𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, September 15, 2022
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Generated Fri 16 Sep 02:43:24 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/2022/09/15/


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

QmZeoDeQynAEb5Yhp8urADxooTvcjp93jYM7aoGTReoxAm
QmUR5BqkVtBjeM3RbDysVaCrQyP93xoRwDKU5C1u5XZdyR
QmS9E4XW4XZrtmFNP12pX65zisQkFTw7frAgGwhna5Fz9m
Qmdj75rdsbiWjm4ms8CTMfcbYno6Pw9hH66AytZ3Hs3qV7
QmWKkufDr5sMvj78wx9nn63R5KYSQipfAGMrMawgr7i6RW
QmVy1ihFnjMRS9u243rmwceZUtn8FwSqLsbXzXsLPS8M37
QmcZN6RDP7J7Dk8c2QYXeoVfYifxDsaK62EM44gSje2HDr
QmcvJBJvcdzE6YbN5kUFP3Cqgwc9K38gcNKU3B86eL6WLr
QmUZ8Zpgu5W6CLgXAAXnvYwpAw9fCGWhqWM6MWMHcNxEwP
QmUtqYa5g8brBCgtMeneus47sgXJXCdgZvkekvW8UuYchF
QmdXKq8frFc6SxT7BErqJC3fnDsbXQfhNmEGEc1BVWprrQ
QmWERMsn1DfZrtyJQLRpzrUSCM3So8WboRGV5qBDKU6pKo
QmeWggouo6JzSCSNPBkF9EbHtca8pg2uefQDca6Z63NbCy
QmPd8eLQ2K4AVwUwwDXWDzcs9Y6q6rEafAqGPGCsRaNu1n
QmfCsH16QBNTRxCFWkRbN8iKEXme1kZFksZvXhwcAkGbv1
QmbPTxQodgGofF9SkH91qnwS4xfGFrHEdPESATQe3KmLup
QmVuPxmX77pHLEiaxQUdUu9Hv2c5on5vmDiepeKvhokhrK
QmSSVivjsb74DwAwvNFUWiXAExS8esEHiJBzykMK9Da4BW
QmYr91F9jQ6C4UgdRQqHE5QbcXGHYUcZYCYnigDogJGkyy
QmVMkxTFB9LnSNGEQQ9wHzrmgcc9R1GBBrkXQwesnZn9sF
QmVp5xT7mzD29ygLxoepcfrYB5u4Vyc9cndBz66AV7cb69


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

⦿ GNU Turns 39 Later This Month and It’s Still Going! | Techrights

⦿ IRC Proceedings: Wednesday, September 14, 2022 | Techrights

⦿ Night Colour in KDE: Small New Feature, Potentially Valuable in This ’Crisis Mode’ Era | Techrights

⦿ [Meme] The Big News is That Big Blue Has Driven Away Tons of Essential Engineers and Managers of Red Hat | Techrights

⦿ Our Static Page Generator in Action: Early Incarnation With Image Support | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/09/15/gnu-39/#comments
		http://techrights.org/2022/09/15/irc-log-140922/#comments
		http://techrights.org/2022/09/15/kde-night-color/#comments
		http://techrights.org/2022/09/15/losing-critical-engineers/#comments
		http://techrights.org/2022/09/15/staging-new-techrights/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/09/15/libadwaita-1-2/#comments
		http://techrights.org/2022/09/15/libreoffice-7-4-1/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 60

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/15/gnu-39/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/15/gnu-39/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ GNU_Turns_39_Later_This_Month_and_It’s_Still_Going!⠀✐


Posted in Deception, Free/Libre_Software, GNU/Linux at 8:42 pm by Dr. Roy
Schestowitz


It has survived all sorts of attacks (on the licence, the founder, the
platform/tools etc.)


                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇bison-being-hit⦈_


                          🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇gnu-39⦈_


Summary: Get ready for another GNU anniversary (11 days from now)); the Linux
Foundation does not want people to know what GNU is and how the GPL works (it
actively works to undermine both)


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

                    ䷩ 𝚕𝚒𝚗𝚎 1247

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/15/irc-log-140922/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/15/irc-log-140922/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Wednesday,_September_14,_2022⠀✐


Posted in IRC_Logs at 2:17 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-140922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-140922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-140922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-140922.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
 QmdPcdAzYcwBjsmXHEovRcq9Q2uRXhW1eFcJ8TVeHpMqd5 #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmVUpRc8wbcoZuAmBY8s5vy2X5pL5CFFkPMa7wNBdiKRS4 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmbSWfLLNtPEdBBCtMeQ4UaarJ281WtNjbU7G6hJqQzjZi social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmSCdzB6QEn3hDwSRymHEGc6yUK5Q7XvQZJFNPVuc4AhXh social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmeDMKusc6i8jr2NvdowPjGvAY3YFumacFZ1MJFJbgzcDM #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmdWaoNmAfaqe87TtQKXLoXtz4xsmJDjwq33ZjGwxpXQzH (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmSMHw2N8mUH1TkvyzFm5fDdqLNFcoH39tx7aeMYVYqhV5 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmbvkBWPaB31uhLN2kxArdy3CeHBQUCUmAxz3QuDtWR4cw (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmVp5xT7mzD29ygLxoepcfrYB5u4Vyc9cndBz66AV7cb69



                    ䷩ 𝚕𝚒𝚗𝚎 1374

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/15/kde-night-color/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/15/kde-night-color/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Night_Colour_in_KDE:_Small_New_Feature,_Potentially_Valuable_in_This_‘Crisis
Mode’_Era⠀✐


Posted in GNU/Linux, KDE at 9:23 am by Dr. Roy Schestowitz


Video_download_link | md5sum 2a337fd2dd58bd8021c8db928783306b
KDE’s Night Colour Mode
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/kde-night-colour.webm


Summary: KDE has made it easier to change contrast/brightness/colours
overnight; the above video shows all the existing options (available in
experimental builds)


THESE days it has become fashionable to discuss how to lessen the burden of
bills. Here in the UK, for instance, lowering brightness on a monitor can save
quite a few pounds per month (certainly when dealing with multiple monitors;
here we have 11). Powering them off is an option, but not when you actually
wish to use them.


“This will probably roll out to more KDE/Plasma-based distros, turned on by
default (or available in the panel by default), over time.”Months ago I started
turning off the monitors whilst away from keyboard (afk) in order to save
energy — or rather to lower our power bills. Working at night when there’s
sufficient contrast (ambiance late at night) is very common for home workers.
There’s some science regarding nocturnal computer work and the brightness
impacts sleepiness (or potentially one’s health). I’ve long been reading about
all those colour shifts, but usually those aren’t built into the desktop
environment — until now!


The above shows KDE’s (Plasma) implementation, which can be found lurking
around in recent builds of KDE Neon.


It should be noted, as a post-mortem-ish, upon recording and after recording I
realised that screen capture in OBS does not capture the colour shifts, but
that’s OK. It’s mostly about demonstrating the existing options and controls.
These will probably evolve over time. Unlike some other new features or
changes, in this one I’ve not found any bugs yet (nothing fatal anyway). This
will probably roll out to more KDE/Plasma-based distros, turned on by default
(or available in the panel by default), over time. █



                    ䷩ 𝚕𝚒𝚗𝚎 1439

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/15/losing-critical-engineers/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/15/losing-critical-engineers/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_The_Big_News_is_That_Big_Blue_Has_Driven_Away_Tons_of_Essential
Engineers_and_Managers_of_Red_Hat⠀✐


Posted in Free/Libre_Software, IBM, Microsoft, Red_Hat at 11:05 am by Dr. Roy
Schestowitz


Big Blue (IBM) has successfully crushed CentOS and Fedora (still_ongoing); but
the real news or the untold story is, many top managers have fled the company,
as did high-profile engineers (3 CEOs in 3 years, new managers came from
Microsoft, brain drain aplenty)


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Remote working: Red Hat tells staff they don't have to
                            return to the office⦈
Some cannot and will not return; they quit or got_fired (lots of them, even the
                            “chief people officer”)


Summary: The above story from a Microsoft media operative in a_Microsoft-_and
IBM-funded site distracts from the simple fact that there’s a longstanding HR
crisis at Red Hat; we wrote about it over the years and salaried IBM staff
actively tried to suppress links to our writings


To some extent, the relentless_attacks_from_IBM/Microsoft against Free software
have driven away talented technical staff that cared about Software Freedom. Is
IBM trying to dissolve what it bought?


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


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

                    ䷩ 𝚕𝚒𝚗𝚎 2427

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/15/staging-new-techrights/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/15/staging-new-techrights/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Our_Static_Page_Generator_in_Action:_Early_Incarnation_With_Image_Support⠀✐


Posted in Site_News at 10:27 am by Dr. Roy Schestowitz


Video_download_link | md5sum 9f82b77961c381c0399b85dc91d26a27
New Static Page Generator
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/new-cms-tuxmachines-staging.webm


Summary: What the future of this site might look like, at least in sections
that shall be managed without a bloated/cluttered front end and a bloated back
end (with or without caching) that are a burden to maintain


THE version of WordPress that we love will run out of support (as in, security
patches) some time soon, as per this_statement_from_eight_days_ago. We've
already_explained_(nearly_a_decade_ago!)_why_we_won't_upgrade_to_future
branches. We’re sure some people will offer unofficial patches, backported to
plug very critical holes. But such patches are risky and unpredictable. They’re
not a long-term solution but a temporary lifeline.


Back in July we started working on our own Content Management System (CMS) or
Static Page Generator. It was deployed to Tux Machines later in the same month
(as “testing”) and went “live” last month. We’re hoping to do the same with
Techrights, but there’s no timeline/deadline set in stone. Probably some time
this coming winter. We’re currently working on the search facility, followed by
basic stuff like archiving. The CMS already supports 3 or 4 different
protocols, not just HTTP/S. Because it is very simple and lightweight (written
mostly in Bash and Perl, plus peripheral libraries) it’s very simple to shape
it into something we want and need, not something that the parent companies of
WordPress and Drupal are pursuing (mostly for business reasons).


The video above demonstrates how new pages are added, updated, and how images
get added to them. It’s not as hard as it looks; it just takes some training to
get into the habit. Debugging is simpler due to the elegance and simplicity of
the system. At the back end there’s one SQLite database, but it’s not accessed
by anyone except administrators, who can use it to generate and regenerate
existing pages. In terms of performance, it’s an amazing improvement over what
we had (more than an order of magnitude) and it runs on a very thin distro
called Alpine Linux. █



                    ䷩ 𝚕𝚒𝚗𝚎 2490

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_15/09/2022:_Libadwaita_1.2_and_Godot_4.0_Reaches_Beta⠀✐


Posted in News_Roundup at 5:55 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Kernel_and_Rust
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o PCLinuxOS
          o SUSE/OpenSUSE
          o Red_Hat_/_IBM
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Productivity_Software/LibreOffice/Calligra
          o Programming/Development
                # Python
    * Leftovers
          o Linux_Foundation
          o Security
          o Civil_Rights/Policing
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
                # Announcements
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ MakeTech Easier ☛ 4_Ways_to_Increase_the_Battery_Life_of
                  Your_Linux_Laptop⠀⇛


                       
                       Linux laptops are known for their high performance
                       and smooth graphics in decently powered devices.
                       But this performance oriented behavior of Linux
                       comes with the cost of battery life of the laptop
                       in comparison to windows counterpart. Recent
                       development of Linux kernel take into account the
                       poor battery life issue and new laptop/desktop
                       oriented distributions like PopOs comes with
                       battery optimization out of the box.


                       Here, we are discussing top 5 ways to increase
                       battery life in Linux laptops. After reading this
                       article, you can surely choose whatever is the best
                       for you and squeeze up more juice from your
                       battery.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Venom_Linux_4.0_overview_|_A_lightweight_source
                  based_distro_for_advanced_Linux_Users_–_Invidious⠀⇛


                       In this video, I am going to show an overview of
                       Venom Linux 4.0 and some of the applications pre-
                       installed.


                # ⚓ Full_Circle_Magazine:_Full_Circle_Weekly_News_#278⠀⇛


                       Based on Sway, a port of LXQt is being developed:


                       https://cartaslinux.wordpress.com/2022/08/28/lxqt-
                       sway-usando-lxqt-para-hacer-que-sway-sea-mas-
                       amigable/


                       Fedora Linux 39 plans to disable SHA-1-based
                       signatures support by default:


                       https://www.mail-archive.com/devel-
                       announce@lists.fedoraproject.org/msg02882.html


                       Apache OpenOffice passed 333 million downloads:


                       https://blogs.apache.org/OOo/entry/more-than-333-
                       million-downloads


                       Release of the QEMU 7.1:


                       https://lists.nongnu.org/archive/html/qemu-devel/
                       2022-08/msg04598.html


                       Armbian 22.08:


                       https://www.armbian.com/newsflash/armbian-22-08/


                       Release of Ubuntu 20.04.5 LTS with graphical stack
                       and kernel update:


                       https://lists.ubuntu.com/archives/ubuntu-announce/
                       2022-September/000283.html


                       Linux From Scratch 11.2 and Beyond Linux From
                       Scratch 11.2:


                       https://lists.linuxfromscratch.org/sympa/arc/lfs-
                       announce/2022-09/msg00000.html


                       Release of the OBS Studio 28.0:


                       https://github.com/obsproject/obs-studio/releases/
                       tag/28.0.0


                       Release of Nmap 7.93, timed to the 25th anniversary
                       of the project:


                       https://seclists.org/nmap-announce/2022/1


                       The webOS Open Source Edition 2.18:


                       https://www.webosose.org/blog/2022/09/02/webos-ose-
                       2-18-0-release/


                       Release of Nitrux 2.4:


                       https://nxos.org/changelog/release-announcement-
                       nitrux-2-4-0/


                       Google Open Source Software Vulnerability Rewards
                       Program:


                       https://security.googleblog.com/2023/08/Announcing-
                       Googles-Open-Source-Software-Vulnerability-Rewards-
                       Program%20.html


                       Peter Eckersley, co-founder of Let’s Encrypt,
                       passed away:


                       https://community.letsencrypt.org/t/peter-
                       eckersley-may-his-memory-be-a-blessing/183854


                       The platform code for Notesnook, has been opened:


                       https://blog.notesnook.com/notesnook-is-going-open-
                       source/


                # ⚓ Video ☛ Enterprise_Linux_Security_Episode_42_–_Do_NOT_Fire
                  Your_Security_Team!_–_Invidious⠀⇛


                       Recent news of Patreon firing their security team
                       is making the rounds online, and in this episode,
                       Jay and Joao will talk about this very strange
                       story and some takeaways from it. This is a
                       developing story as of the day this was recorded,
                       so expect to hear more about this in the near
                       future.


                # ⚓ Video ☛ The_cat_Command_in_Linux_(Featuring_Real_Cats)_–
                  Linux_Crash_Course_Series_–_Invidious⠀⇛


                       In the Linux Crash Course series, we’ll go over one
                       important foundational Linux topic each episode.
                       This series includes tutorials, demonstrations, and
                       more! In this episode, Jay will go over the basics
                       of the cat command.


                # ⚓ Video ☛ EndeavourOS_22.9_Run_Through_–_Invidious⠀⇛


                       In this video, we are looking at EndeavourOS 22.9.


                # ⚓ Linux Made Simple ☛ EndeavourOS_22.9⠀⇛


                       Today we are looking at EndeavourOS 22.9, the KDE
                       Plasma edition. It comes with KDE Plasma 5.25.5,
                       Linux kernel 5.19, and uses about 900MB of ram when
                       idling.


                # ⚓ Video ☛ Was_Grub_On_Arch_Linux_Really_That_Bad?_–
                  Invidious⠀⇛


                       Recently Grub went through some pretty serious
                       issues on Arch and Arch based distros causing boot
                       loops and such but was the problem really that bad
                       looking back in hindsight.


                # ⚓ Video ☛ Fedora_37_Beta_and_GNOME_Shell_mobile_–_Linux_and
                  open_source_News_–_Invidious⠀⇛


                # ⚓ Jupiter Broadcasting ☛ 258:_Linux_Action_News⠀⇛


                       The Linux Foundation takes a victory lap, Google
                       kills another community-loved project, and key
                       moments from the Linux Plumbers Conference.


                # ⚓ The BSD Now Podcast ☛ BSD_Now_472:_Consistent_Exit_Code⠀⇛


                       FreeBSD on the Framework Laptop, Win32 is the only
                       stable ABI on Linux, why OpenBSD’s documentation is
                       so good, configure dma for mail delivery in jails
                       on internet hosts, introducing muxfs, RAID1C boot
                       support, and more


          o § Kernel and Rust⠀➾


                # ⚓ LWN ☛ Linux_5.19.9⠀⇛


                       I'm announcing the release of the 5.19.9 kernel.


                       All users of the 5.19 kernel series must upgrade.


                       The updated 5.19.y git tree can be found at:
                               git://git.kernel.org/pub/scm/linux/kernel/
                       git/stable/linux-stable.git linux-5.19.y
                       and can be browsed at the normal kernel.org git web
                       browser:

                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s...

                       thanks,


                       greg k-h
                # ⚓ LWN ☛ Linux_5.15.68⠀⇛


                # ⚓ LWN ☛ Linux_5.10.143⠀⇛


                # ⚓ LWN ☛ Linux_5.4.213⠀⇛


                # ⚓ LWN ☛ Linux_4.19.258⠀⇛


                # ⚓ LWN ☛ Linux_4.14.293⠀⇛


                # ⚓ LWN ☛ Linux_4.9.328⠀⇛


                # ⚓ Its FOSS ☛ Wow!_Torvalds_Modified_Fedora_Linux_to_Run_on
                  his_Apple_M2_Macbook⠀⇛


                       Linus Torvalds likes to build and fix things. Of
                       course, he has the technical expertise to tinker
                       with various things.


                       Not a surprise if you know that he created Linux as
                       a clone of UNIX from scratch because he could not
                       afford a UNIX system.


                       For a similar reason, he also built Git after
                       BitKeeper was no longer free to use.


                       He continues his tinkerer spirit and the ‘i can fix
                       that’ attitude even today.


                       He managed to run Fedora Linux 36 Workstation
                       edition on his Apple Macbook Air M2.


                # ⚓ TechHQ ☛ Rust’s_implementation_in_the_Linux_kernel_to
                  appear_in_version_6.1⠀⇛


                       Speaking at the Linux Foundation’s Open Source
                       Summit in Dublin, Linus Torvalds, the creator of
                       the Linux kernel (and the Git version control
                       system), confirmed that the new hotness in computer
                       programming languages, Rust, would be included “to
                       a small extent” in the next-but-one kernel release,
                       slated to be 6.1. He also reiterated that the
                       kernel’s version numbers bore more relation to his
                       own inability to differentiate versions in his own
                       mind than it did to the scale of changes in point
                       or full-version nomenclature. Version 6.0,
                       therefore, will not be an especially noteworthy
                       release, despite the rollover from versions 5.19 to
                       6.0.


                # ⚓ ZDNet ☛ Linus_Torvalds:_Rust_may_make_it_into_the_next
                  Linux_kernel_after_all_|_ZDNET⠀⇛


                       As they do at almost every Open Source Summit, Dirk
                       Hohndel, chief open source officer at the Cardano
                       Foundation, and Linus Torvalds, Linux’s founder,
                       talked about all things Linux and the keynote
                       discussion at Open Source Summit Europe in Dublin
                       Thursday. Usually, it’s interesting, but there’s no
                       breaking news. “Usually.” This time was different.
                       Torvalds announced that he would propose adding
                       Rust to the next Linux kernel, Linux 6.1, at the
                       Linux Kernel Maintainers Summit later today.


                # ⚓ Rust Weekly Updates ☛ This_Week_In_Rust:_This_Week_in_Rust
                  460⠀⇛


          o § Applications⠀➾


                # ⚓ Linux Hint ☛ 13_Best_Email_Clients_for_Ubuntu_in_2022⠀⇛


                       Earlier Ubuntu users had limited choices in terms
                       of applications available for Ubuntu. There are
                       still many users who prefer the desktop email
                       clients over browser-based email clients because
                       the desktop email clients offer features such as
                       work schedule, spam filters, etc. You can also make
                       customizations as per your need.


                       Also, managing emails across multiple accounts is
                       made easy by email clients. So, today, we are going
                       to have a quick look at the 13 best email clients
                       for Ubuntu that you can use for your daily work in
                       2022.


          o § Instructionals/Technical⠀➾


                # ⚓ ID Root ☛ How_To_Install_Signal_Messenger_on_Linux_Mint_21
                  –_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Signal Messenger on Linux Mint 21. For those of you
                       who didn’t know, Signal Messenger is a popular,
                       multi-platform application used for sending instant
                       messages, and making audio and video calls. If you
                       need to communicate securely but find it hard
                       because of the restrictions put on traditional
                       messaging apps like WhatsApp, Signal messenger is
                       one of the better forms of communication for those
                       that require the utmost privacy.


                       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 Signal Messenger on Linux Mint 21
                       (Vanessa).


                # ⚓ OSTechNix ☛ Prevent_Command_Arguments_With_Sudo_In_Linux_–
                  OSTechNix⠀⇛


                       In the previous article, we learned how to run
                       commands in a directory as root via sudo. In this
                       guide, we will see how to prevent command arguments
                       with sudo in Linux. Meaning – we allow an user to
                       run commands with sudo, but without command
                       arguments.


                # ⚓ HowTo Forge ☛ How_to_Install_and_Monitor_Servers_with
                  Checkmk_on_Ubuntu_22.04⠀⇛


                       Checkmk is a server and application monitoring
                       software written in Python and C++. It supports the
                       monitoring of servers, applications, networks,
                       containers, and clouds. It has a wide range of
                       features, including, automated monitoring,
                       agentless monitoring via HTTP/SNMP, over 1900
                       plugins to collect data, detailed network traffic
                       analysis, customizable dashboards, and Grafana
                       support.


                       Checkmk comes in four editions. The first version
                       is the open-source Raw edition and uses Nagios as
                       its core. The second version is the free version
                       which has all the features of the standard edition,
                       supports unlimited hosts for the first 30 days, and
                       afterward is limited to 25 hosts. The enterprise
                       standard edition and the enterprise-managed
                       editions are advanced versions with support for
                       unlimited hosts and multiple customers.


                       In this tutorial, you will learn how to install and
                       monitor servers using Checkmk on a Ubuntu 22.04
                       machine.


                # ⚓ HowTo Forge ☛ How_to_Install_JasperReports_with_Nginx_Proxy
                  on_Ubuntu_22.04⠀⇛


                       JasperReports is a free and open-source java
                       reporting engine and class library that helps
                       developers to add reporting capabilities to their
                       applications. It is a stand-alone and embeddable
                       reporting server that provides reporting and
                       analytics functionality. With JasperReports, you
                       can generate professional reports, including
                       images, charts, and graphs. This tool also helps
                       you to write rich content onto the screen, printer,
                       and several file formats. including HTML, PDF, XLS,
                       RTF, CSV, XML, ODT and TXT.


                       In this post, we will show you how to install
                       JasperReports Server on Ubuntu 22.04.


                # ⚓ RoseHosting ☛ How_to_Choose_the_Best_Linux_VPS_Hosting_for
                  Your_Website_–_RoseHosting [Ed: Rather spammy]⠀⇛


                       If you were to search for the “best Linux VPS,” you
                       would most likely just get even more confused with
                       all the industry jargon and tech-speak. What’s
                       more, over half of all VPS servers run on a Linux
                       system.


                       The biggest advantage of using a Linux system is
                       that it is free and open-source. This means that
                       hosting companies generally offer more affordable
                       VPS packages with greater flexibility. Another
                       major benefit is the significant security
                       improvement. This already makes Linux VPS an
                       attractive option for you.


                # ⚓ RoseHosting ☛ How_to_Install_NextCloud_on_Ubuntu_22.04_–
                  RoseHosting⠀⇛


                       In this blog post, we are going to explain step-by-
                       step how to install the latest NextCloud on Ubuntu
                       22.04.


                       NextCloud is an open-source cloud storage service
                       used to store, share, and sync data across multiple
                       devices. NextCloud storage software is written in
                       PHP and Javascript, which makes it very easy to
                       install. In this tutorial, we are going to install
                       and set up NextCloud with the LAMP stack.


                       Installation of NextCloud with the LAMP stack may
                       take up to 15 minutes. Let’s get things working!


                # ⚓ How_To_Install_VMware_On_Linux⠀⇛


                       Installing a hypervisor like VMware can seem
                       intimidating if you’ve never done it before, but in
                       truth, the process isn’t very different from
                       installing any other application. Much like program
                       installation, you must first ensure that certain
                       requirements are met, both in terms of specs and
                       compatibility.


                       The rest of the process is fairly straightforward,
                       but there are a few minor errors users often run
                       into along the way. As such, we’ve detailed the
                       full steps for installing VMware on various Linux
                       distributions and troubleshooting common issues
                       that you may encounter in the process.


                # ⚓ Make Use Of ☛ How_to_Fix_the_“unable_to_resolve_host”_Error
                  on_Linux⠀⇛


                       After changing the hostname on your Linux system,
                       you may encounter the error “unable to resolve
                       host”. Here’s what that means, and what you can do
                       to fix it.


                # ⚓ Make Use Of ☛ How_to_Check_and_Update_Your_Git_Version_on
                  Linux,_Mac,_and_Window⠀⇛


                       Wondering if your git command is as up-to-date as
                       you’d like? Look no further than this simple guide.


                       Git is a popular open-source version control system
                       that you use in your day-to-day workflow as a
                       developer. Like all other software, you need to
                       ensure you’re always using the latest version.


                       Find out how to check the Git version running on
                       your machine and how to update Git if you’re not
                       running the latest update.


                # ⚓ ZDNet ☛ How_to_use_the_handy_SSH_management_tool_in_Chrome
                  OS_|_ZDNET⠀⇛


                       Chrome OS has become quite the platform for users
                       of all types. Whether you’re a typical user who
                       spends most of your time within an operating system
                       browsing social media, writing ad hoc papers, and
                       shopping for the latest trends, or if you’re an
                       administrator who has to work on remote machines
                       throughout the day, Chrome OS has you covered.


                       One tool that I use quite a bit comes by way of
                       Linux. If you’ve already enabled Linux, you
                       understand that Chrome OS is much more than just a
                       web browser. With Linux support enabled, you can
                       install quite a large number of applications to
                       turn Chrome OS into a much more traditional OS.


                # ⚓ Google ☛ Chromium_Blog:_Speeding_up_Chrome_on_Android
                  Startup_with_Freeze_Dried_Tabs⠀⇛


                       We believe that “good enough” is never enough when
                       it comes to pushing the performance of Chrome.
                       Today’s The Fast and the Curious post explores how
                       we sped up the startup times of Chrome on Android
                       by more than 20% by providing an interactive
                       freeze-dried preview of a tab on startup. Read on
                       to see how the screenshot falls short, and freeze-
                       drying your tabs makes for a better browser.


                # ⚓ dwaves.de ☛ Another_genius_toner_saving_reset_howto_Brother
                  L_2370DW_Toner_Reset_Instructions⠀⇛


                       it is a factory-default unsustainable catastrophy
                       that should be forbidden by law:


                       to claim the toner is empty, when toner levels are
                       not even checked


                       but simply the amount of pages printed is counted


                       after x amount of pages, the brother (as many
                       others) printer reports “toner empty, replace”


                       when there might be still plenty of toner in the
                       cardrige


                # ⚓ Red Hat Official ☛ Kubernetes_troubleshooting:_6_ways_to
                  find_and_fix_issues_|_Enable_Sysadmin⠀⇛


                       Kubernetes is the most popular container
                       orchestration platform. It boasts a wide range of
                       functionalities including scaling, self-healing,
                       container orchestration, storage, secrets, and
                       more. The main issues with such a rich solution are
                       mostly due to its complexity. You must be aware of
                       many of its key features to use it adequately. I
                       will attempt to cover some of its less obvious
                       aspects to improve your experience while using
                       Kubernetes in production.


                # ⚓ Weaveworks_Adds_Progressive_Deployment_for_Kubernetes_–
                  Container_Journal⠀⇛


                       Weaveworks this week delivered an update to its
                       GitOps platform that enables application
                       development and deployment teams to progressively
                       deploy applications in a way that makes it simpler
                       to recover in the event there is an issue.


                # ⚓ Make Use Of ☛ How_to_SSH_Into_a_VirtualBox_Ubuntu_Server⠀⇛


                       Setting up virtual machine servers is quick and
                       easy. But is there a way to access your virtual
                       machines remotely using SSH?


                       Virtual machines provide engineers and admins with
                       a good platform to test software, set up IT
                       environments, and maximize the utilization of
                       server hardware resources.


                       VirtualBox is one of the most popular
                       virtualization software on the market today. It’s
                       open source and is packed with lots of nice
                       features. Let’s take a look at how to SSH into an
                       Ubuntu server or desktop running in VirtualBox.


          o § Games⠀➾


                # ⚓ Boiling Steam ☛ TGS_2022_Day_1_–_The_Steam_Deck_Booth_–
                  Boiling_Steam⠀⇛


                       Here’s a quick series of photos and videos of the
                       Steam Deck Booth that were shared online with the
                       first day of the Tokyo Games Show 2022 (aka TGS
                       2022) where the Steam Deck had a huge presence.


                       [...]


                       Below are pictures and a few videos taken by
                       Japanese gamers (press people) who tried out the
                       Steam Deck at the show.


                # ⚓ The_ubuntu.com,_or_Subnautica:_Here’s_Zero._Why_is_there_a
                  major_free_feature?_–_Game_News_24⠀⇛


                       This update has another big feature, Custom Game
                       Mode. A variety of new settings allow you to make
                       the most of the gameplay, including a length of day
                       and night, the frequency of heavy weather, the
                       damage that a player takes, the damage that a
                       person takes, the damage suffered by the predator,
                       the hostility of animals, and even the possibility
                       of a vegetarian diet. The newcomers should bring
                       more freedom and experiences with such situations
                       as Subnautica: Low Zero and veteran explorers need
                       more access. The new Unstuck button, conveniently
                       located in the pause menu, will also allow players
                       to teleport to the last safe place in case they get
                       stuck in tricky geometry.


                       Steam Cloud Save was restored, as well as a number
                       of fixes and optimizations allowing the game to
                       perform more smoothly than ever. With tons of
                       custom game options and new base building options,
                       now is the time to come in to build your new base
                       in Subnautica: below zero.


                # ⚓ Phoronix ☛ Cemu_2.0-2_Released_For_This_Open-Source,_Linux-
                  Supported_Wii_U_Emulator_–_Phoronix⠀⇛


                       The 2.0-2 update has various fixes, including
                       several Linux-specific fixes, some code refactoring
                       and clean-ups, and documentation improvements.


                # ⚓ Godot Engine ☛ Godot_Engine_–_The_next_big_step:_Godot_4.0
                  reaches_Beta⠀⇛


                       It has been a long road to Godot 4.0 with 17 alpha
                       builds distributed in 2022, and continuous
                       development effort since 2019. We aren’t done yet,
                       but today marks a major milestone on the road to
                       Godot 4.0.


                       Today we are pleased to announce that the first
                       beta for the much-anticipated release of Godot 4.0
                       is now ready and available for download. We know
                       that everyone is eager to get their hands on Godot
                       4.0 and this is a major step in getting there. Like
                       in previous release cycles, a beta release means
                       that we are happy with the features that have been
                       included and we don’t plan on adding any major new
                       features before release (except for a few that have
                       been discussed and planned in advance). The goal
                       between now and the stable release will be to
                       continue polishing the current feature set by
                       fixing bugs and optimizing performance.


                # ⚓ Boiling Steam ☛ How_to_Make_Your_Game_in_10_minutes_with
                  Godot_–_Extended_Version_–_Boiling_Steam⠀⇛


                       But there is so much I would like to cover that
                       would not fit in a short video, and some might
                       prefer a written guide.


                # ⚓ Make Use Of ☛ Work_and_Play:_How_to_Use_the_Steam_Deck_as_a
                  Desktop_Replacement⠀⇛


                       Run out of time for gaming? Don’t worry, you don’t
                       have to put your Steam Deck down. Here’s how to
                       switch to desktop mode and get some work done.


                       The Steam Deck is one of the most remarkable game
                       console releases in years, capable of running the
                       latest AAA games. It’s small and light enough for
                       you to take anywhere, and flexible enough for you
                       to hook up some additional controllers and connect
                       it to a TV for traditional console gaming.


                       Behind the user interface, the Steam Deck is
                       running a custom version of Arch Linux. As such, it
                       doesn’t take much effort to turn the Steam Deck
                       into a standard PC.


                       But could it replace your desktop?


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ 9to5Linux ☛ KDE_Plasma_5.26_Desktop_Environment
                        Enters_Public_Beta_Testing,_Here’s_What’s_New⠀⇛


                             Since this is a big update, you can imagine
                             that KDE Plasma 5.26 is packed with lots of
                             new features, starting with re-bindable mouse
                             buttons for multi-button mice to allow you to
                             assign buttons to keystrokes or keyboard
                             shortcuts, full screen reader support for all
                             Plasma widgets, as well as a new Compact mode
                             for the Kickoff applications menu that lets
                             you see more items.


                             However, the biggest new feature is Plasma
                             Bigscreen, a user interface for your TV
                             featuring the Aura Browser for navigating the
                             Internet using just the remote control of
                             your TV, as well as Plank Player as the
                             default multimedia player for playing local
                             files.


                      # ⚓ Liliputing ☛ KDE_Plasma_5.26_Beta_introduces_a
                        Bigscreen_view_for_Linux_apps_on_your_TV_–_Liliputing⠀⇛


                             The latest release of the KDE Plasma user
                             interface for Linux-based operating systems
                             brings a number of improvements including
                             easier previewing of desktop wallpapers,
                             support for animated wallpapers, and a number
                             of UI, navigation, and settings tweaks.


                             But the biggest change in KDE Plasma 5.26
                             Beta? There’s a new Plasma Bigscreen option
                             designed for TVs and other large displays.


                      # ⚓ Plasma_5.26_Beta_–_KDE_Community⠀⇛


                             Today we are bringing you the preview version
                             of KDE’s Plasma 5.26 release. Plasma 5.26
                             Beta is aimed at testers, developers, and
                             bug-hunters. As well as our lightweight and
                             feature rich Linux Desktop this release adds
                             a Bigscreen version of Plasma for use on
                             televisions.


                             To help KDE developers iron out bugs and
                             solve issues, install Plasma 5.26 Beta and
                             test run the features listed below. Please
                             report bugs to our bug tracker.


                             The final version of Plasma 5.26 will become
                             available for the general public on the 6th
                             of October.


                      # ⚓ OMG Ubuntu ☛ KDE_Plasma_Comes_to_the_Big_Screen_(Yes,
                        Your_TV)⠀⇛


                             If you’ve dreamed of being able to KDE Plasma
                             on your TV you’ll want to tune in to the work
                             going into KDE Plasma 5.26, which just hit
                             beta.


                             Why? Because the next major update to the
                             ‘cool’ desktop environment includes a new
                             mode designed to be used on TVs, monitor, and
                             other large display setups. It’s called
                             Plasma Bigscreen and is pitched as a
                             ‘privacy-respecting, open source and secure
                             TV ecosystem’.


                             And we’re not talking the regular Plasma
                             desktop stretched out to a squintfinity. No;
                             Plasma Bigscreen is has a specially designed
                             10 foot UI, ensuring everything shown on
                             screen is visible from afar (i.e. a couch)
                             with ease, as well as being navigable using
                             remote controls.


                      # ⚓ Make Use Of ☛ KDE_Makes_Play_for_Living_Room_With
                        Plasma_5.26_Beta⠀⇛


                             The beta version of the popular Linux desktop
                             includes a new interface for TVs called
                             Plasma Bigscreen. Will hardware makers
                             support it?


                             The developers of KDE have announced a
                             preview version of the KDE Plasma Linux
                             desktop version 5.26. The preview version
                             debuts a new interface for TVs dubbed
                             “Bigscreen.”


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ gnome-info-collect_closing_soon_–_Form_and_Function⠀⇛


                             There has been a fantastic response to gnome-
                             info-collect since Vojtěch announced it three
                             weeks ago. To date we’ve had over 2,200
                             responses. That’s amazing! Thanks to everyone
                             who has run the tool.


                             We now have enough data to perform the
                             analyses we want. As a result, it’s time to
                             close data collection. This will happen next
                             Monday, 19 September. On that day, the data
                             collection server will be turned off.


                      # ⚓ Libadwaita_1.2_–_Just_another_blog⠀⇛


                             So, half a year after 1.1, libadwaita 1.2 has
                             been released.


                             While it doesn’t contain everything I had
                             planned (since I ended up being mostly
                             unavailable for about half of the cycle for
                             reasons outside my control), it still has a
                             bunch of additions, so let’s take a look at
                             the changes.


    * § Distributions and Operating Systems⠀➾


          o § PCLinuxOS⠀➾


                # ⚓ PCLOS Official ☛ FreeFileSync_–_PCLinuxOS⠀⇛


                       FreeFileSync is a graphical folder comparison and
                       synchronization tool for Linux. Updated to version
                       11.25 and shipped to the software repository.


                # ⚓ PCLOS Official ☛ Filezilla_FTP_Client_–_PCLinuxOS⠀⇛


                       FileZilla is a fast and reliable FTP, FTPS and SFTP
                       client with lots of useful features and an
                       intuitive graphical user interface. Updated to
                       version 3.60.2.


                # ⚓ PCLOS Official ☛ Google_Chrome_Browser_–_PCLinuxOS⠀⇛


                       The Google Chrome Browser has been updated to
                       105.0.5195.125 and shipped to the software
                       repository.


                # ⚓ PCLOS Official ☛ Librewolf_Browser_–_PCLinuxOS⠀⇛


                       LibreWolf is designed to minimize data collection
                       and telemetry as much as possible. This is achieved
                       through hundreds of privacy/security/performance
                       settings and patches. Intrusive integrated addons
                       including updater, crashreporter, and pocket are
                       removed too. LibreWolf is NOT associated with
                       Mozilla or its products. Updated to version
                       104.0.2.


                # ⚓ PCLOS Official ☛ Evince_–_PCLinuxOS⠀⇛


                       Evince is the Document viewer. It supports PDF,
                       PostScript and other formats. To view .dvi files as
                       produced by TeX in evince, install the evince-dvi
                       package. Updated to version 42.3.


          o § SUSE/OpenSUSE⠀➾


                # ⚓ SUSE’s Corporate Blog ☛ SUSE_adds_security_automation
                  support_for_Kernel_Live_Patches⠀⇛


                       
                       SUSE has found that security automation is not
                       handling SUSEs kernel livepatches very well.


                       To understand the underlying problem and ways
                       toward a solution, lets first look at the
                       underlying concepts.


                       Kernel livepatching is a technology where functions
                       within a running Linux kernel are patched to fix
                       security issues, without rebooting or even stopping
                       the kernel. This allows uninterrupted use of
                       workloads over long times.


                       Kernel livepatches from SUSE are delivered as
                       loadable kernel modules that are delivered in RPMs
                       seperately from the kernel RPMs.


          o § Red Hat / IBM⠀➾


                # ⚓ Red Hat Official ☛ The_art_and_science_of_secure_open
                  source_software_development⠀⇛


                       Developing software with a greater security posture
                       adds an extra layer of complexity to this process,
                       however, something which not all developers
                       understand or are able to achieve. Open source can
                       help. Open source developers, security researchers
                       and auditors can see your code, spot potential
                       flaws and perhaps even help you make fixes.


                       This doesn’t mean that the developers are free to
                       write insecure software assuming people will
                       correct the flaws or errors for free—it actually
                       means that they now have a greater responsibility
                       to create high-quality code that is free of known
                       vulnerabilities.


                       Red Hat is in a unique position with respect to
                       software security and open source development. Many
                       of our offerings depend on upstream open source
                       projects. While Red Hat is directly involved in a
                       lot of important projects—either through upstream
                       developers who are Red Hat employees, or through
                       other forms of direct and indirect
                       contributions—there are some projects which are
                       wholly independent.


                # ⚓ 5_Years_of_Freedom_with_OpenPOWER_–_tobias_platen’s_blog⠀⇛


                       5 years ago I preorded my Talos II from Raptor
                       Computing Systems. The Talos II is a POWERful
                       system built from the ground up with freedom in
                       mind. In one of its PCIe 4.0 slots, I plugged an
                       AMD Radeon RX 5700 (Navi 10) which I mainly use for
                       playing VR games, but also for multi monitor
                       setups, faster video decoding and many more.
                       Unfortunately all modern graphics cards require
                       non-free firmware, but currently the libre-soc
                       project is developing an OpenPOWER hybrid CPU/VPU/
                       GPU that comes with its own Vulkan drivers.


                       [...]


                       Unlike a modern x86-64, such as the Steam Deck, the
                       Talos II can’t run Steam, so the is no way to play
                       VR games such as Beat Saber, Blade & Sorcery or
                       VRChat. Currenly I can only play the
                       godot4_openxr_demo using Monado and Libsurvice, but
                       I have begun doing a VR port of Minetest, a libre
                       clone of Minecraft and I am also trying to get
                       Godot Beep Saber VR working with my Valve Index
                       using Monado. Currently Beep Saber only works with
                       SteamVR and the Oculus Quest, both non-free
                       platforms incompatible with OpenPOWER systems.


                # ⚓ Red Hat Official ☛ Leveraging_the_Innovative_Optical_and
                  Wireless_Network_(IOWN)_reference_cases_for_core,_edge_and
                  cloud_deployments⠀⇛


                       The Innovative Optical and Wireless Network (IOWN)
                       Global Forum is developing next generation data-
                       centric infrastructure over all photonics networks
                       (APN), to help realize attractive use cases for AI
                       Integrated Communications(AIC) and Cyber-Physical
                       Systems (CPS). IOWN Global Forum’s approach will
                       have a strong influence on telecom, media and
                       entertainment and other industries in the green
                       transformation era.


                # ⚓ Red Hat Official ☛ The_art_and_science_of_secure_open
                  source_software_development⠀⇛


                       For many, writing a computer program isn’t that
                       hard—it simply requires a certain amount of
                       structural and logical thinking and a clear
                       understanding of the syntax of the language you are
                       using.


                # ⚓ IBM Old Timer ☛ Irving_Wladawsky-Berger:_The_Carnegie_Cloud
                  Governance_Project⠀⇛


                       Two years ago, the Carnegie Endowment launched the
                       Cloud Governance Project, a multi-year study on the
                       governance challenges associated with cloud
                       computing. “This project recognizes that the cloud
                       offers huge benefits for individuals,
                       organizations, and national economies through
                       greater IT convenience, flexibility, and cost
                       savings,” said the project’s website. “However, the
                       risks of a major disruption affecting cloud
                       services will invite regulation by governments at
                       the local, national, and international levels.
                       Moreover, as the world grows increasingly dependent
                       on the cloud, other aspects of the technology –
                       related to consumer protection, sustainability,
                       inclusiveness, and human rights – will also attract
                       scrutiny and regulation to protect or advance
                       public interests.”


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Its FOSS ☛ This_Flutter-based_Unofficial_Software_Center
                  Might_Replace_Ubuntu’s_Official_App⠀⇛


                       Ubuntu is often considered one of the best distros
                       for beginners, but the default software center
                       (GNOME Software Center) needs more polishing to
                       make it a pleasing experience.


                       Why? Well, it’s slow and heavy on resources, so
                       most users do not bother using it or just have a
                       bad time with it.


                       Yes, it may have improved over the years, but it is
                       still far from a good experience.


                       And it looks like contributors from Canonical, and
                       others have teamed up together to work on with a
                       lightweight, flutter-based alternative for the
                       Ubuntu software center!


                       Hold on, it is not an official replacement. But, I
                       wonder if it is meant to replace Ubuntu Software
                       Center soon?


                # ⚓ Ubuntu ☛ Ubuntu_Summit_—_Calling_All_Proposals⠀⇛


                       In case you haven’t heard the good news, the Ubuntu
                       Summit is a community-focused event taking place in
                       Prague, Czech Republic from November 7–9th!


                       The Ubuntu Summit Organising Committee would like
                       to bring your attention to our open Call For
                       Proposals. Until September 30th, we are open to
                       your abstract submissions for talks and workshops.
                       (Don’t worry, your entire presentation does not
                       need to be ready just yet!) If your abstract is
                       accepted, we will offer to sponsor your attendance
                       to join us in Prague, Czech Republic!


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ Auto_Xylophone_features_hand-wound_solenoids_|
                  Arduino_Blog⠀⇛


                       A xylophone is, in addition to being one of only
                       two known English words that start with the letter
                       X, an instrument that most of us haven’t touched
                       since we were toddlers. But xylophones produce a
                       very pleasing sound and their construction is about
                       as simple as an instrument gets. That makes them
                       perfect for DIY projects by those of us who aren’t
                       master craftsmen, and is likely why Rachad El
                       Moutaouaffiq chose the instrument for this Auto
                       Xylophone project.


                       As the name implies, this is a xylophone that plays
                       itself. Not only does that let it create beautiful
                       melodies that few of us are capable of hammering
                       out with our clumsy human hands, it can actually
                       exceed the ability of even an accomplished
                       xylophonist. It can strike up to four bars
                       simultaneously, allowing for richer and more
                       complex music than a person could play with only
                       two hands. It works with standard MIDI files and
                       therefore can play a huge range of existing MIDI
                       music or anything new that a musician creates in
                       real time or through other means—such as AI
                       generation that El Moutaouaffiq plans to experiment
                       with.


                # ⚓ Jonathan_Dowland:_things_I’d_like_to_3D_print,_revisited⠀⇛


                       It was pointed out to me that you can’t safely
                       print things to store food in with most materials,
                       as their porous/layered nature facilitates the
                       growth of bacteria. So, I’ll rule out those items.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Ubuntu Pit ☛ 10_Best_YouTube_Vanced_Alternatives_for
                  Android_To_Use_on_2022⠀⇛


                # ⚓ Android_tablet_owners_are_getting_some_really_cool_free_app
                  upgrades_|_T3⠀⇛


                # ⚓ How_To_Delete_My_Activity_Automatically_On_Android?⠀⇛


                # ⚓ GSM Arena ☛ Samsung_Galaxy_Z_Fold2_gets_Android_12L_update
                  with_One_UI_4.1.1_–_GSMArena.com_news⠀⇛


                # ⚓ 9to5Google ☛ Galaxy_Z_Fold_2_gets_Android_12L_update_–
                  9to5Google⠀⇛


                # ⚓ Android_App_Developer’s_Expertise_|_NextPit_Forum⠀⇛


                # ⚓ TechRadar ☛ If_you_use_your_Android_mobile_for_banking_in
                  India,_this_warning_is_for_you_|_TechRadar⠀⇛


                # ⚓ XDA ☛ Samsung_Galaxy_Watch_5_Pro_review:_The_second_best
                  Android_watch_by_default⠀⇛


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


          o ⚓ Sysdig_Adds_gVisor_Support_to_Falco_Container_Security_Platform_–
            Container_Journal⠀⇛


                 Created by Sysdig and contributed to the Cloud Native
                 Computing Foundation (CNCF) in 2018, Falco makes it
                 possible to assess risk and detect threats using a set of
                 rules to trigger security alerts. It detects unexpected
                 behavior, configuration changes, intrusions and thefts of
                 data in real-time that enable IT teams to
                 programmatically enforce security policies.


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ 9to5Linux ☛ LibreOffice_7.4_Office_Suite_Gets_First_Point
                  Release,_80_Bugs_Fixed_–_9to5Linux⠀⇛


                       The Document Foundation announced today the general
                       availability of LibreOffice 7.4.1 as the first
                       point release to the latest and greatest
                       LibreOffice 7.4 open-source, free, and cross-
                       platform office suite.


                       LibreOffice 7.4.1 is here only three weeks after
                       the major LibreOffice 7.4 release to fix various
                       issues, bugs, and annoyances discovered during this
                       time. According to the RC1 and RC2 changelogs, a
                       total of 80 bugs were addressed in this minor
                       maintenance update.


                # ⚓ Eric Hameleers ☛ LibreOffice_7.4.1_for_Slackware_15.0_and_-
                  current⠀⇛


                       LibreOffice Community Edition 7.4.1 was released
                       today and I already have the packages in my
                       repository for Slackware 15.0 and -current.


                # ⚓ Ubuntu Handbook ☛ LibreOffice_7.4_Finally_Available_to
                  Install_via_PPA_in_Ubuntu_22.04_|_UbuntuHandbook⠀⇛


                       For those prefer native .deb packages, LibreOffice
                       7.4 is finally available to install via LibreOffice
                       Fresh PPA.


                       Major release packages always take longer time to
                       be published into PPA. And it’s been almost one
                       month for this new 7.4 release.


                # ⚓ llunak:_16384_columns_in_Collabora_Online⠀⇛


                       Since the Calc core is the same, the underlying
                       functionality works just like in LibreOffice. But
                       the online functionality presented some additional
                       challenges that needed handling, as having more
                       cells in a spreadsheet may mean more data sent over
                       the network, slowing things down. There definitely
                       used to be problems with large spreadsheets, as the
                       tiled rendering used by Online in fact was already
                       limited to 500000 rows compared to 1048576 rows of
                       the desktop version (in fact, git history shows
                       that this started at only 1000 rows initially and
                       then was continually raised over the time as things
                       improved). So together with raising column count to
                       16384 I have raised this to the normal 1048576 rows
                       as well.


                       [...]


                       Now with hopefully all performance problems solved,
                       Collabora Online 22.05 should support these
                       spreadsheet sizes just as fine as the desktop
                       version.


                # ⚓ Tomaz’s_dev_blog:_Chart_Data_Tables⠀⇛


                       Chart data table is a feature of charts, that
                       presents in the chart area a data table with the
                       values that are visualised by the chart. The data
                       table is positioned automatically at the bottom of
                       the chart, and can for certain chart types replace
                       the X-axis labels. Until now this feature has been
                       missing in LibreOffice, but thanks to the funding
                       of NGI, it is now implemented.


          o § Programming/Development⠀➾


                # ⚓ KDE_PIM_in_July_and_August_–_Claudio_Cambra⠀⇛


                       KDE PIM is the set of applications that helps you
                       manage your email, contacts, appointments, tasks
                       and more.


                       Since our last report covering KDE PIM in May and
                       June, the PIM applications and libraries have seen
                       over 1200 changes from almost 30 contributors.
                       Let’s go over some of the biggest updates.


                # ⚓ Andrea_Scarpino’s_blog:_Sniffing_Android_apps_network
                  traffic⠀⇛


                       Back in the days, it was really easy to sniff the
                       network traffic made by the Apps in Android. You
                       could do it in a few minutes by adding mitmproxy’s
                       certificate and setting the HTTP proxy on your wifi
                       network settings. That was it. But things have
                       changed (for good) and that’s no longer the case.
                       However, I still want to sniff the network traffic
                       made by the Apps in Android.


                # ⚓ Drew DeVault ☛ Status_update,_September_2022⠀⇛


                       I have COVID-19 and I am halfway through my
                       stockpile of tissues, so I’m gonna keep this status
                       update brief.


                       In Hare news, I finally put the last pieces into
                       place to make cross compiling as easy as possible.
                       Nothing else particularly world-shattering going on
                       here. I have a bunch of new stuff in my patch queue
                       to review once I’m feeling better, however,
                       including bigint stuff — a big step towards TLS
                       support. Unrelatedly, TLS support seems to be
                       progressing upstream in qbe. (See what I did
                       there?)


                       powerctl is a small new project I wrote to
                       configure power management states on Linux. I’m
                       pretty pleased with how it turned out. It makes for
                       a good case study on Hare for systems programming.


                # ⚓ rec-def:_Dominators_case_study_–_Blog_–_Joachim_Breitner’s
                  Homepage⠀⇛


                       He said “it’s ICFP and I wanted to say the
                       dominance relation has a beautiful set of equations
                       … you can read all these algorithms how to compute
                       this, but the concept is simple”.


                       This made me wonder: If the concept is simple and
                       this formula is beautiful – shouldn’t this be
                       sufficient for the Haskell programmer to obtain the
                       dominator relation, without reading all those
                       algorithms?


                       Before we start, we have to clarify the formula a
                       bit: If a node is an entry node (no predecessors)
                       then the big intersection is over the empty set,
                       and that is not a well-defined concept. For these
                       nodes, we need that big intersection to return the
                       empty set, as entry nodes are not dominated by any
                       other node. (Let’s assume that the entry nodes are
                       exactly those with no predecessors.)


                # § Python⠀➾


                      # ⚓ Linux Hint ☛ 11_Best_Python_IDEs_for_Ubuntu_in_2022⠀⇛


                             Python is one of the most widely used general
                             purpose programming language. Most of the
                             popular websites or application software that
                             you use every day are powered by Python.


                             The reason behind the popularity of this
                             programming language is its simple and easy
                             to understand nature. Data Science and Data
                             Analytics are applications of the Python
                             programming. These fields are responsible for
                             creating many jobs across the world.


                             There are many Integrated Development
                             Environments (IDEs) available for editing and
                             programming in Python. Personally, I prefer
                             Vim in Ubuntu terminal but there many IDEs
                             like PyCharm, GNU Emacs and Pyzo that are
                             available for Ubuntu. So, today we are going
                             to discuss these IDEs one-by-one.


    * § Leftovers⠀➾


          o § Linux Foundation⠀➾


                # ⚓ Linux_Foundation_launches_open_source_digital_wallet
                  project⠀⇛


                # ⚓ HPC Wire ☛ Meta_Transitions_PyTorch_to_the_Linux
                  Foundation⠀⇛


                # ⚓ FOSSLife ☛ Linux_Foundation_Europe_to_Focus_on_Open
                  Collaboration [Ed: Microsoft front group expands to a
                  continent where it can misrepresent Linux users some more]⠀⇛


          o § Security⠀➾


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


                       Security updates have been issued by Debian (nova,
                       pcs, and rails), Fedora (firejail, moby-engine, and
                       pspp), Oracle (.NET 6.0, gnupg2, kernel, python3,
                       and rsyslog rsyslog7), Red Hat (.NET 6.0 and .NET
                       Core 3.1), SUSE (kernel), and Ubuntu (intel-
                       microcode, poppler, and webkit2gtk).


                # ⚓ Dark Reading ☛ Token-Mining_Weakness_in_Microsoft_Teams
                  Makes_for_Perfect_Phish⠀⇛


                # ⚓ GO Media ☛ IOActive_NFC_Relay_Attack_–_Tesla_Y⠀⇛


                       Radio relay attacks are technically complicated to
                       execute, but conceptually easy to understand:
                       attackers simply extend the range of your existing
                       key using what is essentially a high-tech walkie-
                       talkie. One thief stands near you while you’re in
                       the grocery store, intercepting your key’s
                       transmitted signal with a radio transceiver.
                       Another stands near your car, with another
                       transceiver, taking the signal from their friend
                       and passing it on to the car. Since the car and the
                       key can now talk, through the thieves’ range
                       extenders, the car has no reason to suspect the key
                       isn’t inside—and fires right up.


                       But Tesla’s credit card keys, like many digital
                       keys stored in cell phones, don’t work via radio.
                       Instead, they rely on a different protocol called
                       Near Field Communication or NFC. Those keys had
                       previously been seen as more secure, since their
                       range is so limited and their handshakes with cars
                       are more complex.


                       Now, researchers seem to have cracked the code. By
                       reverse-engineering the communications between a
                       Tesla Model Y and its credit card key, they were
                       able to properly execute a range-extending relay
                       attack against the crossover. While this specific
                       use case focuses on Tesla, it’s a proof of
                       concept—NFC handshakes can, and eventually will, be
                       reverse-engineered.


                # ⚓ Security Week ☛ When_It_Comes_to_Security,_Don’t_Overlook
                  Your_Linux_Systems [Ed: At least it does not have known back
                  doors and patching is rapid]⠀⇛


                       As I pointed out earlier this year, Linux systems
                       are a popular delivery mechanism for malware. While
                       they’re not the most popular – that distinction
                       goes to HTML and Javascript – don’t think you can
                       ignore them. Linux-based attacks are very much
                       still happening.


                # ⚓ USCERT ☛ CISA_Releases_Eleven_Industrial_Control_Systems
                  Advisories [Ed: This title is so generic you'd struggle to
                  guess it's all about Siemens]⠀⇛


                       CISA has released eleven (11) Industrial Control
                       Systems (ICS) advisories on September 15, 2022.
                       These advisories provide timely information about
                       current security issues, vulnerabilities, and
                       exploits surrounding ICS.


                # ⚓ CISA ☛ Siemens_Mobility_CoreShield_OWG_Software_|_CISA⠀⇛


                       Successful exploitation of this vulnerability could
                       allow an attacker to leverage the default
                       installation for Windows versions of the CoreShield
                       (OWG) software, which sets insecure file
                       permissions that could result in local escalation
                       of privileges to local administrator.


                # ⚓ Help Net Security ☛ Linux_variant_of_the_SideWalk_backdoor
                  discovered [Ed: It's not a "backdoor"; it's malware. You need
                  to actually install malware. With Windows, on the other hand,
                  the back doors are always there. Microsoft works with the
                  NSA.]⠀⇛


                       ESET researchers have discovered a Linux variant of
                       the SideWalk backdoor, one of the multiple custom
                       implants used by the SparklingGoblin APT group.


          o § Civil Rights/Policing⠀➾


                # ⚓ Public Knowledge ☛ Public_Knowledge_Welcomes_Bill_To
                  Promote_Digital_Equity_–_Public_Knowledge⠀⇛


                       Today, Senators Ben Ray Luján (D-NM), Jeff Merkley
                       (D-OR), Martin Heinrich (D-NM), and Ed Markey (D-
                       MA) introduced the “Digital Equity Foundation Act”
                       to establish a nonprofit foundation to help close
                       the digital divide by leveraging public and private
                       investments. Rep. Doris Matsui (D-CA) introduced a
                       companion bill in the U.S. House.


                       To accomplish this, the bill would supplement the
                       Federal Communications Commission and National
                       Telecommunications and Information Administration’s
                       work to award grants, provide training and
                       education, and overall promote policies to enhance
                       digital equity outcomes across the nation. It would
                       also provide local funding to help connect those in
                       danger of missing out on all the opportunities the
                       internet provides, including telehealth, education,
                       and career training. Public Knowledge applauds
                       Sens. Luján, Merkley, Heinrich, and Markey as well
                       as Rep. Matsui for championing those who need
                       devices and training to participate in our digital
                       world.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ No_bookbinding_for_you⠀⇛


                       I went to a bookbinding shop today asking if they
                       would teach me some of their craft but the owner,
                       an old guy, was so harsh… Almost rude.


                # ⚓ XBCHOSA_Wordo:_ILIUM⠀⇛


                # ⚓ Keeping_Notes_is_Pretty_Awesome_Actually⠀⇛


                       Recently I’ve noticed I’ve been forgetting
                       important things I’d like to remember.


                       I’m not sure if it’s aging, the few years I spent
                       binging (unspecified brain chemical) in an effort
                       to forget the awfulness of human civilization, or
                       just having a life with more important things to
                       forget.


                       It could also be the case that I and most everyone
                       else have always been forgetful but there comes a
                       time when you are both able to accept it and spend
                       some effort putting a system of note-taking in
                       place to mitigate the problem.


          o § Technical⠀➾


                # ⚓ Proof_of_Stake⠀⇛


                       Now, I’m still staying the hell away from all kinds
                       of crypto personally, but no more sleepless nights.


                # § Internet/Gemini⠀➾


                      # ⚓ Boosting_the_Collaborative_Directory_of_Geminispace_
                        (CDG)⠀⇛


                             I just wanted to help boost the signal on
                             this cool initiative in whatever small way I
                             can. I like the idea of a user contributed
                             directory like this.


                             I have a few different themes on my capsule
                             that I would like to share but I don’t want
                             to inundate the Antenna timeline every time I
                             post. Instead I posted links to those pages
                             on the Directory for whoever is interested.


                             If you have your own links or links to other
                             interesting capsules, take a second to add
                             them to the CDG!


                # § Announcements⠀➾


                      # ⚓ nForth⠀⇛


                             And it’s up and running. Defining words, etc.


                             I was just a tiny bit more optimistic about
                             getting to this point yesterday — I would
                             have, but decided to stop for a happy hour
                             drink, and… yeah.


                             [...]


                             While I’ve been making and programming in
                             Forth-like languages for around 40 years, I
                             realized I don’t have a minimal 386
                             implementation suitable for, say, KolibriOS.


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



                    ䷩ 𝚕𝚒𝚗𝚎 4250

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.15.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_15/09/2022:_LibreOffice_7.4.1_and_Red_Hat_Panic_Over_Staff_Exodus⠀✐


Posted in News_Roundup at 8:35 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o Reviews
          o New_Releases
          o SUSE/OpenSUSE
          o Fedora_Family_/_IBM
          o Debian_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Productivity_Software/LibreOffice/Calligra
          o Education
          o FSF
          o Licensing_/_Legal
          o Programming/Development
                # Python
          o Standards/Consortia
    * Leftovers
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Linux_Foundation
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Wildlife/Nature
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Trademarks
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Linux_AppImages_Have_Annoying_Usability_Issues_–
                  Invidious⠀⇛


                       I think AppImages are really cool and I like them
                       for my own use cases but when it comes to the Linux
                       desktop environments they have some interesting
                       design limitations not offered by other solutions
                       like flatpak and snap.


                # ⚓ Video ☛ Let’s_Talk_About_Linux_And_Stuff_–_DT_LIVE!_–
                  Invidious⠀⇛


                # ⚓ Video ☛ Fedora_37_Beta_Run_Through_–_Invidious⠀⇛


                       In this video, we are looking at Fedora 37 Beta.
                       Enjoy!


                # ⚓ Linux Made Simple ☛ Fedora_37_Beta⠀⇛


                       Today we are looking at Fedora 37 Beta. It comes
                       with Gnome 43 Beta 1, Linux kernel 5.19, and uses
                       about 1.7 GB of ram when idling.


                # ⚓ Video ☛ What_is_a_SOC_Analyst??_@Day_Cyberwox_–_Invidious⠀⇛


                # ⚓ Video ☛ Imagine_Letting_a_Power_Company_Control_Your
                  Thermostat_–_Invidious⠀⇛


                       thousands of people had to suffer in their very hot
                       homes because xcel energy had set their smart
                       thermostats to a high temperature to avoid putting
                       additional strain on the grid.


                # ⚓ Video ☛ Enterprise_Linux_Security_Episode_42_–_Do_NOT_Fire
                  Your_Security_Team!⠀⇛


                       Recent news of Patreon firing their security team
                       is making the rounds online, and in this episode,
                       Jay and Joao will talk about this very strange
                       story and some takeaways from it.


                # ⚓ Video ☛ Fedora_vs._Ubuntu_–_2022_Edition_–_Invidious⠀⇛


                       It’s finally time again for a big comparison
                       between Fedora 36 and Ubuntu 22.04 LTS. Both
                       distros were released in the same year and have
                       similar specs.


                # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_971⠀⇛


                       Joel has sad news.


                # ⚓ 3×50:_Two_Riders_Were_Approaching [Ed: Jono_Bacon props up
                  anti-Linux Microsoft moles. Erica Brescia now.]⠀⇛


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ Concurrent_page-fault_handling_with_per-VMA_locks_
                  [LWN.net]⠀⇛


                       The kernel is, in many ways, a marvel of
                       scalability, but there is a longstanding pain point
                       in the memory-management subsystem that has
                       resisted all attempts at elimination: the
                       mmap_lock. This lock was inevitably a topic at the
                       2022 Linux Storage, Filesystem, Memory-Management
                       and BPF Summit (LSFMM), where the idea of using
                       per-VMA locks was raised. Suren Baghdasaryan has
                       posted an implementation of that idea — but with an
                       interesting twist on how those locks are
                       implemented.


                       The mmap_lock (formerly called mmap_sem) is a
                       reader/writer lock that controls access to a
                       process’s address space; before making changes
                       there (mapping in a new range, for example), the
                       kernel must acquire that lock. Page-fault handling
                       must also acquire mmap_lock (in reader mode) to
                       ensure that the address space doesn’t change in
                       surprising ways while a fault is being resolved. A
                       process can have a large address space and many
                       threads running (and incurring page faults)
                       concurrently, turning mmap_lock into a significant
                       bottleneck. Even if the lock itself is not
                       contended, the constant cache-line bouncing hurts
                       performance.


                       Many attempts at solving the mmap_lock scalability
                       problem have taken the form of speculative page-
                       fault handling, where the work to resolve a fault
                       is done without taking mmap_lock in the hope that
                       the address space doesn’t change in the meantime.
                       Should concurrent access occur, the speculative
                       page-fault code drops the work it has done and
                       retries after taking mmap_lock. Various
                       implementations have been shown over the years and
                       they have demonstrated performance benefits, but
                       the solutions are complex and none have managed to
                       convince enough developers to be merged into the
                       mainline kernel.


                       An alternative approach that has often been
                       considered is range locking. Rather than locking
                       the entire address space to make a change to a
                       small part of it, range locking ensures exclusive
                       access to the address range of interest while
                       allowing accesses to other parts of the address
                       space to proceed concurrently. Range locking turns
                       out to be tricky as well, though, and no
                       implementation has gotten close to being considered
                       for merging.


                # ⚓ LWN ☛ What’s_in_a_(type)_name?_[LWN.net]⠀⇛


                       The kernel’s manual pages are in a bit of an
                       interesting position. They are managed as a
                       separate project, distinct from the kernel’s
                       documentation, and have the task of documenting
                       both the kernel’s system-call interface and the
                       wrappers for that interface provided by the C
                       library. Sometimes the two objectives come into
                       conflict, as can be seen in a discussion that has
                       been playing out over the course of the last year
                       on whether to use C standard type names to describe
                       kernel-defined structures.
                       The C <stdint.h> header file defines a number of
                       types for developers who need to specify exactly
                       how they need an integer variable to be
                       represented. For example, int16_t is a 16-bit,
                       signed type, while uint64_t is a 64-bit, unsigned
                       type. This level of control is needed when defining
                       data structures that are implemented by hardware,
                       are exchanged through communications protocols — or
                       are passed between user and kernel space.


                       The kernel, though, does not use these types to
                       define its system-call interface. Instead, the
                       kernel has its own types defined internally. Rather
                       than use uint64_t, for example, the kernel’s API
                       definitions use __u64. That has been the situation
                       for a long time — since before the standard C types
                       existed — and is simply part of how the kernel
                       project does things.


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


                       Kernel code can, at times, be quite inward looking;
                       it often refers to itself. To enable this
                       introspection, the kernel has evolved several
                       mechanisms for identifying specific locations in
                       the code and carrying out actions related to those
                       locations. The code-tagging framework patch set,
                       posted by Suren Baghdasaryan and Kent Overstreet,
                       is an attempt to replace various ad hoc
                       implementations with a single framework, and to add
                       some new applications as well.


                       There are a number of reasons for the kernel to
                       need to identify specific locations within the
                       code. For example, kernel code is not normally
                       allowed to incur page faults, but the functions
                       that access user-space memory will often do just
                       that. To do the right thing in that situation, the
                       kernel build process makes a note of the location
                       of every user-space access operation; when a page
                       fault happens, that list is checked and, if the
                       fault happened in an expected location, it is
                       handled normally. The kernel’s dynamic debugging
                       mechanism is another example; each debugging print
                       statement is tracked and can be enabled
                       independently.


                       The usual trick for implementing this kind of
                       mechanism is to create a special ELF section in the
                       kernel binary; that section is then populated with
                       structures recording the points of interest within
                       the kernel. At run time, the kernel can locate that
                       section, where it will find an array of structures
                       with the needed information. At its core, the
                       tagging framework is a set of functions and macros
                       that make the creation of and access to this
                       special section easier.


          o § Applications⠀➾


                # ⚓ Linux Links ☛ 5_Best_Free_and_Open_Source_OCR_Screen
                  Capture_Tools⠀⇛


                       
                       This article highlights OCR powered screen-capture
                       tools to capture information instead of images. We
                       only feature open source software here.


                       Here’s our verdict of the tools succinctly
                       summarized in a LinuxLinks styled ratings chart.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Shell Tips ☛ How_to_Install_Latest_Python_on_Ubuntu
                  Linux⠀⇛


                       Python is a high-level programming language that is
                       continually taking the interest of many users in
                       the Linux community. The Python general-purpose
                       programming language is in the top ranks with other
                       popular programming languages due to its
                       applicability in web and software development.


                # ⚓ Trend Oceans ☛ 2_Ways_to_Capture_Website_Screenshots_from
                  the_Command-line_on_Linux_–_TREND_OCEANS⠀⇛


                       You might be using ksnip or flameshot to take
                       screenshots of single or multiple web pages. No
                       doubt, both are great tools that provide you with
                       rich full features that make it easy to take
                       screenshots and later edit the image.


                # ⚓ H2S Media ☛ Install_VSFTPD_FTP_Server_on_Ubuntu_20.04_LTS
                  Linux⠀⇛


                       This tutorial is to know how we can install,
                       config, setup, and use the VSFTPD FTP server on
                       Ubuntu 20.04 LTS Focal Fossa using the command
                       terminal.


                       Vsftpd is an FTP server that is very consciously
                       designed for security. For example, the program
                       checks its configuration and the rights of all
                       files it is to access before starting and refuses
                       to start if it is configured incorrectly. We can
                       use this open-source program to set up an FTP
                       server on Ubuntu Linux.


                # ⚓ H2S Media ☛ Install_Discourse_on_Ubuntu_20.04_LTS_Focal
                  Linux_–_Linux_Shout⠀⇛


                       Discourse is open-source forum software that can
                       also be used as a comment system for a website. The
                       creators want to create the basis for modern
                       Internet forums. Here we learn the commands to
                       install the Discourse on Ubuntu 20.04 LTS Focal
                       Fossa Linux to create our own self-hosted Forum.


                # ⚓ Linux Capable ☛ How_to_Install_NVIDIA_Drivers_on_Fedora_37
                  Linux⠀⇛


                       When it comes to graphics processing, speed is
                       often of the essence. For any Linux user who relies
                       on their system for gaming or graphic design,
                       having the fastest drivers possible is essential.
                       While most modern Linux distributions come with
                       Nouveau drivers pre-installed, these are often not
                       the most up-to-date or well-supported drivers
                       available. However, the Nouveau open-source
                       graphics device driver for Nvidia video cards is
                       typically slower than Nvidia’s proprietary or open-
                       source driver and lacks support for the latest
                       hardware features and software technology. In most
                       cases, upgrading to proper NVIDIA drivers will
                       provide a much better experience. In some
                       situations, the improvement in speed and
                       performance can be substantial.


                       The following tutorial will teach you how to
                       install the Nvidia Drivers on Fedora 37 Linux from
                       the Nvidia Proprietary Repository RPM Fusion or
                       Nvidia RPM Cuda REPO using cli with the command
                       line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Brave_Browser_on_Fedora_37
                  Linux⠀⇛


                       Brave is a free and open-source web browser
                       developed by Brave Software, Inc. based on the
                       Chromium web browser. Brave is a privacy-focused
                       internet browser that sets itself apart from other
                       browsers by automatically blocking online
                       advertisements and website trackers in its default
                       settings. Brave claims its browser puts less strain
                       on your computer’s performance than Google Chrome.
                       Even with multiple tabs open at once, the new Brave
                       Software uses 66% less memory and has 50 million
                       more active users than before – a growth of 2X in 5
                       years! In addition to its privacy features, Brave
                       also includes built-in security and performance
                       enhancement tools, making it a well-rounded choice
                       for those looking for a safe and fast browsing
                       experience.


                       In the following tutorial, you will learn how to
                       install Brave Browser on Fedora 37 Linux by
                       importing the official GPG keys and repository with
                       step-by-step instructions on installing, updating,
                       and removing the browser, including disabling/
                       enabling the DNF repository. As a bonus, the beta
                       and nightly optional installation methods are
                       included, installed alongside stable.


                # ⚓ Linux Capable ☛ How_to_Install_Avidemux_on_Linux_Mint_21
                  LTS⠀⇛


                       Avidemux is a free, open-source software
                       application for non-linear video editing and
                       transcoding multimedia files. It supports many file
                       types, including AVI, DVD-compatible MPEG files,
                       MP4, and ASF, using a variety of codecs. It is
                       trendy as it allows users to cut, join, split,
                       rotate videos, and add filters. Avidemux has a wide
                       range of features that makes it a popular choice
                       for video editing, including support for most
                       popular video formats, the ability to cutting and
                       joining video files without re-encoding, and power
                       management features allowing you to automatically
                       shutdown your computer when the job is done and
                       much more. If you are looking for an easy-to-use
                       video editor with all the features you need, then
                       Avidemux is the right choice for you.


                       The following tutorial will teach you how to
                       install Avidemux on Linux Mint 21 LTS using the
                       command line terminal and the LaunchPAD PPA by the
                       XtraDEB team.


                # ⚓ OpenSource.com ☛ 24_of_our_favorite_articles_in_a
                  downloadable_eBook⠀⇛


                       One day in March of 2020, a few of my
                       Opensource.com teammates and I grabbed lunch to
                       talk about how we would work from home for the next
                       couple of weeks until this pandemic got nipped in
                       the bud. At the end of the work day, I packed up my
                       laptop and walked out the door of our office
                       building. Several months later, we were all still
                       working from home. None of us had returned to our
                       office-based workstations. In July 2020, using
                       safety precautions, we were granted access to our
                       workstation solely to retrieve personal items. My
                       desk was left exactly as I left it that afternoon
                       in March. Expiring snacks stashed in my secret
                       drawer. Picture frames collecting dust. Comic
                       strips pinned up.


                       And a pile of several bound copies of Best of a
                       decade on Opensource.com 2010-2019. Our last
                       yearbook that was published (and printed)!


                       Like most folks, the Opensource.com community had
                       to pivot how we operated in order to stay
                       connected. Sure, we continued our weekly video
                       calls. But in-person conferences, a unique time
                       where people would travel from all over the world
                       to be together, were out of the question. Though
                       some of this operational stuff has changed, the
                       connection with one another has strengthened. It is
                       due time to publish a new yearbook to honor that
                       connection. This yearbook was created to celebrate
                       our correspondents.


                       The Opensource.com Correspondent Program recognizes
                       the critical group of our most trusted and
                       committed contributors. We recently closed out yet
                       another successful program year with 24
                       correspondents. Each correspondent selected their
                       favorite article to be included in this
                       downloadable yearbook. In it, you’ll find Raspberry
                       Pi tutorials, career stories, home automation tips,
                       Linux tricks, and much more.


                # ⚓ OpenSource.com ☛ How_I_switched_from_Docker_Desktop_to
                  Colima⠀⇛


                       DDEV is an open source tool that makes it simple to
                       get local PHP development environments up and
                       running within minutes. It’s powerful and flexible
                       as a result of its per-project environment
                       configurations, which can be extended, version
                       controlled, and shared. In short, DDEV aims to
                       allow development teams to use containers in their
                       workflow without the complexities of bespoke
                       configuration.


                       DDEV replaces more traditional AMP stack solutions
                       (WAMP, MAMP, XAMPP, and so on) with a flexible,
                       modern, container-based solution. Because it uses
                       containers, DDEV allows each project to use any set
                       of applications, versions of web servers, database
                       servers, search index servers, and other types of
                       software.


                       In March 2022, the DDEV team announced support for
                       Colima, an open source Docker Desktop replacement
                       for macOS and Linux. Colima is open source, and by
                       all reports it’s got performance gains over its
                       alternative, so using Colima seems like a no-
                       brainer.


                # ⚓ Linux Hint ☛ DOS_Flood_With_hping3⠀⇛


                       This tutorial explains how to execute DDOS
                       (Distributed Denial of Service) attacks using the
                       hping3 tool.


                       After reading this article you will be able to
                       install hping3 to execute both DOS and DDOS tests.
                       Except for the installation process based on
                       Debian, the rest of this document is valid for all
                       Linux distributions.


                       In case you are not familiar with DOS and DDOS
                       attacks, you may want to start by reading a DOS and
                       DDOS introduction.


                       All steps described below include screenshots to
                       make it easy for every Linux user to follow them.


                # ⚓ OSTechNix ☛ Run_All_Programs_In_A_Directory_Via_Sudo_In
                  Linux_–_OSTechNix⠀⇛


                       This brief guide explains how to allow an user to
                       run all programs in a directory via sudo and deny
                       the user to run programs in other directories in
                       Linux and Unix-like systems.


                # ⚓ Its FOSS ☛ How_to_Check_if_You_are_Using_Wayland_or_Xorg?⠀⇛


                       There is a technical transition taking place in the
                       desktop Linux world.


                       Most mainstream distros have started to move to the
                       Wayland display server by default.


                       But not all legacy components are compatible with
                       the newer Wayland. They work only with the good old
                       X or Xorg display server.


                       So, when you are having trouble with your Linux
                       system, it would be wise to check if the problem is
                       coming because of the display server.


                # ⚓ Trend Oceans ☛ How_to_Install_Custom_Fonts_on_Linux_
                  (Ubuntu,_Debian,_RedHat)_–_TREND_OCEANS⠀⇛


                       Linux gives you complete freedom to experiment with
                       the user experience. For this reason, one can try
                       to change the desktop environment to any window
                       manager like i3wm, bspwm, xmonad, etc. Not only
                       that, but you can also change your display manager
                       and audio manager from what you have received from
                       the installed distribution.


                       But we are not here to change any of these things
                       except the font, because after the installation you
                       may not be able to view some of the fonts in
                       Devnangari like Sanskrit, Hindi, Marathi, and
                       Dravidian languages like Telugu, Tamil, Kannada,
                       and Malayalam.


                       Because of that, you might face problems reading
                       content in your regional languages.


                # ⚓ Linux Hint ☛ Install_Wine_on_Linux_Mint_20.3⠀⇛


                       Wine is a helpful tool that allows you to run many
                       Windows applications on Linux. Therefore, if you
                       have just shifted from Windows to Linux, this tool
                       can prove to be your best partner in helping you
                       getting used to the Linux environment. This article
                       is dedicated to the method of installing Wine on a
                       Linux Mint 20.3 system.


                # ⚓ Linux Hint ☛ How_to_Change_the_Password_on_Ubuntu_22.04⠀⇛


                       A password is a word, phrase, or string of
                       characters used to verify the identity of a user
                       during the authentication process. It is used to
                       differentiate an authorized user from an
                       unauthorized user.


                       Today we will explore how to change a password on
                       Ubuntu 22.04 using two different ways. The first
                       method involves changing the password using the
                       command line (Terminal). In the second method, we
                       will see how a password is changed using Graphical
                       User Interface (GUI).


                # ⚓ Vitux ☛ 6_Ways_to_Harden_your_Debian_system_–_VITUX⠀⇛


                       Hardening refers to strengthening the security of
                       your systems. Nowadays when data breaches are very
                       common, even normal users are very much concerned
                       about the security of their critical data.
                       Therefore, in this article, we will share with you
                       some of the best ways for hardening your Debian 11
                       and Debian 10 systems.


                # ⚓ Install_Nagios_Server_on_Oracle_Linux_9_–_kifarunix.com⠀⇛


                       In this guide, you will learn how to install Nagios
                       Server on Oracle Linux 9. Nagios provides
                       enterprise-class Open Source IT monitoring, network
                       monitoring, server and applications monitoring.


                # ⚓ Linux Capable ☛ How_to_Install_Telegram_on_Fedora_37
                  Linux⠀⇛


                       Cross-platform messaging apps are becoming
                       increasingly popular as they offer a convenient way
                       to stay in touch with friends and family no matter
                       where they are. Telegram is one such app that
                       offers several unique features that set it apart
                       from its competitors. Perhaps most notably,
                       Telegram provides end-to-end encryption for all
                       chats, meaning that only the sender and recipient
                       can read the messages. This makes Telegram an ideal
                       choice for those who value privacy and security. In
                       addition, Telegram is entirely free to use and is
                       available on various platforms, making it easy to
                       stay connected with friends and family no matter
                       where they are.


                       In the following tutorial, you will learn how to
                       install the Telegram client on Fedora 37 Linux
                       using the command line terminal with two
                       installation methods and some tips on maintaining
                       Telegram in the future.


                # ⚓ Linux Made Simple ☛ How_to_install_SuperTux_–_Milestone_1
                  on_a_Chromebook⠀⇛


                       Today we are looking at how to install SuperTux –
                       Milestone 1 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.


                # ⚓ Linux Capable ☛ How_to_Install_Signal_Messenger_on_Linux
                  Mint_21_LTS⠀⇛


                       There are a lot of messaging apps on the market
                       these days. Most people probably use the default
                       messaging app that comes with their phone, whether
                       iMessage for Apple users or Messages for Android
                       users. But there are plenty of other options, and
                       more and more people are starting to use them. One
                       of these is Signal messenger.


                       Signal messenger is a free, open-source messaging
                       app that has been around for several years and
                       specializes in end-to-end encryption. This means
                       that your communication is entirely secure from
                       prying eyes, whether it’s the government or someone
                       who happens to get ahold of your phone. If you need
                       to communicate securely but find it hard because of
                       the restrictions put on traditional messaging apps
                       like WhatsApp or Facebook Messenger, Signal
                       messenger is one of the better forms of
                       communication for those that require the utmost
                       privacy.


                       In the following tutorial, you will learn how to
                       install Signal Messenger on Linux Mint 21 LTS
                       release series. The tutorial will use the command
                       line terminal with complete steps to install the
                       official repository and tips on updating and
                       removing the software securely and adequately.


                # ⚓ UNIX Cop ☛ How_to_install_Homebrew_on_CentOS_9_Stream⠀⇛


                       In this post, you will learn how to install
                       Homebrew on CentOS 9 Stream. Sounds interesting?
                       Let’s see.


                # ⚓ Matthew Garrett ☛ mjg59_|_git_signatures_with_SSH
                  certificates⠀⇛


                       Last night I complained that git’s SSH signature
                       format didn’t support using SSH certificates rather
                       than raw keys, and was swiftly corrected, once
                       again highlighting that the best way to make
                       something happen is to complain about it on the
                       internet in order to trigger the universe to retcon
                       it into existence to make you look like a fool. But
                       anyway. Let’s talk about making this work!


                # ⚓ Linux Capable ☛ How_to_Install_Atom_Text_Editor_on_Linux
                  Mint_21_LTS [Ed: Atom is deprecated (dead end) and controlled
                  by Microsoft; it's bloated garbage, nobody should use this]⠀⇛


                       Atom is a free and open-source text and source code
                       editor that supports many cross-platforms such as
                       macOS, Linux, and Microsoft Windows with support
                       for plugins written in JavaScript and embedded Git
                       Control, developed by GitHub. The catchphrase that
                       Atom calls itself is the “hackable text editor for
                       the 21st century”. Atom, compared to competitors,
                       is more user-friendly, with plenty of options for
                       extensions to add syntax highlighting for languages
                       and formats, add dynamic linting, and integrate
                       debuggers, runtime environments, video and music
                       player controls, and much more.


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ Valheim_is_getting_crossplay_with_an_update
                  now_in_testing⠀⇛


                       Iron Gate have announced that Valheim is set for
                       crossplay, with an update now available in testing
                       to ensure you can play with friends anywhere. This
                       is great, as Valheim is coming to consoles next
                       year.


                # ⚓ GamingOnLinux ☛ Isonzo_is_a_new_WW1_FPS_from_the_dev_of
                  Verdun_out_now⠀⇛


                       Isonzo is the latest in the WW1 FPS series from the
                       creator of Verdun and Tannenberg. It’s out now and
                       available with Native Linux support.


                # ⚓ GamingOnLinux ☛ Roadwarden,_one_of_the_best_modern_text-
                  adventures_around_is_out_now⠀⇛


                       For anyone who considers themselves even a remote
                       fan of text-adventures, you should definitely take
                       a look at Roadwarden. Developed by Moral Anxiety
                       Studio, a solo development operation from Poland,
                       and published by Assemble Entertainment.


                # ⚓ GamingOnLinux ☛ Heroes_of_Might_and_Magic_II_&_III_open
                  source_game_engines_get_new_releases⠀⇛


                       This is a bit of a double event. Not only has the
                       Heroes of Might and Magic II game engine fheroes2
                       seen a new release, but a surprise update of VCMI
                       for Heroes of Might and Magic III was also
                       released.


                # ⚓ GamingOnLinux ☛ The_Wandering_Village_is_absolutely
                  mesmerizing⠀⇛


                       The Wandering Village from Stray Fawn Studio, a
                       game about building a village on the back of a
                       massive moving creature has just entered Early
                       Access with Native Linux support.


                # ⚓ Hackaday ☛ 2022_Cyberdeck_Contest:_RPG_Character_Tracker⠀⇛


                       While it would be a mistake to think there are any
                       firm rules for what constitutes a cyberdeck, we can
                       at least identify some common traits that would
                       seem to give us a baseline description. For
                       example, most deck builds we’ve seen have been
                       fully-functional Linux computers, more often than
                       not powered by some Raspberry Pi variant. But that
                       doesn’t mean there isn’t room in the community for
                       less computational powerful decks, or builds that
                       are so bespoke that they can only perform a few
                       selected tasks.


    * § Distributions and Operating Systems⠀➾


          o § Reviews⠀➾


                # ⚓ LWN ☛ A_look_at_Linux_Mint_21_[LWN.net]⠀⇛


                       Linux Mint 21 “Vanessa” was released on July 31.
                       There are no real headline-grabbing features that
                       come with the new release, as the project generally
                       seeks to make incremental changes, rather than
                       larger, potentially disruptive ones. Changes in
                       this release include a new Bluetooth manager that
                       brings several improvements, driverless printing
                       and scanning by default, a process monitor to
                       inform the user about resource-intensive background
                       tasks, new functionality for the Timeshift system
                       backup tool, and several major under-the-hood
                       improvements to the Cinnamon desktop environment.


                       Like previous releases, Linux Mint 21 is available
                       in editions for the Cinnamon, MATE, and Xfce
                       desktop environments. Cinnamon is based on GNOME 3,
                       but with major changes to make it more like other
                       desktop environments with a bottom panel and menu
                       similar to that used in Windows 7 and earlier,
                       rather than the heavily redesigned interface of
                       GNOME 3 and later. Cinnamon was created by the
                       Linux Mint developers due to criticisms of changes
                       in GNOME 3 that were seen as unnecessary. MATE is a
                       continuation of GNOME 2 that was originally forked
                       by an Arch Linux user for the same reason, and Xfce
                       is a lightweight desktop environment designed for
                       computers that may not run other environments well.
                       All of the editions in Linux Mint use X11; Wayland
                       support is not currently on the development roadmap
                       for Cinnamon. MATE and Xfce are working on Wayland
                       support separately from the Mint project, and a
                       future release of Linux Mint is likely to include
                       that work in those editions.


                       [...]


                       Mint 21 replaces Blueberry, the Bluetooth manager
                       used in previous versions, with Blueman, which has
                       more features and provides more information than
                       Blueberry. Blueman also has better headset
                       compatibility and improved audio profile support.
                       Additionally, while Blueberry is a wrapper around
                       the GNOME-specific gnome-bluetooth, Blueman is
                       specifically designed to be cross-desktop.


          o § New Releases⠀➾


                # ⚓ Linuxiac ☛ EndeavourOS_Nova_Released_Primarily_Addresses
                  GRUB_Issue⠀⇛


                       EndeavourOS Nova, the new release in the Artemis
                       series, focused primarily on resolving the GRUB
                       issue that affected Arch Linux-based distros.


                       EndeavourOS is a user-friendly Arch Linux-based
                       rolling release distro with some handy new features
                       that improve the user experience. In other words,
                       it fits into a similar-but-different niche as
                       Manjaro.


                       It might be the perfect solution for less
                       experienced Linux users to get the best Arch Linux
                       offers. Additionally, despite its claim to be a
                       terminal-focused distribution, it has excellent GUI
                       tools that make handling an Arch Linux system
                       simple for new users.


                # ⚓ 9to5Linux ☛ EndeavourOS_Artemis_Nova_Released_with_Linux
                  Kernel_5.19,_Vanilla_GRUB_Experience⠀⇛


                       EndeavourOS Artemis Nova is here a little over a
                       month after EndeavourOS Artemis Neo, which was just
                       a minor update only addressing a GRUB bootloader
                       issue, and two and a half months after the major
                       EndeavourOS Artemis release that introduced a
                       built-in ARM installer and other big changes.


                       Compared to the previous Artemis versions,
                       EndeavourOS Artemis Nova is powered by a newer
                       kernel stack based on the upstream Linux 5.19
                       kernel series. Linux kernel 5.19.7 is included by
                       default in the live/installation image, which, of
                       course, is intended only for new installations as
                       existing users are already up to date.


          o § SUSE/OpenSUSE⠀➾


                # ⚓ Plasma,_Gear,_Frameworks_update_in_Tumbleweed⠀⇛


                       
                       In addition to some changes with YaST affecting
                       grep, the rolling release had snapshots updating
                       Plasma, Gear and Frameworks in that order.


                       Snapshot 20220914 is finishing testing and the
                       snapshot could be released before this article is
                       published, which would make this week another full
                       week of snapshots if the testing passes openQA.


                       Frameworks 5.98.0 arrived in snapshot 20220913. The
                       update deduplicated color loading codes with
                       KConfigWidgets and Kirigami had a fix for a
                       potential crash in imagecolors. Frameworks also
                       delivered a lot of additions and fixes to
                       KTextEditor. There were some fixes of
                       inconsistencies in the completion config tab and
                       KTextEditor enabled the clipboard history with non
                       read-only. An update of fetchmail 6.4.33 removed an
                       upstream patch and a wrapper script for HTMLDOC was
                       added for use with Flatpak because the snapd
                       version was broken. Audio format flac 1.4.0 added a
                       FMA instruction set extension to speed up audio for
                       x86_64 CPUs. There is also now a set of files
                       available to test whether a FLAC decoder implements
                       the format correctly. The update of libstorage-ng
                       4.5.44 fixed the resizing of Linux Unified Key
                       Setup and did some Czech translations. Also updated
                       in the snapshot was the 4.5.4 versions of yast2-
                       bootloader and yast2-kdump.


          o § Fedora Family / IBM⠀➾


                # ⚓ Enterprisers Project ☛ Data_scientist:_A_day_in_the_life⠀⇛


                       Over the last six years, I’ve made a living from
                       modeling, primarily in New York City but also in
                       Seattle and various countries worldwide. While I
                       enjoy dressing up in NYC’s trendiest streetwear, by
                       “modeling,” I mean predictive modeling, a central
                       element of the applied data science I’ve done
                       throughout my career.


                       I started my data science journey at Custora, a New
                       York-based company that built predictive marketing
                       software for eCommerce businesses. After Custora
                       was acquired by Amperity, I joined their data
                       science team, where I’m now a lead data scientist.
                       Amperity is partially remote, which has allowed me
                       to work from anywhere with solid Wi-Fi and even
                       more solid espresso.


                       My experience in data science has been focused on
                       building machine-learning pipelines as part of
                       enterprise software. Such work relies more heavily
                       on engineering prowess, infrastructural
                       considerations, and high performance both
                       computationally and efficaciously (I had to look
                       that one up.) It also requires regular coordination
                       between data scientists, machine learning
                       engineers, back-end engineers, and product
                       managers.


                # ⚓ ZDNet ☛ Remote_working:_Red_Hat_tells_staff_they_don’t_have
                  to_return_to_the_office [Ed: Too late. A lot of the important
                  technical and management staff from Red Hat already left the
                  building. And the company, too.]⠀⇛


                       Enterprise Linux heavyweight Red Hat will let its
                       nearly 20,000-strong workforce choose whether or
                       not to come back into the office.


                       Red Hat chief people officer Jennifer Dudeck said
                       in a blogpost the maker of the enterprise Linux
                       platform Red Hat Enterprise Linux is going for an
                       “office-flex” model where it allows staff to “come
                       to the office as much as they need to, or not at
                       all if they choose.”


          o § Debian Family⠀➾


                # ⚓ IT Wire ☛ iTWire_–_Debian_set_to_start_vote_on_including
                  non-free_packages_in_install_media⠀⇛


                       The Debian GNU/Linux Project is set to start voting
                       on a general resolution which outlines a way to
                       solve the issues it faces in providing proprietary
                       firmware on its install media.


                       The issue was initially raised by former DPL leader
                       Steve McIntyre in April and discussions about a
                       solution have been continuing on the project’s
                       mailing lists.


                       McIntyre told iTWire that he had given a talk on
                       the subject during the annual conference in July
                       and had started the GR process in August.


                       As with every such resolution, there are a number
                       of solutions proposed, in this case five.


                # ⚓ Barry Kauler ☛ Zoom_SFS_created_using_deb2sfs⠀⇛


                       It is on the to-do list that will record these
                       extra dependency requirements somewhere in /usr/
                       local/easy_containers/templates/zoom. So won’t have
                       to remember them when do a future zoom deb2sfs.


                       The SFS has been uploaded, so you can click on
                       “sfs” icon to download and install it. It will only
                       install to the main desktop, as audio is broken in
                       a container.


          o § Devices/Embedded⠀➾


                # ⚓ Linux Gizmos ☛ Industrial_IoT_gateway_based_on_Raspberry_Pi
                  CM4_supports_Ignition_Edge⠀⇛


                       The IGN800 accommodates the Raspberry Pi CM4 which
                       features the Quad-Core ARM Cortex-A72 64-bit SoC.
                       The memory system can be equipped with 4GB/8GB of
                       RAM and a M.2 2280 B-key for SATA 3.0 storage. The
                       specs mentions that the IGN800 can be configured
                       with up to 32GB of eMMC but it seems that model is
                       out of stock for now.


                       The connectivity interface is flexible since the
                       Wi-Fi antenna is optional and the dual GbE LAN
                       ports are Power-over-Ethernet capable (PoE PD
                       Module required).


                       The IGN800 also features one HDMI display port, one
                       USB Type-C, two USB 2.0, one USB 3.2 Gen 1 and a
                       RS-232/422/485 via 5-pin terminal block.


                # ⚓ CNX Software ☛ ModBerry_500_R1_industrial_computer_replaces
                  Raspberry_Pi_CM4_with_Radxa_CM3_module⠀⇛


                # ⚓ Linux Gizmos ☛ Industrial_IoT_gateway_based_on_Raspberry_Pi
                  CM4_supports_Ignition_Edge⠀⇛


                       OnLogic’s IGN800 is a fanless industrial-grade Edge
                       Gateway powered by the Raspberry Pi CM4 and pre-
                       loaded with Ignition Edge software. The device can
                       be customized with up to 8GB of RAM, 32GB of eMMC
                       storage, 2TB of SATA SSD and dual GbE LAN ports.


                       The IGN800 accommodates the Raspberry Pi CM4 which
                       features the Quad-Core ARM Cortex-A72 64-bit SoC.
                       The memory system can be equipped with 4GB/8GB of
                       RAM and a M.2 2280 B-key for SATA 3.0 storage. The
                       specs mentions that the IGN800 can be configured
                       with up to 32GB of eMMC but it seems that model is
                       out of stock for now. 


                # ⚓ Hackaday ☛ ESP32_Adds_Bluetooth_To_An_IPod_Nano⠀⇛


                       The iPod Nano was one of Apple’s masterworks, but
                       it’s really tied down by its dependence on wired
                       headphones. At least, that’s what [Tucker Osman]
                       must have thought, as he spent an unreasonable
                       amount of time designing a Bluetooth mod for the
                       3rd gen Nano. And it’s a thing of beauty —
                       temperamental, brutally difficult to build, and
                       fragile in use, but still beautiful. And while some
                       purists try to keep their signal analog, [Tucker]’s
                       coup d’etat is to intercept the iPod’s audio signal
                       before the DAC chip, keeping the entire signal path
                       digital to the Bluetooth speaker. Oh, and he also
                       managed to make the volume and track skip buttons
                       work, back across the wireless void.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ The_UV_Budgie_shows_IoT_alerts_in_a_fun_way_|
                  Arduino_Blog⠀⇛


                       The Internet of Things (IoT) is now well-
                       established and households around the world contain
                       many IoT devices. Most of them were designed to
                       blend as seamlessly as possible into their owners’
                       lives, which means that they tend to be
                       unobtrusive. But “unobtrusive” is the last
                       adjective you want to describe an important
                       notification, which is why Jude Pullen built the UV
                       Budgie.


                       For those of you without an interest in
                       ornithology, “budgie” is a shortening of
                       “budgerigar” and is a nickname for the common
                       parakeet. That name is appropriate for this device
                       as it features an automata budgie that flaps and
                       squawks according to the peak UV level for the day.
                       UV rays can be dangerous, so this flapping budgie
                       is a great way to get your kids attention and
                       remind them to pack some sunscreen. A ding or
                       announcement from Alexa won’t tear their eyes away
                       from Minecraft, but a fluttering avian might.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ CNX Software ☛ Realtek_RTD1319D_STB_processor_supports_4K
                  H.266_and_AV1_video_decoding_–_CNX_Software⠀⇛


                # ⚓ Business Insider ☛ 2_Ways_to_See_and_Edit_Your_Clipboard_on
                  Android⠀⇛


                # ⚓ 9to5Google ☛ Google_Workspace_brand_comes_to_Keep,_other
                  apps_–_9to5Google⠀⇛


                # ⚓ GSM Arena ☛ One_UI_5.0_Beta_based_on_Android_13_reaches
                  Galaxy_S21_units_in_India_–_GSMArena.com_news⠀⇛


                # ⚓ SamMobile ☛ Samsung_Galaxy_Z_Fold_2_gets_Android_12L_(One
                  UI_4.1.1)_update_for_better_multitasking_–_SamMobile⠀⇛


                # ⚓ Android_tablet_owners_are_getting_some_really_cool_free_app
                  upgrades_|_T3⠀⇛


                # ⚓ Android Headlines ☛ Android_Phone_Security_Issues:_How_To
                  Stay_Safe⠀⇛


                # ⚓ Android Police ☛ How_to_download_Android_apps_without_the
                  Google_Play_Store⠀⇛


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


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ Document Foundation ☛ LibreOffice_7.4.1_Community_available
                  for_download_–_The_Document_Foundation_Blog⠀⇛


                       LibreOffice 7.4.1 Community, the first maintenance
                       release of LibreOffice 7.4, the volunteer-supported
                       office suite for personal productivity on the
                       desktop, is immediately available from https://
                       www.libreoffice.org/download for Windows (Intel and
                       Arm processors), macOS (Apple M1 and Intel
                       processors), and Linux.


                       LibreOffice offers the highest level of
                       compatibility in the office suite market segment,
                       with native support for the OpenDocument Format
                       (ODF) – beating proprietary formats for security
                       and robustness – to superior support for MS Office
                       files, to filters for a large number of legacy
                       document formats, to return ownership and control
                       to users.


          o § Education⠀➾


                # ⚓ IT Wire ☛ Open-source_technology_founder_Dr_Sanjiva
                  Weerawarana_to_visit_Australia⠀⇛


                       The founder of open-source technology provider
                       WSO2, Dr Sanjiva Weerawarana, is visiting Australia
                       this month to discuss the latest in technology
                       innovation and showcase the recently announced
                       Avinya Foundation, a not-for-profit giving more
                       children in Sri Lanka the opportunity for a
                       professional future via vocational careers.


          o § FSF⠀➾


                # ⚓ GNU ☛ LibrePlanet_2023:_Charting_the_Course_|_Call_for
                  sessions_announced!⠀⇛


                       Next year’s LibrePlanet is themed “Charting the
                       Course” and its Web site is now live at https://
                       libreplanet.org/2023


          o § Licensing / Legal⠀➾


                # ⚓ Variety ☛ Why_Disney_Remains_a_Major_Gaming_Licensor_—_Not
                  a_Player⠀⇛


                       But while control of the Marvel Cinematic Universe
                       and “Star Wars” has been incredibly lucrative for
                       the studio’s film and streaming television efforts,
                       Disney’s 2016 decision to close its game publishing
                       unit means Disney had to transition to a licensing
                       model to capitalize on such IP [sic] for games.


                       That decision may have seemed hasty in retrospect,
                       given the continued prominence of the global games
                       market, which is on the verge of hitting a $200
                       billion annual milestone.


          o § Programming/Development⠀➾


                # ⚓ Qt ☛ The_world’s_going_electric – are_you_ready_to_make_a
                  buzz?⠀⇛


                       Where seeing or owning an electric car or hybrid
                       was a rarity a few years back, the global demand
                       for electric vehicles (EVs) has rapidly surged and
                       it does not seem to be slowing down. With this
                       increased need comes a correlated increase in
                       charging points that are easily accessible and
                       convenient to use. E-charging points, as the name
                       suggests, are machines that charge a variety of
                       different electric vehicles and micro mobility
                       devices. The popularity of these has grown so much
                       that the current expectation is for a whopping 25
                       million new charging points to be erected in Europe
                       and in the US by 2030 to help further facilitate
                       the comfort of EV users*.


                # ⚓ rec-def:_Program_analysis_case_study_–_Blog_–_Joachim
                  Breitner’s_Homepage⠀⇛


                       At this week’s International Conference on
                       Functional Programming I showed my rec-def Haskell
                       library to a few people. As this crowd appreciates
                       writing compilers, and example from the realm of
                       program analysis is quite compelling.


                # § Python⠀➾


                      # ⚓ Linux Hint ☛ How_To_Calculate_Matrices_in_Python
                        Without_NumPy⠀⇛


                             The vertical series of objects in a Python
                             matrix is generally known as the “columns,”
                             whereas the horizontal series of things is
                             referred to as the “rows.” Like a nested
                             list, the rows and columns were placed on top
                             of one another. If a matrix has “k” rows and
                             “m” columns, and if “k” and “m” are positive
                             integers, the order of such a matrix object
                             is determined by “k-by-m”.


                             A matrix can hold strings, numbers, and other
                             data kinds of objects. In a matrix, data is
                             stacked in both columns and rows. A key data
                             structure supporting computations in science
                             and math is the matrix. Since Python does not
                             provide a built-in type for a matrix object,
                             we treat either list among lists or even a
                             nested list as a matrix.


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


                             Starting a Python application typically
                             results in a flurry of imports as modules
                             from various locations (and the modules they
                             import) get added into the application
                             process. All of that occurs before the
                             application even gets started doing whatever
                             it is the user actually launched it for; that
                             delay can be significant—and annoying. Beyond
                             that, many of those imports may not be
                             necessary at all for the code path being
                             followed, so eagerly doing the import is
                             purely wasted time. A proposal back in May
                             would add a way for applications to choose
                             lazy imports, where the import is deferred
                             until the module is actually used.


          o § Standards/Consortia⠀➾


                # ⚓ StandICT.eu_2023_–_8th_Open_Call⠀⇛


                       Please note that only the first 70 (seventy)
                       eligible applications submitted in response to the
                       call, taken in chronological order according to the
                       time-stamp of submission will be evaluated by the
                       External Pool of Evaluators for funding


                       The main topic for the 8th Open Call will be
                       “Resilience and Green Transition” .


    * § Leftovers⠀➾


          o ⚓ George ☛ Apostles_Of_Mara⠀⇛


                 Mara, he who tempts with unfulfilled desires and inflicts
                 the sorrows of want and disillusion, came upon a tribe of
                 hunter-gatherers living their happy noble-savage life, in
                 tune with nature and their own bodies, accepting life and
                 death as they accepted day and night.


                 He took the form of a tall man shrouded in dark robes
                 embroidered with golden beetles flapping their wings to
                 create a dissonant symphony of agonizing moans.


                 And he gave them golden robes, but the robes were laced
                 with leaded silk that would slowly drive them to madness.


                 And he thought them ironwork to better hunt but knew the
                 iron arrowheads will be used against their fellow men.


                 And he gave them herbs to cure their sores, and to
                 staunch their fevers, and to prevent childbirth, and to
                 take away pain. But their effects were transitory and
                 lead to greater suffering once treatment ceased.


          o ⚓ Mexico News Daily ☛ Lucha_Libre_legend_‘El_Santo’_retired_40
            years_ago_this_week⠀⇛


                 Forty years ago this week Mexico’s most famous Lucha
                 Libre star retired from the ring, and now his son, El
                 Hijo del Santo, will do the same — but not without one
                 final fight.


          o ⚓ Hackaday ☛ Robot:_Will_Draw_For_Food⠀⇛


                 Biological systems often figure out the best ways to get
                 what they need to survive. Now a robot created by
                 researchers at Worcester Polytechnic Institute, Imperial
                 College London, and the University of Illinois Urbana
                 Champaign can make the same claim. The robot operates in
                 front of a plate that has electrical terminals on one end
                 and various obstacles between those terminals and the
                 robot.


          o ⚓ Hackaday ☛ Making_A_Tape_Echo_The_Traditional_Way⠀⇛


                 [Juan Nicola] has taken inspiration from the musician
                 hackers of old and re-purposed a reel-to-reel tape
                 recorder into a tape-echo for his guitar with a built-in
                 valve amplifier (video in Spanish).


          o ⚓ The Nation ☛ Haiti_Is_On_Fire_Again,_and_Again_the_US_Does
            Nothing_to_Help⠀⇛


                 On Tuesday, in a crescendo of popular anger, Port-au-
                 Prince and Haiti’s provincial towns’ weeklong protests
                 against the de facto government and its policies
                 escalated at a dizzying pace. In preparation for the
                 day’s protests, enormous barricades constructed of
                 building materials, tin roofing, heavy iron gates, and a
                 variety of junked vehicles were erected at important
                 intersections in the capital during the darkness of the
                 previous night. The capital’s population woke to these
                 architectural blockades—interspersed with burning tires
                 and piles of rocks. Hundreds of demonstrators emerged
                 into the morning streets, although warned by news alerts
                 that it might well be dangerous, to protest against gas
                 shortages and soaring prices, the punitive rise in the
                 cost of living, brutal gang violence, and the continued
                 rule of the man presiding over the intensifying crisis,
                 the country’s de facto prime minister, Ariel Henry.


          o ⚓ The Nation ☛ Beauty_in_Harlem⠀⇛


          o ⚓ Hackaday ☛ Big_Noise_From_A_555_And_A_Little_Embroidery⠀⇛


                 [Sam Topley] specializes in making textile based,
                 electronic instruments and sculptures using embroidery,
                 and this little hoop packs some serious sound (Nitter).


          o § Education⠀➾


                # ⚓ Quillette ☛ Math_for_Future_Scientists:_Require_Statistics,
                  Not_Calculus⠀⇛


                       In short, America’s calculus push was launched over
                       60 years ago in the belief that calculus was
                       necessary for national survival in the coming Space
                       Age. But times have changed. We are now in the
                       Information Age, and preparing students to build
                       rockets is not as essential for the majority of
                       science majors as learning to interpret and
                       prioritize a sea of information. And far more
                       scientific information circulates in the form of
                       statistics than in any form related to calculus.


                       Rubin goes on to illustrate how, in the 1980s,
                       American educators began to suggest that statistics
                       might be more important for the future than
                       calculus, which led to the first AP Statistics
                       exams in 1997. He says a college educator told him
                       that this introduction of AP Statistics “occurred
                       despite the best efforts of ‘the calculus mafia.’”
                       The calculus mafia is, unfortunately, still alive
                       and well today: In 2021, roughly 375,000 students
                       took the AP Calculus AB or BC exams, while only
                       about 183,000 took the AP Statistics exam.


                # ⚓ Joinup ☛ High-level_panel_on_personal_data_spaces_with
                  Natalia_Aristimuño_Pérez_and_Sir_Tim_Berners-Lee_Permalink⠀⇛


                       On the 22th of September, Interoperable Europe
                       Digital Services Director Natalia Aristimuño Pérez
                       will take part in a European high-level panel on
                       personal data spaces at Digital Flanders’ annual
                       GovTech Conference. Sir Tim Berners-Lee, the
                       inventor of the World Wide Web, will join as
                       special guest.


                # ⚓ Telex (Hungary) ☛ Why_I_left_public_education_after_13
                  years_–_a_teacher’s_story⠀⇛


                       Dorottya Lendvai knew she wanted to be a teacher
                       when she was six years old. Now, after 13 years as
                       a maths and physics teacher she decided to quit
                       working in the public school system, because she
                       suffered under the ever-increasing burdens, and
                       would have liked to be able to look in the mirror.
                       She had high hopes for the strike and the civil
                       disobedience movement which started at the
                       beginning of this year, but after seeing that this
                       didn’t bring about a change, she had had enough.
                       She says the hardest part was telling her students
                       about it. One of her students’ parents even offered
                       money to the school if she were to stay. She will
                       still do some private tutoring, but seeing her name
                       on the door of her old classroom at a recent visit
                       still made her cry. She would consider returning,
                       but for that to happen, the pay would have to be
                       twice what it is now and the number of lessons
                       limited to 18 per week. This is her story about why
                       she left.


                # ⚓ Telex (Hungary) ☛ Teachers’_Unions_turn_to_European_Court
                  of_Human_Rights_about_their_right_to_strike⠀⇛


          o § Hardware⠀➾


                # ⚓ Middle East Eye ☛ Saudi_Arabia:_Robots_to_relay_sermons_and
                  call_to_prayer_at_Mecca’s_Grand_Mosque⠀⇛


                       Visitors can use their smartphones to scan the
                       robot’s barcodes to show content such as verses
                       from the Quran and download it on their devices.


                # ⚓ RTL ☛ Health_groups_call_for_fossil_fuel_non-proliferation
                  treaty⠀⇛


                       Around 200 health organisations and more than 1,400
                       health professionals on Wednesday called for
                       governments to establish a binding international
                       treaty on phasing out fossil fuels, which they said
                       pose “a grave and escalating threat to human
                       health”.


                       A letter proposing the “fossil fuel non-
                       proliferation treaty” said it could work similarly
                       to the World Health Organization’s Framework
                       Convention on Tobacco Control — except this time
                       the harmful controlled substances would be coal,
                       oil and gas.


                       The WHO was among the health organisations from
                       around the world who signed the letter.


                # ⚓ CNN ☛ Fred_Franzia,_creator_of_‘Two_Buck_Chuck,’_has_died⠀⇛


                       “Core to his vision was a belief that wine should
                       be enjoyed and consumed on every American table,”
                       Bronco’s statement said. “When asked how Bronco
                       Wine Company can sell wine less expensive than a
                       bottle of water, Fred T. Franzia famously
                       countered, ‘They’re overcharging for the water —
                       don’t you get it?’”


                # ⚓ Hackaday ☛ Mokeylaser:_A_DIY_Laser_Engraver_That_You_Can
                  Easily_Build⠀⇛


                       [Mark aka Mokey] borrowed his friend’s open-frame
                       laser engraver for a while, and found it somewhat
                       lacking in features and a bit too pricey for what
                       it was. Naturally, he thought he could do better
                       (video, embedded below.) After a spot of modelling
                       in Fusion 360, and some online shopping at the
                       usual places, he had all the parts needed to
                       construct an X-Y bot, and we reckon it looks like a
                       pretty good starting point. [Mark] had a Sainsmart
                       FL55 5.5W laser module kicking around, so that was
                       dropped into the build, together with the usual
                       Arduino plus CNC shield combo running GRBL.


                # ⚓ Hackaday ☛ Future_Brings_CPU_Modules,_And_The_Future_Is
                  Now⠀⇛


                       Modularity is a fun topic for us. There’s something
                       satisfying about seeing a complex system split into
                       parts and these parts made replaceable. We often
                       want some parts of our devices swapped, after all –
                       for repair or upgrade purposes, and often, it’s
                       just fun to scour eBay for laptop parts, equipping
                       your Thinkpad with the combination of parts that
                       fits you best. Having always been fascinated by
                       modularity, I believe that hackers deserve to know
                       what’s been happening on the CPU module front over
                       the past decade.


                # ⚓ The Next Platform ☛ Arm_Fills_In_Some_Gaps–_And_Details_–
                  In_Server_Chip_Roadmaps⠀⇛


                       Let’s just say it right here at the beginning. The
                       first wave of attempts at creating Arm server chips
                       –Calxeda, Applied Micro, AMD, Marvell, Nvidia, and
                       Samsung, among others – was disappointing. And so
                       was the second wave – with Broadcom, Cavium,
                       Qualcomm, and Nuvia – now that we think on it.


                       But with the third wave of Arm server chips, being
                       led by the hyperscalers and cloud builders (Amazon
                       Web Services, Microsoft, Google, Alibaba, and
                       Tencent – and a few independent chip designers
                       (mainly Ampere Computing, HiSilicon, Nvidia, and
                       SiPearl) working in concert with Arm Ltd, the
                       creator and maintainer of the Arm architecture that
                       is looking to go public (again), it looks like Arm
                       server chips are here for the long haul.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Michael West Media ☛ Paid_pandemic_leave_extended
                  indefinitely_–_Michael_West⠀⇛


                       The payments for infected people off work were set
                       to expire at the end of the month but will remain
                       in place as long as mandatory isolation periods are
                       in effect.


                # ⚓ Scheerpost ☛ NYT_Scolds_China_for_Not_‘Learning_to_Live’—or
                  Die—With_Covid⠀⇛


                # ⚓ TruthOut ☛ Sanders_Calls_State_of_US_Health_Care_an
                  “International_Embarrassment”⠀⇛


                # ⚓ The Nation ☛ The_Half_Measures_of_Public_Health
                  Architecture⠀⇛


                       The sudden onset of the Covid-19 pandemic inverted
                       long-held assumptions. Jobs previously seen as
                       disposable were now regarded as “essential.” Well-
                       heeled professionals walked out on lucrative
                       careers to focus on their lives beyond the market.
                       Conservative politicians who had long taken fee-
                       for-service health care as an article of faith
                       acquiesced to free universal testing and treatment.
                       And the belief that we are all connected changed
                       from a dreamy left-wing mantra to a hard-headed
                       principle of realpolitik.


                # ⚓ Common Dreams ☛ Opinion_|_Covid-19_and_9/11:_Who_Lives,_Who
                  Dies,_Who_Cares⠀⇛


                       On September 9, with virtually no press coverage,
                       President Biden sent an official letter to Congress
                       extending a state of emergency that was first
                       declared in the aftermath of 9/11, more than two
                       decades ago. “The terrorist threat … continues,”
                       the letter declares. George W. Bush’s original
                       declaration of emergency led to trillions of
                       dollars in military spending and the transformation
                       of American society. Thousands of young Americans,
                       and well over a million people in the Middle East,
                       lost their lives.


          o § Proprietary⠀➾


                # ⚓ Krebs On Security ☛ Say_Hello_to_Crazy_Thin_‘Deep_Insert’
                  ATM_Skimmers⠀⇛


                       A number of financial institutions in and around
                       New York City are dealing with a rash of super-thin
                       “deep insert” skimming devices designed to fit
                       inside the mouth of an ATM’s card acceptance slot.
                       The card skimmers are paired with tiny pinhole
                       cameras that are cleverly disguised as part of the
                       cash machine. Here’s a look at some of the more
                       sophisticated deep insert skimmer technology that
                       fraud investigators have recently found in the
                       wild.


                # ⚓ ABC ☛ Iranian_nationals_charged_in_alleged_ransomware
                  conspiracy [iophk: Windows TCO]⠀⇛


                       The four-count grand jury indictment returned in
                       Newark federal court charged the trio with
                       [cracking] conspiracy, two counts of computer
                       [cracking] and a count of computer extortion over
                       an alleged ransomware conspiracy that targeted a
                       range of organizations and critical infrastructure
                       sectors such as healthcare centers, power companies
                       and transportation services inside the U.S. and
                       abroad.


                       Mansour Ahmadi, Ahmad Aghda, and Amir Ravari
                       [broke] into hundreds of computers inside the U.S.
                       and around the world by often exploiting known
                       vulnerabilities in network devices or software
                       programs, the indictment said.


                # ⚓ VOA News ☛ Three_Iranian_[Crackers]_Charged_in_‘Ransomware-
                  Style’_Hacking_Campaign [iophk: Windows TCO]⠀⇛


                       The three Iranian nationals — identified as Mansour
                       Ahmadi, Ahmad Khatibi Aghda and Amir Hossein
                       Nickaein Ravari — are accused of carrying out
                       “computer intrusions and ransomware-style
                       extortion” between October 2020 and August 2022,
                       according to a 30-page indictment unsealed
                       Wednesday.


                       The men remain at large and are believed to be in
                       Iran, according to U.S. law enforcement officials.


                # ⚓ The Hill ☛ DOJ_indicts_Iranians_for_allegedly_[cracking]
                  and_extorting_US_groups [iophk: Windows TCO]⠀⇛


                       U.S. officials accused the defendants of
                       exfiltrating data from the organizations’ computer
                       systems and attempting to extort money from them by
                       either threatening to release the stolen data or
                       keeping the data encrypted unless the hackers were
                       paid.


                       The [crackers] allegedly demanded hundreds of
                       thousands of dollars in ransom payments, which some
                       victims paid to regain access to their data, a
                       senior DOJ official said during a background call
                       on Wednesday.


          o § Linux Foundation⠀➾


                # ⚓ AAAS ☛ CGIAR_and_the_Linux_Foundation_partner_to_unl_|
                  EurekAlert! [Ed: No connection whatsoever to Linux, just
                  openwashing (Microsoft) as a service]⠀⇛


                       CGIAR and the Linux Foundation have formed a
                       research partnership to develop a standard way of
                       sharing data about agricultural fields at scale,
                       which could deliver global benefits, including for
                       the estimated 500 million smallholder farmers that
                       produce about a third of the world’s food.


          o § Security⠀➾


                # ⚓ Istio_/_Support_for_Istio_1.13_ends_on_October_12th,_2022⠀⇛


                       According to Istio’s support policy, minor releases
                       like 1.13 are supported until six weeks after the
                       N+2 minor release (1.15 in this case). Istio 1.15
                       was released on August 31st, and support for 1.13
                       will end on October 12th, 2022.


                       At that point we will stop back-porting fixes for
                       security issues and critical bugs to 1.13, so we
                       encourage you to upgrade to the latest version of
                       Istio (1.15). If you don’t do this you may put
                       yourself in the position of having to do a major
                       upgrade on a short timeframe to pick up a critical
                       fix.


                       We care about you and your clusters, so please be
                       kind to yourself and upgrade.


                # ⚓ Paul Schaub ☛ Using_Pushdown_Automata_to_verify_Packet
                  Sequences_–_vanitasvitae’s_blog⠀⇛


                       As a software developer, most of my work day is
                       spent working practically by coding and hacking
                       away. Recently though I stumbled across an
                       interesting problem which required another, more
                       theoretical approach;


                       An OpenPGP message contains of a sequence of
                       packets. There are signatures, encrypted data
                       packets and their accompanying encrypted session
                       keys, compressed data and literal data, the latter
                       being the packet that in the end contains the
                       plaintext body of the message.


                       Those packets can be sequential, e.g. a one-pass-
                       signature followed by a literal data packet and
                       then a signature, or nested, where for example an
                       encrypted data packet contains a compressed data
                       packet, in turn containing a literal data packet. A
                       typical OpenPGP message can be visualized as
                       follows:


                       [...]


                       From “start” we transition to “OpenPGP Message” by
                       pushing ‘#’ and ‘m’ on the stack. The we read
                       “Compressed Packet from input, pop ‘m’ from the
                       stack and transition to state “Compressed Message”.
                       Since the “Literal Packet” is part of the
                       Compressed Packet”s contents, we now create a new
                       child PDA with input stream “Literal Packet”. After
                       initializing this PDA by pushing ‘#’ and ‘m’ to the
                       stack, we then transition from “OpenPGP Message” to
                       “Literal Message” by reading “Literal Packet” and
                       popping ‘m’, after which we transition to “Valid”
                       by popping ‘#’. Now this PDA is ended up in a valid
                       state, so our parent PDA can transition from
                       “Compressed Message” by reading nothing from the
                       input (remember, the “Compressed Packet” was the
                       only packet in this PDAs stream), popping ‘#’,
                       leaving us with an empty stack and empty input in
                       the valid state.


                       In PGPainless’ code I am planning to implement
                       OpenPGP message validation by using InputStreams
                       with individual PDAs. If a packet contains nested
                       data (such as the Compressed or Encrypted Packet),
                       a new InputStream will be opened on the
                       decompressed/decrypted data. This new InputStream
                       will in turn have a its own PDA to ensure that the
                       content of the packet forms a valid OpenPGP message
                       on its own. The parent stream on the other hand
                       must check, whether the PDA of it’s child stream
                       ended up in a valid state before accepting its own
                       packet stream.


                # ⚓ Help Net Security ☛ 5_Kali_Linux_books_you_should_read_this
                  year_–_Help_Net_Security⠀⇛


                       Kali Linux is a Linux distribution designed for
                       digital forensics, penetration testing, security
                       research, and reverse engineering.


                       Here is a selection of books for different
                       experience levels, you can either start from
                       scratch or get advanced tips – there’s something
                       for everyone.


                # ⚓ The Nation ☛ The_Digital_Soldiers_Taking_America’s_Forever
                  Wars_Online⠀⇛


                       The three men and three women stood with their
                       right arms raised. Behind them the remains of the
                       daylight hued the sky a bluish gray. As a fire
                       danced at their feet, they gazed straight ahead at
                       a camera recording their words. The square-jawed
                       man in the middle, retired Lt. Gen. Michael T.
                       Flynn, spoke first. The others, including members
                       of his family, repeated after him.


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ [Old] Caleb Hearth ☛ Signing_Git_Commits_with_Your
                        SSH_Key⠀⇛


                             You may already be signing your Git commits
                             with a GPG key, but as of today you can
                             instead choose to sign with your SSH key!
                             Signing in SSH is a relatively new feature
                             that lets you use your private SSH key to
                             sign arbitrary text and others to verify that
                             signature with your public key.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Online_Identity_is_Complicated⠀⇛


                             To be clear, I’m not trying to land on one
                             side of the identity debate or another. I’m
                             trying to inject nuance into the conversation
                             and make sure we don’t leave certain groups
                             out of the conversation as a whole, as we
                             have done so many times before. A perennial
                             problem in almost all of tech is we don’t
                             stop to consider externalities, especially in
                             how things will affect marginalized folks.


                      # ⚓ Reuters ☛ S.Korea_fines_Google,_Meta_billions_of_won
                        for_privacy_violations⠀⇛


                             In a statement, the Personal Information
                             Protection Commission said it fined Google
                             69.2 billion won ($50 million) and Meta 30.8
                             billion won ($22 million).


                             The privacy panel said the firms did not
                             clearly inform service users and obtain their
                             prior consent when collecting and analysing
                             behavioural information to infer their
                             interests or use them for customised
                             advertisements.


                      # ⚓ RTL ☛ Google,_Meta_face_record_fines_in_South_Korea
                        over_privacy_violations⠀⇛


                             South Korea has fined Google and Meta more
                             than $71 million collectively for gathering
                             users’ personal information without consent
                             for tailored ads, regulators said Wednesday,
                             the country’s highest-ever data protection
                             fines.


                             Investigations into the two US tech giants
                             found they had been “collecting and
                             analysing” data on their users, and
                             monitoring their use of websites and
                             applications, the Personal Information
                             Protection Commission said.


                      # ⚓ RFI ☛ Google,_Meta_face_record_fines_in_South_Korea
                        over_privacy_violations⠀⇛


                             South Korea has fined Google and Meta more
                             than $71 million collectively for gathering
                             users’ personal information without consent
                             for tailored ads, regulators said Wednesday,
                             the country’s highest-ever data protection
                             fines.


                      # ⚓ CNA ☛ South_Korea_fines_Google,_Meta_billions_of_won
                        for_privacy_violations⠀⇛


                             South Korea levied millions of dollars in
                             fines on Alphabet’s Google and Meta Platforms
                             for privacy law violations, authorities said
                             on Wednesday (Sep 14), as Meta considers
                             fighting the decision in court.


                      # ⚓ Barrons ☛ Google,_Meta_Face_Record_Fines_In_South
                        Korea_Over_Privacy_Violations⠀⇛


                             Regulators said the majority of the users in
                             South Korea — 82 percent for Google and 98
                             percent for Meta — had unknowingly allowed
                             them to collect data on their online use.


                      # ⚓ Internet Freedom Foundation ☛ The_National_Commission
                        for_Safai_Karamcharis_takes_action_to_protect
                        sanitation_workers_from_workplace_surveillance⠀⇛


                             In a significant step, the National
                             Commission for Safai Karamcharis (NCSK) has
                             directed four municipal corporations using
                             GPS tracking devices on sanitation workers to
                             furnish a factual report to them. This step
                             was taken pursuant to our joint letter with
                             All India Lawyers Association For Justice
                             (AILAJ) to the NCSK in which had raised
                             concerns about the increasing surveillance of
                             sanitation workers.


                             [...]


                             After reports concerning the use of GPS
                             tracking devices on Safai Karamcharis by the
                             Ranchi Municipal Corporation came to light,
                             the All India Lawyers Association For Justice
                             (AILAJ) reached out to us to initiate a joint
                             letter to express concerns over such
                             violations. We sent a joint letter dated May
                             30, 2022 to the National Commission for Safai
                             Karamcharis (NCSK) to urge them to
                             investigate this issue and to take the
                             necessary steps to ensure that all Safai
                             Karamcharis are safeguarded from this
                             imposition. The joint letter received
                             endorsements by 18 organisations and 187
                             individuals. However, we did not receive any
                             response from NCSK on the joint letter. As a
                             result, we sent a letter to follow-up on our
                             joint letter on August 8, 2022.


                      # ⚓ Common Dreams ☛ Opinion_|_Down_With_the_Corporate
                        Bean-Counters_Who_Spy_on_Their_Workers⠀⇛


                             For generations, workers have been punished
                             by corporate bosses for watching the clock.
                             But now, the corporate clock is watching
                             workers! They count this as progress.


          o § Defence/Aggression⠀➾


                # ⚓ CBS ☛ Man_who_pinned_D.C._police_officer_in_door_frame
                  during_Jan._6_riot_convicted_of_7_felonies⠀⇛


                       McCaughey was captured on video using a riot shield
                       to pin MPD officer Daniel Hodges in a doorway
                       during the riot. Hodges could be seen screaming out
                       in pain as he was being crushed in the doorway as
                       rioters attempted to enter the Capitol building. In
                       an interview with CBS News, Hodges said that in
                       videos, you can see McCaughey grabbing his gas
                       mask, beating his head against the door, and
                       ripping it away.


                # ⚓ MEMRI ☛ Iranian_Political_Analyst_Emad_Abshenas:_Iran_Has
                  Crossed_The_Nuclear_Threshold;_It_Can_Produce_A_Nuclear
                  Weapon_In_A_Matter_Of_Days⠀⇛


                       “Today, Iran has crossed the nuclear threshold. The
                       basic goal of the nuclear agreement was to keep
                       Iran at least one year away from the nuclear
                       threshold. Today, however, Iran isn’t far from the
                       nuclear threshold. I can tell you that if Iran
                       decides to produce a nuclear weapon, the first
                       nuclear weapon will be ready within two or three
                       days perhaps, if the political decision is made.”


                # ⚓ Medforth ☛ Sweden:_Islam_party_wins_up_to_30%_of_the_vote
                  in_deprived_areas⠀⇛


                       A video showing the party’s supporters in a major
                       Swedish city is currently going viral. Former
                       Austrian People’s Party (ÖVP) politician Efgani
                       Dönmez wrote on Twitter: “If you ask yourself why
                       the right-wing camp is so strong in Sweden, here is
                       an explanation. A party of foreigners is likely to
                       make it into parliament in Malmö. You can see the
                       electorate in the footage. No comment.”


                # ⚓ Pro-Erdoğan_Islamist_party_in_Sweden_sparks_concerns_after
                  it_receives_large_number_of_votes_in_immigrant_districts⠀⇛


                       Many right-wing voters voice concern that an
                       Islamist party has become popular among immigrants.
                       Political experts predict that it is likely for
                       Nyans to enter parliament in future elections,
                       surpassing the electoral threshold, which is only 4
                       percent. Right-wing voters also see it as the
                       failure of integration, blaming leftist
                       governments.


                # ⚓ TruthOut ☛ Report:_DOJ’s_Jan._6_Inquiry_Focusing_on_All
                  Efforts_by_Trump_to_Undo_Election⠀⇛


                # ⚓ Democracy Now ☛ “The_Storm_Is_Here”:_War_Reporter_Luke
                  Mogelson_on_U.S._Right-Wing_Militias,_Violence,_Jan._6_&
                  Trump⠀⇛


                       We speak with The New Yorker’s award-winning war
                       correspondent Luke Mogelson about his new book,
                       “The Storm Is Here: An American Crucible.” The book
                       gives an eyewitness account of right-wing extremism
                       and growing civic unrest in the U.S. since 2020,
                       starting with anti-lockdown protests in Michigan
                       and culminating in the January 6 insurrection.
                       Mogelson, who filmed the attack on the U.S.
                       Capitol, says many of the right-wing rioters viewed
                       the insurrection “not as a political act but as
                       something taking place in a more timeless, kind of
                       cosmic spiritual framework.”


                # ⚓ Meduza ☛ Ukrainian_Prosecutor_General’s_office_says_no
                  Russian_teachers_detained_in_liberated_territories_—_Meduza⠀⇛


                       The Ukrainian Prosecutor General’s office told
                       Current Time that Russian teachers have not been
                       detained on the territory of Kharkiv region that
                       was liberated by Ukrainian troops.


                # ⚓ Meduza ☛ ‘A_complex_situation.’_Ukrainian_troops_approach
                  the_self-proclaimed_Luhansk_People’s_Republic._—_Meduza⠀⇛


                       Andrey Marochko, a spokesman for the so-called
                       People’s Militia of the Luhansk People’s Republic
                       (LNR) says that Ukrainian troops are approaching
                       the border of the self-proclaimed republic, reports
                       news agency TASS.


                # ⚓ Scheerpost ☛ Lee_Camp:_How_the_US_&_UK_Stopped_Peace_Deal
                  in_Ukraine⠀⇛


                       The Headlines Lee Camp proves that NATO and the
                       U.S. want their proxy war in Ukraine to be fought
                       to the last Ukrainian. A new report shows that
                       Russia and Ukraine had negotiat…


                # ⚓ Scheerpost ☛ Scott_Ritter:_Why_Russia_Will_Still_Win,
                  Despite_Ukraine’s_Gains⠀⇛


                       Russia is no longer fighting a Ukrainian army
                       equipped by NATO, but a NATO army manned by
                       Ukrainians. Yet, Russia still holds the upper hand
                       despite its Kharkiv setback.


                # ⚓ Scheerpost ☛ World_BEYOND_War_Volunteers_to_Reproduce
                  “Offensive”_Peace_Mural⠀⇛


                # ⚓ Scheerpost ☛ The_Chris_Hedges_Report:_Nathaniel_Philbrick
                  on_How_George_Armstrong_Custer_Became_a_Martyr_Used_to
                  Justify_Genocide_and_US_Imperialism⠀⇛


                       Custer became in death a martyr to the American
                       empire. He was in popular mythology the last to die
                       in the battle, a symbol of martial valor, although
                       there is scant evidence for this assertion.


                # ⚓ Counter Punch ☛ Colonel_Larry_Wilkerson_Interview:_An
                  Objective_Look_at_U.S._Foreign_Policy⠀⇛


                       We focus on the realities of the international
                       power struggle unfolding in real time, specifically
                       addressing the role of the U.S. in the tensions and
                       its capacity to reduce them. We are looking for
                       paradigm-shift ideas for improving the prospects
                       for peace. His responses below of are exactly as he
                       provided.


                # ⚓ Counter Punch ☛ Russia’s_Underperforming_Military_(and_Our
                  Own)⠀⇛


                       Still, in the view of American military figures,
                       all of those factors take a backseat to Russia’s
                       manifest inability (or refusal) to grasp the basic
                       prerequisites of modern warfare. The fact that
                       Western observers possess a limited understanding
                       of how that country’s military leadership functions
                       makes it all the easier to render such definitive
                       judgments. It’s like speculating about Donald
                       Trump’s innermost convictions. Since nobody really
                       knows, any forcefully expressed opinion acquires at
                       least passing credibility.


                # ⚓ Meduza ☛ ‘A_country_of_denial’:_Ksenia_Mironova,_the
                  fiancée_of_jailed_ex-journalist_Ivan_Safronov,_says_work,_not
                  hope,_is_what_keeps_her_going_—_Meduza⠀⇛


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Techdirt ☛ Gavin_Newsom_Signs_Hugely_Problematic
                  ‘Transparency’_Bill_Into_Law⠀⇛


                       We’re still waiting to see if California Governor
                       Gavin Newsom will sign the California Age
                       Appropriate Design Code (AB 2273) into law, though
                       all indications are that he will. However, he has
                       now signed a different bad bill into law. He has
                       happily signed what he calls the “nation-leading
                       social media transparency measure” AB 587 into law.
                       The bill is a disaster whether or not you support
                       the goal of “transparency” for social media
                       companies. Actually, the bill is a disaster
                       especially if you support more transparency from
                       social media companies.


                # ⚓ The Nation ☛ Biden_vs._Newsom_on_Farmworkers’_Right_To
                  Vote⠀⇛


                       “I strongly support California’s Agricultural Labor
                       Relations Voting Choice Act (AB 2183),” Biden
                       announced on September 6. Noting that farmworkers
                       had worked through the pandemic, he declared, “The
                       least we owe them is an easier path to make a free
                       and fair choice to organize a union. Government
                       should work to remove—not erect—barriers to workers
                       organizing.”


          o § Environment⠀➾


                # ⚓ NBC ☛ Patagonia_founder_gives_away_company,_ensuring
                  profits_go_to_fight_climate_change⠀⇛


                       The founder of the outdoor brand Patagonia has
                       relinquished his ownership in the business and
                       directed its profits to fight climate change.


                       Yvon Chouinard, who became famous for alpine climbs
                       in Yosemite National Park and then as a
                       manufacturer of outdoor gear, has transferred his
                       family’s ownership of Patagonia to two new
                       entities, one of them a nonprofit organization that
                       will use the businesses’ annual profits to fight
                       climate change, the company said in a news release
                       Wednesday.


                # ⚓ The Nation ☛ Want_to_Fight_Climate_Change?_Look_to_Local
                  Politics.⠀⇛


                       In August, Joe Biden signed the Inflation Reduction
                       Act, a reduced version of Build Back Better, that
                       will invest $369 billion in energy and climate. The
                       IRA is poised to cut the nation’s greenhouse gas
                       emissions in half by 2030, according to an analysis
                       by the White House Office of Management and Budget.
                       The plan will give Americans tax credits and
                       rebates for purchasing electric vehicles and create
                       millions of jobs to generate and deploy clean
                       energy. According to the White House, “the
                       Inflation Reduction Act will help ease the burden
                       that climate change imposes on the American
                       public.”


                # ⚓ Common Dreams ☛ Opinion_|_Inside_the_Climate_Movement_and
                  Still_Outside_the_White_House⠀⇛


                       I should have known it wouldn’t work.


                # ⚓ TruthOut ☛ Line_3_Protesters_Win_Protective_Ruling_Against
                  Government_Repression⠀⇛


                # ⚓ Scheerpost ☛ Catastrophic_Climate_Tipping_Points_‘Probable’
                  Above_1.5°C⠀⇛


                       Tim Radford summarizes a harrowing new study about
                       tipping points.


                # ⚓ Common Dreams ☛ ‘Earth_Is_Now_Our_Only_Shareholder’:
                  Founder_Gives_Away_Patagonia_to_Save_the_Planet⠀⇛


                       “Instead of ‘going public,’ you could say we’re
                       ‘going purpose.’”


                # ⚓ Common Dreams ☛ Opinion_|_The_Politics_of_Overconsumption
                  and_Getting_the_Scale_Right⠀⇛


                       This essay is adapted from An Inconvenient
                       Apocalypse: Environmental Collapse, Climate Crisis,
                       and the Fate of Humanity.


                # § Energy⠀➾


                      # ⚓ The Economist ☛ Ireland’s_dreams_of_exporting_wind
                        power_are_plausible⠀⇛


                             The obvious solution is to move production
                             out to sea. Ireland’s only offshore wind
                             farm, off County Wicklow on the east coast,
                             was the largest in the world when it began
                             spinning in 2004, but has since been dwarfed
                             by newer ones elsewhere in Europe. Noel
                             Cunniffe of Wind Energy Ireland, another
                             industry group, says that in theory Ireland
                             could install offshore turbines with a
                             capacity totalling 80 gigawatts, more than
                             triple Britain’s total current wind capacity,
                             and that this figure will probably increase
                             as turbine technology continues to improve.


                      # ⚓ Eesti Rahvusringhääling ☛ Eesti_Energia:_Estonia
                        cannot_produce_enough_electricity_during_peak_hours⠀⇛


                             The report says peak consumption is
                             approximately 1,600 megawatts and Elering’s
                             data shows Estonia’s production capacity is
                             1,700 megawatts. The vast majority — 1,355
                             megawatts — comes from domestic oil shale
                             plants.


                             However, the Iru co-generation power plant,
                             which has a capacity of 94 megawatt, is
                             unlikely to produce electricity this year due
                             to high gas prices.


                      # ⚓ Mexico News Daily ☛ Scientists_refute_Pemex_regarding
                        massive_methane_leak⠀⇛


                             A team of European scientists published a
                             paper earlier this year that details an
                             “ultra-emission event” at Pemex’s Zaap-
                             C platform detected using data from European
                             Space Agency satellites.


                      # ⚓ Common Dreams ☛ Report_Exposes_Decades_of_‘Big_Oil
                        Lies’_as_Industry_Faces_Congressional_Scrutiny⠀⇛


                             “Like Big Tobacco, Big Oil may soon have to
                             pay for its abuses.”


                      # ⚓ Common Dreams ☛ Opinion_|_UK_Reversal_of_Fracking_Ban
                        Is_Anti-Science_and_Anti-Planet⠀⇛


                             It is just shy of three years since the UK
                             Government announced it was withdrawing its
                             support for shale gas extraction or fracking.


                      # ⚓ Common Dreams ☛ WHO_Leads_Global_Health_Coalition
                        Demand_for_Fossil_Fuel_Non-Proliferation_Treaty⠀⇛


                             “It’s time for world leaders to meet the bar
                             for climate leadership by working together to
                             end the fossil fuel era in a way that is fair
                             and fast.”


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ What_History_Can_Teach_Us_About_the
                        Conservation_of_Endangered_Species⠀⇛


                      # ⚓ Counter Punch ☛ Zoo_Troubles:_the_Plight_of_Two
                        Pandas_Lays_Bare_the_Flaws⠀⇛


                             Animals in captivity do not face the
                             challenges and the different stimulations
                             that their counterparts who live in the wild
                             encounter daily. Consequently, they need
                             special enrichment such as toys, different
                             foods and smells, and artificial
                             challenges—like food hiding—to mentally
                             stimulate their senses, deal with boredom,
                             and help these animals live as happily and
                             comfortably as they can in captivity.


                # § Overpopulation⠀➾


                      # ⚓ Middle East Monitor ☛ Half_a_million_children_on
                        Somalia_face_acute_malnutrition⠀⇛


                             An official in one Somali region described
                             famished people walking long distances with
                             children on their shoulders to escape from
                             drought and violence inflicted by Al Shabaab
                             militants. Some children died along the way.


                      # ⚓ California ☛ California’s_drought_regulators_lose_big
                        case._What_it_means_for_state’s_power_to_police_water⠀⇛


                             Earlier this year the board ordered roughly
                             4,500 farms, cities and other entities to
                             stop taking water out of the Sacramento and
                             San Joaquin rivers, the 1,100-square-mile
                             watershed that provides about two-thirds of
                             California’s population with drinking water.
                             The board’s orders this year have included
                             senior rights holders such as the city of San
                             Francisco and the Modesto and Turlock
                             irrigation districts, all of which pull water
                             from the Tuolumne River.


                      # ⚓ The Hill ☛ Can_we_save_the_diminishing_Colorado
                        River?⠀⇛


                             At present, whatever water one state gets,
                             another can expect to lose. And each state
                             has its own body of water law that generally
                             gives priority to historic withdrawal
                             patterns. That body of law is important, but
                             unfortunately, the times have changed. Maybe
                             we should look at some past experiences with
                             extreme water scarcity and consider
                             institutional changes that could make things
                             better for people in the dry southwestern
                             states.


                      # ⚓ New York Times ☛ U.S._Population_Growth_Has_Nearly
                        Flatlined._Is_That_So_Bad?⠀⇛


                             But is a population slowdown as much of a
                             crisis as some have made it out to be, or
                             could it actually bring welcome changes?
                             Here’s a look at a longstanding demographic
                             debate.


          o § Finance⠀➾


                # ⚓ Common Dreams ☛ As_Strike_Looms,_Sanders_Blocks_GOP_Bill_to
                  Force_Rail_Workers_Into_Deal_With_No_Sick_Days⠀⇛


                       Before taking to the Senate floor, Sander (I-Vt.)
                       tweeted that “I will proudly stand up to stop” the
                       legislation proposed by Sens. Roger Wicker (R-
                       Miss.) and Richard Burr (R-N.C.).


                # ⚓ Common Dreams ☛ Even_These_Capitalists_Controlling_$39
                  Trillion_in_Assets_Know_Fossil_Fuel_Era_Must_End⠀⇛


                       “We know that more ambitious action on climate is
                       needed, a fact compounded by increasing
                       geopolitical tension and the devastation caused by
                       intensifying extreme weather events.”


                # ⚓ Counter Punch ☛ Price_Increases_Persist_Despite_Supply
                  Chain_Progress⠀⇛


                       Car prices are still rising sharply: new vehicles
                       up 0.8 percent in August, 10.1 percent year-over-
                       year, added 0.03 percentage points to the month’s
                       inflation.


                # ⚓ TruthOut ☛ Sanders_Tells_Warren_Buffett_to_Treat_Rail
                  Workers_Better_and_Avert_Strike⠀⇛


                # ⚓ Common Dreams ☛ Bernie_Sanders_to_Warren_Buffett:_Give_Rail
                  Workers_Better_Conditions_to_Avoid_Strike⠀⇛


                       “In the midst of a potential rail strike, Warren
                       Buffett, the owner of BNSF Railway’s parent
                       company, worth $100 billion, must intervene,”
                       Sanders (I-Vt.) wrote on social media. “During the
                       pandemic, Mr. Buffett became $36 billion richer. He
                       must ensure that rail workers receive decent wages
                       and safe working conditions.”


                # ⚓ TruthOut ☛ Pelosi_Says_Congressional_Stock_Ban_Bill_Is
                  Ready_to_Come_to_a_Vote_This_Month⠀⇛


                # ⚓ Common Dreams ☛ Warren_Condemns_Deceptive_and_‘Outrageous
                  Behavior’_by_Student_Loan_Giant_Navient⠀⇛


                       “While families breathe a sigh of relief,
                       corporations that made billions off a broken
                       student loan system are now busily laying new traps
                       in a shameless, last-ditch effort to try to line
                       their pockets,” Warren (D-Mass.) said during a
                       hearing of the Senate Banking, Housing, and Urban
                       Affairs Committee.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ NBC ☛ Reality_Winner,_imprisoned_for_leaking_classified
                  report,_calls_case_against_Trump_‘incredibly_ironic’⠀⇛


                       Winner had been working for national security
                       contractor Pluribus International at Fort Gordon in
                       Georgia when prosecutors say she smuggled out a
                       classified report in her pantyhose detailing the
                       Russian government’s efforts to pierce a Florida-
                       based voting software supplier ahead of the 2016
                       presidential election. That information was later
                       reported by The Intercept news outlet.


                       Winner said she was motivated to act on a belief
                       that the American public wasn’t getting the full
                       truth.


                       [...]


                       Winner said she is on probation until November
                       2024, and remains prohibited from traveling out of
                       southern Texas, must adhere to a nightly curfew and
                       report any interaction with the media.


                # ⚓ NBC ☛ Russia_spent_$300_million_secretly_interfering_in
                  foreign_politics,_U.S._says⠀⇛


                       Moscow has covertly funded political parties,
                       officials and politicians in at least two dozen
                       nations across four continents since 2014, the U.S.
                       said Tuesday, as the Kremlin’s role in other
                       countries’ affairs comes under greater scrutiny
                       after its invasion of Ukraine.


                       President Joe Biden’s administration is sharing
                       details of the review with 110 countries as part of
                       its campaign to expose Russia’s actions by making
                       them public.


                # ⚓ VOA News ☛ Indian_Court_Allows_Hindu_Petition_for_Prayer_at
                  17th_Century_Mosque⠀⇛


                       Built by Islamic Mughal emperor Aurangzeb in 1669,
                       allegedly after the demolition of a Shiva temple at
                       the site, the mosque has become the latest
                       potential flashpoint between India’s majority Hindu
                       community and its Muslim minority, who make up some
                       13% of the country’s 1.4 billion people.


                # ⚓ India Times ☛ Why_Twitter’s_former_security_head_is
                  testifying⠀⇛


                       Zatko’s complaint alleges that the company misled
                       regulators about its poor cybersecurity defenses
                       and its negligence in attempting to root out fake
                       accounts that spread disinformation, according to a
                       whistleblower complaint filed with U.S. officials.


                       Among Zatko’s most serious accusations is that
                       Twitter violated the terms of a 2011 FTC settlement
                       by falsely claiming that it had put stronger
                       measures in place to protect the security and
                       privacy of its users. Zatko also accuses the
                       company of deceptions involving its handling of
                       “spam” or fake accounts, an allegation that is at
                       the core of Musk’s attempt to back out of the
                       Twitter takeover.


                       His 84-page complaint alleges that he found
                       “extreme, egregious deficiencies” on the platform,
                       including issues with “user privacy, digital and
                       physical security, and platform integrity/content
                       moderation.”


                # ⚓ Broadband Breakfast ☛ Twitter_Whistleblower_Says_Company
                  Needs_to_Work_to_Permanently_Delete_User_Data⠀⇛


                       Peiter Zatko, who was fired from Twitter in January
                       due to performance issues, blew the whistle on the
                       company last month by alleging Twitter’s lack of
                       sufficient security and privacy safeguards poses a
                       national security risk. He alleged that the company
                       does not delete user data when accounts are
                       deleted.


                       On Tuesday, Zatko told the Senate Judiciary
                       committee that the company needs to take the step
                       of ensuring that the personal information of users
                       are deleted when they destroy their accounts.


                       He alleged company engineers can access any user
                       data on Twitter, including home addresses, phone
                       numbers and contact lists, and sell the data
                       without company executives knowing.


                # ⚓ Techdirt ☛ Twitter_Shareholders_Approve_Sale_Of_The_Company
                  To_Some_Dude_Who_Still_Doesn’t_Understand_He_Signed_A_Binding
                  Contract_To_Buy_It⠀⇛


                       Matt Levine, over at Bloomberg, whose coverage of
                       the Elon Musk/Twitter saga has been excellent (his
                       coverage of most things has been excellent, but
                       especially the Musk/Twitter stuff), recently wrote
                       that he was coming to the conclusion that Elon Musk
                       simply does not know what a merger agreement means.


                # ⚓ TruthOut ☛ The_Queen’s_Death_Brings_Growing_Hope_for_Irish
                  Unification⠀⇛


                # ⚓ The Nation ☛ King_Charles_III_May_Keep_His_Head—His_Kingdom
                  Is_Another_Story⠀⇛


                       London—Charles is a name that most English monarchs
                       have avoided since the 17th century. Let’s
                       therefore start where we really should. A century
                       and a half before the French Revolution, the
                       English fought a civil war and made a bourgeois
                       revolution, funded by merchants. They executed the
                       king (Charles I) on January 30, 1649, abolished the
                       House of Lords and declared a republican state: The
                       Commonwealth that ruled over England, Scotland,
                       Ireland, and Wales may not have lasted very long,
                       but it left an enduring mark. The restoration of
                       1660 was a compromise. The absolutist state could
                       not be resuscitated. The “divine right of kings”
                       was never allowed back. But the reconstituted
                       monarchy proved to be remarkably resilient. From
                       his perch at Princeton, Arno Mayer explained this
                       development in his classic 1981 account, The
                       Persistence of the Old Regime:1The [post 1660]
                       monarchy and landed elite tamed the
                       industrialization of England without succumbing to
                       it…. England never became a “bourgeois order” run
                       by a “conquering” bourgeoisie.… There was no
                       movement to remove the crown, the royal court, the
                       House of Lords, and the ascriptive public service
                       nobility. Despite the decline of agriculture and
                       despite insular security, which vitiated the need
                       for a strong military caste, the landed classes
                       managed to perpetuate the “archaic” political order
                       and culture.2


                # ⚓ Democracy Now ☛ “Major_Step_Towards_a_United_Ireland”:_As
                  Britain_Mourns_Queen,_Northern_Ireland_Considers_Its_Future⠀⇛


                       We speak with journalist and activist Eamonn McCann
                       about Queen Elizabeth II’s legacy in Ireland and
                       the impact of her recent death on the prospects of
                       Irish unification. This comes as King Charles III
                       visited Northern Ireland Tuesday on his national
                       tour commemorating his mother, whose reign oversaw
                       more than 3,600 deaths over three decades in
                       Northern Ireland in fighting between the Irish
                       Republican Army and forces backed by Britain.
                       “There is a great confidence among nationalist and
                       republican leaders in Northern Ireland that we are
                       now moving inexorably towards a united Ireland,”
                       says McCann, a former member of the Northern
                       Ireland Assembly.


                # ⚓ Common Dreams ☛ Opinion_|_No,_MAGA_Republicans_Are_Not
                  Anti-War_Allies⠀⇛


                       Something strange is happening in the United
                       States. As the Biden administration continues to go
                       all in on proxy-war in Ukraine, the only
                       politicians speaking up are… MAGA Republicans? Far-
                       Right leaders like Margerie Taylor Greene and Josh
                       Hawley are some of the only elected officials
                       opposing the constant stream of weapons for war and
                       NATO expansion. This leads some people who oppose
                       war to consider joining forces with MAGA. 


                # ⚓ Counter Punch ☛ The_Queen_is_Dead._Republic_Now!⠀⇛


                       Even John Lydon, who as Johnny Rotten once wrote;
                       “God save the queen. She ain’t no human being.
                       There is no future In England’s dreaming” got
                       involved. He posted the following message on social
                       media: “Rest in peace Queen Elizabeth II. Send her
                       victorious From all at johnlydon.com”.


                # ⚓ Counter Punch ☛ Queenly_Saturation⠀⇛


                       States of class, inequality and hereditary systems
                       of rule are almost titillating, a reminder that the
                       American Revolution was less radical than a revolt
                       begun reluctantly by aristocratic, plantation
                       owning slavers.  Indeed, Britain’s royal
                       institutions, in many ways, were reconstituted and
                       applied to the rough timber of US expansion in the
                       form of a Republic. The batons of empire were
                       changed, but the purpose remained the same.


                # ⚓ Counter Punch ☛ Cotton_Mouth:_Political_Careerist_vs.
                  Ranked_Choice_Voting⠀⇛


                       If this had been a standard “first past the post”
                       election in which a candidate could achieve victory
                       with a mere plurality, Peltola would have won that
                       way too: She received 39.57% of first-round votes
                       to Palin’s 30.79% and Begich’s 28.09%. The ranked
                       choice “instant runoff” merely confirmed that a
                       majority of Alaska’s voters, rather than a mere
                       plurality, preferred Peltola to Palin.


                # ⚓ Counter Punch ☛ Bannon:_Another_Trumpster_in_the_Dumpster⠀⇛


                # ⚓ TruthOut ☛ Poll_Shows_Historic_Tie_Between_Dems_&_GOP_Over
                  Enthusiasm_to_Vote_in_Midterms⠀⇛


                # ⚓ Meduza ☛ Municipal_council_candidate_accuses_Moscow
                  government_of_rigging_election_in_her_favor_—_Meduza⠀⇛


                       Russian Communist Party (KPRF) candidate Daria
                       Bagina, who officially won a seat in her district’s
                       municipal council in an election that ended on
                       September 11, announced Tuesday that she does not
                       consider the results legitimate. On Twitter,
                       Bagina, who ran in Moscow’s Akademichesky District,
                       accused the Moscow Mayor’s Office of using the
                       city’s remote electronic voting (DEG) system to
                       stuff ballots in her favor.


                # ⚓ Common Dreams ☛ Georgia_GOP_Senate_Hopeful_Herschel_Walker
                  Says_He’s_All_In_on_Federal_Abortion_Ban⠀⇛


                       “This November, bodily autonomy is on the ballot.”


                # ⚓ Common Dreams ☛ ‘Extremely_Traumatizing’:_Louisiana_Woman
                  Forced_to_Travel_2,500_Miles_for_Abortion_Speaks_Out⠀⇛


                       “Basically, they said I had to carry my baby to
                       bury my baby.”


                # ⚓ Common Dreams ☛ Opinion_|_Scam_Alert!_Beware_the_GOP’s
                  Other_Midterm_Effort_to_Halt_Democracy⠀⇛


                       Get ready. If you’re a Democratic voter, there’s a
                       chance you’ll show up to vote this November and
                       discover you can’t because you’re no longer
                       registered. Millions will be blindsided this way,
                       and it could turn elections toward Republicans
                       across the nation.


                # ⚓ Pro Publica ☛ For_Donald_Trump,_Information_Has_Always_Been
                  Power⠀⇛


                       It’s true that Trump likes to collect shiny
                       objects, like the framed Time magazine cover that
                       was stowed, according to the U.S. Justice
                       Department, alongside documents marked top secret.
                       It’s true, as The Associated Press reported, that
                       Trump has a “penchant for collecting” items that
                       demonstrate his connection to famous people, like
                       Shaquille O’Neal’s giant shoe, which he kept in his
                       office in New York’s Trump Tower.


                # ⚓ TruthOut ☛ Afropessimism_Forces_Us_to_Rethink_Our_Most
                  Basic_Assumptions_About_Society⠀⇛


                # § Misinformation/Disinformation⠀➾


                      # ⚓ VOA News ☛ Nicaragua_Cuts_Deal_With_Kremlin_Station
                        Sputnik_to_Air_Content⠀⇛


                             Under a new deal between the governments of
                             Nicaraguan President Daniel Ortega and
                             Russian President Vladimir Putin, Russian-
                             produced media content will now be broadcast
                             across Nicaragua.


                             The contract between the Communication and
                             Citizenry Council of Nicaragua, the country’s
                             state media conglomerate, and the Sputnik
                             radio network will make Russian content
                             available to more than 20 Nicaraguan state
                             channels, broadcasting to 6.6 million people.


                      # ⚓ NBC ☛ Michigan_man_who_killed_his_wife_went_down_a
                        ‘rabbit_hole’_of_conspiracy_theories_after_Trump’s_2020
                        loss,_daughter_says⠀⇛


                             Although it’s difficult, Smith said, he
                             believes it’s still possible to reach those
                             who have been sucked into the world of
                             conspiracy theories.


                             “One of things I like to tell my students is
                             when we’re interpreting others, trying to
                             figure what they’re saying, we need to do so
                             charitably,” he said.


                             QAnon and other conspiracy theories have torn
                             apart families across America and
                             occasionally led to violence.


                      # ⚓ Scheerpost ☛ The_Misinformation_Campaign_That_Killed
                        Chile’s_Progressive_New_Constitution⠀⇛


                             Carole Concha Bell writes on the rejection of
                             Chile’s progressive institution.


                      # ⚓ DeSmog ☛ House_Committee_Investigates_the_Role_of_PR
                        Firms_in_Spreading_Climate_Disinformation⠀⇛


                             The hearing, held by the U.S. House Natural
                             Resources Committee, Subcommittee Oversight &
                             Investigations, invited several firms,
                             including Singer Associates, Story Partners,
                             and Pac/West Communications. None of them
                             showed up.


                      # ⚓ TruthOut ☛ Big_Oil_PR_Firms_Reject_Invite_to_Hearing
                        on_Climate_Disinformation⠀⇛


                      # ⚓ Common Dreams ☛ Big_Oil_PR_Firms_a_No-Show_at_House
                        Hearing_on_Climate_Disinformation⠀⇛


                             “This hearing is PR agencies’ worst
                             nightmare.”


          o § Censorship/Free Speech⠀➾


                # ⚓ Alberta_justice_minister_asks_human_rights_chief_to_step
                  down_after_calls_from_Muslim_community⠀⇛


                       On Monday, the National Council of Canadian Muslims
                       (NCCM) released a letter it sent to Justice
                       Minister Tyler Shandro signed by 28 Muslim
                       organizations and mosques in Alberta calling for
                       May’s resignation over comments he made in a book
                       in 2009.


                # ⚓ Teen Vogue ☛ Anti-Royal_Family_Protesters_Are_Being
                  Arrested_in_the_UK⠀⇛


                       Over the weekend, people across the United Kingdom
                       took to the streets after the death of Queen
                       Elizabeth II — some in grief, others in protest, as
                       anti-monarchy sentiment continues to be expressed
                       in tandem with the country’s mourning period. Now
                       concerns about freedom of speech are roiling the
                       UK, as newly passed protest laws are exacerbating
                       the police response to public discourse about the
                       monarchy.


                # ⚓ Common Dreams ☛ House_Dems_Target_Big_Oil_for_‘Weaponizing’
                  Law_Against_Protesters_to_Block_Climate_Action⠀⇛


                       “Thirty-two states and the District of Columbia
                       have enacted commonsense anti-SLAPP legislation.”


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


                # ⚓ Techdirt ☛ CBP_Branch_Retweets_Disgraced,_Bigoted_Trump
                  Advisor,_Gets_Account_Locked_Down_By_CBP_Commissioner⠀⇛


                       Government officials may say acceptable things when
                       pressed for comment by journalists, oversight, and
                       members of the public. But if you really want to
                       know what an agency thinks, just keep your eye on
                       the rank-and-file.


                # ⚓ Don’t Extradite Assange ☛ Free_Assange_Human_Chain_Oct_8⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ NPR ☛ Amazon_warehouse_workers_in_Albany_will_vote_on
                  unionization_in_October⠀⇛


                       In mid-October, 400 workers there will vote on
                       whether to join the upstart Amazon Labor Union, the
                       same independent group that unionized more than
                       8,000 at the massive Staten Island warehouse. It’s
                       run by current and former Amazon workers, and led
                       by a man whom Amazon fired after he led a pandemic-
                       era walkout.


                # ⚓ ‘They_should_be_protecting_us,_not_attacking_us’:_Parents
                  of_man_killed_by_Clear_Creek_County_deputies_speak_out⠀⇛


                       In the end, Glass picked up the knife but never
                       left the car. He was shot and killed by one officer
                       while he remained in the front seat.


                # ⚓ Clear_Creek_County_deputies_shoot_and_kill_man_who_asked
                  for_help_after_car_crash⠀⇛


                       “From beginning to end, the officers escalated and
                       proactively initiated force,” Glass’ family
                       lawyers, Siddhartha Rathod and Qusair Mohamedbhai,
                       said, in a release. “And yet, these officers,
                       including the one who killed Christian, are still
                       in uniform and have paid no price for their
                       conduct. Our country cannot continue to tolerate
                       this level of extreme violence by law enforcement.
                       The act of simply calling 911 for help cannot be a
                       death sentence.”


                # ⚓ Family_of_22-year-old_man_fatally_shot_by_law_enforcement
                  in_Clear_Creek_County_wants_accountability⠀⇛


                       Rathod said Glass had no history of mental illness.
                       When asked about Glass’s abnormal behavior, he said
                       “unfortunately we are not ever going to know.”


                # ⚓ NPR ☛ No_region_is_‘immune’_as_the_number_of_people_in
                  ‘modern_slavery’_climbs_to_50_million⠀⇛


                       That term refers to a spectrum of exploitative
                       practices like forced labor, forced marriage and
                       human trafficking. As of 2021, 50 million people
                       were estimated to endure such conditions. Some form
                       of modern slavery exists in nearly every country in
                       the world, the report found.


                # ⚓ Frontpage Magazine ☛ The_Tragic_Story_of_‘Baby_Shenouda’⠀⇛


                       From the moment when the state seized the child
                       until now, his adoptive parents have been in
                       tears—or, to quote from a recent interview, “living
                       in hell.” They have pled with the state to have the
                       child returned. After sobbingly explaining in the
                       interview how her heart “leapt with joy” when she
                       first heard Shenouda say “mamma,” his mother even
                       offered to work for free as a servant in the
                       orphanage, just to be near him. The father said he
                       would do “anything”—“shoot me with gunfire even,
                       anything, just so long as I can have my child
                       back!”


                       All such pleas have fallen on deaf ears. Nor have
                       Egypt’s so-called “National Council for Human
                       Rights” and “National Council for Motherhood and
                       Childhood” bothered to make any utterances on this
                       matter.


                # ⚓ Firstpost ☛ Ranchi:_Muslim_youth_barge_in_school_with
                  firearms,_tell_Hindu_girls_to_be_their_friends_or_get
                  kidnapped⠀⇛


                       As if the burning, raping and hanging of minor
                       girls was not enough, now a group of Muslim men are
                       reported to have barged in a school brandishing
                       firearms and threatened Hindu girls to fall to
                       their friendship proposals.


                # ⚓ FAIR ☛ ACTION_ALERT:_Crime_Claims_of_CNN’s_New_Police
                  Expert_Don’t_Hold_Up_to_Facts⠀⇛


                       In its latest move to the right, CNN recently hired
                       former NYPD flack John Miller as its “chief law
                       enforcement and intelligence analyst.” As Josmar
                       Trujillo observed more than five years ago
                       (FAIR.org, 6/21/17), Miller “has spun the revolving
                       door between law enforcement and media like perhaps
                       no one else,” moving back and forth between jobs at
                       the NYPD, FBI, ABC and CBS.


                # ⚓ NPR ☛ BYU_apologizes_to_a_banned_fan,_saying_it_found_no
                  proof_they_yelled_racial_slurs⠀⇛


                       “We have not found any evidence that that
                       individual engaged in such an activity,” the
                       department said. “BYU sincerely apologizes to that
                       fan for any hardship the ban has caused.”


                # ⚓ Pro Publica ☛ State_Investigation_Reveals_Racial
                  Disparities_in_Student_Discipline_and_Police_Involvement⠀⇛


                       The information provided to state officials by
                       Township High School District 211 reveals
                       widespread disparities involving not just students
                       of color but also those with disabilities. The
                       Illinois attorney general’s office is in the early
                       stages of a civil rights investigation that aims to
                       determine if some groups of District 211 students
                       have been unfairly disciplined at school.


                # ⚓ Meduza ☛ Jailed_Russian_opposition_politician_Alexey
                  Navalny’s_fellow_inmates_banned_from_looking_at_him_—
                  Meduza⠀⇛


                       Prisoners at Penal Colony No. 6 in Russia’s
                       Vladimir region, where jailed opposition politician
                       Alexey Navalny is serving a nine-year sentence,
                       have reportedly been banned from looking at
                       Navalny. Associates of Navalny described the new
                       policy on their YouTube channel, Popular Politics,
                       after they learned about it from relatives of
                       prisoners in the facility.


                # ⚓ Meduza ☛ Balakliya_resident_says_he_was_tortured_in_Russian
                  captivity_—_Meduza⠀⇛


                       Artem, a resident of the Ukrainian town of
                       Balakliya, told the BBC how he and other detainees
                       were tortured in Russian captivity. The town came
                       under Russian occupation in early March, and was
                       liberated by Ukraine on September 8, 2022.


                # ⚓ Telex (Hungary) ☛ “The_Russians_are_in_the_pantry”_–_the
                  new_mini_statue_of_sculptor_Mihály_Kolodkó_installed_in_the
                  capital⠀⇛


                # ⚓ Techdirt ☛ Judge_Blocks_‘No_Recording_Cops_Within_8_Feet’
                  Law_Even_Arizona_Cops_Don’t_Want_To_Defend⠀⇛


                       In 2016, Arizona state senator John Kavanaugh tried
                       to make it much more difficult to record police
                       officers. He authored a bill that would create a
                       20-foot “no recording” zone around cops, supposedly
                       in the interest of officer safety.


                # ⚓ Counter Punch ☛ America’s_Immigration_Death_Machine⠀⇛


                       Last month, the Guardian published an article
                       entitled, “The Other Death Valley: Hundreds of
                       Migrants Are Dying in Remote Texas Deserts.”


                # ⚓ TruthOut ☛ Here’s_How_We_Stop_the_Republicans’_National
                  Abortion_Ban⠀⇛


                # ⚓ Pro Publica ☛ Meet_the_Woman_Fighting_for_the_Rights_of
                  Voters_Who_Can’t_Read⠀⇛


                       Before 1965, many Southern states forced voters to
                       prove they could read before casting a ballot, a
                       requirement primarily designed to keep Black people
                       from voting. The Voting Rights Act put an end to
                       those polling site exams. But a ProPublica
                       investigation found that the efforts to block
                       people who have difficulty reading from casting a
                       ballot continue, especially in the South. In fact,
                       today’s election system remains a modern-day
                       literacy test.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Techdirt ☛ Colorado_Residents_Lose_Control_Of_Their_‘Smart’
                  Thermostats,_Swelter_In_88_Degree_Heat⠀⇛


                       During a heat wave last summer, some Texans were
                       shocked to wake up and find that their local energy
                       company had turned up their thermostats in the
                       night to save energy. Houston locals weren’t
                       exactly thrilled to wake up sweating in the night
                       to the sound of dehydrated, crying infants.


          o § Monopolies⠀➾


                # ⚓ The Hill ☛ California_sues_Amazon,_alleges_tech_giant
                  stifled_competition⠀⇛


                       California Attorney General Rob Bonta (D) sued
                       Amazon on Wednesday, alleging the e-commerce giant
                       has stifled competition in a way that has increased
                       prices for California consumers.


                       The lawsuit alleges that Amazon requires merchants
                       to enter into agreements that penalize them if
                       their products are offered for a lower price for
                       sale off Amazon, leading to higher prices for
                       consumers.


                # ⚓ NPR ☛ California_sues_Amazon,_alleging_its_policies_cause
                  higher_prices_everywhere⠀⇛


                       The lawsuit, filed by state Attorney General Rob
                       Bonta, focuses on the way Amazon — the largest
                       online retailer — deals with third-party merchants,
                       who account for most of the sales on the platform.


                       California alleges that Amazon penalizes sellers
                       and suppliers that offer cheaper prices elsewhere
                       on the [Internet], including Walmart and Target,
                       for example by displaying their items lower or less
                       prominently or outright blocking their new
                       postings.


                # ⚓ The Hill ☛ Google_must_face_most_of_Texas-led_antitrust
                  case,_court_says⠀⇛


                       Google will have to face most of the Texas-led
                       antitrust case over the tech giant’s ad dominance,
                       a judge ruled Tuesday.


                       U.S. District Judge Kevin Castel ruled against
                       Google’s motion to dismiss the case filed by 16
                       states and Puerto Rico, though he did toss one
                       count alleging Google and Facebook colluded on an
                       advertising agreement.


                # ⚓ India Times ☛ Google_suffers_setback_in_court_fight_against
                  EU_fine⠀⇛


                       The EU General Court largely concurred with the
                       Commission’s conclusion that Google had acted
                       unfairly by forcing mobile phone makers to pre-
                       install its search engine and Chrome apps on
                       devices to carry its Play app store. Additionally,
                       Google placed limitations on mobile network
                       providers.


                       According to the court, the general court accepted
                       the Commission’s finding that Google imposed
                       unlawful limitations on makers of Android
                       smartphones and mobile network operators to
                       consolidate the dominating position of its search
                       engine.


                # ⚓ IT Wire ☛ iTWire_–_EU_gives_Google_little_relief_in_verdict
                  on_record_fine_appeal⠀⇛


                       Google has gained very little from a bid to try and
                       get a €4.34 billion (US$4.33 billion, A$6.42
                       billion) fine imposed by the EU withdrawn, with
                       judges at a tribunal largely confirming the bloc’s
                       decision to impose the fine.


                       The fine was imposed in July 2018, with the EU
                       accusing Google of breaching anti-trust rules
                       relevant to Android. The company appealed the
                       imposition of the penalty to the EU General Court.


                       The Luxembourg-based tribunal said on Wednesday:
                       “The General Court largely confirms the
                       commission’s decision that Google imposed unlawful
                       restrictions on manufacturers of Android mobile
                       devices and mobile network operators in order to
                       consolidate the dominant position of its search
                       engine.”


                       It cut the penalty to €4.1 billion on the grounds
                       that there were some faults in the EU regulator’s
                       analysis and because it agreed that Google’s right
                       to fair trial had been infringed to some extent.
                       Details of the court’s arguments are here.


                # ⚓ RTL ☛ Google_handed_setback_as_EU_court_upholds_record
                  fine⠀⇛


                       The court, however, said the fine should be
                       slightly reduced to 4.125 billion euros ($4.1
                       billion), instead of the 4.3 billion euros decided
                       by the commission in 2018, after reviewing the
                       duration of the infringement.


                # ⚓ Reuters ☛ Google_loses_challenge_against_EU_antitrust
                  decision,_other_probes_loom⠀⇛


                       “The General Court largely confirms the
                       Commission’s decision that Google imposed unlawful
                       restrictions on manufacturers of Android mobile
                       devices and mobile network operators in order to
                       consolidate the dominant position of its search
                       engine,” the court said.


                # ⚓ Indian Express ☛ EU_court’s_ruling_on_record_$4.4_bn_Google
                  fine_may_set_precedent⠀⇛


                       A ruling on Wednesday by Europe’s General Court on
                       whether Alphabet’s Google should face a record EU
                       antitrust fine of 4.34 billion euro ($4.4 billion)
                       for using its Android mobile operating system to
                       quash rivals could set a precedent for other
                       regulators looking into its business practices.


                # ⚓ US News And World Report ☛ Google_Loses_Challenge_Against
                  EU_Antitrust_Decision,_Other_Probes_Loom⠀⇛


                       The Commission in its 2018 decision said Google
                       used Android to cement its dominance in general
                       internet search via payments to large manufacturers
                       and mobile network operators and restrictions.


                # § Trademarks⠀➾


                      # ⚓ Techdirt ☛ Luka_Doncic’s_Trademark_Dispute_With_His
                        Mother_Is_In_Uncharted_Trademark_Territory⠀⇛


                             Normally when we talk about trademark
                             disputes, they tend to look fairly similar.
                             Some entity is upset and/or sues over a
                             trademark they have and we spend some time
                             analyzing whether the trademark itself ever
                             should have been granted, whether there is
                             true customer confusion to worry about,
                             whether the plaintiff is simply bullying,
                             etc. But the story of Luka Doncic’s attempt
                             to wrest control over the trademark for his
                             own name and jersey number is something
                             completely different and has us in uncharted
                             territory.


                # § Copyrights⠀➾


                      # ⚓ Torrent Freak ☛ US_Lawmakers_Urge_Verisign_to_Help
                        Tackle_Online_Piracy⠀⇛


                             A group of U.S. lawmakers wants domain name
                             registry Verisign to help tackle online
                             piracy. The company has a key role in the
                             domain names system, overseeing many popular
                             TLDs including .com, .tv and .net. Verisign
                             believes that it should operate in a content-
                             neutral manner but it doesn’t rule out that,
                             through the right protocols and processes, it
                             can help to address piracy as well.


                      # ⚓ Techdirt ☛ Legacy_News_Orgs’_Hatred_Of_Google_Runs_So
                        Deep_They’re_Willing_To_Give_Up_Fair_Use_To_Punish
                        Google⠀⇛


                             We’ve been writing a bit about the JCPA — the
                             Journalism Competition and Preservation Act —
                             the very bad bill from Senator Amy Klobuchar
                             that would create all sorts of problems, from
                             allowing news orgs to demand money for links
                             (breaking the fundamental nature of how the
                             web works), to creating a “must carry”
                             provision that could force disinformation
                             providers into Google News, to an underhanded
                             method of trying to revamp copyright law,
                             without ever admitting its revamping
                             copyright law. We’ve explained all of these
                             problems in previous posts.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Debord’s_“Society_of_the_Spectacle”⠀⇛


                       i recently read Guy Debord’s 1967 work “The Society
                       of the Spectacle”[a]. i found it dense, but
                       ultimately comprehensible[b]. The following is a
                       collection of quotes that particularly stood out to
                       me, irrespective of whether or not i agree with
                       them. (In particular, i found Debord’s repeated
                       invocations of “false consciousness” to be ….
                       problematic.)


                # ⚓ Guess_who_won_again⠀⇛


                       The Italian Grand Prix always has an atmosphere
                       because of the Italian fans. It’s not always the
                       best race, though. Verstappen had an easy win.
                       Again.


                       During the Schumacher years you knew who was going
                       to win, and it was impressive, but you watched to
                       see if anyone could beat him. This year has become
                       like that with Verstappen.


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


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