𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, January 15, 2026
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Generated Fri 16 Jan 02:49:22 GMT 2026
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/2026/01/15/


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

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


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

⦿ Techrights  -  Coming Soon: Impact With EPO Cocainegate

⦿ Techrights  -  Don't Cry for Gaslighting Media in a Country Which Loathes the Press

⦿ Techrights  -  EPO People Power - Part XXXVI - In Conclusion and Taking Things Up Another Notch

⦿ Techrights  -  GAFAM and IBM Layoffs Outline

⦿ Techrights  -  GAFAM is a National and International Threat to Everybody

⦿ Techrights  -  IRC Proceedings: Wednesday, January 14, 2026

⦿ Techrights  -  Linuxiac May Have Reverted Back to LLM Slop (Updated Same Day)

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Proton Mail compromise, Hannah Natanson (Washington Post) police raid & Debian

⦿ Techrights  -  Red Hat (IBM) is Driving Away Remaining Fedora Users

⦿ Techrights  -  Red Hat is Connected to the Military, Its Chief Comes From Military Family (From Both Sides)

⦿ Techrights  -  Robert X. Cringely Has Already Explained IBM's Bullying Culture (Towards Its Own Staff)

⦿ Techrights  -  Running Techrights is Fun, Rewarding, and Gratifying

⦿ Techrights  -  Slop is a Liability

⦿ Techrights  -  The Creator of Git Probably Doesn't Know How to Install and Deploy Git

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2026/01/15/Coming_Soon_Impact_With_EPO_Cocainegate.shtml
https://techrights.org/n/2026/01/15/Don_t_Cry_for_Gaslighting_Media_in_a_Country_Which_Loathes_the_.shtml
https://techrights.org/n/2026/01/15/EPO_People_Power_Part_XXXVI_In_Conclusion_and_Taking_Things_Up_.shtml
https://techrights.org/n/2026/01/15/GAFAM_and_IBM_Layoffs_Outline.shtml
https://techrights.org/n/2026/01/15/GAFAM_is_a_National_and_International_Threat_to_Everybody.shtml
https://techrights.org/n/2026/01/15/IRC_Proceedings_Wednesday_January_14_2026.shtml
https://techrights.org/n/2026/01/15/Linuxiac_May_Have_Reverted_Back_to_LLM_Slop.shtml
https://techrights.org/n/2026/01/15/Over_at_Tux_Machines.shtml
https://techrights.org/n/2026/01/15/Proton_Mail_compromise_Hannah_Natanson_Washington_Post_police_r.shtml
https://techrights.org/n/2026/01/15/Red_Hat_IBM_is_Driving_Away_Remaining_Fedora_Users.shtml
https://techrights.org/n/2026/01/15/Red_Hat_is_Connected_to_the_Military_Its_Chief_Comes_From_Milit.shtml
https://techrights.org/n/2026/01/15/Robert_X_Cringely_Has_Already_Explained_IBM_s_Bullying_Culture_.shtml
https://techrights.org/n/2026/01/15/Running_Techrights_is_Fun_Rewarding_and_Gratifying.shtml
https://techrights.org/n/2026/01/15/Slop_is_a_Liability.shtml
https://techrights.org/n/2026/01/15/The_Creator_of_Git_Probably_Doesn_t_Know_How_to_Install_and_Dep.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2026/01/15/Gemini_Links_15_01_2026_Ode_to_elinks_envs_net_Pubnix_and_Downt.shtml
https://techrights.org/n/2026/01/15/Links_15_01_2026_Internet_Blackouts_Jackboots_Society_in_US.shtml
https://techrights.org/n/2026/01/15/Links_15_01_2026_Starlink_Weaponised_for_Regime_Change_by_Man_W.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 91

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/Coming_Soon_Impact_With_EPO_Cocainegate.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Coming_Soon_Impact_With_EPO_Cocainegate.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Coming Soon: Impact With EPO
Cocainegate⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


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


As hinted_earlier, on Friday or this coming weekend (we need to provide
sufficient time for "right of reply") we plan to start the next phase of the
Cocainegate series. We welcome any more input readers may have (don't be too
reluctant, we're good at protecting sources). Next_week_industrial_actions
begin. Will_Campinos_survive_2026? █


    * Linuxiac_May_Have_Reverted_Back_to_LLM_Slop_(Updated_Same_Day)
    * Links_15/01/2026:_Internet_Blackouts,_Jackboots_Society_in_US


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣥⣶⣶⣶⣾⣽⣭⣿⣿⢷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⢮⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 143

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/Don_t_Cry_for_Gaslighting_Media_in_a_Country_Which_Loathes_the_.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Don_t_Cry_for_Gaslighting_Media_in_a_Country_Which_Loathes_the_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Don't Cry for Gaslighting Media in a
Country Which Loathes the Press⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026,
updated Jan 15, 2026


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


So the award-winning* Bezos_employee entrusted to cover news got_raided. This
just comes to show that American standards of journalism or this American
regime's (it didn't start with Cheeto [1, 2]) attitude towards the press should
be rejected internationally. To issue a quick reminder to readers:


    * Like_the_Serial_Strangler_From_Microsoft,_Donald_Trump_is_Out_of_Time_and
      Has_Jurisdiction_Issues_in_the_UK
    * How_Americans_View_'Free_Speech'_in_Practice
    * Threats_Against_Techrights_Always_Come_From_Outside_Britain
As_we_said_last_night, an American couple having a fight resulted is us, a
couple based in the UK (different continent!), receiving threats. Yes, my wife
and I received threats for merely writing about Americans. Crazy!!


This is another form of imperialism. It's like colonialism over information, a
gross overreach. █


____


* As_per_Wikipedia:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇...three_part_series_by_Hannah_Natanson,_Sabby_Robinson_and
  Moriah_Balingit_which_investigates_two_separate_shootings_at_Huguenot_High
   School_in_Richmond,_Virginia_and_the_efforts_by_students_for_ways_to_cope
                        during_those_tumultuous_times⦈_


===============================================================================
Image source: Giraffe_sticking_out_tongue


    * Red_Hat_(IBM)_is_Driving_Away_Remaining_Fedora_Users
    * Red_Hat_is_Connected_to_the_Military,_Its_Chief_Comes_From_Military
      Family_(From_Both_Sides)


⠀⠀⣠⣄⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⠄⠀⠀⠀⠀⠀⣬⣤⡀⠀⠀⠀⠀⠀⠀⣀⣠⣷⣄⢰⣾⣿⣦⠀⠀⠋⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣷⣦⣤⣤⡄⠀⠀⣾⠁⠘
⣷⣿⣿⣿⣷⣶⣾⣆⠀⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⠛⠁⠀⠀⡀⠠⣶⢿⣿⣿⡿⠿⠏⢻⣿⣿⣶⣄⣀⡀⠀⠀⠀⠰⣿⠂⠀⠀⢿⣿⣶⠟⢻⣿⣿⣿⣿⣿⣷⣤⣤⣿⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⢾⣼⣿⢤⡄⣌⣹⡆⢠⠈⣿⣿⣿⣿⣿⣷⡄⠀⠀⣀⠀⠀⠀⠀⠀⠛⢋⠀⢾⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠺⣿⡏⠘⡇⣿⣿⣷⣶⣶⣿⣿⣧⣿⣿⣿⣄⣀⠐⠿⠃⠀⠀⠀⢀⣴⣿⣷⡄⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢀⣿⣇⠀⠀⠀⠀⠀⠪⣙⣷⣧⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣬⣾⣿⣿⢯⡉⠻⠿⠛⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⡀⣿⠀⠋⢹⣟⣃⣿⣿⣿⣿⡿⠀⢹⡿⣿⣿⣿⠀⠀⣀⡀⠀⠀⠀⣠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀
⠹⣏⠉⠛⠛⠿⡿⣿⠿⢿⠿⠿⠿⣿⡿⡿⠿⣿⢿⣿⣿⣿⣤⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣄⡀⣡⠇⠀⠀⠘⢡⣤⣤⣴⡿⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀
⣿⣿⣷⣶⣶⣦⣷⣶⣦⣤⣄⣀⣀⣈⣋⣡⣀⡙⡀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣷⠛⠀⠀⢀⣶⣿⣿⠛⠛⠃⠀⠈⠀⢸⣿⣿⣿⣿⣿⡿⠉⢻⣿⠏⠀⠐
⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣏⠉⠉⣿⣦⣬⣴⣿⣿⡿⢫⣙⢀⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣷⡀⠀⢴⠿⢿⡿⠟⠀⣠⣾⣿⠀⣠⣿⣿⢿⣿⣿⣿⣧⣀⣸⣷⠀⠀⠈
⢷⣄⡀⠀⠉⣻⣿⣿⣿⣿⣯⣀⠀⠙⠛⠛⠛⢿⣿⣿⣿⣍⣁⣙⣿⣿⣯⡀⠀⢿⣿⣿⣿⣾⣿⣾⣿⡟⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠓⠘⢳⠀⠀⢀⣤⡀⢀⣀⠛⠟⠃⠐⢿⡇⠀⠉⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠉⢻⣿⡟⠁⠀⠀⠹⣿⣿⣿⣾⣿⣷⣶⣾⣿⣿⣿⣯⠙⠻⣿⣿⣿⣧⡄⣀⠛⠿⣿⣿⣿⣿⣿⣿⣾⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢀⠀⣾⣿⣿⣎⠁⠀⠀⠀⠀⠘⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣦⣴⣿⣿⡿⠶⠿⠿⠿⠿⣿⣿⣿⡿⠛⠉⠉⠙⠿⣷⣥⣤⣼⣿⣿⣿⣷⣾⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠏⢛⢅⡟⠰⣿⣿⣿⣿⣷⡀⠀⠐⠀⠀⠠⢇⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿
⠉⠉⢿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣿⣿⣿⣷⣄⠀⠀⠀⠀⠹⣿⣍⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⠿⣿⣿⣿⠿⣿⣿⣿⣷⣆⣰⣄⠻⣧⠀⠘⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣾⢦⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠃⠀⠈⠙⠛⢦⠄⡀⠀⣿⡿⢆⣀⡠⠶⣿⣿⣿⣿⣽⢫⣿⡃⣿⢴⣿⡹⣦⡀⠈⠁⠀⠀⠉⢼⣿⣿⣿⣏⢡⣽⣧⠀⠀⠈⠀⠈⠂⠀⠀⠀⠀⠀⢨⣯⣈⠀⠀⠀⠀⠀⠹⣿⣯⣸
⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣅⣤⣤⣤⣾⣿⣿⣿⣾⠟⠛⠃⠀⡟⠻⣿⣿⣶⣲⣦⠀⠀⡩⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠓⢶⣶⣌⡀⠰⣿⣿⣿
⠀⠐⠀⠠⣬⣟⣻⣶⣶⡶⠒⠛⢛⡓⠒⠀⠀⢶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⡀⢠⠀⠀⠆⠀⠈⣿⡿⠿⣿⣿⣿⣦⡼⠞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡧⠀⠈⢉⣾
⠀⠀⢠⣾⣿⣏⢹⣿⣯⣄⣀⠀⠉⠁⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡿⠐⠚⡷⣖⠉⠙⣇⠀⠈⢿⣿⣿⣧⡀⠀⠀⠃⠈⣻⣿⣿⣿⣿⣯⣁⠙⢋⠀⢀⣤⣤⡄⠀⠀⠈⠛⠋⠁⠀⠀⠘⣿
⣶⣾⣷⣿⣿⣿⣿⣿⡏⠉⣭⣶⣶⣤⣤⣤⣴⣿⣿⣿⢿⣿⣿⣿⡟⠛⠋⠹⣿⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣈⣦⢀⣸⡆⠀⢠⡿⢉⣿⣧⡤⠀⠀⠀⠈⠀⠙⢿⣿⣿⠻⣷⣤⠀⡀⠉⠛⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙
⠘⠿⣿⣿⣿⣿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⣿⣿⣿⣇⣴⣶⣿⢻⣿⣿⢿⣿⣿⣿⣿⣿⣧⣄⣻⠆⠀⠉⣳⣤⣼⣇⣀⣛⣿⣯⣀⡀⠀⣶⡄⠀⠀⠙⠿⢦⡄⢸⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡶⠀
⠀⠀⠈⠉⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠟⠋⠀⠈⠻⣿⣿⣿⣿⣿⣿⡋⠈⠙⠋⠀⠹⣿⣿⣿⣿⣿⡆⣫⣴⣤⣤⠛⠃⠀⢹⣿⣉⢀⢀⣛⣷⣀⣻⣧⡀⠀⠀⠀⠐⢬⣾⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰
⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⢿⣿⡿⠉⠐⣶⡶⠀⠀⠀⠉⠉⠉⢻⣿⣿⣷⣶⣶⣶⣿⣿⣿⣟⣿⡿⠋⢠⡿⠛⢿⣿⣷⣶⣶⠟⠻⠓⠈⣿⣿⣿⣟⣫⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣻⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠈⠁⠀⠉⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⡿⢿⡿⠇⠀⠀⠀⠀⠈⣻⠿⠟⢀⣀⣀⠀⡀⠙⠛⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣀⢠⣾⣾⡟⠛⠉⠀⠀⠀⠀⠀⢀⣶⣿
⠀⠀⠀⠀⠀⠀⢠⣢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣼⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⣽⣿⣿⣦⣀⠀⣰⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⣰⡦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣤⣄⣤⣾⣶⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⢿⣯⣽⣿⣿⣿
⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⡟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠰⣿⣿⣿⣿⣿⣿⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠉⠉⠉
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                    ䷩ 𝚕𝚒𝚗𝚎 246

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/EPO_People_Power_Part_XXXVI_In_Conclusion_and_Taking_Things_Up_.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/EPO_People_Power_Part_XXXVI_In_Conclusion_and_Taking_Things_Up_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ EPO People Power - Part XXXVI - In
Conclusion and Taking Things Up Another Notch⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Jan 15, 2026


Also see: Part_I | Part_II | Part_III | Part_IV | Part_V | Part_VI | Part_VII |
Part_VIII | Part_IX | Part_X | Part_XI | Part_XII | Part_XIII | Part_Part_XIV |
Part_XV | Part_XVI | Part_XVII | Part_XVIII | Part_XIX | Part_XX | Part_XXI |
Part_XXII | Part_XXIII | Part_XXIV | Part_XXV | Part_XXVI | Part_XXVII | Part
XXVIII | Part_XXIX | Part_XXX | Part_XXXI | Part_XXXII | Part_XXXIII | Part
XXXIV | Part_XXXV


A month after being busted with cocaine the EPO defended him and kept him in
place (it_hid_him_using_fake_and_paid_"sick_leave"_only_two_weeks_later, but
the problem isn't limited to him):


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


The "Alicante Mafia" series (about the EPO "Mafia" which intimidates and
censors the staff [1, 2] like Benoît_Battistelli illegally did) will start
soon, maybe in the weekend if not earlier. It'll last until (at least) next
month. António_Campinos, like Battistelli before him, does not obey orders from
judges. That's how a "Mafia" behaves.


They often say that the law won't deter or stop criminals because it's hard to
enforce laws against people who reject the law. It's often said in relation to
arms control (bans on particular weapons).


And speaking of weapons, remember that Battistelli also broke German laws when
he_brought_weapons_to_the_EPO. In Germany, this is a very serious offence, and
the same goes for lying to police (as Team Campinos apparently did a few months
back).


Campinos may try to act like he's "nice", but he and his friends from Alicante
are a bunch of unskilled Mafioso types and some do cocaine. If the EU continues
to ignore this issue, or if national delegates pretend to themselves that this
scandal will "go away" (or magically "mend itself"), then they're deluded.
Complicity by passivity - more so where professional obligations and
responsibilities exist - means they cannot conveniently distance themselves
from it.


Bad things cannot easily happen (or persist) without enablers. █


    * Running_Techrights_is_Fun,_Rewarding,_and_Gratifying
    * GAFAM_is_a_National_and_International_Threat_to_Everybody


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⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣽⣭⣦⣭⣷⢬⣶⣯⡧⣯⣧⣭⣭⣭⣽⣷⣥⡭⣽⣬⣭⡭⣧⠭⣿⢤⠦⣼⣬⣽⣾⢭⣭⣽⣼⣯⣭⣭⣭⣯⣯⣧⢽⢭⣭⣽⣷⡥⣽⣼⣤⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠾⠾⢷⡶⡶⣷⡶⠾⠲⠷⠶⠶⢾⣿⢶⠞⢶⠶⠷⡶⢿⠶⢿⠞⢶⡾⣖⣷⣷⢾⠶⢶⡺⠾⡻⡿⣿⠾⠖⣶⠾⡾⣾⢶⢷⠖⡿⣶⠿⣷⣶⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣫⣛⣛⣛⣓⣛⣿⣹⣙⣛⣋⣽⣛⣟⣛⣛⣟⣻⣇⣛⣿⣻⣙⣟⣛⣛⣛⣻⣟⣝⣟⣿⣋⣻⣛⣟⣟⣛⠛⣛⣛⣹⣛⣋⣛⢛⣛⣳⣛⣛⣻⣛⣛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣭⣯⣩⣽⣭⣭⣽⣯⣭⣭⣯⣭⣫⣭⣯⣭⣭⣯⣭⣯⣭⣹⣯⣭⣯⣭⣯⣭⣯⣯⣭⣭⣽⣭⣭⣿⣯⣭⣭⣍⣭⣭⣍⣯⣭⣭⣩⣯⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣴⣤⣼⣼⣧⣼⣴⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣻⠿⠟⢿⢻⢿⠿⠟⠿⡿⠿⣟⠻⠟⠛⠟⠿⠟⡿⠿⠿⠟⢿⠻⡿⠿⡿⠿⠿⡿⠿⢿⢿⡿⠿⢟⡻⡟⢛⠻⠿⡿⢿⠿⢿⠿⢿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⣻⣻⣛⣛⣛⣛⣻⣫⣻⣻⣋⣉⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⢿⠿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⣤⣤⣼⣥⣤⣼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠨⠸⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣷⣾⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣈⣽⣽⣇⣼⣍⣽⣹⣏⣈⣽⣍⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⡟⣿⣿⣿⣿⣿⠛⣿⣿⠛⢛⡟⠛⠛⢟⣛⡛⠛⢛⣛⣛⠛⠛⠛⠛⠛⣻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⠁⠀⠀⠀⢹⡇⣿⣿⣿⣿⡿⡀⣿⣿⠀⠹⡇⠀⠀⢿⡏⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠨⣏⣻⣍⡀⠀⠀⠀⢈⡇⣿⣩⠙⣿⠇⢩⣿⣿⠀⠀⠁⠀⠀⠘⠁⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢐⠺⠐⠀⠀⠀⠀⠀⠀⠉⡥⠬⠍⡁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠐⠁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣦⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣧⣤⣬⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣴⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣬⣭⣯⣭⣧⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣭⣤⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣽⣥⣍⣽⣷⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣭⣭⣽⣽⣭⣿⣹⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣯⣭⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣩⣿⣭⣯⣭⣭⣭⣽⣽⣭⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⡿⡿⡿⢿⢿⢿⢿⢿⡿⠿⣿⢿⠿⢿⣿⢿⢿⠿⡿⡿⢿⢿⠿⣿⣿⢿⠿⠿⡿⡿⣿⠿⢿⡿⡿⡿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣼⣼⣼⣧⣇⣠⣼⣧⣤⣼⣧⣯⣧⣮⣥⣦⣿⣼⣥⣼⣰⣧⣽⣥⣼⣧⣿⣧⣤⣥⣤⣧⣼⣼⣧⣤⣿⣤⣬⣤⣤⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⣭⣿⣿⣯⣿⣽⠟⠛⠉⣯⣽⣿⣿⣭⣯⣉⣿⣿⢸⣿⣿⡇⢸⣿⡇⠃⠙⠻⠸⣿⣿⢨⣬⣼⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⠃⠘⢿⠃⠀⠀⠀⠀⣻⣟⠸⠿⡟⡏⣿⣿⡀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣧⠀⠀⠀⢸⣿⣿⣿⢛⣿⡿⣿⣿⢠⠬⣯⡀⠀⠽⠁⠀⠀⠀⠀⠡⢻⡔⠅⠀⠄⣿⣿⠁⠀⠁⣻⣿⣿⠀⠀⠀⠀⠀⡀⢸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⢿⣿⠇⠟⠋⠠⡀⠀⠛⠿⣿⣿⠻⣿⣿⣿⣿⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌⠈⠀⣿⣿⡆⠀⠀⠸⢻⣿⠀⠀⠀⠀⠀⡇⢸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠛⠀⠀⠀⠀⠀⢓⣤⠂⠀⠀⠛⠁⠛⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡁⠈⣿⣿⡇⠠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠿⢿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠷⠾⢾⢿⡶⠶⠿⠿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠷⢶⣶⠾⡾⠶⡾⢷⠾⠶⠶⡾⠿⢿⣿⣿⣿⣿⣿⠶⠶⢶⠿⠾⠶⡶⠾⠿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢳⠷⠶⢲⠶⢷⡺⢾⠿⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣶⣿⣾⣷⣶⣶⣿⣿⣶⣾⣶⣷⣷⣿⣿⣿⣿⣿⣿⣶⣷⣾⣷⣷⣶⣿⣷⣶⣶⣷⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡟⠛⠛⠿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠻⠾⠿⠇⠀⠀⠀⠀⠘⠘⠓⠛⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣭⣭⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣭⣭⣭⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣯⣭⣭⣍⣯⣽⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣭⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 376

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/GAFAM_and_IBM_Layoffs_Outline.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/GAFAM_and_IBM_Layoffs_Outline.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GAFAM and IBM Layoffs
Outline⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


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


A few hours ago: (Noida, Uttar Pradesh, India)


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


GAFAM openly reports layoffs this week, but the M (Microsoft) is said to have
prepared lists of people to cull with_PIPs or pink slips to come out next week
(some said next Monday, another strand said Wednesday). It's possible Microsoft
will delay this until people might already forget some tweet (remember
Microsoft never denied those rumours).


As for IBM, there have been "forever layoffs" [1, 2] in effect for quite some
time (IBM skirts the WARN Act this way), we heard about layoffs at Red Hat (now
"IBM"; they're in many way indistinguishable in 2026), and there's a sort of
ambient atmosphere of woodshedding (similar to the meaning in musical
compositions) - a lot of the layoffs happen in secrecy and involve convincing
people to resign, retire, relocate etc. Not many people will notice this,
sometimes not even the insiders. █


    * Links_15/01/2026:_Internet_Blackouts,_Jackboots_Society_in_US
    * Links_15/01/2026:_Starlink_Weaponised_for_Regime_Change_(by_Man_Who
      Boasted_About_Annexing_South_American_Countries_for_Tesla's_Mining),
      Corruption_in_Switzerland_Uncovered_by_JuristGate


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

                    ䷩ 𝚕𝚒𝚗𝚎 496

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/GAFAM_is_a_National_and_International_Threat_to_Everybody.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/GAFAM_is_a_National_and_International_Threat_to_Everybody.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GAFAM is a National and International
Threat to Everybody⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026,
updated Jan 15, 2026


From_2023/2024:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇BINARY FATA MORGANAS: ByteDance Intel NVIDIA AMD RAND
Corporation Yahoo Facebook Apple Tencent Amazon Microsoft Oracle RedHat Google
                    Alibaba Netflix Atlassian Salesforce⦈


Carole Cadwalladr, who got subjected to lawfare [1, 2, 3] because of her decent
coverage about Brexit and GAFAM's role in Brexit (she had exposed a lot of
legitimate issues and nobody is infallible), recently published "Peter_Thiel's
New_Model_Army" (Thiel_is_raiding_the_NHS - Microsoft being his proxy - and
attacks_the_press_by_proxy to punish his critics). Cadwalladr said: "It sounds
like writerly hyperbole to describe the UK as a vassal state, but I mean it in
its most literal sense. It's explicitly stated in the ur-text of Trump's White
Houses foreign policy, the National Security Strategy document, that US
companies will be used as instruments of state power. There is no hidden agenda
here: Trump has set it all out. (For a breakdown of this document and what it
all means, see this weeks piece in the Nerve by former British diplomat, Arthur
Snell..."


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


Having just_mentioned_Red_Hat's_very_strong_connections_to_the_US_Military and
GAFAM_being_bailed_out_(or_propped_up)_at_taxpayers'_expense_(endless_debt,
inflation), it seems relevant that this_new_article ("The Fed Is Quietly
Bailing Out Wall Street") helps confirm what we wrote just yesterday. As an
associate put it: "Has the federal government taken the opportunity to bail out
Microsoft yet again, too?"


And "apropos technical sovereignty vs software / OS vendors," consider what
Cadwalladr showed.


GAFAM is just a tentacle in service of imperialism.


The world needs to treat GAFAM as what it is; enough with the greenwashing that
we mentioned some_hours_ago. GAFAM is destructive and a net loss. █


    * EPO_People_Power_-_Part_XXXVI_-_In_Conclusion_and_Taking_Things_Up
      Another_Notch
    * Slop_is_a_Liability


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣭⣿⣿⣟⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⢿⣿⣯⣿⣿⣿
⣿⣿⣿⣾⡟⣿⢿⣿⣸⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡿⣻⣟⣿⣿⡿⣿⢻⣿⣿⣸⡟⣻⣻⡟⣿⣿⡿⣿⣿
⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣶⣷⣶⣾⣿⡇
⣿⣿⣿⡿⣿⡿⣿⢿⣿⣿⣿⣿⡿⣿⢿⣿⣿⢿⡿⢿⣿⢿⡿⡿⡿⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀
⠋⠉⠉⠁⠠⠀⠄⠥⡤⣤⣤⣤⣷⣶⣤⣿⣤⣤⣦⣤⣤⣼⣵⣷⣴⣵⣧⣶⣤⣭⣵⣯⣥⣤⣠⣥⣤⣬⣬⣤⣼⣷⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⠟⠟⠛⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠉⠛⠟⢻⠻⣿⣿⣿⣿⣿⣿⣿⣇⣝⣉⣋⣁⣪⣫⣉⣈⣏⣜⣩⣙⣫⣹⣧⣩⣉⣙⣉⣹⣱⣣⣈⣙⣝⣉⣝⣭⣹⣿⣿⣿⢿⠿⠿⠛⠋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠉⠛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⢛⠛⠛⠛⢻⠛⠛⠛⠻⠛⠛⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣠⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⣿⠿⠿⢿⣿⢿⣿⣿⣿⣿⡿⠿⠿⢿⡿⠿⣿⣿⣿⣿⠿⢿⢿⠿⠿⡿⠿⠿
⣉⢥⠅⠀⠤⠀⣂⢁⣔⢩⣐⣡⣀⣀⣀⣉⣢⣴⣆⣦⣼⣶⣴⣵⣾⣿⣶⣭⣾⣶⣷⣿⣺⣮⣭⣯⣿⣽⣿⣽⣿⣿⣥⣧⣭⣽⣷⣿⡲⢶⣴⣷⣶⣾⣷⣾⣪⡌⢥⢷⠟⠰⠦⠾⠶⡶⣬⡃⣜⢑⠂⣁⣠⡀⢀⡐⣀⠀
⠛⠛⠉⠉⠙⠛⠛⠓⠉⠍⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⢋⡙⠟⠉⠈⠉⠩⢭⣙⣛⡛⠉⣟⣋⢉⣏⣉⣩⠿⠻⠟⠋⣟⡯⢏⡟⠛⠛⢻⡿⠿⠿⠭⠅⠀⢉⠀⢉⠈⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⠀⠈⠁⠉⠁⠁⠀
⣤⣄⣤⣤⣷⣦⣾⣷⣶⣴⣦⣶⣤⣾⣶⣴⣥⣦⣤⣤⣥⣤⣮⣴⣶⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣯⣽⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣦⣤⣦⣤⣤⣤
⡏⠩⠯⠉⠋⢉⢹⠍⠋⠛⠛⠿⠿⣿⢻⣻⠿⣟⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠋⠛⣛⣛⣛⣛⢛⡚⠛⠛⠛⠛⠛⠛⠛⣙⣛⡛⠛⢛⠛⠒⠛⠀⠘⢛⠉⠙⠙⠁⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠋⠉⠛⠛⠋⠒⠛⠛⠛⠙⠙⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠋⠉⠉⠉⠉⠙⠀
⣈⣠⣆⣒⣉⡈⡉⣉⣉⣉⣭⣬⣜⣿⣿⣴⣶⣟⣰⣤⣥⣤⣴⣒⣒⣄⣤⣤⣬⣴⣤⣬⣬⣽⣿⣦⣶⣶⣤⣴⣦⣤⣤⣦⣶⣦⣤⣴⣠⣤⣶⣦⣴⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⡤⣤⠄⠀⠠⣤⣤⡤⡠⠄⠀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣋⡀⠤⠟⣿⣤⣄⡀⣀⣤⣵⣞⣤⣤⣧⣶⣶⣶⣶⣐⣒⣾⣯⣿⣶⣟⣁⣴⣾⣾⣿⣷⣾⣾⣾⣾⣿⣿⣿⣿⣯⣽⣯⣭⣿⣿⣿⣷⣶⣿⣿⣤⣽⣿⣶⣶⣶⣶⣾⣿⣷⣶⡿⢶⣶⣾⣻⣻⣿⣶⡤⠤⡤⢴⣖⣲⣶⣦
⠛⠛⠛⠛⠛⢛⣛⢿⡿⠟⠛⠿⢿⣿⡿⣿⡽⠿⠟⢙⡭⢿⣿⣿⢿⢿⣉⡛⠛⢛⢻⣽⣿⣿⡿⣻⡿⠿⢿⣿⢿⣭⣿⣭⢟⠟⡻⢟⣿⣿⣿⣿⣿⣿⠿⢿⣩⡻⢿⡿⠙⠙⣙⢿⣮⠟⠛⠋⠽⠏⠹⠿⠿⠿⠛⢛⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠁⠀⠀⠀⠈⠀⠈⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⠋⣭⡍⡿⠿⡿⠿⡿⠿⠿⠿⢿⡿⢿⡿⢿⣿⠉⢿⠉⢹⠉⢹⡿⠿⣿⡿⢿⠿⣿⣿⠿⠿⣿⡿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⢦⣤⠈⣿⠀⡇⠀⣿⠀⣶⣆⠘⢣⡇⢘⣂⢸⠀⢸⠀⢸⠀⢸⠚⡅⠈⡇⠀⡇⢸⡁⢸⡧⡇⢐⣃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣶⣶⣶⣿⣶⣶⣶⣷⣶⣾⣿⣶⣾⣿⣶⣶⣿⣶⣾⣶⣾⣶⣾⣶⣶⣶⣷⣶⣶⣶⣷⣶⣶⣿⣶⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡂⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣶⣶⣶⣶⣶⣦⡀⣠⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⡀⠃⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⡈⢻⣿⣿⣿⣿⣿⣿⡿⢡⠤⠄⢸⣿⣽⢙⡋⡋⣝⣿⣷⣿⣿⠏⡏⣿⡝⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⣟⣿⣿⣶⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠇⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣗⡇⢸⣿⣿⣿⣿⣿⣿⣧⠘⠤⠂⢸⣟⢟⣛⣟⢿⣿⣟⣿⣿⣿⠿⡟⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣭⣥⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣹⣿⣙⣉⣷⣶⣾⣿⣿⣟⣿⣋⣉⣯⣿⣿⣯⣯⣷⣶⣶⣿⣿⣙⣋⣋⣿⣿⣿⣷⣶⣾⢸⣿⣿⣿⣿⠟⡋⢙⠛⣿⣿⣾⣷⣷⡶⢋⣉⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠧⠿⠿⠼⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⣽⣿⣿⣿⣋⣍⣭⣿⣄⡙⠛⠛⠛⠀⠧⠼⠀⠉⠛⠛⠛⠛⠀⢐⣒⠀⠀⠀⠀⠀⠀⢰⠀⡆⢸⣿⣿⣷⣦⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢴⣾⣿⣿⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⡌⠒⢁⣼⣿⣿⣿⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣉⠑⡏⢐⣙⠋⣴⣽⠀⡇⢸⡆⣵⡄⢸⠀⣾⡄⠓⣼⣿⣿⣿⣿⡏⡠⠠⡀⠹⣯⢻⢻⢛⡿⡟⡟⢻⢛⠟⡛⢻⠻⡇⢸⣿⣿⣋⣹⣘⣿⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣾⣶⣷⣾⣾⣷⣾⣾⣶⣶⣾⣶⣾⣷⣶⣷⣷⣓⣸⣿⣿⣿⣿⣿⣇⠑⠐⠇⠀⠚⠚⠛⠚⠚⠚⠓⠚⠓⠓⠓⠚⠙⠃⢸⣿⣼⣭⣭⣯⣿⠀⠀
⠀⢸⣿⡿⠿⠿⢿⠿⣿⣿⠿⢿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠁⢶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀
⠀⣇⢬⠀⠸⡿⡿⣿⣿⡿⠿⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣠⠾⢾⣷⠻⡿⠶⢶⣿⡶⢢⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠋⠙⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⡀⠀⠀⠀
⠀⠀⠿⣿⣶⣾⣷⣶⣷⣶⣿⣿⣷⣶⣾⣿⣟⣻⣻⣻⣟⣹⣟⣛⣛⣿⣿⡟⠻⣿⣟⠻⢿⢿⣿⣿⣿⣿⢸⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣶⠰⣹⢸⢹⢱⢎⢕⢺⣿⣿⣿⠀⢱⡌⠀⣿⣿⣿⣷⡄⠀
⠀⡄⢠⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣋⣁⣩⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⢸⣿⡷⣿⣿⢿⣶⡶⣾⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣻⡿⡿⣿⢿⡿⢿⢿⡿⢿⢿⡇⢠⣤⣾⣿⣿⣿⣿⡇⠀
⠀⠃⠘⠀⡟⡿⡿⢿⡿⣿⣿⡿⢿⢟⣿⣿⣯⣿⣯⣭⣿⣭⣯⣬⣿⣿⣿⡷⢾⢷⣶⣿⣶⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⢳⡿⣟⣿⣿⣾⡆⠀⠀⠀⠀⠀⠈⠷⣿⣤⣧⣿⣼⣧⣶⣤⣷⣼⣼⡇⢸⣝⣛⣛⣹⣻⣿⡇⠀
⠀⠀⣠⣴⣿⣿⣿⣟⣿⡟⠻⣿⣿⣿⣿⣿⣧⣭⣽⣿⡿⢿⣯⣭⣿⣿⣿⣟⣻⣟⣛⣻⣟⣿⣟⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠮⢅⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢸⣿⣿⣯⣽⣽⣿⡇⠀
⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⣤⣿⣿⣥⣤⣴⡜⢩⡠⠉⢧⣽⣯⣽⣭⣿⣿⣭⡽⠍⠛⢸⣿⣿⣟⣹⣏⣙⣏⣙⣋⠹⠇⠀⠀⠀⠀⠉⢁⣠⣭⡛⢻⢻⠛⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠇⠀
⠀⠀⠀⢠⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠑⠄⢸⣿⣿⣿⣿⣿⣿⣿⠁⡆⠀⠈⣿⣿⣿⣿⣽⣭⣽⣽⠁⣤⢠⡄⠀⠀⠀⠀⢸⡗⣾⢷⡿⣾⢶⣿⡿⢿⢿⠟⡿⡿⣄⠙⠛⠛⠛⠛⠉⠀⠀
⠀⠀⠀⠸⠀⢈⣟⣙⣙⣹⣝⣿⣿⣋⣏⣿⣟⣉⣯⣿⣿⠛⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠃⠂⠃⠀⠀⠀⠀⢸⣧⣵⣼⣮⣦⣬⣬⣧⣼⣶⣥⣮⣬⣬⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⣴⣿⣿⣹⣙⣿⣉⣿⣋⢹⣏⣙⣽⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⡟⡿⠿⡿⢻⡿⢻⢻⠿⡿⡿⠿⡟⣿⠿⡿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣴⣶⣶⣶⣶⠀⢆⡆⠀⢀⣤⣤⣤⣤⣤⣤⡄⢠⠂⡄⢀⣤⣶⣶⣶⣶⣶⣶⠀⣖⡂⠀⢸⣷⣷⣷⣧⣷⣾⣷⣾⣾⣶⣿⣷⣾⣷⣿⣦⣷⣿⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢿⣿⠿⡿⡿⣄⠀⠃⠀⣾⣿⡿⣿⠿⡿⡿⢧⡘⠐⠃⣼⣿⣿⣿⣿⣿⣿⣿⣄⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⢠⣸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣼⣼⣦⣿⣽⣿⣿⣿⡇⣿⣿⣿⣿⣴⣿⣼⣿⣿⣿⠀⣿⣿⣮⣵⣵⣿⣧⣶⣿⣿⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡎⣟⢻⡏⣝⡻⠛⣿⠋⢹⣿⡏⣻⡟⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣮⣥⣽⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠘⠿⠽⠷⠴⠥⠿⠥⠽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣾⣿⣿⣿⣿⣄⠘⠁⠃⣠⣿⣿⣿⣿⣿⣷⣆⠀⣴⣾⣿⣿⣿⣿⣆⠜⠣⢀⣿⣿⣿⣿⣿⣿⣶⣄⢀⣴⣿⣿⣿⣿⡄⠸⠁⢀⣿⣿⣿⣿⣿⣿⣿⣶⡄⢠⣶⣿⣿⣿⣿⣿⣧⠐⠓⠀⣸⣿⣿⣿⣿⣿⣷⡄⠀⠀
⠀⣿⣿⣗⣺⣉⣟⣉⣝⣏⣹⣯⣿⣉⣻⣉⣿⣿⣿⠀⣿⣿⣨⣯⣇⣿⣿⣏⣋⣿⣿⣸⣯⣹⣝⣹⣿⣿⢸⣿⣿⣿⣿⣻⣋⣩⡏⣉⣯⣯⣟⣏⡟⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡻⠲⠚⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⣿⣿⣹⣿⣇⣿⣩⣿⣿⣈⣿⣋⣍⣹⣿⣹⣿⣿⠀⣿⣟⣟⣛⣿⣋⣻⣛⣿⣙⣟⣻⣙⣟⣻⣛⣿⣿⢸⣿⡏⡻⡟⡏⢿⠛⣿⢻⠟⡿⣟⣿⢛⠹⡋⣿⡇⢸⡟⢙⣛⣟⡛⠛⣟⣻⣿⣿⣟⣙⡿⠛⣿⣿⣿⡇⠀⠀
⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 626

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/IRC_Proceedings_Wednesday_January_14_2026.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/IRC_Proceedings_Wednesday_January_14_2026.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Wednesday, January 14,
2026⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Queen_Elizabeth⦈_


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now


    * Gemini_Links_15/01/2026:_"Ode_to_elinks",_envs.net_Pubnix_and_Downtime_at
      geminiprotocol.net
    * Over_at_Tux_Machines...


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⠍⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠀⣿⣿⣿⠿⠟⠓⢫⠯⠚⠳⠾⠶⢿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣧⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠉⣨⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⣿⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 858

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/Linuxiac_May_Have_Reverted_Back_to_LLM_Slop.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Linuxiac_May_Have_Reverted_Back_to_LLM_Slop.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Linuxiac May Have Reverted Back to LLM Slop
(Updated Same Day)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026,
updated Jan 15, 2026


Earlier this week we_were_alerted_that_Linuxiac_may_have_returned_to_state-of-
the-art_plagiarism. So we decided to check the latest two entries. This is the
latest:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNOME_48.8_Released_With_Bug_Fixes_and_Security_Updates⦈_


Two analysers we've used both deem this to be 100% LLM slop. Even a manual
check reveals something is amiss. Second from the top:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Nginx_Proxy_Manager,_a_popular_web-based_and_user-friendly
                reverse_proxy_management_interface_for_Nginx⦈_


We were under the impression that Bobby stopped_doing_this. Is he back off the
wagon? We've contacted him to be sure and will update if or when he gets back
to us. █


Update: 8 hours ago Bobby responded and did not address the issue.


    * The_Creator_of_Git_Probably_Doesn't_Know_How_to_Install_and_Deploy_Git
    * Coming_Soon:_Impact_With_EPO_Cocainegate


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⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⢀⠀⠀⠀⠸⠽⠯⠭⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠠⢧⠇⠣⠀⠀⠀⢘⢘⡛⠉⡃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⠀⢨⣨⣍⣉⡅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣷⢿⣷⣿⢷⡷⣿⢿⣿⣾⡿⠿⡿⡿⢿⣿⣶⣿⢿⢿⣷⣿⣿⡷⣿⣿⣿⠿⢿⣿⡾⡿⢷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣟⣟⣻⣻⣟⣻⣟⣻⣻⣻⣻⣛⣿⣿⣿⣿⣿⣿
⣿⠿⣿⣿⣿⣷⠾⡾⣿⣿⡾⣶⡷⣷⣿⣶⣿⢿⣿⣾⢶⡿⣿⣾⣷⣿⣿⣾⣶⣾⢷⣿⠿⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠶⢿⢾⡿⡿⢿⡿⣿⡿⣿⣷⢷⣿⣾⣿⣿⢿⡿⢾⢿⢿⣿⡾⣿⣿⢿⡾⣿⠿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡾⢿⢿⢿⢷⢾⣶⡷⣷⣾⠾⣷⢾⢿⣾⡿⣷⣾⣷⡶⢿⡾⡿⡿⠶⣿⣷⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣛⣛

                    ䷩ 𝚕𝚒𝚗𝚎 943

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/Over_at_Tux_Machines.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Jan 15, 2026


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Red_Hat_Gives_You_Less_and_Less_Over_Time [original]⠀⇛


           If the future of GNU/Linux is Software Freedom, then this
           future isn't Red Hat or IBM


   2. ⚓ Attacking_People_Accomplishes_Nothing [original]⠀⇛


           When people start attacking those who advocate sharing it's not
           hard to see who the aggressor really is


   3. ⚓ Publishing_Originals_is_Hard [original]⠀⇛


           Perhaps I underestimated how much time would be occupied or
           spent with a growing volume of news


   4. ⚓ Small/Mobile_Systems:_AOSP_(Android),_Raspberry_Pi,_and_RISC-V⠀⇛


           some hardware picks


   5. ⚓ Check_Point_Spreading_Fear_of_Linux,_Without_Explaining_the_Real
      Cause⠀⇛


           as usual from Check Point


   6. ⚓ GNU/Linux_Rose_to_All-Time_High_in_Bolivia_This_Year [original]⠀⇛


           Will it be over 5% by year's end?


      ⚓  New⠀⇛


   7. ⚓ GRUB_2.14_Released_with_EROFS,_Argon2_KDF,_and_Shim_Loader_Protocol
      Support⠀⇛


           GNU GRUB 2.14 has been released today as a major version for
           this popular multiboot boot loader that can be found on almost
           all of today’s GNU/Linux distributions and UNIX-like operating
           systems.


   8. ⚓ Wireshark_4.6.3_Released_with_Updated_Protocol_and_Capture_File
      Support⠀⇛


           Wireshark 4.6.3 has been released today as the third point
           release to the Wireshark 4.6 series of this popular network
           protocol analyzer, with support for new and updated capture
           file and protocol support.


   9. ⚓ Servers_and_Hi-Dee [original]⠀⇛


           Today, for the second day in a row, the server exceeds a
           million requests (this time by 8PM)


  10. ⚓ What_to_Use_Except_Ubuntu_and_Ubuntu-Based_Distros [original]⠀⇛


           There are many fine distros based on Debian and Devuan


  11. ⚓ GNU/Linux_and_BSD_Leftovers⠀⇛


           mostly GNU/Linux


  12. ⚓ Free,_Libre,_and_Open_Source_Software_Leftovers⠀⇛


           FOSS picks


  13. ⚓ Mozilla_Firefox:_Tooling_Announcements,_Developer_Experience,_and
      Firefox_Nightly⠀⇛


           Firefox news


  14. ⚓ Programming_Leftovers⠀⇛


           Development related picks, releases


  15. ⚓ Games:_Playing_Factorio_On_A_Floppy_Disk_Cluster,_Cooking_Pot_For_Doom,
      and_Vanilla_OS_vs._Bazzite⠀⇛


           GNU/Linux and other


  16. ⚓ Fedora_and_Red_Hat_Leftovers⠀⇛


           mostly from Red Hat's site


  17. ⚓ Debian:_Freexian_Collaborators_Outline,_30,000_FAIme_Jobs,_and_Debian
      Libre_Live_13.3.0⠀⇛


           3 updates from Debian teams/people


  18. ⚓ Canonical/Ubuntu:_‘Mass_Rebuild’_of_All_Archive_Packages,_Spring_Boot,
      'Debloated'_Ubuntu_for_a_Fee⠀⇛


           4 picks for today


  19. ⚓ Praises_of_Joplin_and_More⠀⇛


           Free software coverage right now


  20. ⚓ Early_Coverage_About_Upcoming_FOSDEM_2026⠀⇛


           FOSDEM 2026 about to begin


  21. ⚓ today's_howtos⠀⇛


           many howtos for this evening


  22. ⚓ Security_and_Microsoft_Zero-Days_Exploited⠀⇛


           as usual also


  23. ⚓ Android_Leftovers⠀⇛


           Is your Android Phone’s Volume Button Glitching? You’re not
           Alone, Google Says


  24. ⚓ Our_members_help_secure_the_future_of_a_free_society⠀⇛


           Three more days: that's how long we have before our deadline to
           reach our goal of welcoming 100 new FSF associate members


  25. ⚓ Oracle,_MySQL,_and_SQL_Server_Remain_the_World’s_Most_Popular
      Databases⠀⇛


           Relational databases continued to dominate enterprise and cloud
           workloads in 2025


  26. ⚓ Unraid_Plans_Internal_Boot_Support_and_Multiple_Arrays_for_2026⠀⇛


           Unraid’s 2026 plans include booting without USB flash drives


  27. ⚓ Free_and_Open_Source_Software⠀⇛


           This is free and open source software


  28. ⚓ KDE_Ni!_OS_–_Plasma_Login_Manager_teaser⠀⇛


           I’ve read somewhere that Fedora will be the first distribution
           to replace SDDM with Dave’s brand new Plasma Login Manager


  29. ⚓ KDE_Gear_26.04_release_schedule⠀⇛


           This is the release schedule the release team agreed on


  30. ⚓ Games:_"Games_For_Everyone",_Hytale,_Winnie's_Hole,_and_More⠀⇛


           9 stories from GamingOnLinux


  31. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


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


                          Span from 2026-01-08 to 2026-01-14
      2349 /n/2026/01/11/
           Orion_Browser_Takes_First_Step_Toward_Linux_Availability.shtml


      2341 /n/2026/01/11/
           I_replaced_Windows_with_Linux_and_everything_s_going_great.shtml


      2310 /n/2026/01/11/Free_and_Open_Source_Software.shtml


      2307 /n/2026/01/11/5_Windows_like_Linux_distros_you_should_try_out.shtml


      2295 /n/2026/01/11/Manjaro_Is_Arch_Linux_for_Newbies.shtml


      2275 /n/2026/01/11/
           Linux_made_my_old_PC_fast_again_and_it_hasn_t_slowed_down_since.shtml


    * IRC_Proceedings:_Wednesday,_January_14,_2026
    * Proton_Mail_compromise,_Hannah_Natanson_(Washington_Post)_police_raid
      &_Debian


⢠⡄⠀⠘⢃⠠⠶⠀⠁⢹⣷⠀⠀⠘⠛⣿⡿⠟⣶⣿⠻⠟⠉⠀⠀⢩⣶⣶⣾⣿⣯⣏⣹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣴⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀
⠛⠍⣡⠀⢸⣄⠀⠐⠀⠀⠀⠤⠚⠀⠀⠀⠂⣄⣹⣿⠢⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣇⠀
⠀⠚⠀⠀⢸⣿⠟⠀⠀⢠⣶⣦⡀⠀⢀⣸⠵⣿⣿⠿⣿⣿⣾⣤⣄⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⢀⣤⡀⠈⠩⠶⣠⡀⠘⡿⣽⣧⣤⣼⣀⠑⢸⣁⡀⠐⠿⠛⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿
⢁⠀⡀⠁⠀⠀⠀⠉⠁⣀⡶⠈⠛⣿⣿⠟⣸⡏⢽⢿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧⣿⣻⣡⣾⣯⠻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠈⠀⠘⠷⠀⢠⣤⠀⠀⠸⣗⣀⠸⢿⡑⡓⢈⠿⠚⠚⠉⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣤⣽⣿⣿⡟⠁⢾⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠙⠛⠋⠻⣿⣿⣿⣿⣿⣿⣿
⢠⠀⣠⡁⠀⠉⠀⠀⣦⡄⣿⣯⣤⣸⣿⣿⢿⣦⠄⣀⣾⣷⣴⡷⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⠋⠀⣽⣡⣴⣾⡿⣇⢹⢁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠋⠉⠛⠿⠿⢿
⠸⠿⣻⣿⣦⣶⣀⣬⠛⠛⠁⠉⠛⠛⣿⣤⠈⠉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡀⣀⡈⣍⠻⠑⣿⠅⠀⢹⣿⣿⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠆⠲⠸⠷⣿⣿⣿⣶⣄⣊⡉⠀⠙⠻⣷⡆⡀⠌⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣠⣍⣰⣿⣧⡁⡹⠁⢠⣿⣿⣿⡀⣴⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣶⣄⣰⣾⡄⠀⠀⠀⠀⠀⠀
⢸⣥⡄⡈⣡⠟⠻⡿⣯⣿⣿⣶⣦⠄⠐⠋⠹⠀⠀⢀⣴⢿⣷⣦⣩⣥⣹⣷⣼⣟⡿⣿⣿⣿⣽⣹⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡍⠀⢀⣹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣤⣤⠀⠀⠀
⣩⠌⠻⣿⣦⡠⠾⠀⣉⡬⣻⡿⠉⢣⣤⣿⣷⡆⠀⠀⠉⠀⢨⣡⣼⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⡟⡻⣿⣽⣿⣿⣿⣿⣿⣹⡿⠂⢸⣿⣿⡏⣗⣰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀
⢩⠀⡄⣿⣿⣿⣶⡀⠀⣘⠋⠁⣶⡟⢛⣽⣿⣷⣄⣳⠆⡀⢟⠿⣿⣿⣿⣿⣿⣿⡿⣏⣉⣺⣿⣃⣼⣧⣾⣿⣿⣿⠟⣻⣥⠁⠀⠀⣽⣿⢿⣷⣿⢭⢻⣹⣿⡿⢿⣿⣿⣿⣿⣟⡿⢷⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠙⠀⣤⢻⠟⢩⠿⠕⢾⣿⣿⡿⣿⣌⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣿⣿⣤⣄⣾⡿⠃⢀⠉⠀⠀⢀⣘⢄⢳⡬⠻⡿⣿⣿⡿⢻⣾⣡⢺⡿⣿⢏⢿⣿⣿⣿⣿⣿⣿
⡿⡐⠛⠁⢾⣠⣉⠀⠀⠀⠀⠐⢓⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣻⣿⢹⣿⡗⢋⣻⠟⣛⠟⣡⣾⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢡⣷⣶⡀⢿⡿⢙⣧⣅⠀⢺⣾⣿⣿⡟⣿⣿⣤⣿⡎⢈⡈⠟⢿⣿⣿⣿⡟
⠪⠀⣀⣈⢻⣿⣻⣿⠏⢠⣰⣀⣾⣿⣿⣿⣿⣱⣿⣿⡿⡿⣿⣫⣿⣷⣮⣨⡯⠛⣿⣯⡿⣰⣿⢫⡿⣿⣟⢿⣿⣿⣝⢻⣿⣿⣷⣆⡄⠀⣀⣤⠀⠢⣤⣿⣿⣗⢝⣾⠟⢿⠿⣿⣿⣿⣿⣿⣿⢁⡾⢁⣶⣾⣿⣿⣿⣷
⢺⣷⣿⣞⡿⣿⣛⣷⣾⠚⡟⡻⢛⠘⠛⣹⡏⢯⣿⣻⢿⣶⣭⣿⣿⣿⣿⣿⣾⢿⣿⣿⣷⣿⣡⡾⠒⡻⣿⣯⠘⣠⣾⣾⣿⠿⠿⠿⠤⠠⢉⡀⢠⣤⣿⣹⠟⠋⢥⣿⣇⠐⠞⣏⣿⣿⣿⣿⣿⣤⣷⣿⣿⣿⣿⣿⠿⠛
⢷⢂⠀⢐⣶⠟⠁⢻⡿⠚⡒⠉⣼⣿⡤⠀⠫⠾⠻⢁⣙⠚⠟⢡⠒⠒⡉⡅⡌⡻⢾⣿⣿⣿⣿⡇⢆⣿⣟⣛⣵⣿⣿⣿⣿⣧⡆⠀⠀⠈⢰⣿⠇⠨⢞⠁⠀⢠⣶⡟⡹⠇⠒⢀⣸⣇⣽⣽⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀
⠀⣄⠀⠘⢁⡀⡀⠀⠀⠸⣷⣶⣿⡟⢩⣴⣦⣾⡖⠀⠀⠀⠀⠈⠐⠀⠁⠁⠀⠉⠛⠛⠟⣽⣿⢊⠀⣿⣿⠟⠻⢿⡟⣬⣿⣏⠀⠀⠀⠀⢈⡗⢾⣤⡿⠀⣺⣿⣿⡆⠃⠀⠐⢿⣿⣤⠉⡒⢿⡿⡿⠟⡿⠿⣿⣇⣤⣀
⣶⠂⠀⠀⠈⠛⠇⠀⠀⠀⠈⠙⣿⠿⢿⠟⠻⣿⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⠛⠹⢿⡇⠀⠋⢸⣿⡿⣃⣀⡠⡚⠺⠃⠘⠃⢁⣼⠈⠉⢸⡅⡀⠀⠀⠘⣛⣿⢿⣿⡤⠛⢠⣤⠀⠀⢻⡿⣿⣿
⡿⡇⡀⠰⠐⠀⣆⠀⠻⠁⢀⠀⢉⡀⠿⡏⠀⡿⠇⠀⣄⠀⠀⠀⠀⠀⠀⠐⠢⠀⠤⠖⠀⠀⠀⢀⠀⠀⢐⣌⣠⣀⣡⣙⡄⣴⢺⣍⣀⣿⠆⠚⠁⠀⠀⣯⠀⠀⠀⠻⠇⠀⠀⢺⣿⠿⠋⢛⡿⢟⣼⣿⣆⣀⠠⠐⠅⠒
⣼⣿⣴⡶⠃⠈⠙⠀⣸⢶⢮⠀⣾⡅⠁⠁⠁⡠⡠⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠱⣾⡇⠀⠀⠀⠀⠀⢤⣹⠋⢹⣿⣿⣿⣷⣝⣯⣧⣿⣽⣷⣶⡠⠀⠺⠃⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⢻⣹⣁⣼⣿⣿⣷⣷⣿⠳⠄⠀
⠛⣿⣿⡇⡰⠀⠀⢀⣏⠃⣠⣄⡁⠀⠄⠀⠈⠛⢀⡀⠸⢆⠀⢌⠁⠀⠀⢀⡀⠀⠔⢠⠒⠀⠀⠀⠁⢐⠌⠛⠛⢀⣻⣿⣿⣿⣹⣿⡟⠻⢿⣿⣄⣲⣿⣾⣿⡿⠆⠀⠀⠀⣶⠂⠹⠛⠛⠿⠛⣳⣿⣿⣿⣿⣿⣷⣤⡄
⠊⠈⢛⠿⣿⣶⢀⣸⡙⠁⠛⣻⣿⣤⢀⣴⠀⠀⠰⡀⠉⣀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⡀⠈⠀⡀⠈⢩⣟⠿⠗⠚⢣⢴⡿⡝⣷⣹⣽⢿⣿⣧⠀⡤⢀⠀⠘⠂⠀⠀⠀⢀⣀⠀⠈⢛⣿⡿⠉⠙⢿⠁
⠀⠀⠈⠐⠁⠀⠀⢩⠁⢺⡆⠞⡟⢻⠯⣿⣿⠆⠈⢜⠦⢁⠄⣔⠀⠀⠀⠈⢥⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠂⡀⠀⠉⢙⣿⣯⠻⠋⡠⡏⢿⣿⣷⡀⠀⠀⠀⣺⣶⡶⠂⠈⢻⣄⠀⠿⠋⠓⠂⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠀⢾⠊⠐⣿⣿⣄⣀⠀⡀⠀⢹⡷⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠂⠵⣤⣤⣦⣠⣆⣄⣴⠎⠀⠀⠻⣆⠮⢿⣿⡿⠃⣼⣥⣅⢀⣝⠛⠧⠀⠀⠀⢻⣿⣇⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⣠⡀⠀⠀⠀⠄⠀⠀⣴⣾⢿⢯⡻⣑⡐⠇⠀⠈⠀⠀⢶⣿⣦⠄⡀⠀⠀⠀⠀⠀⡀⠹⢻⣿⣾⣯⠁⣿⣷⣵⣴⡶⠃⣸⣟⣋⣀⠀⠠⠀⠀⠀⢨⣷⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⢇⡀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1234

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/Proton_Mail_compromise_Hannah_Natanson_Washington_Post_police_r.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Proton_Mail_compromise_Hannah_Natanson_Washington_Post_police_r.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Proton Mail compromise, Hannah Natanson
(Washington Post) police raid & Debian⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


Reprinted with permission from Daniel_Pocock.


20:30 Wed, 14 Jan 2026


A few days ago, the JuristGate web site published a few words about how Debian
has_tried_to_use_Swiss_police_against_Proton_Mail.


Proton_Mail is based at CERN in Switzerland.


In recent years, activists have tried to reassure journalists and NGOs that
Proton_Mail is somehow safer than other web mail and cloud services.


When I saw news reports today about a police_raid on the home of Hannah
Natanson, a Washington Post journalist, I thought about the possibility that
more journalists are going to be prompted to migrate from Google Gmail to
Proton_Mail. They may simply be jumping from the frying pan and into the fire
(but not the Large Hadron Collider).


Anybody who has any doubts about where this is going only has to read_the
evidence_published_in_the_JuristGate_report.


For those thinking about using the Tor network to protect their privacy, it is
a good moment to read about the_falsification_of_"harassment"_claims_against_Dr
Jacob_Appelbaum.


Remember the Marion_County_Record. I was very fortunate to visit the community
in Marion, Kansas on the_first_anniversary_of_the_raid.


For decades, the American and German spy agencies operated a_fake_security
company_called_Crypto_AG_in_Switzerland. They used the Swiss company domicile
to obfuscate the real ownership of the crypto software. Many other companies
and countries were fooled and put their trust in it. Could Proton_Mail be
another example of the same trick? █


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Daniel_Pocock,_Marion_County_Record,_Kansas⦈_


    * Over_at_Tux_Machines...
    * Robert_X._Cringely_Has_Already_Explained_IBM's_Bullying_Culture_(Towards
      Its_Own_Staff)


⣿⣿⣿⣿⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣟⣏⣿⣿⢿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣶⣶⣦⣤⣤⣤⡀⢉⣉⠉⠻⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣷⢺⣿⣹⡿⢿⣿⣻⣿⣟⢿⣏⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣶⣶⣦
⣤⣤⣤⣤⣬⣍⣉⣙⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣽⣷⣾⢻⣿⣭⡿⢿⣻⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣬⣭⣍⣉⣛⣛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣬⣭⣭⣍⣛⣛⣛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣭⣭⣭⣝⣛⣛⣛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣯⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣭⣭⣭⣙⣛⣛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣭⣭⣭⣝⣛⣛⡛
⠛⠻⠭⠟⠛⢛⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⠛⠛⠋⠹⠿⠿⠿⢛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠁⠁⣩⣧⣍⠛⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⢟⠉⠉⣝⣷⡀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠓⠛⠛⠻⠿⠿⠟⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡸⠓⠚⠻⢿⣿⡏⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⠛⠛⠉⠹⠿⠿⠟⢻⣿⡿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠀⠀⠈⢄⡈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠂⠉⠁⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠂⠂⠀⠀⠀⠄⠠⠠⢄⣀⣀⣀⣀⢀⡀⣀⣰⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣟⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠚⠀⢷⠸⢷⣷⣄⠀⠀⠀⢲⣤⣀⣦⣤
⣿⣿⣾⣶⣶⣶⣦⣤⣤⣄⣀⡀⠀⣀⡀⢀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠤⠤⠴⠤⠔⣂⣀⣤⣤⡤⠬⠭⣽⡀⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣷⠀⢸⣿⣶⣶⣶⣶⣶⣴⣤⣤⣤⠄⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠐⠀⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣤⣤⣤⣠⣤⣤⣄⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠸⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠹⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣷⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⡾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1326

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

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    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Red_Hat_IBM_is_Driving_Away_Remaining_Fedora_Users.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Red Hat (IBM) is Driving Away Remaining
Fedora Users⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


Red Hat (IBM) has been busy trying to help Microsoft [1, 2] inflate the "AI"
bubble [1, 2, 3, 4] and sell Azure (back doors), kill_switches etc.


               🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_and_Red_Hat_(IBM)⦈_


I've not used Fedora since Moonshine. Back then I used it as a postdoc on my
work machine. That was in 2010 and 2011. Then I moved to another distro. Fedora
didn't work for me. Some packages in Fedora didn't work right and I wasted a
lot of time trying to force them to work. Back then, at least, Fedora was
considered a community.


Last month an avid Fedora user told me that he had dumped Fedora.


Why?


He was very clear about it.


He told me that Fedora's fascination was slop (which he called "AI") was the
reason.


"I saw your article about Torvalds's_*vibe_coding*," he said this week, "and I
just want to add that Linuxiac is in the same boat with the others, including
with the AI generated images. He never posted an actual screenshot of a Linux
desktop or software! He continues to mirror everything posted on 9to5Linux and
Phoronx with no shame. Just another bot..."


Call it "vibe" or whatever, LLMs produce slop and it's not of real value. As
for Linuxiac, I spoke to its editor after we had caught him using LLMs. He
didn't deny to me that he tried LLMs, but soon after that he appeared to have
stopped.


In our experience, people who experiment with slop give up at the end. They
realise they relied on nonsense for quantities at the expense of quality.


This was just_a_few_hours_ago:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Deny,_deny,_admit:_UK_police_used_Copilot_AI_“hallucination”
                         when_banning_football_fans⦈_


They'll probably abandon Microsoft "copilot", just like_Manchester_United_did.
Eventually, Microsoft's stock will fall. It's_a_lie,_its_"Value"_is_based_on
"False_Marketing" and false_claims_it'll_improve.


Bitcoin "value":


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


Microsoft "value":


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Market_cap_history_of_Microsoft_from_1996_to_2025:_4,000B+,
            Windows_market_share_~90%;_Windows_market_share_~30%⦈_


As for IBM and Fedora, two days ago we published: IBM_Stock_Compared_to
Bitcoin,_Fake_Articles_About_IBM_Promote_Myths_About_IBM


IBM has put its chips down. It chose losing cards.


By the way, the latest spin from Microsoft and Cheeto (whom_it_sponsored) is
that Microsoft is a "good neighbour" for sucking up lots of water and using up
all the electricity in neighbourhoods. The supine, corrupt (sometimes_bribed)
press is just parroting what Microsoft says about prices of electricity. Like
the Linux_Foundation, they totally invert the narrative by spreading deliberate
lies [1, 2]. █


    * Robert_X._Cringely_Has_Already_Explained_IBM's_Bullying_Culture_(Towards
      Its_Own_Staff)
    * Don't_Cry_for_Gaslighting_Media_in_a_Country_Which_Loathes_the_Press


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠩⠀⠀⠀⠀⠋⣽⣿⣿⣿⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠁⠀⠀⠀⠀⢿⣻⣯⡿⣿⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠚⣿⣿⣿⣿⣿⣿⣿⣿⠃⣔⠜⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠰⠀⠀⠀⠀⠀⠈⠁⣨⣞⡻⡁⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⡤⠏⠘⢿⣿⣿⡿⠋⠉⠠⠄⠊⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠈⣲⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢘⡿⠇⠀⠈⠀⠀⠀⠀⠀⣴⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢠⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣴⣶⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠓⢆⠀⠀⢀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⢤⠄⠀⢀⠀⠀⠀⠀⠀⣸⠀⠻⣿⠿⠃⠀⠈⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡏⡟⣿⡟⢠⠁⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠜⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡷⠃⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣶⢨⢤⠤⡄⡤⢄⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⡾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⠀⠀⠐⣁⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⠒⢺⢠⠭⡇⣿⠀⢸⠃⣿⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠈⠈⠙⠉⠉⠁⠀⠣⠈⠈⠉⠁⠈⠈⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⠟⠀⠀⠀⠀⣠⠂⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡟⠋⠹⠟⠀⠀⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠏⠀⠀⠀⣠⣾⠏⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⣉⡃⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣿⣅⣀⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣸⣶
⡿⠃⠀⠀⢀⣼⣿⡟⠀⠹⣿⣿⣦⣄⡀⠀⠉⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢘⠁⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⢀⡀⢻⣿⣿
⠁⠀⠀⣰⣿⡿⠛⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣶⣿⣿⣿⣿⡇⠀⣄⠄⠀⠁⠀⠐⠀⠀⠀⠀⠀⣰⣷⡄⠀⠀⠀⠀⠀⠀⠈⠅⠐⣿⣿
⡀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠿⠎⠉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠸⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣷⢰⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢘⠒⠃⠐⣒⣀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠛⠃⠀⠀⠳⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⠧⠀⠈⢡⣾⠠⣬⣼⣿⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠁⠀⠀⠀⠀⢿⡿⣿⣿⣟⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⣴⡜⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠠⠀⠀⠀⠀⠀⠈⠁⢻⠨⠜⡁⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠤⠋⠈⠿⣿⣿⣿⠋⠉⠡⠄⠈⠀⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠈⣲⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡷⠁⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢘⣿⠇⠀⠈⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢠⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣴⣶⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠓⢦⠀⠀⢀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⢤⠀⠀⢀⠀⠀⠀⠀⠀⢸⠁⠻⠿⠿⠃⠀⠈⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⡽⢹⡟⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠜⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠃⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣶⢨⢤⠤⡄⡤⢄⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⡾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⠀⢀⠀⠀⠰⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠁⢸⠁⣿⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠋⠉⠁⠀⠣⠈⠈⠉⠁⠈⠈⠁⠉⠜⠀⠀⠀⢀
⣿⣿⣿⠟⠀⠀⠀⠀⣠⠂⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡟⠋⠙⠟⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⠏⠀⠀⠀⣠⣾⠏⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣿⣅⣀⡀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣴
⡿⠃⠀⠀⢀⣴⣿⡟⠀⠹⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠁⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⡀⢺⣿⣿
⠁⠀⠀⣰⣿⡿⠛⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣿⡇⠀⣀⠄⠀⠁⠀⠐⠀⠀⠀⠀⠀⣰⢷⡄⠀⠀⠀⠀⠀⠀⠈⠅⠐⡿⡻
⡀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⠿⠿⠎⠉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣷⢰⣟⢐⣓⣀⡇⢰⣿⠀⣾⡆⢹⠀⣿⡇⣇⢘⠒⠃⠀⢒⣀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠻⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣾⣤⣿⠧⠀⠀⢡⣾⢠⣤⣤⣷⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⠁⠀⠀⠘⠏⣿⣿⣿⣿⣷⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⡟⣿⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠈⢿⣿⣿⣿⣿⣿⣿⣿⠏⣠⡘⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⠀⠀⠀⠀⠈⠁⡠⣌⣈⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢓⡤⠊⠈⢿⣿⣿⣿⠋⠉⠁⠄⠊⠀⠐⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣩⣾⣾⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⠃⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⠆⠀⠈⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⣶⣦⡀⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢅⠀⠀⢀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⠤⠀⠀⢀⢀⠀⠀⠀⠀⢰⠁⠻⣿⡿⠃⠀⠐⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡈⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⣽⢹⡿⠁⠎⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡔⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠃⠈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣶⢨⢤⠤⡄⡤⢄⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⡾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⢀⠀⠀⠐⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠀⢸⠁⣻⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠋⠉⠁⠀⠣⠈⠈⠉⠁⠈⠈⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡟⠀⠀⠀⠀⣠⠂⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠛⠉⠻⠟⠀⠀⠈⠀⠀⠨⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⣠⣾⠏⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⢉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣯⣄⣀⡠⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⡤
⡿⠃⠀⠀⢀⣴⣿⡟⠀⠹⣿⣿⣦⣄⡀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⡿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢾⣷
⠁⠀⠀⣠⣿⡿⠛⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠐⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣶⣿⣿⣿⣿⡆⠀⣀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠰⢖⡀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠿⠿
⡀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠿⠞⠉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠈⠱⡀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⣷⢸⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢘⠒⠃⠐⢒⣀⡄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠲⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣾⣤⣿⠦⠁⠈⢡⣾⠀⣤⣼⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠘⠏⣿⣿⣿⣿⣷⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⠈⠀⠀⠀⠀⠘⢿⢿⣿⣿⣿⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡙⢿⣿⣿⣿⣿⣿⣿⣿⠯⣤⡜⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⠀⠀⠀⠀⠈⠁⡊⡱⣯⠁⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡠⠎⠈⢿⣿⣿⣿⠋⠉⠁⠄⠊⠀⠐⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣥⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠁⠈⠁⠂⠀⠀⠀⠀⠀⠰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠸⣿⠆⠀⠈⠀⠀⠀⠀⠀⣴⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣰⣶⣦⡀⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⢄⠀⠀⢀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⠤⠀⠀⢀⠤⠀⠀⠀⠀⠰⠁⠻⣿⡿⠃⠀⠘⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⡈⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢱⠋⣿⠁⠌⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠔⠀⠀⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠞⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢤⠤⡄⡤⢄⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⡼⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⢀⠀⠀⠐⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠀⢸⠁⣻⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⠈⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠋⠉⠁⠀⠣⠈⠈⠉⠁⠈⠈⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⣠⠎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠛⠉⠛⠟⠀⠀⠈⠄⠀⠨⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠀⠀⠀⢀⣴⡟⣤⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⣉⠙⣉⠀⣉⣿⣿⣯⣄⣀⡴⠀⠀⢀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣼
⣿⠋⠀⠀⢀⣴⣿⡟⠀⠹⣿⣿⣦⣄⣀⠀⠉⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠁⠄⠀⣿⠀⠛⣿⣿⣿⣿⡿⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⠀⠀⠀⢀⠀⢘⣿⣿
⠁⠀⠀⣠⣾⣿⠛⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣶⣿⣿⣿⣿⡆⠀⣀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿
⡀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⠿⠿⠎⠉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠁⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⢰⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢐⠒⠃⠀⢒⣀⡄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠲⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣾⣤⣿⠥⠀⠀⢡⣾⠀⣤⣤⣿⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠘⠉⣿⣿⣿⣿⣷⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠈⠀⠀⠀⠀⠸⣿⢿⣿⣿⣾⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⢿⣿⣿⣿⣿⣿⣿⣿⠏⣠⡜⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢄⠀⠀⠀⠀⠀⠈⣠⡱⠉⠭⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠠⠊⠈⢿⣿⣿⣿⠋⠉⠁⠄⠈⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⠀⠁⡄⠀⠀⠀⠀⠀⠀⣮⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠃⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠰⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⠆⠀⠈⠀⠀⠀⠀⠀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⣶⣦⡀⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⢄⠀⠀⢀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⠤⡒⠀⢀⠤⠄⠀⠀⠀⠐⠁⠻⢿⡿⠃⠀⠈⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⡈⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢱⠃⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠔⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠞⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣶⢨⢤⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠴⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⡾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⢀⠀⠀⠐⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠁⢸⠁⣻⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⠄⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠋⠉⠁⠀⠣⠈⠈⠉⠁⠈⠈⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⣠⠎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠋⠉⠛⠟⠀⠀⠈⠀⠀⠨⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⢀⣴⡟⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⢉⣿⣿⣵⣄⣀⡴⠀⠀⢀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣰⣶
⣿⠋⠀⠀⢀⣴⣿⡟⠀⠹⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠁⠄⠀⣿⠀⠛⣿⣿⣿⣿⡿⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠁⠀⠀⣠⣾⣿⠛⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣷⣶⣿⣿⣿⣿⡆⠀⣀⠀⠐⠁⠀⠐⠀⠀⠀⠀⠀⢰⢫⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿⠻
⡀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⠿⣿⠿⠿⡧⣿⠿⠿⣿⠿⠿⠎⠉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣷⢸⣟⢐⣓⣀⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⢇⢐⠒⠂⠀⣒⣀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠛⠗⠘⠛⠚⠙⠃⠀⠀⠲⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣾⣤⣿⠦⠀⠀⢡⣾⢀⣤⣤⣿⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠁⠀⠀⠸⢉⣿⣿⣿⣿⣳⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠈⠀⠀⠀⠀⠸⣿⣛⡻⠻⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⣰⡎⢻⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠆⠀⠀⠀⠀⠀⠈⡨⠀⣨⡀⡀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠤⠊⠈⠿⣿⣿⣿⠋⠉⠁⠄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⠀⠁⡄⠀⠀⠀⠀⠀⠀⣨⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡷⠃⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⠆⠀⠈⠀⠀⠀⠀⠀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣰⣶⣦⡄⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⢄⠀⠀⢀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣩⣀⣤⠴⡢⠀⢠⠔⠀⠀⠀⠀⠀⠀⠹⢿⠿⠃⠀⠈⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡈⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢱⠃⣿⠃⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠜⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠎⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢤⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⡾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⢀⠀⠀⠐⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠀⢸⠁⣻⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠋⠉⠁⠀⠣⠈⠈⠉⠁⠈⠈⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡟⠁⠀⠀⠀⣠⠆⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⡏⠁⠀⠛⡟⠀⠀⠈⠄⠀⠨⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⢠⣼⡏⣤⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣥⣄⣠⡾⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣴
⣿⠃⠀⠀⢀⣴⣿⡟⠀⠹⣿⣷⣦⣄⡀⠀⠉⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⡿⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⢀⠀⢹⣿⣿
⠁⠀⠀⣠⣾⣿⠛⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣷⣶⣿⣿⣿⣿⡆⠀⣀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⣰⢼⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⢿⣿
⡀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠿⠎⠉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⢰⣟⢐⣓⣂⡇⢰⣿⠀⣶⡆⢹⠀⣾⡇⣇⢘⠒⠃⠐⢒⣀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠲⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⠧⠀⠀⢡⣾⢤⣤⣤⣿⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡋⠁⠀⠀⠘⠉⣿⣿⣿⣿⣶⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⠈⠀⠀⠀⠀⠸⣿⡿⣿⣿⢿⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡋⢻⣿⣿⣿⣿⣿⣿⣿⠿⢠⡆⠻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢆⠀⠀⠀⠀⠀⠀⡐⢁⣁⡀⠆⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠡⠞⠈⠿⢿⣿⣿⠏⠉⠁⠤⠀⠀⠈⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣀⠀⠁⠄⠀⠀⠀⠀⠀⠀⣴⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠸⣿⠆⠀⠈⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⢀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢰⣶⣶⡄⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢇⠀⠀⢀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣫⣤⣤⠴⡢⠀⢀⠔⠐⠀⠀⠀⠀⠁⠘⠿⠿⠇⠀⠈⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠃⡇⢿⡇⠰⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠐⠀⠀⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠗⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢤⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣼⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠈⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⢀⠀⠀⠰⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠍⡇⣿⠁⢸⠃⣿⢸⠒⢪⢸⢱⣰⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠋⠉⠁⠀⠣⠈⠈⠉⠁⠈⠀⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⢠⠎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⡏⠁⠈⠛⡟⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠀⠀⠀⢀⣴⡟⣤⣶⠀⠙⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣦⣄⣠⡾⠀⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣰⣤
⣿⠋⠀⠀⠀⣴⣿⡟⠀⠹⣿⣷⣦⣄⡀⠀⠉⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠁⠄⠀⣿⠀⠛⣿⣿⣿⣿⡿⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢿⡾
⠁⠀⠀⣠⣾⣿⠛⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣶⣿⣿⣿⣿⡇⠀⣀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⢢⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠞⡿
⣀⢀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⠿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠿⠆⠉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠈⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣷⢸⣟⢐⣓⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢘⠒⠊⠀⢒⣀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠛⠇⠘⠛⠚⠙⠃⠀⠀⠚⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣾⣤⣿⠥⠁⠈⢡⣾⠀⣠⣤⣿⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠸⢉⣿⣿⣿⣿⡷⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⡋⠹⣿⣿⣿⣿⣿⣿⣿⠟⢠⡆⠻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢄⠀⠀⠀⠀⠀⠈⠐⠹⠍⠁⠇⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠡⠚⠀⠿⣿⣿⣿⠏⠉⠁⠄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢁⡀⠀⠁⡄⠀⠀⠀⠀⠀⠀⣠⣷⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠋⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⠆⠀⠈⠀⠀⠀⠀⠀⣴⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠁⠀⢀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢰⣶⣶⡄⠀⠀⠀⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢅⠀⠀⢀⠈⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⠴⡲⠀⢀⠔⠂⠀⠀⠀⢀⠁⠘⢿⡿⠇⠀⠈⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⡈⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠃⡏⢿⡏⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⠀⠀⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠷⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢤⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠈⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⢀⠀⠀⠰⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠒⢺⢠⠍⡇⣿⠁⢸⠃⣿⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⠄⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠋⠉⠁⠀⠣⠈⠈⠉⠁⠈⠀⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⢠⡎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⡏⠁⠘⠻⡟⠀⠀⠠⠅⠀⢀⠂⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠀⠀⠀⢀⣴⡟⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⢉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣦⣀⣤⡾⠁⠀⠀⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶
⣿⠋⠀⠀⠀⣴⣿⡿⠁⠹⣿⣷⣦⣄⣀⠀⠈⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠁⠄⠀⣿⠀⠛⣿⣿⣿⣿⡿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣿⣿
⠃⠀⠀⣠⣾⣿⠿⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣿⣇⠀⣀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⢽⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠿⠵
⣀⢀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⠿⣿⠿⠿⡥⣿⠿⠿⣿⠿⠿⠖⠉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠈⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣷⢸⣟⢐⣓⣀⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢘⠒⠋⠐⢒⣀⡄⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠛⠗⠐⠛⠚⠙⠃⠀⠀⠺⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣾⣤⣿⠦⠁⠀⢡⣾⠀⣤⣤⣿⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠹⢹⣿⣿⣿⣿⣷⢀⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⠀⠀⠀⢸⣿⡿⣿⡿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡈⢻⣿⣿⣿⣿⣿⣿⡿⠟⢰⡎⠻⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡄⠀⠀⠀⠀⠀⠉⠀⢩⡝⠛⠆⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠰⠊⠀⠿⢿⣿⣿⠃⠈⠁⠤⠈⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢁⡀⠀⠁⡀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠁⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⠀⠀⠁⠀⠀⠀⠀⢀⣼⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠊⡁⠀⡀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡜⣰⣶⣶⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢅⠀⠀⠀⠈⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣟⣯⣤⣤⠔⡆⠀⠠⠖⠒⠀⠀⠀⢀⠀⠙⠿⠿⠃⠀⠈⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡈⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢡⠇⢿⡇⠰⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠔⠀⠀⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠗⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢤⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⡾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⢀⠀⠀⠰⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠀⢸⠃⣿⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠉⠉⠁⠈⠣⠉⠈⠉⠁⠈⠈⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⠟⠀⠀⠀⠀⣠⠆⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⡿⠉⠀⠉⣻⡟⠀⠀⠈⠀⠀⠠⠁⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⣠⣾⡏⣤⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⣉⠙⣉⠀⣉⣿⣷⣤⣤⣾⡟⠀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣴⣤
⡿⠃⠀⠀⢀⣴⣿⡟⠀⠹⣿⣷⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠁⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⢛
⠁⠀⠀⣰⣿⡿⠛⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣶⣿⣿⣿⣿⡆⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣭⡀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢿⠿
⡀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⡿⠿⠷⠊⢉⡤⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⣷⢸⣟⢐⣓⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⡇⢘⠒⠂⠐⣒⣀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠛⠗⠘⠛⠚⠙⠃⠀⠀⠲⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣾⣤⣿⠧⠀⠈⢥⣶⢠⣤⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡉⠁⠀⠀⠹⢹⣿⣿⣿⣿⣧⢠⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⢺⣿⡿⢿⣿⣟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠟⣈⢻⣿⣿⣿⣿⣿⣿⡿⠏⢴⡎⠻⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡄⠀⠀⠀⠀⠀⠉⠩⡻⡩⣸⠂⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠴⠋⠈⠻⠿⣿⣿⠃⠀⠀⠆⠉⠀⠈⠀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢁⡀⠀⠁⡀⠀⠀⠀⠀⠀⢙⣨⣶⡿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⠀⠀⠁⠀⠀⠀⠀⢀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠊⡀⠀⣀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣴⣿⣶⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⢅⠀⠀⠀⠈⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⠖⠝⠀⠠⠎⠂⠀⠀⠀⢠⠀⠙⠿⠿⠃⠀⠈⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡈⢀⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢡⠇⢿⡇⠘⠀⠀⠁⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠜⠀⠈⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠇⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢶⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠚⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⡾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⢀⠀⠀⠔⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢻⠒⢺⢠⠭⡇⣿⠁⢸⠁⣻⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠉⠉⠁⠈⠣⠉⠈⠉⠁⠈⠈⠁⠉⠜⠀⠀⠀⠠
⣿⣿⣿⠟⠀⠀⠀⠀⣠⠃⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⡯⠀⠈⢉⣻⠟⠀⠀⠈⠄⠀⠰⠁⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠋⠀⠀⠀⣠⣾⠏⣠⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⢉⡁⢸⣿⠀⠸⠿⠀⢸⣋⣉⠙⣉⠀⣉⣿⣶⣤⣴⣿⡟⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣤
⡿⠁⠀⠀⢀⣾⣿⡏⠀⠹⣿⣷⣦⣄⡀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠃⢻⡿⣿
⠀⠀⢀⣴⣿⡿⠛⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣶⣿⣿⣿⣿⡆⠀⣀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠈⠈⠘⠿⡾
⣀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⡿⠿⠷⠊⢉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣷⢸⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⡇⢘⠒⠃⠐⣒⡀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠛⠗⠘⠛⠚⠙⠃⠀⠀⠻⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣿⣤⣿⠧⠀⠈⣥⣶⢤⣬⣬⣷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠀⠀⠀⠸⢹⣿⣿⣿⣿⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠈⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⡄⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢀⢻⣿⣿⣿⣿⣿⣿⡿⠏⠰⡍⠹⠿⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡆⠀⠀⠀⠀⠀⠁⢜⢭⢉⢏⣃⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠔⠙⠈⠻⠿⡿⣿⡃⠀⠀⠖⠋⠀⠈⠀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⠀⠁⡄⠀⠀⠀⠀⠀⠐⣬⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⠀⠀⠉⠀⠀⠀⠀⢀⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡜⣰⣿⣷⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠓⠦⠀⠀⢀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣵⣦⣶⠒⠝⠀⠠⠊⠉⠁⠀⠀⠠⠀⠈⠿⠿⠃⠀⠈⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠄⠀⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡁⡇⢹⡇⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠌⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠛⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢶⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠴⠚⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⡾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠐⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⠀⠀⡘⣁⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠁⢸⠁⣻⢸⠒⢪⢸⢱⣼⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⠂⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⢿⣿⣿⣿⠀⠈⠀⡈⠈⠙⠉⠉⠁⠀⠣⠈⠈⠉⠁⠈⠀⠁⠉⠜⠀⠀⠀⢠
⣿⣿⣿⠟⠀⠀⠀⠀⣠⠃⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⠃⠀⠀⣨⣿⠟⠀⠀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⠋⠀⠀⠀⣠⣾⠏⣤⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡃⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣷⣶⣾⣿⡟⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣖⣾⣦
⡿⠃⠀⠀⢀⣾⣿⡟⠀⠹⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢘⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⠀⢀⣈⢹⣿⣿
⠁⠀⠀⣴⣿⡿⠛⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣶⣿⣿⣿⣿⡆⠀⣄⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⡸⣾⡄⠀⠀⠀⠀⠀⠀⠈⠀⠐⣿⣿
⣄⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⡿⠿⠿⠊⠡⡔⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠼⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋
⢿⠿⠿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣷⢰⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⡇⢘⠒⠃⠀⣒⣀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠟⠘⠛⠚⠙⠃⠀⠀⠙⠿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣿⣤⣿⠇⠀⠀⢡⣾⢠⣭⣼⡷⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠀⠀⠀⠸⢸⣿⣿⣿⣿⣷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠈⠀⠀⠀⠀⠸⣿⣟⣿⡿⣿⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⢻⣿⣿⣿⣿⣿⣿⡿⠏⠰⡇⠙⠿⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡆⠀⠀⠀⠀⠀⠀⣤⢨⠽⣿⣁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠕⠊⠀⠻⠿⣿⢿⡃⠀⠀⠒⠋⠀⠈⠀⣀⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⠀⠁⠄⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠸⣿⠆⠀⠈⠀⠀⠀⠀⢀⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢠⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣿⣿⣆⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠦⡀⠀⢀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⢦⣶⠖⡝⠀⠠⠊⠉⠀⠀⠀⠠⠄⠈⠻⠟⠃⠀⠀⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⡀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡃⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠻⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢪⢴⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠴⠘⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⠀⠀⠘⣁⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠀⢸⠁⣻⢸⠒⢪⢸⢱⣴⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡯⠀⠀⠀⠀⢀⠂⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⠀⠈⠀⡈⠈⠙⢉⠉⠁⠀⠣⠈⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠐
⣿⣿⣿⡟⠁⡀⠀⠀⣠⠎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⡿⡃⠀⠀⣨⣿⡟⠀⠀⣀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⠏⠀⠀⠀⣠⣾⡟⣤⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣶⣾⣿⡟⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿
⡿⠃⠀⠀⢀⣴⣿⡟⠀⠻⣿⣷⣦⣄⣀⠀⠉⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣹⣿⣿
⠁⠀⠀⣠⣿⣿⠋⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣶⣿⣿⣿⣿⡇⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿
⣄⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⠿⠿⠎⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠄⠼⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠊
⢿⠿⠿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⢰⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⡇⢘⠒⠃⠐⣒⣀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠘⠿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣬⣼⣧⣼⣿⠀⣬⣤⣾⣤⣿⠇⠀⠀⢡⣶⣤⣤⠴⠿⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠀⠀⠀⠸⢹⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠆⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢃⡛⣿⣿⣿⣿⣿⣿⡿⠟⠰⡦⠙⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣆⠀⠀⠀⠀⠀⠁⢈⡯⣏⠩⣅⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠔⠚⠈⠻⠿⣿⢿⡇⠀⠀⠒⠁⠀⠀⠀⢀⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣀⠀⡁⠄⠀⠀⠀⠀⠀⠀⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⠆⠀⠈⠀⠀⠀⠀⠀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⠀⢠⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⣿⣷⣆⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠦⡀⠀⢀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢧⣦⣶⠒⡝⠀⠀⠚⠈⠁⠀⠀⠠⠄⠈⠻⠿⠋⠀⠀⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡇⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢪⢴⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠚⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣼⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⠀⠀⠐⣁⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠀⢸⠃⣻⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡯⠀⠀⠀⠀⢀⠆⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⠁⠈⠀⡈⠈⠙⠋⠉⠁⠀⠣⠈⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠐
⣿⣿⣿⡟⠁⠀⠀⠀⣠⠎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣟⠀⠀⢀⣼⣿⡟⠀⠀⢈⠀⠀⠠⠁⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠟⠀⠀⠀⣠⣾⡟⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡃⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣶⣿⣿⡿⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⣶⣴
⣿⠋⠀⠀⢀⣴⣿⡟⠀⠹⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢘⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⡈⣙⣿⣿
⠁⠀⠀⣠⣿⣿⠋⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣶⣿⣿⣿⣿⡇⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠿⣿
⣄⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠿⠎⠁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠢⠀⠚
⢿⠿⠿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⢰⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢘⠒⠇⠀⣒⣀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠘⠿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⠇⠀⠀⢡⣾⢠⣬⣬⣿⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠀⠀⠀⠸⢹⣿⣿⣿⣿⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠈⠀⠀⠀⠀⠸⡿⣿⣿⢛⣹⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣍⢻⣿⣿⣿⣿⣿⣿⡿⠟⠰⡧⠹⠿⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡆⠀⠀⠀⠀⠀⠁⢘⠘⢴⣝⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠔⠚⠀⠻⠿⣿⣿⡋⠀⠀⠖⠈⠀⠈⠀⢀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣀⠀⠁⡄⠀⠀⠀⠀⠀⠀⣧⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠸⣿⠆⠀⠉⠀⠀⠀⠀⠀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⠀⢀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢰⣿⣷⡆⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠦⠀⠀⢀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣶⠒⡝⠀⠠⠊⠈⠀⠀⠀⠠⠄⠘⠻⠿⠃⠀⠀⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡃⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡜⠀⠀⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢴⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⠀⠀⠐⣁⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠀⢸⠃⣿⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡯⠀⠀⠀⠀⢀⠂⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠋⠉⠁⠀⠣⠈⠈⠉⠁⠈⠀⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡟⠀⠀⠀⠀⣠⠎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣇⠀⠀⣠⣽⣿⡟⠀⠀⠈⠀⠀⠠⠁⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⣠⣾⡟⣤⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣷⣾⣿⣿⡟⠀⠀⢀⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶
⡿⠃⠀⠀⢀⣼⣿⡟⠀⠹⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⢀⠀⣙⣿⣿
⠁⠀⠀⣰⣿⡿⠋⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣾⣿⣿⣿⣿⡆⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣄⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠿⠊⠁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠁⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⢿⠿⠿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⢰⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢐⠒⠃⠐⣒⣀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠙⢿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⠇⠀⠀⢡⣾⢤⣤⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠀⠀⠀⠹⢹⣿⣿⣿⣿⡧⢠⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢺⣿⡿⣿⣿⣿⡄⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣃⢻⣿⣿⣿⣿⣿⣿⡿⠟⠰⡎⠻⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡄⠀⠀⠀⠀⠀⠁⠝⢐⠿⠳⡀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠴⠛⠈⠻⠿⣿⣿⡃⠀⠀⠖⠉⠀⠈⠀⢀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⢉⣮⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⣿⠀⠀⠁⠀⠀⠀⠀⢀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠜⢰⣿⣷⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⢆⠀⠀⢀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣶⠒⠝⠀⠠⠊⠉⠀⠀⢀⠠⠀⠘⠿⠿⠃⠀⠈⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡈⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡡⡇⢻⡇⠈⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡜⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢴⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⢀⠀⠀⠐⣁⠀⠀⡠⣀⢀⣀⣀⢀⡀⠈⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠀⢸⠃⣿⢸⠒⢪⢸⢱⣼⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⠂⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠉⠉⠁⠀⠣⠈⠈⠉⠁⠈⠈⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡟⠁⠀⠀⠀⣠⠆⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣿⡁⠀⢀⣴⣿⣿⡟⠀⠀⠨⠀⠀⠠⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⣠⣾⡟⣤⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⣉⠙⣉⠀⣉⣿⣿⣿⣿⣿⡟⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣼⣿
⡿⠃⠀⠀⢀⣴⣿⡟⠀⠹⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢘⠁⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⣁⢹⣿⣿
⠁⠀⠀⣠⣿⡿⠓⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣿⡆⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⢿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿
⣀⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⠿⠿⠊⠡⡤⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠰⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙
⢿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⢰⣿⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⠅⢘⠒⠃⠐⣒⣀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠙⢿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣾⣤⣿⠧⠀⠀⢡⣾⠠⣬⣬⣷⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠻⢹⣿⣿⣿⣿⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⡻⢛⣿⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡒⠻⣿⣿⣿⣿⣿⣿⡿⠏⠰⡎⠻⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡄⠀⠀⠀⠀⠀⠁⠜⠢⢌⢠⡆⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠵⠚⠈⠻⠿⣿⣿⡃⠀⠀⠆⠉⠀⠈⠀⢀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⢐⣵⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⠀⠀⠁⠀⠀⠀⠀⢀⣾⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡜⢰⣿⣷⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⢆⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⡶⠒⠝⠀⡠⠊⠉⠀⠀⠀⠠⠀⠘⠿⠿⠃⠀⠈⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⡈⢠⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡁⠇⢻⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡜⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠓⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢴⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⢀⠀⠀⠐⣁⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⠒⢺⢠⠭⡇⣿⠀⢸⠁⣻⢸⠒⢪⢸⢱⡼⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢿⣿⣿⣿⠁⠈⠀⠈⠈⠙⠉⠉⠁⠀⠣⠈⠈⠉⠉⠈⠈⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡟⠁⠀⠀⠀⣠⠆⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣟⡀⠀⢀⣴⣿⣿⡟⠀⠀⠈⠀⠀⠰⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⣠⣾⡟⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⢉⡁⢸⣿⠀⠸⠿⠀⢸⣋⣉⠙⣉⠀⣉⣿⣿⣿⣿⣿⡟⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡦⡤
⣿⠋⠀⠀⢀⣴⣿⡟⠀⠹⣿⣷⣦⣄⣀⠀⠉⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠘⠀⠀⠀⠀⠀⠀⣀⡁⢐⣷⣛
⠁⠀⠀⣠⣿⣿⠛⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣷⣶⣿⣿⣿⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢫⡄⠀⠀⠀⠀⠀⠀⠈⠄⠐⡟⠹
⣀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠿⠊⠁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣷⢰⣟⢐⣓⣀⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⠇⢐⠒⠃⠀⣒⡀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠙⢷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣾⣤⣿⠧⠀⠀⢡⣾⠠⣤⣤⣷⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠉⠀⠀⠀⠏⣿⣿⣿⣿⣿⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⡀⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⡧⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣃⢻⣿⣿⣿⣿⣿⣿⡿⠏⢰⡎⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠰⡀⠀⠀⠀⠀⠀⢁⢷⡿⣽⢍⡀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠵⠛⠈⠻⠿⣿⣿⡏⠀⠀⠖⠈⠀⠈⠀⢀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⣀⠀⠈⠠⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⠀⠀⠁⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠋⠀⠀⡀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⡜⢰⣿⣶⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢅⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⣧⣦⡶⠚⠍⠀⠐⠊⠉⠀⠀⢀⡡⠀⠘⠿⠿⠃⠀⠈⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⡀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡡⠃⢻⡇⠘⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠜⠀⠈⠻⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣏⣉⠖⣤⣠⣠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢴⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠴⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠈⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⢀⠀⠀⠖⣁⠀⠀⡠⣀⢀⣀⣀⢀⡀⢀⡀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠒⢺⢠⠭⡇⣿⠁⢸⠃⣿⢸⠒⢪⢸⣱⡼⣿⢘⡆⠀⠀⢀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠿⢿⣿⣿⣿⠁⠈⠀⠈⠈⢛⠉⠉⠁⠀⠣⠉⠈⠉⠁⠈⠁⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡟⠁⠀⠀⠀⣠⠎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣃⡀⠀⣠⣾⣿⣿⡟⠀⠀⠈⠀⠀⠒⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⢠⣼⡟⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡃⢸⣿⠀⠸⠿⠀⢸⣋⣉⠙⣉⠀⣉⣿⣿⣿⣿⣿⡟⠀⠀⢰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣼
⣿⠋⠀⠀⢀⣴⣿⡟⠀⠹⣿⣷⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢘⠁⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⡀⢉⢻⣿⣿
⠁⠀⠀⣠⣿⣿⠛⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⣿⡆⢀⣀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⣼⣥⠀⠀⠀⠀⠀⠀⠀⠙⠀⠐⣿⣿
⣀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⠿⠷⠊⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⢰⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢘⠒⠃⠀⣒⣀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠺⢷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣿⣤⣿⠧⠀⠈⢡⣾⢠⣩⣼⣧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠈⡏⣿⣿⣿⣿⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠂⠀⠀⠀⠀⣿⣿⢿⣿⣿⣢⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣃⡻⣿⣿⣿⣿⣿⣿⡿⠟⢰⡦⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⠀⠀⠀⠀⠀⠈⠠⡡⡤⣇⣓⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠵⠛⠈⠻⠿⣿⣿⡏⠀⠀⠤⠈⠀⠈⠀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢀⠀⠈⢠⠀⠀⠀⠀⠀⠈⣮⣷⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⡷⠀⠈⠁⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠊⡀⠀⡀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡼⢰⣿⣶⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢅⠀⠀⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⡵⣶⡶⠚⠏⠀⠔⠛⠁⠀⠀⢀⡠⠀⠘⠿⠿⠇⠀⠈⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡡⠇⢻⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠄⠀⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣤⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢴⠤⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠴⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⢀⠀⠀⠂⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠒⢺⢠⠭⡇⣿⠁⢸⠁⣻⢸⠒⢪⢸⢱⡿⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⠄⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⠿⣿⣿⣿⣿⠃⠈⠀⠈⠈⠛⠉⠉⠁⠀⠣⠉⠈⠉⠁⠈⠀⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⣠⠎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣃⠀⢀⣴⣾⣿⣿⡟⠀⠀⠨⠀⠀⡄⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠏⠀⠀⠀⢠⣾⡟⣤⣴⡀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣿⣿⣿⠟⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣦⣦
⣿⠋⠀⠀⢀⣴⣿⡟⠀⠹⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢘⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⠿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⢹⣿⡿
⠁⠀⠀⣠⣾⣿⠋⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣾⣿⣿⣿⣿⠄⢀⣀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⡿⣿
⣀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠷⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣷⢸⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⡇⢘⠒⠃⠀⣒⣀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠛⠗⠘⠛⠚⠙⠃⠀⠀⠚⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣿⣤⣿⠧⠀⠈⢡⣾⢠⣬⣤⣇⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⢸⢹⣿⣿⣿⣿⡆⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠀⠀⠀⢺⣿⣿⠿⢿⢣⡌⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⡻⣿⣿⣿⣿⣿⣿⡿⠟⢠⡦⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⡄⠀⠀⠀⠀⠀⠋⢙⡨⡀⠠⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠵⠘⠀⠻⠿⣿⣿⡏⠀⠀⠤⠀⠁⠈⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠉⡄⠀⠀⠀⠀⠀⢰⣵⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⠃⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⡆⠀⠑⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢱⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠏⠀⢀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡘⢰⣾⣶⣄⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣅⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⡵⣶⡶⢊⠋⠀⠐⠉⠁⠀⠀⣀⡠⠇⠘⠿⠿⠏⠀⠀⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢠⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡰⠁⢿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠆⠘⠿⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣏⣉⡆⣠⣠⣠⠄⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢴⠦⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣼⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣂⠀⢀⠀⠰⠂⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢺⢠⠭⡇⣿⠁⢸⠁⣽⢸⠒⢪⣸⢳⡸⣿⠈⡆⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠄⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠹⠿⣿⣿⣿⣿⡟⠉⠀⠈⠨⠋⠉⠉⠀⠈⠣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⣠⡎⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠿⣄⠀⣠⣾⣿⣿⣿⡟⠀⠀⠬⠀⢠⠊⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠀⠀⠀⢀⣴⡟⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣿⣿⡿⠟⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡤⡢⣠⣆⣠
⣿⠋⠀⠀⢀⣴⣿⡿⠁⠹⣿⣷⣦⣄⡀⠀⠉⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⠇⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣀⡟⠃⢘⣟⣿
⠁⠀⠀⣠⣾⣿⠛⠁⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣶⣿⣿⣿⣷⠀⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠀⠀⠟⣋
⣀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⢸⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢈⠒⠃⠐⢒⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠛⠗⠘⠛⠚⠙⠃⠀⠀⠚⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣿⣤⣿⠧⠁⠀⢡⣾⠀⣤⣬⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠝⣿⣿⣿⣿⣿⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡹⣿⣿⣿⣿⣿⣿⡿⠿⢰⡦⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⡀⠀⠀⠀⠀⠈⢙⣿⢟⠫⡫⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡱⠜⠁⠻⠿⣿⣿⡏⠈⠁⠤⠀⠁⠈⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠡⠀⠀⠀⠀⠀⠈⣫⣶⡟⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠋⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣿⠀⠀⠃⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢑⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠇⠀⡀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡸⢰⣶⣶⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⡷⣶⡶⢋⠋⠀⠔⠛⠀⠀⠀⣀⣠⠇⠘⠿⠿⠟⠀⠀⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡸⠃⢻⠇⠈⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠹⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣏⣉⡆⣠⣠⣠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢴⠦⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢀⠀⠔⠂⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢺⢠⠭⡇⣿⠁⢸⠁⣿⢸⠒⣪⢸⢳⡸⣟⠈⡆⠀⠀⠀
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠄⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠹⠻⣿⣿⣿⣿⡿⠉⠀⠈⠸⠉⠉⠉⠀⠈⠣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⢠⡞⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⡿⢿⣿⠿⢿⣿⣿⣿⣿⠯⣀⣀⣠⣾⣿⣿⣿⠟⠁⠠⠥⠀⠐⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠀⠀⠀⢀⣴⡿⣤⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡃⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣿⣿⡿⠋⠀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡠⡀⢀⣠⣤
⣿⠋⠀⠀⠀⣴⣿⡿⠁⠹⣿⣿⣦⣄⡀⠀⠉⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣾⡗⠒⢲⣾⡿
⠃⠀⠀⣠⣾⣿⠏⠃⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣶⣿⣿⣿⡇⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⢿⡟⠁⠈⢿⠛
⣀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠿⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣷⢸⣟⢐⣓⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣧⢘⠒⠃⠐⢒⡀⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠛⠗⠘⠛⠚⠙⠃⠀⠀⠘⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⠧⠁⠈⢡⣾⠀⣤⣴⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠘⢻⣿⣿⣿⡇⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⣿⣿⣿⡿⣧⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢇⠻⣿⣿⣿⣿⣿⣿⣿⡿⢠⣦⠛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠀⠀⠀⠀⠘⢙⣿⡧⢉⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡣⠜⠁⠹⣿⣿⣿⡟⠉⠉⠤⠐⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⡃⠀⠀⠀⠀⠀⠘⣿⡾⠋⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠊⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⡆⠁⠃⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡅⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢰⢠⣶⣶⣄⠀⠀⠀⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⡿⡷⣶⡖⠫⠃⠀⠞⠋⠀⠀⣀⣀⣠⠇⠘⢿⣿⠟⠀⠀⠃⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣰⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢸⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢻⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢠⠦⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠇⠈⠆⠓⠔⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⢀⠠⠂⠀⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⡀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠒⢺⢸⠭⡇⣿⠁⢸⠁⢹⢸⠒⢫⢸⢱⡰⣷⢸⡇⠀⠀⠀
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⡀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠛⢿⣿⣿⣿⣿⣿⠋⠀⢨⠌⠉⠉⠈⠀⠈⠣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠁⠀⠀⠀
⣿⣿⣿⡿⠃⠀⠀⠀⢀⡔⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠥⣀⣀⣴⣿⣿⣿⣿⠟⠁⡰⠅⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠁⠀⠀⢀⣴⡿⣥⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣿⡿⠛⠁⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⡀⢀⣤⣤
⣿⠟⠀⠀⠀⣠⣾⣿⠃⠹⣿⣷⣦⣄⣀⠀⠈⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⡇⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠓⠘⢿⡿
⠋⠀⠀⢠⣾⣿⠿⠃⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⠝⠁⠀⢼⠹
⣀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣷⢰⣟⢐⣓⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣧⢘⠒⠊⠀⢀⠀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠰⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⡥⠁⠈⢡⣾⡀⣤⣄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠻⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠠⣿⣿⣿⡷⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠏⠻⣿⣿⣿⣿⣿⣿⣿⡿⢀⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠛⢻⣿⣷⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡣⠜⠁⠻⣿⣿⣿⡟⠉⠉⢤⠐⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠀⠀⠃⠀⠀⠀⠀⠀⢻⣿⠟⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠊⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣷⠀⠘⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⢰⢠⣶⣦⡄⠀⠀⠀⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠖⡹⠁⠠⠞⠃⠀⠀⣀⣀⡀⠇⠘⢿⣿⠟⠀⠀⠂⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠁⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⢸⠈⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠐⣿⡯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢠⠦⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠇⠈⠆⠓⠐⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢀⠀⢀⡴⠀⠀⣀⠀⠀⡠⢀⢀⣀⣀⢀⡀⠀⡀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢺⢨⠭⡇⣿⠁⢸⠁⣼⢸⠒⢪⢸⢱⡰⣿⢸⡇⠀⠀⠀
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⡀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠙⠻⢿⣿⣿⣿⣿⣿⠋⠀⡨⠈⠉⠉⠈⠀⠈⠣⠉⠈⠉⠁⠈⠀⠁⠉⠜⠁⠀⠀⠀
⣿⣿⣿⡿⠃⠀⠀⠀⢀⡔⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿⠄⣀⣀⣾⣿⣿⣿⣿⠟⠁⡴⠅⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠁⠀⠀⢀⣴⡿⣥⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⢉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣿⡟⠛⠁⡠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⣀⠀⣀⣀⡠
⣿⠏⠀⠀⠀⣠⣿⣿⠃⠹⣿⣷⣦⣄⡀⠀⠉⠀⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⠃⢀⠔⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡟⠈⢳⣻⠛
⠃⠀⠀⢀⣾⣿⠿⠃⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣶⣿⣿⣿⠀⠀⠀⠀⠀⢶⠏⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠐⢿⣿⣿⡝⠀⠈⢺⢻
⡀⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⠦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣷⢸⣟⢐⣛⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⣇⢘⠒⠇⠀⠀⢀⣲⠂⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠙⠗⠘⠛⠚⠙⠃⠀⠀⠰⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣿⣤⣿⣧⠀⠈⢥⣶⢀⣥⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠃⠼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣽⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠹⣿⣿⣿⣿⣿⣿⣿⡿⢁⣤⠺⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠹⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡣⠔⠁⠹⣿⣿⣿⡟⠉⠉⢠⠐⠃⠀⠂⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠂⠀⠀⠀⠀⠀⢸⣿⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠀⠀⠀⠀⠀⠈⠀⠁⠂⠀⠀⠀⠀⠀⠀⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣶⡄⠁⠆⠀⠀⠀⢰⡿⢁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠩⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⡁⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠰⢠⣶⣦⡄⠀⠀⠀⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠆⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⣿⣿⣿⣿⣿⣿⡿⡷⣷⡟⢩⠃⠀⢾⠏⠀⠀⢤⣤⠀⢀⡇⠸⢿⣿⡟⠀⠀⠂⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣇⠃⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠍⠁⠀⠀⠀⠀⡀⠀⣏⣉⠆⣠⣠⣀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢰⠦⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠑⠐⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⠀⣠⠀⠀⠀⠀⠀⠠⡤⣀⢀⣀⣀⢀⡀⠀⣀⢤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⠒⢺⢨⠭⡇⣿⡀⢹⠁⢹⢸⠒⢪⢸⢱⡰⣿⢸⡇⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⡄⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠛⢿⣿⣿⣿⣿⣿⣿⡝⢰⠼⠊⠉⠉⠉⠁⠈⠣⠉⠈⠉⠁⠈⠀⠁⠉⠜⠁⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⢀⡞⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣥⠀⣀⣴⣿⣿⣿⣿⣿⠟⢋⡥⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠀⠀⠀⢀⣴⡿⣡⣴⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣿⠟⠛⠁⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⠋⠀⠀⠀⣴⣿⣿⠁⠹⣿⣷⣦⣄⣀⠀⠉⠁⣀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⢾⣷⠶⠐⠋⠸⠛
⠁⠀⠀⣠⣾⣿⠟⠃⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣷⣶⣿⣿⠇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣟⡿⠆⠀⢑⡠⢉
⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣦⠀⠂⠐⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠉⠉
⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⣿⢰⣿⢐⣓⣂⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⠇⣘⠒⠂⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠻⠟⠛⠇⠘⠛⠚⠙⠃⠀⠀⣴⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣿⣤⣿⡧⠀⠈⣥⡆⢠⡀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁⠾⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠁⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠹⣿⣿⣿⣿⣿⣿⣿⣿⠡⣤⠚⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀⢻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡣⠔⠃⠹⢿⣿⣿⡿⠉⠉⢠⠴⠊⠀⠂⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠆⠀⠀⠀⠀⠀⣼⠟⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠁⠉⠂⠀⠀⠀⠀⠀⠀⣴⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣦⡀⠆⠆⠀⠀⠀⣾⠋⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣟⠛⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⠃⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣀⡄⠀⢀⡤⠖⠀⠀⠀⠀⠀⢰⢀⣴⣦⣄⠀⠀⠀⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠂⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⣿⣿⣿⣿⣿⣿⡟⡟⣿⠏⠑⠁⠀⢻⠃⠀⠠⠤⠦⠀⢀⡇⠘⢿⣿⡿⠀⠀⠒⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⡾⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣷⢨⢠⠧⡄⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠃⢈⠂⠑⠔⠘⠂⠃⠀⠀⠀⠀⠀⢐⠄⠀⠀
⣿⣿⣿⣿⣼⣾⣾⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⠀⣀⠀⠀⠀⢀⡤⠀⡠⢀⢀⣀⣀⢀⡀⠀⣀⢤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢺⢨⠭⣇⣿⠁⢸⠁⢸⢸⠒⢪⢸⢱⡸⣿⢸⡇⠀⠀⠀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⡄⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣤⠞⠈⠉⠋⠉⠁⠀⠣⠈⠈⠉⠉⠈⠀⠁⠉⠜⠁⠀⠀⠀
⣿⣿⣿⡿⠁⠀⠀⠀⢀⡾⠀⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣄⠀⣠⣾⣿⣿⣿⣿⣿⡿⠛⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠀⠀⠀⢀⣴⣿⣥⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣿⡟⠛⠋⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⢀⣤
⡿⠋⠀⠀⠀⣴⣿⣿⠃⠹⣿⣷⣦⣀⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠁⠄⠀⣿⠀⠛⣿⣿⠥⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣴⣷⣧⠶⠌⣼⠿⣿
⠁⠀⠀⣠⣾⣿⡟⠋⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠂⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣷⣶⣿⡟⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠆⠀⢻⣟⣝
⡀⢀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣦⠤⠀⠲⠖⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠠⠂
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⣷⢸⣟⢐⣓⣀⡇⢰⣿⠀⣾⡆⢹⠀⣾⡇⠧⣘⠒⠊⠐⢀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠛⠻⠟⠛⠟⠘⠛⠚⠙⠃⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣾⣤⣿⡧⠀⢨⣥⡄⢦⡈⢼⡆⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠛⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠁⠀⠀⠌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⢿⣿⣿⣿⣿⣿⣿⣿⡏⣠⡔⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠇⠚⠈⠻⡿⣿⣿⠏⠉⠁⡤⠞⠁⠐⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⡄⠀⠀⠀⠀⢀⠼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠈⠑⠂⠀⠀⠀⠀⠀⢠⣾⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣄⠀⡠⡀⠀⠀⣼⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⡿⠂⠀⠀⠀⢠⡯⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⡵⡶⠂⣠⣾⠉⠀⣀⡀⠀⠀⠀⠀⡆⣴⣶⣤⡀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢻⡿⠸⠀⠀⢿⠃⠀⠀⢩⠉⠁⠀⠀⣸⠀⢿⣿⣿⠇⠀⠐⠂⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣏⠀⠇⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⢪⣠⠾⡅⡤⢤⠤⣄⣠⠤⢀⠤⣄⢼⢵⠄⠀⢀⠀⠠⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⠀⡀⢄⠡⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⡸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⡘⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⢀⠀⢀⠆⠀⠀⠀⡠⢀⢀⣀⣀⢀⡀⠀⣀⢤⠀⠂⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡒⢺⢨⠭⡇⣿⠀⢰⠁⢸⢸⠒⢪⢸⢱⡸⣿⢘⡇⠀⠀⠀
⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢠⠂⢀⡈⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣟⡙⠛⠈⠉⠉⠈⠀⠈⠣⠈⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⡿⠃⠀⠀⠀⢀⣴⠏⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣥⣀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⡛⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠁⠀⠀⢀⣴⣿⣿⣶⠀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣉⡉⠙⣉⠀⣉⣿⡿⠿⠟⠉⠉⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⣠
⣿⠋⠀⠀⠀⣰⣿⣿⣿⠻⣿⣷⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠛⠃⢸⣿⠀⢰⣶⠀⢘⠁⠄⠀⣿⠀⠛⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠷⠶⢿⣿⣿
⠁⠀⠀⣠⣾⣿⣿⠟⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢠⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣷⣃⠄⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣷⠠⠀⢻⣿⣿
⡀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡶⠿⢿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠉⠀⠀⠘⢻⢯
⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣿⢸⣟⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣾⡇⢧⣐⠓⠈⠐⢂⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠛⠻⠟⠛⠟⠘⠛⠚⠙⠃⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣿⣤⣿⡧⠀⢬⣥⣀⣄⠩⣼⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⣀⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡻⣿⣿⣿⣿⣿⣿⣿⡿⢤⣤⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠉⠁⠙⠿⣿⣿⡟⠉⠉⣤⠶⠋⠐⠛⠒⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⡀⠀⠀⠀⠀⣁⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠀⠀⠀⠀⠀⠀⣶⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣀⠀⢠⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⡿⠀⠀⠀⠀⣼⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠁⢰⡿⠋⠀⠀⠶⠄⠀⠀⠀⠀⡰⣠⣶⣤⡀⠀⠀⠀⠈⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣿⣿⣿⣿⣿⡟⣽⠃⠃⠀⠸⡇⠀⠀⠀⠠⠄⡐⠀⠀⣸⠁⢿⣿⣿⠇⠀⠐⠂⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⠉⠂⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣤⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠿⠛⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠂⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡅⠀⠀⠀⠀⠠⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢻⣤⠼⡅⡤⢤⠤⡄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⢀⠀⡹⣥⢇⠄⠀
⣿⣿⣿⣿⣼⣾⣾⡼⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⢸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⢀⢀⠆⠀⠀⠀⠀⡠⢀⢀⣀⣀⢀⡀⠀⣀⢤⠉⠧⡂⠀
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣺⢨⠭⡇⣯⠀⢰⠁⢸⢸⠒⢪⢸⢱⡸⣿⢘⡇⠀⠀⠀
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢠⡞⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠘⠛⢿⣿⣿⣿⣿⣿⣿⣟⠻⠟⠋⠈⠉⠉⠈⠀⠀⠣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠂⠄
⣿⣿⣿⡿⠃⠀⠀⠀⢀⣴⡿⢀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⣿⡿⢿⣿⠿⢿⣿⠿⢿⣿⣿⣄⣀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠁⠀⠀⢀⣴⣿⣿⣷⡀⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣉⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⣿⣟⡛⠛⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣌⡘⣇⠀⠢⣅⣠⣤⣡
⣿⠋⠀⠀⠀⣰⣿⣿⣿⡿⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠃⢸⣿⠀⢰⣶⠀⢘⠀⠄⠀⣿⠀⠛⠟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣟⣽⣿⣿⣿
⠁⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠉⠛⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢰⡄⠰⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣶⣯⣴⡂⢀⣄⣀⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⢄⢸⣿⣿⣿
⣀⢀⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠸⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡿⠿⢿⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠃⠣⠈⠿⣿⣿
⣿⣿⣿⣿⣾⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣶⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣾⡇⣧⣘⡒⠋⠐⢂⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠙⠛⠻⠟⠛⠟⠛⠛⠚⠙⠃⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⡇⠀⣬⣥⢀⡄⢠⣬⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣁⣠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⡟⢤⣦⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠀⠀⠈⠛⢿⣿⠏⠉⢁⣶⡾⠋⠘⣿⡛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣯⣀⣀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠂⠀⠀⠘⠋⣷⣶⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢀⠀⠈⡀⠀⢠⣾⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣰⠟⠤⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⡇⠀⠁⠀⣼⣿⠟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⠁
⣿⣿⣿⣿⣿⣿⢿⡟⠃⠀⠙⠀⢄⡀⠙⠓⠀⠀⠀⠀⠀⠀⢀⠆⣴⣶⣤⠀⠀⠀⠁⠈⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡌⠃⠀⠀⠀⠀⢀⠈⠁⠀⢀⡤⢀⠂⠀⢀⡞⠸⢿⣿⣿⠇⠀⠐⠂⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⡜⠀⠀⠀⡞⣡⠃⠀⢠⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠜⠀⠀⠀⠈⠠⠁⠀⠀⠸⠟⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⠀⣤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢿⣷⠤⡄⡤⢤⠤⣄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⢀⠀⢰⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⠀⠠⢛⣻⣱⡀⠀
⣿⣿⣿⣿⣼⣾⣾⣼⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⠀⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠃⠭⣭⠂
⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢀⣼⡶⢺⢠⠍⡇⣏⠀⢰⠁⢿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠐⠂⠌
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⣴⢏⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠈⠉⠉⠈⠀⠀⠣⠉⠈⠉⠉⣈⣀⡁⠉⠜⠀⠀⠐⢇
⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⢻⡿⢿⣿⠿⢿⣿⠿⢿⣿⣥⣀⣀⠴⣿⣿⣿⣿⣿⠿⠿⢂⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡠⣁⣂⠁⠠⣀⠄⠀⠔
⣿⣿⡿⠃⠀⠀⠀⣠⣾⣿⣿⡉⠙⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⠟⠀⠀⠀⠀⢈⡁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⣉⡿⠖⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢰⣴⣯⣍⢀⢑⣤⣅⣀⣐⣶
⣿⠟⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠘⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠃⣂⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿
⠋⠀⠀⢠⣾⣿⣿⣿⣿⡟⠈⠉⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣿⣆⠀⠂⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣷⣶⣿⣶⣤⣾⣷⣶⣶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣥⡠⢽⣿⣿⣿
⣄⣀⣴⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣽⠿⠿⣿⡿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠻⠛⠃⢀⠹⢿⣿⣿
⣿⣿⣿⢿⣯⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⣀⢠⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣾⡇⣧⣘⡒⠋⠐⢂⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠛⠛⠻⠟⠛⠟⠛⠛⠚⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣤⣿⣤⣿⠇⠠⣬⣅⣠⠀⣭⡄⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠚⠓⠀⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢿⣿⣿⣿⣿⣿⣿⣿⢅⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠀⠀⠀⠋⠻⣿⡿⠉⠉⣴⣶⠟⠀⢻⣟⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣿⠛⠛⠐⠢⠄⠀⠀⠀⠀⠀⠈⠑⠂⠘⠀⠀⠢⠟⢻⣶⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠃⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⠁⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⡆⠁⠂⠀⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠍⠋⠈
⣿⣿⣿⣿⣿⣿⢹⡏⠀⠀⠈⠀⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣠⣶⣤⡀⠀⠀⠀⠀⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⣀⠀⢀⣀⠀⠀⡰⠀⠀⠀⣠⠄⠘⠀⠀⡸⠁⢻⣿⣿⡇⠀⠠⠂⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡰⠁⠀⠀⢰⢡⠎⠀⠀⣶⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⡰⠁⠀⠀⠀⠀⠍⠀⠀⠀⠟⠣⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⠀⣆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡤⡄⡤⢤⠤⣄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⠀⠠⡾⠴⣶⣄⠀
⣿⣿⣿⣿⣼⣾⣾⣼⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠈⠀⢰⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠩⠽⠷⠔
⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣸⣒⢺⢠⠍⡇⣿⠀⢸⠁⣿⢸⠒⢫⢸⢳⡸⣿⢘⡆⠈⠃⠥
⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣤⣟⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠅⠈⠈⠉⠉⠈⠀⠀⠣⠉⠈⠉⠉⢈⣀⠁⠉⠜⠀⠀⠀⢢
⣿⣿⣿⣿⠟⠁⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡿⢿⣿⠿⢿⣿⠿⢿⣯⣄⣀⣠⠾⣿⣿⠿⢿⣿⠛⠛⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣔⡢⠲⡠⣀⡐⢠⠔⠄⢡
⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⡉⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⠟⡁⠀⠀⠀⠀⠁⢸⣿⠀⠸⠿⠀⢸⣋⡉⠙⣉⠀⡉⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡛⢦⣀⢼⣓⣡⣵⣆⣲
⣿⠟⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⣄⣀⠀⠈⠁⣀⣷⡄⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣶⠀⢘⠀⠄⠀⣿⠀⠓⣥⠄⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠋⠀⠀⢀⣼⣿⣿⣿⣿⡿⠉⠙⠛⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣿⣷⡀⠰⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣾⣿⣿⣶⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣅⠉⣿⣿⣿⣿
⣦⣀⣴⣿⣿⣿⣿⣿⡿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠑⡀⠹⣿⣿⣿
⣿⣿⣿⣯⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⡀⢀⣠⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣾⡇⣧⣘⠒⠋⠐⢂⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠙
⠛⠛⠿⠟⠛⠟⠛⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⠇⢧⣬⣅⢀⠠⣭⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⣰⠆⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠥⣠⡀⠀⠀⠀⠈⠛⢿⡿⠉⣿⣶⣾⠏⠀⠓⠒⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣴⠛⠣⣄⣀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠑⠚⠷⢠⡔⠢⠛⣵⣶⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠰⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠿⣿
⣿⣿⣿⣿⣿⣿⢿⡿⠁⠀⠛⠀⢦⣀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣦⠀⠀⠀⢰⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠟⢫⠈⠉
⣿⣿⣿⣿⣿⣿⣎⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣴⣦⣤⠀⠀⠀⠀⠀⠊⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣶⠃⢰⡜⠀⠀⠀⡤⢀⠂⠀⢀⠇⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡸⠀⠀⠀⡸⣱⠃⠀⢠⣾⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⡁⠀⡔⠀⠀⠀⠀⠠⠁⠀⠀⠸⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⠀⢄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢿⣠⠤⡄⡤⢤⠤⡄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠘⢟⣇⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⠀⠀⠀⣾⠴⢄⡀
⣿⣿⣿⣿⣼⣿⣿⣼⣿⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠉⠀⢰⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠩⠏⣋
⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠒⢺⢠⠍⡇⡏⠀⢰⠁⣿⢸⠒⢪⢸⢳⡸⣿⢘⡆⠀⠀⢠
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣶⡁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠄⣨⢀⠊⠈⠉⠉⠈⠀⠀⠣⠉⠈⡉⠉⣈⣀⠁⠉⠼⠀⠀⢀⠐
⣿⣿⣿⣿⡿⠋⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⢺⣿⠿⢿⣿⠿⢿⣤⣀⣠⣴⠿⣿⣿⣿⡿⠉⠛⠛⠄⠰⠷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢫⠻⣳⠃⡾⢴⣱⠶⠤⢝
⣿⣿⣿⠟⠁⠀⠁⢀⣴⣿⣿⡉⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠟⣉⡙⠀⠀⠀⠀⢸⣿⠀⠸⠛⠀⢸⣋⡉⠙⣉⠀⣉⣿⠁⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⣿⢞⣗⣶⡯⡝⢮⣬⣿
⣿⡿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣿⠀⢰⣶⠀⢘⠀⠄⠀⣿⠀⠛⣿⣿⣧⣦⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⡟⠀⠀⢀⣴⣿⣿⣿⣿⡿⠉⠙⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⡘⣿⣿⡄⠀⠆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣏⡉⢹⣿⣿⣿⣿
⣷⣤⣴⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠿⢿⠟⠀⠀⠀⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠈⠈⢿⣿⣿⣿
⣿⣿⣿⣽⣿⣿⠟⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⠀⠀⢀⣘⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣧⣘⠒⠋⠐⢃⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠋⠙⠛
⠿⠿⠿⠟⠛⠟⠛⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⣤⣿⣤⣽⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⠁⣧⣬⡀⡀⢦⣭⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡁⠸⣿⡿⠀⣆⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠉⠁⣀⣤⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠻⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠷⢤⣄⠀⠀⠀⠀⠙⠿⣿⠛⣿⣿⣶⡟⠁⠘⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣼⠟⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢄⣤⠂⠔⢠⣶⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠙⠀⠲⣤⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣛⠛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡄⠀⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⠛⠛⠃⡌⢀
⣿⣿⣿⣿⣿⣿⣧⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢂⣤⣦⣤⡀⠀⠀⠀⠀⠀⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡧⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⡿⠃⣾⠃⠀⠀⢠⢀⠌⠀⢀⠆⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⠃⠀⠀⢠⢣⠎⠀⢠⣾⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⢟⠀⠠⠃⠀⠀⠀⠠⠁⠀⠀⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢨⣡⠤⡄⡤⢤⠤⡄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠹⠿⣆⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⠀⠀⠐⠶⣧⢦⣄
⣿⣿⣿⣿⣼⣿⣾⣼⣿⠦⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠈⠀⠀⣾⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠀⢀⠀⠀⠀⢀⠀⠀⡠⢀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠈⢞⣷
⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠒⢺⢠⠭⡇⣏⠀⢰⠁⣿⢸⠒⢯⢸⢳⣼⣿⢘⡆⠀⠀⠠
⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣴⡁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠉⠁⠘⠛⣿⣿⣿⣿⣿⡿⠿⣿⣿⠁⡈⠀⢈⠏⠉⠉⠈⠀⠀⠣⠉⠈⡉⡉⡈⣀⡁⠉⠼⠀⠀⢀⣤
⣿⣿⣿⣿⣿⠏⠀⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⣿⠿⢿⣿⠿⢯⣄⣀⣠⣾⠿⣿⣿⣿⠟⡋⠀⠀⠀⠩⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣹⡷⡬⣟⡽⢶⢧⣭⢚⣾
⣿⣿⣿⡿⠁⠀⠊⠀⣠⣾⣿⡉⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⡙⠇⠀⠀⠀⠀⣿⠀⠸⠟⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣥⣖⠀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⡶⢿⣿⣿⣶⣎⣫⣿⣿
⣿⣿⠏⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣄⣀⠀⠈⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠠⠔⡄⠀⠀⠀⠀⢸⠀⢰⣶⠀⢘⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⡿⠁⠀⠀⣠⣾⣿⣿⣿⡿⠉⠙⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⡠⠀⠀⣼⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣏⣩⣹⣿⣿⣿⣿
⣿⣦⣤⣾⣿⣿⣿⣿⠟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠁⠀⠀⠸⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠿⠟⢆⠸⣿⣿⣿⣿
⣿⣿⣿⣽⣿⣿⠟⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣷⠀⠀⠀⣐⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣧⣘⠒⠋⠐⢃⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠙⠛
⠿⠿⡿⠟⠛⠟⠛⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣤⣼⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⠡⣧⣬⠀⡀⢦⣭⠀⠀⠀⠀⠀⠀⠀⠨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠹⣷⣿⠏⢀⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠙⠚⠀⠈⣀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠈⠻⣿⡿⢙⣿⣷⣿⠟⠁⠞⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⠚⠻⠇⠀⠠⢤⠟⣤⣦⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣰⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠛⠛⠋⢕⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⢿⣿⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠆⣠⣤⣤⡀⠀⠀⠀⠀⠂⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⡔⠀⠀⠀⡸⡱⠁⠀⣬⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠙⠛⠛⠿⢿⡋⠀⠔⠀⠀⠀⠀⠌⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⢨⣠⣤⣄⡤⢤⠤⡄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢻⠿⡄⠀⠀⡀⠀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⠀⠀⢀⢨⡰⣀⠀
⣿⣿⣿⣿⣼⣾⣿⣼⣼⡿⠇⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠂⠀⢀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⠂⢀⠀⠀⠀⢀⠀⠀⡠⢀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⢅⠠
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣸⠒⢺⢠⠍⡇⡯⠀⢰⠁⣸⢸⠒⢫⢸⢳⡸⣿⢘⡆⠀⠈⠢
⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⣠⡎⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⢀⣿⣿⣿⣿⡏⠁⠀⠛⢻⣿⣿⣿⣿⣟⠛⠻⠿⠀⠀⣿⠀⠈⢨⠋⠉⠈⠀⠀⠣⠉⢈⠉⠉⠈⠀⠁⠉⠼⠀⠀⠀⠔
⣿⣿⣿⣿⣿⡿⠃⢀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⠿⢿⣿⠿⢥⣀⣀⣴⣿⠿⣿⣿⠅⢀⠀⠀⠀⠀⢰⠃⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠈⠉⠀⠁⢄⠈⠄⢀⢀
⣿⣿⣿⣿⠏⠀⠐⠁⢀⣴⣿⡉⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⢿⠀⠀⠀⠀⢸⠀⠸⠛⠀⢸⣋⡉⠙⣉⠀⣉⣿⣿⣷⣤⣴⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣜⣀⢀⡀⠁⢀⠀⠀⣠⣿
⣿⣿⡿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⠀⠀⠀⠀⠀⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⣷⣍⣿⣾⣾⣿⣿
⣿⠏⠀⠀⢀⣴⣿⣿⣿⣿⠋⠙⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⢀⠄⠀⢀⣿⣿⣿⣿⣿⣷⣾⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣏⡉⢻⣿⣿⣿⣿
⣿⣷⣤⣴⣿⣿⣿⣿⡿⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠑⠀⠀⠀⢾⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⢿⠟⠀⠘⣿⣿⣿⣿
⣿⣿⣿⣟⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⣀⡇⢰⣿⠀⣿⡆⢹⠀⣾⡇⣧⣈⠒⠏⠐⢒⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠛
⠿⢿⡿⠟⠟⠟⠛⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣤⣦⣬⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⢡⣤⣬⠀⠀⣦⡌⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⣿⣿⡏⢀⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠁⠚⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠈⠻⢿⡿⠉⢉⣽⣭⡟⠁⠾⡍⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣯⢀⡠⢤⡾⣻⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠖⠁⠹⠿⢗⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⡿⠟⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠈⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣹⡇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠷⠀⠀⠸⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣅⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠛⠙⠛⠽⢿⡁⠀⠜⠀⠀⠀⠀⠠⠀⠀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⡀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⢨⣠⣤⣄⡤⢤⠤⡄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢿⡷⠀⠀⢀⡀⠀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⠀⢉⢝⠢⣀⣀⠀
⣿⣿⣿⣿⣼⣾⣾⣼⣿⡽⠇⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠂⠀⢠⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⠀⢘⠄⢀⠀⠀⠀⢀⠀⠀⡠⢀⢀⣀⣀⢀⡀⠀⣀⢄⠉⠓⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣸⠒⢺⢠⠍⡇⡿⠀⢰⠁⢸⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⡼⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⢠⣿⣿⣿⣿⠍⠁⠀⠛⢻⣿⣿⡛⠛⠿⠋⠉⠉⠁⠠⣿⠀⠈⢈⠏⠉⠈⠀⠀⠣⠉⠈⠉⠉⠈⣀⠁⠉⠜⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⢀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⢸⠿⢿⣿⠿⢤⣀⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⢂⠀⠀⠒⠀⠐⠀⠀
⣿⣿⣿⣿⠏⠀⠐⠁⢀⣴⣿⡉⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⢿⠀⠀⠀⠀⢸⠀⠘⠛⠀⢸⣋⡉⠙⣉⠀⣀⣠⣤⣤⣄⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣅⡀⠀⢀⣀⠀⠄⠈⠀⡿
⣿⣿⡿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣦⣄⣀⠀⠉⠁⣀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠠⠄⣾⠀⠀⠀⠀⠈⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡭⡷⡱⣲⣻⣖⣮⣶⣮⣿
⣿⠏⠀⠀⢀⣴⣿⣿⣿⣿⡏⠙⠛⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿
⣿⣦⣄⣴⣿⣿⣿⣿⡿⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠱⠀⠀⠀⢼⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡿⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⢿⡿⠁⠀⣿⣿⡿⢻
⣿⣿⣟⣛⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⢀⡇⢰⣿⠀⣿⡆⢹⠀⣾⡇⣧⣘⠓⠏⠐⠒⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠛⠻
⢿⣿⣿⠿⠟⠟⠛⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣤⣤⣤⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⢣⣦⣬⠀⠈⣤⡌⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀⣠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠩⠭⠻⠿⣿⣿⣿⣿⡿⠿⠏⣶⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⠁⠀⠀⠀⠀⠙⠟⠀⠀⢠⣤⡶⠛⠠⠯⠍⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠘⣢⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠰⠀⠀⠀⠀⠀⢡⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣦⠠⢠⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⣀⠀⠀⠀⠀⠈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡋⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡀⢀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡍⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⠿⣷⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠄⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣴⣆⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⢈⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿
⣿⣿⣿⣷⠛⠿⠛⠛⠋⠀⠀⣻⠏⠜⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣦⣤⣶⢨⣤⡤⡆⡥⢤⠤⡄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢤⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠗⠀⠀⠀⡀⠀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⢸⣆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣼⣾⣾⣼⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢰⣦⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⠓⢆⠀⠀⠀⢀⠀⠀⡠⢀⢀⣀⣀⢀⡀⠋⣀⢬⠀⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠙⠃⠘⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⠒⢺⢨⠭⡇⣿⠀⢰⠁⣸⢸⠒⢪⢸⢱⣸⣿⢸⡇⠰⠀⠦
⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣴⣿⣿⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠁⠀⠀⠀⠠⣼⣏⣷⠘⠈⠉⠉⠈⠀⡌⠣⠉⠈⠉⠁⠈⠀⠁⠉⠼⠁⡐⢦⡙
⣿⣿⣿⣿⠟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⠀⢿⣿⠿⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠢⣑⢞⣢⡙
⣿⣿⡿⠃⠀⠀⠀⣠⣾⣿⣿⡉⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠟⣉⠁⠀⠀⠀⠀⢸⣿⠀⠘⠛⠀⢸⣀⡀⠀⣀⠀⣀⣤⣄⣀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣱⠒⠠⣏⠠⢵⣈⡡⣉
⣿⠟⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣖⡿⣇⣷⣷⣣⣾⣾⣿⣿
⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠙⠛⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿
⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡷⠀⠁⠀⠸⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⠀⠀⠀⠺⢿⡿⢿⣿⡖⠈⣿⣿⣿⣿
⣿⣿⠿⣿⣿⣿⠿⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⠀⠀⢘⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣇⣘⠓⠏⢐⡓⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡔⠙⠿⠿⣿
⣿⣿⢿⣿⠛⠟⠛⠛⠛⠙⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣿⣤⣴⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⢧⣧⣬⠠⠜⣠⡤⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⢿⣿⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣹⣿⠿⠿⣿⣿⣿⣿⣿⡿⠿⢷⣶⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠄⠀⠀⠀⢂⣿⣿⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡟⠀⠀⠀⠀⠈⠛⠁⠀⠀⣠⣤⡞⠃⠸⠭⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣤⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠸⠀⠀⠀⠀⠀⠡⣿⣿⡧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣶⡆⠠⠡⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢿⠻⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣴⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡁⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡉⡎⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⢠⣼⠏⢽⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⣿⣧⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠇⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣄
⣿⣿⣿⣿⣿⣿⣿⡟⠈⢠⣾⣿⡏⡂⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣹⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿
⣿⣿⣷⠻⠛⠟⠁⠀⠀⠩⣿⠏⠪⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢤⣹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣯⡦⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⠆⣠⣠⣠⠄⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻
⣿⣿⣿⣶⣦⣤⣶⢨⣤⠶⡅⡤⢤⠤⡄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠻⠿⠟⠀⠀⠀⠀⡀⠀⠀⠀⠃⠈⠂⠓⠐⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣿⣿⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⣶⣶⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⢀⠐⢀⠀⠐⠀⣀⠀⠀⡠⢀⢀⣀⣀⢀⡀⠀⣀⢤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣿⣿⡟⠷⠀⠀⠀⠀⠈⠙⠿⣿⣿⡟⠀⠀⠀⠀⢀⣤⡀⠀⣸⠒⢺⢸⠭⡇⣿⠀⢸⠁⣹⢸⠒⢪⢸⢱⡸⣿⢸⡇⢀⡠⣀
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣴⣿⣿⣿⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⢰⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⣿⣿⣷⣼⡯⣰⣬⠈⠉⠉⠉⠀⠈⠣⠉⠈⠉⠉⠈⠀⠁⠉⠼⢁⣠⣿⣷
⣿⣿⣿⠟⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⢸⡿⢿⣿⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⣧⣭⣷⢟⣽
⣿⡿⠃⠀⠀⠀⣠⣾⣿⣿⣿⡉⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⠟⠀⠀⠀⠀⢈⡃⢸⣿⠀⠘⠛⠀⢸⣋⡉⠑⣀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢟⣷⡿⠻⣯⣯⠁
⠟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠉⠁⣠⣷⡄⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣿⠀⠛⣿⣷⣤⣠⣤⢶⠿⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⢶⣿⣿⣶
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠙⠛⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣴⣿⣿⣟⣿⣿⣿⣿
⢀⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢦⠀⠁⠀⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠰⢿⡿⢿⣿⡶⡒⣺⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⢹⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣧⣘⡓⠏⢐⣓⣀⠟⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⢦⠸⢿⣿⣿
⡿⣿⣿⡿⠟⠟⠛⠛⠛⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣧⣤⣴⣦⣭⣼⣧⣼⣿⠀⣬⣴⣿⣤⣿⣧⣷⣬⢀⡸⠂⣡⠈⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠉⠀⢈⢻⣿⣿⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢁⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣿⡟⣿⣿⣿⣿⣿⠿⣻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣷⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⠟⠋⠉⠉⠉⠙⠀⠀⠀⢠⣶⣼⠟⠢⠿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡄⠀⠀⠀⠀⠈⠟⣿⣿⣿⡇⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⠀⠀⢳⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣤⣿⠛⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⣿⠀⠋⠃⠀⠀⠀⠀⢠⣿⣿⡿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⢛⣿⣾⣿⠉⣓⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢇⢁⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⣿⣿⣿⣿⣿⡿⣣⣤⣿⠿⣿⠏⠁⠂⣰⣿⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⠈⠸⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⠿⣣⣵⣿⣿⣿⣿⠏⠀⢠⣿⣿⡯⣊⢀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠃⠀⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⠃⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⣿⣧⠰⠿⡿⠿⣟⣿⠏⠀⠀⡿⠋⠛⣱⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠀⠀⠙⠛⠿⠟⠙⠊⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⢿⣿⣿⡶⠈⠀⠀⠀⠀⠀⠀⣏⣉⡆⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣧⣴⣦⣶⣶⢿⢡⠤⡄⡤⢤⠤⣄⣥⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠻⠟⠟⠀⠀⠀⢀⠀⠀⠀⠃⠈⠂⠓⠔⠘⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⡞⠟⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⢸⠈⠀⠀⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣀⣀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠁⠀⠀⠀⠀⢀⣴⡄⠀⢸⠒⢺⢸⠭⡇⣿⠁⢸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠀⠀
⣿⣿⠟⠁⠀⠀⠀⣠⣶⣾⣿⣿⣿⡁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⢠⣾⣿⣿⣷⣤⣼⣿⣿⣮⣍⡉⠉⠁⠈⠣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⣿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⠿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡉⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢿⠟⣋⡃⢸⣿⠀⠸⠿⠀⢰⣊⡀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠻⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⣶⠀⠀⡄⠀⠀⠀⠀⢉⣛⠀⠒⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣼⣽
⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣾⣷⣤⣄⡠⣦⣾⣿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠹⢿⡿⠿⣿⣿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠿⣿⡿⠷⢯⣭⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠐⠂⠀⣿⢸⣿⢐⣛⣂⡇⢸⣿⠀⣿⡆⢹⠀⣿⡇⣧⣘⡓⠏⢐⣛⣀⣿⡇⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⣖⠴⣿⣿
⣿⣿⣿⡿⠛⣿⡿⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣬⣽⣦⣭⣼⣧⣼⣿⠀⣭⣴⣿⣴⣿⣧⣷⣬⣥⣾⣦⣭⣼⡿⠁⠀⠀⠀⠀⠀⢀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠋⠈⣆⠝⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠁⠀⠀⢿⣿⣿⣿⣿⢡⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠉⠁⠀⠈⣸⣿⡿⠟⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠈⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡀⠘⡄⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣰⣿⡋⢏⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠆⠰⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⣟⢿⢻⣾⡟⣿⢿⠛⠆⠠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠻⣩⣴⣦⡿⣷⡟⠛⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢅⠀⡅⠀⠀⠀⠀⠀⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠓⣵⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⣞⣾⡿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠀⢀⠃⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣼⣿⠿⠿⢿⣿⡝⠀⠀⠀⠼⠻⠛⢋⡤⠀⠀⠀⠀⠀⠀⠀⠈⠉⣼⠟⠁⠀⠀⢉⣹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣷⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣴⣶⢾⣿⢨⢠⠤⡄⡤⢤⠤⣌⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠇⠈⠂⠓⠔⠘⠢⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠟⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠈⠀⠀⠀⢀⠀⢀⠠⠀⠀⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⢀⡀⠀⢸⠒⢺⢸⠭⡇⣿⠁⢸⠁⣿⢸⠒⢪⢸⢳⡸⣿⢘⡆⠀⠀⠀
⣿⠋⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣇⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠗⠀⠀⠀⠀⣠⣶⣿⣷⠀⣈⣤⣼⣮⣍⡉⢉⡁⠈⠣⠉⠈⠉⠉⠨⠀⠁⠉⠜⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡿⢿⣷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡀⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠟⣉⡙⢿⠟⣉⡁⢸⣿⠀⠐⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠸⠿⡿⠿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣄⣀⠀⠉⠁⣠⣷⡄⠀⠀⠀⠀⠀⠸⡀⠠⠄⣾⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣷⣶⣦⣀⠀⠀⢀⠁⣠⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⡿⠹⢿⡿⠿⣿⣿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠦⣤⡤⠬⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣿⡌⣿⢸⣿⢐⣛⣂⡇⢸⣿⢠⣿⡆⢹⠀⣿⡇⣧⣘⡓⠏⢐⣓⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣿⣮⣽⣦⣭⣼⣧⣼⣿⠀⣭⣴⣿⣴⣿⣧⣷⣬⣥⣾⣦⣭⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⡶⡄⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣿⣿⣿⣿⣷⡴⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢄⠀⠀⠀⠀⠎⣿⣿⣿⣿⡇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣼⣾⢽⣿⣿⣿⣿⣿⣻⣿⠿⣯⢼⣽⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣬⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢯⡼⢫⣽⠿⠛⠛⠋⠁⠀⠈⠀⢀⣤⣭⣽⠏⣛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢡⡄⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢫⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⢀⢸⡟⠋⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠀⢨⢡⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡬⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⡿⣿⣿⣷⢠⡼⠏⢩⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⣴⣶⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⣿⣷⠈⠘⠃⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⡿⠟⢇⣸⣿⣿⢯⡿⣿⡙⠀⣄⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⢁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠋⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⣫⣧⡝⡿⣿⠯⡾⠃⠈⠀⣾⢣⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠈⠸⠀⠀⠀⠀⠀⠘⠛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣖⢢⡾⠃⠀⠀⣰⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⣈⣁⣤⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠁⢰⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣟⠛⠛⡞⠁⠀⠀⠠⣿⣿⠙⡀⡉⢀⠄⠀⠀⠀⠀⠀⠰⢿⣯⣾⠃⠀⠆⢉⣛⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣴⣾⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣏⣉⡆⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢆⢀⣶⢨⢠⠤⡄⡤⢤⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠈⠀⠈⠉⠛⠛⠛⠋⠁⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⣿⣿⣯⠅⠀⠀⠀⠀⠀⠀⠇⠈⠆⠓⠔⠘⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠾⠘⠞⠸⠸⠸⠤⠆⡇⡸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠉⠉⠀⢀⠀⢀⢠⠠⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⢸⠒⢺⢸⠭⡇⣿⠁⢸⡇⣿⢸⠒⢪⢸⢱⣼⣿⢘⡆⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⡀⠂⣿⡟⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⡿⠉⠀⠀⠀⠀⣠⣾⣷⠀⠈⣀⣨⣬⣻⣩⡉⣁⣈⠧⠉⠈⠉⢩⣾⣾⡓⠉⠜⠀⠀⠀⠀
⠀⢀⣴⣶⣿⣿⣿⣿⢸⣿⠁⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⡿⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠻⠛⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀
⣨⣾⣿⣿⣿⣿⠋⣏⣿⣯⣶⡀⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠶⠆⢈⠟⣉⡛⢿⠟⣉⡃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⢸⣾⡟⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠰⠶⣾⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⠿⠟⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠃⣿⣿⠃⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣤⡀⣀⠀⠀⠀⠀⠀⠛⠁⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠄⠀⠀⠀⠀
⣿⣿⣿⣿⡟⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣽⢿⠿⢿⡿⠹⢿⣿⠿⣿⣿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠆⡀⠀⠀⠚⢠⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡺⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⢰⣿⡎⣿⢸⣿⢐⣛⣊⡇⢸⣿⢰⣿⡆⢹⢀⣿⡇⣧⣘⡓⢏⢐⣂⣀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠛⠟⠘⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣼⣿⣧⣷⣬⣥⣾⣦⣭⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⢧⡄⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⣤⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠙⣿⣿⣿⣿⣿⡎⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⢹⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠆⠀⠀⠀⠐⢸⣿⣿⣿⣿⡇⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⣾⣟⣿⣿⣿⣿⣿⢿⣛⡿⠿⠾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡶⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡟⣦⠟⣾⡿⠟⠋⠉⠉⠀⠀⠀⠀⣠⣭⣭⠿⢍⣙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢸⡄⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⣿⣿⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠀⢨⢠⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠬⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⢿⣿⣏⡀⣴⡿⠀⢿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠸⣿⡇⠈⠘⠃⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠏⢣⣰⣿⣿⡟⣱⢿⣏⠀⢠⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⠀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣰⣷⣝⠻⢿⡿⣱⠟⠀⠀⢠⣏⣟⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣍⠀⠆⡏⠀⠀⠀⠀⠀⠚⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⡆⡀⣸⠅⠀⠀⢀⣿⣿⣾⠟⣀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣠⣤⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠀⠰⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢛⠉⠻⠃⠀⠀⠀⠾⢿⠇⢁⢈⠀⡀⠀⠀⠀⠀⠀⠀⠾⢿⣣⡿⠀⠰⠈⣙⣻⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣶⣿⢶⣿⣿⣥⠀⠂⠀⠀⠀⠀⣏⣉⡆⣤⣠⣠⠄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢇⢀⣶⢨⢠⠤⡄⡤⢤⠤⣄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠛⢛⠁⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠸⣿⣿⣿⠄⠀⠀⠀⠀⠀⠇⠈⠆⠓⠔⠘⠢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠘⠞⠸⠸⠸⠤⠆⢇⢸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠉⢀⠀⢀⠀⣄⠠⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠋⠀⠔⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⠒⢺⢠⠭⡇⣿⠁⢸⡇⣿⢸⠒⢪⢸⢱⣸⣿⢘⡆⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⡄⡀⣸⣿⠁⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡟⠁⠀⠀⠀⠀⣠⣾⣇⠈⠀⣈⣈⣩⣩⣭⡅⠈⢧⠉⠈⠉⠉⢨⣤⣥⡍⠜⠀⠀⠀⠀
⠀⠀⣠⣶⣿⣿⣿⢳⠃⣿⠏⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢠⣾⣿⣿⣿⣦⣾⣿⣿⢿⣿⣿⣾⠺⠛⠀⠀⠀⠀⠀⠈⠻⠷⠀⠀⠀⠀⠀
⢀⣴⣿⣿⣿⣿⡏⡞⣸⣿⣶⡀⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢈⠟⣉⡙⢿⠟⣉⡁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢰⣷⡿⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⢰⡄⠻⡀⠠⠔⣾⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠁⠄⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⡿⠛⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⢸⣿⡗⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣤⣄⠀⡀⠀⠀⠀⠀⠀⠻⠁⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡀⠀⠀⠀
⣿⣿⣿⣿⣿⢠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⣿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣿⠿⠷⣄⠀⠀⢀⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀
⣿⣿⣿⣿⣏⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⡎⣿⢸⣿⢐⣛⣊⡇⢸⣿⢰⣿⡆⢹⢐⣿⡇⣧⣘⡓⢏⢐⣒⣀⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠟⠘⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣤⣿⣧⣷⣬⣥⣾⣦⣭⣼⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⢼⡆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣠⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⢻⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡍⠀⠀⠀⠀⡝⣿⣿⣿⣿⣿⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣴⣶⣷⣘⣿⣿⣿⣿⡿⣟⣿⠿⠯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠐⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣌⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⢿⡴⢫⣽⡿⠟⠋⠉⠁⠀⠀⠀⠀⣀⣉⣫⣟⠉⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢫⡀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠖⢻⣿⡿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠁⠀⠈⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⢃⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⡟⣿⡿⣿⠛⣈⣠⡾⠋⠠⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢱⣷⡄⠸⠸⡄⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠿⠋⠑⢴⣮⣿⣿⢩⡞⣿⠁⢀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡟⠣⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⣠⣶⣦⠙⠿⡟⢡⡟⠀⠀⠀⡞⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠄⡧⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣃⡀⣠⠆⠀⠀⠀⣼⣿⢿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠙⠓⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣟⢉⠉⠛⠋⠀⠀⠀⢴⢷⠏⠁⢈⠄⡠⠀⠀⠀⠀⠀⠀⠠⣾⡟⣹⠃⠀⠈⠛⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣠⣌⣀⣴⡷⠄⠀⡀⠀⠀⠀⣏⣉⡆⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢇⢀⣶⢨⢠⠤⡄⡤⢤⠤⣄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠈⠁⠐⠒⠚⠀⠈⠛⠛⠛⠿⠛⠁⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⢿⣿⣿⢷⠀⠀⠀⠀⠀⠇⠈⠆⠓⠔⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠾⠘⠞⠸⠸⠸⠤⠆⢇⠸⠤⠟⠬⠽⠺⠤⠟⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠈⠿⠏⣛⠀⢀⠀⠀⠀⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⠞⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢸⠒⢺⢠⠭⣧⣿⠀⢸⡁⣽⢸⠒⢪⢸⢱⡸⣿⢸⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡀⠄⣸⣿⠋⢀⡀⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣠⡈⠀⠈⠈⠉⠉⣩⣇⠈⠣⠉⠈⠉⠉⠈⠀⢁⣉⣾⡀⠀⠀⠀
⠀⠀⣠⣶⣾⣿⣿⢱⢠⣿⡏⢀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠀⠀⠀⠀⢀⣴⣿⣿⣇⠀⣠⣶⣶⣿⣿⣿⡗⠤⣴⠂⠀⠀⠀⠰⠿⣿⣷⠃⠀⠀⠀
⣠⣾⣿⣿⣿⣿⠃⡏⣼⣿⣶⡀⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢈⠟⣉⡙⢿⠟⣉⡁⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠻⠿⠆⠀⠀⠀
⣿⣿⣿⣿⣿⡟⣸⣼⡿⠻⣿⣿⣦⣄⣀⠀⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣾⡀⠛⠃⢸⣿⠀⢠⣴⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠃⣿⣿⡇⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠿⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀
⣿⣿⣿⣿⡟⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⣿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣶⠤⠤⠀⠀⠀⠀⢀⠙⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣝⣁⠀⠀
⣿⣿⣿⣿⣣⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⢰⣿⡆⣿⢸⣿⢐⣛⣊⡇⢸⣿⢰⣿⡆⢹⢠⣿⡇⣧⣘⡓⠆⢀⠀⣀⣉⣠⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀
⣿⣿⣿⣿⠟⠟⠘⠛⠚⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣼⣿⣧⣷⣬⣥⣾⣦⣥⣬⣙⡿⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣷⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢫⡉⠀⠀⠀⠠⢻⣿⣿⣿⣿⡇⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⠿⣿⢗⣿⣿⣿⣿⣿⠽⢿⡛⠟⠺⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⣶⣟⣶⢁⢾⡿⠛⠉⠉⠁⠀⠀⠀⠀⣤⣬⣭⡿⠏⣘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣅⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⡏⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡾⣿⣿⣿⣿⣿⠌⢉⣿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠈⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⡏⡀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣇⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠿⡝⠿⣝⣿⣏⠠⣠⡾⠃⠐⢿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣾⣷⠀⠇⢧⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠗⠈⠈⣾⣿⣿⡿⢲⡏⠿⠊⢀⡄⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⡈⠛⠿⢱⠏⠀⠀⢀⡾⣱⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⢸⡄⠀⠀⠀⠀⢀⣼⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⡔⣰⠓⠀⠀⠀⣼⣿⣷⢟⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠛⠂⠀⡈⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣭⡀⠸⠋⠀⠀⠀⠸⠷⠏⠂⣠⠆⠔⠀⠀⠀⠀⠀⠀⠀⠾⢿⣹⠇⠀⠀⠙⠻⢿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣤⣁⣠⣶⠦⠀⠀⠀⠀⠀⠀⣏⣉⡆⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢰⢆⢀⣶⢨⢠⠤⡄⡤⢤⠤⣄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠈⠉⠈⠀⠀⠉⠙⠙⠛⡛⠅⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢻⣿⣿⡷⠆⠀⠀⠀⠀⠀⠇⠈⠆⠓⠔⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠗⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠻⠿⠿⣋⠀⢀⠀⠀⠀⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠞⠀⠠⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸⠒⢺⢠⢽⡇⣿⠀⢸⡁⣾⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠀⠀
⠀⠀⠀⢀⣀⣠⡀⠀⣿⣿⠋⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣀⣄⠈⠀⠈⠈⠉⣩⣭⣁⠈⠧⠉⠈⠉⠉⠈⠀⢁⣭⡞⠀⠀⠀⠀
⢠⣴⣿⣿⣿⣿⣝⢸⣿⡏⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠼⠿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠇⠀⠀⠀⠀⣠⣾⣿⣿⡀⢀⣴⣶⣾⣿⣿⣿⣅⣠⡖⠀⠀⠀⠀⢶⣿⣿⡟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢋⢃⣿⡟⣤⣶⡀⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠶⠆⢈⠟⣉⡙⢿⠟⣉⡁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠘⡿⡧⠀⠀⠀⠀
⣿⣿⣿⣿⡏⣼⣼⡿⠀⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡄⠠⠄⣾⡀⠛⠃⢸⣿⠀⢰⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠠⣿⣿⡇⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀
⣿⣿⣿⡏⣼⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣭⣽⢿⠿⢿⡿⠹⢿⣿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡦⣤⠤⠀⠀⠀⠀⢀⠛⠿⠀⠜⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⡁⠀⠀
⣿⣿⣿⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣿⢰⣿⡎⣿⢸⣿⢐⣛⣊⡇⢸⣿⢀⣿⡆⢹⢀⣿⡇⣧⣘⡂⠀⢀⢀⡀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀
⣿⣿⣿⠟⠙⠟⠘⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢀⣭⣴⣿⣴⣿⣧⣷⣬⣥⣾⣦⣌⡸⠿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠘⢿⣿⣿⣿⣿⡞⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣈⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠆⠀⠀⠀⠈⢸⣿⣿⣿⣿⣧⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⡟⢿⢯⣼⣿⣿⣿⣿⠗⠛⠯⠋⠉⠛⢿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠉⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣲⣿⣿⣥⣝⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣶⣶⡾⠛⠢⡍⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⣿⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣷⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣼⠿⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣄⠀⡆⣇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠧⠭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢷⣿⣯⣝⣿⢀⣠⣾⡋⠁⠚⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⠀⠀⠙⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠅⣧⣿⣿⣿⠗⣾⠟⠟⠀⣴⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣇⠙⠻⠏⡾⠁⠀⠀⣸⣧⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⡁⠰⠸⠇⠀⠀⠀⠀⠀⠛⠻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣤⣠⡞⠁⠀⠀⢠⣿⡿⡿⠵⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⣄⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⣭⡈⠟⠀⠀⠀⠀⠾⠿⠃⢠⠞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠼⠃⠁⢦⠈⠙⠿⣿⢿⣿⡿⠗⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣴⣾⡷⣾⣿⣏⣤⠀⠁⠀⠀⠀⣏⣉⡇⣤⣠⣠⠄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⢰⢆⢀⣶⢨⢠⠤⡄⡤⢤⠤⣄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣭⠀⠀⠀⠀⠀⠇⠈⠆⠳⠔⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠗⠸⠘⠞⠸⠸⠸⠤⢆⢇⠸⠤⠟⠬⠽⠺⠤⠟⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢏⠀⠀⠈⠉⠃⢀⠀⢀⠀⠀⡄⣤⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠊⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⠒⢺⢠⠭⣇⣿⠀⢸⡇⣿⢸⠒⢪⢸⢱⡸⣿⢘⡇⠀⠀⠀
⠀⠀⠀⢀⣀⣤⢀⠀⣿⣿⠃⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣤⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡟⠛⠀⠀⠀⠀⢀⣴⣶⡌⠀⠈⣈⣉⣍⣩⣧⡈⠧⠉⡈⠉⠉⠈⢀⣵⣭⣾⡇⠀⠀⠀
⢠⣶⣿⣿⣿⣿⡍⢸⣿⠏⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⣼⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣧⣴⡇⠁⠀⠀⠀⠈⠛⣿⣿⡃⠀⠀⠀
⣿⣿⣿⣿⣿⢳⢃⣿⡏⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠶⠆⢈⠟⣋⡛⢿⠟⢉⡁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀
⣿⣿⣿⣿⡇⣼⣼⡿⠀⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠰⠶⣾⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀
⣿⣿⣿⣿⠠⣿⣿⡇⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠋⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠦⠀⠀
⣿⣿⣿⡏⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣭⣽⢿⠿⢿⡿⠹⢿⣿⠿⣿⣿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣶⠶⠀⠀⠀⠀⢠⠈⡻⠀⠎⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⠂⠀
⣿⣿⣿⢰⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⢰⣿⡎⣿⢸⣿⢐⣛⣊⡇⢸⣿⢰⣿⡆⢹⢀⣿⡇⣧⣘⡃⠄⠀⢀⣀⣴⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀
⣿⣿⣿⡟⠛⠟⠘⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣴⣿⣧⣷⣬⣥⣾⣦⣤⣌⡛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠙⣿⣿⣿⣿⣿⣴⢛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⢁⣾⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠑⡄⠀⠀⠀⠐⢏⣿⣿⣿⣿⣧⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡾⢿⣗⣸⣿⣿⣿⣿⠭⣿⣛⠿⠑⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢥⣜⣷⢘⠨⣿⠟⠋⠉⠉⠀⠀⠀⠀⢠⣤⣭⣽⠯⢁⡛⠛⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣠⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡞⣽⣿⢷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠁⠀⠀⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⠀⠀⡌⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣄⣛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⣟⢻⣯⣿⣿⠛⢁⣤⠟⠀⠼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢿⣷⠄⠠⠹⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⢇⠈⢡⣷⣾⣿⡏⣴⢿⡧⠁⢀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⣡⣴⣶⡈⠻⢿⡏⣰⠋⠀⠀⢠⣏⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⢀⠘⡇⠀⠀⠀⠀⠀⠼⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡀⢀⡶⠃⠀⠀⢀⣟⣿⡼⡡⠔⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⡀⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠉⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⡚⠙⡞⠃⠀⠀⠀⡼⣽⠋⢁⠖⠐⠁⠀⠀⠀⠀⠀⠀⠀⠻⠟⢸⠃⠀⡄⠛⠿⣿⣿⣿⣿⣿⡯⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣤⣅⣠⣾⡷⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢻⢆⢀⣶⢨⢠⠤⡄⡤⢤⠤⣄⣠⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠩⠅⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠋⣿⣿⣿⣓⠀⠀⠀⠀⠇⠈⠆⠓⠔⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡼⠘⠞⠸⠸⠸⠤⠆⢇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠘⠻⣏⠉⢀⠀⠀⠀⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠞⠀⠰⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⠒⢺⢠⠭⡇⣿⠉⢸⡁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣶⣿⠃⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠉⠀⠀⠀⠀⠀⢀⣬⡀⠈⠈⠉⠉⢙⣷⣈⠧⠉⠈⠉⠉⠈⠀⠁⠉⡼⣰⣆⠀⠀
⠀⢀⣤⣶⣶⣿⡟⡸⢰⣿⠏⢀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⠀⠀⠀⠀⣠⣾⣿⣿⣇⠀⣠⣶⣾⣿⣿⣿⣦⣤⣷⡆⠀⠀⠀⠐⠿⣿⣿⡏⠀⠀
⣠⣾⣿⣿⣿⣿⢣⠃⣿⣿⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢈⠟⣉⡙⢿⠟⣉⡁⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠘⠿⠷⠀⠀
⣿⣿⣿⣿⣿⡇⡜⣼⡿⠻⣿⣿⣦⣄⣀⠀⠉⠁⣠⣷⡄⠀⠀⠀⢰⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⢈⠀⠄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⢰⣿⣿⠇⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣄⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡀⠀
⣿⣿⣿⣿⠇⣼⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣭⣽⢿⠿⢿⡿⠹⢿⣿⠿⣿⣿⠿⢿⠿⠿⢿⣿⠿⠿⡧⣶⠀⠀⠀⠀⠀⠀⠀⠿⠉⣧⡀⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⡀
⣿⣿⣿⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⢰⣿⡆⣿⢸⣿⢐⣛⣊⡇⢸⣿⢠⣿⡆⢹⢠⣿⡇⣧⣘⡓⠀⠀⠀⢀⠇⢠⠀⣭⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀
⣿⣿⣿⣿⡿⠟⠛⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣼⣿⣧⣷⣬⣥⣾⣦⣬⡸⢿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡄⡤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠉⠀⠀⠀⡝⣿⣿⣿⣿⣿⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡟⣄⣠⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠑⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣄⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣏⢳⠇⣿⣿⣿⠿⠿⠋⠓⠚⠉⠉⠻⠿⢿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢷⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⠃⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣨⢯⣿⣇⣬⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠉⠐⠆⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠗⠂⠸⠃⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣆⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⣛⢿⣿⣿⣿⡟⠷⠁⣿⠻⢻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠀⠀⢀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣦⡄⠸⢸⡄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠗⠑⠚⣾⣽⡏⣀⣠⣿⠏⠀⢻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣿⠇⠀⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣾⣿⡾⢇⡾⠻⠟⠀⡴⢴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣰⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣦⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣆⠙⠻⢃⡾⠁⠀⠀⣸⣣⢿⡗⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⢦⠀⠃⠈⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣋⠄⠀⠞⠂⠀⠀⢰⣿⡟⡮⣊⢁⠄⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣸⠁⢠⣤⡄⠀⢀⠀⠀⠀⣏⣉⡆⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣥⣅⢰⢆⢀⣶⢨⢠⠬⡌⡤⢤⠥⣄⣤⠤⢀⠤⣄⢼⢵⠄⠈⠉⠘⠃⠒⠒⠀⠉⠙⠻⠛⢛⣟⡏⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⢺⣿⣿⣵⡄⠀⠀⠀⠀⠃⠈⠆⠓⠔⠘⠆⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀
⣿⣿⣧⠸⠘⠞⠸⠸⠸⠤⠆⡇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠘⣿⣿⢷⠆⢀⠀⠀⠀⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⡿⠿⠟⠀⠀⠀⠀⠀⠀⣀⣾⣡⠎⠃⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠁⢹⠒⢺⢠⠭⣷⣿⠂⢸⠁⣺⢸⠒⢪⢸⢳⡸⣿⢘⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠋⢀⡘⢁⣘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⡿⡛⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⣽⢇⠈⠣⠉⠈⠉⠉⠈⠀⠁⠉⢜⣤⠀⠀⠀
⠀⠀⠀⠀⣀⣤⢀⢀⣿⣿⠁⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⣤⣶⣶⣶⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠀⠀⠀⠀⠀⢀⣴⣾⣷⠀⠀⣀⣠⣤⣿⣿⣿⠀⢀⣀⡀⠀⠀⠀⢠⣾⣿⣿⡇⠀⠀
⢠⣶⣿⣿⣿⡟⡘⣸⣿⣧⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠴⠆⢈⠟⣉⡙⢿⠟⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣶⠾⠞⠀⠀⠀⠀⠈⠉⢿⣿⣁⠀⠀
⣿⣿⣿⣿⡿⢱⢃⣿⠏⠻⣿⣿⣦⣄⣀⠈⠉⢁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢠⣤⠀⢰⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀
⣿⣿⣿⣿⠇⣾⣾⡟⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀
⣿⣿⣿⡿⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠿⠤⡀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠉⡋⢡⡤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠦⠀
⣿⣿⣿⢇⣼⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣽⣿⢰⣿⡄⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠠⣿⡇⣧⣐⠀⠀⠀⠀⢀⠉⠻⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡖⠃
⣿⣿⣿⢿⡟⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣼⣿⣧⣷⣬⣥⣄⡠⣤⣤⣴⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⣿⣿⣿⣿⡰⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠡⡀⠀⠀⠀⠰⢹⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣶⣾⣿⣻⣿⣿⣿⣿⣿⣟⣿⠿⠯⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣬⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣯⡼⣩⣾⡿⠛⠛⠛⠁⠀⠉⠈⢀⣈⣏⣻⣿⠛⡙⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠙⣇⠀⠀⠀⠀⠀⠀⠟⢿⣿⣿⣿⣟⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠾⢻⣿⣷⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⠀⠀⠉⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠀⡏⡀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢿⡿⣿⡿⢿⠩⣧⡿⠍⣩⣯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣦⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⣧⠀⠃⠷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢷⣿⣿⣿⡟⣠⣾⣿⠃⢀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⠏⠄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠛⣿⣿⡟⣣⡟⠀⠉⠀⡾⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢠⢸⡄⠀⠀⠀⠀⠀⣴⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⠀⡈⣵⠟⠀⠀⠀⣼⣷⣻⣋⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠆⠈⣨⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠷⠻⠖⠛⠀⠀⠀⢸⣿⡟⠋⡵⠠⠊⠀⠀⠀⠀⠀⠀⠀⠸⢿⡏⣿⠠⢀⠹⠿⣿⣿⣿⣿⣿⣿⠍⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣠⣃⣠⣶⡧⠀⠀⠄⠀⠀⠀⣏⣉⡆⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⡄⢰⢆⢀⣶⢨⢡⠬⡄⡬⢤⠤⣄⣤⠤⢀⠤⣄⢼⢵⠄⠀⠀⠀⠉⠉⠀⠀⠀⠈⠁⠉⠭⠐⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠋⣿⣿⣷⠇⠀⠀⠀⠀⠀⠇⠈⠆⠓⠔⠘⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣻⠇⠸⠘⠞⠸⠸⠸⠤⠆⠇⡸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠹⢿⣟⣋⠀⢀⠀⠀⠀⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠋⠋⠀⠀⠀⠀⠀⠀⢦⣾⣴⠃⠠⡄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⠒⢺⢠⠭⡇⣿⠀⢸⡁⣿⢸⠒⢪⢸⢳⡸⣿⢸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣿⡟⠁⠀⢈⡀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠟⠃⠀⠀⠀⠀⢀⣀⠈⠀⠈⠈⠉⢹⣯⣅⠈⠧⠉⠈⠉⠉⠈⠀⠁⣉⣼⣅⠀⠀⠀
⢀⣀⣤⣤⣶⢠⢀⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⣠⣴⣿⣿⡆⠀⣠⣤⣶⣾⣿⣿⣟⣠⣤⡖⠀⠀⠀⠠⣿⣿⣿⡟⠀⠀⠀
⣿⣿⣿⣿⡏⡞⣸⣿⠃⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠶⠆⢈⠟⣋⡙⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀
⣿⣿⣿⡿⢸⢡⣿⠃⠀⠻⣿⣿⣦⣄⣀⠈⠉⢉⣠⣷⡄⠀⠀⠀⣶⡄⠻⡄⠠⠄⣾⡀⠛⠃⢰⣶⠀⢰⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣿⠃⣿⣿⡏⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀
⣿⣿⡟⢘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣭⣽⢿⠿⢿⡿⠹⢿⣿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠷⠦⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⢀⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠂⠀
⣿⣿⠃⣿⣏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣽⣿⢰⣿⡄⣿⢸⣿⢐⣛⣂⡇⢰⣿⠠⣿⡆⢹⢠⣿⡇⣧⡀⠀⠀⠀⢐⠀⣉⡛⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀
⣿⣿⣻⡟⠛⠟⠛⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣽⣧⣼⣿⢠⣭⣴⣿⣼⣿⣧⣷⣬⣤⣄⡢⣤⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⢀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠉⠉⠀⠀⢈⢻⣿⣿⣿⣿⡏⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣴⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡸⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣏⣹⠷⣿⣿⠿⠿⠿⠋⠓⠚⠉⠉⠓⠿⢟⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣥⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠟⠉⠑⠆⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠠⠀⡷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢂⣿⠛⣙⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⢀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣴⣄⠀⡆⣇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠗⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢾⢿⣿⣿⡇⢀⣴⡿⠁⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢻⡿⠀⠀⠉⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣇⣸⣿⣿⡿⢡⡿⠙⠛⢀⡶⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢀⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⢠⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⣿⣿⣍⠉⠛⣡⡏⠀⠀⠀⣼⣵⣿⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣯⡀⠀⢸⠁⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡷⠂⠐⠗⠀⠀⠀⣸⢿⡿⠗⡋⢀⠄⠀⠀⠀⠀⠀⠀⠀⣤⣤⢤⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠘⠇⠀⣠⡄⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⡄⢰⢆⢀⣶⢨⢠⠥⡌⡤⢬⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠉⠘⠓⠂⠐⠀⠉⠙⠻⠛⠻⡟⠋⠁⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣿⡖⣾⣿⣏⣄⠀⠁⠀⠀⠇⠈⠆⠳⠔⠘⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠜⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣿⣧⡥⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠿⠟⠃⠀⠀⠀⠀⠀⢈⣠⡟⣴⠚⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⢻⠒⢺⢠⠭⡇⣿⠠⢸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⢀⡌⢀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⢫⡡⡈⠣⠉⠈⠉⠉⠈⠀⠁⠉⠜⢀⠀⠀⠀
⠀⠀⠀⢀⣠⡄⠠⢰⣿⡏⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠴⣶⣦⣤⣴⣶⣶⣶⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠃⠀⠀⠀⠀⠀⣠⣴⣷⠀⠀⠀⢀⢀⣸⣿⣯⡀⠀⡀⠀⠀⠀⠀⠀⣠⣶⣿⣧⠀⠀
⣴⣾⣿⣿⣿⢇⠇⣼⣿⣥⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠴⠆⢈⠟⣉⡙⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⣀⣾⣿⣿⣿⣿⣿⣿⣴⡿⠃⠀⠀⠀⠀⠛⢿⣿⡟⠀⠀
⣿⣿⣿⣿⡏⡸⢠⣿⠁⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠤⣼⡀⠒⠂⢠⣤⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀
⣿⣿⣿⣿⢠⣧⣿⠇⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⣿⣿⣿⡇⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠿⠄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠉⡿⠛⣁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀
⣿⣿⣿⢠⣾⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣿⢰⣿⡄⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣦⣀⠀⠀⠀⠀⢀⠛⢿⠀⣷⡔⠁⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡤
⣿⣿⡿⣿⠛⠟⠛⠛⠚⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣴⣿⣧⣷⣬⣄⡀⢀⣀⣈⣠⣶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⠳⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠹⢿⣿⣿⣿⣷⠃⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢀⣀⣘⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⢋⣻⡻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠡⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⡞⠋⡞⣸⣿⣿⡿⢿⠗⠚⠿⠉⠁⠛⢻⡿⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡶⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡞⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⢀⣾⣽⣍⣐⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⠛⠀⠶⠂⠈⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢸⠆⠀⠀⠀⠀⠀⠈⣡⣿⣿⣿⣿⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣟⣿⣿⣿⣿⡿⠻⠈⣸⠿⠿⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠅⠀⠀⠀⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢆⣤⡀⢰⢰⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡷⠬⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡟⡙⢧⣽⣯⢁⣀⡶⠟⠁⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⡇⠈⠈⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣷⣿⠇⣼⠋⠟⠀⢠⢴⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣌⠙⠻⠇⡼⠁⠀⠀⢠⣏⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡍⠀⠆⠛⠀⠀⠀⠀⠀⠐⠛⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⡀⠀⠀⠁⠀⠀⠀⡾⣿⢿⠕⠋⡡⠀⠀⠀⠀⠀⠀⠀⠀⣈⡡⣠⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠀⢰⠁⠀⣀⠀⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⡀⢰⢆⢀⣶⢨⢠⠤⡅⡤⢌⠤⣄⣠⠤⢀⠤⣄⢼⢵⠄⠈⠃⠛⠤⠤⠆⠙⠛⠻⠿⠿⠿⠟⠋⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣴⣷⢤⣾⣿⢃⡀⠐⠀⠀⠀⠇⠈⠆⠓⠔⠘⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠉⢸⣿⣿⣏⡁⢀⠀⠀⠀⣀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⡿⠿⠁⠀⠀⠀⠀⠀⠂⣸⢇⡔⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠙⠋⢺⠒⢺⢠⠭⣇⣿⡀⢸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣵⣟⠞⠀⢢⡃⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⡿⠌⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠹⣏⣁⠈⠣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⣴⣿⠃⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠤⣤⣄⣤⣤⣤⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠿⣟⠀⠀⠀⠀⠀⠀⣀⣴⣆⠀⠀⠀⠀⢀⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣄⠀⠀
⣤⣶⣾⣿⡿⠰⢠⣿⡏⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠶⠆⢈⠟⣉⡙⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣀⣠⣾⣿⣿⣿⣿⣾⣂⣦⣾⠃⠀⠀⠀⠘⠿⣿⣿⠇⠀⠀
⣿⣿⣿⣿⢃⠇⣼⡟⠀⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠂⠀⢠⣴⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠹⠿⠖⠀⠀
⣿⣿⣿⡏⣼⣼⡿⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⣿⣿⣿⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣭⣽⠿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⠉⡿⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀
⣿⣿⡇⣰⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣽⣿⢰⣿⡈⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡆⣤⡀⠀⠀⠀⠀⠀⠿⣿⠀⣄⠘⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣃⡀
⣿⡿⢻⡿⠛⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣤⣿⣧⣷⣤⡀⠀⡀⢀⠀⢠⣮⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣀⡠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠋⠉⠀⠀⠀⡛⣿⣿⣿⣿⣿⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢧⣄⣅⡽⣫⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣯⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠂⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⡈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣯⣿⡿⢑⡽⠉⡿⢃⣿⣿⡿⠿⠟⠛⠒⠋⠉⠙⠹⠿⢻⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢁⡾⣥⣧⣠⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠾⠟⠈⠐⠆⠀⠈⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⡿⣿⣿⣿⣿⠋⠃⢠⡿⠛⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⣀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣤⣄⠀⠇⣧⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠷⠚⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⡏⠡⡻⣭⣿⠅⣈⣼⡻⠁⠀⢻⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⡿⠀⠈⠈⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡎⠐⣼⡿⣿⠟⣰⠏⠸⠃⢀⡖⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⡈⠙⠟⢠⠋⠀⠀⠀⡾⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣯⡀⠘⠈⠃⠀⠀⠀⠀⠀⠋⠙⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣡⠀⠀⠃⠀⠀⠀⣼⣿⢿⠗⡋⢁⠄⠀⠀⠀⠀⠀⠀⠀⢤⣤⢠⡆⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠏⠀⣀⣄⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣭⡀⢰⢆⢀⣶⢨⢠⠥⡌⡤⢬⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠉⠘⠁⠁⠶⠈⠉⠛⠿⠻⠯⠿⣋⠁⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣧⢀⣴⣾⡶⣾⣿⣏⣤⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣅⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣭⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠿⠷⠃⠀⠀⠀⠀⠀⢐⢠⣏⡴⠙⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠡⠀⠀⠈⠉⢻⠒⢺⢠⠭⡇⣿⢀⢸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠝⠁⢀⡋⢀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⢛⣁⠈⠧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡀⡀⢰⣿⡏⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠴⣶⣦⣤⣤⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠛⠃⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⣰⣿⣿⣦⠂⠂⣀⠀⠀⠀⠀⣀⣴⣾⣿⡄⠀
⣰⣶⣾⣿⣿⢃⠃⣾⡟⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠴⠆⢈⠟⣉⡙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣶⣿⣿⣿⣧⣀⣰⣿⣿⣿⣿⣿⣿⣷⣿⡟⠀⠀⠀⠀⠙⢻⣿⣿⠀⠀
⣿⣿⣿⣿⠏⡜⢰⡿⠁⠻⣿⣿⣦⣄⣀⠈⠉⢁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠒⠂⢰⣾⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⠛⠃⠀
⣿⣿⣿⡿⢰⢣⣿⠃⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⠇⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠈⡿⠟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣇⡀
⣿⣿⡿⢠⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣿⢰⣿⡀⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣦⣀⠀⠀⠀⠀⠀⠘⢿⠀⣧⡄⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁
⣿⣿⠻⣿⠛⠟⠛⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣴⣿⣧⣷⣬⣄⠀⢀⡀⡘⢀⣴⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣀⡠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⠿⠻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⠉⠉⠀⠀⠀⡟⣿⣿⣿⣿⣿⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢇⣠⣅⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣼⣭⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠃⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣽⠉⡾⢁⣿⣿⠿⠿⠟⠓⠚⠋⠉⠙⠳⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⠁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⡁⡾⣵⣯⣠⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠏⠈⠐⠂⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠄⠾⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠳⠁⢰⡿⠛⢿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⣀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⣤⠀⠇⢧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢺⣫⢙⡻⣭⣯⢁⣈⣼⠛⠁⠈⢻⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⡿⠀⠈⠈⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠠⣼⣿⣿⠿⣰⠏⠛⠁⢠⡖⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⢀⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣦⡉⠛⠏⢠⠋⠀⠀⢀⡾⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢯⡀⠘⠐⠃⠀⠀⠀⠀⠀⠉⠉⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣅⠀⠐⠁⠀⠀⠀⣼⣿⢷⠷⡊⢁⠄⠀⠀⠀⠀⠀⠀⠀⣤⣤⢤⡆⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠏⠀⣀⣄⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣩⡀⢰⢆⢀⣶⢨⢠⠥⡄⡤⢬⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠉⠚⠁⠁⠶⠈⠉⠛⠿⠛⠯⠿⡋⠁⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⡧⢀⣴⣾⡷⣾⣿⣏⣤⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡥⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢿⣿⣿⣭⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⡿⠷⠃⠀⠀⠀⠀⠀⢐⢰⡏⡴⠙⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⠀⢸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠜⠁⢀⡋⢀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⢙⣥⣈⠧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⡀⠀⠀
⠀⠀⠀⠀⢀⡀⡀⢰⣿⡏⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠴⣶⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠓⠂⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⢀⣠⣿⣿⣆⡨⠅⣀⠀⠀⠀⠀⢀⣴⣾⣿⡄⠀
⣠⣶⣶⣿⣿⢃⠃⣾⡟⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠴⠆⢈⠟⣉⡙⠷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣶⣿⣿⣿⣧⣀⣰⣿⣿⣿⣿⣿⣿⣶⣿⡗⠀⠀⠀⠀⠙⠻⣿⣿⠁⠀
⣿⣿⣿⣿⠏⡜⢰⡿⠁⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠒⠂⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⠛⠃⠀
⣿⣿⣿⡿⢠⢡⣿⠃⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀
⣿⣿⣿⠇⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠉⣿⠟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⣿⣿⡿⢠⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣽⣿⢰⣿⡈⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⢀⣿⡇⣦⣀⠀⠀⠀⠀⠀⡘⠿⠀⣷⡤⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁
⣿⣿⠻⣿⠛⠟⠛⠛⠚⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣤⣿⣧⣷⣬⣥⡀⢀⡀⣘⠁⣴⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡄⡠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠻⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠉⠉⠀⠀⠀⡟⣿⣿⣿⣿⣿⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣨⣘⣎⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⢛⣽⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠃⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣄⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣭⣿⣛⣞⣯⣿⣿⠿⠿⠟⠒⠻⠉⠉⠙⠻⠿⣿⣟⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢃⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⠃⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⣋⠾⣿⣯⣄⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠋⠈⠒⠂⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠈⠄⠺⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⣳⠉⢸⡿⠟⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⣀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣤⣤⠀⠇⢣⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡛⢚⣿⣿⣿⣉⣀⣼⠏⠁⠘⣺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⡿⠀⠈⠈⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢎⢀⣿⣿⣿⠟⣸⠏⠟⠀⢠⢖⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣎⠛⠻⠏⣸⠋⠀⠀⢀⣏⡼⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣯⡀⠐⠀⠃⠀⠀⠀⠀⠀⠚⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣥⠀⠖⠃⠀⠀⠀⡾⣿⢳⠕⡋⢁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠏⠀⢀⣄⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⡀⢰⢆⢀⣶⢨⢠⠤⡅⡤⢬⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠁⠛⠠⠥⠖⠉⠙⠛⠿⠻⠯⠿⡋⠁⠉⠙⢻⣿⣿⣿⣿⣿⣿⡿⡇⢀⣴⣾⡷⣾⣿⣏⣠⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⣿⣭⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⡿⠿⠃⠀⠀⠀⠀⠀⢂⣰⣏⡴⠹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⢀⢸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠞⠀⢠⡃⢀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⢹⣁⡈⠣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠂⠀
⠀⠀⠀⠀⣀⠀⡀⣰⣿⠋⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠴⣤⣤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠿⠀⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⢀⣠⣿⣿⣴⠨⠂⣀⠀⠀⠀⠀⢀⣤⣾⣿⡆⠀
⣤⣶⣶⣿⣿⢡⠁⣿⡟⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠴⠆⢈⠟⣋⡙⢀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⣀⣰⣿⣿⣿⣿⣿⣿⣇⣮⡾⠀⠀⠀⠀⠙⢻⣿⣿⠁⠀
⣿⣿⣿⣿⠇⡎⣸⡿⠁⠻⣿⣿⣦⣄⣀⠈⠉⢁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⠛⠃⠀
⣿⣿⣿⡟⢸⣱⣿⠁⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⠃⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⠿⠿⢿⡿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠈⣿⠟⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⣿⣿⡟⣠⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⡀⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⢐⣿⡇⣦⣀⠀⠀⠀⠀⠀⠘⠿⠀⣷⡄⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉
⣿⣿⢻⣿⠛⠟⠛⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢀⣭⣴⣿⣴⣿⣧⣷⣬⣤⡀⢀⡀⣘⠁⣴⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡄⡠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⠉⠉⠀⠀⠀⡝⣿⣿⣿⣿⣿⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣣⣠⣮⠟⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣯⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠣⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⡄⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣳⣿⡟⢡⡞⢙⡞⢼⣿⣿⠿⠿⠗⠒⠺⠉⠉⠙⠻⠿⣽⠟⠻⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢃⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⠇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⣀⠿⣴⣯⣅⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠋⠀⠑⠂⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⠀⢺⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠙⠉⣸⡟⠟⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⣠⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣴⣤⠀⢃⢳⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠺⠃⢙⢷⣿⣯⣡⣀⣾⠏⠁⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⡿⠀⠈⠈⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠀⣿⣿⣿⠏⣼⠋⠟⠀⣠⢖⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣅⠉⠻⠇⡼⠁⠀⠀⢀⣟⡼⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢯⡀⠐⠐⠃⠀⠀⠀⠀⠀⠚⠉⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣤⠀⠔⠁⠀⠀⠀⡾⣿⢻⠕⡊⢡⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢤⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠟⠀⢀⣤⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⡀⢰⢆⢀⣶⢨⢠⠤⡅⡤⢬⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠃⠛⠠⠥⠖⠉⠙⠛⠿⠻⠯⠿⡋⠑⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣾⡷⣾⣿⣯⣤⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡂⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢿⣿⣿⣭⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⠿⠾⠁⠀⠀⠀⠀⠀⢂⣰⢇⡔⠹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⢀⢸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠞⠀⢠⡃⢀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⢘⣁⣈⠧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠂⠀
⠀⠀⠀⠀⣀⠀⡀⣰⣿⠋⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠛⠀⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⣠⣿⣿⣤⣰⢦⣠⠀⠀⠀⠀⢀⣤⣾⣿⡆⠀
⣤⣶⣶⣿⣿⢰⢁⣿⡏⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠴⠆⢈⠟⣋⡁⢀⠀⠀⡀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⣀⣰⣿⣿⣿⣿⣿⣿⣷⣽⡿⠀⠀⠀⠀⠘⠻⣿⣿⠃⠀
⣿⣿⣿⣿⠇⡎⣸⡟⠀⠻⣿⣿⣦⣄⣀⠈⠉⠉⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠹⠛⠞⠀
⣿⣿⣿⡏⢸⣰⣿⠁⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⢃⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠉⣿⠟⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀
⣿⣿⡏⣠⣿⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣽⣿⢰⣿⡄⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣦⣀⠀⠀⠀⠀⠀⡘⠿⠀⣷⡄⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁
⣿⣿⢻⣿⠛⠟⠛⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣽⣧⣼⣿⢠⣭⣴⣿⣤⣿⣧⣷⣬⣤⡀⠀⡀⣐⠁⣴⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡆⡠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⡝⣿⣿⣿⣿⣿⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣤⣀⣜⣏⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠣⠀⠀⠀⠀⠡⣿⣿⣿⣿⣿⣄⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⠏⣙⡟⢶⣿⣿⠿⠿⠗⠒⠻⠉⠉⠛⠿⠿⣻⠟⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⠏⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⢠⢏⣼⣏⣔⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠉⠀⠓⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⢺⠄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡆⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠟⠁⣸⠿⠛⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⢀⣠⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣴⣤⠀⢃⢱⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⡙⣷⣿⣯⣀⣠⣶⠋⠁⠘⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⡿⠃⠈⠈⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢦⣿⣿⣿⢇⣼⠉⠟⠀⢰⢖⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣄⠙⠻⠇⣼⠁⠀⠀⢠⡏⡾⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢯⡀⠐⠀⠃⠀⠀⠀⠀⠀⠊⠉⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⣀⠀⠚⠁⠀⠀⢀⡾⣿⣹⠕⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣴⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠗⠀⢀⣄⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⠀⢰⢆⢀⣶⢨⢠⠤⡅⡤⢌⠤⣄⣠⠤⢀⠤⣄⢼⢵⠄⠈⠁⠛⠠⠥⠆⠉⠙⠛⠿⠻⠿⠿⡋⠁⠉⠙⢿⣿⣿⣿⣿⣿⣿⣻⡀⢀⣴⣾⡧⣶⣿⣮⣡⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡆⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢻⣿⣿⣬⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⡿⠞⠀⠀⠀⠀⠀⠀⠂⣼⢇⡔⠑⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⠀⢸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⠟⠀⢠⡁⢀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡏⠓⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠘⣡⡈⠣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠂⠀
⠀⠀⠀⠀⣀⠀⠄⣶⣿⠃⠀⢀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡛⠃⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⣠⣿⣿⣆⡠⠥⣀⠀⠀⠀⠀⢀⣠⣾⣿⣦⠀
⣤⣶⣶⣿⡿⠰⢠⣿⡏⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠴⠆⢈⠟⣁⡀⢀⠀⣀⡀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⣀⣰⣿⣿⣿⣿⣿⣿⣯⣿⣿⠁⠀⠀⠀⠘⠻⣿⣿⠃⠀
⣿⣿⣿⣿⠃⠇⣸⡟⠀⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⠛⠞⠀
⣿⣿⣿⡏⣸⣸⡿⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⢁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠉⣿⠟⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⡀
⣿⣿⡇⣠⣿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⠄⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣦⣀⠀⠀⠀⠀⠀⡘⠿⠀⣷⡄⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋
⣿⣿⢻⡿⠛⠟⠛⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣦⣿⣮⣽⣶⣭⣼⣧⣼⣿⠀⣭⣴⣿⣴⣿⣧⣷⣬⣤⡀⠀⣀⣐⠁⣰⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡆⡠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠉⠉⠀⠀⠀⡝⣿⣿⣿⣿⣿⠁⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣠⣤⣬⣋⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠣⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣄⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣽⣿⡟⣠⡯⣙⠿⢼⣿⣿⠿⠿⠖⠚⠿⠉⠃⠻⠿⠿⣿⠟⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⡏⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⣿⣿⣿⣿⣿⡟⣹⢯⣼⣵⣬⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠉⠀⠓⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⢺⠄⠀⠀⠀⠀⠀⠈⣴⣿⣿⣿⣿⡆⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠞⠀⣸⠟⠯⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⣤⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⣤⠀⢃⢱⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⢟⢿⣿⡯⡀⣠⡶⠏⠁⠘⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⡿⢃⠈⠈⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⣿⣿⣿⢇⣾⠉⠿⠀⣠⢶⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣌⠙⠻⢃⡾⠃⠀⠀⢠⣏⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢯⡀⠐⠀⠇⠀⠀⠀⠀⠀⠚⠉⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣀⠀⠘⠀⠀⠀⢀⡟⣿⣹⠕⠉⡡⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣴⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠟⠀⢀⣤⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⠀⢰⢆⢀⣶⢨⢨⠤⡅⡤⢌⠤⣄⣤⠤⢀⠤⣄⢼⢵⠄⠉⠃⠛⠠⠤⠆⠉⠙⠛⠿⠻⠿⠿⡋⠁⠉⠙⢿⣿⣿⣿⣿⣿⣿⣯⡀⢀⣴⣾⡧⣶⣿⣯⣡⠀⠀⠀⠀⠃⠈⠆⠳⠔⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠟⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢻⣿⣿⣭⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⡿⠞⠀⠀⠀⠀⠀⠐⠂⣼⢣⡔⠓⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⠀⢸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣏⠏⠀⢢⡁⢈⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣟⠫⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠸⣡⣈⠧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠂⠀
⠀⠀⠀⠀⣀⠀⠄⣶⣿⠃⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡟⠋⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⣠⣿⣿⣖⡦⠢⢀⠀⠀⠀⠀⢀⣠⣾⣿⣤⠀
⣤⣶⣶⣿⡿⠰⢠⣿⡏⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠴⠆⢈⠟⣀⡀⢠⠀⣀⡀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣴⣿⣿⣿⣧⣀⣰⣿⣿⣿⣿⣿⣿⣶⣾⡿⠀⠀⠀⠀⠘⠿⣿⣿⡇⠀
⣿⣿⣿⣿⠓⠇⣼⡟⠀⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠻⠛⠟⠀
⣿⣿⣿⡇⣼⣸⡿⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠉⣿⠟⠋⢀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀
⣿⣿⡇⣸⣿⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⡀⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣦⣀⠀⠀⠀⠀⠀⡘⠿⠀⣧⡄⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣃
⣿⡿⢻⣿⠛⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣼⣿⣧⣷⣬⣥⡀⢀⡀⣐⠁⣰⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠉⠀⠀⠀⡙⣿⣿⣿⣿⣿⠃⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠡⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢤⡟⢹⠞⢼⣿⣿⠿⠷⠖⠻⠯⠉⠉⠻⠿⠿⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢣⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣟⢨⣯⣼⣭⣔⣿⠁⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⠿⠋⠉⠒⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠉⠆⢸⠆⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠿⠁⣸⠿⠿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⢀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣤⠀⢡⢰⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠒⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠫⠛⢝⢿⣿⣿⣉⣁⡶⠋⡁⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⢇⠈⠈⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣿⣷⣿⢇⣼⠙⠟⠀⢠⢶⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡄⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⠙⠻⠇⡾⠃⠀⠀⢠⡏⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢯⡁⠀⠀⡇⠀⠀⠀⠀⠀⠚⠛⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢟⡀⠀⠘⠁⠀⠀⠀⡾⣾⣹⠕⠊⠡⠀⠀⠀⠀⠀⠀⠀⠀⣄⣡⣰⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠷⠀⢀⣀⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣋⣉⠈⢰⢆⢀⣶⢨⢠⠤⡅⡤⢬⠤⣅⣠⠤⢀⠤⣄⢼⢵⠄⠘⠃⠛⠤⠤⠆⠉⠛⠻⠿⠻⠿⠷⡛⠁⠉⠙⢿⣿⣿⣿⣿⣿⣿⣧⣀⠀⣠⣾⣧⢶⣿⣯⣡⠀⠀⠀⠀⠇⠈⠆⠳⠔⠘⠦⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢺⣿⣿⣭⢀⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⠿⠁⠀⠀⠀⠀⠐⠂⣼⢇⡔⠳⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠙⢻⠒⢺⢠⠭⡇⣿⠀⣸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣟⠟⠀⢠⡃⢈⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠸⣁⣈⠧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⡀⣴⣿⠃⠀⢠⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠤⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡏⠍⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⣀⣿⣿⣶⣶⠂⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⠀
⣤⣴⣶⣿⡿⠰⢠⣿⠏⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢈⠖⣀⡀⢤⠖⣉⡃⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣴⣿⣿⣿⣷⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⠿⣿⣿⡇⠀
⣿⣿⣿⣿⠃⠇⣼⡟⠀⠻⣿⣿⣦⣄⣀⠈⠉⢉⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣾⡀⠛⠃⢸⣿⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠹⠿⠗⠀
⣿⣿⣿⡇⣸⣸⡿⠁⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⢁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠉⣿⠿⠋⢈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⡀
⣿⣿⡇⣸⣿⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⡈⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠠⣿⡇⣦⣀⠀⠀⠀⠀⠀⠘⠿⠀⣿⣄⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⣿⣿⢻⣿⠛⠟⠛⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣬⣿⣧⣷⣬⣤⠀⠀⡀⢀⠃⣰⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣇⣀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡋⠉⠁⠀⠀⣸⢻⣿⣿⣿⣿⡇⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣠⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠱⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣇⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡟⢙⣞⢴⣿⣿⡿⠷⠖⠻⠭⠉⠉⠛⠿⡿⣽⠟⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⢡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⢀⣾⣼⣏⣔⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⠋⠁⠒⠂⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠅⠆⢸⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣻⣿⣿⣿⡿⠷⠉⣸⠿⠟⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⣀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⣤⡀⢰⢸⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠒⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠻⠛⢿⣿⣿⢃⣀⣴⠟⠁⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⠇⠀⠈⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⢠⣿⣿⣿⠇⣼⠋⡟⠀⢠⢆⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣄⠙⠻⠇⣼⠃⠀⠀⢀⡟⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢯⡅⠀⠁⡟⠀⠀⠀⠀⠀⠘⠛⠻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⡀⠀⠘⠃⠀⠀⠀⡾⣿⢻⠵⡊⢁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣡⣠⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠳⠀⢀⣀⠀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣋⣋⠀⢰⢆⢀⣶⢨⢠⠤⡅⡤⢬⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠋⠛⠠⠤⠖⠉⠛⠻⠿⠻⠿⠷⣛⠁⠋⠙⢻⣿⣿⣿⣿⣿⣿⣶⣄⡀⣠⣶⣧⢶⣿⣿⣁⠀⠀⠀⠀⠇⠈⠆⠳⠔⠘⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⢯⢁⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⡿⠁⠀⠀⠀⠀⠀⠂⣸⢇⡔⠱⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⠀⣸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⠞⠀⢀⡃⢈⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡿⠝⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠸⣃⣈⠧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⡀⣰⣿⠃⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡟⠁⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⢀⣿⣿⣦⢤⠂⠀⠀⠀⠀⠀⠀⣀⣴⣾⣧⠀
⣤⣴⣶⣾⣿⢠⢀⣿⡟⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢀⠖⣀⡀⢶⠞⣉⡃⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣀⣠⣾⣿⣿⣿⣿⣿⣿⣽⣿⠁⠀⠀⠀⠘⠿⣿⣿⡏⠀
⣿⣿⣿⣿⠇⡇⣸⡟⠀⠻⣿⣿⣦⣄⣀⠈⠉⢉⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠹⡿⠷⠀
⣿⣿⣿⡏⢸⣰⣿⠁⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⢁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠉⣿⡿⠋⢈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡀
⣿⣿⡏⢨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⠄⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⢀⣿⡇⣦⣀⠀⠀⠀⠀⠀⠐⠿⠀⣿⣄⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⣿⣿⢻⣿⠛⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣴⣿⣧⣷⣬⣥⡀⠀⡀⢀⠃⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⢀⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠛⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡋⠉⠁⠀⠀⢈⢻⣿⣿⣿⣿⡇⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⣀⣊⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣧⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣟⠙⡾⣴⣿⣿⡿⠿⠗⠛⠿⠍⠁⠻⠿⠿⣻⡟⠽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠐⣾⣽⣯⣄⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⠋⠈⠐⠇⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠇⠀⠰⠇⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣧⠸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⣿⣷⠋⢠⡿⠟⢿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⠀⠀⠀⣀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣤⡀⠸⢸⡄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠖⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⢽⢷⣽⣿⠋⣁⣴⠟⠁⠘⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⠇⠀⠁⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢠⣿⣿⣿⡏⣰⠏⠿⠀⢀⡆⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⢀⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣌⠉⠻⠏⣸⠏⠀⠀⠀⡞⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠯⣅⠀⠃⠘⠀⠀⠀⠀⠀⠐⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡁⠀⠒⠋⠀⠀⠀⣼⣽⢳⡧⠊⢁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣩⣤⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠰⠁⠀⣀⡀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⡁⢰⢆⢀⣶⢨⢠⠥⡍⡤⢴⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠋⠛⠡⠤⠴⠉⠛⠻⠿⠿⠿⠿⢛⠁⠈⠙⢻⣿⣿⣿⣿⣿⣾⣷⣤⣀⣠⣶⣷⢴⣿⣿⣁⡄⠀⠀⠀⠃⠈⠆⠓⠴⠘⠢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡁⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⣿⣯⣅⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⡿⠃⠀⠀⠀⠀⠀⠒⢰⣏⡤⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⡀⣸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⡜⠁⢀⡋⢀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠈⢇⣈⠧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⢰⣿⠏⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡟⠋⠁⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⠀⢀⣸⣿⣗⢂⢰⠀⠀⠀⠀⠀⠀⣀⣴⣾⣧⡀
⣠⣴⣶⣾⣿⢁⠁⣿⡟⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢈⠟⣂⡙⢿⠟⣉⡁⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣀⣀⣶⣿⣿⣿⣿⣿⣿⣨⣾⠃⠀⠀⠀⠐⠿⣿⣿⡿⠀
⣿⣿⣿⣿⠏⡌⢸⣿⠁⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠙⡿⠷⠂
⣿⣿⣿⡟⢰⢡⣿⠃⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⠃⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⣿⡿⠟⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣀
⣿⣿⡟⢀⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⡀⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠠⣿⡇⣦⣀⡀⠀⠀⠀⠀⠀⠻⠀⣿⣄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⣿⣿⠻⣿⠛⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣤⣿⣧⣷⣬⣥⡀⠀⣀⢀⠋⢠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⢀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠛⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡋⠉⠁⠀⠀⢈⢻⣿⣿⣿⣿⡏⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣀⣈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢫⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣧⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⣟⠛⡾⢤⣿⣿⡿⠷⠖⠚⠯⠍⠁⠹⠿⡿⣻⡟⠽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣷⣿⣿⣿⣿⡉⡾⣴⣏⣀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠋⠈⠐⠇⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠠⠐⡇⠀⠀⠀⠀⠀⠀⢡⣾⣿⣿⣿⣷⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣿⣿⢿⣿⡿⡷⠉⢠⡿⠟⢿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⠀⠀⠀⣀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣤⡄⠸⠘⡆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠗⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠻⢺⢿⣽⣿⡁⣀⣴⡟⠁⠐⢹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⠷⠀⠁⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⡏⣰⡋⠿⠀⢀⡆⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⢀⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⠉⠻⠏⢸⠏⠀⠀⠀⡞⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠯⣅⠀⠃⠘⠀⠀⠀⠀⠀⠐⠛⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡁⠀⠔⠋⠀⠀⠀⣼⣷⢧⡣⠊⢁⠄⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⡄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⠃⠀⣀⡀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⡁⢰⢆⢀⣶⢨⢠⠥⡄⡤⢴⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠛⠛⠡⠤⠴⠈⠙⠻⠿⠿⠿⠿⠟⠁⠈⠙⢻⣿⣿⣿⣿⣿⣿⣷⣤⣄⣠⣶⣷⢴⣾⣿⣁⡀⠀⠀⠀⠃⠈⠆⠳⠴⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡡⠸⠘⠞⠸⠸⠸⠤⠆⡇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠸⣿⣿⣯⣅⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⠿⠃⠀⠀⠀⠀⠀⠒⢰⣏⡠⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⡀⢸⠁⣿⢸⠒⢪⢸⢳⡸⣿⢘⡆⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⡜⠁⢀⡋⢀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠈⢇⣈⡣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⢰⣾⠏⠀⢀⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡟⠋⠁⠀⠀⠀⠀⣀⣴⣦⠀⠀⠀⠀⢀⣼⣿⣷⣒⣔⠀⡀⠀⠀⠀⠀⣀⣴⣾⣧⡄
⣠⣴⣶⣾⣿⢁⠁⣿⡟⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⠆⢈⠟⣉⡙⢿⠟⣉⡁⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣀⣀⣶⣿⣿⣿⣿⣿⣿⣨⣿⠇⠀⠀⠀⠀⠿⣿⣿⡿⠀
⣿⣿⣿⣿⠏⡜⢰⡿⠁⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠘⠻⠷⠂
⣿⣿⣿⡿⢰⢡⣿⠃⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠈⣿⡿⠟⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁
⣿⣿⡿⢀⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⠀⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠠⣿⡇⣦⣀⡀⠀⠀⠀⠀⠀⠻⠀⣿⣄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⣿⣿⠻⣿⠟⠟⠛⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣤⣿⣧⣷⣬⣥⡀⠀⢀⢀⠋⢠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⢀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡋⠉⠁⠀⠀⢈⢻⣿⣿⣿⣿⡏⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⣀⣈⡛⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣭⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⡄⠀⠀⠀⠈⣼⣿⣿⣿⣿⣧⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣜⠋⡞⣰⣿⣿⡿⠷⠖⠚⠯⠍⠉⠛⠿⠿⣿⡟⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣿⣿⡿⡩⡾⣴⣯⣀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠏⠈⠐⠆⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠐⠧⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣧⠸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⣿⢿⣿⣿⠵⠉⢲⡿⠗⢿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⣀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣤⡀⠸⠘⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠖⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠝⢘⠷⣽⣿⠑⣈⣼⡟⠁⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⠧⠀⠁⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣷⣿⡏⣰⠟⠖⠀⢀⡆⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣀⢀⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣠⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣆⠉⠻⠏⣰⠃⠀⠀⢀⡞⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠫⣅⠀⠃⠘⠀⠀⠀⠀⠀⠐⠛⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡁⠀⠀⠃⠀⠀⠀⣼⣿⢳⡷⠊⢁⠄⠀⠀⠀⠀⠀⠀⠀⣤⣠⢤⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠸⠃⠀⣀⡀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⡁⢰⢆⢀⣶⢨⢠⠥⡌⡤⢴⠤⣅⣠⠤⢀⠤⣄⢼⢵⠄⠈⠃⠚⠡⠤⠴⠉⠙⠻⠿⠿⠿⠿⡛⠁⠈⠙⢻⣿⣿⣿⣿⣿⣿⣷⣶⣄⣠⣶⣷⢴⣿⣿⣁⡀⠀⠀⠀⠃⠈⠆⠳⠴⠘⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡡⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠞⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠸⣿⣿⣯⣅⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⡿⠃⠀⠀⠀⠀⠀⠂⣰⣏⡴⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⡀⣸⠁⣿⢸⠒⢪⢸⢳⡸⣿⢘⡆⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⠜⠁⢐⡇⢀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠈⢇⣈⡧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⡀⢰⣿⠏⠀⢀⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡟⠋⠀⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⠀⢀⣽⣿⣷⠂⡶⠀⣀⠀⠀⠀⠀⣀⣴⣾⣧⡄
⣠⣴⣶⣾⣿⢁⠁⣿⡟⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢈⠟⣉⡙⢿⠟⣉⡁⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣄⣀⣶⣿⣿⣿⣿⣿⣿⣠⣾⠇⠀⠀⠀⠐⠿⣿⣿⡿⠀
⣿⣿⣿⣿⠏⡌⣸⡿⠀⠻⣿⣿⣦⣄⣀⠈⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠘⡿⠷⠂
⣿⣿⣿⡟⢰⢡⣿⠃⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⣾⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⣿⡿⠟⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣁
⣿⣿⡟⢀⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣭⣽⣿⢰⣿⡀⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣦⣀⡀⠀⠀⠀⠀⠀⠻⠀⣿⣄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⣿⣿⠻⣿⠟⠟⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣴⣿⣧⣷⣬⣥⡀⠀⣀⢀⠋⢠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⢀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡋⠉⠁⠀⠀⢈⢻⣿⣿⣿⣿⡏⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣘⡯⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣽⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⡀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣧⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣷⣿⡟⢁⣟⠛⡾⣴⣿⣿⡿⠿⠖⠚⠯⠍⠁⠻⠿⡿⣿⡟⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢯⢿⣿⣿⣿⡿⣋⡾⣴⣯⣄⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⠋⠉⠒⠃⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠐⠇⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣧⠸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣟⡻⣿⣿⣿⡿⠱⠉⢰⡿⠟⢿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⠀⠀⠀⠀⠀⠀⣀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣤⡀⠸⠘⡄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠖⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠋⠚⢷⣿⣯⠁⣈⣴⢟⠁⠘⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⠇⠀⠁⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣾⡟⣼⠏⠿⠀⢠⡆⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣅⠙⠻⠏⣸⠋⠀⠀⢀⡞⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢩⣅⠀⠇⠘⠀⠀⠀⠀⠀⠐⠛⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣀⠀⠖⠃⠀⠀⠀⡾⣽⢳⠷⡊⢁⠀⠀⠀⠀⠀⠀⠀⠀⢄⣡⢠⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣇⠀⠀⠀⠀⠀⠸⠃⠀⣀⡀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⡀⢰⢆⢀⣶⢨⢠⠥⡅⡤⢬⠤⣅⣠⠤⢀⠤⣄⢼⢵⠄⠈⠃⠚⠠⠥⠶⠉⠛⠻⠿⠻⠿⠿⡛⠁⠉⠙⢻⣿⣿⣿⣿⣿⣿⣷⣶⣄⣠⣶⣿⢴⣿⣿⣡⡀⠀⠀⠀⠃⠈⠆⠳⠴⠘⠢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡁⠸⠘⠞⠸⠸⠸⠤⠆⡇⠸⠤⠟⠬⠽⠺⠤⠟⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⣿⢯⣅⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⠿⠁⠀⠀⠀⠀⠀⠂⣰⣏⡴⠹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⡀⣸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠜⠁⢐⡃⢀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠈⢇⣈⡣⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⡀⣰⣿⠋⠀⢀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⣀⣠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡟⠃⠀⠀⠀⠀⠀⣀⣴⣆⠀⠀⠀⠀⢀⣼⣿⣷⣂⠂⠀⠀⠀⠀⠀⠀⣀⣴⣾⣧⡀
⣠⣴⣶⣾⣿⢁⠀⣿⡟⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢈⠟⣉⡙⢿⠟⣉⡁⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣀⣀⣶⣿⣿⣿⣿⣿⣿⣤⣿⠏⠀⠀⠀⠐⠿⣿⣿⡿⠀
⣿⣿⣿⣿⠏⡌⣸⡿⠁⠻⣿⣿⣦⣄⣀⠀⠉⠁⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠘⡿⠷⠂
⣿⣿⣿⡟⢰⢡⣿⠁⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⠃⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⢿⡿⠿⢿⠿⠿⢿⣿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⣿⡿⠟⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀
⣿⣿⡟⢀⣿⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⡀⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠀⣿⡇⣦⣀⠀⠀⠀⠀⠀⠀⠻⠀⣿⣄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⣿⣿⢻⣿⠛⠟⠛⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣦⣿⣮⣽⣶⣭⣼⣧⣼⣿⠀⣭⣴⣿⣴⣿⣧⣷⣬⣥⡀⠀⣀⢀⠃⢠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣧⢀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡋⠉⠁⠀⠀⢘⢻⣿⣿⣿⣿⡇⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠘⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣧⠸⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣿⢻⣞⣼⣿⣿⡿⠿⠾⠚⠯⠉⠉⠻⠿⠿⣽⡟⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⡿⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⢵⣿⣽⣯⣔⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⠋⠉⠒⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠀⠰⠇⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣧⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⡿⠋⣸⠿⠿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⣀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣤⡀⢸⢸⡄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠶⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣛⣿⣿⣯⠁⣚⣴⡟⠁⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⠇⠀⠁⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣿⣯⣿⠟⣼⠋⠿⠀⢠⢦⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣅⠙⠻⠏⣼⠁⠀⠀⢀⡟⡼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠴⠋⢯⡅⠀⠅⡟⠀⠀⠀⠀⠀⠐⠛⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⡀⠀⠐⠃⠀⠀⠀⡾⣿⢹⠵⡊⢁⠀⠀⠀⠀⠀⠀⠀⠀⣥⣡⣤⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⠁⢀⣀⡀⠀⠀⠀⠀⣏⣉⡇⣤⣠⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⠈⢰⢆⢀⣶⢨⢠⠤⡅⡤⢬⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠃⠛⠤⠤⠆⠉⠛⠻⠿⠻⠿⠷⣟⠁⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣶⣧⢶⣿⣿⣣⡀⠀⠀⠀⠇⠈⠆⠳⠴⠘⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡂⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠸⣿⣿⢯⣅⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⡿⠁⠀⠀⠀⠀⠀⠂⣸⢇⡔⠱⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⠀⣸⠁⣿⢸⠒⢪⢸⢱⡸⣿⢘⡆⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⠞⠀⢢⡃⢈⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠘⣗⣈⡧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠑⠀
⠀⠀⠀⠀⣀⠀⡀⣰⣿⠃⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠤⣤⣄⣀⣠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡟⠉⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⢀⣿⣿⣰⣀⡧⠀⡀⠀⠀⠀⠀⣀⣴⣾⣧⠀
⣤⣴⣶⣾⣿⢰⢀⣿⡟⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢈⠟⣋⡙⢿⠟⣉⡃⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣴⣾⣿⣿⣿⣀⣠⣾⣿⣿⣿⣿⣿⣿⣾⣿⠆⠀⠀⠀⠘⠿⣿⣿⡿⠀
⣿⣿⣿⣿⠇⠆⣸⡿⠀⠻⣿⣿⣦⣄⣀⠈⠉⠉⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠹⡿⠷⠂
⣿⣿⣿⡏⣸⣰⣿⠁⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⢁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠉⣿⡿⠏⠈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀
⣿⣿⡏⣨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⡄⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⠠⣿⡇⣦⣀⠀⠀⠀⠀⠀⠐⠻⠀⣿⣄⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⣿⣿⢻⣿⠛⠟⠛⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣽⣧⣼⣿⢠⣭⣴⣿⣴⣿⣧⣷⣬⣥⡀⠀⣀⢀⠃⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣧⢀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡋⠉⠁⠀⠀⢨⢻⣿⣿⣿⣿⡇⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠘⡀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣧⠸⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⢣⣿⣙⣾⢾⣿⣿⡿⠿⠗⠖⠿⠉⠉⠻⠿⡿⣿⢟⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⡟⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢴⣟⣼⣯⡜⣿⠁⠀⠀⠀⠀⠀⠀⠈⠀⣾⣿⠿⠋⠉⠒⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠃⠁⠰⠇⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣧⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⡿⠉⣸⠿⠿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⣀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣦⡀⢸⢸⡄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠖⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⢛⣿⣿⣯⣁⣈⣾⠏⠁⠘⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⠇⠀⠀⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣯⣿⢗⣼⠋⠗⠀⢠⢆⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠃⡀⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣅⠙⠻⠇⣼⠁⠀⠀⢀⣟⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠚⠐⠯⠅⠀⠃⡛⠀⠀⠀⠀⠀⠐⠛⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠂⠐⠁⠀⠀⠀⡾⣿⢹⠵⡊⢁⠀⠀⠀⠀⠀⠀⠀⠀⣥⣥⣤⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠸⠁⢀⣀⡀⠀⠀⠀⠀⣏⣉⡇⣤⣤⣠⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⣉⠈⢰⢆⢀⣶⢨⢠⠤⡅⡤⢬⠤⣅⣤⠤⢀⠤⣄⢼⢵⠄⠈⠃⠛⠤⠤⠆⠉⠛⠻⠿⠻⠿⠷⡋⠁⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣶⣧⢶⣿⣿⣣⡀⠀⠀⠀⠇⠈⠆⠳⠴⠘⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡀⠸⠘⠞⠸⠸⠸⠤⠆⠇⠸⠤⠟⠬⠽⠺⠤⠞⠸⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠸⣿⣿⢯⢅⠀⠀⠀⢀⠀⠀⡠⣀⢀⣀⣀⢀⡀⠀⣀⢄⠀⠀⠀⠀
⣿⠿⠁⠀⠀⠀⠀⠀⠂⣸⢇⡔⠱⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⢻⠒⢺⢠⠭⡇⣿⠀⣸⠁⣿⢸⠒⢪⢸⢳⡸⣿⢘⡆⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠟⠀⢠⡃⢈⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⠓⠂⠀⠀⠀⠀⠈⠀⠈⠈⠉⠉⠘⣇⣈⠧⠉⠈⠉⠉⠈⠀⠁⠉⠜⠀⠀⠑⠀
⠀⠀⠀⠀⣀⠀⡀⣰⣿⠃⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠤⣤⣄⣀⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡟⠈⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⢀⣿⣿⣧⡈⠷⠀⡀⠀⠀⠀⠀⣀⣴⣾⣧⠀
⣤⣴⣶⣾⣿⢰⢀⣿⡏⣤⣶⡈⠛⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⠆⢈⠟⣉⡙⢿⠟⣉⡃⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣴⣾⣿⣿⣿⣀⣠⣾⣿⣿⣿⣿⣿⣯⣾⣿⠆⠀⠀⠀⠘⠿⣿⣿⡿⠀
⣿⣿⣿⣿⠇⠆⣸⡟⠀⠻⣿⣿⣦⣄⣀⠈⠉⠉⣠⣷⡄⠀⠀⠀⣶⡄⠻⡀⠠⠄⣼⡀⠛⠃⢸⣿⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠹⡿⠷⠂
⣿⣿⣿⡏⣸⣰⣿⠁⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⢁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣽⢿⠿⢿⡿⠹⢿⡿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⣿⡿⠟⢈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀
⣿⣿⡇⣨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣽⣿⢰⣿⡌⣿⢸⣿⢐⣛⣂⡇⢰⣿⠀⣿⡆⢹⢠⣿⡇⣦⣀⡀⠀⠀⠀⠀⡀⠻⠀⣿⣄⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟
⣿⣿⢻⣿⠛⠟⠛⠛⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣼⣿⣧⣿⣮⣽⣶⣭⣼⣧⣼⣿⢠⣭⣴⣿⣬⣿⣧⣷⣬⣥⡀⠀⣀⢀⡃⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⡀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠀⠇⠗⠋⠉⠈⡖⠀⠸⠸⠸⠚⠸⠸⠘⠌⠄⠔⠇⠇⠇⠇⠇⠇⠸⠸⠨⠀⠇⠘⠸⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢀⢀⢀⢲⢐⢀⠀⡀⡀⢀⢀⢀⠀⡀⢀⢰⠀⡠⠢⢀⢀⡀⡀⡂⢢⠀⡀⡄⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠘⠐⠘⠘⠘⠐⠀⠋⠁⠘⠘⠈⠃⠋⠘⠘⠀⠑⠐⠑⠊⠇⠊⠃⠘⠓⠊⠃⠀⠊⠑⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢟⢿⢟⡻⡍⣽⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠘⠃⠤⠠⣠⢸⠈⠀⡄⣄⠤⢨⢠⢠⠠⣠⢰⠀⣅⠄⡤⡤⡜⠃⢠⢠⠠⢰⢠⣠⡄⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡟⣭⣭⣟⢽⡍⡏⣿⣸⣜⣼⣮⣥⣿⣶⣿⣿⡿⠿⠿⠛⠃⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠈⠈⠈⠀⠀⢁⠉⠁⠈⠈⠈⢈⠈⠈⠀⠁⠁⡁⠁⠁⢀⣈⡁⠁⡈⠈⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣯⣽⣾⣷⣿⣿⡾⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢰⣠⡆⠒⠂⢰⢰⢰⢰⢰⢰⡔⠀⡇⡆⡆⡂⡆⡇⡇⡆⡦⡄⡇⡇⢸⢐⢴⢰⢰⢐⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⣿⠿⣷⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠈⠀⣭⡍⠉⠀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⢿⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⢻⣿⣿⣿⣿⣿⡇⠀⠀⢹⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠸⠟⠃⣸⡏⣿⡁⣉⣹⢋⣉⣩⡟⢉⣉⠻⣿⢹⣿⢉⣉⡉⣿⣿⣿⣀⣇⣏⠹⣿⠋⣽⣉⣉⠙⣿⢸⡏⢹⣿⡏⣿⠟⣉⡉⢻⣇⣧⣸⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣭⣭⣭⠨⠭⠄⢨⡅⣭⡅⢭⢭⠨⠭⢭⡅⠩⡭⢀⣭⢨⣭⢨⣭⡅⣭⣭⣭⣭⣭⣭⡄⠉⣠⡍⠠⡤⠀⣭⢨⣅⠨⡭⠅⣭⡀⠤⡤⢬⣭⣭⣭⢭⣭⢭⣭⣭⡅⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣿⣷⣶⣾⣷⣶⣾⣿⣶⣶⣾⣿⣾⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣿⣾⣿⣶⣶⣶⣿⣷⣶⣶⣾⣿⣿⡟⠀⠃⠘⢸⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⣿⣿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢠⠀⣭⡭⠍⣬⡈⢭⣭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢭⢡⣭⣭⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⣼⡇⣿⢇⣄⣿⣿⠘⠋⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣷⡉⢸⣿⣿⣿⣧⣿⣷⠛⣿⣿⣿⣿⣿⡿⠟⢿⠻⢿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⢉⣈⡉⣭⢍⣀⣤⣤⣬⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 2803

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/Red_Hat_is_Connected_to_the_Military_Its_Chief_Comes_From_Milit.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Red_Hat_is_Connected_to_the_Military_Its_Chief_Comes_From_Milit.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Red Hat is Connected to the Military, Its
Chief Comes From Military Family (From Both
Sides)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


This (below) was posted some hours_ago. The Shelton Leadership Center is tied
to regime change in South America and the Caribbeans and is called after Red
Hat's real leadership up until the takeover [1, 2] by the_nukes_company.


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Students_a_part_of_the_Shelton_Leadership_Center’s_2026
Global_Leadership_Minor_have_had_two_powerful_experiences_the_last_two_days_to
                            start_their_semester⦈_


If you dislike what the US does militarily right now, then take a moment to
remind yourself that Red Hat's Chairman of the Board (top of Red Hat; he can
fire the CEO) at one time was retired General Hugh Shelton.


Also be aware that IBM's CEO isn't some scientist per se; both his parents
worked for the Indian military and he nowadays governs IBM like a dictator,
based on what staff is saying (it's_not_a_new_problem).


If you think of Red Hat, don't visualise "DEI" or peace or rainbows; think of
military, brutal bombings, and worse_things. The_founder_of_Red_Hat's_parent
company_literally_saluted_Hitler_himself (yes, a Nazi salute). █


    * Don't_Cry_for_Gaslighting_Media_in_a_Country_Which_Loathes_the_Press
    * Running_Techrights_is_Fun,_Rewarding,_and_Gratifying


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣧⡁⠇⠀⠀⠀⢀⣾⣿⣿⠿⣾⣿⡿⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣷⣿⣷⣿⣾⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⣤⣤⣴⣾⣿⣿⣷⣥⣿⣾⣮⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⡟⢿⣿⠻⠿⣿⡿⣿⡿⡿⣿⣿⣟⣿⡿⢻⢿⡿⢿⣿⢻⡿⠿⢻⡿⠿⣿⡟⡿⢿⣿⣿⠿⢿⣿⠿⢿⣿⣟⡻⣿⡿⢻⣿⢿⢿⣟⠛⣻⣻⡻⣟⢻⣿⠟⢿⣿⣿⣿⡿⡿⠟⢿⣿⢿⢻⢿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣾⣿⣶⣷⣿⣿⣾⣶⣧⣷⣿⣿⣿⣷⣾⣿⣷⣾⣿⣾⣷⣾⣾⢷⣶⣿⣷⣷⣷⣾⣿⣾⣾⣿⣷⣾⣿⣷⣷⣿⣷⣾⣿⣾⣷⣷⣷⣾⣿⣷⣷⣿⣿⣶⣶⣿⣿⣿⣿⣷⣶⣾⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣁⣀⣾⣪⣰⣷⣁⣠⣭⣸⣷⣇⣁⣸⣖⣩⣖⣽⢐⣕⣍⣤⣈⣰⣆⣀⣯⣐⣽⣪⣀⣰⣇⣅⣨⣪⣘⣸⣔⣎⣄⣇⣁⣃⣔⣖⣡⣩⣺⣕⣄⡩⣄⣾⣨⣺⣇⣖⣈⣰⣺⣰⣎⣈⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣛⢛⢿⣻⣿⢛⢻⣿⡏⢻⣿⡟⡿⣿⣿⣿⡿⢛⠛⢹⣿⣿⣻⠛⣿⠋⢛⢿⢻⠉⣿⣟⡟⡛⣻⡟⠛⢻⠿⠛⡿⣻⣟⣟⠋⣿⡟⣿⡟⢻⣟⠟⢹⢻⢻⣿⠏⢻⡟⣿⡿⢛⠙⢻⣿⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⢿⣿⣿⡿⠿⣿⢿⢿⡿⡿⣿⢿⡿⡿⢿⡿⢿⡿⡿⡿⣿⣿⢿⢾⢿⣿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⢿⡿⠿⣿⢿⠿⡿⠿⡿⣿⠿⡿⡿⠿⡿⣿⢿⢿⠿⢿⢿⣿⡿⡿⡿⡿⢿⢿⣿⣿⣿⣿
⣿⣿⣿⣯⣴⣥⣼⣮⣼⣔⣹⣧⣼⣯⣼⣿⣵⣤⣬⣯⣾⣤⣧⣼⣥⣼⣿⣯⣤⣿⣤⣤⣿⣽⣵⣤⣼⣯⣼⣧⣤⣿⣧⣶⣤⣧⣦⣤⣤⣶⣼⣥⣧⣼⣧⣼⣨⣥⣯⣤⣥⣷⣽⣿⣤⣿⣵⣬⣧⣥⣿⣬⣤⣽⣿⣿⣿⣿
⣿⣿⣿⣯⣁⣿⣾⣏⣹⣟⢉⣩⣻⣯⣩⣻⣋⣁⣍⣿⣟⣩⣭⣉⣹⣿⣨⣯⣩⣹⣯⢁⣽⣇⣿⣯⣩⣯⣈⣽⣿⣈⣋⣇⣉⣹⣿⣫⣹⣉⣅⣾⣿⣯⣀⣝⣹⣉⣝⣝⣈⣽⡏⣯⣉⣭⣛⣿⣍⣋⣝⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢻⣿⠿⠿⣿⡿⢿⣿⣿⡿⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⣿⣶⣶⣿⣶⣾⣾⣿⣶⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⣽⠛⠹⣿⢿⣟⠻⣿⣿⠟⡿⡛⣻⣿⣿⠛⠙⣿⣿⠟⡏⡿⣿⢿⢟⡟⡛⠏⣿⣿⠛⢛⣿⡏⡏⢻⣿⠛⣻⢛⠛⢹⡟⡏⢛⠿⣻⡟⡛⣿⡿⣿⣿⢉⣿⢻⣿⢛⣿⣏⡟⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⢿⡿⠶⠿⣿⣿⡿⣿⢿⠿⣿⢿⢿⡿⡿⢿⢿⢿⢿⠟⠿⢿⠿⡿⠿⡿⡿⡿⠿⡿⡿⡿⡿⠿⡿⣿⣿⢿⠻⢿⡿⡿⢿⠿⢿⡿⠟⡿⢿⣿⡿⠿⠿⢿⠿⢿⠿⡿⡿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣴⣾⣧⣾⣥⣼⣾⣮⣿⣴⣵⣽⣼⣼⣿⣌⣸⣴⣼⣼⣥⣤⣷⣡⣏⣠⣮⣯⣦⣤⣧⣧⣧⣷⣼⣧⣽⣿⣷⣤⣮⣦⣿⣴⣵⣼⣮⣿⣷⣮⣿⣧⣯⣼⣼⣵⣴⣙⣽⣧⣷⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣘⣿⣉⣿⣷⣣⣩⣹⢻⣿⢉⣻⣿⣩⣹⣏⣸⣈⣿⣽⣹⣍⣩⣝⣹⣯⣙⣿⣉⣹⣸⣿⣅⢉⣹⣿⣸⣹⣍⣟⣿⣏⣽⣸⣏⣩⣏⣿⡉⣿⣯⣹⣿⣯⣉⣏⣽⣸⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⠟⣿⣻⠻⠻⣻⣟⡟⢿⢿⡟⠿⣟⠟⠿⣻⠻⣟⠟⡟⠟⡟⢿⢻⡿⢿⣿⡟⡿⡟⣿⡻⢿⢟⢻⡿⡛⠟⣟⡟⢟⢻⠻⠻⣿⣿⡟⡟⣟⠟⣿⢿⡿⢿⡿⢟⡟⠿⠿⣻⣟⡿⢿⣿⢻⢻⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⡷⣶⣾⣿⣾⣾⣾⣿⣶⣾⣷⣷⣶⡷⣷⢶⣿⡶⣷⣾⣶⣶⡷⣿⣷⣷⣾⣷⣗⠳⣷⣿⣮⣿⣶⡾⣶⡶⢷⣿⣷⣶⣾⣾⡾⣾⣷⣷⣷⣷⣷⣿⣾⢶⣾⣾⣴⣷⣷⡶⣿⣷⣾⣾⣿⣾⣾⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⣶⣤⣺⣧⣴⣻⣷⣷⣦⣾⣿⣼⣷⣴⣧⣧⣬⣾⣦⣿⣧⣬⣬⣿⣽⣧⣷⣥⣴⣿⣼⣤⣤⣥⣻⣄⣰⣤⣼⣱⣧⣤⣧⣼⣿⣿⣶⣿⣶⣱⣿⣮⣷⣤⣾⣾⣹⣿⣦⣾⣯⣼⣾⣦⣦⣬⣞⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡯⢹⡩⢉⢿⠩⡯⠍⣹⡯⠍⣹⡋⣏⢿⠛⢻⡻⣿⡛⣿⢻⡟⣛⡟⣿⡿⠛⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡧⢿⣯⣿⣶⢨⢨⣛⡃⠿⡿⣿⣿⢸⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⣿⢽⣿⣸⣿⣿⣿⡄⣦⠚⣷⣝⣆⠨⡝⢸⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣀⣠⢤⣤⣤⠼⠿⠿⠿⠛⠛⣿⣿
⣿⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⠀⡏⡸⠟⠋⠉⠀⢸⣿⡇⣿⣿⣿⡷⣷⣶⣇⢻⣿⣸⡏⢸⣿⣿⣹⣿⣤⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢻⣿⣿⣿⡿⠿⠿⠿⠿⠿⠭⠽⠼⠟⠛⠛⠛⠛⠒⠓⠚⠛⠋⠉⠉⢹⣿⣿⢻⣟⣻⣷⢸⢿⣿⣸⣿⣿⡇⢸⣿⣿⣭⣿⣿⡗⠛⠛⠛⢿⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠘⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⣿⣿⡟⠈⠉⢻⢻⣿⢿⣇⠈⣿⡿⢿⡿⢿⡓⢂⣀⡀⡟⠀⠀⡶⠒⢿⡿⣶⡶⣶⢶⣶⣶⡶⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣭⡅⠉⠉⠁⠀⠀⢛⠑⠖⠒⢳⠀⠀⠀⠀⠁⠈⠀⠈⠹⠁⠐⠀⠀⠷⢦⣼⣶⣶⣶⣶⣦⣦⡟⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠄⠀⠀⠀⠀⠀⠀⢤⠛⠂⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸⣾⣿⣷⠈⠉⠀⠀⠀⠈⠔⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⠁⠀⠀⠁⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠁⢀⢤⠀⠴⠀⠀⠀⠀⠰⠀⠀⠄⠀⡄⡆⠀⠀⠀⠀⠀⠀⠀⠚⠀⢸⣟⣟⠁⠀⠀⠀⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠀⠀⠈⠀⠀⣿⣿
⣿⣶⣶⣿⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠈⠠⡀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⣨⣴⣶⣷⡶⢆⣿⣿
⣿⡋⠉⣛⡆⠀⠀⠀⢀⠀⠀⢸⣟⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⣿⣿⠃⣽⣿⣿⣿⣿⡯⣿⣿
⣿⣿⣶⣟⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠺⠿⣭⢐⣻⣿⣿⣿⣿⡷⣿⣿
⣿⡿⢟⢈⡅⠀⠀⠐⠀⠀⠀⣽⡃⠀⣠⣿⣇⠀⠀⠀⠀⡀⡀⠀⠀⢸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⢐⣶⣿⣷⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡐⠒⠒⣿⣿
⣿⡷⣼⣿⣷⡆⠀⠀⠀⠀⠀⣱⣿⣿⣿⣿⣿⠂⠀⠀⣼⠟⡃⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 2886

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/Robert_X_Cringely_Has_Already_Explained_IBM_s_Bullying_Culture_.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Robert_X_Cringely_Has_Already_Explained_IBM_s_Bullying_Culture_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Robert X. Cringely Has Already Explained
IBM's Bullying Culture (Towards Its Own Staff)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Jan 15, 2026


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


Robert X. Cringely has been active as a journalist for many years, even
decades. Over a decade ago he devoted a great deal of his professional capacity
and energy to covering IBM's collapse. He has not_blogged_in_3_years (but let's
be fair, he turned 70 around this time and he has no obligation to still be
active).


Published 10 years ago was material of his in sites other than his own, e.g.:


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


13 years ago He explained_how_IBM_bullies_workers_into_silence. Having just
stumbled upon it, that seems to have remained applicable.


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


Notice how workers of IBM laid off by IBM in the latest wave never mention
"RAs" or "layoffs". They almost always use euphemisms such as "last day" and
that's because of NDAs and extortion tactics by IBM [1, 2].


This was just two hours ago:


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Well,_today_marks_my_last_day_at_IBM_after_an_incredible
                    ride_that_started_back_in_August_2021⦈_


IBM tries to keep critics quiet. It wrote to me several times over the years to
try to "control the narrative" and even made an international phonecall to me
(it lasted nearly an hour; it was around 2011). That's because I condemned
their attempts to change what I wrote.


IBM is a fairly nasty company. I keep hearing this from Red Hat people (in
private). I've heard this from two people this past week alone. █


===============================================================================
Image source: Robert_X._Cringely


    * Proton_Mail_compromise,_Hannah_Natanson_(Washington_Post)_police_raid
      &_Debian
    * Red_Hat_(IBM)_is_Driving_Away_Remaining_Fedora_Users


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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 3059

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/Running_Techrights_is_Fun_Rewarding_and_Gratifying.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Running_Techrights_is_Fun_Rewarding_and_Gratifying.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Running Techrights is Fun, Rewarding, and
Gratifying⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


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


I sleep (or slept) as little as my body can tolerate to increase and improve my
output. The "golden era" of the Web is almost 20 years behind us.


Unless you are a Buddhist who believes in karma, you'll probably agree that
each of us lives once. "Be useful" [1, 2, 3] as a motto seems to have regained
visibility this week. "I gave it [life] everything I had," said the creator of
Dilbert, who had also published quite a few successful (widely-read) books.
Yesterday our server handled nearly 1.2 million requests (even more if we count
Gemini too) and I managed to publish over 30 articles across sites. I could do
more had it not been for computer breaks and extra sleep (in 2025 I began
sleeping a lot more to improve my ability to concentrate).


Running this site has always been fun and after almost 20 years it's still fun.
So let's do this for another 20 years. If the Web doesn't last this long, we'll
transition to whatever protocol/standard comes next.


In Geminispace we are already quite dominant. It continues to grow (some_time
soon_5,000_capsules_will_be_known_to_Lupa) and prominent capsules are visited
routinely. Getting 'noticed' is the hard part - same as on the Web.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇There_are_4820_capsules._We_successfully_connected_recently
                              to_3261_of_them.⦈_


It clearly pisses off some people that this site is productive and its people
are generally happy. So they do anything they can in desperate (self-harming)
efforts to sabotage it. They'll never succeed. We always outwit them. █


    * Red_Hat_is_Connected_to_the_Military,_Its_Chief_Comes_From_Military
      Family_(From_Both_Sides)
    * EPO_People_Power_-_Part_XXXVI_-_In_Conclusion_and_Taking_Things_Up
      Another_Notch


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠳⠮⠍⠙⢍⠩⠄⠀⠀⠀⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠙⠛⠓⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⣒⡦⠀⣤⣀
⠿⠿⠿⠿⠻⠿⡿⠟⠛⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠠⠀⠀⠀⠀⠀⠸⠿⢿⢿⡿⢟⢻⣿⣿⣿⣿⣿⡫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⣄⡀⠀⡀⠀⠈⠁⠉⠈⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡀⠀⠀⢠⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠡⠍⠫⠟⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠛⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⣿⣛⠿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡖⢁⣾⣿⣿⠽⣤⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡄⢄⢀⣀⣀⠀⣀⢠⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠀⠛⠷⠑⠃⠃⠚⠘⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠢⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⢀⠀⠀⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠋⠂⠊⠃⠂⠂⠊⠓⠀⠚⠋⠂⠚⠐⠐⠺⠚⠙⠧⡘⠘⠘⠂⠂⠀⠚⠃⠀⠛⠊⠃⠀⠚⠂⠐⠃⠊⠃⠓⠃⠐⠖⠈⠂⠋⠘⠚⠂⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠉⠙⠛⠛⠉⠉⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⢀⣼⣄⠀⠀⣠⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⢿⣿⣟⠿⠿⠿⢟⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠠⠀⠀⠐⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠄⠀⠀⡄⢤⢀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠂⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠄⠀⠀⡀⠀⢀⡄⠀⢠⠀⠀⠄⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠂⠀⠀⠀⠂⠀⠀⠐⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⢤⠀⠀⠀⠄⠀⠀⠤⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠐⠂⠀⠀⠠⠀⠀⠂⠃⠀⠐⠀⠐⠀⠀⠀⠐⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠙⠂⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠀⡰⠀⠄⠄⢠⡀⠠⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠐⠀⠐⠀⠐⠀⠂⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3187

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2026/01/15/Slop_is_a_Liability.shtml
    Gemini version at gemini://gemini.techrights.org/n/2026/01/15/Slop_is_a_Liability.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Slop is a
Liability⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


Slopfarms too will become extinct because people aren't interested in them;
they simply rely on SEO or Google feeding them (at the expense of humans'
patience)


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


"Liability" is a good term by which to go or to describe LLMs (or slop produced
by LLMs). We mentioned it in_relation_to_code_earlier_this_week (too many lines
of code nobody understands), we mentioned it in relation to defamation
(chatbots confidently making false assertions about people or businesses; there
are legal cases), and Google quietly quit displaying slop when people 'google
their symptoms' (due to lawsuits). Aside from that, there are copyright issues
(liabilities), both for_code and for literary works. Google's brand is quickly
being tarnished and even large publishers that were previously Google addicts
(or relied on Google to "get traffic") now truly hate Google and accuse it of
plunder.


More and more scandals like these will pile up, alter public perception, defeat
the_propaganda_("media")_budget_of_slop_pushers_like_Microsoft, and then it'll
inevitably fall over. Microsoft is already moaning that slop is widely loathed
and it tries to change our vocabularies to suit its propaganda [1, 2]. █


    * GAFAM_is_a_National_and_International_Threat_to_Everybody
    * The_Creator_of_Git_Probably_Doesn't_Know_How_to_Install_and_Deploy_Git


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡷⠼⢻⠻⠛⡛⠟⡟⡅⠘⠛⢻⣁⠑⠟⠟⠟⠟⠇⠘⡟⠛⣿⠀⣷⠈⠂⡟⠟⠛⠛⡛⡃⠚⠛⡟⢿⡛⢻⠀⣿⢻⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠮⠥⣾⣬⡴⢦⡵⢡⢌⣡⡴⢤⣾⣮⣥⣦⣤⡧⢤⣦⣤⣤⣤⣾⣤⣭⣾⣤⡯⢴⣤⣤⡧⠥⢤⣤⣮⣴⣬⣬⣤⣿⠬⣴⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣠⡍⡏⡇⢨⢹⢸⠈⡉⠹⢨⠉⠋⣉⠉⣽⡇⢸⡿⠍⢩⠉⠉⣉⠉⠍⡏⠁⢨⢨⣿⠀⣿⢈⡉⢯⠉⣹⢩⣹⣟⡂⢻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢒⢻⣷⣶⣶⣶⣾⣾⣶⡖⢲⣾⡶⣓⢶⣶⣿⣷⣶⣾⣶⣶⣶⣷⣷⣶⣷⡶⢲⣾⣶⣿⣷⣶⣾⣷⣿⣶⣾⣶⣿⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 3250

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Creator of Git Probably Doesn't Know
How to Install and Deploy Git⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


Nobody disputes this: Mr. Torvalds created Git. Because he did.


But how long was he involved in it?


Well, when asked about it Torvalds is being frank; he started it, spent some
months on it, then it was sort of passed on to other people.


Judging by the fact that he's outsourcing_his_own_personal_projects_to
proprietary_prisons, he probably forgot or never knew how to do (or too seldom
practised) Git installations. It's good practice to make one's own, so why
didn't Torvalds? Lack of money isn't a problem, is it?


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


Self-hosting is a very important theme we've been covering for many years
(since around 2019). Seeing that Torvalds - like the Linux_Foundation - fails
at it and gets an "F" (like his_repository_of_choice), and moreover seeing what
GAFAM_has_become, we ought to write about self-hosting a lot more often. █


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇We_refer_to_these_services_by_their_domain_names,_rather
 than_their_common_names_(eg:_savannah.gnu.org_vs._Savannah)._That_is_because
 the_software_for_most_of_these_services_is_also_available_for_self-hosting_as
   free_software._Installing_that_software_on_your_own_server,_and_using_it
         yourself,_avoids_most_of_these_ethical_issues_(all_but_A1).⦈_


    * Slop_is_a_Liability
    * Linuxiac_May_Have_Reverted_Back_to_LLM_Slop_(Updated_Same_Day)


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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠈⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣷⣦⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠛⣿⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠂⠠⠤⠔⡒⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⠀⠀⠀⢠⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⠿⠆⢸⡯⢿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⢀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠉⣆⠀⠀⠀⠈⠙⠛⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⡆⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣤⡠⣤⣤⣤⣤⣤⣤⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠟⣿⠇⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⣿⡛⣽⣽⢿⣿⣯⣿⣿⢫⣯⠐⠙⠛⠒⠂⠀⠀⠀⠀⢀⢀⠀⠀⠀⠁⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⡃⠀⠀⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡡⣿⣿⣿⣻⣿⣿⣿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠀⠀⠀⠀⠀⠉⠙⠀⠈⠁⠀⠀⠁⠀⠀⠀⢰⣿⣻⠻⠇⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣲⠉⡉⠩⢻⣿⣿⣿⣹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⢐⣒⢀⡀⠀⢀⡀⣀⣀⠀⠀⢰⣶⣾⣿⣍⠈⠁⣿⣟⡃⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⣤⣤⣠⣥⣗⣼⣧⣿⣶⣿⣿⣿⣬⣦⣀⣀⣠⣠⣤⣤⣤⣤⡴⠶⢯⢻⣿⣻⡟⠭⠄⣶⣞⣓⡛⡓⣶⣶⣶⣿⡿⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⡤⢄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⠶⠶⠶⠶⠮⠽⠉⠁⠀⠧⠀⠇⠀⠀⠀⠛⠨⠉⢀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠂⠒⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⡿⠟⠋⠉⠈⠀⠈⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣷⡄⠀⠈⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠺⠿⣿⣾⣴⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠠⠤⠴⡲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠈⡭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡀⠀⠀⢰⣶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢺⡁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠻⠋⢛⣿⣗⣘⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢀⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠁⠀⠀⠀⠁⣦⡀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠛⠂⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡄⠘⢄⣠⣤⢀⢤⣤⣤⣤⣤⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠠⢐⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠃⠀⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠠⠤⣜⡧⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢤⢠⣧⡀⣀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⣀⡀⠀⠛⠋⠀⢸⢿⣿⡇⠀⠀⢰⣷⢰⣾⣟⣿⣧⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣫⣻⣻⣿⣿⣽⣿⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⡀⠀⣘⣾⡯⠁⠀⠠⣼⣿⣿⣿⣖⣛⠉⣿⣿⡋⠀⠀⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⣤⣤⣼⣭⣿⣿⣿⣿⣿⣿⣿⣷⣯⣀⣀⣀⣁⣄⣤⣤⣤⣤⣦⠶⢿⣿⣿⣿⡛⠛⡃⣿⣟⣻⣿⡳⣶⣷⣾⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⠄⡀⣀⡀⢀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⡷⠶⠿⠶⠄⠂⠀⠀⠀⠀⠀⠀⠐⠉⠉⠁⠈⠀⠉⠁⠉⠿⠋⠛⠋⠈⠉⠙⠲⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢼⡇⠀⢸⡧⠀⠀⣿⠀⠀⣿⠄⠀⢸⡇⠀⢸⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⣀⡸⠇⢀⡀⣿⣀⣀⠿⠀⠀⠸⠇⠀⢀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢸⡇⣿⡇⠀⢹⡇⢶⢿⣧⠀⠀⠀⣀⡀⢀⣸⣿⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⡧⠛⢧⣤⡝⠃⠛⠛⠋⠠⠤⠀⢼⡧⠀⢴⣶⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⢀⡝⠋⡃⠂⠀⠀⠀⠀⠀⠀⠈⡗⠀⠚⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⡿⠟⠋⢹⡆⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣶⠦⢴⣾⡥⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⠟⠉⠀⠀⠀⠀⠁⠀⡂⠀⣲⣿⣿⣿⡆⠀⠈⠻⢿⣿⣿⣿⣿⠀⠀⠀⢸⡿⠛⠻⠁⢹⡏⠁⠄⣶⠈⠉⡇⠀⠀⢐⡔⠉⢰⣿⠀⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⡀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⢻⢀⠀⡀⠀⠁⡄⠘⢛⠧⠦⣤⠾⠷⣤⠼⠿⢤⡴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐⠶⠶⣷⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠤⠤⠒⠻⠖⠂⠀⠀⠀⠀⢸⡇⠀⢸⡏⠁⠀⠆⠀⠻⠆⢠⣿⠄⠠⣿⡄⠀⣼⡧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣒⡀⠀⠀⠘⠀⢸⡇⠀⢸⡇⠧⠤⠀⠀⠙⣶⡆⠉⢶⡶⠉⢲⣶⠊⠱⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣥⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⠘⠃⠀⢸⡇⠀⠀⠀⠀⠐⡟⠂⠀⢺⡗⠀⢺⣿⠂⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠀⠀⠀⢘⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⡇⠀⠀⣸⠁⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢼⡁⠀⠀⠨⠭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣨⠀⠀⠀⣷⠒⠒⢨⡄⠒⢺⣿⠒⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⢀⡀⠀⠹⠿⢿⣿⣿⡿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢀⣶⣦⣦⠀⠀⠀⠀⠀⠀⣴⠀⠀⢺⡗⠀⠠⣶⡏⢁⣶⠈⠁⣶⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠻⣦⡀⠀⠀⠈⠉⠑⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⢀⡖⠘⠂⡪⠙⠀⠀⠀⠶⠞⠛⢻⣟⢇⢀⠀⠀⠁⣿⠉⠇⠀⠇⠀⠠⠿⠂⠅⣅
⠀⠀⠀⠀⣀⢀⣀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣄⠀⠀⠀⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠀⠀⣛⡀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠙⠿⠀⠀⣿⠄⠃⠀⠇⠨⠀⠀⠀⠀⠀
⠀⠀⢀⣠⣿⣿⣾⣷⣧⣤⣄⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⢑⠘⠘⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢠⣿⣿⡤⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣿⡄⢧⣄⣀⣄⠀⠀⠀⠀⠀
⠠⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠁⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⣬⣁⠀⠀⣀⣠⡄⠠⠀⠀⠀⠀⣴⣿⣧⡄⢸⣿⣿⡇⠀⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⢹⠋⠘⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⡞⠀⠂⠀⢀⡠⣶⣶⠀⢰⣿⣿⡇⠈⠀⢀⣴⢸⣿⣿⣿⡇⣾⣿⣿⡕⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠪⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠐⣷⢰⡂⠀⠀⠀⠉⠉⠀⢘⣿⣯⠁⠀⢠⣼⣿⣾⣿⣿⠏⠃⣿⣿⣿⠁⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀
⣀⢰⣥⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣀⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⠉⠉⣿⣻⡿⠷⢶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣶⠶⠿⠿⠯⠦⠛⠉⣿⣏⠉⢓⣛⡟⣿⠋⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠺⠿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡧⢢⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⢛⣩⡟⡭⠛⢯⡅⢁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡕⣅⣶⣾⣿⣶⣶⣿⣶⣶⣿⣷⣟⣻⣏⣏⡏⢹⣄⣤⡟⠈⣵⢎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠙⠛⢿⡷⣿⡇⠀⢸⣿⣾⣿⣯⡷⠷⠎⢹⣏⣱⢿⣿⠊⠢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡟⢟⠿⠺⢳⣟⣳⡳⠶⠔⠋⡻⢳⣜⡠⢯⢲⢀⡷⣿⠃⠳⠿⡻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⠧⠀⢸⣿⣘⣠⣤⣤⣾⠟⢟⡀⠻⡿⠃⠸⠿⠛⢃⠷⣵⣒⡠⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠶⠋⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⠁⡄⡂⠠⠽⠛⣃⡉⣣⣭⣶⣾⡯⠴⢧⡜⢳⣶⣤⡼⣶⠟⠛⣤⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡀⠀⠐⣰⣲⡤⠋⢡⠙⠋⣍⠙⣷⣶⡉⣅⡌⠛⠉⢡⢻⣖⢢⣽⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣿⣿⣶⣦⣤⠀⠀⠀⠻⠿⠓⠈⡯⠠⣊⢾⣹⣺⣿⢎⣿⢿⠁⣿⣟⡟⣱⠀⢰⣶⡤⡄⣮⢡⠄⠉⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡀⠀⠀⠀⠀⡀⢠⡄⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⢈⡉⠩⠷⣇⠀⠰⠆⠽⢷⣷⡜⢶⡂⠀⣀⠰⢈⠆⠰⢾⢗⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⢦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢹⣿⣄⢀⣀⣸⡯⣶⢎⢟⣗⠋⠿⠀⠴⢇⠿⠿⠿⠿⢿⢿⠫⣰⣂⡀⠿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⠒⠒⠂⢹⣿⡫⠙⠃⠚⡀⠿⠟⠫⠾⢿⣤⣧⢔⣥⣤⣀⣠⣤⢇⣠⣤⡽⠻⣃⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣩⠀⠀⠀⠀⢘⣿⢬⠅⠀⢀⣇⢦⣄⣉⣠⠘⢛⠟⠜⢿⡿⠋⢻⣿⡞⠻⣿⢧⣠⢿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠿⠅⠀⠀⠀⠉⠈⢿⠀⣽⣶⡆⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⡌⠉⣼⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢹⠄⠀⠀⢀⣾⣾⡆⠀⠀⠀⠀⠀⠘⡏⢹⣿⢱⠉⣿⠉⠉⣿⢯⣟⢍⠋⠍⠰⠴⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡗⠀⠀⠀⠛⢆⠀⠀⢀⣼⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣿⠛⠃⠀⠀⠀⠀⠀⠲⣌⡠⢸⣿⣿⣀⡰⣾⢿⣷⠦⡧⡳⢿⡿⠀⠸⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠸⠏⠰⠛⣻⣿⣿⠿⠿⣿⠇⠀⠀⠀⠀⠀⢰⣾⣷⠀⠀⠀⡐⢀⣀⡀⠐⢵⠁⢼⠿⢿⢿⠡⣹⣼⣓⣂⡶⢖⢠⡁⢀⣀⣀⠨⡊
⠀⠀⡀⠀⠈⣷⣷⣀⣠⣀⣤⣤⣤⣤⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠈⠀⠀⠀⢠⣶⠀⢨⣿⣿⡀⠀⣷⡇⣽⠃⠐⣄⠈⣀⢈⡣⣃⠣⡑⠈⣿⣿⣿⢧⣼⡿⣉⢢⡉⢺⡓⠌
⠀⠀⠠⢠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢲⣷⣤⣀⠛⢊⡀⠀⠀⠀⠀⠀⢠⣾⣿⡀⢼⣿⣿⠄⠀⣿⠃⢘⢄⢀⣬⣧⣬⣥⣷⡄⣍⢊⡢⣿⣿⣿⣿⣿⡓⡽⢆⠙⢤⣙⢉
⠀⠀⢨⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⠂⠀⠀⢠⠀⣤⣾⣿⣿⣇⣾⣿⣟⡅⠀⡥⡀⠀⠉⢀⡟⠻⣻⠛⣻⠃⡠⢨⠣⣿⡿⣿⣿⣿⣃⠌⣤⡙⠦⠄⡪
⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⡀⠀⠀⠀⠈⠉⠉⠁⡋⠍⠁⠀⠀⢰⣿⣿⣿⣟⣋⠁⣿⣿⣁⠉⢀⢌⡀⠀⠀⠀⠉⠀⠁⠈⠁⠀⠉⠁⠀⠉⠉⠉⠉⠉⠉⠈⠀⠁⠀⠀⠉
⢀⢀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣀⣀⣀⣀⣀⣤⣤⣤⠤⡶⠶⢿⢿⣟⣟⡿⡙⣶⣒⡞⡷⢖⠒⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠽⣿⣿⣿⢟⠞⠂⠀⠿⢿⣈⠲⠿⠏⠉⠿⢿⣿⣿⣿⡟⠛⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣯⣀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣏⡼⣿⣿⣿⣿⣿⣿⣿⣿⡤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⡟⣟⣷⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⢿⣛⣿⣥⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠟⠛⢻⣿⢎⠉⣉⣙⣭⡭⢛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣯⣉⢻⣿⣿⣻⣿⡷⡻⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠕⠟⠉⠉⠹⠿⠂⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣾⣾⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⣹⣿⠟⠁⠀⠀⢠⣀⣀⠀⢀⡤⢀⣠⣀⡀⠀⢀⣠⣤⠀⠀⠀⠹⠛⠛⠛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣠⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⣿⣗⣾⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣸⣼⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⢿⣻⣿⣿⣺⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣫⣾⣿⣿⣿⣿⣟⢚⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⡄⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣄⠀⠀⢠⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢵⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⢠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⡄⠀⠟⢿⣧⡀⠉⢙⣿⣿⣿⣿⣿⣿⡀⠀⢀⠀⠸⢿⣆⣠⣿⡟⠃⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⡯⣮⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣧⣀⣸⣿⣿⠀⠉⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣛⣿⣇⡷⡧⡀⠀⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⢘⣀⡀⠀⠸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿
⠀⠀⢀⣘⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣄⣄⣀⣀⡀⠀⠀⠀⠀⠐⣩⣿⣿⣿⡏⢙⠀⠀⠀⠀⠀⠿⢿⢿⣿⣿⣿⡇⢰⣿⣠⣵⠀⢸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠓⠂⠀⠀⠀⠰⣿⣼⠟⠁⠢⣤⠀⣤⡄⠀⠀⠀⠀⠀⠉⢘⢳⣾⣿⣿⣿⡆⣼⣿⣿⣧⠀⣿⣿⣿⣿⢿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣷
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠄⣬⣿⢤⣽⣿⣤⣤⣴⡦⠀⠀⣐⠸⣟⣿⣿⣿⣯⣿⣿⣿⣷⢠⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣽⣿⣿⡯⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⠉⠉⣿⣿⣿⣿⣗⣿⣿⡷⠀⠀⣼⣿⣿⣿⣿⣿⣍⣿⣿⣟⡉⢉⣿⣏⡋⢹⣏⣿⣿⣻⡍⢩⣭⠉⣽⢩⠹⢽⠉⠘⠿⠉⠭⠉⠉⠉⠩⠉
⢀⢠⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣠⣤⣤⣤⣤⣤⣴⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣥⣥⣬⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⠈⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⡿⠟⠋⠉⣄⣀⣀⡀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡟⣿⣿⣿⣿⡜⡂⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⠟⠉⠀⠀⠀⠾⠋⠉⠉⠱⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠨⠲⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣇⠅⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠠⣤⣀⠀⣠⣀⡀⠀⠀⠀⠀⠀⡠⣤⠀⠀⠀⠙⠛⠛⠇⠀⠀⠠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡯⣬⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢞⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢩⣿⣂⡝⡞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣥⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣼⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡯⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢽⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⢠⠆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡎⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⠃⣤⡞⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⢀⠀⠀⢀⣿⣿⣿⣷⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡫
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠉⠻⣦⡀⠀⢀⣾⣿⣿⣿⣿⣷⠀⢻⠀⠛⠆⠉⠀⢀⣿⡟⠋⣿⣿⡯⢹⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣽⣿⡯⡛⣿⣿⢗⢕⢜
⠀⠀⠀⢆⣀⣀⣸⣿⣿⠀⠛⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠣⢿⢶⡀⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⢰⣿⣿⡇⠀⣿⣿⣟⡻⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⡱⡻⡜⡴⢇⢫⡺⡎⣳
⠀⠀⠀⢨⣿⣿⣯⣿⣷⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠠⠸⠁⠀⠀⠀⠀⠀⠻⠻⠿⢿⣿⣿⡠⠂⠀⣠⣴⡀⢸⣿⣿⡇⠀⣿⣿⣫⢜⣧⣭⣮⠛⡟⣫⢶⣥⢿⣿⣿⣿⣪⣿⣽⡹⡚⢌⢏⠆⡁⠉
⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠂⠀⠀⠀⢠⣽⠢⠈⠂⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠨⣿⣿⠀⣿⣿⣿⡇⣾⣿⣿⡧⢠⣿⠻⠑⣽⣿⣿⣿⣶⣥⣵⣽⣿⣯⣽⣿⣿⣿⣿⣿⣮⣵⣬⣮⣧⡬⣠
⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣻⣶⡆⠀⠀⣂⣭⣿⣷⣴⣶⣦⡀⠀⠀⠐⣿⣎⣿⣿⣿⣇⣾⣿⣿⣏⠸⣿⣶⢹⣬⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡿
⠀⠀⢾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠰⣿⣩⣅⠀⠀⣼⣿⣿⣿⣮⣹⣯⠁⠀⠀⢰⣿⣿⣿⣯⣿⣋⣿⣿⣿⣋⢀⣛⡋⠘⠈⠃⣹⢿⠉⠹⡉⠋⠽⠉⠉⣿⣿⣿⡿⠋⠉⠙⠛⠛⠛⠑⠛
⣀⢠⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣠⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣴⣴⣤⣤⣀⣀⣀⣀⣀
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣛⣻⠿⣿⠿⠿⣿⢯⡉⠿⢿⣿⡿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⢟⣋⣉⡀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠉⣰⢉⠉⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡄⣿⡟⠁⠀⠀⣠⣤⣀⣀⣀⠂⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠙⠋⠟⠃⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣬⣿⣀⣲⣾⣿⣤⣄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⢀⢀⠰⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢨⣿⡟⢓⢬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠴⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠟⠀⠒⠂⠀⢸⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⡼⣀⡼⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⠀⠀⢀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣄⠀⠉⠻⣦⡀⠀⢀⣾⣿⣿⣿⣿⣷⠀⡟⠀⠀⠆⠈⠀⢠⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡇⡀⠀⠀
⠀⠀⠀⠐⣁⣀⣸⠿⣿⠉⠛⠉⠀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣿⣷⠀⠀⠛⠿⠿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⣿⣿⣿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣚⣛⣅⣠⣃⠀⠀
⠀⠀⠀⢈⣽⣿⣿⣿⣵⣦⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠓⠹⠁⠀⠀⠀⠀⠀⠟⠿⠿⡿⣿⢿⡆⠀⢀⣠⣴⡄⣸⣿⣿⡇⠀⣿⢻⢿⣿⣿⣧⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠂⠀⠀⠀⢨⣿⣿⣤⣤⡀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠙⣻⣷⠒⣿⣿⣿⡇⣿⣿⣿⣇⢠⣿⠩⠪⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠀⠀⠀⠀⠀⠀⣲⣿⠿⢻⣿⣧⣶⣬⣽⣿⣴⣶⣦⡀⠀⠀⠨⣿⣖⣿⣿⣿⣇⣿⣿⣿⣯⢸⣿⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣎⡉⠉⣿⣿⣿⣿⣬⣿⣿⡅⠀⠀⢰⣿⣿⣿⣿⣿⣫⣿⣿⣿⣏⢀⣻⣻⠨⡋⠉⣿⣿⠛⠛⠯⡟⠟⠻⢿⣿⣿⣿⣿⡟⠻⠛⠛⠛⠋⠀⠀
⣀⢠⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣶⣶⣤⣆⣀⣂⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣻⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠠⠖⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⢉⠞⠋⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣩⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠨⢿⡟⠁⠀⠈⣠⣤⣀⡀⢹⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠈⠻⢿⠿⠇⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣉⣟⣿⣁⣾⣿⣟⣽⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣧⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⠀⢰⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡰⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⠟⠒⠒⠒⠒⣺⡿⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡄⠀⢰⣀⡼⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠟⠃⠀⢀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⡀⠀⠀⣀⣀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣄⠀⠉⠻⣦⡀⠀⢀⣿⣿⣿⣿⣿⣷⠘⡟⠀⠁⠄⠈⠀⢠⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠉⠁⠀⢀⣧⣀⡼⣿⣿⡿⠛⠛⠋⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⣻⣿⡿⣷⡀⠀⠛⠿⠿⠿⣿⣿⣿⣿⣿⣧⠀⠈⠀⠀⠀⠀⢠⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣇⣩⣋⣄⣈⠀⠀⠀⠀
⠀⠀⠀⢨⣹⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡛⠻⠃⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⢿⡶⠀⢀⣠⣴⡆⢸⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⠀⠀⠀⠀
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠒⠀⠀⠀⠈⣿⣿⡟⢠⠂⠀⣤⣤⣀⠀⠀⠀⠀⠉⢿⢿⣷⠰⣿⣿⣿⡇⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⠧⠈⠀⣲⣾⣿⣿⣷⣶⣦⡄⠀⠀⠢⣿⣦⣿⣿⣿⣇⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⡀⢈⣿⣿⣿⣿⣍⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣋⣿⣿⣿⣏⣁⣻⣿⠿⢿⣿⣿⣿⣿⡿⢿⣿⣿⠻⢟⣿⣿⣿⣿⡟⠉⠉⠒⠂⠂⠀⠀
⣀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣤⣤⣤⣤⣤⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣭⣿⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣴⣤⣶⣤⣤⣄⣤
⡿⣿⣿⣿⢿⣿⣿⠿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠴⠞⠃⠀⠀
⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠉⡰⠛⠛⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⣠⣤⣀⡀⠙⠄⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠈⠻⣿⣿⡏⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣋⡹⣛⣁⣺⣟⣌⣭⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢹⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⠀⢤⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⡠⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⠟⠒⠒⠒⠒⢺⡿⠀⢙⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢰⣀⡸⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠟⠃⠀⣀⠀⠀⢀⣿⣿⣤⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⠀⠉⠻⣦⡀⠀⢀⣾⣿⣿⣿⣿⣷⠼⡷⠀⠂⠄⠙⠀⢠⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠀⢺⣇⡸⣸⣿⣿⣟⠛⠉⠈⠉⠹⠋⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣷⡀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣗⣈⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⣨⣿⣿⣿⣯⣽⣵⣤⣤⣤⣤⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠿⢿⠿⣿⣿⢿⣦⠀⢀⣠⣴⡄⣼⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣴⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀
⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠒⠤⠀⠀⠀⣿⣿⠟⢿⠀⠀⣤⣤⣀⠀⠀⠀⠀⠙⢛⢿⣷⢠⣿⣿⣿⡇⣿⣿⣿⣧⢸⣿⢻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⠀⠀⠀⠀⣿⡿⣳⣷⢄⣴⣯⣿⣿⣷⣶⣦⡀⠀⠀⢸⣿⣾⣿⣿⣿⣷⣿⣿⣿⣧⣸⣿⠫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡆⠀⠀⠀⠀⠀
⠀⠀⠘⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣀⡈⣿⣿⣿⣿⣏⣿⣿⣯⠀⠀⠠⣿⣿⣿⣿⣿⣏⣿⣿⣿⣏⣈⣙⣋⠉⢩⣹⣿⣿⡿⠏⢫⢙⠟⠋⢿⢿⢭⣝⡿⠟⠛⠁⠀⠀⠀⠀⠀
⢀⣠⣤⣬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣴⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣦⣶⣦⣤⣤⣤
⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⠟⠉⢀⡤⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⣩⣤⣀⠈⠹⡄⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠈⠻⣿⣿⠏⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢋⣚⡏⡁⢂⣉⣙⣈⠀⠀⠀⠀⠈⠉⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡄⢠⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢠⣁⣰⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠞⠃⠀⠀⠀⠀⢀⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣄⠀⠈⠻⣦⡀⠀⢀⣾⣿⣿⣿⣿⣷⠺⡗⠀⠀⠀⠁⠀⢠⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠁⠀⠀⣿⣷⣀⣿⣿⣿⠛⠟⠋⠉⠙⠍⠁⠀⠀⠀⠀⠀⠀⠄⠼⣟⣿⣧⡄⠀⠛⠿⠿⠿⣿⣿⣿⣿⣿⡋⠀⠁⠀⠀⠀⠀⢰⣿⣿⡆⠀⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⢿⣿⣿⡿⢷⣦⠀⢀⣠⣴⠀⣼⣿⣿⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠓⠒⠀⠀⠀⢸⣿⡿⡿⡂⠀⢀⣤⡀⠀⠀⠀⠀⠀⠁⢻⣷⢀⣿⣿⣿⡀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⡆⣤⣤⣿⣿⣶⣶⣤⡀⠀⠀⢸⣿⣴⣿⣿⣿⣷⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢨⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣛⣉⡉⣽⣿⣿⣷⣮⣿⣿⣯⠀⠀⠰⣿⣿⣿⣿⣿⣩⣿⣿⣿⡏⢈⣿⣟⡻⣿⣿⣿⣿⣿⣯⠿⠿⠿⢿⡿⠿⠿⠿⠻⠇⠀⠀⠀⠀⠀⠀⠀
⣀⣠⣤⣤⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣶⣦⣤⣤⣤⣴⣶⣶⣶⣶⣶⣦⣶⣶⣶⣴⣤⣤⣤
⣿⣿⠿⣿⠿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠟⠉⢀⡤⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⠁⠀⠀⣮⣤⣀⠈⢵⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠈⠻⢿⣿⠁⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⢴⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡋⣽⣋⣁⣈⣉⣉⣋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢹⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠠⢼⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣌⣀⠫⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠁⠀⡀⠀⠀⢀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠈⠻⢦⡀⠀⢀⣾⣿⣿⣿⣿⣷⠾⡇⠀⠀⠀⠃⠀⢠⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠛⠀⠀⠨⣞⣂⣨⣿⣿⡟⠛⠛⠉⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡄⠀⠛⠿⠿⠿⣿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠀⠀⢰⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣘⣻⣿⣯⣽⣿⣧⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠂⢸⣿⣿⢿⡇⠀⠀⠀⠀⠀⠿⠿⠿⠿⣿⢳⡤⠀⢀⣠⣴⠀⣼⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠒⠖⠀⠀⠀⢺⣿⣿⣰⠂⡀⢠⣤⣀⠀⠀⠀⠀⠀⠉⢿⣷⢀⣿⣿⣿⡀⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⣾⣿⣿⣿⢁⣶⣤⣿⣿⣶⣶⣦⡀⠀⠀⢸⣿⣼⣿⣿⣿⣷⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢙⣿⣻⣉⡈⣽⣿⣿⣷⣯⣿⣿⣇⠀⠀⠰⣿⣿⣿⣿⣿⣩⣿⣿⣿⡏⢙⣻⣿⡟⢿⣿⣿⣿⣿⣿⡿⢽⣿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀
⣏⣤⣤⣤⣴⣿⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣦⣴⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣦⣷⣶⣦⣤⣤⣤⣶⣶⣶⣶⣦⣦⣤⣦⣶⣦⣤⣤⣤⣴
⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠠⠶⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠈⠈⠘⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠉⠀⠀⠀⣠⠖⠒⣦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⢠⣤⣞⠁⠀⠀⠘⡆⠀⠀⠀⢀⣠⣤⠀⠀⠈⠻⣿⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⡀⣚⣻⣛⣋⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠤⠤⢼⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡼⣀⣼⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠉⠀⠀⠀⠀⢀⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠘⠻⣦⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠘⡇⠀⠇⠀⢠⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠉⠙⠻⠀⠀⠀⣒⡂⣺⣿⣿⠟⠟⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠸⣿⡿⢢⡀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⡛⠁⠇⠀⠀⠀⠀⢰⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣽⣿⣤⣤⣤⣤⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡊⠇⠀⠀⠀⠀⠀⠿⡿⢿⣿⣿⢿⣦⠀⢀⣠⣴⠀⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠒⠦⠀⠀⠀⣿⣋⢠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠉⠉⢸⣷⢠⣿⣿⣿⢀⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣯⣼⠀⢰⣄⣹⣿⣶⣶⣤⡀⠀⠀⠨⣿⣼⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢈⣿⣳⠋⠈⣹⣿⣿⣷⣎⣿⣿⡧⠀⠀⠰⣿⣿⣿⣿⣿⢩⣿⣿⣿⠃⢢⡚⡟⠻⡿⢿⡿⢿⢿⣿⠿⠿⠿⠿⠿⠿⠟⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣧⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⢴⣤⣴⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢿⣿⣋⢿⣿⡿⢿⣿⣻⣿⣿⣽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣁⠤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠟⠋⠉⠉⠁⠀⠁⠈⠋⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⠀⠀⠀⣢⣴⠖⠶⣄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡿⠁⠀⠀⢠⣤⣀⠰⠋⠀⠀⠀⢳⠀⠀⢀⣠⣤⠀⠀⠈⠻⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠿⣻⣿⣿⣿⣿⣿⣿⣷⡘⠋⡿⣛⠀⠀⠀⠀⠈⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣸⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢸⡿⣋⡀⠈⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠉⠀⠀⠀⠀⢀⣻⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⠻⠈⠹⣦⡀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡄⠸⣄⠀⠇⠀⢠⣾⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠿⠋⠛⠧⠀⠀⣀⣠⣤⣼⣿⣿⠺⠖⠒⠚⠚⠒⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠀⠐⠿⠿⠿⣿⣿⣿⣿⣿⣿⠁⡁⠀⠀⠀⠀⢰⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣯⣿⣯⣤⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠀⠀⠀⠀⠀⣿⠿⢿⣿⣿⢿⠀⠇⢀⣠⣤⠀⣿⣿⣿⠀⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠳⠆⠀⠀⠀⣿⣛⣻⠘⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣷⢢⣿⣿⣿⢀⣿⣿⣿⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣿⣯⣽⠀⢠⣄⣩⣶⣶⣶⣶⡄⠀⠛⣻⣿⣾⣿⣿⣿⢸⣿⣿⣿⠀⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢄⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⡗⣋⠈⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠛⠋⠉⣻⣿⣿⢩⣿⣿⣿⠁⡇⠀⠀⠀⢸⢟⣿⡿⠿⠿⠿⠛⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣧⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡍⣫⢿⡯⣿⠿⢿⣿⡿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠇⠀⠀⠀⠘⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠞⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⠿⠛⢉⠉⠽⠀⠈⠙⠉⢉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠉⠀⠀⠀⠀⠁⢀⣤⣟⠛⠻⡄⠁⠀⠀⠈⠻⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡿⠁⠀⠀⢠⣤⣀⠀⢀⠟⢁⣀⣀⠈⠇⣀⣠⣤⠀⠀⠈⠻⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣆⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⠿⢟⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠀⠀⠀⠀⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣰⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠸⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠁⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠈⠿⢢⠉⠀⢨⣾⣿⣿⣿⣿⣿⣿⣷⡸⣠⠰⠆⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠶⣶⣾⠛⠻⠆⠀⠀⣀⡄⢰⣶⣶⡶⠶⠖⠒⢶⠶⠆⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠹⠿⠿⣿⣿⣿⣿⣿⣿⡏⠈⡃⠃⠀⠀⣴⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣠⡀⠀⠀⠀⠀⠀⠀⡻⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠠⣇⣠⡤⠀⣿⣿⣯⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡿⠃⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠦⠄⠀⠈⣿⣿⣿⡇⢡⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣾⣿⣿⣷⢀⣿⣿⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠐⣿⣿⣾⡇⢺⣄⣀⣀⣠⣾⣷⣆⠀⠰⠿⠿⢿⣿⣿⣿⢸⣿⣿⣿⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⢤⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⢩⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣾⣿⣿⢹⣿⣿⣟⠁⡅⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠸⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⣤⣿⣿⣤⣤⣤⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣮⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢶⢀⠀⠀⠠⠦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⡿⢛⣝⠛⠃⠐⢉⣫⣵⣺⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠟⠉⠀⠀⠁⠉⠁⠀⣶⠟⠋⠉⢹⠉⠁⠀⠘⠻⣿⣿⣿⠃⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀⣠⣤⣀⠀⠀⡞⢇⣤⣤⣄⡈⣃⣤⣤⠀⠀⠈⠻⣿⠂⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀
⣶⣶⣄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠿⠿⡿⠿⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠙⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠑⢰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⣼⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⡇⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣆⠀⠈⢺⠇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢳⡆⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣤⣤⣶⡞⠛⢷⠀⠀⢀⢤⡴⣶⣶⣶⠶⡶⠴⠶⣶⠶⠀⠀⠀⠀⠀⢘⢿⣿⣧⡀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⡏⠋⠙⠃⠀⠀⣴⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣀⣀⠀⠀⠀⠀⠀⠀⢘⢿⣿⣿⣿⣿⣀⣂⣄⣠⣍⡀⠀⠀⠀⠀⠀⢘⣽⣿⣿⣿⢺⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆⠀⢠⣧⡄⠀⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⣿⡟⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢦⠤⠀⠘⣿⣿⣾⣿⣾⡇⠀⠀⠀⠀⠉⠁⠀⢸⣿⣷⣶⣾⣿⣧⢠⣿⣿⣧⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣀⣀⣠⣶⣶⣦⠀⠸⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⣤⣤⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⡟⠀⢠⣶⣶⣿⣿⣿⣟⢻⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⣾⣿⣵⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⡿⡿⢿⡿⠟⠛⢿⠿⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⡤⡀⠀⠀⢠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⢿⠟⠛⡟⣮⣿⠟⠛⢿⡯⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⣿⣿⣿⣇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠟⠉⠀⠀⠀⠁⠁⠼⠃⠀⠀⠈⢷⠃⠈⠀⠈⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⣠⣤⣀⠀⢸⢡⣿⣿⣿⣿⡼⣀⣤⣤⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀
⣤⣤⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠋⠓⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡱⣦⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣰⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠻⣟⠉⢁⡋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡴⣶⢈⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣆⠀⠈⢻⡧⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡾⣤
⢀⣠⣤⣶⠶⠶⡆⠀⠀⠀⠠⢤⣴⣦⡦⣴⡤⢴⣤⡤⠀⠀⠀⠀⠀⠀⠼⣿⣦⡀⠀⠁⠈⠉⠻⣿⣿⣿⣿⣿⣿⡗⠁⠙⠀⠀⠀⣼⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠘
⣀⣀⡈⠁⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣇⣸⣆⣸⣿⣧⠀⠀⠀⠀⠀⠀⢽⣿⣿⣗⠀⣅⠀⠀⠀⠿⠿⣿⣿⣿⣿⠆⠀⢀⣾⡄⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀
⣿⣿⠗⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡤⠀⠀⣸⣿⣿⣿⢹⣿⢗⣶⡤⠀⠀⠀⠀⠀⣤⣷⣾⣿⣿⣷⢸⣿⣿⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣯⢨⣿⣿⡿⣿⣷⣿⣷⠀⢀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⡦⣤⣀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢾⣿⣿⠙⢿⣿⣿⣿⣇⣹⣿⡟⠁⢠⣿⣿⣿⣿⣿⣟⢻⣿⣿⡿⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣶⣿⣷⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠙⠉⠛⠛⠀⠋⠉⠛⠻⠿⠟⠀⠛⠙⠛⠻⠻⠿⠿⠿⠿⠿⠟⠻⠋⠛⠋⠛⠛⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠀⠀⠤⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠻⣣⠀⠀⠘⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣿⣿⣿⣿⠟⠯⠹⠋⠀⠈⠛⣿⡿⣾⡻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠁⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⠿⠋⠀⠀⠈⠀⣠⣤⣄⣀⠘⡇⠈⠀⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⢠⣤⣀⢀⣿⣿⣿⣿⡧⡇⠀⣀⣤⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀
⣤⣤⣄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀
⣿⣿⣿⣿⠂⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⠛⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⢹⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⠩⠄⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣽⡿⡏⣓⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠈⠻⡇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⣽⣿⣷⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣇⣩⣴⡄
⠀⠀⣀⣤⣴⠶⢦⡄⠀⢀⣠⣤⣤⣤⣦⣤⣤⠤⣤⣤⠄⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠁⠀⠉⠻⠿⢿⣿⣿⣿⣿⡏⠀⠁⢙⠋⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢸⣿⣿⡿⠈⢿⣿⣷
⣀⣠⣀⡈⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⡀⣦⣀⣀⣷⡀⠀⠀⠀⠀⠀⢼⣿⣿⡿⠀⣄⠀⠀⠀⣄⠀⠉⠻⠿⣿⠇⠀⢀⣿⡄⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⣸⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⣤⡀⠀⢸⣿⣿⣿⢲⣿⣿⣷⣶⣿⣇⡀⠀⠀⠀⠀⣶⣾⣿⣿⢸⣿⣿⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠉⠃⣿⣿⣆⠀⣀⣼⣾⣿⣿⣿⣾⣿⣿⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀
⣿⣿⣿⢄⣠⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⣿⡟⠛⣄⡀⠀⠀⢀⣿⣿⣫⣴⣿⣿⣿⣿⣿⣟⢻⣿⣿⡟⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀
⣿⣿⣿⣦⣿⣯⣤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡶⣶⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀
⠻⠿⠿⣿⠿⢿⠿⠻⠿⠿⠿⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠉⠀⠁⠈⠁⠀⠉⠀⠉⣉⣉⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⢾⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⠾⡆⠀⠐⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠤⠤⠄⠠⠴⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⠟⠋⠉⠀⠈⢻⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠍⠀⠀⢀⣤⣤⣤⡀⢸⡏⡹⠛⠈⠈⢭⡩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⣠⣤⣨⣿⣿⣿⣿⣿⣇⠀⠀⣀⣤⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀
⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠟⠀⠀⠀
⣿⣿⣿⣿⡆⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠓⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⡈⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣯⠀⠄⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⣿⣻⠛⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢴⣄⠀⠈⠻⢇⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⡀⠘⣿⣶⠠⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣭⣼⣌⣉⣤⠀⠀
⠀⠀⣀⣠⣤⡴⠦⡄⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⡩⣿⣦⡀⠀⠀⠹⠿⠿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣈⠉⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠘⣿⣿⡇⠀
⣀⣀⣉⡉⠉⠁⠀⠀⠀⠀⣿⣿⣾⣿⣿⡁⢿⣄⣙⣟⡁⠀⠀⠀⠀⠀⡧⣿⣿⣷⠀⠀⠀⠀⠀⡀⠉⠙⠛⠿⣿⠇⠀⢰⣿⡄⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⣹⣿⣿⠀
⣿⣿⣿⡿⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⢛⣿⣿⣿⢰⣷⣾⣷⣶⣿⣆⡀⠀⠀⠀⠀⢠⣿⣿⡿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⡟⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠈⠙⠛⣿⣿⡄⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣇⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀
⣿⣿⣿⣧⣤⣤⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢰⣿⣿⡟⠛⡀⠀⠀⠀⠀⣿⣿⣫⣶⣿⣿⣿⣿⣿⡟⣻⣿⣿⡟⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀
⣿⣿⣿⣦⣿⣿⣷⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢷⣶⡶⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⡆⠀⠀⠀⣀⣀⣀⡀⠀
⠻⠿⠿⣿⠿⢿⡿⠿⠿⠿⠿⠉⠉⠉⠉⠉⠉⠉⠒⠀⠀⠀⣀⣀⣀⣭⣤⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣍⣩⣭⣭⣭⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⢿⣾⣿⠿⠿⠷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣦⣤⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡿⠛⠋⠉⠀⠀⢻⣯⢯⣯⣽⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠟⠉⠀⠰⣿⣿⣿⣦⠀⡁⠀⠀⠙⠡⠁⠺⢋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣠⣬⣿⣿⣿⣿⣶⣿⠀⠀⠀⣀⣤⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡖⠀⠀⠀
⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀
⣾⣿⣿⣿⡷⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠿⠇⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠒⠒⠒⠒⢒⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⡿⡿⠦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⠀⠀⢻⣧⡀⠐⢚⣿⣿⣿⣿⣿⣿⣟⠹⠿⠀⢠⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⣭⣇⢛⣂⡄⠀⠀⠀
⠀⠀⠀⣀⣠⣤⠤⣤⠀⠀⢀⣠⣤⣤⣤⣄⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⢠⡄⠈⠀⣴⣿⡟⢻⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠉⢻⣿⣷⠀⠀⠀
⠀⢀⣀⣉⠉⠉⠀⠀⠀⠀⢸⣿⣯⣿⣿⡇⠩⠅⠐⣛⡃⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⠃⠀⢸⣰⡄⢸⣿⣿⡆⢨⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠸⣿⣿⡆⠀⠀
⣿⣿⣿⣿⡇⢀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⣾⣿⣆⠀⠰⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡷⢸⣿⣿⡇⣘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⣿⣿⣿⣿⠇⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⢀⠀⢼⣿⣿⣿⣷⣶⣄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⢠⣤⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⡟⢿⣿⣿⣿⣶⣄⣿⡿⢿⣰⣬⣿⣿⣿⣿⡟⣻⣿⣿⡗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀
⣛⠉⣿⣿⣦⣿⣷⣶⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠶⠶⠶⠦⣶⠶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⢶⣦⣀⣀⣀⣀⣀⠀⠀⠀⣠⣶
⠻⠿⠿⣿⠿⢿⡿⠻⠿⠿⠿⠉⣉⣉⣉⣉⣩⣭⣤⣤⣷⣾⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣛⣿⣛⣛⣛⣛⣋⣉⣉⣉⣀⡙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⡄⡄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠛⣿⣿⣿⣷⡀⠨⠽⠯⡋⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣾⠟⠉⠀⢠⣿⣿⣿⣿⣧⣴⡐⠀⠈⠁⠀⠀⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⣾⣧⣬⣿⣿⣿⣿⠀⠀⠀⣀⣤⣤⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀
⣾⣿⣿⣿⣶⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠿⠿⠿⠏⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡎⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⣀⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠒⠒⠒⠒⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⠚⡿⢷⠤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢻⣦⡀⠀⢀⣾⣿⣿⣿⣿⣿⠍⠁⠀⠀⢠⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣾⣌⣅⣄⠘⠂⡀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣤⠤⣤⡀⠀⠀⢀⣀⣀⣤⣄⣠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠯⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⣴⣿⡟⢻⣿⣾⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⢹⣿⣷⠀⠀⠀⠀
⠀⠀⣀⡉⠉⠉⠀⠀⠀⠀⠀⢿⣯⣾⣿⡿⠈⠀⡀⣈⡁⠀⠀⠀⠀⠀⠀⠸⡂⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠻⠁⠀⢀⣠⡀⢸⣿⣿⡂⢹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠈⣿⣿⡀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⢤⡀⠀⠀⢰⣷⣄⠀⢀⣀⣀⣀⠀⢀⡀⠀⠀⠀⢀⣼⣿⣿⡇⢸⣿⣿⡇⣸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⢿⣶⣿⡟⠃⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⠀⠈⣹⣿⣿⣿⣿⣿⡄⠀⠰⢿⣿⣿⣿⣇⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⣄⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢸⣿⡟⢾⣷⣿⣿⣿⣍⣿⡟⢳⡄⠀⣿⣿⣿⣿⡗⣻⣿⣿⡗⢛⠉⢿⢿⣿⣿⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣯⣼⣧⣽⣿⣴⣴⢶⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠶⠶⠴⠶⠶⠶⠟⠿⢷⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀⣀⣀⣀⣀⢀⢠⣶⣿⣿⣿
⠻⠿⠿⣿⠿⢿⠿⠻⠿⠿⠿⠉⠉⣉⣉⣉⣩⣥⣤⣤⣤⣤⣴⣴⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣬⣬⣤⣤⣁⣈⣁⣉⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⡟⠉⢹⣿⣿⣿⣿⡄⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⣻⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠁⠤⢠⣿⣟⡻⢿⣿⣿⣯⠀⠙⠉⡠⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣠⣤⣿⣿⣿⠛⣛⣿⣿⣿⠀⣀⣤⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀
⠠⣿⣿⣿⣷⣄⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⣿⠿⡿⠿⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡄⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠒⠛⠃⡀⢀⣻⣟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⢷⠦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⢀⣼⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⠀⠀⢠⣾⣿⣿⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⣛⣁⠒⠂⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣤⣤⡀⠀⠀⢀⣀⣀⣠⣄⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠉⠻⠿⠿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠈⢀⣴⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⠏⢻⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⣈⠉⠉⠁⠀⠀⠀⠀⢿⣿⣼⣿⣿⠈⠍⠀⠒⠿⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⣿⡏⠁⢀⣠⡀⢸⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢸⣿⣿⣀⠈⣿⡿⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠇⢀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢤⡀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣶⡄⠀⣾⣿⣿⣾⣿⣿⡇⢸⣿⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠟⢿⣷⣿⣯⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⡅⠀⣴⣿⣿⣿⣿⡇⠀⠈⠙⠉⠉⠉⣻⣇⣿⣿⣿⡇⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡄
⣿⣿⣿⣿⣿⢀⣀⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⡿⢺⣾⣿⣿⣿⣽⣿⡟⠀⠀⠀⠀⢀⣴⣿⡟⣻⣿⡿⠗⢹⢙⡿⣿⣿⣿⣿⡿⠟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⢀⣰⣥
⢛⣽⣿⣿⣧⣬⣿⣷⣤⢶⡾⣿⣿⣿⣿⣻⣿⣿⠿⠿⠿⠶⠶⠶⠶⠶⠲⠞⠛⠷⠲⠿⠿⠿⠿⠿⠿⠷⠶⣶⣶⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣲⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⠤⠠⠀⠀⠶⣿⣿⣿⣿⣋⣀
⠻⠿⠿⣿⠿⢿⠿⠻⠿⠿⠿⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠋⠁⣼⣿⣿⣿⣿⣈⢻⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠙⣹⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠀⠱⠄⣰⣿⣟⡻⢿⣿⣿⣏⠡⡀⡧⠞⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣠⣤⣀⢿⣿⣿⣛⣛⣿⣿⡿⣀⣤⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀
⠀⣿⣿⣿⣷⣦⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⠃⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢭⣽⢇⡄⢀⣾⣿⣿⣿⣿⡿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢷⣦⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⠀⠀⢠⣾⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢠⣿⣛⣋⡔⠢⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣤⣤⣄⠀⠀⢀⣀⣀⣠⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠐⠻⠿⠿⢿⣿⣿⡿⠿⢿⠃⠀⠀⠀⠘⢀⣴⣿⡟⣿⣿⣿⣿⣿⣧⣄⣀⠀⣠⣀⠿⠃⠀⠀⢸⣿⣿⡿⠙⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⣈⠉⠉⠁⠀⠈⠀⠀⣾⣿⣿⣿⣿⡇⠯⡑⠲⠟⠀⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠂⢀⣠⡄⢸⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣇⠀⣹⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢀⣶⡄⠀⠿⠿⠿⠿⠿⣿⡇⢸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⠿⠿⣿⣿⣿⡷⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⢸⣿⣿⠑⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣏⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢤⣀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⢀⣼⣿⡿⣿⣿⣿⠗⣋⣹⣿⣿⣿⣿⣿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣄⠀⠀⢀⣤⣤
⢉⣩⣭⣿⣯⣬⣿⣷⣤⢶⡾⣿⣿⣿⣻⣻⣿⣿⠿⠿⠿⠷⠶⠶⠶⠶⠲⠞⠿⠷⠲⠿⠿⠿⠿⠿⠿⠷⠒⠶⠶⢶⡾⣿⣿⣷⣿⣿⣿⣿⣿⣶⣶⣖⣲⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠦⠤⠄⠀⠀⠚⠿⠿⠿⠿⢯⣥⣀
⠸⠿⠿⣿⠿⢿⠿⠻⠿⠿⠿⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠅⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣟⠁⠀⣽⣿⣿⣿⣷⡸⢽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠛⣳⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠈⠀⠁⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠉⠁⠀⢻⡄⣴⣿⡿⢻⣿⣿⡆⠀⠁⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣤⣀⡀⣿⣿⣿⠿⢿⣿⣿⣆⣤⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀
⠀⣶⣿⣿⣶⣦⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀
⠀⢿⣿⣿⣿⡏⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡯⣀⠀⢀⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣼⣿⣿⣿⣿⣿⡉⠁⠀⠀⢀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⢀⠀⠀⠀⣰⣟⣛⣻⠰⠄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣠⣤⣄⠀⠀⠀⣀⣀⣠⣄⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠘⢀⣴⣿⠿⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢻⡿⠃⠀⣿⣿⣿⠏⢻⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡉⠉⠋⠀⠈⠀⠀⠸⣿⣿⣿⣿⡇⠯⡅⠚⡻⠅⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠉⠉⠁⢠⣶⡦⠀⢀⣠⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⡄⠀⠀⠀⢸⣿⣿⡀⠈⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⢀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⣤⡀⠀⣿⣿⣷⣿⣿⣿⡆⣸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠿⠟⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢸⣿⣿⡏⢀⣤⣴⣶⣶⣿⡇⠀⢉⣭⣽⣿⣿⣿⣇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡧⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⣿⢾⣾⣿⣿⣿⣿⣿⡇⠀⠈⠛⠋⠉⠙⢻⡷⣿⣿⣿⠗⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣠⠤⠄
⢈⠉⣭⣭⣿⣭⣿⣷⣴⢶⡖⣿⣿⣿⢻⣛⣿⣛⠛⠻⠿⠷⠶⠶⠖⠒⠒⠞⠛⠷⠂⠿⠿⠿⠿⠛⠟⠓⠒⠒⠲⠖⠶⠶⠿⠷⢿⣿⣿⣿⣗⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠾⠿⠀⠀⠀⠀⠛⠿⠟⠿⠿⠭⣥⣤⣤
⠘⠿⠿⣿⠿⢿⠿⠻⠿⠿⠿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡍⠀⠀⣾⣿⣿⣿⡎⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠇⣧⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠿⠋⠠⡴⠊⣿⣄⣼⣿⣿⣿⣿⣿⢻⠋⠞⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠚⠉⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⣤⣀⡉⢸⣿⣿⣾⣭⣿⣿⣆⣬⣤⠀⠈⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀
⠀⢰⣾⣿⣶⣦⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⡿⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⠤⠤⢀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠿⠟⠋⢀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢀⣿⣻⣻⡗⠦⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣤⣄⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠤⠼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⠘⢀⣴⣿⡿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣤⣤⡄⠸⣿⣿⡿⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡉⠉⠋⠀⠈⠀⠀⢹⣿⣿⣿⣿⡇⠯⣍⠙⠛⠁⠀⠀⠀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⣉⡁⠀⢀⣠⠄⢸⣿⣿⠇⢿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⡈⠉⠀⠈⣿⣿⣇⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⣸⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⠀⠀⠀⠙⠿⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⢸⣿⣿⣿⡀⠀⣀⣤⣤⣿⡇⠀⠾⠿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⡷⣤⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⢻⣶⣿⣿⣿⣿⣿⡗⠀⢰⣾⣿⣿⣿⣿⡷⣿⣿⣿⠷⣟⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⢀⣰⡦⠶⠖
⢉⠈⣬⣤⣤⣭⣯⣷⣴⢶⡖⣿⣿⣿⢻⣛⣻⣛⠟⠛⠛⠓⠲⠖⠒⠒⠒⠚⠛⠗⠢⠟⠿⠿⠛⠛⠛⠓⠂⠚⠛⠋⠻⠛⠛⠳⠿⠿⠿⠧⠯⢬⣭⣷⣶⣷⣾⣿⣿⣿⣶⣖⣛⣛⣃⣀⣀⣀⣈⣛⣛⣛⣛⣯⣥⣤⣤⣤
⠘⠿⠿⣿⠿⢿⠿⠻⠿⠿⠿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⢿⣏⠀⠀⣼⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠇⡇⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠂⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠈⠨⢈⣿⣄⣼⣿⣿⣿⣿⣿⢝⠻⡛⡯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⣤⣀⡉⢸⣿⣿⣶⣮⣭⣿⣇⣤⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀
⠀⢰⣶⣿⣷⣦⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⠤⠤⢀⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠿⠿⠋⢀⢐⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⢠⣇⣻⣺⠰⠆⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣤⣄⡀⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠬⠽⣿⣿⣿⣿⣿⣿⡇⠠⠠⠂⠘⢀⣴⣿⠟⣿⣿⢿⣿⣿⡏⠀⠀⠀⠀⠠⣤⣤⠀⢸⣿⣿⡟⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣋⠉⠛⠀⠀⠁⠀⠘⢿⣿⣿⣿⣇⠯⡍⠚⡛⡃⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⣉⡀⠀⢀⣠⠔⢸⣿⣿⠁⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢈⠁⠀⠸⣿⣿⣅⠀⣿⣿⡇⠀⠀⠀⠀⢀⠀
⣿⣿⣿⣿⣿⣿⠆⡀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⡆⣼⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⠀⠀⠀⠻⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠨⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⠀⣀⣤⣤⣤⣿⡇⠀⠾⢿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⠗⠀⠀⠀⠀⠀⠀⠀⠠
⢿⡿⣿⣿⣿⡿⣤⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⢰⣾⣿⣿⣿⣿⡷⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⠿⠀⠀⠀⠀⠀⢀⣠⣶⣄⠀⢀⣀⡠⠴⠓⠚
⢀⠀⣦⣦⣤⣤⣦⣭⣤⢶⡖⣿⣿⣿⢛⣛⣻⡛⠛⠛⠛⠛⠒⠖⠒⠒⠒⠚⠛⠛⠒⠿⠿⠟⠛⠛⠛⠓⠒⠚⠻⠛⠻⠛⠛⠓⠛⠛⠻⠧⠭⠥⣤⣶⣿⣿⣿⣿⣿⣿⣶⣶⣋⣀⣐⣒⣒⣚⣛⣛⣙⣛⣛⣷⣶⣶⣶⣶
⠸⠿⠿⣿⠿⢿⠿⠻⠿⠿⠿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⢿⣿⣏⠀⠀⣼⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⠞⡆⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠫⡑⢥⠚⣿⣄⣼⣿⣿⣿⣿⣿⠮⣻⠟⢟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣠⣤⣀⡋⢸⣿⣿⣶⣮⣽⣿⣇⣭⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀
⠀⢐⣶⣿⣷⣦⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⡿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠬⢤⠤⢀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠛⠛⠋⢀⢐⠀⢠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣸⣟⣟⣃⠶⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣤⣤⡀⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠶⠾⣿⣿⣿⣿⣿⣿⡇⠲⠆⠀⠘⢀⣴⣿⡿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠐⣶⡦⠀⣿⣿⣿⠟⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣉⠉⠛⠁⠀⠁⠀⠐⣿⣿⣿⣿⣧⠭⡅⠚⠛⡇⠀⠀⠀⠀⠀⢨⣿⣆⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⣩⣀⡀⢀⣠⠔⢸⣿⣿⠇⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⣀⠀⠀⢻⣿⣿⡀⢸⣿⣿⡀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⣿⣿⣿⠇⡀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢤⣄⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⡆⣸⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠈⠻⠿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⠀⣀⣤⣤⣤⣿⡇⠀⠾⢿⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢀⠈⠀⠀
⠻⠿⠿⢿⣿⡿⢤⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⡷⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⣀⣀⠕⠊⠓⠒
⢀⠀⣦⣤⣤⣤⣤⣭⣤⢶⡖⣿⣯⣿⢛⣛⣛⡛⠛⠛⠛⠛⠒⠲⠒⠒⠒⠚⠛⠛⠒⠻⠻⠛⠓⠛⠛⠓⠒⠘⠛⠛⠙⠛⠛⠓⠛⠛⠻⠯⠾⠥⠶⠿⠿⢿⣿⣿⣿⣿⣿⣾⣯⣭⣤⣴⣿⣿⣯⣭⣭⣽⣷⣶⣶⣶⣶⣿
⠘⠿⠿⣿⠿⢿⡿⠻⠿⠿⠿⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠆⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠶⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢈⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣻⢏⠀⠀⣼⣿⣿⣿⡎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠸⣶⡆⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⠁⠈⣿⣄⣼⣿⣿⣿⣿⣯⠲⡰⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠐⠞⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣠⣤⣀⡉⢹⣿⣿⣶⣮⣭⣿⣇⣤⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⠉⣿⣿⡇⠀⠀⠀⠀
⠀⢰⣶⣾⣶⣦⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⠗⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣤⡤⢀⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠛⠛⠛⠉⢀⢀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⣸⣟⣟⡇⠶⢠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣤⣤⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⡇⠓⠑⠄⠘⢀⣴⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⣶⡦⠀⣿⣿⣿⠛⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣈⡉⠛⠁⠈⠁⠀⠐⣿⣿⣿⣿⣿⠭⣍⣟⢻⡗⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠙⠙⠛⠛⠋⣉⣄⡀⢀⣠⠄⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢀⡈⠑⠀⢹⣿⣿⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠇⡀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢤⣄⠀⠀⢠⣿⣿⡆⠀⠀⠀⠀⠀⣀⡀⠀⢨⣿⣿⣿⣿⣿⡖⣼⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠈⠿⠟⣿⣿⣿⡿⠀⠀⠀⠀⢀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⢸⣿⣿⣿⣀⣀⣤⣤⣤⣿⡇⠀⠾⢿⣿⣿⣿⣿⡇⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⠘⢟⢶⣀
⠛⠿⠿⢿⢿⡿⢤⣤⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⡗⠀⢰⣿⣿⣿⣿⣿⡷⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⣤⣶⣦⡀⢀⣀⣤⠼⠟⠛⠉
⢀⡀⣦⣦⣤⣄⣤⣤⣤⢤⡖⣿⣯⣿⢛⣛⣛⡛⠛⠛⠛⠻⠲⠶⠖⠒⠒⠚⠛⠛⠲⠿⠻⠻⠛⠛⠛⠓⠒⠒⠛⠋⠻⠛⠛⠛⠛⠛⠻⠣⠿⠧⠼⠿⠿⠿⠿⠿⠿⢿⣯⣤⣭⣥⣤⣤⣿⣿⣭⣭⣭⣿⣷⣶⣶⣶⣾⣿
⠸⠿⠿⣿⠿⢿⡿⠻⠿⠿⠿⠉⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡴⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠂⠀⠀⠀⠀⠀⠀⠈⠿⠂⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⣻⢿⠀⠀⣴⣿⣿⣷⡎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠸⠾⡆⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠒⠀⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠋⠉⠠⠄⣾⣄⣸⣿⣿⣿⣿⣿⢘⠁⢟⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠐⠞⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣤⣈⡙⣿⣿⣿⣷⣬⣽⣿⣆⣷⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠃⠀⠀⠀⠀
⠀⢀⣶⣾⣶⣤⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⢳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣷⠤⠤⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣴⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠗⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣸⡰⣏⡇⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣁⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠐⠶⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠘⢀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⡿⠓⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣘⡉⠛⠃⠈⠁⠀⠀⣽⣿⣯⣿⣿⠩⣍⠙⠿⡅⠀⠀⠀⠀⠀⠰⣿⣆⠀⠀⠀⠀⠀⠉⠛⠉⠉⢉⣭⣄⣀⢀⣠⠄⢸⣿⣿⡅⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢿⣿⣧⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⢦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⢀⠀⠀⢠⣿⣿⣿⣿⣿⣆⣼⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠀⠀⠘⠿⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠑⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠀⠀⢸⣿⣿⢿⣄⣠⣤⣤⣤⣿⡇⠀⠾⠿⣿⣿⣿⣿⡇⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⡿⠂⠀⠀⠀⠀⠠⠀⢀⠤
⠛⠛⠿⠿⠿⠿⢤⣤⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⢺⣿⣿⣿⣾⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⡗⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⢴⣶⣦⡀⢀⣀⣤⠖⠚⠚⣋
⢀⡀⣦⣤⣤⣤⣤⣤⣤⢶⡖⣿⣯⣽⢛⣛⣛⡛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠚⠛⠛⠒⠘⠛⠛⠛⠛⠛⠓⠒⠒⠛⠛⠟⠛⠛⠛⠋⠙⠋⠐⠐⠲⠶⠾⠿⠿⠿⠿⠿⠿⠭⠯⠥⠤⠭⠥⠭⠥⠤⣬⣭⣭⣷⣶⣶⣶⣾⣯
⠺⠿⠿⣿⠿⢿⡿⠻⠿⠿⠿⠉⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⢿⡿⠁⠀⣠⣤⣤⣔⠨⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠰⠶⡆⠀⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠚⠀⠘⠂⠀⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠏⠂⠌⢫⣧⠀⣰⣿⣿⣿⣿⡇⢻⢟⠓⠯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠐⠛⠃⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⣤⣘⣿⣶⣿⣿⣛⠿⣿⣷⣗⣧⣤⠀⠄⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⠀⠀⠀⠀⠀
⠀⠀⣶⣾⣶⣦⡀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⡟⠫⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣿⡴⠤⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡽⠽⠟⠐⠛⢿⡷⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣼⣾⣏⡇⠾⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣁⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠶⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⢀⣴⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⣿⣿⣿⠓⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢘⠉⠛⠁⠈⠁⠀⠀⣿⣿⣿⣿⣿⠉⢍⠑⣿⡅⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠛⠛⠛⠋⢉⣭⣄⡀⢀⣠⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣧⠀⢹⣿⣏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⡄⠀⠀⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠐⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣼⣿⣿⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠘⠿⠿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⢸⣿⣿⠇⠀⣀⣤⣤⣠⣿⡇⠀⠾⠿⢿⣿⣿⣿⡇⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⢀⠂⠠⠤
⠛⠛⠛⠿⠿⠿⢢⣤⠀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣿⡿⠳⣿⣿⣿⣿⣿⣿⡇⠀⢰⣾⣿⣿⣿⣿⠗⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠅⠀⠀⠀⠀⢠⣶⣶⣤⠀⢀⣀⣠⠶⠗⠛⣉
⢀⡀⣦⣤⣤⣄⣤⣤⣤⢤⡔⣿⣯⣽⢛⣛⣛⡛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠛⠓⠂⠘⠛⠛⠛⠛⠛⠓⠒⠒⠛⠋⠙⠛⠛⠛⠋⠋⠛⠓⠒⠒⠲⠶⠿⠿⠿⠿⠿⠭⠭⠤⠬⠤⠬⠭⣬⣽⣿⣭⣭⣽⣷⣶⣶⣶⣾⣯
⠸⠿⠿⣿⠿⢿⡿⠿⠿⠿⠿⠉⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢸⣿⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣥⣿⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠂⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⢿⣿⣿⣿⣟⡃⠀⠀⠀⠐⠖⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢽⣿⣏⣟⣿⣧⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢿⣿⣾⡿⣿⣻⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣺⣿⣿⣿⣿⣿⣋⢻⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀
⠀⠀⣴⣶⣶⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠀⢸⣟⣩⣼⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡍⢡⣤⣥⡄⠀⢠⣬⣭⣽⡟⣭⣭⣭⣈⣥⣭⣭⣤⣤⣤⣤⣠⣤⣤⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠈⣛⢻⣿⡟⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣧⣺⣿⣏⣱⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⣿⣿⠉⣿⣯⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣿⣿⡇⣿⣿⠀⣬⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡏⠻⠿⢿⢋⡻⠿⠿⢃⠿⠿⠀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣤⣤⣤⣤⣤⡄⢽⣿⢤⢸⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠉⣿⣿⠁⣭⣽⡿⡯⠬⠄⠀⣴⣐⡂⡅⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⠀⣿⣿⢀⣹⣿⠇⠏⠀⠀⠀⣿⣿⡟⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠙⠁⠀⠁⠀⠀⠠⣽⣬⣿⠇⠈⠉⠉⠋⠅⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠉⠉⠛⠻⠛⠋⠉⣩⣭⣿⣿⣿⠃⢸⣿⡿⠿⠿⠿⠿⠀⠿⠿⠶⡿⣿⠁⠀⠀⠀⠀⢿⣿⣇⡀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⢀⠀⠀⠀⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡀⣸⣿⣿⠀⠀⠀⣤⡄⠐⠺⡻⣧⣿⣀⠀⠀⠀⠀⠘⠿⠻⡏⣹⠿⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⣿⣿⠄⠀⠀⢀⣀⣀⣴⡆⠀⠼⠿⣿⣿⣿⣿⡧⣿⣿⣿⠂⡇⠀⠛⡋⡂⠀⠀⠋⠋⣯⣡⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠛⠛⠻⠿⠿⠠⠄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⡏⠙⠑⣶⣾⣿⣿⣯⣿⡇⠀⢰⣾⣿⣿⣿⣿⠓⣿⣿⣿⠖⠁⠀⠂⠤⣀⡂⠀⠀⠀⠥⠌⠀⠀⠀⠀⠀⠠⢶⣦⣄⠀⢀⣀⠀⠀⠀⠀⢀
⢀⠀⣤⣤⣦⣄⣤⣤⣤⢦⡄⣾⡭⣽⢛⢛⣛⡉⠛⠛⠋⠉⠐⠂⠐⠒⠒⠒⠛⠓⠀⠈⠙⠛⠋⠙⠉⠁⠀⠀⠉⠉⠉⠙⠛⠛⠉⠉⠁⠀⠀⠀⠒⠂⠛⠋⠉⠋⠙⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠬⠤⠤⠴⠶⠾⢭
⠸⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠍⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣶⣶⣾⣿⣶⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣎⣉⣿⣿⣿⣿⡻⢹⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠐⠄⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣿⣿⣿⣿⣿⣛⣿⠻⣯⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⡿⠇⠐⡽⣿⣿⣿⣿⣙⣟⡳⣼⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡔⠀⠀⠀⠀⠀
⠀⠀⠰⢔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣠⣴⣴⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢡⣤⣥⡄⠀⢠⣤⣥⣤⡅⣬⣤⣤⣛⣬⣤⣥⣤⣤⣤⣤⣠⣤⣤⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠺⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣸⣿⣏⡱⠖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⣿⣿⠉⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣿⣿⡇⣿⣿⠀⣬⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠿⠿⠏⠻⠿⠿⣏⠻⠿⢿⡃⠿⠿⠀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣤⣤⣤⣤⣤⡄⢹⣷⢰⠀⠄⠄⠀⠀⠠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠉⣿⣿⠁⢼⠱⠺⠂⠿⠆⠀⣀⡰⡀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠀⣨⣿⣯⣿⣿⣭⣯⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⠀⣿⣿⠈⣖⣷⡁⠸⠀⠀⠀⢿⣿⡟⠀⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠉⠛⠁⠀⠀⠀⠀⠠⣿⣨⠿⡇⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠈⠉⠙⠋⠉⠉⣩⣭⣿⣿⣿⠇⢸⣿⡿⠿⠿⠿⠿⠀⠿⠿⢐⣌⣻⠀⠀⠀⠀⠀⢸⣿⡇⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡦⠤⠀⠀⠀⠀⡛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡄⢸⣿⣷⠀⠄⠀⠀⠀⠀⢰⢪⠊⠓⡀⠀⠀⠀⠀⠘⠛⠛⡇⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢵⠑⠀⠀⠀⠀⡀⢀⣤⡄⠀⠸⠿⣿⣿⣿⣿⡇⣿⣿⣿⡀⡄⠀⠠⠥⠄⢜⠨⢠⢤⣿⢀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠛⠛⠻⠿⠿⠤⠀⠀⠀⠀⢈⠉⠉⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠐⣲⣾⣿⣷⣿⣿⡇⠀⢰⣾⣿⣿⣿⣿⠓⣿⣿⡿⠗⠁⠀⠐⡒⢖⡆⠒⠂⠀⠁⠠⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⢀
⢀⠀⣦⣤⣤⣄⣤⣤⣤⢤⡄⣤⣭⣥⠛⢛⣛⠃⠈⠉⠉⠑⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠾⣭
⠼⠿⠿⣿⠿⢿⣿⠿⠿⠿⠿⠏⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⣿⣿⣿⣿⣿⡟⠅⢰⣤⣤⣄⡀⠘⣿⣿⣿⣿⣿⡗⠀⠀⠈⠀⠀⠀⠈⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡎⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠿⠏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢑⢚⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣌⣠⣤⡤⠖⢽⣿⣿⣿⣿⣿⣿⣿⣥⡄⢠⣤⣤⡄⠀⢠⣤⣤⣤⡄⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣷⣤⣿⣿⣿⣛⢻⣿⣿⣿⣿⡇⢸⣿⣏⡁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⣿⣿⠉⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣿⣿⡇⣿⣿⠀⣬⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠑⣦⠸⠿⠿⠿⠏⠻⠿⠿⠋⠻⠿⠿⠃⠿⠿⠀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠈⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣬⣤⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡇⠀⠈⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⠿⣿⣿⠉⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⣗⣥⣔⣛⡉⡈⣿⣿⣿⣍⠈⠉⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⠇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⣯⣿⡟⢻⠀⠀⢻⠿⠿⠿⠿⠿⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠇⠀⢘⡴⠀⠀⠀⠀⠀⠀⠀⠀
⢲⣶⣶⣾⣶⣶⠂⠀⠀⠀⠀⠀⠄⣒⠒⣷⣶⣶⣦⢠⡶⣤⠠⠤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢳⣾⠀⢠⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⣤⡀⠀⠈⠿⠿⠷⣾⣿⡀⠮⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠋⠉⠹⠟⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠏⠽⢿⣿⠉⠋⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡷⠮⣿⠂⠀⢠⣾⣿⣿⣿⣏⠁⣿⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⣄⣄⣤⣄⢀⣤⣤⠤⡄⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠠
⠽⠿⡿⣿⢿⢿⣿⠿⠿⠿⠿⠍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣤⣤⡄⣤⡄⢠⣤⣤⡄⠀⠀⣤⡄⣤⡄⣠⣤⣄⠀⣠⣤⣄⢠⣤⣤⣤⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡛⠃⣿⣏⡁⣿⡇⢸⣿⣏⠁⠀⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠈⢹⣿⠉⣿⣧⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡝⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡄⢸⣿⠀⣬⡝⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠁⠛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠛⠿⠛⠀⠛⠿⠛⠁⠘⠛⠀⠙⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠿⠇⣿⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠃⠛⠛⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣠⣴⣶⣾⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠀⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⠀⠀⠀⢸⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⠄⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⢿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡄⠀⠀⠀⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⢻⣭⣭⡝⢿⢿⣤⡄⣤⡝⣻⣿⣅⠀⣠⣭⣝⢻⣭⣭⣽⣻⣯⣿⡻⡇⠀⢿⡇⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⢻⣿⣏⡁⣿⡇⢸⣿⣏⡁⠬⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⣮⣽⣿⣉⣿⣧⡛⢣⡇⠀⢸⡇⠘⠛⠃⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣬⡟⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠙⠻⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡎⢻⣿⣿⣮⡝⣿⡇⠃⠀⢸⡇⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⡻⣿⣿⣿⣿⣿⣿⣿⣧⣛⠿⢟⠁⠛⢛⣇⣿⣿⣿⣟⣣⣧⣹⣔⣛⡃⠛⠃⠛⠿⣟⣅⣛⣿⣟⠁⠘⣿⣿⣿⣿⣿⣧⡆⠀⠈⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⠋⠛⢋⣭⣽⡛⣯⣤⣤⣤⣤⡝⣿⣿⣿⡿⠁⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠏⠀⣼⣿⣿⣿⣿⣿⡄⠀⣿⡏⠿⠇⣿⣿⠉⣿⡏⢡⣄⣸⣿⠁⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠇⠀⣿⡟⣿⡇⣿⣿⠀⣿⡇⢼⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⠿⠛⠇⠻⠟⠀⠻⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⣠⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⡇⠘⢿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣯⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠹⣿⣿⢸⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡾⡝⢻⣾⣏⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⣷⣄⡀⠀⠸⣿⡄⢻⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢧⠜⣺⡿⡄⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⢸⡇⠀⠀⠈⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣿⣿⡟⠀⠀⣼⡷⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⣠⣾⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⣀⣀⡀⠀⠀⠈⣿⣿⣿⣿⣿⣯⣾⣿⣿⡟⠁⠀⡃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⡏⣻⣇⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢺⣿⠀⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⠸⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⣿⠀⠀⠀⠀⡂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠫⣭⡜⣿⡿⣯⣤⣄⠀⣠⣿⣿⢯⣭⣭⣭⣹⣭⣽⡻⠐⠀⣿⠀⠀⠀⠀⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⢻⣿⣏⡙⣿⡏⢻⣿⣏⡑⡿⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠈⢹⣿⢉⣿⣧⡛⠃⠀⠀⣿⡇⢺⡿⠀⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣭⡟⣿⡎⣿⡟⠃⣿⡇⢸⣿⣏⣽⣿⠇⣿⡏⣿⡇⣿⡇⣿⡇⣬⡿⣿⡎⢸⣿⠘⣭⡝⣿⡇⣧⠀⢸⡇⠀⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣚⣿⣿⣿⣿⣿⣿⣿⣧⡛⠿⣟⣑⡟⣛⣇⠟⠛⣛⣿⣿⣿⣿⣴⠛⠃⠛⠃⠛⠿⢛⡡⠛⠿⠛⠁⡘⠛⣠⣟⡿⣿⣷⣿⡇⠘⡇⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠟⠻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⣿⣿⣟⣭⣭⡂⣴⣭⣴⣤⣤⡄⠀⠿⣿⣷⣤⣿⣿⣿⡋⣿⣿⣿⣿⡅⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠉⢻⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡏⠿⠇⣿⣿⠉⣿⡏⠁⠀⢀⣿⡿⢿⣿⣿⠟⠁⢸⣿⣿⣿⣿⡀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠂⢨⡽⢙⣿⣿⣿⣿⣿⣿⡟⣿⡇⣿⣿⠀⣿⡇⠀⠘⢋⣷⣤⣴⣯⡄⠀⠀⠸⣿⣿⣿⣿⣷⡅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠇⢻⣿⡀⠛⠃⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣿⣿⣿⣿⣿⣿⠀⠀⣶⣿⣿⡿⡆⠀⢠⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣷⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⡟⢏⡀⠀⠀⢙⣿⣿⣿⣿⣿⠃⠀⠀⢠⣦⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣿⣾⣿⣿⣿⡟⣿⣿⣿⡟⠁⠀⠀⠀⠀⢠⣾⣷⠀⢠⣾⣿⣿⣿⣿⡏⠀⠀⠀⠺⠏⠀⢸⣿⣿⣿⣿⣿⣿⡋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⢝⣾⣿⣿⣿⡟⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣟⡄⣈⣿⣿⣿⣿⣿⠀⠀⠀⢰⣦⠀⠀⣿⣿⣿⡏⢸⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣶⣿⡟⡽⣪⣾⣿⣿⠁⢸⣿⣿⣿⠁⠀⠀⠀⠀⢠⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣷⠀⠀⣿⣿⡟⠀⠈⠙⠻⠛⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢠⣿⣿⡿⠁⠀⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣼⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⣾⣿⣿⡿⠋⠀⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣴⣿⣷⣶⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⣿⣷⣾⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⢻⡇⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣯⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⢸⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⣿⠀⠀⠀⠸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣥⣄⠀⣠⣤⣿⣿⣿⣿⣿⣻⣯⣿⡻⠗⢘⣿⡀⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣏⡻⣿⡿⣿⣿⣏⡉⠿⠻⣿⣧⣿⡇⣿⡟⣿⡗⣿⣟⡛⠋⢹⣿⠉⣿⣧⡛⠃⡔⠀⣿⡆⣶⣶⡶⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡟⣿⡾⣿⡟⠃⣿⡇⢹⣿⣟⣽⣿⣿⣿⡏⣿⡷⣿⡇⣿⡇⣬⡿⣿⡆⣾⣿⠸⣯⡝⣿⣇⣄⠀⢻⡇⠀⠁⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⣙⣻⣿⣿⣿⣿⣿⣿⣯⣛⡿⣟⣛⣟⣻⣷⣿⠛⣻⣿⣿⣿⣿⣴⠛⠃⠛⠃⠛⠿⢛⣥⠛⠿⠛⠁⠙⠛⣤⣿⣿⣿⣿⣿⡇⠘⡇⠀⠀⠀⠰⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣟⣯⣭⡂⣴⣽⣶⣿⣤⡄⠁⢾⣿⣶⣤⣿⣿⣿⡿⣻⣿⣿⣿⡟⠀⡇⠀⠀⠀⢘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠿⠗⣿⣿⠉⣿⡏⠁⠀⢀⣿⣿⣿⣿⣿⣿⠟⠙⢻⣿⣿⣿⡆⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⣿⣿⠀⣿⡇⠀⠰⠟⣿⣥⣼⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠈⢊⡻⣿⣿⣿⣿⣿⣿⠿⠻⠇⢻⣿⣆⠟⠃⠀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⣶⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣆⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣿⣿⡏⠉⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣄⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣺⣯⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢻⣇⣻⣿⡄⠀⣰⣿⣿⣿⣿⣿⠁⠀⠀⠀⢰⡏⠀⢰⣿⣿⣿⣿⣿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡴⣸⣿⣿⣿⣿⡿⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠸⠋⢿⣿⠃⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⠁⠀⢸⣿⣿⣿⢹⣿⣷⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣰⣵⣿⣿⠿⣿⣿⣿⠃⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⣸⣦⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣧⠀⠸⣿⣿⠇⠸⠿⣿⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢠⣿⣿⡿⠁⠀⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⣾⣿⣿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣏⣼⣿⣿⡿⠋⠀⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⡿⢿⣿⣷⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⢹⡇⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⣟⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⠉⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢻⣿⠀⠀⠀⢸⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣫⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢺⣿⠀⠀⠀⠸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⡭⣽⡿⣿⣥⣄⠀⣠⣴⣿⣿⣭⣽⣿⣻⣯⣿⡻⢾⢘⣿⠁⠀⠀⠀⡃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⣿⣏⣹⣿⡟⣿⣿⣏⣹⣿⣿⣿⣧⣿⣧⣿⣏⣿⡇⣿⣟⡛⣊⣹⣿⢉⣿⣧⣛⠃⠘⠤⣿⡦⣾⣿⣯⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡿⣿⣾⣿⡟⢻⣿⡇⢸⣿⣿⣿⡿⢟⣿⡟⣿⡏⣿⣷⣿⡇⣬⡿⣿⡎⢿⣿⠘⣭⡝⣿⣷⣦⡀⢽⡇⠈⠉⠉⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⡉⢭⣙⣿⣿⣿⣿⣿⣿⣿⣧⣛⢿⣟⣻⣿⣿⣟⡿⠛⣿⣿⣿⣿⣿⣿⣛⣃⣿⣣⣿⡿⠛⠃⣻⣿⣟⠁⣼⣛⣴⣿⣿⣿⣿⣿⣇⢸⡇⠀⠀⠀⢰⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⣿⣿⣏⣥⣬⡻⣿⣿⣿⣭⣥⡄⠀⠙⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⡏⠨⡇⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠋⠻⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⣿⣿⠉⣿⡏⠁⢠⣼⣿⣿⣿⣿⣿⠿⠉⠉⢹⣿⣿⣿⡆⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡖⣿⡇⠀⠈⣡⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠋⢻⣻⣿⣿⣿⣿⣿⡟⠿⠻⡿⣿⣿⣦⠿⠇⠀⢺⣿⣿⣿⣿⣿⡟⠀⠀⠀⠸⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣿⣿⣿⣿⣿⡿⠁⠀⢸⣿⣿⣿⡿⠷⠀⢀⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠙⠿⢿⣿⣿⣶⣦⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣻⣿⣿⡟⠏⠁⠀⠀⠀⣿⡿⣿⣇⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣽⣿⡿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⡆⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣿⠀⠀⣿⣿⣿⣿⣿⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⡿⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣁⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⢸⣿⣿⣿⠒
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⡄⠀⢿⣿⡇⠸⠿⣏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⣿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣢⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣾⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣀⣀⣀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠋⢐⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⢿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢸⣯⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠐⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢺⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⣥⣬⡟⣻⣿⣤⠀⣤⣼⣿⢿⣭⣭⣿⣻⣯⣿⣻⣿⡿⣿⡇⠀⡀⠘⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣏⣻⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⣿⣟⡛⢮⣽⣿⢩⣿⣧⣛⠃⠻⣧⣿⣿⣿⣿⣾⣗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣾⣿⡟⢻⣿⡟⢹⣿⣿⣿⣿⢯⣿⡟⣿⡇⣿⣿⣿⡇⣬⡿⣿⡆⢻⣿⠈⣭⡟⣿⣷⣦⠘⣿⡏⠉⠉⠉⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣻⣿⣿⣿⡿⠛⣿⣿⣿⣿⡿⣿⣿⣷⣿⣧⣿⠿⠛⠁⣿⣿⣿⣁⣾⣿⣴⣿⢿⣿⣿⣿⡇⢸⡇⠀⠀⠀⢿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠘⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣏⣤⣼⡻⣿⣿⣿⣥⣤⡄⠀⢀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡏⢸⡷⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠯⠙⠛⢿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣿⣿⣉⣿⡏⠁⢰⡿⣿⣿⣿⣿⣿⡟⠁⠉⣹⣿⣿⣿⣾⣿⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡏⣿⡇⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠋⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⣿⣿⣿⣧⡿⠇⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣼⣽⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⡟⠛⠀⢠⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠹⢿⣿⣿⣿⣶⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠈⣽⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⠛⣿⣿⣿⠋⢰⠀⠀⠀⠀⠀⣿⡿⣿⣿⡇⠀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣾⠀⠀⣿⣿⣿⣿⣿⡟⠟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣾⣿⣿⣿⣿⣿⡏⠀⣿⡿⠁⢠⣿⠀⠀⠀⠀⠀⣿⣇⣿⣿⣥⢠⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣉⠀⠀⢿⣿⣿⢸⣿⣿⣿⠿
⠀⠀⠲⠆⠀⠒⠀⠀⠐⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⣰⡿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⡆⠀⢸⣿⡇⠸⠿⡿⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⡿⠃⠀⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣼⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢹⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣾⣿⣻⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢸⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡶⠀⠀⠸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣭⣤⣬⡝⣻⣿⣿⠂⣤⣿⣿⢻⣭⣭⣽⣻⣯⣽⣿⣿⣿⣿⡇⠀⠀⠸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣏⣻⣿⣿⣿⣿⣏⣿⣿⣾⣿⣿⣿⡷⣿⣿⣿⡇⣿⣿⡛⠪⣽⣿⢩⣿⣧⣛⠃⠻⢿⣿⣿⣿⣿⣶⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡿⣿⣾⣿⡟⢻⣿⡇⢸⣿⣿⣿⣿⢷⣿⣟⣿⡇⣿⣿⣿⡇⣬⡿⣿⡆⢹⣿⠀⣭⡟⣿⣿⣦⠈⣿⡏⠉⠉⠉⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣸⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⡿⠛⣿⣿⣿⣿⠛⣹⣿⣿⣿⣷⡛⠿⠛⠁⠻⣿⣿⣥⣿⣿⣶⠟⠿⣿⣿⣿⡇⢸⡇⠀⠀⠀⣯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠁⠻⠟⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣇⣬⣿⡛⣿⣿⣿⣧⣤⡄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡧⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠭⠉⠹⢿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣿⣿⣍⣿⡏⠁⠸⠟⣿⣿⣿⣿⣿⣏⠀⠉⣹⣿⣿⣿⣞⣷⠀⠀⠀⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⠃⣿⡇⠀⣠⣾⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠟⠻⢹⡿⣿⣿⣿⣿⣿⣿⡿⠙⠿⠿⣿⣿⣿⣶⡿⠇⠀⣙⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢸⣿⣿⣿⡟⠛⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣶⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⡏⢁⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠀⢀⣼⣿⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣜⣿⣿⣿⣿⡟⢹⣿⣿⠟⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⣿⡇⠀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡸⠀⠀⣿⣿⣿⣿⣿⠟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⠃⠈⠿⠏⠀⣴⡿⠀⠀⠀⠀⠀⣿⣧⣿⣿⣶⢠⣾⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣁⠀⠀⣿⣿⡏⢸⣿⣿⣿⠿
⠀⠀⠳⠖⠀⠒⠀⠀⠐⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣄⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣆⠀⢸⣿⡇⠸⢿⣿⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⠃⠀⣷⣿⣗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠋⠀⣰⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⣴⣴⣤⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⣿⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢻⣿⠀⠀⠀⢹⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡥⣤⡝⣩⣭⣍⠛⣫⣭⣝⢩⣤⣤⣭⣩⣭⣿⡻⠹⢸⣿⠀⠀⠀⠘⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣟⡻⣿⡿⢻⣿⣏⡿⡿⠈⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠊⢹⣿⠉⣿⣧⡛⠃⠈⠘⣿⣠⣤⣤⣰⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣿⡞⣿⡟⠣⣿⡇⢸⣿⣟⡹⠻⢇⣿⡏⣿⡇⣿⡇⣿⡇⣬⡿⣿⡆⣸⣿⠀⣬⡝⣿⡇⣄⠀⣿⡏⠛⠛⠙⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣟⣱⣿⣻⣧⣟⣻⣿⣿⣿⡁⢸⣾⣿⣓⣛⣧⡛⠿⠛⢁⣻⣿⣿⣿⣿⣿⣦⣙⡿⣿⣷⣿⠀⢹⠁⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣤⣭⡀⣬⣽⣿⣭⣤⡄⢾⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⠿⠇⣿⣿⠉⣿⡏⠁⢠⣿⣿⣿⣿⣿⣿⠇⠀⢈⣿⣿⣿⣧⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⡟⣿⡇⣿⣿⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⠗⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢻⣿⣿⣿⢿⡿⠃⠀⠘⠿⠿⣧⣿⣿⡄⠿⠃⢀⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⠀⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⢠⡄⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠸⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⢹⣿⣦⣦⣄⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣻⠀⢸⣿⣿⡏⢠⣿⡇⠀⠀⠀⠀⠀⣿⡏⣿⣿⣏⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣵⣿⣿⠀⣾⣿⣿⠁⣾⣿⣿⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣿⣿⣿⣥⣄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⣿⣷⣾⣿⣿⠀⣿⣿⠃⣾⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⠻⢿⣿⣿⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⠃⢸⣤⣼⣷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠁⢀⣸⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣴⣶⣶⣦⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢣⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣼⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣇⠀⠀⠀⢿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣥⣤⣤⡌⣩⣭⣍⠉⣩⣭⣍⢡⣤⣤⣬⣩⣭⣽⡛⢫⣸⣿⠀⠀⠀⠘⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣟⣻⣿⡏⢸⣿⣏⡿⠿⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠊⢹⣿⠉⣿⣧⡛⠃⠙⢻⣿⣤⣤⣤⣼⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣿⡿⣿⡟⠳⣿⡧⣾⣿⡟⠹⣿⣧⣿⡏⣿⡏⣿⡇⣿⡇⣬⡿⣿⣦⣾⣿⠈⣬⡝⣿⡇⠀⠈⣿⠉⠻⠟⠹⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣳⣿⣿⣷⣿⣿⣿⣿⣇⠘⢻⡟⠛⣓⣛⣧⡛⠿⢛⣥⣿⣿⣿⣿⣿⣿⡶⠟⢿⣿⣷⡀⠀⢿⠀⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣤⣤⡘⣿⣿⣯⣤⣤⡜⠻⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣷⡄⢸⡇⠀⠀⠀⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⡏⠿⠷⣿⣿⠉⣿⡏⠁⣼⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⡿⠿⡿⠟⠁⠀⣿⡟⣿⡟⣿⣿⠀⣿⡇⠀⢿⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿⣿⠘⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⡀⠀⠀⠀⠙⠿⠿⣷⣿⣿⡀⠿⠃⢠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⣿⣿⡀⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣰⣶⣾⡆⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠈⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣷⣷⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⡿⢀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⢠⣾⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⠀⣿⣿⠇⣼⣿⣿⣿⣿⡄⠀⠀⠀⣿⡇⣹⣿⡟⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣼⣿⣿⡿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⡆⢿⣿⢰⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⣿⣿⣷⣶⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣿⣿⣽⣿⡇⢸⣿⡌⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠙⠻⢿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⠋⢹⣀⣴⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠃⢀⣼⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣠⣾⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠟⣥⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣴⣶⣶⣶⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣼⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡆⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⠀⠀⠘⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣩⣭⡍⣿⡿⣿⣥⣤⡶⣿⣿⣿⢻⣿⣿⣿⣻⣿⣿⡛⢧⢼⣿⠀⠀⠀⢻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿⡟⢻⣿⣏⡿⠟⠛⣿⣧⣿⡇⣿⣏⣿⡇⣿⣟⡛⠎⢹⣿⣉⣿⣧⣛⠃⠀⢼⣿⣤⣤⣤⣾⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣿⡟⢻⣿⡇⣼⣿⡟⠹⢿⢧⣿⣏⣿⡇⣿⣿⣿⡇⣬⡿⣿⡆⣺⣿⠹⣯⡝⣿⡇⠀⠸⣿⠟⠿⠟⢻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣟⠃⠛⠿⢛⣷⣿⣿⣿⣷⣿⣿⣬⣿⣿⣿⣣⠀⠀⣿⠀⠀⠀⢸⡂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣭⣭⡙⣿⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣄⠀⣿⡄⠀⠀⠈⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠙⠹⠋⠻⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠿⠷⣿⣿⠉⣿⡏⠉⣹⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣧⢹⡇⠀⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣱⠀⣿⣿⣿⣿⣿⣿⠀⣿⡇⢰⣿⣿⣿⣿⣿⣿⠃⠀⠀⢿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢈⣽⣿⣿⠏⠉⢡⡴⢿⡄⠙⠿⠿⠟⢿⣿⣤⡿⠇⠈⣹⣿⣿⣿⣿⠃⠀⠀⠀⠈⢿⣿⣿⣿⠈⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢁⣿⣿⣶⣾⡇⠀⠀⢿⣿⣿⣿⡟⠃⠀⢰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣄⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢸⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⣹⣿⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡇⢸⣿⡿⢡⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⢻⣿⣿⠀⢰⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⡏⢹⣿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡇⢸⣿⢁⣿⣿⣿⣿⣿⣿⣿⣇⠀⢰⣿⣿⣾⣿⣿⡄⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⠿⠟
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⣀⣤⣴⣿⣿⣿⣿⣿⠃⢽⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣼⣿⣿⠏⢿⣀⣴⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⡿⠁⢀⣼⣿⣿⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⣾⣿⣿⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠟⣥⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣤⣤⣤⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣰⣿⣏⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢹⡅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠟⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⡟⣿⡿⣧⣤⣄⡰⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⠀⠀⠀⢿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿⡿⢻⣿⣯⡿⠿⠻⣿⣧⣿⣇⣿⣯⣿⡇⣿⣿⡛⣊⣹⣿⣉⣿⣧⣛⠃⡸⢻⣿⣤⣤⣤⣼⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣿⡟⢻⣿⡇⢸⣿⡟⠹⣿⢃⣿⣏⣿⡇⣿⣿⣿⡇⣬⡿⣿⡆⣼⣿⢻⣿⡟⣿⡇⠀⡻⣿⠛⠿⠟⢻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣿⣿⣿⣿⡟⠃⠛⠿⢛⣷⣿⣿⣿⣿⣿⣛⣺⣿⣿⣿⣧⠀⠀⣿⠀⠀⠀⢸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣭⣭⡙⣿⣿⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣯⣀⠀⣿⡆⠀⠀⠈⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠉⠙⠛⠙⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠿⠷⣿⣿⠉⣿⡏⠙⣽⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣆⢻⡇⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⣿⣿⣿⣿⣿⣿⠀⣿⡇⢠⣿⣿⣿⣿⣿⣿⠂⠀⠀⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢋⣽⣿⣿⡏⠙⣽⢷⣿⡆⠙⠿⠿⢿⣿⣿⣄⠿⠇⠘⣻⣿⣿⣿⣿⠃⠀⠀⠀⠹⣿⣿⣿⣿⠘⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠂⣷⣿⣷⣿⡇⠀⠀⢿⣿⣿⣿⡟⠓⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣧⣤⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⡟⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣷⡄⠀⠈⢹⣿⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⡇⢸⣿⡟⢡⣾⣿⣿⣿⣿⣿⡆⠀⢨⣿⣿⢿⣿⣷⠀⢰⣿⡟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⢻⣿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡇⢸⣿⢡⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣾⣿⣯⣀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠛
⠀⠀⠠⠆⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⣀⣤⣾⣿⣿⣿⣿⠀⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⣼⣿⣿⠏⢳⣀⣴⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃⢀⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢆⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠟⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣸⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⣡⣤⣄⡀⣼⣿⣿⢿⣿⣿⣿⣿⣿⣽⡛⢿⣿⣿⠀⠀⠘⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿⡿⢻⣿⣿⣿⡿⢿⣿⣧⣿⣧⣿⣿⣿⡏⣿⣿⡛⢊⣹⣿⢉⣿⣧⣛⢣⣼⣿⣿⣤⣤⣤⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣿⡟⢿⣿⡇⢸⣿⡿⢻⡿⢃⣿⡟⣿⡿⣿⣿⣿⡇⣬⡿⣿⡆⣹⣿⣿⣿⡟⣿⡇⢹⣺⣿⠿⠿⠟⢿⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣼⣿⣿⣿⣿⡛⠃⠛⠿⢿⣷⣿⣿⣿⣷⣿⠿⢿⣿⣿⣿⣧⠈⠉⣿⠀⠀⠀⢸⡂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡠⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢙⣽⣭⡛⣿⣧⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠨⣿⡄⠀⠀⠈⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠑⠟⠉⠉⠟⠿⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠿⠿⣿⣿⠉⣿⡟⠛⣿⣿⣿⣿⣿⣿⠅⠁⢹⣿⣿⣿⣿⡄⣿⡇⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣿⣿⣿⣿⣿⣿⠀⣿⡇⢠⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠻⡿⢿⣿⣿⣿⠿⣻⣿⣿⡇⠙⠿⢿⠿⣿⣿⣀⠿⠇⠸⢿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⢠⣿⣿⣿⠇⣿⣿⣷⣿⡷⠀⠀⣿⣿⣿⣿⡿⠇⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠛⣿⣿⣿⣦⣧⣄⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢸⣿⣿⡿⢀⣿⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣷⡀⠀⠘⢹⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣌⣯⡏⢸⣿⣿⢃⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣷⠀⢠⣿⡟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠟⣿⣿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣿⣿⣿⣿⡇⢸⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣾⣿⣏⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠟
⠀⠀⠳⠆⠀⠂⠀⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⣀⣀⣰⣥⣿⣿⣿⣿⣿⣿⡇⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣗⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠄⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠟⣿⣀⣼⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠪⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⡆⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⣾⣿⣿⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣼⣿⣿⢿⡆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣷⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠄⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢹⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⡟⣠⣤⣌⠉⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⡻⣿⣿⣿⠀⠀⠸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⢿⣿⣯⣿⡿⢿⣿⣧⣿⣿⣿⣿⣿⡟⣿⣿⡛⠊⣹⣿⠉⣿⣧⣛⢣⣿⣿⣿⣷⣿⣶⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣿⣿⡟⢿⣿⡇⢸⣿⡿⢿⠿⠋⣿⡟⣿⡿⣿⣿⣿⡇⣬⡿⣿⡆⣻⣿⣿⣯⡟⣿⡏⢻⣿⣿⡿⢿⠟⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⣷⣾⣿⣿⠿⠃⠛⠿⣿⣧⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣧⠘⣟⣿⠀⠀⠀⢹⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠔⠀⣴⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢛⣿⣿⡛⣿⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⡆⠀⠀⢸⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠻⠛⠛⠻⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠿⠿⣿⣿⠉⣿⡿⠟⣿⣿⣿⣿⣿⣿⠇⠛⢻⣿⣿⣿⣿⡞⣿⡇⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⡇⢠⣿⣿⣿⣿⣿⣗⠀⠀⢸⣿⣿⣿⣿⣷⢸⡇⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠙⠿⡿⢿⣿⣿⡀⠿⠇⠸⢿⣿⣿⣿⣿⠁⠀⠀⠸⣿⣿⣿⣿⣿⣸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠠⣿⣿⣿⡇⣿⣿⣿⣿⡟⠀⠘⣿⣿⣿⣿⡿⠆⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣾⣧⣄⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠀⣿⣿⣿⠃⣿⣿⣿⣿⣿⡆⠀⢻⣿⣿⣿⣧⠀⠀⠘⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢸⣿⣿⠇⣰⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣧⠀⢠⣿⠇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⣿⡿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣶⣾⣿⣿⣿⣿⢸⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣼⣿⡟⠀⣼⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⠿⢿
⠀⠀⠳⠖⠀⠖⠀⠀⠘⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣷⣿⣿⣿⣿⣿⣿⡏⣾⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⠀⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠁⢀⣿⣿⣿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⡇⠀⠀⢸⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡯⣤⡄⣩⣭⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡛⠃⣿⡇⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣟⣿⣿⡿⢻⣿⣏⡙⠛⠀⣿⣧⣿⡇⣿⡏⣿⡗⣿⣟⡛⠊⢹⣿⠉⣿⣧⣛⠃⠐⢹⣧⣀⣢⡠⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣿⡾⣿⡟⢳⣿⡇⢸⣿⡏⠹⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡆⢸⣿⠐⣬⡝⣿⡇⠀⢸⣿⠉⠛⠁⢻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣟⣹⣟⣿⣷⡟⣻⣿⡛⠃⣴⣰⣔⣛⠃⠛⠃⠛⢿⣟⣡⣛⣿⣟⣵⣿⣿⣿⣿⣿⠟⢃⠀⠈⣿⠀⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢉⣭⣽⡻⣧⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⠀⣿⠀⠀⠀⠘⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠹⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣿⡏⠿⠇⣿⣿⠉⣿⡏⣽⣿⣿⣿⣿⠋⠀⣿⣿⣿⣿⣿⣿⡆⠀⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣻⢿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡟⣿⡇⣿⣿⠀⣿⡇⣿⣿⣿⣿⡏⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡀⡀⠙⠿⠿⢗⡻⠿⠀⠛⠇⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣷⠀⢐⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣷⣶⡀⢘⣷⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠹⣿⣿⣿⣿⣿⢀⣾⣷⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣇⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣽⠀⣿⣿⡿⠋⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⡄⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣯⠀⣿⣿⠃⢀⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠟⣿⣿⣿⣿⡏⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣜⣿⣿⣿⣿⣿⡏⠀⣿⠃⢠⣿⣿⣿⣿⣿⣿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣷⠀⠀
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⠟⡇⠀⣸⣗⠀
⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣴⣿⣿⠃⠀⣿⣾⣿⠟⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣴⣿⣿⠋⠀⠀
⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣿⣿⠿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣤⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⠀⠀⢿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡂⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⡇⠀⠀⢸⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣭⡭⣿⡿⣿⣯⣍⠙⣻⣿⣿⢿⣿⣿⣿⣿⣯⣽⡛⠀⣿⡇⠀⠀⠘⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣟⣿⣿⡏⢹⣿⣏⡉⠋⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⣎⢹⣿⣭⣿⣧⣛⠃⠀⢸⣇⢀⣀⣀⡅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣿⣿⣿⡟⠃⣿⡇⢸⣿⡏⠙⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡿⣿⡟⣿⣿⠙⣯⡝⣿⡇⠀⢸⣷⠙⠿⠏⡯⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣻⣿⡟⢃⣿⣛⠛⠛⢃⣤⣴⡄⠛⠃⠛⣣⣻⣿⣿⣥⡛⢿⣿⣷⣿⣿⡀⣻⣿⣿⣣⡀⠘⣿⠀⠀⠀⠹⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡻⢛⣿⣥⡀⣤⣤⣭⣭⣽⡟⠛⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⣿⠀⠀⠀⠸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠉⠹⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠿⠇⣿⣿⠉⣿⣏⣥⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⣿⣿⠀⣿⣿⣿⣇⠀⠹⣿⣿⣿⣿⣿⣷⠹⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠁⠀⠀⠙⢿⣿⣷⣿⠟⠀⠿⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⡇⠀⠻⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣣⣤⣶⡆⠀⢿⣿⣿⣿⣷⠀⢸⣿⣿⣿⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⢹⡷⢠⣴⣧⣄⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⠉⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣦⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⢸⣿⣿⡿⠀⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠀⣿⣿⠃⢰⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⠀⠈⣿⣿⣿⣿⡏⠙⢻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣶⡶⠒⠺⣿⣿⣿⣿⠀⣿⠃⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠉⠛⠿⢷⣦⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣴⣽⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⡿⠁⠀⢀⠀⠀⠀⠀
⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣴⣿⣿⠁⠀⣤⣶⡟⠀⠀⠀
⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⣤⣾⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣠⣄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣾⣿⡿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⣿⣿⣇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣦⠀⠀⠀⢠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⢘⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢸⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⢫⣭⣬⡟⠄⠠⣤⡭⣿⡍⣠⣤⣄⠰⣨⣥⣄⢩⣿⣿⣿⣻⣭⣭⡁⠀⠸⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⣿⣿⣿⣿⣿⣿⣇⣿⣯⡛⢻⣿⣏⡁⣿⡇⢸⣿⣏⡁⠄⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣿⡛⣮⢹⣿⠉⣿⣧⡛⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡿⣬⡟⣿⡞⣿⡏⠁⣿⡇⢸⣿⡏⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡿⣿⣿⣿⣿⡘⣬⡝⣿⡇⠀⠀⡇⠀⠋⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢿⣿⣿⣧⡛⠿⠟⣑⣛⣛⡃⠛⠛⠛⠛⢣⣶⣿⠂⠛⠃⠛⠃⠛⠿⢟⠁⠛⢿⣿⣿⣿⣿⣷⣟⠿⠟⣃⠀⠀⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠴⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⢉⣭⣥⡀⢤⣤⣤⣤⣤⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠰⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⠿⠇⣸⣿⠉⣿⡏⣥⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⣿⡿⣿⡇⣿⣿⠀⣿⡇⢿⡆⠀⠀⠀⠀⠈⠿⢿⣿⣿⡷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢗⣿⠛⠀⣿⡇⣼⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⣀⣠⣠⠀⠀⠀⢸⣿⣿⣿⣃⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠖⠀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⣐⣶⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⠉⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⡆⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⣿⣿⣿⣿⣟⣉⠉⠙⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠉⠛⠿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⡿⠃⠃⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣾⡿⠃⠀⢠⡄⣒⠀⠀
⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⠁⢀⣴⣿⡗⠁⠀⠀
⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢙⣶⣿⣿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣀⣤⣄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣸⣿⣿⣿⣇⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠼⣏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⠀⠀⠀⢰⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢺⡄⠀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠉⠛⣿⣿⣿⡟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⡇⠀⠀⠨⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⢩⣥⣼⡟⠄⢠⣤⡼⣿⡍⣠⣤⣄⡼⣿⣿⣇⢩⣿⣿⣿⣻⣭⣽⡁⠀⢸⡇⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠽⣿⣿⣿⣿⣿⣿⡿⣿⣯⡛⢻⣿⣏⡁⣿⡇⢸⣿⣏⡡⠀⠀⣿⣧⣿⡇⣿⡏⣿⡗⣿⣿⣻⣏⣽⣿⢉⣿⣧⣛⠃⠀⠈⡇⢀⣄⠀⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢽⢿⣿⣿⣿⣿⣿⣬⡿⣿⡞⣿⡏⠃⣿⡇⢸⣿⡏⠙⠛⠃⣿⡏⣿⡇⣿⣧⣿⡇⣬⡿⣿⣿⣿⣿⣼⣮⡝⣿⡇⠀⠀⡇⠈⠛⠁⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢻⣿⣿⣿⣧⠛⠿⢟⣙⣿⣿⡇⠛⠛⠛⠛⣧⣶⣶⠖⠛⠃⠛⣧⡻⢿⣟⡅⠛⠿⣿⣿⣿⣿⣿⣿⡿⢟⣃⠀⠀⢷⠀⠀⠀⢐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢶⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠚⠛⢛⣭⣤⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠋⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⠿⠇⣿⣿⠉⣿⣏⣥⡀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⠀⣿⡏⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢷⣿⠛⢀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⡀⣠⣤⣄⠀⠀⠀⢻⣿⣿⣿⢀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡏⠐⠐⣦⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡃⢠⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠟⠁⠀⡄⠈⡴⣶⣿⣿⣿⣿⣿⣷⡀⠀⠈⠛⠻⠿⠿⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣯⣭⣉⣹⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣄⢰⢿⣽⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠷⢿⢺⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣾⡿⠃⠀⠠⢄⠀⠀⠀
⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⠁⢀⣴⣷⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢘⣶⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣠⣤⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣰⣽⣿⣿⣇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠏⣻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢰⠀⠀⠀⢰⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⡆⠀⠀⠘⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⠛⣿⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⡇⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡍⢩⣤⣽⡗⠀⢠⣤⡼⣿⡍⣠⣤⣤⣼⣿⣿⣷⢩⣽⣿⣿⣻⣭⣭⡋⠀⠈⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⡜⡿⣿⣿⣿⣿⣿⡯⣿⣯⡛⢻⣿⣏⡁⣿⡇⢼⣿⣏⡁⡀⠀⣿⣧⣿⡇⣿⣿⣿⡗⣿⣿⣻⣯⣽⣿⠉⣿⣧⣛⠃⠀⠀⣇⢀⣀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⢽⣿⣿⣿⣿⡿⣬⡟⣿⡞⣿⡟⠳⣿⡇⢸⣿⡏⠙⠛⠃⣿⡏⣿⡇⣿⣧⣿⡇⣬⡿⣿⣿⣿⣿⣼⣬⡝⣿⡇⠀⠀⡏⠈⠉⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⣿⣿⣿⣇⠛⠿⠟⣻⣿⣿⡃⠛⠛⠛⠛⣧⣶⣶⠖⠛⠃⠛⣧⣿⣿⣟⡅⠛⠿⢿⣿⣿⣿⣿⣿⡿⠟⣃⠀⠀⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⣿⢿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⠛⢛⣭⣤⡀⣤⣤⣤⣤⣤⡍⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⠿⠇⣿⣿⠉⣿⣏⣥⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠄⠀⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⣿⣿⠀⣿⡟⣿⡇⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣷⣿⠟⢀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠉⠀⠀⠀⣀⣀⣤⡀⠀⠀⠀⢺⣟⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠇⠀⢤⣦⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠁⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠄⣀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠋⠀⠀⠀⠈⠠⠼⣿⣿⣿⣿⣿⣧⠀⠀⠈⠛⠿⠿⠿⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠁⣟⠈⠁⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⢤⣶⣂⣠⠀⠀⢥⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⢉⣿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⢀⣼⣿⠇⠁⠀⠀⠀⠀
⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣠⣿⡿⠃⠀⣠⣄⠀⠀⠀
⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣼⣿⣿⠁⢀⣴⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⣶⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣄⣤⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣼⣿⣿⣿⣧⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⢘⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣀⣤⣧⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣻⠄⠀⠀⢸⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⡇⠀⠀⠘⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠎⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠉⠙⠛⣿⣿⣿⠙⠛⠛⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡍⢡⣤⣽⡇⠀⢠⣤⡼⣿⡍⣠⣤⣤⣼⣿⣿⣿⢬⣭⣿⣿⣫⣭⣭⡛⠀⠈⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣯⣿⣯⡛⢻⣿⣏⡁⣿⣧⣼⣿⣏⡁⠀⠀⣿⣧⣿⡷⣿⣿⣿⡟⣿⣿⣛⣿⣿⣿⠉⣿⣧⣛⠃⠀⠀⣇⢠⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣿⣿⣿⣿⣿⣬⡿⣿⣾⣿⡟⢷⣿⡇⢸⣿⡟⠙⠛⠃⣿⡏⣿⡇⣿⣿⣿⡇⣬⡿⣿⣿⣿⣿⣾⣬⡝⣿⡇⠀⠀⣿⠀⠉⠃⠀⠀⠀
⢼⠄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣧⠛⠿⢟⣻⣿⣿⠋⠛⠛⠛⠛⣣⣠⣤⡄⠛⠃⠛⣧⣿⣿⣟⣥⠛⠿⠟⣿⣿⣿⣿⣿⣿⠿⣃⠀⠀⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢶⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠬⠛⢛⣿⣤⡀⣤⣤⣬⣭⣬⡍⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⠿⠇⣿⣿⠉⣿⣏⣥⡀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣽⡇⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣿⣿⣿⡷⣿⣿⠀⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣷⣿⠟⢠⣿⢗⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠁⠀⠀⢀⣀⣠⣤⠀⠀⠀⠀⢺⣾⣿⣿⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⡆⢶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠁⢄⢀⢺⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢷⣦⣤⣄⠀⠈⠳⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠠⢠⠱⢾⣿⣿⣿⣿⣿⡆⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⠀⠀⠀⠀⠀⠨⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣀⣀⣀⣠⣤⢠⢼⡭⣹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠉⠻⠇⠀⠀⠀⠀⠐⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠈⠃⠀⠀⢠⢶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⡿⢿⣭⣤⡍⠁⠩⣬⡍⣭⡝⣫⣭⣟⠿⣿⣿⣿⢿⣿⣿⣿⣻⣭⣭⡉⠀⠀⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⡇⣿⣇⡛⢻⣿⣏⡁⣿⡇⢸⣿⣏⡁⠀⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⣮⢹⣿⣩⣿⣧⡛⠃⠀⠀⠇⠀⠀⠀⠀⠀⠀
⢀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⡿⣬⡟⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡎⢸⣿⣿⣯⡝⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀
⣲⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣺⢿⣿⣿⣧⣛⣿⣟⣵⡛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠛⠿⠛⡁⠛⠿⠛⣡⣾⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣻⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣄⡀⢤⣤⣤⣤⣤⡌⠋⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⡲⢌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⡏⠿⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠴⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠃⠘⠛⠀⠿⢇⣴⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⠿⠀⢀⣴⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣴⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠀⠀⠀⠀⠀⠀
⠀⠐⢤⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠾⢿⡿⣿⣷⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀
⣰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⣿⣿⣿⣿⣿⣏⠙⠿⡿⠻⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀
⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⣻⣿⣿⢿⣿⣿⡿⣿⡍⢠⣤⣤⡄⢿⠿⣭⡿⣿⡟⣠⣤⣄⠀⣠⣿⣟⢫⣽⣿⣿⣿⣿⣭⡻⡇⠀⠀⠃⠀⠀⠀⠀⠀
⠠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⣿⣯⡛⠻⣿⣏⡁⣿⡇⢸⣿⣏⠁⠀⠀⣿⣧⣿⡇⣿⡇⣿⡇⣿⣟⡛⡊⢹⣿⣩⣿⣧⡛⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠼⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⠃⣬⡟⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡆⢸⣿⣿⣯⡝⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠈⡁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠛⠿⠛⠁⠛⢛⣃⣛⠛⠛⠛⣷⡶⠆⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⣵⣿⣿⣿⣿⡿⠟⢃⣴⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣺⡻⠯⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠉⢀⣤⣄⡀⣤⣤⣤⣤⣤⡔⠃⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠁⠁⠿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣭⣀⠀⠀⠀⠀⣿⡏⠿⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠶⠟⠻⠻⠉⠓⢔⠘⣸⣻⣇⡺⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡆⠀⠀⠀⣿⡟⣿⡇⢸⣿⠀⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢢⣿⣿⣮⠖⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠘⠿⠛⠃⠘⠛⣀⠿⣇⣾⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡭⡿⡇⠀⠺⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠐⣿⣷⣀⠀⠀⠈⠙⠟⣦⠘⢿⣷⠖⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⠘⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠐⣷⣦⣤⣀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣷⠛⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢀⠘⢿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⡀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢠⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⠁⣠⣄⠀⠀⠀⠀
⠀⠀⠀⢰⣼⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣼⣿⡟⠀⠀⠀⠀
⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠏⠀⠀⠀⠀⠀
⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀
⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣤⣶⣶⣦⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣀⣰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⢿⣿⣿⠿⢿⣿⣿⣷⣄⠻⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⡟⣫⣭⣿⢿⣿⣿⡿⣿⡏⢠⣤⣤⡄⠁⠠⣤⡤⣽⡿⣿⣥⣄⠀⣠⣤⣄⢠⣭⣿⣿⣿⣿⣿⡻⣿⡇⠀⠐⠀⠀⠀⠀⠀
⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢿⠀⣿⣯⡛⢻⣿⣏⡁⣿⡇⢸⣿⣏⠁⠀⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⣮⢹⣿⠉⣿⣧⡛⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠐⠚⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⣬⡟⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡏⢸⣿⠀⣬⡝⣿⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠁⠛⠛⣃⣟⣻⣟⠛⠃⣶⣿⠖⠛⠃⠛⠃⠛⠿⠛⠀⠛⠿⠛⠁⠘⠛⣀⣙⠿⠟⠃⣸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⠿⠟⠀⠀⢀⣥⣄⡀⢤⣤⣤⣤⣤⡄⠀⠀⠀⢀⣤⣴⣾⣿⣿⠛⠟⠙⠛⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⡯⠍⠁⠀⠕⠸⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣄⠀⠀⣿⡏⠿⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠿⣿⢿⠐⠧⠧⠀⠀⠀⠠⢰⡀⢈⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⣿⡟⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠂⠀⠀⠀⠀⠀⠑⡃⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠙⠿⠛⠃⠘⠛⡀⠿⢇⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⢠⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠈⠛⠂⠀⠸⣿⣿⣷⣤⣤⣤⣤⣾⣿⡿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠐⠂⠘⠛⠛⠉⠀⠀⠀⠀⢠⣤⣄⠀⠀⠈⣿⣿⡎⠻⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢍⡧⢄⠀⠘⢿⣇⠀⠈⠉⠙⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⣀⢻⣿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⠙⣾⣆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢼⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡟⠉⣀⣤⡿⠀⠀⠀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣼⣿⡿⠃⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠏⠀⠀⠀⠀⠀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀
⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢠⣶⡶⠿⣷⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣠⣤⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠿⣿⣿⠿⢛⣿⣿⣿⣦⣄⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡟⣫⣭⣿⢻⣿⣿⡿⣿⡍⢠⣤⣤⡄⠀⢠⣤⡬⣽⡟⣻⣥⣄⠀⣠⣤⣄⢠⣬⣽⣿⣻⣿⣿⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⠀⣿⣯⡛⢻⣿⣏⡁⣿⡇⢸⣿⣏⡁⠀⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡻⣮⣽⣿⠉⣿⣧⣛⠃⣿⡇⠀⠀⡄⠀⠀⠀⠀
⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠀⣬⡟⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠙⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡿⣿⡿⢻⣿⠀⣬⡝⣿⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀
⠉⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠁⠛⠛⣃⣿⣿⣿⠛⠓⠻⣿⠛⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⠁⠙⠛⣀⣙⠿⣟⣃⣼⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠇⠸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠛⣿⡟⠋⠁⠀⢀⣤⣄⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣟⠛⢿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠔⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡄⠀⣿⡏⠿⠇⢿⣿⠉⣿⡏⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⣿⡟⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠉⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠋⠊⠈⢘⠻⢛⢻⣿⣿⣿⣿⣿⣿⠳⠿⣿⣿⣿⣻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠙⠿⠛⠇⠚⠻⡀⠿⠇⠀⠀⠀⠀⢀⣀⠈⠻⣿⣿⣦⠀⠀⠀⠐⠂⢠⣴⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠋⠉⠑⠛⠛⠃⠘⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠉⠉⠀⠀⢹⣿⣿⣷⣶⣶⣶⣶⣾⡿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⣶⣶⣦⠀⠀⢹⣿⣿⠙⠿⣿⣿⣿⣷⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠻⣿⡀⠀⠀⠈⠉⠛⠃⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢸⡟⠉⠙⠧⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣽⣷⣧⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⣿⣷⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣸⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⡌⠷⣞⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⣾⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠉⣤⣶⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣼⣿⡿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠾⠻⠛⢻⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣶⣾⣿⣿⣷⣯⡝⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⡟⠻⠿⣿⣫⣿⣿⣿⣿⢶⣶⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⡟⣫⣭⣿⢿⣿⣿⡟⣯⡅⢠⣤⣤⡕⠀⢠⣬⡭⣭⡝⣻⣭⣄⠀⣠⣤⣄⢠⣤⣭⣿⣿⣿⣿⣻⣿⣷⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠨⠀⣿⣯⡛⢻⣿⣏⡁⣿⡇⢸⣿⣏⡁⠀⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣿⣻⣯⣿⣿⠉⣿⣧⣛⠃⣿⣿⠀⠀⡇⠉⠁⠀⠀
⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⣬⡟⣿⣾⣿⡏⠁⣿⡗⢾⣿⣟⣹⣿⣧⣿⡏⣿⡇⣿⣿⣿⡇⣬⡿⣿⡿⣿⣿⠀⣬⡝⣿⡇⢹⣿⠀⠀⢁⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠿⠟⠙⠛⠛⢃⣿⣿⣿⠟⠃⠉⠻⠋⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠟⠁⠙⠛⣠⣛⠿⢟⣃⣼⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢨⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠀⢃⠀⠀⠀⣹⣿⣄⡀⠀⢀⣤⣤⡀⣤⣤⣤⣤⣤⡄⠁⠀⠀⢰⣶⣶⣾⣿⣿⠿⠟⣙⣻⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠔⠬⢟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⣿⣿⠿⠇⣿⣿⠉⣿⡏⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣷⣀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⡑⢲⣿⣉⢳⣿⡿⢿⡋⢛⣑⣾⣿⣻⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡆⣿⣿⣿⡇⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠈⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢉⠀⢋⠘⡊⠔⠉⠸⠿⠟⠉⢻⠹⠿⠛⢟⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠁⠙⠿⠛⠇⠛⠻⠀⠿⠇⠀⠀⠀⠀⣤⡀⠈⢻⣿⣿⣦⠀⠀⠀⠚⠃⢰⣶⣶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠐⣛⠠⣁⠀⠠⠀⡈⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⣦⢴⣿⡿⠟⠃⠀⠀⠀⠉⠉⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣾⡿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠂⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣆⠀⠙⣿⣿⡇⠛⠿⢿⣿⣿⣿⠂⠀⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠙⠉⠀⠱⠀⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠹⣿⡇⠀⠢⠄⠀⠉⠛⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣶⠄⠀⠀⠈⠻⡟⠉⠑⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠇⠐⠐⠀⠂⠘⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢤⣤⣾⣶⣦⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣳⠀⢈⠈⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣾⣿⠏⠀⣀⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣧⣶⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠐⠊⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣼⣿⣿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣀⣤⣄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠛⢟⠉⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣾⣿⣿⣿⣿⣿⣮⡙⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣃⠀⣿⠈⠛⠻⣯⣼⣿⣿⣿⠏⢓⠿⠿⠏⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠟⣫⣽⣿⢿⣿⣿⡟⣭⡅⢠⣤⣤⡌⠓⢠⣤⣬⣥⡍⣫⣥⣄⠀⣠⣤⣄⢠⣤⣬⣿⣿⣿⣿⡻⣿⣿⠀⠀⣇⢀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⠀⣿⣯⡛⢻⣿⣏⡁⣿⡇⣸⣿⣏⡁⠀⠀⣿⣧⣿⡇⣿⣯⣿⡗⣿⣿⣻⣿⣿⣿⠉⣿⣧⣛⢣⣿⣿⠀⠀⡯⠈⠉⠀⠀
⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⠀⣬⡟⣿⣾⣿⡏⠁⣿⡟⢿⣿⡟⠹⣿⣷⣿⡟⣿⡧⣿⣿⣿⡇⣬⡿⣿⡟⣿⣿⠀⣬⡝⣿⡇⢿⣿⡀⠀⢻⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠛⠿⠟⣙⠛⠛⠃⠿⠿⠟⠛⠃⠀⠉⠉⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠟⠁⠚⠛⣠⣟⠿⣿⣣⣿⣿⡂⠀⢰⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠺⠛⠩⡇⠀⠀⣾⣿⣶⣦⠀⢀⣤⣤⡀⣤⣤⣤⣤⣤⡄⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⠂⠀⠀⠀
⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⣿⣿⠿⠇⣿⣿⠉⣿⡏⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣇⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠉⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡉⡿⣿⣿⣿⣷⡿⣛⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠙⠿⠛⠟⠻⠿⣀⠿⠇⠀⠀⠀⠀⣤⡄⠈⢿⣿⣿⣆⠀⠀⠀⠘⠉⢱⣶⣶⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠛⠋⠈⠀⠀⢙⡾⢻⣿⠃⡋⣁⠈⡉⡉⡙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣾⠠⣿⣿⣿⣇⠀⠀⠀⠀⠶⠰⠿⠟⠋⠁⠀⠀⠀⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠍⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡈⠾⠁⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⢹⣿⣿⠉⠛⠛⠿⣿⣿⣿⡗⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠙⠋⠂⣨⣧⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠐⢿⣿⠀⢈⣤⡄⠀⠈⠙⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢖⣒⣪⣿⣿⣧⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠉⣿⣟⠛⠀⠀⠙⡆⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠳⠏⠘⠇⠐⠒⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣻⢿⣾⣿⣿⣿⣦⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⣿⠟⠃⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣟⣼⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣅⡷⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠰⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡡⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢨⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠹⣿⠟⣫⣭⣿⢿⣿⣯⡍⣭⡝⢻⣭⣥⡄⠀⠠⣤⡄⣤⡄⣨⣭⣍⠙⣩⣭⣍⢫⣭⣭⣽⣻⣿⣿⣿⣿⣿⡇⠀⠰⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠋⠀⣿⣇⡛⢃⣿⣏⡁⣿⡇⢸⣿⣏⡁⠀⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠊⢹⣿⠉⣿⣧⣛⣻⣿⣿⡇⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣬⡝⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡆⢸⣿⠀⣬⡝⣿⡏⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠿⠟⣁⡛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⣡⣚⣛⣀⢙⣿⣟⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠻⢿⣿⡇⠀⠀⢺⣿⣿⠂⢀⣤⣄⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠀⠘⣿⣿⠀⣿⡏⠿⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡟⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠙⠿⠛⠃⠘⠛⠀⠛⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⢾⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠘⣻⠛⠋⠁⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡝⣟⠋⠠⡂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠙⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⣿⠃⠍⠙⠻⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠇⠘⣿⠡⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠃⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⡿⠇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⢻⡇⢸⡏⠂⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣴⡾⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⡟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⡇⠀⠀⣠⣀⣀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣷⣦⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⣀⣠⡄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣴⣧⣬⣿⣿⣦⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⠰⠄⢸⣿⣿⣿⣿⣿⣿⣿⡅⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣤⣄⠩⣭⣽⡿⣿⡏⢡⣤⣤⡄⠀⠀⣬⡄⣤⡍⣩⣭⣽⠿⣣⣤⣄⢠⣤⣬⣭⣻⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⡛⠃⣿⣏⡁⣿⡇⢸⣿⣏⡁⠀⠀⣿⣧⣿⡇⣿⡇⣿⡇⣿⣏⡛⠈⢹⣿⠉⣿⣧⡛⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣬⡝⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⣙⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡝⣿⡆⢸⣿⠀⣬⡝⣿⡇⢻⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠿⠛⠁⠛⠛⠃⠛⠛⠛⠛⠋⠻⠉⠀⠛⠃⠛⠃⠛⠿⠛⠀⠛⠿⠛⢱⣞⣻⣤⠙⠿⠟⢃⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠐⠀⠀⠀⡿⣙⠛⠇⠋⠛⢛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⢀⣤⣄⡀⢤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠙⠛⠁⣠⡘⢷⣿⡟⢉⠉⠇⠀⠀⠀⠀⠀
⠀⠉⠙⠉⠋⠛⠿⢿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠊⠀⠐⠊⠙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⣿⡏⠿⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⣿⣿⣷⣿⣿⠛⠉⠈⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣿⡏⢻⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⢀⡀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡙⠿⠛⠃⠘⠛⠀⠛⠃⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢿⣿⣄⣀⣀⣀⣀⣠⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⣀⣀⠈⠉⠙⠻⠿⣿⣿⣿⡟⠉⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⡿⣿⡟⠀⢒⡀⡀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠉⠀⡢⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⢧⣤⡄⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⠇⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣤⣶⡟⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡀⠀⢰⣿⣷⣦⡀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣄⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣀⣀⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢠⣍⡉⡉⣽⣦⡘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⡿⠿⡿⡿⠿⣿⣿⡄⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⣩⣭⣍⠀⣤⣤⡝⣿⡟⢻⣭⣤⡄⠀⠀⣤⡄⣤⡄⣠⣤⣄⠘⣫⣤⣄⢠⣤⣬⣽⣻⣿⣿⣿⣿⣿⣿⠓⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⣿⣇⡛⠃⣿⣏⡁⣿⡇⢸⣿⣏⡱⠷⠀⣿⣧⣿⡇⣿⡇⣿⡇⣿⣏⡛⠈⢹⣿⠉⣿⣧⡛⠃⠙⢻⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡿⣿⠀⣬⡝⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠹⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡆⢸⣿⠀⣬⡝⣿⡇⢸⣾⡿⠀⠀⠀⠀⠀⠀
⠘⠋⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠐⠟⠉⠀⠘⠀⠛⠿⠟⠁⠛⠛⠃⠛⠛⠛⠛⠃⣀⡀⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⠁⠘⠛⠀⠙⠿⠟⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠅⠉⡟⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⣿⣻⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢉⣥⣄⡀⢤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣀⣀⣠⣴⣿⠶⠆⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⡏⠿⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠪⠿⠿⠻⢟⠂⠹⠽⠣⠞⣩⠺⠭⠿⠿⠿⡷⠘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣿⡟⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⡅⠀⢸⣷⡀⠀⠀⠀⠀⠀⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠃⠘⠛⠀⠛⠃⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠘⠛⠻⢿⣿⣿⣿⡿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠐⠍⠓⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡑⢄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢹⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠛⠃⠲⠑⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣾⡿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⡀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣷⣄⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢀⣀⣀⣀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣌⣉⣋⣹⣧⡘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⡾⠻⢿⢿⣿⣿⣿⡄⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠟⣡⣤⣭⠁⣤⣤⡍⣿⡟⢻⣭⣤⡄⠀⠀⣤⡄⣤⡄⣠⣤⣄⠘⣫⣤⣄⢠⣤⣤⣽⣻⣿⣿⣿⣿⣿⣿⡑⠆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣧⡛⠃⣿⣏⡁⣿⡇⢸⣿⣏⡹⡿⠠⣿⣧⣿⡇⣿⡏⣿⡇⣿⣏⡛⠈⢹⣿⠉⣿⣧⡛⠃⢉⢙⣿⠉⠀⠀⠀⠀⠀
⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⢿⣿⠀⣬⡟⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠹⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡆⢸⣿⠘⣬⡝⣿⡇⢸⣾⡿⠀⠀⠀⠀⠀⠀
⠀⠙⠉⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠉⠈⠉⠀⠛⠿⠟⠁⠛⠛⠃⠛⠛⠛⠛⠃⣀⣄⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⠁⠘⠛⠀⠙⠿⠟⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀
⡀⠈⠀⠄⠀⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣥⣄⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣠⣀⣤⣴⣿⠶⠆⠀⠰⣶⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡸⣽⣿⣿⣿⣿⣿⣿⣿⣿⡻⣻⢿⣿⣿⣿⣿⡢⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⣿⡏⠿⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⠀⠹⠿⣿⣿⡿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠐⠟⣹⢛⣿⣫⣳⣯⣿⣿⡝⠇⠀⠉⢛⠿⠐⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡟⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⣠⣼⣿⡅⠀⢸⣿⣅⣀⡀⠀⠀⢀⣶⣶⣶
⠀⠀⠀⠀⠁⠀⠀⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠘⠛⠀⠛⠃⠀⠀⠀⠀⣠⣾⣿⠿⠋⣀⣀⠈⠛⠛⠿⣿⣿⣿⣿⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⠰⢟⣉⠀⠂⠀⠀⠀⠈⠉⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠀⠀⠀⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠲⢈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡑⠄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢿⣿⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠻⠀⠟⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣶⡿⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣄⡀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠊⠀⢰⣿⣿⣶⣄⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣷⣦⡀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣀⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⣐⣛⢛⢛⣧⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⢸⠿⢿⣿⣿⣿⣿⡆⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡅⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠟⣩⣤⣭⠩⣤⣤⡌⣭⡟⢻⣭⣤⡄⣀⠠⣤⡄⣤⡄⣠⣤⣍⠘⣫⣥⣄⢠⣤⣬⣽⣻⣿⣿⣿⣿⣿⣿⡟⡗⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⠀⣿⣯⡛⢣⣿⣏⡁⣿⡇⢸⣿⣏⡿⣿⢾⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠈⢹⣿⠉⣿⣧⡛⠃⠙⢛⣿⡏⠇⠀⠀⠀⠀
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠀⣬⡟⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠹⠟⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡿⣿⡞⢿⣿⠿⣬⡝⣿⡇⠸⣿⡿⠀⢀⠀⠀⠀⠀
⡉⠩⠁⠈⢩⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠉⠉⠉⠁⠀⠀⠀⠀⠟⠋⠁⠀⠛⠿⠟⠑⠛⠛⠃⠛⠛⠛⠛⢣⣴⣶⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⠁⠛⠿⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣐⣺⢯⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠈⢉⣤⣄⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣠⣤⣤⣴⣿⠖⠒⠀⠀⢾⣆⠀⠀⠀⠀⠀⠀
⠂⠀⠷⠸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⣿⣿⠿⠇⣿⣿⠉⣿⡏⠁⠀⠀⠀⠀⠙⠻⢿⣿⣿⠀⢀⡀⠀⠀⠉⠀⢀⡀⠀⠀⠀
⠀⠀⠀⢀⣻⠿⣿⡿⠿⢟⠻⠽⠿⡿⠿⠿⠿⠏⠀⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⣠⣤⣿⡇⠀⠸⣿⣧⣠⣀⣀⣀⣀⣸⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠃⠛⠛⠀⠛⠇⠀⠀⠀⢀⣴⣿⣿⠟⠋⢠⡤⠀⠉⠙⠻⢿⣿⣿⣟⠅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠳⣖⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠟⠋⠀⠠⠐⠕⠉⠁⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⡴⠟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠁⠀⠀⠙⠉⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠳⠇⠐⠇⠈⠙⠘⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣽⣿⣿⡟⠀⠀⣀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢦⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠢⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠀⠹⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⢠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⡇⢸⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣶⡿⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠀⢠⡀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⢐⣿⣿⣷⣤⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠐⣿⣿⣿⣿⣿⣶⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣠⣤⣤⡀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⣴⣍⣙⣩⣷⣄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⢸⠟⢿⣿⣿⣿⣿⡇⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡟⣫⣭⣭⢩⣤⣤⡌⣭⡟⢻⣥⣤⣴⣦⣠⣤⡄⣤⡄⣠⣤⣍⠉⣩⣥⣄⢠⣤⣤⣽⣻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⣿⣯⡛⢻⣿⣏⡁⣿⡇⢸⣿⣏⡿⡿⠿⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠊⣹⣿⢉⣿⣧⡛⠃⡹⢉⣿⡟⣳⠀⠀⠀⠀
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⠀⣬⡟⣿⣞⣿⡏⠁⣿⡇⢸⣿⡏⠹⠿⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡿⣿⡞⣿⣿⠛⣬⡝⣿⡇⠹⠿⠿⠄⠑⠀⠀⠀⠀
⡙⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣩⠍⠀⠀⠀⠀⠸⡛⠹⠀⠛⠿⠟⠙⠛⠛⠃⠛⠛⠛⠛⠃⣶⡆⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⠁⠛⠛⠀⣙⠿⠟⠃⣀⣀⠀⠀⠈⠄⠀⠀⠀
⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣤⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣴⣦⣴⣾⣿⠛⠃⠈⠋⠻⣧⡀⠀⠀⠀⠀⠀
⢉⡙⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠎⠀⠀⠀⠀⠀⠈⠸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿⣿⠿⠇⣿⣿⠉⣿⡏⠁⠀⠀⠀⠀⠙⠛⠿⣿⣿⠀⢀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀
⠺⠷⠃⠶⠿⠿⠿⠛⠟⠛⠻⠿⠽⠟⠻⠛⠛⠛⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⣿⣿⡇⣿⣿⠀⣿⡇⠀⠀⠀⠀⢀⣠⣦⣾⣿⠟⠒⠸⣿⣧⣤⣤⣀⣀⣀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠃⠛⠛⠀⠻⠇⠀⠀⢀⣴⣾⣿⠿⠋⠁⢠⣤⡄⠉⠙⠛⠿⢿⣿⡿⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠂⠀⠻⡁⠀⠀⠀⠀⠀⠀⠀⣶⡿⠛⠉⢀⡀⢶⠉⡵⡿⠛⠙⠂⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⠴⡖⢶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠤⢀⢆⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠈⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢔⡀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠃⠈⠉⠀⠀⠀⠀⠀⢀⣠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⡴⣀⡆⢃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⠢⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠻⠟⠘⠟⠛⠛⠛⠛⠃⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⣱⢀⢠⣤⠙⠀⠀⠀⠀⠙⠈⣰⡀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠘⢻⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⠋⣩⣤⣌⠉⣤⣤⡄⣭⡝⢻⣥⣤⡌⠁⠀⣤⡄⣤⡄⣠⣤⣄⠀⣠⣤⣄⢠⣤⣭⣭⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⣿⣇⡛⠂⣿⣏⡁⣿⡇⢸⣿⣉⠁⠀⠀⣿⣇⣿⡇⣿⡇⣿⡇⣿⣅⡛⠈⢹⣿⠉⣿⣧⡛⢳⣿⣿⣿⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠉⠀⣬⡝⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡝⣿⡄⢸⣿⠀⣬⡝⣿⡇⢻⣿⣿⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠁⠛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠙⠿⠛⠀⠛⠿⠛⠁⠘⠛⠀⠙⠿⠟⠃⣸⠛⡛⠀⠀⠀⠀⠀⠀
⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠻⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠃⠘⠛⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢸⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣄⢀⣀⣀⣠⣤⣤⠼⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⡿⠿⠏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⢸⣠⣤⣄⠈⣤⣬⡍⣭⡟⢫⣤⣤⡄⠀⠀⣤⡄⣤⡄⣠⣤⣄⠀⣠⣤⣄⢠⣤⣤⣤⣠⣤⣄⡀⠀⠀⠀⠀⠀⠸⠛⠁⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⢰⣿⣦⠀⢠⣿⣇⡛⠃⣿⣏⡁⣿⡇⢸⣿⣏⠁⠀⠀⣿⣧⣿⡇⣿⡇⣿⡇⣿⣟⡛⠈⢹⣿⠉⣿⣧⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣿⣹⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⢰⣿⣿⣿⡿⢸⣿⣿⠀⢸⣬⡝⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡄⢸⣿⠀⣬⡝⣿⡆⠀⠀⠀⠀⠀⠀⠰⡿⠻
⠀⠀⠀⠀⢸⣿⣿⣻⣿⡟⠉⠉⠋⢸⣿⡿⣿⣿⣿⠀⢸⡇⣿⣿⣿⠸⣿⣿⣿⡇⠘⣿⠿⠀⢰⠛⠿⠛⠁⠛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠛⠿⠛⠀⠛⠿⠛⠁⠘⠛⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡿⠿⠻⠛⠃⠀⠀⠀⠀⣿⡇⣿⣿⣿⠀⢹⡇⣿⡿⠛⠀⠛⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⣿⡿⢻⠀⢹⡇⣁⠀⠀⠀⠀⠀⠾⠇⠀⠋⠁⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠿⠇⣽⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⢸⠀⢸⡇⠁⠀⣀⣀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣷⣶⠀⢀⠀⠀⠀⢀⠀⠀⠀⣿⡟⣿⡇⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢰⠀
⣀⣾⣿⣀⢸⡇⠀⢰⠦⠀⢀⣤⣦⣤⣦⣴⣴⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣃⢻⠀⠀⠀⢸⠆⠀⠀⠙⠿⠿⠇⠻⠿⠀⠿⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⣿⣿⣿⣟⣸⢠⣶⣇⠀⣰⡻⣿⣿⣿⣆⠀⠈⠉⠉⠉⠉⠉⠉⠁⠁⠀⠈⠈⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠂⠄⠐⠰⠒⠂⠠⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀
⠿⠿⢻⣿⢿⣿⣿⢿⣿⡿⢿⡿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣎⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⢸⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⣿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⢿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠋⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢼⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣼⣿⣿⣦⣀⣀⣀⣠⣤⣤⠐⠟⠋⠀⣀⣠⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠻⠟⠙⠛⠛⢿⣽⣿⣷⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀
⠀⠐⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⢠⣠⣤⣄⠀⣤⣤⡄⣬⡟⢻⣥⣤⡄⠀⠀⣤⡄⣤⡄⣠⣤⣄⠀⣠⣤⣄⢠⣤⣤⣤⣠⣤⣄⡀⠀⠀⠀⠀⠀⠸⠛⠁⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣯⣭⣤⢸⣿⣷⠀⢨⣿⣇⡛⠃⣿⣏⡁⣿⡇⢸⣿⣏⠁⠀⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠈⢹⣿⠉⣿⣧⡛⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣿⣹⣿⢿⣿⣿⣿⣿⣿⡟⣿⡿⣯⣵⣴⢰⣿⣿⣿⣿⢸⣿⣿⠀⢸⣬⡝⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡆⢸⣿⠀⣬⡝⣿⡆⠀⠀⠀⠀⠀⠀⠸⡿⠛
⠀⠀⠀⠀⢸⣿⣿⢻⣿⡏⠉⠉⠃⢸⡿⠟⣿⣿⣿⠀⣸⣇⣿⣿⣿⠸⣿⣿⣿⡇⠸⣿⡿⠀⢰⠛⠿⠛⠁⠛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⠁⠘⠛⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡿⠛⠛⠛⠃⠀⠀⠀⠀⣾⡇⣿⣿⣿⠀⣿⡇⣿⡿⠟⠀⠛⠋⠉⠀⠀⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠿⠿⢻⠀⢹⡇⣁⠀⠀⠀⠤⠀⠿⠇⠀⠛⠁⣀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠿⠇⣻⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠶⠖⢸⠀⢸⣇⣉⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⡂⣀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⣿⣿⠀⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢸⠀
⢀⣴⣿⣀⢸⠇⠀⣰⠷⠀⠀⣴⣦⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣟⣦⢻⠀⠀⠐⣷⠀⠀⠀⠙⠿⠿⠇⠻⠿⠀⠿⠇⠀⣨⠠⠠⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⢿⣿⣿⡏⢹⠀⣾⡇⠀⣈⡛⣿⣿⣿⣅⠁⠉⠈⠀⠈⠉⠈⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠘⠆⠀⠀⠈⡀⠀⠀⠀⠀⣶⣖⡶⢦⣤⡦⠦⢄⣮⠒⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠉
⠿⠿⠻⠿⢿⢿⣾⣿⣿⣿⣻⡟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢸⡃⠀⣀⣼⣿⣇⣿⣿⣿⣿⣿⣿⣟⣵⣿⣟⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⡏⣰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠿⠇⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠁⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣐⣐⣒⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠍⠉⠋⠉⠉⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⣿⣿⠧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠋⠙⠛⠃⠀⠀⠀⢀⣀⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀
⠀⠈⠀⠀⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣉⠀⢠⣠⣤⣄⢠⣤⣤⡄⣤⡄⢨⣯⣽⣿⡏⠀⣤⡄⣤⡄⣠⣤⣄⠀⣠⣤⣄⢠⣤⣤⣤⣠⣤⣤⡀⠀⠀⠀⠀⠀⠸⠋⠁⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣭⣭⣶⢸⣿⣿⠀⢸⣿⣯⡛⠃⣿⣏⡁⣿⡇⢸⣿⣏⡙⠁⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠈⢹⣿⠉⣿⣧⡛⠃⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣿⣸⣿⣿⣿⣿⣿⣿⣿⠍⣿⣿⣯⣵⣶⢸⣿⣿⣿⡇⢸⣿⣿⠀⢸⣬⡟⣿⡆⣿⡏⠁⣿⡇⢸⣿⡏⠙⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡟⣿⡆⢸⣿⠀⣬⡝⣿⡇⠀⠀⠀⠀⠀⠀⢾⣿⠛
⠀⠀⠀⠀⢸⣿⣿⣹⣿⠋⠀⠉⠋⢹⠿⠟⣻⣽⣿⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⢸⣿⠿⠀⢰⠛⠿⠟⠁⠛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⠁⠘⠛⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡟⠛⠛⠛⠃⠀⠀⠀⠀⣿⡇⣿⣿⣿⠀⣿⣿⣿⡿⠏⠘⠛⠋⠁⠀⠀⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠿⠿⢻⠀⣿⡇⣁⢠⠀⠀⠤⠰⠿⠇⠘⠛⢁⣀⣸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠇⣿⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀
⠐⠰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠶⠟⢻⠀⣸⣇⣁⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡗⡆⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⠀⣿⡇⠀⣶⣐⡦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢺⠶
⢀⣴⣿⣀⢸⠇⣴⣪⠷⣁⠀⣶⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡦⣿⠀⠈⢿⣦⢀⠀⠀⠙⠿⠿⠗⠿⠿⠀⠿⠇⣰⣿⣿⡷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀
⢽⣿⣿⣆⣾⠐⣿⣗⠀⣈⡛⣿⣿⣿⡍⠁⠈⠁⠀⠉⠉⠀⠉⠀⠈⠉⠁⠈⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠳⠸⠆⠀⠈⢻⣠⠀⠀⠀⠀⣷⣶⡶⢾⣿⡶⣶⣿⣿⡿⠖⡻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠈⠉
⠿⠿⠻⠿⢻⣿⣾⣿⣿⣿⣻⡟⠋⠋⠉⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⠀⠉⠊⠃⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠈⠒⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣧⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠓⠆⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⢸⠀⠀⣠⣾⣿⣧⣿⣿⣿⣿⣿⣿⣟⣽⣿⣟⣛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⡏⢀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢴⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠘⠁⠄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠺⢿⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡒⣒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⡿⠿⠭⠟⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠒⠒⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡧⣿⣿⣿⠧⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⠀⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠉⢋⣶⡄⠀⠀⠀⠀⠸⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⡀⠀
⠀⠰⠀⠀⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⡉⠀⡇⣠⣤⣄⢠⣤⣼⡿⣥⡄⢠⣤⣤⣴⣶⠠⣤⣄⣤⡄⣠⣤⣄⠀⣠⣤⣄⢠⣤⣤⣤⣠⣤⣤⡀⠀⠀⠀⠀⠀⠿⠋⠁⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⠿⣛⣭⣷⡆⣼⣿⣿⠀⡇⣿⣯⡛⢻⣿⣏⡁⣿⡇⢸⣿⣏⡹⠟⠀⣿⣧⣿⡇⣿⡏⣿⡇⣿⣟⡛⠊⢹⣿⠉⣿⣧⡛⠃⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣿⣸⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣭⣴⣦⢸⣿⣿⣿⡇⢿⣿⡿⠀⡇⣬⡟⣿⡞⣿⡏⠁⣿⡇⢸⣿⡏⠙⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡿⣿⡆⢸⣿⠀⣬⡝⣿⡇⠀⠀⠀⠀⠀⠰⢾⠟⠛
⠀⠀⠀⠀⢸⣿⣿⣹⣿⠋⠀⠉⠋⢿⠿⠟⣻⣽⣿⠀⣿⣿⣿⣿⡿⢸⣿⣿⣿⡇⢸⣿⠇⠀⡇⠛⠿⠟⠁⠛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠛⠁⠘⠛⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡟⠛⠛⠛⠃⠀⠀⠀⢰⣿⡇⣿⣿⣿⠀⣿⢿⣿⡿⠇⠘⠛⠋⠁⠀⢀⣀⡀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇⠿⠿⣿⠀⣿⢀⣀⣠⠀⠠⠆⠸⠿⠃⠘⠛⣁⣀⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠇⣿⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠶⠟⣿⣀⣿⣈⣁⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠈⠀⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⡇⠠⡶⢔⣴⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠒
⢀⣴⣿⣀⢸⢇⣔⣨⢿⣇⠐⣶⣦⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⡜⡇⠀⠀⢿⣦⢀⠀⠀⠙⠿⠿⠟⠿⠿⠀⠿⠇⢸⡿⢺⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀
⢾⣿⣿⣂⣾⠘⣟⡇⠀⣨⡙⣿⣿⣿⡉⠉⠉⠈⠉⠀⠀⠉⠀⠉⠉⠉⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠿⠀⠀⠀⢿⡠⠀⠀⠀⢰⣷⣶⣶⣿⣿⣷⣾⣿⣿⣾⣿⣿⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉
⠿⠿⠻⠿⢻⣿⣾⣿⣿⣿⣻⠟⠋⠉⠉⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⠈⠁⠙⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣧⡀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠳⠇⠀⠂⠀⠀⠐⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢀⢸⠀⠀⣠⣾⣿⣹⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢺⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣿⠇⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣛⣟⣿⡷⣯⣿⡃⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠾⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣃⣀⡀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠁⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠶⡶⡄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠛⠻⠟⠛⢇⠒⠒⠒⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣅⢄⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣤⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢐⠀⠀⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠋⣶⣶⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⡀⠀
⠀⠐⠀⠀⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⢙⣿⠀⣠⣤⣄⢠⣤⣤⣿⣯⡄⢠⣤⣤⡄⣀⢨⣥⣤⣤⡄⣠⣤⣄⠀⣠⣤⣄⢠⣤⣤⣤⣠⣤⣤⡀⠀⠀⠀⠈⣿⡿⠋⠁⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⢿⣻⣭⣥⢠⣿⣿⠉⣿⡀⣿⣯⡛⠻⣿⣏⡛⣿⡇⢸⣿⣏⡁⠻⠸⣿⣿⣿⣷⣿⣿⣿⡇⣿⣟⡛⠊⢹⣿⠉⣿⣧⡛⠃⠀⠀⠀⠀⠈⠀⠀⣀⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣿⣸⣿⣿⣿⣿⣿⣿⡷⢸⣿⣋⣭⣴⡄⣿⣿⣿⣿⢸⣿⣿⠄⡿⠃⣬⡿⣿⡶⣿⡟⠁⣿⡇⢸⣿⡏⠹⠛⠃⣿⡟⣿⡿⣿⣿⣿⡇⣬⡿⣿⡆⢸⣿⠀⣬⡝⣿⡇⠀⠀⠀⠀⠰⠦⠾⠿⠻
⠀⠀⠀⠀⢸⣿⣿⣹⣿⠋⠈⠉⠻⣿⠿⢟⣿⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⣿⡇⠐⣿⡿⠀⠀⠀⠛⠿⠟⠙⠛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠛⠿⠛⠁⠛⠿⠟⠁⠘⠛⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡟⠛⠛⠛⠀⠀⠀⠀⢰⣿⢸⣿⣿⡇⢸⣿⣿⣿⡿⠁⠛⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠸⠿⠿⡇⢸⡿⣁⣠⣤⠀⢰⠦⠸⠏⠐⠛⢃⣀⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠇⣿⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀
⠰⢴⠀⠀⢸⡇⠀⢀⣠⠀⠀⠀⠀⢠⠴⠰⠾⢻⡇⣈⣇⣉⣁⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠁⢶⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⡇⢰⣿⣿⣖⠐⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⠲
⣠⣾⣿⣤⢸⢧⣶⣿⢿⣟⡒⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠻⣧⠀⠀⠀⠙⠿⠿⠟⠿⠿⠀⠿⠗⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀
⢿⣿⣿⡕⣾⠸⣿⡗⠀⣨⡛⣿⣿⣮⡉⠉⠉⠉⠙⠋⠋⠛⠛⠛⠛⠟⠛⠛⠋⠉⠙⠉⠉⠀⠉⠉⠻⠿⠿⠦⠀⠀⠀⢿⡀⠀⠀⢀⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢰⡄⠀⠀⠉
⠿⠟⠻⠿⢹⣷⣾⣿⣿⣿⣿⡟⠉⠉⠉⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡿⠬⠀⠛⠋⠉⠁⠁⠁⠉⠀⠀⠀⠀⠁⠘⠛⠂⠐⠀⠀⢀⣀⣠⣤⣿⣿⣿⣽⣧⡀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⠻⠗⠘⠗⠒⠒⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣼⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⣀⢸⡃⠀⣠⣾⡇⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⣸⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣛⣻⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣿⣗⣭⣞⢿⠤⣑⠀⠠⢴⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⢳⠆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡨⠀⠀⠀⠀⠀⠀⠚⠛⠉⠁⠉⠛⠛⠀⠀⠠⠅⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣮⣭⣬⣁⠀⡀⢀⠀⠠⣠⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠶⢿⡗⠂⠀⠴⠐⠲⠦⠀⠀⠄⠀⠤⠄⠀⢈⠉⡉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣻⣿⣟⣛⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣾⣹⣿⣿⣉⣉⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠉⣴⡶⠆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣤⡀⠀
⠀⠈⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢹⡇⠀⣠⣤⣄⢠⣤⣤⣽⣭⡄⢠⣤⣤⡄⠀⢨⣧⣤⣤⡄⣠⣤⣄⠀⣠⣤⣄⢠⣤⣤⣤⣠⣤⣤⡀⠀⠀⢸⣿⣿⣿⠋⠁⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⣭⡅⣾⣿⡇⢸⡇⠀⣿⣯⡛⢻⣿⣏⣿⣿⡇⢸⣿⣏⡁⠀⢸⣿⣿⣿⣷⣿⣿⣿⡇⣿⣟⡛⠊⢹⣿⠉⣿⣧⡛⠃⠀⠀⠈⠛⠋⠀⢀⣀⣠
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣿⣸⣿⣿⣿⣿⣿⣿⡿⣿⡟⣻⣭⣥⢰⣿⣿⣿⠇⣿⣿⡇⢸⡏⠁⣬⡿⣿⣾⣿⡟⠷⣿⡇⢸⣿⡏⠙⠛⠃⣿⣿⣿⡿⣿⣿⣿⡇⣬⡿⣿⡆⢸⣿⠀⣬⡝⣿⡇⠀⠀⠀⢀⠟⠶⢿⠟⠋
⠀⠀⠀⠀⢸⣿⣿⢹⣿⠉⠈⠙⠻⣿⠿⢟⣯⣽⡇⣸⣿⣿⣿⣿⢸⣿⣿⣿⠁⣿⣿⠃⢸⡇⠐⠿⠿⠟⠙⠛⠟⠃⠛⠛⠛⠛⠃⠀⠀⠐⠛⠛⠛⠃⠛⠿⠛⠁⠛⠿⠟⠁⠘⠛⠀⠙⠿⠟⠃⠀⠀⠀⠄⣆⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡟⠛⠛⠛⠀⠀⠀⠀⣶⣿⣿⣿⣿⠂⢹⡷⣿⣿⡿⠸⠟⠛⠛⠀⢀⣀⠀⢸⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠁⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⢿⠀⢻⡇⣁⣤⡄⠀⣤⠴⠲⠀⠻⠛⢀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠷⣿⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀
⢸⠰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⠾⢻⠀⢸⣇⣉⣉⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣗⣆⠀⠀⠀⠈⢰⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⡇⢀⣮⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⠖
⣠⣶⣿⡤⢼⠣⣦⣶⠷⣗⠂⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⠀⠀⠀⠈⣷⠀⠀⠀⡙⠿⠿⠟⠿⠿⠀⠿⠗⣸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀
⢿⣩⣿⣇⣾⠰⣾⡇⠀⣠⡛⣿⣿⣇⠉⠁⠙⠉⠉⠋⠹⠛⠻⠟⠟⠛⠛⠻⠻⠿⠉⠁⠀⠀⠈⠉⠟⡾⠦⠄⠀⠀⠀⢽⡄⠀⢀⣿⢿⣿⣿⣾⣿⣿⣾⣷⣿⢿⣾⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⢰⡄⠀⠀⠉
⠷⠟⠻⠿⢹⢷⣼⢽⣿⡿⢿⠟⠉⠉⠁⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⠼⡿⠜⠛⠙⠉⠀⠀⠉⠁⠀⠈⠁⠀⠀⠒⠛⠓⠀⠀⠀⢀⣀⣀⣦⣿⣿⣿⣯⣭⣧⡀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⠛⠛⠿⠟⠒⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠻⠗⠘⠗⠐⠒⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡀⢹⣿⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⡏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⣾⣷⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⠁⠀⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣤⣤⡌⣤⡄⢠⣤⣤⡄⠀⠀⣤⡄⣤⡌⣩⣽⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⣿⣇⡛⠂⣿⣏⡁⣿⡇⢸⣿⣉⠀⠀⠀⣿⣧⣿⡇⣿⡇⣿⡇⣿⣟⡛⠊⢹⣿⠉⣿⣧⡛⠻⣿⠿⠟⠻⠏⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⣬⡝⣿⡆⣿⡏⠃⣿⡇⢸⣿⡋⠘⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡝⣿⡄⢸⣿⠀⣬⡝⣿⡆⠈⠀⠀⢀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠁⠛⠛⠃⠛⠛⠛⠛⠃⠀⢀⡀⠛⠃⠛⠃⠛⠿⠛⠀⠛⠿⠛⠁⠘⠛⠀⠙⠻⠟⠃⠀⣰⣷⣾⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⠛⢿⣿⣿⣿⣿⡿⠋⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⣤⣭⡛⣥⣤⣤⣤⣤⡄⠀⠀⠀⠀⣦⣤⣠⠀⠀⢠⣷⣿⡆⠹⡟⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⡇⠀⢸⣿⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠿⠇⢼⣿⠉⣿⡏⠁⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠋⢻⠇⠀⠀⠀⠀⢀⠀⠀⠀
⠀⢰⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⢸⠁⠁⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠸⠀⠀⠀
⢠⣿⣇⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡙⠿⠛⣇⣺⣿⣤⣿⣷⣆⠀⠀⣀⣾⡄⠀⠀⠀⡄⠀⢀⡇⠀⡗⣦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡶⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣄⢀⣠⣿⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢺⣿⣿⣿⣷⣦⣤⣠⣷⣶⣿⣧⣠⣿⣿⡄⠀⠀⠀⠀⠀
⠈⠀⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠷⠠⠻⠿⢿⠿⢶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠸⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢨⣿⣿⣥⣤⣤⣦⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⠀⠈⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢛⡿⠇⠀⠶⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀
⠀⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡄⢠⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⠋⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠙⣧⠿⣿⣿⣿⣤⣤⠾⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠛⠟⠛⠛⠛⠋⠀⣸⣿⣿
⢀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢶⣾⣷⡄⠀⠀⠀⠀⠀⣨⣬⣄⠀⣤⣤⡍⣭⡅⢠⣤⣤⣤⡄⠠⣤⡄⣤⡄⣀⣤⣄⠀⣠⣤⣄⢠⣤⣤⣤⣠⣤⣤⣠⣤⣤⣤⣤⣾⣿⣿⣿⣿
⢸⣿⣿⣿⡇⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⢹⣿⣿⠆⠀⠀⠀⠀⣿⣇⡛⠂⣿⣏⡁⣿⣿⣿⣿⣏⡿⠿⠀⣿⣇⣿⡇⣿⡇⣿⡆⣿⣍⡛⠈⢹⣿⠁⣿⣧⡛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟
⢸⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣟⠃⠀⠀⠀⠀⠀⣬⡝⣿⡆⣿⡏⠁⣿⡇⢹⣿⡏⠙⠛⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡝⣿⡄⢸⣿⠀⣬⡝⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⡟⠃⠀⠀⠀⠀⢠⠛⠿⠛⠁⠛⠛⠃⠛⠛⠛⠛⠃⠀⠀⠀⠛⠃⠛⠃⠙⠻⠛⠀⠛⠿⠛⠁⠘⠛⠀⠙⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠛⢿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣤⣀⠀⠀⡀⣸⡶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⣄⡀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⠁⠀⠀⡴⣶⡟⠁⠎⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠿⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣦⣀⠀⠀⠟⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⢠⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⡀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⡀⢸⣿⣤⣤⣤⣾⣿⣧⠀⠀⠀⣀⡀⠘⠿⠛⠃⠻⠛⠀⠻⡇⣰⣶⣶⣾⣿⣿⣷⣶⣄⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣟⣀⠀⠀⠀⠒⡀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠐⠿⠿⡿⢿⣿⣿⣿⣿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠉⠙⠿⠛⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢘⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⡶⠈⠻⢿⣯⣭⣭⣭⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠁⠀⠤⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⠟⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀
⠀⠀⢸⡿⠛⠘⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢠⣿⣿⡟⠻⣿⣿⣿⣿⣿⡿⠻⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿
⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠯⠻⣤⢼⣿⣿⣧⣀⣬⣽⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠀⠀⠈⠀⠀⣀⣴⣿
⠀⠀⣿⡃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⣤⣾⣦⠀⠀⠀⠀⣠⣤⣌⠁⣤⣤⡄⣤⡍⢩⣤⣤⡄⣠⣀⣤⡄⣤⡄⣠⣤⣄⠀⣠⣤⣄⢠⣤⣤⣤⣠⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣃⣀⠀⠀⠀⠉⣿⣿⣧⠀⠀⠀⣿⣇⡛⠃⣿⣏⡁⣿⡇⢿⣿⣏⣵⣿⠿⣿⣧⣿⡇⣿⡇⣿⡇⣿⣏⡛⠈⢹⣿⠁⣿⣧⡛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣻⡿⠉⠀⠀⠀⣬⡝⣿⡆⣿⡏⠁⣿⡇⢸⣿⣟⣽⠿⠃⣿⡏⣿⡇⣿⡇⣿⡇⣬⡝⣿⡄⢸⣿⠀⣬⡝⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠴⠾⣿⡷⠄⠀⠀⠀⠛⢿⠟⠁⠛⠛⠃⠛⠛⠛⠛⠻⠿⠂⠀⠛⠃⠛⠃⠙⠿⠛⠀⠛⠿⠛⠁⠘⠛⠀⠙⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠟⢿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣸⣿⣇⣀⠀⠀⠀⠀⣻⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡟⠉⠉⢀⣬⣴⡿⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠿⠇⢸⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣾⣿⣧⡀⠀⠈⠹⡏⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣶⡀⠀⠶⠆⣀⣀⣀⣶⣷⡀⠀⠀⠀⠙⠿⠛⠇⠚⠿⠀⠛⠃⢸⡄⢤⣤⣬⣿⣿⣷⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠂⠀⠉⠉⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣶⣶⣶⣶⣶⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⢾⡇⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⢒⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠛⠉⠛⠛⠛⠛⠋⠙⠛⠛⠛⠋⠋⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠹⠿⠿⠟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠾⣿⣿⡿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣤⣼⣤⣤⣤⣼⣤⣼⣤⣤⣤⣤⣧⣤⣴⣦⣵⣥⣿⣵⣿⣬⣤⣬⣼⣤⣼⣦⣥⣥⣼⣬⣭⣤⣤⣬⣧⣮⣭⣬⣥⣾⣥⣥⣤⣧⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⣴⣤⣤⣤⣤⣤⣅⣠⣤⣬⣮⣆⣾⣽⣼⣷⣥⣮⣼⣾⣾⣾⣼⣿⣿⣬⣾⣾⣧⣧⣤⣷⣤⣤⣬⣼⣼⣤⣽⣤⣤⣤⣴⣶⣦⣷⣤⣴⣷⣦⣤⣤⣷⣴⣤⣮⣤⣤⣡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣉⣈⣍⣏⣉⣍⣀⣉⣨⣈⣟⣞⣹⣏⣩⣓⣙⣍⣩⣛⣻⣻⣏⣹⣷⣫⣍⣿⣝⣗⣋⣽⣉⣍⣿⣘⣋⣟⣙⣀⣉⣉⣇⣈⣉⣹⣩⣁⣨⣭⣙⣋⣭⣋⣹⣩⣫⣋⡹⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⣉⣉⣉⣏⣏⣉⡉⣹⣏⣟⣉⣉⣩⣉⣿⣽⣉⣩⣭⣉⣉⣯⣽⣍⣯⣯⣽⣏⣝⣍⣩⣿⣉⣯⣉⣩⣿⣍⣉⣉⣉⣽⣉⣉⣹⣉⣋⣹⣝⣹⣙⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣆⣈⣩⣩⣁⣩⣩⣝⣟⣉⣻⣹⣯⣭⡿⣩⣮⣈⣭⣽⣽⣤⣭⣽⣽⣿⣿⣯⣿⣇⣧⣟⣭⣏⣭⣹⣅⣩⣹⣍⣉⣩⣋⣁⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠬⠉⢿⣿⣿⢊⡌⠉⣿⠸⡹⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠿⠋⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣻⠁⠀⠁⠂⠀⠀⠀⠆⠐⠒⠆⠿⠻⠛⠫⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠆⠀⠘⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠀⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣷⣿⢸⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣾⠿⣿⢸⣝⣽⣿⣿⣿⢟⠛⠻⠙⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠸⣇⣀⣉⣀⣀⣀⣈⣚⣑⢀⣀⣃⣑⣂⣿⢸⣿⣿⣁⣿⣿⣿⣿⣧⣤⣤⣥⣱⣤⣬⣤⣴⣿⢸⣿⣿⣿⣿⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠚⠛⠛⠛⠛⢛⢛⠻⣛⠛⠛⠛⠛⠛⠛⠘⠛⡛⠛⢛⠙⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠘⠛⠛⠛⠛⠛⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⡄⠆⠀⢜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡤⠀⠀⠐⠀⠀⠀⠋⠁⠀⠀⠨⠂⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣞⣷⠀⠀⡐⢀⠀⠀⠀⠀⠈⢸⡷⠀⣠⣷⣦⣶⣿⣿⣿⣿⣿⣿⣯⣵⣿⣶⣶⢰⣶⣬⣤⣀⠀⠀⠀⠠⡀⢀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⡄⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣮⣤⣤⣤⣤⣠⣧⣤⣸⣿⣿⣿⣾⣿⣿⣼⣿⣿⣿⣿⣯⣿⣯⣿⣧⣭⣬⣭⣯⣿⣻⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣤⡈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⣻⣿⣿⣟⠛⠛⠛⢻⠛⣻⡟⣟⣟⢻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣟⡿⣟⢻⣿⣿⣿⣿⣟⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⡟⢛⡻⠁⠂⠀⠙⠛⢿⣿⣿⣿⢸⣿⣿⣟⣿⣿⣿⣿⡿⠛⠛⢟⡿⠟⠛⠙⡻⣿⢸⢽⢟⣽⣿⣷⣲⠆⠄⢊⣋⣨⣿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣷⣾⣏⡃⣁⣶⣿⣿⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣭⣄⡥⣶⡿⠏⠁⢠⣮⣸⡙⢙⣷⣟⣣⣦⣼⣟⢁⣏⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⠿⠿⢿⢿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣠⣀⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⢽⣿⣿⣷⣿⣿⣿⣿⣯⣬⣦⣧⣷⣴⣿⣤⣵⣿⢿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠘⠛⠛⢛⣟⠻⣟⣿⡻⣿⣿⣿⣿⣿⢿⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⡿⣿⢻⣿⣿⣿⣿⣿⡛⣟⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠑⠈⠘⠋⠛⠚⠛⠟⠛⠛⣿⣮⢸⣿⣿⢋⣿⣿⣯⣿⡯⠀⡉⠏⡿⠋⢹⠙⢭⣿⢸⣿⣿⣿⣿⣿⠿⠏⣷⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣋⡨⠂⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣯⣞⣧⣤⣿⣿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 5043

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 15/01/2026: "Ode to elinks",
envs.net Pubnix and Downtime at
geminiprotocol.net⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Technology and Free Software⠀➾


                # ⚓ SONOFF_Announces_Matter_Support_—_If_You_Self-Host
                  eWeLink's_CUBE_O⠀⇛


                       Home automation and Internet of Things (IoT)
                       specialist SONOFF has announced official support
                       for the Matter vendor-neutral interoperability
                       standard — providing you self-host a copy of
                       eWeLink's CUBE OS, that is.


                       "Now all your SONOFF devices work with Matter
                       easily," the company announced this week. "Bringing
                       SONOFF Wi-Fi & Zigbee devices into the Matter
                       ecosystem is now official and simple. Works
                       seamlessly with Matter platforms like Apple Home
                       and Google Home."


                       Originally known as Project Connected Home over IP,
                       Matter — developed by a consortium formed of
                       Amazon, Apple, Google, Samsung, and what was known
                       at the time as the Zigbee Alliance — aims to
                       address the fragmentation of the smart home
                       connectivity sector. Any Matter device can be
                       connected to any Matter network and controlled with
                       any Matter-compliant software — regardless of the
                       manufacturer of the device, hub, or app. In some
                       cases, adding Matter support is as simple as a
                       firmware upgrade; in others, it requires new
                       hardware.


                # § Internet/Gemini⠀➾


                      # ⚓ 2026-01-14⠀⇛


                             I've written an "Ode to elinks" on my #Gemini
                             capsule before, and I recently stumbled upon
                             this great article that goes into more
                             details and reasons why #elinks is one of the
                             best text web browsers out there. Excellent
                             for when you want to access information from
                             a #RaspberryPi Zero or other low-powered
                             device.


                      # ⚓ My_Signup_on_the_envs.net_Pubnix⠀⇛


                             I signed up for a pubnix account on envs.net
                             on Mon, 12 Jan 2026. Thanks to ~creme for
                             squeezing me in between moving the servers to
                             different locations! It's my first membership
                             in a pubnix ever. I already introduced myself
                             in the #meta channel of the Tildeverse IRC
                             servers, and as far as I can tell so far, the
                             tilde members are really nice, friendly and
                             helpful people.


                      # ⚓ Yet_more_downtime,_spontaneous_second_migration⠀⇛


                             Unfortunately geminiprotocol.net has been
                             unexpectedly down for the past several days.
                             Thank you to everyone who wrote to let me
                             know about the situation. The outage was due
                             once again to network problems on the VPS
                             provider's end. I was less than impressed
                             with the competence and practices of the
                             provider in trying to restore connectivity,
                             and in light of this happening so shortly
                             after the tedious and poorly documented
                             datacenter migration process I was required
                             by that provider to carry out at the end of
                             last year, I spontaneously decided to just
                             cut my losses and migrate the server to a new
                             provider in the hopes of better service. If
                             you are reading this, I guess it worked!
                             There might still be a few loose ends for me
                             to tie up over the coming days but hopefully
                             things will be essentially stable from now
                             on. Sorry for the inconvenience!


                      # ⚓ a_small_catch-up⠀⇛


                             So starting off a new year with something
                             new, a /proper/ gemlog. Never really felt it
                             was necessary but honestly, I am hoping to
                             spend more time here!


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


    * Still_Condoning_Child_Labour_and_Exploiting_Unpaid_Children_Developers_as
      PR_Props_(to_Raise_Monopoly_Money)
    * IRC_Proceedings:_Wednesday,_January_14,_2026



                    ䷩ 𝚕𝚒𝚗𝚎 5181

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 15/01/2026: Internet Blackouts,
Jackboots Society in US⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026,
updated Jan 15, 2026


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


Reminder: ALL the attacks on Techrights were_from_the_US, a country that Roy
has not set a foot in since 2006.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights_/_Policing_/_Accessibility
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Patents
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Manuel Moreale ☛ How_You_Read_My_Content⠀⇛


                 In conclusion, is it still worth serving content via RSS?
                 Yes. Is the web overrun by bots? Also yes. Is somebody
                 watching me type these words? Maybe. If you have a site
                 and are going to run a similar experiment, let me know
                 about it, and I’ll be happy to link it here. Also, if you
                 want some more data from my logs, let me know.


          o ⚓ The Register UK ☛ AI_is_everywhere,_but_nowhere_in_recent
            productivity_data⠀⇛


                 During our conversation, Gownder cited US Bureau of
                 Labour Statistics that suggest the advent of the personal
                 computer also did not improve productivity, which
                 improved by 2.7 per cent annually from 1947 to 1973, but
                 just 2.1 percent between 1990 and 2001.


                 “So despite all those PCs, it [productivity growth] was a
                 lot lower. And [from] 2007 to 2019 it was 1.5 percent. If
                 you look at these numbers, productivity is the foundation
                 of job replacement and of job growth and a whole bunch of
                 things. But when you look at this … you begin to get the
                 picture that information technology isn't measured always
                 in as linear a way into productivity as people assume. It
                 just isn't there.”


          o ⚓ Riccardo Mori ☛ My_2025_in_review⠀⇛


                 In what, exactly? This is another thing I’ve tried to
                 explore in 2025 and I’m still on it at the moment. I’ve
                 looked into Linux a bit more. I have enjoyed using older
                 Macs with older Mac OS versions and older applications
                 that are still very useful to me today. I have enjoyed my
                 Nothing Phone (2a) and don’t regret my switch to Android
                 in the least. But going back to reading more — and
                 reading more physical books — has been especially grand.


          o § Science⠀➾


                # ⚓ The Independent UK ☛ Nasa_brings_four_astronauts_back_to
                  Earth_in_first-ever_medical_evacuation⠀⇛


                       Launched in August, Cardman, Fincke, Japan’s Kimiya
                       Yui and Russia’s Oleg Platonov were due to remain
                       on the space station until late February.


                # ⚓ Futurism ☛ Union_Representing_NASA_Workers_Says_Space
                  Agency's_New_Administrator_Is_a_Straight-Up_Liar⠀⇛


                       Of particular concern is the campus’ main library,
                       which was unceremoniously shut down last month, as
                       the New York Times reported on December 31. NASA
                       officials tried to downplay these concerns
                       seemingly to no avail — as former and current
                       staffers, advisors, and union representatives
                       continue to watch in horror as the GSFC closures go
                       on.


                       NASA insiders cried foul following the library’s
                       closure, warning that critical and still-
                       undigitized materials could be thrown out in what
                       they said were reckless efforts by the Trump
                       administration.


                # ⚓ Futurism ☛ NASA_Has_Some_Very_Bad_News_About_Its_Mars
                  Spacecraft⠀⇛


                       But weeks later, things aren’t looking much better.
                       As SpaceNews senior writer Jeff Foust pointed out,
                       NASA planetary science division director Louise
                       Prockter conceded during a Tuesday meeting that the
                       agency is “very unlikely” to recover the MAVEN
                       orbiter.


          o § Hardware⠀➾


                # ⚓ Jérôme Marin ☛ China’s_breakthrough_in_chips⠀⇛


                       “The laws of physics in China are the same.” In
                       early 2023, Peter Wennink, then CEO of ASML,
                       sounded the alarm: export restrictions imposed by
                       Western countries would push Beijing to “double up
                       its efforts” to develop its own technologies —
                       particularly the most advanced lithography
                       machines, still marketed exclusively by the Dutch
                       group and indispensable for producing cutting-edge
                       chips. Three years later, that prediction is
                       beginning to come true.


                # ⚓ India Times ☛ Battle_over_Chinese-owned_chipmaker_Nexperia
                  rages_in_Dutch_court⠀⇛


                       A Dutch court held hearings Wednesday to weigh
                       whether to order an investigation into Nexperia, a
                       Chinese-owned chip company at the centre of a
                       global tug-of-war over critical semiconductor
                       technology.


                       The firm, based in the Netherlands but whose parent
                       company is China's Wingtech, has been the subject
                       of a standoff between Beijing and the West that
                       threatened to cripple car manufacturers that rely
                       on its chips.


                # ⚓ Macworld ☛ An_obscure_material_used_in_every_Apple_device
                  is_suddenly_in_very_short_supply⠀⇛


                       The material is called “glass cloth” and it is an
                       important component in a particular type of
                       substrate (essentially a little pad that the chip
                       is mounted on to attach it to the circuit board).
                       There aren’t may companies that make it at a high
                       quality level and high volume. There’s essentially
                       only one major supplier: the Japanese company Nitto
                       Boseki, or Nittobo.


                # ⚓ Ruben Schade ☛ The_BookArc_and_Bolt_laptop_stands⠀⇛


                       Spot the issue? The entire stand rests on four tiny
                       rubber feet mounted to the aluminium frame and…
                       that’s it. The whole feet design is weird; most of
                       the rubber doesn’t interface the table at all,
                       meaning you’ve got about a millimetre-wide contact
                       surface at it narrowest point. That’s not much
                       resistance between you and accidentally moving or
                       bumping the stand. Which, given the high centre of
                       gravity and the fact the laptop is a massive sail
                       made of metal and silicon, happened constantly.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Science Alert ☛ The_Best_Medicine_For_Joint_Pain_Isn't_What
                  You_Think,_Says_Expert⠀⇛


                       The best medicine isn't found in a pill bottle or
                       an operating theatre – it's movement. Yet across
                       countries and health systems, too few patients are
                       being guided toward the one therapy proven to
                       protect their joints and ease their pain: exercise.


                # ⚓ El País ☛ Inactive_people_can_reduce_risk_of_death_by_30%
                  with_five_minutes_of_exercise_a_day⠀⇛


                       The same study points to another easy measure that
                       can improve the health of millions of people:
                       reducing sitting time by 30 minutes a day, with
                       short walks of a couple of minutes every hour, for
                       example, could prevent between 3% and 7% of
                       premature deaths.


                # ⚓ The University of Leeds ☛ Microplastics_detected_in_rural
                  woodland⠀⇛


                       “This shows that microplastic deposition is shaped
                       not just by human activity, but also by
                       environmental factors, which has important
                       implications for monitoring, managing, and reducing
                       microplastic pollution.


                       “The widespread presence of smaller microplastics
                       raises concerns about potential health risks from
                       inhalation, regardless of whether people live in a
                       city or a rural village.”


          o § Proprietary⠀➾


                # ⚓ Meta_Closes_Twisted_Pixel,_Armature_&_Sanzaru_Games⠀⇛


                       Meta shut down Twisted Pixel Games (Deadpool VR),
                       Sanzaru Games (Asgard's Wrath), and Armature Studio
                       (Resident Evil 4 VR).


                       The New York Times reported earlier that Meta is
                       laying off more than 10% of its Reality Labs
                       division, specifically targeting teams working on
                       VR and Horizon Worlds.


                       Now, UploadVR can confirm that these layoffs are
                       being conducted today, and we've seen a document
                       indicating the entirety of three of Meta's acquired
                       VR games studios are affected: Twisted Pixel Games,
                       Sanzaru Games, and Armature.


                # ⚓ Bobby_Kotick:_Embracer_Group_Tried_to_Disrupt_the_Deal
                  Between_Microsoft_and_Activision_Blizzard⠀⇛


                       The former head of Activision Blizzard revealed
                       this during the ongoing legal proceedings with AP7.
                       According to Bobby Kotick, Embracer Group aimed to
                       sabotage the deal with Microsoft to improve its
                       market position in California.


                       Kotick explained that at the time, Embracer Group
                       was actively expanding its presence in California,
                       so it was beneficial for them to weaken Activision
                       Blizzard—one of the largest players in the local
                       market. The company hoped that the lawsuit filed by
                       AP7 would hinder Activision Blizzard's ability to
                       "hire talented employees and grow through M&A,"
                       thus clearing space for Embracer Group.


                # ⚓ Michael Tsai ☛ Gmail_Ending_Support_for_Gmailify_and_POP
                  Fetching⠀⇛


                # ⚓ The Register UK ☛ Judge_tosses_CrowdStrike_shareholder_suit
                  over_2024_outage⠀⇛


                       The update was malformed, and CrowdStrike's
                       internal validation system, designed to ensure
                       updates didn't cause serious snafus, failed to
                       catch the issue, as the company later explained in
                       a post-mortem. CrowdStrike acknowledged it had made
                       a mistake, causing its share price to plummet and
                       leaving the company with months of uncertainty for
                       investors, many of whom are institutional.


                       One such institutional group was the Plymouth
                       County Retirement Association, which filed a
                       lawsuit in July 2024. Other parties signed on to
                       the suit, turning it into a class action complaint
                       under the leadership of New York State Comptroller
                       Thomas DiNapoli, who oversees the New York State
                       Common Retirement Fund, one of the institutional
                       CrowdStrike investors who lost money following the
                       outage. Pitman dismissed the case this week.


                # ⚓ The Register UK ☛ New_Linux_malware_targets_the_cloud,
                  steals_creds⠀⇛


                       While malware operators have traditionally focused
                       on Windows-based systems, VoidLink's cloud-first
                       focus is significant. Government agencies, global
                       enterprises, critical infrastructure and other
                       high-value attack targets increasingly run on
                       cloud-based services and host their most sensitive
                       systems in the cloud - so malware that hunts for
                       infected machines' public cloud providers is likely
                       to reap bigger rewards for government-sponsored
                       spies as well as financially-motivated ransomware
                       gangs.


                # ⚓ Rob Knight ☛ Bullet_Journal_Is_a_System_for_Selling_More
                  Bullet_Journal⠀⇛


                       12 months later and it's as if a completely
                       separate entity runs the website having only been
                       given a vague description of what it was before. I
                       would go to the site to find a guide on a specific
                       concept I'd previously seen and those pages were
                       either impossible to find just by navigating or
                       when I did find them via Google search they would
                       404. Not found. Get fucked. Pay us for a course
                       instead.


                # § Artificial Intelligence (AI) / LLM Slop / Plagiarism⠀➾


                      # ⚓ Futurism ☛ Opposition_to_MElon’s_Hey_Hi_(AI)
                        Stripping_Clothing_Off_Children_Is_Nearly_Universal,
                        Polling_Shows⠀⇛


                             Good.


                      # ⚓ Futurism ☛ Financial_Expert_Says_OpenAI_Is_on_the
                        Verge_of_Running_Out_of_Money⠀⇛


                             The AI industry continues to pour tens of
                             billions of dollars into resource-intensive
                             models and the infrastructure to run them. In
                             the face of it all, their promises of
                             kickstarting a technological revolution that
                             could one day be immensely profitable remain
                             convincing enough for investors to prop up
                             sky-high valuations — at least for now.


                      # ⚓ Futurism ☛ Tech_Billionaires_Have_No_Answer_for
                        What'll_Happen_If_AI_Takes_All_Jobs⠀⇛


                             Speaking at a press conference last month,
                             Geoffrey Hinton — a pioneer in the field of
                             neural networks, the bedrock of modern AI —
                             remarked that “it’s clear that a lot of jobs
                             are going to disappear: it’s not clear that
                             it’s going to create a lot of jobs to replace
                             that.”


                      # ⚓ Walled Culture ☛ Walled_Culture_the_book,_three_years
                        on⠀⇛


                             What’s really problematic about the rise of
                             services based on generative AI is not that
                             they are using huge amounts of copyright
                             material – those will probably be licensed in
                             one way or another – but that the creators of
                             that material are unlikely to see much
                             benefit from the payments made to publishers,
                             recording companies and studios. Generative
                             AI is portrayed as a novel and exciting
                             chapter in technology, but actually, it’s not
                             new, since much of the foundational work goes
                             back decades. And as far as ordinary people
                             and creators are concerned, it is definitely
                             the same old copyright story: companies
                             reaping the benefits and profits, while
                             everyone else is expected to accept with
                             gratitude the few scraps tossed their way.


                      # ⚓ RTL ☛ Sexualised_photos_of_children_and_women:_Musk's
                        Grok_barred_from_undressing_images_after_global
                        backlash_-_RTL_Today⠀⇛


                             X said it will “geoblock the ability” of all
                             Grok and X users to create images of people
                             in “bikinis, underwear, and similar attire”
                             in those jurisdictions where such actions are
                             deemed illegal.


                      # ⚓ Yarn Spinner Pty Ltd ☛ Why_We_Don't_Use_AI⠀⇛


                             We get asked about AI a lot. Whether we’re
                             going to add it to Yarn Spinner, whether we
                             use it ourselves, what we think about it.
                             Fair questions. Time to write it all down.


                             Yarn Spinner doesn’t use the technology
                             that’s currently being called AI. We don’t
                             have generative AI features in the product,
                             and we don’t use code generation tools to
                             build it, and we don’t accept contributions
                             we know contain generated material. Let’s
                             talk about why.


                             TL;DR: AI companies make tools for hurting
                             people and we don’t want to support that.


                      # ⚓ Tidepool Heavy Industries ☛ Stop_using_natural
                        language_interfaces⠀⇛


                             There's a classic CS diagram visualizing
                             latency numbers for various compute
                             operations: nanoseconds to lock a mutex,
                             microseconds to reference memory,
                             milliseconds to read 1 MB from disk. LLM
                             inference usually takes 10s of seconds to
                             complete. Streaming responses help
                             compensate, but it's slow.


                      # ⚓ Rolling Stone ☛ Who_Is_Sienna_Rose_and_Is_She_AI?_All
                        Signs_Point_to_'Yes'⠀⇛


                             In a statement to Rolling Stone, streaming
                             platform Deezer confirmed “that many of
                             Sienna Rose’s albums and songs are detected
                             and flagged as AI on Deezer.”


                      # ⚓ Futurism ☛ Tech_Startup_Hiring_Desperate_Unemployed
                        People_to_Teach_AI_to_Do_Their_Old_Jobs⠀⇛


                             And while debate swirls about whether AI is
                             actually replacing jobs in any serious
                             numbers, many tech startups are trying to
                             make it a reality. As the Wall Street Journal
                             reports, a buzzy San Francisco-based AI
                             company called Mercor is hiring desperate
                             job-seekers for a particularly ghoulish task:
                             training AI models to one day do the work
                             they used to do.


                      # ⚓ Futurism ☛ AI_Has_Basically_Killed_Stack_Overflow⠀⇛


                             “Of course, one could point to 2022 and say
                             ‘look, it’s because of AI,’ and yes, AI
                             certainly accelerated the decline, but this
                             is the result of consistently punishing users
                             for trying to participate in your community,”
                             one Reddit user argued. “People were just
                             happy to finally have a tool that didn’t tell
                             them their questions were stupid.”


                             Others pointed out that the most important
                             questions simply may have already been asked.


                # § Social Control Media⠀➾


                      # ⚓ RTL ☛ Museveni's_40-year-rule:_Uganda_votes_under
                        internet_blackout_and_police_crackdown_-_RTL_Today⠀⇛


                             With President Museveni looking to extend his
                             40-year-rule in the upcoming election,
                             Ugandans are voting on Thursday amid expected
                             police crackdowns and an [Internet] blackout.


                      # ⚓ Rodrigo Ghedin ☛ Is_it_possible_to_live_without
                        WhatsApp?_⁄_Manual_do_Usuário⠀⇛


                             In many parts of the world outside the US,
                             the “big boss” of those who decide to get rid
                             of Meta is WhatsApp. And how could it not be?
                             Some research on phone habits shows that up
                             to 99.1% of Brazilians over the age of 16 use
                             the messaging app. Here, it is ubiquitous;
                             the standard means of communication for many
                             people and companies.


                      # ⚓ Zimbabwe ☛ Warning:_Fake_Accounts_Impersonating
                        Techzim_and_Editor⠀⇛


                             Techzim is aware of fake Facebook accounts
                             pretending to be Leonard Sengere and Techzim
                             following our recent coverage of EcoCash-
                             related scams.


                      # ⚓ [Repeat] BIA Net ☛ Social_media_platforms_turn_to
                        censorship_to_protect_commercial_interests⠀⇛


                             However, this compliance did not create
                             genuine legal accountability. In practice,
                             social media platforms have moved away from
                             transparency and effectively turned into
                             mechanisms of “digital obedience” for the
                             state.


                      # ⚓ Tech Central (South Africa) ☛ Uganda_shuts_down_
                        [Internet]_ahead_of_pivotal_election⠀⇛


                             The Uganda Communications Commission ordered
                             mobile service providers to shut down public
                             [Internet] connections from 6pm (5pm SAST) on
                             Tuesday in order to curb “misinformation,
                             disinformation, electoral fraud and related
                             risks”.


                      # ⚓ The Atlantic ☛ Elon_Musk_Cannot_Get_Away_With_This⠀⇛


                             If there is no red line around AI-generated
                             sex abuse, then no line exists.


                      # ⚓ US News And World Report ☛ US_Teachers_Union_Says_It
                        Is_Leaving_X_Over_Sexualized_AI_Images_of_Children⠀⇛


                             The American Federation ‌of ​Teachers says it
                             is leaving X, ‌citing the social media site's
                             creation and dissemination of "sickening"
                             images of ​children in various states of
                             undress.


                      # ⚓ The Verge ☛ X_claims_it_has_stopped_Grok_from
                        undressing_people,_but_of_course_it_hasn’t⠀⇛


                             UK communication regulator Ofcom has opened
                             an investigation, and the UK is bringing a
                             law into force this week that makes creating
                             nonconsensual intimate deepfake images a
                             criminal offense. Earlier on Wednesday, Prime
                             Minister Keir Starmer told MPs that “To
                             update the House, I have been informed this
                             morning that X is acting to ensure full
                             compliance with UK law. If so, that is
                             welcome, but we’re not going to back down,
                             and they must act.” The BBC reports that the
                             prime minister’s official spokesperson called
                             it a “qualified welcome,” based on media
                             reports that X had taken action on the
                             issues, but our testing indicates that isn’t
                             true yet.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Site36 ☛ Access_to_biometric_police_data:_EU
                        Commission_wants_to_negotiate_secretly_with_the_U.S.⠀⇛


                             The U.S. is demanding automated access to
                             biometric police and asylum data in EU
                             states. Also Trump’s infamous anti-migrant-
                             militia ICE could use the fingerprints and
                             facial images. Nevertheless, the Commission
                             is starting negotiations under high secrecy.


                      # ⚓ Techdirt ☛ DHS_Wants_To_Harvest_Biometric_Data_From
                        Anyone_Helping_A_Foreigner_Stay_In_This_Country
                        Legally⠀⇛


                             This was first pitched by the DHS back in
                             November, as “Papers Please” reports. Public
                             comments are being accepted, but probably not
                             being welcomed unless they’re sufficiently
                             congratulatory of this expansion of
                             surveillance power. Here’s what Papers Please
                             has to say about it in its recent post: [...]


                      # ⚓ Techdirt ☛ ICE_Is_Going_On_A_Surveillance_Shopping
                        Spree⠀⇛


                             There are many different agencies under U.S.
                             Department of Homeland Security (DHS) that
                             deal with immigration, as well as non-
                             immigration related agencies such as
                             Cybersecurity and Infrastructure Security
                             Agency (CISA) and Federal Emergency
                             Management Agency (FEMA). ICE is specifically
                             the enforcement arm of the U.S. immigration
                             apparatus. Their stated mission is to “
                             [p]rotect America through criminal
                             investigations and enforcing immigration laws
                             to preserve national security and public
                             safety.”


                      # ⚓ Pete Brown ☛ 🔗_Congress_Pushes_DHS_for_Details_on
                        ICE’s_New_Facial_Recognition_App:...⠀⇛


                             I’m glad they are pushing Noem et al. on
                             this, but the accuracy (or the lack thereof)
                             of the tool is beside the point. Even if this
                             app were 100% accurate and never generated
                             any false positives, it is a blatant invasion
                             of privacy and ought to banned outright.


          o § Defence/Aggression⠀➾


                # ⚓ Marisa Kabas ☛ ICE_is_headed_to_Maine⠀⇛


                       As ICE continues its deadly assault on Minneapolis
                       and communities throughout the country, its likely
                       next target has been revealed: The state of Maine.
                       On Tuesday I learned that people were gearing up
                       for enforcement actions based on rumors, and by
                       Wednesday the mayors of the state's two largest
                       cities addressed it, decrying ICE tactics as a
                       “paramilitary approach.”


                       Mayor of Portland Mayor Mark Dion issued this
                       statement Wednesday afternoon: [...]


                # ⚓ Garrett Bucks ☛ What_a_rage-filled_heart,_an_exhausted
                  heart,_a_terrified_heart,_and_a_grieving_heart_have_in
                  common⠀⇛


                       I will not lecture you. But I will offer this.


                       What you are feeling right now, be it volcanic
                       anger or exhaustion or guilt or confusion or
                       incapacitation isn’t just real, it is sacred. It is
                       your heart reacting, in any number of ways, to its
                       own sudden expansion. You are feeling something
                       deeply, and it may or not yet be pulling you in a
                       clear direction, but in either case it is a
                       gorgeous reminder: You are human. And you are
                       reacting to horrors being rained down on other
                       human beings. You ache for them and rage for them
                       and feel incapacitated on their behalf because that
                       is what human beings do when we don’t turn off the
                       part of us that knows we are made for more than
                       cruelty.


                # ⚓ US Navy Times ☛ Former_US_sailor_sentenced_to_16_years_for
                  selling_ship_intel_to_China⠀⇛


                       A federal judge in San Diego sentenced Jinchao Wei,
                       25, to 200 months. A federal jury convicted Wei in
                       August of six crimes, including espionage. He was
                       paid more than $12,000 for the information he sold,
                       the U.S. Department of Justice said in a statement.


                # ⚓ Allbritton Journalism Institute ☛ Democrats_Say_DOJ_Is
                  Probing_Their_Involvement_in_‘Illegal_Orders’_Video_-_NOTUS_—
                  News_of_the_United_States⠀⇛


                       In fiery statements Wednesday, the lawmakers
                       accused the Trump administration of seeking to
                       silence its enemies and politicize the Justice
                       Department.


                # ⚓ Truthdig ☛ What_Happens_When_the_People_Refuse_to_Be
                  Afraid?⠀⇛


                       None of this means that we’re home safe. Trump and
                       his right-wing billionaire funders are still openly
                       opposed to democracy, red state governors are
                       actively purging people in their blue cities from
                       the voting rolls with the approval of five corrupt
                       Republicans on the Supreme Court, and billionaire-
                       owned and -run media operations from CBS to Fox to
                       Sinclair daily sing his praises.


                       But there’s also an active and growing resistance
                       across media and in local communities that’s
                       emerging within both parties. Even as Facebook and
                       Twitter censor anti-Trump posts and armies of
                       trolls and bots attack Democrats and progressives,
                       average working-class people are waking up hard and
                       fast from coast to coast.


                # ⚓ Common Dreams ☛ Further_|_One_People,_Realm,_Leader:_But
                  Don't_Call_Them_Nazis_|_Opinion⠀⇛


                       The atrocities and the fury mount. Astoundingly,
                       after a murderous thug shot a mother of three in
                       the face in broad daylight - "He didn't kill her
                       because he was scared, he killed her because she
                       wasn't" - state terror has ramped up with more
                       lies, goons, attacks on "gangs of wine moms,"
                       brutish agitprop literally echoing the Nazis'. So
                       when mini-Bovino went to take a leak at a store,
                       the people's wrath, a bittersweet splendor,
                       erupted. Their/our edict: "Get the fuck out."


                # ⚓ Common Dreams ☛ Fossil_fuel_phaseout_urgent_as_1.5°C_target
                  likely_to_be_passed_by_2030⠀⇛


                       The report notes that air temperature over global
                       land areas was second warmest, while the Antarctic
                       saw its warmest annual temperature on record.
                       Temperature rise in 2025 was mainly due to “the
                       build-up of greenhouse gases in the atmosphere,
                       from continued emissions and reduced uptake of
                       carbon dioxide by natural sinks”–underscoring the
                       urgent need for a fossil fuel phaseout.


                # ⚓ Dark Reading ☛ Taiwan_Endures_Greater_Cyber_Pressure_From
                  China⠀⇛


                       The report comes as the relationship between China
                       and Taiwan suffered setbacks in the past year.
                       China considers the island — a former Japanese
                       colony that became independent when the Nationalist
                       Party retreated to the island following its defeat
                       in a civil war against the Chinese Communist Party
                       in 1949 — as part of its territory. The island
                       democracy, however, continues to resist political
                       efforts to absorb it into the mainland. In
                       December, the US committed to an $11 billion arms
                       sale to Taiwan, and Japan's recently elected prime
                       minister caused a kerfuffle by stating that if
                       China attacked Taiwan, it would threaten Japan's
                       survival and allow the country to exercise its
                       right of self defense.


                # ⚓ The Guardian UK ☛ After_the_shooting_of_Renee_Good,_we_see
                  dissent_can_be_fatal_in_Trump’s_America_–_all_bets_are_off⠀⇛


                       She looked at me coldly. “You’re a fucking idiot,”
                       she said, when I told her how rude I’d been. “What
                       if they’d asked you where the girls’ father is? And
                       why aren’t you travelling with their birth
                       certificates?” I couldn’t believe that I was
                       getting grief off this person who has never met a
                       cab driver she couldn’t start a fight with – but
                       then, her antecedents were murdered by Nazis. She
                       understands a real threat when she sees it. Nothing
                       should take away from Good’s courage or
                       convictions. But there are lessons to be learned: a
                       system that puts paramilitaries on US streets to
                       round people up willy-nilly should be approached by
                       those protesting with the understanding that there
                       is nothing – nothing – it won’t do to shut them up.


                # ⚓ YLE ☛ Finnish_PM_floats_social_media_ban_for_under-15s⠀⇛


                       Speaking at the mobility-focused summit on
                       Wednesday, Orpo said he supports banning social
                       media use for those under 15, citing screen time as
                       one of the biggest obstacles to kids moving more.


                # ⚓ The Zambian Observer ☛ It_would_be_‘stupid’_to_have_Elon
                  Musk’s_Starlink_in_South_Africa_—_Parliament_committee
                  chairperson⠀⇛


                       • In a video shared on X, Zibi said the government
                       would be “stupid” to allow Starlink to operate due
                       to Musk’s open disdain for South Africa.


                       • Zibi accused Musk of being a “white supremacist”
                       who had declared himself an enemy of South Africa’s
                       constitutional order and who frequently spread lies
                       and misinformation about the country.


                # ⚓ Task And Purpose ☛ Kelly_and_Hegseth_fight_over_‘unlawful
                  orders’_video_headed_to_court⠀⇛


                       The suit is the latest escalation in the fight
                       between the senator and the secretary after Hegseth
                       moved to censure Kelly and start a process to
                       reduce his rank last week. Hegseth had previously
                       threatened to prosecute Kelly, a retired Navy
                       captain, combat pilot and astronaut, for a Nov. 18
                       video urging troops not to follow unlawful military
                       orders. Kelly was one of six current members of
                       Congress with intelligence and military backgrounds
                       who released a video aimed at American service
                       members in the early weeks of the Pentagon’s
                       bombing campaign of vessels in the Caribbean and
                       eastern Pacific.


                # ⚓ C4ISRNET ☛ Swedish_military_to_pump_forces,_money_into
                  mobile_drone-defense_units⠀⇛


                       The plan entails several independent company-sized
                       units that will be required to be mobile and
                       modular to mix and match different weapons,
                       including guns and radar systems. Assets requiring
                       protection will include bridges, rail hubs, nuclear
                       and hydroelectric power plants, as well as cities,
                       according to a government press release.


                # ⚓ University of Michigan ☛ The_Right_Finnish:_Ukraine’s_Deal
                  Will_Decide_Who_Writes_the_Rules_of_the_21st_Century⠀⇛


                       After fighting bravely against the Soviet invasion
                       in 1939–40, Finland ceded 10% of its territory. But
                       territorial loss was only the beginning. The 1948
                       Agreement of Friendship, Cooperation, and Mutual
                       Assistance between Finland and the Soviet Union
                       preserved nominal independence at a steep price:
                       Finland could not join NATO, criticize Soviet
                       actions or pursue an independent foreign policy.


                       For example, the treaty obligated Finland to defend
                       against an attack “by Germany or its allies” on the
                       Soviets — Cold War code for the Western European
                       alliances that eventually became NATO. Moscow
                       reinforced these constraints through election
                       interference, ministerial pressure and support for
                       Finnish communists, keeping Helsinki politically
                       subdued.


                       Finland preserved independence by surrendering
                       sovereignty. Current peace proposals threaten to
                       replicate this model for Ukraine.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Marcy Wheeler ☛ Where_We_Go_from_Here⠀⇛


                       In my opinion, the Epstein scandal is a tool. It
                       undercuts Trump’s ability to grab and redirect
                       attention. It can create moments of cognitive
                       dissonance, as it did for MTG. It is a way to turn
                       Trump’s conspiracism and populism against him and
                       may make other related narrative lines more
                       salient. And if there’s a surprise disclosure —
                       perhaps about Melania’s origin story — all the
                       better. But as you keep the focus on Epstein,
                       remember that there needs to be a direction beyond
                       Epstein as well, a direction which incorporates the
                       oligarchs who are still key players in Trump’s
                       network of power.


                # ⚓ FAIR ☛ ACTION_ALERT:_Why_Didn’t_NYT,_WaPo_Report_What_They
                  Knew_About_Venezuelan_Invasion?_—_FAIR⠀⇛


                       In a 2,000-word play-by-play, the Post (1/3/26)
                       called it a “surprise strike” in a headline, and a
                       “secretive operation” in the article. The Times,
                       for its part, dubbed it a “surprise nighttime
                       operation” (1/3/26), noting that “the military took
                       pains to maintain so-called tactical surprise” (1/
                       3/26).


                       But word quickly got out that it was not a surprise
                       to either paper. Semafor (1/3/26), an outlet co-
                       founded by former Times media columnist Ben Smith,
                       reported that both the Times and Post “learned of a
                       secret US raid on Venezuela soon before it was
                       scheduled to begin,” but chose not to report on it,
                       to “avoid endangering US troops.” Semafor sourced
                       its report to “two people familiar with the
                       communications between the administration and the
                       news organizations.”


                # ⚓ TruthOut ☛ Ford_Plant_Suspends_Worker_After_Trump_Flips_Him
                  Off_|_Truthout⠀⇛


                       Sabula’s remark that Trump is a “pedophile
                       protector” is a reference to the president stalling
                       the release of files relating to Jeffrey Epstein,
                       an alleged child sex trafficker and former close
                       friend of the president’s. After campaigning in
                       2024 in favor of releasing the Epstein files, Trump
                       reneged on that promise once he re-entered the
                       White House, and has since wrongly derided
                       bipartisan calls to make the files public as a
                       Democratic Party-led “hoax.”


                       After Trump reluctantly signed a bill into law that
                       required the Epstein files to be made public, the
                       DOJ recently admitted that only about 1 percent of
                       files have been added to an online database for
                       viewing, missing by far a mid-December deadline.


          o § Environment⠀➾


                # ⚓ Project Censored ☛ Illegal_Gold_Rush_Strips_140,000
                  Hectares_from_the_Peruvian_Amazon⠀⇛


                       A new report published by Monitoring of the Andean
                       Amazon Project (MAAP) and its Peruvian partner
                       organization, Conservación Amazónica, found that
                       140,000 hectares of land in the Peruvian Amazon
                       have been cleared for illegal gold mining. The
                       illegal miners use dredges, “floating machines that
                       chew up and spit out riverbeds—leaving the toxic
                       mercury used to extract gold from sediment in their
                       wake.” MAAP used ultra-high resolution aerial
                       images to locate dredges alongside deforestation.
                       This investigation revealed that the environmental
                       crisis that was previously limited to the south of
                       Peru has moved further north, according to a
                       Guardian report by Luke Taylor, also published in
                       Earth Island Journal.


                # § Energy/Transportation⠀➾


                      # ⚓ Court House News ☛ States_clash_with_Trump_admin_over
                        electric_vehicle_infrastructure⠀⇛


                             In June, U.S. District Judge Tana Lin granted
                             the states’ motion for a preliminary
                             injunction requiring the Federal Highway
                             Administration to restore funding for the
                             National Electric Vehicle Infrastructure
                             Formula (NEVI) Program, which allocated $5
                             billion to states to build electric vehicle
                             charging networks across the country.


                      # ⚓ JURIST ☛ US_federal_court_deems_Trump's_clean_energy
                        grant_cancellation_illegal⠀⇛


                             The court concluded that while cancellation
                             of the grants may have constituted a
                             legitimate government purpose, the different
                             treatment for of Democratic-led states and
                             Republican-led states was not rationally
                             related to that purpose. The court stated:


                             "In fact, Defendants concede that Plaintiffs’
                             seven terminated grants are “comparable” to
                             awards to grantees in Red States that were
                             not terminated. The only identifiable
                             difference—the grant recipient’s state’s
                             political identity and, specifically, its
                             electoral votes cast against President
                             Trump—does not provide a rational basis for
                             why Defendants chose to terminate Plaintiffs’
                             grants over others to advance their stated
                             interest of aligning grant funding with
                             agency priorities."


          o § Finance⠀➾


                # ⚓ The Economist ☛ Why_Europe_is_rediscovering_the_virtues_of
                  cash⠀⇛


                       Enter a church in Sweden in the bleak midwinter and
                       you will find one of its recesses faintly aglow. A
                       thicket of candles, lit by visitors commemorating a
                       loved one, offers a break from the bustle of modern
                       life. Once, such contemplative scenes were
                       disturbed only by the sound of coins clinking into
                       a metal box accepting donations for each candle. No
                       longer. In these modern times, the candles remain
                       but the cash box has often been replaced by a QR
                       code. Instead of rummaging through their change
                       purses, prospective candle-lighters zap a few
                       kronor to the church through Swish, a ubiquitous
                       payment app. The sound of coins against metal has
                       been replaced by the dull buzz of mobile phones
                       announcing that a payment has gone through.


                # ⚓ Europe_is_Rediscovering_the_Virtues_of_Cash⠀⇛


                       Over one in three cinemas in the Netherlands no
                       longer accept notes and coins. Cash usage across
                       the euro area dropped from 79% of in-person
                       transactions in 2016 to just 52% in 2024. Sweden
                       leads the digital shift where 90% of purchases now
                       happen digitally and cash represents under 1% of
                       GDP compared to 22% in Japan.


                       The policy change stems from concerns about
                       financial inclusion for elderly and poor
                       populations who struggle with digital systems.
                       Resilience worries also drove the decision after
                       Spaniards facing nationwide power cuts last spring
                       found themselves unable to buy food. European
                       officials worry about dependence on American
                       payment giants Visa and MasterCard. The EU now
                       recommends citizens store enough cash to survive a
                       week without electricity or internet access.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Futurism ☛ Grok_Is_Getting_Access_to_Classified_Military
                  Networks⠀⇛


                       In addition to the Grok integration, Hegseth
                       announced the creation of a new role within the
                       Department of Defense, the “Chief Digital and
                       Artificial Intelligence Officer,” to be filled by
                       Cameron Stanley. Stanley was most recently the
                       national security transformation lead at Amazon Web
                       Services, a role he began after a lengthy career as
                       as science and tech advisor at the Pentagon.


                # ⚓ Scoop News Group ☛ Executive_branch_budget_pact_includes_IT
                  investments,_less_for_DOGE⠀⇛


                       On the executive branch funding released Sunday for
                       the fiscal year ending Sept. 30, lawmakers agreed
                       on $124.3 million for salaries and expenses in the
                       White House’s Office of Administration, with up to
                       $12.8 million used for IT modernization. No more
                       than $10 million of that IT pie should be spent for
                       security and continuity of operations improvements.


                # ⚓ Jacobin Magazine ☛ The_Fed_Is_Quietly_Bailing_Out_Wall
                  Street⠀⇛


                       The Federal Reserve has quietly delivered nearly
                       half a trillion dollars to Wall Street with few
                       strings attached over the past few months through
                       an obscure government financial program intended
                       for banks struggling to make cash payments.


                       These cash infusions could signal instability in
                       the broader financial sector — and come as the
                       central bank is besieged by potentially market-
                       rattling turmoil following the Trump
                       administration’s launch of a criminal investigation
                       into Federal Reserve chair Jerome Powell.


                # ⚓ [Repeat] Scoop News Group ☛ Hill_warning:_Don’t_put_cyber
                  offense_before_defense⠀⇛


                       “I’m concerned we’re putting the cart before the
                       horse, when we have not had a hearing on why the
                       [Cybersecurity and Infrastructure Security] Agency
                       has lost one-third of its workforce in the last
                       year,” the top Democrat on the full committee,
                       Bennie Thompson of Mississippi, said. “We ought to
                       be cautious about pursuing an approach involving
                       the use of offensive cyber tools that could result
                       in retaliation or escalation if we’re not in a
                       position to help defend U.S. networks.”


                # ⚓ Scoop News Group ☛ TSA_plans_to_beef_up_its_IT_help_desk⠀⇛


                       “TSA requires an IT contractor who can locally
                       support the users and IT equipment and provide a
                       central help desk for rapid responses and trouble
                       resolution,” per the forecast, which was published
                       Thursday on APFS.


                       DHS estimates a formal request for offers will go
                       live next week.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ RTL ☛ Amid_[Internet]_blackout:_AI-created_Iran
                        protest_videos_gain_traction_-_RTL_Today⠀⇛


                             US disinformation watchdog NewsGuard said it
                             identified seven AI-generated videos
                             depicting the Iranian protests -- created by
                             both pro- and anti-government actors -- that
                             have collectively amassed some 3.5 million
                             views across online platforms.


                      # ⚓ Open Caucasus Media ☛ Russia’s_soft_power_project
                        focused_on_Armenia_funded_through_presidential_grant⠀⇛


                             In May 2025, the Russian daily Vedomosti
                             reported that Kiriyenko would be ‘tasked’ to
                             advance Russian interests in Armenia ‘through
                             soft power’ ahead of the 2026 parliamentary
                             elections.


                      # ⚓ Techdirt ☛ Elon_Musk_Plays_Disinfo_Telephone:_How
                        Oregon’s_Mundane_Voter_Roll_Cleanup_Is_Turned_Into
                        False_Claim_Of_‘Fake_Voters’⠀⇛


                             The game works like this: Someone takes a
                             factual but largely unremarkable story, gives
                             it a slight spin, and passes it along. The
                             next person picks it up, adds another layer
                             of spin, and passes that along. By the time
                             it reaches someone with a massive
                             audience—say, the richest man in the
                             world—the original mundane fact has been
                             transformed into a full-blown conspiracy
                             theory. And that final, mangled version is
                             what millions of people see and believe.


                             So let’s trace this particular game of
                             telephone from start to finish.


          o § Censorship/Free Speech⠀➾


                # ⚓ The Record ☛ Ugandan_officials_turn_off_[Internet]_on_eve
                  of_national_elections⠀⇛


                       “It is especially alarming coming as it does just
                       before a crucial election already marred by massive
                       repression and an unprecedented crackdown on
                       opposition parties and dissenting voices.”


                       Chagutah called the fact that no end date has been
                       given for when the blackout will lift “ominous.”


                # ⚓ The Independent UK ☛ University_free_speech_row_as_students
                  want_Reform_UK_banned⠀⇛


                       Nearly half (47 per cent) of students believe
                       universities are becoming less tolerant of diverse
                       viewpoints, a figure that has almost doubled since
                       2016.


                # ⚓ BBC ☛ Uganda_elections_2026:_Communications_authority
                  imposes_an_[Internet]_blackout_ahead_of_vote⠀⇛


                       Earlier this month, the Uganda Communications
                       Commission (UCC) described reports of an [Internet]
                       blackout as "mere rumours", saying the commission's
                       role was to guarantee uninterrupted connectivity
                       nationwide.


                # ⚓ Le Monde ☛ Uganda_cuts_[Internet]_access_ahead_of
                  elections⠀⇛


                       Ugandan authorities shut down [Internet] access
                       nationwide on Tuesday, January 13, two days ahead
                       of elections in which President Yoweri Museveni has
                       overseen a crackdown on the opposition as he seeks
                       to extend his 40-year rule. The 81-year-old leader,
                       who once said African rulers should not overstay
                       their time in office, is widely expected to win a
                       seventh term on Thursday due to his total control
                       over state and security bodies.


                # ⚓ Deutsche Welle ☛ Uganda:_Crackdown,_[Internet]_blackout
                  ahead_of_vote⠀⇛


                       Journalists in the capital Kampala say they lost
                       [Internet] access after the Uganda Communications
                       Commission ordered [Internet] providers cut access
                       to prevent the spread of "misinformation" and
                       electoral fraud.


                       Some international phone calls were also being
                       blocked said the journalists.


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


                # ⚓ Northwestern University ☛ Newspaper_family_saves_Oregon
                  paper⠀⇛


                       The goal is to preserve independent newspapers,
                       which accounted for a majority of newspaper
                       closures and mergers over the last year, according
                       to data gathered by Northwestern University’s Local
                       News Initiative.


                       But there’s no single — or simple — solution to
                       ensure the survival of America’s 5,400 or so
                       remaining newspapers. Many approaches are needed,
                       including community and public support, to sustain
                       these essential local businesses.


                # ⚓ Washingon-Baltimore News Guild ☛ WBNG_condemns_FBI_search
                  of_Washington_Post_Guild_member's_home_-_Washington-Baltimore
                  News_Guild⠀⇛


                       The Washington-Baltimore News Guild unequivocally
                       condemns the reported search of a Washington Post
                       reporter’s home and the seizure of her electronic
                       devices by federal agents. Such actions represent a
                       dangerous escalation that threatens press freedom
                       and the fundamental role of journalists in holding
                       power accountable.


                # ⚓ TruthOut ☛ Free_Press_Advocates_Decry_FBI_Search_of
                  Washington_Post_Reporter’s_Home⠀⇛


                       Post reporter Hannah Natanson, whose reporting
                       focuses extensively on the consequences of
                       President Donald Trump’s attempts to fire workers
                       and dismantle entire government agencies, was at
                       her home when federal investigators arrived. Agents
                       seized her electronic devices, including her phone
                       and laptop computers, and searched her entire home
                       as part of the raid.


                # ⚓ Techdirt ☛ Bari_Weiss_Is_Sad_That_People_Aren’t_Enjoying
                  Her_Clumsy_Destruction_Of_CBS_News⠀⇛


                       If you missed it, Trump-allied billionaire Larry
                       Ellison and his nepobaby son David hired an
                       unqualified troll named Bari Weiss to “run” CBS
                       News. And by “run” CBS news, I mean destroying what
                       little journalism was left at the media giant and
                       creating an alternate-reality safe space for right
                       wing billionaires and their increasingly radical
                       ideologies. While pretending to be “restoring trust
                       in journalism.”


                       It’s… not going well.


                # ⚓ TruthOut ☛ “CBS_Evening_News”_Has_Lost_Over_a_Million
                  Viewers_Since_Bari_Weiss_Takeover⠀⇛


                       Data from media audience measurement firm Nielsen
                       shows that the show lost nearly a quarter of its
                       viewership in the first five days of Dokoupil
                       taking over the program, from January 5 to January
                       9, compared to the same period last year.


                # ⚓ The Tyee ☛ Stop_Blocking_Media,_BC_Human_Rights_Report_Will
                  Tell_Police⠀⇛


                       The commissioner wants police to stop using
                       “exclusion zones” to bar the media from areas where
                       officers are undertaking enforcement activities,
                       unless they have judicial permission or are facing
                       an immediate public safety threat.


                       And with police forces continuing to restrict media
                       access despite legal rulings calling the practice
                       unconstitutional, the commissioner is asking the
                       province to formally restrict the practice, while
                       also asking for more education for frontline
                       officers.


                # ⚓ BoingBoing ☛ FBI_raids_Washington_Post_reporter's_home⠀⇛


                       Searching a journalist's home is an extraordinary
                       step. Even past administrations that aggressively
                       pursued leak investigations — and the Obama
                       administration was notably aggressive — stopped
                       short of raiding reporters' homes. "Searches of
                       newsrooms and journalists are hallmarks of
                       illiberal regimes, and we must ensure that these
                       practices are not normalized here," said Jameel
                       Jaffer, executive director of the Knight First
                       Amendment Institute.


                # ⚓ The Guardian UK ☛ FBI_raids_home_of_Washington_Post
                  reporter_in_‘highly_unusual_and_aggressive’_move⠀⇛


                       The reporter’s home and devices were searched, and
                       her Garmin watch, phone, and two laptop computers,
                       one belonging to her employer, were seized, the
                       newspaper said. It added that agents told Natanson
                       she was not the focus of the probe, and was not
                       accused of any wrongdoing.


                # ⚓ Mediaite ☛ FBI_Search_Washington_Post_Journalist's_Home,
                  Seize_Devices⠀⇛


                       The move to search and seize is noted by The Post
                       as rare, even in aggressive leak investigations
                       where authorities typically pursue journalists’
                       phone or email records rather than physically
                       searching their homes.


                       Natanson has spent the past year closely covering
                       the Trump administration’s campaign to fire large
                       numbers of federal workers and reshape the civil
                       service to more directly serve the president’s
                       agenda. Her reporting documented widespread anger
                       and fear inside government agencies as employees
                       confronted pressure to fall in line or risk losing
                       their jobs.


                # ⚓ The Dissenter ☛ Coalition_Opposes_Rep._Luna's_Effort_To
                  Silence_Journalist⠀⇛


                       “The subpoena has few parallels or precedents in
                       recent history and poses a grave danger to the
                       First Amendment’s guarantee of press freedom,” the
                       coalition declared in a letter [PDF] addressed to
                       the House of Representatives.


                       “Luna’s comments on social media have made clear
                       that she lacked a legitimate legislative purpose
                       for proposing the subpoena. In one post explaining
                       the subpoena, she claimed the purpose was for Harp
                       to ‘face accountability’ as ‘the media has gotten
                       away with too much for too long and I’m sick of
                       it.’”


                # ⚓ Techdirt ☛ Prosecutors_Flee_DOJ_After_Being_Told_To
                  Investigate_The_Murdered_Woman,_Not_The_Murderer⠀⇛


                       Last week, we wrote about how ICE agent Jonathan
                       Ross murdered Renee Nicole Good, a 37-year-old poet
                       and mother, on a Minneapolis street in broad
                       daylight. We wrote about how the Trump
                       administration immediately began lying about it
                       despite multiple video angles showing exactly what
                       happened. We wrote about how the media called
                       documented murder a “dispute.”


                       This week, we’re writing about how career Justice
                       Department prosecutors—people who’ve spent their
                       careers putting away fraudsters, drug dealers, and
                       actual criminals—looked at how the administration
                       is handling this case and said: we want no part of
                       this.


          o § Civil Rights / Policing / Accessibility⠀➾


                # ⚓ Manuel Matuzović ☛ Workshop:_Deep_Dive_on_Accessibility
                  Testing⠀⇛


                       Once again, I’ve teamed up with my friends at
                       Smashing Magazine 😻 to share with you everything I
                       know about web accessibility testing! In this
                       smashing workshop we’ll talk about automatic and
                       manual testing, screen reader basics, Single Page
                       Applications, Dev Tools, and more.


                       Sounds interesting? Great! Here are some more
                       details about the workshop: [...]


                # ⚓ Adam Bonica ☛ The_Wall_Looks_Permanent_Until_It_Falls⠀⇛


                       Start with work and economic life. Americans work
                       longer hours, pay more out-of-pocket for college
                       and childcare, lack parental leave, and enjoy less
                       economic mobility. The share of income going to the
                       top 1 percent is nearly double the OECD average.
                       American CEOs earn, on average, 354 times as much
                       as their workers. More workers are trapped in
                       poverty-wage jobs. Collective bargaining covers
                       fewer workers. And social protections are less
                       generous for those who fall on hard times, with the
                       government raising less in taxes and spending more
                       on the military.


                       The economy is just the beginning.


                       We spend nearly twice as much on healthcare as
                       other wealthy countries do. Yet life expectancy is
                       well below average, infant and maternal mortality
                       rates are alarmingly high, and more Americans
                       remain uninsured.


                # ⚓ Futurism ☛ ICE_Reportedly_Stole_a_10th_Grader's_Phone,_Then
                  Seemingly_Sold_It_for_Cash⠀⇛


                       One of these civilians was tenth grader Arnoldo
                       Bazan, who was getting McDonald’s with his father,
                       Arnulfo Bazan Carrillo, when they were pulled over
                       by masked agents. According to Arnoldo, after
                       several agents violently tackled his father — who
                       is undocumented — to the ground, with one pressing
                       a knee into his neck, another put the 16-year-old
                       in a suffocating chokehold. When he told the agent
                       that he was a citizen and a minor, the agent didn’t
                       stop.


                # ⚓ Truthdig ☛ 'Now_Is_the_Time':_Minnesota_Calls_for_General
                  Strike_to_Drive_Out_ICE⠀⇛


                       On Jan. 13, a coalition of faith leaders, union
                       presidents, business owners and community figures
                       in Minneapolis called on “every worker in Minnesota
                       to refuse to show up to work” and “every single
                       Minnesotan to not spend a dime” on Jan. 23 to
                       demand an end to the “violence and horror” that
                       Immigration and Customs Enforcement has unleashed
                       on the community and the agency’s complete removal
                       from the state.


                       “We are going to leverage our economic power, our
                       labor, our prayer for one another,” said JaNaé
                       Bates, co-executive director of Isaiah MN, a
                       multiracial interfaith community organizing
                       network.


                       “We are not going to shop, we are not going to
                       work, we are not going to school on Friday, January
                       23.”


                # ⚓ MinnPost ☛ ICE_occupation,_unlike_Floyd_protests,_is_an
                  intentional_disruption_-_MinnPost⠀⇛


                       This month, the same kind of insecurity is not an
                       accident, but fundamental to a named federal
                       operation sending unaccountable SUVs full of masked
                       men to sow chaos for political propaganda. The ICE
                       officer who killed Renee Good last week was filming
                       himself while doing it, not with a body camera but
                       with his personal cell phone: one hand on a gun,
                       and one hitting record for personal posterity. Much
                       recent Trump-orchestrated activity in the Twin
                       Cities seems similarly oriented to creating
                       “content” to feed a right-wing media machine.


                       The only meaningful pushback against the terror
                       campaign comes in the form of my neighbors, regular
                       people doing extraordinary and difficult work. They
                       are coordinating themselves from the bottom up,
                       grassroots, using phone chat apps. They are
                       patrolling outside schools and immigrant
                       businesses. They are putting in hours tailing ICE
                       agents, blowing whistles, and witnessing the
                       questionable incarceration of vulnerable neighbors.
                       I know many people who have done this work every
                       day, and I am in awe of their courage.


                # ⚓ MinnPost ☛ Two-plus_dozen_ICE_vehicles_lack_necessary
                  lights,_sirens⠀⇛


                       More news on the ICE front: [...]


                # ⚓ TwinCities Pioneer Press ☛ Remarks_of_Gov._Tim_Walz’s
                  address_on_ICE_actions_in_Minnesota_–_Twin_Cities⠀⇛


                       My fellow Minnesotans,


                       What’s happening in Minnesota right now defies
                       belief.


                       News reports simply don’t do justice to the level
                       of chaos and disruption and trauma the federal
                       government is raining down upon our communities.


                       Two to three thousand armed agents of the federal
                       government have been deployed to Minnesota.


                # ⚓ TwinCities Pioneer Press ☛ Walz_calls_for_Minnesotans_to
                  record_ICE,_continue_resistance_to_immigration_crackdown⠀⇛


                       As a federal immigration enforcement surge
                       continues in Minnesota, Gov. Tim Walz on Wednesday
                       called on Minnesotans to peacefully resist the
                       administration of President Donald Trump and to
                       record videos of immigration agents operating in
                       the state.


                       “Help us establish a record of exactly what’s
                       happening in our communities. You have an absolute
                       right to peacefully film ICE agents as they conduct
                       these activities,” Walz said in a five-minute
                       speech. “So carry your phone with you at all times,
                       and if you see these ICE agents in your
                       neighborhood, take out that phone and hit record.
                       Help us create a database of the atrocities against
                       Minnesotans, not just to establish a record for
                       posterity, but to bank evidence for future
                       prosecution.”


                # ⚓ Techdirt ☛ We_Found_More_Than_40_Cases_Of_Immigration
                  Agents_Using_Banned_Chokeholds_And_Other_Moves_That_Can_Cut
                  Off_Breathing⠀⇛


                       In nearly 20 cases, agents appeared to use
                       chokeholds and other neck restraints that the
                       Department of Homeland Security prohibits “unless
                       deadly force is authorized.”


                       About two dozen videos show officers kneeling on
                       people’s necks or backs or keeping them face down
                       on the ground while already handcuffed. Such
                       tactics are not prohibited outright but are often
                       discouraged, including by federal trainers, in part
                       because using them for a prolonged time risks
                       asphyxiation.


                       We reviewed footage with a panel of eight former
                       police officers and law enforcement experts. They
                       were appalled.


                # ⚓ Jacobin Magazine ☛ Most_Americans_Condemn_ICE’s_Murder_of
                  Renee_Good⠀⇛


                       By an average margin of more than 22 points,
                       Americans overwhelmingly find that ICE’s killing of
                       Renee Good was unjustified (a scenario we
                       traditionally describe as “murder”). Republicans
                       weren’t just wrong in predicting a landslide of
                       support for ICE; the landslide went in the exact
                       opposite direction. Ahmari’s prediction was wrong
                       by a hilarious margin of 62 points, a failure that
                       should permanently discredit his media branding as
                       a post-partisan populist who’s in touch with the
                       American people.


                       And as bad as these numbers are, the details are
                       even worse. Just look at the crosstabs: [...]


                # ⚓ Jacobin Magazine ☛ ICE_Has_Become_a_Rogue_Paramilitary⠀⇛


                       Ross shot Good as she attempted to leave, which we
                       know because we can see in his own footage that she
                       was dramatically cranking the wheel away from him.
                       The car had passed him by when he fired the first
                       of three shots, which we know because both of his
                       legs are visible on the ground to the left of the
                       car in the footage from several angles. His life
                       was not under threat, which we know because killing
                       her had no bearing on the car’s immediate course
                       and he walked away unharmed. And if he had actually
                       been under threat, shooting her would have
                       contributed nothing to his self-defense, which we
                       know because cars do not stop instantly when their
                       drivers die.


                # ⚓ Pro Publica ☛ Immigration_Agents_Using_Banned_Chokeholds_on
                  U.S._Citizens⠀⇛


                       • Former Police Are Appalled: We showed former
                       police and immigration officials videos of
                       incidents. They said agents are out of control. One
                       said it’s “the kind of action which should get you
                       fired.”


                       • Banned Tactics, No Punishment: There is a federal
                       ban on chokeholds and similar tactics. But there is
                       no sign of punishment for officers who’ve used
                       them.


                # ⚓ The Tyee ☛ Is_It_Time_to_Ban_Tipping?⠀⇛


                       Tipping and tipflation signal a growing shift in
                       responsibility for workers’ pay from employers to
                       customers, with significant consequences like
                       income volatility and workplace inequity.


                       The spread of tipping isn’t the best way to help
                       workers make ends meet.


                       Instead Canadians should consider a bold
                       alternative: banning tipping and replacing it with
                       a living-wage floor, ensuring decent wages for all
                       workers and transparent pricing for customers.


                # ⚓ RFERL ☛ Iranian_Doctor_Says_Security_Forces_'Shooting
                  Inside'_Hospitals⠀⇛


                       A doctor inside Iran has told RFE/RL's Radio Farda
                       that security forces have stormed hospitals and
                       executed wounded protesters amid a brutal state
                       crackdown on nationwide antiestablishment protests.


                # ⚓ Boston Globe ☛ Iran_signals_fast_trials_and_executions_for
                  protesters⠀⇛


                       The Human Rights Activists News Agency said 2,403
                       of the dead were protesters and 147 were
                       government-affiliated. Twelve children were killed,
                       along with nine civilians it said were not taking
                       part in protests.


                       More than 18,100 people have been detained, the
                       group said.


                # ⚓ TwinCities Pioneer Press ☛ Oglala_Sioux_Tribe_says_three
                  tribal_members_arrested_in_Minneapolis_are_in_ICE_detention⠀⇛


                       “The Oglala Sioux Tribe’s memorandum makes clear
                       that ‘tribal citizens are not aliens’ and are
                       ‘categorically outside immigration jurisdiction,’”
                       President Frank Star Comes Out said.


                # ⚓ Techdirt ☛ Following_Murder_Of_Renee_Good_By_ICE_Officers,
                  ICE_Blocks_Congressional_Reps_From_Its_Detention_Facility⠀⇛


                       The wagons are circling even tighter — a metaphor
                       that ICE has made extremely apt now that it’s just
                       the extension of the administration’s xenophobic
                       id: an invading force that’s meant to rid America
                       of anyone not sufficiently white enough to
                       “deserve” to live in the United States.


                       It’s back on its old bullshit, continuing to
                       pretend it’s not legally obligated to allow members
                       of Congress to tour its detention facilities. DHS
                       and ICE have claimed (without legal support) that
                       they need advance notice, citing unspecified
                       “security” concerns of the “national” variety. The
                       government continues to place obstacles in the path
                       of congressional representatives who are engaged in
                       acts that are supported by law and legal precedent:
                       oversight of ICE operations.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ US News And World Report ☛ Verizon_Outage_Disrupts_Calling
                  and_Data_Services_for_Wireless_Customers_Across_the_US⠀⇛


                       The carrier acknowledged that there was an “issue
                       impacting wireless voice and data services for some
                       customers." Verizon didn't specify what was causing
                       the disruptions, but said in updates shared on
                       social media that it had deployed its engineering
                       teams and was working to resolve the problem “as
                       quickly as possible.”


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ Mexico News Daily ☛ Trump_says_he_doesn't_care_about_USMCA;
                  Sheinbaum_says_US_businesses_do⠀⇛


                       Trump’s remarks came 5 1/2 months before the
                       commencement of the formal review of the USMCA,
                       which superseded the North American Free Trade
                       Agreement, or NAFTA, on July 1, 2020.


                # ⚓ Semafor Inc ☛ US_patent_data_shows_where_tech_growth_lies⠀⇛


                       The push for green inventions comes from car
                       companies, with Honda and auto component-maker
                       Toshiba dominating those grant filings. It’s a
                       signal that companies continue to see real business
                       value in developing those new technologies, outside
                       of the political ESG discourse that has tempered in
                       recent years. And as energy becomes a focal point
                       in the AI race, innovation on the battery front
                       will continue in the coming years.


          o § Copyrights⠀➾


                # ⚓ Decrypt ☛ Google_Seeks_Dismissal_of_Publisher_Lawsuit_Over
                  AI_Search_Summaries⠀⇛


                       Google and its parent company Alphabet have filed a
                       motion to dismiss antitrust claims from Penske
                       Media Corporation and its subsidiaries, saying that
                       displaying AI-generated summaries on its search
                       engine constitutes lawful product improvement
                       rather than anti-competitive behavior.


                       Filed on Monday in the U.S. District Court for the
                       District of Columbia, this marks Google’s third
                       attempt to kill the lawsuit after publishers
                       amended their complaints twice following earlier
                       dismissal motions.


                       Penske Media, which owns Rolling Stone, Variety,
                       Billboard, and Deadline, sued Google last
                       September, alleging the search giant forces
                       publishers to surrender content for AI training and
                       republishing as a condition of appearing in search
                       results.


                # ⚓ Society for Scholarly Publishing ☛ Guest_Post_—_AI_Use:
                  From_Policies_to_Reality⠀⇛


                       Last month, the Committee on Publication Ethics
                       (COPE) hosted its third Publication Integrity Week,
                       featuring a week-long series of online events
                       bringing together a diverse group of speakers,
                       practitioners, and community members to examine
                       pressing challenges and opportunities in scholarly
                       publishing. As part of the week, Gráinne McNamara
                       hosted a panel discussion to continue the
                       conversation around AI (artificial intelligence)
                       use: policies and reality — with a range of
                       perspectives shared by Jeremy Ng, Elizabeth Moylan,
                       Coco Nijhoff, and Lauren Flintoft.


                # ⚓ The Conversation ☛ Wikipedia_at_25:_can_its_original_ideals
                  survive_in_the_age_of_AI?⠀⇛


                       The scale of human labour that goes into Wikipedia
                       is easy to take for granted, given its disarming
                       simplicity of presentation. Statista estimates 4.4
                       billion people accessed the site in 2024 – over
                       half the world and two-thirds of internet users.
                       More than 125 million people have edited at least
                       one entry.


                       Wikipedia carries no advertising and does not trade
                       in users’ data – central to its claim of editorial
                       independence. But users regularly see fundraising
                       banners and appeals, and the Wikimedia Foundation
                       has built paid services to manage high-volume reuse
                       of its content – particularly by bots scraping it
                       for AI training. The foundation’s total assets now
                       stand at more than US$310 million (£230 million).


                # ⚓ Torrent Freak ☛ Groupon_'Redeems'_Itself_With_Rapid
                  Takedown_of_Pirate_IPTV_Deal⠀⇛


                       Groupon, the global marketplace that aims to offer
                       users some of the best online deals, recently
                       featured an offer that was too good to be true.
                       After Dutch anti-piracy group BREIN flagged an
                       illegal IPTV service on the platform, Groupon
                       reportedly took swift action to remove it. BREIN
                       credits this rapid response to its new 'Trusted
                       Flagger' status under the EU’s Digital Services Act
                       (DSA).


                # ⚓ Torrent Freak ☛ Court_Orders_Porkbun_and_Other_Registrars
                  to_Hand_Over_PornXP_Domains_to_Aylo⠀⇛


                       Formerly known as Mindgeek, Aylo is the driving
                       force behind free ‘tube’ sites such as Pornhub,
                       YouPorn, and RedTube. It also owns many adult
                       brands, including Brazzers and Reality Kings, that
                       charge for subscriptions.


                       The company controls an impressive library of more
                       than 40,000 registered copyrighted works. When this
                       content appears on third-party sites, it doesn’t
                       hesitate to take legal action.


                # ⚓ Digital Music News ☛ Fifth_Circuit_Hands_Down_Landmark
                  Vetter_v._Resnik_Decision⠀⇛


                       Keeping the focus on brass tacks, per the initial
                       suit from Vetter, despite the recapture, Resnik
                       refused “to relinquish claim to the Double Shot
                       copyright outside of the United States” and
                       purported “to retain the exclusive right to exploit
                       the work in all foreign countries.”


                       “‘FYI, under the U.S. Copyright law, a termination
                       of transfer notice only terminates a transfer for
                       the United States,’” counsel for the defendant
                       wrote in 2023. “‘All rights outside of the United
                       States do not revert so Mr. Resnik/Windsong Music
                       retain the copyright to ‘Double Shot’ outside of
                       the United States for the life of copyright.’”


                # ⚓ Techdirt ☛ Online_Gaming’s_Final_Boss:_The_Copyright
                  Bully⠀⇛


                       For decades, that participatory experience was a
                       key part of one of the longest-running video games
                       still in operation: Everquest. Players had the
                       official client, acquired lawfully from EverQuest’s
                       developers, and modders figured out how to enable
                       those clients to communicate with their own servers
                       and then modify their play experience – creating
                       new communities along the way.


                       Everquest’s copyright owners implicitly blessed all
                       this. But the current owners, a private equity firm
                       called Daybreak, want to end that independent
                       creativity. They are using copyright claims to
                       threaten modders who wanted to customize the
                       EverQuest experience to suit a different playstyle,
                       running their own servers where things worked the
                       way they wanted.


    * Coming_Soon:_Impact_With_EPO_Cocainegate
    * GAFAM_and_IBM_Layoffs_Outline



                    ䷩ 𝚕𝚒𝚗𝚎 7191

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 15/01/2026: Starlink Weaponised for
Regime Change (by Man Who Boasted About Annexing South American Countries for
Tesla's Mining), Corruption in Switzerland Uncovered by
JuristGate⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jan 15, 2026


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
                # Artificial_Intelligence_(AI)_/_LLM_Slop_/_Plagiarism
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights_/_Policing_/_Accessibility
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ New York Times ☛ NASA_Begins_Astronaut_Space_Station
                  Medical_Evacuation:_What_to_Know⠀⇛


                       Four astronauts departed from the I.S.S. about a
                       month earlier than scheduled because a crew member,
                       who was not identified, has an undisclosed medical
                       issue.


                # ⚓ New York Times ☛ Toby_Kiers,_World_Champion_of_Mycorrhizal
                  Fungus⠀⇛


                       This year’s recipient of the Tyler Prize for
                       Environmental Achievement talks about “punk
                       science,” microbial economics and thinking like a
                       mycorrhizal fungus.


                # ⚓ Science Alert ☛ CPR_on_TV_Shows_Can_Save_Real_Lives_–_if
                  They_Do_It_Right⠀⇛


                       Time for a refresher.


                # ⚓ Science Alert ☛ Spiral_Galaxy_Caught_Spraying_Huge_Jets_of
                  Super-Hot_Gas_Like_a_Sprinkler⠀⇛


                       The largest of their kind ever found.


                # ⚓ Science Alert ☛ Just_One_Gene_May_Be_Responsible_For_Over
                  90%_of_Alzheimer's_Cases⠀⇛


                       A "neutral" variant is not-so-neutral after all.


                # ⚓ Science Alert ☛ An_Ancient_Wolf_Cub's_Last_Meal_Just
                  Rewrote_The_Woolly_Rhino_Extinction_Story⠀⇛


                       Wild.


                # ⚓ Science Alert ☛ WATCH:_NASA_Conducts_First-Ever_Medical
                  Evacuation_From_The_ISS⠀⇛


                       "Our timing of this departure is unexpected."


          o § Hardware⠀➾


                # ⚓ Daniel Lemire ☛ How_stagnant_is_CPU_technology?⠀⇛


                       Sometimes, people tell me that there is no more
                       progress in CPU performance. Consider these three
                       processors which had comparable prices at release
                       time. The AMD Ryzen 7 9800X3D (Zen 5, with up to
                       5.3 GHz boost) was released in 2024.


                # ⚓ Tom's Hardware ☛ Chinese_customs_told_to_block_H200
                  imports,_report_claims_—_directive_would_effectively_ban_the
                  Nvidia_Hey_Hi_(AI)_chip_from_China⠀⇛


                       Chinese customs officers were allegedly told to
                       disallow the entry of Nvidia H200 chips,
                       effectively banning the entry of these Hey Hi (AI)
                       processors into the country. The command comes as
                       other sources say that Beijing will only allow the
                       import of these Hey Hi (AI) GPUs for 'special
                       circumstances.'


                # ⚓ Tom's Hardware ☛ Beijing_reportedly_limiting_H200_purchases
                  to_those_with_‘special_circumstances’_—_sources_suggest_only
                  university_R&D_labs_can_acquire_Nvidia_GPUs_in_China⠀⇛


                       After weeks of deliberation, sources suggest that
                       China will only allow companies to purchase H200
                       GPUs for "special circumstances," although Beijing
                       has yet to define exactly what that means.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ British_Columbia_Ends_Program_That_Aimed
                  to_Curb_Arrests_of_Drug_Users⠀⇛


                       The three-year pilot program did not deliver the
                       results hoped for, the health minister said. It had
                       allowed drug users to avoid criminal charges for
                       possessing small amounts of illegal substances.


                # ⚓ New York Times ☛ Is_Whole_Milk_Healthier_for_Kids?⠀⇛


                       A new law will allow full-fat and 2 percent milk to
                       be served in schools. Here’s what to know.


                # ⚓ New York Times ☛ H.H.S._Reverses_Decision_to_Cut_$2_Billion
                  for_Mental_Health_and_Addiction_Services⠀⇛


                       A day after funding termination notices went out to
                       more than 2,000 programs nationwide, the
                       administration reversed itself and reinstated the
                       money.


                # ⚓ The Straits Times ☛ Bangkok_wakes_up_to_toxic_air_choking
                  central_business_districts⠀⇛


                       Toxic smog has become Bangkok’s annual public-
                       health emergency during colder months.


                # ⚓ Bridge Michigan ☛ 40,000_fewer_Michiganders_seek_Affordable
                  Care_Act_health_insurance⠀⇛


                       About 40,000 fewer state residents are signing up
                       through HealthCare.gov, as health care subsidies
                       expire and premiums increase.


                # ⚓ PHR ☛ Israel_Has_Systematically_Undermined_Women’s_and
                  Newborn_Health_in_Gaza:_Two_Reports⠀⇛


                       Physicians for Human Rights (PHR) in the United
                       States (co-publishing with the Global Human Rights
                       Clinic at the University of Chicago Law School
                       [GHRC]) and Physicians for Human Rights -Israel
                       (PHRI) published two independent reports
                       documenting the severe harm to women and children’s
                       health in Gaza since October 7, 2023 [...]


                # ⚓ The Straits Times ☛ More_than_1_in_7_newborns_in_South
                  Korea_conceived_through_infertility_treatment⠀⇛


                       The number of government supported treatment cases
                       grew by 142.6 per cent from 2020 to 2024.


                # ⚓ New York Times ☛ China’s_Coal_Ban_Improved_Air_Quality,_but
                  Villagers_Are_Paying_the_Price⠀⇛


                       China banned the burning of coal for heat around
                       Beijing, but natural gas subsidies have run out,
                       leaving many villagers vulnerable in dangerously
                       cold weather.


                # ⚓ The Straits Times ☛ Beijing_won_its_war_for_blue_skies_but
                  villagers_are_paying_the_price⠀⇛


                       Across Hebei province, villagers are confronting
                       the full cost of China's push for cleaner air.


                # ⚓ Science Alert ☛ Exercise_Is_Emerging_as_a_Powerful
                  Treatment_For_Depression⠀⇛


                       Do try this at home, if you can.


                # ⚓ Science Alert ☛ Scientists_Are_Finally_Closing_In_on_a
                  Treatment_For_Huntington's_Disease⠀⇛


                       Hopeful progress at last.


                # ⚓ Science Alert ☛ A_Ketamine-Related_Health_Problem_Is
                  Surging_in_Young_People,_Doctors_Warn⠀⇛


                       Substantially increasing patient admissions.


                # ⚓ Science Alert ☛ Mosquitoes_Are_Feeding_on_Us_More_Often_–
                  And_Scientists_Say_We're_to_Blame⠀⇛


                       The consequences are more dire than just an itch.


                # ⚓ Bridge Michigan ☛ Michigan_nears_school_cellphone_ban._What
                  to_know⠀⇛


                       Michigan House OK’s ban on using smartphones in
                       public and charter schools across the state.
                       Students could still carry ‘dumb’ phones without
                       access to TikTok.


          o § Proprietary⠀➾


                # § Artificial Intelligence (AI) / LLM Slop / Plagiarism⠀➾


                      # ⚓ Futurism ☛ Grok_Is_Getting_Access_to_Classified
                        Military_Networks⠀⇛


                             What could possibly go wrong?


                      # ⚓ Futurism ☛ Duffer_Brothers_Accused_of_Using_Abusive
                        Monopolist_Microsoft_Chaffbot_for_Final_Season_of
                        “Stranger_Things”⠀⇛


                             Some watchers are wondering why the "Stranger
                             Things" finale didn't live up to expectations
                             and are now blaming OpenAI's ChatGPT.


                      # ⚓ Tarek_Ziadé:_The_Economics_of_Hey_Hi_(AI)_Coding:_A
                        Real-World_Analysis⠀⇛


                             My whole stream in the past months has been
                             about Hey Hi (AI) coding. From skeptical
                             engineers who say it creates unmaintainable
                             code, to enthusiastic (or scared) engineers
                             who say it will replace us all, the discourse
                             is polarized. But I’ve been more interested
                             in a different question: what does Hey Hi
                             (AI) coding actually cost, and what does it
                             actually save?


                             I recently had Claude help me with a
                             substantial refactoring task: splitting a
                             monolithic Rust project into multiple
                             workspace repositories with proper dependency
                             management. The kind of task that’s tedious,
                             error-prone, and requires sustained attention
                             to detail across hundreds of files. When it
                             was done, I asked Claude to analyze the
                             session: how much it cost, how long it took,
                             and how long a human developer would have
                             taken.


                      # ⚓ The Verge ☛ UK_police_blame_Microsoft_Copilot_for
                        intelligence_mistake⠀⇛


                             The chief constable of one of Britain’s
                             largest police forces has admitted that
                             Microsoft’s Copilot AI assistant made a
                             mistake in a football (soccer) intelligence
                             report. The report, which led to Israeli
                             football fans being banned from a match last
                             year, included a nonexistent match between
                             West Ham and Maccabi Tel Aviv.


                      # ⚓ Digital Music News ☛ Bandcamp_Takes_a_Stand_and_Bans
                        AI-Generated_Music⠀⇛


                             Bandcamp takes an official stance against
                             artificial intelligence by banning AI-
                             generated audio and music from its platform.
                             Bandcamp keeps providing users with even more
                             reasons to love its platform.


                      # ⚓ Scoop News Group ☛ California_AG_launches
                        investigation_into_X’s_sexualized_deepfakes⠀⇛


                             California Attorney General Rob Bonta
                             announced an investigation Wednesday into xAI
                             over allegations that its artificial
                             intelligence model Grok is being used to
                             create nonconsensual sexually explicit images
                             of women and children on a large scale,
                             marking the latest escalation in regulatory
                             efforts to address AI-generated deepfakes.


          o § Defence/Aggression⠀➾


                # ⚓ The Straits Times ☛ Australia’s_hate_speech_and_gun_law
                  reforms_face_free_speech_concerns⠀⇛


                       Conservative opposition lawmakers say the Bill also
                       threatens religious freedom.


                # ⚓ New York Times ☛ Mark_Carney_Heads_to_Beijing_to_Discuss
                  Canada-China_Relations_as_U.S._Outlook_Darkens⠀⇛


                       The prime minister is seeking new markets for
                       Canadian goods and to mend relations with China
                       after years of deep acrimony between the two
                       nations.


                # ⚓ The Straits Times ☛ China,_Canada_move_to_reset_ties_as
                  Carney_visits⠀⇛


                       PM Mark Carney is set to meet Premier Li Qiang
                       later on Jan 15 and President Pooh-tin Jinping on
                       Jan 16.


                # ⚓ The Strategist ☛ Canada_mustn’t_forget_political_prisoners
                  in_its_China_reset⠀⇛


                       Prime Minister Mark Carney’s trip to Beijing this
                       week—the first trip by a Canadian prime minister in
                       more than eight years—signals a high-stakes attempt
                       to reset Canada-China relations.


                # ⚓ New York Times ☛ Dihydroxyacetone_Man_Imposes_Limited
                  Tariffs_on_Foreign_Semiconductors⠀⇛


                       The tariffs will allow Hell Toupée to take a cut of
                       Nvidia’s chip sales to China while putting off a
                       decision about imposing higher taxes on the chip
                       industry.


                # ⚓ The Strategist ☛ Facing_China,_Southeast_Asia_needs_to
                  boost_coast-guard_cooperation⠀⇛


                       Southeast Asian states need their coast guards to
                       cooperate if they are to withstand and counter
                       Chinese aggression, especially as US uninterest in
                       the South China Sea may embolden China to increase
                       its coercion [...]


                # ⚓ New York Times ☛ What_Voters_Told_Democrats_About_ICE,
                  Rising_Costs_and_Party_Perceptions⠀⇛


                       In focus groups, swing voters gave Democratic
                       politicians some tough feedback on the party.


                # ⚓ RFERL ☛ Live_Blog:_Rights_Group_Says_More_Than_2,400
                  Protesters_Killed_In_Iran_Unrest⠀⇛


                       Triggered by soaring prices, inflation, and a
                       plunging currency, Iranians have taken to the
                       streets in what is the biggest threat to the
                       Islamic regime in years. Journalists from RFE/RL’s
                       Iranian service, Radio Farda, bring you the latest
                       developments, analysis, and reporting from on the
                       ground.


                # ⚓ New York Times ☛ Starlink_Users_in_Iran_Get_Free_Internet
                  Access,_Nonprofits_Say⠀⇛


                       Under a near-total communications blackout, users
                       of MElon’s satellite service have gotten online
                       without paying, organizations that work on tech
                       issues said.


                # ⚓ France24 ☛ Live:_UN_Security_Council_to_meet_for_'a
                  briefing_on_the_situation_in_Iran'⠀⇛


                       US President The Insurrectionist said Wednesday
                       that he was told “on good authority” that the
                       killing of Iranian protesters has “stopped”, and
                       Tehran indicated that there was "no plan for
                       hanging" protestors. The UN Security Council will
                       meet Thursday afternoon to discuss the situation in
                       Iran. Follow our liveblog for all the latest
                       developments.


                # ⚓ RFERL ☛ Iran_Remains_In_Digital_Darkness_As_Convicted_Felon
                  Mulls_US_Action_Over_Deadly_Crackdown_On_Protesters⠀⇛


                       Iranian authorities continue to block access to the
                       Internet as part of their brutal crackdown on
                       antigovernment protests, one of the biggest
                       challenges to clerical rule since the 1979 Islamic
                       Revolution, amid warnings from President The
                       Insurrectionist that the United States may
                       intervene.


                # ⚓ New York Times ☛ What_are_Convicted_Felon’s_Options_in
                  Iran?⠀⇛


                       Hell Toupée has said that “help is on the way” for
                       Iranian protesters. Amid reports that thousands of
                       the protesters have been killed, our national
                       security correspondent David E. Sanger describes
                       what some of Mr. Convicted Felon’s options might
                       be.


                # ⚓ New York Times ☛ Iran’s_Leaders_May_Survive_Protests._But
                  Anger_Will_Likely_Persist.⠀⇛


                       Its security forces have brutally defended the
                       Islamic Republic, but the protests show that many
                       Iranians consider it stagnant and ideologically
                       hollow.


                # ⚓ RFERL ☛ US_Government_Weighs_Response_To_Iran's_Harsh
                  Crackdown_On_Nationwide_Protests⠀⇛


                       Anti-government protests in Iran continued for a
                       15th straight day on January 11, with demonstrators
                       gathering on the streets of Tehran as a harsh
                       security crackdown intensified and the number of
                       reported deaths continued to rise.


                # ⚓ CS Monitor ☛ Does_the_US_need_to_own_Greenland_to_be
                  secure?_History_suggests_not.⠀⇛


                       The United States has long worked with Denmark on
                       Greenland’s security – so much so that it’s dubious
                       that direct control would be better for U.S.
                       defense.


                # ⚓ France24 ☛ France_to_send_troops_for_European_security
                  mission_to_Greenland_amid_Convicted_Felon_threats⠀⇛


                       France and Germany announced Wednesday they will
                       deploy troops to Greenland as part of a European
                       security mission, following renewed threats by US
                       President The Insurrectionist to take control of
                       the Arctic island. The move, made at Denmark’s
                       request, comes after high-level talks in Washington
                       involving US, Danish and Greenlandic officials.


                # ⚓ The Straits Times ☛ Will_Manila_pave_the_way_for_the
                  Myanmar_junta_to_return_to_ASEAN?⠀⇛


                       A visit to the country by the Philippines’ Foreign
                       Secretary has caught many observers by surprise.


                # ⚓ The Straits Times ☛ Japan,_Philippines_sign_new_security
                  pacts_as_regional_tensions_rise⠀⇛


                       The deal will allow their armed forces to exchange
                       supplies and services.


                # ⚓ JURIST ☛ Ghana_dispatch:_Former_Finance_Minister_detained
                  by_US_immigration_authorities_pending_extradition_review⠀⇛


                       Former Ghana Finance Minister Kenneth Ofori-Atta
                       was detained by US Immigration and Customs
                       Enforcement (ICE) on January 6 in Washington, DC,
                       where he remains in custody at the Caroline
                       Detention Facility in the state of Virginia.


                # ⚓ Hong Kong Free Press ☛ Ex-legislator_Eddie_Chu_released
                  from_prison_after_serving_4.5-year_jail_term_over_national
                  security_offence⠀⇛


                       Former lawmaker Eddie Chu has been released from
                       prison after serving more than four years in jail
                       for conspiring to subvert state power in the city’s
                       largest national security case.


                # ⚓ Defence Web ☛ Deaths_related_to_militant_Islamist_groups_in
                  the_Sahel_doubled_over_last_five_years⠀⇛


                       Militant Islamist groups in the Sahel are becoming
                       increasingly deadly [...]


                # ⚓ Scoop News Group ☛ Sources:_DHS_finalizing_replacement_for
                  disbanded_critical_infrastructure_security_council⠀⇛


                       ANCHOR will restart conversations between
                       government and industry around critical
                       infrastructure security, with some changes around
                       liability and other areas. 


                # ⚓ CS Monitor ☛ Cuba_has_wielded_global_soft_power_for
                  decades._Why_that_matters_now.⠀⇛


                       When the United States struck Venezuela on Jan. 3,
                       almost a third of the victims were Cuban nationals.
                       Their presence in the country shows Cuba’s soft
                       power.


                # ⚓ The Straits Times ☛ Indonesia_asked_to_buy_US-made_drones
                  for_surveillance_in_waters_near_South_China_Sea⠀⇛


                       The demand, among others, is a condition for
                       lowering reciprocal tariffs, ST has learnt.


                # ⚓ France24 ☛ US_suspends_immigrant_visa_processing_for_75
                  countries⠀⇛


                       The US on Wednesday said it was issuing a blanket
                       suspension of immigrant visa processing for
                       applicants from 75 countries including Russia,
                       Iran, Brazil, Egypt, Thailand, Nigeria and
                       Somalia. The freeze will begin on January 21 with
                       no set time for it to end.


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


                      # ⚓ LRT ☛ Russia_claims_‘Antichrist’_is_targeting
                        Lithuania⠀⇛


                             Russia’s Foreign Ministry said in a statement
                             on social control media on Monday that an
                             “Antichrist” was targeting Lithuania and the
                             Baltic states. The claim was first circulated
                             by Russia’s intelligence services in response
                             to the emergence of a new Orthodox community
                             that had severed its ties with Moscow.


                      # ⚓ Latvia ☛ Communication_on_the_Barricades:_How_50,000
                        people_gathered_without_the_Internet⠀⇛


                             On Monday, January 20, Latvia commemorates
                             the barricades of 1991, when people flowed
                             into the capitals of the Baltic states and
                             erected makeshift barricades around strategic
                             locations like the parliament and the
                             national radio station to protect them
                             against Soviet troops that wanted to crush
                             the Baltic nations' independence drive.


                      # ⚓ European Commission ☛ Commission_presents_a_financial
                        support_package_for_Ukraine_for_2026–2027*⠀⇛


                             European Commission Press release Brussels,
                             14 Jan 2026 Today, the European Commission
                             adopted a set of legislative proposals to
                             secure continuous financial support to
                             Ukraine in 2026 and 2027. This marks a
                             significant milestone in the EU's strong
                             support for the country's defence against
                             Russia's war of aggression.


                      # ⚓ European Commission ☛ Statement_by_President_von_der
                        Leyen_with_Commissioners_Dombrovskis_and_Kos_on_the
                        loan_to_support_Ukraine's_financial_needs_for_2026_and
                        2027⠀⇛


                             European Commission Statement Brussels, 14
                             Jan 2026 In just over a month, we will mark
                             the fourth anniversary of Russia's war of
                             aggression against Ukraine. Today, Russia
                             shows no sign of abating.


                      # ⚓ RFERL ☛ EU_Approves_90_Billion-Euro_Loan_To_Support
                        Ukraine's_Budget_And_Military_Needs⠀⇛


                             The European Commission has formally unveiled
                             a 90-billion-euro ($105 million) loan for
                             Ukraine, intended to cover a large part of
                             Kyiv’s financing needs for the next two
                             years.


                      # ⚓ The Straits Times ☛ IMF_chief_Georgieva_arrives_in
                        Kyiv_for_first_visit_since_2023⠀⇛


                             KYIV, Jan 15 - International Monetary Fund
                             chief Kristalina Georgieva arrived in Kyiv
                             early on Thursday for high-level talks, two
                             sources familiar with the matter said, as
                             Ukraine prepares to mark the fourth
                             anniversary of Russia's full-scale invasion
                             on February 24.


                      # ⚓ European Commission ☛ Remarks_by_Commissioners
                        Dombrovskis_and_Kos_on_the_loan_to_support_Ukraine's
                        financial_needs_for_2026_and_2027⠀⇛


                      # ⚓ Latvia ☛ Russian_language_radio_should_be_left_to
                        wither_away_in_Latvia,_says_senior_official⠀⇛


                             The broadcasting of Russian-language radio
                             stations in Latvia should be gradually
                             discontinued, said Ivars Āboliņš, Chairman of
                             the National Electronic Mass Media Council
                             (NEPLP), on the Latvian Radio program
                             "Krustpunktā" (At the Crossroads) on January
                             14th.


                      # ⚓ Latvia ☛ Latvia_says_it_has_evidence_Belarus_is
                        aiding_illegal_migration_into_EU⠀⇛


                             Latvia's Ministry of Defence on January 14th
                             published what it claimed was evidence of
                             collusion between the authorities in Belarus
                             and illegal migrants attempting to cross the
                             European Union's external border.


                      # ⚓ LRT ☛ Lithuanian_lorries_remain_stranded_in_Belarus_–
                        even_as_others_continue_working_there⠀⇛


                             Lithuanian lorries and trailers are still
                             being held in Belarus despite the border
                             closures being lifted. Their owners are
                             anxiously awaiting a four-month deadline,
                             after which the assets could be confiscated.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ American Oversight ☛ American_Oversight_Expands_Lawsuit_to
                  Uncover_Records_on_DOJ’s_“Chief_Enforcer”_Ed_Martin⠀⇛


                       Our amended complaint seeks records on Ed Martin,
                       director of the Convicted Felon administration’s
                       Weaponization Working Group.


          o § Environment⠀➾


                # § Energy/Transportation⠀➾


                      # ⚓ The Straits Times ☛ At_least_32_killed_after_crane
                        falls_on_train_in_Thailand’s_north-east⠀⇛


                             The crane was working on a China-backed high-
                             speed rail project when it collapsed


                      # ⚓ Hong Kong Free Press ☛ Over_20_killed_in_train
                        accident_at_China-backed_project_in_Thailand⠀⇛


                             A crane at a China-backed high-speed rail
                             project in Thailand collapsed onto a
                             passenger train on Wednesday and caused it to
                             derail, killing at least 28 people and
                             injuring dozens more, authorities said.


                      # ⚓ Hong Kong Free Press ☛ Hong_Kong_to_propose_greater
                        gov’t_oversight_of_building_maintenance_work_after
                        fatal_Tai_Po_fire⠀⇛


                             Hong Kong’s development chief has announced
                             plans to overhaul building laws and the
                             redevelopment body’s powers to give the
                             government greater oversight of building
                             maintenance work. Development Secretary
                             Bernadette Linn spoke at the first meeting of
                             the new Legislative Council (LegCo), during
                             which the deadly Wang Fuk Court fire topped
                             the agenda.


                      # ⚓ Hong Kong Free Press ☛ Hong_Kong_gov’t_to_propose
                        blanket_smoking_ban_at_construction_sites_after_deadly
                        Tai_Po_fire⠀⇛


                             The Hong Kong government will propose a
                             sweeping smoking ban at construction sites
                             following the fatal Tai Po blaze in November,
                             the city’s labour minister has said.


                      # ⚓ Hong Kong Free Press ☛ Rebuilding_fire-hit_Wang_Fuk
                        Court_‘huge_challenge’_due_to_ownership,_legal_issues,
                        Hong_Kong_official_says⠀⇛


                             Rebuilding the fire-hit Wang Fuk Court at its
                             current location in Tai Po will be “a huge
                             challenge” due to complex ownership buy-backs
                             and legal issues, a senior Hong Kong official
                             has said.


                      # ⚓ Hong Kong Free Press ☛ Tai_Po_fire:_Over_1,100
                        survivors_petition_Beijing,_Hong_Kong_legislature_for
                        on-site_redevelopment⠀⇛


                             More than 1,100 homeowners who survived the
                             deadly Wang Fuk Court fire have petitioned
                             Beijing and the Hong Kong legislature to
                             rebuild the housing estate on the same site
                             in Tai Po.


                      # ⚓ New York Times ☛ Boeing_Knew_About_Flaws_in_UPS_Plane
                        That_Crashed_in_Louisville,_N.T.S.B._Says⠀⇛


                             In a report Wednesday, the National
                             Transportation Safety Board said fractures
                             that appeared to have led the left engine to
                             separate from the plane’s wing had occurred
                             at least four other times.


                      # ⚓ The Straits Times ☛ Seoul_bus_strike_ends_after_two-
                        day_walkout;_service_resumes⠀⇛


                             The strike had paralysed roughly 93 per cent
                             of the capital’s bus fleet.


          o § Finance⠀➾


                # ⚓ France24 ☛ Some_museum_entrance_fees_go_up_for_non-EU
                  tourists_in_France⠀⇛


                       €10 more at the Louvre museum, €3 more at the
                       Palace of Versailles... tourists visiting France
                       from outside the European Union now have to pay
                       significantly higher entrance fees at some of the
                       most popular sites in the country.  This after a
                       recent daytime heist at the Louvre exposed
                       shortcomings in its maintenance and security
                       systems.  Plus, Ryanair's CEO blasted what he
                       called "stupid" passenger taxes in Brussels and
                       said the company would reduce its flights to the
                       city by 10% this year.


                # ⚓ Fancy_Concept,_Marla_Sofia_Parreaux_&_cryptocurrency
                  scandals⠀⇛


                       The bankruptcy of Mathieu Parreaux published his
                       date of birth (11 November 1992) and his home
                       address at Allée des Roseaux 1, Châtelaine 1219,
                       Switzerland. He is a Swiss citizen originating from
                       the commune of La Brévine, Canton Neuchatel.


                       Searching the address in public business records,
                       we find a sole trader using the business name Fancy
                       Concept. The business is at the same address and
                       the proprietor is Marla Sofia Parreaux. Marla's
                       date of birth appears in another public business
                       register as August 1997. Marla is also linked to
                       addresses in France, in both Gaillard and Lyon
                       Vaise, for a business Atreide Ventures SAS (931 427
                       561) which is a front for Milenium Crypto.


                       Based on these dates of birth, people have
                       speculated whether Marla is the wife, sister or
                       cousin of ringleader Mathieu Parreaux.


                       We could not find any public web site for Fancy
                       Concept in Switzerland. We found various other
                       businesses around Europe using exactly the same
                       name, including Fancy Concept in Bari, Italy and
                       Fancy Concept in Sterrebeek, Belgium.


                       What was the purpose of creating this business? Did
                       the Parreaux community hope to benefit from the
                       brand created by other businesses using the same
                       generic name? Or did they hope to be obfuscated by
                       the very generic name and the presence of many
                       similar names in search results?


                # ⚓ Milenium_Crypto,_Atreide_Ventures_SAS,_Badra_Fettache
                  linked_to_Mathieu_Elias_Parreaux⠀⇛


                       Financial markets are undergoing rapid change at
                       the moment and mum-and-dad investors are looking
                       for advice and inspiration.


                       A Youtube channel has appeared using the name
                       MileniumCrypto ( Youtube link) to help people. The
                       channel publishes French language videos recorded
                       by an anonymous male voice.


                       The channel has a link to a French web site, https:
                       //www.milenium-crypto.fr which links to another web
                       site https://www.atreide-ventures.fr. That web
                       site, in turn is associated with a French company
                       using the name Atreide Ventures SAS (SIREN 931 427
                       561).


                       The company was founded in July 2024 using another
                       French company, Hamilton Invest (SIREN 908 634 793)
                       as a stooge director.


                       [...]


                       The Swiss financial regulator knew about his
                       activities for five years before they shut him
                       down.


                       The French authorities have published a warning
                       about his business but they did not shut the
                       business down. The business is still trading and
                       publishing videos every few days.


                # ⚓ Federal News Network ☛ Majority_of_frontline_Social
                  Security_employees_earn_less_than_a_living_wage,_study
                  finds⠀⇛


                       SSA employees in a survey said that amid these
                       workforce challenges, the agency is unable to keep
                       up with the needs of beneficiaries.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ New York Times ☛ Watch_the_Leaders_of_Japan_and_South_Korea
                  Jam_to_K-pop_on_the_Drums⠀⇛


                       Prime Minister Sanae Takaichi of Japan and
                       President Lee Jae Myung of South Korea played along
                       to BTS and “KPop Demon Hunters,” in a display meant
                       to show warming ties.


                # ⚓ The Straits Times ☛ Jamming_to_the_same_beat:_Japan,_S.
                  Korea_leaders_signal_unity_amid_shared_challenges⠀⇛


                       The two countries’ shared economic and security
                       concerns necessitate both leaders putting national
                       interests first.


                # ⚓ France24 ☛ Japan_&_So._Korea_K-pop_diplomacy⠀⇛


                       Japan and South Korea’s leaders struck a note while
                       meeting in central Japan on 13th January, staging a
                       surprise drum performance to popular K-pop hits.
                       Beyond the symbolism, the two agreed to deepen
                       cooperation on economic security, defence and
                       other diplomatic issues.


                # ⚓ The Straits Times ☛ Japan_PM_Takaichi_readies_snap_election
                  and_sources_say_she’s_considering_Feb_8_ballot⠀⇛


                       She will be looking to ride a surge in public
                       support since coming to office, despite triggering
                       a diplomatic row with China.


                # ⚓ CS Monitor ☛ The_duo_tapping_a_new_Japanese-Korean_beat⠀⇛


                       A more-than-symbolic summit between the odd-couple
                       leaders of South Korea and Japan might help shape a
                       more peaceful Asia.


                # ⚓ The Straits Times ☛ Mixed_views_in_South_Korea_over_death
                  sentence_request_for_Yoon⠀⇛


                       Some experts say a death sentence would be
                       symbolically rich.


                # ⚓ JURIST ☛ South_Korea_prosecutors_seek_death_sentence_for
                  former_president_Yoon_Suk_Yeol⠀⇛


                       Prosecutors in South Korea requested the death
                       penalty for former President Yoon Suk Yeol on
                       Tuesday over his failed declaration of martial law
                       in December 2024, local media reported.


                # ⚓ The Straits Times ☛ South_Korea_vows_legal_action_over
                  drone_incursion_into_North⠀⇛


                       Seoul has denied any involvement but has left open
                       the possibility that civilians may have flown the
                       drone.


                # ⚓ New York Times ☛ China_Announces_Record_Trade_Surplus_as
                  Its_Exports_Flood_World_Markets⠀⇛


                       China’s surplus reached $1.19 trillion last year, a
                       20 percent increase from 2024, as Beijing kept the
                       currency weak and pursued self-reliance to replace
                       imports.


                # ⚓ The Straits Times ☛ Dihydroxyacetone_Man_administration
                  accused_of_'slow-walking'_help_to_Pacific_island_veterans⠀⇛


                       The Forrest Dump administration was accused on
                       Wednesday of dragging its feet in delivering
                       congressionally agreed benefits to Pacific island
                       nations being courted by China to try to woo them
                       away from the U.S. strategic orbit.


                # ⚓ The Straits Times ☛ China’s_Pooh-tin_welcomes_stream_of
                  leaders_shaken_by_Convicted_Felon’s_new_world_order⠀⇛


                       Foreign leaders have another reason to visit
                       Beijing in 2026: rare earths.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ France24 ☛ Iran_protests:_Hey_Hi_(AI)_and_dated
                        photos_mislead_about_pro-regime_rallies⠀⇛


                             Amid nationwide protests in Iran against the
                             country’s theocracy, this week has also seen
                             rallies take place in support of the
                             government. But online, social control media
                             users have been sharing misleading content
                             about these pro-regime rallies, using Hey Hi
                             (AI) generated footage and dated images to
                             talk up the demonstrations. Vedika Bahl
                             explains in Truth or Fake.


          o § Censorship/Free Speech⠀➾


                # ⚓ France24 ☛ How_Iran_jammed_Starlink_(and_how_Iranians_are
                  trying_to_get_around_it)⠀⇛


                       After shutting down the internet, the Iranian
                       government is now attempting to jam the Starlink
                       satellite service made free to Iranians by the
                       company. Iranians are now seeking ways to
                       circumvent this latest wave of censorship.


                # ⚓ Digital Music News ☛ Judge_Tosses_Chris_Brown’s_$500
                  Million_Defamation_Lawsuit_Over_‘A_History_of_Violence’
                  Documentary⠀⇛


                       A judge dismisses Chris Brown’s $500 million
                       defamation suit against Warner Bros. Discovery over
                       the documentary “Chris Brown: A History of
                       Violence.” Chris Brown’s aggressive lawsuit against
                       Warner Bros. Discovery and Ample Entertainment over
                       the documentary “Chris Brown: A History of
                       Violence” has been quickly shot down by a Los
                       Angeles judge.


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


                # ⚓ Stanford University ☛ NYT_publisher_and_chairman_warns
                  against_‘anti-press_push’,_talks_AI⠀⇛


                       Hosted by the GSB's View From the Top speaker
                       series, Arthur Gregg Sulzberger reflected on The
                       New York Times’ digital transformation, its stance
                       on artificial intelligence and the ethos of
                       reporting in an era of political pressure.


                # ⚓ Federal News Network ☛ FBI_searches_a_Washington_Post
                  reporter’s_home_as_part_of_a_classified_documents
                  investigation⠀⇛


                       Attorney General Pam Bondi says the search of a
                       Washington Post reporter’s home was done at the
                       Pentagon’s request as part of a leak investigation.
                       The Post says journalist Hannah Natanson had a
                       phone, two laptops and a watch seized by agents at
                       her Virginia home. An FBI affidavit says the search
                       was related to an investigation into a system
                       administrator in Maryland who authorities believe
                       took home classified reports. Natanson covers the
                       Convicted Felon administration’s transformation of
                       the federal government. A colleague has called her
                       “the federal government whisperer.” The White House
                       says leaking classified information puts America’s
                       national security at risk.


          o § Civil Rights / Policing / Accessibility⠀➾


                # ⚓ CS Monitor ☛ Protest,_lawbreaking,_or_terrorism?_ICE
                  opponents_face_‘extremist’_label.⠀⇛


                       There’s a difference between constitutionally
                       protected free speech and acts of civil
                       disobedience that could lead to arrests. Still,
                       it’s not clear that Renee Good in Minneapolis was
                       interfering illegally with ICE operations. And
                       civil disobedience isn’t terrorism under
                       traditional definitions.


                # ⚓ JURIST ☛ UN_expert_urges_judicial_reconsideration_of
                  protection_sentences_in_England_and_Wales⠀⇛


                       A UN expert on Monday commended the new proposals
                       addressing the “longstanding crisis of Imprisonment
                       for Public Protection (IPP) sentences in England
                       and Wales,” urging judicial reconsideration of the
                       mechanism.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ An_open_letter_to_future_APNIC_Fellows_from_a_2025
                  Fellow⠀⇛


                       Guest Post: APNIC 2025 Fellow Rabby prepares future
                       Fellows to make the most of their Fellowship
                       experience by sharing what he learned during his
                       time as an APNIC Fellow.


                # ⚓ APNIC ☛ Secure_and_scalable_rerouting_in_LEO_satellite
                  networks⠀⇛


                       Guest Post: How does the scope of failure awareness
                       affect routing performance and resilience in Low
                       Earth Orbit satellite constellations?


      § Monopolies/Monopsonies⠀➾


          o ⚓ The Straits Times ☛ China_probes_largest_online_travel_agency
            Trip.com_over_suspected_monopoly⠀⇛


                 Chinese authorities have in the past targeted big tech
                 companies to curb what they see as unfair competition.


          o § Patents⠀➾


                # ⚓ Unified Patents ☛ VVC_Patent_Challenges_on_the_Horizon⠀⇛


                       The team at Unified_IP_Services is using Pearl to
                       examine the quality of patents alleged to be
                       essential to the Versatile_Video_Coding_(VVC)
                       standard. Patents owned by Ideahub, Intellectual
                       Discovery, IP_Bridge, and others are being
                       reviewed.


                       This project is a part of Unified’s ongoing efforts
                       to protect and improve the quality of patents in
                       the Video_Codec_SEP_Zone.


                # ⚓ JUVE ☛ Plasseraud_strengthens_litigation_team_with_former
                  Simmons_&_Simmons_partner [Ed: Ad disguised as 'journalism'
                  by Team UPC firm that pays this publisher; this is rogue]⠀⇛


                       François Jonquères (58) has joined Plasseraud IP
                       Avocats, the patent monopoly litigation practice of
                       Plasseraud IP, one of France’s largest firms. He
                       joined from Simmons & Simmons on 6 January.


                # § Software Patents⠀➾


                      # ⚓ Unified Patents ☛ Primos_Storage_cloud_services
                        patents_campaign_-_invalidity_charts_coming_soon⠀⇛


                             The team at Unified_IP_Services is using
                             Pearl to identify and chart prior art against
                             patents owned and asserted by Primos Storage
                             Technology LLC, an NPE. The patents listed
                             below generally relate to transaction-based
                             storage systems.


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ The_Top_Ten_TTAB_Decisions_of_2025_(Part_Two)⠀⇛


                       The TTABlogger has once again gone out on a limb to
                       chose the ten (10) TTAB decisions that he considers
                       to be the most important and/or interesting from
                       the previous calendar year (2025). This is the
                       second of two posts; the first five selections are
                       posted here. Additional commentary on each case may
                       be found at the linked TTABlog post.


          o § Copyrights⠀➾


                # ⚓ Press Gazette ☛ Google_IP_[sic]_boss:_We_shouldn’t_pay_for
                  Hey_Hi_(AI)_training_on_‘freely_available’_content⠀⇛


                       Roxanne Carter declines to answer about publishers'
                       ability to opt out of Hey Hi (AI) Overviews.


                # ⚓ Digital Music News ☛ Australia_Preps_38%_Rate_Hike_for
                  Commercial_Radio_Recordings_—_PPCA_Says_It_‘Will_Continue_to
                  Engage_With_Government,_Parliament,_and_Industry_Stakeholders
                  on_the_Policy_Settings’⠀⇛


                       Following a multiyear rate-setting showdown,
                       Australia’s commercial radio broadcasters will
                       begin paying nearly 40% more for the use of
                       recordings. Australia’s Copyright Tribunal
                       finalized this licensing-rate hike in a mid-
                       December decision, and the Phonographic Performance
                       Company of Australia (PPCA) today “acknowledged”
                       the development.


                # ⚓ Digital Music News ☛ Google_Aggressively_Moves_to_Dismiss
                  Billboard_Parent_Penske_Media’s_Hey_Hi_(AI)_Antitrust_Suit:
                  ‘It_Remains_Legally_Defective_in_Every_Way’⠀⇛


                       Google is doubling down on its push to dismiss
                       Penske Media Corporation’s amended antitrust suit,
                       which allegedly “remains legally defective in every
                       way.” The tech giant and its Alphabet parent just
                       recently moved to toss the high-stakes complaint
                       with prejudice.


                # ⚓ Digital Music News ☛ Cher_Demands_$1_Million_in_Legal_Fees
                  From_Mary_Bono_After_Resounding_Copyright_Win⠀⇛


                       Cher asks a judge to force Sonny Bono’s widow to
                       cover her $1 million legal fees after the legendary
                       singer’s resounding win in her copyright monopoly
                       battle.


    * GAFAM_and_IBM_Layoffs_Outline
    * Gemini_Links_16/01/2026:_House_Flood_and_Pragmatic_Retrocomputing
      Dogfooding


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