𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, November 25, 2024
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Generated Tue 26 Nov 02:49:20 GMT 2024
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/2024/11/25/


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

QmbHjgPAAcGNUG9Sej4vSKhK8DfUYokfFkXLdKwr1JtGJG
QmdLsuRLzrwb58dZaSmJah6oCmNNZ6cW4ick4chqJmHjmY
QmTNR3uqcbMYjPAbbHjBqyNJb3ib8kytQvdFnATzkBFVvo
QmfCHrqMLfMsHXYnQeAvVuNYt91Zw2AmMJ5mx4RqsrWy3b
QmR2rr1yXDANjQBEz2oGtd2UMgy9U37FHdjpUhPfAk7h5z
QmWE6ucdKk9Q1pi6ce3ko9xPWd9Y4BjpLij3W7tJ5TMjG3
QmaoEDiALTYYZdaq3SQ86aQpMwUji1nqCeLbXAoszFRYvJ
QmSTkZUY74BcgbgqS6JKwwNbVnbzY5uqwpgWtYonGJua8s
QmXZcp3rXLYa24pYd7jUu6sPDrhziRCNCok875WLJTLysP
QmUE7nd24kx2soZFbSYKDsb1ik1wpirFTRTBhDTj6w9sjh
QmdKeWBhfnjgQLYU48wto7DdStpXsB5mE1yEEnWcxQ53vu
QmfSnnTnjcAe3YvtRsVgAwUJfpcEk1dM5J5yjJLyv7MxqM
QmQ16CkpxBbMzPZ6wZcuKBUcxH1RZ8uAEhcvdBsPRpVZe9
QmT3gTQRv33wEDtJveL8DiqiacGeRaxEbRFDUyVSJEAvDL
QmTs9qcwghZPs5oBh9qzsu8a11T4s6xHrJjVNyk5miFy3X
Qmdqd6mb8mj27qVvQZRR7sjshrXYYirWm9vRttLkNB5rW6
QmSjY85vxbu9nNFHUMmuK7CxRame2VYuhb523CJaK5zRkj
QmZwah9nZHVvSzbJWEAMxumYDpanFPqTahnqoNP83tuZbx
QmQWSrGfeYwgf6HE9N3742DJrJwq8uNSCUAz469CnuUFGe
QmcgTTyseF5zFd4MLquM4PtJZzkFcBEqaUbqDe4eaUx6Na
QmZMEFKvpgvjxAcV9Pwu7yF74LYZwS7ktdLFdYb988Ncfu


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

⦿ Techrights  -  BetaNews is Run and Written by Bots That Make Clickbait

⦿ Techrights  -  IRC Proceedings: Sunday, November 24, 2024

⦿ Techrights  -  Latest Mass Layoffs at Microsoft Are Confirmed, Bing and Vista 11 Losing Market Share

⦿ Techrights  -  [Meme] Microsoft: Our "Hey Hi" Hype is Going So Well That We Have MASS Layoffs Every Month. Makes Sense?

⦿ Techrights  -  On Groupthink, Mindless 'Sheep', and Toxic Online Cults

⦿ Techrights  -  Over at Tux Machines...

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/11/25/BetaNews_is_Run_and_Written_by_Bots_That_Make_Clickbait.shtml
https://techrights.org/n/2024/11/25/IRC_Proceedings_Sunday_November_24_2024.shtml
https://techrights.org/n/2024/11/25/Latest_Mass_Layoffs_at_Microsoft_Are_Confirmed_Bing_and_Vista_1.shtml
https://techrights.org/n/2024/11/25/Meme_Microsoft_Our_Hey_Hi_Hype_is_Going_So_Well_That_We_Have_MA.shtml
https://techrights.org/n/2024/11/25/On_Groupthink_Mindless_Sheep_and_Toxic_Online_Cults.shtml
https://techrights.org/n/2024/11/25/Over_at_Tux_Machines.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/11/25/Gemini_Links_25_11_2024_Purity_and_Cory_Doctorow_s_Ulysses_Pact.shtml
https://techrights.org/n/2024/11/25/Links_25_11_2024_Climate_News_Daniel_Pocock_Receives_a_Fake_Fra.shtml
https://techrights.org/n/2024/11/25/Links_25_11_2024_Egypt_Harasses_Bloggers_The_University_of_Mich.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 64

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/25/BetaNews_is_Run_and_Written_by_Bots_That_Make_Clickbait.shtml
    Gemini version at https://techrights.org/n/2024/11/25/BetaNews_is_Run_and_Written_by_Bots_That_Make_Clickbait.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ BetaNews is Run and Written by Bots That
Make Clickbait⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 25, 2024,
updated Nov 25, 2024


                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇BetaNews,_Inc.⦈_


At least one author is doing this:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Brian_Fagiol_=_Microsoft_LLM_spam_(slop),_Microsoft_spew_or
                             PR,_Microsoft_hype⦈_


The latest two stories in the entire Web site!! They're both fake! Aside from
marketing spam for products they're producing botspam. That site is basically
DONE.


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Chess,_the_age-old_strategy_game,_continues_to_inspire
advancements_in_artificial_intelligence._Google,_known_for_its_AI_breakthroughs
like_AlphaZero,_has_used_chess_as_a_proving_ground_for_cutting-edge_technology.
   AlphaZero_famously_taught_itself_to_master_chess_without_prior_knowledge,
 showcasing_AI’s_potential_for_creative_problem-solving._This_innovation_even
   extends_beyond_games,_influencing_real-world_projects_like_AlphaFold_for
       protein_structures_and_AlphaDev_for_discovering_new_algorithms.⦈_


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


The_"Trump"_piece_is_also_slop.


Also see: BetaNews_Has_Become_a_SPAM/Slop_Factory,_Brian_Fagioli_Publishes_Fake
'Articles' | It's_Morbid_to_Talk_About_Living_People_as_If_They're_Dead |
BetaNews,_Inc._Became_a_Spam_Operation/Web_Site,_LLM_Spew_(Slop)_for_SEO
Disguised_as_"Articles" | BetaNews_is_Beta-Testing_the_Site_as_LLM_Slop_With
Microsoft_Propaganda_Thrown_In | Even_the_Managing_Editor_of_BetaNews_is_Doing
Slop_and_Spam | At_BetaNews,_"Most_Commented_Story"_Is_Not_a_Story_But_LLM
Slop!_(Readers_Talking_to_Bots)




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⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠘⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣴⣦⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡻⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠉⠀⠀⢻⣿⣿⣿⣿⠫⢍⡟⣻⣽⣛⡿⣟⢿⣿⢩⣭⣟⣻⢟⡛⣯⢟⡻⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⡏⣭⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠁⡄⠉⠀⣺⣿⣿⣿⣿⣾⣧⣷⣧⣧⣧⣧⣿⣿⣯⣿⣿⣼⣽⠼⣱⣽⣼⣵⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣻⣻
⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠈⠐⠆⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⡿⢛⢿⠟⠙⢻⡿⡟⣿⡟⠟⡿⣿⢿⡛⡛⡿⡟⣿⠛⣿⠿⢻⣿⡟⠛⣿⡝⢹⡿⣿⠟⣿⠿⣿⠏⣿⣿⡟⢻⡿⡛⡻⢻⣿⢿⠛⣿⡿⡛⢿⡿⣿⠟⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⢿⣿⡿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠚⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠡⢸⣿⣲⠾⡿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣟⣻⣩⣿⣟⣻⣿⣽⣿⣍⣯⣹⣛⣻⣟⣫⣫⣿⣿⣛⣟⣟⣻⣻⣻⣻⣟⣟⣿⣟⣻⣯⣛⣿⣻⣿⣯⣿⣯⣯⣋⣽⣿⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣹⣹⣛⣟⣿⣛⣟⣿⣹⣿⣻⣛⣻⣿⣟⣿⣹⣯⣻⣙⣻⣟⣍⣿⣻⣻⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣻⣹⣻⣟⣟⣻⣿⡇⠀⠀⠀⣠⣶⡾⠙⢿⣶⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣏⣏⣿⣙⣭⣹⣍⣏⣻⣍⣏⣍⣏⣫⣽⣍⣿⣯⣹⣹⣯⣉⣯⣩⣹⣙⣟⣍⣩⣏⣻⣩⣽⣭⣭⣿⣏⣟⣏⣍⣉⣽⣯⣽⣭⣯⣹⣿⡇⠀⠀⣾⣿⣿⣿⠀⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣯⣿⣽⣽⣽⣿⣭⣽⣽⣯⣯⣭⣽⣽⣯⣭⣽⣭⣯⣽⣽⣽⣿⣽⣽⣽⣽⣯⣭⣏⣽⣽⣭⣭⣿⣭⣿⣿⣭⣯⣯⣿⣿⣿⣿⣿⣿⡧⠦⠞⠛⢻⡿⠿⠀⢿⡏⡏⠛⠃⠀⢤⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣽⣯⣽⣽⣍⣿⣿⣿⣯⣽⣭⣭⣭⣯⣯⣽⣯⣽⣯⣭⣭⣯⣯⣿⣩⣽⣯⣏⣿⣿⣽⣻⣿⣽⣭⣯⣯⣏⣿⣭⣿⣯⣯⣯⣿⢇⠀⢀⠅⠘⣠⢀⡀⢀⡀⠀⣄⢀⠀⣀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣯⣿⣽⣽⣭⣯⣿⣿⣿⣽⣽⣯⣿⣭⣯⣿⣿⣽⣿⣭⣿⣯⣯⣿⣭⣯⣿⣽⣽⣿⣯⣯⣯⣿⣯⣿⣯⣽⣿⣭⣭⣿⣿⣿⣿⡇⠁⠀⠀⢀⡀⠀⠙⢠⡌⠀⡇⠀⡇⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠀⠈⢁⡀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⢿⢿⡿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⢿⣿⡿⡿⢿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣶⣦⣤⣾⣥⣤⣼⣷⣤⣤⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣾⢾⣾⣶⣾⣷⣿⣷⣶⣿⣾⣿⣷⡷⡿⢿⠷⢾⡾⠷⠿⡾⢶⢷⣿⠶⡷⡶⢶⣶⢷⠾⢷⠷⢿⢷⢾⢷⢿⢿⢿⢿⢿⠿⢿⢿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⣿⣿⣿⣶⣿⣿⣿⣾⣿⣷⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣹⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣟⡻⢟⣿⣿⢻⣿⠛⣻⡻⡟⣻⣻⣻⡛⣟⣿⣿⠟⣿⣟⠟⣻⡟⣿⢛⣿⢟⡿⣿⢻⣻⣻⣟⣿⠻⣟⢛⡻⣿⢻⡟⠛⣟⣟⣟⠿⣻⣿⣻⣛⢟⣟⢟⠟⡟⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡿⣿⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠻⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡈⠁⢸⣿⣾⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⣈⣻⣿⣾⣷⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣟⣻⣟⣟⣛⣛⣿⣟⣻⣛⣿⡟⣻⣻⣟⣻⣿⣻⣛⣟⣻⣟⣿⣻⣿⣿⣟⣛⣿⣟⣻⣻⣛⣿⣿⣟⣿⣟⣻⣿⣛⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⡍⡉⠩⠉⠍⠉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣟⣿⣻⣻⣟⣛⣻⣛⣿⣛⣿⣻⣻⣿⣛⣿⣿⣛⣿⡟⣿⣛⣿⣛⣿⣿⣻⣟⣟⣻⣟⣟⣻⣿⣿⣿⣿⣿⣿⠁⢠⢹⢸⣿⣿⣿⠿⡇⠃⢠⠀⠄⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣻⣟⣿⣻⣻⣛⣟⣻⣻⣿⣻⣟⣟⣛⣟⣿⣿⣿⣟⣿⣛⣻⣟⣟⣻⡛⣻⣛⣛⣿⣿⣟⣛⣛⣿⣻⣟⣻⣿⣻⣟⣟⣿⣿⣿⡏⠁⠀⠊⠈⡙⠉⠉⠀⠁⠀⠈⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣻⣟⣻⣻⣿⣟⣿⣿⣿⣻⣟⣿⣿⣻⣛⣟⣛⣿⣻⣿⣻⣿⣟⣿⣻⣛⣟⣿⣟⣿⣻⣹⣟⣟⣟⣿⣻⣟⣟⣻⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⣏⣛⣿⣿⣏⣛⣟⣿⣿⣯⣟⣛⣟⣛⣫⣿⣛⣻⣟⣟⣿⣻⣝⣿⣟⣿⣿⣻⣻⣿⣻⣿⣛⣟⣛⣿⣻⣛⣿⣿⣛⣽⣿⣏⣿⣛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣏⣻⣻⣟⣟⣛⣝⣟⣿⣹⣻⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣷⣶⣾⣷⣾⣷⣾⣾⣷⣿⣧⣾⣶⣾⣷⣷⣿⣷⣷⣮⣾⣾⣼⣾⣾⣶⣷⣾⣶⣷⣷⣶⣿⣾⣿⣶⣿⣾⣾⣿⣾⣾⣿⣿⣿⣧⣤⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣷⣷⣵⣾⢿⣶⣿⣿⡾⣴⣷⣾⣮⢷⣷⣷⣾⣾⡿⣷⣷⣷⣷⣶⣷⢿⣷⣿⣷⣷⣷⣷⣾⣶⣿⣿⣾⣶⢾⣿⣿⡶⢾⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢷⢾⣿⣶⣶⣿⢷⣾⣷⣾⣿⣿⣿⣷⣿⣷⣶⣾⣷⡾⣾⣷⢾⢾⣿⣶⣶⣿⣷⣶⢷⣾⣿⣿⣶⣶⡿⣿⣾⣾⣿⡿⣾⣶⣾⣾⣶⣷⣿⣿⠾⣿⣷⣶⣶⣶⣾⣾⣷⣷⣾⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣷⣾⣷⣿⣾⣾⣷⣿⣶⡿⣾⣶⣷⣿⣿⣷⢾⣶⣾⣶⣾⣾⣿⡶⣿⣷⣿⢷⡾⣶⡷⣾⣿⣷⣷⣿⣿⣾⣷⣷⣿⣾⢾⣶⣶⣾⣶⣷⣿⣷⣾⣾⣾⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⢖⣾⢶⣶⣶⣤⣤⣤⣴⣴⣤⣤⣤⣤⣴⣤⣤⣴⣶⣤⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣟⣵⣿⣿⣺⣿⣿⡿⣿⠿⡿⡿⠿⡿⣿⠿⢿⡿⠿⢿⢿⡿⠟⢿⢿⢿⠿⡟⠿⡿⠿⡿⠿⢿⢿⡿⢿⣿⢿⢿⢿⣿⡿⡿⠻⣿⡿⠿⢿⢿⠿⠿⢿⣿⠿⢿⢿⢿⠿⣿⢿⡿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⡿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣮⣮⣴⣦⣿⣷⣼⣿⣤⣽⣼⣯⣧⣷⣼⣼⣴⣧⣼⣯⣮⣿⣵⣴⣼⣷⣾⣿⣼⣷⣾⣧⣾⣧⣼⣿⣿⣤⣿⣵⣶⣴⣿⣧⣷⣾⣾⣵⣮⣿⣼⣧⣤⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⡿⣿⣥⣿⣿⣧⣶⣄⣾⣶⣴⣷⣧⣤⣾⣾⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣿⣿⢻⣿⣿⣿⣿⣿⠃⠀⠈⣿⣏⣙⣏⣿⣙⣿⣽⣙⣝⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣼⣿⣟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠛⣧⣼⣴⣤⣦⣧⣨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣾⣶⣿⣾⣷⣶⣷⣶⣾⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣽⣽⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⠿⢿⠿⠿⡿⠿⡿⠿⠿⢿⢿⡿⡿⠿⢿⡿⠿⠿⠿⡿⡿⡿⢿⠿⠿⠿⢿⠿⠿⠿⠿⠿⢿⠿⠿⡿⢿⠿⠿⠿⠿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⠾⠶⠾⠶⠾⡶⡶⠷⢶⢷⡾⠶⢾⠶⡷⠶⡿⢶⢷⡶⠷⠶⠶⠷⠷⡾⠷⢶⢾⠾⡶⡷⡶⢶⠶⡶⣾⠶⠷⣿⡶⠾⡶⠶⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⢶⡶⠾⠶⠶⢷⠶⡷⠾⢶⠿⢶⠶⠾⢿⠶⠷⡾⠷⣷⠿⠶⡶⠶⠷⢶⡾⢾⠾⢶⡿⠶⡿⠶⠶⢿⠿⢶⠶⠷⠶⢶⠷⠾⢶⠶⣿⣿⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⠶⠷⣷⠶⠿⠾⡾⠾⠾⢾⢷⡿⠶⢾⢾⠾⠷⠶⠶⠷⡶⡶⠷⠷⡷⠶⡿⢶⠶⡶⠶⡶⠷⠶⠿⡖⠾⡾⡶⠾⢶⢿⣷⣷⣿⣶⣿⣿⠀⠀⡀⠀⢠⣾⡇⢸⣿⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢿⡿⢿⠿⠾⠶⡿⢿⣿⢗⢿⢶⡷⡿⠾⢿⢿⠿⠶⢿⡷⣿⠾⢿⡿⠺⠿⣶⡿⠿⠾⠶⡶⢷⡶⢿⡾⢷⢷⡶⣷⡾⣿⢿⢿⠿⢿⡿⠠⠀⡇⠠⠼⡉⠀⠠⡉⠠⠀⠀⠀⠈⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⡿⠿⡿⢿⢾⠿⠻⠿⠻⠿⡿⠿⠿⠿⢿⠿⣿⡟⠿⠿⢿⠿⢿⡗⡿⠻⠟⡺⠿⡿⢿⢿⡿⣿⠿⠿⠿⣿⡿⠿⢿⣿⣿⣿⡗⠁⠀⠇⠃⠀⠃⠠⠀⠇⢠⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠿⡟⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣛⣏⣉⣏⣉⣏⣉⣹⣉⣉⣍⣉⣽⣩⣭⣋⣟⣋⣋⣹⣉⣝⣉⣹⣉⣝⣩⣍⣏⣉⣉⣉⣻⣙⣉⣉⣉⣏⣹⣩⣹⣏⣏⣯⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣯⣯⣹⣹⣍⣏⣭⣯⣹⣹⣩⣽⣉⣻⣉⣉⣉⣩⣹⣉⣉⣩⣭⣯⣻⣏⣉⣹⣉⣙⣉⣩⣉⣏⣍⣉⣉⣫⣉⣉⣉⣏⣩⣏⣉⣏⣍⣙⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣶⣿⣶⣾⣾⣦⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣻⣈⣸⣮⣺⣮⣿⣇⣟⣀⣴⣗⣽⣕⣗⣅⣨⣸⣏⣿⣬⣼⣿⣪⣰⣿⣼⣀⣼⣨⣪⣕⣇⣕⣅⣿⣊⣀⣿⣆⣢⣽⣇⣟⣀⣼⣺⣈⣀⣅⣯⣇⣅⣨⣺⣨⣊⣼⣸⣨⣸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣍⣽⣍⣉⣩⣯⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠙⣿⡟⠻⡟⣿⢻⣻⣿⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠿⣯⣏⣿⣛⣟⣻⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⣽⣿⣿⣟⣿⣿⣮⣽⣯⣯⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣬⣷⣤⣼⣤⣥⣼⣬⣤⣴⣯⣥⣬⣴⣤⣤⣯⣴⣼⣬⣧⣥⣶⣧⣴⣤⣶⣥⣧⣤⣥⣧⣦⣯⣿⣤⣼⣦⣥⣬⣼⣮⣤⣼⣭⣿⣿⠸⠋⠙⡇⣾⠋⡟⢿⣿⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣶⣤⣿⣿⣵⣦⣧⣾⣤⣤⣤⣧⣥⣴⣶⣤⣼⣼⣤⣼⣤⣤⣦⣴⣮⣧⣤⣼⣤⣼⣧⣾⣶⣦⣴⣯⣤⣤⣤⣼⣤⣼⣦⣼⣼⣿⣿⣿⠀⠀⠀⠀⠿⠀⠇⠈⠁⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣵⣦⣤⣼⣤⣴⣧⣴⣤⣬⣧⣤⣦⣽⣾⣴⣼⣤⣶⣧⣥⣦⣤⣧⣿⣤⣤⣧⣤⣤⣶⣤⣧⣧⣤⣤⣴⣦⣷⣦⣦⣶⣧⣴⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣴⣼⣧⣴⣴⣴⣼⣴⣦⣧⣥⣴⣼⣤⣦⣷⣽⣤⣤⣼⣵⣼⡴⣴⣤⣦⣧⣴⣼⣼⣬⣤⣥⣤⣷⣦⣤⣦⣦⣯⣦⡦⣷⣼⢤⣿⣿⡿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣼⣧⣷⣦⣼⣿⡽⡼⣮⣥⣼⣷⣦⣧⣧⣬⣾⣶⣯⣧⣷⣤⣼⣿⣶⣥⣶⣧⣵⣧⣷⣧⣦⣤⣥⣷⣼⣧⣶⣤⣭⣶⣼⣯⣾⣿⣴⣼⣿⠐⠄⠀⡇⠀⠈⠂⠐⠁⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣷⣷⣾⣶⣴⣧⣷⣷⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠁⠈⠀⠁⠈⠀⠁⠐⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢻⡻⠛⠟⢻⢛⠛⡟⠛⢛⠻⡛⡟⠻⠛⠻⠛⢛⢿⢛⠛⠛⠛⠟⡟⢛⠻⢻⠛⠛⢛⢻⠛⠛⡿⠛⣻⢛⡟⡟⠛⡛⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⡛⠛⠛⣟⡛⢛⢻⠛⢻⠻⠻⢛⢻⠛⡟⠛⢻⣻⢛⠛⣟⡛⣛⠛⢻⢻⠛⠛⢛⠛⠛⠛⡿⡛⡟⡛⡟⠟⣻⢛⣟⠛⡟⢟⠛⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⠛⢿⣛⠛⡿⠛⠛⠛⠛⣻⢛⡟⡟⣛⢻⠛⢻⠛⠛⠛⡛⣟⠛⢻⠛⠛⣻⡛⠛⠛⣻⠛⡟⢛⠛⠛⡟⠟⣟⢻⠛⠛⡛⡛⠛⢻⠛⡛⡟⡟⡟⠛⠛⡛⠟⠛⢻⢛⠛⡟⠛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢟⠛⣛⡟⠟⡛⡟⡟⢻⢛⠛⠻⠛⢛⠛⣛⣿⠛⠟⡛⣟⡛⡟⠛⣛⠛⢻⠻⣻⠛⡛⢛⢛⠛⢻⢛⡛⠻⣿⣛⢻⠻⡛⡟⡛⢛⠛⠛⢛⢻⢛⡟⡻⣛⡛⢛⣻⠛⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⣟⢛⡛⣽⡛⣛⣟⡛⢛⡛⡛⡋⣟⡛⣿⢛⡛⡙⣛⡛⣻⡟⢻⣛⣋⡟⣏⢏⡻⢻⡟⢙⢛⣻⢹⢻⡛⣟⣟⣛⠛⡛⢏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣿⣽⣭⣿⣭⣥⣼⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀⠀
⣿⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⢻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤
⣿⣿⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣾⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠒⡒⠒⠒⢻⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⠟⢉⣀⣀⡈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣗⠒⡒⠲⠒⢲⠒⠒⠒⢲⠒⠒⣒⢲⠒⠒⠒⢒⠒⡒⠒⢒⠒⠒⠚⢻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⠃⢰⣿⡿⡿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⢛⠛⠛⠛⠛⠻⡟⠛⡛⠛⠛⢛⢻⡻⡛⡟⠛⢛⡛⠛⣛⢛⢛⣛⠛⣛⢻⠛⠛⣛⡛⣻⣿⣿⣿⠀⣿⣿⢸⣿⡀⢹⣿⣷⣶⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣅⣨⣿⣟⣉⣉⣉⣍⣹⣍⣉⣿
⣿⣿⣟⣛⣛⣛⢻⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣷⣄⠉⠛⠛⠋⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠻⠛⣿⡿⢿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣧⣤⣤⣤⣀⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣧⣤⣼⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣧⣨⣿⣷⣤⣤⣤⣧⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣶⣶⣶⣶⣶⣶⣶⣦⣶⣦⣴⣶⣶⣶⣾⣦⣿⣿⣿⣿⣿⢸⣿⡗⢹⣿⣿⣛⢋⣛⣛⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣉⣫⣛⣟⣛⣛⣛⣛⣏⣛⣟⣛⣟⣛⣛⣛⣏⣻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣷⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⡆⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣦⣴⣤⣦⣤⣤⣴⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡾⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣉⣛⣙⣛⣏⣉⢛⣙⣛⣛⣙⣙⣛⣛⣟⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⠿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⠿⠶⠶⢶⠶⠶⡦⠶⠶⠶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣼⣶⣶⣶⣷⣼⣾⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⡿⠋⣠⣤⣤⣄⠉⢻⣿⣿⡏⡉⢹⠉⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⠁⣸⣿⣿⣿⣿⣷⠀⣿⣿⡿⠟⢿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⡄⠸⣿⣿⣿⣿⠟⢀⣿⣿⡷⣶⢾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣦⣈⠉⠉⣁⣤⣾⣿⣿⣧⣤⣴⣤⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 247

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/25/IRC_Proceedings_Sunday_November_24_2024.shtml
    Gemini version at https://techrights.org/n/2024/11/25/IRC_Proceedings_Sunday_November_24_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Sunday, November 24,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 25, 2024


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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The corresponding text-only bulletins for_Tux_Machines and for_Techrights
contain all the text.


                          Enter_the_IRC_channels_now




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⠂⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠉⠁⠀⠀⠀⢠⣴⣿⡿⠀⠀⠈⣻⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠀⠠⣤⣶⡆⠀⠀⢠⣾⣿⡿⢻⣿⣿⣿⡇⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⣿⣿⣆⣠⣾⣿⣿⠃⠈⠿⠋⠉⢹⡾⠿⠛⠉⠁⠉⠙⢿⣿⣿⣿⠟⠋⠉⠙⠻⠿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⢿⣿⠏⠀⠀⠀⣤⣶⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣴⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⠀⠀⠀⠈⢸⣿⣿⣿⣽⣴⣦⣾⣿⡿⠁⠀⠀⢹⣿⣿⣿⣶⣆⣿⣿⣿⣿⣩⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠈⠿⣿⡿⢿⣿⣿⣿⣿⣿⢩⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣿⣷⣴⣶⣾⣿⣿⣷⠘⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠛⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⡏⡠⠀⢰⡞⢡⣿⣿⣿⣿⠍⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠞⠀⢀⡼⠁⢨⣿⣿⣖⣿⡭⠙⢻⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣯⠥⢠⠎⠀⣠⡿⡗⠈⢐⢾⣶⠤⢌⣽⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠠⣐⡴⠁⢄⡺⢛⣿⣿⣷⡦⢯⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣿⣿⣿⣿⣟⠠⢡⡿⠋⠠⠚⡿⠶⠿⠾⢿⢿⣿⣬⣹⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⣿⣿⣿⣿⡟⠀⠀⡀⠀⠀⠀⠔⣦⣶⣄⠐⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣏⣿⣿⣿⣿⡟⡣⠖⠉⠠⠄⠀⠹⢧⢿⣿⣿⣷⣎⣿⣿⣽⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡝⠛⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠻⣿⣿⡏⠃⠀⢀⠀⢀⢀⣤⣠⣀⠈⠙⠿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⢠⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⠿⠿⣿⡯⠀⠀⠀⠀⠀⠀⠀⣀⠨⠹⣷⡒⠄⡹⣿⣿⣿⣷⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣰⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 469

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/25/Latest_Mass_Layoffs_at_Microsoft_Are_Confirmed_Bing_and_Vista_1.shtml
    Gemini version at https://techrights.org/n/2024/11/25/Latest_Mass_Layoffs_at_Microsoft_Are_Confirmed_Bing_and_Vista_1.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Latest Mass Layoffs at Microsoft Are
Confirmed, Bing and Vista 11 Losing Market
Share⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 25, 2024


Recent (3 days ago): This_Month_is_the_11th_Month_of_This_Year_With_Mass
Layoffs_at_Microsoft_(So_Far_It's_Happening_Every_Month_This_Year,_More
Announced_Hours_Ago)


So we're proven right again, having mentioned this very early. Now some Indian
media serves to affirm_the_above, even some of the biggest publishers in India.
This is from 2 hours ago:


    * ⚓ LinkedIn_lays_off_around_200_employees:_Report⠀⇛


           Professional networking platform LinkedIn has let go of around
           200 employees, according to a report from tech outlet The
           Information


They tried to hide this. They misuse NDAs.


We've meanwhile noticed that Bing_is_down_this_month and Vista 11's share is
also_down_this_month, based on this one surveyor.


Judging by Microsoft-funded fake 'cases' by the_serial_harasser and serial
strangler, we must be very obnoxious to Microsoft. Fake 'cases' merit strong
response [1, 2]. Microsoft has been attempting to silence me for about 20 years
and it backfired every single time. It'll backfire this time too. Not just
because of the Streisand Effect. They waste money exposing their_own_misogyny -
a losing strategy from a law firm that nearly always loses (it earned notoriety
for taking cases no other firm would take because of utterly low chances of
winning, no merit). If Microsoft money is used to 'troll' us, it won't end well
for Microsoft either. █





                    ䷩ 𝚕𝚒𝚗𝚎 523

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/25/Meme_Microsoft_Our_Hey_Hi_Hype_is_Going_So_Well_That_We_Have_MA.shtml
    Gemini version at https://techrights.org/n/2024/11/25/Meme_Microsoft_Our_Hey_Hi_Hype_is_Going_So_Well_That_We_Have_MA.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Microsoft: Our "Hey Hi" Hype is
Going So Well That We Have MASS Layoffs Every Month. Makes
Sense?⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 25, 2024


Contradiction (messages versus actions):


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_layoffs;_How_about_our_amazing_vapourware?⦈_


Context: Latest_Mass_Layoffs_at_Microsoft_Are_Confirmed,_Bing_and_Vista_11
Losing_Market_Share | This_Month_is_the_11th_Month_of_This_Year_With_Mass
Layoffs_at_Microsoft_(So_Far_It's_Happening_Every_Month_This_Year,_More
Announced_Hours_Ago)




⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢒⣴⣾⣿⣿⠿⣿⡿⠿⣿⣿⠻⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣯⣶⣷⣿⣽⣤⣮⣯⣼⣿⣿⣿⣿⣧⠀⠀⠀⣤⡶⠳⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠉⠹⣯⣿⠉⢹⣿⠍⢯⣿⡏⠉⣿⣿⣿⣿⠆⣧⡾⠛⠻⢿⣿⣿⣿⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⡿⠿⢿⡿⠿⣿⡿⣿⠿⠿⣿⠿⣶⢻⣿⣿⡟⣸⣯⣠⣶⣿⣿⣿⣟⢿⣿⣿⣿⣦⠀⢖⣀⣀⣀⢀⢀⣃⣀⣤⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣷⣮⣼⣧⣬⣿⣧⣧⣾⣥⣿⣴⣷⣿⡿⠋⢠⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡟⣰⣿⣿⠿⠿⠿⠿⣿⡿⠿⠿⠿⠛⠋⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠼⢛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⡱⢟⣫⡴⠀⣶⣶⣷⣶⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠻⠟⠛⠉⠉⠉⠉⠁⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣷⡀⠐⢻⡯⠑⠚⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣥⣶⣿⣿⡧⣰⣿⣿⣿⣿⣿⣿⣦⣤⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⡟⠿⠁⢈⡩⠀⠀⢤⣼⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢴⣶⠀⠀⠺⡇⠀⠀
⠈⠉⠛⠛⠛⠛⠿⠛⠉⠀⠈⠿⢶⠀⠀⠈⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣾⣿⣿⣿⣷⣄⠀⠀⢹⣿⣟⢛⣿⡿⠟⣿⡿⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⠀⠻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⡿⣿⣿⣟⢀⣸⣿⣿⡿⠿⠿⡿⠒⠒⠂⢹⡭⠉⠉⢀⣴⣫⡟⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⢿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡇⠀⣟⠛⠒⠉⠐⠀⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣴⣬⣍⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠶⠀⠙⢿⠏⠙⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡠⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠱⣾⣿⣿⣿⣿⣿⣯⣤⣤⡀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣀⠀⢛⠛⠉⠓⠲⠛⢿⣿⣿⣷⡀⢠⣀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠑⠀⠀⠀⠀⠀⠀⠙⠻⢿⣽⣿⣿⣷⣄⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⣿⣿⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠰⠆⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡏⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⠛⠶⣦⡤⢤⠄⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢻⣿⢿⡿⣿⣅⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠶⠶⣤⣌⢠⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣠⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢿⣿⠏⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⠀⠀⠀⣤⣶⣶⣶⡶⠿⠿⢿⠷⠖⠀⢉⣉⣭⣤⣤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠘⢿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡻⣿⣿⠀⠀⠀⣤⡤⢤⣶⡶⠿⠷⠾⠂⠄⠀⠉⠉⠉⠀⠀⠁

                    ䷩ 𝚕𝚒𝚗𝚎 574

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/25/On_Groupthink_Mindless_Sheep_and_Toxic_Online_Cults.shtml
    Gemini version at https://techrights.org/n/2024/11/25/On_Groupthink_Mindless_Sheep_and_Toxic_Online_Cults.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ On Groupthink, Mindless 'Sheep', and Toxic
Online Cults⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 25, 2024,
updated Nov 25, 2024


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


This week, treat yourself to a life free of social control media


Back in 2016 ("ahead of his time" as the saying goes; also ahead of his death)
Pieter Hintjens explained_why_he_had_quit_Twitter. His explanation aged very
well, predating by more than half a decade Musk's fatal takeover of Twitter.


Daniel Pocock cautioned about it in_November_2018_at_the_UN_Forum_on_Business
and_Human_Rights:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Daniel_Pocock_spoke_about_Facebook_and_Twitter_while
attending_the_UN_Forum_on_Business_and_Human_Rights_in_Geneva,_Switzerland⦈_


As he_put_it_yesterday (days ahead of Irish_elections), with us noting that he
consistently says "social control media" (a term we coined):


     Mr Pocock makes the point that social control media gives activists
     like Hutch Hussein a false sense of empowerment. People have come to
     see the truth in this during 2024 as Elon Musk's Twitter / X appeared
     to help one US election candidate more than the other. The Guardian
     newspaper recently decided to stop using the Twitter / X platform.


     Mr Pocock's point is equally valid for all enterprises, whether they
     be political parties, non-profits, small businesses or whatever.


     Let's not forget Operation Trojan Shield, whereby the secure
     messaging app ANOM was really controlled by the FBI and Australian
     Federal Police (AFP). Social control media is really not much better
     than this and unlike an app operated by the police, social control
     media can sell information about their users to just about anybody.


Days ago he wrote


     Nonetheless, by using social control media for her campaign Brigid is
     giving power to billionaires in Silicon Valley. Brigid is giving
     power to a lot of privileged white men who work in the social control
     media ecosystem. Every minute Brigid spends on social control media
     is unpaid work adding to the share price of Meta and X. Every friend
     she connects with through these platforms increases the value of
     those networks and their share prices based on the theory proposed by
     Metcalfe's law.


     Therefore, by building up social control media, People Before Profit
     are augmenting the capital accounts of billionaires. Those same
     billionaires have the power to manipulate their message in very
     subtle ways or in a very big way at any time. Artificial Intelligence
     is only going to make it more difficult.


     Daniel Pocock is the only candidate building a campaign without
     social control media.


The catchy term "social control media" is used 29 times in this_page. Many
politicians all around the world have surrendered sovereignty to GAFAM and
social control media. All their communication (both ways) is controlled by
hostile and sometimes private interests. GMail spies on them, Microsoft culls
their outgoing/incoming mail, Facebook suspends them, Twitter subjects them to
extreme-right propaganda, YouTube shadowbans them etc.


You want freedom? Be ready to pay the price of letting go of pure nonsense.


One of our favourite coffee shops (or pubs) decided to do the same nearly 7
years ago. Quoting Wikipedia: "On 16 April 2018, Wetherspoons deleted all of
its social media profiles. Chairman Tim Martin cited the "current bad publicity
surrounding social media, including the trolling of MPs and others"..."


What I've found the 'hard' way, based on personal experience, is that social
control media attracts some of the most toxic interactions. Some_aren't_worth
having_at_all. So in 2020 I quit "engaging" and in spite of that Twitter_would
still_sanction_me for merely linking to verified facts. Nobody needs nonsense
like that! Twitter then censors_evidence_of_its_own_censorship_(a_very_common
tactic_of_dictators). This_is_how_absurd_it_has_become.


Being outside of social control media does not mean having no visibility. The
Web isn't just a handful of domains like Facebook, Twitter, Netflix etc.


Perhaps Dr._Andy_Farnell's_latest_explanation_of_this is a lot clearer (it's
certainly more detailed) than mine.


Some people say utterly shitty and really dumb things like, if it's not indexed
in Google, then it does not exist. Oh, really? Are you working for Google?
Google determines your pages' existence like Mark Zuckerberg determines who
your real friends are.


As my wife put it yesterday, "there's no regret and I'm better off without
social control media."


Groupthink and abuse aren't a desirable feature or facet of society. Crowds can
indeed be large and noisy; their size isn't indicative of anything but sheep
mentality. █


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




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

                    ䷩ 𝚕𝚒𝚗𝚎 1703

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/11/25/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2024/11/25/Over_at_Tux_Machines.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Over at Tux
Machines...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 25, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Rich_thick_ground_cover_of_3_leaf_clovers⦈_


⚓  Updated This Past Day⠀⇛


   1. ⚓ TuxCare_and_Cloudimg_Partner_to_Bring_Patches_to_Dead_Linux_Cloud
      Images⠀⇛


           TuxCare has partnered with UK-based Cloudimg, to bring its
           customers TuxCare Endless Lifecycle Support for keeping end-of-
           life Linux distributions supported


   2. ⚓ Android_Leftovers⠀⇛


           Here's what I'll miss about Chrome OS once it turns into
           Android


   3. ⚓ Just_Starting_in_the_Linux_Terminal?_Here_Are_Some_Setup_Tips⠀⇛


           The Linux terminal is useful, but it sometimes gets a bad rap
           for being boring


   4. ⚓ Free_and_Open_Source_Software⠀⇛


           This is free and open source software


   5. ⚓ today's_leftovers⠀⇛


           GNU/Linux and FOSS links


   6. ⚓ dpb_(Distributed_Ports_Builder),_Warp_and_Wireshark⠀⇛


           Applications in focus


   7. ⚓ Games:_Humble_Bundle,_Social_Media_Card_Game,_and_Snake⠀⇛


           With Linux twist


   8. ⚓ Programming_Leftovers⠀⇛


           coding related links


   9. ⚓ Open_Hardware_Leftovers⠀⇛


           ESP32 and more


  10. ⚓ Audiocasts_and_Videos:_Collection_From_Invidious_and_TLLTS⠀⇛


           from the past week


  11. ⚓ today's_howtos⠀⇛


           many howots for today and some older ones


  12. ⚓ FreeBSD_14.2-RC1_Now_Available⠀⇛


           The first Release Candidate build of the 14.2-RELEASE release
           cycle is now available


  13. ⚓ 10_Best_Linux_FTP_Clients_for_Every_User_in_2024⠀⇛


           Looking for reliable FTP clients on Linux


  14. ⚓ Moksha_–_modern_iteration_of_the_Enlightenment_window_manager⠀⇛


           This is free and open source software


  15. ⚓ RELIANOID_Load_Balancer_Community_Edition_v7.5_Release_Notes⠀⇛


           We are thrilled to announce the release of RELIANOID 7.5.0
           (Community Edition)


  16. ⚓ GhostBSD_24.10.1_Is_Now_Available⠀⇛


           We’re excited to announce the release of GhostBSD 24.10.1


  17. ⚓ KaOS_2024.11⠀⇛


           More application are now ready to use Qt6 and Frameworks 6
           including Freecad, Sqlitebrowser, Cantor, Kalzium, Webacmoid
           and Liquidshell


  18. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


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      888  /n/2024/11/17/
           Linux_Kernel_6_12_Officially_Released_This_Is_What_s_New.shtml




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⠘⣟⣻⣿⣿⣿⣿⡆⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⣶⣿⣿⣿⣧⣴⣷⣶⣄⣬⡟⣛⡈⠀⠈⠀⠀
⠀⠀⠐⠀⠀⠀⠀⢠⣶⡀⡦⡀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠋⣻⣿⣿⣿⠏⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣣⣤⣦⣄⠈⠻⠿⠿⠃⠈⠉⠉⠁⠀⠀⠀⠀⢩⣿⣿⣿⣯⣿⣿⣿⣿⣇⠀⠀⠻⠭⠟⠊⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⣾⣷⠰⠝⣀⣀⡀⠴⣾⣷⡆⡠⠀⠀⠀⠀⠀⠀⢠⠙⠋⠁⠀⠀⠈⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⡎⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⢶
⠀⢠⡄⠀⠀⢠⣶⡶⢶⣶⣤⡍⢡⣼⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⡻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠿⠟⠀⠀⠈⠛⠻⢿⡭⣹⣿⡎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠆⠀⠀⠀⠀⠀⠀⣤⣤⣤⡻⣿⣿⣿⣿⣿⣷⠉⠙⠻⠿⠿⠿⠿⠃⠀⠀⠀⠀⢀⣤⣦⡀⣾⣧⣴⣤⣤⣿⣿⣷⣈⡻⣴⣿⣶⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣄⠀⠈⠛⠻⠛⣵⣄⣀⣠⣿⣿⣿⣿⣯⠉⠑⡀⠀⣠⣀⣠⣶⡤⣠⠼⣿⣿⣿⣿⣶⣶⣿⣿⠛⠁⠈⠁⠀⠀⣴⣶⣦⡄⣠⣶⣶⣤⣿⣿⣿⣿⠻⠛⣡⠿⠃⠙⠻⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡿⠛⢳⣆⠀⠇⣾⣿⣽⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⣆⠀⢀⢾⣿⣿⣿⣿⡻⣿⢿⣿⣦⡶⣶⣍⣥⣤
⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠀⠉⠉⠉⠉⠀⠴⣾⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⡍⠁⣈⣤⡉⠛⠛⣷⣿⡏⠈⠉⠻⠿⠿⠃⢭⣿⣿⣿⣼⣗⠘⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡝⣼⣿⣿⣿⣿⣿⣦⠏⠙⠛⠋⠉⠀⠀⣿⣿⣿⣿⠏⠀⠀⠠⣿⣿⣿⠿⠛⠿⠛⠛⠛⠛⣁⣰⣿⣿⡇⠀⣠⣽⣿⣿⣶⣤⣿⣿⡂⠤⠉⠉⠘⠛⠟⠛⣠⠜⠻
⠻⠟⠋⣀⠛⠿⠛⠋⠀⠀⢰⣶⣄⣀⠀⢠⠀⠠⠿⠃⠀⠙⠛⠉⠀⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣿⡿⠿⠛⠋⣤⣶⣿⣿⢿⣿⣿⡞⠿⠿⢓⡦⠀⢐⣔⣀⠀⣀⣀⡀⠀
⠀⣠⣾⣿⣦⠔⣠⣤⣄⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣯⠀⠀⠈⠉⣴⢿⣿⣿⣿⣿⣿⣿⣷⡤
⣿⣿⣿⣿⣿⣾⣿⣿⠏⠀⠀⠀⠉⠁⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠⣾⣦⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣋⢀⠀⠀⢑⣷⣈⡛⣚⣭⣾⣿⣿⣿⣄
⠿⠿⠟⠛⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⢀⣠⣄⡀⣠⣶⣦⡄⠀⠀⢰⣫⣽⣢⣿⣿⣿⣿⣿⣿⣷⣦⣤⠤⢨⣅⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣷⣷⣿⣿⣿⣿⣝⠿⢿⠛⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠟⠡⢄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⣿⣿⣿⣿⣿⣿⣿⣽⠾⣿⣷⣮⣍⠛⠁⠀⠀⣴⣿⣷⡄⠈⠛⠋⠁⠸⢿⡿⠿⠉⠁⠀⠀⣽⣿⣿⣿⣿⣇⣠⣤⡈⠙⠲⢴
⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠙⠛⣋⣾⣷⡴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠙⠛⢩⣿⣿⣿⣿⣾⠟⠛⢛⠋⠀⣴⣿⣶⣽⣿⣾⣄⠀⠠⠀⠈⢠⡀⠀⠀⠀⠀⠀⠀⣡⣽⣛⣛⣿⣿⣿⣿⣿⡆⠀⠠
⣿⣿⣿⣷⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⢇⡈⣉⣥⣴⣿⣿⣿⣿⠿⠃⠀⠀⠀⣠⣤⣴⣿⣿⡟⠋⠁⠀⠈⢿⣿⣦⣜⣿⣿⣿⣿⣿⣿⣷⣶⣼⣇⣈⣿⣿⡆⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣤⣄⠀⠘⢿⣿⣷⣝⠻⣿⣭⣿⣿⣥⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠀⣐⡀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠉⠛⠃⠀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠈⠀⠀⠘⣟⣿⣷⣈⡀⠉⠉⠁⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣢⣽⠿⣿⣿⣷⣾⣿⣇⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣴⣶⣿⣶⣾⣿⣷⡄⠠⠜⠃
⣿⣿⣿⣿⡏⠉⠛⠋⠁⠀⠀⠀⠀⠙⢻⣿⣿⡿⠃⠀⢀⣤⣾⡻⣿⣿⣿⡿⣋⣠⣤⣄⡘⢿⠇⢀⣤⣿⡏⡋⣹⣿⣷⡦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿
⠉⠛⠛⠋⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠂⠈⠛⠛⠛⢩⣾⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣛⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡟⣻⣅⠀⢉⣿⣿⣿⣷⣦⣚⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⣈⣥⣴⣿⣿⣿⣿⡿⠟⠋⠙⠻⠿⣿⣿⣿⠿⠛⠛⠛⠁⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠀⠀⢦⡄⠀⢀⠶⠀⠀⠀⠈⠉⠉⠁⠀⠘⢿⣿⣿⠟⣿⣿⣿⣷⣿⣏⢙⡿⠛⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡙⠿⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢢⣾⣾⣥⣕⡌⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠻⠿⣿⣿⣿⣟⣩⣾⣿⣷⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⣿⣷⣽⣦⡀⠀⢀⣠⣦⣠⣾⣿⣶⣄⠀⣀⣤⡀⠀⠀⢀⣠⣶⣦⣴⣤
⠀⠀⠀⠀⢠⡈⠀⢺⣿⣴⣿⣿⣿⣻⣦⡀⢔⣤⢾⡆⢠⣶⣶⣾⣧⣾⣦⣤⣤⣄⠀⠀⠘⣿⣿⣿⣹⣿⣿⣿⣦⣀⣠⣾⣿⣶⣤⡶⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠾⠿⠿⠿⣿⣻
⡀⠀⠀⢶⣾⣼⠟⠁⠘⢿⣿⣿⣿⣿⡿⢁⡀⢛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠁⣿⣿⡿⠿⠋⠉⠛⢿⠉⢓⣋⣀⡀⢀⣀⣀⠀⠀⠙⠛⠋⠛⠛⠋⠘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣠⠀⠀⢠⣿⣿
⣁⠀⢀⣤⡀⠀⠐⠀⠀⠀⠉⠉⢉⣥⣶⣿⣿⠰⣿⣮⡙⠛⣫⣭⣿⣿⣿⣯⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢿⣿⣿⣿⣿⣿⣿⡷⣀⣤⣄⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣴⣦⣄⣻⣿
⠟⠰⠀⠉⠙⢀⠶⠖⠀⠀⠀⠀⠺⣿⣿⣿⣿⣾⣿⡿⠏⢸⣿⣿⣿⣿⡿⠟⠀⠀⠀⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⣿⡏⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠛⠻⣿⣿⣿⣿⡇⣩⠉⠁⣀⣄⡘⣿⣿⣿⣿⣿
⠀⠀⠘⢶⠐⣀⣄⠀⣤⣾⡛⢧⠀⠀⠀⠈⠆⠀⠀⢠⣾⣿⣿⣷⣿⣿⣷⡄⠀⡀⠀⠀⣠⣶⣾⣿⣿⣿⠀⣠⣶⣤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠙⠛⠉⠀⠁⠀⢸⣿⣿⣿⣌⣿⣿⣿⣿
⠀⠄⠀⣰⠮⠙⠲⣿⡜⢯⣩⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣴⣵⡇⠀⠻⣿⣿⣿⣿⡟⣰⣿⣿⣿⣏⠀⠈⠻⢿⣿⡿⠛⠛⡛⣙⡻⠿⠿⠟⠱⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈⣿⣿⣿⣿⠟⢱⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1886

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 25/11/2024: Purity and Cory
Doctorow's Ulysses Pact, Smolnet Portal and
SGI⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 25, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal/Opinions
          o Technology_and_Free_Software
                # Internet/Gemini
    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ The_final_top_gear/grand_tour_episode⠀⇛


                       It's been 22 years since I as a young lad took up
                       watching Top Gear. It might only have been 20 or 19
                       years for me, but regardless, I was still a
                       teenager.


                       I said the nostalgia was layered on thick, but to
                       me Top Gear was also more than a show. It's like
                       the other major hits, Friends, Big Bang Theory,
                       Desperate Housewives and so on, they aren't great
                       because of the content per se, but because of the
                       people.


                       It's the same reason the networks tried and failed
                       at creating subsequent copies of these things, it's
                       not the same.


                # ⚓ ALLEN_DAM⠀⇛


                       A hot day yesterday, and forecast rain today. Not
                       ideal for exploring the dam I plotted a route to
                       last weekend. So I decided to go on Friday instead,
                       with an 18degC forecast and light winds being
                       perfect for some quiet bushwalking.


                       Allen/Allenvale Dam/Reservoir (naming for these
                       places is traditionally inconsistent) is among the
                       last dam within comfortable day-trip range that I
                       haven't visited yet. The Web provides every
                       suggestion that it's not accessible to the public,
                       but since it's in a national park with lots of
                       walking tracks running between the innumberable
                       waterfalls dotted around the coastal township of
                       Lorne, the tracks cross the gated road to the
                       reservoir and present a convenient backdoor route.


                # ⚓ Greetings⠀⇛


                       Hello all. I was ambling my way home after a beer
                       or two, and happened to glance down the alleyway
                       and saw the sign for the Midnight Pub. I strolled
                       up, but was not sure whether to enter. I waited
                       outside for a bit listening to some of the
                       conversations. What I heard made me think it was my
                       kind of place - so here I am.


                # ⚓ My_home⠀⇛


                       I'm moving in a couple weeks. I wouldn't like to
                       leave this place, but alas. The new place is very
                       nice and it has its own, different pros and cons. I
                       just gotta get my stuff gathered up. I'll have
                       time.


                       I need some new bookshelves. Somewhere to put all
                       my board games and books and decorations more
                       neatly than I now have them.


                       I also need to make myself a proper music statiom
                       in the living room. A chair and a note stand are
                       decent enough when I actually get myself to
                       practice for real, but I've spread myself out a lot
                       in my living room.


                # ⚓ I_Regret_to_Inform_You_the_Poets_are_Elsewhere:_Purity_and
                  Cory_Doctorow's_Ulysses_Pact⠀⇛


                       Every so often, someone asks Cory Doctorow if he's
                       going to sign up for Bluesky. I've seen a couple of
                       these, and the answer is always no, with an
                       asterisk: he isn't interested in new platforms
                       unless he can exit without switching costs.
                       Doctorow has a big following in the Fediverse:
                       almost 60k followers (enormous, by Fedi standards -
                       at time of writing, the 52nd most-followed
                       account), and still posts on Twitter. Presumably
                       his self-enforced rule is carefully constructed to
                       exclude new services like Bluesky and Threads, and
                       to allow him to keep posting on Twitter. Because if
                       he's got platform concerns, I don't see how he
                       reconciles that with continuing to post at a site
                       owned by a fascist, that pushes violent posts,
                       trolls, and fascist propaganda into people's feeds.
                       But, I guess we each make our decision. I left last
                       year and left behind a good chunk of my community,
                       something that I haven't fully found elsewhere, and
                       whose loss I've keenly felt for the last year and a
                       half (more on that later).


          o § Technology and Free Software⠀➾


                # ⚓ HTB_season_ended_and_team_was_top_100_world_wide!!!⠀⇛


                       Hola! Happy Hacking to all hackers, DIY, Creators
                       and tinkers out there. - Yes our team got into the
                       top teams, most, I personally got to the top of the
                       holo label, finishing all boxes, we did all boxes
                       in a matter of hours or a 1-2 days for the insane
                       ones, very good considering this used to take me
                       weeks, but yes I have to admit this insame boxes
                       were easier because they had non-intended ways that
                       later on got patched after I did them.


                # ⚓ Fast_computer_and_magic⠀⇛


                       As I wrote here some weeks ago I updated my MNT
                       Reform 2 laptop with the latest RCORE CPU. So now I
                       have a really fast ARM laptop. My own code runs
                       here 2 times slower than it does on my OpenPOWER
                       workstation with the POWER9 CPU. White slower, the
                       reform also consumes many times less power (and it
                       is way more portable than my desktop workstation,
                       too!).


                       Other things are black magic, though. The Reform 2
                       uses a system controller to start and to shutdown
                       the machine, to report battery status and so on (as
                       the OpenPOWER does). The Linux requires a kernel
                       module to acces the system controller. I do have
                       the thing and it used to work well before the
                       upgrade. After that it sometimes works.


                # § Internet/Gemini⠀➾


                      # ⚓ Smolnet_Portal_and_SGI⠀⇛


                             I remember times when I was able to do almost
                             all on-line work on the IRIX. Internet
                             banking, browsing, online shopping and so on.
                             The IRIX 6.5 has been able to run the
                             Netscape up tp 4.7, the Firefox up to 3.0.19
                             and the latest Lynx, among others. Some
                             things required helpers like youtube_dl, some
                             thing were unavailable at all (do you
                             remember then ActiveX or the Flash?)


                             But these times are gone. There is no recent
                             SSL implementation available and even if if
                             will be then many modern cyphers are too CPU-
                             demanding so even my 250 MHz MIPS R10k CPU
                             will not be able to handle them. So, no
                             https:// at all.


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





                    ䷩ 𝚕𝚒𝚗𝚎 2095

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 25/11/2024: Climate News, Daniel
Pocock Receives a Fake/Fraudulent €17,000 Electricity
Bill⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 25, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
                # Patents
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Forget_Pixel_Art:_Try_Subpixels⠀⇛


                 [Japhy Riddle] was tired of creating pixel art. He went
                 to subpixel art. The idea is that since each color pixel
                 is composed of three subpixels, your display is actually
                 three times as dense as you think it is. As long as you
                 don’t care about the colors, of course.


          o ⚓ Hackaday ☛ RFID_From_First_Principles_And_Saving_A_Cat⠀⇛


                 [Dale Cook] has cats, and as he readily admits, cats are
                 jerks. We’d use stronger language than that, but either
                 way it became a significant impediment to making progress
                 with an RFID-based sensor to allow his cats access to
                 their litterbox. Luckily, though, he was able to salvage
                 the project enough to give a great talk on RFID from
                 first principles and learn about a potentially tragic
                 mistake.


          o ⚓ Habib Cham ☛ Unplanned_Writing_and_Publishing_Hiatus⠀⇛


                 Despite my blogging endeavours, I have fallen into a
                 writing and publishing hiatus over the past four months.
                 Given the amount of blog posts I consume daily — one of
                 the sources of inspiration and thought triggers, I didn't
                 feel compelled to write. Nevertheless, I decided not to
                 force the issue and allow for the desire to return,
                 naturally.


                 The hiatus could’ve been longer had it not been for the
                 fact my Ghost subscription auto-renewed, which lead me to
                 log back into my Ghost Pro account after a couple of
                 months. Whilst taking care of my subscription setup, I
                 decided to tidy things up and reconfigure the site. I
                 also spent time reading the published posts, and what do
                 you know, it triggered the desire to write, and I started
                 digging into my drafts folder to pick up where I left
                 off.


                 The unplanned hiatus is over! 🙌🏾


          o ⚓ Jacky Alciné ☛ Creating_with_Intention_-_Jacky_Alciné⠀⇛


                 Art is what pulls people across class, regions and other
                 markers of division together. The ability to produce art
                 in this time is vital and controlled. I always encourage
                 folks to check out the independent arts of every medium
                 to help give air to stories that you want to see more of
                 — photography, food, music, clothing, jewelry; you name
                 it. I'm glad to see many of them grow over the last
                 decade[4]. There's a lot we can do when it comes to
                 having more control over how we tell stories and what we
                 can teach each other. Art serves as a medium that can be
                 as accessible, if not more so, than reading. In a well
                 planned out approach, it could help improve our
                 intelligence in multiple ways.


          o ⚓ Facundo Olano ☛ my_blogging_setup_is_my_writing_process⠀⇛


                 The entry sits there for weeks, months, even years.
                 Whenever I think about something relevant, I attach a
                 note to the entry. Or I jot something down in any of the
                 notebooks I keep around—on the desk, in my bag, in my
                 nightstand drawer.


                 Eventually I find myself thinking about the post when I
                 wake up, or while I’m running, instinctively composing it
                 in my head, one sentence after another. Then I know it’s
                 time to start writing.


          o § Science⠀➾


                # ⚓ Tech Central (South Africa) ☛ The_biggest_prime_number_ever
                  found⠀⇛


                       First, it’s a prime number (meaning it is only
                       divisible by itself and one). Second, it’s what is
                       called a Mersenne prime (we’ll get to what that
                       means). And third, it is to date the largest prime
                       number ever discovered in a mathematical quest with
                       a history going back more than 2 000 years.


                # ⚓ Science Alert ☛ Physicists_Transformed_a_Quantum_Computer
                  Into_a_Time_Crystal⠀⇛


                       Time crystals are groups of particles that display
                       repeating patterns. Where the patterns that make up
                       regular crystals like diamond and quartz echo
                       through 3D space, time crystals move periodically
                       like a pendulum, tick-tocking through time.


                       What makes them unique is their ability to do this
                       in absence or in contrast to a driving 'push'. Time
                       crystals oscillate in their lowest energy state to
                       their own rhythm, like a child kicking out in their
                       swing in defiance of their parent's repetitive
                       nudges.


                # ⚓ Omicron Limited ☛ New_tools_filter_noise_from_evolution
                  data⠀⇛


                       While rates of evolution have appeared to
                       accelerate over short time periods, new analysis
                       suggests that statistical noise is affecting the
                       data patterns. A professor at the University of
                       Tennessee, Knoxville, and his colleague have
                       developed new tools to help researchers filter the
                       data.


                # ⚓ Science Alert ☛ Mysterious_Inca_Objects_Reveal_a_Hidden
                  Link_We_Never_Saw_Before⠀⇛


                       After examining and manipulating the data, I
                       realised the smaller and more complex khipu is a
                       summary and reallocation of the information in the
                       larger khipu. In other words, the two khipus record
                       the same data, but represent it differently.


          o § Career/Education⠀➾


                # ⚓ University of Michigan ☛ The_University_of_Michigan_is_a
                  corporation⠀⇛


                       This confusion is derived from a belief that the
                       University operates as an institution of higher
                       education, dedicated to knowledge, critical
                       thinking, free expression and student growth. But
                       its operational strategy does not comport with such
                       a mission. Rather, the University operates more
                       like a corporation. At the same time, it flouts
                       obvious corporate solutions that would benefit
                       students — the institution’s most important
                       stakeholders.


                # ⚓ Alex Ewerlöf ☛ Staff_Engineer_vs_Engineering_Manager⠀⇛


                       These are actual questions I’ve got in the past few
                       years:


                       • An EM: I don’t want to deal with people anymore.
                       I want to focus on the tech. Is Staff Engineering
                       for me?


                       • A Senior EM responsible for multiple teams: I
                       have so much admin work: 1:1s, skip levels,
                       promotion, performance review, architectural
                       decisions, engineering strategy, etc. Should I hire
                       a Staff Engineer to take over the technical part of
                       my job?


                       • A Staff Engineer for a team without an EM: I’m
                       practically acting as the team manager and like it.
                       Should I just switch lanes to become an EM?


                       So I thought it’s time to settle all these
                       questions once and for all.


                # ⚓ Alex Ewerlöf ☛ How_can_engineer_leaders_stay_technical?⠀⇛


                       I reached out with this question to one of my
                       friends who is the CTO at a mid-size company (500-
                       1000 employees).


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ $40_Ham_Antenna_Works_Six_Bands⠀⇛


                       [My Ham Radio Journey] wanted to see if a “common
                       person” (in his words) could build an effective
                       vertical ham radio antenna. If you look at the
                       video below, the answer is apparently yes.


                # ⚓ India Times ☛ Ex-Google_CEO_Schmidt_to_the_US_Army:_Give
                  tanks_away,_instead_buy_a_...⠀⇛


                       Google's former CEO and chairman Eric Schmidt is
                       asking for a radical shift in America's military
                       strategy. He proposes that the US military should
                       replace its traditional tank fleets with AI-powered
                       drones. Schmidt served as Google’s CEO for almost
                       10 years -- from 2001 to 2011, a time of rapid
                       growth for the search giant. He later became
                       executive chairman for Google, and in 2015, for its
                       new parent company, Alphabet, before resigning as
                       chairman in the year 2018.


                # ⚓ India Times ☛ AI_revolution_drives_surge_in_gold_demand_for
                  smartphones,_autonomous_vehicles,_and_data_centres:_report
                  [Ed: "AI revolution" = Microsoft et al propaganda and Ponzi
                  scheme.]⠀⇛


                       Gold demand in the electronics sector peaked in
                       2010 at 328 tons but gradually declined to 249 tons
                       by 2023. Recent quarters, however, have shown a
                       modest recovery, driven in part by the expansion of
                       AI-enabled devices.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Future US Inc ☛ After_awards_haul,_Helldivers_2_devs_lament
                  the_"dire_state"_of_the_games_industry:_"We_need_to_be_there
                  to_help_each_other"⠀⇛


                       "The games industry is in turmoil"


                       [...]


                       One major source of layoffs in 2024 has been
                       Microsoft, which has reportedly laid off more than
                       2,500 workers alone, with several successful
                       studios shutting down in the process, such as Hi-Fi
                       Rush develop Tango Gameworks and Arkane Austin,
                       developer of the Dishonored series and Redfall.


                # ⚓ 9to5Mac ☛ 2024-11-19_[Older]_Apple_Devices_May_Learn_to
                  Ignore_‘Hey_Siri’_Command_From_TV_Ads⠀⇛


                # ⚓ Neil Selwyn ☛ AI_…_minding_our_language⠀⇛


                       Mitchell makes the point that the use of such
                       language matters – shaping how society is
                       responding to the rise of genAI. The more that we
                       presume this technology to be thinking like a human
                       then the more that we feel comfortable with human-
                       related rights and responsibilities being afforded
                       to the technology. Thus, we are now seeing
                       organisations decide that it is acceptable to
                       replace human counsellors with chatbots. We are now
                       seeing legal debates over the moral rights of
                       robots. We are now seeing credulous discussions of
                       how AI software can ‘perform’ when taking an
                       examination or an IQ test


                # ⚓ CNBC ☛ Will_AI_replace_humans?_Yoshua_Bengio_warns_of
                  artificial_intelligence_risks⠀⇛


                       "Intelligence gives power. So who's going to
                       control that power?" he said. "Having systems that
                       know more than most people can be dangerous in the
                       wrong hands and create more instability at a
                       geopolitical level, for example, or terrorism."


                # ⚓ Futurism ☛ Godfather_of_AI_Warns_of_Powerful_People_Who
                  Want_Humans_"Replaced_by_Machines"⠀⇛


                       The head of the University of Montreal's Institute
                       for Learning Algorithms, Bengio was among the
                       public signatories of the "Right to Warn" open
                       letter penned by leading AI researchers at OpenAI
                       who claim they're being silenced about the
                       technology's dangers. Along with famed experts Yann
                       LeCun and Geoffrey Hinton, he's sometimes referred
                       to as one of the "Godfathers of AI."


                       "Intelligence gives power. So who’s going to
                       control that power?" the preeminent machine
                       learning expert told the outlet during the One
                       Young World Summit in Montreal.


                # ⚓ The Atlantic ☛ The_Right_Has_a_Bluesky_Problem⠀⇛


                       The number of people departing X indicates that
                       something is shifting, but raw user numbers have
                       never fully captured the point of what the site
                       was. Twitter’s value proposition was that
                       relatively influential people talked to each other
                       on it. In theory, you could log on to Twitter and
                       see a country singer rib a cable-news anchor,
                       billionaires bloviate, artists talk about media
                       theory, historians get into vicious arguments, and
                       celebrities share vaguely interesting minutiae
                       about their lives. More so than anywhere else, you
                       could see the unvarnished thoughts of the
                       relatively powerful and influential. And anyone,
                       even you, could maybe strike up a conversation with
                       such people. As each wave departs X, the site
                       gradually becomes less valuable to those who stay,
                       prompting a cycle that slowly but surely diminishes
                       X’s relevance.


                # ⚓ The Register UK ☛ Thousands_of_PAN-OS_devices_compromised
                  by_critical_exploits⠀⇛


                       Roughly 2,000 devices had been hijacked as of
                       Wednesday - a day after Palo Alto Networks pushed a
                       patch for the holes - according to Shadowserver and
                       Onyphe. As of Thursday, the number of seemingly
                       compromised devices had dropped to about 800.


                # ⚓ WikiBooks ☛ Wikibooks:Artificial_Intelligence_-_Wikibooks,
                  open_books_for_an_open_world⠀⇛


                       Large language models (LLMs), often referred to as
                       "AI chatbots" or simply "AI", can be beneficial.
                       However, like human-generated text, machine-
                       generated text can also contain errors, flaws, or
                       even be entirely useless. In particular, requesting
                       a language model to write a book or an essay can
                       sometimes cause the production of complete
                       fabrications, including fictitious references. The
                       output may be biased, libel living people, infringe
                       on copyrights, or simply be of poor quality. As
                       such, LLMs may not be used to generate original
                       material or ideas at Wikibooks, and their sources
                       should not be blindly trusted.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ US News And World Report ☛ 2024-11-12_[Older]
                        Facebook_and_Instagram_Users_in_Europe_Can_Opt_for_Less
                        Personalized_Ads⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-11-18_[Older]_Germany:
                        Compensation_for_Facebook_data_breach_victims⠀⇛


                      # ⚓ Make Tech Easier ☛ 2024-11-14_[Older]_Apple’s_Shazam
                        Can_Now_Remember_Where_You_Identified_a_Song⠀⇛


                      # ⚓ International Business Times ☛ 2024-11-14_[Older]_Is
                        'Bluesky'_The_New_Twitter?_Platform_Gains_1.25M
                        Followers_During_X's_Mass_Exodus_After_US_Elections
                        [Ed: Boosting another flavour of the same toxin]⠀⇛


                      # ⚓ Vox ☛ 2024-11-14_[Older]_Bluesky_feels_more_like_old
                        Twitter_than_X_does⠀⇛


                      # ⚓ Omicron Limited ☛ Wildlife_monitoring_technologies
                        used_to_intimidate_and_spy_on_women,_study_finds⠀⇛


                             Remotely operated camera traps, sound
                             recorders and drones are increasingly being
                             used in conservation science to monitor
                             wildlife and natural habitats, and to keep
                             watch on protected natural areas. But
                             Cambridge researchers studying a forest in
                             northern India have found that the
                             technologies are being deliberately misused
                             by local governments and male villagers to
                             keep watch on women without their consent.


                      # ⚓ Thomas Rigby ☛ Create_an_account⠀⇛


                             I've heard good things about another place in
                             town. I won't name-and-shame them because
                             this isn't about them; it's about every
                             largely unnecessary account.


                             To book an appointment, I tapped the "Book
                             appointment" button on their website which
                             took me to a third party booking system where
                             I needed to create an account.


                      # ⚓ JURIST ☛ Federal_court_allows_illegal_data_collection
                        claims_against_Target_to_move_forward⠀⇛


                             A US federal judge on Thursday denied Target
                             Corporation’s motion to dismiss a class-
                             action lawsuit alleging the retailer
                             collected and stored customers’ biometric
                             data without proper notice or consent.


                             A class-action lawsuit was filed in May 2024
                             by four Illinois residents on behalf of
                             shoppers in the state. The plaintiffs allege
                             that Target violated the Illinois Biometric
                             Information Privacy Act (BIPA), which
                             regulates the collection, storage, and use of
                             biometric data such as facial scans and
                             fingerprints.


          o § Defence/Aggression⠀➾


                # ⚓ US News And World Report ☛ 2024-11-13_[Older]_Israel_Says
                  It_Attacks_Hezbollah_Arms_Smuggling_Routes_in_Syria⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-14_[Older]_Israel_Will
                  Attack_Any_Attempt_to_Bring_Arms_to_Hezbollah_From_Syria_-
                  Army_Spokesperson⠀⇛


                # ⚓ CoryDoctorow ☛ Pluralistic:_The_far_right_grows_through
                  “disaster_fantasies”⠀⇛


                       This individualistic approach to problem solving
                       does useful work for powerful people, because it
                       keeps the rest of us thoroughly powerless. Voting
                       with your wallet is casting a ballot in a rigged
                       election that's always won by the people with the
                       thickest wallets, and statistically, that's never
                       you. That's why the right is so obsessed with
                       removing barriers to election spending: the wealthy
                       can't win a one-person/one-vote election (to be in
                       the 1% is to be outnumbered 99:1), but unlimited
                       campaign spending lets the wealthy vote in real
                       elections using their wallets, not just just
                       ballots.


                # ⚓ NDTV ☛ Sambhal_News:_Internet_Snapped,_Schools_Shut_As
                  Violence_Over_Shahi_Jama_Masjid_Mosque_Survey_Kills_3_In_UP⠀⇛


                       Internet services have been suspended and schools
                       shut after three people were killed in violence
                       over the survey of a mosque in Uttar Pradesh's
                       Sambhal on Sunday.


                       Chaos erupted in Sambhal Sunday morning when a
                       court-ordered survey of the Mughal-era Shahi Jama
                       Masjid led to violent clashes between the locals
                       and the police. The mosque is at the centre of a
                       contentious legal battle over claims that it was
                       built on the site of a Hindu temple.


                # ⚓ Jacobin Magazine ☛ Democracy_Is_Not_a_Customer_Loyalty
                  Program⠀⇛


                       Liberal democracy’s assumption that political
                       parties must compete for votes in the same way that
                       businesses compete for customers is a dangerous
                       trap. It reduces voting to a mere transactional
                       choice and erases the participatory vision of self-
                       governance


                # ⚓ Tom's Hardware ☛ Hackers_breach_Wi-Fi_network_of_U.S._firm
                  from_Russia_—_daisy_chain_attack_jumps_from_network_to
                  network_to_gain_access_from_thousands_of_miles_away⠀⇛


                       The hackers were able to access their target by
                       first compromising the network of a neighboring
                       firm (Company B). In their first attack, they
                       looked for a computer that was connected via
                       Ethernet to the initially compromised network
                       (Company B) but could also connect via Wi-Fi. From
                       there, they connected to the wireless network of
                       their final target (Company A). Another attack
                       showed the hackers penetrating the network of a
                       third company (Company C) to then connect to
                       Company B’s Wi-Fi. They then used that connection
                       to Company B to advance their cyberattack on
                       Company A.


                # ⚓ The Register UK ☛ Russian_cyberspies_access_target_by
                  compromising_neighbors⠀⇛


                       To get around the fact it was targeting a Wi-Fi
                       network thousands of miles away, APT28 breached the
                       target's neighboring organizations, identified
                       devices with both wired and wireless network
                       adapters, and used them to connect to the target's
                       Wi-Fi network with the stolen credentials. Once
                       connected, the attackers moved laterally within the
                       network and routed exfiltrated data through
                       compromised machines on neighboring networks.


                # ⚓ Deccan Chronicle ☛ Yazidis_Seek_India_Support_at_UNSC⠀⇛


                       The IS had killed thousands of Yazidi men,
                       thousands of women have been abducted and made sex
                       slaves and their children were forced into slavery.


                       The delegation of Yazidi National Union (YNU),
                       which represents the community, is seeking
                       intervention of Prime Minister Narendra Modi to
                       represent their cause at the United Nations
                       Security Council (UNSC) for the protection of one
                       of the ancient communities in the world from
                       disappearance and creation of a safe zone in their
                       territory.


                # ⚓ [Repeat] RFA ☛ What_happens_when_China_puts_boots_on_the
                  ground_in_Myanmar?⠀⇛


                       It now appears to be a question of “when, not if”
                       Chinese security personnel will arrive in Myanmar,
                       with Beijing looking to secure its strategic
                       interests in the war-torn country and those of its
                       ally, the military junta that has lost large chunks
                       of the country since the 2021 coup.


                # ⚓ The Atlantic ☛ What_the_Broligarchs_Want_from_Trump⠀⇛


                       After Donald Trump won this month’s election, one
                       of the first things he did was to name two
                       unelected male plutocrats, Elon Musk and Vivek
                       Ramaswamy, to run a new Department [sic] of
                       Government Efficiency. The yet-to-be-created
                       entity’s acronym, DOGE, is something of a joke—a
                       reference to a cryptocurrency named for an
                       [Internet] meme involving a Shiba Inu. But its
                       appointed task of reorganizing the federal
                       bureaucracy and slashing its spending heralds a new
                       political arrangement in Washington: a broligarchy,
                       in which tremendous power is flowing to tech and
                       finance magnates, some of whom appear indifferent
                       or even overtly hostile to democratic tradition.


                # ⚓ New York Times ☛ Trump_Is_Running_His_Transition_Team_on
                  Secret_Money⠀⇛


                       Mr. Trump has so far declined to sign an agreement
                       with the Biden administration that imposes strict
                       limits on that fund-raising in exchange for up to
                       $7.2 million in federal funds earmarked for the
                       transition. By dodging the agreement, Mr. Trump can
                       raise unlimited amounts of money from unknown
                       donors to pay for the staff, travel and office
                       space involved in preparing to take over the
                       government.


                       Mr. Trump is the first president-elect to sidestep
                       the restrictions, provoking alarm among ethics
                       experts.


                # ⚓ Los Angeles Times ☛ Trump_wanted_to_ban_TikTok._Will_his
                  return_to_office_help_save_it?⠀⇛


                       But there are factors that complicate the app’s
                       position. Several legal experts and tech industry
                       observers said the path forward for TikTok is still
                       precarious.


                       “It’s just a huge mess, and it isn’t clear,” said
                       Carl Tobias, a law professor at the University of
                       Richmond.


                # ⚓ Deutsche Welle ☛ Nordic_countries_ramp_up_civil_defenses⠀⇛


                       Finland, Sweden and Norway have all issued updated
                       preparedness guides to their citizens. Finland has
                       issued theirs in a digital format, while Norway and
                       Sweden are sending physical copies of instructions
                       to all households.


                # ⚓ Axios ☛ The_Resistance_to_Trump_goes_quiet⠀⇛


                       That could change as Trump moves to implement his
                       agenda. But experts and activists expect the
                       renewed resistance to come in different forms.


                       Flashback: Trump won in 2016 despite trailing in
                       the polls, and within weeks of the infamous Access
                       Hollywood tape and multiple sexual assault
                       allegations.


                # ⚓ RFERL ☛ Romanians_Vote_In_Presidential_Election_As_Ukraine
                  Aid_Could_Lay_In_Balance⠀⇛


                       At three polling stations, turnout was reported at
                       more than 150 percent. It was not immediately clear
                       if the figure was the result of irregularities or
                       due to supplemental lists holding more names than
                       the permanent lists.


                # ⚓ RFERL ☛ Police_Violence_Against_Foreign_Students_In_Kazan
                  Leads_To_Iranian_Diplomatic_Protest⠀⇛


                       The violent detentions of brawling foreign
                       university students, including from Iran, in
                       Tatarstan has led to a protest by the Iranian
                       consul-general.


                # ⚓ France24 ☛ LGBT_harassment_in_Russia;_destruction_of
                  monuments_in_the_West_Bank_(16/12/2023)⠀⇛


                       A weekly news show produced with photos, videos and
                       personal accounts from France 24 Observers around
                       the world - all checked by our staff here in Paris.
                       This show was broadcast on 16/12/2023.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ New York Times ☛ What’s_Behind_Ukraine_and_Russia’s
                        Missile_Brinkmanship?⠀⇛


                             Tit-for-tat moves this week included the use
                             of American-made ballistic missiles to strike
                             inside Russia, and new nuclear threats from
                             Moscow. Neither appear to have influenced the
                             war on the ground.


                      # ⚓ RFERL ☛ EU_Parliament_Leader_Wants_Germany_To_Send
                        Taurus_Missiles_To_Ukraine⠀⇛


                             EU Parliament President Roberta Metsola
                             supports the use of long-range missiles by
                             Ukraine in its defense against Russia's full-
                             scale invasion and said Germany should
                             quickly deliver its long-range Taurus system
                             to the embattled country.


                      # ⚓ RFERL ☛ Trump_Reportedly_Considers_Ex-Intelligence
                        Chief_Richard_Grenell_For_Ukraine_Post⠀⇛


                             U.S. President-elect Donald Trump is
                             considering tapping Richard Grenell, his
                             former intelligence chief, to be a special
                             envoy for the Russia-Ukraine conflict,
                             according to four sources familiar with the
                             transition plans.


                      # ⚓ RFERL ☛ Russia's_Claim_Of_Emissions_In_Occupied
                        Ukraine_Regions_Draws_Protests_At_COP29⠀⇛


                             Russia has included the territories it
                             occupies in Ukraine in its recent greenhouse
                             gas inventory report to the United Nations,
                             drawing protests from Ukrainian officials and
                             activists at the COP29 climate summit in
                             Baku.


                      # ⚓ JURIST ☛ Ukraine_prosecutor_accuses_Russia_of
                        executing_POWs⠀⇛


                             The Donetsk Regional Prosecutor’s Office on
                             Friday accused Russian soldiers of executing
                             five Ukrainian prisoners of war (POWs) near
                             the village of Vuhledar in Donetsk Oblast,
                             Ukraine. The office stated: “The killing of
                             prisoners of war is a gross violation of the
                             Geneva Conventions and is classified as a
                             serious international crime.”


                      # ⚓ France24 ☛ Ukraine_faces_rapid_demographic_decline⠀⇛


                             Ukraine's population has declined by 10
                             million, or around a quarter, since the start
                             of Russia's invasion in 2014 as a result of
                             refugees leaving, collapsing fertility and
                             war deaths, according to the United Nations.
                             Catherine Norris-Trent, senior reporter at
                             France 24, reports.


                      # ⚓ France24 ☛ Ukraine_loses_more_than_40%_of_territory
                        it_seized_in_Russia's_Kursk_region⠀⇛


                             Ukraine lost more than 40% of the territory
                             in Russia's Kursk region that it captured in
                             a surprise offensive in August with the
                             Russians launching multiple counter-attacks,
                             a senior source in Kyiv's army said. While
                             the Kursk invasion caught Moscow unprepared,
                             Russian forces are still steadily advancing
                             in Ukraine’s eastern Donetsk region.


                      # ⚓ France24 ☛ "The_Ukrainian_army_is_outnumbered,_in_men
                        and_equipment"⠀⇛


                             Ukraine was bound to lose the territory it
                             held in Russia, said FRANCE 24's
                             correspondent in Ukraine Emmanuelle Chaze.
                             "At the height of the Ukrainian offensive in
                             the Kursk region, the Ukrainian army
                             controlled over 1300 square kilometres of
                             land, and within four months, Russia has
                             managed to reclaim 40% of this land," she
                             said. "This didn't come as a surprise for the
                             Ukrainians, simply because the Ukrainian army
                             is outnumbered, in men and equipment," she
                             added.


                      # ⚓ Atlantic Council ☛ Biden’s_Ukraine_moves_are_a_gift
                        to_Trump⠀⇛


                             The outgoing administration is “emptying the
                             barrel,” which could improve the incoming
                             president’s chances at negotiating a deal
                             worth having.


                      # ⚓ New York Times ☛ With_Memes_and_in_State_Media,_Many
                        Russians_Cheer_on_Putin’s_Threats⠀⇛


                             While support for Vladimir V. Putin’s threats
                             resounded in pro-war venues, some Russians
                             reacted with worry, gallows humor and apathy
                             to the suggestions of striking the West and
                             using nuclear weapons.


                      # ⚓ RFERL ☛ Putin_Says_Russia_Will_Use_New_Missile_Again
                        In_'Combat_Conditions'_After_Ukraine_Strike⠀⇛


                             Russian President Vladimir Putin said the
                             country's new intermediate-range ballistic
                             missile, a nuclear-capable weapon, will
                             continue to be tested, including in combat
                             conditions, as Moscow struck several
                             Ukrainian regions with other weapons.


                      # ⚓ RFERL ☛ Zelenskiy_Says_Putin_Aiming_To_Regain_Kursk
                        Territory_Before_Trump_Takes_Office⠀⇛


                             Ukrainian President Volodymyr Zelenskiy said
                             that Russia is seeking to drive his forces
                             out of the Kursk region before U.S.
                             President-elect Donald Trump takes office
                             next year but added that the military
                             situation in the Donetsk region is the most
                             critical for his country.


                      # ⚓ France24 ☛ Lt_Gen_Hodges:_Putin's_war_on_Ukraine
                        'could've_ended_last_year'_had_West_provided_Kyiv_'the
                        tools'⠀⇛


                             As Ukrainian President Volodymyr Zelensky
                             appeals to allies for updated air-defence
                             systems to meet the new threat from Russia,
                             involving an experimental hypersonic missile,
                             FRANCE 24's Gavin Lee welcomes Retired US
                             Lieutenant General Ben Hodges, former
                             Commanding General of US Army Europe. Lt.
                             Gen. Hodges asserts that, despite numerous
                             threats, Russia will never start a nuclear
                             war "because there are zero positive
                             upsides," including the US threat of
                             "catastrophic consequences."


                      # ⚓ RFERL ☛ Georgian_Dream_To_Open_Parliament_Despite
                        Protests,_Without_Foreign_Diplomats⠀⇛


                             The Moscow-friendly Georgian Dream party,
                             fresh off a contested victory in
                             parliamentary elections last month that
                             ignited calls for fresh polls and pro-EU
                             demonstrations in Tbilisi, is preparing to
                             hold its first parliamentary session on
                             November 25.


                      # ⚓ European Commission ☛ Address_by_Mr_Janusz
                        Wojciechowski_at_the_International_Summit_on_Food
                        Security,_Kyiv⠀⇛


                             It is my great pleasure to join you here in
                             Kyiv, at this important event, and at this
                             important moment.


                      # ⚓ New York Times ☛ Russia_Supplies_Antiaircraft
                        Missiles,_to_North_Korea,_the_South_Says⠀⇛


                             Pyongyang has long coveted an advanced air-
                             defense system to guard against missiles and
                             war planes from the United States and South
                             Korea.


          o § Environment⠀➾


                # ⚓ The Independent UK ☛ What_to_know_about_the_plastic
                  pollution_treaty_talks_in_South_Korea⠀⇛


                       Nations are deciding what actions they'll take


                       National delegations still have a lot to hammer out
                       before there is a treaty. Most contentious is
                       whether there will be a limit on the amount of
                       plastic that companies are allowed to produce.


                # ⚓ The Independent UK ☛ In_South_Korea,_nations_meet_in_final
                  round_to_address_global_plastic_crisis⠀⇛


                       It's the fifth time the world's nations convene to
                       craft a legally binding plastic pollution accord.
                       In addition to the national delegations,
                       representatives from the plastics industry,
                       scientists and environmentalists have come to shape
                       how the world tackles the surging problem.


                       The planet is “ choking on plastic, ” according to
                       the United Nations. It's polluting lakes, rivers,
                       oceans and people's bodies.


                # ⚓ The Korea Times ☛ Global_attention_centers_on_reducing
                  plastic_production_as_5th_round_of_negotiations_begins_in
                  Busan⠀⇛


                       The two major issues that will be the focus at the
                       INC-5 are whether to prioritize the regulation of
                       plastic production or promote reuse and whether to
                       specify a target year for international plastic
                       agreements.


                       The key issue in the debate over production
                       regulation is whether to impose limits on the
                       production of primary polymers, which are raw
                       materials used to make plastics extracted from
                       fossil fuels.


                # ⚓ VOA News ☛ $300B_climate_change_deal_sparks_hope_in_some,
                  outrage_in_others⠀⇛


                       The $300 billion will go to developing countries
                       who need the cash to wean themselves off the coal,
                       oil and gas that causes the globe to overheat,
                       adapt to future warming, and pay for the damage
                       caused by climate change’s extreme weather. It’s
                       not near the full amount of $1.3 trillion that
                       developing countries were asking for, but it’s
                       three times a deal of $100 billion a year from 2009
                       that is expiring. Some delegations said this deal
                       is headed in the right direction, with hopes that
                       more money flows in the future.


                # ⚓ Counter Punch ☛ 2024-11-19_[Older]_In_Baku,_at_the_Latest
                  Global_Confab_on_Climate,_Hand-Wringing_Abounds⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-19_[Older]_Should_major_fossil
                  fuel_companies_pay_for_climate_damage?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-19_[Older]_What_will_happen_if
                  Argentina_quits_Paris_Climate_Agreement?⠀⇛


                # ⚓ The Age AU ☛ 2024-11-19_[Older]_Coral_bleaching_on_the
                  Great_Barrier_Reef,_September_2024⠀⇛


                # ⚓ Copenhagen Post ☛ 2024-11-18_[Older]_Danish_government
                  strikes_major_green_deal⠀⇛


                # ⚓ Mexico News Daily ☛ 2024-11-18_[Older]_​​Sheinbaum_included
                  in_TIME’s_list_of_top_100_climate_titans⠀⇛


                # ⚓ University of Michigan ☛ 2024-11-18_[Older]_Presentations
                  scheduled_for_campus_climate_survey_findings⠀⇛


                # ⚓ TruthOut ☛ 2024-11-18_[Older]_COP29_Activists_Demand_$5
                  Trillion_in_Annual_Climate_Financing_From_Global_North⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-18_[Older]_How_has_Germany's
                  collapsed_coalition_scored_on_climate?⠀⇛


                # ⚓ Truthdig ☛ 2024-11-18_[Older]_The_Question_Looming_Over
                  COP29:_Who’s_Rich_Enough_To_Pay_for_Climate_Change?⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-18_[Older]_Andrea_Illy
                  Takes_Aim_at_Coffee’s_Climate_Crisis⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-17_[Older]_Methane_From
                  Tropical_Wetlands_Is_Surging,_Threatening_Climate_Plans⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-17_[Older]_G20_Talks_in
                  Rio_Reach_Breakthrough_on_Climate_Finance,_Sources_Say⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-15_[Older]_Where_are_we_at_with
                  countries'_climate_contributions?⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-15_[Older]_New_York
                  Judge_Rejects_State_Efforts_to_Shutter_Bitcoin_Mine_Over
                  Climate_Concerns⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-15_[Older]_Climate
                  Change_Activist_Gets_2_Years_in_Prison_for_Dumping_Red_Powder
                  on_Constitution_Display⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-15_[Older]_Australia
                  Eyes_US_Climate_Policy_Shift_for_Green_Energy_Boost⠀⇛


                # ⚓ Vox ☛ 2024-11-15_[Older]_I_saw_the_Hurricane_Helene
                  response_up_close._This_is_how_disaster_relief_actually
                  works.⠀⇛


                # ⚓ Modern Diplomacy ☛ 2024-11-14_[Older]_Social_Media_and
                  Climate_Discourse:_A_Double-Edged_Sword_for_Global_Advocacy⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-14_[Older]_G20:_Lula_faces_high
                  stakes_on_climate,_taxing_billionaires⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-14_[Older]_Is_climate_finance
                  reaching_the_most_vulnerable?⠀⇛


                # ⚓ Renewable Energy World ☛ 2024-11-14_[Older]_Companies_are
                  buying_up_cheap_carbon_offsets_−_data_suggest_it’s_more_about
                  greenwashing_than_helping_the climate⠀⇛


                # ⚓ The Age AU ☛ 2024-11-14_[Older]_Extinction_Rebellion
                  climate_activists_block_traffic_during_peak_hour_in
                  Melbourne⠀⇛


                # ⚓ Vox ☛ 2024-11-14_[Older]_We_were_supposed_to_hit_peak
                  emissions._Why_won’t_they_stop_rising?⠀⇛


                # ⚓ Modern Diplomacy ☛ 2024-11-13_[Older]_Climate_Change:
                  Science,_Impacts,_Mitigation,_and_Financing_at_COP29⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-13_[Older]_Climate_disaster_fund
                  to_start_paying_out_in_2025⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-13_[Older]_COP29:_Climate_change
                  in_10_charts⠀⇛


                # ⚓ NL Times ☛ 2024-11-12_[Older]_Climate_group_can't_force
                  Shell_to_set_and_achieve_CO2_reduction_targets:_Appeals
                  Court⠀⇛


                # ⚓ TruthOut ☛ 2024-11-12_[Older]_Climate_Groups_Decry_Dutch
                  Court’s_Reversal_of_Shell_Ruling_as_“Setback”⠀⇛


                # ⚓ Counter Punch ☛ 2024-11-12_[Older]_The_Military-Industrial
                  Complex_Is_Fueling_Climate_Catastrophe⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-11-12_[Older]_What_is_Big_Oil_and
                  what_does_it_mean_for_the_climate?⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-12_[Older]_Development
                  Lenders_Set_$120-Billion_Climate_Finance_Goal_for_Poorer
                  Countries⠀⇛


                # § Energy/Transportation⠀➾


                      # ⚓ Daniel Pocock ☛ Energy_shock:_€17,000_circuit_court
                        claim,_threat_of_judgment_for_fraudulent_charges⠀⇛


                             The home in Dublin suffered a fire in January
                             2023. A lodger had made a mistake with a
                             candle. The feeling when I go back there is a
                             feeling of grief. The environment has become
                             toxic. The work required to restore it is
                             beyond what most individuals could
                             comprehend, let alone execute. Yet going back
                             there one day in July 2024, when it would
                             seem that nothing could get worse, it did.


                             Imagine it is days before you are to leave on
                             your summer vacation and a sinister looking,
                             hand-written, red envelope arrives in your
                             letterbox.


                             In my case, there was no summer vacation. I
                             was on the way to an event in the United
                             States.


                             Opening up the red envelope, I found court
                             documents insisting that I have used €17,000
                             of energy in the eighteen months that the
                             home has been vacant.


                      # ⚓ Dan Langille ☛ Optimizing_UPS_power_use_when_the
                        power_goes_out⠀⇛


                             This post is mostly for myself. I’m just
                             putting my Sunday morning thoughts down for
                             later review and consideration.


                             When Selecting replacements batteries for my
                             Eaton 5PX UPS (5PX2200RT & 5PXEBM48RT), I
                             began to think about: when the power goes
                             off, why can’t I keep using my laptop?


                      # ⚓ Los Angeles Times ☛ Solar_glut_boosts_California
                        power_bills_—_other_states_reap_the_benefits⠀⇛


                             In the last 12 months, California has
                             curtailed production of enough solar energy
                             to power 518,000 homes for a year.


                             Californians, whose electric rates are
                             roughly twice the national average, are
                             essentially paying for power capacity they
                             are unable to use.


                      # ⚓ Los Angeles Times ☛ With_bitcoin_surging,_here's_a
                        refresher_on_cryptocurrency⠀⇛


                             Now, bitcoin is at the doorstep of $100,000,
                             just two years after dropping below $17,000
                             after the collapse of [cryptocurrency]
                             exchange FTX. The dramatic rally arrives as
                             industry players expect the incoming Trump
                             administration to bring a more
                             [cryptocurrency]-friendly approach to
                             regulating the digital currency.


                      # ⚓ CS Monitor ☛ Recurring_blackouts_roiled_Cuba._What’s
                        behind_the_crisis?⠀⇛


                             Blackouts have been a regular feature in Cuba
                             for decades. But in recent months, the
                             problem has escalated – lasting longer and
                             occurring more frequently. Here’s a look at
                             the factors driving outages on the island.


                # § Wildlife/Nature⠀➾


                      # ⚓ EcoWatch ☛ ‘Mind-Blowing’:_Study_Shows_Fungal
                        Networks_Can_Solve_Problems_and_Make_Decisions⠀⇛


                             If the fungi did not have decision-making
                             skills, they would spread out from the center
                             without being affected by the placement of
                             the blocks. However, this is not what
                             happened.


                      # ⚓ Omicron Limited ☛ Slender-billed_Curlew_may_be
                        extinct,_marking_the_disappearance_of_a_third_bird
                        species_from_the_Western_Palaearctic⠀⇛


                             In their paper published in the journal Ibis,
                             the group notes that the extinction would
                             also represent the first bird species from
                             Mainland Europe, West Asia and North Africa
                             to go extinct.


          o § Finance⠀➾


                # ⚓ BIA Net ☛ 2024-11-15_[Older]_Two_million_children_in_Turkey
                  in_‘absolute_poverty’⠀⇛


                # ⚓ Robert Birming ☛ Don't_buy_me_a_coffee..._yet⠀⇛


                       I don’t think I offer anything that justifies a
                       call to donate money. I write some blog posts and
                       let others use my theme. That’s it!


                # ⚓ Seth Michael Larson ☛ How_do_I_pay_the_publisher_of_a_web
                  page?⠀⇛


                       URLs tell you where to get content on the web, but
                       they don't tell you anything about how to support
                       the person who created the content. This story
                       might sound similar to paying open source
                       maintainers, where a user can almost abstract an
                       entire project to a single download URL.


                       There are tons of people creating content for the
                       web and plenty of ways to get paid (Patreon, Kofi,
                       GitHub Sponsors, YouTube Paid Membership), but
                       there's no standardized way to direct someone
                       interested in paying for the content of a page in
                       the right direction.


                       We have HTML meta headers for many things,
                       including where to find an RSS feed or what my
                       Fediverse handle is, but none for enumerating
                       options to pay the creator of the content. I wish I
                       could click a button to easily send a "tip" to
                       someone who created something I enjoy or to browse
                       other options for supporting them.


                # ⚓ International Business Times ☛ 2024-11-17_[Older]_UK_Women
                  Save_Over_£6K_On_Cosmetic_Surgeries_In_Turkey—But_Some_Go
                  From_Surgery_Table_To_Coffin⠀⇛


                # ⚓ BIA Net ☛ 2024-11-15_[Older]_Landlords_in_Turkey_accused_of
                  trapping_refugees_into_deportation_scheme⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Deccan Chronicle ☛ Amazon_Invests_an_Additional_$4_Billion
                  in_AI_Firm_Anthropic⠀⇛


                       Amazon is investing an additional $4 billion in
                       artificial intelligence startup Anthropic, boosting
                       its stake in one of OpenAI’s chief rivals.


                # ⚓ The Verge ☛ Tech_CEOs_want_to_replicate_Tim_Cook’s_Donald
                  Trump_playbook⠀⇛


                       Cook used direct appeals to influence Trump’s 2017
                       tax policy and to get him to dial back his 2019
                       tariffs in ways that benefitted Apple. In exchange,
                       Trump got to look good; as the Journal points out,
                       Cook didn’t correct Trump when claimed
                       responsibility for Apple opening an Austin
                       manufacturing plant that had already been around
                       for years and wasn’t even owned by Apple.


                # ⚓ US News And World Report ☛ US_Plans_to_Reduce_Intel's_$8.5
                  Billion_Federal_Chips_Grant_Below_$8_Billion_-_New_York
                  Times⠀⇛


                       The change took into account a $3 billion contract
                       Intel had been offered to make chips for the
                       Pentagon, the people told the Times.


                # ⚓ Pivot to AI ☛ Roll_out_the_barrels_of_pork:_Congressional
                  committee_recommends_AI_‘Manhattan_Project’⠀⇛


                       Helberg just happens to be a senior advisor to the
                       CEO of Palantir and a close friend of Sam Altman at
                       OpenAI. In fact, Altman officiated at Helberg’s
                       2019 wedding to Keith Rabois of the PayPal Mafia.


                # ⚓ Kansas Reflector ☛ Some_in_the_venture_capital_community
                  backed_Trump._Here’s_what’s_next⠀⇛


                       While Trump didn’t receive unanimous support from
                       the tech sector, many American tech giants and
                       investors are excited about the light-handed
                       approach to tech regulation that’s likely to come
                       in the next four years. Congress has struggled to
                       pass any federal laws around emerging technology
                       like AI, though states have done so on their own on
                       issues like data privacy, transparency,
                       discrimination, and on how AI-generated images can
                       be used.


                # ⚓ [Repeat] New Yorker ☛ The_Rise_of_4B_in_the_Wake_of_Donald
                  Trump’s_Reëlection⠀⇛


                       A “Lysistrata”-style political sex strike in the
                       U.S. is unlikely to take off. But there hasn’t
                       really been one in South Korea, either. I wouldn’t
                       describe 4B as a movement or an ideology as much as
                       a feeling, a name for what many women are doing (or
                       not doing), intentionally or not. The country has
                       one of the world’s lowest fertility rates, and the
                       marriage rate has fallen by forty per cent in the
                       past decade. Many straight women, twentysomething
                       through middle age, have given up on the layers of
                       bullshit that come with dating and reproduction:
                       sexist dudes, in-law drama, holiday rituals, dead-
                       end job prospects. There’s also the untenable cost
                       of family housing and childhood education in Seoul
                       and other major cities. 4B is catchy and
                       provocative, but it’s also way too slight to help
                       us through this moment of crisis.


                # ⚓ IT Wire ☛ iTWire_-_Nokia_wins_five-year_deal_to_supply
                  Azure_data_centre_networks⠀⇛


                       Telecoms equipment vendor Nokia has won a five-year
                       expansion of its existing multi-year agreement to
                       supply Microsoft Azure with data centre routers and
                       switches.


                # ⚓ BIA Net ☛ 2024-11-18_[Older]_Turkish_state_media_says
                  Israel’s_president_had_to_skip_COP29_after_Turkey_denied
                  airspace_access⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-19_[Older]_Turkey's
                  Erdogan_Says_Israel's_Herzog_Was_Denied_Airspace_En_Route_to
                  Azerbaijan⠀⇛


                # ⚓ US News And World Report ☛ 2024-11-18_[Older]_US_Warns
                  Turkey_Against_Hosting_Hamas_Leaders⠀⇛


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ VOA News ☛ Australia_withdraws_misinformation_bill
                        after_critics_compare_it_to_censorship ⠀⇛


                             The bill would have granted the Australian
                             Communications and Media Authority power over
                             digital platforms by approving an enforceable
                             code of conduct or standards for social media
                             companies if self-regulation fell short.


                      # ⚓ Google ☛ Seeing_Through_a_GLASSBRIDGE:_Understanding
                        the_Digital_Marketing_Ecosystem_Spreading_Pro-PRC
                        Influence_Operations_|_Google_Cloud_Blog⠀⇛


                             This blog post details GLASSBRIDGE—an
                             umbrella group of four different companies
                             that operate networks of inauthentic news
                             sites and newswire services tracked by the
                             Google Threat Intelligence Group (consisting
                             of Google’s Threat Analysis Group (TAG) and
                             Mandiant). Collectively these firms bulk-
                             create and operate hundreds of domains that
                             pose as independent news websites from dozens
                             of countries, but are in fact publishing
                             thematically similar, inauthentic content
                             that emphasizes narratives aligned to the
                             political interests of the People’s Republic
                             of China (PRC). Since 2022, Google has
                             blocked more than a thousand GLASSBRIDGE-
                             operated websites from eligibility to appear
                             in Google News features and Google Discover
                             because these sites violated our policies
                             that prohibit deceptive behavior and require
                             editorial transparency.


                             We cannot attribute who hired these services
                             to create the sites and publish content, but
                             assess the firms may be taking directions
                             from a shared customer who has outsourced the
                             distribution of pro-PRC content via imitation
                             news websites.


                             These campaigns are another example of
                             private public relations (PR) firms
                             conducting coordinated influence campaigns—in
                             this case, spreading content aligned with the
                             PRC’s views and political agenda to audiences
                             dispersed across the globe. By using private
                             PR firms, the actors behind the information
                             operations (IO) gain plausible deniability,
                             obscuring their role in the dissemination of
                             coordinated inauthentic content.


                      # ⚓ NPR ☛ What_happens_when_your_partner_has_an_overnight
                        political_conversion? [Ed: NPR is whitewashing Bill
                        Gates, who bribes NPR; criticism of Gates is not
                        disinformation]⠀⇛


                             Vaillancourt's social media feeds kept
                             showing her more and more QAnon content,
                             including posts and videos claiming the
                             alleged cabal had planned the pandemic to
                             institute authoritarian control. "Once you
                             fell into this QAnon rabbit hole, that became
                             the entire online ecosystem," Vaillancourt
                             said. "My Facebook, my YouTube, my Google
                             searches — everything was giving me more and
                             more of this information that I found so
                             fascinating that I believed myself to be
                             waking up," she said.


                      # ⚓ Deutsche Welle ☛ 2024-11-12_[Older]_Fact_check:
                        Amsterdam_video_doesn't_show_attack_on_Israelis⠀⇛


                      # ⚓ NL Times ☛ 2024-11-17_[Older]_Police_identified_45
                        suspects_in_Amsterdam_riots,_unblurred_photos_of
                        suspects_released⠀⇛


                      # ⚓ US News And World Report ☛ 2024-11-12_[Older]
                        European_Fake_Art_Network_Involving_Banksys,_Warhols,
                        Modiglianis_Uncovered_in_Italy⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ BIA Net ☛ 2024-11-14_[Older]_Director_Luca_Guadagnino_says
                  Turkey’s_ban_on_his_film_‘Queer’_will_boost_its_cult_status⠀⇛


                # ⚓ RFERL ☛ Pakistani_Capital_Locked_Down,_Internet_Partially
                  Suspended_Ahead_Of_Protest⠀⇛


                       Pakistani authorities have locked down Islamabad
                       and partially suspended mobile phone and Internet
                       services as supporters of imprisoned former Prime
                       Minister Imran Khan geared up for a protest in the
                       capital, calling for his release.


                # ⚓ Deccan Chronicle ☛ Pakistan_cuts_mobile,_[Internet]
                  services_ahead_of_pro-Imran_Khan_protest⠀⇛


                       Pakistan on Sunday suspended mobile and internet
                       services “in areas with security concerns” as
                       supporters of imprisoned former premier Imran Khan
                       geared up for a protest in the capital .


                       The government and Interior Ministry posted the
                       announcement on social media platform X, which is
                       banned in Pakistan. They did not specify the areas,
                       nor did they say how long the suspension would be
                       in place.


                # ⚓ Deccan Chronicle ☛ Internet_ban_extended_in_Manipur_as_7
                  arrested_for_arson_in_Imphal⠀⇛


                       Amid continuing unrest in Manipur, the state
                       government has extended its ban on mobile
                       [Internet] and data services, including VSAT and
                       VPN services, in nine districts for an additional
                       two days. This move comes as tensions remain high
                       following violent incidents, including arson
                       attacks on the residences of elected officials.


                # ⚓ New York Times ☛ Egypt_Feuds_With_Travel_Blogger,_Issuing
                  1,100-Word_Response_to_Complaints⠀⇛


                       But this month, Egypt found itself facing an
                       opponent it could not silence so easily.


                       “Cairo Airport: Is There a Worse Major Airport?”
                       the travel blogger Ben Schlappig pondered in a no-
                       holds-barred post on his website, One Mile at a
                       Time. He cited the “actively hostile and rude”
                       staff, the “endless requests for tips,” the
                       “disorder” in line, the “weak” dining options and
                       the “yuck” lounges.


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


                # ⚓ CPJ ☛ 2024-11-13_[Older]_CPJ_joins_call_for_Turkey_to
                  release_arrested_journalist_Furkan_Karabay⠀⇛


                # ⚓ BIA Net ☛ 2024-11-13_[Older]_‘Covering_ECtHR_rulings_could
                  become_an_offense_with_Turkey’s_new_agents_of_influence
                  bill’⠀⇛


                # ⚓ The Dissenter ☛ Democrats_Responsible_For_Slow_Death_Of_The
                  PRESS_Act⠀⇛


                # ⚓ ANF News ☛ Prison_sentence_against_journalist_Beritan
                  Canözer_confirmed⠀⇛


                       Beritan Canözer has been working as a journalist
                       for ten years. During this time, her home was
                       searched six times by the police. She was arrested
                       five times and was twice in custody for several
                       months. Eight criminal proceedings were initiated
                       against her. In three cases, she was accused of
                       membership in a terrorist organization and
                       acquitted in court. She was sentenced to a total of
                       seven and a half years in prison in four different
                       trials on charges of propaganda for a terrorist
                       organization.


                # ⚓ Nebraska Examiner ☛ Nebraska_newspapers_in_Ainsworth,
                  Valentine_slated_to_close_unless_buyers_are_found⠀⇛


                       The Worrells are not alone.


                       A combination of higher production and mailing
                       costs, a shift by advertisers to social media and
                       other outlets and the difficulty in hiring staff to
                       cover night and weekend community meetings and
                       local ball games have put a squeeze on community
                       newspapers.


                # ⚓ Axios ☛ Jim_VandeHei:_Why_clear-eyed_journalism_matters⠀⇛


                       "But at the core of that is maybe transparency,
                       maybe a free press, maybe the ability to do your
                       job without worrying about going to jail, maybe the
                       ability to sit in a war zone and tell people what's
                       actually happening ... The work that we do
                       matters."


                # ⚓ VOA News ☛ Prominent_Cambodia_environmentalist_arrested
                  while_investigating_illegal_logging⠀⇛


                       A prominent Cambodian environmentalist was arrested
                       along with five others while investigating illegal
                       logging in a national park, a rights group and a
                       government official said Sunday.


                # ⚓ Breach Media ☛ Police_spied_on_Albertan_journalist_accused
                  of_vandalizing_Nazi_monuments⠀⇛


                       Journalist Duncan Kinney is charged with mischief
                       for allegedly spray-painting two Nazi monuments—a
                       charge he says the Edmonton Police is using to
                       silence him


          o § Civil Rights/Policing⠀➾


                # ⚓ HRW ☛ 2024-11-20_[Older]_Saudi_Arabia:_Public_Investment
                  Fund_Linked_to_Abuses⠀⇛


                # ⚓ BoingBoing ☛ Justice_Department_shuts_down_DEA_airport_cash
                  grab_scheme⠀⇛


                       Inspector General Michael E. Horowitz's
                       investigation revealed that one airline employee
                       alone received "tens of thousands of dollars" for
                       flagging passengers who committed the suspicious
                       act of… buying tickets within 48 hours of their
                       flight. Meanwhile, the DEA hasn't bothered
                       documenting these encounters or training their
                       agents since 2023, ignoring their own policies from
                       a 2015 oversight report.


                # ⚓ The Telegraph UK ☛ Taliban_divided_over_'isolated'_leader's
                  crackdown_on_women⠀⇛


                       Her crime was selling honey to male customers as a
                       female business owner, which is forbidden under the
                       Taliban regime. She ended up in jail.


                       Since returning to power in August 2021, the
                       Taliban has systematically curbed women’s rights in
                       Afghanistan.


                       The restrictions affect their daily lives, ranging
                       from preventing them showing their faces in public
                       or driving a car, to forbidding conversations with
                       men and restricting how they dress.


                # ⚓ Futurism ☛ CEO_Fires_99_Out_of_110_Workers_for_Missing
                  Morning_Meeting⠀⇛


                       This sudden departure isn't as unwarranted as it
                       sounds. The self-described intern explained that
                       every fired Musician's Club employee is an unpaid,
                       remote worker — so this isn't a story of lost
                       income as much as it is a moral tale about a CEO-
                       sized ego.


                # ⚓ VOA News ☛ New_Zealand's_founding_treaty_is_at_a
                  flashpoint._Why_are_thousands_protesting_for_Māori_rights?⠀⇛


                       A proposed law that would redefine New Zealand's
                       founding treaty between the British Crown and Māori
                       chiefs has triggered political turmoil and prompted
                       tens of thousands of people to show up in protest
                       at the country's Parliament on Tuesday.


                       The bill is never expected to become law. But it
                       has become a flashpoint on race relations and a
                       critical moment in the fraught 180-year-old
                       conversation about how New Zealand should honor its
                       promises to Indigenous people when the country was
                       colonized – and what those promises are.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ Is_it_bandwidth_or_latency?⠀⇛


                       You can’t ignore the laws of physics, especially
                       the speed of light. While people often know that
                       light travels at 3 × 10^8 metres per second, that’s
                       only true in a vacuum. When signals travel over
                       electrical wires, they slow down to about 2.7 ×
                       10^8 metres per second or roughly 97% of that
                       speed. Through fibre optics, it’s even slower
                       —around 2 × 10^8 metres per second — so a signal
                       travelling at two-thirds the speed of light is
                       actually expected.


                       The key point here is that distant locations are
                       often much farther than people realize. For
                       example, if your data packets are being served from
                       Japan while you’re in Europe, the signal delay,
                       even without any routers or switches along the way,
                       is around 60 milliseconds. This is noticeably
                       longer than the delay you’d experience receiving
                       the same data from a nearby Content Delivery
                       Network (CDN).


                # ⚓ Deccan Chronicle ☛ Experts:_GIS_Tech_to_Boost_Governance⠀⇛


                       Geographic Information Systems (GIS) were
                       highlighted as essential tools for governance,
                       sustainable development, and societal progress
                       during the International GIS Day celebrations held
                       at the Institution of Engineers, on Wednesday.
                       Experts discussed how GIS technology could
                       transform decision-making, planning, and education,
                       emphasising its role in achieving Sustainable
                       Development Goals (SDGs).


                # ⚓ Kev Quirk ☛ AMA_-_Do_I_See_a_Future_for_the_Federated_Web⠀⇛


                       The TL;DR is that I do see a future in the
                       federated web, but maybe not in its current form.
                       Let me explain...


                       As I alluded above - to me, the "federated web"
                       (aka fedi for the purposes of this post) isn't just
                       Mastodon and its ilk. To me, the backbone the fedi
                       are personal sites, like this one.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ [Old] Free Software Foundation ☛ About_the_DRM-free_label_|
                  Defective_by_Design⠀⇛


                       Would you ever shop at a book, video, or record
                       store that demanded permission to send employees to
                       your home to take back movies, novels, or CD's for
                       any reason? Would you buy something that broke when
                       you tried to share it with someone else?


                       Digital Restrictions Management is technology that
                       controls what you can do with the digital media and
                       devices you own. When a program doesn't let you
                       share a song, read an ebook on another device, or
                       play a single-player game without an [Internet]
                       connection, you are being restricted by DRM. In
                       other words, DRM creates a damaged good. It
                       prevents you from doing what would normally be
                       possible if it wasn't there, and this is creating a
                       dangerous situation for freedom, privacy and
                       censorship.


                # ⚓ Lee Yingtong Li ☛ Investigating_a_historical_Android_anti-
                  root_protection_system⠀⇛


                       This article concerns a specialised Android app
                       used as part of a proprietary authentication
                       protocol, developed in the late 2010s. Given the
                       intended use case, the app features a number of
                       aggressive security measures – the app uses
                       FLAG_SECURE and does not run when developer options
                       are enabled; it also incorporates root detection
                       and tamper prevention.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ Tom's Hardware ☛ Applied_Materials_MAX_OLED_screens_touted
                  to_offer_5x_lifespan_—_tech_claimed_to_produce_brighter_and
                  higher_resolution_screens_too⠀⇛


                       The patented OLED pixel design combined with a
                       revolutionary manufacturing process enhances all
                       types of OLED displays by delivering superior
                       brightness, sharper clarity, improved energy
                       efficiency, and extended lifespan.


                # ⚓ IP Kat ☛ 2024-11-13_[Older]_[GuestPost]_How_the_European
                  Patent_Office_uses_AI_to_facilitate_patent_searches [Ed: It's
                  not "AI", it's just hype and nothing new]⠀⇛


                # ⚓ 2024-11-13_[Older]_USPTO_Director_Announces_Resignation
                  [Ed: Now she can go back to working for her beloved
                  Microsoft]⠀⇛


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ 'Piracy'_Scam_Exploited_Movie_Fans_For_20
                  Years,_Suddenly_Cited_as_Major_Threat⠀⇛


                       One of the most enduring online movie scams
                       involves sites that claim to offer premium content,
                       but turn out to be some type of scam. These
                       services do not discriminate, so whether
                       'customers' are pirates or just regular people
                       hoping to buy content, everyone is a potential
                       victim. The scam has been running for at least 20
                       years yet, seemingly out of nowhere, pro site-
                       blocking studies now describe it as a major piracy-
                       related security threat.





                    ䷩ 𝚕𝚒𝚗𝚎 3970

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 25/11/2024: Egypt Harasses Bloggers,
The University of Michigan Has Become Like a
Corporation⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 25, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Monopolies/Monopsonies
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Flyback,_Done_Right⠀⇛


                 A common part used to create a high voltage is a CRT
                 flyback transformer, having been a ubiquitous junk pile
                 component. So many attempts to use them rely on brute
                 force, with power transistors in simple feedback
                 oscillators dropping high currents into hand-wound
                 primaries, so it’s refreshing to see a much more nuanced
                 approach from [Alex Lungu]. His flyback driver board
                 drives the transformer as it’s meant to be used, in
                 flyback mode relying on the sudden collapse of a magnetic
                 field to generate an output voltage pulse rather than
                 simply trying to create as much field as possible. It’s
                 thus far more efficient than all those free running
                 oscillators.


          o ⚓ Hackaday ☛ Double_Your_Analog_Oscilloscope_Fun_With_This_Retro
            Beam_Splitter⠀⇛


                 These days, oscilloscope hacking is all about enabling
                 features that the manufacturer baked into the hardware
                 but locked out in the firmware. Those hacks are cool, of
                 course, but back in the days of analog scopes, unlocking
                 new features required a decidedly more hardware-based
                 approach.


          o ⚓ Hackaday ☛ Aftershock_II:_How_Students_Shattered_20-Year_Amateur
            Rocket_Records⠀⇛


                 When it comes to space exploration, we often think of
                 billion-dollar projects—NASA’s Artemis missions, ESA’s
                 Mars rovers, or China’s Tiangong station. Yet, a group of
                 U.S. students at USC’s Rocket Propulsion Lab (RPL) has
                 achieved something truly extraordinary—a reminder that
                 groundbreaking work doesn’t always require government
                 budgets. On October 20, their homemade rocket, Aftershock
                 II, soared to an altitude of 470,000 feet, smashing the
                 amateur spaceflight altitude and speed records held for
                 over two decades. Intrigued? Check out the full article
                 here.


          o § Science⠀➾


                # ⚓ Science Alert ☛ Experiments_Reveal_What_Happens_When_You
                  Hand_in_Work_Late⠀⇛


                       Spoiler alert: It's not good.


                # ⚓ Science Alert ☛ Voyager_1_Just_Activated_a_Radio_That's
                  Been_Offline_Since_1981⠀⇛


                       Weird happenings in interstellar space.


                # ⚓ Science Alert ☛ A_Mysterious_Explosion_of_Color_in_Animals
                  Has_Lasted_100_Million_Years⠀⇛


                       But where did it come from?


                # ⚓ Science Alert ☛ A_Huge_Design_Flaw_in_CPR_Dummies_Could
                  Have_Deadly_Consequences⠀⇛


                       A grave omission.


          o § Career/Education⠀➾


                # ⚓ University of Michigan ☛ The_University_of_Michigan_is_a
                  corporation⠀⇛


                       The past two years have been eventful for the
                       University of Michigan, to say the least. Community
                       stakeholders have grappled with a strike by the
                       Graduate Employees’ Organization, outspoken student
                       protests, disapproval from student and alumni
                       groups, and national criticism of the University’s
                       diversity, equity and inclusion initiatives.


          o § Hardware⠀➾


                # ⚓ New York Times ☛ Washington_Curtails_Intel’s_Chip_Grant
                  After_Company_Stumbles⠀⇛


                       The Biden administration is reducing its award to
                       the chip maker, partly to account for a
                       multibillion-dollar military contract.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ World_Seeks_an_End_to_Plastic_Pollution_at
                  Talks_in_South_Korea⠀⇛


                       Many nations hope to reduce the half a billion tons
                       of plastic made each year. But pushback from
                       plastic and oil producers, and Donald Trump’s
                       election, could scuttle an agreement.


                # ⚓ The Straits Times ☛ Johor_to_ride_medical_tourism_wave⠀⇛


                       Malaysia has been stepping up efforts to pull in
                       medical tourists from Africa to Indonesia.


                # ⚓ The Straits Times ☛ Malaysia_boosts_efforts_to_fight
                  pneumonia,_the_leading_cause_of_death_in_country⠀⇛


                       Pneumonia became the principal cause of death for
                       the first time in two decades.


                # ⚓ The Straits Times ☛ China’s_local_governments_step_up
                  public_safety_measures_after_attacks⠀⇛


                       The safety initiatives come nearly two weeks after
                       the deadliest mass attack in China in a decade.


                # ⚓ Science Alert ☛ Should_You_Be_Worried_About_The_Mold
                  Growing_in_Your_Home?⠀⇛


                       Here's what we know.


                # ⚓ The Straits Times ☛ Nurses_at_Ramsay_Health_Care_hospitals
                  in_New_South_Wales_announce_24-hour_strike⠀⇛


                       Hundreds of nurses and midwives across Ramsay
                       Health Care's 17 hospitals in Australia's New South
                       Wales will go on a 24-hour strike on Tuesday,
                       demanding a pay hike and better staffing, a union
                       representing them said on Monday.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Tom's Hardware ☛ Researchers_jailbreak_Hey_Hi_(AI)_robots
                  to_run_over_pedestrians,_place_bombs_for_maximum_damage,_and
                  covertly_spy⠀⇛


                       Researchers from the University of Pennsylvania
                       have discovered that a range of AI-enhanced
                       robotics systems are dangerously vulnerable to
                       jailbreaks and hacks.


                # ⚓ Tom's Hardware ☛ Microsoft_Flight_Simulator_2024_gets_a_new
                  patch_to_address_ongoing_stability_issues_—_Abusive
                  Monopolist_Microsoft_suggests_users_install_1.1.9.0_patch,
                  relocate_Community_Folder_to_mitigate_long_loading_times⠀⇛


                       The latest hotfix for Abusive Monopolist Microsoft
                       Flight Simulator 2024 rectifies a few stability
                       issues and advises users to move the Community
                       Folder.


                # ⚓ Neil Selwyn ☛ Hey_Hi_(AI)_…_minding_our_language [Ed: Well,
                  they totally distort the term to mean almost anything]⠀⇛


                       As Melanie Mitchell argues in a recent article in
                       Science, experts and non-experts alike have long
                       struggled with finding the right words to describe
                       AI.


                # ⚓ New York Times ☛ Do_Coding_Boot_Camps_Make_Sense_in_an_Hey
                  Hi_(AI)_World? [Ed: This "Hey Hi (AI) World" nonsense from NY
                  Times helps companies lie about the capabilities of LLMs and
                  some garbage as such]⠀⇛


                       Coding boot camps once looked like the golden
                       ticket to an economically secure future. But as
                       that promise fades, what should you do? Keep
                       learning, until further notice.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ The Straits Times ☛ Thai_medical_tycoon_wanted_for
                        fraud_fled_to_China,_police_say⠀⇛


                             Scam victims believed they were investing in
                             medical businesses in Thailand, Laos and
                             Vietnam.


                # § Privacy/Surveillance⠀➾


                      # ⚓ The Straits Times ☛ Australia_PM_plays_down_privacy
                        fears_of_social_control_media_ban_for_children⠀⇛


                             Australia Prime Minister Anthony Albanese
                             said on Monday social control media firms
                             would be required to destroy personal data
                             used to verify ages of users, as part of what
                             the government says is a world-leading ban on
                             under-16s using the services.


          o § Defence/Aggression⠀➾


                # ⚓ The Straits Times ☛ Japan_mayor_regrets_South_Korea’s
                  absence_from_wartime_memorial⠀⇛


                       The South Korean Foreign Ministry said officials
                       will hold a separate memorial on Nov 25.


                # ⚓ The Strategist ☛ Australia_needs_a_coastguard_to_meet
                  modern_maritime_threats⠀⇛


                       The maritime domain is increasingly contested. From
                       attacks on shipping and undersea cables in Europe
                       to grey zone threats in the South China Sea, risks
                       to maritime security are mounting.


                # ⚓ Hong Kong Free Press ☛ 2_men_arrested_over_flying_drones
                  near_Chinese_army_assault_ship_docked_in_Hong_Kong⠀⇛


                       Two men have been arrested on suspicion of flying
                       drones in a restricted zone where a Chinese army
                       assault vessel was docked during a five-day visit.
                       A 35-year-old man surnamed Wong, and a 18-year-old
                       man surnamed Yeung, were apprehended at the China
                       Merchants Wharf near Kennedy Town on Friday and
                       Saturday. They were suspected of […]


                # ⚓ The Straits Times ☛ Philippine_V-P’s_assassination_threat
                  against_President_‘a_national_security_matter’⠀⇛


                       Ms Sara Duterte says she has instructed an assassin
                       to kill Mr Ferdinand Marcos Jr and his wife if she
                       is herself killed.


                # ⚓ JURIST ☛ Halifax_dispatch:_protesters_at_annual_security
                  forum_declare_‘Warmongers_are_not_welcome_in_Kjipuktuk!’⠀⇛


                       William Hibbitts is JURIST’s Deputy Editorial
                       Director, based in Halifax, Nova Scotia, Canada. He
                       filed this dispatch from Halifax.  The atmosphere
                       in Halifax was marked by contrasts Saturday.


                # ⚓ France24 ☛ Live:_Hezbollah_fires_about_250_rockets_and
                  other_projectiles_into_Israel_in_massive_barrage⠀⇛


                       Hezbollah fired about 250 rockets and other
                       projectiles into Israel on Sunday, wounding seven
                       people in one of the militant group's heaviest
                       barrages in months, in response to deadly Israeli
                       strikes in Beirut. This comes as the EU's foreign
                       policy chief Josep Borrell called for an "immediate
                       ceasefire" in the Israel-Hezbollah war while on a
                       visit to the Lebanese capital for talks.


                # ⚓ NYPost ☛ Hezbollah_fires_about_250_rockets_and_other
                  projectiles_into_Israel_in_heaviest_barrage_in_weeks⠀⇛


                       BEIRUT — Hezbollah fired about 250 rockets and
                       other projectiles into Israel on Sunday, wounding
                       seven people in one of the militant group’s
                       heaviest barrages in months, in response to deadly
                       Israeli strikes in Beirut while negotiators pressed
                       on with cease-fire efforts to halt the all-out war.
                       Some of the rockets reached the Tel Aviv area in
                       the...


                # ⚓ CS Monitor ☛ Israel-Hezbollah_conflict_widens_after_Israeli
                  strike_kills_Lebanese_soldier⠀⇛


                       Israel's attacks are aimed at Hezbollah militants,
                       but a fatal weekend strike hit Lebanon's army
                       center, igniting a heavy barrage in the ongoing
                       war.


                # ⚓ New York Times ☛ Hezbollah_Fires_Waves_of_Projectiles_Into
                  Israel_After_Deadly_Strike_in_Lebanon⠀⇛


                       The waves of attacks on Sunday came amid diplomatic
                       efforts to reach a cease-fire in the conflict.


                # ⚓ New York Times ☛ Israel_Conducts_Widespread_Strikes_Near
                  Beirut⠀⇛


                       As negotiators inch toward a cease-fire deal, the
                       conflict between Israel and Hezbollah in Lebanon
                       has intensified.


                # ⚓ New York Times ☛ Palestinians_See_Echoes_of_Israel’s_Gaza
                  War_in_West_Bank_Raids⠀⇛


                       West Bank residents say Israeli forces are adopting
                       tactics similar to the ones they are deploying in
                       Gaza, including airstrikes and the use of
                       Palestinians as human shields.


                # ⚓ Cambodia,_Laos_sack_foreign_ministers_in_preparation_for
                  more_combative_geopolitics⠀⇛


                       The new top diplomats in Phnom Penh and Vientiane
                       are likely to heed China’s concerns.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ RFERL ☛ Russia_Set_To_Name_New_Ambassador_To_United
                        States⠀⇛


                             Aleksandr Darchiyev is slated to be appointed
                             as Russia’s ambassador to Washington, the
                             Kommersant newspaper reported on November 24,
                             citing three unidentified sources.


                      # ⚓ Tom's Hardware ☛ U.K._closely_monitoring_Russian_spy
                        ship_as_it_passes_near_British_Isles_—_'undersea_cables
                        are_a_shared_concern'_says_Ministry_of_Defense⠀⇛


                             The U.K. government is concerned about the
                             presence of the Russian ship and has been
                             closely monitoring it since it entered its
                             waters.


                      # ⚓ The Straits Times ☛ North_Korea_and_Russia_agree_on
                        sports_exchanges_in_2025,_says_KCNA⠀⇛


                             The Russian delegation also toured North
                             Korean stadiums and viewed a taekwondo
                             demonstration.


                      # ⚓ RFERL ☛ Russia-Friendly_Candidate_Takes_Surprising
                        Lead_In_Romanian_Presidential_Vote,_Runoff_Expected⠀⇛


                             Pro-Russia candidate Cailin Georgescu has
                             edged ahead in Romania's presidential vote,
                             partial preliminary results showed, throwing
                             the race into unexpected territory and
                             setting up a likely runoff against Prime
                             Minister Marcel Ciolacu.


                      # ⚓ LRT ☛ In_Russia’s_war_economy,_the_warning_lights_are
                        blinking⠀⇛


                             Prices of milk, potatoes, and butter are
                             soaring in Russia. Retailers are beefing up
                             security to prevent shoplifting. Mortgage
                             rates are skyrocketing as the sales of new
                             apartments plummet.


                      # ⚓ JURIST ☛ Belarus_opposition_figure_faces_terrorist
                        charges_following_extradition_to_Minsk⠀⇛


                             Belarusian opposition activist Vasil
                             Verameichuk has been detained in Vietnam and
                             extradited to Belarus, where he faces
                             accusations of terrorism and a possible death
                             penalty, the opposition in exile said
                             Thursday.


                      # ⚓ JURIST ☛ IAEA_condemns_Iran_for_non-compliance_over
                        nuclear_program⠀⇛


                             The International Atomic Energy Agency (IAEA)
                             condemned Iran for insufficient cooperation
                             regarding its nuclear program, in a
                             resolution passed Thursday. The resolution is
                             supported by nineteen member states,
                             including the US, the UK, France and Germany.
                             However, China, Russia and Burkina Faso
                             opposed the resolution, with 12 other
                             countries abstaining.


                      # ⚓ France24 ☛ Pro-Russia_candidate_surges_in_Romania
                        presidential_vote⠀⇛


                             Hard-right candidate Călin Georgescu appears
                             to be on track to make it to the final round
                             of presidential elections in
                             Romania. Georgescu is leading with 22 percent
                             followed closely by center-left Prime
                             Minister Marcel Ciolacu on 20.6 percent,
                             according to partial results on Sunday.


                      # ⚓ The Straits Times ☛ Survivors,_sniffing_dogs_join
                        anti-mine_march_at_Cambodia’s_Angkor_Wat⠀⇛


                             The protest comes after the US decision to
                             send anti-personnel mines to Ukraine.


                      # ⚓ RFERL ☛ Zelenskiy_Calls_For_More_Air-Defense_Systems
                        For_Ukraine⠀⇛


                             Ukrainian President Volodymyr Zelenskiy said
                             on November 24 his country “needs more air-
                             defense systems” to protect its people as
                             Russia continues to target Ukraine with
                             aerial bombs, combat drones, and missiles.


                      # ⚓ RFERL ☛ Russia_Reportedly_Recruiting_Fighters_From
                        Yemen_Through_Huthi_Intermediaries⠀⇛


                             The Financial Times reports that Russia has
                             recruited hundreds of Yemeni men to fight in
                             Ukraine, lured by the promise of high
                             salaries and potential Russian citizenship.


                      # ⚓ JURIST ☛ International_community_to_establish_special
                        tribunal_for_crime_of_aggression_against_Ukraine⠀⇛


                             The Core Group on the Establishment of a
                             Special Tribunal for the Crime of Aggression
                             against Ukraine has reaffirmed its commitment
                             to establishing an effective and legitimate
                             tribunal, in a resolution adopted on Friday.
                             The resolution marks a significant step
                             towards holding those responsible for the
                             aggression against Ukraine accountable.


                      # ⚓ France24 ☛ 'The_Ukrainian_army_is_outnumbered,_in_men
                        and_equipment'⠀⇛


                             Ukraine was bound to lose the territory it
                             held in Russia, said FRANCE 24's
                             correspondent in Ukraine Emmanuelle Chaze.
                             "At the height of the Ukrainian offensive in
                             the Kursk region, the Ukrainian army
                             controlled over 1300 square kilometres of
                             land, and within four months, Russia has
                             managed to reclaim 40% of this land," she
                             said. "This didn't come as a surprise for the
                             Ukrainians, simply because the Ukrainian army
                             is outnumbered, in men and equipment," she
                             added.


                      # ⚓ France24 ☛ PM_Marcel_Ciolacu_leads_first_round_of
                        Romanian_presidential_vote,_show_exit_polls⠀⇛


                             In the first round of Romania's presidential
                             election on Sunday, far-right leader George
                             Simion is campaigning to replace President
                             Klaus Iohannis, a liberal and staunch Ukraine
                             ally. The election is being held amid a surge
                             in inflation and fears over the war in
                             neighbouring Ukraine.


          o § Environment⠀➾


                # ⚓ Hong Kong Free Press ☛ COP29_summit_ends_with_‘paltry’
                  US$300_billion_climate_finance_deal;_no_change_for_China’s
                  contribution⠀⇛


                       By Nick Perry, Laurent Thomet and Shaun Tandon The
                       world approved a bitterly negotiated climate deal
                       Sunday but poorer nations most at the mercy of
                       worsening disasters dismissed a US$300 billion a
                       year pledge from wealthy historic polluters as
                       insultingly low.


                # ⚓ New York Times ☛ Monday_Briefing:_U.N._climate_talks_End
                  With_a_Deal⠀⇛


                       Plus, photographing the world’s food.


                # § Energy/Transportation⠀➾


                      # ⚓ RFERL ☛ Freight_Train_Arrives_In_Afghanistan_From
                        China_As_Beijing_Looks_To_Increase_Ties⠀⇛


                             The first train carrying goods from China to
                             Afghanistan arrived in Mazar-e Sharif on
                             November 23 after crossing through Kazakhstan
                             and Uzbekistan, the de facto Taliban rulers
                             said.


                      # ⚓ Hackaday ☛ Modular_Multi-Rotor_Flies_Up_To_Two
                        Hours⠀⇛


                             Flight time remains the Achilles’ heel of
                             electric multi-rotor drones, with even high-
                             end commercial units struggling to stay
                             airborne for an hour. Enter Modovolo, a
                             startup that’s shattered this limitation with
                             their modular drone system achieving flights
                             exceeding two hours.


                      # ⚓ The Strategist ☛ Chinese_electric_vehicles_are_a
                        rolling_security_threat⠀⇛


                             Senate estimates earlier this month heard the
                             remarkable revelation that Home Affairs
                             Minister Tony Burke has had to take
                             ‘precautions’ based on warnings from his own
                             department to protect himself and the
                             nation’s sensitive information...


                # § Wildlife/Nature⠀➾


                      # ⚓ Hackaday ☛ Hacking_The_Soil_To_Combat
                        Desertification⠀⇛


                             While the Sahara Desert is an important
                             ecosystem in its own right, its human
                             neighbors in the Sahel would like it to stop
                             encroaching on their environment. [Andrew
                             Millison] took a look at how the people in
                             the region are using “half moons” and zai
                             pits to fight desertification.


          o § Finance⠀➾


                # ⚓ NL Times ☛ School_kids_often_regret_in-game_purchases,
                  UNICEF_survey_finds⠀⇛


                       Many children in the Netherlands between the ages
                       of eight and 12 regret in-game purchases, a recent
                       UNICEF survey has found. This refers to additional
                       purchases of computer or video games in which users
                       can buy money for loot boxes, weapons, skins
                       (outfits), or virtual surprise chests, NOS reports.


                       Around 188,000 Dutch primary school pupils who play
                       games in their free time took part in the survey.
                       The results showed that almost half of them
                       (92,000) had made in-game purchases during a
                       computer game.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Tedium ☛ Corporate_Casserole⠀⇛


                       Pondering Thanksgiving through an exceedingly
                       corporate lens. Some of the holiday’s most
                       important elements were brought to you by marketing
                       and lobbying.


                # ⚓ Ruben Schade ☛ We_must_not_be_done_with_kindness⠀⇛


                       Paul Kafasis concluded_a_post about the recent
                       elections in the US with this, but I think it
                       broadly applies:


                       Even as cruelty is ascendent, we must not be done
                       with kindness. Let us also not be done with joy.
                       Instead, we should locate humor wherever we can and
                       revel in it. The darkest times still contain
                       something to laugh about. We’re going to continue
                       to find it right here, together.


                # ⚓ The Straits Times ☛ Wealthy_South_Korean_parents_ditch
                  passports_to_get_kids_into_international_school⠀⇛


                       “Citizenship by investment” programmes serve as
                       crucial pathways for some of South Korea’s wealthy.


                # ⚓ The Straits Times ☛ South_Korea_pushes_for_better_work-life
                  balance_to_ease_falling_birth_rate⠀⇛


                       Poor work-life balance has been cited as a key
                       reason for the country's record low 0.72 births per
                       person in 2023.


                # ⚓ The Straits Times ☛ Countries_remain_divided_as_fifth_UN
                  plastics_treaty_talks_begin_in_South_Korea⠀⇛


                       South Korea is hosting the fifth and ostensibly
                       final UN Intergovernmental Negotiating Committee
                       meeting.


                # ⚓ The Straits Times ☛ South_Korean_man_convicted_after_binge
                  eating_to_avoid_military_service⠀⇛


                       He followed a regimen cooked up by his friend.


          o § Censorship/Free Speech⠀➾


                # ⚓ New York Times ☛ Egypt_Feuds_With_Travel_Blogger,_Issuing
                  1,100-Word_Response_to_Complaints⠀⇛


                       When a blogger criticized Cairo’s airport, Egypt’s
                       government fired back, citing security footage,
                       threatening legal action and asking, “Is it
                       reasonable for a passenger to visit two lounges
                       before a single flight?”


                # ⚓ Hong Kong Free Press ☛ Who_are_the_45_Hong_Kong_pro-
                  democracy_figures_jailed_for_subversion?_Part_II_–_Activists,
                  ex-lawmakers⠀⇛


                       Hong Kong’s largest national security case came to
                       a close on Tuesday as 45 prominent pro-democracy
                       advocates were jailed for up to 10 years over
                       taking part in a conspiracy to commit subversion.


          o § Civil Rights/Policing⠀➾


                # ⚓ Digital Music News ☛ SiriusXM_Made_It_Too_Difficult_for
                  Customers_to_Cancel_Subscriptions,_New_York_Judge_Rules⠀⇛


                       A New York judge rules that SiriusXM made it too
                       difficult for customers to cancel their service,
                       weeks after federal regulators enact a click-to-
                       cancel rule for subscriptions.


      § Monopolies/Monopsonies⠀➾


          o § Copyrights⠀➾


                # ⚓ The Straits Times ☛ ‘We_need_to_talk’:_Artist_surprised_to
                  see_his_iconic_Penang_mural_artwork_on_AirAsia_plane⠀⇛


                       Artist Ernest Zacharevic said AirAsia didn't seek
                       his consent for using his Children On A Bicycle
                       artwork.




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