𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, June 17, 2021
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Generated Fri 18 Jun 02:40:39 BST 2021
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/2021/06/17/


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

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QmcDA7FbLzad36FKCSkeVFEjFXPwpcrt1a9h9kg77mG1fr
QmajwF31nmyxxm7e5imo4QUnrAmMGNU9jkY4beybcxWevv
QmXeVCbTbi5P1GkGm1gYJnWmeN4nbuehzDpz7Egwwm6Zy1
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QmbBtrgn5vZv4zAnCwEsSEbNfqZyMc1GXjrxGtjFJubZo6


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

⦿ [Meme] Tilting the Scales for Software Patents | Techrights

⦿ Virtual Injustice  -  Part 9: Heli, the EPO’s Nordic Ice-Queen | Techrights

⦿ Heli Pihlajamaa Promoting Software Patents to Patent Maximalists | Techrights

⦿ IRC Proceedings: Wednesday, June 16, 2021 | Techrights

⦿ The Lying by Team UPC, Led Again by Kevin Mooney | Techrights

⦿ Too Much Noise and/or Distraction and General Loss of Focus (on the Real and Urgent Issues, Such as the Ongoing Anti-FSF ’Coup’) | Techrights

⦿ [Meme] The Enlarged Bored People With Presidential Decrees | Techrights

⦿ Response to Misinformation From EPO Officials | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/06/17/epo-ip-expansionism/#comments
		http://techrights.org/2021/06/17/heli-pihlajamaa/#comments
		http://techrights.org/2021/06/17/heli-pihlajamaa-swpats/#comments
		http://techrights.org/2021/06/17/irc-log-160621/#comments
		http://techrights.org/2021/06/17/kevin-mooney-upc-lies/#comments
		http://techrights.org/2021/06/17/loss-of-focus/#comments
		http://techrights.org/2021/06/17/meme-the-enlarged-bored-people-with-presidential-decrees/#comments
		http://techrights.org/2021/06/17/swpats-epo-officials/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/06/17/cutelyst-3/#comments
		http://techrights.org/2021/06/17/linux-kernel-rust/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 69

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/06/17/epo-ip-expansionism/#comments
    Gemini version at gemini://gemini.techrights.org/2021/06/17/epo-ip-expansionism/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ [Meme]_Tilting_the_Scales_for_Software_Patents⠀✐


Posted in Deception, Europe, Patents at 2:53 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇BOA,_Team_Campinos._Are_they_from_Finland?_I_hereby_declare
software_patents_are..._Hey_hi!⦈_


Summary: Shovelling up lots of patents, even worthless patents such as software
patents, dooms the EPO (EPC violations, lawlessness), dooms European
professionals, but the wrong people have been put in charge and courts are
being intimidated by them


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_and_Finland:_EPO_'IP'_expansionism⦈_


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⠀⠀⠐⠀⠀⠀⠀⠠⣤⣤⣲⣦⣶⣖⣲⣒⣭⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⢸⣿⡇⣸⣿⡟⠃⣿⣯⣿⣇⣿⡟⣿⡿⣿⣼⣿⣟⡿⠟⣣⣯⣭⣾⣷⣶⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣂⠀⠴⡀⢲⣻⣮⣭⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡇⣿⣧⠀⣿⣷⠾⠿⢇⣙⣛⣽⣭⠿⠷⠶⠿⠛⠛⠻⡾⠿⠿⠿⡿⢿⣿⠤⣤⡀⠀⠀⠀⠀⣤⡀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣾⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣯⣷⣿⣾⣧⣭⣭⣾⣶⣶⣿⣿⣿⣿⣿⢟⣤⣄⠀⠀⠀⠀⠀⣠⡆⣤⣤⣭⣛⠙⣫⡆⠿⠿⢆⠀⠀⣠⠻⠿⠆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⣯⣯⣬⣯⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣦⡀⠀⠾⣿⣷⠸⠛⠻⠿⠈⢻⡇⠀⢀⡆⠀⣰⠃⠀⡞⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⣛⣷⣿⣿⣿⣶⣶⣿⣿⣿⡿⢻⣶⣶⠀⣰⣾⣿⠏⠀⢀⣼⠀⢠⣾⠃⠀⣸⠀⢠⠃⠀⣈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢗⣚⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⡄⣸⣿⣿⡆⠀⠸⡟⠀⢨⣿⠀⢠⡇⣰⣾⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣧⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠁⣷⣿⣿⣿⣿⠀⢰⣿⢸⣿⣿⡆⣾⣧⢻⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⡿⠟⠟⢿⠋⠩⣙⣿⣿⡿⣿⣿⠿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⠶⣾⣿⡄⣿⣿⣷⢸⣿⣼⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣄⡠⠄⠈⣨⣁⡉⢹⣹⣿⣽⡻⣿⢯⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⡇⢻⣿⣿⡄⢻⡟⣿⣿⡄⢻⡾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿
⡿⢶⣶⡂⣾⣧⣽⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⡿⢿⣻⣯⣯⠛⣿⣟⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⢷⢸⣿⠿⠧⢨⢧⣻⣴⣆⣰⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣥⣿⣿⣿⡒⢻
⣟⣛⣳⠶⡟⣟⢫⣩⣶⣾⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⡿⣿⣿⣵⣷⡿⠋⠉⣖⢧⡺⣫⡖⣾⣞⡶⢷⣶⣾⡉⠚⣿⣿⡿⠃⢁⠉⠉⠈⡇⠁⠘⡇⢀⣤⣊⡿⢞⣶⣶⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣤⣔⢈⣣⣼⣷⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠿⢻⣭⣷⣼⠿⠛⠟⠻⠛⠛⠊⠊⡛⠛⠁⠁⠊⠠⣼⣿⣁⣡⣀⣀⣂⠀⢧⣀⣰⣇⣿⣿⣿⣟⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠘⣿⣿⡇⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⠀⢀⡀⡀⠉⠀⠀⣀⣀⠀⠀⠀⣀⠀⡀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢠⠀⣄⠀⠀
⣧⡄⠀⠀⢀⣴⡁⠀⣿⠀⡟⢲⢴⠶⠆⠀⠀⢸⠷⢿⢰⡶⠦⡖⣶⢲⣤⡶⠦⡖⠂⠀⠀⢾⠀⣸⢿⠂⠀⠀⢸⢳⡇⠀⠀⢸⡁⢸⡇⠀⠀⢿⠀⡇⠀⠀⠀⠸⣀⡇⠀⣿⣸⣿⣉⣟⣻⡄⡀⠀⠘⠫⠄⣸⣀⡏⢹⠀
⠿⠏⠠⠦⠈⠿⠃⠀⠉⠀⠁⠈⠈⠉⠡⠤⠤⠈⠀⠈⠈⠉⠁⠁⠉⠈⠁⠉⠁⠁⠠⠤⠤⠈⠉⠁⠈⠠⠤⠤⠈⠀⠁⠤⠤⠄⠉⠉⠠⠤⠤⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣾⣿⣰⡖⢲⣶⣶⠀⢸⡗⡿⢲⣦⣶⣶⢶⣠⡆⠀⢺⣷⡖⢲⡖⣶⣶⢲⡖⣶⠀⢸⣧⣤⢰⣶⡖⣶⣿⣰⣶⣶⡶⢲⣴⡖⣿⠉⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠋⠉⠛⠃⠘⠳⠓⠀⠘⠗⠃⠘⠛⠳⠚⣈⡿⠀⠀⠘⠛⠃⠘⠷⠛⠛⠘⠃⠛⠀⠘⠃⠀⠘⠛⠃⠛⠛⠻⠞⠛⠃⠘⠛⠷⠛⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣖⡶⣒⣶⣒⣲⢖⣒⣲⡶⣖⣒⣶⣒⣲⡶⣖⡶⣒⣶⣶⣒⣶⣶⣶⣲⣶⣶⣒⣶⣶⣲⣶⢶⣒⣶⢶⣲⣶⠶⣖⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣩⢸⣿⣿⡇⣿⣏⣽⣿⣹⡷⣹⣷⡿⣾⢿⣿⢹⣷⣿⣏⡇⣿⣿⣿⢸⣿⣿⣿⣿⣇⢸⣿⣿⡇⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣩⢸⣿⣿⡇⣿⣯⣿⣿⣹⣿⡏⣿⣷⣿⣾⣿⣸⣿⣿⣏⡅⣿⣿⣿⢸⣿⣋⣿⣿⣿⢸⣿⣿⡆⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣼⣿⣿⣧⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣾⣟⢿⣵⣟⠛⠃⣙⡛⣿⣾⣿⣿⣿⣿⣿⣼⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣶⡿⣿⢻⣿⢿⡟⣿⡿⠷⢶⣶⢶⣶⣸⣿⢹⣿⢹⣿⡟⢹⣿⣷⡏⣿⡿⣽⡇⣶⣶⣮⢰⣶⣇⡷⣶⡶⢶⣶⠶⣶⣆⣶⣶⣾⣿⣯⣿⢿⣿⣿⢿⣿⣧⢰⣶⢶⡆⣶⡶⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⢀⣾⣝⣿⣶⢸⣿⢸⡇⣿⡷⠆⢸⣿⡞⣿⣿⣿⣾⡇⣿⣿⣿⢸⣿⣿⡇⣿⡷⣽⡇⣿⡿⡟⣿⣿⣿⠇⣿⣿⢸⣿⠶⣿⣿⣿⡿⣿⣿⢯⣻⣷⣝⠿⣼⣏⣿⢸⣿⢿⡇⣿⡷⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⢷⠿⠙⠿⡿⠇⠿⠇⠀⠸⠿⠀⠿⠿⠸⠿⠇⠿⠿⠿⠸⠿⠿⢇⠿⠷⣿⣧⠿⣿⣧⠿⣿⠿⣀⠿⢿⡸⠿⠶⠿⠟⠿⢇⠿⠿⡘⠿⡾⠏⠄⠿⠏⠿⠿⠿⠸⠇⠿⠷⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠍⠁⠁⠀⠀⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠫⣿⣯⣿⣿⣥⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠟⢻⡿⠯⠍⠉⠉⢛⡋⡁⢐⣖⣐⣈⣁⢠⣽⣶⣿⣿⣿⣿⣿⣿⠿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⣶⣶⣿⣿⣷⣿⣿⣼⣿⣿⣿⣿⣟⣿⣿⣿⣿⣯⣿⣿⣟⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⣿⣿⣿⣭⣽⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⣠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⡦⠘⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠻⠿⠿⠇⠀⠀⠉⠛⠟⢿⣿⣶⣶⡄⠀⠀⠀⠈⢻⣿⣿⣿⣭⣭⣭⣬⣭⣽⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡧⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀
⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⠉⠁⠀⠉⠁⢹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡏⠀⠀⠀⠀⠀⠿⠿⢶⣶⣤⣤
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡻⣿⣷⣦⠀⠀⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿
⣿⣿⣿⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣌⣿⣇⣠⣾⣽⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠹⠮⠟⠉⠙⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣠⣆⠀⠀⠀⠀⠀⣠⣌⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶
⠿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⣸⣿⣿⣿⣟⠀⢀⣀⢿⣿⣿⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⢻⢿⣿⡿⠀⢸⣿⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⠻⡟⣿⠃⠀⢸⣿⣿⡇⣿⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢘⠛⠛⣧⠛⠀⠀⠘⠛⠛⣣⢛⠃⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⡿⠟⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢒⠨⢭⣭⣅⠀⠂⢙⠟⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⡁⠉⠀⠀⣴⣶⣦⣐⣸⠏⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣗⣬⣤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣀⣴⣤⠿⣿⣷⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠾⠛⠋⠁⠘⠋⠉⠁⠀⠃⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⡿⢿⡅⢀⣨⣿⣿⣿⣿⣻⣿⣿⠀⠀⠀⣀⣀⠀⠀⠀⢀⣼⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⡟⢡⣬⢋⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠀⣠⣶⣿⢿⣶⣽⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠹⠟⠉⠈⠀⠀⠀⢻⣿⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⠄⠠⡀⠈⠀⡀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣏⢺⢹⡷⠀⠀⢀⣸⣅⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴
⡿⣿⣿⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣒⢯⠞⠺⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠴⠋
⠋⣟⡻⡤⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⣝⢘⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣷⣚⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠄⠀
⡦⡃⠐⠊⠁⠺⠩⠋⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⡨⣾⡇⣿⣿⠻⠀⠉⠙⠛⠹⡟⠛⢁⣾⣿⡐⣒⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡓⢒
⠖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣻⢿⡟⣿⣿⣿⣿⣿⣷⣿⣯⣼⣿⠏⢊⠀⠀⠐⠀⠂⠀⢒⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣪⡔⢋⠙⡙⣩⣿⣿⣿⣿⣿⣿⣿⡡⠈⠈⠐⠲⠖⠠⢤⣤⠈⢨⣿⣿⣿⣛⡿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⢄⣟⣷⡕⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠠⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⠒⡠⠀⠀⠀⠀⠀⠀⠠⠁⡗⣻⣾⡿⢿⢿⣏⢻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⡀⡀⣀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠻⠿⠋⠉⠉⢙⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣝⠻⠁⠗⠀⠀⣿⣿⣯⣿⣿⣿⣿⣿⡼⢿⠿⣿⡃⠘⠁⠛⠤⠶⠉⠭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⠀⠀⠀⠠⣤⣾⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣡⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠻⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⢀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⡀⣿⡇⣿⣿⠉⠁⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠋⠛⠃⠛⠛⠛⠀⣖⣶⣶⠦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢛⡿⠟⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢐⠠⢤⣬⣄⠀⠃⢙⡏⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⡁⠁⠀⠀⣴⣶⡦⣐⣸⠏⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣗⣬⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣀⣰⣤⡿⢿⣷⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠾⠛⠋⠁⠘⠋⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣿⢿⡇⢀⣨⣿⣿⣿⣷⣻⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⢀⣽⠿⢷⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⡟⢡⣌⢉⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠀⣠⣶⣿⢿⣶⣽⣾⣿⡟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠟⠉⠈⠀⠀⠀⢹⣿⡰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢤⠄⠠⠠⠈⠀⡀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣟⣘⢱⡷⠀⠀⢀⣰⣅⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴
⡿⣿⢿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣚⠏⣺⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠴⠋
⡟⣿⡟⠜⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣜⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣷⣚⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠄⠀
⠁⡇⠈⠈⠈⠹⠙⠗⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⡨⣾⡓⣿⣿⠻⠀⠉⠛⠛⠙⡛⠛⢁⣾⣿⡐⣒⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⢒
⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠟⡿⣿⠟⣿⣿⣿⣿⣿⣿⣮⣭⣼⣿⠏⢈⠁⠀⠠⠀⠂⠀⢔⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡐⢋⠙⠙⣩⣾⣾⣿⣿⣿⣿⣿⡡⠈⠈⠐⠲⠖⠠⢤⣤⠈⢨⣿⣿⣟⣛⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣄⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢖⣽⡮⣷⣍⣯⣼⣼⣿⣿⣿⣿⣿⣿⣿⣶⡾⠠⠄⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⠂⡆⠀⠀⠀⠀⠀⠀⠀⠓⡗⣺⣽⡟⣾⣿⡟⢛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⢀⣀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠻⠿⠛⠉⠉⢩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢱⠻⠷⠏⠀⠀⣽⣿⣏⣿⣿⣿⣿⣿⣼⢟⠿⣿⡃⠘⠀⠛⠤⡶⠛⠭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣾⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠗⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣭⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣡⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠹⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⢀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣯⣿⡇⣿⣿⣿⣿⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⡀⣿⡇⣿⣿⠉⠁⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠓⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠋⠛⠃⠛⠛⠛⠀⣦⣶⣶⡦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢛⡟⠟⡟⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢒⠠⢤⣤⣤⠀⠃⢙⡯⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⡁⠁⢀⣴⣶⣶⣦⣐⣸⠏⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣗⣬⣤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣁⣴⣤⡿⢿⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡿⠾⠛⠋⠁⠘⠋⠉⠁⠀⠃⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣿⢻⣅⢀⣸⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⣀⣀⠀⠀⠀⢀⣼⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⡟⢡⢬⢋⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣠⣶⣿⢿⣶⣽⣾⣿⡟⣿⣿⣿⡿⣿⣿⣿⡁⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠹⠟⠉⠈⠀⠀⠀⢹⣿⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⠀⠠⠄⠈⠀⡀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣸⢱⡵⠀⠀⢀⣰⣄⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴
⡿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣀⡿⡷⠹⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠴⠋
⣣⡯⢝⠔⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠎⣝⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣚⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠄⠀
⡶⠆⠀⠀⠀⠉⠚⠮⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⢿⡗⣿⣿⠿⠀⠉⠙⠛⠙⠛⠛⢁⣾⣿⡐⣒⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡓⢒
⣌⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠻⠿⡻⣿⠟⣿⣿⣿⣿⣿⣷⣷⣯⣾⣿⠏⢂⠀⠀⠠⠀⠂⠀⢐⣿⣟⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣔⡐⢊⠙⡙⣩⣷⣿⣿⣿⣿⣿⣿⡡⢈⠀⠐⠲⠖⠰⢤⣤⠈⢨⣿⣿⣟⣛⡿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⢞⡮⢵⣝⣵⣼⣼⣿⣿⣿⣿⣿⣿⣿⣶⡾⠠⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⠂⡆⠀⠀⠀⠀⠀⠀⠐⠙⢝⢻⡶⣟⣾⣮⣏⢋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⡀⣀⣀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠿⠿⠋⠉⠉⠩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣮⠻⠤⠓⠀⠀⣽⣿⣯⣿⣿⣿⣿⣿⢜⢿⠿⣿⣇⠐⠀⠛⠤⠷⠚⠭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣾⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠶⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣡⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠻⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⢀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⡀⣿⡇⣿⣿⠉⠁⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠋⠛⠃⠛⠛⠛⠀⣆⣶⣶⠦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢛⡿⠟⡟⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢒⠠⢤⣤⣤⠀⠃⠙⠟⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⡁⣁⣄⣼⣿⣿⣷⣖⣸⠏⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣬⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣀⣴⡦⣿⣿⣿⣿⣿⣷⣿⣿⣿⠄⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡿⠾⠛⠋⠁⠘⠋⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⡿⢿⡃⢈⣿⣿⣿⣿⣟⣿⣿⣿⣀⠀⠀⣀⣀⠀⠀⠀⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⡟⣡⡛⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⢈⣤⣶⡿⣷⣷⣿⣾⣿⡿⣿⣿⣿⣟⣿⣿⣿⡁⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠹⠟⠉⠈⠀⠀⠀⢹⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⣸⠄⠀⡤⠁⠀⡀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣟⣔⢵⡷⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴
⡿⣿⢿⡛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣀⡏⡾⣹⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠴⠋
⣻⡧⠜⠲⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠮⡕⣂⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣷⣟⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠄⠀
⠉⡅⠀⠈⠀⠘⠉⠗⠹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⣩⣿⡃⣿⣿⠿⠀⠉⠙⠛⠛⠛⠛⢁⣾⣿⣐⣒⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⢒
⡃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⢿⢿⠟⣿⣿⣿⣿⣿⣿⣾⣟⣾⣿⠏⢀⠐⠀⠠⠀⠂⢀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢅⡑⢎⡉⡙⣫⣗⣿⣿⣿⣿⣿⣿⡢⢀⠈⠐⠲⠖⠠⢤⣤⡈⣨⣿⣿⣿⣟⡿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⢥⣟⣷⣍⣿⣼⣼⣿⣿⣿⣿⣿⣿⣿⣶⡾⠠⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⠂⡆⠀⠀⠀⠀⠀⠀⠀⠬⢪⠝⣷⡟⣿⣿⣟⢛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⡀⣀⣀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠿⠻⠛⠉⠉⢩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠡⣏⠿⠕⠍⠀⠀⣹⣿⣏⣿⣿⣿⣿⣿⡼⢻⠿⣾⣇⠐⠀⠛⠤⡶⠙⠭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠠⣤⣾⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣭⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣡⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠻⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⣯⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠑⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⣟⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠋⠛⠃⠛⠛⠛⠀⣖⣶⣶⡦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢟⣻⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢒⠠⢤⣬⡄⠀⠃⠙⡟⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣹⣧⣍⣶⣿⣿⣿⣿⣶⣾⠏⠩⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣗⣬⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣀⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠠⠄⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡿⠾⠛⠋⠁⠘⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣿⢿⠉⣿⣿⣿⣿⣿⣟⣻⣿⣿⣀⡤⠄⣀⣀⠀⠁⠀⢀⣹⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⡟⣑⠱⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⢠⣤⣶⣿⣧⣿⣷⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠟⠉⠈⠀⠀⠀⢻⣷⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢼⠀⠀⠀⠀⠀⡀⢸⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣏⣜⢸⡷⠀⠀⢀⣠⣄⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⡿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣺⡏⢹⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣖
⡷⣟⠬⠻⡟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠪⣓⠐⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣶⣞⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⣀
⠁⡇⠈⠀⠈⠊⠛⠝⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣨⣿⡇⣿⣿⠻⠀⠉⠘⠛⠹⠛⠻⣀⣾⣿⡐⣒⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂
⡃⠅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠿⣻⢿⠟⣿⣿⣿⣿⣿⣿⣟⣟⣼⣿⠏⠀⠀⠀⠀⠀⠂⢀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠕⣂⠉⡝⣹⣿⣿⣿⣿⣿⣿⣿⡠⢀⠀⠐⠶⠖⠠⢦⣤⡈⢨⣿⣿⣟⣏⡿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⢥⡿⣳⣔⣵⣼⣾⣷⣿⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⣒⡤⠀⠀⠀⠀⠀⠀⠠⠩⠣⣼⣽⡯⣿⣷⣟⣫⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⡁⠀⣀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠽⠻⠛⠉⠉⢙⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡹⠻⠅⠗⠁⠀⣽⣿⣯⣿⣿⣿⣿⣿⡞⢛⠿⡾⠃⠐⠀⠛⠤⡶⠙⡭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⠀⠀⠀⠠⣤⣾⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠾⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣥⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠻⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠐⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣖⣶⣶⠦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢐⠠⢤⣤⣤⠀⠃⢑⠏⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣹⣿⣿⣿⣿⣿⣿⣿⣶⣾⠏⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣗⣬⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣀⣴⣤⣿⣿⣿⣿⣿⣯⣿⣿⣿⠗⠀⠠⠄⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠿⠛⠋⠂⠘⠉⠉⠁⠀⠃⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⡿⢿⡿⢿⣿⣿⣿⣿⣗⣿⣿⣿⣰⡶⠄⣀⣀⠀⠁⠀⢀⣽⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⡟⣑⠩⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠀⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⢠⣤⣶⣿⣧⣿⣷⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⠟⠉⠈⠀⠀⠀⢻⣿⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⣸⠀⠀⠀⠀⠀⡀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣟⢐⢵⡷⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⡿⣿⡿⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣈⠰⡞⢸⣿⣷⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣖
⡷⡸⠂⠙⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⡃⠖⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣶⣞⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀
⡉⠀⠀⠀⠀⠀⠘⠈⠙⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⢨⢖⡧⣿⣿⠿⠀⠉⠙⠛⠹⠟⠛⢀⣾⣿⡐⣒⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂
⢞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⡻⣿⡟⣿⣿⣿⣿⣿⣯⣾⣋⣼⣿⠏⠀⠀⠀⠠⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡐⢋⠉⠙⣹⣿⣿⣾⣿⣿⣿⣿⡀⢈⠈⠐⠶⠖⠠⣦⣤⠌⢪⣿⣿⣿⣛⡿⢷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⢷⣟⣳⣍⣿⣼⣽⣷⣿⣿⣿⣿⣿⣿⣶⡾⡀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⠂⡆⠀⠀⠀⠀⠀⠀⠠⠀⠗⢺⡷⣟⣿⡖⣟⢛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡁⠄⣀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠦⠻⠻⠛⠉⠉⢩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡕⠻⠞⠑⠀⠀⣽⣿⣯⣿⣿⣿⣿⣿⡼⢟⠿⣿⡇⠘⠄⠛⠤⣾⠙⡭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠾⣤⡄⣤⡄⣤⣬⣭⣩⣭⠋⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡈⢠⣤⣤⢡⣤⡄⣭⡍⣡⣭⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣭⣭⠹⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⢀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠄⣿⡇⣿⣿⠉⠁⠐⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⡿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠠⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣖⣶⣶⠦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢐⠠⢤⣤⣤⠀⠛⣙⡋⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣹⣿⣿⣿⣿⣿⣿⣷⣶⣿⠏⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣗⣬⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣀⣴⣦⣿⣿⣿⣿⣿⣯⣿⣿⣿⠗⠀⠀⠄⠀⠀⠈⠛⠿⣿⣿⣯⠉⣛⣿⡷⠾⠛⠋⠁⠘⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣠⡿⢿⡿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣠⡶⠄⣀⣀⠀⠁⠀⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⡟⣹⠕⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠠⣤⣶⣿⣛⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⠟⠉⠈⠀⠀⠀⢻⣷⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⣸⠀⠀⠀⠀⠀⡀⢸⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⢰⢱⡷⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⡿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣤⢙⠊⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣖
⡷⢘⠅⠘⠪⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣶⣞⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⣀
⠁⡀⠁⠁⠀⠆⠐⠘⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⢀⢑⡗⣿⣿⠻⠀⠉⠙⠛⠙⠟⠟⣁⣾⣿⡀⣒⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠻⢿⡟⣿⣿⣿⣿⣿⢯⣾⣋⣼⣿⠏⢈⠀⠀⠀⠀⠂⢀⢐⣿⣿⣿⣿⣿⣿⢫⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡕⠊⠙⠉⣩⣿⣿⣿⣿⣿⣿⣿⡀⢈⠈⠐⠖⠖⠠⢦⣤⠌⢪⣿⣿⣟⣛⡿⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⢍⡷⣲⣝⣭⣽⣾⣷⣿⣿⣿⣿⣿⣿⣶⡾⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⣷⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⣂⠇⠀⠀⠀⠀⠀⠀⠐⠑⢝⢝⣿⡟⣿⣿⣟⢛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⡀⠄⡀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠛⠿⠋⠉⠉⢩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠻⠽⠊⠀⠀⣹⣿⣏⣿⣿⣿⣿⣿⡼⠟⠿⡾⠇⠐⠠⠟⠦⣶⠙⡭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠶⣤⡄⣤⡄⣤⣬⣭⣡⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣡⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠻⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⡀⣿⡇⣿⣿⠉⠁⠐⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠠⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣖⣶⣶⠦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠒⠠⢤⣤⣤⠀⠊⣐⡿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣹⣿⣿⣿⣿⣿⣿⣷⣶⣾⠏⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣗⣬⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣀⣰⣦⣿⣿⣿⣿⣯⣯⣿⣿⣿⠗⠀⠄⠄⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠾⠛⠋⠁⠘⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⡿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣰⡶⠄⣀⡀⠀⠁⠀⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⡟⣡⡉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠀⣤⣶⣿⣧⣽⣷⣾⣿⣟⣿⣿⣿⣟⣻⣿⣿⡛⠃⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠟⠉⠈⠀⠀⠀⢻⣯⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢘⠄⠀⠀⠀⠀⡀⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣟⣸⢰⡷⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣻⠗⣺⠸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣖
⠋⡞⠘⠜⢯⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠪⢑⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣗⣚⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀
⠦⠄⠀⠀⠁⠐⠙⠋⠻⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⢻⡗⣿⣿⠿⠀⠉⠘⠛⠹⠟⠛⣁⣼⣿⡀⣒⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂
⡧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⡟⣿⣿⣿⣿⣿⣷⣿⣻⣸⣿⠏⢀⠀⠀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠓⢂⡉⠋⣩⣾⣿⣻⣿⣿⣿⣿⡀⠈⠈⠒⠶⠖⠠⣦⣤⠌⢪⣿⣿⣿⣟⡿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣔⢮⡯⣿⡍⣯⣵⣽⣷⣾⣿⣿⣿⣿⣿⣶⡾⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⣖⡄⠀⠀⠀⠀⠀⠀⠠⠐⡗⡹⣿⣷⣿⣿⣟⢋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠄⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠟⠿⠛⠉⠉⢩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⡣⠻⠯⠗⠀⠀⣽⣿⣯⣿⣿⣿⣿⣿⢞⠟⠿⡿⠇⠐⠠⠟⠦⡤⠉⡭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠠⣤⣾⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠾⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣥⣭⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠹⣿⣿⣿⠿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠄⣿⡇⣿⣿⠉⠁⠑⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⢀⣖⣶⣶⡦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢐⠠⢬⣤⣤⠀⠋⣼⣯⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣹⣿⣿⣿⣿⣿⣿⣷⣾⣾⠏⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣬⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣀⣼⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠗⠀⠀⠄⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡿⠾⠛⠋⠁⠘⠋⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⡿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣰⡶⠄⣀⡀⠀⠁⠀⢀⣹⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢀⣼⡟⢥⡈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠤⣤⣶⡿⣧⣽⣵⣾⣿⡿⣿⣿⣿⣟⣿⣿⣿⡛⠓⡆⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠟⠉⠈⠀⠀⠀⢹⣷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⠀⠀⠀⠀⠀⡀⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣟⣐⢰⡷⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⢿⡟⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡐⠐⡲⠺⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣔
⣫⠘⠃⠂⢨⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠨⢇⠬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣟⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀
⢒⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⢂⡗⣿⣿⠟⠀⠉⠙⠛⠙⠟⠻⣁⣼⣿⡀⣲⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠠
⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠻⣿⠟⣿⣿⣿⣿⣿⣷⣿⢻⣾⣿⠏⢀⠀⠀⢀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⣫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡃⠎⠙⢉⣩⣿⣾⣻⣿⣿⣿⣿⡀⠈⠈⠒⠖⠔⠠⣤⣬⠜⢪⣿⣿⣿⣟⡻⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢗⡼⣓⡤⣼⣦⣾⣿⣿⣿⣿⣿⣿⡿⣶⡾⡀⠀⠀⠀⠀⠀⠀⢥⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⣖⠠⠀⠀⠀⠀⠀⠀⠀⠑⠴⠔⣿⠻⣿⣷⡹⢋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⡀⡄⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠿⠛⠉⠉⢙⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢈⠃⠷⠀⠀⠀⣹⣿⣯⣿⣿⣿⣿⣿⢾⢞⠿⣿⡇⠑⠸⠛⠦⣤⠘⡭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠾⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣥⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣭⣭⠻⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠈⣿⡀⣿⡇⣿⣿⠉⠁⠁⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣯⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣖⣶⣶⡦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⠐⠠⢬⣤⡄⠀⠓⣙⠾⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣗⣬⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣛⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠁⠠⠄⠀⠀⠉⠛⠿⣿⣿⣯⠉⣙⣿⡿⠿⠛⠋⠃⠘⠋⠉⠁⠀⠃⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⣠⡿⢿⣿⣿⣿⣿⣺⣻⣿⢿⣿⣿⣶⣶⣄⣀⣀⠀⠉⠀⢀⣽⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⢀⣼⡟⢷⡤⠈⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⠀⣿⡿⠿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠐⣠⣶⣿⠗⣾⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠟⠉⠈⠀⠀⠀⢹⣿⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⠄⠀⠀⠀⠀⡀⢸⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣯⢢⢵⠷⠀⠀⢀⣠⣄⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⠁⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣸⢐⠫⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢔
⠃⢠⡅⠘⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠠⡂⠢⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣚⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀
⣖⠀⠀⠀⠀⠐⠘⠈⠝⢿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡅⢐⢑⣗⣿⣽⠿⠀⠙⠙⠛⠹⠟⠛⣁⣼⣻⡀⣒⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠒
⡂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⢻⢟⡟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠏⢀⠀⠀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⣫⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡘⡊⠙⣉⣩⣶⣾⣿⣿⣿⣿⣿⠀⢈⠉⠒⠳⠔⠨⢤⣬⠌⢨⣿⣿⣯⣝⡿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢀⢯⡇⣳⣤⣿⣥⣭⣿⣿⣿⣿⣿⣿⣿⣶⡾⡄⢄⠀⠀⠀⠀⠀⢥⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣴⣾⣿⣿⣿⣿
⣂⠇⠀⠀⠀⠀⠀⠀⠀⠚⡽⣿⠯⡧⣿⣷⣟⢚⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠻⠿⠛⠉⠉⢩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡱⠻⠶⠇⠀⠀⣹⣿⣯⣿⣿⣿⣿⣿⢾⢟⠷⡾⡇⠐⠨⢛⠦⡴⢚⡽⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠞⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡈⢠⣤⣤⢡⣤⡄⣭⡍⣥⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣭⣭⠹⣿⣿⣿⢿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⡀⣿⡇⣿⣿⠉⠁⠑⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣶⠦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢐⠠⢬⣬⣤⠀⠃⣙⠞⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣬⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠔⣛⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣟⡃⠄⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠾⠛⠋⠁⠘⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⣶⣿⣍⣀⡀⠀⠉⠀⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⢀⣼⡟⢵⡸⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠐⣤⣶⣿⡗⣾⣵⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⠟⠋⠈⠀⠀⠀⢹⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⠀⠀⠀⠀⠀⡀⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢯⠀⢹⡷⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠁⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡿⢻⠟⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⢐⡐⣹⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢔
⡟⢚⠁⠒⢺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡂⢠⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣇⣚⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀
⠁⠀⠀⠀⠀⠁⠁⠪⠙⢟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣗⣏⣿⣽⠿⠀⠉⠙⠛⠹⠟⠛⡁⣴⣺⡀⣒⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠒
⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⢟⠟⣿⣿⣿⣿⣿⢿⣾⣹⣾⣿⡟⢀⠀⠀⠀⠀⠂⠀⢐⣿⣟⣿⣿⣿⣿⣫⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⣃⠉⣉⣨⣾⣾⣻⣿⣿⣿⣿⠠⠈⠉⡒⠾⠔⠰⢤⣵⠌⢪⣿⣿⣯⣏⡿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⢃⡿⢷⣤⣿⣤⣾⣷⣿⣿⣿⣿⣿⣿⣶⡾⠄⠅⠀⠀⠀⠀⠀⢥⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⠂⡆⠀⠀⠀⠀⠀⠀⠠⠀⡳⣾⣟⣯⣿⣿⣏⢚⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠽⠿⠛⠉⠉⢩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⠿⠂⠯⠀⠀⣽⣿⣯⣿⣿⣿⣿⣿⠼⢟⢿⣾⡃⠙⠠⢛⠧⡤⢀⠽⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠋⢩⣭⣤⣤⣤⣠⡤⣤⣤⣤⡈⢠⣤⣤⢡⣤⡄⣭⡍⣥⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣭⣭⠻⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠄⣿⡇⣿⣿⠉⠁⠑⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣖⣶⣶⢦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢐⠠⢤⣤⡤⠀⠃⣛⠮⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣏⡽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣤⡤⠉⠘⠋⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣻⣿⣿⣿⣿⣿⣿⡻⡽⣿⣿⣿⣿⣿⣇⡀⢀⣀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠾⠛⠋⠀⠘⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣿⣿⣶⣿⣍⣀⣀⠀⠈⠀⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⠀⣼⡟⢛⡻⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⡿⠿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠐⣤⣶⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢽⠟⠉⠈⠀⠀⠀⢹⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⠀⠀⢀⠀⠀⡀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣟⠀⢹⡶⠀⠀⢀⣰⣄⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⣨⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⢿⡟⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡬⠘⠃⣹⣿⣷⣶⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢴
⡟⡴⠂⠍⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⡁⣶⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⣞⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀
⠉⠐⠁⠀⠀⠀⠊⠚⡹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢀⣛⡑⣯⣷⠿⠀⠉⠙⠛⠹⠟⠛⣁⣼⣻⡀⣒⣺⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠒
⡯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡻⢟⠛⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⡏⢀⠀⠀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡥⠃⢊⠉⡙⣹⣼⣿⣻⣿⣿⣿⣿⡠⠈⠈⡒⠪⠖⠤⠴⣤⠈⢨⣿⣿⣯⣟⡿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣂⡷⣷⠭⣼⣥⣿⣿⣾⣿⣿⣿⣿⣿⣶⡾⢂⠅⠀⠀⠀⠀⠠⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣷⣶⣴⣴⣿⣿⣿⣿⣿
⣬⠒⠀⠀⠀⠀⠀⠀⠠⠨⢣⣼⣯⡟⣿⣧⣯⣘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⠀⠀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠙⠛⠋⠉⠉⠉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡩⠫⠗⠑⠀⠀⢽⣿⣯⣿⣿⣿⣿⣿⠜⢟⠷⠾⡉⠘⠥⢛⠦⡔⠂⠽⠿⢿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡈⢠⣤⣤⢡⣤⡄⣭⡍⣥⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠹⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠄⣿⡇⣿⣿⠉⠅⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⣀⣀⣀⣘⡛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠋⠛⠃⠛⠛⠛⠀⣒⣶⣶⡦⣉⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢐⠠⢤⣤⣤⠀⠃⣙⣏⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣾⣿⣷⣤⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣻⣿⣿⣿⣿⣿⣷⡿⣟⣿⣿⣿⣿⣿⣇⡀⠀⡀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠾⠛⠉⠁⠘⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣿⣿⣿⣿⣿⣿⣿⣮⡿⣿⣿⣿⣶⣿⣍⣀⣀⠀⠈⠀⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⢀⣼⡟⢿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠐⣤⣶⣿⣳⣿⣽⣾⣿⣿⣿⣿⣿⣿⣶⣶⡿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠟⠉⠈⠀⠀⠀⢻⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢘⠀⠀⢀⠀⠀⡀⢸⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢯⡂⢱⡷⠀⠀⢀⣰⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⣨⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⢿⡟⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡁⢨⠆⡹⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣏⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢴
⣟⠔⠀⠉⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢠⡁⣠⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀
⠾⠀⠀⠀⠀⠀⠠⠪⠝⢻⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡅⢀⣛⣗⣿⣷⠿⠀⠈⠙⠛⠙⠟⠛⣁⣼⣻⡀⣒⣺⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠒
⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢛⢟⡛⣿⣿⣿⣿⣿⣿⣷⣯⣼⣿⡏⢂⠀⠀⠠⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠙⢊⠉⡉⣽⣾⢷⣿⣿⣿⣿⣿⡠⠌⠈⠐⠛⠔⠄⡦⣤⠈⢨⣿⣿⣯⣟⡿⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⢷⡵⣷⣭⣼⣤⣿⣿⣾⣿⣿⣿⣿⣿⣶⡾⢂⠅⠀⠀⠀⠀⠠⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⣒⢠⠀⠀⠀⠀⠀⠀⠀⠙⡜⣻⣼⡟⣿⡯⡟⠘⡹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⠀⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠛⠻⠛⠉⠉⠉⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡗⠏⠷⠕⠀⠀⣽⣿⣏⣿⣿⣿⣿⣿⠞⢟⠗⠾⡁⠘⠡⠛⡮⡼⠃⡽⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠞⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡌⣭⡍⣡⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠅⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⡿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⣀⣀⣀⣘⡛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠋⠛⠃⠛⠛⠛⠀⣦⣶⣦⠦⣉⠻⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢒⠢⢤⣤⣤⠀⠃⣙⠞⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣏⡹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣷⣬⡤⠉⠘⠋⠥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣻⣿⣿⣿⣿⣿⡿⣟⣻⣿⣿⣿⣿⣿⣇⡠⠤⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠾⠛⠋⠁⠘⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣶⢿⣿⣿⣿⣿⣍⣑⣚⠛⠀⠀⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⠄⣤⣶⡿⣦⣬⣵⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠟⠉⠈⠀⠀⠠⢹⣧⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣘⠀⠀⠀⠀⠀⡀⢸⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢟⡐⣱⡷⠀⠀⢀⣠⣄⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⣸⡿⠆⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⢿⠟⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣃⢰⠅⢺⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠳⢯⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢤
⣽⠐⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠪⡀⣴⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀
⠉⠀⠀⠐⠀⠂⠈⠘⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡍⠀⣑⡗⣝⣷⠿⠀⠉⠙⠛⠙⠛⠛⣀⣼⣻⡐⣒⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡒
⡬⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠟⠿⢟⡟⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡏⢀⠀⠀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⠊⢊⠙⡉⢸⣶⣾⣻⣿⣿⣿⣿⡀⠈⠘⠒⠞⠖⠤⠤⣤⠈⢪⣿⣾⣯⣝⡟⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣲⡎⢇⣽⣼⣦⣿⣿⣾⣿⣿⣿⣿⣿⣶⡾⠂⠀⠀⠀⠀⠀⠀⢥⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⡕⣿⠻⣿⡏⡻⠊⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⡀⠀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠟⠿⠋⠉⠉⢙⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠃⠕⠈⠀⠀⢽⣿⣯⣿⣿⣿⣿⣿⠼⢎⠿⠾⠁⠄⠀⡻⠬⡶⢀⠭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠾⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣥⣭⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣭⣭⠹⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠅⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⢀⣖⣶⣖⡦⣉⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢐⠠⢤⣤⣤⠀⠁⣑⠿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣷⣤⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⡿⢟⣻⣿⣿⣿⣿⣿⣇⡠⠄⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠉⠁⠘⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣹⣿⣿⣿⣿⣿⣿⣿⣽⢶⢻⣿⣿⣿⣿⣍⣑⣚⠛⠀⠀⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⡄⣠⣶⣿⣮⣼⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠟⠉⠈⠀⠀⠀⢹⣷⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⡀⢸⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢟⠀⢽⡶⠀⠀⢀⣰⣄⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⣸⡿⠇⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⡚⢠⡐⣨⣿⣷⣶⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢯⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠
⠍⢸⡃⠪⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠘⡀⠐⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀
⣶⠈⠀⠀⠀⠁⠒⠈⠛⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣓⣓⣝⣿⠟⠀⠉⢙⠛⠙⠛⠛⣁⣼⣻⣐⣒⣺⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒
⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠻⢟⡛⣿⣿⣿⣿⣿⣟⣽⣩⣾⣿⡏⠀⢀⡀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡜⢊⠉⡉⣹⣾⣿⣻⣿⣿⣿⣿⡀⡄⠈⠐⠾⠔⠤⠠⣤⠈⢨⣿⣿⣯⣍⡿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⡎⣧⣭⣼⣦⣿⣿⣾⣿⣿⣿⣿⣿⣾⡾⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣴⣴⣿⣿⣿⣿⣿
⣧⠐⠀⠀⠀⠀⠀⠀⠀⠐⠘⡕⣻⢻⣾⡟⢘⡊⠹⣿⣿⣿⣿⣿⣽⣿⣿⣷⡶⠀⠀⣀⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠻⠿⠛⠉⠉⢩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠇⠵⠈⠀⠀⢽⣿⣮⣿⣿⣿⣿⣿⠾⢏⠷⠽⠁⠔⠠⠻⠤⠦⠒⠼⠿⢿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠶⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡥⣤⣤⣤⡀⢠⣤⣤⢡⣤⡌⣭⡍⣡⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠹⣿⣿⣿⡿⣾⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣟⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠈⣿⠄⣿⡇⣿⣿⠉⠅⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⡁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⢀⣖⣶⣖⡦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⢐⠠⢤⣤⣤⠈⠂⣓⢿⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣷⣤⡤⠉⠘⠃⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⠀⠀⠈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠋⠁⠘⠋⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⡷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣑⣚⠛⠀⠀⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠻⠋⡄⣤⣶⣿⣧⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣻⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠛⠉⠈⠀⠀⠀⢻⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣘⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⠀⢱⡶⠀⠀⢀⣠⣄⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⣸⡿⠟⠊⠁⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡿⢿⡿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡶⠰⠆⢺⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠻⢯⠀⣸⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠
⠛⢘⡂⠉⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢨⡁⠼⣿⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣞⠠⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀
⡪⠀⠀⠁⠀⠀⠓⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢀⣚⣫⣽⣷⠟⠀⡩⠙⠙⠙⠛⠛⣁⣼⣻⡐⣒⣺⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗
⡧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠻⣟⠟⣿⣿⣿⣿⣿⣏⣽⢹⣼⣿⡏⢠⡂⠀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢊⠉⡉⣼⣼⣿⣻⣿⣿⣿⣿⡀⢈⠉⠐⠳⠔⠠⠤⣤⠈⢪⣿⣿⣯⣝⡿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢄⣷⣵⣗⣤⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⠀⢀⠀⠀⠀⠀⠀⢥⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣴⣴⣾⣿⣿⣿⣿
⡄⠠⠀⠀⠀⠀⠀⠀⠀⠽⠘⢘⣿⡟⢿⣿⡫⡚⡹⣿⣿⣿⣿⣿⣽⣿⣿⣷⡶⠀⠀⣀⠀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠟⠿⠛⠉⠉⢙⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠟⠐⠀⠀⢽⣿⣯⣿⣿⣿⣿⣿⠾⠯⠷⡿⡉⠔⠀⠛⠧⡶⠂⠽⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠾⣤⡄⣤⡄⣤⣬⣬⣩⣭⠉⢩⣭⣤⣤⣤⣠⡥⣤⣤⣤⡀⢠⣤⣤⢡⣤⡌⣭⡍⣥⣯⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠻⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠈⣿⠀⣿⡇⣿⣿⠉⠅⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣢⣶⣖⡦⣉⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢐⠠⢤⣤⣤⠀⠃⣙⢶⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣤⡤⠉⠘⠃⠥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣾⡿⣻⣿⣿⣿⣿⣿⣷⣤⣕⣄⢈⠛⠿⣿⣿⣯⠉⣙⣿⡷⠾⠛⠋⠁⠘⠋⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣾⣿⠷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣹⣿⣿⣿⣿⣿⣿⣿⣾⡽⢞⢿⣿⣿⣿⣿⣿⣿⣿⠀⠁⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⡄⣤⣶⣿⣷⣬⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣽⢟⣻⣿⣿⣿⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠟⠉⠈⠀⠀⠠⢹⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢟⣻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢟⠀⢻⡷⠀⠀⢀⣠⣄⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠁⣹⣿⣷⠋⠁⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⢻⠟⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡮⠀⡀⠺⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢯⠀⣸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠
⡟⢀⠀⠀⠘⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢀⢘⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣎⠀⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄
⡁⠀⠀⠁⠀⠀⠰⠀⠙⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⣑⡇⣿⡿⠿⠄⠈⠙⠛⠙⠛⠛⠁⣼⣻⡐⣒⣺⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗
⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢛⡟⠛⣿⣿⣿⣿⣿⣗⣽⡹⣼⣿⡏⢢⠀⠀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠑⢊⠉⡉⣸⣰⢾⣻⣿⣿⣿⣿⡀⠀⠀⠐⠿⠔⠠⣤⢤⡈⣪⣿⣿⣯⣙⡿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣬⡒⢧⣴⣼⣤⣾⣿⣾⣿⣿⣿⣿⣿⣶⡶⠀⠄⠀⠀⠄⠀⠀⢥⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⣬⢐⠀⠀⠀⠀⠀⠀⠀⠑⠸⡞⢼⠹⠗⡿⡙⠎⠹⣿⣿⣿⣿⣿⣽⣿⣿⣷⡶⠂⠀⣀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠻⠿⠛⠉⠉⢙⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⡊⠏⠈⠀⠀⣹⣿⣯⣿⣿⣻⣿⣿⠾⠯⠿⠾⠅⠔⠀⢛⠮⡔⠐⠭⠿⢿⣿⣿⣷⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠞⣤⡄⣤⡄⣤⣬⣬⣩⣭⠉⢩⣭⣥⣤⣤⣠⡥⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣡⣭⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣭⣭⠻⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠄⣿⡇⣿⣿⠉⢡⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣯⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣒⣶⣦⡦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢒⠠⢤⣤⣄⠀⠃⣙⢶⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣤⡤⠉⠘⠃⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣯⣾⢟⣿⣿⣿⣿⣿⣷⣿⣇⣆⣈⡛⠿⣿⣿⣯⠉⣙⣿⡷⠾⠛⠉⠁⠘⠋⠉⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⡷⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣹⣿⣿⣿⣿⣿⣿⣿⣷⣞⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⡿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠋⡄⣤⣶⣿⣧⣬⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⠟⠉⠈⠀⠀⠀⢻⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⡿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⠟⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⡀⢿⡷⠀⠀⢀⣰⣄⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⣽⣿⣿⣿⠁⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡿⣿⡛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡮⠐⠂⣺⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠳⣯⠀⣻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀
⡬⠐⠂⠛⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣄⢹⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣟⣞⠰⠋⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠉⢀⠀⠀⠈⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡅⢀⣟⡇⣿⣿⠿⠆⠉⠙⠙⠙⠛⠛⠁⣼⣾⡐⣒⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡻⢟⠟⣿⣿⣿⣿⣿⣷⣾⣹⣼⣿⡏⢀⠀⠀⢀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡜⢂⠉⡙⣹⣶⢶⣻⣿⣿⣿⣿⡐⠀⠈⢒⠢⠄⠠⢤⣤⡈⢪⣿⣾⣯⣙⡿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣷⡪⣵⣼⣽⣦⣿⣿⣾⣿⣿⣿⣿⣿⣶⡶⠀⠄⠀⠀⠄⠀⠀⢭⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⡇⠠⠀⠀⠀⠀⠀⠀⠀⢐⠨⡅⢾⠫⡿⡟⡙⠚⠹⣿⣿⣿⣿⣿⣽⣿⣿⣷⡶⠀⠄⣀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠿⠛⠉⠉⢩⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠋⠗⠈⠀⠀⣽⣿⣯⣿⣿⣻⣿⣿⡾⠿⠿⡾⠃⠜⠀⠻⠦⡄⠐⠬⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠾⣤⡄⣤⡄⣤⣬⣬⣩⣭⠉⢩⣭⣤⣤⣤⣠⡥⣤⣤⣤⡀⢠⣤⣤⢡⣤⡌⣭⡍⣥⣭⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⣄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣭⣭⠻⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠈⣿⠄⣿⡇⣿⣿⠉⢡⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣒⣶⣦⡦⣙⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⢝⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠢⢤⣤⡤⠀⠂⣐⣦⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣧⣷⢟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠉⠀⠘⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣑⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠻⠋⠐⣤⣶⣿⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⣯⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠨⠛⠉⠈⠀⠈⠀⢻⣧⣨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢲⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⢈⠀⠀⠀⠀⠀⡀⢸⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠟⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠇⠀⣀⠴⠀⠀⢀⣠⣄⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠸⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠛⠛⠋⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠪⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⡏⠀⣻⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀
⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠛⣟⠽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣶⣞⠐⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣁⠀⠘⡆⣽⡇⠴⠀⠈⠘⠋⠙⡟⠛⢀⣼⣾⣐⢂⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠹⠛⣻⣿⣿⣿⣿⡧⣏⡄⣼⣿⡏⢀⢀⠀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠉⠉⠈⣠⣹⣻⣷⣿⣿⣿⡀⠌⠸⠒⠺⠞⠠⢤⣤⠈⣨⣿⣿⣏⣛⡟⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠑⠀⣤⣤⣥⣿⣿⣿⣿⣿⣿⣿⣶⡶⢂⠅⠀⠀⠀⠀⠀⢥⣾⣿⣿⣿⣿⣿⣿⣇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠠⠉⠈⠹⣿⣿⣿⣿⣿⣽⣿⣿⣷⡶⠀⡀⣀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠙⠛⠋⠉⠉⠉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⣿⣏⣿⣿⣿⣿⣟⠞⠮⠶⡸⠃⠀⠀⠛⠤⡤⢀⠭⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣤⣤⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠋⢩⣭⣥⣤⣤⣠⡥⣤⣤⣤⡀⢠⣤⣤⢡⣤⡌⣭⡍⣡⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣢⣶⣆⡦⣉⠻⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠒⠢⢤⣤⡤⠀⠂⣘⠦⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣤⡤⠉⠘⠃⠉
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠉⠀⠘⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⡷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣇⣿⣿⣿⣹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣑⣸⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣼⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⢬⣿⡿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠻⠋⠐⣤⣶⣿⣛⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣧⣵⣻⣿⣿⣿⣿⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠛⠉⠈⠀⠈⠀⢹⣧⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢈⠀⠀⠀⠀⠀⡀⢸⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠏⠀⣐⠶⠀⠀⢀⣠⣄⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⡿⠸⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠛⠛⠋⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠀⠀⠸⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠱⡏⠀⣻⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀
⠀⠀⠀⠀⠈⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠐⢰⠏⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣟⣟⠐⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠘⡂⣐⡧⠹⠃⠈⠘⠛⠙⠛⠛⢀⣼⣾⣐⣂⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢛⠛⣿⣿⣿⣿⣿⡇⣇⣁⣼⣿⣏⢀⢀⠀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠉⠉⠈⣨⣹⣻⣿⣿⣿⣿⡀⠌⠸⠒⠲⠜⠠⠴⣤⡈⣨⣿⣿⣯⣋⡟⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⢄⠀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣶⡶⢀⠅⠀⠀⠀⠀⠠⢥⣿⣿⣿⣿⣿⣿⣿⣇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣷⣶⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠈⠹⣿⣿⣿⣿⣿⣽⣿⣿⣷⡶⠀⡄⣀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠙⠛⠋⠉⠉⢉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢽⣿⣎⣿⣿⣿⣿⣟⡾⠯⠿⣺⠃⠘⠀⠛⠤⡔⢀⠭⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡥⣤⣤⣤⡀⢠⣤⣤⢡⣤⡌⣭⡍⣡⣮⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠅⠀⠀⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡿⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠋⠛⠃⠛⠛⠛⠀⣒⣶⣦⡦⣙⠻⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢙⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⢤⣤⡤⠀⠂⡒⠧⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣮⣯⣗⣤⡤⠉⠘⠃⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠉⠁⠘⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣿⡿⣛⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⠻⠋⠀⣠⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣷⣿⣿⣻⡟⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠠⠛⠉⠈⠀⠀⠀⢻⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⡏⢀⢐⡴⠀⠀⢀⣠⣄⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⢸⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠛⠛⠛⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠚⣿⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠱⣏⠘⣿⣿⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠼⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠐⠀⠀⢹⡫⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣾⣷⣎⠰⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡁⠀⠘⡒⣉⡪⠟⠂⠈⠙⠋⠙⠛⠛⡀⣼⣾⡀⣂⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠹⠛⣿⣿⣿⣿⣿⣧⡗⠇⣼⣿⣏⣀⢀⠀⠀⠀⠂⠀⢒⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠊⠉⠉⣉⣨⣽⣻⣷⣿⣿⣿⡀⠄⠈⠐⠀⠔⠤⠀⣤⠈⣮⣿⣿⣏⣋⡿⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢀⠈⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣶⡶⡀⠅⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣷⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣷⠌⡏⠊⠹⣿⣿⣿⣿⣿⣽⣿⣿⣷⣾⠀⡀⣀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠙⠛⠋⠉⠉⠉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠩⠀⠀⢼⣿⣧⣿⣿⣿⣿⣟⠜⠎⠿⡺⠃⠘⠀⠛⠤⠤⠒⠬⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣡⣭⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⢿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⡿⠟⣻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣶⣦⠦⣉⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢐⠢⠤⣤⡤⠀⠂⣒⠦⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣤⡤⠉⠘⠃⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠉⠁⠘⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⡷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣷⣿⡿⣛⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⠻⠋⠄⣠⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣹⡞⣿⣿⣿⣿⣿⣿⣶⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠠⠛⠁⠈⠀⠀⠀⢹⣇⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠹⠃⠀⢠⡴⠀⠀⢀⣤⣄⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣿⣸⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠛⠛⠛⠉⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⠀⠀⠀⠐⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠱⡏⠹⣿⣿⢿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠈⠢⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡈⡕⡊⣽⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣶⣚⠐⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⡖⣝⣯⠟⠀⠈⠘⠋⠙⠛⠛⢁⣼⣾⡀⣂⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠛⠙⠛⣻⣿⣿⣿⣿⣏⡖⠡⣼⣿⣯⠀⢀⠀⠀⠠⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠉⠉⠈⣢⣹⣻⣷⣿⣿⣿⡠⠄⠈⠒⠢⠜⠤⡤⣤⠨⣪⣿⣿⣏⣋⡿⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⢈⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣶⡶⡀⠄⠀⠀⠀⠀⠀⢥⣾⣿⣿⣿⣿⣿⣿⣇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣧⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⣶⡈⡏⠊⠹⣿⣿⣿⣿⣿⣽⣿⣿⣷⡾⠃⠀⣀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠙⠻⠋⠉⠉⢉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⣿⣟⠜⠎⢟⡺⠃⠘⠀⠛⠤⡤⠘⠮⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡌⣭⡍⣡⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠹⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⢛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣒⣾⣦⡦⣉⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢣⢎⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢐⠠⢤⣤⡤⠀⠀⣘⠞⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣽⣯⣷⣾⣯⣷⣤⡤⠉⠘⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠉⠀⠘⠈⠁⠁⠀⠁⠀⠀⠀⠀⠀
⣿⣿⣿⡷⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣿⣟⣏⣿⣻⡿⣿⡿⡯⣿⡿⢿⣿⣿⣿⣿⣿⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠻⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣾⣶⣿⣽⡟⣿⢻⣿⣿⣿⣿⣶⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠰⠛⠉⠈⠀⠀⠀⢻⣯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠍⡃⠀⢠⠦⠀⠀⢀⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀
⠙⠻⠋⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠲⡿⢷⡶⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡝⠹⠿⢿⣿⡿⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣄⠀⠀⢀⠎⢠⠔⠢⡀⠳⡀
⠀⠀⠀⠀⠀⠫⠕⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣧⡛⠽⣿⣿⢭⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣎⠐⠋⠁⠀⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠴⣉⣁⣛⠀⠀⠘⡀⢸⡀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⡀⠀⠘⠂⣚⣮⠞⠀⠈⠘⠛⠙⠙⠋⢁⣼⣾⡀⢒⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⢄⠀⢧⠀⠀⠳⢄⣙⣒⣃⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠟⡓⣻⣿⣿⣿⣿⣧⡇⠎⣸⣿⡏⢑⠀⠀⠀⠀⠂⠀⢐⣿⣟⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣑⣒⣩⡤⠋⠀⠀⠀⠀⠉⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⣉⣠⣼⣳⣷⣿⣿⣿⡀⠈⠈⠐⠖⠔⠤⠤⣤⠈⣪⣿⣿⣏⣙⡿⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⣤⣤⣤⣿⣾⣿⣿⣿⣿⣷⣶⡦⠀⠄⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⡉⠂⠊⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠁⠀⣀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠙⠛⠋⠉⠉⠉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣎⣯⣿⣿⣿⣟⠼⠊⢟⠺⡃⠐⠠⠛⠤⡄⠐⠬⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣡⣭⠋⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣡⣭⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⡿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⣸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣿⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⠛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣾⣦⡦⣉⠻⣿⡿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⡿⢻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⠤⣤⡤⠀⠂⣐⠥⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣡⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣖⣤⡤⠁⠘⠃⠉
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠊⠀⠘⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠷⠿⠿⢟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣾⣿⡟⣏⣿⣻⣿⣿⡿⡯⣿⡿⢿⣿⣿⣿⣿⣿⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⢻⣿⣿⣿⠻⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⡱⣾⣿⣿⣿⣿⣾⣶⣿⣽⡟⣿⢻⣿⣿⣿⣿⣶⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠉⠈⠀⠀⠀⢻⣇⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡫⠍⠉⠁⠀⠀⠴⠀⠀⢀⣤⣄⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣵⣖⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀
⠀⠓⠂⠀⠈⠽⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠳⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡗⠱⢿⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣄⠀⠀⢀⠚⢠⠔⠠⡀⠳⡀
⠀⠀⠀⠀⠀⠀⠠⠗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⢐⠒⠼⣿⣿⣥⡿⣿⣿⣿⢿⡿⣿⣿⢻⣿⣿⣿⣷⣞⠐⠋⠁⠀⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢴⣉⣁⣛⠀⠀⠘⡀⢸⡀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡀⠀⠐⠂⣐⡢⠐⠀⠈⠘⠋⠙⠉⠃⠀⣼⣺⣀⢂⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⢄⠀⢣⠀⠀⠳⢄⣙⣒⣃⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠙⠛⣻⣿⣿⣿⣿⣇⠀⠀⣸⣿⣟⢁⠀⠀⠀⠀⠂⠀⢒⣿⣟⣿⣿⣟⣿⢫⣥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣁⣒⣩⡤⠋⠀⠀⠀⠀⠉⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⢠⢩⣓⣷⣿⣿⣿⡂⠈⠁⠐⠂⠔⠠⠤⣤⠈⣪⣿⣿⣏⣙⡿⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⣾⣿⣿⣿⣿⣷⣶⡦⠀⠄⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣧⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠹⣿⣿⣿⣿⣿⣽⣿⣿⣷⡷⠇⠀⣀⡠⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠝⠛⠋⠉⠉⠉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣎⣿⣿⣿⣿⣟⠼⠺⢟⠾⡃⠐⠠⠟⠤⡤⠐⠬⠻⢿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣤⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣬⣩⣭⠉⢩⣭⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣡⣭⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠂⢸⣿⠉⢹⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⡛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣶⣖⠢⣉⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⢄⣻⡹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⢤⣤⡤⠀⠂⡐⠄⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣱⣼⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣻⣯⣷⣮⣯⣆⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⢿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⠷⠞⠛⠉⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀
⣷⣟⣿⠷⠿⠿⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⣿⣿⣻⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣧⣿⣿⣿⣻⣟⣻⣿⣿⡻⣫⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠩⢿⣿⣿⣿⠻⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⡕⣿⣿⣿⣿⣿⣶⣶⢿⣳⡏⣻⣿⣭⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠙⠁⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣮⣭⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠣⠉⠉⠁⠀⠐⠤⠀⠀⢀⣠⣄⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣷⣖⠛⣿⣿⣿⣿⣷⣿⣿⣿⣿⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⢄⡀⠀
⠂⠒⠂⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⢻⠷⠶⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢿⣿⡗⠱⢿⡿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠠⠀⠀⠀⡼⠁⡔⠒⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠫⠓⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⢀⠂⠾⣿⣯⢧⠿⡿⣯⡿⢿⡿⠿⣿⢻⣿⣿⣷⣶⣋⠑⠉⠁⠉⠉⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠎⠉⢉⡁⠀⠀⢇⠀⣇⠀⢸⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣟⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠂⣐⡢⠐⠀⠀⠘⠉⠙⠙⠓⡁⣼⣾⡀⢒⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠤⠤⡄⢘⡆⠀⠘⠢⣈⣛⣃⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢙⠑⣻⣿⣿⣿⣿⡇⠂⠀⣸⣿⣏⢁⠀⠀⢀⠀⠂⠀⢒⣿⣿⣿⣿⣿⣿⢫⣥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣉⣭⠥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⣀⡉⣑⣷⣿⣿⣿⡀⢀⠀⠐⠢⠐⠠⠀⣤⠈⢪⣿⣾⣏⣙⡿⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢠⣤⣤⣿⣾⣿⣿⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣷⣿⣿⣿⣧⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠀⠊⠹⣿⣿⣿⣿⣷⣽⣿⣿⣶⣷⠂⠀⣀⡀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠙⠛⠋⠉⠉⠉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣿⣿⣿⣗⠼⠲⢟⠺⠇⠀⠀⢙⠤⠄⠈⠼⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣡⣭⠉⢩⣭⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣡⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣠⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⡟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⠛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣶⣆⠢⣉⠻⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠢⢤⣤⡤⠀⠂⣐⠄⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣻⣿⣷⣮⣿⣖⣤⡤⠉⠘⠃⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠋⠁⠘⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⠷⠿⠿⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣯⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣽⣿⣟⣿⣽⣻⣿⣿⣻⣿⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿⣿⠻⠏⠀⣠⣿⣿⣿⣿⣿⣿⣿⣗⣾⣿⣿⣿⣿⣯⣾⣸⡞⣶⢿⡿⣭⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠠⠙⠁⠈⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣧⣽⣽⣿⣿⣿⡷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠨⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠟⠋⠉⠁⢁⠴⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢄⡀⠀
⠛⠛⠛⠉⠉⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⡀⠀⠀⢺⣻⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠱⢿⣿⣿⣿⣿⣿⣿⠯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠠⡀⠀⠀⡼⠁⡔⠒⢄⠈⢆
⠀⠀⠀⠂⠈⠡⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⢉⡊⢾⣿⣯⣿⡿⣿⣿⣿⣿⡿⢿⣿⢻⣿⣿⣿⣷⣋⠙⠋⠉⠉⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠎⠉⢉⡁⠀⠀⢧⠀⣇⠀⢸⠆⢸
⢀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣄⠀⠐⡃⢊⡶⠝⠀⠈⠙⠋⠙⠛⠒⡁⣼⣾⡀⣒⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠤⠤⡄⢘⡆⠀⠈⠢⣀⣛⣃⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠛⠙⠛⣻⣿⣿⣿⣿⣧⡍⡃⣼⣿⣏⢃⠀⠀⢀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣿⢫⣵⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣉⣭⡥⠚⠁⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⢉⣠⡽⣿⣶⣿⡿⣿⡂⠀⠀⠐⠐⠖⠠⠠⣤⠈⢪⣿⣾⣏⣙⡟⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠌⣤⣤⣽⣿⣾⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣀⠈⠷⡨⠈⠊⠹⣿⣿⣿⣿⣿⣽⣿⣿⣷⣷⠂⠄⣀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠙⠿⠋⠉⠉⠉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⢸⣿⣮⣿⣿⣿⣿⣟⠼⠲⢖⠺⠃⠀⠀⢛⠦⠤⠐⠮⢻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣭⡍⣥⣭⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠹⣿⣿⣿⢿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠄⣿⡇⣿⣿⠉⠅⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⡇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⡛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣾⣖⠢⣉⠻⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣸⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠢⢤⣤⡄⠀⠂⣐⠆⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣤⡤⠉⠘⠃⠡
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠉⠁⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣽⠷⠿⠿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣼⣿⣏⡿⣿⣻⣟⣿⡿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⠻⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⡽⣯⣿⣿⣿⣿⣿⣥⣽⡿⣵⠻⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠠⠛⠉⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣟⣩⣿⣿⣿⡷⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠟⠃⠀⡐⠴⠀⠀⢀⣰⣄⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⠀
⠛⢛⠋⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠐⣻⢷⡺⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣗⢹⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠠⡀⠀⠀⡼⠁⡔⠓⢢⠈⢧
⠀⠀⡀⠒⠀⠀⠟⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣾⠇⠀⠀⢀⣀⣊⠾⣿⣿⢷⣿⣿⣿⣿⢿⣿⣿⣿⢻⣿⣿⣿⣾⣛⠻⠿⠿⠙⠉⠉⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠎⠩⢉⣁⠀⠀⢷⠀⢇⠀⢈⡆⢸
⠈⠀⠀⠀⠀⠀⠐⠀⠀⠚⠙⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⡁⠀⠐⠁⣫⡆⠏⠂⠈⠉⠋⠙⠛⠛⠁⣴⣾⡀⣖⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⠠⠤⡄⠈⡇⠀⠈⠣⢄⣛⣋⠤⠋
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠝⠛⣿⣿⣿⣿⣟⣯⢺⡅⣼⣿⣏⠁⠀⠀⠀⠀⠂⠀⠐⣿⣟⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⣭⠥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⡈⢀⣥⣿⣶⣿⡿⣿⡁⠀⠀⠒⠠⠔⠠⠀⣤⠈⢨⣿⣯⣏⣙⡽⢳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⢴⣤⣼⣿⣿⣿⡿⣿⣿⣿⣶⡾⠀⠀⠀⠀⠀⡀⡀⢰⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣧⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡸⠨⡅⠸⠈⠊⠻⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⠆⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠙⠻⠉⠉⠉⠉⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠀⢹⣿⣏⣿⣿⣿⣿⣿⠌⠦⢗⠾⠇⠀⠀⠓⠦⠄⠀⠬⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣡⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣠⣄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣬⣭⠹⣿⣿⣿⢟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠅⠀⠂⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⢇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⡛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣶⠢⣉⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠢⢤⣤⡄⠀⠂⣐⠆⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣿⣗⣤⡤⠉⠘⠃⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⡷⠞⠛⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⠷⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣼⣿⣏⡿⣿⣻⣿⣿⣿⡿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⣿⣿⣿⠻⠏⠀⣠⣿⣿⣿⣿⣿⣿⣿⡽⣯⣿⣿⣿⣿⣯⣬⣽⡿⣵⠻⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠠⠛⠉⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣛⣫⣿⣿⣿⡷⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠟⠃⠀⢐⡵⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⠀
⠛⠛⠛⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠲⢿⣷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⡀⠀⠀⣸⠁⡔⠒⢢⠈⢧
⠀⠀⡂⠙⠀⠀⠿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣾⠇⠀⠀⢀⢀⣚⢶⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣟⣟⠻⡿⠿⠉⠉⠙⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠎⠩⢉⣁⠀⠀⢳⠀⢇⠀⢈⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡅⠀⢀⡇⣢⡮⠫⠀⠈⠙⠛⠘⠛⠛⢁⣴⣾⡀⣖⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⠤⠤⡄⠘⡇⠀⠈⠣⢀⣛⣋⠤⠋
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠝⠛⣿⣿⣿⣿⣟⣇⣚⡍⣼⣿⣟⢃⠀⠀⠀⠠⠂⠀⠒⣿⣟⣿⣿⣿⣿⢫⣭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⣭⠥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⢈⢀⣷⣿⣶⣿⣿⣿⡀⠀⠀⠒⠀⠔⠠⠀⣤⠈⢨⣿⣿⣏⣙⡿⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⠀⢤⣦⣼⣿⣿⣿⡿⣿⣿⣿⣶⡾⠀⠀⠀⠀⠀⡄⡀⢰⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣿⣿⣿⣧⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⢒⠀⠥⠒⠉⠟⠹⣿⣿⣿⣿⣿⣽⣿⣿⣶⣿⠄⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠝⠛⠉⠉⠉⠉⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⣿⣿⠬⠧⢗⠼⠇⠀⠀⠓⠤⠤⠀⠼⠿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣴⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠋⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣡⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣠⡤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠅⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⢇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⡛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣖⠢⣉⠿⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠐⣟⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣀⠐⠠⢤⣤⡄⠀⠂⣐⠆⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣑⣲⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣻⣯⣷⡮⣿⣅⣤⡤⠉⠘⠃⠉
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⠷⠞⠋⠉⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣞⣽⠷⠿⠿⢟⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣧⣿⣟⣹⢻⣿⣿⣹⣾⣟⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢻⣿⣿⣿⠻⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⡕⣯⣿⣿⣷⣿⣿⣥⡇⣿⢣⣹⢻⣿⣿⣿⣿⣿⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠰⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣺⣟⣾⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⡇⠀⢈⠀⠀⠀⠀⠀⡀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠉⠍⠉⠀⠀⠤⠀⠀⢀⣠⣄⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⠀
⠂⠐⠂⠀⠀⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠺⡷⡺⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠒⡄⠀⠀⢰⠃⡤⠒⠢⡀⢳
⠀⠀⠀⠀⠀⠀⠐⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣀⠊⠚⣿⣿⢦⡿⣿⣿⡿⢿⡿⣿⣿⢻⣿⣿⣿⣟⣿⣹⡿⣿⠿⠉⠻⠅⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠾⠩⠍⣉⠀⠀⢸⠀⢳⠀⠀⡇⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣟⣾⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⣐⡀⠬⠀⠈⠙⠙⠑⠙⠃⠀⣴⣶⡀⣒⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠀⠠⣤⠀⡃⠀⠀⠣⢄⣙⣋⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠛⠛⣿⣿⣿⣿⣟⡇⡀⠀⣺⣿⣟⠁⠀⠀⠀⠀⠂⠀⠒⣿⣟⣿⣿⣿⣿⢫⣥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⣭⡥⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠈⢀⢡⣗⣶⣿⣿⣿⡁⠀⠀⠂⠢⠔⠀⠀⢤⠈⢨⣿⣿⣏⣙⡟⢳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢤⣤⣤⣷⣾⣿⡿⣿⣿⣷⣶⡮⠀⠀⠀⠀⠀⡀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣽⣾⣿⣦⣶⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠠⠀⠀⠊⠹⣿⣿⣿⣿⣷⣽⣿⣿⡦⡾⠆⠄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣯⣿⣻⣿⣿⠜⠧⢖⠼⠇⠐⠀⠒⠤⠄⠀⠸⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣡⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣥⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠅⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⡿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⢇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⡛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣶⣦⠠⣉⠻⣿⡿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⣟⢻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣀⠐⠠⢤⣤⡄⠀⠂⣐⠆⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣺⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣹⣯⣷⣮⣿⣅⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⠿⣿⣿⢷⣯⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣙⣿⠷⠞⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣽⠷⠿⠿⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡟⢭⢟⣿⣟⢞⣼⡿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣻⣿⣿⣿⠻⠋⠀⣰⣿⣿⣿⣿⣿⣿⢿⡑⣯⣿⣿⣿⣾⣽⣿⢼⢸⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠠⠋⠉⠈⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣼⣇⣿⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⢽⣿⣿⣿⣿⡇⠀⢀⠄⠀⠀⠀⠀⡀⢰⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠉⠉⠁⠀⠀⠤⠀⠀⢀⣠⣄⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀⠀
⠂⠐⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⢷⡸⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣖⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⢤⠀⠀⢠⠆⢠⠒⠢⡄⠹
⠀⠀⠀⠀⠀⠀⠒⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠊⠲⣿⣷⢧⠿⡿⣻⡿⢿⡿⣿⣿⢻⣿⣿⣿⣿⣿⣹⣿⣿⠿⠹⠿⠃⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠰⠍⠍⣉⡀⠀⠸⡄⠸⡀⠀⡷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣟⣿⣿⣿⣿⣿⣿⣽⡀⠀⠀⠀⣀⡀⠍⠀⠈⠉⠛⠐⢉⠟⡀⣴⣶⡀⣆⣸⣿⣿⣿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡀⠤⢤⠀⢱⠀⠀⠑⠤⣉⣛⡡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠓⣻⣿⣿⣿⣿⡇⡀⠀⣰⣿⡟⢓⠁⠀⠀⠀⠂⠀⠐⣿⣿⣿⣿⣿⣿⢫⣥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣭⣭⡭⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠈⠀⠁⣁⣶⣿⡿⣿⡡⢀⠀⠂⠢⠐⠄⠠⢠⠈⣨⣿⣿⣏⣉⡿⣳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣤⣷⣾⣿⣿⣿⣿⣷⣶⡾⠠⠀⠀⠀⠀⡄⠂⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠊⠹⣿⣿⣿⣿⣿⣽⣿⣿⣦⣾⠆⠄⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡧⣿⣿⣻⣿⣿⠬⠿⢗⠾⠇⠐⠀⠑⠤⠄⠀⠸⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣡⣭⠉⢩⣭⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣥⣭⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⣤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⢿⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠡⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠛⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣛⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣶⣖⠢⡉⠿⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢐⣛⢛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣀⠐⠠⢤⣤⡄⠀⠂⣐⠆⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣁⣺⣿⣿⣾⢾⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣽⣯⣷⣾⣭⣖⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⢿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠞⠛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣽⠷⠿⠿⢋⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣍⣟⣽⣟⡞⣼⣯⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠩⢻⣿⣿⣿⠻⠋⠀⣰⣿⣿⣿⣿⣿⣿⣟⡽⣿⣾⣿⣿⣿⣽⣷⣥⡏⣿⢻⡾⣾⣿⣿⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠨⠋⠉⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣿⣿⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡍⠍⠉⠃⠀⠠⠤⠀⠀⢀⣠⣄⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢄
⠊⠐⠁⠀⠀⠸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠻⡷⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⣒⢢⠀⠀⠀⡎⢠⠞⠓⡄
⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣷⠁⠀⠀⠀⠀⢊⠸⣿⣯⣬⠽⣿⣿⡿⠿⡿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⠻⠇⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠯⠭⠍⡀⠀⠀⡇⠸⡄⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⣁⡠⠐⠀⠈⠘⠛⠙⡓⠻⠁⣴⣶⡀⣆⣸⣿⣿⣿⠋⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣒⠂⣀⡄⢘⠀⠀⠘⠤⢈⣉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠛⣻⣿⣿⣿⣟⡃⣁⠀⣸⣿⣏⠁⠀⠀⠀⠀⠂⠀⠐⣿⣿⣿⣻⣿⣻⢮⢤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠈⠠⠄⣁⣶⣿⡿⣿⡂⢀⠀⠀⠂⠐⠔⠠⣠⠈⢪⣿⣾⣏⣉⡟⣲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣷⣾⣿⣿⣿⣿⣷⣶⡾⠀⠆⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣿⣿⣿⣧⣦⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⠀⠀⠈⠹⣿⣿⣿⣿⣿⣹⣿⣿⣦⣷⠆⠄⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣸⣿⣇⣯⣿⣿⣿⣻⠜⠏⠷⡺⠇⠀⠀⠓⠤⠄⢀⠽⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣬⣡⣬⠉⢩⣭⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣡⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣶⣆⠠⣉⠻⣿⣿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢐⣛⢛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⢤⣤⡄⠀⠂⣐⠆⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣺⣾⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣽⣯⣷⣬⣯⣖⣤⡤⠉⠘⠃⠉
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⡿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡷⠾⠋⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣿⠷⠿⠿⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣟⣿⣟⢏⣿⡏⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠨⢻⣿⣿⣿⠻⠋⠀⣰⣿⣿⣿⣿⣿⣿⣟⡕⣯⣿⣿⣿⣾⣽⣟⣼⣼⣿⣿⡿⣾⣽⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠸⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣾⣷⣿⣿⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠉⠉⠁⠀⠠⠤⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢄
⠂⠀⠀⠀⠀⢉⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠰⠹⣷⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢐⣒⢢⠀⠀⠀⡎⢠⠞⠓⡄
⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠂⠲⣿⣿⣬⢿⡿⣻⡿⠿⡿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⠻⠋⠁⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠯⠭⠍⡀⠀⠀⡇⠸⡄⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⡀⠐⠀⠈⠘⠋⠙⠋⠻⠁⣴⣾⡀⣆⣸⣿⣿⣿⠃⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣒⠂⣀⡄⢘⠀⠀⠘⠤⢈⣉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠏⠙⣻⣿⣿⣿⣟⡇⡠⠀⣼⣿⣏⠃⠉⠀⠀⠀⠂⠀⠐⣿⣿⣿⣿⢿⣻⢧⢬⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⢠⡥⣃⣶⣿⡿⣿⡃⠀⠀⠐⠂⠔⠰⢠⣤⠈⢪⣿⣾⣏⣛⡟⣲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣷⣾⣿⣿⣿⣿⣷⣶⡾⠀⠆⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣿⣿⣾⣦⣦⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠊⠹⣿⣿⣿⣿⣿⢽⣿⣿⣷⣷⠇⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠋⠉⠉⠉⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⣿⡧⣯⣿⣻⣿⣿⠜⠏⠷⡺⠇⠀⠀⠒⠤⠄⢀⠹⠻⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣡⣬⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣥⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣠⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⡿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢀⣶⣦⠠⣉⠻⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⣟⡫⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣀⠐⠠⢤⣤⡄⠀⠂⢐⠆⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣻⣿⣷⣮⣽⣆⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠞⠛⠋⠁⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣮⣽⠷⠿⠯⠝⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣟⣿⡿⢯⡟⣽⡿⡟⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠩⢿⣿⣿⣿⠻⠋⠀⣰⣿⣿⣿⣿⣿⣿⣟⡹⣥⣿⣿⣽⣷⣟⣿⣱⡏⣿⢻⡾⣿⣿⣿⡟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣾⣷⣿⣾⣿⣷⣿⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠉⠉⠁⠀⠀⠤⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣲⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢄
⠂⠃⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠉⡷⠾⡿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣒⢢⠀⠀⠀⡞⢠⠞⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠟⢿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣾⠂⠀⠀⠀⠀⢂⠼⣷⣿⣽⠿⣿⣫⣯⡿⡟⢿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠻⠃⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠯⠭⠍⡁⠀⠀⡇⠸⡆⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣟⣾⣿⣿⣿⣿⣿⢿⡁⠀⠀⠀⢁⡄⠐⠀⠈⠈⠋⠙⠛⠛⠀⣴⣳⡀⢒⣸⣿⣿⣿⠃⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣒⠀⣀⡄⢘⠀⠀⠘⠤⢌⣉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⢻⣿⣿⣿⣟⡣⣀⠀⣸⣿⣟⢃⠀⠀⠀⠀⠂⠀⠐⣿⣿⣿⣻⣿⣫⢣⠨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠀⠀⢠⣁⣷⣿⡿⣿⡀⠀⠀⠒⠂⠀⠠⠀⣴⠈⢨⣿⣾⣍⣙⡝⢲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣷⣿⣿⣿⣿⣿⢷⣶⡦⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠹⣿⣿⣿⣿⣿⣽⣿⣿⣶⣷⠆⠀⢀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣻⣿⡿⠬⠏⠷⡼⠃⠀⠀⠛⠤⠄⠐⠬⠻⢿⣿⣿⣯⣿⡿⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⢨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣬⠉⢩⣥⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣥⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡤⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠅⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣆⠢⡉⠿⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⣯⢛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣀⠐⠠⠤⣤⡄⠀⠀⣐⠆⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⢿⣯⣷⣼⣽⣖⣤⡤⠉⠘⠃⠉
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠞⠓⠉⠁⠘⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣽⠷⠿⠿⢏⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣇⣿⡿⢯⡿⣽⡿⡟⣿⣟⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠩⠿⣿⣿⣿⠻⡋⠀⣰⣿⣿⣿⣿⣿⣿⣟⡉⣶⣿⣿⣵⣗⣻⣿⣑⡋⣿⢻⡾⣿⣯⣿⡟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠈⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣷⣿⣾⣿⣷⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⠉⠍⠁⠀⠀⠤⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢄
⠊⠒⠁⠀⠈⠍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⢷⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⣒⢢⡀⠀⠀⡞⢠⠞⠓⣄
⠀⠀⠀⠀⠀⠀⠠⠻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠂⠼⣿⢿⣴⠽⣿⣿⣯⡿⡿⢿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡻⠿⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠯⠭⠍⡁⠀⠀⣇⠘⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣟⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢀⡄⠀⠀⠨⠈⠊⠙⠉⠛⠀⣴⣺⡀⢂⣸⣿⣿⣿⠃⠸⠟⠛⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⠀⣀⡄⢈⠀⠀⠘⠤⢌⣉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠉⠛⣻⣿⣿⣿⣟⡇⣂⠀⣸⣿⣟⢃⠁⠁⠀⠀⠂⠀⢐⣿⣿⣿⣿⣿⣻⢯⢭⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠈⠀⢀⣓⣶⣿⡿⣿⡀⠀⠀⠐⠂⠀⠠⠀⢬⠈⢨⣿⣾⣏⣙⡽⢲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⡀⠀⠀⠀⠀⠀⢀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣷⣿⣿⡿⣿⣿⠿⣶⡦⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣿⣿⣾⣧⣦⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠹⣿⣿⣿⣿⣿⣽⣿⣿⣶⣾⠆⠀⢀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣎⣿⣿⣻⣿⡳⢼⢋⠷⡾⠃⠘⠀⠻⠤⠄⠐⠬⠻⢿⣿⣿⣯⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣡⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣥⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠋⡶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠅⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣦⠠⣉⠿⣿⣿⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⣟⢑⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣀⠐⠠⠤⣤⡄⠀⠀⣐⠆⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣽⣿⣷⣮⣯⣆⣤⡤⠉⠘⠃⠁
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠞⠛⠉⠁⠘⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣽⠷⠿⠿⠋⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣽⣷⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣟⢏⣿⣿⣿⢟⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⣿⣿⣿⠻⠋⠀⣴⣿⣿⣿⣿⣿⣿⣟⡿⣾⣿⣯⣿⣸⡎⣼⣼⣿⡟⣿⢿⣿⣽⣟⡿⣿⡿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠠⠉⠁⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣼⣇⣛⣱⣯⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡋⠉⠉⠁⠀⠀⠢⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀
⠂⠋⠁⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠀⢀⡛⡳⠺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣒⠢⡀⠀⠀⡞⢠⠜⠓⣄
⠀⠀⠀⠀⠀⠈⠪⠟⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⠀⠀⠀⠈⠈⠂⠼⣿⢷⣷⡽⣿⣻⡿⣿⠽⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠯⠭⠍⣁⠀⠀⣇⠘⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣟⣾⣿⣿⣿⣿⣿⣿⡁⠀⠀⠂⢀⡥⠃⠁⣁⠈⠋⠑⠑⠛⠀⣼⣺⡀⢒⣸⣿⣿⣿⠃⠸⠟⠛⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⠀⣀⡄⢈⠄⠀⠈⠦⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠛⣿⣿⣿⣿⣟⡇⡀⠀⣼⣿⣏⢁⠐⠁⠀⠀⠂⠀⢐⣿⣿⣿⣻⢿⣻⢭⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠈⠀⣠⣰⣷⣿⣿⣿⡁⠈⠁⠐⠠⠔⠠⠠⢴⠀⢨⣿⣿⣏⣙⡍⣲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣷⣾⣿⣿⣿⣿⣷⣶⠴⠂⠂⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣽⣾⣿⣧⣶⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣽⣿⣿⡶⡾⠆⠄⣀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠻⠉⠉⠉⠉⣿⣿⣿⣿⢟⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⣿⣿⡷⠬⢟⠿⡺⠃⠘⠐⠑⠤⠀⠀⠭⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣬⠉⢩⣥⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣥⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠋⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⠃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣦⠠⣈⠻⣿⣿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⠀⢘⣟⢑⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⠤⣤⡄⠀⠀⣐⠆⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣲⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣽⣿⣶⣮⣭⣆⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠷⠞⠋⠉⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣽⠷⠿⠿⠏⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣽⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣻⣿⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠩⠹⣿⣿⣿⠛⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⡝⣾⣾⣯⣿⣾⡈⡟⣿⡿⡟⡽⣿⣯⣿⣿⡟⣟⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣶⣿⣽⣷⣸⣇⣿⣹⣧⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀
⠀⠃⠂⠀⠀⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠿⠳⠲⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣒⠢⡀⠀⠀⡞⢠⠜⠓⣄
⠀⠀⠀⠀⠀⠈⠀⠟⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⢀⡀⠼⣿⢿⣦⡼⣿⡻⡿⣿⠿⠿⣽⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠯⠭⠍⣁⠀⠀⣇⠘⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⣿⢟⣾⡟⣟⣿⣿⣿⣸⠀⠀⠀⠂⣁⡡⠉⠀⡈⠈⠋⠐⠃⠋⠀⣼⣢⡀⢒⣸⣿⣿⣿⠃⠸⠟⠛⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⠂⣀⡄⢈⠄⠀⠈⠦⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠑⣻⣿⣿⣿⣟⠃⡂⠀⣴⣿⣏⢁⠀⠁⠀⠀⠂⠀⢒⣿⣿⣿⣿⢿⣻⢡⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢠⢰⣡⣷⣿⣿⣿⡁⠈⠁⠐⠐⠔⠠⠄⢴⠀⢩⣿⣿⣍⣙⡯⣲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣷⣾⣿⡷⣽⣿⣷⣶⡶⠂⠂⠀⠀⠀⠀⠀⢤⣼⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣷⣿⣶⣢⣦⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠹⣿⣿⣿⣿⣷⣽⡿⣿⣷⡾⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣯⣿⣻⣿⡷⠜⢯⠾⡾⠃⠈⠀⠉⠤⠄⠀⠭⠻⢿⣿⣯⣯⣿⡿⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣬⣡⣬⠉⢩⣥⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣥⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠠⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢛⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⣀⣀⣀⣘⡛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⡶⣆⠠⣈⠻⣿⡿⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠘⣯⡯⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⠤⣤⡄⠀⠀⢐⠆⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣼⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣯⣷⣮⣭⣕⣤⡤⠁⠘⠃⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠷⠞⠓⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⠷⠿⠿⢛⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⠛⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠭⠻⣿⣿⣿⠻⠋⠀⣶⣿⣿⣿⣿⣿⣿⢿⡝⣾⣿⣯⣿⣾⡎⡟⣿⣟⡟⡿⣿⣯⣽⣿⡟⣿⣻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠉⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣷⣿⣷⣼⣇⣟⣹⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡉⠙⠉⠁⠀⠀⠀⠀⠀⢀⣠⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀
⠂⠋⠉⠁⠀⢹⣹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⢀⡻⠳⠾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣒⠢⡀⠀⠀⡞⢠⠜⠓⣄
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣗⠄⠀⠀⢈⢰⡀⠼⣿⣯⣽⢿⣿⣻⡿⡿⠿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠯⠭⠍⣁⠀⠀⣇⠘⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⣿⣿⣟⣾⢿⣿⣿⣿⣿⣝⡃⠀⠈⠃⢠⡀⠠⠀⠨⠘⠋⠙⠛⠓⠀⣼⣢⡀⢂⣸⣿⣿⣿⠃⠸⠟⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⠀⣀⡄⢈⠄⠀⠈⠦⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠟⠙⣿⣿⣿⣿⣿⠏⠀⡀⣰⣿⡏⢁⠀⠀⠀⠀⠂⠀⢒⣿⣿⣿⣿⣿⣿⣯⠥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠀⢨⣔⣲⣷⣿⣿⣿⡀⠈⠁⠐⠂⠜⠠⠠⢴⠀⢉⣿⣾⣏⣙⡵⣲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣀⡀⡀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣷⣾⣿⡿⣿⣿⢿⣶⡴⠀⠀⢠⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣷⣿⣿⣿⣷⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠹⣿⣿⣿⣿⣿⣽⣿⣿⡶⡾⠂⠄⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣯⣿⣻⣿⣷⠜⢿⢿⡾⠃⠘⠘⠛⠤⠄⠀⠬⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣬⣡⣭⠋⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣡⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⢏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⡿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠾⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣶⠂⣈⠻⣿⣿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⡏⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⢤⣤⡄⠀⠀⣐⠆⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣲⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣾⣭⣇⣤⡤⠁⠘⠃⠁
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠞⠛⠋⠁⠘⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⠷⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⠟⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⢻⣿⣿⣿⠻⠏⠀⣶⣿⣿⣿⣿⣿⣿⣟⡽⣼⣿⣏⣻⣸⡞⣼⣼⣿⡟⡿⣿⣯⣽⣿⣿⣿⡿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠠⠙⠁⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣼⣇⣛⣳⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠍⠉⠁⠀⠀⠢⠀⠀⢀⣠⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀
⠒⠃⠀⠈⠈⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢠⠿⠳⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣒⠢⡀⠀⠀⡜⢠⠜⠓⣄
⠀⠀⠀⠀⠀⠊⠪⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠈⣀⡄⠼⣿⢿⣿⣾⣿⣿⣿⢿⣿⢿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠯⠭⠍⣁⠀⠀⣇⠘⡆⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣃⠀⠀⡃⣀⡄⠱⠀⠉⠙⠋⠙⠛⠙⠀⣼⣪⡀⢒⣸⣿⣿⣿⠃⠸⠟⠛⠯⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⠂⣀⡄⢈⠄⠀⠘⠦⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠙⠛⣿⣿⣿⣿⣟⡇⠊⡀⣸⣿⡏⢁⠀⠀⠀⠀⠂⠀⢒⣿⣿⣿⣿⣿⣿⣯⠥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠉⠈⢠⣳⣷⣿⣿⣿⡁⠈⠉⠐⠂⠔⠡⠠⢴⠀⢩⣿⣮⣏⣛⡷⢶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣠⡀⡀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣷⣾⣿⣿⣿⣿⢿⣶⠶⠀⠀⢠⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣷⣿⣿⣿⣧⣶⣤⣴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠠⠊⠹⣿⣿⣿⣿⣿⣽⣿⣿⣶⡶⠆⠄⣀⡀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠛⠛⠋⠉⠉⠉⣿⣿⣿⣿⣿⠿⢿⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⢸⣿⣷⣯⣿⣿⣿⣷⠬⢫⢿⡾⠃⠐⠀⠙⠤⡔⠀⠬⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣡⣭⠋⢩⣭⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣥⣭⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⢟⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⡯⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣛⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣻⣿⣧⣬⣽⣿⣿⣿⡇⣿⡿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡷⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⣀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣦⠢⣉⠻⣿⡿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠸⢹⠑⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⢤⣤⡄⠀⠀⢐⠀⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣯⣿⣿⣷⣮⣽⣇⣤⡤⠁⠘⠃⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠷⠞⠛⠉⠀⠘⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⠷⠿⠿⣟⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣯⣿⣿⠏⢿⣿⣿⠿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⠻⣿⣿⣿⠻⠋⣤⣶⣿⣿⣿⣿⣿⣿⣟⡹⣼⣿⣏⣿⣾⡜⡾⣿⣿⡟⡿⣿⣯⣽⣿⡿⣿⡿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠙⠁⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣾⣷⣿⣼⣇⣛⣳⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣽⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠍⠍⠁⠀⠀⡰⠀⠀⢀⣠⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀
⠊⠐⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⢀⠹⠷⠺⣻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣒⠢⡀⠀⠀⡜⢠⠜⠓⣄
⠀⠀⠀⠀⠀⠀⠉⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠂⠀⠀⠀⢀⡁⠼⣿⢿⢽⣾⡿⣻⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠯⠭⠍⣁⠀⠀⣇⠘⡆⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⡟⣾⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⣀⡀⠐⠀⠈⠘⠁⠙⠛⠿⠀⣴⣪⣀⢒⣸⣿⣿⣿⠃⠸⠿⠟⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⠂⣀⡄⢈⠄⠀⠘⠦⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠛⢻⣿⣿⣿⣿⡃⠀⠀⣼⣿⡏⠁⠈⠀⠀⠀⠂⠀⢐⣿⣿⣿⣿⣽⣿⣯⠥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠈⢠⣠⣱⣶⣿⡿⣿⡀⠈⠈⠐⠂⠔⠠⠠⣴⠀⢉⣿⣾⣏⣙⡕⢲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣤⣤⣷⣾⣿⡿⣿⣿⣿⣶⠦⠀⠀⢠⠠⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣵⣶⣷⣧⣦⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠈⠹⢿⣿⣿⣿⣿⣽⣿⣿⣶⣷⠂⠄⢀⡀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢿⠿⢿⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡿⣿⣿⣿⡷⠼⠯⠿⡸⠃⠈⠀⠛⠤⡀⠀⠬⠻⢿⣿⣽⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣌⣡⣬⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢡⣤⡄⣬⡍⣡⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣛⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣻⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣶⣦⠢⢉⠻⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠇⠀⠐⣿⠌⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⢤⣤⡄⠀⠂⣠⡢⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣽⣯⣷⣬⣭⣄⣤⡤⠉⠘⠁⠁
⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠷⠞⠋⠉⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣽⠷⠿⠿⢍⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣥⣿⣿⢩⡟⣻⡿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⢻⣿⣿⣿⠻⠋⣤⣶⣿⣿⣿⣿⣿⣿⢿⡡⣼⣿⣯⢡⠇⣿⡿⡟⣵⢺⣿⢻⣿⣽⡟⣿⡟⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣾⣿⣼⣧⣸⣇⣻⣡⣷⣯⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠉⠉⠁⠀⠀⠂⠀⠀⢀⣠⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀
⠒⠈⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠹⡲⠾⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣒⠢⡀⠀⠀⡜⢠⠜⠓⢄
⠀⠀⠀⠀⠀⠀⠩⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⠼⣿⢯⢽⡾⡿⡻⠿⢿⠹⢿⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠯⠭⠍⣁⠀⠀⣇⠘⡆⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⢟⣾⡿⣿⣿⣿⣿⢜⠀⠀⠀⠀⢀⡀⠐⠀⠀⠘⠉⠝⠓⠶⠀⣼⣪⣀⢒⣸⣿⣿⣿⠃⠸⠿⠟⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⠂⣀⡄⢈⠄⠀⠈⠦⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠑⣻⣿⣿⣿⣟⠃⠀⠀⣰⣿⣏⠂⠀⠀⠀⠀⠂⠀⠒⣿⣿⣿⣻⣿⣿⣧⠥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠀⠐⣰⣷⣿⡿⣿⡁⠀⡈⠀⠂⠔⠠⠠⢴⠀⢉⣿⣾⣍⣉⡵⢲⡿⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⡀⠀⠀⠀⠀⠀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣤⣤⣷⣾⣿⡷⣿⣿⢿⣶⠶⠀⠁⠀⠀⠆⠀⠀⢬⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣿⣾⣿⣧⣶⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠹⢿⣿⣿⣿⣿⣽⣿⣿⣶⣷⠂⠀⣀⡀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢟⡟⢿⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣯⣿⣻⣿⣷⠼⠯⠿⡿⠃⠘⠀⠘⠤⡄⠀⠬⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣬⣡⣭⠉⢩⣥⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣡⣬⣅⣠⣤⡄⣠⣤⣤⠀⣤⡄⣠⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠋⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣛⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣻⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢛⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⠛⢛⠛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣆⠠⢈⠻⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡃⠀⢘⢙⠑⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣀⠐⠠⠤⣤⡄⠀⠀⢠⠀⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣷⢾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣷⣬⣭⣆⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠷⠞⠋⠉⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣿⠷⠿⠿⠍⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣽⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣡⣿⣿⢩⡟⣻⡿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠋⡻⣿⣿⣿⠻⠋⣤⣶⣿⣿⣿⣿⣿⣿⣟⡡⣼⣿⣯⢡⠗⣿⡿⡟⣵⢹⣿⢻⣿⣽⡟⣿⡟⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣾⡿⣾⣿⣼⣧⣸⣇⣻⣡⣷⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣾⣾⣽⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡉⠈⠋⠀⠀⠀⡠⠀⠀⢀⣠⣄⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀
⠊⠐⠂⠀⠀⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢈⢹⠲⡾⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣒⠢⡀⠀⠀⡜⢠⡜⠓⢄
⠀⠀⠀⠀⠀⠀⠛⠹⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠐⠃⠻⣿⢯⢭⠽⡿⡿⠿⢿⠹⣿⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠯⠭⠍⣁⠀⠀⣇⠘⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣟⣾⣿⣿⣿⣿⣿⣘⡀⠀⠀⠂⣐⡢⠑⠀⠈⠙⠋⠙⠋⠢⠀⣼⣲⣀⢂⣸⣿⣿⣿⠃⠸⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⠀⣀⡄⠈⠄⠀⠈⠢⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠑⣻⣿⣿⣿⣟⡋⠠⠀⣼⣿⡏⠁⢀⠀⠀⠀⠂⠀⠐⣿⣿⣿⣻⣿⣿⢧⠤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⢠⠀⣲⣶⣿⡿⣿⡁⠈⠀⠐⠂⠐⠠⠠⢴⠀⢉⣿⣮⣍⣉⡕⣲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⡀⠀⠀⠀⠀⠀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣷⣾⣿⡷⣿⣿⣿⣶⠶⠀⠄⠀⠀⠀⠁⠀⢬⣾⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣽⣾⣶⣧⣶⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠈⠹⢿⣿⣿⣿⣿⣽⣿⣿⣶⡷⠁⠀⠀⡀⠠⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢟⠿⢿⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⡯⣿⣻⣿⡷⢼⢋⠿⠾⡇⠐⠀⠚⠤⠄⠀⠬⠻⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣬⣡⣬⠉⢩⣭⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣡⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣠⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⡿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⡛⣛⡛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣆⠀⢈⠻⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣛⠑⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⢤⣤⡄⠀⠀⢐⠀⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣼⣯⣇⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠞⠛⠊⠁⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⠷⠿⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣼⣿⡟⣹⢏⣹⡟⡟⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠍⠻⣿⣿⣿⠻⠋⣤⣶⣿⣿⣿⣿⣿⣿⣟⡣⣽⣾⣯⣱⡓⠿⣯⢊⠖⣹⣿⢲⣿⣽⡟⣿⡟⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣧⣿⣓⣻⣡⣷⣯⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠋⠋⠁⠀⠀⠰⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢄
⠊⠊⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠻⠳⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣒⠢⡀⠀⠀⡜⢀⡜⠓⢄
⠀⠀⠀⠀⠀⠐⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠣⠟⣿⢿⢽⡿⣿⣿⣿⢿⣿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠮⠭⠍⣁⠀⠀⣇⠈⣇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣟⣾⣿⣿⣿⣿⣿⣟⡁⠀⠀⠂⣀⡤⠁⠀⠈⠈⠋⠙⡛⠻⠀⣼⣺⣀⠂⣸⣿⣿⣿⠃⠸⠿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⡂⣀⡄⠈⠄⠀⠈⠢⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠛⣻⣿⣿⣿⣟⡇⠓⠀⣸⣿⡏⢁⠈⠀⠀⠀⠂⠀⢒⣿⣿⣿⣿⢿⣿⣮⣥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠈⠀⢔⣱⣷⣿⡿⣿⡁⠈⠀⠐⠂⠄⠠⢠⣴⠀⢈⣿⣾⣏⣛⡶⢲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⣾⣿⣿⣿⣿⣿⣶⠮⠀⠀⠀⠠⠆⠁⠀⢬⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣽⣶⣷⣧⣦⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠈⠹⢿⣿⣿⣾⣿⣽⣿⣿⣶⣾⠀⠀⠀⡀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢏⠯⢿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣌⣿⣿⣻⣿⡷⢌⢫⠿⠼⠇⠀⠀⠚⠤⠄⠀⠬⠻⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣤⣤⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣤⣬⣡⣭⠉⢩⣥⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣡⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣛⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣻⣿⣧⣬⣽⣿⣾⣿⡇⣿⡷⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡷⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣆⠠⣉⠻⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡃⠀⠐⣻⡁⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⣀⠐⠠⢤⣤⡄⠀⠀⢀⡀⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣯⣷⣾⣽⣖⣤⡤⠁⠘⠃⠁
⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠷⠖⠋⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣿⠷⠿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣼⣿⡟⣹⢋⣹⣟⡟⣿⣏⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⢻⣿⣿⣿⠻⠋⣤⣶⣿⣿⣿⣿⣿⣿⡿⡡⣽⣾⣯⣹⠰⢿⣿⠋⠆⢻⣿⣾⣿⣽⡟⣿⡻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣇⣿⣳⣿⣡⣷⣯⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣯⣽⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠈⠉⠁⠀⠀⠤⠀⠀⢀⣤⣄⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢄
⠊⠂⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠸⢗⠒⣻⣿⢻⣿⣿⣽⣿⣿⣻⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣒⠢⡄⠀⠀⡜⢀⡔⠓⢄
⠀⠀⠀⠀⠀⠀⠬⢋⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡆⠄⠀⠀⠀⠀⠄⠴⣿⢧⣤⡽⡿⣿⠿⡿⠽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠮⠭⠍⣁⠀⠀⢇⠈⢇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⣿⢟⣾⡿⣟⣿⣿⣿⣬⡀⠀⠀⠂⢐⡔⠅⠀⠁⠈⠉⠙⠋⠣⠀⣴⣰⣀⢀⣸⣿⣿⣿⠃⠸⡿⣿⠿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⠀⢀⡄⠀⠆⠀⠈⠢⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠋⠉⠓⢻⣿⣿⣿⣟⠃⠀⠀⣴⣿⡏⢀⠀⠀⠀⠀⠂⠀⢒⣿⣿⣿⣻⢿⣿⣯⣅⣿⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⣀⠉⣉⣶⣿⡿⣿⡁⠈⠀⠂⠀⠐⠀⠠⣴⠀⢉⣿⣾⣍⣉⡶⢲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣷⣾⣿⡷⣿⣿⣷⣶⠶⠀⠁⠀⠠⠀⠀⠀⢼⣼⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣿⣾⣿⣦⣦⣤⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠊⠀⠈⠹⣿⣿⣿⣿⣿⣽⣿⣿⣶⡿⠂⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢟⠏⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⣯⣟⣻⣿⣷⢮⢋⠗⠸⠃⠀⠀⠒⠤⠄⠀⠬⠻⢿⣿⣿⣯⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣤⣬⣡⣭⠉⢩⣥⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣡⣭⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣬⠸⣿⣿⣿⠏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣯⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⡿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⡿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⡛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣴⣦⠠⢈⠻⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠐⣻⡁⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⠤⣤⡄⠀⠂⢐⡂⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣮⣯⣆⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠞⠛⠉⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣯⠷⠿⠿⢝⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣧⣿⣿⡟⣿⢉⣻⣿⠟⣿⣟⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⢻⣿⣿⣿⠻⠋⣤⣶⣿⣿⣿⣿⣿⣿⣿⡥⣿⣾⣏⣹⠸⢿⣿⠋⠆⣿⣿⣾⣿⣽⡟⣿⡻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠉⠉⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣹⣿⣡⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠉⠉⠁⠀⠀⠤⠀⠀⢀⣰⣄⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⢄
⠒⠁⠀⠀⠀⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠹⡷⠖⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣒⠢⡄⠀⠀⡜⢀⡔⠓⢄
⠀⠀⠀⠀⠀⠀⠦⠛⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡧⠄⠀⠀⠀⠀⠀⠜⣷⢿⣭⡽⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠮⠭⠍⣁⠀⠀⢇⠈⢇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣟⣾⣿⣿⣿⣿⣿⣏⡀⠀⠀⠃⢀⡀⠀⠀⠈⠈⠋⠙⠋⠫⠀⣼⣲⣀⢀⣸⣿⣿⣿⠃⠸⡿⣿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⡀⢀⡄⠀⠆⠀⠈⠢⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠛⢻⣿⣿⣿⣟⡇⠠⠈⣼⣿⡏⠀⠀⠀⠀⠀⠂⠀⢒⣿⣿⣿⣻⢿⣿⣯⣅⣿⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠈⢀⡋⣉⣶⣿⡿⣿⡁⠈⠁⠂⠀⠐⠀⠠⣴⠀⢉⣿⣾⣏⣙⡶⢲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣾⣿⣿⣿⣿⣷⣶⠶⠀⠀⠀⠠⠄⠁⠀⢴⣼⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣿⣾⣿⣦⣦⣤⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠹⢿⣿⣿⣿⣿⣽⣿⣽⣶⡿⠂⠀⣀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢟⠏⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⣿⣿⣷⢬⢋⠗⠼⠃⠐⠠⠙⠤⠄⠀⠬⠻⢿⣿⣽⣯⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣡⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠸⣿⣿⣿⠏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣯⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠉⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠂⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣗⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢛⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣴⣦⠠⢉⠻⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⣟⢙⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⢤⣤⡄⠀⠂⢀⡂⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣧⣮⣽⣖⣤⡤⠉⠘⠃⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠞⠛⠉⠀⠘⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⠷⠿⠿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣇⣟⣿⡏⣿⢉⣻⣿⢟⣿⣯⣿⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠩⠻⣿⣿⣿⠻⠋⣤⣶⣿⣿⣿⣿⣿⣿⡿⡥⣿⣾⣏⣹⠺⢿⣿⢋⠆⢿⡿⣾⣿⣽⡟⣿⡻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠐⠉⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣾⣿⣿⣆⣿⣹⣿⣡⣷⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡋⠉⠍⠁⠀⠀⠥⠀⠀⢀⣠⣅⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⢄
⠊⠋⠀⠀⠀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠽⢳⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣒⠢⡄⠀⠀⡜⢀⡔⠓⢄
⠀⠀⠀⠀⠀⠀⠉⠏⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡦⠂⠀⠀⠀⠀⠀⠼⣿⢿⣽⣽⣿⣻⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠮⠭⠍⣁⠀⠀⢇⠈⢇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣟⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠃⣄⡠⠂⠀⠈⠘⠉⠑⠋⠺⠀⣴⣼⣀⢀⣸⣿⣿⣿⠃⠸⣿⣿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⡀⢀⡄⠀⡆⠀⠈⠢⢌⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠛⢻⣿⣿⣿⣟⡇⡆⠈⣼⣿⡏⠁⠀⠀⠀⠀⠂⠀⢖⣻⣿⣿⣿⣿⣯⣮⣭⣿⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠈⠀⡡⣛⣷⣿⡿⣿⡀⠀⠈⠂⠂⠔⠠⠰⠴⠊⢈⣿⣮⣏⣙⡿⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣿⣾⣿⡿⣿⣿⣷⣶⠆⠀⠀⠀⠀⢀⠀⠂⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣽⣷⣶⣧⣦⣤⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣽⣿⣽⣶⡿⠂⠀⣀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠋⠉⠉⠉⣿⣿⣿⣿⢟⠏⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⣿⣏⣿⣿⣿⣿⣷⢼⢫⠗⢾⠁⠘⠘⠙⠤⠄⠀⠬⠻⢿⣿⣿⣯⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣿⣿⣿⣿⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣭⣩⣭⠉⢩⣭⣤⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣡⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠸⣿⣿⣿⠏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⡿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡷⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣶⣆⠢⢉⠻⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡃⠀⢘⢙⠁⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠐⠠⢤⣤⡄⠀⠂⢀⠀⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣯⣷⣮⣭⣆⣤⡤⠁⠘⠃⠁
⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠷⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣯⠷⠽⠟⠏⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣽⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣧⣟⣿⡟⣿⢉⣻⣟⠟⣿⣟⣺⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠉⢿⣿⣿⣿⠻⠋⣤⣶⣿⣿⣿⣿⣿⣿⡿⠥⣿⣾⣏⣹⠺⣿⣷⢋⠆⣿⣿⣾⣿⣽⡟⣿⡻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠉⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣆⣿⣹⣿⣡⣷⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣽⣯⣽⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⠁⠀⠀⠤⠀⠀⢀⣤⣅⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⢄
⠂⠑⠀⠀⠀⠙⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠸⠳⠶⣿⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣒⠢⡄⠀⠀⡜⢀⡔⠓⢄
⠀⠀⠀⠀⠀⠁⠛⠘⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠄⠀⠀⠀⠀⠁⠰⣷⢿⣭⡿⡿⡻⡿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠮⠭⠍⣁⠀⠀⢧⠀⢇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⣿⡟⣾⣻⣟⣿⣿⣿⣌⡀⠀⠀⠀⢠⡀⠀⠀⠈⠘⠉⠑⠋⠪⠀⣴⣾⢀⠈⣻⣿⣿⣿⠃⠸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⡀⢀⡄⠀⠆⠀⠈⠢⢄⣉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠑⢻⣿⣿⣿⣟⠁⠀⠀⣰⣿⡏⠀⠐⠀⠀⠀⠂⠀⢔⣻⣿⡿⣿⣿⣯⣮⡉⣿⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢭⠭⠔⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢀⠁⣋⣶⣿⡿⣿⡀⠀⠀⠆⠂⠔⠰⠰⠤⠈⢉⣿⣮⣍⣑⡶⢳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣷⣾⣿⡿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⡄⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣽⣿⣿⣦⣦⣤⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣽⡿⣿⣶⣶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⡄⣯⣟⣻⣿⣷⢄⢋⠷⠸⠁⠘⠀⢙⠤⠄⠀⠤⠻⢿⣿⣿⣧⣿⡿⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⢤⣤⣿⣿⣿⣟⠀⠀⢸⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣤⣬⣡⣬⠉⢩⣥⣤⣤⣤⣠⡤⣤⣤⣤⡈⢠⣤⣤⢠⣤⡄⣬⡍⣥⣬⣅⣠⣤⡄⣠⣴⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣬⠹⣿⣿⣿⠏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣉⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⡿⠟⠻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⡇⠛⠃⠛⠛⠀⢀⣀⣀⣘⡛⣛⢛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣴⣆⠠⣈⠻⣿⡿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⢝⠁⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠐⠠⢤⣤⡄⠀⠂⢠⠀⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣯⣧⣾⣭⣆⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠞⠛⠉⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣭⠷⠿⠟⠏⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⢿⣿⣿⢟⡟⢻⣻⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⢻⣿⣿⣿⠻⠋⣤⣶⣿⣿⣿⣿⣿⣶⠿⢹⣧⣷⠋⡏⣾⣿⣷⢫⣼⣿⡟⣻⣿⣿⡿⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠙⠉⠈⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣾⣿⣷⣶⣆⣿⣹⣧⢁⡿⢸⣿⢸⣻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣽⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⠉⠉⠁⠀⠀⠤⠀⠀⢀⣠⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤
⠒⠈⠂⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢽⠷⠒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⡒⢤⠀⠀⢀⠋⢠⠒⠲
⠀⠀⠀⠀⠀⠀⠚⠛⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠂⠀⠀⠀⠈⠁⠺⣷⢿⣭⡼⡿⢿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡏⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠰⠭⠍⢉⡀⠀⠈⡄⠸⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⣿⢟⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠂⣠⡠⠔⠀⠨⠘⠉⠙⠛⠺⠀⣼⣺⣈⠙⣻⣿⣿⣿⠛⠻⣿⣿⢿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⠀⢤⠄⢹⠀⠀⠑⠤⣈⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠛⢻⣿⣿⣿⣟⣃⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠂⠀⠒⣻⣿⣿⢻⠿⣯⢿⡋⢿⡆⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣭⣭⡭⠔⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠀⣀⠈⣓⣶⣿⡿⣿⡀⠀⠈⠀⠀⠐⠀⠠⠴⠄⣉⣿⣮⣏⣙⡶⢲⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣤⣤⣿⣾⣿⡿⣿⣿⣿⣶⠎⠀⠇⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣽⣷⣿⣦⡦⣤⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣽⣿⣿⡶⡷⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢏⠯⢿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⣿⣏⣿⣿⣻⣿⡷⢔⢛⡖⠼⠁⠐⠀⠘⠤⠄⠀⠤⠻⢿⣿⣿⣯⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣿⣿⣿⣿⠀⠀⢨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣬⣍⣩⣭⠉⢩⣭⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣥⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣬⠹⣿⣿⣿⠋⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠠⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⡷⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⡟⠟⢻⢿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⣛⣛⣛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣴⣆⠠⢈⠛⣿⡿⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⢙⠑⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠐⠠⢤⣤⡄⠀⠀⢀⠂⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣶⣿⣶⣷⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣽⣭⣷⣮⣯⣅⣤⡤⠁⠘⠃⠁
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠷⠞⠋⠉⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⠷⠿⠿⢋⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⢯⣿⣿⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠍⢿⣿⣿⣿⠻⣋⣤⣶⣿⣿⣿⣿⣿⣶⡿⢹⣧⣾⠏⡟⣼⣿⣟⢟⣹⣿⡟⢻⣿⣿⡿⠿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⠉⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣭⣻⣏⣬⣍⣿⢯⣧⠁⣿⢸⣿⢘⣿⣿⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣷⢽⣾⣷⣾⣿⣿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡙⠋⠃⠁⠀⠀⠥⠀⠀⢀⣠⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤
⠂⠐⠂⠀⠀⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠹⡶⠸⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⡒⢤⠀⠀⢀⠏⢠⠒⠲
⠀⠀⠀⠀⠀⠀⠻⠙⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠂⠀⠀⠀⠈⠄⠺⣿⢿⣭⡽⡿⠻⡿⡿⠿⢳⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠰⠭⠍⢉⡀⠀⠈⡄⠸⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⣿⣟⣾⡿⣟⣿⣿⣿⣌⡀⠀⠀⠀⢠⡠⠅⠀⠈⠙⠙⠝⠙⠲⠀⣼⣊⣻⢻⣿⣿⣿⣿⠿⠿⣿⣿⢿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⠀⢤⠄⢹⠀⠀⠙⠤⣈⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠓⢻⣿⣿⣿⣟⠁⠀⠀⣴⣿⡏⠁⠀⠀⢠⠀⠂⠀⢐⢻⣿⣿⢿⣿⣟⣿⠻⢿⡆⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣭⣭⡭⠔⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⢀⠅⣑⣶⣿⡿⣿⡁⠀⠈⠐⠂⠔⠰⠐⠴⠆⣉⣿⣿⣏⣛⡾⢲⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣾⣿⡷⣿⣿⡿⣶⡞⠀⠅⠀⠀⠀⠀⠢⢤⣾⣿⣿⣿⣿⣿⣿⣇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣷⣾⣿⣦⢦⣤⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠹⢿⣿⣿⣿⣿⣽⡿⣿⡶⡶⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⢟⡟⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⣿⡄⣯⣟⣻⣿⡷⢜⢛⡗⠼⠁⠐⠀⠙⠤⠄⠀⠤⠻⢿⣿⣿⣯⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣤⣴⣿⣿⣿⣟⠀⠀⣨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣤⣬⣩⣬⠉⢩⣥⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣭⡍⣡⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣬⠹⣿⣿⣿⠋⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⣿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣭⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣿⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⡿⠟⠻⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⠿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⡛⡛⡛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⢂⣴⣆⠠⣈⠛⣿⡿⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⡟⠐⢪⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢤⡀⠐⠠⢤⣤⡄⠀⠀⢠⠀⠧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣯⣷⣮⣿⣄⣤⡤⠉⠘⠃⠁
⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠷⠞⠋⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣾⣭⠷⠿⠿⢏⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣶⣾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣯⣿⣿⢿⣷⣿⢟⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⡯⠄⠛⣿⣿⣿⣿⣋⣤⣶⣿⣿⣿⣿⣿⣾⡿⢸⣧⣾⠋⡏⣾⣿⣿⢫⣹⣿⡟⢻⣿⣽⡿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠉⠁⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣷⣿⣿⣧⣶⣎⣿⣹⣇⢁⡿⢸⣿⢸⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⢿⣿⣿⣷⣿⣿⣽⣿⣷⣾⣷⣾⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡑⠘⠉⠀⠀⠀⠴⠀⠀⠀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤
⠀⠀⠀⠀⠀⠈⠋⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢽⠲⠚⣟⡿⢛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠂⢠⠀⠀⠀⠎⢠⠒⠲
⠀⠀⠀⠀⠀⠀⠺⠳⢿⣯⣿⣿⣿⢿⣿⣿⣿⣿⣯⡿⡕⠄⠀⠀⠀⠀⠀⠢⣿⢿⢤⡾⡿⠛⡿⣿⡿⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡟⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠭⠍⢉⡀⠀⠀⡆⠸⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⣾⡻⣟⣿⣿⣿⣪⡀⠀⠀⠀⢀⡢⠍⠀⠈⠘⠈⠑⠋⠛⠀⣴⣔⢿⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⠠⢤⡄⢸⠀⠀⠙⠤⣈⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠛⠉⠒⢻⣿⣿⣿⣟⠁⡀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠂⠀⠒⡻⣿⣿⣻⠿⣏⢿⡛⢿⡏⠁⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣭⣭⡭⠔⠊⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠄⣐⣶⣿⡿⣿⡀⠀⠈⠀⠀⠔⠠⠠⠴⠄⢨⣿⣿⣍⣛⡾⢶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣷⣾⣿⡷⣿⣿⡿⣲⠞⠀⠀⠀⠀⠀⠀⠢⢠⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣿⣾⣿⣶⣦⣤⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣽⣿⣿⡶⡷⠆⠀⠀⠀⠀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⠟⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⣿⡄⣯⣿⣻⣿⣗⠼⢋⡶⡼⠁⠘⠀⠙⠤⠄⠀⠤⠻⢿⣿⣿⣯⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿⠀⠀⢨⣿⣿⣿
⠀⠀⣤⣤⣤⣤⣤⣤⣀⣠⣤⣤⡀⠖⣤⡄⣤⡄⣤⣤⣬⣡⣬⠉⢩⣥⣥⣤⣤⣠⡤⣤⣤⣤⡀⢠⣤⣤⢠⣤⡄⣬⡍⣥⣬⣅⣠⣤⡄⣠⣤⣤⡀⣤⡄⣤⡄⣤⣤⣠⣴⣤⡀⣤⣤⣤⣤⣭⠹⣿⣿⣿⠏⣶⣿⣿⣿⣿
⠀⠀⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⢘⠃⣿⡇⣿⣇⣿⡟⠛⠀⢸⣿⣈⢸⣿⣿⡇⣿⣿⣸⡿⣿⣿⣿⢸⣿⣷⣿⡟⣿⣿⣛⢻⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⢿⣧⣟⠛⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿
⠀⠤⣿⣿⠉⣿⣿⠭⠁⣿⣿⣿⡇⠀⣾⠀⣿⡇⣿⣿⠉⠁⠀⠀⢸⣿⠉⢸⣿⣿⣇⣿⣿⠉⠁⣿⣯⣿⣿⣿⣿⣿⣧⣬⣽⣿⣾⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣬⡝⣿⣷⣿⡏⣿⣿⣿⠀⣿⠟⠛⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠻⢻⡟⠿⠿⡿⠻⠿⠟⠿⠿⢿⣇⠛⠃⠛⠛⠀⢀⣀⣀⣘⡛⢛⠛⣛⡘⠛⠛⠛⠀⠐⠛⠃⠛⠛⠛⠋⠛⠃⠙⠿⠟⣙⡛⢃⣙⡿⠟⣁⣛⣃⣛⣓⣛⣛⣙⠻⠟⠉⠛⠃⠛⠛⠛⠀⣂⣶⣆⠠⣈⠻⣿⡿⢏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⠁⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣀⠐⠠⠤⣤⡄⠀⠂⢰⠂⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⢿⣯⣷⣮⣽⣇⣤⡤⠉⠘⠃⠁
⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠞⠛⠉⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣞⣽⠷⠽⠿⢍⣟⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣽⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⢿⣟⣿⢟⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠙⢿⣿⣿⣿⣿⣋⣤⣶⣿⣿⣿⣿⣿⣿⡿⢹⣧⣾⠋⡏⣾⣿⣿⢫⢹⣿⡟⢻⣿⣽⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⠙⠁⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣷⣿⣿⣧⣾⣎⣿⣹⣇⢁⡿⢸⣵⢹⣷⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠄⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣽⣾⣷⣾⣵⣾⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠉⠉⠁⠀⠀⠴⠀⠀⢀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠑⠂⠀⠀⠙⣛⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠹⠷⠚⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠢⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠂⠀⠀⠀⠀⠀⠖⣿⢿⣧⣽⡿⢻⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⢟⣾⣿⣿⣿⣿⣿⣾⡀⠀⢀⠀⣠⡀⠹⠀⠉⠘⠋⢝⠛⠛⡁⣾⣜⢿⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠉⠋⢻⣿⣿⣿⣟⡇⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠂⠀⠐⢻⣿⣿⢿⢿⣿⢿⠻⣿⡟⠃⠉⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠀⠀⠅⣕⣶⣿⡿⣿⡁⠀⠀⠀⠀⠄⠐⠤⠰⠀⢌⣿⣮⣍⣛⡿⢶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⢠⣤⣤⣷⣾⣿⡿⣿⣿⣷⣿⠖⠀⠀⠀⠀⠀⠀⠢⢠⣾⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣷⣽⣷⣿⣦⢦⣤⣰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣽⣿⣿⡶⡶⠆⠄⠀⠀⢀⠂⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠛⠉⠉⠉⠉⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 1214

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

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✐ Virtual_Injustice_—_Part_9:_Heli,_the_EPO’s_Nordic_Ice-Queen⠀✐


Posted in Europe, Patents at 2:33 am by Dr. Roy Schestowitz


Previously in the series:


   1. Virtual_Injustice_—_Part_1:_António’s_Increasingly_Wonky_Legal_Fudge
      Factory
   2. Virtual_Injustice_—_Part_2:_The_ViCo_Oral_Proceedings_of_28_May_2021
   3. Virtual_Injustice_—_Part_3:_All_the_President’s_Men…
   4. Virtual_Injustice_—_Part_4:_Mihály_Ficsor,_the_EPO’s_Hungarian_“Fixer”
   5. Virtual_Injustice_—_Part_5:_Benoît’s_“Friends”_in_Budapest
   6. Virtual_Injustice_—_Part_6:_Best_Buddies_With_António
   7. Virtual_Injustice_—_Part_7:_Musical_Chairs_and_Revolving_Doors
   8. Virtual_Injustice_—_Part_8:_A_Well-Connected_‘IP’_Maximalist
                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Heli_Pihlajamaa⦈_
           Heli Pihlajamaa, Director of Patent Law in the EPO’s DG5.


Summary: Team Campinos is full of people who instead of grasping and working to
promote innovation are boosting the agenda of litigation (scientists are not
being employed)


We now turn our attention to the second-in-command on the legal team
representing the President of the Office in the high-profile referral case no.
G 1/21.


The person in question is the EPO‘s Nordic Ice-Queen, Director of Patent Law
Heli_Pihlajamaa, affectionately known to her underlings as “Ms Pyjamas”.


“During her time as a lawyer in the EPO’s Directorate of Patent Law, she was
responsible for legal issues relating to search and examination procedure and
acted as legal member for the hearing of witnesses in opposition
proceedings.”Heli studied law at the University of Helsinki in Finland and
completed her postgraduate studies at the Max_Planck_Institute_for_Intellectual
Property_and_Competition in Munich.


Before moving to Munich in 1996 to take up a post as lawyer in the Directorate
of Patent Law at the European Patent Office’s Directorate of International and
Legal Affairs (DG 5), she worked for the Finnish Patent and Registration Office
and for a patent attorney’s office in Helsinki.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Finlandia hall⦈ Heli also taught Industrial Property Law at
the Technical University of Helsinki and has published books and newspaper
articles on patent law in Finnish.


During her time as a lawyer in the EPO’s Directorate of Patent Law, she was
responsible for legal issues relating to search and examination procedure and
acted as legal member for the hearing of witnesses in opposition proceedings.


Her current_duties as Director of Patent Law include responsibility for
“supporting EPO policy by developing, strengthening and promoting the EPC,
including proposals for legal changes, compliance of operations with patent
law-related norms and case law” and she “advises EPO higher management on
policy issues and legal amendments”.


Despite her job title as Director of Patent Law, Heli doesn’t seem to do a lot
of work on actual patent cases.


            🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Heli_Pihlajamaa_on_early_certainty⦈_
        Heli promoting the EPO’s “early certainty” initiative in 2018.


As a matter of fact she appears to spend most of her time on the global IP
conference circuit, turning up as a speaker at various EPO-financed junkets to
deliver pre-cooked presentations on the latest self-promotional gimmicks of the
EPO’s senior management team, such as the “early_certainty” initiative in 2018.


                🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Heli_Pihlajamaa_on_HEY_HI⦈_
           Heli giving the EPO spiel on “Patenting AI” (March 2018).


Apart from that she is in her element holding forth about the latest_“hot
topics”_and_buzzwords (warning: epo.org link) in the IP world such as
“patenting_AI” (software_patents).


Whatever private opinions Heli might have had about the excesses of the Benoît
Battistelli regime at the EPO she seems to have kept these to herself.


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Helsinki Cathedral⦈ Living with a_more_powerful_and_at_times
aggressive_and_expansionist_neighbour on their doorstep, history has taught the
Finns how to keep their mouths shut in the interests of self-preservation.


Whatever about that, the fact of the matter is that Heli survived the
Battistelli era and managed to come out unscathed at the other end.


Less charitable souls have been heard to suggest that she might not have had
too much difficulty accommodating herself to the authoritarian regime of the
Sun-King and his minions.


                🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Heli_Pihlajamaa_and_Bergot⦈_
  In recent years, Heli (left) seems at times to have morphed into a clone of
                            Elodie Bergot (right).


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Finnish flag⦈ EPO insiders have observed that at times,
during recent years, Heli has given the impression that she had morphed into a
clone of Elodie Bergot – at least in terms of her outward appearance.


That concludes our look at the members of the legal term representing the
President of the Office in G 1/21.


In the next part we will review the coverage of the oral proceedings of 28 May
in the IP blogosphere. █


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⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣻⣿⣛⣛⡛⠛⣻⣿⡻⢿⣿⠿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⣿⠘⠿⣌⡀⢂⠠⠺⠌⢨⣿⢀⣀⣿⠔⠂⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠃⠩⠀⡶⠑⠀⠀⠁⡄⡭⢔⣹⠸⠿⡩⢹⡇⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡨⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠠⠄⠀⠀⠐⡀⠀⠀⠸⠿⢸⣟⣁⠐⠂⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡁⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠆⢰⣤⠀⠀⣶⡆⠀⡡⣸⣿⢸⣲⣻⠀⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⢘⡋⠀⠄⠉⠈⠹⠁⢸⣞⢸⣏⡹⠂⠀⠤⠀⠀⠀⠀⠀⠸⣛⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠅⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⢶⠼⠇⠀⠀⣀⠐⠀⠀⢸⣠⢸⡋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡏⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠙⠛⠿⠿⢿⣿⣿⣿⢰⠴⣿⣿⣿⣿⣿⣿⣿⡇⠀⢨⣬⣿⡇⠀⠀⠀⠀⠀⢀⢰⣙⢸⡾⡶⠄⠀⠁⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠘⠛⠿⢿⣿⣿⣿⣿⡇⠠⠘⢋⠀⠀⠀⠀⠀⢀⣀⠂⠸⠇⠰⠡⣰⠹⠡⠂⠀⠀⠀⠀⠀⠀⣸⣫⣽⠿⢹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠃⠀⠀⢀⠀⠀⠀⠀⡆⠈⠟⠀⢸⣥⠸⡃⡚⠲⢤⠀⠂⠀⠀⠀⠀⠀⠰⢐⣟⣿⢺⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠘⠯⢐⣀⠔⠀⢀⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠨⠨⠃⣷⢸⣿⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣧⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣤⠀⠁⠀⠻⢧⠀⡆⣄⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣯⣼⣿⣿⣿⣿⣼⣿⣻⣿⣇⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠉⠀⠀⢀⠾⢫⠀⠇⡁⠀⠀⠀⠐⠀⠀⠐⠀⠄⢴⡶⠦⠄⢿⡿⠾⠛⢿⡏⣹⢛⢻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡇⠿⡏⢸⣿⡃⣾⣿⢽⣟⣶⣦⣤⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⡞⣏⢽⢹⣻⡿⣾⣿⡅⣿⣿⣿⣿⢽⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠅⡾⡿⠈⢻⡇⢿⣶⠕⣬⣸⢛⡛⡾⡿⣽⣿⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣠⠈⠈⡅⠆⡹⢱⠿⣯⣸⣷⣻⣷⠗⣾⣯⣿⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⠈⢿⠀⣿⡄⢸⡆⢿⣧⡇⣛⢣⠻⢢⠿⢭⣿⣊
⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⡀⠁⢀⠙⢈⡋⡏⢿⢀⢿⢬⢾⣞⢳⠾⠨⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠰⠿⡀⢿⠘⢲⡌⢨⡌⢈⡑⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠑⠀⠀⠀⠁⠀⠁⡈⠁⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⢀⠀⢤⠀⠀
⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⡃⣸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠿⠛⠋⠁⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⡇⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠟⠛⠛⠉⠉⠁⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡧⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣺⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⣉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠴⡿⠿⠇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣴⡷⣦⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⣿⣿⣿⣇⢟⠀⠁⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠍⠀⠀⠀⠀⠙⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⣀⣀⣀⣀⣀⣤⡤⠤⠤⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⢁⣄⠀⠀⣇⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠊⠉⠉⠉⠉⠁⠀⠀⢸⣿⣟⣤⣽⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢼⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠙⠿⠛⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣀⡤⡦⢰⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢤⣤⣴⡶⢶⣶⡴⣶⣶⣶⠶⢾⣏⣱⣦⣴⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠉⠁⠈⠐⠒⠒⠒⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⡀⠀⠀⠁⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠤⣁⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡯⡈⠙⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣽⡀⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⢻⣆⠀⠀⠁
⠀⢸⠀⠀⠀⢰⣿⠀⠈⠄⣿⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠀⠀⠀⠀⣻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠲⢶⣆⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢘⠀⠀⠀⠀⣽⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠠⠄⠈⠉⠉⠥⠄⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀
⠀⢸⠀⠀⠀⡀⣿⠢⠀⠀⣿⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠉⠙⠁⠈⠁⠀⠀⠀⢀⣀⣀⠀⣄⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠻⠀⠀⠀⠁⣿⠤⠄⠑⣿⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⠀⠀⠀⠀⣏⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠀⠀⠀⠀⡿⡉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⣤⣤⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⠀⠀⠀⠀⡇⠑⡀⠀⡇⠀⠀⠀⠀⠀⠀⡂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣐⣾⡇⢠⣄⢲⣧⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠠⠂⠀⡄⡇⠀⠘⢄⡇⠀⠀⠀⠀⠀⠀⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢍⠀⠀⠀⡆⡇⠀⠀⡨⡇⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⣿⣿⣀⣀⣀⣐⣶⣶⣶⣶⣶⣶⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⠀⠦⠀⡇⡇⠀⠔⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠀⠈⢂⠃⣇⠊⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠂⠄⠀⡀⡧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠀⠒⠁⣷⡇⠱⡀⢸⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⣿⡇⠀⠘⢼⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡟⠀⠀⠀⣿⡇⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣀⠀⠀⣿⣗⢆⠎⢸⡇⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⡢⠠⢲⢻⡧⣷⡂⢸⡇⣈⣢⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠁⡁⡴⣸⣿⣿⠃⢸⣧⣾⣩⡁⠀⢸⡿⠿⣿⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡝⠛⠛⠛⠛⠛⠛
⣀⣿⣀⣎⣀⣹⣟⣹⣀⣸⣿⣽⣿⡇⠀⢼⣧⣤⣼⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠾⢿⣿⣻⣿⣿⣿⠿⠿⣿⣿⣿⣿⣧⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢻⣿⠁⢀⢴⡄⠀⠀⠀⠀⡀⣩⣉⣉⣉⣩⣍⣠⡇⣿⣿⠿⠛⠻⣿⣸⣿⣿⡇⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⣶⠀⠀⠀⠠⠀⠄⠀⠀⠀⢀⣀⣀⣀⣄⣠⡅⢸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⢇⡿⠷⠶⠖⠒⠛⠉⠻⠋⠁⠀⠀⠀⠀⠀⢯⠀⠀⢀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢡⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣧⣤⢰⣉⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿⣾⣿⣾⣧⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⣾⣶⣿⣿⣽⣿⣯⣽⣟⣃⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠁⠁⠀⠀⠁⠁⠛⢿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣤⣤⣤⣤⣤⣴⠒⠒⠒⠀⠀⠠⠤⠤⠄⡤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⣿⣇⠀⠀⠈⠉⠉⠉⠉⠉⠀⠒⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⣶⣶⣶⣦⢤⣤⣤⣀⣀⣀⣀⣠⣀⣀⣀⣀⣤⣤⣤⣤⣼
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠇⢸⣿⣇⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡆⠠⠄⠀⠀⣤⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢻⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣟⣻⣛⣿⣿⣗⣿⣿⣿⣿⣿⣿
⢰⡖⠘⣆⣨⣿⣐⣜⣁⣿⣹⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⣶⣶⣿⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠶⠶⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⢭⣝⠓⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡶⢾⠶⣮⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣈⣿⣿⣿⣿⣿⣧⣸⣀⣇⣹⣿⣿⣿⣃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⢿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⠠⣤⣤⡶⢂⡀⠏⠄⢲⢶⣶⣷⣵⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡟⢠⣀⣦⣼⣶⣿⣿⣿⣷⣶⣧⣼⣈⠅⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣭⣭⣿⣿⣟⣱⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⠶⠶⠖⠐⠔⠛⠀⠬⠭⠭⠅⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣧⣠⢄⣦⠀⢠⡆⠀⠀⣦⠀⢀⡆⠀⠀⠰⠲⢀⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣦⡹⣧⣿⣯⣿⠟⣿⣿⣿⣿⣿⣾⣿⣶⣾⣷⣶⣶⣿⣶⣼⣧⣤⢰⠰⢸⡆⠀⣶⠂⣶⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠸⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⢹⣿⣿⣿⣿⠃⠀⠀⠸⡗⠂⣿⣶⢻⠀⠸⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⠛⠿⠛⠀⠉⠉⠉⠉⠛⠛⠛⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡿⠿⣿⡏⠉⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠃⢸⣿⣿⢸⠀⠀⠟⠿⠟⠀⠀⠀⠈⠰⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠿⠿⠿⠿⠿⠿⠿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣾⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠰⠋⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⠀⠀⠀⠀⣠⣼⣿⣿⠟⠋⠁⠀⠙⣿⣿⣟⡩⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⠀⠀⠠⠰⢿⣿⣿⣿⣶⣦⣤⣶⣶⣿⣿⣧⣠⣽⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢡⣿⣯⣽⣯⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡰⣷⣄⡇⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡾⣿⣿⡿⠯⠟⠀⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠛⠃⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡇⠀⠈⠛⠿⠶⠂⢘⡆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⣀⣼⣳⣤⣼⣶⣄⡀⣠⣾⣿⣶⣦⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣀⡒⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢰⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⡀⠀⢨⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣸⣿⣶⡬⢁⡠⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⠙⡟⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣷⣿⣿⣷⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠻⠿⠿⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠷⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⣛⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣤⣄⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⣶⣶⣶⢐⣒⡒⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣄⣘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠸⠭⠝⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢄
⠀⠀⠀⠀⢀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠈⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠤⠠⠀⠀⠈⠓⢌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⠇⠀⠨⢿⣶⢠⣄⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠠⠠⡾⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢰⠠⣿⣿⣿⡮⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢥⣈⣉⣻⣿⢹⣯⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿⣮⣝⡁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣻⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢤⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1597

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/06/17/heli-pihlajamaa-swpats/#comments
    Gemini version at gemini://gemini.techrights.org/2021/06/17/heli-pihlajamaa-swpats/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Heli_Pihlajamaa_Promoting_Software_Patents_to_Patent_Maximalists⠀✐


Posted in Deception, Europe, Patents at 7:28 pm by Dr. Roy Schestowitz


Video_download_link


http://techrights.org/videos/epo-pyjamas.webm


Summary: "Ms_Pyjamas" from the EPO is promoting illegal software_patents to a
bunch of patent zealots (CIPA)


Having worked for the regime of Benoît_Battistelli and António_Campinos, Heli
Pihlajamaa (known inside EPO as “Ms Pyjamas”) should know that the judges in
Haar lack independence and should not even be in Haar. But in pursuit of money
and power she carries water for the regime and we’re still seeing evidence of
presidential_tampering_in_ongoing_cases. They just can’t leave the judges
alone, can they?


“Does it strictly require being a liar (who is eager to violate the EPC) or is
that a prerequisite in order to become an EPO official?”Less than a day ago we
mentioned how “Ms Pyjamas” had been promoting ‘Hey Hi’ (AI) patents, in effect
patents on algorithms. And based on this article from earlier this week, only
weeks ago she also vainly_promoted illegal software patents disguised as “CII”
(“computer-implemented inventions”), another misleading name for software
patents. It feels like a ‘collusion’ with the litigation giants, at the expense
of science. To quote some passages: “On Tuesday 25 May 2021, Heli Pihlajamaa,
director of patent law at the European Patent Office, gave a presentation to
CIPA’s computer technology committee on the Patentability of computer-
implemented inventions after the Enlarged Board of Appeal’s decision in G 1/19.
G 1/19 relates to the assessment of inventive step in relation to computer-
implemented simulations and considered whether to have a technical effect, a
simulation must have a direct link to physical reality going beyond its
implementation on a computer. In the presentation, Pihlajamaa discussed how the
decision of G 1/19 emphasised that the approach in T 641/00 applies to all
computer implemented inventions including simulations. In T 641/00 it was
decided that while a claim can have a mix of technical and non-technical
features, novelty and inventive step can only be based on the technical
features. In T 641/00 it was also stated that when assessing inventive step,
the claim should solve a technical problem which the skilled person in the
particular technical field might be asked to solve.”


These are the sorts of people who keep meddling in the online Zoom ‘case’.
Along with her Hungarian colleague, who lies about opponents of software
patents, important decisions will be made. Does it strictly require being a
liar (who is eager to violate the EPC) or is that a prerequisite in order to
become an EPO official? It certainly seems so. More in the video above. █



                    ䷩ 𝚕𝚒𝚗𝚎 1663

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/06/17/irc-log-160621/#comments
    Gemini version at gemini://gemini.techrights.org/2021/06/17/irc-log-160621/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ IRC_Proceedings:_Wednesday,_June_16,_2021⠀✐


Posted in IRC_Logs at 2:31 am by Needs Sunlight


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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                                    #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⠀➾


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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmbBtrgn5vZv4zAnCwEsSEbNfqZyMc1GXjrxGtjFJubZo6



                    ䷩ 𝚕𝚒𝚗𝚎 1777

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/06/17/kevin-mooney-upc-lies/#comments
    Gemini version at gemini://gemini.techrights.org/2021/06/17/kevin-mooney-upc-lies/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ The_Lying_by_Team_UPC,_Led_Again_by_Kevin_Mooney⠀✐


Posted in Deception, Europe, Patents at 7:04 pm by Dr. Roy Schestowitz


Video_download_link


http://techrights.org/videos/team-upc-kluwer.webm


Summary: Team UPC, or specifically Mr. Mooney, lies to the public about the
prospects of the UPC; similarly, EPO and EU officials keep bringing up false
claims about the UPC, so while the UPC itself has likely died for good the lies
have not


ABOUT a day ago (actually a bit less than that) FFII wrote_about_UPC_lies,
reiterating the role of the European Commission and the EPO in such lies.


“Basically, Mr. Mooney decided to lobby for his money.”There seems to be — not
for the first time one might add — a complete and total disregard for facts.
“FFII has received a testimony that the European Commission has recycled an old
Impact Assessment (IA) of the Unified Patent Court (UPC),” it said, “in order
to hide the controversial self-financed aspect of the Court, which is why the
Court is too expensive for SMEs. Countries are ratifying this dangerous treaty
without any real Impact Assessment of the new Court system which will exclude
most SMEs with its super high costs. The Impact Assessment was recycled from
old treaty project of 2009, the UPLS, with lots of changes in the meantime,
similar to what happened recently with the recycling of the Impact Assessment
of the Mercosur treaty.”


It also noted: “Around early 2012, after some requests to redo the impact
assessment by the Scrutiny committee of the British parliament, the
representative of the European Commission Margot Frohlinger apparently refused
to procure an updated one, according to a testimony we received she did not
want to “redo the impact assessment because it would attract critics”. After
taking this decision at the European Commission, she left to continue her
career at the European Patent Office (EPO), the other self-financed
administration that will grant the Unitary Patent. A self-financed patent court
is controversial, because the cost is passed on to companies that litigate in
front of the court, and no courts in Europe have a self-financed objective
(Art36.3 UPCA “the objective of a self-financing Court”), as courts are not
companies and should not be driven by financial targets to guarantee the
integrity of the justice system. If courts are driven by profit, judges will
tend to apply “patent maximalism” just to guarantee their salary.”


It says “patent maximalism” — a term we used a lot about a decade ago (based on
“copyright maximalism”). The same observation is made in the comments_here,
citing Techrights. Basically, Mr. Mooney decided to lobby for his money. He
decided to lie again about the UPC and people are reacting. The video above
does too. █



                    ䷩ 𝚕𝚒𝚗𝚎 1846

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/06/17/loss-of-focus/#comments
    Gemini version at gemini://gemini.techrights.org/2021/06/17/loss-of-focus/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Too_Much_Noise_and/or_Distraction_and_General_Loss_of_Focus_(on_the_Real_and
Urgent_Issues,_Such_as_the_Ongoing_Anti-FSF_‘Coup’)⠀✐


Posted in Deception, Free/Libre_Software, FSF, GNOME, GNU/Linux, IBM,
Microsoft, Windows at 5:55 am by Dr. Roy Schestowitz


Video_download_link


http://techrights.org/videos/distraction_galore.webm


Summary: The media is full of Microsoft fluff and technical blog posts still
focus on the Freenode fiasco, among other things that don’t matter all that
much; but we certainly need to talk about steps undertaken to undermine the
FSF’s power because long-term ramifications may be huge


THIS past week, especially the past few days, may have seemed rather turbulent.
Microsoft has resorted to vapourware (they really could use a distraction from
all the scandals, which extend to and include Bill Gates) and many projects
that rely on IRC are (or were) still on Freenode, so there’s a big debate about
what_happened and what to do next.


“It’s about giving more control to monopolies.”Sadly, I worry that many people
lost sight of what GNU_C_Library_(glibc)_and_GNU_Portability_Library_(gnulib)
are_doing — a_subject_we_covered_here_before. There are efforts to weaken the
FSF, in effect giving more control (over GNU projects) to companies such as
IBM. We’re talking about this at this very moment in IRC. There’s a lot at
stake because licensing and copyright assignments are a very big deal from a
legal perspective. As somebody put_it this week, “MsPL has a clause added
specifically and only to make it incompatible with the GPL and related
licenses.” It’s about giving more control to monopolies. █



                    ䷩ 𝚕𝚒𝚗𝚎 1895

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/06/17/meme-the-enlarged-bored-people-with-presidential-decrees/#comments
    Gemini version at gemini://gemini.techrights.org/2021/06/17/meme-the-enlarged-bored-people-with-presidential-decrees/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ [Meme]_The_Enlarged_Bored_People_With_Presidential_Decrees⠀✐


Posted in Europe, Patents at 5:30 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Classic_Rodney:_Oh,_hi!_Hey_hi!_(AI);_The_President_said_to
'OK'_software_patents;_No_matter_the_actual_facts⦈_


Summary: The laughable state of the EPO‘s EBA (or EBoA) is rarely commented on
anymore, not even in so-called ‘IP’ blogs; maybe they’re just so eager to see
patents on everything, even European_software_patents, so tyrants [1, 2] who
destroy the courts (with UPC lobbying and removal of EBA independence) don’t
bother them so much anymore


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⢤⡄⣤⢠⡬⢹⢩⡭⣥⣤⣤⡄⣤⠤⣤⢦⡄⣤⢠⡤⣤⢠⡤⢠⡄⣤⢤⣤⠄⢠⡴⣤⢠⣤⡄⣤⢠⡤⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢰⡟⣶⠀⠿⠿⣴⢻⡆⣿⣼⠿⠿⢇⢳⣟⠷⢰⡟⣶⢸⡟⠛⣿⢻⣇⣾⣶⡿⣼⣿⢰⣿⣶⢸⡟⠃⢸⡟⣶⢸⣿⡖⢻⡟⢸⡟⢸⣧⣿⠚⣿⢣⣾⠷⢹⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇⣿⠀⠀⠀⣿⣸⡇⣿⢿⡄⣿⣿⣣⣝⣷⢸⣇⣿⢸⡏⠀⣿⠀⣿⡟⣿⡇⣿⣼⣿⣿⣿⢸⣟⡁⢸⡟⠋⣼⣿⡇⢸⡇⢸⣏⣸⡿⣿⠀⣿⠠⣽⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠈⠉⠁⠉⠈⠁⣿⣿⣷⣭⠉⠈⣉⣁⣬⣥⣤⣭⣶⣩⣁⠉⠁⠉⡈⠉⠉⠉⠈⠉⠁⠈⠁⠀⠉⠈⠉⠈⠁⠈⠉⠉⠁⠉⠀⠉⢴⣭⣭⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢿⠞⠏⠑⠀⠀⠉⠛⠛⠿⠙⣫⡄⢺⡟⣄⢅⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⡵⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠋⠀⠀⠠⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⣆⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⣿⣿⣿⣿⠿⠃⣀⣀⡀⣰⠋⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠋⣵⣠⣾⣿⣿⣧⡉⠰⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⡟⣿⣿⣿⢻⣿⠛⠿⠆⠀⠀⠀⠉⣁⠀⢀⢀⣄⠠⢀⢠⣈⣿⣿⣿⣿⣿⣿⣿⢲⡿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣦⠀⠈⢻⣿⠋⢧⡄⠀⠀⠀⠀⡠⡄⣿⣦⡘⣷⡶⠶⢛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠈⠈⠿⣿⣧⡀⠘⠿⠆⠀⠀⢀⠀⠀⠐⠾⢁⣿⣿⣿⣷⢶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢫⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⠿⣧⠀⠐⠀⠀⢀⣾⣶⠀⢠⣴⡿⠿⠏⠉⠉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠇⢻⣿⠀⠀⠀⠀⠀⠢⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣷⣤⣤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⢄⣾⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣿⠿⠿⠟⢛⣛⣉⣙⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⠿⠿⠿⢿⣟⣱⡽⠍⠂⠀⠀
⠀⠀⠀⢀⣎⠁⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡⠁⠀⠊⠉⣉⣹⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠀⠀⠀
⠀⠀⢀⣾⣿⣦⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢿⣿⣿⡩⠿⣛⢀⡀⣀⣀⠀⢀⣀⢀⣀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⠀⢀⣀⡀⣀⣀⣐⣛⣃⣀⣀⡀⢀⣀⠀⣀⠀⢀⣀⡀⣀⣀⢀⣀⣀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠉⠉⠀⣿⣾⡇⣿⣿⡇⢸⣿⣿⣿⢸⣿⡇⢹⡏⠉⣿⠁⣿⡅⣿⣼⡇⠈⢹⡏⢸⣿⣿⣿⣯⠀⢸⣿⡇⣿⠸⢯⢹⡏⣿⣿⡇⣼⢻⡆⣿⠀⢸⣿⡅⣿⣿⢸⡇⠿⠈⣿⠙⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠇⠿⠿⠃⠸⠇⠿⠿⠼⠟⠷⠸⠇⠀⠿⠀⠿⠦⠿⠸⠇⠀⠸⠇⠸⠿⠿⠿⠷⠀⠿⠻⢧⡿⠼⠇⠸⠇⠻⠿⠇⠿⠻⠇⠿⠄⠸⠿⠸⠿⠿⠼⠧⠿⠀⠿⠈⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣟⣛⠟⣛⡛⣛⡛⣿⣿⡟⣛⡛⣛⣛⢛⣛⢛⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢹⣿⡄⣿⣇⣿⡇⣿⣿⡇⣿⣇⣿⣿⢸⣿⠘⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⡇⣿⡟⣿⡇⣿⣿⡇⣿⡟⣿⣿⢸⣿⠀⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣾⠿⡁⣿⡇⣿⡇⣶⢹⡇⣿⡇⣿⡿⢸⣿⠀⣶⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣾⣿⣶⣾⣇⠚⢷⣶⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠹⣻⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢈⢽⣿⣿⡿⠛⠀⠀⠀⠀⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⠛⣿⣿⣿⣇⣀⣐⡭⢤⡀⠀⠀⠘⣿⣿⡟⠛⠉⠙⠛⠿⢿⣿⡟⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⠋⠂⠤⠿⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣯⣤⣤⣴⢪⣼⣿⣿⣿⠀⢀⠂⠒⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⠿⠛⠛⠙⢩⣴⣿⣿⣿⣿⣿⣧⡀⠈⠉⣡⣮⠅⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠛⠻⢿⢿⠧⠻⣿⣶⣾⣿⠛⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡄⠘⠻⠟⠃⠀⢀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠎⠁⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢴⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠑⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀⣀⣀⢊⢁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⠀
⡻⢛⡛⠋⠉⠩⠭⠉⠉⠉⢩⡞⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠈⠀⠙⠾⠿⢿⠿⠿⠃⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡞⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠖⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢩⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⠿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⠿⢿⡋⣼⣿⣿⠿⣿⣿⣿⣿⣿⣏⡫⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣾⣿⣿⠋⣼⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣷⣤⣤⣶⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠯⢿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠉⠷⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠣⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣹⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣻⣿⠻⣿⣿⣿⠟⠛⣙⣟⡻⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢫⡶⢾⡇⢀⣿⣿⣿⣷⠈⠧⣽⣷⣿⣿⡄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣟⣿⣿⣿⣿⣿⣿⠋⠿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢏⣴⣷⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠁⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠈⠉⠁⢠⣾⣿⠟⢡⣾⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣛⠉⠉⣉⣀⣠⠖⢹⣿⣿⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣿⣿⢻⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣷⣴⣿⣿⡏⡀⢀⣿⣿⣿⣷⣶⣾⣿⠟⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡻⣿⣦⠻⢿⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢱⡟⣿⣿⣿⣿⣿⣿⣿⣿⠃⣱⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡙⣿⣷⡙⠿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⠁⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣿⣿⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠆⠼⠿⣿⠿⢿⣿⣿⠿⡿⡿⡿⠀⣿⣿⣿⣿⣿⠿⢩⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣶⢰⣶⡆⣶⣶⠆⣶⡆⣶⡆⡝⢰⣶⢰⣶⠀⣶⡆⣶⣶⢸⢡⣶⠖⢰⣶⣶⡀⣶⣶⠰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⡇⣿⣧⡄⠸⣷⣿⢰⡟⢸⣿⣾⣿⠀⣿⡇⣿⡏⢸⢸⣿⠀⣸⡟⣿⡇⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡝⠻⣿⣿⣿⣿⣿⣿⣿⡻⣻⣿⣿⣿⡟⢸⣿⢸⣿⡇⣿⣇⣐⠂⣿⡇⣾⡇⢸⣿⢸⣿⠀⣿⡇⣘⡃⢿⢸⣿⠀⣿⡷⣿⣧⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⠻⡿⠿⡙⢛⣿⣿⣿⣿⡿⠀⠈⠉⠈⠉⠁⣋⣉⣉⣤⣉⣁⣽⣧⣈⣉⣈⣉⣀⢉⣡⣉⣁⣼⣦⣉⣉⣉⡁⢉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣸⣿⣿⣿⠘⠿⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢉⣿⣾⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿

                    ䷩ 𝚕𝚒𝚗𝚎 2000

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/06/17/swpats-epo-officials/#comments
    Gemini version at gemini://gemini.techrights.org/2021/06/17/swpats-epo-officials/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Response_to_Misinformation_From_EPO_Officials⠀✐


Posted in Deception, Europe, Patents at 4:54 am by Dr. Roy Schestowitz


Video_download_link


http://techrights.org/videos/epo-rebuttals.webm


Summary: Opponents of European_software_patents are clearly being
mischaracterised by EPO officials, who also use meaningless buzzwords to
promote such patents; as an aside or footnote that relates to our ongoing
series we’re making this quick video, which is days late


Due complete catastrophes associated with IRC, notably Freenode, we didn’t make
any videos yesterday and the day before that. We lost a ton of time (and sleep)
over the urgent need to set up contingencies and regain control over the “new”
Freenode. The new deployment has caught up with about 60 users who are still on
it, but they don’t say much. IRC isn’t about the number of users and how much
they talk, however, but how many say something and how many say something of
value (to retain high s/n ratio).


“In the meantime, those wishing to join us in IRC are encouraged to come to
irc.techrights.org (default port numbers).”In any event, this video is my
personal view about recent parts of the EPO series about António_Campinos
‘hatchets’ inside the Boards of Appeal and the Enlarged Board of Appeal’s
hearings [1, 2, 3]. I have had a lot more to say, but we lost an incredible
amount of time this week. We won’t be catching up fully any sooner than Monday.


Tomorrow we’ll continue with Virtual Injustice — Part 10. This series is by far
our highest priority. Some time in the future we’ll write about Freenode and
explain things never covered elsewhere (we have some exclusive inside
knowledge).


In the meantime, those wishing to join us in IRC are encouraged to come to
irc.techrights.org (default port numbers). This is the predictable network that
won’t be scrapped overnight and/or become unavailable for a whole day. █



                    ䷩ 𝚕𝚒𝚗𝚎 2057

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Links_17/6/2021:_Cutelyst_3_and_Lenovo_Move_Towards_ThinkPad_BIOS
Configuration_From_Within_Linux⠀✐


Posted in News_Roundup at 8:49 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Audiocasts/Shows⠀➾


                # ⚓ The_Linux_Link_Tech_Show_Episode_910⠀⇛


                       upgrading raspberry pi to buster, sd card imaging
                       woes, apple replacement woes, food


                # ⚓ FLOSS_Weekly_634:_Web_Development_with_Wasp⠀⇛


                       Martin Sosic, Co-Founder and CTO of Wasp joins Doc
                       Searls and Katherine Druckman on FLOSS Weekly. Wasp
                       is a simple and exciting new open-source language
                       for developing full-stack web apps with less code.
                       Sosic shares more about Wasp as well as where web
                       development is going and many of the issues
                       involved for both developers and users.


                # ⚓ Freenode_Is_Now_Dead:_Birth_Of_A_New_Freenode⠀⇛


                       Andrew Lee can’t just let Freenode collapse, every
                       step of the way he keep kicking it faster down the
                       hill and now he has actually done it, Freenode
                       might now be actually dead.


          o § Kernel Space⠀➾


                # ⚓ Continued_collaboration_with_AMD_brings_powerful_solutions
                  to_customers⠀⇛


                       The Oracle Linux and Virtualization team
                       congratulates AMD for the recently released AMD
                       EPYC™ 7003 Series CPUs, which includes one of the
                       most powerful server processors in the world, the
                       EPYC 7763. Oracle Cloud Infrastructure and AMD
                       teams have worked together for several years to
                       bring high-performance solutions, based on the 1st
                       and 2nd Generation EPYC processors, to our mutual
                       customers and we’re doing the same with the latest
                       offerings from Oracle and AMD.


                # ⚓ VirtIO-GPIO_Guest_Driver_Updated_For_The_Linux_Kernel_–
                  Phoronix⠀⇛


                       There has been a number of new VirtIO driver
                       additions recently to the Linux kernel like for
                       sound and Bluetooth for the expanding VirtIO
                       specification while one still in the works for
                       mainlining is the GPIO guest driver.


                       The latest VirtIO-GPIO guest driver was published
                       on Tuesday as a new GPIO driver for complying with
                       the VirtIO-GPIO protocol and ultimately mapping
                       from a guest virtual machine either to virtual/
                       simulator devices or from the guest mapping to real
                       GPIOs on the host hardware.


                # ⚓ Lenovo_To_Support_Configuring_ThinkPad_BIOS_From_Within
                  Linux_–_Phoronix⠀⇛


                       In conjunction with supported Lenovo systems, a new
                       “Think-LMI” driver is on its way to the mainline
                       Linux kernel for allowing some BIOS/firmware
                       settings to be accessed and configured within
                       Linux.


                       The Think-LMI driver allows for changing BIOS
                       settings on supported ThinkPads and other
                       unspecified Lenovo systems where the WMI interface
                       is supported.


                # ⚓ PSA:_kernel_5.12.11_is_safe_for_bcache,_again⠀⇛


                       With the release of Linux kernel 5.12.11, bcache is
                       safe to use, again. The patch bcache: avoid
                       oversized read request in cache missing code path
                       has been merged.


                # § Graphics Stack⠀➾


                      # ⚓ KDE_Goals_Update_–_June_2021⠀⇛


                             With every recent Plasma update (and
                             especially the just released version 5.22)
                             the list of features that are X11 exclusive
                             gets smaller and smaller.


                             Conversely, many users may not be aware that
                             the opposite is also happening: every day
                             there are more features available on Wayland
                             that cannot be found on X11!


                             There are many resources available describing
                             the security advantages of Wayland over X11,
                             but the ageing protocol has some other
                             shortcomings as well. For example, the last
                             update we highlighted was the recently
                             released VRR support in 5.22. Among other
                             things, this enables an important use case
                             for me: it allows each of my connected
                             displays to operate at their highest refresh
                             rate. I have a 144Hz main display, but
                             occasionally I plug in my TV, which works at
                             60Hz. Because of limitations of X11, for
                             everything to work, my main display needs to
                             be limited to 60Hz when both of them are
                             active. But not any more thanks to Wayland!


                             While the KDE developers always try to bring
                             new functionalities to all users, the above
                             example shows that sometimes, either due to
                             X11 limitations or for other reasons, feature
                             parity will not be possible.


                             [...]


                             As announced on the community mailing list
                             and the Goals matrix room, there was a
                             meeting last Monday to discuss the way
                             forward with the huge list of topics
                             mentioned in the previous update.


                             In the meeting, the conclusion was to start
                             with the topics regarding the different
                             platforms we support, as well as the
                             automation of the build/release process of
                             apps.


                             Taking advantage of the upcoming Akademy, the
                             topics will be discussed during the BoF
                             sessions. Check out the schedule to see when
                             you can attend! Also, don’t miss the
                             “Creating Plasma Mobile apps” BoF!


                             Of course, like the other Goal Champions,
                             Aleix will have a talk on the first day of
                             Akademy, don’t miss it!


                      # ⚓ Mike_Blumenkrantz:_Suballocate_Me⠀⇛


                             There’s a lot that goes into this item. The
                             post you’re reading now isn’t about to go so
                             far as to claim that zink(-wip) is usable for
                             gaming. No, that day is still far, far away.
                             But this post is going to be the first step.


                             To begin with, a riddle: what change was made
                             to zink between these two screenshots?


                             [...]


                             A suballocator is a mechanism by which small
                             blocks of memory can be suballocated out of
                             larger one. For example, if I want to
                             allocate an 64byte chunk of memory, I could
                             allocate it directly and get my block, or I
                             could allocate a 4096byte chunk of memory and
                             then take 64bytes out of it.


                             When performance is involved, it’s important
                             to consider the time-cost of allocations, and
                             so yes, it’s useful to have already allocated
                             another 63 instances of 64bytes when I need a
                             second one, but there’s another, deeper issue
                             that’s also necessary to address, especially
                             as it relates to gaming: 32bit environments.


                             In a 32bit process, the amount of address
                             space available is limited to 4GB, regardless
                             of how much actual memory is physically
                             present, some of which is dedicated to system
                             resources and unavailable for general use.
                             Any time a buffer or image is mapped by the
                             driver in a process, this uses up address
                             space in order to create an addressable
                             region of memory that can be read or written
                             to. Once all the address space has been used
                             up, no other resources can be mapped, and it
                             becomes impossible to continue normal
                             operations.


                      # ⚓ Zink_OpenGL-On-Vulkan_Hits_Another_“Massively
                        Improved_Performance”_Milestone_–_Phoronix⠀⇛


                             The Zink component to Mesa that provides a
                             generic OpenGL implementation built atop the
                             Vulkan API recently hit another “massively
                             improved performance” milestone by Valve
                             contractor Mike Blumenkrantz.


                             Mike began work on a suballocator for Zink
                             that is based on the Gallium3D auxiliary/
                             pipebuffer code originally started by the
                             RadeonSI Gallium3D driver. After making
                             significant changes to that code, Zink’s new
                             suballocator implementation is showing off
                             significant performance improvements in just
                             shy of 700 lines of new code.


                      # ⚓ OpenGL_over_Vulkan_driver_Zink_gets_a_huge
                        performance_boost⠀⇛


                             We heard you like performance and it seems
                             the new OpenGL over Vulkan driver Zink is
                             going to bring some FPS friends whenever the
                             next release lands. Developer Mike
                             Blumenkrantz who has been contracted by Valve
                             has continued hacking away at the code, and
                             in a new blog post detailed a massive change
                             to the driver to improve gaming performance.


                             Don’t know what Zink is? It’s “an OpenGL
                             implementation on top of Vulkan. Or to be a
                             bit more specific, Zink is a Mesa Gallium
                             driver that leverages the existing OpenGL
                             implementation in Mesa to provide hardware
                             accelerated OpenGL when only a Vulkan driver
                             is available” – Collabora.


          o § Instructionals/Technical⠀➾


                # ⚓ [Old] Tarsnap_Architecture⠀⇛


                       That said, i’m also interested in tarsnap from a
                       technical standpoint. Tarsnap manages to provide
                       all three of compression, encryption, and
                       deduplication, while also allowing you to delete
                       old backups. The two other deduplicating backup
                       systems i’ve looked at (camlistore and bup) don’t
                       support deletion, which is an instant disqualifier
                       for me, since i’m always running out of disk space.


                # ⚓ SSH_with_a_SmartCard-HSM_and_EC_keys⠀⇛


                       The six year-old HSM I have has support for 2048
                       bit only RSA keys which is enough reason to attempt
                       using EC keys, but as Remy pointed out when he
                       wrote the article in 2016, OpenSSH had no PKCS#11
                       support for them then.


                       It turns out my client of choice has OpenSSH_8.1p1
                       which isn’t recent enough either, so I install
                       portable OpenSSH version 8.6p1.


                # ⚓ Joey_Hess:_typed_pipes_in_every_shell⠀⇛


                       Powershell and nushell take unix piping beyond raw
                       streams of text to structured or typed data. Is it
                       possible to keep a traditional shell like bash and
                       still get typed pipes?


                       I think it is possible, and I’m now surprised noone
                       seems to have done it yet. This is a fairly
                       detailed design for how to do it. I’ve not
                       implemented it yet. RFC.


                # ⚓ Stephen_Smoogen:_Working_with_Raspberry_PI4_systems⠀⇛


                       While my current work is aimed at ARM-64 hardware,
                       many of the boards are not Server Ready Hardware
                       and thus do not have things like EUFI to boot, ACPI
                       to query the hardware stack, or various other
                       things which are added later as firmware updates.
                       They also end up having ‘developer kit boards’ of
                       US$6000.00+ systems which having one at home is
                       hard to justify. {Sorry kid, no college this
                       semester… Dad bought himself a board that the
                       customer may dump next week.}


                       In looking for proxy systems, my team has been
                       focusing first on the classic ARM for small
                       projects: The Raspberry Pi. The raspberry pi4 with
                       4 GB of ram works out as a proxy for all kinds of
                       ‘low-end’ systems where you may need to play with a
                       small GPU and try to make it work with a Server
                       Ready operating system like CentOS Stream.


                # ⚓ How_to_update_the_Discord_app_on_Linux⠀⇛


                       Do you use Discord on Linux? Do you need to update
                       to the latest features but don’t know how? We can
                       help! Follow along in this guide as we go over how
                       to update Discord on Linux!


                # ⚓ How_to_install_Veloren_on_a_Chromebook⠀⇛


                       Today we are looking at how to install Veloren 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.


                # ⚓ How_to_Set_Up_Razer_Devices_on_Linux_for_Lighting_Effects⠀⇛


                       You have a shiny new Razer hardware, but you cannot
                       find the Razer Synapse software for Linux. And you
                       end up with no proper RGB sync and do not get to
                       customize it. What do you do?


                       Well, for certain functionalities, like adding
                       macros to your mouse, you will still need access to
                       Razer Synapse (on Windows or macOS).


                       But, to tweak a few other options like macros for
                       the keyboard, changing the DPI of your mouse, or
                       lighting effects, you can easily set up your Razer
                       peripherals on Linux.


                # ⚓ How_To_Install_and_Configure_Drupal_on_Fedora_34/33_–
                  TecAdmin⠀⇛


                       Drupal is a free and open-source content management
                       system (CMS), is flexible for building blogs and
                       websites. It is written in PHP programming language
                       and uses MySQL as a backend database. Drupal is
                       available with thousands of add-ons, which makes it
                       highly customizable.


                       You can deploy Drupal on any web server that
                       supports the PHP programming language. In this
                       tutorial, we will provide you with steps to install
                       Drupal with Apache on Fedora Linux systems.


                # ⚓ How_to_deliver_decision_services_with_Kogito_|_Red_Hat
                  Developer⠀⇛


                       This article is the first of two presenting new
                       support for developing decision services in Red Hat
                       Business Automation Manager and Red Hat Process
                       Automation Manager. We specifically address support
                       for the Decision Model and Notation (DMN) standard.
                       Process Automation Manager now supports Kogito’s
                       cloud-native runtime engine for creating rules,
                       decisions, and resource-planning optimization
                       solutions based on the Predictive Model Markup
                       Language (PMML).


                       We’ll present an example using Kogito with Drools
                       Rules Language, both backed by the KIE group. By
                       expanding Kogito with the power of Quarkus, you can
                       enjoy hot-reload during the development phase and
                       compile decision services into fast, lightweight
                       services.


                       For resource planning, Process Automation Manager
                       7.11 brings full support for OptaPlanner 8, the
                       most recent version of this artificial intelligence
                       (AI) constraint solver technology.


                       All these new features are now part of the Red Hat
                       Process Automation stack.


                # ⚓ How_to_install_htop_on_Almalinux_or_Rocky_8_–_Linux_Shout⠀⇛


                       htop is a lightweight to available for Linux
                       systems to show a dynamic overview of the running
                       processes and the system resources used. Compared
                       to the classic top this process manager offers some
                       convenient functions. Here we see the steps to
                       install it on AlmaLinux, CentOS, 8, Rocky, Oracle,
                       or RHEL.


                       The program has a ncurses interface, ncurses stands
                       for new curses, it is a free C – program library to
                       a character-based user interface (Text user
                       interface – TUI) independently of the illustrative
                       text terminal or terminal emulator display. Htop
                       can easily be operated with the keyboard without
                       having to type long commands. If htop is started in
                       a terminal within a desktop environment, the mouse
                       can also be used. If you want to use the mouse in a
                       virtual terminal, gpm must be installed.


                # ⚓ How_to_install_Gitlab_on_FreeBSD_–_Unixcop_Unixcop⠀⇛


                       GitLab is a web based version control system and
                       collaborative software development based on Git.
                       Its features include things like the code
                       repository, wiki or issue-tracking system. In this
                       article I will show you how to install the
                       Community Edition of GitLab on FreeBSD.


                # ⚓ How_to_install_Joomla_3.9_on_Ubuntu_20.04⠀⇛


                       Joomla is an award-winning content management
                       system (CMS) that is used for making dynamic
                       websites. It is open-source and is available for
                       free under GPL (general public license). It is
                       based on a model–view–controller framework. It
                       powers millions of websites around the world. It
                       can be used to develop websites for different
                       purposes like business websites, online magazines,
                       e-commerce, portals etc. Joomla has large community
                       of users to provide support.


                # ⚓ How_to_resize_and_growing_disks_in_FreeBSD_–_Unixcop⠀⇛


                       I work a lot with virtual nachines. In fact, most
                       of my servers are virtual machines (last time I’ve
                       counted, there where around 100vms) running on top
                       of four physical servers and couple of SAN/NAS.
                       Sometimes you -or the one who asked for the
                       machine- underestimate the hardware resources
                       needed. Or simply after a while you end up with a
                       nice “Filesystem full” error.
                       In this article I’ll show how to resize a partition
                       and grow the filesystem to get more free space.


                # ⚓ yum/dnf_Package_Manager_Basics⠀⇛


                       Every modern Linux distribution comes with a set of
                       tools for installing and updating software. Such
                       tools are called package managers.


                       Package managers help you find software, download
                       it to your computer and install or upgrade it. When
                       a certain software package can’t work without
                       additional components, relevant software packages
                       will be installed automatically.


                       In Red Hat family of operating systems the package
                       manager is called yum. In recent years it’s been
                       replaced with backward-compatible tool called dnf.


                # ⚓ Copy_A_File_To_Multiple_Directories_In_Command_Line_On
                  Linux⠀⇛


                       In this brief guide, we will discuss how to copy a
                       file to multiple directories from command line
                       using find, cp, echo, xargs and tee commands on
                       Linux.
                       The other day I wanted to copy some videos to
                       different folders in my Arch Linux desktop. As you
                       already know, we can easily do it by right-clicking
                       on the file, select Copy option from the context
                       menu and paste it on the destination directory/
                       folder.
                       However, I’d like to know if there are any other
                       way to copy the file into multiple directories in
                       one go. I thought It would help when I want to copy
                       a single file into number of different directories
                       at once. I did a few web searches and come up with
                       following solutions.


                # ⚓ Defining_and_distributing_SELinux_policies_–_Linux
                  Concept⠀⇛


                       Enabling SELinux does not automatically start the
                       enforcement of access. If SELinux is enabled and it
                       cannot find a policy, it will refuse to start
                       because the policy defines the behavior of the
                       system (what SELinux should allow). SELinux
                       policies are generally distributed in a compiled
                       form (just like with software) as policy modules.
                       These modules are then aggregated into a single
                       policy store and loaded in memory to allow SELinux
                       to enforce the policy rules on the system.


                # ⚓ Install_NVIDIA_Drivers_on_Debian_/_Ubuntu_/_Linux_Mint_/
                  LMDE_[Manual_Install]_–_If_Not_True_Then_False⠀⇛


                       This is guide, howto install NVIDIA proprietary
                       drivers on Debian Sid/11/10, Ubuntu 21.10/21.04/
                       20.10, Linux Mint 20.1, LMDE 4 and disable Nouveau
                       driver. This guide works with GeForce 8/9/200/300/
                       400/500/600/700/800/900/10/20/30 series cards. This
                       is alternative way to install NVIDIA drivers,
                       because Debian based Linux distros have NVIDIA
                       drivers directly from repos too.


                # ⚓ The_ultimate_guide_to_EAPI_8⠀⇛


                       Three years ago, I had the pleasure of announcing
                       EAPI 7 as a major step forward in our ebuild
                       language. It introduced preliminary support for
                       cross-compilation, it finally provided good
                       replacements for the last Portagisms in ebuilds and
                       it included many small changes that made ebuilds
                       simpler.


                       Only a year and a half later, I have started
                       working on the initial EAPI 8 feature set.
                       Similarly to EAPI 6, EAPI 8 was supposed to focus
                       on small changes and improvements. The two killer
                       features listed below were already proposed at the
                       time. I have prepared a few patches to the
                       specification, as well as the initial
                       implementation of the respective features for
                       Portage. Unfortunately, the work stalled at the
                       time.


                       Finally, as a result of surplus of free time last
                       month, I was able to resume the work. Along with
                       Ulrich Müller, we have quickly prepared the EAPI 8
                       feature set, got it pre-approved, prepared the
                       specification and implemented all the features in
                       Portage and pkgcore. Last Sunday, the Council has
                       approved EAPI 8 and it’s now ready for ~arch use.


                       What’s there in EAPI 8? Well, for a start we have
                       install-time dependencies (IDEPEND) that fill a gap
                       in our cross-compilation design. Then, selective
                       fetch/mirror restriction make it easier to combine
                       proprietary and free distfiles in a single package.
                       PROPERTIES and RESTRICT are now accumulated across
                       eclasses reducing confusion for eclass writers.
                       There’s dosym -r to create relative symlinks
                       conveniently from dynamic paths. Plus bunch of
                       other improvements, updates and cleanups.


                # ⚓ Linux_package_management_with_dnf_|_Opensource.com⠀⇛


                       Installing an application on a computer system is
                       pretty simple. You copy files from an archive (like
                       a .zip file) onto the target computer in a place
                       the operating system expects there to be
                       applications. Because many of us are accustomed to
                       having fancy installer “wizards” to help us get
                       software on our computers, the process seems like
                       it should be technically more complex than it is.


                       What is complex, though, is the issue of what makes
                       up an application. What users think of as a single
                       application actually contains code borrowing from
                       software libraries (i.e., .so files on Linux, .dll
                       files on Windows, and .dylib on macOS) scattered
                       throughout an operating system.


                       So that users don’t have to worry about that
                       veritable matrix of interdependent code, Linux uses
                       a package management system to track what
                       application needs what library, and which library
                       or application has security or feature updates, and
                       what extra data files were installed with each
                       software title. A package manager is, essentially,
                       an installer wizard. They’re easy to use, they
                       provide both graphical interfaces and terminal-
                       based interfaces, and they make your life easier.
                       The better you know your distribution’s package
                       manager, the easier your life gets.


                # ⚓ Providing_more_security_for_Linux_–_Linux_Concept⠀⇛


                       Seasoned Linux administrators and security
                       engineers already know that they need to put some
                       trust in the users and processes of their system in
                       order for the system to remain secure. This is
                       partly because users can attempt to exploit
                       vulnerabilities found in the software running on
                       the system, but a large contribution to this trust
                       level is because the secure state of the system
                       depends on the behavior of the users. A Linux user
                       with access to sensitive information could easily
                       leak that out to the public, manipulate the
                       behavior of the applications they launch, and do
                       many other things that affect the security of the
                       system. The default access controls active on a
                       regular Linux system are discretionary; it is up to
                       the users how the access controls should behave.


                       The Linux discretionary access control (DAC)
                       mechanism is based on the user and/or group
                       information of the process and is matched against
                       the user and/or group information of the file,
                       directory, or other resource being manipulated.
                       Consider the /etc/shadow file, which contains the
                       password and account information of the local Linux
                       accounts…


                # ⚓ Editing_files_with_the_vi_editor_–_Linux_Concept⠀⇛


                       The vi editor is the most popular editor used to
                       edit or create new files from a shell prompt. It
                       comes in text-based as well graphical interface
                       form, with extended features. This text-based
                       editor is used to write a script, edit system
                       configuration files, or develop the source code of
                       a programming language. The name vi is pronounced
                       as vee-eye.


                       The vim (short for vi improved) version of the vi
                       editor comes with many enhancements to make working
                       with the vi editor easier. It supports extended
                       features, such as syntax highlighting for many
                       configuration files and programming languages.
                       Whatever we learn about vi editor is applicable to
                       vim also, so we will learn about the vi editor in
                       this section.


                # ⚓ Different_methods_to_create_a_text_file_–_Linux_Concept⠀⇛


                       Text files can be viewed and edited using any text
                       editor that exists in Linux. However, before
                       learning the editing part, we must have a basic
                       understanding of different ways that can be used to
                       create plain text files. Depending on the
                       requirement, different methods can be used for text
                       file creation. The most popular ones are described
                       next.


                # ⚓ Managing_archives_and_compressed_files_–_Linux_Concept⠀⇛


                       Archiving is the process of fetching multiple files
                       from the same or different locations and putting
                       them into a single file bundle. It is generally
                       done together with compression, or immediately
                       followed by compression. This helps in streamlining
                       the backup process, as discussed in the following
                       section.


                # ⚓ Micro_–_A_Command_Line_Based_Text_Editor_for_Linux⠀⇛


                       Tired of using a Nano text editor? Then surely you
                       have to try Micro – is a simple terminal-based text
                       editor written in Go Language and released under
                       MIT license.


                # ⚓ Recover_Lost_Space_on_a_USB_Flash_Drive [Ed: Newly
                  updated]⠀⇛


                # ⚓ Set_up_a_service_mesh_on_Istio_|_Opensource.com⠀⇛


                       Service mesh and serverless deployment models
                       represent the next phase in the evolution of
                       microservice architectures. Service mesh enables
                       developers to focus on business feature development
                       rather than managing non-functional microservices
                       capabilities such as monitoring, tracing, fault
                       tolerance, and service discovery.


                       Open source service mesh projects, including Istio,
                       LinkerD, and Kuma, use a sidecar, a dedicated
                       infrastructure layer built right into an app, to
                       implement service mesh functionalities. So, for
                       example, developers can improve monitoring and
                       tracing of cloud-native microservices on a
                       distributed networking system using Jaeger to build
                       an Istio service mesh.


                # ⚓ 13-_BASH_Scripting_–_Creating_Bash_Functions_for_shell
                  script_–_LinuxTechLab⠀⇛


                       In our last tutorial, we discussed advanced uses of
                       I/O redirection & we will now learn to create
                       functions for our Bash / shell scripts. Learning
                       how to create a function is an important skill
                       required for BASH scripting.


                       When we are writing our scripts, we might see
                       ourselves using a section of the script over and
                       over again like using a loop that is checking a
                       condition many times in a script. So rather than
                       writing a section of the script over & over again,
                       we will create that section of script as a
                       Functions aka Bash Functions also.


          o § Games⠀➾


                # ⚓ Godot_Engine_–_Godot_Web_progress_report_#8:_Progressive
                  Web_Apps⠀⇛


                       Howdy Godotters! Time for another update on the
                       status of Godot on the web.


                       It’s been a while since the last web report as we
                       were busy releasing Godot 3.3 and the following
                       hotfixes, but as we move onto preparing for Godot
                       3.4 and the first alpha of Godot 4.0 (soon™), I’m
                       happy to announce that starting from Godot 3.4 you
                       will finally be able to export your HTML5 game as a
                       Progressive Web App (PWA)!


                # ⚓ Return_a_wasteland_to_green_glory_in_the_upcoming_Terra_Nil
                  |_GamingOnLinux⠀⇛


                       Terra Nil is an absolute gem you can play right now
                       on itch.io free (which is now named as the
                       Prototype) but it’s also getting a total rewrite to
                       be a full commercial game and the new Terra Nil is
                       coming to Linux. Developed by Free Lives, who are
                       at this point a pretty well-known name that created
                       the likes of Broforce and Genital Jousting but this
                       is a very different game. No violence, only the
                       greens.


                       Compared with the prototype it’s going to be a much
                       bigger and more open-ended strategy game where you
                       progress through multiple stages of restoration,
                       including cultivating biodiversity, fixing the
                       climate and even recycling the buildings you use
                       along the way. You will do this across a whole
                       planet as you restore different geographical
                       regions, each with their own unique challenges,
                       flora, and fauna.


                # ⚓ BOY_BEATS_WORLD_is_an_overlooked_fun_and_quirky_rhythm
                  action_adventure_|_GamingOnLinux⠀⇛


                       Underrated and criminally overlooked, the rhythm
                       action adventure BOY BEATS WORLD is officially out
                       now. Note: our key was provided by the developer.


                       At first glance, BOY BEATS WORLD really doesn’t
                       look like much. The graphical style is very
                       simplistic but if you do actually give it a go, you
                       will find a bizarre yet completely charming musical
                       adventure that really is worth playing through.
                       There’s not a whole lot of modern releases like
                       this and the music is pretty good too. It’s got a
                       really great vibe going that will have you happily
                       tapping along to the music to defeat all sorts of
                       weird enemy types.


          o § Desktop Environments/WMs⠀➾


                # ⚓ Windows_11_Look_“Inspired”_by_KDE_Plasma_and_GNOME?_We_try
                  to_find_out.⠀⇛


                       The images of the upcoming Windows 11 Operating
                       system from Microsoft resemble a mixture of our
                       beloved KDE Plasma and GNOME. How much they are
                       similar? We try to find out.


                # ⚓ Dash_to_Panel_GNOME_Shell_Extension_Turns_GNOME_40_Into_KDE
                  Plasma_or_Windows_10⠀⇛


                       If you’ve been waiting for Dash to Dock to support
                       GNOME 40, you’ll have to wait a little longer, but
                       there’s another great extension that now supports
                       the latest version of the popular desktop desktop
                       environment, Dash to Panel, which is an icon
                       taskbar for the GNOME Shell.


                       Once installed, Dash to Panel automatically moves
                       GNOME’s Dash to the GNOME Panel, which is moved to
                       the bottom of the screen to create a look similar
                       to that of the KDE Plasma desktop environment or
                       Windows 7 or later systems.


          o § Distributions⠀➾


                # ⚓ elementary_OS_6_Beta_2_is_the_First_Step_to_Have_Flatpak
                  Apps_Out-of-the-box⠀⇛


                       elementary OS 6 “Odin” beta release gave us a sneak
                       peek on a variety of interesting things that are in
                       motion for the final release.


                       Now, the second beta release, i.e. elementary OS 6
                       Beta 2 is starting to make sense of the ambitious
                       plans that the development team has for the stable
                       release soon.


                       [...]


                       First, the improvements to the installer.


                       There are a few UI tweaks to the installer for a
                       cleaner and consistent look. You will also find a
                       subtle animation with the installation progress
                       instead of a static icon.


                # § Screenshots/Screencasts⠀➾


                      # ⚓ Linux_Mint_20.2_Beta_XFCE⠀⇛


                             Today we are looking at LinuxMint 20.2 Beta,
                             the XFCE edition. It comes with Linux Kernel
                             5.4 (upgradeable to 5.8), XFCE 4.16, and uses
                             about 900MB of ram when idling.


                      # ⚓ Linux_Mint_20.2_Beta_MATE⠀⇛


                             Today we are looking at LinuxMint 20.2 Beta,
                             the MATE edition. It comes with Linux Kernel
                             5.4 (upgradeable to 5.8), MATE 1.24.0, and
                             uses about 900MB of ram when idling.


                      # ⚓ Linux_Mint_20.2_Beta_Cinnamon⠀⇛


                             Today we are looking at LinuxMint 20.2 Beta,
                             the Cinnamon Edtion It comes with Linux
                             Kernel 5.4 (upgradeable to 5.8), Cinnamon
                             5.0, and uses about 900MB of ram when idling.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ SUSE_Linux_Enterprise_/_openSUSE_Leap_Pursuing
                        x86_64-v2_Optimized_Libraries_–_Phoronix⠀⇛


                             In addition to the rolling-release openSUSE
                             Tumbleweed looking at HWCAPS / x86-64 feature
                             levels for being able to provide greater out-
                             of-the-box performance by selectively loading
                             more tuned libraries depending upon the CPU
                             in use, SUSE Linux Enterprise / openSUSE Leap
                             are also looking at offering similar
                             functionality that may turn up in time for
                             the next point release / service pack.


                             On the table for openSUSE Leap 15.4 / SUSE
                             Linux Enterprise 15 SP4 is offering x86_64-v2
                             enabled libraries of important base system
                             packages. The developers admit though that
                             this might not all come to pass until the
                             second update from now, Leap 15.5 / SUSE
                             Linux Enterprise 15 SP5, given the work at
                             hand.


                      # ⚓ Survey_For_openSUSE_Leap_15.3_Release_Closes⠀⇛


                             Our survey about the release of openSUSE Leap
                             15.3 has ended and the results will be
                             discussed in a release retrospective at the
                             openSUSE Conference in the coming days.


                             “I’d like to give big thanks to all of those
                             who participated…,” wrote release manager
                             Lubos Kocman in an email. “We’ve received 605
                             responses, which is almost 200 more than in
                             15.2. I’m grateful for the increased
                             participation as it shows us that it makes
                             sense to have this type of feedback loop.”


                             Kocman will give a talk at the openSUSE
                             Conference on June 19 at 09:00 UTC and
                             discuss the results.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Red_Hat_Shares_―_Kubernetes_in_depth⠀⇛


                             According to the 2021 Kubernetes Adoption
                             Survey by Portworx (PDF), 68% of IT
                             professionals increased their Kubernetes use
                             due to the COVID-19 pandemic. Further, the
                             third-annual Red Hat State of Enterprise Open
                             Source report found that the use of
                             containers and Kubernetes is likely to
                             continue growing throughout this year.


                      # ⚓ Shipwright:_A_framework_for_building_container_images
                        on_Kubernetes_|_Red_Hat_Developer⠀⇛


                             The container ecosystem explosion began with
                             developers running docker build and docker
                             push on their local machines. But
                             increasingly, developers have discovered the
                             benefits of building container images
                             remotely in the cloud, such as better
                             automation, supply chain security, visibility
                             and observability, increased efficiency from
                             caching, and more.


                             With supply chain security becoming a hot
                             topic in 2021, operators don’t want to manage
                             and secure a separate bespoke build
                             infrastructure. In the past, this “build
                             infrastructure” has sometimes been as simple
                             as a shared computer running under a
                             developer’s desk. However, that build
                             environment was difficult to manage, upgrade,
                             and secure. Furthermore, often, it ran with
                             very privileged access to production
                             environments, making it a prime target for
                             attackers.


                             Instead, operators want to lean on the tools
                             and experience they’ve gained to secure and
                             observe their production environments running
                             on Kubernetes. Moving container image builds
                             into the cluster is a natural fit, but
                             running docker build in a cluster can be very
                             hard to secure properly.


                             To meet this need, engineers from the Red Hat
                             OpenShift build and IBM Cloud Code Engine
                             teams developed Shipwright.


                      # ⚓ Stories_from_the_amazing_world_of_release-
                        monitoring.org_#11_–_Fedora_Community_Blog⠀⇛


                             The sun is shining on the land as I walk
                             through the streets of one of the cities on
                             Anitya. My staff is doing clinking sounds on
                             the stone road under my feet. Everything
                             looks peacefully and seems to be in order.
                             This is how I like it.


                             Not many citizens have noticed my humble
                             presence. The life here is too busy and I’m a
                             frequent guest in these parts. My steps are
                             going towards the local tavern. I know who
                             will wait for me there and this makes my
                             heart happy. Traveler is always coming back
                             to visit me and his visits are always good
                             way to spent my time.


                             The tavern is a little dark like most of the
                             taverns in these parts of the land. I looked
                             around searching the faces sitting here,
                             looking for the one that seems familiar to
                             me. I found it! Traveler was sitting in
                             corner sipping his pint of beer and looking
                             at the fire crackling in the heart of the
                             tavern. I came closer to his table: “Hello
                             traveler, it’s nice to meet you again. It was
                             few months till we saw each other last time.
                             The times were busy, but I have plenty of
                             good news for you. I know you want to know
                             what is happening around. So let’s begin.” I
                             sat on the stool beside his table and started
                             talking.


                      # ⚓ Learn_more_about_your_Linux_system_with_inxi_|_Enable
                        Sysadmin⠀⇛


                             Gathering information about Linux systems is
                             an essential sysadmin task. There are many
                             tools that can help in this regard. However,
                             one command that can gather a lot of
                             information with only a few options and
                             parameters is inxi.


                             The inxi tool is a full-featured CLI utility
                             that displays all kinds of system information
                             in your console/terminal/shell or in your IRC
                             client. It gathers this information from a
                             variety of sources about your system, so you
                             can see what you want in an easy-to-use
                             format.


                      # ⚓ Low-code_and_no-code_tools:_4_considerations_for_CIOs
                        |_The_Enterprisers_Project⠀⇛


                             As CIOs look for ways to help their teams
                             maximize software delivery efforts, low-code/
                             no-code tools offer a compelling solution for
                             some organizations. In addition to empowering
                             “citizen developers” with few or even no
                             development skills, low-code/no-code tools
                             can help experienced developers maximize
                             outputs and scale.


                             For the CIO, the decision to adopt low-code/
                             no-code depends on organizational challenges,
                             risk management, and needs among DevOps
                             teams. To get some high-level insights, I
                             asked several DevOps Institute Ambassadors
                             for some factors CIOs should consider when it
                             comes to low-code/no-code adoption.


                      # ⚓ Linux_sysadmins:_6_reasons_you_should_write_technical
                        articles_|_Enable_Sysadmin⠀⇛


                             My goal is to convince you to write
                             articles—specifically, technical articles.
                             The six reasons to write technical articles
                             also apply to other types of written pieces,
                             such as documentation and project proposals.
                             I can’t promise that you’ll become a
                             billionaire or that this will improve your
                             romantic life, but the benefits for you will
                             be higher than for those who choose not to
                             write.


                             Why should you put effort into something that
                             is voluntary work and (apparently) won’t help
                             you pay your bills?


                             Below, I give you six reasons to write, or in
                             some cases, remind you of what you already
                             know.


                      # ⚓ Write_for_Fedora_Magazine,_please!⠀⇛


                             Fedora Magazine is always looking for content
                             to publish from the Fedora Community as well
                             as from Fedora Project. This content comes
                             from the community members like you. I’d like
                             to begin with how I got started writing for
                             Fedora Magazine, highlighting the community
                             interaction that led to it, and finishing
                             with my thoughts on the results. Also, the
                             content itself, what is it Fedora Magazine is
                             looking for specifically? What steps does a
                             community member need to take to contribute?
                             What is the process that an article follows?


                      # ⚓ The_State_of_Kubernetes_Security⠀⇛


                             Twice each year for its State of Kubernetes
                             Security report, StackRox examines how
                             companies are adopting Kubernetes, containers
                             and cloud-native technologies while meeting
                             the challenges of securing these
                             environments.


                             Prior to being acquired by Red Hat, StackRox
                             surveyed more than 500 DevOps, engineering
                             and security professionals for the summer
                             2021 report, uncovering new findings about
                             what keeps IT leaders up at night when it
                             comes to containers and how organizations are
                             embracing DevSecOps initiatives to protect
                             their cloud-native environments. The full
                             report is available here and we’ve
                             highlighted some of the key findings below.


                      # ⚓ Old_school_lessons_for_modern_architectures⠀⇛


                             More than a decade ago, the launch of public
                             cloud services was the beginning of a seismic
                             shift in the foundation of IT architectures.
                             It was a natural evolution – the first SaaS
                             services started in the late 1990s and
                             virtual machines (which had been around since
                             the 1970s) began growing in popularity for
                             optimizing physical server resources. But
                             virtual machines and even SaaS still had the
                             central core of a traditional IT
                             infrastructure, building on physical systems
                             in server rooms and data centers.


                             Public cloud introduced a new, decentralized
                             architecture with built-in services and self-
                             service catalogs. The adoption has changed
                             the nature of IT infrastructure. Red Hat’s
                             2021 Global Tech Outlook report shows that a
                             majority of our customers have a cloud
                             strategy that involves one or more public
                             clouds and 17% that have a private cloud
                             strategy.


                             But cloud services introduce other challenges
                             for system administrators (and for IT leaders
                             planning projects or trying to manage
                             budgets) because the very thing that makes
                             cloud so easy to adopt makes it very
                             difficult to manage.


                      # ⚓ Explore_Red_Hat’s_virtual_training_and_certification
                        options⠀⇛


                             If there’s one thing the past year has taught
                             professionals across the globe, it’s that it
                             is time to rethink how they work. Virtual has
                             become a standard method of working and
                             learning, and its flexibility has made it the
                             new norm. Red Hat Training and Certification
                             has sought to adapt to how global events have
                             changed the requirements of our audience.
                             This post will highlight some enhancements
                             we’ve made to help you and your organization
                             remain competitive in today’s economy.


                             As software becomes more and more complex, IT
                             teams have to keep up with the increasing
                             demands of their organization. Maintaining
                             high technical proficiency can help ensure
                             success, both individually and
                             organizationally. Therefore, high-quality
                             technical training is imperative for
                             developing the skills necessary to keep up
                             with industry trends and practices.


                             Whether teams or individuals are expanding on
                             a current skill set or looking to develop an
                             entirely new one, Red Hat Training and
                             Certification can help you on any technical
                             professional development journey.


                      # ⚓ Week_3_&_4_—_Madeline_Peck⠀⇛


                             Decided to combine two weeks into one blog
                             post because unfortunately my grandmother
                             passed away on the 4th and I took some time
                             off to help and be with my family.


                             Last week I was able to talk to Gabbie about
                             the details for the Research Podcast
                             thumbnails! Super exciting but I’m just
                             awaiting the reference photos of the first
                             few guests and then I can draw up a proper
                             schedule.


                             I’ve been chugging along on the Kubernetes
                             coloring book.


                             [...]


                             I worked on the new pride fedora logo and I
                             came up with these below but honestly, they
                             were relatively simple. Going over the
                             previous ticket there was some debate about
                             how much could be done with the logo, and my
                             skills with Inkscape are still slowwwww and
                             simple since I use it for drawing the
                             majority of the time. Honestly, the worst
                             thing is when you know it’s possible to do
                             something in a program but not sure how, and
                             Google is your best friend. But the ticket is
                             here and Mo has come up with some really
                             great variations!


                      # ⚓ Fedora_Cloud_35_Approved_To_Use_Btrfs_By_Default_–
                        Phoronix⠀⇛


                             Last month plans were published for Fedora
                             Cloud 35 to use the Btrfs file-system by
                             default, similar to Fedora Workstation using
                             Btrfs by default for several releases. That
                             plan has now been signed off on by FESCo
                             allowing for this change to happen.


                      # ⚓ Deploy_self-hosted_GitHub_Actions_runners_for_Red_Hat
                        OpenShift [Ed: Red Hat is not competing with Microsoft
                        and proprietary software; instead it is embracing
                        both]⠀⇛


                             To date, Red Hat has released a series of
                             GitHub Actions and an OpenShift starter
                             workflow to ease integrating Red Hat
                             OpenShift with GitHub’s popular CI/CD
                             platform. Since the initial announcement,
                             we’ve been hard at work responding to
                             community feedback to improve our existing
                             actions as well as adding a few new ones.


                             In addition to our direct work, we’ve
                             implemented a way to self-host GitHub Actions
                             runners on a Red Hat OpenShift cluster so you
                             can run workflows on your own cluster instead
                             of GitHub’s.


                      # ⚓ IT_metrics:_5_measurement_mistakes_to_avoid⠀⇛


                             In a world fueled by data, enterprises that
                             aren’t measuring and analyzing their
                             performance are doomed to fall behind their
                             competitors. Without the consistent
                             refinement enabled by accurate, insightful
                             measurements, companies are likely to
                             stagnate and miss opportunities for growth.


                             However, not all technology metrics are
                             created equal, and a poor measurement
                             strategy can be nearly as problematic as
                             having no strategy at all. Even the best
                             tools are useless in the hands of an inept
                             craftsman, which is why modern enterprises
                             must develop a well-considered measurement
                             approach tied to business outcomes.


                             [...]


                             On the other hand, collecting too few
                             measurements could lead to biased or
                             distorted results. Zeroing in on just a
                             couple of performance metrics leads to a lack
                             of context, meaning the insights provided by
                             these data points could lead your enterprise
                             astray. Finding the right scope of
                             measurements for your team means finding a
                             number that is manageable but that provides a
                             balanced view of your innovation apparatus.


                # § Debian Family⠀➾


                      # ⚓ FrostWire⠀⇛


                             There is a new application available for
                             Sparkers: FrostWire


          o § Devices/Embedded⠀➾


                # ⚓ JingPad_A1_Linux_Tablet_Sets_to_Begin_Crowdfunding
                  Campaign⠀⇛


                       JingPad A1 is an ARM-based tablet powered by JingOS
                       an especially developed open-source Linux
                       distribution.


                       Chinese startup Jingling has been promoting the
                       upcoming tablet for a few months, and now the
                       company has launched a crowdfunding campaign with
                       Indiegogo. At the time of writing this post 171
                       backers have pledged a combined total of almost
                       $102,000. With 59 days left to go this figure is
                       sure to rise.


                       The consumer tablet market is saturated with either
                       Google’s Android and Apple’s iPadOS as the only
                       valiable oprions for OS. However, this changed back
                       in March, when JingLing Tech, the Chinese startup
                       company, unveiled a tabled running JingOS. JingOS
                       is a convergent Linux-based open source OS. It
                       offers a brand new way to merge mobile and desktop
                       experiences. It can run both Linux apps and Android
                       apps. JingOS is adapted to run naturally with touch
                       screen, stylus, keyboard, and trackpad. The Linux
                       distribution will open the door to all types of use
                       but not necessarily to applications designed for
                       touch.


                # ⚓ JingPad_Linux_Tablet_Crowdfunding_Campaign_is_Now_Live⠀⇛


                       After months of teasing one, Chinese company
                       Jingling has launched its crowdfunding campaign for
                       the JingPad A1 Linux tablet on IndieGoGo.


                       And within mere hours of the effort going live the
                       JingPad reached its (peculiarly modest) goal of
                       $20,000.


                # ⚓ JingPad_A1_Linux_tablet_launched_for_consumers_on
                  Indiegogo⠀⇛


                       There have been Linux tablets in the market for
                       years if you consider that Android is Linux-based.
                       There have also been attempts to put “proper” Linux
                       flavors on phones and tablets, but most of those
                       have been aimed at developers and tinkerers. Linux
                       mobile devices that are designed specifically for
                       the consumer market are far and few in between,
                       making the JingPad Linux tablet a rather
                       interesting venture, one that seems to have
                       resounded with quite a few backers on Indiegogo.


                # ⚓ Xilinx_announces_Versal_AI_Edge_Series_with_Cortex-A72_&_R5
                  cores,_FPGA_fabric_–_CNX_Software⠀⇛


                       Edge AI solves the latency and security issues
                       through on-device AI acceleration for optimal
                       computations at a low power supply. Xilinx
                       announces its Versal AI Edge Series which is 4th
                       member of the Adaptive Compute Acceleration
                       Platform (ACAP) family. The versal series consists
                       of seven models ranging from VE2002 to VE2802 with
                       the processor fabrication on 7 nm silicon
                       technology.


                # ⚓ Safety_conscious_TI_AM64x_debuts_on_$99_dev_kit⠀⇛


                       TI’s 16nm Sitara AM64x offers up to 2x -A53, up to
                       4x Cortex-R5F, and a Cortex-M4F core for FuSa and
                       ships with a Linux SDK and choice of $99 and $299
                       eval kits. Phytec, SolidRun, and TQ have also
                       unveiled AM64x based modules.


                       The Texas Instruments Sitara AM64x was announced on
                       Embedded Computing in early May, but we did not
                       hear about it until TQ Embedded sent us an
                       announcement this week for a TQMa64xx module based
                       on the new SoC. Then we saw that TI quietly
                       announced the industrial-focused AM64x in a
                       February blog post and has posted “preview” product
                       pages for the 5x AM64x models. We also see that
                       Phytec has posted a product page for a PhyCore-
                       AM64X module and SolidRun has a page for an AM64x
                       SOM.


                # ⚓ NVIDIA_Jetson_AGX_Xavier_Industrial_module_adds_lockstep
                  Cortex-R5_cluster,_ECC_RAM,_and_more_–_CNX_Software⠀⇛


                       NVIDIA Jetson AGX Xavier is the most powerful
                       module from the Jetson family packing 32 TOPS of AI
                       inference performance. But with some customers
                       wanting to use the embedded AI computer in harsher
                       conditions, the company has now introduced a rugged
                       version of the module with NVIDIA Jetson AGX Xavier
                       Industrial.


                       Some changes included a slightly lower performance
                       (30 TOPS) to cater for an expanded temperature
                       range, a dual-core Cortex-R5 cluster in lockstep,
                       ECC memory, and compliance with shock and vibration
                       standards.


                # ⚓ Build_a_Raspberry_Pi_Pico_piano⠀⇛


                # § Open Hardware/Modding⠀➾


                      # ⚓ Purism_shows_off_new_features_coming_to_PureOS_for
                        the_Librem_5_smartphone_(camera_software,_wireless
                        toggles,_screen_rotation_and_more)⠀⇛


                             The next major release of the PureOS
                             operating system that ships with the Librem 5
                             smartphone will bring a number of new
                             features and improvements.


                             Code-named Byzantium, the new version of
                             PureOS will bring a handful of new
                             applications plus user interface tweaks that
                             let you do things like enable automatic
                             screen rotation, toggle WiFi, Bluetooth, or
                             cellular functionality, or change keyboard
                             styles.


                             And while some of those features are likely
                             tied to the hardware of Purism’s $799
                             smartphone, it’s likely that some may
                             eventually find their way to other Linux
                             distributions for other phones, because
                             Purism is the lead developer of the Phosh
                             user interface that’s also available for
                             other mobile Linux distributions including
                             postmarketOS, Manjaro, Mobian, Arch,
                             openSUSE, and Fedora.


                      # ⚓ The_Other_First_Computer:_Konrad_Zuse_And_The_Z3⠀⇛


                      # ⚓ Daniel_Vrátil:_Building_RC_LEGO_with_Arduino_and_Qt⠀⇛


                             Recently my 4 year-old stepson saw a kid with
                             an RC racing car in a park. He really wanted
                             his own, but with Christmas and his birthday
                             still being a long way away, I decided to
                             solve the “problem” by combining three things
                             I’m really passionate about: LEGO,
                             electronics and programming.


                             In this short series of blogs I’ll describe
                             how to build one such car using LEGO, Arduino
                             and a bit of C++ (and Qt, of course!).


                      # ⚓ RC_skateboard_moves_in_any_direction_|_Arduino_Blog⠀⇛


                             Skateboards are great for going in a straight
                             line, or gently curving one way or the other,
                             but Proto G Engineering’s “omnidirectional
                             board” takes things to a whole new level.
                             Thanks to four 3D-printed Mecanum-style hub
                             wheels, this device can not only move
                             forwards and backwards, but can slide left
                             and right and even spin like a tank!


                             The system is powerful enough for human
                             riders, but currently has some issues
                             carrying such a load at low speeds, making it
                             a mostly unmanned vehicle for the time being.
                             Steering is handled by a remote control unit
                             while a GoPro camera setup provides a first-
                             person view. An Arduino Nano is implemented
                             on each of the hub motors to translate RC PWM
                             signals into the proper driver format. The
                             Nanos also control the forward/reverse/brake
                             pin input on the motor drivers, making this
                             unique board possible.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ ‘Enhanced_notifications’_replace_Adaptive
                        Notifications_in_Android_12,_but_they’re_basically_the
                        same⠀⇛


                      # ⚓ LG_Velvet_LTE_gets_Android_11_stable_update_–
                        GSMArena.com_news⠀⇛


                      # ⚓ Nokia_Mobile_releases_a_new_Android_10_build_for
                        Nokia_5.4._Size,_markets,_changelog_|_Nokiapoweruser⠀⇛


                      # ⚓ Google_Plans_to_Move_All_Android_TV_Devices_Sold_in
                        Retail_to_Google_TV_–_The_Streamable⠀⇛


                      # ⚓ Motorola_may_revive_a_‘classic’_rugged_Android_phone
                        –_Android_Authority⠀⇛


                      # ⚓ Best_Android_app_deals_of_the_day:_SPHAZE,
                        Planescape,_more_–_9to5Toys⠀⇛


                      # ⚓ GTA_San_Andreas_vs_GTA_Liberty_City_on_Android
                        smartphones:_File_size,_gameplay,_system_requirements,
                        and_more_compared⠀⇛


                      # ⚓ How_to_Make_a_Song_Your_Ringtone_on_Android⠀⇛


                      # ⚓ New_Honor_50_phones_will_support_Google’s_Android
                        apps_–_BGR⠀⇛


                      # ⚓ You_can_now_buy_fastest_Android_phone_for_a_price_you
                        won’t_believe_|_Express.co.uk⠀⇛


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


                # ⚓ Everyone_struggles!⠀⇛


                       It’s been 3 weeks since I started the Outreachy
                       internship, I’ve done a lot but at the same time, I
                       don’t think I’ve done anything.


                       In the first week, it was that week of setup
                       machine, fighting with IRC to be able to send
                       messages, sending some information necessary for
                       Outreachy organizers. I also needed to configure my
                       blog’s RSS Feed (yes, at a time when I was in doubt
                       whether I wanted to work with backend or frontend,
                       I decided to learn how to develop a blog) as I use
                       Gatsby as the base of the blog, it was relatively
                       easy to configure the RSS (Hooray!! One thing
                       worked \o/)


                # ⚓ Blender_3.0_Likely_Delayed_2_Months_For_Post-Lockdown
                  Breather,_Cycles_X_Might_Land_–_Phoronix⠀⇛


                       The wildly successful Blender 3D open-source
                       modeling software has been working hard towards its
                       Blender 3.0 release but will likely now be
                       proactively delayed to allow developers more time
                       to relax with COVID-19 lockdowns/restrictions
                       loosening, the possibility of developer meetups
                       pre-3.0, and letting more changes flow into this
                       big feature release.


                # § Web Browsers⠀➾


                      # § Chromium⠀➾


                            # ⚓ Top_5_Chrome-like_Browsers_That_Are_Better_Than
                              Google_Chrome_in_2021⠀⇛


                                   Want to switch away from Google? But,
                                   looking for something potentially
                                   better than Google Chrome (and similar)
                                   for your Linux system?


                                   Fortunately, there are multiple Google
                                   Chrome alternatives that you can try.


                                   Each of them brings something
                                   interesting to the table, while also
                                   keeping the fantastic compatibility
                                   Chrome is known for. Read on to find
                                   out more about these browsers.


                # § SaaS/Back End/Databases⠀➾


                      # ⚓ Metabase:_The_ultimate_Swiss_knife_open-source_for
                        getting_insightful_answers_from_databases⠀⇛


                             Metabase is a no- and low-code open-source
                             (Libre) project that removes all hassle of
                             getting insightful data from databases. It
                             does a lot without having to deal with SQL
                             code or even know any SQL to begin with.


                             It is built for anyone with basic technical
                             skills, as well as data engineers and
                             scientists. That makes it the right tool for
                             marketeers, sales managers, project planners
                             and marketing strategist.


                             Metabase helps user to learn from their data
                             by asking meaningful questions which it
                             translates into a complex SQL queries in the
                             background.


                             Currently, we are using it to work with
                             several databases, and we recommend it to
                             some of our clients.


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ Did_you_know_that_you_can_100%_legally_get_&_run
                        WordPerfect_for_free?⠀⇛


                             In fact, there are two free versions: one for
                             Classic MacOS, made freeware when WordPerfect
                             discontinued Mac support, and a native Linux
                             version, for which Corel offered a free,
                             fully-working, demo version.


                             But there is a catch – of course: they’re
                             both very old and hard to run on a modern
                             computer. I’m here to tell you how to get
                             them and how to install and run them.


                      # ⚓ LibreOffice_7.1.2.2_compiled_in_OE⠀⇛


                             The last time that I compiled LibreOffice
                             (LO) in OpenEmbedded (OE) was in the Pyro-
                             series. My port of OE back then is still on
                             github, search for “oe-qky-src’.


                      # ⚓ Hossein_Nourikhah_joins_the_TDF_team_as_Developer
                        Community_Architect⠀⇛


                             Next week, Hossein Nourikhah will join the
                             team at The Document Foundation, the non-
                             profit behind LibreOffice, as Developer
                             Community Architect. Hossein is a developer,
                             university lecturer and FOSS advocate. He
                             writes programs, teaches programming to
                             students, and is an advocate for the use of
                             free software applications, because they have
                             a huge positive impact on the quality of our
                             life by providing the essential freedoms that
                             we all deserve.


                             Hossein has a B.Sc. in Computer Engineering
                             (Software) from Isfahan University of
                             Technology, and a M.Sc. and a Ph.D. in
                             Information Technology from Amirkabir
                             University of Technology, also called the
                             Tehran Polytechnic. Since 2016 he has been an
                             instructor at the Amirkabir University of
                             Technology, teaching various courses
                             including C/C++ programming, operating
                             systems, software design, and many others.


                             Hossein started programming in BASIC and
                             Pascal when he was 12, and after two and a
                             half decades he is still involved in
                             programming for fun and profit. He has worked
                             with several programming languages, including
                             C/C++, Java, Pascal, PHP and many more.


                # § FSF⠀➾


                      # ⚓ Open-source_projects_glibc_and_gnulib_look_to_sever
                        copyright_ties_with_Free_Software_Foundation⠀⇛


                             The GNU C Library (glibc) and GNU Portability
                             Library (gnulib) are laying the groundwork to
                             divorce themselves from the troubled Free
                             Software Foundation by removing the
                             requirement for copyright assignment.


                             This move follows in the footsteps of the
                             same shift by the GNU Compiler Collection
                             (GCC) on 2 June.


                             Like many projects under the GNU umbrella,
                             glibc and gnulib – the GNU Project’s C
                             standard library and a collection of
                             subroutines designed to ease cross-platform
                             porting respectively – allow anyone to
                             contribute code. Those doing so are asked to
                             assign copyright to the Free Software
                             Foundation – for now, at least.


                      # ⚓ My_internship_at_the_FSF,_and_the_domino_effect_of
                        thoughts_—_Free_Software_Foundation_—_Working_together
                        for_free_software⠀⇛


                             Hello! My name is Panos Alevropoulos. I was
                             born in and live in Thessaloniki, Greece, and
                             I am a law student at Aristotle University of
                             Thessaloniki. This is my introductory post in
                             the course of my internship at the Free
                             Software Foundation. Specifically, I will
                             work remotely with the campaigns and
                             licensing teams, contributing to areas that
                             could benefit from someone with legal
                             experience. The campaign I will focus on most
                             is End Software Patents, a legal topic that I
                             find particularly fascinating, and which I
                             hope to delve into. In this short article, I
                             would like to briefly recount how I came to
                             know about free software.


                             In general, I have had a great interest in
                             technology since I was a young child. I
                             started using a computer at the age of about
                             four (an old Mac), and then my father bought
                             me my first personal computer when I was
                             seven (a Windows XP system). From a very
                             early age, I became familiar with the logic
                             of computers, and felt the need to adapt my
                             system to my liking (for example, I wanted
                             the word “start” in Windows XP to be changed
                             to spell my name — I managed to do it by
                             tweaking the Windows Registry). For many
                             years, I used Windows, but slowly I realized
                             that I was using a very closed system. The
                             ability to configure Windows seemed to be
                             minimal to none; when I encountered a
                             technical problem, the information available
                             to solve it was laconic and inadequate. Then,
                             if I wanted to research a particular
                             technical aspect on the Internet, I only came
                             across Windows support sites, with bland and
                             vague answers that not even the most familiar
                             Windows user would understand. I could not
                             provide any answer as to why the world’s most
                             widespread operating system felt like a black
                             box. However, for many years, I truly
                             believed that there was no alternative.


                # § Programming/Development⠀➾


                      # ⚓ Cutelyst_3_is_out!_–_Dantti’s_Blog⠀⇛


                             Cutelyst, the C++/Qt web framework just got a
                             new major release.


                             Under the hood it now has both Qt5 and Qt6
                             support, but because of this a few things had
                             to be changed, the most important one was
                             QMap usage as a multi-key container had to be
                             changed to QMultiMap, if you used
                             ParamsMultiMap types or auto when assigning
                             there’s probably little to do, one major
                             exception is that if you still use Grantlee
                             it might not work well, but Cutelee is there
                             with fixes and is almost ported to Qt6.


                      # ⚓ U.S._Supreme_Court_sends_LinkedIn_data-scraping_suit
                        back_to_lower_court⠀⇛


                             The justices threw out a lower court ruling
                             that had barred LinkedIn from denying hiQ
                             access to the information that LinkedIn
                             members had made publicly available.


                             At issue is whether companies can use a
                             federal anti-hacking law called the Computer
                             Fraud and Abuse Act, which prohibits
                             accessing a computer without authorization,
                             to block competitors from harvesting or
                             “scraping” vast amounts of customer data from
                             public-facing parts of a website.


                             The justices sent the dispute back to the San
                             Francisco-based 9th U.S. Circuit Court of
                             Appeals to reconsider in light of their June
                             4 ruling that limited the type of conduct
                             that can be criminally prosecuted under the
                             same law. In that case, the justices found
                             that a person cannot be guilty of violating
                             that law if they misuse information on a
                             computer that they have permission to access.


                      # ⚓ ProgressUI_|_nintyfan⠀⇛


                             Recently, I nearly create ProgressUI – tool
                             to setup triggers (condition/action pair)
                             related to task of programs. Currently It’s
                             very simple, because it supports only one
                             kind of action – running external program.
                             User must also type program name and
                             parameters. In future, we would read .desktop
                             files and allow to select from dropdown list
                             (for example). Also, I will add possibility
                             to invoke DBus method and allow to define
                             method name/path/etc. in special files, so
                             user could also select method. Also, I must
                             enhance my set of tools in other ways – for
                             example allowing to send watch fd to daemon,
                             so It could report exit code of application.


                      # ⚓ Learning_Awk_Is_Essential_For_Linux_Users⠀⇛


                             One of my favorite command line utilities is
                             “awk” which is a text-processing program. It
                             is mostly used for pattern scanning and
                             processing. In this video, I will give
                             examples of some of the basic awk commands,
                             and show you some of the ways that I often
                             use awk.


                      # ⚓ GNU_C_Library_Lands_Year_2038_Handling_For_Legacy
                        ABIs_–_Phoronix⠀⇛


                             The GNU C Library (Glibc) saw another batch
                             of Year 2038 “Y2038″ preparations on Tuesday
                             for the Unix timestamp for when the time
                             since 1 January 1970 can no longer be stored
                             in a signed 32-bit integer.


                             There were several Y2038 patches to be merged
                             to Glibc in the past day but ultimately the
                             main highlight is support for 64-bit time
                             with the legacy ABIs.


                      # ⚓ Wasmer_2.0_Released_With_Significantly_Faster_Runtime
                        Performance,_Quicker_Deserialization_–_Phoronix⠀⇛


                             Going along with a number of other recent
                             WebAssembly interpreter/run-time releases,
                             Wasmer 2.0 has been released as this popular
                             WebAssembly WASI and EmScripten run-time.


                             Following the recent RC, Wasmer 2.0 is now
                             officially available. Wasmer 2.0 is quite
                             exciting on the performance front with more
                             optimal float handling with LLVM leading “up
                             to +50% faster runtime speeds!” and usage of
                             their Cranelift back-end providing another
                             “+40% faster runtime speed.” These big items
                             plus other smaller enhancements make the
                             Wasmer 2.0 run-time all the more exciting and
                             performant.


                      # ⚓ Integrating_sandboxed_Vala_apps_with_the_host_system
                        through_xdg-desktop-portals_–_Felipe_Borges⠀⇛


                             Portals are a mechanism through which
                             applications can interact with the host
                             environment from within a sandbox. They give
                             the ability to interact with data, files, and
                             services without the need to add sandbox
                             permissions.


                             Examples of capabilities that can be accessed
                             through portals include opening files through
                             a file chooser dialog, or printing. More
                             information about portals can be found in
                             Sandbox Permissions.


                             Some portals, such as the FileChooser one,
                             provide an almost seamless experience without
                             much extra code on the app side. For other
                             portals, you usually need some code to talk
                             to the portal’s DBus interface or use
                             libportal.


                             Vala was designed specifically for the
                             development of GNOME apps, and it has some
                             nice syntax-sugar that makes the
                             communication with DBus pretty simple to
                             implement.


                      # § Python⠀➾


                            # ⚓ How_to_use_the_logging_module_in_Python⠀⇛


                                   The logging module in Python has five
                                   different log levels as standard, which
                                   can be used depending on the type and
                                   severity of the program error.


                            # ⚓ Python_For_Loop_(with_Examples)_–_TecAdmin⠀⇛


                                   Python is a general-purpose programming
                                   language, which emphasizes making
                                   programming easy, efficient coding, and
                                   unleashes the user’s potential. Loops
                                   are the vital part of programming as it
                                   allows the user to repetitive use a set
                                   of codes using loops. So in the
                                   following article, we will see how to
                                   use for loops in python.


                      # § Rust⠀➾


                            # ⚓ This_Week_in_Rust_395⠀⇛


    * § Leftovers⠀➾


          o ⚓ The_World_According_to_Satyajit_Ray⠀⇛


                 Yes, it’s the one-hundrerth anniversary of Ray’s birth,
                 but the Indians are not celebrating the occasion very
                 enthusiastically. The director, who was born in 1921 and
                 who died in 1992 at the age of 70, belongs in large part
                 to an India that Indians want to believe no longer
                 exists. Call it a world of poverty where men, women and
                 children go barefoot, live in what might be described as
                 “hovels,” and subsist on a meager diet of rice. They eat
                 with their hands, not knives, forks and spoons.


                 I spent two weeks in and around New Delhi a couple of
                 years ago, breathed the terribly polluted air, spent
                 hours stuck in traffic and saw mile after mile of Indians
                 living in cardboard shacks along the sides of roads. I
                 also visited modern Hindu and Moslem universities, met
                 students who spoke English with a British accent and
                 called me “sir” at every possible opportunity, a legacy I
                 assumed of the British Empire and its insistence on
                 hierarchy.


          o ⚓ The_IOC_Says_the_2032_Olympics_Are_Coming_to_Brisbane⠀⇛


                 The Olympic Games are in the midst of their biggest
                 crisis in decades. With more than 80 percent of the
                 population in Japan in staunch opposition to this
                 summer’s Tokyo Olympics and the winter Games arriving in
                 less than eight months in China, an indisputable human
                 rights violator in plain sight, you’d think the
                 International Olympic C0mmittee might slow down and
                 engage in a little introspection


          o ⚓ Loss_Runs_Like_a_River_Through_My_Life⠀⇛


                 Dedicated to my mother, Janet Cyril; my wife, Alana
                 Devich-Cyril, my aunts Sandy and Marion, my godsister
                 Kafi, my Uncle Tony, my cousins Javana, Njuzi, and BJ; my
                 friends Margo, Sia, Art, Yulanda, Elandria, Lana, Rahwa;
                 and all those lost but here, unnamed.


          o ⚓ The_Streets_Are_Empty⠀⇛


                 Just as globalization moved jobs first to the US South
                 and then to Southeast Asia, the Far East, and Mexico,
                 never to return, I fear that any hope for peace or
                 movement toward peace and funding domestic needs are
                 relics of the past also never destined to return.


                 Nuclear weapons are refurbished and modernized and US
                 weapons pour into the tinder box of the Middle East.
                 Biden is the consummate cold warrior and is no better
                 than Trump when the light of day shines on the US
                 military budget, up $10 billion from FY2021 at $705
                 billion to FY2022 at $715 billion. And it’s anybody’s
                 guess how much money goes to secret operations around the
                 world carried out by the CIA and other agencies? It’s
                 mind- boggling!


          o ⚓ What’s_the_Difference_Between_a_Waitress_and_a_Private_Equity
            Partner?_(Their_Tax_Rate)⠀⇛


                 The ostensible rationale for allowing PE partners to pay
                 a lower tax rate on their carried interest is that these
                 payments involve risk. If the funds don’t meet some
                 threshold rate of return, then they don’t earn any money.


                 The New York Times had a major piece on tax avoidance and
                 evasion by private equity partners, which gave this
                 rationale. However, the piece neglected to point out that
                 millions of workers take this sort of risk, since they
                 get paid, in large part, on commission. This list would
                 include realtors, car salespeople, and waiters and
                 waitresses. In all of these cases, the money earned as a
                 commission is taxed as normal income. It is only PE
                 partners, or hedge fund and venture capital partners,
                 that get to pay a lower tax rate.


          o § Science⠀➾


                # ⚓ Git_for_Computer_Scientists⠀⇛


                       Quick introduction to git internals for people who
                       are not scared by words like Directed Acyclic
                       Graph.


                # ⚓ The_Sperm_Count_Culture_War⠀⇛


                       Before deconstructing their argument, it’s helpful
                       to understand the political and ideological prism
                       through which the Harvard-MIT team views this issue
                       in particular, and science in general. Neither
                       Boulicault nor Richardson is a scientist. Both are
                       philosophers, who openly proclaim their fealty to
                       feminist scholarship—the focus of the GenderSci
                       Lab, a cooperative started by Richardson in 2018.


                # ⚓ What_is_“old”_water?_And_what_do_researchers_learn_from_the
                  age_of_water?⠀⇛


                       “If, for example, pesticides seep into the ground
                       and then penetrate further into the groundwater,
                       one would like to know how long they remain there
                       and when the groundwater reservoir was replaced
                       with new water”, says Pfister.


          o § Hardware⠀➾


                # ⚓ Abhijith_PA:_Changing_LCD_screen_of_car_infotainment
                  system⠀⇛


                       I have a 2013 model used car that I bought two
                       years ago. It came with a 7 inch touch screen
                       infotainment system on its dash board with features
                       like navigation, Bluetooth phone connectivity and a
                       good FM AM radio. Except the radio I rarely use
                       navigation or Bluetooth phone sync. After couple of
                       months the touch started to become non-responsive.
                       Since all important things such as call
                       termination, mute and volume control have physical
                       switches, I was happy with it.


                       During a periodic car check up on a local workshop,
                       mechanic pulled battery terminals making the
                       infotainment system locked. Now it ask for 4 digit
                       pass code. Its one of their ant-theft mechanism and
                       in order to enter those digits you need a touch
                       responsive screen. So now I am completed locked
                       out.


                       I visited service center of this car to get it
                       changed, turns out they don’t repair it and only
                       change by the unit. And will cost me Rs 50,000.
                       Considering my usage is restricted to radio. That
                       price is way too much.


          o § Health/Nutrition⠀➾


                # ⚓ Pandemic_Recovery_Must_Include_Care_Worker_Protections⠀⇛


                # ⚓ Watchdog_Demands_FDA_Chief_Resign_Over_‘Reckless’_Approval
                  of_Biogen_Alzheimer’s_Drug⠀⇛


                       A leading consumer advocacy group on Wednesday
                       demanded the immediate resignation or removal of
                       the acting head of the Food and Drug Administration
                       as well as other U.S. government officials involved
                       in the recent approval of Biogen’s aducanumab, a
                       purported Alzheimer’s treatment whose effectiveness
                       has been widely questioned by independent experts.


                       “This decision is a disastrous blow to the agency’s
                       credibility, public health, and the financial
                       sustainability of the Medicare program.”—Dr.
                       Michael Carome, Public Citizen


                # ⚓ It’s_Time_to_End_the_War_on_Drugs_Once_and_For_All⠀⇛


                       Fifty years ago this month, on June 17, 1971,
                       President Richard Nixon declared a “full scale
                       attack” on drug use. It was the beginning of the
                       War on Drugs.


                # ⚓ Unions_Demand_Pelosi_and_Schumer_Include_Lower_Medicare
                  Age,_Drug_Pricing_Reform_in_Infrastructure_Plan⠀⇛


                       Echoing earlier demands from progressive groups and
                       lawmakers, over 100 labor unions and their allies
                       on Wednesday called on the Biden administration and
                       Democratic congressional leaders to include
                       expanded Medicare eligibility and prescription drug
                       pricing reform in the $1.8 trillion American
                       Families Plan, part of President Joe Biden’s three-
                       part Build Back Better economic and infrastructure
                       proposal.


                       “The Biden administration and Congress have a
                       chance to deliver important progress at a crucial
                       time.”—Dan Bauer, CWA


                # ⚓ Delta_variant_spreads_to_74_countries_as_data_suggests_it
                  will_become_dominant_coronavirus_mutation_worldwide⠀⇛


                       The Delta variant of the coronavirus, first
                       detected in India, has now spread to at least 74
                       countries, according to reports aggregated by the
                       World Health Organization, threatening a massive
                       resurgence of the pandemic as reopenings worldwide
                       continue apace.


                       The variant was first sampled last October, and is
                       most likely responsible for the 35-fold increase in
                       cases reported in India from February to May,
                       reaching a peak of more than 390,000 cases each
                       day, with a corresponding 45-fold increase in daily
                       deaths, topping out at 4,500 reported fatalities.
                       To date, India has suffered 29.6 million known
                       coronavirus cases and at least 377,000 officially
                       counted deaths, a number widely understood to be
                       far lower than the actual death toll.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ FBI’s_Recovery_Of_Colonial_Pipeline_Bitcoin_Ransom
                        Highlights_How_The_‘Ban_Crypto_To_Stop_Ransomware’
                        Cries_Were_Wrong_Again⠀⇛


                             Last month we highlighted what seemed like a
                             fairly silly Wall Street Journal op-ed
                             arguing that banning cryptocurrency was the
                             best way to stop ransomware, in response
                             (mainly) to the well publicized ransomware
                             attack on Colonial Pipeline, which resulted
                             in the company shutting down the flow of oil
                             while it sorted things out. As we pointed
                             out, not only was the idea of banning
                             cryptocurrency unworkable, it was unlikely to
                             do much to stop ransomware. Unfortunately, it
                             appears that a number of other cryptocurrency
                             haters jumped on this moment to push the idea
                             even further, claiming that “society has a
                             Bitcoin problem.”


                      # ⚓ Ryuk_ransomware_recovery_cost_us_$8.1m_and_counting,
                        says_Baltimore_school_authority [iophk: Windows TCO]⠀⇛


                             An organisation whose network was infected by
                             Ryuk ransomware has spent $8.1m over seven
                             months recovering from it – and that’s still
                             not the end of it, according to US news
                             reports.


                             The sum, spent by Baltimore County Public
                             Schools, will doubtless raise some eyebrows
                             and the public breakdown of the costs will be
                             eye-opening for the infosec industry and
                             potential corporate ransomware victims alike.


                             A spreadsheet obtained by Fox 45 News
                             Baltimore, a TV station, revealed the $8.1m
                             spending and also broke it down into
                             individual line items.


                      # ⚓ AWS_S3_Glacier_Deep_Archive_–_Difficulty_deleting
                        files_with_accents⠀⇛


                             And to the second point, it gets more
                             complicated with S3 Glacier Deep Archive,
                             because I’m used to some operations taking 12
                             hours or longer, so I got lazy and didn’t
                             double-check on the delete operations.


                      # ⚓ The_methods_and_menace_of_the_new_bank_robbers
                        [iophk: Windows TCO]⠀⇛


                             Such activity represents the handiwork of a
                             new breed of bank robber. Forget the hold-ups
                             of yore. Today’s smartest [crackers] are
                             likely to be backed by rogue states, such as
                             North Korea and, to a lesser extent, Iran, or
                             tolerated by countries such as Russia and
                             China. They benefit from unprecedented
                             resources and protection from law-enforcement
                             agencies. As well as attempting to empty
                             accounts, they also target data for insider
                             trading.


                             As one of the first industries to offer
                             online transactions, banks have been fending
                             off [crackers] since the dawn of the
                             [Internet]. They spend more on cyber-security
                             than any other sort of firm—$2,691 per
                             employee—and manage to foil a lot of the
                             attempted thefts. Nonetheless, since 2016, no
                             industry has suffered more from attacks than
                             banks (see chart).


                      # § Security⠀➾


                            # ⚓ Ukrainian_Police_Nab_Six_Tied_to_CLOP
                              Ransomware⠀⇛


                                   Authorities in Ukraine this week
                                   charged six people alleged to be part
                                   of the CLOP ransomware group, a
                                   cybercriminal gang said to have
                                   extorted more than half a billion
                                   dollars from victims. Some of CLOP’s
                                   victims this year alone include
                                   Stanford University Medical School,
                                   the University of California, and
                                   University of Maryland.


                            # ⚓ Security_updates_for_Wednesday⠀⇛


                                   Security updates have been issued by
                                   Debian (prosody, python-urllib3, and
                                   xen), Fedora (dino, dotnet3.1,
                                   dotnet5.0, and vmaf), Oracle (gupnp,
                                   kernel, and kernel-container), Red Hat
                                   (gupnp), Scientific Linux (kernel),
                                   SUSE (java-1_8_0-openjdk, kernel,
                                   snakeyaml, and xorg-x11-libX11), and
                                   Ubuntu (bluez).


                            # ⚓ Microsoft_Teams_security_flaw_left_users
                              defenseless_against_serious_cyberattacks⠀⇛


                                   Microsoft Teams exploit exposed
                                   sensitive files, emails and chat logs


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ FBI_Director_Ignores_More_Than_500
                                    Ongoing_Capitol_Raid_Prosecutions_To
                                    Complain_That_Encryption_Is_Keeping
                                    Criminals_From_Being_Caught⠀⇛


                                         FBI Director Chris Wray needs to
                                         shut the fuck up about
                                         encryption.


                                  # § Confidentiality⠀➾


                                        # ⚓ Security_flaw_found_in_2G_mobile
                                          data_encryption_standard⠀⇛


                                               Cybersecurity researchers
                                               in Europe say they have
                                               discovered a flaw in an
                                               encryption algorithm used
                                               by cellphones that may have
                                               allowed attackers to
                                               eavesdrop on some data
                                               traffic for more than two
                                               decades.


                                               In a paper published
                                               Wednesday, researchers from
                                               Germany, France and Norway
                                               said the flaw affects the
                                               GPRS – or 2G – mobile data
                                               standard.


                                        # ⚓ Researchers_discover_flaw_in_2G
                                          mobile_encryption_algorithm⠀⇛


                                               Researchers discovered a
                                               flaw in a 2G mobile
                                               encryption algorithm that
                                               leaves cellphones
                                               vulnerable to attackers.


                                        # ⚓ Security_flaw_found_in_2G_mobile
                                          data_encryption_standard⠀⇛


                                               The vulnerability in the
                                               GEA-1 algorithm is unlikely
                                               to have been an accident,
                                               the researchers said.
                                               Instead, it was probably
                                               created intentionally to
                                               provide law enforcement
                                               agencies with a “backdoor”
                                               and comply with laws
                                               restricting the export of
                                               strong encryption tools.


          o § Defence/Aggression⠀➾


                # ⚓ After_Far-Right_Marchers_Chant_‘Death_to_Arabs,’_New
                  Israeli_Government_Bombs_Gaza⠀⇛


                       Just hours after far-right marchers chanted “Death
                       to Arabs!” during a demonstration in the streets of
                       Jerusalem, Israeli war planes bombarded the
                       occupied Gaza Strip early Wednesday morning in the
                       first series of airstrikes launched by the new
                       government of Prime Minister Naftali Bennett, a
                       former IDF officer who once boasted that he has
                       “killed a lot of Arabs.”


                       “This is a genocidal chant. Let’s call it what it
                       is.”—U.S. Rep. Jamaal Bowman


                # ⚓ Opinion_|_By_Your_Actions_Ye_Shall_Be_Known:_Implacable
                  Israel_Again_Bombs_Gaza,_Still_Shattered_By_Its_Last
                  Atrocities⠀⇛


                # ⚓ Biden_Urged_to_Embrace_Top_Democrat’s_Call_to_End_Deadly_US
                  Sanctions_Against_Venezuela⠀⇛


                       Advocates for more a more humane U.S. foreign
                       policy are urging President Joe Biden to embrace
                       Rep. Jim McGovern’s call for an end to “all
                       secondary and sectoral sanctions imposed on
                       Venezuela by the Trump administration.”


                       “If something is a war crime when people are
                       shooting and dropping bombs, it is an equally
                       serious crime when there is technically no war
                       taking place.”—Mark Weisbrot, CEPR


                # ⚓ ‘Great_News’:_Biden_Backs_2002_AUMF_Repeal_as_Schumer
                  Announces_Senate_Vote⠀⇛


                       Just ahead of Senate Majority Leader Chuck Schumer
                       announcing a vote on repealing the Iraq war
                       authorization later this year, the White House this
                       week declared its support for legislation to end
                       the 2002 measure—a development welcomed by
                       Democratic lawmakers and progressive groups that
                       have demanded an end to “endless wars.”


                       At issue is Rep. Barbara Lee’s (D-Calif.) H.R. 256,
                       which would repeal the Authorization for Use of
                       Military Force (AUMF) Against Iraq Resolution of
                       2002 that passed in the wake of the September 11
                       attacks. The repeal measure—whose supporters now
                       include even right-wing groups like Americans for
                       Prosperity—has 134 bipartisan co-sponsors. The
                       House is set to vote on the bill Thursday.


                # ⚓ The_US_Government’s_Jailing_Of_A_Drone_Whistleblower⠀⇛


                       The following was published as part of The
                       Dissenter Newsletter, a project of Shadowproof.
                       Become a subscriber here.


                       When the United States government had drone
                       whistleblower Daniel Hale arrested and the judge
                       revoked his bail, they deprived him of the ability
                       to tie up loose ends and prepare for incarceration
                       before his sentencing in July.


                # ⚓ The_Biden-Putin_Summit_Is_an_Opportunity_to_Ban_Nuclear
                  Weapons⠀⇛


                       Presidents Joe Biden and Vladimir Putin meet
                       Wednesday for a summit that will discuss strategic
                       stability, which includes nuclear weapons. The
                       summit takes place in Geneva, the international
                       city renowned for advancing peace and disarmament,
                       and will be held between two individuals who
                       control 90% of the world’s nuclear arsenals.


                # ⚓ Biden_and_Putin_Meet_in_Geneva_for_Summit_on_“Mutual
                  Interests”⠀⇛


                # ⚓ Activists_Frustrated_That_Biden,_Putin_Won’t_Reduce_Nuclear
                  Arsenals⠀⇛


                       Anti-nuke campaigners around the world expressed
                       frustration on Wednesday after U.S. President Joe
                       Biden and Russian President Vladimir Putin met in
                       Geneva and released a joint statement but did not
                       commit to cut down their nations’ nuclear
                       arsenals—let alone full disarmament.


                       “Following the Geneva summit, Presidents Putin and
                       Biden have made no further commitments to reduce
                       their nuclear arsenals in line with the Treaty on
                       the Prohibition of Nuclear Weapons and global
                       opinion,” said Beatrice Fihn, executive director of
                       International Campaign to Abolish Nuclear Weapons
                       (ICAN).


                # ⚓ Masha_Gessen_on_the_Biden-Putin_Summit,_Alexei_Navalny_&
                  the_Future_of_U.S.-Russia_Relations⠀⇛


                       President Joe Biden and Russian President Vladimir
                       Putin are meeting in Geneva for a closely watched
                       summit between the world’s two largest nuclear
                       powers. Topics expected to be discussed include
                       nuclear arms, cybersecurity, Syria, the Iranian
                       nuclear deal, Afghanistan, Ukraine, the Korean
                       Peninsula, Putin’s crackdown on dissent inside
                       Russia and the U.S. military presence near the
                       Russian border. The two world leaders are coming to
                       the summit with fundamentally different goals, says
                       Russian American journalist and writer Masha
                       Gessen. Putin “accomplishes what he has come to
                       Geneva for by simply having the summit,” Gessen
                       says. “Biden is concerned … with finding areas of
                       common interest, and he is alone in that. He is
                       alone in actually trying to negotiate in good
                       faith.” Gessen also discusses the ongoing
                       imprisonment of Russian opposition figure Alexei
                       Navalny, Russia’s low vaccination rate and their
                       own experience with COVID-19.


                # ⚓ House_hearing_exposes_complicity_of_FBI_and_Pentagon
                  officials_in_January_6_coup_attempt⠀⇛


                       On Tuesday, the House Committee on Oversight and
                       Reform held its second hearing on “Unexplained
                       Delays and Unanswered Questions” regarding former
                       President Donald Trump’s attempted coup on January
                       6. The hearing featured stunning revelations
                       related to the refusal of the Federal Bureau of
                       Investigation to issue an intelligence bulletin or
                       threat assessment prior to January 6, despite
                       having received detailed reports on plans for
                       violence at the Capitol from the social media
                       company Parler.


                       In addition to taking testimony from FBI Director
                       Christopher Wray, the committee questioned two top
                       generals who, in the midst of the violent attack on
                       Congress, ignored multiple appeals from besieged
                       lawmakers, as well as then-D.C. National Guard
                       Commander William Walker and then-Capitol Police
                       Chief Steven Sund, for authorization to deploy
                       National Guard forces to clear the mob from the
                       Capitol.


                # ⚓ The_Real_Welfare_Cheats_Are_War_Profiteers⠀⇛


                       As my friends and I have noticed, President Joe
                       Biden remains super-glued to the same old
                       post–World War II agreement between the two major
                       parties: They can differ vastly on domestic
                       policies, but they remain united when it comes to
                       projecting US military power around the world and
                       to the government spending that sustains it. In
                       other words, the US “national security” budget is
                       still the third rail of politics in this country.


                # ⚓ France_Arrests_‘High-Ranking’_Islamic_State_Fighter_in
                  Mali⠀⇛


                       According to the United Nations’ Mali mission,
                       MINUSMA, the armed men were suspected of belonging
                       to EIGS.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ In_Alaska,_Commercial_Aviation_Is_a_Lifeline._The_State_Is
                  Also_Home_to_a_Growing_Share_of_the_Country’s_Deadly
                  Crashes.⠀⇛


                       On a clear day in May 2019, the tourist season was
                       just starting up in Ketchikan, Alaska, a
                       southeastern city of 8,000 that had become a cruise
                       ship hot spot. For Randy Sullivan, that meant
                       another day — his fifth in a row — of flying
                       sightseeing tours and charters.


                       Sullivan and his wife, Julie, owned Mountain Air
                       Service, a single-plane family business that had
                       allowed Randy to realize his dream of becoming his
                       own boss. Randy was born and raised in Alaska. He
                       grew up in Ketchikan and had been flying in the
                       area for more than 17 years. He, more than most,
                       knew the dangers of commercial aviation in the
                       state.


                # ⚓ What_We_Know_About_Alaska’s_Recent_Series_of_Fatal_Flight
                  Collisions⠀⇛


                       Even though much of Alaska has uncongested
                       airspace, in recent years it has seen a series of
                       midair collisions involving commercial operators.


                       In the past five years alone, there have been five
                       such fatal collisions. There haven’t been any in
                       the rest of the U.S. since 2009. (There was one
                       fatal midair collision involving a for-hire
                       sightseeing plane in Idaho last year, but it flew
                       under the Federal Aviation Administration’s
                       regulations typically meant for private aircraft.)


                # ⚓ How_We_Tallied_Alaska_Aviation_Deaths⠀⇛


                       A KUCB and ProPublica analysis has found that in
                       recent years, Alaska has accounted for a growing
                       share of the country’s fatalities from crashes
                       involving small commercial aircraft.


                       Since 2016, 42% of the country’s deaths in these
                       crashes occurred in Alaska, up from 26% in the
                       early 2000s. And in recent years, the state has
                       seen a series of midair collisions involving
                       commercial flights, a type of crash that has
                       largely been eliminated in the rest of the country
                       thanks to greater oversight by the federal
                       government and advances in technology.


                # ⚓ New_York_Times_marks_50_years_since_Pentagon_Papers,
                  ignoring_persecution_of_Julian_Assange⠀⇛


                       This week marks 50 years since the publication in
                       the New York Times of the Pentagon Papers, which
                       played a significant role in galvanizing popular
                       opposition to the Vietnam War. The manner in which
                       the Times itself chose to commemorate the
                       anniversary provides a case study in the profound
                       shift to the right by the media and the entire
                       political establishment in the intervening five
                       decades.


                       Nowhere is this shift expressed more nakedly than
                       in the newspaper’s stony silence on the case of the
                       imprisoned WikiLeaks editor Julian Assange, whose
                       persecution by the US and British governments pose
                       the issue of basic democratic rights to free speech
                       and a free press even more sharply than the events
                       of 50 years ago.


          o § Environment⠀➾


                # ⚓ Mr._Trash_Wheel_is_gobbling_up_millions_of_pounds_of
                  trash⠀⇛


                       Trash interceptors are becoming more common in
                       large cities, helping to stop garbage as it floats
                       down waterways. Mr. Trash Wheel is the pride of
                       Baltimore, helping to make a cleaner, more
                       beautiful city waterfront.


                # ⚓ Record_Heat_and_Flimsy_Power_Grid_Across_US_Illustrates
                  Urgent_Need_for_Green_Infrastructure⠀⇛


                       With states across the southern and western United
                       States facing record high temperatures weeks before
                       the hottest months of the year, scientists and
                       progressive lawmakers on Wednesday doubled down on
                       calls for green infrastructure to ensure
                       the nation is prepared for increasing levels
                       of extreme weather on a rapidly warming planet. 


                       For the second time in four months, state
                       regulators in Texas on Monday warned residents that
                       the demand for energy was straining the state’s
                       power grid, asking millions to set their
                       thermostats to 78 degrees or higher, turn off
                       lights, and avoid washing clothes and cooking. 


                # ⚓ Building_a_Global_Green_New_Deal⠀⇛


                       The Senate recently demonstrated that the only
                       adhesive capable of uniting the two parties is a
                       good, old-fashioned enemy. Although the Democrats
                       and Republicans continue to bicker over the Biden
                       administration’s infrastructure legislation, they
                       achieved rare accord in passing a major technology
                       bill that directs investment into key sectors of
                       the economy.


                # ⚓ Scientist_Who_Spent_Year_at_‘Epicenter’_of_Climate_Crisis
                  Warns_World_May_Already_Have_Hit_Arctic_‘Tipping_Point’⠀⇛


                       The atmospheric scientist that led a major year-
                       long Arctic research expedition said Tuesday that
                       the world may have already hit one of the so-called
                       climate “tipping points.”


                       “The disappearance of summer sea ice in the Arctic
                       is one of the first landmines in this minefield,
                       one of the tipping points that we set off first
                       when we push warming too far,” said Markus Rex of
                       the Alfred Wegener Institute, reports Agence
                       France-Presse.


                # ⚓ Laws_Must_Adapt_for_Climate_Refugees⠀⇛


                # ⚓ Rising_floods_threaten_Danish_financial_system⠀⇛


                       Stormier seas and more frequent floods can cause
                       havoc anywhere. The Danish financial system is now
                       growing apprehensive.


                # ⚓ Planet_in_Distress⠀⇛


                # § Energy⠀➾


                      # ⚓ Trump-Appointed_Judge_Blocks_Biden_From_Pausing_New
                        Oil_Drilling_Leases⠀⇛


                      # ⚓ ‘A_Deeply_Dangerous_Order’:_Trump-Appointed_Judge
                        Blocks_Biden_From_Pausing_New_Oil_Drilling_Leases⠀⇛


                             A Trump-appointed federal judge on Tuesday
                             blocked the Biden administration from
                             enforcing a temporary pause on new leases for
                             oil and gas drilling on public lands and
                             waters, a decision the Interior Department
                             said it “will comply with” amid warnings
                             about the order’s potentially destructive
                             climate impact.


                             “This is a deeply dangerous order that
                             heightens the imperative for bold, urgent
                             climate action on our public lands and
                             ocean.”—Randi Spivak, Center for Biological
                             Diversity


                # § Wildlife/Nature⠀➾


                      # ⚓ Was_American_Indian_Overhunting_Responsible_for_the
                        Near-Extinction_of_the_Buffalo?⠀⇛


                             My first encounter with this trend was with
                             Frank Furedi’s sect in the early 90s that
                             published a magazine called Living Marxism,
                             better known as LM. (They still exist as
                             Spiked today, long after dispensing with the
                             idea that they are Marxist.) When I saw an LM
                             article around that time denouncing Survival
                             International as a group that sought to keep
                             the Brazilian indigenous peoples “preserved
                             in amber” like in the Museum of Natural
                             History, I could not believe my eyes. The
                             Yanomami were in danger of extinction as a
                             result of mining and ranching excursions into
                             their territory and these self-described
                             Marxists were attacking the main group trying
                             to protect them.


                             Furedi’s group in England was called the
                             Revolutionary Communist Party that shared a
                             name with Bob Avakian’s cult in the USA but
                             little else politically except their belief
                             that the left should not believe in the
                             “noble savage”. In a debate with leaders of
                             the American Indian Movement in 1980,
                             Avakian’s spokesman referred to the “second
                             harvest”, a practice from around 7,000 years
                             ago when some indigenous peoples stored dried
                             feces so that in the event of a famine, they
                             could extract undigested seeds and other
                             products for food. In other words, Indians
                             ate shit.


          o § Finance⠀➾


                # ⚓ Wealth_Hoarding_by_‘Silver_Spoon_Oligarchs’_Is_Endangering
                  US_Democracy:_Report⠀⇛


                       The growing concentration of wealth in fewer
                       hands—including among corporate robber barons’
                       descendants who continue, after multiple
                       generations, to wield the “financial, political,
                       and philanthropic clout” afforded by enormous
                       inheritances to “advance their dynasty-building
                       agenda”—intensifies working-class suffering in the
                       U.S. and poses a threat to society and democracy.


                       “By 2020, the 50 families had amassed $1.2 trillion
                       in assets. By comparison, the bottom half of all
                       U.S. households—an estimated 65 million
                       families—shared a combined total wealth of just
                       twice that, at $2.5 trillion.”—IPS


                # ⚓ Generous_Unemployment_Benefits_Are_Not_the_Problem—Poverty
                  Wages_are⠀⇛


                       Ending enhanced unemployment benefits has become
                       the signature economic agenda for the GOP, a party
                       with little else to promote. Unfortunately the
                       largely low- key response of the President on this
                       issue has been disappointing. The failure to mount
                       a vigorous defense of these benefits is bad ethics,
                       bad policy, and bad politics. As for ethics, let us
                       assume for the minute that some workers lie around
                       idle at home while enjoying the extra $300 from the
                       government. Should economic leaders cut off any
                       additional assistance to all workers who currently
                       cannot find any job at all, in order to incentivize
                       the return to the workplace of the few who could?


                # ⚓ 25_Richest_Americans_Pay_Few_Taxes_—_Partly_Thanks_to_the
                  “Family_Fund”_Loophole⠀⇛


                # ⚓ Who_Pays_More_Taxes:_Jeff_Bezos,_Elon_Musk,_or_You?⠀⇛


                       While Rev. Martin Luther King Jr. proclaimed, “I
                       have a dream,” it was full of lofty ethical stuff
                       like “justice for all” and … well, it was so 1963.


                # ⚓ Progressives_Push_for_High-Speed_Rail_Funding_in
                  Infrastructure_Deal⠀⇛


                       Clean transportation supporters in Congress joined
                       with environmental and labor advocates for a
                       Wednesday rally to demand funding for high-speed
                       rail, a call that was echoed in a new letter from
                       five Democratic lawmakers amid ongoing
                       infrastructure talks.


                       “High-speed rail connects communities. It brings
                       people together. It’s the way of the future.”—Rep.
                       Seth Moulton


                # ⚓ The_Global_COVID-19_Inequality_Virus⠀⇛


                       Thanks to the wonders of global capitalism,
                       globalisation, neoliberalism and adjacent
                       ideologies, we live in a world where nearly half of
                       humanity is forced to scrape by on less than $5.50
                       a day – roughly the price of a Big Mac in the USA.
                       Worse, during the last 40 years – around the same
                       time neoliberalism was introduced – the wealthiest
                       1% more than doubled their income, leaving the rest
                       behind. Still worse, the global elite (1%) causes
                       twice as much carbon as the bottom half of the
                       world.


                       Just before the coronavirus pandemic started to
                       bite, over three billion people did not have access
                       to healthcare, 75% of all workers had no access to
                       social protection like unemployment benefits and
                       sick leave. Moreover, over 50% of all workers were
                       part of the precariat and working poor in low and
                       middle-income countries.


                # ⚓ Leading_Manhattan_DA_Candidate_Has_Repeatedly_Paid
                  Virtually_No_Federal_Income_Taxes⠀⇛


                       The leading candidate to take over the
                       investigation relating to former President Donald
                       Trump’s taxes paid virtually no federal income
                       taxes in four of six recent years.


                       Tali Farhadian Weinstein, who is married to hedge
                       fund manager Boaz Weinstein, is running for
                       Manhattan district attorney in the Democratic
                       primary, in which early voting has already begun.
                       She and her husband reported income as high as $107
                       million in 2011, and she recently donated $8.2
                       million to her campaign — more than her seven
                       Democratic rivals have raised in total.


                # ⚓ [Old] What’s_Next_For_Dogecoin⠀⇛


                       Now if you want to get a little bit more in-depth,
                       the Dogecoin code is based on Luckycoin, which is
                       derived from Litecoin. It was used as a randomized
                       reward for block mining, and it was changed to a
                       static reward in March of 2014. Dogecoin uses
                       Litecoin’s scrypt technology and is a proof-of-work
                       coin.


                       Scrypt is a password-based key derivation function
                       that was created by Colin Percival and was for the
                       Tarsnap online backup service. The algorithm was
                       designed with the intention of making it costly to
                       perform large-scale custom hardware attacks, where
                       they required a large amount of memory to
                       efficiently execute.


                # ⚓ Three_million_job_cuts_coming_at_Indian_services_giants_by
                  next_year,_says_Bank_of_America⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Will_Democratic_Court_Nominations_Live_Up_to_Biden’s
                  Promises?⠀⇛


                       During his four years in office, former President
                       Donald Trump reshaped the courts, successfully
                       pushing through a record number of young, deeply
                       conservative judges to fill lifetime positions
                       throughout the country. He left the White House
                       having appointed 234 judges to the federal bench,
                       including 54 appellate judges and a third of the
                       Supreme Court—a legacy that will shape the country
                       for decades to come. Now, Democrats are
                       prioritizing their judicial confirmation effort,
                       confident that they can work faster than they did
                       in the Obama era, while making good on President
                       Joe Biden’s promise to diversify the courts.


                # ⚓ Vague_Alternatives_and_G7_Summitry:_The_Build_Back_Better
                  World_Initiative⠀⇛


                       Never let contradiction get in the way of such a
                       united front.  Babbling about liberal democratic
                       values matters little when it comes to crusty
                       realpolitik.  The UK and the US continue to supply
                       armaments to their favourite theocracy, Saudi
                       Arabia, even as they take issue with Russia and
                       Chinese actions they deem aggressive, cruel or
                       authoritarian.   Germany’s position on dealing with
                       Russia remains distinct within the grouping, not
                       least on the issue of energy politics and the Nord
                       Stream 2 gas project.  Nor does the G7 necessarily
                       share the same attitude in dealing with China, each
                       having had its slant in coping with Beijing’s
                       actions in recent years.


                       The China Syndrome has produced some form of united
                       response at the summit.  Welcome, then, to the
                       Build Back Better World (B3W) initiative.  This
                       will entail, according to a White House factsheet,
                       “a values-driven, high-standard, and transparent
                       infrastructure partnership led by the major
                       democracies to help narrow the $40+ trillion
                       infrastructure need in the developing world, which
                       has been exacerbated by the COVID-19 pandemic.” 
                       The initiative will also involve “the G7 and other
                       like-minded partners” coordinating and mobilising
                       “private-sector capital in four areas of focus –
                       climate, health and health security, digital
                       technology, and gender equity and equality – with
                       catalytic investments from our respective
                       development finance institutions.”


                # ⚓ China’s_Flawed_Claims_to_Internal_Sovereignty⠀⇛


                       To contest the global criticism of its policies
                       inside and outside the country, China appeals to
                       sovereignty. At various international
                       organizations, including the U.N. Security Council
                       and the U.N. Human Rights Council, China summons
                       sovereignty and the related concepts of
                       “territorial integrity,” “political independence,”
                       “sovereign equality,” and non-interference “in
                       matters which are essentially within the domestic
                       jurisdiction of any state.” These are indeed the
                       fundamental principles of the 1945 U.N. Charter, a
                       global treaty now ratified by 193 nations.


                       As a matter of legal rhetoric, China is the chief
                       proponent of sovereignty in international affairs.
                       However, China is most vociferous about non-
                       interference when the human rights organizations
                       and U.N. special rapporteurs point out systematic
                       human rights violations of ethnic and religious
                       minorities in Xinjiang and Hong Kong. In addition
                       to contesting the “truth” of allegations, China
                       makes the legal argument that the world has no
                       lawful basis to investigate what China does within
                       its sovereign borders.


                # ⚓ Mediocre_Men_Have_Failed_New_York⠀⇛


                       New York state Senator Alessandra Biaggi recently
                       said something that so completely encapsulated
                       American patriarchy at this moment, it should be
                       tattooed on every woman’s exhausted face: “We’ve
                       got to move on past talking about the bad behavior
                       of below-average men.”


                # ⚓ What_I’d_do_as_NYC_Mayor⠀⇛


                       Media coverage has focused on the fading fortunes
                       of former presidential candidate and tech
                       entrepreneur Andrew Yang, the dearth of
                       progressives in a wide field and the new, confusing
                       ranked-choice voting scheme. (I have a lot of
                       doubts about ranked-choice voting, which I will
                       enumerate in this space at another time.)


                       A New Yorker by choice most of my life and, unlike
                       Yang, a guy who moved back to the city during the
                       COVID-19 pandemic while others were running for the
                       exurbs, I’ve been thinking a lot about what the
                       next mayor should prioritize and what I would do if
                       I were in charge of the city. Most of my readers
                       don’t live in New York. But most do live in urban
                       areas. Many who live in rural regions work and shop
                       in cities. So New York’s problems are your problems
                       too.


                # ⚓ After_Weeks_of_Wasted_Time,_Senate_Democrats_Demand_Action
                  on_Infrastructure⠀⇛


                # ⚓ Ayanna_Pressley_Calls_Out_Biden’s_DOJ_for_Moving_to
                  Reinstate_the_Death_Penalty⠀⇛


                # ⚓ Chomsky:_Republicans_Are_Willing_to_Destroy_Democracy_to
                  Retake_Power⠀⇛


                # ⚓ Schumer_and_Pelosi_Are_Urging_Fellow_Democrats_to_Go_Easy
                  on_Joe_Manchin⠀⇛


                # ⚓ Leaked_Call_Reveals_Manchin_Colluding_With_Wall_Street_to
                  Preserve_Filibuster⠀⇛


                # ⚓ Nina_Turner_Kicks_Off_‘$27_Dollar_Donation_Challenge’_After
                  Hillary_Clinton_Endorses_Establishment_Candidate_in_Ohio⠀⇛


                       Ohio congressional candidate Nina Turner said
                       Wednesday that “the establishment is doing
                       everything they can to stop our movement” shortly
                       after erstwhile Democratic presidential nominee
                       Hillary Clinton publicly threw her support behind
                       Shontel Brown, the leader of the Cuyahoga County
                       Democratic Party and Turner’s biggest competitor in
                       the race to fill the vacant U.S. House seat in the
                       Buckeye State’s 11th district.


                       “I’m not taking any corporate PAC or lobbyist
                       money.”—Nina Turner


                # ⚓ Close_Encounters_of_an_Unprecedented_Kind⠀⇛


                       A tumultuous Israeli parliament narrowly approved a
                       government aiming at centrism Sunday, an
                       unprecedented alliance that included an Arab party
                       for the first time in Israel’s 73-year history that
                       brought down the 12-year reign of a right-wing
                       divisive prime minister.


                       “I’ll be back,” defeated former Prime Minister
                       Benjamin Netanyahu told the Knesset, in a line from
                       the Terminator.


                # ⚓ New_Israeli_Government,_Same_Israeli_Apartheid⠀⇛


                       In 2013, as Middle East peace talks were set to
                       resume after a five-year freeze, Bennett reportedly
                       proclaimed to Israeli National Security Adviser
                       Ya’akov Amidror, “I’ve killed lots of Arabs in my
                       life – and there’s no problem with that.”


                       In 2014, Bennett, who had previously been the
                       director of the Yesha Settlements Council,
                       contradicted Netanyahu by asserting that all Jewish
                       Israelis living in the West Bank, even those living
                       in outposts that violate Israeli law, should remain
                       under Israeli sovereignty, and called for more
                       settlement construction. “This is the time to act,”
                       he said. “We must continue building in all corners
                       of the Land of Israel, with determination and
                       without being confused. We are building and we will
                       not stop.”


                # ⚓ American_Backstory,_While_Biden_Struts_Abroad⠀⇛


                       U.S. President Joe “Nothing Will Fundamentally
                       Change” Biden on Sunday boasted in England that
                       “America is back at the table,” leading the charge
                       against grave challenges like “China.”


                       Let’s take a look back at some facts of U.S.-
                       American life that are escaping serious “free
                       press” attention (imagine) during Joe Defender of
                       the Status Quo Biden’s visits with the cartoon
                       Queen of England and the ostensible heads of
                       European states.


                # ⚓ Boris_Johnson_Toadies_Up_to_Biden_at_the_G7⠀⇛


                       BoJo made the 210-mile journey from London to
                       Cornwall by private plane, for which he was widely
                       criticized on social media. Many thought it was a
                       bit rich of him to travel by plane to a conference
                       highlighting action on climate change (there are
                       regular train services between London and the
                       location of the summit).


                       BoJo has spent his life ignoring any measures or
                       rules that could apply to him; these are for the
                       little people, not His Eminence. So, it was the
                       private plane and not a train. Trains are for plebs
                       and tree huggers like Greta Thunberg and her ilk.


                # ⚓ Why_The_Two-Party_System_Is_Wrecking_American_Democracy⠀⇛


                       The new scholarship on comparative polarization is
                       crucial in understanding this dynamic. In one
                       sense, it offers a very depressing view: Given the
                       current binary structure of American party
                       politics, this conflict is mostly locked in. No
                       level of social media regulation or media literacy
                       or exhortation to civility is going to make much of
                       a difference. But it also offers a kind of master
                       key: If the structure of a party system is as
                       crucial as these studies suggest it is, then the
                       solution is obvious: The U.S. may want to change
                       its voting system to become more proportional.


                # ⚓ Survey:_1_in_3_US_Election_Workers_Feels_Unsafe⠀⇛


                       Many of the election officials surveyed blamed
                       false information spread by social media for their
                       problems — much of it making baseless claims of
                       widespread voting fraud. According to the study,
                       78% of officials said social media made their jobs
                       “more difficult,” while 54% percent said they
                       believed social media made their job “more
                       dangerous.”


                # ⚓ Amazon_says_it’s_all_social_media’s_fault_for_letting_fake
                  review_schemes_thrive⠀⇛


                # ⚓ Edelman_PR_and_the_Manufacturing_of_“Trust” [Ed: Microsoft
                  propaganda firm, bribery instrument, and a source of entryism
                  and infiltration operations (also inside LF)]⠀⇛


                       “We need to regain trust” is the theme of the year,
                       according to remarks made by the World Economic
                       Forum’s executive chairman Klaus Schwab in January
                       2021. But trust may be hard to engineer in an age
                       of professional disinformation campaigns by
                       governments, the mainstream media, and a handful of
                       powerful elite public relations companies.


                       Edelman, an American public relations and marketing
                       consultancy firm founded by Daniel J. Edelman in
                       1952, is the largest public relations firm in the
                       world by revenue, and some would also say by
                       reputation. Today, the company is run by Daniel
                       Edelman’s son, Richard Edelman. It is a firm with a
                       rich history of controversial efforts to completely
                       change the narrative of some of the most
                       contentious modern issues. It also boasts close
                       ties to the World Economic Forum and the Forum’s
                       attempt to engineer “trust” in its various agendas.


                       Edelman is often found representing organizations
                       experiencing what could be best termed as public
                       relations nightmare scenarios. Edelman, with its
                       previous experience representing the American
                       Petroleum Institute—the trade association for the
                       oil and gas industry that lobbied for the Keystone
                       XL pipeline and the fossil fuel exploration of the
                       Canadian tar sands—is no stranger to advocating for
                       companies stuck in atypical negative PR situations
                       with little, if any, possible positive outcomes. If
                       you are a giant corporation with a reputation to
                       launder, then Edelman is the go-to professional
                       firm to help your organization rebuild its image or
                       to simply help mitigate as much reputational damage
                       as possible.


                       Edelman has worked on behalf of some of the most
                       powerful businesses in the corporate world,
                       including Microsoft, Pfizer, Johnson & Johnson,
                       Unilever, Wal-Mart, and General Electric to name
                       just a tiny fraction of their past and present
                       clientele. The company is one of the largest PR
                       firms in the world for a reason: it fights dirty,
                       and in doing so it often uses imaginative, yet
                       underhanded, methods of manufacturing public
                       consent.


          o § Censorship/Free Speech⠀➾


                # ⚓ Content_Moderation_Case_Study:_YouTube_Relocates_Video
                  Accused_Of_Inflated_Views_(2014)⠀⇛


                       Summary: The internet is the way that many new
                       musical artists get discovered these days, with
                       perhaps the most famous story being that of that of
                       Justin Bieber on YouTube. Some of this came from
                       finding undiscovered musicians who had talent, and
                       some of it came from finding otherwise unsigned
                       artists who had managed to build large followings
                       themselves.


                # ⚓ Ai_Weiwei’s_artwork_in_support_of_Julian_Assange_rejected
                  by_Firstsite_UK_exhibition⠀⇛


                       Ai’s Postcard for Political Prisoners was explicit
                       in its aim to enlist support for Assange, under
                       conditions in which days before the exhibition was
                       to open Assange had just undergone a show trial in
                       London, with the US government seeking his
                       extradition on Espionage Act charges that could see
                       him locked up forever with a 175 year prison
                       sentence.


                       Ai said he was “honoured” by the rejection, which
                       “gave a real meaning to my artwork.” He explained,
                       “I think the reason is related to Assange who has
                       been incarcerated in HM Prison Belmarsh in London
                       since his arrest on 11 April 2019, and that they
                       don’t want to touch on a topic like Assange.”


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


                # ⚓ Zimbabwe_Court_Grants_Bail_to_New_York_Freelancer_After_3
                  Weeks_in_Prison⠀⇛


                       “It’s a typical tactic which is used to extend the
                       detention of prisoners after they have been granted
                       bail, which is why the legal team specially
                       requested to see the warrant of liberation before
                       leaving the Magistrates Court,” Coltart said. “That
                       request was denied, which is why when prison
                       officials started claiming that there was an error
                       on it late in the evening last night (Tuesday)
                       again, the legal team requested to see the warrant
                       of liberation. That request was again denied.”


          o § Civil Rights/Policing⠀➾


                # ⚓ Advocates_Cheer_DOJ_Reversal_of_Trump_Policy_Denying_Asylum
                  to_Victims_of_Violence⠀⇛


                       Immigrant rights advocates hailed the Wednesday
                       reversal by U.S. Attorney Merrick Garland of a
                       Trump-era rule denying asylum in the United States
                       to victims of domestic or gang violence as a
                       “critically important” step toward restoring the
                       right of refuge to migrants fleeing countries where
                       their lives are often in danger.


                       “This was the right move. We are thrilled for our
                       client and for the many deserving individuals
                       fleeing persecution who will have a fair chance to
                       seek refuge in the United States.”—Karen Musalo,
                       CGRS


                # ⚓ The_Demand_of_Freedom⠀⇛


                       Racism is not regional. I often hear people refer
                       to it as though it were trapped in the South. White
                       Northerners who are appalled by the blatant racism
                       around them will say things like “This isn’t
                       Mississippi” or “Take that attitude back to
                       Alabama.” But whether white Northerners like to
                       recognize it or not, slavery was in every colony in
                       the United States for more than a century and a
                       half. It was part of the fabric of America—all of
                       America. After Charleston, South Carolina, New York
                       City had the largest urban enslaved population; by
                       the mid-18th century, one in five people in the
                       city of New York was Black. It is important to note
                       that the North was not the utopian refuge that
                       public memory likes to romanticize it as.
                       Prosperous Black communities in places like
                       Philadelphia during the antebellum period were more
                       the exception than the rule. And even the City of
                       Brotherly Love experienced several major anti-Black
                       riots in the 1830s and ’40s.


                # ⚓ Trump_Toady_Mark_Meadows_Is_Running_a_Legal_Group_That
                  Promotes_White_Rights⠀⇛


                       Most recently seen in public (via e-mail, anyway)
                       hawking a conspiracy theory that Italian satellites
                       stole the 2020 election for President Joe Biden,
                       former White House chief of staff Mark Meadows
                       actually has a terrible new project: working with
                       Stephen Miller on an effort called America First
                       Legal, which should really be called Whites First
                       Legal. On behalf of white Texans who run at least
                       one of the 25 restaurants in the Lost Cajun chain,
                       they recently succeeded in getting a federal judge
                       to stop the Small Business Administration’s
                       disbursement of restaurant Covid relief funds that
                       prioritized businesses owned by women, veterans,
                       and people of color, blocking money already
                       approved for almost 3,000 struggling businesses.


                # ⚓ A_GOP_Lawmaker_Wants_to_Ban_Critical_Race_Theory_—_Without
                  Knowing_What_It_Is⠀⇛


                # ⚓ GOP_Attack_on_Education_Continues_as_Texas_Bans_Teaching_of
                  ‘Critical_Race_Theory’_in_Schools⠀⇛


                       Texas Gov. Greg Abbott became the latest Republican
                       state leader to approve legislation aimed at
                       controlling public school teachers’ ability to
                       accurately teach U.S. history and discuss current
                       events, signing a bill late Tuesday that bars
                       educators from including “critical race theory” in
                       their classroom work. 


                       Under Senate Bill 2202, starting on September 1
                       public school teachers in Texas will be required to
                       “give deference to both sides” when discussing
                       current events like the racial justice uprising
                       which began last spring following the police
                       killing of George Floyd In Minneapolis. 


                # ⚓ FBI_Ignored_Its_Own_Warrant_And_Search_Policies_To_Seize
                  Millions_From_People’s_Safety_Deposit_Boxes⠀⇛


                       This brief clip from an FBI training film helps
                       explain the actions undertaken by agents during a
                       raid on a secure storage facility earlier this
                       year:


                # ⚓ Protest_Song_Of_The_Week:_‘Zami’_By_Moor_Mother⠀⇛


                       The following post was originally published at
                       Ongoing History of Protest Music.Experimental
                       musician and acclaimed spoken word artist Camae
                       Ayewa had a prolific 2020 with the free jazz
                       project Irreversible Entanglements and a few
                       projects released under her spoken word alias Moor
                       Mother. As Moor Mother, Ayewa released “Circuit
                       City,” her punk-inspired “True Opera” album
                       featuring producer Mental Jewelry, and her
                       collaboration with rapper Billy Woods.“Zami’” is
                       Moor Mother’s first release in 2021, and since
                       announcing that she has signed to the record label
                       ANTI-. The short but powerfully ominous tune gets
                       its name from Audre Lorde’s 1982 book.According to
                       Ayewa, “‘Zami’ speaks to a number of different
                       themes. Using the lenses of Black Quantum Futurism,
                       the lyrics speak to time and space, injustice,
                       racism, erasure of African identity.”“‘Zami’ speaks
                       of agency and something beyond freedom. It speaks
                       of another future. It speaks about connections free
                       from the stains of colonialism. It speaks about the
                       expansive temporalities of Afro Diasporan people
                       around the world,” Ayewa added.Black Quantum
                       Futurism refers to the collective Ayewa co-founded
                       with Rasheedah Phillips, dedicated to “a new
                       approach to living and experiencing reality by way
                       of the manipulation of space-time in order to see
                       into possible futures, and/or collapse space-time
                       into a desired future in order to bring about that
                       future’s reality. “This vision and practice derives
                       its facets, tenets, and qualities from quantum
                       physics and Black/African cultural traditions of
                       consciousness, time, and space.”Through various
                       artistic expressions, the collective seeks to
                       “explore personal, cultural, familial, andcommunal
                       cycles of experience, and solutions for
                       transforming negative cycles into positive ones
                       usingartistic and holistic methods of
                       healing.”Listen to Moor Mother’s “Zami”:


                # ⚓ Shake_Shack_manager_accused_of_poisoning_shakes_sues_NYPD
                  officers,_union_for_defamation⠀⇛


                       The manager of a New York City Shake Shack
                       restaurant said he was unlawfully detained by
                       police and “taunted” after he was falsely accused
                       last year of poisoning three officers’ milkshakes.


                       The manager, Marcus Gilliam, is now suing members
                       of the New York Police Department, the City of New
                       York, as well as the unions that represent police
                       and detectives. Gilliam’s lawsuit is seeking
                       damages for alleged defamation and deprivation.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ AT&T_Whines_About_Biden_Focus_On_Community_Broadband⠀⇛


                       We noted how while the Biden broadband plan was
                       arguably vague, a big part of its core focus was
                       community broadband. In stark contrast to the Trump
                       administration and GOP — which think such efforts
                       should be banned — the Biden administration seems
                       to recognize such efforts are a helpful and organic
                       local response to market failure. While such
                       efforts aren’t a mystical panacea, they’re a
                       helpful way to both drive some needed regional
                       broadband improvements to underserved areas, and
                       force regional telecom monopolies to try just a
                       little harder.


                # ⚓ Null_and_Void:_Speaker_of_the_House_of_Commons_Strikes_Down
                  Numerous_Bill_C-10_Amendments⠀⇛


                       Canadian Heritage Minister Steven Guilbeault and
                       the government can undo the Speaker ruling by
                       bringing back the null and void amendments for a
                       vote, but the government, the Minister and the
                       Liberal, NDP and Bloc Heritage committee MPs cannot
                       undo their embarrassing conduct in which they
                       sacrificed democratic principles for the sake of
                       rushing through Bill C-10.


                # ⚓ Symmetrical_Gigabit_Internet_Attracting_Business,
                  Municipalities_Attest⠀⇛


                       Municipalities have been attesting to the allure of
                       symmetrical gigabit internet and voice-over
                       internet protocol services to keeping businesses in
                       cities across the United States.


                       Experts on a panel discussing municipal broadband
                       on Tuesday discussed advanced technologies that
                       have attracted businesses and, as a consequence,
                       jobs to their cities.


                # ⚓ Funny_how_Sir_Tim_Berners-Lee,_famous_for_hyperlinks,_is
                  into_NFTs,_glorified_hyperlinks⠀⇛


                       Internet trailblazer Sir Tim Berners-Lee is
                       auctioning off a link to his very early World Wide
                       Web browser and server source code in the form of a
                       non-fungible token.


                       Yup, another NFT. These are tokens that are
                       embedded in a blockchain, and can be sold for
                       millions and exchanged between traders. Buyers
                       really aren’t getting much. Typically, the data
                       they paid for isn’t actually stored in a
                       blockchain, they just get a token, and the tokens
                       include a link to the material they represent that
                       anyone can see and access. It’s a receipt stored in
                       an append-only database. You’re essentially bagging
                       bragging rights for stuff that’s public.


                       And in the case of Sir Tim’s code, it’s definitely
                       public: you can find at least his earliest WWW
                       browser code here for free, web server code here
                       for free, and the first website he crafted at CERN
                       recreated here for free.


          o § Monopolies⠀➾


                # ⚓ FOSS_Patents:_Former_Assistant_Attorney_General_Makan
                  Delrahim,_fighting_for_his_legacy,_says_yet-to-be-named
                  successor_should_have_‘regulatory_humility’_in_face_of_court
                  rulings⠀⇛


                       As the keynote speaker of a Concurrences webinar
                       held today (and ongoing as I write this post),
                       former Antitrust Assistant Attorney General–and now
                       UPenn professor–Makan Delrahim gave an impassioned
                       speech. He’s trying to dissuade his successor, who
                       (as Mr. Delrahim noted) has yet to be named almost
                       eight years after the elections, from undoing his
                       patentee-friendly policies.


                       [...]


                       In today’s webinar speech, Mr. Delrahim mostly
                       focused on access to injunctive relief over SEPs,
                       but he twice referenced the Ninth Circuit’s FTC v.
                       Qualcomm decision, in which case Qualcomm’s refusal
                       to grant exhaustive SEP licenses to chipset makers
                       played a key role. The former U.S. antitrust chief
                       also lauded a couple of European high-court
                       rulings: the UK Supreme Court’s Unwired Planet v.
                       Huawei and the German Federal Court of Justice’s
                       Sisvel v. Haier opinions.


                       Mr. Delrahim’s position is that the “ability to
                       exclude” is a key “incentive” for filing for
                       patents, and this right should not be limited
                       except by the legislature. He does say–as he could
                       hardly claim the opposite–that FRAND commitments
                       should be enforced under contract law. That works
                       in the U.S., which recognizes third-party
                       beneficiaries’ rights, but in some jurisdictions it
                       would not even be an option. Judge Hoffmann noted
                       toward the end of today’s webinar that in Germany
                       the courts have no problem applying the antitrust
                       laws to a duty to extend licenses, and Germany’s
                       seminal Orange-Book-Standard case involved a de
                       facto standard without a FRAND commitment.
                       Microsoft v. Motorola Mobility is an example Mr.
                       Delrahim mentioned for the enforcement of
                       contractual rights. But violations of a FRAND
                       pledge “do not somehow conjure up an antitrust
                       violation,” said Mr. Delrahim. He went on to stress
                       that a breach of a FRAND contract “should NEVER be
                       a violation of the antitrust laws.” And this line
                       of thought culminated in the view that “using
                       antitrust law with its triple damages and hammers
                       in [his] view is a misuse.”


                # § Patents⠀➾


                      # ⚓ Think_Tech_Companies_Are_Too_Monopolistic?_Then_Stop
                        Giving_Them_Patent_Monopolies⠀⇛


                             There is a lot of sturm and drang in the
                             halls of government these days about
                             corporate mergers – or, at least, tech
                             company mergers (oddly, this ire doesn’t seem
                             to necessarily extend to all mergers). But
                             despite all the gnashing and wailing there’s
                             not a lot of understanding of why they
                             happen. Which is strange, because if you
                             think there’s a problem, it would help to
                             understand WHY there is a problem, because
                             that understanding will give clues on how to
                             fix it.


                # § Trademarks⠀➾


                      # ⚓ Miley_Cyrus_can_use_name_as_trademark_in_Europe_after
                        long-running_row_|_Reuters⠀⇛


                             U.S. pop star Miley Cyrus has won the right
                             to use her name as a trademark on a wide
                             range of products in the European Union,
                             after Europe’s top court on Wednesday
                             annulled a decision by the EU patent office
                             to limit the scope of her brand.


                             The case dates to 2014 when the 28-year-old
                             “Wrecking Ball” singer’s company Smiley Miley
                             Inc. sought to trade mark MILEY CYRUS with
                             the EU Intellectual Property Office (EUIPO)
                             for audio and video discs, mobile phone
                             cases, e-books, electronic board games,
                             calendars and other goods.


                # § Copyrights⠀➾


                      # ⚓ “Destiny_2″_Creator_Bungie_Sues_Cheat_Seller
                        AimJunkies_for_Copyright_Infringement⠀⇛


                             Game developer Bungie has filed a lawsuit
                             against cheat seller AimJunkies.com for
                             offering the popular ‘Destiny 2 Hacks’ suite
                             for sale. The complaint, filed at a federal
                             court in Seattle, also targets the alleged
                             maker of the cheats. All defendants stand
                             accused of various forms of copyright and
                             trademark infringement.


                      # ⚓ Court_Sentences_Operator_of_Danish_Torrent_Trackers
                        to_Prison⠀⇛


                             A 50-year-old man was handed a four-month
                             prison sentence this week for his involvement
                             with the Danish torrent trackers Asgaard and
                             NordicBits. The man, who is seen as one of
                             the ringleaders behind the now-defunct sites,
                             helped to arrange servers and provided
                             customer service, among other things. The
                             Danish prosecution, meanwhile, warns that
                             users of these sites can be targeted too.



                    ䷩ 𝚕𝚒𝚗𝚎 5934

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.17.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


✐ Links_18/6/2021:_RasPad_3_and_Pushing_Rust_Into_the_Linux_Kernel⠀✐


Posted in News_Roundup at 8:20 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Audiocasts/Shows⠀➾


                # ⚓ The_RasPad_3_–_Unboxing_and_Assembly_(Full_review
                  tomorrow!!!)⠀⇛


                       The RasPad 3 is a neat project that enables you to
                       turn your Raspberry Pi 4 into a full tablet! In
                       this video, I’ll unbox the RasPad 3 and I’ll also
                       show you the entire assembly process. Be sure to
                       check out my full review as well.


                # ⚓ Ubuntu_Podcast_from_the_UK_LoCo:_S14E15_–_Tanks_Crash
                  Clash⠀⇛


                       This week we’ve been learning Davinci Resolve and
                       instrumenting our house with DHT11 sensors. We
                       round up the goings on from the Ubuntu community
                       and discuss our favourite picks from the wider tech
                       news.


                       It’s Season 14 Episode 15 of the Ubuntu Podcast!
                       Alan Pope, Mark Johnson and Martin Wimpress are
                       connected and speaking to your brain.


                # ⚓ BSDNow_407:_The_jail_Detail⠀⇛


                       Confining the omnipotent root, Jails with ZFS and
                       PF on DigitalOcean, NomadBSD 130R is out, KDE
                       Plasma Wayland on FreeBSD, Firefox under FreeBSD
                       with Privacy, Using NetBSD’s pkgsrc everywhere, and
                       more.


          o § Kernel Space⠀➾


                # ⚓ Auditing_io_uring⠀⇛


                       The io_uring subsystem, first introduced in 2019,
                       has quickly become the leading way to perform high-
                       bandwidth, asynchronous I/O. It has drawn the
                       attention of many developers, including, more
                       recently, those who are focused more on security
                       than performance. Now some members of the security
                       community are lamenting a perceived lack of thought
                       about security support in io_uring, and are trying
                       to remedy that shortcoming by adding audit and
                       Linux security module support there. That process
                       is proving difficult, and has raised the prospect
                       of an unpleasant fallback solution.


                       The Linux audit mechanism allows the monitoring and
                       logging of all significant activity on the system.
                       If somebody wants to know, for example, who looked
                       at a specific file, an audit-enabled system can
                       provide answers. This capability is required to
                       obtain any of a number of security certifications
                       which, in turn, are crucial if one wants to deploy
                       Linux in certain types of security-conscious
                       settings. It is probably fair to say that a
                       relatively small percentage of Linux systems have
                       auditing turned on, but distributors, almost
                       without exception, enable auditing in their
                       kernels.


                       The audit mechanism relies, in turn, on a large
                       array of hooks sprinkled throughout the kernel
                       source. Whenever an event that may be of interest
                       occurs, it is reported via the appropriate hook to
                       the audit code. There, a set of rules loaded from
                       user space controls which events are reported to
                       user space.


                       When io_uring was being developed (which is still
                       happening now, of course), the developers involved
                       were deeply concerned about performance and
                       functionality. Supporting security features like
                       auditing was not at the top of their list, so they
                       duly neglected to add the needed hooks — or to
                       think about how auditing could be supported in a
                       way consistent with the performance goals. Now that
                       io_uring is showing up in more distributor kernels
                       (and, in particular, the sorts of kernels where
                       auditing is relatively likely to be enabled),
                       security-oriented developers are starting to worry
                       about it. Having io_uring serve as a way to
                       circumvent the otherwise all-seeing audit eye does
                       not seem like a good way to maintain those security
                       certifications.


                # ⚓ The_runtime_verification_subsystem⠀⇛


                       The realtime project has been the source of many of
                       the innovations that have found their way into the
                       core kernel in the last fifteen years or so. There
                       is more to it than that, though; the wider realtime
                       community is also doing interesting work in a
                       number of areas that go beyond ensuring
                       deterministic response. One example is Daniel
                       Bristot de Oliveira’s runtime verification patch
                       set, which can monitor the kernel to ensure that it
                       is behaving the way one thinks it should.


                       Realtime development in the kernel community is a
                       pragmatic effort to add determinism to a production
                       system, but there is also an active academic
                       community focused on realtime work. Academic
                       developers often struggle to collaborate
                       effectively with projects like the kernel, where
                       concerns about performance, regressions, and
                       maintainability have been the downfall of many a
                       bright idea. As a result, there is a lot of good
                       academic work that takes a long time to make it
                       into a production system, if it ever does.


                       Imagine, for a moment, a project to create a
                       realtime system that absolutely cannot be allowed
                       to fail; examples might include a controller for a
                       nuclear reactor, a jetliner’s flight-control
                       system, or the image processor in a television set
                       showing that important football game. In such a
                       setting, it is nice to know that the system will
                       always respond to events within the budgeted time.
                       Simply observing that it seems to do so tends to be
                       considered inadequate for these systems.


                       One way to get to a higher level of assurance is to
                       create a formal model of the system, prove
                       mathematically that the model produces the desired
                       results, then run that model with every scenario
                       that can be imagined. This approach can work, but
                       it has its difficulties: ensuring that the model
                       properly matches the real system is a challenge in
                       its own right and, even if the model is perfect, it
                       is almost certain to be far too slow for any sort
                       of exhaustive testing. The complexity of real-world
                       systems makes this approach impractical, at best.


                # ⚓ It’s_Good_But_Maybe_Bad:_LVFS_Skyrockets_With_More_Than
                  100k_Firmware_Updates_In_One_Day_–_Phoronix⠀⇛


                       The Linux Vendor Firmware Service (LVFS) with Fwupd
                       has been serving on average around 40k~50k firmware
                       updates per daay to Linux users relying on this
                       cross-vendor, open-source firmware distribution
                       service with FWUPD for applying firmware updates
                       under Linux. But yesterday its usage just
                       skyrocketed with more than 100,000 firmware updates
                       in a single day… That’s great for adoption but the
                       motivation for the mass firmware updates may be
                       something rough on the horizon.


                # ⚓ Intel_Speed_Select_Driver_Issue_Was_Hurting_Performance_In
                  Some_HPC_Benchmarks_–_Phoronix⠀⇛


                       Intel’s Speed Select Technology introduced since
                       Cascade Lake for providing more granular power/
                       performance controls was done in the name of
                       performance but it turns out an ISST Linux driver
                       inefficiency could lead to a 10%+ performance hit
                       for some HPC benchmarks.


                       Public details are scarce on this latest Intel
                       Speed Select Technology Linux driver change but
                       when making use of this ISST code on select systems
                       and for unspecified HPC workloads it could lead to
                       reported 10%+ performance penalties for some high
                       performance computing benchmarks. The issue stems
                       from the CPU to PCI device mapping carrying out a
                       linear search of PCI devices on systems and in
                       particular for massive servers this could prove to
                       be very expensive.


                # ⚓ AMDGPU_For_Linux_5.14_To_Report_Throttler_Status,_Many
                  Fixes_Sent_Out_–_Phoronix⠀⇛


                       Last week marked the end of feature work for the
                       AMDGPU driver (and other DRM drivers) for the
                       upcoming Linux 5.14 cycle. Sent out today though
                       were the first set of AMDGPU fixes targeting Linux
                       5.14 that does include a recently talked about
                       throttler status feature.


                       Prior feature pull requests to DRM-Next for the AMD
                       Radeon kernel graphics driver for Linux 5.14
                       included the introduction of Beige Goby and Yellow
                       Carp GPU support, HMM SVM, more Aldebaran
                       accelerator work, PCI Express ASPM being enabled by
                       default, GPU hot unplug support, AMD Smart Shift
                       support for laptops, 16 bpc support, and various
                       other changes. Linux 5.14 will be another exciting
                       cycle for AMD Radeon open-source driver users
                       particularly if running newer GPUs.


          o § Applications⠀➾


                # ⚓ 7_Best_Free_and_Open_Source_HTML_Editors⠀⇛


                       An HTML editor is computer software for creating
                       web pages. As this type of editor helps to remove
                       the frustration out of creating web pages, it
                       represents an indispensable tool for graphic and
                       web designers. Specialized HTML editors provide
                       convenience and added functionality.


                       There are three main types of HTML editors. The
                       most common type is the WYSIWYG HTML editor. Here
                       the editor provides an editing interface which
                       resembles how the page will be displayed in a web
                       browser. This is achieved by embedding a layout
                       engine. For example, in the case of BlueGriffon,
                       the layout engine that is used is Gecko, which is
                       also used in the Firefox web browser. The other
                       types of editor are text source editors and object
                       editors.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_update_the_Telegram_Linux_desktop_app⠀⇛


                       Are you excited about the latest Telegram Desktop
                       features, but your Linux client is out of date? Do
                       you need to know how to update Telegram to the
                       latest and greatest on your Linux PC but can’t
                       figure it out? We can help! Follow along as we go
                       over how to update Telegram on Linux!


                # ⚓ How_to_edit_a_system_file_with_sudoedit_preserving_the
                  invoking_user_environment⠀⇛


                       On Linux and other Unix-based operating systems,
                       sudo is used to run a program with the privileges
                       of another user, often root. When we need to modify
                       a file which requires administrative privileges to
                       be edited, if we launch our favorite text editor
                       directly with sudo, it will run without the
                       customization and settings we use when we invoke it
                       normally, since the environment of the invoking
                       user is not preserved. In this tutorial we will see
                       how can we easily solve this problem and how we can
                       modify system files securely by using sudoedit.


                # ⚓ How_to_Install_Plex_Media_Server_on_Ubuntu_20.04⠀⇛


                       Plex is a streaming media server that lets you
                       organize your video, music, and photo collections
                       and stream your media to your computer, phone,
                       tablet, or TV at any time and from anywhere. Plex
                       media server can be installed on all major
                       operating systems and devices.


                       This article explains how to install Plex Media
                       Server on Ubuntu 20.04.


                # ⚓ How_to_Make_a_Bootable_USB_Drive_With_Etcher_in_Linux⠀⇛


                       Boot disks (or bootable drives) are a vital tool
                       for troubleshooting system issues on any operating
                       system. They allow you to temporarily access the
                       file system of a broken computer and fix the
                       problem that caused the breakdown.


                       Moreover, bootable drives also serve as live USB
                       drives and facilitate access to your system on any
                       device, anywhere. To create a bootable drive, you
                       need to flash an image file onto your removable
                       device using an image flashing utility.


                       If you’re on Linux, you can use Etcher to create a
                       bootable drive. Here’s a guide to help you through
                       the process.


                # ⚓ How_to_install_Sort_The_Court_on_a_Chromebook⠀⇛


                       Today we are looking at how to install Sort The
                       Court 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.


                # ⚓ Using_text_file_manipulation_tools_in_CentOS_Linux_–_Linux
                  Concept⠀⇛


                       System administrators, developers, and users need
                       to work with text files, configuration files, and
                       log files when working on Linux. Some of these
                       files are large; some of them are small or medium.
                       The data contained in these files frequently needs
                       to be viewed, updated, or extracted. In this
                       section, we will learn how to manage and manipulate
                       text files on Linux.


                # ⚓ Redirecting_output_to_files_and_programs_in_CentOS_Linux_–
                  Linux_Concept⠀⇛


                       When we execute any program, by default, its output
                       or error is displayed on the screen. We can
                       redirect the text output of a program to a file
                       using the input/output redirection operator or to
                       another program using pipes. For this, when any
                       command is executed, there are three standard file
                       streams (file descriptors) created and opened by
                       the operating system. The streams are known as
                       standard input (stdin), standard output (stdout),
                       and standard error (stderr).


                       The first stream is associated with stdin (numbered
                       as 0) used to read input from keyboard. The second
                       file stream is associated to stdout (numbered as 1)
                       used by program to print output on screen, and the
                       last file stream is stderr (numbered as 2), used by
                       our program to print errors onscreen.


                # ⚓ Basic_DHCP_concepts_|_Ubuntu⠀⇛


                       Let’s step back and take a very basic look at DHCP.
                       In fact, let’s look at the analogy of assigning an
                       address to your house. Usually, this is done by the
                       local 911 dispatch office, or some other central
                       authority. They typically use either a survey map
                       or a latitude, longitude pair to locate you, before
                       they assign your house numbers from a pool of
                       available addresses, compatible with other
                       addresses in the area.


                # ⚓ Enrico_Zini:_Reimagining_Ansible_variables⠀⇛


                       This is part of a series of posts on ideas for an
                       ansible-like provisioning system, implemented in
                       Transilience.


                       While experimenting with Transilience, I’ve been
                       giving some thought about Ansible variables.


                # ⚓ How_to_Upload_and_Share_Files_From_the_Terminal_Using
                  Transfer.sh⠀⇛


                       Generally, file sharing involves logging into a
                       storage provider, manually locating the file, and
                       uploading it via the graphical user interface of a
                       web browser or application. While the time wasted
                       during these intermediate steps may not seem like
                       much, it keeps on adding up every time you wish to
                       upload or share a file.


                       But sharing files doesn’t have to be tedious
                       anymore. With the Linux terminal, you can do this
                       in a jiffy. Thanks to tools like transfer.sh, all
                       it takes is a simple command on your terminal to
                       upload a file.


                # ⚓ LXD_and_Docker_containers_nesting_–_Tutorial⠀⇛


                       Welcome to Arcane Weekly. Today, I want to talk to
                       you about a problem you’re not likely to encounter,
                       but if you do, then you’d want a quick and handy
                       solution. Tools at hand: LXD containers, Docker.
                       Mission at hand: You want to run the two at the
                       same time. More specifically, you want to spawn a
                       LXD container, and then inside it, start a Docker
                       container. Why? Why not.


                       Then, the problem you have is as follows. The
                       Docker execution fails with the following error:
                       docker: Error response from daemon: OCI runtime
                       create failed: container_linux.go:367: starting
                       container process caused: process_linux.go:495:
                       container init caused: rootfs_linux.go:60: mounting
                       “proc” to rootfs at “/proc” caused: permission
                       denied: unknown. Lots of text there. Let’s debug
                       this, shall we?


                # ⚓ How_to_watch_or_monitor_log_files_in_Debian_10⠀⇛


                       Log files are simply plain text files that contain
                       the set of records, events, or messages about the
                       server, applications, and services running on your
                       Linux operating system. They are used by system
                       administrators for troubleshooting purposes
                       whenever an issue arises.


                # ⚓ How_to_quickly_deploy_a_static_website_with_Hugo_–
                  TechRepublic⠀⇛


                       There are several reasons why your business might
                       want to start employing a static website generator.
                       One reason is because you need to be able to
                       quickly roll out websites without having to bother
                       coding them. Or, you might want to eventually get
                       to the point of automating this process for regular
                       static site deployment.


                       With tools like Hugo (which has been around for
                       nearly 10 years), you can use pre-defined templates
                       to generate a full static website. The pages are
                       served very fast, so if speed is what you’re
                       looking for, this might be the tool you need. One
                       thing you must know about Hugo-built sites is that
                       there’s no database backend or plugins to expand
                       the feature set. These are static sites at their
                       heart.


                       However, with the right developer magic, you can
                       use these types of sites to bolster your companies
                       online presence, using them in kiosks, embedded
                       systems or just about any use-case that could
                       benefit from lightning-fast static sites.


                       If this sounds like something you might want to
                       try, you’re in luck, because I’m going to walk you
                       through the steps of deploying your first site with
                       Hugo.


                # ⚓ Opensearch_and_syslog-ng⠀⇛


                       Opensearch is a fork of the Elastic stack code
                       base, made right before the license change. The
                       first release candidate (RC1) has been released
                       recently. Next to plain text files, Elasticsearch
                       is one of the most popular destinations in syslog-
                       ng, but after the license change people started to
                       look for alternatives. I did some quick tests and
                       using the elasticsearch-http() destination, syslog-
                       ng seems to work fine with Opensearch as well.


                       Opensearch is not yet production ready. It is still
                       in testing phase. However, if the licensing changes
                       of Elastic makes you search for alternatives,
                       switching to Opensearch might be the easiest. RC1
                       is already in a good enough shape to start testing
                       it, so you can switch easier once it is ready for
                       production.


                       You can learn from this blog how to get started
                       with Opensearch, dashboards and syslog-ng. Another
                       alternative that syslog-ng users explored is
                       Grafana Loki.


                       Disclaimer: covering a given technology or brand on
                       the syslog-ng blog is not an endorsement. The
                       syslog-ng blog covers new syslog-ng features, new
                       trends in log management or questions, problems
                       coming up in the syslog-ng community.


                       [...]


                       From this blog, you could learn how to quickly set
                       up a set environment for Opensearch and syslog-ng.
                       Now comes the hard part: reading the documentation,
                       learning how to configure individual components,
                       rolling out your own PKI, and more. Those topics
                       are well beyond the scope of a syslog-ng blog.


                # ⚓ Refactor_your_applications_to_Kubernetes_|_Opensource.com⠀⇛


                       Application modernization developers must be able
                       to understand database operations and transaction
                       processes inside applications precisely. Tackle-
                       DiVA (Data-intensive Validity Analyzer) is an open
                       source data-centric Java application analysis tool
                       in the Konveyor Tackle project that aims at
                       refactoring applications to Kubernetes.


                       This article gives an overview of Tackle-DiVA and
                       presents example instructions and analysis results.


                # ⚓ How_To_Install_Microsoft_SQL_Server_on_Ubuntu_20.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Microsoft SQL Server on Ubuntu 20.04 LTS. For those
                       of you who didn’t know, MS SQL is a relational
                       database system by Microsoft that was open-sourced
                       in 2016. As a database server, it is a software
                       product with the primary function of storing and
                       retrieving data as requested by other software
                       applications which may run either on the same
                       computer or on another computer across a network
                       (including the Internet).


                       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 Microsoft SQL Server 2019 on
                       Ubuntu 20.04 (Focal Fossa). You can follow the same
                       instructions for Ubuntu 18.04, 16.04, and any other
                       Debian-based distribution like Linux Mint.


                # ⚓ How_to_Hide_All_The_User_Accounts_in_Ubuntu_20.04,_21.04
                  Login_Screen_|_UbuntuHandbook⠀⇛


                       Ubuntu lists all the available user accounts in the
                       GDM login screen. You can however remove them to
                       protect your privacy.


                       Gnome, the default desktop environment, has a
                       hidden option to force users to type the username
                       and then password to login. If you’re working on
                       public places, it will be good to enable this
                       option for privacy concern.


                # ⚓ croc_–_another_file_transfer_method_|_Fitzcarraldo’s_Blog⠀⇛


                       I have lost count of the number of times I have had
                       to send a large file to someone at work, usually in
                       a hurry. I’ve used Dropbox, ownCloud, Firefox Send
                       (no longer available) etc. Transferring large files
                       became a bit easier when e-mail service providers
                       increased the size limit for attachments, but that
                       is still not a solution for very large files. The
                       xkcd cartoon FILE TRANSFER sums up the situation
                       nicely.


                       I recently discovered the command line utility
                       croc, which the author claims is a way to ‘easily
                       and securely transfer stuff from one computer to
                       another.’ I thought I’d give it a try, if only to
                       have another tool to fall back on in an emergency.
                       It does rely on both ends having croc installed,
                       but hopefully that should not be a show-stopper as
                       croc is available for Linux, Windows, macOS and
                       BSD.


                # ⚓ Checking_Linux_system_performance_with_sar_|_Network
                  World⠀⇛


                       Sar is a system utility that gives us many ways to
                       examine performance on a Linux system. It provides
                       details on all aspects of system performance
                       including system load, CPU usage, memory use,
                       paging, swapping, disk usage, device load, network
                       activity, etc.


                       The name “sar” stands for “system activity report,”
                       and it can display current performance, provide
                       reports that are based on log files stored in your
                       system’s /var/log/sa (or /var/log/sysstat) folder,
                       or be set up to automatically produce daily
                       reports. It’s part of sysstat – a collection of
                       system performance monitoring tools.


                # ⚓ How_to_install_Fast_Disk_Usage_Analyzer_[Gdu]_for_Linux_–
                  Unixcop⠀⇛


                       The gdu tool is created for SSD drives where
                       parallel processing can be utilized. This tool can
                       also work with HDD with less performance compared
                       to SSD drives. You can also check benchmark
                       results. There are many other similar tools and you
                       have to play with gdu first to see if satisfy your
                       needs.


                # ⚓ Distinguishing_between_SELinux_policies_–_Linux_Concept⠀⇛


                       The most common SELinux policy store names are
                       strict, targeted, mcs, and mls. None of the names
                       assigned to policy stores are fixed though, so it
                       is a matter of convention. Hence, we recommend
                       consulting the distribution documentation to verify
                       what the proper name of the policy should be.
                       Still, the name often provides some information
                       about the SELinux options enabled through the
                       policy.


                # ⚓ Jira_as_Requirements_Management_Tool_(RMT)_|_SUSE
                  Communities⠀⇛


                       Safety-critical industries can be flippantly
                       defined as those where a software failure could
                       kill you. Think automotive, aviation, or medical
                       devices as examples. Safety-critical industries use
                       heavy processes to ensure that (especially but not
                       exclusively) software is developed in a safe
                       manner. Heavy processes often need heavy tools. In
                       terms of requirements management, those heavy
                       requirements management tools (RMT*) include DOORS,
                       DOORS Next Generation, Polarion, Jama, just to name
                       drop a few. These heavy RMTs require a substantial
                       investment of time and money to use properly.


                       I’ve been a requirements engineer for many years
                       and I’ve done time at avionics and automotive
                       suppliers who had the resources to deploy those
                       heavy RMTs. I’m used to having their advanced
                       features at my fingertips. Now I’m the requirements
                       engineer for the Automotive Linux Team here at SUSE
                       and it’s my job to use the resources available to
                       me to successfully manage requirements for our
                       automotive projects. We took a long hard look at
                       investing resources into a heavy RMT. But we
                       already had Jira in place, so we took up the
                       challenge to see if it could serve as our RMT.


          o § Games⠀➾


                # ⚓ God_sim_sandbox_‘WorldBox’_has_a_huge_release_out_with_lots
                  of_fun_new_toys⠀⇛


                       WorldBox gives you a pixel-art god game all about
                       doing whatever they hell you want. It’s actually
                       fantastic and a new release is out now. They only
                       recently started supporting Linux with it (back in
                       April), and now we’re seeing all updates across all
                       platforms at the same time which is great.


                       I wasn’t actually aware of just how popular it was
                       until recently. The developer announced even just
                       on their Discord, they’ve hit 200,000 people – so
                       that gives you an idea of just how big it is. It’s
                       available for mobile too like Android, where there
                       it’s seen over 388,000 ratings so it’s fantastic to
                       have it on Linux too now. Not seen it?


                # ⚓ NVIDIA_Resizable_BAR_Performance_–_A_Big_Boost_For_Some
                  Linux_Games_–_Phoronix⠀⇛


                       Back in March NVIDIA announced they would be
                       supporting the GeForce RTX 30 series with Resizable
                       BAR support via a video BIOS update for supported
                       systems. Recently I’ve been looking at the
                       performance of a GeForce RTX 3080 once flashing the
                       graphics card under Linux with Resizable BAR
                       support and the performance is quite compelling for
                       Vulkan-based games where this functionality is
                       working.


                       Like with the AMD Smart Access Memory / Resizable
                       BAR support, it requires a compatible CPU and
                       motherboard and having the support enabled within
                       the system BIOS. There is also graphics driver
                       support required for Resizable BAR. NVIDIA hasn’t
                       talked much about the Linux driver for Resizable
                       BAR but in fact the support is there with the
                       latest stable driver series, assuming your video
                       BIOS has the support available. It is important to
                       note though the Resizable BAR support is
                       implemented just for their Vulkan driver and not
                       for OpenGL.


                # ⚓ Loop_Hero_adds_saving_during_a_run_and_more_speed_options
                  in_the_1.1_update⠀⇛


                       Loop Hero, the big hit from Four Quarters and
                       Devolver Digital that released back in March has a
                       major 1.1 update out now with some really wonderful
                       additions.


                       Making an already great game that little bit
                       better, you can now actually save and quit to come
                       back during a run through the expeditions. So you
                       no longer have to run back to camp and lose a bunch
                       of resources just because you have to leave. That
                       alone will make me put a lot more time into it. You
                       can also speed the game up an additional two times,
                       card deck switching is in, new titles and enemies
                       and more.


                # ⚓ Absolute_Drift_from_the_art_of_rally_devs_arrives_on_GOG
                  and_free_for_48_hours_|_GamingOnLinux⠀⇛


                       Yet another chance to bag yourself a free game.
                       During the GOG Summer Sale, Absolute Drift from the
                       art of rally developer has been released on GOG and
                       free for 48 hours.


                       “This is a driving experience like no other.
                       Journey from apprentice to master drifter as you
                       hone your skill in a gorgeous minimalist world.
                       Push yourself to the limit on drifting tracks and
                       wild mountain roads while you work to unlock
                       trophies and elite events. Compete against ghosts
                       of the top players in the world, or refine your
                       skills by out-scoring your own ghost. Chill out to
                       over 3 hours of original electronic music by C41
                       and NYTE as you challenge your driving skills at
                       every turn until you finally master the art of
                       drifting.”


                # ⚓ Godot_Engine_–_Tiles_editor_progress_report_#4⠀⇛


                       This is the part 4 of the progress reports about
                       the TileMap and TileSet editors rework. You can
                       find the previous report here.


                       We are close to the end of this huge work.
                       Hopefully in the coming few weeks, the Tiles
                       editors should be ready to be included in the first
                       4.0 alpha. Some improvements still have to be done,
                       but we are getting close to feature completeness.
                       Until then, here is the summary of the work done
                       during the last two months.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ KDE_Plasma_5.22_Released_with_Better_Stability_and
                        Usability_Across_the_Board⠀⇛


                             The KDE Plasma desktop development has kicked
                             into high gear and the latest release
                             reflects newfound popularity and drive behind
                             the open-source environment.


                             The KDE Plasma developers have been
                             incredibly busy this cycle, refactoring code,
                             fixing bugs, and adding new features, all of
                             which come together to bring even more
                             performance to the desktop environment. The
                             developers are so proud of this release (and
                             the work they’ve achieved) that they created
                             a showcase site to highlight everything found
                             in KDE Plasma 5.22.


                             The latest release is all about general eye
                             candy and usability. And it shows.


                             One of the most exciting new features to be
                             found in KDE Plasma is called Adaptive
                             Transparency, which will transition between
                             translucent to opaque, depending on if there
                             are any maximized windows. So when an app
                             window is maximized, the panel will be
                             opaque. If there are no maximized windows,
                             the panel will be translucent. Of course,
                             users can opt-out of this feature and make
                             the panel always translucent or always
                             opaque.


                      # ⚓ GitHub_Notification_Actions [Ed: KDE projects that
                        outsource to Microsoft proprietary software and help a
                        malicious monopoly]⠀⇛


                             Calamares, a Linux system installer used by a
                             few dozen different distro’s, is hosted on
                             GitHub. The source code and issues live
                             there, and the website is run from GitHub
                             pages. This post meanders around GitHub
                             actions – things that happen in response to
                             changes in a project – and how I built a
                             Matrix-notification-thing for Calamares.


          o § Distributions⠀➾


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ Digest_of_YaST_Development_Sprint_125⠀⇛


                             Time flies and another two weeks of YaST
                             development have passed. As in the previous
                             report, we have to mention we invested quite
                             some time learning and experimenting with
                             technologies that will shape the role of YaST
                             in particular and Linux installers in general
                             in the future.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ The_evolution_of_Software_Defined_Networking⠀⇛


                             As the world digitizes and software is eating
                             the world, there is a growing expectation to
                             have on-demand and customizable services for
                             both enterprise and end users. As an end
                             user, we expect sub-millisecond latency and
                             jitter when playing online. We want to hear
                             the goal at the same time as our neighbor
                             when watching a game; and above everything,
                             we want the video and audio to be stable when
                             doing a video call.


                             All these things, and many more, require a
                             lot of automation and orchestration. Software
                             Defined Networking (SDN) is a piece to the
                             puzzle. In this first post, we’ll provide an
                             overview of the role it plays and how it has
                             transformed the way communication service
                             providers operate their network.


                      # ⚓ IBM_Collaborates_with_30_Organizations_to_Re-Skill_&
                        Connect_the_Workforce_with_Real_Career_Opportunities
                        [Ed: IBM is laying off tons of people while paying for
                        press releases that somehow portray it as a charity
                        looking to get people employer]⠀⇛


                             At VivaTech today, IBM (NYSE: IBM) CEO Arvind
                             Krishna announced a new collaboration with 30
                             global organizations including governments,
                             community colleges, non-profits, and
                             employment agencies, focused on helping
                             underserved populations improve their skills
                             and employability.


                      # ⚓ A_primer_on_containers⠀⇛


                             Remember when people used cloud computing
                             because it was cheaper? It (often) still
                             is—but what began as a way to cut costs has
                             led to a sea change in IT. Similarly,
                             containerization, which started as an
                             incremental shift in how code is packaged and
                             deployed, has fundamentally altered how code
                             is written, as well as the architecture of
                             the services it supports. For example, most
                             large software companies used to release new
                             code once a month at most. Now, the most
                             successful teams release code to production
                             at least once a day, an acceleration made
                             possible by containerization.


                             A container, in simple terms, is a bundle of
                             everything an application needs in order to
                             run, including libraries and dependencies.
                             Unlike a virtual machine (VM), a container
                             doesn’t include a full operating system
                             kernel, relying instead on containerization
                             platforms such as Docker, LXC, or rkt to get
                             what it needs from the operating system
                             layer. Containers can offer a range of
                             benefits over VMs. For one, they generally
                             use less memory and storage space when
                             running applications. More broadly, they
                             enable architecture that’s flexible and
                             resilient, in which software runs
                             consistently and scales smoothly.


                             As with most tools, however, containers
                             aren’t a universal solution. They work best
                             when used to fulfill specific engineering
                             needs—something to keep in mind as we explore
                             their advantages and disadvantages. Let’s
                             dive in, shall we?


                      # ⚓ 3_Reasons_to_choose_RHEL_for_SAP_Solutions_on_Alibaba
                        Cloud⠀⇛


                             Alibaba Cloud is an important partner for Red
                             Hat and the choice of public cloud for many
                             of our customers in the Asia Pacific region.
                             For those customers looking to modernize and
                             migrate SAP workloads to SAP S/4HANA we can
                             offer several reasons to consider RHEL for
                             SAP Solutions in the Alibaba cloud.


                             Moving to SAP S/4HANA by 2027


                             The year 2027 is an important one –
                             modernizing legacy SAP ERP solutions to S/
                             4HANA means that organizations must
                             standardize their underlying SAP databases to
                             use SAP HANA running on Linux.


                             This critical migration event presents an
                             excellent opportunity for organizations to
                             modernize their IT infrastructure, compelling
                             them to not only decide on which operating
                             system to pick, but also whether or not they
                             should move to the cloud to further
                             streamline costs and improve business
                             agility.


                             With Alibaba Cloud leading the pack among the
                             cloud service providers in the Asia Pacific
                             region and building on the successful
                             availability of Red Hat Enterprise Linux 8.1
                             on the Alibaba cloud, Red Hat, SAP, and
                             Alibaba Cloud have been working closely to
                             bring Red Hat Enterprise Linux (RHEL) for SAP
                             solutions with High Availability and Update
                             Services to the Alibaba Cloud Marketplace
                             with on-demand pricing options for RHEL 7 and
                             RHEL 8.


                      # ⚓ Fedora_contemplates_the_driverless_printing_future⠀⇛


                             Back in a distant time — longer ago than he
                             cares to admit — your editor managed a
                             system-administration group. At that time,
                             most of the day-to-day pain reliably came
                             from two types of devices: modems and
                             printers. Modems are more plentiful than ever
                             now, but they have disappeared into interface
                             controllers and (usually) manage to behave
                             themselves. Printers, instead, are still
                             entirely capable of creating problems and
                             forcing a reconsideration of one’s life
                             choices. Behind the scenes, though, the
                             situation has been getting better but, as a
                             recent conversation within the Fedora project
                             made clear, taking advantage of those
                             improvements will require some changes and a
                             bit of a leap of faith.


                             Traditionally, getting a printer working on
                             Linux has involved, among other things,
                             locating and installing the appropriate
                             printer drivers and PostScript printer
                             definition (PPD) files to allow the system to
                             communicate with the printer using whatever
                             special dialect it favors. Often that
                             involves installing a separate package like
                             hplip, often supplied by the printer vendor.
                             Some vendors have traditionally supported
                             Linux better than others, but none of their
                             products seem to work as smoothly as one
                             would like. While printer setup on Linux has
                             definitely improved over the years, it still
                             easy to dread having to make a new printer
                             work.


                      # ⚓ Why_FreeDOS_has_16_colors_|_Opensource.com⠀⇛


                             To explain why text only comes in sixteen
                             colors, let me tell you a story about the
                             first IBM Personal Computer. Parts of this
                             story may be somewhat apocryphal, but the
                             basics are close enough.
                             IBM released the Personal Computer 5150 (the
                             “IBM PC”) in 1981. The PC used a simple
                             monitor screen that displayed text in green.
                             Because this display only worked with one
                             color, it was dubbed monochrome (the “IBM
                             5151 monochrome display,” with the IBM
                             Monochrome Display Adapter card, or “MDA”).


                             That same year, IBM released an updated
                             version of the PC that sported an amazing
                             technical achievement—color! The new IBM 5153
                             color display relied on a new IBM Color
                             Graphics Adapter, or “CGA.” And it is because
                             of this original CGA that all DOS text
                             inherited their colors.


                             But before we go there, we first need to
                             understand something about color. When we
                             talk about colors on a computer screen, we’re
                             talking about mixing different values of the
                             three primary light colors—red, green, and
                             blue. You can mix together different levels
                             (or “brightnesses”) of red, green, and blue
                             light to create almost any color. Mix just
                             red and blue light, and you get magenta. Mix
                             blue and green, and you get cyan or aqua. Mix
                             all colors equally, and you get white.
                             Without any light colors, you see black (an
                             absence of color).


                      # ⚓ A_more_sustainable_future_should_be_a_more_open
                        future [Ed: "Sustainable" is a pretty meaningless
                        buzzword and no wonder IBM Red Hat embraces that for
                        marketing and openwashing purposes]
                        ⠀⇛


                             In the first part of this extended review of
                             The Age of Sustainable Development” by
                             Jeffrey Sachs, I outlined the author’s
                             argument about the environmental impacts of
                             economic development. In the second article,
                             I discussed the author’s argument about
                             impacts on humans. In this final piece, I
                             will discuss how to address those impacts.
                             I’ll outline Sachs’ suggestions but will also
                             further explain how taking an open
                             organizational approach to the issues will be
                             critical to addressing them.


                # § Debian Family⠀➾


                      # ⚓ Dependable_Debian_is_like_a_rock_in_a_swirling_gyre
                        of_‘move_fast_and_break_things’,_and_version_11_is_no
                        different⠀⇛


                             The Debian 11 is the venerable Debian
                             Project’s first new release in more than two
                             years, nicknamed “Bullseye” after the Toy
                             Story character and supplanting Debian 10
                             “Buster” (all Debian releases bear names from
                             the kids’ film).


                             Since Debian is the source from which dozens
                             of other distros draw, notably Ubuntu, its
                             major updates are well worth paying attention
                             to, even if you aren’t a Debian user. If you
                             are a Debian user and you’ve been patiently
                             waiting for an updated kernel to work with
                             all the latest hardware, I have good news,
                             the 5.10 LTS Linux kernel is here. More on
                             that in a minute.


                             First, for the Linux newcomers, it might help
                             to understand why Debian only releases new
                             versions every couple of years when most
                             popular distros crank out several new
                             versions each year.


                      # ⚓ Debian_11_Bullseye:_Full_Freeze_and_Preliminary
                        Release_Dates_have_been_set_–_Market_Research
                        Telecast⠀⇛


                             The start date of Debian GNU / Linux 11 in
                             the “Full Freeze” phase has been fixed since
                             last weekend: From July 17, 2021, packages
                             that now want to be included in the upcoming
                             version of the Linux distribution require
                             explicit approval (“manual unblock”) by the
                             Debian release team. The full freeze is
                             followed by the publication – and there is
                             now a date for which the developers are
                             aiming for July 31, 2021 as well.


                             The Debian developers have July 17th rolled
                             into one Post on the announcement mailing
                             list debian-devel-announce announced. The
                             appointment was also included in the Bullseye
                             Freeze Timeline and Policy recorded, which
                             depicts the total of four freeze phases. Last
                             week, the team agreed on July 31, the
                             cautiously targeted release date: A Mailing
                             list post by developer Paul Gevers describes
                             the date as a tentative release date, after
                             possible dates in August had also been
                             discussed.


                      # ⚓ Raphaël_Hertzog:_Submit_your_ideas_for_Debian_and_+1
                        those_that_you_find_important⠀⇛


                             A while ago, I got a request from Kentaro
                             Hayashi on the project I use to manage
                             funding requests addressed to Freexian. He
                             was keen to see some improvements on the way
                             reimbursement requests are handled in Debian.
                             In my opinion, the idea is certainly good but
                             he’s not part of the treasurer team and was
                             not willing to implement the project either,
                             so it was not really ready to be submitted to
                             us.


                             To be able to fund a useful project, we need
                             either someone that is willing to do the work
                             and try to push it further in Debian, or we
                             need a Debian team interested in the result
                             of the project (and in that case, we can try
                             to find someone willing to implement the
                             project). In this case, it’s a bit sad that
                             the treasurer team didn’t comment at all… but
                             in general, what should we do with those
                             suggestions ?


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Two-factor_authentication_coming_to_Ubuntu_One [Ed:
                        The brand Ubuntu One is back... just to confuse
                        people]⠀⇛


                             Two factor authentication (2FA) increases
                             your account security further than just using
                             a username and password. In addition to a
                             password (the first factor), you need another
                             factor to access your account. A great
                             example to demonstrate this is when you
                             withdraw money from an ATM. To access your
                             bank account you need both your physical bank
                             card and to know your PIN number. These are
                             the two factors you need to withdraw money =
                             2 factor authentication!


                             Common ways to provide this extra level of
                             security are a specific application on your
                             phone or computer, a physical security key/
                             USB (Yubikey, for example), or a smart card.
                             By using more than one of these factors, you
                             can greatly increase the security of your
                             account or system.


                             [...]


                             After many years in beta, we have created a
                             comprehensive code recovery experience.
                             Following this, we are happy to announce that
                             we will be implementing 2FA for all Ubuntu
                             One accounts. This change is coming in the
                             next few weeks, so keep your eyes peeled for
                             instructions on how to enable 2FA for your
                             account. With a reliable backup mode of
                             authentication, lockouts should be a thing of
                             the past.


                      # ⚓ 5_awesome_backup_services_that_support_FTP,_Rsync_and
                        SCP⠀⇛


                             Some weeks ago I wrote about backing up your
                             important files on Ubuntu to Google Drive.
                             It’s a trivial process that will save your
                             hide on the day disaster strikes. You lose
                             your laptop unexpectedly for example or you
                             fall prey to a ransomware gang as has become
                             trendy these days. But what if for some
                             reason you cannot use Google Drive? What
                             should you do?


                             I found myself in such a situation recently.
                             While in the process of trying to add a new
                             tool to my webhost, I later discovered the
                             tool was not meant for sites in Zimbabwe and
                             wanted it removed from my hosting platform. I
                             wrote an email to the web hosts support with
                             this request and the person who answered the
                             ticket was a French guy. English is not his
                             first language and he thought I wanted out of
                             their service. He wanted to delete
                             everything. I mean everything including the
                             backups they had of my sites.


                      # ⚓ Design_and_Web_team_summary_–_4_June_2021⠀⇛


                             The web team at Canonical run two-week
                             iterations building and maintaining all of
                             Canonical websites and product web
                             interfaces. Here are some of the highlights
                             of our completed work from this iteration.


                             Meet the team


                             My name is Beth Collins and I’m a Web
                             Engineer in the Web squad. We work on
                             maintaining Canonical’s sites and also some
                             web based projects. I started at Canonical in
                             September 2020, since then it’s been a steep
                             learning curve (in a good way) – with some
                             exciting projects to get my teeth stuck into.


                             I actually studied dentistry at university,
                             and worked in the field for a couple of years
                             before I realised it wasn’t for me (not your
                             usual career change – I know). But it’s
                             surprising how many similarities there are,
                             problem solving is problem solving whether
                             it’s teeth or code!


                             When I’m not working I love running, dancing
                             to old school disco music, going to
                             festivals, going climbing and the occasional
                             cold water wild swim (dip). In the past 5
                             years I’ve travelled and lived in many places
                             all over the world, including Melbourne,
                             Hanoi, India, Barcelona, but have settled and
                             now live in a small town on the border of
                             Wales called Oswestry.


          o § Devices/Embedded⠀➾


                # § Open Hardware/Modding⠀➾


                      # ⚓ Picovoice_offline_Voice_AI_engine_now_works_on
                        Arduino⠀⇛


                             Last year, I wrote about Picovoice support
                             for Raspberry Pi enabling custom wake-word
                             and offline voice recognition to control the
                             board with voice commands without relying on
                             the cloud.


                             They used ReSpeaker 4-mic array HAT to add
                             four “ears” to the Raspberry Pi SBC. I also
                             tried to generate a custom wake-word using
                             the “Picovoice Console” web interface, and I
                             was able to use “Dear Master” within a few
                             minutes on my computer. No need to provide
                             thousands of samples, or wait weeks before
                             getting a custom wake-word. It’s free for
                             personal projects.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Android_12_features_you’ll_love,_like_Quick_Tap_and_a
                        new_privacy_dashboard:_Here’s_how_they_work_–_CNET⠀⇛


                      # ⚓ The_LG_Velvet_LTE_gains_Android_11_in_South_Korea;_OS
                        upgrade_slips_for_it,_the_G8S_ThinQ_and_G8X_ThinQ_in
                        other_markets_–_NotebookCheck.net_News⠀⇛


                      # ⚓ How_to_download_Minecraft_Bedrock_Beta_versions_for
                        Android_smartphones⠀⇛


                      # ⚓ How_to_download_and_play_GTA_5′s_latest_version_on
                        Android_smartphones_through_PS_Play_in_2021⠀⇛


                      # ⚓ Android_Auto_Is_Getting_A_Little_Update_With_Many
                        Helpful_Tweaks⠀⇛


                      # ⚓ New_updates_on_the_Google_Assistant_will_make
                        controlling_your_Android_phone_through_voice_much
                        easier_than_before_/_Digital_Information_World⠀⇛


                      # ⚓ Leica_launched_its_first_Android_phone_with_a
                        revolutionary_new_camera_–_BGR⠀⇛


                      # ⚓ 10_Best_Writing_Apps_For_Android_To_Unleash_Your
                        Creativity⠀⇛


                      # ⚓ Android_Auto_update_coming_this_summer_with_new_and
                        enhanced_features_|_Autoblog⠀⇛


                      # ⚓ Lincoln_will_use_native_Android_Auto_starting_in_2023
                        –_9to5Google⠀⇛


                      # ⚓ These_40_Android_games_and_apps_are_temporarily_free
                        or_on_sale_today⠀⇛


                      # ⚓ 5_best_Android_games_like_GTA_5_available_on_low-end
                        Android_smartphones_in_2021⠀⇛


                      # ⚓ 5_Dangerous_Android_apps_that_you_should_avoid
                        downloading_on_your_mobile⠀⇛


                      # ⚓ A_security_bug_in_Google’s_Android_app_put_users’
                        data_at_risk_–_TechCrunch⠀⇛


                      # ⚓ Your_Android_phone_under_attack!_3_hidden_dangers_you
                        must_not_ignore_|_Express.co.uk⠀⇛


                      # ⚓ Android_12_gesture_bar_won’t_be_hidden_on_Pixel
                        Launcher-_9to5Google⠀⇛


                      # ⚓ Xiaomi_upgrades_the_Redmi_Note_9_Pro_to_Android_11,
                        but_holds_back_on_MIUI_12.5_for_now_–_NotebookCheck.net
                        News⠀⇛


                      # ⚓ How_to_turn_on_dark_theme_on_Android:_Step-by-step
                        guide_–_Information_News⠀⇛


                      # ⚓ How_to_Extract_a_Color_Palette_From_an_Image_on
                        Android⠀⇛


                      # ⚓ How_to_Use_Nearby_Share_on_Android_and_Chromebook⠀⇛


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


                # § Web Browsers⠀➾


                      # § Mozilla⠀➾


                            # ⚓ The_Mozilla_Blog:_What_is_the_difference
                              between_the_internet,_browsers,_search_engines
                              and_websites?⠀⇛


                                   Real talk: this web stuff can get
                                   confusing. And it’s really important
                                   that we all understand how it works, so
                                   we can be as informed and empowered as
                                   possible. Let’s start by breaking down
                                   the differences between the internet,
                                   browsers, search engines and websites.
                                   Lots of us get these four things
                                   confused with each other and use them
                                   interchangeably, though they are
                                   different. In this case, the old
                                   “information superhighway” analogy
                                   comes in handy.


                                   [...]


                                   The internet is the superhighway’s
                                   system of roads, bridges and tunnels.
                                   It is the technical network and
                                   infrastructure that connect all the
                                   computers and devices that are online
                                   together across the world. Being
                                   connected to the internet means
                                   devices, and whoever is using them, can
                                   communicate with each other and share
                                   information.


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ LibreOffice_Annual_Report_2020:_Website,_blogs_and
                        social_media⠀⇛


                # § CMS⠀➾


                      # ⚓ Blogging_with_WordPress_|_WordPress_101⠀⇛


                             Welcome back to WordPress 101 series. In this
                             series, we’re learning the basics of
                             WordPress. WordPress is used to create all
                             types of websites such as eCommerce, Forums,
                             Social networking sites, etc.


                             But majorly WordPress is known for blogging.
                             The majority of blogs on the Internet are
                             hosted by WordPress.


                # § FSF⠀➾


                      # ⚓ GNU_C_Library:_Change_of_copyright_policy_for_glibc
                        is_under_discussion⠀⇛


                      # § GNU Projects⠀➾


                            # ⚓ Rewriting_the_GNU_Coreutils_in_Rust⠀⇛


                                   As movement toward memory-safe
                                   languages, and Rust in particular,
                                   continues to grow, it is worth looking
                                   at one of the larger scale efforts to
                                   port C code that has existed for
                                   decades to Rust. The uutils project
                                   aims to rewrite all of the individual
                                   utilities included in the GNU Coreutils
                                   project in Rust. Originally created by
                                   Jordi Boggiano in 2013, the project
                                   aims to provide drop-in replacements
                                   for the Coreutils programs, adding the
                                   data-race protection and memory safety
                                   that Rust provides.


                                   Many readers will be familiar with the
                                   Coreutils project. It includes the
                                   basic file, process, and text
                                   manipulation programs that are expected
                                   to exist on every GNU-based operating
                                   system. The Coreutils project was
                                   created to consolidate three sets of
                                   tools that were previously offered
                                   separately, Fileutils, Textutils, and
                                   Shellutils, along with some other
                                   miscellaneous utilities. Many of the
                                   programs that are included in the
                                   project, such as rm, du, ls, and cat,
                                   have been around for multiple decades
                                   and, though other implementations
                                   exist, these utilities are not
                                   available for platforms like Windows in
                                   their original form.


                                   Collectively, the Coreutils programs
                                   are seen as low-hanging fruit where a
                                   working Rust-based version can be
                                   produced in a reasonable amount of
                                   time. The requirements for each utility
                                   are clear and many of the them are
                                   conceptually straightforward, although
                                   that’s not to suggest that the work is
                                   easy. While a lot of progress has been
                                   made to get uutils into a usable state,
                                   it will take some time for it to reach
                                   the stability and maturity of
                                   Coreutils.


                                   The use of Rust for this project will
                                   help to speed this process along since
                                   a huge swathe of possible memory errors
                                   and other undefined behavior is
                                   eliminated entirely. It also opens the
                                   door to the use of efficient, race-free
                                   multithreading which has the potential
                                   to speed up some of the programs under
                                   certain conditions. The uutils rewrite
                                   also provides an opportunity to not
                                   just reimplement Coreutils but to also
                                   enhance the functionality of some of
                                   the utilities to yield a better user
                                   experience, while maintaining
                                   compatibility with the GNU versions.
                                   For example, feature requests that have
                                   long been rejected in the Coreutils
                                   project, like adding a progress bar
                                   option for utilities like mv and cp,
                                   are currently being entertained in this
                                   Rust rewrite.


                            # ⚓ 2021-6:_SUERF_Policy_Brief_“How_to_issue_a
                              privacy-preserving_central_bank_digital_currency”
                              published⠀⇛


                                   We are happy to announce the
                                   publication of our policy brief on “How
                                   to issue a privacy-preserving central
                                   bank digital currency” by The European
                                   Money and Finance Forum.


                                   Many central banks are currently
                                   investigating Central Bank Digital
                                   Currency (CBDC) and possible designs. A
                                   recent survey conducted by the European
                                   Central Bank has found that both
                                   citizens and professionals consider
                                   privacy the most important feature of a
                                   CBDC. We show how a central bank could
                                   issue a CBDC that would be easily
                                   scalable and allow the preservation of
                                   a key feature of physical cash:
                                   transaction privacy. At the same time
                                   the proposed design would meet
                                   regulatory requirements and thus offer
                                   an appropriate balance between privacy
                                   and legal compliance.


                            # ⚓ gdbm_@_Savannah:_Version_1.20⠀⇛


                                   Version 1.20 is available for download.


                # § Openness/Sharing/Collaboration⠀➾


                      # ⚓ “Free_Software_and_Open_Science”_marks_the_XVI
                        International_Congress_of_Scientific_Research⠀⇛


                             The Ministry of Higher Education, Science and
                             Technology (MESCYT) held the XVI
                             International Congress of Scientific Research
                             on “Free Software and Open Science”, an
                             annual symposium to which this year national
                             and international experts with vast
                             experience were invited in the publication
                             and dissemination of both topics.


                             These are conceptually articulated in the
                             open knowledge (open knowledge).


                             The event was held on June 9, 10 and 11 under
                             the direction of Dr. Manuel Madé, researcher
                             professor and coordinator of management and
                             scientific dissemination of the Technological
                             Institute of Santo Domingo (INTEC).


                # § Programming/Development⠀➾


                      # ⚓ Modelplace.AI_is_an_app_store_for_OpenCV_compatible
                        AI_models⠀⇛


                             OpenCV open-source computer vision library is
                             used in a wide variety of projects and
                             products, and last year, the community also
                             launched the OpenCV AI Kit (OAK) Myriad X-
                             based hardware solution for computer vision.


                             However there’s a learning curve to use the
                             library, especially in combination with
                             artificial intelligence models, and it can be
                             challenging and time-consuming to newcomers.
                             So in order to broaden the reach of the
                             solution, OpenCV has now introduced
                             Modelplace.AI, an app store/marketplace for
                             AI models working with the OpenCV library.


                      # § Perl/Raku⠀➾


                            # ⚓ vrurg:_A_Long_Promised_Article_About_Roles⠀⇛


                                   A while ago I promised a couple of
                                   people an article about Raku roles. To
                                   be frank, it was a long time ago. The
                                   plan was to cover a number of other
                                   subjects needed to better understand a
                                   few concepts behind the role model
                                   implementation in Rakudo.


                                   Unfortunately, it turned out to be one
                                   of those perfect examples of the
                                   principle: “wanna make the God laugh?
                                   tell him your plans!” But promise is
                                   promise and a few days ago the WTF mood
                                   took me over, all actual tasks were
                                   pushed back, and my note-taking app was
                                   ready for a new draft.


                      # § Python⠀➾


                            # ⚓ When_and_how_to_evaluate_Python_annotations⠀⇛


                                   Annotations in Python came late to the
                                   party; they were introduced in Python 3
                                   as a way to attach information to
                                   functions describing their arguments
                                   and return values. While that mechanism
                                   had obvious applications for adding
                                   type information to Python functions,
                                   standardized interpretations for the
                                   annotations came later with type hints.
                                   But evaluating the annotations at
                                   function-definition time caused some
                                   difficulties, especially with respect
                                   to forward references to type names, so
                                   a Python Enhancement Proposal (PEP) was
                                   created to postpone their evaluation
                                   until they were needed. The PEP-
                                   described behavior was set to become
                                   the default in the upcoming Python 3.10
                                   release, but that is not to be; the
                                   postponement of evaluation by default
                                   has itself been postponed in the hopes
                                   of unwinding things.


                      # § Rust⠀➾


                            # ⚓ Supporting_Miguel_Ojeda’s_Work_on_Rust_in_the
                              Linux_Kernel [Ed: Pushing_more_Microsoft-
                              connected_frameworks as requirements for
                              compiling Linux]⠀⇛


                                   ISRG’s Prossimo project for memory
                                   safety aims to coordinate efforts to
                                   move the Internet’s critical software
                                   infrastructure to memory safe code.
                                   When we think about what code is most
                                   critical for today’s Internet, the
                                   Linux kernel is at the top of the list.
                                   Bringing memory safety to the Linux
                                   kernel is a big job, but the Rust for
                                   Linux project is making great progress.
                                   We’re pleased to announce that we
                                   started formally supporting this work
                                   in April 2021 by providing Miguel Ojeda
                                   with a contract to work on Rust for
                                   Linux and other security efforts full
                                   time for one year. This was made
                                   possible through financial support from
                                   Google. Prior to working with ISRG,
                                   Miguel was undertaking this work as a
                                   side-project. We are happy to do our
                                   part in supporting digital
                                   infrastructure by enabling him to work
                                   full-time on it.


                                   We’ve worked closely with Dan Lorenc,
                                   Software Engineer at Google to make
                                   this collaboration possible. “Google
                                   has found time after time that large
                                   efforts to eliminate entire classes of
                                   security issues are the best
                                   investments at scale. We understand
                                   work in something as widely used and
                                   critical as the Linux kernel takes
                                   time, but we’re thrilled to be able to
                                   help the ISRG support Miguel Ojeda’s
                                   work dedicated to improving the memory
                                   safety of the kernel for everyone,” Dan
                                   said.


                            # ⚓ Supporting_Miguel_Ojeda’s_Work_on_Rust_in_the
                              Linux_Kernel_(Prossimo_blog)⠀⇛


                                   The Prossimo project has announced that
                                   it has contracted with Miguel Ojeda to
                                   work on Rust in the Linux kernel for
                                   the next year. Prossimo is a new name
                                   for the memory-safety projects being
                                   run by the Internet Security Research
                                   Group (ISRG), which is the organization
                                   behind the Let’s Encrypt certificate
                                   authority (CA) project. Google provided
                                   the funds to enable Ojeda to work full-
                                   time on the project starting back in
                                   April.


                            # ⚓ Google-backed_Linux_project_could_make_Android,
                              Chrome_OS_harder_to_hack⠀⇛


                                   Google said Thursday it’s funding a
                                   project to increase Linux security by
                                   writing parts of the operating system’s
                                   core in the Rust programming language,
                                   a modernization effort that could
                                   bolster the security of the internet
                                   and smartphones.


                                   If the project succeeds, it’ll be
                                   possible to add new elements written in
                                   Rust into the heart of Linux, called
                                   the kernel. Such a change would mark a
                                   major technological and cultural shift
                                   for an open-source software project
                                   that’s become foundational to Google’s
                                   Android and Chrome operating systems as
                                   well as vast swaths of the internet.


                            # ⚓ Google_Backs_Linux_Project_To_Make_Android,
                              Chrome_OS_Harder_To_Hack⠀⇛


                            # ⚓ Google_Wants_To_See_Rust_Code_In_The_Linux
                              Kernel,_Contracts_The_Main_Developer⠀⇛


                                   Google wants to see Rust programming
                                   language support within the Linux
                                   kernel so much so that they have
                                   contracted the lead developer working
                                   on “Rust for Linux” as the work aims to
                                   get mainlined.


                                   Google is going public today with their
                                   formal support for Rust in the Linux
                                   kernel to enhance memory safety and
                                   that they have contracted developer
                                   Miguel Ojeda to further his work on
                                   Rust for the Linux kernel and related
                                   security efforts. This contract is
                                   going through at least the next year.


          o § Standards/Consortia⠀➾


                # ⚓ ZFS_fans,_rejoice—RAIDz_expansion_will_be_a_thing_very
                  soon⠀⇛


                       OpenZFS founding developer Matthew Ahrens opened a
                       PR for one of the most sought-after features in ZFS
                       history—RAIDz expansion—last week. The new feature
                       allows a ZFS user to expand the size of a single
                       RAIDz vdev. For example, you can use the new
                       feature to turn a three-disk RAIDz1 into a four,
                       five, or six RAIDz1.


                       FURTHER READING
                       ZFS 101—Understanding ZFS storage and performance
                       OpenZFS is a complex filesystem, and things are
                       necessarily going to get a bit chewy explaining how
                       the feature works. So if you’re a ZFS newbie, you
                       may want to refer back to our comprehensive ZFS 101
                       introduction.


                # ⚓ Explainer:_What_is_an_API?_|_TechSpot⠀⇛


                       Direct3D. OpenAL. Winsock. You’ve probably heard of
                       these, you might have even used them before, but
                       one thing is certain: everyone who’s ever used a
                       computer will have run a piece of software that’s
                       made good use of them.


                       We’re talking about APIs — the golden fleece to
                       programmers around the world. Join us as we explain
                       just what an API is, and take a quick look at where
                       and how they get used.


                # ⚓ W3C_Promotes_Web_Audio_API_To_Official_Standard⠀⇛


                       The W3C has promoted the Web Audio API to now being
                       an official standard as a JavaScript API for
                       creating and manipulating audio content directly
                       within web browsers.


                       The W3C sums up the Web Audio API as “a JavaScript
                       API for creating, shaping, and manipulating sounds
                       directly in a Web browser. It is already widely
                       deployed for the creation of music and sound
                       effects on Web pages, for the creation of online
                       musical instruments, for Web games, and for
                       collaborative artworks such as sound
                       installations.”


                       The Web Audio API is focused on creation and
                       manipulation of audio rather than just audio
                       playback. The Web Audio API was also engineered to
                       support collaborative, multi-user environments.


    * § Leftovers⠀➾


          o ⚓ Episode_35,_screenshot_before_release⠀⇛


                 Tomorrow will be the release of Pepper&Carrot episode 35!
                 🥳 I’m currently working on the final details of this big
                 episode. Here is a sneak peek into page 1.


          o § Science⠀➾


                # ⚓ Your_spacesuit_ran_into_a_problem_and_needs_to_restart⠀⇛


                       There are two things a spacewalker doesn’t want to
                       hear: “Can you turn it off and turn it on again?”
                       and “What’s that hissing sound?”


                       The IT solution of the ancients reached orbit
                       yesterday as one of a pair of astronauts tasked
                       with fitting a new solar array to the International
                       Space Station (ISS) had to make his way back to the
                       airlock in order to restart his spacesuit.


                       NASA astronaut Shane Kimbrough was not in any great
                       danger during what the US space agency delicately
                       called an “issue” with his spacesuit’s display and
                       control module (designed to provide a spacewalker
                       with information on the status of the suit).
                       Controllers also noted a spike in the pressure
                       reading for his sublimator (used to keep things
                       cool) and so sent the astronaut back to the airlock
                       to perform a restart.


          o § Health/Nutrition⠀➾


                # ⚓ Amy_Coney_Barrett,_Trump’s_controversial_final_Supreme
                  Court_pick,_votes_to_uphold_Obamacare⠀⇛


                # ⚓ Antibody_drug_cuts_deaths_for_some_severe_COVID_patients:
                  study⠀⇛


          o § Integrity/Availability⠀➾


                # ⚓ You_had_one_job:_Akamai’s_Prolexic_Denial-of-Service
                  protection_system_fingered_after_users_in_Australia_denied,
                  er,_services⠀⇛


                       A wide range of internet-connected services in
                       Australia, including banking systems, are
                       experiencing an outage – and it looks like a hiccup
                       at Akamai was at the heart of the problem.


                       Reports of issues with news sites, gaming services,
                       and – more critically – banking systems began to
                       spread on Australian social media early Thursday
                       afternoon local time. Uptime-tracking service
                       Downdetector concurred, showing a massive spike in
                       issues at Commonwealth Bank, Westpac, Bankwest,
                       St.George Bank, Bank Australia, Bank of Melbourne,
                       and others.


                # § Proprietary⠀➾


                      # ⚓ Microsoft_loves_Linux_so_much_that
                        packages.microsoft.com_has_fallen_and_can’t_get_up⠀⇛


                             Microsoft demonstrated its deep and
                             meaningful affection for all things penguin
                             overnight by borking packages.microsoft.com
                             and leaving some Linux fans bereft of the
                             company’s wares.


                             For some of the hardcore, an absence of
                             Microsoft software on their fiercely open-
                             source setups might not be such a bad thing.
                             For others, however, getting a 404 from an
                             apt-get is a major workflow blocker.


                             The issue looks, at first glance, to be
                             related to the Ubuntu paths as users
                             struggled with the likes of Microsoft’s
                             OpenJDK and its flagship .NET platform.


                             ODBC packages were also borked, as well as
                             the package link for Visual Studio Code and
                             even poor old Microsoft Edge.


                             Microsoft has yet to respond to our request
                             for more information, although a software
                             engineer at the Windows behemoth, Rahul
                             Bhandari, posted on GitHub: “Our infra team
                             is still working to resolve this issue. They
                             ran into some space issues but this issue
                             should be resolved quickly. Unfortunately, I
                             do not have an ETA yet.”


                      # ⚓ Microsoft’s_Linux_repositories_were_down_for_18+
                        hours_|_Ars_Technica⠀⇛


                             Yesterday, packages.microsoft.com—the
                             repository from which Microsoft serves
                             software installers for Linux distributions
                             including CentOS, Debian, Fedora, OpenSUSE,
                             and more—went down hard, and it stayed down
                             for around 18 hours. The outage impacted
                             users trying to install .NET Core, Microsoft
                             Teams, Microsoft SQL Server for Linux (yes,
                             that’s a thing) and more—as well as Azure’s
                             own devops pipelines.


                             We first became aware of the problem
                             Wednesday evening when we saw 404 errors in
                             the output of apt update on an Ubuntu
                             workstation with Microsoft Teams installed.
                             The outage is somewhat better-documented at
                             this .NET Core issue report on Github, with
                             many users from all around the world sharing
                             their experiences and theories.


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation⠀➾


                                        # ⚓ Linux_Foundation_Announces_Software
                                          Bill_of_Materials_(SBOM)_Industry
                                          Standard,_Research,_Training,_and
                                          Tools_to_Improve_Cybersecurity
                                          Practices⠀⇛


                                        # ⚓ Linux_Foundation_Announces_Software
                                          Bill_of_Materials_(SBOM)_Industry
                                          Standard,_Research,_Training,_and
                                          Tools_to_Improve_Cybersecurity
                                          Practices⠀⇛


                                               The Linux Foundation, the
                                               nonprofit organization
                                               enabling mass innovation
                                               through open source, today
                                               announced new industry
                                               research, training, and
                                               tools – backed by the SPDX
                                               industry standard – to
                                               accelerate the use of a
                                               Software Bill of Materials
                                               (SBOM) in secure software
                                               development.


                                        # ⚓ Linux_Foundation_Advances_Adoption
                                          Of_Software_Bill_Of_Materials⠀⇛


                                               The Linux Foundation has
                                               announced new industry
                                               research, a new training
                                               course, and new software
                                               tools – backed by the SPDX
                                               industry standard – to
                                               accelerate the use of
                                               Software Bill of Materials
                                               (SBOMs) in development.


                                        # ⚓ Free_Training_Course_Explores
                                          Software_Bill_of_Materials⠀⇛


                                               At the most basic level, a
                                               Software Bill of Materials
                                               (SBOM) is a list of
                                               components contained in a
                                               piece of software. It can
                                               be used to support the
                                               systematic review and
                                               approval of each
                                               component’s license terms
                                               to clarify the obligations
                                               and restrictions as it
                                               applies to the distribution
                                               of the supplied software.
                                               This is important to
                                               reducing risk for
                                               organizations building
                                               software that uses open
                                               source components.


                      # § Security⠀➾


                            # ⚓ Security_updates_for_Thursday⠀⇛


                                   Security updates have been issued by
                                   CentOS (gnupnp and postgresql), Fedora
                                   (dino, microcode_ctl, and xen), Mageia
                                   (apache, gsoap, libgd, openssh, perl-
                                   Image-ExifTool, python-bleach, and qt4
                                   and qtsvg5), openSUSE (chromium,
                                   containerd, docker, runc, djvulibre,
                                   htmldoc, kernel, libjpeg-turbo,
                                   libopenmpt, libxml2, spice, squid, and
                                   ucode-intel), Red Hat (dhcp and glib2),
                                   SUSE (apache2, inn, java-1_8_0-openjdk,
                                   and webkit2gtk3), and Ubuntu (nettle).


                            # ⚓ UChecker_Linux_Security_Tool_Released⠀⇛


                                   UChecker is part of KernelCare, a live
                                   patching solution for Linux kernels,
                                   which now rolls up under the company’s
                                   TuxCare offerings. TuxCare, which is
                                   specifically targeted for enterprises,
                                   puts the CloudLinux products
                                   KernelCare, Extended Lifecycle Support,
                                   and Linux Support Services all under
                                   one roof.


                            # ⚓ Open_source_UChecker_tool_detects_vulnerable
                              libraries_on_Linux_servers⠀⇛


                                   CloudLinux announced UChecker, a free
                                   open source tool that scans Linux
                                   servers for vulnerable libraries that
                                   are outdated and being used by other
                                   applications. This provides detailed
                                   actionable information regarding which
                                   application is using which vulnerable
                                   library and needs to be updated, which
                                   helps improve the security awareness
                                   patching process.


                            # ⚓ How_To_Protect_Your_Computer_From_Viruses,
                              Hackers,_And_Surveillance⠀⇛


                                   Is your computer safe? How can you
                                   protect your operating system? Should
                                   you cover your laptop camera?


                                   In this article, we teach you how to
                                   secure your device, whether you are a
                                   Windows user or a Mac user. Or you run
                                   GNU/Linux on your system.


                                   An operating system is an interface
                                   between software and hardware. It
                                   performs various tasks such as file
                                   management, process management and
                                   memory management.


                            # ⚓ IoT_Supply_Chain_Bug_Hits_Millions_of_Cameras⠀⇛


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ Papa_don’t_breach:_UK_data_watchdog_fines
                                    that_other_pizza_place_£10,000_over
                                    unsolicited_marketing_blitz⠀⇛


                                         Pizza takeaway and delivery
                                         outfit Papa John’s has been fined
                                         £10,000 by the UK’s data watchdog
                                         for sending marketing fluff to
                                         punters without their say-so.


                                         Following a year-long
                                         investigation, the Information
                                         Commissioner’s Office (ICO) found
                                         that the company had sent 168,022
                                         “nuisance marketing messages to
                                         its customers without the valid
                                         consent required by law.”


                                         One of the unnamed complainants
                                         said they had “never [given
                                         their] consent for marketing text
                                         messages” resulting in
                                         “distress.”


                                         Another said they had received
                                         almost 100 messages in what was
                                         described as the “textbook
                                         definition of harassment.”


                                  # ⚓ Amazon_Sidewalk:_Open_Your_Wi-Fi_To_The
                                    Public⠀⇛


          o § Finance⠀➾


                # ⚓ El_Salvador_seeing_influx_of_Bitcoiners_and_Bitcoins,_but
                  some_predict_disaster_–_Stockhead⠀⇛


                       British podcaster Peter McCormack has declared that
                       El Salvador’s adoption of Bitcoin is the “real
                       deal” after meeting with President Nayib Bukele in
                       the presidential palace.


          o § Misinformation/Disinformation⠀➾


                # ⚓ Amazon_Blames_Social_Media_for_Spreading_Fake_Reviews⠀⇛


                       If you’re a regular customer of Amazon, you’re
                       fully aware of the fake reviews. They are sometimes
                       obviously fake. After removing its third recent
                       major company from its online storefront, Amazon is
                       laying the blame for the fake reviews at the feet
                       of social media


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ BT_sues_supplier_for_£72m_over_exchange_gear_that_allegedly
                  caused_wave_of_ADSL_outages_•_The_Register⠀⇛


                       BT is suing a supplier for £72m after it delivered
                       nearly 100,000 defective landline connection blocks
                       that caused ADSL broadband outages, London’s High
                       Court has heard.


                       Legal filings reveal that Tii Technologies is said
                       to have supplied 95,000 faulty jack test (JT)
                       blocks to BT over a period spanning 2006-2016. The
                       one-time state monopoly claims these faulty blocks
                       led to a spate of ADSL outages in the mid-2010s
                       that mainly affected Sky Broadband’s customers –
                       and cost BT more than £40m in engineer callouts to
                       trace the problem’s cause.


                # ⚓ Complicated_Changes_Confuse_Concerned_Citizens⠀⇛


                       I tossed that one-liner out there in an interview
                       earlier today. It shows that I’ve been following
                       the news a wee bit. There’s been more going on that
                       directly impacts my situation than I like.


                       Previously I have mentioned that I participate in
                       Ashtabula County’s broadband task force. That’s an
                       effort by the county government to try to improve
                       economic development by improving part of our local
                       infrastructure. It has been mentined by local
                       public radio stations looking at how we have
                       problems with broadband in my local area as
                       recently as March of this year.


                       That is why a report from Ars Technica by Jon
                       Brodkin might have been confusing to some folks out
                       there that saw it today. If anything I am still
                       baffled by the situation especially when I learned
                       of it on Wednesday from local media sources. Mr.
                       Brodkin reported that the state legislature is
                       proposing to outlaw municipal broadband in Ohio
                       while also prohibiting the continued operation of
                       municipal broadband efforts like FairlawnGig that
                       already exist. Ohio News Connection/Public News
                       Service also talks about the situation a bit.


                       Due to the offices of my local state representative
                       and local state senator not being very responsive
                       to any contacts I have not reached out to them.
                       They’re both first-term backbenchers. Nobody in the
                       statehouse press corps has been able to track down
                       who sponsored this particular provision in the
                       omnibus budget bill required to be passed by June
                       30th to cover the biennium.


                # ⚓ Xen_IRC_channels_have_moved⠀⇛


                       Due to circumstances, all Xen subprojects have now
                       moved their IRC channels off of Freenode.


                       The following channels have been moved to OFTC:
                       #xendevel, #xen, #xeninfra #xcp-ng, #xcp-ng-dev.
                       #mirage has moved to Libera Chat.


          o § Monopolies⠀➾


                # ⚓ FTC_approves_$61.7m_settlement_with_Amazon_for_pocketing
                  driver_tips_•_The_Register⠀⇛


                       The US Federal Trade Commission on Friday announced
                       the approval a consent order against Amazon that
                       requires the company to pay $61.7m to resolve
                       charges that for two and a half years it took tips
                       intended for Amazon Flex drivers and concealed the
                       diversion of funds.


                       The deal was proposed in February but required
                       sign-off from the US trade watchdog. It arises from
                       FTC charges that Amazon misrepresented both to
                       Amazon Flex drivers and to the public what the
                       company would pay for delivery work.


                # § Patents⠀➾


                      # ⚓ How_Patent_Extensions_Keep_Some_Drug_Costs_High⠀⇛


                             PRITI KRISHTEL’S first case as a legal aid
                             lawyer in India was as tragic as they come.
                             One day in 2004, she recalls a couple walking
                             into her office in Bengaluru with their three
                             children. Unable to afford life-saving
                             medicine to keep their HIV infections in
                             check, the parents were dying of AIDS. With
                             no other options, they wanted Krishtel to
                             draw up guardianship transfer papers: The
                             rambunctious siblings were to be sent to an
                             orphanage before their parents died.


                             Even though drugs that could save the
                             parents’ lives were available, the cost at
                             the time was out of reach for the couple, who
                             were living in poverty. Krishtel and the
                             collective of lawyers she was working with at
                             the time went on to handle many similar
                             cases. By 2007, she came up with a strategy
                             to slash the cost of HIV drugs in India: On
                             behalf of patients’ rights groups, lawyers
                             with the nonprofit Initiative for Medicines,
                             Access, and Knowledge (I-MAK) she had
                             cofounded would challenge specific patent
                             applications on brand-name drugs, opening
                             opportunities for generic manufacturers.
                             Through a combination of patent expirations
                             and legal challenges, price competition in
                             India drove down the cost of the most common
                             HIV therapy by more than 80 percent between
                             2003 and 2008.


                      # ⚓ European_Commission_cheated_Unitary_Patent’s_Impact
                        Assessment_to_hide_its_high_costs_for_SMEs⠀⇛


                             FFII has received a testimony that the
                             European Commission has recycled an old
                             Impact Assessment (IA) of the Unified Patent
                             Court (UPC), in order to hide the
                             controversial self-financed aspect of the
                             Court, which is why the Court is too
                             expensive for SMEs. Countries are ratifying
                             this dangerous treaty without any real Impact
                             Assessment of the new Court system which will
                             exclude most SMEs with its super high costs.
                             The Impact Assessment was recycled from old
                             treaty project of 2009, the UPLS, with lots
                             of changes in the meantime, similar to what
                             happened recently with the recycling of the
                             Impact Assessment of the Mercosur treaty.


                             [...]


                             Around early 2012, after some requests to
                             redo the impact assessment by the Scrutiny
                             committee of the British parliament, the
                             representative of the European Commission
                             Margot Frohlinger apparently refused to
                             procure an updated one, according to a
                             testimony we received she did not want to
                             “redo the impact assessment because it would
                             attract critics”. After taking this decision
                             at the European Commission, she left to
                             continue her career at the European Patent
                             Office (EPO), the other self-financed
                             administration that will grant the Unitary
                             Patent.


                             A self-financed patent court is
                             controversial, because the cost is passed on
                             to companies that litigate in front of the
                             court, and no courts in Europe have a self-
                             financed objective (Art36.3 UPCA “the
                             objective of a self-financing Court”), as
                             courts are not companies and should not be
                             driven by financial targets to guarantee the
                             integrity of the justice system. If courts
                             are driven by profit, judges will tend to
                             apply “patent maximalism” just to guarantee
                             their salary.


                      # § Software Patents⠀➾


                            # ⚓ EPO_approach_to_examining_computer_implemented
                              inventions [Ed: Heli_Pihlajamaa_(known_inside_EPO
                              as_“Ms_Pyjamas”) is promoting illegal software
                              patents]⠀⇛


                                   On Tuesday 25 May 2021, Heli
                                   Pihlajamaa, director of patent law at
                                   the European Patent Office, gave a
                                   presentation to CIPA’s computer
                                   technology committee on the
                                   Patentability of computer-implemented
                                   inventions after the Enlarged Board of
                                   Appeal’s decision in G 1/19.


                                   G 1/19 relates to the assessment of
                                   inventive step in relation to computer-
                                   implemented simulations and considered
                                   whether to have a technical effect, a
                                   simulation must have a direct link to
                                   physical reality going beyond its
                                   implementation on a computer.


                                   In the presentation, Pihlajamaa
                                   discussed how the decision of G 1/19
                                   emphasised that the approach in T 641/
                                   00 applies to all computer implemented
                                   inventions including simulations. In T
                                   641/00 it was decided that while a
                                   claim can have a mix of technical and
                                   non-technical features, novelty and
                                   inventive step can only be based on the
                                   technical features. In T 641/00 it was
                                   also stated that when assessing
                                   inventive step, the claim should solve
                                   a technical problem which the skilled
                                   person in the particular technical
                                   field might be asked to solve.


                # § Trademarks⠀➾


                      # ⚓ European_Intellectual_Property_Office_Announces_That
                        Its_Official_ERegister_Is_Now_Live [Ed: It’s a
                        trademark office, not “Intellectual Property Office”,
                        and it_is_profoundly_corrupt]⠀⇛


                             One year after the launch of its beta
                             version, the first official eRegister is now
                             live. eRegister allows access to historical
                             records of EU trade marks and registered
                             Community designs and allows users to see
                             what information has been changed, when it
                             was changed and why it was changed.


                             [...]


                             In addition, the record of any given IP
                             right, including its history, can be
                             downloaded free of charge as a certified
                             copy. Records downloaded from eRegister are
                             deemed to be authentic extracts from the EUTM
                             and RCD Registers, and can be verified
                             online.


                             eRegister can be accessed via the EUIPO’s
                             search tool eSearch plus. Users will first
                             need to search for a particular trade mark or
                             design and then click on the eRegister button
                             located towards the top right-hand corner of
                             their screens.


                # § Copyrights⠀➾


                      # ⚓ Roger_Waters_tells_Facebook_CEO_to_Zuck_off_after
                        ‘huge’_song_rights_request_•_The_Register⠀⇛


                             Grouchy former Pink Floyd bassist/vocalist
                             Roger Waters launched an expletive-laden
                             attack on human-impersonating Facebook CEObot
                             Mark Zuckerberg after receiving a request
                             from Instagram to use one of his songs in a
                             promotional film.


                             Speaking at an event in New York to advocate
                             for the release of Julian Assange, Waters
                             held up a printed piece of paper he said he
                             received “on the internet this morning”,
                             which included a request to use the Pink
                             Floyd song ‘Another Brick In The Wall (Part
                             2)’ in exchange for what Waters described as
                             “a huge, huge amount of money.”


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