𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, February 02, 2022
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Generated Thu 3 Feb 02:42:14 GMT 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/2022/02/02/
╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
Previous bulletins in IPFS (past 21 days, in chronological order):
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QmRXpMsysY15jnTdXabNj8RQWyYQoA287zCaWvJJjNWzB2
QmaSCmshgLNtetvtehrJTkVzA4UKVtdrEf2DcHz8b5gBoV
QmZWJhSMSsSbuTS3JfxxEo3tfs2QfTCENeVipKSaQVU5b2
Qmehhm7o1VbxWg8uyeTcYkk6Hr1Cp4Ho21X2wCnesY9asd
Qmf3TSbMJS9koYs7ieZ1w3WBpaDp6x7rx5xnhC6B134fFL
QmbAVHY5Ges1nF9HNsiNn6FsQW8UdTFHURKDG1QgSKpKw7
QmZnZkCBXLzZg5rkewh3peFLzQ5xAZRm6HpjAvmtf39ELR
QmZeHUaFKnCwMohgf9hT7KAvQEFvHbBZ8MUZTtceSkoLZc
QmQLbqvdSXzQ59gWzwwt9RARegF8vZB68qihXTbNcDNoxy
QmXRhRDa28yw47e5ym8hgWTNSCTtmH5t22GCpvFvaGYDwN
QmNrH8cLM4mYaiBXzhdkhAQm8XM54JzRQa3Z1Ng4a41kcV
QmZjLA2jtgeEhSJihNxjJW3q7KaEU6iyCKve9pmkci3m61
QmTWgjCkngZ2r4jN8fZGmd7bpEdJL3pBfU6vKWFNxPmkYf
QmUa6NW563bcVpbJi9K42Aap4iTTXYmJcu5bTsjAcRc9yG
QmPENr81muU2jHsHXxDP2oXCR4itHu2Pb54BpV4z2a6v8g
QmT1WmWT8oyJF7h6FDnkDWXE6tEV7sUdo6MyboEn1kLiFx
Qmd7o1W8PgtXmeAFmAGFoVreMpLA1AVtvVjUMvVr7zc1YQ
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QmS1wrYoYvTPNPTvZYppVeYPXTR8rHjtMkwCEYGCEaEWUU
╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕
⦿ AMD Apparently Sends Crates of CPUs to Phoronix (But It’s Definitely Not a Bribe!) | Techrights
⦿ IBM Has Not Been Good to Red Hat (the Company Should Never Have Been Sold) | Techrights
⦿ IRC Proceedings: Tuesday, February 01, 2022 | Techrights
⦿ Linux.com Used to Clock Millions of Hits Every Week, But Linux Foundation Can Barely Keep Thousands | Techrights
⦿ Darkening the Counterpart’s Reputation: Microsoft-Friendly (Sometimes Microsoft-Funded) Media Describing Every Security Issue - Even Windows Issues - as ’Linux’ | Techrights
⦿ One Year Since We Joined Geminispace and the Effort Has Paid Off | Techrights
䷼ Bulletin articles (as HTML) to comment on (requires login):
http://techrights.org/2022/02/02/epyc-trove/#comments
http://techrights.org/2022/02/02/ibm-ruins-red-hat/#comments
http://techrights.org/2022/02/02/irc-log-010222/#comments
http://techrights.org/2022/02/02/lets-talk-linux-com/#comments
http://techrights.org/2022/02/02/security-perception-manipulation/#comments
http://techrights.org/2022/02/02/year-of-geminispace/#comments
䷞ Followed by Daily Links (assorted news picks curated and categorised):
http://techrights.org/2022/02/02/easyos-3-3/#comments
http://techrights.org/2022/02/02/gstreamer-1-18-6/#comments
http://techrights.org/2022/02/02/weston-10-0-0/#comments
䷩ 𝚕𝚒𝚗𝚎 64
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/02/epyc-trove/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/02/epyc-trove/
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Gemini_version_available_♊︎
✐ AMD_Apparently_Sends_Crates_of_CPUs_to_Phoronix_(But_It’s_Definitely_Not_a
Bribe!)⠀✐
Posted in Hardware at 7:34 pm by Dr. Roy Schestowitz
Posted earlier today:
🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇amd-crate⦈_
Either those ads pay Phoronix a lot of money, or electricy costs have gone down
considerably, or…
🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇EPYC_shop⦈_
🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇AMD_EPYC_Milan_X_EPYC_7773X_64_Core_Server_CPU⦈_
Summary: Over a decade ago AMD earned some notoriety for the way it was
schmoozing bloggers, so we don’t rule out anything…
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⣿⠀⢀⠠⢊⡗⡊⡼⣁⠀⠈⢊⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⡛⠛⠋⠀⠀⠀⣰⣿⣿⠏⠀⣤⣿⣿⣿⣿⣿
⣿⣔⡫⠔⣸⠚⣡⠞⠁⠀⠀⠀⠪⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣿⣿⠏⠀⣼⣻⣿⣿⣿⣿⣿
⣿⠛⣵⢎⣵⠞⢀⠀⠀⠀⠚⠉⠀⠁⣻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣀⣴⣿⣶⣌⠛⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣼⣿⣿⡿⣂⣼⣿⣿⣿⣿⣿⣿⣿
⣿⡓⠄⠛⢁⣾⣿⡅⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠛⣿⣿⣿⣿⣿⣿⣿⣶⣌⡙⠿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣾⡟⠈⠙⢥⣿⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣵⣿⣿⣿⠃⠀⠀⠀⢀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡙⠻⡿⠿⠃⠀⠀⠀⢀⣾⠏⢀⠀⢀⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣬⣤⣤⣾⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢠⣾⣟⣠⣿⡗⡾⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠉⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⢟⣯⡻⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠀⠀⠀⠀⢠⣿⣿⣳⣿⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣾⣿⡿⢿⣿⣿⣿⣿⣻⣿⣿⡇⠔⠉⠂⠙⢿⣝⢿⡻⣿⢿⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡻⠃⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣤⣴⣸⣿⣿⠿⣿⣽⡿⢛⣮⣶⣦⣤⣵⣄⡈⢿⣯⡻⣷⣝⡞⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡝⠁⠀⠀⠀⠀⣰⣿⡿⢁⣾⣿⠿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⢿⠟⢑⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣮⡛⢿⣿⣝⢝⢿⡿⠏⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣴⣿⣿⣷⣾⣿⣿⡄⢨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣷⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡔⣂⢰⠢⢴⠀⡆⢰⢀⡍⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠁⠈⠈⠀⠈⠀⠉⠁⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⠸⠘⡟⠛⠛⣿⠉⡏⠋⠉⡍⣏⠩⠛⠟⡻⠛⢻⢻⡏⢉⠛⡛⢛⠛⠛⠛⢻⠛⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣿
⣿⣷⣶⣶⣷⣶⣰⣿⣶⣶⣿⣶⣶⣿⣶⣶⣷⣷⣷⣾⣾⣷⣿⣶⣶⣶⣶⣶⣾⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣠⣀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⠛⢟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⡿⠿⣶⠶⠶⠶⡶⠶⣖⡶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣿
⣿⣷⣷⣷⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣙⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⡿⣿⢿⢿⡿⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⣶⣦⣷⣷⣿⣾⣶⣷⣾⣿
⣿⡏⠙⠋⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣀⣁⣉⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
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䷩ 𝚕𝚒𝚗𝚎 188
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/02/ibm-ruins-red-hat/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/02/ibm-ruins-red-hat/
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Gemini_version_available_♊︎
✐ IBM_Has_Not_Been_Good_to_Red_Hat_(the_Company_Should_Never_Have_Been_Sold)⠀✐
Posted in Deception, GNU/Linux, IBM, Red_Hat at 12:09 pm by Dr. Roy Schestowitz
Video_download_link | md5sum 60c2a78d757c755fa338bb6e347ca54c
IBM does not get Red Hat
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/ibm-ruins-redhat.webm
Summary: More than three years after IBM said it would be buying Red Hat the
latter company is a shadow of its former self and many_IBM_layoffs_carry_on
while Red Hat staff — including many executives — leave in droves
A COUPLE of years ago we wrote about what_IBM_had_done_to_Red_Hat_less_than_2
years_after_the_takeover. We occasionally touched the subject again after that.
It has not improved; it seems to have only worsened. The oversensitive but
racist IBM does not tolerate any criticism!
Today, as in so far in 2022, Red Hat’s Web site is occasionally boosting
Microsoft and other “clown” partners, which make IBM seem a bit like SUSE —
mostly a reseller of proprietary software and seller of IBM’s legacy (very
expensive) systems. We keep posting links about that trend in our Daily Links,
though lately we’ve not composed any actual articles about the subject. In a
nutshell, IBM does to Red Hat as a company what it did to Fedora as a community
and to CentOS as a project. IBM is run (ruined) by truly incompetent managers.
They only care about short-term “compensation” of theirs. They don’t know the
people. They don’t care about the product (they don’t even use it).
“These people actually decide to leave their jobs.”This is very sad to me. It
really is. Those who have been reading this site since 2006 very well know that
we were supportive of Red Hat, which many perceived as the archenemy of SUSE/
Novell back when we campaigned to “Boycott Novell” (it was this site’s name!)
and when Jim Whitehurst became CEO we wrote an open letter to him. He later
offered to do an interview with us — a short interview that we published over
10 years ago.
After the takeover Whitehurst became a president at IBM (a “dream job” maybe;
just maybe… if you worked in the IBM of the 1970s!), but that didn’t last long.
This former CEO left IBM and several other CxO-level folks from Red Hat did the
same, including presidents and vice presidents. It’s a lot like IBM of Ginni
Rometty, except now it happens at Red Hat. It’s alarming because it’s difficult
to run a business with a ‘leadership turnover’ quite so profound and quite so
rapid. Those shake-ups aren’t strategic. These people actually decide to leave
their jobs. Is Chris Wright (CTO) next to quit? CEOs rarely leave or resign
unless there’s a major scandal, as that tends to cause a major PR/morale crisis
and the Board members (for shareholders) don’t like that, so they prefer to
spin the whole thing as a peaceful transition of power from one person to
another person. Maybe that’s even in the contract (CEOs never resign in anger
or ‘ragequit’). Look what happened in Microsoft’s GitHub a couple of months
ago. It’s like a_face-saving_cover-up.
“That’s why many people leave (those who can anyway).”Shown above (as video
posted) is the latest high-profile departure (the financial department). Yet
another top-level executive, the CFO of the company (and a lot more, also a
token ‘activist’), just_leaves. It was announced about a day ago (ignore the
face-saving headline and read between the lines), reaffirming what we’ve long
said about IBM ruining what became of Red Hat after more than 20 years. Sooner
or later IBM too will die (while faking its finances, e.g. by offloading losing
units), so the writings on the wall are generally there. That’s why many people
leave (those who can anyway). It is willful.
“IBM has basically discarded red hat, I’m not sure what the point of the
acquisition even was given how things have been (mis-)handled,” an associate of
ours said today.
Wrong assumptions had been made about Red Hat and then they paid too much
mostly for a brand, not recognising how GPL (or copyleft) actually works. It’s
anti-monopoly. A source once told us that attacks on Linus Torvalds and his
undeserved_'suspension' (very shortly after the announcement of a mega-
takeover) were meant to lower the price of buying Red Hat. That was a year
before quote-mining a decade-old RMS on the most problematic issues, not
technical_or_legal_issues. That’s mentioned in passing in the video above. █
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IBM and the Hat⦈
IBM and the (tall) Hat
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣩⣾⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣿⣿⣿⣿⣿⣿⣇⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⣨⠟⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠯⠀⣰⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢐⢀⣾⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢼⣯⣶⣥⣽⣿⣿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠄⣺⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣐⠰⠒⣿⣽⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢙⣫⣼⣚⣊⡘⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣂⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠨⣭⣱⣿⡺⣿⠃⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠛⠛⠀⠀⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠁⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣴⣻⣝⣿⡿⢿⡠⢾⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡷⠀⣾⣿⣄⠀⠀⠀⠨⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣥⡐⠒⠻⢿⣿⣿⡿⣶⣮⣿⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣦⡀⠠⣭⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣼⣻⢿⡳⣿⣿⣿⣿⣿⠃⣹⣿⡟⣻⣿⠋⢿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠥⠀⣿⣿⣿⡿⡿⡾⡿⡿⠋⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⠙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣿⣿⣿⢿⣿⡿⠀⡟⣿⠀⢾⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣯⠚⠒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣌⡉⠛⠛⠐⢹⣦⣄⣷⢽⣜⣧⣿⡀⢺⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢻⣿⣇⣿⣿⢻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣝⠘⣿⣿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣴⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣘⣶⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⣿⣿⣿⣇⠀⢠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣄⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣸⠟⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠯⠀⣰⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⢴⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢼⣯⣶⣤⣿⣿⡿⠿⠟⡿⣿⣿⣷⣶⣤⣀⠀⣺⣿⠿⠿⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⢀⡀⢘⣁⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢈⢰⣻⣳⣿⠂⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣔⣔⠷⠚⠾⠂⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠋⠛⠛⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠀⠑⠋⠋⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣴⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣴⣻⣿⣿⣿⡿⣆⣼⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡇⠀⣾⣿⣄⠀⠀⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣥⡲⠛⠷⢿⣿⣿⣿⣻⣄⣾⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣦⡀⠰⣨⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣼⣿⡿⠯⣿⣿⣿⣿⣿⠃⣹⣿⡟⣻⣿⠋⢿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⠥⠀⣿⣿⣿⣿⣿⡯⡟⠿⠋⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⠙⣿⣿⣷⣼⣿⣿⠛⢿⣿⣦⣷⡽⠿⢻⡿⠀⡟⣿⠀⢾⠷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣯⠒⠒⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠛⠓⠑⢩⣦⣄⣷⢽⣜⣧⣿⡀⢺⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢻⣿⣇⣿⣿⣻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣝⠘⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣴⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠸⣿⣿⣯⣽⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⡀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣘⣶⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣾⣿⣿⣿⣿⣿⣇⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣦⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⣸⠟⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠯⠀⣰⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣯⣶⣥⣿⣿⣿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠀⣺⣿⠿⠿⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⢀⢀⢘⡅⡠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⢹⣿⣿⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢀⣻⣛⣿⡂⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⣄⣴⣗⠻⠾⠁⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠒⠓⠀⠀⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠉⠁⠋⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣴⣿⣿⣿⡿⣿⣿⢾⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡧⠀⣾⣿⣄⠀⠀⠀⠈⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣥⡀⠓⠱⢿⣿⣿⡿⣖⣽⣿⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣦⡀⠰⣦⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣼⣿⡿⠷⣿⣿⣿⣿⣿⠃⣹⣿⡿⣻⣿⠋⢿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠤⠀⣿⢿⣿⣿⡿⡿⡿⠿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⠙⣿⣿⣷⣬⣿⣿⠛⢿⣿⣮⣿⣿⡿⢿⡟⠀⡟⣿⠀⢾⠷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣿⣿⣿⣿⣿⣿⣯⠀⠒⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠛⠛⠃⢹⣦⣄⣿⢿⣜⣧⣿⡀⢺⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢻⣿⣇⣿⣿⣻⣿⣷⢿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣝⠘⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣴⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣩⣾⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣶⣾⣿⣿⣿⡇⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣿⣿⣿⣿⣿⣿⣇⠀⢀⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣨⠟⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠯⠀⣸⡃⠸⣿⢿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢐⠠⢼⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢼⣯⣶⣤⣿⣿⣿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠀⣸⣿⠿⠿⠿⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢈⣘⡬⢿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠜⡲⣻⣩⣫⠐⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠱⣗⣕⣿⡽⣛⠅⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠛⠛⠛⠁⠀⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠙⠋⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣔⣻⣿⣿⣻⣿⢟⣹⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡧⠀⣾⣿⣄⠀⠀⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣥⡖⠚⠛⢿⣿⣿⣿⣮⣿⣿⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⡿⠀⣰⣿⣿⣿⣦⡀⠨⣦⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣼⣻⡿⢧⣽⣿⣿⣿⣿⠃⣹⣿⡟⣻⣿⠋⢿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠧⠀⣿⣿⣿⣿⣿⡟⡾⠿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⠙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⣿⣿⣟⢿⡟⠀⡟⣿⠀⢾⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾⣿⣿⣿⣿⣿⣯⠀⠒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣍⡉⠛⠛⠛⢨⣦⣄⣷⢽⣜⣧⣿⡀⢺⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢻⣿⣇⣿⣿⣻⣿⣿⢿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣝⠘⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣴⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⣄⡈⠘⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣩⣾⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣶⣾⣿⣿⣿⡇⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣿⣿⣿⣿⣿⣿⣇⠀⢀⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⣨⠟⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠯⠀⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢐⠠⢬⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣿⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢼⣯⣶⣥⣿⣿⡿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠀⢾⣿⠿⠿⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣘⡬⢿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠜⡲⣻⣩⣓⠃⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣔⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠱⣗⣕⣿⡽⣟⠆⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠛⠛⠛⠁⠀⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠋⠛⠉⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣴⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣴⣻⣽⣿⣿⣿⣕⣿⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡧⠀⣾⣿⣄⠀⠀⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣥⡐⠒⠘⢿⣿⣿⡿⣄⣫⣿⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣦⠀⠨⣽⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣄⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣼⣻⢿⣿⣿⣿⣿⣿⣿⠃⣹⣿⡿⣻⣿⠋⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⠧⠀⣿⣿⣿⣿⣿⡟⢾⡿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⠙⣿⣿⣷⣼⣿⣿⠛⠿⣿⣮⣿⣝⡿⣿⡿⠀⡟⣿⠀⢾⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾⣿⣿⣿⣿⣿⣯⠀⠒⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠛⠛⠈⢸⣦⣄⣷⢽⣜⣧⣿⡀⢺⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢻⣿⣇⣿⣿⢻⣿⣷⣻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣝⠘⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣴⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧⣄⡈⠘⠿⣿⣶⣤⡀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣼⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢲⣦⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⣿⣿⡇⠀⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⣔⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⠟⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠯⠍⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢴⣯⣶⣤⣽⣿⡿⠿⠟⠿⣿⣿⣷⣶⣤⣀⠀⣸⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣗⢟⣲⠃⢸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⣄⡭⠝⠟⠇⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢞⠣⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠓⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠈⠉⠋⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢠⠇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣴⣿⣿⣿⣿⣿⣯⣺⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡟⠁⢸⣿⣷⡀⠀⠀⠨⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣯⣄⡂⠒⠘⢿⣿⣿⣿⣬⣉⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⡠⣿⣿⣿⣷⡀⠈⣷⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣼⣻⠿⠳⣿⣿⣿⣿⣿⠃⣿⣿⡿⣻⣿⠋⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡗⠀⣿⣿⣿⣿⣿⡿⡽⠿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡛⠛⠿⢿⠟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⠐⠒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠒⠂⢠⣦⣄⣿⢹⣔⣧⣿⡀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠀⣿⣿⣯⡿⠉⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⣄⡈⠙⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣴⣷⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣧⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣸⡿⡏⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠅⣴⣁⡸⣿⣿⠇⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⡿⠿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⣠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢴⣯⣶⣥⣿⢿⡿⠿⠟⢿⣿⣿⣷⣾⣤⣀⠀⣾⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠸⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⡾⢶⣝⠃⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⣼⢛⠿⠿⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠚⠛⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠃⠈⠑⠉⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⢔⣻⣿⣿⣿⣟⣛⣽⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡿⠁⢸⣿⣷⡀⠀⠀⠈⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣅⡒⠂⠺⢿⣿⣿⣿⣠⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⢀⡠⣿⣿⣿⣷⡀⠸⣷⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣳⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣻⢹⣷⣿⣿⣿⣿⣿⠁⣽⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⡿⡟⢟⡿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣼⣿⣿⠛⠿⣿⣯⡩⣿⣛⣿⡟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⠒⠒⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣅⡉⠓⠛⠈⢡⣦⣤⣷⢻⣔⣧⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢹⣿⣇⣿⣿⣻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠉⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣎⠙⣿⣿⣿⣼⣿⣿⣹⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣴⣦⡄⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣕⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣾⣿⣿⣿⣿⣿⣇⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⣑⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣸⡿⡏⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠅⣼⡁⠸⣿⣿⠇⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⡒⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣤⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢴⣯⣶⣤⣽⣿⡿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠀⣼⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⡸⡊⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢘⣚⣼⣘⠣⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣰⢛⠓⠿⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠖⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠚⠋⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠃⠘⠘⠉⠈⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣔⣿⣿⣿⣿⣿⣄⣸⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡿⠁⢸⣿⣷⡀⠀⠀⠈⡲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣅⡚⠚⠻⢿⣿⣿⣿⣯⣭⣿⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⢀⡠⣿⣿⣿⣷⡀⠸⣗⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣄⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡟⣳⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⠽⢷⣿⣿⣿⣿⣿⠁⣽⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡿⢫⡿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣷⡻⡿⠿⢿⠟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⠐⠒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠂⠙⢢⣦⣤⣷⢹⣔⣧⣿⡀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢹⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣼⣿⣿⣽⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣦⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣽⣿⣿⣿⣿⣿⣧⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣸⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠅⣰⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⡿⢿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢴⣯⣶⣥⣽⣿⡿⠿⠟⣿⣿⣿⣷⣶⣤⣀⠀⣾⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⠁⡸⠫⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣛⣾⣛⠇⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣸⢓⠚⠿⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠑⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠛⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠃⠈⠉⠉⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣔⣺⣿⣿⣻⣿⣮⣼⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡿⠁⢸⣿⣷⡀⠀⠀⠈⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣯⣥⡲⠲⠻⢿⣿⣿⣿⣔⣼⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⢈⡠⣿⣿⣿⣷⣀⠰⣷⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⣽⠯⣿⣿⣿⣿⣿⠃⣻⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡯⡯⡿⠯⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣮⡻⠿⣿⡿⠟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⠘⠒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠛⠉⠉⢠⣦⣤⣷⢻⣔⣧⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢹⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣎⠙⣿⣿⣿⣴⣿⣿⣹⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣵⣾⣮⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣴⣷⣿⣿⣿⡇⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣰⣿⣿⣿⣿⣿⣿⣧⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⣸⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠅⣰⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⡿⠿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠜⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⡂⣾⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢴⣯⣶⣥⣿⣿⣿⠿⠟⣿⣿⣿⣷⣶⣤⣀⠀⣾⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⢀⢸⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⡀⣿⣿⣻⣿⣛⠯⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⣨⣿⣿⣷⣿⣿⠕⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠋⠛⠛⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⢐⣻⣽⣿⣿⣿⣔⣺⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡿⠁⢸⣿⣷⡀⠀⠀⠈⢲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣥⡒⠚⠟⢿⣿⣿⣿⣷⣹⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⢈⡤⣿⣿⣿⣷⣀⠸⣗⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⠽⠏⣿⣿⣿⣿⣿⠁⣽⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡛⢯⡿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣷⣻⣿⢿⣿⡟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⠘⢒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣅⡉⠓⠂⠈⢡⣦⣤⣿⢻⣔⣧⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢹⣿⣇⣿⣿⣻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣎⠙⣿⣿⣿⣼⣿⣿⣽⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣰⣦⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣽⣿⣿⣿⣿⣿⣧⠀⢀⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣸⠿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠅⣰⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢴⣯⣶⣤⣼⢿⣿⠿⠟⣿⣿⣿⣷⣶⣤⣀⠄⣸⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⠁⡸⠫⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣛⣾⣛⠇⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣸⢓⠚⠿⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠔⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠛⠚⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠁⠘⠉⠉⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⢄⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣰⣻⣽⣿⣻⣿⣍⣾⣿⡇⣿⣿⣿⣿⡟⠛⠛⠉⠀⣠⣼⡿⠁⢸⣿⣷⡀⠀⠀⠈⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣥⡚⠒⠻⢿⣿⣿⣿⣐⣽⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⢀⡠⣿⣿⣿⣷⡀⠨⣯⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡟⣳⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⠽⠟⣿⣿⣿⣿⣿⠁⣻⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡯⢏⠿⠍⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⣿⢿⠿⡿⡟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⠒⠒⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠛⠁⠚⢰⣦⣤⣷⢻⣔⣧⣿⡀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢹⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠃⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣎⠙⣿⣿⣿⣼⣿⣿⣹⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣮⣷⣿⣿⣿⡇⠀⠀⢀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣕⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⣩⡟⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠯⠅⣼⣃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢐⣠⣾⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢴⣯⣶⣵⣿⣿⣿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠄⣼⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⣸⣿⣿⣿⣂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣃⣿⣿⣭⣿⣟⡧⢸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⣜⣿⣿⣿⣻⣿⡅⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠛⠀⠀⠀⠀⢹⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣲⣿⣽⣿⢯⡿⢝⣻⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣼⡿⠁⢸⣿⣷⡀⠀⠀⠈⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣅⡒⠒⠘⢿⣿⣿⣿⣐⣟⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⢈⣠⣿⣿⣿⣷⡄⠸⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣳⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣻⠽⢿⣿⣿⣿⣿⣿⠃⣹⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡿⢟⠿⠏⠡⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣧⡛⣟⣛⡻⡟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⠒⢒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠛⠓⠊⢡⣦⣤⣷⢻⣔⣧⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣯⡿⠁⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⡿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⣿⣿⣯⣿⣿⣿⡿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣇⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣤⣶⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⣨⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠅⣰⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣤⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢴⣯⣾⣤⣿⣿⡿⠿⠟⠿⣿⣿⣷⣶⣤⣀⠀⣾⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣨⡫⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢙⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⢹⢿⣓⠃⢼⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣰⢋⠟⠿⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠔⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠒⠑⠀⠀⠀⠀⢻⣿⣿⣿⣿⠓⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠈⠉⠉⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢤⣖⣿⣟⣿⣻⣟⢲⣼⣿⡇⣿⣿⣿⣿⡟⠛⠛⠋⠀⣠⣾⡿⠁⢸⣿⣷⡀⠀⠀⠈⠲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣥⡚⠓⠻⢿⣿⣿⡿⣷⣚⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⢀⡠⣿⣿⣿⣷⣄⠰⣾⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣳⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⠽⠿⣿⣿⣿⣿⣿⠁⣽⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⡿⢯⡿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣯⡙⢛⡻⢿⠟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⠘⠒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠉⠁⢠⣦⣤⣷⢻⣜⣧⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢹⣿⣇⣿⣿⣻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣫⡿⠃⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠘⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣆⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⡧⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣕⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣾⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⡀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣨⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫⠍⣸⣃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢴⣯⣶⣥⣿⣿⣿⠿⠟⣿⣿⣿⣷⣶⣤⣀⠀⣾⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠸⡋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⡞⡜⣳⣚⠓⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣒⡧⠳⠳⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡢⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠓⠊⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠃⠈⠑⠉⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⡆⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣰⣿⣿⣿⣿⣿⢤⣾⣿⡏⣿⣿⣿⣿⣟⠛⠛⠉⠀⣠⣾⡟⠁⢘⣿⣿⣇⠀⠀⢈⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⣄⡐⠊⠂⢿⣿⡏⡘⣿⢉⣱⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⣀⣸⣿⣿⣿⣧⠀⣧⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣻⠫⡍⣯⣿⣿⣿⣿⠃⣽⣿⡿⣿⣿⠋⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡷⠿⠿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣿⣾⣿⡿⡿⡟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠐⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠐⢡⣦⣄⣷⢹⣼⣧⣿⡀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⠿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⢹⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣤⣾⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⡀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣨⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠅⣸⡃⠸⣿⢿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡴⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢴⣯⣶⣥⣿⣿⡿⠿⠟⢿⣿⣿⣶⣶⣤⣀⠀⣼⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠰⣋⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢙⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠺⡪⣲⣚⠂⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⡢⣒⠛⠻⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠃⠃⠐⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠁⠙⠉⠀⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢠⡆⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠤⣲⣿⣿⣿⢿⣿⣔⣾⣿⡏⣿⣿⣿⣿⣟⠛⠛⠉⠀⣠⣾⡿⠀⢘⣿⣿⣆⠀⠀⠀⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣄⡐⠒⠚⢿⣿⡿⣘⣟⢭⣽⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣾⣿⣿⣿⠀⢀⣸⣿⣿⣿⣧⠀⣤⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣋⠓⢀⣝⣿⣿⣿⣿⠃⣽⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡷⣯⡿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣶⡿⠿⡿⣿⡟⠀⡏⣿⠁⢸⡷⠀⢘⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠁⢩⣦⣄⣿⢹⣼⣧⣿⡀⢸⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣶⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠂⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⠿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⡀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⢽⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣤⣾⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⡀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣨⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠅⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢴⣯⣶⣤⣵⢾⡻⠟⠛⠿⣿⣿⣷⣶⣤⣀⠀⣨⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⢉⢫⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢙⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢲⣻⢟⡝⠃⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⡴⣓⠚⠿⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡳⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠊⠓⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠃⠉⠙⠁⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢠⡇⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢤⡒⣺⣽⣿⣿⣿⢆⢿⣿⡏⣿⣿⣿⣿⣟⠛⠛⠉⠀⣠⣾⡿⠀⢘⣿⣿⣆⠀⠀⠀⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⢿⣿⣿⣅⡘⠓⠀⢿⢿⡿⡚⡏⢿⣻⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⢀⣸⣿⣿⣿⣧⠀⣵⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣛⠻⡁⣿⣿⣿⣿⣿⠃⣽⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡭⢾⠿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣧⡹⢿⠿⢿⠟⠀⡏⣿⠁⢸⡷⠀⢘⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠊⠐⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠁⢰⣦⣄⣿⢹⣼⣧⣿⡀⢸⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠊⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⠿⣿⣿⣧⣄⡈⠘⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⣶⣵⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⣶⣶⣿⣿⣿⡇⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣶⣾⣿⣿⣿⣿⣿⣇⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣨⡿⡏⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠅⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣰⣻⣻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢴⣯⣶⣤⣿⣿⡿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠀⣾⣿⠿⠿⠿⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⢀⢈⢝⡻⡿⠋⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢹⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣈⢊⡼⣛⢭⣮⠁⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢡⢶⣞⣣⡽⢿⠄⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⡇⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢤⣔⣿⣟⣿⣛⣿⢃⣸⣿⡇⣿⣿⣿⣿⡟⠛⠛⠉⠀⣠⣾⡟⠀⢐⣿⣿⣧⠀⠀⠈⢱⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣄⡀⠃⠚⢟⣛⠻⠟⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⢀⣸⣿⣿⣿⣇⠀⣀⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⡳⠍⣬⣿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⡭⣽⡿⠯⠈⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣯⡿⡭⢿⢿⡟⠀⡏⣿⠁⢼⡿⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢻⣦⣄⣿⢹⣼⣧⣿⡀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠘⣿⣿⣿⡿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⠿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⡀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⣶⣵⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣶⣶⣿⣿⣿⡇⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣞⣮⣿⣿⣿⣿⣿⣿⣇⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣨⡿⡏⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠅⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢤⣿⣟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢴⣯⣶⣥⣿⣿⡿⠿⠿⢿⣿⣿⣷⣶⣤⣀⠀⢮⣿⠿⠿⠿⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⢨⠴⡿⡿⡃⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠌⠯⣊⣵⣊⢾⠭⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⢩⣽⣎⣺⠯⣿⠆⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠓⠀⠁⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣔⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⢠⡗⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡤⣒⣿⣽⣟⣟⣿⣿⣽⣿⡇⣿⣿⣿⣿⡟⠛⠛⠉⠀⣠⣾⡿⠀⢐⣿⣿⣦⠀⠀⠀⢵⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣆⡀⠓⠺⢿⣝⣻⢿⣿⣯⣽⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⢀⣸⣿⣿⣿⣧⠀⣐⣾⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣍⢁⣐⣙⣿⣿⣿⣿⠃⣾⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⡿⣿⠿⠏⠈⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡿⠿⡿⢿⡿⠀⡏⣿⠁⢸⡿⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠀⠄⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠃⢠⣦⣄⣿⢹⣼⣧⣿⡀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⠿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⡀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⣶⣵⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⣶⣶⣿⣿⣿⡇⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣲⣾⣿⣿⣿⣿⣿⣇⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣨⡿⡏⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠅⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⢐⣷⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢴⣯⣾⣤⣿⣿⣿⠿⠟⢿⣿⣿⣶⣶⣤⣀⠀⣸⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⢨⢎⢿⢿⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⢂⠭⡑⢃⣕⠝⠾⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠡⣫⣚⣿⠿⣻⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡠⡄⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢠⡗⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡤⣴⣻⣽⣿⣿⣿⡷⣺⣿⡏⣿⣿⣿⣿⡟⠛⠛⠉⠀⣠⣾⡟⠀⢐⣿⣿⣧⠀⠀⢈⠵⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⣄⡐⠃⠒⢿⣛⠿⣻⣿⣷⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⢀⣸⣿⣿⣿⣇⠀⣠⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⠉⢜⣿⣿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣽⡿⠏⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣿⡿⡿⢿⣿⡟⠀⡏⣿⠁⢼⡿⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠕⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠈⢠⣦⣄⣿⢹⣼⣧⣿⡀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣯⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⠿⣿⣿⣧⣄⡈⠘⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⣶⣵⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣶⣶⣿⣿⣿⡇⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣕⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⣶⣥⣿⣿⣿⣿⣿⣿⣇⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣮⣦⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣨⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠅⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣞⢽⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣤⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢴⣯⣶⣥⣿⣿⡿⠿⠟⣿⣿⣿⣷⣶⣤⣀⠄⣺⣿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣨⠼⢿⣿⢵⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢄⣚⣔⡝⢃⣝⠽⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢡⣶⣦⣾⡿⢾⠄⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠋⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⠛⠛⠛⠛⠋⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⢄⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢠⡇⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢤⣰⣻⣽⣿⣿⣾⢏⣿⣿⡏⣿⣿⣿⣿⡟⠛⠛⠉⠀⣠⣾⡟⠀⢐⣿⣿⣧⠀⠀⠈⢱⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⣄⡐⠃⠐⢾⣝⠫⣿⣿⣟⣾⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⢀⣸⣿⣿⣿⣇⠀⣠⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣻⠉⢸⣽⣿⣿⣿⣿⠁⣽⣿⡿⣿⣿⠋⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣽⡿⠯⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣿⡿⠯⢿⢿⡿⠀⡏⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠈⠄⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠊⢩⣧⣄⣿⢹⣼⣧⣿⡀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠊⣿⣿⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⠿⣿⣿⣧⣄⡈⠘⠿⣿⣶⣤⡀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣮⣺⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣵⣾⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠨⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠂⣼⡃⢸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠝⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡤⣵⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢴⣯⣶⣥⣿⣿⣿⠿⠿⣿⣿⣿⣷⣶⣤⣀⠔⣾⣿⠿⠿⠿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⣠⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠉⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠨⡿⣿⣿⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⣽⡿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠚⠛⠓⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠉⠉⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣤⡆⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣿⣿⣿⣿⣿⢫⣽⣿⡗⣿⣿⣿⣿⣛⠛⠉⠁⠀⣠⣾⡿⠀⠀⣿⣿⣿⡄⠀⠀⢓⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣥⡰⠣⠚⢯⣽⣉⣟⠿⡷⣺⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⣀⣀⣿⣿⣿⣿⡀⣠⣾⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡿⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⣁⣴⣾⣿⣿⣿⣿⠁⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⣿⡿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣾⡻⠟⢿⣿⡟⠀⡏⣿⠁⢼⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠋⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠓⢢⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢻⣿⣿⣿⣿⣿⠿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⡿⡟⠉⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠂⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣥⣠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢴⣯⣶⣤⣽⢿⡿⠿⠟⠿⣿⣿⣶⣶⣤⣀⠀⢬⣿⠿⠿⠿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⡠⡄⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠉⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠨⠯⠚⣠⠏⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠕⠘⠓⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠂⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡴⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⡆⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣔⣿⡽⡿⣻⣳⠆⢹⣿⡇⣿⣿⣿⣿⡛⠛⠋⠁⠀⣠⣾⠏⠁⠀⣿⣿⣿⡄⠀⠀⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⡐⠒⠲⠿⡯⠿⠷⠯⡽⣾⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠀⣀⢀⣿⣿⣿⣿⡀⣀⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣖⣅⡺⣽⣿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣯⣿⠧⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡿⡼⡿⠿⡿⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⡐⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠂⢠⣦⣄⣷⢹⣼⣧⣿⡀⢸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣽⣿⣽⠈⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣢⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠀⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡿⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠂⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣥⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢴⣯⣶⣴⣿⢿⡿⠿⠟⠿⣿⣿⣷⣶⣤⣀⠀⢨⣿⠿⠿⠿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⣠⡤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠉⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠸⠮⡈⢠⡂⠘⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠐⢉⠵⠂⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠽⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠒⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣴⣿⣽⣿⣸⣷⡂⣽⣿⡏⣿⣿⣿⣿⡛⠛⠋⠁⠀⣠⣾⠿⠁⠀⣿⣿⣿⡄⠀⠀⢲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣥⡀⠂⠋⠿⡍⣾⢻⣳⣺⣾⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⣀⢀⣿⣿⣿⣿⡠⣄⣺⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣎⢀⠐⣴⣾⣿⣿⣿⠃⣽⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⣿⠿⠧⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣮⡻⣏⡿⢿⠟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⡂⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠈⢲⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⡀⠐⠿⣿⣶⣤⡀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣢⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⢀⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡿⡟⠌⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠃⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣅⣠⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢴⣯⣶⣤⣿⣿⡿⠿⠟⠿⣿⣿⣷⣾⣤⣀⠀⢬⣿⠿⠿⠿⠻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⣠⡤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠉⢹⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠸⠮⡈⢠⡊⠘⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠐⢉⠵⠃⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠒⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠀⠀⠀⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣴⣿⣿⣿⣹⣿⡀⣿⣿⡇⣿⣿⣿⣿⡛⠛⠉⠁⠀⣠⣾⠟⠁⠀⣿⣿⣿⡄⠀⠀⠲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⡀⠂⠚⠾⡏⠾⠿⠼⣿⣺⣿⣿⠇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠀⣀⣀⣿⣿⣿⣿⡠⣄⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡟⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣄⢀⠐⣿⣿⣿⣿⣿⠃⣽⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣿⡿⠧⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣮⡻⠟⡿⡿⠟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⣀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠈⢰⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢻⣿⣿⣿⣿⣿⢿⣿⣿⣥⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠠⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡿⡟⠈⣩⣭⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠂⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣇⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢴⣯⣶⣤⣷⣿⡿⠿⠛⢿⣿⣿⣷⣶⣤⣀⠀⣸⣿⠿⠿⠿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⣈⢆⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠉⢹⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠘⠮⣺⣄⠏⠘⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠘⠽⡓⠄⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⠭⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠂⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠈⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣴⣿⣿⣿⣽⣻⣁⢼⣿⡇⣿⣿⣿⣿⡛⠛⠉⠁⠀⣠⣾⠿⠀⠀⣿⣿⣿⡄⠀⠈⢲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⡀⠂⠹⠾⠧⣮⠥⡟⣾⣺⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠀⣀⣀⣿⣿⣿⣿⡀⣄⣹⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣮⢿⡉⣴⣿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣿⡿⠧⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡚⠋⡿⠿⡟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⡐⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠁⢠⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢻⣿⣿⣿⣿⣿⢿⣿⣿⣥⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠠⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣨⡿⡟⠈⣩⣭⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠂⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣧⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢴⣯⣶⣤⣷⣿⡿⠿⠛⢿⣿⣿⣷⣶⣤⣀⠀⣼⣿⠿⠿⠿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⣈⢆⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠉⢹⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠘⠮⣺⣄⠏⠘⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠘⠽⡓⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠂⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠀⠀⠈⠈⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣔⣿⣿⣿⣿⣻⣂⢺⣿⡏⣿⣿⣿⣿⡛⠛⠉⠁⠀⣠⣾⠟⠀⠀⣿⣿⣿⡄⠀⠀⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⡐⠒⠻⠻⡍⢎⢱⡿⣝⣾⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⣀⢀⣿⣿⣿⣿⡀⣄⣾⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡟⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣏⠴⠨⣿⣿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⣟⡿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡬⠿⣿⠿⡟⠀⡏⣿⠁⢸⡿⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠒⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠉⢡⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢻⣿⣿⣿⣿⣿⢿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣹⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡿⡟⠉⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠂⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢴⣯⣶⣤⣿⣿⡿⠿⠟⠿⣿⣿⣷⣶⣤⣀⠀⢼⣿⠿⠿⠿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⣠⢄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠉⢹⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠘⠮⣚⣠⠏⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠘⠝⡾⠇⠀⣿⣿⣿⣿⣿⣿⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠂⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠀⠀⠀⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢴⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣴⣿⣿⣿⢿⣿⠖⣿⣿⡇⣿⣿⣿⣿⣛⠛⠋⠁⠀⣠⣾⡟⠁⠀⣿⣿⣿⡄⠀⠀⠱⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣥⡀⠂⠚⠿⠯⠾⠻⠝⢟⣾⣿⣿⠇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⠀⣀⢀⣿⣿⣿⣿⡀⣄⣾⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡿⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣀⣴⡀⣝⣿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣟⡿⠯⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣷⣬⣿⣿⠛⠿⣿⣶⡺⡿⢿⠿⡟⠀⡏⣿⠁⢸⠷⠀⢘⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠁⢡⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠠⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠂⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢴⣯⣮⣤⣿⣿⡿⠿⠛⢿⣿⣿⣷⣶⣤⣀⠀⣨⣿⠿⠿⠿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⣠⢄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠉⢹⣿⣿⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠘⠮⣚⣠⡏⠚⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠘⠝⡾⠁⠀⣿⣿⣿⣿⣿⣿⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠂⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡖⣿⣟⣿⣻⣽⣄⢾⣿⡇⣿⣿⣿⣿⣛⠛⠋⠁⠀⣠⣾⠏⠀⠀⣿⣿⣿⡄⠀⠀⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⡀⠊⠺⠿⠽⠻⢟⢿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⠀⣀⣀⣿⣿⣿⣿⡀⣄⣾⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣔⡂⣠⣶⣿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⣿⡿⠯⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣿⣻⣿⡿⠿⡟⠀⡏⣿⠁⢸⡿⠀⢘⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠘⢢⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣯⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⢻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⢽⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣦⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠎⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠁⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣯⣦⣥⣽⣿⡿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠀⣸⣿⠿⠿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣢⢨⡢⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠸⣣⢟⠯⡲⠘⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠘⠋⡙⠋⠂⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠂⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠟⠉⠈⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢴⣶⣻⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⣤⡇⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣴⣿⣿⣿⣤⠊⡐⣾⣿⡇⣿⣿⣿⣿⡛⠛⠁⠀⢀⣴⣿⠟⠀⠀⣽⣿⣿⣆⠀⠈⠱⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⢿⣿⣿⣷⡖⠒⠀⠎⢆⠈⡹⠿⣟⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⣀⣀⣻⣿⣿⣿⡀⣄⣺⣿⣿⣿⣿⢷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣄⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣾⣿⡟⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⣿⣥⠬⠿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡻⣝⡿⠯⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡸⠀⢛⢻⡟⠀⡏⣿⠁⢸⡿⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠈⢡⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⡃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⣿⣇⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠎⡏⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠁⣸⡃⡸⣿⢿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣠⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣯⣶⣦⣽⣿⡿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠀⢨⣿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣠⣗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠉⢹⣿⣿⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢸⢷⡿⠦⠣⠘⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⠁⠘⠋⡹⠙⠂⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡕⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠛⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠛⠋⠁⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⣤⡆⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣴⣻⣽⢿⡤⣡⡗⣼⣿⡏⣿⣿⣿⣿⡛⠛⠁⠀⢀⣴⣿⠟⠀⠀⣽⣿⣿⣆⠀⠈⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡔⠂⠀⠆⡡⣋⡽⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⠀⣀⣀⣻⣿⣿⣿⡀⣄⣾⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣾⣿⡿⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣾⢤⠥⢴⣟⣿⣿⣿⠁⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⣿⡟⣿⣿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡰⠁⢙⣫⡟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⠆⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠈⢠⣦⣄⣿⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣇⠙⣿⣿⣿⣴⣿⣿⣽⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣢⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡤⠞⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠁⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠅⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣯⣦⣤⣽⢿⡻⠟⠟⠿⣿⣿⣷⣶⣤⣀⠀⡮⣿⠿⠿⠿⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣭⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠉⢹⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠨⢵⠘⠌⠃⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡣⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠤⣉⡚⠝⠙⢛⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠅⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠓⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⣤⡇⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢔⣿⣿⣿⡵⣌⡛⣹⣿⡏⣿⣿⣿⣿⡛⠛⠁⠀⢀⣼⣿⡟⠁⠀⣽⣿⣿⣆⠀⠈⠲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡔⠁⠀⠨⡷⡯⣳⡟⣿⣼⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⣀⣀⣻⣿⣿⣿⡀⣠⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣾⣿⡟⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣢⠯⠹⠲⠿⣿⣿⣿⠁⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⣿⡿⢿⡿⠯⠈⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡓⠊⠿⢿⡿⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠁⢡⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⡿⠿⠿⠾⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⠿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⡀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣢⣠⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡤⠎⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠁⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣯⣶⣥⣿⣿⡿⠟⠻⢿⣿⣿⣷⣶⣤⣀⠀⣼⣿⠿⠿⠿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣼⠄⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠉⢹⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⢨⣵⠜⠎⡃⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡢⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠨⠩⠏⠻⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠆⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠒⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠓⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⠋⠈⠁⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⣴⡇⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣴⣪⣽⣿⡢⡦⢥⣼⣿⡏⣿⣿⣿⣿⡛⠋⠁⠀⢀⣼⣿⠿⠁⠀⣽⣿⣿⣆⠀⠈⠲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡔⠚⠀⠬⡵⡌⠕⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠂⣀⣀⣻⣿⣿⣿⡀⣤⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣾⣿⡟⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣷⣚⣓⠒⢿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⣿⡿⣟⡿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡀⠿⡻⣿⡟⠀⡏⣿⠁⢸⡷⠀⢘⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠊⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢀⣦⣄⣿⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⡿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⡿⣿⣿⣥⣄⡀⠐⠿⣿⣶⣤⡀⠁⠚⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣦⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣴⣴⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣢⣀⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡤⠎⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠁⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⡇⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡿⢿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣯⣦⣤⣽⢿⡻⠟⠟⢿⣿⣿⣶⣶⣤⣀⠀⡸⣿⠿⠿⠿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣼⠄⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠉⢹⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⢨⣵⠜⠞⠃⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠨⠩⠏⠹⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠇⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠒⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠂⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⣴⡇⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢔⣻⣿⣿⠀⡶⠦⢻⣿⡏⣿⣿⣿⣿⡛⠛⠁⠀⢀⣼⣿⡿⠁⠀⣿⣿⣿⣆⠀⠀⠱⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡔⠄⠈⠄⡀⡒⠢⡼⣿⣶⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⣀⣀⣻⣿⣿⣿⡀⣀⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣾⣿⡟⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣳⠭⠑⠚⢿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⣿⡿⣿⡿⠏⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡊⠀⢛⠻⡟⠀⡏⣿⠁⢸⡿⠀⢘⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⠋⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠁⢀⣦⣄⣿⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⡿⣿⣿⣥⣄⡈⠐⠿⣿⣶⣤⡀⠁⠚⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⢽⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣦⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣴⣴⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣢⣀⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡤⠎⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠁⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⡇⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡿⢿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣯⣦⣤⣽⢿⡻⠟⠟⢿⣿⣿⣶⣶⣤⣀⠀⡸⣿⠿⠿⠿⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣼⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠉⢹⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⢨⣵⠜⠌⠅⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠨⠩⠏⠻⠀⠀⣿⣿⣿⣿⣿⣿⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠅⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠒⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠈⠉⠈⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⣴⡇⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣔⣯⣽⣿⠠⣤⠍⣾⣿⡏⣿⣿⣿⣿⣛⠛⠁⠀⢀⣼⣿⡿⠁⠀⣿⣿⣿⣆⠀⠀⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡤⠀⠸⠌⠁⠀⠣⣜⣟⣾⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⣀⣀⣻⣿⣿⣿⡀⣤⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣾⣿⡟⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣣⢍⠸⠉⢽⣿⣿⣿⠃⣽⣿⡿⣿⣿⠃⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣟⡿⠯⠈⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡛⠀⠛⢛⡟⠀⡏⣿⠁⢸⡿⠀⢘⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠊⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢨⣦⣄⣿⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠊⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⡿⣿⣿⣥⣄⡀⠐⠿⣿⣶⣤⡀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣢⣠⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡤⠎⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠈⠁⣸⣃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣯⣦⣤⣽⢿⡿⠟⠟⠿⣿⣿⣷⣶⣤⣀⠀⢼⣿⠿⠿⠿⢟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣼⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⢹⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⢨⣵⠜⠌⠅⠸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠨⠩⠏⠻⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠒⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠓⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⢴⣶⣻⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⣤⡇⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢔⣻⣽⣿⣶⢭⢄⣸⣿⡟⣿⣿⣿⣿⡛⠛⠁⠀⢀⣼⣿⡟⠁⠀⣽⣿⣿⣆⠀⠈⢲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡜⠀⠈⠨⣰⣥⢔⢿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⠂⣀⣀⣻⣿⣿⣿⡠⣔⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣾⣿⡟⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣚⢑⡣⣝⢿⣿⣿⣿⠁⣿⣿⡿⣿⣿⠃⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⣿⡿⣿⣿⠯⠈⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣿⡛⠀⠹⣻⡟⠀⡏⣿⠁⢸⡷⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠂⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣹⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠈⢡⣦⣄⣷⢹⣴⣧⣿⡀⢸⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢹⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⡿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⡿⣿⣿⣥⣄⡀⠐⠿⣿⣶⣤⡀⠁⠚⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣾⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣷⣿⣿⣿⡧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⠀⢀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣖⢛⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⡃⣸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⡇⠅⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠝⣻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⢖⣶⡖⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣾⣥⣿⣿⡿⠿⠿⣿⣿⣿⣷⣾⣤⣀⠔⣾⣿⠿⠿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⢸⣷⣿⣿⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡉⢹⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢼⣲⣿⣿⣿⣿⡿⢽⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢋⣿⣿⣿⣿⣿⣿⠟⠀⣿⣿⣿⣿⣿⣿⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠋⠙⠂⠀⠀⠀⢻⣿⣿⣿⡿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠟⠋⠉⠉⠉⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣰⣶⡇⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣔⣪⣽⣿⢄⡦⡡⣾⣿⡇⣿⣿⣿⣯⣉⣁⢀⣀⣴⣾⣿⡟⠀⠀⣿⣿⣿⡄⠀⠀⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡆⠇⠀⠠⡹⣝⡙⣿⣧⣽⣾⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⠀⣀⢀⣽⣿⣿⣿⠀⣤⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣄⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡟⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣤⠶⠊⢟⠿⣿⣿⣿⠇⣽⣿⡟⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡿⣿⣿⠏⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡒⠉⠛⣿⣿⠀⡟⣿⠁⢾⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡈⠂⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢠⣧⣄⣷⢻⣼⣧⣿⡀⢺⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣖⣾⣷⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣷⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣷⣿⣿⣿⣿⣿⣿⣷⠀⠠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣖⠛⡯⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⡷⠂⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⢀⠀⠁⠍⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⠦⣶⣖⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⣶⣵⣿⣿⡿⠿⠟⠿⣿⣿⣷⣾⣦⣀⠄⣼⣿⠿⠿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡠⠀⢸⣾⣟⣷⣗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡉⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣷⣻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡢⣳⣿⣿⣿⣿⣿⡇⠁⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠑⠙⠛⠛⠛⠓⠀⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠋⠉⠉⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⣴⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⣰⣶⡇⠀⣠⣶⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢴⣩⣿⣿⣀⠖⠦⣾⣿⡇⣿⣿⣿⣯⣉⣁⡀⣠⣤⣾⣿⠟⠀⠀⣿⣿⣿⡄⠀⠀⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡎⠇⠀⠢⠶⠰⢆⣼⣧⣼⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⡿⠀⣀⣀⣽⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡟⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣂⠒⢓⠾⠻⣿⣿⣿⠇⣿⣿⡿⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡿⣟⣿⠏⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡣⠉⠛⢻⣿⠀⡿⣿⠁⢾⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡈⠀⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢨⣧⣄⣷⢻⣼⣧⣿⡀⢺⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⡿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⡷⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡰⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣾⣿⣿⣿⡯⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⠀⢀⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⡖⢛⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣁⢸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠨⡇⠆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⡒⣾⡖⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣷⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⣶⣵⣿⣿⡿⠿⠛⢿⣿⣿⣷⣶⣤⣀⠀⣬⣿⠿⠿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡍⣹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⢶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣫⣲⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠛⠛⠛⠉⠃⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠋⠉⠉⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⡠⢴⣶⣿⣿⣿⣿⣿⣿⣿⠿⠉⠁⠀⣰⣾⡇⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣔⣮⣽⣿⡀⠻⠆⣼⣿⡇⣿⣿⣿⣯⣉⣁⣀⣠⣴⣾⣿⡿⠀⠀⣿⣿⣿⡄⠀⠀⠵⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡖⠗⠐⠲⠕⡱⠙⣟⣏⣵⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⠀⣀⣄⣽⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣾⣿⡿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣀⢍⢹⣿⣿⣿⣿⣿⠇⣿⣿⡟⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡿⣟⣿⠏⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡙⠰⠛⢻⣿⠀⡿⣿⠁⢾⡷⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⠂⣀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢨⣧⣄⣷⢻⣼⣧⣿⡀⢺⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⠿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣗⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣶⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠓⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣵⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣖⢛⡿⠉⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⡃⣸⣿⢿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠅⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠁⠍⣻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⢰⣶⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣯⣾⣵⣿⣿⡿⠿⠟⢿⣿⣿⣷⣾⣤⣀⠐⣾⣿⠿⠿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⣸⣷⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡉⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢢⢲⣿⣿⡿⢿⣻⠽⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡣⡳⡿⣿⣿⣫⣿⠆⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠛⠛⠀⠁⠀⠀⠀⢻⣿⣿⣿⡿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠋⠉⠉⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⣠⡀⠴⣶⡿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⣰⣶⡇⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣔⣾⣿⣟⢥⠀⡁⣻⣿⡇⣿⣿⣿⣯⣉⣁⢀⣀⣤⣾⣿⠿⠀⠀⣿⣿⣿⡄⠀⠈⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡞⠇⠐⠲⡓⠪⡜⣿⣗⣾⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⠀⣀⢄⣽⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡿⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣄⢓⠒⠿⢿⣿⣿⣿⠇⣿⣿⡟⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡿⣟⡿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡒⠪⠛⣿⣿⠀⡟⣿⠁⢾⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⠂⣀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠁⢨⣧⣄⣷⢻⣼⣧⣿⡀⢺⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⡿⠿⠿⠾⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⡷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠓⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣿⣿⣿⣿⣿⣿⣷⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣖⠛⣟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⣃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⣧⠃⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⡀⠁⠝⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢐⢖⣶⡖⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣾⣤⣿⣿⡿⠿⠿⢿⣿⣿⣷⣾⣤⣀⡔⣾⣿⠿⠿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣷⣿⣿⣧⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡍⣹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣶⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣋⣴⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠑⠙⠓⠛⠋⠃⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠙⠉⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⠠⢶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣰⣾⡇⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣔⣪⣽⣿⣍⡭⡤⣼⣿⡇⣿⣿⣿⣯⣉⣁⣀⣠⣴⣾⣿⠟⠀⠀⣿⣿⣿⡆⠀⢀⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡖⠟⠐⠤⡗⠧⠕⢺⣏⣲⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⠀⣀⢀⣽⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡿⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣓⢤⢕⠹⠿⣿⣿⣿⠃⣿⣿⡟⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡿⣿⣿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡀⠁⠛⣿⣿⠀⡿⣿⠁⢾⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢨⣧⣄⣷⢻⣼⣧⣿⡀⢺⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⡿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⡀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣽⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣶⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷⣶⣾⣿⣿⡧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⣮⣾⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣶⠛⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⡀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⡿⢿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢐⣷⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣯⣾⣤⣿⣿⡿⠿⠿⢿⣿⣿⣷⣶⣦⣁⡄⣾⣿⠿⠿⠿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣸⣗⣿⣟⡧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡉⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢐⣿⣿⣿⢿⣷⡦⠼⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣐⣿⣿⣿⣯⣯⠏⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠚⠛⠛⠁⠀⠀⠀⠀⢻⣿⣿⣿⡿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠉⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⢔⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣠⣿⡇⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢴⣻⣿⣿⠂⣀⣕⣼⣿⡏⣿⣿⣿⣯⣉⡀⠀⣀⣠⣿⣿⡟⠀⠀⣿⣿⣿⡄⠀⠀⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡎⠛⠐⠪⡗⢶⣪⣿⣿⣼⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠁⣀⣀⣿⣿⣿⣿⠠⣴⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡟⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣭⠭⢡⣽⣿⣿⣿⣿⠇⣹⣿⡟⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡿⣿⡿⣟⣿⠏⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡋⠒⡻⢿⣿⠀⡿⣿⠁⢾⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢠⣦⣄⣷⢻⣜⣧⣿⡀⢺⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⡿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⣿⣿⣿⣿⣿⡿⣿⣿⣧⣀⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣷⣮⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣿⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣶⠛⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣸⡃⡸⣿⢿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⡇⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⢀⡀⠁⠌⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢔⣽⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣯⣶⣥⣿⣿⡿⠿⠿⣿⣿⣿⣷⣾⣦⣀⠀⣼⣿⠿⠿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢀⢸⣎⣿⣟⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡉⢹⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⣿⣿⣿⡿⣿⡿⠼⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢄⣸⣿⣿⣿⣿⣿⠕⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠛⠛⠂⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⡠⢖⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⣰⣿⡇⠀⣠⣶⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢴⣻⣻⣿⡑⣖⢪⣽⣿⡇⣿⣿⣿⣯⣉⣁⠀⣀⣠⣿⣿⡟⠀⠀⣿⣿⣿⡆⠀⢈⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡎⠟⠀⠘⠃⣞⢱⣿⣿⣾⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠁⣀⣀⣽⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡟⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣿⣠⠒⠿⠿⣿⣿⣿⠇⣽⣿⡟⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡿⣟⠿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡚⠚⣛⣻⣿⠀⡿⣿⠁⢾⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡂⠀⣀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢡⣦⣄⣷⢻⣜⣧⣿⡀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣷⣮⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣷⣿⣿⣿⡧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣢⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣖⠛⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⡿⠿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠌⣻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢐⣿⣏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣯⣾⣥⣿⣿⣿⠿⠿⢿⣿⣿⣷⣶⣦⣀⠔⣾⣿⠿⠿⠿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⢀⢸⣗⣿⣟⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡉⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢰⣿⣿⠿⣿⢯⡿⢼⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢄⣰⣿⣷⣿⣿⣿⠍⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠛⠛⠂⠀⠀⠀⠀⢻⣿⣿⣿⡿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠋⠉⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⢖⣾⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⢀⣰⣾⡇⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢴⣯⣿⣿⠞⣞⠊⢹⣿⡇⣿⣿⣿⣯⣉⣀⣀⣀⣠⣿⣿⠟⠀⠀⣿⣿⣿⡆⠀⠀⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡎⠟⠐⠊⠁⠊⢁⣿⣻⣿⣿⣿⡇⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠁⣀⣄⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡟⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣬⣷⠛⡿⣿⣿⣿⣿⠇⣽⣿⡟⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⡿⢟⢿⠏⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡘⠝⠙⣿⡿⠀⡿⣿⠁⢾⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢸⣦⣄⣷⢻⣜⣧⣿⡀⢺⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⢿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⡀⠁⠚⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⣿⣿⣾⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣷⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠋⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠝⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣜⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣯⣄⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣶⣥⣽⣿⡿⠿⠿⣿⣿⣿⣷⣶⣤⣀⠄⣺⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢖⣼⣿⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣉⣹⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⢸⣿⣿⣿⣿⣿⡯⠾⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢬⣽⣿⣿⣽⣿⣿⠝⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠛⠿⠛⠛⠛⠁⠀⠀⢿⣿⣿⣿⡿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠋⠉⠛⠙⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⢠⣾⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⣠⣾⣿⠃⢀⣴⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣶⣙⡗⣿⠀⡀⢂⣻⣿⡏⣿⣿⣿⣶⣤⣤⣀⣄⣾⣿⣿⡏⠀⣿⣿⣿⣆⠀⠀⠈⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⠂⠐⠺⡇⠀⠸⢿⣟⣿⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⢀⣠⣽⣿⣿⣿⡆⠠⣴⣼⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣇⣶⣿⡿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣀⠉⠨⢍⠻⠿⣿⣿⠇⣻⣿⡟⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⡿⣿⠿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡀⠀⠀⢼⡿⠀⡿⡿⠀⣿⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠒⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢈⣦⣄⣷⢷⣞⣷⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⣿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠘⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⢹⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣼⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣢⣿⣿⣾⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡂⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠋⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⡂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⡧⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⣻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣔⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣯⣠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣾⣥⣿⣿⣿⠿⠿⢿⣿⣿⣷⣾⣦⣀⠔⣾⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣼⣿⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣉⣹⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⢾⣿⣿⣾⣿⣿⣽⠾⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢬⢾⣿⣾⣿⣾⣿⠎⠃⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠛⠻⠛⠛⠛⠋⠀⠀⢻⣿⣿⣿⡿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⢀⣾⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⣠⣾⣾⠃⢀⣴⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢶⣽⣿⣟⠠⡘⢁⣸⣿⡏⣿⣿⣿⣶⣤⣤⣀⣤⣾⣿⣿⡟⠀⣿⣿⣿⣆⠀⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⠂⠐⠖⡀⠉⠀⠿⣻⣿⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⢀⣠⣽⣿⣿⣿⡆⠀⣴⣽⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣎⣶⣿⡿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣃⠄⠀⠺⡿⢿⣿⣿⠇⣿⣿⡿⣿⣿⠋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⡿⣿⠿⠏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡀⠀⠀⢹⡿⠀⡿⡿⠀⣿⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢀⣦⣄⣷⢷⣞⣷⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⣿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⢻⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣽⣿⣿⣇⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠋⡯⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡣⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢨⣶⣿⣏⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣥⣽⣿⡿⠿⠿⢿⣿⣿⣷⣶⣤⣀⠀⣬⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣰⣰⣾⣿⣿⣯⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣍⣹⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⡸⣭⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣺⣽⣿⣿⣿⣿⡮⠂⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠛⠛⠛⠋⠍⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠙⠛⠉⠋⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⣾⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣠⣶⣿⠇⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣶⢻⢿⡿⢀⠼⠄⣿⣿⡇⣿⣿⣿⣶⣦⣤⣀⣤⣾⣿⣿⡟⠀⣿⣿⣿⣆⠀⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣦⠒⠂⠀⠀⠦⠄⣿⣯⣶⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⢀⢤⣽⣿⣿⣿⡆⠀⣶⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣏⣶⣿⡿⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣃⠊⠂⠂⠻⣿⣿⣿⠇⣿⣿⡿⣿⣟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⣿⠿⠯⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡀⠀⠀⢼⣿⠀⡿⡿⠀⣿⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢀⣦⣄⣧⢷⣞⣷⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⣿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⢹⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣼⣿⣿⣹⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣷⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⣾⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠉⡯⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⡃⢸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠢⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡧⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢨⣶⣿⣟⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣤⣽⣿⡿⠿⠿⠿⣿⣿⣷⣶⣤⣀⠀⣬⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡰⣠⣺⣿⣿⣟⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⡍⣹⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⣸⣿⣿⠿⣿⣿⢿⢸⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⣿⣿⣯⣟⣿⣟⡋⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠟⠛⠛⠋⠉⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉⠙⠉⠙⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠉⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣠⣾⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣠⣶⣾⠇⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢶⣻⢻⢿⡀⢁⡀⣾⣿⡇⣿⣿⣿⣶⣦⣤⣀⣤⣾⣿⣿⡟⠀⣿⣿⣿⣆⠀⠀⠈⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⠒⠂⠡⠀⠄⢀⡿⣷⣾⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⢀⢤⣽⣿⣿⣿⡆⠀⣶⣻⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣄⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣶⣿⡿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣃⠚⠖⢖⠼⣿⣿⣿⠇⣿⣿⡿⣿⣟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡿⣿⠿⠯⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡀⠐⠈⢾⡿⠀⡿⡿⠀⣿⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠂⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢀⣦⣄⣧⢷⣞⣷⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⣿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⢹⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣼⣿⣿⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣷⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⣾⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠉⡯⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⡃⢸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠢⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡧⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢨⣶⣿⣟⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣥⣿⣿⡿⠿⠿⢿⣿⣿⣷⣶⣤⣀⠀⣬⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡰⣠⣺⣿⣿⣟⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡍⣹⣿⣿⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⣸⣿⣿⠿⣿⣿⢿⢸⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⣿⣿⣯⣟⣿⣟⡋⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠟⠛⠛⠋⠉⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠉⠛⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⡠⡤⢠⣾⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⣠⣾⣿⠃⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠶⢻⡿⣿⠤⣸⡄⣻⣿⡇⣿⣿⣿⣶⣤⣤⣀⣠⣾⣿⣿⡏⠀⣿⣿⣿⣆⠀⠀⠀⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣷⣶⠒⠀⢀⠀⡂⢨⠿⢧⣽⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⢀⢤⣽⣿⣿⣿⡆⠀⣶⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣄⢻⣯⣤⣤⣄⠉⠙⢿⣿⣆⣶⣿⡿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣁⠠⢐⠲⠯⣿⣿⣿⠃⣿⣿⡿⣿⣟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⡿⣿⠿⠯⠡⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡀⠀⠈⢽⣿⠀⡿⡿⠀⣿⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢠⣦⣄⣧⢷⣞⣷⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⣿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⢹⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣼⣿⣿⣽⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣷⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⣾⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠋⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠢⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡧⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢨⣶⣿⣟⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣤⣽⣿⣿⠿⠿⢿⣿⣿⣷⣶⣤⣀⠀⣸⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡰⣠⣺⣿⣿⣟⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣍⣹⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⣸⣿⣿⠿⣿⣿⢿⢸⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⣿⣿⣯⣟⣿⣟⡋⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠟⠛⠛⠋⠉⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠉⠛⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⣠⣾⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⣠⣶⣿⠃⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣶⢻⣿⡿⢔⠂⠀⣽⣿⡇⣿⣿⣿⣶⣦⣤⣀⣠⣾⣿⣿⡏⠀⣿⣿⣿⣦⠀⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣶⠒⠘⠐⠂⢰⢐⠿⢏⣶⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⢀⢠⣹⣿⣿⣿⡆⠀⣵⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣄⢻⣯⣤⣤⣄⠉⠙⢻⣿⣇⣶⣿⡿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣀⠶⠜⠀⢜⣿⣿⣿⠇⣿⣿⡿⣿⣟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⡿⣿⠿⠯⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡀⠀⠀⢼⣿⠀⡿⡿⠀⣿⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠂⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢈⣦⣄⣧⢷⣞⣷⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⣿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⢻⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣼⣿⣿⢹⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣷⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣾⣼⣿⣿⣿⡯⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠉⡯⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⡃⣸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠁⠈⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢨⣦⣿⣏⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⣧⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣥⣿⣿⡿⠿⠻⣿⣿⣿⣷⣶⣤⣀⠐⣾⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢐⢜⣾⣿⣿⣯⡧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣍⣹⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠽⣿⣿⣿⡿⣻⡿⠺⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠖⣾⣿⣿⣾⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠛⠟⠋⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉⠙⠛⠉⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣠⣾⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣠⣾⣿⠃⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢶⢻⢿⢿⢈⡨⢆⣿⣿⡇⣿⣿⣿⣶⣦⣤⣀⣤⣾⣿⣿⡏⠀⣿⣿⣿⣆⠀⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣶⠒⠂⠊⡀⠤⠠⢿⣻⣴⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⢀⢠⣽⣿⣿⣿⡆⠀⣶⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣄⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣶⣿⡿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣃⠦⠀⠲⠺⣿⣿⣿⠃⣿⣿⡿⣿⣟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⡿⣿⠿⠯⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡒⠒⠤⢽⣿⠀⡿⡿⠀⣿⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠂⠂⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢀⣦⣄⣷⢷⣞⣷⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⣿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⢹⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠘⠿⣿⣶⣤⣀⠁⠚⢿⣷⣶⣿⣏⠙⣿⣿⣿⣼⣿⣿⢹⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣽⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣿⣿⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡠⣪⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠋⡯⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⡃⢸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⢦⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡗⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠜⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣰⣿⡏⡁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣴⣿⣿⣿⠿⠻⣿⣿⣿⣷⣶⣤⣀⠄⣮⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣑⣽⣾⣿⣿⣟⣗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣍⣹⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠞⡯⣿⣿⣷⣿⣿⡍⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠙⠛⠛⠛⠛⠛⠀⠀⢻⣿⣿⣿⡿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠙⠙⠛⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⢠⣾⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⣠⣾⣿⠃⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣶⣿⣿⠷⢀⢥⠀⣿⣿⡇⣿⣿⣿⣶⣦⣤⣀⣠⣾⣿⣿⡟⠀⣿⣿⣿⣆⠀⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣶⠒⠀⠬⡀⣤⠐⣟⣫⣼⣿⣿⡇⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⢀⣤⣽⣿⣿⣿⡆⠀⣶⣾⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣎⣶⣿⡿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣤⣁⠐⠎⡲⢜⣿⣿⣿⠇⣿⣿⡿⣿⣟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣿⣿⡿⣟⠿⠯⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣶⡐⠒⠀⢺⡿⠀⡿⡿⠀⣿⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⠂⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢈⣦⣄⣧⢷⣞⣷⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⣿⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠛⠻⣿⣿⣮⣿⣿⣝⠈⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠋⢹⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠘⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣼⣿⣿⢹⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣯⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣷⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠟⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠀⣸⣃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣄⢄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⡿⢿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠝⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣹⣿⡩⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣯⣶⣴⣿⣿⡿⠿⠟⠿⣿⣿⣷⣾⣤⣀⠔⣨⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣠⣿⣾⣿⣿⣇⡖⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠉⢹⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠸⡵⢷⣿⣿⣾⡯⡸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢛⣧⡯⣿⣿⣿⣷⡦⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠛⠛⠛⠙⠈⠀⠀⢻⣿⣿⣿⡿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠉⠛⠉⠙⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⢀⣴⡇⠀⣠⣴⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣶⣿⢿⣿⣂⡰⡅⢻⣿⡏⣿⣿⣿⣿⣛⡛⠁⠀⣀⣴⣿⣿⠃⠀⣿⣿⣿⣆⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣷⡆⠒⠀⠩⢻⣻⢏⢐⣘⣶⣻⣿⡇⢻⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣋⣀⣤⣽⣿⣿⣿⡀⣾⣾⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣇⣾⣿⡟⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣹⠭⢥⡤⡿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⡿⣿⡿⠏⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣮⡛⠽⣧⠿⠿⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢠⣧⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣽⠈⣿⣿⣿⡿⠸⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣍⣹⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡠⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡾⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⠀⢠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠟⣿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠀⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣄⢄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡿⢿⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠹⣻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣹⣿⣩⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣷⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣯⣶⣥⣽⣿⡿⠿⠿⠿⣿⣿⣷⣾⣤⣀⠀⣼⣿⠿⠿⠿⢛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣠⣿⣾⣿⣿⣎⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⠉⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠸⡵⢷⣿⣿⣿⡯⠹⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢛⣧⡯⣿⣿⣿⣿⠎⠈⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠛⠛⠛⠛⠉⠉⠀⠀⢻⣿⣿⣿⡿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠙⠋⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣴⡗⠀⣠⣴⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣶⣿⣻⣿⠼⡘⠄⣹⣿⡟⣿⣿⣿⣿⣛⡋⠁⠀⣀⣴⣿⣿⠃⠀⣿⣿⣿⣆⠀⠀⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡆⠐⠚⠓⣮⡜⣘⣳⣒⣷⣾⣿⡇⢻⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣋⢀⣤⣽⣿⣿⣿⡠⣾⣟⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣇⣾⣿⡿⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣺⠫⢭⣽⣽⣿⣿⣿⠃⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⡿⣿⣿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡟⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣮⡲⠬⣤⡿⠿⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⠒⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢁⣦⣄⣿⢹⣴⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣽⣿⣽⠈⣿⣿⣿⡿⠙⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣻⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡠⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣥⠾⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣦⣾⣿⣿⣿⣿⣿⣿⣿⠀⢀⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡥⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠀⣸⣃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠜⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣱⣿⡝⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣯⣶⣶⣿⣿⡿⠿⠟⢿⣿⣿⣷⣾⣤⣀⠀⣺⣿⠿⠿⠿⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢣⣶⣿⣿⣿⣵⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⠉⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣻⢿⢿⣷⢽⢸⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢛⣇⡯⣾⣿⣷⣿⡵⠀⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠚⠉⠛⠛⠋⠀⠀⠀⢻⣿⣿⣿⡿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉⠙⠋⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⢐⣺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣴⡗⠀⣠⣴⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡠⣶⣿⣟⣿⢷⠨⡇⢻⣿⡏⣿⣿⣿⣿⣛⡛⠉⠀⣀⣴⣿⣿⠁⠀⣿⣿⣿⣆⠀⠀⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣷⡆⠀⠀⠀⢭⠑⢇⣀⣇⣼⣿⣿⡇⢻⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣋⢀⣤⣽⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢿⣿⣇⣾⣿⡟⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣝⠛⠍⢚⢿⣿⣿⣿⠃⣽⣿⡿⣿⣿⠋⢿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡉⠻⡩⠽⠟⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⠃⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢠⣧⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠈⣿⣿⣿⣿⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠟⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⣸⡃⣸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⣰⣿⡷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⣾⣵⣷⣿⡿⠿⠟⣿⣿⣿⣷⣾⣤⣀⠔⣾⣿⠿⠿⠿⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣾⣿⣿⣯⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠉⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⢱⣿⣿⣿⣿⣿⡟⢼⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠞⡸⣿⣿⣯⣿⣿⡯⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠛⠛⠛⠛⠛⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⢀⣼⡇⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⡶⣿⡷⠤⠬⠀⠅⣼⣿⡏⣿⣿⣿⣿⣛⠛⠁⠀⣀⣴⣿⡟⠀⠀⣿⣿⣿⣆⠀⠈⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣶⡄⠀⠛⠠⠆⢽⠊⠥⢥⣤⣿⣿⡇⢿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠁⣀⣄⣹⣿⣿⣿⡀⣶⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡿⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣆⠭⠭⣔⠝⢿⣿⣿⠇⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⡇⣺⣿⣿⣿⣿⡿⣟⡽⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡋⠐⠁⠚⠛⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠢⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢠⣦⣄⣿⢹⣴⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠀⣿⣿⣻⣿⠉⢻⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⡀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⡇⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣼⣵⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢈⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣲⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠟⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⣸⣃⢸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⢴⣴⡥⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⣶⣥⣿⣿⡿⠿⠟⢿⣿⣿⣷⣾⣤⣀⠐⣾⣿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢜⣷⣾⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠉⢹⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡈⢫⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠗⡸⣿⣷⣿⣿⣿⡣⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⢀⣼⡇⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡴⣾⣷⠔⠻⠐⠀⣹⣿⡟⣿⣿⣿⣿⣛⠛⠁⠀⣀⣴⣿⣿⠁⠀⣿⣿⣿⣆⠀⠈⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡄⠀⠀⠘⢅⣖⠞⣐⢤⣠⣾⣿⡇⢿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠁⣀⣀⣹⣿⣿⣿⡀⣾⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡟⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣦⠄⠐⢪⡭⣿⣿⣿⠃⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣟⡻⠏⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡉⠚⠃⡛⠛⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠁⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢠⣦⣄⣷⢹⣜⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠂⣿⣿⣻⡿⠉⢻⣿⣿⣿⣿⣿⣿⣟⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⡇⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣼⣵⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢈⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣲⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠟⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⣸⣃⢸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠜⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣤⣶⣥⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⣶⣥⣿⣿⣿⠿⠟⢿⣿⣿⣷⣾⣤⣀⠐⣺⣿⠿⠿⠿⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢼⣶⣿⣿⣿⣗⡗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠉⢹⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡈⢫⣿⣿⡿⣿⣿⡿⠾⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠗⡸⣿⣿⣿⣿⣿⡭⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣼⡇⠀⣠⣶⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡶⣾⡧⠠⢠⠆⡁⢸⣿⡟⣿⣿⣿⣿⣛⠛⠁⠀⣀⣴⣿⡟⠀⠀⣿⣿⣿⣆⠀⠈⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡄⠀⠀⠨⠑⢆⠈⡬⣋⣤⣾⣿⡇⢿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠁⣀⣄⣽⣿⣿⣿⡀⣶⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡟⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣦⠀⠺⠏⣘⣿⣿⣿⠃⣾⣿⡿⣿⣿⠋⢿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⡿⣿⣿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡘⠃⠀⡉⠛⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠁⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢀⣦⣄⣷⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠂⣿⣿⣿⡿⠉⢻⣿⣿⣿⣿⣿⣿⣟⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣾⣿⡇⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣼⣵⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢈⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣲⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠟⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⣸⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢐⣶⣾⣥⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣷⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⣶⣦⣿⣿⡿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠀⣾⣿⠿⠿⠿⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢜⣿⣾⣿⣿⣯⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡉⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡈⢫⣿⣿⢿⢿⡿⡿⠿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⡸⣿⣿⣿⣽⣿⡭⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⠛⠛⠛⠛⠀⠀⢿⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⢀⣼⡇⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⡶⣾⡧⠀⠈⠘⠃⢹⣿⡏⣿⣿⣿⣿⣛⠛⠁⠀⣀⣴⣿⡟⠁⠀⣿⣿⣿⣆⠀⠈⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡄⠀⠂⠨⠍⣽⡠⣭⢀⣠⣿⣿⡇⢿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠁⣀⣤⣽⣿⣿⣿⡀⣾⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣾⣿⡿⣿⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣤⣪⠭⠡⣗⣙⣿⣿⣿⠇⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⡿⣟⡿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⡉⠉⠐⠛⠟⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠐⠃⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠀⠀⢠⣦⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⢻⣿⣷⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠊⣿⣿⣿⡿⠉⢻⣿⣿⣿⣿⣿⣿⣟⣿⡿⢿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣾⣾⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⣿⣿⣿⣿⣿⣇⠀⠐⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣹⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⣸⡃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⡠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢐⣲⣾⣷⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢼⣯⣶⣤⣿⣿⣿⠿⠟⢿⣿⣿⣷⣶⣤⣀⠀⣸⣿⠿⠿⠿⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣤⣾⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠈⢹⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡘⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡝⣺⣿⣿⣿⣿⣿⡯⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠙⠛⠛⠛⠛⠛⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠋⠉⠉⠉⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢰⡇⠀⣀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⡶⢾⣗⣰⡽⠋⣇⣻⣿⡏⣿⣿⣿⣿⣿⡛⠛⠉⠀⣠⣴⡟⠀⢘⣿⣿⣧⠀⠀⠈⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣥⡀⠐⠓⠰⣴⠿⢊⡁⣦⣾⣿⣿⡇⢿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠃⢀⠸⣿⣿⣿⣇⠠⣷⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣷⢒⢓⣢⣿⣿⣿⣿⠇⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣧⣶⣿⣿⣽⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣿⠿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣷⣼⣿⣿⠛⠿⣿⣦⡛⢝⠻⠟⠛⠀⡏⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⠘⠃⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠋⠒⢣⣦⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠂⣿⣿⣻⣿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣘⣾⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣾⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣵⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣹⡿⣿⠉⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠉⣼⡃⡸⣿⢿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢀⣆⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠝⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣼⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢴⣯⣶⣤⣿⣿⣿⠿⠿⡿⣿⣿⣷⣾⣤⣀⠀⣸⣿⠿⠿⠿⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢄⣼⣿⣿⣿⣷⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣨⢺⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣮⣪⣿⣿⣽⣿⣿⡯⠁⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠑⠙⠛⠛⠛⠛⠋⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢠⡇⠀⣀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡠⣶⣻⢿⢿⠒⣭⣫⣿⣿⡇⣿⣿⣿⣿⣿⡛⠛⠉⠀⣀⣴⡏⠀⢘⣿⣿⣇⠀⠀⠈⣳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⡐⠃⠙⠡⣺⠾⢏⣓⣓⣸⣿⣿⡇⢿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠁⢀⠸⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣫⠿⡭⢽⣿⣿⣿⣿⠇⣾⣿⡿⣿⣿⠋⢿⣿⣿⣿⣷⣶⣿⣿⣽⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣿⣿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣷⣼⣿⣿⠛⠿⣿⣮⡑⣽⠿⠟⠛⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⠘⠠⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠙⠛⢣⣦⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠀⣿⣿⣻⣿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⠅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣵⣶⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣿⣿⣿⣿⡇⠀⠀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣨⡿⡟⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠉⣼⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢄⣼⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣦⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢴⣯⣶⣥⣿⣿⡿⠿⠿⠿⣿⣿⣷⣾⣤⣀⠀⣾⣿⠿⠿⠿⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢤⣼⣿⣿⣿⣯⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣨⢸⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣮⣹⣿⣿⣿⣿⣿⡯⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠑⠛⠛⠛⠛⠙⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠙⠉⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢠⠇⠀⣀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡠⣴⣻⢽⢿⣯⡵⠳⣽⣿⡇⣿⣿⣿⣿⣟⡛⠛⠉⢀⣀⣴⡟⠀⢘⣿⣿⣇⠀⠀⠈⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣥⡰⠖⠋⠻⢮⣗⡝⠥⣶⣼⣿⣿⡇⢿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠃⢀⠸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣇⣿⣿⡟⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣺⠯⠎⢙⣿⣿⣿⣿⠇⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣿⣶⣿⣿⣽⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣿⣿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣼⣿⣿⠛⠿⣿⣾⣍⢩⣿⠟⠛⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⡐⠡⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠁⠈⢡⣦⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠀⣿⣿⣻⡿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣾⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣾⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣷⣾⣿⣿⣿⡇⠀⠈⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣦⣶⣿⣿⣿⣿⣿⣿⣧⠀⢨⣅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡧⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣩⡿⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠉⣼⣃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣸⣷⡻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣢⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢴⣯⣶⣧⣿⣿⣿⠿⠟⣿⣿⣿⣷⣶⣤⣀⠔⣼⣿⠿⠿⠿⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠴⣤⣿⣿⣿⡏⣗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢸⣿⣿⡿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣺⣭⣯⣟⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠘⠛⠛⠛⠙⠙⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⣠⡇⠀⣀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⢴⣿⡼⢿⣯⡬⢹⣻⣿⡇⣿⣿⣿⣿⣿⡛⠛⠉⠀⣀⣶⡏⠀⢘⣿⣿⣇⠀⠀⢈⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⡐⠃⠈⠲⣛⡭⠯⣙⣄⣸⣿⣿⡇⢻⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⠁⠀⠸⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣇⣿⣿⡿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⣫⢡⠼⣻⣿⣿⣿⠃⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣿⣿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣼⣿⣿⠛⠿⣿⣾⡝⢿⣿⡟⠛⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⠘⠠⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠒⠀⢠⣦⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠀⣿⣿⣻⣿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣾⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣷⣾⣿⣿⣿⡇⠀⠈⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣦⣶⣿⣿⣿⣿⣿⣿⣧⠀⢨⣅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡧⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣩⡿⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠉⣼⣃⠸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣸⣷⡻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣢⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢴⣯⣶⣧⣿⣿⣿⠿⠟⣿⣿⣿⣷⣶⣤⣀⠔⣼⣿⠿⠿⠿⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠴⣤⣿⣿⣿⡏⣗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢸⣿⣿⡿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣺⣭⣯⣟⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠘⠛⠛⠛⠙⠙⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠙⠉⠉⠋⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣠⠇⠀⣀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡠⣶⣿⣜⣿⠑⣩⢿⣺⣿⡇⣿⣿⣿⣿⣟⡛⠛⠉⠀⣀⣴⡟⠀⢘⣿⣿⣇⠀⠀⢈⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣦⡐⠎⠀⠲⣻⠿⡾⢞⢵⣻⣿⣿⡇⢿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⠃⢀⠸⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣯⣤⣤⣄⠉⠙⢻⣿⣇⣿⣿⡿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⡿⠶⣝⣻⣿⣿⣿⠃⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣷⣶⣿⣿⣽⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣿⣿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣦⣅⣦⣿⡟⠛⠀⡟⣿⠁⢹⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⡐⠣⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠉⠁⢢⣦⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠀⣿⣿⣻⡿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣵⣰⣾⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢢⣶⣾⣿⣿⣿⡇⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣰⣯⣿⣿⣿⣿⣿⣿⣧⠀⢠⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣹⡿⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠉⣼⡃⡸⣿⢿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣇⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣸⣾⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣧⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢴⣯⣶⣧⣿⣿⣿⠿⠿⣿⣿⣿⣷⣶⣤⣀⠔⣼⣿⠿⠿⠿⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠴⣤⣿⣿⣿⡟⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢸⣿⣿⡿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⢺⣭⣯⣾⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠈⠛⠛⠛⠚⠙⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠙⠉⠉⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣀⡇⠀⣀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡠⣶⣿⡽⣿⠫⡥⢝⢸⣿⡇⣿⣿⣿⣿⣿⡛⠛⠉⠀⣠⣴⡟⠀⢘⣿⣿⣇⠀⠀⢀⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣦⡐⠞⠛⠹⢺⣓⣽⡿⣟⣻⣿⣿⡇⢿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⠁⠀⠸⣿⣿⣿⣇⠠⣷⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢿⣿⣆⣿⣿⡿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣿⠡⢄⣽⣿⣿⣿⣿⠃⣿⣿⡿⣿⣿⠋⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣿⣿⠯⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡏⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣷⣼⣿⣿⠛⠿⣿⣮⣩⢹⢿⠟⠛⠀⡟⣿⠁⢸⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⠐⠤⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠑⠂⢣⣦⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠀⣿⣿⣻⣿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣶⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣐⣾⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣧⠀⢀⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣨⡿⡿⠈⣩⣽⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⣼⡃⡸⣿⣿⠇⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠂⡂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣇⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⢿⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠍⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣨⣿⡙⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣯⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢴⣯⣶⣧⣿⣿⣿⠿⠿⣿⣿⣿⣷⣾⣤⣀⠀⣺⣿⠿⠿⠿⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢔⣦⣿⣿⣿⡴⣎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢹⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢸⣿⡿⢿⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⣺⣿⣯⣯⣿⣿⡧⠁⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠙⠛⠛⠛⠚⠋⠀⠀⢿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠼⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢠⠇⠀⣀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⢶⣻⢟⣿⠓⠥⣏⣽⣿⡇⣿⣿⣿⣿⣟⡛⠛⠉⠀⣀⣴⡏⠀⢘⣿⣿⣇⠀⠀⠈⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡇⠀⢀⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣧⡀⠆⠛⠩⣽⡪⣭⣥⢃⣾⣿⣿⡇⢿⣿⣿⣿⣛⣻⣿⣿⣿⣿⡿⠁⢀⠸⣿⣿⣿⣇⠀⣷⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⠀⣀⣀⣤⣤⢻⣭⣤⣤⣄⠉⠙⢻⣿⣆⣿⣿⡿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣤⣞⠵⠾⢼⢿⣿⣿⣿⠃⣾⣿⡿⣿⣿⠋⢿⣿⣿⣿⣷⣶⣿⣿⣽⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣿⣿⠏⠉⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣇⣿⣿⡟⠛⢸⣿⡟⣿⣿⡿⣷⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢙⣿⣿⣷⣬⣿⣿⠛⠿⣿⣮⣭⢡⠿⠟⠛⠀⡟⣿⠁⢹⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⠘⠡⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⡏⢸⣿⣷⣶⢸⣿⣷⣿⣿⣇⣀⢹⣿⣿⣿⣿⡇⣿⣿⣻⣿⡿⣿⣿⡏⠙⣿⣿⣶⣦⣄⡉⠓⠁⠈⢠⣦⣄⣿⢹⣼⣯⣿⡀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡏⣿⣿⢸⣿⣿⣀⣸⣿⣿⣿⣿⡟⠋⢸⣿⣿⢸⣿⣇⣿⣿⣻⣿⣿⢻⣿⡇⠀⣾⣿⣌⠙⠻⢿⣷⡆⢀⡈⠙⠻⣿⣿⣦⣿⣿⣝⠀⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣷⡿⢿⠾⠿⣿⣿⣿⡿⠿⠛⠿⠇⠀⠘⠛⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡈⠐⠿⣿⣶⣤⣀⠁⠘⢿⣷⣶⣿⣏⠙⣿⣿⣿⣴⣿⣿⣿⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
䷩ 𝚕𝚒𝚗𝚎 1722
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/02/irc-log-010222/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/02/irc-log-010222/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ IRC_Proceedings:_Tuesday,_February_01,_2022⠀✐
Posted in IRC_Logs at 2:28 am by Needs Sunlight
Also available via the Gemini protocol at:
* gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-010222.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-010222.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-social-010222.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-010222.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
QmTbbJTLsuocaQdNBqMoxuzxUzWQ6WL9TvutFmNCxZH7PY #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell
QmVSDV8PizHf9JEjaGh7Yj4HoX6vhvAsjUotXwR96AAVVT (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
#boycottnovell-
Qmaq2FoeXuCaPxPrw8xBhFhcoJk5oicpFdW7PqsD7QwENF social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#boycottnovell-
QmQ9E4iSqqTPYEmZHRkJ2qkQYSJQaExfgHb3FtieJnvA5Z social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
(full IRC log
as plain/ASCII
text)
IRC log for
QmUotrz7nTZsghj67nNnNpYuso51Pc2tUcFzSe4CKxN53e #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techbytes
Qmc6yEioiXfk4rjB33jxucvxZA732wCQS4EYNHEDfyqY6M (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
IRC log for
QmTTZMiRLUGvg9szBeZPj2DDtPgcAwT7xug8xi7fwDY2aK #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
(full IRC log
as HTML)
IRC log for
#techrights
QmWSYCk7AyR1enUwdtjDLYq38ivew2cZkhLrg2j48Ju34X (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
as plain/ASCII
text)
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈
§ Bulletin for Yesterday⠀➾
Local_copy | CID (IPFS): QmS1wrYoYvTPNPTvZYppVeYPXTR8rHjtMkwCEYGCEaEWUU
䷩ 𝚕𝚒𝚗𝚎 1849
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/02/lets-talk-linux-com/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/02/lets-talk-linux-com/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Linux.com_Used_to_Clock_Millions_of_Hits_Every_Week,_But_Linux_Foundation_Can
Barely_Keep_Thousands⠀✐
Posted in GNU/Linux, Kernel, Marketing at 3:47 pm by Dr. Roy Schestowitz
Let’s Talk… about what happened to Linux.com over the past 3 years
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Linux.com hit⦈
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Go away, Linux users⦈
Summary: After the Linux_Foundation attacked Linux.com by firing all the staff
and all the editors we’re left with a site called Linux.com that makes Linux
look insignificant, often misused for Spamnil’s crude, self-promotional
activities [1, 2]
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣻⣫⣹⢻⣍⣥⣭⣻⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣄⠀⠈⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠉⠙⠈⠑⠁⠙⡏⠀⠀⣾⣿⣿⣿⣿⣿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⣡⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣟⡈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⠿⠿⠿⠿⠿⠛⢛⣓⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣻⣫⣽⢻⣍⣥⣭⣻⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣄⠀⠈⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣆⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⡿⠟⠏⠁⠀⠁⠹⠿⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣻⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣿⣿⣿⣶⣦⣀⡀⠀⠉⠉⠉⠙⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠷⠿⠛⠛⠛⢛⣋⣉⣭⣭⣤⣦⠤⠤⠀⠀⠀⠀⠀⣠⣄⣈⣉⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣻⣫⣹⢻⣍⣵⣭⣿⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣆⠀⠈⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⡿⠟⠋⠟⠛⠯⠿⠹⡿⠑⢸⣿⣿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⣈⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠛⠉⠉⣉⣩⣽⣽⣿⣿⣿⣿⣿⣿⣇⣄⣀⣄⣴⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣻⣫⣹⢻⣍⣵⣭⣿⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣆⠀⠈⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣼⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠟⠛⠿⠍⠋⠻⠻⡿⠋⢸⣿⣿⣿⣿⣿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡜⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡿⠹⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡉⠙⠛⠛⠛⠛⠛⠛⠛⠟⠙⠛⠻⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⢠⣤⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⢉⣩⣽⣿⣿⣿⣿⣿⣿⣿⡟⢀⣀⣀⣀⣀⣀⣈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣻⣫⣹⢻⣍⣥⣭⣻⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠟⠝⠀⠉⠀⠊⠉⠯⠁⣿⣿⣿⣿⣿⣿⡎⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡈⢧⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣆⡉⠉⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣭⣉⠉⠁⠉⠉⠉⠀⠈⠙⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣷⣶⣶⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠋⠋⠉⣥⣬⣽⣿⣿⣿⣿⣿⣿⣿⠇⠀⠚⠛⠹⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢊⡷⢆⣀⣰⣦⡤⣠⠶⠠⢾⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡃⢀⣾⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣛⣫⣹⢻⣍⣥⣭⣹⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠟⠛⠿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠛⠛⠟⠛⠿⠟⠛⠿⠿⠛⠛⠿⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⠻⢿⡿⠈⠩⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡏⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠉⢹⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⠈⢷⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣭⣍⣉⣉⣉⠙⠛⠛⠛⠋⠙⠛⠻⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢻⣿⣿⣿⣷⣶⣿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠚⠛⢹⢿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣯⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣛⣫⣹⢻⣍⣥⣭⣹⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠿⠿⠿⠿⠿⠟⠟⠛⠟⠟⠻⠻⠛⠛⠛⠛⠛⠟⠟⠟⠛⠛⠿⣿⡿⠿⠿⠛⠀⠀⠀⠀⠀⠄⠃⢸⣿⣿⣿⣿⣿⣿⠏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⢸⢹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⢶⠍⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣟⡿⠿⠿⠿⣿⠻⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣹⣿⣿⣿⣿⣿⣶⣶⣄⢴⣶⣶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢛⣻⠿⠿⠿⢿⡿⠁⠀⠀⠉⠀⠛⠻⣿⣿⣿⠿⡿⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⢀⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢐⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡧⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠇⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⣿⣷⡄⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠋⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢻⣿⡇⣿⣿⣿⣿⣹⣿⢸⣿⣷⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣻⣿⣿⢻⣤⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡀⢿⡽⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢒⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠃⠘⡇⠹⡎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣦⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣻⣀⣑⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⢙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⡍⠻⡙⢟⠛⠛⠉⠛⠛⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢦⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⢤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⣙⣈⣶⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣀⣥⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀
⢠⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀
⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡣⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣥⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⡇⢨⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⢼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣦⣬⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣷⣾⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣿⣿⣿⢿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⣿⣶⣿⣷⡄⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠀⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⡿⣿⣿⣿⡿⣿⢿⣿⣿⢿⢿⡏⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⢿⣿⡿⢿⠿⠿⠟⢹⣿⡇⢸⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣷⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡶⠀⢹⡏⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣷⡾⠃⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷⠿⠿⠿⠏⠀⠀⠀⠀⠀⠁⠈⠛⠻⣟⠿⡟⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⢦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡀⠀⠀⢀⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣦⣴⣶⣆⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⣉⠁⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢀⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀
⣂⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣄⡀⠀⠀
⣭⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡰⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣯⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⡇⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⣿⣦⣝⣷⡄⠀⠀⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠈⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢷⣿⡿⢿⣿⡏⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⢿⣿⠟⠿⠿⠿⠟⢹⣿⡇⢸⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣷⣶⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣄⣤⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⠉⢿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣼⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⡧⠿⠼⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣦⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠏⠀⠀⠀⠀⠀⠋⠙⢿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣇⡟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉⠉⠁⠀⠀⠀⣠⡤⠀⠀⠈⠓⠀⠀⠀⠀⠑⢄⠱⡌⢻⣿⣿⣿⣿⣶⣯⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠂⠘⣆⠹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣆⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣶⣦⣶⣶⡄⠀⠙⠛⠛⠛⠛⠛⠛⠻⠛⠟⠿⠿⠛⠛⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢀⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀
⣕⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⣀⠀⠀
⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡥⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⢿⣳⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣌⢻⣆⠀⠀⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢻⣿⣿⣾⣿⠀⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢷⣿⣿⠿⣿⡝⠀⠟⠃⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⢿⣿⢿⢿⡿⠿⠟⢹⣿⡇⢸⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣷⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠞⠛⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣼⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⡾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠸⣿⣿⣿⣥⡤⠶⠟⠛⠁⠀⠀⣀⣀⠀⠀⠈⠙⠻⡿⠿⡟⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣦⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⣦⡀⠀⠀⠀⢀⠘⢄⠻⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⣿⣷⠿⠙⠳⣆⠀⠀⠁⡈⢢⡘⣿⣿⣿⣿⣿⣼⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢟⡛⠁⠀⠀⠁⠀⢠⣆⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣯⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣶⣿⣶⣆⠀⠘⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢀⡥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⡄⠀⠀⠀⠀
⠔⢻⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⠀⠀⠀
⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣭⣶⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⡇⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⢿⣗⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⣬⡻⢦⠀⠀⠉⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠀⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣧⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⠿⣿⡿⠀⠟⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⣿⠿⠿⠿⠿⠟⢹⣿⡇⢸⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣷⣶⣷⣶⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠟⠉⡝⠉⢩⡿⢻⣦⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⣿⣿⠃⠀⠀⠀⠀⠚⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣷⠴⠾⠛⠁⠀⠀⠀⢠⣀⠀⠀⠀⠙⠛⠻⣏⠻⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⢀⠘⢦⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣦⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣆⠀⠀⠀⢀⠐⣄⢻⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣶⣿⣿⣿⣿⣷⢄⡀⡌⢡⣀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢩⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢟⠛⠛⠋⠁⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣾⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣷⣾⣷⣿⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢰⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⡀⠀⠀⠀
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢇⡀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⡀⠀
⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣧⣶⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⡇⠨⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⣾⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡟⢴⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣦⡙⢦⠀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠀⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⢿⢾⣿⡿⢿⣿⡿⠀⠟⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣿⡟⠻⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⢿⠿⠿⠿⡿⠿⢿⡿⢻⣿⡇⢸⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣷⣶⣶⣶⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠋⠀⡚⠀⣰⠏⢨⣽⣧⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠈⠟⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣼⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠟⠛⠉⠁⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠳⣈⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⡀⠀⠀⠢⠈⠂⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣦⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠈⠢⡐⠦⡙⢂⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢶⣿⣿⣿⣿⣿⣤⣾⡦⣱⣮⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⠀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢚⢻⡋⠙⠛⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⣿⣿⣿⣿⣿⣷⣿⠀⠈⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡤⠀⠀⠀⠀
⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡗⣨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡇⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢚⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣦⡙⢦⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣾⣿⠀⣧⡅⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⢿⣿⠿⠿⣿⡿⠀⠟⠃⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠟⢉⡉⢉⠽⠛⠛⠻⠿⠙⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⢿⠿⡿⣿⢿⠟⠿⠟⢹⣿⡇⢸⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣷⣶⣷⣶⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡄⠘⡴⣾⣷⣶⣤⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢶⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⣛⠛⠛⠛⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢰⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣷⣥⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡷⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⢴⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣦⡙⢧⡀⠀⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠀⣧⡌⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢠⣿⣿⣱⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡿⠂⠟⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠉⠠⠀⠈⠁⠀⠀⠀⠀⠸⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⣿⠿⠿⠿⣿⠟⢿⡿⢹⣿⡟⢸⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣷⣶⣷⣶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⢛⡛⠋⠛⠛⠉⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠀⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣽⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡋⢀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠋⠈⢈⣦⡙⢧⡀⠀⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠘⣯⡕⠁⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠿⠿⠿⠟⠁⠀⠀⠀⣽⣿⣿⣱⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠟⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠋⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢻⣿⡇⣿⣿⣿⣿⣹⣿⢸⣿⣷⣾⣿⣶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⡛⠛⠙⠛⠋⠉⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠉⠀⠀⢰⣦⡙⣳⡀⠀⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠉⣿⡅⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⢋⠉⠉⠉⠀⠀⠀⠀⠊⠉⠻⣵⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠂⠿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⣶⣶⣾⣿⣯⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⡿⠿⣿⢿⢹⣿⡏⢸⣿⡇⣿⣿⣿⣿⣹⣿⢸⣿⣿⣶⣷⣶⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⢠⣤⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⡛⠋⠙⠛⠋⠉⠁⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠀⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢦⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠢⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⡀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡖⡐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡡⢤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣽⣭⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣽⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⢻⠓⡠⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣤⡙⢷⡀⠀⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡐⣭⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠉⠀⠐⠁⠀⠀⠀⠀⠁⠉⠑⢳⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠇⠀⠀⠀⠀⢀⣀⣤⣤⡤⠀⣾⣿⣶⣿⣯⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢿⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣿⣶⣿⣶⠂⠀⠀⠀⠀⠀⠀⣼⡿⠿⠛⠀⠀⠀⠀⢀⡀⢹⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⢠⣤⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢛⡛⠋⠙⠛⠋⠉⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢢⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⣿⣿⣾⡀⠀⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣧⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡗⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣿⣿⣿⣿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠤⡀⠀⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠘⣽⡄⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡟⠋⠩⠁⠀⠉⠀⠀⠀⠀⠈⠀⠀⠱⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠃⠟⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⠀⢀⡀⣠⣤⡤⠐⣾⣿⣷⣿⣧⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⣿⡿⣿⠿⡿⡿⠿⢿⢹⣿⡇⢼⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣷⣶⣷⣶⠂⠀⠀⠀⠀⠀⠀⣾⣿⠿⠟⠁⠀⠀⠀⠀⡀⢸⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⢠⣤⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣦⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢛⡛⠛⠙⠛⠋⠉⠁⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣾⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⣿⣿⣾⡀⠀⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣺⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡿⢿⠟⠛⠂⠉⠀⠙⠳⠀⠀⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠋⣯⡅⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡟⠋⣠⠞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆⠿⠃⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠁⢺⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⡟⢻⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣿⣶⣿⣶⠂⠀⠀⠀⠀⠀⠀⣿⠟⣻⠿⠃⠀⠀⠀⠀⡀⢻⣿⣿⣷⣶⣤⣤⣉⢑⣴⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠐⠗⠉⠀⠀⠀⠀⡠⠒⠋⢠⣈⣹⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢚⡛⠛⠛⠛⠛⠉⠁⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣆⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣿⣿⣷⣿⣿⣷⣾⡀⠀⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀
[22A⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣚⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣥⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢥⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⣽⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣽⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⣻⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣾⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡧⡅⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⠟⣻⠟⠛⠋⠛⠂⢩⣷⡀⠀⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠹⣯⡍⠁⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⠟⠉⠘⠃⠀⠃⠀⠀⠀⠀⠈⠲⣍⠓⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠃⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⡏⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠐⠠⠀⠉⠲⣬⡉⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢿⣿⡏⣿⣿⣿⣿⣽⣿⢸⣿⣿⣾⣿⣶⠀⠀⠀⠀⠀⠀⢠⣿⠏⣻⡾⠋⠀⠀⠀⠀⡀⢿⣿⣷⣦⣤⣤⣀⡐⢦⣀⣐⠆⢈⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠉⠁⠉⠁⠁⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠸⠗⠊⠁⠀⠀⠀⡠⠒⠋⢀⣈⣿⣿⣿⢻⣿⣿⣿⣷⣄⣝⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢚⡛⠛⠛⠛⠋⠉⠁⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⣆⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢦⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⣿⣿⣿⣿⣿⣷⣾⡀⠀⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣅⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣿⣭⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠛⢻⠛⠛⠋⠛⠂⢙⣷⡀⠀⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠘⣯⡄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠁⠈⠁⠀⠊⠀⠀⠀⠀⠈⠳⣍⠓⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠂⠿⠃⠀⠀⠀⠀⠀⢀⣶⣿⢿⣿⡏⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠠⢀⠙⠲⢬⡉⠻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⣿⡿⣿⠿⠿⢿⡿⣿⢹⣿⡏⢸⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣷⣶⣷⣶⠀⠀⠀⠀⠀⠀⢠⣿⠏⣻⡾⠉⠀⠀⠀⠀⠀⢿⣿⣿⣦⣤⣤⣀⡒⠦⣀⣐⠢⢈⣙⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠸⠇⠈⠁⠀⠀⠀⡠⠒⠋⢀⣈⣻⣿⣿⢻⣿⣿⣿⣷⣄⣙⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣦⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢚⠛⠛⠛⠛⠋⠉⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠀⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣆⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢲⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⣿⣿⣿⣿⣿⣷⣾⡀⠀⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣾⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⢿⠟⠉⡜⠉⠉⠀⠛⢂⣙⣷⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠘⣽⡅⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⢷⡍⠓⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠂⠿⠃⠀⠀⠀⠀⠀⢠⣾⣿⢿⣫⠃⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠄⡈⠓⢢⡘⠻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⣿⡿⣿⠿⠿⣿⡿⣿⢹⣿⡇⢸⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣷⣶⣿⣶⠂⠀⠀⠀⠀⠀⢀⡿⠏⡿⠟⠀⠀⠀⢀⣠⠌⢻⣿⣿⣦⣦⣤⣀⠲⣄⡀⠦⠍⠃⢾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠸⠃⠁⠀⠀⠀⢀⠤⠛⠋⢠⣈⣹⣿⣿⢹⣿⣿⣷⣬⡙⣷⣦⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠈⠉⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢷⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢚⣛⡛⠛⠛⠉⠉⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣆⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢦⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣿⣿⣿⣿⣾⣷⣾⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣅⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣽⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⢿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣾⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⡻⢁⠜⠉⠉⠀⠉⠀⠙⠳⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠉⣯⡅⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⠃⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡅⠿⠃⠀⠀⠀⠀⠀⣠⣾⡿⣻⡟⠃⠀⠀⠀⠀⣴⣦⣀⡀⠀⠀⣀⠐⠂⣀⣀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⣿⣿⣿⣿⡿⣿⡿⢿⢿⣿⡏⢹⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣿⣶⣷⣶⠀⠀⠀⠀⠀⠀⠀⡿⠋⠔⠋⠀⠀⠀⢀⣤⠆⢻⣿⣿⣿⣷⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠴⠋⠉⢠⣈⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⢛⡛⠛⠛⠛⠋⠉⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⣦⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⣿⣷⣾⡀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣥⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠿⢟⠟⠛⠉⠀⠁⠀⠀⠀⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢱⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠂⠿⠃⠀⠀⠀⠀⠀⣠⣾⡿⣻⡟⠃⠀⠀⠀⠀⢠⣶⣴⣶⡦⠀⣤⣄⡀⠉⣢⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⡏⢺⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣿⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⡟⠉⠐⠉⠀⠀⠀⠀⣠⠄⢻⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠉⢠⣬⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⡛⠛⠙⠛⠉⠉⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢦⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⣿⣷⣾⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀
[22A⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣽⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⢀⡘⠳⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⡌⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠱⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠿⠃⠀⠀⠀⠀⠀⢀⣾⡿⣻⡟⠃⠀⠀⠀⠀⢀⣤⣤⣶⡤⠀⣶⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⢹⣿⡇⣿⣿⣿⣿⣽⣿⢹⣿⣿⣶⣿⣶⠂⠀⠀⠀⠀⠀⠀⡟⠹⠜⠉⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⢠⣬⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⣻⠛⠙⠛⠉⠉⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⣿⣷⣾⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣯⡁⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣼⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⢠⡈⠳⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠑⣯⡅⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠂⠟⠃⠀⠀⠀⠀⠀⢀⣾⡿⣻⡿⠃⠀⠀⠀⠀⢀⣤⣶⣶⡤⠀⣶⣶⣶⣿⣧⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⠿⠿⡿⢿⣿⡏⢻⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣿⣶⣷⣶⠂⠀⠀⠀⠀⠀⠀⡿⠫⠴⠋⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣷⣴⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⢠⣤⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠀⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⡻⠛⠙⠛⠉⠉⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⣿⣷⣾⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣦⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢿⠿⠋⠀⠀⠀⢀⡈⠳⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠛⣯⡅⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠟⠉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠛⠑⣵⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠃⠿⠃⠀⠀⠀⠀⠀⢀⣴⣿⢻⡿⠇⠀⠀⠀⠀⢀⣤⣲⣦⡄⠀⣤⣶⣦⣾⣧⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢻⣿⡏⢻⣿⡏⣿⣿⣿⣿⣹⣿⢸⣿⣿⣶⣿⣶⠂⠀⠀⠀⠀⠀⠀⡿⢋⠴⠋⠀⠀⠀⠀⢀⠀⢺⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⢠⣬⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⣛⠛⠛⠛⠋⠉⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⣿⣷⣾⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀
⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣅⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣿⣤⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⠛⠃⠉⠀⠀⠀⠀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠈⣯⡄⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠟⠉⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠂⠟⠃⠀⠀⠀⠀⠀⢀⣶⣿⢿⡿⠏⠀⠀⠀⠀⢀⣀⢀⣄⠀⠀⡀⠀⠀⠙⢥⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⡿⣿⣿⢿⣿⠿⠿⠿⢻⣿⡇⢸⣿⡇⣿⣿⣿⣿⣹⣿⢸⣿⣷⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⡿⢛⡵⠛⠀⠀⠀⠀⢀⠀⢻⣿⣿⣿⣷⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⢠⣈⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⡛⠋⠙⠛⠋⠉⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣿⣷⣾⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⣻⠿⠿⠏⣿⣦⡉⠳⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⣯⡍⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠋⠁⠴⠃⠰⠁⠀⠀⠀⠀⢦⠀⠑⠳⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃⠿⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⢄⠈⠂⠀⠀⠀⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡯⢻⣿⡏⣿⣿⣿⣿⣽⣿⢸⣿⣿⣶⣿⣶⠂⠀⠀⠀⠀⠀⢀⡿⢟⡽⠟⠀⠀⠀⠀⣀⠄⢻⣷⣤⣄⡀⢄⠑⠄⠀⢰⣶⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠠⠚⠉⢠⣈⣿⣿⣿⢹⣆⠠⢄⠺⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡞⣿⣷⣬⣷⣐⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⡻⠋⠙⠛⠉⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠰⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣿⣷⣾⡀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡗⣱⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⣻⠿⢿⡇⣿⣦⡉⠱⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠉⣿⡍⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠋⢀⠼⠁⢰⠁⠀⠀⠀⠀⢧⠙⠵⣷⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠂⠟⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠈⠣⡀⠀⠀⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⢿⣿⡏⢹⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣿⣶⣷⣶⠂⠀⠀⠀⠀⠀⠀⡿⢟⡿⠛⠀⠀⠀⠀⣀⠄⢻⣷⣄⡀⠀⢀⠑⢤⡐⠈⢦⣀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠠⠚⠉⢠⣈⣿⣿⣿⢻⣄⠡⣀⠸⡆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡞⣿⣷⣬⣶⣄⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⡻⠋⠉⠛⠉⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠰⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣿⣷⣾⠀⠘⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⡿⠋⣻⠟⢿⡟⣿⣦⡉⢳⡀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣥⡌⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⠉⠀⠞⠁⠸⠁⠀⠁⠑⠻⣿⠻⢵⣷⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠃⠿⠃⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠁⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⢧⠀⠉⠻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡟⢹⣿⡇⣿⣿⣿⣿⣽⣿⢸⣿⣿⣾⣿⣶⠂⠀⠀⠀⠀⠀⠀⡿⣟⡿⠟⠀⠀⠀⠀⣀⠄⢿⣷⣄⡀⠀⠈⠢⡠⡁⠐⢦⣀⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⢀⠠⠚⠉⢠⣈⣿⣿⣿⢲⣌⠂⠈⠠⡄⠈⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠁⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡞⣿⣷⣄⣥⡀⢕⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢛⡛⠋⠙⠛⠋⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠰⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣿⣷⣾⡀⠈⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣥⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⡿⠋⣻⠟⠿⡿⣿⣦⡙⢦⠀⠀⠉⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠉⣯⡅⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⠋⠀⠞⠁⠘⠁⠀⠀⠀⠀⢎⠑⠱⠷⡀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⣿⣿⠁⠿⠃⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠁⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣻⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡏⢻⣿⡇⣿⣿⣿⣿⣽⣿⢸⣿⣿⣶⣿⣶⠂⠀⠀⠀⠀⠀⠀⡿⢟⡿⠟⠀⠀⠀⠀⣀⠄⢿⣷⣤⣀⠀⠀⠀⢱⣄⠀⠻⣿⣿⣿⣿⣿⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⠀⠠⠚⠉⢠⣘⣿⣿⣿⢳⣄⠀⢦⡈⣳⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡞⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⢛⡛⠛⠛⠛⠋⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣆⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣿⣷⣾⠀⠘⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣥⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡗⣼⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣦⡙⢦⠀⠀⠉⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠉⣯⡄⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠟⠉⠀⠂⠐⠁⠀⠀⠀⠀⠀⠁⢀⣰⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⠂⠿⠃⠀⠀⠀⠀⠀⢀⣶⣿⢿⡿⠏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣬⣿⣿⣿⣿⣿⣻⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⢿⣿⠿⣿⡿⢹⣿⡏⢹⣿⡏⣿⣿⣾⣿⣽⣿⢸⣿⣿⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⡿⢛⠹⠟⠁⠀⠀⠀⢀⠀⢿⣿⣶⡆⣤⣴⣴⣷⣦⣠⣬⣿⣿⣿⣿⣿⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠉⢠⣘⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣦⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⢛⡻⠛⠛⠛⠋⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣆⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣼⣿⣿⣿⣿⣿⣷⣾⠀⠘⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣅⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣯⡿⠀⠀⠀⠀⠀⠀⢤⠀⠀⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠟⣿⡌⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠟⠛⠟⠙⠀⠀⠀⠀⠀⡠⣶⢳⣧⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⠃⠿⠃⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣿⣬⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢽⣿⡏⢺⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣾⣿⣶⠂⠀⠀⠀⠀⠀⠀⡾⢛⡱⠟⠃⠀⠀⠀⠀⠀⢠⣶⣼⣶⣦⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠁⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣛⣛⠛⠙⠛⠉⠉⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣾⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣾⣿⣿⣿⣿⣿⣷⣾⠀⠘⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣳⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡢⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡮⢕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡋⣸⣾⠛⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢢⣼⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣾⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡻⠁⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢦⠀⠀⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡻⣿⡧⢲⢁⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠿⠿⠟⠛⠀⠀⠀⠀⠀⣤⡦⢻⣧⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⢃⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣬⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⣾⢻⣫⠾⠋⠀⠀⠀⠀⠀⢀⣴⣴⣦⣦⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠉⠉⠉⠁⠈⠈⠈⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⢠⣼⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠙⠙⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣛⡻⠛⠛⠛⠉⠉⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣾⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣼⣿⣿⣿⣿⣿⣷⣿⠀⠘⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣥⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣦⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣽⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⢦⠀⠀⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣯⡌⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⢿⠿⠋⠀⠀⠀⠀⢀⣦⢻⣧⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠁⠿⠃⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣼⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⢹⣿⡇⣿⣿⣿⣿⣹⣿⢸⣿⣿⣶⣿⣶⠂⠀⠀⠀⠀⠀⠀⣾⢿⣫⡿⠏⠁⠀⠀⠀⠀⢀⣤⣠⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠟⠈⠁⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣛⡛⠛⠛⠛⠉⠉⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣶⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣼⣿⣿⣿⣿⣿⣷⣿⠀⠈⠙⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣮⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡩⣷⣷⡒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣸⡷⠠⠀⠀⠀⠀⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡍⠁⠂⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢠⣦⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⠃⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠛⠛⠟⠻⠋⠀⠀⠀⠀⣀⣼⣿⣼⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡏⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢻⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡿⠟⠚⠛⠁⠀⠀⠀⠀⠀⢠⣴⡄⣆⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⣾⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠘⣛⡟⠟⠛⠋⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣾⣿⣿⣿⣿⣿⣿⣇⡀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣧⡁⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣹⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣼⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⣌⢙⢆⠀⠀⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠘⣿⡍⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠂⠿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣾⣿⣼⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢽⣿⡏⢻⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣿⣶⣷⣶⠂⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣧⠾⠝⠋⠀⠈⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⣿⣿⣿⠟⠁⠀⠀⠂⠘⠛⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠉⠁⠁⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣾⡶⣶⣤⣤⣦⣤⣼⣿⣿⣿⣿⣿⣿⡇⡟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠱⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⣿⣿⣿⣿⣿⣿⠟⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⣛⠿⠝⠛⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣷⣄⠀⠀⡀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠠⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣾⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⢉⠁⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡷⣔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣽⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣼⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⣌⢛⣆⠀⠀⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠉⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⠿⣿⢿⠿⡿⢹⣿⡏⢸⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣿⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡽⢿⠹⡏⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⢛⣻⣽⣿⣿⠟⠁⠀⠀⠀⣥⠛⠛⠉⠁⠀⠀⢀⣀⣼⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡇⢫⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣶⣿⣿⣧⣆⣶⣤⣀⣠⣀⡀⠙⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⣿⣿⣿⣿⡿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⠀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⡻⠿⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⣷⣄⢀⠀⣀⠀⡀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⢼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⣌⠻⣆⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠈⣽⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠂⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣽⣿⣼⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⢿⣿⣿⣿⢿⢻⣿⡏⢹⣿⡇⣿⣿⣾⣿⣽⣿⢸⣿⣷⣶⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡻⡏⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠉⠀⠉⠉⢻⣿⣿⠟⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠾⠛⠹⠛⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢰⣦⣄⣀⣀⣄⢀⡄⠀⠀⠀⠀⠀⡄⠘⠗⠈⠛⠛⠋⠉⠉⠙⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢦⠀⠐⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⡈⢄⠀⠄⠸⣄⣠⣶⣄⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣼⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣿⣿⣿⣿⡿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⢸⣷⣌⢻⣆⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠉⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠂⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣹⣿⣿⣿⣧⣽⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡟⢿⣿⡏⣿⣿⣿⣿⣽⣿⢸⣿⣿⣶⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡟⣯⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠚⢻⣿⣿⣿⣿⣿⣿⣿⠃⠉⠈⠁⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⡄⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠊⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠹⢿⣯⣿⣿⣿⣿⣿⣿⠏⠁⠉⠻⢿⣛⠛⠿⠿⠿⠿⠟⠿⠻⠿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢑⡻⠿⣿⠟⠁⠀⠀⠀⢀⣘⣿⡗⣤⣀⠀⢀⣤⡀⠀⣶⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣦⠀⠀⠄⠠⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⣿⣷⣦⣤⣶⣤⣦⣤⣄⠑⠋⠀⠟⠹⠿⣿⣿⣷⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣮⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⡿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣿⢸⣷⣌⢻⡆⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡞⣿⡆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠇⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣻⣿⣿⣻⣧⣽⣿⣿⣿⣿⣿⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⡯⢹⣿⡏⣿⣿⣿⣿⣽⣿⢹⣿⣿⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⡇⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⠀⠉⠉⠉⠉⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠉⠛⠋⠉⠉⠉⠛⠛⠻⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠯⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠲⣦⣄⣀⢀⣴⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢦⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢰⣶⣭⣛⠻⡿⠋⠀⠀⠀⠀⢰⠿⣿⣿⣿⣿⣿⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢋⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡱⢀⡁
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠊⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⣍⣥⣭⣙⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣉⣲⡶⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⣤⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣨⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⣿⣿⣿⡿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣶⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⢸⣷⡝⢷⡄⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠫⣿⡝⣙⡄⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡼⣿⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣷⣿⣧⣿⣿⣿⣿⣿⣽⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠉⠉⠉⠉⠉⠉⠀⠁⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡛⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠉⠙⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠈⠃⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⣿⣿⣿⣿⣿⡿⡿⠿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⡀⠀⠀⠀⠀⣠⡀⠀⣤⣤⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⢴⣤⣼⣿⣇⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⣤⣟⠻⠿⣿⣿⣿⣿⣿⠏⠀⠈⠀⣽⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣅⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⡠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣹⣿⣛⣫⣘⢹⣍⣅⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⡖⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⡶⣤⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢗⢞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣿⢸⣧⡙⣷⡄⠀⠀⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠹⡎⠀⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣽⣿⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠿⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣷⢿⣧⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡏⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣥⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡋⣿⣿⣿⣿⣿⣿⣿⡏⠙⠛⠉⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠘⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣘⣛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣿⣿⠉⢸⣿⢻⣿⢀⣬⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⣠⢰⣶⣶⣮⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠶⣤⣴⣿⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣦⣤⣄⣖⡛⠛⠿⠿⠿⣿⣿⠃⣀⣀⡀⠀⠀⠀⠙⠛⢿⡳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⡷⡂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣼⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣼⣧⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⢀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⢸⣧⡙⣷⡄⠀⠀⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢽⡇⠀⠀⠀⠀⠨⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣹⣿⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠿⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⣧⢿⣧⣿⣿⣿⣿⣿⡷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡏⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢹⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠋⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠙⠙⠛⠻⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠄⣶⣶⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⠻⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⠈⠀⠉⠛⠿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣄⣤⡀⠉⠛⠛⠛⠛⢛⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣹⣿⣛⣫⣘⢹⣍⣥⣭⣙⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣯⣷⡿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⣾⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣼⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣸⣧⡙⣷⡀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣽⡎⠀⠀⠀⠀⠐⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣷⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠿⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣏⣿⣧⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⡏⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⢰⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣂⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣄⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣿⣿⠉⢸⣿⢹⣿⢄⣬⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⣠⢠⣤⣤⣴⣶⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣶⣶⣦⣤⢀⣀⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⡅⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣹⣿⣛⣫⣘⢹⣍⣥⣭⣙⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣶⣿⡗⠆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⢤⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣾⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢸⣧⡙⣷⡀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣽⣿⡍⠍⡃⠀⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣿⣿⡏⣿⣦⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡏⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣳⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠳⠚⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠋⠙⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢉⡔⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣼⣃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣏⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣅⣉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣿⣿⠉⢸⣿⢹⣿⢀⣬⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣀⠀⢀⡀⠈⠙⠻⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⠛⠻⠟⠛⢋⣉⡭⠽⠷⠶⢀⠀⢀⣼⡟⠀⣾⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣶⠀⠰⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣄⣠⣶⣶⣾⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣛⣫⣘⢹⣍⣥⣭⣙⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡫⣦⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣦⣽⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣾⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣸⣧⡙⣷⡄⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣿⣿⡏⣿⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡇⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⣿⣿⣾⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⡳⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡯⡿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡿⠾⠞⣿⣿⣿⣿⣿⣿⣿⡿⠈⠉⠉⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠙⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢩⡖⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣯⣦⣠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⣆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣼⡃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣀⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣬⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠛⠛⠿⠛⢛⣛⣯⡭⠷⠆⠀⠀⠀⢀⠀⠀⣶⣶⡆⣤⣬⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣶⠀⠠⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣶⣶⡀⢠⣶⣶⣾⣿⣿⣶⣾⣿⣧⣴⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣥⣭⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣾⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣿⣼⣧⡙⣷⡀⠀⠀⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠇⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⡞⣿⣬⣿⣿⣿⣿⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢿⣿⣿⣿⣿⣿⡿⡿⠿⢹⣿⡿⢺⣿⡇⣿⣿⣿⣿⣽⣿⢸⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣴⣿⣯⣿⣧⢿⣿⣿⣿⣿⣿⣿⢭⡏⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡏⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⢯⢽⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠁⠁⠉⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠂⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣣⠄⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⡿⢅⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⡿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣭⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣿⣿⣿⣿⣿⣦⣤⡀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠟⣿⠿⠿⠛⠻⠭⢓⡀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠟⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⣤⣤⠀⠀⣈⣩⣍⣥⣤⣄⣀⣀⠀⠀⠀⣰⣶⢀⣤⣬⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣛⣫⣘⢹⡍⣅⣍⣙⣻⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣿⣦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣸⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣬⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣿⣿⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⣶⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣾⡏⣾⣦⡹⣧⡀⠀⠀⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠐⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣧⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠂⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⠿⠿⢿⣿⠿⢹⣿⡇⢸⣿⡇⣿⣿⣾⣿⣹⣿⢸⣿⣷⣾⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⠇⢸⣿⠇⣿⣿⣿⡟⣿⣿⢸⣿⢘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⢸⣿⢀⣿⠹⣿⡇⣿⣿⣾⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠄⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠋⠁⠛⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⣴⡶⣶⡆⢰⣶⣶⠀⣤⣤⣤⡀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠱⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣿⡇⠻⣷⣬⡁⢸⣿⣤⢰⣿⣇⣿⠇⣿⣇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣯⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠇⣶⡎⣿⡇⣾⣿⠉⢸⣿⢹⣿⢀⣌⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣽⣿⣿⣿⣿⣟⠘⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠁⠛⠛⠛⠘⠛⠸⠿⠈⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⣿⣿⣿⢿⠿⠶⡀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢶⠀⠀⠄⠠⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢀⣀⡁⠀⠀⠀⢀⣒⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣻⣫⣽⢻⣍⣥⣭⣿⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣧⡀⠀⠈⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⢿⣿⣿⣿⢿⡿⠝⠋⠉⠻⠫⣿⡿⠅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡏⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢳⣿⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⡁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠄⠀⠈⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠉⠉⠛⠋⠉⠑⠨⢭⣅⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣻⣫⣽⢻⣍⣥⣭⣿⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣦⣿⣷⡄⠀⠈⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠉⠉⠁⠹⢯⠿⠛⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢯⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣮⣿⠃⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣿⣿⣷⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠀⠙⠋⠋⠉⠙⠂⣤⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣻⣫⣽⢻⣍⣥⣭⣿⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣧⡄⠀⠈⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠏⠉⠍⠹⠹⢿⠿⠍⠥⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠿⢿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣶⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣮⣿⠗⢸⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣿⣿⣷⠆⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣿⣿⣿⣶⣦⡄⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠂⠙⠙⠉⠉⠉⠒⢨⣄⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠽⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣻⣫⣹⢻⣍⣵⣭⣿⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣧⡄⠀⠈⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠟⠀⠋⠛⠈⠾⠿⠅⠨⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⣶⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⠗⠼⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣿⣿⣷⠆⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⣿⣿⣿⣿⣿⣶⣦⣄⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠍⠀⠘⠛⠛⠉⠉⠒⣠⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣻⣫⣹⢻⣍⣵⣭⣻⣻⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣷⡄⠀⠈⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠩⠏⠘⠑⠸⠫⠿⠛⠀⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⣶⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⡗⢐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡆⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣼⣿⣿⣿⣿⣿⣶⣦⣄⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠍⠃⠘⠛⠛⠋⠉⠑⣂⠀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
䷩ 𝚕𝚒𝚗𝚎 3196
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/02/security-perception-manipulation/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/02/security-perception-manipulation/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Darkening_the_Counterpart’s_Reputation:Microsoft-Friendly(Sometimes
Microsoft-Funded)Media_Describing_Every_Security_Issue—Even_Windows_Issues—
as_‘Linux’⠀✐
Posted in Deception, FUD, GNU/Linux, Microsoft, Security, Windows at 6:22 pm by
Dr. Roy Schestowitz
Video_download_link | md5sum 50e30a74c66758c9b3e9173defb765cd
Microsoft Culprit Spun as Expert
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/security-narrative-inverted.webm
Summary: The perception manipulation campaign (it certainly feels like one)
keeps Linux in the headlines in relation to security issues that aren’t even in
Linux; we know who stands to benefit from it and the people who promote these
messages are sometimes ex-Microsofters [1, 2]
THE Microsoft-connected_CrowdStrike_is_once_again_attacking_Linux in an effort
to sell its so-called ‘products’ and disservices, trying to twist a bunch of
generic or Microsoft issua as (somehow) a “Linux” thing. With the media in
their pockets, and parrots as messengers, they can probably get away with it
too. A VFS-related issue (or Samba) gets spun as “Linux”, attacks on VMware are
spun as a “Linux” issue, and systemd is apparently a kernel now, based on how
media reports on it. The video above takes stock of the media’s campaign of
obfuscation and distraction, apparently compensating for Microsoft’s most
terrible year by shifting negative media attention to Linux and then [cref
telling officials to blame Free software]. █
䷩ 𝚕𝚒𝚗𝚎 3245
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/02/02/year-of-geminispace/#comments
Gemini version at gemini://gemini.techrights.org/2022/02/02/year-of-geminispace/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ One_Year_Since_We_Joined_Geminispace_and_the_Effort_Has_Paid_Off⠀✐
Posted in Site_News at 1:20 pm by Dr. Roy Schestowitz
Video_download_link | md5sum 8ed5666be758c4245573ad1c1cc4815d
Our Gemini Adoption One Year Later
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/gemini-growth-one-year.webm
Summary: It looks like Geminispace will more than double in size in 2022, based
on the trends we saw in the month of January
IN FEBRUARY last year we set up our Gemini capsule and later_shared_some
instructions/guidance_on_setting_up_one's_own_Gemini_server_at_home. It’s a lot
simpler than setting up a Web site!
“There’s an advantage associated with being an “early adopter”.”As we noted
earlier_this_week, Gemini had expanded a lot in January, a lot more than other
alternatives_to_the_Web (like Web0). As the graphs_shown_in_the_video_make
clear, Geminispace added a net of 73 capsules in the past 2.5 weeks alone, at
least based on Lupa. That’s a gain of 5% in less than 20 days! It took almost 3
years — yes, years — to reach 1,600 and now we’re seeing gains of over 100 per
month. Will Geminispace double in size in 2022? Will it triple in size? We can
only hope because we’ve sunk or invested a lot of time/effort in it. There’s an
advantage associated with being an “early adopter”. We’ve probably served about
2-3 million pages over gemini:// this past year.
As Andre_Alves_Garzia_put_it_last_week: “Since the markup language is so
simple, it lowers the barrier of entry for those wanting to produce content.
There is no need to learn web design and have a pretty site (nothing against
those, I like them but they add friction to newcomers). One can learn all about
Gemtext in less than an hour and be happy. [...] The world is not made richer
by having less options for hypertext networks. Gemini is not the Web, and it
doesn’t want to be the Web. Gemini is its own thing that will co-exist with the
Web.” █
䷩ 𝚕𝚒𝚗𝚎 3304
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_2/2/2022:_EasyOS_3.3_and_Kiwi_TCMS_11.1⠀✐
Posted in News_Roundup at 3:04 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Distributions
o Devices/Embedded
* Free_Software/Open_Source
* Leftovers
* § GNU/Linux⠀➾
o § Desktop/Laptop⠀➾
# ⚓ How_I_switched_to_Ubuntu_after_using_Windows_for_20_years_
(the_2022_guide)_|_by_Dmitrii_Eliuseev_|_Jan,_2022_|_Medium⠀⇛
I was a Windows user for many years, but after
buying a new computer I decided to use Ubuntu as
the main OS.
o § Kernel Space⠀➾
# § Graphics Stack⠀➾
# ⚓ First_Blog_Post_for_SoK_2022!⠀⇛
As a painter who also likes software
development, I first came across Krita when I
was looking for digital painting applications
on Windows. Later on, I learned about open
source and decided to start contributing as a
way to build my development skills while
working on something that I myself use. I
spent the last few months of 2020 building
Krita, first in Windows (a nightmare :P),
then in Linux, and started learning Qt since
I was already familiar with some basic C++
from school.
# ⚓ AMD_HIP_Linux_GPU_Acceleration_For_Blender_Delayed_To
v3.2_Release_–_Phoronix⠀⇛
Last year Blender 3.0 added AMD HIP
acceleration to its Cycles X render code with
OpenCL having been removed. That AMD HIP
support for Blender 3.0 was limited to
Windows with plans to then enable Linux
support for Blender 3.1. Sadly due to AMD
driver delays, that HIP Linux support is
postponed to Blender 3.2.
Blender 3.1 is due to be released in March
and sadly will be lacking AMD HIP support on
Linux.
# ⚓ Intel_Patches_To_Make_It_Easier_To_Run_Their_Discrete
Graphics_On_Arm,_Other_Architectures_–_Phoronix⠀⇛
A change currently being evaluated for
Intel’s “i915″ Linux kernel graphics driver
would make it easier for building driver
support for their forthcoming discrete
graphics products for targeting other non-x86
CPU architectures like Arm
Sent out today as a “request for comments”
were patches that change the Intel Linux
kernel graphics driver to allow it to
optionally build without support for
integrated graphics — leaving the driver just
capable of discrete graphics support. While
Intel graphics have traditionally been about
their integrated graphics on their
processors, Intel is moving hard and fast on
bringing up their discrete graphics support
under Linux with DG2/Alchemist for Intel Arc
graphics cards coming together as well as
their Xe HPC accelerator.
# ⚓ NVIDIA_510.47.03_Linux_Driver_Released_With_Vulkan
1.3_Support,_RTX_3050_Compatibility_–_Phoronix⠀⇛
While it was just yesterday NVIDIA released
the 470.103.01 Linux driver, today they have
made public the 510.47.03 Linux driver as
their first stable version in the NVIDIA 510
Linux driver series.
This is the stabilized version from their
prior NVIDIA 510 Linux beta that brought
Vulkan dynamic rendering, AV1 VDPAU decode
support, and a variety of other updates
predominantly driven by Vulkan API
improvements. There is also improved GBM API
support for what was originally introduced in
the 495 driver series.
o § Benchmarks⠀➾
# ⚓ NVIDIA_Linux_Gaming_Performance_For_Wayland_vs._X.Org_On
Ubuntu_22.04⠀⇛

With NVIDIA’s newly-introduced 510 Linux driver
series paired with the latest XWayland and a modern
Wayland compositor like the newest GNOME/Mutter
packages, the NVIDIA (X)Wayland experience is in
great shape and delivering comparable performance
to a traditional X.Org session. The NVIDIA Wayland
support with GBM usage has stabilized and appears
to be in good shape for the upcoming Ubuntu 22.04
LTS release. Here are some benchmarks of the NVIDIA
510 driver on the current state of Ubuntu 22.04
LTS.
In the past we’ve looked at the Radeon Linux gaming
performance for X.Org vs. Wayland. Modern Wayland
support in the likes of KDE Plasma and GNOME Shell
have worked out well with that open-source Radeon
driver stack. Now with the latest NVIDIA drivers,
their Wayland support is in good shape too.
o § Instructionals/Technical⠀➾
# ⚓ How_to_install_Oracle_Solaris_11.4⠀⇛
Some time ago, I wrote an article on how to install
OmniOS CE on VirtualBox. OmniOS is a distribution
of illumos, which is based on (now discontinued)
OpenSolaris, which was based on Oracle Solaris.
For this article I’m going back to the “source” to
show how to install Oracle Solaris 11.4, screen by
screen. Last year I’ve switched from VirtualBox
(also from Oracle) to gnome-boxes, but the general
procedure should be pretty similar to any VM
system. Anyway, to use in production, a real server
would do better.
# ⚓ Convert_PDF_To_EPUB_In_Linux_–_OSTechNix⠀⇛
In this modern era, everything is digitized. The E-
Books have became mainstream. EBooks are available
in various formats such as PDF, EPUB, MOBI, AZW3
and IBA Etc. Most e-Book readers does support
almost all formats. However, some e-Book reader may
not support a specific format. For example, ASW3
files will only be viewed by Amazon Kindle. In such
cases, we need to convert the e-Books from one
format to another supported format. In this quick
tutorial, we will see how to easily convert EBooks
from PDF to EPUB format (and vice versa) in Linux.
There are many online and offline applications
exists to convert an EBook from one format to
another. For the purpose of this tutorial, we will
be using Calibre e-book suite, which let us to
convert ebooks from both CLI and via GUI.
# ⚓ How_To_Install_RethinkDB_server_on_Ubuntu_20.04_LTS_Focal
fossa⠀⇛
RethinkDB is an open-source NoSQL database for
production use, it is meant to simplify the
creation and scaling of real-time applications.
This distributed NoSQL database intended for
storing schemaless JSON documents
Although MongoDB is already quite popular in the
field of NoSQL databases, however, MongoDB lags
behind Cassandra, CouchDB, or Riak in terms of
scalability. Well, this means RethinDB has to
compete with all of them, well it already trying to
provide ease of usage like MongoDB with good
scalability.
# ⚓ How_To_Install_Terraform_on_Fedora_35_–_idroot⠀⇛
In this tutorial, we will show you how to install
Terraform on Fedora 35. For those of you who didn’t
know, Terraform is an open-source infrastructure as
a code software tool that provides a consistent CLI
workflow to manage hundreds of cloud services.
Terraform codifies cloud APIs into declarative
configuration files. 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 a Fedora 35.
# ⚓ How_to_install_KDE_Plasma_on_Ubuntu_22.04_Jammy_JellyFish⠀⇛
There was a time when KDE was considered as a
resource binger Desktop UI but not anymore, it is
similar to Gnome in terms of performance but with a
much beautiful interface and wide range of
applications. It comes already comes as a default
GUI in many Linux systems such as OpenSUSE, MX
Linux, Kubuntu among others. The main focus here is
on the many customization options.
Although the KDE desktop is beautiful, a bit more
confusing at first glance, however as you start
using the same, it is very reminiscent of Windows
with its taskbar. This also contains the “Activity
Manager” with which different desktop versions can
be displayed, for example, to access a photo
collection directly. The display of windows or the
positioning of widgets – almost every element of
the user interface can be customized in KDE.
However, the variety of options can quickly
overwhelm inexperienced users. You should therefore
invest some time in your very own KDE experience.
Also, the applications from the KDE community are a
lot more extensive and, like the KDE desktop, with
a wide range of setting options. Great for power
users, unfortunately often too overloaded for
newcomers.
# ⚓ DNS_RPZ:_A_DNS_Firewall_to_filter_Sites_and_Users⠀⇛
Hello flocks, today we are going to learn some DNS
stuffs. We all know about what’s a DNS, how DNS
works, its types, etc. So, wrap things up and let’s
dive into our today’s topic about DNS Response
Policy Zone (RPZ).
[...]
DNS Response Policy Zone (RPZ) is a DNS zone which
enables DNS administrators to customize policy in
DNS servers, so that the server returns modified
answers to Client’s DNS queries. In other words,
RPZ provides a way to alter a DNS response in real
time. It can be used to modify potentially unsafe
DNS Data to block communication or provide local
data to redirect to a “walled garden”. As we can
alter query response or block any domain using RPZ
it is also known as DNS firewall.
# ⚓ Grep_Command_Cheat_Sheet_With_Examples_[Free_PDF
Download]⠀⇛
Grep is a powerful UNIX command that lets you
search inside the file contents on a variety of
parameters. It’s specially helpful when you are
troubleshooting or debugging.
The grep command has a huge number of options and
use cases. You probably will never need or use all
of them. However, you’ll end up using a handful of
grep commands most of the time.
This article lists the most common grep commands
with quick examples. Linux Handbook already has a
detailed article on grep, so I won’t go in depth
here. I’ll just the common options and their
explanation here.
# ⚓ Increment_and_Decrement_Variables_in_Bash_–_ByteXD⠀⇛
A variable is a placeholder that is used to store
any numerical or text value so that it can be used
during the execution of a computer program. It is
normally used in computer programming languages,
but you can also use it in Bash scripts.
In this tutorial, you will learn about increment
and decrement variables and different ways of
incrementing and decrementing variables in Bash
scripts.
In traditional programming languages, there is a
proper syntax to define a variable. Also, you have
to specify the well-known data type (integer,
float, char, etc.) that defines the type of value
the variable would contain and allocates memory for
it accordingly.
o § Games⠀➾
# ⚓ CodeWeavers_advertising_for_a_Wine_developer_and_Linux
gaming_tester_|_GamingOnLinux⠀⇛
Looking for a job in the Linux space? Now is your
chance! CodeWeavers, the company that sponsors
development on the Wine compatibility layer and
works with Valve on Steam Play Proton are hiring
again.
Similar to one they offered before is a “General
Wine Developer”. This position needs a programmer
to hack away on open source to improve Wine’s
ability to run games and all sorts of other
software. CodeWeavers say there’s multiple
positions available here between working on their
own CrossOver UI, Proton for Valve and various
other CodeWeavers’ stuff. One of the key points
though is you cannot have had exposure to Microsoft
code or reverse-engineering of Microsoft software,
as everything Wine related has to be totally clean-
room.
# ⚓ Cyberpunk_adventure_Technobabylon_gets_a_modern_native
Linux_build_|_GamingOnLinux⠀⇛
Wadjet Eye Games and Technocrat Games have returned
with a fresh upgrade of Technobabylon, a 2015
cyberpunk adventure. This follows on from updates /
new Linux ports of Unavowed, Gemini Rue and The
Blackwell Bundle.
# ⚓ Steam_announces_changes_to_sales_for_devs,_next_set_of_sale
dates_up_|_GamingOnLinux⠀⇛
For developers, the time they have to wait between
running sales has been decreased. Instead of having
to wait six weeks between sales, they now only have
to wait four (28 days). Although, this rule does
not apply to the four most major site-wide sales
being the Lunar New Year, Summer, Autumn, and
Winter sales. Valve are also provided developers
with a new tool to manage participating in sale
events, where developers get a centralized area to
see all the events their games qualify to be
included in. Sounds pretty useful.
# ⚓ Total_War:_WARHAMMER_III_gets_a_nice_long_official_Let’s
Play_video_|_GamingOnLinux⠀⇛
We don’t yet know the exact date of the Linux
version, with it coming “as close to launch day as
possible” with the main release date being February
17.
# ⚓ If_you_still_don’t_own_Stellaris_it’s_currently_free_with
Amazon_Prime_Gaming_|_GamingOnLinux⠀⇛
Quick tip – GOG and Amazon Prime Gaming have teamed
up to give subscribers an offer they can’t refuse –
another free game! Get a copy of Stellaris from
Paradox Interactive / Paradox Development Studios.
How to get it? Easy. Just head over to Prime Gaming
and click the Games header, then you will see that
you can redeem Stellaris on GOG. The offer is open
until March 1 and the deal is open to any region
that is available with GOG, so you should be good
to go. Always nice to get another free game and
Stellaris is one where you can happily sink 100s of
hours into even without any DLC.
# ⚓ Valheim_getting_Steam_Deck_tweaks,_more_new_content_teased
|_GamingOnLinux⠀⇛
Valheim, absolutely one of the best games available
natively for Linux is going to get some upgrades
for the Steam Deck.
# ⚓ First_big_Jump_in_Steam_Deck_Verified_Games⠀⇛
Today marks the first time where the Steam Deck
Verified and Playable games are listed at a much
faster rate – nothing like what we have seen in the
past week. Just in the past 24 hours since our last
refresh, 56 titles have been added in total,
bringing the current status to…
o § Desktop Environments/WMs⠀➾
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ KDE’s_Falkon_Browser_Adds_Screen_Capture_and_PDF
Reader_with_its_Latest_Update_in_3_Years⠀⇛
If you’re a KDE fan, you must have certainly
come across or even used Falkon. So, you must
be pleasantly surprised to find out that KDE
has managed to release a new major upgrade of
their web browser.
Unlike other mainstream web browsers, Falkon
does not receive frequent updates. And, the
latest release is an exciting update, after a
gap of almost three years!
For those unaware, Falkon is a simple open-
source web browser built upon the
QtWebEngine. It was initially known as
QupZilla, later rebranded to Falkon under
KDE.
o § Distributions⠀➾
# ⚓ FSF-Tailored_Trisquel_10.0_Released_–_Adds_32-bit_Arm,
Defaults_To_GNU_Linux-Libre_5.4_–_Phoronix⠀⇛
Trisquel 10.0 was released on Tuesday as the latest
major release of this operating system that is one
of the few GNU/Linux distributions endorsed by the
Free Software Foundation. While it has the blessing
of the FSF, it’s a bit behind on the software
feature front.
Trisquel 10.0 is the FSF-endorsed distribution’s
rebase to… Ubuntu 20.04 lTS. Two years after the
release of Ubuntu 20.04 LTS and two months ahead of
Ubuntu 22.04 LTS, Trisquel 10.0 is now onto this
Ubuntu long-term support release. Trisquel 10.0 for
meeting the free software requirements defaults to
using the GNU Linux-Libre 5.4 kernel by default,
which is also a bit unfortunate for a 2022+
distribution considering all of the improvements
since in recent kernels. There is though 5.8 and
5.13 based GNU Linux-libre builds available within
Trisquel 10.0 as alternatives but surprisingly not
any option based on Linux 5.15 LTS.
Besides migrating to an Ubuntu 20.04 LTS base,
Trisquel 10.0 adds initial support for ARM devices.
However, that’s an “armhf” target. Next the project
will be working towards 64-bit Arm and POWER
architecture support. They did drop 32-bit x86
support though with Trisquel 10.
# ⚓ Trisquel_GNU/Linux_10.0_“Nabia”_Is_Here_with_Support_for
ARM_Devices⠀⇛
The Trisquel team released Trisquel GNU/Linux 10.0
“Nabia” and we’re going to take a look at it today.
Very few Linux distros have the privilege of being
endorsed by the Free Software Foundation (FSF). One
of those distros is Trisquel GNU/Linux.
You can be forgiven if you haven’t heard of
Trisquel. It is an Ubuntu-based desktop oriented
distro which features free and open source software
exclusively. This means that there is no closed
source proprietary software of any kind included in
this distro. That includes the kernel, all the
apps, all the libraries, drivers, everything.
Keep in mind that if you wanted to go out and get
proprietary drivers, Trisquel doesn’t provide any
easy tools for you to use to get those proprietary
drivers. Certainly, you’re not gonna like spending
a ton of money on that high-end Nvidia graphics
card and then having to run the nouveau drivers.
# § EasyOS⠀➾
# ⚓ EasyOS_version_3.3_released⠀⇛
# ⚓ EasyOS_Dunfell-series_3.3⠀⇛
EasyOS was created in 2017, derived from
Quirky Linux, which in turn was derived from
Puppy Linux in 2013. Easy is built in woofQ,
which takes as input binary packages from any
distribution, and uses them on top of the
unique EasyOS infrastructure.
Throughout 2020, the official release for
x86_64 PCs was the Buster-series, built with
Debian 10.x Buster DEBs.
EasyOS has also been built with packages
compiled from source, using a fork of
OpenEmbedded (OE). Currently, the Dunfell
release of OE has been used, to compile two
sets of binary packages, for x86_64 and
aarch64.
The latter have been used to build EasyOS for
the Raspberry Pi4, and first official
release, 2.6.1, was in January 2021.
The page that you are reading now has the
release notes for EasyOS Dunfell-series on
x86_64 PCs, also debuting in 2021.
Ongoing development is now focused on the
x86_64 Dunfell-series. The last version in
the x86_64 Buster-series is 2.6.2, on June
29, 2021, and that is likely to be the end of
that series. Releases for the Pi4 Dunfell-
series are still planned but very
intermittent.
The version number is for EasyOS itself,
independent of the target hardware; that is,
the infrastructure, support-glue, system
scripts and system management and
configuration applications.
The latest version is becoming mature, though
Easy is an experimental distribution and some
parts are under development and are still
considered as beta-quality. However, you will
find this distro to be a very pleasant
surprise, or so we hope.
# ⚓ Should_EasyOS_be_shipped_as_an_uncompressed_image
file?⠀⇛
The upcoming Easy 3.3 will be a 616MB
download, compressed .img.gz file.
However, if I was to build it with a 4MB
second partition, and not compress the file,
the .img file will be 1 + 639 + 4 +1 equals
645MB. Those 1MB at start and end are
padding.
Then there will be no need to uncompress the
file, just one click to open it. But, I don’t
know if this is really such a big issue,
might put it on the back burner. Reconsider
sometime later.
# ⚓ More_exotic_cross-compile_path_fixing⠀⇛
# ⚓ Hack_to_fix_OE_cross-compile_paths⠀⇛
This topic is somewhat esoteric, of interest
to developers only. The OpenEmbedded cross-
compile environment can cause some unexpected
side-effects when the executables are run in
the target system.
# § IBM/Red Hat/Fedora⠀➾
# ⚓ Cockpit_Project:_Cockpit_262⠀⇛
# ⚓ Technical_debt_lessons_from_the_pandemic_|_The
Enterprisers_Project⠀⇛
If your technology organization is like most,
the volume of requests you receive can
outpace your ability to keep up with the
architecture you need to support innovation
and growth. Over time, this situation can
cause technical debt, hindering
responsiveness and speed to market.
Like many organizations, our company faced
challenges during the pandemic that left us
with the burden of technical debt. Here’s how
we responded to come out ahead.
# ⚓ Red_Hat_EMEA_Digital_Leaders_Awards_2021:_And_the
regional_winners_are…⠀⇛
In our previous post we shared the names of
the winners of Red Hat EMEA Digital Leaders
Awards across three categories: Open
Transformation, Cloud Native, and Hybrid
Cloud.
The awards were launched in July 2021 in
collaboration with Intel and IDC with the
goal of identifying innovative and
transformative digital leaders using Red Hat
technologies and services. The awards shine a
spotlight on the innovations of our
customers, while focusing on the business
value and impact of their projects.
Philip Carter, group vice president, European
chief analyst and WW C-Suite tech research
lead at IDC said: “With close to 120
applications, we were able to capture and
showcase unique use cases of technology and
share some of the best practices for making
projects a success.
We had the pleasure of reviewing many
successful practices across industries in
EMEA, from large blue chip organisations to
local heroes, all of whom provided incredible
insights into their projects and operations.”
# ⚓ The_State_of_Customer_Experience_at_Red_Hat:
Technical_support_and_subscription_management
enhancements⠀⇛
In the first post of our three-part series,
we discussed enhancements made to several Red
Hat products and product documentation based
on customer feedback in the past year. In
this post, we’ll look at some additional
areas where we have been working to improve
the experience we deliver to customers and
partners.
Other areas that we have made improvements to
based on what we’ve heard from our customers.
Let’s take a look at some of the enhancements
we made to the areas of support delivery and
subscription management.
# ⚓ Protect_secrets_in_Git_with_the_clean/smudge_filter_|
Red_Hat_Developer⠀⇛
When working on public Git repositories, you
need to pay close attention so that you don’t
accidentally push secret information such as
tokens, private server addresses, personal
email addresses, and the like. One of the
tools that can help you is Git’s clean/smudge
filter.
# ⚓ Edge_computing_strategy:_5_potential_gaps_to_watch
for_|_The_Enterprisers_Project⠀⇛
In financial terms, edge has already arrived:
IDC predicts that companies will spend $176
billion on edge computing worldwide this
year, roughly a 15% increase from 2021.
Ultimately, that’s just a (big) number. There
may be more qualitative signs of edge
computing’s maturation in terms of
architectural approaches, technical
capabilities, enterprise use cases, security
tactics, and more.
“Even if we see echoes of older architectures
in certain edge computing deployments, we
also see developing edge trends that are
genuinely new, or at least quite different
from what existed previously,” Gordon Haff,
technology evangelist at Red Hat, wrote
recently in his analysis of edge trends to
watch in 2022. “And they’re helping IT and
business leaders solve problems in industries
ranging from telco to automotive, for
example, as both sensor data and machine
learning (ML) data proliferates.”
IT leaders don’t often tackle business
problems without a plan, which is why edge
strategies – and related categories like IoT
and machine learning – figure prominently on
their roadmaps. In Red Hat’s 2022 Global Tech
Outlook report, for example, 61% of
respondents reported plans to run IoT or edge
workloads (or both) in the next 12 months.
# § Debian Family⠀➾
# ⚓ How_to_install_Envoy_Proxy_on_Debian_11_–
NextGenTips⠀⇛
Envoy is an L7 proxy and communication bus
designed for large modern service-oriented
architecture. The project was born out of the
belief that the network should be transparent
to applications. When network and
applications problems occur, it should be
easy to determine the source of the problem.
Envoy is an open-source edge and service
proxy, designed for cloud-native
applications. Let’s dive in and learn how to
install Envoy on Debian 11.
# ⚓ Ben_Hutchings:_CI_for_the_Debian_kernel_team⠀⇛
Starting just after Christmas, I have been
working on CI for all the kernel team’s
packages on Salsa. The salsa-ci-team has done
great work on producing a common pipeline
that is usable for most packages with minimal
configuration. However, for some packages a
lot more work was required.
# ⚓ Ben_Hutchings:_Debian_LTS_work,_January_2022⠀⇛
In January I was assigned 24 hours of work by
Freexian’s Debian LTS initiative. I worked 16
hours, and will carry over the remaining time
to February.
I sent various backported security fixes for
Linux to the stable mailing list, and they
have been included in subsequent stable
releases. I rebased the linux package on the
latest 4.9-stable release, but did not yet
upload it.
# ⚓ Which_version_of_Debian_consumes_less_RAM_?_–
LinuxStoney⠀⇛
Among the many Linux distributions that we
can get our hands on today, Debian is one of
the most loved and used for different
reasons. Many users install it not only for
its functionality, but also for its interface
and external appearance.
For many, this is an alternative that is not
suitable for users with little experience in
Linux environments, but it is also true that
it has improved a lot in recent years. Little
by little it has been adapting to all types
of users and devices, hence its growth and
acceptance by the majority. Debian is an open
source operating system valid for both
corporate environments and end users. Of
course, depending on the capabilities of our
computer, we can customize the behavior of
the software .
Although in most cases these Linux
distributions are prepared to work smoothly
on somewhat more limited computers, we must
also take some precautions. Generally, the
most modern versions of Windows have higher
demands than Linux systems, hence precisely
one of its attractions. This is something
that refers directly to the consumption that
the system makes of both the CPU and the RAM
memory of the computer.
Precisely because of all this that we are
telling you and if you have made the decision
to download and install Debian on your PC, we
are going to focus on the resource
consumption section. More specifically, we
are going to talk about the version of this
Linux that consumes less RAM . It is evident
that all this will be useful in the event
that you have an old PC or a somewhat limited
one in terms of internal specifications.
o § Devices/Embedded⠀➾
# ⚓ Linux_Arcade_Cab_Gives_Up_Its_Secrets_Too_Easily_|
Hackaday⠀⇛
Sometimes reverse engineering embedded systems can
be a right old faff, with you needing to resort to
all kinds of tricks such as power glitching in
order to poke a tiny hole in the armour, giving you
an way in. And, sometimes the door is just plain
wide open. This detailed exploration of an off-the-
shelf retro arcade machine, is definitely in that
second camp, for an unknown reason. [Matthew Alt]
of VoidStar Security, took a detailed look into how
this unit works, which reads as a great
introduction to how embedded Linux is constructed
on these minimal systems.
# § Open Hardware/Modding⠀➾
# ⚓ Ultimate_Raspberry_Pi_Computer_Build_–_Water_Cooled
CM4_with_NVMe_SSD_–_The_DIY_Life⠀⇛
If you’ve been following my projects for a
while then you’re probably aware that I like
to do unnecessary things, like building a
water-cooled Raspberry Pi cluster, or this
desktop version of a water-cooled Pi. As cool
as these may look, they’re not all that
practical, so today we’re going to build
something that is a little more practical,
although is still a bit unnecessary.
We’re going to build the ultimate water-
cooled Raspberry Pi desktop computer and try
to give it all of the bells and whistles,
including front-facing USB ports, a power
button, an OLED stats display and an NVME
SSD.
I’m going to be using a Raspberry Pi Compute
Module 4, or CM4 for short, for this build so
that I can use the CM4 IO Board for a number
of features which we’ll get into in a bit.
# § Mobile Systems/Mobile Applications⠀➾
# ⚓ The_Google_One_VPN_for_Android_just_got_a_little
safer_–_Android_Authority⠀⇛
# ⚓ Google_bans_nasty_Android_app!_If_you’ve_downloaded
it,_delete_it_now_|_Express.co.uk⠀⇛
# ⚓ Samsung_Galaxy_Tab_A8_review⠀⇛
# ⚓ The_best_chemistry_apps_for_Android_–_Android
Authority⠀⇛
# ⚓ Best_Free_Android_Apps_[February_2022]:_5_Must-Have
Apps_|_NDTV_Gadgets_360⠀⇛
# ⚓ Sony’s_4K_OLED_Xperia_PRO_5G_Android_smartphone_sees
first_discount_at_$500_off_–_9to5Toys⠀⇛
# ⚓ Fly_around_your_phone_with_Android’s_hidden_voice
command_center_|_Computerworld⠀⇛
# ⚓ How_to_minimise_the_risk_of_smartphone_snooping_
(Android_privacy_tips)_–_Cybershack⠀⇛
# ⚓ How_to_clear_your_Galaxy,_Pixel_or_other_Android
phone’s_cookies_and_cache_–_CNET⠀⇛
# ⚓ How_to_Leave_a_Group_Text_on_Android_in_2022⠀⇛
# ⚓ You_told_us:_You’re_split_about_plans_for_an_Indian-
made_Android,_iOS_rival⠀⇛
When you think of mobile phone operating
systems, Android and iOS probably come to
mind. Beyond these two, very few other OSes
enter the public discourse. However, the
Indian government is considering changing
this by creating a rival to these two
industry juggernauts.
But is this a good idea or another fool’s
errand that many companies have fallen foul
of? Well, we asked our readers this in a
recent poll. Here are the results.
o § Free, Libre, and Open Source Software⠀➾
# ⚓ SteveCo:_Video_from_OLF_2021⠀⇛
I had two talks at OLF in December. I just noticed
that videos are up on YouTube for both of them.
# ⚓ Kiwi_TCMS:_Kiwi_TCMS_11.1⠀⇛
We’re happy to announce Kiwi TCMS version 11.1.
# ⚓ Open_source_cloud_platform:_meet_OpenStack⠀⇛
Are you looking for an open source cloud platform
and you don’t know where to start? Are you getting
lost in all the independent rankings and cloud
platform comparison pages?
Try OpenStack and get your open source cloud
platform up and running today. OpenStack works at
any scale: from a single workstation to thousands
of nodes and installs in minutes.
Sounds impossible? Give it a try or continue
reading to explore where is it coming from.
# ⚓ Open_Source_Apache_CloudStack_Powers_Government_Services_in
India⠀⇛
A division of the government of India went with the
open source Apache CloudStack instead of a public
cloud provider to bring services to millions of
citizens.
# ⚓ Apache_Month_in_Review:_January_2022⠀⇛
Welcome to the latest monthly overview of events
from the Apache community.
# ⚓ joinpeertube.org_–_a_free_decentralized_federated_video
platform_alternative_to_centralize_YouTube_Dailymotion
Vimeo⠀⇛
# § Productivity Software/LibreOffice/Calligra⠀➾
# ⚓ LibreOffice_7.3_Community_is_better_than_ever_at
interoperability⠀⇛
LibreOffice 7.3 Community, the new major
release of the volunteer-supported free
office suite for desktop productivity, is
available from https://www.libreoffice.org/
download. Based on the LibreOffice Technology
platform for personal productivity on
desktop, mobile and cloud, it provides a
large number of improvements targeted at
users migrating from Microsoft Office to
LibreOffice, or exchanging documents between
the two office suites.
# ⚓ LibreOffice_7.3_Released,_This_is_What’s_New⠀⇛
This release sees a score of improvements
aimed at making it easier for users to
migrate from Microsoft Office to LibreOffice,
as well as those who regularly swap documents
between the two office suites.
To this end, LibreOffice devs have spent time
developing new features to handle change
tracking in tables and text within documents.
This, The Document Foundation say will have a
“positive impact” on interoperability
throughout all Microsoft Office formats.
# ⚓ LibreOffice_7.3_Released_With_Better_Interoperability
For_Microsoft_Office_Files⠀⇛
The Document Foundation has released
LibreOffice 7.3 as the newest half-year
update to this leading open-source, cross-
platform office suite.
LibreOffice 7.3 is introducing support in
Writer for hyperlinks attached to shapes,
Writer better tracks and indicates changes to
text, various performance improvements, Bash-
like auto-completion for Calc spreadsheets, a
new bullet mode editing feature, and much
more. As usual, LibreOffice 7.3 has many
import/export improvements to its Microsoft
Office DOC, DOCX, XLSX, and PPTX file format
handling. The Document Foundation is
particularly promoting LibreOffice 7.3′s
improved interoperability with Microsoft
Office files as one of the key pillars of
this release.
# ⚓ Compiling_LibreOffice_with_Meson_even_further⠀⇛
After building the basics of LO on Windows
and macOS the obvious next step is to build
all of it. This is just grunt work and quite
boring at that actually. I almost got it done
apart from the fact that at the end I got
lazy and skipped those bits that require
weird dependencies (of which more later).
The end result has approximately 7800
individual compilation and linking steps. It
takes about 30 minutes on a 16 core Ryzen
3700X CPU using Windows and Visual Studio. On
a 7 year old 4 core Macbook it takes around 3
hours.
Quite a bit, actually. The most pertinent
would be all the configuration files that get
installed. There are a lot of them and they
need to be exactly right, otherwise the end
result fails to start with cryptic error
messages, if any. Unlike code compilation
there is no easy way to know in advance what
should be done or how things should behave.
Ideally you’d get help with people who know
the innards of the program and all the
configgen bits.
# ⚓ LibreOffice_7.3_released⠀⇛
Version 7.3 of the LibreOffice “Community”
edition is out. “In addition to the majority
of code commits being focused on
interoperability with Microsoft’s proprietary
file formats, there is a wealth of new
features targeted at users migrating from
Office, to simplify the transition”.
# ⚓ Install_LibreOffice_7.3_On_Ubuntu_/_Rocky_Linux_&
Fedora_|_Tips_On_UNIX⠀⇛
This tutorial will be helpful for beginners
to install LibreOffice 7.3 on Ubuntu 20.04
LTS, Ubuntu 22.04, LinuxMint 20.3, Rocky
Linux 8, AlamLinux 8, and Fedora 35.
LibreOffice is open-source software and it is
based on OpenOffice.org also an alternative
for Microsoft office, unlike others
LibreOffice supports lots of tools.
LibreOffice suite contains the following
Writer, Calc, Impress, Draw, and Math
The Document Foundation today (02-02-2022)
has released the newer version of LibreOffice
7.3 and this is the newest half-year update.
# § FSFE⠀➾
# ⚓ Welcome_to_the_Matrix:_the_FSFE_now_runs_its_own
server⠀⇛
The FSFE is eager to support its community
with diverse Free Software communication
channels. We are happy to announce that we
have recently added Matrix to this list.
After successful beta tests, every FSFE
supporter and volunteer can now create their
own Matrix account. We will also use our
instance for the FSFE’s virtual booth during
FOSDEM!
For over a decade now, the FSFE has been
offering an XMPP (also known as Jabber)
server as well as a traditional IRC channel
for our community to quickly exchange
messages. Today we officially open the gates
to our new Matrix server, which has been
successfully tested for a few months and has
a few advantages over XMPP.
# § FSF⠀➾
# § GNU Projects⠀➾
# ⚓ GNU_Guix:_Meet_Guix_at_FOSDEM⠀⇛
As usual, GNU Guix will be present at
FOSDEM this week-end, February 5th and
6th. Due to the pandemic, FOSDEM takes
place on-line for the second year, but
we’re confident the wires will be able
carry enthusiasm to the homes of the
thousands of attendees.
# § Programming/Development⠀➾
# ⚓ Qt_Allstack_I_–_Setup_–_KDAB_–_KDAB_on_Qt⠀⇛
Writing mobile apps can be a lot of fun,
especially with Qt and QML. But if your
background is all about C++ and Qt, writing
the entire required stack for a mobile app
can be challenging. Adding push
notifications, storing information, and
having to write that with another language
and framework might make you give up. But we
got you covered!
# ⚓ LLVM/Clang_14_Ends_Feature_Development_With_Better
C++20_Support,_Armv9_Added_–_Phoronix⠀⇛
LLVM release manager Tom Stellard has
branched the LLVM 14.0 code and that of its
sub-projects like Clang within the mono
repository. As such, LLVM 14.0 feature
development is now over with the main Git
branch working towards what will become LLVM
15.0 later this calendar year.
LLVM 14.0 will now undergo weeks of bug
fixing and testing before being released as
stable likely in March. A first release
candidate is expected later this week while a
second release candidate in early March. If
all goes well, LLVM 14.0 stable could be out
in mid-March at the earliest.
# ⚓ Robert_Foss:_Git_Alias_function_syntax⠀⇛
A basic example of the git alias function
syntax looks like this.
* § Leftovers⠀➾
o ⚓ Will_A_Kettle_Filled_With_Alcohol_Boil_Dry?_|_Hackaday⠀⇛
The average home kettle is set up to switch off
automatically when water reaches its boiling point. But
would a kettle filled with alcohol, which has a
significantly lower boiling point, actually turn off?
[Steve Mould] set out to find out.
The prediction was that a kettle full of 40% strength
vodka would boil dry, as the vodka would evaporate before
it actually got to a hot enough temperature to cause the
kettle’s cutout mechanism to kick in. The experiment was
done outside to minimise the dangers from the ethanol
vapor. As it turns out, the vapor from the boiling vodka
is about 80% ethanol and just 20% water, so eventually
the mixture left in the kettle is mostly water and it
boils hot enough to trigger the cutout mechanism.
However, the experiment doesn’t end there. Trying again
with 99% ethanol, when the fluid started boiling, the
kettle switched off even more quickly. So what’s going
on?
o § Science⠀➾
# ⚓ You_have_a_BIG_cognitive_degradation_problem…⠀⇛
The book is about how and why everyone is losing
their capacity for concentration. As one of many
examples, Hari describes a couple a couple he met,
in front of a tourist attraction, looking at a
picture of that attraction on a tablet screen,
instead of enjoying the real thing they had around
them.
# ⚓ The_first_four_words_you_see_are…_|_Stop_at_Zona-M⠀⇛
It’s amazing to which lenghts people will go to
work for free for the already extremely rich
stockholders of social media companies. Yes, the
mere act of having and using a social media account
today is equivalent to sending money to them. But
this is another level.
# ⚓ Misleading_Packaging_History:_Maybe_Double-Check_the
Label⠀⇛
A few years ago, I wrote a tweet, which I imagine
is shocking to many of you, but this tweet was
quite the tweet. It was just five words, attached
to an image that highlighted the risks of
misleading packaging, and yet, somehow I apparently
captured the zeitgeist of clickbait on the internet
in 2018. It was, honestly, weird, and it pulled
some crazy numbers (while making my phone totally
useless for a while). But now that the dust has
long settled on that tweet, I got to thinking about
the central theme of it: Why do we put up with
misleading packaging? And who decides that
something is misleading, anyway? Today’s Tedium
looks on the other side of the personal pan pizza
that is product design.
[...]
In a lot of ways, the definition of misleading can
be in the eye of the beholder, especially if that
beholder knows how to contact a lawyer.
Let me give you a fairly recent example. Last year,
a woman filed a lawsuit, seeking class action
status, over branding on a common product that had
been sold for decades that she felt was inaccurate?
The product? Morningstar Farms veggie burgers. What
was her problem? Simply put, she felt that the term
“veggie” implied more vegetables than the burgers
actually contained. The patties were largely made
of wheat and corn syrup.
Kellogg’s, the makers of these popular patties
(which have a history that goes back more than a
century), defended itself in court, and won a quick
dismissal of the case just last week, after a judge
agreed with the cereal-maker that “veggie” was a
common way to refer to vegetarian products.
o § Integrity/Availability⠀➾
# § Proprietary⠀➾
# ⚓ Demand_for_Rapid_Risk_Elimination_for_Linux_at_Scale
Fueled_TuxCare’s_Meteoric_Growth_in_2021⠀⇛
With ever-changing compliance requirements
and shrinking timelines to apply security
updates, enterprises find themselves in a
constant, multipronged race to remain
compliant, competitive, and fortified against
increasingly sophisticated threat vectors.
Live-patching is one way engineering teams
can stay ahead of system vulnerabilities
without the downtime.
# ⚓ Microsoft:_Keep_your_Windows_PC_online_for_this_long,
or_it_won’t_update_properly [Ed: You know Microsoft is
in for a severe crisis when even Liam Tung (Microsoft
booster) admits Windows_is_a_sordid_chaotic_mess]⠀⇛
# § Security⠀➾
# ⚓ SureMDM_bug_chain_enabled_wholesale_compromise
of_managed_devices⠀⇛
Vulnerabilities in SureMDM could have
been chained to compromise every device
running the popular mobile device
management (MDM) platform within a
targeted enterprise, security
researchers have revealed.
The vendor, Indian tech firm 42 Gears,
has patched the bugs, which led to
remote code execution (RCE) via the web
console, along with RCE, command
injection, hardcoded password, local
privilege escalation, and information
disclosure flaws affecting the Linux
agent.
# ⚓ Security_updates_for_Wednesday_[LWN.net]⠀⇛
Security updates have been issued by
CentOS (samba), Debian (apache2 and
python-django), Fedora (kernel and
phpMyAdmin), Mageia (kernel and kernel-
linus), openSUSE (samba), Oracle
(nginx:1.20 and samba), Red Hat
(cryptsetup, java-1.8.0-ibm, kernel,
nodejs:14, rpm, and vim), SUSE (kernel,
python-Django, python-Django1, and
samba), and Ubuntu (cron).
# ⚓ Samba_bug_may_allow_code_execution_as_root_on
Linux_machines,_NAS_devices_(CVE-2021-44142)_–
Help_Net_Security⠀⇛
A critical vulnerability (CVE-2021-
44142) in Samba, a widely used open
source implementation of the Server
Message Block (SMB) networking
protocol, could allow attackers to
execute arbitrary code as root on
affected Samba installations.
Several updated versions of Samba have
been released on Monday, fixing CVE-
2021-44142 and two other flaws (1, 2),
but since the software is included in
most Linux and Unix-like operating
systems (including Apple’s macOS and
macOS Server), users of those are
advised to keep an eye out for specific
updates by those developer teams.
# ⚓ Tripwire_Patch_Priority_Index_for_January_2022
|_The_State_of_Security⠀⇛
Tripwire’s January 2022 Patch Priority
Index (PPI) brings together important
vulnerabilities for Apache, Open Source
Policy Kit, Adobe, and Microsoft.
# ⚓ PostgreSQL:_PostgreSQL_JDBC_42.3.2/42.2.25
Security_update⠀⇛
A security advisory has been created
for the PostgreSQL JDBC driver. The
driver provides the facility to
instantiate plugin instances based on
class names provided via
authenticationPluginClassName,
sslhostnameverifier, socketFactory,
sslfactory, sslpasswordcallback
connection properties.
However, the driver did not verify if
the class implements the expected
interface before instantiating the
class.
# § Privacy/Surveillance⠀➾
# ⚓ Digital_Transparency:_A_Right_to
Information_Report_for_January_2022⠀⇛
One of our key areas of work is
ensuring that public authorities
respect data privacy and engage
in practices that will ensure
that the right to privacy is
protected. We filed 9 RTI
requests and 1 first appeal with
various authorities this month to
ask for information pertaining to
newly introduced projects which
affect the data privacy of Indian
citizens.
[...]
Another focus of our work is to
ensure that freedom of speech and
expression on the internet is
protected and that unnecessary
censorship does not lead to a
chilling effect on people’s
fundamental rights. For this, we
routinely file RTI requests to
demand accountability for
instances that may hamper free
speech on the internet such as
website blocking or internet
shutdowns.
In the last month, we have filed
1 RTI request to demand
accountability for violations of
free speech on the internet with
the National Internet Exchange of
India on the notice to seek
written approval of NIXI CEO on
.in domain registrations.
We also filed one first appeal
with the Ministry of Information
and Broadcasting for their
incomplete reply dated 14/01/2022
to our original reply requesting
information on the list of
publishers to whom communications
were sent by the Ministry of
Information and Broadcasting.
䷩ 𝚕𝚒𝚗𝚎 4876
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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_3/2/2022:_System76_Scheduler_and_GStreamer_1.18.6⠀✐
Posted in News_Roundup at 8:53 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Distributions
o Devices/Embedded
* Free_Software/Open_Source
* Leftovers
* § GNU/Linux⠀➾
o § Desktop/Laptop⠀➾
# ⚓ System76_refreshes_Kudu_Linux-based_laptops_with_Ryzen_9
5900HX_processor_and_Nvidia_RTX_3060_GPU⠀⇛
Linux-based laptop OEM System76 is updating the
Kudu lineup with a 2022 model that combines the
high-end performance of the AMD Ryzen 9 5900HX APU
with the mid-range Nvidia RTX 3060 GPU and the
versatility of a Linux distro. Users can choose
among System76’s proprietary Pop!_OS versions or
the Ubuntu 20.04 LTS.
Besides the powerful APU and GPU combo, the latest
Kudu6 laptops feature 15.6-inch screens with 1080p
resolution and 144 Hz refresh rate, up to 64 GB of
DDR4-3200 RAM, and up to 4 TB of NVMe SSD storage
via 2x M.2 slots. Connectivity includes 2.5 GbE +
Wi-Fi 6 + BT 5, while the system can support up to
three external video sources through a USB-C 3.2
Gen 2 with DP 1.4, miniDP 1.4 connector, plus an
HDMI video out.
Additionally, there are ports such as 1x USB-A 3.2
Gen 1, 1x USB-A 3.2 Gen and 1x USB 2.0, plus audio
jacks. The new model weighs 4.85 lbs (2.2 kg) and
comes equipped with a rather small 48.96 Wh
battery. Standard features like a 720p webcam and
multi-color keyboard are offered, as well.
Price-wise, the base model with 8 GB of RAM and 240
GB storage starts at US$1,799, while a fully
equipped model that includes mechanical keys and
carrying bag would cost $US3,906.
# ⚓ System76-Scheduler_Is_A_New_Pop!_OS_Rust_Effort_To_Improve
Desktop_Responsiveness⠀⇛
Quietly making its v1.0 debut today is system76-
scheduler as a Rust-written daemon aiming to
improve Linux desktop responsiveness and catering
to their Pop!_OS distribution.
System76 Scheduler describes itself as…
# ⚓ System76_Releases_AMD-Powered_Kudu_Laptop⠀⇛
Denver-based System76 welcomes back a familiar face
to their laptop lineup with the Kudu.
System76 has finally brought back the popular Kudu
laptop workstation powerhouse. This time around the
laptop is equipped with a 3rd-gen AMD (Zen 3) Ryzen
9 5900HX H-class processor with 8 cores and 16
threads. The CPU runs at 3.3 GHz but can be boosted
up to 4.6 GHz.
The Kudu is paired with NVIDIA RTX 3060 graphics
and up to 64GB of Dual Channel DDR4 memory.
According to Ben Shpurker, Product Manager at
System76, “This combination makes it the perfect
machine for creating on the go.”
The 15″ FHD matte display and a thin bezel, but for
creators of all kinds, the Kudu laptop can manage
up to three external displays with one HDMI port,
one mini DisplayPort, and one DisplayPort over USB-
C.
# ⚓ 11_Funniest_Linux_Meme_Distros,_Software,_and_Commands_–
Linux_Stans⠀⇛
We’ve already featured serious Linux distros like
distros for servers and distros for programming.
Now, it’s time to blow off some steam with a few
funny Linux distros and software.
All of these Linux distros and software are
actually usable, and they have a funny spin to
them. We won’t include unique distros like Damn
Vulnerable Linux, GoboLinux, or certain religious
Linux distros. We might create a different list for
them. In this article, we’ll only feature funny
distros and software that are just a meme.
o § Audiocasts/Shows⠀➾
# ⚓ Hackaday_Invades_the_FLOSS_Weekly_Podcast⠀⇛
Regular Hackaday readers will know that we’re big
supporters of free/libre and open source software
(FLOSS) around these parts. There’s an excellent
chance you are too, as so many of the incredible
projects you send our way make it a habit to share
their innermost details, from firmware source code
to the OpenSCAD files that generate its 3D printed
components. So when our recently minted Editor in
Chief [Elliot Williams] was invited to join This
Week in Tech’s FLOSS Weekly podcast, he jumped at
the chance to represent our little corner of the
Internet to the wider world of open source
aficionados.
# ⚓ Hackaday_(FLOSS_Weekly_666:_Hackaday_–_Elliot_Williams,
Open_Source_&_Hacking)⠀⇛
Hackaday.com is what its new editor-in-chief,
Elliot Williams, calls “a library of Alexandra for
fugitive hacks”—and that’s just one of the many
deep and quotable things he shares with Doc Searls
and co-host Jonathan Bennett, who is also a veteran
Hackaday writer. Topics range from hackable gizmo
and the hacker mindset, to how great open firmware
hacks become bait for cool new hackable products
coming out of China.
# ⚓ Steam_Deck_Only_Has_200_Verified_Games?!?_–_Invidious⠀⇛
o § Kernel Space⠀➾
# ⚓ Parallel_x86_64_CPU_Bringup_Linux_Patches_Revised_For
Quicker_Boot_Times_–_Phoronix⠀⇛
The Linux kernel patches that alow bringing up
x86_64 CPU cores in parallel when booting the
system have been revised for faster boot times on
today’s systems from high core count desktops to
massive servers.
This patch series led by longtime kernel developer
David Woodhouse is about allowing secondary x86_64
CPU cores to be brought up in parallel. While prior
versions of the patch series noted a 15x speed-up,
his testing of the new “v4″ patches on other
hardware is showing a drop from around 500ms down
to 100ms.
# ⚓ Lenovo’s_Platform_Profile_Support_For_AMD_Systems_On_Linux
Has_Been_Busted_–_Phoronix⠀⇛
ACPI Platform Profile support on Linux has been
useful for catering to balancing your power or
performance preferences with modern laptops on
Linux. It has worked well in general across various
devices tested but it turns out to be a dud
currently when it comes to AMD Ryzen powered Lenovo
systems.
ACPI Platform Profile support allows setting the
power/balance/power-savings preference (among other
possible profiles) on Linux with recent kernel
activity that so far has seen major support
available for major laptop brands like Lenovo,
Dell, and ASUS. The user’s profile preference can
be set via a sysfs interface or desktops like KDE
Plasma and GNOME have already added convenient user
interfaces for setting it nicely from the system
settings area.
# § Graphics Stack⠀➾
# ⚓ Download_NVIDIA_510.47.03_Graphics_Driver_For_Linux_|
Itsubuntu.com⠀⇛
Finally, NVIDIA 510.47.03 proprietary
graphics driver is available for Linux-based
operating systems. In this driver software,
you can find support for Linux 5.17 kernel
series and support for the d Vulkan 1.3
graphics API.
# ⚓ Mike_Blumenkrantz:_Wew⠀⇛
Nothing too exciting. Mostly bug fixes. I
managed to sneak ARB_sparse_texture_clamp in
for zink just before the branchpoint, so all
the sparse texturing features supported by
Mesa will be supported by zink. But only on
NVIDIA since they’re the only driver that
fully supports Vulkan sparse texturing.
The past couple days I’ve been doing some
truly awful things with gl_PointSize to try
and make this conformant for all possible
cases. It’s a real debacle, and I’ll probably
post more in-depth about it so everyone can
get a good chuckle.
o § Intel⠀➾
# ⚓ Intel’s_“Software_Defined_Silicon”_Linux_Support_Moving
Along_–_Phoronix⠀⇛
While Intel has not publicly announced their plans
around Software Defined Silicon (SDSi), the Linux
kernel patches allowing activation of licensed CPU
features is continuing to move forward toward
mainline integration.
# ⚓ Intel_Announces_“Project_Circuit_Breaker”_To_Expand_Its_Bug
Bounty_Program_–_Phoronix⠀⇛
Intel today is announcing Project Circuit Breaker
as a broadening of its bug bounty program for
“elite hackers” to help discover areas for
improvement within Intel’s hardware/software
security.
# ⚓ Intel’s_Vulkan_Linux_Driver_Adds_Experimental_Mesh_Shader
Support_For_DG2/Alchemist_–_Phoronix⠀⇛
Intel’s open-source “ANV” Vulkan driver for Linux
systems now has experimental support for mesh
shaders that work with their forthcoming Intel Arc
DG2/Alchemist graphics cards.
o § Applications⠀➾
# ⚓ XMPP_and_Mail_Clients_–_WindfluechterNet_Blog⠀⇛
I really like XMPP, but I’m a little unhappy about
the current general situation of XMPP. I think XMPP
could do better if there were some benefits of
having an XMPP address. For me one of those
benefits is to have the option to have just one
address I need to communicate to others. If
everything is in place and well-configured, a user
can be reached by mail, XMPP and SIP (voice/video
calls) by just one address.
To address this I would like to see XMPP support in
mail clients (MUAs). So when you reply to a mail or
write a new one, the client will do a lookup in
your addressbook if the address has an XMPP field
associated with it and (if not) do a DNS lookup for
_xmpp-server._tcp.example.com (or the matching
domain part of recipients address). If there is an
XMPP address listed in mail header, that JID will
be used. When the lookup is successful and an xmpp:
protocol handler is configured in the system, the
MUA offers an option to begin a chat with the
recipient and/or displays the presence status of
the recipients (depending on available web-presence
or presence subscription).
# ⚓ Standard_Notes_–_A_tidy_little_note-taking_program⠀⇛
Note taking. This is one of those things that
everyone does, and often, in a rather unique,
individual way. Some people leave themselves
reminders using physical sticky notes glued to the
door of their fridge. Others have reminders in
their calendar. Others yet keep information in text
files on their desktop. Or you hire a person whose
job is to do it for you. Many ways indeed. How
about a dedicated tool?
[...]
‘Tis a short review, I admit. But then, Standard
Notes delivered on its promise. It’s a program that
helps you keep a bunch of notes sorted and
organized, you can tag your notes, protect them in
case they contain sensitive information, and if you
go for a full account, you can then also back them
up online. Quite handy.
Now, does that mean my days of desktop files are
over? Well, no. There’s one more thing that notes
are supposed to do – constantly remind you of what
you should be doing. Hence the desktopness of the
whole idea, in me book. But then, you can also have
calendar reminders, alerts and alarms, and you
could just keep notes of practical things worth
remembering, in which case, notes become bookmarks,
citations, or diaries. I don’t think I can solve
the bigger philosophical problem of how people are
meant to work with notes. If you like it tidy,
Standard Notes does a pretty decent job. And we’re
done.
o § Instructionals/Technical⠀➾
# ⚓ Gathering_Information_on_Your_Wi-Fi_NIC_and_Connection_on
Linux_—_Virtualization_Review⠀⇛
I have been working with a lot of edge devices and
virtual desktop infrastructure (VDI) clients lately
and one of the issues that I have encountered is
that many of these devices have built-in Wi-Fi that
I need to monitor and gather information about.
Because many edge devices run Linux — which in turn
means a wide variety of Linux versions and GUI
interfaces that each supports — I have found it
easier to use the command line to monitor the Wi-Fi
of these devices.
In this article, I will show you some of the
command-line tools that I use to monitor Wi-Fi NICs
on Linux edge devices.
# ⚓ Install_osTicket_Ticketing_System_on_Ubuntu_22.04/Ubuntu
20.04_–_kifarunix.com⠀⇛
In this tutorial, you will learn how to install
osTicket Ticketing system on Ubuntu 22.04/Ubuntu
20.04. osTicket is an opensource ticketing system.
# ⚓ How_to_install_Crab_Game_by_Dani_on_a_Chromebook_–_Updated
Tutorial⠀⇛
Today we are looking at how to install Crab Game by
Dani on a Chromebook. Please follow the video/audio
guide as a tutorial where we explain the process
step by step and use the commands below.
This tutorial will only work on Chromebooks with an
Intel or AMD CPU (with Linux Apps Support) and not
those with an ARM64 architecture CPU.
# ⚓ How_to_install_Inkscape_on_Zorin_OS_16_–_Invidious⠀⇛
In this video, we are looking at how to install
Inkscape on Zorin OS 16. Enjoy!
# ⚓ How_To_Install_Lighttpd_on_Linux_Mint_20_–_idroot⠀⇛
In this tutorial, we will show you how to install
Lighttpd on Linux Mint 20. For those of you who
didn’t know, Lighttpd is a free, open-source, and
high-performance web server designed for speed-
critical environments. Lighttpd doesn’t require a
lot of memory and CPU usage which makes it one of
the best servers for any project that needs speed
in deploying web pages. Moreover, it also provides
full support for HTTPS.
This article assumes you have at least basic
knowledge of Linux, know how to use the shell, and
most importantly, you host your site on your own
VPS. The installation is quite simple and assumes
you are running in the root account, if not you may
need to add ‘sudo‘ to the commands to get root
privileges. I will show you the step-by-step
installation of a Lighttpd on a Linux Mint 20
(Ulyana).
# ⚓ How_to_Backup_&_Restore_MongoDB_on_Ubuntu_–_TechAcute⠀⇛
MongoDB is one of the most renowned NoSQL Database
Engines. It is widely regarded as a Database that
is highly powerful, scalable, and reliable to use.
MongoDB leverages JSON-like documents with optional
schemas to function efficiently. MongoDB supports a
unique Document-based Data Model that helps
developers map data and code. MongoDB further
empowers application development by providing a
unified and robust API for querying.
MongoDB lets you optimize, scale, and deploy your
applications seamlessly with built-in sharding,
replication, performance tools, and indexing to
help you run confidently in production. MongoDB
ensures that your performance SLAs are met in any
conducive environment irrespective of whether it’s
450 million users around the world or your first
customer.
# ⚓ How_to_install_Manjaro_21.2.2_–_Invidious⠀⇛
In this video, I am going to show how to install
Manjaro 21.2.2
# ⚓ How_to_Install_Magento_2.4_With_OpenLiteSpeed_on_Ubuntu
20.04_–_RoseHosting⠀⇛
This blog post is about installing Magento 2.4 with
OpenLiteSpeed as a web server on Ubuntu 20.04 OS.
Magento is an open-source e-commerce platform
written in PHP that uses multiple PHP frameworks
such as Symfony and Laminas. OpenLiteSpeed is an
open-source web server that offers high
performance, security and can be used for handling
huge traffic for the website. Magento with a
combination of OpenLiteSpeed can provide a very
powerful and fast website performance.
For this setup, we will need about 30 minutes for
everything to be configured properly. Let’s get
started!
# ⚓ Linux_Whatis_Command_–_ByteXD⠀⇛
Linux whatis command is used to display the brief
manual page description of Linux commands. The
manual page contains a detailed description of each
specified command or option. So, we can say that it
helps you to provide a quick short description of a
Linux command. It searches for the arguments from
its index databases that are provided with the
whatis command to view the short manual page
description.
We will explore in this article what is the purpose
of the whatis command. We can use whatis along with
different options.
o § Desktop Environments/WMs⠀➾
# § GNOME Desktop/GTK⠀➾
# ⚓ GStreamer_1.18.6_stable_bug_fix_release⠀⇛
The GStreamer team is pleased to announce
another bug fix release in the stable 1.18
release series of your favourite cross-
platform multimedia framework!
This release only contains bugfixes and
security fixes, and it should be safe to
update from 1.18.x.
# ⚓ Jean-François_Fortin_Tam:_Year_MMXVI_in_1_½_minute⠀⇛
I completed my 2nd term on the board of the
GNOME Foundation, and wrote a report
summarizing my duties that year.
At the end of these two terms, I decided to
leave the GNOME Foundation board, as I felt
like I had accomplished what I had to
accomplish, and because I wanted to get back
some balance in my personal life, as well as
the ability to focus on my other non-profit
work and professional duties.
# ⚓ Christian_Hergert:_GSignalGroup_and_GBindingGroup⠀⇛
Some of the first abstractions we made when
creating GNOME Builder are now available to
everyone in GObject!
In particular, writing Text Editors requires
tracking lots of information and changes from
various sources. Sometimes those changes come
from 2nd-degree objects via the object you
really care about.
For example, with a GtkTextView that might
mean tracking changes to a GtkTextBuffer,
GtkTextTagTable, or many other application-
specific accessory objects through the form
of signals and properties.
o § Distributions⠀➾
# § New Releases⠀➾
# ⚓ Tiny_Core_Linux_13_Released:_Needs_Just_46MB_of_RAM,
50MB_of_Disk⠀⇛
Tiny Core Linux has been updated to v13.0,
following its recently established annual
cadence. This veteran ultra light Linux
distribution is remarkably compact by today’s
standards, requiring a mere 22MB download.
However, it installs and presents the user
with a fully graphical UI, with a modern
Linux kernel, and allows you to install and
run modern applications (but keep it simple
if you install this OS due to your PC being
ancient).
# § Arch Family⠀➾
# ⚓ Arch_Linux_–_News:_Debug_packages_and_debuginfod⠀⇛
We are very happy to announce that debug
packages are now available in Arch Linux.
Debug symbols and source listing are provided
through our debuginfod instance which can be
utilized by debuggers such as gdb and delve.
https://debuginfod.archlinux.org/ A couple of
sponsored mirrors are providing the debug
repositories while we figure out and
communicate the new mirror requirements.
# § IBM/Red Hat/Fedora⠀➾
# ⚓ Máirín_Duffy:_Wacom_calibration_troubleshooting_on
Fedora⠀⇛
My colleague Madeline Peck have the same
laptop that we each got late this past fall.
It’s the Lenovo Thinkpad X1 Yoga Gen 6, and
it is a dream computer, with integrated Wacom
screen and stylus
Recently though, Madeline noticed the cursor
was a bit off from where she placed the
stylus on the screen. The issue only seemed
to be happening in Krita, but was enough to
cause an issue. I suggested trying the GNOME
Wacom calibration tool in GNOME Settings,
thinking that even though there was a slim
chance it’d help (since the issue only
affected Krita), at the very least it
wouldn’t do any harm and might improve the
X,Y calibration of the tablet.
It threw the calibration off a good 4 inches.
Repeated calibrations using the tool didn’t
improve the issue.
# § Debian Family⠀➾
# ⚓ Raspberry_Pi_OS_enters_the_64-bit_era_(but_32-bit_is
still_the_default_option)⠀⇛

Raspberry Pi has been using 64-bit processors
for its tiny, low-cost computers since the
organization launched the Raspberry Pi 3 in
early 2016. But up until now the official
Raspberry Pi OS has been 32-bit only.
Now, after months of beta testing, the folks
at Raspberry Pi have released the first
official build of Raspberry Pi OS that’s
available in either 32-bit or 64-bit
versions.
# ⚓ Raspberry_Pi’s_Raspbian_OS_Finally_Spins_64-bit
Version⠀⇛
# ⚓ Raspberry_Pi_OS_(64-bit)⠀⇛
# ⚓ Raspberry_Pi_OS_(64-bit)_Now_Available⠀⇛
Massive good news for the Raspberry lover as
the Raspberry Pi OS 64 bit edition is now
available for download. Raspberry Pi OS was
available only as a 32-bit operating system.
Raspberry Pi Zero 2 W, Raspberry Pi Compute
Module 4 (CM4), Raspberry Pi Compute Module 3
(CM3), Raspberry Pi Compute Module 3+ (CM3+),
Raspberry Pi 4, Raspberry Pi 400, Raspberry
Pi 3A+, Raspberry Pi 3B+, and Raspberry Pi 3B
will support Raspberry Pi OS.
# ⚓ Sparky_news_2022/01⠀⇛
The 1st monthly Sparky project and donate
report of 2022:
– Linux kernel updated up to 5.16.4 & 5.17-
rc1
– Added to repos: Signal Desktop, Mullvad VPN
– NsCDE Desktop updated up to 2.0 (twice);
debs built for amd64, i386, armhf & arm64
– all sparky services, including repos moved
to a new, bigger server
– mirror de1.repo.sparkylinux.org canceled
– Sparky 5.16 Nibiru of the oldstable line
released
– Sparky Center LXDE updated so can be
installed back to LXDE desktop
# § Canonical/Ubuntu Family⠀➾
# ⚓ Linux_Server_Management_in_2022_|_Ubuntu [Ed: server
push of Landscape, which is non-free]⠀⇛
Linux server management is an integration of
cybersecurity and business objectives. Linux
server management at scale is a vastly
different activity from interacting with a
terminal on one machine. The best Linux
server management tools universally offer a
server management GUI within a web browser.
Implementation details matter, especially in
a pay-for-compute world. Sysadmin tools that
don’t have a lightweight footprint increase
overall compute costs. Some of the most
popular open source and free Linux server
management tools scale poorly, when managing
more than one machine. Requiring system
administrators to perform the same tasks
repetitiously across several machines
increases the time it takes to manage the
entire estate. Beyond inefficiency, manual
administration also introduces risks
associated with human error. Server
management should be automated as much as
possible, through policy-aware tooling that
can define when different groups of machines
get patched.
# ⚓ The_International_Space_Station_Starts_Minting_NFTs⠀⇛
The hardware powering Celestium is located in
NASA’s part of the ISS. The servers run
Ubuntu Linux, with a custom kernel designed
to operate on resource-constrained systems.
Despite its seemingly playful nature, the
project has a very serious goal: to
demonstrate data storage, onboard processing,
and edge of network computing as a prototype
of lunar-based cloud services.
The NFTs minted by Celestium won’t be sold
for cash. In order to receive the tokens,
individuals must contribute images to a
collaborative artwork that will be sent into
space in March 2022 as a contemporary
portrayal of humanity. They can then exchange
their ‘fungible tokens’ into NFTs that
signify the ownership of a specific asteroid,
and its accompanying AI-generated image.
o § Devices/Embedded⠀➾
# ⚓ Amlogic_based_home_automation_hubs_start_at_$52⠀⇛
JetHome’s $52-and-up “JetHub H1” and $57-and-up,
DIN-rail ready “JetHub D1” home automation hubs run
Linux on Amlogic S905W and A113X SoCs,
respectively, and provide 10/100 LAN, WiFi/BT, USB,
and Zigbee. The D1 adds RS485, 1-Wire, relays, and
more.
St. Petersburg, Russia based JetHome has launched a
pair of low-cost, Arm-based automation controllers
with Fast Ethernet, WiFi/Bluetooth, and Zigbee
connectivity. The more affordable JetHome JetHub H1
is focused on basic home automation while the more
I/O-rich, DIN-rail form-factor JetHome JetHub D1
supports more sophisticated automation networks.
# ⚓ A_Portable_Projecting_Pi_For_Education_|_Hackaday⠀⇛
We cover a lot of cyberdeck projects here at
Hackaday, custom portable computers often built
around the Raspberry Pi. It’s not often that we
cover a computer that perfectly achieves and
exceeds what a cyberdeck is trying to do without
being a cyberdeck in any way, but that’s what
[Subir Bhaduri] has done. In addressing the need
for Indian schoolchildren to catch up on two years
of COVID-disrupted schooling he’s created the pπ, a
Raspberry Pi, projector, and keyboard all-in-one
computer in a neat sheet-metal case that looks as
though it might be just another set of spanners or
similar. At a stroke he’s effortlessly achieved the
ultimate cyberdeck, because this machine is no sci-
fi prop, instead it has a defined use which it
fulfills admirably.
# ⚓ Did_You_Know_That_The_Raspberry_Pi_4_Has_More_SPI,_I2C,
UART_Ports?_|_Hackaday⠀⇛
We’ve gotten used to the GPIO-available functions
of Raspberry Pi computers remaining largely the
same over the years, which is why it might have
flown a little bit under the radar: the Raspberry
Pi 4 has six SPI controllers, six I2C controllers,
and six UARTs – all on its 40-pin header. You can’t
make use of all of these at once, but with up to
four different connections wired to a single pin
you can carve out a pretty powerful combination of
peripherals for your next robotics, automation or
cat herding project.
The datasheet for these peripherals is pleasant to
go through, with all the register maps nicely laid
out – even if you don’t plan to work with the
register mappings yourself, the maintainers of your
preferred hardware enablement libraries will have
an easier time! And, of course, these peripherals
are present on the Compute Module 4, too. It might
feel like such a deluge of interfaces is excessive,
however, it lets you achieve some pretty cool stuff
that wouldn’t be possible otherwise.
# § Open Hardware/Modding⠀➾
# ⚓ This_DIY_power_bank_can_deliver_up_to_60W_and
displays_info_in_real-time⠀⇛
The advent of USB-C and the power delivery
(PD) standard have allowed for a single cable
to carry both large amounts of data and power
for a wide range of devices. So, while
looking for a PD-capable power bank for his
laptop but only coming across expensive
units, Instructables user Toby Chui decided
to make his own — with additional
improvements, of course.
# ⚓ Golioth_IoT_development_platform_offers_Zephyr_SDK,
support_for_nRF9160,_ESP32,_and_over_100_other
platforms_–_CNX_Software⠀⇛
There are already plenty of IoT development
platforms, but here’s another one with
Golioth that relies on a Zephyr SDK, “first-
tier” support for Nordic Semiconductor
nRF9160 (cellular) and Espressif Systems
ESP32-C3 (WiFi), as well as a QEMU-based
simulator for easy testing.
The use of an open-source Zephyr SDK even
enables them to support over 100+ hardware
components, and the company, also called
Golioth, says their platform scales from one
device for evaluation to one million devices
during deployment, thanks notably to a free
Dev Tier account to get started at no cost.
# ⚓ Repairing_Librem_14_Part_1:_RAM/WiFi/Storage/Battery
–_Purism⠀⇛
The Librem 14 is deliberately made easy to
repair and upgrade. By removing just a few
screws, you can easily replace the battery,
wifi module, RAM, or the M.2 ssd. This is
really nice if you already own hardware you’d
like to put in a barebones Librem 14 order,
or if you want to upgrade the hardware in
your current Librem 14.
# ⚓ Open_Hardware_5V_UPS_Improves_On_Cheap_Powerbank
Design_|_Hackaday⠀⇛
Often, we need to power a 5V-craving project
of ours on the go. So did [Burgduino], and,
unhappy with solutions available, designed
their own 5V UPS! It takes a cheap powerbank
design and augments it with a few parts vital
for its UPS purposes.
You might be tempted to reach for a powerbank
when facing such a problem, but most of them
have a fatal flaw, and you can’t easily tell
a flawed one apart from a functioning one
before you buy it. This flaw is lack of load
sharing – ability to continue powering the
output when a charger is inserted. Most
store-bought powerbanks just shut the output
off, which precludes a project running 24/
7 without powering it down, and can cause
adverse consequences when something like a
Raspberry Pi is involved.
# § Mobile Systems/Mobile Applications⠀➾
# ⚓ Android_13:_Release_Date,_Compatible_Devices,
Features_and_More⠀⇛
# ⚓ One_UI_4.0_based_on_Android_12_comes_to_Galaxy_Z_Flip
5G_users_in_the_US_–_NotebookCheck.net_News⠀⇛
# ⚓ The_Google_One_VPN_for_Android_just_got_a_little
safer_–_Android_Authority⠀⇛
# ⚓ 5_Tips_to_improve_Android_battery_life_–_Geeky
Gadgets⠀⇛
# ⚓ Top_9_Ways_to_Fix_Keyboard_Typing_Lag_on_Android⠀⇛
# ⚓ Genius_Android_trick_can_help_you_find_closest_free
internet_in_your_city⠀⇛
# ⚓ How_to_use_your_phone_as_an_Android_TV_remote
control⠀⇛
# ⚓ Scrcpy’s_latest_update_brings_keyboard_and_mouse
passthrough_without_USB_debugging⠀⇛
# ⚓ Lenovo_Tab_P11_Plus_review:_Striking_the_perfect
budget_balance_|_Android_Central⠀⇛
o § Free, Libre, and Open Source Software⠀➾
# ⚓ curl_dash-dash-json⠀⇛
The curl “cockpit” is yet again extended with a new
command line option: –json. The 245th command line
option.
curl is a generic transfer tool for sending and
receiving data across networks and it is completely
agnostic as to what it transfers or even why.
To allow users to craft all sorts of transfers, or
requests if you will, it offers a wide range of
command line options. This flexibility has made it
possible for a large number of users to keep using
curl even as network ecosystems and its (HTTP) use
have changed over time.
# § Events⠀➾
# ⚓ CFP:_Binary_T00ls_Summit_2022⠀⇛
The Binary T00ls Summit 2022 (https://binary-
tools.net/summit) is an informal, technical,
online event oriented to authors, users and
enthusiasts of FLOSS programs that deal with
binary data.
This includes binary editors, libraries to
encode and decode data, parser generators,
binary data description languages and
frameworks, binary formats and encodings,
assemblers, debuggers, reverse engineering
suites, and the like.
The goal of this event is for developers to
get in touch with each other, introduce their
tools, have interesting and hopefully
productive discussions, and finally what is
most important: to have fun.
The venue of the event will be an instance of
the Big Blue Button web conferencing system,
accessible using Firefox, Chromium and other
web browsers. We will be having a single
track that will span for three days during a
weekend.
The summit will be held on the first weekend
of March 2022, From Friday 4 to Sunday 6.
# § Web Browsers⠀➾
# § Chromium⠀➾
# ⚓ Chrome_Releases:_Stable_Channel_Update_for
Desktop⠀⇛
The Chrome team is delighted to
announce the promotion of Chrome 98 to
the stable channel for Windows, Mac and
Linux. Chrome 98 is also promoted to
our new extended stable channel for
Windows and Mac. This will roll out
over the coming days/weeks.
Chrome 98.0.4758.80/81/82 for windows
and 98.0.4758.80 for mac and linux
contains a number of fixes and
improvements — a list of changes is
available in the log. Watch out for
upcoming Chrome and Chromium blog posts
about new features and big efforts
delivered in 98.
# ⚓ Google_Chrome_98_Released_With_COLRv1_For
Smaller_Emoji_Files_–_Phoronix⠀⇛
Chrome 98 is available today as
Google’s second web browser update of
the new year. The Chrome 98 changes are
mostly on the developer-side but with
some user-impacting differences.
Among the changes in Chrome 98 as
Google’s stable browser update for
February 2022 are:
- COLRv1 color gradient vector fonts
support that is motivated by wanting
smaller emoji files for the web while
delivering better quality. COLRv1 fonts
compress well, are vector-based, and
work well with gradients. Google Chrome
and Google Fonts teams consider the
COLRv1 specification as their successor
format to the Google Noto emoji font.
The emoji font size is around 20% the
size as previously while also having
greater rendering fidelity. More
details on COLRv1 via
developer.chrome.com.
# ⚓ Google_Releases_Security_Updates_for_Chrome_|
CISA⠀⇛
Google has released Chrome versions
98.0.4758.80/81/82 for Windows and
98.0.4758.80 for Mac and Linux. These
versions address vulnerabilities that
an attacker could exploit to take
control of an affected system.
# § Mozilla⠀➾
# ⚓ Hacks.Mozilla.Org:_Retrospective_and_Technical
Details_on_the_recent_Firefox_Outage [Ed: A
reminder that under ‘new’_Mozilla Firefox became
spyware that phones “mother ship”]⠀⇛
On January 13th 2022, Firefox became
unusable for close to two hours for
users worldwide. This incident
interrupted many people’s workflow.
This post highlights the complex series
of events and circumstances that,
together, triggered a bug deep in the
networking code of Firefox.
[...]
As part of the incident response
process, we quickly discovered that the
client was hanging inside a network
request to one of the Firefox internal
services. However, at this point we
neither had an explanation for why this
would trigger just now, nor what the
scope of the problem was. We continued
to look for the “trigger” — some change
that must have occurred to start the
problem. We found that we had not
shipped updates or configuration
changes that could have caused this
problem. At the same time, we were
keeping in mind that HTTP/3 had been
enabled since Firefox 88 and was
actively used by some popular websites.
[...]
With the load balancer change in place,
and a special code path in a new Rust
service now active, the necessary final
ingredient to trigger the problem for
users was deep in Necko HTTP/3 code.
When handling a request, the code
looked up the field in a case-sensitive
way and failed to find the header as it
had been lower-cased by viaduct.
Without the header, the request was
determined by the Necko code to be
complete, leaving the real request body
unsent. However, this code would only
terminate when there was no additional
content to send. This unexpected state
caused the code to loop indefinitely
rather than returning an error. Because
all network requests go through one
socket thread, this loop blocked any
further network communication and made
Firefox unresponsive, unable to load
web content.
# § SaaS/Back End/Databases⠀➾
# ⚓ MariaDB_announces_plans_to_go_public_for_$672m_via
SPAC_•_The_Register⠀⇛
MariaDB Corporation Ab, which sells the
popular open source database by the same
name, said on Tuesday that it intends to
become a public company with the help of
Angel Pond Holdings Corporation.
The deal, announced in a S-1 filing with the
US Securities and Exchange Commissio,n [PDF]
describes the Cayman Islands-based biz as a
special purpose acquisition company (SPAC).
It was formed by Shihuang “Simon” Xie, a co-
founder of Alibaba Group, and Theodore Wang,
a former Goldman Sachs partner, to raise
capital from investors in order to acquire
another company.
SPAC-driven deals have become popular in
recent years partly as a defense against
market volatility, which can complicate
initial public offerings when companies try
to go the traditional route to market. They
also provide a clearer exit path for
investors, allowing acquired firms to go
public more quickly and at less cost, and to
negotiate their value directly with the SPAC.
However, US government regulators have
expressed concern about the rising number of
SPAC-based deals. SEC Chairman Gary Gensler
last May said, SPACs raise a number of policy
questions, like whether retail investors are
appropriately protected and how SPACs fit
into the SEC mission to maintain fair
markets.
# § Productivity Software/LibreOffice/Calligra⠀➾
# ⚓ LibreOffice_7.3_Released_with_an_Attention_for_Those
Switching_from_MS_Office⠀⇛
The Document Foundation has released
LibreOffice 7.3, including a large number of
fixes intended to compatibility with
Microsoft Office.
A new version of the open source office suite
LibreOffice has been released earlier today.
LibreOffice 7.3 is available for all
supported platforms. Core improvements
include better interoperability with
Microsoft Office document formats,
performance improvements, and new handling of
change tracking in tables.
LibreOffice is one of the best-known open
source office suites. It is a free Microsoft
Office alternative, complete with a
spreadsheet program, database tool,
presentation maker, and word processor. The
project was forked from OpenOffice after
Oracle inherited the latter through its
acquisition of Sun Microsystems in 2009.
Reading and writing to Microsoft Office file
formats, like DOCX, XLSX, and PPTX remains a
key ask of this open source office suite and
something its millions of users rely on
daily. Well, with the new 7.3 release, things
get even better.
# ⚓ LibreOffice_7.3.0_Released!_How_to_Install_in_Ubuntu
20.04,_21.10_&_18.04_|_UbuntuHandbook⠀⇛
Ubuntu’s default office suite LibreOffice
released new major version 7.3.0 today.
Here’s what’s new and how to install it in
all current Ubuntu editions.
LibreOffice 7.3 provided a large number of
improvements to Microsoft Office file formats
support. It now loads large DOCX and XLSX/
XLSM files and some complex documents faster!
# § Programming/Development⠀➾
# ⚓ Design_and_Prototypical_Implementation_of_an_IRC_Chat
Server_in_Erlang_OTP_|_Linux_Journal⠀⇛
By the time of this article, digital services
provide key functionality to businesses and
everyday life. Due to the progress of
digitization, the reliance on digital
services has been growing rapidly. This
process is not only shown by the growing
number of inter connected devices that
communicate with each other but also by the
impact of unavailable services during an
incident: On the 4th of October 2021, Meta
(former Facebook) and all of its
organizations (e.g. Instagram, WhatsApp,
Facebook Messenger) were unavailable for up
to seven hours. The outage resulted in a huge
profit loss for the company and connected
businesses. [1]
This outrage shows that modern solutions must
be designed resiliently to enable service
provisioning during incidents. There are
multiple solutions to develop high-available
and reliable services that can be applied to
various levels in a system’s architecture and
design. Some programming languages are
specifically designed to meet these
challenges. The functional programming
language Erlang provides inherent
functionality to develop these resilient
services.
Therefore, this article presents the
exemplary design and development of a
communication service based on the Internet
Relay Chat (IRC) protocol in Erlang to
investigate its availability features.
# § Shell/Bash/Zsh/Ksh⠀➾
# ⚓ 50_lines_of_Bash_to_bring_a_Wordle_fan_out_of
their_shell_•_The_Register⠀⇛
Of course, those 50 lines do not
include all the gubbins required to
render things on a browser nor the
hooks to send a smug little post out to
social media so your friends can see
how clever you are. However, the
requisite colours are present and
correct, as is the frustration factor
as the attempts mount up without
success.
Thankfully, a thoughtful command line
parameter (unlimit) will up the limit
from six tries to quite a bit more.
We took the script for a spin on a tame
Linux box (in this case, running Ubuntu
20.04 LTS) and can confirm that, after
a quick chmod to make things
executable, tapping in ./wordle.sh got
us our fix.
* § Leftovers⠀➾
o ⚓ Digital_transformation_in_Eastern_Europe_|_Stop_at_Zona-M⠀⇛
Among many other things, the European Union the EU
supports digital transformation in partner countries.
This week, for example, they signed a Joint Declaration
with Armenia, Azerbaijan, Georgia, Moldova and Ukraine.
In this area, that currently suffers from high
instability, digitization is a priority and an important
element of dialogue at several levels, from physical
infrastructures to roaming agreements and training. These
are the parts that I personally find more interesting in
the full Joint Declaration:
A: Modernisation and innovation efforts at all levels of
education and training will be pursued. This includes
structured cooperation between EU and partner countries’
universities, VET institutions and youth organisations,
as well as the promotion of youth employment,
employability, entrepreneurship and skills, including
addressing brain drain.
o ⚓ Building_Forged_Carbon_Fiber_Wings_For_Radio_Control_Cars_|
Hackaday⠀⇛
When it comes to building decent aerodynamic devices, you
want to focus on getting your geometry accurate, and
making sure your parts are strong enough to deal with the
force they’re generating. This build from [Engineering
After Hours] delivers on those fronts, consisting of a
high-downforce wing for a small RC car.
The video points out that, at best, even a decent RC car
will have pretty crappy aerodynamic parts from the
factory, with a lift-to-drag (L/D)ratio of 2-3:1 at best.
This means that, while they may create some small amount
of downforce, they’re also creating plenty of drag at the
same time.
The dual-element wing designed here is much more
efficient, hitting an L/D ratio in the vicinity of 17:1 –
a huge improvement. Even a casual eye can note that the
design looks a lot more like something you’d see on a
full-size car, versus some of the whackier designs seen
on toys.
The wing is built with a forged carbon fiber process
using 3D-printed molds, to give the wing plenty of
strength. Given that it’s built for an RC car that can do
over 100 mph, making sure the wing is stiff enough to
perform at speed is key.
o § Science⠀➾
# ⚓ Simple_Setup_Answers_Complex_Question_On_The_Physics_Of
Solids_|_Hackaday⠀⇛
Thought experiments can be extremely powerful;
after all, pretty much everything that [Einstein]
came up with was based on thought experiments. But
when a thought experiment turns into a real
experiment, that’s when things can get really
interesting, and where unexpected insights crop up.
Take [AlphaPhoenix]’s simple question: “Are solid
objects really solid?” On the face of it, this
seems like a silly and trivial question, but the
thought experiment he presents reveals more. He
posits that pushing on one end of a solid metal rod
a meter or so in length will result in motion at
the other end of the rod pretty much instantly. But
what if we scale that rod up considerably — say, to
one light-second in length. Is a displacement at
one end of the rob instantly apparent at the other
end? It’s a bit of a mind-boggler.
# ⚓ Time_And_Accuracy_In_Las_ATMegas_|_Hackaday⠀⇛
Do you ever have to ensure that an exact amount of
time passes between two tasks in your
microcontroller code? Do you know what’s the
difference between precision and accuracy? Today,
[Jim Mack] tells us about pushing timers and
interrupts to their limits when it comes to
managing time, while keeping it applicable to an
ever-popular ATMega328P target! Every now and then,
someone decides to push the frontiers of what’s
possible on a given platform, and today’s rules is
coding within constraints of an Arduino
environment. However, you should check [Jim]’s post
out even if you use Arduino as a swearword – purely
for all of the theoretical insights laid out,
accompanied by hardware-accurate examples!
[...]
Keeping our projects true to the passage of time
can be an issue, and we’ve been at it for ages –
calibrating your RC oscillator is a rite of passage
for any ATTiny project. If you ever decide to have
an interrupt peripheral help you with timing
issues, we’ve gone in-depth on that topic in the
past, with a three-part series describing the
benefits, the drawbacks and the edgecases of
interrupts. Going for a more modern target? Our
piece on using interrupts with STM32 is a great
path for trying out tools of the modern age.
o § Hardware⠀➾
# ⚓ Analog_Computer_Made_From_LEGO_Predicts_Tides_|_Hackaday⠀⇛
Although the tides in the ocean are caused by the
motion of the Sun and the Moon, both of which are
easy to observe, accurately predicting the tide
more than a few days in advance turns out to be
rather difficult. The math behind the tidal
movement is so complex that some of the earliest
analog computers were built specifically to perform
tide calculations. Sir William Thomson (better
known as Lord Kelvin) designed one such “tide-
predicting machine”, an impressive arrangement of
gears and pulleys, back in the late 19th century.
# ⚓ The_Wanhao_Duplicator_CNC_Heat_Sealer_|_Hackaday⠀⇛
[Thane Hunt] needed to find a way to make a variety
of different heat-seal patterns on a fluid heat
exchanger made from polyolefin film, and didn’t
want all the lead time and expense of a traditional
sealing press machined from a steel plate. Pattern
prototyping meant that the usual approach would not
allow sufficient iteration speed and decided to
take a CNC approach. Now, who can think of a common
tool, capable of positioning in the X-Y plane, with
a drivable Z axis and a controlled heat source? Of
course, nowadays the answer is the common-or-garden
FDM 3D printer. As luck would have it, [Thane] had
an older machine to experiment with, so with a
little bit of nozzle sanding, and a sheet of rubber
on the bed, it was good to go!
# ⚓ Defective_3D_Printing_For_Great_Strength_|_Hackaday⠀⇛
Most of us want our 3D prints to be perfect. But at
Cornell University, they’ve been experimenting with
deliberately introducing defects into printed
titanium. Why? Because using a post-print treatment
of heat and pressure they can turn those defects
into assets, leading to a stronger and more ductile
printed part.
The most common ways to print metal use powders
melted together and this leads to tiny pores in the
material which weakens the final product. Using Ti-
6Al-4V the researchers deliberately made a poor
print that had more than the usual amount of
defects. Then they applied extreme heat and
pressure to the resulting piece. The pressure
caused the pores to close up, and changed the
material’s internal structure to be more like a
composite.
# ⚓ Know_Audio:_A_Mess_Of_Cables_|_Hackaday⠀⇛
We’ve now spent several months in this series
journeying through the world of audio, and along
the way we’ve looked at the various parts of a Hi-
Fi system from the speaker backwards to the source.
It’s been an enjoyable ride full of technical
detail and examining Hi-Fi myths in equal measure,
but now it’s time to descend into one of the
simplest yet most controversial areas of audio
reproduction. Every audio component, whether
digital or analogue, must be connected into
whatever system it is part of, and this is the job
of audio cables, sometimes referred to as
interconnects. They are probably the single
component most susceptible to tenuous claims about
their performance, with audiophiles prepared to
spend vast sums on cables claimed to deliver that
extra bit of listening performance. Is there
something in it, or are they all the same bits of
wire with the expensive ones being a scam? Time to
take a look.
o § Integrity/Availability⠀➾
# § Proprietary⠀➾
# ⚓ Oracle_Linux_8.5_now_available_through_the_Microsoft
Store_|_Windows_Central⠀⇛
Lovers of Linux have a new option to use on
Windows PCs. Oracle Linux 8.5 recently
launched through the Microsoft Store,
allowing developers, IT admins, and
enterprise users to run another Linux
distribution on their PCs. Oracle Linux 8.5
installs through the Windows Subsystem for
Linux, which is available on both Windows 11
and Windows 10.
# ⚓ Oracle_Linux_appears_somewhere_unexpected:_The
Windows_Store⠀⇛
On the last day of January, Oracle Linux 8.5,
the current version of Big Red’s RHEL-alike,
quietly appeared on the Windows Store.
# § Pseudo-Open Source⠀➾
# § Openwashing⠀➾
# ⚓ CIQ_Provides_Commercial_Enterprise
Services_for_Apptainer⠀⇛
Singularity, the container that
powers HPC, has been moved into
the Linux Foundation and renamed
to Apptainer, and CIQ is here to
help with the transition
# ⚓ Alpha-Omega_Project_Launched_to_Improve
Open_Source_Software_Security⠀⇛
# ⚓ OpenSSF_Announces_The_Alpha-Omega_Project
to_Improve_Software_Supply_Chain_Security
for_10,000_OSS_Projects⠀⇛
# ⚓ Standard_electric_charging⠀⇛
It’s become an LF Energy project,
Shuli Goodman, Linux Foundation
Energy’s Executive Director,
explained because, “At LF Energy,
we firmly believe that only open
source has the speed and
transformative power to change
industries fast. Our mission is
to decarbonize the global economy
by enabling the transformation of
power systems, the transition to
electric mobility, and the
radical efficiency of the built
environment. In this regard,
EVerest is the perfect addition
to our ecosystem.”
# § Security⠀➾
# ⚓ New_SureMDM_Vulnerabilities_Could_Expose
Companies_to_Supply_Chain_Attacks⠀⇛
A number of security vulnerabilities
have been disclosed in 42 Gears’
SureMDM device management solution that
could be weaponized by attackers to
perform a supply chain compromise
against affected organizations.
Cybersecurity firm Immersive Labs, in a
technical write-up detailing the
findings, said that 42Gears released a
series of updates between November 2021
and January 2022 to close out multiple
flaws affecting both the platform’s
Linux agent and the web console.
# ⚓ New_Malware_Used_by_SolarWinds_Attackers_Went
Undetected_for_Years [Ed: Microsoft-connected
CrowdStrike_once_again_attacking_Linux, trying to
twist_a_Microsoft_issue_as_(somehow)_a_“Linux”
thing]⠀⇛
According to cybersecurity firm
CrowdStrike, which detailed the novel
tactics adopted by the Nobelium hacking
group last week, two sophisticated
malware families were placed on victim
systems — a Linux variant of GoldMax
and a new implant dubbed TrailBlazer —
long before the scale of the attacks
came to light.
# § Privacy/Surveillance⠀➾
# ⚓ Wanna_go_to_a_public_school?_Tell_Google!
|_Stop_at_Zona-M⠀⇛
(*) the official explanation that
Pinassi received for the presence
of Google Analytics would be that
“it is exclusively aimed at
logging for reasons of security
of the access operations” and
that (this is the best part IMHO)
“it does not record and use any
user tracking data” In other
words, it is not clear what is it
used for, period.
o § Environment⠀➾
# § Energy⠀➾
# ⚓ Electric_cars_are_not_middle_class?_That’s_bad,_IF…⠀⇛
Carlos Tavares, CEO of the automaker giant
Stellantis, is quite skeptical, and worried
too, about the real benefits of electric
cars. In a recent interview Tavares made two
main critiques, both aimed at ecological
benefits of electric cars, and above all
against what he described as a forced push,
by many governments, to buy electric instead
of traditional cars with internal combustion
engines (ICE).
# ⚓ Underwater_Tanks_Turn_Energy_Storage_Upside-Down_|
Hackaday⠀⇛
Pumped hydro storage is one of the oldest
grid storage technologies, and one of the
most widely deployed, too. The concept is
simple – use excess energy to pump a lot of
water up high, then run it back through a
turbine when you want to get the energy back
later.
With the rise in renewable energy deployments
around the world, there is much interest in
finding ways to store energy from these
often-intermittent sources. Traditional
pumped hydro can help, but there is only so
much suitable land to work with.
However, there could be a solution, and it
lurks deep under the waves. Yes, we’re
talking about underwater pumped hydro
storage!
o § Finance⠀➾
# ⚓ Kazakhstan_dispels_a_big_myth_behind_Bitcoin⠀⇛
It seems that the recent riots in Kazakhstan are
due at least parts of them is strictly linked to
the “mining” processes of the cryptocurrency called
Bitcoin. On one side, it seems that the arrival in
Kazakhstan of many Bitcoin mining datacenters
forced to leave China has increased the overall
energy consumption of the whole country enough to
push the government to raise energy prices, which
in turn contributed to cause the riots.
[...]
Regardless of how things will end up in Kazakhstan,
and sincerely wishing the best to all Kazakh
people… the specific effect of the riots that I
summarized above is great. Maybe Bitcoin or its
successors will save the world, or maybe they wont.
That is another issue.
In both cases, the effects on Bitcoin of the riots
in a place many “First World” residents could not
locate on a map if their life depended on it are
another wonderful, perfect reminder that there is
no separate “cyberspace”. There is no digital
utopia where digitally savvy people live and trade,
untouched by the miseries of the one, real world.
We are all in this together, with or without
cryptocurrencies.
# ⚓ When_data_favour_the_rich_|_Stop_at_Zona-M⠀⇛
Lies, damn lies and socioeconomical indicators.
A recent post by Filippo Celata presents a textbook
example of how and why data are not neutral and,
regardless of their quality, can tell stories very
far froom reality if one just accepts them as they
are, without further judgment.
On December 31st, 2021 the italian government
published the decree that assigns the COVID
recovery funds specifically allocated for urban
regeneration projects. Celata explains clearly how
and why those assignments do not really match local
needs.
o § Internet Policy/Net Neutrality⠀➾
# ⚓ The_web_of_power_that_has_less_masters_every_year_|_Stop_at
Zona-M⠀⇛
Google, Amazon, Meta and Microsoft are weaving what
I would call a worrying “Fiber-Optic Web of Power”.
Here is why you should be worried too.
[...]
Whatever answer you give to the question above, one
thing is certain: the oceans of the world are
becoming more and more digital every year, first at
the (privatized!) data level and now at the
physical level, thanks exactly to the (privatized,
again!) cables that run on their floors. This is
even less reassuring, when you also consider how
fragile, that is needy of really effective and
transparent supervision, those cables really are:
we are talking about stuff highly vulnerable to
anyone that could “deploy underwater submersibles
to destroy them”.
o § Monopolies⠀➾
# § Copyrights⠀➾
# ⚓ Portrait_of_a_Scaphander_–_The_Public_Domain_Review⠀⇛
Brad Fox tells a history-story that follows
the fuzzy logics we associate with a “shaggy
dog”. An aquatic dog? Maybe. The sea bends
everything — even light.
䷩ 𝚕𝚒𝚗𝚎 6728
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 02.02.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_2/2/2022:_Weston_10.0.0_and_LibreOffice_7.3⠀✐
Posted in News_Roundup at 7:56 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Distributions
o Devices/Embedded
* Free_Software/Open_Source
* Leftovers
* § GNU/Linux⠀➾
o § Desktop/Laptop⠀➾
# ⚓ System76_Kudu_is_a_Linux_laptop_with_Ryzen_9_5900HX_and
NVIDIA_RTX_3060⠀⇛
The System76 Kudu is a laptop with a 15.6 inch,
1920 x 1080 pixel matte display with a 144 H screen
refresh rate, an AMD Ryzen 9 5900HX 8-core, 16-
thread processor, and NVIDIA GeForce RTX 3060
graphics. And while most laptops with those specs
ship with Windows, the Kudu is designed to run
Linux.
System76 first introduced the laptop earlier this
year, and now the Kudu is available for purchase
for $1799 and up.
# ⚓ CutiePi_Tablet_review:_The_open-hardware_Linux_tablet⠀⇛
Over the last years, we have seen many Linux-
powered tablets, all of which developed with
different approaches to “openness”. For instance,
the PineTab trades performance and a somewhat
conservative design for a very low selling price
and full Linux support, which made its demand high
to the point of becoming essentially impossible to
find on the used market. The JingPad offered a
modern, premium feel and near-flagship performance,
but it is more of a Linux userspace over an Android
kernel, and it did not particularly open to third-
party projects.
The CutiePi, on the other hand, seems to hit a
sweet spot: it is arguably the most open project
among those mentioned, being certified open-
hardware (code JP000005) to the point that anyone
with a 3D printer, good SMD soldering equipment,
and a lot of time on their hands could replicate it
entirely at home.
o § Audiocasts/Shows⠀➾
# ⚓ Lock_Your_Terminal_Sessions_With_Vlock_–_Invidious⠀⇛
Vlock is a nifty little program that allows you to
lock out your virtual console (tty) session. This
is especially useful for Linux machines which have
multiple users with access to the console. You can
lock your own session(s) while still allowing other
users to use the system on other virtual consoles.,
or lock the entire virtual console display.
o § Kernel Space⠀➾
# § Graphics Stack⠀➾
# ⚓ weston_10.0.0⠀⇛
Weston 10.0.0 has been released! This new
version contains a whole
bunch of new features and improvements. Here
are some highlights:
- Add building blocks for color management:
color transformations, gamma
correct blending, color profiles. These are
only internal changes invisible
to users for now, but will allow to enable
color management features in a
future release.
- Add feedback to linux-dmabuf-unstable-v1,
enabling zero-copy scanout in more
situations.
- libseat support has been added. It will
supersede all launchers in a future
release.
- The test suite has been expanded.
- All example clients have been converted to
xdg-shell.
- Weston can now automatically launch a
client after startup.
- The wl_shell interface, the fbdev backend,
and weston-launch are deprecated.
Notes for packagers:
- libdrm 2.4.95, libwayland 1.18.0 and
wayland-protocols 1.24 are now required.
- libpipewire 0.3 is required for the
PipeWire remoting plugin.
- Support for the deprecated wl_shell
interface is now disabled by default (it
will be removed in a future release, re-
enable it with the Meson option
-Ddeprecated-wl-shell=true).
- Support for the fbdev backend is now
deprecated and disabled by default (it
will be removed in a future release, re-
enable it with the Meson option
-Ddeprecated-backend-fbdev=true). Migrating
to KMS is recommended.
- Support for weston-launch is now deprecated
and disabled by default (it will
be removed in a future release, re-enable
it with the Meson option
-Ddeprecated-weston-launch=true). Systems
without systemd can use seatd (or
seatd-launch) instead.
- A KMS driver supporting universal planes is
now required for the DRM backend.
Thanks to all contributors!
Commit history since RC1 below.
Kenny Levinsen (4):
meson: Print deprecation warning for
weston-launch
meson: Set weston-launch as disabled by
default
meson: Rename to deprecated-weston-
launch
ci: Enable weston-launch explicitly for
test
Simon Ser (2):
clients/simple-dmabuf-feedback: fix
bound global versions
build: bump to version 10.0.0 for the
official release
git tag: 10.0.0
# ⚓ Wayland’s_Weston_10.0_Compositor_Released_With_DMA-
BUF_Feedback,_Libseat_Support⠀⇛
Weston 10.0 has been released as the newest
feature update to Wayland’s reference
compositor that often works as a proving
grounds and compositor showcasing shiny new
features for Wayland.
Arguably most exciting with Weston 10.0 DMA-
BUF feedback support is added to allow zero-
copy direct scanout in more situations like
with hybrid/multi-GPU laptop setups. Other
Wayland compositors have also been quick to
support the DMA-BUF feedback extension.
o § Instructionals/Technical⠀➾
# ⚓ Ansible_playbook_to_upgrade_Ubuntu/Debian_servers_and
reboot_if_needed⠀⇛
I realized I’ve never posted this playbook to my
blog… I needed to grab it for a project I’m working
on, so I figured I’d post it here for future
reference.
Basically, I need a playbook I can run whenever,
that will ensure all packages are upgraded, then
checks if a reboot is required, and if so, reboots
the server. Afterwards, it removes any dependencies
no longer required.
# ⚓ Cascade_Layers:_First_Contact⠀⇛
Earlier this week I learned about CSS Cascade
Layers and now I’m all hyped up because I really
like the concept. I’m eager to find out how we can
use them to improve and rethink the architecture of
our styles.
I will not explain how CSS Cascade Layers work
because Bramus and Stephanie have already done that
and they did it much better than I ever could. I
just want to get my feet wet and share my first
impressions. If you’re new to the topic, read their
articles first.
# ⚓ Read_RSS_feeds_on_Mastodon⠀⇛
My daily routine when it comes to staying informed
of what happens in the world is to read RSS feeds
from various sources. To do so, I created an
account on Feedly and use their iOS App. But I
noticed that I often “forget” to launch the app ;
whereas I check Mastodon several times a day. So I
decided to configure a Bot that will parse my RSS
feeds and publish them on my Masto Home page.
# ⚓ Using_an_Ansible_playbook_with_an_SSH_bastion_/_jump_host⠀⇛
Since I’ve set this up a number of times, but I
just realized I’ve never documented it on my blog,
I thought I’d finally do that.
I have a set of servers that are running on a
private network. That network is connected to the
Internet through a single reverse proxy / ‘bastion’
host.
But I still want to be able to manage the servers
on the private network behind the bastion from
outside.
# ⚓ How_I_Manage_Content_With_Jekyll⠀⇛
The problem as I see it is two fold. Firstly,
inserting images using HTML is a pain, and there’s
no real way of doing anything except adding an alt
attribute using Markdown.
What if you want to add a caption to the image? Or
a class? Or make it lazy loading? You’re fresh out
of luck if you want to use Markdown, so you will
have to revert to good old HTML.
# ⚓ Install_GrandCMS_on_Ubuntu_20.04_–_Make_your_own_blog_for
free_with_this_CMS!⠀⇛
GrandCMS is an open source CMS that is based on the
OpenCart core. The developer says that he has
removed all the commercial stuff and focused on
providing an attractive, robust and competent CMS.
In addition to this, GrandCMS stands out for being
very fast and easy to use so in a matter of minutes
we can have a new website up and running.
So it is a good idea to try it out and keep it in
mind for personal and private projects.
Let’s get started.
# ⚓ How_to_share_files_with_Samba_|_Enable_Sysadmin⠀⇛
The Samba project provides file sharing and print
services for computers on a network. It uses the
Server Message Block and Common Internet File
System (SMB/CIFS) protocol, so the services created
by running Samba are available to Linux, macOS, and
Windows clients. It’s an essential service to run
in organizations that support multiple operating
systems, and it’s even useful on homogenous
networks.
It’s not difficult to set up, and all you need is
at least one server you want to designate as a
file-share host (it doesn’t have to be rack mounted
and could even be a dedicated workstation). For
client access, Samba is either built into the
operating system or easily installed from a
repository.
# ⚓ How_to_install_Clonezilla_on_Ubuntu_21.10_–_NextGenTips⠀⇛
Clonezilla is a suite of open-source, disk cloning
programs used for bare metal backup Fand recovery
and also used during system deployment. Clonezilla
server edition uses multicast technologies to
deploy a single image file to a group of computers
in a local area network.
In this tutorial guide, we are going to explore how
to install and use Clonezilla on Ubuntu 21.10.
# ⚓ How_To_Install_Google_Chrome_98_In_Ubuntu_/_Rocky_Linux_&
Fedora_|_Tips_On_UNIX⠀⇛
Google Chrome is one of the common and most widely
used web browsers in the world. It is blazing fast
and easy to use with security features.
Google Chrome’s newer version is 98 and it is the
second web browser update of the year. This release
contains changes related to the developer side and
some user-impacting differences.
This tutorial will be helpful for beginners to
install Google Chrome 98 on Ubuntu 20.04 LTS, Linux
Mint 20.3, Rocky Linux 8, AlmaLinux 8, and Fedora
35.
# ⚓ How_to_Install_LAMP_Apache,_MySQL,_PHP_on_Debian_11⠀⇛
How to Install LAMP Apache, MySQL, PHP on Debian
11. In this guide you will learn how to install
Apache2, MySQL 8.0 and PHP 8.1.
You will also install some common PHP extensions
and adjust the PHP configurations. Finally you will
secure your setup with Let’s Encrypt SSL and
configure HTTPS redirection.
This setup is tested on Google cloud, so it will
work on all cloud hosting services like AWS, Azure
or any VPS or any dedicated servers running Debian
11.
# ⚓ How_to_Install_OpenNMS_Horizon_Network_Monitoring_System_on
Debian_11⠀⇛
OpenNMS is a free, open-source, and one of the most
powerful network monitoring and network management
platforms used for monitoring remote devices from a
central location. It supports many functionalities
including, Provisioning, Services Monitoring, Event
managing, chart support, and more. OpenNMS uses
SNMP and JMX and gathers information from remote
systems. It runs on Linux and Windows operating
systems and provides a web-based interface to easy
monitoring.
In this tutorial, I will show you how to install
OpenNMS on Debian 11.
# ⚓ How_to_Setup_a_Kubernetes_Cluster_with_K3S_in_Rocky_Linux
8⠀⇛
Kubernetes is an open-source container
orchestration system for automating software
deployment, scaling, and management. Google
originally designed Kubernetes, but the Cloud
Native Computing Foundation now maintains the
project. It groups containers that make up an
application into logical units for easy management
and discovery.
K3S is a certified lightweight kubernetes built for
IoT & Edge Computing. K3s is a highly available,
certified Kubernetes distribution designed for
production workloads in unattended, resource-
constrained, remote locations or inside IoT
appliances. K3s is packaged as a single <50MB
binary that reduces the dependencies and steps
needed to install, run and auto-update a production
Kubernetes cluster.
In this tutorial, we will set up a kubernetes
cluster with K3S in Rocky Linux 8.
# ⚓ How_to_Use_the_nmcli_Command_to_Manage_NetworkManager⠀⇛
The nmcli command, available in many Linux
variants, is a command-line tool for managing
NetworkManager. Using nmcli, a Linux administrator
can perform various tasks, such as managing the
network connections and displaying the network
interface adapter’s status.
o § Games⠀➾
# ⚓ Intel_Arc_GPUs_could_raise_the_bar_for_gaming_on_Linux_|
Windows_Central [Ed: Interesting to find it in a site such as
this]⠀⇛
Intel ARC graphics cards look like they’ll have
Resizable BAR (ReBAR) support at or near launch.
ReBAR technology can boost the frame rate
performance of games that support the feature. That
list is rather short at the moment, but support for
ReBAR would still be nice to see on Intel’s
upcoming ARC GPUs.
A report by Phoronix explains that Intel’s open-
source developers are working on Linux driver
support. ReBAR support is on the way, according to
the notes for the most recent kernel patches (via
PC Gamer).
# ⚓ Left_4_Dead_2_gets_updated_ready_for_the_Steam_Deck_|
GamingOnLinux⠀⇛
Looks like playing Left 4 Dead 2 on the upcoming
Steam Deck will be a pretty good experience, with
Valve pushing out a fresh update today to be ready
for it.
Part of all titles getting to the status of
Verified, gamepad input needs to be rock solid. Not
only that, games need to use the correct controller
input icons on-screen too. This upgrade for Left 4
Dead 2 brings all that. Valve of course want their
own games to be Verified as much as possible too
for their own hardware!
# ⚓ Custom_Macintosh_With_A_Real_486_|_Hackaday⠀⇛
Older Apple computers can often be something of a
collector’s item, with the oldest fetching an
enormously high price in auctions. The ones from
the late ’80s and early ’90s don’t sell for quite
as much yet, but it’s possible that museums and
collectors of the future will one day be clamoring
for those as well. For that reason, it’s generally
frowned upon to hack or modify original hardware.
Luckily, this replica of an Apple Macintosh didn’t
harm any original hardware yet still manages to run
software on bare metal.
# ⚓ Arcane:_An_Exceptional_TV_Show⠀⇛
“Hey have you watched Arcane yet?” – “Me: Not yet,
heard about it on Reddit. It’s based on League of
Legends right? I’ve never played the game.” – “Just
watch it NOW.”
If someone had told me that there was going to be
something better than Squid Game to watch on TV in
2021, I’d have laughed. Now I would have the admit
they were right. The best TV show of the year 2021,
in my opinion, is most certainly Arcane, developed
as a collaboration between Riot Games (characters
and story) the French studio Fortiche (for the
production itself. By the way, Fortiche is a casual
word to mean strong, and they earned it). You may
be aware that Riot Games’ reputation is not so hot
lately, but do not let that detract you from
checking out Arcane.
o § Desktop Environments/WMs⠀➾
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ What_a_FreeBSD/KDE_user_misses_on_macOS⠀⇛
Ed Maste asked what everyone’s favourite
changes were to FreeBSD over the last year. I
replied that FreeBSD 13 was a great release
for the desktop, and that coupled with KDE
even made me miss stuff when I’m working on
macOS.
A few people asked me to expand on what I
meant by that. There’s probably nothing
surprising here, but here goes: [...]
o § Distributions⠀➾
# ⚓ Tiny_Core_Linux_13.0_released_for_older_or_lower-end_x86
hardware⠀⇛
Tiny Core Linux is a lightweight (~22MB SIO) Linux
distribution with an FLTK (Fast Light Toolkit)/FLWM
(Fast Light Windows Manager) desktop and based on
the Core Project that integrates a recent Linux
kernel, vmlinuz, and a root filesystem with low
footprint libraries such as busybox. It’s mostly
interesting for older or low-end hardware that may
be slow and/or unusable with more common Linux
distributions like Ubuntu or Debian.
I’ve quickly tried the 32-bit ISO in VirtualBox and
was offered to boot it with a GUI or command line,
but an option for slow devices waiting for USB for
a period of time. The desktop environment (shown in
the first screenshot above) is very basic with just
five icons are the bottom. The only application
installed is the Terminal, but you can add more
including Firefox through the menu.
# § New Releases⠀➾
# ⚓ Trisquel_GNU/Linux_10.0_“Nabia”_Released_with_GNU
Linux-Libre_5.4_Kernel,_ARM_Support⠀⇛
Trisquel GNU/Linux continues to keep the
spirit of free software alive in 2022 and the
new release promises an Ubuntu 20.04 LTS
(Focal Fossa) based computer operating system
that doesn’t include any proprietary software
or firmware and uses the GNU Linux-libre 5.4
LTS kernel rather than Ubuntu’s Linux 5.4 LTS
kenel.
Dubbed “Nabia,” Trisquel GNU/Linux 10.0 is
here more than 15 months after Trisquel GNU/
Linux 9.0 “Etiona” with new releases of its
privacy-oriented software, including Abrowser
96.0 web browser and Icedove 91.5.0 email,
calendar and news client as rebranded
versions of the Mozilla Firefox and
Thunderbird apps.
# ⚓ Linux_Lite_5.8_Release_Includes_Neofetch,_Updated
Theme,_and_New_Wallpapers_–_It’s_FOSS_News⠀⇛
One of the best Windows-like distribution and
lightweight distros out there, Linux Lite is
an impressive choice for modern computers and
old systems.
And, to improve the experience, finally,
Linux Lite 5.8 is here!
The latest release includes a host of changes
in terms of UI, with performance tweaks and
bug fixes.
# § BSD⠀➾
# ⚓ GoT_all_the_things⠀⇛
Hola, I was basically using cvs for a long
time for OpenBSD and some Github for open
source projects, until this thread on ports
made me decide to just move all my repos to
GoT, which I had the privilege to see an
early version long time ago in a hackthon :).
So my setup is pretty easy and I will explain
the “migration” and how to keep in sync my
“new” GoT repos with upstream providers such
as Codeberg, Sourcehut and Github.
# ⚓ FreeBSD_13_on_Thinkpad_T460s⠀⇛
For some reasons, I decided to use FreeBSD on
my laptop. Several times have I tried it in
the last few years. Several times have I
stopped after the first issue that I felt was
sign of it not being built for me.
This time, I’ll go for at least a whole month
of using it. So I can really decide if I keep
using it ; or switch back to OpenBSD.
# § Arch Family⠀➾
# ⚓ First_Arch_Linux_ISO_Powered_by_Linux_Kernel_5.16_Is
Now_Available_for_Download⠀⇛
Arch Linux 2022.02.01 is now available for
download and it comes pre-installed with
Linux 5.16 as default kernel for new
installations and system rescue/recovery
tasks. The ISO image includes Linux kernel
5.16.4, but it looks like Linux kernel 5.16.5
was also released today and you should expect
it to land in the stable archives by the end
of the week.
In addition to the new kernel, the Arch Linux
2022.02.01 snapshot incorporates all the
updated packages and security patches that
have been released through the distribution’s
software repositories during the month of
January 2022.
# § IBM/Red Hat/Fedora⠀➾
# ⚓ [Old] CentOS_Linux_8_will_reach_End_of_Life_on
December_31,_2021._Here’s_what_that_means.⠀⇛
Additionally, with this deadline falling
during a time when many of our team, as well
as many of our users, will be out of the
office, we intend to bend the usual EOL
process by keeping this content available
until January 31st.
# § Debian Family⠀➾
# ⚓ Full_64-bit_Official_Raspberry_Pi_OS_Now_Generally
Available⠀⇛

Until today, Raspberry Pi OS (formerly
Raspbian) was available only as a 32-bit
operating system for all Raspberry Pi models,
from Raspberry Pi 1 to the latest Raspberry
Pi Zero 2 W. This is was the recommend
version offered by the Raspberry Pi
Foundation, due to compatibility issues and
to avoid customer confusion.
During the past few months, since April 2021,
the Raspberry Pi Foundation announced a beta
release of a full 64-bit version of their
Debian-based Raspberry Pi OS, which is now
finally out of beta testing and ready for
mass deployment.
o § Devices/Embedded⠀➾
# § Open Hardware/Modding⠀➾
# ⚓ Celebrate_Black_history_this_month_with_code!⠀⇛
# ⚓ Some_Small_Updates⠀⇛
Hi everyone! The X2100 BIOS has been updated
and the only change is the GPIO voltage for
the Intel_HDA pin. The change from 3.3v to
1.8v should mitigate/eliminate EC issues with
new motherboards (<100hrs of power up time).
Huge thanks to jwise once again for his
contributions.
# ⚓ Silicon_die_teardown:_a_look_inside_an_early_555
timer_chip⠀⇛
Eric Schlaepfer (@TubeTimeUS) recently came
across the chip above, with a mysterious part
number. He tediously sanded through the epoxy
package to reveal the die (below) and
determined that the chip is a 555 timer.
Signetics released the 555 timer in mid-1972
4 and the chip below has a January 1973 date
code (7304), so it must be one of the first
555 timers. Curiously, it is not labeled 555,
so perhaps it is a prototype or internal
version.3 I took detailed die photos, which I
discuss in this blog post.
# ⚓ It’s_dire:_Raspberry_Pi_availability_tracker_is
launched⠀⇛
André has tried including all the official Pi
vendors (who contractually will sell Pi
models at MSRP and not the insane markups
you’ll find on eBay or Amazon), but some
block script-based access, so only about half
the vendors are currently accounted for.
Checking yesterday, two models were
available—across all the 29 models tracked.
And today that number’s down to one, a lonely
CM4 model with 2 GB of RAM, 32 GB eMMC
storage, and WiFi/Bluetooth.
# ⚓ Soldering_Workbench_Tour⠀⇛
Over the past couple of years I have been
upgrading the soldering equipment that I used
to mostly repair Amigas and build new Amiga
parts. Today I’m going to go through what I
use and why I decided to purchase each one.
The hope is that will help people trying to
make similar purchasing decisions in the
future.
I have a workshop with a 6 meter kitchen
counter on it and my soldering section takes
up half that counter. I’m going to go from
right to left in this post.
# ⚓ LTO_Tape_data_storage_for_Linux_nerds⠀⇛
One of the common reasons to look towards LTO
Tape is that it’s much cheaper than hard
drives, where a 12TB SATA drive costs around
£18.00 per TB (at the time of writing), a
LTO-8 tape that has the same capacity costs
around £7.40 per TB (at the time of writing).
That’s a significant price difference. So,
you may ask what is the catch?
# ⚓ Learn_how_to_make_your_old_pedal_generator_work_with
Zwift_|_Arduino_Blog⠀⇛
Zwift is a neat cycling simulator app that
lets you experience a variety of bicycle
adventures from the comfort of your living
room. You can participate in bike races,
cruise your favorite trails, or go on a
leisurely ride through the country. Zwift’s
key feature is that it reacts to your
pedaling and vice-versa. So an uphill section
increases the pedaling difficulty and your
in-game speed correlates to your pedaling
speed. Gene’s Green Machine found a way to
integrate an existing bike with Zwift using
Arduino.
In order for this to work, you will need an
indoor bike setup with a pedal generator. The
generator creates resistance and its voltage
output is proportional to the gear ratio and
pedaling speed. By monitoring the voltage,
you can tell Zwift how fast your virtual bike
should move. Conversely, Zwift can adjust the
real world pedaling resistance based on the
virtual conditions. Steering isn’t a factor
here, but that isn’t a major part of cycling
at speed anyway. You also don’t get to
experience the virtual weather elements, but
that is a good thing as far as most people
are concerned.
# § Mobile Systems/Mobile Applications⠀➾
# ⚓ Updating_SailfishOS_(Suomenlinna)⠀⇛
Long story short (read this part of the
release notes), I decide to remove the
packages the updater complains about and a
few more.
# ⚓ the_smart_modem⠀⇛
I think I’ve mentioned occasionally that
various devices, mostly cellular modems, just
use the Hayes or AT command set. Recently I
obtained a GPS tracking device (made by
Queclink) that is, interestingly, fully
configured via the Hayes command set. It’s an
example of a somewhat newer trend of
converging the functionality of IoT devices
into the modem baseband. But what is this
Hayes command set anyway?
# ⚓ YouTube_for_Android_rolls_out_video_player_redesign_–
9to5Google⠀⇛
# ⚓ Samsung’s_Galaxy_S22_Is_Near_—_Don’t_Buy_a_New
Android_Phone_yet⠀⇛
# ⚓ Repainter_App_Lets_You_Customize_Android_12_Theme
Colors⠀⇛
# ⚓ Nokia_7.2_receiving_Android_11_Build_update_|
Nokiamob⠀⇛
# ⚓ Android_Auto_is_looking_more_like_CarPlay_in_new
leaked_images_–_The_Verge⠀⇛
# ⚓ 7_BestPhoto_Collage_Apps_for_Android_–_Phandroid⠀⇛
# ⚓ Android_app_deals_of_the_day:_Monopoly,_Sheltered,
Worms_3,_Twilight_Pro_Unlock,_more_–_9to5Toys⠀⇛
# ⚓ How_to_sign_a_document_on_your_Android_smartphone⠀⇛
# ⚓ The_Google_One_VPN_for_Android_just_got_a_little
safer_–_Android_Authority⠀⇛
o § Free, Libre, and Open Source Software⠀➾
# ⚓ How_radical_transparency_is_transforming_open_source
healthcare_software⠀⇛
At Tidepool, where I work as a Community and Clinic
Success Manager, the company’s mission is to make
diabetes software more accessible, meaningful, and
actionable. Operating in the open is how we achieve
that. Tidepool’s diabetes management software is an
open source platform free for both clinicians and
people impacted by diabetes. And, because the
company is a nonprofit, it also operates according
to the transparency rules that govern 501(c)(3)
organizations.
This approach means that open source healthcare
software can be driven by the people most affected
by it—in the case of Tidepool, the diabetes
community. The solutions that come from this
process put the needs of individual users first,
from the design phase to implementation.
# ⚓ Best_Free_and_Open_Source_Alternatives_to_Apple
Compressor⠀⇛

Apple, Microsoft, Alphabet (Google’s parent),
Amazon and Facebook dominate the tech landscape.
Their dominance is so broad they account for more
than 20% of the S&P 500.
There are many things to admire about Apple’s
hardware and software. Apple make great looking
(albeit expensive) hardware. Over the years key
successes include the iPhone, iPad, iPod, and the
MacBook Air. The company designs its own hardware
and software. This gives them the power to make an
operating system and suite of apps that are tailor-
made and optimized for their hardware. Apple also
operates the Apple Music and Apple TV media
distribution platforms.
macOS is Apple’s proprietary operating system for
its line of Macintosh computers. Its interface,
known as Aqua, is highly polished and built on top
of a BSD derivative (Darwin). There’s a whole raft
of proprietary applications that are developed by
Apple for their operating software. This software
is not available for Linux and there’s no prospect
of that position changing.
# ⚓ How_open_source_supports_businesses’_impact_on_climate
change_|_Opensource.com⠀⇛
In the coming decade, climate changes will compel
the creation of new ecological norms and rules for
our economy. The financial industry will be at the
center of this transition, determining which
companies and technologies are granted the
resources they need to spearhead this evolution.
So far, objectively evaluating the ethics and
environmental impact of individual businesses has
proved challenging. Many currently used metrics
make it easy for companies to promote a message of
ecological responsibility while continuing
unsustainable practices, a discordance sometimes
referred to as greenwashing. A movement toward
measuring corporate sustainability based on
quantitative values, open source practices, and
open science can potentially circumvent this threat
to economic transformation.
# § Events⠀➾
# ⚓ FOSDEM_2022⠀⇛
The annual FOSDEM conference is kicking off
in a matter of days as software developers
prepare for thoughtful discussions on the
latest open source developments.
This two-day virtual event is organized by
volunteers to promote the widespread use of
free and open source software. With over 50
devrooms and nearly 700 talks, this jam-
packed weekend is sure to satisfy the most
curious of minds.
Within this rigorous lineup, you’ll have the
chance to get an in-depth look at Mobian: an
open-source project aimed at bringing Debian
GNU/Linux to mobile devices. Presented by
Collabora’s very own Arnaud Ferraris, he’ll
take you through the significance of the
project’s advancements and contributions to
the FLOSS ecosystem.
# § Productivity Software/LibreOffice/Calligra⠀➾
# ⚓ LibreOffice_7.3_Open-Source_Office_Suite_Officially
Released,_This_Is_What’s_New⠀⇛

As with previous updates in the LibreOffice
7.x series, the LibreOffice 7.3 release is
here to further improve document
interoperability with proprietary formats
from the MS Office suite in an attempt to
ease the migration from Microsoft Office to
LibreOffice.
Highlights include handling of change
tracking in tables and when text is moved,
which have a positive impact on
interoperability with Microsoft Office
documents, faster opening of large DOCX and
XLSX/XLSM files of over 200 pages, improved
rendering speed of some complex documents, as
well as improvements to import and export
filters.
# § FSF⠀➾
# § GNU Projects⠀➾
# ⚓ GNU_findutils_4.9.0_released_[Savannah]⠀⇛
This is to announce findutils-4.9.0, a
stable release.
See the NEWS below for more details.
GNU findutils is a set of software
tools for finding files that match
certain criteria and for performing
various operations on them.
Findutils includes the programs "find",
"xargs" and "locate".
More information about findutils is
available at:
https://www.gnu.org/software/findutils/
Please report bugs and problems with
this release via the the
GNU Savannah bug tracker:
https://savannah.gnu.org/bugs/
?group=findutils
Please send general comments and
feedback about the GNU findutils
package to the mailing list (<mailto:
bug-findutils@gnu.org):
https://lists.gnu.org/mailman/listinfo/
bug-findutils
There have been 35 commits by 6 people
in the 55 weeks since 4.8.0:
Andreas Metzler (1) Helge
Kreutzmann (1)
Andrew Gaul (1) James
Youngman (1)
Bernhard Voelker (33) Renaud
Pacalet (1)
This release was bootstrapped with the
following tools:
Autoconf 2.69
Automake 1.16.5
M4 1.4.18
Gnulib v0.1-5153-g6ef3d78333
Please consider supporting the Free
Software Foundation in its fund
raising appeal; see .
Thanks to everyone who has contributed!
Have a nice day,
Bernhard Voelker [on behalf of the GNU
findutils maintainers]
# ⚓ When_is_GIMP_version_3.0_coming?_–
LinuxStoney⠀⇛
Of greater or lesser complexity, almost
everyone now has a photo editor
installed on their computer. Although
Adobe Photoshop is the most popular, we
don’t need to go for a solution of that
level either. Serve as a clear example
of all this, GIMP, a very interesting
alternative solution.
It is not for nothing that these two
programs are considered the most
popular and used all over the world
when it comes to editing our images .
However, there is a clear difference
between the two. While the giant
Adobe’s proposal is a paid program,
with GIMP we are faced with a
completely free open source project. It
is true that for some time now, this
program is considered one of
Photoshop’s main competitors. However,
many consider that, in order to
continue on this path, its top managers
will speed up some movements.
With this, what we really mean is that
for some time the usual users of this
software solution have been waiting for
the arrival of GIMP 3.0 . It’s been too
many months now that this new version
has been talked about, which initially
would revolutionize the future of the
editor. To date, some test versions
have been seen, although it seems that
its developers have not made up their
minds about its launch. At the moment,
the previous versions that are
currently on the market continue to be
improved. We refer specifically to
version 2.1 and later.
# § Programming/Development⠀➾
# ⚓ Git_2.34_has_changed_how_you_configure_fast-forward
only_pulls_and_rebasing⠀⇛
As of Git 2.34, two things have changed.
First, the default behavior of ‘git pull’ is
now to abort if it can’t fast-forward the
upstream into your local branch (ie, ‘git
pull –ff-only’); basically, the previous
warning has become an error. Second, the
configuration setting of ‘pull.ff only’ now
takes priority over ‘pull.rebase true’
(although not over an explicit –rebase on the
command line). If you have both in a
repository with things to rebase, you
effectively wind up running ‘git pull –ff-
only’, which fails because you have
additional local changes that Git thinks
would have to be merged. The behavior of
‘pull.ff only’ here may be an accidental bug
and is certainly not historical behavior, but
we have to deal with the Git release we get,
not the one we’d like.
# ⚓ Regexes_are_Cool_and_Good⠀⇛
No, where regex really shines is in
interactive use. When you’re trying to
substitute in a single file you have open, or
grep a folder, things like that. Readability
doesn’t matter because you’re writing a one-
off throwaway, and fragility is fine because
you’re a human-in-the-loop. If anything goes
wrong you will see that and tweak the regex.
# ⚓ A_thesis:_most_websites_are_implicitly_designed_with
a_short_lifetime⠀⇛
I don’t think people building websites
explicitly think about the expected lifetime
and plan for whatever specific lifetime they
expect (at least, not usually). But I do
think it influences what technologies they
consider and choose, and in particular I
think people are influenced by a general
feeling that no matter what they do, it’s
probably not lasting for all that long. Or,
to put things another way, they won’t be
stuck with what they’ve built for all that
long, left to operate and maintain it no
matter what. Something will change enough to
force changes regardless of what they do.
# ⚓ Fortran_newsletter:_February_2022⠀⇛
Welcome to the February 2022 edition of the
monthly Fortran newsletter. The newsletter
comes out at the beginning of every month and
details Fortran news from the previous month.
# § Perl/Raku⠀➾
# ⚓ A_brief_guide_to_perl_character_encoding⠀⇛
I originally wrote this at work, after
my team spent far too many days yelling
at the computer because of Mojibake.
Thanks to my employer for allowing me
to publish it, and the several
colleagues who provided helpful
feedback. Any errors are, naturally,
not their fault.
# § Rust⠀➾
# ⚓ Arti_0.0.4_is_released:_Refactoring,_rustls,
and_more!⠀⇛
Arti is our ongoing project to create a
working embeddable Tor client in Rust.
It’s nowhere near ready to replace the
main Tor implementation in C, but we
believe that it’s the future.
We’re working towards our 0.1.0
milestone in early March, where our
main current priorities are stabilizing
our APIs, and resolving issues that
prevent integration. We’re planning to
do releases every month or so until we
get to that milestone.
# ⚓ Trio_of_Rust_Core_Team_members_take_their
leave⠀⇛
There is only drama in the open source
community when the day has a “y” in it,
and sure enough a trio of members have
decided to step back from the Rust Core
Team, including a nine-year veteran of
the language.
It has been a busy few months for the
Rust project. The entire moderation
team quit in November 2021. The
resignation was, according to the post
in GitHub on the matter, “in protest of
the Core Team placing themselves
unaccountable to anyone but
themselves.”
This week has kicked off with three of
Core Team taking their leave. Florian
Gilcher, a Core Team observer and
project director on the Rust foundation
board, is departing to focus on his
company.
Pietro Albini, meanwhile, reckoned he
had too much to do, and is off to
“focus on other parts of the project.”
o § Standards/Consortia⠀➾
# ⚓ A_toy_DNS_resolver⠀⇛
Hello! I wrote a comic last week called “life of a
DNS query” that explains how DNS resolvers work.
In this post, I want to explain how DNS resolvers
work in a different way – with a short Go program
that does the same thing described in the comic.
The main function (resolve) is actually just 20
lines, including comments.
I usually find it easier to understand things work
when they come in the form of programs that I can
run and modify and poke at, so hopefully this
program will be helpful to some of you.
The program is here: https://github.com/jvns/tiny-
resolver/blob/main/resolve.go
* § Leftovers⠀➾
o ⚓ Heeding_James_Joyce’s_“Ulysses”⠀⇛
The mythical figures in Homer’s epic – Ulysses is the
Latin name for Homer’s hero Odysseus – are reincarnated
in the lives of the Irish working-class. Ulysses, the
Greekking of Ithaca, whose ruse of the Trojan Horse made
him the architect of the victory against Troy, who spent
ten years trying to get home after ten years at war and
slaughtered the suitors who besieged his wife and ravaged
his court during his absence, becomes in Joyce’s hands
Leopold Bloom, a 38-year-old ad canvasser for the
nationalist newspaper Freeman’s Journal. Leopold, whose
father was an observant Hungarian Jew, throughout the
novel mourns his infant son Rudy, who died over a decade
earlier, a loss that severed his sexual relations with
his wife Molly. Ulysses’ son Telemachus, who grew up
without his father and who, when he reached manhood, left
Ithaca to search for Ulysses, becomes Stephen Dedalus, a
fictionalized version of Joyce’s precocious younger self.
Penelope, the loyal wife of Ulysses, is reinvented as
Molly, the wife of Leopold Bloom, who during the day has
a tryst with her lover, Hugh “Blazes” Boylan, and whose
approximately 22,000-word monologue, one of the greatest
in literature, affirming the sanctity of love and life –
along with graphic descriptions of digestion, orgasms,
and farts – concludes the book.
“Unimpressive as Bloom may seem in so many ways,” writes
Joyce’s biographer Richard Ellman, “unworthy to catch
marlin or countesses with Hemingway’s characters, or to
sop up guilt with Faulkner’s, or to sit on committees
with C.P Snow’s, Bloom is a humble vessel elected to bear
and transmit unimpeached the best qualities of the mind.
Joyce’s discovery, so humanistic that he would have been
embarrassed to disclose it out of context, was that the
ordinary is the extraordinary.”
o ⚓ Of_Mice_and_Men⠀⇛
This recent controversy on Maus’s suitability (or not)
for Tennessee schoolchildren, though, has reinforced an
unease I’ve had for quite a while on the uses and misuses
of the extermination of European Jewry.
It should be said that the fact that the Holocaust is
treated as such a matter of importance in the United
States—which is, after all, a Christian country—is
something that needs to be acknowledged. Considering the
brutality meted out to Jews over the centuries, this is
no small thing. (And the Holocaust and Nazi oppression
were not just directed at Jews, of course.)
o ⚓ Hunter_S._Thompson: Literary_Gentleman_from_Louisville⠀⇛
Thompson always had a nose for notoriety as well as for
the news, though he didn’t really find himself until 1970
at the age of 33 when Hinckle published in the pages
of Scanlon’s, his sensational article, “The Kentucky
Derby Is Decadent and Depraved.” Alas, the magazine soon
folded. Steadman provided the art for Thompson’s expose
of Louisville’s filthy rich. Apparently, he drew the
illustrations with lipstick and eyeliner.
Peter Richardson tells the riveting story of the Hinckle/
Steadman/Thompson triumvirate in Savage Journey
(University of California Press; $27.95), a biography, in
which he also traces what he calls the “Weird Road to
Gonzo.” True, the road could be bumpy with twists and
turns, but Thompson’s journey looks and feels a lot more
civilized than Richardson makes it seem. At times, Hunter
—as friends called him— even appeared to be a gentleman
of the old school, especially with his long cigarette
holder and shiny bald head and in photos of him sitting
next to Senator George McGovern in 1972. Gonzo was a
genuine part of his act; much as Beat was a genuine part
of Kerouac’s act.
o ⚓ The_Militant_Passion_of_Emma_Tenayuca⠀⇛
Some knew her as la Pasionaria de Texas—the Texas
Passionflower. Others called her Red Emma. But most of
the people she fought alongside just called her
“comrade.” Emma Tenayuca was born in San Antonio, Texas,
in 1916 to parents of Spanish and Comanche descent, and
spent her childhood learning about Mexican identity, the
evils of Jim Crow, and revolution from her grandfather.
Emma was also constantly running off to Plaza del Zacate
in San Antonio’s Milam Park to listen to anarchists and
activists speak about politics and workers’ rights from
their soapboxes. Her first experience on the picket line
came when she was only 16. In 1933, she joined a group of
Mexican women workers from the H.W. Finck Cigar Company,
who were out on a wildcat strike over low wages and
unsanitary working conditions. The teenager was horrified
to witness the violent police response to the strike, and
was arrested herself. That early baptism into the labor
struggle convinced the young Tejana that she’d found her
place—and her purpose.
o ⚓ ‘The_Thaw’_in_black_and_white_Photographer_Vladimir_Lagrange
chronicled_the_Soviet_1960s_and_1970s._Meduza_looks_back_at_his
main_works.⠀⇛
Vladimir Lagrange, who died in Moscow on January 22 at
the age of 82, was an icon of national photography with
work published in both the Soviet and foreign press. From
1959 to 1963, he worked in the news photography division
of TASS. Until 1989, he was a special photo correspondent
for the magazine Sovetsky Soyuz. He also worked for the
magazine Rodina and in the Moscow bureau of the French
agency Sipa Press. Following a memorial service on
January 25, Meduza is publishing some of Lagrange’s
classic images, with comments by Natalia Grigorieva-
Litvinskaya, the director of the Lumière Gallery, which
hosted an exhibit in 2019 titled “Lagrange Street.”
o ⚓ The_Great_Social_Media_Retreat⠀⇛
A few weeks ago I changed my life on a whim. I deleted my
Reddit and Twitter accounts. To be fair, I have deleted
my Twitter account before, so perhaps that one isn’t a
big deal. My Reddit account on the other hand was
practically a prized possession. So what caused me to
delete it?
People. All of them. Myself included.
o ⚓ Life_in_the_neighborhood⠀⇛
I’ve worked from home since 1998. All along I’ve hoped
many more people would enjoy the privilege and share in
the benefits. Now that it’s finally happening, and seems
likely to continue in some form, let’s take a moment to
reflect on an underappreciated benefit: neighborhood
revitalization.
o ⚓ Titanium_Edition⠀⇛
I still recall how hard it was to find where the right
song was, especially once I had had a few drinks.
Carrying around a stack of CDs wasn’t fun either. Music
discovery was hard and friends, TV channels and radio
stations were my main sources of ideas. Pirating music
wasn’t exactly easy either, given how slow and expensive
internet was back then. I think my first subscription for
Internet over LAN was $20/month for something like 300MB/
month total traffic. We’d exchange music with friends and
I’d spend a lot of time scouring the LAN (usually with
the help of DC). Younger people here probably have no
idea what I’m talking about. I’m trying to make a point,
though – because it was so hard to build a music
collection, one had a lot of pride in theirs. Efforts
give meaning to stuff.
o ⚓ Radio_Amateurs_&_Skywatchers_Rejoice,_Sat_Operators_Worry:_Solar
Storm_Incoming_|_Hackaday⠀⇛
How do you look back over your life and divide it up?
Maybe by decades, cultural moments, or geopolitical
events. For radio amateurs with older callsigns there’s a
temptation to do so by solar cycles, as the roughly 11-
year period of the Sun’s activity had a huge effect on
radio propagation through the charge it creates in the
upper atmosphere. We’re now in solar cycle 25, numbered
since the 18th century when the science of solar
observation began, and as never before we’re surrounded
by information from experts such as [Dr. Tamitha Skov],
the so-called [Space Weather Woman]. When she says
something is on the way we listen, so a recent Tweet
predicting a direct hit from a solar storm with a good
probability of auroras in lower latitudes is very much
worth sharing.
o § Science⠀➾
# ⚓ The_Controversy_Surrounding_Hybrid_Cryptography⠀⇛
Despite the risks of greenfield cryptographic
algorithms, the NSA has begun recommending a
strictly-PQ approach to cryptography and have
explicitly stated that they will not require hybrid
designs.
# ⚓ The_Perils_and_Promises_of_Virtual_Reality⠀⇛
Thus begins David Chalmers enchanting new
book Reality + which engages imaginatively with
philosophical issues connected to Virtual Reality
(VR).
In his book, Chalmers argues for:
o § Education⠀➾
# ⚓ Where_are_All_the_Substitute_Teachers?⠀⇛
Some schools have even called on parents to step in
to provide adult supervision in classrooms. In New
Mexico, the governor has asked National Guard
members to serve as substitute teachers.
Normally schools hire substitutes to cover teacher
absences. But there are so many teachers out with
COVID-19 that the demand is much higher than usual.
o § Hardware⠀➾
# ⚓ An_old_photo_of_a_very_large_BBS⠀⇛
Nearly 30 years ago, I was given this picture. I
wanted to present it in a post all by itself to
give it a chance to “sink in” before I went and
used it in an analogy. First, I’ll just show the
image and explain what you’re looking at here.
# ⚓ One_machine_can_go_pretty_far_if_you_build_things
properly⠀⇛
I’ll admit: when I first saw that picture in 1993,
I was in awe of the scale. It had never occurred to
me what kind of layout you would need to run some
of these systems at that level of scale. Some small
part of me probably wanted to at least experience
that, but I never actually went that far.
# ⚓ Renaissance-Style_Drone_Would_Make_Da_Vinci_Proud_Four
Times_Over_|_Hackaday⠀⇛
For as much of a genius as Leonardo da Vinci
obviously was, modern eyes looking upon his
notebooks from the 1400s tend to see his designs as
somewhat quaint. After all, his concept of a
vehicle armored with wood would probably only have
survived the archers and pikemen of a Renaissance
battlefield, and his curious helicopter driven by
an Archimedes screw would certainly never fly,
right?
Don’t tell that to [Austin Prete] and his team from
the University of Maryland, who’ve built a da
Vinci-style quadcopter that actually flies. Called
the “Crimson Spin”, the quad is based on a standard
airframe and electronics. Details are sparse — the
group just presented the work at a vertical flight
conference — but it appears the usual plastic props
are replaced with lightweight screws made from wire
and some sort of transparent plastic membrane.
Opposing pairs of screws have the opposite
handedness, which gives the quad yaw control.
There’s a video embedded in the link above that
shows the quad being tested both indoors and out,
and performing surprisingly well. We’d imagine that
Crimson Spin might not do so well on a windy day,
given the large wind cross-section those screws
present, but the fact it got off the ground at all
is cool enough. It kind of makes you wonder where
we’d be today if da Vinci had access to BLDCs.
# ⚓ Rainbow_DIP_Switch_Is_The_Coolest_Way_To_Configure_Your
Project_|_Hackaday⠀⇛
Oftentimes, when programming, we’ll put
configuration switches into a config file in order
to control the behaviour of our code. However,
having to regularly open a text editor to make
changes can be a pain. This colorful little DIP
switch dongle from [Glen Aikins] makes for a fun
alternative solution.
o § Health/Nutrition/Agriculture⠀➾
# ⚓ Data_Highlights_‘Egregious’_Pandemic_Profiteering_by_US
Food_and_Oil_Giants⠀⇛
A new analysis released Tuesday ahead of a
congressional hearing on pandemic-era price gouging
shows that U.S. corporations in the food and energy
sectors—from Tyson to Exxon Mobil—are pushing
higher costs onto consumers while raking in ever-
increasing revenues and handing executives massive
pay packages.
Conducted by the advocacy group Food & Water Watch
(FWW), the analysis spotlights the fact that
skyrocketing food and energy—specifically
gasoline—prices have been major contributors to the
overall rise of inflation in the U.S.
Between December 2019 and December 2021, the
nation’s Consumer Price Index (CPI) jumped by 8.5%.
# ⚓ ‘Five_Alarm_Crisis’:_Teachers_Union_Warns_Pandemic_Burnout
Destroying_Schools⠀⇛
New polling out Tuesday reveals pervasive burnout
among the nation’s educators as pandemic-related
staffing shortages and other difficulties drive a
potential exodus from the teaching profession.
Released by the National Education Association, the
nation’s largest union of any profession, the
member survey shows, according to NEA president
Becky Pringle, that “after persevering through the
hardest school years in memory, America’s educators
are exhausted and increasingly burned out.”
# ⚓ The_Limits_of_Understanding_the_Pandemic_Philosophically⠀⇛
The Covid-19 pandemic has brought death to the
forefront of daily life. Whether in the
overwhelming moments of intimate grief or the
omnipresent background hum of irrepressible dread,
the virus’s deadly ramifications have been
impossible to avoid. It is the ways in which we
have responded to this crisis, however, that
philosopher Byung-Chul Han’s latest work, The
Palliative Society, wants to take up as the basis
for cultural analysis. For, as Han writes in the
opening to his book, “Our relation to pain reveals
what kind of society we are.” Written in German in
2020 and now translated into English by Daniel
Steuer, this short book (or perhaps, more
accurately, long essay) attempts to position our
social reaction to the pandemic as being of a piece
with our contemporary inability to reckon with
pain. Han seeks to utilize an extended reading of
our relation to pain as a means of opening up a
critique of our social, cultural, and political
lives. But this work demonstrates both the
possibilities and the pitfalls of taking up such a
weighty historical moment in media res. Stuck
somewhere between genuine insight and banal
truisms, radical critique and reactionary
entrenchment, The Palliative Society is never quite
able to position the pandemic as a historic event,
using it merely to confirm an argument that feels
already well-rehearsed.
# ⚓ Theranos_Verdict:_In_the_U.S.,_It_Is_Fine_to_Lie_to
Consumers_but_Not_to_Investors⠀⇛
The evidence presented during the trial showed that
Theranos technology did not work, and Holmes, while
fully aware of it, knowingly falsified the results
and forged reports. These “doctored reports” showed
that major pharmaceutical companies endorsed her
products, and even the U.S. military was using
Theranos equipment in the field.
Holmes got major names in the industry to invest
almost a billion dollars in Theranos. The investors
included the Walton family, who owns Walmart;
Rupert Murdoch, the major media mogul; the family
of Betsy DeVos, who was the former secretary of
education under the Trump administration; Larry
Ellison, the founder of Oracle; and many other
people with deep pockets. Meanwhile, Theranos’
board of directors also had dazzling names
including former U.S. secretaries of state Henry
Kissinger and George Shultz and former U.S.
secretaries of defense James Mattis and William
Perry.
# ⚓ Opinion_|_Abortion:_What_a_Complex_Web_They_Weave⠀⇛
Did you know?
# ⚓ Native_American_tribes_agree_to_$590M_settlement_with
Johnson_&_Johnson,_drug_distributors_over_opioid_epidemic⠀⇛
“The Native American population has suffered some
of the worst consequences of the opioid epidemic of
any population in the United States. Indeed,
American Indians have suffered the highest per
capita rate of opioid overdoses,” the tribal
leadership committee said in a statement filed with
the court. “American Indians and Alaska Natives had
the highest drug overdose death rates in 2015 and
the largest percentage increase in the number of
deaths over time from 1999-2015 compared to other
racial and ethnic groups.”
Johnson & Johnson agreed to pay $150 million over
the next two years while not admitting liability or
wrongdoing. The company defended its promotion of
the medications.
o § Integrity/Availability⠀➾
# § Proprietary⠀➾
# ⚓ How_to_Delete_Your_Spotify_Account_–_Plus_5
Alternative_Music_Streaming_Services⠀⇛
If you’re ready to switch to one of many
Spotify alternatives, you can delete your
Spotify account. Just don’t forget to export
all of your playlists with a service like
Soundiiz. If you have Spotify Premium, you’ll
need to head to the Spotify website to get
the process started.
# ⚓ Lock-in_and_Multi-Cloud⠀⇛
But that’s today. Let’s think ahead to 2030
and zero in on on a hypothetical future
version of AWS. First, there was that
unfortunate accident involving one of Elon’s
satellites and the Blue Origin rocket Jeff
was on. And Andy, a multibillionaire via that
Amazon-CEO package, bought out the rest of
the Kraken owners, then put in a surprise
grab and owns the Seahawks too. He’s
discovered that being a sports mogul beats
the hell out of testifying on live TV to
Pramila Jayapal.
In this scenario, activist investors and big-
time PE players have won a majority on the
Amazon board and they don’t want any of their
business units missing any chances to turn
screws that maximize revenues. Data egress
charges ratchet up every corner, as do high-
level proprietary services like Kinesis and
Lambda.
A whole lot of customers have lost control of
their cloud-computing spend; they pay
whatever their AWS account manager tells them
they’re gonna pay.
# ⚓ FBI_says_cyber_actors_could_‘disrupt’_Beijing
Olympics,_Paralympics [iophk: Windows TCO]⠀⇛
The FBI noted it was not aware of any
specific cyberattacks that were planning on
being carried out but emphasized that
athletes and others associated with the Games
should remain vigilant, including by
recommending that people leave their personal
devices at home and use a temporary phone
while in China.
# ⚓ Cyber-attack_strikes_German_fuel_supplies [iophk:
Windows TCO]⠀⇛
It has declared “force majeure” for the
majority of its inland supply activities in
Germany.
The declaration of force majeure excuses a
company from contractual agreements when an
extraordinary event occurs which is beyond
its control.
# ⚓ What_I_Learned_When_My_Parents_Got_Arrested⠀⇛
My parents, who had owned a software-resale
business, had nothing to do with the piracy
ring itself. Instead, they were charged with
30 counts of conspiracy, mail fraud, wire
fraud, and money laundering in what
authorities described as a scheme to defraud
Microsoft of millions of dollars by obtaining
discounted academic software under false
pretenses.
Microsoft initially alleged that it lost as
much as $100 million, and the local newspaper
ran with that number. Overnight, everyone
heard that my parents had been scooped up in
a massive anti-piracy raid. Their faces were
plastered on the FBI website for days, and
people assumed I was somehow sitting on $100
million stashed away in domestic and foreign
accounts.
Oh, how I wish it were true. I really could
have used that money in the weeks and months
that followed.
# ⚓ [Old] How_to_Set_Up_SSH_2fa_(Two-Factor
Authentication)⠀⇛
This tutorial guides you through setting up
Google Authenticator PAM to enable SSH 2FA
for users connecting to a Linux server. We’ll
use nano as our editor in examples.
# § Security⠀➾
# ⚓ Update_now:_Samba_prior_to_4.13.17_hit_with
remote_root_code_execution_bug_|_ZDNet⠀⇛
Samba has fixed a vulnerability in all
versions of its software prior to
version 4.13.17 that allowed for a
remote actor to execute code as root,
thanks to an out-of-bounds heap read
write vulnerability.
# § Privacy/Surveillance⠀➾
# ⚓ Snowden_Slams_Ongoing_Impunity_for_NSA’s
Domestic_Spying⠀⇛
Exiled U.S. whistleblower and
former National Security Agency
contractor Edward Snowden on
Tuesday called out years of
impunity for the NSA violating
Americans’ civil liberties and
privacy rights.
Snowden’s tweet came in response
to CNN reporting that the NSA
“failed to follow both court-
approved and internal procedures
designed to prevent officials
from using a controversial
foreign surveillance law to
inappropriately monitor
Americans’ communications.”
# ⚓ ID.me_Finally_Admits_It_Runs_Selfies
Against_Preexisting_Databases_As_IRS
Reconsiders_Its_Partnership_With_The
Company⠀⇛
Tech company ID.me has made
amazing inroads with government
customers over the past several
months. Some of this is due to
unvetted claims by the company’s
CEO, Blake Hall, who has asserted
(without evidence) that the
federal government lost $400
billion to fraudulent COVID-
related claims in 2020. He also
claimed (without providing
evidence) that ID.me’s facial
recognition tech was sturdy,
sound, accurate, and backstopped
by human review.
# ⚓ Suicide_Hotline_Collected,_Monetized_The
Data_Of_Desperate_People,_Because_Of_Course
It_Did⠀⇛
Another day, another privacy
scandal that likely ends with
nothing changing.
# ⚓ Chicago_Cops_Love_Them_Some_Facebook
Sharing,_According_To_Internal_Facial
Recognition_Presentation⠀⇛
Somewhere between the calls to
end encryption and calls to do
literally anything about crime
rate spikes at this time of year,
at this time of day, in [insert
part of the country], localized
entirely within [add geofence]
lies the reality of law
enforcement. While many continue
to loudly decry the advent of by-
default encryption, the reality
of the situation is people are
generating more data and content
than ever. And most of it is less
than a warrant away.
# ⚓ Birthday_wishes_inadvertently_give_away
private_information_online⠀⇛
Dilara Kekulluoglu at the
University of Edinburgh, UK, and
her colleagues found more than 18
million Twitter posts that
mentioned “happy birthday” in a
45-day period. Of those, 2.8
million directly mentioned a
user, so they could be used to
ascertain an individual’s
birthday. More than 66,000 of
these tweets also gave away the
age of the user, and therefore
their full date of birth.
Only around 2 per cent of the
Twitter users mentioned in those
posts shared their birth years on
their profiles, so the team warns
that well-wishers are exposing
this information for users who
haven’t proactively shared it
themselves.
# ⚓ The_EARN_IT_Act_is_back_in_Congress⠀⇛
The original EARN IT Act’s
sponsors touted endorsements from
the National Center for Missing
and Exploited Children and other
groups, and it took aim at a
surge of online child sexual
abuse content. But the bill was
strongly condemned by the
American Civil Liberties Union
and many advocates for online
civil liberties, sex workers, and
LGBT rights — who argued that it
would encourage companies to
abandon strong encryption and
privacy protections for users.
Some of these groups, including
Fight For the Future, have issued
statements against the revived
bill as well. The bill is
scheduled to be discussed by the
Senate Judiciary Committee on
Thursday.
# ⚓ EU:_Mass_travel_surveillance:_no_problem,
says_court⠀⇛
The Passenger Name Record (PNR)
Directive was agreed in April
2016 and mandates the
surveillance and profiling of
almost all air passengers
entering, travelling within, or
leaving the EU. Passenger data
has to be transmitted by travel
companies and airlines to
Passenger Information Units
(PIUs) operated by national
police forces.
# ⚓ A_cautious_green_light_for_technology-
driven_mass_surveillance⠀⇛
This cursory analysis sheds light
on some of the AG’s Opinion’s
shortcomings. It thus follows
that the CJEU should deviate from
Pitruzzella’s recommendations.
The PNR Directive, due to the
severity of its effects and its
inherent inefficiency in
fulfilling its stated purpose,
produces disproportionate
interferences with Articles 7 and
8 CFR. It ought to be
invalidated.
# ⚓ IRS_plan_to_scan_your_face_prompts_anger
in_Congress,_confusion_among_taxpayers⠀⇛
Millions of Americans could soon
have to scan their faces to
access their Internal Revenue
Service tax accounts, one of the
government’s biggest expansions
yet of facial recognition
software into people’s everyday
lives.
For now, taxpayers can still file
their returns the old-fashioned
way; the IRS began accepting
returns for 2021 earnings on
Monday, encouraging electronic
filing.
But by this summer, anyone
wanting to access their records —
including details about child tax
credits, payment plans or tax
transcripts — on the IRS website
could be required to record a
video of their face with their
computer or smartphone, and send
it to the private contractor
ID.me to confirm their identity.
# ⚓ Facial_recognition_for_all_online_IRS
accounts:_What’s_up_with_ID.me?⠀⇛
The IRS uses ID.me — a third-
party service with a thorough
registration process that
includes uploading a “video
selfie” through ID.me’s facial
recognition software — to manage
new signups for the agency’s
online tax services.
Soon, everyone who wants to use
IRS services online — including
viewing and making payments
online, updating a mailing
address, and accessing the Child
Tax Credit Update Portal — will
need to register through ID.me.
# ⚓ The_IRS_is_reportedly_looking_for_ID.me
alternatives_amid_privacy_concerns⠀⇛
Last year, the IRS announced its
plans to start requiring people
who file their taxes online to
register with third-party facial
recognition company ID.me.
Through the service, users will
have to submit a video selfie
using a webcam or mobile device
to verify their identity. The IRS
is supposed to roll out the
program this summer.
Although ID.me previously claimed
it only uses one-to-one facial
matching, which involves matching
a user’s face with images of the
same face, ID.me CEO Blake Hall
admitted it uses technology that
matches faces against a larger
database. This only exacerbates
privacy concerns — politicians,
the American Civil Liberties
Union, and digital rights
advocates have already spoken out
about the IRS’ use of the
software.
# ⚓ Website_fined_by_German_court_for_leaking
visitor’s_IP_address_via_Google_Fonts⠀⇛
Earlier this month, a German
court fined an unidentified
website €100 ($110, £84) for
violating EU privacy law by
importing a Google-hosted web
font.
The decision, by Landgericht
München’s third civil chamber in
Munich, found that the website,
by including Google-Fonts-hosted
font on its pages, passed the
unidentified plaintiff’s IP
address to Google without
authorization and without a
legitimate reason for doing so.
And that violates Europe’s
General Data Protection
Regulation (GDPR).
# ⚓ Website_operator_fined_for_using_Google
Fonts_“the_cloudy_way”⠀⇛
The court agreed, demanded that
the website operator start
hosting fonts locally, and
awarded the complainant damages
of €100 (about $110).
The court’s argument doesn’t seem
to be suggesting any and all
other third party “widget
linking” is now considered
illegal in Germany (or, more
particularly, in the region where
this court holds sway), but only
that websites are expected to
host content locally if that’s
easily possible: [...]
# § Confidentiality⠀➾
# ⚓ Why_I_won’t_use_Let’s_Encrypt⠀⇛
Why do not I forcefully
redirect people from HTTP
to HTTPS?
First reason is that I just
do not have geographically
distributed servers under
my control. Most of my
websites are hosted both on
my own home server and on
some VPS in another city. I
can not set up TLS on VPS,
because its hosting company
obviously will have access
to all of its internals,
including TLS private keys.
Currently my websites have
two IP addresses, with two
independent HTTP servers,
but with only single HTTPS
server and single dummy
TCP-proxy located on VPS.
If my main server is down,
then the whole HTTPS is
down too. If I give TLS
private keys to the hosting
company, then what is the
point of using TLS and
lying that it can
authenticate the endpoint
domain?
Second reason is that it is
not my responsibility to
impose user the desired
security protocol usage.
Possibly there is already
IPsec transport session,
transparently securing the
link. Possibly we use some
overlay network like
Yggdrasil, where TLS is
just pointless. My tarballs
and Git tags are always
signed with OpenPGP key.
TLS even won’t give any
metadata privacy there
because of known tarballs/
pages sizes.
Next point is that there
just can not be some
objectively absolutely
valid and proper global
scale PKI certificate.
Because its validity fully
depends on your exact point
of view, specifically on
what trust anchors you use
and validation rules you
apply.
o § Defence/Aggression⠀➾
# ⚓ McEnany’s_Texts_Lead_to_Request_for_Ivanka_Trump_to_Speak
With_Jan._6_Committee⠀⇛
# ⚓ More_Than_a_Dozen_HBCUs_Faced_Bomb_Threats_on_First_Day_of
Black_History_Month⠀⇛
# ⚓ NATO_Nonsense_and_Panic⠀⇛
Many or most U.S. media overlooked it – that is,
buried it. Or emasculated it. In Germany they
couldn’t fully ignore it – though unpleasant as a
messy cat cadaver near the red carpet at a major
film event. This was no star-studded premiere,
however, but a dangerous, frightening political and
military program, and the disturbing element was
not a raggedy, dead alley-cat but the elegantly-
uniformed boss of the German Navy. Yet here, too, a
demise was involved – that of the vice-admiral’s
career!
What sin earned him such a fate? When asked about
the month-long NATO-Washington campaign against
Putin and Russia, based only on vague, dubious
assumptions and prophesies by anonymous experts yet
rushing headlong toward military catastrophe, this
top-level expert had the temerity to puncture the
foundation of the whole campaign with one word:
“Nonsense!”
# ⚓ International_Support_Grows_for_Mexico’s_Lawsuit_Against_US
Gun-Makers⠀⇛
In a big boost to the Mexican government’s historic
federal lawsuit against American gun-makers, 13
U.S. states, the District of Columbia, two
countries, a coalition of attorneys general, and
numerous advocacy groups on Monday filed or joined
amicus briefs supporting Mexico’s litigation, which
seeks to hold weapons manufacturers accountable for
the violence they facilitate.
“The defendant gun manufacturers send guns to
Mexico, where transnational drug cartels use them
to inflict violence on both sides of the border.”
# ⚓ Opinion_|_How_Much_More_Deadly_Will_the_Next_Variant_of
Trumpism_Be?⠀⇛
Imagine that you were experiencing all of this (and
by this, I mean our lives right now) as if it were
a novel, à la Daniel Defoe’s A Journal of the
Plague Year. The famed author of Robinson Crusoe —
Defoe claimed it had been written by the fictional
Crusoe himself — was five years old in 1665. That
was when a year-long visitation of the bubonic
plague decimated London. It probably killed more
than 100,000 of that city’s residents or 15% of its
population. As for Defoe, he published his
“journal” in 1722, 57 years later. He wrote it,
however, as if he (or his unidentified protagonist)
had recorded events as they were happening in the
way that all of us, whatever our ages, have been
witnessing the ravages of the many variants of
Covid-19 in our own all-too-dismantled lives.
# ⚓ Opinion_|_North_Korea,_Perpetual_Victim_of_the_US_Military-
Industrial_Complex⠀⇛
It seems hard to believe that in these possible end
times in the midst of a global pandemic with an
endless succession of catastrophic climate
disasters and thousands of nuclear weapons poised
and pointed in the U.S. and Russia, ready to
destroy life on earth, we are beset by a bought,
corrupted mainstream media that assaults us with
the “wrongdoings” of Russia and China, and most
recently North Korea, with barely a mention in
their assaultive reporting of how the U.S. might be
the cause in the matter. Nor do they report on the
many remedies that have been rejected by the United
States in its drive for global domination. Instead
of promoting the critical opportunities we must now
seize—all nations and peoples of the world—to work
cooperatively to save Mother Earth, the western
news reports serve up a steady daily diet of the
harm that could be inflicted upon an innocent
United States, echoing shades of the dreadful 1950s
McCarthy Era in a new Cold War II and maybe World
War III.
# ⚓ A_Police_Car_Hit_a_Kid_on_Halloween_2019._The_NYPD_Is
Quashing_a_Move_to_Punish_the_Officer.⠀⇛
It was a little more than two years ago that I
really started learning about the reality of police
oversight in America.
On Halloween night in 2019, my wife and our then-6-
year-old daughter were walking home from trick-or-
treating in our Brooklyn neighborhood when they saw
a New York Police Department car go the wrong way
down a street and smack into a teenager, who fell
and then ran away.
# ⚓ Amid_US-Russia_Escalation,_Activists_Emphasize_NATO_Is_“Not
About_Security”⠀⇛
# ⚓ ‘We_have_other_problems’_As_the_world_worries_about_an_all-
out_war_between_Russia_and_Ukraine,_Meduza_reports_from_the
border_with_the_Donbas⠀⇛
Since the fall of 2021, media outlets around the
world have been discussing the possibility of
another Russian invasion of Ukraine. Moscow has had
troops massed near the Ukrainian border for several
months now — in response, NATO countries, led by
the United States, have deployed additional forces
to Eastern Europe and are threatening the Kremlin
with sanctions. What do people living near the
Russian border with Ukraine think about these
escalating tensions? For Meduza, journalist Gleb
Golod traveled to towns and villages in Russia’s
Rostov region to find out.
# ⚓ 100+_Anti-War_Groups_Demand_Biden_End_Brinkmanship_With
Russia⠀⇛
More than 100 advocacy organizations representing
millions of people across the U.S. demanded Tuesday
that the Biden administration take immediate steps
to defuse tensions with Russia as the two nuclear-
armed powers remain perilously close to war over
Ukraine.
“We call upon President Biden to end the U.S. role
in escalating the extremely dangerous tensions with
Russia,” the progressive groups said in a joint
statement spearheaded by CodePink and
RootsAction.org. “It is gravely irresponsible for
the president to participate in brinkmanship
between two nations that possess 90% of the world’s
nuclear weapons.”
# ⚓ The_Exit_From_the_Ukraine_Crisis_That’s_Hiding_in_Plain
Sight⠀⇛
The crisis over Ukraine grows simultaneously more
dangerous and more absurd. Russia has amassed more
than 100,000 troops on the Ukrainian border,
demanding that NATO not admit Ukraine and stop its
expansion east. Russian officials want those
demands answered immediately, but President
Vladimir Putin also says he won’t make war.
# ⚓ Russia_Gains_Much_From_Threats_to_Invade_Ukraine,_But_Knows
That_Actually_Doing_So_Would_be_a_Disaster⠀⇛
Russian troops might be able to capture Kyiv in a
week, but this would only be the start of a long
war that Russia would find it impossible to win. A
more limited Russian offensive in east Ukraine –
such as seizing a land corridor between the Russian
separatist Donbas and Russian annexed Crimea – is
scarcely a more attractive option. It would push
the rest of Ukraine further into the embrace of
Nato, which would be exactly the opposite of what
Russia wants.
President Putin may be vindictive and
unpredictable, but he has never overplayed his hand
as Russian leader in military conflicts from
Chechnya in 1999 to Syria in 2015. In all cases,
Western hopes and expectations that he was plunging
into a quagmire were disappointed.
# ⚓ More_Than_100_Antiwar_Groups_Call_on_Biden_to_End
Brinksmanship_With_Russia⠀⇛
# ⚓ “It’s_Not_About_Security”:_Belgian_Peace_Activist_Says_NATO
Has_Outlived_Its_Purpose⠀⇛
To speak about the key role NATO is playing in the
Ukraine crisis, we speak with Ludo De Brabander,
spokesperson of the peace organization Vrede vzw in
Belgium, where NATO is headquartered. De Brabander
says NATO has outlived its purpose, and touches on
how activists in NATO countries like Belgium are
pushing against narratives in the media that war
with Russia is necessary.
# ⚓ Germany_Refuses_to_Send_Arms_to_Ukraine_Despite_Pressure
from_U.S._&_NATO⠀⇛
Germany’s new coalition government is refusing to
send lethal weapons to Ukraine but has offered to
send over 5,000 combat helmets to protect Ukrainian
soldiers in case of a Russian attack. The move has
been ridiculed as the U.S. and other NATO countries
continue to send military support to Ukraine. In
response, German Chancellor Olaf Scholz has
promised his country will stay in tune with
European Union and NATO policies toward Russia. To
speak more about Germany’s stance toward Ukraine,
we’re joined by German peace activist and executive
director of the International Peace Bureau Reiner
Braun, who calls on the European Union to establish
a more “common politics with Russia” to prevent a
war in Central Europe. He also says war in the
region could result in use of nuclear weapons that
would lead to “the end of Europe.”
# ⚓ Ukrainians_Doubt_a_Russian_Invasion_Is_Imminent_as_U.S.
Peace_Groups_Urge_Biden_to_Halt_Escalation⠀⇛
The United States and Russia sparred on Monday over
the crisis in Ukraine at the United Nations
Security Council. Meanwhile, U.S. senators are
preparing to unveil a bill that would target
Russian President Vladimir Putin, Russian banks and
other entities with sanctions. To discuss the
Ukraine crisis, we’re joined by the co-founder of
CodePink, Medea Benjamin, who says “we need the
voice of the American people” to oppose U.S.
escalation and also calls on U.S. progressives to
vocalize their opposition to fueling a war in
Europe. We also speak with Ukrainian sociologist
Volodymyr Ishchenko, who says Ukrainian
intelligence does not see a Russian invasion as
likely or economically wise for Russia.
# ⚓ How_US_meddling_split_Sudan,_creating_an_oil_republic
drowning_in_poverty_and_conflict⠀⇛
# ⚓ Nigeria_and_Indonesia_cement_defence_ties⠀⇛
Following a meeting between the Indonesian
Ambassador to Nigeria Usra Harahap and the
executive vice-chairman of Nigeria’s National
Agency for Science and Engineering Infrastructure
(NASENI), Mohammed Sani Haruna, both countries
accepted a draft letter of intent on bilateral
defence cooperation.
The NASENI’s mission is to further the transfer of
technologies to Nigeria in various areas including
defence and aeronautics. Haruna told The Guardian
Nigeria that Indonesia would assist the country in
developing “aircraft, both civil and military, the
armoured personnel carrier, and other equipment
needed by the military”, with approval from the
Nigerian Federal government.
# ⚓ Taiwan_Detects_Chinese_Electronic_Warfare_Aircraft_Near
Island⠀⇛
The Taiwanese MND stated that the aircraft flew on
Monday between Taiwan and Pratas, an island in the
northern South China Sea, which the government
controls in Taiwan.
# ⚓ Ambitious_China_gears_up_to_flex_power_in_the_conflict-
riven_Horn_of_Africa⠀⇛
The Horn of Africa – located in the easternmost
corner of the African continent, takes its name
from the horn-shaped land formation at the southern
end of the Red Sea and on the Gulf of the Aden.
Five of the region’s seven countries – the Sudan,
Eritrea, Djibouti, Somalia and landlocked Ethiopia,
are situated looking into the Indian Ocean south of
the Arabian Peninsula. Located on the main shipping
route for the transport of oil from the Persian
Gulf to Europe and the United States, the Horn of
Africa is considered one of the most strategically
important regions in the world. Sadly the region is
endowed with rivers, lakes, forests and livestock,
and has untapped rich deposits of natural resources
including gold, petroleum, salt and natural gas
etc. Yet its two hundred million people remain one
of the poorest on the earth.
# ⚓ Accused_American_ISIS_leader_‘highly_intelligent’_and
‘marksman’:_Former_friend⠀⇛
One former friend, who said she last spoke to
Fluke-Ekren more than 10 years ago, painted a
picture of a woman who was close with her family
but then became increasingly radicalized. Fluke-
Ekren was arrested in Syria, where she moved a
decade ago and married a “prominent” ISIS leader,
according to court documents.
# ⚓ Turkey_Helps_ISIS_Attack_Rojava⠀⇛
It’s no accident that the time bomb exploded on the
fourth anniversary of Turkey’s invasion and
occupation of Afrin in 2018. Turkey’s support of
ISIS and other jihadis is an open secret. A Turkish
drone even bombed an SDF vehicle that was racing to
Hasaka to help recapture ISIS prisoners. According
to an October 2021 report on ISIS sleeper cells,
raids resulting in the arrest of ISIS members
brought to light documents showing links to Turkish
intelligence, suggesting that the two coordinate
closely. The SDF believes the Hasaka attack was
organized by Turkish forces and their proxies in
territories Turkey occupied in 2019, including
Serekaniye and Tal Abyad, and the plan was for the
ISIS prisoners to flee there and regroup.
# ⚓ Trump_Steals_a_Strategy_From_Mussolini’s_Playbook⠀⇛
That was a dangerous signal in and of itself, as it
came from a former president with a track record of
abusing his pardon authority for political
purposes. It suggested a willingness to employ the
power of the presidency to circumvent legitimate
and necessary legal accountability for those who
launched a deadly attack on the US Capitol, and for
himself—as the man who told those at the January 6
rally to head to the Capitol and “fight like hell”
to overturn the results of the 2020 election.
# ⚓ Trump_Says_He_Would_Consider_Pardons_for_Jan._6_Defendants
if_Elected⠀⇛
At least 700 people have been arrested in
connection with the Jan. 6 [insurrection],
including 11 who have been charged with seditious
conspiracy. Some have said they believed they were
doing Mr. Trump’s bidding.
o § Environment⠀➾
# ⚓ As_China_replants_its_own_forests,_it_is_destroying_the
world’s⠀⇛
These developments might be interpreted as proof of
China’s dedication to protecting trees. Is there
substance to such an interpretation, or is the
declared appreciation for forests merely a mirage?
If history is any guide, reality hews to the
latter. That’s because China has a very long record
of razing forests to feed its development.
Alongside its economic rise in recent decades, it
has taken on an outsize and accelerating role in
global deforestation.
# ⚓ First_Latin_American_e-waste_report_published⠀⇛
The report was produced by the Sustainable Cycles
(SCYCLE) Programme, co-hosted by the UN University
(UNU) and the UN Institute for Training and
Research (UNITAR). It covers the 13 countries
participating in the UNIDO-GEF LAC E-waste project:
Argentina, Bolivia, Chile, Costa Rica, Ecuador, El
Salvador, Guatemala, Honduras, Nicaragua, Panama,
Peru, Uruguay and Venezuela.
# ⚓ Biden_Praised_for_Reversing_Trump_Effort_to_Unleash_More
Toxic_Air_Pollution⠀⇛
The Biden administration on Monday won strong
praise from public health defenders following the
Environmental Protection Agency’s move to restore
the legal basis for regulating mercury and other
toxic air pollutants from coal- and oil-fired power
plants.
“Administrator Regan has taken a critical step
forward in restoring vital public health
protections.”
# ⚓ After_Passing_‘Point_of_No_Return’_in_2014,_Hot_Oceans_Are
Now_‘New_Normal’⠀⇛
A study published Tuesday revealed that ocean
heatwaves fueled by human-caused climate change
passed the “point of no return” in 2014 and have
become the “new normal.”
“These dramatic changes we’ve recorded in the ocean
are yet another piece of evidence that should be a
wake-up call to act on climate change.”
# § Energy⠀➾
# ⚓ North_Carolina_Fertilizer_Plant_Fire_Forces_Thousands
to_Evacuate⠀⇛
Thousands of residents who live within a one-
mile radius of a fertilizer plant in Winston-
Salem, North Carolina were ordered to
immediately evacuate after a fire broke out
at the facility Monday night.
Although firefighters initially battled the
blaze at the Winston Weaver Co. fertilizer
plant, located at 4440 N. Cherry St., the
crews were pulled back after about an hour
and a half due to the explosion risk, Fire
Chief Trey Mayo said during a Tuesday morning
press conference.
# ⚓ Climate_Groups_Urge_Biden_Not_to_Fight_Ruling_Against
Oil_and_Gas_Lease_Sale⠀⇛
# ⚓ Biden_Urged_Not_to_Fight_Court_Ruling_Against_Massive
Oil_and_Gas_Lease_Sale⠀⇛
As the fossil fuel industry clamors for an
appeal, the Biden administration on Tuesday
faced pressure from environmentalists to
adhere to a judge’s decision blocking a
massive oil and gas lease sale in the Gulf of
Mexico, the site of the catastrophic
Deepwater Horizon spill.
“We urge you to comply with the court’s
ruling and not appeal the court’s decision,”
more than 70 climate groups wrote in a letter
to President Joe Biden and Interior Secretary
Deb Haaland. “The [Department of the
Interior] should not continue to defend
unlawful drilling for oil and gas in public
waters in appellate court given the impacts
on our climate, clear violations of federal
environmental standards, and public
commitments made by President Biden to end
the practice.”
# ⚓ Protests_Erupt_in_Argentina_Over_Plan_for_Offshore
Oil_Drilling⠀⇛
On January 4, thousands of people took to the
streets of Mar del Plata, a coastal city
roughly 250 miles south of Buenos Aires,
Argentina. They were there to protest the
plans by Norwegian oil company Equinor to
begin offshore oil exploration later this
year.
They held signs that read “the sea is ours!”
and “an ocean free of oil,” and they chanted,
shouted, and sang. The protests were focused
in Mar del Plata, a beach town closest to the
offshore blocks, but spread to other cities
in the province and around the country.
# ⚓ Lobbyist_Behind_The_Sun’s_Petrol_Car_Ban_Survey
Admits_He_Used_‘Loaded’_Question⠀⇛
A survey supposedly showing public opposition
to the government’s plans to phase out petrol
and diesel cars was carried out by a motoring
lobbyist who admits he “doesn’t care” that
the poll involved a “loaded” question.
The Sun reported on Saturday that “fuming
voters” oppose the UK’s 2030 ban on new
fossil fuel-powered cars, with three in five
people saying they would not vote for an MP
who supports it.
# ⚓ Oil_Is_Killing_the_Planet_—_And_Driving_Inflation⠀⇛
Today’s inflation isn’t just caused by a
post-pandemic rebound in fuel prices, but a
long-term exhaustion of oil production. We
need to end our dependency on fossil fuels
without it becoming the pretext for another
wave of austerity.
# ⚓ The_Case_Against_[Cryptocurrency]⠀⇛
I’ve long been extremely skeptical of
[cryptocurrency]1, regardless of all the hype
surrounding it, and me being surrounded by
many people who are very passionate about it.
Seems there’s no shortage of believers in
[cryptocurrency] and blockchain in the tech
circles, and no shortage of people who are
drawn to “get rich quick” schemes. I’ve been
meaning to write a bit of thoughts on the
subject for a while now, but Martin O’Leary
saved me some work by writing a fantastic
article that perfectly reflects my own
sentiment. In a nutshell: [...]
# ⚓ Should_I_get_my_paycheck_in_crypto?_Experts_weigh_in
as_America_Competes_Act_looms⠀⇛
In December 2020, Russell Okung became the
first NFL player to be paid part of his
salary in Bitcoin. Other pro-athletes have
followed suit, with Aaron Rodgers announcing
in October 2021 that he would also be paid
partially in Bitcoin and Trevor Lawrence
placing his signing bonus in a cryptocurrency
account in April 2021.
# ⚓ Bitcoin_miners_pressed_on_climate_impact,_power
consumption⠀⇛
Cryptocurrencies have come under increasing
fire for the industry’s power consumption,
which is now comparable to the entire country
of Argentina.
The letters raise the stakes in Senator
Warren’s campaign to crack down on wasteful
Bitcoin operations after she sent a similar
request in December to Greenidge Generation
Holdings, which powers its upstate New York
facility with a natural gas plant.
# ⚓ We’re_in_a_Climate_Crisis_—_But_the_Pipelines_Keep
Coming⠀⇛
The Spire case is exceptional in a number of
ways, and yet experts say the project’s
problems exemplify everything that is wrong
with the natural gas pipeline approval
process.
# ⚓ Meta_abandons_its_cryptocurrency_venture,_Diem⠀⇛
The Facebook-backed digital currency project
Diem announced Monday the winding down and
$182-million sale of its technology, capping
a years-long initiative that drew significant
concern from regulators.
# ⚓ Facebook_Is_Reportedly_Trying_To_Sell_Off_Its_Botched
Cryptocurrency⠀⇛
Facebook made a huge splash in 2019 when it
announced Libra, a “stable digital
cryptocurrency” meant to revolutionize global
financial technologies. Even the likes of
Uber, Spotify, PayPal, Visa, and Mastercard
were on board, signing on as corporate
partners with a $10 million stake each.
But the ambitious venture imploded after
facing fierce backlash from US regulators and
even governments around the world.
# § Overpopulation⠀➾
# ⚓ Anti-natalism_(and_other_problems)⠀⇛
My main annoyance is, and I’ve (anecdote
alert) encountered this time and time again,
is people who are like “I don’t need to eat
plants or cut down on air travel because I’m
not gonna have kids”… and then they do end up
having kids.
It’s such a science-fiction, implausible,
scapegoat of a solution.
o § Finance⠀➾
# ⚓ Government_Contracting:_the_Next_Big_Battleground_for_a
More_Equal_America?⠀⇛
# ⚓ Opinion_|_No_Quick_Fixes:_Working_Class_Politics_From_Jim
Crow_to_the_Present⠀⇛
With a new book out Tuesday reflecting on his years
growing up within—and moving through—the racist
apartheid order that loomed over the U.S. South in
the 1950s and 60s during his upbringing and early
adulthood, political scientist Adolph Reed Jr.
offers his unique perspective on the Jim Crow era,
but please do not call it a memoir.
# ⚓ A_Wall_Street_Veteran_Speaks_Out_–_Bubbles_&_the_Planet⠀⇛
Nowadays, a lot of the air has come out of hot
stocks of the covid era, losing 30%-40%-50%, or
more, in only a couple of months, e.g. Netflix
falling from $700 down to $390/share within 3
weeks. That’s a lot of hot air wheezing out
quickly. As Joe Granville, market technician 1923-
2013, famously said: They (investors) are “bag-
holders.”
The title of the Bloomberg Grantham article refers
to more than overvalued stocks, wherein he claims a
Goldilocks period over “the past 25 years is
ending, and the world needs to prepare for a future
of inflation, slower growth, and labor shortages,”
as stated in the Bloomberg Front Row interview.
# ⚓ More_Thoughts_on_the_Great_Inflation_Debate⠀⇛
There are three main components to the Summers-
Furman (SF) argument. (Their arguments are not
identical, so I’m being a bit unfair to both in
trying to mash them together.) The first is that
the Biden administration provided excessive
stimulus to the economy with the American Recovery
Act (ARA) passed by Congress last February. They
argue that demand for goods and services far
exceeded the economy’s ability to supply them,
leading to a sharp uptick in the rate of inflation.
Second, the SF position is that this jump in
inflation has unmoored inflationary expectations.
While households and businesses had long come to
expect low and stable inflation, the surge in
inflation we saw in the last year has changed
people’s expectations. Just to be clear, this is
more Summers’s concern than Furman’s. Also, he
views this as a serious risk, but not a necessary
outcome from the current situation.
# ⚓ We_Can’t_Let_Build_Back_Better_Be_Replaced_With_Manchin’s
Wish_List⠀⇛
# ⚓ Poor_People’s_Campaign_Denounces_Dems’_Push_for_Means-
Tested_Child_Tax_Credit⠀⇛
Leaders of the Poor People’s Campaign on Tuesday
blasted Sen. Joe Manchin’s proposal to means-test a
child tax credit that expired because the Senate
hasn’t passed the House-approved Build Back Better
Act—largely due to opposition from the West
Virginia Democrat.
“Sen. Manchin and others want to do away with it
now—not because it didn’t work, but because it
did.”
# ⚓ Inflation_Policies_Must_Deal_With_Impact_of_Rising_Food
Prices_on_the_Poor⠀⇛
# ⚓ Amid_Push_for_Ban,_Lawmakers_Traded_$355_Million_of_Stock
in_2021⠀⇛
As the coronavirus pandemic continued to roil the
U.S. economy and take lives in 2021, congressional
lawmakers and their family members went on a stock
buying and selling spree, trading an estimated $355
million worth of shares in Facebook, Apple, and
other prominent corporations.
According to a new analysis of financial
disclosures by Capitol Trades and reporting from
MarketWatch, at least 113 members of Congress have
divulged stock transactions completed by themselves
or members of their families in 2021.
# ⚓ ‘Puerto_Rico_Hasn’t_Had_the_Opportunity_to_Develop_Its_Own
Economic_Future’⠀⇛
Janine Jackson interviewed the Center for Popular
Democracy’s Natalia Renta about the Puerto Rican
debt deal for the January 28, 2022, episode of
CounterSpin. This is a lightly edited transcript.
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ Nature_on_the_Political_Chopping_Block⠀⇛
# ⚓ New_5-Minute_Video_Summarizes_Joe_Manchin’s_‘Brazen’
Corruption⠀⇛
Although right-wing Sen. Joe Manchin’s financial
conflicts of interest have been well-documented, a
new video released Monday details how the West
Virginia Democrat’s “brazen” corruption has
derailed his party’s immensely popular economic
policies.
Not only did Manchin take more than $1 million from
corporate-tied PACs last year as he watered down
and obstructed the Build Back Better Act (BBB), but
he “repeatedly timed his key attacks on [President
Joe] Biden’s agenda to occur at events with his
largest corporate donors,” according to pro-worker
media group More Perfect Union, which summarizes
its research in the following five-minute video.
# ⚓ Pro-government_media_outlets_receive_preference_at
government_briefings⠀⇛
Regardless of viewership, popularity, or
readership, the government gives preference to pro-
government journalists and their media outlets
during its regular press conferences. Critical
media outlets, such as Telex, are left standing at
the back of the line. This became clear when we
carefully looked through all the government
briefings in 2021 and noted the order in which
journalists present were addressed by the
politicians leading the events. Translation by
Dominic Spadacene
# ⚓ Big_tech_should_reimburse_victims_of_online_scams:_British
lawmakers⠀⇛
Big tech companies whose online platforms carry
advertisements for scams should be made to
reimburse victims, British lawmakers said, as part
of wider efforts to combat a growing epidemic of
online fraud in Britain.
While banks have signed up for a voluntary code to
reimburse fraud victims who do enough to protect
themselves, there is not sufficient regulation
governing social media and other websites where
victims are often first lured in, Mel Stride,
chairman of the cross-party Treasury committee,
told Reuters
# ⚓ Twitter’s_algorithm_favours_the_political_right,_a_recent
study_finds⠀⇛
In this climate, Twitter commissioned a study to
understand whether their algorithm may be biased
towards a certain political ideology. While Twitter
publicised the findings of the research in 2021,
the study has now been published in the peer-
reviewed journal PNAS.
# ⚓ Nord_Stream_2:_Russia-Germany_gas_pipeline_becomes_a
geopolitical_lever⠀⇛
The crisis surrounding Ukraine has been a harsh
reminder to Europeans of just how dependent they
are on Russian energy supplies. While the European
Union weighs its options for a united and robust
response to Russia if Vladimir Putin decides to
invade Ukraine, the bloc is feeling a new sense of
unease over its dependence on Russian oil and gas.
# ⚓ Nord_Stream_2:_The_gas_pipeline’s_second_power_struggle⠀⇛
Germany is almost totally reliant on natural gas
imports, with Russia accounting for more than half
of supplies in 2020, according to IHS Markit.
Europe’s No.1 economy needs to wean itself off coal
and nuclear as part of its energy transition, and
wants to use natural gas as a bridge until it can
build or import enough renewable energy.
o § Misinformation/Disinformation⠀➾
# ⚓ Neil_Young,_Joe_Rogan,_and_a_Swedish_Billionaire⠀⇛
I think part of the reason why I feel like I’m not
communicating well when I write about Spotify is I
focus so much on the negative aspects of the
operation. Another reason is I tend to forget that
just because it is by far the most popular music
streaming platform on the planet, what this means
in practice is that there are hundreds of millions
of mostly young people around the world for whom
listening to music means opening Spotify, but then
there are billions of other people around the
world, largely middle-aged or older folks, who have
never used a music streaming app of any kind.
So I’d just like to put it out there now at the
outset that I completely understand why Spotify is
so popular, and I use the platform regularly,
despite all my complaints about the way the company
is run. I am also a regular user of so many other
platforms that are run by other very large
corporations with predatory corporate practices,
including but not limited to Facebook, Google,
Uber, and Airbnb.
# ⚓ Joe_Rogan_row_puts_cost_of_Spotify_podcasts_under_investor
microscope⠀⇛
Spotify investors will focus on how much its
‘Netflix for audio’ strategy is costing the
streaming service when it reports fourth-quarter
results on Wednesday against the backdrop of
several angry high-profile artists withdrawing
their tracks.
Over the past four years, Spotify has spent more
than $1 billion on podcasts such as Joe Rogan’s in
an attempt to triumph over rival music subscription
services from Apple and Amazon.
# ⚓ The_Joe_Rogan_controversy_is_what_happens_when_you_put
podcasts_behind_a_wall⠀⇛
We’re moving away from a world in which a podcast
player functions as a search engine and toward one
in which they act as creators and publishers of
that content. This means more backlash and room for
questions like: why are you paying Rogan $100
million to distribute what many consider to be
harmful information? Fair questions!
This is the cost of high-profile deals and attempts
to expand podcasting’s revenue. Both creators and
platforms are implicated in whatever content’s
distributed, hosted, and sold, and both need to
think clearly about how they’ll handle inevitable
controversy.
# ⚓ Joe_Rogan_Issues_Absolutely_Terrible_Apology_For_Covid
Misinfo⠀⇛
He posted a video on his Instagram on Sunday
wherein he addressed the criticism that his show
has spread COVID misinformation. While he was quick
to offer a full apology to Spotify, he stopped
short of a complete mea culpa to Young and
Mitchell, nevermind the public to whom he’s been
spreading extremely dubious fear about vaccines.
# ⚓ Oh_Spotify…⠀⇛
If you’ve been living under a rock for the last few
days, you wouldn’t have heard about the shit show
that is Joe Rogan sharing COVID misinformation on
his podcast and Spotify doing nothing about it.
Needless to say, this has caused uproar all over
the Internet and it seems that people are
boycotting the platform, with Neil Young being the
most vocal on the matter.
# ⚓ Spotify’s_Joe_Rogan_Problem_Isn’t_Going_Away⠀⇛
Mr. Rogan could double down on Covid-19
misinformation, daring Spotify to de-platform him
and casting himself as a “victim of the woke mob,”
censored for speaking too many uncomfortable
truths. He could wriggle out of his Spotify deal
and head back to YouTube and to the other platforms
that used to carry his show. (He could even go to a
right-wing social network like Gettr or Parler, but
I’m guessing he’d prefer an audience.)
# ⚓ Spotify_Isn’t_Really_About_the_Music_Anymore⠀⇛
The company’s deal with Rogan was part of a larger
strategic shift whose implications listeners may
not fully understand. Since launching in 2008,
Spotify has transformed the music world by helping
make on-demand streaming a reality for millions of
listeners and rescuing the industry’s coffers from
a years-long decline. But Spotify pays most of its
revenues from songs back to labels and artists and
has rarely turned a profit. In 2019, the company
announced a new focus on “audio,” meaning recorded
books, live chats, and the booming medium of
podcasts. Spotify began paying out millions in
exclusive deals with such creators as Rogan, the
Obamas, Bill Simmons’s Ringer network, and Prince
Harry and Meghan Markle.
# ⚓ Spotify_is_more_than_just_a_bystander_to_Joe_Rogan’s
misinformation⠀⇛
In response to the growing boycott fronted by Young
and Mitchell, Spotify has promised to amend its
protocols, applying a “content advisory” to podcast
episodes that discuss covid-19, which the company
says will link to reliable sources about the
pandemic. It’s a move straight from the social
media company playbook, reminiscent of Facebook and
Twitter’s efforts to rein in misinformation that
could cause real-life harm to its users. It’s a
response that might befit Spotify if an unknown
podcaster uploaded an episode exclaiming the
benefits of ivermectin, the horse-deworming drug
that Rogan has falsely claimed helps treat covid-
19.
But Rogan isn’t an unknown podcaster uploading to a
platform, getting paid fractions of a cent per
stream. Rogan is on Spotify’s payroll to the tune
of $100 million.
# ⚓ Insult_atop_injury_to_Syrian_photographer_as_China_diplomat
misuses_war_photos⠀⇛
Lijian, seeking a correction and apology for the
use without permission of his work and the
misrepresentation of the images. Zhao’s Jan. 24
tweet said: “This is 20 years of war, America’s
consequences for children in ‘Afghanistan’.”
Suleiman noticed it on Jan. 27.
“These large and small shells are the Syrian Assad
regime supported by Russia…the legacy of attacks
against Syrian civilians and children,” wrote
Suleiman, who at 23 has spent half his life with
his country embroiled in a brutal civil war.
“He did not contact me and did not apologize after
deleting the tweet,” Suleiman told RFA’s Mandarin
Service in an interview by text, translated from
Arabic to English.
# ⚓ Spotify_CEO_Daniel_Ek_Officially_Responds_to_Neil_Young’s
Pullout_—_Here’s_His_Complete_Statement⠀⇛
# ⚓ Spotify’s_Joe_Rogan_Mess_Exposes_Larger_Rift_Over_Rules,
Streaming_Revenues⠀⇛
But as Spotify is under the spotlight for its
handling of Rogan — who released an episode in
December featuring a vaccine skeptic who baselessly
claimed people were being “hypnotized” to believe
facts about COVID, sparking 270 medical pros to
write an open letter in protest — the rift is
exposing issues that artists and content creators
have long been frustrated about. Even Young, who
left “because Spotify is spreading fake information
about vaccines,” added elsewhere in his exit letter
on his website that Spotify “continues to peddle
the lowest quality in music reproduction.”
# ⚓ Graham_Nash_and_India_Arie_join_Neil_Young’s_Spotify
boycott_over_‘problematic’_Rogan⠀⇛
Nash declared his support for his Crosby, Stills,
Nash & Young bandmate Tuesday after “having heard
the COVID disinformation spread by Joe Rogan on
Spotify.” Young previously pulled much of his music
library from the app after Spotify failed to cut
ties with Rogan, a controversial podcast host known
for fueling conspiracy theories about COVID-19
treatments and vaccines.
“I am requesting that my solo recordings be removed
from the service,” Nash said in a statement. “There
is a difference between being open to varying
viewpoints on a matter and knowingly spreading
false information which some 270 medical
professionals have derided as not only false but
dangerous.
# ⚓ Fact_check:_WikiLeaks_did_not_release_footage_that_proves
moon_landing_staged⠀⇛
The claim was fact-checked by Reuters and found to
be false.
o § Censorship/Free Speech⠀➾
# ⚓ As_the_Right_Censors_Public_Libraries,_Families_Are_Forming
Banned_Book_Clubs⠀⇛
# ⚓ Eleanor_Goldfield_and_Nolan_Higdon_Return_to_the_Program_–
The_Project_Censored_Show⠀⇛
Eleanor Goldfield is a creative radical,
journalist, artist, and organizer. She is co-host
of the Common Censored podcast with Lee Camp. She
also produced a documentary, Hard Road of Hope,
about West Virginia communities confronting
pollution from fracking. The Craig Murray article
she mentions (about Julian Assange) can be found
here.
# ⚓ YouTube_Dusts_Off_Granular_National_Video_Blocking_To
Assist_YouTuber_Feuding_With_Toei_Animation⠀⇛
Hopefully, you will recall our discussion about one
YouTuber, Totally Not Mark, suddenly getting
flooded with 150 copyright claims on his YouTube
channel all at once from Toei Animation. Mark’s
channel is essentially a series of videos that
discuss, critique, and review anime. Toei Animation
produces anime, including the popular Dragon Ball
series. While notable YouTuber PewDiePie weighed in
with some heavy criticism over how YouTube protects
its community in general from copyright claims, the
real problem here was one of location. Matt is in
Ireland, while Toei Animation is based out of
Japan. Japan has terrible copyright laws when it
comes to anything resembling fair use, whereas
Ireland is governed by fair dealing laws. In other
words, Matt’s use was just fine in Ireland, where
he lives, but would not be permitted in Japan.
Since YouTube is a global site, takedowns have
traditionally been global.
# ⚓ Cal_State_Poly,_Pomona_Professor_Accused_of_Anti-Semitism_–
Censored_Notebook⠀⇛
Jaime Scholnick, a Los Angeles-based artist and
adjunct professor at California State Polytechnic
University, Pomona is under pressure from
university administration as a result of unfounded
accusations of “anti-Semitism” by a former student.
# ⚓ How_to_Get_Teenagers_to_Read_Important_Books?_Ban_Them.⠀⇛
The real reason I wanted to read The Catcher in the
Rye was it had been banned from the library. I knew
the librarian kept one copy behind her desk, and I
was determined to get it. She reluctantly handed it
to me. I read it voraciously.
# ⚓ Swedish_publishers_demand_China_free_jailed_bookseller_Gui
Minhai⠀⇛
A group of Swedish publishers on Monday demanded
Beijing release Chinese-Swedish bookseller Gui
Minhai, who was sentenced to 10 years in prison in
2020 on charges of illegally providing intelligence
abroad.
Gui, one of five Hong Kong-based booksellers known
for publishing salacious titles about China’s
political leaders, has been at the centre of
diplomatic tensions between Stockholm and Beijing
for more than six years.
# ⚓ Controversial_House_Bill_1134_would_limit_classroom
curriculum⠀⇛
“Contrary to some social media post, HB1134 was NOT
adopted into law. It simply passed out of the House
after multiple amendments (some comments have
reflected the original draft). It now moves over to
the Senate for further consideration, amendment, or
to die. I appreciate the passion shown around this
legislation and welcome the attention and debate
it’s drawn. Bullet points for HB1134 as it stands
today: [...]
# ⚓ University_of_Hong_Kong_covers_up_33-year-old_Tiananmen
tribute_painted_on_bridge,_weeks_after_removing_statue⠀⇛
Residents at Swire Hall painted the slogan on the
bridge after the Tiananmen crackdown in 1989. A
bloody military intervention ended months of
student-led demonstrations on June 4 that year. It
is estimated that hundreds, perhaps thousands, died
in Beijing when the People’s Liberation Army
cleared the protests.
Every year since then, HKU students have retouched
the slogan leading up to the anniversary. The 20-
character inscription reads: “Souls of martyrs
shall forever linger despite the brutal massacre;
Spark of democracy shall forever glow for the
demise of evils.”
# ⚓ Chinese_censors_give_Fight_Club_movie_a_new_ending_where
police_win⠀⇛
The first rule of Fight Club in China? Don’t
mention the original ending. The second rule of
Fight Club in China? Change it so the police win.
o § Freedom of Information/Freedom of the Press⠀➾
# ⚓ Pirates_nominate_whistleblower_Julian_Assange_for_the_Nobel
Peace_Prize⠀⇛
The Pirates in the European Parliament have
submitted the nomination of Julian Assange for the
Nobel Peace Prize to the Norwegian Nobel Committee.
For the Pirates, the case of Assange, who is
currently imprisoned in the United Kingdom, is a
symbol for the oppression of freedom of speech and
the public’s right to information
# ⚓ Foreign_journalists_in_China_face_lawsuits,_intimidation,
state-backed_trolling_attacks,_media_group_says⠀⇛
Threats of legal action, online troll campaigns and
dwindling numbers after the expulsion of colleagues
— foreign journalists in China are facing
“unprecedented hurdles” from efforts to discredit
independent reporting, a press group said Monday.
Beijing appears to be “encouraging a spate of
lawsuits”, or the threat of legal action against
foreign journalists, often filed long after sources
agreed to interviews, the Foreign Correspondents’
Club of China (FCCC) said in its annual report.
# ⚓ Apply_For_The_2022_Marvel_Cooke_Fellowship_For_Abolition
Journalism⠀⇛
Shadowproof is proud to welcome applications for
the 2022 Marvel Cooke Fellowship.
The fellowship’s mission is to fund reporting from
writers of color on abolition movements around the
world. We are specifically looking for journalists
who have a history of engagement and experience
with abolition, and who produce journalism with an
abolitionist ethic.
# ⚓ Criminalising_journalists_for_telling_the_truth_is_in
nobody’s_interest⠀⇛
State manipulation of the media is why journalism
has developed beyond the mainstream print and
broadcast worlds, which seem to have lost the
ability to challenge authority and embarrass
governments and big business. Today, though, there
is a new breed of journalist operating in the realm
of social media; much to the mainstream media’s
annoyance, we are seeing the continued growth of a
new and very valid kind of journalism, accompanied
by a vicious backlash to discredit the new media
kids on the block.
o § Civil Rights/Policing⠀➾
# ⚓ Opinion_|_The_Absurdity_of_Protecting_Kids_From_the
Holocaust_Narrative_‘Maus’⠀⇛
Nudity and bad language. That’s a Tennessee school
board’s excuse for banning Art Spiegelman’s graphic
novel “Maus.” Not Holocaust denial. Not
antisemitism.
# ⚓ ‘Shame_on_Them’:_DOJ_Will_Not_Reopen_Tamir_Rice_Case⠀⇛
The mother of Tamir Rice, who was shot to death at
age 12 by a Cleveland, Ohio police officer,
condemned the U.S. Department of Justice’s decision
not to reopen her son’s case.
“Shame on them,” Samaria Rice told Buzzfeed News
Monday after receiving a letter from the DOJ
regarding the Biden administration’s decision. “I
think they’re pitiful and pathetic, and at this
point no one is going to get justice when it comes
to police shootings in America. It’s disgusting I
don’t have an indictment for my 12-year-old son.”
# ⚓ Anti-BDS_Law_in_Texas_Violates_Free_Speech_Rights,_Federal
Judge_Rules⠀⇛
Progressives welcomed a federal judge’s recent
ruling that Texas cannot forbid an engineering firm
hired by Houston city officials from boycotting
Israel to protest its subjugation of
Palestinians—and vowed to keep fighting until the
state’s anti-boycott law is thrown out completely.
As The Texas Tribune reported Monday:
# ⚓ Opinion_|_US_Supreme_Court_Nomination_Debates_Are
Dangerous⠀⇛
Justice Breyer has announced his resignation from
the Supreme Court and a Biden/Harris pick is
expected to win confirmation. The Democrats’ choice
is unlikely to shift the court’s balance, we’re
told, but the media’s milquetoast reassurance
misses the point that when it comes to balance
it’s not just the court, it’s also the public
debate that’s shifted dramatically to the right.
And nomination fights have a nasty habit of playing
a big role in that.
# ⚓ Progressive_Urge_Biden_to_Nominate_Justice_on_Side_of
Workers,_Not_Corporations⠀⇛
Following a number of U.S. Supreme Court rulings
favoring powerful corporations, progressives are
demanding that President Joe Biden nominate a
successor to Justice Stephen Breyer who will
represent the interests of working people,
continuing the trend he began with his nominations
to lower federal courts.
The one potential nominee the White House has
confirmed is on the president’s shortlist—U.S.
District Judge J. Michelle Childs—is not reassuring
labor advocates that their call will be answered.
# ⚓ Opinion_|_The_Moral_Panic_of_Critical_Race_Theory_Is_a
Right-Wing_Tool⠀⇛
The moral panic currently sweeping America about
Critical Race Theory (CRT) has been covered ad
nauseum by the press and commentators across the
political spectrum. That’s what typically happens
with moral panics (more on that in a moment).
# ⚓ Mayoral_Candidate_Faces_Backlash_After_Saying_She_Wants_to
“Eradicate”_Islam⠀⇛
# ⚓ The_Hypocrisy_of_American_Islamophobia⠀⇛
Fox News anchor Tucker Carlson excused one of the
leaders of the extremist Oath Keepers organization
implicated in the January 6 insurrection by
describing him as “a devout Christian.” It’s safe
to surmise that he wouldn’t have offered a similar
defense for a Muslim American. Since September 11,
and even before that ominous date, they have
suffered bitterly from discrimination and hate
crimes in this country, while their religion has
been demonized. During the first year of the Trump
administration, about half of Muslim Americans
polled said that they had personally experienced
some type of discrimination.
# ⚓ Massachusetts_Court_Says_Breathaylzers_Are_A-OK_Less_Than
Three_Months_After_Declaring_Them_Hot_Garbage⠀⇛
Breathalyzers are like drug dogs and field tests:
they are considered infallible right up until
they’re challenged in court. Once challenged, the
evidence seems to indicate all of the above are
basically coin tosses the government always claims
to win. Good enough for a search or an arrest when
only examined by an interested outsider who’s been
subjected to warrantless searches and possibly
bogus criminal charges. But when the evidentiary
standard is a little more rigorous than roadside
stops, probable cause assertions seem to start
falling apart.
# ⚓ Tibetan_former_political_prisoner_in_failing_health_still
watched_by_police⠀⇛
“He is succumbing to weak health due to the
beatings he received in prison, and is now in
critical condition with both his legs crippled,”
RFA’s source said, citing contacts in the Draggo
area and speaking on condition of anonymity to
protect his sources.
# ⚓ ‘Low-Skill’_Workers_Don’t_Exist,_But_Low-Wage_Workers_Do⠀⇛
On day four of his tenure as mayor of New York
City, Eric Adams made a gaffe that drew the ire of
many who know the lie of “low-skill” labor.
Advocating for the return of workers to their
midtown offices, he said, “My low-skill workers, my
cooks, my dishwashers, my messengers, my shoe-shine
people, those who work at Dunkin’ Donuts — they
don’t have the academic skills to sit in a corner
office.” His poor choice of words drew backlash
from across the internet (myself included). He
rephrased his poor choice of words soon after, and
Twitter moved on.
But the harm perpetuated by the myth of low-skill
labor lingers. It’s an old lie, one that has
implications much bigger than what Mayor Adams was
alluding to. Historically, enforcing the idea that
a worker is low-skilled has proved to be an
excellent way to justify suppressing their wages.
o § Internet Policy/Net Neutrality⠀➾
# ⚓ Techdirt_Podcast_Episode_309:_Remembering_The_SOPA_Fight,
With_Rep._Zoe_Lofgren⠀⇛
As many of you know, last week we hosted an online
event for the latest Techdirt Greenhouse edition,
all about looking back on the lessons learned from
the 2012 protests against SOPA and PIPA. Our
special guest was Rep. Zoe Lofgren, one of the
strongest voices in congress speaking out against
the disastrous bills, who provided all kinds of
excellent insight into what happened then and
what’s happening now. In case you missed it, for
this week’s episode of the podcast (yes, we’re
finally back with new episodes!) we’ve got the full
conversation and Q&A from the event.
# ⚓ Senate’s_New_EARN_IT_Bill_Will_Make_Child_Exploitation
Problem_Worse,_Not_Better,_And_Still_Attacks_Encryption⠀⇛
You may recall the terrible and dangerous EARN IT
Act from two years ago, which was a push by
Senators Richard Blumenthal and Lindsey Graham to
chip away more at Section 230 and to blame tech
companies for child sexual abuse material (CSAM).
When it was initially introduced, many people
noticed that it would undermine both encryption and
Section 230 in a single bill. While the supporters
of the bill insisted that it wouldn’t undermine
encryption, the nature of the bill clearly set
things up so that you either needed to encrypt
everything or to spy on everything. Eventually, the
Senators were persuaded to adopt an amendment from
Senator Patrick Leahy to more explicitly attempt to
exempt encryption from the bill, but it was done in
a pretty weak manner. That said, the bill still
died.
# ⚓ Senators’_‘Myths_&_Facts’_About_EARN_IT_Is_Mostly_Myths,
Not_Facts⠀⇛
I already wrote a long post earlier about the very
very real problems with the EARN IT Act — namely
that it would make the problem of child sexual
abuse material significantly worse by repeating the
failed FOSTA playbook, and that it would attack
encryption by making it potential “evidence” in a
case against a tech company for any CSAM on its
site. But with the bill, the sponsors of the bill,
Senators Richard Blumenthal and Lindsey Graham,
released a “Myth v. Fact” document to try to
counter the criticisms of EARN IT. Unfortunately,
the document presents an awful lot of “myths” as
“facts.” And that’s a real problem.
o § Monopolies⠀➾
# ⚓ Google_parent_company_Alphabet_broke_$200_billion_in_annual
revenue_for_the_first_time⠀⇛
Google parent company Alphabet hit a new record for
annual revenue in 2021, showing no ill effects from
the lingering coronavirus pandemic or ongoing
issues with the global supply chain. For full-year
2021, the company saw a 41 percent year-over-year
jump in revenue to $257 billion. The company
reported revenue of $75.3 billion in the fourth
quarter of 2021, up 32 percent from the year
earlier.
# § Patents⠀➾
# § Software Patents⠀➾
# ⚓ Podcast_Episode:_Saving_Podcasts_from_a_Patent
Troll⠀⇛
That’s exactly the situation faced by a
group of podcasters several years ago,
including comedian Marc Maron, who
hosts the WTF podcast. They were being
threatened by a patent troll called
Personal Audio, which claimed that
podcasters were infringing on a patent
that covered “disseminating media
content in a serialized sequence.”
On this episode of How to Fix the
Internet, Marc Maron and his producer
Brendan McDonald join EFF’s Cindy Cohn
and Danny O’Brien to talk about how
they decided not to give in, and how
podcasters came together to support
EFF’s work to defeat the patent.
Click below to listen to the episode
now, or choose your podcast player:
# § Copyrights⠀➾
# ⚓ Anime_YouTuber_Battle_Against_Copyright_Results_In
New_YouTube_Rule⠀⇛
YouTube decided not to honor Toei’s removal
request because it would violate the
platform’s fair use policy. Instead, YouTube
asked Toei to provide further justification
for why Fitzpatrick’s channel should be
removed. Rather than provide that evidence,
Toei used YouTube’s automated claim system to
have the videos blocked.
# ⚓ U.S._Seeks_Significant_Prison_Sentence_for_SPARKS
Member_to_Deter_Other_Pirates⠀⇛
Later this month, a 52-year old British man
will be sentenced by a New York federal court
for his role in the SPARKS piracy Scene
group. Mr. Bridi, who was extradited to the
US from Cyprus previously pleaded guilty.
While the defense argues that a reduced
sentence is warranted, the U.S. Government is
asking the court to award a significant 27 to
33-month term to deter other pirates.
# ⚓ Anti-Piracy_Group_Received_$290K_in_Settlements_from
Usenet_Pirates_in_2021⠀⇛
Dutch anti-piracy group BREIN has revealed
that during 2021, it took down five Usenet
indexing platforms and approached 38
uploaders of content for settlement. Overall,
BREIN collected cash payments of $290K from
pirates, with settlements presented as an
alternative to protracted and expensive legal
battles.
# ⚓ Episode_1:_Open_Culture_VOICES_–_Medhavi_Gandhi⠀⇛
We are excited to share the first episode of
Open Culture VOICES, a vlog series of short
interviews with open GLAM (galleries,
libraries, archives, and museums) experts
from around the world. The Open Culture
Program at Creative Commons aims to promote
better sharing of cultural heritage in GLAMs
collections. With Open Culture VOICES, we’re
thrilled to bring you various perspectives
from dozens of experts speaking in many
different languages on what it’s like to open
up heritage content online. In this
interview, we hear from Medhavi Gandhi,
founder of The Heritage Lab, India’s first
digital platform that connects museums and
citizens through engaging campaigns, content
and resources.
# ⚓ That’s_A_Wrap_On_The_Public_Domain_Game_Jam!_Check
Out_All_This_Year’s_Great_Entries⠀⇛
Last night at midnight, we reached the end of
Gaming Like It’s 1926, our fourth annual
public domain game jam celebrating the new
works that entered the public domain this
year. At final count, we got 31 entries
representing a huge variety of different
kinds of digital and analog games!
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