirations⠀⇛


                      # ⚓ Latvia ☛ Around_4,000_Russian_citizens'_Latvian
                        residence_permits_expire_this_year⠀⇛


                             For around 4000 Russian citizens in Latvia,
                             their temporary residence permit expires at
                             the end of the year. The authorities are
                             already preparing for a busy year as these
                             people will have to take a language test to
                             get a permanent European Union residence
                             permit, Latvian Radio reports on March 12.


                      # ⚓ LRT ☛ Lithuanian_ex-politician_Paleckis_found_guilty
                        of_contempt_for_partisans⠀⇛


                             The Kaunas Regional Court on Thursday
                             acquitted Algirdas Paleckis, a controversial
                             former politician already serving a sentence
                             for spying for Russia, of defaming MP
                             Laurynas Kasčiūnas but found him guilty of
                             denying international crimes by expressing
                             contempt for partisans.


                      # ⚓ RFERL ☛ China_Hosts_Iran,_Russia_In_Talks_Over
                        Tehran's_Nuclear_Standoff_With_West⠀⇛


                             Beijing urged “calm” and “restraint” has it
                             prepared to host three-party talks with
                             Tehran and Moscow in pursuit of a diplomatic
                             solution to the Iran nuclear issue.


                      # ⚓ Meduza ☛ German_newspaper_links_CDU_lawmaker’s
                        employee_to_Russian_FSB⠀⇛


                      # ⚓ Meduza ☛ Moscow_court_logs_administrative_case
                        against_Meduza_journalist_Lilia_Yapparova_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russia_considers_trials_in_absentia_for
                        ‘foreign_agents’⠀⇛


                      # ⚓ Meduza ☛ Russia’s_Defense_Ministry_announces_control
                        over_Sudzha_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russia_opposes_temporary_ceasefire,_Kremlin
                        says_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russia_publishes_images_from_retaken_Kursk
                        settlements⠀⇛


                      # ⚓ Atlantic Council ☛ Vladimir_Putin_does_not_want
                        peace._He_wants_to_subjugate_Ukraine.⠀⇛


                             Russian President Vladimir Putin's evasive
                             response to US President The
                             Insurrectionist's ceasefire proposal
                             underlines his commitment to continue with an
                             invasion that aims to extinguish Ukraine as a
                             state and nation, writes Mykola Bielieskov.


                      # ⚓ The Strategist ☛ Europe_can_still_prevent_a_Russian
                        victory⠀⇛


                             When Russian President Vladimir Putin
                             launched his full-scale invasion of Ukraine
                             in February 2022, he knew that he was
                             upending Europe’s security order.


          o § Environment⠀➾


                # § Energy/Transportation⠀➾


                      # ⚓ Hackaday ☛ Have_Li-ion_Batteries_Gone_Too_Far?⠀⇛


                             The proliferation of affordable lithium
                             batteries has made modern life convenient in
                             a way we could only imagine in the 80s when
                             everything was powered by squadrons of AAs,
                             or has it? [Ian Bogost] ponders whether
                             sticking a lithium in every new device is
                             really the best idea.


                      # ⚓ The Straits Times ☛ Air_Busan_fire_likely_caused_by
                        power_bank_with_faulty_insulation:_South_Korea⠀⇛


                             170 passengers and six crew members were
                             evacuated when the plane caught fire on Jan
                             28.


                # § Overpopulation⠀➾


                      # ⚓ Hong Kong Free Press ☛ Hong_Kong_proposes_axing_10-
                        year_storage_limit_for_frozen_eggs_and_embryos_amid
                        declining_fertility_in_city⠀⇛


                             Hong Kong authorities have proposed scrapping
                             a law that limits the storage duration for
                             frozen eggs, sperm, and embryos to 10 years
                             amid the city’s declining birth rate.


          o § Finance⠀➾


                # ⚓ China’s_exports_to_be_hit_hard_by_US_tariffs:_businesses⠀⇛


                       The sector has been a bright spot amid economic
                       gloom, but will struggle to make a profit as costs
                       rise.


                # ⚓ Hong Kong Free Press ☛ China_and_other_US_trading_partners
                  hit_back_on_Convicted_Felon’s_steel,_aluminium_tariffs⠀⇛


                       Major US trading partners announced countermeasures
                       Wednesday after The Insurrectionist’s blanket
                       tariffs on steel and aluminum imports took effect,
                       prompting the president to vow a further response.


                # ⚓ New York Times ☛ See_How_MElon’s_Team_Inflated,_Deleted_and
                  Rewrote_Its_Savings_Claims⠀⇛


                       The cost-cutting group removed hundreds of
                       contracts from its “wall of receipts,” added back
                       many of them, and inflated savings values.


                # ⚓ The Straits Times ☛ Dihydroxyacetone_Man_hits_ally
                  Australia_with_tariffs,_sparking_alarm_over_security_ties⠀⇛


                       Some question whether the US will still honour the
                       deal to acquire its nuclear-powered submarines.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ France24 ☛ Federal_judge_orders_Convicted_Felon_to_rehire
                  agency_workers_laid_off_in_mass_firings⠀⇛


                       In a show of resistance to US President The
                       Insurrectionist's drastic efforts to reduce the
                       federal workforce, a District Judge on Thursday
                       ordered the Convicted Felon administration to
                       rehire probationary workers it had laid off since
                       coming into power. The White House swiftly appealed
                       the ruling – a lawsuit jointly filed by numerous
                       labor unions – labeling it an encroachment on
                       executive powers.


          o § Censorship/Free Speech⠀➾


                # ⚓ China_pushes_patriotic_education_in_Tibet_with_propaganda
                  movies_and_storytelling⠀⇛


                       The campaign is to promote ‘ethnic unity’ and
                       assimilate Tibetan and other ethnic groups into Han
                       Chinese culture.


                # ⚓ Silicon Angle ☛ Meta_says_it’s_almost_ready_to_start
                  testing_Community_Notes⠀⇛


                       Meta Platforms Inc., the parent company of
                       Facebook, Instagram and Threads, announced today
                       that it will begin testing its crowdsourced fact-
                       checking program, Community Notes, on March 18.


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


                # ⚓ The Straits Times ☛ Malaysian_journalist_charged_in_court
                  for_allegedly_taking_bribe⠀⇛


                       He allegedly receiving $6,000 in exchange for
                       retracting and not uploading articles about a
                       foreign workers cartel. 


                # ⚓ The Straits Times ☛ China_amplifies_newspaper’s_attack_on
                  CK_Hutchison_over_Panama_ports_deal⠀⇛


                       The company agreed to sell a controlling stake in
                       Panama ports that had become a political lightning
                       rod.


                # ⚓ Press Gazette ☛ As_some_publishers_seek_full_return_to
                  office,_most_staff_favour_hybrid_working⠀⇛


                       Eight in ten respondents to a Press Gazette survey
                       backed hybrid/flexible working.


                # ⚓ Press Gazette ☛ News_media_staff_share_views_in_the_great
                  work_from_home_debate⠀⇛


                       Everyone from national news CEOs to local
                       newspapers reporters share their views on office
                       versus remote working.


          o § Civil Rights/Policing⠀➾


                # ⚓ The Straits Times ☛ China_deports_Japanese_tourists_over
                  Great_Wall_buttocks_pic⠀⇛


                       Exposing the lower half of the body in a public
                       place is against the law in China.


          o § Internet Policy/Net Neutrality⠀➾


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Android Police ☛ Google_is_changing_how_you_answer
                        calls_with_a_major_Phone_app_redesign⠀⇛


                             Google's stock Phone app on Pixel smartphones
                             is pretty minimal, focusing on the basics
                             with an easy-to-use UI. While the Phone app
                             still lacks some useful features found in
                             competing dialer apps, it looks like Google
                             is at least working on a redesigned call
                             screen.


                      # ⚓ Android Authority ☛ Google_could_change_the_way_you
                        answer_your_phone_calls⠀⇛


                             With Phone v166.0.735169223 beta, Google is
                             testing a new interface for answering
                             incoming calls.


                      # ⚓ Andrea Contino ☛ Profiles_-_Andrea_Contino_-_Go_With
                        The_Flow⠀⇛


                             I decided that to slow down at the end of the
                             day, completely abandon the phone, and only
                             reach for it in emergencies, I needed a
                             drastic and clear action. And so I did. Now,
                             as soon as my iPhone geolocates to home, it
                             automatically activates the “Personal”
                             profile, and what appears before my eyes is
                             this: the bare essentials.


      § Monopolies/Monopsonies⠀➾


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ CAFC_Affirms_TTAB's_Dismissal_of_BULLSHINE
                  FIREBULL_Opposition_Despite_Commercial_Strength_of_FIREBALL
                  for_Whisky⠀⇛


                       In a precedential opinion, the U.S. Court of Appeal
                       for the Federal Ciruit affirmed the TTAB's decision
                       (here) dismissing Sazerac Brand's opposition to
                       registration of the mark BULLSHINE FIREBULL for
                       "alcoholic beverages except beers." The Board found
                       Sazerac's FIREBALL mark (for whiskey and liqueurs)
                       to be commercially strong but conceptually weak,
                       that the goods were purchased without great care,
                       and that Bullshine Distillery did not act in bad
                       faith in choosing its mark. But the Board concluded
                       that confusion is unlikely because of the
                       differences in the marks. The CAFC ruled that the
                       Board did not err in its conclusion. Sazerac
                       Brands,_LLC_v._Bullshine_Distillery_LLC, Appeals
                       Nos. 2023-1682 and 2023-1900 (Fed. Cir. March 12,
                       2025) [precedential].


    * Gemini_Links_14/03/2025:_Löjl_and_Docker_Context_Stuff
    * Slopwatch:_linuxsecurity.com_and_hamradio.my_(in_Planet_Ubuntu)_Are_at_It
      Again_With_LLM_Slop_About_"Linux"



                    ䷩ 𝚕𝚒𝚗𝚎 6263

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 14/03/2025: ProPublica Admitting That
It Uses Slop (Foolish Move), RIP Mark Klein⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Monopolies/Monopsonies
                # Patents
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ MWL ☛ 80:_Mentally_Stable_People⠀⇛


                 I’m gonna finish this book. I’m gonna finish this book.
                 It doesn’t matter how much life tries to stop me, I’m
                 gonna finish this book… One of the great problems of
                 civilization is disposing of unwanted stuff.


          o § Science⠀➾


                # ⚓ Hackaday ☛ Tracking_Deep-Sky_Objects⠀⇛


                       Astrophotography, and astronomy in general, takes
                       some fairly specialized tools and a high amount of
                       precision. Setting up the equipment can also take a
                       lot of time, especially for amateurs traveling to
                       various locations with their equipment, so anything
                       that can reduce the amount of time spent looking
                       for objects and increasing the amount of time
                       looking at them is a welcome addition, especially
                       since nights where conditions are ideal for these
                       activities can be rare. [Anton] developed this
                       real-time tracking tool for deep sky objects (DSOs)
                       to keep tabs on most of the interesting things out
                       there a telescope can be pointed at.


          o § Career/Education⠀➾


                # ⚓ Johns_Hopkins_lays_off_2,000_employees_after_Trump's
                  funding_cut⠀⇛


                       Johns Hopkins University, a top US institution in
                       scientific research, has announced plans to lay off
                       over 2,000 employees.


                       The decision comes after the Donald Trump
                       administration made deep cuts in foreign aid
                       funding.


                       The university said that the termination of more
                       than $800 million in USAID funding is now forcing
                       them to wind down critical work here and
                       internationally.


                # ⚓ IT Pro ☛ Laid-off_workers_are_ditching_full-time_work:_70%
                  of_staff_caught_up_in_brutal_layoffs_opted_for_part-time
                  roles_and_freelance_gigs_–_and_flexibility_was_the_big_appeal
                  for_many⠀⇛


                       Flexible working practices have proven so popular
                       that a significant number of workers laid off from
                       full-time jobs have opted for part-time work.


                       That's according to a survey from job platform
                       Intch, which showed 96% of laid-off professionals
                       moved to flexible work after being made redundant,
                       with 70% planning to shift to part-time, freelance,
                       or project-based roles.


                       Of those polled, 84% had previous corporate
                       experience, but only 15% said they would return to
                       a large company, which Intch suggested was a sign
                       that traditional roles and work structures were
                       losing appeal.


                       "Our research confirms that especially after more
                       than 150,000 job cuts across 542 companies in [the]
                       last three years, flexible work has evolved from a
                       fallback option into a strategic and preferred
                       career path for many professionals," said Yakov
                       Filippenko, CEO and founder of Intch.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ Renesas_RZ/V2N_low-power_Hey_Hi_(AI)_MPU
                  integrates_up_to_15_TOPS_Hey_Hi_(AI)_power,_Mali-C55_ISP,
                  dual_MIPI_camera_support⠀⇛


                       Renesas has recently introduced the RZ/V2N low-
                       power Arm Cortex-A55/M33 microprocessor designed
                       for machine learning (ML) and computer vision
                       applications. It features the company’s DRP-AI3
                       coprocessor, delivering up to 15 TOPS of INT8
                       “pruned” compute performance at 10 TOPS/
                       W efficiency, making it a lower-power alternative
                       to the RZ/V2H.


                # ⚓ CNX Software ☛ Geniatech_AIM_M2_M.2_module_features_Kinara
                  Ara-2_40_TOPS_Hey_Hi_(AI)_accelerator⠀⇛


                       There are plenty of M.2 Hey Hi (AI) modules based
                       on accelerators such as Hailo-8, MemryX MX3, or
                       Axelera AI, but the Geniatech AIM M2 module is
                       based on the Kinara Ara-2 40 TOPS Hey Hi (AI)
                       accelerator that we’ve yet to cover here on CNX
                       Software. The Key-M module is designed to handle
                       Generative Hey Hi (AI) and transformer-based models
                       such as Stable Diffusion at a lower price point
                       than competitors, and operates at a typical sub-2W
                       power consumption in computer vision workloads.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Stanford University ☛ George_Steinmetz_on_the_hidden_costs
                  of_our_food_system⠀⇛


                       Photographer George Steinmetz ’79 returned to
                       Stanford to unveil his new book, sharing images of
                       global food production and bringing the realities
                       of meat consumption home to students.


                # ⚓ Science Alert ☛ Expired_Cans_of_Salmon_From_Decades_Ago
                  Contained_a_Big_Surprise⠀⇛


                       A real can of worms.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_police_arrest_74_in_anti-
                  triad_operation,_seize_HK$1.6_million_of_drugs⠀⇛


                       Hong Kong police have arrested 74 people in an
                       anti-triad operation and seized HK$1.6 million of
                       drugs, including “space oil,” an addictive
                       substance popular among local youth.


                # ⚓ The Straits Times ☛ Chinese_tourist_critically_injured
                  after_leaning_out_of_Sri_Lanka_train_for_photos⠀⇛


                       The woman reportedly hit her head on a tunnel wall
                       and fell off the train.


                # ⚓ University of Michigan ☛ ‘Redefining_the_Crown’_exhibit
                  highlights_Black_breast_cancer_survivors⠀⇛


                       Each year, the University of Michigan Women’s and
                       Gender Studies Department and Institute for
                       Research on Women and Gender host two exhibits in
                       Lane Hall. Until Aug. 8, the exhibit space features
                       “Redefining the Crown,” a portraiture series
                       displaying six Black breast cancer survivors and
                       their journeys with chemotherapy-induced hair loss.


                # ⚓ New Yorker ☛ “An_Unfinished_Film”_Puts_the_Pandemic_in_the
                  Spotlight⠀⇛


                       This historical docufiction, directed by Lou Ye,
                       boldly dramatizes the outbreak of *COVID*{: .small}
                       in China by way of its impact on a movie shoot.


                # ⚓ Latvia ☛ What_did_Latvia_learn_from_the_Covid_crisis?⠀⇛


                       It has been five years since the day when a state
                       of emergency was declared in Latvia due to
                       increasing morbidity and mortality caused by Covid-
                       19.


          o § Proprietary⠀➾


                # ⚓ Junichi_Uekawa:_Filing_tax_this_year_was_really_painful.⠀⇛


                       Filing tax this year was really painful. But mostly
                       because my home network.


                       It was ipv4 over ipv6 was not working correctly.
                       First I swapped the Router which was trying to
                       reinitialize the MAP-E table every time there was a
                       dhcp client reconfiguration and overwhelming the
                       server. Then I changed the DNS configuration not
                       use ipv4 UDP lookup which was overwhelming the ipv4
                       ports.


                       Tax return itself is a painful process. Debugging
                       network issues is making things was just making
                       everything more painful.


                # ⚓ The Strategist ☛ South_Korea_has_acted_decisively_on
                  DeepSeek._Other_countries_must_stop_hesitating⠀⇛


                       South Korea has suspended new downloads of
                       DeepSeek, and it was were right to do so. Chinese
                       tech firms operate under the shadow of state
                       influence, misusing data for surveillance and
                       geopolitical advantage.


                # ⚓ Security Week ☛ DeepSeek’s_Malware-Generation_Capabilities
                  Put_to_Test⠀⇛


                       Researchers have analyzed the ability of the
                       Chinese gen-AI DeepSeek to create malware such as
                       ransomware and keyloggers.


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ Pro Publica ☛ How_ProPublica_Uses_AI_Responsibly_in
                        Its_Reporting [Ed: ProPublica has just ousted and
                        discredited itself by saying it tries LLM slop]⠀⇛


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ BIA Net ☛ Turkey's_independent_media_protest
                        Surveillance_Giant_Google_over_‘algorithmic
                        censorship'⠀⇛


                             An analysis of website traffic shows that
                             conglomerate and state media benefit
                             significantly more from searches on
                             Surveillance Giant Google and its news app
                             than independent outlets.


                      # ⚓ Xe's Blog ☛ Opsec_and_you:_how_to_navigate_having
                        things_to_hide⠀⇛


                             A discussion on operational security and
                             privacy in modern life.


                      # ⚓ Privacy International ☛ Our_challenge_against_UK's
                        secret_TCN_powers⠀⇛


                      # ⚓ OpenRightsGroup ☛ Joint_letter:_Make_the
                        Investigatory_Powers_Tribunal_on_Fashion_Company_Apple
                        Encryption_a_Public_Hearing⠀⇛


                             Joint letter from Open Rights Group, Big
                             Brother Watch and Index on Censorship.


                      # ⚓ OpenRightsGroup ☛ Make_the_Investigatory_Powers
                        Tribunal_on_Fashion_Company_Apple_Encryption_a_Public
                        Hearing⠀⇛


                             Rights groups call for Apple’s closed appeal
                             against the Home Office’s encryption-
                             breaching order to be opened to the public.


                      # ⚓ Bruce Schneier ☛ RIP_Mark_Klein⠀⇛


                             2006 AT&T whistleblower Mark Klein has died.


          o § Defence/Aggression⠀➾


                # ⚓ New York Times ☛ After_al-Assad’s_Ouster,_Many_Syrians
                  Struggle_With_Returning_Home⠀⇛


                       Syria’s interim president has said that millions
                       would return after President Bashar al-Assad’s
                       ouster, but many houses and other buildings were
                       destroyed in 13 years of civil war.


                # ⚓ Defence Web ☛ Peace_in_Sudan:_a_fresh_mediation_effort_is
                  needed_–_how_it_could_work⠀⇛


                       Intense fighting has ravaged Sudan since 15 April
                       2023. The war between the Sudanese Armed Forces and
                       its erstwhile comrades-in-arms, the paramilitary
                       Rapid Support Forces, has created one of the worst
                       humanitarian crises in the world. Famine,
                       displacement and mass atrocities are wreaking havoc
                       in the country. International mediation efforts
                       have been lacklustre and fruitless.


                # ⚓ Atlantic Council ☛ What_airstrikes_in_Somalia_show_about
                  the_war_on_terror⠀⇛


                       With terrorist groups increasingly prevalent
                       throughout Africa, the United States is likely to
                       devote more attention to counterterrorism efforts
                       on the continent.


                       >


                # ⚓ Site36 ☛ After_30_years_in_exile:_Left-wing_radicals_stand
                  trial_for_two_major_attacks⠀⇛


                       Two people wanted as militant leftists are
                       returning to Berlin this week. Their story is
                       characterised by a long escape and exile in
                       Venezuela. The surveillance by the German police
                       was unprecedented. In October 1994, the
                       ‘K.O.M.I.T.E.E.’ carried out an arson attack on the
                       military replacement office in Bad Freienwalde.


          o § Environment⠀➾


                # § Energy/Transportation⠀➾


                      # ⚓ Hong Kong Free Press ☛ Civil_service_job_cuts_and
                        HK$2_transport_fare_revamp_‘insignificant,’
                        legislature’s_research_office_says⠀⇛


                             Hong Kong government’s proposals to downsize
                             the civil service and revamp the HK$2 elderly
                             transport fare scheme are likely to result in
                             “insignificant” cost savings, the research
                             office of the city’s legislature has said.


                      # ⚓ European Commission ☛ Opening_statement_of
                        Commissioner_Jørgensen_in_the_European_Parliament
                        Plenary_debate_on_the_Action_Plan_for_Affordable
                        Energy⠀⇛


                             According to Google, in my home country the
                             name most searched for last year was actually
                             Taylor Swift.


                      # ⚓ The Straits Times ☛ Malaysia’s_PM_Anwar_denies
                        bailout_claims_after_pumping_$331_million_into_ailing
                        Sapura_Energy⠀⇛


                             The PM was previously strongly against
                             bailing out Sapura Energy, once one of the
                             world's top oil and gas firms.


          o § Finance⠀➾


                # ⚓ New York Times ☛ S&P_500_Dips_Into_Correction_as_Stock
                  Market_Sours_on_Convicted_Felon⠀⇛


                       The S&P 500 is now more than 10 percent below its
                       last record high — a line in the sand for investors
                       worried about a sell-off gathering steam.


                # ⚓ Digital Music News ☛ En_Vogue’s_Dawn_Robinson_Says_She’s
                  Been_Living_In_Her_Car_for_Almost_Three_Years⠀⇛


                       En Vogue’s Dawn Robinson reveals she’s been living
                       in her car for nearly three years, breaking the
                       news in a video on her YouTube channel. But it’s
                       not the “woe is me” situation fans might expect.


                # ⚓ France24 ☛ How_to_stop_the_escalation?_Convicted_Felon_hits
                  back_after_EU_retaliation_to_US_metal_tariffs⠀⇛


                       The Insurrectionist has said it many times...: "The
                       most beautiful word in the dictionary to me is
                       tariff." But the tariffs that Convicted Felon is
                       imposing on business and commerce across the
                       borders is having a less than beautiful effect.
                       Convicted Felon came to power promisong prosperity
                       for the United States, a "new golden age", but now
                       the country is teetering towards recession.


                # ⚓ Federal News Network ☛ How_to_ensure_your_financial_and
                  physical_health_in_uncertain_times⠀⇛


                       Federal employees worried about their jobs are also
                       worried about their family finances and health care
                       coverage.


                # ⚓ New Yorker ☛ Will_Convicted_Felon’s_Tariffs_Trigger_a
                  Recession?⠀⇛


                       “I always compare tariffs to a boxing match,” the
                       staff writer John Cassidy says. “The other guy
                       punches you back, you punch, and who’s gonna stop
                       it?”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ US_hands_over_Tibetan_Buddhism_relics_to_China⠀⇛


                       Experts said Chinese authorities may misuse the
                       artifacts to justify their territorial claims in
                       Tibet.


                # ⚓ Pro Publica ☛ Amid_Trump,_Musk_Cutbacks,_D.C._Faces_Gloomy
                  Future⠀⇛


                # ⚓ Atlantic Council ☛ Soofer_interviewed_on_War_on_the_Rocks
                  podcast_about_Convicted_Felon’s_‘Iron_Dome’⠀⇛


                       On March 12, Forward Defense senior fellow Robert
                       Soofer was interviewed by Ankit Panda, host of the
                       “Thinking the Unthinkable” podcast on War on the
                       Rocks. The episode discussed the Convicted Felon
                       administration’s plan for an American “Iron Dome”
                       and the questions it raises for US missile defense
                       and the strategic vulnerability in the United
                       States today.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ The Straits Times ☛ Fuelled_by_disinformation_online,
                        Myanmar_migrants_in_Thailand_face_surge_in_hate_speech,
                        resentment⠀⇛


                             Social media platforms have been flooded by
                             claims that Myanmar workers were demanding
                             higher wages.


          o § Censorship/Free Speech⠀➾


                # ⚓ Chinese_doll_sold_in_Vietnam_shows_disputed_map_of_South
                  China_Sea,_ministry_says⠀⇛


                       Photos show a map on doll’s cheek resembling the
                       ‘nine-dash-line’ marking off China’s claims to
                       waters off Vietnam.


                # ⚓ Digital Music News ☛ Andrew_Tate’s_Podcast_Removed_from
                  Spotify⠀⇛


                       Andrew Tate’s podcast has been removed from Spotify
                       after several complaints from both employees and an
                       online petition garnering 92,000 signatures. The
                       misogynist influencer has been de-platformed by
                       both YouTube and Fentanylware (TikTok) previously.
                       Spotify removed a podcast dubbed a ‘degree course’
                       created by the influencer with the title ‘pimping
                       hoes.’


          o § Civil Rights/Policing⠀➾


                # ⚓ Rlang ☛ Diversity_Champion_Updates⠀⇛


                       I am excited to announce that the pharmaverse
                       council has approved additional organizational
                       characteristics required for council membership.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ Unified Patents ☛ $2,000_awarded_for_Granite_Vehicle_self-
                  driving_patent_monopoly_prior_art⠀⇛


                       Unified is pleased to announce PATROLL
                       crowdsourcing contest winners, Ritu Tyagi and
                       Calvin Zhong, who split a cash prize of $2,000 for
                       their prior art submissions on U.S._Patent
                       12,037,004, owned and asserted by Granite Vehicle
                       Ventures LLC, an NPE. The ‘004 patent monopoly
                       relates to the field of vehicles, and specifically
                       to the field of self-driving vehicles. It has been
                       asserted against Tesla.


                # ⚓ Dennis Crouch/Patently-O ☛ EcoFactor_v._Google:_Listen_Live
                  This_Morning⠀⇛


                       EcoFactor v. Surveillance Giant Google is the
                       Federal Circuit’s first en banc utility patent
                       monopoly case in years.  The court will beholding
                       oral arguments this morning, starting at 10:00 am
                       Eastern.


                # ⚓ Dennis Crouch/Patently-O ☛ EcoFactor_v._Google:_Quick
                  Review_of_Oral_Arguments⠀⇛


                       The Federal Circuit recently heard oral arguments
                       in the much-anticipated en banc review of
                       EcoFactor, Inc. v. Surveillance Giant Google LLC, a
                       case focusing on how courts evaluate expert
                       testimony on patent monopoly damages.  And, in
                       particular, when a court should step-in to bar
                       expert testimony that does not have sufficient
                       factual basis for its conclusions.  The arguments
                       focused on whether EcoFactor's damages expert
                       improperly derived royalty rates from license
                       agreements that contained performative non-binding
                       "whereas" clauses stating EcoFactor's belief about
                       rates, while the operative provisions specified
                       lump-sum payments.  It seems clear to me that these
                       provisions were added as elements of the patentee's
                       smaller license agreements in order to later be
                       used in larger cases, such as the one against
                       Google.


                # ⚓ Unified Patents ☛ $2,000_awarded_for_ShopSee_interactive
                  video_patent_monopoly_prior_art⠀⇛


                       Unified is pleased to announce PATROLL
                       crowdsourcing contest winners, Ekta Aswal, Ritu
                       Tyagi, and Gaurav Yadav, who split a cash prize of
                       $2,000 for their prior art submissions on U.S.
                       Patent_11,134,316, owned and asserted by ShopSee
                       Inc., an NPE. The ‘316 patent monopoly relates to
                       video processing technology, and more particularly,
                       relates to a method and apparatus for providing one
                       or more interactive video layers with video media.
                       The patent monopoly has been asserted against
                       TikTok.


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


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ Mannheim_local_division_favours_practical
                        approach_for_calculating_damages [Ed: UPC is illegal;
                        this is basically more puff piecing by JUVE, funded by
                        Team UPC, for a kangaroo court that must not exist and
                        its very presence is a violation of constitutions, so
                        it contributes to EU being discredited as corruption
                        hub]⠀⇛


                             The Korean kitchen appliance manufacturers
                             Hurom and NUC have taken their global patent
                             monopoly dispute to the UPC. The case
                             concerns slow juicers that both companies
                             sell worldwide. Hurom sued its competitor at
                             the local divisions in Mannheim and Paris
                             over two different patents.


          o § Copyrights⠀➾


                # ⚓ Creative Commons ☛ Community_in_2025⠀⇛


                       Regent Street Looking Towards the Duke of York’s
                       Column, plate twelve from Original Views of London
                       as It Is by Thomas Shotter Boys is marked with CC
                       1.0 In case you missed it, we recently published
                       our 2025-2028 Strategy which sets the stage for our
                       goals and activities over the next few years.


                # ⚓ Digital Music News ☛ OpenAI_Says_Copyright_Training
                  Restrictions_Would_Equal_‘Forfeiting_Our_Hey_Hi_(AI)_Lead’_to
                  China [Ed: Allow plagiarism or "China wins"?]⠀⇛


                       OpenAI hopes for a nation where Hey Hi (AI)
                       training on copyrighted works counts as fair use —
                       or else, the company says, the US might ‘forfeit’
                       its Hey Hi (AI) lead to China.


                # ⚓ Carl Svensson ☛ Copyright_and_the_Demo_Scene⠀⇛


                       Scandal, scandal!


                # ⚓ Digital Music News ☛ Sony_Music_Sues_the_University_of
                  Southern_California_Over_Alleged_Social_Media_Infringement:
                  ‘USC_Chose_to_Flaunt_Copyright_Law’⠀⇛


                       Sony Music Entertainment (SME) has fired off
                       another social control media copyright monopoly
                       complaint – this time against the University of
                       Southern California (USC), which is accused of
                       “blatantly willful” infringement. The major label
                       just recently slapped USC with the straightforward
                       action.


    * Windows_is_Fast_Becoming_Insignificant_to_Zimbabweans
    * Gemini_Links_14/03/2025:_Grizzy_Bear_and_Prime_Beats



                    ䷩ 𝚕𝚒𝚗𝚎 6972

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 14/03/2025: Scam Currencies in the US
and Oligarchs (Including GAFAM) Controlling All the Major
Policies⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Mar 14, 2025


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          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 Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ James G ☛ Website_reflections⠀⇛


                 Guided by wondering “what would I say to my younger self
                 starting a website?”, I started taking notes. Here they
                 are: [...]


          o ⚓ Kevin Kelly ☛ The_Technium:_Public_Intelligence⠀⇛


                 Imagine 50 years from now a Public Intelligence that was
                 a distributed, open-source, non-commercial artificial
                 intelligence, operated like the [Internet], and available
                 to the whole world. This public AI would be a federated
                 system, not owned by any one entity, but powered by
                 millions of participants to create an aggregate
                 intelligence beyond what one host could offer. Public
                 intelligence could be thought of as an inter-
                 intelligence, an AI composed of other AIs, in the way
                 that the [Internet] is a network of networks. This AI of
                 AIs, would be open and permissionless: any AI can join,
                 and its joining would add to the global intelligence. It
                 would be transnational, and wholly global – an AI
                 commons. Like the [Internet], it would run on protocols
                 that enabled interoperability and standards. Public
                 intelligence would be paid for by usage locally, just as
                 you pay for your [Internet] access, storage, or hosting.
                 Local generators of intelligence, or contributors of
                 data, would operate for profit, but in order to get the
                 maximum public intelligence, you need to share your work
                 in this public non-commercial system.


          o ⚓ Joel Chrono ☛ I'm_a_fake_fan_of_many_things⠀⇛


                 There's lots of things I like where I don't really have
                 what it takes to be a true fan, someone in the know, but
                 well


          o ⚓ Thomas Rigby ☛ Reorganising_tags_and_categories⠀⇛


                 I like to tag my posts on this website. I thought it
                 would be helpful — to me as well as others. But then the
                 number of tags grew. And grew. So many tags with one (1)
                 post!


          o ⚓ University of Toronto ☛ Doing_multi-tag_matching_through_URLs_on
            the_modern_web⠀⇛


                 This isn't because the idea of stacking selections like
                 this is bad; 'site/wiki/foo/bar' is a perfectly
                 reasonable and good way to express 'a list of articles
                 tagged foo and bar'. Instead, it's because of how
                 everything on the modern web eventually gets visited
                 combined with how, in the natural state of this feature,
                 'site/wiki/bar/foo' is just a valid a URL for 'articles
                 tagged both foo and bar'.


          o ⚓ Andy Bell ☛ We_gave_The_Index_a_much_needed_design_refresh_and
            introduced_advertising,_site-wide⠀⇛


                 I’m a big fan of curating links, so I set Piccalilli up
                 originally as a newsletter, then evolved it into a blog
                 and newsletter.


                 Unfortunately, I had to stop curating the old newsletter
                 because I just didn’t have the time for it anymore. The
                 Index gives a massive nod to that old newsletter though,
                 which I’m really happy with.


          o ⚓ Vintage Everyday ☛ Edward_Penfield:_The_Father_of_the_American
            Poster⠀⇛


                 Penfield’s style played a significant role in bridging
                 the gap between illustration and graphic design as we
                 understand it today. Here is a collection of impressive
                 covers of Harper’s Magazine illustrated by Edward
                 Penfield in the 1890s.


          o ⚓ Bitdefender ☛ Man_found_guilty_of_planting_infinite_loop_logic
            bomb_on_ex-employer's_system⠀⇛


                 When directed to hand in his company laptop following his
                 dismissal, Lu was found to have erased encrypted data -
                 but his [Internet] search history showed that he had
                 researched on the web methods to hide processes, rapidly
                 delete files, and escalate his privileges. Prosecutors
                 claimed that this was a deliberate attempt to prevent his
                 co-workers from fixing the issues that he had caused.


                 Investigators found the code for Lu's malicious Java
                 program on an internal Kentucky-based development server,
                 and evidence that it was his user account that had been
                 used to execute the malicious code on the company's
                 production systems. Lu was found to be the only member of
                 staff who had access privileges to the development server


          o § Science⠀➾


                # ⚓ Science News ☛ A_quantum_computing_milestone_is_immediately
                  challenged_by_a_supercomputer⠀⇛


                       In just minutes, a special quantum processor,
                       called a quantum annealing processor, solved a
                       complex real-world problem that a classical
                       supercomputer would take millions of years to
                       complete, researchers claim March 12 in Science.
                       And that supercomputer, the team reports, would
                       consume more energy to run the whole computation
                       than the entire globe uses in a year. However,
                       another group of researchers claims to have already
                       found a way for a classical supercomputer to solve
                       a subset of the same problem in just over two
                       hours.


                # ⚓ Deutsche Welle ☛ Trump's_'assault_on_science':_Bad_for_the
                  US,_good_for_EU?⠀⇛


                       The prospect of a US science brain drain is seen as
                       "a great opportunity for Europe as a research
                       location," said Cramer.


                       Applications from US scientists to the group of 84
                       Max Planck Institutes have at least doubled and, in
                       some cases, tripled.


                       "But for research as a whole, it is a clear step
                       backwards, something that worries me greatly," he
                       said.


          o § Career/Education⠀➾


                # ⚓ CNET ☛ Department_of_Education_Rocked_by_Layoffs:_Will_It
                  Be_Abolished?⠀⇛


                       President Donald Trump announced recently that
                       roughly half of the Education Department's staff
                       was being cut, amid his contentious plans to axe
                       the department altogether.


                # ⚓ Robert Birming ☛ The_Writer's_Engine⠀⇛


                       Now, I pick up a book whenever I have a moment. I'm
                       immediately immersed in the story, finding the
                       whole experience both relaxing and inspiring.


                # ⚓ [Old] OMG Ubuntu ☛ Our_Exclusive_Interview_with_Linus
                  Torvalds_-_OMG!_Ubuntu⠀⇛


                       His early work to establish the Linux kernel as a
                       reliable, feature-rich and flexible basis for
                       Operating Systems made Linux one of the most
                       prominent and widely used examples of Free Software
                       in the world.


                       Torvalds has been named as one of the “most
                       influential people in the world” by TIME Magazine
                       in 2004, and was voted 17th in their “Top 100 Most
                       Important People of the Century” in 2000.


                # ⚓ The Takeda Foundation ☛ The_Takeda_Foundation⠀⇛


                       [...] The technical achievement honored by the
                       Takeda Award 2001 Techno-Entrepreneurial
                       Achievements for Social/Economic Well-Being is "the
                       origination and the advancement of open development
                       models for system software - open architecture,
                       free software and open source software." The prize
                       is awarded jointly to Ken Sakamura (University of
                       Tokyo), Richard M. Stallman (Free Software
                       Foundation) and Linus Torvalds (Transmeta
                       Corporation). Ken Sakamura is honored for
                       developing and promoting the TRON open
                       architecture, a real-time operating system
                       specification for embedded systems. Richard M.
                       Stallman is honored for starting the free software
                       movement and leading the development of the GNU
                       operating system. Linus Torvalds is honored for
                       developing the Linux operating system kernel by the
                       open source process for software development. [...]


                # ⚓ [Old] uni MIT ☛ Stallman_shares_Takeda_award_of_nearly
                  $1M⠀⇛


                       This new award from Japan's Takeda Foundation is
                       intended to honor and encourage contributions in
                       science and technology that "enhance the value of
                       human life and lead to an increase in the wealth,
                       richness and happiness of life for humanity." It is
                       aimed at individuals who have demonstrated
                       outstanding achievements in creating and applying
                       new engineering intellect and knowledge. An awards
                       ceremony will be held in December.


                       Stallman shares the prize of $800,000 to $900,000
                       (100 million yen) with Linus Torvalds and Ken
                       Sakamura, for "the origination and the advancement
                       of open development models for system software--
                       open architecture, free software and open source
                       software."


                # ⚓ [Old] GNU ☛ Richard_Stallman_Receives_Takeda_Award_-_GNU
                  Project_-_Free_Software_Foundation⠀⇛


                       Stallman shares the full 2001 Takeda award of 100
                       million yen with two other recipients. Ken Sakamura
                       receives the award for developing and promoting the
                       TRON architecture, a real-time operating system
                       specification for embedded systems. Linus Torvalds
                       is honored for his work on the operating system
                       kernel called Linux, which is normally used
                       together with GNU. The GNU/Linux system, which
                       combines GNU and Linux, has over 20 million users
                       worldwide.


                       The Takeda foundation will bestow this year's award
                       in a ceremony in Tokyo on December 4th. Stallman
                       will attend the event, and speak about his work in
                       the Free Software Movement.


                # ⚓ Vox ☛ Department_of_Education:_Why_Trump_is_firing_staff
                  and_dismantling_it⠀⇛


                       That’s where the third change comes in: the entry
                       of Elon Musk and DOGE [sic] to the conservative
                       coalition. They have modeled a new approach to
                       dismantling the agencies they dislike, something
                       that has never really been tried at this scale. And
                       now it’s the Department of Education’s turn in the
                       barrel.


          o § Hardware⠀➾


                # ⚓ RFERL ☛ Fiber-Optic_Drones_The_New_Must-Have_In_Ukraine
                  War⠀⇛


                       The cable transmits a high-quality image back to
                       the ground, right up to the moment of detonation.


                       "These drones can fly up to 60 kilometers per hour,
                       perform maneuvers, and within a range of 10
                       kilometers, the fiber does not break," says Serhiy
                       Beskrestnov of the Ukrainian military.


                # ⚓ Nico Cartron ☛ Trail_running_training_and_treadmill⠀⇛


                       As I explained above, I went for a simpler
                       treadmill with no fancy screen or connectivity,
                       with the idea to use external services such as
                       Kinomap for advanced activities.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ The Register UK ☛ AI_models_hallucinate,_and_doctors_are
                  okay_with_that⠀⇛


                       Their work, published in a preprint paper titled
                       "Medical Hallucinations in Foundation Models and
                       Their Impact on Healthcare" and in a supporting
                       GitHub repository, argues that harm mitigation
                       strategies need to be developed.


                # ⚓ India Times ☛ Apollo_Hospitals_bets_on_AI_to_tackle_staff
                  workload⠀⇛


                       Apollo, which has more than 10,000 beds across its
                       hospital network, making it one of the largest in
                       the country, set aside 3.5% of its digital spend on
                       AI over the past two years and plans to increase it
                       this year, Joint Managing Director Sangita Reddy
                       said, without providing further details.


                # ⚓ Michal Zelazny ☛ Socialized⠀⇛


                       We do not need another social media app.


                       What we do need are friends.


                       Nothing more. Nothing less.


                # ⚓ [Old] BBC ☛ Social_media_apps_are_'deliberately'_addictive
                  to_users⠀⇛


                       Social media companies are deliberately addicting
                       users to their products for financial gain, Silicon
                       Valley insiders have told the BBC's Panorama
                       programme.


                       "It's as if they're taking behavioural cocaine and
                       just sprinkling it all over your interface and
                       that's the thing that keeps you like coming back
                       and back and back", said former Mozilla and Jawbone
                       employee Aza Raskin.


                       "Behind every screen on your phone, there are
                       generally like literally a thousand engineers that
                       have worked on this thing to try to make it
                       maximally addicting" he added.


                # ⚓ [Old] CBS ☛ Facebook_is_addictive_as_cigarettes,_former
                  executive_claims⠀⇛


                       Kendall, CEO of time-management app Moment and
                       former director of monetization for Facebook, told
                       the hearing held by the House Committee on Energy
                       and Commerce: "Tobacco companies initially just
                       sought to make nicotine more potent. But eventually
                       that wasn't enough to grow the business as fast as
                       they wanted. And so they added sugar and menthol to
                       cigarettes so you could hold the smoke in your
                       lungs for longer periods, At Facebook, we added
                       status updates, photo tagging, and likes."


                # ⚓ [Old] Recovery Worldwide LLC ☛ Facebook_Addiction_-_Signs,
                  Symptoms,_And_Treatment⠀⇛


                       Facebook addiction is often included under the
                       umbrella term of social media addiction, but it is
                       important to note that different social media
                       platforms come with their own unique symptoms and
                       risks. When Facebook use becomes a replacement for
                       face-to-face connection, becomes compulsive, or
                       starts causing health issues like sleep
                       disturbances, it may be time to evaluate if there
                       is a social media addiction present.


                # ⚓ [Old] Time ☛ Will_2022_Be_the_Year_of_Reckoning_for
                  Addictive_Algorithms?⠀⇛


                       Often compared to Big Tobacco for the ways in which
                       their products are addictive and profitable but
                       ultimately unhealthy for users, social media’s
                       biggest players are facing growing calls for both
                       accountability and regulatory action. In order to
                       make money, these platforms’ algorithms effectively
                       function to keep users engaged and scrolling
                       through content, and by extension advertisements,
                       for as long as possible.


          o § Proprietary⠀➾


                # ⚓ Ubisoft_Silently_Negotiating_Acquisition_Bids_From
                  Microsoft,_Tencent_and_EA⠀⇛


                       Ubisoft is facing financial difficulties, game
                       performance issues, and large-scale layoffs. Titles
                       like Avatar: Frontiers of Pandora, Skull and Bones,
                       and XDefiant failed to meet expectations, leading
                       to stock losses and studio closures. Assassin's
                       Creed Shadows (delayed to 2025) is Ubisoft's hope
                       to turn its fortunes around. Ubisoft is also
                       considering strategic alternatives, including
                       mergers or acquisitions, to stabilize its future.


                       Ubisoft is "horribly mismanaged" and has not
                       disclosed supposed negotiations with Microsoft and
                       EA regarding possible acquisition bids. That's what
                       the Ubisoft minority shareholder AJ Investments
                       stated, suggesting in a memo that it will organize
                       a protest outside Ubisoft's Paris headquarters to
                       help raise its concerns and be heard.


                # ⚓ Nick Heer ☛ Rotten_in_Cupertino⠀⇛


                       Those are personal context, onscreen awareness, and
                       in-app actions. As Gruber astutely broke down the
                       existing Apple Intelligence features by their
                       degree of reality, I think it is worth picking
                       apart these three, even though Apple is lumping
                       them together under the “more personalized Siri”
                       banner.


                # ⚓ Bitdefender ☛ Chromecast_chaos_-_2nd_gen_devices_go_belly-
                  up_as_Google_struggles_to_fix_certificate_issue⠀⇛


                       Indeed, Google goes on to explain that if you
                       perform a factory reset while trying to
                       troubleshoot the issue with your Chromecast, you
                       may find yourself unable to re-setup your device.


                # ⚓ 9to5Google ☛ Google_rolling_out_Cast_fix_for_2nd-gen
                  Chromecast_and_Audio⠀⇛


                       Some interpreted this message to mean that Google
                       was deprecating those two models, with nobody
                       offering a true successor to the Chromecast Audio.
                       Meanwhile, the $99 Google TV Streamer might be a
                       cost-prohibitive upgrade, especially if you have
                       multiple 2nd-gen Chromecasts.


                       Google has since confirmed that this is a bug
                       rather than any attempt to end support. To date,
                       Google has only stopped updating the original
                       Chromecast. Even then, it can still be used to
                       Cast.


                # ⚓ PC World ☛ Google_issues_a_fix_for_Chromecast_‘untrusted’
                  bug⠀⇛


                       The Chromecast bug cropped up on Sunday, when the
                       owners of older Chromecast players and the
                       Chromecast Audio started getting errors that read,
                       “Untrusted device: [name] couldn’t be verified.
                       This could be caused by outdated device firmware.”
                       The devices then refused to play.


                # ⚓ The Verge ☛ Google_is_rolling_out_a_fix_for_broken
                  Chromecasts⠀⇛


                       Google is rolling out a fix for Chromecast device
                       issues that left many users with “untrusted device”
                       errors that disabled casting.


                       The issue, which appeared over the weekend, seemed
                       to widely affect Chromecast 2nd generation and
                       Chromecast Audio devices. Google has not said what
                       caused the errors, but a user on Reddit claimed it
                       could be because the certificate baked into the
                       devices expired.


                # ⚓ Howard Oakley ☛ USB_ports_on_Apple_Silicon_Macs:_Accessory
                  Security_and_liquid_detection⠀⇛


                       If there’s liquid in one of their USB-C receptacles
                       (ports) when a USB-C cable is connected to it, a
                       sensor should detect it and alert the user,
                       advising them to shut the Mac down, disconnect all
                       cables and leave it to dry. Full details are given
                       in this support note, dated 23 November 2024.


                # ⚓ Greece ☛ Rising_concerns_over_US_control_of_F-35_software⠀⇛


                       According to this theory, Washington has the power
                       to block the use of F-35s in operations it has not
                       authorized. This issue is of particular interest to
                       Greece, as Athens has placed an order for 20 F-35s,
                       with an option for an additional 20.


                       In recent days, the “kill switch” controversy has
                       triggered concerns in several countries – both
                       within and beyond the EU – that have invested
                       heavily in these 5th-generation fighter jets from
                       the US.


                # ⚓ India Times ☛ Musk-led_cuts_drive_US_consumer_protection
                  agency_to_ask_for_Amazon_trial_delay⠀⇛


                       The FTC accused Amazon in 2023 of using "deceptive
                       user-interface designs known as 'dark patterns' to
                       trick consumers into enrolling in automatically-
                       renewing Prime subscriptions."


                       Cohen said the case over what he called the world's
                       largest subscription program - which Amazon says
                       has more than 200 million subscribers worldwide -
                       involves claims worth at least $1 billion.


                # ⚓ The Record ☛ China_continues_cyberattacks_on_routers,_this
                  time_targeting_Juniper_Networks_devices⠀⇛


                       The researchers said the state-backed group —
                       dubbed UNC3886 — was behind a campaign last year to
                       deploy custom backdoors on the company’s Junos OS
                       routers. The group appears to be “focused mainly on
                       defense, technology, and telecommunication
                       organizations located in the US and Asia,” they
                       said.


                # ⚓ Matt Birchler ☛ I’m_not_used_to_seeing_this⠀⇛


                       This is a pretty scathing piece from Gruber on what
                       Apple’s done in the past year talking about Apple
                       Intelligence to both the press and customers.


                # ⚓ John Gruber ☛ Something_Is_Rotten_in_the_State_of
                  Cupertino⠀⇛


                       What Apple showed regarding the upcoming
                       “personalized Siri” at WWDC was not a demo. It was
                       a concept video. Concept videos are bullshit, and a
                       sign of a company in disarray, if not crisis. The
                       Apple that commissioned the futuristic “Knowledge
                       Navigator” concept video in 1987 was the Apple that
                       was on a course to near-bankruptcy a decade later.
                       Modern Apple — the post-NeXT-reunification Apple of
                       the last quarter century — does not publish concept
                       videos. They only demonstrate actual working
                       products and features.


                       Until WWDC last year, that is.


                # § Artificial Intelligence (AI)⠀➾


                      # ⚓ Android Police ☛ Google_responds_to_the_Trump
                        Administration’s_AI_Action_Plan⠀⇛


                             Google highlighted three key areas where it
                             says AI policy must focus: infrastructure,
                             government modernization, and pro-innovation
                             policies. This is in response to an executive
                             order signed by President Trump looking for
                             input into how to position America as the
                             strongest player in artificial intelligence.


                      # ⚓ Digital Camera World ☛ Is_generative_AI_ready_for
                        streaming?_Probably_not,_as_the_[Internet]_reacts_to
                        “horrible”_upscaling_of_classic_sitcoms_|_Digital
                        Camera_World⠀⇛


                             Fans of the shows, which were recently added
                             to Peacock (Roasanne) and Netflix (A
                             Different World), are taking to social media
                             to point out odd facial distortions and
                             nonsensical text that’s like the result of
                             using AI to upscale the old show, with many
                             users calling the footage “horrible.” For
                             creatives in the video industry, however, the
                             criticism highlights some of the shortcomings
                             that generative AI has yet to scale (pun
                             intended).


                      # ⚓ Tom's Hardware ☛ AI_tool_tells_user_to_learn_coding
                        instead_of_asking_it_generate_the_code⠀⇛


                             Upon trying to generate code for skid mark
                             fade effects within a racing game, Cursor AI
                             halted its code generation. Instead of
                             continuing, Cursor responded that further
                             coding should be done manually, highlighting
                             the importance of personal coding practice
                             for mastering logic and system understanding.


                      # ⚓ New Scientist ☛ Revealed:_how_the_UK_tech_secretary
                        Peter_Kyle_uses_ChatGPT_for_policy_advice⠀⇛


                             Now, New Scientist has obtained records of
                             Kyle’s ChatGPT use under the Freedom of
                             Information (FOI) Act, in what is believed to
                             be a world-first test of whether chatbot
                             interactions are subject to such laws.


                      # ⚓ Pivot to AI ☛ UK_science_secretary_Peter_Kyle_cribs
                        ChatGPT_for_advice⠀⇛


                             We wrote here in November and in Foreign
                             Policy in March how the United Kingdom’s all-
                             government AI push came out of Tony Blair
                             Institute reports that just faked all their
                             numbers using ChatGPT. These made-up numbers
                             were used to justify the whole UK AI push.


                # § Social Control Media⠀➾


                      # ⚓ Ethan Zuckerman ☛ Focus_on_the_player,_not_the_puck:
                        Finnish_approaches_to_combatting_electoral_interference
                        -_Ethan_Zuckerman⠀⇛


                             For Robert Fife, Ottawa bureau chief for the
                             Globe and Mail, disinformation operations
                             have forced reporters to look around the
                             world and deeply into local communities.
                             Disinfo often targets Chinese speakers,
                             Punjabi speakers and other groups who often
                             aren’t reading the Globe and Mail, but
                             WeChat, Indian-language media and other
                             sources of information that routinely
                             distribute state sponsored disinformation.
                             The most powerful weapon to counter
                             disinformation is transparency, Fife argues,
                             but to be transparent and effective, Canadian
                             reporters have to better represent what
                             Canada looks like – it speaks not just
                             English and French, but Chinese and Punjabi
                             as well.


                      # ⚓ Sara Jakša ☛ IndieWeb_Secret_Santa_Gift_for_Antonio:
                        How_Small_Online_Communities_can_be_a_Better_Place_than
                        Large_Social_Network_Websites?⠀⇛


                             It was also the time when Snowden revealed
                             the extent the US, the place where the
                             majority of the largest social media were
                             located, was collecting the data on people.


                             Meaning, that if I was using the large social
                             media afterwards, I was literally made to do
                             it, and run away as quickly as I could. I
                             left Twitter in 2014, LinkedIn in 2016 and
                             Facebook in 2019 (and I still hate that I
                             needed to create an account there for the
                             study purposes) and Tumblr around that time
                             as well. I was never on TikTok, I was never
                             on Instagram, on Fediverse, on BlueSky, on
                             Google+, never had an account on Reddit.


                             But as the the weeks progressed, the more I
                             realised the people talk about it a lot.


                      # ⚓ Crooked Timber ☛ Unbundling_and_Abundance⠀⇛


                             But mostly today I want to talk about the
                             graduate seminar I just finished teaching,
                             about Media, Social Media and Politics. The
                             syllabus is here. To summarize what we spent
                             the most time talking about in class, I’ll
                             quote a sentence from Green et al (2025):
                             “The online information ecosystem in the
                             early twenty-first century is characterized
                             by unbundling and abundance.”


                             I taught a similar class four years ago, and
                             let me tell you, the academic literature has
                             not changed nearly as fast as the underlying
                             pheonomena have. The lag is getting worse.
                             But even if it’s slow, scientific progress
                             has been made. In my view, the most important
                             results come not from fancy causal inference
                             but from large-scale quantitative
                             description; this should not be surprising
                             coming from the editor of the Journal of
                             Quantiative Description: Digital Media.


                      # ⚓ Hindustan Times ☛ Two_journalists_arrested_for
                        posting_‘derogatory’_video_against_Telangana_CM⠀⇛


                             P Viswaprasad, the additional commissioner of
                             police (crimes and SIT), said, “The alleged
                             video was shot at BRS headquarters in Banjara
                             Hills in February and released on March 10,
                             just ahead of the budget session, as per an
                             orchestrated plan to insult, defame, and
                             abuse the CM. The content of the video is
                             vulgar, derogatory, insulting, and abusive,
                             crossing all levels of decency. The accused
                             have been doing this repeatedly and posting
                             on social media for fame and views. We have
                             evidence that they have received monetary
                             incentives from the BRS. We will investigate
                             every aspect.”


          o § Security⠀➾


                # ⚓ Reuters ☛ White_House_instructs_agencies_to_avoid_firing
                  cybersecurity_staff,_email_says⠀⇛


                       The White House is urging federal agencies to
                       refrain from laying off their cybersecurity teams,
                       as they scramble to comply with a Thursday deadline
                       to submit mass layoff plans to slash their budgets,
                       according to an email seen by Reuters.


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ New York Times ☛ Meta_Tries_to_Stop_Sarah_Wynn-
                        Williams_From_Further_Selling_Scathing_Memoir⠀⇛


                             Sarah Wynn-Williams last week released
                             “Careless People: A Cautionary Tale of Power,
                             Greed, and Lost Idealism,” a book that
                             describes a series of incendiary allegations
                             of sexual harassment and other inappropriate
                             behavior by senior executives during her
                             tenure at the company. Meta pursued
                             arbitration, arguing that the book is
                             prohibited under a nondisparagement contract
                             she signed as a global affairs employee.


                             During an emergency hearing on Wednesday, the
                             arbitrator, Nicholas Gowen, found that Meta
                             had provided enough grounds that Ms. Wynn-
                             Williams had potentially violated her
                             contract, according to a legal filing posted
                             by Meta. The two parties will now begin
                             private arbitration.


                      # ⚓ Threat Source ☛ Abusing_with_style:_Leveraging
                        cascading_style_sheets_for_evasion_and_tracking⠀⇛


                             Features of HTML and CSS can be used together
                             to include comments and irrelevant content
                             that are not visible to the victim (or
                             recipient) when the email is rendered in an
                             email client but can impact the efficacy of
                             parsers and detection engines. We discussed a
                             few examples in our recent blog post, and we
                             will share more throughout the rest of this
                             section. We will not cover cases that are
                             well-known to the security community, such as
                             including zero-sized fonts.


                             Threat actors can use the text_indent
                             property of CSS to conceal content in the
                             email’s body. Below is an example of a
                             phishing email that contains text in
                             different places, but the text is not visible
                             when rendered in an email client.


                # § Privacy/Surveillance⠀➾


                      # ⚓ US Senate ☛ Letter_from_US_Congress_to_UK
                        Investigatory_Powers_Tribunal [PDF]⠀⇛


                             The U.K.’s attempted gag has already
                             restricted U.S. companies from engaging in
                             speech that is constitutionally protected
                             under U.S. law and necessary for ongoing
                             Congressional oversight. Apple has informed
                             Congress that had it received a technical
                             capabilities notice, it would be barred by
                             U.K. law from telling Congress whether or not
                             it received such a notice from the U.K., as
                             the press has reported. Google also recently
                             told Senator Wyden’s office that, if it had
                             received a technical capabilities notice, it
                             would be prohibited from disclosing that
                             fact. The U.K. embassy has also not responded
                             to a recent request from Senator Wyden’s
                             office regarding potential demands from the
                             U.K. to other U.S. companies.


                             The security of U.S. technology companies’
                             products against surveillance by foreign
                             governments is an important topic for ongoing
                             Congressional oversight because of several
                             recent hacks of the communications of senior
                             U.S. government officials. This includes:
                             [...]


                      # ⚓ US Senate ☛ Bipartisan_Members_of_Congress_to_UK_Spy
                        Court:_UK_Gag_Orders_for_Surveillance_Backdoors
                        Threaten_Americans’_Security_and_Privacy,_Impede
                        Congressional_Oversight⠀⇛


                             “Given the significant technical complexity
                             of this issue, as well as the important
                             national security harms that will result from
                             weakening cybersecurity defenses, it is
                             imperative that the U.K.’s technical demands
                             of Apple— and of any other U.S. companies —
                             be subjected to robust, public analysis and
                             debate by cybersecurity experts,” the members
                             wrote. “Secret court hearings featuring
                             intelligence agencies and a handful of
                             individuals approved by them do not enable
                             robust challenges on highly technical
                             matters.”


                      # ⚓ NL Times ☛ Police_databases_need_stricter
                        supervision:_Amnesty_International⠀⇛


                             Amnesty International wants the governments
                             regulators to sharpen their supervision on
                             the police databanks. Civilians can submit a
                             complaint to the police against the
                             collection and storage of their data, but
                             these are “not effective legal means,” the
                             human rights organization said.


                             The organization said in a statement that
                             they have supported 31 demonstrators in their
                             case against the police in the last years. it
                             is reported that many of the complaints are
                             not even dealt with by the police.


                             Amnesty pointed out that the police store the
                             identity details of demonstrators, look at
                             what people are putting on social media, and
                             infiltrate group chats. The supervision of
                             this is insufficient, the organization said.


          o § Defence/Aggression⠀➾


                # ⚓ Techdirt ☛ It_Is_Long_Past_Time_For_Democrats_To_Start
                  Pounding_The_Impeachment_Drum⠀⇛


                       Because the question is not whether impeachment can
                       yet succeed (although in a sane Congress there
                       would be no question). The question is whether and
                       when Democrats are going to collectively put their
                       foot down and finally say no to the lawless,
                       unconstitutional sledgehammer Trump and his
                       associates have been taking to our federal
                       government and constitutional order. The question
                       is how much are they going to allow to be
                       destroyed—how many lives are they going to allow to
                       be destroyed—before they finally say enough is
                       enough. How much scientific discovery will be
                       squandered, disease spread, expertise ignored,
                       government services gutted, agencies dismantled,
                       public servants fired, infrastructure vandalized,
                       contracts breached, resources wasted, bigotry
                       celebrated, voices censored, persecutions pursued,
                       civil rights violated, human beings disappeared,
                       rule of law upended, national security compromised,
                       military readiness forfeited, veterans betrayed,
                       allies attacked, alliances trashed, wars
                       threatened, businesses bankrupted, taxes
                       uncollected, corruption enabled, and economies
                       crashed before the national Democratic party shows
                       up to be the party against all these things.


                # ⚓ Ethan Zuckerman ☛ Freedom_Interrupted:_Electoral
                  Interference_-_Ethan_Zuckerman⠀⇛


                       That’s not to say we’re not seeing old-fashioned
                       election interference. Marcus Kolga of DIsinfowatch
                       offers a chilling overview of Russian interference
                       in Moldovan and Romanian elections. Russia directly
                       paid hundreds of thousands of Moldovans to vote
                       against a pro-EU candidate, and ran massive pro-
                       Russian campaigns on Telegram. These were
                       unsuccessful and the pro-EU candidate was re-
                       elected.


                       But Russian disinfo did manage to spoil the first
                       round of Romanian elections, Kolga tells us. Calvin
                       Georgescu, an obscure fringe candidate, rose in
                       prominence during the first round of the elections
                       through a suspiciously successful TikTok campaign.
                       There’s lots of evidence that Georgescu, who
                       advocates ties between Romania and Russia, perhaps
                       most compellingly the fact that investigators found
                       $10 million dollars and a ticket to Moscow buried
                       under his house. While Romania threw out results
                       from the first round of the election, JD Vance
                       spoke in favor of Georgescu, complaining that
                       Romania was unfairly overturning results.


                # ⚓ The Washington Spectator ☛ Senator_Claude_Malhuret_on_the
                  End_of_American_Democracy_|_Washington_Spectator⠀⇛


                       Senator Claude Malhuret on the End of American
                       Democracy, speaking in the French Senate, Tuesday,
                       March 4, 2025.


                # ⚓ Nebraska Examiner ☛ Immigrants_help_push_Omaha_metro_past
                  1M_population_mark_as_more_Nebraska_counties_grow⠀⇛


                       Also revealed in population estimates released
                       Thursday are county-level growth patterns that
                       showed 48 of Nebraska’s 93 counties gaining
                       population and two remaining the same in the latest
                       year tracked, mid-2023 to mid-2024.


                # ⚓ Alabama Reflector ☛ Immigration_buoyed_population_in_large
                  counties,_agricultural_Midwest⠀⇛


                       The surge of newcomers to the United States was the
                       primary driver in population changes for 38% of
                       counties nationwide and for most counties in states
                       across a large swath of the Midwest: Illinois,
                       Iowa, Kansas, Nebraska and North Dakota.
                       Immigration also was the largest growth factor in
                       most counties in Louisiana and Massachusetts.


                # ⚓ US News And World Report ☛ Pentagon_Asked_for_Military
                  Options_to_Access_Panama_Canal,_Officials_Say⠀⇛


                       Any move by a foreign power to take the canal by
                       force would almost certainly violate international
                       law.


                       The U.S. and Panama are treaty-bound to defend the
                       canal against any threat to its neutrality and are
                       permitted to take unilateral action to do so.


                # ⚓ Greece ☛ Hooked_on_TikTok?_Tool_developed_by_Athens
                  University_helps_you_find_out⠀⇛


                       A research team from the University of Athens has
                       developed the world’s first tool specifically
                       designed to measure addiction to TikTok.


                       The TikTok Addiction Scale (TTAS) consists of 15
                       questions assessing six dimensions of problematic
                       use: preoccupation, mood changes, tolerance,
                       withdrawal, conflict and relapse. Respondents rate
                       statements on a scale from “very rarely” to “very
                       often.” A score above 3.2 suggests excessive use,
                       prompting the need for a professional evaluation.


                # ⚓ The Local SE ☛ 'I_would_love_to_see_Sweden_set_age
                  regulations_on_smartphones'⠀⇛


                       With young children of her own, Katie Dodd Syk kept
                       returning to these questions and soon found she had
                       an ally in her neighbour Roksana Schnittger.
                       Noticing that their conversations increasingly
                       revolved around this issue, the pair decided to
                       take action and set about forming Smartphone Free
                       Childhood Sverige, the Swedish chapter of a global
                       grassroots organisation.


                # ⚓ NL Times ☛ Instagram’s_‘teen_accounts’_provide_false_sense
                  of_security,_consumer_group_warns⠀⇛


                       Instagram’s newly introduced “Teen Accounts”
                       feature is meant to provide better online
                       protection for young users, but a new study by the
                       Dutch Consumers’ Association (Consumentenbond)
                       finds the safeguards largely ineffective. The
                       organization warns that Meta, Instagram’s parent
                       company, is misleading consumers with promises of
                       automatic protections that do not adequately
                       address the platform’s risks.


                       Instagram has implemented several default settings
                       for accounts belonging to users between 13 and 17
                       years old. These accounts are automatically set to
                       private, preventing strangers from viewing their
                       posts. Additionally, teenagers can only receive
                       private messages from users they already follow.
                       While these measures reportedly offer minor
                       improvements, the study finds that they fail to
                       tackle the platform’s fundamental issues, including
                       addictive algorithms, harmful content that may
                       damage self-esteem, and extensive data collection
                       on teenage users.


                # ⚓ The Local SE ☛ US_imposes_sanctions_on_Sweden's_Foxtrot
                  Network_and_its_leader⠀⇛


                       Describing Foxtrot as one of Sweden's "most
                       notorious criminal gangs [sic]," the US Treasury
                       and State Departments also placed sanctions on its
                       leader Rawa Majid, with both agencies saying in
                       statements that he had "specifically cooperated
                       with the Iranian Ministry of Intelligence and
                       Security."


                       "Iran's brazen use of transnational criminal
                       organizations and narcotics traffickers underscores
                       the regime's attempts to achieve its aims through
                       any means, with no regard for the cost to
                       communities across Europe," Treasury Secretary
                       Scott Bessent said.


                # ⚓ The Strategist ☛ More_than_ever,_airpower_will_depend_on
                  sharing_data._Watch_Sweden⠀⇛


                       Such teaming means that more-numerous, less-costly,
                       even expendable uncrewed vehicles can bring more
                       weapons to the fight and force the adversary to
                       deal with more targets. More-expensive and
                       survivable crewed vehicles, meanwhile, can stand
                       back, offering human supervision of the entire
                       formation.


                       But none of that will work without maintaining
                       real-time common operational pictures. Everyone and
                       everything in a team needs to know what the others
                       know—about each other and about the enemy.


                # ⚓ International Business Times ☛ MPs_Compare_Photos_of_Muslim
                  Women_Without_Hijabs_to_Child_Abuse_Images_and_Call_for
                  Criminalisation⠀⇛


                       Members of Parliament have sparked controversy with
                       a new proposal recommending that possessing
                       photographs of Muslim women without their
                       hijabs—taken without consent—should legally qualify
                       as possessing 'non-consensual intimate images'. If
                       adopted, this offence could become law by the end
                       of 2025, and be treated with the same severity as
                       the possession of child sexual abuse material. This
                       unprecedented move has ignited debate, as it would
                       provide unique protections to Muslims under British
                       law, a privilege not currently extended to other
                       religious groups.


                # ⚓ The Record ☛ At_Ukraine’s_major_cyber_conference,_Europe
                  takes_center_stage_over_US⠀⇛


                       For 2025, however, the situation was different. The
                       U.S. loomed large as an unspoken presence, but no
                       Trump administration officials attended the
                       conference amid geopolitical tensions between Kyiv
                       and Washington, which hold different visions of how
                       to end the war with Russia.


                       Unlike last year, when U.S. representatives openly
                       discussed ongoing cooperation and continued donor
                       support for Ukraine, the conversations this week
                       largely steered clear of questions regarding future
                       collaboration between the countries.


                # ⚓ New Eastern Europe ☛ The_digital_Trojan_Horse_in_Romania’s
                  elections⠀⇛


                       TikTok played a crucial role in Georgescu’s rise to
                       fame, as the platform saw a sharp increase in
                       engagement with his content in the weeks leading up
                       to the election. According to the data below, the
                       hashtag #călingeorgescu surged during this period.
                       This spike illustrates how TikTok’s algorithm can
                       effectively disseminate political messages and
                       influence public opinion on a large scale.


                # ⚓ C4ISRNET ☛ Space_Force_teaming_with_Air_Force_on_Joint
                  Simulation_Environment⠀⇛


                       “The Space Force needs to provide space effects to
                       the joint warfighter to ensure the joint warfighter
                       can validate in their training events and their
                       exercises, whether or not they’re going to be
                       effective,” Klopstein said March 5 at the Air
                       Warfare Symposium in Aurora, Colorado. “The Space
                       Force also needs a high-fidelity environment to be
                       able to validate not just our system performance in
                       the threat environment that we anticipate, but also
                       our tactics, and validate our tactics.”


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Wired ☛ Researchers_Propose_a_Better_Way_to_Report
                  Dangerous_AI_Flaws⠀⇛


                       In a proposal released today, more than 30
                       prominent AI researchers, including some who found
                       the GPT-3.5 flaw, say that many other
                       vulnerabilities affecting popular models are
                       reported in problematic ways. They suggest a new
                       scheme supported by AI companies that gives
                       outsiders permission to probe their models and a
                       way to disclose flaws publicly.


                # ⚓ The Record ☛ Calls_grow_for_UK_to_move_secret_Apple
                  encryption_court_hearing_to_public_session⠀⇛


                       Politicians and civil society groups in the United
                       Kingdom are calling for a secret court hearing
                       expected on Friday about the British government’s
                       encryption demands on Apple to be held in public.


                       It follows warnings from experts, including from
                       Britain’s own intelligence community, that the
                       government’s attempts to access encrypted messaging
                       platforms should be more transparent. Academics
                       described the Home Office's ongoing refusal to
                       either confirm or deny the legal demand as
                       unsustainable and unjustifiable.


                # ⚓ Jacobin Magazine ☛ Supreme_Court_Lobbyists_Don’t_Want_to
                  Reveal_Their_Funders⠀⇛


                       A government committee in charge of federal
                       judiciary rules wants to make Supreme Court
                       lobbyists disclose who is funding them. Some of the
                       most powerful corporate and conservative forces in
                       DC are trying to keep that information secret.


                # ⚓ Semafor Inc ☛ Newsmax_deletes_interview_criticizing_FCC⠀⇛


                       Within hours, the piece had been removed from the
                       news organization’s website without explanation.
                       Network chief Chris Ruddy sought its removal, a
                       person familiar with the decision-making process
                       said. In an email to Semafor, a Newsmax
                       spokesperson said that removing the article was an
                       editorial decision, but did not elaborate on why
                       the article was taken down.


                # ⚓ Federal News Network ☛ Gov_tech_layoffs_could_hamper_SHARE
                  IT_Act_software_mandates⠀⇛


                       Experts say recent cuts at the General Services
                       Administration’s Technology Transformation Services
                       and elsewhere could hinder implementation of the
                       “Source Code Harmonization and Reuse In Information
                       Technology Act,” or the SHARE IT Act.


                       Signed into law late last year, the SHARE IT Act
                       requires agencies to share their custom-developed
                       software code publicly or on a private listing that
                       can be accessed by other agencies.


          o § Environment⠀➾


                # ⚓ Truthdig ☛ Trump_Administration_Launches_All-Out_Assault_on
                  Environmental_Protection⠀⇛


                       Zeldin’s announcements mark the start of a
                       dismantling process that could take months or even
                       years. To undo regulations that go back decades,
                       EPA staff would have to write proposals, gather
                       public comments and possibly hold hearings and
                       create a scientific and legal record justifying any
                       decision. The latter will be needed to defend
                       against inevitable lawsuits by environmentalists
                       and states. All of this will have to be carried out
                       by an agency that is severely hobbled by firings
                       and plans to slash its funding to the lowest levels
                       in its 55-year history.


                # ⚓ Omicron Limited ☛ In_LA,_cooking_emissions_rival_fossil
                  fuels_as_ozone_pollution_source⠀⇛


                       According to new research from NOAA, the potent and
                       often pungent volatile organic compounds (VOCs)
                       given off from cooking food are now responsible for
                       over a quarter of the ozone production from VOCs
                       generated by human activity in the LA basin. This
                       is roughly equal to the amount of ozone produced by
                       VOCs from on-road and off-road motor vehicles.


                       The new study, published in Atmospheric Chemistry &
                       Physics, takes a more complete look at the mix of
                       VOCs in urban air by adding chemical compounds
                       specific to cooking emissions to an air quality
                       model set up to replicate the conditions in and
                       around Los Angeles.


                # § Energy/Transportation⠀➾


                      # ⚓ GreyCoder ☛ Bitcoin's_Growing_Role_in_Government_and
                        Business⠀⇛


                             Some companies have made notable Bitcoin
                             purchases recently. Metaplanet added 162
                             Bitcoin to its holdings, bringing its total
                             to 3,050 BTC. Rumble, another company,
                             announced it holds $17.1 million in Bitcoin.
                             It sees it as a way to guard against
                             inflation. They purchased 188 BTC for around
                             $91,000 each. This is part of their $20
                             million Bitcoin strategy they announced
                             earlier. The company, backed by Tether, may
                             buy more based on market conditions and cash
                             needs.


                      # ⚓ Wired ☛ What’s_Lost_When_the_Human_Drivers_Are
                        Gone?⠀⇛


                             If you’ve spent time in San Francisco or
                             Phoenix in the past couple years, chances are
                             you’ve probably seen a self-driving car
                             making its way around. This week, we’re
                             joined by WIRED’s Aarian Marshall to talk
                             about the race to flood our streets with
                             self-driving cars. We’ll get into safety
                             regulations, the pros and cons of robotaxis,
                             and we imagine a future where driverless cars
                             become mainstream.


                      # ⚓ The Register UK ☛ Microsoft_says_natural_gas_needed
                        to_keep_up_with_AI⠀⇛


                             The rapid expansion of bit barns from
                             Microsoft and others has, however, created
                             problems in accessing enough energy to power
                             them all, coupled with warnings that their
                             energy requirements could expand 160 percent
                             by 2027, exceeding the ability of utility
                             providers to keep pace.


                             At the CERAWeek Global energy conference in
                             Houston this week, Microsoft indicated there
                             was plenty of potential for wind and solar
                             expansion in the US, but conceded it is
                             "open" to deploying natural gas with carbon
                             capture technology to meet its energy
                             requirements.


                      # ⚓ Public Citizen ☛ Senate_Banking_Committee:_Vote_NO_on
                        [Cryptocurrency]_Stablecoin_Bill_(GENIUS_Act)⠀⇛


                             What inescapably explains this Committee’s
                             and Congress’ unreasonable attention to
                             [cryptocurrency] is the flood of political
                             spending by a handful of [cryptocurrency]
                             financiers in the 2024 election cycle, and
                             the threat of more in the next cycle.
                             Lawmakers must not allow political spending
                             by an inherently harmful sector to shape
                             important policy.


                             What follows is a description of stablecoins,
                             an outline for responsible legislation, and a
                             critique of the GENIUS Act.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ A_Gulf_of_Misunderstanding⠀⇛


                      # ⚓ Nature ☛ Ecological_drivers_of_ultraviolet_colour
                        evolution_in_snakes⠀⇛


                             Ultraviolet (UV) colour patterns invisible to
                             humans are widespread in nature. However,
                             research bias favouring species with
                             conspicuous colours under sexual selection
                             can limit our assessment of other ecological
                             drivers of UV colour, like interactions
                             between predators and prey. Here we
                             demonstrate widespread UV colouration across
                             Western Hemisphere snakes and find stronger
                             support for a predator defence function than
                             for reproduction. We find that UV colouration
                             has evolved repeatedly in species with
                             ecologies most sensitive to bird predation,
                             with no sexual dichromatism at any life
                             stage. By modelling visual systems of
                             potential predators, we find that snake
                             conspicuousness correlates with UV
                             colouration and predator cone number,
                             providing a plausible mechanism for
                             selection. Our results suggest that UV
                             reflectance should not be assumed absent in
                             “cryptically coloured” animals, as signalling
                             beyond human visual capacities may be a key
                             outcome of species interactions in many taxa
                             for which UV colour is likely underreported.


                      # ⚓ Omicron Limited ☛ Snakes'_secret_language_of
                        ultraviolet_color:_A_hidden_world_of_predator_evasion
                        and_camouflage⠀⇛


                             The researchers discovered that UV color is
                             found widely across the snake tree of life,
                             and that it is frequently used for predator
                             avoidance, says study co-author Hayley
                             Crowell, a doctoral student in the U-
                             M Department of Ecology and Evolutionary
                             Biology.


                      # ⚓ Omicron Limited ☛ Study_says_endangered_Asian
                        elephant_population_in_Cambodia_is_more_robust_than
                        previously_thought⠀⇛


                             "With sufficient suitable habitat remaining
                             in the region, the population has the
                             potential to grow if properly protected," the
                             report concludes.


                      # ⚓ US News And World Report ☛ Study_Says_Endangered
                        Asian_Elephant_Population_in_Cambodia_Is_More_Robust
                        Than_Previously_Thought⠀⇛


                             From their work they estimated that there are
                             51 elephants in the Prey Lang, Preah Roka,
                             and Chhaeb Wildlife Sanctuaries, with greater
                             genetic diversity — a “critical factor for
                             long-term viability,” the researchers said —
                             than in two other areas of the country in
                             which they live.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The New Stack ☛ Intel's_New_CEO_Will_Make_Changes_to
                  Reshape_Software_Strategy⠀⇛


                       The new CEO has experience with software as the
                       former CEO of Cadence Systems, but a different kind
                       of software — development tools to design chips. He
                       has limited experience in software application
                       development and open source.


                # ⚓ Los Angeles Times ☛ Water_officials_knew_Trump's_demand_to
                  open_dams_was_ill-advised⠀⇛


                       “To intentionally create a situation where that
                       could have been the outcome, it’s depraved and
                       mind-blowing,” Willis said.


                       Indeed, many California water officials and experts
                       agreed that the plan had the potential to be
                       ruinous. Local water managers pushed back when they
                       learned of the plan by corps officials to release
                       water from the dams, telling the agency that the
                       water wasn’t needed this time of year and that the
                       abrupt surge of water could do damage.


                # ⚓ Reuters ☛ Exclusive:_TSMC_pitched_Intel_foundry_JV_to
                  Nvidia,_AMD_and_Broadcom,_sources_say⠀⇛


                       Under the proposal, the Taiwanese chipmaking giant
                       would run the operations of Intel's foundry
                       division, which makes chips adapted for the needs
                       of customers, but it would not own more than 50%,
                       the sources said. Qualcomm (QCOM.O), opens new tab
                       has also been pitched by TSMC, according to one of
                       the sources and a separate source.


                # ⚓ Silicon Angle ☛ Report:_TSMC_could_launch_joint_venture
                  with_partners_to_run_Intel’s_fabs⠀⇛


                       The company is said to have pitched the idea to
                       Nvidia Corp., Advanced Micro Devices Inc., Broadcom
                       Inc. and Qualcomm Inc. Under the plan, the
                       chipmakers would take stakes in a joint venture
                       tasked with operating Intel’s fabs. TSMC, which is
                       reportedly eyeing a stake of up to 50%, would be
                       responsible for the day-to-day management of the
                       plants.


                # ⚓ Linuxiac ☛ Rust_Takes_Root_in_Ubuntu_25.10⠀⇛


                       However, recent efforts like uutils’ re-
                       implementation of these tools in Rust signal a
                       major transformation on the horizon. In light of
                       this, starting with Ubuntu 25.10 and continuing
                       into Ubuntu 26.04 LTS, if everything goes according
                       to plan, the distro is set to adopt some of these
                       Rust-based tools as the new default.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ VOA News ☛ Foreign_bloggers_help_China_spread
                        propaganda,_analysis_finds⠀⇛


                             "It is a long-standing tradition of the
                             Chinese Communist Party to use foreigners to
                             voice its propaganda for added credibility,"
                             said Mareike Ohlberg, a senior fellow at the
                             German Marshall Fund.


                             Foreign influencers cooperate with the
                             Chinese government, the media and third
                             parties to create and boost content that
                             supports government narratives, Ohlberg said.
                             One of the most common topics that foreign
                             influencers focus on is whitewashing human
                             rights abuses in Xinjiang. The U.N. Human
                             Rights Office and groups like Amnesty
                             International estimate that more than 1
                             million people – mostly Uyghurs – have been
                             confined in internment camps in Xinjiang.


                      # ⚓ Ethan Zuckerman ☛ Taylor_Owen:_Canadians_now_see_the
                        US_as_the_most_serious_disinfo_threat⠀⇛


                             Owen warns that Silicon Valley companies have
                             changed their status. It’s not just
                             performative alignment with Trump: major
                             platforms are ending the ten year era of
                             “trust and safety”, turning moderation over
                             to crowdsourcing. These platforms are moving
                             from minimal transparency to complete
                             opacity. These US government as well as US
                             platforms are participating in the
                             persecution of disinformation researchers.
                             And we’re no longer worried about ideological
                             segregation within platforms so much as we
                             are worried about platforms becoming tightly
                             aligned with political points of view.


                      # ⚓ Indian Express ☛ Newsmax_to_pay_$40_million_to_settle
                        defamation_suit_over_2020_election_claims⠀⇛


                             Newsmax Media has agreed to pay $40 million
                             to settle a defamation lawsuit brought by
                             voting technology company Smartmatic, which
                             accused the broadcaster of spreading false
                             claims that it helped rig the 2020 US
                             presidential election in favour of Joe Biden
                             over Donald Trump, according to a court
                             filing, reported by Reuters.


                      # ⚓ CNN ☛ Newsmax_faces_‘bet-your-company’_defamation
                        trial_over_2020_election_lies⠀⇛


                             The Newsmax case revolves around the same
                             false claims, championed by former President
                             Donald Trump and his Republican allies, that
                             the 2020 election was rigged by Smartmatic
                             software and others. The Florida-based
                             company sued Newsmax and other right-wing
                             outlets and figures in 2021, alleging that
                             its reputation was destroyed by the lies.


                      # ⚓ The Independent UK ☛ Newsmax_reached_a_‘confidential’
                        settlement_with_Smartmatic_last_year._We_now_know_how
                        much_the_MAGA_outlet_paid⠀⇛


                             In a regulatory filing released this week by
                             Newsmax as part of its planned initial public
                             offering, the channel revealed that it agreed
                             to pay Smartmatic $40 million as well as
                             issue a “five-year cash exercise warrant” for
                             the voting machine firm to purchase 2,000
                             shares of preferred stock in the conservative
                             cable channel.


                             The investment prospectus also noted that
                             there was an inherent risk to investors due
                             to the ongoing defamation case brought by
                             Dominion Voting Systems, which is set to go
                             to trial next month.


                      # ⚓ [Old] The Guardian UK ☛ Newsmax_and_Smartmatic_settle
                        2020_US_election_defamation_lawsuit⠀⇛


                             After the 2020 election, Newsmax aired
                             several false claims about the company, whose
                             voting machines were only used in Los Angeles
                             county in 2020. The network repeatedly aired
                             false claims from Trump allies that the
                             software was widely used across the country
                             and that it had been hacked to change votes.


          o § Censorship/Free Speech⠀➾


                # ⚓ Techdirt ☛ Meta,_Apparently,_Really_Wants_Everyone_To_Read
                  This_Book_(By_Trying_To_Ban_It)⠀⇛


                       By going to arbitration and trying to block
                       publication, then, suddenly, it all gets that much
                       more attention.


                       The arbitrator’s ruling reads like a corporate
                       revenge fantasy rather than enforceable legal
                       reality. Yes, Wynn-Williams probably should have
                       engaged with the arbitration process rather than
                       just appearing on podcasts to discuss Meta’s
                       attempts to silence her. But the arbitrator’s order
                       is nonsensical: telling her not to make disparaging
                       remarks about Meta, not to promote a book that’s
                       already on sale, and to stop distribution “to the
                       extent within [her] control” (which is effectively
                       zero since Macmillan controls distribution and
                       isn’t bound by the arbitration).


                       This fits a pattern for Meta. For all of
                       Zuckerberg’s grand pronouncements about free speech
                       and open dialogue, the company seems pretty quick
                       to freak out when strong criticism comes along.


                # ⚓ Futurism ☛ Facebook_Is_Desperately_Trying_to_Keep_You_From
                  Learning_What's_in_This_Book⠀⇛


                       The memoir, "Careless People: A Cautionary Tale of
                       Power, Greed, and Lost Idealism," released this
                       week, rips into Meta's toxic work culture and
                       provides a behind-the-scenes look at how the
                       company handled some of its worst scandals. Among
                       her cavalcade of damning allegations, Wynn-Williams
                       also reveals the repeated sexual harassment she
                       faced from senior Meta executives.


                # ⚓ Techdirt ☛ My_New_Podcast_‘Otherwise_Objectionable’
                  Explains_Why_Everyone’s_Wrong_About_Section_230⠀⇛


                       The episode explores how gutting Section 230 would
                       reshape the [Internet] in ways most of its critics
                       haven’t considered. Small websites and communities
                       would face an impossible choice: either become
                       purely broadcast platforms with no user
                       interaction, or be forced to host truly toxic
                       content with no ability to moderate it. The result
                       wouldn’t just be fewer places to comment — it would
                       fundamentally break the [Internet]’s ability to
                       foster genuine communities and enable collaborative
                       knowledge-sharing. The only survivors would be the
                       largest tech companies with enough lawyers and
                       content moderators to manage the risk.


                       Neither would be a great outcome.


                # ⚓ RFA ☛ Hong_Kong_media_urged_to_back_up_Facebook_protest
                  videos_–_Radio_Free_Asia⠀⇛


                       There are concerns that much of the online footage
                       of those protests, most of which is banned in the
                       city amid an ongoing crackdown on dissent, will no
                       longer be available to the general public.


                       That will make it easier for the authorities to
                       impose their own narrative on events in the city’s
                       recent history.


                       Facebook notified users last month that it will be
                       deleting archived live video streams from June 5,
                       while newly streamed live video will be deleted
                       after 30 days from Feb. 19, 2025.


                # ⚓ Organization for Transformative Works ☛ OTW_Signal,
                  February_2025_|_Organization_for_Transformative_Works⠀⇛


                       Chinese censors have arrested dozens of writers in
                       the national crackdown on Taiwan-based online
                       erotic fiction website Haitang (海棠) Literature. A
                       translated article from Radio Free Asia (RFA)
                       discusses the way Chinese [Internet] censors ban
                       explicit adult writing to “anything below the neck”
                       and even vaguely euphemistic phrases such as love
                       and nature, which may mean sex when combined in a
                       certain way. Similarly, Chinese online fiction
                       platform Jinjiang Literature City (晋江文学城) was also
                       summoned by consumer protection officials, but
                       refused to turn up, accusing authorities of
                       “fishing”, according to the Lianhe Zaobao (联合早报).


                # ⚓ VOA News ☛ Zimbabwe_journalist_still_in_custody_after_case
                  adjourned⠀⇛


                       A High Court judge in Zimbabwe on Wednesday
                       adjourned the case of a journalist arrested over
                       his interviews with a war veteran-turned-politician
                       who criticized the country's president.


                # ⚓ New Yorker ☛ The_Silencing_of_Russian_Art⠀⇛


                       Bi-2’s members soon learned that they had landed on
                       a list of undesirable artists, which had circulated
                       among regional administrations and cultural
                       departments. “Officially these lists don’t exist,”
                       a concert promoter, who was forced to remove Bi-
                       2 and a half dozen other bands from the lineup of a
                       rock festival that summer, said. “They don’t have
                       any legalistic basis.” Rather, he went on, they
                       functioned as “indications of undesirability.” A
                       producer described seeing a color-coded list—black,
                       yellow, and red—with dozens of musicians and other
                       performers on it. “It was like an intern prepared
                       it,” the producer said. In some cases, first and
                       last names were mixed up; other entries listed band
                       members who had left their groups years earlier.
                       “The whole thing looked awfully unserious,” the
                       producer told me. “But the consequences were as
                       serious as it gets.”


                # ⚓ [Old] Quote Investigator ☛ The_Trouble_About_Fighting_for
                  Human_Freedom_Is_That_You_Have_To_Spend_Much_of_Your_Life
                  Defending_Sons-of-Bitches_–_Quote_Investigator®⠀⇛


                            “The trouble about fighting for human
                            freedom,” he remarked once, “is that you
                            have to spend much of your life defending
                            sons-of-bitches; for oppressive laws are
                            always aimed at them originally, and
                            oppression must be stopped in the
                            beginning if it is to be stopped at all.”


                       In this version of the quotation, the term “sons-
                       of-bitches” occurred instead of “scoundrels”. The
                       bowdlerized variant with “scoundrels” began
                       circulating by 2003.


                # ⚓ Jacobin Magazine ☛ Democrats_Must_Defend_Mahmoud_Khalil⠀⇛


                       It’s fair to say that the overall Democratic
                       response so far to what has roundly and correctly
                       been called the most serious assault on the First
                       Amendment in years has been a mixed bag. The case
                       is the exact kind of authoritarian overreach that
                       high-ranking Democratic officials have claimed to
                       be fighting the last eight years.


                # ⚓ Jacobin Magazine ☛ Free_Speech_Means_Free_Mahmoud_Khalil⠀⇛


                       Mahmoud Khalil’s arrest is a cut-and-dry free
                       speech issue that makes two things clear. First,
                       the Right was always disingenuous when it claimed
                       to care about free speech. Second, the Left should
                       never have ceded the issue.


                # ⚓ CPJ ☛ CPJ,_partners_urge_FCC_to_stop_threatening_press
                  freedom_and_free_speech⠀⇛


                       The Committee to Protect Journalists and 16 other
                       organizations, led by the nonprofit group Public
                       Knowledge, sent a letter to Federal Communications
                       Commission (FCC) Chairman Brendan Carr on March 7,
                       expressing concern about recent developments that
                       threaten to erode long-established safeguards for
                       editorial independence and free expression.


                # ⚓ The Telegraph UK ☛ Starmer's_plan_to_redefine_terrorism
                  'would_threaten_free_speech'⠀⇛


                       Mr Hall was asked to investigate whether the
                       definition should be widened after Sir Keir pledged
                       to tackle the threat of loner misfits fixated on
                       violence in a speech the day after Southport killer
                       Rudakubana pleaded guilty. Current terrorism law
                       requires the suspect to have carried out an act in
                       the name of a specific ideology, but Sir Keir said
                       he would change it, if needed, to include
                       perpetrators who commit violence for the sake of
                       violence.


                # ⚓ [Old] Clouse Brown PLLC ☛ Can_You_Fire_Someone_for
                  Participating_in_Public_Protests?⠀⇛


                       From an employment standpoint, this means that
                       government employees cannot be terminated for
                       participating in public protests. However, these
                       protections do not apply to private employers.
                       Therefore, under federal law, private sector
                       employers may terminate at will employees for
                       voicing political beliefs or participating in
                       political activities that the employer deems
                       offensive.


                       In the social media age, employees should be
                       mindful that their off-duty tweets and updates may
                       garner employer scrutiny. Roseanne Barr learned
                       this the hard way when she tweeted a racially
                       charged comment about a former White House advisor
                       and was fired by ABC within hours. While many
                       employers have social media policies, it’s a good
                       idea to review and update them periodically to
                       cover new technologies and increased social
                       activism.


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


                # ⚓ Ethan Zuckerman ☛ Jay_Rosen_and_Taylor_Owen:_Can_journalism
                  survive_Trump?_Can_democracy?⠀⇛


                       Now that the Republican Party has gone “off the
                       rails in a direction we can call anti-democratic”,
                       it created an asymmetry. The Democratic Party is
                       still a recognizable political party, but the
                       Republicans are not. The press still has not
                       adjusted to this shift. Owen suggests we need to
                       start further back than 2016 to examine the
                       collapse of journalism and the transformation of
                       American politics – Trump is the middle of the
                       story, not the beginning.


                       Jay got interested in “the savvy style of political
                       journalism” some years ago – it’s a focus on who’s
                       ahead, who are the winners and the losers. Who are
                       the spin doctors and what tactics have them come up
                       with? This journalism appealed to many people in
                       Washington DC, NY and in many state capitols… but
                       it’s enormously alienating to folks who are not
                       interested in politics as a game.


                # ⚓ El País ☛ Former_Spanish_military_man_who_spied_on_Assange
                  for_the_CIA_is_investigated_for_falsifying_evidence⠀⇛


                       A new legal battle has begun for David Morales, a
                       former Spanish military man who spied on Julian
                       Assange for the CIA during the latter’s time at the
                       Ecuadorian Embassy in London. Madrid Court No. 45
                       is officially investigating Morales — who is the
                       owner of UC Global S.L., the company that was in
                       charge of security at the Ecuadorian embassy in
                       London — for allegedly falsifying official
                       documents and committing procedural fraud. Judge
                       Fernando Fernández Olmedo has summoned Morales to
                       testify as a suspect, according to court documents
                       obtained by EL PAÍS.


                # ⚓ VOA News ☛ ‘I_was_there_to_try_to_kill_the_journalist,’
                  gunman_tells_New_York_court⠀⇛


                       The Islamic Revolutionary Guard Corps of Iran was
                       allegedly behind the plot, according to
                       prosecutors. Amirov and Omarov, both from
                       Azerbaijan, have pleaded not guilty. If convicted,
                       they face decades in prison.


                       Media advocates say the case highlights how far the
                       Iranian government will go to silence its critics.
                       Iran’s Foreign Ministry did not immediately reply
                       to VOA’s email requesting comment.


                # ⚓ CPJ ☛ CPJ,_partners_call_for_Guatemalan_journalist_José
                  Rubén_Zamora’s_release⠀⇛


                       Judge Erick García ordered Zamora’s return to
                       prison on March 10, executing a appeals court order
                       that revoked the journalist’s house arrest. At the
                       hearing, García reported threats and intimidation,
                       raising concerns over judicial independence and
                       press freedom in Guatemala.


                       The UN Working Group on Arbitrary Detention ruled
                       in July 2024 that Zamora’s continued imprisonment
                       violated international law. A TrialWatch report
                       detailed severe due process violations in Zamora’s
                       case, concluding that his prosecution was likely
                       retaliation for his investigative journalism.


          o § Civil Rights/Policing⠀➾


                # ⚓ FAIR ☛ ‘These_Strikes_Are_a_Good_Example_of_Why_We
                  Shouldn’t_Just_Succumb_to_Despair’:CounterSpin_interview_with
                  Eric_Blanc_on_worker-to-worker_organizing⠀⇛


                # ⚓ FAIR ☛ Did_Left_Journalists_Buy_Into_Right-Wing_Ideology–or
                  Were_They_Bought?⠀⇛


                       Some wonder if their political conversion is
                       related to their departure from traditional
                       journalism to new, high-tech platforms for self-
                       publishing and self-production. In Owned: How Tech
                       Billionaires on the Right Bought the Loudest Voices
                       of the Left (2025), Eoin Higgins focuses on the
                       machinations of the reactionary tech industry
                       barons, who live by a Randian philosophy where they
                       are the hard-working doers of society, while the
                       nattering nabobs of negativism speak only for the
                       ungrateful and undeserving masses. Higgins’ book
                       devotes about a chapter and a half to Elon Musk and
                       his takeover of Twitter, but Musk is refreshingly
                       not the centerpiece. (Higgins has been  a FAIR
                       contributor, and FAIR editor Jim Naureckas is
                       quoted in the book.) The tech billionaire class’s
                       desire to crush critical reporting and create new
                       boss-friendly media isn’t just ideological.
                       Higgins’ story documents how these capitalists have
                       always wanted to create a media environment that
                       enables them to do one thing: make as much money as
                       possible. And what stands in their way? Liberal
                       Democrats and their desire to regulate industry
                       (Guardian, 6/26/24). 


                # ⚓ Truthdig ☛ Workers_Respond_as_Trump_Tries_To_Bust_Airport
                  Screeners_Union⠀⇛


                       In a memo that that one TSA employee said sounded
                       like “a teenage blogger writing about someone they
                       don’t like,” the Department of Homeland Security
                       announced March 7 that it was cancelling the union
                       contract for 47,000 workers at the Transportation
                       Security Administration.


                       The American Federation of Government Employees
                       signed its contract with TSA in May 2024, and it
                       wasn’t set to expire until 2031.


                       DHS also stopped deducting union dues, and ordered
                       all union officers to immediately return to their
                       duties. Workers voted in the union in 2011.


                # ⚓ Federal News Network ☛ Unions_sue_DHS_to_save_TSA
                  collective_bargaining_contract⠀⇛


                       In addition to AFGE, the plaintiffs include the
                       Communications Workers of America and its affiliate
                       union, the Association of Flight Attendants.


                       Meanwhile, Noem, DHS, TSA and Adam Stahl are named
                       as defendants. Stahl is TSA’s chief of staff and is
                       currently performing the duties of the TSA
                       administrator.


                # ⚓ CoryDoctorow ☛ Pluralistic:_The_future_of_Amazon_coders_is
                  the_present_of_Amazon_warehouse_workers⠀⇛


                       When you have a new, abusive technology, you can't
                       just aim it at rich, powerful people, because when
                       they complain, they get results. To successfully
                       deploy that abusive tech, you need to work your way
                       up the privilege gradient, starting with people
                       with no power, like prisoners, refugees, and mental
                       patients. This starts the process of normalization,
                       even as it sands down some of the technology's
                       rough edges against their tender bodies. Once
                       that's done, you can move on to people with more
                       social power – immigrants, blue collar workers,
                       school children. Step by step, you normalize and
                       smooth out the abusive tech, until you can apply it
                       to everyone – even rich and powerful people. Think
                       of the deployment of CCTV, facial recognition,
                       location tracking, and web surveillance.


                       All this means that blue collar workers are the
                       pioneering early adopters of the bossware that will
                       shortly be tormenting their white-collar colleagues
                       elsewhere in the business. It's as William Gibson
                       prophesied: "The future is here, it's just not
                       evenly distributed" (it's pooled up thick and
                       noxious around the ankles of blue-collar workers,
                       refugees, mental patients, etc).


                # ⚓ RFA ☛ Dalai_Lama_book_excerpt:_Tibetans’_only_leverage_is
                  ‘power_of_truth’⠀⇛


                       In the case of Tibet, for instance, it has now been
                       more than seventy years since Communist China’s
                       invasion in 1950. Despite the physical control of
                       the country, through brutal force as well as
                       economic inducements, the Tibetan people’s
                       resentment, persistent resistance in various forms,
                       and moments of significant uprising have never gone
                       away.


                       Even though generations and economic conditions
                       have changed, very little has changed when it comes
                       to the Tibetan people’s perception and attitude
                       toward those they still view as occupiers. The
                       simple fact is that insofar as the Tibetans on the
                       ground are concerned, the Communist Chinese rule in
                       Tibet remains that of a foreign, unwanted, and
                       oppressive occupying power.


                       The Tibetan people have lost so much. Their
                       homeland has been forcibly invaded and remains
                       under a suffocating rule. The Tibetan language,
                       culture, and religion are under systematic attack
                       through coercive policies of assimilation. Even the
                       very expression of Tibetanness is increasingly
                       being perceived as a threat “to the unity of the
                       motherland.”


                # ⚓ RFA ☛ Dalai_Lama_says_his_successor_will_be_born_in_‘free
                  world,’_outside_China_–_Radio_Free_Asia⠀⇛


                       China took control of Tibet in 1950, leading to
                       tensions and resistance.


                       Nine years later, at the age of 23, the 14th Dalai
                       Lama fled to India with thousands of other Tibetans
                       after a failed uprising against the rule of Mao
                       Zedong’s Communists.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ RouteViews_Peering_Policy_updated⠀⇛


                       Most of us will know that the Internet, true to its
                       name, is a network of networks. Each network,
                       whether a local ISP or a global content provider,
                       must connect with others to enable the worldwide
                       flow of data we know as the Internet. We have two
                       ways to interconnect: Transit, where one network
                       pays another for connectivity to the rest of the
                       Internet, and peering, where networks agree to
                       exchange traffic directly.


                # ⚓ Tom's Hardware ☛ Public_IPv4_addresses_are_now_valuable
                  loan_collateral_and_can_be_worth_millions⠀⇛


                       IPv4. Global has launched a new lending program
                       that uses a borrower's IPv4 addresses as
                       collateral. The firm, which describes itself as
                       "the world's largest, most trusted and transparent
                       IPv4 marketplace," says the new loan facility is a
                       first-of-its-kind offer to customers.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Macworld ☛ M3_Ultra_exposed:_Inside_Apple's_hybrid_chip
                  powerful_enough_to_take_on_Nvidia⠀⇛


                       That means the M3 Ultra is an in-between chip,
                       mostly based on the older M3 generation, but with a
                       few high-end additions that push it up toward the
                       M4 in terms of capability. In my conversations with
                       Apple representatives, I’ve gotten the impression
                       that these changes, including the upgrade to
                       Thunderbolt 5, had an impact on the release date of
                       the chip.


                # ⚓ Authors Alliance Inc ☛ Updates_on_AI_Copyright_Law_and
                  Policy:_Section_1202_of_the_DMCA,_Doe_v._Github,_and_the_UK
                  Copyright_and_AI_Consultation⠀⇛


                       Authors Alliance has been closely monitoring the
                       impact of Digital Millennium Copyright Act (DMCA)
                       Section 1202. As we have explained in a previous
                       post, Section 1202(b) creates liability for those
                       who remove or alter copyright management
                       information (CMI) or distribute works with removed
                       CMI. This provision, originally intended to prevent
                       wide-spread piracy, has been increasingly invoked
                       in AI copyright lawsuits, raising significant
                       concerns for lawful use of copyrighted materials
                       beyond training AI. While on its face, penalties
                       for removing CMI might seem somewhat reasonable,
                       the scope of CMI (including a wide variety of
                       information such as website terms of service,
                       affiliate links, and other information) combined
                       with the challenge of including it with all
                       downstream distribution of incomplete copies
                       (imagine if you had to replicate and distribute
                       something like the Amazon Kindle terms of service
                       every time you quoted text from an ebook) could be
                       potentially very disruptive for many users.


                       In order to address the confusion regarding the
                       (somewhat inaptly named) “identicality requirement”
                       by the courts in the 9th Circuit, we have released
                       an issue brief, as well undertaken to file an
                       amicus brief in the Doe v. Github case now pending
                       in the 9th Circuit.


                       Here are the key reasons why we care—and why you
                       should care—about this seemingly obscure issue:
                       [...]


      § Monopolies/Monopsonies⠀➾


          o ⚓ The Register UK ☛ Mozilla_tells_DOJ_to_let_Google_continue_search
            payments⠀⇛


                 Mozilla, which in 2023 received about 75 percent of its
                 revenue from royalties paid by Google and other search
                 providers for search engine usage in Firefox, worries
                 that the US Justice Department's proposed ban on the very
                 same Google Search payments would be rather harmful.


                 American federal prosecutors last week filed their
                 revised proposed remedies [PDF] in their case against
                 Google to restore competition in the web search market,
                 which the [Internet] titan was found to have unlawfully
                 monopolized.


          o ⚓ Mozilla Petition ☛ Mozilla:_it’s_time_to_ditch_Google⠀⇛


                 The open, global [Internet] is a remarkable resource that
                 connects us all and empowers individuals to share ideas,
                 collaborate, and innovate. It embodies our collective
                 hopes for a better future, fostering learning,
                 understanding, and solutions to the challenges we face
                 together.


                 As passionate supporters of Mozilla and its mission, we
                 want to express our thoughts on the current landscape,
                 especially in light of the ongoing U.S. v. Google LLC
                 case and its implications for Mozilla’s search
                 partnerships. While Mozilla has always championed user
                 privacy and an open web, the increasing reliance on
                 Google for revenue raises important questions about our
                 shared commitment to these values.


          o ⚓ India Times ☛ Apple_blocks_Tinder_owner,_startups_from_commercial
            secrets_in_India_antitrust_case⠀⇛


                 An investigation by the Competition Commission of India
                 (CCI) last year found Apple exploited its dominant
                 position in the market for app stores on its iOS
                 operating system to the detriment of app developers,
                 users and other payment processors.


                 Apple has denied wrongdoing and said it is a small player
                 in India where phones using Google's operating system are
                 dominant.


          o § Copyrights⠀➾


                # ⚓ Carl Svensson ☛ Copyright_and_the_Demo_Scene⠀⇛


                       The irony is apparent, bordering on parody: A bunch
                       of hardened game crackers complaining about
                       software theft. The floppy disk copy program Fast
                       Lightning was a commercial title (which later
                       evolved into the famous X-Copy), and its code,
                       "byte for byte", was defended by a cracker group
                       because one of their members wrote it. Of course,
                       both Fast Lightning and X-Copy were, in turn,
                       cracked and spread by other groups.


                       This paradoxical duality of writing commercial
                       software and cracking games defines the complex and
                       often incomprehensible attitude towards copyright
                       or intellectual property - for lack of a better
                       word - on the demo scene.


                # ⚓ BoingBoing ☛ Record_labels_attempt_to_bankrupt_Internet
                  Archive_over_grandpa's_dusty_old_78s⠀⇛


                       This time they're targeting the Internet Archive
                       for the unforgivable crime of preserving history.
                       According to Ars Technica, major labels are now
                       seeking a $700 million in damages over the
                       Archive's Great 78 Project, which digitizes those
                       ancient, crackly records your great-grandparents
                       stored in their basement.


                # ⚓ Ars Technica ☛ Music_labels_will_regret_coming_for_the
                  Internet_Archive,_sound_historian_says_-_Ars_Technica⠀⇛


                       Labels told the court the new complaint was
                       warranted, since these 493 new recordings are
                       evidence of alleged ongoing infringement that they
                       claimed occurred after the case was filed in 2023.
                       If the motion is granted, the recordings at issue
                       in the case would then total 4,624, potentially
                       each worth $150,000 in damages in an IA loss.


                       The case still has a long way to go before a
                       verdict will be reached and IA's fate potentially
                       decided. IA continues to argue that the Great 78
                       Project is a fair use under copyright law, and not
                       everyone agrees that the maximum potential damages
                       will be awarded, even if IA loses. In September,
                       Sam Trust, a music-publishing vet currently
                       overseeing the Doris Day estate, told Rolling Stone
                       that the potential damages that labels seek are
                       "absolutely absurd," suggesting that he "would be
                       surprised if it’s $41,000 worth of damages."


                # ⚓ Society for Scholarly Publishing ☛ Guest_Post_–_The_Future
                  Is_Not_Perpetual_(But_it_could_be_yours_for_just_several
                  thousand_dollars_per_year...)⠀⇛


                       Clarivate, the provider behind a number of
                       resources key to academic libraries, including
                       ProQuest, recently announced that it is shifting to
                       a “subscription-based access strategy,” meaning
                       that it will no longer allow academic libraries to
                       purchase perpetual licenses to content. This is bad
                       news for libraries. Leo Lo, the president of the
                       Association of College and Research Libraries, told
                       Publishers Weekly that “Clarivate’s move away from
                       any ownership option forces libraries into a cycle
                       of ongoing payments, intensifying concerns about
                       collection stability and the ability to preserve
                       scholarly materials for future use.”


                # ⚓ Authors Alliance Inc ☛ Fair_Use,_Censorship,_and_Struggle
                  for_Control_of_Facts⠀⇛


                       While most websites disappear from benign neglect,
                       others are intentionally taken down to remove
                       records from public scrutiny. Exhibit A may be the
                       8,000+ government web pages recently removed by the
                       new presidential administration, but there are many
                       other examples (even whole “reputation management”
                       firms devoted to scrubbing the web of information
                       that may cast one in an unfavorable light).


                       The most well-known bulwark against disappearing
                       [Internet] content is the Internet Archive, which
                       has, at this point, archived over 900 billion web
                       pages. Over and over again, we’ve seen its WayBack
                       Machine used to shine a light on history that
                       powerful people would rather have hidden. It’s also
                       why the WayBack Machine has been blocked or
                       threatened at various times in China, Russia,
                       India, and other jurisdictions where free
                       expression protections are weak.


                       It’s not just the open web that is disappearing. A
                       recent report on the problem of “Vanishing Culture”
                       highlights how this challenge pervades modern
                       cultural works. Everything from 90s shareware video
                       games to the entirety of the MTV News Archive are
                       at risk. As Jordan Mechner, a contributor to the
                       report explains, “historical oblivion is the
                       default, not the exception” to the human record. As
                       the report explains, it’s not just disappearing
                       content that poses a problem: libraries and
                       consumers must grapple with electronic content that
                       can be remotely changed by publishers or others as
                       well. As just one example among many, in just the
                       last few years we’ve seen surreptitious
                       modifications to ebooks on readers’ devices—some
                       changing important aspects of the plot—for works by
                       authors such as RL Stine, Roald Dahl, and Agatha
                       Christie.


                # ⚓ Digital Music News ☛ Turbo_Beats_$10_Million_Copyright
                  Infringement_Lawsuit⠀⇛


                       Britt alleged in his suit that he “was never given
                       notice that his voice was being used, never
                       properly credited for his contributions to the
                       songs in question, and was never compensated from
                       any of the royalty payments, profits, or other
                       income generated from the exploitation of his
                       recorded voice.”


                # ⚓ JURIST ☛ France_creative_sector_brings_copyright_action
                  against_Meta_under_EU_AI_Act⠀⇛


                       Several French publishing associations filed a
                       joint legal complaint on Wednesday against Meta for
                       its alleged unauthorized use of copyrighted work to
                       train its generative artificial intelligence,
                       contrary to the EU Artificial Intelligence (AI)
                       Act.


                       The National Publishing Union (SNE), the Société
                       des Gens de Lettres (SGDL) and the National Union
                       of Authors and Composers (SNAC) filed a complaint
                       to be heard before the Paris Judicial Court. In a
                       joint press release, the SNE said that it is taking
                       action against Meta for its non-compliance with the
                       EU AI Act, which entered into force in August 2024.


                # ⚓ Torrent Freak ☛ Disqus_is_Deleting_Pirate_Site_Communities
                  on_Short_Notice⠀⇛


                       After 15 years or so of relatively plain sailing,
                       comment platform Disqus is cracking down on sites
                       that violate its terms of service. Pirate manga and
                       anime sites have received notifications that Disqus
                       will no longer provide services after copyright
                       infringement came to its attention. With evictions
                       now spreading to sites including FitGirl Repacks
                       and KickassAnime, it's a race against the clock to
                       export years of chat in the 24/48 hours notice
                       given.


    * Antisemitic_Attacks_on_Richard_Matthew_Stallman_(RMS)_in_Wikipedia_This
      Week
    * Gemini_Links_14/03/2025:_Löjl_and_Docker_Context_Stuff


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