𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, September 01, 2022
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Generated Fri 2 Sep 02:43:17 BST 2022
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/2022/09/01/


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

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QmY8oB1Qg87HBxwHopNxS6LMozLiwmSxad31Ttse73Fh2q
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QmZeoDeQynAEb5Yhp8urADxooTvcjp93jYM7aoGTReoxAm
QmUR5BqkVtBjeM3RbDysVaCrQyP93xoRwDKU5C1u5XZdyR
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QmcZN6RDP7J7Dk8c2QYXeoVfYifxDsaK62EM44gSje2HDr


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

⦿ The Fall of Ubuntu (Other GNU/Linux Distros Rising) | Techrights

⦿ IRC Proceedings: Wednesday, August 31, 2022 | Techrights

⦿ The Linux Foundation Has Formally Changed Its Mission! (Based on IRS Files) | Techrights

⦿ Linux Foundation’s New Cybersecurity Report Made Using Proprietary Software for Microsoft Partners Under the Guise of ’Research’ | Techrights

⦿ [Meme] Squeezing the Brand (Linux Mark) | Techrights

⦿ The Propaganda Mill of EPO.org Pushes Illegal, Unconstitutional UPC (’Fake It Till You Make It’) Ahead of Further Perils | Techrights

⦿ Going Live With Tux Machines’ Holistic Front Page | Techrights

⦿ [Meme] The Limits of Lobbying and Lying | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/09/01/fall-of-ubuntu/#comments
		http://techrights.org/2022/09/01/irc-log-310822/#comments
		http://techrights.org/2022/09/01/linux-foundation-mission-creep/#comments
		http://techrights.org/2022/09/01/proprietary-software-cybersecurity-report/#comments
		http://techrights.org/2022/09/01/squeezing-linus-and-linux/#comments
		http://techrights.org/2022/09/01/tanned-propaganda/#comments
		http://techrights.org/2022/09/01/tux-machines-front-page/#comments
		http://techrights.org/2022/09/01/upc-blahblah/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/09/01/microsoft-burned-by-systemd/#comments
		http://techrights.org/2022/09/01/obs-studio-28-0/#comments
		http://techrights.org/2022/09/01/ubuntu-20-04-5-lts/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 70

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/01/fall-of-ubuntu/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/01/fall-of-ubuntu/

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Gemini_version_available_♊︎


✐ The_Fall_of_Ubuntu_(Other_GNU/Linux_Distros_Rising)⠀✐


Posted in GNU/Linux, Ubuntu at 8:01 pm by Dr. Roy Schestowitz


Recent: Moving_From_Ubuntu_to_Another_GNU/Linux_Distro_Would_Harm_Microsoft_(or
Its_Efforts_to_Control_the_Competition)


            🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇SteamOS_is_Arch-based_now_as_well⦈_
           Top of this list used to be particular versions of Ubuntu


Summary: GNU/Linux_“market_share”_in_Steam grew by a quarter this past year,
boosted by SteamOS perhaps, but watch the trends in distributions; even the
Ubuntu-based distros aren’t near the top (and SteamOS moved from Debian to
Arch, so expect Ubuntu to stagnate further)


⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡄⠀⣤⣤⣤⡄⠀⠀
⡇⠀⠀⡀⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⠀⠉⠩⣍⣩⣩⣍⣉⢭⡍⣭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣭⣩⣍⠉⣩⣭⣭⡉⠉⢹
⡇⠀⠀⠁⠘⠑⠃⠉⠐⠈⠑⠘⠑⠈⠛⠈⠈⠃⠋⠈⠈⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣤⣀⣄⣀⣤⣀⣠⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣀⠀⣀⣀⣀⡀⠀⢸
⡇⠀⠀⠂⡲⠔⠄⡶⡲⠠⠦⢶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣥⣭⢤⣥⣬⡤⢥⡬⣤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣥⣥⡤⠤⣤⣤⣤⡤⠤⠼
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣛⣛⣛⣛⣛⡓⢛⡓⣛⢚⡓⠒⠒⠒⠒⠒⠒⠒⠒⠒⣛⣛⡓⠒⢚⣛⣛⠓⠒⠒
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⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉⠁⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 126

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/01/irc-log-310822/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/01/irc-log-310822/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Wednesday,_August_31,_2022⠀✐


Posted in IRC_Logs at 2:40 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-310822.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-310822.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-310822.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-310822.gmi
Over HTTP:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 QmV43xPgHUWBWYLC7oermonPN7jjy2ATdbAgMykYXKbH7C #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmQcm1sxhehE2pD9pNVu7PmE4AQ3HUqJjaSzZ195jAabcJ (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmRAYpiviZ9o3oNBJuyyV6mM4okqb5fNA4M87Ph8nm6LB7 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmRCei4ztSsv7Hbqw23CffzcaToZqnjd2JLvfCnzg6mNWA social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 Qmeif4MZfQfKtjDkNa9m5136JqueCfED9Rwuof5zjgGV9C #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmTRdENkzoUsVFm7tkzeY9H9MfEvUzfaByPvpF1a29Qw2m (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmVVMAScbYns4rd8BKRxoN6RbyRvupzPTriEopkPsAFqog #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmWUkrBSKrNiSt1rXpUkaTEiQzLoUSQPTdpgWFVdctNpaU (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmcZN6RDP7J7Dk8c2QYXeoVfYifxDsaK62EM44gSje2HDr



                    ䷩ 𝚕𝚒𝚗𝚎 253

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/01/linux-foundation-mission-creep/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/01/linux-foundation-mission-creep/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_Linux_Foundation_Has_Formally_Changed_Its_Mission!_(Based_on_IRS_Files)⠀✐


Posted in Kernel at 6:08 am by Dr. Roy Schestowitz


Summary: Rather than stick to its mission, which defines the name of the
institution, we’ve witnessed an expansion to promotion of Microsoft GitHub and
non-technical things that have nothing to do with Linux (this enables grifting,
openwashing etc.)


LATELY we have been digging into this informal_copy of the Linux_Foundation IRS
files, which the IRS appears to be suppressing (we wrote about this many times
before). Jim Zemlin signed the 2019 IRS form in 2020 (November 12th to be
precise) and yet the_IRS_isn't_releasing_the_PDF_yet. What’s going on? It has
been nearly 2 years already. This is not normal!


“Is this a legitimate way to raise money?”Looking at this suppressed document,
we find that in less than five years the ‘Linux’ Foundation almost doubled the
number of board seats. This might sound OK until people realise those seats are
for sale (the Foundation itself admits as such, as we showed earlier_this_year
and in_2020). Imagine if SCOTUS added more Justices… only for corporations that
pay to plant their “Justice” (or even up to two per corporation). Since then
Microsoft has bought two seats, not just one. Is this a legitimate way to raise
money?


“Between 2018 and 2019 the non-salaries expenses of the ‘Linux’ Foundation went
up by a stunning 20%.”As we noted the other day, there are Linux_Foundation
layoffs while operating_costs_go_up_considerably_for_no_good_reason. It’s
costly_showoff_and_graft. 2-3 years ago the “Linux” Foundation had already
stockpiled about $60,000,000 in the bank, just sitting there. Nevertheless they
decided to effectively kill Linux.com by firing all the workers there.
“Salaries, other compensation, employee benefits” in the Linux Foundation
increase by about 10% per year. Imagine inflation going up at this pace every
year. This isn’t about Linux but about people who don’t even use Linux helping
themselves to the bank account, just like in the_corrupt_EPO. It’s a familiar
pattern; they just use the name/brand and the good (past) reputation, not to
mention goodwill of communities (volunteers). They monetise their own harm.


Between 2018 and 2019 the non-salaries expenses of the ‘Linux’ Foundation went
up by a stunning 20%. That’s aside from sky-rocketing salaries the managers
deposited in their bank accounts. Remember: they don’t even use Linux.


Last but not least, they’ve changed the mission of the Foundation. Here’s when
and how:


⚓  2015⠀⇛


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Foundation's_mission_in_2015⦈_


⚓  2016⠀⇛


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Foundation's_mission_in_2016⦈_


⚓  2017⠀⇛


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Foundation's_mission_in_2017⦈_


⚓  2018⠀⇛


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Foundation's_mission_in_2018⦈_


⚓  2019⠀⇛


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Foundation's_mission_in_2019⦈_


Who knows what it says now. The IRS releases copies for nothing_later_than_the
2008_forms! █


⡶⣶⠶⡶⡶⢶⢶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⠶⣶
⡗⠒⠓⠓⠓⠚⢲⡗⠾⠾⠿⠿⠿⠿⢿⠿⢻⠻⠿⠿⠿⠿⠿⡟⠿⠿⢿⠿⢿⡟⠿⠿⠿⠿⠿⡻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣾⣶⣿
⣧⣤⣤⣤⣤⣤⣼⡷⡶⠾⡶⡶⡶⠾⠾⠶⠾⡾⢶⠶⠾⡾⠶⢷⢶⠾⠾⠶⠾⢶⠶⡾⠶⠶⠾⡷⠶⢶⠶⠶⠷⡾⢿⢿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿
⣿⢻⣿⣿⢛⡛⡛⢳⠓⣲⠓⡓⢳⢒⢳⠒⠓⣓⡟⠒⡒⣒⣲⠚⠚⡟⡖⣾⣶⣾⣾⣿⣾⣷⣷⣷⣷⣾⣶⣿⣾⣷⣾⣾⣷⣷⣷⣶⣿⣾⣿⣾⣿⣾⣿⣾⣿⣾⣿⣾⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣟⣟⢛⣟⢻⡛⡻⡟⢻⡟⢻⣿⣻⢻⢟⢻⢛⡛⡟⣻⡛⣛⡛⣿⣛⠟⡛⢛⢛⣻⠛⣟⣛⢿⣻⣿⣻⢻⣻⣻⣻⣻⢛⣛⣟⡻⢛⠛⣿⣟⡟⡿⣟⢻⣻⣿⢟⣻⣛⣻⣻⣿⢛⢟⣛⣿⢿⡛⣟⣟⡿⣿⣿⣿⣿⣿⣿⣿
⡧⡭⠥⢤⠧⠬⠼⠼⠬⡧⠬⡬⡥⠤⢯⠾⡿⢽⣼⠥⠯⡦⡥⢤⠥⢾⣤⣽⣯⣬⣽⣴⣧⣼⣽⣾⣼⣧⣬⣽⣽⣼⣥⣽⣾⣤⣯⣧⣷⣥⣼⣮⣾⣤⣥⣾⣥⣼⣤⣧⣤⣬⣿⣤⣧⣽⣾⣽⣤⣭⣧⣭⣷⣬⣼⣿⣿⣿
⣧⣬⣤⣬⣤⣤⣤⣤⣤⣥⣤⣭⣭⣬⣬⣤⣤⣤⣬⣤⣤⣥⣤⣤⣬⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⣒⣒⣒⣒⣲⡖⣒⣶⡒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⠒⣖⠖⣶
⠀⠀⠀⠀⠀⠄⣶⣀⣀⣂⣐⣐⣐⣀⣆⣰⣠⣀⣂⣐⣀⣰⣀⣐⣔⣀⣐⣂⣒⣀⣂⣀⣂⣀⣀⣐⣀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⠿⠿⠿⠿⠿⠿⠿⠉⠝⠋⠟⠍⠛⠋⠛⠛⠏⠹⠛⠍⠙⠋⠟⠟⠛⠉⠛⠛⠟⠟⠛⠛⠟⠛⠛⠻⠫⠻⠟⠏⠛⠏⠛⠹⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠟⠿⠟⠿⠟⠿⠟⠿⠟⠿⠿⠀⠿⣿
⠿⡿⡿⣧⠦⡴⢾⠴⡦⡴⠼⡶⣼⡴⢶⠤⣦⠤⢴⣤⡾⢴⢤⣼⠴⡿⢿⢿⠿⡿⣿⣿⡿⣿⠿⠿⠿⢿⡿⣿⣿⡿⣿⡿⠿⡿⣿⠿⣿⠿⣿⢿⣿⣿⣿⡿⢿⢿⠿⢿⢿⣿⠿⡿⣿⢿⣿⣿⠿⣿⡿⠿⠿⣿⢿⢿⣿⣿
⣟⣲⡳⣒⡲⣚⣲⢖⡟⣚⣻⡒⢓⣚⢖⣺⣖⡚⡗⣒⣓⡲⣻⣒⢒⣓⣖⡓⢲⡞⣖⣲⢗⣖⣻⢳⠞⡻⢖⢚⢖⣖⡓⣚⢲⣚⣒⡒⢾⡗⢶⡚⣗⡒⠒⣗⡖⡾⣿⡓⣒⣞⢗⣖⣺⣒⠒⡖⣳⡗⣚⡚⣓⣗⢶⣾⣿⣿
⣂⣁⣒⣀⣀⣃⣀⣘⣀⣁⣀⣐⣂⣋⣈⣀⣘⣀⣀⣃⣒⣃⣂⣃⣐⣀⣃⣁⣁⣀⣐⣀⣀⣒⣐⣀⣁⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⣩⣫⣙⣍⣉⣏⣉⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡛⣛⣍⣿
⠀⠀⠀⠀⠀⠂⣶⣀⣀⣀⣀⣀⣀⣀⣆⣰⣠⣀⣂⣀⣀⣰⣀⣀⣄⣀⣀⣂⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⡫⡟⣋⣟⣍⡻⡛⢛⣛⣋⣙⣛⡋⢛⡛⣟⣟⠛⠛⣛⡛⣛⣟⡛⠛⣟⡛⣛⢻⣛⢻⣛⣏⡛⣏⢛⣹⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣿⡿⣿⣿⠠⣿⣿
⣏⣻⣿⣧⣭⣥⣽⣭⣭⣿⣬⣥⣬⣭⣭⣩⣭⣭⣭⣭⣬⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠧⠧⠤⠬⠴⢤⡤⠤⢬⠤⡤⢬⢧⢤⠤⢤⡴⠦⠶⠥⠦⢦⡬⡤⠤⠬⣧⠴⠤⢥⠴⠤⠬⡤⢬⡬⠤⠤⢼⠤⣬⠬⠦⠧⠴⠴⢤⡴⠦⢤⡼⠤⡧⡬⡤⠦⠤⢬⡼⠦⡬⡭⠴⣭⠿⡤⠤⠧⠵⣤⢯⠤⠦⠭⣭⣿⣿
⠤⠂⠇⠨⠂⠰⠀⠉⠨⠔⠰⠟⠖⠓⠲⠑⠢⠁⠀⠀⠐⠲⠐⠃⠀⠤⠂⠚⠰⠀⠏⠑⠱⠅⠂⠠⠕⠀⠛⠀⠆⠚⠉⠂⠴⠀⠢⠓⠋⠺⠜⠐⠶⠷⠿⠾⠾⠶⠿⠿⠶⠷⠶⠾⠾⠷⠿⠷⠶⠶⠿⠾⠷⠷⠿⠿⠿⣿
⠠⠤⢤⢀⠄⣤⠀⡠⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠤⠤⡄⣤
⠉⠉⠉⠉⠉⠉⣭⠉⠉⠩⠉⠩⠉⢭⠍⢩⢉⡍⠭⠍⠍⢩⠩⠩⠭⠍⢩⠍⠩⠉⠍⠍⠉⠉⠉⠩⠉⠍⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⣶⣶⣶⣶⣶⣶⣿⢿⠿⠿⡿⡿⠿⠿⠿⠿⣿⠿⠶⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⡿⠿⢿⠿⢿⠿⠿⠿⡟⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢻⣿⣿
⡟⣿⣿⡏⣛⣋⢻⠛⣛⣛⠛⡗⡛⡟⡚⡛⣛⠛⠛⡛⢻⣛⣻⢛⡟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿
⣛⠛⡿⢛⣛⣻⣛⡻⡛⢟⣛⠻⡛⡟⢛⣛⢛⣛⢻⣿⡛⣟⣟⢛⣟⠻⡛⡿⣻⢛⠛⣿⡛⣻⡛⠛⣛⣛⢛⢻⠛⡻⣛⠟⡟⡻⠟⣟⢻⡟⣛⢻⢛⣟⢛⢟⣻⠛⣛⢻⡛⣛⣛⣻⢟⢿⣛⡻⡟⣻⡟⠟⢛⢟⢛⡻⣿⣿
⠬⢤⠤⠧⠵⠴⠼⡤⡵⠬⢥⠤⠿⢴⠾⠬⠼⢷⠥⢬⠤⠿⢤⠥⢤⠦⠥⣿⡤⢴⡧⠤⡤⢥⡴⠦⢥⡥⠦⠬⡤⠧⡤⠼⢤⠥⠦⢬⠤⠧⡴⠭⡤⠤⠼⠮⠤⢦⠦⠤⡤⡽⠧⢴⠬⠥⢬⣼⠤⠥⠴⠮⠴⡼⠤⢶⣽⣿
⢒⠲⡲⠒⡖⡒⡲⣓⠒⢒⣓⣒⢓⣶⣖⢲⣖⡚⡲⡛⢒⡓⢛⣲⢖⣓⣒⣚⡒⢒⣖⢒⣖⣚⠗⡒⢚⣲⣷⣶⣿⣶⣶⣶⣶⣷⣶⣾⣾⣶⣷⣷⣷⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⣾⣷⣶⣿⣶⣷⣶⣷⣶⣶⣷⣶⣾⣿⣿
⣿⡛⣛⡟⢛⡟⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⠻⢻
⣿⠀⠀⠀⠀⠀⢰⣶⣀⣀⣀⣀⣀⣠⣠⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⣿⠿⠿⠿⠿⠿⠿⠿⠉⠛⠹⠹⠉⠍⠙⠉⠍⠟⠋⠛⠉⠏⠋⠉⠛⠛⠛⠻⠉⠻⠉⠛⠻⠩⠻⠹⠉⠹⠍⠉⠉⠿⠿⠿⠿⠟⠿⠟⠿⠟⠿⠿⠿⠿⠿⠿⠿⠻⠿⠻⠿⠻⠿⠿⠿⠿⠿⠿⠿⠤⠿⠿⠿⠿⠿⠿⠿⢿
⣿⢯⠿⢿⠶⠶⡦⠶⡶⠶⠶⠷⣾⡶⡴⠶⠶⠶⠶⠷⡶⡶⠶⠿⠿⠿⣿⠿⡿⠿⠿⣿⠿⠿⢿⢿⠿⠿⣿⠿⢿⢿⠿⡿⠿⠿⠿⠿⠿⠿⢿⢿⡿⢿⠿⠿⠿⠿⡿⠿⠿⠿⠿⢿⠿⠿⡿⠿⠿⠿⠿⠿⡿⢿⣿⣿⣿⣿
⣿⣀⣆⣔⣂⣂⣙⣲⣐⣀⣚⣁⣐⣗⣦⣛⣂⣆⣖⣁⣂⣱⣶⣐⣊⣂⣊⣖⣓⣐⣘⣂⣐⣄⣢⣒⣰⣐⣪⣂⣐⣒⣒⣷⣰⣀⣂⣘⣁⣒⣸⣄⣏⣲⣒⣒⣐⣒⣟⣒⣖⣒⣂⣚⣐⣰⣁⣊⣰⣔⣐⣹⣒⣘⣛⣉⣿⣿
⣿⠒⠲⠒⠒⠒⠳⠲⠒⠛⠖⠒⠓⠚⠳⠲⠒⠒⠶⠒⠒⠚⠖⠒⠓⠗⠒⠒⠒⠶⠒⠟⠓⠚⠖⠒⠲⠷⠷⠶⠶⠾⠾⠶⠷⠶⠶⠶⠷⠶⠿⠶⠿⠷⠶⠷⠶⠷⠶⠶⠾⠾⠷⠶⠶⠿⠶⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⢿

                    ䷩ 𝚕𝚒𝚗𝚎 385

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/01/proprietary-software-cybersecurity-report/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/01/proprietary-software-cybersecurity-report/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Linux_Foundation’s_New_Cybersecurity_Report_Made_Using_Proprietary_Software
for_Microsoft_Partners_Under_the_Guise_of_‘Research’⠀✐


Posted in Deception, FUD, Security at 5:20 pm by Dr. Roy Schestowitz


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


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Addressing_Cybersecurity_Challenges_in_Open_Source_Software:
What_you_need_to_know_-_proprietary_software⦈_


Summary: The Linux_Foundation rejects “Open Source”; and judging by its
liaison, it’s interested in pushing Microsoft talking points (it’s paid to do
this), instead of defending Free software/Open Source from such talking points


⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣩⣹⣳⣿⣯⣉⣝⣈⣿⣇⣘⣽⣏⣙⣹⣫⣙⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⣿⣟⢻⣿⣿⣿⢿⡿⠿⣿⣿⣿⢿⣿⡿⢿⣿⢿⢿⣿⠿⣿⡿⢿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣿⣿⣾⣿⣿⣷⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣽⣿⣼⣿⣿⣿⣽⣿⣽⣧⣿⣿⣿⣿⣽⣿⣥⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⣽⣼⣿⣿⣿⣽⣿⣯⣿⣿⣯⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣯⣿⣯⣯⣯⣿⣿⣿⣻⣿⣿⣭⣿⣿⣿⣿
⣿⡿⢿⡟⣻⣿⣿⢻⣿⢻⣿⡟⢿⣿⠻⡟⢻⣿⣿⡟⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⢻⡻⢿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣿⠛⣿⣿⠛⣿⣿⢛⣿⣿⢿⣿⣟⣻⣿⢻⣿⢿⡟⢻⣿⡿⢻⡿⣿⠛⣿⣿⢿⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⡀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⡀⢀⢀⣀⠀⡀⡄⠀⣠⢀⣀⢠⢄⢠⣠⣀⡀⣀⠠⣀⡀⠀⢀⠀⠀⠀⡄⣄⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣅⣄⢄⡤⡤⠀⣅⢠⡄⠄⢄⡤⡤⡄⠌⡄⠀⠀⠀⠁⠀⠀⠀⠀⠈⠈⠀⠁⠁⠁⠀⠁⠉⠁⠈⠀⠀⠁⠁⠀⠁⠁⠈⠈⠈⠈⠈⠁⠉⠉⠀⠀⠀⠀⠁⠁⠈⠈⠀⠀⠉⠉⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠈⠀⠁⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣟⢛⣿⣿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⣀⣀⣀⡀⠀⢸⣿⣿⣸⣷⣶⣇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⢾⣿⣿⣿⣿⣿⡇⠀⢸⣿⡇⢸⣿⣿⠁⢸⡇⠈⢻⠀⣿⠀⣿⡇⢸⣧⡀⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⡇⠘⠛⢻⠀⢸⡇⢰⡄⠀⣿⡀⠹⠃⢸⡿⠁⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⠿⠿⠿⢿⡿⠇⠀⢸⣿⣗⣒⢖⡺⣷⣾⡗⢾⢻⣒⣿⣟⣖⣚⡛⢗⣺⡟⣶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣸⣇⣀⣀⣸⣿⣷⣾⣝⣻⣟⣟⣇⣯⣸⣛⣿⣼⣼⣿⣇⣜⣟⣇⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣭⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣯⣾⣯⣦⣤⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⣖⣤⣄⡄⣠⡄⣖⣤⣤⠄⠤⣄⣤⣴⣤⡄⡶⡤⡤⢢⢤⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡶⠆⣆⣶⣶⢰⡀⡦⡆⢠⣢⢲⠂⣶⣒⣴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢠⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⠹⣧⠀⣴⡟⢺⣿⢠⣾⠓⣿⡇⢸⡷⠛⢰⣞⣻⣦⢰⣟⣛⡃⢰⣟⣛⠂⢸⡇⢸⡷⠛⣷⠀⣾⠛⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠼⠟⠛⠻⠇⠹⠧⠼⠿⠈⠿⠤⠿⠇⠸⠇⠀⠘⠧⠤⠶⠰⠬⠽⠇⠰⠬⠽⠇⠸⠇⠸⠇⠀⠿⠀⠻⠶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢿⡄⣾⠃⣿⡗⢻⣦⢠⣞⣛⣶⠀⣿⠞⠃⣾⣛⡛⢀⣾⣛⣷⡄⣴⠟⠛⠀⣿⠀⣿⡇⢸⡷⠛⢸⣧⠘⣿⠛⠘⣷⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠿⠦⠶⠀⠈⣿⠏⠀⠿⠷⠼⠏⠘⠷⠤⠴⠀⠿⠀⠀⠦⠭⠿⠈⠻⠤⠴⠀⠻⠦⠴⠀⠿⠶⠿⠇⠸⠇⠀⠸⠏⠀⠿⠶⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⡟⢻⡆⢘⣛⣻⣦⠀⣿⠀⣿⠀⣴⣟⣻⡆⢸⡷⠛⣷⠀⣾⠛⢾⡇⢰⣟⣛⣦⠰⣿⣛⡃⠀⠀⠀⣿⠀⣿⡞⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⠶⠶⠀⠿⠇⠸⠇⠸⠧⠼⠿⠀⠿⠀⠿⠀⠹⠧⠤⠆⠸⠇⠀⠿⠀⠻⠶⣻⡇⠘⠷⠤⠶⠰⠦⠽⠇⠀⠀⠀⠿⠀⠿⠇⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠀⢸⣿⠀⣿⠛⢿⡄⣴⣟⣻⡆⢸⣿⠛⣷⠀⠀⠀⠸⠷⣦⣄⢠⣾⠛⣷⡄⣿⡇⢸⡇⢸⣿⠛⢣⣾⠛⠃⢰⣟⣛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⠶⠾⠋⠀⣿⠶⠾⠃⠙⠧⠴⠆⠸⠿⠀⠿⠀⠀⠀⠰⠶⠾⠟⠈⠻⠶⠟⠁⠻⠷⠾⠇⠸⠿⠀⠈⠻⠶⠆⠘⠷⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⢤⡄⠀⠀⠀⠀⠀⢠⡴⠆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠷⢶⣤⠀⣾⠛⢻⡆⢻⡟⠛⣿⡟⠃⢿⣄⣿⣄⣿⠀⣛⣿⣷⠀⣿⡟⠛⣴⣟⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⠶⠶⠟⠀⠻⠶⠾⠃⠸⠇⠀⠹⠷⠆⠸⠿⠁⠿⠇⠀⠿⠴⠿⠀⠿⠇⠀⠙⠷⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠛⠛⠛⢻⡇⠀⠀⠀⡀⡀⢀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠘⠛⠁⢰⠀⠀⢀⣀⢀⡀⣀⢀⡀⢀⢠⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣶⠀⠀⠀⢸⡇⠸⣄⠀⠇⡟⠾⠸⡠⠇⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣇⣀⠀⡁⣸⠀⠀⡻⣮⢸⡏⢹⠈⢧⡞⢸⡗⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠿⠶⠶⠆⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠸⠤⠇⡿⠀⠀⠉⠁⠈⠁⠈⠠⠜⠁⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⢻⡄⢀⡶⠲⣿⠀⡴⠲⣼⠀⣶⠴⢠⡖⢲⡄⢰⡒⠦⠠⡖⠲⠀⣶⠀⡦⠒⣦⠀⡴⠒⢴⠀⠀⣼⠋⠉⠓⠐⣆⠀⡖⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠗⠚⠷⠈⠷⠤⠿⠀⠷⠤⠾⠀⠿⠀⠘⠧⠭⠀⠠⠭⠷⠀⠬⠽⠂⠿⠀⠇⠀⠸⠀⠷⠤⢺⠀⠀⠘⠦⠤⠖⠀⠘⡎⠁⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⣤⣀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢼⡁⠀⠉⠀⣿⠉⢻⠀⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣈⣈⣁⣀⣀⣁⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣈⣁⣁⣈⣀⣁⣈⡀⠀⠀
⠀⠈⠓⠒⠋⠀⠛⠀⠘⠀⠙⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⢠⡖⠦⠀⢀⣀⡀⢀⣾⡃⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⢈⡙⢲⡄⣿⠀⣹⠀⣿⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠈⠉⠉⠀⠈⠉⠁⠀⠉⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠘⠘⠁⠉⠀⠘⠁⠘⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀
⠀⢠⢀⠀⠀⠀⢀⠄⢠⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠈⠀⠁⠀⠈⠀⠁⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢀⠀⠀⠀⡀⡤⢠⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢀⠤⣄⢀⠤⣼⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠹⣀⡤⠣⣀⡼⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 532

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/01/squeezing-linus-and-linux/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/01/squeezing-linus-and-linux/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Squeezing_the_Brand_(Linux_Mark)⠀✐


Posted in Deception, Kernel at 6:31 am by Dr. Roy Schestowitz


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


Summary: The brand “Linux” is under attack, just like its community and its
leadership; the Linux_Foundation actively serves_foes_of_Linux, which casually
badmouth “Linux” (even_this_week)


⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣿⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⡿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠘⢹⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⣶⣶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⣰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣦
⠈⣿⣶⣷⣶⡟⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠠⣶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⡆⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⡏⢀⣿⣿⣿⡿⠋⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⣀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠄⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡈⠙⢻⠟⠂⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠈⠀⠀⡀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠈⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠲⠾⣿⣿⣿⣿⣷⣴⠃⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⠀⠈⣷⢰⠿⢻⠛⠓⠑⡄⡄⠂⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠰⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣭⣿⡿⠿⠦⠧⠥⡌⣧⣿⣿⣝⣀⣁⣈⢂⣀⢘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⡐⠀⠀⢀⣭⣏⠩⠋⢹⠛⠙⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣧⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠛⣿⣿⣿⣄⢸⠇⢸⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠏⠀⠀⢀⠀⢸⣿⣿⣿⡷⠄⢸⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡾⠀⢀⢸⣗⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡀⢤⣁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⣾⢸⣿⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⣆⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣧⣼⣿⣼⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣶⠀⣶⡄⣿⡆⠀⠀⠀⠀⣀⠐⣹⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠛⢿⡟⢻⣿⢻⣿⠘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣛⠋⢀⡤⢸⣿⠼⣿⠇⣿⡇⠀⠀⢀⣴⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢉⡄⢸⡇⠀⣿⠁⢹⣶⢹⣿⠻⣿⡏⢻⣿⢿⣿⠻⠏⠉⠟⢀⠀⠀⠈⠃⠈⠛⠀⢿⠀⢈⠁⠀⠀⠸⣿⣿⣧⣿⣿⠁⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠁⢸⡟⠀⣾⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢰⣿⠃⣿⡆⢠⣧⠀⢸⡀⠀⣅⠀⢸⡇⠀⣷⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣽⣿⠇⠀⠀⣸⡇⢰⣿⠀⣼⡇⢀⣿⠀⣸⣿⣶⣿⣷⣼⣿⣤⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⣇⠀⣿⠀⢸⣇⠀⢿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⠀⣀⣀⣰⣿⣿⠀⠀⣈⣿⣁⣸⣟⠀⣿⣧⣸⣿⣤⣿⣇⣙⣿⣴⣿⣿⣉⣿⣇⣼⣿⣀⣿⣇⣀⣿⢀⣸⣿⣆⣿⣇⣸⣿⣀⣸⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⣄⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⡿⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠘⢱⣵⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠿⣷⣶⣶⣶⠒⠚⠑⠀⠒⣶⣶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⣰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣆
⠈⣿⣶⣷⣶⠟⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠆⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⡏⠀⣿⣿⣿⡿⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠂⠀⠀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⡇⠀⣶⡆⢸⣿⣿⡈⠉⠙⠛⠁⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⢀⠀⡃⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠿⣿⣿⣿⣿⣷⣴⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⠄⠀⠀⢠⠀⠈⣷⠰⢿⠻⢛⣓⢽⡏⡍⠃⣿⣿⣿⣿⠟⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣿⣿⡿⠿⠂⠧⠥⡌⣧⣛⣫⣝⣀⣀⣀⣾⣶⣿⣷⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⣀⠀⠀⠀⠀⠀⠀⡦⠄⢀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠛⣿⣿⣿⣄⢸⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣷⠀⠀⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⠀⠀⠀⠠⠀⢸⣿⣿⣿⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡾⠀⢀⢸⢧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⣿⠀⠀⠀⠀⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡾⢸⣿⢹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢰⡿⠀⠀⠀⣄⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣴⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣧⣼⣿⣼⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣦⠀⣶⡄⣿⡆⠀⠀⠀⠀⣀⠐⣹⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠛⢿⡟⢻⣿⢻⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⡤⢸⣿⠳⣿⠇⢿⡇⠀⠀⢀⣴⣿⡀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢉⡄⢸⡇⠀⣿⠋⢻⡶⢿⣿⠻⣿⡏⢹⣿⢿⣿⣻⡏⡿⠿⣀⠀⠀⡞⠃⠸⠿⠀⡟⠀⠈⠀⠀⡀⠸⣿⣿⣧⣿⣿⠁⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠁⢸⡏⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠀⣿⡏⢹⣿⠃⣿⡆⢰⣧⠀⢸⡀⠀⣆⠀⢺⡆⠀⣦⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⡇⠀⠀⣼⠇⢰⣿⠀⣼⡇⢠⣿⠀⣼⣿⣶⣿⢶⣼⣿⣤⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⣇⠀⣿⡄⢸⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⠀⣀⣀⣀⣀⣰⣿⣿⠀⠀⣀⣿⣀⢸⣟⡀⣿⣇⣸⣿⣤⣿⣇⣘⣿⣴⣿⣿⣉⣿⣣⣸⣿⣀⣿⣇⣘⣿⢀⣸⣿⣆⣿⣇⣸⣿⣀⣸⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⣄⠠⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣻⠿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢹⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⣶⣶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⡆⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⡏⠀⣿⣿⣿⡿⠃⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠂⠀⠠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠄⠀⠀⠀⢘⡇⠀⣶⡆⢸⣿⣧⡨⠍⠛⠏⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠈⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⣀⠀⡇⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⢿⣿⣿⣿⣿⣷⣔⠁⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢿⣿⣿⣿⣟⡆⡀⠀⠀⣠⠀⠀⡷⠰⠿⢻⣻⣓⢹⡏⡍⠇⣿⣿⣿⠙⠟⠟⠿⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠰⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣽⣾⣿⣭⣿⡿⠿⠢⢦⠤⡐⣤⣊⣃⣄⣀⣀⣾⣿⣶⣿⣷⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⢀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣷⠀⢀⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⠀⣷⠀⠀⠀⠠⠀⢸⣿⣿⣿⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⢀⢸⣇⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢙⠀⣿⠀⠀⠀⠀⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡞⢸⣿⢸⣾⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢴⣿⢰⠿⠀⠀⠀⣀⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣴⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣼⣧⣼⣿⣼⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣦⢀⣶⡄⣿⡆⠀⠀⠀⠀⣀⠐⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠛⢿⡟⢻⡿⢻⣿⠹⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣻⠃⢀⡦⢸⣿⠳⣿⠇⢿⡇⠀⠀⢀⣴⣿⡀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢉⡀⢸⡇⠀⣷⠃⢻⡶⢿⣿⠻⣿⡏⢹⣿⣿⣿⣻⡏⣿⣿⣀⠀⠀⡎⠁⠸⠿⠀⡟⠀⢘⠀⠀⡀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠁⢸⡏⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠀⣿⡏⢻⣟⠂⣿⡆⢸⣷⠀⣸⡀⠀⣆⠀⢻⡆⠀⣧⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣾⠇⢰⣿⠀⣼⡇⢰⣿⠀⣼⣿⣶⣿⡤⣼⣿⣤⣿⡇⣸⣿⠀⣿⡇⢸⣿⠀⢸⣇⠀⣿⡄⢸⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⠀⣀⣀⣰⣿⣿⠀⠀⣀⣿⣀⢸⣟⡀⣿⣇⣸⣿⣤⣿⣇⣸⣿⣴⣾⣿⣉⣿⣣⣼⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣇⣸⣿⣀⣹⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣖⠰⠶⠶⠖⠀⠀⠀⣄⠤⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⠞⠉⢋⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢰⣽⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⣶⣶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⢰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠂⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⠋⢀⣿⣿⣿⡿⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⢘⡇⠀⣶⡆⢸⣿⣧⡈⠉⠙⠋⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⣁⠀⡇⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢿⣿⣿⣿⣟⡆⠀⠀⠀⠀⠀⠀⠷⠰⠛⢻⣻⣓⢹⡏⡍⠃⣿⣿⣧⠙⠛⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠐⢀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣯⣾⣿⣭⣿⡿⠿⠣⠃⠤⡀⣥⣎⣓⣀⣀⣀⣾⣿⣶⣿⣷⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⡐⠀⠀⢀⣭⣏⠉⠋⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣷⠀⠀⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⠀⣷⠀⠀⠀⠠⠀⢸⣿⣿⣻⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⢀⢸⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢐⠀⣿⠀⠀⠀⠀⠀⢘⡿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢃⣳⡀⠤⣉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡎⢸⣽⢸⣉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢴⣿⢸⡿⠀⠀⠀⠁⠀⠀⠹⠂⠀⠀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣼⣇⣼⣿⣼⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣦⢀⣶⣄⣿⡆⠀⠀⠀⠀⣀⠐⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠛⢿⡟⢻⣿⢻⣿⠹⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣛⠁⢀⡤⢸⣿⠛⣿⠏⢿⡇⠀⠀⢀⣴⣿⡀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢉⡄⢸⡆⠀⣷⠊⢻⡶⢿⣿⠚⣿⡏⢹⣿⣿⣿⣻⡟⣿⣿⣠⠈⠀⡜⠃⠸⠿⠀⠏⠀⢨⠀⠀⡀⠸⣿⣿⣿⣿⣿⠁⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣾⠁⢸⡏⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠈⣿⡏⢻⣿⠀⣿⡄⢸⣷⠀⢸⡀⠀⡀⠀⢸⡄⠀⣄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⠇⢠⣿⠀⣼⡇⢸⣿⠀⣿⣿⣶⣿⠄⣸⣿⣠⣿⡇⣸⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⣿⡄⢸⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⡀⡀⣀⣀⣰⣿⣿⠀⠀⢀⣿⣀⣸⣟⠀⣿⣇⣸⣿⣤⣿⣇⣘⣿⣴⣿⣿⣉⣿⣃⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣇⣸⣿⣀⣸⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⢄⠄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⠿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢵⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⣶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⢰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣽⣆
⠈⣿⣶⣷⣶⡞⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠆⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠋⢀⣿⣿⣿⡿⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⣀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠁⠀⠀⠀⠘⡇⠀⣶⡆⢸⣿⣧⡈⠏⢻⠟⠁⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠈⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⣀⠀⡇⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⢈⣼⣿⣿⣿⣿⣟⡆⡀⠀⠀⢠⠀⠈⡷⠰⠻⠻⢛⣓⢽⡏⡍⠃⣿⣿⣿⡟⠛⠿⠻⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠰⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣿⣿⡿⠿⠢⠤⠥⡀⣤⣐⣁⣄⣀⣀⣀⣾⣶⣿⣷⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⢀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⠀⢐⠀⠀⠀⢀⣠⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⣷⠀⠀⠀⠠⠀⢸⣿⣿⣿⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡾⠀⢀⢸⣧⣾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠀⣿⠀⠐⠀⠐⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡀⢤⡉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡎⢸⣯⢹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⢰⡿⠀⠀⠀⠆⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣷⣾⣤⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣿⣼⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣦⢠⣶⣄⣦⡄⠀⠀⠀⠀⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠟⢿⡟⢻⣿⢻⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣛⠁⢐⡠⢸⣿⠾⣿⠏⢻⡇⠐⠀⢀⣴⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢉⡄⢸⡆⠀⣵⠋⢻⣶⣿⣿⠚⣿⡇⢹⣿⣿⣿⣻⡟⣿⣿⣤⠉⢀⡜⠇⠸⠿⠀⠏⠀⢨⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⣀⣴⠀⠀⣠⡿⠀⣾⠁⢰⡿⠀⣾⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡏⢻⣿⠁⣿⡄⢸⣷⠀⢸⡄⠀⣤⠀⢸⡄⠀⣀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⡇⠀⠀⣿⠇⢠⣿⠀⣼⡇⢸⣿⠀⣾⣿⣶⣿⣇⣸⣿⣤⣿⡇⣸⣿⠀⣿⡇⢸⣿⠀⢸⣇⠀⣿⡄⢸⣇⠀⣿⠀⢸⣿⡉⠀⠹⠀⠀⢸⠇⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⠀⣀⣀⣰⣿⣿⠀⠀⠀⣟⣀⢸⣿⡀⣿⣇⣸⣿⣤⣿⣇⡈⣿⣽⣿⣿⣉⣿⣧⣸⣿⣀⣿⣇⣈⣿⢀⣸⣿⣆⣿⣇⣸⣿⣀⣹⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⢄⠤⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⠿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢽⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠓⠀⠐⣶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⡞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠄⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⠋⢀⣿⣿⣿⡿⠉⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡈⠋⢹⠟⠃⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⢀⠀⡃⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡄⠀⠀⢠⠀⠈⡷⠰⠿⠻⠛⣓⢽⡏⡍⠇⣿⣿⣿⣿⠟⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠐⢀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣿⣿⡿⠿⠢⠤⠥⡴⣦⣆⣛⣔⣀⣀⡀⣼⣶⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠤⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡃⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣷⠀⢐⠀⠀⠀⢀⣠⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⠀⠀⠀⢀⠀⢸⣿⣿⣿⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡾⡀⢀⢸⣇⣾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⣿⠀⠀⠀⠀⠀⢘⣿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢁⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡞⢸⣿⢹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢸⡿⠀⠀⠀⢆⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣷⣿⣤⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣇⣼⣿⣼⣶⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣶⢀⣴⣄⣤⡄⠀⠀⠀⠀⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠟⢿⡟⢻⣿⢻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣟⠁⢐⡠⢸⣿⠾⣿⠟⢻⡇⠀⠀⢀⣴⣿⡄⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢉⡄⢨⡆⠀⣵⠈⢻⣶⣿⣿⠞⣿⡏⢩⣿⣿⣿⣿⣟⣿⣿⣠⠉⢀⡜⠇⠸⠿⠀⠏⠀⢨⠀⠀⠀⠸⣿⣿⣯⣿⣿⠃⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⣀⣴⠀⠀⣰⡿⠀⣾⠁⢰⡿⠀⣾⠇⢸⣿⠀⣿⡇⢸⣿⠈⣿⡏⢹⣿⠉⣿⡄⢸⣷⠀⢸⡄⠀⣦⠀⢸⡄⠀⣄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⠇⢠⣿⠀⣼⡇⢸⣿⠀⣾⣷⣶⣿⣇⣸⣿⣤⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⣇⠀⣿⡄⢸⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⠀⣀⣀⣰⣿⣿⠀⠀⡀⣟⣀⢸⣿⡀⣿⣇⣸⣿⣤⣿⣇⣈⣿⣵⣿⣿⣉⣿⢧⣸⣿⣀⣿⣇⣈⣿⢀⣸⣿⣆⣿⣇⣸⣿⣀⣹⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠰⠶⠶⠶⠀⠀⠀⢄⠄⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⡿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠘⢽⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠓⠀⠒⣶⣶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣦
⠈⣿⣶⣷⣶⡞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠆⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⠋⢀⣿⣿⣿⡿⠉⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠂⠀⢠⡿⠀⠀⣿⡇⠀⠀⢀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠉⠹⠛⠃⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡀⠀⠀⢠⠀⠈⡷⠰⢿⠻⠛⠓⢱⡏⡍⠃⣿⣿⣿⣿⣿⠿⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣿⣿⡿⠿⠦⠄⠥⡰⣦⣏⣃⣠⣀⣀⡀⠀⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠋⠙⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⠀⠀⠀⠠⠀⢸⣿⣿⣿⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣈⢻⣷⣾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀⠀⠀⠀⢘⣿⠟⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢂⣤⡌⢃⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡞⢸⡟⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿⠀⠀⠀⣆⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣼⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣦⠀⢶⣄⠹⡆⠀⠀⠀⢀⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠟⢿⡟⢻⡿⢻⣿⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⡧⢸⣿⠺⣿⠟⢿⡇⠐⠀⢀⣴⣿⣀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣈⡄⢈⡀⠀⣡⠈⢻⣶⣿⣿⠚⣿⡏⢹⣿⣿⣿⢟⠛⣿⣿⢀⠉⠀⠘⠁⠸⠟⠀⠏⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⣀⣴⠀⠀⣸⡏⠀⣼⠁⢰⡟⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠈⣿⡏⢹⣿⠋⣿⡄⢸⣧⠀⢸⡇⠀⣿⠀⢸⡄⠀⣄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⠃⢠⣿⠀⣼⡇⢸⣿⠀⣾⡇⣦⣿⣇⣸⣿⣤⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⣿⡀⢸⣇⠀⣿⠀⢸⣿⡉⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⠀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣀⢸⣟⠀⣿⣇⣸⣿⣤⣿⣇⣈⣿⣼⣿⣿⣉⣿⣇⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣇⣸⣿⣀⣹⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⢁⢄⣻⠿⠋⢻⣿⣷⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠿⣷⣶⣶⣶⠒⠚⠑⠀⠒⣶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⡄⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠋⢀⣿⣿⣿⡿⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠂⠀⢠⡿⠀⠀⣿⡇⠀⠀⢀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡸⠉⠹⠉⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠈⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣆⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡄⠀⠀⢀⠀⠈⢷⠰⠿⠻⠛⠓⢱⡏⡍⠃⣿⣿⣿⣿⣿⠻⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠘⠀⠀⠰⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣽⣿⡿⠿⠦⠠⠤⡄⣦⣫⣙⣀⣀⣀⡀⠀⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⡀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠋⠙⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢐⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⢰⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⠀⠀⠀⠠⠀⢸⣿⣿⣻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⡀⢈⢹⣷⣾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀⠀⠐⠀⢘⡿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡂⣤⡌⢃⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡟⢸⡟⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿⠀⠀⠀⣆⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣳⣿⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣸⢏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣦⠀⣶⣄⢹⡆⠀⠀⠀⢀⣀⠐⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣾⠟⢿⡟⢻⡿⠻⣿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⡧⢸⣿⠸⣿⠿⢲⡇⠀⠀⢀⣴⣿⣀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣘⡄⢈⡄⠀⣁⠘⣻⣶⣿⣿⠜⣿⡏⢹⣿⣿⣿⣟⢛⣿⣿⢀⠈⠀⠘⠃⠘⠏⠀⠏⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⣀⣴⠀⠀⣸⡏⠀⣼⠁⢰⡟⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠈⣿⡇⢸⣿⠟⣿⡄⢰⣧⠀⢹⡇⠀⣿⠀⢸⡄⠀⣄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⠃⢠⣿⠀⣼⡇⢸⣿⠀⣾⣧⣶⣿⢇⣸⣿⣤⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⣿⡀⢸⡇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⠀⠀⢀⣀⣰⣿⣿⠀⠀⠀⣿⣁⢸⣟⠀⣿⣇⢸⣿⣤⣿⣇⣈⣿⣼⣿⣿⣉⣿⢃⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣇⣸⣟⣀⣹⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣖⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠇⢈⣿⡿⠉⢛⣿⣷⣿⣋⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢷⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠿⣷⣶⣶⣶⠒⠚⠓⠀⠒⣶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢴⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⡇⠀⠀⣶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⡆⠀⠈⠛⠻⡅⠀⠟⠻⢿⣟⠋⢀⣿⣿⣿⡿⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠂⠀⢠⡿⠀⠀⣿⡇⠀⠀⡀⠀⠀⠀⠀⢲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠉⠙⠙⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⡄⠀⠰⠾⣿⣿⣿⣿⣷⣔⠁⠀⠀⠀⠐⠙⢿⣿⢿⣿⣿⣿⣆⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⡈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⢀⠀⠈⡷⠰⠿⠻⠛⠓⢱⡏⡍⠃⣿⣿⣿⣿⣿⡿⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠰⢀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⣀⣯⣿⣿⣽⣿⡿⠿⠦⠤⠤⣤⣦⣱⣓⣤⣀⣀⡀⠀⣰⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠩⠋⢹⠋⠙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢐⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠀⠀⠀⠠⠀⢸⣿⣿⣻⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣘⢻⣷⣼⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⠀⠀⠀⠀⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠂⣤⡌⢃⣳⡠⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡟⢸⡿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿⠀⠀⠀⣆⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣇⣾⣧⣼⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣦⢀⣴⣄⣽⡆⠀⠀⠀⢀⣀⠐⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⢸⠟⢿⡟⢻⡷⠻⣿⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⡧⢸⡿⠺⣽⠿⢭⡇⠀⠀⢀⣴⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣬⠄⢈⡄⠀⣀⠘⣿⣶⣿⣷⠜⣿⡏⢩⣿⣿⣿⡟⢻⣿⣿⢀⠉⠀⠘⠃⢘⠃⠀⡏⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡏⠀⣼⠃⢰⡏⠀⣿⠇⢸⡿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠟⣿⡀⢰⣧⠀⢹⡇⠀⣿⠀⢸⡄⠀⣄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠨⣿⣿⠇⠀⠀⣿⡇⢀⣿⠀⣼⡇⢸⣿⠀⣾⣧⣶⣿⣇⣸⣿⣠⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⣿⡀⢸⡇⠀⣿⠀⢸⣿⡁⠁⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⠀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣁⣸⣟⡀⣿⣇⣸⣿⣤⣿⣇⣈⣿⣼⣿⣿⣈⣿⢧⣸⣿⣀⣿⣇⣨⣿⢀⣸⣿⣆⣿⣁⣸⣏⣀⣹⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣖⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⡿⠋⢋⣿⣷⣿⣋⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠿⣷⣶⣶⣶⠒⠚⠑⠀⠒⣶⡶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⡆⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⠋⠀⣿⣿⣿⡿⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠂⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠉⠙⠉⠁⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣔⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠉⣼⣿⣿⣿⣿⣟⡆⡄⠀⠀⢀⠀⠈⣷⠰⠿⢻⠛⠓⠑⠀⡄⠃⣿⣿⣿⣿⣿⣿⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠰⠄⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡈⣯⣿⣿⣽⣿⡿⠿⠦⠆⠥⣀⣤⣌⣋⣤⣀⣀⡀⠀⠀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠋⠙⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠀⠀⠀⠠⠀⢸⣿⣿⣻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡾⡀⣿⢿⣷⣼⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠂⣤⡌⢃⣳⡀⢤⡉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡟⢸⡿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠀⠀⠀⡆⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣼⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠈⢸⣇⣾⣧⣼⣯⣠⣿⣿⣿⣷⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣦⢀⣶⣄⣹⡆⠀⠀⠀⢀⣀⠐⣽⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⢸⠟⢿⡟⠻⠟⠻⣿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡦⢸⣿⠲⢿⠟⢿⡇⠀⠀⢀⣴⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣶⠆⢀⡀⠀⢀⠈⣿⣶⣿⣷⠘⣿⡏⢩⣿⣿⣿⡟⢻⣿⣿⠈⠉⠁⠘⠃⢨⠁⠀⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡏⠀⣼⠃⢠⡟⠀⣿⠇⢸⡟⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠟⣽⡀⢰⣧⠀⢸⡇⠀⣿⠀⢸⡄⠀⣀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⠇⠀⠀⣿⡇⢀⣿⠀⣸⡇⢸⣿⠀⣼⣷⣶⣿⣅⣸⣿⣠⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⣿⡀⢸⣇⠀⣿⠀⢸⣿⡁⠁⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⠀⠀⢀⣀⣰⣿⣿⠀⠀⠀⣿⣁⢸⣟⡀⣿⣇⢸⣿⣤⣿⣇⣈⣿⣽⣿⣿⣉⣿⢇⣸⣟⣀⣿⣇⣰⣿⢀⣸⣿⣆⣿⣁⣸⣏⣀⣹⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢌⣿⣿⠋⢛⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⣻⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⣶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⣰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⡶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠄⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⠋⢀⣿⣿⣿⡟⠉⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠂⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡨⠋⠙⠉⠁⠀⠀⣸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠁⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠈⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠿⣿⣿⣿⣿⣷⣔⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡦⠐⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⡈⣼⣿⣿⣿⣿⣿⡆⠄⠀⠀⣠⢀⠈⡷⠰⡿⢻⠛⠓⠑⡀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠘⠀⠀⠰⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣠⣯⣿⣿⣿⣿⡿⠿⠦⠧⡥⣤⣧⣟⣿⣭⣀⣀⣀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⣀⠀⠀⠀⠀⠀⠀⡧⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⢂⣭⣏⠉⠋⢹⠋⠙⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⢿⣿⣻⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣿⢿⣷⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢘⡿⠟⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⢤⣉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⢇⢰⡿⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡄⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣿⣴⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣼⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣦⠀⣰⡄⣽⡆⠀⠀⠀⢀⣀⠐⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⢸⡟⣿⡟⢻⡟⠻⣿⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡤⢸⡿⠲⣿⠟⢿⡇⠀⠀⢀⣴⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣾⡇⠉⡀⠈⢁⠀⣿⣷⢿⣿⠙⣻⡏⢻⣾⣿⣿⣿⢿⣿⣯⠉⠙⠉⠘⠁⣠⠁⠀⡙⠀⠘⠃⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡟⠀⣼⠇⢠⡟⠀⣿⠇⢸⡿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⡟⣿⡀⢠⣇⠀⢹⡇⠀⣿⠀⢰⡀⠀⡀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⠇⠀⠀⣿⡇⢠⣿⠀⣼⡇⣸⣿⠀⣼⣧⣤⣿⣇⣸⣿⣠⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⣿⠀⢸⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⡀⠀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⣸⣏⡀⣿⣇⣸⣿⣤⣿⣇⣨⣿⣼⣿⣿⣉⣿⢣⣸⣟⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣹⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⠰⠶⠶⠶⠀⠀⠀⣄⢄⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠅⠀
⣼⠀⠀⠙⠃⣎⣿⠿⠉⠫⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠿⣷⣶⣶⣶⠒⠚⠑⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣋⣽⣷⣦
⠘⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⠏⠀⣿⣿⣿⠟⠉⠀⢀⠀⠀⠃⠋⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠉⠹⠟⠀⠀⠀⣸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⠤⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠸⠿⣿⣿⣿⣿⣷⣄⠃⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡀⠀⠀⣠⢀⠈⣷⢰⠿⠻⠛⠓⠑⡀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠰⡀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⣀⣯⣾⣿⣿⣿⡿⠿⠦⠧⠅⡬⣧⣹⣿⣭⣀⣀⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⢀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⡐⠀⠀⢀⣭⣏⠉⠋⢹⠋⠙⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠠⠀⢸⣿⣿⣻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣽⢿⣧⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣴⡌⢃⣳⡀⢤⣁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡿⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⡄⠀⠀⠻⠂⠀⠀⠀⣾⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣷⣿⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠈⢸⣇⣾⣧⣼⡏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣦⠀⣶⣄⣿⡆⠀⠀⠀⢀⣀⠘⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢶⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠹⡟⣿⡟⢿⡟⠻⣿⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡤⢸⣿⠲⣿⠿⢿⡇⠀⠀⢀⣴⣿⣠⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣾⡇⠙⠀⠘⣃⠀⣿⡷⢿⣿⠛⢳⡟⢻⣾⣿⣿⡿⢿⣿⣯⠉⠛⠉⠘⠁⣠⠁⠀⡝⠀⠘⠇⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡟⠀⣼⠃⢠⡟⠀⣿⠃⢸⡿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⡿⣿⠀⢰⣇⠀⢿⡆⠀⣷⠀⢸⡀⠀⠄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⠇⠀⠀⣿⡇⢀⣿⠀⣼⡇⣰⣿⠀⣼⣇⣤⣿⣇⣸⣿⣠⣿⡇⢸⣿⠁⣿⡇⢸⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⢿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⣀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣁⣸⣇⠀⣿⣇⣸⣿⣤⣿⣇⣸⡿⣽⣿⣿⣉⣿⢣⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣹⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⠰⠶⠶⠶⠀⠀⠀⣄⢀⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⢃⢌⣿⡿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢷⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠚⢻⡿⠿⣷⣶⣷⣶⠒⠚⠑⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⣴⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣦
⠘⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⡀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠋⠀⣿⣿⣿⡿⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠂⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠉⠹⠋⠁⠀⠀⣸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠸⠿⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡄⠀⠀⡠⠀⠈⣷⢰⠿⠻⠛⠓⠑⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠀⠖⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⣀⣯⣾⣯⣿⣾⡿⠿⠦⠥⠄⡄⣧⣻⣟⣍⣀⣀⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⡐⠀⠀⢀⣭⣏⠩⠋⢹⠋⠙⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡄⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⠅⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⡇⢀⣿⣿⣿⣇⣿⢘⣿⣿⣿⣄⢸⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠠⠀⢸⣿⣿⣹⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⢀⣳⢾⣧⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣴⡌⢃⣳⡆⢤⣡⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡿⢸⣿⢸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⡄⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣿⣴⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣼⡿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣦⠀⣶⡄⣿⡆⠀⠀⠀⢀⣀⠐⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⡟⣿⡟⢻⡟⠻⣿⡻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣸⡿⠲⣿⠟⢿⡇⠀⠀⢀⣴⣿⣄⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣾⠇⠙⡀⠘⠃⠀⣽⡿⢿⣿⠿⣷⡿⢿⣾⣿⣿⡟⢻⣿⣟⢉⣿⡋⠈⠁⣤⠁⠀⡘⠀⠘⠇⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⠀⠀⢸⡟⠀⣼⠃⢠⡿⠀⣿⠇⢸⡟⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⡿⣿⠇⢰⣇⠀⢿⡆⠀⣷⠀⢰⡀⠀⡀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣾⡇⢠⡿⠀⣼⡇⣸⣿⠀⣼⣧⣦⣿⣅⣸⣿⣤⣿⣇⢸⣿⠁⣿⡇⢸⣿⠀⢸⡇⠀⣿⡀⢸⡇⠀⢿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⡀⣀⣀⣰⣿⣿⠀⠀⢀⣿⣓⣻⣃⠀⣿⣁⣸⣿⣤⣿⣇⣸⣿⣸⣽⣯⣉⣿⢣⣸⣿⣀⣿⣇⣘⣿⢀⣸⣿⣆⣿⣁⣘⣿⣀⣸⣌⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣖⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣕⣂⠁⠀
⣼⠀⠀⠙⢁⢈⣿⢿⠋⢛⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣦
⠘⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⠏⠀⣿⣿⣿⡟⠁⠀⢀⠀⠀⠃⠋⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠉⠹⠉⠁⠀⠀⣸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⢀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡄⠀⠀⡠⢀⠈⡷⠰⠿⠻⠛⠓⠑⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠈⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⣈⣯⣿⣿⣽⣾⡿⠿⠆⠇⠥⡴⣧⣛⣿⣍⣠⣀⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⢀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠩⠋⢹⠋⠙⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡌⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣤⡆⣿⡇⠀⢸⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⡇⢀⣿⣿⣿⣇⣿⣸⣿⣿⣿⣄⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣶⣴⡾⢠⣦⢾⣧⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡂⢤⣁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢨⡟⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⠀⠀⠀⡄⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣼⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣇⣾⣧⣼⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢰⣤⠀⣶⡄⣿⡆⠀⠀⠀⢀⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⠏⣿⡟⢻⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡀⠸⡿⠲⣿⠟⢿⡇⠀⠀⢀⣴⣿⣀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣼⠏⠘⠁⠘⣃⠀⣹⡿⢿⣿⠿⣷⡾⢿⣾⣿⣿⡟⢻⣿⣟⢉⣿⠋⠚⠁⣤⠁⠀⠘⠀⠸⠇⠀⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⣿⠀⣠⠀⢰⡿⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⣿⣿⡿⢸⣇⠀⢻⡆⠀⣷⠀⢠⡀⠀⠀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢠⡟⠀⣼⡇⢠⣿⠀⣸⣷⣤⣿⢇⣸⣿⣤⣿⣇⢸⣿⠋⣿⡅⢸⣿⠀⢸⡇⠀⣿⡀⢸⣇⠀⣺⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⡀⠀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⢻⣇⠀⣿⣀⣸⣿⣤⣿⣇⣹⣿⣼⣿⣿⣉⣿⢧⣸⣿⣁⣿⣃⣀⣿⢀⣸⣿⣆⣿⣁⣘⣿⣀⣸⣇⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠰⠶⠶⠖⠀⠀⠀⣄⠄⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⢁⢀⣻⠿⠋⠋⣻⣷⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣷⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠏⢀⣿⣿⣿⣿⣿⡆⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⣠⣿⣿⣿⣿⣿⠁⣸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣿⠋⣹⣿⡏⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣿⠟⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡄⠀⠀⣠⠀⠀⡷⢰⠿⠻⠛⠓⠑⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⣀⣯⣾⣿⣭⣾⡿⠿⠦⠇⠅⡴⣧⣝⣿⣍⣀⣀⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠩⠋⢹⠋⠙⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣥⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡌⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⠅⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣠⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⣸⣿⣿⣿⣄⢸⣷⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡟⠁⠀⠠⠀⢸⣿⣿⣻⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⢠⣂⢸⣇⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠒⠀⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⠤⡉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣼⡏⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠀⠀⠀⡄⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣷⣾⣴⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⡇⣾⣧⣼⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣦⠀⣶⡄⣿⡄⠀⠀⠀⢀⣀⠐⣹⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠘⣃⣿⡟⢻⡟⠻⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢋⡠⠸⡿⠲⣿⠗⢿⡇⠀⠀⢀⣴⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣤⠙⠘⠁⠘⣣⠀⣻⡿⢻⣿⢿⣿⡾⢿⣾⣿⣿⡟⢻⣿⣿⠉⣿⠋⢨⠀⢀⠀⠀⡘⠀⠸⠃⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⡿⠀⣀⠀⢰⡏⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⣿⢼⠿⢠⣇⠀⢸⡀⠀⣇⠀⢀⡀⠀⠀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠽⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣽⣿⠇⠀⠀⣼⡇⢸⡇⠀⣿⠁⢠⣿⠀⣸⣯⣴⣿⢁⣼⣿⣤⣿⣇⢸⣿⠋⣿⡇⠘⣿⠀⢸⡇⠀⣿⠀⢸⣷⠀⢻⡆⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⡀⠀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⢸⣇⠀⣿⣀⣸⣿⣤⣻⣇⣸⣿⣰⣿⣿⣉⣿⢣⣸⣿⣀⣿⣇⣀⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣸⣇⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣗⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣾⣿⠉⢋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢴⣴⣶⣶⣶⣶⡀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣷⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠃⠀⢿⣿⣿⣿⣿⣿⣇⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⣠⣿⠟⠉⠉⣹⣿⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣿⠀⠀⣰⣿⠇⣿⣿⢀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⠀⠀⠠⡆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡄⠀⠀⢠⢀⠀⡷⢰⠿⠻⠛⠓⠑⡀⠀⠀⣴⣾⣿⣿⣿⣿⣿⢿⣿⣿⠏⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣿⣿⡿⠿⠦⠃⠥⡴⣧⣽⣿⣭⣀⣀⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠩⠋⢹⠋⠙⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⣿⡇⠀⢸⣿⣧⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⢀⣿⠛⣿⣿⣿⣄⢸⠁⢸⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣠⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⢰⡇⢀⣿⣿⣿⣇⣿⣸⣿⣿⣿⣄⢸⣷⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣻⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⢠⣀⢸⡇⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠒⠀⠀⢘⡿⠟⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡄⠤⡡⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣼⡏⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠀⠀⠀⡄⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣴⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⡇⣾⣧⣼⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣤⠀⣶⡄⣿⡄⠀⠀⠀⢀⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠘⣃⣿⡟⢻⡟⠻⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⢃⡠⠘⡿⠲⣿⠗⢿⡇⠀⠀⢀⣴⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣤⠙⠘⠁⠘⣣⠀⣻⡿⢻⣿⢿⣷⡾⣿⣾⣿⣿⡏⢻⣿⣿⠉⣿⠋⢈⠀⠀⠀⠀⡸⠀⠸⠃⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⡿⢀⡴⠀⣰⡏⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⣿⣼⡿⢠⣆⠀⢸⡄⠀⣇⠀⢠⠀⠀⠀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣼⡇⢸⡇⠀⣿⡁⢠⣿⠀⣸⣿⣴⣷⢁⣼⣿⣤⣿⣇⢸⣿⠋⣿⡇⠈⣿⠀⢸⡇⠀⣿⠀⢸⣿⠀⢻⡆⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⡀⢀⣀⣀⣰⣿⣿⠀⠀⡀⣿⡃⢺⣇⠀⣿⣀⣸⣿⣤⣿⣇⣸⣿⣸⣿⣿⣉⣿⢣⣸⣿⣀⣿⣇⣀⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣸⣇⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣖⠰⠶⠶⠖⠀⠀⠀⣄⠄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣻⠾⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠘⢱⣵⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣿⢿⠂⠘⣿⡇⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣋⣽⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠐⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣗⠀⠀⢿⣿⡿⠉⠀⠀⢰⣿⠁⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⣀⣾⠟⠀⠀⠀⠀⣼⣯⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣏⠀⢀⣠⣶⣾⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣿⡿⣿⡿⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢿⣿⣿⣿⣟⡆⡄⠀⠀⢠⠀⠀⡷⠰⠿⠻⠛⠓⠑⡀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⠓⣭⣿⠃⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⡀⣯⣾⣿⣽⣾⡿⠿⠦⠧⠥⡼⣧⣽⣟⣽⣀⣀⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⢿⠋⠆⢠⣿⠇⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠩⠋⢹⠛⠙⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢠⡾⠃⠀⠀⣿⡇⠀⢸⣿⣧⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⡿⠁⢀⣤⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣠⡇⢀⣿⣿⣿⣇⣿⣘⣿⣿⣿⣄⢸⣿⣿⣿⣿⣯⣛⣿⣿⣿⣿⣿⠟⠛⠋⠀⠀⢸⣻⣿⣹⡇⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⢀⠀⢸⡏⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣹⣿⣿⠀⠀⠒⠀⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣼⡇⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣤⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢹⡆⣼⣿⣼⣿⣠⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣢⠀⣶⡄⣿⡄⠀⠀⠀⢀⣀⠐⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠇⣿⡟⢻⡟⠻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣵⣭⣿⣿⢋⠠⠀⡿⠲⣿⠟⣿⡇⠀⠀⢀⣴⣿⡀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣠⠄⠚⠁⠘⣧⠀⣿⡿⢿⣿⢿⣷⡾⣟⣾⣿⣿⡏⢻⣿⣿⠉⣻⠋⠈⠀⠀⠀⠀⠙⠀⠸⠃⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⣿⢠⡤⠀⣠⡇⠀⣿⠇⢸⣿⠀⡿⡇⢸⣿⠀⣿⡇⢸⣿⣿⣴⡿⢠⣆⠀⢸⠀⠀⣧⠀⢠⡀⠀⣀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣼⡇⢸⡇⠀⣿⡄⢠⣿⠀⣸⣧⣴⣿⣠⣼⣿⣤⣿⣇⢸⣿⠋⣿⡇⠈⣿⠀⢸⡆⠀⣿⠀⢸⣷⠀⢻⡆⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⡿⣋⣁⣀⣀⢀⢀⣀⣰⣿⣿⠀⠀⡀⣿⣃⢘⣃⠀⣿⣀⣸⣿⣤⣿⣇⣸⣿⣸⣿⣿⣉⣿⢣⣸⣿⣀⣿⣇⣀⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣸⣇⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⣄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣿⠏⠀⠀⢹⣿⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣺⠾⠉⠋⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⢸⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢸⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠁⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣿⢿⠂⠀⠀⠀⠀⣿⠃⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣗⠂⠀⢞⣿⡿⠑⠀⠀⢀⠀⠀⢸⡏⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠂⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⣼⡟⠁⡀⠀⠀⣸⣧⣤⣿⠁⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣏⠀⣸⣷⣾⣟⣿⣿⢉⠁⠀⠀⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⣿⣿⠀⠀⠠⡦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣻⣿⣿⣿⣟⡆⡀⠀⠀⢠⠀⠀⡷⠰⠛⠛⠛⠓⠑⡄⠀⠀⣀⣰⣿⣿⣿⣿⡛⢿⣿⣿⣿⡇⢀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠠⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣽⣾⡿⠿⠠⠧⠥⠔⣧⣛⣿⣍⣀⣀⡀⠀⠀⠀⢀⣵⣿⣿⣿⣿⣿⣿⡿⠁⢈⣿⠏⠈⠀⢸⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠩⠋⢹⠋⠙⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢀⠀⠀⢠⡏⣿⡇⠀⢸⣿⣧⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⠅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡰⠐⠻⠁⣠⣿⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣠⡇⣀⣿⣿⣿⣇⣿⣘⣿⣿⣿⣄⢸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⢹⣿⣿⡻⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⢀⠀⢸⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⢹⣿⣿⠀⠀⣠⡆⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡀⠤⡡⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⡎⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠇⠏⡆⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣷⣾⣴⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⡀⣾⣧⣼⣿⣠⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣷⠆⣶⡄⣿⡄⠀⠀⠀⢀⣀⠐⣽⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠃⣿⡟⢻⡟⠻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⣏⠄⠀⠾⠂⣿⠟⣿⡇⠀⠀⢀⣴⣿⣀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣠⠆⠛⠁⠘⡧⠀⣿⡿⢻⣿⢿⣧⡞⢟⣽⣿⣿⡟⢳⣦⣿⠉⢻⠋⠘⠀⠀⠀⠀⠙⠀⠸⠁⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⣿⢀⣿⠀⢸⡇⠀⣿⠇⢸⣿⠀⣯⠇⢸⣿⠈⣿⡇⢸⣿⣿⣶⡿⢰⣷⠀⢸⡀⠀⣧⠀⢰⡄⠀⣦⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣼⡇⢸⡟⠀⣿⡇⢠⣿⠀⣸⣧⣴⣿⣠⣼⣿⣴⣿⣇⢸⣿⠃⣿⡇⠈⣿⠀⢸⡇⠀⣿⠀⢸⣿⠀⣿⡆⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⢀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣃⢸⣃⠀⣿⣀⣸⣿⣤⣻⣇⣸⣿⣸⣿⣿⣉⣿⢣⣸⣟⣀⣿⣇⣀⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣸⣇⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⣄⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⢠⣾⣿⣿⣿⣷⣿⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⠿⠉⠋⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢼⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⣦⣾⠟⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣟⣽⣽⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠖⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣗⠀⠀⠾⣿⣿⢏⣵⡿⢃⠀⠀⠃⠂⠀⣠⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠂⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠙⢫⣾⠏⠀⢸⣧⠠⠰⠂⣠⣏⣼⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⣴⣿⠃⠀⠀⣿⣿⢱⠀⠀⠤⣼⠟⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠟⠐⣶⣿⣿⣿⠀⠀⢠⣾⠟⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡀⠀⠀⣠⢀⠈⣷⠰⠿⠻⠛⠓⠑⠄⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣃⣀⢠⣹⣿⣿⣿⠀⢰⣾⠏⠰⠀⠖⠀⠀⠀⠈⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣯⣿⡿⠿⠦⠣⠄⡤⣧⣛⣿⣝⣀⣀⡀⢀⠀⠀⢁⣪⣥⣿⣿⣿⣿⣿⡁⣱⡿⠛⠛⠁⠘⢃⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠩⠋⢹⠋⠙⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⢀⠎⣿⡇⠀⢸⣿⣧⢤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⠅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⢠⣾⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀⢸⢿⣿⣻⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣝⡻⠿⢿⣿⣿⣿⣿⠀⠀⢀⡄⠀⢘⡿⠟⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⡎⢸⣿⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡾⠀⡄⠞⣇⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣷⣾⣼⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⡇⣾⣯⣼⣿⣠⣿⣻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣷⡀⣷⡄⣿⡄⠀⠀⠀⢀⣀⠐⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠿⠋⢿⡟⢻⡟⠻⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢠⠾⡿⠇⣿⠟⢿⡇⠀⠀⢀⣴⣿⡀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣠⠆⣻⠃⢈⡇⠂⢸⡿⢿⣿⠿⡯⡟⢏⣿⣿⣼⡆⠀⣄⡍⣉⠛⠋⡀⠀⠀⠀⠀⡛⠀⠈⠁⠀⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⢀⣿⠀⢸⡇⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠙⣿⡇⢸⣿⣿⣿⡿⢰⣿⠀⢰⡀⠀⣧⠀⢻⡇⠀⣿⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢸⡏⠀⣿⡇⢀⣿⠀⣸⣷⣴⣿⣠⣼⣿⣤⣿⡇⢸⣿⠁⣿⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⣷⠀⣿⡆⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣃⢸⣃⡀⣿⣁⣸⣿⣤⣻⣇⣸⣿⣴⣿⣿⣉⣿⣧⣸⣿⣀⣿⣇⣀⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣸⣃⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣗⠰⠶⠶⠶⠀⠀⠀⣄⠄⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢡⣾⣿⣿⣿⣶⣿⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⡿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠀⠀⠒⢶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠂⠀⣴⡿⠃⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠀⠀⡞⣿⣿⠟⠁⣠⣾⠋⠀⠋⠋⠀⣠⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠂⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠈⠁⢀⣴⠟⢹⣧⠀⠐⠀⢰⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⣠⣾⣫⣴⣿⣿⠉⡆⠀⠬⠀⣰⡿⠁⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⣿⣿⠀⠺⠠⣶⣲⡿⠁⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡄⠀⠀⢠⠀⠈⡷⠰⢿⠻⠛⠓⠑⡄⡀⠀⣴⣾⣷⣝⠛⣻⣿⡿⠏⠁⠀⠀⠀⣿⣿⠀⢰⣄⣰⡿⠂⠖⠀⠀⠀⠈⠀⠀⠰⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣭⣾⡿⠿⠤⠧⠅⡼⣧⣛⣿⣽⣀⣀⡐⠀⠀⠀⠁⢯⣿⣿⣿⣿⣿⣾⡿⠋⠀⠀⠀⠀⠀⢀⣿⣿⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠩⠋⢹⠋⠙⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠛⠛⠂⠀⠀⠀⠀⢀⠆⣿⡇⠀⢸⣿⣧⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡃⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠀⠀⠀⣠⣾⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⠀⢸⣿⣿⡻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⠀⢸⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⠀⢘⡿⠟⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡂⢤⡉⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⡎⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣯⢭⣿⣿⢿⡿⠀⡄⠜⣇⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣼⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⡇⣼⣯⣼⣿⣠⣿⢻⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣷⡔⣷⡀⣿⡄⠀⠀⠀⢀⣀⠐⣽⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⡟⢻⡟⢻⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣻⣿⡋⣡⡾⣿⠇⣿⠿⢿⡇⠀⠀⢀⣴⣿⣄⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣠⠆⣻⠃⢈⡇⠀⢸⡿⢿⣿⢿⡏⡜⢧⣿⣯⣽⡍⠉⡍⡉⣉⠛⢋⡀⠀⠀⠀⠀⠛⠀⢈⠁⠀⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⣀⣴⠀⠀⢠⣿⢀⣿⠀⢸⡇⠀⣿⡇⢸⣿⠀⣿⠇⢸⣿⠙⣿⡇⢸⣿⡿⣿⡟⢰⣿⠀⢠⡀⠀⣧⠀⢻⡇⠀⣿⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣸⡇⢸⡏⠀⣾⡇⢠⣿⠀⣸⣿⣴⣿⣠⣼⣿⣤⣿⡇⢸⣿⠁⣿⡇⠈⣿⠀⢸⡇⠀⣿⡀⢸⣷⠀⢿⡇⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣃⢸⣇⡀⣿⣁⣸⣿⣤⣻⣇⣸⣿⣤⣿⣿⣉⣿⣧⣸⣿⢀⣿⣇⣀⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣸⡃⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⣄⠄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠅⢈⣻⣾⠋⢋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠿⣷⣶⣶⣶⠒⠚⠁⠀⠒⢶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⣀⣾⡿⠋⣻⣿⣿⣿⣿⣛⣛⣽⣷⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣗⠀⠀⡿⣿⣿⠛⠃⠀⢀⠀⢀⣵⡿⠃⣰⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠂⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠈⠉⠉⠀⠀⠀⣸⣧⡾⠋⠀⣴⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠄⠀⠀⠀⢨⣿⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣰⡿⣿⣿⠀⠀⠠⠆⠀⠀⠀⣾⠧⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⢠⢀⠈⣷⠰⣿⠻⠛⠓⠑⡄⡀⠀⣶⣤⣄⠙⠛⠛⠛⠛⢃⣤⡾⠋⠀⣿⣿⠀⢰⡄⠀⠰⢂⣾⠇⠀⠀⠘⠀⠀⠐⢀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⣀⣯⣾⣿⣯⣿⡿⠟⠠⠧⠥⣤⣧⣿⣿⣍⣀⣚⣈⠤⠀⠈⠆⣿⣿⣿⣿⣷⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⣿⣿⠀⢸⣷⣤⢀⣾⠏⠀⠀⠀⡧⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⡐⠀⠀⢀⣭⣏⠩⠋⢹⠋⠙⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⡘⣿⡇⠀⢸⣿⣿⢿⣧⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡌⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠁⢸⣧⣾⣿⣿⣿⣿⣿⣿⣿⡋⣿⠀⠀⠀⠀⠀⣠⣾⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠀⠀⠀⠠⠀⢹⣿⣿⣻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⠀⢸⣗⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⣀⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣴⡌⢃⣳⡀⢤⣁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⡎⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡿⣿⣿⣿⢻⡿⠀⡀⠸⣏⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⡇⣾⣯⣼⣿⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⡇⢸⣦⡰⣷⡆⣿⡄⠀⠀⠀⢀⡀⠐⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⡟⢻⡿⢻⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⢛⣦⣾⣿⠁⣿⠿⣿⡇⠀⠀⢀⣴⣿⡀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣹⡆⣹⠅⢈⡇⠈⢹⡿⢿⣿⢿⣇⡜⢷⣿⣿⣩⡍⠉⡉⡉⠉⠛⠋⡀⠉⠊⠋⠀⠛⠀⣈⠀⠀⡀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣿⡇⢸⣿⠀⣿⠇⢸⣿⠻⣿⡇⢸⣷⡇⣿⡟⢸⣷⠀⢰⡀⠀⣧⠀⢻⡇⠀⣿⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢸⡏⠀⣿⡇⣀⣿⠀⣸⣿⣶⣿⣤⣼⣿⣤⣿⡇⢸⣿⠁⣿⡇⠸⣿⠀⢸⡇⠀⣿⡀⢸⣧⠀⣿⡄⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⣸⣇⡀⣿⣁⣸⣿⣤⣿⣇⣸⣿⣰⣿⣿⣉⣿⣧⣸⣿⢀⣿⣇⣀⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣻⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠅⢈⣿⣾⠋⢋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⢘⢱⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠿⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣛⣽⣷⣦
⠉⣿⣶⣷⣶⠞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠉⠀⣿⣿⣿⠟⠃⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⢙⠋⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⣠⣾⠟⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠸⠾⣿⣿⣿⣿⣷⣤⠃⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⣦⣾⠟⠁⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⡈⣼⢻⣿⣿⣿⣟⡆⡀⠀⠀⡠⠀⠈⣷⠰⣿⢻⠛⠓⠑⡄⡄⠂⣦⢠⢤⠝⠟⠿⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⣾⠟⠱⠂⠆⠀⠀⢀⣾⠇⠀⠰⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡈⣭⣾⣯⣭⣿⡿⠟⠠⠧⠥⠴⣧⣙⣟⣽⣘⣙⣌⡔⠀⡸⣷⣿⣿⣿⣇⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⢿⣷⡀⠀⠀⢀⠀⠀⣾⡯⠄⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⢀⣴⣾⣿⣿⣿⣿⣟⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⢀⣿⡿⠁⢸⣿⣿⣿⣿⣻⣿⣾⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠻⣿⣿⣿⣄⢸⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣷⠀⠀⠀⠀⠀⣠⣶⡿⣿⡇⠀⢸⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⡇⢀⣿⣿⣿⣇⣿⠸⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣷⠀⠀⠀⣠⣤⢿⣿⣿⣻⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⠠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⠀⢸⣇⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣤⣴⡿⠟⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣴⡌⢃⣳⡀⢤⡉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡎⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢝⡿⣿⣿⣿⢸⡿⠀⠀⠀⣶⠀⠀⠻⠂⠀⠀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣇⣾⡏⣸⣿⣠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣶⠠⣶⡆⣿⡄⠀⠀⠀⢀⡀⠐⣽⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⡟⢻⡿⢻⣿⠸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣻⣦⣾⣿⠏⣿⠿⣿⡇⠀⠀⢀⣴⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣹⡆⣸⡇⠈⣷⠀⢿⡿⢿⣿⢿⣷⡞⢿⣿⣿⣹⣽⠉⡉⠉⠉⠛⠃⡝⠋⢙⡟⠁⠋⠀⣬⠀⠀⡀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⣆⣿⡇⢸⣷⡇⣿⡖⢸⣿⠀⣿⡀⠀⣧⠀⢻⡇⠀⣷⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢸⣿⠀⣼⡇⣀⣿⠀⣸⣿⣶⣿⣥⣼⣿⣼⣿⡇⢸⣿⠁⣿⡇⠈⣿⠀⢸⡇⠀⣿⠀⢸⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⣀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣇⣸⣟⡀⣿⣇⣸⣿⣤⣿⣏⣘⣿⣴⣿⣿⣨⣿⣧⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣿⣁⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⣄⢄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⠿⠋⢋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠘⢹⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⡶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣏⠋⠀⣿⣿⣿⠟⠋⠀⢀⠀⠀⠁⠂⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠁⠘⠉⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣀⢀⠈⣷⢰⠿⢻⠛⠓⢱⡆⡄⠆⡀⠠⠄⠙⠛⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣏⣿⣯⣭⣾⡿⠟⠂⠥⠥⠘⣇⣻⣿⣽⣠⣓⣔⠔⠀⣿⣷⣿⣿⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⣀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⢹⣶⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⢿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠛⣿⣿⣿⣄⢸⣣⣿⣿⣿⣿⣿⣿⣿⣿⣇⣅⠀⣷⠀⠀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⣷⠀⠀⠀⢠⠀⢸⣿⣿⣻⡷⡄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⠀⢹⣇⢸⣷⣿⣿⣿⣿⣿⣿⣷⣿⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⠀⣿⠀⠀⠀⠐⠀⢘⣿⠿⠃⠣⠄⢸⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡀⠤⣁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡞⢸⣧⢸⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⢰⡿⠀⠀⠀⣀⠀⠀⠹⠂⢀⡄⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣧⣾⣏⣸⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⢸⣦⢀⣶⡄⣿⡄⠀⠀⠀⢉⣀⠐⣹⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⡗⢻⡿⠻⣿⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢁⣼⣾⣿⡋⣿⠗⣿⠇⠠⠀⢀⣴⣿⣀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢹⡆⢸⡆⠀⣴⠀⢻⡿⢿⣿⠿⣿⡇⢹⣿⣿⢻⣿⣟⡟⠛⢠⠛⠁⣼⠟⣿⡟⡥⠏⠀⣦⠀⢀⡀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠹⣿⡿⢻⣿⡇⣿⡇⠸⣿⠀⢻⡟⠠⣧⠀⢹⡇⠈⣿⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢰⣿⠀⣼⡇⣀⣿⠀⣸⣿⣴⣿⣧⣼⣿⣤⣿⡇⢸⣿⠁⣿⡇⢀⣿⠀⢸⠇⠀⣿⠀⢸⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⠀⣀⣀⣰⣿⣿⠀⠀⢀⣻⣃⣸⣟⡀⣿⣇⢸⣿⣄⣿⣇⡈⣿⣴⢿⣿⣀⣿⣣⣸⣟⣀⣿⣇⣀⣿⢀⣸⣻⣆⣿⣇⣸⣿⣀⣿⡄⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠰⠶⠶⠖⠀⠀⠀⢄⠄⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⢿⠋⠋⣿⣿⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢹⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠁⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢠⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣛⣽⣷⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠁⠀⣿⣿⣿⠟⠁⠀⢀⠀⠀⠁⠂⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠁⠸⠋⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⡀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠸⠿⣿⣿⣿⣿⣷⣄⠂⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠠⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⠄⠀⠀⣠⠀⠈⣷⠰⡿⠻⠛⠓⢱⡆⡅⠂⡀⠄⠄⠙⠛⠻⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣭⣿⣾⣽⣿⡿⠟⠀⢥⠅⠴⣧⣹⣿⣽⣨⣛⣌⡀⣐⣿⣷⣿⣿⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⣀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⣹⣾⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡂⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⢅⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣏⡀⣷⠀⠀⠀⢠⠀⢸⣿⣿⡻⡷⡄⢸⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡾⠀⠀⢹⣇⢸⣷⣿⣿⣿⣿⣿⣿⣷⣿⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠀⣿⠀⠀⠀⠀⠀⢘⡿⠿⠃⠣⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡂⢤⡩⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡞⢸⣇⢸⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣽⣿⣿⣿⢰⡿⠀⠀⠀⠀⠀⠀⠹⠂⣀⡄⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣧⣾⣏⣸⣿⢠⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢸⣦⢀⣶⡄⣿⡄⠀⠀⠀⢉⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠟⢿⡟⢻⡿⠻⣿⠻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⢀⣧⣼⣿⡛⣿⠷⢿⡇⠀⠀⢀⣼⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢹⡆⢸⡆⠀⣴⠀⢻⡾⢿⣿⠿⣿⡇⢹⣿⣿⢿⣿⣟⡟⠛⢠⠛⠁⣼⠿⠿⡟⠧⠋⠀⣾⠀⢀⡄⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣾⡇⢸⣿⠀⣿⡇⢸⣿⠹⣿⣿⣿⣿⣧⣿⡇⠸⣿⠀⢿⡇⢐⣇⠀⢻⡆⠈⣷⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠠⣼⣿⠇⠀⠀⣸⡇⢰⣿⠀⣼⡇⢀⣿⠀⣸⣿⣴⣿⣧⣼⣿⣤⣿⡇⢸⣿⠁⣿⡇⢐⣿⠀⢸⡇⠀⣿⡀⢸⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⢀⣻⣁⣸⣟⡀⣿⣇⣸⣿⣤⣿⣇⣘⣿⣸⣿⣿⣀⣿⢣⣸⣟⢀⣿⣇⣘⣿⢀⣸⣻⣆⣿⣇⣸⣿⣀⣿⡄⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣕⠰⠶⠶⠖⠀⠀⠀⢄⠄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⠿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⡶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣇⠁⠀⢾⣿⣿⠟⠃⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠁⠘⠋⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⡀⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⡈⣼⢿⣿⣿⣿⣟⡆⡄⠀⠀⣠⠀⠀⣷⠰⠿⠻⠛⢓⢹⡏⡍⠂⠄⡤⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣏⣿⣯⣭⣿⡿⠟⠂⠥⠥⠠⣧⣹⣿⣝⣠⣉⣄⣤⣴⣿⣷⣿⣟⣚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⣀⠀⠀⠀⠀⠀⠀⡦⠄⠀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⢛⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣇⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣏⡀⣷⠀⠀⠀⠀⠀⢸⣿⣿⣻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⠀⢹⣇⣼⣷⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡇⣩⠀⣿⠀⠀⠀⠀⠀⢘⡿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⣾⢸⡇⢸⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣿⢰⡿⠀⠀⠀⢀⠀⠀⠻⠂⣀⡄⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣧⣼⡇⣸⣶⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡀⠀⢸⣦⠀⣴⡄⣾⡄⠀⠀⠀⢉⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠟⢿⠗⢻⡿⠻⣿⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣶⣼⣿⠻⣿⠇⣿⡇⠀⠀⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢹⡆⢰⡆⠀⣴⠀⢻⡶⣿⣿⢾⣿⡇⢹⣿⣿⣻⣿⣻⡟⠛⢠⠛⠁⣼⡿⡿⡟⠷⠟⠐⣾⠀⢠⡄⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣾⡇⢸⣿⠀⣿⡇⢸⣿⢹⣿⣿⣿⣿⡇⣿⡇⢸⣿⠁⢿⡇⢀⣇⠀⢻⡆⠈⣧⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣽⣿⠇⠀⠀⣼⡇⢰⣿⠀⣼⡇⣠⣿⠁⣼⣿⣴⣿⣧⣼⣿⣬⣿⡏⢹⣿⠁⣿⡇⢸⣿⠀⢸⣇⠀⣿⡀⢸⡇⠀⣿⠀⢸⣿⡁⠀⠸⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣻⣀⣸⣟⡀⣿⣇⢸⣿⣀⣿⣇⣘⣿⣼⣿⣿⣀⣿⢣⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣇⣸⣿⣀⣿⣂⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣖⠰⠶⠶⠶⠀⠀⠀⣄⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⢁⢈⣻⠿⠋⠫⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠘⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠃⠀⡿⣿⣿⠟⠃⠀⢀⠀⠀⠁⠂⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠹⠋⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⡀⠀⠀⣠⠀⠈⣷⠰⠿⢻⠛⢓⢹⡏⡅⠂⣤⣠⢄⠙⠿⠻⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣭⣾⣾⣭⣿⡿⠟⠠⠧⠤⢴⣧⣛⣿⣝⣘⣛⣈⣶⣶⣿⣷⣿⣟⣉⣓⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⢫⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⣿⣿⣛⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣆⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣏⣀⣷⠀⠀⠀⠀⠀⢸⣻⣿⣻⡷⠀⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⠈⢹⣇⢼⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠇⢡⠀⣿⠀⠀⠀⠐⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣴⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⣞⢸⡏⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⢶⣿⢸⡿⠀⠀⠀⠀⠀⠀⠻⠂⣀⡄⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣳⣾⣿⣿⣿⣿⣷⣾⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣸⣧⣾⡇⢸⣃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡀⠀⢸⣦⢀⣲⡄⣸⡆⠀⠀⠀⢉⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⠏⢻⡿⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣻⣟⢈⣦⣸⣿⠻⣿⡇⢿⠇⠀⠀⢀⣼⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢡⡆⢠⠄⠀⣴⠀⢻⡶⣿⣷⢾⣿⡇⢹⣿⣿⣻⣿⣻⣿⡟⢠⠛⠁⣾⡟⡿⡟⠒⠟⠘⣇⠀⢰⠄⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣿⡇⢸⣿⠈⣿⡇⢸⣿⢻⣿⣿⣿⣿⡇⣿⡆⢸⣿⠀⢻⡇⠐⣄⠀⢹⡄⠐⣇⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣾⠇⢰⣿⠀⣼⡇⣰⣿⠀⣾⣿⣴⣿⣧⣼⣿⣬⣿⡏⢹⣿⠁⣿⡇⢸⣿⠀⢸⣧⠀⣿⡀⢸⡇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⢀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣻⣀⣸⣟⠀⣿⣇⣸⣿⣄⣿⣇⣈⣿⣼⢿⣿⣀⣿⢣⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣇⣸⣏⣀⣿⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⢄⢄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣻⠿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠲⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠃⠀⣿⣿⣿⡟⠃⠀⢀⠀⠀⠁⠂⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠸⠋⠀⠀⠀⣸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⣁⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠘⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⣿⣿⡆⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⢼⢻⣿⣿⣿⣟⡆⡀⠀⠀⣠⠀⠈⣷⠰⢿⢻⠛⠓⢹⡏⡄⠀⠠⣄⠄⠙⠿⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣍⣾⣾⣭⣾⡿⠟⠂⠡⠥⠴⣧⣹⣿⣝⣘⣹⣐⢢⣴⣿⣷⣿⣿⣏⣍⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⣹⣾⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⣇⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢏⠀⣷⠀⠀⠀⠀⠀⢸⣻⣿⣻⡷⠀⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⢐⢺⣇⣾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⠀⣿⠀⠀⠀⠀⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡄⢤⡡⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡾⢸⡟⢸⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠭⣿⣿⣧⣿⢸⡿⠀⠀⠀⠀⠀⠀⠻⠂⣀⡄⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣶⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣸⣧⣾⡇⢸⡏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⢸⣦⢀⣶⡄⢸⡆⠀⠀⠀⢉⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠟⢿⠟⢺⡗⢻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠉⣙⣛⢁⣴⢸⣿⠿⣽⡏⢨⠅⠐⠀⢀⣼⣿⣀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢁⡆⢠⡀⠀⣴⠈⢿⣶⢿⣷⢾⣿⡏⢻⣿⣿⣻⣿⣻⣿⣟⢠⠛⠁⡼⠛⠿⠇⠀⠿⠘⢅⠀⠲⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⣠⡿⠀⣾⠀⢰⡇⢀⣾⡇⢸⣿⠀⣿⡇⢸⣿⠹⣿⣿⣿⣿⡏⣾⡆⢸⣧⠀⢸⡀⠀⣄⠀⢸⡄⠈⣆⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⠇⢠⣿⠀⣼⡇⣸⣿⠀⣾⣧⣶⣿⣧⣼⣿⣤⣿⡏⢹⣿⠁⣿⡇⢸⣿⠀⢸⣇⠀⣿⡄⢸⡇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⢀⣀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣻⣀⢸⣟⠀⣿⣇⣸⣿⣄⣿⣇⣈⣿⣼⣿⣿⣀⣿⢣⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣇⣸⣏⣀⣿⣌⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣖⠰⠶⠶⠖⠀⠀⠀⢄⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣻⢿⠋⠋⣿⣷⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠢⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⢸⠿⠻⡇⠀⠟⠻⢿⣟⠉⠀⣿⣿⣿⡟⠃⠀⢀⠀⠀⠁⠂⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⢘⡇⠀⣶⡆⢸⣿⣧⡀⠁⠙⠃⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⣁⠀⠁⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⢸⣿⣿⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⡆⠀⠀⠀⠀⠄⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⡀⠀⠀⣠⠀⠈⣷⢰⢿⢻⠛⠓⢹⡏⡅⠀⠤⣀⠤⠙⠛⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠘⠀⠀⠠⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣍⣾⣿⣭⣿⡿⠟⠠⢥⠥⡴⣧⣿⣿⣝⣘⣒⣌⢀⣤⣾⣷⣿⣿⣇⣌⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⢙⣤⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡃⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⢣⣾⣿⣿⣿⣿⣿⣿⣷⠀⣇⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣋⠀⣷⠀⠀⠀⠠⠀⢸⣿⣿⣹⡷⠀⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⢐⢺⣷⣾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠉⣿⠀⠀⠀⠐⠀⢘⣿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢃⣳⡂⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⣞⢸⡟⢸⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⡧⣿⢸⡿⠀⠀⠀⢀⠀⠀⠹⠂⣀⡄⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⡇⢸⡏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡅⠀⢸⣦⢀⣶⡄⣸⡆⠀⠀⠀⢉⣀⠐⣽⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠟⢿⠟⢹⡇⢻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠉⣛⡛⢁⣥⢸⣿⠻⣻⡗⢘⠃⠀⠀⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢉⡆⢠⡀⠀⣤⠈⢿⡶⣿⣷⢾⣿⡏⢻⣿⣿⣻⣿⣻⣿⣟⢠⠛⠁⡜⠛⣛⠇⠀⠿⠚⢍⠀⠒⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⣠⡿⠀⣾⠀⢰⡏⠀⣾⠇⢸⣿⠀⣿⡇⢸⣿⢹⣿⣿⣿⣿⡏⣿⡆⢸⣧⠀⢸⡀⠠⣤⠀⢾⡀⠀⣆⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣿⠇⢠⣿⠀⣼⡇⣸⣿⠀⣾⡧⣴⣿⣧⣼⣿⣤⣿⡏⢹⣿⠁⣿⡇⢸⣿⠀⢸⣇⠀⣿⡄⢸⡇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⡀⡀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣻⣀⣸⣟⡀⣿⣇⣸⣿⣄⣿⣇⣈⣿⣼⣿⣿⣀⣿⢡⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣇⣸⣏⣀⣿⣎⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣧⠰⠶⠶⠖⠀⠀⠀⢄⢤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⠿⠋⢋⣿⣷⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠁⠀⠒⠶⠶⣶⣿⣿⡟⠛⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⡇⠀⠟⠻⢿⣏⠃⠀⣿⣿⣿⡟⠁⠀⢀⠀⠀⠁⠂⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⢘⡇⠀⣶⡆⢸⣿⣧⡀⠉⠙⠁⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⣁⠀⡇⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⣿⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢿⣿⣿⣿⡟⡆⠀⠀⠀⣠⠀⠈⣷⠰⢿⢻⠛⠓⠑⡏⡍⠃⡠⡀⠄⠙⠛⠻⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣏⣾⣯⣭⣾⡿⠟⠂⠦⠤⠤⣧⣻⣿⣽⣔⣰⣬⠀⠠⢠⣷⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠩⠋⢹⠛⠙⠀⣠⣾⣿⣿⣿⡿⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⣸⣿⣿⣿⣿⣿⣿⣷⡀⣇⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⢍⠀⣷⠀⠀⠀⢀⠀⢸⣿⣿⣹⡷⠀⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⢠⢸⣷⣾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⣿⠀⠀⠀⠀⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢁⣳⡠⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡞⢸⡿⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿⠀⠀⠀⠀⠀⠀⠹⠂⣀⡄⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣇⣸⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⡇⡀⢸⣦⢀⣶⣄⣸⡆⠀⠀⠀⢉⣀⠐⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣼⠟⢿⠟⠹⠇⢻⣿⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⣛⣛⣁⣶⢸⣿⠻⢿⡏⠸⠇⠀⠀⢀⣼⣿⡀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢈⡆⢠⡀⠀⣠⠈⢻⡶⢿⣷⢾⣿⡏⢻⣿⣿⣻⢿⣻⣟⡇⢠⠛⠀⠘⠛⠻⠃⠀⢀⠈⠈⠀⢒⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⣰⡟⠀⣾⠃⢰⡏⠀⣿⠇⢸⡿⠀⣿⡇⢸⣿⠉⣿⣿⣿⣿⡇⣾⡆⢀⣇⠀⢸⡄⠀⣶⠀⢶⡀⠀⣆⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⡇⢠⣿⠀⣼⡇⣸⣿⠀⣼⣧⣴⣿⣧⣼⣿⣤⣿⡏⢹⣿⠁⣿⡇⢸⣿⠀⢸⣇⠀⣿⡄⢸⡇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⢀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣹⣀⣸⣿⡀⣿⣇⣸⣿⣄⣿⣇⣈⣿⣼⢿⣿⣀⣿⣣⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣇⣸⣟⣀⣿⣏⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⣄⠄⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⠟⠋⠫⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⠶⣶⣶⣾⡟⠛⣿⣿⣶⣶⣶⠆⢰⣴⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣆
⠘⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣗⠋⠀⣿⣿⣿⠟⠋⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⢘⡇⠀⣶⡆⢸⣿⣧⡀⠁⠙⠋⠀⠀⠀⣸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠃⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣆⠁⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⢸⣿⣿⡏⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⢼⢻⣿⣿⣿⣟⡆⡀⠀⠀⣠⠀⠈⣷⠰⣿⢻⠛⠓⠑⡄⡈⠃⣿⣇⠄⠙⠛⠿⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣍⣾⣿⣭⣿⡿⠟⠠⠧⠥⡴⣧⣹⣻⣝⣸⣻⣜⠀⠀⢾⠇⣿⣿⣿⣋⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⠀⠀⢰⣿⣿⣿⣿⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⡇⣸⣷⣾⣿⣿⣿⡏⣆⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⡇⣋⠀⣷⠀⠀⠀⢠⠀⢸⣿⣿⣻⡷⠀⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣱⢹⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⣻⠀⠀⠀⠐⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣴⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡿⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿⠀⠀⠀⢀⠀⠀⠻⠂⣀⡄⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣼⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣧⣸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⠀⢸⣦⢀⣶⣤⢼⡆⠀⠀⠀⢉⣀⠘⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⠟⣿⡟⢻⡟⠻⣿⠻⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣋⡦⢸⣿⠻⣿⡟⢻⡇⠐⠀⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣀⡄⢩⡀⠈⣁⠈⣻⡶⣿⣷⠙⣿⡏⢹⣿⣿⣟⣻⢫⡍⠀⢀⠙⠉⠙⠓⠸⠃⠀⠙⠁⠈⠃⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡏⠀⣾⠃⢰⡟⠀⣿⠃⢸⡿⠀⣿⡇⢸⣿⠙⣿⣿⣼⣿⡃⣸⠀⠀⡅⠀⢸⡆⠀⣿⠀⣶⡀⠀⣄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⡇⢠⣿⠀⣸⡇⣸⣿⠀⣼⣧⣴⣿⣧⣸⣿⣄⣿⡏⢸⣿⠁⣿⡇⢠⣿⠀⢸⣇⠀⣿⡀⢸⡇⠀⣿⡀⢸⣿⡁⠀⠸⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⣀⠀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣻⣀⣸⣿⡀⣿⣇⢸⣿⣄⣿⣇⣘⣿⣼⣻⣿⣈⣿⢣⣸⣿⣀⣿⣇⣸⣿⢀⣸⣿⣆⣿⣃⣸⣏⣀⣿⣍⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣅⠰⠶⠶⠶⠀⠀⠀⢄⢄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠑⠁⢀⣹⠾⠃⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢸⣵⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠀⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣷⣆
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣿⣿⠏⠉⠁⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠀⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠠⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⡟⡆⠀⠀⠀⣠⠀⠀⣷⠰⠿⠻⠛⠓⠑⡄⡀⠀⣤⢸⣿⣿⣿⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣭⣾⣾⣽⣿⡿⠟⠂⠅⠥⡐⣧⣻⣻⣝⣌⣲⣌⡠⠠⢶⣷⣿⣿⣧⣺⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⣀⣼⣿⣿⣿⡿⢻⣿⠟⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠂⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⣿⣿⣿⣿⣿⣿⣧⣾⣏⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⣀⣿⣿⣿⣇⣿⢘⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣷⠀⠀⠀⠀⠀⢸⣿⣿⣺⡷⠄⢸⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢀⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⢠⣢⢾⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⢀⢻⠀⠀⠃⠀⠀⢘⡿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢃⣳⡀⠤⡁⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡞⢸⣿⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣾⢨⠹⠀⠀⠀⢀⠀⠀⠹⠂⣀⡀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣷⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣯⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⡇⠀⢸⣦⣀⣶⣄⢸⡆⠀⠀⠀⢉⣀⠐⣹⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⠟⣿⡟⢻⡟⠻⣿⠻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣁⡧⢸⣿⠿⣿⡟⢻⡇⠀⠀⢀⣼⣿⡔⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣴⠀⢙⡁⠘⢁⠀⣿⡶⢻⣷⡼⣿⣿⣿⣽⣿⣿⣿⢫⣿⠏⢩⠻⠁⠘⠁⢸⡇⠀⣿⠀⠘⠃⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡏⠀⣼⠇⢠⡟⠀⣿⠃⢸⣿⠀⣿⡇⢸⣿⠉⣿⣧⢸⣿⡆⣼⡀⠀⡆⠀⢸⡇⠀⣿⠀⢶⡀⠀⡄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠽⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⡇⠀⠀⣾⡇⢠⣿⠀⣸⡇⣠⣿⠀⣼⣧⣤⣿⣧⣸⣿⣠⣿⡏⢸⣿⠀⣿⡇⠀⣿⠀⢸⣇⠀⣿⡀⢸⡇⠀⣿⡀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣙⣃⣸⣿⠀⣾⣇⣸⣿⣄⣿⣇⣨⣿⣹⣿⣶⣉⣿⢣⣸⣿⢀⣿⡇⣰⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣿⣏⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣅⠰⠶⠶⠖⠀⠀⠀⢄⠄⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣸⠾⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠀⢰⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣿⣷⣿⣿⣿⣿⣿⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣷⣆
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠐⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣿⣿⣿⡟⠉⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠀⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠄⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⠄⠀⠀⢠⠀⠀⣷⠰⢿⠻⠛⠓⠑⡄⡀⠀⣀⠀⢸⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣭⣾⣾⣽⣿⡿⠿⠆⠃⠥⠐⣧⣛⣿⣝⣀⣈⣄⠦⡀⢞⣥⣿⣷⣦⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⢀⣸⣿⣿⣿⣿⠛⢻⣿⠟⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠀⠀⡇⠀⣿⢀⣿⠛⣿⣿⣿⣄⢸⠇⢸⣷⣿⣿⣿⣿⣿⣇⠀⣿⡏⣷⠀⢀⠀⠀⠀⣠⣶⡖⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⣀⣿⣿⣿⣇⣿⢘⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⠀⠀⡀⠠⠀⢸⣿⣿⣹⡷⠄⢸⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢀⠁⠀⠀⠀⠀⠀⢀⣦⣴⡾⢠⢢⢾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢻⠀⠀⠃⠐⠀⢘⣿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢁⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡿⢸⣿⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠹⠀⠀⠀⢀⠀⠀⠻⠂⣀⡀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣲⣾⣿⣿⣿⣿⣶⣾⣬⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣯⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣢⣼⣿⡿⠁⢸⣦⢀⣶⣄⢸⡆⠀⠀⠀⢉⣀⠐⣹⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⠟⣿⡟⢻⡿⠻⣿⠻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡤⢸⣿⠿⣿⡿⢻⡇⠀⠀⢀⣼⣿⡀⣿⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣴⠀⢘⡁⠘⢁⠀⣿⡶⢻⣷⡼⣿⡿⣿⣽⣿⣿⣿⢩⣿⠏⢩⠻⠁⠈⠁⢸⡇⠀⣿⠀⠘⠇⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡟⠀⣼⠃⢠⡞⠀⣿⠇⢸⣿⠀⣿⡇⢹⣿⠉⣿⣧⢸⣿⡄⢨⡀⠀⡄⠀⢸⡇⠀⣿⠀⢶⡀⠀⣄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⡇⠀⠀⣾⡇⢠⣿⠀⣸⡇⣠⣿⠀⣸⣧⣤⣿⣧⣸⢿⣀⣿⡏⢸⣿⠀⣿⡇⠀⣿⠀⢸⣇⠀⣿⡀⢸⡇⠀⣿⡀⢸⣿⡃⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⠀⢀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣙⣃⣸⣿⠀⣿⣇⣸⣿⣄⣿⣇⣨⣿⣽⣽⣿⣈⣿⢇⣸⣿⢀⣿⡇⣀⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣿⡎⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⢄⠄⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣹⠾⠈⠉⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠈⢰⣵⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠲⣶⣶⣶⡖⠒⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣋⣭⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠐⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠀⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠄⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⡈⢼⢻⣿⣿⣿⣟⡆⠀⠀⠀⢠⠀⠀⣷⢰⡿⢻⠛⠓⠑⡄⡀⠀⣀⡀⠤⠙⢻⣿⣿⣿⠏⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⠀⣭⣾⣾⣽⣾⡿⠟⠢⠇⠅⠐⣇⣻⣿⣝⣰⣨⣀⡄⣀⠲⣣⣿⣶⣦⠄⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⠀⢐⣿⣿⣿⣿⠟⠛⠛⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠀⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⣧⣾⣿⣿⣿⣿⣿⠀⣅⠀⣿⣿⢁⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⣀⣿⣿⣿⣇⣿⢘⣿⣿⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣆⢍⠀⣿⠁⠀⡀⢀⠀⢸⣿⣿⣺⡷⠄⢸⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡾⢠⣦⢾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣸⣿⠀⠀⠃⠀⠀⢘⡿⠟⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢁⣳⡀⠠⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢘⡏⢸⣿⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠀⠀⠀⡄⠀⠀⠻⠂⣀⡀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣬⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣯⣸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣨⣿⣿⣷⣤⣿⣧⢀⣶⣄⢸⡄⠀⠀⠀⢉⣀⠐⣹⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⠟⣿⡟⢻⡿⠻⣿⠻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⠻⣿⠿⢺⡇⠀⠀⢀⣼⣿⡄⣿⣿⠇⠀⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣴⠀⠘⠁⠘⠁⠀⣿⡷⢻⣿⣼⣿⡟⢻⣽⣿⣿⡏⢩⣽⠏⢩⢿⣿⣿⣿⣿⠁⠀⣻⠀⠘⠃⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡟⠀⣼⠃⢠⡏⠀⣿⠇⢸⡿⠀⣿⡇⢸⣿⠉⣿⡇⢸⣿⡄⢀⠀⠉⣿⠋⢹⡇⠀⣿⠀⣵⡀⠠⣄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠽⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⡇⠀⠀⣾⡇⢠⣿⠀⣸⡇⣠⣿⠀⣸⣧⣤⣿⣧⣸⣛⣤⣿⡇⢸⣿⠁⣿⡇⢀⣿⠀⢸⡇⠀⣿⡀⢸⣇⠀⣿⠀⢸⣿⡃⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⡀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣙⣁⢸⣿⠀⣾⣇⣸⣿⣀⣿⣇⣈⣿⣽⣿⣿⣈⣿⢃⣸⣿⢀⣿⣇⣈⣿⢀⣸⣿⣆⣿⣁⣸⣿⣀⣿⣏⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⢄⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⡂⠁⠀
⣼⠀⠀⠑⠁⢈⣸⠾⠈⠉⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠈⢰⣴⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠰⣶⣶⣶⡖⠒⣶⣶⡶⣶⣶⠆⢠⣶⣶⣿⣿⣾⣿⣿⣿⣿⡃⠀⠀⠈⢻⣿⣿⣿⣟⣛⣋⣽⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡁⠀⠟⠻⢿⣌⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠁⠀⢠⠏⠀⠀⢹⣿⣯⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢹⣿⣀⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠀⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠠⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⡟⣿⣟⠆⡀⠀⠀⢠⠀⠈⣷⢰⠿⢻⠛⠓⠑⡄⡀⠀⡀⡀⠀⠙⠛⠛⠛⠛⠃⣿⣿⣿⠟⣿⣿⠀⢰⡄⠀⠰⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⠀⣭⣾⣾⣭⣿⡿⠟⠀⠣⠤⠴⣃⣻⣿⣽⣀⣀⡈⡀⡀⠰⢃⣯⣦⣔⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⠀⠀⣿⣿⣿⣿⡟⠛⠛⠛⠛⠂⠀⢸⣿⡟⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠂⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⣇⣴⣿⣿⣿⣿⡟⠀⢄⠀⣷⠀⠀⠀⣿⡟⢠⣶⡆⣿⡇⠀⢸⣿⡇⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⣘⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣆⢉⠀⣧⠀⠀⣀⣿⠁⢸⣿⣿⣸⡧⠀⢸⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⢀⣦⢾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⢿⠀⠀⣸⡿⠀⢘⡿⠿⠃⠃⠀⢸⣿⡇⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡄⢁⣳⡀⠠⡁⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣼⡏⢸⣿⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡿⠀⠀⣿⡇⠀⠀⠹⠂⣀⡀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣲⣿⣿⣿⣿⣿⣶⣶⣤⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢰⣧⣼⣏⣸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢩⣿⣿⡏⠀⢨⣤⢀⣾⣿⣿⡄⠀⠀⠀⢉⡀⠐⣹⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⠛⢿⡟⢿⡟⠻⣿⡻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣉⣿⣋⣁⠤⢸⡿⠺⣿⣿⢼⡇⠀⠀⢀⣼⣿⡀⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣤⠁⠈⡁⠘⠃⠀⣹⡏⢻⣿⣾⣷⡟⢻⣹⣟⣯⡏⢁⣬⠍⠉⢹⡏⠀⠀⢠⠀⢀⣿⡇⡘⠃⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⡟⠀⣼⠃⢠⡞⠀⣿⠇⢸⡿⠙⣿⡇⢸⣿⠈⣿⡇⢸⣿⡄⡀⢸⣷⡀⠀⢻⡆⢸⣿⠇⢤⡀⠰⡦⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⠼⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣼⡇⢠⣿⠀⣸⡇⣠⣿⠀⣸⣧⣤⣿⣧⣸⣶⣤⣿⡇⢸⣿⠀⣿⣿⣿⣿⠀⢸⡇⣼⣿⡀⢸⡇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⢿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⡿⣋⣁⠀⠀⡀⣀⣀⣰⣿⣿⠀⠀⠀⣛⣁⢸⣛⠀⣟⣃⢸⣿⣀⣻⣇⣨⣿⣹⢿⣿⣈⣿⢃⣸⣿⢀⢿⣿⣿⣿⣷⣼⣿⣿⣿⣁⣸⣿⣀⣿⣋⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⢄⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣿⣿⣿⠿⣿⣿⣿⣤⣾⣿⣿⣿⣶⣾⣕⡂⠁⠀
⣼⠀⠀⠑⠁⢀⣸⠞⠈⠉⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢯⢻⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠀⢰⣵⣿⠂⠀⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠆⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠒⠀⠀⠐⠒⠰⣶⣶⣶⡖⠒⣶⣶⡶⡶⡶⠆⢠⣴⣶⣶⣿⣿⡏⠀⠀⣆⣻⣿⣿⡏⣻⣿⣿⣿⣟⣛⣋⣩⣵⣆
⠈⣿⣶⣶⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡁⠀⠟⠻⢿⣄⠀⠀⠘⣻⣿⠟⢿⣿⣷⠀⠀⠛⢻⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡲⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠈⠁⠀⠸⣿⣿⣷⡀⠀⢰⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢸⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣷⣀⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⡇⠀⡸⣿⣿⣷⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡄⠠⣿⣿⣿⠀⠀⠀⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⢜⢻⣿⣟⣿⡟⠆⠀⠀⠀⢠⠀⠀⣷⢰⢿⠻⠛⠓⠑⡄⡀⠀⠄⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⢸⣿⣿⠈⢱⣄⣼⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⠀⣭⣾⣮⣭⣾⡿⠿⠆⠀⠠⠴⣧⣟⣿⣽⣈⣈⡈⠀⠀⠐⠃⡿⢃⣂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⡄⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⠀⠀⢠⣶⣿⣿⣟⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⣧⠀⣸⣿⣿⣿⣿⣻⣷⣶⣶⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠀⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠇⢸⡇⢀⡇⣸⣿⣿⣿⡿⢄⠀⣷⠀⢀⠀⠀⠀⢠⣶⣆⣿⣷⣴⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣠⡇⢀⣿⣿⣿⣇⣿⣘⣿⣿⣿⣄⢸⣧⣾⣿⣿⣿⣿⣿⡀⢉⠀⣵⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣦⣴⡞⢀⣄⢼⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⢿⠀⠀⠀⠀⠀⢘⡿⠟⣿⣿⣿⣿⣿⡇⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡄⢁⣳⡀⠠⡁⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣼⡟⢸⣿⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡾⠀⠀⠀⡄⠀⠀⠸⠂⣿⣿⡿⣿⣿⡇⠀⠀⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣲⣾⣾⣿⣿⣿⣶⣶⣤⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢿⣧⣼⣯⣸⣿⢠⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⡿⠁⢸⣶⠀⣶⡄⣿⡄⠀⠀⢸⣿⣏⠐⣹⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠛⢿⡏⢻⡿⠻⣿⣻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⡄⣈⣏⣉⡁⠤⠸⡿⠻⣿⠿⢺⡇⠀⢠⣿⣿⣿⡀⣿⣿⠇⠀⢸⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⡿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢠⠀⠈⠁⠈⠁⠀⢸⡟⢹⣿⣿⣷⡞⢿⣹⢟⣁⡌⠁⡀⠇⢸⣿⠉⠀⠀⢠⠀⠀⠝⠀⠈⠁⠀⣾⣿⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢙⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⣴⠀⠀⢠⡿⠀⣴⠃⢠⡆⠀⣿⠇⢸⣿⠸⣿⡇⢘⣛⠈⣿⡇⢰⣶⡀⢘⡇⠀⡄⠀⢹⡆⠀⣷⠀⢴⠀⢸⣿⣿⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣸⡇⢠⡿⠀⣼⠇⣀⣿⠀⣸⣿⣤⣿⣧⣸⣿⣀⣿⡇⢸⣿⠀⣿⣿⣸⣿⠀⢸⡇⠀⣿⠀⢸⣇⣾⣿⡟⢸⣿⡁⠀⠸⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⡿⡋⡁⠀⠀⠀⣀⣀⣰⣿⣿⠀⠀⠀⣙⡃⢘⣃⠀⣟⣀⢸⣿⣄⣹⣇⣘⣿⣠⢿⣗⣈⣿⢃⣸⣿⠀⢸⣻⣿⣿⣆⣸⣿⣆⣿⣁⣈⣿⣟⣻⣇⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣯⣷⣄⠰⠶⠶⠖⠀⠀⠀⢄⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢠⣾⣿⣿⣿⣶⣶⣕⡂⠁⠀
⣼⠀⠀⠑⠀⢀⣸⠾⠁⠋⣳⣷⣷⣉⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠀⢰⣵⣿⠂⠀⠒⠫⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠒⠀⠀⠐⠒⠐⣶⣶⣶⡖⠒⣶⣶⡶⡶⣶⠆⢠⣴⣶⣶⣶⠆⢠⣿⣿⣿⣿⣿⡆⠈⢻⣿⣿⣿⣟⣛⣋⣩⣵⣆
⠈⣿⣶⣶⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡁⠀⠟⠻⢿⣅⠀⠀⠘⣿⣿⠿⠁⣴⣿⣿⣿⣿⣿⣿⣷⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠘⠁⠀⣼⣿⣿⣿⠋⠹⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢹⣿⣀⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⣿⠀⠀⢽⣿⣿⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠋
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠄⠀⠀⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⢼⣿⣿⠀⠀⠀⠀⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣯⠀⠁⠀⣎⠈⢜⢻⣿⣟⣿⡟⠆⠀⠀⠀⢠⠀⠀⣷⠰⡿⠻⠛⠓⠑⡄⡀⠀⡄⠄⠄⠙⠛⠛⠛⠛⠃⠀⠀⢿⣿⣿⣿⠀⢰⡼⣿⣿⡆⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⠀⣭⣾⣮⣭⣾⡿⠿⠆⠦⠅⠰⣧⣟⣿⣽⣀⣈⡀⠂⠀⠰⠇⢿⢣⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⢸⣷⣿⣿⡇⠀⠀⠀⠀⡄⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⠀⠀⠀⣰⣿⣿⡟⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⢿⣿⡿⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠂⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠇⢸⡇⢀⡇⢸⣿⣿⣿⣿⣄⠀⣷⠀⠀⠀⠀⠀⢠⣶⣾⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣠⡇⢀⣿⣿⣿⣇⣿⡘⣿⣿⣿⣄⢸⡇⣸⣧⣾⣿⣿⣿⠏⣉⠀⣥⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣦⣴⡾⢀⣄⢼⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⢿⠀⠀⠀⠀⠀⢘⡿⠟⣿⣿⣧⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡀⢁⣓⡀⠠⡁⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⡟⢸⣿⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡾⠀⠀⠀⡄⠀⠀⠹⠂⣿⣿⣿⣿⣿⣿⠏⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣳⣿⣿⣿⣿⣿⣶⣶⣤⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣧⣼⣏⣸⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠁⢸⣶⠀⣶⡄⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠛⢿⡟⢻⡿⠻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⠿⠶⡄⠈⣋⣉⡁⠠⠸⡾⠛⣿⠿⢸⡇⠀⠀⢀⣿⣿⣿⣿⣿⠇⠀⢰⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣀⠀⠈⠁⠘⠁⠀⢸⡏⢹⣿⣿⣷⡞⢟⣫⢟⡁⡈⠁⠀⠇⠀⣿⠁⠀⠀⢀⠀⠀⡝⠀⠈⠃⠀⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢙⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⣴⠀⠀⢰⡿⠀⣴⠃⢀⡆⠀⣿⠇⢸⣿⠘⣿⡇⢸⣻⠈⣿⡇⢠⣷⠀⠀⡇⠀⡄⠀⢸⡆⠀⣷⠀⢾⠀⠈⠡⢠⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣼⡇⢠⡿⠀⣼⠇⣀⣿⠀⣸⣷⣴⣿⢥⣼⣿⢀⣿⡇⢸⣿⠀⣾⡷⣰⣿⠀⢸⡇⠀⣿⠀⢸⣇⠀⣿⣾⣿⣿⡁⠀⠸⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⠀⣀⣀⣰⣿⣿⠀⠀⠀⡛⡃⢸⣃⠀⣿⣀⢸⣿⣄⣹⣇⣈⣿⣠⢿⣟⣀⣿⢁⣸⣿⠀⢸⣻⣿⣿⣆⣸⣿⣆⣿⣁⣈⣿⣀⣸⣿⣋⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣯⣶⣄⠰⠶⠶⠖⠀⠀⠀⢄⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣻⠾⠉⢋⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠈⢰⣵⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠀⠀⠒⢶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣋⣽⣷⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠐⠀⠀⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡅⠀⠟⠻⢿⣟⠀⠀⠾⣿⣿⠟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠘⠋⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠀⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⢼⢻⣿⣿⣿⣟⡆⠄⠀⠀⢠⠀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡀⠀⡄⠄⣤⣙⠛⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⠀⣭⣾⣮⣭⣾⡿⠿⠦⠧⠥⠔⣧⣻⣿⣝⣨⣘⡔⠀⢀⣾⢧⣿⣃⣘⣺⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⣿⣟⣿⡿⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠆⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠇⢸⡇⢀⡇⢰⣿⣿⣿⣿⣇⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⡇⢸⣇⣼⣿⣿⣿⡏⣉⠀⣷⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢀⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣔⢸⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⡧⢁⠀⣿⠀⠀⠀⠀⠀⢘⣿⣿⡿⠟⢿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡀⢤⡉⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⡿⢸⣿⢹⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⠀⠀⠈⣇⠀⠀⣿⣿⣇⣀⢸⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣬⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣧⣼⣏⣸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣶⢀⣶⡄⣿⡄⢰⣿⣿⢋⣈⢹⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⠛⢿⡟⢿⡿⠻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⢷⠿⠉⡉⢻⣟⣋⠁⠠⠸⠻⠺⣿⠿⢿⡇⠘⣿⣿⣼⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣀⠀⠈⠁⠈⠃⠀⢸⡟⢸⣿⣿⣷⡾⢿⣻⣿⡀⡈⠀⠀⠇⠈⣿⠁⠀⠀⠠⠀⠀⡝⠀⠘⠀⣀⢹⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⡿⠀⣼⠃⢠⡖⠀⣿⠇⢸⣿⠘⣿⡇⢨⣭⠈⣿⡇⢠⣴⠀⢀⡻⠀⣀⠀⢿⡆⠀⣧⠀⢯⡀⠈⣋⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠁⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢰⡏⠀⣾⡇⣠⣿⠀⣸⣿⣴⣿⢣⣼⣟⠀⣿⡇⢸⣿⠀⣾⡷⡰⣿⠀⢸⡇⠀⣿⠀⢸⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⠀⡀⣀⣀⣰⣿⣿⠀⠀⠀⣻⡃⢘⣃⠀⣿⣀⣸⣿⣄⣹⣇⣸⣿⣨⢿⣿⣈⣿⢁⣸⣿⠀⢿⡿⣷⣿⣇⣸⣿⣆⣿⣁⣘⣿⣀⣸⣻⣿⣿⣿⣿⣿⣿⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣔⠰⠶⠶⠖⠀⠀⠀⢄⠤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣷⣂⠅⠀
⣼⠀⠀⠙⢃⣌⣿⣿⠋⢻⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠒⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⣶⢶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣻⣛⣽⣿⣦
⠈⣿⣶⣷⣶⠞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⡴⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⡀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠁⠀⣿⣿⣿⠟⠉⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠹⠏⠀⠀⠀⣸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⡀⠀⠛⠀⠘⢹⠀⢸⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⣤⡄⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠿⣿⣿⣿⣿⣷⣔⠃⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⡉⣼⢻⣿⣿⣿⣟⡆⡀⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡄⠀⣤⣤⣤⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣭⣿⡿⠿⠧⣧⡥⡼⣧⣿⣿⣽⣼⣛⣼⡦⢠⣾⣧⣿⣧⣿⣦⣿⣿⣛⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⢂⣭⣏⠩⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⣟⣿⠟⠛⢻⣿⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣷⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⡇⢘⡇⢐⣧⣤⣿⠏⣇⠀⣿⠛⢓⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠸⣿⣿⣿⣄⢸⡇⢸⡇⣿⣿⣿⣿⡇⣏⠀⣷⠀⠀⠀⢠⠀⢹⣿⣿⣿⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣴⢼⣯⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣇⣼⣧⣼⣿⣿⣿⢃⣛⠀⣿⠀⠀⠐⠀⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣐⣴⡌⢃⣳⡂⢤⣩⢿⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⣿⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⢸⣿⠀⠀⠐⣇⠀⠀⠻⠂⣀⡀⠀⣾⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣷⣿⣿⣿⣿⣿⣶⣿⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣯⣼⣯⣸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣶⢀⣶⡄⣿⡄⠀⠀⠀⢉⣀⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠿⠟⢻⡟⢻⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣟⡹⢸⣿⠻⣿⠿⢿⡇⠀⠀⢀⣼⣿⣤⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣠⠀⠈⡁⠘⢃⠀⢸⡟⢸⣿⣿⣷⣾⣿⣿⣿⠀⡀⠀⠀⠋⢹⣿⠉⠀⠀⣰⠀⠀⡝⠀⡘⠀⣀⡀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⠀⠀⢰⡿⢀⣼⠇⣠⡿⠀⣿⠇⢸⣿⠘⣿⡇⢸⣾⠉⣷⡇⢠⣄⠀⣘⣧⠀⡀⠀⢿⡆⠠⣷⠀⢶⡀⠀⣡⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠐⣾⣿⠇⠀⠀⣼⡇⢸⡏⠀⣿⡇⣠⣿⠀⣸⣿⣶⣿⢠⣼⣿⢁⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⣿⡀⢸⣷⠀⣿⡇⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⢀⣀⣀⣿⣃⣸⣇⠀⣿⣀⣸⣿⣄⣻⣇⣸⣿⣸⣿⣟⣀⣿⣣⣸⣿⣀⣿⣿⣾⣿⣄⣸⣿⣆⣿⣁⣸⣿⣶⣾⣇⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠁⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠰⠶⠶⠶⠀⠀⠀⣄⣤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣶⣶⣕⡂⠁⠀
⣼⠀⠀⠐⠁⢀⣸⠞⠉⠋⣲⣷⣿⣉⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠀⢰⣴⣿⠂⠀⠒⠫⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣤⣶⣴⠖⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠒⠀⠀⠐⠖⠔⣶⣶⣶⡖⠒⣶⣶⡶⢶⠶⠆⢰⣴⣶⣶⣾⣿⠏⠀⢸⣿⣿⣿⣿⡏⢻⣿⣿⡿⣟⣛⣋⣩⣵⣆
⠈⣿⣶⣶⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡁⠀⠟⠻⢿⣆⠀⠀⠈⣿⣿⣿⣿⡏⢀⠀⢸⣿⣿⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠘⣽⣿⡿⠀⢸⣧⢸⣿⣿⣿⣿⣿⡄⢹⣿⣯⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣷⣀⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⢠⣿⣿⠁⠀⣿⣿⢸⣿⣿⣿⣿⡿⠃⠀⢻⣽⣽⣿⣿⣿⣿⠋
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠄⠀⠐⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⢸⣿⣿⣿⣿⠃⠀⠀⠀⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣯⠀⠀⠀⣎⠈⢼⢻⣿⡟⣿⣟⠆⠀⠀⠀⢠⠀⠀⣷⠰⣿⠻⠛⠓⠑⡄⡀⠀⡄⡀⠀⠙⠛⠛⠛⢻⣿⡟⠀⠀⠀⣿⣿⣸⣿⣿⣿⠿⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⠀⣭⣾⣮⣭⣾⡿⠿⠂⠂⠠⠴⣇⣛⣿⣝⣄⣀⡜⠂⠀⠶⠧⠿⢆⣠⡀⡀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠲⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣛⣳⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠀⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⡇⢀⣧⣤⣇⠀⡇⠀⣅⠀⣷⠀⣼⡿⠀⠀⢠⣶⣆⣿⣿⣿⢿⣿⡇⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⡇⢾⣿⣿⣿⣇⣁⠀⢁⠀⣧⠀⣿⡇⠀⠀⢸⣿⣿⣿⣿⠏⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣤⢸⢿⢽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣯⣼⣿⣿⣿⣿⣿⡀⢈⠁⣿⣸⣿⠡⠀⠀⢘⣿⣿⣿⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡄⢁⣳⡀⠠⡁⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⣿⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣼⣿⣿⡇⠀⣄⠀⠰⣿⣿⣯⡀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣲⣾⣾⣿⣿⣿⣶⣶⣤⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣧⣼⣏⣸⣿⢠⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⣿⣿⣿⣷⡀⣿⡄⠀⢿⣿⣟⡀⠘⣽⣿⡇⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠟⢻⡟⢻⣿⠻⣿⣻⣿⣿⣿⡿⢿⣿⣿⣟⠻⠿⠿⣿⣿⡿⣛⣋⢁⡰⢺⣿⠸⣿⠗⢿⡇⠀⠀⢉⣼⣿⡀⣿⣿⠃⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⢻⡟⢻⣿⢿⣧⡞⠟⣛⠿⠀⠐⠀⠈⢻⡄⢩⠉⠈⠁⢈⠛⠀⠉⠀⢨⣤⠄⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢙⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⣴⠀⠀⢀⡾⠀⣾⠁⢸⡇⠀⣾⠇⢸⣿⠈⣿⠇⢸⣿⠀⣤⠁⢠⡀⠀⢹⡓⠐⣶⠀⢰⡄⠀⣄⠀⣼⣿⠀⣆⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠽⢿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣸⡇⢸⡇⠀⣾⡇⢀⣿⠀⣸⣧⣴⣿⢠⣼⣿⠀⣿⡀⢸⣷⠀⣿⡇⠨⣿⠀⢸⡇⠀⣿⠀⣿⣿⡆⢿⡄⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⢿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⡿⡋⣁⣀⠀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣻⣃⢘⣇⠀⣿⣀⣸⣿⣄⣸⣇⣈⣿⣰⢹⣟⣀⣿⢁⣸⣿⠀⢹⣗⣶⣿⣀⣸⣿⣆⣿⣁⣿⣿⣇⣘⣁⣀⣿⣃⣀⣀⣀⣀⣀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿
⣿⣞⣾⣿⣯⣷⣆⠰⠶⠶⠖⠀⠀⠀⢄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⢸⣿⣿⣿⣿⣶⣾⣕⡂⠁⠀
⣼⠀⠀⠙⠁⢈⣸⠾⠈⠉⣻⣷⣷⣉⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠀⢰⣴⣿⠂⠀⠒⠫⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠒⠀⠀⠐⠲⠔⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠂⢰⣴⣶⣶⣶⠂⣰⣿⣿⠃⡀⠀⠀⣿⣿⣿⣿⣿⣟⣛⣋⣭⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠐⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡁⠀⠟⠻⢿⣇⠀⠀⠘⣿⣿⠟⠁⢠⣿⣿⠏⠁⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠘⠁⠀⠀⣼⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢹⣿⣀⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⠋
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠐⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⠀⠀⠠⢶⣿⣿⣿⣿⠏⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⣎⠈⢼⢻⣿⣿⣿⣟⡆⡀⠀⠀⣠⠀⠀⣷⢰⣿⠻⠛⠓⠑⡄⡀⠀⡄⠀⠄⠙⠛⠛⠛⠛⠃⠀⣸⣿⠇⣿⣿⠀⢰⡄⢸⣿⣿⣿⡏⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⠀⣭⣾⣮⣭⣾⡿⠿⠦⠂⠠⠴⣧⣛⣿⣝⣨⣠⡸⠂⠀⠰⠧⠿⢂⣃⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⣿⡟⠀⢸⣷⣿⣿⣿⣿⠀⠀⠀⡤⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⣼⣿⠃⠀⣿⡇⠀⢸⣿⣿⣿⣿⣟⣷⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠀⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⡇⣠⣧⣤⣇⠀⡇⠀⢅⠀⣷⠀⠀⠀⢰⣿⣹⣶⡆⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⢸⡷⣿⣿⣿⣿⣄⣁⠀⢁⠀⣧⠀⠀⠀⣴⡏⢸⢿⣿⣸⡧⢀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣤⢸⠿⢾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣯⣿⣿⣿⡟⠿⣿⣷⣌⠁⣿⠀⠀⣰⣿⠃⢘⡿⠟⠃⢃⣾⣿⣿⡟⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡄⢃⣳⡀⠠⡁⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⣿⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⢿⣿⣿⡿⠀⠀⣿⣿⠀⠀⠹⠂⣀⣾⣿⣿⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣲⣾⣿⣿⣿⣿⣶⣾⣤⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣧⣼⣯⣸⣿⢠⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢿⣷⣴⣾⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠟⢿⡟⢻⣿⠻⣿⣻⣿⣿⣿⡿⢿⣿⣿⣟⠿⠿⢿⣿⣿⡛⣛⣋⢀⡰⢸⣿⠿⣿⠟⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⠃⠀⢸⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⢻⡟⢿⣿⢿⣧⡎⠟⣛⢿⠀⠀⠀⠈⢿⣄⢽⠉⠈⠁⢈⠟⠀⠙⠀⣼⣄⠄⠀⠹⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢙⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢀⡿⢀⣿⠀⢸⡇⠀⣾⠇⢸⣿⠘⣿⠃⢸⣿⠀⣤⡀⢠⡄⠀⢹⡍⢰⣶⠀⢸⡄⠀⣆⢰⣿⣿⠀⣦⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠀⠽⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣸⡇⢸⣇⠀⣾⡇⢀⣿⠀⣸⣿⣴⣿⢠⣼⣿⠀⣿⡀⢸⣯⠀⣿⡇⠘⣿⠀⢸⡇⠀⣿⢸⣿⣿⠀⢿⡄⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⡿⣋⡁⠀⡀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣻⣃⢘⣇⠀⣿⣀⣸⣿⣄⣸⣇⣘⣿⣠⣻⣟⣀⣿⢀⣸⣿⠀⢹⣳⣶⣿⣀⣸⣿⣆⣿⣁⣻⣿⣄⣘⣀⣀⣿⣃⣀⣀⣀⣀⣀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿
⣿⣷⣿⣷⣯⣷⣄⠰⠶⠶⠖⠀⠀⠀⢄⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣶⣕⡂⠁⠀
⣼⠀⠀⠑⠀⢀⣰⠞⠀⠉⣲⣷⣿⣉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠀⢰⣵⣿⠂⠀⠒⠻⠿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠰⣤⣶⣴⠆⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠒⠀⠀⠐⠂⠐⣶⣶⣶⡖⠒⣶⣶⣶⡶⣶⠂⢰⣴⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡿⣟⣛⣋⣩⣵⣆
⠈⢿⣶⣶⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡁⠀⠟⠻⢿⣅⠀⠀⠊⢻⣿⠏⠀⠀⢀⠀⠀⠁⠂⠀⣰⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠘⠁⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢹⣿⣀⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣼⣿⣿⠏⢻⣽⣽⣿⣿⣿⣿⢫
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠠⠾⣻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⡿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⣶⣿⣿⠏⠀⠀⠻⣿⣿⠿⢛⣵⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣶⣿⠀⠁⠀⣎⠈⢼⢻⣿⣿⣿⣟⠆⠄⠀⠀⢠⠀⠀⣷⠰⠿⢻⠛⠓⠑⡄⡀⠀⣤⠀⠀⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⣿⣿⠀⢰⣤⣿⣿⡿⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⠀⣭⣾⣮⣭⣾⡿⠿⠆⠀⠀⠰⣧⣛⣿⣝⣀⣈⣘⡆⠠⠴⠧⠿⠂⣆⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⡏⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣟⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠀⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⡇⣰⣿⣿⣿⣿⣿⣦⡇⠀⣷⠀⠀⠀⠀⠀⢠⣶⡆⣿⡇⢀⣿⣿⡏⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠈⣿⣿⣿⣄⣸⣿⣿⣿⣿⡇⠀⣙⣿⣿⣄⣥⠀⠀⠀⠀⠀⢸⣻⣿⣸⣧⣾⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣤⣴⡞⠀⣄⢸⣷⢺⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⣿⣿⡃⠠⠿⠈⢻⣿⣿⠀⠀⠀⠀⠀⢘⡿⠟⠃⢻⣿⣿⣿⡇⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡄⢁⣰⡀⠠⡁⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⡏⢸⣷⢸⣬⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⢴⣿⣿⣿⣆⠀⠀⡀⠀⠀⠰⠂⣠⣿⣿⣿⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣲⣾⣾⣿⣿⣿⣶⣶⣤⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣧⣼⡇⣸⣿⢠⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣶⡀⣿⡄⠀⠀⢀⣿⣿⡟⣻⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⡏⢻⡿⠻⣿⢻⣿⣿⣿⡿⢿⣿⣿⣿⠿⡿⢿⣿⣿⡛⣛⣋⢀⡠⢸⣿⢿⣿⣇⣿⠇⢀⣴⣾⣿⣿⡁⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⣀⠁⢈⡁⠀⢻⡟⢿⣿⢿⣧⡎⢛⣛⢿⠀⠀⠀⠉⢿⣄⡉⠉⠘⠁⢈⠏⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⣴⠀⠀⢀⣾⠀⣿⠀⢸⡇⠀⣾⠇⢸⣿⠈⣿⠃⢸⣿⠉⣤⠀⢠⡄⠀⢰⡌⢸⣿⠀⢨⡄⠀⣇⠈⣿⣿⠻⣿⠉⣿⣿⣿⢿⣿⣠⣿⣿⣿⣿⠋⠽⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣸⡇⢸⣇⠀⣾⡇⢀⣿⠀⣸⣯⣴⣿⢠⣼⣿⠀⣿⡄⢸⣧⠀⣿⡇⠈⣿⠀⢸⡇⠀⣿⠀⣿⣿⠀⣻⠂⢸⣿⡁⠀⢸⣿⣿⣿⡿⠃⠀⠠⣻⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⢀⣀⠀⣀⣀⣰⣿⣿⠀⠀⠀⣿⡃⢘⣇⠀⣿⣁⣘⣿⣄⣸⣇⣘⣿⣠⢹⣟⣀⣿⢃⣸⣟⠀⢹⣗⣤⣿⣄⣸⣿⣆⣿⣁⣿⣿⣀⣘⣀⣀⣿⣃⣰⣿⣿⣿⣟⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿
⣿⣖⣿⣾⣏⣷⣄⠰⠶⠶⠖⠀⠀⠀⢄⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣻⠾⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠘⢹⣵⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠁⠀⠒⠶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠐⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣏⠃⠀⣿⣿⣿⡟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠹⠋⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠄⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⠀⠀⠀⣠⢀⠈⣷⠰⠿⢻⠛⠓⠑⡄⡄⠀⡄⠤⠄⠙⠻⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣍⣾⣿⣭⣿⡿⠿⠡⠧⠅⠴⣧⣿⣿⣝⣨⣛⣼⢲⣤⣾⣧⣿⣗⣏⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⢾⡟⠛⠛⢻⣿⣿⣿⣟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡄⠀⡇⠀⣿⢀⣿⠙⣿⣿⣿⣄⢸⠃⢸⣿⣿⣧⣤⡇⠀⡟⢿⣿⣷⣷⠀⠀⠀⠀⠀⢠⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⣸⣿⣿⣿⣿⣧⠀⣇⠀⢙⣿⣿⣆⠀⠀⠀⠀⢹⣿⣿⣻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣄⢸⣧⢾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⡏⠠⡿⠀⢈⠈⣿⣿⣷⡀⠀⠀⢘⣿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⠤⡉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⡏⢸⣟⢸⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠄⢶⣿⢸⡿⠹⣿⣷⡇⠀⠀⠹⠂⣀⡀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⡧⣼⣇⣸⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠀⢸⣶⣠⣿⣿⣷⡄⠀⠀⠀⢉⣀⠘⣽⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⡟⢻⡟⠻⣿⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡼⢺⣿⠻⣿⣿⣿⣧⠐⠀⢀⣼⣿⡄⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⣨⠃⢈⡇⠀⢻⡿⢿⣿⢿⣷⡎⢻⣿⣿⠀⠀⠀⠉⣿⠄⠛⢋⣼⠁⠘⠟⠀⠉⢹⣿⣿⡄⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣿⡇⢸⣿⠘⣿⡇⢸⣿⠉⣦⠀⢠⡄⠀⢰⡄⢸⣿⠀⢾⡄⠀⣧⢨⣿⣿⡇⣿⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢸⣿⠀⣾⡇⢠⣿⠀⣸⣿⣴⣿⢤⣼⣿⠀⣿⡄⢸⣿⠀⣿⡇⠀⣿⠀⢸⡇⠀⣿⠈⣿⣿⣿⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⣀⣿⣃⣸⣇⡀⣿⣁⣸⣿⣄⣹⣇⣈⣿⣠⣻⣿⣀⣿⣃⣸⣿⠀⣻⣷⣤⣿⣄⣸⣿⣆⣿⣁⣽⣿⣿⣿⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠰⠶⠶⠶⠀⠀⠀⢄⠄⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣄⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣻⣿⠋⢋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣿⣶⣶⣶⠒⠚⠑⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣛⣽⣿⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢰⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠃⠀⣿⣿⣿⡟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠉⠘⠉⠀⠀⠀⣸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢿⣿⣿⣿⣟⠆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡄⠀⣤⣄⠤⠝⠿⠿⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣭⣾⣿⣿⣿⡿⠿⠥⠣⠥⡼⣯⣻⣿⣽⣸⣟⣼⠦⣀⣾⡧⣿⣧⣏⣋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⢀⣭⣏⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠄⠀⡇⠀⣿⢀⣿⠛⣿⣿⣿⣄⢸⠃⢸⣷⣾⣷⣤⡇⠀⡇⠀⣇⠀⣷⠀⢀⠀⠀⠀⣠⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⢀⣿⣿⣿⣇⣿⠘⣿⣿⣿⣄⣸⣟⣿⣿⣿⣿⣦⣃⠀⣏⣀⣷⠀⠀⠀⠠⠀⢸⣿⣿⣻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣜⢻⣷⣾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣆⣙⠀⣿⠀⠀⠀⠄⠀⢘⣿⠿⠋⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣴⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡏⢸⣿⢸⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡿⣿⣿⣾⡿⠀⠀⠀⣇⠀⠀⠹⠂⣀⡀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣼⣇⣼⣧⣼⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⣿⣿⣦⣀⣒⡄⣙⡆⠀⠀⠀⢉⣀⠘⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⡟⢻⡿⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣑⡿⢿⣿⣿⣿⠏⢿⡇⠀⠀⢀⣼⣿⣤⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠉⠀⢸⠇⢀⡷⠀⢻⡿⣿⣿⣿⣿⡏⢻⣿⣿⠀⢠⠀⠙⡏⠀⠙⢹⣾⠃⠘⢿⣿⣿⣤⣾⡄⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣾⠀⣿⠀⢸⡇⠀⣾⡇⢸⣿⠘⣿⡇⢸⣿⠉⣤⡀⢀⡄⠁⢰⡀⢘⣿⠀⢿⡀⢹⣿⣿⣿⣇⠀⣿⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢰⣿⢀⣾⡇⢀⣿⠀⣸⣿⣶⣿⣠⣼⣿⣀⣿⡇⢸⣿⠀⣿⡇⠀⣿⠀⢹⡇⠀⣿⣿⣿⣿⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⡀⣀⣿⣃⣸⣏⠀⣿⣇⣸⣿⣤⣻⣇⣈⣿⣰⣻⣿⣀⣿⣇⣸⣿⣀⣿⣷⣦⣿⣄⣸⣿⣆⣿⣿⣿⣿⣆⣸⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣗⣂⠁⠀
⣼⠀⠀⠙⠁⣈⣻⡿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⣹⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣛⣭⣵⣦
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠔⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠃⠀⣿⣿⣿⠟⠀⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠁⠙⠋⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⡀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣿⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⢻⣿⣿⣿⣟⠆⡀⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡄⠀⣄⣄⠤⠝⠿⠿⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣭⣾⣿⣯⣿⡿⠿⠤⠧⠥⡵⣧⣿⣿⣽⣸⣟⣸⠦⣤⣾⡧⣿⣧⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⣹⠀⢸⠃⢸⡇⢘⣧⣴⣇⠀⡇⠀⣇⠀⣷⠙⢐⠀⠀⠀⣤⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢠⡇⠀⣿⡀⣿⣀⣿⠀⣿⠀⢸⣀⣸⣇⣿⣿⣿⣿⡇⣿⠀⣿⠀⣿⠀⢰⠀⢰⠀⢻⣿⣿⣿⡧⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣜⢻⣷⣾⡇⢠⣯⡟⣿⣿⣿⣦⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣁⣿⠂⣿⠀⣿⠠⣼⠀⡴⠆⢘⣿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡟⢸⣿⢹⣿⠀⣿⡇⣿⡏⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠈⣿⠀⣧⡄⠀⠹⠂⣀⡀⠀⣼⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣷⣿⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⡇⣾⣧⣸⣇⣠⣿⣥⣿⣿⣿⣷⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣀⢿⡄⠹⡇⠀⠀⠀⢉⣀⠘⣽⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠓⢿⡟⢻⡿⠻⣿⠻⣿⣿⢿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⣿⡇⠀⠀⢀⣼⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠉⠀⢸⠇⢀⣷⠀⢻⡿⢿⣿⣿⣿⡏⢿⣿⣿⠁⢰⠀⠈⡏⠀⠙⢹⣿⣿⣿⣟⠀⠉⢠⣾⡄⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢀⣿⠀⣿⠀⢸⡇⠀⣾⡇⢸⣿⠘⣿⠇⢸⣿⠁⣤⡀⢀⣄⠁⢰⡀⠘⣿⠙⣿⣿⣾⣇⢸⣿⡇⠀⣿⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢰⣿⠀⣾⡇⢀⣿⠀⣸⣿⣶⣿⢤⣼⣿⣀⣿⡇⢸⣿⠀⣿⡇⠀⣿⠀⢸⣿⣿⣿⡀⢻⣟⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⣀⣿⣃⣸⣏⡀⣿⣇⣸⣿⣄⣿⣇⣈⣿⣰⣻⣿⣀⣿⣇⣸⣿⣀⣿⣷⣤⣿⣄⣸⣿⣿⣿⣷⣼⣿⣀⣸⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣖⠰⠶⠶⠖⠀⠀⠀⢄⠄⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣗⣂⠁⠀
⣼⠀⠀⠙⢁⢈⣻⡿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢱⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠑⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣦
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠔⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣏⠇⠀⣿⣿⣿⠟⠀⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠈⠹⠛⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⡀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⡀⠀⠀⣠⢀⠈⣷⠰⣿⢻⠛⠓⠑⡄⡀⠀⣤⢤⠤⠝⠿⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣭⣾⣿⣿⣿⡿⠿⠧⠥⠥⠴⣯⣻⣿⣽⣼⣿⣼⢶⡠⢾⢧⣿⣷⣟⣈⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⠀⣿⠀⣿⠀⣹⠀⢸⠇⢸⡇⢐⣧⣶⣧⡀⡇⠀⣇⠀⣷⠑⢐⠀⠀⠀⣤⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢠⡇⠀⣿⡀⣿⠀⣿⠀⣿⠀⢸⡀⢸⡇⢾⣿⣿⣿⡷⣿⠀⣿⠀⣿⠀⢰⠀⢰⠀⢻⣿⣿⣿⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣼⢺⣧⣼⡇⢠⣷⡗⣿⣿⣿⣆⣿⣄⣸⣿⣾⣿⣿⣿⣿⣿⣁⣿⠂⣿⠀⣿⠠⣼⠀⣴⠂⢘⣿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡟⢸⣿⢹⣿⠀⣿⡇⣿⡏⣿⣿⢹⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⠘⣿⠀⣧⡅⠀⠹⠂⣀⡀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣼⡇⣾⣇⣸⣧⣠⣿⣥⣿⣿⣿⣷⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣀⣿⡄⢹⡇⠀⠀⠀⢉⣀⠘⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠓⢿⡟⠿⡶⠻⣿⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢿⣿⠿⣿⠗⢸⡇⠀⠀⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠉⡀⢨⡆⠀⡶⠀⢻⡾⣿⣿⢿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣟⠀⠙⢹⣿⠃⠘⠟⢀⡉⢰⣿⡄⠀⡀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢀⣾⠀⣿⠀⢸⡇⠀⣼⡇⢸⣿⠈⣿⠇⢸⣿⠁⣿⣿⣿⣿⣿⣿⡄⠈⣿⠀⢸⡀⠸⣇⠸⣿⡇⠀⣧⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢰⣿⠀⣼⡇⢠⣿⠀⣸⣿⣶⣿⢢⣼⣿⣀⣿⡇⢸⣿⢻⣿⣿⣴⣿⠀⢸⡇⠀⣿⠀⢹⣇⠀⢿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣹⣃⣸⣇⠀⣿⣁⣸⣿⣄⣿⣇⣉⣿⣰⢻⣟⣀⣿⢃⣸⣿⣀⣿⣿⣿⣿⣀⣸⣿⣇⣿⣇⣸⣏⣀⣸⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⢄⠄⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣗⣢⠁⠀
⣼⠀⠀⠙⠁⢌⣿⣿⠋⠻⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⣹⣿⣿⠒⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣟⣽⣿⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⡂⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠃⠀⣿⣿⣿⡿⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠈⠽⠏⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⡀⠀⠓⠀⠘⢹⠀⢸⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠸⠾⣿⣿⣿⣿⣷⣔⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⡿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⡄⠀⠀⣠⠀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡄⠀⣤⣤⢤⠝⠿⠿⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢸⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣿⣿⣿⣽⣿⡿⠿⠧⠧⢥⠼⣯⣿⣿⣽⣸⣿⣼⣷⢤⣾⣷⣿⣯⣿⣯⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠂⠉⠋⠩⠋⢹⠛⠙⠂⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⠀⣿⠀⣿⠀⣿⠀⢸⠇⢸⡇⢸⣷⣿⣿⣆⡇⠀⣇⠀⣷⠙⢐⠀⠀⠀⣤⣶⡦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⡇⠀⡿⠀⣿⠀⣿⠀⣿⠀⢸⠀⢸⡇⢸⣿⣿⣿⣿⣿⠀⣿⠀⣿⠀⢰⠀⢰⠀⢻⣿⣿⣿⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⢀⣦⣴⡾⡀⣼⢻⣧⣼⡇⢠⣯⡇⣿⣿⣿⣶⣿⣄⣸⣿⣼⣿⣿⣿⣿⣿⣧⣿⠤⣿⠀⣿⢠⣼⠀⣴⡆⢘⣿⠿⠃⠃⠄⢸⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣴⡌⢃⣳⡂⢤⡩⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡟⢸⣿⢸⣿⠀⣿⡇⣿⡏⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⠘⣿⠀⣿⡁⠀⠻⠂⣀⡀⠀⣼⣿⡇⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣼⣇⣾⣧⣼⣯⣠⣿⣥⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣯⣀⣿⡀⣿⡇⠀⠀⠀⢉⣀⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠃⢿⡟⠻⠏⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠟⣻⣿⣿⡿⢻⣿⠿⢿⠗⠻⠇⠐⠀⢀⣼⣿⣄⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠁⠀⢠⡆⢀⣴⠀⢻⣶⣿⣷⢾⣿⡏⢿⣿⣿⡍⣹⠏⣿⠻⠀⠛⢹⣿⠃⠈⠏⢀⡀⢸⣿⡀⠀⡄⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣾⠀⣿⠀⢸⡇⠀⣼⡇⢸⣿⠈⣿⡇⢸⣿⠉⣿⣧⢠⡿⠀⢰⡀⢘⣿⠀⢾⡀⠠⣇⠹⣿⡇⠈⣧⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠐⣾⣿⠇⠀⠀⣼⡇⢠⣿⢀⣼⡇⢠⣿⠀⣸⣿⣶⣿⣤⣼⣿⣼⣿⡏⣿⣿⠀⣿⡇⠈⣿⠀⢸⡇⠀⣿⡀⢹⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⣀⣻⣁⣸⣏⡀⣿⣇⣸⣿⣄⣿⣇⣈⣿⣬⣿⣿⣀⣿⣣⣿⣿⣀⣿⣷⣴⣿⣀⣸⣿⣇⣿⣇⣸⣏⣀⣿⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⢄⠄⢤⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣗⣂⠁⠀
⣼⠀⠀⠙⠅⢌⣿⣿⠋⠛⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢻⡿⠿⣿⣿⣷⣶⠒⠚⠑⠀⠒⠶⡶⣶⣶⣶⡖⠛⣿⣷⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣛⣭⣽⣦
⠈⣿⣶⣷⣶⡟⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣗⠋⠀⣿⣿⣿⡟⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠂⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠈⠹⠉⠀⠀⠀⣸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⢰⣿⡏⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⠆⡀⠀⠀⣠⢀⠌⣷⢰⢿⢻⠛⠓⠑⡄⡄⠀⣿⣧⢤⠝⠛⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣿⣿⡿⠿⠤⠧⠥⠴⣧⣿⣿⣽⣘⣿⣬⠠⠠⢺⠧⣟⣿⣿⣛⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡧⠄⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢺⣿⣿⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠻⢿⣿⠛⠋⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⣿⠀⢸⠁⢸⡇⢘⡇⣴⣿⣿⣿⠀⣇⠀⣷⠙⢐⠀⠀⠀⣴⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⡇⠀⡏⠀⣿⠀⣿⠀⣿⠀⢸⠀⢸⡇⢸⣯⣿⣿⣿⣿⠀⣿⠀⣿⠀⢰⠀⢰⠀⢻⣿⣿⣿⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣔⢻⣇⣼⣇⢠⣗⡆⣿⣿⣿⣶⣿⣄⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣄⣿⠀⣻⢠⣸⠀⣰⠀⢸⣿⠿⠃⠃⠄⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⢇⢰⡟⢸⣿⢸⣿⠀⣿⡇⣿⡏⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⣿⠸⣿⠀⣿⡀⠀⠻⠃⣀⡀⠀⣾⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠈⣼⣧⣾⣧⣼⣇⣤⣿⣥⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢸⣯⣀⣿⡀⣿⡇⠀⠀⠀⢉⣀⠘⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠋⣿⠏⢻⡟⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⡿⢻⣿⠿⣿⣇⣿⡇⠀⠀⢀⣼⣿⣤⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠁⠀⢩⡆⠈⡷⠀⢹⡶⣿⣷⢺⣿⡏⢹⣿⣿⣍⣿⡏⡙⡿⢀⠛⢹⡿⠁⠘⠇⠠⡛⣿⣿⠃⠰⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⠀⠀⢠⣾⠀⣿⠁⢸⡇⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠏⣿⣏⣹⣿⠇⣸⡇⢸⣧⠀⢿⠀⢸⣇⠉⣿⡇⠀⣆⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⠇⢰⣿⣀⣼⡇⢸⣿⢀⣾⣧⣶⣿⣤⣼⣿⡴⣿⡿⣿⣿⠀⣿⡇⢨⣿⠀⢸⣇⠀⣿⡀⢹⡇⠀⣿⠀⢹⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⣀⣀⣀⣿⣀⣸⣏⡀⣿⣇⣸⣿⣄⣿⣇⣈⣿⣴⣻⣿⣀⣿⣣⣿⣿⣀⣿⣷⣾⣿⣀⣸⣿⣆⣿⣃⣸⣏⣀⣿⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣦⠰⠶⠶⠶⠀⠀⠀⣄⠄⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⠿⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠚⢻⡿⠿⣿⣷⣿⣶⠒⠚⠑⠀⠐⠶⠖⣶⣶⣶⡖⠒⣿⣿⣿⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣽⣦
⠈⣿⣶⣷⣶⠞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣇⠋⠀⣿⣿⣿⡟⠃⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠁⠙⠉⠀⠀⠀⣸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⢀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⣿⣿⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠉⣼⣻⣿⣿⣿⣟⡆⡄⠀⠀⣠⢀⠈⣷⢰⢿⠻⠛⠓⠑⡄⡄⠀⣿⣏⠤⠙⠟⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣏⣾⣿⣽⣿⡿⠿⠦⠧⠥⡴⣧⣿⣿⣽⣼⣰⣨⠤⠀⢺⡧⣿⣿⣿⣍⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⡐⠀⠀⠀⠉⠋⠉⠋⢹⠋⠙⠀⠀⠀⠀⢲⣿⣿⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠀⠈⠙⠻⢿⣿⠛⠋⠁⠀⠀⡆⠀⡇⠀⣿⠀⣿⠀⣿⠀⣿⠀⢸⠃⢸⡇⢘⡇⣰⣿⣿⣿⠀⣇⠀⣷⠑⢐⠀⠀⠀⣴⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⡇⠀⡏⠀⣿⠀⣿⠀⣿⠀⢸⠀⢸⡇⢸⣧⣿⣿⣿⣿⠀⣿⠀⣿⠀⢰⠀⢰⠀⢻⣿⣿⣻⡷⠄⢸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⢀⣦⣴⡞⠀⣰⢸⣇⣼⡇⢠⣇⡆⣿⣽⣿⣾⣿⣌⣻⣏⢸⣷⣿⣿⣿⣿⣿⣿⡄⣿⠀⢻⢠⣸⠀⣰⠂⢸⣿⠿⠉⠃⠄⢸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡟⢸⣿⢸⣿⠀⣿⡇⣿⡏⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠸⣿⠀⣽⠀⠀⠻⠃⣀⡀⠀⣾⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣼⣧⣼⣧⣸⡇⣠⣿⣥⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣯⢀⣿⡀⣿⡇⠀⠀⠀⢉⣀⠘⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠋⣿⡏⢻⡟⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⡿⢺⣿⠻⣿⣇⣿⡇⠀⠀⢀⣼⣿⣄⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠁⠀⢩⡄⠈⡷⠀⢹⡶⢿⣿⠚⣿⡟⢻⣿⣿⣏⣿⡟⡛⣿⢀⠟⢻⣿⠁⠘⠃⠠⡛⣿⣿⠃⠰⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⠀⠀⢠⣾⠀⣾⠀⢸⡇⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠏⣿⣏⣹⣿⠇⣸⡇⢘⣧⠀⢿⠀⢸⣇⠉⣿⡇⠀⣄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⠇⢰⣿⢀⣼⡇⢸⣿⠀⣾⣧⣶⣿⣤⣸⣿⡶⣿⡿⣿⣿⠀⣿⡇⢠⣿⠀⢸⣇⠀⣿⡀⢹⣇⠀⣿⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⢀⠀⣀⣿⣀⣸⣟⡀⣿⣇⣸⣿⣄⣿⣇⣈⣿⣴⣿⣿⣀⣿⢣⣿⣿⣀⣿⣷⣾⣿⣀⣸⣿⣇⣿⣃⣸⣏⣀⣿⣀⣀⣿⣃⣀⣀⣀⣀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⠰⠶⠶⠖⠀⠀⠀⢄⠄⢠⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠑⠁⢈⣻⡾⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⡄⠀⠈⢱⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣿⣶⣶⣶⠒⠚⠁⠀⠒⠶⠴⣶⣶⣶⡖⠒⣶⣿⣿⣷⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣏⠁⠀⣿⣿⣿⠟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠉⠋⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠐⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠄⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⡈⣼⢻⣿⣿⣿⣟⡆⡄⠀⠀⣠⠀⠈⣷⠰⣿⠻⠛⠓⠑⡄⡀⠀⣤⣿⡇⠙⠛⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡈⣍⣾⣿⣭⣿⡿⠿⠤⠇⠡⠴⣧⣿⣿⣽⣘⣵⣔⠢⠀⢾⠇⢿⣿⣻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⣀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⣿⣿⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠋⠁⠀⠀⠆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠃⢸⡇⢘⡇⢠⣷⣿⣿⣿⣇⠀⣷⠱⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣻⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣾⣿⣿⣿⠇⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣺⡇⠖⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢠⠀⠼⠤⠤⠠⠿⢄⣿⣴⡿⠄⢹⢼⣿⣼⡧⢹⡧⡸⣿⣻⣿⣾⣿⣮⢹⣷⢼⣵⣿⣿⣿⣿⣿⣿⣦⣿⢤⣽⢠⣿⠁⣶⠊⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢃⣳⡀⠤⡉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡟⢸⣿⢸⣿⠀⣿⡇⣿⡟⣿⣿⢻⣿⣹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣾⠸⣿⠀⣿⠁⠀⠻⠂⣀⡀⠀⣼⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣧⣸⣇⣠⣿⣥⣿⣿⣽⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣯⢀⣿⡄⣿⡇⠀⠀⠀⢉⣀⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠏⣿⡏⢻⡏⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢺⣿⠻⣿⣇⣿⡇⠀⠀⢀⣼⣿⡀⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⢫⡄⠈⣕⠀⢉⡶⣿⣷⠺⣿⡿⢿⣿⣿⣿⣿⣟⡿⣿⢀⣿⢿⡟⠁⢈⠃⢠⠻⣿⣿⠃⠐⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⠀⠀⣠⣾⠀⣾⠀⢸⡟⢀⣾⠇⢸⣿⠀⣿⡇⢸⣿⠋⣿⡟⣹⣿⠀⣸⡄⠈⣯⠀⢻⡀⠸⣤⠉⣿⡄⠀⡆⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣿⡇⢠⣿⠀⣼⡇⢸⣿⠀⣾⣧⣶⣿⣤⣸⣿⣔⣿⣟⣿⣿⡀⣿⡇⢀⣿⠀⢸⣇⠀⣿⡀⢸⡇⠀⣿⠀⢸⣿⡁⠀⠸⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⣀⣀⣀⣿⣀⣸⣏⣀⣿⣇⣸⣿⣄⣿⣇⣈⣿⣴⣽⣿⣀⣿⢣⣿⣿⣀⣿⣿⣾⣿⣀⣸⣿⣇⣿⣃⣸⣏⣀⣿⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⢄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣻⡿⠋⠋⣿⣷⣿⣋⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢑⡄⠀⠘⢹⣷⣿⠒⠀⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣿⡿⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⣿⠃⣿⣿⣿⡟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣿⡀⠉⠘⠋⠀⠀⠀⢸⣧⠀⠀⠀⢠⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⢈⣼⢿⣿⣿⣿⣟⡆⠀⠀⠀⣠⢀⠈⣷⠰⠿⠻⠛⠓⠑⡄⡀⠀⣴⣿⡿⢹⡟⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣍⣾⣿⣯⣿⡿⠿⠦⠧⢅⠴⣧⣿⣿⣝⣨⣺⣬⠤⠀⢺⣧⣿⣯⣿⣟⡁⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡤⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⣿⡟⠛⠛⡟⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡟⠀⢸⣿⣿⢿⣟⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣄⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠀⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠀⢸⠇⢸⡇⢀⡇⢀⣧⣿⣇⠀⣽⡇⣷⠹⣔⠀⠀⠀⣤⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⣠⡷⣆⡿⠀⣿⠀⣿⢴⣿⢀⣸⡆⣾⡇⣾⣷⣿⣿⣿⣿⠂⣿⠑⣿⠀⣿⡀⢰⢠⣿⣿⣿⣸⡇⠖⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣴⡿⢄⣹⢾⣿⢼⣧⠹⡯⡸⣿⣷⣿⣿⣿⣮⢹⣷⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⠤⣹⢠⢿⠃⢶⡎⢻⣿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣰⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢨⡝⢸⣿⢸⣿⠀⣽⡇⣿⡟⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣻⢸⣿⡀⣼⠅⠀⠹⠂⣀⡀⠀⣼⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣤⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣏⣸⡏⢠⣿⣧⣿⣿⣽⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⢀⣿⡀⣿⡆⠀⠀⠀⢉⣀⠐⣹⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣼⠟⣿⡟⢻⡟⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠇⢿⡇⠀⠀⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⣵⠀⢹⣶⢿⣷⠾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⢿⡟⠁⠈⠃⢠⢿⣿⣿⠇⠂⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⣸⡟⠀⣾⠁⢰⡟⠀⣿⠃⢸⡿⠀⣿⡇⢹⣿⠛⣿⡟⣿⣿⠀⣼⡆⠀⣧⠀⢹⡆⠘⣾⠁⢿⡄⠀⡄⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⢾⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⡇⠀⠀⣿⡇⢠⣿⠀⣼⡇⢸⣿⠀⣼⣧⣶⣿⣧⣸⣿⣄⣿⣷⣽⣿⡀⣿⡇⢠⣿⠀⢸⣇⠀⣿⡀⢸⡇⠀⣷⠀⢸⣿⡁⠀⠸⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⣀⣀⣀⣿⣁⣸⣏⣀⣿⣇⣸⣿⣤⣿⣇⣈⣿⣴⣽⣿⣈⣿⣣⣿⣿⣀⣿⣿⣾⣿⣀⣸⣻⣇⣿⣃⣸⣏⣀⣻⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⢄⠄⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⣿⣿⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣸⡾⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠈⠋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢕⡄⠀⠘⢱⣷⣿⡒⠀⠒⠻⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠰⣤⣶⣴⠖⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠒⠁⠀⠒⠶⠒⢶⣶⣶⡖⠒⣶⣶⣷⣷⣶⠆⢠⣼⣿⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣋⣭⣽⣆
⠈⣿⣶⣷⣶⡞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠂⠀⠀⠓⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡁⠀⠟⠻⢿⣏⠉⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠁⠋⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⣟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⢹⡿⠁⠀⠀⠀⢸⣧⠀⠀⠀⢠⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣾⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠐⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⣾⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠠⠦⠀⠀⠀⠀⠠⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⢼⢻⣿⣿⣿⡟⡇⡀⠀⠀⣠⠀⠀⣷⢰⠿⠻⠛⠓⠑⡄⡀⠀⢰⡇⠤⠘⠻⠛⢻⡟⠃⠀⠀⠀⠀⣾⣿⠀⢰⡤⠀⠠⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣭⣾⣿⣭⣿⡿⠿⠢⠃⠥⡴⣇⣿⣿⣝⣐⣐⣀⠀⠀⢲⠧⣿⣷⣿⣁⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠈⠋⠉⠋⢹⠛⠙⠄⠀⠀⠀⢰⣿⡟⠛⠛⠛⠛⢛⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠀⠀⡇⠀⣿⠀⣺⠀⣿⠀⢸⠄⢸⡇⢸⡇⠀⡇⢀⣧⣾⣇⠀⢰⠀⣷⣹⣿⠀⠀⠀⣤⣶⣆⣿⡯⠀⢸⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⠀⣷⢠⡷⣆⣿⠀⣿⠀⣿⣴⣹⣀⣸⡇⣾⡇⣶⣷⣿⣿⣿⣿⠀⣿⠐⣿⣿⣿⡀⢰⢤⣿⣿⣿⣾⡇⠖⢸⣿⣷⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢀⠁⠼⠤⠤⠀⠿⢄⣿⣤⡿⠄⢹⢼⣿⣝⣧⠹⡯⡸⣿⣶⣿⣿⣿⣾⣹⣶⣼⣵⣿⣿⣿⣿⣿⣿⣆⣿⠤⢼⣿⣿⡃⢶⡎⢻⣿⠏⠻⠧⠀⢸⣿⣻⡇⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢃⣳⡀⠤⡁⢟⣾⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⣿⢸⣿⢸⣿⠀⣿⡇⣿⣿⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡀⣼⠀⠀⠹⠂⣀⡀⠀⣼⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣬⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢰⣧⣼⣯⣸⣿⢠⣾⣇⣿⣿⣿⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢠⣽⣏⣿⠀⣿⡇⠀⠀⠀⢉⣀⠐⢹⣿⡇⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⠟⢿⡟⢻⡟⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠇⢿⡇⠀⠀⢀⣼⣿⡄⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣤⠀⢸⡁⠈⣷⠀⣽⣴⢿⣷⢾⣿⡟⢻⣿⣿⣿⣿⣻⣿⡿⢀⣿⠋⡏⠀⣸⡏⢀⣿⣿⣿⠃⠀⠀⠸⣿⣿⣧⣿⣿⠃⠀⢸⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡟⠀⣼⠁⢠⡷⠀⣿⠃⢸⣿⠀⣿⡇⢸⣿⠙⣿⡟⢿⣿⠀⣿⡇⠀⣿⣦⣿⡇⠀⣿⠀⢻⡄⠀⡄⠀⢿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠽⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣻⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⡇⠀⠀⣿⡇⢠⣿⠀⣸⡇⢠⣿⠀⣸⣧⣦⣿⣧⣸⣿⣤⣿⣇⣸⣿⠀⣿⡇⢰⣿⠿⢿⠇⠀⣿⡀⢸⡇⠀⣷⠀⢸⣿⡃⠀⠸⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⡀⠀⡀⣿⣃⣸⣿⡀⣾⣇⣸⣿⣀⣻⣇⣈⣿⣭⣽⣿⣀⣿⣧⣿⣿⣀⣿⣿⣾⣿⣀⣸⣿⣇⣿⣁⣸⣟⣀⣻⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⢄⠀⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠉⠛⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠀⢈⣼⠾⠉⠉⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⢱⣄⠀⠈⢱⣷⣿⠂⠁⠒⠫⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢻⡿⠿⣿⣿⣷⣶⠒⠚⠁⠀⠐⠶⠴⣶⣶⣶⡖⠒⣶⣶⣾⣷⣶⠆⢰⣶⣶⣿⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣆
⠈⣿⣶⣷⣶⡞⢿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠂⠀⠀⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠃⠀⣿⣿⣿⠿⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⢸⡿⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⣿⠃⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠀⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⣼⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠄⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⠄⠀⠀⣠⠀⠀⣷⢰⠿⠻⠛⠓⠑⡄⡀⠀⣤⡟⠤⠘⠛⠛⠻⣿⡇⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣍⣾⣿⣭⣿⡿⠿⠦⠥⠤⠴⣧⣿⣿⣝⣜⣄⣈⡀⡠⢾⢧⣿⣟⣾⣃⡀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡤⠄⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⣿⡟⠛⠛⠛⠛⠛⢲⡟⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠋⠁⠀⠀⡆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠃⢸⡇⢘⡇⢀⣧⣼⣇⠀⣅⠀⣷⠹⣼⠇⠀⠀⣤⣶⡦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⣴⣿⣀⣸⡆⣾⡇⣾⣷⣿⣿⣿⣿⠀⣿⠐⣿⡀⣿⠀⢰⢠⣿⣿⣿⣺⡇⠖⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡀⠀⠠⠁⠼⠤⠤⠠⠿⢄⣿⣴⡿⠄⢹⢼⣿⣽⣧⠹⡧⡸⣿⣶⣿⣿⣿⣿⣹⣶⣼⣵⣿⣿⣿⣿⣿⣿⣆⣿⠤⣿⣰⣿⠀⢶⡊⢻⡿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⣿⢸⣿⢸⣿⠀⣿⠃⣿⡿⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⣼⠀⠀⠻⠂⣀⡀⠀⣼⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣳⣾⣿⣿⣿⣿⣶⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢹⣧⣼⣯⣼⣿⣠⣽⢠⣿⣿⣿⣿⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢘⣻⣿⣿⡀⣿⡆⠀⠀⠀⢉⡀⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡏⠟⢿⡟⢻⡇⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⡿⣿⠗⣿⡇⠀⠀⢀⣼⣿⡀⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣤⠀⢘⠁⠈⣷⠀⣽⣴⣿⣷⢾⣿⡟⢻⣿⣿⣿⣿⣻⣿⠟⢀⣿⠉⡋⠀⢨⣿⢇⣿⢿⣿⠃⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⠀⠀⢸⡏⠀⣾⠁⢠⡟⠀⣿⠁⢸⡿⠀⣿⡇⢸⣿⠛⣿⡟⢻⣿⠀⣿⡇⢀⣇⠀⢸⡿⠀⣿⠀⢿⡀⠀⡀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠀⠽⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣿⡇⢠⣿⠀⣼⡇⢰⣿⠀⣼⣧⣶⣿⣧⣼⣿⣤⣿⣇⣸⣿⠄⣿⡇⢸⣿⡀⣸⣇⠀⣿⡀⢸⡇⠀⣷⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣁⣸⣿⠀⣿⣇⢸⣿⣄⣿⣇⣈⣿⣴⣾⣿⣈⣿⣣⣿⣿⣀⣿⣿⣾⣿⣿⣿⣿⣆⣿⣁⣸⣏⣀⣿⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⢄⠀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠑⠁⢈⣻⠾⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢹⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠒⠁⠀⠐⠶⠔⣶⣶⣶⡖⠒⣶⣶⣶⣿⣶⠆⢰⣴⣶⣶⣶⣿⡇⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣆
⠈⣿⣶⣷⣶⡞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠐⠀⠀⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⠃⠀⣿⣿⣿⠻⣿⣿⢁⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡈⠉⠘⠉⢰⣿⠃⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⣸⡏⠀⢹⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠐⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⡇⢀⣿⠁⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⡀⠀⠀⣠⢀⠀⣷⢰⠿⠻⠛⠓⠑⡄⡀⠀⣠⣼⠇⠘⠛⠻⠛⠛⠃⣸⡏⠀⠀⣿⣿⠀⢰⡄⠀⠰⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣭⣿⡿⠿⠢⠧⠅⡴⣧⣛⣿⣽⣰⣐⣘⠢⠠⠾⠧⣿⣧⣟⣿⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡤⠄⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⣿⠛⠛⠛⠛⠛⠂⠀⢸⠃⠀⠀⠀⣿⡟⠀⢸⣿⣿⢿⣿⣿⣷⣶⣶⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠂⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠄⢸⠇⢸⡇⢀⡇⢀⣧⣦⣟⠀⣥⠀⣷⠹⣔⠀⡾⠀⣤⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⣴⣿⣀⣸⡆⣾⡇⣾⣷⣿⣿⣿⣿⠀⣿⠐⣿⠀⣿⢠⣷⢠⣿⣿⣿⣺⡇⠖⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣴⡿⠄⢹⢼⣿⣼⣧⡹⣯⡸⣿⣶⣿⣿⣿⣿⣹⣦⣼⣧⣿⣿⣿⣿⣿⣿⣄⣿⠤⣿⢠⣿⣺⢶⡎⢻⡿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣠⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⣿⢸⣿⢹⣿⠀⣿⡇⣿⣿⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⡟⣾⠁⠀⠻⠂⣀⡀⠀⣼⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣤⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢿⣧⣼⣿⣼⣿⢰⣿⢠⣿⣿⣿⣿⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠸⣿⢈⣿⡅⣿⡆⠀⠀⠀⢉⣀⠐⣹⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠘⠟⢿⡟⢻⡏⠻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⢰⡿⠿⣿⠇⣿⡇⠐⠀⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣴⠀⢸⠁⠈⡵⠀⣿⡶⢿⣷⢼⣿⡟⢿⣿⣿⣿⣟⣻⣿⠟⠁⠼⠉⠉⠀⢬⡁⢸⣿⠶⡾⠃⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡟⠀⣼⠁⢠⡟⠀⣿⠃⢸⣿⠀⣿⡇⢸⣿⠙⣿⡟⢻⣿⠀⣿⡆⢠⣦⠀⢸⡇⣼⣿⠀⢫⡄⠀⡀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣻⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣾⡇⢠⣿⠀⣼⡇⢠⣿⠀⣸⣧⣦⣿⣧⣸⣿⣠⣿⣇⢸⣿⠀⣿⡇⢘⣿⠀⢸⣇⡟⣿⡀⢸⡇⠀⣷⠀⢸⣿⡃⠁⠸⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⡿⣋⣁⠀⣀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣃⣸⣿⠀⣿⣃⢸⣿⣄⣻⣇⡈⣿⣽⣽⣿⣈⣿⢇⣿⣿⣀⣿⣷⣾⣿⣶⣾⣿⣇⣿⣅⣸⣿⣀⣿⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣄⠰⠶⠶⠖⠀⠀⠀⢄⠄⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣻⠞⠉⢛⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢸⣽⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠚⠀⠀⠐⢶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣾⠆⢰⣴⣶⣶⣶⠂⠀⣿⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣷⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠠⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⠃⠀⣾⣿⣿⠟⠉⠀⢀⡇⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠈⠃⠀⠀⠀⣸⣧⠀⠀⠀⢠⠇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⢿⣀⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣾⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠙⣿⣿⢿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣻⣿⣿⣿⣟⡆⠄⠀⠀⣠⢀⠈⣷⢰⠿⠻⠛⠓⠑⡄⡀⠀⣠⡄⢴⡟⠿⠛⠛⠛⠁⠀⠀⠀⣼⣿⣿⠀⢰⡄⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⡀⣯⣾⣿⣭⣿⡿⠿⠦⢧⡁⠴⣧⣛⣿⣽⣐⣤⣀⠀⢀⣲⣧⣿⣇⣥⣄⣾⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⢻⡟⠛⠛⠛⠂⠀⠀⠀⠀⣼⡟⣿⡇⠀⢸⣿⣿⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢀⡇⢀⣧⣤⡇⢸⣇⠀⣷⠹⣔⠀⠀⠀⣤⣿⣇⣿⡇⠀⢸⣿⡇⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⢿⣿⣿⣿⠃⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣻⡇⠖⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣤⡿⠄⢹⢼⣿⣾⣷⣹⣧⡸⣿⣶⣿⣿⣿⣿⣹⣶⣼⣅⣿⣿⣿⣿⣿⣿⡄⣿⠤⣿⢠⣿⠀⢶⡊⣿⡿⠏⠻⠧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣤⣤⣄⣀⣼⣿⣿⠇⢰⣿⢸⣿⢹⣿⠀⣿⠇⣿⣿⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⠀⣾⢱⠇⠹⠂⣀⡀⠀⣼⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣤⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣧⣼⣿⣼⣿⣰⣿⢠⣿⣿⣿⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⢈⣿⡀⣿⡿⠀⠀⠀⢉⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠙⠟⢿⡟⢿⡟⠻⣿⠺⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠘⣻⠾⣿⠇⣿⡇⠀⠀⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣴⠂⢘⠁⠈⢿⠀⣿⡷⢿⣿⢼⣿⡟⢛⣿⣟⣿⣟⢻⣿⠙⠁⠐⠋⠙⠀⢰⠁⠀⣿⠶⣿⠇⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡿⠀⣼⠀⢠⡟⠀⣿⠃⢸⡿⠀⣿⡇⢸⣿⠙⣿⡟⢹⣿⠀⣿⡄⢠⣦⠀⢸⡇⠀⣿⢠⢯⡀⠀⡀⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣻⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⡇⠀⠀⣾⡇⢠⣿⢀⣼⡇⢠⣿⠀⣸⣧⣦⣿⣧⣸⣿⣀⣿⣇⢸⣿⠀⣿⡇⢸⣿⠀⢸⣇⠀⣿⡜⢸⡇⠀⣷⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⡀⣀⢀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣃⣸⣿⠀⣿⣀⢸⣿⣤⣻⣇⣉⣿⣼⣽⣿⣈⣿⣧⣿⣿⣀⣿⡷⣾⣿⣷⣾⣿⣶⣿⣇⣸⣯⣀⣿⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⣄⠄⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡏⠀⠀⠀⠀⠸⡀⠀⠀⡾⢸⢯⣾⣿⣿⣿⣷⣿⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⣿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡇⠀⢸⣷⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠀⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠒⠁⠀⠒⠶⠴⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⢸⣶⣶⣶⣶⠂⠀⠀⢱⣴⡟⠁⠀⠈⣻⣿⣿⣿⣿⣛⣛⣭⣽⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠰⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣿⡙⠀⣿⣿⣿⡟⠃⠀⢀⠀⠀⢫⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡈⠉⠘⠃⠁⠀⠀⢸⣧⠀⡘⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⢠⡇⠀⠤⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣻⣿⢸⠇⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣻⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⢿⢻⠛⠓⠑⡄⡄⠀⣤⣄⠤⢹⠟⠛⠟⠛⠃⠀⠀⠀⠀⣿⣿⡟⢰⡄⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣏⣾⣿⣭⣿⡿⠿⠦⣥⢥⣼⣧⣟⣿⣽⣬⣚⣀⠒⣤⣺⣧⣿⣯⣿⣏⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠂⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡟⠀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠄⢸⠇⢸⡇⢀⡇⢀⣏⣀⡇⠀⣵⠀⣷⠹⣔⠀⠀⠀⣤⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⢿⣿⣿⣿⡄⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠖⢸⣿⣷⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠽⠤⠤⠠⠿⢄⣿⣤⡿⠄⢹⢼⣿⣜⣧⠹⣯⡸⣿⣶⣿⣿⣿⣿⣹⣶⣼⣇⣿⣷⣿⣿⣿⣿⡥⣿⠤⣿⠠⢿⠀⢖⠎⢻⣿⢿⠿⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡂⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⣾⢸⣿⢹⣿⠀⣿⡇⣿⣿⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢰⣿⢸⣿⠀⣮⠀⠀⠹⡾⣀⡀⠀⣼⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣳⣾⣿⣿⣿⣿⣷⣾⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣧⣼⣿⣼⣿⣠⣿⣥⣿⣿⣿⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⠀⣿⡄⣿⡅⠀⢀⡇⢉⣀⠐⣽⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠛⢿⡟⢻⣿⢻⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⢸⣿⠾⣿⠇⣿⡇⠐⣼⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣴⠇⠘⠁⠈⠑⠀⣸⡟⢻⣿⠿⢻⡟⠻⣿⣛⣿⣟⢻⣿⠈⡉⡰⠋⠛⠁⢸⡉⠀⣿⠲⠚⠁⣀⡇⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡿⠀⣼⠀⢠⡗⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠘⣿⡟⢸⣿⠀⣿⡄⢀⣦⠀⢸⡇⠀⣿⠀⢠⡀⣿⡿⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣻⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⡇⠀⠀⣼⡇⢠⣿⠀⣼⠇⢀⣿⠀⣸⣷⣦⣿⣧⣸⣿⣀⣿⡇⢸⣿⠀⣿⡇⢸⣿⡀⢸⡇⠀⣿⠀⢸⣇⠀⣿⠀⢸⣿⡋⠁⠸⠀⠀⢸⠇⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⢀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⣸⣇⠀⣿⣀⢸⣿⣤⣻⣇⣸⣿⣨⢿⣿⣈⣿⣧⣾⣿⣀⣻⣷⣾⣿⣷⣿⣿⣾⣿⣥⣼⣿⣀⣙⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣖⠰⠶⠶⠶⠀⠀⠀⢄⠄⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠏⠀⠀⠀⢸⡿⠀⠀⢰⠇⢨⣿⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣻⢾⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠘⡀⠀⠀⡾⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢱⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠒⠀⠀⠐⠖⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣾⣶⣶⣶⠂⠀⠀⡇⠀⣀⡇⣰⡿⣻⣿⣿⣿⣟⣛⣛⣽⣵⣆
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠰⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣏⡘⠀⣿⣿⣿⠟⠁⠀⢀⠀⢠⠁⣾⢠⣿⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠙⠂⠀⠀⠀⢸⣧⠈⠀⠃⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠁⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⡈⠀⠀⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣔⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠇⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣻⣿⣿⣿⣟⡆⡀⠀⠀⣠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡀⠀⡤⢀⠤⢹⠟⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⢸⢰⡄⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣏⣾⣿⣭⣿⡿⠿⠧⢧⠥⢼⣧⣟⣿⣽⣼⣄⣈⠀⣤⣾⣧⣿⣏⣇⣈⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠂⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⣿⠃⢸⣿⣿⣿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠄⢸⠇⢸⡇⢀⡇⢀⣏⣀⡇⠀⣴⠀⣷⠹⣔⠀⠀⠀⣤⣶⣆⣿⡏⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⡷⣿⣿⣿⣿⡀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣾⡇⠖⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣤⡿⠄⢹⢼⣿⣜⡧⠹⣧⡸⣿⣾⣿⣿⣿⣯⣹⣶⣼⣅⣿⣷⣿⣿⣿⣿⣥⣿⠤⣿⠠⢿⠀⢖⡎⢻⣿⠯⡿⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⣿⢸⣿⢹⣿⠀⣿⡇⣿⣿⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⢸⣿⠀⣾⠀⠀⠹⢲⣁⡀⠀⣼⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣧⣼⣿⣼⣿⣰⣿⢤⣿⣿⣿⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⢀⣿⡄⣿⡇⠀⠀⡘⢉⣀⠐⣹⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠛⢿⡟⢻⣿⢻⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⢸⣿⠺⣿⠇⣿⡇⠐⠸⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣼⠃⠘⠁⠈⢓⠀⣹⡟⢹⣿⠻⢻⡞⠻⣿⠛⣿⣟⢻⣿⠈⡉⡴⠛⠛⠁⣰⡋⠀⣿⠢⠘⠁⣴⣦⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⡿⠀⣼⠀⢠⡏⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠐⣿⡏⢸⣿⠀⣿⡏⢠⣧⠀⢸⡇⠀⣿⠀⢠⡀⠹⡟⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠽⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⡇⠀⠀⣼⡇⢠⣿⠀⣼⠇⢀⣿⠀⣸⣧⣶⣿⣷⣼⣿⣠⣿⣇⢸⣿⠀⣿⡇⢸⣿⡀⣸⣇⠀⣿⠀⢸⣇⠀⣷⠀⢸⣿⡃⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⣸⣇⠀⣿⣀⣸⣿⣄⣻⣇⣸⣿⣸⣿⣿⣈⣿⢧⣼⣿⣀⣻⣷⣾⣿⣷⣿⣿⣿⣿⣤⣾⣿⣀⣹⣈⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⢄⠄⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠚⢉⣿⠃⠀⠀⢠⣿⣿⣿⣿⣶⣾⣵⣂⠁⠀
⣼⠀⠀⠙⢁⢀⣿⠿⠋⠫⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣼⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢹⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠿⣿⣶⣷⣶⠒⠚⠁⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⢰⣶⣶⣾⣷⠂⠀⢀⣿⠁⡀⠀⢸⢹⣻⣿⣿⣿⣟⣛⣛⣭⣽⣦
⠈⣿⣶⣷⣶⠞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠰⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡝⠀⣿⣿⣿⠟⠁⠀⢀⢸⠁⠁⠃⢀⣶⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡈⠁⠙⠂⠀⠀⠀⢸⣿⠀⠀⠀⣸⠏⡆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⠇⢀⠃⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⢀⡯⠆⢸⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣻⣿⣿⣿⣿⡆⡀⠀⠀⢠⢀⠈⣷⢰⠿⠻⠛⠓⠑⡄⡀⠀⡤⢀⠤⢹⠟⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⣼⣤⠀⣽⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣭⣾⣿⣭⣿⡿⠿⠦⠧⠥⠼⣧⣟⣿⣽⣼⣂⣐⠶⢤⣾⢧⣿⣧⣓⣛⠁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠃⢸⡇⢘⡇⢀⡏⣀⡇⠀⣿⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⡷⣿⣿⣿⣷⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣾⡇⠖⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⢹⢼⣿⣼⡷⢹⣷⡺⣿⣿⣿⣿⣿⣾⣹⣶⢼⣇⣿⣿⣿⣿⣿⣿⡦⣿⠤⣿⠠⢿⠀⠖⠊⢻⣿⠯⠻⡧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣤⡌⢃⣳⡀⢤⣁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡾⢸⣿⢸⣿⠀⣿⡇⣿⣿⣿⣿⢻⣿⣹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⢰⣿⠀⣴⠀⠀⠹⠂⣼⡀⠀⣼⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣳⣿⣿⣿⣿⣿⣷⣾⣤⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣧⣼⣿⣼⣿⣴⣿⣤⣿⣿⣿⣿⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⢈⣿⡄⣿⡄⠀⠀⡘⢉⣀⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⡟⢿⡿⢻⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⢸⣿⠺⣿⠇⣿⡇⠈⠀⢀⣼⣿⡄⣿⣿⠃⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣴⠃⠘⠁⠈⠑⠈⣻⡏⢹⣿⢹⢻⡞⠛⣿⠛⣯⡟⢻⣷⠞⡁⠼⠉⠛⠁⣨⠛⠀⡻⠠⠸⠁⣤⢄⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡿⠀⣼⠀⢠⡟⠀⣿⠇⢸⡿⠀⣿⡇⢸⣿⠈⣿⡏⢸⣿⠀⣿⡇⢠⣇⠀⢼⡆⠀⣿⠀⢀⡀⠸⠛⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠁⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢠⣿⢀⣼⠇⢠⣿⠀⣸⣧⣶⣿⣧⣼⣿⣀⣿⣇⢸⣿⠀⣿⡟⢸⣿⡀⣸⡇⢀⣿⠀⢸⣧⠀⣧⠀⢸⣿⡁⠀⠹⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⣀⣀⣀⣰⣿⣿⠀⠀⣀⣿⣃⣺⣇⠀⣟⣀⣸⣿⣄⣻⣇⣸⣿⣸⣿⣿⣈⣿⣣⣾⣿⣀⣻⣷⣾⣿⣷⣿⣿⣿⣿⣤⣾⣿⣀⣸⣀⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⢄⠄⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⠿⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢱⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢻⡿⠿⣿⣾⣶⣶⠒⠚⠁⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠖⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣟⣛⣛⣭⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣏⡙⠀⣿⣿⣿⠟⠁⠀⢀⠀⠀⠁⠃⠀⣰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠁⠘⠊⠀⠀⠀⢸⣧⣾⣿⠀⢠⠏⢸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⢸⠏⠀⠀⠀⠈⣿⠉⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⢀⣱⡿⠀⠠⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⡆⡀⠀⠀⢠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡀⠀⣤⠀⠅⢸⠛⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⣼⡿⠇⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣯⣿⣿⣭⣿⡿⠿⠦⠥⠥⠼⣧⣻⣿⣽⣼⣈⣐⡦⡤⣾⢧⢿⣯⣾⡃⡀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⣿⠁⠀⠀⠀⠀⡤⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⢠⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠃⢸⡇⢘⡇⣀⣏⣀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⢀⣿⣀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣾⣿⣿⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣾⡇⠖⢸⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⠹⢼⣿⣼⣧⣽⣷⡺⣿⣿⣿⣿⣿⣾⣹⣶⢼⣧⣿⣿⣿⣿⣿⣿⣦⣿⠤⣿⠠⠿⠀⠖⡊⢻⣿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣠⡌⢃⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡎⢸⣿⢸⣴⠀⣿⡇⣿⣿⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⢠⣭⠀⣀⠀⠀⠹⢃⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣳⣿⣿⣿⣿⣿⣷⣾⣤⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣸⣧⣼⣿⣼⣿⣤⣿⣥⣿⣿⣿⣿⣶⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⢈⣿⣄⣿⡆⠀⠀⡘⢉⣁⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢻⡟⢻⣿⠻⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣿⣿⡿⢸⣿⠻⣿⠇⢿⡇⠀⠀⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣴⠏⠈⠁⠈⠁⠀⣻⡟⢻⣿⠻⢻⡞⠻⣿⠿⣿⡿⣿⣿⡿⡟⣿⠋⣹⡄⠾⠟⠀⡝⠀⠘⠠⢄⣀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⡿⠀⣼⠀⢠⡗⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⣷⣴⣯⠀⣼⡇⠀⣷⠀⢀⡀⠈⠉⠀⣿⣿⣿⢿⣿⠀⠀⢸⣿⠃⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢸⡟⢀⣿⠇⢠⣿⠀⣸⣧⣶⣿⣧⣼⣿⣠⣿⣇⣸⣿⠀⣿⡟⠹⣿⡆⣿⣇⢀⣿⠀⢸⣷⠀⢣⡀⢸⣿⡁⠀⠸⠀⠀⢸⠃⠀⠀⠠⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⠀⢀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣃⣸⣇⡀⣿⣀⣸⣿⣄⣸⣇⣘⣿⣨⣿⣿⣈⣿⣧⣾⣿⣀⣻⣷⣶⣿⣷⣿⣿⣿⣿⣧⣸⣿⣀⣸⣁⣀⣿⣃⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⢄⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⠿⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢹⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢻⡿⠿⣷⣶⣶⣶⠒⠚⠁⠀⠒⠶⠒⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣴⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠖⠀⠀⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡙⠀⣾⣿⣿⠿⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠙⠋⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠐⠾⣿⣿⣿⣿⣷⣔⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣻⣿⣿⣿⡟⡆⡄⠀⠀⣠⢀⠀⣷⢰⠿⠻⠛⠓⠑⡄⡀⠀⣄⣄⠤⢼⠛⠛⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⢠⣦⣶⠄⠀⠀⢾⠆⠀⣰⣶⡆
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣭⣿⣿⣭⣿⡿⠿⠦⠧⠥⠼⣧⣿⣿⣽⣼⣘⣀⠒⡤⢾⢧⣿⣋⣩⣉⡂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣾⠿⠠⠶⠆⠀⠈⡿⠤⢀⡉⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢠⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠉⣿⢿⣿⠛⠛⠁⠀⠀⡆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠀⢸⠇⢸⡇⢘⡇⣴⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⢀⣿⣀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣾⣿⣷⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣾⡇⠒⣿⣿⣷⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⡀⠀⢠⠁⠿⠤⠤⠠⠿⢄⣿⣴⡿⡄⢹⢼⣿⣜⡧⣹⣯⡸⣿⣿⣿⣿⣿⣾⣹⣯⣼⣏⣿⣿⣿⣿⣿⣿⣶⣿⠤⣿⠠⠿⠀⠖⠎⢻⣿⠏⠻⠧⠀⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡀⢤⡉⢞⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡞⢸⣿⢹⠛⠁⣿⡇⣿⣿⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⠀⠮⠀⠣⠀⠀⠹⢂⣴⡀⢠⣿⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣼⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣸⣧⣼⣿⣼⣿⣴⣿⣧⣿⣿⣿⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣯⣠⣿⣄⣶⡄⠀⠀⡚⢉⣅⣼⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⣻⡿⢿⣿⠻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⢸⣿⠻⣿⠏⢿⡇⠐⠀⢀⣼⣿⣿⣿⣿⠇⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣠⠎⠘⠁⠈⠁⠀⢻⡿⢿⣿⠻⢷⡟⠛⣿⣿⣿⡿⣿⣿⣿⣟⣿⠛⣿⡁⢚⠛⠀⡛⠀⠈⠀⢄⣀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⡿⢀⣴⠂⢰⡆⠀⣿⠇⢸⣿⠀⣾⡇⢸⣿⠀⣿⡇⢸⣿⠁⣿⣿⣿⣿⡇⣿⡇⢀⣷⠀⢠⡄⠀⢈⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢸⡏⠀⣿⡇⣀⣿⠀⣸⣷⣶⣿⣴⣼⣿⣠⣿⣇⣸⣿⠀⣿⡟⠛⣿⡅⣿⣇⠀⣿⡀⢸⣿⠀⢸⡆⢸⣿⣹⠁⠸⠀⠀⢸⠃⠀⠀⠰⢿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⢀⣀⣿⣃⣸⣇⠀⣿⣁⣸⣿⣤⣺⣇⣈⣿⣨⣿⣿⣈⣿⣧⣾⣿⣀⣻⣿⣶⣿⣷⣿⣿⣾⣿⣧⣼⣿⣀⣸⣀⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⢄⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⢁⢈⣻⣾⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⣹⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣽⣦
⠈⣿⣶⣷⣶⠞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡙⠀⣿⣿⣿⠟⠃⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡈⠁⠘⠁⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠄⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣔⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢻⣿⣿⣿⣟⠆⡀⠀⠀⣠⠀⠈⣷⢰⣿⠻⠛⠓⠑⡄⡀⠀⣄⠠⠤⢹⠿⠿⠿⠟⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣭⣿⣿⣽⣿⡿⠿⠦⢧⠥⡴⣧⣿⣿⣽⣘⣒⣠⣦⣤⣾⣧⡿⣧⣋⣀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠂⠉⠋⠩⠋⢹⠛⠙⠄⠀⠀⠀⣰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢠⢸⣿⣿⢿⣿⣻⣳⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡂⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠄⢸⠇⢸⡇⢀⣇⣼⡏⠀⡇⠀⣿⠀⣷⠹⣔⠀⠀⠀⣤⣶⡦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⣀⣿⣀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣾⣷⣶⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣽⡇⠒⣸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣤⡿⡄⢹⢼⣿⣼⡧⣹⣯⡹⣿⣿⣿⣶⣿⣶⣹⣯⣽⣏⣿⣿⣿⣿⣿⣿⣶⣿⠤⣿⠠⢿⠀⠶⠎⢻⣿⠯⠻⠧⡼⢹⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣴⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡞⢸⣟⢹⠿⠀⣿⡇⣿⣿⣿⣿⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣼⠀⢧⡀⠀⠻⢂⣰⣠⡇⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣇⣼⣿⣼⣿⣤⣿⣧⣿⣿⣿⣿⣶⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣀⣶⣄⣦⡄⠀⠀⡚⢉⣽⡗⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⣻⡿⢿⣿⠻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠟⢿⡇⠀⠀⢀⣼⣿⣇⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣠⠊⠙⠁⠀⠁⠀⢻⡿⣿⣿⠻⢯⡟⠛⣿⣿⣷⣿⣿⣿⣿⣟⣼⠛⣻⠁⢚⠛⠀⡛⠀⠈⠀⠀⢀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⣿⢀⣾⠀⢰⡆⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠁⣿⣿⣿⣿⡄⣿⡆⢰⣧⠀⢠⡄⠀⣌⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢸⡏⠀⣿⡇⢀⣿⠀⢸⣿⣶⣿⣤⣼⣿⣠⣿⣇⣸⣿⠀⣿⡟⠋⣿⡁⣿⣇⠀⣿⠀⢸⣿⠀⢸⠂⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⡀⡀⣀⣀⣰⣿⣿⠀⠀⢀⣿⣇⣸⣇⠀⣿⣁⢸⣿⣤⣻⣇⣘⣿⣨⣿⣿⣉⣿⣯⣿⣿⣀⣻⣷⣶⣿⣷⣿⣿⣶⣿⣥⣼⣿⣀⣸⡀⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⣄⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⢁⢈⣿⠿⠉⠫⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢱⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠾⣷⣶⣶⣶⠒⠚⠀⠀⠐⠶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣽⣆
⠈⣿⣶⣷⣶⠞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡙⠀⣾⣿⣿⠛⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠈⠋⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠐⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⡈⣼⢿⣿⣿⣿⣿⡆⡄⠀⠀⢠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡀⠀⣄⡀⠤⢹⠟⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠠⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣭⣿⡿⠿⠧⠧⠥⡼⣧⣿⣿⣽⣬⣉⣰⢤⣤⣾⡧⡿⣏⣭⣅⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠂⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⢠⢸⣿⣿⢿⣿⣻⣷⣶⣶⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠃⢸⡇⢀⣇⣼⣿⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⣀⣿⣀⣿⢴⣿⠀⣸⣆⣾⡇⣾⣷⣾⣿⣶⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣽⡇⠒⣸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠀⠿⠤⠤⠠⠿⢄⣿⣴⡿⠄⢹⢼⣿⣼⡧⣹⣧⣹⣿⣿⣿⣶⣿⣶⣹⣿⢼⣟⣿⣿⣿⣿⣿⣿⣤⣿⠤⣿⠠⢿⠀⠶⠊⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣤⣤⣄⣀⣼⣿⣿⠇⢠⡟⢸⡟⢹⣿⠀⣿⡏⣿⣟⣿⣿⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣾⠀⣦⡀⠀⠻⢂⣰⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣷⣬⣥⣤⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣀⣿⡄⣈⡁⠀⠀⡞⣽⡆⠘⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣽⠛⢻⡟⢿⣿⠻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠟⢻⡇⠐⠀⢀⣼⣿⡔⣿⣿⠇⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣠⠀⠘⠁⠀⡁⠀⢻⡿⣿⣿⠻⣧⡟⢋⣿⣿⣷⣿⣧⣴⣿⣇⣘⠛⣻⠀⣉⠋⠀⡙⠀⠈⠀⠀⠀⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⡿⢀⣿⠀⢸⡇⠀⣾⠇⢹⣿⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠁⣿⣿⣿⣿⡄⣿⡆⠠⣇⠀⢰⡆⠀⣾⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣼⣿⠇⠀⠀⣼⡇⢸⣏⠀⣿⡇⣠⣿⠀⢸⣧⣶⣿⣠⣼⣿⣠⣿⣧⣸⣿⠀⣿⡟⢙⣿⡀⣿⣇⠀⣿⠀⢸⣧⠀⢹⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⠀⠀⠀⢀⣀⣰⣿⣿⠀⠀⠀⣿⣇⢸⣇⠀⣿⣁⢸⣿⣄⣻⣇⣘⣿⣸⢿⣿⣉⣿⢫⣽⣿⣀⣿⣷⣾⣿⣷⣿⣿⣶⣿⣥⣼⣿⣀⣸⣀⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⣄⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣻⣿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢹⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠑⠀⠐⠶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣛⣭⣽⣦
⠈⣿⣶⣷⣶⠞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡙⠀⣿⣿⣿⡟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡈⠁⠉⠉⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠸⠾⣿⣿⣿⣿⣷⣔⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⢼⢻⣿⣿⣿⣟⡇⡄⠀⠀⣠⠀⠈⣷⢰⠿⢻⠛⠓⠑⡄⡄⠀⣤⣤⠤⢹⠿⠿⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣭⣿⣿⣭⣿⡿⠿⠦⢧⢥⡴⣧⣿⣿⣽⣸⣞⣨⣤⣤⣾⣧⣿⣧⣏⣃⡀⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠂⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢠⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠀⢸⠇⢸⡇⢘⣇⣀⡏⠀⡇⠀⣿⠀⣷⠹⣔⠀⠀⠀⣤⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⡀⣿⣀⣿⢴⣿⠀⣸⡆⣾⣇⣾⣷⣿⣷⣶⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣴⡿⠄⢹⢼⣿⣼⡧⣹⣯⣻⣿⣿⣿⣶⣿⣶⣹⣷⣾⣟⣿⣿⣿⣿⣿⣿⣤⣿⠧⣿⠠⣿⠐⠶⠎⢻⣿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡟⢸⡟⢹⣿⠀⣿⡏⣿⣿⣿⣿⢻⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⠀⣿⠀⣦⡁⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣼⢯⣴⣿⣧⣿⣿⣿⣿⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣀⣿⣄⢿⡇⠀⠀⡞⣽⡇⠐⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣼⠟⢻⡟⢿⡿⠻⣿⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠿⢲⡇⠀⠈⢀⣼⣿⡄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣀⠄⣨⡅⢀⡅⠀⢻⡿⣿⣿⠻⣿⡟⢫⣿⣿⣧⣿⣇⣠⡝⣍⡙⢛⣻⠁⣭⠋⠀⡛⠀⠈⠀⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠀⣿⣿⢻⣿⠀⣿⡆⢀⣧⠀⢸⡇⠀⣿⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠠⣾⣿⠇⠀⠀⣼⡇⢸⣿⠀⣾⡇⢀⣿⠀⣸⣯⣶⣿⣤⣼⣿⣤⣿⣇⣸⣿⠀⣿⡟⠸⣿⡀⣿⣇⠀⣿⠀⢸⣧⠀⢻⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣃⣸⣇⠀⣿⣃⣸⣿⣄⣻⣇⣙⣿⣸⣿⣿⣉⣿⣯⣼⣿⣀⣻⣷⣾⣿⣷⣿⣿⣶⣿⣥⣸⣿⣀⣸⡁⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣖⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⣿⠋⢋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣽⣦
⠘⣿⣶⣷⣶⡞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡝⠀⣿⣿⣿⡟⠃⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣓⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠈⠸⠋⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣔⠂⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⠆⡄⠀⠀⣠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡄⠀⣤⣤⣄⢽⠟⠛⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣽⣿⡿⠿⠧⢧⣥⣽⣧⣿⣿⣽⣼⣍⣨⢤⢤⣾⣧⣿⣿⣿⣇⣀⣸⣀⠀⠀⠀⠂⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢲⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠀⢸⠇⢸⡇⢈⣇⣀⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⡀⣿⡀⣿⢴⣿⠀⣸⡆⣾⣇⣾⣷⣿⣷⣶⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠽⠤⠤⠠⠿⢄⣿⣴⡿⠄⣹⢿⣿⣼⡧⢹⣿⣻⣿⣿⣿⣶⣿⣶⣹⣿⢼⣍⣿⣿⣿⣿⣿⣿⢄⣿⠦⣽⠠⣿⠐⢶⠊⢻⣿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡂⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡿⢸⣿⢸⣿⠀⣿⡏⣿⣿⣿⣿⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢲⣿⠀⣿⠀⣦⡀⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣿⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣼⣷⣴⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣀⣿⣄⣽⡇⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⠟⢻⡟⢻⠛⠻⣿⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠛⠿⠟⠻⠇⠐⠀⢀⣼⣿⡔⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⠀⣸⠇⢀⡗⠀⢻⡿⣿⣿⠛⣿⡎⢻⣿⣿⣯⣿⣇⣀⠛⣿⡙⢻⣿⠁⣬⠃⠀⠉⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠀⣿⣇⢸⣿⠀⣿⡆⠰⣷⠀⢸⡇⠀⣿⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢸⡿⠀⣾⡇⢀⣿⠀⢸⣯⣶⣿⣤⣼⣿⣤⣿⣇⣸⣿⠀⣿⡏⢸⣿⡀⣿⣇⠀⣿⠀⢸⣧⠀⢻⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⢸⣇⠀⣿⣣⢸⣿⣤⣿⣇⡈⣿⣸⣿⣿⣉⣿⣧⣼⣿⣀⣿⣷⣾⣿⣷⣿⣿⣶⣿⣥⣸⣿⣀⣸⡁⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣦⠰⠶⠶⠖⠀⠀⠀⣄⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠉⠀
⣼⠀⠀⠙⢁⢈⣿⠿⠋⠛⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠐⠶⠲⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣛⣭⣵⣆
⠘⣿⣶⣷⣶⡞⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡝⠀⣿⣿⣿⠟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠉⠈⠉⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣔⠂⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣿⣿⣿⣿⣿⠆⣄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡄⠀⣤⣠⡤⢹⠟⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣿⣿⡿⠿⠧⠧⢥⣽⣧⣿⣿⣽⣼⣾⣼⢄⠤⣾⣧⣿⣏⣟⣛⣂⣸⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠂⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠀⢸⠇⢸⡇⢀⣇⣀⡏⠀⡇⠀⣵⠀⣷⠹⣔⠀⠀⠀⣤⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⠀⣿⡀⣿⢴⣿⠀⣸⡆⣾⣇⣾⣷⣿⣷⣴⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣾⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠀⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⣻⢿⣿⣼⣧⢹⣿⣿⣿⣿⣿⣶⣿⣶⣹⣿⣼⣍⣿⣿⣿⣿⣿⣿⠄⣿⠦⣽⠠⣿⠠⢶⠎⢻⡿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡿⢸⡿⢸⣿⠀⣿⡏⣿⣿⣿⣿⢻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡟⣿⣿⢺⣿⠀⣿⠀⣆⠀⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣳⣾⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣼⣯⣤⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣀⣿⡄⣽⡇⠀⠀⡞⣽⣆⠐⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⠟⢿⡟⠻⠟⠻⣿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠟⢿⡇⠀⠈⢀⣼⣿⡔⣿⣿⠇⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⠀⣸⡇⢀⡷⠀⢻⡿⢿⣿⠛⣿⡎⢹⣿⣿⣭⣿⣇⣈⠛⣿⡙⢻⣿⠁⣬⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠁⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡆⠰⣷⠀⢸⡇⠀⣷⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢸⣿⠀⣾⡇⢀⣿⠀⣸⣧⣶⣿⣤⣼⣿⣤⣿⡇⣸⣿⠀⣿⡇⢸⣿⡀⣿⣇⠀⣿⠀⢸⣧⠀⢿⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣃⢸⣇⠀⣿⣇⣸⣿⣤⣿⣇⣈⣿⣰⣿⣿⣉⣿⣧⣼⣿⣀⣻⣷⣾⣿⣿⣿⣿⣶⣿⣥⣸⣿⣀⣸⡀⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⣄⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠉⠀
⣼⠀⠀⠙⠁⣈⣻⡿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⣹⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡶⠶⣷⣶⣶⣶⠒⠚⠑⠀⠐⠶⠒⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢴⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣽⣦
⠈⣿⣶⣷⣶⡞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠒⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠄⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡙⠀⣿⣿⣿⡟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠉⠨⠋⠁⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡄⠀⣤⣠⠤⢽⠿⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣿⣿⡿⠿⠧⡧⠵⡼⣧⣿⣿⣽⣼⣾⣼⡢⠤⢾⣧⣿⣏⣿⣏⣀⣸⢀⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢰⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢀⢸⣿⣿⣿⣿⣻⣶⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢘⣇⣀⡏⠀⡇⠀⣵⠀⣷⠹⣔⠀⠀⠀⣤⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣿⣷⣔⣷⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣴⡿⠄⣿⢿⣿⣼⡧⢹⣿⡻⣿⣿⣿⣶⣿⣶⣹⡷⢼⣝⢿⣿⣿⣿⣿⣿⠄⣿⡷⣿⠠⢿⠠⣶⠎⢻⡿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡂⢤⡁⢟⣿⣷⣶⣤⣤⣄⣀⣼⣿⣿⠇⢰⡿⢸⣿⢸⣿⠀⣿⡏⣿⣟⣿⣿⢻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡏⣿⣿⢻⣿⠀⣿⠀⣆⠀⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣳⣾⣿⣿⣿⣿⣷⣿⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣼⣟⣤⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⢸⣯⣀⣿⣄⣽⡇⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⢸⠟⣿⡟⢻⡟⠻⣿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠟⢿⡇⠀⠀⢀⣼⣿⡔⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⠀⣸⠇⢀⡷⠀⢻⡿⢿⣿⠛⣿⡏⢹⣿⣿⣍⣿⣏⣉⠿⣿⠛⢻⣿⢣⣬⠃⠀⠉⠀⠈⠁⠀⠀⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡇⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠉⣿⣿⢾⣿⠀⣿⡇⢸⣿⠀⣿⡆⠸⡗⠀⢸⡇⠀⣷⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣸⡇⢰⡟⠀⣾⡇⢠⣿⠀⣸⣧⣶⣿⣤⣼⣿⣤⣿⣇⢸⣿⠀⣿⡇⢸⣿⡀⣿⣇⠀⣿⠀⢸⣇⠀⣿⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⠀⣀⣀⣀⣀⣰⣿⣿⠀⠀⣀⣿⣃⢸⣇⡀⣿⣇⢸⣿⣄⣿⣇⣈⣿⣰⣿⣿⣉⣿⣧⣼⣿⣀⣿⣷⣾⣿⣷⣿⣿⣦⣿⣤⣸⣿⣀⣸⡀⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣖⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠉⠀
⣼⠀⠀⠙⠁⢌⣻⣿⠋⠫⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣽⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠲⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢴⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣽⣦
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡝⠀⣿⣿⣿⠟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠁⠘⠋⠀⠀⠀⣸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠸⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡄⠀⣄⣠⠤⢽⠿⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠀⠆⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣿⣿⡿⠿⠧⢧⠵⡽⣧⣿⣿⣽⣼⣿⣬⣦⡦⣾⣧⣿⣯⣯⣍⣂⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢐⡿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⢀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠆⠀⡇⠀⣿⠀⣿⠀⣿⠀⣻⠀⢸⠇⢸⡇⢘⣇⣀⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣿⣷⣐⣷⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣽⡇⠒⢸⣿⣷⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⡀⠀⠠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⣻⢾⣿⣼⡧⢹⣷⡹⣿⣿⣿⣾⣿⣮⣹⣧⢼⡝⢿⣿⣿⣿⣿⣿⠄⣿⡿⢿⠢⢿⢀⣶⠎⢻⣿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⢤⡉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡿⢸⣿⢸⣿⠀⣿⡏⣿⣟⣿⣿⢻⣿⣿⣿⣿⣻⣶⣿⣿⣿⣿⡏⣷⣿⢻⣿⠀⣾⠀⣍⠀⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣾⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣼⣯⣤⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣯⣀⣿⣄⣿⡇⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⢸⠟⣿⡟⢻⡟⠻⣿⠿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠟⢿⡇⠀⠀⢀⣼⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⠀⢹⡇⠈⣵⠀⢹⡿⢿⣿⠛⣿⡟⢻⣿⣿⣯⣿⣯⣍⠿⣽⠛⢻⣿⢳⣮⠃⢀⡛⠀⢨⠃⠀⠀⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡏⠀⣾⡇⢸⣿⠀⣿⠃⢸⣿⠉⣿⣿⣸⣿⠀⣿⡇⢸⣿⠀⣿⡆⠈⣇⠀⢻⡆⠀⣷⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠐⣾⣿⠇⠀⠀⣸⡇⢰⡟⠀⣾⡇⢠⣿⠀⣸⣧⣶⣿⣤⣼⣿⣤⣿⣏⣹⣿⠀⣿⡇⢸⣿⠀⣿⣇⠀⣿⠀⢸⣇⠀⣿⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣰⣿⣿⠀⠀⣀⣿⣃⣸⣇⠀⣿⣃⣸⣿⣤⣿⣇⣸⣿⣴⣿⣿⣉⣿⢣⣾⣿⣀⣿⣷⣾⣿⣿⣾⣿⣦⣿⣧⣸⣿⣀⣸⣀⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡽⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠑⠁⢈⣻⠿⠋⠫⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠑⠀⠐⠶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣆
⠈⣿⣶⣷⣶⡞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡙⢀⣿⣿⣿⠟⠃⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠁⠘⠉⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡄⠀⣄⣤⠤⢽⠿⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣭⣿⡿⠿⠧⠧⠥⣼⣧⣿⣿⣽⣼⣟⡸⡀⢤⣶⣇⡿⣏⣻⣏⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡤⠄⢀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢒⠿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢀⢸⣿⣿⢿⣿⣻⣶⣶⣶⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢘⣇⣀⡏⠀⡇⠀⣵⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⢀⣸⡆⣾⡇⣾⣷⣿⣷⣐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣺⡇⠒⣸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠽⠤⠤⠠⠿⢄⣿⣴⡿⢤⣻⢾⣿⣼⣧⢹⣧⡻⣿⣷⣿⣿⣿⣾⣹⣦⢼⣷⡿⣿⣿⣿⣿⣿⣾⣿⣶⣿⢲⢿⠃⢶⡎⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⡟⢸⣿⢸⣿⠀⣿⡏⣿⣿⣿⣿⢻⣿⣹⣿⣽⣫⣿⣿⣿⣿⣿⣏⣍⣽⢫⣹⠐⣾⠀⣾⠁⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣇⣾⣧⣼⣿⣤⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⢀⣿⣄⣿⡆⠀⠀⡞⣽⣆⠐⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⠟⣿⡟⢻⡟⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠟⢿⡇⠐⠀⢀⣼⣿⡴⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⠀⢹⡅⠈⣵⠀⢹⣶⢿⣷⠿⣿⡏⢻⣿⣿⣯⣿⣿⣭⠿⣿⡙⢹⣿⢱⣾⠃⢠⡝⠀⢘⠃⠀⡀⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡟⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠙⣿⣿⣹⣿⠀⣿⡇⢸⣿⠀⣿⡇⠀⣄⠀⢲⡆⠀⣧⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⠇⢠⣟⠀⣼⡇⢠⣿⠀⣼⣷⣶⣿⢤⣸⣿⣤⣿⣏⣹⣿⠀⣿⡇⢸⣿⠀⢻⣇⠀⣿⡄⢸⣇⠀⣿⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⠀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣀⢸⣇⠀⣿⣃⢸⣿⣤⣿⣇⣘⣿⣰⣿⣿⣉⣿⣧⣽⣿⣀⣿⣷⣾⣿⣶⣾⣿⣦⣿⣧⣸⣿⣀⣸⣀⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣤⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠉⠀
⣼⠀⠀⠙⠃⢈⣻⡿⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠶⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡛⠀⡿⣿⣿⠟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠀⠸⠋⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣔⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⡈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡄⠀⣄⡀⠤⢽⠿⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣿⣿⡿⠿⠧⠧⠥⢴⣧⣿⣿⣽⣼⣯⣸⡤⣤⣾⣇⡿⣯⣯⣍⡂⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠂⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢀⢸⣿⣿⣿⣿⣻⣶⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡆⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠄⢸⠇⢸⡇⢘⣇⣀⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⣴⣿⢀⣸⡆⣾⡇⣾⣗⣿⣷⣐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣴⡿⢤⣿⢾⣿⣼⣧⢹⣧⡻⣿⣷⣿⣿⣿⣾⣹⣦⢼⣷⡿⣿⣿⣿⣿⣿⣶⣿⣶⣿⢰⣿⠃⢶⠎⢻⣿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⡟⢸⣿⢸⣿⠀⣿⡏⣿⣿⣿⣿⢻⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣯⡛⣻⢛⣻⠘⣾⠀⣾⠁⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣬⣗⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣇⣾⣧⣼⣿⣠⣿⣧⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⢀⣿⡄⣿⡆⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⠟⣿⡟⢻⡟⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠟⢿⡇⠀⠀⢀⣼⣿⡴⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⡀⢻⡇⠈⣽⠀⢹⣶⢿⣷⠿⣿⡏⢿⣿⣿⣯⣿⣿⣭⡿⣿⡛⢹⣿⢱⣾⠃⢠⡟⠀⠘⠃⠀⡀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢠⣿⠀⣿⠀⢸⡏⠀⣾⡇⢸⣿⠀⣿⠇⢸⣿⠙⣿⣟⢹⣿⠀⣿⡇⢸⣿⠀⣿⡇⠀⣆⠀⢣⡆⠀⣇⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣾⠇⢠⣯⠀⣼⡇⢰⣿⠀⣼⣷⣶⣿⠤⣼⣿⣤⣿⣏⣹⣿⠀⣿⡇⠸⣿⠀⢹⡇⠀⣿⡄⢸⣇⠀⣿⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⣀⣀⣀⣰⣿⣿⠀⠀⢀⣿⡀⢸⣟⡀⣿⣇⢸⣿⣤⣿⣇⣘⣿⣴⣾⣿⣉⣿⢣⣽⣿⣀⣿⣷⣶⣿⣶⣾⣿⣦⣿⣥⣸⣿⣀⣹⡀⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣤⠰⠶⠶⠖⠀⠀⠀⣄⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣕⣂⠉⠀
⣼⠀⠀⠙⠁⢀⣿⠿⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⠶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣏⡙⠀⣿⣿⣿⠟⠃⠀⢀⠀⠀⠁⠂⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠹⠋⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠈⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡀⠀⣄⡠⡤⢹⠿⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠠⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣾⣿⣿⣿⡿⠿⠧⠧⠥⠼⣧⣿⣿⣽⣼⣚⣨⠠⠤⣾⠧⡿⣯⣍⣁⣂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠂⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢐⠿⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⢀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢈⣇⣀⡏⠀⡗⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⣴⣿⣀⣸⡆⣾⡇⣾⣟⣿⣷⣐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠿⠤⠤⠠⠿⢄⣿⣴⡿⢤⣿⢾⣿⣽⣧⢹⣧⡻⣿⣷⣿⣿⣿⣾⣹⣧⣼⣷⣿⣿⣿⣿⣿⣿⣶⣿⣴⣿⢠⣿⠓⢶⠎⢻⣿⠏⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣠⡌⢃⣳⡂⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⡟⢸⣿⢸⣿⠀⣿⡏⣿⣿⣿⣿⢻⣿⣹⣿⣿⣻⣿⣿⣿⣿⣿⣿⠿⢿⠻⢿⠈⣿⠀⣮⠁⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⡇⣾⣧⣼⣿⣤⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⢸⣿⠀⣿⡄⣿⡆⠀⠀⡞⣽⣆⠐⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⠏⣿⡟⢻⡟⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⠟⢿⡇⠀⠀⢀⣼⣿⡴⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⡀⢹⡆⠈⣽⠂⢹⣶⢿⣷⠾⣿⡏⢿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢻⣿⢱⣶⠃⠤⠽⠀⢘⠃⠀⠀⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢀⣿⠀⣾⠀⢸⡏⠀⣾⡇⢸⣿⠀⣿⡇⢸⣿⠛⣿⡟⢻⣿⠀⣿⡇⢸⣿⠀⢿⡇⠀⡄⠀⢳⡄⠀⣄⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⠇⢠⣿⠀⣼⡇⣸⣿⠀⣾⣧⣶⣿⡤⣸⣿⣤⣿⣇⣼⣿⠀⣿⡇⠘⣿⠀⢸⡇⠀⣿⡄⢸⣇⠀⣿⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⢀⣀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣿⡀⣸⣟⠀⣿⣇⢸⣿⣄⣿⣇⣈⣿⣴⣿⣿⣉⣿⢧⣼⣿⣀⣿⣷⣶⣿⣶⣾⣿⣦⣿⣧⣸⣿⣀⣹⡀⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣔⠰⠶⠶⠖⠀⠀⠀⣄⠀⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⡿⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠒⠐⠀⠐⡶⠒⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠂⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡝⠀⣿⣿⣿⣟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠸⠃⠁⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠂⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡀⠀⣤⣠⡤⢹⠟⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣭⣿⡿⠿⠧⠧⢥⡼⣧⣿⣿⣽⣼⣿⣜⢠⠤⣾⠧⣿⣣⣟⣙⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⢀⢸⣿⣿⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠃⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢸⡧⣄⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⣴⣿⣀⣸⡆⣾⡇⣾⣿⣿⣷⡐⣷⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣹⡇⠒⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠀⠾⠤⠤⠠⠿⢄⣿⣴⡿⢤⣻⢼⣿⣽⣧⢹⣧⡺⣿⣶⣿⣿⣿⣿⣹⣧⢼⣷⣿⣿⣿⣿⣿⣿⣴⣿⣤⣿⢠⣿⠒⢶⠊⢻⣿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣠⡌⢃⣳⡀⢤⡉⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣼⡏⢸⣿⢸⣿⠀⣿⡏⣿⣿⣿⣿⢿⣿⣹⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⢻⣿⠘⣿⠀⣌⠀⠀⠻⢃⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⡇⣾⣷⣼⣿⣤⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⢨⣭⢀⣿⣄⣿⡆⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⠟⣿⡟⢻⡟⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⣿⠻⣿⠟⢿⡇⠀⠀⢀⣼⣿⣴⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⡄⢹⠀⠈⣵⠋⢻⣶⢿⣷⢿⣿⡏⢿⣿⣿⣿⣿⣿⣿⡿⣽⡿⢻⣿⢷⣦⠁⠤⠿⠀⢸⠃⠀⠀⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⣠⡿⠀⣾⠀⢰⡟⢀⣾⠇⣸⡿⠀⣿⡇⢸⣿⠛⣿⡟⢻⣿⠀⣿⡆⢸⣿⠀⢿⡇⠀⣄⠀⢺⡄⠀⣀⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⠃⢠⣿⠀⣼⡇⣸⣿⠀⣿⣧⣶⣿⢄⣼⣿⣤⣿⣇⣸⣿⠀⣿⡇⠈⣿⠀⢸⡇⠀⣿⡀⢸⡇⠀⣿⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⡀⢀⣀⣀⣰⣿⣿⠀⠀⡀⣛⣀⢸⣿⠀⣿⣇⣸⣿⣄⣿⣇⣙⣿⣴⣿⣯⣉⣿⣡⣼⣿⣀⣿⣷⣶⣿⣶⣾⣿⣦⣿⣥⣸⣿⣀⣹⣈⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣄⠰⠶⠶⠶⠀⠀⠀⣄⠄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⡿⠉⠛⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠑⠀⠐⣶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣦
⠈⣿⣶⣷⣶⡞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡝⠀⣿⣿⣿⡟⠃⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠀⠙⠉⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⣿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣻⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡀⠀⡤⣤⡄⢹⠿⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠠⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣭⣿⡿⠿⠧⡧⠥⡼⣧⣿⣿⣝⣼⣯⣰⡤⢤⣾⠧⣿⣯⣯⣹⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢐⡻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⢀⢸⣿⣿⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢘⣧⣄⡏⠀⡇⠀⣿⠀⣷⠱⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⣴⣿⣀⣸⡆⣾⡇⣾⣿⣿⣷⠐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣴⡿⢄⢹⢼⡿⣼⣧⢹⣧⡾⣿⣶⣿⣿⣿⣿⣻⣷⢼⣇⣿⣷⣿⣿⣿⣿⣄⣿⡤⣿⢠⣿⢠⣶⠊⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣠⡌⢃⣳⡀⢤⡑⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⡏⢸⣿⢹⣿⠀⣿⡏⣿⣿⣿⣿⢿⣿⣹⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⢻⣿⢸⣿⠀⣾⠀⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⡇⣾⣿⣼⣿⣠⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣀⣿⣄⣿⡆⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠸⠃⢿⡟⢻⡟⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠰⡾⠛⣿⠟⣿⡇⠈⠀⢀⣼⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⢀⡀⢘⠀⠘⣱⠈⣿⣶⣿⣷⢾⣿⡏⢿⣿⣿⣿⣿⣻⣿⡿⣿⣿⢹⣿⣷⣤⠁⠀⠛⠀⠘⠁⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⣸⡏⠀⣼⠀⢰⡟⠀⣿⠇⢸⡟⠈⣿⡇⢸⣿⠻⣿⡟⢻⣿⠀⣿⡇⢸⣿⠁⣹⡇⠀⣿⠀⢰⡄⠀⣄⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⠃⢠⣿⠀⣼⡇⢸⣿⠀⣾⡧⣶⣿⣀⣸⣿⣤⣿⡇⢸⣿⠀⣿⡇⠈⣿⠀⢸⡇⠀⣿⡄⢸⡇⠀⣿⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣀⢸⣿⠀⣿⣇⣸⣿⣤⣿⣇⣈⣿⣼⣿⣿⣈⣿⣧⣼⣿⣀⣿⣷⣶⣿⣶⣾⣿⣦⣿⣅⣸⣿⣀⣻⣈⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣄⠰⠶⠶⠖⠀⠀⠀⣄⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣻⠿⠉⠛⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠈⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠶⣷⣶⣶⣶⠒⠚⠁⠀⠒⡶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣽⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡟⠀⣿⣿⣿⡟⠁⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠀⠹⠉⠁⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⢿⣿⣿⣿⣟⡆⡄⠀⠀⣠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡀⠀⣤⣤⡤⢽⠿⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣭⣿⡿⠿⠧⢧⠥⡼⣧⣿⣿⣽⣼⣏⣘⡂⢤⣾⠧⣿⣏⣋⣉⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠄⢸⠇⢸⡇⢘⣧⣄⡏⠀⡗⠀⣿⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⣴⣿⣀⣸⡆⣾⡇⣾⣿⣿⣷⠐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⢄⠹⢼⣿⣾⣷⠹⣧⣺⣿⣦⣿⣿⣿⣿⣻⣶⢼⣇⣿⣷⣾⣿⣿⣿⣄⣿⡤⣿⢠⣿⢠⣶⠎⢻⣿⠯⠻⠧⠄⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣠⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⡇⢸⣿⢹⣿⠀⣿⡏⣿⣿⣿⣿⢿⣿⣹⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⢺⣿⠸⣿⠀⣮⠁⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⡇⣾⣿⣼⣿⣠⣿⣧⣿⣿⣿⣿⣶⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⡀⣿⣄⣿⡆⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠸⠋⢿⡟⢻⡿⠻⣿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠨⡽⠿⣿⠟⣿⡇⠘⠀⢀⣼⣿⡤⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣀⡄⠘⠀⠈⣣⠀⣻⣶⢿⣷⢾⣿⡏⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢻⣿⣷⢦⠁⠀⠛⠀⠘⠁⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⣸⡟⠀⣼⠀⢰⡟⠀⣿⠇⢸⡟⠀⣿⡇⢸⣿⠻⣿⡟⢻⣿⠀⣿⡇⢸⣿⠁⢹⡇⠀⣿⠀⢰⡄⠀⣀⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⠃⢠⣿⠀⣸⡇⢸⣿⠀⣾⡧⣶⣿⣃⣸⣿⣤⣿⣇⣸⣿⠀⣿⡇⠈⣿⠀⢸⡇⠀⣿⡀⢸⣇⠀⣿⠀⢸⣿⣿⠇⢹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⠀⠀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣁⢸⣟⠀⣿⣇⣸⣿⣤⣿⣇⣈⣿⣼⣿⣿⣈⣿⢧⣼⣿⣀⣿⣷⣾⣿⣶⣾⣿⣦⣿⣡⣸⣿⣀⣻⣈⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣔⠰⠶⠶⠖⠀⠀⠀⣄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⡿⠉⠋⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢼⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠶⣷⣶⣶⣶⠒⠚⠑⠀⠐⡶⠲⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡟⠀⣿⣿⣿⡟⠉⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠙⠉⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠴⠾⣿⣿⣿⣿⣷⣔⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠠⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡄⠀⣤⣤⣤⢹⠟⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠰⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣭⣿⡿⠿⠧⢧⠥⡼⣧⣿⣿⣽⣸⣟⣼⡂⢄⣾⡧⣿⣇⣿⣛⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢘⣧⣄⡏⠀⡗⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⣀⣸⡆⣾⡇⣾⡷⣿⣷⠐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣻⡇⠒⢸⣿⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⠹⢼⣿⣾⣿⣹⣷⣸⣿⣦⣿⣿⣿⣿⣹⣶⣼⣇⣿⣯⣿⣿⣿⣿⣄⣿⠤⣿⠠⢿⢠⣶⠎⢻⣿⠏⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣠⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣤⣤⣄⣀⣼⣿⣿⠇⣸⡎⢸⣿⢹⣿⠀⣿⡏⣿⣿⣿⣿⢿⣿⣹⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⢹⣾⢸⣿⠈⣿⠀⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⡇⣾⣿⣼⣿⣠⣿⣧⣿⣿⣿⣿⣶⣿⣭⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⡀⣿⣄⣿⡄⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⠛⠋⢿⡟⢻⡿⠻⣿⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠿⠟⣿⠿⣿⡇⠈⠀⢀⣼⣿⣄⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣠⠄⠘⠁⠈⣡⠀⣹⣶⢿⣷⢼⣿⡟⢿⣿⣿⣿⡟⢻⣿⣿⣿⡿⢿⣿⠷⣦⠀⠀⣿⠀⠙⠁⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⣸⡏⠀⣼⠀⢠⡏⠀⣿⠃⢸⡟⠀⣿⡇⢸⣿⠻⣿⡏⢸⣿⠀⣿⡇⢸⣿⠀⣽⡇⠀⣿⠀⢸⡄⠀⣄⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⡇⢠⣿⠀⣸⡇⢰⣿⠀⣼⡇⣶⣿⣁⣸⣿⣤⣿⣇⣸⣿⠀⣿⡇⢀⣿⠀⢸⡇⠀⣿⡀⢸⣇⠀⣿⠀⢸⣿⣿⠇⢹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣿⡀⢸⣷⠀⣿⣇⣸⣿⣤⣿⣇⣈⣿⣴⣿⣿⣉⣿⣧⣼⣿⣀⣿⣷⣾⣿⣶⣾⣿⣦⣿⣡⣸⣿⣀⣻⡈⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⣄⠀⢤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣷⣂⠉⠀
⣼⠀⠀⠙⠁⢀⣿⡿⠋⠋⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠒⠑⠀⠐⣶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠂⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡟⢀⣿⣿⣿⡟⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠉⠹⠋⠀⠀⠀⢸⣧⠀⠀⠀⢰⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢐⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠼⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠌⣷⢰⣿⢻⠛⠓⠑⡄⡄⠀⣤⣤⡤⢽⠟⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣈⣯⣿⣿⣿⣿⡿⠿⠧⢧⠥⡽⣯⣿⣿⣽⣼⣯⣼⡶⡤⣶⣧⣿⣏⣿⣙⣀⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠤⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢐⡹⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⢀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡃⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢸⡧⣄⡏⠀⡗⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣿⣷⠐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠀⠿⠤⠤⠠⠿⢄⣿⣴⡿⠄⠹⢼⣿⣼⡧⢹⣧⣸⣿⣦⣿⣿⣿⣿⣹⣷⣼⣇⣿⣗⣿⣿⣶⣿⣤⣿⠤⣿⠠⣿⢀⣖⠎⢻⣿⠯⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡂⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⣸⡎⢸⣿⢹⣿⠀⣿⡏⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣟⣿⣿⢸⣿⢰⣾⠈⣿⠁⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣇⣾⣯⣼⣿⣠⣿⣧⣿⣿⣿⣿⣶⣿⣭⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⡈⣿⣄⣿⡅⠀⠀⡞⣽⣆⠐⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠋⢿⡟⢻⡿⢻⣿⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠟⣿⠿⢿⡇⠘⠀⢀⣼⣿⣤⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣴⠀⠘⠁⠈⣡⠀⣽⡦⢿⣷⢼⣿⡟⢻⣿⣟⣿⡟⢻⣿⣿⣿⣿⣿⡿⠳⣦⡉⠀⣿⠀⠘⠁⠀⠀⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡟⠀⣼⠃⢠⡏⠀⣿⠃⢸⡿⠈⣿⡇⢸⣿⠻⣿⡇⢸⣿⠁⣿⡇⢸⣷⠀⢿⡇⠀⣿⠀⢰⡄⠀⣆⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣿⡇⢀⣿⠀⣼⡇⢰⣿⠀⣼⡇⣶⣿⣁⣸⣿⣤⣿⡇⣸⣿⠀⣿⡇⢠⣿⠀⢸⡇⠀⣿⠀⢸⣇⠀⣿⠀⢸⣿⣿⠇⢹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⠀⢀⣀⣀⣰⣿⣿⠀⠀⡀⣿⣁⣸⣿⡀⣿⣇⣸⣿⣤⣿⣇⣈⣿⣼⣿⣿⣉⣿⢧⣼⣿⣀⣿⣷⣶⣿⣶⣾⣿⣦⣿⣡⣸⣟⣀⣹⣈⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣖⠰⠶⠶⠖⠀⠀⠀⣄⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣕⣂⠉⠀
⣼⠀⠀⠙⠁⢈⣿⡿⠉⠋⣿⣷⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠶⣷⣶⣶⣶⠒⠚⠑⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣿⣛⣛⣭⣵⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡟⠀⣿⣿⣿⠟⠉⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠀⠹⠁⠀⠀⠀⣸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣯⣿⣿⣿⣿⣿⣿
⢀⣹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⢾⣿⣿⣿⣿⣷⣔⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⡈⣼⣿⣿⣿⣿⣟⠆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡀⠀⣤⣠⡤⢹⠟⠛⠛⠛⠁⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣿⣿⡿⠿⠧⠧⠥⠼⣧⣿⣿⣽⣼⣏⣔⡀⠤⣾⣧⣿⣯⣛⣟⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⣀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⢐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⢀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢸⡧⣄⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣿⣷⠐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣻⡇⠒⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⠹⢼⣿⢼⠷⣹⣯⣸⣿⣾⣿⣿⣿⣦⣻⣿⣽⣇⣿⣗⣾⣿⣄⣿⢤⣿⠤⣿⠠⠿⠀⠖⠎⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣰⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢸⡎⢸⣿⢸⣿⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⡟⣿⣿⢲⣿⠀⣼⠀⣿⠀⠀⠻⢃⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣧⣾⣯⣸⣿⣠⣿⣧⣿⣿⣿⣿⣶⣿⣭⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⡸⣿⣄⣿⡄⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠋⢿⡟⢻⡿⢻⣿⠸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠗⣿⠿⢿⡇⠈⠀⢀⣽⣿⣴⣿⣿⠇⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣾⠇⠈⠀⠈⢁⠈⣿⡷⢿⣿⢼⣿⡟⢿⣿⠿⣿⡟⢻⣿⣿⣿⣿⣿⡟⠁⣾⡏⢰⡟⠀⠘⠀⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡟⠀⣼⠇⢠⡟⠀⣿⠃⢸⡿⠈⣿⡇⢸⣿⠐⣿⡇⢸⣿⠁⣿⡇⢘⣿⠀⢻⡇⠈⣿⠀⢰⡀⠀⣄⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣾⡇⢀⣿⠀⣼⡇⣠⣿⠀⣸⡧⣶⣿⢁⣸⣿⣴⣿⣇⣸⣿⠀⣿⡇⢘⣿⠀⢸⣇⠀⣿⡀⢸⡇⠀⣿⠀⢸⣿⣿⠇⢹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⠀⠀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣁⣸⣇⢀⣿⣅⣸⣿⣤⣿⣇⣨⣿⣴⣿⣿⣉⣿⣣⣼⣿⣀⣿⣷⣾⣿⣶⣾⣿⣦⣿⣡⣸⣯⣀⣸⣈⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⣄⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣕⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣻⠿⠋⢛⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠁⠀⠒⡶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣽⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠂⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡟⠀⣿⣿⣿⠟⠉⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠁⠙⠋⠀⠀⠀⣸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠙⣿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠉⠀⣎⠈⣼⢿⣿⣿⣿⣟⡆⡄⠀⠀⣠⢀⠈⣷⢰⢿⢻⠛⠓⠑⡄⡀⠀⣤⢤⠄⢹⠻⠿⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣿⣿⡿⠿⠧⠧⠥⠼⣧⣿⣿⣽⣼⣟⣜⡂⠤⣾⠧⡿⢳⣫⣽⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡤⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢐⡻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢸⡧⣤⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣴⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⢀⣿⢴⣿⠀⣸⡆⣾⡇⣾⡷⣿⣷⠐⣷⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠀⠼⠤⠤⠠⠿⢄⣿⣴⡿⠄⠹⢼⣿⢼⣧⣹⣯⣸⣿⣾⣿⣿⣿⣦⣻⣷⣼⣏⣿⣷⣾⣿⣄⡿⢄⣿⠤⣿⠠⠿⠀⠖⠊⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣠⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡾⢸⣿⢸⣶⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⣿⣿⢹⣿⠀⣼⠀⣶⠀⠀⠻⢃⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣇⣾⣯⣸⣿⣠⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣰⣿⣄⣿⡄⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠋⢿⡟⢻⡿⢻⣿⠹⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠇⣿⠿⢿⡇⠈⠀⢀⣼⣿⣴⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⢀⣿⠇⠈⠁⠈⢡⠈⣿⡷⢿⣿⢸⣿⡟⢿⣾⣿⣿⡟⢻⣿⣿⣿⣿⣿⡟⠀⣾⠇⢰⡟⠀⠸⠀⠀⠀⠸⣿⣿⣯⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡟⠀⣼⠃⢠⡿⠀⣿⠃⢸⡿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠁⣿⡁⢸⣧⠀⢻⡇⠈⣿⠀⢰⡀⠀⡄⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣾⡇⢀⣿⠀⣼⡇⢠⣿⠀⣼⡇⣶⣿⣀⣸⣿⣴⣿⣇⣸⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⣿⡀⢸⡇⠀⣿⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⠀⠀⢀⢀⣀⣰⣿⣿⠀⠀⡀⣿⣁⣸⣇⡀⣿⣁⣸⣿⣤⣿⣇⣸⣿⣴⣿⣿⣉⣿⣧⣼⣿⣀⣿⣷⣾⣿⣶⣼⣿⣦⣿⣡⣸⣿⣀⣹⣈⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⣄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⡿⠋⢛⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠁⠀⠐⢶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣽⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡝⢀⣿⣿⣿⡿⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠀⠻⠋⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠠⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣟⡆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡀⠀⣤⣠⡤⢹⠟⠻⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠰⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣿⣿⡿⠿⠧⢧⠥⡼⣧⣿⣿⣽⣼⣏⣠⡀⠤⣾⠧⣿⣯⣯⣭⢀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢐⡻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢸⡧⣄⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⡆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⢀⣿⣀⣿⢴⣿⠀⣸⡆⣾⣇⣾⣷⣿⣷⠐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣽⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠽⠤⠤⠠⠿⢄⣿⣴⡿⠄⠹⢽⡿⢼⡧⣹⣧⣸⣿⣿⣿⣿⣿⣦⣹⣿⣼⣏⣿⣷⣿⣿⣄⣿⢄⣿⠤⣿⢠⢿⠀⠖⠎⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣴⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⡾⢸⣿⢸⣭⠀⣿⡇⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢾⣿⠀⣩⠀⣤⠀⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣿⣧⣾⣿⣸⣿⣠⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣯⣽⣿⣿⣿⣿⣿⣷⣿⣯⢸⣿⣠⣿⣄⣿⡄⠀⠀⡞⣽⣆⠘⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⠛⢿⡟⢿⡿⠻⣿⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠟⣿⠿⣿⡇⠀⠀⢀⣽⣿⣴⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣿⡇⠈⠁⠈⣃⠀⣿⡟⢿⣿⢹⣿⡟⢿⣶⣿⣿⡟⢿⣿⣿⣿⣿⣿⡟⠁⣿⡏⢰⡟⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡿⠀⣸⠃⢠⡟⠀⣿⠃⢸⡿⠀⣿⡇⢸⣿⠈⣿⡇⢸⣿⠁⣿⡅⢸⣧⠀⢿⡇⠘⣿⠀⢰⡀⠀⡇⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣻⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣾⡇⢠⡿⠀⣼⡇⢠⣿⠀⣸⣧⣶⣿⣁⣸⣿⣴⣿⣇⣸⣿⠀⣿⡇⢸⣿⠀⢸⡇⠀⣿⡀⢸⡇⠀⣿⠀⢸⣿⣿⠇⢹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⠀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⣚⣇⡀⣿⣀⢸⣿⣤⣿⣇⣸⣿⣸⣿⣟⣉⣿⢧⣼⣿⣁⣿⣷⣾⣿⣶⣼⣿⣦⣿⣩⣸⣿⣀⣸⣈⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠖⠀⠀⠀⣄⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⡿⠋⠋⣿⣷⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠶⣷⣶⣶⣶⠒⠚⠁⠀⠐⣶⠖⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⡇⠀⠀⢲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠂⠀⠈⠛⠻⡇⠀⠟⠻⢿⣝⡙⢀⣿⣿⣿⣿⠁⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠇⠀⣶⡆⢸⣿⣧⡀⠁⠹⠏⠀⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠁⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠠⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡀⠀⣤⣤⠤⢹⠿⠻⠟⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣭⣿⡿⠿⠧⣧⢥⡼⣧⣿⣿⣽⣬⣛⣼⠄⢤⢾⠧⣟⣏⣋⣁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠂⠉⠋⠉⠋⢹⠛⠙⠀⠀⠀⠀⠐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⢿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢹⠄⢸⡇⢸⡇⢘⡧⣄⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⡀⣿⣀⣿⢴⣿⠀⣸⡇⣾⣇⣾⣷⣿⣷⠐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣴⡿⠄⠹⢽⣿⢼⡧⣹⣧⣻⣿⣿⣿⣶⣿⣶⣹⣿⣼⣇⣿⣷⣿⣿⣆⣿⢄⣿⠤⣿⢠⢿⠀⠖⠎⢻⣿⠏⠻⠧⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣠⡌⢃⣳⡀⠤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡾⢸⣇⢸⠿⠀⣿⡏⣿⣟⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢸⣿⠘⠿⠀⢰⠅⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣬⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣾⣷⣾⣿⣸⣿⢠⣿⣧⣿⣿⣿⣿⣶⣿⣭⣿⣯⣽⣿⣿⣿⣿⣿⣿⣽⣯⢸⣿⣀⣿⣄⣿⡅⠀⠀⡞⣽⣆⠐⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⠛⢿⡟⢿⡿⠻⣿⣻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠟⣿⠿⢿⡇⠐⠀⢀⣽⣿⣬⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣿⠇⠈⠁⠈⣁⠀⣿⡟⢿⣿⢿⣿⡞⢻⣶⣿⣿⡟⢻⣿⣿⣿⣿⣿⡟⠁⣿⡏⢸⡟⠀⠈⠀⠀⠀⠸⣿⣿⣧⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡿⠀⣸⠀⢠⡟⠀⣿⠇⢸⣿⠀⣿⡇⢸⣿⠉⣿⡇⢸⣿⠇⣿⡟⢸⣧⠀⢹⡇⠘⣿⠀⢰⡀⠀⡆⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢠⡟⠀⣼⠇⢠⣿⠀⣸⣧⣤⣿⣇⣸⣿⣤⣿⣇⣸⣿⡀⣿⡇⢸⣿⠀⢸⣇⠀⣿⡀⢸⣇⠀⢻⠀⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⢀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⣻⣅⡀⣿⣀⢸⣿⣄⣿⣇⣸⣿⣸⣿⣿⣉⣿⣧⣼⣿⣁⣿⣿⣶⣿⣶⣼⣿⣦⣿⣩⣸⣿⣀⣸⣇⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠉⠀
⣼⠀⠀⠙⠁⢈⣿⠿⠋⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠀⠀⠒⡶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠴⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠂⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡟⠠⣿⣿⣿⡟⠑⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡈⠈⠙⠋⠀⠀⠀⣸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠉⣼⣿⣿⣿⣿⣿⡆⡀⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡀⠀⣤⣠⠤⢽⠟⠿⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠖⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⣯⣿⣿⣽⣿⡿⠿⠧⠯⠥⡽⣧⣿⣿⣽⣼⣟⣸⡶⠤⣾⢧⣿⣯⣋⡿⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⢐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡃⠀⡇⠀⣿⠀⣿⠀⣿⠀⣻⠀⢸⠃⢸⡇⢸⡧⣤⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⢀⣿⣀⣿⢴⣿⠀⣸⡆⣾⣇⣾⣷⣿⣷⠐⣿⡀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣽⡇⠒⣸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⢹⢽⣿⢼⣧⣹⣿⣻⣿⣿⣿⣶⣿⣶⣻⣿⣾⣏⣿⣧⣾⣿⣄⣿⠄⣿⠤⣿⠠⢿⠀⢶⡊⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⣾⢸⡏⢸⣿⠀⣿⡇⣿⡟⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⣿⣿⢾⣿⠘⣿⠀⢰⡀⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣼⣧⣼⣇⢸⣣⣠⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣯⢸⣿⢀⣻⣄⣼⡇⠀⠀⡟⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⣟⢻⡏⢿⡿⢻⣿⣛⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠿⣿⠿⢿⡇⠈⠀⢀⣽⣿⣴⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣬⠉⠀⠀⠘⣡⠀⣿⡟⢿⣿⢿⣿⡞⢛⣶⣿⣿⡿⢻⣿⣿⣻⣿⢿⣿⠟⣿⡏⢹⡟⠀⠈⠀⠀⠀⠸⣿⣿⣷⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢸⡿⠀⣠⠀⢠⡏⠀⣿⠇⢸⣿⠈⣿⡇⢸⣿⠋⣿⡇⢸⣿⠃⣿⡿⢸⣧⠀⢿⡇⠈⣇⠀⢤⡀⠀⠆⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠁⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢸⡇⠀⣿⡁⣠⣿⠀⣼⣧⣴⣿⣀⣼⣷⣤⣿⣇⢸⣿⡀⣿⡇⠘⣿⠀⢸⣇⠀⣿⡀⢸⣷⠀⢳⡆⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⡀⠀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⣻⣃⡀⣿⣀⣸⣿⣤⣿⣇⣸⣿⣸⣿⣯⣉⣿⣧⣼⣿⣀⣿⣿⣶⣿⣷⣼⣿⣦⣿⣩⣸⣿⣀⣸⣇⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠶⠀⠀⠀⣄⠄⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠉⠀
⣼⠀⠀⠙⠁⢀⣿⠿⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠶⣷⣶⣶⣶⠒⠚⠁⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣴⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣽⣦
⠈⣿⣶⣷⣶⠞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠰⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡝⠀⣿⣿⣿⡟⠑⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠁⠘⠋⠁⠀⠀⣸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⡀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡀⠀⣤⣄⡤⢽⠿⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣯⣿⣿⣿⣿⡿⠿⠦⠧⢥⡽⣧⣿⣿⣽⣼⣟⣸⠂⠤⣾⠧⣿⣯⣯⣟⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡤⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠂⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⠐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠃⢸⡇⢸⡧⣤⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⡀⣿⣀⣿⢴⣿⠀⣸⡆⣾⣇⣾⣷⣿⣷⠐⣿⣀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣼⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡀⠀⢠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⠹⢽⣿⣼⣧⣹⣿⣻⣿⣿⣿⣶⣿⣶⣻⣷⣾⣏⣿⣧⣾⣿⣄⣿⠄⣿⠤⣿⠠⢿⠀⢶⠊⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⣿⢸⡏⢸⣿⠀⣿⡇⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⣿⣿⢾⣿⠘⣿⠀⢰⡄⠀⠻⢂⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣼⣧⣾⣇⢸⣃⣠⣿⣧⣿⣿⣿⣷⣾⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⣧⣿⣯⢸⣿⣀⣿⣄⣸⡇⠀⠀⡟⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⣛⠿⡟⢻⡿⠻⣿⣛⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠿⣿⠿⢿⡇⠘⠀⢀⣽⣿⣴⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣤⠉⠀⠁⠘⣡⠀⣿⡟⢿⣿⢿⣷⡞⢛⣶⣿⣿⡿⢹⣿⡿⣻⣿⢿⣿⠟⣿⡋⢹⡟⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⡿⢀⣤⠀⢠⡏⠀⣿⠇⢸⣿⠈⣿⡇⢸⣿⠋⣿⡇⢸⣿⠁⣿⡟⢸⣧⠀⢻⡇⠈⣇⠀⢴⡀⠀⠆⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢸⡇⠀⣿⡁⣠⣿⠀⣼⣧⣴⣿⣠⣼⣷⣴⣿⣇⢸⣿⠀⣿⡇⠘⣿⠀⢸⣇⠀⣿⡀⢸⣷⠀⢻⡆⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⠀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⣻⣃⡀⣿⣀⣸⣿⣤⣿⣇⣸⣿⣸⣿⣯⣉⣿⣣⣼⣿⣁⣿⣷⣾⣿⣷⣼⣿⣦⣿⣩⣸⣿⣀⣸⣇⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣆⠰⠶⠶⠶⠀⠀⠀⣄⠄⢤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢀⣿⠿⠉⠛⣻⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣷⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡾⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⣶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢴⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣽⣿⣆
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡽⠀⣿⣿⣿⡟⠑⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠈⠘⠛⠁⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠛⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠏
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣻⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡀⠀⣤⡠⡤⢹⠿⠻⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠘⠀⠀⠐⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣠⣯⣾⣿⣽⣿⡿⠿⠧⠧⢥⠽⣧⣿⣿⣽⣼⣿⣜⡶⢤⣾⢧⣿⣯⣟⣻⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠀⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⠐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⢿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢸⡧⣤⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣦⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⡀⣿⣀⣿⢴⣿⠀⣸⡆⣾⣇⣾⣷⣿⣷⠐⣿⡀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⡀⠀⢠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⢹⢾⣿⣼⣷⣹⣿⣻⣿⣿⣿⣶⣿⣶⣹⣷⣾⣏⣿⣧⣾⣿⣄⣿⠄⣿⠤⣿⠠⢿⠀⢶⠊⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢰⣾⢸⡟⢸⣿⠀⣿⡇⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⣿⣿⢾⣿⠘⣿⠀⢠⡀⠀⠻⢃⣴⡀⠀⣾⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣾⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⣸⣧⣾⣇⢸⡯⣠⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣯⣽⣿⣿⣿⣿⣿⣧⣿⣯⢸⣿⣀⣿⣄⣸⡇⠀⠀⡟⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣿⡟⢿⡟⢺⡿⠻⣿⣟⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠻⣿⠿⢿⡇⠐⠀⢀⣽⣿⣴⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⣡⠀⣿⡟⢿⣿⢿⣷⡞⢛⣴⣿⣿⡿⢻⣿⠛⣿⣿⢿⣿⡟⣿⠋⢻⡿⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⣿⢀⣤⠀⣰⡏⠀⣿⡇⢸⣿⠈⣿⡇⠸⣿⠋⣿⡇⢸⣿⠀⣿⡏⢸⣿⠀⢿⡇⠈⣧⠀⣶⡀⠐⡂⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢸⡇⠀⣿⡇⣠⣿⠀⣸⣧⣴⣿⣠⣼⣿⣴⣿⣇⢸⣿⠀⣿⡇⠀⣿⡀⢸⣇⠀⣿⡀⢸⣿⠀⢹⡇⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⠀⠀⣀⣀⣀⣰⣿⣿⠀⠀⢀⣿⣃⣚⣃⠀⣿⣀⣸⣿⣤⣿⣇⣸⣿⣨⣿⣿⣉⣿⢧⣼⣿⣀⣿⣷⣶⣿⣷⣼⣿⣦⣿⣩⣸⣿⣀⣸⣇⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⣄⠄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣻⡿⠉⠋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢵⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠑⠀⠒⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⣰⣶⣶⣶⣶⠆⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠲⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡝⠀⣿⣿⣿⡿⠋⠀⢀⠀⠀⠁⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠉⠙⠉⠁⠀⠀⢸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢹⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠀⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠄⠀⠰⢾⣿⣿⣿⣿⣷⣔⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠆⠀⠀⠀⠀⠤⠻⣿⣿⠿⠛⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⠈⣼⣿⣿⣿⣿⣿⡆⡀⠀⠀⣠⢀⠈⣷⢰⡿⢻⠛⠓⠑⡄⡀⠀⣤⣤⡤⢽⠟⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⡀⣯⣾⣿⣿⣿⡿⠿⠧⠧⠥⡽⣧⣿⣿⣽⣼⣛⣸⠦⢄⢾⢧⣿⣯⣟⣇⣂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠀⠀⠂⠉⠋⠩⠋⢹⠛⠙⠄⠀⠀⠀⠐⠹⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⠇⠀⡇⠀⣿⠀⣿⠀⣿⠀⢻⠀⢸⠇⢸⡇⢘⡧⣄⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⣿⠀⣿⡀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣿⣷⠐⣿⡀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣽⡇⠒⢸⣿⣷⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⡀⠀⢠⠁⠾⠤⠤⠠⠿⢄⣿⣴⡿⠄⢹⢾⣿⣼⣷⣹⣿⣻⣿⣿⣿⣶⣿⣦⣹⣷⣾⣝⣿⣇⣼⣿⡄⣿⡌⣿⠤⣿⠠⢿⠀⢶⡎⢻⣿⠯⠻⠧⠀⢸⣿⣻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⣾⢸⣿⢸⣿⠀⣿⡇⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢼⣿⠘⣾⠀⢰⡀⠀⠻⢃⣴⡀⠀⣾⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣷⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣾⣧⣸⣧⣠⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣯⣽⣿⣿⣿⣿⣿⡅⣿⣯⢸⣿⣀⣿⣄⣼⡇⠀⠀⡟⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⣽⡟⢿⡟⢽⡟⠻⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⣻⠿⢟⠇⠐⠀⢀⣽⣿⣴⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⡤⠀⣿⡿⢿⣿⢿⣧⡞⢟⣤⢿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⠋⢻⡯⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⣿⢠⣶⠀⢰⡏⠀⣿⡇⢸⣿⠈⣿⠇⢸⣽⠘⣿⡇⢸⣿⠀⣿⡇⢸⣿⠃⣿⡆⠀⣧⠀⢿⡄⠈⣦⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠈⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⠇⠀⠀⣼⡇⢸⡇⠀⣾⡇⣠⣿⠀⣸⣿⣴⣿⣤⣼⣿⣴⣿⣇⢸⣿⠀⣿⡇⠸⣿⠀⢸⣇⠀⣿⠀⢸⣿⠀⣿⡆⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁⢀⠀⢀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣇⢘⣃⠀⣿⣁⣸⣿⣤⣿⣇⣸⣿⣨⣿⣿⣉⣿⣧⣼⣿⣀⣿⣷⣾⣿⣷⣼⣿⣦⣿⣡⣸⣿⣀⣹⣇⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣷⣄⠰⠶⠶⠖⠀⠀⠀⣄⠄⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣾⣗⣂⠁⠀
⣼⠀⠀⠙⠁⢈⣿⡿⠉⢋⣿⣷⣿⣉⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢱⡄⠀⠘⢽⣿⣿⠂⠁⠒⠻⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣴⠖⠒⠒⠒⢲⡿⠾⣷⣶⣶⣶⠒⠚⠀⠀⠐⠶⠶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⠆⢰⣶⣶⣶⣶⠂⠀⠀⠀⠀⡀⠀⠀⠈⣻⣿⣿⣿⣟⣛⣛⣭⣵⣦
⠈⣿⣶⣷⣶⠞⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠶⠀⠈⠳⠤⠟⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡇⠀⠟⠻⢿⣟⡛⠀⣿⣿⣿⡟⠉⠀⢀⠀⠀⠃⠃⠀⣰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣾⣿⣿⣿⡟⠋⠱⠴⠰⠦⠆⠀⠀⠀⠀⠀⠂⠀⢠⡿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰⣾⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⠇⠀⣶⡆⢸⣿⣧⡀⠈⠛⠋⠀⠀⠀⣸⣧⠀⠀⠀⢠⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣻⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⢻⣿⣄⠀⠈⠀⠀⠀⠀⠓⠀⠘⢹⠀⢘⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠛⠁⣸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⠤⠀⠀⠀⠀⢻⣽⣽⣿⣿⣿⣿⠟
⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠄⠀⠰⠾⣿⣿⣿⣿⣷⣔⠁⠀⠀⠀⠐⠙⢿⣿⢿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠠⠦⠀⠀⠀⠀⠤⠻⣿⣿⠿⠟⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠁⠀⣎⡈⣼⣿⣿⣿⣿⣿⡆⡄⠀⠀⣠⢀⠈⣷⢰⣿⢻⠛⠓⠑⡄⡀⠀⣤⣤⡤⢹⠿⠟⠛⠛⠃⠀⠀⠀⠀⣿⣿⠀⢰⡄⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣠⣯⣿⣿⣿⣿⡿⠿⠧⠧⢥⡵⣧⣿⣿⣽⣼⣿⣼⠂⠤⣾⢧⣿⣧⣿⣿⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⡦⠄⢀⡀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠀⠐⠂⠀⠂⠉⠋⠩⠋⢹⠛⠙⠀⠀⠀⠀⠐⠻⡟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠈⠙⣿⢿⣿⠛⠛⠁⠀⠀⡆⠀⡇⠀⣿⠀⣿⠀⣿⠀⣻⠀⢸⠇⢸⡇⢸⡧⣄⡏⠀⡇⠀⣷⠀⣷⠹⣔⠀⠀⠀⣤⣶⣆⣿⡇⠀⢸⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣻⠀⠀⠀⣶⠀⣶⠐⣶⠀⣶⢠⣷⢠⡷⣆⡿⠀⣿⠀⣿⢴⣿⠀⣸⡆⣾⡇⣾⣷⣿⣷⠐⣿⠀⣿⠐⣿⠀⣿⠀⢰⢠⣿⣿⣿⣿⡇⠒⢸⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⡀⠀⢠⠁⠼⠤⠤⠠⠿⢄⣿⣴⡿⠄⣹⢼⣿⣼⣧⣹⣧⡺⣿⣿⣿⣾⣿⣦⣹⣷⣼⡝⣿⣇⣼⣿⡄⣿⠼⣿⠤⣽⠢⢿⠀⢶⡎⢻⡿⠯⠻⠧⠀⢸⣿⣿⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣤⡌⢃⣳⡀⢤⡁⢟⣿⣷⣶⣦⣤⣄⣀⣼⣿⣿⠇⢠⡿⢸⣿⢹⣿⠄⣿⡇⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⣷⣿⢰⣿⢸⣾⠀⢠⡀⠀⠻⢃⣴⡀⠀⣾⣿⡏⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣳⣿⣿⣿⣿⣿⣶⣾⣼⣟⣹⣿⣿⣿⣿⡿⣿⡿⠟⠀⢸⣧⣼⣧⣸⣿⣠⣿⣧⣿⣿⣿⣿⣾⣿⣭⣿⣯⣽⣧⣿⣿⣿⣿⣅⣽⣯⢸⣿⢀⣿⣤⣸⡇⠀⠀⡟⣽⣆⠘⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢴⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⠀⢸⠟⣿⡟⢻⡟⠻⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⠿⣿⡟⢿⡇⠐⠀⢀⣽⣿⣴⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⣰⠆⣉⠁⢈⡅⠀⣻⡿⣿⣿⠻⣧⡜⠏⢤⢻⣿⣿⣽⣿⠿⣿⣿⣿⣿⣿⣿⠋⠻⡏⠀⡈⠁⢀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣴⠀⠀⢰⣿⢀⣿⠀⢸⡇⠀⣿⡇⢸⣿⠀⣿⠇⢸⣿⠘⣿⡏⢸⣿⠀⣿⡇⢸⣿⠃⣿⡀⠸⣇⠀⢿⡇⠀⣿⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⠃⠀⠿⣿⣿⣿⣿⣿⣿
⠀⠀⣹⣿⣿⣷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⠇⠀⠀⣼⡇⢸⡇⠀⣿⡇⣀⣿⠀⣼⣿⣴⣿⣠⣼⣿⣴⣿⣇⢸⣿⠀⣿⡇⢸⣿⠀⢹⣇⠀⣿⠀⢸⣷⠀⣿⡆⢸⣿⣿⠇⠹⠀⠀⢸⠃⠀⠀⠰⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⠀⠀⣀⣀⣀⣰⣿⣿⠀⠀⠀⣿⣃⣸⣃⠀⣿⣁⣸⣿⣤⣿⣇⣘⣿⣸⣿⣿⣉⣿⣧⣾⣿⣀⣿⣷⣶⣿⣶⣼⣿⣦⣿⣡⣸⣿⣀⣸⣃⣀⣿⣿⣀⣀⣀⣀⣈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣆⠰⠶⠶⠖⠀⠀⠀⢄⢄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2386

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/01/tanned-propaganda/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/01/tanned-propaganda/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_Propaganda_Mill_of_EPO.org_Pushes_Illegal,_Unconstitutional_UPC_(‘Fake_It
Till_You_Make_It’)_Ahead_of_Further_Perils⠀✐


Posted in Deception, Europe, Patents at 8:23 am by Dr. Roy Schestowitz


Video_download_link | md5sum d650dc59180bc475f4d3817830b423a7
EPO Propaganda Mill Resumes
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-org-is-back.webm


Summary: The usual Unified Patent Court (UPC) propaganda is back as managers of
Europe’s second-largest institution come back to rob it by breaking_the_law_and
besieging_the_staff


THE EPO‘s Web site is writing again for the first time in nearly 5 weeks and
António_Campinos is back with a tan… and vengeance. Like Benoît_Battistelli in
2014, he needs to impress nobody; he already bought his second time and after 4
years in the Office it seems clear he sees no need to obey rulings from the
ILOAT. He just does the corrupt and the illegal without facing any consequences
whatsoever.


“September will be a busy month for us in terms of EPO coverage.”The video
above discusses today’s_lies (warning: epo.org link) and also mentions that the
copyright troll that threatens to sue me over EPO material (pages which concern
the EPO breaking the law) is still sending more threats [1, 2] — even as
recently as yesterday!


September will be a busy month for us in terms of EPO coverage. █



                    ䷩ 𝚕𝚒𝚗𝚎 2438

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/01/tux-machines-front-page/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/01/tux-machines-front-page/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Going_Live_With_Tux_Machines’_Holistic_Front_Page⠀✐


Posted in Site_News at 7:49 am by Dr. Roy Schestowitz


Video_download_link | md5sum 0ead9fdb3314011273b62c9e42a8a6e5
Front Page Changes in Tux Machines
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/cms-live-frontpage.webm


Summary: This past weekend and yesterday were devoted mostly to Tux Machines, a
sister site which is where a lot of research and curation gets done, focusing
on GNU/Linux and Free software issues


LESS than 24 hours ago we made big changes to Tux Machines, which we try to
“modernise” by making_things_simpler_and_lighter,_not_to_mention_supporting_a
lot_more_protocols.


The CMS we develop for Tux Machines will later be used here in Techrights, so I
go through some of the work and the changes, which can be seen as they_happen
in the_Git_repository. █



                    ䷩ 𝚕𝚒𝚗𝚎 2481

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/01/upc-blahblah/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/01/upc-blahblah/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_The_Limits_of_Lobbying_and_Lying⠀✐


Posted in Courtroom, Deception, Europe, Law, Patents at 8:34 am by Dr. Roy
Schestowitz


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


Summary: The EPO‘s management is writing some blahblah about the UPC again
(today_in_EPO.org), but the law isn’t on its side


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

                    ䷩ 𝚕𝚒𝚗𝚎 3155

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_01/09/2022:_Nitrux_Linux_2.4.0_Released_and_Microsoft_Burned_by
Systemd⠀✐


Posted in News_Roundup at 12:02 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o New_Releases
          o BSD
          o Fedora_/_Red_Hat_/_IBM
          o Debian_Family
          o Canonical/Ubuntu_Family
          o Devices/Embedded
    * Free,_Libre,_and_Open_Source_Software
          o Productivity_Software/LibreOffice/Calligra
          o Education
          o Programming/Development
                # Rust
          o Standards/Consortia
    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Patents
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o § Applications⠀➾


                # ⚓ Linux Links ☛ Best_Free_and_Open_Source_Software_–_August
                  2022_Updates⠀⇛


                       We’ve also published new articles in the fields of
                       graphics, games, system administration, education,
                       productivity and internet/networking.


                       As always, we welcome suggestions for new articles
                       or additional open source software to feature.


          o § Instructionals/Technical⠀➾


                # ⚓ Earthly ☛ Grafana_&_Prometheus_Kubernetes_Cluster
                  Monitoring⠀⇛


                # ⚓ Manuel Matuzovic ☛ Parents_counting_children_in_CSS⠀⇛


                       I’ve built a demo to illustrate what can be done.
                       If you click on the element, start typing and press
                       Enter, the parent element tells you how many items
                       you should add.


                # ⚓ uni Toronto ☛ A_thought_on_presentational_versus_semantic
                  HTML⠀⇛


                       One of the realities of life is that as people, we
                       care about how things look, partly because in
                       practice you can’t divorce content from
                       presentation. This means that most people are
                       always going to care about how their HTML looks. If
                       you write semantic HTML, making your HTML look
                       right is a two step process; first you write
                       carefully taxonomized (‘semantic’) HTML, and then
                       you get it to look right with CSS or whatever. If
                       you write presentational HTML, you have only one
                       step; you write your HTML (and CSS) and directly
                       tweak things if necessary.


                # ⚓ uni Toronto ☛ ZFS_DVA_offsets_are_in_bytes,_not_(512-byte)
                  blocks⠀⇛


                       In ZFS, a DVA (Device Virtual Address) is the
                       equivalent of a block address in a regular
                       filesystem. For our purposes today, the important
                       thing is that a DVA tells you where to find data by
                       a combination of the vdev (as a numeric index) and
                       an offset into the vdev (and also a size). However,
                       this description leaves a question open, which is
                       what units are ZFS DVA offsets in. Back when I
                       looked into the details of DVAs in 2017, the code
                       certainly appeared to be treating the offset as
                       being in bytes; however, various other sources have
                       sometimes asserted that offsets are in units of
                       512-byte blocks. Faced with this uncertainty, today
                       I decided to answer the question once and for all
                       with some experimentation.


                # ⚓ Dan Langille ☛ da12_in_my_FreeBSD_zfs_array_disappeared_at
                  :02_and_came_back_at_:04⠀⇛


                       Details about this host (disks, zpool, gpart, etc)
                       are in this post.


                # ⚓ Jan Schaumann ☛ The_Sender_Policy_Framework_(SPF)⠀⇛


                       Take the Sender Policy Framework (SPF), for
                       example. Seems pretty straight forward, right? If
                       you’re, say, a Mail Transfer Agent (MTA) for a
                       popular public email service, and a new connection
                       is made to you trying to deliver mail, you perform
                       a few checks and, by way of SPF, determine whether
                       or not you should even bother to accept the mail:
                       [...]


                # ⚓ H2S Media ☛ How_to_install_Thinkorswim_on_Ubuntu_22.04_LTS
                  Linux⠀⇛


                       Thinkorswim was launched in 1999 as an options
                       brokerage platform. However, later it was acquired
                       by TD Ameritrade, although Thinkorswim’s brokerage
                       services were shut down, the trading platform is
                       still active and distributed by TD Ameritrade for
                       its clients. Besides the trading feature,
                       Thinkorswim users also have access to trading and
                       analysis tools, online courses, etc.


                       Unlike TradingView which can be linked to the
                       trading accounts of many different brokers,
                       Thinkorswim is only used by TD Ameritrade clients.


                       Thinkorswim allows users to freely set alerts based
                       on parameters of technical indicators and price
                       movements. Meanwhile, TradingView allows users to
                       receive only 12 different alert conditions. However


                       Thinkorswim is a bit more complicated for
                       beginners. It is confusing even for many
                       experienced traders. However, the platform has a
                       fairly detailed and comprehensive system of study
                       guide documents that users can use when they need
                       to study.


                       Thinkorswim is completely free for customers, which
                       is a big plus. For traders with TD accounts,
                       Ameritrade has provided extensive knowledge for
                       traders who want to learn about trading and
                       investing.


                # ⚓ OpenSource.com ☛ Use_Tracee_to_solve_for_missing_BTF
                  information_|_Opensource.com⠀⇛


                       Tracee is a project by Aqua Security for tracing
                       processes at runtime. By tracing processes using
                       Linux eBPF (Berkeley packet filter) technology,
                       Tracee can correlate collected information and
                       identify malicious behavioral patterns.


                # ⚓ TecMint ☛ How_to_Install_Rocky_Linux_9.0_Step_by_Step⠀⇛


                       Rocky Linux 9.0 was made generally available on
                       July 14, 2022. It comes with a boatload of new
                       features and improvements and will enjoy support
                       and maintenance until May 31, 2032. The previous
                       release, Rocky Linux 8, will still continue to
                       receive support until May 31, 2029.


                       In this guide, we will walk you through the
                       installation of Rocky Linux 9.0.


                # ⚓ OSTechNix ☛ Convert_Arch_Linux_Packages_To_AppImage_Format
                  –_OSTechNix⠀⇛


                       We already have discussed how to convert a DEB
                       package to an Arch Linux package format with Debtap
                       utility. We also have seen how to use Alien tool to
                       convert Linux packages to different formats. Today,
                       we will be discussing yet another Linux package
                       converter tool named Arch2appimage. In this guide,
                       we will see a brief introduction to Arch2appimage,
                       and how to install Arch2appimage in Linux and how
                       to convert Arch Linux packages to AppImage format
                       with Arch2appimage application.


                # ⚓ ID Root ☛ How_To_Install_XanMod_Kernel_on_Ubuntu_22.04_LTS
                  –_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       XanMod Kernel on Ubuntu 22.04 LTS. For those of you
                       who didn’t know, XanMod is a popular Linux kernel
                       modification that provides enhanced performance and
                       stability for gaming, streaming, and other
                       resource-intensive tasks Compared to the stock
                       Linux Kernel found in many other Linux
                       distributions, you will find some custom settings
                       and new features enabled to enhance your experience
                       with it.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the XanMod Kernel on Ubuntu 22.04
                       (Jammy Jellyfish). You can follow the same
                       instructions for Ubuntu 22.04 and any other Debian-
                       based distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ ID Root ☛ How_To_Install_Zoom_on_Linux_Mint_21_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Zoom on Linux Mint 21. For those of you who didn’t
                       know, Zoom is a communications technology platform
                       that provides video telephony and real-time online
                       chat services through a cloud-based peer-to-peer
                       software platform. Zoom is not only used as a
                       platform for audio or video conferencing but is
                       also used for chats, and conducting several
                       webinars. It is available on Windows, Linux, macOS,
                       Android, and iOS systems.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of a Zoom video conference on Linux
                       Mint 21 (Vanessa).


                # ⚓ LinuxOpSys ☛ How_to_Install_Ubuntu_on_a_USB_Flash_Drive_
                  (Solution)⠀⇛


                       Ubuntu is one of the most widely used Linux
                       operating systems among home users and enterprises.
                       Ubuntu is normally installed by booting from a USB.


                       Installing the entire Ubuntu on a USB Flash drive
                       is simple and straightforward. We need a bootable
                       usb and another USB to which complete Ubuntu to be
                       installed.


                       You can use ubuntu installed USB as a portable
                       computer and bootable device. In this tutorial, we
                       learn how to install the entire Ubuntu on a USB
                       Flash Drive.


                # ⚓ TechRepublic ☛ How_to_install_Webmin_2.0_on_Ubuntu_Server
                  22.04_|_TechRepublic⠀⇛


                       Jack Wallen demonstrates how to install the latest
                       version of the powerful Webmin web-based admin tool
                       for Linux.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Arcane_Waters_is_an_upcoming_open-world
                  pixel-pirate_adventure_game⠀⇛


                       Want to sail the high seas? Love pixel artwork?
                       Check out the upcoming game Arcane Waters which
                       will let you do some pirating adventures alone or
                       online with others too but it’s mainly an online
                       focused game.


                # ⚓ GamingOnLinux ☛ Steam_Deck_Tips_and_Tricks_Part_2⠀⇛


                       Since a lot of people liked the first set of tips
                       and tricks for the Steam Deck, here’s a Part 2 with
                       just a few more that some of you might find useful.
                       Some done before in other videos or articles but
                       this is an easy reference for you.


                # ⚓ GamingOnLinux ☛ The_Zachtronics_Solitaire_Collection
                  releases_September_6⠀⇛


                       Okay so perhaps Last Call BBS being their actual
                       final game was a sweet little lie from Zachtronics.
                       Well, sort of, as The Zachtronics Solitaire
                       Collection is technically not exactly a new game.


                # ⚓ GamingOnLinux ☛ Futuristic_drift-racer_Neodash_is_out_now
                  on_Steam_and_looks_wild⠀⇛


                       Neodash is a fresh Native Linux racing game that
                       combines futuristic bright neon visuals with crazy-
                       fast drifting. What you get is something that
                       clearly resembles the awesome racing-platformer
                       Distance, but pumped up on some serious steroids
                       and a little Trackmania too even.


                # ⚓ Vice ☛ Navy_Looking_for_Gamers_After_Disastrous_Esports
                  Launch⠀⇛


                       Goats and Glory, the U.S. Navy’s esports team, is
                       looking for new sailors to refresh its roster of
                       Twitch streamers. According to an August 22 admin
                       memo, Goats and Glory needs new sailors to play
                       games in front of a camera to help with the
                       military’s recruitment effort.


                # ⚓ The Verge ☛ Chinese_tech_giant_buys_Detroit:_Become_Human
                  developer_Quantic_Dream⠀⇛


                       NetEase is a China-based internet technology
                       company with a growing division dedicated to PC,
                       console, and mobile games. It first became a
                       minority shareholder in Quantic Dream in 2019,
                       shortly after the release of Detroit: Becoming
                       Human. Quantic Dream joins a growing list of game
                       companies that NetEase has acquired and marks its
                       first studio located in Europe.


                # ⚓ GamingOnLinux ☛ Infinity_Engine_reimplementation_GemRB
                  continues_improving_Icewind_Dale_2⠀⇛


                       Classics like Baldur’s Gate, Planescape: Torment,
                       Icewind Dale and more running on the Infinity
                       Engine should live on forever thanks to open source
                       reimplementations like GemRB.


                # ⚓ GamingOnLinux ☛ SokoChess_combines_Chess_with_the_Sokoban
                  block-pushing_formula⠀⇛


                       SokoChess is certainly an intriguing game blending
                       together two very different types of gameplay, to
                       create something that’s a little peculiar but quite
                       fun. Note: key provided by the developer.


                # ⚓ GamingOnLinux ☛ Valheim_gets_patched_to_prevent_the_world
                  resetting⠀⇛


                       Quite an important update has rolled out for the
                       open-world survival game Valheim, with a bunch of
                       changes related to the saving system to prevent
                       some big problems. For a little while some people
                       have unfortunately seen their worlds getting reset,
                       which this patch solves.


    * § Distributions and Operating Systems⠀➾


          o § New Releases⠀➾


                # ⚓ Linuxiac ☛ Nitrux_Linux_2.4.0_Released,_XanMod_Kernel_Is
                  Now_the_Default⠀⇛


                       Nitrux OS has released a new 2.4.0 version,
                       bringing us the latest software updates, bug fixes,
                       and performance improvements.


                       Nitrux is a free, beautiful, open-source, desktop-
                       oriented Linux distro. It’s powered by Debian, KDE
                       technologies, and Qt, emphasizing aesthetics, user
                       efficiency, and portable universal app formats.


                       The distro features a modified version of the KDE
                       Plasma desktop called NX Desktop. On top of that,
                       Nitrux Linux comes with a set of applications that
                       are not typical KDE apps. Instead, a large number
                       of these are MauiKit-based. So, as a result, it is
                       a very different type of desktop Linux
                       distribution.


          o § BSD⠀➾


                # ⚓ “OpenBSD_Mastery:_Filesystems”_Status_Report⠀⇛


                       I just finished the ‘non-native filesystems’ part
                       of “OpenBSD Mastery: Filesystems.” I wouldn’t say
                       I’ve finished the hard part, but I have finished
                       the “intertwined to an unholy degree” part.


          o § Fedora / Red Hat / IBM⠀➾


                # ⚓ Red Hat Official ☛ 4_things_to_know_about_programming_using
                  Ansible_|_Enable_Sysadmin⠀⇛


                       Maybe this isn’t new information for you, or
                       perhaps you’ve just never thought about it. Ansible
                       works really well, so what does it matter whether
                       it’s a programming language?


                # ⚓ Enterprisers Project ☛ 5_ways_data_can_make_you_a_better_IT
                  leader⠀⇛


                       All successful organizations require strong
                       leadership, whether it comes from a captain on a
                       baseball team, officers in the military, or a
                       founder/CEO at a tech startup. We’ve all seen
                       first-hand how poor leadership results in
                       inefficiencies, lack of organization, poor
                       collaboration, and overall lack of innovation.
                       Today, all companies rely on software and tech, so
                       effective IT management can make or break an
                       organization.


                       Future-ready CIOs, CTOs, and other IT leaders
                       require certain skill sets to run teams efficiently
                       and effectively, no matter the size or scope of the
                       project. Some of these skills are soft skills such
                       as empathy, compassion, and open communication, but
                       data also plays a key role. You can’t manage what
                       you don’t measure, and data is essential to
                       measuring anything – including IT leadership
                       quality.


                # ⚓ OpenShift_vs._AWS_product_mapping_–_formicapunk⠀⇛


                       OpenShift is Red Hat’s Kubernetes distribution: it
                       is basically the upstream Kubernetes delivered with
                       monitoring, logging, CI/CD, underlying OS, tested
                       upgrade paths not found with a manual kubernetes.io
                       kubeadm install.


                # ⚓ Red Hat ☛ My_advice_on_why_you_should_build_containers_on
                  your_PC_|_Red_Hat_Developer⠀⇛


                       In this article, I will present options for
                       building containers that will run in Kubernetes and
                       Red Hat OpenShift. There are many reasons against
                       development in the environment that will ultimately
                       run the container, such as cost, speed, tooling,
                       and so on. Creating a container that works on your
                       PC requires a local development environment that
                       gives you the complete experience of coding,
                       building, debugging, and running—and then pushes
                       all pieces of the container to a host or cloud
                       service. The best way to describe this process is
                       tantamount to encapsulating your entire software
                       building experience into one file and then sending
                       it off to a server.


                       Container development offers a new way of thinking
                       about software development. It is an application
                       development model in which you decide which
                       operating system and runtimes run your application,
                       and which libraries to include. A software
                       container holds the application, libraries,
                       runtimes, operating system, as well as
                       specifications for the network port, environment
                       variable values, and more.


                # ⚓ Fedora Project ☛ F37_Pre-Beta_release_validation_kicks_off
                  –_Fedora_Community_Blog⠀⇛


                       Fedora Linux is foremost a community-powered
                       distribution. Fedora Linux runs on all sorts of
                       off-the-shelf hardware. The QA team relies on
                       looking at bugs and edge cases coming out of
                       community-owned hardware, so testing pre-release
                       composes is a crucial part of the release process.
                       We try to fix as many of them as we can! Please
                       participate in the pre-beta release validation test
                       week now through 7 September. You can help us catch
                       those bugs at an early stage.


                # ⚓ Red Hat ☛ 3_essentials_for_writing_a_Linux_system_library
                  in_Rust_|_Red_Hat_Developer⠀⇛


                       Learn how to implement 3 practices for writing
                       Linux system libraries: backward compatibility,
                       event-driven asynchronous programming, and logging.
                       (Part 1 of 4)


          o § Debian Family⠀➾


                # ⚓ Jeff Geerling ☛ apt_key_deprecated_in_Debian/Ubuntu_–_how
                  to_fix_in_Ansible⠀⇛


                       This way of adding apt keys still works for now (in
                       mid-2022), but will stop working in the next major
                       releases of Ubuntu and Debian (and derivatives). So
                       it’s better to stop the usage now. In Ansible, you
                       would typically use the ansible.builtin.apt_key
                       module, but even that module has the following
                       deprecation warning: [...]


                # ⚓ Paul_Wise:_FLOSS_Activities_August_2022⠀⇛


                       This month I didn’t have any particular focus. I
                       just worked on issues in my info bubble.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ 9to5Linux ☛ Canonical_Accepts_Ubuntu_Unity_as_Official
                  Ubuntu_Flavor_Starting_with_Ubuntu_22.10⠀⇛


                       Ubuntu Unity (formerly Ubuntu Unity Remix) saw the
                       light of day a few years ago as part of the Ubuntu
                       20.04 LTS (Focal Fossa) operating system series,
                       but as an unofficial flavor because Canonical
                       abandoned its beloved Unity7 desktop environment
                       more than five years ago.


                       It was hard to believe that Ubuntu Unity will be
                       recognized one day as an official flavor
                       considering Canonical’s past with the Unity7
                       desktop environment, but today, the miracle
                       happened and Canonical will recognize it as an
                       official Ubuntu flavor starting with the upcoming
                       Ubuntu 22.10 (Kinetic Kudu) release in late October
                       2022.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ $5_CH347_board_is_a_USB_2.0_bridge_to_I2C,
                  SPI,_UART,_JTAG,_and_GPIO_–_CNX_Software⠀⇛


                       MuseLab USB-HS-Bridge is an inexpensive ($5) board
                       based on WCH CH347 chip with a USB 2.0 Type-
                       C interface that acts as a bridge for I2C, SPI,
                       UART, and JTAG interfaces, as well as GPIOs.


                       It’s notably useful to debug and download
                       bitstreams to FPGA development boards, but it can
                       also be used to connect various peripherals such as
                       I2C sensors, SPI flash devices, UART devices to
                       basically any host with a spare USB 2.0 host port.


                # ⚓ SparkFun Electronics ☛ A_Day_for_Oscilloscopes_–_News_–
                  SparkFun_Electronics⠀⇛


                       I was rummaging in the basement of SparkFun HQ and
                       came across an ancient oscilloscope. With my
                       interest piqued, I thought it’d be entertaining to
                       dive into its history and see how this device has
                       evolved into the modern-day oscilloscope. This
                       measurement tool has been a tremendous asset in its
                       contribution to SparkFun’s success, so let’s take
                       the time to understand its birth and evolution.
                       Let’s get started…


                # ⚓ CNX Software ☛ Arducam_ToF_camera_adds_depth_sensing_to
                  Raspberry_Pi_for_$30_(Crowdfunding)_–_CNX_Software⠀⇛


                       Arducam has launched of Time-of-Flight (ToF) camera
                       module for Raspberry Pi that enables depth sensing
                       by capturing 3D data (at 240×180 resolution) at a
                       distance of up to 4 meters.


                       Arducam has launched several cameras for Raspberry
                       Pi boards over the years, more recently the Arducam
                       Pi HawkEye 64MP camera, but the Arducam ToF camera
                       is quite different, as while it still connects to
                       the MIPI CSI connector of the SBC, it is used to
                       measure distances and depth and display 3D data.


                # ⚓ Linux Gizmos ☛ ICP_releases_low_cost_industrial_router_with
                  4G_LTE/3G_support⠀⇛


                       The UR32L Lite is an industrial router with
                       automated failback between ethernet and cellular
                       connectivity. This router integrates a single ARM
                       Cortex A7 processor, two 10/100Mbps LAN ports and a
                       SIM slot. The UR32L is available for 109,80€.


                       According to the UR32L datasheet, the industrial-
                       grade processor featured is a single ARM Cortex-A7
                       with a maximum frequency of 528MHz along with 180MB
                       of DDR3 RAM and 128MB of flash. 


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


          o ⚓ Hillel Wayne ☛ Software_Mimicry⠀⇛


                 Mimicry is when software X reimplements at a higher level
                 a core feature of software Y. The produced facsimile has
                 some, but not all, of the same properties, enough to
                 “look like” it’s the same thing but missing many of the
                 nuances. This exists in every kind of software. One
                 language can mimic another, a library can mimic a
                 language, a database engine can mimic a product, etc.


          o ⚓ OpenSSH ☛ Commit_signing_for_portable_OpenSSH⠀⇛


                 We are in the process of converting the portable OpenSSH
                 repository to require signed commits, tags and pushes,
                 using git’s recent ssh signature support. So far it’s
                 gone very smoothly, and we hope to have it enforced for
                 all commits soon.


                 We maintain our own git repository for portable OpenSSH,
                 that is automatically mirrored to github. We use “pre-
                 receive” and “update” hooks to check for signed pushes
                 and tags/commits respectively, using an in-repository
                 allowed_signers file.


          o ⚓ MJ Fransen ☛ Texinfo_as_Personal_Knowledge_Base⠀⇛


                 As soon as you start capturing information for your
                 personal reference, it is time to start thinking about a
                 Personal Knowledge Base.


                 A Personal Knowledge Base helps to structure the
                 information, store it, and make sure you can retrieve the
                 information later on.


                 One of the use-cases for a Personal Knowledge Base are
                 all tasks you have to perform only once in a while, f.e.
                 like installing a new server (if that is not your daily
                 job).


                 You can document all the necessary steps, in the right
                 order, and additional information you might need, and so
                 on.


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ What_is_Miklos_hacking_–_Cropped_video_for_media_shapes_in
                  Impress⠀⇛


                       Impress now supports cropped videos in slide edit
                       mode and during slideshow for documents imported
                       from PowerPoint.


                       [...]


                       The first problem was that the Impress preview was
                       picked from the 3rd second of the video (presumably
                       to avoid a black preview in many videos that start
                       with a short black fade-in), while PowerPoint can
                       store an explicit preview from the video (seems to
                       be the first frame), so no matter what effects you
                       apply, the previews were just different as the
                       source bitmap was different. This could be fixed by
                       looking for an explicitly provided bitmap for the
                       video first, and only then asking the various
                       avmedia/ backends to produce a preview.


                       Once the preview’s initial bitmap was OK, it was
                       necessary to take cropping into account. This was
                       first done for the preview bitmap, and then also
                       for the gstreamer backend (the relevant one for
                       Linux, as a start) of avmedia/, which is
                       responsible for the actual video playback. The
                       gstreamer bits were done by first creating a
                       videocrop element and then connecting that to the
                       existing playbin.


          o § Education⠀➾


                # ⚓ [Old] The_Good_Research_Code_Handbook⠀⇛


                       I’ve tried to write this book in a progressive
                       manner: some content is targeted at complete
                       novices, other to programmers who are farther along
                       on their journey. However, I generally assume that
                       you have some familiarity with the following:


                       Python: this intro is Python-centric. You can write
                       good code for Matlab, R, or Julia, but we won’t
                       cover that here. You don’t need to be a Python
                       expert, but you’ll get the most out of this if
                       you’ve been using Python on a regular basis for at
                       least a month, and if you have some passing
                       familiarity with the python data science ecosystem
                       (numpy, matplotlib, pandas, etc.).


                       Git & Github: a lot of the practices introduced
                       here will require you to change your code, which
                       could cause existing functionality to break. You
                       might even accidentally delete something important!
                       Mastering git and github means you will have a time
                       machine for your code, so you can revert to an
                       earlier state. There’s a great intro to git for
                       beginners from software carpentries.


                       The command line: You will need to run some
                       commands on the command line to implement some of
                       the advice in this book. I’m going to assume that
                       you have some familiarity with running commands
                       from a Unix-style shell (e.g. bash). There’s a
                       great intro to the unix shell from software
                       carpentries. If you’re using Windows, you will
                       still be able to run many tools from the Windows
                       command prompt. Long term, your life will be easier
                       if you install the Windows Subsystem for Linux
                       (WSL) which will give you access to a Unix-style
                       shell.


          o § Programming/Development⠀➾


                # ⚓ Lee Yingtong Li ☛ Robust_Poisson_regression_in_medical
                  biostatistics⠀⇛


                       Robust Poisson regression, on the other hand, seems
                       harder to justify. Under the usual parametric view
                       of generalised linear models, it seems to assume a
                       Poisson distribution for a binary outcome, which is
                       incorrect, as a Poisson-distributed variable can
                       take any non-negative integer value, but the
                       outcome can only either happen or not.


                       It turns out that robust Poisson regression can be
                       justified under a quasi-likelihood framework.


                # ⚓ Rlang ☛ Python_is_superior_to_R_for_writing_quality_codes⠀⇛


                       Python is superior to R for writing quality codes!.
                       R is good for short and dirty analysis, but Python
                       is better if you want to perform significant work,
                       we frequently hear or read.


                       We vehemently disagree with this claim because it
                       is entirely feasible to develop production-quality
                       code in R; we have done it, and others can do it as
                       well.


                # ⚓ Matt Rickard ☛ Design_in_OSS⠀⇛


                       A key advantage of open source is the ability to
                       customize the application to your needs (through
                       interfaces, design systems, or even modifying the
                       code). While this method covers most use cases, it
                       will suffer from being the least common denominator
                       API – you can’t make everyone happy.


                # ⚓ Cobol-mode_(Emacs_Mode_for_editing_COBOL_code)_version_1.1_
                  (stable)_released_on_29_August_2022⠀⇛


                # ⚓ GCC ☛ C++:_add_-std={c,gnu}++{current,future}⠀⇛


                # ⚓ How_to_Check_an_Array_Is_Empty_in_PHP_–_Pi_My_Life_Up⠀⇛


                       In this tutorial, we will take you through some of
                       the ways you can check if an array is empty in PHP.
                       We will touch on using the not operator, the empty
                       and count function. These will come in handy if you
                       use many arrays in your code.


                # ⚓ Medevel ☛ Bullet_Train_is_an_Open-source_SaaS_Platform
                  Builder_for_Ruby_on_Rails⠀⇛


                       Bullet Train is a free open-source SaaS building
                       bundle that aid developers set their SaaS platform
                       in no-time.


                       It comes with dozens of outstanding features fit
                       for building a scalable large enterprise-ready SaaS
                       apps.


                       Bullet Train is built on top of Ruby-on-Rails
                       framework, so it inherits all of its amazing
                       features as scaffolding, organization and more. It
                       also plays well with the popular Ruby packages and
                       gems.


                       The project offers two editions: the first one is a
                       free open-source project that is released under the
                       MIT license. The other one comes with more pro/
                       enterprise features as payment workflow, chat and
                       messaging options, auditing, task management, and
                       Kanban boards.


                # § Rust⠀➾


                      # ⚓ Rust Weekly Updates ☛ This_Week_In_Rust:_This_Week_in
                        Rust_458⠀⇛


          o § Standards/Consortia⠀➾


                # ⚓ OpenSource.com ☛ Usability_and_accessibility_starts_with
                  open_communication_|_Opensource.com⠀⇛


                       Amazing though it may seem, we each experience the
                       world differently. That’s one reality with over 6
                       billion interpretations. Many of us use computers
                       to broaden our experience of the world, but a
                       computer is part of reality and so if you
                       experience reality without, for instance, vision or
                       sound, then you also experience a computer without
                       vision or sound (or whatever your unique experience
                       might be.) As humans, we don’t quite have the power
                       to experience the world the way somebody does. We
                       can mimic some of the surface-level things (I can
                       close my eyes to mimic blindness, for example) but
                       it’s only an imitation, without history, context,
                       or urgency. As a result of this complexity, we
                       humans design things primarily for ourselves, based
                       on the way we experience the world. That can be
                       frustrating, from an engineering and design
                       viewpoint, because even when you intend to be
                       inclusive, you end up forgetting something
                       “obvious” and essential, or the solution to one
                       problem introduces a problem for someone else, and
                       so on. What’s an open source enthusiast, or
                       programmer, or architect, or teacher, or just
                       everyday hacker, supposed to do to make software,
                       communities, and processes accessible?


    * § Leftovers⠀➾


          o ⚓ Counter Punch ☛ Living_in_a_Sci-fi_World⠀⇛


                 If you want a bizarre image, just imagine him in the
                 company of Abraham Lincoln. I mean, really, what’s
                 happened to us?


          o ⚓ Counter Punch ☛ The_Law_of_Proximity⠀⇛


                 Notes.


          o ⚓ Counter Punch ☛ The_Best_Defense_._._.⠀⇛


                 Sadly, missing from these gimmicky TV spots is the self-
                 evident truth that women who become pregnant—whether they
                 plan to or not—are also human and have value. Women are
                 not simply baby-makers whose reproductive functions need
                 to be controlled by patriarchal politicians and self-
                 appointed religious busy bodies. Importantly, pregnant
                 women have the constitutional right to determine for
                 themselves whether or not to bear a child.


          o ⚓ Counter Punch ☛ The_Dance_of_Sympathy⠀⇛


                 This was just one of the issues raised last week.


          o ⚓ The Nation ☛ The_NFL_Disrespects_Women._What_Else_Is_New?⠀⇛


                 The NFL finds itself in a familiar place: trying to
                 convince women, who make up as much as 47 percent of the
                 league’s fan base, that they should give a damn about it.
                 This has been an ugly off-season for the league. First,
                 quarterback Deshaun Watson—who has been accused of
                 coercive, “improper contact” with countless massage
                 therapists in behavior as compulsive as it is
                 repugnant—signed a deal for the most guaranteed money in
                 the history of the sport. In a statement that reads as if
                 it were ghostwritten by a PR flack at a men’s rights
                 meeting, owners Jimmy and Dee Haslam apologized if anyone
                 was “triggered” by the news. Watson is now suspended for
                 the first 11 games by Commissioner Roger Goodell, but
                 only after outrage after an independent arbitrator,
                 former US district judge Sue L. Robinson, handed him only
                 a six-game suspension.


          o ⚓ Counter Punch ☛ Shaq_Dunks_the_Voice⠀⇛


                 Opponents and sceptics have been lingering in the bushes,
                 but the appearance of Shaq provided grist to the mill. 
                 While movie stars, tartlets and personalities find their
                 mark in the politics of some countries (the Philippines
                 comes to mind), Australia remains unaroused by the tinsel
                 and bling.  Generally speaking, the celebrity factor duds
                 when it comes to proposing substantive political change.


          o ⚓ The Nation ☛ The_Secret_Powers_of_William_Klein⠀⇛


                 One of photography’s secret powers is to turn time inside
                 out. It takes a constellation of happenings that occupied
                 a fraction of a second and makes it available to
                 attention over a long span of time. And yet the picture
                 always collapses back into instantaneity. This is
                 something that William Klein has thought about. “A
                 picture is taken at 125th of a second,” he once observed.
                 That means that when you see 125 images by any
                 photographer, you’re seeing one second of their life.
                 “The life of a photographer, even a great photographer as
                 they say: two seconds.” That’s about what’s encompassed
                 by the photographs alone in the current exhibition at New
                 York’s International Center of Photography, “William
                 Klein: YES: Photographs, Paintings, Films, 1948–2013.”
                 But even with some 300 works on view—two and a half
                 seconds of life!—the ICP exhibition, curated by David
                 Campany and on view through September 12, left me hungry
                 for more; every one of those tiny morsels of time
                 encapsulated in his imagery is so teeming with energy,
                 with life. The brash optimism of the three-letter upper-
                 case affirmation in the show’s title reflects the
                 enthusiasm that permeates all of Klein’s endeavors: His
                 willingness to try anything, his will to experience
                 everything, his determination not to miss out on
                 witnessing and participating and fighting, are just what
                 we need in these most discouraging of times.


          o § Science⠀➾


                # ⚓ Hackaday ☛ The_Cheat_Way_To_Perfectly_Split_An_Oreo⠀⇛


                       Believe it or not, much research has been done in
                       how to perfectly split Oreos with an even amount of
                       cream on both sides. Early studies suggested it
                       simply wasn’t possible, with one side always
                       getting the majority of the cream.  However, [Ian
                       Charnas] has now found a sneaky workaround.


                # ⚓ Hackaday ☛ Water_Level_Sensor_Does_Not_Use_Water_Level
                  Sensor⠀⇛


                       When interfacing with the real world, there are all
                       kinds of sensors available which will readily
                       communicate with your microcontroller of choice.
                       Moisture, pH, humidity, temperature, location,
                       light, and essentially every other physical
                       phenomenon are readily measured with a matching
                       sensor. But if you don’t have the exact sensor you
                       need, it’s sometimes possible to use one sensor as
                       a proxy for another.


          o § Education⠀➾


                # ⚓ Jim Nielsen ☛ Trying⠀⇛


                       Ultimately, I don’t think any of my words helped
                       much. What did help, I think, was just being there
                       alongside him as he went through it.


                # ⚓ Eesti Rahvusringhääling ☛ Maria_Mölder:_Free_use_of
                  libraries_a_basic_human_right⠀⇛


                       We have to admit that not everyone can afford to
                       buy books (or will in the near future) and that the
                       use of public libraries is still an integral aspect
                       of education in society, and hence a
                       constitutionally protected human right. The
                       introduction of fees for library lending as a means
                       of solving the issue of compensation is
                       inconceivable, writes Maria Mölder in a comment
                       originally published in Estonian in Sirp magazine
                       last Friday.


                # ⚓ Scheerpost ☛ Want_More_Teachers?_Start_Valuing_Education⠀⇛


                       Too many lawmakers are happy to dole out subsidies
                       for the rich and corporations while resisting pay
                       increases for educators.


          o § Hardware⠀➾


                # ⚓ The Hill ☛ Commerce_secretary_urges_states_to_compete_for
                  semiconductor_funds:_‘This_is_a_race’⠀⇛


                       Raimondo gave remarks while touring a microchip
                       manufacturing facility at the university with Sen.
                       Mark Kelly (D-Ariz.). President Biden signed the
                       CHIPS and Science Act into law earlier this month,
                       providing more than $50 million in incentives for
                       semiconductor manufacturers to build domestic
                       plants.


                # ⚓ Hackaday ☛ Converting_An_Old_ATV_To_Electric_Drive⠀⇛


                       [RCLifeOn] happened upon an old petrol-powered ATV
                       that had seen better days. He decided it was the
                       perfect candidate for a conversion to electric
                       drive.


                # ⚓ Hackaday ☛ Solar_Cells_As_Art_Form⠀⇛


                       When most of us approach a project, we have a
                       certain problem to solve. 3D printing,
                       microcontrollers, batteries, and all kinds of
                       technologies are usually tools to accomplish some
                       task. This is not necessarily true in the art
                       world, though, where the intrinsic nature of these
                       tools can be explored for their own sake rather
                       than as a means to an end. The latest one that came
                       across our desk is this light-powered sound
                       generator.


                # ⚓ Hackaday ☛ MH-Z19-like_NDIR_CO2_Sensor_HC8_Found_And
                  Explored⠀⇛


                       While on the search for an alternative to directly
                       buying the fairly expensive MH-Z19 CO2 sensor,
                       [spezifisch] came across a ‘BreeRainz’ branded
                       gadget (also found under other brands) that claimed
                       to use an NDIR (Non-Dispersive Infrared) sensor for
                       measuring CO2 levels, while costing only €25. This
                       type of sensor allows for CO2 levels to be measured
                       directly, rather than inferred, making them
                       significantly more precise.


                # ⚓ Hackaday ☛ Backup_Camera,_Digital_Dash,_Road_Assist…_In
                  1969?⠀⇛


                       If your friend told you their car had a backup
                       camera, a digital dashboard, climate control, could
                       scan for radio stations, and even helped stay on
                       the road, you wouldn’t think much about it. Unless
                       the year was 1969. The car — the Hurricane by
                       Australian automaker Holden — was never a
                       production vehicle. But it was way beyond the state
                       of the art in 1969 and isn’t too dated, even
                       today.  The concept car was actually found in 1988
                       and restored by 2011. Honestly, it still looks
                       great.


                # ⚓ Hackaday ☛ Hackaday_Prize_2022:_A_Sun-Chasing_Robot⠀⇛


                       There’s plenty of power to be had from the sun, but
                       you need to be out of the shade to receive it.
                       [Dennis] built a robot by the name of Sun Chaser
                       that has the smarts to go where the sun is shining.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ Life_Expectancy_in_US_Drops_for_Second_Straight
                  Year⠀⇛


                # ⚓ NPR ☛ An_ode_to_city_parks:_a_climate_refuge_under
                  pressure⠀⇛


                       At the same time, climate change demands ever more
                       attention from parks departments, and dozens of
                       cities have added new positions to meet those
                       demands.


                # ⚓ Terence Eden ☛ You_can’t_smile_in_the_Metaverse⠀⇛


                       The current range of VR headsets have to be
                       strapped tight to your face. In order to prevent
                       your eyes going out of alignment with the lenses or
                       the focus suddenly changing, the mask clings tight
                       to your face. Sure, it has a foam/rubber seal to
                       soften the pain, but it can still be pretty
                       uncomfortable.


                # ⚓ Democracy Now ☛ “We_Can’t_Go_It_Alone”:_Jackson,_Miss.,
                  Mayor_Lumumba_on_Water_Catastrophe_in_Majority-Black_City⠀⇛


                       We get an update on the water crisis in Jackson,
                       Mississippi, from Mayor Chokwe Antar Lumumba, where
                       more than 180,000 residents of the majority-Black
                       city are without running water. President Biden
                       declared a federal emergency on Tuesday. Water has
                       been cut off since the main water treatment plant
                       flooded amid torrential rains. Lumumba says the
                       emergency is the result of three decades of
                       disinvestment from the state. “We’ve been investing
                       the money that we have,” says Lumumba, who took
                       office in 2017 and started alerting the state
                       government of the challenges with the water system
                       starting in 2018. “We can’t do it alone. We don’t
                       have a billion dollars’ worth of resources to make
                       it happen.”


          o § Security⠀➾


                # ⚓ The Verge ☛ A_‘high_severity’_TikTok_vulnerability_allowed
                  one-click_account_hijacking⠀⇛


                       The bug and its resulting attack, labelled a “high
                       severity vulnerability,” could have been used to
                       hijack the account of any TikTok user on Android
                       without their knowledge, once they clicked on a
                       specially crafted link. After the link was clicked,
                       the attacker would have access to all primary
                       functions of the account, including the ability to
                       upload and post videos, send messages to other
                       users, and view private videos stored in the
                       account.


                # ⚓ California18 ☛ Azure:_Ubuntu_VMs_paralyzed_by_systemd
                  update,_Kubernetes_services_disrupted⠀⇛


                       A recent systemd update creates an error when
                       resolving DNS requests on virtual machines with
                       Ubuntu Bionic Beaver (version 18.04). Systemd
                       version 237-3ubuntu10.54 contains a bug that causes
                       network connections to drop. The automatic
                       installation of the update on VMs in Azure led to
                       various failures. The Azure Kubernetes Service
                       (AKS) in particular is severely affected globally.
                       The Ubuntu and Azure teams are working to fix the
                       bug and its impact. The problem is limited to
                       Ubuntu 18.04.


                # ⚓ Krebs On Security ☛ Final_Thoughts_on_Ubiquiti⠀⇛


                       Last year, I posted a series of articles about a
                       purported “breach” at Ubiquiti. My sole source for
                       that reporting was the person who has since been
                       indicted by federal prosecutors for his alleged
                       wrongdoing – which includes providing false
                       information to the press.


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Terence Eden ☛ What’s_the_most_malicious_thing_you
                        can_do_with_an_injected_HTML_heading_element?⠀⇛


                             While fuzzing around with the input, I made
                             an interesting mistake. I mistyped <svg> as
                             <sgv>. That invalid element was added to the
                             page’s HTML! That means there’s a parser
                             somewhere which is stripping out only the
                             elements it knows about. Browsers typically
                             ignore elements they don’t understand – so
                             there’s no danger to users there. But it
                             points to the idea that there may be some
                             elements the sanitiser doesn’t know about.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Pro Publica ☛ Inside_a_Million-Dollar_Instagram
                        Verification_Scheme⠀⇛


                             Jugenburg’s physician-influencer tendencies
                             led to a six-month suspension of his Ontario
                             medical license in 2021 after he admitted to
                             filming patient interactions and sharing
                             images of procedures without consent. He
                             apologized for the lapse and is currently
                             facing a class-action lawsuit from female
                             patients who say their privacy was violated.


                      # ⚓ NBC ☛ Surviving_Monkees_member_Micky_Dolenz_sues_the
                        FBI,_asks_for_files_on_him_and_his_bandmates⠀⇛


                             “If I had to guess, it would pertain to who
                             they hung around with within the
                             counterculture, anti-war and drug
                             entertainment community,” he said in a
                             statement to NBC News.


                      # ⚓ Vice ☛ FTC_Sues_‘Massive’_Data_Broker_for_Selling
                        Location_Info_on_Abortion_Clinics⠀⇛


                             The Federal Trade Commission (FTC) has sued
                             Kochava, a large location data provider, for
                             allegedly selling data that the FTC says can
                             track people at reproductive health clinics
                             and places of worship, according to an
                             announcement from the agency.


                      # ⚓ Bert Hubert ☛ Tracker_Beeper⠀⇛


                             The video above beeps only on Google, and it
                             shows how the official Dutch government jobs
                             site (which also advertises for the
                             intelligence and security services) sends
                             your every click to Google – despite never
                             asking for your permission to do so. It also
                             reports to Google if you clicked the button
                             “apply for this job”, or even “call us for
                             information”. Nice.


                      # ⚓ YLE ☛ Finland_set_to_introduce_digital_ID_cards⠀⇛


                             An upcoming reform is set to allow electronic
                             identification in Finland, making proving
                             one’s identity possible directly from a phone
                             using a mobile app, alongside traditional
                             identification with a passport or ID card.


                             A draft law on the digital identity cards
                             will be presented to Parliament in autumn by
                             the Ministry of Finance.


                      # ⚓ EFF ☛ Fog_Data_Science_Puts_our_Fourth_Amendment
                        Rights_up_for_Sale⠀⇛


                             This post explains that the Fourth Amendment
                             sharply limits how police use Fog. At a
                             minimum, the Fourth Amendment prohibits
                             police from using Fog’s device search feature
                             without first obtaining a warrant from a
                             judge. Additionally, the Fourth Amendment
                             likely bars Fog’s dragnet searches—in which
                             police request information about any mobile
                             device in a geographic area— even when police
                             get a warrant. 


                      # ⚓ EFF ☛ Inside_Fog_Data_Science,_the_Secretive_Company
                        Selling_Mass_Surveillance_to_Local_Police⠀⇛


                             Troublingly, those records show that Fog and
                             some law enforcement did not believe Fog’s
                             surveillance implicated people’s Fourth
                             Amendment rights and required authorities to
                             get a warrant. 


                      # ⚓ EFF ☛ How_Law_Enforcement_Around_the_Country_Buys
                        Cell_Phone_Location_Data_Wholesale⠀⇛


                             In our first post about Fog Data Science, we
                             described how Fog’s Reveal service works,
                             where its data comes from, and why it is so
                             dangerous. In this post, we will examine the
                             records received by EFF to better understand
                             how Fog Data Science’s service is actually
                             used. We will also dive deeper into the legal
                             issues at stake and discuss how lawmakers and
                             platform developers can shut down Fog’s
                             business model once and for all.


                      # ⚓ Techdirt ☛ FTC_Sues_Data_Broker_Over_Location_Data,
                        But_May_Face_Steep_Uphill_Climb⠀⇛


                             The reversal of Roe is resulting in dramatic
                             new pressures on privacy reform, given how
                             easily consumer location data can be
                             weaponized against abortion seekers and those
                             helping them. Not just by authoritarian-
                             leaning state governments, but potentially by
                             vigilantes who’ll find little trouble buying
                             such data on the cheap from a wide array of
                             irresponsible data brokers.


                      # ⚓ EFF ☛ How_Ad_Tech_Became_Cop_Spy_Tech⠀⇛


                             You can probably guess where this is going.


                      # ⚓ EFF ☛ Fog_Revealed:_A_Guided_Tour_of_How_Cops_Can
                        Browse_Your_Location_Data⠀⇛


                             Fog Reveal offers law enforcement a powerful
                             and incredibly invasive tool for sifting
                             through huge datasets of phone location data.
                             Reveal’s workflow allows cops to perform
                             “geofenced” device searches, i.e. a search
                             for all devices in a specified region on a
                             map, and then find all other locations those
                             devices were at other times. A powerpoint
                             presentation we received from the Chino
                             Police Department describes how cops use
                             these features to identify so-called “bed-
                             down” locations and build up “patterns of
                             life” for device’s owners. These features
                             clearly undercut Fog’s claim that their
                             product only contains “anonymized” data with
                             “no PII [personally identifiable
                             information]”.


                      # ⚓ EFF ☛ What_is_Fog_Data_Science?_Why_is_the
                        Surveillance_Company_so_Dangerous?⠀⇛


                             This means that police can open up their Fog
                             map and do a number of things. They can draw
                             a box and see identifiers representing every
                             device within that geographical area at a
                             given time frame. They can also use a
                             device’s ID to trace that device’s precise
                             location history over months or even years.
                             Fog does not require police officers to
                             obtain a warrant or other court order before
                             acquiring this location data (unlike
                             communication service companies that hold
                             their customers’ location data and generally
                             do require a court order). Likewise, many
                             police departments that use Fog do not
                             require their officers to get a warrant.


                      # ⚓ Techdirt ☛ Wikimedia,_ACLU,_Knight_Institute_Ask
                        Supreme_Court_To_Hear_Challenge_Of_NSA_Bulk
                        Surveillance⠀⇛


                             More than nine years of news cycles ago, the
                             initial Snowden leak dropped. The next few
                             years were filled with lawsuits, extensive
                             news coverage, reform efforts (some better
                             than others), the unplanned retirement of one
                             bulk collection program, and an uptick in
                             public outcry against large-scale government
                             surveillance programs.


                      # ⚓ Techdirt ☛ The_Downside_Of_Apple’s_Lockdown_Mode:
                        Websites_Call_Tell_If_You’re_Using_It⠀⇛


                             Israeli exploit developer NSO Group has drawn
                             a lot of heat over the past several months
                             after it was revealed its malware had been
                             deployed by its customers to target
                             dissidents, journalists, opposition leaders,
                             and other people governments don’t like but
                             aren’t normally considered to be terrorists
                             or criminals.


                      # ⚓ EFF ☛ The_SECURE_Notarization_Act_Will_Create_a_Race
                        to_the_Bottom_for_Privacy⠀⇛


                             If passed as written, the SECURE Notarization
                             Act would require states to recognize out-of-
                             state notarizations that do not comply with
                             potentially stronger state standards. This
                             encourages a race to the bottom. States will
                             have a clear incentive to establish the
                             weakest possible standards in a bid to
                             attract notary businesses to their state. Not
                             only does this diminish the rights of
                             consumers, but it would also create
                             significant enforcement problems, as states
                             do not have regulatory oversight of out-of-
                             state notaries.


                      # ⚓ PIA ☛ The_Patriot_Act:_Mass_Surveillance_Before_and
                        After_9/11⠀⇛


                             Anti-terrorism legislature was introduced
                             left and right. It didn’t take long to pass
                             the US Patriot Act, which provided the
                             government with broad surveillance
                             capabilities. Now, any group, individual, or
                             entity known to be conspiring with terrorists
                             could be monitored legally. It was the
                             solution and comfort Americans needed at the
                             time. 


                      # ⚓ TruthOut ☛ US_Government_Sues_Data_Broker,_Saying_It
                        Sold_Abortion_Clinic_Visitors’_Data⠀⇛


                      # ⚓ Techdirt ☛ France_Uses_AI_To_Find_Swimming_Pools_For
                        Tax_Purposes⠀⇛


                             As humanity marches on towards the expansion
                             of artificial intelligence, we are finding
                             many ways to use this technology while
                             waiting for it to get smart enough to kill us
                             all and bring on the Age of the Robot.
                             Platforms have attempted to solve the
                             impossibility of moderation at scale by
                             employing AI, with no real success. The UK
                             tried to employ AI to make decisions for when
                             to charge certain people with crimes based on
                             a likelihood to re-offend… largely based on
                             where they live. And, of course, there are
                             those that have used AI to create
                             intellectual property in order to throw the
                             IP world into chaos over whether AI can claim
                             IP rights or not.


          o § Defence/Aggression⠀➾


                # ⚓ Salon ☛ Trump’s_Truth_Social_rants_against_the_FBI
                  inadvertently_undercut_his_main_January_6_defense⠀⇛


                       To be certain, this is just more confirmation of
                       what was already obvious, that Trump knows he’s
                       lying when he says he’s the rightful winner of the
                       2020 election. As Dan Friedman at Mother Jones
                       reported in July, a leaked tape shows Trump’s close
                       friend and advisor Steve Bannon outlining the plan
                       to a group of associates: “What Trump’s gonna do is
                       just declare victory. Right? He’s gonna declare
                       victory. But that doesn’t mean he’s a winner. He’s
                       just gonna say he’s a winner.”


                # ⚓ The Sunday Times UK ☛ ‘Western_spy’_took_Shamima_Begum_to
                  Syria⠀⇛


                       An inquiry was demanded last night as it emerged
                       that Canada knew about the teenagers’ fate but kept
                       silent while the Metropolitan Police ran a frantic,
                       international search for the trio. Canada privately
                       admitted its involvement only when it feared being
                       exposed, and then successfully asked the British to
                       cover up its role, the book claimed.


                # ⚓ Medforth ☛ France:_A_literature_teacher_in_a_Paris_suburb
                  anonymously_reports_on_the_penetration_of_Salafism_into_the
                  school,_an_Islamist_ideology_that_has_been_affecting_his
                  teaching_for_about_ten_years_now⠀⇛


                       In the Paris suburbs, most high schools are schools
                       of social decline. The first problem is the ethnic
                       mix: there is no mixing. In my première class, for
                       example, all the pupils have an immigrant
                       background. They feel forgotten and abandoned by
                       the Republic and, in response, they turn to
                       Salafism. They are looking for meaning and find it
                       in this all-encompassing religion that has an
                       answer to everything or almost everything. The
                       Muslim Brotherhood is proselytising, some
                       communities are proving compliant. And conversion
                       to Islam is easy and quick. What is the outcome?
                       For the last ten years or so, the school, which is
                       a mirror image of society, has become permeable to
                       these religious zealots. The abaya – a veil that
                       covers the whole body except the face, hands and
                       feet – has become commonplace there. More and more
                       girls dress in it, sometimes even putting on Saudi-
                       style hoods and gloves when they leave school.
                       Fifteen years ago, this kind of clothing did not
                       happen.


                # ⚓ TruthOut ☛ What_Can_We_Expect_From_Biden’s_Speech_on_the
                  Rise_of_Fascism_Among_Republicans?⠀⇛


                # ⚓ Medforth ☛ “80_fascists_killed”:_Islamo-Leftists_mock_the
                  victims_of_the_Islamist_terrorist_attack_in_Nice,_France⠀⇛


                       Such statements come just a few days before the
                       start of the trial for the July 14 attack. Eight
                       defendants are due to appear before Paris’ special
                       jury court in connection with the attack, which
                       took place on the Promenade des Anglais in 2016 and
                       killed 86 people and injured more than 400. The
                       perpetrator, a 31-year-old Tunisian named Mohamed
                       Lahouaiej-Bouhlelqui, will not stand trial. On the
                       evening of July 14, Mohamed Lahouaiej-Bouhlelqui
                       was shot dead by police after firing at the
                       security forces himself. He had just driven a 19-
                       tonne truck into the crowd that had gathered on the
                       Promenade des Anglais in Nice to watch the
                       fireworks.


                # ⚓ The Hill ☛ Five_of_the_biggest_takeaways_from_FBI’s_Trump,
                  Mar-a-Lago_filing⠀⇛


                       A new filing released late on Tuesday casts more
                       light on a case that exploded into public view when
                       the former president’s Florida estate was raided on
                       Aug. 8.


                # ⚓ RTL ☛ Secret_files_‘likely_concealed’_at_Trump_home_to
                  block_FBI_probe⠀⇛


                       Top secret documents found at Donald Trump’s
                       Florida home were “likely concealed” to obstruct an
                       FBI probe into the former US president’s potential
                       mishandling of classified materials, the Department
                       of Justice said in an explosive new court filing.


                # ⚓ The Hill ☛ DOJ:_Classified_documents_at_Mar-a-Lago_‘likely
                  concealed_and_removed’⠀⇛


                       Among the details revealed by the filing were that
                       classified documents were found in Trump’s own desk
                       during the search, as they recovered some 33 boxes
                       containing more than 100 classified records when
                       agents searched Mar-a-Lago on Aug. 8.


                # ⚓ Counter Punch ☛ Ukraine’s_Imperiled_Zaporizhzhia_Nuclear
                  Complex:_What_Could_Go_Wrong⠀⇛


                       How safe was the Zaporizhzhia power plant before
                       the Russian attack?


                # ⚓ Meduza ☛ International_Atomic_Energy_Agency_mission_arrives
                  in_Zaporizhzhia_for_nuclear_plant_inspection_—_Meduza⠀⇛


                       A delegation from the International Atomic Energy
                       Agency (IAEA) has arrived in Zaporizhzhia,
                       according to the Ukrainian state energy company
                       Enerhoatom. The representatives, led by IAEA
                       Director General Rafael Grossi, plan to travel from
                       the Ukrainian-held city to the Zaporizhzhia Nuclear
                       Power Plant to conduct an inspection.


                # ⚓ Meduza ☛ Russian_authorities_to_hold_‘referendum’_in
                  Zaporizhzhia_region_in_September_as_planned_—_Meduza⠀⇛


                       A “referendum” on whether to join Russia will be
                       held in the occupied parts of Ukraine’s
                       Zaporizhzhia region in September, according to
                       Alexander Saulenko, the Russian-appointed mayor of
                       Berdyansk.


                # ⚓ Meduza ☛ ‘The_entire_country_is_being_held_hostage’:_Human
                  rights_lawyer_Ivan_Pavlov_on_why_the_Russian_authorities_are
                  targeting_ex-journalist_Ivan_Safronov_—_Meduza⠀⇛


                # ⚓ Meduza ☛ A_Soviet_Hamlet_Scholar_Artemy_Kalinovsky_suggests
                  a_Shakespearian_perspective_on_Mikhail_Gorbachev’s_legacy_—
                  Meduza⠀⇛


                # ⚓ The Nation ☛ Gorbachev’s_Legacy⠀⇛


                       On March 11, 1985, Mikhail Gorbachev became leader
                       of the Soviet Union. Within a few weeks, the full-
                       scale reformation he attempted to carry out both
                       inside his country and in its Cold War relations
                       with the West, particularly the United States,
                       began to unfold. Perestroika (“restructuring”)—as
                       Gorbachev called his reforms—officially ended with
                       the Soviet Union and his leadership in 1991. The
                       historic opportunities for a better future it
                       offered Russia—and the world—have been steadily
                       undermined ever since.


                # ⚓ The Gray Zone ☛ Jon_Stewart_and_the_Pentagon_honor
                  Ukrainian_Nazi_at_Disney_World⠀⇛


                # ⚓ Counter Punch ☛ The_Stained-Glass_Teddy_Bear⠀⇛


                       I had intended to write a column this week about
                       the nature of the U.S. security state and the
                       country’s trillion-dollar, only minimally
                       challenged annual “defense” — actually, offense —
                       budget, but then I came upon a journal entry I
                       wrote in 1988, when my daughter, who is a stained-
                       glass artist and poet living in Paris, was 2 years
                       old.


                # ⚓ Counter Punch ☛ The_Missing_“Peace”_in_the_$13.5_Billion
                  Military_Package⠀⇛


                       The latest announcement from the DOD brings the
                       total in weapons, ammunition and military training
                       to escalate the war in Ukraine to at least $13.5
                       billion dollars.


                # ⚓ Common Dreams ☛ Opinion_|_The_Missing_‘Peace’_in_$13.5
                  Billion_of_Military_Aid_to_Ukraine⠀⇛


                       The Department of Defense recently announced it
                       would send nearly $3 billion more in weapons and
                       assistance to Ukraine. The White House news of the
                       largest Ukraine arms package yet—rockets, drones,
                       350,000 rounds of ammunition—was drowned out by
                       President Biden’s announcement to cancel federal
                       student loan debt for almost half of the country’s
                       43-million debt-saddled people. So while our nation
                       debated whether U.S. citizens should be burdened
                       with huge predatory interest for seeking an
                       education; predatory weapons of war were given the
                       greenlight for Ukraine, even though there’s no
                       accountability for who will receive those weapons,
                       including the neo-Nazi Azov Batallion, an official
                       wing of the Ukrainian military.


                # ⚓ Common Dreams ☛ Outrage_After_Ohio_Cop_Kills_Unarmed_Black
                  Man_Donovan_Lewis_in_Bed⠀⇛


                       “Columbus police shot Donovan Lewis within a second
                       of opening the door to his room, and then, while he
                       was dying, told him to ‘stop resisting.’”


                # ⚓ Democracy Now ☛ “Freedom_Dreams”:_Historian_Robin_D._G.
                  Kelley_on_20th_Anniversary_of_His_Book_&_Why_Movements
                  Matter⠀⇛


                       On the last day of Black August, as President Biden
                       calls for an assault weapons ban and more funding
                       for police, we speak with UCLA professor Robin D.
                       G. Kelley, who recently published the revised and
                       expanded 20th anniversary edition of his book
                       “Freedom Dreams: The Black Radical Imagination,”
                       with an added foreword by poet Aja Monet. The new
                       edition was inspired by the Black Lives Matter
                       uprisings in 2020 and covers topics from critical
                       race theory to state militarism that Kelley says
                       “continues to this day.” Kelley says the book’s
                       legacy conveys that “we don’t have the luxury to
                       just fight for reform. We can’t survive that way.
                       We’ve got to fight for revolutionary change.”


                # ⚓ Democracy Now ☛ “Total_Terror”_in_Iraq:_Muqtada_al-Sadr
                  Supporters_Fight_Rivals_in_Baghdad_Amid_Political_Deadlock⠀⇛


                       At least 30 people were killed and hundreds more
                       injured in Iraq after armed supporters of the
                       powerful Iraqi cleric Muqtada al-Sadr clashed with
                       security forces in the capital of Baghdad following
                       the cleric’s announcement Monday he would be
                       quitting politics. The violence comes after months
                       of political turmoil in Iraq that has seen
                       politicians unable to form a government since
                       parliamentary elections in October, and the prime
                       minister said Tuesday he would “vacate his post” if
                       the complicated political situation in the country
                       continues. “The political parties that came to
                       power are in reality just militias who cannot talk
                       politics, do not understand democracy, do not
                       understand what it means to step down once you did
                       not win,” says Yanar Mohammed, president of the
                       Organization of Women’s Freedom in Iraq, who joins
                       us from Baghdad. Mohammed says the fighting fueled
                       by the political parties “held the totality of the
                       Iraqi people in ransom” for almost 24 hours,
                       forcing people to stay at home “because it felt
                       like a civil war.”


                # ⚓ Common Dreams ☛ Opinion_|_Failure_of_the_Nuclear
                  Nonproliferation_Treaty_Review_Conference_Leaves_Humanity
                  Increasingly_Vulnerable⠀⇛


                       The failure of the Nuclear Nonproliferation Treaty
                       Review Conference to adopt a final conference
                       statement adopting specific goals and deadlines for
                       further disarmament weakens humanity’s ability to
                       defend itself against the existential and increased
                       danger of nuclear war. (The conference was held at
                       the United Nations in New York, August 2-26)


                # ⚓ TruthOut ☛ Alabama_Hides_the_Horrors_of_Its_Executions_by
                  Classifying_Them_as_Homicides⠀⇛


                # ⚓ Techdirt ☛ Alabama_Town_Disbands_Police_Force_After_Racist
                  Text_Message_Surfaces⠀⇛


                       Were you ever so terrible at your job that your
                       entire place of employment was put out of business?


                # ⚓ The Nation ☛ The_ACLU_Fights_for_Minneapolis⠀⇛


                       Minneapolis, Minn.—In the 16 months since Derek
                       Chauvin was sentenced to 22.5 years in prison for
                       the murder of George Floyd, the streets of
                       Minneapolis have only occasionally been filled by
                       protesters. The police killings of 22-year-old Amir
                       Locke and 20-year old Tekle Sundberg this year
                       sparked outrage, though to a lesser degree. Despite
                       dwindling boots-on-the-ground action, however, the
                       fight over policing in Minneapolis rages on.


                # ⚓ The Nation ☛ Harlem_Beauty⠀⇛


                # ⚓ Counter Punch ☛ Western_Sahara_Conflict:_Analyzing_the
                  Illegal_Occupation_(1973-Present)⠀⇛


                       Zunes talks about how this foreign policy and human
                       rights issue is to play out since the election of
                       Biden as he further unpacks Western Sahara-Morocco-
                       US relations in terms of a thematic bipartisan
                       consensus. He breaks down MINURSO (the United
                       Nations Mission for the Referendum in Western
                       Sahara) and provides to the reader the background,
                       proposed goals, and the state of the political
                       situation, or dialogue, at the institutional level.


                # ⚓ Counter Punch ☛ Baiting_Tigers_and_Poking_Dragons_–_A
                  Kungfu_Perspective_on_China_and_Taiwan⠀⇛


                       Communist China regards Taiwan as a renegade
                       province. Some say China has a legitimate claim,
                       and maybe that’s true. As far as I’m concerned, the
                       claim of any state has about as much moral weight
                       as the claim John Wayne Gacy had to the children he
                       raped and murdered. The Right of Might has inspired
                       many imperial powers to occupy Taiwan, from the
                       Dutch to the Japanese. I get it that there are
                       strategic reasons why China won’t consider
                       Taiwanese independence—particularly considering how
                       cozy Taiwan’s government has always been with the
                       U.S.—but strategy is not the same as morality.
                       Regardless, my basic feeling on the China vs.
                       Taiwan matter is that it’s none of my business.
                       Then again, I’m not the CIA.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Common Dreams ☛ DOJ_Releases_Photo_of_‘Top_Secret’
                  Documents_Seized_From_Trump’s_Home⠀⇛


                       The heavily redacted photo, which shows documents
                       clearly marked “secret” and “top secret” sprawled
                       out on carpet, accompanied a new 36-page filing in
                       which the Department of Justice said it compiled
                       evidence that “efforts were likely taken to
                       obstruct” its investigation, a finding that puts
                       members of Trump’s team and potentially the former
                       president himself in even more legal jeopardy.


                # ⚓ Counter Punch ☛ The_Mar-a-Lago_Dumpster⠀⇛


                       Law enforcement by the Democrats under President
                       Joe Biden is treating Trump as if he shot someone
                       on Fifth Avenue, illustrating Garland’s repeated
                       admonition that no one is above the law. Trump said
                       when running for president in 2015 that he could
                       shoot someone on that busy street, a positive
                       symbol of New York City, and still remain popular.
                       We’ll see, as he used to say.


                # ⚓ TruthOut ☛ Trump_Mocks_Image_From_DOJ_Showing_He_Kept
                  Classified_Docs_in_Unsecured_Places⠀⇛


                # ⚓ Internet Freedom Foundation ☛ Digital_Transparency:_A_Right
                  to_Information_Report_for_August_2022⠀⇛


                       For the month of August 2022, IFF has filed 45
                       Right to Information (“RTI”) applications, 3 first
                       appeals and appeared in 1 second appeal before the
                       Central Information Commission.


          o § Environment⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_My_Country_Is_Drowning._Here’s
                  What_You_Can_Do_Right_Now_for_Pakistan⠀⇛


                       A third of my country is under water right
                       now—bridges, roads, schools, and other critical
                       infrastructure sinks, and people run to evacuate
                       their homes. At least 33 million people are
                       displaced—that’s 1 in every 7 Pakistani. These are
                       33 million dreams broken, 33 million hopes
                       shattered, and 33 million futures destroyed as a
                       result of the havoc wreaked upon their lands by no
                       fault of their own.


                # ⚓ TruthOut ☛ GOP_Opposed_Infrastructure_Upgrades;_Now_This
                  Mississippi_City_Has_No_Safe_Water⠀⇛


                # ⚓ Democracy Now ☛ Cooperation_Jackson’s_Kali_Akuno:_Climate
                  Crisis_Impact_Worse_in_Black_Cities_Facing_Disinvestment⠀⇛


                       We speak with an evacuated resident of Jackson,
                       Mississippi, where over 180,000 residents are on
                       their third day without access to running water. We
                       speak with longtime Jackson activist Kali Akuno,
                       co-founder of Cooperation Jackson, who joins us
                       from New Orleans, where he went when floods
                       recently inundated the majority-Black city and shut
                       down the main water plant. He attributes the water
                       crisis to decades of white flight and the
                       subsequent disinvestment in majority-Black and
                       Brown cities. “What we are experiencing now is
                       literally just the crumbling of the empire’s
                       infrastructure,” notes Akuno, who also says he
                       fears the state government will push to privatize
                       or regionalize Jackson’s water system instead of
                       giving the city adequate resources to stabilize it.


                # ⚓ Pro Publica ☛ Storm_Drain_Dangers_Are_Starting_to_Be
                  Addressed⠀⇛


                # ⚓ TruthOut ☛ The_Climate_Crisis’s_Impact_Is_Worse_in_Black
                  Cities_Facing_Disinvestment⠀⇛


                # § Energy⠀➾


                      # ⚓ Vice ☛ The_USPS_Underestimated_the_Benefit_of_Going
                        Electric,_Study_Shows⠀⇛


                             The United States Postal Service dramatically
                             underestimated the benefits of an electric
                             delivery fleet in its environmental review
                             when it agreed to purchase nearly all gas-
                             powered trucks, a peer-reviewed study by
                             University of Michigan researchers found. The
                             lead author of the study, Maxwell Moody,
                             called the USPS’s environmental review
                             “significantly flawed” in a press release,
                             adding yet another layer of criticism to the
                             USPS’s handling of its new delivery fleet
                             procurement.


                      # ⚓ uni Cambridge ☛ Spain_To_Make_Some_Rail_Passengers
                        Free_Of_Charge_From_September⠀⇛


                             The Spanish Ministry of Transport noted that
                             “This measure encourages to the maximum the
                             use of this type of collective public
                             transport to guarantee the needed daily
                             commute with a safe, reliable, comfortable,
                             economic and sustainable means of
                             transportation, amid the extraordinary
                             circumstances of the steady increase of
                             energy and fuel prices.”


                      # ⚓ The London Economic ☛ Near-free_rail_travel_in
                        Germany_saved_1.8_million_tons_of_CO2⠀⇛


                             The 9-euro ($9) monthly ticket, which allows
                             nationwide travel on regional trains,
                             subways, trams and buses, prevented 1.8
                             million tons of CO2 because commuters didn’t
                             use their cars as much, according to the VDV
                             public-transport lobby.


                      # ⚓ RTL ☛ Californians_told_not_to_charge_EVs_as_grid
                        struggles_in_heat_wave⠀⇛


                             Californians were told Wednesday not to
                             charge their electric vehicles during peak
                             hours, just days after the state said it
                             would stop selling gas-powered cars, as the
                             aging electricity grid struggles with a
                             fearsome heatwave.


                             Temperatures as high as 112 degrees
                             Fahrenheit (44 degrees Celsius) were forecast
                             in some Los Angeles suburbs as a huge heat
                             dome bakes a swathe of the western United
                             States.


                      # ⚓ Common Dreams ☛ Heatwave_‘Supercharged’_by_Climate
                        Crisis_Poised_to_Intensify_Fires_in_US_West⠀⇛


                             Extreme heat—”supercharged” by the fossil
                             fuel-driven climate crisis, as environmental
                             scientist Jonathan Overpeck put it—has been
                             building this week and is only projected to
                             get worse in the coming days.


                      # ⚓ Common Dreams ☛ ‘Simply_Immoral’:_Leaked_Doc_Shows_UK
                        Energy_Giants_to_Make_£170_Billion_in_Excess_Profits⠀⇛


                             “Ministers must tax these profits and
                             urgently cancel the energy bill increase.”


                      # ⚓ Common Dreams ☛ Climate_Groups_Gear_Up_for_Massive
                        Mobilization_Against_Manchin’s_Dirty_Deal⠀⇛


                             The Stop MVP coalition and People vs. Fossil
                             Fuels coalition said they plan to convene in
                             the nation’s capital to speak out against
                             Manchin’s deal and the Mountain Valley
                             Pipeline (MVP) project, a fracked gas
                             pipeline that would transport shale gas 300
                             miles from West Virginia to Virginia.


                      # ⚓ Telex (Hungary) ☛ Hungary_signs_new_agreement_with
                        Gazprom_to_buy_more_gas_from_Russia⠀⇛


                # § Wildlife/Nature⠀➾


                      # ⚓ Counter Punch ☛ The_Forest_Nearest_Me⠀⇛


                             Consider that the snow on the needles of the
                             hemlocks in the last cold storms is lit by
                             that peculiar angular light that only occurs
                             in these latitudes in spring and fall (light
                             never seen in summer, when the high sun
                             oppresses and flattens).  The sight of snow
                             on the needles is a miraculous enveloping
                             almost spiritual thing, such that you can
                             stare at it for a time and forget who you are
                             and enter if only fleetingly a kind of
                             consciousness of light on ice and snow on the
                             evergreen branches.


          o § Finance⠀➾


                # ⚓ India Times ☛ Internet_shutdowns_hit_cash-strapped_Lebanon
                  due_to_strike⠀⇛


                       Internet shutdowns rippled through cash-strapped
                       Lebanon on Tuesday after employees of the country’s
                       state-owned telecom company went on strike,
                       demanding higher wages. It was the latest
                       reflection of one of the world’s worst economic
                       disasters, which has pulled three quarters of
                       Lebanon’s 6 million people into poverty.


                # ⚓ Common Dreams ☛ Behind_Starbucks_Union-Busting_Stands_CEO
                  Who_Got_$940,000,000_Richer_During_Pandemic⠀⇛


                       Compiled by the progressive group Americans for Tax
                       Fairness (ATF), Billion-Dollar Union Busters: How
                       Starbucks and Its Rich CEO Are Stifling Worker
                       Organizing was published as the nationwide
                       unionization drive at the coffee chain continues to
                       grow in the face of increasingly brazen opposition
                       from management, with more than 200 locations
                       voting to join Workers United since December 2021.


                # ⚓ TruthOut ☛ CEO_Who_Got_$940_Million_Richer_in_Pandemic_Is
                  Behind_Starbucks_Union-Busting⠀⇛


                # ⚓ Common Dreams ☛ Pandemic,_Profit-Driven_Healthcare_System
                  Blamed_for_Historic_Decline_in_US_Life_Expectancy⠀⇛


                       “Has our failure to provide universal healthcare
                       access contributed to many unnecessary deaths? Yes…
                       Is it finally time to build an effective public
                       health system? Yes.”


                # ⚓ Common Dreams ☛ In_UK_Speech,_Sanders_Says_‘Stand_Together
                  and_Tell_the_Oligarchs_They_Cannot_Have_It_All’⠀⇛


                       “Our job right now, internationally, is to stand
                       together.”


                # ⚓ Common Dreams ☛ Green_Group_Blasts_Biden_for_Backing_Big
                  Oil’s_California_Offshore_Fracking_Push⠀⇛


                       “It’s incredibly disappointing to see the Biden
                       administration doing the oil industry’s bidding.”


                # ⚓ How_Visibility_Can_Ease_the_Pain_of_Long_Chassis_Return
                  Times_|_SupplyChainBrain⠀⇛


                       After a year of steady increases in freight prices,
                       the U.S. trucking industry is experiencing a
                       cooldown in demand, with linehaul rates declining
                       significantly from their highs at the start of
                       2022. Trucking capacity has loosened considerably,
                       thanks to new space entering the system, and a
                       plateauing of consumer demand across major
                       geographic markets.


                       The rise in trucking capacity also has to do with
                       an improvement in efficiency across different nodes
                       in the end-to-end supply chain, be it at ports,
                       intermodal yards or warehouses. Transportation
                       networks work in partnership, meaning that any
                       tangible improvement in efficiency within one
                       logistics segment has ripple effects on the
                       efficiency of other segments.


                # ⚓ CoryDoctorow ☛ Tory_Britain_is_crashing_and_burning⠀⇛


                       After 43 years of Tory policies (including the 12
                       years of Tory-lite Blairism), Margaret Thatcher has
                       been vindicated – there truly no longer is “any
                       such thing as a society.” As Thatcher predicted,
                       “there are individual [ultra-rich] men and women,
                       and their families [whom they pass vast
                       inheritances on to].”


                       [...]


                       What has Brexit delivered? Well, it led to
                       deregulation of the water system (which Tories had
                       largely privatised), permitting water companies to
                       flush raw sewage into Britain’s rivers and coastal
                       waters, rendering them unsafe to swim in. To be
                       fair, even if they wanted to treat the sewage,
                       they’d couldn’t, because Brexit stopped water-
                       treatment at the border.


                       There’s runaway energy prices everywhere, but
                       Britain’s version is extra-special, with contracts
                       coming in at 400-1000% higher than last year,
                       triggering a wave of small business closures. Care
                       homes are warning that they might have to turn off
                       the heat this winter.


                       But even if they manage to keep paying their bills,
                       it might not help, because energy experts are
                       forecasting unscheduled, UK-wide rolling blackouts
                       this winter. The Tories’ backup plan is to import
                       energy from France, Belgium and the Netherlands,
                       these being three countries that are slowing or
                       halting energy exports.


                       SNP leader Nicola Sturgeon has proposed re-
                       nationalising the energy companies (36% of Scots
                       households are headed to fuel poverty by October).
                       The Tories have categorically rejected this, which
                       is great news for anyone hoping to convince
                       Scotland to leave the UK.


                       Tory rule – starting with Thatcher’s airdrop of the
                       nation’s stock of public housing – destroyed the
                       nation’s capacity to supply housing to working
                       people, and what affordable housing remained was
                       turned into deathtraps after it was sheathed in
                       highly flammable cladding.


                       Conservative ideology has produced a country that
                       can’t provide shelter, or food, or water, or
                       energy. But what about health-care? The NHS is OK,
                       right?


                       Yikes. England’s NHS – a patchwork of underfunded
                       public providers and hollowed out, private
                       providers – has suffered from worsening annual
                       winter crises for years. This year’s winter crisis
                       arrived early – in the summer, with overflowing
                       A&Es and hospitals out of beds.


                # ⚓ Positech Games ☛ You_are_unimportant._This_is_ok._–
                  Cliffski’s_Blog⠀⇛


                       How psychopathic narcissist CEOs teamed up with
                       money obsessed statisticians to trick gamers into
                       thinking they are heroes


                       [...]


                       Twitter is currently in a furious legal dispute
                       with Elon Musk over whether or not twitter lies
                       about how many of its accounts are bots, and
                       therefore likely fake. Some bots are to be
                       expected… but more than 5%? Some say its vastly
                       higher, and when you think about it, twitter has a
                       huge vested interest in artificially inflating
                       follower counts. Why on earth would you bother
                       tweeting when you know you have 0 or 2 followers?
                       Give a man 1,000 followers and they will feel
                       special. Give them 10,000 followers and they will
                       feel amazing.


                       Last time I looked I had about 10k followers, but
                       I’m determined not to care. If they swept out fakes
                       and it turns out I have 100 followers I’d just find
                       it funny. I’m just a middle aged dude who makes
                       computer games and plays guitar as a hobby. How do
                       I have *any* followers? I’m not a famous
                       philosopher or the prime minister. Why should
                       anybody care about my life unless they actually
                       know me? Do you REALLY want to know what meal I ate
                       yesterday? or what I think of some new TV show?
                       Why?


                       [...]


                       Game CEOs: Please get some fucking therapy. Not
                       everyone wants to be you, not everyone is you, not
                       everyone wants a thousand spotlights on them, not
                       everyone daydreams about being on the cover of
                       Newsweek. Blame that private school education that
                       gave you an overinflated ego, and an inability to
                       understand other people.


                       Yes. This is a rant, as all my blog posts turned
                       into, but its a rant from the heart from a gamer
                       who just despairs at how the industry he is a tiny
                       tony (and happy to be so) part of has been ruined
                       so dramatically.


                # ⚓ Common Dreams ☛ GOP_Attacks_on_Social_Security_Makes
                  Popular_Program_Key_Midterm_Issue⠀⇛


                       “This November 8, our earned benefits are on the
                       line.”


                # ⚓ Common Dreams ☛ Opinion_|_A_Hot_Topic_for_Labor_Day:
                  Extreme_Heat_Kills_Workers⠀⇛


                       Here’s a hot topic for Labor Day: heat.


                # ⚓ Scheerpost ☛ Craig_Murray:_Marx_Was_Right⠀⇛


                # ⚓ Counter Punch ☛ Behind_the_‘Economic_Policy’_Façade,_It’s
                  Class_War⠀⇛


                       “Quantitative easing” (QE) intoned Treasury
                       Secretary Janet Yellen, repeating what Fed Chair
                       Jerome Powell had said while offering a policy
                       solution to recession. The technical-sounding
                       phrase simply referred to the Federal Reserve’s
                       particular economic policy to slow or stop the
                       sharp economic downturn that had started in 2020
                       and was worsened by the COVID-19 pandemic. That Fed
                       policy created a vast new amount of money and
                       provided it, via loans and security purchases to
                       big banks and other large financial institutions.
                       To be clear here, the Fed made vast new monetary
                       resources available to some of the largest and
                       richest financial employers. The stated goal was to
                       stimulate “the economy.” The Fed hoped that the
                       financial employers it enriched would find it
                       profitable to use this money to lend more to non-
                       financial employers who would then hire unemployed
                       workers. Note that QE favors the employer class. It
                       works first and foremost to enrich the top 1
                       percent and then “hopes” the latter’s gains trickle
                       down to the other 99 percent. Note further that the
                       fresh new money is not provided to the mass of
                       workers with the hope that they spend it thereby
                       generating sales and profits for employers. Such a
                       “trickle-up” approach to “stimulate the economy”
                       would favor workers. That is why it is rare and
                       almost never the primary focus of “expansionary
                       monetary policy.”


                # ⚓ Counter Punch ☛ Why_Talk_about_Loans?⠀⇛


                       The 1960s and early 1970s seemed to promise greater
                       progress.  But then the Empire struck back.


                # ⚓ Scheerpost ☛ The_Federal_Reserve_Is_Wrong:_Corporations
                  Should_Pay_To_Stop_Inflation,_Not_Workers⠀⇛


                       The Federal Reserve says wages should go down to
                       get inflation under control. What if we just
                       stopped corporate profiteering and the lax rules
                       that make it possible?


                # ⚓ The Nation ☛ Democrats_Need_to_Start_Talking_About_Class⠀⇛


                       After a year and a half of doomsaying about
                       Democratic prospects for the 2022 midterms, a
                       certain anticipatory hush has come over the
                       sanctums of the center left. The Biden White House
                       has reeled off an impressive and mostly unexpected
                       run of major policy wins—from the passage of the
                       landmark climate change package in the Inflation
                       Reduction Act to a substantive and far-reaching
                       student-debt-relief program. Unemployment is low,
                       inflation is subsiding, and Biden’s approval rating
                       is ticking steadily upward. The fallout from the
                       Supreme Court’s disastrous Dobbs ruling also seems
                       likely to elevate Democratic turnout, particularly
                       among the coveted swing constituency of white
                       suburban women. Meanwhile, Trumpian conspiracy-
                       mongering over bogus election fraud—together with
                       Trump’s latest venal forays into sedition—already
                       appears to be dampening GOP primary turnout and
                       right-wing confidence alike.


                # ⚓ Common Dreams ☛ Opinion_|_Young_Voters_in_America_Are_Our
                  Best_Hope_for_Saving_the_Planet⠀⇛


                       For America’s young voters, famished for positive
                       action on climate change, the Inflation Reduction
                       Act of 2022 is cause for celebration. The passage
                       of this landmark legislation is a signal to young
                       climate activists across the countrythat
                       unprecedented progressive change is possible.


                # ⚓ Counter Punch ☛ Bailing_Out_Corporate_Higher_Education:
                  What_is_Really_Wrong_with_the_Biden_Student_Debt_Relief
                  Plan⠀⇛


                       For many students and parents, paying off student
                       debt is a life-time experience, forcing them into
                       long term debt that precludes them from  being able
                       to buy a home, start a family, or take public
                       service jobs that may not pay a lot but which may
                       be personally satisfying or socially useful. 
                       College education may be critical to the American
                       dream for many, but pursuing it may also be a
                       nightmare.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Counter Punch ☛ How_Mikhail_Gorbachev_Became_the_Most
                  Reviled_Man_in_Russia⠀⇛


                       As with nearly all of the Soviet Union’s
                       leadership, Gorbachev had provincial origins, in
                       his case born in 1931 in Stavropol Krai just
                       southeast of Ukraine. His maternal grandparents
                       were ethnic Ukrainian. He rose through the party
                       ranks with a reputation for hard work and finding
                       solutions to vexing challenges. By 1979 he was in
                       the USSR’s highest governing body, the Politburo,
                       and by 1985, selected to the country’s highest post
                       as General Secretary to lead the Soviet Union out
                       of its economic stagnation.


                # ⚓ Counter Punch ☛ Florida_Gubernatorial_Election:_Swamp
                  Monster_Cage_Match⠀⇛


                       Fried, a former lobbyist, spent her entire term as
                       the state’s only statewide elected official
                       (agriculture commissioner) issuing “oh no you
                       didn’t” press releases every time DeSantis so much
                       as yawned, and pulling stupid tricks like adding
                       her photo to the inspection stickers on every
                       Florida gas pump as publicly funded campaign ads
                       (the legislature nixed that one in short order).


                # ⚓ Telex (Hungary) ☛ Far_right_party_Mi_Hazánk_unveils_bust_of
                  controversial_Miklós_Horthy_in_Parliament_Office⠀⇛


                # ⚓ Counter Punch ☛ Make_Congress_Accountable⠀⇛


                       Our 1972 Congress Project provides a context for
                       measuring the decline of Congress, both in its near
                       abandonment of its constitutional powers vis-à-vis
                       the executive branch and its collective
                       subservience to the many forces of corporatism over
                       the people’s necessities.


                # ⚓ Counter Punch ☛ The_Most_Important_Election_in_the_Americas
                  is_in_Brazil⠀⇛


                       The book release took place during Lula’s campaign
                       for president against the current
                       incumbent—and deeply unpopular—President Jair
                       Bolsonaro. Lula is now in the lead in the polls
                       ahead of the first round of Brazil’s presidential
                       election to be held on October 2.


                # ⚓ Counter Punch ☛ Let’s_Revive_FDR’s_Four_Freedoms_and_the
                  Atlantic_Charter⠀⇛


                       As it happens, “appeasement” is the only road
                       humanity can take in the nuclear age.  It is the
                       road that our ancestors mapped in the UN Charter,
                       when “we the people” demanded measures to spare
                       succeeding generations from the scourge of war. Our
                       leaders, however, are simultaneously provoking two
                       nuclear powers with vast stockpiles of nuclear
                       weapons and means to deliver them.  This is highly
                       undemocratic, because people do not want war and do
                       not consent to needless provocation.  People want
                       and are entitled to peace and prosperity. It is the
                       corporate “elites”, the military-industrial-
                       financial complex who want war. Indeed, there are
                       too many war profiteers around us.


                # ⚓ Counter Punch ☛ FPOTUS_and_Rare_Liberals_Stoking_the
                  Schedule_F_Burn_Pit⠀⇛


                       Within a couple days the long New York Times
                       Magazine feature piece on the Jones Day law firm
                       identified Jones Day partner and former Detroit
                       Emergency Manager Fascist (EMF) Kevyn Orr as “a
                       rare liberal” in their rightwing dog pen.


                # ⚓ Counter Punch ☛ A_Firm_Grasp_of_the_Obvious⠀⇛


                       It would be one thing if we could simply say “well,
                       it’s a dry year in the West” — but that’s a great
                       simplification given lie by the equally dire
                       conditions afflicting major rivers across the
                       globe. The great Yangtze River in China, the third
                       longest river in the world at 3,975 miles, is
                       drying up. The Yangtze provides water to an
                       estimated 400 million Chinese (more than the entire
                       population of the U.S.) but is so low it’s
                       “affecting hydropower, shipping routes, limiting
                       drinking water supplies, and even revealing
                       previously submerged Buddhist statues.” The reason?
                       Higher than normal temperatures and “record-
                       breaking drought.”


                # § Misinformation/Disinformation⠀➾


                      # ⚓ New York Times ☛ Elon_Musk_Cites_Whistle-Blower
                        Report_as_Reason_to_Scrap_Twitter_Deal⠀⇛


                             The requests, revealed in regulatory and
                             legal filings on Tuesday, are an effort by
                             the billionaire to incorporate Mr. Zatko’s
                             allegations in the coming trial that will
                             determine whether Mr. Musk must complete the
                             purchase. On Tuesday, Mr. Musk asked a judge
                             to delay the trial for one month while his
                             lawyers investigate the whistle-blower
                             claims.


                             Mr. Zatko has accused Twitter of years of
                             “material misrepresentation and omissions”
                             about security and privacy protections built
                             into its platform. Twitter executives have
                             strongly rejected Mr. Zatko’s claims.


                      # ⚓ Common Dreams ☛ Far-Right_Floods_Chile_With
                        Misinformation_Ahead_of_Vote_on_New_Constitution⠀⇛


                             Even though Chileans voted by a 4-to-1 margin
                             during a historic October 2020 plebiscite to
                             create a new constitution to replace the
                             neoliberal charter imposed by Gen. Augusto
                             Pinochet’s military dictatorship, the
                             resulting document is at risk of being
                             rejected in Sunday’s referendum, polls have
                             consistently shown.


                      # ⚓ Scheerpost ☛ Factchecking_the_Factchecker_on_Chomsky,
                        Russia_and_Media_Access⠀⇛


                             Millions of people in the Soviet Union,
                             including virtually all intellectuals, had
                             access to and tuned into Western media in the
                             1970s.


                      # ⚓ Scheerpost ☛ We’re_Being_Trained_to_Worry_About
                        ‘Russian_Propaganda’_While_Drowning_in_US_Propaganda⠀⇛


                             The entire western world is being trained to
                             freak out about “Russian propaganda” — which
                             barely exists in the west — while ignoring
                             the fact that we are spending every day
                             marinating in billions of dollars worth of US
                             empire propaganda.


                      # ⚓ The Nation ☛ How_Emmett_Till’s_Death_Led_to_the
                        Invention_of_the_“Liberal_Media”⠀⇛


                             It was on an early morning in late August 67
                             years ago that Roy Bryant and his half-
                             brother J.W. Milan abducted Emmett Till from
                             his great uncle Mose Wright’s home in Money,
                             Miss. Till, who was visiting from Chicago,
                             had reportedly whistled at and flirted with
                             Bryant’s wife, Carolyn, at the couple’s
                             grocery store.


          o § Censorship/Free Speech⠀➾


                # ⚓ TruthOut ☛ Virginia_Judge_Throws_Out_Republican_Attempt_to
                  Ban_Book_About_LGBTQ_People⠀⇛


                # ⚓ Index On Censorship ☛ Saudi_woman’s_“death_sentence”_for
                  using_her_voice⠀⇛


                       On the 15th of every month (she was initially
                       arrested on 15 January 2021), we will tell her
                       story. Shining a light on her plight. And in the
                       coming months we will work with partners both in
                       the UK and across the world to make sure her case
                       doesn’t get forgotten as just another case of human
                       rights abuse by Saudi Arabia.


                # ⚓ Norbert Preining ☛ [Repeat]_Debian_complaining_to_KDE_…⠀⇛


                       So now some Debian boohoos are complaining about my
                       blog which is aggregated at Planet KDE, directly to
                       KDE, how nice. They were bothered by the following
                       statement:


                       Usual disclaimer: (1) Considering that I don’t have
                       a user-facing Debian computer anymore, all these
                       packages are only tested by third parties and not
                       by myself. Be aware! (2) Funny to read the Debian
                       Social Contract, Point 4. Our priorities are our
                       users and free software, obviously I care a lot
                       about my users, more than some other Debian
                       members.


                # ⚓ NPR ☛ A_Saudi_woman_gets_a_45-year_prison_sentence_for
                  social_media_use_that_remains_unclear⠀⇛


                       A Saudi court has sentenced a woman to 45 years in
                       prison for allegedly damaging the country through
                       her social media activity, according to a court
                       document obtained Wednesday. It was the second such
                       sentence that has drawn scrutiny of the kingdom
                       this month.


                       Little is known about Nourah bint Saeed al-Qahtani,
                       who hails from one of the biggest tribes in Saudi
                       Arabia and has no apparent history of activism. An
                       official charge sheet seen by The Associated Press
                       and human rights groups describes her case as
                       involving her social media use, though Saudi
                       officials did not respond to requests for comment.


                # ⚓ Middle East Eye ☛ Saudi_woman_sentenced_to_45_years_in
                  prison_over_social_media_posts⠀⇛


                       A Saudi court has sentenced a woman to 45 years in
                       prison for using social media to express her
                       opinions, a rights group said on Tuesday.


                # ⚓ The Times Of Israel ☛ 2nd_Saudi_woman_jailed_for_decades
                  for_social_media_posts_—_rights_group⠀⇛


                       Nourah al-Qahtani received the heavy sentence on
                       appeal after she was convicted of “using the
                       internet to tear the [country’s] social fabric” and
                       “violating public order” via social media,
                       Democracy for the Arab World Now (DAWN) said.


                       She was convicted under the kingdom’s Counter-
                       Terrorism and Anti-Cyber Crime Law, DAWN added.


                # ⚓ TheNewArab ☛ Saudi_Arabia:_Woman_receives_45_years_prison
                  sentence_over_social_media_use⠀⇛


                       An official charge sheet seen by The Associated
                       Press and human rights groups describes her case as
                       involving her social media use, though Saudi
                       officials did not respond to requests for comment.


                # ⚓ Irish Examiner ☛ Saudi_woman_gets_45_years_in_prison_for
                  social_media_use⠀⇛


                       It remains unclear what al-Qahtani posted online or
                       where her hearing was held. She was taken into
                       custody on July 4 2021, according to the
                       Washington-based human rights watchdog Democracy
                       for the Arab World Now, which is critical of the
                       kingdom.


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


                # ⚓ VOA News ☛ In_covering_violence_in_Tijuana,_Mexico,_the
                  city’s_journalists_give_voice_to_a_community_demanding
                  change.⠀⇛


                       Outside of war zones, Mexico ranks as the most
                       dangerous place for journalists, with at least 60
                       slain in connection with their work since 1992, the
                       year the Committee to Protect Journalists, or CPJ,
                       started to track those killed.


                       Covering organized crime presents the greatest
                       risk, according to CPJ data. And official efforts
                       to ensure media safety fall short, reporters say.


                       As one of the first female journalists assigned to
                       cover Tijuana’s violence, García has witnessed some
                       of the worst brutality that humanity can offer. But
                       she has also seen how shining a light on the city’s
                       problems can effect positive change.


                # ⚓ Scheerpost ☛ Patrick_Lawrence:_When_Correspondents_Came
                  Home,_Part_2⠀⇛


                       September 11 was a paradigm shifting moment in
                       American journalism.


          o § Civil Rights/Policing⠀➾


                # ⚓ AccessNow ☛ U.S._must_stand_up_to_human_rights_abuses_in
                  MENA⠀⇛


                       U.S. President Joe Biden has ignored activists and
                       civil society groups’ call to address the extreme
                       human rights abuses perpetrated by leaders from the
                       Middle East and North Africa during a recent visit
                       to the region. Access Now stands in solidarity with
                       civil society organizations demanding an end to the
                       unconditional support by the U.S. and other
                       governments given to oppressive regimes in MENA.


                       “The MENA region doesn’t need a savior, it needs
                       consistency and respect,” said Marwa Fatafta, MENA
                       Policy and Advocacy Manager at Access Now. “We
                       cannot continue to hear companies and world leaders
                       publicly condemn human rights abuses, then keep
                       silent when an oil deal is on the table. U.S.
                       President Joe Biden had the opportunity to look
                       Saudi Crown Prince Mohammed bin Salman in the face
                       and demand accountability. He chose not to.”


                       Since Biden’s visit, Saudi Arabia has continued its
                       civil society persecution, handing a 34-year prison
                       sentence to Salma al-Shehab, a UK-based PhD student
                       and human rights defender, for simply re-tweeting
                       and following dissidents and activists on her
                       personal Twitter account. Salma’s online activities
                       led to what is considered the “longest prison
                       sentence ever for a peaceful activist.” This ruling
                       sends a chilling message from Crown Prince Mohammed
                       bin Salman (MBS) on how peaceful activism will
                       continue to be dealt with in the Kingdom.


                # ⚓ Meduza ☛ Navalny_associates_announce_plans_to_release
                  ‘Smart_Vote’_recommendations_for_September_elections_—
                  Meduza⠀⇛


                       Russian opposition politician Alexey Navalny’s team
                       of anti-corruption activists announced the launch
                       of its “Smart Vote” initiative for this year’s
                       Moscow municipal elections, which will take place
                       from September 9–11. The team announced on Twitter
                       that the recommendations will focus on municipal
                       elections in Moscow.


                # ⚓ George ☛ Why_Remote_Works⠀⇛


                       After working remotely for 4 companies over 5
                       years, interviews with hundreds of others, managing
                       fully remote teams, interviewing hundreds of
                       employees for remote roles, chatting with thousands
                       of remote workers, and voyeuring the activities of
                       many amazing remote teams, I concluded that, to my
                       surprise, I need to write a different take about
                       why, when and how remote work is worth it.


                # ⚓ DNA India ☛ In_another_barbaric_move,_Taliban_restricts
                  female_students_from_leaving_Kabul_for_studies⠀⇛


                       Around 80 percent of women working in the media
                       have lost their jobs, it said adding that almost 18
                       million women in the country are struggling for
                       health, education, and social rights.


                # ⚓ Scheerpost ☛ Corporate_Media_Has_Failed_to_Report_on_the
                  Threats_to_Women’s_Reproductive_Rights⠀⇛


                       In the weeks since the Supreme Court overturned Roe
                       v. Wade, the corporate media has been saturated
                       with analyses and reports about the implications of
                       the ruling for women’s lives and health. Legal
                       observers have weighed in on the conservative
                       majority’s reasoning in the case. The impact of the
                       ruling on the 2022 midterm elections has been
                       discussed endlessly.


                # ⚓ TruthOut ☛ “Roe”_Overturn_Has_Driven_Spike_in_Young_People
                  “Very”_Motivated_to_Vote⠀⇛


                # ⚓ Common Dreams ☛ Fetterman_Vows_to_Fight_for_Reproductive
                  Rights_After_Oz_Calls_Abortion_‘Murder’⠀⇛


                       “Oz would be a rubber stamp to criminalize abortion
                       and send doctors, nurses, and patients to jail.” 


                # ⚓ Common Dreams ☛ Opinion_|_This_US_City_Is_Creating_a_Model
                  for_Fighting_Mass_Incarceration⠀⇛


                       In the late spring and summer of 2020, protests for
                       racial justice erupted in response to the police
                       murder of George Floyd. Mobilizations spread
                       throughout the country and continued for months,
                       producing what scholars identified as arguably the
                       largest wave of mass protest in U.S. history.


                # ⚓ Common Dreams ☛ Opinion_|_Calling_the_GOP_Semi-Fascist_Is
                  Half_Right⠀⇛


                       In an August 25 speech in Rockville, Md., aimed at
                       drumming up support for Democrats ahead of the
                       midterms, President Biden tarred Donald Trump and
                       the MAGA movement with the dreaded “F” word. 


                # ⚓ Counter Punch ☛ The_Blank_Check_Protection_Program:_a
                  Religious_Experience⠀⇛


                       The amounts are shocking, but perhaps the most
                       astounding numbers are the five separate donations
                       from the Archdiosese of Kansas City, Kansas. The
                       amounts are as follows: $1,250,000, $850,000,
                       $380,000, $350,000, and yet another $350,000. In
                       excess of 3 million dollars spent, not on charity,
                       not on helping infants be fed, not on paying for
                       obstetrical care. No, this was over 3 million spent
                       trying to get Kansans to allow a path for the
                       Republican legislature to deny reproductive
                       freedoms. When I saw this colossal amount of cash,
                       I had to marvel at the donations that individuals
                       must have extended to the church. And I wondered
                       how many must have left their estates to the church
                       to allow such a large amount of money to be used in
                       such a manner. This, by an institution that I
                       imagine is financially taxed not by the government,
                       but financially taxed by having to pay out an awful
                       lot of lawsuits for some downright horrifying
                       criminal behavior.


                # ⚓ Counter Punch ☛ Mother’s_Love_for_the_Motherland⠀⇛


                       Indeed, there have been many women who have invoked
                       versions of this sentiment, from Julia Ward
                       Howe to Jane Addams right down to a persecuted
                       union of Russian and Belarusian women leading a
                       dangerous, principled opposition to Putin’s
                       invasion right now.


                # ⚓ Counter Punch ☛ Who_Should_Forgive_Who?⠀⇛


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Techdirt ☛ Chattanooga’s_City-Owned_ISP_Pushes_25_Gbps
                  Broadband⠀⇛


                       Chattanooga, Tennessee is one of a growing number
                       of U.S. cities to build its own broadband network.
                       The ISP, tacked on to the city’s existing EPB
                       electricity utility, has routinely delivered speeds
                       faster and more affordable than the services
                       provided by regional utilities like Comcast.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Common Dreams ☛ Experts_Fear_Repeat_of_Covid_Failures
                        as_US_Hoards_80%_of_Monkeypox_Vaccines⠀⇛


                             “Once again, vaccines for an outbreak are not
                             available in the vast majority of countries.”


                      # ⚓ Techdirt ☛ The_Public_Paid_For_Moderna’s_mRNA_Vaccine
                        Tech;_The_Fact_That_Moderna_Is_Suing_Over_The_Patent_Is
                        A_Travesty⠀⇛


                             You may have heard last week that Moderna is
                             suing Pfizer, claiming that Pfizer’s COVID
                             vaccine violates Moderna’s patents. You can
                             read the legal complaint which is full of
                             bluster about how brilliant Moderna is and
                             how it saved the world and blah blah blah.
                             While it does mention that Moderna teamed up
                             with the National Institutes for Health, it
                             leaves out that it was the US taxpayer and US
                             government employees who were critical in
                             helping Moderna develop its mRNA technology.


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ HDFilme_&_xCine_Latest_to_Fall_in
                        Relentless_ACE_Anti-Piracy_Campaign⠀⇛


                             The Alliance for Creativity and Entertainment
                             has added the scalps of more pirate streaming
                             sites to its growing collection. Earlier
                             distress signals suggested that HDFilme and
                             xCine might be in trouble, but their domains
                             diverting to ACE leaves no doubt.
                             Importantly, both sites were operated from
                             Vietnam, an increasingly big player in global
                             piracy that has the MPA worried.


                      # ⚓ Torrent Freak ☛ Court_Orders_Telegram_to_Disclose
                        Personal_Details_of_Pirating_Users⠀⇛


                             The High Court in Delhi ordered Telegram to
                             share the personal details of copyright-
                             infringing users with rightsholders. The
                             messaging app refused to do so, citing
                             privacy concerns and freedom of speech, but
                             the court waved away these defenses, ordering
                             the company to comply with Indian law.


                      # ⚓ Torrent Freak ☛ Fake_‘YouTube’_DMCA_Notices_Exploit
                        Suspension_Fears_to_Install_Malware⠀⇛


                             To make their victims more compliant, online
                             scammers often imply that something of value
                             is under threat if immediate action isn’t
                             taken. Bank accounts are often mentioned but
                             nothing is off limits. A scam currently doing
                             the rounds warns of copyright strikes on
                             genuine YouTube accounts, but after targeting
                             a security researcher, the scam’s secrets are
                             now public.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Bookkeeping_in_the_megadungeon⠀⇛


          o § Technical⠀➾


                # § Internet/Gemini⠀➾


                      # ⚓ Browsers_and_life_choices⠀⇛


                             For the last few days, I’ve been trying out
                             three new web browsers — amfora (cli),
                             bombadillo (cli) and Min (gui) — and have
                             become very heartened at how simple and fast
                             they are.


                             No joke, when I alt-tab from anything to
                             Firefox these days, there’s a 1-2 second
                             delay before the application loads up. Until
                             last week I’d convinced myself I made the
                             right choice switching from Chrome to FF, but
                             I’m getting the sense that the Big 5 browsers
                             might all be kinda same-same but different.


                             Maybe it’s the same story with the Big 5
                             anything anywhere — social platforms, tech
                             companies, creative agencies, SMEs. When
                             you’re competing for widespread adoption,
                             there are certain sacrifices you have make in
                             order to maintain a competitive advantage.
                             And competitive business culture means you
                             make it. And those sacrifices just happen to
                             include speed, simplicity and performance…
                             and maybe sometimes privacy, freedom and
                             humanity too.


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



                    ䷩ 𝚕𝚒𝚗𝚎 6311

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_01/09/2022:_OBS_Studio_28.0_and_New_LFS⠀✐


Posted in News_Roundup at 4:17 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Applications
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o New_Releases
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Content_Management_Systems_(CMS)
          o Programming/Development
                # Python
    * Leftovers
          o Censorship/Free_Speech
    * Gemini*_and_Gopher
          o Personal
          o Politics
          o Technical
                # Science
                # Programming
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Tuxedo_Pulse_15_Gen_2_Unboxing_–_First_impressions!⠀⇛


                       Today’s article is special for us Linux users as we
                       will experience the unboxing of a laptop built with
                       Linux in mind: the Tuxedo Plus 15 Gen 2 from
                       TuxedoComputers.


                       Disclaimer: TuxedoComputers does not sponsor this
                       article, meaning that the article will express my
                       own experience with all credibility and
                       impartiality.


          o § Server⠀➾


                # ⚓ Istio_/_Announcing_Istio_1.15⠀⇛


                       This is the third Istio release of 2022. We would
                       like to thank the entire Istio community for
                       helping to get Istio 1.15.0 published. Special
                       thanks are due to the release managers Sam Naser
                       and Aryan Gupta from Google, Ziyang Xiao from Intel
                       and Daniel Hawton from Solo.io. As always, our
                       gratitude goes to Test & Release WG lead Eric Van
                       Norman (IBM) for his help and guidance.


                # ⚓ Istio_/_Istio_1.15_Upgrade_Notes⠀⇛


                       When you upgrade from Istio 1.14.x to Istio 1.15.0,
                       you need to consider the changes on this page.
                       These notes detail the changes which purposefully
                       break backwards compatibility with Istio 1.14.0.
                       The notes also mention changes which preserve
                       backwards compatibility while introducing new
                       behavior. Changes are only included if the new
                       behavior would be unexpected to a user of Istio
                       1.14.x. Users upgrading from 1.13.x to Istio 1.15.0
                       should also reference the 1.15.0 change logs.


                # ⚓ Istio_1.15.0_Change_Notes⠀⇛


                # ⚓ LWN ☛ The_container_orchestrator_landscape_[LWN.net]⠀⇛


                       Docker and other container engines can greatly
                       simplify many aspects of deploying a server-side
                       application, but numerous applications consist of
                       more than one container. Managing a group of
                       containers only gets harder as additional
                       applications and services are deployed; this has
                       led to the development of a class of tools called
                       container orchestrators. The best-known of these by
                       far is Kubernetes; the history of container
                       orchestration can be divided into what came before
                       it and what came after.


                       The convenience offered by containers comes with
                       some trade-offs; someone who adheres strictly to
                       Docker’s idea that each service should have its own
                       container will end up running a large number of
                       them. Even a simple web interface to a database
                       might require running separate containers for the
                       database server and the application; it might also
                       include a separate container for a web server to
                       handle serving static files, a proxy server to
                       terminate SSL/TLS connections, a key-value store to
                       serve as a cache, or even a second application
                       container to handle background jobs and scheduled
                       tasks.


                       An administrator who is responsible for several
                       such applications will quickly find themselves
                       wishing for a tool to make their job easier; this
                       is where container orchestrators step in. A
                       container orchestrator is a tool that can manage a
                       group of multiple containers as a single unit.
                       Instead of operating on a single server,
                       orchestrators allow combining multiple servers into
                       a cluster, and automatically distribute container
                       workloads among the cluster nodes.


                # ⚓ PR Web ☛ Linux_and_Open_Source_Veterans_Sign_On_to_Form_CIQ
                  Leadership_Team⠀⇛


                       Nine cloud and Linux veterans have signed on to
                       form the leadership team for CIQ, the company
                       building the next generation of software
                       infrastructure for enterprises running data-
                       intensive workloads atop the Rocky Linux enterprise
                       Linux distribution. This follows a successful
                       funding round in May and a teaming with Google
                       Cloud in July.


          o § Audiocasts/Shows⠀➾


                # ⚓ The BSD Now Podcast ☛ BSD_Now_470:_0mp_interview⠀⇛


                       In this special episode, we are interviewing
                       Mateusz Piotrowski about his various roles in the
                       FreeBSD project, his ports work, and a few other
                       interesting things he’s involved with. Enjoy this
                       interview episode, we’ll be back with a regular
                       episode next week.


                # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_969⠀⇛


                       Joel says the automation rocks.


                # ⚓ FLOSS_Weekly_696:_Tailscale_Gets_Hot_–_Avery_Pennarun,
                  Tailscale_NAT-Traversal_and_Zero_Config_VPN⠀⇛


                       Avery Pennarun was previously on FLOSS Weekly
                       discussing his startup Tailscale as it aims to make
                       creating secure network connections super easy.
                       Since Pennarun’s last appearance, Tailscale has
                       received $100 million in funding to push the
                       service into the mainstream further, all while
                       honoring open source values. Doc Searls and Aaron
                       Newcomb have a great conversation with Pennarun
                       about Tailscale’s journey.


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ The_growing_image-processor_unpleasantness_
                  [LWN.net]⠀⇛


                       There was a time when care had to be taken when
                       buying hardware if the goal was to run Linux on it.
                       The situation has improved considerably in recent
                       decades, and unsupported hardware is more the
                       exception than the rule. That has, for many years,
                       been especially true of Intel hardware; that
                       company has made a point of ensuring that its
                       offerings work with Linux. So it is a bit
                       surprising that the IPU6 image processor shipped
                       with Alder Lake CPUs lacks support in Linux, and is
                       unlikely to get it anytime soon. The problem
                       highlighted here goes beyond just Intel, though.


                       The IPU6, like most image processors, exists to
                       accept a data stream from a camera sensor and turn
                       it into a useful video stream. These processors can
                       take on a lot of tasks, including rotation,
                       cropping, zooming, color-space conversion, white-
                       balance correction, noise removal, focus
                       management, and more. They are complex devices; the
                       kernel community has responded by creating some
                       equally complex APIs, including Video4Linux2 (V4L2)
                       and media controller, to allow user space to manage
                       them. As long as a device comes with a suitable
                       driver, the kernel can make a camera device
                       available to user space which, with care, can work
                       with it without needing to know the details of the
                       hardware.


                       As Paul Menzel recently pointed out on the linux-
                       kernel mailing list, there is no such driver for
                       the IPU6, so a mainline Linux kernel cannot drive
                       it. As a result, the kernel lacks support for MIPI
                       cameras on some current laptops, including some
                       versions of the Thinkpad X1 Carbon and Dell XPS 13,
                       which are relatively popular with Linux users
                       (cameras using other interfaces, such as USB UVC,
                       are generally supported). To get around this
                       problem, Dell ships a closed-source, user-space
                       driver in the Ubuntu build it offers on the XPS 13.
                       Lenovo, instead, is not selling the affected
                       systems with Linux preloaded at all at this point.


                # ⚓ LWN ☛ LRU-list_manipulation_with_DAMON_[LWN.net]⠀⇛


                       The DAMON subsystem, which entered the kernel
                       during the 5.15 release cycle, uses various
                       heuristics to determine which pages of memory are
                       in active use. Since the beginning, the intent has
                       been to use this information to influence memory
                       management. The 6.0 kernel contains another step in
                       this direction, giving DAMON the ability to
                       actively reorder pages on the kernel’s least-
                       recently-used (LRU) lists.


                       The kernel’s memory-management developers would
                       like nothing better than the ability to know which
                       pages of memory will be needed in the near future;
                       the kernel could then make sure that those pages
                       were resident in RAM. Unfortunately, current
                       hardware is unable to provide that information, so
                       the memory-management code must make guesses
                       instead. Usually, the best guess is that pages that
                       have been used in the recent past are likely to be
                       used again soon, while those that have gone
                       untouched for some time are probably not needed.


          o § Applications⠀➾


                # ⚓ Make Use Of ☛ Is_VirtualBox_Safe_or_Is_It_a_Security
                  Risk?⠀⇛


                       What are the potential security risks of virtual
                       machines in Oracle VirtualBox? Is it actually safe
                       to use? And how can you protect your host system?


                       VirtualBox is a popular open-source virtualization
                       program used by individuals and enterprises. If you
                       have tried creating virtual machines on your
                       Windows or Linux system, you may have already used
                       it.


                       Considering it can be used for so many purposes,
                       and by a wide range of people, you need to ask
                       yourself: is it entirely safe for use? What are
                       some of the risks that you should be aware of? Let
                       us highlight a few details regarding the security
                       of VirtualBox.


                # ⚓ DebugPoint ☛ OBS_Studio_28.0_Released_with_HDR_Encoding,
                  Apple_Silicon_Builds⠀⇛


                       The latest instalment of OBS Studio 28.0 brings
                       native Apple Silicon support and many new features.


                       OBS Studio 28.0 marks the 10th anniversary of the
                       project, making it one of the successful open-
                       source media streaming software for Linux and other
                       systems. Although there are other players in the
                       same category, OBS Studio is the standard when it
                       comes to free and open-source streaming software.


                       The application is loaded with features and
                       supports screen recording, streaming over YouTube,
                       Twitch and other major platforms.


                # ⚓ Its FOSS ☛ OBS_Studio_28.0_is_a_Massive_Upgrade_With_Qt6,
                  HDR_Support;_Also_Works_on_Apple_Silicon⠀⇛


                       One of the most popular pieces of open-source
                       software, OBS Studio, gets a major upgrade.


                       It is one of the best screen recorders on Linux,
                       and for that matter, pretty much every other
                       desktop platforms too (Windows/macOS). This release
                       brings a boatload of new features, which build upon
                       the numerous previous features as well.


                       Let’s take a look at what’s new!


                # ⚓ 9to5Linux ☛ OBS_Studio_28.0_Released_with_10-Bit_Color
                  Support,_HDR_Video_Encoding,_and_Qt_6_Port⠀⇛


                       Highlights of OBS Studio 28.0 include 10-bit color
                       support, HDR video encoding, a new color format and
                       color space settings to let you tweak these options
                       in the advanced settings, as well as a port to the
                       latest Qt 6 application framework for a more modern
                       interface with a new default theme called “Yami”.


                       Other exciting changes include support for sending
                       chat messages to YouTube from within OBS, obs-
                       websocket 5.0 as a first-party plugin, native SRT/
                       RIST outputs, the ability to automatically split
                       recordings based on file size or duration, and a
                       new “Accessibility” section in settings to let you
                       change colors of certain UI elements. Linux users
                       also get a new “What’s New” dialog.


                # ⚓ Productivity_on_Linux:_Yakuake_|_KDE_|_Terminal_Emulator_|
                  Konsole⠀⇛


                       Whether you refer to it as a command line
                       interface, console, or terminal, the terminal is
                       one of the most important tools available on Linux.
                       To that extent, it is important to always have
                       rapid access to the terminal, and a little style
                       has never hurt anyone. Yakuake brings the console
                       to the forefront of your desktop with the press of
                       a key, allowing you to quickly perform your tasks
                       with ease.


                       Of course, one of the greatest advantages of Linux
                       and Open Source is the flexibility to build an
                       environment that best suits the end user. Some will
                       argue that tiling window managers provide quicker
                       access to the terminal, but to each their own. KDE
                       has been my desktop of choice since the 2.0 days,
                       so Yakuake fits the bill for a fast-access terminal
                       emulator – and it can for you, too.


                       Before we move on, how about trying to say
                       “yakuake” five-times fast?


                # ⚓ Its FOSS ☛ Micro:_Making_File_Editing_Easier_in_Linux
                  Terminal⠀⇛


                       While modern open source code editors have taken
                       the programming world by storm, Linux command line
                       is still ruled by a selected set of text editors.
                       Popular command line editors like Vim and Emacs are
                       also infamous for their weird keyboard shortcuts.


                       There are several jokes about those weird keyboard
                       shortcuts in the programming world. Exiting Vim is
                       perhaps the most common of them all. Here’s an
                       example.


                # ⚓ Linux Shell Tips ☛ MusicPlayerPlus_–_A_Terminal_Music
                  Player_for_Linux⠀⇛


                       Being considered a Linux user does not
                       automatically translate to a routine of coding and
                       constant file configuration efforts.
                       MusicPlayerPlus brings life to the Linux terminal
                       environment through its music support features.
                       This character-based console is an impressive music
                       player for your Linux terminal window.


                       [...]


                       Playback and visualization are derived from
                       MusicPlayerPlus inputs which are in turn derived
                       from the MPD streamed audio server outputs (the
                       Music Player Daemon (MPD) is responsible for audio
                       streaming).


                       As for the MPD and ALSA configurations, they are
                       managed and controlled by the MusicPlayerPlus
                       components.


                       The character-based terminal user is the primary
                       target of MusicPlayerPlus’s integrations and
                       extensions. This music player’s integrations and
                       extensions make visualization, music library
                       management, and audio streaming & playing under a
                       lightweight character-based environment much easier
                       to control.


                # ⚓ Help Net Security ☛ 5_open-source_vulnerability_assessment
                  tools_to_try_out_–_Help_Net_Security⠀⇛


                       A vulnerability assessment is a methodical
                       examination of network infrastructure, computer
                       systems, and software with the goal of identifying
                       and addressing known security flaws. Once the
                       vulnerabilities are pinpointed, they are classified
                       based on how critical it is to fix/mitigate them
                       sooner rather than later. Usually, the
                       vulnerability scanning tool also provides
                       instructions on how to remediate or mitigate the
                       discovered flaws.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Made Simple ☛ How_to_install_RPG_Maker_XP_on_a
                  Chromebook⠀⇛


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


                # ⚓ Enabling_ARM64_CPU_Capabilities_in_the_Linux_Kernel_|_Adam
                  Young’s_Web_Log⠀⇛


                       ARM64 design defines features long before there is
                       a CPU that can implement those features. Since the
                       ARM ecosystem is so varied, there are many
                       different CPU designs out there with different
                       capabilities. A general purpose linux Kernel build
                       put out by a major distribution has to work across
                       a wide array of chips by a large nuymber of
                       vendors. Thus, there is an enumeration of the
                       capabilities inside the Kernel and mechnism for
                       describing how to probe each of these capabilities.


                # ⚓ UNIX Cop ☛ How_to_install_MySQL_8_on_Ubuntu_22.04⠀⇛


                       In this post, you will learn how to install MySQL 8
                       on Ubuntu 22.04. This post is for newbies, but it
                       is always good to have it handy for everyone.


                # ⚓ Linux Shell Tips ☛ How_to_Install_SELinux_to_Harden_Nginx
                  Webserver⠀⇛


                       For Linux users that have exposed themselves to
                       RHEL-based distributions like RHEL, Fedora,
                       AlmaLinux, and Rocky Linux, SELinux is not a new
                       concept to them as it mostly comes pre-installed on
                       their systems.


                # ⚓ MakeTech Easier ☛ How_to_Use_a_Servo_Motor_With_the
                  Raspberry_Pi_–_Make_Tech_Easier⠀⇛


                       DC motors are great, but it’s hard to make them
                       control robotic hands and fingers. You just can’t
                       get the angle right. But with servo motors, you can
                       always be sure that they’ll stop at the right
                       angle, all the time.


                       So pick up your jumper wires, we’ll spin a servo
                       motor with the Raspberry Pi and make it stop at any
                       angle!


                # ⚓ How_to_install_PostgreSQL_14_and_configure_it_to_use_md5
                  connection_on_Fedora_36_–_NextGenTips⠀⇛


                       In this guide, we will walk through installing
                       PostgreSQL 14 and then configure I to use an md5
                       connection whenever you are login into Postgres.


                       PostgreSQL is a powerful, open-source object-
                       relational database system that uses and extends
                       the SQL language combined with many features that
                       safely store and scale the most complicated data
                       workloads. It was designed to handle a range of
                       workloads from single machines to data warehousing.


                       Every database must conform to ACID properties i.e
                       Atomicity, Consistency, Isolation, and Durability.
                       This is true for PostgreSQL as well, it must
                       conform to those features for transactions to pass
                       the tests.


    * § Distributions and Operating Systems⠀➾


          o § New Releases⠀➾


                # ⚓ 9to5Linux ☛ Nitrux_2.4_Released_with_Linux_Kernel_5.19,_KDE
                  Gear_22.08,_and_New_Maui_Apps⠀⇛


                       The monthly Nitrux releases are back, and Nitrux
                       2.4 is a major update to the Debian-based
                       distribution that ships with the XanMod-flavored
                       Linux 5.19 kernel to provide the best possible,
                       out-of-the-box hardware support for new
                       installations.


                       TSince Nitrux is a KDE-oriented distribution, you
                       can guess that the new release includes the latest
                       and greatest KDE software, starting with the KDE
                       Plasma 5.25.4 desktop environment and continuing
                       with the recently released KDE Gear 22.08 and KDE
                       Frameworks 5.97 software suites.


                # ⚓ LFS_and_BLFS_Version_11.2_are_released⠀⇛


                       The Linux From Scratch community is pleased to
                       announce the release of
                       LFS Version 11.2, LFS Version 11.2 (systemd), BLFS
                       Version 11.2, and
                       BLFS Version 11.2 (systemd).

                       This release is a major update to both LFS and
                       BLFS.

                       The LFS release includes updates to gcc-12.2.0,
                       glibc-2.36, and
                       binutils-2.39. The
                       Linux kernel has also been updated to version
                       5.19.2. Changes to text
                       have been made throughout the books.

                       The BLFS version includes approximately 1000
                       packages beyond the base
                       Linux From Scratch Version 11.2 book. This release
                       has over 1100 updates
                       from the previous BLFS version including package
                       updates and numerous text
                       and formatting
                       changes.

                       Thanks for this release goes to many contributors.
                       Notably:

                       Douglas Reno
                       Pierre Labastie
                       Xi Ruoyao
                       Thomas Trepl
                       Ken Moffat
                       Tim Tassonis


                       You can read the books online[0]-[3], or download
                       [4]-[7] to read locally.

                       Please direct any comments about this release to
                       the LFS development
                       team at lfs-dev@lists.linuxfromscratch.org or
                       blfs-dev@lists.linuxfromscratch.org. Registration
                       for the mailing lists
                       is required to avoid junk email.

                       -- Bruce Dubbs
                       LFS
          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Controlling_a_bionic_hand_with_tinyML_keyword
                  spotting_|_Arduino_Blog⠀⇛


                       Traditional methods of sending movement commands to
                       prosthetic devices often include electromyography
                       (reading electrical signals from muscles) or simple
                       Bluetooth modules. But in this project, Ex Machina
                       has developed an alternative strategy that enables
                       users to utilize voice commands and perform various
                       gestures accordingly.


                       The hand itself was made from five SG90 servo
                       motors, with each one moving an individual finger
                       of the larger 3D-printed hand assembly. They are
                       all controlled by a single Arduino Nano 33 BLE
                       Sense, which collects voice data, interprets the
                       gesture, and sends signals to both the servo motors
                       and an RGB LED for communicating the current
                       action.


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


          o § Content Management Systems (CMS)⠀➾


                # ⚓ People_of_WordPress:_Bud_Kraus_–_WordPress_News⠀⇛


                       This month, as we approach WordCamp US, we feature
                       Bud Kraus, a WordPress trainer who has made a
                       career in helping others learn about software. He
                       also shares how he has developed an approach to
                       using technology in order to overcome longstanding
                       difficulties with his eyesight.


                       [...]


                       Bud has taught web design since 1998, with students
                       from more than 80 countries online or in person. He
                       was determined not to let his sight difficulties
                       stop him from his wish to help others learn website
                       building and maintenance skills.


                       As WordPress evolves and new features release, Bud
                       decided to extend his training services around
                       helping new and existing users improve and practice
                       their skills. He supports others in open source
                       through volunteering to speak at WordPress events,
                       and encourages others to do so too. He also gives
                       time to help produce material for the free-to-
                       access resource Learn WordPress, which is part of
                       the WordPress.org project.


                       As a contributor to the Test and Training teams,
                       Bud is keen for others to try contributing to these
                       areas and help support the project’s future
                       development. One of his current training priorities
                       is to help people with using the block editor and
                       Full Site Editing. He is an advocate for the
                       usability of WordPress today, saying: “I can design
                       all aspects of a website now with a block.”


          o § Programming/Development⠀➾


                # ⚓ LWN ☛ The_ABI_status_of_ELF_hash_tables_[LWN.net]⠀⇛


                       It is fair to say that some projects are rather
                       more concerned about preserving ABI compatibility
                       than others; the GNU C Library (glibc) project
                       stands out even among those that put a lot of
                       effort into preserving interface stability, So it
                       may be a bit surprising that a recent glibc change
                       is being blamed for breaking a number of
                       applications, most of which are proprietary games.
                       There is, it seems, a class of glibc changes that
                       can break applications, but which are not deemed to
                       be ABI changes.
                       When the dynamic linker starts a program, it must
                       resolve all of the symbol references into shared
                       libraries (including glibc). That can involve
                       looking up thousands of symbols in long lists.
                       Since this process must complete before an
                       application can actually start running, it needs to
                       happen quickly. Nobody likes a long delay between
                       starting nethack and facing off against that first
                       kobold, after all. So it is not surprising that
                       some effort has gone into optimizing symbol lookup.


                       When the ELF file for a shared object is created by
                       the linker, one of the sections stored therein
                       contains a hash table for the symbols in that file.
                       This hash table can be used to speed the lookup
                       process and get the application underway. For many
                       years, the System V standard for the format of this
                       table has been DT_HASH; that format is supported by
                       the toolchains on Linux. In 2006, though, the
                       DT_GNU_HASH format was added as well; it includes a
                       number of improvements intended to get nethack
                       players into their dungeons even more quickly,
                       including a better hash algorithm and a Bloom
                       filter to short-circuit the search for missing
                       symbols. This format is not well documented, but
                       this 2017 blog post gives an introduction.


                       Since the hash table lives in its own ELF section,
                       there is nothing preventing an ELF file from having
                       more than one of them. Linkers on Linux systems can
                       be told to create one format or the other — or to
                       create both, each in its own section. Until
                       recently, glibc has been built (by default) with a
                       linker option explicitly requesting that both
                       formats be created. That changed, though, with the
                       glibc 2.36 release at the beginning of August; it
                       contained a simple patch from Florian Weimer
                       causing only the DT_GNU_HASH format to be
                       generated.


                # § Python⠀➾


                      # ⚓ LWN ☛ From_late-bound_arguments_to_deferred
                        computation,_part_2_[LWN.net]⠀⇛


                             Discussion on PEP 671 (“Syntax for late-bound
                             function argument defaults”) has been going
                             on—in fits and starts—since it was introduced
                             last October. The idea is to provide a way to
                             specify the default for a function argument
                             that is evaluated in the scope of the
                             function call, which will allow more concise,
                             and visible, defaults. But there has been a
                             persistent complaint that what the language
                             needs is a more-general deferred computation
                             feature; late-bound defaults would simply
                             fall out as one specific user of the feature.
                             The arrival of a proposal for deferred
                             computation did not really accomplish that
                             goal, however.


    * § Leftovers⠀➾


          o ⚓ Culture,_Books,_Friends_–_Experiences_in_the_community⠀⇛


                 For e.g. while I do not know which culture or which
                 country this comes from, somebody shared that in some
                 cultures one can talk/comment ‘May your poop be easy’ and
                 with a straight face. I dunno which culture is this but
                 if somebody asked me that I would just die from laughing
                 or maybe poop there itself.


          o § Censorship/Free Speech⠀➾


                # ⚓ AccessNow ☛ Civil_society_to_Meta:_Stop_censoring
                  reproductive_rights_content_–_Access_Now⠀⇛


                       Meta did not reply to civil society’s outreach by
                       the August 31 deadline. Access Now will continue to
                       advocate for uncensored access to information on
                       reproductive rights for all.


                # ⚓ Bloomberg ☛ Taliban_Continues_Censorship,_Web_Blocks_As_It
                  Promises_4G⠀⇛


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Self-observation_Log_001⠀⇛


                       This morning, while having a cigarette out on the
                       front porch, I noticed something — an object of
                       some sort — on the sidewalk in front of the house.
                       By the way it looked, the first thought that
                       crossed my mind was a fist-sized woodlouse — also
                       known as a “pill bug”, “rolypoly”, and a variety of
                       other names depending on locale — and it was lying
                       on its back, dead. That’s what it looked like from
                       where I was sitting, but I knew that woodlice that
                       size do not even exist, nor does any insect
                       resembling that shape and size exist in this area.


                       I have an irrational fear of insects, and it’s
                       interesting that, out of all the other
                       possibilities of what the object could be, my brain
                       prioritized my fears. But another level of my
                       consciousness knew that the object was not likely a
                       fist-sized insect. As a surge of disgust/horror ran
                       through me, my brain flitted through other abstract
                       possibilities that match what my perception and
                       fears insisted was a fist-sized insect. It’s like
                       “fist-sized insect” was the starting point, and I
                       could not see it in terms of anything else, for the
                       time being.


                # ⚓ Quiet_quitting⠀⇛


                       I came across this phrase in a news story. If you
                       feel that you’re working extra hard and getting no
                       recognition, no pay rise, no kudos, no whatever,
                       but you aren’t at the point of resigning, you can
                       “quiet quit” which means just doing the minimum.
                       It’s not a long term plan. All the people in the
                       article had later left those jobs. Why would you
                       stay somewhere that didn’t treat you well? But
                       conversely, while you’re still there, why would you
                       do anything extra?


                # ⚓ Tang_ping_(Re:_“Quiet_Quitting”)⠀⇛


                       I’d like to share some of my thoughts on quiet
                       quitting, since the original post understandably
                       didn’t explore the concept more broadly than
                       sharing a couple of thoughts. This doesn’t directly
                       address freeshell’s post, but does provide further
                       context to the points raised in it.


          o § Politics⠀➾


                # ⚓ quite_apocalyptic⠀⇛


                       This sounds like a background news report playing
                       on a video monitor in the background of an 80′s
                       sci-fi movie’s protaganist’s kitchen while they sip
                       their morning coffee in the opening scene set far
                       into the future.


          o § Technical⠀➾


                # § Science⠀➾


                      # ⚓ Nuon_Rechargeable_NiMH_Batteries⠀⇛


                             I have been using Nuon rechargeable NiMH
                             batteries for about a year now. I use AA,
                             AAA, and 9V, and I have bought the batteries
                             and chargers from Batteries and Bulbs. Now
                             that I have some credibility from long-term,
                             heavy use of these batteries, I want to give
                             my own thoughts on this product and NiMH
                             batteries in general. (To date) I am not a
                             paid advertiser for Nuon and I have never
                             received any free materials.


                             I’m just going to give my general
                             perspectives, and not bother with references
                             or the hard numbers on cost effectiveness,
                             mA-hours, and such like. You should be able
                             to find that information on the Internet
                             without much difficulty.


                # § Programming⠀➾


                      # ⚓ We_could_have_skipped_writing_a_program⠀⇛


                             A bit of background—“Project: Sippy-Cup [1]”
                             uses data from a single column from a
                             database to do its job. It doesn’t query the
                             database directly since we have a tight
                             deadline, so there’s a custom binary file
                             that contains around 100,000,000 records,
                             each record having a unique key and a 32-bit
                             value. It doesn’t matter what the key or the
                             value is, just that this file exists. So,
                             with that out of the way …


                      # ⚓ RE:_Having_a_Dot_File_Repo?⠀⇛


                             Funny how this post was made right around the
                             time that I started using a dotfile repo. I
                             was against it for a while, but actually find
                             it kind of useful. Primarily because it’s a
                             much more narrow subset of using git on your
                             entire home directory. The concerns were:
                             what do we do about credentials? And how do
                             we scrub the scripts when pushing it to a
                             remote repository.


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



                    ䷩ 𝚕𝚒𝚗𝚎 7265

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.01.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_01/09/2022:_*ubuntu_20.04.5_LTS_and_Unity_Now_Official_Flavour⠀✐


Posted in News_Roundup at 8:33 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Audiocasts/Shows
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o Fedora_and_Red_Hat
          o Debian_Family
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Google
          o Web_Browsers
                # Mozilla
          o Programming/Development
                # PHP
                # C
          o Standards/Consortia
    * Leftovers
          o Hardware
          o Misinformation_from_Microsoft/Linux_Foundation
          o Entrapment_(Microsoft_GitHub)
          o Security
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Finance
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Notebook Check ☛ Kubuntu_Linux_developers_launch_Focus_NX
                  mini_PC_with_Intel_Tiger_Lake_CPU_and_two_Thunderbolt_3
                  connectors_–_NotebookCheck.net_News⠀⇛


                       Linux-based mini PCs usually feature very modest
                       specs in order to offer solutions that are as easy
                       on the wallet as possible, but there are
                       exceptions. Take for example the new Focus NX model
                       launched by the developers of the popular Kubuntu
                       Linux distro themselves. Instead of integrating ULV
                       processors from the Intel Celeron series, the
                       Kubuntu Focus NX is powered by up to a Core i7-
                       1165G7 CPU with 28 W TDP and Iris Xe iGPU. Prices
                       are obviously more spicy, yet the Kubuntu team is
                       offering premium features such as Thunderbolt
                       connectors and an SDXC card reader.


                       Besides the i7 CPU, users may opt to equip the
                       Kubuntu Focus NX mini PC with the more affordable
                       i5-1135G7 model. The DDR4-3200 RAM capacity can be
                       configured to include between 8 GB and 64 GB, while
                       the storage options range from a single 250 GB NVMe
                       SSD up to 2 GB of NVMe + 4 TB SATA SSDS with
                       optional disk encryption.


          o § Server⠀➾


                # ⚓ Ubuntu ☛ Canonical_Kubernetes_1.25_is_now_generally
                  available_|_Ubuntu⠀⇛


                       The Canonical Kubernetes team is delighted to
                       announce that Canonical Kubernetes 1.25 is now
                       generally available, with Charmed Kubernetes
                       joining our Microk8s release last week, following
                       the release of upstream Kubernetes on 23 August.


                       We consistently follow the upstream release cadence
                       to provide our users and customers with the latest
                       improvements and fixes, together with security
                       maintenance and enterprise support for Kubernetes
                       on Ubuntu. This blog is a quick overview of the
                       latest development highlights available in
                       Canonical Kubernetes 1.25 as well as a look at our
                       favourite upstream enhancements.


                # ⚓ Kubernetes Blog ☛ Sidhartha_Mani_(Minio,_Inc):_Introducing
                  COSI:_Object_Storage_Management_using_Kubernetes_APIs⠀⇛


                       This article introduces the Container Object
                       Storage Interface (COSI), a standard for
                       provisioning and consuming object storage in
                       Kubernetes. It is an alpha feature in Kubernetes
                       v1.25.


                       File and block storage are treated as first class
                       citizens in the Kubernetes ecosystem via Container
                       Storage Interface (CSI). Workloads using CSI
                       volumes enjoy the benefits of portability across
                       vendors and across Kubernetes clusters without the
                       need to change application manifests. An equivalent
                       standard does not exist for Object storage.


                       Object storage has been rising in popularity in
                       recent years as an alternative form of storage to
                       filesystems and block devices. Object storage
                       paradigm promotes disaggregation of compute and
                       storage. This is done by making data available over
                       the network, rather than locally. Disaggregated
                       architectures allow compute workloads to be
                       stateless, which consequently makes them easier to
                       manage, scale and automate.


          o § Audiocasts/Shows⠀➾


                # ⚓ Makulu_Max_Progress_Update_–_MakuluLinux⠀⇛


                       I’ve Compiled a little video showing what’s up with
                       Makulu Max …


                # ⚓ Video ☛ What_Is_TiVoization_–_Why_You_Should_Care!_–
                  Invidious⠀⇛


                       Every so often you’ll hear FOSS and Linux advocates
                       discuss something called TiVoization as being one
                       the reasons for GPLv3 existing but what exactly is
                       that and why should you even care?


                # ⚓ Linux_Action_News_256⠀⇛


                       Debian’s firmware future is up for debate, Pine64
                       teases a RISC-V SBC, and some of your favorite
                       tools just got new tricks.


                # ⚓ Video ☛ GNOME_Telemetry,_GRUB_broke_Arch,_and_Steam_Deck_2
                  Confirmed_:_Linux_and_Open_Source_News_–_Invidious⠀⇛


          o § Graphics Stack⠀➾


                # ⚓ Khronos_Releases_Vulkan_Mesh_Shader_Pipeline_Extension⠀⇛


                       With the release of the VK_EXT_mesh_shader
                       extension Vulkan gets an alternative geometry
                       rasterization pipeline. This extension brings
                       cross-vendor mesh shading to Vulkan, with a focus
                       on improving functional compatibility with DirectX
                       12.


                       Mesh and Task shaders follow the compute
                       programming model and use threads cooperatively to
                       generate meshes within a workgroup. The vertex and
                       index data for these meshes are written similarly
                       to shared memory in compute shaders. Mesh shader
                       output is directly consumed by the rasterizer, as
                       opposed to the previous approach of using a compute
                       dispatch followed by an indirect draw. Therefore
                       mesh shading applications can avoid preallocation
                       of output buffers.


          o § Applications⠀➾


                # ⚓ Linux Links ☛ 16_Best_Free_and_Open_Source_Podcast_Tools⠀⇛


                       To provide an insight into the quality of software
                       that is available, we have compiled a list of 16
                       high quality open source podcast tools that offer
                       an excellent way to manage and download podcasts.
                       The selection includes both graphical and console
                       based tools, software which includes built-in
                       podcast management, as well as stand-alone tools,
                       so all tastes should be catered for here.


                # ⚓ MakeTech Easier ☛ The_Best_Open_Source_Tools_to_Secure_Your
                  Linux_Server⠀⇛


                       While Linux does have a variety of security
                       features to help make it safer, it’s not
                       impenetrable, which is why you need open-source
                       tools to secure your Linux server. You need the
                       right software to sniff out potential attacks and
                       vulnerabilities. On its own Linux isn’t going to
                       keep your server safe. It’s the other security
                       measures you take. Luckily, open-source tools make
                       this job easier.


                # ⚓ Ubuntu Handbook ☛ OBS_Studio_28.0_Released!_How_to_Install
                  it_in_Ubuntu_22.04_|_20.04_|_UbuntuHandbook⠀⇛


                       Free open-source video capturing, recording and
                       live streaming software, OBS Studio, just got a big
                       update with exciting new features!


                       It’s the 10th anniversary release that features 10-
                       bit & HDR video encoding support! Thought, the new
                       feature so far works only with AV1 and HEVC
                       encoders, and 10-bit HEVC encoding requires NVIDIA
                       10-series, AMD 5000 series, or newer GPU.


                       OBS Studio 28.0 also adds native Apple Silicon
                       support, many third-party plugins may not yet be
                       ready for the native build.


                       The release is also porting to Qt6. Except for
                       Ubuntu 20.04 PPA package, all others are now based
                       on Qt6. Meaning many plugins may not work until the
                       developers updated with Qt6 support. See most
                       common plugins, that works with OBS Studio 28.0.


                # ⚓ 9to5Linux ☛ VirtualBox_6.1.38_Released_with_Initial_Support
                  for_Linux_Kernel_6.0⠀⇛


                       The big news in VirtualBox 6.1.38 is that it
                       introduces initial support for the upcoming Linux
                       6.0 kernel. This means that users will be able to
                       virtualize GNU/Linux distributions powered by Linux
                       kernel 6.0, when it will be officially released
                       later this fall, as well as to install VirtualBox
                       in a Linux 6.0-powered distribution.


                # ⚓ FocusWriter_1.8.2_released⠀⇛


                       FIXED: Could not change language in portable mode
                       FIXED: Crashed during paste from context menu
                       FIXED: First line indent was lost on empty
                       paragraphs
                       Always write RTF as Latin1
                       Replaced ICU with iconv
                       Improved Linux deployment
                       Translation updates: German, Korean, Portuguese
                       (Brazil), Russian, Swedish


          o § Instructionals/Technical⠀➾


                # ⚓ HowTo Forge ☛ How_to_Set_Up_WireGuard_VPN_on_Ubuntu_22.04⠀⇛


                       Wireguard is an open-source cross-platform Virtual
                       Private Network (VPN) implementation that uses
                       state-of-the-art cryptography. It supports IPv4 and
                       IPv6 connections. It is faster, simpler, and more
                       functional than IPSec and OpenVPN protocols. It is
                       designed as a general-purpose VPN to run on
                       embedded interfaces and super computers and runs on
                       Linux, Windows, macOS, iOS, Android, and various
                       other platforms.


                       Wireguard’s encryption works using private and
                       public keys for peers to establish an encrypted
                       tunnel between themselves.


                       This tutorial will cover how to install Wireguard
                       VPN on a Ubuntu 22.04 server and connect to it
                       using a Ubuntu client.


                # ⚓ Make Use Of ☛ How_to_Fix_the_“sudo:_command_not_found”
                  Error_on_Linux⠀⇛


                       When setting up a new Linux desktop or virtual
                       machine, you may encounter the error: “sudo:
                       command not found”. This Linux error message can be
                       infuriating, and prevent you from progressing
                       further with your setup. Here’s what it means and
                       how to fix it.


                # ⚓ Speed_up_Ansible_SSH_with_Multiplexing⠀⇛


                       Ansible opens an SSH connection for every playbook
                       run. When you have multiple servers you need to
                       configure in parallel with multiple playbooks being
                       applied to them then it all adds up.


                # ⚓ TechTarget ☛ DNS_server_troubleshooting_for_Linux_and
                  Windows⠀⇛


                       Steps in DNS server troubleshooting include
                       checking the DNS status, looking at zone
                       configurations and evaluating logs. Follow these
                       best practices for Windows and Linux servers.


                # ⚓ Linux Made Simple ☛ How_to_install_WebStorm_2022_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install WebStorm
                       2022 on a Chromebook. Please follow the video/audio
                       guide as a tutorial where we explain the process
                       step by step and use the commands below.


                # ⚓ Video ☛ How_to_install_Olive_video_editor_on_Pop!_OS_22.04
                  –_Invidious⠀⇛


                       In this video, we are looking at how to install
                       Olive video editor on Pop!_OS 22.04.


                # ⚓ Video ☛ How_to_install_MX_Linux_21.2._–_Invidious⠀⇛


                       In this video, I am going to show how to install MX
                       Linux 21.2.


                # ⚓ Make Use Of ☛ apt_update_vs._apt_upgrade:_What_Are_the
                  Differences?⠀⇛


                       The entire Linux ecosystem works on the concept of
                       packages; each package on Linux is crucial for
                       ensuring the smooth functioning of the operating
                       system.


                       To update your packages on Debian and Ubuntu-based
                       distributions, you might need to run from pillar to
                       post, trying to figure out the best way to update
                       all the essential software.


                       When looking for ways to update packages, you will
                       come across commands like apt update, apt upgrade,
                       and related versions. But the point is, what’s the
                       difference between these commands, and how can you
                       use them to update your Linux packages?


                # ⚓ Linux Capable ☛ How_to_Install_FileZilla_Client_on_Linux
                  Mint_21_LTS_–_LinuxCapable⠀⇛


                       FileZilla is a free FTP client with cross-platform
                       support. It can be downloaded for Windows or Linux
                       on both server and client sides. FileZilla supports
                       sftp connections which helps transfer files without
                       wrapping them up in archives. This reduces traffic
                       on your network while still getting the job done
                       quickly. Another helpful feature of FileZilla is
                       that it allows you to resume interrupted transfers.
                       If your connection drops in the middle of a
                       transfer, you can pick up right where you left off
                       without starting over from scratch. Whether you’re
                       a web developer who regularly uploads files to a
                       server or a network administrator who needs to
                       transfer large amounts of data between computers,
                       FileZilla is a helpful tool in your arsenal.


                       In the following tutorial, you will learn how to
                       install the latest version of FileZilla on Linux
                       Mint 21 LTS using a recommended Launchpad PPA
                       repository or the alternative third-party package
                       manager Flatpak to provide the most up-to-date
                       version using the command line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Firefox_ESR_on_Linux_Mint_21
                  LTS_–_LinuxCapable⠀⇛


                       The extended support release (ESR) for Firefox is
                       specially designed for organizations that require
                       stability and security but may not have access to
                       the latest features. ESR versions are officially
                       supported by Mozilla and do not contain any known
                       bugs or unfinished products. The extended support
                       release cycle is perfect for universities, large
                       businesses, and other organizations that must
                       carefully plan and test their software before
                       upgrading. The standard release cycle is
                       recommended for individual users who want the
                       latest features and can tolerate a few bugs.
                       Firefox ESR is an excellent choice for anyone who
                       values stability and security over cutting-edge
                       features.


                       The following tutorial will teach you how to
                       install Firefox ESR on Linux Mint 21 LTS using a
                       recommended Launchpad PPA repository to provide the
                       most up-to-date version using the command line
                       terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Liquorix_Kernel_on_Linux
                  Mint_21_LTS_–_LinuxCapable⠀⇛


                       Liquorix Kernel is a free, open-source general-
                       purpose Linux Kernel alternative to the stock
                       kernel. It features custom settings and new
                       features and is built to provide a responsive and
                       smooth desktop experience, especially for new
                       hardware. Liquorix Kernel is popular amongst Linux
                       Gaming, streaming, and ultra-low latency
                       requirements and often boasts the latest Linux
                       Kernels, having multiple branches for different
                       Hardware requirements. For users looking for more
                       performance out of their systems or just wanting to
                       use the newest kernel, Liquorix Kernel is an
                       excellent option. The company that builds the
                       Liquorix Kernel offers commercial support and
                       development services should you need them. If
                       you’re looking for a rock-solid and well-supported
                       Linux Kernel alternative, Liquorix Kernel is worth
                       checking out.


                # ⚓ Linux Capable ☛ How_to_Install_MariaDB_10.5_on_Debian_11
                  Bullseye_–_LinuxCapable⠀⇛


                       MariaDB is one of the most popular open-source
                       databases next to its originator MySQL. The
                       original creators of MySQL developed MariaDB in
                       response to fears that MySQL would suddenly become
                       a paid service due to Oracle acquiring it in 2010.
                       With its history of doing similar tactics, the
                       developers behind MariaDB have promised to keep it
                       open source and free from such fears as what has
                       happened to MySQL. In addition, they have also made
                       sure that MariaDB is compatible with existing MySQL
                       installations, making it an ideal drop-in
                       replacement. As a result, MariaDB has become the
                       preferred choice for many businesses and
                       organizations looking for a robust and reliable
                       open-source database solution.


                       In the release of MariaDB 10.5, an LTS edition,
                       there are many new features and capabilities that
                       will help improve the performance and stability of
                       MariaDB installations from previous versions. One
                       of the most notable changes is the inclusion of a
                       new storage engine, Aria, which is designed to
                       replace MyISAM as the default engine for MariaDB.
                       In addition, there have been several improvements
                       to InnoDB, including better support for full-text
                       search and a reduction in I/O overhead. Other
                       changes include improved KILL statement handling,
                       enhanced PARTITIONING options, and support for
                       parallel creation and dropping databases. With
                       these and other changes, MariaDB 10.5 provides a
                       more robust and scalable database solution that
                       suits demanding production environments.


                # ⚓ Linux Capable ☛ How_to_Install_MariaDB_10.6_on_Rocky_Linux
                  9_–_LinuxCapable⠀⇛


                       Oracle’s acquisition of MySQL in 2010 led to fears
                       that the popular open-source database would become
                       a paid service. In response, the original creators
                       of MySQL developed MariaDB, and MariaDB is now one
                       of the most popular open-source databases. Like
                       MySQL, it is free and can be used for various
                       purposes, including web development, data analysis,
                       and application development. The developers behind
                       MariaDB have promised to keep it open source and
                       free from the same fears that led to its creation.
                       This commitment has helped to solidify MariaDB’s
                       position as a leading open-source database.


                       MariaDB 10.6 brings several significant
                       improvements to the popular open source database,
                       including improved performance, scalability, and
                       new features such as a crash-safe replication
                       mechanism and improved SQL compatibility. In terms
                       of performance, MariaDB 10.6 includes several
                       optimizations that can help to speed up database
                       operations. For example, the new version contains
                       several changes that can help to reduce disk IO and
                       improve caching. These changes can result in a
                       significant performance boost for high-traffic
                       databases. MariaDB 10.6 also introduces a new
                       replicated log much more resilient to crashes and
                       other failures. This feature can help to ensure
                       that data is always safe and available, even in the
                       event of an unexpected shutdown. Finally, MariaDB
                       10.6 includes several improvements to SQL
                       compatibility, making porting applications and data
                       from other database systems easier. Overall,
                       MariaDB 10.6 is a significant step forward for the
                       popular open source database and will provide
                       substantial benefits for users looking for a high-
                       performance, scalable, and feature-rich option.


                # ⚓ Linux Capable ☛ How_to_Install_PHP_8.0_on_Debian_11
                  Bullseye_–_LinuxCapable⠀⇛


                       PHP is a programming language used to develop
                       server-side applications. It is one of the most
                       popular languages to date, with code that can be
                       embedded into HTML pages. PHP code is executed on
                       the server, producing HTML or other types of
                       output, which is then sent to the client’s web
                       browser. PHP can be used for many tasks, such as
                       developing dynamic web pages, generating images,
                       and even sending and receiving cookies. In
                       addition, PHP can connect to databases and access
                       files on the server. As a result, PHP is an
                       essential tool for developing modern web
                       applications.


                       PHP 8.0 is a significant update of the PHP
                       language, released on December 3, 2020. This new
                       version includes many features that improve
                       performance and enable greater flexibility in
                       coding. For example, PHP 8.0 introduces union
                       types, allowing a single variable to hold multiple
                       data types. This can be handy when working with
                       complex data structures. Other new features include
                       Named Arguments, which make it easier to call
                       functions with multiple arguments, and the Printf
                       Directive, which allows printf-style string
                       formatting within PHP code. In addition, this
                       release has updated or improved many existing
                       features. Overall, PHP 8.0 is a welcome addition
                       that will help make PHP an even more powerful and
                       flexible language.


                # ⚓ Linux Capable ☛ How_to_Install_Redis_on_CentOS_9_Stream_–
                  LinuxCapable⠀⇛


                       Redis is an open-source database frequently used as
                       a cache or message broker. Unlike other databases,
                       Redis stores data in memory, making it
                       significantly faster. In addition, Redis supports a
                       wide range of data structures, including strings,
                       hashes, lists, sets, sorted sets, bitmaps, and
                       streams. This makes Redis an incredibly versatile
                       tool that can be used for various purposes. For
                       example, Redis can be used as a simple key-value
                       store, or it can be used to implement more complex
                       data structures such as queues or leaderboards.
                       Additionally, Redis comes with a built-in
                       replicated caching system that can be used to
                       improve the performance of web applications. As a
                       result, Redis is an incredibly popular database
                       that is used by thousands of companies all over the
                       world.


                       In the following tutorial, you will learn how to
                       install Redis on CentOS 9 Stream workstation or
                       server using the terminal command line with two
                       methods: appstream or Remi Redis pm, along with
                       basic setup instructions to get you started using
                       the command line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Spotify_on_Linux_Mint_21_LTS
                  –_LinuxCapable⠀⇛


                       Spotify is a digital music streaming service with
                       both free and paid features. As of September 2022,
                       it is the world’s largest music streaming service
                       provider, with over 443 million monthly active
                       users, including 187 million paying subscribers.
                       Spotify can give instant access to a vast online
                       library of music and podcasts and has been very
                       popular as you can listen to the content of your
                       choice whenever you feel like it. You can also
                       create your playlists or listen to those created by
                       Spotify. In addition, Spotify offers several
                       features for its premium users, such as ad-free
                       listening, high-quality audio, offline mode, and
                       more. Spotify is available on various devices,
                       including smartphones, tablets, computers, and
                       more.


                       The following tutorial will teach you how to
                       install Spotify on Linux Mint 21 LTS using the
                       official Spotify repository or alternative flatpak
                       installation manager using the command line
                       terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Thunderbird_Mail_on_Linux
                  Mint_21_LTS_–_LinuxCapable⠀⇛


                       Thunderbird Mail is a free, open-source email
                       client that can be used on your desktop computer
                       and mobile devices like iPhone or Android. The mail
                       client software was initially developed by the
                       Mozilla Foundation but is now maintained by the
                       Thunderbird community for community. Thunderbird
                       offers support for multiple email accounts, a
                       personal address book, and built-in search tools to
                       help you find messages quickly. It also includes
                       message filtering and tagging to help you organize
                       your inbox. In addition, Thunderbird supports both
                       POP and IMAP protocols, making it easy to set up
                       and use with most email providers.


                       In the following tutorial, you will learn how to
                       install Thunderbird Mail on Linux Mint 21 LTS using
                       one of two installation methods: APT or Flatpak
                       using the command line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_XanMod_Kernel_on_Linux_Mint
                  21_LTS_–_LinuxCapable⠀⇛


                       XanMod is a popular Linux kernel modification that
                       provides enhanced performance and stability for
                       gaming, streaming, and other resource-intensive
                       tasks. The XanMod team is known for its timely
                       release of new kernels, which often include support
                       for the latest hardware before it is available on
                       other distributions. For desktop users who are not
                       into gaming or streaming, XanMod can still be a
                       desirable choice for its up-to-date hardware
                       support. In addition to its kernel modifications,
                       XanMod offers many other features and tweaks that
                       make it an appealing option for many users.


                # ⚓ Linux Capable ☛ How_to_Install_Zoom_on_Linux_Mint_21_LTS_–
                  LinuxCapable⠀⇛


                       Zoom is a communications technology platform that
                       provides video telephony and real-time online chat
                       services through a cloud-based peer-to-peer
                       software platform. Zoom’s easy-to-use platform lets
                       users connect with colleagues, classmates, and
                       customers in real-time from any device. Zoom’s
                       features include high-definition video and audio,
                       screen sharing, and the ability to record meetings.
                       Zoom also offers a variety of enterprise features,
                       such as single sign-on, integration with
                       calendaring systems, and support for large-scale
                       deployments. Zoom is used by businesses of all
                       sizes, from small businesses to Fortune 500
                       companies. Zoom is also popular with educational
                       institutions and non-profit organizations.


                       In the following tutorial, you will learn to
                       install Zoom on Linux Mint 21 LTS using the flatpak
                       package manager or the snapcraft package manager,
                       with some tips for maintaining or removing software
                       in the future.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Dedoimedo ☛ RescueZilla_–_Fast,_efficient,_reliable_–_perfect
            imaging_tool⠀⇛


                 RescueZilla is a wonderful tool, and it definitely makes
                 using CloneZilla easier and more accessible. The only
                 downside the program has is the somewhat clunky GUI – the
                 desktop, the application itself. The information should
                 be more presentable, but other than that, I really had no
                 worries or complaints. The most important thing is, the
                 software is solid, robust and fast.


                 Hopefully, this tutorial gives you what you need to make
                 your first steps with RescueZilla. I strongly endorse
                 this program, it’s another step on my journey away from
                 Windows. Plus, recently I discovered that Acronis True
                 Image (ATI) no longer offers perpetual-license keys for
                 their software, it’s all subscription now, nope, and so
                 the still truly offline editions that I currently own
                 (2019 and 2020) will be the last ever for this product.
                 In this regard, RescueZilla comes as a beautiful falcon
                 of poetic justice. Anyway, this is a fantastic system
                 toolbox, and you should have it, and use it, and enjoy
                 it. Dedoimedo out.


          o ⚓ Linux Mint ☛ The_Linux_Mint_Blog:_Monthly_News_–_August_2022⠀⇛


                 Wil Wheaton runs Linux Mint. It’s official! I really like
                 him so it made my day to know about it. I just thought
                 I’d mention it


                 To all the really cool people out there who haven’t come
                 out yet. If you like what we do, don’t be a stranger, let
                 us know!


                 Another piece of cool news this month is the Steam Deck.
                 It’s starting to become available. I managed to get one.
                 I’m hoping we’ll manage to get a few more for the team.
                 It’s brilliant as a portable gaming device but it’s also
                 fantastic for the future of gaming in Linux. A lot of
                 people will get a Steam Deck. Many studios will want
                 their games to be “Deck Verified” and thus this is going
                 to significantly boost the compatibility of games with
                 Linux, or at least with Proton.


                 Other than Linux and Proton, the Deck relies on an
                 immutable version of Arch, Flatpak and KDE so its
                 ecosystem is a little bit different than the one we have
                 in Linux Mint. The development of SteamOS and Linux Mint
                 isn’t likely to have much in common or to converge in any
                 way. That said there will likely be some use cases we’ll
                 be able to help with. Warpinator for instance, which we
                 made available as a Flatpak, proved to be useful to share
                 files between computers, smartphones and the Steam Deck.


          o § Fedora and Red Hat⠀➾


                # ⚓ Fedora Magazine ☛ Contribute_at_the_i18n,_Release
                  Validation,_CrytoPolicy_and_GNOME_43_Final_test_weeks_for
                  Fedora_Linux_37_–_Fedora_Magazine⠀⇛


                       There are 4 upcoming test days/weeks in the coming
                       weeks. The first is Wed 31 August through Wed 07
                       Sept. It is to test Pre-Beta Release Validation.
                       The second is Tuesday 6 Sept through Monday 12
                       Sept. It focuses on testing i18n. The third is
                       Monday 5 Sept the Crypto Policy test day. The
                       fourth is Wed 7 Sept through Wed 14 Sept to test
                       GNOME 43 Final. Please come and test with us to
                       make the upcoming Fedora 37 even better. Read more
                       below on how to participate.


                # ⚓ Video ☛ Technically_Speaking_(E15):_Machine_learning_model
                  drift_–_MLOps_pipelines_–_Invidious⠀⇛


                # ⚓ SDTimes ☛ Improvements_to_the_developer_experience_in
                  OpenShift_4.11_–_SD_Times⠀⇛


                       The team at Red Hat OpenShift, an enterprise ready
                       Kubernetes container platform for an open hybrid
                       cloud strategy, recently released the platform’s
                       newest update, Red Hat OpenShift 4.11. With this,
                       developers gain several improvements to the
                       developer experience in the OpenShift Container
                       Platform web console.


                       The OpenShift console now offers users dark mode, a
                       long-awaited feature according to the company.
                       Users can set their theme preferences by going to
                       User Preferences and selecting either Light, Dark,
                       or System Default.


                       Customer requested usability enhancements are also
                       included in 4.11, such as the ability to easily
                       create and edit routes and ConfigMaps with a form-
                       based interaction. Additionally, users can now
                       connect to the Red Hat console from the Application
                       Launcher as well as share their project with other
                       members of a team by clicking the Sharing card on
                       the Add page.


          o § Debian Family⠀➾


                # ⚓ Linuxiac ☛ Deepin_20.7_Released_with_Hardware_Enablement
                  Kernel_5.18⠀⇛


                       Deepin 20.7 arrives precisely two months after the
                       previous version’s release, bringing a new set of
                       desktop features and improvements.


                       Deepin is a Chinese-made Linux distribution based
                       on the Debian stable branch aimed at the average
                       desktop computer user.


                       It has a long history of paying attention to visual
                       detail that is more akin to macOS than Windows.
                       Like elementary OS, is visually attractive straight
                       out of the box, with no customization. In other
                       words, it is one of the most good-looking Linux
                       distros.


                # ⚓ Sparky_news_2022/08⠀⇛


                       The 8th monthly Sparky project and donate report of
                       2022:
                       – Linux kernel updated up to 5.19.6 & 5.15.64-LTS
                       (6.0 RC1 is also available)
                       – Added to repos: g4music
                       – Created a new script/package called ‘sparky-
                       openbox-diagnose’ which check default application
                       which should be started with Openbox; and print
                       message if something wrong; this output is helpful
                       to help you if any problem with loading Openbox
                       – Finished adding es_ES locales to Sparky tools,
                       thanks to depaz
                       – Sparky 6.4 of the stable line released
                       – LXQt desktop updated up to version 1.1.0 (Sparky
                       testing (7) amd64 only); can be installed from
                       Sparky ‘extra main’ repos


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ DebugPoint ☛ Ubuntu_Team_Accepted_Unity_As_the_Official
                  Flavour⠀⇛


                       Ubuntu Unity is now an official Ubuntu flavour, and
                       the first release will be Ubuntu Unity 22.10.


                # ⚓ Its FOSS ☛ Unity_Desktop_Makes_a_Comeback_With_the_Upcoming
                  Ubuntu_22.10⠀⇛


                       I loved the Unity desktop but not enough to keep on
                       using it when Ubuntu ditched it in 2017 for GNOME.


                       I have started liking the customized GNOME Ubuntu
                       offers. And the old flame enters again.


                       Ubuntu Unity is going to be an official Ubuntu
                       flavor with the release of version 22.10 Kinetic
                       Kudu.


                # ⚓ Ubuntu_Unity_Is_Now_Official_Ubuntu_Flavor⠀⇛


                       The good news for the Ubuntu Unity lover as
                       Canonical has accepted Ubuntu Unity as the official
                       flavor of Ubuntu. Ubuntu Unity is a remix of Ubuntu
                       featuring the Unity7 desktop environment Ubuntu
                       Unity which was formerly known as Ubuntu Unity
                       Remix was started a few years ago. It was based on
                       Ubuntu 20.04 LTS (Focal Fossa).


                # ⚓ The Register UK ☛ Kubuntu_and_Lubuntu_get_desktop_upgrades,
                  as_optional_extras⠀⇛


                       Kubuntu and Lubuntu desktops have been upgraded but
                       you won’t automatically get the new versions.
                       Here’s how to get the optional lifts.


                       There’s only one official flavor of Ubuntu. The
                       standard desktop is GNOME, and if you pay for
                       optional support, that’s the only supported
                       edition. But if you don’t care for GNOME – and we
                       entirely understand and sympathize with that –
                       there are seven other “flavours”. We took a look at
                       all of them recently, after they were updated for
                       22.04.1.


                       The underlying OS is the same for all of them, and
                       it will get five years of updates, just like the
                       standard version. It’s important to be aware,
                       though, that these alternative desktop versions
                       don’t get the full five years of updates, and they
                       aren’t supported by Canonical.


                       That means two things. Firstly, you should plan on
                       upgrading at least every two years, because unlike
                       the baseline GNOME edition, after three years, the
                       flavours won’t get updates for anything except the
                       text-mode OS underneath.


                       Secondly, if you want the latest and greatest
                       versions of their component desktops, you have to
                       install the newer desktop yourself – and you
                       should. Fortunately, that is quite easy to do, and
                       once you add the relevant repos to your system, the
                       desktop will get updated along with everything
                       else.


                # ⚓ The_Fridge:_Ubuntu_20.04.5_LTS_Released⠀⇛


                # ⚓ Ubuntu_20.04.5_LTS_released⠀⇛


                       The Ubuntu team is pleased to announce the release
                       of Ubuntu 20.04.5 LTS
                       (Long-Term Support) for its Desktop, Server, and
                       Cloud products, as well
                       as other flavours of Ubuntu with long-term support.

                       Like previous LTS series, 20.04.5 includes hardware
                       enablement stacks
                       for use on newer hardware. This support is offered
                       on all architectures.
                       Ubuntu Server defaults to installing the GA kernel;
                       however you may
                       select the HWE kernel from the installer
                       bootloader.

                       As usual, this point release includes many updates,
                       and updated
                       installation media has been provided so that fewer
                       updates will need to
                       be downloaded after installation. These include
                       security updates and
                       corrections for other high-impact bugs, with a
                       focus on maintaining
                       stability and compatibility with Ubuntu 20.04 LTS.

                       Kubuntu 20.04.5 LTS, Ubuntu Budgie 20.04.5 LTS,
                       Ubuntu MATE 20.04.5 LTS,
                       Lubuntu 20.04.5 LTS, Ubuntu Kylin 20.04.5 LTS,
                       Ubuntu Studio 20.04.5 LTS,
                       and Xubuntu 20.04.5 LTS are also now available.
                       More details can be found
                       in their individual release notes:

                       https://wiki.ubuntu.com/FocalFossa/
                       ReleaseNotes#Official_flavours

                       Maintenance updates will be provided for 5 years
                       for Ubuntu Desktop,
                       Ubuntu Server, Ubuntu Cloud, and Ubuntu Core. All
                       the remaining
                       flavours will be supported for 3 years. Additional
                       security support is
                       available with ESM (Extended Security Maintenance).
                # ⚓ Lubuntu ☛ Lubuntu_20.04.5_LTS_Released!_–_Lubuntu⠀⇛


                       Thanks to all the hard work from our contributors,
                       we are pleased to announce that Lubuntu 20.04.5 LTS
                       has been released!


                # ⚓ OMG Ubuntu ☛ Ubuntu_20.04.5_LTS_Released_with_Linux_Kernel
                  5.15_–_OMG!_Ubuntu!⠀⇛


                       The fifth point release of Ubuntu 20.04 LTS is
                       available to download.


                       Now, now: don’t get too excited. Ubuntu 20.04.5 LTS
                       is a freshly-spun install image composed of Ubuntu
                       22.04 LTS plus all major security patches, bug
                       fixes, and app updates issues since the release of
                       Ubuntu 20.04.4 LTS, which was back in February.


                       Periodic refreshes to install media are necessary
                       as they cut down on the number of post-install
                       updates a user has to install after (or during, as
                       that is an option) install.


                       So if you already run Ubuntu 20.04 LTS and you have
                       installed all updates as/when released you do not
                       need to reinstall anything to ‘get’ 20.04.5
                       LTS.You’re not missing out on anything; you have
                       everything included in these new images — in fact,
                       you’ve had it for a while!


                       But if you don’t currently use Ubuntu 20.04 LTS and
                       you plan to, this all-new ISO is the one to use.


                # ⚓ 9to5Linux ☛ Ubuntu_20.04.5_LTS_Released_with_Linux_Kernel
                  5.15_LTS_from_Ubuntu_22.04_LTS_–_9to5Linux⠀⇛


                       Canonical released today Ubuntu 20.04.5 as the
                       fifth and last planned point release to its long-
                       term supported Ubuntu 20.04 LTS (Focal Fossa)
                       operating system series.


                       Ubuntu 20.04.5 LTS is here a little over six months
                       after the release of Ubuntu 20.04.4 LTS, which
                       shipped with the Linux 5.13 kernel and Mesa 21.2
                       graphics stack from the now obsolete Ubuntu 21.10
                       (Impish Indri) release.


          o § Devices/Embedded⠀➾


                # ⚓ Notebook Check ☛ ODROID-Go_Ultra:_New_gaming_handheld
                  previewed_with_a_5-inch_display_and_Ubuntu_support_for_US$111
                  –_NotebookCheck.net_News⠀⇛


                       Hardkernel has revealed the ODROID-Go Ultra,
                       another gaming handheld in the ODROID-Go series. To
                       recap, the company released the ODROID-Go Super for
                       US$89.95 in January 2021, which featured the
                       Rockchip RK3326 SoC and a 5-inch display running at
                       854 x 480 pixels. Seemingly, the ODROID-Go Ultra
                       utilises the same display as the ODROID-Go Super,
                       but with a more potent chipset powering it.


                       Specifically, the ODROID-Go Ultra has the 5-inch
                       LCD display from the ODROID-Go Super, but with the
                       Amlogic S922X, a chipset on which Hardkernel bases
                       the ODROID-N2 Plus. For reference, the Amlogic
                       S922X has four ARM Cortex-A73 CPU cores running at
                       2.2 GHz, another two Cortex-A53 CPU cores clock at
                       2.0 GHz and a Mali-G52 MP4 GPU that peaks at 846
                       MHz. Additionally, the ODROID-Go Ultra comes with
                       16 GB of eMMC flash storage, expandable via a
                       microSD card slot (UHS-1), and 2 GB of LPDDR4 RAM
                       running at 1,608 MHz.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Arduino_improves_the_compilation_terms_for_the
                  free_plan_in_the_online_IDE_|_Arduino_Blog⠀⇛


                       Online interactive development environments (IDE)
                       have taken off during the recent years.
                       Traditionally, local IDEs were considered the best
                       tools for programming as they were usually faster
                       than their online counterparts. But the arrival of
                       new web programming frameworks and the
                       standardisation of high-speed internet connections
                       have improved the user experience of interactive
                       editors using browsers.


                       Arduino’s popular online IDE is a widely used tool
                       for programming not only Arduino boards but also
                       3rd party hardware. Improving the user’s experience
                       including or changing features is part of its
                       dynamic nature, always based on the developers’
                       experience and feedback.


                # ⚓ Arduino ☛ Convert_an_old_telephone_into_a_MIDI_instrument_|
                  Arduino_Blog⠀⇛


                       MIDI (Musical Instrument Digital Interface) is a
                       fantastic standard because it is versatile enough
                       to encompass almost all instruments, but simple
                       enough to work with using low-power digital
                       hardware. A typical MIDI message contains three
                       bytes. The first is a status byte that describes
                       the action (like “note on”) and the channel to use,
                       the second byte contains the note to play, and the
                       third byte defines the velocity. Because a single
                       switch can act as a trigger to send a MIDI message,
                       one can turn an old touch tone telephone into a
                       MIDI instrument.


                       The phone used in this project and most others like
                       it have numeric keypads set up in the same way as
                       keyboards, with a matrix reducing the number of I/
                       O pins needed on a connected microcontroller.
                       Multiply the number or rows in the matrix by the
                       number of columns to get the maximum number of
                       keys. This particular keypad had a combined row/
                       column total of 11, which means it could support up
                       to 30 unique keys. But only 12 of those are
                       connected, so the tutorial includes instructions on
                       how to identify the key that each row/column combo
                       triggers. Once you know that information, you can
                       connect the row and column wires to the I/O pins of
                       an Arduino.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ The Sun ☛ Urgent_warning_for_over_a_MILLION_Android_users_–
                  you_must_delete_an_app_now_|_The_US_Sun⠀⇛


                # ⚓ Android Authority ☛ How_to_remove_malware_from_an_Android
                  device_–_Android_Authority⠀⇛


                # ⚓ Android Authority ☛ Motorola_Edge_(2022)_review:_Edge-
                  appropriate_–_Android_Authority⠀⇛


                # ⚓ Android Central ☛ Samsung_Galaxy_Z_Flip_4_review:_The
                  perfect_foldable_|_Android_Central⠀⇛


                # ⚓ Kim Kommando ☛ Fix_these_7_annoying_Android_problems_and
                  get_more_out_of_your_phone⠀⇛


                # ⚓ XDA ☛ Support_for_satellite_connectivity_arriving_to
                  Android_14⠀⇛


                # ⚓ 9to5Google ☛ Android_14_to_feature_satellite_connectivity
                  support_–_9to5Google⠀⇛


                # ⚓ Android Authority ☛ Android_13_comes_to_the_Galaxy_S7,_S8,
                  and_Note_8_thanks_to_a_custom_ROM_–_Android_Authority⠀⇛


                # ⚓ CNET ☛ Android_12_Has_Some_Tricks_Up_Its_Sleeve,_But_You
                  Have_to_Know_Where_to_Look_–_CNET⠀⇛


                # ⚓ Liliputing ☛ Lilbits:_Samsung_brings_Android_12L_to_the
                  Galaxy_Tab_8_series,_HMD_introduces_the_Nokia_T21_tablet_–
                  Liliputing⠀⇛


                       Samsung is one of the few companies making premium
                       Android tablets these days… and the company’s been
                       at it for years, even when Google seemed to have
                       largely given up on the space.


                       But now that Google has remembered that tablets are
                       a thing and started releasing versions of Android
                       optimized for large screens, Samsung is starting to
                       incorporate some of Google’s new features (like the
                       Android 12L taskbar) into the software for Samsung
                       Galaxy Tab S8 series.


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


          o ⚓ Purism ☛ Introducing_PureBoot_Basic_–_Purism⠀⇛


                 PureBoot is our high-security, tamper-detecting boot
                 firmware that we offer as an alternative to our default
                 coreboot firmware on hardware like our Librem 14 and
                 Librem Mini. The combination of PureBoot, our anti-
                 interdiction services, and the option of Qubes as the
                 pre-installed OS makes hardware like the Librem 14 among
                 the most secure computers you can buy. We are constantly
                 adding improvements to PureBoot, and the release of
                 PureBoot version 22 has added a new feature we are
                 calling “PureBoot Basic” that lets you optionally disable
                 the tamper detection. In this blog post I will discuss
                 why we created this feature, where it’s useful, and some
                 of our future plans for it.


          o § Google⠀➾


                # ⚓ Hacker News ☛ Google_Launches_New_Open_Source_Bug_Bounty_to
                  Tackle_Supply_Chain_Attacks⠀⇛


                       Google on Monday introduced a new bug bounty
                       program for its open source projects, offering
                       payouts anywhere from $100 to $31,337 (a reference
                       to eleet or leet) to secure the ecosystem from
                       supply chain attacks.


                       Called the Open Source Software Vulnerability
                       Rewards Program (OSS VRP), the offering is one of
                       the first open source-specific vulnerability
                       programs.


                # ⚓ FOSSLife ☛ Google_Announces_New_Open_Source_Bug_Bounty [Ed:
                  Still working for the NSA while pretending to value
                  security]⠀⇛


                       Google has introduced a new bug bounty program for
                       open source projects, with payouts ranging from
                       $100 to $31,337 to tackle supply chain attacks.


                # ⚓ Google ☛ Chromium_Blog:_Chrome_106_Beta:_New_CSS_Features,
                  WebCodecs_and_WebXR_Improvements,_and_More⠀⇛


                       Unless otherwise noted, changes described below
                       apply to the newest Chrome beta channel release for
                       Android, ChromeOS, Linux, macOS, and Windows. Learn
                       more about the features listed here through the
                       provided links or from the list on
                       ChromeStatus.com. Chrome 106 is beta as of
                       September 1, 2022. You can download the latest on
                       Google.com for desktop or on Google Play Store on
                       Android.


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ Mozilla ☛ Hello_from_the_new_developer_advocate_|
                        Mozilla_Add-ons_Community_Blog⠀⇛


                             Hello extension developers, I’m Juhis, it’s a
                             pleasure to meet you all. In the beginning of
                             August I joined Mozilla and the Firefox add-
                             ons team as a developer advocate. I expect us
                             to see each other quite a lot in the future.
                             My mom taught me to always introduce myself
                             to new people so here we go!


                             My goal is to help all of you to learn from
                             each other, to build great add-ons and to
                             make that journey an enjoyable experience.
                             Also, I want to be your voice to the teams
                             building Firefox and add-ons tooling.


          o § Programming/Development⠀➾


                # ⚓ Paul Schaub ☛ Creating_a_Web-of-Trust_Implementation:
                  Accessing_Certificate_Stores_–_vanitasvitae’s_blog⠀⇛


                       In this post, I will outline some progress I made
                       towards a full WoT implementation. The current
                       milestone entails integrating certificate stores
                       more closely with the core API.


                       On most systems, OpenPGP certificates (public keys)
                       are typically stored and managed by GnuPGs internal
                       key store. The downside of this approach is, that
                       applications that want to make use of OpenPGP
                       either need to depend on GnuPG, or are required to
                       manage their very own exclusive certificate store.
                       The latter approach, which e.g. Thunderbird is
                       taking, leads to a situation where there are
                       multiple certificate stores with different
                       contents. Your GnuPG certificate store might
                       contain Bobs certificate, while the Thunderbird
                       store does not. This is confusing for users, as
                       they now have to manage two places with OpenPGP
                       certificates.


                       There is a proposal for a Shared PGP Certificate
                       Directory nicknamed “pgp.cert.d” which aims to
                       solve this issue by specifying a shared, maildir-
                       like directory for OpenPGP certificates. This
                       directory serves as a single source for all OpenPGP
                       certificates a user might have to deal with. Being
                       well-defined through the standards draft means
                       different applications can access the certificate
                       store without being locked into a single OpenPGP
                       backend.


                # ⚓ new_month,_new_brainworm_—_wingolog⠀⇛


                       Today, a brainworm! I had a thought a few days ago
                       and can’t get it out of my head, so I need to pass
                       it on to another host.


                       So, imagine a world in which there is a a drive to
                       build a kind of Kubernetes on top of WebAssembly.
                       Kubernetes nodes are generally containers,
                       associated with additional metadata indicating
                       their place in overall system topology (network
                       connections and so on). (I am not a Kubernetes
                       specialist, as you can see; corrections welcome.)
                       Now in a WebAssembly cloud, the nodes would be
                       components, probably also with additional
                       topological metadata. VC-backed companies will duke
                       it out for dominance of the WebAssembly cloud
                       space, and in a couple years we will probably
                       emerge with an open source project that has become
                       a de-facto standard (though it might be dominated
                       by one or two players).


                       In this world, Kubernetes and Spiffy-Wasm-Cloud
                       will coexist. One of the success factors for
                       Kubernetes was that you can just put your old
                       database binary inside a container: it’s the same
                       ABI as when you run your database in a virtual
                       machine, or on (so-called!) bare metal. The means
                       of composition are TCP and UDP network connections
                       between containers, possibly facilitated by some
                       kind of network fabric. In contrast, in Spiffy-
                       Wasm-Cloud we aren’t starting from the kernel ABI,
                       with processes and such: instead there’s WASI,
                       which is more of a kind of specialized and limited
                       libc. You can’t just drop in your database binary,
                       you have to write code to get it to conform to the
                       new interfaces.


                # ⚓ FSF ☛ August_GNU_spotlight_with_Amin_Bandali:_12_new_GNU
                  releases⠀⇛


                # ⚓ KDAB ☛ KDChart_3.0.0_Released_–_KDAB⠀⇛


                       We just released KDChart version 3.0.0!


                       KDChart is a comprehensive business charting
                       package with many different chart types and a large
                       number of customization options. We are constantly
                       improving the package, and have been doing so for
                       years.


                       This is the first release of KDChart that supports
                       Qt 6, and both Qt 5 and Qt 6 can be co-installed.


                       And get this: KDChart 3.0.0 is completely free!
                       We’ve relicensed KDChart from the GPL to the MIT
                       license and removed our commercial offering. This
                       means that you can use it as you want without
                       license restrictions. Find out more about the MIT
                       license, here.


                # § PHP⠀➾


                      # ⚓ Remi_Collet:_PHP_version_8.0.23_and_8.1.10⠀⇛


                             RPMs of PHP version 8.1.10 are available in
                             remi-modular repository for Fedora ≥ 34 and
                             Enterprise Linux ≥ 8 (RHEL, Alma, CentOS,
                             Rocky…) and in remi-php81 repository for EL
                             7.


                             RPMs of PHP version 8.0.23 are available in
                             remi-modular repository for Fedora ≥ 34 and
                             Enterprise Linux ≥ 8 (RHEL, Alma, CentOS,
                             Rocky…) and in remi-php80 repository for EL
                             7.


                # § C⠀➾


                      # ⚓ Paul E. McKenney ☛ Confessions_of_a_Recovering
                        Proprietary_Programmer,_Part_XIX:_Concurrent
                        Computational_Models_–_Paul_E._McKenney’s_Journal_—
                        LiveJournal⠀⇛


                             The September 2022 issue of the
                             Communications of the ACM features an
                             entertaining pair of point/counterpoint
                             articles, with William Dally advocating for
                             concurrent computational models that more
                             accurately model both energy costs and
                             latency here and Uzi Vishkin advocating for
                             incremental modifications to the existing
                             Parallel Random Access Machine (PRAM) model
                             here. Some cynics might summarize Dally’s
                             article as “please develop software that
                             makes better use of our hardware so that we
                             can sell you more hardware” while other
                             cynics might summarize Vishkin’s article as
                             “please keep funding our research project“.
                             In contrast, I claim that both articles are
                             worth a deeper look. The next section looks
                             at Dally’s article, the section after that at
                             Vishkin’s article, followed by discussion.


                             TL;DR: In complete consonance with a
                             depressingly large fraction of 21st-century
                             discourse, they are talking right past each
                             other.


          o § Standards/Consortia⠀➾


                # ⚓ IBM Old Timer ☛ Irving_Wladawsky-Berger:_Web3:_The_Promise
                  of_a_Blockchain-Based_Internet_of_Value⠀⇛


                       On June 30, MIT hosted the Imagination in Action
                       Web3 Summit, an event jointly organized by MIT
                       Connection Science, Forbes, and Link Ventures. The
                       Summit brought together almost 600 developers,
                       entrepreneurs, investors, and academics to discuss
                       the present state and potential evolution of Web3.
                       The agenda featured a number of panels and talks.
                       Speakers included Alex (Sandy) Pentland, – MIT
                       professor and Connection Science Director, Michael
                       Federle, – CEO of Forbes, John Werner, – Managing
                       Director at Link Ventures, and Esther Dyson, –
                       investor, journalist, and philanthropist.


                       The MIT Summit is the first in a series of
                       Imagination in Action conferences. The next one
                       will take place on October 6 in San Francisco,
                       followed by one on January 17 at Davos, and back to
                       MIT in June of 2023. The summits aim “to take us
                       from reflections on the last major social and
                       economic transformation precipitated by the arrival
                       of the Internet era, to the economics to build and
                       the governance to sustain Web3,” as well as to
                       envision the possibilities of a Web3 future and to
                       try to discern hype from reality in these early
                       days of a potential new internet era.


                       I wasn’t able to attend the Summit in person, but I
                       watched the recordings of a number of the sessions,
                       where I heard a variety of opinions on what Web3 is
                       about. This is not surprising. In their early
                       years, major new technologies are generally
                       accompanied by a mixture of excitement, speculation
                       and confusion, as people sort out what the
                       technology might be about and how it’s likely to
                       evolve. Something important is going on out there,
                       but it takes time and marketplace experience to
                       sort things out.


    * § Leftovers⠀➾


          o § Hardware⠀➾


                # ⚓ The Next Platform ☛ GPU_Engines_Are_So_Strategic_China_Will
                  Have_To_Use_Its_Own⠀⇛


                       China is the world’s second largest economy, it has
                       the world’s largest population, and it is only a
                       matter of time before has a world-class technology
                       ecosystem spanning the smallest transistors to the
                       largest hyperscale and HPC systems. It simply has
                       enough money, and enough time, and enough smart
                       people, to get there.


                       But that does not mean that the United States wants
                       to make that transition for the Middle Kingdom an
                       easy one. And so, every now and then, export
                       controls and licenses are put into effect by the US
                       Department of Commerce to restrict the sale of
                       hardware, software, and other vital pieces of
                       technology to China. And even before it was waging
                       war against Ukraine, sales of technology to Russia
                       were also restricted.


          o § Misinformation from Microsoft/Linux Foundation⠀➾


                # ⚓ Bleeping Computer ☛ New_ransomware_hits_Windows,_Linux
                  servers_of_Chile_govt_agency [Ed: This targets VMware
                  (proprietary) and Microsoft (proprietary), not "Linux"; this
                  Microsoft-connected site does not want to tell it like it
                  is]⠀⇛


                       The attack started on Thursday, August 25,
                       targeting Microsoft and VMware ESXi servers
                       operated by the agency.


                       [...]


                       Conti [Windows] has been previously linked to
                       attacks on entire nations, such as the one on Costa
                       Rica in July 2022, which took five days from
                       gaining initial access to stealing and encrypting
                       the systems.


                # ⚓ Linux Foundation’s Site/Blog ☛ Addressing_Cybersecurity
                  Challenges_in_Open_Source_Software:_What_you_need_to_know
                  [Ed: Linux_Foundation’s_New_Cybersecurity_Report_Made_Using
                  Proprietary_Software_for_Microsoft_Partners_Under_the_Guise
                  of_‘Research’]⠀⇛


                       June 2022 saw the publication of Addressing
                       Cybersecurity Challenges in Open Source Software, a
                       joint research initiative launched by the Open
                       Source Security Foundation in collaboration with
                       Linux Foundation Research and Snyk. The research
                       dives into security concerns in the open source
                       ecosystem. If you haven’t read it, this article
                       will give you the report’s who, what, and why,
                       summarizing its key takeaways so that it can be
                       relevant to you or your organization.


          o § Entrapment (Microsoft GitHub)⠀➾


                # ⚓ TechRadar ☛ Dodgy_Microsoft_Azure_update_knocks_Ubuntu_VMs
                  offline [Ed: Microsoft systemd; Microsoft: even when our own
                  broken stuff breaks down we blame "Linux"]⠀⇛


                # ⚓ Microsoft_to_Use_the_Mariner_Linux_Distro_Exclusively_for
                  Its_Xbox_Storefronts [Ed: Microsofters love to pretend
                  Microsoft 'owns' Linux]⠀⇛


          o § Security⠀➾


                # ⚓ LWN ☛ Security_updates_for_Thursday_[LWN.net]⠀⇛


                       Security updates have been issued by Fedora (pdns-
                       recursor, thunderbird, and vim), Gentoo (firefox,
                       thunderbird-bin, virtualbox, and webkit-gtk), Red
                       Hat (convert2rhel), SUSE (gstreamer-plugins-good,
                       open-vm-tools, postgresql12, rsync, and ucode-
                       intel), and Ubuntu (linux-azure, linux-gcp, linux-
                       hwe).


                # ⚓ ‘Dirty_Cred’_security_patched_kernels_available⠀⇛


                       All users that use any 5.10, 4.19 and 4.9 kernels
                       are strongly advised to upgrade to the latest
                       versions in the antiX repos. This applies to 64 bit
                       and 32 bit pae and non-pae kernels for antiX-19,
                       antiX-21 and testing/sid users.


                # ⚓ ZDNet ☛ Linux_devices_‘increasingly’_under_attack_from
                  hackers,_warn_security_researchers [Ed: ZDNet is, as usual,
                  helping Microsofters and their partners distract from the
                  real culprit, which moreover has NSA back doors]⠀⇛


                # ⚓ Bruce Schneier ☛ Clever_Phishing_Scam_Uses_Legitimate
                  PayPal_Messages_–_Schneier_on_Security⠀⇛


                       Basically, the scammers use the PayPal invoicing
                       system to send the email. The email lists a phone
                       number to dispute the charge, which is not PayPal
                       and quickly turns into a request to download and
                       install a remote-access tool.


                # ⚓ CISA ☛ CISA_releases_two_Industrial_Control_Systems
                  Advisories_|_CISA⠀⇛


                       CISA has released two Industrial Control Systems
                       (ICS) advisories on September 01, 2022. These
                       advisories provide timely information about current
                       security issues, vulnerabilities, and exploits
                       surrounding ICS.


                # ⚓ CISA ☛ Apple_Releases_Security_Updates_for_Multiple
                  Products_|_CISA⠀⇛


                       Exploitation of this vulnerability could allow an
                       attacker to take control of affected device.


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ Public Knowledge ☛ New_Public_Knowledge_Paper
                        Emphasizes_That_New_Copyright_Protection_Measures
                        Require_Consensus_–_Public_Knowledge⠀⇛


                             Today, we’re happy to announce our newest
                             white paper, “Consensus, Not Command: A
                             Smarter Approach to Standard Technical
                             Measures,” by Public Knowledge Policy Counsel
                             Nicholas P. Garcia.


                             The paper explores a little-known facet of
                             the Digital Millennium Copyright Act, or
                             DMCA, that outlines a voluntary and
                             consensus-driven process for adopting
                             “standard technical measures,” or STMs, that
                             enable copyright identification and
                             enforcement. Codified at Section 512(i) of
                             Title 17, this law has been in place for
                             almost 25 years. Through the inclusive and
                             multistakeholder approach in this law, no
                             technical measure has ever garnered the broad
                             consensus needed to become standard under
                             this section, and for good reasons. The paper
                             examines the technological, legal, and
                             economic factors that have weighed against
                             STMs and highlights the success of the
                             current decision-making model in avoiding
                             impractical, costly, and harmful technology
                             mandates.


                      # ⚓ The_JCPA_Hasn’t_Improved_with_Age_–_Disruptive
                        Competition_Project⠀⇛


                             After an initial introduction in 2018 and
                             reintroduction in March 2021, Congressional
                             sponsors released the revised version of S.
                             673, the Journalism Competition and
                             Preservation Act (“JCPA”) on August 23, 2022.
                             What began as an effort to give journalism
                             organizations an antitrust “get-out-of-jail-
                             free” card has morphed into a vast link-tax-
                             and-spend scheme under which leading digital
                             services would be compelled to distribute and
                             subsidize online content publishers, at
                             prices set by a government-mandated panel of
                             arbitrators.


                             There are numerous reasons why this effort is
                             misguided. First, it is constitutionally
                             unsound in multiple ways. Second, it
                             prohibits content moderation practices that
                             are used to remove hate speech and fight
                             misinformation online. Third, the bill runs
                             afoul of existing U.S. copyright law, with a
                             ‘savings clause’ too narrow to save anything.
                             Fourth, the JCPA remixes two failed 20th
                             century competition policies: it grants a
                             special interest antitrust exemption in a
                             government-guided effort to make prices
                             subjectively “fair”. Yet, antitrust
                             exemptions have historically fallen flat,
                             including one specifically given to
                             journalism producers, and the government’s
                             New Deal foray in “fairness” regulation for
                             pricing is widely regarded as a disaster.
                             Finally, national and international
                             experience shows that special treatment for
                             news publishers has done little for
                             independent journalists and instead resulted
                             in government-mandated negotiations
                             controlled by large and influential
                             publishers. Each of these problems are
                             discussed below.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Re:_Spending_My_Own_Money_for_Office_Comfort⠀⇛


                       Tip: instead of thinking of the office as the place
                       where you sell your soul, think of it as free real
                       estate and make it as nice for yourself as you can!


                # ⚓ Reporting_from_procastinationland⠀⇛


                       I have always been a procrastinator. But each time,
                       the deadline would get closer, and I would
                       eventually do the thing in time, usually being
                       satisfied with the end product. But this time it
                       feels different, the rut that I am in seems
                       inescapable. Most of my time is spent stressing
                       over the fact that I am not working on my master’s
                       thesis, but also feeling paralyzed, unable to start
                       the work.


                       I have tried many things, and was able to get some
                       things done, but I can’t seem to be able to get
                       into the rhytm of research. I tried pomodoros, they
                       sort of work sometimes, but they don’t allow me to
                       really get into reading, I feel that stopping after
                       25 minutes interrupts the flow and “removes” me
                       from the text in a way that makes it harder to get
                       back into, and also to understand the big picture.
                       I tried going to the library instead of staying at
                       home, which again, works, but for some reason, I
                       tire much faster there, and cannot get as much work
                       done as I would at home. I have divided my tasks
                       into smaller sections, but they are still daunting.
                       Thinking about the thesis makes me anxious.


                       [...]


                       I am sending this message out to you, nice people
                       of Gemini, in the hopes that someone might have a
                       suggestion on how to beat this. Thank you for
                       reading.


                # ⚓ Beetles_in_Pennsylvania_39⠀⇛


                       The other day I had the idea to use a bip39
                       mnemonic seed in a poem. It would be the perfect
                       place to hide it, right? But you’d have to be a
                       really good poet in order to make it make sense.


                       No one would know which words to use other than
                       you, and you can hide it in plain sight! No need to
                       worry about others seeing it, and you can use
                       something like archive.org to make sure you don’t
                       lose it. And since bip39 produces a seed rather
                       than a single key, you could use the seed for all
                       your keys! I don’t really know if that’s a security
                       risk or not…


                       Due to my terrible creative writing, I will not be
                       attempting this.


                # ⚓ HIKMNTS_Wordo:_VAPES⠀⇛


          o § Finance⠀➾


                # ⚓ Budgeting_Strategy⠀⇛


                       I have a problem with impulsive spending when it
                       comes to credit cards. I understand that the
                       temptation of having easy access to credit is the
                       whole point of them, from a capitalist perspective.
                       Losing track of my credit balance and racking up a
                       ton of debt is as easy as just *not* checking the
                       balance, which is something I excel at.


          o § Technical⠀➾


                # ⚓ Zero_Copy_OpenCL_Buffers⠀⇛


                       This is another subject that is complicated to
                       explain. But is crucial to understand to write
                       efficient code. Especially on embedded systems and
                       integrated GPUs. I explained this with my coworkers
                       recently. I figure to write it down as a reminder.
                       This post mostly references Intel’s article on
                       minimizing memory copy[1] and AMD’s ROCm OpenCL
                       optimization guide[2].


                # ⚓ Being_Offline⠀⇛


                       Over that last couple of years I’ve gone more and
                       more offline. And by offline, I mean I’m growing
                       more disconnected from internet culture. It’s been
                       a big change, and definitely for the better.


                       For most of my 20′s I was one of the more ‘online’
                       people in my circle. I knew what the latest memes
                       were, what was trending on Reddit and Twitter, and
                       was just glued to social media feeds all day.


                       However, the thing that I was most aware of on any
                       given day, and the thing that ultimately pushed me
                       to disconnecting, was what the internet was mad
                       about at that time. And not just what they were mad
                       about, but what every influencer, celebrity, and
                       viral tweet had to say about said thing.


                # § Internet/Gemini⠀➾


                      # ⚓ Announcing_ROOPHLOCH_2022⠀⇛


                             Long time no see, Gopherspace!


                             September is here again, bringing with it not
                             only the hope of lower


                             temperatures for those of us suffering
                             through recent heatwaves, but


                             also the fourth installment of the annual
                             Remote Outdoor Off-grid


                             Phlogging Challenge, ROOPHLOCH 2022!


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


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