𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, April 09, 2022
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Sun 10 Apr 02:40:34 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/2022/04/09/


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

QmYTPvdifyTSUV9CuZ5gpuZVC7pHshJvZhZ5niheQb2vzE
QmZkDEgYNnUUQtaGwFdmteyZ5W9URPTE1mBXTnYquZ1fsa
QmYDUiQWeiJU7WCsdP3xeCnELkr2V2Y9aQVLP4Z8n6efVs
QmVmhebNywnTu6B8SmaNwvmpQrK5uGfyPHsAeM383HwKRx
QmbtCnKikT7Qr6XTD9CLjRmtU6T3bRTyVqgASiAa1S3VBY
QmZAPYrP7hETWM5jGJE8DCf5TgW4hE1qdRnTa5DiwUyy2i
QmbZUGxupu36yFf72bxj4yCNrYAfeMKD4kf3TzSvrLqGkT
QmfLQGVUofEiaUy33j7d2fYbyaYzAQJvw2ZWN6FztbPGc6
QmRLV4LzQCcbGE4VJXvT8zja7a8Ehkc6z5ALTVvwBbNgA7
QmVsotEYMNPE1dyPEZpAQ81YQFtSrxNxJNRyba9tPacbNr
Qma6RvSv1ESUzDxUh7arsCZmoLXUaaSzK11P7gLczW1TKT
QmcKAXzUKRMGp3YdQETGwbF7nS2hNTSzE84u2fb9P3tEDf
QmYX7yxkzNPmi6NC3UHnNT3dqZ5FfkpgUrstQa95hPuvgt
Qmc3h1ndVkwPrqkr5MwUe6DdA5S7dDpBHt61UHELCc9ewf
QmTQQuAATQ3bx7aaCvuFeFsB7QuviwS2MdAiz9SW34tZeV
QmanAKUKZgCyqdLttoPwN8UdE5JSFDVuH8vEncfJwtmqZ9
QmPA9baiheMyYvoirRpVxfonAnbATaW9SCDexu9yzCdwpR
QmPP37AxLbRc3k9bp8hVPgJLkqdNKMo4NwWGy77QCsCNmS
QmPTFnSBK7s4hJa6dWKXhRFqz7rSTw2b3nyJfUHGke9zsy
QmTXSm48sqA6HLeyyDAbAxdJ8GTxKK6mhdZHkkxWhkTEcn
QmPokuDJbuL2FN7E9h2TvVkafexTCncL78fivWTmKvQBfi


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

⦿ [Meme] EPO Moving Backwards | Techrights

⦿ For EPO Staff on Dutch Territories Purachasing Power Fell 12% in Just One Year While EPO Increased Its Fees | Techrights

⦿ IRC Proceedings: Friday, April 08, 2022 | Techrights

⦿ Microsoft GitHub the King of DMCA Censorship (Removing Free Software) | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/04/09/epo-employment/#comments
		http://techrights.org/2022/04/09/epo-purachasing-power/#comments
		http://techrights.org/2022/04/09/irc-log-080422/#comments
		http://techrights.org/2022/04/09/microsoft-github-is-censorship/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/04/09/kde-frameworks-5-93/#comments
		http://techrights.org/2022/04/09/links-09042022/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 57

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/09/epo-employment/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/09/epo-employment/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_EPO_Moving_Backwards⠀✐


Posted in Europe, Finance, Patents at 6:02 pm by Dr. Roy Schestowitz


           🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Inflation? Let's take salaries down⦈
                        Violating the EPC, using a lie…


Summary: As we’ve just_seen, the EPO isn’t interested in employing the people
it absolutely must employ


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣟⣻⣿⣿⣿⣿⡟⣽⠹⢿⣯⢯⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠠⠘⠓⠋⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠑⠢⢝⣿⣿⣿⣟⣇⠚⠱⠈⠘⢿⣶⣶⣊⣭⣛⡫⣭⡓⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⠉⠉⠉⠉⣿⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡄⠀⠀⠀⣿⣀⣀⡀⠀⣸⣄⡀⠀⠀⢀⣯⡀⠀⣀⣀⢠⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⢟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣷⠀⠀⢀⣿⣿⣿⣿⢸⣿⣿⣿⡆⣾⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⡀⠀⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢹⣿⣿⣿⡐⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⢈⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣷⡇⣰⣿⣿⣿⣿⣿⣷⠂⠛⢻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢺⣿⣿⣿⣧⣿⣿⣿⡏⣾⣿⣿⣿⣻⣿⣿⣿⣿
⡿⣿⣄⣀⣸⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣦⡄⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡦⣄⢀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡈⠉⠉⠉⢹⣿⣿⣿⣿
⣷⠄⠀⠀⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⡿⠿⠇⣿⣿⣿⣿⠈⠋⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡆⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⠁⠀⠀⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣀⣸⣿⣿⣿⡷⠆⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡅⠀⠀⣿⣿⣿⣿⣿⣸⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⠿⢿⣿⣿⣿⡇⢀⠀⣿⣿⣿⣏⠙⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⠀⠀⣿⣿⡿⠿⠛⣿⣿⡿⠟⠀⢻⣿⠟⢿⣿⣿⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⢸⣿⣿⣿⣷⠾⢿⣿⣿⣷⣿⣿⣿⣿⣿⣏⡄⠚⡻⢿⣿⣿⣿⣿⣿⠛⠛⣿⠏⠘⠛⠛⠛⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿
⡍⠉⠉⠒⣟⠛⠿⠤⠤⣿⣿⣿⣀⠀⣾⡯⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠅⢰⡟⠃⣧⡗⢰⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣿⡀⠀⢀⣿⣧⠀⠀⠀⣷⡄⠀⠉⠉⡯⠙⢻⡇⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠨⣥⢸⣾⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠄⠀⢸⣿⣿⠀⠀⢰⣿⣿⡀⠀⠀⡇⢸⢶⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣴⣭⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠍⠙⠛⠛⠛⢀⠀⠈⣾⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠀⢸⣿⣿⠀⠀⢸⣿⣿⢐⠀⢰⡇⠈⢚⣻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠉⠀⠀⠀⠀⠀⠴⠆⠀⠙⠓⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠢⢼⣿⣿⣖⠀⣼⣿⣿⡇⠀⢸⡇⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣶⡶⠀⠀⠉⠀⠀⠀⠀⠈⣼⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⣼⣦⡀⠈⠉⣿⡛⠻⠧⠤⣼⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⠿⠃⠀⠉⠉⠉⠙⠛⢻
⣿⠂⠀⣿⣿⡇⠀⠀⣿⣿⡀⠀⠀⣿⣄⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢀⢐⡚⣋⣀⡀⠀⠀⠀⠀⠀⠀⣚
⣿⠂⠀⣿⣿⡇⠀⢀⣿⣿⡗⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣭⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⠿⠿⢿⡿⠛⠀⠂⠀⠘⢻⣶⣶⣷⣤⣤⣭⡅⠐⠒⢒⣶⣿
⠻⠧⢴⣿⣿⣧⠀⢸⣿⣿⡷⠀⢰⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠦⠤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣦⣤⣄⣀⣠⠤⠤⣀⣀⣤⣶⠒⠒⠀⠀⠛⠻⣿⣿⣿⣟⣛⣿⣸⣿⣧⢺⣿⣿
⡄⠀⢰⣷⡉⠙⠛⢻⠿⣿⣷⣀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⠀⠀⠉⠉⠝⠛⠻⠿⠿⣶⣶⣿⣿⣤⣤⣄⣀⣀⣀⣿⣿⣿⣿⣯⣽⣿⣛⣿⣿⡿⠛
⡃⠀⢸⣿⣷⠀⠀⢸⣦⡀⠈⠉⢹⡛⠿⢿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀
⡧⠀⢸⣿⣿⠀⠀⣾⣿⣧⠀⠀⣿⣿⡄⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⠃⠐
⠿⢦⣾⣿⣿⣄⣀⣿⣿⣿⠀⠀⢛⣭⣥⠄⠀⢸⣛⣛⠿⣦⡄⠀⠀⠀⠉⠙⠓⠲⠆⣼⣿⣿⣿⣿⣷⣮⣭⣿⣿⣿⣿⣯⠉⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣰⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀
⣄⡀⠀⠉⠛⠻⠿⣿⣿⣿⣂⣰⣮⣛⠿⠀⠀⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣷⣶⣿⣿⣿⣿⡥⣤⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢿⣿⣯⣿⣿⣿⣿⡇⠀⠀⣤
⣿⣿⣿⣶⣤⣄⡀⠀⠈⠙⠛⠿⢿⣿⣷⣤⣀⣻⢿⣿⣿⠟⠫⠷⣶⠶⠶⡦⣀⠄⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢿⣿⣿⣿⣿⣿⣯⣼⠗⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿
⣛⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠉⠛⠻⠿⠿⠶⠁⠀⡀⠀⠀⠀⡐⠁⠀⢠⢦⣗⢝⢿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠟⠛⠛⠛⠿⢧⣭⠴⠿⠺⠰⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⡀⢀⠘⠿⣷⣶⢌⣀⠤⠀⡼⢸⣿⣷⣕⡿⠻⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⠀⠉⠀⠀⠀⠀⠀⠻⢀⣴⠆⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠿⣯⣶⡯⢭⡛⠻⢠⠇⣺⣿⣿⡟⠛⣛⣉⣈⡛⠛⠿⡿⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⠀⠹⣿
⠋⢁⣀⣥⣀⣈⠉⠉⠉⠉⠉⠉⠙⠻⢯⣿⣿⡿⠟⠛⠛⠋⠛⢻⣿⣿⡿⢟⣯⣿⣟⡯⠏⢀⠀⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣿⣆⠀⠘
⡾⠋⠉⠁⠈⠉⠛⢦⣄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠈⠉⠀⠀⢀⠔⠘⠂⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣧⠀
⠀⠀⡀⠀⠀⠀⣄⡀⠙⢷⡀⠀⠀⠀⠈⠀⣰⣄⣴⣤⣤⣄⣴⣿⣿⣿⡷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣷
⠀⡀⠡⠀⠀⠀⣿⣿⣷⣦⠹⡄⠀⠀⠄⠘⠋⠉⠉⠉⠨⠾⣿⣿⣿⢿⠏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⠀⠀⡉⡉⡉⡍⠠⠀
⠀⢑⠀⠆⠢⠀⠺⡟⠿⣿⡢⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠻⠿⡆⠸⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢠⠠⠠⠠⠀⠀⠀
⣦⡈⡮⡺⡀⡐⢘⠌⠀⠀⠂⠄⢿⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠂⠂⠂⢀⣥
⣷⣦⣐⡀⠉⠤⡀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣼⣯⣀⢸⣶⣄⡀⠀⡉⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠐⠒⠶⣿⠟⠛⣿
⢻⣿⣯⡇⠀⡀⠀⠐⠠⠀⠀⢤⣼⣧⣤⣼⣿⣿⡟⠋⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣤⣀⣤⠤⠖⠒⠛⠀
⠘⣿⣿⣿⣿⣿⣮⣦⡀⠁⠀⠲⠿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠊
⠄⠙⣿⣿⣿⣿⣿⣿⣿⣶⣶⣟⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⡶⣾⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣠⣶⣦⣀⡀⠀⠀⣀⡸
⣆⠀⢈⢿⣿⣿⣿⣿⣿⣿⣿⢫⡿⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣠⠄⠂⠀⢀⠢⣄⣱⢰⡝⣟⡿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠿⠍⠀⠈⠀⠀⠀
⡙⢷⣄⠀⠉⠋⢻⣿⡿⠟⢁⡾⠃⠀⠀⠐⠀⠀⠀⠀⠀⠈⢸⣮⣦⠁⠀⠄⢸⠸⣿⣿⣿⣾⣽⣐⢤⣚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣝⡷⣦⣤⣄⣤⣤⡶⠟⠁⠠⣾⣶⣶⣶⣦⣤⣄⡀⠀⠐⠁⡀⡲⣶⠀⢸⣾⣿⣿⣿⣿⡰⣾⢛⣿⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣮⣭⣉⡀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣷⣦⣀⠈⠙⠿⣴⢸⣿⣿⣿⣿⣿⣿⣶⣶⣼⣸⣭⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⡀⠀⣀⣙⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣧⣘⡻⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣮⣽⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠧⢹⠟⠛⠻⣿⣿⣿⣿⣿⣿⠟⠋⣀⣤⣴⣶⣶⣾⣿⣿⣷⣶⣶⣤⣄⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⡆⢺⡀⢿⡇⢹⠟⣉⠻⠟⣡⣴⣿⠟⠋⠉⠁⠀⠀⢀⠀⠀⠀⠈⠉⠛⠻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣅⣼⡛⣤⡄⢸⡀⠿⢁⣾⡿⠋⠀⢀⠀⠄⠀⠀⠀⢰⠀⠑⠆⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⡓⢠⣿⠏⠀⢀⣴⣿⣄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠰⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⠏⠀⢀⣿⣿⡗⢙⠋⠀⠀⢂⡀⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠛⠿⣿⣿⣿⣿⡏⣾⡟⠀⠀⣼⣿⣿⠇⢀⠡⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⠻⢿⣇⣿⠇⠀⢰⣿⣿⣿⠀⠀⠈⠒⡤⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⢸⣿⠀⠀⢺⣿⣿⣟⠂⡀⠀⠀⠈⠢⡈⠘⡤⢈⡢⢶⡛⠻⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⡄⠀⠘⠻⣿⡇⠀⠈⠣⡀⠄⡄⠈⠢⠐⡀⡃⠀⠉⢳⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠉⠉⠁⠩⡳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠄⠸⣿⣶⣦⡂⠐⠒⠀⠀⠰⠿⠀⠀⠀⠀⠑⠢⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣧⠀⠀⢹⣿⣿⣷⣷⣤⡀⠀⠀⠀⠀⠀⠀⠂⠡⠢⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣆⠀⠀⠻⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⠑⠧⣘⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠈⢿⣦⠀⠀⠘⠿⣿⣿⣿⣿⣿⣷⣷⣤⡑⠀⠀⠈⡌
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠈⠻⣷⡀⠀⠈⠫⣿⣿⣿⣿⣿⣿⣿⣿⡯⢢⡀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠙⢿⣦⡀⠀⠈⠸⠿⣻⡿⢿⣿⣯⣿⣶⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡻⣿⣦⡀⠈⠢⠈⠃⠼⢛⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⢿⣷⣤⣀⠀⠀⠠⠉⠀⠀⠘⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⠿⣿⣶⣤⣄⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣙⠛⠿⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡂⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠳⡦⡄⠀⣀⢄⣆⣤⣤⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠛⠛⢀⣀⡀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠹⣥⡀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣿⣿⣿⣿⢾⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⢠⣶⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⠿⣶⣄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣾⣿⣶⣦⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣜⣿⣷⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡅⣀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣭⣭⣥⣈⡙⠛⠿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣽⣮⣾⣟⢏⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡈⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣷⣗⠤⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣟⣻⣿⣿⣿⣿⡟⢹⢽⢿⣿⢯⢿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠟⠛⠠⠘⠓⠋⣻⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠢⢝⣿⣿⣿⣿⣆⠚⠳⠈⠘⠿⣶⣶⣊⠭⣛⣋⣭⡓⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⣿⠉⠉⠉⠉⢹⠉⠉⠉⠉⠛⡟⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠀⠀⣿⣅⣀⣀⡀⢸⣆⣀⡀⠀⠀⣯⣀⡀⠀⢀⢀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠩⠙⠛⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆⢸⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢺⣿⣿⣿⠩⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⡆⣠⣿⣿⣿⣿⣿⣿⣷⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣧⣿⣿⣿⡗⢼⣿⣿⣿⢿⣿⣿⣿⣿
⣿⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⣿⣿⣿⣿⣵⡿⣹⣿⣿⣿⣿⣿⣿⣅⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠍⠛⢸⣿⣿⣿⣿
⡄⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⠇⣿⣿⣿⡟⠛⠈⣽⣿⣿⣿⣿⣿⣿⡏⠑⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣯⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣿⣿⣯⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣇⠀⠈⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⣿⣿⡿⠟⠛⣿⣿⣿⠿⠛⢸⣿⠿⢿⣿⣿⠛⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⣿⣿⡿⠿⣶⣶⣿⣿⣿⣿⣷⣴⣿⣿⣟⡃⠐⠺⠿⣿⣿⣿⣿⣿⡆⠘⣿⡟⠛⠸⠛⠛⠛⠃⠘⠛⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠒⣟⠛⠷⠤⠤⣿⣿⣿⣠⠀⢸⣿⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⡇⢢⣿⠗⣆⣶⢠⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⣿⣧⠀⠀⠀⣷⡄⠀⠉⠉⡯⠛⢓⡏⢩⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠸⣧⢀⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡃⠀⢰⣿⣿⠅⠀⢠⣿⣿⡄⠀⠀⡗⢰⢶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣩⣭⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡍⠉⠿⠛⠿⠀⠀⠈⣼⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⢸⣿⣿⠁⠀⢸⣿⣿⣇⠀⢠⡇⠈⢚⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠀⠀⠈⠉⠀⢀⡀⠐⠛⠯⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠓⠦⢼⣿⣿⣗⠄⣼⣿⣿⡇⠀⢸⣧⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣦⡀⠉⠉⣿⡛⠻⠧⢤⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠟⠉⠉⠉⠙⠛⠛⢻⣿
⠂⠀⣿⣿⡇⠀⠀⣿⣿⡄⠀⠀⣾⣆⠉⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠒⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⡂⠀⣿⣿⡇⠀⢠⣿⣿⣿⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠟⠛⠿⠿⠿⢿⣿⡿⠟⠀⠒⠀⠸⠻⣷⣤⣽⣤⣄⣭⡔⠐⠒⠲⣶⣿⣿
⠷⢴⣿⣿⣧⠄⢸⣿⣿⣿⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠦⢤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣤⣤⣄⣠⠤⠤⢄⣀⣀⣔⣶⡖⠂⠀⠤⠼⠿⢿⣿⣿⣟⠻⢿⣹⣿⣧⢾⣿⣿⣿
⠀⢠⣧⡉⠙⠛⢿⢿⣿⣿⣀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠬⠉⠭⠛⠛⠿⠿⢷⣶⣾⣯⣿⣤⣄⣀⣀⣀⣀⣸⣿⣿⣿⣯⣟⣛⡿⣿⣿⣿⠿⠿
⠀⢸⣿⣷⠀⠀⢸⣧⡀⠈⠉⢻⡛⠿⢿⣷⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀
⠀⢸⣿⣿⠀⠀⣼⣿⣧⠀⠀⣼⣷⡄⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣿⠃⠐
⢦⣾⣿⣿⣄⠀⣿⣿⣿⠄⠀⡿⣛⣳⠀⠀⢘⣛⡿⠿⣶⡄⠀⠀⠀⠉⠙⠓⠲⠆⣸⣿⣿⣿⣿⣷⣯⣭⣿⣿⣿⣿⣿⡏⠙⠿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⢠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠉⠛⠻⢿⣿⣿⣿⣂⣀⣧⣙⠿⠀⠀⣼⣿⣿⣿⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣿⣿⣿⣿⣂⣀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⣿⣿⣿⣿⣿⣿⣶⠆⠀⠀⣤
⣿⣿⣶⣤⣀⡀⠀⠉⠙⠛⠿⢿⣿⣷⣦⣄⣻⢿⣿⡿⡟⠓⢦⣷⠶⣶⡦⣀⡄⡘⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣾⣿⣿⣿⣿⣿⣇⣹⡟⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⣰⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠈⠉⠛⠻⠿⠿⠶⠭⠀⡀⠀⠀⠀⡠⠁⠀⢀⣆⣕⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠿⠿⠿⠿⢿⢏⣋⣵⠷⠖⣰⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⠀⡀⠈⠿⣷⣶⣄⣀⠤⡀⣸⢸⣿⣿⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⠐⠉⠁⠀⠀⠀⠈⠟⢀⣤⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⣏⣴⣯⢮⣛⠻⢂⡏⣸⡿⣿⣿⠟⠾⣓⣚⠛⠛⠿⣿⡿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢻⣿
⠉⣉⣉⣉⡉⠉⠑⠈⠉⠉⠛⠛⠿⢿⣛⣻⣿⡿⢟⣛⠓⠛⢿⣷⣴⣶⠶⢞⣶⣿⣟⣿⠇⡀⠈⠉⠉⠉⠛⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣷⡄⠀⠻
⠟⠋⠉⠉⠉⠛⠶⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠉⠉⠁⠀⡠⠠⠷⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣄⠀
⠀⢀⠀⠀⠀⢀⡀⠈⠳⣄⠀⠀⠀⠀⠁⢀⣄⣤⣀⣠⣤⣀⣴⣿⣿⣶⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⣸⣿⣿⣿⣿⣆
⢇⠈⣆⠀⠀⢸⣿⣷⣦⡙⣦⠀⠀⡀⠀⠛⠋⠉⠉⠉⢽⣿⣿⣿⡿⡿⠋⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠃⠀⠀⠛⡛⠋⢉⠉⠉
⠘⣂⢰⠁⠀⠸⠿⠟⣿⡯⠜⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠀⠀⠀⠺⠿⣆⠀⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⡈⢀⠀⠀⠄⠄⠀
⡀⢳⠕⡇⢈⢆⢇⠀⠀⡀⣠⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠄⠠⠐⢂⣠
⣕⡈⠌⠘⠆⠀⠀⠀⠀⠀⠀⠂⣿⠀⠀⣢⣭⣀⠀⣶⣄⡀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠲⠶⣶⣶⠶⠿⣿
⣿⣯⡍⠀⠀⡄⠀⢄⡀⡀⢠⣤⣿⣤⣤⣿⣿⣿⠛⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⡨⣀⣀⣠⡤⠤⠶⠒⠉
⣿⣿⣿⣿⣿⣮⣢⡀⠨⠀⠤⠾⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠉⠉⠀⠀⠀⠀⠀⡆
⡜⣿⣿⣿⣿⣿⣿⣷⣶⣧⣶⣛⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⣶⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣠⣤⣄⠀⠀⠀⠀⢐⣀
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣤⡴⠀⠀⡀⣄⡈⡎⣭⢿⠿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⡛⠍⠀⠐⠁⠉⠀
⢷⣄⠀⠁⠏⢿⢿⣿⡿⠟⣰⡟⠀⠀⠀⠠⠀⠀⠀⠀⢀⠑⣿⣜⠓⠀⠀⠀⠁⣻⣿⣿⣮⣞⣏⢆⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣝⣷⣦⣄⣀⣀⣀⣤⡾⠋⠀⣴⣶⣦⣤⣤⣤⣀⡀⠀⠐⠉⢡⡵⣶⡆⠀⣷⣿⣿⣻⣿⡏⢬⡿⢾⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣯⣍⣉⠉⠁⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣷⣤⣀⠈⠘⢷⣇⡄⣿⣿⣿⣿⣿⣿⣶⣧⣏⡇⣮⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⡀⠀⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⣀⢈⣻⣿⣿⣿⣿⣿⣷⣦⣀⠈⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣲⣍⡹⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣬⣭⣙⢻⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡌⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⠿⠛⢀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣧⡐⣿⢰⣷⡌⣿⠟⠛⢿⠟⢁⣴⣾⡿⠟⠛⠉⠉⠁⠀⠈⠉⠉⠙⠛⠿⢿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⣁⣿⢦⣉⠁⣇⢰⡿⢀⣴⡿⠛⠁⠀⠀⢄⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣠⣿⠆⣠⣿⠟⠀⢀⣴⣏⡀⠀⠀⠀⠀⠈⠂⠀⠈⠸⢄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⠏⠀⠀⣾⣿⠟⠻⠇⠀⠈⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⠛⠿⣿⣿⣿⣿⣿⠇⣿⡏⠀⠠⣾⣿⣿⠑⢄⢃⠀⠀⠀⠓⠀⠀⠀⢰⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠙⠻⢿⣿⢸⣿⠁⠀⢸⣿⣿⣿⠀⠀⠘⢖⠄⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⢸⣿⠀⠐⢺⣿⣿⡗⠀⡀⠀⠀⠑⢄⠑⠰⣀⠐⣠⡤⠶⢶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢸⣿⠀⠀⠸⢿⣿⠇⠀⠑⢔⠠⠐⡀⠑⢄⠡⠈⡇⠊⠓⣦⡙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⡀⠀⠀⠀⠉⠀⠀⠀⠀⠑⢄⠁⠀⠀⠀⠀⠓⠂⠀⠽⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣇⠀⡀⢿⣶⣄⡀⠐⠀⠀⠀⠁⢰⣶⠀⠀⠀⡀⠀⡈⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⡄⠀⠈⣿⣟⣿⣷⣤⡀⠀⠀⠀⢀⠀⠀⠠⡘⢂⣄⡐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣷⡀⠀⠘⢿⣿⣿⣿⣿⣷⣄⡀⠀⠠⡈⠒⢤⡄⢂⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠹⣷⡄⠀⠈⢻⣿⣽⣿⣿⣿⣿⣼⣆⡐⠄⠀⠈⢂⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⣿⣄⠀⠀⠙⢼⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠈⢢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢿⣷⡀⠀⠀⠉⢿⢏⣿⢿⣿⣿⣼⣧⣽⣤⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⢿⣦⣄⠀⠢⡈⠛⢬⡿⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣷⣤⡀⠀⠀⠀⣀⠀⠁⠙⠟⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⡛⠿⢿⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡟⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠓⢦⣀⣀⠀⠀⡀⢄⠂⣀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠛⠃⣀⣀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢙⢏⣍⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢾⣯⣿⣷⠇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⣰⣶⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠈⠿⣿⣦⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠿⢛⠆⣧⣷⣦⡀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠾⣿⣌⣿⡿⠿⠃⠀⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣛⣋⣉⣭⣉⡉⠛⠻⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣏⣄⣠⡨⢄⠄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣦⣄⠘⢻⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⠇⠈⠐⠂⠀⢀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣻⢿⣿⣿⣿⣟⢻⢽⢿⡿⣫⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠟⢀⣘⠻⠏⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢝⣿⣿⣿⣿⡏⠚⠳⠚⠸⠷⣶⣴⣩⠝⣛⣯⣍⡻⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠙⣿⠉⠉⠉⠉⢻⠛⠛⠛⠛⠛⣟⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⡀⢀⣀⡀⣸⡆⣀⣀⠀⠀⣿⣀⣀⠀⠀⢀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢉⠉⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡒⢸⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣠⣾⢣⣿⣿⣿⣿⣿⣷⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣯⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣷⣦⡌⣿⣿⣿⣿⡿⡡⢸⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⠻⢽⣿⣿⣿⣿⣿
⠀⠀⢸⣧⢀⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⣿⣿⣿⣿⠈⠀⣼⣿⣿⣿⣿⣿⣿⡿⢍⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣟⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣛⢹⣿⣿⣿⡏⠉⠹⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠷⢾⣿⣿⣿⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⡍⠛⠛⣿⣿⣿⠿⠛⢻⣿⠛⢿⣿⣿⠙⠛⠛⠛⠁⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⡿⣿⣿⣶⣶⣿⣿⣿⣷⣤⣔⣿⣟⡛⠳⠶⣾⣿⣿⣿⣿⣿⡇⠐⣿⡟⠻⠻⠇⠛⠛⠛⠃⢘⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠒⣟⠛⠿⠤⢤⣿⣿⣿⡄⠀⣸⣿⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⡇⢢⣿⠇⣆⡦⢠⣶⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣧⠀⠀⠀⣧⡄⠀⠉⠉⡿⠛⢓⡟⢩⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣇⢰⣽⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⠁⠀⢠⣿⣿⡀⠀⠀⡗⢰⢶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⡉⠙⠿⠻⠿⠀⠀⠘⣼⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⠀⠀⢸⣿⣿⠇⠀⢠⡏⠈⢚⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠀⠀⠉⠀⠀⣀⣀⠒⠛⠧⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠦⢼⣿⣿⣇⢤⣼⣿⣿⣧⠀⢸⡇⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⠁⠀⠙⠃⠀⠀⠀⠀⢰⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣼⣦⠀⠉⠉⣿⠛⠻⠧⢤⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠏⠉⠉⠛⠛⠛⠿⠿⣿⣿
⠀⣿⣿⡇⠀⠀⣿⣷⡄⠀⠀⣸⣌⠉⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠲⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿
⠀⣿⣿⡇⠀⢠⣿⣿⡷⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣭⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⠿⠿⠿⣿⣿⡿⠟⠀⠂⠀⠰⠯⣷⣭⣭⣀⣀⣐⡒⠐⠢⢤⣶⣿⣿⣿
⢼⣿⣿⣧⠀⢸⣿⣿⣯⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠤⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣤⠤⠤⣄⣀⣀⣰⣶⡀⠠⠄⠤⠿⠾⢿⣿⣿⡟⠿⠿⣻⣿⣦⣾⣿⣿⣿⣿
⢸⣧⡉⠙⠛⢾⢿⣿⣿⣂⢸⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⡉⠉⠙⠛⠻⠿⠿⣶⣶⣿⣭⣿⣇⣀⣀⣀⣀⠀⣻⣿⣿⣿⣟⣛⣛⣿⣿⣿⣿⠿⠿⠿
⢸⣿⣧⠀⠀⢸⣧⡀⠈⠉⢻⠻⠿⢿⣷⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⠔
⢸⣿⣿⠀⠀⣾⣿⣧⠀⠀⣼⣷⡄⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⡗⠀⠂
⣾⣿⣿⣀⢀⣿⣿⣿⠀⠀⣿⢟⣓⡀⠀⢘⣻⠿⠿⣷⡄⠀⠀⠈⠉⠙⠓⠶⠄⢸⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⢠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠈⠉⠛⠻⢿⣿⣿⣿⣀⣠⣿⣝⠿⠀⠀⣾⣿⣿⣿⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⣼⣿⣿⣿⣿⣀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⣿⢿⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⢀⣀
⣿⣶⣤⣀⡀⠀⠉⠙⠛⠿⣿⣿⣷⣦⣄⡻⢿⣿⣿⡟⠷⢲⣦⠽⣶⣧⣀⡄⡘⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣿⣿⣿⣿⣿⣿⣋⣾⠅⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿
⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠈⠉⠛⠻⠿⠿⠶⠭⠁⡀⠀⠀⠀⠠⠁⠀⢀⡆⣝⡯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⠿⠿⠿⢿⣿⣛⣋⣵⣦⢄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⠀⠀⠀⠿⣷⣶⣄⣀⠤⡀⣸⢹⣿⣿⣮⡪⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡠⠓⠉⠁⠀⠀⠀⢹⠏⣀⡤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡼⣏⣴⣯⢮⣛⠻⢃⡏⣸⡿⣿⣿⡿⠷⠗⠚⠛⠻⠿⣿⣿⠃⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠹⣿⣿
⠉⣉⣉⠉⠙⠛⠓⠚⠛⠛⠛⠿⢿⣿⣿⣿⣿⡿⠟⠓⠞⠿⣗⣶⣶⡶⡾⣷⣿⠿⣻⡿⡀⠀⠋⠉⠙⠛⠶⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣆⠀⠙⣿
⠛⠋⠉⠙⠛⠶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠀⠈⠛⠉⠁⢀⠤⠸⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⠁⠀⢠⣿⣿⣧⠀⠈
⠀⡀⠀⠀⢀⡀⠈⠳⣄⠀⠀⠀⠀⠂⠀⣤⣤⣄⣀⣄⡀⣠⣾⣷⣶⡦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⠀⠀⣾⣿⣿⣿⣷⡀
⠀⢱⠀⠀⢸⣿⣷⣤⡈⢧⠀⠀⢀⠀⠞⠟⠋⠛⠛⢻⣿⣿⣿⣿⣿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠀⠀⠘⠛⠛⠛⠛⢉⠉
⡇⡀⡌⢄⠀⡿⣿⣿⡿⠊⢷⡀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠰⢶⣶⠀⢸⡷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⡈⡀⢁⠡⠠⠄
⠘⢈⢣⢠⠢⢡⠀⠈⢉⢀⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠠⠀⠄⠤⣀⣀
⣀⠂⠘⠐⠀⠉⠀⠀⠀⠠⠄⢹⡄⠀⢩⣶⣂⠀⢰⣄⡀⠀⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢤⣤⣤⡶⢶⣿⣿
⣿⣽⠀⠀⢀⠀⠀⠀⠀⠰⢶⣾⣧⣤⣾⣿⣿⠿⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠀⠀⠀⣀⠀⢀⣀⣨⠤⠤⠌⠉
⣿⣿⣷⣾⣯⣧⡀⠱⠳⢘⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠌⠀⠉⠉⠀⠀⠀⠀⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣦⣤⣍⣩⣽⣿⣿⡿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⢀⣤⣄⠀⠀⠀⠀⠐⠀⠀
⠈⠺⢿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣠⡤⠔⠄⠀⠀⢁⡀⢹⢩⣻⠿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣛⠁⠀⠀⠉⠉⠀
⣄⠃⠁⠟⢿⣿⣿⣿⡿⢃⣿⠃⠀⠀⠠⠀⠀⠀⠀⠀⠈⢹⣿⢶⠁⠀⡀⠈⠘⣻⣿⣮⣵⣹⠠⡉⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠂⠁⠁⠀⠀⠀⠀⠀⠀⠀
⣝⢷⣤⣀⡀⠉⢉⣠⣴⠿⠁⣠⣦⣤⣤⣄⣀⣀⡀⠀⠀⠈⠉⢉⣦⣤⠀⢸⣤⣿⣿⣿⣿⢩⣽⡾⣿⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣾⣭⣛⡛⠛⠉⠁⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣤⣀⠀⠑⢿⡭⡀⢸⣿⣿⣿⣿⣿⣧⣭⣬⣹⢩⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣦⣀⠈⠃⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⡙⣏⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣉⣋⠻⢻⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣠⣤⢹⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡍⢼⡇⣴⣆⢻⡿⠿⢿⣿⠟⢁⣤⣶⡿⠿⠛⠛⠉⠉⠉⠉⠛⠛⠻⠿⣷⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⢸⡷⣘⠋⢸⡁⣶⡆⢁⣶⡿⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣙⠃⣸⡷⠈⣰⣿⠏⠀⢀⣴⡀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⠃⠀⠠⣾⣿⠛⠷⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⢱⣿⠃⠀⢠⣿⣿⡟⠔⡈⢀⠀⠀⠈⠶⠀⠀⠀⢈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⢿⣿⡏⣼⡟⠀⠀⣾⣿⣿⡇⠀⠀⠘⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠃⣿⡇⠀⠀⣿⣿⣿⡓⢀⠀⠀⠨⠢⡁⠂⢅⠀⠂⣀⣤⣤⣠⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⣿⡇⠀⠀⣿⣿⣿⠀⠈⠣⠂⠄⡂⠈⠢⡀⠌⠚⠉⠗⢦⡌⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣧⠀⠀⠀⠉⠃⠀⠀⠀⠈⠢⠈⠄⠀⠈⠘⠠⠄⠀⠐⣟⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡀⠀⠰⣶⣤⡀⠀⠂⠀⢀⠈⠀⣤⡄⠀⠀⠀⠀⠀⢁⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣇⠈⠀⢻⢿⣻⣷⣤⡀⠀⠀⠀⠨⠁⠀⠀⡀⠦⢈⠂⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣆⠀⠀⢻⣿⣿⣿⣿⣷⣦⣀⠀⠀⡈⠂⢌⡈⢋⠑⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠞⢿⣆⠀⠀⠹⣟⣯⣿⣿⣿⣿⣆⣦⣈⠆⠀⠉⠢⠠⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⢿⣦⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣴⣤⡀⠀⢠⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠻⣷⣄⠀⠀⠉⢿⢏⣿⣿⣿⣿⣯⣇⣱⣄⣤⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⢿⣷⣄⠀⠀⣈⠚⢽⢿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣷⣤⡀⠁⠀⠈⠑⠀⠀⠉⠻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⢿⣷⣤⣀⡈⠉⠀⠀⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⡻⢿⣿⣶⣶⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠉⠉⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠛⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢺⣦⣦⠀⢄⣀⣤⣶⣴⡄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⢀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⠋⠀⠀⣠⣾
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⣫⠁⠀⠀⠀⠀⠀⠈⠻⣾⣾⣿⣿⣿⣿⣿⣿⢦⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⢀⣾⣾⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⣰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣌⢻⢿⣶⣀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣷⣿⣷⣦⡄⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠷⣠⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠿⢛⣉⣉⣉⡉⠛⠿⠿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⣾⣝⣻⣦⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣶⣄⡈⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡯⢘⡦⡀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠷⠿⣀⠸⠿⠗⢾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡡⠔⢦⠂⢶⣶⣤⡭⠟⡻⠿⢟⣛⣯⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣟⠛⠛⠒⠒⢲⠒⠚⠛⠛⠳⡶⠿⠿⠿⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠀⠀⠀⠀⣸⣀⡀⠀⠀⢀⣇⠀⠀⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⡄⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣇⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠋⣿⣿⣿⣿⠆⠀⢠⣿⣿⣿⣿⣿⣷⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣧⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⠀⢀⣼⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣍⠉⠉⠙⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡿⠿⠿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣷⠀⢉⣿⣿⣿⣿⣿⣿⣿⣷⣂⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠄⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠨⣿⣿⣿⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⣿⣿⠿⠟⠘⢿⡿⠟⣽⣿⣿⠛⠃⠘⠛⠛⠛⠁⠀⠀⠛⠛⠛⠛⠛⠛⢻⣿⣿⣧⣽⣿⣿⣿⣯⣈⣿⣟⣛⡧⣠⡀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣯⡹⠛⢻⠟⠋⠁⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⢦⣄⣀⣿⣿⢇⡀⠀⣿⡇⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣾⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣸⣿⣿⣿⣿⣿⠀⢠⣿⡄⢀⡄⢠⣤⣄⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣄⠀⠀⢠⣧⡉⠉⠙⠓⡟⠛⢶⡟⢛⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢽⠇⢨⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⢸⣿⣷⠀⠀⠀⡇⢶⣮⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣛⠛⠻⡿⢿⣿⠀⠐⠉⣼⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⠀⠀⣾⣿⣿⠀⠀⢸⡇⠉⠽⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠒⠀⠀⠀⠀⠤⠿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⡀⣿⣿⣿⡄⠀⢸⡇⠀⠀⠵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⠀⠀⠺⠁⠀⠀⠀⠀⣬⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣌⠉⠉⠛⡿⠿⠿⣧⣄⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⡿
⣿⠄⠀⠀⣿⣦⠀⠀⠀⣯⡉⠙⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠤⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷
⣿⠀⠀⢸⣿⣿⡇⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⡷⠀⠄⠀⢰⢶⣤⣐⣆⡀⠀⡢⠤⠤⢤⣠⣴⣷⣿⣿⣿⣿
⣿⡄⠀⢸⣿⣿⡆⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢤⣤⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣁⡀⠀⣀⣀⣀⠀⠈⣩⣥⠤⠄⠀⡀⣶⣾⣿⣿⣿⠿⣿⣟⣷⣶⣄⣼⣿⣿⣿⣿⣿⣿
⠙⠛⠷⢿⣿⣿⣯⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠙⠛⠛⠿⠿⣷⣶⣿⣭⣽⣿⣿⣀⡀⠀⠀⠀⠀⣻⣯⣿⣷⡖⠾⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠀⣾⣆⠉⠉⠛⣿⠿⣿⣿⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡠⠊⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⠛
⡇⠀⠀⣿⣿⡆⠀⠀⣿⣶⠀⠀⠉⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣷⣶⣤⠄⡀⠀
⣧⠀⢸⣿⣿⣷⠀⢀⣿⣿⠧⠀⠀⠼⠿⣿⣷⣄⡀⠀⠀⠉⠛⠒⠶⢤⠄⢸⣿⣿⣿⣿⣯⣝⣛⣿⣿⣿⣿⣿⣿⠀⡟⠿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣦⣤⢀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠀⠀⢾
⠻⢿⣿⣿⣿⣿⡀⢸⣿⡕⠾⠀⠀⣿⣿⣷⣶⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣷⣄⣉⣿⣿⣿⣿⠂⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀
⣀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣆⣀⣀⠿⣿⣿⣿⠿⢷⣶⢶⣶⣲⣄⣂⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣭⣽⣿⣿⣿⣿⣿⡿⣫⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣰⣷⣶
⣿⣿⣷⣶⣤⣄⡀⠀⠈⠉⠛⠿⢿⣿⣷⣯⣙⠂⠀⠀⠈⠀⠠⠃⠁⠀⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣲⣿⣿⣿⣿⣿⠿⠿⣟⣅⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⢰⣶⣤⡔⡁⢀⠀⠸⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠁⠫⠕⠛⠉⠉⠀⢿⡟⠉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⢒⣭⣟⣞⠻⠷⠀⡅⣸⣿⣿⣿⣿⣦⣤⡽⠿⠿⣿⣿⣿⠇⠀⠀⠸⠧⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠋⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⣿
⠟⠛⠻⠿⠿⠯⠽⠿⠿⢿⣷⣾⣿⣿⣿⣿⣿⣦⢬⢿⣯⢬⣥⣤⣤⣤⣿⣿⣿⢿⢿⠁⠀⠖⠒⠲⠦⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣄⠀⠹⣿⣿
⠿⠷⠶⣤⣄⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠉⠐⠒⠀⠀⠐⠛⠛⡛⠉⠾⠿⠛⠒⠙⠁⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣆⠀⠹⣿
⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣧⡀⠘
⢀⠀⠀⣿⣦⣄⡈⢷⡀⠀⠀⠀⠀⣮⠿⠿⠚⠾⢿⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⢠⣿⠿⠿⠿⠿⠓⠀
⠀⠀⠀⢿⣿⣿⣿⣆⢻⡄⠀⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠋⠀⣠⣤⡄⠀⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠰⠐⠐⠐⠀⠈⡁⠀
⠀⠀⢠⣈⡉⠉⠛⠋⠈⢿⡀⠀⣠⡄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠂⠂⠃⢁⡉⣀⠀⠀
⠠⠀⠀⠀⠀⠀⢠⣥⣬⣼⣧⣀⣼⣷⡤⠠⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣈⣈⣈⣀⣤⣶⣿⡇
⠆⠀⠀⠀⠀⠀⠐⠶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠈⣉⠛⣋⣈⣉⠻⠤
⣧⣤⣤⡀⠀⠀⠐⢛⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⡸⠶⠖⠛⠉⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣧⣄⣉⠉⠙⢛⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠐⠄⠀⠀⠀⢰⠶⠖⠐⠄⠀⠀⠀⠉⠹⢻⠿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠲⢿⣷⡦⠄⠀⠠⠐⠂⠀⠀
⠀⠹⢿⣿⣿⣿⣿⡿⢻⣿⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⢄⠂⠀⠀⠀⠀⡆⠰⠤⣶⣙⢺⢨⣙⢛⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠠⠒⠈⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠈⠛⠛⢋⣠⡿⠃⢀⣀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⣿⣿⢚⢥⣐⣦⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠶⣶⣶⠶⠟⠋⠀⠀⠛⠿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠐⢯⢿⡃⠀⣿⣿⣿⣿⣿⣿⣜⡛⣙⢿⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣶⣄⡀⠉⠣⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣮⡣⣲⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣄⡀⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣍⣿⣿⣿⣿⣿⢉⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠛⢨⡏⣩⣉⢿⣿⣿⣿⣿⣿⠿⠋⣀⣤⣶⣾⡿⠿⠿⠿⠿⠿⢿⣶⣶⣤⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣷⢘⣇⠻⠿⠈⡏⣠⣍⠛⢁⣴⣿⠿⠋⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣏⠳⠶⢠⣧⠹⠋⣴⣿⠟⠁⠀⡀⠀⠀⠀⠁⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣯⢁⣾⡿⠁⠀⣠⣾⣷⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡏⣼⡿⠁⠀⣰⣿⣿⠈⠪⡀⠄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠉⠛⠿⣿⣿⣿⣿⢱⣿⠇⠀⢰⣿⣿⡏⠀⠀⠈⢰⢄⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠙⠻⢟⢸⣿⠀⠀⢹⣿⣿⡏⠀⠀⠀⠀⠓⢅⠠⠀⡄⠀⠀⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣿⣿⠀⠀⢹⣿⣿⠇⠀⠒⠤⢄⠠⠈⢢⡀⢱⠀⠴⡞⣛⠓⢧⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠀⠀⠉⠻⢿⠀⠀⠀⠀⠀⠈⠒⠠⠑⠄⠅⠀⠀⠈⢻⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⡄⠀⠀⣄⡀⠀⠐⠀⢤⠀⠀⠀⠀⠀⠀⠀⠈⡐⠀⠨⢦⣚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣧⠀⠄⢻⣿⣶⣄⡀⠀⠈⠁⠂⠸⠿⠀⠀⠀⠈⠢⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⡆⠀⠈⢿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠂⠀⠠⠤⢀⣈⡑⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠈⢻⣿⣿⣷⣿⣿⣷⣀⡀⠀⠀⠑⠠⠀⠀⠉⠩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠹⣿⣆⠀⠀⠙⣽⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠈⠀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠘⢿⣧⡀⠀⠈⠹⡿⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣿⣄⠀⠀⠀⠺⢟⠿⣿⡿⣿⣿⣶⣶⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⢻⣷⣦⡀⠐⠦⠉⠁⠄⣈⠙⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⢿⣶⣄⡀⠀⠀⠠⠄⠀⠀⠈⠙⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣻⢿⣷⣦⣤⣀⣀⠈⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⡛⠻⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠈⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⢧⣀⠀⠀⠀⠀⠀⢄⡀⡀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠟⠛⠀⣀⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡿⠋⠀⠀⣠⣾⣿⢿⣿
⣿⣿⣿⣿⣿⡿⠟⠟⠿⡿⠋⠀⠀⠀⠀⠀⠉⠳⣶⣦⣾⣿⣿⣿⣷⣦⠄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⢀⣶⣶⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⢸⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣷⣦⣄⠂⠸⣿⣦⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠃⢀⢰⣤⣀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠀⠀
⣿⣿⣶⣬⣿⣿⣿⣿⣿⣤⣈⣙⣿⣶⡀⠀⠀⠀⠀⠀⠈⠛⠿⣥⣼⢷⣽⢿⠿⠀⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣆⢀⡤⢭⠒⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣶⣿⣿⣿⣿⣶⣤⡀⠉⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣛⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⠏⢉⢿⣾⠧⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠡⠶⡬⢩⣷⣤⣬⣙⡻⠿⣿⡿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠓⠒⠶⡶⠶⠾⠿⠷⢶⠿⠶⠿⠿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⡀⢀⣀⠀⢸⣇⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢃⣿⣿⣿⣇⣀⠀⢠⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣦⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠓⠒⣛⠛⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⠗⣿⣿⣿⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣧⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡛⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⢺⣿⣿⣿⣿⢸⣿⣿⣿⠘⣿⣿⣿⡇⢸⣿⣿⣿⡀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡉⠛⠻⣿⡟⠸⣿⣿⡿⠀⠙⠛⠛⠃⠘⠛⠛⠛⠀⠀⠀⠛⠛⠛⣿⣿⣿⣟⣛⣛⣃⣘⡛⢛⣿⡀⠀⢛⠛⠻⠋⣙⣛⣿⣿⣿⣿⣿⣟⠛⢻⡿⣿⡟⢙⠻⠟⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣸⣿⣿⡇⠀⢀⣿⡇⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣷⣿⣶⣧⣉⡉⢻⣿⣿⣿⣿⣿⠀⢰⣟⡀⠀⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢹⣍⠙⠛⠒⠺⡿⠧⣼⡟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠋⢡⣾⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⣽⣿⡆⠀⠀⢸⣷⣤⣮⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⣿⣿⣿⡇⠀⠻⠆⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⢀⣿⣿⣿⠀⠀⣸⡏⠻⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡗⠀⠈⠅⠉⠉⠤⠀⣰⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⢸⣿⣿⣿⠀⠀⣿⠀⠀⠉⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣠⠤⠀⠰⣶⠂⠀⠈⠑⡛⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⢾⡿⣿⣿⣡⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⢸⣷⡄⠀⠈⢩⣟⠛⠲⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣺⣿⡟⠉⠀⠀⠀⠀⠈⠉⠉⣻⣿⣿⣿⣥⣄⣀⣀
⣾⣿⣿⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⡀⠀⣠⣤⡭⠤⠅⠠⠄⣀⣀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠁⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠁⡉⠁⠈⠉⠉⠉⠛⣛⣋⡁⠀⠀⠀⣭⣽⣿⣿⣷⣶⣶⣶⣢⣌⢉⣿⣿⣿⣿⣿⣿⣭⣿⣿⠿
⣿⣿⣿⡇⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠻⠿⢿⣷⣶⣭⣭⣗⣒⣶⣿⣿⡾⠉⠉⠉⠉⠉⣿⣿⣿⣧⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⡉⠛⠛⠿⣿⣿⣿⣯⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠒⠀⠀⠉⠉⠛⠛⠻⠿⢿⣿⣶⣶⣶⣶⣶⣿⣿⣻⣿⣷⣶⣾⣿⣿⣿⠋⠉⠉⠙⣿⣿⣿⣿⠤
⣿⣿⡀⠀⠀⣿⣄⠈⠉⠛⢻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣡⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⠠⠂⠀⠀⠀
⣿⣿⡇⠀⢸⣿⣿⡄⠀⠀⣿⣿⣿⣶⡀⠀⠀⠀⠒⠲⠤⣤⣄⡀⢸⣿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⡟⠀⠃⣤⣬⣝
⣿⣿⣇⠀⣸⣿⡿⠅⠀⠀⣷⣿⣭⣭⣝⡃⠀⠀⠀⠀⠀⠀⠈⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣦⡀⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛
⠛⠿⢿⣿⣿⣿⣿⡤⠀⠸⣿⣿⣿⣿⢿⣧⣤⣤⣤⡤⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢉⢻⣿⣿⣿⣿⣿⣿⣿⡦⣤⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣤⣄⣀⣀
⣤⣀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣯⣝⡻⠀⠈⠉⠉⠀⢉⠉⠉⠁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠮⢝⣿⣿⣿⣿⣿⣿⣯⡾⡟⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣦⣤⣀⣀⠀⠈⠉⠉⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⣰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠛⠛⠛⠛⠛⠿⣩⠥⠞⠛⠢⣾⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⠈⣻⣟⡵⣿⣮⠀⡃⢿⣿⣿⣿⣿⣦⣉⢻⣿⣿⣿⣿⣿⡇⠀⠀⢰⣶⣄⣀⠄⠁⠀⠀⠀⠀⠀⠘⠃⠴⠖⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠰⣿⣿⣿⣿⣿⡇
⣿⡿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣚⣿⣋⣙⣁⠀⠐⠃⣿⣿⣿⣿⣿⠟⠛⢫⣭⣭⣍⣙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⠀⠘⣿⣿⣿⣿⠁
⣀⠈⠁⠀⠈⠉⠁⠛⠻⠿⠯⠿⠟⠛⠭⠉⠉⠉⠽⠿⣿⠿⢛⣯⣿⡿⠭⠿⠣⡄⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣼⣧⡀⠈⢿⣿⣿⠀
⠉⠛⢦⣄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡔⠂⠓⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠃⠀⢰⣿⣿⣷⡄⠀⢻⡇⠀
⢠⣄⡀⠙⢧⡀⠀⠀⠀⠀⣀⣤⣶⣶⣤⣦⣤⣴⣿⣿⣿⡿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣆⠀⠀⠀
⢸⣿⣿⣷⣌⢻⡄⠀⢰⣤⡉⠉⠁⠀⠀⠰⠿⣿⣿⣿⠿⠟⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⢈⢉⢉⡉⠅⠤⠀⠀⠀⠀
⠘⠻⠿⢿⣿⣦⣿⣤⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠄⠄⠄⠤⠐⠐⠀⠀⠀⠀
⠀⠋⠀⢻⡶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠐⠐⠂⢂⣭⣤⠆⠀⢠
⠀⠀⠀⣙⣛⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠐⣒⣶⡶⢟⠻⣿⡿⠀⠀⢸
⠀⢀⠀⠈⠉⠉⠉⠙⡏⠉⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⢀⢤⣄⣴⠿⠵⠒⠛⠀⠀⠀⢀⡤
⣷⡄⠹⠦⠈⠢⣞⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⠀⣤⢄⣤⡒⠀⠘⢻⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣦⣄⣿⡇⠀⠀⠠⡀⠀⠀⠀⠀⢸⣽⣿⠮⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣶⣦⣀⠀⠀⢀⣀⣀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠐⠀⠀⢀⠈⠀⠁⠀⠀⠀⠀⡀⣄⣈⡎⣮⢿⢿⢿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣉⡻⠍⠐⠈⠀⠀⠀⠀⠀⠁⠒
⠙⠿⢿⣿⠟⣱⣿⠃⠀⠀⠐⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡓⣠⣿⣿⣶⣾⣽⡆⢐⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣠⣶⠟⠁⡠⣶⣶⣤⣤⣤⣤⣀⡀⠀⠀⠀⣀⢶⣶⠀⠀⣿⣿⣿⣿⣿⣏⢴⣿⢳⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣟⡛⠛⠉⠁⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣶⣤⡀⠀⠙⢿⢆⢀⣿⣿⣿⣿⣿⣿⣶⣷⣷⣿⡼⣽⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡂⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣤⣀⢀⡀⠀⠤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣜⣦⠽⠿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣟⢛⣛⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⢹⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠈⠙⠳⢦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣄⢺⡇⣾⣷⢸⡿⠛⠻⣿⠟⢁⣠⣶⡿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣶⣤⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣉⣸⡿⣌⣉⠀⡇⢾⡷⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠆⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣁⣼⡿⠌⣡⣿⡟⠁⠀⣠⣆⡀⠀⠀⠀⠀⠉⠆⠀⠀⠀⠄⡀⠀⠀⢀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⠏⠀⢀⣼⣿⠛⢟⠅⠨⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⡇⣿⡟⠀⠀⣾⣿⣿⠀⠀⠈⠢⣢⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠉⠛⠿⣿⣿⢸⣿⠁⠀⢨⣿⣿⡟⠢⡀⠀⠀⠹⢷⠀⠀⠰⠁⠀⠀⠠⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠙⢸⣿⠀⠀⢸⣿⣿⡇⠐⠚⢤⡀⢀⡈⢣⠀⠠⡀⢠⣤⡴⢶⣠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢸⣿⠀⠀⢸⣿⣿⡀⠀⠀⠀⠊⠑⢠⣀⠁⡐⠃⠉⠈⣒⣦⡘⢯⠤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡀⠀⠀⠀⠉⠈⠐⠤⣀⠀⠐⠀⠈⠁⠈⠈⠥⣀⠀⠘⡅⣺⡾⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣇⠀⠀⢷⣦⣄⠀⠀⠀⠀⠂⠈⢀⣤⡄⠀⠀⠂⡈⠐⠚⠦⢄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⡀⠁⠘⣿⣿⣷⣦⠄⡀⠀⠀⠀⠉⡀⠀⠀⠀⠐⠲⠂⠁⠀⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣷⡀⠀⠘⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠈⠁⠒⠲⠬⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢻⣷⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠈⠄⠀⠀⠀⡀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠻⣷⡄⠀⠀⠉⣿⠿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠂⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠙⣿⣦⡀⠀⠀⠚⢿⡛⣿⣿⣿⣿⣭⣀⣠⣤⣤⣄⣠⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⣿⣦⡀⠀⢀⡙⠻⡋⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⣿⣦⣄⠈⠀⠀⠉⠂⠀⠈⠙⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡿⣿⣦⣄⣀⠀⠁⠀⠀⠄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣛⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡉⠉⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠝⠉⠁⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⡟⠻⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⢠⣀⢀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠉⣠⣤⣄⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠋⠀⠀⢠⣼⣿⡟⠻⠿⣿⣿⣿⣿
⣿⡿⠟⠿⢿⡿⠛⠀⠀⠀⠀⠈⠙⢷⣤⣶⣷⣷⣿⣷⣷⣶⠄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⣸⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠠⣿⣿⣿⡧⠀⠀⠀⠙⠻⢿
⣿⣧⣀⣀⠀⢿⣷⣄⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣋⣀⢰⣦⣄⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠇⡁⡁⠄⠀⠀⠀
⣽⣿⣿⣿⣷⣄⡈⢹⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⢿⣭⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢥⡡⣄
⠛⠟⠛⠛⠿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⣴⣶⠖⡷⣄⡀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲
⣶⣿⣿⣶⣦⣄⡈⠉⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣺⠧⠉⠈⢄⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢉⣹⣿⡿⣼⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⢷⣤⣌⣝⣛⠿⢿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢶⠶⠾⠿⠷⠶⡿⠷⠾⠿⠧⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠀⠀⠀⢀⣷⣀⡀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⠁⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⡏⣿⣿⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠿⠿⠤⠤⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⠿⣷⣿⣿⣿⣿⠶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡄⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠁⠀⠛⣿⣿⣿⣿⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⡇⢸⣿⣿⣿⣇⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣇⠀⠀⢸⣿⠿⢿⣿⣿⠟⠛⠛⠀⠛⠛⠛⠃⠘⠛⠛⠛⠁⠈⠉⢛⣿⣿⣛⣛⣛⣻⠛⡛⠃⣸⣟⠛⠛⠂⠀⠛⠛⠻⠿⣿⣿⣿⣿⡿⠿⠙⣻⢿⣿⢿⠿⠿⠇⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⣿⣟⠀⠀⣼⡧⠀⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣻⣿⣿⠿⢿⣿⣿⣾⣷⣴⡈⠙⢛⣿⣿⣿⣿⣿⡇⠈⣿⡊⠀⠘⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠙⠛⠓⠲⡿⠿⢤⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⢯⣷⡗⢰⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⣇⠀⠀⠀⡟⣤⣜⣧⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠉⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠀⣺⣷⢸⣾⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀
⣿⡇⠀⢰⡟⠛⣻⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⠀⢛⣉⠛⠀⠉⠉⣾⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⣿⡇⠀⢸⣏⠀⠀⣒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣠⠀⠀⠀⠲⣢⡄⠉⠉⠓⠞⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⣿⣯⡀⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠉⠉⣿⡛⠳⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⠉⠀⠀⠉⠉⠉⠛⢿⣿⣿⣿⣇⣀⡀⠐⠒⠐⠠
⡆⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣀⡉⢉⡭⠄⠀⣀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣷⡾⠉⢩
⣿⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢩⠉⠉⠉⠛⠛⠛⠻⠿⠉⠀⠈⠀⢈⣙⣿⣷⣿⣶⣴⣶⣌⣉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⣿
⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿⣿⣾⣯⣬⣖⣒⣶⠤⣾⣿⣿⣯⠅⠀⠈⠛⢻⣿⣿⣯⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤⣤
⠻⠷⢾⣿⣿⣿⣇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠠⠉⠉⠙⠛⠻⠿⠿⣿⣷⣶⣶⣦⣤⣤⣾⣿⣿⡿⣿⣿⣯⣽⣿⣿⠏⠙⠛⠛⢻⣿⣿⣿⣁⣸⣿⣿
⠀⠀⣸⣆⠉⠉⠛⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⠄⣠⣭⡿⠋⠉⠁⠀⠀
⠀⠀⣿⣿⣦⠀⠀⢰⣿⣿⣶⣄⠀⠀⠀⠐⠦⢤⣤⣀⣀⠀⣾⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⠇⠠⢀⣐⡶⠦⠀
⠄⢀⣿⣿⣿⡂⠀⢨⣭⣽⣟⣛⡛⠀⠀⠀⠀⠀⠀⠈⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣨⡍⠹⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⣸⣿⣿⣿⣿⣾⣿⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠚⠻⠿⠿⠀
⣶⣾⣿⣿⣿⡄⠀⢾⣿⣿⣿⣿⣿⣀⣀⣤⣤⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠐⠻⣿⣿⣶⣾⣿⣿⣿⣯⣀⡀⠀⠀⢠⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⣀⣀⠀⠀⠀⠀
⠀⠉⠛⠻⠿⣿⣷⣷⣮⣝⡻⠇⠈⠉⠛⠋⠉⠻⠒⠒⢠⣘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣙⢿⣿⣿⣿⣿⣿⣿⣫⣾⠇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣿⣿⣿⣿⡆⠀
⣶⣦⣤⣀⡀⠀⠈⠉⠉⠉⠉⠁⣄⡄⣀⡀⠐⠀⠀⠀⡞⣿⣿⣿⣽⡮⡻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠰⠶⠿⠟⠿⠿⠿⢿⢛⣩⡿⠶⣠⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⠁⠀
⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣤⣤⣄⠑⣻⢿⣾⣶⡄⢘⠃⣿⣿⣿⣿⣯⣌⡊⢻⣿⣿⣿⣿⣿⠀⠀⠀⣴⣶⣄⠀⡀⠐⠈⠁⠀⠀⠀⠈⠿⢁⣤⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢼⣿⣿⣿⣿⣿⠀⠀
⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢧⠿⠛⠗⠊⠁⡞⢸⣿⣿⣟⡿⣿⡿⠗⠿⣛⣛⣛⠛⠟⠀⠀⠀⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀
⠉⠉⠉⠛⠛⠿⢿⣿⣻⣿⣿⠿⣛⡛⠋⠛⢛⣿⣾⣷⠾⢟⣿⡿⣟⣿⠾⡀⠀⠉⠉⠉⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣷⡀⠀⠻⣿⣿⠃⠀⠀
⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠈⢠⠤⠱⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⣄⠀⠹⣿⠀⠀⣴
⠈⠳⣄⠀⠀⠀⢡⣧⠄⣠⣄⣠⣀⣠⣀⣀⣴⣿⣷⣶⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣆⠀⠁⠀⠀⣿
⣷⣾⣿⣷⣶⣤⣬⣿⣿⠛⠛⠉⠉⠙⣽⣿⣿⣿⣿⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠚⠛⠛⢛⠋⡉⠁⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⢁⢁⠉⡀⠄⠀⠀⠀⠀⠀⠛
⡌⣩⣭⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡈⡈⡄⠤⠀⢄⣀⡠⠀⠀⡀⠀
⠀⠀⠀⠀⠈⢸⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⢤⣤⣴⠶⣾⣿⠃⠀⢰⡷⠀
⠀⠂⠀⢀⡀⠀⣇⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠄⠀⠀⢀⣸⢿⣷⣦⡤⠵⠎⠉⠁⠀⠸⠇⠀
⢀⡀⠀⣀⣨⡇⣿⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠨⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠍⠉⠉⠉⠀⠀⠀⠀⠂⠀⠀⠉⠀⠀
⣶⣭⣀⣀⠈⢱⡟⠀⠀⣀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣈⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠄⡀⠀
⣿⣿⣿⣿⣷⣾⠇⠀⠀⠈⠙⠀⠄⠀⠀⢈⠋⠉⠁⢈⠀⠀⠀⡂⡐⢻⢛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠙⠻⠟⠫⠤⠂⠉⠉⠁⠀⠒⠿⣶⣦
⣿⣿⣿⢟⣽⡟⠀⠀⠀⡀⠀⠀⠀⠀⠐⠑⠁⢉⣀⠀⠀⠀⣧⣻⣿⣿⣬⣽⣷⣫⣩⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠌⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠛⠋⣡⣾⠟⠀⣠⣄⣀⡀⣀⡀⠀⠀⠈⠀⠁⠙⣿⣿⣆⠁⣾⣿⣿⣿⣿⣿⢛⣷⣾⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠿⠛⠁⠀⠀⠘⠛⢿⣿⣿⣿⣿⣷⣤⣀⠀⠘⠻⣿⣟⠀⣿⣿⣿⣿⣿⣿⣮⣟⣱⣽⣯⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠠⠀⠀⠀⠀⠀⠂⠀⠀
⣦⣄⣀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠈⠙⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣼⡻⢯⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⣤⣀⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣽⣿⣿⣿⣿⣏⣤⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠦⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠙⠻⠷⣧⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⠁⣾⢁⣤⡌⢿⣿⢿⣿⣿⡿⠛⢁⣤⣶⣿⠿⠿⠛⠛⠛⠛⠛⠿⠿⣷⣶⣤⣄⡀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⠇⣹⣆⠻⠃⢸⠀⣶⣌⠋⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠈⠉⠛⠿⣷⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣌⠻⠃⣼⣆⠛⢁⣾⡿⠋⠀⢀⠀⠀⠀⠀⠀⠐⠥⠀⠀⠂⠀⠀⠀⠀⠀⠀⡈⠙⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢡⣿⡟⠀⢀⣴⡿⠿⣾⢀⠠⡀⠀⠀⠀⡀⠀⠀⠉⠀⠅⠀⠁⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⢇⣿⡟⠀⢀⣼⣿⡇⠀⠀⠈⠢⣡⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠲⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠻⣿⣿⣿⡟⢸⣿⠁⠀⣸⣿⣿⡇⠡⡀⠀⠀⠘⡡⠀⠀⠀⠡⠀⠀⠀⠄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠛⠇⣿⡟⠀⠀⣾⣿⣿⠀⠑⠺⣠⣀⠀⠈⢄⠑⢄⠀⠀⢀⣠⠄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠈⠍⠂⢁⠀⢂⠠⠐⠓⠫⢭⡉⢻⣦⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠉⠻⠏⠈⠂⠄⠀⡀⠠⠀⠁⠀⠡⠀⢀⠀⠐⢻⠒⣻⣧⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡀⠀⠠⣤⡀⠀⠀⠀⠀⠂⠌⠑⠀⣀⠀⠀⠉⠐⠠⢌⡚⠉⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣇⠠⠀⢻⣿⣷⣤⣀⡀⠀⢀⠈⠘⠛⠁⠀⠀⡈⣀⡀⡀⠵⢆⠤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⡄⠀⠈⢻⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠐⠠⠀⡂⡀⢂⠀⠀⠣⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⡄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠀⡀⠀⠈⠉⡒⠤⢀⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠐⠘⣿⣆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠠⠀⢀⠀⠘⢆⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢿⣧⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡁⢇⣀⣐⣄⣇⠱⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠹⣿⣦⡀⠀⠈⠁⢿⡋⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⣿⣦⡀⠀⠢⠀⠛⠁⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⢿⣷⣤⣀⠀⠀⠠⠤⠀⠀⡙⠛⠛⠛⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⡿⣿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣉⠛⠻⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠂⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⢿⣿⡢⡀⠀⢀⣤⠀⢀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠙⠿⣷⣶⣎⣢⣄⣤⣼⣦⣤⡀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣩⣅⣥⣶⣶⣤⣀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠋⠀⠀⣴⣿⣿⣿⣟⠛⠻⢿⣿⣿⣿⣿⣿⣿
⡿⢿⠿⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⢠⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⣄⡀⠉⠛⠿⣿⣿⣿
⣄⠸⠿⣶⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣶⡀⠀⠈⠙⠻
⣿⣧⣀⣘⣿⣷⣆⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣷⣾⣄⠀⠀
⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷
⣶⣦⣄⡈⠙⢿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣬⣭⣛⠿⢿⣿⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⠿⠿⠶⡾⠷⠶⠿⠿⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣀⣀⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠀⢰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⠟⠛⠁⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⢸⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣧⣸⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠷⠦⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢲⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⣾⣠⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡟⠋⠻⣿⣿⣿⣿⡑⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⠸⣿⣿⣿⡇⢸⣿⣿⣿⣇⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠐⠛
⡀⠀⢠⣿⠍⢻⣿⣿⡏⠈⠛⠛⠛⠀⠛⠛⠛⠃⠘⠛⠛⠛⠉⠉⣩⣟⣛⣛⣛⡻⠟⢛⠛⢛⣇⡘⠛⠟⠛⠁⠙⠛⠿⣿⣿⣿⣿⣿⠿⠟⠻⢶⣭⠟⠻⣿⡿⠛⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⡀⠀⢸⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⡿⠿⣿⣷⣿⣷⣷⣤⣖⠛⠻⣿⣿⣿⣿⣿⡿⠀⢹⡗⠉⠡⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⠓⠶⢾⠿⣦⣼⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠠⣿⣿⡸⣼⠀⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀
⠀⠀⣸⢠⣄⣫⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⢸⣿⡆⣷⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⣿⠒⣟⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠀⠙⡋⠛⠃⣘⠛⢱⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⢀⣧⠁⠀⣒⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣩⠀⠀⢀⠌⢠⣤⠌⠉⠙⠦⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⡅⢸⣿⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠉⠀⠀⠀⠀⢱⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠉⢻⡟⠿⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⡿⠿⠀⠈⠉⠉⠙⠛⢻⣿⣿⣿⣟⣀⠀⠂⠀⠠⣤⣀⢀
⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣈⢛⣛⠁⣀⡀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠍⢉⣓⡚
⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡛⠋⠙⠛⠛⠛⠿⠿⠟⠁⠈⠁⠀⣛⣻⣷⣾⣦⣤⣤⣭⣉⡐⠒⣶⣿⣿⣿⣿⣟⣿⣿⣿⡟⠀⢸⣿⠃
⠀⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⣷⣾⣯⣴⣖⣒⡶⠤⣤⣿⣿⣿⡖⠐⠒⠛⢛⣿⢿⣯⣝⣛⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣨⣭⣄
⣶⣿⣿⣿⣯⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⡉⠛⠛⠿⠿⠿⣿⣿⣿⣬⣤⣤⣤⣤⣿⡿⢿⣿⣿⣭⣿⣿⣿⡿⠛⠛⠛⠿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⢰⣯⡉⠙⠛⠿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣷⣶⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢀⠀⢈⣭⡟⠋⢐⠞⠿⠟⠉⠉
⢸⣿⣷⡀⠀⠀⣿⣿⣷⣤⡀⠀⠀⠀⠤⢤⣀⣀⡀⠀⢰⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣷⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣗⡒⢁⠀⠠⣤⣄⠀
⣼⣿⣿⡇⠀⠀⣛⣛⣛⣟⡷⠆⢀⠀⠀⠀⠀⠉⠉⠃⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⣾⣻⠛⣻⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⣾⣿⣿⣇⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠉⠉⠙⠛⠀⠁⠰⢿⣷⣶⠀
⣿⣿⣿⣧⠀⠸⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⠀⠁⢰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⣿⣿⣦⣤⣿⣿⣿⣿⣟⠀⠀⠀⠀⢠⣿⣿⣿⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀
⠛⠿⢿⣷⣶⣾⣶⣽⣻⠿⠉⠙⠛⠛⠙⠛⠋⠈⠀⡍⣝⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⢦⣾⣿⣿⣿⣿⣿⣿⢛⣭⠆⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣿⣷⣶⣦⠀⠀
⣄⣀⠀⠀⠉⠙⠛⠛⠛⠛⢰⣄⣀⠀⠀⠈⠀⠀⢰⢳⣿⣿⣾⣗⢯⡻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣭⣵⣿⣿⣿⣿⣿⡟⠿⣛⣯⡤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⡿⡛⠀⠀
⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣀⡛⠟⡾⣱⣶⣦⠄⡻⢸⣿⣿⣿⣿⣛⣊⠪⣻⣿⣿⣿⣿⡇⠀⠀⢀⣷⣤⣅⡀⠀⠀⠨⠛⠉⠉⠁⠀⢹⡿⠉⣀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⣿⣿⣷⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢷⣿⠐⠳⠌⠉⢰⡇⣾⣾⣿⣿⢿⣿⣿⣿⣷⡿⠿⠿⠿⠁⠀⠀⢸⠿⠛⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀
⠛⠚⠿⢿⣿⢿⣿⣿⣿⣿⣶⣶⠶⢶⠲⣶⣤⣾⣦⣿⣿⣿⣿⣿⢿⣯⡆⠀⠘⠛⠛⠲⢦⡌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣤⠀⠈⢿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣭⠉⠉⠉⠑⠈⠛⠒⠒⠀⠩⠙⠛⠁⠑⠻⠛⠛⠋⢉⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣿⣷⡀⠀⢻⠀⠀⠀⠀
⢳⣿⣿⣿⣿⣶⣿⣷⡀⡀⡀⡀⠀⠀⠀⢀⣴⣶⣤⣄⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣷⡄⠈⠀⠀⠀⠀
⣭⣭⣿⣿⣿⣿⣿⣿⣿⠃⠈⠈⠉⠉⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⣸⣿⠿⠿⠿⠛⠀⠀⠂⢸⠀
⣷⣾⣿⢿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠂⠂⠒⠐⠀⠀⠀⠀⠀⠀⡄
⠙⠛⠉⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠐⠐⠘⠀⢁⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠃⠚⠘⡇⠀⠀⡆⠠⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⣁⣈⣠⣴⣟⠃⠀⠀⠁⠀
⠀⠀⠀⠀⠀⢿⠀⠀⢺⣿⣶⣦⣽⡿⠒⠀⠠⣬⣚⢟⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⣿⣶⠍⠙⣋⣈⣙⡷⠄⠀⡀⠀⠀
⠉⢐⠀⠀⣲⢸⡆⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠛⠙⠇⢾⢻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣨⠷⠾⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣦⠈⠃⠘⠻⣸⡇⠀⠈⠁⠀⠀⠀⠀⠀⢀⣠⣶⡔⠅⠂⠈⢻⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⢄⣿⠀⠀⠀⠲⢄⠀⠀⠀⠀⠾⠞⠻⠓⠆⠀⠀⠸⠙⢻⣿⢿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠲⠿⣿⡷⠆⠀⠤⠖⠒⠀⠀⠲⣯⠀⣒
⣿⣿⣿⢟⣾⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠆⠀⠀⠀⠀⢠⣴⣶⣦⣧⡿⢹⢹⢻⠿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⡤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺
⠿⠟⣫⣾⠟⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠐⠦⣷⣦⣤⡐⢸⣿⣿⣿⣿⣿⣿⢾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣾⠿⠋⠀⠐⡿⣶⣤⣶⣶⣶⣦⣀⠀⠀⠀⢾⣿⣿⡃⢸⣿⣿⣿⣿⣿⣿⡺⡿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠉⠻⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣹⡼⢯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀
⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣾⣆⣛⣻⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠙⠳⣦⣄⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠆⣿⠋⣙⠻⣿⣿⣿⣿⣿⣿⡿⠟⠉⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀⠀⠈⠙⠲⢦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣷⡌⣿⠸⣿⡇⢻⠋⣉⠻⡿⠋⣠⣶⣿⠿⠛⠉⠉⠀⠀⠀⡀⠀⠀⠉⠉⠛⠿⢷⣦⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣤⣿⠳⣤⠄⣸⡘⣿⠇⣠⣾⡿⠋⠀⢀⠀⠀⠈⡄⢀⡀⠘⠓⡆⠀⠁⠀⠀⠀⠈⠛⠿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⠓⠆⣴⣿⠋⠀⢀⣼⣤⡑⢌⢄⠀⢀⠈⠀⠠⠀⠘⠢⠄⠀⠀⠄⢀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣼⣿⠃⠀⣠⣿⣏⢋⠁⠀⠑⢆⢻⠀⠀⠀⢠⠀⠀⠀⠈⠐⠂⠖⣂⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⢡⣿⠇⠀⢀⣿⣿⡇⠁⢆⠀⠀⠀⢻⢄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠛⠿⣿⡿⢸⣿⠀⠀⣼⣿⣿⠁⠀⠂⢇⢀⠀⠀⠣⠁⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠁⣿⡿⠀⠀⣿⣿⣿⠀⠀⠀⠀⢃⠪⡐⠀⠡⡀⠀⣦⣶⠾⠧⣴⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢿⣷⠀⠀⠹⣿⡏⠈⠀⢤⢀⡀⠀⠈⠆⢄⠡⠁⠃⠀⠉⢳⡌⣯⢂⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡁⠃⠀⠀⠀⠁⠀⡈⠀⠉⣣⠿⢟⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡆⠀⠈⣿⣶⣄⡀⠀⠀⠀⠈⢐⠀⣶⠆⠀⠀⠀⠁⠢⠄⡄⠀⠁⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⡀⠀⠘⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠠⠤⡔⠄⠤⡈⠒⠢⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣷⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⡄⠀⠈⠠⠁⠐⠠⢄⠃⠀⠁⠑⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⢻⣧⡀⠀⠈⢿⢿⣿⣿⣿⣿⣿⣷⣤⣀⢐⠂⠀⠀⠸⡀⠤⢀⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠻⣷⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⢄⠀⠘⢄⠠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⢿⣦⡀⠀⠈⠑⢿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣷⣶⣤⡣⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠻⣿⣦⡀⠀⠀⡙⠻⢰⡿⢻⢿⣿⣿⣿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⢿⣶⣄⡈⠁⠀⠀⠐⠂⠘⠙⣿⡿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣻⢿⣶⣤⣀⡀⠉⠀⠀⠐⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⠿⢿⣿⣶⣶⣦⣤⣤⣴⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠉⠉⠉⠛⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⠂⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⡛⣵⣦⠠⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⢿⣿⣧⣄⠐⣾⡿⢾⢠⢀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠙⠻⣿⣿⣿⣿⣿⣾⣿⣿⣧⣄⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⣶⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⣾⣿⣿⣿⣿⣭⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠁⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣧⣤⠈⠉⠻⢿⣿⣿⣿⣿
⢿⣶⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣆⠀⠉⠻⣿⣿
⣄⣹⣿⣿⣆⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣆⣢⣴⣿⠉
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣯⣆
⣄⡈⠻⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢽⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣌⣜⡛⠿⣿⣾⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠶⡾⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣷⢀⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡟⠛⠁⣿⣿⣿⣇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠷⣿⣿⣿⣇⣸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣤⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⠸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯
⠀⠀⣷⡀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⡏⠻⠴⣿⣿⣿⣿⡬⣐⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄
⠀⠀⣿⠁⢠⣿⣿⣿⣿⢸⣿⣿⣿⠘⣿⣿⣿⡇⣸⣿⣿⣿⡇⢐⡲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠂
⠀⢰⣿⠄⣺⣿⣿⡟⠋⠈⠛⠛⠛⠀⠛⠛⠛⠃⠘⠛⠛⠛⠋⣻⣙⣛⣛⠿⠿⠟⠛⠟⢛⣟⠃⡘⠛⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣭⠟⠿⣿⡿⠿⠛⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⠀⢸⣿⡀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢷⣾⣿⣷⣶⣧⣶⣤⣔⠛⠿⣿⣿⣿⣿⣿⡷⠀⢹⡷⠉⠠⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀
⠦⢼⣿⣇⣾⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣯⢂⣾⣿⣰⣶⠀⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⠀⣸⣄⣀⣋⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣷⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⡺⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠉⠙⡛⠛⠇⣘⠻⢱⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⢀⣿⠃⠘⡻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⡉⠀⡀⣀⠭⢠⣶⠀⠘⠛⠤⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠
⢸⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠈⠉⠀⠀⠀⠀⢡⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡤
⢻⡿⠿⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠈⢽⣿⡿⡿⠋⠉⠉⠉⠛⠛⣿⣿⣿⣿⣟⠀⠀⠀⠀⠤⢤⣀⣀⡀
⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣈⣛⣛⣁⣀⡀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣯⠍⢒⣛⡚⠓
⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡟⠛⠛⠛⠛⠻⠿⠿⠟⠃⠀⠃⠀⡛⣻⣶⣾⣦⣤⣬⡭⢁⠒⠒⣶⣿⣿⣿⣿⣻⣿⣿⣿⡟⠀⢸⣿⠃⠀
⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣷⣶⣽⣖⣒⣲⠦⢤⣤⣿⣿⣶⠒⠒⠒⠛⢛⣿⣿⣿⣛⣻⣻⣿⣯⢾⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⣠⣬⣭⣄⠀
⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⣿⣾⣿⣯⣤⣤⣤⣄⣠⣿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣇
⣯⡉⠛⠻⠿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣶⣶⡖⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⢀⣽⣿⠛⠀⢚⠿⠿⠟⠋⠉
⣿⣷⡀⠀⠀⣿⣿⣧⣄⡀⠀⠀⠠⠤⣤⣀⣀⠀⠀⢰⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣯⣽⣗⣒⡶⢂⠀⢀⣄⣀⠀
⣿⣿⣷⠀⠀⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠈⠉⢙⠃⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣾⡟⠻⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣿⣿⣇⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠁⠊⢰⣶⣶⣿⠀
⣿⣿⣿⠀⠰⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⡀⠠⠁⢰⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣤⣉⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣳⡟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠀
⠿⣿⣿⣶⣾⣶⣽⣻⢿⡉⠙⠻⠿⠛⠿⠟⠕⠂⡈⣟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⡷⣬⣿⣿⣿⣿⣿⣿⣿⠗⡖⠀⠀⣠⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣶⣶⣦⠀⠀⠀
⡀⠀⠈⠉⠛⠛⠛⠛⠛⢰⣄⣀⠀⠀⠄⠀⠀⢰⢇⣿⣿⣿⣽⡫⣟⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣕⣶⣿⣿⣿⣿⣿⡿⠿⢟⣏⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⡿⡛⠀⠀⠀
⣿⣿⣶⣶⣤⣤⣄⣤⣄⣈⡛⠿⡇⣣⣶⣤⡀⡾⢸⣿⣿⣿⣿⣛⣺⠵⢝⣿⣿⣿⣿⡇⠀⠀⢀⣿⣯⣍⡉⠈⠉⠉⠩⠕⠚⠋⠉⠁⢿⡿⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣿⣿⣷⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢷⣾⡇⠲⠭⠙⢰⡇⣼⣿⣿⣿⢿⣿⣿⣿⣿⣯⠿⠿⠿⡇⠀⠀⢸⣿⠿⠟⠛⠂⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀
⠭⠿⡿⢿⣿⣿⣿⣿⣿⣶⣤⣭⣤⣤⣤⣤⣾⣤⣿⣿⣿⣿⣿⣿⣟⣫⠅⠈⠐⠒⠶⢦⣤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣠⠀⠘⢿⡇⠀⠀⠀⠀
⠀⠀⢀⣈⠁⡙⠛⠛⠛⠛⠉⠒⠶⢦⠄⠐⠛⠛⡟⠉⠵⠿⠿⠳⠛⠋⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣧⡀⠈⠀⣴⠀⠀⢠
⣾⣿⣿⣿⣿⣿⣷⣦⣤⡄⠀⠀⠀⠀⠀⢀⣤⣤⣁⡀⠀⠀⠀⠀⠰⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣷⡀⠈⠅⠀⠀⣼
⢋⣵⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⢸⣿⣿⣿⡿⠡⠄⠀⢂⠸⣟
⣿⣴⡛⡍⠛⠋⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠄⠄⠄⠰⠀⠀⠀⠀⠀⠁⡁
⠻⠿⠃⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠠⠰⠐⠀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠰⠀⠦⢹⡀⠀⠀⢄⣀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠂⠁⢈⣵⣶⠊⠀⢠⠀⠀
⠀⠀⠀⠀⠈⡇⠀⠈⣵⣶⣤⣀⣿⣶⡄⠀⣀⣞⠕⣖⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢶⠌⠙⠛⠋⢙⡵⠿⠀⠀⠀⠀⠀
⠀⢀⠀⠠⡅⣿⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠘⠿⢻⡮⢹⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠘⣮⣤⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠃⠂⠶⡇⣿⠀⠀⠛⠁⠀⠀⠀⠀⠀⢀⢠⣄⣤⠆⠈⠛⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⣷⣶⣦⣄⢀⣿⠀⠀⠰⢤⡀⠀⠀⠀⢠⣿⣿⢗⢣⠄⠀⠀⢘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠴⣾⣷⣶⡤⠀⡀⡤⠴⠄⠀⣬⠀⣒⡭
⣿⣿⣿⣏⣾⠇⠀⠀⠀⠀⠉⠂⠀⠀⢈⡋⠼⠗⠙⠂⠀⢀⣺⣼⣥⡇⣾⢿⣻⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⢀⡭⠕⠂⠉⠀⠀⠀⠀⠀⠀⠉⠚⠿
⣿⠿⢫⣾⠏⠀⠀⠐⠢⠀⠀⠀⠀⢀⠀⠠⣴⣦⣠⣤⣬⢸⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣴⡿⠋⠀⠴⣶⣤⣠⣤⣤⣤⣄⠀⠁⠀⢈⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣏⢾⡿⡻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠉⠀⠀⠁⠀⠉⠻⣿⣿⣿⣿⣿⣿⣦⣄⡀⠉⠻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣷⣷⣻⡞⣹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⣅⡀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣤⣠⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠉⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣷⣹⠿⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠳⢦⣤⡄⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⡌⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠂⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠉⠋⠳⢦⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣦⠰⣿⢰⣿⡆⢿⠟⠛⢿⣿⠟⠉⣠⣶⣿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠛⠛⠿⢷⣦⣤⣀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣁⣿⢦⣉⡁⢸⠀⣿⡆⢉⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠄⠀⠀⠀⠀⠈⠙⠻⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣠⣿⠧⡉⢡⣾⡿⠃⠀⣠⣄⠀⠀⠐⡀⠀⠑⠀⠀⠈⠀⢤⡀⠀⠀⢐⡠⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢡⣿⡟⠀⠠⣼⡿⠙⡇⠀⠈⠲⡄⡀⠀⠀⠀⢄⠀⠀⠀⠀⠤⣨⠤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⠇⣿⡟⠀⠀⣼⣿⡇⢀⠰⡀⠀⠀⠘⣦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠑
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⠙⠿⣿⣿⣿⢸⣿⠃⠀⢰⣿⣿⠇⠀⠑⠰⣀⠀⠀⠘⡄⢄⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠛⢸⣿⠀⠀⢸⣿⣿⢄⠀⠀⠀⠑⠫⡐⠠⠐⡀⠀⢨⣠⣤⣆⣠⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⢸⣿⠀⠀⢸⣿⡿⠀⠑⢤⣀⡀⢀⡈⠀⠀⠘⡐⠹⠙⠒⢦⡈⢿⢆⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⠁⠑⠄⠀⠀⠀⠠⠤⠤⠤⠇⣸⣿⣆⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⣶⣤⡀⠀⠀⠀⠀⠈⠂⠀⢀⣄⠀⠀⠀⠠⢀⠩⠁⠑⠠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⠀⠄⠸⣿⣿⣷⣦⣀⠈⠀⠐⠀⠙⠋⠀⠀⠀⠠⠄⡀⠒⢄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣧⠀⠀⠸⣿⣿⣿⣿⣾⣶⣄⡀⠀⠀⠅⠂⢤⡡⠀⠍⠙⠩⣌⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣧⠀⠀⠘⡿⣿⣿⣿⣿⣿⣶⣷⣀⠀⠠⡀⠀⠑⠤⠀⡀⠀⠓
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠊⢻⣧⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢀⠀⠈⢢⠙⠐⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣿⣄⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣧⣤⣵⣴⣤⡱⡈⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢻⣷⣄⠀⠀⠈⠻⢧⣿⠻⢽⣿⣿⣿⣿⣿⣿⣿⣟⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠿⣷⣤⡀⠁⠢⠈⠁⠣⠨⠩⢿⣯⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⢿⣷⣤⣀⠀⠀⠐⠄⠀⢉⡉⠉⠋⠁⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⠿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣉⠛⠛⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⡄⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠛⣿⣿⣷⣢⣼⣾⣿⣾⣖⣀⡀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢀⣀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠋⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣶⣶⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠰⣿⣿⣿⣿⣿⣷⣬⡝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣾⣧⣙⠛⢿⣿⣿⣿⣿⣿
⣦⣄⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣦⠀⠙⢿⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡟⡉⣻
⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣿⣿
⠉⢿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢽⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣝⡛⠿⣿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠷⡾⠷⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣷⠀⠀⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⡥⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠟⠛⠁⣿⣿⣿⣏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⡷⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⡾⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⢂⣿⣿⣿⣇⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣤⣼⣿⣟⣻⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⣷⠀⠀⠈⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⡿⠔⢀⣿⣿⣿⣿⣐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠷
⠀⣿⠀⠀⣾⣿⣿⣿⣿⢸⣿⣿⣿⠘⣿⣿⣿⣇⣸⣿⣿⣿⣗⡳⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠀⠁⠀
⢰⣿⠆⣺⣿⣿⡟⠛⠋⠈⠛⠛⠛⠀⠙⠛⠛⠋⠙⠛⠛⠛⢛⣋⣛⣛⠿⠿⠿⠛⠟⢛⣿⠛⡃⠙⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣏⡟⠿⣿⡿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⢸⣿⡀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣻⣿⣿⡿⢷⣾⣿⢷⣶⣮⣶⣤⣆⠛⡻⢿⣿⣿⣿⣿⣿⠀⢸⡧⠉⠃⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⢼⣿⣇⣼⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠒⣾⣿⢲⣰⠆⣶⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⢸⢀⣀⣟⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⢰⣿⡟⣾⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠
⣿⠰⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠉⠙⡛⠛⠗⣘⠛⢣⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣽
⣿⡀⠙⡻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⡉⠀⠀⢀⡨⢄⣴⠄⠘⠛⠣⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⡿
⣿⣅⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠈⠉⠁⠂⠀⠀⠁⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡤⠀
⡿⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⠿⠏⠉⠉⠉⠛⠛⢻⣿⣿⣿⣿⡀⠀⠀⠀⠠⢤⣀⣀⡁⠀
⣿⣆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⣀⣛⣛⣋⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠙⣛⡛⠙⠭
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⠛⠛⠛⠛⠛⠿⠿⠟⠋⠀⠃⠀⡟⣻⣶⣾⣦⣤⣬⣭⢉⡒⠒⣶⣿⣿⣿⣿⣟⣿⣿⣿⡿⠀⢸⣿⠃⠀⠀
⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⣿⣷⣶⣿⣶⣒⣲⡦⠤⣤⣿⣿⣷⡶⠒⠒⠛⠛⣿⣿⣿⣟⣻⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢠⣬⣭⣤⠀⠀
⣿⣿⣿⡅⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣠⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣧⠀
⡙⠛⠻⠿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣶⣶⣤⡔⠋⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⠀⠀⣭⣿⠋⠐⠚⠋⡭⢿⠿⠛⠂
⣷⡀⠀⠀⢸⣿⣷⣄⡀⠀⠀⠀⠤⣄⣀⡀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣷⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣟⣒⣲⠶⠎⠀⢀⣀⣀⠀
⣿⣷⠀⠀⣿⡿⠿⢿⣿⡞⠀⠀⠀⠀⠈⠉⠛⠊⣸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⣿⣿⣴⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠁⠊⢠⣶⣾⣯⠀
⣿⣿⠀⠀⢾⣿⣿⣿⣿⡆⠀⣀⣀⣀⡀⠀⠊⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣷⣀⣹⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⣿⣇⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠉⠉⠀
⣿⣿⣦⣼⣷⣭⣛⢿⡏⠛⠻⠿⠛⠿⠿⠥⠶⡨⣘⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣧⣽⣿⣿⣿⣿⣿⣿⡿⢗⡶⠀⠀⢠⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⠄⠀⠀⠀
⠀⠈⠙⠛⠛⠛⠛⠛⢲⣀⡀⠀⠀⠀⠁⠀⠃⡇⣿⣿⣿⣯⣾⢽⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣓⣬⣿⣿⣿⣿⣿⣿⣷⢿⣋⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⢻⠀⠀⠀⠀
⣿⣶⣦⣤⣤⣀⣀⣀⣈⡻⠿⣿⢇⣶⣤⡄⠸⢃⣿⣿⣿⣿⣟⣳⠯⡪⡻⣿⣿⣿⡿⠀⠀⠀⣾⣿⣍⣛⠉⠉⠉⠉⠛⠷⠒⠛⠉⠑⣿⡿⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⢫⣾⣯⠞⡭⠛⠃⡟⢰⣾⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⣠⠀⢀⣿⣿⡿⠿⠿⠂⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⣭⣥⣤⣠⣄⣸⣃⣸⣿⣿⣿⣿⣾⣿⣻⣫⠉⠉⠶⠶⠦⣤⣀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⠘⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠛⠾⠿⠟⠛⠫⠥⢤⣥⡍⢹⠾⠿⠟⠛⣽⣿⡿⠽⠾⠋⠤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⣧⡀⠀⢰⣶⠀⠀⢰
⣶⣿⣿⣿⣿⣶⣶⣤⣤⡄⠀⠀⠀⠬⠀⢀⣤⡘⠁⠀⠀⠀⠀⠀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⡷⠀⠈⠁⠀⠀⡾
⢛⣽⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⢠⣿⣿⣿⣇⠿⠄⠀⢢⠀⠀
⣾⡱⢟⡛⠉⠩⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠀⠀⡌⡍⠅⠤⠀⠐⠀⠀⠀⠡⡀
⢿⣟⠃⢳⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠠⠠⠠⠰⠀⠂⠀⠀⠀⠀⠀⠐
⠀⠠⢠⡌⣧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠆⠂⠂⠈⣠⣶⠎⠀⠀⠀⠀
⠀⠐⠐⠂⢸⡄⠀⢰⣮⣯⣁⠸⣷⣤⡀⠀⢈⡽⣲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⡄⠁⠒⠻⠟⠙⠻⣿⡀⠀⠀⠀⢠
⡀⢀⠀⣀⡀⡇⠀⠀⣿⣿⡿⠛⠉⠁⠀⠀⢼⣿⣶⣿⡫⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⣥⣠⡤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠻
⠨⠲⠤⣴⠇⣿⠀⠀⠟⠋⠀⠀⠀⠀⠀⠀⣠⣤⣭⣌⠀⠿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣴⣄⡀⢡⡿⠀⠀⢤⡀⠀⠀⠀⠀⢰⣾⣿⣯⣌⡀⠀⠀⠛⡿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣶⣶⣶⡤⠄⢀⡠⡤⠄⠀⢄⢒⣨⠄
⣿⣿⣿⡟⣼⠇⠀⠀⠀⠈⠓⠀⠀⠀⢹⣿⣿⣿⠿⠄⠀⢀⣴⣱⢣⡯⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢈⣩⡥⠖⠘⠉⠀⠀⠀⠀⠈⠙⠻⢯
⢿⣿⢛⣾⡟⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⢁⣼⣄⣄⡄⣀⢹⣿⣿⣿⣿⣯⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢉⣴⣿⠏⠀⣠⣄⠀⣀⣀⣀⣀⠀⠀⠈⠈⠝⣿⣿⣧⣼⢸⣿⣿⣿⣿⣿⡏⣽⣿⠿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠋⠁⠀⠠⠚⠻⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠚⢿⣟⣻⢸⣿⣿⣿⣿⣿⣿⣾⣯⣧⢿⡽⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⣀⣀⣲⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠈⠛⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠳⢦⣄⡀⡤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⣴⡌⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀⡀⠈⠈⠉⠛⠳⢦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⡡⣿⠠⣶⡌⢿⡿⠿⢿⣿⣿⠟⢁⣠⣶⣾⡿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⣶⣦⣄⡀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡛⠃⣽⢦⡙⡃⢸⠀⣶⣦⠙⢁⣴⣿⠟⠋⠀⠀⠀⠤⠀⠀⢐⢦⡄⠄⠀⠀⠀⠉⠙⠻⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⢁⣼⣧⣙⠋⣴⣿⠟⠁⢀⣀⠀⠀⠀⠐⡀⠑⠸⠀⠀⠁⢠⡀⠀⢀⣀⠠⡀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⣼⣿⠃⠀⢠⣾⠙⠿⡀⠀⠀⠰⡀⡀⠀⠀⠀⢨⠉⠁⠀⢀⣈⡒⡢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⠃⠀⢠⣿⣿⡢⠈⠰⠀⠀⠀⠱⡅⠀⠀⠀⢰⠀⠀⠀⠀⠈⠉⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠙⠻⢿⣿⣿⣿⡇⣿⡏⠀⠀⣿⣿⡇⠀⠈⠂⢥⡀⠀⠀⠨⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⠙⠿⢸⣿⠇⠀⢰⣿⣿⡇⡀⠀⠀⠀⠛⢅⠂⠄⢁⠀⢄⢀⣠⣤⡄⡀⠀⠠⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⢸⣿⠀⠀⠸⣿⣿⠀⠈⠰⡄⣀⠈⠀⠑⢄⢈⢖⠸⠛⡫⢤⡉⢻⣢⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇⠀⠀⠙⠛⠀⠀⠀⠀⠀⠉⠂⠆⠀⠑⠈⠄⣀⣀⠀⢹⠀⣣⣧⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣇⠀⠀⢢⣄⡀⠠⠀⠀⠀⠀⠒⠀⠀⣀⠀⠀⠀⠀⡀⠘⡛⠉⢕⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⡀⢀⠘⢿⣿⣶⣤⡀⠈⠀⠀⠀⠘⠛⠁⠀⠀⠠⣀⠑⠴⡀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣷⠀⠀⠘⣿⣿⣿⣿⣷⣦⣄⡀⠀⠐⠐⠠⢀⠒⠒⠓⠲⢚⠔⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣧⡀⠀⠘⢿⣿⣿⣿⣿⣿⣶⣧⣄⡀⠢⠈⠁⠃⠌⠀⠀⠉⢢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⢻⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣔⠀⠀⠀⠄⠓⠤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠙⣿⣄⠀⠀⠈⢿⡿⣿⣿⣿⣿⣿⣿⣿⣈⣢⣤⣌⣆⢁⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⢻⣷⣄⠀⠀⠀⠻⢻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⢿⣷⣄⡀⠀⠠⡉⠸⠅⣻⡏⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣻⣿⣶⣄⡀⠀⠀⠀⠄⠀⠃⠛⠁⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣻⢿⣷⣶⣤⣄⣀⡀⠈⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣍⡛⠻⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣦⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⣿⣿⣿⣿⣿⣿⣷⣆⣀⡀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣀⣄⡀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠟⠁⠀⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⣾⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣭⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣶⣼⡿⠻⣿⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣷⣓⣘⣿⡿⣿⣿⣿
⣿⣷⣄⡀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⢧⣤⣽⣿
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣿⣿⡟
⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⡀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⡻⠿⣿⠛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⡶⠿⠷⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣷⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⣆⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⡟⢻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡷⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣧⣾⣿⣿⣿⡟⠛⠁⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣯⠀⢠⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣾⣤⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⣤⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣄⣸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⠀⠀⢀⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡷⠀⠀⣿⣿⣿⣿⡂⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢇
⣿⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⠘⣿⣿⣿⣇⣸⣿⣿⣿⣗⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠃⠀⠀⢠
⣿⠀⢺⣿⣿⡟⠛⠛⠋⠈⠛⠛⠛⠀⠙⠛⠛⠋⠙⠛⠛⢻⣅⣙⣛⣛⠛⠟⢛⠛⠛⣻⡛⠛⠓⠘⢛⠛⠛⠿⢿⣿⣿⣿⣿⡿⠟⠛⢿⣿⡟⠺⢿⡿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⣼
⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣻⣿⣿⡿⢿⣿⣿⣿⣿⣾⣤⣆⠛⡛⢿⣿⣿⣿⣿⣿⠀⢈⣷⠁⠃⠞⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢩
⢿⣴⣾⠿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠘⣼⣟⢳⢰⡆⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣨
⢄⣀⣋⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⣿⡿⣼⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣿
⠰⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠌⠙⣛⠛⠳⢘⠻⡃⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣯
⡀⠘⣺⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣩⠤⢀⡀⣠⢡⣴⠦⠁⠛⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡿⢿
⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠉⠁⠐⠀⠀⠀⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀
⠿⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠟⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣁⠀⠀⠀⠠⠤⣄⣀⡁⠀⠀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣀⣛⣛⡋⣀⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⣚⣛⠛⠯⠤
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣶⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠛⠛⠛⠛⠛⠿⠿⠿⠋⠀⠃⠀⣘⢻⣷⣶⣧⣤⣤⣭⢍⡑⠒⣲⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⢀⣿⡏⠀⠀⠀
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⢿⣷⣶⣯⣶⣒⣲⡦⠤⣤⣾⣿⣿⣶⠒⠒⠛⠛⣿⣿⣿⣯⣛⣛⣿⣿⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣬⣭⣥⠀⠀⠀
⣿⣿⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣧⡀⠀
⠛⠻⠿⢾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣴⣶⣦⣤⠔⠉⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⡀⣭⣽⠋⠁⠒⠛⠭⣽⣿⠿⠖⠂
⡀⠀⠀⢸⣿⣷⣤⡀⠀⠀⠀⠤⣄⣀⣀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣟⣿⣿⣿⣷⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣽⣿⣒⣲⡶⠤⠜⡀⠀⣀⣄⠀
⣿⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠉⠙⠋⠸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠿⢿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⢠⣿⣰⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠃⠊⢀⣾⣭⣽⠀
⣿⠀⠀⣵⣶⣿⣿⣶⡖⠀⣀⣀⣀⡀⠀⠊⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣼⣿⣿⣿⣆⣈⣻⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣏⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠉⠉⠛⠀
⣿⣦⣼⣿⣮⣛⠿⡏⠛⠻⠿⠟⠿⠿⠡⠶⠨⢸⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⢗⢦⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣴⡄⠀⠀⠀⠀
⠈⠉⠛⠛⠛⠛⠛⢲⣀⡀⠀⠀⡠⠁⠀⠂⡟⣿⣿⣿⣿⣕⡯⣿⢿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣢⣽⣿⣿⣿⣿⣿⣿⣿⢾⣃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⢻⠁⠀⠀⠀⠀
⣶⣦⣤⣄⣀⣀⣀⣘⣹⠿⣿⣿⣰⣦⡄⢸⠇⣿⣿⣿⣿⣟⣻⠮⣗⢝⢿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣛⡛⠉⠉⠋⠙⣻⠴⠖⠛⠛⠐⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⢫⣶⣯⠶⠩⠛⠃⡾⢰⣾⣿⣟⡿⣿⣿⣿⣿⣷⣽⣻⣿⡟⠀⠀⠀⣿⣿⣿⣿⠿⠷⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠐⠇⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣭⣿⣿⣧⣤⢭⣥⣤⣄⣤⣰⣇⣸⣿⣿⣿⣿⣷⣿⣿⢟⣫⠉⠑⠶⠦⣤⣀⡐⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⠻⠀⠀⠀⠀⠀⠀
⠈⠉⠀⠋⠛⠿⠿⠿⠿⠛⠯⣭⣭⣈⠉⠿⠿⣿⠟⢛⣽⣿⡿⡽⠿⠃⡄⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣦⠀⠐⣶⡴⠀⠀⠈
⢀⣠⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠉⣉⢀⢀⣀⠐⠁⠀⠀⠀⠀⢀⠔⠐⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠀⠀⣸⣿⣿⢀⡀⠈⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠃⠀⢠⣿⣿⡇⣸⡷⠄⠀⢂⠀⠀
⢡⡾⣿⣿⡿⠿⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⡈⡉⡉⠡⠀⠀⠀⠀⠀⠡⠀
⣿⠸⠋⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⢠⢠⠠⠠⠄⠂⠀⠀⠀⠀⠀⠐
⠉⡅⣠⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠄⠄⠆⠐⣠⣤⠖⠀⠀⠀⠀
⠀⠀⠀⠀⣷⠀⠀⢫⣬⣃⠀⢰⣦⣄⠀⠀⠨⢶⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠐⢲⢖⠒⠛⢳⣯⣀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⡄⠀⢸⣿⣿⡿⠚⠋⠉⠀⠈⣿⣷⣮⢺⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⣄⣀⣤⡤⠖⠚⠃⠀⠀⠀⠀⠠⠀
⡢⢆⣑⣾⢸⡇⠀⢸⠟⠉⠀⠀⠀⠀⠀⢀⣌⣉⣋⠀⠿⢿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠒⠉⠉⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀
⣌⣄⡀⠋⢸⡇⠀⠀⣀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣴⣶⣤⣄⠄⢀⣠⣵⠀⢀⣰⣂⠤⠀
⣿⣿⣿⢇⣿⠁⠀⠀⠈⠑⠠⠀⠀⠈⢿⢿⣿⡿⣿⡀⠀⠀⣯⣻⢿⢻⡿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠉⣛⣩⠤⠆⠁⠁⠀⠀⠀⠑⠻⠿⣀
⣿⣿⢫⣾⠏⠀⠀⢄⠀⠀⠀⠄⠀⠀⠉⢉⣫⡁⢀⡄⡄⣿⣿⣿⣿⣿⣥⣇⣧⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢋⣵⣿⠋⠀⣀⣀⠀⣈⣀⠀⠀⠀⠁⠀⠙⢿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⡟⣿⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠛⠁⠀⡐⠞⢻⣿⣿⣿⣿⣿⣷⣤⣀⠀⠘⠿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣷⣿⣣⡟⡏⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣊⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⢰⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠈⠑⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣀⡀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣁⣤⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠂⠀⠛⠻⢶⣄⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⢡⣿⢠⣦⡈⣿⣿⠿⣿⣿⣿⠿⠋⣁⣤⣶⣾⡿⠿⠿⠟⠛⠻⠿⠿⢿⣶⣦⣤⣀⠐⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠿⠂⣿⣌⠻⠃⢸⠁⣶⣌⠻⢁⣤⣾⡿⠛⠉⠀⠀⠀⠀⠀⠠⢤⡀⢀⡀⠀⠈⠙⠻⢿⣶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣌⠛⠃⣼⣆⠛⠟⣠⣿⡿⠋⠀⡀⠀⠀⠀⠀⢁⠂⠄⠀⠉⠀⣀⠀⠀⠐⠀⢀⡈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠋⣰⣿⠏⠀⢀⣾⠻⢶⢀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠰⠀⣈⠑⡊⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⠇⠀⢀⣿⡿⢑⢄⠀⡄⠀⠀⠈⢄⠀⠀⠀⠀⡄⠀⠀⠀⠉⠓⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠉⠛⠿⣿⣿⣿⣿⡇⣿⡟⠀⠀⣾⣿⡇⠀⠀⠑⢔⣀⠀⠀⠈⡀⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠙⠻⢿⢰⣿⡇⠀⠠⣿⣿⠗⢄⠀⠀⠀⠱⢅⠂⢀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠱⢄⣀⠀⢀⠑⢄⠈⢂⠴⡿⠫⣉⡙⢿⣖⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⡆⠀⠈⠛⠟⠀⠀⠀⠀⠀⠁⠒⠄⠄⠑⠀⠄⠀⠈⠈⢫⠀⢧⣦⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡇⠀⠀⢤⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠲⠗⠫⠭⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡀⠀⠘⣿⣷⣦⣄⠀⠈⠀⠀⠀⠀⠿⠂⠀⠀⢀⠑⠤⡠⠁⠈⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣧⠈⠀⠙⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⢀⠀⠤⠥⠦⢈⢱⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣧⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢄⠈⠂⢄⡁⠀⠁⠠⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠊⢿⣧⠀⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣷⣤⡂⡀⠀⠈⠐⠄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠻⣷⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠑⣀⣀⣡⡀⠈⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⢿⣦⡀⠀⠀⠙⢟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡙⢿⣦⣀⠀⠀⢌⡑⠗⢹⡟⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠠⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣷⣤⣀⠀⠀⠀⠈⣀⠂⠙⠟⠻⠟⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠐⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡿⣿⣶⣤⣀⣀⠀⠀⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣛⠻⠿⣿⣿⣿⣶⣶⣶⣿
⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠉⠀⠀
⣿⣿⣿⣿⣤⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⣿⣿⣿⣿⣿⣷⣦⣤⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣟⢛⣡⣤⣤⡀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⡿⠉⠀⣼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣼⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⡙⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣷⣿⣿⡿⠛
⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡟⠀⠀
⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣛⣭⣟⢿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⡀⠀⠀⠀⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣷⡏⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣻⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⢰⣿⡿⠃⢽⣿⣛⣇⠀⣯⠆⣠⣶⠀⠀⠀⣄⡀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠉⠉⠩⠛⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛
⣿⡧⠀⠀⣼⣿⣧⠀⠀⠈⠙⠿⢰⣿⣰⡿⡣⠀⢀⣼⡿⣾⣁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠩⣋⣰⣤⣤⣤⣄⡈⠀⠠⢝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠈
⠿⠿⢧⣾⣿⡏⠐⠁⠀⠀⠀⠀⠸⠛⠿⠕⠁⢠⣾⣿⡄⠀⠉⠻⢆⠤⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠃⠙⣿⡟⣿⣿⣿⣿⣷⣶⡄⠈⠑⠺⢝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⠀⠀⣤
⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠓⠃⠀⠀⠀⠉⢒⡬⢘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢔⠻⣸⣿
⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣤⣤⣭⣛⣿⣿⣾⣷⠮⠭⠏⠘⠻⠾⢽⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣬⠿⣿⣙⣻⣿⣿⡏⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⠐⠒⠐⣿⣿
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣬⣭⣭⣛⣒⣁⣔⠀⢰⣦⠀⠀⡁⠂⢀⠉⣙⠿⢿⣿⣿⣿⣿⡿⠉⣛⢷⣽⢙⡻⠿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢠⣿⡿
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⣿⣿⣾⣷⣾⣜⡩⠛⣿⣿⣿⣿⣿⡇⠀⣽⡎⠘⠘⠛⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣭⣭
⢼⡛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠄⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣟⣇⣿⢰⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡦⣤
⣯⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠉⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⡇⣿⣿⣷⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⣧⣄
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠹⣉⡛⠋⠉⠹⢸⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣿⡏⣹
⠭⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⡤⠀⠶⢶⣾⣯⠈⠉⠙⠖⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⠿⠣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠊⠁⠀⠒⠀⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⠄⠀⢤⣴
⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠇⠀⠉⠉⠉⠻⣿⣿⣿⣿⣇⣀⡀⠒⠒⠠⢶⣤⣂⣀⣀⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⡈⠋⣿⠧⢀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⠉⢩⣴⡚⠛⠺⠿⠿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⠉⠙⠛⠛⠛⠻⠿⠟⠁⠈⠁⢀⣋⣿⣿⣾⣶⣆⣶⣯⣉⡉⢛⣿⣿⣿⣿⣿⣿⣿⡿⢿⠇⠀⣾⣿⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⣿⣾⣯⣽⣿⣓⣶⡤⢼⣿⣿⣿⡿⠂⠚⠛⢻⣿⣿⣿⣭⣻⣽⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤⣬⣥⣄⠀⠀⠀⠀
⣿⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⢻⠿⢿⣿⣿⣿⣷⣤⣤⣤⣼⣿⣿⢿⣿⣿⣯⣿⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⠃⢰⣿⣿⣿⣿⣄⠀⠀⠀
⠻⢿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣶⣶⣤⠔⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⣀⠄⢠⣿⡿⠉⠀⠚⠛⠤⢽⣯⡷⠶⠒⠀
⠀⢸⣿⣿⣷⣄⡀⠀⠀⠠⠤⣤⣀⣀⡀⡀⣼⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣽⣗⣲⡶⠶⡤⢁⠀⢀⣤⠀⠀
⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠉⡙⢀⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⣧⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠟⠐⠃⣰⣿⣿⡇⠀
⠀⣾⢵⣾⣿⣿⣿⣀⣀⣀⣀⣀⣀⠔⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣧⣈⣹⣿⣿⣿⣿⡏⠀⠀⠀⠀⢰⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠉⠉⠙⠃⠀
⣶⣿⣷⣮⣟⠿⠉⠛⠻⠟⠛⢛⠏⠞⠂⢂⣽⣻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⡿⢗⣢⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⠀⠀⠀⠀⠀⠀
⠙⠛⠛⠛⠛⠛⣦⣀⣀⠀⠠⠂⠀⠀⣸⢹⣿⣿⣿⣾⣵⣫⣟⢿⣿⣿⣿⣿⡿⠀⠀⠀⣾⣿⣿⣳⣽⣿⣿⣿⣿⣿⣿⣷⢿⣋⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡎⠀⠀⠀⠀⠀⠀
⣦⣤⣤⣤⣤⣄⣙⡻⢿⡿⣱⢰⣦⢄⡻⢸⣿⣿⣿⣿⣟⣛⠷⣝⢿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣟⡛⠋⠉⠛⠛⢻⠦⠖⠛⠛⠓⢿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠛⣵⣿⠝⢺⠈⠙⢸⠃⣿⣿⣿⣟⡿⣿⣿⣿⣿⣷⣕⣿⣿⠃⡀⠀⢸⣿⣿⣿⣿⡿⠷⠄⠤⠈⠀⠀⠀⠀⠀⠀⠈⠃⠀⠚⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡟⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣽⣿⣿⣤⣬⣥⣶⣦⣄⣄⣿⣀⣿⣿⣿⣿⣿⣷⣿⣟⢟⣫⠉⠙⠶⠶⣤⣄⡘⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡀⠸⠄⠀⠀⠀⠀⠀⠀
⠙⠈⠋⠛⠿⠿⠿⠿⢛⣯⣭⣭⣉⠉⠽⠿⢿⠟⢛⣽⣿⡿⡭⠿⠛⡄⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⡿⠀⠈⢢⢔⠃⠀⠀⠄
⠀⠐⠠⠀⡠⡀⠀⠀⠀⠀⠀⠉⠉⠑⢀⣀⡘⠃⠀⠀⠀⠀⠀⡔⠐⠘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠇⠀⢀⣿⡇⣾⣆⠀⠳⠀⠀⠀⠀
⣶⣶⣿⣶⣮⣄⣠⣦⣤⣦⣤⣦⣴⣴⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⠀⠀⣼⣿⢰⣿⣿⣦⠀⠐⡀⠀⠀
⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠁⠀⢀⢉⢉⠉⡅⠀⠀⠀⠀⠈⢄⣖
⠟⡾⠿⠿⠿⠟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⡈⡄⡄⠤⠠⠀⠀⠀⠀⠀⠈⠂
⡍⣡⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠠⠠⠰⠀⣒⣤⡴⠀⠀⢀⠀⠀
⠀⠈⠀⣷⠀⠀⢩⣶⣂⠀⢠⣤⣀⠀⠀⠠⣄⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⠲⣶⡓⠒⢟⣯⣃⡀⠀⡬⠀⢀
⠀⠀⠐⢸⡄⠀⢸⣿⣿⣿⠞⠛⠉⠁⠀⣿⣷⣯⣾⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⣀⣀⣀⣥⡴⠖⠛⠀⠀⠀⢨⡟⠀⣼
⢀⣠⣽⢸⡇⠀⢸⠿⠋⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠋⢿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠐⠋⠉⠉⠀⠀⠠⢤⡄⠀⠀⣖⠀⠀⠛
⣁⡪⡙⢸⡇⠀⢀⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⣮⣿⡆⠀⢠⣓⡀⠀⠀
⣿⣿⠆⣾⠃⠀⠀⠉⠓⠤⠀⠀⢸⣿⣿⣿⣿⣿⡁⠀⠀⣥⣳⢯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢰⠇⠀⠀⠀⠉⢛⣋⡥⠴⠚⠉⠀⠀⠀⠈⠚⠧⣄⡀
⣿⢟⣼⡟⠀⠀⣀⠀⠀⠀⠄⠀⠐⠻⣿⣿⣿⣹⡄⠀⣾⣿⣿⣿⣿⣿⣿⣾⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣵⣿⠟⠀⣀⣀⡀⠉⠂⠀⠀⠀⠈⠔⡿⣿⣿⣿⣧⣩⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠁⠠⣾⠿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠈⠘⠿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣖⢿⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣥⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠓⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⡀⢀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠋⢛⠷⣦⣠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⣸⡇⣤⣌⢻⣿⣿⣿⣿⣿⣿⠟⠋⣀⣤⣶⣾⣿⠿⠿⠿⠿⠿⠿⢿⣶⣦⣤⣀⠁⠀⠙⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⠇⢸⣇⠹⠿⠀⡏⢠⣤⠙⠟⢁⣴⣾⡿⠛⠉⠀⢀⠀⠀⠀⢤⣀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣏⠻⠞⢠⣧⡘⠿⠃⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠒⡄⠀⠈⠒⢀⣈⠀⠀⠀⠀⡀⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⡙⢃⣾⡿⠃⠀⣠⡾⣷⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠂⠢⣘⠁⢒⠡⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⠁⠀⢰⣿⡇⠈⠢⡀⠆⠀⠀⠀⢃⡄⠀⠀⠀⠀⠀⠀⠈⠙⠲⠵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠿⣿⣿⣿⣿⣿⢰⣿⠇⠀⢀⣿⣿⡀⠀⠀⠈⠨⣆⠀⠀⠀⡆⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠉⠛⢿⡟⣸⣿⠀⠀⢸⣿⣿⠈⢄⠀⠀⠀⠐⢅⠂⢀⠰⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣿⣿⠀⠀⣾⣿⡇⠈⠀⠑⠦⣀⠀⠀⢑⡀⠀⠢⠶⢿⢋⣙⠳⣷⡄⠠⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⠀⠀⠚⠿⠃⠀⠀⠀⠀⠀⡈⠒⠄⢀⠢⡈⡀⠀⠀⠙⠧⠸⣼⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡀⠀⠠⣀⠂⠀⠠⠤⢀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠂⠀⠵⠞⡛⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣇⠀⠀⢻⣿⣶⣄⡀⠀⠀⠀⠀⠄⢰⡷⠀⠀⠀⠁⠠⡠⡄⠂⠪⡉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⡄⠁⠀⢿⣿⣿⣿⣷⣦⣄⡀⠠⠈⠀⢄⠠⠄⠙⣀⡈⠐⢄⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣄⡀⢂⠈⠒⢄⠐⠀⠑⠥⠁⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠽⣿⣄⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⢉⠂⢐⠂⠈⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⠘⢿⣦⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣤⣧⡐⠑⠢⡱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠸⠿⡯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⣷⣄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠐⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠻⣷⣄⡀⠀⠀⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣋⠻⢿⡌⢉⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣿⣦⣄⡈⠁⠀⠈⠁⡃⠛⠇⠿⢿⢿⡿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣘⠛⠁⢀⣭⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣻⢿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡁⠈⠡⢮⠈⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⡛⠿⢿⣿⣷⣶⣶⣶⣶⣿
⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠠⠀⡝⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠉⠉⠉⠀
⣿⣿⣷⣌⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠈⠑⠂⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀
⣿⣿⣿⣿⣷⣶⣦⡊⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⣈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠋⠀⠉⠻⣿
⣷⣄⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠃⠀⠀⠀⢀⣾
⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠙⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⢲⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⢀⣿⣿⡿⣿⣿⣾⡇⠀⣀⠀⠀⡀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀⣬⣀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿
⡆⠀⠀⢸⣿⡏⠁⠺⢿⣭⣇⢠⣷⠁⣴⡿⠀⠀⢀⣶⢤⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠉⢙⡻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⡆⠀⢠⣾⣿⠷⡀⠀⠀⠈⠙⢸⣿⣾⣟⡔⠀⢠⣿⠛⠿⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡘⣥⣼⣶⣶⣶⣦⣄⡀⠐⠪⢝⡺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠀⠀⠀
⠛⢻⣿⡿⠅⠀⠀⠀⠀⠀⠀⠘⠉⠋⠊⠀⠰⣿⢿⡆⡀⠀⠙⠣⣒⠤⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢑⠈⣿⡏⣿⣿⣿⣿⣷⣿⣆⠀⠈⠑⠪⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢲⣒⠀⣶⣶
⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⢀⢀⣈⢩⣖⣨⢙⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣛⢁⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠶⠛⣼⣿⡟
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠶⡖⢭⣿⣿⣿⢿⡓⠒⠂⠈⠙⠛⢲⡙⠛⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣛⡿⣬⣟⣿⣿⡏⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠉⠀⠀⣿⣿⠃
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣭⣭⣤⣮⣀⣾⣷⣀⣀⢄⡁⠠⢀⣉⣛⣻⣿⣿⣿⣿⡛⠀⣭⢻⢾⠉⡝⠛⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢰⣿⣟⣆
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⣔⣉⣿⣿⣿⣿⣿⡇⡀⣾⣇⣈⣈⠉⣀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡶⠶⢷
⢩⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠂⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⡿⣧⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⡷⠶⢀
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⣿⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠻⠿⣿⣿⣿⡇⢽⣿⣷⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⣷⣧⡼
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠘⠤⠉⣁⠀⢘⣸⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢠⣿⡇⣽⢳
⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣆⣀⡭⠻⠿⣶⡂⠀⠈⠋⢙⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⠛⠧⠟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢢⣴⣿
⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢀⣻⣿⡿⠛⠁⠀⠀⠀⠉⢛⣿⣿⣿⣿⣧⣤⣀⣁⣀⣐⡷⢠⡥⣤⣀⣀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⡀⠀⣤⣤⡡⢿⠀⠤⠄⣀⣀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣭⠍⠉⠚⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣀⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢳⣯⢁⠈⠉⠉⠉⠛⣛⣋⣀⡀⠀⢠⣍⣿⣿⣿⣿⣶⣶⣶⣤⣌⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠻⠿⠿⣷⣾⣯⣽⣟⣒⣾⣿⣿⣿⡟⠋⠉⠉⢹⣿⣿⣿⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣶⣶⣶⣆⠀⠀⠀⠀⠀
⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠉⠉⢛⡛⠿⠿⢿⣿⣶⣶⣶⣶⣾⣿⣿⣻⣿⣿⣶⣿⣿⣿⡟⠉⠉⠙⢻⣿⣿⣿⠃⢰⣿⣿⣿⣿⡦⠀⢀⠀⣠
⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢰⣿⣿⣷⣶⡶⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣂⣰⣶⡿⠁⠈⠉⠓⠒⠛⡧⣴⠾⠗⠂⠻
⢸⣿⣿⣷⣦⣀⠀⠀⠐⠲⠦⢤⣤⣀⡀⣾⣿⣿⣿⣿⣛⡿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣻⣿⣿⣿⣿⣶⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣯⣭⣿⣛⣲⡶⠖⡀⠀⣠⣦⠀⠀
⢸⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠜⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠠⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠃⠚⢁⣾⣿⣿⠀⠀
⣿⣗⢿⣿⣿⣿⣤⣤⣤⣤⣤⣄⢊⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⣄⣉⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀
⣿⣿⣷⣯⣛⠄⠉⠙⠛⠙⢻⠓⢛⠣⢁⣚⣙⣛⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⠿⣲⡆⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠉⠉⠉⠉⠉⣷⣤⣄⣀⡰⠁⠀⠀⣸⢸⣿⣿⣿⣿⣾⣵⡯⣿⢿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣟⣪⣿⣿⣿⣿⣿⣿⣿⠾⣛⣁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⣤⣤⣭⡝⣻⣟⢽⣇⣶⢀⡝⣸⣿⣿⣿⣿⣭⣝⣛⣾⣷⣝⣿⣿⡇⠀⠀⢀⣿⣿⣿⣯⣛⡛⠉⠙⠉⢛⡻⠖⠚⠋⠉⠺⣿⠟⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣟⠉⢾⣿⠞⠓⠂⠉⣸⠃⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣫⡿⠁⠄⠀⢸⣿⣿⣿⣿⣿⠿⠷⠠⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠃⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠠⡀⠀⠀⠀⠄⠀⠀⠠
⣿⣿⣿⣿⣿⣶⣦⣴⣶⣶⣶⡠⣿⣀⣻⣿⣿⣿⣿⣿⣿⣿⣟⣫⡅⠉⠱⠶⠶⢤⣌⡙⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⠀⠑⡀⠀⢸⠁⠀⠀⠀
⠉⠙⠉⠛⠿⠿⠛⠛⠯⠵⣬⣅⣌⠙⡿⠿⠿⠛⣫⣿⣿⠿⠶⠛⢡⠄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⢠⡀⠈⢎⢽⠀⠀⠀⠀
⠀⠀⢤⢤⡂⠀⠀⠀⠀⠀⠀⠈⠁⡀⣠⣀⡋⠀⠀⠀⠀⠁⢠⠊⠀⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠁⠀⢰⡇⣾⣷⡄⠀⢣⠀⠀⠀⢬
⣤⣴⣦⣤⣀⢀⣶⣶⣶⣶⣶⣦⣶⣿⣿⣿⣿⠟⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⢀⣿⢸⣿⣿⣿⠄⠀⠡⡀⡜⠊
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠀⠀⡈⡉⡀⡄⠠⠄⠀⠀⠀⠰⡄⠀
⢟⣽⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⢀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀
⢨⡄⢧⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠀⠄⠂⠒⣠⡴⠆⠀⠀⡐⠀⠀
⠀⠄⢸⡄⠀⠘⣬⣽⣀⠀⣀⣀⣀⠀⠀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⡄⡴⡽⠖⠛⢳⣥⣀⠀⢘⠆⢠⣦
⠀⣀⠂⣇⠀⠀⣿⣿⣿⠗⠋⠉⠁⠀⠹⣿⣶⣽⣻⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⢤⣈⣤⡴⠖⠛⠋⠀⠀⠀⡞⠀⣼⣿
⢢⣢⡇⣿⠀⠀⠿⠋⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⡟⠸⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠀⠀⠀⠐⠊⠉⠀⠀⢀⡠⠄⠀⠀⢀⠀⠀⠉⠛
⣢⠈⠃⣿⠀⠀⢀⡀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣁⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⠀⢲⣿⣿⠀⠀⣬⡀⠀⠀⠀
⣿⡿⢸⡏⠀⠀⠈⠙⠳⠤⠀⠀⣿⣿⣿⣿⣿⣇⠀⠈⢠⣞⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠜⠀⠀⠀⠀⠉⣙⣩⠴⠖⠃⠈⠀⠀⠀⠉⠓⠦⣄⡀
⡿⣡⣿⠁⠀⠠⣀⠀⠀⠠⠀⠀⠙⣻⣟⣿⣎⣥⢀⢸⣿⣿⣿⣿⣮⣷⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣾⡿⠁⢀⣀⣀⣀⣁⡀⠀⠀⠈⠂⢊⢽⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠴⡿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠉⠻⢿⣿⡛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣳⡾⡏⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣈⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠐⣦⣤⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠉⠚⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣃⣬⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡤⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠛⠻⢶⣤⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⢁⣿⢁⣤⡌⢿⣿⢿⣿⣿⣿⡿⠟⢁⣠⣴⣶⣿⡿⠿⠿⠿⠿⠿⠿⢿⣶⣶⣤⣀⠀⠀⠉⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠿⠂⣿⣄⠻⠇⢸⠁⣴⣌⠻⠋⣠⣶⣿⠟⠋⠁⠀⠀⡀⠀⠀⢄⣀⠀⠀⠀⠈⠉⠛⠿⣶⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣌⠻⠃⣼⣆⠛⠟⢀⣾⡿⠋⠁⠀⠀⠀⠁⠀⠀⠒⠆⠀⠉⠂⢀⡀⠁⠀⠀⠀⡀⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠛⢠⣿⡟⠁⠀⣴⠿⢶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠄⣨⠁⢂⠥⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⡟⠀⠀⣾⣿⠈⠀⠑⠀⢠⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠉⠑⠺⢕
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠉⠛⢿⣿⣿⣿⣿⡟⣼⣿⠀⠀⣸⣿⣟⠀⠀⠀⠈⠲⡆⠀⠀⠀⠖⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠻⢿⡇⣿⡏⠀⠀⣿⣿⡇⠀⠢⡀⠀⠀⠈⠢⠀⢀⠰⠀⠀⢀⣈⡀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣿⡇⠀⠀⣿⣿⠁⠀⠈⠐⠖⢄⡠⠄⠑⣀⣈⠢⠾⢿⢉⡙⠺⣦⡁⡀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⡛⠿⠄⡀⠀⠀⠀⠀⡈⠐⠤⢌⠢⠈⠀⠀⠒⠻⡏⠵⣵⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣷⠀⠀⢠⣈⠀⠀⠑⠂⠄⠔⠈⢂⠀⠀⠀⠀⠁⠁⠂⠤⢕⡟⠉⠁⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⡄⢀⠈⢿⣿⣶⣄⡀⠀⠀⠀⠂⠄⢾⡳⠀⠀⠀⠐⢄⢠⠄⠙⢅⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣷⡈⠀⠘⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠠⠌⢁⡀⠀⢂⡈⠁⠑
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣧⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠁⠣⡀⠂⠈⠋⠈⠒⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⢻⣷⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠘⡐⢄⡐⠈⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠹⣿⣄⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣴⣄⣈⠢⣘⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⠉⠭⢭⢟⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢿⣷⣄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⢙⣿⣻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⢿⣷⣄⠀⠀⠨⡑⠻⣓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣻⢞⢦⢶⠍⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡻⣿⣦⣄⠈⠁⠀⠈⠁⡛⠓⠻⢽⢿⡿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣖⠒⠓⠌⠞⡩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡻⣿⣶⣤⣄⣀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠈⠐⠀⠆⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣝⡛⠿⢿⣿⣿⣶⣶⣶⣿⣿
⣎⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠄⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠈⠁⠀⠠
⣿⣿⣦⣈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠁⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀
⣿⣿⣿⣿⣿⣶⣄⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⣤⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡿⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⠁⠀⠀⠀⣸⣿⣿
⣦⣄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⠻⣿⣿⣿⣿⣿⣿⣅⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣅⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠈⠙⠿⣿⣿⣿⣿⣷⣤⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⢰⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢍⣙⠯⣿⣿⣿⣿⣿⣿⣿⣏⣭⣭⣽⣭⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣾⣿⣿⣹⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⡿⢙⣿⡿⢿⠀⢠⣢⠀⢠⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠚⠒⠒⠠⠿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⣩
⠀⠀⢀⣾⣿⡀⠀⠉⠛⠿⡆⢸⡏⣴⡿⠁⠀⢀⣼⣯⡖⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⠟⠷⠦⣀⣀⣀⡀⠀⠂⠉⠙⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠒⠒⠓
⣤⣠⣾⡿⠃⠐⠀⠀⠀⠀⠀⡿⢿⡟⠔⠁⢠⣾⣏⠉⠉⠲⢆⢀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⡿⠦⡈⢆⣯⡿⢿⣿⣷⣦⢤⣀⠀⠀⠍⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⠀⠀⠀⠀
⠀⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠻⠐⠀⠀⠀⠑⠪⢀⡂⠼⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣤⣀⣼⣿⠛⢸⣿⣿⡿⣾⣿⣾⠀⠀⠀⣁⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢙⡠⢠⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢐⡲⠶⣤⣤⣤⣤⣓⣒⠡⠶⣨⣝⡻⢿⡏⠀⣿⣿⣿⣿⣿⣯⣿⣿⣘⣀⣿⡟⢿⡷⣿⣿⡿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠉⠁⠀⣼⣿⢏
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢻⣉⣛⡛⠻⠯⠕⠀⠀⠀⣀⠀⠀⠉⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⡗⠳⢯⣝⣳⠾⣯⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣿⡿⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⣿⣿⡿⠿⣶⣶⣿⣷⣶⣦⣴⣄⠄⠐⠶⢶⣿⣿⣿⣿⣷⠀⠐⣦⠏⠁⣰⠈⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⠿⢧⠧
⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⡀⣰⡿⡆⢤⡄⢠⣤⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻
⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣂⢠⣸⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣴⠏⠂⢰
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⡉⠙⠟⠻⠿⠀⠀⠙⣸⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⡿⠿⢶⢋
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⠀⠀⠉⠀⠀⢨⠄⠂⠿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⡿⢀⡏⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠀⠀⠐⠀⠀⠀⠀⠐⢸⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⢠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢀⣾⣿⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠟⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢳⣾⣽
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠤⠽⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣤⣄⡠⠤⢁⣀⠀⠀⠀⠀⠽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣭⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠻⠿⠿⠿⣿⣿⣿⠿⠀⠠⠀⠰⠶⣤⣔⣆⣀⢀⣒⠤⠤⢤⣠⣼⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⡶⠀⠀⠈⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠤⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣄⣀⡤⠤⠄⣀⣀⠀⢀⣩⣤⠤⠀⠀⠰⣶⣿⣿⣿⠿⢾⡿⣳⣶⣀⣼⣿⣿⣿⣿⣿⣿⣿⣭⡟⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠉⠛⠛⠿⠿⢿⣶⣾⣭⣿⣿⣇⣀⡀⠀⠀⠀⣸⣿⣿⣶⣶⡾⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⣾⣷⣦⠀⠀⠀⠀⠀
⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣄⣀⣀⠀⠀⡀⠈⠉⠙⠛⠛⠻⠿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⣹⣿⡿⠀⠀⠀⠀⠹⠿⡿⠏⠀⣾⠿⠻⣿⠿⠂⠀⠀⢠⣴
⣿⣷⣄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣷⣦⣬⣤⣞⠿⣀⣀⣀⡀⠈⠉⠈⡰⠲⠟⠋⠁⠉
⣿⣿⣿⣷⣠⡀⠀⠀⠀⠉⠙⠓⠶⠆⠸⣿⣿⣿⣿⣧⣭⣽⣻⣿⣿⣿⣿⣿⠃⠀⠀⢀⣧⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣷⣶⣾⣭⣽⣛⠂⡠⠀⣠⣶⠀⠀
⣿⣟⣫⣭⣭⡅⠀⠀⠀⠀⠀⠀⠔⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣽⠙⢻⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⣼⣿⣿⣟⣿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠀⠀⣼⣿⣿⡆⠀
⣿⣧⡙⠿⠛⠷⢶⣶⢾⣶⣶⢂⣄⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⡿⣿⣿⣦⣤⣼⣿⣿⣟⠍⠀⠀⠀⠀⢠⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀
⠿⠿⠿⠷⢠⠀⠀⠀⠀⠀⠂⠀⠄⡂⣬⣽⣷⣯⣍⡟⣻⢿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣿⣿⣿⣿⢦⣿⣿⣿⣿⣿⣿⣿⢟⣹⡁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢲⣶⣶⡤⣡⡀⡀⢰⠃⣿⣿⣿⣿⡿⣿⣾⣕⣯⡻⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣯⣵⡾⠿⢿⠿⢿⣿⠻⢟⣫⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣶⣿⢖⣨⡟⣜⡻⠱⡇⡾⢠⣿⣟⡿⣿⣿⣶⣮⣽⣿⣯⣪⣿⡟⠀⠀⠀⣼⣿⣿⣿⣯⣭⣁⡀⠀⠀⠀⠐⠊⠉⠀⠀⠙⣿⠟⠉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⣄⠈⠛⢋⣀⡁⠀⢠⡇⢸⣿⣿⣿⣷⣯⣟⡿⣿⣿⣿⠿⣷⡇⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣷⣶⢠⣤⣤⣤⣤⣤⣤⣤⢠⣴⣬⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠛⠿⢿⣿⡿⣿⣿⣿⣿⠿⠿⠞⠶⢶⣟⣿⣿⣿⠿⢿⣿⣷⠯⣶⠇⠀⠈⣿⣿⣿⣧⡈⠛⢹⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠁⠐⠀⠂⠈⠙⠛⠋⠀⠚⠿⠛⠚⠋⣉⠰⡀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣌⡉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⡄⠀⠠⠠⠀⠀⠀⠀
⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣏⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠘⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣿⣿⣆⠀⠀⠀⠀⠀⠀
⣴⣶⣶⣤⣄⣴⣵⠶⠿⠿⠿⢶⣾⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⡿⠀⠤⠀⠀⠀⠀⠀
⢾⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠘⣿⣿⡟⠀⠀⠀⠠⠀⠄⠐⠀⠀⠀⠀⠀⠀⢠
⢛⡽⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠻⣿⠁⠀⠀⠄⠄⠐⠐⠀⠀⠀⠀⠀⠀⠀⠘
⠰⠆⢧⠀⠀⠠⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠂⠁⣠⠖⠊⠀⠀⠀⢀⠀
⠀⠀⠸⡆⠀⠸⣶⣶⣄⣀⣀⡀⠀⢀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⣶⠀⠀⠀⠀⠀⠐⠒⠭⠋⠙⠣⠦⡀⠀⠀⠀⣾⣷
⠀⠬⠀⡇⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠂⠩⣿⣿⣶⣦⣄⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠋⠀⠀⠀⢀⣤⣤⡴⠶⠚⠋⠉⠀⠀⠀⠀⢸⣿⣿
⠀⢾⠁⣧⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⣤⣰⣿⣿⣿⠀⠀⠀⢸⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⡦⠂⠀⠀⠀⠈⠀⠀⠀⠀⢔⣀⠀⠀⠀⠀⠀⠀⠉⠙
⣦⣀⢠⡇⠀⠀⠰⡀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⢸⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⣿⣿⣿⠸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⢠⣶⣶⣦⡄⠘⣺⡭⠇⠀⠀⠄⠀⠀⠀⠀
⣿⠇⣼⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣬⣏⣎⣾⣹⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⠀⢸⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠎⠀⠀⠀⠀⢈⣉⠥⠒⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀
⢃⣾⠟⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣷⣾⣼⡱⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⡇⢻⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡿⠋⠀⠐⣀⢀⣀⣤⣄⣀⡀⠀⠀⠀⡀⣠⢤⣸⡆⢸⣿⣿⣿⣿⣿⣿⢹⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠲⢦⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠹⣿⣿⣿⣿⣷⣤⣀⠀⠙⠫⣫⠇⢸⣿⣿⣿⣿⣿⣿⣷⣾⣼⣝⣯⢍⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣠⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠉⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣂⡌⠻⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠙⠳⢦⣄⡀⡤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣤⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣇⣀⣶⣿⣿⣿⣿⣿⣦⠈⠛⠶⢦⣄⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢸⣿⣿⣿⡍⣿⣿⣿⢿⣿⣿⣿⡏⢀⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⠿⣿⣿⣿⣤⣄⡀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⢸⣿⣿⣿⣷⣿⣿⣿⣆⢻⣿⣿⣿⡿⣿⣿⣿⣧⣤⡤⠈⢿⣿⣿⣶⣤⡀⠀⠉⠛⠿⣷⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⣟⠋⢸⣿⣿⡏⠀⣿⣿⣿⡿⠿⠏⠓⠨⠙⠿⣿⣿⣿⣶⠀⠀⠀⡀⠉⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣇⣴⣿⣿⣿⡇⢠⠀⢰⣷⣷⣶⠈⣿⣿⣿⡇⢀⠁⠂⠡⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣾⣶⠈⣿⣿⣿⣤⣿⣿⣿⠁⠀⠈⠀⠒⠅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⡛⠛⠙⠻⣿⣿⣿⣿⡟⣿⡿⠘⠛⣻⣿⡇⠻⡛⠛⠛⠛⢟⡀⠈⠙⠻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠉⠛⠿⠇⣿⡇⠀⠀⣿⣿⠓⠠⢑⣄⡀⠀⠀⠁⡀⠠⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⢰⣿⣷⡆⢰⣿⣿⡆⠀⣶⣾⣾⠢⠐⠀⠈⢄⠀⢑⠏⠫⢍⡙⠻⡤⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡄⣿⣿⣿⠀⠀⠈⠢⠄⠀⠀⠄⠀⠀⠛⡦⠻⣽⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣧⣿⣿⣿⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⣓⡛⠉⠁⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⠺⠃⠀⠀⠀⠀⢀⣀⠀⠅⠒⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠠⠀⢁⠀⠀⠄⠁⠐⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⡏⢿⣿⣿⣿⣷⣿⣿⢠⡄⠀⠀⠐⠀⠀⠀⠁⠀⡑⠠⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⢻⣿⡿⠇⠈⠿⠿⣿⣿⣿⣿⣾⣿⣴⣄⣀⠀⠀⠂⠀⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠹⣿⣄⠀⠀⠐⠽⣩⢿⣟⣽⣿⢹⣿⠃⡀⢀⣂⣄⠐⢄⢁⠀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⢻⣷⣄⠀⠀⠉⠳⣛⢛⠿⠻⣿⣼⣿⢿⣿⣿⣧⢋⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⢿⣷⣄⠀⠀⠠⡙⠂⢄⡀⠘⠿⢾⣿⣿⣿⣏⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡻⣿⣦⣄⠀⠀⠀⠀⠀⣀⠀⠈⠻⡻⢿⠟⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⡻⢿⣶⣦⣄⣀⡀⠀⠀⠁⠀⠀⠀⠀
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⡛⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡿⠋⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀
⠀⠀⢀⣠⣄⡄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⣉⣡⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠋⠀⠀⣾⣿⣿⣿⡆⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣷⣤⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣤⣀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡤⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣀⣤⣶⡗⠀⠈⢻⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣀⣤⣿⠃⠀⠈⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠏⠀⠀⠀⠀⢀⣿⣿⣿
⣦⣄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⡽⣟⠯⡀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣶⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⠿⣿⣿⣷⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⣄⣀⣀⢰⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿
⠀⠀⢰⣿⡟⠁⠺⢿⣿⡇⠀⣷⠇⣠⡿⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠉⠻⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣼
⠀⢀⣼⣿⠣⠀⠀⠀⠈⠛⢰⣿⣴⡟⡁⠀⢀⣾⠿⢾⣄⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠐⣹⣿⣿⣿⣿⠉⢍⢩⣶⣶⣶⣦⣄⡀⠀⠂⠉⠒⠿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⢲⣾⡿⠁⠀⠀⠀⠀⠀⠀⠸⠉⠟⠈⠀⠠⣾⢿⡆⡄⠀⠙⠳⡐⠄⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⠉⣿⣿⣿⡿⣶⣆⡀⠀⠀⠀⠙⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢢⠀⠀⣤⣤
⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠀⠀⠈⢑⣂⠌⡛⠻⢿⣿⣿⣿⡷⢠⣿⣿⣿⣿⣿⣿⣾⡿⡏⢀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⠌⠃⢸⣿⡿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣤⣤⡤⢭⣽⣿⣿⣾⠷⠊⠌⠉⠛⠛⠾⡟⠻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣺⣿⣇⣻⣿⣿⣿⠙⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⣿⠃
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣭⣭⣉⣁⣅⣀⣠⣦⡀⠀⡀⡀⠀⠈⣙⣛⣿⣿⣿⣿⣿⡛⠋⢙⡛⣦⡏⢛⠿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣿⡟⡄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡉⠙⢿⣿⣿⣿⣿⣟⠀⢸⣗⠀⠁⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣭⣽⣿
⣋⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣾⢹⢸⣼⠃⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⡤⠀⢈
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇⠀⢻⡄⣴⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣾⣅⡂⣸
⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠘⠋⠙⠃⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣯⠉⡿⢥
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⢤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣀⠀⠀⠀⠀⠀⡀⠀⠉⠙⠲⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⠏⢐⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⣰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠫⠉⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⡀⠃⣙⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⣀⡀⠀⠀⠀⠀⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠋⠙⠛⠛⠛⠿⠿⡟⠃⠀⠃⠀⡟⢻⣶⣾⣧⣤⢨⣭⠀⠒⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡏⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠲⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣶⣶⣦⣴⣂⣠⠄⠀⣠⣤⣿⠄⠀⠀⠀⠛⠿⣿⣿⣿⣟⢿⣏⣿⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣶⠅⢀⣈⣙⣁⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣾⣿⣿⣦⣤⣄⣀⣀⣀⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⡟⠀⣸⣿⣿⣿⣇⠀⠀⠀⠀⠀
⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣶⣤⣤⣀⣀⡀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⠀⠀⢀⠀⠛⢛⠛⠃⠀⠩⠋⣻⡿⠛⠀⠀⣀⣰⣾
⣿⣷⣄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣷⣾⣦⣼⣛⠠⠄⣀⣀⣀⡀⠀⠀⠔⠚⠛⠁⠀
⣿⣿⣿⣇⣆⠀⠀⠀⠀⠈⠉⠙⠳⠁⢻⣿⣿⣿⣿⣴⣶⣭⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⣴⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣷⣶⣶⣯⣭⠉⡄⢀⣴⠁⠀
⣿⡟⣩⣭⣬⠀⠀⠀⠀⠀⠀⠀⠁⠸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠈⣿⠉⠛⢿⣿⣿⣿⣶⠂⠀⠀⢀⣿⣿⣿⣽⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠙⠃⠀⠀⠾⢿⣿⡇
⣿⣷⣍⠘⠙⠻⠿⠟⠿⠿⠟⠴⠄⠆⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣦⣤⣬⣿⣿⣿⣯⣀⡀⠀⣸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠃⢀⠀⠀⠀⠀⠈⠀⠐⢰⢠⣽⣿⣶⣾⣿⣫⣟⡿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⡧⣬⣽⣿⣿⣿⣿⣿⣿⣯⣸⠄⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠉⠿⣿⣶⢢⣤⡄⠀⡟⢸⣿⣿⣿⣿⠿⠿⣿⣿⣻⣟⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣓⣒⣼⣿⣿⣿⣿⡿⠻⣿⡯⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠿⣣⣾⡳⢭⠛⠃⢰⠃⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⡿⠁⠀⠀⢰⣿⣿⣿⣿⣿⣍⣛⡋⠀⠈⠉⠁⠀⠉⠀⠀⠀⣿⡟⠉⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣀⣈⣋⣤⣀⣀⠀⠾⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠾⣆⣀⣀⠸⠿⣿⣿⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠛⠻⠽⣿⣿⣿⣿⣿⡿⠿⠷⠆⠲⠾⣻⣿⣿⣿⠿⣿⣿⣿⢯⣶⡏⠀⠈⣿⣿⣿⡶⣄⠙⢫⣤⣤⣤⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠀⠂⠈⠉⠉⠋⠀⠚⠻⠛⠈⠋⡁⡈⡄⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⡷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀
⣄⣀⣀⣀⠀⢰⣽⡿⠿⠿⠿⢿⣾⣿⣿⣿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⢿⣿⡏⠀⠀⠀⠀⠐⠀⠀
⣻⣽⣿⣿⣿⣷⣅⣀⡀⠀⠀⠉⠛⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⢻⣿⣿⠇⠀⠀⡄⡄⠄⠠⠀⠀⠀⠀⠀⠀⠸
⢉⢞⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣇⢀⣿⣿⣿⠀⠀⠀⠘⢿⡟⠀⠀⠠⠠⠠⠀⠂⠂⠀⠀⠀⠀⠀⠀
⠐⠛⢩⡙⠛⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠈⠁⠀⠀⠆⠆⠂⠐⢀⡴⠖⠁⠀⠀⣼⣆
⠀⠀⡀⡇⠀⠀⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠒⠢⠍⠉⠙⠠⠄⠀⠀⢰⣿⣿
⠁⠒⠄⢿⠀⠀⣿⡿⠛⠀⠀⠀⠀⠀⠀⠠⠀⠐⠏⢸⣿⣿⣶⣤⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠘⠃⠀⠀⠀⠠⡄⣠⡤⠶⠛⠉⠉⠀⠀⠀⣾⣿⣿
⠒⠾⡇⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⢰⠔⠀⠀⠀⠀⠂⠀⠀⡀⣤⣀⠀⠄⠀⠀⠀⠀⠉⠙
⣶⣄⠀⣿⠀⠀⠰⢤⡀⠀⠀⠀⠀⠦⠵⠀⠀⠠⠀⠀⠀⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⢸⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣤⠛⠋⣈⠤⠇⠀⠀⠀⠀⠀⠀
⣿⡟⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣮⣏⣸⢸⡝⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠸⠁⠀⠀⠀⠀⢉⡩⠤⠂⠈⠀⠀⠀⠀⠀⠁⠒⠤⣀
⢋⣴⡟⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣷⣶⣿⣷⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢸⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠋⠀⠰⣢⣠⣄⣤⣤⣤⣄⠀⠀⠀⠀⡄⣤⣶⠀⠈⣿⣿⣿⣿⣿⣿⡱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠙⢿⣿⣿⣿⣿⣶⣄⡀⠈⠚⢿⢀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣼⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀
⣤⣀⣀⣂⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠈⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣁⣉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡀⢀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⣴⡌⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠙⠳⢤⣤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠛⢻⣿⣿⣿⢛⣿⣿⣿⣦⣹⣿⣿⣷⣾⣿⣿⣿⡏⠉⡁⢸⣿⣿⣿⠀⣿⣿⣿⠉⠛⠻⢿⣶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢹⣿⣿⡟⠁⣿⣿⣿⣯⣤⡅⠘⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⠃⣼⣿⣿⡇⢀⣿⣿⣿⣿⠿⡿⠀⠀⠙⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⣿⣿⣿⣿⡗⠡⡘⣶⣷⣶⣾⠊⣿⣿⣿⡆⠀⠀⠐⠁⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⢿⣿⣿⣿⣼⣿⣿⣿⠁⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⡛⠛⠙⠻⡟⣿⣿⠘⠛⢻⣿⡇⠛⠛⠛⣿⡛⠛⠈⠫⡙⢟⠿⠛⠏⠁⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⣿⣏⠀⠀⢻⣿⠃⠀⠀⠀⠈⢛⠦⡀⠆⠑⣄⠘⢳⡞⢏⡛⠲⣷⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡆⢰⣾⣿⡆⠀⣶⣶⣶⠀⠡⡀⠱⠤⢈⢆⠈⢈⠈⠈⢷⠨⣯⣤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⣿⣿⣿⠉⠒⠒⠌⠀⠀⠀⠀⠂⠀⢀⠸⠔⠛⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⡾⠆⠀⠀⠀⠀⠈⠘⠂⡄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⡀⠒⢄⠉⠉⠀⠨⢦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣶⢀⡀⠀⠀⠀⢑⠀⠁⠑⢄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠑⠀⠀⠀⠱⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠸⠿⢿⣧⡈⠿⠿⠿⢯⣿⣟⣾⣿⣿⣿⢻⠀⠀⢄⣀⠢⡀⠂⠁
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⣷⣄⠀⠀⠈⠀⠅⣻⡿⣿⣯⣿⣷⣼⣿⣿⣏⣬⣺⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠻⣷⣄⡀⠀⠀⡈⠀⠮⠁⢾⠟⣿⣿⣿⣿⡼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⣿⣶⣄⡈⠁⠀⠀⠀⠀⠀⠉⠹⠛⡿⠹⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣻⢿⣶⣤⣄⣀⠈⠁⠀⠙⠀⠁⠀⠀
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⠛⠿⢿⣿⣶⣶⣶⣶⣶⣶
⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠉⠉⠉⠉⠉
⢷⣒⣤⡀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⡿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀
⣧⣿⣿⣿⣷⣦⣀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢡⣤⣴⣾⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⢰⣿⣿⣿⣿⣄⣄⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣦⣄⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⠖⠀⠀⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⢀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣾⣿⠇⠀⠙⣿⡿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣴⣿⡿⠁⠀⠉⠻⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣷⣄⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣧⣀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣯⡽⡾⠆⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠾⠟⠀⠀⠀⠀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠿⠏⠀⣼⣳⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢻⣏⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⠿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣧⣿⣿⡟⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⠻⣿⣿⣷⠀⠠⠄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠀⠠⠤⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉
⠀⠀⠀⣿⡟⠀⠈⠛⠷⣾⠀⣾⡇⣰⡿⠁⠀⢀⣼⣆⡖⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠤⠀⠀⠀⠀⠀⠀⠉⠉⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠒⠛
⠀⢀⣼⣿⠙⠂⠀⠀⠀⠈⠁⣿⣷⡟⡕⠀⢀⣾⡛⠛⠲⢄⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡯⢽⣿⣿⣿⡿⠤⡰⠄⣟⣿⣻⣿⣶⣤⣀⡀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⢉⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠀⠀⠻⠟⢟⡠⠀⠀⠉⠪⣑⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣧⣀⡀⢸⣿⠃⢸⣿⣿⣿⣼⣿⣤⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣡⠀⣸⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣠⣀⣤⠭⢔⢂⣭⢛⡿⣿⣿⡇⠂⣿⣿⣿⣿⣿⣟⣻⣿⠹⠀⣿⡿⣿⣷⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠋⠋⠀⢠⣿⣿
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠲⠶⠶⠲⠶⢾⣿⣟⡋⠁⡁⠀⠀⠉⡙⠃⠉⠃⠸⢿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⡃⢮⣽⣽⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⠇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣯⣦⣤⣄⣠⠀⡀⠤⣬⣭⣿⣿⣿⣿⣯⠁⠠⣌⡛⡇⢰⠉⠋⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⣸
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣭⣽⣿⣿⣿⣿⣿⣷⣤⣄⣸⣿⣿⣿⣿⣿⠠⢠⣿⡄⢀⡈⢀⣀⣀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠺⠛⠳
⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠇⢡⢸⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡶⠠⠀
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⢿⣿⠀⠈⠻⣸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⡴
⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣿⠆⢸⢱
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠋⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠏⠙⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠠⡤⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⣀⢻⡟⠃⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣧⣀⣀⡀⢀⢀⡒⠀⠀⠀⠀⠀⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⣠⡌⠤⡄⠀⠀⣀⣀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⡖⠀⣨⣭⠁⠀⠀⠁⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⢈⠁⠀⠉⠉⠉⠉⢛⣋⡁⠀⠀⠀⣬⣩⣿⣿⣷⣶⣰⣶⢂⣌⠉⢹⣿⣿⣿⣿⣯⣿⣿⡻⠿⠁⠀⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠛⠻⠿⢿⣷⣶⣭⣥⣔⣂⣴⣴⣿⡏⠀⠀⠈⠉⠉⣿⣿⣿⢯⣵⣣⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣤⣤⡄⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣶⣶⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⠋⠉⠙⠛⢻⣿⣿⡿⠀⢸⣿⣿⣿⣿⡄⠀⡀⠀⣀
⣧⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣯⣄⣀⡠⠄⢀⣉⡅⠁⠀⠀⠒⠨⠽⠍⠀⠀⢀⣴⣿
⣿⣿⣷⡂⡀⡀⠀⠀⠲⠦⣤⣄⣀⠀⠰⣿⣿⣿⣿⣟⠿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣷⣿⣦⣴⣖⣒⡲⠶⣤⣄⣀⣤⠎⠉⠉⢁
⣿⣿⣿⣿⣦⡇⠀⠀⠀⠀⠀⠀⠉⠁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣶⡶⠀⠄⢀⣄⣈
⣿⣿⢩⣶⢶⣆⣀⣀⣠⣄⣀⡀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣇⢈⣿⠉⠉⣿⣿⣿⣿⣿⠀⠀⠀⣾⣹⣿⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠻⠿
⣿⣿⣷⣌⠈⠉⠛⠋⠙⠛⠏⠚⠃⡆⣶⣯⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣿⣿⣿⣿⡠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⡄⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⢠⣄⣀⣀⢀⠌⠀⠀⢐⠁⣿⣾⣿⣿⣷⣮⣞⡿⣻⢿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⠦⢤⣽⣿⣿⣿⣿⣿⣿⣯⡿⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣀⣀⣄⡘⢻⡿⢣⣿⣶⠆⡜⢸⠿⣿⣿⣿⣩⣛⡻⣿⣾⣗⢝⢿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣑⣒⣤⣿⣿⣿⣿⣿⣛⠿⠧⢾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠛⢵⣿⡗⠳⠎⠉⢠⡇⢸⣿⣷⣯⣟⣿⣿⣿⣿⣿⣿⣷⣕⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣭⣙⡋⠁⠉⠉⠀⠀⠀⠀⠀⠘⠿⠏⢀⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⣤⣤⣶⣶⣤⡄⡄⠀⢺⣿⣿⣿⣿⣿⣿⣮⣿⡿⡿⢟⡛⠳⢦⣤⣈⡙⠻⢿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠄⠀⠀⠀⠀⠀
⠉⠙⠛⠻⣿⣿⣿⣿⠾⡟⢛⡛⠋⠛⣻⣽⣿⡿⠟⢟⣿⣿⣟⣾⡻⡁⠀⣴⣤⣬⡟⠳⣦⢸⣤⣤⣤⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⡄⠀⠠⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠈⢀⠤⠘⠄⣿⣿⣿⣇⠀⠀⢸⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣞⠀⠀⠀⠀⡀⠀⠀
⡀⠀⠀⠈⠁⠀⢀⡀⣀⣄⣀⣀⢀⢀⣴⣿⣶⣶⡤⠀⠀⠀⠀⠁⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⢻⣿⣿⣿⣿⣿⡏⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀
⡹⣄⣀⣀⣀⠀⠾⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⢀⠻⠏⠀⠀⠀⠀⠀⠈⠀
⣷⣛⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠒⠃⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠆⠆⠂⠀⠂⠀⠀⠀⠀⠀
⠒⢫⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠀⠀⠘⢿⡏⠀⠀⠐⠐⠐⠀⠃⠀⠀⠀⠀⢀⣆
⠁⠀⠛⢙⠛⠿⠿⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠃⡁⢈⡀⠖⠋⠀⠀⣸⣿
⠀⠀⠀⠸⡆⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠈⠉⠒⠀⢀⣉⡰⠦⠀⢠⣿⣿
⠌⠀⢒⠄⡇⠀⠀⡿⠛⠁⠀⠀⠀⠀⠀⠒⠒⠒⠂⢘⢿⣿⣿⣶⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠈⠀⠀⠀⠀⠔⣆⠴⠖⠛⠉⠁⠀⠀⠀⠺⠿⣿
⠈⠈⠻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠖⠊⠀⠀⠀⠀⠉⠀⣀⣠⠤⠀⣂⠀⠀⠀⠀⠀⠀
⣿⣶⡤⢸⡇⠀⠀⠐⠦⡀⠀⠀⠀⠠⠖⠢⠀⠀⠀⠀⠀⢸⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣸⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⢶⣾⣦⠬⠋⢀⠼⠾⠁⠀⠀⠀⠀⠀
⣿⡿⢃⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣼⣾⣬⣧⠷⢹⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠊⠀⠀⠀⠀⢀⡨⠤⠒⠂⠀⠀⠀⠀⠀⠀⠈⠑⠢
⢛⣡⣾⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⢸⣿⣿⣿⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠰⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠟⠁⠀⠜⢧⣤⣤⣶⣶⣴⣄⡀⠀⠀⠀⣼⣿⣷⣿⢸⣿⣿⣿⣿⣿⣿⡰⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠩⢿⣿⣿⣿⣿⣶⣤⣀⠈⠙⠷⣾⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢫⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⢬⣀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⣬⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣩⣍⢹⠿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣦⣀⠠⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⡌⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠄⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠻⠶⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣽⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣹⣿⣿⣿⣙⣿⣿⣿⣾⣿⣿⣿⣧⣴⣿⣿⣿⡏⠉⠁⢸⣿⣿⣿⠀⣿⣿⣿⠀⠈⠉⠛⠿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⣈⣻⣿⣿⣿⠟⣿⣿⣿⣧⣤⡵⠈⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢹⣿⣿⡇⠀⣿⣿⣿⡿⢿⠇⢡⡇⠙⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⡇⣰⣿⣿⣿⡇⠀⠙⢾⣿⣿⣶⠈⣿⣿⣿⡆⠀⠀⠀⠁⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⣿⣿⣿⣤⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠈⠛⠻⠟⣿⡟⠛⠛⣿⣿⠟⠛⠛⠛⢿⢟⠀⠈⠛⡟⠻⡛⠋⢃⢀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠩⡓⠄⠃⠈⢄⢈⢺⠟⢏⡉⠓⢷⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⢰⣶⣿⡏⠀⣶⣶⣶⡀⣀⠐⡀⠸⠢⠈⢂⠈⡀⣈⠈⢷⠈⣯⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡀⣿⣿⣿⠈⠀⠍⠀⠂⠀⠀⠀⠀⠃⠀⠀⠸⠒⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠰⡟⠆⠀⠀⠀⠀⠠⠐⠂⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠒⠄⠈⡅⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣐⡀⠀⠀⠀⢁⠈⠀⠢⠬⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢹⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣶⣤⣀⠈⠓⢀⠀⠀⠢⡈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡸⠿⠿⢿⣎⠿⠿⠿⠨⡿⣿⣻⣿⣿⣿⣟⡿⠀⠰⣀⡑⢄⠐⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠻⣷⣄⠀⠀⠀⠀⢟⠛⣞⣿⣿⣿⢹⣿⣿⣷⢻⣷⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠻⣷⣄⡀⠀⠀⣁⠻⠂⣙⠟⡿⣿⣿⣿⣏⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⢿⣶⣄⡀⠁⠀⠀⠁⠀⠀⠘⠙⢿⠼⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣻⢿⣷⣦⣄⣀⠀⠀⠀⠐⠉⠀⠀
⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⡛⠿⠿⣿⣶⣶⣶⣶⣶
⣀⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠈⠉⠉
⣿⣽⣿⣦⣄⣀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠟⠛⣀⣤⣀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡿⠁⠀⣴⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⣰⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠰⢿⣿⣿⣿⣷⣾⣷⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣧⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣯⢄⣀⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣄⣨⣽⡿⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠁⠀⠀⠈⢻⣿⣿⣿
⣦⣀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⣸⣿⣿⣿
⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⣿⣤⣀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣷⣭⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣯⡏⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⡻⢽⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣏⡟⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⠉⢫⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⠏⣻⣿⠿⡇⠀⣔⡄⠀⣴⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠒⠒⠚⠻⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢠
⠀⠀⢰⣿⣇⠀⠈⠙⠻⣷⠀⣿⢃⣾⠏⠀⠀⣠⣿⣳⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠛⠓⠂⣀⣀⣀⡀⠀⠀⠀⠘⠻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠈
⣀⣰⣿⡟⠀⠂⠀⠀⠀⠀⢹⠿⣿⢫⠊⠀⣰⣿⡉⠉⠓⠦⡀⣀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠨⣼⣿⣿⣿⡟⠦⠘⢣⣿⢯⢿⣿⣿⣶⢠⣀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡀⠀⢀⣀
⣸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⠙⠯⠂⠀⠀⠈⠂⢅⣂⠠⢿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣧⣤⣠⣼⡿⠈⣿⣿⣿⡟⣿⣿⣞⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⢦⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠤⠤⣤⣶⣶⡖⡒⠏⠴⢎⣽⣛⡿⣿⠇⢰⣿⣿⣿⣿⣿⣯⣽⣧⣂⣶⣿⡟⢿⡿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠁⠉⠀⢸⣿⡟
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⣋⡙⠻⠿⠿⠯⠅⠀⠈⠀⡀⠀⠈⠁⠀⠁⠘⠿⣿⣿⣿⣿⣿⣿⣿⡗⠶⣯⣑⡿⠼⣯⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⢁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣻⣿⡿⢷⣶⣶⣶⣾⣿⣧⣶⣦⣦⣈⠀⠶⠶⣾⣿⣿⣿⣿⣶⠀⠐⣆⠋⠇⡴⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⡦
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿⣿⣿⣿⣿⠰⣸⡿⢂⢠⡄⣠⣤⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠛⢉⠙
⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣻⣠⢸⣾⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢰⠇⠈⢠
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣉⠛⠻⡿⢿⡇⠀⠈⠃⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠠⡿⡿⢷⡞
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⠀⠀⠂⠀⠀⠀⠤⠿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣷⠀⣾⢸
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⠀⠀⠲⠀⠀⠀⠀⠀⣭⣝⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠐⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠰⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⡌⠿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣶⣤⣤⣤⠬⠩⣁⣀⡂⠀⠀⠀⢹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⡶⠀⡄⠀⣤⣲⣒⣒⡆⠒⠀⠤⠀⢀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣶⣶⠀⠉⠁⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⢤⣄⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣀⠀⣀⡀⠀⠀⠀⠉⠩⣧⣀⣀⣀⠀⣦⣼⣿⣿⣿⣿⡼⡟⣤⣤⢀⣼⣿⣿⣿⣿⣷⣿⣭⣟⡛⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⠛⠛⠿⠿⢷⣶⣿⣤⣤⣒⣷⣿⠅⠀⠀⠀⠀⠀⣿⣹⣿⣷⣼⣷⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣶⣶⣶⣄⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⡀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣷⣶⣶⣯⣽⣟⣛⣿⣿⣿⣿⣿⣿⠁⠈⠉⠉⢽⣿⣿⡏⠀⠾⠿⢿⣿⣿⠄⠀⠄⠀⣤
⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣷⣦⣄⣐⡀⣼⡤⠀⠀⠀⠈⠉⠐⠚⠀⠠⡀⣀⣨⡿
⣿⣿⣷⡆⡄⡀⠀⠀⠓⠲⠶⢤⣤⡀⣠⣿⣿⣿⣿⣛⣛⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣷⣮⣭⣭⣛⣒⡶⠦⢤⠒⡾⠁⠉⢀
⣿⣿⣿⣿⠷⠁⣀⠀⠀⠀⠀⠀⠔⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⢷⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⠇⠠⠁⣠⣬
⣿⣿⡏⢶⢺⣤⣤⣤⣤⣤⣤⢄⠀⡘⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣷⠀⣻⡉⠩⢽⣿⣿⣿⣿⠁⠀⠀⡼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⣿⣿⣿⣦⠀⠈⠉⠁⠉⠉⠃⠉⢁⡅⣿⡶⠯⢟⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣷⣵⣶⣿⣿⣿⣿⡤⠄⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠂⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠀⠴⣤⣤⣄⡀⠁⠀⠀⡸⢨⣷⣿⣿⣿⣿⣷⣯⣺⢽⡻⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠤⣬⣿⣿⣿⣿⣿⣿⣗⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⣤⣤⡍⣻⣟⠼⣿⣿⠂⡌⢸⣻⢿⣿⣿⣬⣭⣛⣿⣷⣯⡻⡻⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣒⣢⣿⣿⣿⣿⡿⡋⠯⠟⠸⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠉⠺⡿⠊⠙⠂⠈⠀⠃⣼⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⣿⣮⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣙⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⡄⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣶⣶⣾⣶⣶⣆⣇⡀⣻⣿⣿⣿⣿⣿⣿⣷⣯⣟⠿⢛⣩⠛⠣⣤⣬⣉⡙⠻⢿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⢄⠀⠀⠀⠀
⠉⠈⠛⠛⠿⠿⠿⠿⠿⢟⠋⣉⠓⡙⠛⣿⣿⣿⠿⢛⣽⣿⣟⡯⡿⢃⡀⣦⣤⣤⡌⠙⠶⣴⣥⣤⣤⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀
⠀⠀⠂⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⠄⠀⠧⣿⣿⣿⣇⠀⠀⢸⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⠀⠀⠀⠀⠠⠀⠀
⣄⠀⠀⠈⠈⠁⠀⣀⣀⣤⣀⣠⣀⣀⣴⣿⣿⣶⡶⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⡏⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀
⡈⢦⠀⠀⠀⠀⠚⠿⠛⠋⠙⠛⢻⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀
⣿⡶⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠠⠦⠀⠰⠛⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠰⠐⠐⠀⢁⠀⠀⠀⠀⠀
⢃⠘⣹⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠀⠀⠀⠹⣷⠁⠀⠀⠂⠂⠃⠉⠈⠀⢀⠀⠀⣿
⠈⠈⠱⠟⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⡀⠀⠀⠈⠀⠀⠘⠘⢈⣨⣀⡰⠛⠁⠀⢰⣿
⠀⠀⠀⠄⣇⠀⠀⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣐⡙⠀⠀⣼⣿
⢀⠀⢰⡆⢽⠀⠀⡿⠟⠁⠀⠀⠀⠀⠀⠠⠤⠤⢄⠀⢲⣶⣾⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠔⠦⠶⠛⠉⠁⠀⠀⠀⠀⠛⠿
⠠⠈⡙⠂⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠐⠆⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠋⠁⠀⠀⠀⠈⠀⣠⣤⠒⠀⢥⣒⠀⠀⠀⠀⠀
⣿⣿⣦⢁⡿⠀⠀⠐⠓⢀⡀⠀⠀⠀⠘⠥⠁⠀⠀⠀⠀⠀⡾⣹⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠰⢾⣷⠦⠁⠀⠼⠟⠉⠀⠀⠀⡀⠀
⣿⣿⠋⣼⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣬⣷⣷⣼⣼⠏⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠁⠀⠀⠀⢀⠀⡤⠒⠊⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠛⣡⣾⠏⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⣤⠔⡮⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠟⠁⠀⠘⠿⢶⣶⣶⣶⣶⣦⣄⠀⠀⠀⢎⣿⣿⠀⡆⣿⣿⣿⣿⣿⣿⣗⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣄⡀⠉⠻⢠⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀
⣶⣶⣦⣴⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣉⡻⡿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⢹⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠛⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣶⣦⣤⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣭⣿⣿⣿⢰⣿⣿⣿⣏⣠⣿⣿⣿⡏⠉⠁⢸⣿⣿⣿⢠⣿⣿⣿⠀⠀⠈⠉⠛⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡿⢤⣹⣿⣿⣿⡿⣿⣿⣿⣧⣬⣄⠈⣿⣿⣿⣷⣤⡁⠀⢀⠀⠀⠀⠠⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣹⣿⣿⡟⠀⣿⣿⣿⡿⠿⠯⣢⠈⣹⠿⣿⣿⣿⣦⠈⠀⠀⠀⡈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⡇⠀⣿⣿⣿⣇⠀⠀⢸⣿⣿⣷⠈⣿⣿⣿⡆⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⢿⣿⣿⣿⠇⣿⣿⣿⡇⣼⣿⣿⣿⣷⣶⣶⠈⣿⣿⣿⣤⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠛⠛⠻⢠⣿⡟⠛⠓⣿⣿⠛⠛⠛⠛⠻⡠⢈⠙⠟⠟⠛⡛⢁⢀⣀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢸⣿⡇⠀⠐⣿⡯⢀⢀⠀⠀⠀⠡⡑⠄⡃⠊⢦⠀⢾⠟⢍⡉⠓⣷⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣶⡏⠁⣶⣾⣷⠢⡄⢀⡐⠀⠈⠂⠀⢂⠈⡀⠀⠈⣇⣸⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⠀⠀⠐⠄⡉⠂⠀⠀⠀⠀⠂⠀⠀⠸⠚⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⠀⡀⠈⠀⠰⡿⠀⠀⠀⠀⡀⠁⠂⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⡀⢀⠀⠂⠒⠒⠒⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⠀⠀⠀⠊⡀⠀⠒⢀⢅⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣷⣹⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣷⣤⣀⠨⠠⠀⠀⠑⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠿⠿⣿⣿⠿⠿⠈⠿⢫⢯⣿⣿⣿⡿⣿⣟⠀⣄⣀⡀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⢿⣷⣄⠀⠀⠉⠸⣿⣸⡿⢿⣿⣯⣿⣿⣿⣽⣿⣮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⢿⣷⣄⠀⠀⠀⡙⠁⢀⠟⢱⢻⣿⣿⣷⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡻⣷⣦⣄⠈⠁⠀⠀⠀⠀⠀⠈⠻⠎⡿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡻⢿⣶⣤⣄⣀⠈⠁⠀⠘⠀⠀
⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣙⠻⠿⢿⣿⣶⣶⣶⣶
⡷⣄⣀⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠉⠉
⣿⣿⣿⣷⣦⣄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢛⣋⣩⣤⣦⣄⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡿⠋⠀⢠⣾⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢀⣾⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣶⣦⡹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣷⡄⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣴⣦⣿⡿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣇⠠⣴⣿⠏⠙⠻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠏⠀⠀⠀⠀⢹⣿⣿⣿
⣷⣄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣄⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿
⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣾⣷⣿⣿⣤⣄⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠉⠁⠀⠀⠀⠠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⡏⣻⣿⣿⣷⣔⣄⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢭⣽⢶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣇⡏⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢡⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⣿⣿⠿⢘⣿⣟⣻⠀⣠⡆⠀⣴⡄⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠉⠁⠚⠳⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⢰
⠀⠀⢠⣿⣏⠀⠀⠈⠛⠿⡄⣿⣇⣾⢏⠀⠀⣠⣷⣷⡃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠉⢉⠁⣤⣤⣤⣄⣀⠀⠀⠈⠙⠫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀
⣄⣰⣿⡟⠀⠃⠀⠀⠀⠀⢀⠟⢿⠫⠊⠀⣰⣿⣄⠀⠉⠛⢆⡄⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⡟⠗⠌⢣⣷⣟⢻⣿⣿⣿⢲⣤⠀⠀⠀⠨⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠄⠀⢠⣤
⣰⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠀⠀⠀⠀⠁⠢⠅⣂⠻⢿⣿⣿⣿⣿⡯⠀⣿⣿⣿⣿⣷⣦⣴⣾⢿⠈⣸⣿⣿⡟⣾⣿⣿⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡦⣤⠛⠀⣾⣿
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣐⡒⣲⣶⣦⣄⣈⡛⣂⠚⠰⠎⣭⡿⠿⡃⢠⣿⣿⣿⣿⣿⣷⣿⣿⡬⠤⣿⡏⠻⢟⣿⣿⡟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠐⠁⠀⢸⣿⡟
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣵⣈⣙⣛⠛⠻⠆⢀⠀⢀⣄⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣾⡿⠟⠛⠷⣭⡽⠚⢷⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣾⣿⢣
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣛⣿⣿⠿⢿⣾⣿⢷⣶⣧⣶⣄⡂⠛⡻⢿⣿⣿⣿⣿⣿⠀⠈⣧⠋⠁⠼⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣙⣻⣞
⢿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠐⣸⡟⢇⢢⡆⢴⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢍⣀⠉
⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢺⣭⢸⣼⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣏⡈⢐
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠉⠙⠟⠻⠯⠀⠀⠈⣾⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡿⡟⢻⠏
⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠀⠀⠉⠀⠀⢈⡀⠒⠛⠧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢰⣿⠀⣼⢰
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⠀⠀⠚⠀⠀⠀⠀⠐⢰⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡈⠀⠈⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢃⣤⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⠟⡉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⠀⠈⠀⠀⠈⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠤⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣖⣂⠠⠤⠀⠅⣀⡀⡂⢰⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣭⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠀⠄⠀⠰⢶⣤⣅⣆⣁⢀⣒⠀⠤⠤⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣸⣿⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠦⠤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⣒⠤⠀⣀⣀⠀⠀⢀⣡⡤⠤⠀⠀⢰⣾⣿⣿⣿⡿⢞⡟⢰⣶⣠⣼⣿⣿⣿⣿⣿⣿⣾⣯⡍⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠉⠙⠛⠛⠿⠿⣶⣶⣯⣤⣿⣿⣁⣀⡀⠀⠀⠀⣸⣿⣿⣷⣾⠾⠿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣧⠀⠀⠀⠀⠀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣾⣯⣭⣿⣿⣿⣻⣿⣿⠁⠀⠀⠀⠸⠿⡿⠟⠀⠘⡛⠻⢿⠿⠃⠀⠀⠀⣴
⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⡿⣿⣿⣿⣿⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣷⣦⣬⣤⣘⡟⢁⣀⣀⣀⠀⠉⠉⠀⢐⠄⣤⣀⣽
⣿⣿⣿⣦⡠⡄⠀⠀⠉⠙⠒⠶⠤⡄⠘⣿⣿⣿⣿⣯⣭⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⣿⣷⣶⣯⣭⣭⣟⣒⣲⡽⣛⡟⠁⠀
⣿⣿⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⠏⠐⠁⣰
⣿⣿⣿⡱⠾⢷⣶⣶⣶⣶⣦⢌⡀⢘⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢘⣯⠉⠩⢿⣿⣿⣿⡏⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣯⠀⠀⠈⠉⠀⠉⠃⠉⠅⡆⣾⣿⠷⣯⣟⡿⠿⢿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣶⣾⣿⣿⣿⣴⣔⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⢶⣦⣤⡤⣁⡀⠀⢰⠃⣽⣾⣿⣿⣿⣿⣷⣯⣾⢽⡻⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠳⠤⣿⣿⣿⣿⣿⣿⣿⣷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⡦⣩⡟⡱⠿⣿⡇⡆⢨⣽⣻⢿⣿⣷⣮⣭⣿⣿⣿⣯⡪⡋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣙⣒⣶⣿⣿⣿⡿⠟⠩⠝⠓⢿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡉⠘⠿⠋⠉⠉⠀⢠⠀⢸⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣭⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠠⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣥⣤⣶⣿⣿⣿⣆⣌⣀⣉⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⠟⣫⡅⠛⠳⠦⣤⣍⡙⠻⢿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠆⠀⠀⠀
⠉⠁⠀⠙⠛⠿⠯⠿⠿⠟⠯⢍⡉⠁⠙⠹⠷⣿⡿⠛⣫⣿⡿⣿⡽⠟⢁⣤⣦⣤⡄⠈⠙⢶⣤⣤⣤⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣴⣶⣶⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠁⠀⠠⠐⠀⣿⣿⣿⡇⣀⠄⢸⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠳⣄⠀⠀⠀⠀⠀⢀⣄⣤⣤⣤⣤⣀⣠⣾⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⡁⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⣤⡘⢦⠀⠀⢀⠀⠻⠿⠛⠋⠉⠛⣿⣿⣿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠠⠀⠀⠀⡀⠁⠀
⣿⠿⢎⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠠⠆⠀⣾⡿⠈⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⢿⠃⠀⠀⠐⠐⠐⠈⢁⠀⠀⠀⠀
⠉⠁⢰⢾⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣧⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠹⡟⠀⠀⠀⠂⠃⢁⠁⠀⠄⣀⠀⠀
⠀⠀⠈⢫⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠈⠄⢀⡔⠋⠁⠀⢸
⠀⠀⠀⠀⠆⡎⠉⠛⣿⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⠛⠀⠀⣾
⠀⣄⠀⣉⡇⣇⠀⠀⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⢤⣤⣴⣶⣶⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠴⠶⠞⠛⠉⠀⠀⠀⠀⠀⠛
⣀⢈⠈⠙⠁⡿⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡈⠂⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠘⠉⠀⠀⠀⠀⠈⠀⣠⠀⣆⣲⣭⡅⠀⠀⠀⠀
⣿⣿⣿⣦⢰⡇⠀⠀⠉⠲⢀⡀⠀⠀⠀⠛⠉⠂⠈⠀⠀⠀⠘⡸⣹⢻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⢀⠀⠀⡀⠀⠀⠀⠰⢿⣷⠖⠀⠈⠙⠖⠓⠀⠀⢄⣀
⡿⣿⡿⢃⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣯⣾⡹⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠈⠀⠀⠀⠀⢀⠠⡤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈
⠟⠊⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠒⠄⡀⠨⡐⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡿⠟⠁⠀⠈⠿⣶⣶⣿⣶⣶⣦⣀⠀⠀⠈⢺⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢤⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣄⡀⠉⠻⢦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⠀
⣿⣷⣶⣦⣾⣿⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣙⡛⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡦⢹⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣷⡌⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣷⣶⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣇⢸⣿⣿⡿⠋⣿⣿⣿⡟⠋⠁⢸⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠈⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⣿⣿⣧⣾⣿⣿⣿⣧⣤⡄⠘⣿⣿⣿⣷⣤⡀⠀⢦⢀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⣿⣿⣿⡿⡿⠇⠀⠈⣟⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡍⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⡇⠘⡄⢰⣾⣿⣿⡋⣿⣿⣿⡷⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⠻⣿⣿⣿⣭⣿⣿⣿⡇⠀⣿⣿⣿⣷⣶⣾⣄⣿⣿⣿⣵⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠛⠛⠛⠿⢛⣿⡟⠃⠀⣿⣿⡛⠛⠛⠛⠛⢮⡽⣛⠻⢻⠛⠁⠀⠀⣀⡀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢸⣿⡇⠀⢀⣿⡟⠨⢦⡀⠀⠀⠈⠌⠢⣈⠐⢳⡄⣺⡟⢍⣉⠓⢵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣷⣶⡆⡙⣷⣶⣶⠈⠓⢖⠀⢈⢂⠀⠑⠄⠱⠀⠁⠀⠈⢷⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣠⣿⣿⣿⠀⠀⠀⠁⠢⡈⠀⠀⠀⠀⠀⠁⠈⠀⠹⡝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣧⣿⣿⣿⣄⡀⠄⠀⠀⠀⠄⠀⡶⡆⠀⠀⠀⡀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⡀⠀⠀⠀⠀⡀⢀⠀⠠⠈⢔⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠠⠈⠐⠐⢄⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠛⣿⣿⡿⣿⣿⣿⣿⣷⢰⣀⠈⠀⠀⠀⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠹⣿⣿⠿⠀⠀⢩⡞⣿⡿⣿⣿⣟⣾⡟⠀⠀⠐⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⢻⣷⣄⠀⠀⠁⠹⣡⡟⠟⣿⣿⣽⣿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⢿⣷⣄⠀⠀⠀⡙⠡⣽⠉⠛⡿⡿⣿⡟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⣷⣦⣀⠈⠑⠀⠈⠑⠀⠀⠘⠛⠻
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡻⣿⣶⣤⣀⡀⠈⠉⠀⠑⠂
⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣛⠻⠿⣿⣶⣶⣶⣶
⣷⣥⣤⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠟⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠈⠉⠉
⣿⣿⣿⣿⣶⣦⡄⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢉⣭⣭⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠟⠋⠀⢀⣿⣿⣿⣿⣇⣙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢀⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣧⣄⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⡄⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⡀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣆⣴⣿⣟⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣣⣄⣶⣿⠃⠈⠙⠿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣦⣀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣂⣀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⣿⣯⣷⣶⢀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣶⡝⣿⣿⣿⠖⠠⣄⡀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⡝⢼⣿⣿⣿⣿⣿⣿⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣧⡏⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⣿⡿⠣⣸⣿⣟⡇⠀⣦⡆⢀⣶⠄⠀⠀⣠⡀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠉⠉⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣸
⠀⠀⣰⣿⣇⠀⠀⠉⠙⢷⡀⣿⢡⣾⢃⠀⠀⣰⣷⣵⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣻⣿⣿⣿⣿⠉⢉⠁⣦⣤⣤⣤⣀⠀⠀⠈⢙⠫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⣤⣴⣿⠟⠀⠃⠀⠀⠀⠀⢸⠟⠿⠳⠃⠀⣼⣿⣄⠀⠉⠓⢆⠤⡀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⡏⠑⠈⢱⣾⢳⣻⣿⣿⣿⣰⣤⢀⠀⠀⠨⢝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢲⠂⠀⣠⣤
⣼⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠃⠁⠀⠀⠀⠁⠢⠥⣐⠻⢿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣷⣶⣤⡾⠟⠀⣿⣿⣿⣇⣿⣿⣿⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡶⠔⠛⢤⣿⣿
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣰⣒⣲⣶⣿⣿⣛⠏⣃⠚⢡⠾⢭⡟⠿⡃⢸⣿⣿⣿⣿⣿⣷⣾⣿⣥⠽⣿⡏⣻⢿⢿⣿⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣺⣿⠇
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣥⣄⣙⣛⣛⡛⠂⢀⠀⢀⣄⡀⠀⠄⠀⢀⠈⠛⠿⢿⣿⣿⣿⣿⠿⠏⢙⡳⣮⡟⢛⢿⠿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢠⣿⣿⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣟⣛⣿⣿⠿⠿⣿⣿⣿⣷⣷⣤⣀⠛⠛⣿⣿⣿⣿⣿⣿⠀⢈⣷⠁⠃⠞⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣭⣭⣯
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠘⣼⠟⢱⢰⡆⣲⣶⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡠⠠⠈
⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⢽⡰⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣃⡂⢰
⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠉⠙⡟⠛⠇⠀⠀⠆⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣟⠋⢻⢍
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣄⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠁⠀⠀⠀⠁⠄⠂⠂⠐⠛⢧⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⠗⣸
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⡶⠀⠀⠉⠀⠀⠀⠀⠀⢶⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣶⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⠉⠉⠛⠛⠛⠿⣿⣿⣿⣿⠃⠀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠈⠿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠒⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣤⡖⠒⢀⡴⠤⠀⠩⠅⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠟⠻⠿⠿⠿⢿⣿⡿⠟⠀⠂⠀⠰⢽⣶⣭⣇⣀⢀⣐⡒⠀⠤⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⡟⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠦⢤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣤⣎⣠⠤⢄⣀⣀⣀⣔⣶⡒⠤⠤⠤⠿⠾⣿⣿⣟⠛⠾⠟⣾⣷⡠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡍⠀⡀⢙⡃⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠈⠉⠙⠛⠛⠿⠿⣷⣶⣿⣿⣿⣦⣀⣀⣀⡀⠀⣿⣿⣿⣽⣿⣛⣿⢿⢷⣿⡿⠿⠿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⣤⣀⣀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢚⢻⠟⠃⠄⠛⣛⡻⢿⠛⠁⠀⠂⠠⣾
⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣿⣷⣶⣶⣶⣛⡾⠤⢤⣄⣀⣀⡀⠀⠉⣤⣤⡤⣄⢸
⣿⣿⣿⣧⣄⡆⠀⠀⠉⠉⠛⠲⠶⠄⣤⣿⣿⣿⣿⣯⣭⣝⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⢀⣀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⢿⣿⣶⣾⣯⣭⣽⣚⣿⡿⡿⠇⠀
⣿⣿⣿⣿⣗⠇⠀⠀⠀⠀⠀⠀⠌⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⠁⠊
⣿⣿⣿⡟⠰⢶⣶⣶⢶⣶⡶⣢⡄⡸⣘⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⢻⡋⠉⢹⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠁⠀⠀⡇⣿⣿⣿⠶⣯⣟⡿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣤⣶⣽⣿⣿⣿⣦⡦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣶⣶⣦⡔⣁⣀⠀⢸⢣⢟⣽⣾⣿⣿⣿⣿⣷⣯⣾⢽⡻⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠦⣬⣽⣿⣿⣿⣿⣿⣿⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣶⣶⣶⢆⣩⣏⣜⠿⢿⠇⡏⢠⣯⣿⣿⢿⣶⣶⣮⣿⣿⣿⣷⣿⡂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣒⣒⣽⣿⣿⣿⡿⠟⠭⠛⠛⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡀⠙⠿⢋⠈⠉⠀⢸⠃⢸⣿⣿⣿⣿⣾⣿⣟⡿⣿⣿⣿⣿⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣯⣛⡛⠛⠁⠁⠀⠀⠀⠀⠀⠀⠛⠛⠁⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⣿⣿⣿⣯⣭⣿⣿⣿⣿⣇⣮⣀⣈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡿⢟⣠⡄⠛⠳⠤⣤⣉⡙⠻⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣀⠀⠀⠀⠀⠑⡀⠀
⠁⠉⠀⠒⠛⠻⠿⠭⠿⠿⢿⡯⣍⡉⠁⠛⠽⢷⣿⡿⠛⣫⣿⢿⣿⡽⠟⣧⣴⣦⡄⠀⠈⢻⣶⣶⣤⣤⣤⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣴⣶⣶⣶⣭⡛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠀⣾⡿⠀⠀⠀⠀⠀⠈⠄
⡀⠀⠀⠰⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠈⠉⠁⠀⠠⠒⣿⣿⣿⡇⢀⣀⢼⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⣘⣿⠁⠀⠀⠀⠀⠀⠀⠈
⠙⢦⡀⠀⠀⠁⠉⠀⢠⣄⣠⣤⣤⣤⣀⣠⣾⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⡁⢻⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⢞⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣄⡹⣄⠀⠀⢀⠐⠻⠿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⠞⡁⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠘⣿⣿⠇⣼⡖⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣗⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠰⠆⢠⣞⢧⠁⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣻⢠⣼⠁⠀⠀⠂⠂⠃⠈⠁⠀⠀
⠈⠙⠀⢠⣿⣿⣿⣶⣶⣄⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣧⢀⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠙⠼⠇⠀⠀⠐⠘⠈⢀⠁⠠⢀⡀
⠀⠀⠁⠉⣯⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠁⠁⣡⣀⣠⠚⡏⠀
⠀⠀⠀⠀⠰⠾⢿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⡛⠑⠀
⠁⢢⠄⠀⢲⡆⡇⠀⠉⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡴⠶⠶⠛⠋⠁⠀⠀⠀⠀
⣄⡈⢀⠉⠻⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⡤⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠁⠀⢠⣰⠶⡅⠀⠀⠀⠀
⣿⣿⣿⣶⡄⢸⡇⠀⠀⠛⠦⣀⠀⠀⠀⠸⠿⠞⠘⠀⠀⠀⠠⠸⠹⣹⢻⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⠶⠂⠉⡠⠗⠒⠀⠀⠠
⣿⣿⣿⡿⢁⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣯⣾⡺⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠐⠁⠀⠀⠀⠀⡀⢤⠶⠚⠁⠁⠀⠀⠀⠀⠀
⠿⠿⠋⣠⣾⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢒⠤⢀⢀⣠⠒⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣿⠟⠁⠠⠚⣿⣷⣶⣶⣶⣶⣤⡀⠀⠁⠠⣻⣿⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢦⣄⡀⠀⠀⢀⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣷⣤⣀⠈⠙⠳⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢮⣄⡀⠀⠀⠀
⣿⣷⣶⣦⣴⣿⣿⣶⣶⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣟⣊⡿⠿⣿⣿⣿⣿⣽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣧⣴⣦⠘⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣶⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⠁⣸⣿⣿⣧⠹⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⠀⣿⣿⣿⡀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣿⣿⣿⣏⠀⣿⣿⣿⣯⣤⣄⡈⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⠿⠿⠠⠈⠙⠿⣿⣿⣿⣦⠀⠀⠀⠛⠐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡀⢰⣷⣾⣷⠈⣿⣿⣿⡆⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠙⣿⣿⣿⣽⣿⣿⣿⣿⡇⣿⣿⣿⣿⣶⣾⠶⣿⣿⣿⣤⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣛⠛⠛⠛⠿⡟⢻⣿⠀⠛⢻⣿⡿⡛⠛⠀⠈⠛⢿⡿⠛⠛⠡⠐⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⣾⣿⠀⠀⢸⣿⠈⠘⠢⢀⠀⠀⠈⠌⠢⡀⠀⢡⡠⣶⣿⡛⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡆⠀⣾⣿⣶⠀⠀⠈⠑⢖⠠⠐⡂⠈⠲⠂⢃⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⠀⠀⠀⠀⠀⠑⢄⡀⠄⠀⠀⠀⠂⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣦⣄⡀⠀⠠⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠈⠁⠀⠀⠀⡈⣂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢽⣿⣿⣿⡿⣿⣧⣄⡀⠀⠀⠢⠑⠂⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⠀⠩⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠐⠄⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⠿⢿⣿⠀⠀⠀⠸⠏⣯⣿⣿⣿⣿⣿⣿⡇⠀⠠⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠻⣷⣄⠀⠀⠈⠻⣼⣽⢟⣿⣿⣽⣇⣢⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡘⢿⣷⣄⠀⠀⠈⠉⠾⡟⣹⠻⣿⣼⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⠻⣷⣦⣀⠀⠐⠤⠉⠀⠀⠁⠍⠋
⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⠿⣷⣦⣄⡀⠀⠁⠑⠒⠀
⣀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡻⠿⣿⣶⣦⣤⣤
⣿⣷⣶⣤⡀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⠟⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡉⠛⠛
⣿⣿⣿⣿⣿⣶⣄⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢩⣥⣴⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⢠⣿⣿⣿⣿⣟⣤⣝⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣷⣦⣽⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣷⡀⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣿⣿⣯⣀⡈⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⡀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣾⣿⣿⠃⠀⠈⠛⢿⣿⣿⣿
⣄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⠀⠀⠀⠀⢠⣿⣿⣿
⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡻⣧⠄⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣯⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠾⠟⠀⠀⠀⠀⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⡀⠀⠀⠀⠙⠻⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⣲⢄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣙⡯⣽⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠓⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣾⣿⣿⣫⡏⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣈⣀⣀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢛
⠀⠀⢠⣿⡿⠏⣻⣿⢿⡇⠀⣶⠆⢀⣶⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠈⠉⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠤⠼
⠀⠀⣸⣿⠇⠀⠈⠙⠻⢧⢠⣿⣠⣿⢃⠀⠀⣴⣿⣽⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣟⠉⠉⢩⣶⣶⣶⣤⣄⡀⠀⠀⠉⡓⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⣀⣰⣿⠗⠀⠀⠀⠀⠀⠀⢸⠻⡿⡱⠁⢀⣼⣿⡄⠀⠉⠳⢆⠄⡀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⡇⠑⠉⣸⣿⠑⣿⣿⣿⡿⣶⣆⡀⠀⠁⠒⠌⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠹⣁⠀⣾⣷
⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠃⠃⠀⠀⠀⠑⠢⠥⣒⠻⢿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣶⣼⡿⡏⢀⣿⣿⣿⣷⣿⣿⣷⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠏⠊⠉⢸⣿⡟
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣒⣒⣲⣶⣿⣟⡛⠍⢁⠚⠣⠾⢭⡟⠿⡊⢸⣿⣿⣿⣿⣿⣷⣿⣿⣇⡺⢿⣏⣻⢯⣿⣿⠙⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠁⣿⣿⠃
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣥⣈⣛⣛⣛⠛⠂⣀⠀⢠⣄⡀⠀⠅⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⡿⠋⢙⡻⣦⡏⢙⠻⠞⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣿⣿⣄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣯⣿⣿⣿⣟⣛⣿⣿⠿⠿⣿⣿⣿⣷⣷⣴⣁⠉⠛⢻⣿⣿⣿⣿⣿⠀⢨⣗⠀⠃⠋⠂⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠶⠶⠷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣾⢛⢱⣸⠇⣺⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⡔⠲⢀
⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⡿⠀⠸⠴⣸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⡸
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠀⠘⣋⠙⠓⠀⠀⠀⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⠁⣸⢠
⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡈⠀⠀⠀⠀⠀⢠⠆⠉⠉⠓⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠸⠻⠤⠟⣼
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡖⠀⠀⠉⠀⠀⠀⠀⠀⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢤⣤⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠯⠀⠀⠈⠉⠉⠙⠛⢻⣿⣿⣿⣇⣀⠀⠐⠒⠀⠠⠄⠀⠀⠀⡀⢛⡿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢀⠙⣙⡁⣀⡀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣶⡿⠉⢠⣔⠓⠒⠒⠀⠐⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⣭⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠿⠿⠿⢿⡿⠛⠀⠂⠀⠘⢻⣶⣶⣧⣤⢠⣭⠅⡐⠒⢲⣾⣿⣿⣿⣿⣿⣿⡿⣿⠃⠀⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠤⢤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⣤⣜⣀⣠⠤⢄⣀⣀⣤⣴⡖⠒⠂⠀⠙⠛⢿⣿⣿⣟⣪⣟⣾⣿⡵⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣄⣈⣥⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⣷⣾⣿⣿⣤⣤⣤⣀⣀⣀⡼⢿⣿⣿⣿⣭⣹⣻⣿⣿⠿⠛⠛⠿⢿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣄⠀⠀⠀⠀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣷⣾⣿⣿⣿⣬⣿⣟⣀⠀⠀⡀⢈⡻⡋⠁⠀⠈⠩⠬⠻⡋⡁⠀⠀⠀⢿
⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡟⣿⣯⣿⣿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣷⣬⣽⣓⣲⠶⠤⣤⣤⣀⡀⣴⣦⣾⣶⢸
⣿⣿⣿⣦⣠⡄⠀⠀⠉⠙⠒⠶⠦⡄⠘⣿⣿⣿⣿⣯⣭⣝⣻⣿⣿⣿⣿⣿⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⣿⣷⣶⣶⣭⣾⣿⣿⣃⣈
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠁
⣿⣿⣿⣿⡟⣥⣴⣶⣶⣶⣦⢄⡄⢰⢙⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⠋⠙⣻⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⠀⠈⠉⠀⢉⠃⠈⠅⡄⣼⣿⣿⣷⡾⠽⡻⠿⢿⣿⣿⣿⣿⠇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣦⣢⣬⣿⣿⣿⣷⣤⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⢶⣦⣤⣤⢂⣀⠀⠠⡇⣿⢟⣯⣶⡿⣿⣿⣿⣾⣵⡫⣟⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠽⣉⣽⣿⣿⣿⣿⣿⣿⣗⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⡦⣉⡿⣱⠿⢿⡏⡼⢀⢧⣿⣻⠿⣷⣶⣮⣽⣿⣿⣿⣷⡝⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡲⠦⣬⣽⣿⣿⣿⡿⡏⠯⠛⠻⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡏⠘⠿⠟⠁⠉⠀⢀⡇⢸⢸⣿⣿⣿⣷⣯⣿⣻⢿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠛⠛⠀⠴⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣟⣸⣁⠈⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⡿⢃⣠⡄⠛⠳⢤⣤⣉⠛⠿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣤⡀⠀⠀⠀⠀⠈⠢
⠉⠉⠛⠉⠟⠛⢿⣿⣿⣿⡷⢿⣛⣛⡛⠈⠛⣫⣿⣿⡿⠟⣻⣿⣿⣟⣽⣿⣦⣴⡄⠀⠀⢹⣿⣦⣾⣥⣤⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣴⣶⣶⣶⣤⡉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⠁⣼⣿⠃⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⢠⡀⣀⡀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠠⣿⣿⣿⡇⠀⠀⣸⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⡟⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠉⠳⣄⠀⠀⠁⠋⠑⠀⢀⣀⣀⣀⣀⣀⡀⣠⣾⣿⣷⣶⡤⠀⠀⠀⠀⠁⣿⣿⣿⡇⠀⠈⣻⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃⡘⠿⡛⠀⠀⠀⠀⠀⠀⠀
⣦⣄⡈⢳⡀⠀⠀⡀⠰⢿⡿⠿⠛⠻⠿⣿⣿⣿⣿⣿⣯⡖⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠘⢿⡿⠰⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⡹⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠉⠋⠀⠠⡄⢰⣶⢧⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠇⣿⣿⡅⠀⠀⠐⠘⠈⢁⠁⠀
⡉⠙⠛⠈⠀⣹⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⢁⢁⠁⡀⠀⣀
⠃⠀⠀⠁⠚⣯⣿⣿⣿⣿⣷⡤⠀⢠⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠂⠀⠀⠈⠈⠠⠄⣤⣸⣿
⠀⠉⠉⠁⠉⢹⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠋
⠐⠤⣠⡄⠀⣮⡍⡛⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡵⠶⠟⠋⠉⠀⠀⠀
⣦⡂⠘⠁⠒⢿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⡔⢲⠀⠀⠀⠀
⣿⣿⣷⣶⣦⣄⢰⡇⠀⠀⠳⢤⠀⠀⠀⠀⣤⣴⠖⠲⠑⠂⠀⠠⠸⡹⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⢿⠷⠆⠁⢠⠔⠞⠃⠀
⣿⣿⣿⣿⣿⠇⣾⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣧⣧⣼⣸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀⠠⡴⠞⠉⠀⠀⠀⠀⠀
⣿⣿⣿⠟⢃⣼⠇⠀⠀⠐⠀⠀⠀⠁⠀⠠⠀⠤⣦⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣤⣴⡿⠋⠀⢴⣶⣦⣴⣶⣤⣤⣄⠀⠀⠈⠐⣾⣷⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢤⣀⠀⠠⠀⡀⠀⠀
⠛⠛⠛⠉⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣶⣄⡀⠈⠛⢿⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀
⣿⣶⣶⣤⣄⣠⣶⣶⣦⣤⣄⣀⣹⣿⣿⣿⣿⣿⣿⣷⣤⡀⠈⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣷⡍⠿⠿⣿⣿⣿⣿⣯⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⣤⣶⡌⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠔⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣶⣾⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⢁⣴⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⡙⢻⣿⣿⣷⣶⣿⣿⣿⣏⣩⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⡄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢻⣿⣿⣏⠛⣿⣿⣿⣿⣿⡏⠈⢿⣿⣿⣷⣬⡓⠢⠀⠀⠉⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⣿⣿⡿⠿⢇⠴⠏⠙⢿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⡇⢠⡟⢰⣶⣷⣿⡈⣿⣿⣿⣆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣷⣿⣷⠈⣿⣿⣿⣵⣿⣿⣿⠉⡂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠈⠛⠿⣿⡇⣿⣿⠛⠛⢻⣿⠛⠀⠈⠙⠛⠟⠻⡋⠁⠀⠘⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠁⣿⡇⠀⠀⣽⡿⠀⠀⠑⢄⠀⠀⠀⠈⠢⡈⠀⠰⡀⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣇⣶⣶⣿⠇⠀⠀⠀⠈⠁⢐⠀⢄⣀⠈⠲⡐⢳⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⡈⠄⠁⠈⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣤⡀⠀⠒⠒⠔⠀⠀⠀⢀⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠉⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⢤⡀⠀⠀⠀⢈⠐⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡀⠀⠀⠺⡿⣻⣿⣾⣿⣿⣿⣦⣄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠿⠿⠿⣿⣄⠀⠀⠘⠏⣽⡿⣿⣿⣿⣿⣿⣷⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠘⢿⣧⡀⠀⠀⠙⢸⣿⢟⣻⣿⣹⣛⣠⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⢿⣦⡀⠀⠀⠈⠪⠽⡨⠛⢿⡏⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⢿⣷⣄⡀⠀⠢⠌⠀⠀⠀⠈
⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡻⢿⣶⣤⣀⠀⠀⠁⠐
⣤⠄⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⠿⣿⣶⣦⣤
⣿⣿⣶⣤⣄⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⢆⣀⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡿⠋⠀⣠⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣉⠛
⣿⣿⣿⣿⣿⣿⣦⣄⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢰⣷⣾⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⢿⣿⣿⣿⣿⣶⣤⣬⡝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣷⡏⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⠡⢀⣠⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣯⠀⣀⣸⡿⠛⠻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣾⣿⣿⠁⠀⠀⠀⠙⣿⣿⣿
⣦⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⢠⣿⣿⣿
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢿⣵⣧⣤⣀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣷⣬⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠘⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣟⡿⢿⣿⣿⣷⣠⡄⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣓⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⢿⣿⣿⣾⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⣻
⠀⠀⣸⣿⠛⠪⢿⣿⣽⠀⢸⣽⠀⣴⡗⠀⠀⢀⢤⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠿
⠀⢠⣿⡿⠄⠀⠀⠈⠙⠇⣸⣇⣾⢟⡄⠀⢠⡿⠷⢏⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⠀⣄⢰⢶⣶⣶⣦⣄⡀⠀⠀⠍⡚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⢤⣿⣟⠁⠈⠀⠀⠀⠀⠀⠟⠹⠏⠊⠀⢠⣿⣷⠄⠀⠈⠛⢔⠠⢀⠀⢠⣿⣿⣿⣿⣿⣿⡿⢥⣿⣿⣿⣿⡘⠑⠈⣿⡿⣏⣿⣿⣿⣇⣿⣆⡄⠀⠉⠒⠌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢏⡀⢠⣿⣶
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠂⠀⠀⠀⢉⣒⡠⢜⡛⠿⣿⣿⣿⣿⠙⢸⣿⣿⣿⣿⣿⠷⣾⡟⡅⢰⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡻⠻⠊⠁⣾⣿⢟
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⠭⣭⣿⣿⣦⡤⠬⠫⠌⠁⠛⠰⠯⠙⠻⢐⣾⣿⣿⣿⣿⣿⣿⣿⣷⣒⣺⠿⣨⣛⣿⣿⡿⠈⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢠⣿⡟⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣬⣭⣍⣉⣚⣀⣄⡀⣴⣦⠀⢀⠀⡀⠄⢈⣙⣛⣿⣿⣿⣿⣿⡛⠀⣉⠳⢶⠉⡝⠻⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⣇⣣
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣟⣛⣻⣿⡟⣿⣿⣾⣷⣬⣌⡩⠙⣿⣿⣿⣿⣿⡇⠀⣸⣏⠀⠀⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠠⠶⠾⢾
⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⣿⠹⡸⣾⠀⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⠒⠆⢠
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⡇⠀⢷⡆⣷⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣴⣄⡞
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠙⢉⡙⠃⠀⠀⢰⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣸⡧⢈⡏⣸
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⠀⠀⠀⠀⠊⡀⠈⠉⠙⠲⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠟⠧⠼⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⠆⠀⠀⠉⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣤⣼⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠛⠁⠀⠈⠉⠉⠙⠛⢻⣿⣿⣿⣀⡀⠀⠒⠂⢀⠤⠄⠀⠀⢀⠘⣻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣀⢃⣙⡀⢀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣶⡏⠉⣥⣚⠚⠀⠒⠦⠺⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠛⠋⠛⠛⠛⠻⠿⠿⡟⠃⠀⠃⠀⡛⢺⣶⣶⣧⣤⣠⣩⢁⡐⠒⣲⣿⣿⣿⣿⣿⣿⣿⢿⡿⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣶⣶⣤⣵⣒⣒⡤⠤⣤⣠⣬⣿⠆⠒⠒⠀⠛⠛⣿⣿⣿⣓⣻⣃⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢀⣀⣩⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣷⣶⣾⣿⣥⣤⣤⣄⣀⣀⡿⣿⣿⣿⣿⣽⣟⣿⣿⣿⠟⠛⠻⠿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣧⡀⠀⠀⠀⢀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣶⣤⣤⣀⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣋⡀⠀⢀⠀⣉⣻⠋⠁⠀⠙⠭⠝⢟⣉⠀⠀⠀⠸⣿
⣿⣧⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣧⣽⣟⣒⡶⠦⠤⣤⣄⣀⢀⣶⣴⣷⡖⣿
⣿⣿⣿⣤⣆⠀⠀⠀⠈⠉⠛⠓⢶⠂⣾⣿⣿⣿⣿⣴⣯⣭⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣸⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⣿⣶⣶⣮⣽⣿⣿⣻⣀⣙
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠂⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣽⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿
⣿⣿⣿⡟⠸⠰⣶⡶⢶⣶⡖⣠⡄⡌⣽⣟⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⠛⠛⢻⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⠷⠀⠀⠀⠀⠀⡐⠁⠀⢠⠆⣿⣿⣿⣿⡷⠯⣟⡿⠿⢿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣧⣀⣈⣿⣿⣿⣏⣤⠤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠺⣶⣶⣦⢄⣄⣀⡀⡸⢸⣿⡿⣫⣷⠿⣿⣿⣿⣷⣯⣞⢽⡓⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢫⡙⣛⣻⣿⣿⣿⣿⣿⣿⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣶⣶⣷⢆⣽⢏⣞⡿⢿⢁⡏⢸⡞⣬⣟⣿⢿⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⢉⣻⣿⣿⣿⣿⡿⡻⠟⠻⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠙⠛⢁⡈⠁⠀⢸⠁⣾⡿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⠀⠀⠀⢨⢿⣿⣿⣿⣿⣿⣿⣿⣟⠾⠿⠿⠉⠉⠉⠀⠀⠀⠀⠀⠙⠛⠃⢠⠆⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣇⣀⣸⣷⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⡛⢀⣠⣤⠚⠛⢤⣤⣉⡙⠻⣿⣿⣿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣤⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠉⠛⠛⠛⠿⣿⣿⣿⠿⢾⣛⣋⣙⠃⠛⢻⣽⣿⣿⠿⢛⣿⣿⣟⣫⣿⣧⣤⡆⠀⠀⢨⣿⣶⣶⣯⣤⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣴⣶⣶⣶⣤⡉⠛⠟⠻⠿⣿⣿⣿⣿⣿⡏⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀
⣄⡀⠀⠀⢠⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⣿⣿⣿⡇⠀⠀⣸⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠀⠀⠈⢻⣿⣿⣿⠃⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠈⠙⢦⡀⠀⠈⠉⠑⡀⠀⣀⣀⣀⣀⣀⡀⢀⣴⣿⣷⣶⣤⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⢻⣿⡿⢀⡻⠟⡟⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣀⠹⣄⠀⠀⠀⢀⢾⣿⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿⡵⠃⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢼⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢻⡇⢾⣿⡧⠂⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣷⡘⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠋⠛⠁⠀⡆⢀⣖⣾⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣧⡄⠀⠀⠀⠂⠂⠂⠈⣀
⡛⠉⠛⠂⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠃⠀⠀⠐⠐⠈⢈⠁⠠
⠉⠀⠀⠀⠘⢳⠿⣶⣶⣶⣤⡤⠄⠀⣄⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠒⠀⠀⠀⠃⠁⣁⣀⣠⣾
⠀⠒⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣶⠀⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⡛
⠀⢄⣀⡀⢀⢐⡶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠰⠲⠶⠞⠋⠁⠀⠀
⣠⡀⠊⠂⢔⠳⠇⡇⠈⠛⠛⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣦⣄⢀⡇⠀⠀⠲⢦⠀⠀⠀⠀⠀⢀⣀⣠⡤⠐⠀⠀⢀⡏⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⠮⠀⢁⣠⠖⠖⠀
⣿⣿⣿⣿⣿⠏⣸⠃⠀⠀⠀⠀⠈⠁⠀⠀⠉⢛⣅⠀⠀⠐⠀⠀⣠⣶⣼⣡⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⠴⠞⠉⠀⠀⠀⠀
⡻⣿⣿⠿⠋⣴⠏⠀⠀⠐⠂⠀⠀⠈⠀⠠⠀⠠⣤⣄⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣈⣀⣴⡾⠋⠀⢰⣶⣶⣤⣤⣤⣤⣄⠀⠈⠀⠁⡤⣷⣶⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀
⠿⠟⠛⠉⠀⠀⠀⠀⠉⠙⠿⠿⣿⣿⣿⣿⣶⣄⡀⠈⠙⠿⣭⡃⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣾⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣀⠀⠀
⣿⣶⣦⣤⣀⣀⣲⣦⣤⣄⣀⣀⣻⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠁⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣲⡭⡹⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯⣠⣤⠹⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡏⢰⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠋⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⡈⢻⣿⣿⣇⣴⣿⣿⣿⡟⢉⣥⣾⣿⣿⣿⠉⣿⣿⣿⠀⢀⡀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢻⣿⣿⣇⠛⣿⣿⣿⣷⣿⡟⠋⢿⣿⣿⣷⣤⣑⠪⣀⠀⠈⠂⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣿⡿⠿⠇⠀⢾⠙⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⢳⣿⣶⣾⠈⣿⣿⣿⡆⢢⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣾⣿⠀⣿⣿⣿⣤⣿⣿⣿⠁⠀⠣⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠈⠛⠻⣿⣿⢠⣿⡟⠛⠛⣿⡟⠈⠊⠙⠛⠿⠛⠻⡃⠀⠀⠈⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠉⢸⣿⠇⠀⠀⣿⡇⠐⠠⠁⣠⠀⠀⠀⠈⠢⡀⠀⠔⣠⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣶⣶⡿⠀⠀⠀⠀⠀⠙⢝⠡⢈⡀⠘⠖⠀⢋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⡀⠀⠀⠀⠀⠀⠑⢀⠀⠃⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣶⣤⡀⠀⠁⠐⠠⠀⠀⠒⠀⢀⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣵⣦⣄⡀⠀⠀⠀⠀⠘⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠻⣿⣿⣿⣿⡿⣤⣂⠀⠀⠀⠈⠐⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⠿⢿⣦⠀⠀⠈⠱⢿⢟⣾⣿⣿⣿⣿⣿⢰⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⠻⣷⣄⠀⠀⠈⠸⡿⢋⣿⡿⣽⣽⢸⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠙⢿⣷⣄⠀⠀⠀⠛⠏⡞⠚⠿⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⢿⣷⣤⡀⠀⠀⢌⣐⠀⠀⠀
⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⢿⣷⣤⣀⠀⠈⠀⠂
⣄⢀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠟⠁⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⠿⣿⣶⣦⣤
⣹⣿⣶⣦⣄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢙⣭⣭⣶⣷⣦⣄⠀⠀⠀⠀⠀⠀⠉⠙⠿⠟⠁⠀⢰⣿⣿⣿⣿⣿⣪⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡙⠛
⣿⣿⣿⣿⣿⣷⣶⣄⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣷⣮⡌⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⡇⣀⠀⢹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣿⣿⡁⠀⠈⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡿⠁⠀⠈⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⢀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣦⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⡿⡿⢃⡀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣇⣶⢿⣿⣷⢦⠤⠀⠀⠀⠀⠈⠙⠿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣤⡏⣯⣯⣷⣶⣦⡠⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣽⣿⣿⣿⣿⣧⠣⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣻⣿⣿⣿⣿⣿⣿⣿⢛⣛⣛⣛⣛⣛⣛⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣧⣿⣿⡟⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⡟⢻⣿⣷⡇⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠠⠤⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣽
⠀⢀⣿⡟⠉⠐⠿⣧⣧⠀⣿⡇⣰⡿⠃⠀⠀⣴⣆⡴⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⡷⠤⠀⠀⠀⠀⠀⠈⠉⠉⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠒⠒⠛
⢀⣼⣿⠓⡄⠀⠀⠀⠉⠂⣿⣷⡿⡱⠁⢀⣾⡛⠛⠶⣄⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏⢿⣿⣿⣿⣿⢇⡀⠤⣞⣿⣿⣿⣶⣤⡄⡀⠐⠀⠉⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⠀
⣾⡿⠇⠀⠀⠀⠀⠀⠀⠐⠁⠙⠘⠀⠀⢾⡿⣷⢠⠀⠀⠙⠣⡒⠄⢀⣸⣿⣿⣿⣿⣿⣿⢛⢸⣿⣿⣿⣿⣀⠀⣀⣿⡇⢹⣿⣿⣿⢳⣿⡧⠂⠀⠈⠑⠢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢣⡀⢰⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⣀⡀⠀⠠⢭⡖⣨⣝⣻⠿⣿⣿⡏⠀⣾⣿⣿⣿⣿⣿⣿⣿⡽⠠⣼⣿⢿⣿⣾⣿⣿⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡝⠙⠃⠀⣿⣿⢫
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠶⠦⣶⠲⣾⣿⣿⣷⣖⠊⠒⠀⠈⠋⠚⢊⠉⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⡻⢤⣟⣾⣿⡇⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢰⣿⡟⠀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣶⣤⣭⣭⣴⣄⣀⣾⣦⣀⡠⢀⡀⠠⢠⣭⣽⣿⣿⣿⣿⣯⡍⠀⣬⠹⢻⢀⡌⠛⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠿⢿⣧⣴
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣭⣽⣿⣟⣹⣿⣿⣿⣷⣷⣤⣂⣉⣿⣿⣿⣿⣿⡇⡀⣾⣇⠀⣈⠈⣀⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠰⠛⠛⠶
⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⡿⠄⣇⡟⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⠐⠃⣰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢛⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⣿⣿⣿⠃⠀⠠⢢⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠨⠄⠉⠁⠀⢀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⡌⢠⡏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⡄⠀⠀⢠⡆⠀⠀⠉⠃⡛⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠜⢡⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠹⠛⢻⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⢤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣼⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠉⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣯⣀⣀⣀⣀⠐⠒⡀⡬⠀⠄⢀⣘⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⡈⠉⣉⠠⠀⢀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠂⠉⣭⡌⠉⠒⠃⠓⠻⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠉⠙⠉⠉⠛⠛⠛⠻⠿⠋⠁⠈⠀⢀⡉⣿⣿⣾⣶⣆⣶⣆⣁⡉⠙⣿⣿⣿⣿⣿⣿⣟⣿⠿⠏⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⢿⣶⣾⣥⣴⣒⣒⡦⠤⣴⣶⣿⣍⠁⠀⠀⠛⢛⣿⣿⣯⣭⣺⣼⣿⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣷⣶⣤⣤⣤⣤⣴⣿⡿⢿⣾⣿⣭⣽⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⡇⠀⣿⣿⣿⣿⣧⠀⠀⠀⢀⣀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣇⣀⠀⠄⢀⣍⡙⠉⠀⠈⠒⠠⠭⠏⠁⡀⠀⠀⠺⣿
⣿⣦⡀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣽⣿⣒⣒⡶⠦⢤⣤⣀⣰⣧⣼⣵⠆⣿
⣿⣿⣿⣶⢰⠀⠀⠀⠀⠉⠉⠛⡓⢰⣾⣿⣿⣿⣿⣶⣶⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣶⣶⣿⣿⣿⣯⣀⣙
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠔⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠟
⣿⣿⣿⠃⠛⠗⢾⡿⠿⢿⢯⠦⢠⢲⣿⣽⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⡿⠛⠿⣿⣿⣿⣿⡖⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠇⡀⠀⠀⠀⠀⠊⠀⠀⣸⢸⣿⣿⣿⣿⣿⠶⣯⣛⡿⠿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣧⡠⣈⣹⣿⣿⡿⣁⡠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⢿⣶⡶⣡⣤⣄⢀⡃⡾⣿⣿⢿⣽⡾⢿⣿⣿⣿⣷⣵⡪⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡏⡟⠛⢿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣠⣾⡵⣟⡻⠟⢸⠁⣿⣷⣲⣽⣻⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣙⣛⣿⣿⣿⣿⣿⢛⡻⠗⢿⣿⣿⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣇⣀⣙⣋⣄⣀⣀⠀⡏⢠⣿⣿⣿⣿⣿⣿⣷⣯⣿⣻⢿⣿⡟⠀⠀⠀⣜⡝⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠿⠟⠛⠋⠉⠈⠀⠀⠀⠘⠛⠛⠀⡤⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣛⣿⣿⣿⣯⣿⣿⣿⣿⣼⣂⣀⣾⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣾⡅⠀⣀⣤⡔⠛⠣⣤⣌⡉⠛⢿⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣦⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠙⠛⠛⠻⢿⣿⣿⠿⠿⣟⣋⣉⡛⠘⢛⣿⣿⣿⡿⠟⣻⣿⣿⣛⣿⣿⣤⡄⠀⠀⢠⣽⣷⣶⣾⣥⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣴⣶⣶⣶⣤⡈⠙⠻⠿⠿⢿⣿⣿⣿⣿⡇⢰⣿⡋⠀⠀⠀⠀⠀⠀⠀
⣦⡀⠀⠀⠀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⠡⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢷⡄⠀⠀⠈⠉⠀⠀⣀⣀⣀⣀⣀⣀⠀⣠⣾⣿⣶⣦⡄⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠈⢿⡇⣘⡻⠿⠃⠀⠀⠀⠀⠀⠀⢠
⣶⣤⣀⠙⢦⠀⠀⢀⠀⡺⣿⡿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣯⠞⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠾
⣿⣿⣿⣿⢌⢧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠙⠃⠀⢠⠀⣴⡶⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠄⠆⠒⠘
⣉⡋⠛⠓⠁⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠰⠐⠐⠀⠁
⠊⠀⠀⠈⠐⠛⣸⣄⣀⡀⡄⠤⠠⠀⣀⡀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠃⢁⣈⣀
⠀⠀⠄⠀⠀⢀⣭⣽⣿⣿⣿⣿⡔⠄⠛⠛⠒⠤⠠⠜⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣀⣉
⠀⢄⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠆⠀⠀⢐⣤⡴⠶⠛⠉⠁
⣤⣀⠱⠁⡐⠲⡟⢛⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣾⣮⡢⠀⣾⠀⠀⠈⠭⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡤⠀⠀⡠⡴⠶
⣿⣿⣿⣿⣿⡷⢰⡇⠀⠀⠀⠀⠈⠀⠀⠀⢠⣤⣲⢘⠉⠸⠂⠀⢀⣴⣤⣏⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣤⠖⠛⠀⠀⠀
⢿⠿⡿⡿⠟⣠⡟⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠠⢵⣆⠄⠀⠀⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠑⠉⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣠⣾⠟⠀⢠⣶⣶⣤⣤⣤⣤⣤⡀⠀⠐⠁⣠⢰⣦⡆⢠⢸⣿⣿⣿⣿⣿⣿⣿⣯⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⣄⡀⠀⠀⠀⠀⠀
⠿⠿⠟⠋⠁⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣶⣤⡀⠀⠙⠿⡯⣹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢮⣄⡀⠀
⣿⣶⣦⣤⣀⣀⣰⡦⢤⣤⣀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠈⠙⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣯⢝⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⢿⣿⣿⣿⣃⣤⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣆⢹⣿⣿⡟⢀⣿⣿⣿⣿⡿⠋⣸⣿⣿⣿⠿⣿⣿⣿⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢻⣿⣿⣷⡈⣿⣿⣿⣧⣤⣾⡿⢿⣿⣿⣷⣤⡀⠲⢆⠈⠈⠑⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⣿⣿⣿⣿⣿⠏⠀⢈⡽⡿⣿⣿⣿⣦⠀⠂⢀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣰⣿⣷⣾⠊⣿⣿⣿⡆⠀⠁⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣾⣿⣿⣿⣿⠿⣿⣿⣿⣷⣶⣶⡟⣿⣿⣿⣤⣿⣿⣿⠃⠀⠀⠐⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠈⠛⠻⣿⣿⣿⢻⣿⡟⠛⠛⣿⡇⠈⠙⡟⠻⠛⠛⠙⣦⠀⠀⠀⢊⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠉⠋⢸⣿⠀⠀⢸⣿⠀⠁⠒⠨⣢⣀⠀⠀⢠⠣⡀⠂⠈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⢸⣿⣶⣶⢸⡏⡀⠀⠀⠀⠀⠈⢝⠢⢀⠖⠘⢄⠀⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⠐⠀⠀⠀⠠⢀⠀⠀⠀⠁⡀⠙⡐⠀⠑⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠀⢲⣤⡀⠀⠀⠈⠘⠁⠀⠐⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣷⣦⣄⠀⠀⠀⠈⠐⠀⠸⠛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣾⣦⣢⣀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⢿⣾⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠿⠻⣷⡄⠀⠀⠘⠿⣿⣿⣿⡿⣿⣿⣷⢲⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⣿⣦⠀⠀⠀⠻⠝⣩⣿⣿⣿⣿⢹⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠻⣷⣄⠀⠀⠀⠙⢡⣍⠻⠿⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠻⣷⣦⡀⠀⠀⠀⡀⡀⠀⠀
⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⢿⣷⣤⣀⠈⠁⠐⠀
⣶⣄⡀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢆⣀⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠏⠀⣰⣾⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⠿⣿⣶⣤⣀
⣿⣿⣷⣷⣄⡀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣷⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠰⢿⣿⣿⣿⣷⣾⣧⣉⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡛⠻
⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⡦⡀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣤⣀⣼⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣡⢀⣦⣿⠏⠙⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠏⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⣶⣄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣤⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡻⣭⣾⣧⣤⡀⣀⠀⠀⠀⠉⠻⢿⣿⣿⣄⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣮⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣼⠫⣻⣿⣷⣷⣢⡀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣾⣟⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⢹⠁⢀⣀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣹⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡟⣿⣿⣾⡄⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠠⠴⠤⠤⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣩⣯
⠀⢸⣿⠋⠁⠺⢿⣵⡇⢰⣿⢀⣼⡟⠀⠀⢀⣶⢠⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢦⠀⠀⠀⠀⠀⠀⠉⠉⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠒⠒⠓⠊
⢠⣿⣟⠢⠀⠀⠀⠈⠙⢸⣿⣾⢏⠄⠀⣠⣟⠛⠻⢤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡧⡀⣢⢸⣻⣿⣿⣷⣦⣄⠀⠀⠂⠍⡛⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⠿⠀⠀⠀⠀⠀⠀⠀⠘⠈⠋⠃⠀⠰⣿⢿⡆⡄⠀⠈⠛⢔⠢⠀⣀⣿⣿⣿⣿⣿⣿⡿⣏⣿⣿⣿⣿⣆⡈⢀⣾⡿⠀⣿⣿⣿⣏⣿⣧⠄⠀⠀⠉⠒⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⢣⡄⢠⣿⣿⠿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣀⣀⠀⠀⢬⣵⢂⣭⣛⡿⢿⣿⣿⢗⢼⣿⣿⣿⣿⣿⣿⣿⣏⠇⢠⣿⣿⣿⣽⣿⣿⢧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡏⠙⠃⠀⣾⣿⢯⢩
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠶⠖⠾⣿⣿⣿⣶⠒⠑⠂⠀⠙⠑⠓⡉⠙⠨⢼⣿⣿⣿⣿⣿⣿⣿⣿⡯⣽⣟⠦⣭⣿⣿⢿⠈⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢠⣿⡿⠀⣸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣬⣭⣥⣤⣄⣰⣷⣄⣀⢄⡄⠂⠀⣬⣭⣿⣿⣿⣿⣿⣍⠁⢠⣝⠷⡅⣬⠙⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠼⠿⢧⢧⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣏⣿⣿⣿⣿⣾⣦⣔⣈⣹⣿⣿⣿⣿⣯⢀⣸⣯⢀⢀⡁⣀⣀⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠐⠛⠛⠷⠎
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠡⠸⣾⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣴⡇⠎⢰⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠿⢿⣿⣿⡏⠀⡁⡄⣶⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣶⣦⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠠⠈⢁⠀⢀⣀⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⡏⣹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠶⠶⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⣴⠀⠀⠀⠙⠉⣛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠘⢁⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣘⢿⡟⠋⠁⠀⠀⠀⠀⠉⠉⣹⣿⣿⣿⣤⣄⣀⢉⣀⡰⠒⢈⠀⠀⠀⡈⢹⣟⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⡀⠀⢀⣠⠭⠭⡤⠤⠄⣀⡀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣮⣭⠁⠀⠙⠃⠛⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢉⠉⠉⠉⠉⠙⠛⠛⣏⠁⠀⠁⠀⣌⣹⣿⣿⣷⣶⣰⣶⢀⣈⠉⣹⣿⣿⣿⣿⣯⣿⣿⡿⠿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⠿⢿⣶⣾⣭⣭⣗⣒⣦⠤⣷⣿⡿⠉⠁⠀⠉⠉⣿⣿⣿⣯⣵⣧⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣤⣴⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⢿⣿⣶⣶⣶⣤⣤⣤⣟⣻⣿⢿⣿⣿⣯⣿⣿⣿⠋⠉⠛⠛⣻⣿⣿⡟⠀⣼⣿⣿⣿⣿⠄⠀⡀⠀⣠⣴
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀⣠⠄⣄⣭⠁⠀⠀⠐⠒⠊⠹⠤⠀⠀⠀⠘⣿⣿
⣿⣤⡀⠀⠀⠀⠠⢤⣄⣀⡀⠀⠀⠐⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣷⣾⣯⣭⣟⣓⣲⠶⠤⣄⣠⣷⣾⣿⡏⢿⣿
⣿⣿⣿⡆⡆⠀⠀⠀⠀⠈⠉⢛⠃⣦⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⠿⣿⣷⣶⣿⣿⣽⣤⣌⣛
⣿⣿⣿⣿⠁⠀⠀⡀⠀⠀⠠⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠹
⣿⣿⣿⠘⠛⠿⠟⠺⠿⡟⠵⠆⡔⣶⣿⣭⣿⣛⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢻⠿⠿⢿⣿⣿⣿⣿⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⢠⡀⠀⠀⠀⠐⠀⠀⢠⡇⣿⣿⣿⣿⣿⣿⣿⣾⠽⠻⠿⢿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣇⠀⣙⣿⣿⣿⣿⢝⣀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⢀⡘⠿⢿⣿⢎⣶⣤⡄⣨⢀⣻⢿⣿⣿⢟⡩⠶⣿⣿⣿⣿⣾⡕⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡏⡛⢛⣿⣿⣿⣿⣿⣿⣿⡭⣺⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣣⣶⡧⢮⡝⠛⢁⡏⢸⣿⣿⣷⢣⣟⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⠤⠍⣛⣾⣿⣿⣿⣿⠿⣟⠷⠼⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣄⣈⣋⣡⣤⣀⡀⢸⠃⠸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⡿⣿⠃⠀⠀⢠⣷⣕⡽⣿⣿⣿⣿⣿⣿⣿⠾⠿⠟⠉⠉⠋⠋⠁⠀⠀⠀⠀⠻⠿⠇⢠⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣀⣠⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣘⣭⡕⠛⢧⣤⣉⡙⠻⢿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣻⣿⡾⣟⣛⣛⠛⠙⢛⣭⣿⣿⡿⠟⣻⣿⣿⣿⣿⣷⡆⠀⠀⢤⣭⣿⣶⣶⣯⢠⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣴⣶⣶⣶⣤⡀⠉⠛⠿⠿⠿⣿⣿⣿⡟⢠⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀
⢶⣄⡀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠉⠀⠈⠉⠛⠀⣿⣿⣿⡿⠄⠀⢸⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⠇⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠛⢦⡀⠀⠀⠘⠋⠂⠀⠀⠀⡀⠀⢀⠀⠀⣠⣾⣷⣶⣤⡄⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⢠⣙⡛⠏⠀⠀⠀⠀⠀⠀⠀⣼
⣷⣦⣄⡀⠹⣄⠀⠀⠀⠀⢶⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣏⡄⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁⠀⠀⠀⠀⠀⠀⢰⣿
⣿⣿⣿⣿⣷⡘⣆⠀⠀⠉⠀⠈⠀⠀⠀⠀⠈⠙⠛⠿⠿⠛⠋⠀⡀⠀⣄⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠠⠠
⡿⣋⠛⠻⠯⠍⠘⡆⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠆
⠟⠮⠀⠀⠀⠐⠖⢹⡀⠀⠠⢄⣀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠐⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣧⣀⡀⣴⣷⢦⡄⠿⠗⠂⠄⣀⣠⡶⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠐⠲⠟⠉
⠀⠀⠀⠁⡐⠀⢤⣬⣽⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠆⠁⠀⠀⠤⣤⣤⠶⠛
⣿⡖⠀⠤⠈⠀⢰⡳⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢋⠀⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀
⣿⣿⣿⣶⣶⣤⡉⠙⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⣤⣤⡤⠀⠀⣠
⣿⣿⣿⣿⣿⣿⠛⢰⠇⠀⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⣠⣎⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⡠⠴⠈⠀
⢿⢿⣿⣿⣿⠟⣠⡟⠀⠀⠀⠤⠀⠀⠐⠀⠀⡀⢰⣾⣿⡇⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⣇⡟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠍⠋⠀⠀⠀⠀
⠈⠀⠈⠉⣀⣴⠟⠀⢠⣦⣤⣤⣤⣤⣀⣀⠀⠁⠊⠋⢍⡢⣶⡆⢠⢸⣿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⠀
⢿⣿⣿⠿⠟⠁⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠈⠺⢿⣗⣸⢸⣿⣿⣿⣿⣿⣿⣷⣭⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣂⠀
⣷⣶⣤⣄⣀⡀⠀⠀⢀⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠉⠻⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡻⣭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣽⣿⣿⣿⣿⡟⢉⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣠⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⡇⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⠿⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡇⣸⣿⣿⣿⣧⣿⡏⢈⣿⣿⣿⣿⣭⡀⢀⠠⣄⠀⠀⡢⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢿⣷⣿⡟⠛⠿⣿⣿⣿⣦⢢⠀⠉⠂⠘⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⢻⣶⣶⣾⠉⣿⣿⣿⡇⢂⡄⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣧⣿⣿⣿⠛⢎⢧⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠈⠙⠻⢿⣿⣶⣿⡟⢻⣿⡟⠛⢀⣾⠛⠟⠛⠿⡟⠁⠀⠀⠹⡄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠈⠙⠻⡇⣾⣿⠀⠀⣸⡟⠀⠀⠈⠰⠼⢦⡀⠀⠀⠝⢌⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⣶⣿⣿⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈⠣⠢⠀⢲⠨⢦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠁⠐⠐⠄⣀⠀⠀⠑⡀⠁⠂⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⠀⠀⠀⠀⠀⠁⠩⠀⠈⠤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠁⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢻⠿⣿⣿⣷⣢⣂⠒⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⡄⠀⠀⠻⣿⣿⣿⣿⣷⣿⣦⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⡹⣿⣆⠀⠀⠙⢛⣿⣿⣿⣿⣿⣽⣦⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⢿⣧⡀⠀⠀⠛⣫⠿⡟⣫⣾⡏⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠻⣿⣄⠀⠀⠈⠁⢼⢛⡟⠿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠻⣷⣄⡀⠀⠀⢈⡢⠀⠀
⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⣿⣦⣄⠀⠉⠰⢌
⣶⣄⣀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣃⣤⣄⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠃⠀⣴⣿⣿⣿⡏⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⠻⢿⣶⣄⡀
⣿⣿⣿⣷⣤⣀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⣨⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣦⣴⣍⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡻⠿
⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣶⣤⣼⡟⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣆⣾⣶⣿⠃⠈⠙⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⣷⣦⡀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣻⣳⡄⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣶⠄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⠎⢸⡦⠤⡀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣷⣮⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣮⡈⢙⠻⠞⡁⢠⣀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣽⣾⣭⣻⣿⣷⣦⠄⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⡋⣢⠀⣠⣄⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣓⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⢿⣿⣿⣼⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣄⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⢿⡛
⠀⣼⣿⠛⠪⢿⣿⣽⠀⢸⣾⢀⣼⡗⠀⠀⢠⢤⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠤⠼⠷⠥
⢠⣿⡿⠄⠀⠀⠈⠙⠇⣸⣇⣾⢏⠄⠀⣰⡿⠷⢧⣀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣏⣧⣿⣿⣿⣿⣃⠁⡀⡾⣶⢶⣶⣦⣄⡀⠀⠠⢉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀
⣿⣟⠁⠈⠀⠀⠀⠀⠀⠏⠹⠃⠋⠀⢰⡿⣷⢄⠀⠈⠓⢔⠢⢀⠀⢸⣿⣿⣿⣿⣿⣿⠻⢸⣿⣿⣿⣿⠀⠁⢠⣿⡏⢹⣿⣿⣿⢻⣿⣀⠀⠀⠑⠂⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠸⣁⠀⣾⣷⣶⣶
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⢀⡀⢈⣒⣢⠍⣛⠿⣿⣿⣿⣿⠣⣾⣿⣿⣿⣿⣿⢷⣾⢻⠀⣸⣿⢿⣿⣿⣿⣷⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠍⠟⠉⢲⣿⡿⡟⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣤⣤⣬⠮⣭⣽⣿⣿⠿⠓⠈⠌⠉⠚⠃⠾⠙⠣⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣛⠿⣭⣽⣟⣿⡇⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣼⣿⠃⢀⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣬⣭⣭⣉⣈⣀⣀⣶⣦⣀⣐⢀⠀⢄⢈⣉⣛⣻⣿⣿⣿⣟⡛⠀⣭⢻⢞⠨⡝⠛⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠰⣿⣿⣜⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⣯⣭⣿⣿⣟⣛⣻⣿⣿⣿⣷⣦⣄⣈⡩⣿⣿⣿⣿⣿⡇⡀⣿⡅⠈⣈⠁⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠶⠲⠷⢾⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⡟⠃⣧⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⡷⠰⢀⣄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠿⢿⣿⣿⣿⠁⠀⢠⢰⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⣷⣦⡼⢧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡃⠀⠩⠄⠉⠀⠀⢠⣸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣿⠆⣸⢃⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⠀⠀⠀⢰⡆⠀⠀⠉⠚⢛⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⠏⣸⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠢⣤⣯⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣤⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⠋⠁⠀⠀⠀⠀⠉⠉⢩⣿⣿⣿⣧⣀⣀⣀⣀⠐⠒⠀⢄⠀⠀⠀⠙⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⣀⡨⠉⣉⠤⠄⢀⡀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⡷⠀⢨⣭⡍⠁⠒⠚⠛⠷⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⡉⠉⠉⠉⠉⠛⠛⢻⡉⠀⠈⠀⢠⣉⣿⣿⣿⣶⣆⣶⢆⣀⡉⢉⣿⣿⣿⣿⣿⣽⣿⣿⠿⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠿⠿⣷⣶⣯⣭⣷⣒⣲⡤⢴⣷⣿⠉⠉⠀⠈⠉⢹⣿⣿⣿⣭⣾⣼⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣶⣶⣶⣦⣤⣤⣼⣛⣿⡿⣿⣿⣯⣽⣿⣿⡟⠉⠛⠛⢛⣿⣿⣿⠃⢠⣿⣿⣿⣿⡧⠀⠀⠀⢀⣤⣴
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣷⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣥⣀⣀⣤⢠⣬⡍⠀⠀⠀⠐⠒⠩⠧⠀⠀⠀⠀⢻⣿⣿
⣷⣄⠀⠀⠀⠀⠠⢤⣀⣀⠀⠀⠀⣼⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣶⣿⣭⣽⣓⣒⡶⠦⠤⣀⣴⣶⣯⡽⢸⣿⣿
⣿⣿⣷⣴⠀⠀⠀⠀⠀⠉⠉⡛⢠⣸⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣶⣾⣿⣯⣥⣤⣝⣛
⣿⣿⣿⣿⠀⠀⢀⣀⡀⠀⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠿
⣿⣿⡟⠙⠻⠿⠟⠳⠶⠦⠶⢀⢂⣶⣿⣭⣿⣛⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⢿⣿⣿⣿⣿⣷⡖⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠓⣄⡀⠀⠀⢀⠀⠀⠐⣸⢸⣿⣿⣿⣿⣿⣿⣿⣾⣽⣻⠿⣿⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⢀⣸⣿⣿⣿⡿⣇⣀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⢀⡛⠿⣿⡷⣡⣦⣤⠀⡎⢸⣻⢿⣿⣿⣛⠛⢭⣷⣾⣿⣿⣷⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣛⣻⣿⣿⣿⣿⣿⣿⢁⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠟⣵⣾⡵⢭⠝⠛⢸⠃⣿⣿⣿⣷⡿⣵⣻⢿⣿⣿⣿⣿⣿⠀⠀⠀⢨⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⢭⣹⣿⣿⣿⣿⡿⠻⣻⠷⠖⣼⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣀⣈⣩⣤⣤⣄⠀⡿⠀⢿⣿⣿⣿⣧⣿⣿⣿⣿⣯⣟⡿⡟⠀⠀⠀⣼⣿⣮⣪⣻⣿⣿⣿⣿⣿⣿⠻⠟⠋⠉⠉⠉⠉⠋⠁⠀⠀⠀⠘⠿⠿⠀⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⢿⣿⣿⣿⣟⣻⣿⣴⣆⣀⣸⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢟⣋⣭⠵⠶⣤⣉⡙⠻⢿⣿⣿⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠋⠉⠛⠹⠿⠿⣿⣟⣻⣿⣿⣿⠟⠛⠛⠋⠻⢟⣿⣿⣿⣿⢷⣲⣶⣶⣾⣿⡖⠀⠀⢤⣬⣿⣷⣶⣾⢡⣤⣤⣤⣤⣤⣤⣤⢠⣤⣤⠀⣠⣴⣶⣶⣶⣤⡀⠈⠉⠻⠿⠿⠿⣿⣿⠇⣸⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀
⠶⣤⡀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠉⠀⠂⠘⠉⠉⠁⠀⠚⠛⠃⣿⣿⣿⡇⢫⠀⢸⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢰⣿⣿⡟⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⢶⣄⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣤⣄⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣦⣄⡀⠙⢦⡀⠀⠀⠀⠠⣶⣿⣿⣿⠿⣿⣶⣾⣿⣿⣿⣿⣋⠄⠀⠀⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⣆⢳⡀⠀⠐⠈⠈⠁⠀⠀⠀⠀⠙⠛⠿⢿⠟⠿⠃⠀⠀⢠⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠿⠟⡛⠻⠿⠝⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⡢⠳⡁⠀⠀⠀⠶⠎⣇⠀⠀⢠⣀⣀⡀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤
⢁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢨⣶⣦⢄⠸⠿⠦⠄⡀⢀⣼⡽⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠠⠤⠴
⠀⠈⠀⠂⠀⡈⠐⣨⣼⣦⣄⣸⣻⠃⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢥⡂⠀⠀⢀⣀⣀⣤
⣷⣤⢀⡀⠘⠤⢄⡾⣶⣽⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⠘⠁⠀⠀⠀⠤⠚⠉⠀
⣿⣿⣿⣷⣤⣤⣤⣟⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠏⡝⠻⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⣴⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢀⣤⠦
⢿⣽⣿⣿⡿⣿⠌⣸⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀⡀⣿⣿⣿⣿⣿⣿⣧⣷⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠞⠉⠀⠀
⠈⠀⠙⠛⠉⣠⡾⠃⠀⣠⣤⣀⣀⣀⣀⢀⠀⠀⠈⢛⠟⣛⣷⣼⡀⠀⣿⣿⣿⣿⣿⣿⣿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀
⣶⣶⣶⣶⠿⠋⠁⠀⠚⠻⢿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠋⢞⣿⡣⡀⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠈⠺⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⡿⢭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣷⣷⣮⣵⣧⣶⣦⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣤⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣭⣚⣻⡿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠷⢸⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢺⣿⣿⣿⡆⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣶⣶⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣸⣿⣿⣏⡁⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣿⣿⣿⣿⠿⠟⢁⣼⣿⠿⣿⣿⣿⣦⠐⠀⠉⠓⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⣿⣿⣶⠈⣿⣿⣿⡆⠐⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⣿⣿⣿⣥⣿⣿⣿⠃⠀⠘⢆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠈⠙⠻⢿⣿⣭⣿⣿⣿⠛⣿⡿⠀⠈⢹⡟⠛⠿⡛⠱⡄⠀⠀⠀⠳⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠈⠛⠿⣿⣿⢸⣿⡇⠀⠠⣿⠀⠈⠀⠊⠲⢕⣄⠀⠀⠀⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⡀⣶⣷⣾⣿⠁⠀⢰⣏⡑⠄⡀⠀⠀⠀⠈⠇⢔⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠃⠀⠁⠚⠢⢀⠀⠀⠈⢀⠁⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⠙⠁⡐⠀⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠰⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⡆⠀⠀⢿⣿⣿⣶⣄⡀⠀⠀⠀⠒⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⡀⠀⠈⢛⣿⣷⣟⣿⣶⣦⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣷⡄⠀⠀⠛⣽⣿⣿⣿⣿⣗⣠⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠁⠹⣿⣄⠀⠀⠙⢙⢯⣷⠿⠫⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⢿⣦⡀⠀⠀⠁⢄⡈⠸⣿⣸
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠹⣿⣦⡀⠀⠀⢁⡂⠀⠉
⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠻⣿⣦⡀⠀⠈⠠⡐
⣀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠟⢛⣠⣤⣀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⠟⠁⢠⣾⣿⣿⣿⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⢿⣷⣤⣀⠀
⣾⣿⣿⣶⣄⡀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⣼⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣾⣷⣄⣄⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣛⢿⣷
⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣆⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡖⣀⣠⣾⠍⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⢀⢀⣰⡟⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣷⣄⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠏⠝⡐⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣏⡂⠀⠀⠀⢤⣀⡀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⢄⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣁⡀⠤⠡⡸⣤⣄⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣧⣽⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⣏⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⢻⣿⣷⡇⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠤⠤⠤⠤⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢩⣿⡍⠛
⠀⣿⡟⠉⠐⠿⢯⣇⠀⣿⡇⣰⡿⠁⠀⢀⣔⢄⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⣤⠄⠀⠀⠀⠀⠀⠉⠉⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠒⠚⠛⠒⠐
⣼⣿⠓⡄⠀⠀⠀⠉⠂⣿⣾⡟⡵⠁⢠⣾⠛⠛⠦⣄⡀⠀⢀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠻⣾⣿⣿⣿⡯⢀⠦⢸⣻⣟⣿⣷⣦⡄⡀⠀⠀⠉⠛⠻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⡀⠀⠀⠀
⡿⠁⠀⠀⠀⠀⠀⠀⠘⠁⠙⠈⠀⠀⢿⠿⡗⠀⠀⠀⠑⠤⡀⠀⢀⣿⣿⣿⣿⣿⣿⡏⡀⣿⣿⣿⣿⣇⣠⢀⣿⡿⠂⣿⣿⣿⣧⣿⣧⡆⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡘⡀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠭⠖⣬⣍⢛⢿⣿⣿⢇⢰⣿⣿⣿⣿⣿⣻⣿⣏⠇⢰⣿⢿⣿⣾⣿⣿⠇⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠊⠋⠀⢸⣿⡟⠍⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠶⠶⠞⠲⠶⣿⣿⣿⡋⠉⠁⠀⠈⠉⠙⠃⠉⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⡿⢭⣟⡲⡶⣿⣽⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿⢃⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⣶⣶⣶⣦⣴⣤⣼⣷⣦⣤⣄⣤⠀⡀⠤⣬⣭⣿⣿⣿⣿⣬⠀⢰⣎⠛⠄⡆⠉⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢻⣿⡾⠾⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣭⣽⣿⣿⣿⣿⣷⣤⣤⣽⣿⣿⣿⣿⣷⠀⣼⢷⢠⢠⡀⣠⣄⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠉⠙⠿⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠈⡘⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⡿⠠⠀⡆⠃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣉⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣙⠛⠻⡿⢿⡇⠀⠀⠁⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢺⠿⠯⡞⣱⢰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⢀⠀⠀⠀⠤⢿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⢡⣇⣿⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⠀⠀⠈⠀⠀⠀⠈⠈⣭⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠁⣸⣹⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠉⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠟⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢻⣟⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣧⣀⠀⠀⠀⠀⠀⠀⠤⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⣤⣀⡤⠬⠠⠤⠀⠄⣰⡀⣾⣯⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⡷⠀⠄⠀⢠⣶⣄⣒⣆⣀⠀⠀⠄⠤⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⡇⠀⠀⠀⠀⠀⠙⡛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣀⣀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⡀⢀⡀⠀⠀⠀⠀⣉⣥⡄⠀⠀⠀⣶⣼⣿⣿⣿⡿⣼⡿⣴⣦⡀⣾⣿⣿⣿⣿⣿⣿⣿⣭⡁⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠉⠙⠛⠛⠿⠿⣶⣶⣿⣤⣴⣿⣻⣉⡀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿⣾⣿⡄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠿⡿⠟⠃⠀⠛⠛⠻⡿⠟⠀⠀⠀⣰⣾⣿⣯
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣶⣤⣬⣄⣴⠖⢀⣀⣀⣀⠀⠉⠉⠀⣄⡠⣄⡈⣿⣿⣿
⣷⣄⢀⠀⠀⠀⠐⠒⠶⢤⣄⡠⢠⣿⣿⣿⣿⣏⣛⡛⢻⣿⣿⣿⣿⣿⠃⠀⠀⢀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⠿⣿⣶⣶⣯⣭⣭⣑⣚⣿⣿⡿⠁⢿⣿⣿
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⠁⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠐⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⣿⣿⣶⢾⣶
⣿⣿⡏⣧⣤⣤⣤⣤⣤⠀⡀⢀⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣟⡅⠈⠉⠉⠉⠉⠛⠘⠉⣨⢸⣿⣿⣿⣾⣯⣭⣛⡿⢿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠀⢰⣦⣤⣄⣀⢈⠀⠀⢀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⣝⣟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⡾⣖⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣌⢙⣿⡃⢿⣿⡗⢸⠁⣿⣿⣿⣻⢧⣬⠉⣹⣾⣿⣿⣿⣿⠀⠀⠀⢨⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠭⡽⣿⣿⣿⣿⣿⣿⣷⣿⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠑⢿⠗⠉⠒⠀⠁⡟⢰⣿⣿⣿⣿⣿⣗⣾⣿⣻⣿⣿⣿⡇⠀⠀⠀⣿⣮⣗⢝⢿⣿⣿⣿⣿⣿⣿⣏⣶⡾⠿⢿⢿⣿⣿⣙⠽⠛⠋⠐⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣶⣶⣶⣿⣶⡶⢰⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠃⠀⠀⢀⣿⣿⣿⠿⠫⠻⢿⣿⣿⣿⣿⣿⣙⣁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠃⠰⠞⠀⣽⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡿⣟⣛⣿⣿⣿⣿⣯⣿⣿⣶⣦⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣀⠀⠀⣾⣿⣧⡶⠶⠘⢻⣶⣶⣼⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⢠⣤⣤⠀⣠⣴⣶⣶⣶⣤⡀⠻⠿⣿⣿⣿⣿⣿⣿⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠈⠀⠀⠀⠀⠁⠐⠏⠻⠿⣯⡿⠿⠿⢟⣯⣉⡉⣊⠛⣿⣿⣿⡿⠻⣻⣿⣿⣿⣿⡟⢃⡀⢾⣿⣿⡿⠿⠿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠀⠉⠉⠙⠛⠟⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿
⠛⠳⢦⣄⠀⠀⠀⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠉⠉⣿⣿⣿⡇⠀⠓⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⣼⡟
⣀⠀⠀⠉⢳⣄⠀⠀⠈⠉⠀⠀⠀⢀⣀⣀⣀⣀⠀⣠⣾⣿⣷⣶⡤⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⡿⠀
⣿⣿⣶⣤⣀⡘⢦⡀⠀⠀⠀⠺⢿⡿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣿⣿⣿⡇⠀⠀⢾⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀
⣿⣿⣿⣿⣿⣿⣆⢳⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠋⠋⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀
⢿⠻⠛⡉⠛⠛⠉⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠠
⢷⠑⠳⠀⠀⠀⠀⠛⠈⡇⠀⠀⠄⢠⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠇⠀⠀⠂
⠂⠀⠀⠀⠀⠀⠀⠀⢠⢹⠀⠀⢸⣿⠶⠂⠘⠛⠓⠀⠀⣠⡕⠿⠓⠒⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠠⣤⢸⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢲⠀⠀⠀⠀⣤⣠
⣾⣿⣔⣄⠀⠃⠐⠰⣾⠻⢿⣶⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣠⣤⣼⣿⣿⢿⣿⣿⡆⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠐⠀⠀
⣿⣿⣿⣿⣶⣦⣦⣸⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⣤⠤⠀
⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣭⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠴
⠟⠹⣿⣿⣿⡿⠀⢁⡞⠀⠉⠛⠿⠟⠛⠛⠂⠀⠀⠀⠀⠀⣤⠄⠀⠀⡄⣿⣼⣿⣿⣿⣯⣵⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠁⠀
⠀⠀⠀⠈⠀⢀⣴⠟⠁⠀⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⣁⢄⢾⠀⡅⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⣿⣷⣶⡶⠿⠛⠁⠀⠀⠐⠻⠿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠙⠀⣽⠀⡇⣿⣿⣹⣭⣿⣿⣿⣯⣽⣩⡏⣯⣹⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦
⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠙⠇⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠳⣽⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣤⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣼⣿⣿⣿⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⡟⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⡟⣿⣿⣿⣿⣯⣽⡿⣿⣿⣿⣿⣿⣯⣁⣀⣤⣶⣾⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣷⣤⣿⣿⣿⡿⣿⣧⠘⡿⡟⢿⣿⣿⣿⣿⠛⠋⠉⠀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣿⣿⣿⣧⣉⡁⢰⣿⣷⣿⣿⣿⣿⣿⡆⠀⠀⠈⠉⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⣿⣿⣿⣥⣿⣿⣿⠋⡀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣼⣿⠟⠛⠻⠛⠛⠁⠀⠸⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⠛⠿⢿⣾⣽⣿⣿⡿⢰⣿⡏⠀⠀⣼⠁⠀⠨⢂⢀⠡⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆⠉⣿⣿⣿⡇⣼⣿⠁⠀⢰⡗⠀⠀⠀⠀⠀⠑⠱⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⠁⣿⣿⠀⠀⣸⠁⠐⠀⠢⡀⠀⠀⠀⠈⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⠀⠀⠘⠀⠀⠀⠀⠈⠰⢀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⡇⠀⠀⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⡀⠀⠈⣿⣿⣶⣦⡀⠀⠉⠉⠀
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣧⠀⠀⠘⢿⣿⣿⣿⣦⣤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣧⡀⠀⠈⢻⣿⣿⣿⣿⣷⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠊⢻⣷⡀⠀⠀⠘⠻⠛⠛⠧⠮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠹⣿⣆⠀⠀⠀⠢⠀⠀⠀
⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⢻⣷⣄⠀⠀⠀⡀⢀
⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡿⠁⠀⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣷⣄⡀⠀⠃
⣔⣀⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⣭⣤⣴⣾⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⣾⣿⣿⣿⡆⣀⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⠻⣿⣦⣄
⣿⣿⣿⣧⣦⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣧⣶⡄⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⠿
⣿⣿⣿⣿⣿⣿⣷⣧⡀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣴⣆⠀⠀⢠⣺⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣴⣾⠏⠀⠀⣩⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣶⣴⡿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⡯⠄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡿⣁⠀⠉⠑⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣦⣀⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡢⢤⡄⠐⠐⠵⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣾⣿⣿⢹⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⠍⣿⣿⢿⠀⢀⣠⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠂⠀⠠⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢉⢽⡛⠛
⣼⣿⠀⠀⠉⠛⠿⡇⢸⣿⣠⣿⢃⠀⠀⣰⣿⡴⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠦⢄⣀⠀⠀⠀⠀⠉⠉⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠒⠶⠶⠥⠤
⣿⠃⠐⠀⠀⠀⠀⠀⣸⢿⡿⡱⠃⠀⣼⣏⠉⠙⠲⢦⡀⢀⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⠌⣿⣿⣿⣿⠇⠀⠶⣸⣿⣿⣿⣷⣦⡄⣀⠀⠀⠉⠛⠿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⠃⠂⠀⠀⠉⠢⣐⡀⢸⣿⣿⣿⣿⣿⣿⠓⢺⣿⣿⣿⣿⣤⣠⣤⣿⠇⢻⣿⣿⣿⢻⣿⣧⡀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⡀⠀⣾⣷⡿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⢤⣦⣤⠴⢖⡚⠡⠶⣭⣛⣻⢿⣿⠀⢸⣿⣿⣿⣿⣿⣙⣿⣙⢰⣸⣿⠻⣿⢿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉⠙⠈⢰⣿⡟⡏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢛⣋⠙⠻⠿⠿⢯⠁⠀⠁⠀⡀⠈⠉⠀⠈⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⠾⢭⣟⢲⠦⣿⣟⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣾⣿⠁⢨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⡿⢶⣶⣷⣶⣾⣿⣴⣶⣠⣄⠠⠀⠶⢾⣿⣿⣿⣿⣿⡆⠀⢶⡹⠛⢀⡆⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠸⠿⠿⡦⣾⡟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⣿⣿⡇⠄⣾⠧⠀⣤⠀⣤⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠛⠛⠻⠷⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠈⠏⠀⣧⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⡏⠘⢀⡠⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⡙⠛⢿⠿⢿⡇⠀⠀⢡⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⠿⢧⡜⡄⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠃⠀⠀⠀⠀⠠⠀⠠⠼⢿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣷⠁⣼⢱⢧⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⡄⠀⠀⠁⠀⠀⠀⠁⠀⣯⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⠉⠐⠁⣾⣾⢧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⢉⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠟⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⣶⣷⡟⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⡀⠀⠀⠀⠀⠀⠠⡍⡻⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣤⣤⡤⠀⢁⣀⠒⠀⠀⠀⠩⠟⣗⡂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠿⣿⣿⣿⣿⣿⣿⠆⠀⠄⠀⣴⣶⣐⣲⠀⠐⠠⠄⠀⣀⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣶⠂⠀⠈⠁⠀⠚⠛⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠤⣤⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣀⠀⠀⠀⡀⠀⠀⠀⢩⣥⡀⠀⠀⡀⣦⣾⣿⣿⡿⢧⣿⣏⣴⡄⣠⣿⣿⣿⣿⣿⣾⣿⣭⣛⠃⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠙⠛⠻⠿⠿⣶⣶⣥⣤⣾⣚⣟⡀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣶⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⡏⠀⠀⠈⠩⢿⣿⠿⠁⣰⠿⠿⣿⡿⠇⠀⠀⠀⣤⣶⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣶⣤⣤⣴⠀⣔⡄⠀⣀⠀⠈⠁⠀⠃⢀⠀⣀⡀⢹⣿⣿⣿
⣷⣀⣠⠀⠀⠈⠑⠒⠲⠤⣤⠀⢿⣿⣿⣿⣿⣩⣛⣛⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶⠄⠠⠐⠒⠂⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣶⣶⣮⣭⣽⣛⣒⠦⠾⣾⣷⡟⠸⣿⣿⣿
⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠂⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣷⣶⣶⣭⣭⣭
⣿⡿⢿⣤⣤⣶⣤⣤⡤⣀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠛
⣿⡇⠀⠀⠉⠁⠈⠉⠁⠁⢰⢠⣿⣿⣷⣶⣾⣯⣽⣛⣻⢿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣷⣦⣤⣄⢔⡀⠀⠀⡬⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣹⣿⣿⣿⢯⣤⣤⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣴⣦⢈⣹⢋⠾⣿⣿⢠⠃⣸⣿⣾⣽⣻⡖⣬⣽⣿⢿⣫⣽⣶⠆⠀⠀⢀⣚⢽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⣿⣿⣿⣿⣿⣿⣁⣿⠇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡏⠁⠻⠿⠋⠉⠁⠀⣸⠀⣿⣿⣿⣿⣿⣿⣷⣯⢩⣻⢿⣿⣿⠀⠀⠀⢸⣿⣿⣮⡳⣝⢿⣿⣿⣿⣿⣿⣿⡷⢉⣸⣿⣿⣿⣿⠻⢛⣽⣷⠄⠀⣼⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣶⣶⣶⣿⣿⣶⢠⡉⠀⢹⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣶⡍⠀⠀⠀⣼⣿⣿⣿⣿⣯⡷⣹⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠉⠻⠖⠋⠉⠀⠀⠀⠘⣿⡏⢀⣤⠈⢻⣿⣿⣿⣿⣿⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⡿⠿⣿⣿⣿⣿⣿⣷⣶⣦⣾⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣟⣩⣭⣵⣶⣮⣿⣿⣿⢿⣿⣷⣶⣦⣤⣴⣤⢠⣤⣤⠀⣠⣴⣶⣶⣶⣤⡉⠀⢼⣿⣿⣿⣿⣿⡇⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠛⠉⠁⠁⠉⠙⠋⠉⠿⠿⣿⣛⣿⣿⣿⡿⠟⠛⠛⠏⠻⢿⣿⣷⣷⣶⠶⣿⣿⣿⣟⣷⡶⢾⣿⣿⡿⠿⠿⢼⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠉⠙⠻⠿⠿⠀⢾⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠓⠒⠂⠉⠉⠉⠉⠀⠚⣿⣿⣿⡏⠉⠀⢻⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿
⢀⡀⠀⠈⠙⢦⡀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣀⡀⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⢸⣿⣶⣤⣀⠀⠙⢦⠀⠀⠀⠀⢤⣶⣾⣿⣾⣷⣶⣶⣾⣿⣿⣿⣿⠟⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣶⣌⢳⡀⠀⠐⠀⠈⠉⠀⠀⠀⠈⠛⠻⢿⣿⡿⢿⠇⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⡄⣿⡿⢿⠿⠿⣟⠛⠂⢳⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣗⠫⣱⠳⠀⠀⠀⠀⣦⡌⣧⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇
⠙⠩⠀⠀⢀⠀⠀⠀⠀⢀⢸⡀⠀⢠⣽⣥⡀⠸⠷⠤⠀⠀⠀⡨⣷⣦⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠛⠛⠀
⠀⠀⡀⠀⠀⠀⠀⠀⢀⠘⠘⡇⠀⠈⡿⠘⠀⠀⠀⠀⠀⠀⠈⠹⠓⠋⢸⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠀⠀⠀⠀⠀⠀
⣶⣶⣔⠀⠐⢠⡂⠄⣄⣽⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⢸⣿⣿⢿⣿⣿⡆⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢻⣿⣶⣤⣀⣀⢈⠑⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⣤⣶⣿⣿⣿⣾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣙⣿⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⠀⠀⠠⠶
⠃⠹⠿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠉⠉⠏⠂⢁⣴⠷⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢀⡔⢠⡄⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀
⣶⣤⣤⣤⣤⣤⡶⠟⠁⠀⢰⣾⣿⣿⣿⣿⣿⣶⣦⣀⠀⠈⠀⢂⡍⠢⣁⠀⣿⡭⣉⣉⣿⣿⣿⣏⠿⣿⢛⢿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⣿⣿⣭⣉⡉⠁⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠈⠙⢠⡀⣿⢿⣿⠿⢿⣿⣿⣿⣿⣷⣾⣸⠗⣎⣽⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣑⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣼⣿⣿⣿⣨⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣷⣤⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⣿⣿⣿⡿⡿⢏⣉⠙⢿⢿⣿⣿⣿⣿⠁⣀⣤⣴⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣷⣇⠸⣿⣷⣾⣿⡿⣿⣿⣿⣿⡿⠟⠋⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣤⣿⣿⣿⠋⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⠛⣻⣿⡿⠋⠁⢀⠀⠠⡀⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠉⠛⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡏⢰⣿⡟⠀⠀⢀⠀⠀⠢⢐⢦⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣰⣶⣾⡟⠻⣿⣷⣾⣿⣿⡿⢀⣿⡿⠀⠀⡰⢀⠁⡀⠀⠀⠉⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⠿⣿⡇⢸⣿⠇⠀⠀⠇⠀⠁⠪⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠁⣼⣿⠀⠀⠘⠀⠀⠈⠐⠀⢙⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⢻⣿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣇⠀⠀⢱⣠⣄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⡄⠀⠀⢻⣽⣷⡄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣷⡀⠀⠈⢿⣿⣿⣿⣷⡖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣷⡀⠀⠈⠛⣻⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⢻⣷⡄⠀⠀⠈⠁⢿⠏
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⣿⣦⠀⠀⠠⠀⠀
⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⠟⠁⠀⣴⣿⣿⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⢻⣷⣄⠀⠘⠀
⣀⡀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣤⣤⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⢾⣿⣿⣿⣆⣄⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡘⢿⣷⣄⠀
⣿⣿⣾⣶⡄⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣵⣶⡆⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⠻⣿
⣿⣿⣿⣽⣿⣷⣦⡀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⠀⠀⢐⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢾⣶⣾⠁⠀⠀⣼⡏⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣴⣼⡟⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠭⠂⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣀⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⢅⠅⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡅⠀⠀⣈⣿⣿⣿⣿⣿⣿⣷⣮⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⣿⣿⣿⣿⣿⣧⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣇⡏⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠛⢸⣿⣟⣻⠀⢠⡄⠀⣴⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠒⠒⠂⠀⠰⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣟⠛⠛
⣿⡇⠀⠀⠈⠙⠻⡀⣿⣇⣾⠟⠀⠀⢠⣾⣯⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⡏⣿⣿⣿⣿⡿⠳⠦⢀⣀⣀⡀⠀⠀⠉⠙⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠢⠤⠿⠿⠤⠤
⠟⠀⠂⠀⠀⠀⠀⠀⠟⢿⠯⠊⠀⣠⣿⣆⠀⠉⠓⢆⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡯⢹⣿⣿⣿⡿⠢⡠⠄⣯⡿⢿⣿⣷⣦⣄⣀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠔⠀⠀⠀⠑⠢⠅⡂⠼⣿⣿⣿⣿⣿⣿⠑⣼⣿⣿⣿⣿⣤⣀⣼⣿⠃⢸⣿⣿⣿⣼⣿⣴⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢉⠀⢠⣿⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢐⡓⢶⣦⣤⣤⣦⣁⣒⠃⠶⣨⣝⡻⢿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⡘⣀⣾⡿⢿⣷⣿⣿⡿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠩⠩⠋⠈⣼⣿⢏⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣹⣈⣙⣛⠻⠭⠕⠀⠀⠀⣀⠀⠀⠉⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⡷⠶⢭⣑⢲⢼⣯⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣿⡟⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣻⣿⡿⠿⣷⣶⣿⣷⣶⣦⣴⣄⠁⠐⠶⢶⣿⣿⣿⣿⣷⠄⠀⣶⠙⠳⢰⠈⠉⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠸⢿⣧⣧⣿⡏⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣶⣬⣿⣿⣿⣿⣿⡂⢠⡿⡆⡄⡤⢠⣤⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠐⠛⠛⠶⡏⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠸⠃⢠⣹⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣴⠃⠂⢠⡰⢠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣍⡉⠙⠿⠻⢿⠀⠀⠘⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣿⣶⣆⢏⡄⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠀⠀⠀⠐⠀⠠⠀⠠⠿⣟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣸⡷⠀⡏⣼⣸⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠃⠘⢡⣏⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⣹⣿⢛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⡿⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢲⣾⣽⡇⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⣤⣤⡀⠈⣉⣁⡂⠀⠀⠀⠌⢹⣻⡒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣭⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠿⣿⣿⣿⣿⣿⡷⠀⠠⠀⢠⣔⣆⣒⣒⠐⠂⠤⠄⢀⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⣶⡦⠀⠉⠈⠀⠐⠸⠿⢷⣶
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠦⠤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣁⣀⠀⠀⢀⡀⠀⠀⢈⣩⡤⠀⠀⠀⢰⣤⣿⣿⣿⢿⣺⣿⢡⣦⢄⣸⣿⣿⣿⣿⣷⣿⣽⣟⡛⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠙⠛⠛⠿⠿⣶⣶⣥⣤⣾⣻⣆⡀⠀⠀⠀⠀⢸⣿⣿⣳⣶⣶⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⣿⣶⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⠃⠀⠉⠉⢹⣿⡿⠏⠀⡼⠿⢿⣿⡷⠄⠀⠀⢠⣤⣴⣟⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣦⣤⣄⡆⣰⣠⡀⠀⠀⠀⠈⠐⠚⠀⠀⢀⡀⠈⣿⣿⣿⣿
⣦⡀⡄⠀⠀⠈⠉⠓⠲⠦⡄⠘⣿⣿⣿⣿⣯⣭⣙⣻⣿⣿⣿⣿⣿⠇⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡤⠤⠤⠐⠂⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣷⣶⣧⣭⣟⣓⣲⠦⠴⣧⣶⣾⠃⢿⣿⣿⣿
⣿⣧⡇⠀⠀⠀⠀⠀⠀⠐⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣶⣦⣬⣿⣛⣉
⡯⠹⢶⣶⣶⢶⣶⣶⢈⡄⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠘⠻⠿
⡿⢀⠀⠀⠈⠀⠀⠃⠀⠀⠄⣶⣶⣷⣶⣶⣿⣯⣽⣟⣻⠿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡂⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⢶⣦⣤⡤⣁⣀⠀⢰⠂⣟⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣮⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢻⣿⣿⣿⢏⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⢆⣩⡟⣔⠿⢿⠇⡾⢠⣿⣿⣿⣯⣗⡖⣨⣽⣿⣿⡿⣟⡯⠀⠀⠀⣸⣍⡭⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⣿⣿⣿⣿⣿⠁⣺⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⠀⠙⠿⢋⠈⠉⠀⢠⠇⢸⣿⣿⣿⣿⣿⣿⣷⣯⣽⢻⢾⣿⡇⠀⠀⠀⣿⣿⣿⣿⣝⢮⡻⣿⣿⣿⣿⣿⣿⣿⣷⢋⣿⣿⣿⣿⡿⠟⣩⣿⣤⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣿⣿⣿⣿⣿⡇⡌⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣷⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣪⣻⣿⣿⣿⣿⣿⣷⡏⠀⠀⠉⠛⣳⠿⠛⠉⠀⠀⠀⠹⣿⡟⠉⣀⠙⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣿⣿⣿⠿⠿⣿⣿⣿⣟⣒⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⡿⠟⣛⣽⣥⣥⣿⣿⣿⢿⣿⣷⣦⣴⣤⣴⣶⢠⣤⣤⠀⣠⣴⣶⣶⣾⣥⡈⠉⠀⣼⣿⣿⣿⣿⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠟⠛⠈⠉⠉⠉⠙⠿⠿⠿⣿⣿⣿⢿⣿⣽⣿⠿⠿⠿⠞⢿⣷⣲⣶⣶⣶⣿⣿⣿⣷⡭⣭⣽⣿⣿⡿⠿⠿⣼⡿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠈⠛⠻⢿⡇⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠶⠶⣦⣤⡀⠀⠀⠀⢀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠒⠢⠦⠄⠽⠛⠛⠋⠉⣿⣿⣿⡗⠞⠛⢻⣿⣿⡇⠀⠀⠀⠉⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⢀⡀⠀⠈⠙⠷⣄⠀⠈⠉⠷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⣿⣿⣿⡏⠀⠁⢹⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⢨⣿⣶⣤⣀⠀⠈⠳⡄⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣤⣄⣴⣿⣿⣿⣿⡟⣿⣿⣿⡇⠀⠀⢺⣿⣿⣏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣶⣤⡙⣦⠀⠀⠄⠈⠛⠋⠉⠉⠉⠉⠿⢿⣿⣿⣿⣯⡔⣿⣿⣿⣧⣤⣄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡀⣿⣿⢿⠿⡿⣿⡟⠵⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠿⠿⠿⣿⡿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⡀⠙⢍⣳⣦⠀⠈⠉⢀⣔⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠚⠸⡈⠉⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢉⣶⡂⠀⢰⣤⣀⠀⠀⠀⢐⢤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠛⠻⠿⢿
⠆⠀⠀⠀⠐⠀⠤⢀⡀⠀⠼⢸⡆⠀⢸⣿⠃⠁⠀⠀⠀⠀⠀⠐⢷⣯⢿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀
⣤⣤⣄⢄⡀⠀⠀⠢⠀⠈⣶⠘⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⠊⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡄⣌⣁⠐⠘⢼⢌⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠐⣿⣿⣿⠀⠀⠀⣿⣿⣿⣼⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⣰⠀⠀⠀⠀
⣿⣿⢿⣿⣿⣿⣿⣿⣷⣄⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⡠⣶⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⡤⠀⠀
⠋⠻⠹⣿⢿⣿⣿⣿⡿⠛⢛⠿⣷⣦⣶⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇⣰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢂⠀⠉⠘⢿⠋⠏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⣦⣄⣀⡀⠀⣀⣀⣤⠾⠋⠉⣹⣿⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⢀⠄⠷⣤⠐⠈⡿⠉⡉⠝⣿⣿⣿⡏⣭⣿⡯⣽⣍⣝⡋⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣽⣟⡛⠛⠛⠋⠁⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⢿⣿⣷⣤⡀⠀⠁⠠⢪⢀⡇⣿⠤⠥⠀⢿⣿⣿⣷⣬⣏⣼⠸⡏⣟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣰⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣼⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⣿⣿⣿⣿⠿⣿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣿⣿⣿⣏⠀⣟⢰⣶⣶⣿⣯⣿⣿⣿⡏⢀⣠⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣄⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠛⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠛⠛⢻⠟⢛⣿⣿⠟⠁⠀⢀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣾⡿⠃⠀⠀⠄⠀⠐⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣰⣶⣿⡟⠿⣷⣿⣿⣻⣿⣿⣛⡏⢀⣿⡿⠁⠀⠀⠒⡀⢢⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⢿⣿⣿⣿⠃⣼⣿⠃⠀⠀⠀⠤⣀⠀⠹⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠿⠀⣿⡿⠀⠀⠈⠁⠐⠂⠭⠆⢝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⣿⡇⠀⠀⠁⠠⢀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡇⠀⠀⠉⠐⠂⠥⢦⣀⠀
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⡆⠀⠀⢳⣷⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⡀⠀⠈⢿⣿⣿⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣧⠀⠀⠈⢽⣷⡶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡎⢿⣷⡀⠀⠈⠱⠾⢿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢻⣷⡄⠀⠐⢀⠘
⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⠋⠀⣴⣾⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠙⢿⣦⡀⠈⠀
⣀⡀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣶⣶⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠸⣿⣿⣿⡇⣀⡀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠻⣿⣦⡀
⣿⣿⣷⣶⡀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣴⣠⣆⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠻⣿
⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣦⠀⠀⢀⡜⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮
⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢾⣿⡏⠀⠀⣰⠟⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠴⣶⡿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢟⠄⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣤⡄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢠⣴⠂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣇⡀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣬⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣥⣤⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿
⣿⣿⣟⡛⣫⣻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢠⠐⡀⢀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣾⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠨⣿⣟⣻⠀⢰⣴⠀⣰⡦⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠀⠀⠴⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⠿⠿⠿
⠇⡀⠀⠀⠁⠻⠆⣼⣇⣾⡟⡀⠀⢀⣾⣮⡞⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⠦⢄⣀⠀⠀⠀⠀⠉⠉⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⠤⣯⣞⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠟⠻⠏⠎⠀⣠⣿⣧⡀⠈⠙⠦⡀⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡯⢃⣿⣿⣿⣿⠣⠀⠶⣾⡿⣻⣿⣷⣤⡄⡀⠀⠀⠉⠛⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠘⠀⠀⠀⠈⠂⠅⣂⠼⢿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣤⣀⣤⣿⠇⢻⣿⣿⣿⢻⣿⡤⠀⠀⠈⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠓⡀⢀⣶⣶⣶⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣐⣒⣒⣶⣤⣄⣄⣉⢒⠛⠰⢎⣝⣻⢿⡿⠀⣾⣿⣿⣿⣿⣿⣽⣿⣛⢐⣼⣿⢻⣿⢿⣿⡿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠛⠊⠀⣼⣷⣟⢺⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣄⣉⣛⡛⠫⠵⠀⠠⠀⣠⡀⠀⠉⠀⠈⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⠶⢭⣟⢲⠮⣯⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣿⣿⠈⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣛⣿⣿⠿⢷⣶⣿⡿⣶⣶⣴⣆⡁⠐⠲⢶⣿⣿⣿⣿⣿⡆⠀⢲⡹⢻⢠⠮⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣇⣣⣿⡯⠽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⣶⣤⣿⣿⣿⣿⣿⡇⢄⣿⠧⡀⣤⢀⣤⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠶⠾⢶⡍⠛⢶⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠏⠀⣷⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣰⡖⡂⣠⣰⢠⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⡉⠙⠿⠿⢿⠀⠀⠀⢱⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣿⣶⣤⢿⡄⡀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠃⠀⠀⠐⠀⠠⠀⠠⠼⢿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣷⠀⡟⣸⢸⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡄⠀⠀⠂⠀⠀⠀⠀⢨⣭⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠛⠋⠸⢁⣏⣿⠑⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠀⣹⣿⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢲⣾⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣄⡀⠀⠀⠀⠀⠀⠠⠜⡿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⣤⣀⡈⠀⣀⠁⣀⠀⠀⠀⠈⢻⣿⡢⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⣭⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⠆⠠⠀⠀⣔⣦⣐⣲⠀⠒⠠⠄⠀⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⣰⣦⠁⠁⠀⠀⠘⠺⠿⣷⣶⣀
⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠤⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣌⣀⡠⠀⢀⡀⡀⠀⢈⣩⣤⠄⠀⠀⢰⣦⣿⣿⣿⡿⢷⣷⢧⣤⣄⣸⣿⣿⣿⣿⣷⣿⣽⣟⡛⠀⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠈⠉⠛⠛⠻⠿⢷⣶⣮⣥⣼⣟⣇⣀⠀⠀⠀⠀⢸⣿⣿⣷⣶⢾⣾⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠈⠉⠹⣿⡿⠿⠀⡸⠿⢿⣿⣿⠄⠀⠀⢀⣤⣴⣟⣒⠶
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⢿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣶⣤⣤⣆⢀⣆⡀⠀⠀⠀⠁⠐⠚⠀⠀⢀⡀⠈⣿⣿⣿⣿⣿
⡠⡄⠀⠀⠀⠉⠙⠓⠶⠔⢰⣿⣿⣿⣿⣿⣭⣽⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀⡠⠤⠄⠀⠈⠉⠉⠛⠛⠿⠿⢿⣷⣶⣯⣭⣽⣓⣒⠶⠤⣿⣶⣿⠏⢿⣿⣿⣿⣟
⣧⡇⠀⠀⠀⠀⠀⠀⠐⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣿⣶⣦⣬⣽⣛⣙⣚
⠙⠷⣶⣶⢶⣶⣶⢊⣄⢠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠘⠛⠿⠿
⢀⠀⠀⠀⠀⢀⠊⠀⠀⡔⢸⣭⣽⣿⣯⣭⣭⣿⣛⣻⡿⢿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣷⣶⣦⡴⣀⣀⠀⢠⠃⣾⣟⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⠅⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣟⠁⡄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣶⢆⣨⡟⣔⡻⠿⠇⣼⢀⣿⣿⣿⣾⣵⣲⢦⣽⣿⣿⣿⣿⡿⠀⠀⠀⢠⣬⣍⡻⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣾⣿⣿⣿⣿⠋⣾⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠙⠻⢋⡀⠉⠀⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡻⢫⡆⠀⠀⠀⣼⣿⣿⣿⣷⣽⡺⣝⢿⣿⣿⣿⣿⣿⣿⣧⠛⣛⣿⣿⣿⣿⡶⣫⣿⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⡏⠨⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⡳⡽⣿⣿⣿⣿⣿⣯⣾⠉⠈⠛⠻⣷⣶⠿⠛⠋⠉⠈⠙⣿⣿⡟⠉⠉⠻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⠀⠀⠀⠈⠑⣿⣿⣿⣿⠿⠛⣻⣿⣾⣾⣿⣿⢿⣿⣿⣷⣶⣶⣶⣶⢽⣥⣤⠀⣠⣴⣶⣶⣾⣯⡀⠐⠃⠀⣿⣿⣿⠃⣸⣿⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠿⠟⠒⠊⠛⠛⠻⠟⣻⣯⣿⣿⠿⣿⣿⣿⣿⡿⠿⠿⣇⢻⣶⣶⣤⣤⣤⣿⣿⣿⣷⣼⣛⣻⣿⣿⡿⠿⠿⣼⡿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠈⠻⠿⣿⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠙⠓⠒⠶⠦⠤⠤⠘⡛⠻⠿⠋⣿⣿⣿⣟⠥⠾⢿⣿⣿⡇⠀⠀⠀⠉⢺⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠉⠛⠷⣄⠀⠀⠙⢲⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣿⣿⣿⡇⠈⡐⢹⣿⣿⣿⣿⣟⡀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⣷⣦⣄⡀⠀⠈⠳⣄⠀⠀⠁⠀⢀⣀⣤⣤⣤⣤⣤⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢼⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣷⣦⣄⡘⢧⡀⠀⠀⠨⠛⠟⠛⠛⠛⠛⢻⣿⣿⣿⣿⡿⣣⣿⣿⣿⣧⣤⣄⣸⣿⣿⣧⣥⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣇⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⢿⣿⣿⢗⠌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠋⠿⠿⠿⠿⡿⠟⠹⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⢂⢸⠿⡑⣤⠄⠈⠉⡀⣀⡌⢧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠜⠌⠜⠑⠋⠀⠀⠀⠀⠉⠁⠸⡆⠀⠐⢠⡦⠀⢠⣤⡀⠀⠀⠀⠠⢤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠻⠿⣿
⣄⠀⠀⠂⠄⡀⠀⠀⠀⠀⢠⡆⣷⠀⠀⣿⡿⠂⠈⠉⠉⠁⠀⠠⣴⣭⣺⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀
⣌⡀⣀⡀⢀⠀⠁⣖⠀⢐⢲⡄⢻⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠈⣿⣿⣿⠀⠀⠀⢸⣿⣿⢿⣿⣿⡆⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀
⣿⣿⣿⣷⣆⣶⡄⠈⢒⠢⠿⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⢸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⣠⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣦⣣⡀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠠⠆⠊⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠋⠀⢀⠀
⠙⡟⢿⡿⣿⣿⣿⣿⣿⣿⠋⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣠⠘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀
⠔⠀⠘⠃⢻⡿⢿⢿⡍⢃⣴⣧⣤⣤⣤⣤⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⡟⣷⣿⣿⣿⡿⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⡀⠀⠀⠀⠀⠈⢁⣠⣾⣶⣶⣾⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢀⢤⣦⡥⠊⢩⡭⡭⣅⡨⡭⣿⣿⠛⡳⣯⣝⣟⡍⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠶⠶⠶⠿⠛⠉⠰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠑⠊⡩⠓⢄⢸⣿⣗⣁⢆⠒⢼⣿⣦⡛⠟⠨⢿⢛⠿⣶⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠈⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣸⡱⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣦⣀⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣼⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⡟⠿⠃⢸⣿⣶⣾⠙⣿⣿⣿⣿⣿⠟⠉⢀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣦⣿⣿⣿⠋⢀⣠⣾⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⡿⠛⣿⠟⠁⣴⣿⡿⠋⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠉⠛⠿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⠏⢠⣾⡿⠋⠀⠀⠐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⢰⣶⣿⡿⢿⣿⣿⣿⠿⣿⣿⣿⣿⠿⠋⢠⣿⡿⠁⠀⠀⠈⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠁⠀⠀⠀⠐⠤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠉⠛⠿⣿⡇⢸⣿⡇⠀⠀⡀⠀⠈⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠁⢸⣿⠀⠀⠠⠀⠑⠄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⢸⣿⠀⠀⠀⠀⠀⠀⠊⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣇⠀⠀⢰⣤⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⡀⠀⠀⣿⣿⣷⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣷⠀⠀⠈⢿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣧⠀⠀⠜⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⢿⣷⡀⠀⠡⠁
⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⢀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⡿⠁⠀⣰⣿⣿⣯⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠹⣿⣄⠀⠀
⡀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣀⣶⣾⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠿⢿⣿⣿⣠⡆⣀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠈⢿⣷⣄
⣿⣶⣦⣀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⢿
⣿⣿⣿⣿⣶⣦⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣷⠄⢀⣤⡼⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣇⠀⠀⣼⠏⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡟⠕⠦⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣶⣤⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠰⠾⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣍⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣆⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿
⣿⣻⣯⣩⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢤⣢⣈⠠⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣯⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠟⠛⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣯⣽⡀⢀⣶⠀⣴⣿⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠒⠀⠠⠬⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⠀⠀⠙⠃⣸⣯⣾⡿⡁⠀⢀⣼⠿⢟⡁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⠟⠷⠦⣀⡀⡀⠀⠀⠈⠉⠩⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣸⣿⠇⠀⠀⣈⣿⣿
⠀⠀⠀⠀⠏⠙⠟⠋⠀⢠⣾⣿⡆⠀⠉⠓⢄⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⡿⠠⠐⢠⣿⣿⣿⣿⣦⣤⣀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉⠉⢙⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠁⠀⠀⠀⠁⠂⠄⣒⠿⢿⣿⣿⣿⣿⡗⢰⣿⣿⣿⣿⣧⣄⣠⣼⡿⠀⣿⣿⣿⣿⣿⣯⢤⠀⠀⠀⠂⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠂⠀⣤⣤⣤⣤⣄⡀⠈⠓⢀
⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣄⣀⣭⣒⣒⣶⣾⣿⡛⠏⣀⠋⠴⢯⣝⠿⢿⠃⢸⣿⣿⣿⣿⣿⣯⣿⣿⣃⣠⣿⡿⢿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠲⠊⢠⣿⣿⠯⣿⣿⣿⣶⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⣤⣍⣙⣛⡒⠂⣀⠀⢀⣄⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⡷⠮⣭⣓⣶⢽⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠁⠀⠀⣸⣿⠏⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣛⣿⣿⠿⣿⣿⣶⣶⣤⣶⣄⡀⠒⠲⢶⣿⣿⣿⣿⣷⠀⠐⣎⠛⠃⣰⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢠⣿⣿⣁⣼⣿⢿⣿⣿⡿⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣼⣿⣿⣿⣿⣿⠠⢴⡿⠆⢠⡄⣠⣄⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠴⠾⢿⣽⠻⢶⣤⣿⠗⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠀⢀⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣴⠐⠂⠈⠄⣴⡟⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⠉⠻⠟⠻⠯⠀⠀⠀⣾⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⣤⣰⣇⣀⠥⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠦⠤⢤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠀⠀⠀⠀⠀⠠⠀⠤⠿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⢳⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠀⠀⢀⠀⠀⠀⠀⠀⣽⣝⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠛⠃⠟⣸⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⣀⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣽⡏⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⣤⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣧⣀⠀⠀⠀⠀⠀⠀⠬⠻⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣤⣄⡀⠁⣀⠐⠀⠀⠠⠀⠀⠚⡿⡿⠄⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠟⠻⠿⠿⢿⣿⣿⣿⠷⠀⠄⠀⢠⣲⣆⣒⡂⠐⠀⠤⠀⢀⣀⣀⣶⣯⣿⣿⣿⣿⣿⣿⣿⠂⢠⣮⡅⠀⠀⠀⠀⠂⠿⣷⣦⡄⠀⠀⠀
⠀⠀⠀⠀⠉⠙⠓⠲⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣤⣄⣀⠄⠤⣀⠀⠀⠀⢈⣥⡤⠀⠀⠀⣶⣼⣿⣿⣿⢿⣻⣿⣡⣤⢀⣿⣿⣿⣿⣿⣾⣭⣿⣛⠋⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠛⠯⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠛⠛⠿⠿⢷⣶⣦⣤⣾⣛⣃⡀⠀⠀⠀⠀⣺⣿⣿⣲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣴⣴⣦⡀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠁⠈⠉⠉⢿⣿⣿⠇⢀⠿⠿⣿⣿⡧⠀⠀⠀⣠⣤⣾⡇⠲⣶⣶⣼
⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣷⣦⣤⣰⡂⣠⣂⠀⠀⠀⠀⠐⠚⠃⠀⠀⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠙⠓⠲⠀⣾⣿⣿⣿⣿⣤⣭⣍⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⣀⠀⢀⣀⣀⠉⠉⠙⠛⠻⠿⢿⣿⣶⣾⣭⣽⣓⣒⠦⠤⢼⢣⣾⡟⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣦⣤⣽⣛⣋⣛⠛⠻⠿
⣿⠿⢿⣶⣆⣤⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠻⠿⠿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⢠⣸⣿⣛⣿⣿⣿⣿⣿⣛⣛⡿⠿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⡤⣠⣄⡀⠀⡆⣿⣿⣟⢿⣿⠿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⣟⣤⣛⠻⠇⢰⠀⣿⣿⣿⣿⣾⣽⣲⢮⣿⣿⣿⣿⣿⡇⠀⠀⠀⣓⣋⣙⡛⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣟⡤⢒⣦⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⢋⣀⡁⠀⠀⡌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣟⡿⡿⠃⠀⠀⢰⣿⣿⣿⣿⣷⣯⣳⣽⡻⣿⣿⣿⣿⣿⣿⣾⡹⠿⣿⣿⣿⣿⣧⡼⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⣿⣿⣿⣟⡀⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠱⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣝⢮⣻⣿⣿⣿⣿⣿⣋⡀⠈⠛⠿⣯⣭⣴⣿⡿⠖⠀⠚⢻⣿⣿⡿⠛⠛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠓⠫⠟⣿⣿⣿⡿⠿⠛⢷⣷⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⢻⣥⣤⠀⣠⣴⣶⣿⣿⣥⡠⠆⠈⣿⡿⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠋⠗⠒⠚⠛⡿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠴⣶⣦⣤⣀⣀⣀⣀⣿⣿⣿⣷⡛⠛⣻⣿⣿⡿⣿⣿⠹⢿⣿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠘⢿⠇⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⣀⣀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠛⠻⠿⠯⢤⣤⣄⣁⡈⠵⠿⢿⡿⠛⢉⣿⣿⣿⡯⣵⠆⢻⣿⣿⡇⠀⠉⠓⠀⢹⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠉⠙⠻⢶⣄⡀⠀⠒⠦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠀⠀⣼⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⣦⣀⠀⠀⠈⠻⣦⠀⠀⠉⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣴⣿⣿⣷⣶⡄⣿⣿⣿⡇⠁⠀⢺⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣤⣀⡈⢳⡄⠀⠀⠀⠺⢿⠿⠿⠛⠛⠿⣷⣿⣿⣿⣿⣿⠋⡐⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⠑⠋⠀⣿⣿⣿⡿⡿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿
⣻⡟⢫⡉⠉⠛⠋⠁⢀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⢻⠾⠾⠀⠀⠀⠈⠘⠛⠂⢿⠀⠀⠠⣀⡀⠀⢀⡀⠀⠀⢀⠀⠀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢿⣿⣿⣿
⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡇⠀⠀⣿⡂⠄⠘⠛⠐⠀⠀⢀⣰⡮⠗⢺⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠉⠙
⠀⠀⡀⠀⠀⣀⣀⠀⣀⣉⠀⣧⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠔⠀⠀⠀⠀⠀
⣶⣦⣐⢀⠀⠘⠓⠤⣬⠻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⠸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢀⢀⠀⠀⠀
⣿⣿⣿⣿⣶⣤⣤⣀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡾⠋⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⡹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠐⠃⠀
⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡦⣧⣾⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠨⠀⠀⠀⠙⠛⠿⣿⡿⠿⠿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣧⡀⠠⢈⠉⣭⣿⣿⣿⣿⣿⠯⢧⣋⠩⢍⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣤⣤⣤⣴⠾⠋⠀⡀⠰⣾⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠐⠾⠫⠿⠇⠀⢰⣾⣿⣿⣿⣿⣿⣿⡀⠶⡿⠛⢿⣶⣮⣽⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣷⣯⣍⣉⠁⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣎⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣴⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⢸⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣏⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣷⣶⣾⡄⣿⣿⣿⣼⣿⣿⣿⠟⠋⢀⣠⣴⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⠻⣌⣙⡛⢻⣿⡟⠁⢀⣴⣿⡿⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡉⣀⣼⠏⢀⣴⣿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡎⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣾⡿⠋⠀⠀⠀⠈⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⡙⣿⣿⣿⣭⣿⣿⣯⣽⡞⠀⣾⡿⠁⠀⠀⠂⠀⠐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠛⢿⣿⣿⣿⠇⣸⣿⠃⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠈⠙⠻⠀⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⠀⠀⠀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⡆⠀⠀⢻⣿⣢⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⡀⠀⠀⢻⣿⣿⠯
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣷⡀⠀⠦⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠎⢻⣷⡀⠀⠂⠛⣻
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢃⣠⣄⡀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠟⠁⠀⣴⣿⣾⣯⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠻⣿⣄⠀⠐⠈
⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢀⣾⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣤⡟⢀⡀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠙⢿⣦⡀⠀
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣤⣀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠻⣿⣦
⣿⣶⣤⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠖⢠⣲⡧⠀⠀⠈⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻
⣿⠟⡋⣱⣶⡀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⠀⣀⣼⠇⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣾⣾⣿⣿⡏⡧⡦⣀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠿⣿⣿⣯⡠⠸⢟⠗⠤⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠙⢿⣯⡦⣵⠙⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣶⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣝⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣤⣀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿
⠻⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿
⣠⣰⣼⡿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣽⣛⣛⣛⣛⣛⣛⣻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣇⣼⣿⠃⠀⠀⣠⣷⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠈⠉⠉⠀⠘⠺⢽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⠃⠀⠀⣼⣏⠙⠒⢤⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠋⣾⣿⣿⣿⣿⠏⠉⠁⣤⣤⣤⣀⠀⠀⠀⠐⠻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣀⣠⣿⡇⠀⠀⢈⣿⣿⡿⠿⢿⣿
⠀⠈⠀⠀⠀⠺⠟⢿⡢⠄⠀⠈⠻⢔⠠⢀⠀⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣟⠑⠀⢰⣿⡟⣿⣿⣿⣶⣤⣀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠉⢙⢿⡿⣿⣷⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠩⢔⠨⢙⡛⢿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣶⣴⣾⡟⠁⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢂⠀⢠⣶⣤⣤⣄⡀⠈⠃⢀⡺⢽⡟⠳
⠀⠀⠈⠙⠛⠒⠶⠶⠒⠲⣾⣿⡷⠶⠒⠒⠀⠈⠑⠃⠶⠍⠛⠁⢸⣿⣿⣿⣿⣿⣷⣾⣿⡬⢤⣿⡟⠹⣿⣿⣿⡿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠓⠄⢠⣿⣿⠿⣿⣿⣿⣶⡄⠀⠙⠢⠁⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣶⣶⣶⣬⣭⣤⣀⣀⣰⣦⠀⣀⡀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⡿⠟⠛⠶⣍⣿⠻⢿⣿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⡏⠀⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⣭⣽⣟⣛⣿⣿⣿⣾⣿⣦⣄⡈⠙⢻⣿⣿⣿⣿⣿⠀⠈⣯⠌⠁⠼⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣃⣸⣿⠿⣿⣿⡟⠰⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⠐⢲⡟⠂⢠⡆⢠⣤⣤⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠴⠶⢿⣭⡗⢶⣦⣿⠗⠤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣟⡓⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣤⠒⠂⠀⡄⣰⡟⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠙⠛⠙⠟⠀⠀⠀⢸⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣤⣰⣇⣀⠥⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠓⠒⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡁⠀⠀⠀⠈⠀⠀⠀⠒⠛⠧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⡇⢸⢗⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⢿⣿⣶⡶⠀⠀⠐⠀⠀⠀⠀⠀⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠛⠃⠝⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠒⠠⠤⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⢀⣬⠁⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⢚⣾⣿⠯⠟⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⣤⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⡧⣿⣷⣄⡀⠀⠀⠀⠀⠀⠤⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣤⣀⠈⣀⡀⠂⠀⠠⠀⠀⠘⡿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⠛⠛⠛⠛⠿⠷⠿⣿⣿⠟⠀⠀⠀⠰⠶⣤⣔⣦⣀⠀⠠⠤⠀⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⣦⡍⠀⠀⠒⠀⠣⠿⣷⣦⡄⠀⠀⠀⠀⠀⢸⣿
⠀⠈⠉⠙⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣶⣶⣤⣤⣀⡀⠠⢀⡀⠀⠀⣲⡦⠄⠀⠀⠰⢶⣿⣿⣿⠿⢿⣿⣳⣶⣄⣾⣿⣿⣿⣿⣷⣿⣿⣟⠛⠀⠠⢿⠁⠀⠀⠀⠀⠀⠀⠀⠾⠟⠻⠧⠐⢖⣦⣾⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠙⠛⠻⠿⢷⣶⣶⣦⣽⣄⣀⣀⡀⠀⠀⣸⣿⣿⣷⣶⠶⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⣶⣤⣦⡀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⣄⣀⡀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⠁⠀⠈⠉⠿⣿⡿⠏⠀⠾⠿⣿⣿⡷⠄⠀⠀⣀⣤⣶⡆⠶⣦⣤⣼⣿⣿⣿⢃
⣀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣷⣶⣤⣤⡆⢀⣂⠀⠀⠀⠀⠁⠒⠋⠀⠀⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠉⠉⠃⢀⣿⣿⣿⣿⣿⣶⣶⣭⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣄⣀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣷⣶⣭⣭⣛⣒⡲⠤⢴⢤⣾⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣷⣿⣦⣤⣽⣛⣋⣙⠛⠻⢿⣿⡏⢸⣶
⠥⠦⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠻⠿⠿⣿⣿⣶⣦⣤⣤⣀
⠀⠀⡐⣿⣿⣿⡿⢿⣛⣛⣛⣿⣿⠿⢿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿
⡄⢀⠇⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣷⡖⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⠅⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡀⠀⠀⠀
⠂⠸⢠⣿⣿⣿⣿⣿⣮⣕⣲⢿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡷⠿⠽⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢉⣿⣿⣧⠄⡀⠤⢄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣶
⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣛⡿⠁⠀⠀⢠⣷⣾⣿⣿⣿⣿⣮⣗⣯⣟⢿⣿⣿⣿⣿⣿⣿⣛⢻⣿⣿⣿⣿⣿⣇⣸⢿⡄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⡐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⣝⢿⣿⣿⣿⣿⣿⣧⠀⠘⠿⣿⣿⠛⣩⣿⣿⣶⠦⠼⠿⣿⣿⣿⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠙⠒⠯⢟⡿⣿⣿⣿⣿⣿⡿⠮⠳⣿⣿⣿⣿⣿⣷⢰⣶⣶⣶⣿⣿⣿⣿⢡⣤⣤⠀⣠⣼⣿⣿⣷⣤⡀⠀⣾⣟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠽⠿⢿⣿⡷⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⣶⣐⣀⣀⣀⠀⠠⠥⢶⠆⢉⣿⣿⣿⡷⠶⠶⢿⣿⣿⡿⠿⣿⡾⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣷⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠘⠓⠻⠿⠯⡭⠯⣿⣿⣛⣉⣉⡙⠃⠙⣫⣿⣾⣿⠿⠻⣋⣿⣿⣿⣿⣧⠄⠀⢸⣿⣿⣟⠆⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⠸⣿⣿⣷⣄⠉⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣄⡀⠀⠀⢤⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠘⠉⠀⠘⠛⠛⣿⣿⣿⡇⠀⢃⢸⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠻⣦⡀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⣀⠀⠀⣿⣿⣿⡇⠀⠀⢹⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⣴⣾⣿⣦⠀⠀⠀⠠⢴⣶⣿⣿⣶⣶⣦⢄⣾⣿⣿⣿⣿⡿⢁⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣴⣤⠀⠀⠈⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠟⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⡟⠛⠋⠉⠉⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠉⠉⠛⠻⠿⣿
⠀⠀⠀⠀⠒⠒⠤⠿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢤⣲⢼⡵⣦⣴⣿⣿⣿⠀⠀⠀⢸⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀
⠄⠑⣀⣀⣀⠀⠁⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣤⣀⠀⣿⣿⣿⠸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠊⠀⠀⠀⠀⠀⠀⠀
⣷⣤⣀⡀⠀⠉⠙⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⠀⢸⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣶⡶⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣄⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠋⠀⣠⡄⠀⠀
⣿⣿⣿⣿⣿⡿⡏⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⣿⢡⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⢿⣿⡤⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠠⠀⣿⣿⣿⣿⣿⣷⣤⣽⣹⢩⠍⣪⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⢀⣠⡾⠋⠀⢀⣆⣤⣄⣤⣤⣤⣄⣀⠀⠀⠂⠀⠤⢺⢿⡇⠀⢸⣿⣿⣿⣿⢿⣿⣿⡏⢩⣳⡦⣽⣿⣺⠛⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣷⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠈⠁
⣷⣦⣤⣀⡀⠀⠀⠠⣤⣄⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣯⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣴⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣼⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡛⢬⣟⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡧⣾⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣷⣾⣷⣠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣜⡛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⢛⣿⣟⠹⠿⠟⢻⡿⣿⡿⠋⠀⣠⣴⣿⡿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡈⠳⠶⠀⣸⡇⠏⠀⣠⣾⡿⠋⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡿⠁⢠⣾⡿⠋⠀⢀⠀⠢⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣯⣿⣿⣿⠿⡿⠿⢿⣫⠂⢠⣿⡟⠁⠀⢀⠀⠁⠢⢈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⡟⠀⠀⠠⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⢿⣿⠇⣸⣿⠃⠀⠀⠀⠀⠑⠈⠢⠀
⣿⣟⡉⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠉⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣁
⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣿⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⠀⠠⠄⠀⢀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡄⠀⠀⢶⣤⡀⠀⠈⠁
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣧⠀⠀⠼⣻⣋⣀⡀⢀
⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣆⠀⠐⠹⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠟⠁⢠⣾⣿⣟⡛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣆⠀⠀⠘⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣩⣤⣴⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠿⣿⣿⡟⢁⠴⠆⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠙⣿⣦⠀⠀⠀⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⢼⣷⡮⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠈⢿⣷⡀⠀⠀⠀
⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠺⢤⡄⣀⣠⡖⠀⠀⠙⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠹⣿⣦⡀⠀
⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢇⢀⣠⣼⠁⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠻⣿⣦
⠄⣤⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻
⠩⡏⠠⣀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣺⣳⠎⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣦⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠹⢏⡈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣶⣌⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠑⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠠⣀⢂⣂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿
⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⣷⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣭⣭⣭⣭⣭⣭⣭⣛⣛⣛⣛⣛⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠛⠛⠛⠒⠺⠿⠿⠿⠿⢿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣴⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⢉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣿⠋⠀⠀⢠⣾⢧⠎⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⠁⠺⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢛⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⡣⠃⠀⣰⣿⡍⠉⠓⠦⡄⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⡏⠈⠉⢡⣦⣤⣤⣄⠀⠀⠀⠙⠻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⠤⢵⣟⣀⣀⡠⣿⣿⣿⡿⠿⠿⣿⣿
⠀⠀⠀⠈⠻⠛⠏⠰⠀⠀⠈⠃⢅⡀⠀⣸⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⠁⠐⠀⣾⡾⡓⣿⣿⣿⡷⣤⡄⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢉⡛⠿⢿⣿⣦⡀⠀⠀
⠀⣀⡀⠀⠀⠀⠠⠤⢤⣄⣀⡀⣀⠠⠕⢂⡍⣛⠿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣶⣤⡿⡇⢠⣿⣿⣿⣻⣿⣿⡇⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠱⡀⢀⣶⣶⣴⣤⣄⠀⠙⠂⣜⡫⣿⡝⠆⠀
⠀⠈⠉⠙⠛⠛⣋⠉⠻⠶⣻⣛⡫⠉⠐⠂⠈⠉⠘⠂⠉⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠼⣿⣛⠻⣻⣿⣿⠣⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠋⠂⠁⣸⣿⣟⢺⣿⣿⣿⣶⠀⠈⠙⠮⠁⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠷⣶⣶⣤⣴⣤⣄⣾⣆⣀⣀⢀⡀⠠⢀⣉⣛⣿⣿⣿⣿⣿⠿⠉⠛⠷⣬⠟⠻⣿⡯⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⠈⢸⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣷⣾⣿⣯⣭⣿⣛⣿⣿⣿⣿⣦⣄⣈⠉⣿⣿⣿⣿⣿⡏⠀⢹⡖⠁⠀⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠸⣿⣇⣂⣿⡿⢿⣿⣿⠡⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⣿⣿⣟⣿⣿⣯⠁⠾⠙⢰⣴⠆⣶⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠶⠾⢶⡝⠻⢦⣾⡏⢂⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣉⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⡇⠀⠀⡀⣀⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⡖⠒⢠⣰⢠⣾⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠙⡉⠛⠃⡀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣶⣧⠾⡄⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠈⠉⠙⠛⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠤⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⠀⡞⣺⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠿⣿⠿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠚⠛⠐⢁⣏⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠐⠒⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣠⣾⡄⢹⣆⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠯⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢲⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣐⣿⣿⣿⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⣦⣤⣤⠄⠉⡁⡀⠀⠀⠀⠈⢹⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣀⣀⠀⠀⣼⣿⣿⣿⣿⣯⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠙⠉⠘⠛⠛⠛⠿⣿⡟⠃⠀⠂⠀⠶⢽⣤⣼⣆⣀⣐⣂⠠⠤⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⢰⣶⠀⠁⠀⠀⠘⠺⠿⣶⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠉⠉⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠿⣷⣶⣦⣤⣐⣂⠠⠀⡀⠀⠀⣶⠒⠀⠀⠀⠷⠾⣿⣿⡿⠿⢿⡟⣶⣦⡠⣿⣿⣿⣿⣿⣷⣿⣿⣛⠃⠀⠾⠏⠀⠀⠀⠀⠀⠀⠈⢰⠛⠛⠛⠻⢴⣶⣶⣿⡿⠿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣶⣶⣶⣯⣤⣀⣀⣀⡀⠀⣻⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢸⣿⣿⣿⠡⣤
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣶⣤⣤⣀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠉⠿⣿⠿⠁⠰⠿⠿⣿⣿⠆⠀⠀⢀⣤⣴⣗⣒⠶⣶⣴⣿⣿⣿⡏⣸⣿
⡀⠀⢰⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣶⣤⣤⣄⢀⣄⣀⣀⠀⠈⠀⠘⠂⠀⢀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣔⣨
⠉⠁⣆⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣠⣤⣀⣀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣷⣶⣯⣭⣝⣓⣲⠤⢲⣲⣶⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡿⠟⠛⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣶⣬⣽⣋⣑⣋⡙⠻⢿⡿⠠⢦⣼⣭
⠆⡜⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠉⠉⠙⠘⠛⠿⠿⣿⣿⣶⣦⣤⣤⣀⣀
⢠⠇⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿
⡸⢀⣿⣿⣿⣿⡗⠻⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣀⠀⠀⠀⠀
⡃⢸⣿⣿⣿⣿⣿⣷⣭⣚⢿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣷⣯⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢉⣿⣿⣿⠄⠀⠤⢤⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⣿⣶⣶
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣟⡿⠀⠀⠀⠸⣻⣽⣶⣿⣿⣿⣷⣯⣶⢭⣻⢿⣿⣿⣿⣿⣿⣿⣛⠻⣿⣿⣿⣿⣿⣗⣨⣿⡆⠀⠀⠀⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣸⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡳⣝⢿⣿⣿⣿⣿⣿⣮⠄⠘⠿⣿⣿⣛⣉⣾⣿⡷⠖⠒⠛⢿⣿⣿⣿⠿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠙⠓⠺⠽⣻⢿⣿⣿⣿⣿⣿⡿⠮⠳⣿⣿⣿⣿⣿⣷⢰⣶⣶⣶⣶⣿⣿⣿⢠⣤⣤⠀⣠⣼⣿⣿⣷⣤⡀⠘⡗⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠽⠿⢿⣿⣶⠶⣾⣿⣿⣿⣿⣿⣿⣿⣬⣶⣂⣀⣀⠀⠀⠠⠝⢶⠈⠈⢙⣿⣿⣿⡷⠶⠶⢿⣿⣿⡿⠿⡿⠸⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣷⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⢈⣻⣿⣷⣿⠿⣽⣽⣿⣷⣿⣛⣋⡛⠛⠃⠻⣿⣿⣿⣿⣿⠿⢟⣿⣿⣿⣿⡗⡶⠀⢸⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⠄⠀⠉⠉⠉⠉⠑⠛⠒⠘⠉⠩⠉⠀⠐⠛⠛⣿⣿⣿⡏⠀⠓⢺⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⣛⣿⡿⠻⣟⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣶⡤⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿
⡿⠿⢿⣿⠋⠓⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⣦⠂⠀⠈⡄⣠⣠⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠈⠁⠀⢸⡆⠀⠀⣲⡂⠀⢰⡦⡄⠀⠀⠀⢠⣄⣄⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠛⠻⠿⣿⣿
⠐⠀⠤⠀⠀⠀⠀⠶⠄⣇⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠠⢶⣮⣕⡫⢯⣶⣤⣐⣿⣿⣿⠀⠀⠀⢸⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈
⠁⢄⠀⠐⢄⠀⠐⡲⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠙⣿⣿⣿⣿⣿⣄⡀⠀⣿⣿⣿⠸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀
⣇⢀⡐⠂⠡⠵⣋⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣀⣿⣿⣿⠀⢸⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣦⣤⠄⠀⠀⠀
⣿⣿⣿⣿⣷⣦⡀⠢⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⠛⠁⠀⣠⠀⠀
⣿⣿⣿⣿⣿⣿⢟⠂⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣄⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⡏⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠉⠀⠀
⠿⣿⣿⡿⢿⠑⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣿⣿⣿⣡⠀⣠⢀⡆⣿⣿⣿⣿⣿⣧⣍⣹⢩⣋⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠊⠉⢀⣴⠟⠁⠀⣄⣀⣀⠀⣀⢀⣀⣀⠀⠀⠉⠹⣿⣿⣾⡿⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⢛⢻⣯⣛⣲⠎⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⣶⣶⠶⠿⠛⠁⠀⠄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠑
⣦⣤⣀⡀⠀⠀⠀⢀⣀⣀⢈⣻⢹⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣸⣿⣿⣯⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣦⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⣿⠉⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⠀⠈⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣘⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣟⠻⠿⠛⢻⣟⠘⣿⣿⠛⣿⢿⣿⣿⠟⠁⢀⣤⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⡟⢳⣤⡄⠀⣿⢸⠟⠁⣠⣶⣿⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠈⢹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣾⣟⠊⢀⣾⣿⠟⠁⠀⠠⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡏⢹⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⢿⣫⠂⢠⣿⡿⠁⠀⠀⢄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡏⢠⣿⡿⠀⠀⠀⠑⢄⠱⡄
⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⠀⣾⣿⠁⠀⠀⠁⠂⢄⡉⠊
⣍⡀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠈⠉⠻⢀⣿⡟⠀⠀⠀⠈⠁⠐⠊⠐
⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⢸⣿⡇⠀⠀⠁⠂⢄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⡇⠀⠀⠉⠀⠒⠈⠴⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣷⠀⠀⠩⣄⠀⠀⠀⠀
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⡄⠀⢈⢿⣷⣦⣄⡀
⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣷⠀⠀⠈⢽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠦⢀⣀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠛⠀⣠⣾⣿⣿⣍⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣧⠀⠈⠘⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⣠⣶⣾⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⡾⣷⣆⣄⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠌⢿⣷⡀⠀⠀⠹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣦⠀⠀⠀⡘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠈⢻⣷⣄⠀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠧⣴⣿⣿⠀⠀⣨⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠙⢿⣦⡀⠀
⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢴⣶⡿⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⠻⣿⣦
⣤⡀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠻
⣿⣿⣆⡄⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣟⡿⠂⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣶⠄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣯⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⡛⠠⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣦⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠛⠿⣆⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠙⢷⣦⣄⢀⡀⠀⣀⣄⡀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠘⢻⣧⣿⣿⣟⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢳⡷⠺⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿
⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣮⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠉⠉⠉⠙⠛⠛⠛⠓⠲⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣴⡷⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠤⠄⢀⣀⣲⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⡟⡀⠀⢀⣼⣿⣼⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣄⡀⠀⠀⠀⠈⠙⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣩⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠎⠀⢠⣾⣷⡀⠀⠉⠲⣤⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⠇⠈⡀⣼⣶⢶⣶⣤⣀⠀⠀⠍⠙⠾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠒⠒⠻⠯⠤⠤⣐⣿⣿⣿⡛⠛⠛⠿⠿
⠀⠀⠀⠀⠉⠘⠃⠃⠀⠀⠀⠑⠬⣀⠠⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣀⠀⢀⣿⡏⢹⣿⣿⣿⢷⣶⣀⠀⠀⠀⠍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠠⣝⠛⢻⣿⣷⣄⠀⠀
⠀⣤⣀⣀⣀⣠⣒⠒⠶⢤⣤⣤⣴⣒⠊⠴⢨⡝⡻⢿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠿⣾⣛⠀⣸⣿⣿⣿⣾⣿⣯⡄⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢁⡄⢰⣿⣿⣾⣶⣦⣀⠈⡀⢮⡑⢿⠎⠃⠀
⠀⠀⠀⠉⠉⢩⣅⣈⡛⠋⠽⠽⠅⠀⠉⠀⠀⠀⠉⠑⠈⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣻⠿⣉⡻⣽⣿⡏⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠙⠁⢀⣾⣿⢫⢹⣿⣿⣿⣟⠀⠀⠈⠂⠁⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣛⣿⣿⠷⣶⣾⣶⣼⣿⣦⣤⣄⣠⡀⠀⠠⣬⣽⣻⣿⣿⣿⣟⡋⠀⣉⢳⢼⠉⡻⠿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢠⣿⡿⠀⣸⣿⣿⡿⣾⢧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣯⣼⣿⣿⣿⣿⣷⣤⣄⣈⣿⣿⣿⣿⣿⡇⡀⣾⣂⠈⠘⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⠿⢧⢴⣿⠛⠻⢿⣿⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣟⣿⡇⠐⡟⠁⣄⡿⢠⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠐⠛⠛⠷⠎⠙⢷⣾⠇⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⡭⣭⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠿⠿⣿⣿⣿⠁⠀⠃⢀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣴⠋⠃⣠⠄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣀⣀⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠩⠀⠉⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⡿⠿⡴⢣⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⡞⢀⡏⡿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⠛⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠊⢰⢷⡟⠄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠉⠉⠐⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⣿⣶⣿⣤⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠟⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢲⣾⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⢟⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠘⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣶⣤⣀⣠⠄⠉⠀⡀⠀⠀⠈⠽⢟⡂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⢤⣀⡀⢀⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠙⠛⠛⠿⠿⠛⠁⠘⠀⠀⠛⣷⣶⣽⣤⡄⣄⡒⠂⠤⠤⣼⣿⣿⣿⡿⣿⣿⣿⣿⠇⠀⣿⡖⠀⠀⠈⠀⠑⠛⠿⢷⣖⣀⡀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠿⠿⣷⣶⣥⣤⣀⣀⠄⠀⡤⣩⣷⠀⠂⠀⠈⠛⢻⣿⣿⡟⠻⠿⣳⣿⣦⢼⣿⣿⣿⣿⣿⣿⣾⣯⡍⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⢙⠋⠙⠛⠛⢽⣴⣾⣿⠟⠻
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣷⣶⣷⣤⣤⣄⣀⣀⣨⣿⣿⣿⣿⣛⣻⣿⣿⣾⣿⠿⢿⣿⣿⣿⣿⣿⠃⢰⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⣸⣿⣿⡟⢰⣶
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣷⣶⣿⣿⣿⣿⣻⡿⠃⠀⠀⠀⠘⠿⠿⠟⠀⢼⠛⠻⣿⠿⠂⠀⠀⢠⣴⣾⣗⣛⣷⣶⣶⣿⣿⣿⠃⣾⣿
⣀⠀⣶⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣶⣦⣥⣀⡥⠄⣀⣀⣀⠀⠉⠉⠀⣀⣤⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⣶⡖
⠉⢠⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⢀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣦⣤⣄⣀⡀⠀⠀⠀⣀⣉⠉⠛⠛⠿⠿⣿⣶⣾⣭⣭⣛⣒⣺⠲⣿⡿⠀⣿⣿⣿⡿⣹⣿⣿⣿⣿⠁⠨⣿⣿
⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⣯⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⢿⣿⣷⣶⣮⣭⣭⣂⣉⣙⠻⠿⠇⠬⠴⣶⣤
⢀⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠛⠻⠿⢿⣿⣶⣶⣤⣤⣄⣀
⣸⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿
⠇⢸⣿⣿⣿⣿⢙⠘⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢨⣟⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣀⣀⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣿⣷⣽⣻⢿⣿⣿⡏⠀⠀⠀⣸⣿⣿⣿⣾⣭⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢉⣿⣿⣿⡄⡀⠔⣢⡀⠀⠀⠀⢀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣶⣶
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⡃⠀⠀⠀⣿⡿⣛⣭⣶⣾⣿⣿⣶⣴⣫⣽⡻⣿⣿⣿⣿⣿⣿⣿⣛⡛⣿⣿⣿⣿⣿⣗⣀⣿⣇⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿
⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⢍⣺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣾⡿⣿⣿⣿⣿⣿⣿⣿⡤⠈⠻⠿⣿⣛⣋⣾⣿⠿⠟⠑⠛⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠉⠛⢲⠯⣟⡿⣿⣿⣿⣿⣿⣿⠿⠞⣮⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⢻⣤⣤⠀⣠⣴⣶⣿⣿⣦⣀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠭⢽⣿⣿⣿⣶⢶⣿⣿⣿⣿⣿⣿⣷⣼⣏⣂⣀⠀⠀⠀⠶⠿⡇⠈⠁⠉⣿⣿⣿⡷⠶⠶⣿⣿⣿⡿⠿⢿⠿⠿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⠁⠀⠑⠐⣲⣶⣾⣿⣭⣯⣺⣿⣷⣿⣟⡛⠛⠻⠎⠿⣻⣿⣿⣿⣷⢶⢾⣿⣿⣿⣗⣖⡖⢼⣿⣿⣿⠦⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⠉⠐⠀⠊⠉⠉⠙⠋⠀⠐⠿⣿⣿⣿⡏⠋⠀⢺⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡾⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣴⡏⣿⢹⡿⢻⡋⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣧⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣦⣥⣘⣧⣄⠹⣆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠾⠗⠘⣇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠂⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⢽⣤⠀⠈⠉⠀⣀⣂⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠑⠉⠀⠀⠐⠈⠉⠁⠀⢻⠀⠀⢀⡲⠂⠀⣦⣄⠀⠀⠀⠀⢠⢠⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠘⠿⢿⣿⣿
⠂⠀⢀⠀⠀⠀⢀⠀⣶⠸⡇⠀⠈⠋⠁⠀⠁⠀⠀⠀⠀⢠⣼⣽⡫⢟⣲⣤⣰⣿⣿⣿⠀⠀⠀⢸⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈
⡀⢀⠀⠈⢐⠀⠀⣀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠈⢹⣿⣿⣿⣿⣄⡀⠀⣿⣿⣿⠸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠊⠀⠀⠀⠀⠀
⣷⣒⡱⠄⠀⠉⠲⠆⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠓⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣀⣿⣿⣿⠀⢸⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⣴⣄⣀⠀⠀
⣿⣿⣿⣿⣶⣦⣔⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⠧⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠸⠿⠟⠉⠀⢀
⣿⣿⣿⣿⣿⡿⡿⣋⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣤⡄⠀⠀⠂⠀⠀⢹⣿⣿⣿⣫⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠚⠃
⡿⣿⣿⣿⡿⢟⠐⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⣿⣿⣆⢀⠀⡆⡀⢸⣿⣿⣿⣿⣿⣮⣛⣹⢩⢍⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⡁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠈⠋⠓⠃⢀⣴⠟⠁⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠩⠋⢿⠛⣿⢿⠇⠡⢸⣿⣿⣿⣿⣿⣿⣿⡿⠾⣼⣽⠿⠯⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣤⣶⠾⠛⠁⢀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀
⣦⣤⣀⡀⠀⠀⠀⢰⣤⣅⣩⣿⢹⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⣸⣿⣿⣯⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣘⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣧⣠⣿⡟⢻⣟⡛⢛⣇⠈⣿⣿⠟⢿⣿⣿⣿⣿⡿⠟⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣤⣉⣀⣼⡿⢦⣉⢛⠀⣸⣿⣿⡿⠋⢀⣠⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠈⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣌⠛⠋⣠⣿⣻⠋⢀⣴⣿⡿⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡏⢻⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⠃⢠⣿⡿⠋⠀⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣽⣿⣟⣿⣯⣽⣾⠃⣰⣿⡿⠁⠀⡀⠈⠠
⣿⠿⠛⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⢿⣿⣿⣿⣿⡏⢠⣿⡿⠁⠀⠀⠀⠐⠤
⣧⣄⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠙⠻⣿⠃⣼⣿⠇⠀⢀⡀⠀⠈⠀
⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣿⣿⠀⠀⠀⢈⠐⢄⠀
⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⣿⣿⠀⠀⢀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⡇⠀⠀⢷⣦⣀⠀
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣷⠀⠀⠐⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠗⣀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⡿⠋⠀⣼⣿⣿⣿⣌⣍⡝⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣧⠀⠀⠘⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣴⣶⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣴⣤⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣦⠀⠀⠈⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣖⣀⣌⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⢿⣧⡀⠀⠀
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣾⣿⣿⡀⣀⣽⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣷⣄⠀
⡀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣿⡿⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠙⢿⣷
⣿⣶⣄⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠙
⣿⣿⣿⣿⣄⡀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣲⡄⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⡆⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣦⣾⣾⣆⣀⣀⡀⠀⠀⠀⠉⠻⢿⣿⣷⣤⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣻⣿⡿⣿⣿⣷⣷⣄⡦⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠿⣿⡿⣶⣾⣽⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠻⢿⣿⣿⣿⣿⣿⣄⣲⣶⣬⣀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿
⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⢿⣧⡆⠄⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿
⣛⣛⣛⣛⡻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⡿⠃⠀⠀⣠⡦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠒⠒⠂⠠⠴⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⡡⠀⠀⣴⡟⠣⢧⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢿⢻⣿⣿⣿⣿⠛⠷⠦⣀⠀⠀⠀⠀⠈⠉⠹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡀⣖⡏⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠀⠀⢾⡿⣷⢀⠀⠈⠙⢔⠠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⣿⡟⠠⠀⢂⣿⣟⣿⣿⣦⣄⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠈⠛⠓⠒⠲⠽⣿⣿⣿⣍⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⢂⠤⣐⠻⢿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣧⣄⡀⢸⡿⠘⣾⣿⣿⣿⣼⣿⣠⠀⠀⠁⠨⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⡀⠀⢀⣀⠀⡀⠀⠀⠰⢮⠉⢹⢿⣷⢄⠀⠀
⠰⠶⠤⣤⣤⣤⠬⣽⣟⣳⣴⣶⠮⠍⠀⠚⠴⢮⣝⠿⢿⠃⢰⣿⣿⣿⣿⣿⣿⣻⣿⠁⠀⣿⡿⣿⣷⣿⣿⣿⠀⠀⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣄⠡⠂⣸⣿⣿⣿⣿⣶⣄⡀⠐⠳⣝⠿⡀⠁⠀
⠀⠀⠀⠀⠀⣴⣦⣬⣭⣙⣒⡒⠀⡀⠀⢀⣄⠀⠀⠃⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡿⢭⣝⠣⢮⣱⣟⢿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠀⠁⢤⣿⡿⠈⣼⣿⣿⣿⣳⡀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣽⣿⣿⣛⣿⡿⠿⣿⡿⣶⣶⣤⣶⣀⠄⠲⠶⣾⣿⣿⣿⣿⣯⠁⠠⣌⠟⡇⢠⠙⠛⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⢇⢀⣿⣿⣿⣯⣿⢹⠀⠀⠀⠀⠀⠀
⠠⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿⣿⣿⣿⣿⠠⢠⣿⡄⢀⡉⢀⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢛⣛⣺⠾⣿⣉⢛⣿⢏⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢙⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⢸⠁⢠⣸⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣉⡉⠛⠀⢙⡿⣿⠁⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣉⠛⠻⡿⢿⣏⠀⠀⠐⣸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣟⠠⠀⡆⠃⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠤⢤⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠂⠀⠀⢀⠀⣀⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣸⠻⠻⢞⡰⣰⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⠈⠁⠀⠀⠀⠉⢘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣿⡇⣸⢠⣇⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠉⣹⡟⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⣚⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⠁⠉⠁⣼⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣳⣷⣆⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠋⠁⠀⠀⠉⠉⠛⠛⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⡀⠀⠁⠀⠈⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣭⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣛⣿⣿⣷⣦⠀⢀⠀⢀⣀⠈⢈⡁⠀⢀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣤⡖⠀⡠⠄⠁⠀⠀⠐⠫⣯⣁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠦⠤⣄⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠀⢀⠀⠀⠀⠉⠉⠙⠛⣋⠁⠀⠀⠀⢈⣙⣿⣷⣷⣦⣠⣬⠅⡐⠒⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⠃⠀⠀⠀⠀⠉⠛⣛⣿⣧⣄⣀⡀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠙⠛⠻⠿⢷⣶⣦⣤⣔⣂⣠⢶⢾⠏⠁⠀⠀⠈⠛⢻⣿⣿⣉⣚⢛⣸⣿⡔⣿⣿⣿⣿⣿⣿⣿⣿⣦⠅⢀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢏⠉⠉⠉⠘⣹⣿⣿⣿⠛⢛
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣶⣶⣦⣤⣤⣤⣼⣿⢿⣾⣿⣭⣽⣿⣻⣿⠟⠻⠿⠿⣿⣿⣿⡟⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣰⡀⠀⠀⢀⣿⣿⣿⠇⣺⡷
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⡷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡀⠀⢀⠀⠙⠛⠛⠃⠠⠛⣋⡻⡟⠋⠀⠐⠀⣶⣾⣿⣭⣝⣻⣿⣾⣿⣿⡿⠀⠿⣿
⡄⢰⣾⣿⣿⣿⣿⣝⣛⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣿⣿⣶⣦⣾⣟⠤⠤⢤⣀⣀⡀⠈⢠⣄⣤⢄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣻⡤
⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⣤⣄⣀⣀⠀⠀⠀⣀⣈⣉⠙⠛⠻⠿⢿⣷⣶⣯⣭⣕⣛⣿⡿⠏⠘⣿⣿⣿⢏⣿⣿⣿⣿⡏⠀⠸⠽⣷
⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⢻⣿⣿⣿⡿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣷⡶⣯⣤⣭⣤⣉⡛⠻⠁⠀⠴⠾⣿
⡌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣶⣶⣦⣤⣄
⠇⣾⣿⣿⣿⣿⣿⣿⢿⣛⣛⣛⣛⣛⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻
⠀⣿⣿⣿⣿⣏⣭⣁⡻⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣭⣟⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣀⣀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣾⣷⣭⣻⢿⣿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣶⣭⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢙⣿⣿⣟⠀⡀⠤⢤⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣽⣿⣽⣿⣿⣿⣿⣶
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⢸⣿⣿⢟⣫⣵⣶⣿⣿⣿⣶⣔⡯⣟⢿⣿⣿⣿⣿⣿⣿⣿⣛⠻⣿⣿⣿⣿⣿⣗⣈⣿⡆⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠶⡯⣱⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⢮⡻⣿⣿⣿⣿⣿⣿⣮⡄⠉⠻⢿⣿⣛⣫⣾⣿⣷⠶⠒⠛⢻⣿⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣟⣿⣿⣿⣿⣿⣿⣿⠁⣀⡀⠀⠀⠀⠈⠉⢟⣲⠭⣛⠿⣿⣿⣿⣿⡿⠿⠷⣽⣼⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣥⠀⣠⣴⣶⣶⣷⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽
⠭⠿⠿⢿⣿⣶⢾⣿⣿⡿⣿⣿⣿⣵⣾⣈⣀⣀⡀⡀⠘⠻⢹⠀⠀⠈⠈⣿⣿⣿⡷⠶⠶⢿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⠿⠿⢸⣿⡟⢸⣿⣿⡟⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿
⠀⠉⠉⠐⠒⠲⠶⠿⢧⣽⣽⣿⣷⣿⣟⣛⣛⠛⠳⠹⢟⣿⣿⣿⣿⣿⡾⣿⣿⣿⡗⣒⣒⣾⣿⣿⡟⠳⣤⠈⠀⢸⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⢦⣤⣀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣍⠉⠉⠉⠛⠛⠒⠶⡘⢍⠉⠝⠁⠀⠚⣿⣿⣿⡟⠛⠁⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢺⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⣶⣤⣀⠨⡿⣿⣿⣿⡟⠛⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⡄⢸⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣇⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⠘⠏⢳⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⠿⡿⢿⣿⠣⠟⢂⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⣤⢷⡄⠀⠈⠉⢠⣐⡄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠋⠁⠁⠀⠀⠀⠭⠍⠄⠈⣇⠀⠀⣐⠖⠂⢰⣤⠀⠀⠀⠀⠀⢤⣄⡀⢠⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢻⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⣤⣯⣟⡽⣳⣦⢼⣿⣿⣿⠀⠀⠀⢸⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠈
⢠⠂⠀⠁⢲⢄⠀⢐⢠⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠍⢿⣿⣿⣿⣄⣀⠀⣿⣿⣿⠘⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠔⠀⠀⠀⠀
⣿⣆⣵⡰⠀⠉⠒⠔⠋⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⠀⢸⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠀⣀⣀⠀⠀
⣿⣿⣿⣿⣷⣶⣤⣀⠀⠂⣼⠀⠀⠀⠀⠀⠀⠀⠀⢞⠽⠊⠑⠀⠀⠆⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣿⠟⠋⠀
⣿⣾⣿⣿⣿⣿⣿⠟⠌⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⠄⠄⠐⠀⠀⢸⣿⣿⣿⡟⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠶
⠿⣿⣿⣿⡿⡟⠣⠑⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⣿⣿⣋⡀⢀⠠⠀⣾⣿⣿⣿⣷⣷⣝⢋⡯⣭⢛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠊⠂⠑⠛⠉⣠⣴⠏⠀⣀⣀⣀⠀⢀⣀⣀⠀⠀⠊⠝⢽⡛⢻⡷⡾⠨⡅⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⣟⠿⠯⠝⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣤⣴⡶⠟⠋⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣴⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⣶⣤⣄⡀⠀⠀⠀⠀⢠⣤⣤⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⣸⣿⣿⣏⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣾⣧⣨⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣶⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣿⣶⠘⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣘⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣛⣿⠿⣟⣛⡛⢀⡏⢹⣿⣿⠛⣿⣿⣿⣿⣿⣿⡿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⠛⢀⣼⣷⡀⠛⠟⠀⣹⣿⣿⣿⠟⠉⢀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠿⠃⢠⣿⢻⡟⠁⢀⣴⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡏⢹⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣏⠏⠀⣴⣿⠟⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣛⣯⣷⠏⢀⣾⣿⠋⠀⠀⢄
⠿⠋⠁⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⡟⠀⣾⣿⠃⠀⠀⠀⠀
⣶⣤⡀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠙⠿⣿⣿⡇⢸⣿⡏⠀⠀⠢⠀⠀
⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠉⠀⣿⣿⠁⠀⠐⠂⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⠀⠀⠒⠂⠀⠀
⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡆⠀⠀⣦⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣧⠀⠀⠸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠟⢛⣃⣤⣤⡀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠋⠀⢰⣿⣿⣿⣿⣂⣤⡝⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣆⠀⠀⠹⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⣰⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣶⢍⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣆⠀⠀⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣖⣀⣬⡯⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠹⣿⣆⠀⠀
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣿⣿⣧⡰⣴⣿⠏⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠘⢿⣧⡀
⡀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⢿⣿⠏⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠈⠻⣿
⣿⣧⣠⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠘
⣿⣿⣿⣿⣀⡀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⡟⣹⣯⣶⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣙⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣷⣃⠻⡻⢿⣧⣷⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠻⢿⣵⣌⣋⡛⠷⠿⢵⣴⣤⢠⡠⡀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⢿⠛⣶⣷⣼⣷⣿⣻⣿⠂⡀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣯⣮⣷⣷⡶⡀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿
⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡛⣐⣼⠿⣠⡄⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿
⣛⣛⣛⣛⣛⡛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠭⠽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⠟⠀⠀⢀⣔⢄⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠒⠒⠂⠤⣽⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢏⠆⠀⢠⣾⠛⠺⢄⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣟⡏⣿⣿⣿⣿⡟⠛⠒⢀⣀⣀⡀⠀⠀⠉⠉⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣔⣷⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠰⣿⢿⡆⡀⠀⠈⠣⢆⠄⡀⠀⢸⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⠓⠄⠁⣼⡽⡿⣿⣷⣦⡄⡀⠀⠀⠉⠻⢿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠉⠉⠉⠁⠐⠒⢿⣿⣿⣦⡀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⢁⣂⠅⡛⠿⢿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣤⣄⣠⣿⠇⢹⣿⣿⣿⢷⣿⣧⠀⠀⠈⠐⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢤⠀⠀⣤⣄⣀⣀⡀⠈⠳⠆⠨⢟⣿⡷⡄⠀⠀
⠒⠶⠦⢤⣤⡴⠭⣭⣿⣷⣤⠤⠌⠕⠀⠚⠴⠩⡟⠻⡇⠀⣿⣿⣿⣿⣿⣿⣭⣿⣀⣐⣼⣿⢻⣿⢾⣿⣿⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠦⠄⠀⢰⣿⡿⣻⣿⣿⣦⣄⠀⠙⠮⡙⠆⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣦⣬⣭⣉⣑⣂⡀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⠶⢯⣝⢲⢮⣯⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣾⣿⠓⢸⣿⣿⣿⢧⡥⠀⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣷⣶⣿⣯⣽⣿⣟⣛⣿⠿⢿⣷⣾⣯⣾⣦⣄⠐⠲⠶⣾⣿⣿⣿⣿⡆⠀⢲⡹⢛⢀⡎⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢰⣿⡏⡄⣼⡿⣿⣟⣾⠇⡄⠀⠀⠀⠀⠀⠀
⠄⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣿⢿⣿⣿⣿⡇⠄⣾⢧⠀⣤⠀⣀⣀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣽⣿⣚⡿⣥⡍⣹⡿⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⣹⣿⣿⣿⡿⠭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⡇⠈⠏⠈⣦⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡀⡀⠉⢃⠀⣹⠿⠇⠐⠁⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⣿⣿⣿⣿⣧⣵⣖⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⡉⠙⢿⠿⣿⡅⠀⠀⢡⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⣁⡀⡸⠊⠘⡋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠦⠤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠛⠁⠀⠀⠂⠀⠀⠀⠠⠸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣏⠛⡻⢵⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⡀⠀⠀⠄⠀⠀⠀⠈⠉⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⠛⢠⠇⡟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠀⢘⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣀⣸⢳⡟⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣲⣿⣿⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⡘⢿⠃⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣇⡀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠘⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣧⡭⢍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠬⢿⣿⣿⣻⣿⣿⣷⡄⠀⠀⠀⣠⢄⡀⢬⠀⠀⢀⡀⠀⠀⠀⠀⣜⣻⣿⣿⣿⣿⣿⣾⡥⠀⢒⣀⠀⠀⠈⠁⢘⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠶⠤⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⡀⠀⠀⡀⠀⠀⠈⠉⠙⣁⣀⠀⠀⠀⣄⣽⣿⣿⣶⣆⣶⣆⣀⡉⢙⣿⣿⣿⣿⣿⣻⣿⣿⣿⠃⠀⣿⡟⠀⠀⠀⠀⠀⠈⠉⢟⣻⣤⢄⠤⢀⣀⣀⣿⣿⣿⣛
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠙⠛⠿⠿⣷⣶⣧⣤⣐⣀⣰⠇⠀⠀⠀⠀⠉⠩⣿⣿⡮⣉⣘⣼⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣀⣉⣁⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⢡⣿⣿⣿⠋⡉⠉
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿⣾⣯⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⠁⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣄⣃⣀⣀⡀⣼⣿⣿⡟⢨⣟⣛
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣯⣅⡀⠀⠀⠈⡉⠋⠁⠀⠊⠭⠙⣻⠋⠁⠀⠁⠸⣿⣿⣷⣦⣭⣿⣿⣿⣿⣿⠁⠚⠻⠿
⠀⣶⣿⣿⣿⣿⣯⣭⣛⣻⣿⣿⣿⣿⣿⠇⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⣿⣦⣾⣒⣒⡶⠤⣤⣀⡀⢀⡂⣔⣂⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡧⣇⠺
⢠⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣷⣶⣶⣤⣄⣀⣀⠀⠀⠀⢀⣉⣉⣙⠛⠻⠿⢿⣷⣶⣯⣭⣿⣲⣂⡀⠻⣿⡿⢟⡾⢿⣿⣿⣿⢀⡀⢓⠺⠁
⡜⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣾⣿⣿⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠂⡀⠀⠈⠉⠙⠛⠻⠿⠿⡿⢳⣶⣶⣦⣤⣍⣛⡃⠈⠐⠐⠿⠟
⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣷⣶⣦⣤
⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛
⢸⣿⣿⣿⣿⣴⣭⣝⣿⡺⣿⣿⣿⣿⠀⠀⠀⢰⣾⣭⣟⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣶⣦⣤⣀⣀⡀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡻⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣯⣝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢻⣿⣿⣇⢀⠠⠢⡄⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢱⣿⣧⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⣿⡿⢟⣯⣽⣶⣶⣶⣦⣞⡭⣟⢿⣿⣿⣿⣿⣿⣿⣿⣟⣛⢿⣿⣿⣿⣿⣿⣂⣹⣷⡀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠿⢶⣯⢟⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⢮⡻⣿⣿⣿⣿⣿⣿⣿⣥⡀⠙⠿⡿⣟⣛⣵⣿⣿⣶⡶⠾⠇⢰⣦⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣾⣯⣿⣻⣿⣿⣿⣿⣿⡇⠤⣀⡀⠀⠀⠀⠀⢬⣝⣓⠾⣽⣻⢿⣿⣿⣿⣿⣿⡿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣯⣶⣶⣶⣶⣼⣿⣾⠋⣩⣴⣶⣶⣶⣬⡻⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⡯⣽⣿⣿⣿⣶⡶⣿⣿⣿⣿⣧⣽⣇⣀⣀⡀⠀⠀⠹⠋⡇⠀⠀⠀⠉⣿⣿⣿⣧⠴⠶⢾⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⢸⣿⡗⢰⣿⣿⡟⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿
⠈⠉⠓⠒⠒⠶⠧⠦⣿⣯⣟⣙⣟⣿⣾⡿⠛⠛⠿⠿⠹⢿⣿⣧⣶⣶⣶⣿⣿⣿⣧⡤⣤⣾⣿⣿⡏⠙⠶⠶⠿⢿⣿⣿⣿⠀⠀⠘⠛⠃⢸⣿⣿⣷⣄⠉⠉⠉⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿
⣦⣤⣀⡀⠀⠀⠀⣀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠳⠶⠶⡈⢍⠛⢛⠋⠁⣿⣿⣿⡗⠺⠛⢻⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠛⠷⣤⡀⣈⣻⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠉⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿
⣷⣦⣄⡀⠀⠨⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⠀⠀⣄⣤⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⢺⣿⣿⣧⣤⣤⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣇⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠛⠛⠛⠿⠛⠁⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡯⠊⡛⠛⡟⠛⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⡿⣿⢠⣤⠠⠙⢓⠀⡀⡂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⡏⡟⠓⠁⠀⠀⠈⠘⠛⠃⠀⢷⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⢠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣿
⠈⠃⠀⠐⠒⠀⠀⠀⠤⢤⣤⢸⡇⠀⠀⠓⠂⠀⠀⠀⠀⠀⢀⣀⣴⣢⢔⡦⢠⣿⣿⣿⠀⠀⠀⢸⣿⣿⢿⣿⣿⡄⠀⢸⣿⣿⣇⣾⣿⣿⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀
⠀⠀⠀⠀⠄⠀⡀⠀⠀⢤⡁⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠮⢸⣿⣿⣿⣤⣀⡀⣿⣿⣿⠘⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⠀⠀
⣾⣷⣈⢠⠉⠨⡊⠧⠌⠛⠃⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⠀⢸⣿⣿⡿⣿⣿⣷⠀⠀⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⠀⡀⠀
⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣿⡇⢻⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣸⣿⠷
⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⠏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⡈⠁⠂
⢯⣿⣿⣿⣿⣿⣟⢏⠐⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣤⡄⠀⠀⡅⠀⣹⣿⣿⣿⣯⣿⡽⢿⢹⣟⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀
⠈⠒⠉⠽⠭⠿⠚⠀⣠⡾⠋⠀⠀⠀⠀⣀⣀⡀⠀⠀⠠⡺⢟⠿⣿⡿⠶⡧⢻⢸⣿⣿⣿⣿⣿⣿⣷⣾⣼⡱⠻⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣄⣀⣠⣤⣴⠿⠋⠀⠀⠘⢯⣾⣿⣿⣿⣿⣿⣦⡀⠀⣽⣿⣿⣿⣿⡇⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⣴⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀
⣶⣭⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣸⣿⣿⣯⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣶⣦⣄⣀⢐⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣷⣶⣤⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣜⡛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠛⠛⠛⣿⣟⠛⠿⠟⠙⡟⠛⣿⡋⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣌⠻⠶⠂⣰⣇⠘⢿⣿⠀⢹⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠀⢹⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣷⣶⣶⣿⡍⢳⣤⡤⠀⣼⣿⣿⡿⠋⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡏⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣼⡿⣸⠟⠀⣠⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⡿⣟⣿⠃⢀⣾⣿⠟
⠛⠁⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣷⣶⣿⣶⣶⣿⣿⡏⢀⣾⣿⠋⠀
⣶⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠈⠙⠻⢿⣿⣿⣿⣿⠀⣾⣿⠇⠀⢀
⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠈⠛⠿⡇⢰⣿⡿⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⢸⣿⡇⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⡇⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡇⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢛⣋⣩⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⣾⣿⣿⣿⣷⣦⡦⢉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⢠⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣷⣂⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣏⢀⣰⣼⡏⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⡄
⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣿⣿⡢⣶⣾⠟⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠂⠻⣿
⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠙
⣿⣤⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⣿⣿⣿⣖⢄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠰⠾⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢋⣿⠧⠀⢀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡃⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣮⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣾⣧⠀⡨⠘⢿⣢⣐⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠛⢷⣥⣠⠀⠀⡸⣋⢄⣱⡠⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠻⠗⣿⣾⢾⣾⣷⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣏⣄⣵⣤⣧⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿
⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡏⠉⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷

                    ䷩ 𝚕𝚒𝚗𝚎 2758

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/09/epo-purachasing-power/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/09/epo-purachasing-power/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ For_EPO_Staff_on_Dutch_Territories_Purachasing_Power_Fell_12%_in_Just_One
Year_While_EPO_Increased_Its_Fees⠀✐


Posted in Europe, Patents at 5:49 pm by Dr. Roy Schestowitz


Video_download_link | md5sum ee33fa5440e3ff966c0c83596b29e2ba
Lowered Salaries at EPO
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/inflation-epo-issues.webm


Summary: Multinational corporations and billionaires may not mind this (they
profit even more; price hikes all across the board!), but the EPO is making
itself extremely unattractive to much-needed researchers and it’s pricing
itself out of the reach of SMEs (which the EPO itself has just admitted are no
more than a fifth of all patent applications)


THE number of patents granted by the EPO has plunged thanks to industrial
actions, which culminated in a strike last month. The EPO is back with António
Campinos where it was with Benoît_Battistelli just half a decade earlier; the
Office is just faking “health” by granting loads of fake patents, including a
lot of European_software_patents.


“…for workers stationed in The Netherlands the living expenses are soaring
while the EPO suspends the standard salary increase (keeping up with national
inflation rates).”The document discussed above concerns the vastly lowered
incentive to join the EPO; not only is there no work security anymore (5-year
contracts); for workers stationed in The Netherlands the living expenses are
soaring while the EPO suspends the standard salary increase (keeping up with
national inflation rates).


In the words of the union:


     08 April 2022
     su22011hp – 0.2.1


     § Inflation at 11.9%⠀➾


     § Extraordinary times request extraordinary measures – Request for
     intermediate salary adjustments.⠀➾


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


     Inflation is at an all-time high since the euro was launched in 1997.
     It is not a mere indicator anymore; it is here to hurt. The inflation
     index published by Eurostat for March 2022 is 7.5% for the eurozone
     and 11.9% for The Netherlands when compared with prices a year before
     on March 2021. And still growing. The trend stays worrying upwards,
     with no visible signs of a stabilisation, let alone a downward trend.
     In fact, the problem of inflation is that once established in the
     economy it hardly finds a downward trend. We all maybe remember
     efforts of European economies in the late 80s to reduce inflation
     levels, during a period of both long-term inflation and economic
     stagnation, called stagflation.


     Double digit inflation figures seemed to belong to a remote past.
     This is no longer true. If salaries remain nominally the same while
     losing purchasing power, employee salaries will melt like ice in the
     sun. In a short period of time, salaries and pensions will be reduced
     to a shadow of what they are today.


     EPO’s management looks at this economic disaster as an opportunity to
     award its staff no inflation adjustment at all, using a sophisticated
     intellectually dishonest structured scheme which purpose is to never
     grant any nominal salary adjustment. Therefore, permanently eroding
     all career and pension prospects. EPO’s management reminds us of
     bankers, advertising for complex structured financial products that
     promise a “potential” return on investment to customers. However, the
     vast array of mala fide exception clauses in those investments always
     and hopelessly produced 0% returns at the product maturity. Sounds
     familiar? It is not a coincidence, knowing that our salary adjustment
     procedure was produced by such bankers, in order to achieve a 0% by
     design.


     SUEPO expects in these extraordinary times, extraordinary leaders
     able to amend their decisions for the best of the EPO and their most
     valuable asset, staff.


     SUEPO requests a sustainable workforce management by intermediate
     salary adjustments as done at the Coordinated Organisations and the
     EU.


     Your SUEPO The Hague Committee


     They are the butlers of a whole universe
     Lords by force lawless dispatchers
     They fill their pockets, drink new wine
     And dance around at the king’s pine forest


     Zeca Afonso – “Os Vampiros” (The Vampires)


The way things are going, the Office will quickly run out of people capable of
doing the job it was entrusted to do. It’s a disaster in the making and those
who make the mess are profiting some_other_way. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2917

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/09/irc-log-080422/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/09/irc-log-080422/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_April_08,_2022⠀✐


Posted in IRC_Logs at 2:02 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-080422.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-080422.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-080422.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-080422.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
 QmapJV7TxerQRKg8hXkq4NT5AaUg1SVDJT7uvTXoJ4cmVz #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmXUSYMQRzoSEUWMQ551RNF2NbcsgqcgjMUPfzFVkKrero (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmVrJSkHKAWpycr6eReDspmFiaCVwuS8fL7ZH4zcyRNi7g social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmeMDrbiudGdXYvrHLPjfu65gCs9A9b8ccycUexLSS5jyK social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmTW6ZyHcKoGtsUGBNS4X7Mwv7cv1jvAvQXwjLjjUAQRCh #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmYXJTNMmH6XPa7EZzV97k7AkGGrjCv22b289KBsgYSk1P (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmXiUwsU5FLqEjVdjhshe3zrCYcaqSrMKeAioAjxCxQun8 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmbUVh2sqbuh2YaFusAmuLaqXY1PpHzLdUof7SVPyG6771 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmPokuDJbuL2FN7E9h2TvVkafexTCncL78fivWTmKvQBfi



                    ䷩ 𝚕𝚒𝚗𝚎 3044

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/04/09/microsoft-github-is-censorship/#comments
    Gemini version at gemini://gemini.techrights.org/2022/04/09/microsoft-github-is-censorship/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Microsoft_GitHub_the_King_of_DMCA_Censorship_(Removing_Free_Software)⠀✐


Posted in Free/Libre_Software, Microsoft at 6:58 am by Dr. Roy Schestowitz


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇DMCA Notices Took Down 19,276 GitHub Projects Last year⦈
                 If this is what “love” is like, what is hate?


Summary: Notice the very_high_acceptance_ratio; Microsoft loves “open source”
like it loves the OSI — in its back pocket and inside the bin


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠉⡆⡿⡀⡜⢀⠊⠑⠀⡞⡄⠀⢸⢆⢸⠠⠠⡀⡆⡅⡠⠤⢠⢠⢠⠤⠀⠈⢹⠉⡠⢤⢠⠤⡄⣇⠄⠀⠎⠙⡆⡄⢄⢄⣠⢠⢠⠤⡀⠀⢺⠀⢎⢱⠀⠘⢉⠊⢉⠏⣰⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠐⠃⠃⠑⠀⠀⠂⠘⠘⠉⠑⠀⠘⠈⠛⠐⠔⠁⠃⠃⠃⠐⠘⠀⠐⠈⠃⠀⠘⠀⠓⠘⠘⠀⠃⠋⠂⠀⠃⠐⠁⠃⠚⠘⠃⠋⠘⠀⠃⠀⠘⠀⠀⠚⠰⠐⠁⠀⠈⠀⠑⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠤⡀⠀⢀⢠⠀⢠⠀⠀⠀⡄⠀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⠐⡆⠀⢹⢸⠒⢺⢸⠀⡇⡏⢱⠀⢸⠒⠃⡏⢸⠉⡆⡇⡍⠃⡎⢑⢹⢐⠩⡄⠀⡇⠀⡌⢹⢘⢭⠈⠁⠀⢃⠇⡏⠑⠨⢹⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠁⠁⠈⠁⠀⠈⠀⠀⠁⠀⠁⠐⠁⠈⠀⠈⠁⠈⠀⠉⠀⠀⠉⠁⠈⠈⠀⠁⠀⠁⠀⠘⠀⠈⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠤⠦⠐⠢⠂⠒⠂⠂⠶⠂⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡻⣿⣿⣻⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣟⣿⣿⣿⣿⣻⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⡿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣿⣿⣿⣿⣯⣟⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣯⣿⣯⣿⣹⣻⣿⣿⣿⣝⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣝⣿⣻⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣾⣽⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣯⣮⣯⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣽⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣶⣷⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3096

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_09/04/2022:_KDE_Frameworks_5.93⠀✐


Posted in News_Roundup at 8:28 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


⚓ Video ☛ Fedora_vs_Debian_and_Arch_Linux_–_Invidious⠀⇛


     Lets breakdown Linux Distributions and figure out which one is good
     at what.


⚓ Video ☛ How_do_you_prefer_writing_your_if_statements?_–_Invidious⠀⇛


⚓ Video ☛ Can_I_Fit_A_Tiling_Window_Manager_On_My_Mouse?_–_Invidious⠀⇛


     I have a gaming mouse for playing FF14 but I wondered if I can fit my
     tiling window manager onto it and have it be remotely usable, turns
     out it’s a terrible idea but it works.


⚓ 379.5_–_Phishing_Season⠀⇛


     1:06 Linux Innards
     42:46 Check This Out
     44:16 Announcements & Outro


     In our Innards section, we talk about how much security is enough.


§ Applications⠀➾


⚓ Linux Links ☛ 4_Best_Free_and_Open_Source_Linux_Flickr_Tools⠀⇛


     
     Flickr is an online photo management and sharing application created
     in 2004 and subsequently acquired by the web portal organisation,
     Yahoo! Inc. Flickr has a large user base that rely on this storage
     site to host and share their 6 billion images with family and
     friends. The application is particularly popular among the blogging
     community, but faces stiff competition from the likes of Picasa,
     Facebook, and others. There is a free version of Flickr which allows
     limited space. If users need more bandwidth, the ability to show HD
     video, archiving, and ad-free browsing, they can upgrade to a
     relatively inexpensive Pro account.


     Whilst there have been no official Flickr tools released for Linux,
     the developers have made the Application Programming Interfaces
     (APIs) available to software developers. The APIs allow Flickr to be
     integrated into other Linux software.


⚓ Linux Links ☛ 4_Best_Free_and_Open_Source_Web_Application_Firewalls⠀⇛


     
     A web application firewall (WAF) is a type of application firewall
     that lets you see and analyze HTTP traffic to and from a web
     application. It has the objective of preventing attacks that seek to
     deny service and steal data. It gives the administrator direct
     control over the requests and the responses passing through the
     system without needing to modify backend code. A WAF differs from a
     standard firewall by protecting a specific web application or set of
     web applications. And it does this without actually touching web
     applications.


     Unprotected web applications are the easiest entry point for
     criminals and vulnerable to a number of attack types. Once a web
     application security vulnerability is discovered, it must be promptly
     fixed. Virtual patching using a WAF or patching the web application
     code directly are two solutions. Preventing attacks in application
     code can be difficult and may need painstaking maintenance, patching
     and monitoring at multiple layers of the application topology. And
     web application attacks are the main cause of data breaches. About
     75% of all attacks are focused at the web application level. Most
     websites suffer dozens of attacks every day and some popular sites
     suffer, on average, a thousand attacks per hour. WAFs are deployed to
     add an external security layer; this improves a system’s security.
     They detect and prevent attacks before they reach web applications.


⚓ Mastersearch_released⠀⇛


     Like announced in my previous post, I released mastersearch,
     “Searching the web from the CLI”.


§ Instructionals/Technical⠀➾


⚓ H2S Media ☛ How_to_install_Steam_on_Ubuntu_22.04_LTS_Jammy⠀⇛


⚓ H2S Media ☛ How_to_install_Microsoft_SQL_Server_on_Ubuntu_20.04_LTS [Ed: It
is proprietary, poorly built (DrawBridge), and not trustworthy)]⠀⇛


⚓ Linux Capable ☛ How_to_Install_Opera_Browser_on_Fedora_36_Linux⠀⇛


     Opera is a freeware, cross-platform web browser developed by Opera
     Software and operates as a Chromium-based browser. Opera offers a
     clean, modern web browser that is an alternative to the other major
     players in the Browser race. Its famous Opera Turbo mode and its
     renowned battery saving mode are the best amongst all known web
     browsers by quite a margin, with a built-in VPN and much more.


     In the following tutorial, you will learn how to install Opera
     Browser on Fedora 36 Linux workstation desktop with optional branches
     stable, beta, or the nightly development version using the command
     line terminal with tips on maintaining and removing the browsers if
     required.


⚓ ID Root ☛ How_To_Install_Seafile_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


     In this tutorial, we will show you how to install Seafile on Ubuntu
     20.04 LTS. For those of you who didn’t know, Seafile is an open-
     source, self-hosted file sync that shares the solution with high
     performance and reliability. Seafile enables you to put files on your
     own server and allow others and your different devices to sync and
     access it. Seafile is written in C and Python programming language
     and provides similar features like Dropbox, mega.co.nz, and others.


     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 Seafile open-source file-hosting and cloud storage
     system on Ubuntu 20.04 (Focal Fossa). You can follow the same
     instructions for Ubuntu 18.04, 16.04, and any other Debian-based
     distribution like Linux Mint.


⚓ ID Root ☛ How_To_Install_Terraform_on_AlmaLinux_8_–_idroot⠀⇛


     In this tutorial, we will show you how to install Terraform on
     AlmaLinux 8. For those of you who didn’t know, Terraform is an open-
     source infrastructure as a code software tool that enables you to
     safely and predictably create, change, and improve infrastructure.
     Terraform is built by Hashicorp and released under Mozilla Public
     License. It supports public, private as well as hybrid cloud, as of
     now Terraform supports 145 providers, which includes popular
     providers like AWS, Azure cloud, GCP, Oracle cloud, and many others.


     This article assumes you have at least basic knowledge of Linux, know
     how to use the shell, and most importantly, you host your site on
     your own VPS. The installation is quite simple and assumes you are
     running in the root account, if not you may need to add ‘sudo‘ to the
     commands to get root privileges. I will show you the step-by-step
     installation of the Terraform on an AlmaLinux 8. You can follow the
     same instructions for CentOS and Rocky Linux.


⚓ ELinux ☛ How_to_set_watermarks_in_video_using_FFMPEG⠀⇛


⚓ ELinux ☛ How_to_install_LetsEncrypt_SSL_on_Bitnami_WordPress_Server?⠀⇛


     To install a free LetsEncrypt SSL certificate on bitnami WordPress
     installation, do the following…


⚓ Specify_the_Timezone_with_Linux_date_Command_–_Putorius⠀⇛


     The date command is a powerful tool provided by the GNU Core
     Utilities package. The formatting options are incredibly useful when
     writing scripts. If you are unfamiliar with this tool read our primer
     The Linux Date Command – Display, Format & Set the Date on Linux. In
     this Linux quick tip we are going to use the TZ environmental
     variable to specify the timezone with the Linux date command. I use
     this often when I am working with servers that are geographically
     distant from me. For example, when I need a script to send me an
     email when an action completes. Having the date time sent to me using
     my timezone stops me from needing to do time conversions. It is also
     handy if you simply want to display the date and time in a different
     time zone.


⚓ How_to_Flush_Local_DNS_Cache_on_Linux_–_Putorius⠀⇛


     We aren’t going to go into how the whole DNS protocol works. However,
     it is important to know that all the name and IP address mappings are
     cached locally. This is done for speed and efficiency. So the next
     time you go to putorius.net, the DNS resolver can read it’s local
     cache instead of doing a lookup over the internet. Sometimes it is
     necessary to flush the DNS cache of your system. Maybe the IP address
     of the system you are trying to reach has changed? If so, you need to
     flush your local DNS cache or you will not be able to reach it.


⚓ Specify_the_Timezone_with_Linux_date_Command_–_Putorius⠀⇛


     The date command is a powerful tool provided by the GNU Core
     Utilities package. The formatting options are incredibly useful when
     writing scripts. If you are unfamiliar with this tool read our primer
     The Linux Date Command – Display, Format & Set the Date on Linux. In
     this Linux quick tip we are going to use the TZ environmental
     variable to specify the timezone with the Linux date command. I use
     this often when I am working with servers that are geographically
     distant from me. For example, when I need a script to send me an
     email when an action completes. Having the date time sent to me using
     my timezone stops me from needing to do time conversions. It is also
     handy if you simply want to display the date and time in a different
     time zone.


⚓ Ubuntu Handbook ☛ Hide_Username_&_Enable_Tap_to_Click_in_Ubuntu_22.04_Login
Screen_|_UbuntuHandbook⠀⇛


     This simple tutorial shows how to hide user list and/or enable
     touchpad tap clicking in login screen of Ubuntu 22.04 LTS.


     GNOME, the default desktop environment, has some hidden keys to
     configure the login screen options. However, you need gdm (Gnome
     Display Manager) user privilege who handles the default login.


     After following this tutorial, Ubuntu will no longer display
     usernames in login screen. Instead, you need to manually type user-
     name and then password to login.


⚓ Ubuntu Handbook ☛ [Quick_Tip]_Enable_‘Open_as_Administrator’_Option_in_Ubuntu
22.04_|_UbuntuHandbook⠀⇛


     Want to open folder or edit file as administrator (aka root in
     Linux)? Here’s how to do the trick by adding menu option in Ubuntu
     22.04 file manager.


     The ‘Files’ (aka nautilus) has an extension called nautilus-admin to
     do administrative operations. With it, you may right-click on folder
     and select “Open as Administrator“, or right-click on file and select
     “Edit as Administrator“.


     Don’t like MS Windows, it however does not support running an app as
     root.


⚓ Configure_TOTP_Two-Factor_Authentication_on_Apache_Guacamole_–
kifarunix.com⠀⇛


     In this tutorial, you will learn how to configure TOTP two-factor
     authentication on Apache Guacamole. Time-based One-time Password,
     TOTP, is a kind of multi-factor authentication which adds an extra
     layer of authentication on top of the usual username/password based
     authentications. This improves the security of your accounts.


⚓ Install_Wireshark_on_Rocky_Linux_–_kifarunix.com⠀⇛


     In this guide, we are learn how to install Wireshark on Rocky Linux.
     Wireshark is the world’s foremost and widely-used network protocol
     analyzer.


⚓ Configure_Guacamole_MySQL_Database_Authentication_–_kifarunix.com⠀⇛


     In this tutorial, you will learn how to configure Guacamole MySQL
     database authentication. Guacamole supports various authentication
     mechanisms including database authentication via MySQL, PostgreSQL,
     or SQL Server databases.


     So how can you can enable and configure Guacamole MySQL database
     authentication?


⚓ Guacamole:_How_to_fix_RDP_server_closed/refused_connection:_Security
negotiation_failed_(wrong_security_type?)_–_kifarunix.com⠀⇛


     This short tutorial shows you how to fix RDP server closed/refused
     connection: Security negotiation failed (wrong security type?) error
     while connecting to Windows systems using Apache Guacamole.


§ Games⠀➾


⚓ PS_Vita_release:_osu!octave_(osu!_port_for_PS_Vita)_–_Wololo.net⠀⇛


     osu!octave is a free and open source rhythm game designed to play
     osu!standard beatmaps, optimized for best performance and playability
     on PlayStation Vita.


     Its core (as in, the very base of hit objects logic and some parts of
     architecture) is based on osu-ds, an unfinished osu! port to Nintendo
     DS made by Echo in 2009 and released under the BSD-2 license.


⚓ PSN_Bug_Causing_Game_Licenses_to_Expire_on_PS3,_Vita [Ed: DRM in action,
punishing those who followed the "official" routes]⠀⇛


     A PlayStation Network bug is causing game licenses to suddenly
     expire, preventing users from playing games on the PS3 and Vita.
     First reported for purchased and downloaded versions of Chrono Cross,
     the bug has also affected games like Chrono Trigger and many others.
     Evidence points to the phenomenon being a network glitch. [Thanks,
     Prima Games!]


⚓ Users_report_their_digital_PlayStation_classics_are_‘expiring’_and_unplayable
[Ed: Lessons on DRM]⠀⇛


⚓ GO Media ☛ Chrono_Cross_And_Other_Classics_Suddenly_‘Expiring’_On_PS3,_Vita
[Ed: Lessons on DRM again]⠀⇛


⚓ Every_Unreal_Engine_5_Game_So_Far_–_GameSpot⠀⇛


     Unreal Engine 5 is the latest version of Epic Games’ popular game
     development software and has been available for use since the start
     of 2021. A year later, more studios have begun to adopt the software
     as the foundation for projects that can leverage its versatile power
     to create detailed games.


§ Desktop Environments/WMs⠀➾


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


⚓ 9to5Linux ☛ KDE_Frameworks_5.93_Brings_Multi-Cursor_Support_for_Text_Editor
Apps,_over_280_Changes⠀⇛


     KDE Frameworks 5.93 comes with lots of improvements for your favorite
     KDE apps, including multi-cursor support for Kate and other
     KTextEditor-based apps. Users are given three ways to create multiple
     cursors, including Alt+Click in different places, Alt+Ctrl+up/down on
     lines above or below the current one, and Alt+Shift+I after selecting
     multiple lines of text.


⚓ KDE_Ships_Frameworks_5.93.0_–_KDE_Community⠀⇛


     KDE today announces the release of KDE Frameworks 5.93.0.


     KDE Frameworks are 83 addon libraries to Qt which provide a wide
     variety of commonly needed functionality in mature, peer reviewed and
     well tested libraries with friendly licensing terms. For an
     introduction see the KDE Frameworks release announcement.


     This release is part of a series of planned monthly releases making
     improvements available to developers in a quick and predictable
     manner.


§ Distributions⠀➾


⚓ Web Pro News ☛ Elementary_OS_Founders_Split,_Putting_Project_In_Question⠀⇛


     The co-founders of the Elementary OS project have split, leaving many
     open questions about one of the most popular Linux distributions
     (distro).


     Danielle Foré and Cassidy James Blaede co-founded the Elementary OS
     project in an effort to help further Linux on the desktop. Elementary
     is based on Ubuntu LTS (Long-Term Support) and is often compared to
     macOS, providing a similar default look and feel. The distro has won
     its fair share of praise, and currently sits at number 11 on
     DistroWatch.com.


     Unfortunately, there appears to be trouble in paradise, with the two
     co-founders parting ways, according to Foss Force.


⚓ Paul Thurrott ☛ Elementary_Founder_Exits_the_Company⠀⇛


     Elementary founder Cassidy James Blaede revealed that he’s left the
     company, opening questions about the future of its Linux
     distribution. It appears that he was basically forced out of
     Elementary by co-owner Dani Foré.


     “Over the last decade, I’ve worked to help build elementary into what
     it is today: a world-class operating system lead by a team who is
     involved in and oftentimes driving the direction of the greater open
     source desktop space,” Blaede writes in his goodbye post. “In 2011 I
     founded elementary, LLC. so we could have a legal entity under which
     to do business, sign agreements, etc. I owned and ran the company for
     seven years, bearing the entirety of the legal responsibility and
     handling much of the administration and logistics.”


⚓ Barry Kauler ☛ Consolidation_of_date_and_time_menu_entries⠀⇛


     Earlier today I posted about an improvement to the Setup menu:


     https://bkhome.org/news/202204/remove-duplicate-pupcontrol-entries-
     in-setup-menu.html


     Now for something that I have wanted to do for a very long time…


⚓ Barry Kauler ☛ Remove_duplicate_PupControl_entries_in_Setup_menu⠀⇛


     In ye olden days, Puppy had an entry “Wizard Wizard” in the Setup
     menu, which was a frontend to the other “wizards”.


     This idea of a “wizard” was inherited from Windows 95:


     http://toastytech.com/guis/win952.html


     Quoting:


     To simplify some of the more complicated operations in Windows,
     Microsoft added “wizards”.


     A “wizard” is usually a dialog box that walks you through each
     specific step needed to complete the operation.


     Typically a wizard presents a few discrete choices at a time across
     several pages you can navigate with a “Back” and “Next” button. The
     last page will usually have a “Finish” button that completes the task
     using your selected choices.
     I do think that the term “wizard” has had its day, and intend to
     phase it out of the Setup menu. Firstly, though, in Easy 3.4.5 these
     two entries circled in red, both run PupControl:


§ New Releases⠀➾


⚓ 9to5Linux ☛ MX_Linux_21.1_Released_with_Linux_5.16_for_AHS_Edition,_Based_on
Debian_GNU/Linux_11.3⠀⇛


     Based on Debian GNU/Linux 11.3, MX Linux 21.1 brings back the disk-
     manager utility to the ISO images, adds various improvements to the
     installer, updates many of the pre-installed packages, and introduces
     the mx-samba-config utility for those who want to configure Samba and
     CIFS shares in a desktop-agnostic way.


     On top of that, this release bumps the kernel version on the AHS
     (Advanced Hardware Support) image, which features the Xfce desktop
     environment by default, to Linux 5.16.


§ Gentoo Family⠀➾


⚓ Make Use Of ☛ Sick_of_Compiling_Gentoo_Linux?_Then_Try_the_New_LiveGUI
Distro!⠀⇛


     The Gentoo project has announced a new LiveGUI image in a post on its
     official blog.


     The Gentoo Linux distribution is known for giving users as much
     manual control over what’s installed on the system, to the point
     where users are encouraged to compile most of Gentoo’s software from
     source to tailor its performance to the user’s CPU architecture.


     However, the LiveGUI version is intended to allow prospective users
     to test drive a full desktop system by extracting the image to a USB
     stick or optical media before committing to the installation process.


     True to the distribution’s fast-moving nature, Gentoo plans to offer
     a new LiveGUI version every week.


     While the Gentoo project supports multiple architectures, the ISO
     image is for x86-64 systems. It weighs in at 4.8 GB and can be
     obtained from Gentoo’s download page.


§ Debian Family⠀➾


⚓ OS News ☛ Raspberry_Pi_OS_no_longer_defaults_to_user_“pi”_–_OSnews⠀⇛


     This is a pretty substantial change that might break some
     applications that assume the default “pi” user exists.


⚓ Raspberry_Pi_Just_Made_Two_Huge_Changes_for_Security_and_Convenience⠀⇛


     A new update to Raspberry Pi OS (formerly Raspbian) offers several
     improvements over previous releases, though one of these
     “improvements” may be a bit controversial. On the one hand, setup is
     more convenient and the Pi is more secure. But it’s time to say
     goodbye to the default user.


     From here on out, Raspberry Pi OS won’t come with a default user
     called “pi.” Additionally, the operating system won’t give you the
     default “raspberry” password. That means the Raspberry Pi setup
     wizard is now unskippable, as you must enter custom login
     credentials. (That said, the default user won’t disappear if you
     update your Pi, and the new setup wizard won’t stop you from using
     the “pi” username or “raspberry” password.)


     This change is probably overdue. Default usernames and passwords
     present a security risk for remote access devices, and of course, the
     Pi is a popular home server solution. (You can run the sudo rename-
     user command to change the default credentials on an older Pi.)


§ Devices/Embedded⠀➾


⚓ Linux Gizmos ☛ Alfa_Network_long_range-low_power_Wifi_HaloW_AHPI7292S_RPI
HAT⠀⇛


     
     The AHPI72992S by Alfa Network is a Raspberry Pi HAT that guarantees
     long distance wireless communication for low power due to its WiFi
     HaLow(IEEE 802.11ah) standard protocol.


     The expansion board is built around the NRC7292 SoC that is IEEE
     802.11ah compliant and Qorvo’s RFFM6901 single chip front end module
     (FEM). Due to its design, the AHPI72992S module is optimized to
     operate in the sub 1GHz license-exempt band.


§ Mobile Systems/Mobile Applications⠀➾


⚓ Tech Times ☛ Android_13’s_Photo_Picker_Might_Get_an_Upgrade_|_Seen_on_Android
12_June_Feature_Drop?_|_Tech_Times⠀⇛


⚓ Android Police ☛ Hands-On:_Android_12L_is_a_big_step_in_the_right_direction
for_tablets⠀⇛


⚓ Good_News,_LG_Just_Confirmed_at_Least_Three_Phones_Will_Get_Android_12_–
Review_Geek⠀⇛


⚓ Giz China ☛ Top_10_Android_UI_with_the_most_fluent_and_fast_performance⠀⇛


⚓ Make Use Of ☛ 6_Really_Useful_Google_Widgets_to_Add_to_Your_Android_Home
Screen⠀⇛


⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss_this_week_–_Android
Apps_Weekly⠀⇛


⚓ Motorola_MA1_Wireless_Android_Auto_Car_Adapter_review_–_It_just_works!_(most
of_the_time)_–_The_Gadgeteer⠀⇛


⚓ Android Central ☛ These_Android_phones_emit_the_most_radiation,_study_claims
|_Android_Central⠀⇛


⚓ Bypass_FRP_Lock_on_Samsung_devices_with_iToolab_UnlockGo_(Android)⠀⇛


⚓ Motorola_MA1_Wireless_Android_Auto_Car_Adapter_review_–_It_just_works!_(most
of_the_time)_–_The_Gadgeteer⠀⇛


⚓ Make Use Of ☛ What_Is_an_XAPK_File_and_How_Do_You_Install_One_on_Android?⠀⇛


⚓ Make Use Of ☛ iPhone_vs._Android:_Which_Is_More_Secure?⠀⇛


§ Free, Libre, and Open Source Software⠀➾


    * § Programming/Development⠀➾


⚓ Cardano_Hackathon_in_Argentina_–_Cardano_Feed⠀⇛


     The term is believed to have been created in 1999 independently by
     the OpenBSD developers and the Sun Microsystems marketing team.


⚓ Unix_Command_Cheat_Sheet_for_Busy_Developers_|_by_Koushik_Thota_|_Apr,_2022_|
Medium⠀⇛


     As a developer, you might have had to use the terminal quite often,
     especially if your organization doesn’t use Microsoft products.
     Having knowledge of the most important UNIX commands can improve your
     life as a developer.


⚓ The Register UK ☛ Languages?_Compiling_the_future_is_where_the_real_fun’s_at
•_The_Register⠀⇛


     Here’s a recipe for happiness. Don’t get overexcited by the latest “C
     is not a language” kerfuffle.


     Proper coders have known since its inception that C is as much a
     glorified library of assembler macros as anything else. Don’t sweat
     it. That business with operating systems being infected by their old
     C genes, crippling all the new cool Rusts and Swifts? So what? If
     your code is limited by its OS interactions, you should probably go
     write a kernel.


     There is one place, and one place only, where you should invest your
     emotional and intellectual energies. Compilers. They saved the world
     once, and they’re about to do it again.


     For most young code-slingers, compilers are slightly mystical
     interfaces to the data divinities. If things are good, the completion
     messages flow down the terminal window like a high priest’s blessings
     on the faithful. If you’ve done bad, the compiler heaps fire and
     brimstone on you, and you must repent. When judgement day comes, your
     executable is your reward.


§ Perl/Raku⠀➾


⚓ Perl ☛ Perl_Advent_Calendar_articles_about_Moose_|_simbabque_
[blogs.perl.org]⠀⇛


     At $work, one of my colleagues who is not in a developer role has
     started to get into writing code more and more, and I am mentoring
     him. He’s about to work on a productive ticket with Moose for the
     first time, so I gave him a little reading list, mostly involving
     selected parts of the documentation as well as Ricardo Signes’
     excellent talk Moose is Perl.


     But then I thought I must have read lots of great blog posts about
     Moose on the Perl Advent Calendar over the years. I tried to find a
     few, but had some trouble identifying them easily. So I wrote a quick
     scraper. Here are all articles that mention Moose since 2010 (where
     the format of the website changed). Most of them are about Moose or
     one of the numerous MooseX modules.


    * § Leftovers⠀➾


          o § Education⠀➾


⚓ Moodle,_the_Perth-based_open-source_software_platform_that_has_taken_global
education_by_storm⠀⇛


     While making software free seems counterintuitive to the core of
     running a profitable business, it’s exactly what Moodle founder
     Martin Dougiamas did when he launched his course management system in
     2001.


     Since then, the Perth-based edtech has grown to accommodate more than
     311 million users and operates in approximately two-thirds of
     universities worldwide.


     Speaking with Business News Australia Dougiamas explains how keeping
     aspects of Moodle free is a “sensible” approach towards software
     development in a field like education, where teamwork is paramount.


     “To me, it’s very natural. It comes out of academic tradition [where]
     you learn, share and work together – it’s very collaborative. It’s
     not about competition,” he says.


     “It’s a very healthy ecosystem for open source. Most of the lower
     layers of the internet and operating systems like UNIX are all built
     with this model because it works.


     “The dotcoms like Google, Microsoft, Apple and Facebook completely
     operate on open-source software.”


§ Integrity/Availability⠀➾


    * § Proprietary⠀➾


          o § Security⠀➾


⚓ How_to_Use_and_Automate_PKI_in_DevOps?⠀⇛


⚓ IT Wire ☛ New_ASPI_tool_offers_means_to_check_website,_email_and_net
connection⠀⇛


     iTWire asked Russell Coker, a senior developer with the Debian GNU/
     Linux project and a veteran sysadmin to evaluate the site.


⚓ AboutChromebooks ☛ Chrome_OS_adds_Stability_to_the_three_core_principles_of
Speed,_Simplicity_and_Security [Ed: Still not freedom, only more spying over
time...]⠀⇛


     Earlier this week, I shared information on what Chrome OS 100 brings
     to Chromebooks. Aside from new features, such as the improved
     Launcher, there’s a huge behind-the-scenes addition. The original
     three core principles of Speed, Simplicity, and Security in Chrome OS
     are now four. After more than a decade, Stability is a primary
     function of Chrome OS.


§ Privacy/Surveillance⠀➾


⚓ The Register UK ☛ Google_will_have_to_pay_€150_million_fine_to_the_French
Competition_Authority,_court_orders⠀⇛


⚓ Axios ☛ Clean_energy_players_eye_home_power_consumption⠀⇛


     A trio of clean-energy players are enabling the nation’s largest
     competitive wholesale electricity market to reduce load by expanding
     demand-response to residential customers’ thermostats.


§ Defence/Aggression⠀➾


    * ⚓ #_No_3G⠀⇛


           We have new neighbors from Ukraine. The owners of the flat
           dropped a letter into everyone’s mailbox to inform us and to
           ask that maybe we could share our wlan access with the family
           (mother, 2 children and mother-in-law).


           From an email at work I learned that Telekom is giving away
           free SIM cards to refugees from Ukraine with an unlimited data
           plan. They only require some Ukrainian ID as all SIM cards have
           to be registered in Germany. So I just wrote an email to the
           landlord informing him about this as I really just would not
           like to share our internet access even with the guest option in
           the router. He did not know about the free cards and wrote me
           back that they would visit a Telekom shop the next day.


⚓ The Register UK ☛ Huawei_CFO_who_was_detained_in_Canada_promoted_to_chair_•
The_Register⠀⇛


     Huawei executive Meng Wanzhou – who was famously held in Canada and
     is the daughter of company founder Ren Zhengfei – has quietly been
     named as one of three people who share the role as chair of the
     Chinese company’s board.


     Huawei rotatesits CEO and chair every six months, appointing the new
     leaders from a panel of three who each take turns in the top jobs
     before reverting to be mere senior advisors.


     While critics of the system may question the resulting continuity and
     accountability, founder Ren Zhengfai justifies the unique approach by
     saying the rotating and acting CEOs “sought harmony in diversity,”
     helping the company “adapt quickly to changes in the environment.”


     “They make decisions collectively, which avoids corporate rigidity
     caused by any particular individual being too obstinate and also
     avoids the uncertainties caused by unexpected risks to company
     operations,” said Ren. In 2018, the co-CEO role was downgraded to
     “rotating deputy chairperson.”


⚓ The Register UK ☛ China_moves_to_protect_offshore_tech_company_listings_•_The
Register⠀⇛


     China’s Securities Regulatory Commission has opened a consultation on
     revised regulations aimed at avoiding trouble for local tech
     companies that list on US stock markets.


     In recent weeks the NASDAQ stock exchange warned Chinese tech
     companies Baidu and Weibo – and more besides – that they face
     suspension from the bourse because they don’t allow the US government
     to see audits of their finances.


     Washington wants to see those audits under the Holding Foreign
     Companies Accountable Act (HFCAA) – a law that requires some
     companies that issue securities in the US to disclose how many of
     their shares are owned by governments, if governments exercise
     control over the company, and whether any officials or regulations
     are connected to the Chinese Communist Party.


§ Finance⠀➾


⚓ Medium ☛ Capitalism_Is_The_Problem,_………._(Part_Two:_A_republic,_if_you_can
keep_it)⠀⇛


     Some of the most important inventors you may not have heard of, are:
     Charles Babbage, Ada Lovelace, Herman Hollerith, Semyon Korsakov,
     Alan Turing; where to start? The truth is; Hollerith was the only one
     that succeeded financially. How do I define this? Well, several of
     these people were born into privilege or married into or inherited
     significant wealth; and their inventiveness did not expand their
     wealth significantly. So, the definition of success is: that they
     grew their own wealth within their inventions.


§ AstroTurf/Lobbying/Politics⠀➾


⚓ Foreign Policy ☛ Macron_Begins_His_Fight_for_a_Second_Term⠀⇛


     French voters go the polls this Sunday in the presidential election
     first round, with Macron’s old rival Marine Le Pen likely to advance
     with him.


§ Civil Rights/Policing⠀➾


    * ⚓ Re:_Wholesomedonut’s_thoughts_on_work⠀⇛


           It makes plenty of sense to work multiple days a week,
           throughout the whole day, if you’re a farmer who has to respect
           the life cycles of his work animals, and doesn’t have giant
           spotlights with which to light up his whole field as he tills.


§ Internet Policy/Net Neutrality⠀➾


    * ⚓ The_future_of_dimension.sh⠀⇛


           dimension.sh is nearly 2 years old. I initially started
           dimension as I wanted to rekindle a love of an old ‘pubnix’ I
           used to be a member of back when I was in college, it ended up
           being a small community where I met a few good friends to which
           i’m still in contact with twenty years later. I happened to
           come across the the tilde community one day and was reminded of
           this fun part of my life.


    * ⚓ tldr_in_gemtext⠀⇛


           For command line help, man pages are thorough. The information
           you want is probably in there somewhere. But I’d prefer a few
           examples to get me started. The tldr project does exactly that.
           So I translated their pages to gemtext, and put up a list of
           them.


    * ⚓ Is_gemini_a_read-only_protocol?⠀⇛


           I got to know the gemini protocol by reading Drew DeVault’s
           blog. In a post from last year he argues that gemini is
           supposed to be a read-only protocol, that the INPUT response
           code is only for searching, and that the SENSITIVE INPUT code
           should be removed. Forms, file uploads, commenting systems, and
           other kind of interactive use cases simply fall out of gemini’s
           scope according to him.


§ Monopolies⠀➾


⚓ The Register UK ☛ Russian_media_watchdog_bans_Google_from_advertising_its
services⠀⇛


     Russia’s communications scold is fed up with all the misinformation
     online, at least with regard to Google and its YouTube subsidiary.


     Roskomnadzor, the agency charged with monitoring and controlling
     media in Russia, introduced “coercive measures” that ban Google from
     promoting services deemed to be distributing “fake” – as defined by
     the Russian government – content.


     Affected services, according to Russian business publication
     Kommersant, include Google Search, Google Play, YouTube, YouTube
     Music, Google Chat and Gmail. The measures also include requiring
     search engines (e.g. Yandex) that present information about Google
     services (i.e. link to them) to inform users that Google is violating
     Russian law.


     “YouTube video hosting has become one of the key platforms spreading
     fakes about the course of a special military operation on the
     territory of Ukraine, discrediting the Armed Forces of the Russian
     Federation,” the agency said.


⚓ The Register UK ☛ EU_appeals_overturned_$1.2b_Intel_antitrust_fine⠀⇛


     The European Commission (EC) is going ahead with an appeal against a
     court decision earlier this year to drop a $1.2 billion fine imposed
     against Intel for anti-competitive behavior.


     The case stretches back many years and concerns deals between Intel
     and some system vendors to favor Intel chips over those from rivals
     such as AMD.


     A spokesperson for the EC confirmed to The Register that it has
     decided to file an appeal against the General Court judgment of 26
     January, which found Intel was no longer required to pay an
     approximate $1.15 billion fine imposed by the EC for anti-competitive
     behaviour.



                    ䷩ 𝚕𝚒𝚗𝚎 4113

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 04.09.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_09/04/2022:_Outages_and_Clown_Computing_Failures⠀✐


Posted in News_Roundup at 10:20 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Server⠀➾


⚓ The Register UK ☛ Atlassian_outage_lingers,_sparking_data_loss_fears⠀⇛


     Atlassian is still scrambling to recover from a recent software
     script fiasco and is hoping no customer data gets lost, which may be
     more than Microsoft can manage if OneDrive, as some have reported,
     has been intermittently corrupting large uploads for at least two
     months.


     Four days after some Atlassian customers began encountering problems
     with the cloud giant’s collaboration software, recovery efforts
     continue and a few folks are worried they may not get their data
     back.


     One wrote to The Register wondering about that possibility after the
     company, via Twitter, responded to a request to confirm that customer
     data is backed up and failed to actually do so.


     “We expect most site recoveries to occur with minimal or no data
     loss,” the biz said on Thursday.


§ Applications⠀➾


⚓ Linux Links ☛ Best_Free_and_Open_Source_Alternatives_to_Adobe_Acrobat
Reader⠀⇛


     
     Adobe Acrobat Reader is a multi-platform PDF reader. It lets users
     view, print, sign and comment on PDF documents.


     While Acrobat Reader is free to download, it’s proprietary software.
     And support for Linux was discontinued in 2014, although it’s
     possible to run the Windows software using WINE.


     We recommend free and open source alternatives that run natively
     under Linux.


§ Instructionals/Technical⠀➾


⚓ How_To_Install_NotepadQQ_On_Linux_[Updated]_|_Itsubuntu.com⠀⇛


     How To install NotepadQQ On Linux


     Notepadqq is an amazing text editor. It is promoted as an editor
     designed by developers, for developers. Notepadqq is free to use and
     open-source text editor that has support for almost 100 languages. If
     you are looking for a perfect text editor for Linux then NotedpadQQ
     must be your choice.


⚓ Run_Commands_As_Another_User_Via_Sudo_In_Linux_–_OSTechNix⠀⇛


     Picture this scenario. You are managing a Linux server that is
     accessed by multiple users. All users have sudo rights. You want to
     test certain Linux commands with different users. How would you do
     that? Log in as one user and test the commands, and then log out and
     log back in as another user and test commands? Yes, It is one way to
     do it. However, there is a simple way to run commands as another user
     via sudo in Linux. Read on to find out.


⚓ Ubuntu Pit ☛ Set_Up_Cron_Jobs_for_Linux_and_10_Best_Online_Tools_for_Cron
Jobs⠀⇛


     The term cron job is a task that we need to do regularly, and we can
     schedule the tasks to be automatically done. In Linux, there are many
     built-in commands and online tools that might help you organize and
     initialize your tasks on your behalf on the system. With command line
     codes and online tools, you can link your tasks and assign the tools
     to perform tasks. One of the most used and useful syntax for cron
     jobs in Linux is the crontab (cron tables). To maintain these cron
     jobs in Linux, we can either write a script, use online tools, or use
     terminal commands.


     If you’re a system admin where you need to perform multiple repeating
     and scheduled tasks in many different systems, the cron jobs can save
     your time and efficiently complete your tasks.


⚓ ELinux ☛ Secure_Memcached_on_CentOS/RHEL_7?⠀⇛


     By default memcached on CentOS 7 is set to run on all IP address on
     the server. This allow attackers to abuse the service.


⚓ ELinux ☛ Cpanel_find_recently_logged_in_users?⠀⇛


⚓ ELinux ☛ How_to_Install_Supervisord_on_CentOS_7?⠀⇛


     Supervisor is a program used to monitor and control programs. It can
     auto startup application on server boot time, restart if the
     application fails.


⚓ ELinux ☛ How_to_install_PHP_ssh2_module_in_Cpanel_Server⠀⇛


     PHP ssh2 module allows you to connect to SSH servers. On Cpanel
     servers, this module is not available under EasyApache. You need to
     install using PECL. The PECL module installer in WHM does not list
     this module. The module is available to download from


⚓ ELinux ☛ How_to_fix_Cpanel_Server_shared_IP_address_show_customer_site?⠀⇛


     On a Cpanel Server, when you visit a shared IP address used by
     multiple websites, you will see the website of the first VirtualHost
     entry. This is not good when you have multiple customer websites as
     your other customers may visit the IP and see the site associated
     with the first VirtualHost entry and complain about this. I had
     customers reporting that their site is hacked when this happened to
     them.


⚓ ELinux ☛ How_To_Fix_Video_Conversion_Problem_in_Clipbucket?⠀⇛


     This topic has been discussed many times so i am going to write a
     complete guide to track your video conversion problem and fix it. I
     am using ClipBucket 2.0.9, if you have not already update to latest
     version, please download it from http://clip-bucket.com/latestAdding
     some of my Forum post content, here is what we are going to track our
     problem.


⚓ ELinux ☛ ACME_(acme.sh)_Free_SSL_Certificate?⠀⇛


     ACME (acme.sh) is a shell script for generating LetsEncrypt SSL
     certificate. acme.sh is written in bash, so it works on any Linux
     server without special requirements. For getting SSL, another popular
     option is to use certbot.


⚓ ELinux ☛ acme.sh_SSL_using_manual_DNS_method?⠀⇛


     When you run this command, you will get DNS TXT entry that needed to
     be added to your DNS server. Login to your DNS provider, add the DNS
     entry, then run the following command to confirm the SSL creation.


⚓ ELinux ☛ Run_rsync_if_not_running_using_cronjob?⠀⇛


     I want to rsync files from one server to another server every 5
     minutes, but only want to start the rsync if the previous rsync
     command has finished. Time for one rsync depends on how much data
     changed on the source server, so the time taken to finish rsync
     cronjob varies.


⚓ ELinux ☛ Run_rsync_if_not_running_using_cronjob⠀⇛


⚓ Linux Capable ☛ How_to_Install_Ristretto_on_Ubuntu_22.04_LTS⠀⇛


     Imagine being able to scroll through your favorite images and watch
     them come alive on screen or view a slideshow of all the best moments
     in life. Ristretto is an innovative image viewer that allows you to
     scroll through images and view them in a slide show. You can also
     open multiple files with other applications like your computer’s
     built-in photo editor or use it as wallpaper on its own!


     In the following tutorial, you will learn how to install Ristretto on
     Ubuntu 22.04 LTS Jammy Jellyfish using the Ubuntu default repository
     or alternative flatpak installation manager for those that require
     the latest released version as Ubuntu’s releases can be behind due to
     stability factors in what long term releases are meant for.


⚓ Linux Capable ☛ How_to_Install_NVIDIA_Drivers_on_Fedora_36_Linux⠀⇛


     Most modern Linux Desktop systems such as Fedora come with an NVIDIA
     driver pre-installed in the Nouveau open-source graphics device
     driver for Nvidia video cards. For the most part, this is acceptable;
     however, if you are using your Linux system for graphical design or
     gaming, you may get better drivers.


     Historically, the Nouveau proprietary drivers are slower than
     Nvidia’s, which lacks the latest graphics card hardware features,
     software technology, and support. In most situations, upgrading your
     Nvidia Drivers with proper NVIDIA drivers is more beneficial than
     not. In some cases, you may see some substantial improvements
     overall.


     In the following tutorial, you will learn how to install the Nvidia
     Graphic Drivers from the Nvidia Proprietary Repository RPM Fusion,
     giving you the latest software available on Fedora 36 Workstation,
     the command line terminal.


⚓ Linux Capable ☛ How_to_Install_Tor_Browser_on_Fedora_36_Linux⠀⇛


     Tor, also referred to as The Onion Router, is open-source, free
     software that permits anonymous communication when using online
     services like web surfing. The Tor network directs the web traffic
     through an accessible worldwide volunteer overlay network with over
     six thousand relays and continues to grow. Many users want to search
     out more ways to stay their information and activities anonymous or
     as private as possible, which has led to Tor Browser growing quite
     popular in recent years because it conceals a user’s location and
     usage from anyone conducting network surveillance or traffic
     analysis.


     The Tor network is intended to protect the personal privacy of users
     and their freedom and ability from conducting communication without
     having their activities monitored, and data were taken without their
     consent and used to sum it up.


     In the following tutorial, you will learn how to install Tor Browser
     on Fedora 36 Linux workstation desktop using Fedora 36’s default
     repository or downloading the browser manually and how to install it
     manually with tips on registering the application icon.


⚓ Linux Capable ☛ How_to_Install_PHP_8.1_on_Ubuntu_22.04_LTS⠀⇛


     PHP 8.1 is a significant update of the PHP language that was
     “officially” released on November 25, 2021. This is a standard
     upgrade going forward from the existing PHP 8.0 release. The new PHP
     8.1 brings enums, fibers, never return type, final class constants,
     intersection types, and read-only properties, among new features and
     changes.


     In the following tutorial, you will learn how to import the Ondřej
     Surý PPA and install PHP 8.1 on your Ubuntu 22.04 LTS Jammy Jellyfish
     using the command line terminal.


⚓ Linux Capable ☛ How_to_Install_OpenJDK_11_on_Ubuntu_22.04_LTS⠀⇛


     Java is a general-purpose, class-based, object-oriented multipurpose
     programming language that is popular due to the design of having
     lesser implementation dependencies, meaning that the compiled Java
     code can be run on all platforms that support Java without the need
     for recompilation. Java is also fast, secure, and reliable,
     therefore. It is widely used for developing Java applications in
     laptops, data centers, game consoles, scientific supercomputers, cell
     phones, etc.


     The tutorial will look at installing the OpenJDK version instead of
     the default Oracle JDK. The difference between these two is
     licensing. OpenJDK is an entirely free, open-source Java with a GNU
     General Public License, and Oracle JDK requires a commercial license
     under the Oracle Binary Code License Agreement. Other differences are
     release schedules and other factors that come into play; however,
     performance is the same.


     In the following tutorial, you will learn how to install OpenJDK 11
     LTS or better known as Java 11 LTS, on Ubuntu 22.04 LTS Jammy
     Jellyfish with the standard APT installation from Ubuntu’s repository
     along with the PPA version, which may suit some users better. The
     tutorial will also demonstrate how to switch Java alternative default
     versions.


⚓ Linux Capable ☛ How_to_Install_SciTE_Text_Editor_on_Ubuntu_22.04_LTS⠀⇛


     SciTE is an easy-to-use text editor that has many features for
     programming. Its footprint size and functionality make it perfect for
     installing on any system, even if you don’t have experience with
     Scintilla or GTK.


     More valuable features include syntax styling, error indicators, and
     code completion. It also has a selection margin that can be filled
     with markers like those found commonly used by debuggers to indicate
     breakpoints or other vital points when exploring an application’s
     functionality (e). The user interface provides greater control than
     what you might find elsewhere; this makes it easier for developers
     who need these types of tools but don’t want something too
     complicated-looking while still offering plenty of ” Done deal!”
     style options if that more their speed!


     In the following tutorial, you will learn how to install SciTE on
     Ubuntu 22.04 LTS Jammy Jellyfish using the Ubuntu default repository
     or alternative flatpak installation manager for those that require
     the latest released version as Ubuntu’s releases can be behind due to
     stability factors in what long term releases are meant for.


⚓ Linux Capable ☛ How_to_Install_Firefox_ESR_on_Ubuntu_22.04_LTS⠀⇛


     Firefox ESR is the perfect choice for enterprise users who need
     stability and security updates but may not have access to newer
     features. The Firefox Extended Support Release (ESR) versions are
     officially supported by their respective organizations because they
     do not contain any bugs or unfinished products within their
     programmed functions! The Firefox extended support release is perfect
     for university or government networks where they need more support
     than just updated software.


     In the following tutorial, you will learn how to install Firefox ESR
     on Ubuntu 22.04 LTS Jammy Jellyfish using a recommended Launchpad PPA
     repository to provide the most up-to-date version using the command
     line terminal.


⚓ Linux Capable ☛ How_to_Install_RawTherapee_on_Ubuntu_22.04_LTS⠀⇛


     The RawTherapee application is a powerful and versatile tool for
     processing raw photos. This program, which runs on both PC & Mac
     systems using GTK+ as its interface, uses patches of DCRAW with added
     support from their in-house team that enhances accuracy where needed
     most – ensuring every photo comes out beautifully regardless of the
     type or model device was used when taking them!


     In the following tutorial, you will learn how to install RawTherapee
     on Ubuntu 22.04 LTS Jammy Jellyfish using the Ubuntu default
     repository or alternative flatpak installation manager for those that
     require the latest released version as Ubuntu’s releases can be
     behind due to stability factors in what long term releases are meant
     for.


⚓ Linux Capable ☛ How_to_Install_Shotwell_on_Ubuntu_22.04_LTS⠀⇛


     Shotwell is a simple and easy-to-use photo organizer for the GNOME
     desktop. You can import photos from your camera or disk, organize
     them by date and subject matter, and ratings on how you want to
     present these memories in this application with its basic editing
     features, including cropping red eyes away!


     In the following tutorial, you will learn how to install Shotwell on
     Ubuntu 22.04 LTS Jammy Jellyfish using the Ubuntu default repository
     or alternative flatpak installation manager for those that require
     the latest released version as Ubuntu’s releases can be behind due to
     stability factors in what long term releases are meant for.


⚓ Linux Capable ☛ How_to_Install_Freetube_on_Manjaro_21_Linux⠀⇛


     FreeTube is a free, open-source YouTube player that lets you watch
     videos without advertisements and prevents Google from tracking your
     browsing activity with cookies or JavaScript. Thanks to Electron, you
     can use it for Windows, Mac & Linux!


     In the following tutorial, you will learn how to install Freetube on
     Manjaro 21 Linux. The tutorial will use the command line terminal
     with yay AUR helper. Ideally, most users may be using some wrapper
     for Pacman; for new users, it is essential to install one to keep
     your packages up-to-date while you learn Arch/Manjaro.


⚓ Marian Bouček ☛ Installing_Ubuntu_from_FreeBSD⠀⇛


     I want to install Ubuntu for playing games on external SSD, so I
     don’t have to touch my boot loader. I got inspired by Ruben’s post. I
     decided to buy a new SSD external drive and install Ubuntu on it. I’m
     pretty sure I’ve told the Ubuntu installer to NOT override boot
     record on my main drive, but sadly the installer ignored my choice
     and happily installed GRUB on it. At this point, I was really scared
     of not being able to boot my FreeBSD anymore.


⚓ Rachel ☛ Lots_of_feedback_about_/bin/true,_and_more_empty_file_fun⠀⇛


     Okay, wow, my post about an empty file has generated a lot of
     feedback, mostly for the throwaway line at the bottom about an empty
     file being the smallest version of /bin/true possible.


⚓ India Times ☛ How_QR_codes_work_and_what_makes_them_dangerous:_A_computer
scientist_explains⠀⇛


     QR codes are not inherently dangerous. They are simply a way to store
     data. However, just as it can be hazardous to click links in emails,
     visiting URLs stored in QR codes can also be risky in several ways.


⚓ ID Root ☛ How_To_Install_Pixeluvo_on_Ubuntu_20.04_LTS_–_idroot⠀⇛


     In this tutorial, we will show you how to install Pixeluvo on Ubuntu
     20.04 LTS. For those of you who didn’t know, Pixeluvo is an
     affordable image editor tool designed to transform the entire view of
     an image in Linux distributions. Pixeluvo contains a wide range of
     advanced features including non-destructive editing via adjustment
     layers, powerful color correction tools, full support for raw image
     formats, realistic pressure-sensitive drawing tools, and many image
     enhancement filters. To use it, you need a commercial license and a
     license for Pixeluvo full version costs $34 and includes all future
     updates for that major version number.


     This article assumes you have at least basic knowledge of Linux, know
     how to use the shell, and most importantly, you host your site on
     your own VPS. The installation is quite simple and assumes you are
     running in the root account, if not you may need to add ‘sudo‘ to the
     commands to get root privileges. I will show you the step-by-step
     installation of the Pixeluvo image editor on Ubuntu 20.04 (Focal
     Fossa). You can follow the same instructions for Ubuntu 18.04, 16.04,
     and any other Debian-based distribution like Linux Mint.


⚓ Trend Oceans ☛ How_to_resolve_VMware_Workstation_no_Internet_connection_–
TREND_OCEANS⠀⇛


     When I was logging into the virtual machine via SSH connection, I was
     not prompted to enter the password and the connection terminated with
     the Connection timed out message.


     At first, I thought maybe the IP address had changed, but it’s not
     possible because I have set the static address, even though the
     firewall is not implemented on the system. Still, I pinged the
     network and found the connection was unreachable.


     So, I directly logged in to the VMware machine and checked the IP
     address. I found the IP address was the same. Then why is it not
     getting connected through SSH? Therefore, again, I tried to ping
     Reddit and found it was also not working.


⚓ Install_MariaDB_10.7_on_Ubuntu_20.04_–_kifarunix.com⠀⇛


     Follow through this guide to learn how to install MariaDB 10.7 on
     Ubuntu 20.04. MariaDB 10.7.3 is the current stable release version of
     MariaDB.


⚓ Install_MariaDB_10.8_on_Ubuntu_20.04_–_kifarunix.com⠀⇛


     Follow through this guide to learn how to install MariaDB 10.8 on
     Ubuntu 20.04. MariaDB 10.8.2 is the current RC release version of
     MariaDB.


⚓ OpenSource.com ☛ Explaining_Git_branches_with_a_LEGO_analogy_|
Opensource.com⠀⇛


     Creating a new branch in a code repository is a pretty common task
     when working with Git. It’s one of the primary mechanisms for keeping
     unrelated changes separate from one another. It’s also very often the
     main designator for what gets merged into the main branch.


     Without branches, everything would either have to be cherrypicked, or
     else all your work would be merged effectively as a squashed rebase.
     The problem is, branches inherit the work of the branch from which
     they’re forked, and that can lead to you accidentally pushing commits
     you never intended to be in your new branch.


     The solution is to always fork off of main (except when you mean not
     to). It’s an easy rule to say, but unfortunately it’s equally as easy
     to forget, so it can help to look at the reasoning behind the rule.


⚓ nixCraft ☛ How_to_install_GIMP_2.10_on_Ubuntu_or_Debian_Linux⠀⇛


     This quick tutorial explains how to download and install the latest
     GIMP application on Ubuntu or Debian Linux and friend using the CLI.


⚓ UNIX Cop ☛ How_To_Enable_mod_rewrite_For_Apache_in_Rocky_Linux_8_/_Alma_Linux
8⠀⇛


     Hello, friends. On Debian and Ubuntu, it is effortless to enable
     mod_rewrite, which is an Apache utility to rewrite addresses in our
     applications. However, in the case of Rocky Linux 8 / Alma Linux 8
     the issue is not the same. So, you will learn how to enable
     mod_rewrite for Apache in Rocky Linux 8 / Alma Linux 8.


⚓ Bifrost_Spike_on_an_Ampere_AltraMax_|_Adam_Young’s_Web_Log⠀⇛


     For the past week I worked on getting a Ironic standalone to run on
     an Ampere AltraMax server in our lab. As I recently was able to get a
     baremetal node to boot, I wanted to record the steps I went through.


     Our base operating system for this install is Ubuntu 20.04.


⚓ HowTo Forge ☛ How_to_Install_Memcached_on_Alma_Linux_8⠀⇛


⚓ The_Unexpected_Importance_of_the_Trailing_Slash_–_Tookmund_–_A_place_for_my
random_thoughts_about_software⠀⇛


     For many using Unix-derived systems today, we take for granted that /
     some/path and /some/path/ are the same. Most shells will even add a
     trailing slash for you when you press the Tab key after the name of a
     directory or a symbolic link to one.


     However, many programs treat these two paths as subtly different in
     certain cases, which I outline below, as all three have tripped me up
     in various ways.


⚓ Barry Kauler ☛ How_to_fiddle_with_JWM_tray_height_and_width⠀⇛


     This blog post is prompted by a forum post by BologneChe, who set the
     tray width to full width of screen, by editing the “width” attribute
     in the “Tray” tag, but found that sometimes had to reset it…


⚓ Jump Cloud ☛ How_to_Launch_an_Amazon_Linux_EC2_Instance_Using_Terraform⠀⇛


⚓ How_to_Check_Kernel_Version_in_Ubuntu_20.04⠀⇛


     The kernel is one of the most important parts of a system. In the
     case of Ubuntu or Debian, the kernel is rarely upgraded to major
     versions, although it is patched frequently. As with the entire
     system, it is also a good idea to check the kernel version because it
     will tell you more about the system and provide better support.


§ Wine or Emulation⠀➾


⚓ GamingOnLinux ☛ Wine_7.6_out_now_with_more_PE_conversion_work,_Mono_updated_|
GamingOnLinux⠀⇛


     Wine is the compatibility layer that allows you to run games and
     applications developed for Windows – on Linux (plus also macOS and
     BSD). A new development release is out with Wine 7.6. It’s a major
     part of what makes up Steam Play Proton and enables a ton of games to
     work on the Steam Deck. Once a year or so, a new stable release is
     made.


§ Games⠀➾


⚓ Boiling Steam ☛ Top_7_New_Games_to_Play_on_Linux_with_Proton_–_April_2022
Edition_–_Boiling_Steam⠀⇛


     We are back with our usual monthly update! Boiling Steam looks at the
     latest data dumps from ProtonDB to give you a quick list of new games
     that work (pretty much?) perfectly with Proton since March 2022 – all
     of them work out of the box or well enough with tweaks…


⚓ GamingOnLinux ☛ Godfall_Ultimate_Edition_seems_to_run_well_on_Linux_and_Steam
Deck_|_GamingOnLinux⠀⇛


     Godfall Ultimate Edition released onto Steam on April 7, a former
     Epic Store exclusive, and now thanks to the Steam release it runs
     very nicely on Linux and Steam Deck with Proton.


     “Aperion is on the precipice of ruin. You are the last of the
     Valorian knights, god-like warriors able to equip Valorplates,
     legendary armor sets that transform wielders into unstoppable masters
     of melee combat. Ascend in Godfall, the first-of-its-kind, looter-
     slasher, melee action-RPG.”


⚓ GamingOnLinux ☛ Duck_Game_gets_a_patch_for_Proton,_now_works_on_Steam_Deck_|
GamingOnLinux⠀⇛


     With their changes, it should now work out of the box! Released
     originally on Steam back in 2015, it went onto receive wide
     recognition with an Overwhelmingly Positive rating from 20,944 (at
     time of writing) user reviews. Always nice to see such a title
     running well on Linux and Steam Deck.


⚓ Its FOSS ☛ 10_Best_Indie_RPG_Games_for_Linux_in_2022⠀⇛


     
     Whether it is Windows, Linux, or macOS, you will find plenty of Indie
     games to play.


     There are chances to find incredibly exciting games that are often
     underrated, which makes it exciting to explore Indie games.


     But, here, I focus only on the best Indie RPG games (i.e. developed
     by small teams) available for the Linux platform.


§ Desktop Environments/WMs⠀➾


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


⚓ This_week_in_KDE:_a_feast_for_the_eyes⠀⇛


     Those finger-following touchscreen gestures have started to land, and
     we have a lot more than that too! This week is overflowing with
     positive visual changes that I think you’re all really going to like…


§ GNOME Desktop/GTK⠀➾


⚓ Blender_Eevee_is_Magic_–_Even_a_Stopped_Clock⠀⇛


     Georges wrote a great little app to configure Elgato Stream Deck
     buttons on non-proprietary platforms. I’ve been following Georges’
     ventures into streaming. He’s done amazing job promoting GNOME
     development and has been helping with OBS a lot too.


     To make Boatswain work great by default, rather than just presenting
     people with a monstrous shit work mountain to even get going, Georges
     needed some graphical assets to have the configurator ship with ready
     made presets.


§ Distributions⠀➾


    * § BSD⠀➾


⚓ OpenSSH ☛ OpenSSH_9.0_Release_Notes⠀⇛


     This release switches scp(1) from using the legacy scp/rcp protocol
     to using the SFTP protocol by default.


     Legacy scp/rcp performs wildcard expansion of remote filenames (e.g.
     “scp host:* .”) through the remote shell. This has the side effect of
     requiring double quoting of shell meta-characters in file names
     included on scp(1) command-lines, otherwise they could be interpreted
     as shell commands on the remote side.


     This creates one area of potential incompatibility: scp(1) when using
     the SFTP protocol no longer requires this finicky and brittle
     quoting, and attempts to use it may cause transfers to fail. We
     consider the removal of the need for double-quoting shell characters
     in file names to be a benefit and do not intend to introduce bug-
     compatibility for legacy scp/rcp in scp(1) when using the SFTP
     protocol.


     Another area of potential incompatibility relates to the use of
     remote paths relative to other user’s home directories, for example –
     “scp host:~user/file /tmp”. The SFTP protocol has no native way to
     expand a ~user path. However, sftp-server(8) in OpenSSH 8.7 and later
     support a protocol extension “expand-path@openssh.com” to support
     this.


     In case of incompatibility, the scp(1) client may be instructed to
     use the legacy scp/rcp using the -O flag.


§ Debian Family⠀➾


⚓ Raspberry Pi ☛ An_update_to_Raspberry_Pi_OS_Bullseye⠀⇛


     Up until now, all installs of Raspberry Pi OS have had a default user
     called “pi”. This isn’t that much of a weakness – just knowing a
     valid user name doesn’t really help much if someone wants to hack
     into your system; they would also need to know your password, and
     you’d need to have enabled some form of remote access in the first
     place. But nonetheless, it could potentially make a brute-force
     attack slightly easier, and in response to this, some countries are
     now introducing legislation to forbid any Internet-connected device
     from having default login credentials.


     So with this latest release, the default “pi” user is being removed,
     and instead you will create a user the first time you boot a newly-
     flashed Raspberry Pi OS image. This is in line with the way most
     operating systems work nowadays, and, while it may cause a few issues
     where software (and documentation) assumes the existence of the “pi”
     user, it feels like a sensible change to make at this point.


⚓ MRT ☛ Raspberry_Pi_OS_updated_based_on_Debian_Bullseye⠀⇛


     The Raspberry Pi Foundation has now put the official Raspberry Pi OS
     on the basis of Debian Bullseye. This means that the operating system
     for the handicraft boards has an up-to-date substructure again.
     However, as in the past with such releases, the Foundation does not
     recommend a direct in-place upgrade.


     the Name developers only a few visible changes. You highlight the
     switch to the GTK + 3 toolkit, which works with the Compositing
     Window Manager Mutter. This first renders the display in RAM and can
     display nicer windows with rounded corners, for example. However,
     this has the disadvantage that it only works with Raspberry Pis with
     more than 2GB of RAM. Smaller versions of the Pi keep the old GTK + 2
     framework with OpenBox window manager. In the future, however, the
     development will move further away from the X Windows Manager towards
     Wayland, announces the Raspberry Pi Foundation.


⚓ The Register UK ☛ Raspberry_Pi_OS_update_beefs_up_security⠀⇛


     An update to the Debian Bullseye-based Raspberry Pi OS is being
     rolled out with both quality-of-life improvements and one very
     important tweak: an overdue departure of the default user.


     Previously, all installs of the Raspberry Pi OS (formerly known as
     Raspbian) had a default user called “pi”.


     This was handy for quick setups and convenience but a bit of an open
     goal on the security front. “This isn’t that much of a weakness,”
     insisted the Pi team, pointing out that you’d need to know the
     password as well to get access (and you’d need to have enabled remote
     access for miscreants to do their dirty work anywhere but locally)
     but still.


     There is no getting away from the fact that its presence could expose
     credentials and “potentially make a brute-force attack slightly
     easier.”


⚓ Alexander_Wirt,_Bucha_executions_&_Debian_political_prisoners⠀⇛


     When and why are these tactics used in Debian? It usually involves
     questions about money. If you ask why a woman who had a shared travel
     history with the Debian leader received a $6,000 internship, you are
     almost certain to be subject to one of these secret bans/censorship
     too. Debian oligarchs do not want to draw any attention to these
     cases, not even on debian-private so they blackmail people to
     disappear quietly.


§ Devices/Embedded⠀➾


⚓ CNX Software ☛ MangoPi_MQ_Pro_–_A_$20_RISC-V_alternative_to_Raspberry_Pi_Zero
W⠀⇛


     
     MangoPi MQ Pro is an Allwinner D1 RISC-V SBC that offers an
     alternative to Raspberry Pi Zero W with the same form factor, and
     most of the same features including WiFi and Bluetooth connectivity


     The board has been in the works for several months, but the MangoPi
     MQ Pro board can now be purchased for around $20 on Taobao with 512MB
     RAM, and I’d expect it to show up on Aliexpress and/or Seeed Studio
     within the next few weeks.


§ Open Hardware/Modding⠀➾


⚓ Hackaday ☛ It’s_Almost_A_New_Raspberry_Pi_Compute_Module_4._But_Not_Quite⠀⇛


     We know that readers are familiar with the global chip shortage and
     its effects on product availability. The Raspberry Pi folks haven’t
     escaped its shadow, for even though they’ve managed to preserve
     availability of their RP2040 microcontroller, it’s fair to say that
     some of their flagship Linux-capable boards have been hard to find.
     All of this has had an unlikely effect in the form of a new Raspberry
     Pi, but unexpectedly it’s one which few end users are likely to get
     their hands on.


⚓ Ruben Schade ☛ Computers_and_the_passing_of_time⠀⇛


     My coffee-fuelled retrocomputing adventures have reached the point
     where I’ve realised these machines are not only older than people at
     school now, or at university, but even people I meet professionally.
     I then realise the 1990s weren’t “a decade ago”, and suddenly it
     makes sense why finding parts for these things is becoming more
     difficult.


⚓ PIA ☛ How_to_​Escape_The_‘Smartphone_Duopoly’_of_Apple_&_Google_with_Sailfish
OS⠀⇛


     Both the Windows Phone and Windows Mobile OS are long dead after an
     extended period of mockery. The once-loved Blackberry shut down its
     servers earlier this year, rendering handsets from what was formerly
     the most popular business choice finally obsolete.


§ Mobile Systems/Mobile Applications⠀➾


⚓ Notebook Check ☛ Xiaomi_12_Lite_5G_surfaces_on_the_EEC_and_FCC_with_Android
12,_MIUI_13_and_multiple_memory_configurations_–_NotebookCheck.net_News⠀⇛


⚓ Android Central ☛ These_Android_phones_emit_the_most_radiation,_study_claims
|_Android_Central⠀⇛


⚓ GSM Arena ☛ Samsung_Galaxy_A52_is_receiving_Android_12-based_One_UI_4.1
update_–_GSMArena.com_news⠀⇛


⚓ Express ☛ Android_apps_that_promise_to_destroy_malware_could_BREAK_your_phone
|_Express.co.uk⠀⇛


§ Free, Libre, and Open Source Software⠀➾


⚓ Daniel Stenberg ☛ More_steel [Ed: Showing off 'gifts' from Microsoft while
insisting on putting a Free project in proprietary hosting of a company which
commits crimes, including mass bribery]⠀⇛


     I didn’t expect this, and this year I wasn’t asked ahead of time if I
     wanted to receive this gift. It is however something of a collector’s
     item that I find very enjoyable.


     I received my GitHub contribution matrix printed in steel. This is my
     2021 contribution skyline. (Click the images for higher resolution.)


§ Web Browsers⠀➾


    * § Mozilla⠀➾


⚓ Its FOSS ☛ Firefox_99_Brings_These_Two_Changes_for_Linux_Users⠀⇛


     Mozilla’s Firefox is one of the most popular open-source browsers
     which is the reason it is used as the default browser in many Linux
     distributions such as Mint and Ubuntu.


     Recently, Mozilla released Firefox version 99.0 which brings new
     security and UI features to Linux.


§ FSF⠀➾


    * § Licensing/Legal⠀➾


          o ⚓ Market Screener ☛ VMware_:_Open_Source_License_Compliance_and_Why
            It_Matters [Ed: Serial_GPL_violator_VMware is trying to ‘lecture’
            us on copyleft just months after starting an anti-Linux FUD
            campaign; VMware became_so_malicious_this_past_year that even Dirk
            Hondahl, their damage-controlling spinner, resigned]⠀⇛


                 Open source license compliance isn’t glamorous. It has
                 little to do with cranking out code. It’s a messy,
                 nuanced undertaking that is in no way amenable to a
                 simple technical fix. But it’s something we ignore at our
                 peril.


                 Any open source user – or community – that fails to take
                 software license compliance seriously is risking serious
                 harm. It’s worth reminding ourselves why that is, and
                 what we can do about it.


§ Programming/Development⠀➾


⚓ One_year_of_sales⠀⇛


     A breakdown of selling 640 copies of my first product Deployment from
     Scratch.


     [...]


     You signed up for two jobs if you decided to write a book. Writing
     and marketing. And marketing is likely even more vital if you want
     people to find and read your work.


⚓ Requiring_passing_unit_tests_on_KDE’s_CI⠀⇛


     In its default configuration, KDE’s Gitlab CI will only consider
     compilation or license validation failures a failure of the CI job,
     which follows what the previous Jenkins-based system did. Unit test
     failures would be shown in the results of a job, but would not be
     considered fatal and stop integration.


     In projects with reliable and maintained tests this is obviously not
     ideal, and therefore this can now be changed. The require-passing-
     tests-on setting controls on which platform(s) tests need to pass for
     the CI to pass. Making this a per-platform setting allows phasing
     this in gradually, without the least well supported platform holding
     everything back.


⚓ Brian Callahan ☛ Hand-optimizing_the_TCC_code_generator⠀⇛


     I am on a number of different compiler mailing lists. One of those is
     the mailing list for the Tiny C Compiler. Imagine my surprise when a
     recent email mentioned our latest series and suggested trying a
     similar approach to improve the code generator in TCC. I was
     interested to see if there were any low-hanging fruit that could
     produce similar gains as O provides for QBE.


⚓ Dirk Eddelbuettel ☛ Dirk_Eddelbuettel:_RcppEigen_0.3.3.9.2_on_CRAN:
Maintenance⠀⇛


     A new release 0.3.3.9.2 of RcppEigen arrived on CRAN today (and
     already went to Debian). Eigen is a C++ template library for linear
     algebra: matrices, vectors, numerical solvers, and related
     algorithms.


     This update was (as it happens) requested by CRAN as R aims to bring
     the Fortran / C interface to best practices. We call dgesdd twice in
     one example and use a character argument, and the-powers-that-be now
     prefer better control over that character argument. So we did.
     Another change, kindly contributed by Mikael Jagan, switches row and
     column indices for R_xlen_t allowing for greater range. Plus some
     more small tweaks mostly to CI, see the NEWS entry below for full
     details.


§ Shell/Bash/Zsh/Ksh⠀➾


⚓ Anders Borch ☛ Making_Nvm_And_Volta_Co-exist_With_Zsh⠀⇛


     Some of the magic of not having to do any chpwd hooks at all are
     clearly negated by this, but such is the world of working on multiple
     heterogenous projects.


    * § Leftovers⠀➾


⚓ Counter Punch ☛ Travelers,_Sour_and_Sentimental⠀⇛


     For the roots of our contemporary attitudes toward travel we must go
     back to the eighteenth century, to the golden age of the Grand Tour,
     when extended journeys on the European continent were made not only
     by royals and aristocrats, whose families had long been embarking on
     extended trips abroad, but by ever larger numbers of middle-class
     travelers as well.


     The period spawned a huge travel literature, much of it unpublished
     journals like those of Boswell and Edward Gibbon. But books flooded
     the market, too, from personal accounts such as Joseph
     Addison’s Remarks on Several Parts of Italyof 1705, to general travel
     guides like Thomas Nugent’s four-volume The Grand Tour, the first of
     its many editions printed in 1749. These books were re-issued
     continuously in the course of the eighteenth century to feed the
     appetites both of those intent on making the journey themselves, or
     for stay-at-homes eager to experience it vicariously.


⚓ Unix Sheikh ☛ Don’t_use_Reddit_for_Linux_or_BSD_related_questions⠀⇛


     If you want to get valuable information, why would you try to locate
     it at a place that is mainly occupied by childish, immature, hostile
     and selfish people?


     This is not unique to Reddit, but it generally relates to most social
     places on the Internet, especially those with point based voting. By
     the very nature by which these places work, they not only attract,
     but often nurture the most hollow and miserable people. Reddit and
     other places like it are often toxic and superfluous.


     Occasionally you will find something useful by someone who stands out
     from the crowd, but in most cases, it’s a complete waste of time.
     People mainly spend their time with empty, personal, emotional, and
     myth based discussions and statements.


⚓ Quillette ☛ I’m_Being_Investigated_by_the_British_Columbia_College_of_Nurses
Because_I_Believe_Biological_Sex_Is_Real⠀⇛


     Before this happened, I did not self-identify as any kind of active
     feminist, let alone the “radical” kind. However, I could not ignore
     the harms that gender-identity ideology was inflicting on women and
     children. And over the last six years, I’ve written and spoken on the
     issue of gender; organized large events about gender-identity
     ideology; hired lawyers to prevent the Vancouver Public Library from
     cancelling one such event; attended a human-rights tribunal and court
     hearings involving the notorious grifter formerly known as Jonathan
     Yaniv; been investigated and threatened with arrest by police when
     the aforementioned grifter falsely accused me of rape and voyeurism
     in a courthouse bathroom; faced hundreds of protesters—some of them
     former friends—chanting at me and my six-week-old infant, “Save the
     baby from the TERF”; received threats of death and sexual violence;
     had my Member of Parliament refuse to speak to me; and, with a former
     friend, helped erect a Vancouver billboard expressing support for my
     fellow “TERF,” J.K. Rowling.


§ Science⠀➾


⚓ New Scientist ☛ An_extreme_form_of_encryption_could_solve_big_data’s_privacy
problem⠀⇛


     Fellay’s concerns are a microcosm of one of the world’s biggest
     technological problems. The inability to safely share data hampers
     progress in all kinds of other spheres too, from detecting financial
     crime to responding to disasters and governing nations effectively.
     Now, a new kind of encryption is making it possible to wring the
     juice out of data without anyone ever actually seeing it. This could
     help end big data’s big privacy problem – and Fellay’s patients could
     be some of the first to benefit.


§ Education⠀➾


⚓ San Fancisco ☛ California_math_wars_get_ugly:_Accusations_of_racism_and
harassment_ignite_battle_between_Stanford_and_Cal_profs⠀⇛


     Boaler said after his retweet that she contacted Nelson via email,
     notifying him that police and lawyers were taking up “the sharing of
     private details about me on social media.”


     “I was shocked to see that you are taking part in spreading
     misinformation and harassing me online,” she wrote to him in an
     email.


⚓ uni Stanford ☛ Stanford_and_Cal_professors_level_accusations_as_debate_over
state_math_curriculum_rages⠀⇛


     This is not the first time that Boaler has received threatening
     messages in response to her work in education. In 2012, Boaler took
     to the Internet to call out “harassment and persecution” by two
     mathematics scholars amid a national debate about the future of
     education policy. In October, Boaler’s photo and personal details
     were posted on Fox News in an attempt to ridicule her work, which she
     said resulted in death threats.


⚓ teleSUR ☛ UNESCO_Warns_That_132_Million_Children_Do_Not_Receive_Education⠀⇛


     A report by the organization revealed that, in several countries,
     boys are at greater risk than girls of repeating years of schooling,
     as well as the level of learning, although they insist that girls
     face more disadvantages in this area.


     In addition, UNESCO considers that among the elements identified with
     school dropout are severe discipline, corporal punishment and other
     forms of violence in schools. This is in addition to school closures,
     loss of learning and economic hardship arising from the pandemic.


§ Hardware⠀➾


⚓ Hackaday ☛ Just_In_Case_You_Want_To_Charge_Your_Neighbor’s_Tesla⠀⇛


     Tesla vehicles have a charging port that is under a cover that only
     opens on command from a charging station. Well, maybe not only.
     [IfNotPike] reports that he was able to replay the 315MHz signal
     using a software defined radio and pop the port open on any Tesla he
     happened to be near.


⚓ Hackaday ☛ A_Bargain_In_Bionic_Knees⠀⇛


     You probably don’t want to lose a leg, but if you have to there are
     many options now that were unthinkable not long ago. That is, if you
     can afford them. A microprocessor knee — a prosthetic with some
     smarts in it — can run anywhere from $25,000 to well over $100,000.
     However [Lucas Galey], a PhD candidate at the University of Texas El
     Paso in a recent paper claims to be able to produce a comparable
     artificial knee for under $1,000. If the paper is too long to read,
     Amplitude has a good summary including what it means to people who
     need them.


⚓ Hackaday ☛ Wordle_Comes_To_The_Nokia_N-Gage_Thanks_To_New_SDK⠀⇛


     You probably never imagined you’d be reading about new software
     getting developed for Nokia’s infamous N-Gage handheld game system in
     2022, and we certainly never thought we’d be writing about it. But
     here we are. Of course, we aren’t talking about a commercial title —
     this is an unofficial port of Wordle by “taco phone” superfan
     [Michael Fitzmayer].


⚓ Hackaday ☛ A_Close_Look_At_A_Little_Known_8-bit_Computer⠀⇛


     If you read about the history of personal computing, you hear a few
     familiar names like Microsoft, Apple, and even Commodore. But there
     were a host of companies that were well known and well regarded back
     then that are all but forgotten today. Godbout computing, Ohio
     Scientific, and Southwest Technical Products (SWTP). SWTP is probably
     best remembered for having a relatively cheap printer and “TV
     typewriter”, but they also made a 6800-based computer and [Adrian]
     takes us inside of one.


⚓ Hackaday ☛ PCB_Thermal_Design_Hack_Gets_Hot_And_Heavy⠀⇛


     Thanks to the relatively recent rise of affordable board production
     services, many of the people reading Hackaday are just now learning
     the ropes of PCB design. For those still producing the FR4 equivalent
     of “Hello World”, it’s accomplishment enough that all the traces go
     where they’re supposed to. But eventually your designs will become
     more ambitious, and with this added complexity will naturally come
     new design considerations. For example, how do you keep a PCB from
     cooking itself in high current applications?


⚓ Hackaday ☛ Hackaday_Podcast_163:_Movie_Sound,_Defeating_Dymo_DRM,_3DP_Guitar
Neck,_Biometrics_Bereft_Of_Big_Brother⠀⇛


     Join Hackaday Editor-in-Chief Elliot Williams and Assignments Editor
     Kristina Panos as we spend an hour or so dissecting some of the more
     righteous hacks and projects from the previous week. We’ll discuss a
     DIY TPM module that satisfies Windows 11, argue whether modern guts
     belong in retrocomputer builds even if it makes them more practical,
     and marvel at the various ways that sound has been encoded on film.
     We’ll also rock out to the idea of a 3D-printed guitar neck, map out
     some paths to defeating DYMO DRM, and admire a smart watch that has
     every sensor imaginable and lasts 36+ hours on a charge. Finally,
     we’ll sing the praises of RS-485 and talk about our tool collections
     that rival our own Dan Maloney’s catalogue of crimpers.


§ Health/Nutrition/Agriculture⠀➾


⚓ Common Dreams ☛ Drop_in_Life_Expectancy_‘Speaks_Volumes’_About_How_US_Handled
Covid:_Expert⠀⇛


     Just over a month into year three of the Covid-19 pandemic, research
     revealed Thursday that life expectancy in the United States declined
     again in 2021—which followed a well-documented drop in 2020 and
     contrasted a recovery trend in other high-income countries.


     “The life expectancy gap between the United States and its peer
     income countries is now over five years, which is an incredible gap.”


⚓ Project Censored ☛ Global_Displacement_of_COVID_Orphans:_The_Pandemic’s
Hidden_Consequence_–_Validated_Independent_News⠀⇛


     Children process grief differently than adults, but signs of
     emotional suffering are easy to miss when you don’t know what to look
     for. Nelson believes the longer a child has to wait for help, the
     harder the treatment will be. Lack of early intervention may account
     for social, emotional, and cognitive challenges down the road and can
     also lead to childhood depression and anxiety. The physiological
     effects of trauma and stress can be equally devastating, often
     causing chronic conditions. While these are all highly sought out
     issues to aid in America, only ten percent of bilateral funding, one
     government transferring funds to a recipient country, is invested
     toward vulnerable and orphaned children.


⚓ Project Censored ☛ Homeless_Students_Further_Marginalized_by_COVID-19_–
Validated_Independent_News⠀⇛


     Noting that homelessness is “not an identity” but, instead, an
     “experience” and an “indicator of other vulnerabilities,” Merohtra
     reported that students of color, students with disabilities, English
     learners, and students who are LGBTQ+ are among the vulnerable groups
     that experience homelessness at “disproportionate rates.”


⚓ The Revelator ☛ Best_Practices_to_Confront_Pandemics_at_the_Source⠀⇛


⚓ TruthOut ☛ Vaccinations_for_Medicaid_Patients_Are_Far_Behind_Those_for
Privately_Insured⠀⇛


⚓ YLE ☛ One_in_three_teens_buys_snus_on_social_media,_study_finds⠀⇛


     The most recent School Health Promotion study found that up to 43
     percent of students in grades 10-12 and 67 percent of vocational
     school students have used a tobacco product at least once last year,
     with snus becoming increasingly popular.


     The survey also showed that roughly one in three snus users got hold
     of the product via social media platforms.


⚓ The Verge ☛ The_US_is_trying_to_fix_medical_devices’_big_cybersecurity
problem⠀⇛


     The new document is still just a draft, and device makers won’t start
     using it until it’s finalized after another round of feedback. But it
     includes a few significant changes from the last go-around —
     including an emphasis on the whole lifecycle of a device and a
     recommendation that manufacturers include a Software Bill of
     Materials (SBOM) with all new products that gives users information
     on the various elements that make up a device. An SBOM makes it
     easier for users to keep tabs on their devices. If there’s a bug or
     vulnerability found in a bit of software, for example, a hospital
     could easily check if their infusion pumps use that specific
     software.


§ Integrity/Availability⠀➾


    * § Proprietary⠀➾


⚓ VOA News ☛ Chinese_[Crackers]_Reportedly_Target_India’s_Power_Grid [iophk:
Windows TCO]⠀⇛


     Over the last several months, the Insikt Group, the threat research
     division of Massachusetts-based Recorded Future, said it has
     collected evidence that hackers targeted seven Indian state centers
     responsible for carrying out electrical dispatch and grid control
     near a border area disputed by the two nuclear neighbors.


     The group primarily used the trojan ShadowPad, which is believed to
     have been developed by contractors for China’s Ministry of State
     Security, leading to the conclusion that this was a state-sponsored
     hacking effort, the group reported.


⚓ Secureworks ☛ ShadowPad_Malware_Analysis [iophk: Windows TCO]⠀⇛


     The majority of ShadowPad samples analyzed by CTU researchers were
     two-file execution chains: an encrypted ShadowPad payload embedded in
     a DLL loader. ShadowPad DLL loaders are [installed] by a legitimate
     executable vulnerable to DLL search order hijacking. The DLL loader
     then decrypts and executes the embedded ShadowPad payload in memory
     using a custom decryption algorithm specific to the malware version.
     Table 1 lists legitimate executable and malicious DLL pairs that CTU
     researchers observed in analyzed samples.


⚓ Isle of Wight ☛ Electric_vehicle_chargepoints_[cracked]_to_show_porn⠀⇛


     Screens on devices at the council’s car parks are meant to show its
     website, but some featured explicit images instead.


⚓ LRT ☛ Security_startup_becomes_Lithuania’s_second_unicorn⠀⇛


     Founded in 2012, Nord Security is now valued at 1.6 billion dollars.
     This makes the company Lithuania’s second unicorn, after the clothing
     resale platform Vinted.


     According to one of the founders, Eimantas Sabaliauskas, Nord
     Security is now striving to become the world’s biggest cybersecurity
     company.


⚓ Duncan Lock ☛ Using_Windows_after_15_years_on_Linux⠀⇛


     I am a software & web developer – and Linux is a toolbox, full of
     highly polished tools, crafted over decades by software developers,
     for software developers. Windows is… not that. It’s a commercial OS,
     aimed at users of Word, Excel & Outlook, pretty much. You can feel
     this difference all the time that you’re using it – it pervades
     everything.


     Non-composable Software


     The command line tools (echo, cat, grep, sed, awk, find, cut, sort,
     curl, ssh, etc…) which make up the standard Linux/Unix toolbox are
     all composable and general purpose. You can join them together like
     Lego bricks, in whatever combination you like, to make new tools on
     the fly. You do this on the command line, by piping streams of text
     from one tool to another and using them to transform it however you
     need.


     Sadly, nobody has ever really figured out how to make GUI software
     like this – general purpose & composable. Windows has always focussed
     heavily on the GUI, to the almost complete exclusion of the command
     line – which means that it doesn’t have this foundation of composable
     software tools. Almost everything is a special purpose piece of GUI
     software. Which you have to go and find. And then download and
     install.


⚓ CS Monitor ☛ Why_did_you_make_that_decision?_AI_systems_learn_to_explain.⠀⇛


     While AI scientists have no problem designing systems that make
     accurate predictions on all sorts of business outcomes, they are
     discovering that to make those tools more effective for human
     operators, the AI may need to explain itself through another
     algorithm.


     The emerging field of “Explainable AI,” or XAI, has spurred big
     investment in Silicon Valley as startups and cloud giants compete to
     make opaque software more understandable and has stoked discussion in
     Washington and Brussels where regulators want to ensure automated
     decision-making is done fairly and transparently.


⚓ YLE ☛ Finnish_foreign_affairs_and_defence_ministry_websites_hit_by_cyber
attacks [iophk: Windows TCO]⠀⇛


     The websites of Finland’s defence and foreign affairs ministries were
     out of service on Friday, the ministries announced in separate tweets
     at just before 1pm.


     The defence ministry said its website was taken down by a denial of
     service (DoS) attack and that it was investigating the matter.


⚓ PC Mag ☛ US_Disrupts_‘Cyclops_Blink’_Botnet_by_Hacking_Infected_Devices
[iophk: Windows TCO]⠀⇛


     The US blames Russia’s military intelligence, the GRU, for creating
     the botnet as a way to spy on company networks. Back in February,
     federal officials warned that a new strain of Linux-based malware,
     called Cyclops Blink, had been found targeting vulnerable routers and
     firewall devices from PC maker Asus and network security provider
     WatchGuard.


⚓ CSO ☛ What_is_a_botnet?_When_infected_devices_attack [iophk: Windows TCO]⠀⇛


     A botnet is an example of a distributed computing system operating
     over the internet—a fairly early example of this idea’s widespread
     real-world use. The people or teams who run a botnet, called
     controllers or herders, need to recruit unwilling computers into
     their army and then coordinate their activity for profit. There are a
     number of components to the architecture that helps botnets form and
     perpetuate themselves.


⚓ Nigeria ☛ ALERT:_Malware_targeting_routers,_Windows_PCs_in_circulation,_NCC
warns [iophk: Windows TCO]⠀⇛


     “To hide the malicious activity, the ransomware displays a fake
     window update screen, cancels specific processes and services, and
     completely disables the task manager, windows error reporting,
     machine firewall and windows defender of the compromised system.


⚓ Science Nigeria ☛ NCC_Uncovers_Cyber_Threats_to_Windows_Platforms,_Routers
[iophk: Windows TCO]⠀⇛


     The first cyber threat is ransomware ‘Lokilocker’, capable of wiping
     data from all versions of Windows systems or platforms. It causes
     data loss and denial of service (DoS) which reduces user
     productivity.


⚓ Security Affairs ☛ DirtyMoe_modules_expand_the_bot_using_worm-like
techniques⠀⇛


     The Windows botnet has been active since late 2017, it was mainly
     used to mine cryptocurrency, but it was also involved in DDoS attacks
     in 2018. The DirtyMoe rootkit was delivered via malspam campaigns or
     served by malicious sites hosting the PurpleFox exploit kit that
     triggers vulnerabilities in Internet Explorer, such as the CVE-2020-
     0674 scripting engine memory corruption vulnerability.


     The operations behind the DirtyMoe botnet rapidly changed since the
     end of 2020, when the malware authors added a worm module that could
     increase their activity by spread via the internet to other Windows
     systems.


⚓ The Register UK ☛ Microsoft_hikes_prices_for_non-profit_customers,_ends_on-
prem_software_grants [Ed: Clown computing is a bait-and-switch trap; Microsoft
is a bunch of criminals, preying on the poorest]⠀⇛


§ Security⠀➾


⚓ Kevin Cox ☛ Maybe_Passwords_are_the_Future⠀⇛


     A wide variety of new approaches are vying for popularity. WebAuthn
     removes passwords and instead uses keys that are managed by the
     browser. Email “magic links” use the ability to receive email as
     authentication. SSO delegates the problem to another provider.
     However these approaches all have major downsides. Let’s take a quick
     look at some of these and try to squeeze them into a pass/fail score,
     ignoring most of the nuance.


⚓ Techdirt ☛ WatchGuard_Plays_The_Ostrich,_Patches_Exploit_Without_Informing
Customers⠀⇛


     Firewalls. You know, boring old IT stuff. So why are we talking about
     them at Techdirt? Well, one thing we regularly talk about is how
     companies tend to respond to exploits and breaches that are uncovered
     and, far too often, how horrifically bad they are in those responses.
     Often times, breaches and exploits end up being far more severe than
     originally reported, and there are some companies that actually try
     to go after those reporting on breaches and exploits legally.


⚓ Hacker News ☛ Hackers_Exploiting_Spring4Shell_Vulnerability_to_Deploy_Mirai
Botnet_Malware⠀⇛


     The recently disclosed critical Spring4Shell vulnerability is being
     actively exploited by threat actors to execute the Mirai botnet
     malware, particularly in the Singapore region since the start of
     April 2022.


§ Privacy/Surveillance⠀➾


⚓ Techdirt ☛ NSO_Confirms_It_Gave_Israeli_Police_Access_To_Malware_To_Spy_On
Israelis⠀⇛


     Nearly every rumor about NSO Group has been proven true, despite
     plenty of early denials by the (oh, I guess we’ll be nice…)
     “embattled” malware merchant. The world’s foremost purveyor of zero-
     click exploits capable of completely compromising phones of targets
     is still in damage control mode. The damage can no longer be
     controlled, though. So, it’s basically just NSO admitting the nasty
     things said about have been mostly true.


⚓ Project Censored ☛ Major_Media_Outlets_Lobby_against_Regulation_of
“Surveillance_Advertising”_–_Validated_Independent_News⠀⇛


     Revenues from surveillance advertising drive the lobbying efforts
     against regulation. Media corporations argue that targeted
     advertising—and, by extension, the siphoning of user data—has become
     necessary due to declining revenues from print sales and
     subscriptions. However, despite a decline in print sales,
     surveillance advertising profits have soared for most media
     conglomerates over the last decade. While non-digital advertising
     revenue has decreased from $124.8 billion in 2011 to $89.8 billion in
     2020, over the same time period digital advertising revenue has risen
     from $31.9 billion to $152.2 billion, according to Pew Research.


⚓ India Times ☛ China_uses_AI_software_to_improve_its_surveillance
capabilities⠀⇛


     According to more than 50 publicly available documents examined by
     Reuters, dozens of entities in China have over the past four years
     bought such software, known as “one person, one file”. The technology
     improves on existing software, which simply collects data but leaves
     it to people to organise.


     “The system has the ability to learn independently and can optimize
     the accuracy of file creation as the amount of data increases. (Faces
     that are) partially blocked, masked, or wearing glasses, and low-
     resolution portraits can also be archived relatively accurately,”
     according to a tender published in July by the public security
     department of Henan, China’s third-largest province by population.


⚓ NYOB ☛ UPDATE:_CNIL_decides_EU-US_data_transfer_to_Google_Analytics_illegal⠀⇛


     Only weeks after the groundbreaking decision by the Austrian Data
     Protection Authority that the continuous use of Google Analytics
     violates the GDPR, the French Data Protection Authority (CNIL)
     ordered three French websites to comply with the GDPR. All these
     decisions are based on noyb’s 101 model complaints which were filed
     after the Court of Justice ruling invalidating Privacy Shield. noyb
     expects similar decisions by the other authorities.


⚓ CS Monitor ☛ Elon_Musk_became_Twitter’s_biggest_shareholder._What’s_next?⠀⇛


     Mr. Musk’s ultimate aim in acquiring 73.5 million shares, worth about
     $3 billion, isn’t clear. Yet in late March Mr. Musk, who has 80
     million Twitter followers and is active on the site, questioned free
     speech on Twitter and whether the platform is undermining democracy.


⚓ Futurism ☛ Gun_Shot_Detection_Cameras_Alerting_Cops_To_Slamming_Doors
Instead⠀⇛


     A police reform group says the cameras cops are using to
     automatically detect and report gun shots should be taken down,
     citing their proclivity for picking up the sound of slamming doors
     instead.


     According to a new Axios report, Campaign Zero is lobbying local city
     governments to stop using the tech, called ShotSpotter, after a year-
     long study. The group says ShotSpotter doesn’t significantly reduce
     gun violence, rarely leads to physical evidence a gun was fired,
     increases the likelihood of police violence, and costs tax payers
     millions.


⚓ You_are_Tracked_Online_–_How_To_Avoid_Being_Tracked_Online⠀⇛


     The internet, as well as the threats that cybercriminals use to
     exploit their victims, are constantly evolving and often users will
     fall short in implementing best practices. Tracking users online is
     not only seen as a marketing strategy for websites, it is often a
     resource for third parties to buy your information. Once this
     information has gotten into the wrong hands, there is a strong
     possibility of eventually facing a phishing or ransomware attack.
     Because of this, it is important to have as many safeguards in place
     as possible and change methods frequently to protect yourself online.
     Consider Tor and Tor Browser (based on Firefox), a web browser that
     anonymizes your web traffic when using the Tor network, making it
     easy to protect your identity online. This can be very appropriate
     for navigating without being tracked at specific times.


⚓ The Register UK ☛ Apple_iOS_privacy_clampdown_‘did_little’_to_reduce_tracking
[Ed: Apple works for NSA. You need to be as gullible as an Apple "consumer" to
believe otherwise (in the face of verifiable facts).]⠀⇛


     Apple’s ramp up in iOS privacy measures has affected small data
     brokers, yet apps can still collect group-oriented data and identify
     users via device fingerprinting, according to a study out of Oxford.


     What’s more, the researchers claim, Apple itself engages in and
     allows some forms of tracking, which serve to strengthen its control
     over the iOS market.


     In a paper titled, “Goodbye Tracking? Impact of iOS App Tracking
     Transparency and Privacy Labels,” due to be published in June for the
     ACM Conference on Fairness, Accountability, and Transparency 2022,
     Oxford academics Konrad Kollnig, Max Van Kleek, Reuben Binns, and
     Nigel Shadbolt, with independent US-based researcher Anastasia Shuba,
     describe what they found after analyzing 1,759 iOS apps from the UK
     App Store, both before and after the introduction of iOS 14.


     “While Apple’s changes make tracking individual users more difficult,
     they motivate a counter-movement, and reinforce existing market power
     of gatekeeper companies with access to large troves of first-party
     data,” they state in their paper.


§ Defence/Aggression⠀➾


⚓ Common Dreams ☛ Opinion_|_Opposing_War:_Standing_Together_for_Peace⠀⇛


     The soul of humanity cries out from the crowded streets of Moscow,
     from steps near the Kremlin, as a man—an artist in the deepest
     sense—brings the slaughter of civilians in Bucha back to the home
     country…not by killing a bunch of Russians, but by posing, publicly,
     as dead himself, with his hands tied behind his back.


⚓ Common Dreams ☛ Russian_Airstrike_Reportedly_Kills_30+_at_Train_Station_Used
to_Evacuate_Civilians⠀⇛


     A Russian missile attack on Friday reportedly killed more than 30
     people at a train station in the eastern Ukrainian city of
     Kramatorsk, where civilians gathered to flee escalating violence in
     the region.


     Pavlo Kyrylenko, the regional governor of Donetsk, said in a
     statement that “thousands of people were at the station during the
     missile strike, as residents of Donetsk region are being evacuated to
     safer regions of Ukraine.”


⚓ TruthOut ☛ Report:_Jan._6_Committee_Finds_Connections_Between_Militias_&
Rally_Organizers⠀⇛


⚓ Democracy Now ☛ End_the_Double_Standard:_U.S._Accuses_Russia_of_War_Crimes
While_Continuing_to_Oppose_the_ICC⠀⇛


     The United Nations General Assembly voted to suspend Russia from the
     U.N. Human Rights Council on Thursday, a resolution that accused
     Russia of committing human rights abuses in Ukraine. We speak with
     human rights lawyer Wolfgang Kaleck about the apparent double
     standards and weaknesses in the current international criminal
     justice system in light of the U.S. committing similar crimes in Iraq
     and Afghanistan. Nations like the U.S. have refused to submit
     themselves to any kind of international jurisdiction because “they
     want to lead their wars,” says Kaleck. “The International Criminal
     Court will only get off the ground in the near future if Western
     states agree to apply universal standards.”


⚓ Common Dreams ☛ Kremlin_Shutters_Amnesty,_Human_Rights_Watch_Offices_in
Moscow⠀⇛


     The Moscow offices of Amnesty International, Human Rights Watch, and
     other groups were shuttered by the Kremlin on Friday—a move that
     comes amid widespread condemnation of abuses and possible war crimes
     that have taken place during Russia’s ongoing attack on Ukraine.


     “Amnesty’s closing down in Russia is only the latest in a long list
     of organizations that have been punished for defending human rights
     and speaking the truth to the Russian authorities,” said Agnès
     Callamard, secretary-general of Amnesty International, in a
     statement.


⚓ Mint Press News ☛ Kyiv_Independent_Deep_Dive:_The_West’s_In-Kind_Answer_to
Putin’s_Propaganda⠀⇛


     As the Russian attack on Ukraine has come to dominate global news
     feeds, so has a previously little-known outlet called The Kyiv
     Independent. Since its inception in November of last year, the
     Independent’s profile has risen rapidly and has been promoted and
     endorsed by both social media giants and the corporate press.


⚓ The Nation ☛ Our_Planet’s_Long_History_of_War⠀⇛


     Excuse me if I wander a little today—and if it bothers you, don’t
     blame me, blame Vladimir Putin. After all, I didn’t decide to invade
     Ukraine, the place my grandfather fled almost 140 years ago. I
     suspect, in fact, that I was an adult before I even knew such a place
     existed. If I could be accused of anything, maybe you could say that,
     for most of my life, I evaded Ukraine.


⚓ The Nation ☛ The_Little_Picketers_of_Russia⠀⇛


     On a recent snowy day in Moscow, a figure held a poster of a peace
     sign across the river from the Kremlin. Unlike other protesters, this
     one was not arrested, because it stood only a few inches tall and was
     made of plasticine clay.


⚓ Common Dreams ☛ Opinion_|_The_Idea_of_a_Clean_and_Efficient_War_Is_a
Dangerous_Lie⠀⇛


     The war in Ukraine resuscitated a certain dangerous fascination for
     war. Notions such as patriotism, democratic values, the right side of
     history, or a new fight for freedom are mobilized as imperatives for
     everyone to take a side in this war. It is not surprising then that a
     large number of so-called foreign fighters are willing to go to
     Ukraine to join one side or the other.


⚓ Common Dreams ☛ Russia’s_Invasion_of_Ukraine_Has_Pushed_Global_Food_Prices_to
All-Time_High:_UN_Agency⠀⇛


     The U.N. Food and Agriculture Organization declared Friday that
     “supporting agricultural resilience in Ukraine and around the world
     has never been more important to avert a global food crisis” and
     reported that food commodity prices just hit their highest levels
     ever.


     The FAO’s Food Price Index—which tracks monthly international price
     changes in food commodities—hit a new high in March, surpassing
     February’s record level.


⚓ Common Dreams ☛ Opinion_|_From_US_Invasion_in_Iraq_to_Russia’s_Assault_on
Ukraine,_We_Need_a_Global_Standard_for_War_Crimes⠀⇛


     In early April, shocking video surfaced revealing the brutal murder
     of civilians by an occupying army. The year was 2010, however, not
     2022, in Iraq, not Ukraine, and the soldiers were American, not
     Russian. On April 5th, 2010, Wikileaks, the whistleblower website,
     released a classified U.S. military video it called “Collateral
     Murder.” The video was recorded on July 12, 2007 aboard a U.S. Army
     Apache helicopter gunship as it fired on a crowd in Baghdad. Two
     Reuters employees were killed, along with at least eight others, and
     two children were seriously injured. The video includes audio of U.S
     soldiers laughing and swearing as they kill, as well as radio
     transmissions authorizing the attacks from their chain of command.
     Ultimately, only one U.S. soldier was prosecuted: Army Private
     Chelsea Manning was court martialed, not for participating in that
     attack on civilians, but for revealing it to the world.


⚓ Common Dreams ☛ Opinion_|_As_US_Funds_Pentagon_Bloat,_China_Investments_in
Green_Energy_Soar⠀⇛


     China is beating the pants off the United States in the burgeoning
     new energy vehicle market, out-producing and out-selling America with
     regard to plug-in vehicles by a massive margin. Whereas the Chinese
     government is supporting this new industry, the US government is
     still subsidizing fossil fuels and is spending $728.5 billion a year
     on the Pentagon at a time when the US is not even at war. The result
     is bloated and problematic engines of destruction like the failed F-
     35.


⚓ Meduza ☛ Verified_video_appears_to_show_Ukrainian_troops_killing_Russian
captives._Here’s_what_we_know_about_it.⠀⇛


     On April 6, the New York Times reported that its journalists had
     verified a video that appears to show Ukrainian soldiers killing
     captured Russian troops. This footage surfaced on April 4, amid the
     international outcry over the civilian killings revealed in Bucha
     following the withdrawal of Russian forces from the Kyiv region. Pro-
     Russian media outlets, which have been pushing false narratives about
     the atrocities in Buch being “staged” and/or a “false flag” (despite
     ample evidence of war crimes), already claim to have identified the
     Ukrainian troops seen in the video. The Ukrainian authorities have
     yet to confirm the authenticity of the video, but earlier promised to
     investigate alleged war crimes against Russian forces.


⚓ Meduza ☛ Worse_than_Bucha_Meduza_speaks_to_Borodyanka_residents_about_how
they_survived_under_Russian_occupation⠀⇛


     Bucha and Borodyanka are two small towns in the vicinity of Kyiv that
     were recently occupied by Russian troops. The images of murdered
     civilians in Bucha sent shockwaves around the world after journalists
     arrived in the village following its liberation. According to Kyiv
     authorities, upwards of 400 people died in Bucha while it was under
     Russian control. However, Iryna Venediktova, the Ukrainian Prosecutor
     General, has said that the situation in liberated Borodyanka may be
     even worse. Meduza spoke to people from Borodyanka and a few other
     Kyiv suburbs about how they survived the occupation.


⚓ Meduza ☛ Russian_missile_hits_Kramatorsk_train_station:_The_attack_killed_at
least_50_civilians_and_overwhelmed_local_hospitals⠀⇛


     The Kramatorsk train station in eastern Ukraine was hit by a missile
     strike, Ukrainian state railway company head Oleksandr Kamyshin
     reported on Friday. According to Kamyshin, two missiles were fired at
     the station. He published photos and videos of wreckage from the
     strike on Telegram.


⚓ Meduza ☛ ‘You_see_this_line?_It’s_all_Russians.’_In_a_dispatch_from_Almaty,
Meduza_meets_Russian_citizens_flocking_to_Kazakhstan_following_Moscow’s
invasion_of_Ukraine⠀⇛


     Thousands have left Russia in response to Moscow launching an all-out
     war against Ukraine. While Turkey, Georgia, and Armenia have been the
     most popular destinations for émigrés, others fleeing repressions and
     economic sanctions have found themselves in former Soviet republics,
     including Kyrgyzstan, Uzbekistan, and Kazakhstan. Kazakh journalist
     Daniyar Moldabekov spoke to newly-arrived Russians in Almaty about
     how they chose their path, whether they planned to return to Russia,
     and how they envision their futures.


⚓ Meduza ☛ A_new_wave_of_old_lies:_More_false_claims_about_the_Mariupol
maternity_hospital_bombing,_debunked⠀⇛


     In early April, Denis Seleznyov, a blogger from the self-proclaimed
     Donetsk People’s Republic (DNR), posted a new video on his YouTube
     channel: an interview with Marianna Vyshemirskaya (who also goes by
     her maiden name, Podgurskaya). Marianna is a beauty blogger from
     Donetsk who caught the world’s attention after AP journalists
     Mstyslav Chernov and Yevgeny Maloletka photographed her at a
     maternity hospital in Mariupol immediately after it was bombed on
     March 9, 2022. The Ukrainian authorities reported that the hospital
     had been hit by a Russian airstrike.


⚓ Hungary ☛ Borodyanka_was_once_a_town_full_of_life_–_now_they_are_pulling
bodies_from_under_the_rubble⠀⇛


     Borodyanka was once a quiet little town about 50 kilometres west of
     Kyiv until Russian forces took control of it in the first few days of
     the war. The town, is not too far from Bucha – which has been
     mentioned due to potential war crimes having been committed there –
     and it was under Russian occupation for a month. We arrived just a
     few days following the sudden, overnight retreat of the Russian
     forces.


⚓ Counter Punch ☛ An_antidote_to_the_“Split”_in_the_US_Peace_Movement:_Anti-
interventionism._No_more_US_Arms_to_Ukraine._End_the_Racist_Sanctions._Stop_the
Russia_Bashing.⠀⇛


     A recent piece by its Assistant Director, Brian Garvey, provides an
     astute analysis of the ideological differences in the progressive
     part of the US peace movement and properly criticizes its inability
     to unite around a common program. He asks the two crucial questions:


     “What do we do now? and


⚓ Counter Punch ☛ Conflict_Dynamics⠀⇛


     How did it come to this?


     Having worked in war zones, I have wondered if that violence could
     happen again here. One way to prevent it is to understand how
     conflict escalates.


⚓ Counter Punch ☛ Big_Oil’s_War_Bonanza⠀⇛


     Yes, a tight oil market and inflationary prices are good for electric
     car production. But the oil and gas industry is doing even better,
     not just because of high gas prices, but also because they can demand
     more access to public lands for drilling—and blame the administration
     for the high gas prices if the companies don’t get to drill more.
     This is a false argument on five counts.


     Drill, Baby, Drill


⚓ Counter Punch ☛ Putin_and_the_Church:_an_Unholy_Alliance⠀⇛


     Lest anyone has doubts as to Putin’s racist and imperialistic vision,
     he was quoted as saying:


     “The United States continues to receive more and more immigrants,
     and, as far as I understand, the white, Christian population is
     already outnumbered … White Christians have become a minority, less
     than 50 percent now. … Russia is a vast territory, from its western
     to eastern borders, it is a Eurasian space. But as regards culture,
     even language group and history, this all is undoubtedly a European
     space, as it is inhabited by people of this culture. … we have to
     preserve all this to remain a significant centre in the world.”


⚓ Counter Punch ☛ War_is_the_Crime._Its_Perpetrators_Seldom_Face_Justice.⠀⇛


     “You may remember I got criticized for calling Putin a war criminal,”
     says US president Joe Biden. “Well, the truth of the matter — we saw
     it happen in Bucha — he is a war criminal.”


     What actually happened in Bucha is uncertain  and may remain so
     forever. The Ukrainians claim that Russian soldiers murdered the
     civilians. The Russians seem to alternately claim the entire scene
     was staged, or else that the victims were suspected Russian
     sympathizers/collaborators killed by fellow Ukrainians.  Probably
     mass murder, but who did it?


⚓ The Nation ☛ The_Ukraine_Crisis_Comes_to_the_UN⠀⇛


     Not long ago, any ordinary crisis worked its way through the United
     Nations with some predictability: A meeting of the Security Council
     was announced. Official briefings took place and predictable speeches
     were made. A resolution may or may not have been passed, or a
     presidential statement issued. Not a lot of global media reported on
     these events.


⚓ The Nation ☛ Life_Under_Russian_Occupation_in_Bucha⠀⇛


     Lviv, Ukraine—Before the war came, the commuter town of Bucha, near
     Kyiv, was well-known as a glass-making hub. In the last week, as
     pictures of mass graves and bodies left to rot on its streets have
     begun to circulate, it has taken on a grimmer renown. According to
     the mayor of the town, at least 300 civilians were executed by
     Russian troops. (The Russian government has called the allegations
     “fake” and insists Ukrainian troops killed the civilians as part of a
     false flag operation.)


⚓ Counter Punch ☛ Can_Israel_Exist_without_America:_Numbers_Speaks_of_a
Changing_Reality⠀⇛


     One may explain Israel’s political significance to the Russian-
     Ukrainian talks based on Tel Aviv’s strong ties with Kyiv, as opposed
     to Russia’s trust in Israel. This is insufficient to rationalize how
     Israel has managed to acquire relevance in an international conflict,
     arguably the most serious since World War II.


     Immediately following the start of the war, Israeli officials began
     to circumnavigate the globe, shuttling between many countries that
     are directly or even nominally involved in the conflict. Israeli
     President Isaac Herzog flew to Istanbul to meet with his Turkish
     counterpart, Recep Tayyip Erdogan. The outcome of this meeting could
     usher in “a turning point in relations between Turkey and Israel,”
     Erdogan said.


⚓ Counter Punch ☛ The_Lies,_Damned_Lies_of_War_–_and_the_Statistics_to_Prove
It⠀⇛


     I spoke with Heidi by Zoom yesterday.  Here is the edited transcript
     of the interview.


     John Hawkins: You are part of the Costs of War Project at Brown
     University. Can you say more about the project and what your role has
     been?


⚓ Counter Punch ☛ Suspending_Russia:_a_Precedent_That_Undermines_the
Credibility_of_the_Human_Rights_Council⠀⇛


     I do not wish to overestimate the consequences of the GA decision. 
     Obviously, it is a blow to Russia’s prestige, and adds to the general
     atmosphere of Russophobia that we have seen over the decades. We can
     expect in the future that efforts will be made to exclude other
     countries from membership in the Human Rights Council – one could
     think of excluding several NATO countries for the war crimes and
     crimes against humanity committed by their forces during the wars of
     aggression against Yugoslavia, Afghanistan, Iraq, Libya, Syria.  We
     could think of excluding Saudi Arabia because of its genocidal war
     against the people of Yemen. We could think of excluding India for
     its systematic war crimes and gross violations of human rights
     against the people of Kashmir, including widespread extra-judicial
     executions.  Another credible candidate for suspension would be
     Azerbaijan because of its aggression against the hapless Armenians of
     Nagorno Karabakh during the Blitzkrieg of September-November 2020,
     where war crimes and crimes against humanity were committed,
     including torture and execution of Armenian prisoners of war. We
     could think of excluding Colombia because of its lethal para-military
     activities and consistent pattern of killing human rights defenders,
     social leaders, syndicalists and indigenous peoples.


     Let us not shed too many tears over the Human Rights Council, whose
     authority and credibility are questionable, and whose resolutions are
     routinely ignored by many countries, including the United States, the
     United Kingdom and Israel. Since its creation in 2006 the Human
     Rights Council has not served human rights well – but it has
     certainly served the geopolitical and informational interests of the
     United States and the European Union


⚓ Counter Punch ☛ Why_Hasn’t_the_US_Been_Kicked_Off_of_the_UN_Human_Rights
Council?⠀⇛


     While there are calls for independent investigations into those
     allegations, the US and NATO member state governments have been
     pushing the claim that Russia is committing war crimes in Ukraine
     including the major war crime of invading another country, the
     unasked question in the US media is: Why hasn’t the US been kicked
     out of the Human Rights Council for similar war crimes that aren’t at
     all allegations, but are well-documented fact? Why indeed, for all
     the accusations that Russian President Vladimir Putin is himself a
     war criminal responsible for all these crimes, haven’t a number of US
     presidents still living been accused of war crimes?


     Let’s look at some of those crimes…


⚓ Counter Punch ☛ Get_In_Line:_Investigate_U.S._Atrocities_First⠀⇛


     CP published part of this list of headlines in 2012, but in view of
     continuing U.S. wars and the outpouring of legitimate, agonized of
     grief for civilian victims of Russia’s illegal war, an updated
     compilation is in order.


     The U.S. military has a long record of apparent atrocities during its
     attacks and its unprovoked wars of aggression or occupation in
     Afghanistan, Iraq, Syria, Libya, Pakistan, Yugoslavia and elsewhere.
     Like Russia in Ukraine today, the crimes include bombing hospitals,
     desecrating corpses, attacks on civilians and civilian objects,
     attacking allied troops, torturing and executing prisoners, and using
     banned cluster bombs.


⚓ Counter Punch ☛ Chronicle_of_a_Genocide_Foretold⠀⇛


     Studying American history, one inevitably notices that the white
     supremacist philosophy which underlaid both the genocide of Native
     Americans and the Transatlantic slave trade was expressed openly at
     the time – constantly, in fact, and by everybody from US Presidents
     to Sunday school teachers to fur traders. The same is true of the
     Nazi genocide of Jews, Roma and other minority groups in mid-20th C.
     Europe. Preceding the Holocaust, blithely antisemitic, genocidal
     language was used in Germany for years – in public speeches and
     newspaper editorials, in legislation and in children’s books. This
     was also the case surrounding the genocide which occurred in Rwanda
     in 1994. As the BBC details, in the months leading up to the campaign
     of terror against the Tutsis, “The Hutu extremists set up a radio
     station, RTLM, and newspapers which circulated hate propaganda,
     urging people to ‘weed out the cockroaches’ meaning kill the Tutsis.
     The names of prominent people to be killed were read out on radio.”
     We appear to be witnessing a similar phenomenon today when the
     Russian state speaks about its the war in Ukraine.


     On April 3, 2022 – the same day the world learned of the apparent war
     crimes and atrocities carried out the Russian army in Bucha and other
     cities north of Kiev – the prominent Russian state-owned news agency
     RIA Novosti published an article titled “What Should Russia Do with
     Ukraine?” The piece is openly genocidal in its language. That is, it
     promotes and seeks to justify “acts committed with intent to destroy,
     in whole or in part, a national, ethnical, racial or religious group,
     as such” – which is how the United Nations defines the crime of
     genocide. The conceptual device which author Timofey Sergeytsev
     employs in order to make his demented argument is the that the
     pursuit of Ukrainian national identity is indistinguishable from
     Nazism. Given what is at stake, it is important to examine the
     article’s at once turgid and terrifying prose.


⚓ Counter Punch ☛ Bucha_Massacre_Evidence_and_Russia’s_Propaganda⠀⇛


     Exploring the newly emerging evidence of a Russian atrocity in the
     village of Bucha and debunking the fraudulent narratives of the
     Kremlin disinformation army on the Left.


⚓ Counter Punch ☛ Ukraine_Conflict_a_Platform_for_Racism_and_Rewriting
History⠀⇛


     In a rare admission of moral responsibility, Oleksiy Arestovych, an
     adviser to the Ukrainian President, quickly reminded Ukrainian
     fighters of their responsibility under international law. “I would
     like to remind all our military, civilian and defense forces, once
     again, that the abuse of prisoners is a war crime that has no amnesty
     under military law and has no statute of limitations,” he said,
     asserting that “We are a European army”, as if the latter is
     synonymous with civilized behavior.


     Even that supposed claim of responsibility conveyed subtle racism, as
     if to suggest that non-westerners, non-Europeans, may carry out such
     grisly and cowardly violence, but certainly not the more rational,
     humane and intellectually superior Europeans.


⚓ Counter Punch ☛ Plots_and_Counter-Plots:_Western_Skulduggery_to_Realign
Central_Asia⠀⇛


     This malodorous silence, whiffling through our press and TV, means no
     focus, ever, on western machinations to engineer regime change. That
     skullduggery may be alluded to as the wild charges of some unreliable
     non-western politico, but that’s it. They’ll tell you that Pakistan’s
     president, Imran Khan, who is not very friendly with Washington,
     faced a no-confidence vote and to get out of it precipitated a
     constitutional crisis and that Kazakhstan foiled a foreign agent’s
     attempt to kill President Kassym Jomart Tokayev, but they’re
     strangely reluctant to draw lines of causality between the likely
     shadowy culprits, and those who pull their strings, namely
     Washington’s rulers.


     Pakistan prime minister Khan told a huge crowd on March 27 that
     “foreign powers are engineering a regime change in Pakistan.” He
     claimed to have proof in a letter and, based on that, later the
     Foreign Office reprimanded the U.S. ambassador. The letter mentions a
     no-confidence motion against Khan, according to an April 2 article in
     the Cradle, “about eight times.”


⚓ Counter Punch ☛ Letter_From_Crimea:_Is_the_Ukraine_War_a_Pogrom?⠀⇛


     Most of what I did on my first day in Moscow was get the hang of
     bicycle riding in traffic that is a perpetual motion machine.


     I had read that Moscow, as a way of alleviating its car congestion,
     had laid down some bicycle lanes around the city, but when I went in
     search of these segregated paths I found that many ended abruptly at
     the steps of underground passages that pedestrians use to pass
     beneath the city’s multi-lane boulevards. In order to cross busy
     streets, I often had to carry the bicycle down and up long
     staircases, as if portaging a canoe from one Wisconsin lake to
     another.


⚓ Counter Punch ☛ How_the_U.S._Exports_Its_Border_to_Ukraine⠀⇛


     The INL caught my eye because this was one of the agencies I examined
     in my book Empire of Borders: The Expansion of the U.S. Border around
     the World, which traces U.S. border externalization from the Americas
     and the Caribbean to East Africa, the Philippines, and the Middle
     East. The armored vehicles caught my eye too, because the INL
     transferred similar equipment to newly formed border forces in
     Central America and to fortify Mexico’s border with Guatemala in the
     2010s. The INL—an agency whose goal is to counter crime, illicit
     drugs, and instability abroad “to keep Americans safe”—works in 90
     countries across the globe, often orchestrating U.S.-instigated
     border enforcement in places like Guatemala and Ukraine.


     For Washington, the post-9/11 strategy of pushing out the border has
     become an overlooked yet fundamental part of its enforcement scheme.
     According to former CBP commissioner Alan Bersin, there has been a
     “paradigm shift” toward this emphasis on international enforcement.
     Bersin is the same high-ranking official who in 2012 said, “The
     Guatemalan border with Chiapas is now our southern border.” While
     much of the U.S. border externalization does occur in the Western
     Hemisphere, its scope is far wider. It has followed the spirit of the
     9/11 Commission Report, which stated, “The American homeland is the
     planet.”


⚓ Counter Punch ☛ Why_Ukraine?⠀⇛


     Similarly, when authorization was given by the ICC to investigate
     crimes by the United States in Afghanistan, the decision was
     denounced as void because the U.S. was not a party to the Rome
     Statute governing the operations of the ICC. The Trump presidency
     went so far as to impose personal sanctions on the ICC prosecutor,
     presumably for daring to challenge the U.S. in such a manner even
     though her behavior was entirely respectful of her professional role
     and consistent with relevant canons of judicial practice.


     Against such a background, there is a typical liberal quandary when
     faced with clear criminality on one side and pure geopolitical
     hypocrisy on the other side. Was it desirable after World War II to
     prosecute surviving German and Japanese political leaders and
     military commanders at the ‘legal’ cost of overlooking their
     criminality because there was no disposition to investigate the
     dropping of atom bombs on Japanese cities or the strategic bombing of
     civilian habitats in Germany and Japan? I am far from sure about what
     is better from the perspective of either developing a global rule of
     law or inducing respect for the restraints of law. The essence of law
     is to treat equals equally, but world order is not so constituted. As
     suggested, there is ‘victors’ justice’ imposing accountability on the
     defeated leadership but complete non-accountability for the crimes of
     the geopolitical winners. Beyond this, the UN Charter was drafted in
     ways that gave a constitutional status to geopolitical impunity by
     granting the victors in World War II an unconditional right of veto,
     and this of course includes Russia. In these respects, liberalism
     defers to geopolitical realism, and celebrate the one-sided
     imposition of legality, with the naïve hope things will be different
     in the future. Yet the post-Nuremberg record shows that geopolitical
     actors go on treating restraints on recourse to war as a matter of
     discretion (what American liberals called ‘wars of choice’ in the
     course of the debate about embarking upon a regime-changing attack on
     and occupation of Iraq in 2003) rather than an obligation. When it
     comes to accountability double standards are still operative,
     illustrated by the execution of Saddam Hussein for war crimes after a
     war of aggression against Iraq.


⚓ Counter Punch ☛ Roaming_Charges:_News_From_Never-Neverland⠀⇛


     What needs to be done? Nothing less than a revolution in the way the
     world’s economy functions and the fuels that drive it. What can be
     done? Not much. What will be done? Almost nothing. That’s my read on
     the latest (and reportedly the final) consensus report from the IPCC,
     a document reads less like the Book of Revelations than an after-
     bombing damage assessment. The bottom-line is that the 1.5C warming
     goal set by the panel in 2015 is obsolete. It’s unattainable.
     Defunct. Moreover, it’s always been unattainable. The international
     plans to slow global warming from Kyoto to Paris would not have been
     able to keep the climate below that threshold, even had they been
     fully-implemented. Needless to say, they haven’t been fully
     implemented. Far from it.


     Consider this: the average annual greenhouse gas emissions over the
     last 10 years were the highest in … human history. In 2019, carbon
     emissions were about 54% higher than in 1990. Sixty percent of all
     historical emissions were produced in the lifetime of the average
     American, who is 38. Almost 90 percent were produced since the birth
     of Joe Biden in November 1942.


⚓ Counter Punch ☛ Wartime_Dispatches⠀⇛


     From Micanopy, Florida to Kyiv, Ukraine is 5,559 miles, almost a
     quarter way around the world, but the war feels dangerously close.
     Putin, however, is criminal not crazy and the Russian policy on first
     use is little different from ours, so the likelihood of a nuclear
     attack is small. But for anybody who lived through the Cuban Missile
     Crisis, the shadow cast by the mushroom cloud is hard to evade.


     I was only a child, on October 22, 1962, but I can remember the dread
     silence in our Forest Hills apartment the evening we watched the
     president announce his plan to stop, by force, if necessary, the
     installation of missile launchers in Cuba. A little more than a year
     later, we gathered again – two parents, three children and three
     grandparents — to watch Kennedy’s funeral on the same black and white
     TV. This time, the silence was broken by sobs. For the children, it
     was just as before: something big and distant threatened to destroy
     what was intimate and close. The Russian war against Ukraine, far
     away though it is, resurrects that traumatic memory, albeit dimly.


⚓ The Gray Zone ☛ US_lawmakers_welcomed_notorious_Georgian_warlord_now_boasting
of_war_crimes_in_Ukraine⠀⇛


⚓ TruthOut ☛ Why_Is_Merrick_Garland_Throttling_the_Trump_Investigation?⠀⇛


⚓ TruthOut ☛ Russian_Airstrike_Reportedly_Kills_30+_at_Train_Station_Used_for
Evacuations⠀⇛


⚓ VOA News ☛ 2_Acquitted,_Hung_Jury_for_2_More_in_Michigan_Kidnap_Case⠀⇛


     A jury on Friday acquitted two men of all charges in a plot to kidnap
     Michigan Governor Gretchen Whitmer but couldn’t reach verdicts
     against the two alleged leaders, a stunning defeat for the government
     after a weekslong trial that centered on a remarkable FBI sting
     operation just before the 2020 election.


     Whitmer did not immediately comment on the outcome, though her chief
     of staff was critical, saying Americans are “living through the
     normalization of political violence.”


⚓ BBC ☛ Gretchen_Whitmer:_Michigan_governor_kidnap_plot_case_collapses⠀⇛


     A US federal jury has acquitted two men accused of plotting to kidnap
     Michigan’s governor and failed to reach a verdict for two other
     defendants.


⚓ NBC ☛ The_dangerous_message_sent_by_the_Gov._Whitmer_kidnapping_verdict⠀⇛


     But again, this pattern extends far beyond the Mitten State, as
     conservatives desperate to whitewash the revolting spectacle of bat-
     wielding, police-beating Capitol insurrectionists who shared the same
     anti-government ideology as the Michigan men engage in Houdini-level
     logical contortions.


     The acrobatic effort has welded together some of the strangest
     bedfellows in American history. Carlson, a backer of the police’s
     thin blue line if there ever was one, has been ridiculing and
     downplaying the seriousness of the alleged plot for more than a year.
     He has given a platform to a variety of activists who have made a
     cottage industry of comparing the Michigan case to what they now call
     the “entrapment operation” of the Capitol insurrection. Such claims
     are amplified across the right-wing echo chamber. (Osama bin Laden’s
     niece Noor bin Laden even wrote a letter to the U.N. on behalf of the
     jailed Jan. 6 “political prisoners.”)


⚓ CISSAR ☛ As_another_genocide_looms,_Western_virtue_signaling_won’t_cut_it⠀⇛


     Virtue signaling is a placebo, not a remedy. It’s increasingly clear
     that the Biden administration has not learned any lessons from its
     mistakes.


⚓ France24 ☛ ‘Bad_intelligence’_behind_Mali_military_operation_that_‘killed_300
civilians’⠀⇛


     “They are attacking many jihadi strongholds,” Nasr continued. “But
     the thing is, the jihadis aren’t resisting, or at least they weren’t
     – up til the beginning of last month. They counter-attacked after
     absorbing the new force, which is the Russians actually, and counter-
     attacked in Mondoro, causing the deaths of more than 40 Malian
     military. In the last two months, the Malian military lost up to 160
     men in this region.”


⚓ Defence Web ☛ Mali_tri-border_security_worrying⠀⇛


     The security situation on Mali’s borders with Burkina Faso and Niger
     has deteriorated to the stage where the UN mission in the landlocked
     west African country notes “significant” population displacement.


     “Attacks by armed terrorist groups have a devastating impact on an
     already distressed civilian population, resulting in dozens of deaths
     and significant displacement of populations in Gao and Ansongo
     towns,” a MINUSMA statement reads.


⚓ NPR ☛ 2_men_impersonated_federal_agents_to_get_close_to_the_Secret_Service,
FBI_says⠀⇛


     Taherzadeh allegedly provided rent-free apartments, iPhones,
     surveillance systems, a flat screen television and other items to win
     over Secret Service agents and one employee of DHS. He also offered
     what he called “official government vehicles” and offered to purchase
     a $2,000 assault rifle for the Secret Service agent assigned to the
     first lady, the affidavit said.


§ Environment⠀➾


⚓ Modern Diplomacy ☛ Earth_Day_2022:_Earth_is_calling._We_must_act_now_before
it’s_too_late⠀⇛


     Every year on 22 April, the world marks Earth Day. It is an occasion
     to raise awareness and show support for the protection of the
     environment, with actions organised worldwide around a common
     message: save the Earth.


     Almost 2 million children under the age of five die every year due to
     environmental factors like pollution. One in three people do not have
     access to safe drinking water. And things are only getting worse. The
     temperature on Earth will rise by 2.7°C this century, even if we meet
     our 2030 climate targets, affecting food supplies, lives and
     livelihoods.


     Time is running out: every action counts, and every second counts.


⚓ Counter Punch ☛ The_Great_Barrier_Reef_on_Life_Support⠀⇛


     Recent news of another (the 6th) bleaching event at the Great Barrier
     Reef is but one more example in a long list of recent climate-related
     events that depict a scenario that can only be described as triple-
     alarm climate emergencies, as ecosystems breakdown across the world.


     But, those breakdowns are not happening where people live. Therefore,
     other than scientists, who sees cascading ice sheets, crumbling
     permafrost, tens of thousands of Alaskan and Siberian thermokarst
     lakes bubbling methane, Greenland’s Helheim glacier cascading into
     the sea, or depleting ocean kelp forests amongst horrendous loss of
     prime fishing stock at crucial northern latitudes?


⚓ Counter Punch ☛ Being_a_Bit_Serious_About_Oil_Prices⠀⇛


     There are a couple of points here worth noting. First, the projected
     impact of this sort of additional supply would not be all that
     trivial. The short-term demand elasticity is usually estimated to be
     quite low, typically around -0.15. That would imply that a 1 percent
     increase in the supply of oil should lead to a roughly 7 percent
     decline in oil prices. If we apply that to the current price of gas,
     that would be a drop of more than 25 cents a gallon.


     A price increase of that size would likely be sufficient to prompt a
     raff of news pieces about how higher gas prices were bankrupting
     families. A price decline of this size should be equally momentous.


⚓ Counter Punch ☛ Capital’s_New_Face_is_Intersectional⠀⇛


     To celebrate this past International Women’s Month, Pipeline Equity’s
     CEO Katica Roy has been promoting the company’s proprietary SaaS
     platform using artificial intelligence to assess and address
     intersectional inequity (the overlap of multiple identities- race,
     gender, sexuality, etc) in business hiring, pay, and promotion
     practices.


     In its promotional materials, Pipeline announced that its customers
     saw a “65% increase in their intersectional equity progress” within
     the first three months of using their platform. The company cited a
     “massive economic opportunity to the tune of $12 trillion globally”
     for companies when addressing workplace intersectional inequity- for
     every 10% increase in intersectional gender equity, an increase of 1-
     2% in revenue.


⚓ The Nation ☛ We_Can’t_Wait_for_Our_Institutions_to_Take_Action_on_Climate
Change⠀⇛


     Students and alumni of Pennsylvania State University—my school and
     Pennsylvania’s flagship land-grant institution—recognize that the
     climate crisis is personal. The Keystone State accounts for nearly 1
     percent of the world’s greenhouse gas emissions and is expected to
     warm nearly 6 degrees Fahrenheit by 2050, after already sustaining
     hundreds of millions of dollars worth of infrastructure damage.


⚓ The Nation ☛ Fueling_Disaster⠀⇛


⚓ Common Dreams ☛ Fight_Climate_Emergency_by_Nationalizing_US_Fossil_Fuel
Industry,_Says_Top_Economist⠀⇛


     In the wake of a United Nations report that activists said showed the
     “bleak and brutal truth” about the climate emergency, a leading
     economist on Friday highlighted a step that supporters argue could be
     incredibly effective at combating the global crisis: nationalizing
     the U.S. fossil fuel industry.


     “With at least ExxonMobil, Chevron, and ConocoPhillips under public
     control, the necessary phaseout of fossil fuels as an energy source
     could advance in an orderly fashion.”


⚓ Common Dreams ☛ Climate_Groups_Say_Canadian_Government_‘Bowed_to_Big_Oil’
With_New_Budget⠀⇛


     Climate campaigners are charging that the federal budget unveiled
     Thursday by Canada’s Liberal government fails to deliver on Prime
     Minister Justin Trudeau’s three-year-old promise to bring about a
     “just transition” from fossil fuels and instead caters to polluters.


     “This federal budget is stuck in the mindset of more highways and
     fossil fuel subsidies.”


⚓ Common Dreams ☛ NY_Leaders_Commit_to_Nation’s_First_Fully_Zero-Emission
School_Bus_Fleet⠀⇛


     “New York, a clean ride for kids is coming your way!”


     So declared the Electric School Bus Initiative at the World Resources
     Institute (WRI) on Friday after Democratic New York Gov. Kathy Hochul
     announced an agreement on a budget that includes a historic plan to
     fully electrify the state’s fleet of school buses.


§ Energy⠀➾


⚓ TruthOut ☛ West_Virginians_Gear_Up_for_“Coal_Baron_Blockade”_at_Joe_Manchin’s
Coal_Plant⠀⇛


⚓ Common Dreams ☛ Opinion_|_Gas_Prices_Are_High…So_Electrify⠀⇛


     When Russia’s invasion of Ukraine drove up gasoline prices, members
     of Congress from oil and gas producing states called for increased
     fossil fuel production. In his March 31 speech, President Biden also
     seemed to put most of his emphasis on increasing the oil supply. But
     a growing number of voices are saying that we should use this
     occasion to move away from fossil fuels as quickly as possible.


§ Overpopulation⠀➾


⚓ VOA News ☛ Fishy_Business:_Report_Details_Chinese_Fleet’s_Illegal_Operations
in_West_Africa⠀⇛


     China is the world’s biggest fish producer and has the largest
     distant-water fleet (CDWF) — officially 2,701 vessels but likely
     thousands more — many of which engage in high instances of illegal,
     unreported and unregulated fishing, according to an NGO, the
     Environmental Justice Foundation.


     The group’s report this week found that some 90% of Ghana’s
     industrial trawl fleet is actually owned by Chinese corporations
     using local “front” companies to register as Ghanaian and get around
     the law.


§ Finance⠀➾


⚓ Counter Punch ☛ The_Dollar_Devours_the_Euro⠀⇛


     As President Biden and U.S. national-security reports announced,
     China was seen as the major enemy. Despite China’s helpful role in
     enabling corporate America to drive down labor’s wage rates by de-
     industrializing the U.S. economy in favor of Chinese
     industrialization, China’s growth was recognized as posing the
     Ultimate Terror: prosperity through socialism. Socialist
     industrialization always has been perceived to be the great enemy of
     the rentier economy that has taken over most nations in the century
     since World War I ended, and especially since the 1980s. The result
     today is a clash of economic systems – socialist industrialization
     vs. neoliberal finance capitalism.


     That makes the New Cold War against China an implicit opening act of
     what threatens to be a long-drawn-out World War III. The U.S.
     strategy is to pry away China’s most likely economic allies,
     especially Russia, Central Asia, South Asia and East Asia. The
     question was, where to start the carve-up and isolation.


§ AstroTurf/Lobbying/Politics⠀➾


⚓ Common Dreams ☛ Far-Right_Nationalist_Le_Pen_Gaining_on_Macron_Ahead_of
French_Election⠀⇛


     Far-right French presidential candidate Marine Le Pen is closing in
     on President Emmanuel Macron’s lead, according to poll numbers
     released ahead of Sunday’s first-round presidential election.


     Polling data collected by French journalist Alexandre Léchenet this
     week showed that as of Thursday, centrist Macron is leading the
     presidential field with more than 25% of respondents saying they
     would support him on Sunday, while Le Pen’s support hovers in “the
     low 20s.”


⚓ Techdirt ☛ GOP_Social_Media_Experiments_Fail_(In_Part)_Because_They_Break_The
Troll/Amplification_Cycle⠀⇛


     We’ve noted for a while that Trump’s alternative social media
     platform, Truth Social, isn’t doing particularly well. Being a Trump
     product, the platform (surprise!) began with a lot of money slushing
     around that wasn’t spent in any coherent way. It’s also just
     generally glitchy and terrible. And it’s not helped much by the fact
     that after all of his whining about social media “censorship” (read:
     minimal accountability for saying stupid and sometimes dangerous
     things), Trump doesn’t even use the product.


⚓ Democracy Now ☛ Trita_Parsi:_War_Could_Be_on_Horizon_If_Iran_Nuclear_Deal_Is
Not_Restored_Soon⠀⇛


     Will the U.S. and Iran revive the 2015 nuclear deal abandoned by the
     Trump administration? President Biden is facing heat from lawmakers
     in both parties who oppose the deal, which would relax U.S. sanctions
     on Iran in exchange for limits on its nuclear program. At the crux of
     the debate is the Iranian request for Biden to lift the designation
     of Iran’s Revolutionary Guard Corps as a terrorist organization,
     which would have a high political cost for the administration. With
     threats between the two nations mounting, a deal becomes more urgent
     to avoid the situation spiraling into military confrontation, says
     Trita Parsi, author of multiple books on U.S.-Iran relations.


⚓ Techdirt ☛ How_Would_Senator_James_Lankford_React_If_A_Democratic_Senator
Demanded_Fox_News_Explain_Its_Editorial_Policies?⠀⇛


     A month ago, we wrote about a bizarre, nonsensical, Twitter rant from
     Senator James Lankford of Oklahoma that followed a bizarre,
     nonsensical appearance at the CPAC conference in which he lashed out
     at “big tech” for supposedly “censoring conservatives.” This fact-
     free grievance has been an item of blind faith among the Trumpist
     set, that big tech is somehow out to get them. The smart ones know
     it’s not true, but it plays well to the base, so they play it up. The
     dumb ones truly believe it, even as the evidence shows that Twitter
     and Facebook both have actually bent over backwards to give
     Republican politicians more leeway to violate the rules and not face
     any enforcement actions.


⚓ Counter Punch ☛ The_Quiet_Revolution_in_the_San_Francisco_Public_Library⠀⇛


     Libraries reflect and validate the cross cultural character
     and personality of the towns and cities where they’re located. This
     is as true for San Francisco, where I live, as it is for other places
     which I have known, whether Oaxaca, Mexico, London, England, Saint-
     Sulpice sur Tarn in France, and Huntington, Long Island where I was
     born and raised. In my hometown, books with titles such as Labor’s
     Untold Story (1955) by Herbert Morris and Richard O. Boyer, were
     removed from the shelves in the days of the Red Scare. My father, who
     was a civil rights and civil liberties lawyer, saved Labor’s Untold
     Story from a bonfire that would have made it unavailable in
     Huntington.


     Lefty books matter, and so do books by Latin, Asian, African, Black
     and LQBTQ writers. Theirs is one of literature’s untold stories over
     the past half-century. Libraries have changed because readers have
     signed petitions, marched, demonstrated and demanded books that
     weren’t on the shelves. Too often libraries purge old books to make
     room for new books especially in the US where the new is king, queen,
     jack and ace. Store them, don’t get rid of them.


⚓ Counter Punch ☛ A_Milestone:_Venezuela’s_Communard_Union_Stages_Its
Foundational_Congress⠀⇛


     Why build a league or union of communes? That is, what is the role of
     a commune in Venezuela and why try to unify them? Communes became
     important during Hugo Chávez’s last years when he developed a
     strategy of advancing toward socialism by using these grassroots
     spaces of self-managed production and substantive democracy as its
     basic cells. Since the president’s death, the communal project has
     faced numerous challenges, including the post-Chávez government’s
     rightward turn under the pressure of sanctions and hybrid war.
     Despite these challenges, commune-building goes forward in an almost
     miraculous way in the country, driven by grassroots bases whose
     commitment can be explained by a combination of loyalty to the former
     president, the pressing necessity to produce food, and their
     political consciousness. Sown across the country and without much
     support, Venezuela’s functioning communes are embattled outposts,
     weakened by their isolation. However, there have been attempts to
     build unity and coordinate these efforts. The most important of these
     is the Communard Union (Unión Comunera).


     The urgent need to overcome the isolation of communes and accumulate
     forces in the popular movement is both the raison d’être for the
     Communard Union and explains the huge draw of its first Congress.
     Hosted in Lara state by El Maizal Commune, the Foundational Congress
     brought together – so the organizers said – almost 500 delegates from
     48 communes. Since March is always dry and hot in this low-lying
     region, the organizers had a constant, more or less Sisyphean battle
     against heat and dust. To this effect, they initially seated
     delegates under the roof of El Maizal Commune’s machinery shed,
     before the event migrated to a huge thatched caney that had been
     expanded to provide shade for the participants. Despite the torrid
     atmosphere, the congress was kicked off with a great deal of
     “mística,” a passionate interchange of slogans, and the intoning of
     revolutionary songs. Among the slogans, the most common was “Commune
     or Nothing!” This slogan was also employed in an expanded form:
     “Commune or Nothing, that is the mission, as Chávez said in Golpe de
     Timón!”


⚓ Counter Punch ☛ ‘We_Will_Prevail’:_A_Conversation_With_Cuba’s_President
Miguel_Díaz-Canel⠀⇛


     In March, I spent a few hours talking to Díaz-Canel, who—born in
     1960—has lived his entire life as Cuba struggled against the
     suffocating policies from Washington to shape its socialist path.
     Raised by a teacher and a factory worker, Díaz-Canel saw firsthand
     the Cuban Revolution’s comprehensive program of social justice in
     which millions of members of the working class, peasants, Black
     people, and women began to access for the first time on equal terms
     the right to work, study and live with dignity. Díaz-Canel’s
     generation grew up in a period under Fidel Castro’s leadership in
     which, despite the existence of a U.S. blockade, most Cubans saw
     their standards of living and quality of life rise significantly due
     to national development plans, favorable trade relations with the
     Soviet Union and a growing network of support in the nonaligned
     world. Díaz-Canel studied electrical engineering at the Central
     University of Las Villas, but early on in his career teaching
     engineering there, he devoted much of his time to local activism with
     the Young Communist League. That led him to an internationalist
     mission in Nicaragua where, along with thousands of Cuban doctors and
     teachers, he served among the poorest, often in remote corners of
     this Central American country that was then trapped under a U.S.-
     funded war of counterinsurgency.


     Díaz-Canel returned from Nicaragua in 1989 as the USSR neared its
     final days and as the U.S. government seized the opportunity to
     tighten restrictions on Cuba. In 1991, Cuba entered a Special
     Period as trade fell by 80 percent. Cubans were eating less (caloric
     intake decreased by 27 percent from 1990 to 1996), long queues for
     food became common, electricity became a rare occurrence, and
     millions took to riding bicycles as the island faced a severe oil
     shortage under an intensified blockade. Díaz-Canel was one of those
     on a bicycle. Cuba’s resilience during the Special Period shaped his
     view of the world.


⚓ New York Times ☛ Legal_Effort_Expands_to_Disqualify_Republicans_as
‘Insurrectionists’⠀⇛


     In all three suits, the plaintiffs claim that the politicians are
     disqualified from seeking office because their support for rioters
     who attacked the Capitol made them “insurrectionists” under the
     Constitution and therefore barred them under the little-known third
     section of the 14th Amendment, adopted during Reconstruction to
     punish members of the Confederacy.


     That section declares that “no person shall” hold “any office, civil
     or military, under the United States, or under any state, who, having
     previously taken an oath” to “support the Constitution,” had then
     “engaged in insurrection or rebellion against the same, or given aid
     or comfort to the enemies thereof.”


§ Misinformation/Disinformation⠀➾


⚓ Orac ☛ Antivax_rhetoric_from_Dr._Lee_Hieb_in_2015:_The_Song_Remains_the
Same⠀⇛


     After my last post about an COVID-19 contrarian surgeon echoing old
     antivax and other science denial tropes about the “scientific
     priesthood,” which was even longer than my usual posts, I thought I’d
     slow things down and try something that I’ve been meaning to try for
     a while. I’ve repeated the refrain that there is nothing new under
     the sun in antivaccine rhetoric, pseudoscience, and conspiracy
     theories. Antivax rhetoric about COVID-19 just seems new to most
     people because they never paid much attention to it before and are
     discovering it for the first time, much as I did in the late 1990s.
     (I will concede, however, that since the pandemic the antivax
     rhetoric has assaulted us in a more concentrated form than I’ve ever
     seen.)


⚓ Creative Commons ☛ Global_Report_on_the_State_of_Journalism_Released⠀⇛


     A new global report on the state of journalism has been published by
     Creative Commons (CC) which identifies the growing challenges of
     combatting disinformation and the disconnect between the public and
     the media.


⚓ The Atlantic ☛ Anne_Applebaum:_Social_Media_Made_Spreading_Disinformation
Easy⠀⇛


     Applebaum: In a way, this is the dark side of globalization, namely
     that we all now live in the same information market. Whereas in the
     past the Russians or the Soviet Union would have had to try and get
     something going in the Indian market and then the Italian market and
     then somehow seed that into the American market, it’s now essentially
     one market. There’s an ease with which they can, first of all, study
     American politics and understand it in a way that wasn’t possible
     before, because they can use the same microtargeting and research
     tools that marketers use. They can tailor messages to different
     groups in specific ways, again, in the same way that marketers use.
     The people who are selling soap powder or washing machines—they also
     have ways of targeting particular audiences, changing the message
     whether you’re in Illinois or Florida or Wyoming, or whether you’re
     rich or poor. And the Russians took those tools and they used them to
     target Black Lives Matter activists in one part of the country and
     immigration activists in another part. Of course, it’s important to
     understand that what they did was no different from what American
     political campaigns do. The tools were available. And where those
     kinds of tools, in the past, wouldn’t have been available to
     outsiders or foreigners, now they are because everything’s available.
     They can reach into our markets and send whatever messages they want.


⚓ RSF ☛ Facebook_must_explain_how_Feed_bug_made_disinformation_more_visible⠀⇛


     According to the report obtained by The Verge, the technical problem
     dates back from 2019 and began causing a noticeable surge in
     disinformation in October 2021 and was not fixed until last month.
     Meta spokesperson Joe Osborne claimed in a tweet that the bug had no
     “meaningful long-term impact” but provided no evidence to support
     this claim.


§ Censorship/Free Speech⠀➾


⚓ Techdirt ☛ Checking_In_On_Twitter’s_Attempt_To_Move_To_Protocols_Instead_Of
Platforms⠀⇛


     With Elon Musk now Twitter’s largest shareholder, and joining the
     company’s board, there have been some (perhaps reasonable) concerns
     about the influence he would have on the platform — mainly based on
     his childlike understanding of free speech, in which speech that he
     likes should obviously be allowed, and speech that he dislikes should
     obviously be punished. That’s not to say he won’t have some good
     ideas for the platform. Before his infamous poll about free speech on
     Twitter, he had done another poll asking whether or not Twitter’s
     algorithm should be open sourced.


⚓ Common Dreams ☛ 1,100+_Banned_Books_Across_26_States:_Report_Shows_‘Shocking’
Censorship⠀⇛


     A report published Thursday by the free expression group PEN America
     details an “alarming” and unprecedented surge in book banning across
     the United States, with 86 school districts in 26 states prohibiting
     more than 1,100 titles in classrooms and libraries over just the past
     eight months.


     “Book challenges in American schools are nothing new, but this type
     of data has never been tallied and quite frankly the results are
     shocking.”


⚓ Techdirt ☛ State_Legislators_Are_Demanding_Websites_Moderate_Less_AND
Moderate_More;_Federal_Law_Prohibits_Both⠀⇛


     Local politicians across the political spectrum are trying to force
     websites to moderate their content in a manner the politicians want.
     Some (mainly Democrats) are trying to push for companies to remove
     more content. Some (mainly Republicans) are pushing companies to stop
     removing certain kinds of content. In both cases, trying to force
     specific editorial stances — either hands on or hands off — raises
     serious Constitutional issues. And this is partly why Congress,
     wisely, decided in 1996 with Section 230 of the Communications
     Decency that no state could pass a law that interfered in the
     editorial decision making process of websites. Because without that,
     websites would have to deal with a confusing and contradictory
     patchwork of laws — some of which demanding certain types of content
     not be hosted, with others demanding certain types of content must be
     hosted.


⚓ Foreign Policy ☛ West_Seeks_to_Pierce_Russia’s_Digital_Iron_Curtain⠀⇛


     Russia’s last remaining independent media outlets in the country were
     forced into closure or exile and much of the foreign press corps
     decamped abroad as a new law signed last month effectively
     criminalized reporting on the conflict, banning the use of the words
     “war” or “invasion.”


     As a digital iron curtain descends on Russia, Western governments and
     free press advocates are scrambling for ways to punch through it and
     reach average Russians with accurate reporting on the war—in methods
     that vary from the creative to the high tech to the antiquated.


     Major Western media outlets are publishing their stories on Telegram,
     a popular messaging app in Russia that hasn’t been banned. The free
     media advocacy organization Reporters Without Borders set up a system
     allowing Russians to access independent news if they type Russia’s
     constantly changing national lottery numbers into Twitter’s search
     bar, a move that redirects them to mirrored news sites blocked by the
     Russian government.


     There’s even a push among some U.S. broadcasting officials to revive
     Cold War-era radio infrastructure to beam U.S.-funded media outlets,
     such as Voice of America and Radio Free Europe/Radio Liberty, into
     Russia for any Russians with shortwave radios.


§ Freedom of Information/Freedom of the Press⠀➾


⚓ VOA News ☛ Jailed_Belarusian_Journalist_Charged_With_Treason_5_Months_Before
Her_Release⠀⇛


⚓ France24 ☛ Turkish_court_suspends_Khashoggi_trial,_confirms_transfer_to_Saudi
Arabia⠀⇛


     The Istanbul court’s decision comes despite warnings from human
     rights groups that turning the case over to the kingdom would lead to
     a cover up of the killing, which has cast suspicion on the crown
     prince.


     It also comes as Turkey, which is in the throes of a deep economic
     downturn, has been trying to repair its troubled relationship with
     Saudi Arabia and an array of other countries in its region. Some
     media reports have claimed that Riyadh has made improved relations
     conditional on Turkey dropping the case, which had inflamed tensions
     between two countries.


⚓ [Old] RSF ☛ Turkey:_RSF_shocked_by_Khashoggi_murder_proceedings’s_transfer_to
Saudi_Arabia⠀⇛


     Reporters Without Borders (RSF) is deeply shocked by Istanbul High
     Criminal Court’s decision to send Jamal Khashoggi murder case to
     Saudi Arabia. This transfer dashes the remaining hopes of criminal
     justice for the 2018 assassination. RSF will keep on challenging by
     all means this unacceptable impunity.


⚓ [Old] RSF ☛ Greece_facing_a_systemic_press_freedom_crisis,_say_the_Media
Freedom_Rapid_Response_and_RSF⠀⇛


     Today, the Media Freedom Rapid Response (MFRR) publishes the report
     “Controlling the Message: Challenges for independent reporting in
     Greece”, which details the findings and recommendations of its online
     fact-finding mission to Greece. The mission, involving interviews
     with more than thirty local stakeholders, was implemented by the MFRR
     together with Reporters Without Borders (RSF) in December 2021. The
     partner organisations conclude that challenges to the independence of
     the media and the safety of journalists are systemic in the country.
     While the problems are not unique, their intensity is highly
     problematic and sets it apart from most other EU Member States.


     The result of this crisis is that news that is inconvenient or
     unflattering for the government, which includes reporting on serious
     human rights violations, does not get reported in many outlets. This
     creates a significant obstacle for the public’s access to information
     and, subsequently, their informed participation in the democratic
     process.


§ Civil Rights/Policing⠀➾


⚓ TruthOut ☛ A_Third_of_DHS_Law_Enforcement_Staff_Have_Experienced_Sexual
Harassment_at_Work⠀⇛


⚓ TruthOut ☛ Biden’s_Proposed_Budget_Leaves_Out_the_Hyde_Amendment_—_for_Now⠀⇛


⚓ TruthOut ☛ Starbucks_Workers_Have_Filed_to_Unionize_200_Stores⠀⇛


⚓ Democracy Now ☛ Law_Professor_Michele_Goodwin_Condemns_Wave_of_“Unprecedented
&_Unfathomable”_Anti-Abortion_Laws⠀⇛


     Anti-abortion legislation is sweeping the U.S., including in Texas,
     Oklahoma and Missouri. We speak with Michele Goodwin, author of
     “Policing the Womb: Invisible Women and the Criminalization of
     Motherhood,” about the links between current conflicts between state
     and federal law and their historic precedents, such as Brown v. Board
     of Education and the Fugitive Slave Acts. “Bounty hunter” provisions
     in Texas’s new abortion restrictions are “plucked right out of
     antebellum slavery,” says Goodwin. “These are horrific times for
     reproductive liberty.”


⚓ Pro Publica ☛ Changes_in_Police_Policy,_Payouts_to_Latino_Victims_of_Traffic
Stops_and_Arrests_Following_Investigations⠀⇛


     The state of Pennsylvania has agreed to pay $865,000 to settle a
     federal lawsuit alleging that its state troopers routinely and
     unconstitutionally pulled over Latino drivers, demanded their
     “papers” and held them and their passengers for pickup by federal
     immigration authorities — a practice that escalated markedly after
     President Donald Trump took office in 2017.


     The complaint, filed by the Pennsylvania ACLU and drawing in part on
     a 2018 series of ProPublica articles published in collaboration with
     The Philadelphia Inquirer, detailed cases of state troopers stopping
     and then detaining immigrants under the auspices of federal
     immigration laws, which it alleged they had no authority to enforce.
     The immigrants were engaged in ordinary, legal activities, according
     to the complaint: traveling to see family members, driving to or from
     work, buying a soda in a state police barracks, awaiting medical help
     following a traffic accident or, in one case, returning from a job
     interview accompanied by a wife who was nine months pregnant.


⚓ Common Dreams ☛ 4,500_Unionized_Nurses_Vote_to_Authorize_Strike_at_California
Hospitals⠀⇛


     More than 4,500 nurses at Stanford Health Care and Stanford
     Children’s Health in Northern California voted on Friday to authorize
     a strike, capping off dozens of negotiating sessions that have
     stretched on for 13 weeks, including this past week when the
     healthcare workers completed their jobs without any contract in
     place.


     The nurses’ union, the Committee for Recognition of Nursing
     Achievement (CRONA) said that out of its 5,000 members, 93% voted in
     favor of going on strike to combat management’s insistence that
     nurses work with inadequate resources and staff support, all while
     being forced to pick up extra shifts and having their benefits cut.


⚓ Techdirt ☛ Bar_Security_Camera_Exposes_Off-Duty_Officers’_Lies_About_Their
Unprovoked_Assault_Of_Another_Bar_Patron⠀⇛


     Cops lie.


⚓ Papers Please ☛ Amtrak_gave_train_reservations_to_the_TSA_for_a_profiling
test⠀⇛


     [“Secure Flight” process flow used by the TSA for airline passengers
     and being tested on Amtrak passengers. The red box at right center is
     the “black box” for algorithmic profiling, blacklist/blocklist
     enforcement, and fly/no-fly decision making.]Amtrak has reportedly
     given the Transportation Security Administration several months of 
     archives of Amtrak passenger reservations and frequent rider
     profiles. At Amtrak’s request, the TSA has used these records to test
     the TSA’s ability to extend to Amtrak passengers the ID-based
     profiling and blacklisting algorithms the TSA already applies to air
     travelers.


     If you aren’t allowed to travel by air, the right to travel by train
     is critical. And while all common carriers have an obligation to
     transport all would-be passengers, Amtrak as a government agency
     should be most strictly held to that obligation.


     The plans to run a batch of historical Amtrak reservations through
     the TSA’s “threat assessment” black box were disclosed in a Privacy
     Impact Assessment (PIA) quietly posted on the Department of Homeland
     Security website last December, and first noted in a news report by
     Mark Albert of Hearst Television earlier this week.


⚓ The Nation ☛ ATROCITIES⠀⇛


⚓ The Nation ☛ Will_Biden_Keep_His_Word_and_Pardon_Federal_Cannabis
Offenders?⠀⇛


     In the fall of 2020, Daniel Muessig was urging everyone he knew to
     get out and vote. He lived in the swingiest of swing states and,
     while he’d supported Bernie in the primaries, he was now convinced of
     the importance of carrying Pennsylvania for Joe Biden.


⚓ Counter Punch ☛ The_Metaphysics_of_Memory⠀⇛


     The idea of the human mind as operating akin to a machine, as a
     recording device with a given amount of storage space, is a belief
     which only comes into its own in the 19th century, at the time of the
     industrial revolution when those ‘dark satanic mills’ were springing
     up in and around the great cities; such a doctrine takes shape in a
     society where technological production has been ratcheted up to its
     zenith, its product effectively measured and quantified according to
     the relentless rhythms of the conveyer belt, and where human labour
     itself has been inexorably fused with the pistons and levers of the
     factory monolith.


     Perhaps the first human ‘thinking machine’ was Conan Doyle’s
     fictional detective Sherlock Holmes who appeared in the 1880s, a
     product of the Victorian epoch. Conan Doyle was at pains to emphasise
     not only the brilliance of his seminal detective but also the way in
     which Holmes’ mind had a given quantitative capacity which could be
     tweaked and refined in much the way one might refine a sophisticated
     piece of machinery in order to yield its optimum capacity.  Doyle has
     his eponymous detective describe how:


⚓ Counter Punch ☛ Abortion_Rights:_Beyond_the_Killing_Confines_of_Liberal_Mis-
leadership⠀⇛


     United States “democracy” is plagued by the presence of an elitist
     liberal mis-leadership class that fears the “mob” and “rabble” –
     everyday citizens and the working-class majority – more than it
     worries about right-wing (now neofascist) rule. This liberal “elite”
     is militantly opposed to popular movements. It rejects popular
     demands and indeed sees “demand” as a bad word. It maintains a dogged
     faith in existing bourgeois-“democratic” and constitutional rules,
     methods, institutions, and procedures no matter how completely those
     rules, methods, institutions, and procedures have been subverted and
     captured by the right. It is doctrinally committed to lobbying and
     litigation, work by professionals, which they see as the only safe
     and effective way to “get things done.” It works to tamp down rank-
     and-file energies and channel popular anger into the nation’s regular
     candidate-centered major party electoral extravaganzas. The liberal
     mis-leadership class, loaded with Ivy League graduates, will let the
     nation go fascist before it will mobilize masses by the millions to
     fight for human rights, equality, and decency.


     The Right-Wing Campaign to Kill Roe Hits the Jackpot


⚓ TruthOut ☛ GOP_Disrespect_on_Full_Blast_Amid_Ketanji_Brown_Jackson’s_Historic
Confirmation⠀⇛


⚓ Democracy Now ☛ Justice:_Ketanji_Brown_Jackson_Makes_“Herstory”_as_First
Black_Woman_Confirmed_to_Supreme_Court⠀⇛


     The U.S. Senate voted 53-47 on Thursday to confirm Judge Ketanji
     Brown Jackson to the Supreme Court. She will be the first Black woman
     and first former public defender to serve on the country’s top court.
     While Jackson’s confirmation was a “monumental moment in United
     States history,” it was undercut by the “shameful spectacle” of
     Republican senators behaving disrespectfully toward Jackson, says law
     professor Michele Goodwin. The confirmation process remains broken
     more than three decades after Anita Hill faced hostile questioning,
     she adds.


⚓ The Nation ☛ Did_Ranked-Choice_Voting_Make_It_Easier_for_2_Republicans_to
Back_Ketanji_Brown_Jackson?⠀⇛


     The days of broad bipartisan support for the confirmation of US
     Supreme Court nominees are, by every indication, behind us. But it
     still matters that Judge Ketanji Brown Jackson was confirmed to serve
     on the court Thursday with a 53-47 Senate majority that included both
     Democrats and Republicans. And it is worth noting that two of the
     three Republican votes came from senators who represent states where
     election systems have been reformed to allow for ranked-choice
     voting.


⚓ FAIR ☛ Racism_‘Hovers’_Over_Events_Like_Jackson_Hearings_Because_It_Goes
Unnamed⠀⇛


     The confirmation of Ketanji Brown Jackson to the Supreme Court
     occasions a look back at some of the media coverage of her hearings.
     While media reported GOP senators’ grandstanding harassment and
     aggressive repetition of baseless accusations, their need to always
     be signaling “balance” led to some mealy-mouthed avoidance tactics,
     like C-SPAN‘s tweet (3/23/22) describing a “heated exchange between
     Supreme Court Nominee Judge Ketanji Brown Jackson and Sen.
     @LindseyGrahamSC on child pornography sentencing”—when anyone
     watching would tell you only one side was heated.


⚓ FAIR ☛ Marjorie_Cohn_on_Prosecuting_Trump,_Mike_Liszewski_on_Marijuana
Justice⠀⇛


⚓ Teen Vogue ☛ What_Is_Retaliation_in_the_Workplace?_Here_Are_Your_Rights_and
What_to_Know⠀⇛


     Recognizing what is officially retaliation and what is generally a
     toxic workplace is tricky, especially since they can overlap. And not
     knowing the difference feels like another obvious advantage for
     exploitative workplaces, because if we don’t know how to recognize
     retaliation, we’ll assume this is just what work is.


     But there are real differences to unpack. “The workplace in modern
     America is a terribly imbalanced place when it comes to the power
     dynamic,” says Benjamin Dictor, a labor lawyer. (Disclosure: Dictor
     is counsel for the News Guild of New York, which represents workers
     at several publications owned by Teen Vogue publisher Condé Nast.)
     “Unfortunately, there’s no law that says that your boss is not
     allowed to be an asshole.” That means not everything they do is going
     to be an act of unlawful retaliation.


⚓ Hungary ☛ In_his_own_words:_Orbán_explains_why_he_turned_to_Putin⠀⇛


     At a rare press conference, where he answered questions of both
     Hungarian and foreign journalists, Orbán talked about the price cuts
     on utility costs, told the opposition to pull themselves together,
     and described at length why he changed his policy towards Russia – a
     Telex video summary.


⚓ Hungary ☛ Péter_Márki-Zay:_I_do_not_wish_to_maintain_the_impression_that
Hungary_is_a_parliamentary_democracy⠀⇛


⚓ FAIR ☛ Right-Wing_US_Media_Applaud_Hungary’s_Orban_as_Example_to_Follow⠀⇛


     Viktor Orbán has been re-elected the Hungarian prime minister, a win
     for the global far-right movement. Now the European Union’s longest-
     lasting leader, he has served as prime minister since 2010.


§ Monopolies⠀➾


⚓ Techdirt ☛ Streaming_Providers_Tell_FCC_That_Taxing_Streaming_TV_Would_Be
Dumb⠀⇛


     For years, we’ve noted how telecom and media giants have been trying
     to force “big tech” to give them huge sums of money for no reason.
     The shaky logic usually involves claiming that “big tech” gets a
     “free ride” on telecom networks, something that’s never actually been
     true. This narrative has been bouncing around telecom policy circles
     for years, and recently bubbled up once again thanks to telecom
     industry BFF and FCC Commissioner Brendan Carr.


§ Copyrights⠀➾


⚓ Torrent Freak ☛ DMCA_Notices_Took_Down_19,276_GitHub_Projects_Last_year⠀⇛


     GitHub received 1,828 valid DMCA takedown notices last year, which
     resulted in the removal of 19,276 projects. Less than one percent of
     these projects were reinstated following retractions or counter-
     notices. The developer platform uses automated tools to scan for
     abuse, but this technology is not used for copyright infringements.


⚓ Torrent Freak ☛ MPA_Asks_EU_For_IPTV,_Torrents_&_Piracy_Support_Services
Crackdown⠀⇛


     Major Hollywood studios and Netflix have asked the European
     Commission for assistance in their global anti-piracy fight. While
     many pirate IPTV, torrent and streaming sites are named directly, the
     MPA believes that greater pressure needs to be applied to other
     players in the ecosystem that help pirate services stay online and
     generate revenue.


╘══════════════════════════════════════════════════════════════════════════════╛
                       ¶ Lines in total: 7496
    ➮ Generation completed at 02:41, i.e. 50 seconds to (re)generate ⟲