𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Tuesday, July 30, 2024
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Generated Wed 31 Jul 02:49:17 BST 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/2024/07/30/


╒═══════════════════ 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  -  August Will be Productive, the Future Bears Much Promise

⦿ Techrights  -  EPO Workers Blow the Whistle on Extremely Worrying Discontinuation of the CFS, a Central File Store (Which Means Examination Will Be Hard to Do)

⦿ Techrights  -  Microsoft Lost Taiwan a Long Time Ago, About a Decade Ago

⦿ Techrights  -  Guest Post on the Cost of Debian Taking Bribes From Microsoft (and Letting Microsoft Vote Inside Debian!)

⦿ Techrights  -  IRC Proceedings: Monday, July 29, 2024

⦿ Techrights  -  [Meme] Microsoft Pundits 'Reporting' the 'Results'

⦿ Techrights  -  [Meme] The Only File You Need is the Patent

⦿ Techrights  -  Offending Accounts Removed, Even Without Help From the Police

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  Truth and Microsoft Aren't Compatible

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/07/30/August_Will_be_Productive_the_Future_Bears_Much_Promise.shtml
https://techrights.org/n/2024/07/30/EPO_Workers_Blow_the_Whistle_on_Extremely_Worrying_Discontinuat.shtml
https://techrights.org/n/2024/07/30/GNU_Linux_adoption_has_been_high_in_Taiwan.shtml
https://techrights.org/n/2024/07/30/Guest_Post_on_the_Cost_of_Debian_Taking_Bribes_From_Microsoft_a.shtml
https://techrights.org/n/2024/07/30/IRC_Proceedings_Monday_July_29_2024.shtml
https://techrights.org/n/2024/07/30/Meme_Microsoft_Pundits_Reporting_the_Results.shtml
https://techrights.org/n/2024/07/30/Meme_The_Only_File_You_Need_is_the_Patent.shtml
https://techrights.org/n/2024/07/30/Offending_Accounts_Removed_Even_Without_Help_From_the_Police.shtml
https://techrights.org/n/2024/07/30/Over_at_Tux_Machines.shtml
https://techrights.org/n/2024/07/30/Truth_and_Microsoft_Aren_t_Compatible.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/07/30/Gemini_Links_30_07_2024_Burnout_and_Plan_9.shtml
https://techrights.org/n/2024/07/30/Links_30_07_2024_Atrocities_in_Sudan_Escalations_Near_Lebanon.shtml
https://techrights.org/n/2024/07/30/Links_30_07_2024_Microsoft_Admits_Lying_About_ClownStrike_Windo.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 76

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/07/30/August_Will_be_Productive_the_Future_Bears_Much_Promise.shtml
    Gemini version at https://techrights.org/n/2024/07/30/August_Will_be_Productive_the_Future_Bears_Much_Promise.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ August Will be Productive, the Future Bears
Much Promise⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024


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


YESTERDAY was a fruitful_day, we belatedly completed a full site backup, and
then tidied up the digital desk to make way for future articles, based on
patient research. We try to cover things exclusively - focusing on topics other
sites do not touch or barely touch. That pays off on many levels, except
financial.


Overnight we'll be working on some long-form publications and tomorrow - seeing
there's a bit of a heatwave on the way - we might have to take a break. This
site has been smoothly operating for a long time and the vandals foolishly
resort to crimes, which only means they get_reported_to_the_cops (the cops very
much encourage updates on this).


In the month of August we don't plan to travel abroad or do anything very
special, so it'll be another very productive month for sure.


https://lists.gnu.org/ has been offline for hours already, we're not too sure
why (better not to guess), but the FSF has in general done well recently. It
spoke_out_against_Microsoft (good!) and belatedly_met_its_fundraising_goal. Its
new leadership is_decent and it recently_improved_some_more.


From the lenses of an optimist (which I am not, although my wife and my father
insist that I am), Free software seems to have a positive future. As a
pessimist (by nature) I recognise that lots of work will be needed for decades
to come. It's a constant struggle and we need to ensure we have more people on
our side than the likes of Microsoft have on theirs (Microsofters).


Eventually justice can prevail and the_truth_will_prevail. Convincing people of
a lie take more time, effort and money than convincing people of something that
is evidently true. █


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇He who asks a question is a fool for a minute, he who does
            not remains a fool forever. - Famous Chinese Proverb⦈




⡁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⠀⠀⠀⠘⠿⣿⣇⠙⠁⠀⠀⢀⣚⡯⠀⠀⠈⡁⢀⢿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⣿⣿⣿⣿⠀⠀⠀⠘⣷⣿⣿⣷⡀⢀⠿⣇⠀⢸⣿⣼
⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⣷⣶⣭⠁⠀⠀⠀⠚⠉⠁⠀⠀⢠⣄⣘⠮⠻⣾⣧⡀⠀⢠⡆⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⣸⣿⣿⣿⡟⣷⠀⢀⡠⡽⣿⣿⣝⢷⣾⣿⠆⢀⢀⠙⠿
⣇⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⢀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡄⠀⠈⣿⣿⣿⣶⡌⠍⣀⠶⠘⠁⠀⠀⠀⠀⠈⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⡿⣷⣾⠂⢸⣷⡸⡹⣿⣿⣷⣿⠉⢰⠿⠈⢳⠀
⡿⠀⠀⠀⠰⢢⠀⠀⠹⠁⠀⠀⠐⠻⠿⣿⣿⣿⠀⠀⣼⣿⣦⣄⠙⠿⣄⠀⠘⣿⣿⣿⣿⣦⡹⣷⡄⠀⠀⠀⠀⠀⠀⢰⣷⣷⡿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢧⣿⣿⣿⣴⣯⣖⣈⠸⣿⣿⡯⢀⣦⡀⠰⢇⠀
⠀⠀⠀⠀⢀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⢠⣿⣿⣿⣿⣿⣆⠘⢤⣠⣿⣿⣿⣿⣿⣿⣮⡂⠀⠀⢳⣶⣤⡀⣘⠿⡿⠁⠀⠀⠀⢨⣆⢀⠀⠀⠀⠀⠀⠘⢏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡛⠁⣦⠽⠇⠦⠀⠘
⠀⠠⠄⠀⠏⠀⠀⠁⠀⠀⠲⣤⡀⠀⠀⠀⠀⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣧⢄⡀⣠⣝⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠸⢿⣶⣄⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣬⡀⠠⡆⠁⣤
⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠑⢾⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠛⢿⣿⣿⣿⣿⣾⣿⣮⡻⢿⡿⣿⢛⠁⠀⠀⠀⠀⢰⣦⡀⢉⣙⡃⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⢀⣤⠀⠙
⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣉⠛⠻⣿⢹⣿⣿⣿⣦⡅⠰⢯⠀⠀⠀⣧⠀⢸⣿⣿⣆⠹⣿⣷⣤⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⢰⣿⣿⡇⢸⡏⠁⣿
⣰⣿⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣱⣦⣀⢸⣿⣿⣿⡿⠛⠉⠀⠀⠀⠉⠙⢿⣿⢿⣿⣦⣄⠘⠻⢿⡿⣫⠞⣴⣬⡁⠀⢰⣿⣆⡈⣿⣿⣿⣦⡘⢻⣿⣿⣦⡀⠀⠀⠀⠘⣿⢿⣿⣏⠀⣿⣿⣿⡇⠟⢧⡆⢿
⡜⠡⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣽⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⣿⣿⡇⣷⢢⣄⠉⠀⠿⣿⣿⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣦⡀⠀⠀⠈⠘⣿⡇⢸⣿⣿⣿⡇⣀⣿⡇⢸
⠀⣴⣮⣝⠇⠀⠀⠠⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡻⡇⣴⣿⡏⠀⠀⣄⢈⡉⠀⠀⣷⣦⣌⠻⢿⣿⣿⣿⣿⣷⢌⠹⣿⣿⣳⡀⠀⠀⠀⠈⠃⢸⡅⣽⣿⡇⢸⣿⣷⢰
⡄⢻⣿⣿⣷⣆⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣿⠀⣿⣻⠧⠀⠀⢻⣿⢿⡄⣤⡈⠛⠿⡟⠲⣬⣙⡻⠿⣿⣿⡧⠈⠻⢻⣿⡄⠀⠀⠀⠀⠘⢷⣿⣿⡇⢸⣿⣿⠈
⣇⠈⡿⠃⣫⡅⠀⢨⣝⢆⠀⠀⣴⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣤⣿⣿⠠⢿⣿⣿⡆⠀⢨⣭⡜⣛⠨⠙⣶⣦⡀⠀⠙⢿⣿⣷⣶⣶⣶⣦⣄⠈⠻⣧⡀⢀⠀⠀⠀⠀⠙⠿⡿⠸⣿⣿⡆
⠉⠀⢲⣿⣿⣧⠀⢸⣿⣷⣄⠀⠈⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢰⣾⣿⣿⣷⠀⢸⣿⣿⣿⣷⢳⣿⣶⣦⣀⢠⣀⡈⠙⠻⣿⣿⣿⣿⢸⣦⣌⠙⠀⢣⡀⠀⠀⠀⠀⠀⠀⠙⠻⣧
⠶⣄⠀⠈⠛⠋⠀⢸⣿⣿⣿⣦⢰⣄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⠈⡟⣿⣿⣿⣁⣿⣿⣿⣌⢿⣧⢻⣿⣿⣿⣷⡙⢿⣷⣦⣄⡈⠙⠻⠸⣿⣟⣓⣀⡀⠀⠰⣄⠀⠀⠀⠈⠳⡀⠈
⣀⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣆⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠛⠻⠿⣿⡟⠸⣣⣿⣿⣷⣿⣟⣿⣿⣿⣮⢿⣧⠁⣿⣿⣿⣿⣮⡛⣿⣿⣿⣷⣦⡄⡀⠛⠿⢭⣽⣂⡀⠈⠑⠀⠀⠀⠀⠈⠑
⠛⠛⠻⠿⠿⠒⠀⠀⠀⠈⠙⠿⣿⣆⠻⣿⣿⣿⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠫⣶⣿⣿⣿⣿⣿⣯⣻⡇⣿⣿⣿⣿⣿⣿⣎⡻⣿⣿⣿⣿⢿⣷⣦⣄⣈⠙⠛⠂⠐⢄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠈⠉⠁⠹⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢷⠁⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣀⠀⠀⠀⠀⠻⠿⠟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⡀⠀⠀⠉⠉⠛⠻⠿⠿⣿⣿⣿⣮⡙⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡤⢀⠀⠀⠀⠘⠻⣿⣿⣶⣾⣿⣿⣿⡜⣿⣿⣿⣿⡿⢛⠀⢸⣷⣦⣄⣐⣺⠿⠿⣧⣄⣉⢙⣿⣇⢸⣿⣶⣦⣴⣤⣄⠀⠀⠈⠉⠛⠓⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠆⣄⡀⠀⠀⠉⠛⠿⣿⣿⣿⣇⢻⣿⣿⣿⡇⣿⡆⢘⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⠸⢿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣰⣤⣀⡀⠀⠄⠉⢙⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣎⣛⠷⢤⣀⠀⠀⠀⠉⠉⠉⠘⣿⣿⣿⣷⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣦⣀⠀⣉⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣄⣀⣀⠀⠀⠀⠀⠈⠙⠙⠿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠉⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣙⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣯⢿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠈⠛⠿⣿⣿⣿⣧⢹⣿⣿⠿⣿⣏⣿⣿⣿⣿⣿⣧⡻⢿⡅⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠈⠙⠻⣿⡆⢻⣿⡀⢛⣾⣿⣿⣿⣮⣭⣭⣥⣌⠹⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠉⠈⠻⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⢀⡤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣾⣁⣴⠏⣀⣀⠀⠀⣀⠀⠀⢀⣀⢀⠞⢚⠁⢀⣀⡀⠀⠀⠀⣀⣀⢀⣀⣠⢠⡞⣒⡁⢀⣀⡄⠀⠀⢀⣀⠀⠀⠀⣀⣀⡀⡠⠀⣀⠀⣀⡀⢀⣀⡤⢠⢞⣐⢂⣀⡀⠀⣀⢀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣸⢏⣾⠤⠋⠀⢰⣇⣴⢃⡼⢡⡿⠊⡿⣼⠁⣾⠗⠀⣰⢋⣴⠊⢻⡌⢡⡿⣪⠜⠙⢧⡘⠀⢠⡞⣡⠖⠀⢠⣏⣠⠖⣼⢁⣴⢣⣯⠴⠃⢿⡘⣱⠏⡼⣵⠃⢾⢗⡼⠓⣹⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠋⠈⠓⠀⠀⠀⠛⠁⠙⠉⠠⠟⠀⠚⠀⠙⠒⠁⠀⠀⠛⠉⠃⠤⠚⠁⠉⠀⠸⡠⠔⠋⠀⠀⠘⠋⠙⠀⠀⠘⣩⡯⠈⠛⠁⠃⠘⠃⠠⠴⠚⠑⠏⠘⠁⠙⠒⠁⠈⠁⠐⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⢠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠱⠃⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡴⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢘⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣴⠒⠞⠀⢀⠴⢒⠂⠀⢐⣾⡒⣢⢒⣷⣄⡔⣚⣦⢀⡞⠀⠐⣾⡗⣢⢖⣱⡄⣰⡦⡶⠀⢀⡤⢒⡒⠀⢀⣴⠤⣶⡤⣶⢰⠖⣴⡦⢶⢆⡾⢁⡴⢢⡞⡴⢒⡇⠠⠖⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⣨⠇⠀⠀⣿⠴⠏⠀⢀⠎⢸⠿⣧⡤⠋⢺⣄⠽⠁⡞⠀⢀⡞⢠⠟⢧⡨⠏⡼⠋⠀⠁⠀⣾⠔⡟⠀⢀⡾⠁⠼⠃⡼⢡⠏⠼⠋⣠⠏⢾⠷⠺⢡⡏⢸⣏⠉⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡞⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠞⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢩⠏⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠋⣊⠀⣀⣤⠀⠀⣠⠀⠀⢀⣀⢀⡞⢒⡁⢀⡠⡀⠀⠀⠀⣀⣠⢞⡠⣄⠀⣀⣤⡀⣀⣠⠄⠀⢀⡀⣀⡀⢀⣠⡀⠀⣰⠋⠀⢀⢀⣠⢀⣠⡄⢀⠀⡀⠀⣀⠀⢀⣀⡀⣐⠃⡀⢀⣀⢀⣀⣤⠀⠀⢀⣀⡀
⠀⠀⣰⠗⢉⡟⣾⠥⠋⠀⢠⣏⣴⡇⡸⢃⡾⠊⡽⣱⠃⢲⠟⠀⢰⠏⣠⢯⡏⢰⡿⣿⠥⠞⠘⣧⠉⠀⢠⡿⠋⡽⣱⠃⢲⠟⣼⠃⠀⣰⠟⠹⢱⡯⠔⣳⠟⢩⡟⢩⢏⡞⣡⡖⣰⢋⡾⠋⣹⠇⠻⡌⠁⠀⣴⢁⡴⠀
⠀⠰⠋⠀⠋⠀⠓⠀⠀⠀⠘⠉⠘⠉⠀⠞⠁⠘⠁⠈⠛⠁⠀⠀⠙⠉⠋⠈⠛⠉⠀⠙⠂⠀⠒⠋⠀⠀⠉⠀⠚⠁⠘⠛⠁⠸⠃⠀⠐⠃⠀⠀⠘⠂⠐⠋⠀⠉⠀⠋⠘⠋⠈⠀⠃⠈⠀⠐⠁⠐⠚⠁⠀⠈⠋⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠂⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⢀⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠡⠋⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡰⠣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⣗⣢⢞⣹⣦⡴⢊⣷⢄⡞⠀⠀⡶⣗⣢⠖⣹⡦⣠⡦⡶⣣⠖⡿⣰⠀⣺⢫⠖⡹⢠⡶⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡏⠯⠤⠏⠸⠧⠼⠃⡾⠀⠀⡜⢁⡟⠿⠤⠞⠰⠋⠀⠁⣿⠉⠀⡿⠞⠁⣿⡉⢠⠟⠀⠈⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡼⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡔⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠿⢡⠎⠜⠁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀
⠀⠀⠀⠀⢠⡾⠉⢉⡵⢊⡝⣴⡧⣶⡤⣺⢧⠞⣹⡧⣰⠋⣠⠞⣶⠹⠋⠀⣸⡇⠀⢀⣠⡯⢶⡇⡴⢃⡾⠔⣿⣠⢊⡽⢰⡊⠟⣵⢊⡿⠀⢀⡾⠓⠒⠛⣱⠧⡾⡵⢊⣽⢄⡖⢀⡟⡵⣉⠇⣴⠧⡾⣱⠗⢻⠂⠀⠀
⠀⠀⠀⠠⠟⠀⠀⠾⠖⠟⠼⠋⠰⠋⢰⠃⠻⠤⠞⠠⠿⠊⢏⣀⡼⠃⠀⠀⠻⠷⠖⣱⠏⠀⠞⠼⠡⠟⠀⠼⠁⢿⠉⣀⣠⠟⠐⣏⠁⠀⠀⠾⠁⠀⠀⠴⠃⠀⠙⠧⠴⠋⠸⠗⠋⠸⣏⠁⠼⠃⠀⡴⠧⠔⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 205

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/07/30/EPO_Workers_Blow_the_Whistle_on_Extremely_Worrying_Discontinuat.shtml
    Gemini version at https://techrights.org/n/2024/07/30/EPO_Workers_Blow_the_Whistle_on_Extremely_Worrying_Discontinuat.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ EPO Workers Blow the Whistle on Extremely
Worrying Discontinuation of the CFS, a Central File Store (Which Means
Examination Will Be Hard to Do)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024


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


And, by default, patents will just be granted without sufficient scrutiny


A letter was sent at the end of last week to the EPO's António_Campinos. Signed
by Derek Kelly, Chairman of the Central Staff Committe (elected, unlike
Campinos), it shows that things continue to deteriorate even further after
Benoît_Battistelli and his cronies began the demolition. Team Battistelli and a
friend of Campinos, a Microsoft collaborator (see EPO_and_Microsoft_Collude_to
Break_the_Law_--_Part_II:_Steve_Rowan_Announces_Microsoft_“Outlook_Migration”),
are once again involved. To quote: "In this open letter to the President and Mr
Rowan (VP1), we request a proper information policy allowing meaningful
exchange of informed views as well as concrete measures rather than generic
references to team managers and directors for "appropriate support" for
"individual cases"."


The core issues: "The next far-reaching measure would obviously be the
discontinuation of the Central File Store (CFS). The following discussion
points appear vital: 1. How can colleagues with different working styles and/or
medical conditions be accommodated? 2. How can quality within the meaning of
legal certainty be assured for granted patents if annotations on paper are
lost? After all, a sizable fraction of CFS-applications and patents in
opposition are older than 10 years, pre-dating Ansera et al."


Here is the full open letter as it was sent to the Administration (Corrupt
Cabal, pure nepotism like Team Battistelli) last Friday:


     European Patent Office
     80298 Munich
     Germany


     Central Staff Committee
     Comité central du personnel
     Zentraler Personalausschuss


     Tel. +49 -89- 2399 - 2120
     +49 -170- 2251 - 7271


     centralSTCOM@epo.org


     Reference: sc24048cl


     Date: 26.07.2024


     European Patent Office | 80298 MUNICH | GERMANY


     Mr. António Campinos
     President of the EPO


     Mr. Steve Rowan
     Vice-President DG1


     § OPEN LETTER⠀➾


     § Discontinuation of the Central File Store⠀➾


     Dear Mr. President,
     Dear Mr. Vice-President of DG1,


     In the last six months, several actions have been undertaken by the
     administration related to the paper consumption. First the
     substantial reduction of printer capacity by over 80% in late 20231,
     second the discontinuation of central printing and storage of (new)
     paper dossiers2 and third the absence of a file store in the new
     Berlin sub-office (C1)3. In the Berlin case, to date only a vague
     statement has been made that the “availability” of the files is
     assured, only the “time component is dilated”. All three actions
     occurred within half a year, the second and third essentially without
     warning or major explanations beyond the obvious tip that files may
     be printed by the examiners themselves.


     If no new input is allowed and the stock present eventually expires
     (e.g. abandoned, refused or granted patents past the opposition time
     limit), such a file store “evaporates” and becomes obsolete.


     This was confirmed in informal talks on several management levels,
     and in the most recent LOHSEC meeting in Munich by the CSO.


     At which point in time the staff representation and the COHSEC as
     statutory bodies will be formally involved in this far-reaching
     measure? The following discussion points appear vital:


     - How can colleagues with different working styles and/or medical
     conditions be accommodated?


     - How can quality within the meaning of legal certainty be assured
     for granted patents if annotations on paper are lost? After all, a
     sizable fraction of CFS-applications and patents in opposition are
     older than 10 years, pre-dating Ansera et al.


     ____


     1 Where have all the printers gone? LSCMN, published 12.01.2024


     2 Discontinuation of central printing and storage of paper dossiers
     CSC Open letter, published 22.04.2024


     3 Comparison table, annex to LSCBE meeting report with new site
     manager, published 31.05.2024


     =====================================================================
     We request clarification and would appreciate concrete measures
     rather than generic references to team managers and directors for
     “appropriate support” for “individual cases”. We note that an
     information policy serving the purpose of allowing meaningful
     exchange of informed views is needed for changes in working
     conditions of such a magnitude4. Ad hoc implementations achieve the
     opposite.


     Yours sincerely,


     Derek Kelly
     Chairman of the Central Staff Committee


     ____


     4 Staff survey 2024 […] CSC, published 05.07.2024


So we can expect the examiners to have even less tools (i.e. poorly equipped)
for rejecting European_software_patents. Never mind the pressure already put_on
them_to_grant irrespective of the illegality. █




⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⢘⣛⣛⣛⣿⣛⣿⣿⣿⣿⣟⣻⣟⣻⣃⣛⣿⣿⣿⣟⣿⢘⣿⣿⣿⣿⣿⣿⣟⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⣿⣿⣿⣿⣽⠻⡿⠿⡿⠿⠿⡿⠿⠿⠿⡿⠿⠿⡿⠏⡿⠽⢿⣿⣿⣾⣿⣿⣿⣿⢹⣿⣿⣿⣿⣯⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣛⣿⣿⣿⣿⢻⢿⣿⣟⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⣟⣛⣋⣭⣭⣭⣭⣽⣛⣛⣿⠿⣿⣿⣿⡿⣶⢶⣯⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⢭⣿⣿⣿⣿⣯⣭⢩⣭⣿⣿⣷⢼⣿⣿⣿⣿⣿⣿⡱⢶⣿⣽⣹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢫⣶⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣽⣿⣿⣶⡌⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣷⣤⣶⠉⣿⣿⣿⣿⣷⣿⣿
⣼⣻⠿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⠝⠛⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣫⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣯⣭⣭⣩⣭⣭⢽⣿⣾⠛⠻⣿⣷⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠛⠻⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠈⣿⣿⠀⠀⣿⣿⡿⠿⣿⣿⠀⢈⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⠀⠀⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⠀⢸⡿⠻⡿⢿⣿⣃⡟⠉⠉⢻⣿⣿⠈⣿⢻⣿⣿⣿⣿⡟⠉⠛⠹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⡤⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⣿⡁⠀⣿⣿⣿⣿⣿⣿⡆⠈⠀⣨⠀⢸⣿⣟⣤⣶⠂⢘⣿⣛⠀⡏⠀⢛⣛⣛⣻⢻⠁⠀⠀⣿⡉⠛⠙⢹⣤⣿⣿⣿⣿⣿⣿⣿⠋⠉⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⢹
⣸⣶⡇⣿⣿⣿⣿⣿⣿⣝⣿⣿⣷⡆⠟⠀⠀⠉⠛⠿⣽⣿⢿⡇⢀⡾⠁⠀⠸⠿⠿⠛⠟⠀⠚⠿⠟⠀⠇⠀⠸⠿⠟⠋⠈⠀⠘⠀⠇⠛⠆⠀⠘⠿⡏⢹⣿⣿⣏⣋⠀⠀⠀⠀⢀⣍⣿⣿⡇⠀⣧⢀⠀⢀⣼⣟⡟⠘
⠿⠋⠉⠉⠉⠙⠛⢿⣿⡿⢻⡿⠻⡄⠀⠀⠀⠀⡀⠸⠿⢿⡼⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠙⠋⢉⡀⠀⠀⡰⠛⠉⠉⠛⠇⠀⢻⠘⠀⢸⣿⢻⠗⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⣁⣀⣄⢠⠾⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡘⣤⣌⠀⠀⠀⠀⠀⣿⣿⠃⠸⠿⣄⠃⠀
⢀⣀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣠⠀⡞⢠⣽⣯⣿⠀⠀⠀⠀⠟⠛⠀⠀⠀⠀⠐⡆
⣈⣾⠰⣿⣗⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢠⠲⡄⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠄⠀⠀⠈⢰⠁⢸⠐⣻⠇⢀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠻⣿⡄⠈⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⢐⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠓⡗⢻⣀⠗⠓⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣀⠀⠀⠀⠀⠀⠸⠦⠀⢰⡟⠁⢀⢸⡿⢿⣷⡀⠀⠀⠀⢧
⠀⠙⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⢟⣛⣉⣉⠀⠀⢀⠀⠀⠀⠀⣀⡀⡀⡀⢀⢀⢀⢀⣀⠀⣀⣀⡀⠀⢀⠀⠀⡀⡀⠀⠀⠀⣿⣋⣉⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢺⣹⣻⣿⣿⣿⠿⠀⠀⢸
⠀⠀⠀⠐⠀⡚⡇⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠿⠿⠟⠛⠛⠛⠋⠉⠀⠀⠈⠉⠋⠁⠀⠉⠉⠛⠉⠈⠉⠉⠈⠉⠉⠉⠉⠁⠀⠈⠉⠁⠉⠈⠁⠀⠀⠋⠙⠛⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠭⢿⣿⠟⠃⠀⠀⠀
⠀⠀⠀⠀⢙⣃⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠀⠀⠉⠚⠎⠘⠚⠁⠛⠙⠙⠘⠉⠂⠈⠃⠘⠙⠃⠈⠚⠫⠛⠀⠉⠚⠗⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⢰⣿⣤⣾⠫⣶⡀⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⢀⣴⡿⠿⢿⣿⣿⣿⣿⣿⣷⣶⡾⣿⣿⠀⠀⠢⠶⠲⠀⠔⠖⠖⠂⠀⠖⠒⠢⠲⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢛⣻⣿⣿⣿⣯⣥⣀⣀⡀⠀⠀⠸⢿⡇⠀⣼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⢿⣿⣿⡿⠿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢺⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⣾⣿⣿⣿⣧⣀⣀⣠⣤⣤⣤⣶⣿⣿⣿⣟⣛⣿⣿⣿⣿⡿⠿⣿⣿⡟⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⢀⣐⣺⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠉⠙⠛⠻⠿⠿⣿⣀⣉⣭⣥⠤⠶⠶⠒⠒⣺⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⡄⠀⢀⣀⣄⠴⢤⡎⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣥⣤⣄⣀⣀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠠⣯⡭⠵⠶⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣠⣴⣦⡀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⡉⠙⣿⣇⢠⠘⠿⣿⣿⣿⣿⣿⠿⣿⣿⣶⡞⠛⠻⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⣀⣠⣤⣶⣶⣿⠿⠿⠿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣶⣾⣿⡿⠛⠛⠛⠛⠿⠿⠿⠇⣀⣤⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠉⠁⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠟⠛⠛
⠁⠨⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠿⠗⠛⠛⠉⠉⠉⠛⠿⢿⣿⣿⣿⣿⣦⣄⣠⣄⠀⠀⠀⠀⣀⣀⣀⣤⣤⠔⠲⠾⢟⣟⣻⣿⣿⣿⣤⣥⣿⠿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣄⣀⠀⠀⠀⢰⣶⣤⣀⠀⠉
⠀⢀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠈⠉⠀⠀⠀⠈⢉⣻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣤⣤⣴⣾⡿⣿⣿⣿⣿⣿⣿⣥⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣷⣾⣿⣿⣿⣯⣿⠟⠉⠉⠉⣻⣿⣿⣯⣤⣌⡁⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣶⣤⣀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 417

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Lost Taiwan a Long Time Ago,
About a Decade Ago⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Taiwan⦈_ The shift happened around_2012-2015:


           🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Operating System Market Share Taiwan⦈


GNU/Linux_adoption_has_been_high_in_Taiwan.


                  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Taiwan Flag and Linux⦈




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢶⣷⢹⣭⣽⢉⣹⣯⡭⣉⡇⣽⢸⣭⢹⠩⢩⣿⣜⣻⣹⢫⡩⢯⣽⢉⣹⢩⣭⡍⣿⡇⡹⢣⡿⣉⢹⣭⡟⢩⢉⣹⣭⣿⣧⣛⡇⣭⠹⣉⢹⣩⢋⣉⣿⣿⢸⢍⣹⢸⠛⣹⡹⣉⢹⣭⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣿⣶⣾⣶⣾⣿⣷⣶⣿⣾⣾⣿⣾⣒⣪⣿⣶⣾⣣⣿⣶⣾⣾⣶⣾⣾⣿⣷⣿⣷⣷⣿⣷⣶⣾⣿⣿⣷⣶⣾⣷⣿⣷⣶⣷⣿⣶⣶⣾⣿⣷⣶⣿⣿⣾⣶⣾⣾⣷⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣒⡯⢽⢨⢻⣿⢎⣧⡎⢱⢽⣒⢹⡿⣿⣗⣺⠭⡏⡝⣿⡷⣹⣶⣯⣼⣗⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣶⣾⣷⣶⣷⣾⣷⣾⣶⣿⣿⣿⣿⣿⣶⣷⣶⣿⣶⣾⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣉⣩⣙⡟⠛⠛⠛⠿⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣀⣀⣈⣉⣉⣉⣉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣦⣄⣉⡉⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⢉⡙⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠈⢉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠛⢛⠻⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠉⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠈⠹⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⠀⠀⠀⢈⣿⠿⠿⠻⡿⠿⠟⢿⠿⢿⠿⢿⢿⠿⠿⠿⠟⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⡏⠈⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⠇⠀⠀⢀⣿⠀⣸⠘⡃⠀⡃⢋⡐⢢⡘⣀⠘⡀⠀⡆⡇⢃⡈⢸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡄⢸⣿⣿⣿⣿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⣿⣿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡈⡉⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⡿⠛⠛⠟⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣶⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⢀⣀⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠇⢠⣄⣴⣿⣿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣀⣆⠀⣾⣿⣿⣿⣿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢁⣰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⡿⠿⠿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣧⣤⣬⣦⡇⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠖⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢉⣀⠴⠶⠛⠛⠛⠛⠛⠛⠛⠛⠉⣁⣀⣤⣤⣤⣤⣤⣤⣴⣿⣿⣶⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⡿⠿⡿⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠙⠉⠉⠉⠉⢸⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣧⣤⣬⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣀⣠⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣼⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⣡⣿⣿⣿⣿⣿⣿⣿⣿⠏⢐⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⣣⣾⣿⣿⣿⣿⣿⣿⣿⠯⢐⣰⣿⣿⣿⣿⣿⣿⣿⡿⡏⣂⣾⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣰⣿⣿⣿⣿⣿⣿⣿⣿⡧⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⢥⣢⣿⣿⣿⣿⣿⣿⣿⣿⡯⣔⣰⣿⣿⣿⣿⣿⣿⣿⣿⢵⣀⣾⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣸⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠃⣰⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠿⠿⠿⢿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣾⣦⣼⣤⣤⣤⣥⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣽⣵⣧⣦⣧⣤⣴⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣮⣥⣾⣤⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡑⠀⠀⢉⠉⠉⠛⠛⠛⠻⠿⡿⢿⣿⣿⣯⣭⣭⣭⣭⣉⣉⣉⡉⢴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣇⠀⠀⠀⠀⠁⠒⠤⣜⣶⣤⣿⡆⢰⣟⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⡄⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣾⣶⣞⡁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣧⠀⠀⠀⠀⠀⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⠀⠐⠢⣄⠀⠀⠰⠛⠋⣟⠻⣿⠛⣫⡛⠿⣮⠉⠛⠻⠿⢿⣻⢶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⡆⠀⠀⠀⠉⠛⢶⣶⣴⣁⠀⢻⠀⠈⠣⠀⠈⠉⠲⣦⣄⣀⠀⠁⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣯⣙⠛⠻⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣾⣿⣶⣶⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠟⠛⣛⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡉⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣻⣻⣿⣿⣿⣿⣿⣿⣟⣯⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣽⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣬⣭⣭⣭⣭⣉⣛⣻⣿⣿⣿⣿⣿⣿⡜⠹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣤⡘⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣛⣋⣡⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 544

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/07/30/Guest_Post_on_the_Cost_of_Debian_Taking_Bribes_From_Microsoft_a.shtml
    Gemini version at https://techrights.org/n/2024/07/30/Guest_Post_on_the_Cost_of_Debian_Taking_Bribes_From_Microsoft_a.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Guest Post on the Cost of Debian Taking
Bribes From Microsoft (and Letting Microsoft Vote Inside
Debian!)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024,
updated Jul 30, 2024


    🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Bits from Debian: DebConf24 welcomes its sponsors!⦈


Recent: Debian_it_Taking_Bribes_(Gold_Sponsorship)_From_Microsoft_Again |
Microsoft_Inside_Debian_is_Sabotaging_Debian_and_Its_Many_Hundreds_of
Derivatives_With_SystemD_(Microsoft/GitHub_Slopware_With_Catastrophic_Bugs_is
Hardly_a_New_Problem)


Guest post:


I found something_here which almost made me double over and vomit. I can't
believe it!


DebConf24 welcomes its sponsors!


A Gold Sponsor is this: "Microsoft, who enables digital transformation for the
era of an intelligent cloud and an intelligent edge. Its mission is to empower
every person and every organization on the planet to achieve more."


You've got to be FUCKING KIDDING ME.


I wouldn't be surprised if Debian is undermined by Microsoft in the long run,
which of course I know could be one of their sinister goals.


Look how many distros are based on Debian!


For one thing, that is.


Look at the mess which is snaps in Ubuntu.


IMO Ubuntu/Canonical should just be considered to be a lost cause and Microsoft
should just outright buy them out.


Not that I favor it, but I find it to be eventual anyway...


Now to get inside and rot out Debian would be a grand accomplishment for
Microsoft.


I'm just TIRED of the public doing NOTHING in regards to the continued monopoly
and dirty tricks of Microsoft.


I suppose you've already read about this news, but if not, please spread the
information! I'm actually shocked at this bullshit.


In the past, when I've read about a company or individual standing against
Microsoft and in such a place where they WON'T allow Microsoft to fuck them
over, time and time again, like clockwork, they eventually come out and say
they are either now a partner with and/or their attitude has changed, like
something out of a body snatchers movie.


I mean, they undergo a complete transformation!


Do they dispatch a bunch of hookers and blow or something or do they
participate in blackmail?


It's just unfucking canny.


It seems like wherever and whenever Microsoft wants to be somewhere or do
something, a situation always presents itself with a golden key and they get
what they want. █


Please note this is a guest post which we didn't editorialise, sanitise, or
censor. This is how some people truly feel.




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠈⡁⠙⡁⠈⢙⠈⠉⠉⠉⠉⠉⠉⠉⡀⠈⣊⠉⠉⠉⠉⠁⠁⠉⡆⠉⠘⠁⡏⠁⠉⠈⠉⠈⠛⠉⠉⢸⠉⠉⠁⠈⠉⠁⢉⢹⠉⢹⠉⠁⠉⢹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡧⣤⢤⣴⢤⣤⡤⢤⡽⡤⣶⣤⣧⢴⣥⣤⣤⡤⣧⣼⣠⣦⡤⣧⡤⣴⢤⣤⣤⣤⣤⣦⣤⣴⣧⣤⣾⢤⡤⣿⣤⡤⣧⡴⣧⣵⣧⣤⣤⢼⠄⡤⣷⠦⣧⠤⣯⣤⡧⣴⡧⢿⣤⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⢥⠾⠤⡤⠿⡮⡧⠢⠠⢼⠿⡦⠼⠿⠶⣤⣷⣶⣿⣧⣯⣵⣧⣼⣧⣬⣦⣴⣾⣧⣦⣦⣴⣾⣴⣴⣧⣶⣾⣧⣼⣦⣧⣦⣦⣴⣾⣽⣯⣦⣼⣤⣧⣬⣶⣿⣯⣤⣧⣤⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣷⣶⣷⣶⣷⣷⣾⣶⣷⣶⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 680

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/07/30/IRC_Proceedings_Monday_July_29_2024.shtml
    Gemini version at https://techrights.org/n/2024/07/30/IRC_Proceedings_Monday_July_29_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Monday, July 29,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024


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


                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇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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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠰⠒⡿⢛⠛⠿⠀⠛⣛⠒⡿⢛⠛⠻⠛⢛⠛⢻⠛⣛⠻⠛⠛⠛⠛⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠿⠀⠀⠀⡀⠻⠷⢻⠀⢿⢿⠀⡇⠸⣷⠀⠀⢸⡇⠘⠠⡤⠀⠀⢸⣿⠀⢿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣶⣶⣷⣦⣶⣿⣷⣴⣾⣶⣿⣦⣴⣾⣶⣾⣷⣾⣶⣶⣶⣶⣾⣿⠂⠰⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠂
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠰⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠤⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡟⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 919

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/07/30/Meme_Microsoft_Pundits_Reporting_the_Results.shtml
    Gemini version at https://techrights.org/n/2024/07/30/Meme_Microsoft_Pundits_Reporting_the_Results.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Microsoft Pundits 'Reporting' the
'Results'⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Microsoft Pundits: I'll tell them every product became 'AI'
and thus there is 'growth'; Alright, I will focus on something about 'cloud'⦈


Context: Truth_and_Microsoft_Aren't_Compatible




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⣿⡟⣭⣿⣟⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣭⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⣾⣯⣷⣻⣹⡗⣎⠙⡝⢿⣟⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⢿⢿⡿⣯⣯⣾⣧⣘⠻⣭⡭⣿⠛⢷⠿⣿⣿⣯⣻⣋⣏⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣉⣙⣉⣙⣉⠛⢿⣿⣷⣌⠻⢿⣿⣿⣾⣦⣘⣿⡌⢿⣏⣛⣿⡻⢷⠿⣽⣾⣻⣽⣜⣌⣿⠏⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠊⣾⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣦⣍⠻⣿⣿⣿⣿⣿⣿⣾⣿⣧⣵⣆⣧⡆⣾⣍⢽⢿⡛⠻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⠿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠃⠀⡏⠉⢁⣄⠉⣙⣷⡄⢹⣛⣿⡿⠟⢡⣾⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣌⣮⣷⡘⣿⣿⣿⣿⠿⠛⠁⠀⣄⠀⠂⠉⠉⠉⢹⣿⣟⡋⠉⠀⠉⠉⠛
⠿⣿⣿⣻⣿⣿⣿⣿⣿⠿⠿⠶⠒⠶⢾⣷⠀⠁⠙⠙⠛⠉⠋⠩⠷⢿⣿⠟⠀⠐⢛⣋⣉⣥⣤⣶⣶⣶⣶⣤⣭⣭⣉⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠐⠊⠁⠀⠈⣤⣤⣤⣤⣶⠎⠉⠁⠁⠀⠀⠀⠀⠀
⠀⠈⠉⠉⢉⣿⡇⠈⠀⣀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⠀⠸⣴⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣧⣤⣄⣀⣀⣀⠀⢠⣠⡤⠶⠏⠀⠉⠉⠠⣴⣶⣦⣴⣿⣶⣶⢶⣶
⣶⣶⣀⠀⢸⡟⠓⢶⣶⣟⣱⣤⣄⣀⣀⠀⣀⡃⠀⠀⠀⠀⠀⠀⠐⠁⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⣀⣈⠈⠻⣿⣿⣧⣤⣽
⣿⣿⣿⣿⠆⢀⡀⢠⣼⡿⣿⡿⣁⣨⣤⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠉⢽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣴⡿⠇⠀⠀⠀⠀⣿⣿⣿⡇⡘⣻⠁⠀⢸
⣿⡿⠋⠁⠀⠉⠀⠀⠀⠀⢻⣾⣿⡟⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣴⣧⣤⠤⣠⠶⠄⠀⣿⣿⣿⣿⣿⣯⡀⠀⢸
⠉⠀⠀⠀⠠⠂⠊⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⠛⠀⠀⠀⠀⠠⠴⠾⢿⣿⣿⣿⣿⡟⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣦⡀⠘⣿⡟⠁⠛⠃⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠀⠀⠀⠀⣿⣿⠃⢀⠋⠀⠀⠀⠀⢀⣦
⠟⠀⢸⣿⠀⠘⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠔⠀⠀⠐⠖⢻⡟⠀⢿⣱⣶⣴⣤⣤⣾⣿
⠴⠂⠙⠈⠁⠀⢀⣾⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⣷⣄⣸⢻⣿⣿⣿⠿⠿⣯
⣀⣀⣀⣰⣆⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⠉⣠⡜⢿⣦⠀⠉
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠘⢛⣉⣉⣩⣭⣭⣉⣉⣛⡚⠫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣯⣄⣀⣉⡀⠐
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣽⢹⢹⡉⣿⢽⣛⣯⣿⣷⣦⣌⡉⠻⠛⠿⠿⠀⠀⠩⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⣿⣿⡿⠿⠃⠀
⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⡤⠀⠀⢀⡀⣠⠀⠀⠀⠀⠀⠀⣤⣤⠀⡀⠀⠀⣤⣤⣤⣤⣤⠄⣠⣾⣿⣿⡿⣿⡷⣷⡾⡾⣶⡷⠾⢿⠷⡯⣿⠿⣿⣿⣦⡀⢿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣬⣭⣥⣭⣭⣥⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠈⠜⠁⠀⠀⠀⠀⠀⢸⣿⠛⠀⠀⠀⣴⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⡇⣿⢱⢹⡇⠇⢿⡇⡇⢇⠸⡂⢿⠮⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣻⢻⣿⢛⣟⣻⢻⢻⣻⢛⢻⠛⡿⣿⣛⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣇⢻⣿⣿⣿⣟⣻⣠⣿⣕⣟⣻⣈⣼⣺⣸⣰⣀⣿⣼⣓⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⠿⣦⡙⢿⣿⣿⣹⢹⡏⡟⢹⢹⣿⡟⣯⢹⣿⢹⡏⣿⢩⣿⠟⣡⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣅⠺⣿⣿⣿⣿⣦⣉⠳⠷⣾⣷⣿⣾⣿⣿⣿⣷⣾⣿⣾⣷⣿⣞⠡⣾⣿⣿⡟⠁⣀⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⣼⣿⣿⣿⣿⣿⣿⡶⡄⢨⣍⣉⣉⣉⠉⣉⣉⣥⣌⠙⠿⣿⡆⢹⣾⣛⣷⣼⠿⢿⣶⣆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣙⣻⣤⣌⡙⠀⢻⢛⡿⣿⣷⠾⣤⢌⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿
⣿⡿⠋⠉⢿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡃⠀⣴⣇⠨⡏⠀⢁⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⢻⡆⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⠙⠛⢶⡻⣿⣤⡀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⠀⠀⠈⠁⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⠯⠇⠀⠀⢢⣶⡆⠀⢻⣿⣿⣿⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠶⣶⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⢿⠏⠀⠀⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠁⠀⠰⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⢠⣿⣷⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠐⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠠⢪⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⠟⠃⠈⢻
⠛⠛⠛⠋⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⣠⠀⠀⠀⠈⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢠⡴⠀⢻⣿⣿⣿⣿⡿⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢸⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣻⣿⣿⣿⠏⠸⡒⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣃⠀⠈⠉⠋⢹⣏⣋⣀⣀⣀⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣯⣭⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣇⣘⣠⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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posted by Roy Schestowitz on Jul 30, 2024


Monopoly. Monopolies everywhere! Monopoly for everyone!


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇It looks like you're trying to get work done. Don't. Just
                              grant the patent.⦈


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⣿⠀⡆⢰⡇⢸⠀⠀⠀⠀⠀⠀⠠⠀⢺⡇⢸⠀⠀⠀⡇⢐⣷⠀⡄⠀⠈⠀⠀⣼⠀⢸⠀⣸⡆⢰⠀⠀⡇⢠⠀⡇⠀⠀⠀⢸⣷⠀⡆⠀⢸⠀⠀⠀⢀⡆⢰⣇⠀⠀⢀⠀⠀⠀⠀⡇⠀⣾⠀⡆⡇⠀⠀⠀⢸⢀⣺⣿
⣿⣤⣧⣼⣧⣤⣦⣤⣧⣤⣦⣤⣴⣤⣼⣧⣤⣤⣤⣦⣤⣤⣿⣤⣷⣤⣼⣤⣴⣿⣤⣼⣤⣼⣧⣼⣤⣤⣧⣼⣤⣧⣦⣴⣤⣼⣿⣤⣧⣤⣾⣧⣤⣤⣤⣧⣼⣿⣤⣦⣼⣤⣴⣤⣤⣧⣤⣼⣤⣤⣧⣤⣦⣤⣼⣤⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡤⠤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⠛⢿⣿⣿⣿⣿⣿⣇⣀⣂⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⡏⠉⡛⢻⠛⣛⠉⠙⠛⡟⠛⠛⠛⢻⠛⠛⡛⢙⡋⢙⠛⡟⠛⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣶⣷⣶⣶⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠛⠛⠛⢿⠛⠛⠛⠛⠛⠛⠻⠛⠛⠻⠛⢻⠛⠻⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⣶⣦⣼⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠛⠻⠛⠛⡟⠛⠛⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⠛⠙⢿⠛⡟⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⡟⠋⠛⠛⠛⢻⣿⠛⠙⢻⠛⠛⢿⠛⠛⡟⠻⠛⠛⠛⠛⣿⠛⠛⠛⢻⠛⡟⠛⢻⡟⠛⠛⡟⠛⠛⠛⠛⠛⠛⡟⠻⠛⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⠀⡇⢸⠀⠀⢰⣾⠀⢸⣿⣿⠀⠀⠀⠀⡧⠀⠐⣿⠀⣿⡿⠀⠂⢸⠀⠁⠘⠀⠀⡇⠀⠀⣿⠀⣿⣿⡇⢸⡇⢈⠀⡇⠈⢹⡇⠀⢀⠅⠀⠸⠀⢸⠀⠈⡇⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣀⣁⣸⣀⣀⣼⣀⣀⣸⣿⣀⣈⣹⣏⣀⣦⣀⣀⣧⣈⣀⣿⣀⣿⣿⣀⣁⣸⣀⣇⣀⣀⣀⣀⣰⣀⣿⣀⣿⣿⣇⣸⣇⣸⣀⣇⣈⣹⣇⣀⣿⣀⣀⣀⣀⣸⣀⣈⣁⣰⣀⣿⣀⣏⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1030

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/07/30/Offending_Accounts_Removed_Even_Without_Help_From_the_Police.shtml
    Gemini version at https://techrights.org/n/2024/07/30/Offending_Accounts_Removed_Even_Without_Help_From_the_Police.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Offending Accounts Removed, Even Without
Help From the Police⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024


Anti-Free_Software_Militants_Reported_to_the_Police_for_Second_Time_This_Month


We have just been notified that the offending accounts have been suspended and
we'll report on the matter some time in the future, probably by the end of this
year. Not agreeing with someone does not entitle one to commit crimes against
that someone.


The community must identify and properly deal with such militants, who disguise
themselves as "diversity". █


                     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Justice is blind⦈




⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠘⡀⠘⣿⣿⣻⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣇⢀⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣸⠀⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢳⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡭⠻⢭⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣏⡸⡇⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⡏⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰
⣿⣆⠀⠀⡌⢻⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠂⠉⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⢸⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣸⣿⣿⣿⡇⢹⣿⡇⣿⣿⣿⣿⣿⣷⣿⡇⣿
⣿⣿⣦⢆⣧⠀⣇⡴⠃⠉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣼⣇⣀⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣹⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣿
⢹⣿⣿⣷⡟⠛⣻⡻⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡻⢜⠻⣿⣿⣿⣿⣿⣿⣿⠷⣤⣶⣿⣿⡿⠇⢁⣿⠋⢹⠈⠻⠿⢿⣿⢿⣸⣠⣶⣴⡆⠀⣶⣎⠙⡉⠙⢹⣦⠈⠁⠁⠀⢹⡇⠘⠄⠁⢸⡏⠈
⠈⣿⣿⠥⠥⠀⠿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢿⢤⡄⢱⠟⠀⠀⠀⠀⠈⡉⠃⠀⠀⠙⡛⡛⠂⠘⠛⠀⠸⠷⠤⠤⠼⠿⠾⣿⠟⠛⠛⠗⠻⠃⠛⠓⠲⠒⠺⠃⠀⢀⣤⣄⢸⡇⢀⣰⣿⣿⣧⣤
⠀⠹⣿⢸⠀⣀⣶⡶⠆⡟⠻⡻⣩⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⡼⠋⠁⣿⣿⠗⠂⠂⢀⣬⣷⣾⠁⠀⢿⡇⠀⠀⢹⢰⡄⠀⠙⠛⢻⣿⡶⣹⡟⠁⢘⡁⠀⠀⠁⠀⣀⣠⣤⣿⡄⠙⠉⠙⢸⣷⣾⣿⣿⣿⣿⣿
⠀⣀⠁⢸⠟⠋⠁⠀⠀⡐⠀⢀⡟⢿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣽⠛⠉⠀⠀⠀⠀⣡⣀⠀⠀⠀⡻⣿⣏⣀⢀⣈⡟⠀⠀⡋⢈⡃⡀⠀⠈⠛⠋⠊⠈⣵⡆⠘⠃⠀⠀⠀⠃⠀⠛⠋⢛⠓⠒⠊⠉⣽⣿⣿⣿⣿⣿⣿⣿
⠐⢻⠀⠀⠀⠀⠀⢀⡆⣇⠀⣈⠉⠘⠋⠈⣿⡿⣿⣿⣷⣄⣹⠋⠀⠀⠀⠀⠀⠀⠻⠿⣶⡏⠀⠉⣽⣿⢸⣿⣿⣧⣄⣀⣿⣻⣷⣿⣆⡀⠘⣄⠀⢰⣯⣶⡂⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣿⡿⠋⠀
⠀⠀⠀⠀⠀⠀⣀⢀⣇⢃⠀⠀⢈⣉⣌⢙⣿⣀⠹⣿⣿⠿⠃⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣶⣶⣆⡀⠿⠁⢻⣿⡛⢋⡙⣟⣟⣸⠀⣨⡟⢉⠉⠉⠈⠉⠀⢈⠹⡏⠉⠉⠉⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀
⣿⣿⣾⣿⣿⢀⡏⣸⣿⣿⣗⣿⣿⣿⣿⣿⣿⡿⠀⠻⣏⣤⣼⣿⣿⣿⣷⣿⣷⣶⣶⡶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢤⣤⣀⣀⣤⣤⣠⣾⣿⣿⣟⠷⣾⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣷⣶⣧⢿⠛⠸⣟⠛⠻⡌⠀⠠⡤⠁⢿⣿⣿⣿⣿⡯⠀⠀⢀⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣭⣿⣿⣷⣤⣄⣉⡀⠀⣤⣄⠀⠀⠀⣸⠟⢳⣖⠀⣾⣇⠈⢻⣿⣿⣿⠃⣴⣶⣾⣿⠿
⠀⠘⠻⠿⠿⠿⠻⠻⠟⠛⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣵⣿⣿⣿⣿⣗⣴⣿⡏⠶⢿⣿⠟⠋⠃⢠⣿⣿⣿⣿⡀⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠙⠏⠁⠃⠀⠀⠻⠃⠋⠈⠣⡿⠉⠿⠏⠉⣿⡧⣬⠽⠋⠉⢉⠛⠉⢩⠉⠈⠋⠛⠃⠀⠐⠃⣭⠿⠿⠿⠟⠋⠹⣿⠟⢯⡹⠋⠿⠇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠁⠛⠻⠿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⢠⣦⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⣰⡿⠟⠁⠀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⠐⣤⢤⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢐⠀⠀⠀⢠⣆⢸⣿⠛⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⣰⡆⠀⠀⠀⠀⠁⠀⠁⢀⢰⡎⢀⡯⠁⠀⠀⠀⠀⠀⣾⣾⠇⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢰⡿⠛⠃⡀⢠⠄⠀⠀⢀⣶⡿⠄⠿⢿⣷⡦⡤⠀⠀⢠⣾⡿⠿⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⢠
⣿⣿⢀⡾⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠚⠀⠈⢱⠀⠀⠒⠀⢾⠟⠁⠀⠀⠀⢨⡀⠀⣿⣿⣷⣆⠀⠀⠀⠀⠈
⣿⠅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡀⠀⠀⠀⠀⡐⠻⡛⠂⠈⢻⣿⣿⣷⡀⠀⠀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣧⡀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣀⣀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠀⠘⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢊⣀⠀⠈⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠿⠉⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⡀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣉⡀⠀⠀⠀⠀⠘⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠄⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠉⠉⢛⣿⣿⣿⠋⠉⠀⠀⠀⠀⣨⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⣀⣤⣠⣠⣀⣄⣴⣶⣶⣾⣿⣿⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠁⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣫⣷⣿⣿⠝⣐⠫⣵⣼⣿⡿⣿⣿⣿
⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⣠⣤⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣠⣼⣿⣿⣿⣿⡿⡫⢖⠶⣶⣌⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠶⠊⠁⠀⠀⢹⣿⣿⣿⣿⡟⣵⣾⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⣿⣿⣿⠛⢻⠟⠿⡿⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⣿⡿⠛⠋⠈⠛⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⠛⠛⠟⠛⠷⠃⠀⠀⠀⠀⠀⠘⡦⠀⠀⠀⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⢸⠀⠀⡇⠀⡇⠀⠂⣀⣀⡄⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠘⠀⠀⡇⠀⡿⠦⡀⠈⢻⡇⠀⣿⡇⠀⠀⠀⠀⠀⠚⠀⠀⣀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣠⣄⠀⠀⢀⣇⡀⠁⢀⣼⡇⠀⢹⡇⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠶⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣾⣿⣿⡟⠀⠀⠀⠀⠙⢋⠋⠀⠀⠀⠀⠿⣿⣿⣶⣦⣤⣤⣀⠀⣹⣿⣿⡇⠀⠙⠟⠹⠉⢽⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠻⣿⡿⠉⠀⢀⣀⣼⣿⣷⣿⣿⣿⣿⣿⣷⣤⣤⣤
⢺⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣅⠀⣿⣿⣽⣿⣿⣿⣧⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣮⠄⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡏⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⢳⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡗⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⢀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣯⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⡟⣼⣿⣿⣇⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⡏⢠
⣿⣧⠀⠀⣄⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠁⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⠛⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⣱⣿⣿⣿⣿⢹⣿⣟⣹⣿⣿⣿⣿⣿⣿⣇⣼
⣿⣿⣷⣦⣻⣀⣛⣶⣋⣈⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⣠⣿⣿⣿⣿⣿⠻⠿⣾⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣸⣿⣷⣼⣿⣿⣿⣿⣿⣿⣧⣿
⢸⣿⣿⣿⡟⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⣿⡽⢯⡹⢿⣿⣿⣿⣿⣿⣿⡧⢴⣶⣿⣿⣟⡏⠀⣿⠃⢹⡁⠙⠛⠿⣿⢿⣴⣶⣶⣦⡆⠀⣾⣷⠩⠉⠉⢹⣷⠈⠈⠀⠀⠋⣟⡘⠁⠀⢸⣿⠉
⠁⢿⣿⡿⠣⠆⠿⠃⠠⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⢦⡄⠘⣿⡓⠀⠀⠀⠀⢊⡵⠐⠀⠘⣛⡛⠃⠀⢛⠒⠸⠿⠴⠶⠖⡿⢻⣿⣛⡛⢛⡛⠛⠛⢛⠛⠓⠒⠚⢛⠀⢀⣸⣗⣸⣿⣀⠀⠀⠀⠋⠀
⠀⠸⣿⢹⡀⣀⣼⠶⠞⢿⠛⢝⢩⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⡼⠋⠁⣿⣿⡟⠚⠓⠀⣤⣿⣾⠇⠀⢻⣿⠀⠀⢸⢰⡆⠀⠈⠛⢻⣿⣿⣿⡟⠁⠈⡏⠁⠀⠀⠀⣤⣤⣤⣿⡆⠘⠉⢉⢹⣏⣲⠉⠉⢩⣡⡝
⠀⣠⡉⠠⠟⠋⠁⠀⢀⡸⠀⢀⣼⢻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠟⠉⠀⠀⠀⠀⢡⣄⡀⢀⠀⣹⣿⣿⢀⣀⣬⣭⠁⠀⣉⢈⡅⣀⠀⠀⠙⠋⠉⠈⣷⡖⠈⠃⠀⠀⠀⠙⠂⠙⠛⢙⡋⠉⠋⠉⠹⢿⣿⣷⠷⠿⠝⠻
⠒⢻⠅⠀⠀⠀⠀⠀⡎⢰⠀⣀⣉⣀⢋⣀⣿⣿⣿⣿⣿⣦⣹⠛⠀⠀⠀⠀⠀⠀⠙⠿⣿⡏⠁⡉⣸⣿⢸⣿⣿⣿⣤⣆⣿⢿⣷⣿⣧⣀⣀⣠⠀⢠⣿⣶⡆⢦⣀⡀⠀⠀⠀⠀⠀⢸⣧⣀⣀⠀⢸⡿⠊⠀⠀⠀⠀⠀
⣀⡀⠀⠀⣀⠀⣀⢀⣧⣸⡀⠀⣀⣠⣬⣍⣿⣀⡹⣿⣿⡿⠃⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣾⣿⣿⣆⣀⢻⢁⢹⣿⡟⢫⣉⣛⣟⣰⠃⠠⡟⢩⠉⠁⠀⠉⠁⢈⡉⣏⠉⢉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢃⡟⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠓⠻⣿⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣀⣤⣴⣶⣤⣾⣿⣿⣿⠻⣿⣿⣍⡀⣴⣀⣀⢀⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣾⣧⡿⡏⠁⣿⡉⣉⠗⠂⠲⠦⠀⠹⣿⠁⠛⠁⣰⡾⠟⠃⣰⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣷⣶⣦⣍⣀⠀⣤⣤⡀⠀⢀⣸⠟⢹⣗⡀⣾⣏⠀⠀⠀⠀⠀⠏⢻⣷⣼⣿⡿
⠀⠘⠻⠿⠿⠿⠛⠛⡟⠛⢿⣟⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣸⣿⣿⣿⣿⣿⣴⣿⡏⠴⠻⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠁⠛⠟⠁⠃⠀⠀⠹⠋⠐⠈⠁⡿⠅⠻⠟⠋⢿⠷⣬⠝⠋⠉⢉⠛⠁⢨⠉⠀⠉⠙⠋⠀⠀⠃⣭⡿⠿⠿⠟⠛⠘⡿⠟⠻⢥⠏⠛⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⣦⣄⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⠀⠌⢀⡄⠀⠀⣦⠶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢘⠀⠀⠀⢀⣷⣸⣿⡟⠁⠀⠀⠁⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠌⠩⠦⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠁⠀⢁⢠⣰⣾⣀⣝⠁⠀⠀⠀⠀⠀⣾⣿⠧⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠟⢿⠰⡿⠛⠓⠀⢠⡦⠄⠀⢀⣾⡿⢶⠿⣿⣿⣶⣆⡀⠀⣠⣾⣿⣿⣶⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠲⢀⡾⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠁⠀⠀⠚⠉⠀⠘⠀⠈⢹⣁⣿⣿⣿⣿⣿⣏⢠⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠔⠀⠀⠀⠀⢰⡄⠀⢸⢿⣿⣿⡿⠻⠛⠉⢟⣿⣿⣯⣼⣿⣿⣷⣤⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⡇⠀⠀⣿⣿⠟⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠏⠀⢰⢿⣿⣿⡀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀
⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣤⠀⠀⢐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢋⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠤⠄⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠐⠲⢍⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣴⣆⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⣟⣿
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⣀⣤⣠⣠⣀⢄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠐⠻⡻⠿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣫⣷⣿⣿⠕⣐⠫⣵⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⠄⠀⠰⠂⠀⠀⠀⠀⠀⠀⢰⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆⠀⠀⣠⣼⣿⣿⣿⣿⡿⡫⢖⠶⣶⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠛⠀⠀⠀⣹⣿⣿⣏⠁⠀⠀⠀⠀⠒⢺⣿⣷⠀⠀⠀⠀⠀⠀⠀⠜⠋⠁⠀⠀⢹⣿⣿⣿⣿⡟⣵⣾⣷⣾⣿⣿⡆⠀⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⠁⠀⠀⠀⠀⢠⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠙⠛⠇⠀⠀⠀⠀⠀⠀⠘⣶⠀⠀⠀⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⣀⣿⡿⠀⠰⠀⠈⠀⠀⣤⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠓⠀⠀⠈⠉⠁⠀⠀⠀⠈⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⣿⣿⣻⣭⣽⣿⣿⣿⢯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢹⣿⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠈⠙⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⢰⣿⠿⠿⠟⠋⠛⠐⠋⠻⣷⠀⠀⠘⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣤
⣸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣷⣤⣿⣿⣿⣿⣿⣿⣿⠀⣠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣧⠃⣾⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣇⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⠟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢿⠠⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢘⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡟⣼⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀
⣿⣿⣄⣐⣶⣩⣿⠛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⢾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⢺
⢿⣿⣿⣿⣾⣤⣿⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠿⢿⣿⣿⣿⣿⢿⣿⠿⠿⢟⠾⣿⣿⢿⣿⠿⢿⣿⡾
⣚⣿⣿⣿⡿⡉⣿⣿⠹⢿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣮⣻⣿⠿⠿⠿⠿⣿⣟⠛⠟⢻⣿⣿⣟⠀⣿⡇⠀⣧⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣯⣟⣄⢀⣿⠃⠰⢿⣍⠊⣿⣜⠋⠁⠀⣿⠀
⠙⢸⣿⣿⡝⠃⢻⡋⣰⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⡿⢻⣯⣦⣂⣄⠀⠿⣕⣉⡥⠀⢭⣭⠉⠀⢩⡍⠙⡛⠟⣿⣿⣿⣿⣿⣿⣭⠫⣭⡉⠉⠩⠉⠉⠉⢉⢽⡔⢁⡿⢿⣯⣿⣷⣄⣀⣀⣨⣔
⠀⠘⣿⠏⣆⣤⡾⠟⠋⢸⠈⠻⢡⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⡟⠃⠀⠸⠿⠟⠉⠉⠀⢶⣾⣿⡇⠀⠘⣿⡄⠀⢸⢀⣿⠀⠀⢉⣩⣿⣿⣿⣿⡁⢀⣷⠀⠀⠀⢀⡒⣶⣾⣿⣿⣀⣀⣰⣷⣿⣿⣿⢠⣲⣾⣿
⠂⣰⡆⠀⠋⠁⠀⠀⢀⢸⠀⠀⣾⠹⣿⠿⣿⣿⣿⣿⣿⡛⣿⣿⡏⠀⠀⠀⠀⠀⢰⣶⣤⣠⡄⢸⣽⣿⠠⣤⣶⣶⠀⠀⣤⣤⡶⣠⣄⠀⠘⡇⠀⠁⣿⠿⡁⠈⠀⠐⠀⠈⠉⠀⠉⠈⣅⠀⠁⠀⠈⣿⡿⡿⠟⠛⠻⠉
⠉⠩⠃⠀⠀⠀⠀⠀⢾⢸⠀⠴⠤⠤⠥⣤⣽⡿⢻⣿⣿⣿⣼⠃⠁⠠⠄⠀⠀⠀⠈⠙⠺⠟⠀⣤⣼⣿⣆⣿⣿⣿⠶⢶⣿⣿⣿⣿⣿⣦⣤⣽⡆⣴⠿⣿⣿⣽⣤⣤⣤⡤⠀⣤⣤⣤⣿⣤⣤⣄⣠⡿⠙⠀⠀⠀⠀⠀
⣤⣤⣀⣠⣤⡄⢤⣤⣾⣬⣆⣤⣤⣴⣾⣦⣿⣷⡌⣿⣿⡟⠁⣤⣠⣠⣄⣰⣶⣁⡀⡀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣦⣘⣀⣬⣿⣧⣱⣦⣼⣿⣽⠇⠠⠟⠡⠀⠀⠀⠀⢀⣀⣄⣻⣄⣀⣄⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣃⣿⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣋⣩⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣿⣷⣶⡶⣿⣷⣿⣿⡿⠿⠟⢻⢿⣷⣦⣼⣷⢤⣤⣴⣦⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢿⡿⠿⠿⠟⡏⠁⠿⠅⣬⣟⣉⡉⠛⣂⠘⠿⠃⠙⠁⣠⣿⣋⠙⣼⣿
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡷⢶⣶⣤⣶⣾⣦⡀⣠⣴⡟⣹⣿⣧⣹⣿⡄⠀⠀⠀⠀⠉⠘⣿⣿⣿⡟
⠀⠀⠉⠛⠛⠛⠋⠉⠏⠉⠉⡿⡿⢿⣿⡿⣛⠿⣿⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⣿⡟⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣷⣼⠿⣿⣿⣿⡿⣿⣿⣿⠘⠛⢿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⡀⠀⠰⡀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠀⠉⠉⠈⠀⠉⠿⠃⠈⠛⠁⠻⠿⠛⠚⠃⠀⠂⠮⠀⠰⠋⠀⠀⠀⠃⠀⠀⠉⢹⡟⠛⠋⠉⠉⠈⠛⠛⠙⢷⡏⠈⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡻⠛⠃⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠁⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⢠⠇⠀⠰⡀⡔⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⣿⣷⣤⡀⠀⡠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠒⠂⠊⠠⠰⠀⢀⣷⡟⢆⠒⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⠃⠡⠀⠀⢀⡿⢾⣿⠟⠊⠈⠀⠀⢀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠛⠿⠏⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⣴⣿⣿⠀⠀⠀⠀⠀⠀⢀⣱⣞⣿⣤⣼⡁⠀⠀⠀⠀⢀⣺⣿⡟⠒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠈⠟⣻⠇⣿⡉⠉⠳⠠⡿⠂⠀⢠⣿⠟⢛⡛⣿⣿⣿⡿⣆⡀⢠⣾⣿⠿⠁⠈⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠙⠢⡾⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠀⠀⣇⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠘⠀⠈⢸⡇⠀⠈⠉⠘⠋⠁⠀⢀⠀⣠⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠄⠘⠚⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠁⠀⠀⠀⠚⠀⡀⠈⠀⢀⠀⠀⠘⠇⠀⠀⠀⠰⠀⠀⠀⠀⠸⠉⠻⠍⠲⣄⣤⣤⡀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠐⠚⠂⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⣾⠀⢈⠉⠓⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⣠⠀⠠⢀⣤⠀⠀⡄⠀⠀⠈⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣤⣴⠶⠀⠀⠀⠶⠇⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠻⢩⠶⠆⠀⠀⠀⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠖⠀⠀⠀⠼⠀⠀⠀⠀⠀⠊⠀⠘⢦⣦⡀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⠳⠦⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠒⠒
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⡂⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⣂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⣀⢀⣀⣤⣠⣠⣠⣄⣴⣶⣶⣾⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣫⣷⣿⣿⠝⣐⠫⣵⣼⣯⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢶⡾⠋⠀⠀⠀⠀⠀⠀⠸⠂⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣨⡷⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⠶⣾⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢛⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⢻⣿⣿⣿⣿⡟⣵⣾⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⠛⠛⠛⠁⠀⠀⢀⣿⠻⠛⠃⠀⠀⠀⠀⠛⠛⠟⠛⢿⠀⠀⠀⠀⠠⠀⠀⠽⠀⠀⠀⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠀⠀⠀⠀⠀⣀⣾⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣀⣄⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠷⠄⠀⠈⣿⡿⠀⠠⠀⠈⠀⠀⣤⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⡏⠀⣰⣄⠀⠁⣀⣇⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⠀⠀⡄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣦⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠁⣰⣿⣷⣶⣀⠀⠀⢀⣴⣷⠈⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣷⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⣿⣿⣿⣿⣿⣿⡆⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⡶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣾⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢀⣔⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⣿⣾⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢯⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣇⠿⢹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠀⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢻⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⡛⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⣏⣻⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⠇⢹⣿⠉⣿⡘⠛⠛⢻⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⡿⡋⣻⡷⢈⣿⣿⣿⣿⣿⢿⢿⠃⣿⡏
⠛⠛⣿⣿⡟⠾⢾⣿⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣶⣿⣿⣿⣻⣄⣤⠈⢻⣿⣶⣒⡀⢛⣻⡛⠂⠛⡛⠒⢿⣷⣶⣶⣾⣿⣿⣿⣟⡛⣛⡛⠻⢻⡟⠛⠿⢿⣿⡇⠶⣿⣿⣿⣿⣿⣍⣀⣼⣿⣷
⠀⠐⣿⡿⣧⢀⣤⡿⠿⠛⡏⠻⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣶⠾⠉⠸⣿⣿⠟⠛⠃⢰⣽⣿⣿⠁⠘⣿⣇⠀⠀⡇⣷⠊⠉⠙⠛⣿⣿⣿⣿⡟⠁⢹⡉⠀⠀⠁⢠⣤⣾⣿⣿⡀⠉⢈⣿⣿⣿⣿⣿⣽⣿⣿
⠀⢀⣼⠃⠼⠛⠉⠀⠀⣠⠇⠀⣰⡟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠉⠁⠈⠀⠀⢀⣤⣤⣀⣀⢨⣿⣿⡏⣄⣤⣬⡍⠀⢈⣁⣩⢡⣄⠈⠙⣿⠍⠹⣿⣿⠖⠙⠃⠴⠲⠚⠷⠺⠟⠛⣻⠉⠻⠟⠉⢻⣿⣿⡿⠿⢿⡿
⠀⠛⡿⠀⠀⠀⠀⠀⢴⡇⡆⢠⣌⣁⣘⣁⣸⣿⣿⣿⣿⣿⣯⡿⠃⢀⣀⡀⠀⠀⠈⠻⠿⣿⠍⢈⣩⣿⣇⣿⣿⣿⣧⣼⣼⣿⣿⣾⣿⣄⣀⣛⣦⣀⣾⣿⣾⣱⣆⣀⣀⣀⢀⢀⣀⣀⣿⣇⣀⣀⡀⣾⡿⠟⠁⠀⠀⠀
⣀⣀⡀⢀⣀⣀⢀⣀⣸⣇⣇⢀⣀⣀⣤⣭⣿⣿⣄⣿⣿⣿⠟⣁⡀⣀⣀⠀⣤⠄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣥⡘⢟⣙⣻⣿⣛⣭⣹⣿⣇⡟⠀⣽⠏⡍⠉⠉⠉⠉⠉⣉⢹⡋⠉⡉⠉⠉⠉⠻⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡟⣼⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣶⣤⣤⣶⣦⣴⣿⣿⣿⣿⢿⣿⣯⣭⢸⣷⣄⣀⣠⣤⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣟⢙⣻⠟⠒⠶⠮⠹⢿⡟⠺⠟⢉⣿⡟⠛⢷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣶⣬⣭⣀⣠⣴⣮⡀⠈⣠⣿⢛⣿⣧⣴⣿⡇⠀⠀⠀⠀⠘⠛⣿⣷⣿⣿
⠀⠀⠹⠿⠿⠿⢿⢻⢿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣷⣿⣿⡷⠾⢿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠒⠉⠉⠻⠿⠟⠘⠃⠉⠛⠿⣟⠋⠙⢹⠿⠘⠻⢿⢹⣿⣷⠿⠟⠉⡯⣭⠋⠀⡿⠉⠈⠉⢿⡅⠀⠹⢿⣿⡿⠿⠿⠟⠧⢿⡿⠿⣿⣿⠙⠿⠀⠀⠙⠉⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠁⠀⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠂⢀⢶⠶⢿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠂⠀⠀⠀⠀⠃⠐⠛⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠤⠠⠿⠋⡄⠀⠀⠀⠀⠀⠀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠤⠀⢠⣾⠀⠰⡆⣠⠦⠄⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠻⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇⠈⠉⠁⢀⠀⣶⣶⣀⠀⠀⢀⣠⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠶⠶⢮⠇⡠⡄⠉⣻⣶⣶⡠⠖⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠄⠐⠤⣺⣿⣿⣿⠿⠟⠒⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠄⡀⠳⠿⠿⢿⣷⠓⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⢀⣠⣤⠀⢰⣶⣿⡇⠀⠀⠈⠈⠉⠙⣷⣼⢿⣧⣬⡟⠀⠀⠀⠀⠀⢰⣿⣿⣆⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⡻⣿⡏⣿⡟⠛⠳⣀⣾⠤⠀⢀⣴⣿⠿⡾⣿⣿⣿⣶⣶⠀⠀⣴⣿⣿⡗⠺⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠛⠳⣼⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⡀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠶⠁⠀⣶⢀⡄⠀⠈⠁⠈⠁⠀⠀⠈⠹⠀⠀⠙⠋⠁⢠⠃⠘⢻⣏⠀⠉⠛⠘⠿⢿⠃⠀⠀⢀⣵⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠐⠞⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠐⠂⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⡔⠂⠀⠀⠀⠸⠇⠀⠘⢁⠀⠀⠀⠸⠿⠀⠀⠀⢰⣔⠿⠂⠈⢠⠛⠻⠿⢷⣀⣀⣄⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⡀⠀⠀⠀⠠⠶⠓⡠⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠋⠀⠁⢸⡄⠀⡖⠾⠅⠀⠀⠀⢷⡀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈
⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⢲⡦⡆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠹⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣠⣤⡀⠀⢠⠠⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠛⣠⣄⣤⣤⠄⠀⠀⢤⡦⠀⠀⠀⠐⠟⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠁⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢤⡄⠀⠺⢿⡷⠾⠉⠋⠀⢀⣈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠐⠆⠀⠀⠀⡀⠰⠀⠁⠀⣰⡇⠀⠀⠀⠀⢠⡖⢺⣶⣴⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠙⠻⠦⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠁⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠉⠹⣿⠟⠀⠀⠤⠤
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠿⢶⠄⠀⢀⡀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠄⠓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⣀⣤⣠⣠⣠⢄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⣲⣶⠟⠀⠀⠀⠀⠀⠀⠠⠧⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣈⣷⠀⠀⠀⢀⣾⣿⣯⣷⣿⣿⠝⣐⠫⣵⡼⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠻⠛⢿⣿⣿⣿⠿⠟⠛⠛⣛⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⣉⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣾⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⢸⣿⣿⡿⠛⠉⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠙⠻⣿⣿⣿⡀⠀⠀⣠⡀⠀⢹⡇⠀⠀⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠿⡿⠛⠃⢠⣴⣿⠻⠿⠿⢿⠓⠒⣶⠂⠀⠄⠀⢿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣀⣿⠟⠀⠀⠀⠈⠀⠀⣿⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠷⠄⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⡙⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣻⣭⣽⣿⣿⣿⢿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⡄⠀⠀⢀⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⡃⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⣛⣛⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣴⣿⠟⠉⠈⠁⠀⠀⠀⠈⠙⢻⣧⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣤
⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡇⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠋⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⢻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿
⡿⡿⣿⣿⣿⣷⣾⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣽⣷⣿⣿⣏⣹⡟⣿⣿⣯⣭⡉⠹⠿⡿⣧⣼⣿⣦⣸⣷⣤⣤⣤⣿⣿⣿⣿⣿⡿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡄⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠼⣿⣿⣷⠀⣤⣿⣿⠟⡿⢿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣩⣹⠟⠋⣿⣿⣿⡿⠧⢉⣻⣿⣷⡾⠆⣿⣷⠀⠀⢹⢰⡍⠿⠻⢿⣿⣿⣿⣿⣿⠟⠸⡟⠆⠀⠚⠀⣘⣉⣿⣿⣆⠹⠟⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢘⣿⢸⡿⠛⠉⠀⠀⡡⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠟⠀⠔⠀⠙⢋⣁⠀⠀⠈⣿⣿⣿⠃⢀⣘⣿⠆⠀⠾⠸⡧⡠⠀⠠⣾⡿⣿⣿⣷⣦⠴⢿⣤⣠⣤⣶⣯⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠴⢿⠀⠀⠀⠀⠀⢀⡎⡇⠀⡘⠛⠸⢿⠛⣿⣿⣿⣿⣿⣽⣿⠿⠁⠀⠀⠀⠀⠀⢿⣿⣷⡶⠂⠻⣿⣿⢸⣿⣿⣿⡀⠄⣿⣾⣿⣿⣦⠁⠸⣏⠁⢰⣿⣧⡤⣮⠁⠁⠀⠀⠀⠀⠀⢸⣷⠀⠈⠁⢀⣿⣿⠟⠁⠈⠉
⠀⠀⠈⠀⠀⠀⠀⠀⢈⣧⢿⠉⠉⠙⢋⣛⣿⣿⡏⢻⣿⣿⣿⠋⠁⠀⠈⠁⠀⣀⠀⠀⠈⠉⠉⣀⣿⣿⣿⣾⣿⣿⡟⠛⢿⠿⢿⣿⡿⢿⠳⣶⣿⢿⠟⣻⣿⠿⠟⠖⠲⠶⠞⠒⠶⣶⠶⠿⠶⠒⠒⢾⣿⠉⠀⠀⠀⠀
⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣣⣾⣷⣶⣶⣶⣿⣿⣦⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣶⣾⣿⣷⣾⣿⣿⣿⣿⣄⣉⣧⣌⣀⣀⣠⢀⣴⣶⣷⣿⣶⣴⣦⡤⣤⣤⣗⠀⠀⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⢿⣿⡟⣿⣽⡻⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣛⡟⡻⠛⠛⣻⣿⠇⠘⠛⢹⣷⣿⣦⢀⣭⣶⠙⠋⠁⠈⠀⣾⣿⣤⣨⣿
⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣾⣿⣿⣧⣠⣶⣿⣷⣾⣿⣿⣿⡿⢀⠀⣠⠄⠀⠀⠹⠿⣿⣿
⠀⠀⠂⠀⠈⠉⠉⢭⡉⠋⢰⠘⠛⢿⣿⣿⠿⣏⣛⢿⣿⣿⡿⢿⣿⣿⣛⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⡿⣻⠟⠻⠿⢿⠿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠉⠼⡿⠛⠋⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠂⠀⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⣦⡆⠨⠉⠀⠐⠛⠉⣿⣋⠉⠻⠈⠁⠉⠷⠀⠉⠁⢀⣠⠃⣫⣬⣼⣿⣿⠏⠉⠈⠀⠀⠉⠋⠉⠙⠛⠃⠀⠁⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠊⡶⠶⠀⠆⣀⠛⠑⠠⠆⠀⠀⢀⢄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢘⣣⣰⣾⠋⠉⠋⠛⠀⢀⠀⢲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⡀⣸⡇⠀⣤⢤⣤⣤⠀⠀⠀⠠⠄⠀⠀⠈⠓⠐⠀⠀⠐⠒⠀⠁⠁⠀⠀⠀⠈⢻⣧⡄⠀⠀⠂⠉⠁⠉⠀⠘⠀⠀⠀⠀⢠⠤⠾⠟⠀⣈⣠⣤⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡂⣀⣀⣿⣀⡀⠘⢿⣧⣤⡀⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐⠖⡄⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⡇⢀⣀⣠⣷⣿⣿⣿⣶⠤⣴⠋⠋⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢥⣤⠈⠉⠙⣗⣴⣾⣿⣿⣾⣄⠒⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠃⠀⠃⠂⠀⠀⡐⠂⠀⠀⢀⢀⣠⣴⣦⠄⠀⠑⠙⠿⠻⣧⣀⣤⣾⢙⣿⠟⠁⠀⠀⠀⢀⣾⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣆⠀⠨⠟⠂⠈⠀⠁⠀⠨⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠂⣺⣿⣧⢶⣿⠿⢿⡀⣠⣄⡀⠀⢀⣾⣿⣿⣿⣿⣿⣤⣤⡀⠀⢀⣴⣿⣿⡼⣿⣶⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⢧⣀⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠰⠄⢄⠀⠀⣠⡾⠛⢢⡄⢀⠈⠙⠟⠘⠇⠀⠀⠙⢿⡇⠁⠰⡿⠛⠉⡿⠙⠿⣿⠛⠻⠷⠦⣾⣿⡿⠅⠀⠀⢻⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣬⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⢴⠀⠠⠀⠒⠄⠀⡀⠁⠀⠚⠓⠃⠀⠀⠀⠀⡠⠤⠀⠀⠀⢰⣦⠀⠀⡄⠈⠁⠀⠀⣿⠀⠀⠀⠀⣈⣭⡄⠀⠆⣴⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠶⡄⠀⠀⠐⠀⠀⠀⣤⣴⠤⡀⡄⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠧⠀⠀⠀⠀⠈⠁⢴⠀⠐⢳⡆⠄⣤⣽⡞⠃⠀⢈⣿⡅⠁⠀⠀⠡⠈⠉⠉⠛⠻⠿⠿⠓⠀⠀⠀
⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄⠀⠑⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⣄⣤⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠸⠇⠰⠟⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⣀⢘⡀⠀⢠⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠾⠛⠋⡀⠸⠿⣀⣀⣀⣀⣀⠀⠀⢈⣡⠀⠀⠀⢀⣷⡆⠀⠀⠀⠀⠀⠂⠀⡁⠀⠀⢠⡆⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢀⣠⠄⢴⣿⣿⣦⠟⠛⠣⠀⠸⠍⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠉⠉⠀⠀⠈⣅⠈⠀⠀⠀⢠⠆⠀⠀⢀⡶⠀⠀⠀⠁⢀⣄⢸⣇⣸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣠⠼⢶⣏⣀⡀⠀⠂⠀⠛⠃⣠⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠌⠈⠀⠀⠀⠈⠁⠠⠀⠀⠒⠈⡏⠀⠛⠿⣶⣴⡄⢀⣀⣀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣄⡀⠀⠀⠀⠀⠀⠐⠃⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠋⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠈⠉⣅⡐⢯⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣤⣀⠐⣆⣴⠆⠀⠀⠀⠀⠀⢤⣿⣶⣾⣧⣤⢹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣀⡀⠈⠁⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠈⠁⠀⠙⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢢⠤⢤⣦⣶⠆⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⢉⣁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⠟⠋⠉⣿⣿⣿⣿⡆⠀⠀⠀⠀⠰⠟⠉⠀⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⡆⠀⠀⣾⣿⣿⣏⣥⣄⡀⢀⣠⣿⣿⣿⣷⠀⠀⡀⠉⠙⢿⣿⣿⡀⠀⢀⡀⠀⢻⡆⠀⠀⠀⢀⣾⣿⣯⣷⣿⣿⠝⣐⠫⣵⡼⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣿⣿⡇⠀⠈⠁⠀⠀⠁⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⠶⣾⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⠁⠉⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡄⠤⠀⡤⠀⠀⢻⣿⣿⣿⣿⡟⣵⣾⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠿⡿⠛⠛⠛⣻⣿⠛⠛⠻⢶⠀⠀⣶⠛⠛⠛⠛⢿⠛⢻⠓⠀⠀⠀⠈⠀⠐⠀⠀⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣿⡟⠀⠐⠀⠈⠀⠀⢿⠀⠀⠀⠀⠘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠷⠄⠀⠈⣯⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣯⣿⣿⣿⣿⢯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣄⠀⠀⢀⣿⣿⠀⠈⠀⢀⠀⠀⠀⠀⠀⡆⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣫⣿⣌⣛⣋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⠋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣟⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⡿⠛⠹⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠿⠿⢿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⢿⣿⣿⣷⡿⠛⠉⠁⢸⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⣻⠧⠸⣿⣿⡋⠁⠀⢻⣿⣿⣿⣥⣜⣿⣷⡀⢀⣇⣿⣧⣄⣈⣹⣿⣿⣿⣿⣏⣀⣼⣯⣤⣀⣀⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⢴⣿⣏⠈⠁⠀⠀⠀⣰⢻⠀⢰⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⠀⠀⠀⠀⢿⣿⣷⣤⡤⢸⣿⣿⡿⣿⣿⣿⡏⢈⣿⣾⣿⣻⣿⡿⠿⣿⣿⣿⣾⣿⣋⣽⡿⠿⢟⠛⠛⠛⠻⠿⢿⣟⠛⠻⠛⢻⣿⣿⣿⠛⠻
⠀⠀⠘⠁⠀⠀⠀⠀⠐⣿⢾⠐⠛⠒⠶⢶⣾⣿⣿⢻⣿⣿⣿⡿⠟⠓⠶⠲⠂⠀⠀⠀⠛⠛⠛⠀⣼⣿⣿⣧⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣄⣬⣴⣧⣠⣤⣤⣼⣯⣤⣤⣤⣼⣿⠋⠱⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣶⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣦⣤⣴⣾⣶⣾⣧⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣎⣯⣭⣿⣿⣽⣿⣿⣿⣯⡟⣿⣿⣯⠇⠀⠀⠉⢁⣀⣴⣼⣧⣄⣤⣀⣀⣀⣹⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣤⣿⣿⡏⢿⣿⡽⠿⠟⠛⠛⢣⣿⣟⣛⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⣶⣴⣿⣿⣿⣧⣽⣶⣿⣿⣿⣿⣾⣿⣷⡀⢀⡀⡀⠸⢻⣿⣿⣿
⠉⠀⠹⠋⠙⠛⢿⢿⣿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⡿⣻⡟⠚⠋⠁⠀⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⡴⠀⠹⠇⠈⠁⡀⠀⠙⢙⠁⡉⠙⠛⠉⠻⢿⣤⢙⢿⠛⠻⡿⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⠸⠟⠃⢉⣿⣿⡗⢸⣿⣿⣿⠿⠟⠛⠛⠋⣿⠿⠻⢿⣿⠛⠻⠀⠀⠹⠉⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⢀⣀⠡⢂⣀⣸⣦⡥⠴⣶⣖⡀⠻⠿⣼⣍⠀⠀⠀⠘⠛⠛⠁⠀⢰⠀⠀⠀⠙⢷⡤⢄⣿⣉⣘⣿⡿⣿⣿⠏⠀⣀⣤⣤⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠃⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠋⣁⡀⠛⠁⢼⣿⠀⠀⣥⣀⣀⢀⠻⠉⢁⣌⠀⠈⠉⢳⠤⠝⠋⠠⣠⡠⠪⢧⣢⠲⠰⠒⢷⣶⡀⠀⠙⣷⠾⠿⢿⠋⢹⠆⠀⠀⠀⠈⠋⣸⣿⡆⢠⣇⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⣿⢁⣄⣿⣟⠀⠰⢿⣿⣿⣏⣀⣠⡀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣅⣤⡀⠈⠻⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣼⣯⠀⡀⠀⣸⣿⣿⣿⣦⣀⣠⣤⠶⢶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀
⠀⠀⠄⠀⠋⢉⡍⠛⠓⣿⢧⣴⣿⣿⣿⡏⠁⢻⠿⠁⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡿⠉⠹⠭⠯⠃⣠⡥⠄⠀⠀⣀⣤⣀⣠⣀⠀⠂⠼⣿⡿⣿⡀⣈⣺⡿⢿⣿⠟⠛⠉⠙⠁⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⠀⠈⠙⠿⠘⠶⠿⠏⢙⠻⠟⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠁⠃⠁⠀⠀⠀⠁⠘⣿⠏⣤⣶⣾⣡⣿⣿⣿⡇⢀⣀⠀⠀⠀⣹⣿⣾⣿⣿⣾⡇⠀⠀⠀⠀⢀⣿⣿⣿⣷⣶⡦⠀⠀⠂⠀⠀⠀⠀⠀⠀
⠐⣾⣿⡀⢰⣦⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣱⠇⠀⢀⣤⡾⢿⡀⠀⢸⢟⣿⡯⣿⣍⠙⠿⣾⣿⠛⢀⣶⡿⠟⢻⡿⣿⣿⣿⣿⣷⣀⢠⣿⣿⣿⠋⠛⢿⡇⠁⢀⠄⠀⠀⠀⠀⠀⠀
⠂⠀⢀⣙⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠓⠀⠉⠂⠀⢠⣄⢀⠉⣽⡶⠋⠉⠛⢃⠸⣯⣴⣎⠀⠀⠀⠀⠀⡀⠀⠀⠋⣠⢀⢉⣀⠀⠟⠀⠈⣿⡇⠀⠉⠉⠙⢿⡟⠉⣀⢠⣼⣷⣤⣾⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠋⠙⠉⠉⠀⢆⡋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡄⡦⠤⢤⣤⠈⢉⣩⣅⠀⠈⣴⠟⠀⠤⠀⢀⠈⠑⠠⠤⣤⣾⡋⠀⠀⠀⠐⠛⣠⡄⢩⡴⣠⣀⡀⢹⣧⣴⠂⠀⣾⣿⢛⠁⠀⠺⠙⠛⠛⣿⣤⣾⣿⣇⠄⠀⠀
⠀⣀⣀⣠⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⣉⠁⠳⠤⠈⠀⠀⠙⠉⣱⡇⠀⠈⠀⠀⠀⣀⠻⠀⠀⣀⣀⠀⠉⠁⠀⠀⣠⠀⠀⠈⠅⠀⢠⣿⢠⣾⠟⠿⢇⠀⠀⠻⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢀⠀⠀⢰⡇⠀⢀⡘⠁⠀⣠⣤⠀⠀⠀⠁⠈⠚⢾⣿⣿⡇⠀⣶⣄⠀⠘⠀⠀⣀⠀⠠⠓⡇⣀⠃⠀⣰⣶⠀⠀⠀⠀⠀⡄⠀⢶⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣈⣀⣤⣴⣿⣧⣾⢿⠿⡀⠸⣷⠃⠀⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢨⣿⣿⣾⡟⠛⠓⠘⠛⢛⠋⠻⡄⠐⠙⡋⢠⡀⠀⣰⣄⠀⠀⠻⢷⡀⠀⣿⢿⠇⠀⠀⣠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣩⣯⣿⡛⠁⢀⠀⠰⣾⠿⢠⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠈⠋⠀⠀⠘⠋⢀⡀⠀⠤⠼⡿⠙⢿⣿⣷⣀⡀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠉⠉⠉⠉⠀⡈⠿⠈⠉⠁⠉⠙⠃⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⡀⠀⠻⠛⠏⣾⡚⠟
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠶⠆⠀⠈⠁⠀⡄⠀⠀⠀⢠⢔⣓⠰⣿⣿⣿⣶⣾⣶⣶⣶⣶⣶⣤⡄⠀⡘⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠉⣻⣶⣦⣽⣿⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠓⠀⠀⢠⡀⠀⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠛⠓⠴⣷⣿⠁⠠⠤⠲⢿⡷⣿⠿⠟⠻⠛⠛⠻⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣶⠀⠀⠀⠀⠀⠚⣻⡇⠀⠀⠀⠈⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠛⠁⠀⠀⣬⡄⠀⣸⡿⢿⣥⡄⠀⠀⠀⠀⠛⢋⠀⠀⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠵⠾⠛⣛⣉⠀⠀⠀⠠⡀⠀⠉⠉⢂⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⡶⠟⠃⠀⠛⠁⣸⠟⠱⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠓⠀⠀⠐⣾⠀⠀⢸⣿⣿⣿⣯⣥⣤⣀⣠⣾⣿⣿⣿⣇⢀⣀⣈⣙⢿⣿⣿⡀⠀⠀⠀⠈⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣈⠁⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⢠⠐⣢⠀⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣠⣄⣤⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⡈⠀⠧⠀⠀⠀⢀⣾⣿⣯⣷⣿⣿⠝⣐⠫⣵⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣿⣿⠟⠛⠛⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⠶⣾⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠠⠏⠁⠀⢀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣿⣶⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⠿⠻⠿⠛⠛⢿⣿⣿⠟⠛⠿⢿⠛⠛⣿⠛⠛⡟⠛⢿⠛⢻⠛⠛⠂⠀⠀⠀⠀⠁⠀⢀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣀⣿⡟⠀⠐⠀⢈⠀⠀⣿⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠈⣿⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣯⣽⣿⣿⣿⢿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣄⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⢀⡟⠀⠀⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠽⠛⠻⣃⡛⠛⠛⠁⠲⠂⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄⠀⠈⠏⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣎⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿
⠠⣴⣿⣿⣿⣷⡿⠟⠉⠁⢘⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⢹⣿⡿⢿⣿⣟⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⣀⣸⣧⣿⣴⣤⣉⣽⣿⣿⣿⣿⣯⣄⣼⣷⣦⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠼⢿⡇⢾⠁⠀⠀⠀⢠⢺⡀⠰⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠏⡍⠀⠀⠀⠘⣿⣿⣧⣤⣄⣿⣿⣿⢿⣿⣿⣿⠉⢩⣿⣮⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⡟⠛⢿⡿⢿⣟⠛⠻⠛⢻⣿⣿⣿⡿
⠀⠀⠈⠃⠀⠀⠀⠀⠀⢻⣿⡇⠛⠳⠲⢶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠲⠶⠲⠀⠀⠀⠙⠛⠛⠛⢰⣿⣿⣿⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣬⣽⣿⣿⣿⣿⣿⣿⣿⣥⣧⣴⣧⣠⣄⣄⣼⣿⣤⣄⣄⣸⣿⡿⣿⡿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣷⣶⣶⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣦⣤⣤⣾⣿⣶⣿⣄⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣟⣽⣿⣿⣽⣿⣽⣿⣽⣿⣿⣿⣿⠇⠀⠈⠉⢁⣀⣤⣸⣯⣍⣭⣉⣁⣈⣹⣿⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣭⣿⣿⡿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣧⣿⣿⣿⣿⣷⣿⣼⣿⣿⣿⣿⣾⣿⣿⣄⣀⣄⣄⣺⣿⣿⣿
⠿⠛⢿⠟⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛
⠀⠀⠀⠀⡀⠀⣾⠏⠻⠯⠙⠉⣀⡀⢹⣿⡟⢋⠛⠻⠏⢹⣿⣭⡝⣿⡟⠛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠻⢿⣟⣿⣿⡧⣽⣿⣿⣿⣿⣿⢻⢿⣿⣿⡿⢿⣿⣿⡿⣿⠁⡉⣿⡟⠉⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣀⠀⠀⠀⢠⣄⣀⣀⣰⣻⣿⣀⣹⣷⣯⣴⣶⣶⣖⠻⢿⣷⣿⡇⠀⠄⣾⣿⠿⠟⠁⠈⣏⡀⠈⠙⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⢻⣹⣿⡎⠈⠈⣶⠄⠈⠁⠀⠀⠀⢿⡁⠀⠸⠏⢿⠗⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠟⣛⡀⡺⠃⣿⣿⡏⠉⣻⣅⡈⢙⣿⡟⠛⢿⣿⠛⠿⣷⣾⣿⣿⣷⣢⣌⠳⣿⣶⡴⡶⢶⠿⣷⣦⣀⠘⣿⣿⣿⣿⣿⠛⣿⠋⠉⠉⠀⢹⢛⣿⣷⡀⣴⣃⠀⡀⠀⠀⠀⠀⠘⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠁⠈⠋⡋⢻⣿⣻⣿⣿⠂⠘⣿⣿⣿⣿⡏⣁⡆⠘⠁⣠⣀⡁⠁⠀⠈⠀⠀⠀⠀⠈⢉⣿⣧⡀⠀⠻⣿⠿⠂⠛⢿⠄⠀⠈⠀⠋⠀⢠⣶⣿⣾⡏⠉⠉⢀⣿⣿⣿⣿⣄⣀⣀⣠⣤⣴⡾⠒⠓⠂⠀⠀⠀⠀⠀⢸⠀⠀
⠤⠄⠀⠗⠊⣛⣙⠛⠛⢺⣟⣄⣾⣿⣿⣿⢋⢸⣿⣿⠃⠀⠁⠀⠀⠀⠀⢀⣤⠀⢻⡿⢛⣿⣿⣿⣿⣿⣶⠦⠈⠀⣠⣤⣀⣀⡀⠀⢸⣿⣿⣿⡇⠐⢶⣾⣿⣿⣿⠿⠿⠛⠻⠃⢠⣼⡇⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀
⣃⣀⣬⡴⠀⣽⣿⠃⠛⠾⠿⠛⣿⡿⠿⠋⠙⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡄⠙⠛⠛⠉⠀⠤⠘⠛⢿⣿⣷⣶⣶⣞⣻⣿⣿⣿⡉⠀⠀⠉⠁⢈⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣀⣿⣿⣿⣶⣼⣂⡀⠸⠁⠀⠀⠀⠀⠀
⠽⢿⣿⣏⠀⣾⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⣬⣹⣶⣖⠀⣠⣶⣿⣟⠁⠈⣿⣿⣿⣿⣿⡿⠿⣿⣿⣷⡆⣠⣾⣿⠿⣿⣿⣿⣿⣿⣿⣦⠀⣼⣿⣿⡿⠛⢳⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢏⠀⣉⣻⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠓⠀⠠⠤⠀⢀⣤⡀⣉⢹⣿⣿⢛⠿⠟⡉⣿⣦⣾⡁⠉⠁⠀⠉⠃⠀⠁⣽⣯⣷⣿⡏⢁⣰⡏⠈⢿⣿⠁⠈⠙⠁⢻⣿⡿⢃⠀⣤⣽⣦⣰⣷⠀⠀⣀⠀⠀⠀
⠀⠘⠛⠛⠟⡛⠗⣷⡿⠛⠀⠀⠀⠀⠀⠀⠉⢀⣠⣤⣤⣶⣤⣤⣤⡀⠛⢋⣩⠀⠉⢙⣿⠗⢲⠗⢠⡀⠿⠃⣤⣤⣶⣿⠋⠀⠀⠰⠿⢿⣄⠘⣧⣄⡀⠀⠘⢿⣥⣶⠀⢰⣿⣿⣿⠈⠁⡟⠻⠿⢿⣧⣤⣾⣿⣦⡀⠀
⠀⢀⣄⣠⡏⠀⠀⠉⠙⠀⠀⠀⠨⠀⠐⠒⠉⠹⠟⣝⡛⢻⢿⣿⠋⢁⠘⠛⣯⣾⠐⠊⠉⠀⠀⣰⡾⠇⠀⢤⠀⡘⠿⠋⠁⠀⠀⣤⠀⠘⣛⠀⠈⣿⡿⣿⣿⣿⣿⡅⠀⠾⢿⡿⡿⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠈⠀
⠀⠨⠉⠀⠄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠋⡀⠀⢠⣿⠂⠈⣀⠟⠀⢀⣤⡜⠁⠀⠙⠙⠓⢶⣿⣿⣿⠀⣶⣦⣀⠀⠟⠀⠀⣀⣀⡾⢿⣣⡿⠁⢀⣴⡗⠀⠀⠀⠀⢀⡀⢠⣶⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⣡⣤⣶⣿⣿⣶⣿⣿⣇⣈⣿⣿⠁⠸⠿⠿⠀⠀⠁⠀⠀⠀⠉⠀⠹⠏⠩⣿⣿⣷⣶⠞⠛⠽⠿⠿⡿⠻⣧⡀⣞⢛⢇⡀⠀⢠⣄⡈⠀⢰⣿⣦⠀⣾⣿⣷⠂⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⡟⠛⣁⠀⠸⣿⣿⡏⣤⣀⢀⣠⠐⠁⠀⠠⠀⠀⠀⠀⠀⠀⢐⠛⠉⠛⠁⠀⠀⠀⠀⠈⠋⠀⠈⠁⡄⡟⠁⠁⠸⠿⠟⠁⡀⣀⣨⣿⡿⢿⣿⣿⣄⡀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣟⠁⠙⠛⠛⠙⢃⣌⠻⠟⠓⠛⠉⠛⠛⠃⠀⢀⣀⣀⠀⠀⠀⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠀⣀⠶⠇⠀⠀⠁⠰⠦⠀⠀⠀⠀⠉⢀⠀⠁⠹⢣⣄⠉⠿⠿⢿⣧⣷⣶
⠀⠀⠀⠀⠘⠁⠠⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠉⠙⠛⠁⠴⡶⠰⡮⠋⠀⢠⠀⠀⡀⠀⣤⣾⡧⢼⣿⣿⣶⣶⣶⣶⣷⣶⣶⣶⣤⠄⠠⠆⠀⠀⠀⠀⠀⠀⢺⠇⠀⣀⠀⠀⣤⣄⣀⡀⠀⠀⠀⢸⣿⣷⣤⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠛⠀⠀⠸⠂⠀⠀⡆⠀⠚⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⠋⠁⠀⠀⠀⠀⢀⠾⠇⠈⠻⠿⣶⣿⣿⡟⠁⣠⠤⢾⣿⣿⡿⣿⠿⡿⠟⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣠⣴⣤⣴⣤⣴⡆⠀⠀⠀⠀⠰⢛⣿⠀⠀⠁⠠⠅⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢤⠾⠋⠀⠀⣬⣥⡀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠙⠛⠇⠀⠠⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡻⠫⠶⠿⢿⣯⡅⠀⠀⠀⢤⠀⠈⠉⠒⡂⠀⠀⢠⣿⣿⣿⣿⡿⠿⢟⠛⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⣾⡿⠟⠁⠺⠋⢈⡿⠻⢶⣷⡄⠀⠀⣉⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠑⠂⠒⠂⠸⠃⠀⠀⢺⠇⠀⠀⣾⣿⣿⣿⣷⣶⣶⣷⣾⣿⣿⣿⣿⣆⣠⣤⣽⣿⣿⣿⣇⢀⠀⠁⠀⠿⣦⠀⠀⠀⠀⢀⠀⠀⠀⠈⡹⡿⠿⢧⣀⠀⠀⠀⠻⣀⣄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⢀⡠⠀⠀⠀⠀⠀⠀⠈⠐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠈⠑⠛⠀⠀⠛⠓⠀⠈⠉⠹⢅⠀⠲⠟⠁⠀⠀⠀⠛⠀⠀⠀⠶⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⣿⡷⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣠⣿⣿⣿⣿⣿⣿⣿⡆⠀⣀⢠⡖⣶⣤⣤⠀⠀⣴⡾⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⡌⠃⠸⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⠊⠉⠀⠀⣀⡠⠀⠀⢀⡀⠀⣠⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣀⣀⣀⡀⠈⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⠀⠀⠀⢠⡿⠃⠀⠠⣄⣀⠀⠀⠈⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣯⣿⣿⣿⠝⣐⠻⣷⣼⣯⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣶⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠙⠛⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠓⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⢼⡿⠛⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠐⠶⣶⡦⠀⠀⣠⣅⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⠀⢸⠀⠀⠀⣀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠋⢀⠀⢰⡟⠛⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⠀⠀⠀⠀⣤⣿⣿⠀⢸⠷⠄⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⣋⠀⣀⣁⠀⠀⠀⠻⣿⣿⣻⣯⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣾⣇⠀⢠⡀⠀⠀⠰⠀⣀⣉⣿⣿⠀⠸⢆⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢸⠀⠀⢀⣀⣟⣯⠟⣫⡏⠀⢠⣀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠑⠿⠛⠻⠃⠛⠛⠛⠃⣀⣠⣤⣽⣿⡿⠿⠃⠀⠈⠛⠋⢠⣿⣿⣿⡿⡟⠁⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣶⣾⡿⠿⣿⣿⣿⣿⠘⣿⣿⣷⡖⣶⣿⣷⠄⠻⢉⣀⣀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⣠⣤⣶⣿⣾⣿⣷⣷⣶⣶⣄⣼⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⢻⢿⣿⣿⣿⣦⢻⣿⡟⠉⠉⠀⠀⢰⣿
⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿
⠉⠉⠀⠉⠁⠀⠘⣿⡿⣿⡿⠻⡿⠛⠛⢿⣿⡿⢿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⢹⣿⡿⠟⢻⣿⣿⠿⠏⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠋⠁⠈⠋⠀⠰⣶⣶⠛⢩⣄⡄⠀⡉⣁⠸⢻⣿⡇⣾⡗⠀⠛⠿⣿⣿⣿⠿⠿⠿⠟⢻⠿⣏⣾⠉⢀⣷⣿⣿⣧⣼⣿⣿⣿⣿⡟⣿⣿⠛⠿⡿⠛⠛⠿⠟⠛⠋⠀⠀⠙⠀⢠⡼⣿⣇⠀⠀⠀⠀⠀
⠚⠀⢠⣾⡦⢀⣤⡤⣽⣷⡶⠴⣶⢛⠻⢷⣶⣿⣿⣿⣿⣿⣯⣝⣻⢟⣷⡮⠀⢐⠼⡿⡏⢁⣀⣀⣰⣤⡌⠀⡸⣿⣶⣿⣿⣿⣿⣿⡿⠿⠿⠏⠈⣿⣿⣿⡁⠀⢼⠷⠀⠀⠀⠀⠀⠀⠒⡀⠈⠉⠀⠻⠋⠀⠀⠀⠀⠀
⠀⠐⠻⣤⣷⣾⣻⣁⣾⣿⠇⢨⣿⣷⣦⣴⣟⠊⠁⢿⡿⠉⢍⠟⠟⠛⠿⡁⠴⠖⠈⠛⣻⣿⡟⠛⠝⢿⣿⣦⡰⣹⣿⡟⠻⠟⠉⢹⠇⡀⠀⠀⢀⣄⣽⣿⠧⢰⣾⣼⣰⡄⠀⠀⠀⠀⠀⢀⡐⢀⡀⠀⠀⠀⠀⠀⠀⢀
⡀⠀⠀⠐⡁⣸⣧⣮⣽⣿⣰⡜⠛⣿⣿⣯⣷⣾⢧⣀⣄⣰⠊⠇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣷⣦⣦⡸⣿⣟⠀⠈⠀⠃⠀⠀⠀⠀⠀⠨⢨⣿⣿⣿⠅⠀⢀⣾⣿⣿⣿⣷⣦⣤⣴⠞⠺⢟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠘
⣯⡇⠀⡔⡙⠠⣽⣦⡀⡀⣹⣿⣶⣿⣿⣿⣿⣴⠺⢿⡛⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣹⣿⠀⠟⠿⣿⣟⣿⣟⠓⡀⢀⣴⣷⣦⣤⡄⠀⠀⡾⣿⠿⣿⣄⣪⣽⡿⣿⣿⠟⠉⠉⠉⠁⢠⣷⣷⡄⠀⢁⠀⠀⢐⠀⠀⠀⠀
⣿⢷⣶⣿⣆⠀⣸⠟⠀⠘⠛⠋⠀⣿⠋⠛⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⢈⢉⠁⠀⠀⠀⣥⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⢥⣾⣿⣿⣿⣷⣾⣶⠀⠉⠀⠀⠀⠀
⣩⣼⣟⠻⢶⣸⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⢶⣴⣿⣿⣄⣿⣿⣿⣿⡄⢀⡿⠻⠿⠿⣿⣬⠙⣿⢿⣿⣿⣿⣿⠿⠏⣹⠿⣿⣿⡿⢿⣿⣦⢰⣿⣿⣿⠁⠙⠻⣇⠀⢀⠴⠀⠀⠀⠀
⠿⠛⣀⣤⣤⣿⣿⡏⣁⣀⣀⠀⠀⠀⠀⠀⠀⢤⠈⠁⠁⠉⠁⠀⠛⠀⠀⣶⣤⣴⡲⢿⢿⣫⣉⠉⣤⢾⠿⣿⡇⠀⠀⠀⣀⣉⡇⠀⠸⢿⣶⠈⣭⡤⠠⠏⠀⠘⣿⡇⠀⠈⠁⢘⣿⣿⠀⣠⢠⣴⣿⣦⣾⡇⠀⣠⡄⠀
⠆⠀⠈⠉⠀⣥⠎⠀⡿⢟⠁⠀⠀⢀⣠⢀⣀⡠⣤⣴⣿⣶⣿⣶⡾⣷⠤⢈⣡⣶⣥⣀⣤⡿⠉⠙⠋⢐⡆⠚⠁⠲⠷⣶⣿⠇⠀⠀⠈⠛⢻⣷⠀⢷⣞⣤⣄⣀⣻⣿⠿⠆⢀⣿⣿⣿⡀⠀⠻⠉⠛⠛⢿⣷⣾⣿⣷⡆
⠐⠀⢰⡶⠶⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠸⠻⢨⣭⣙⠛⠺⣁⣀⣭⡩⣴⡿⠈⠁⢀⡠⠀⢶⣎⡃⣀⣮⣦⣬⡉⣃⡀⠀⠀⣿⠀⠈⠽⠀⢀⣽⣿⢹⣿⠿⠿⣷⡀⠘⠛⠿⠛⠂⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠉⣙⣧⣀⣨⣿⡉⠀⣤⣋⡀⢰⣶⣮⡀⠀⠈⠈⠈⠙⢿⠿⣿⡇⣿⣿⣶⣀⣉⣀⣀⣰⣶⣼⣻⣧⣿⠁⢠⣾⣷⠁⠀⠀⠀⠀⡄⠐⣿⡁⠀⠀⣥⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠻⠷⣄⣿⣿⡃⠈⠛⠛⠀⢀⠀⠀⠀⣠⡄⠀⠈⠁⠀⠙⢿⣿⣿⠟⠉⠉⠛⢻⣿⠛⢿⠶⠾⣻⣿⡤⣤⣤⣶⣦⡀⠠⠿⣿⣂⣷⣿⣻⡇⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣿⠿⢿⣯⣭⣴⡀⠀⢻⣿⣇⣿⣶⣤⣴⣆⠀⠀⠀⣵⣿⣶⣶⣶⣶⣶⣶⣶⣮⣁⠀⠀⠀⠀⠀⠀⣀⠉⠁⡶⠸⠀⠀⠈⠛⠋⢩⡇⠴⠦⢿⡟⠛⢿⣿⣿⣤⡄⠀
⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⢀⠄⠒⠀⠀⠀⠀⢼⣿⣦⣬⠃⣀⠀⣹⣶⠘⠛⠉⠁⠀⠉⠉⢻⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠐⠚⠛⠀⢠⣅⠘⠋⠂⠀⠀⠀⠀⠀⠂⠀⠀⣱⣶⡄⠙⠛⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⣿⠈⣿⠀⠀⢰⡆⠀⠦⠀⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣈⡁⢰⣶⣶⣴⣴⢗⣤⡤⠀⠀⢀⣸⣿⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⣠⣤⡌⠁⣠⠠⠷⣰⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣦⠀⢀⣀⠀⠛⠓⠀⠉⠙⣿⣿⣿⡟⠀⠐⠚⠻⢿⣿⡿⠿⠋⡻⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⢟⣻⣿⣿⡿⠀⠀⠀⠀⠈⠡⣿⡆⠀⠀⠂⢰⣿⣿⣿⣿⣷⣤⣤⣦⣼⣿⣿⣿⣿⠀⠀⠈⠛⢿⣿⣿⣇⠘⠁⠀⢀⣴⣶⠆⢸⣿⢿⣿⣷⣰⣖⡀⠀⠈⠻⠅⠀⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠋⠉⠉⠉⢹⢿⡇⡀⠀⡀⢹⡄⠀⠀⣈⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⠀⠀⠀⣿⣛⠁⠀⠘⠁⠀⠉⠁⠛⢿⣆⣀⣀⡀⠋⠂⠆⢀⣠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⢄⣀⠀⠉⡿⠀⠰⠠⠤⠤⡄⠀⠀⣧⡜⠛⠛⠓⣷⠄⠐⠀⣈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⡥⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⢀⡀⠀⠀⠀⡘⣒⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣾⣿⡿⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠺⠏⢹⠗⠂⠀⢠⣿⣏⡀⠀⠀⠀⠁⠻⠃⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡤⠤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠀⠀⠈⠹⢿⡄⠃⠀⠀⠀⠀⠄⠀⠻⡿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣀⠀⠀⠀⠀⢠⡶⠒⠁⣄⠀⠂⠀⠀⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣶⣶⣶⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⢠⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠛⠀⣠⡄⠀⠛⠁⠀⠀⠛⠻⠅⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠤⠀⢀⣤⡄⠀⢨⡷⠀⢰⡀⢸⣦⡀⠀⠀⠂⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠀⠀⠀⠘⠁⠁⠙⠛⠁⠀⢘⡃⠈⠈⢻⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠟⠛⠿⠛⠿⠿⠻⢿⣟⣻⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠁⠀⠛⣤⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⠂⠀⠐⠀⠀⣠⣤⢆⣴⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡄⠀⣠⣶⣶⡄⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⠀⠀⠸⠦⠀⠀⢸⣿⣿⣿⣶⣤⣴⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣧⣄⣻⣿⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣶⠶⠀⠀⣀⣾⣿⣿⠿⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⣿⣿⡔⡀⠀⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣤⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣼⣿⣿⡿⠛⠋⠀⠀⠙⠙⢠⣿⣿⣿⣿⢻⠁⠀⠀⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣴⣶⠾⣿⣿⣿⣿⡷⢸⣿⣿⣿⠶⠂⠀⠀⢠⣾⣿⣯⣿⣿⣿⠝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠿⠟⠋⣿⣿⢸⡀⠀⠀⠈⢻⣿⣿⣿⣿⠀⠀⠀⢀⣶⣿⡿⠁⠀⠈⢻⣿⣿⢃⣿⣿⣿⠛⠋⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢻⣿⣿⣿⣇⣀⢠⣶⡖⠀⠀⣶⣾⣿⣿⢸⣿⣷⣦⡀⠀⠙⢿⣧⡁⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣾⣿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠛⠻⡟⠸⠿⠿⡟⠛⢻⠃⠀⠐⢶⠺⠿⠿⣿⣿⠘⠻⡿⠛⠓⢄⡀⠀⠛⠓⠰⢿⠛⠛⠿⠛⠋⠀⠀⠀⠘⢿⠛⠿⠿⢦⣤⠀⠀⠀⠀⠀⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠢⣤⡇⡄⠀⣶⡇⠀⠀⠀⠀⠀⠈⠀⠈⣶⣿⣿⠀⢠⠀⠀⢀⣀⣿⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⣿⠀⠀⢀⣐⠄⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⡀⠈⢁⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⡄⠀⣤⣿⣿⠀⠈⠷⠄⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣤⣤⠀⠉⠀⣀⠀⢻⣿⣿⣿⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⣀⣧⡀⠁⢀⢸⣇⣀⡟⠀⠀⢀⠀⠀⠀⣰⣇⣀⣉⣿⣿⠀⠀⣄⠀⠁⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⢀⢀⡈⣀⣠⡟⠉⠉⠀⣀⠀⠿⢤⡀⡙⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⡇⠀⠐⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⡇⠀⠀⠺⠿⠀⠀⠀⣀⣐⣠⣾⣶⣿⣿⣿⣿⣿⣿⣧⣄⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⡟⠛⣿⣿⣿⣿⠻⠋⢻⣿⣿⣿⣦⣿⣿⡿⠍⠉⠁⠀⢸
⢽⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣾⣿⣿
⠸⠉⠉⠉⠁⠀⠙⣻⡿⢿⣿⠛⠹⠉⠛⢿⣿⣿⢿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢸⣿⡿⠻⢿⣿⡏⠚⠓⠀⠀
⠀⠀⠀⠀⠀⠃⠀⠛⠀⠀⠉⠀⠀⢠⡀⠈⠀⣤⣰⡄⢉⠁⣀⡬⣿⣶⣰⡿⡋⠉⠛⣿⣿⣿⣿⠟⢿⡟⠟⣿⢿⣧⡏⠀⣠⣺⡿⣿⣽⣿⣿⣿⣿⣿⣋⣙⣉⠹⢿⠟⠛⠛⠿⠛⢛⠁⠠⠑⠁⠀⣴⡿⣿⡄⠀⠀⠀⠀
⠸⠾⢢⣶⣦⠀⣠⣤⣾⣷⣤⠶⣴⣴⠀⠠⣶⣿⣿⣿⣿⣿⣿⣇⡛⡟⢿⣷⡇⠠⣠⣺⣿⠉⠁⠀⢈⣧⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠋⢡⣿⣿⣿⠀⠀⡾⠧⠀⠀⠀⠀⠀⠰⣷⠁⠈⠉⠀⠟⠁⠀⠀⠀⠀
⣶⡷⢿⣯⣿⣦⣿⣝⣿⣿⣷⣴⣾⣾⣦⣤⣿⣿⣟⢻⣿⠏⠉⣿⡿⠓⣽⣟⠦⢶⠟⠻⠿⢿⣮⠘⠻⠻⣿⣧⣦⠞⣽⠿⠛⠿⠟⠉⡿⠀⠀⠀⣄⣸⣭⣿⣿⠆⣰⣧⣆⣤⡀⠀⠀⠀⠀⠘⣀⣾⣀⡀⠀⠀⠀⠀⠀⠀
⣭⡀⠀⠈⣯⣸⣿⣿⣿⣿⣿⣾⡿⢿⣿⣿⣿⣷⣿⣄⣙⣠⣆⣽⠀⠘⠁⠀⠀⠀⠀⠀⣠⣴⢿⣦⣤⡀⢽⣟⠋⠉⠀⠋⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣤⣀⣤⣿⣿⣿⣿⣷⣤⣤⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⠻⣿⣿⠿⣿⣿⡏⣉⣻⣿⣷⣾⣿⣿⣿⣧⡾⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⢦⡤⣈⣿⡇⠘⠻⣿⣿⣿⣿⣇⡀⠀⣀⣶⣶⣤⣤⣀⣨⢿⣿⣿⢿⣧⣸⣿⣿⣿⣿⡿⠛⠛⠙⠻⣇⣸⣿⣿⡀⠉⣷⠀⠀⡖⠀⠀⠀
⣿⣿⣿⣿⣿⠀⣸⡿⠇⠘⠟⠛⠋⢿⡿⡟⠃⠀⠀⠙⠋⠀⠀⠀⠀⠀⠤⢂⡸⠀⢠⠉⣀⡀⠐⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣙⣋⠀⢸⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣶⣄⣇⠀⠀⠀
⣭⣿⣿⡿⢷⣤⣿⣷⣦⡄⠀⡀⠀⡀⠀⠁⠀⠀⠀⣀⣤⣤⣄⠀⡀⠀⠁⠀⠀⠰⣷⣿⣿⣅⣠⣿⣿⣿⣇⠀⣸⠟⣿⠿⢿⣿⣟⢻⣿⣿⣿⣿⣿⣿⠿⢋⡿⢿⣿⣿⠿⣿⣷⣆⣼⣿⣿⡿⠙⠻⢿⡏⠉⣻⡿⠀⠀⠀
⡿⠿⢛⣣⣴⣿⣿⣿⣧⣤⣀⡅⠀⠀⠀⠀⠀⣠⣄⠈⠉⠉⢛⠂⠛⠂⠀⢰⣿⣤⣶⢿⣿⢟⣬⡛⢋⡼⣿⣷⣿⠀⠀⠀⢀⣀⣹⡎⠠⢿⣿⣷⢡⣥⡤⠼⠁⠀⢹⣿⠀⠀⠉⠁⣻⣿⣿⣇⡄⣿⣾⣿⣶⣿⠆⣀⣦⣦
⠷⠀⠀⠉⠁⣩⣿⠇⣹⣿⡉⠁⠀⠀⢀⡀⣀⣠⣤⣴⣾⣷⣾⣷⣶⣷⣦⠌⣩⣴⣮⣤⣠⣼⠏⠉⠞⠃⣦⠜⠛⠠⠶⣾⣿⡿⠁⠀⠀⠘⠛⢻⣦⠈⠷⣣⣤⣀⣘⣿⣿⣿⠀⣴⣿⣿⣿⠃⠉⣿⠙⠛⠛⣿⣷⣿⣿⣿
⠀⠦⢄⣶⠶⠿⠉⠀⠀⠀⠄⠐⠀⠐⠽⠁⠉⠉⠸⢟⣯⣿⣍⠟⠛⢏⡀⣨⣭⢹⣿⠏⠉⠀⣀⠄⠰⣷⣿⢀⣐⣷⣖⡟⠛⡁⠀⠀⢸⡇⠈⠙⠇⠀⣠⣿⠟⣿⡿⠿⢿⣷⠂⠟⠻⠿⠛⠀⠀⣘⠀⠀⢀⣀⠘⠉⠀⠀
⠀⠀⠘⠋⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠉⢿⣷⡄⣀⣺⣿⠠⣤⣜⣡⠀⣶⣾⡋⠀⣀⠉⠉⠉⢻⣿⣿⡿⠸⣿⣷⣄⡈⢃⣀⣀⣴⣶⣛⣻⣿⡏⠀⣰⣿⡏⠁⠀⠀⠀⢰⡆⢸⣿⠀⠀⢨⣧⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢠⣾⣾⣾⣿⣿⣿⣿⠟⠿⢧⣩⣿⡟⠀⠛⠻⢣⡀⡀⠀⢀⣦⣯⣭⣤⣤⣤⣤⣭⣿⣿⣿⠋⠉⠛⠿⣿⡿⠻⣷⡾⠟⣿⣷⣤⣤⣤⣶⣄⠀⠸⢿⣿⣄⣾⣿⣿⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣽⣾⠿⣿⣭⣵⣶⢂⠙⣿⣿⣹⣶⣤⣴⣾⠀⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠈⢁⡘⠉⢠⡇⠇⠀⠀⠛⠛⠫⣵⣦⣶⡼⣿⡟⠿⣿⣿⣷⣤⢀
⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⡠⠔⠂⠀⠀⠀⠰⣿⣧⣤⡞⢉⡀⢨⣶⡆⠛⠉⠉⣀⡈⠉⠙⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠖⠛⠃⠀⣼⡀⠚⠚⠂⠀⠀⠀⠀⠦⠀⠀⢘⣿⣶⡀⠛⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠰⢻⡏⢹⡇⠀⠀⣷⠀⢸⣄⣴⣾⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣨⠠⣶⣶⣦⣤⣾⣧⣤⠄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢀⡀⠼⠏⠀⠀⣃⣤⣤⠉⢀⠰⢿⣾⣿⣿⣿⣭⣭⣌⣽⣧⣿⣿⣿⣿⡇⠀⠀⠛⠻⣿⣿⣧⠀⢀⡀⠸⠛⣇⠈⠉⢛⣿⣿⣿⡃⡤⠒⠚⢻⣿⣿⡿⡿⠛⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣟⣚⣿⣿⣿⠇⠀⠀⠀⠀⠏⢿⠧⣀⠠⠛⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣶⣾⣿⣿⡄⠋⠉⢀⣵⣶⡶⠀⣿⡿⣿⣿⣿⣦⣦⠀⠀⠛⣿⠃⠀⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠍⣽⠉⠉⠿⠿⢂⠀⢀⠈⣧⡀⢀⣀⣿⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣏⠁⠀⠙⠁⠈⠉⠈⢻⣯⣀⣀⣼⠼⠗⠒⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠋⠿⠀⢀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣠⡄⠀⠙⠋⣠⠗⠤⢦⣤⠄⠀⣠⣤⠟⠛⠛⢰⡾⠛⠃⢄⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣯⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣤⠀⠀⠀⢰⣛⡇⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⢻⡿⠟⠂⠀⣼⣯⣁⠀⠀⠀⠘⠸⠟⠀⢀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠤⠦⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠉⠀⠀⠀⠋⠻⣧⠘⠀⠀⠀⠀⠰⠄⠻⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣶⠟⠉⢠⣄⡘⠁⠈⠻⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⠄⠀⠀⢤⠀⡄⠀⠐⠖⣄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⢀⣴⡄⠉⠁⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⠀⢐⣶⣦⠀⢀⣽⠆⠰⣇⢸⡿⣦⡀⠀⠐⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠛⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⡿⣿⣿⣿⣿⡿⢽⡟⢀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠙⠃⠀⠀⠛⠈⠁⠘⣷⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠘⠀⠈⢡⣤⡖⠒
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⡀⠀⠀⢶⣾⣿⣿⣿⣶⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⡄⢠⣶⣶⡦⠀⠀⢈⣿⠓⠖⢶⣄⠀⠠⠟⣷⣄⢲⣀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⣀⢀⣀⡛⠒⠄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣀⠀⢠⡿⠿⠀⠀⠀⠹⠀⠀⠀⠉⢹⠏⢉⠀⠓⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣃⡀⣾⣿⡿⠿⠁⠀⠹⠿⠟⢉⣿⣿⣿⡿⡟⠉⠀⠹⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣵⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡶⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣾⠿⢫⣿⡇⣧⠀⠀⠀⠻⣿⣿⡿⣿⡿⠀⠀⠀⢀⣴⣿⣿⠉⠀⠙⢿⣿⣿⢇⣿⣿⣿⠷⠽⠉⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣿⣿⣿⣿⡀⠀⣤⣤⡀⠈⢀⣤⣼⣿⡇⣿⣷⣆⡀⠀⠙⢿⣿⣞⠁⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⢸⣿⡟⣾⣿⠉⠉⠀⠀⠀⠀⡀⠀⣀⣘⣿⣶⣠⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡟⠉⠁⣠⣤⣼⣿⣿⣿⡇⢻⣿⣿⣿⣦⡀⠀⠘⢿⣆⣠⣾⣿⣿⣿⡿⠟⠀⠀⠀⢸⣿⢹⣿⣿⣀⡀⠀⠀⠀⠀⢀⡾⣿⣫⣿⣿⣿⣽⣖⣻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢹⣿⣿⣿⠉⠉⣷⣶⡆⠛⢻⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣶⣄⠀⠈⠛⠛⠉⠉⠀⠀⠀⠀⣠⣾⣿⡇⣾⣿⣿⣿⡗⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡯⣶⣾⣿⣮⡻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣾⣿⣿⣿⣶⡄⠙⠛⢃⣀⣼⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠃⣿⣿⣿⣿⣧⣤⡄⠁⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⠀⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠟⠛⠻⡇⠿⢿⠿⠛⠛⢃⠀⠀⠛⢿⠿⡿⠿⣿⣿⠟⠀⠿⠛⠛⢿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⡟⠛⢿⠟⠋⠀⠿⠿⢿⣿⡏⠛⠃⣀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠂⣀⢀⡆⠐⣦⠀⠀⠀⠀⠀⠀⠀⡆⠂⣶⣿⣿⠀⠀⠀⠀⢠⣤⣿⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⢰⠀⠀⣿⣇⣀⠀⣿⣿⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠦⡀⠀⢸⡇⠀⠻⠀⠀⠀⠀⠀⠒⢸⡇⠁⣤⣿⣿⠀⠀⠰⠄⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇⠀⠀⢰⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⠀⠁⣀⣧⡀⠁⠀⣼⣇⡀⠀⠀⠀⢠⡀⠀⠀⣸⣇⣀⣉⣿⣿⣀⣀⠀⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⣇⠀⢠⣀⣈⣀⣠⣿⠀⠀⢀⣶⡦⠘⠀⠀⣿⡻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠛⠓⠿⢻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣦⡦⠘⠻⢷⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⣸⣿⣿⣿⣿⣿⢀⣄⠘⠛⠟⠀⠀⢀⣀⣡⣾⣿⣶⣿⣿⣿⣿⣿⣷⣤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⠘⠟⠀⢉⣀⠀⢨⠻⠋⢙⠛⡿⠋⠙⠛⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡟⠻⣿⣿⢿⡿⣿⣿⢿⡟⠈⡈⡿⠋⢀⣸⣿⡇⠀⠀⠀
⠀⢰⣴⢠⣤⣄⠀⢀⢀⢶⣆⣀⣀⣀⡃⠀⣀⣠⣿⣿⣤⣷⣾⣷⡊⠿⢿⣿⣿⡆⠀⣠⣿⡿⠛⠋⠀⢹⡋⠈⠋⠙⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⢟⣮⣴⣶⠀⠀⢶⣦⠔⠀⠀⠠⠁⠠⣷⠗⠐⠟⠋⠸⠟⠀⠀⠀
⢀⣀⣴⣾⣟⣿⣼⣿⣟⣿⣿⣇⢹⣻⣄⡀⢹⣿⣿⡿⣿⣿⠟⠛⣿⣾⠧⣿⡧⣮⣥⣿⣿⣷⣦⣢⠠⣶⣿⣶⣦⡀⢹⣿⣿⣿⣿⣿⡿⣿⠉⠙⠋⡀⢸⠟⣿⣿⡆⢀⣾⣰⢀⡀⠀⠀⠀⠀⠸⠆⣰⠀⠀⠀⠀⠀⠀⠀
⣀⠙⠉⠉⠻⡏⣿⣿⢿⣿⣿⣇⣸⣿⣿⣿⣿⣟⣻⣷⡘⠟⣀⡀⣿⠁⠖⠩⠗⠁⠈⠀⠀⠉⢹⣿⡀⢀⠘⢿⣿⣷⠼⠟⡯⠀⠈⠀⠀⠋⠀⣷⢲⣿⣾⣿⠋⠉⢁⣼⣿⣿⣿⣷⣀⣀⣀⣤⣤⣶⣾⡛⠟⠃⠀⠀⠀⠀
⣿⣿⡶⢤⢰⣷⠿⣿⣏⠟⠻⣿⣿⣤⣽⣿⣿⣿⣛⣹⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⣀⡀⠰⣿⠟⢻⣿⣷⡿⣿⣟⡀⠠⠀⠀⣤⣤⣀⣀⠀⠀⢿⣿⣿⣿⡟⢐⡶⣾⣿⣿⣿⡿⠿⠟⢿⡏⢹⣿⣿⡂⠀⢅⠀⠀⢀⠀⠀
⢿⣭⣤⣴⣴⣄⠈⣻⣿⡀⢷⣿⡿⠛⣿⣿⣿⠛⠛⠊⠽⡟⠀⠀⠀⠀⠀⠀⡆⣀⠙⠃⠞⠟⠀⣀⠈⢿⠿⣿⣿⣷⣷⣤⣟⣿⣿⣿⣿⣛⡁⠙⠛⠛⠹⣿⣾⣿⣿⣧⣿⡏⠀⠀⠀⠀⡊⣾⣿⣿⣷⣆⣸⣄⡀⢼⠀⠀
⣾⠛⣿⣿⣿⣏⢀⣿⣀⡀⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠋⢀⡔⣴⣶⠒⢠⣤⣼⣿⡟⠉⢹⣿⣿⣿⣿⣟⡿⣿⣿⣿⣷⣆⣤⣶⣿⡿⣿⣿⣿⣿⣿⣶⣦⡀⢀⣿⣿⣿⠿⢿⣿⡟⠛⠇⣽⠆⠀
⣿⣿⣿⣿⡉⣙⣿⣿⣿⠟⠄⠐⠀⠈⠀⠀⠀⠀⠀⠀⠺⠿⠿⠷⠄⣶⠀⠀⢠⡀⢘⣙⣿⣿⡿⢾⡿⠿⢻⣿⣤⣾⠁⠉⠉⠙⠻⢷⡔⠋⣿⣿⣾⣟⡟⠉⣠⡟⠉⢻⣿⠉⠋⠻⡟⢾⣿⣿⣿⠀⣀⣨⣷⣄⣴⡇⠀⣤
⣿⣏⠉⠑⠛⠻⣿⣿⠋⣼⣿⠿⠂⠀⠀⠀⠀⠀⠉⠁⣀⣠⣄⣴⣄⣠⣄⣀⠹⠟⢛⡛⠛⠛⣲⣿⠦⣸⠏⡋⢻⣿⢀⣀⣤⣼⣶⠚⠁⠉⢹⣿⣿⡟⠻⣋⡍⡀⠀⠸⣿⣤⣤⠀⢀⣾⣿⣿⠟⠛⣾⠿⣿⣿⣿⣤⣨⣿
⠉⢉⡀⠀⣄⣠⡿⠟⠀⠊⠋⠂⠀⠀⢀⠺⠉⠶⠚⠻⣿⣿⣿⠛⣿⣽⡿⠋⠱⠿⣿⣿⡷⠟⠛⠁⠀⣠⣄⣿⠄⢀⣌⠉⣿⡿⠛⠀⠀⢀⡄⠀⢼⣟⠀⠛⣹⣿⣶⣶⣾⣿⡟⠂⣿⣿⣿⣿⡆⠀⢘⠀⠀⠀⠙⢻⠟⠛
⠀⠀⠀⠹⢋⠀⠀⠀⠠⠌⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡈⠿⢿⣇⠀⠈⣷⣦⠐⡃⣸⠏⢀⣀⣠⡞⠋⠈⠿⠿⠤⣴⣿⣶⣇⣀⣀⡀⠀⠸⡇⠀⠈⢁⣠⣾⣿⣧⡿⠋⢉⣽⣿⠗⠁⠀⠁⣀⡁⢠⣿⡇⠀⠀⡒⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⣼⣧⣤⣾⣿⣶⣶⣿⣿⣄⢻⣧⡿⠀⣿⣿⡆⠀⠂⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣶⣿⣿⣇⣀⣾⢿⣏⡀⠀⠠⣄⠘⠁⢸⣿⣯⠀⣸⣿⣷⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣻⣿⣿⠟⢏⣈⡉⣿⣾⣿⢧⣄⡈⢉⣀⠖⠒⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠻⠏⢨⡿⠉⡝⡟⠛⠛⢻⣿⣿⣿⠀⣌⣘⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣏⢙⡿⠻⠛⠻⣥⣈⣿⠿⠾⠛⠿⢿⠿⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⠆⠀⣸⠃⣵⣤⡀⠀⠀⠉⠛⣋⡉⠛⢻⣧⣄⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⡙⠟⠛⢠⣶⡆⣾⡿⠃⠀⣄⠀⠶⠀⢀⣴⣿⣿⣿⢿⣛⠉⠙⠟⣽⣿⣿⣿⣿⠋⠉⠨⢿⣿⣿⣿⡀⠀⠀⠛⠀⡀⠀⡀⠀⣀⡄⠀⠁⠀⠀⠀⣿⣿⣧⣤⣰⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣜⠁⠹⠃⢀⠀⠿⠀⡘⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣄⣈⢿⣿⡇⠀⢠⣶⡈⠛⠿⢿⣾⣿⣾⡟⠁⣀⣠⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣀⣤⣦⣤⣶⣴⣶⠄⠈⠈⠀⢠⠾⣿⡗⠀⠸⣷⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠚⠁⢀⣳⣄⢀⣾⣿⣿⣿⡇⢋⣀⠀⠘⣿⢿⡏⠁⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠿⠷⠾⠿⣿⣯⠀⠀⠀⢠⡎⠊⠙⠙⣷⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⣿⣦⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⡋⠸⣿⠋⠹⠟⠙⣿⣿⠀⠀⠙⢻⣧⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠛⠀⠀⠉⠉⠐⠀⠀⠀⠿⠀⠲⠶⣿⠂⠀⣾⣿⣿⣿⣿⣿⡿⣽⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢿⡖⠀⡄⠀⣀⠀⠀⠀⢈⡉⣿⣶⣿⢡⣷⠶⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢻⣿⣯⣿⣿⣿⣿⣿⣅⠀⠀⠀⠘⠁⠉⠉⠿⡁⠀⠾⠟⠀⠀⠀⠸⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠭⣿⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⣿⣤⡄⠀⣸⡶⠇⠀⠀⠀⡠⣠⣤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⣀⣄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠷⠀⠀⠰⠿⣿⣞⢢⠀⠀⠀⠈⢁⡀⢰⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠀⠉⠀⠀⢀⣠⡤⠞⠁⠀⡠⠤⠤⣶⡆⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⠀⠀⠀⠈⠛⠀⠀⢀⣀⠀⠀⠀⠈⠋⠁⠀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠚⠟⠚⠶⠗⠀⣀⡀⠺⠟⠀⠀⠻⠷⣶⠤⠄⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⢀⠀⠀⣀⡀⠉⠀⣧⡀⢤⡈⢱⣦⡄⠠⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠈⠀⠰⠏⠛⠠⠶⠟⠁⠈⣿⠚⠋⢻⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⡀⠀⠀⠀⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠃⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠤⠈⢻⡃⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣤⣤⣄⠀⠀⠲⣤⣤⣤⣤⠀⠀⢠⡧⣄⡀⣀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠐⠶⣄⢀⣼⣿⣿⡿⠋⠙⣿⣿⠟⣻⣿⣿⣿⣿⠟⠛⠙⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢹⣿⣿⣿⡄⣰⣾⣯⠀⠀⠉⢷⠀⠀⠘⠟⢳⠛⠆⠠⡦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⣾⣾⣷⣵⣾⣿⡟⠁⠀⠀⠀⠀⠀⣠⣿⡿⢻⣿⢰⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣶⣿⠟⠉⠻⣿⣿⡿⢸⣿⣿⣿⣿⠛⠛⠓⢤⣤⣶⣾⣶⣤⠀⠀⠉⠁⠙⠸⢧⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⡦⠀⢀⣀⡀⠀⠋⢁⣀⣿⣿⠘⣷⣄⠀⠀⠘⢿⣿⡍⠿⠃⠀⠀⣠⣾⣿⣿⡃⠀⠀⠀⣿⣿⢱⣿⡟⠛⠃⠉⠀⠀⠀⠈⠛⣿⣿⣿⡿⠰⣶⣿⣆⠀⠀⠸⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢹⣿⣿⣿⣿⣶⡚⠛⢉⣀⣠⣾⣿⣿⣿⠀⣿⣿⣷⣆⠀⠀⠙⢿⣆⠀⢠⣾⣿⣿⣿⣿⡗⠀⠀⠀⣿⡏⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢠⣬⣉⡉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⣿⣿⣿⡿⠟⢻⣤⣀⠼⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣦⣄⠀⠈⠺⠿⠿⠛⠛⠉⠁⠀⠀⣠⣴⣿⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⣈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢧⣿⣿⣿⣧⣀⠸⠿⠿⠀⠀⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⣼⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡀⠀⠀⠀⠀⠈⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⢸⣿⣿⣿⠿⢿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⣿⣿⣿⣿⡿⠇⠀⠀⡀⠀⣀⢀⣠⣿⣷⣠⣠⣤⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡏⣼⣿⣿⡇⠀⠀⣿⣷⠀⠈⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣯⣿⣿⣿⣿⣒⢻⣿⣼⣿⣿⣿⣿⣿
⠀⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠀⠉⢉⣦⣤⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣷⢶⣿⣮⠻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠀⠠⣤⣠⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⣿⣿⣿⣿⣿⠉⠉⢁⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠐⠿⡿⠛⡿⠛⠛⠻⡟⠸⠿⠿⡇⠐⠸⠟⠛⠁⢀⠿⠿⠿⣿⣿⠿⢿⡿⠃⠘⢿⣿⣿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠘⢿⠛⠃⠸⠿⠿⢿⣿⣿⣀⡀⠸⠇⢿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠂⣀⡄⠀⠀⣶⡇⠀⠀⠀⠀⠀⢸⡄⠀⣶⣿⣿⠀⢸⠀⠐⠀⢀⣿⣿⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⢰⠀⠀⣿⡿⣿⣿⠀⠀⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠁⠀⢸⠀⠀⡇⠀⡿⠦⠀⠀⢣⠀⠀⣿⠇⠀⠀⠀⠀⠘⢻⠇⠀⣤⣿⣿⠀⢸⠷⠤⡀⠈⣿⡿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⣿⡇⠀⢸⣶⣶⡖⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣆⠀⠁⣀⣧⡀⠀⢀⣼⠀⠀⣿⡄⠀⢠⡀⠀⠀⣸⠀⠀⠉⣿⣿⠀⢸⣄⡀⠁⡀⢹⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣀⣈⣀⣠⣿⣿⣿⠆⠈⠉⠀⣠⡀⠙⠻⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡀⠀⠀⠀⠉⢀⣀⣠⣾⣿⣿⣾⣿⣿⣿⣿⣷⣤⣠⣤
⠀⢀⣤⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠀⠀⢈⣷⣾⣤⣤⣤⣮⠹⣿⣿⣿⡫⠁⠀⣨⣿⣿⡿⠏⠉⠉⣏⠁⠈⠙⠻⣇⣀⣤⣿⣿⣽⣷⣿⣿⣿⣿⣿⣏⣡⣭⡀⠈⠡⣤⡀⠈⠁⠀⠅⠀⣸⢈⠀⢘⠿⢉⡿⠃⠀⠀
⠀⢀⣁⢼⡟⣻⣀⣿⡿⣿⣿⡏⠻⣿⣇⠀⠐⣿⣿⠿⣿⣿⠿⠿⣷⣶⡬⣿⣽⣠⣀⣼⣿⣯⣀⠀⢀⣤⣿⣦⣄⠀⢰⢿⣿⣿⣿⣿⣿⢿⡟⠛⠛⠉⠀⡿⢿⣿⣧⠀⣀⢃⠄⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠊⠋⠛⠘⠻⠟⢿⣿⢲⣿⣿⠏⠺⣿⣿⣿⣾⡟⠛⣶⠸⠟⠃⠀⣻⠛⠅⠈⠐⠊⠉⠁⠀⠙⠛⣿⡀⠈⠈⣿⣿⣷⠄⠸⢍⠁⠉⠋⠁⠹⠁⢐⢀⣴⣦⣷⡞⠛⠛⢰⣿⣿⣶⣧⡀⠀⠀⣠⣀⣠⣶⡷⠒⠀⠀⠀⠀⠀
⣾⣶⣤⢄⢈⣦⡟⠻⡟⠿⠯⢶⣿⢈⣹⣿⣿⣿⡟⣛⣷⣶⣾⠛⠛⠀⠁⠀⠀⠀⠀⠀⠠⣶⡾⢻⣿⣦⡶⣘⣋⡁⠀⠀⠀⢀⣠⡀⠀⠀⠀⢸⣾⣿⣿⣿⠈⠰⣤⣾⣿⣿⣿⣿⠿⢿⣿⠋⣩⣯⡏⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⡄⣀⡀⠁⢺⣿⡆⢶⣼⣿⠿⢿⣿⣿⠟⠓⠉⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⡤⠿⠃⠈⠉⢻⠿⣾⣿⣧⣤⣤⣴⢿⣿⣿⣿⠳⠀⠀⠻⠿⠋⢻⣧⣶⣾⣿⣻⣿⠋⠀⠀⠀⠉⢰⣿⣿⣷⣄⠀⡆⠀⢀⠇⠀
⣶⠿⣿⣿⣿⡿⠀⣾⡃⠁⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠵⠞⠀⡸⢤⣤⠄⠀⣀⣠⣶⡶⠋⠹⣿⣿⣿⣿⣿⢿⣿⣾⣷⣶⣄⢀⣠⣾⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⣰⣾⣿⡿⢿⣿⣿⠷⠛⠀⠆⠀
⣿⣶⣿⣿⡏⠛⢷⣿⣿⡿⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⣰⣿⢶⣦⡄⢠⡀⠀⢀⡀⠐⠛⣿⣿⣷⢶⣿⣿⠛⣿⣄⣴⠋⠙⠛⠙⠟⣷⡈⠟⢻⣿⡯⣽⠿⠋⠁⣼⠋⠻⣿⡟⠛⠻⡷⢴⣿⣿⣿⠃⠀⠈⣿⣄⢀⣾⠁⢀
⣿⣟⡛⠑⠿⠿⠿⣿⠟⢓⣷⣶⠀⠀⠀⠀⠀⠀⠐⠃⠀⣀⣀⢠⣄⠈⣀⠀⠸⡿⠶⢿⠛⠟⢳⣶⣆⢀⡂⠙⠛⣿⡆⠀⣀⣠⣴⠼⠛⠀⠈⣿⣿⠁⠰⡖⢈⠃⠀⠀⣿⣇⣀⡀⠀⣠⣿⣿⡿⠶⢢⡿⣿⣿⣿⣿⣀⣼
⠉⠉⠁⠀⣀⠀⣳⡿⠀⠘⠛⠀⠀⠀⠀⠀⠆⣤⠴⠒⣿⣿⢿⠿⢿⣻⣿⠟⠃⣴⡾⡗⣶⢴⠺⠋⠀⠉⡀⣸⡆⠈⢀⠛⠻⠿⠿⠀⠀⠀⣀⠀⢙⣿⠀⠘⢋⣶⣠⣴⣬⣿⣿⠃⢠⣿⣿⣿⡏⠀⠈⠇⠀⠉⠙⠛⡿⠿
⠀⠈⠁⢠⡟⠉⠉⡀⠀⡀⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠳⣿⡆⠈⠉⢱⣤⠀⠶⢐⡿⠃⡀⢀⡐⠆⠀⠿⡯⠇⣨⣿⣶⣀⣀⣀⡀⠀⠀⠿⠀⠀⠉⠀⣰⣾⣏⢸⠟⠛⢛⣿⡦⠈⠉⠉⠉⠁⠀⣤⣦⠀⠀⠰⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣴⣿⣧⣤⣾⣿⡄⠺⣾⣴⠄⢿⣿⣧⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣯⣽⣿⣿⠀⣰⣿⣿⠀⠀⠀⡀⠀⠟⠀⣿⣿⡀⢀⣾⣦⣤⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠿⠿⠿⣿⣿⡿⠿⠉⠛⢻⣴⣿⣿⡀⠈⠉⢁⠀⠂⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠹⠿⠉⣿⡟⢉⢷⠿⠛⢳⣶⣿⠷⡤⠠⠛⣿⣧⣼⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⡿⠛⣿⠷⠶⢶⡀⠀⣿⣫⣤⠿⢿⣾⡿⢄⣴⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣧⡀⢠⣤⠀⠰⡟⢸⣄⡀⠀⠉⠁⠾⠗⠛⠛⠻⣟⡉⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠔⠉⠁⠀⠀⠀⠀⠿⠿⠷⠋⣤⡤⣨⣟⠷⠉⣀⠀⠠⠄⢀⣀⣿⣿⣿⣋⣅⣀⡈⢂⣼⣿⣿⣿⣏⠁⠀⠐⠻⢿⣿⣿⠉⠁⠀⠘⠃⠈⠀⠉⠀⠀⡀⠀⠈⠁⠀⠀⠹⣿⣇⣈⡩⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⠇⠘⡗⠀⠀⢿⠀⠈⣇⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣿⣿⡇⠀⠀⣤⡎⠞⢶⣾⣷⣿⣧⣶⠓⠀⢀⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣤⣀⣤⣤⣤⡄⠈⠁⠂⠀⣥⣾⣷⠀⠀⢒⡘⢳⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠰⠈⠉⣐⣀⡀⢠⣿⣿⣿⣇⠒⠉⠉⠉⢻⣿⣿⠙⣡⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣯⣭⣿⣿⣟⡃⠀⠀⠀⡀⠃⠛⠛⣶⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣽⣿⠿⠁⢼⡟⠻⠿⠋⢾⣿⠇⠀⠀⢶⣁⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⡠⠀⠀⠙⠛⠀⠀⠀⠀⢿⠆⠠⣤⣼⡇⠀⣴⣿⣿⣿⣿⣿⣏⣼⣿⠟⠉⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣷⠀⢀⠈⠀⠀⠀⠀⠘⠛⢲⣴⣶⣃⣨⣤⣤⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⢀⣠⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠡⢤⠟⠒⠚⣳⡂⠀⠴⠷⠊⠉⠉⠁⠙⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠹⣿⡿⠂⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣟⣤⡤⣶⣄⣀⠀⢀⣧⠧⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⠛⠁⢯⠉⠁⠀⡾⣿⣆⢂⡄⠀⠀⠀⠛⠁⠠⣤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠀⠘⠋⠉⠀⢀⣀⡴⠂⠀⢀⣀⠀⣤⡄⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠁⠈⠻⠆⠀⢀⡀⠀⠘⠁⠀⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠷⠤⣶⠀⠀⠀⠤⡿⠃⠀⠸⣶⣤⡄⠀⠈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⠋⠛⠃⠀⠀⢀⠈⢁⠀⠀⠘⠂⢶⡀⢀⡈⠑⣤⣀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠃⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⣤⣄⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠉⠉⠙⠛⠛⣿⣿⣿⣷⣤⠀⠀⠀⠀⠈⠁⠀⡾⠻⠤⣤⡾⠃⠀⣳⡢⠟⢹⣆⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢠⡀⢻⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⣀⣀⣄⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⣯⡄⠀⢀⠀⠀⠙⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢶⡄⢀⣾⣿⣿⡿⠋⠉⣿⣿⠟⣻⣿⣿⣿⢿⠛⠉⠙⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⡟⣿⣿⣿⣤⢀⣴⣿⡇⠉⠙⢷⠀⠈⠁⠾⠧⣸⠖⠀⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣶⣦⣶⣶⣥⣾⣿⡏⠀⠀⠀⠀⠀⠀⣰⣿⠿⢻⣿⢸⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⣿⠏⠀⠙⢿⣿⣿⠁⣿⣿⣿⢿⠉⠛⠛⢧⣤⣴⣾⣶⣦⡀⠀⠐⠃⠐⢢⣅⣀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⣀⡀⠀⠉⢁⣀⣿⣿⠘⣷⣄⠀⠀⠈⠻⣿⣌⠟⠁⠀⠀⣠⣾⣿⣿⡏⠀⠀⠀⢸⣿⣇⣾⣿⠛⠋⠀⠀⠀⠄⠐⠛⢻⣿⣿⣿⠃⢠⣶⣆⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⡚⠛⢓⣀⣀⣾⣿⣿⣿⠀⣿⣿⣿⣦⡀⠀⠈⠻⣧⡀⣠⣾⣿⣿⣿⣿⠿⠀⠀⠀⢸⣿⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡄⣀⡛⠙⠐⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⣿⣿⣿⡟⠛⠻⣤⣄⠾⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣶⣤⡀⠀⠘⠟⠛⠋⠉⠉⠀⠀⠀⣠⣴⣾⠃⣿⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⢛⠿⡇⣿⣿⣿⣷⣦⣀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢧⣿⣿⣿⣧⣀⠈⠛⠿⣀⡀⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢸⣿⣿⣿⣿⣧⣄⠀⠉⠁⠀⠀⠀⢀⢚⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢸⣿⣿⡿⠿⠿⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠇⣼⣿⣿⣿⣿⠙⠛⠀⠀⠀⠀⠀⠀⠌⠺⠅⠀⠀⠀⠀⠈⣿⣿⣇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⣼⣿⣿⡇⠀⠀⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⣀⢀⣠⣶⣾⣠⣤⢄⣴⣾⣿⣿⣿⣿⣿
⠀⠈⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣿⠀⠀⠉⣤⣤⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⠇⠀⠀⢀⣾⣿⣯⣿⣿⣿⣿⣟⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⡟⠀⠈⣤⣄⠘⠙⢻⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⣸⣿⣿⣿⣿⡇⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣶⣷⣾⣮⠻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣧⣤⠶⠿⠿⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⢿⣿⡟⢀⣿⣿⣿⣿⣿⣇⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠉⠛⠛⢛
⠀⠀⠀⠀⠀⠸⠟⠟⠛⡿⠛⠛⠻⡟⠘⠿⠿⡿⠟⠀⠀⠀⠰⢿⡿⠿⠿⣿⣿⠿⢿⡿⠛⠃⠸⣿⣿⠛⠛⠿⢿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠸⠿⠿⢿⣿⣿⠿⢿⠃⠀⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠀⠀⠁⠀⡇⠀⠀⣀⣠⠀⠀⣶⡇⠀⠀⠀⢀⠀⢸⠇⠀⣶⣿⣿⠀⢸⠀⠐⢤⡀⢻⣿⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⣿⣿⡀⠀⣶⣶⡎⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⡀⠀⡿⠆⠀⠀⢻⡀⠀⢿⡇⠀⠀⠀⢘⠀⠛⠀⠀⣤⣿⣿⠀⢸⠷⠤⡀⠀⠘⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣄⠀⠀⢀⣇⡀⠀⠀⣼⡇⠀⣸⡇⠀⣠⡀⠈⢀⣸⡀⠀⠉⣿⣿⠀⢸⣄⡀⠁⣠⣇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣸⣀⣈⢀⣠⣿⣿⣿⢁⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⢿⣿⣿⣷⠀⠀⠀⠀
⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠀⠙⠿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣅⠘⠿⠿⠿⠁⠀⣀⣠⣾⣿⣿⣾⣿⣿⣿⣿⣷⣤⣠⣤
⠀⠀⠀⠀⠛⠃⠀⡲⠆⠀⣴⡆⠈⠙⠀⠀⠀⢶⡟⠟⢻⡿⠙⠉⠓⢦⡄⡈⠄⡀⣀⡀⠸⣆⣀⠀⠀⠠⢼⣦⣄⠀⠀⢿⡇⡿⢧⠬⠹⢻⡟⠈⠉⠁⠀⠘⠛⣻⣿⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠒⠚⢛⣗⠀⣰⣿⠇⠀⢻⣿⣗⠶⠛⠀⣠⠈⠛⠀⠀⠀⠈⠁⠀⠀⠈⠈⠀⠀⠈⠁⣰⡀⠀⠀⠹⣿⣷⠀⠀⠅⠀⠀⠀⠀⠘⠁⠀⠀⣠⣄⣶⡞⠛⠙⠀⣾⣶⣧⣦⡀⠀⠀⢀⣀⣀⣠⡆⠂⠀⠀⠀⠀⠀
⣴⡶⢤⠀⡀⣤⡜⠛⡛⠻⠷⠶⣶⠀⣸⣿⣿⣧⡞⠋⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⠻⣷⣦⣤⢒⠹⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠠⠤⣼⣿⣿⣿⡿⠻⠟⠿⠏⢁⡀⣭⠁⠀⠀⠀⠀⢀⠀
⠙⢛⢓⡀⣀⡈⠀⢸⣿⡇⢰⣴⢿⠟⠿⣿⢿⠟⠓⠁⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⡙⠃⡤⠾⠁⠀⠉⠹⠂⢴⣿⣞⣀⣄⣰⠲⣿⣿⣿⠒⠀⠀⠹⠟⠋⠹⣷⣾⣾⣿⣠⣿⠏⠀⠀⠀⠀⠀⣾⣿⣿⣤⣀⠠⠀⠀⡜⠀
⣴⠿⢗⣿⣿⣟⠀⣼⡄⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠀⠀⠠⣠⡄⠀⠀⠀⣶⡤⠋⠉⢻⣟⣿⢻⣿⠛⢿⣶⣴⣶⣤⢀⣀⣼⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⢠⣾⣿⣿⠻⢿⣿⡿⠞⠀⡁⠀
⣾⣶⣶⠏⠉⠙⢷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣤⡄⢠⡀⠀⠀⡀⠀⠛⢻⣭⣔⠤⣾⣿⠋⣷⣄⣠⡆⠘⠛⠈⠿⢻⡀⠙⠻⣿⠁⠈⠿⠛⠉⢸⠟⠻⣿⡟⠙⠛⠿⠆⣿⣿⣿⠃⠀⠈⢹⣇⡀⣴⠀⠀
⣿⣟⡉⠀⠴⠾⢟⣿⠟⢰⣶⣤⠀⠀⠀⠀⠀⠀⠐⠒⠀⢀⡀⢀⡀⢀⣁⠀⠰⠿⠶⠟⠉⠻⠋⣤⡤⡀⡀⠈⠉⢻⡇⠀⠀⢀⣤⠤⠃⠀⠀⣻⣿⠂⠀⠶⢀⠊⠀⠀⢹⣇⢀⡀⠀⢠⣸⣿⡷⠀⠂⡿⢿⣿⣿⣿⠀⣀
⠉⠉⠁⠀⣀⠀⢨⡿⠀⠘⠛⠀⠀⠀⠀⠀⠆⢠⡄⠒⢚⣛⠻⠿⢿⡋⡽⠿⠃⣤⣶⠷⣲⢄⠺⠛⠀⠈⠀⢠⡆⠀⠀⠈⠛⠿⠿⠇⠀⠀⠀⠀⢈⣿⠆⠀⠋⣾⢂⣠⣤⣿⡟⠃⠀⣾⣿⣵⣧⠀⠀⠃⠀⠀⠈⠛⡛⠿
⠀⠀⠉⠁⠙⠉⠉⡀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠾⠇⠈⠉⢩⣤⠄⠠⠀⡿⠋⠀⠀⡀⠆⠀⠸⠧⣧⣖⣉⣠⣤⣤⣤⣤⣄⣀⣹⡂⠀⠈⠁⢀⣼⡟⢈⡟⠋⠉⡛⠂⠀⠉⠉⠉⠀⠀⢠⣴⠀⠀⠀⠄⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠇⡀⣠⣴⣦⣠⣾⣿⡄⠰⣶⣰⡄⢸⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣯⣵⣿⣾⠀⢠⣾⡿⠀⠀⠀⠀⠀⠟⠀⢽⣧⠀⠀⣼⣷⣤⠀
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠾⠿⡟⣿⣿⡿⠿⠋⠉⢙⣦⣿⡟⡀⠀⠉⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠩⠿⠈⣙⡟⢁⢢⠧⠒⠓⣶⣾⠷⠂⠀⠉⢱⣷⣴⣿⣦⣏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡿⠋⢻⠶⠶⢶⡄⠀⢻⣹⣧⡿⢷⣶⡶⣦⣿⣿⣿⣿⣿⣟⢻⢿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣷⡀⢀⣤⠀⠀⠞⠈⣄⡀⠀⠉⠉⠰⠖⠀⠛⠈⡿⠁⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠛⠿⠞⠏⣠⣤⢰⣞⠛⠈⢀⠀⢠⠄⠀⣸⣿⣿⣟⣭⣤⣄⣀⣡⣾⣿⣿⣿⡇⠀⠀⠉⠛⠿⣿⣿⡀⠁⠀⠐⠃⠈⠁⠁⠀⠀⡀⠀⠀⠁⠀⠀⠈⢿⣇⣀⠩⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡨⠇⠈⠷⠀⠀⢸⠄⠠⠠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣷⣴⣾⣷⣶⣤⣽⣿⡇⠀⠀⣤⡄⠘⢷⣶⣦⣾⣧⣶⠖⠀⢀⣀⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⣤⣀⣠⣄⣤⡄⠀⠀⠀⠀⣠⢶⣷⠂⠀⠠⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣷⠠⠄⠉⢨⣤⡄⠠⣽⣿⣿⣧⡘⠋⠉⠉⢻⡿⠿⠙⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠯⣭⠾⢿⣟⡃⠀⠀⠀⣀⠁⠚⠛⢴⠄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⠿⠁⢸⡿⠙⠿⠋⠙⡿⠄⠀⠀⠲⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⡒⠂⠀⠈⠉⠁⠀⠀⠂⠼⠆⠀⢤⢴⡇⢠⣾⣿⣿⣿⣿⣿⣯⣾⣿⠟⠉⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⢻⣿⠆⢠⠈⠀⠀⠀⠀⠈⠛⢲⣴⣶⡃⢀⣡⠄⡉
⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⢀⡠⠀⠀⠀⠀⠀⠀⠘⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠤⠠⠏⠑⠒⣲⣆⠀⠠⣷⠊⠉⠉⠀⠙⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⣼⡿⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣠⡤⣴⣆⡀⠀⠀⣧⠶⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡝⠃⠸⠍⠀⠀⡶⣿⣆⠂⡄⠀⠀⠀⠙⠁⣠⣴⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠃⠘⠋⠉⠁⢀⣀⡰⠓⠀⢀⡀⠀⣤⣄⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⡀⠀⠁⠈⠙⠄⠀⠀⣀⣀⠈⠁⠀⠛⠋⠀
⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠦⢶⠄⠀⠀⠠⠾⠃⠀⠘⣷⣦⣄⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⡟⠁⠙⠁⠀⠀⠀⡀⠁⠀⢀⠈⠳⢺⡀⠀⡔⠛⣷⣄⠀⡀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣵⠆⠀⠀⠀⠈⠁⠀⡾⠛⠦⢤⣾⠋⠀⢱⡀⠟⠹⣧⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠙⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣻⣿⣿⠟⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⢠⡄⠹⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣧⣤⣤⣤⠀⠀⠒⣤⣤⣀⣠⡀⠀⠒⣾⣄⠀⢀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠲⠦⣠⣾⣿⠿⠟⠈⠹⠿⣿⠟⣻⣿⣿⣿⠿⠛⠋⠙⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⠏⣿⣿⣿⡦⠠⣶⣾⡇⠀⠈⢳⡄⠈⠁⠾⠳⢘⠓⠀⣤⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠸⣧⣵⣾⡝⣿⣿⠇⠀⠀⠀⠀⠀⠀⣠⣿⡿⢻⣿⢰⠀⠀⠀⠹⣿⣿⡿⣿⣿⡆⠀⠀⠀⠀⣠⣶⣿⠏⠈⠙⣿⣿⣿⢀⣿⣿⣿⠿⠍⠉⠉⠱⣤⣴⣿⣷⣦⡄⠀⠘⠉⠙⠲⣦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢻⣿⣿⣷⡆⠀⢀⣀⣀⠀⠋⣁⣀⣿⣿⠸⣷⣄⠀⠀⠘⢿⣿⣌⡟⠁⠀⠀⢠⣼⣿⣿⡿⠀⠀⠀⢸⣿⢧⣿⡟⠉⠁⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⠃⢲⣿⣦⠀⠀⠀⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣼⣿⣿⣿⣷⣶⠋⠉⢹⣤⣤⣿⣿⣿⣿⠀⣿⣿⣷⣄⡀⠀⠈⠻⣧⠀⢀⣾⣿⣿⣿⣿⠿⠂⠀⠀⢸⡟⣾⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡄⣤⣍⣉⠀⡂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣿⣿⣿⡏⠉⢹⣦⣤⠛⠿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣦⣄⡀⠈⠘⠟⠛⠛⠋⠉⠀⠀⠀⣀⣤⣿⢁⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣄⣿⣿⡇⣿⣿⣿⣿⣷⣄⣨⡁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢱⣿⣿⣿⣧⣤⠀⠛⠛⣀⣀⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⢸⣿⣿⣿⣿⣆⣤⠀⠛⠛⠀⠀⠸⠿⠛⠿⡇⢿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢸⣿⣿⡟⠛⠻⡀⠀⠠⡿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⠋⠛⠃⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠙⠿⣿⣿⣿⣧⠼
⠀⠀⣀⡠⢄⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⣾⣿⣿⡃⠀⢰⣿⣯⠀⠀⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⢷⣷⠀⠀⢈⣦⣤⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⣀⢀⣠⣶⣦⣠⣤⢄⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⣤⣄⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⣾⣿⣯⣿⣿⣿⣿⣗⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣤⠾⠿⠿⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⠃⢸⣿⣿⣿⣿⣿⣄⡀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣶⠶⣾⣮⠻⢿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠸⠏⢠⣿⣿⣿⣿⣿⡟⠛⠇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠉⠛⠛⢛
⠀⠀⠀⠀⢰⠟⠛⠟⠛⡿⠛⠛⠻⡗⠀⠿⠿⠇⠀⢤⠄⠀⠘⢿⠿⠿⠿⣿⣿⠿⢿⡿⠛⠛⠀⢿⣿⠛⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⢿⣿⣇⡀⠀⣿⣇⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠆⠀⡇⠀⠀⣀⣠⡀⠀⢰⡆⠀⠀⠀⢀⠀⠈⠀⠀⣶⣿⣿⠀⢸⠀⠐⢤⣄⠸⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⣿⣿⣿⠇⠀⠀⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⡗⠂⠀⠀⢹⡁⠀⢸⡇⠀⠀⠀⢸⠛⢛⠀⠀⣤⣿⣿⠀⢸⠷⠤⡀⠘⡄⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⣿⣿⡏⣀⣀⠀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⢀⣸⣄⠀⠀⢀⣇⠀⠀⠀⣸⠃⠀⢸⡇⠀⣰⡀⠈⢀⣸⡀⢀⠉⣿⣿⠀⢘⣄⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣇⣀⣸⠀⠀⠀⠀⢿⣯⡀⠻⠿⠿⠿⠀⠀⠈⠻⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀⠀
⡀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⢛⢿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⢰⣶⣶⣶⣭⣵⣀⣀⠀⠀⠀⠀⣀⣼⣿⣷⣾⣿⣿⣿⣿⣷⣤⣀⣤
⠀⠀⠀⠀⡀⢰⣄⡌⠁⠀⣼⡇⠀⣤⣄⣀⡀⡸⡏⠀⠘⣦⠄⠀⠐⠹⠦⠀⠀⠨⠺⠭⠉⠱⡰⠀⠀⠀⠘⢿⣧⣀⠀⠹⠹⠛⠫⠉⠈⢹⡇⠀⠀⠀⠀⣀⢀⣾⣿⠀⢠⢁⡆⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠁⠹⣧⣠⣸⡿⠃⢀⠙⢻⣯⣭⡍⣀⣸⢀⡁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆⡀⠀⠘⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣿⠏⠀⠀⢀⣿⣿⣿⣿⣦⣤⣤⣤⠖⠲⠞⡛⠁⠀⠀⠀⠀⠀
⢿⣯⡕⠐⠀⠹⠋⢡⣬⡍⠉⢙⣟⣠⣼⣿⣿⣷⡇⠀⠿⡟⠂⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣹⠏⠉⠿⣿⠏⢐⣀⣄⠀⠀⠀⢀⣆⣠⣤⣀⠀⠀⣷⣿⣿⢿⡄⠘⣑⣼⢿⣿⡿⠛⠉⠉⠉⠁⣠⣦⣷⠀⠀⠀⠀⠀⢠⠀
⠀⣤⣤⣤⣴⣦⠀⠨⠟⠇⠘⠘⠛⠉⢙⡙⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⠚⠉⠀⠀⠄⠈⠀⠛⡿⠻⣴⣷⣾⣠⣾⣿⣿⡀⠀⡀⠉⠈⠀⢈⣿⣿⣿⣿⣾⣿⡁⠀⠀⠀⠀⢀⣿⣿⣿⣷⣦⣎⢀⠀⠇⠀
⣻⡋⢉⣻⠿⣧⡀⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣐⢾⠂⠀⢠⣤⣿⣏⠁⠀⡸⢻⣿⢸⣿⣩⠙⢿⣿⣿⠗⢠⣶⣾⡿⢻⣿⣿⣿⣿⣿⣿⣤⡀⣰⣿⣿⡟⠉⠻⣿⡏⠁⢀⡀⠀
⣿⣽⣿⠅⠀⣠⣹⣿⣽⠃⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠐⠂⠀⠆⠀⢀⣤⢀⣀⡹⣿⡾⠉⠛⠟⠁⠿⠧⣾⡇⠀⠀⠀⠉⠘⠆⠀⠈⣟⣤⡀⠉⣁⠀⠼⠁⠈⢻⣧⠀⠀⠉⠁⢻⣿⡩⠁⡀⣤⣼⣷⣤⣾⠀⠀
⠾⠶⠄⠀⠛⠉⠉⣌⡉⢀⣿⠛⠂⠀⠀⠀⠀⠀⠀⣀⣀⢤⣄⣰⢦⣠⣤⣄⡈⠋⠉⣩⢀⠉⢡⣿⠓⢠⠄⠀⡀⠸⠇⢠⣤⣤⣿⠋⠀⠀⠀⠾⠿⣁⡀⢉⡤⣀⡀⠀⠘⣿⣴⡆⠈⢰⡾⠿⡯⠀⠀⡟⠛⠿⠿⣿⣤⣴
⠀⠀⠤⡀⢦⠤⠼⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠊⠀⢶⢀⣹⡋⠻⠦⡮⠉⠀⠚⠛⣩⣿⠑⠈⠁⠀⠀⢠⡼⡇⢠⠄⠀⠀⠉⠋⠁⠀⠀⢤⠀⠀⢙⠁⠀⢠⣿⠂⣼⡿⠿⣏⡀⠐⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠬⠉
⠀⠀⠀⠀⠎⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠣⡀⠀⢈⣷⠀⢉⣁⢟⠀⢠⣤⡆⠉⠀⠈⠙⣿⣶⣶⣶⣿⣿⣿⣷⣶⣶⣾⣇⠀⠀⣤⡰⠟⣋⣠⠋⠀⣠⣾⡁⠀⠀⠀⠀⢠⠀⢸⡿⠀⠀⢠⡁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⣠⣥⣤⣴⣷⣷⣶⣿⡿⣇⡈⣿⣾⠁⠘⢿⠟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⠿⢿⡤⠐⠟⡟⢀⣀⢀⣠⣄⠀⠀⠸⢳⣄⢀⣾⡟⡿⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣥⣿⣿⣛⠉⣄⠀⠼⣿⣿⡏⣶⣄⣀⣠⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠉⠀⠐⠀⣠⠘⠋⠀⠈⠿⠿⠉⠁⠀⣤⡸⣿⠛⢿⣷⣷⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣯⣀⣹⠙⠋⠉⣣⣄⠸⠎⠛⠋⠙⠿⢻⣿⣿⣿⠟⠛⠛⠆⠉⣿⣿⣿⣿⠟⠋⠉⢭⣿⣿⣿⣆⠰⠾⠀⠀⣅⠠⠃⠀⠀⠀⠀⠈⠉⡀⠀⠀⢟⣴⡌⠉⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠙⠉⠁⠺⡟⠸⣃⠉⠀⢠⠀⠐⠀⢀⣿⣿⣿⣷⣾⣷⣶⣦⣾⣿⣿⣿⣿⣆⢀⣠⣀⣀⠙⣿⣿⡄⠀⠀⠀⠁⢀⣀⣀⡀⣀⡄⣀⣀⠀⠀⠀⢀⠹⣷⣶⣆⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢀⣀⡘⠂⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠶⢆⠈⠙⠛⢿⣾⣷⡿⢁⣀⠤⠴⣿⢿⣿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡾⠦⢶⣶⣾⡇⠀⠀⠀⠀⠞⣻⣿⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⣀⣻⣿⣿⣿⣿⣿⣿⣧⠛⠀⠠⣬⣿⠇⢰⣿⣿⣿⣿⢀⣀⡀⠀⠘⠛⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡋⢛⡛⠛⢹⣿⠆⠀⠀⡀⢶⡀⠀⠁⠙⡄⠀⣸⣿⣿⣿⣿⣿⡟⣾⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⡋⠀⠘⠋⠀⠉⠁⠠⣯⣀⠀⠀⡁⠀⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠙⠃⠀⠑⢻⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠐⠿⠁⡰⢄⣀⣀⡀⠀⠀⣀⣸⠿⠷⠆⣠⠌⠃⢤
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡯⡅⠠⠆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢉⠁⠁⠀⠀⡚⢳⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⠆⢿⠷⠂⠀⣀⣿⡋⡀⠀⠀⠀⠂⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡤⠤⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠘⠂⠀⠀⠏⠻⣧⠀⠇⠀⠀⠀⢠⠤⠚⢿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡀⠀⠀⡀⠀⠀⠀⣠⡶⠊⢀⣀⠐⠒⠒⠻⠗⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇⠀⠀⠀⠀⠆⠀⠰⢠⣈⢁⠀⠐⠒⣢⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠛⠃⣠⡤⠉⠋⠁⠀⠀⠛⠻⠗⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣇⠄⠀⠀⠀⠀⠠⠄⠀⣠⣴⡀⠀⢸⡦⠀⢯⠀⣾⠷⡄⠂⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠋⠉⠉⠙⠛⠛⠻⣿⣿⣿⣿⣾⠀⠐⠀⠀⠀⠀⠀⠋⠈⠁⠛⠛⠀⠀⠘⠂⠃⠀⣿⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣧⣤⣄⣀⣀⣠⣤⣤⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠉⠂⠘⠃⠈⠣⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⢀⠀⠀⣰⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣶⣷⡄⠀⢀⣿⠓⠒⢶⣆⠀⠠⠟⣷⣤⢰⣀⠀⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠘⠶⢠⡄⡦⡉⠷⣾⣿⠟⠛⠁⠀⠘⠛⠛⠈⣾⣿⣿⡿⠛⠉⠀⠈⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⣿⣿⣿⣿⠁⣿⣿⣿⣿⡰⠿⢿⠇⠀⢀⣘⣇⡀⠀⠉⣉⠵⢬⣀⡻⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣀⠀⠀⠀⠀⠀⢀⣼⠿⠋⣿⣷⢠⠀⠀⠀⠙⣿⣿⡟⢿⣿⠃⠀⠀⠀⢀⣾⣿⣿⠁⠀⠈⢿⣿⡟⣠⣿⣿⡿⠛⠃⠀⠀⠘⣿⣿⣿⣿⣿⡆⢀⣠⡀⠀⠘⠛⡶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡟⣾⣿⣿⣿⣁⣀⢰⣶⡆⠀⠀⣴⣴⣿⣿⢸⣿⣦⡀⠀⠈⠻⣿⣾⠋⠀⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⢸⣿⢳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⠀⠙⠿⠷⢄⡀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣿⣿⣿⣿⠿⠟⠀⠀⢰⣶⣾⣿⣿⣿⣿⢸⣿⣿⣿⣦⣄⠀⠀⠙⠧⢀⣴⣿⣿⣿⡿⠿⠋⠀⠀⠀⢸⡏⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⣷⣶⣤⣄⡇⠀⠠⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢹⣿⣿⣿⠃⠀⢸⣿⣦⠈⠋⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⣦⣄⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⣴⣾⣿⢠⣿⣿⣿⣿⠁⠀⠀⢀⢀⠀⠀⢰⣶⣿⣿⡇⣿⣿⣿⣿⣿⣶⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣸⣿⣿⣿⣶⣶⠈⠉⢀⣄⣰⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⢸⣿⣿⣿⣿⣶⣶⠀⠀⠀⣀⣀⡼⠿⠿⠿⡇⢿⣿⣿⣿⣿⣿⡏⣻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⣾⣿⣿⠏⠉⠡⣀⡀⠘⠿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠿⣿⣿⣿⣧⢁
⠀⠀⠄⠊⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣀⡀⠠⠟⠇⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢠⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣟⠛
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢠⣿⣿⡿⠻⠟⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⡿⠇⠀⠀⡀⠀⣀⢀⣠⣶⣦⣠⣤⢄⣴⣾⣿⣿⣿⣿⣷
⠄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡇⠀⢠⣶⣆⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣾⣿⣯⣿⣿⣿⣿⣗⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⡶⠛⠛⠛⢢⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⣸⣿⣿⣿⣿⣿⣶⣀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣶⠶⣾⣮⠻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⣿⣿⣿⣿⣿⡿⠛⠙⣀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠉⠛⠛⢛
⠀⠀⠀⠀⢸⠟⠛⠟⠛⡿⠛⠛⠻⡗⠀⠻⠿⠇⠚⢶⠖⠂⠘⢿⠿⠟⠿⣿⣿⠿⢿⡿⠛⠛⠀⢹⣿⠛⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⢿⣿⣧⣤⡀⠻⠇⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⣀⣠⠀⠀⢰⡆⠀⠀⠀⢠⠀⠈⠀⠀⣶⣿⣿⠀⢸⠀⠐⢤⣤⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⣿⣿⣿⠇⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⢻⡁⠀⢸⡇⠀⠀⠀⢸⠛⢛⠀⠀⣤⣿⣿⠀⢈⠷⠤⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⣿⣿⠇⢰⣤⣤⣤⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣄⠀⠀⢀⣆⠀⠀⠀⣸⠀⠀⢸⡇⠀⣰⡀⠈⢀⣸⡀⠀⠉⣿⣿⠀⢘⣄⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣇⣀⣸⠀⠀⠀⠀⠛⠻⢦⣈⠛⠛⠛⠀⠀⠈⠻⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀⠀
⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣑⣟⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣶⣶⣶⠦⠀⠀⠀⣀⣼⣾⣶⣾⣿⣿⣿⣿⣷⣤⣀⣤
⠀⠀⠀⠀⠀⠊⢿⣆⡀⣺⡿⠀⠀⢶⣿⡞⠒⠏⠀⠀⠈⠓⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠈⢀⠀⠀⠀⠈⡄⠖⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣀⣶⠎⠋⠉⢀⣴⣾⣷⣷⣄⠀⠀⢀⣄⡠⢴⠶⠀⠀⠀⠀⠀⠀
⣶⡖⡠⠀⠠⢆⠘⢚⡛⠛⠅⠴⠆⢀⣸⣿⣿⣲⠞⠁⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡖⢛⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠄⠀⠤⣼⣿⣿⣿⡿⠛⠛⠻⠋⢀⣄⣗⠀⠀⠀⠀⠀⢀⠀
⠀⣉⠁⠀⣡⡄⠀⢻⢿⠀⠠⠰⠿⠛⠿⠻⢿⠟⠓⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠴⠛⠁⢀⡉⠉⠀⢴⣶⣃⣀⣤⣴⢈⣯⣿⣿⠉⠀⠀⠈⠙⠉⠙⣷⣿⣿⣿⣸⣿⠁⠀⠀⠀⠀⢀⣾⣿⣿⣤⣀⡀⠀⠀⡎⠀
⡶⠟⣿⢿⣿⡛⠀⣼⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⢀⣠⣶⡴⠊⠁⣿⢟⣿⢻⣿⠛⠿⣶⣴⣷⣤⢀⣠⣼⣿⢿⣿⣿⣿⣿⣶⣶⡀⠀⢠⣾⣿⣿⠟⣿⣿⡿⠂⠀⠀⠀
⣟⣶⣾⠈⠉⠙⢶⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠄⢀⡀⠀⠀⢀⠐⠛⢶⣅⡰⠶⣾⣿⠋⣶⣀⣴⠃⠈⠋⠈⠛⠱⠀⠘⠹⣿⡀⠁⠛⠋⠁⣸⠋⠙⣿⡏⠉⠙⠛⠆⢿⣿⠿⠋⠀⣀⣹⣇⣀⣴⠁⠀
⣿⣉⠁⠀⠴⠛⠻⠛⠟⠐⣤⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⡀⠀⡀⠀⣁⠀⠸⠟⠶⠻⠈⠛⢁⣤⠄⢀⡀⠈⠉⢻⡇⠀⢀⢀⣶⠴⠀⠀⠀⣫⣿⠁⠀⠒⣀⠀⠀⠀⢻⣏⢀⡀⠰⢰⣼⣿⡖⠀⢃⡿⢿⣿⣿⣯⣀⣠
⠉⠉⠀⠀⣀⢀⣰⡏⠀⠘⠉⠀⠀⠀⠀⠀⠀⠢⠀⠒⣾⡙⠷⠾⢮⡁⡹⠟⠃⠴⠶⠗⣶⠴⠘⠋⠀⠈⠀⢸⡆⠀⡀⠉⠙⠻⠿⠂⠀⠀⠀⠀⠀⡾⠆⠈⠁⣿⠀⣠⣦⣿⠟⠃⢠⣾⣿⣴⣆⠀⠀⠁⠀⠀⠈⠙⣻⠛
⠀⠀⠉⠁⠋⠉⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠇⠀⠉⢡⣤⠀⠰⠀⡟⠁⢀⠀⡀⠂⠀⠘⢧⣧⣈⣤⣤⣤⣤⣤⣤⣠⣀⣾⠀⠀⠈⠁⢠⣾⠟⢈⠟⠉⠉⣑⠄⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠐⠂⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠘⠇⣀⣠⣤⣦⣠⣼⣿⡄⠐⣮⣰⠀⢹⣿⡧⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣧⣬⣤⣶⣽⡀⢠⡿⣿⠀⠀⠀⢀⠀⠋⠀⢬⣇⠀⠀⣼⣳⣴⠀
⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠛⣿⣿⠿⠿⠉⠉⢱⣤⣯⡏⡀⠀⠉⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠦⠀⠙⠍⢀⢢⠦⠛⠒⣶⣾⠛⠂⠀⠈⢹⣷⢾⣿⣦⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⠟⠉⢻⠶⠶⠲⠄⠀⣻⡹⠤⠟⠷⠶⣶⣾⣿⣿⣿⣿⣟⠛⢿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣦⠀⢠⣤⠀⠀⡛⢀⣄⡀⠀⠈⠁⠐⠒⠀⠙⠉⡿⣀⠘⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠛⠿⠶⠂⣤⡦⢠⣙⠛⠀⢀⠀⠠⠄⢰⣿⣿⣿⣋⣤⣄⡀⠀⣠⣿⣿⣿⣿⠀⠀⠀⠘⠻⣿⣿⣇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠉⢛⣇⣀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠗⠀⠀⠼⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣷⣶⣌⣿⣿⠀⠀⠀⣤⡄⠘⠷⢯⣄⣼⣧⣿⠟⠀⣀⣠⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣀⣤⣀⣤⣤⣤⡄⠀⠀⠀⠀⡥⢶⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠉⠀⠈⠙⣿⣿⣮⣽⣿⣿⣿⡇⠤⠀⢀⣐⣶⡄⢠⣼⣿⣿⣧⠘⠉⠁⠈⢻⠼⠿⠉⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠻⠯⠴⠿⢿⣟⡃⠀⠀⠀⡤⠀⠛⠛⠶⠀⠀⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣿⡋⠁⠸⠟⠙⠛⠋⢙⡿⠁⠀⠐⠂⠁⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠚⠂⠀⠈⠉⠀⠀⠀⠀⠼⠆⠀⠠⢴⢇⣼⣿⣿⣿⣿⣿⣿⣠⣿⣿⠿⠛⠛⠛⠿⢿⣿⣿⣮⣿⣿⣿⣿⣿⣧⠀⠀⢩⣿⠃⢠⠀⠀⠀⠀⠀⠀⠙⢱⣶⣦⡁⡀⠀⠠⣈
⠠⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⠀⢀⡠⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣧⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⣿⣿⣿⣿⡖⠀⠐⠀⠀⠀⠁⠚⠰⣇⠀⠴⡿⠂⠀⠀⠀⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠉⣸⡷⠃⠈⠀⠂⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣇⣠⡤⣲⣦⡀⠀⠀⣷⠲⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠽⠄⠀⠀⡾⢿⣆⢃⠄⠀⠀⠀⢉⡀⠠⣶⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠁⠈⠉⠉⠁⢀⣠⠬⠋⠀⢠⠀⠠⢴⡆⠀⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡀⠀⠀⡀⠀⡀⠀⠙⠀⠀⠠⠤⣄⠈⠡⠀⠙⠁⠀
⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠐⠿⠒⠶⠶⠀⠀⡀⠴⠿⠋⠀⠘⠷⣶⣤⠤⠈⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠋⠀⠀⠀⢀⡈⠡⠤⢤⠈⠁⢺⣀⠀⡄⠈⣽⣄⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠒⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣏⣴⠀⠠⠀⠀⠈⠁⠀⠾⠙⠂⠦⡾⠁⠀⣽⠀⠏⠸⣦⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠉⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⠀⠀⠉⠉⠙⠙⢹⣿⣿⣿⡐⠃⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠄⠰⠄⠹⣇⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣧⣤⣠⣤⣤⡀⠀⠒⣤⡤⣤⣤⡀⠀⢂⣷⣄⠀⣠⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⢀⠠⡀⠲⣦⣴⣿⣿⡿⠉⠹⣿⣷⡟⢛⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⢹⣿⣿⡿⠥⢤⣶⣶⡀⠀⠈⢳⠀⠀⠀⠛⠓⣜⠛⠀⣶⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠾⢷⣾⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣤⣶⠛⠛⢿⣿⣿⡇⣸⣿⣿⡿⢿⠉⠉⠉⢧⣤⣿⣿⣶⣦⠀⠀⠉⠁⠉⠳⠧⣤⢼
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢧⣿⣿⣶⡄⠀⠀⢀⡀⠀⠾⠛⡁⣸⣿⡄⣇⣀⠀⠀⠘⢿⣿⣈⣿⡿⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⣿⡿⣼⣿⠋⠙⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡍⠰⢿⣿⣧⢀⠀⠠⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢸⣿⣿⣿⣷⣶⡞⠛⠛⣀⣀⣼⣿⣿⣿⡇⣿⣿⣷⣄⠀⠀⠙⢿⣿⠀⠀⢠⣴⣿⣿⣿⣿⡇⠀⠀⠀⣿⢧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣇⢠⣤⣀⡀⠈⠏⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣾⣿⣿⡿⠛⠋⣄⣄⠰⠿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣷⣦⣀⠀⠉⠓⢴⡿⠿⠿⠛⠋⠁⠀⠀⢀⣤⡟⢸⣿⣿⣿⡗⠀⠀⠀⡀⠀⠀⠀⣀⣸⣿⣿⢸⣿⣿⣿⣿⣧⣀⣬⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⣿⣿⣿⡇⣀⡀⠿⠿⠁⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠇⣿⣿⣿⣿⣇⣀⡀⠀⠚⠀⠀⢀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢡⣿⣿⣿⠿⠿⠁⠀⠀⣰⣾⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⢠⣿⣿⣿⣿⡟⠛⠃⠀⠀⢸⣿⣿⡿⠿⠟⠿⠘⣿⣿⣿⣿⣿⣿⣦⣛
⠀⢀⣀⠐⠦⠀⠀⢠⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠀⠀⣦⣴⠀⠈⢨⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠁⠀⠀⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣧⣤⡀⠁⠉⠀⢀⣸⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣇⠀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠉⠉⢀⣀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿⠀⠁⠀⠀⡀⠀⣀⢀⣠⣶⣦⣠⣠⣄⣴⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣀⣀⣾⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⣼⣿⣿⣿⣿⣇⣀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣝⢐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⠃⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠃⣰⣿⣿⣿⣿⣿⣿⣻⡀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣶⢶⣾⣮⠻⢿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⠋⣀⣀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁⠀⣰⣦⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⠀⠀⠀⠸⠻⠛⠛⠟⠛⡿⠛⠛⠻⡇⠈⠛⠛⠀⠛⠻⠟⠃⠘⢿⠛⠿⠿⣿⣿⠿⢿⡿⠛⠛⠀⢻⣿⠿⠟⠿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⢿⠿⠿⠿⢿⣿⣿⣷⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⣠⡀⠀⢰⡆⠀⠀⠀⢰⠀⠸⠀⠀⣶⣿⣿⠀⠸⠀⠐⢤⣄⠈⠏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⠰⠀⠀⣿⣿⢁⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢹⠄⠀⢹⡇⠀⠀⠀⢸⠛⢻⠀⠀⣤⣿⣿⠀⠘⠷⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⣿⣅⠈⠻⠿⠿⠃⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⣀⡏⢀⣠⣄⠀⠀⢀⣆⠀⠀⠀⠸⠀⠀⣸⡇⠀⣰⡀⠈⢀⣸⡀⠀⠉⣿⣿⠀⢐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⢸⠀⠀⠀⢀⣤⣬⣭⣂⣀⣀⣀⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣷⣤⣀⣤
⢀⠀⠀⠀⠀⠀⡿⢄⢀⣽⠃⠀⡀⠙⣿⣥⣵⢀⣠⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢶⣿⠁⠀⠀⢰⣿⣿⣿⣷⣦⣀⣤⡴⠖⠲⢻⠉⢀⠀⠀⠀⠀⠀
⢿⡭⠒⠐⠐⠟⠈⣠⣍⠉⠁⢛⣃⣤⣿⣿⣿⣾⠁⠰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣻⠃⠸⠿⣷⠇⣀⣄⠄⠀⠀⠀⢀⠀⣠⣄⣀⠀⠀⠺⣿⡿⣟⡀⣀⣲⣿⢿⣿⡿⠋⠉⠉⠉⠀⣠⣦⣧⠀⠀⠀⠀⠀⡄⠀
⢠⣤⣦⣤⣴⡄⠀⠙⠛⠀⠃⠚⠋⠉⢩⠙⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠉⠀⠠⠄⠈⡈⢻⣿⣷⣴⣶⣏⣤⣿⣿⣿⠀⢀⡀⠀⠀⠀⢨⣿⣿⣿⣿⣾⣏⠀⠀⠀⠀⠀⣸⣿⣿⢻⣶⣤⣄⡀⠀⠃⠀
⡟⠙⠛⣷⢿⣅⠠⣷⣄⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣲⣞⠁⠀⣤⣴⣿⡍⠀⠀⡿⢻⣿⣽⣏⡍⠙⣿⣿⡿⠞⢠⣴⣿⠟⢻⡿⣿⣿⣿⣿⣧⣤⠀⣼⣿⣿⠟⠑⠻⣿⠛⠁⢀⠄⠀
⣭⣿⡏⠀⠀⣈⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠓⠂⠠⠀⠀⢠⡄⢈⡉⣿⣿⡏⠙⠿⠟⠀⠿⣤⣾⠀⠀⠀⠀⠁⠲⠄⠀⠸⣿⣄⠈⠙⢀⠀⡞⠀⠙⣿⡇⠀⠈⠙⠁⢻⣟⡍⢁⡀⣠⣼⣷⣤⡿⠀⢠
⣿⣤⠀⠐⠛⠉⢛⡍⠁⢸⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣴⣤⢀⣤⣄⠘⠋⢉⡁⠀⢉⣱⡿⠂⡰⠀⢀⡀⠼⠃⣤⣤⣴⡿⠋⠀⠀⠠⠿⠿⣆⠉⢋⠄⣀⠀⠀⠻⣧⣴⡀⠀⢼⡾⠿⠃⠀⠰⡟⠛⠿⢿⣷⣤⣶
⠀⠠⣀⠠⣤⣠⡾⠃⠀⠉⠀⠀⠀⠀⠀⠘⠀⠓⠊⠈⠟⢙⣻⡛⢳⢤⡝⠉⠐⠛⢋⣩⡏⠒⠈⠁⠀⠀⣤⢶⠇⡠⠄⠀⠈⠙⠉⠁⠀⠀⣄⠀⠀⣛⠀⠀⢠⡿⢢⣿⣷⣿⣅⠀⠰⠿⠿⠿⠇⠀⠀⠁⠀⠀⠀⠀⡿⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠛⠃⠀⠀⢸⡆⠀⢉⡸⠃⠀⣤⣤⠀⠁⠀⢹⣿⣦⣶⣶⣶⣶⣶⣶⣶⣦⣼⣧⠀⠀⢀⣀⠰⢿⣇⣼⠋⠀⣠⣼⠀⠀⠀⠀⠀⡀⠀⣾⡏⠀⠀⣩⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣼⣠⣤⣼⣿⣷⣾⣿⠿⡀⠘⣷⡆⠀⠻⢿⠇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠶⡿⠿⣯⡄⠸⠛⢟⣀⡀⠀⣦⣄⠁⠀⡿⢧⡀⢀⣿⢻⡟⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣩⣿⣿⡛⠋⣀⠠⢼⣾⣿⠁⣄⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠛⠀⠊⠀⣠⠸⠉⠉⠩⠿⠿⠉⠁⣀⣀⢼⡿⠻⢿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⢈⣿⣏⣀⠏⠉⠋⠋⣠⡀⠿⠜⠛⠋⠻⣿⣿⣿⣿⠿⠿⠯⠙⢿⣿⣿⣿⡿⠟⠛⢛⣻⣿⣿⣷⡤⠤⠶⠇⠀⢠⡃⠨⠦⠄⠀⠀⠀⠉⢉⡀⠀⠀⢧⣖⡈⠹⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠖⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⢶⠇⢰⡎⠁⠀⣤⠀⠐⢰⣿⣿⣯⣤⣶⣤⡄⣀⣾⣿⣿⣿⣧⠀⠀⣀⠈⠙⢿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣤⡄⣀⣀⠀⠀⠀⢈⣽⣷⣦⣎⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠅⢀⡀⠛⠀⢐⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠿⠿⠿⢿⣷⣿⡟⠿⣷⣦⣿⣿⡄⠀⠀⠀⠶⠀⠉⠛⠳⢶⣿⣶⡟⣁⡠⠤⠶⣿⣿⣿⢿⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣴⡶⠴⣶⣶⣶⡆⠀⠀⠀⠀⠞⣿⣟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⡀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⡇⠘⠋⠀⠠⣽⣿⠂⢰⣿⣿⣿⣷⣀⣤⡀⠀⠘⢛⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠛⢒⠛⠛⣿⣥⠀⠀⠀⠀⣆⠀⠈⠁⢋⣠⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣶⣶⣟⢻⣿⣿⣿⣿⣿⣧⠀⠀⢀⣾⣿⠁⠀⠸⠃⠈⠉⠁⠸⣯⡀⠀⢈⡍⠙⠃⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠛⠂⠈⠒⢹⣿⣿⣿⣿⣿⣿⡏⣼⣿⠟⠉⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⠲⠿⠀⢠⠀⣀⣀⡀⠀⠀⣀⡸⠿⠷⢄⣦⠉⠐⣤
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⠥⡀⢠⠆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⣿⣿⣿⣿⣿⣿⡟⠉⠀⠈⣉⠁⠀⠀⠁⡞⠇⠀⠛⠋⠀⠀⠀⠀⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠿⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡤⣶⠃⡿⠶⠀⠀⣠⣿⠁⡀⠀⠀⠐⠸⡿⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡤⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠱⠀⠀⠛⠂⠀⠀⠏⠿⣇⠸⠁⠀⠀⠀⢠⡄⠚⣿⡷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⠀⠈⢀⠀⠀⠀⠀⣠⡖⠚⢁⡀⠐⠐⠒⢺⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⠄⢀⠀⢀⡈⣀⠀⠐⢒⣦⣀⠐⠀⠀⠀⠀
⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠀⣠⡄⠙⠋⠁⠀⠘⠻⠿⠲⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣉⠉⣻⣿⣿⣿⣿⣿⣿⡏⣀⠉⠀⠀⠀⠀⠰⠀⠀⣠⣤⠀⠀⣹⠄⠐⣇⠀⡿⢦⠀⠂⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡿⢿⣿⣿⣿⠷⢳⡟⠙⠂⠀⠀⠀⠀⠘⠋⠈⠘⠛⠃⠀⠀⠛⠘⠃⠸⣧⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣾⣯⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡟⠁⠂⠙⠀⠙⠤⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⢶⣦⣶⣶⣶⡄⠀⣉⡟⠓⠒⢶⡀⠀⠴⠛⣦⡄⢆⣀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠺⠶⢰⡶⢤⡽⣿⣿⠿⠿⠁⠀⠿⠿⠿⠙⣿⣿⣿⣿⡿⠛⠋⢻⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢨⣿⣿⣿⣛⣳⣾⣿⣿⠀⢀⡀⢿⠀⠀⠈⠉⣩⠦⣄⣘⡟⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣙⣿⣿⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⡇⠀⠀⠀⠀⢻⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⣠⣴⣾⠋⠈⠙⣿⣿⡿⣀⣿⣿⡿⠛⠃⠀⠈⠙⣶⣾⣿⣿⣿⡆⣤⣠⣤⡀⠀⠙⢓⡖⠛
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⣾⣿⣿⣷⠀⠀⣠⣤⡀⠘⠋⣁⣠⣿⣷⢸⣤⣄⠀⠀⠙⢿⣦⣹⠟⠀⠀⠀⢀⣼⣿⣿⣇⠀⠀⠀⢸⣿⢳⣿⡏⠈⠁⠀⠀⠉⠀⠀⠀⠹⣿⣿⣧⠀⠈⠻⠿⠧⣤⡀⠘⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣿⣿⣿⣿⣾⡟⠈⠉⣥⣤⣴⣿⣿⣿⣿⢸⣿⣿⣶⣄⠀⠀⠙⢿⡄⠀⢠⣾⣿⣿⣿⣿⠟⠀⠀⠀⢸⡿⣾⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣶⣦⣄⣀⣽⠇⠀⠴⠐
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢸⣿⣿⣿⠉⠉⢡⣤⡄⠛⠿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣷⣤⣄⠀⠈⠸⠟⠛⠛⠉⠉⠀⠀⠀⣀⣴⣿⢁⣿⣿⣿⣿⠁⠀⠀⣠⡀⠀⠀⢠⣤⣿⣿⡇⣿⣿⣿⣿⣿⣧⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢸⣿⣿⣿⣤⣄⠘⠿⠃⠀⢠⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢸⣿⣿⣿⣿⣦⣤⠀⠉⠁⢀⣀⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣏⢉⣿
⠀⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⣾⣿⣿⡟⠿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⠉⠉⠀⢀⠀⠻⠿⣿⣿⡿⠟⠇⢹⣿⣿⣿⣿⣿⣿⣾⣶
⠀⠀⠒⠈⠓⠀⠀⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡀⠀⠸⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣟⠛⠛
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⡶⠀⠀⠀⣤⣠⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣀⠀
⠄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⣠⣀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⣀⣀⣠⣶⣦⣠⣠⣄⣴⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣧⣤⠨⠿⠿⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⢠⣿⣿⣿⣿⣿⣇⣤⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠒⣼⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠏⢀⣾⣿⣿⣿⣿⣿⠳⠾⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣖⢶⣾⣮⠻⢿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⡏⢠⣤⣀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣀⠀⠿⢧⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⠀⠀⢀⠟⠻⠛⠛⠟⠛⡿⠛⠛⠻⡄⠘⠛⠓⠈⠛⠛⠛⠀⠛⢿⠿⠿⠿⣿⣿⠿⢿⡿⠛⠓⠈⢿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⣠⠀⠀⢠⡆⠀⠀⠀⢰⠀⢸⠀⠀⣶⣿⣿⠀⢸⠀⠐⢤⣄⠘⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⠀⠀⠀⣿⠟⢠⣄⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⢰⣿⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢹⠀⠀⣻⡇⠀⠀⠀⢸⠛⠻⠀⠀⣤⣿⣿⠀⠘⠷⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠿⣤⡈⠛⠟⠛⠀⠊⠻⣿⣿⣿⣯⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀
⢁⣿⡋⠀⣠⣄⠀⠀⢀⣆⠀⠀⠀⣈⠀⠀⣻⡇⠀⣰⣀⠈⢀⣸⡀⠀⠉⣿⣿⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⣇⠀⢸⠀⠀⠀⢀⣷⣶⣾⣤⣤⣤⣤⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠏⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠿⠻⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣷⣤⣀⣤
⡴⢤⢀⠀⠀⠀⠃⠰⠾⠿⠤⣤⠀⢈⣿⣿⢗⡄⠒⢡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠖⣳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡼⠛⠀⠄⡀⣿⣿⣿⣿⠿⠗⠺⠟⠁⣀⣂⡀⠀⠀⠀⠀⠀⠀⠀
⠉⠓⠀⠀⡀⠀⠐⢻⡆⠠⠀⡾⠟⠿⠿⣿⡿⠻⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠰⠃⠀⠉⠉⠃⢠⣴⣄⠀⣠⣀⠆⢐⣶⣿⡗⠂⠀⠀⠙⠛⠉⢳⣄⣴⣾⣏⣹⡟⠁⠀⠀⠀⠀⢰⣿⣿⣇⣀⠀⠂⠀⢀⠃⠀
⡾⠌⢻⣶⡿⠂⢠⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠉⠀⣠⣤⠝⠁⢸⣿⢿⡟⣿⡿⠿⣧⣤⣶⣦⣄⢀⣀⣾⣿⣿⣿⣿⣿⣧⣤⡄⠀⠀⣴⣿⣿⡿⢛⣿⡷⠶⠀⠀⠀⠀
⠦⣤⠞⠉⠙⠢⣼⡿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣦⡀⠀⠀⠀⠀⠀⠀⠺⠲⣶⡆⠄⢴⣿⡟⢱⡄⢀⡜⠀⠛⠋⠹⠃⠄⠀⠋⣿⠇⠀⠹⠟⠋⠁⡿⠉⠿⣿⠋⠛⠻⠷⢸⡿⡿⡿⠀⠀⢈⣷⡀⢀⡎⠀⠀
⡚⠛⠀⢠⠴⠾⠿⠿⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠾⠠⠶⠂⠛⠓⠀⣤⡀⣀⠈⠉⠛⣦⠀⠀⠀⣠⣤⠄⠀⠀⢉⣾⡇⠀⠠⠆⡘⠁⠀⠘⣿⠃⣀⠀⠀⣄⣷⣶⠅⠐⢸⣿⣿⣿⣿⡅⢀⣲
⠙⠁⠀⠀⠀⠀⡴⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⣀⠀⢠⡚⠿⡶⣮⡛⠘⠷⠖⢠⣤⡾⢤⡄⡂⠿⠂⠀⠁⠀⣱⠀⠀⠀⠛⠹⠿⠷⠀⠀⠀⠈⠉⠡⡶⠀⠋⢱⣆⠀⣤⣭⣿⠛⠀⣠⣿⣤⣤⡀⠀⠘⠀⠈⠁⠘⠻⡿⠟
⠀⠉⠒⠘⠋⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⠀⠉⠉⢀⡀⠠⠄⢴⠟⠀⠀⠀⠀⠀⠈⣶⡏⣀⣤⣤⣤⣤⣄⣀⣀⠀⣸⠆⠀⠐⠂⠀⣀⠿⠇⠸⠟⠉⠉⡇⠀⠈⠁⠁⠁⠀⠀⣤⡆⠀⠀⠦⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⣀⣠⣀⣠⣽⣆⠀⢰⣅⡄⠀⣿⣷⡄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡤⣼⣆⣭⣤⣴⡇⠀⣰⣿⡇⠀⠀⠀⠀⠀⠂⠀⣽⡀⠀⢠⡖⣤⡄⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠴⣶⡟⢻⡿⣿⣿⡟⠉⠋⣄⣸⣿⢀⠀⠉⠉⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠭⠍⠉⢛⠃⠀⡤⠔⠒⢒⣴⡿⠦⠀⠀⠉⣿⣶⣾⣧⣽⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣾⠟⠻⡷⠤⠤⠆⠉⠹⡏⣭⣼⠷⢦⣴⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣦⠀⠀⠀⣠⡄⠀⠰⠃⢡⠀⠀⠈⠉⠁⠶⠂⠘⠃⠹⢃⠈⠻⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠦⠀⡀⠀⠀⠠⠂⠉⠀⠀⠀⠀⠸⠿⡶⠄⢀⣠⡀⣀⠻⠎⠉⠀⠀⢀⣼⣿⣿⠟⣁⣀⠉⠁⣠⣿⣿⣿⣿⠀⠀⠀⠒⠻⣿⣿⣧⠈⠉⠈⠀⠀⠚⠂⠉⠉⠀⠀⠀⠀⠀⠊⠀⠀⠀⠛⢷⣀⣈⠭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⢽⠅⠀⠀⡇⠀⢸⣿⣿⣿⣿⣟⣫⣭⣶⣿⣿⣿⣿⣿⣧⣤⣴⣦⣤⣌⣻⣿⡆⠀⠀⠀⢀⣀⠀⠲⣶⡒⢉⣿⣰⡶⠂⠀⢀⣠⣤⣽⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⡀⢀⣀⣀⣤⡀⠀⠀⠀⢀⡤⢶⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠉⠀⠈⠙⣿⣷⣬⣭⣿⣿⣿⡇⠀⢤⡄⠈⢉⣤⣤⠀⣬⣯⣿⣿⡄⠛⠉⠉⠙⣏⠿⠏⠉⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣻⡷⣩⣽⢿⡿⢛⠀⠀⠀⢀⡈⠐⠻⠇⣄⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⣶⣦⣤⣤⣿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣭⣿⠃⠀⣿⠛⠻⠟⠙⠻⠷⠀⠀⠤⠰⢠⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠦⠀⠀⠛⠋⠤⠀⠄⠈⣦⠀⠤⠠⣼⣿⣿⣿⣿⣿⣿⠃⣿⣿⡿⠛⠛⠻⠿⠿⣿⣿⣎⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⣛⡿⠀⡀⠀⠀⠀⡀⠀⠙⠓⣦⣴⣚⢀⡀⠄⢈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠁⠀⠀⠁⠀⣠⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣼⣿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣷⢼⣿⣿⣿⣿⣿⣷⠶⠆⠀⠠⠅⠀⠁⠐⢒⣶⡀⠠⣼⠖⠉⠉⠉⠸⠃⠀⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⢳⡯⠝⠂⠉⠠⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣿⣿⣿⣿⣿⠀⢀⣄⢴⣦⣀⠀⠀⢰⡴⠄⠀⠀⠀⢀⣠⣤⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⠇⠘⣏⠁⠀⢲⢿⣷⠐⡠⠀⠀⠀⠈⠁⠀⣤⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠓⠀⠚⠉⠉⠀⣀⣀⠾⠀⠀⣀⣀⣠⣤⡈⠛⠋⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⢀⠀⠀⠀⠀⠈⠀⠙⠇⠁⠀⢤⣀⡀⠙⠀⠘⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠾⠥⢤⣆⠀⠀⠠⢴⠿⠂⠀⢶⣶⣤⣄⡀⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠃⠀⠀⠀⠀⡀⠉⠤⠠⠄⠓⠒⣇⠀⢔⠚⢻⣦⡄⢂⠀⣀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⠄⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣧⣠⣋⡶⠄⠀⠀⠀⠉⠀⠴⠏⠧⠤⣴⠋⠀⢸⡇⠾⠉⣤⡀⠀⠈⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠃⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠏⠉⠈⠉⠉⠋⠁⣾⢿⣿⣧⠀⠸⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⠤⡄⠘⣟⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣶⣶⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣧⣄⣀⣠⣠⡀⠀⠐⢢⣤⣄⣀⣀⠀⠐⣺⣤⡀⣀⡀⠀⠀⠙⠋⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠄⠄⣤⡀⢀⣀⠠⢦⣤⣿⣿⡿⠋⢻⣿⣷⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⣿⣿⣿⠿⠿⣄⣤⣾⡆⠀⠈⠑⣆⠀⠉⠰⠟⢦⡓⠂⣤⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡿⣭⣿⣿⣿⡏⠉⠁⠀⠀⠉⠉⠁⣼⣿⣿⣿⠋⠁⠀⠀⢻⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⢀⣤⣶⠚⠻⣿⣿⣿⠇⣿⣿⣿⡿⡿⠉⠉⠳⣤⣴⣶⣶⣷⡄⠀⠀⠈⠉⠉⠳⠿⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣇⣿⣿⣥⡀⠀⠀⠀⠀⠀⣼⠿⠋⢸⣿⡐⣄⡀⠀⠀⠹⣿⣯⠹⣿⡃⠀⠀⠀⢀⣴⣿⣿⠇⠀⠀⠘⣿⡏⣼⣿⠛⠛⠀⠀⠀⠀⠀⠉⠹⣿⣿⣯⠁⠘⠿⣿⣷⠀⠀⠀⠾⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢸⣿⣿⣿⣇⣄⡜⠿⠿⠀⠀⣰⣷⣿⣿⡇⣿⣿⣦⡀⠀⠈⠻⣷⡆⠀⠀⢀⣴⣿⣿⣿⣿⠆⠀⠀⠀⣿⢷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡆⣦⣄⣀⠈⠘⢿⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣸⣿⣿⣿⠿⠟⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣶⣄⡀⠈⠙⠂⣴⣿⡿⠿⠟⠋⠁⠀⠀⣀⣴⡟⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⡇⣿⣿⣿⣿⣿⣿⣀⣠⣁⠀
⠀⠀⠀⠀⠒⠀⠀⠀⣸⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃⣿⣿⣿⣿⣧⣀⡀⠘⠛⠀⠀⢸⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡿⠻⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⠃⠀⠀⣰⣶⣾⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⢰⣿⣿⣿⣿⡟⠛⠁⠀⠀⢰⣾⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣧⣺⡡
⠀⢀⣀⠰⣄⠀⠀⣾⣿⣿⣿⣿⣿⢠⣿⣿⡿⠀⠀⢠⣤⠀⠙⠛⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⠀⠀⠀⣻⡄⠀⠀⢹⣿⣿⠿⠛⠸⣿⣿⣿⣿⣿⣿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢸⣿⣿⣇⣠⡀⠘⠛⠁⠀⢰⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠟⠛⠃⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⣿⣿⣿⡏⢰⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣇⣀⠸
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡀⠀⢰⣿⡦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⡀⠀⣀⣀⣠⣴⣤⣠⣠⣄⣴⣶⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡏⠀⠉⠉⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⠃⢰⣿⣿⣿⣿⣿⣿⣼⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡟⢁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⣰⣀⠀⣠⣼⣿⣿⣿⣿⣿⡯⣶⢶⣾⣮⠛⢿⣿⣿⣿⣿
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣇⠻⠿⣿⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⠀⠀⣾⠛⠻⠛⠛⠟⠛⡿⠛⠛⠛⡄⠘⠛⠛⠗⠒⢶⠞⠛⠛⢿⠿⠿⠿⣿⣿⠿⢿⡿⠛⠓⠀⢻⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⡰⠿⣿⠿⢿⠿⠿⠿⢿⣿⢁⣀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⢰⣿⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⣠⠀⠀⢴⡆⠀⠀⠀⢰⠀⢘⠀⠀⣶⣿⣿⠀⢸⠀⠐⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠸⠀⠀⠀⠀⣇⠈⠻⠿⠿⠃⠬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⣾⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢙⠀⠀⢸⡇⠀⠀⠀⢸⠛⢻⠀⠀⣤⣿⣿⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⣬⣭⣄⣀⣀⣤⠄⠀⠻⣿⣿⣻⣭⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⢠⣿⡏⠀⣠⣄⠀⠀⢀⣆⡀⠀⠀⠀⠀⠀⣿⡇⠀⣰⡀⠈⢀⣸⡀⠀⠉⣿⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠇⠀⣇⠀⠘⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⢀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣷⣤⣠⣤
⣒⡢⠀⠀⢄⠈⢀⣀⠛⠓⠒⡆⣀⣴⣿⣿⣧⡏⠀⢼⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢘⡿⠉⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣴⣿⣿⡇⠀⠀⢶⡿⣿⣿⡿⠋⠙⠙⠋⠀⣤⣴⡀⠀⠀⠀⠀⢀⠀⠀
⣉⢡⠀⣠⣄⠀⠹⠿⠁⠠⠠⠛⠉⠛⠛⠻⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠊⠁⠀⠀⠈⠀⠰⣶⣖⣠⣤⣴⢁⣹⣿⣿⡏⠁⠀⠀⠈⠉⠉⣹⣶⣾⣿⣥⣿⠏⠀⠀⠀⠀⠀⣾⣿⣿⣧⣤⡀⠀⠀⠘⠀⠀
⠛⠘⢿⣿⣟⠀⣴⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠴⠄⠀⠀⣀⣴⣶⠋⠀⢹⠿⣿⡏⣿⠛⠛⠧⣶⣿⠦⠆⣀⣴⣿⠿⣿⢿⣿⣿⣷⣶⣄⡀⢀⣾⣿⣿⠟⠹⢿⡟⠃⠀⡠⠀⠀
⣲⣶⠀⠀⠈⢳⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⡄⠀⠀⣀⠀⠉⠹⣗⡔⠂⠾⡿⠃⢹⣇⣰⡆⠀⠉⠁⠘⠁⠄⠀⠀⡿⣂⡀⠙⠋⠁⢠⡏⠈⢛⣿⠉⠈⠙⠓⠸⡿⠟⠉⠀⢀⣠⣿⣄⣰⡇⠀⡤
⣍⡁⠀⠒⠛⠙⠋⠋⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠄⡀⢀⡀⡀⠛⠒⢛⠀⠉⠁⡐⠦⢄⡄⠀⠉⠩⠗⢀⣀⣀⣴⠖⠂⠀⠀⠨⣾⡇⠀⠑⣁⠄⠀⠀⠸⣿⣀⣄⠀⢀⣦⠿⠿⠂⠉⣼⠿⢿⡿⣿⣄⣤⣾
⠉⡀⠀⣄⣀⣠⠟⠀⠈⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠩⠉⠛⠓⠦⣄⣈⠛⠁⠴⠶⠛⣺⠀⠍⠋⠀⠀⠀⣠⣷⠀⠀⠀⠉⠛⠛⠂⠀⠀⢠⡀⠀⠼⠇⠀⠁⣸⡇⣰⣶⣾⣿⠉⠀⢴⣿⣶⣶⠀⠀⠈⠀⠀⠀⠈⢩⡟⠛
⠀⠀⠁⠌⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠀⠀⠀⣦⠀⠐⠂⡾⠉⠀⣀⡀⠀⠀⢘⣿⣥⣶⣶⣶⣶⣶⣶⣤⣤⣤⣿⠁⠀⠈⢁⠀⣦⠟⠀⡟⠉⢀⣸⡀⠀⠀⠀⠀⠀⠀⠠⣾⠂⠀⠈⣃⠀⠐⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⢃⣀⣠⣦⣷⣤⣴⣿⣆⠀⢻⣤⠂⠸⣿⣷⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠶⠷⠾⣧⣶⣿⣾⣇⠀⡿⢿⠃⠀⠀⢀⣀⠘⠁⢀⣷⡠⠀⣸⡟⣶⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡛⣻⣿⡿⠛⠃⢀⣈⣶⣼⡟⢀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠒⠂⠈⠭⢁⡀⡞⠈⠉⣱⣿⡟⠓⠀⣀⣀⣿⠾⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢲⣟⠋⠙⠛⠒⠚⠇⣀⢸⡷⠧⠞⠛⣶⣿⣿⣿⠿⠿⠍⠛⢿⣿⣿⣿⡿⠟⠋⢛⣿⣿⣿⣆⠀⢀⡠⢴⠁⠀⣘⠁⡤⢀⠀⠄⠀⠐⠛⣁⠈⠁⢸⣠⡀⠙⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠘⠃⠠⠄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠙⠻⠟⠂⢠⣶⠄⡼⠟⠂⢀⡀⠀⣴⣿⣿⣫⣤⣶⣤⣄⣠⣾⣿⣿⣿⣇⠀⢀⡀⣈⠙⢿⣿⡆⠀⠀⠀⠀⠀⠉⠀⡀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠈⠹⢯⣤⣔⣲⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠞⠀⢓⠂⠀⠘⠇⢠⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⠿⠿⠿⢿⣿⣿⠿⠿⣷⣾⣿⣿⠀⠀⠀⠀⣠⡦⠀⠻⠿⢤⣼⣿⣾⠟⣁⣀⣠⣶⣷⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢂⣀⣴⣄⣤⣤⣴⣶⠀⠀⠀⠀⢰⢞⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣅⣠⣀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠐⠶⠂⢀⣴⣶⡶⠀⣶⣿⣿⣿⣎⣁⡀⠀⠈⠶⠻⠀⠁⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠿⠴⠾⢻⣏⡍⠀⠀⠀⢤⠀⠈⠙⠰⢦⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣾⡿⠀⠈⡿⠉⠉⠉⠈⣽⡋⠀⠀⣛⠁⠒⠂⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠐⠓⠀⠈⠉⠁⠂⠐⠂⠸⠗⠀⠒⠖⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠉⠁⠈⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⢭⠁⠠⡄⠀⠀⠠⠀⠀⢌⠙⣿⣿⡥⣤⡄⠀⢤⣀
⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⣖⢂⠀⣠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠂⠀⠒⠒⠂⠀⠉⠹⠿⠀⠐⠾⠋⠀⠀⠀⠍⠁⠀⠈⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⢸⣗⠊⠀⠀⠐⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣠⡶⢿⣷⡄⠀⢀⣸⡞⠀⠀⠀⠀⠇⣶⡖⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⡌⠁⠘⠦⠀⠀⢹⠻⣿⡈⡖⠀⠀⠀⠀⣄⠴⢶⣶⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠃⠀⠉⠀⠀⢀⣤⠴⠛⡀⠀⠤⠤⠴⣶⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⠀⠀⠄⠀⠀⣄⠀⠠⢀⡈⢃⡀⠐⠒⢲⣄⠁⠂⠈⠉⠀⠀
⠀⠀⠀⢀⡈⠀⠀⠀⠄⠀⠀⠛⠛⠒⠺⠇⠀⣀⠐⠺⠛⠁⠀⠻⠿⣧⠦⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣍⣙⣿⣿⣿⣿⣿⣿⣿⠃⠀⡈⠀⠀⠀⠀⠀⣄⠀⢒⣒⡀⠉⢙⣧⠀⢯⠉⢹⣷⠄⠢⠠⢤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠑⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⡿⢿⣿⣿⣿⠧⠼⣴⠗⠂⠀⠀⠀⠀⠀⠛⠉⠃⠒⠾⠁⠀⠼⠏⠟⠐⢷⣄⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⣰⣶⣆⡀⠀⠀⣀⣀⣁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠙⠋⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣧⠀⠋⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠐⠒⠂⠘⠧⣠⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠈⠀⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣤⣶⣼⣄⠀⠈⠱⠶⠶⢶⡆⠀⢩⣽⢶⣄⢠⣄⠀⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠂⠂⢦⡄⣠⢤⣘⣦⣾⡿⠿⠏⠈⠹⢿⣿⠛⣹⣿⣿⣿⡿⠟⠋⠹⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠃⣿⣿⣿⣛⣓⣶⣾⡿⠆⢀⣀⣘⡇⠀⠀⠙⢉⡳⣉⡀⣿⠶⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⣛⣶⣟⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⣿⢀⠀⠀⠀⠻⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠙⢿⣿⡿⣀⣿⣿⡿⠟⠃⠀⠀⠸⣿⣿⣿⣿⣿⡆⢀⣀⣀⡀⠀⠙⠛⣶⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢻⣿⣿⣶⡆⠀⢀⣀⣀⠀⠟⢉⣀⣿⣿⠘⣦⣄⠀⠀⠙⢿⣷⣼⠟⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⢘⣿⣧⣿⡿⠀⠀⠀⠀⠈⠉⠀⠀⠸⠿⣿⣷⠀⠉⠛⠿⠽⣀⣀⡀⠓⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣼⣿⣿⣿⣷⣶⠊⠉⢩⣄⣠⣿⣿⣿⣿⠀⣿⣿⣷⣄⡀⠀⠉⠻⣆⠀⢀⣴⣿⣿⣿⣿⠟⠀⠀⠀⢸⡿⣸⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⣷⣶⣤⣄⣈⣿⠀⢠⡄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⣿⣿⣿⡟⠉⠉⣤⣤⠈⠻⢿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣦⣄⡀⠈⠀⠟⠛⠛⠉⠉⠀⠀⠀⣠⣴⣿⠇⣿⣿⣿⣿⡇⠀⠀⢠⣤⠀⠀⢰⣶⣿⣿⡇⣿⣿⣿⣿⣿⣷⣤⣶⣤⣀
⠀⠀⠀⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⡇⣿⣿⣿⣇⣀⠈⠟⠛⠀⠀⣼⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢰⣿⣿⣿⣿⣷⣤⡄⠀⠀⢀⣀⣸⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⡏⢹⡟
⠐⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢠⣿⣿⣿⠿⠿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠁⠉⠀⣀⡀⠙⠿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣷⣶⣿⣖
⠀⠠⠤⠑⠆⠀⢠⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠀⠀⢸⣶⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣄⣀⠈⠿⠇⠀⠀⣿⣿⡿⠿⠃⠸⣿⣿⣿⣿⣿⣟⠛⠛⠛
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢸⣿⣿⣷⣶⠆⠀⠈⢠⣄⣼⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⠿⢿⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠀⠀⢠
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⠀⠀⢀⣀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⢸⣿⣿⣿⣿⡇⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣇⣀⠈
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣤⡄⠿⠿⢇⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⡏⢀⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⡀⢀⣀⣀⣠⣴⣤⣠⣠⣄⣴⣶⣿⣿⣿⣿⣿
⠀⠀⠠⠄⣼⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠟⠀⣼⣿⣿⣿⣿⣿⠋⠙⢀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⡃⣤⣤⣄⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⣄⠚⠀⠀⣠⣼⣿⣿⣿⣿⣿⡯⣶⢶⣿⣮⠛⢿⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣧⡙⠛⠛⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⠀⠀⢸⠛⠻⠛⠛⠛⠛⡿⠛⠛⠻⡆⠘⠛⠛⠟⠛⢿⠟⠛⠻⢿⠿⠿⠿⣿⣿⠿⢿⡿⠛⠛⠀⢹⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⡾⠿⣿⠿⢿⠿⠟⠻⠿⠟⠠⣦⣤⣤⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⣴⡆⠀⠀⠀⢰⠀⠸⠀⠀⣶⣿⣿⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠈⠀⠀⠀⠀⠳⠤⠈⠉⠉⠀⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣸⡇⠀⡄⠀⢸⠛⢻⠀⠀⣤⣿⣿⠀⢸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡇⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣷⣶⣶⣿⠀⠀⠻⣿⣿⣻⣭⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⢰⣿⡏⠀⣠⣄⠀⠀⢀⣆⡀⠀⠀⠀⠀⠀⣿⡇⠀⣱⡀⠈⢀⣸⡀⠀⠉⣿⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⣇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⢠⠀⠈⠻⢿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⢀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣷⣤⣠⣤
⠐⠀⠀⠈⠀⠠⢶⡆⠀⡀⢹⡴⣶⣿⢿⣶⠷⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠀⠘⠓⠃⠀⣀⡀⠀⠀⠀⡠⠀⢤⣶⣶⠀⠀⠀⠐⠻⠛⠻⣧⣠⣴⣿⣉⡿⠋⠀⠀⠀⠀⠀⣼⣿⣿⢀⠀⠀⠀⠀⠐⠀⠀
⡀⢒⣦⡻⠆⠀⡂⠙⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠩⠋⠱⣾⣿⣧⢶⣿⢿⣿⣀⣠⣤⣀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⢀⣴⣿⣿⡟⣻⣿⣶⠆⠀⠀⠀⠀
⢀⡜⠛⠛⢆⣸⣿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⣀⡈⠀⣀⣼⣾⠛⣦⠀⢠⠏⠹⠿⠘⠷⠀⠀⠹⢻⣯⠁⠸⣿⠿⠋⢹⠇⠻⣿⡟⠛⠻⣶⡄⣾⣿⡿⠏⠀⠈⢻⡄⠀⣠⠁⠀⠑
⠛⠃⠀⣀⡤⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⢰⡆⣤⡄⠸⠶⠀⢀⡉⠉⠀⠛⠲⢿⡄⠀⠀⠀⣀⣀⠀⠀⠀⢋⣶⠀⠠⢤⠀⠏⠀⠀⢺⡿⠀⠀⠀⢀⢹⣴⣬⠠⠄⣾⣿⣿⣶⣟⠀⢐⣿
⠖⠀⠀⠀⠀⢀⠄⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣦⣌⠀⠀⢠⡤⠄⢀⣠⡆⣄⠠⢴⡦⠉⠐⠁⠐⡀⠈⠁⠲⠶⠾⠃⠀⠀⠀⠀⠋⠙⣤⡄⠰⠞⣤⡀⢀⣈⣷⡾⠇⢀⢸⣏⣩⡇⠀⠈⠃⠈⠉⠙⠿⢷⣿⢷
⠐⠠⠐⠖⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢀⣬⡀⠘⠒⠂⡀⠀⢉⢀⡤⠇⠈⠀⠀⠀⠀⢤⣞⣡⣤⣤⣤⣤⣤⣤⣄⣀⢠⣧⠀⠀⠥⠀⢀⡴⡿⠀⡿⠛⠛⢱⠀⠈⠛⠛⠉⠁⠀⠀⣄⠀⠀⠠⠀⠛⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡄⢀⣨⣇⠀⠀⡔⢁⠀⢰⣶⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣦⣘⣃⣤⣼⠀⠀⣾⣿⠀⠀⠀⠀⠀⠴⠀⢹⡇⡀⠀⣴⢆⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣤⣴⠶⣾⣿⣿⣿⠛⠛⢀⠀⢿⡇⠀⠘⠛⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠈⠩⣉⠉⠛⠒⠈⢉⣋⠤⠤⣄⣶⡦⡀⠀⠘⢻⣦⣴⣿⣌⡏⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣡⣶⠟⣿⣥⣀⣤⠒⠒⣿⢛⣁⣧⣤⣠⣿⣿⣿⣿⣏⠛⠿⣿⣿⣿⣿⠿⠿⠛⠻⣿⣿⣿⡄⠀⠀⠀⣀⠀⠀⠼⠘⡀⠀⠀⠛⠛⢠⡤⠐⠶⠊⡟⠉⠻⠿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠷⣦⣄⠀⢀⣀⢀⠠⢆⠚⠈⠉⠀⣸⣿⣿⣋⣡⣤⣀⡀⣠⣿⣿⣿⣿⠀⠀⢀⡉⠙⠿⣿⣿⡀⠙⠉⠃⠀⠠⠆⠘⠉⠃⠠⠀⠀⠀⠐⠂⠀⠀⠳⠷⠄⠐⣛⣋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⢸⣉⠀⠀⢲⠀⢀⣿⣿⣿⣿⣿⣯⣿⣿⣿⠿⠿⠿⢿⣷⣶⡿⠷⣿⣤⣽⣿⣇⠀⠀⠀⠀⢀⡀⠰⣤⡄⠂⢲⣆⣤⡤⠀⠀⢀⣄⣅⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢂⣠⣤⠈⠀⣼⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⠀⠀⠀⠘⣿⣿⣷⣾⣿⣿⣿⣿⠀⢀⣀⠀⠋⢡⣄⡀⢉⣹⣿⣿⣏⠲⠒⠒⠙⢿⣻⡟⠙⠉⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⢶⡝⣒⢿⣿⡿⠇⠀⠀⠀⠀⠉⠴⣿⣀⣠⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣷⣶⣿⢿⣿⣿⣿⣿⣿⣿⠀⠉⠁⠀⣊⣿⡟⠁⢸⣿⠻⠿⠏⠲⢿⠆⠀⠨⣥⠀⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠁⣨⠉⠁⠷⠞⠃⡀⣀⡀⣣⡄⢀⣀⣨⣿⣿⣿⣿⣿⣿⢡⣿⡿⠛⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠟⠿⠇⠀⠈⠁⠀⠀⠀⠘⠷⢤⣤⡠⠆⡀⠠⠀⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⣀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣦⡤⠀⠈⣉⠀⠘⠠⠤⣤⡆⠀⣀⡦⠜⠛⠋⠁⠟⠀⠀⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡀⠀⠀⠀⠀⠴⣸⣒⠄⠐⠋⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣀⣤⡄⠀⠀⠀⣏⣍⠀⠀⠀⢀⠄⣄⡉⠁⠀⠀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢞⠻⠁⣟⡛⠁⠀⣴⣿⡄⢄⡀⠀⠀⠈⠛⠁⢀⣤⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⠖⠒⠀⠀⠀⢠⡆⠀⠀⠀⠀⢀⡀⠈⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠁⠀⠀⠀⠀⠀⠃⠉⢷⠘⠀⣀⣀⡀⠘⢃⠈⠿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣤⣐⣀⣤⠀⠀⠀⣀⣶⠏⠁⢠⣤⣈⣉⣉⠙⠛⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⢙⣿⣿⣿⣿⣿⣿⣿⠃⠀⠁⠂⠀⠀⠁⠀⠐⠂⡐⣀⠐⠂⢴⠀⢠⠤⠙⣶⣀⢠⠀⠀⠀⢀
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠴⠦⠈⠁⠀⠀⠀⠉⠙⠃⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣯⢿⣿⣿⣿⠀⡴⣠⠤⠀⠀⠀⠘⠃⢀⡶⠺⢀⣄⡼⠃⠀⣣⢠⡏⢩⡄⠁⠉⠁⠾
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⠠⢄⣤⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠐⡿⠟⣿⣿⡍⠩⠏⠠⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⣠⠉⡀⢠⠈⢿⡂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⣼⣿⣿⣿⣷⡶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣤⣄⣀⣀⡄⠀⠀⠤⣄⣀⣀⣀⠀⠠⠤⣧⡀⠀⡀⠀⠀⠙⠛⠋⢉
⠀⠀⠀⠀⠀⠀⠀⢈⢩⢀⡀⠀⠀⠀⢠⣀⣾⡿⠿⠏⠉⠹⣿⣷⠛⣻⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⢸⣿⣿⣟⣛⣲⣤⣴⠭⠈⠉⠛⢤⠀⠉⠁⠿⠧⡙⠒⢀⣤⡀⠀⠠
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢰⣏⣳⣖⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣇⠀⠀⠀⠘⢿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⣠⣶⣿⠁⠉⢻⣿⣿⡇⣸⣿⣿⡿⠿⠁⠀⠈⢶⣶⣿⣿⣿⣦⠀⠀⠀⠒⠉⠒⢶⣇⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⣾⣿⣿⢹⣿⣿⣶⡆⠀⢀⣀⡀⠐⠟⣁⣀⣿⣷⢰⣤⡀⠀⠀⠻⣿⣮⣿⠏⠀⠀⠀⣠⣾⣿⣿⡁⠀⠀⠀⣿⣿⣸⣿⡇⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⢾⣶⡶⡆⠀⠀⢰⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⣿⣿⣿⣿⣷⣶⠈⠉⢡⣄⣠⣿⣿⣿⣿⠠⣿⣿⣦⣀⠀⠈⠙⢿⡀⠀⣠⣾⣿⣿⣿⡿⠇⠀⠀⠀⣿⢇⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⣦⣬⣉⠉⠳⠖⠀⢀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⣿⣿⣿⡏⠉⢁⣤⣤⠘⠿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣷⣤⣀⠀⠁⠸⠟⠛⠛⠉⠉⠀⠀⢀⣤⣴⣿⢸⣿⣿⣿⣿⠀⠀⢀⢄⠀⠀⠀⣦⣼⣿⣿⢸⣿⣿⣿⣿⣿⡃⣀⣉⠀⠐
⠀⠀⠀⠀⠄⠀⠀⠀⣾⣿⣿⣿⣿⢡⣿⣿⣿⣥⣤⠐⠛⠃⠀⠀⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠇⣾⣿⣿⣿⣿⣤⡤⠀⠀⢁⣀⣠⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠿⢷⡶
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢸⣿⣿⡿⠛⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⣿⣿⣿⣿⡏⠉⠀⣀⣀⠘⠻⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢰⣋⠠
⠀⠀⠀⢄⠀⠀⢠⣿⣿⣿⣿⣿⡟⢸⣿⣿⡇⠀⠀⠾⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣇⣀⡀⠙⠿⠀⠀⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢾⣷⠶
⠀⠉⠁⠈⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠹⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⠿⠿⠇⠀⠀⢰⣾⣾⣿⣿⡿⠟⠀⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⣠⣤⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢹⣿⣿⡏⢀⣿⣿⣿⣿⣿⠀⠀⠀⡔⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⠀⠀⠗
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣷⣤⠄⠛⠿⢇⡀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⣸⣿⣿⣿⣿⣿⡤⡄⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣖⣒⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠁⢿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⠃⢰⣿⣿⣿⣿⣿⡟⠉⢃⣀⡀⠀⠀⡀⣤⣀⣀⣠⣴⣠⣠⣠⣄⣴⣶⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⠀⣤⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣧⣄⡘⠛⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣦⣈⣉⣉⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣠⣼⣿⣿⣿⣿⡿⡫⣶⢶⣾⣮⠛⢿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣶⣤⣤⡤⢹⣿⣿⣿⣿⣿⣵⣾⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⠀⠀⣿⠛⠻⠛⠛⠛⠛⠿⠛⠛⠛⠇⠈⠛⠛⠟⠟⢿⠟⠛⠛⢿⠿⠿⠿⣿⣿⠿⠿⡿⠋⠉⠀⠈⠙⠛⠃⠀⠀⠀⠀⢀⡾⠿⡿⠿⣿⠟⠀⠀⠉⠙⠓⠦⠈⠉⠉⠁⠀⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⡏⠀⢰⠀⢸⠀⠀⣶⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣾⡇⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⢀⣼⣿⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⠛⢻⠀⠀⣤⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣨⣿⡏⠀⣠⣄⠀⠁⢀⡇⠀⠀⠀⢀⡄⠀⣿⡇⠀⣰⡀⠈⢀⣸⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡇⢰⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⣿⠟⠛⠃⢀⣠⣿⣿⣿⣿⣿⣿⠏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣷⣤⣤⣤
⠃⠀⠀⠀⠀⠘⠿⠇⠠⠀⢷⠞⠿⠿⢿⣿⠻⠌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠁⠀⠈⠁⠀⠀⣤⡄⠀⢠⣄⡄⠐⣶⣿⣿⠀⠀⠀⠈⠛⠉⠙⣷⣴⣾⣿⣸⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣀⡀⠆⠀⠀⠇⠀⠀
⠈⢸⣾⡟⠀⢠⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣤⠼⠀⠙⣿⢟⣗⣿⡿⠿⠿⣤⣴⣦⣤⢀⣀⣼⣿⣿⣿⡿⣿⣷⣶⡤⠀⠀⣠⣾⣿⡿⠰⣽⣿⠷⠀⠀⠀⠀⠄
⣤⡎⠉⠙⢢⣼⣿⡗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠘⠃⣄⠂⡤⢤⣿⡿⠹⣧⠀⣴⠁⠚⠛⠉⠇⢀⠀⠍⢻⣇⠀⠘⠿⠛⠁⡾⠃⠻⣿⡟⠛⠙⠷⠂⣿⡿⠿⠃⠀⢈⣹⣄⠀⣾⠀⠀⡁
⠛⠀⢠⡴⠲⠿⠿⠂⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠺⠢⠶⠆⠘⠗⢀⢄⣀⢀⠐⠉⠉⢳⠀⠀⠀⢀⣤⠤⠀⠀⢈⣹⣷⠀⠒⡖⣈⠁⠀⠀⣿⡇⢀⠈⠐⣠⣸⣶⠆⠐⢢⡾⣿⣿⣿⣗⢀⣸⡿
⠃⠀⠀⠀⠀⠰⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣄⠀⢄⡚⠻⢷⢀⡀⠀⢿⠒⢀⣤⠴⠆⡆⡐⠺⠂⠀⠋⠀⣰⡀⠀⠀⠛⠻⠿⠰⠀⠀⠀⠈⠁⠐⡶⠀⠘⢃⣶⠀⣴⡌⣿⠟⠂⢠⣿⣯⣬⡆⠀⠈⠃⠀⠉⠈⠛⣿⠟⠛
⠑⠒⠘⠛⠛⠁⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢴⣶⠀⠈⠉⢀⡄⠀⠤⢰⠞⠁⠀⠀⠀⠀⠈⣻⣥⣴⣶⣶⣶⣶⣶⣶⣤⣔⡲⡇⠀⠀⠒⠀⢰⡸⠇⢐⠟⠉⠉⡷⠀⠀⠉⠉⠁⠀⠀⣠⡤⠀⠀⠶⠀⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⢀⣰⡀⣠⣼⣧⠀⢰⣎⡠⠀⣿⣷⡄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⢤⣿⣭⣼⣦⠗⠀⣰⣿⣿⠀⠀⠀⠀⠀⠞⠀⢹⡃⠀⢀⣾⢥⣤⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠀⠰⣶⡿⢻⡿⣿⣿⡟⠉⠉⢀⣀⣛⠃⠀⠈⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠸⠤⠈⠉⠉⢨⢠⠇⠒⢲⣲⡟⠛⠀⠀⠉⢽⣦⣶⣿⣮⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣼⠞⠛⠿⠦⠤⢶⠈⠙⣯⣩⣰⠦⢦⣾⣿⣿⠿⠛⠣⠉⠻⣿⣿⣿⡿⠛⠉⠉⢭⣿⣿⣷⡀⠀⣀⢠⡄⠀⠀⠗⢨⣄⠀⠀⠉⠁⠲⠂⠈⠋⠸⡇⡀⠙⢻⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠖⠈⠀⠀⠀⠀⠘⠿⡶⠦⠄⣠⣄⣀⢘⠆⠉⠀⠀⢀⣾⣿⣯⣤⣶⠶⠦⣠⣾⣿⣿⣿⣷⠀⣀⣤⣀⡌⠻⣿⣷⠈⠉⠈⠀⠀⠚⠃⠉⠁⢁⠀⠀⠀⠀⠈⠀⠀⠈⠛⠟⣂⣈⠭⣭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡹⠅⢰⠄⠀⠀⣧⠀⢸⣿⣿⣿⣿⣿⣾⣿⡿⠛⠛⠛⠛⠻⢿⣿⣝⣛⣻⣷⣿⣿⡄⠀⠀⠀⠀⣠⠀⠸⣶⣆⣉⣹⣧⣶⠂⠀⢀⣠⣶⣷⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⣀⢀⣤⡀⠀⠀⠀⠀⣠⢴⡦⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠤⡤⠈⢉⣤⣤⠀⣠⡭⣿⣿⣧⠛⡉⠉⠉⢯⡽⠏⠋⠀⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⢻⢯⣋⣍⣿⣿⠟⠀⠀⠀⢀⡠⠀⠺⠧⣤⣼⣿⣿⣿⣿⣿⠯⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣥⡼⠋⠀⢼⠟⠛⠛⠉⢙⡿⠃⠀⠒⠲⠠⠤⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠤⠀⠀⠛⠛⠠⠀⠤⠀⣷⠀⠠⠠⣼⣿⣿⣿⣿⣿⣿⣸⣿⠏⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⣟⡛⠀⣀⠀⠀⠀⠀⠀⠈⠛⢶⣴⣘⣀⣠⠂⢀⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠶⠆⠀⠠⠀⠀⠈⠐⢒⣶⡂⠀⢼⠒⠊⠉⢁⣐⠃⠀⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠐⠋⣮⠥⠂⠈⠁⠄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣠⡴⣶⣀⠀⠀⢰⡦⠇⠀⠀⠈⢀⣠⣦⠄⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢇⠓⠀⠯⠁⠀⠐⡾⣷⡆⢢⠄⠀⠀⠀⢀⠀⣤⣦⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠀⠘⠋⠙⠂⢀⣀⡰⠆⠀⢀⣀⣀⣤⡄⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠀⠈⢀⡀⠀⢀⠀⠀⡀⠈⠳⠈⠀⠤⠤⣄⠉⠡⠈⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⡦⠭⠤⣴⡀⠀⠀⣤⡿⠃⠀⢰⣲⣤⣤⢤⠘⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠁⠀⠀⠀⢀⠈⠩⠡⠌⠉⠔⢳⡀⢴⡂⢩⣷⣄⠠⠀⣀⠀⣰
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠛⠣⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠉⠙⠛⠛⢡⣾⣿⣿⣿⣀⣏⣶⠂⠀⠀⠀⠈⠀⠰⠟⠻⠠⢴⡟⠁⢨⣵⢸⠃⢴⣄⠀⠀⠀⠋
⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠄⠀⠀⠀⠁⠀⡀⢀⣠⣄⡀⠀⠀⣀⣀⣁⣂⣤⣶⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢿⣿⣿⡄⠸⠃⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠄⠦⠈⢿⣁⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢶⣤⣤⣄⣄⠀⠀⠢⣤⣤⣤⣤⢀⠐⣲⣧⣄⡀⡄⠀⠀⠈⠉⠀⠤
⢀⠀⠀⠀⠀⠀⠀⠠⠠⣠⣀⠀⣀⠀⢶⣴⣿⡿⠿⠁⠀⠻⠿⠇⢉⣿⣿⣿⡿⠟⠋⠁⢻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣀⣠⡴⢿⣿⣿⣿⡏⢸⣿⣿⣯⣭⡽⠷⢞⠓⠀⣤⣉⣦⠀⠀⠐⠛⠣⡝⠃⢰⡦⠀⣀⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣼⣦⣽⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⣿⡇⡆⠀⠀⠈⠻⣿⣿⢻⣿⣿⠀⠀⠀⠀⢠⣾⣿⡟⠀⠀⠙⣿⣿⢃⣾⡿⠿⠋⠉⢀⣀⠀⠿⢿⣿⣿⡿⠇⢀⡀⠀⠉⠈⠙⠿⢦⡤⣿⣟
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⣼⣿⣿⣿⠀⠀⣤⣤⡄⠈⠉⣤⣼⣿⡇⢰⣶⣄⠀⠀⠙⠿⣿⡿⠃⠀⠀⣠⣾⣿⣿⣿⣆⠀⠀⠀⣿⡟⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡆⠘⠻⢿⣿⡆⠀⠀⠸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⠀⠀⣵⣦⣼⣿⣿⣿⣇⢸⣿⣿⣷⣦⡀⠀⠈⠻⠆⢀⣼⣿⣿⡿⠿⠛⠁⠀⠀⠀⣿⢳⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣷⣶⣤⣀⣙⠃⠀⣤⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢃⣿⣿⣿⠃⠀⢰⣶⡄⠙⠛⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⣦⣀⠀⠈⠉⠉⠀⠀⠀⠀⢀⣴⣾⣿⡏⣸⣿⣿⣿⣿⠀⠀⢰⠄⠄⠀⠀⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⡄⣤⣦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣦⡄⠈⠉⢠⣀⣠⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠃⣿⣿⣿⣿⡿⠟⠆⠀⠀⢠⣶⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡟⠛⣿⠓
⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢸⣿⣿⡟⠙⠃⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⢠⣿⣿⣿⣿⡇⠀⠀⣤⣤⠀⠉⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣧⣼⡥⠒
⠀⣀⡠⢤⠀⠀⢰⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⠟⠃⠀⠀⣾⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣧⣤⡆⠈⠉⣀⣀⣸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠛⠺⠟⠛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠳⠷⠀⠀⠀⣶⣴⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⠋⠙⢃⡀⠀⠹⠿⣿⣿⣿⡿⠟⠘⠿⢿⣿⣿⣿⣿⡇⠀⢀⡘
⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⢃⣿⣿⡏⠀⠀⣶⣶⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠹⣿⣿⡇⢠⣿⣿⣿⣿⣿⠀⠀⠘⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡇⠀⠈⠁
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣶⠒⠛⠛⠠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⣼⣿⣿⣿⣿⣿⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣍⣉⠀
⠀⠀⣀⠄⣼⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⠛⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿⣿⣿⡇⠀⢐⣶⡆⠀⠀⡀⣤⣀⣀⣠⣴⣠⣠⣠⣄⣴⣶⣾⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⠐⣷⣶⣶⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⡄⠉⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣷⣤⣤⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⡿⡫⣶⢶⣾⣮⠛⢿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠛⢿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠿⠻⢿⣿⣧⡀⠻⢿⡿⠇⢻⣿⣿⣿⣿⣿⣵⣾⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⠀⠀⣿⠛⠻⠛⠛⠛⠛⠿⠛⠛⠛⠇⠀⠛⠛⠟⠻⢿⠟⠛⠻⢿⠿⠿⠿⣿⣿⠿⢿⡟⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣴⡿⠿⡿⠿⣿⠿⠀⠐⠀⠀⠬⣭⣒⣀⣀⣀⡀⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠂⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠋⠀⢰⠀⠸⠀⠀⣶⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⢰⣿⣿⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⣿⡇⠀⠄⠀⢸⠛⢛⠀⠀⣤⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢀⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣼⣿⡏⠀⣠⣄⠀⠀⢀⠇⠀⠀⠀⣠⡆⠀⣿⡇⠀⡰⠀⠈⢀⣸⠀⠀⠉⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡇⢸⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠃⠀⣶⣿⣿⣿⣿⣿⣿⡇⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠀⢀⣀⣴⣾⣶⣿⣿⣿⣿⣿⣷⣤⣤⣤
⢠⣀⣠⡄⠀⠈⠙⠁⠐⠀⠋⠉⠙⠉⠻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠄⠀⠀⠘⢿⠤⣤⣾⣶⣠⣼⣿⣿⡇⠀⣀⡀⠀⠀⠀⣸⣿⣿⣿⣷⣾⣇⡀⠀⠀⠀⢀⣼⣿⣿⣿⣶⣦⣀⠄⠐⠀⠀⠠
⠀⠾⠿⣅⠀⣾⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣔⠁⠀⢀⣤⣾⣷⠁⠀⢸⠏⣾⡇⢿⡏⠉⠁⣿⣿⡛⠃⢰⣶⡿⠛⣿⠻⣽⣿⣿⣿⣧⣀⢀⣿⣿⣿⠋⠙⠻⣿⠉⠀⣐⠀⠸⠀
⡿⠀⠀⢀⣹⣿⣬⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠂⠀⠄⠀⠀⣠⠀⣉⠘⣷⡌⠉⠛⠛⠁⠸⣧⣼⡃⠀⠀⠀⠈⠀⠃⠀⠀⠻⣇⡀⠈⡁⡀⢠⠏⠀⠩⣿⡆⠀⠈⠉⠘⡟⣋⠉⣀⢀⣦⣿⣦⣴⡇⠀⢶⣦
⠀⠀⠚⠉⠉⢉⠉⠀⣁⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⡀⠀⠀⢠⣀⡀⠉⠉⢉⢀⡈⣀⣎⠓⢂⠆⠀⡀⠀⠗⢀⣤⣤⡚⡋⠉⠀⠀⠰⠟⢏⣀⠀⣥⢆⡀⠀⠀⢿⣤⣶⠀⠀⡷⠟⠛⠁⠀⢼⡉⠻⠿⢿⣷⣴⣿⣭
⣀⡀⣤⣀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠰⠢⢉⡓⠒⠦⡤⠃⠁⠐⠛⢋⣹⠐⠂⠉⠀⠀⢠⣴⣻⠆⠂⣀⣀⣈⣉⣉⠁⠀⣠⡀⠀⠘⡉⠀⢀⣸⡗⢤⣿⢿⢿⡄⠀⠻⠿⠿⠞⠀⠀⠀⠁⠀⠀⡀⠈⠏⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠙⠋⡀⠀⠀⣶⠂⠈⢁⠟⠁⢠⣄⡀⠁⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣗⠀⠀⢠⣀⠾⢌⣁⡘⠀⢀⣴⣇⠀⠀⠀⠀⠀⡄⠐⢾⠃⠀⢀⣩⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢀⣁⣤⣄⣾⣿⣤⡿⢿⠇⠀⢹⣶⠁⠘⠿⡿⠀⢀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⠫⠗⠻⠟⠻⣧⠄⠻⢻⣃⣀⣀⢐⣤⣀⢀⢠⠿⢦⠀⣶⡇⢻⠇⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠛⣃⣹⣿⡟⠛⠃⠀⠠⢷⡶⠆⢠⣀⡀⢀⣰⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠉⠃⢠⠀⢀⡄⠟⠈⠀⠸⠾⠏⣉⡀⢠⡤⢻⡟⠻⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⡁⠈⠝⠉⠉⠁⣀⠸⠥⠓⠛⠉⠙⣿⣿⣿⠟⢋⡉⠁⠀⢈⣿⣿⣿⡟⠉⠀⠀⠾⣿⣿⣿⡤⠴⠺⠃⠀⣨⡀⠴⠦⠀⠒⠀⠀⠉⡀⠀⠀⠭⣷⣆⠈⠾⠿⢿⣡
⠀⠀⠀⠀⠀⠈⠉⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⡙⠋⠉⠰⠶⠂⢃⠍⠃⢠⡀⠀⢒⣸⣿⣿⣷⣾⣟⣛⣣⣴⣿⣿⣿⣿⣿⣀⣠⣴⣠⣄⠹⣿⣷⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⣤⢀⣀⡀⠀⠀⢀⡀⢿⣶⣶⣭⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢙⠀⠀⠘⠃⢀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠙⢿⣿⣥⣍⣿⣿⣿⣿⡀⠀⠀⠰⠾⠀⠈⠛⠲⠶⣿⣾⠫⡤⠤⠴⢿⡿⣿⠿⡟⠛⣿⠟
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⢉⣤⡔⣦⢴⣦⣴⣶⠀⠀⠀⠀⠰⢋⣽⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣶⣤⣤⣤⣨⣿⣿⣿⣿⣿⣿⣿⡇⠙⠃⠠⠶⣿⡏⠀⣾⣽⣿⣿⠧⣤⣄⠀⠀⣛⣻⠁⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡝⠛⠒⠚⢹⣯⡤⠀⠀⠀⠰⡀⠀⠉⠉⢋⣀⣿⣿⣿⣿⣿⣿⢋⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡇⠀⠀⣰⣿⣍⠁⠀⠛⠁⠀⠀⠀⢶⣌⢀⣀⡨⠃⢈⠉⠲⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠃⠀⠀⠀⠀⡁⠀⠉⠐⠛⠀⠁⠂⡿⣻⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠀⠈⠹⣿⡿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠲⠅⠀⠆⣀⣀⣀⠂⠀⢠⣈⠿⠿⠖⢰⡆⠀⢰⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⣶⢂⡀⡤⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⢈⡉⠂⠀⠀⢐⢛⠂⠈⠛⠉⠀⢀⠐⠂⠀⠀⠀⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠱⠷⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⡞⢹⡿⠖⠀⣀⣽⣏⢁⠀⠀⠀⠒⠾⠟⠀⠀⠀⠀⠘⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⣄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⠀⠈⠓⠀⠀⠸⠙⢻⡄⠮⠀⠀⠀⠀⠦⠈⢹⡿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⢀⣴⠒⠂⣀⠀⠒⠀⠒⢿⠆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⢿⣿⣿⣿⣿⣿⣻⡏⠙⠛⠀⠀⠐⠀⠀⠤⠀⠀⠄⢄⣁⡄⠈⣉⣝⢦⡀⠑⡀⠀⠀⠀⢰
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠋⠙⠛⠇⠀⣤⡐⠛⠋⠁⠀⠙⠻⢷⠆⠂⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⣤⣾⣿⣿⡋⡾⣿⣿⠀⡤⣀⠀⠀⠀⠀⠶⠀⢉⣨⡅⠀⢀⡷⠀⠱⠀⣸⠛⣃⠐⠐⠒⢠⣇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⡏⠈⠀⠀⠉⠉⠁⡼⠟⣿⣿⡐⣺⠃⡁⠀⠀⠀⢀⠀⠉⠁⠀⠉⠛⠀⠀⠚⠃⠋⡀⢻⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠤⠆⢠⣾⣷⣶⣦⣴⡶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣷⣄⡀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣸⠉⠘⠉⠁⠈⠣⠶⠾⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠼⠂⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠛⢻⣿⣤⡿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢹⣿⣿⡿⠷⢤⣀⣸⣛⠛⠛⢗⡂⠐⠞⢻⣶⡒⢦⡀⣀⠄⠀⠀⣉
⠐⠀⠀⠀⠀⠀⠀⠁⠁⠲⠦⣠⠲⣤⣹⣿⣿⡏⠉⠁⠀⠀⠉⠉⠁⣼⣿⣿⣟⢉⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣴⡞⠛⢿⣿⣿⡏⢸⣿⣿⡿⣿⠋⠉⠛⣤⣤⣶⣶⣷⡄⠀⠈⠠⠝⠦⢤⣽⠋⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⣿⣿⣿⣇⣿⣿⣥⡄⠀⠀⠀⠀⠀⣼⠟⠋⣼⣿⠰⣀⠀⠀⠀⠻⣿⣅⢻⣿⠁⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⢻⣿⢱⣿⡏⠙⠀⠀⠀⠀⠀⠉⠙⣿⣿⣯⠃⠠⣤⣤⣄⠀⠈⠉⡻⠛⠛⠀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢹⣿⣿⣿⣧⣤⡜⠛⠛⠀⠀⣼⣿⣿⣿⠀⣿⣿⣦⡀⠀⠈⠻⣿⡁⠀⠀⣠⣾⣿⣿⣿⡷⠀⠀⠀⢸⡏⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⣤⣍⣙⠚⠀⣤⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢸⣿⣿⣿⠛⠻⢁⠀⠰⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣶⣄⡀⠀⠙⠀⡾⠿⠿⠟⠛⠉⠀⠀⢀⣠⣿⢹⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⢀⣄⣼⣿⡇⢿⣿⣿⣿⣶⣎⠀⢐⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⣿⣿⣿⣇⠀⠀⠿⠿⠀⠀⣸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇⣼⣿⣿⣿⣿⣄⡀⠀⠃⠀⣀⣠⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⣿⣿⣿⣿⡟⠉⠃⠀⠀⠸⠿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠇⡼⢋⣀
⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⣿⣿⡿⠀⠀⢠⣤⠀⠉⢹⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⢰⣿⣿⣿⣿⡇⠀⠀⠿⠿⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣥⣥
⠀⠒⠉⠓⠀⠀⣸⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣤⡄⠈⠈⠀⢀⣸⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⡿⣿⠇⠀⠀⢴⣶⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠉⠉⠁⣰
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⠏⠉⢀⣀⡀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⣿⣿⣿⣿⣿⠀⠀⢀⣄⠀⠈⠙⣿⣿⣿⡿⠏⠘⠿⢿⣿⣿⣿⣿⡄⠀⢰⠄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣤⡀⠸⣿⣗⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⠁⣸⣿⣿⣿⣿⣧⣤⡀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡥⠤⠌⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⠃⢠⣿⣿⣿⣿⣿⡟⠛⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣗⣄⠄
⠀⠐⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⡇⣤⣄⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⣀⠐⠿⠇⠀⠀⣀⣤⣀⣀⣠⣤⣠⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣧⣈⠛⠛⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣤⣤⣀⡀⣠⣽⣿⣿⣿⣿⡿⡫⣶⢶⣾⣮⠻⢿⣿⣿⣿⣿
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠀⠀⠙⠿⠇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⢈⡉⠛⠳⠤⡉⠛⠛⠁⢻⣿⣿⣿⣿⡟⣵⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⢛
⠀⢠⣿⠛⠻⠛⠛⠛⠛⠋⠛⠒⠙⠟⠀⠛⠛⠟⠿⣿⠟⠛⠻⢿⠿⠿⠿⣿⣿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠿⡿⠿⢿⠟⠀⠙⠛⠻⢿⣿⣷⣶⣶⣾⡆⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⢀⣼⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⣴⡆⠀⡍⠀⢰⠀⠸⠀⠀⣶⣿⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣠⣿⣿⠀⠀⠀⠀⠆⠀⡿⠂⠀⠀⢀⡄⠀⣿⡇⠀⠂⠀⢸⠛⢻⠀⠀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⡏⠀⣠⡄⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣿⡇⠀⠀⠀⠈⢀⣸⠀⠀⠉⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡇⢸⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡃⠈⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠉⠀⣀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣷⣤⣠⣤
⠰⣀⠴⠆⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⣈⡇⠐⢴⡿⣿⢴⣾⣿⣿⡅⣀⣠⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⣠⣾⣿⣏⡿⣿⣦⡤⠀⠘⠀⠀⠀
⣠⠛⠛⠦⢀⣿⢤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢈⡙⡀⠀⣰⣶⠛⣑⡀⢀⡘⠁⠿⠂⢿⠀⡀⢈⠟⣿⠉⠀⢶⡿⠟⠉⡿⠸⣾⣿⠿⠿⣶⣄⢰⣿⣿⣿⠁⠉⠹⣇⠀⢀⡜⠀⠐⠀
⠇⠀⣀⡠⣽⣿⡆⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠂⠀⠠⣤⣀⣄⠨⢦⠄⢀⠙⠉⠀⠸⠧⢾⡁⠀⠀⠀⢀⣀⡁⠀⠀⠛⣴⡄⠀⣀⠀⠸⠀⠀⢰⣿⠀⠀⠂⡀⡈⣯⣤⠀⠤⣰⣾⣿⣷⣾⠃⠀⣿⣶
⠀⠈⠉⠀⠀⠀⠀⢠⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⢶⣦⠀⠀⠀⠴⢠⡀⠀⣁⣄⡀⠀⢄⡌⠉⠰⠂⠠⡄⠘⠃⠠⠤⣤⣯⡁⠀⠀⠀⠒⠛⣁⡄⠈⠖⢣⡀⢀⣈⣻⣶⠧⠀⠘⣿⠙⢋⠀⠀⢻⠈⠛⠛⠿⡷⣾⣿⣶
⠤⠀⠦⠴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠠⣤⡉⠑⠒⠌⠁⠀⢉⠉⣥⠾⠀⠀⠀⠀⠀⢦⣾⣿⠂⣀⣀⣀⣀⣀⣈⣀⠤⢰⡀⠀⠩⠅⠀⡄⣾⠃⢺⠟⠛⢻⡄⠀⠘⠛⠛⠋⠀⠀⣀⡀⠀⢠⣄⠘⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠁⡄⠀⢀⣟⠀⠀⣠⠋⠀⢠⣤⡀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣇⠀⡀⡰⠄⢓⣤⡀⠄⠀⣰⣾⡗⠀⠀⠀⠀⢠⠄⠸⡟⠁⠀⢠⡄⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡀⠀⠀⣠⣤⡶⣴⣿⣿⣾⠿⠿⠃⠀⠹⡦⠀⠈⠻⠏⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠛⣛⡋⠻⠶⠂⠋⣹⠤⠤⢄⣹⣦⣄⠀⠰⠛⣦⣀⣾⣇⣻⠁⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣤⠶⢾⣏⡉⣀⡀⠀⢿⠟⡃⣰⢠⣀⣤⣼⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣧⡀⠀⠈⢁⠔⠂⣠⠆⠃⠀⠀⠛⠛⠠⣤⠄⠲⠆⣿⠉⠙⣿⢿⣦⣤⡀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣥⣀⡀⠈⠀⠀⠀⣄⠘⠒⠉⠉⠈⢩⣿⣿⡿⣋⣡⣀⡀⠀⣠⣿⣿⣿⣇⠀⠀⠈⠛⠿⣿⣿⡒⠂⠛⠀⠀⠴⠠⠛⠒⠀⠀⠀⠀⠀⠄⠀⠀⠺⢾⡥⠀⢛⣛⣻⣼
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠁⠀⠘⢛⠘⣇⠂⠁⢰⡀⠀⢁⣸⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⡿⢿⣿⣶⡶⠷⣾⣦⣹⣿⣇⠀⠀⠀⠀⠀⠀⣄⣤⠴⠲⡶⢠⡤⠄⠀⠀⣀⣐⣾⣿⣿⣼⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠩⣀⣀⡈⠁⢠⢠⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡀⠀⠀⠀⠹⣿⣶⣶⣿⣿⣿⣿⢀⣀⠀⠘⢛⣀⡈⠉⢓⣚⣿⣿⡳⠖⠒⠚⢿⢛⣿⠻⠛⢉⡿⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠠⣤⡫⠶⢶⣶⣾⡟⠀⠀⠀⠀⠘⢩⣿⢄⠀⠀⣼⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣷⣶⣶⡟⢿⣿⣿⣿⣿⣿⡀⠉⠀⢐⣛⣿⠃⢈⣿⡹⣿⡿⠲⢶⡦⠀⢀⡍⠅⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣛⢉⡙⠉⢹⣧⠆⡀⠀⠀⢲⡀⠀⠀⢈⣥⣰⣿⣿⣿⣿⣿⡿⢠⣿⡿⠛⠉⠉⠉⠛⠻⣿⣿⢼⣿⣿⣿⣿⣿⡇⠀⠀⠾⢿⡆⠐⠈⠋⠀⠀⠀⠐⠳⢦⣀⡠⠔⢀⠠⠀⠘⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠅⠀⠀⠈⠁⠀⠀⠉⠟⣿⣿⣿⣿⣿⣿⣷⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⣿⡎⣿⣿⣿⣿⣿⣧⣤⡀⠈⣛⣂⠈⠃⡤⢤⡬⠁⢀⣢⡤⠛⠛⠃⠽⠇⠀⠻⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡿⣡⠀⠖⢁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⡈⠁⠀⢀⣭⣹⡀⠈⠁⠄⠀⣀⡀⠑⠀⠀⠐⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠂⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⠲⠅⢹⠛⠋⠀⢠⣿⣆⠠⣀⠀⠀⠉⠛⠋⢀⣀⣀⠀⠈⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠴⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠃⠀⠈⠉⠀⠀⠈⠈⠻⡌⠃⣀⣀⡀⠠⠂⠀⠺⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⠀⠀⠀⣀⣖⡊⠁⣤⣀⡒⠀⠙⠿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣸⣿⣿⣿⣿⣿⣿⠃⠈⠁⠀⠀⠈⠀⠀⠓⡀⢀⡀⠦⢰⡄⢀⡬⠜⣳⣄⠁⡀⠀⠀⠀⡜
⠀⠀⠰⠂⠀⠀⠀⠂⠀⠀⠈⠁⠉⠉⠃⣰⣴⣈⠉⠀⠀⠀⠙⠛⠯⠈⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⠛⠿⠿⢻⣿⣿⣿⢠⢂⡄⡀⠀⠀⠀⠓⠀⣠⠴⡆⣀⣰⠗⠀⢻⡤⡿⢉⡅⠁⠈⠁⠸⠣
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⢽⠿⣿⣿⡀⠽⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡉⢁⣁⡀⢻⡗⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠒⠀⣴⣿⣿⣶⣶⡶⠛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⣷⣤⣀⣀⣀⠀⠀⠠⣀⣀⣀⢀⡀⠀⠤⢸⡀⠀⠀⠀⠀⠙⠛⠋⢉⡉
⠀⠀⠀⠀⠀⠀⠐⠋⡁⠀⠀⠀⠀⢀⣀⢠⣼⣿⣿⡟⠉⠹⣿⣶⠛⢻⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⢸⣿⣿⣟⠓⢤⣤⣮⡍⠉⠙⢫⡅⠘⠉⡽⠿⡙⠴⠀⣔⡂⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⣴⡣⣤⡽⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣏⠁⠀⠀⠀⠻⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⣠⣶⣿⠏⠀⠙⢿⣿⡇⣸⣿⣿⠿⠏⠉⠁⠑⣶⣶⣿⣿⣷⡄⠀⠀⠐⠊⠒⢶⣏⣁⣺⣿⠷
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣰⣿⣿⣿⢧⣿⣿⣶⡆⠀⠀⣀⣀⠀⠾⢋⣁⣿⣿⠐⣤⣄⠀⠀⠘⢿⣷⣽⡿⠁⠀⠀⢀⣴⣿⣿⣯⠀⠀⠀⢸⣿⣸⣿⡇⠉⠀⠀⠀⠀⠀⠀⠉⠿⣿⣷⠁⢲⣶⣶⣆⠀⠀⠀⡏⠉⠉⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢸⣿⣿⣿⣷⣶⠆⠋⠉⣀⣀⣿⣿⣿⣿⠀⣿⣿⣷⣄⡀⠀⠈⠻⣇⠀⢀⣼⣿⣿⣿⡿⠟⠀⠀⠀⢸⡏⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣶⣬⣉⡉⠲⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣼⣿⣿⡟⠉⠉⣤⣀⠈⠻⢿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠛⠛⠋⠉⠁⠀⠀⢀⣤⣶⣿⢰⣿⣿⣿⣿⠀⠀⠠⣀⠀⠀⠠⣶⣾⣿⡇⣿⣿⣿⣿⣿⣇⢀⣨⡀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⣿⣿⣿⣇⡀⠀⠛⠛⠀⠀⣼⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⣸⣿⣿⣿⣿⣦⡄⠈⠉⢀⣤⣴⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣽⡿⢷⣶⠤
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⣿⣿⣿⠿⠻⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⣿⣿⣿⣿⡏⠀⠀⣄⣀⠘⠛⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣟⣀⣚⣡⠤
⠀⠀⣀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⣿⣿⣟⠀⠀⢰⣦⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣇⣀⡀⠛⠛⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢿⣿⠶⢆
⠐⠊⠀⠉⠀⠀⣸⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣶⠆⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⢿⣿⣿⣿⠇⢸⣿⣿⣿⣿⠟⠻⠇⠀⠀⢽⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠞
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⠁⠀⢀⣤⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⣿⣿⣿⣿⣿⠀⠀⢘⣿⠆⠀⠀⣿⣿⣿⡿⠏⠘⠿⢿⣿⣿⣿⣿⠀⠀⠓⠀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡷⢻⣿⣿⣶⡤⠘⠿⠏⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢹⣿⠁⣸⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣖⠒⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⣿⣿⣿⣿⣿⡏⠈⠁⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣟⣒⢢
⠀⠈⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⡇⢰⣦⣤⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣦⡌⠉⠁⠀⠀⡀⢤⣀⣀⣠⣤⣠⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣷⣤⣉⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠿⣿⣿⣿⠀⠿⣷⣀⠀⣠⣼⣿⣿⣿⣿⡿⡫⣶⢶⣾⣮⠻⢿⣿⣿⣿⣿
⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⢠⣤⣤⣭⣽⣂⣀⣀⣀⢹⣿⣿⣿⣿⡟⣵⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⠀⢀⣿⠛⠻⠛⠛⠟⠛⠙⠁⠁⠉⠏⠀⠘⠛⠟⠿⣿⠟⠛⠻⢿⠿⠿⠿⣿⣿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⠿⡿⠿⣿⠛⠀⠘⠛⠻⢿⣿⣿⣿⣿⣿⡇⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠠⣾⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⣴⡆⠀⡌⠀⢰⠀⠘⠀⠀⣶⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣰⣿⣿⠀⠀⠀⠀⠀⠀⠟⠂⠀⠀⢀⡄⠀⣿⡇⠀⡂⠀⢸⠛⠻⠀⠀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⡏⠀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣿⡇⠀⣳⠀⠈⠀⠸⠀⠀⠉⣿⣿⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡇⢸⣦⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠈⠛⠻⢿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠈⠉⢹⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠇⠸⠉⠀⣀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣷⣤⣠⣤
⢱⣶⡋⠀⢠⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⣀⢰⣶⠚⠀⠈⡿⢛⣿⢹⡟⠛⠛⢤⣼⡷⠤⢀⣠⣾⡿⢿⡿⣟⣿⣿⣶⣶⡀⠀⣠⣾⣿⡿⠃⠸⣿⠟⠂⠀⠀⠀⡀⠀
⠊⠀⠉⠠⣼⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠘⠃⢖⡀⠀⠰⠿⠏⠀⣶⣀⡰⠀⠘⠉⠀⠃⠀⠀⠀⢸⠇⠀⠀⠛⠉⠁⣼⠁⠘⣻⣏⠉⢉⠛⠂⢿⠿⠛⠁⠀⢀⣸⣧⣀⣴⠀⢀⣄⣀
⠀⠠⠔⠘⠛⠛⠀⢀⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠀⠀⠸⠱⠒⠂⠈⠛⢀⠠⠄⣀⠀⠈⠈⢱⠀⠀⠀⠀⢶⠄⠀⠀⢀⣠⡿⠀⠀⠒⣠⠁⠀⠀⢸⣇⣠⡄⠀⢰⣼⣾⡗⠈⠁⡞⠿⣿⢿⣧⣀⣠⣏⣋
⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣤⠔⢒⣉⠛⠷⠠⢄⠈⠹⠛⠠⠴⠾⠃⡄⢈⠙⠃⠀⠁⣀⣸⣆⡀⢀⠉⠙⠿⠶⠆⠀⠀⠀⠀⠠⠶⠀⠈⠁⣿⠀⢰⣶⣾⡏⠁⠀⢸⣷⣤⡄⠀⠀⠑⠀⠀⠀⠉⣹⠛⠛⠛
⠐⠈⠉⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠶⠀⠈⠈⢠⡄⠀⠂⢰⠟⠁⠀⠀⠀⠀⠀⢻⣷⣿⣡⣤⣶⣶⣶⣶⣶⣤⣌⣑⡀⠀⠉⠀⢠⡙⠇⢀⠟⠁⢀⣼⠂⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠘⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠹⠀⠀⣠⣼⣄⣤⣾⣧⠀⠰⣇⠰⠀⣿⣿⡄⠀⠐⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠆⠉⣤⣴⢶⣞⣀⣰⡿⣿⠀⠀⠠⢄⠀⠈⠀⣬⣧⡤⢤⣾⠳⡶⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠴⠶⠟⠻⣿⣿⠿⠟⠉⠉⢢⣀⣩⠁⠀⠀⠉⠀⣐⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠐⠶⠀⣈⡉⢁⢠⠟⠛⠛⣖⣟⠛⠂⠀⣁⢸⣷⣾⣿⣷⣇⣀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡾⠟⠉⡻⠶⠒⠶⠀⠈⣏⡹⠰⠇⠧⡶⣾⣿⣿⣿⠿⠿⠯⠉⠻⣿⣿⣿⣿⠿⠛⠛⣻⣿⣿⣦⣀⣠⡎⠀⠀⡛⢈⣤⡀⠀⠀⠀⠐⠋⠀⠉⠐⣏⣠⠈⠋⣿⣿⡟⣤
⠀⠀⠀⠀⠐⠖⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠻⡿⠶⠀⣠⡄⢠⢘⠧⠁⡀⠀⠠⠤⢈⣿⣿⣟⣥⣴⣦⣄⢀⣴⣿⣿⣿⣧⠀⠀⣀⠉⠛⢿⣿⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⣂⡀⠀⠈⠁⠀⠀⠈⠹⣥⣄⡔⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠀⠰⠦⠀⠀⢷⠀⠐⠃⣼⣿⣿⣿⣿⣿⣷⣿⣿⠿⠿⠿⠿⢿⣷⣟⠛⠾⣷⣬⣿⣿⠀⠀⠀⣤⡄⠘⠾⢏⣉⣽⣷⣿⣋⣀⣀⣠⣾⣶⣿⣿⡿⢿⣿⠿
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⢀⢤⢀⣀⣀⣤⡄⠀⠀⠀⢀⡥⢾⡶⠀⠀⠃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⠐⠦⠀⣀⣴⣶⠀⢤⡾⢾⣿⣷⣈⣀⠀⠀⠹⠾⠇⠈⠀⠚⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠷⢭⣭⠻⣿⢛⠀⠀⠀⢀⡀⠀⠛⠫⠤⠀⠀⣸⣿⣿⣿⣿⣿⠋⣼⣿⣿⣿⣿⣿⣿⣷⣾⣜⣿⣿⣿⣿⣿⣿⡆⠀⠀⣴⣞⠋⠀⢺⠏⠙⠋⠁⢈⣉⠁⠀⠐⠊⠀⠂⠀⣄⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠶⠀⠀⠛⠋⠠⠀⠀⠀⡵⠄⠠⠠⢴⡗⢶⣿⣿⣿⣿⣿⡏⣰⣿⠟⠉⠉⠀⠉⠉⠛⢿⣷⣸⣿⣿⣿⣿⣿⡇⠀⠈⢯⣟⠀⢠⠀⠀⠀⠤⠀⢀⠉⢳⣦⣬⡥⣤⠀⠠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠤⠄⢈⡠⠀⠀⠀⠀⠀⠀⠈⠐⣿⣿⣿⣿⣿⣿⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⡈⣿⣿⣿⣿⣿⣷⠖⠀⠐⠒⠤⠀⠐⠋⠿⡇⠀⠶⢟⠃⠀⠀⠌⡉⠀⠀⢩⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠄⠀⢀⠀⠀⠋⣾⠭⠃⠈⠁⠄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⠰⣶⣤⠄⠀⠰⣷⠂⠀⠀⠈⠠⢡⡶⡀⠀⠀⠀⠀⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠇⡘⠀⠯⠄⠀⠀⡟⢿⡆⢡⠂⠀⠀⠀⢀⡀⢲⣶⡦⠀⠀⠛
⠀⠀⢀⠀⠀⠀⠀⠀⢀⣈⠀⠀⠘⠀⠘⠋⠉⠀⢀⣀⠼⠇⠀⢠⡀⠠⣤⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⢿⣿⣿⣿⣿⣿⣿⡟⢿⡟⠀⠀⠄⠀⢀⡀⠀⠀⠀⠙⠀⠀⠒⠆⢤⡁⠡⠀⠉⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠶⠮⠤⣶⡀⠀⡀⠴⡾⠓⠀⠸⣷⣶⡄⠤⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⡿⣿⣿⣿⢁⠀⠀⠀⠀⠀⢠⡀⠐⠀⣒⠈⠁⢻⡀⠼⡉⠐⡿⡤⠰⠄⢤⠀⣼⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠂⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠀⠀⠉⠉⠋⢑⣾⣭⣿⣿⠧⡶⠒⠤⠀⠀⠀⠀⠐⠏⠙⠐⠶⠏⠀⠠⠧⠹⠁⠰⣄⡀⠀⠐⠉⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠠⠆⠀⠀⠀⠁⢀⣀⡀⢠⣤⣤⣄⣀⣀⣤⣼⣴⣔⣦⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣶⣿⣿⡄⠃⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠒⠒⠀⢻⢤⣤⠶⠤⠄
⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠂⢠⣤⣿⣿⣿⠿⠿⣟⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡟⣶⣶⣶⣧⡀⠀⢙⠶⠦⠤⣤⠤⠈⣥⠷⣤⡀⡄⡀⠀⣀⠀⠀⠒⠈
⡀⠀⠀⠀⠀⠀⠠⠰⢠⣄⢀⢠⣀⠲⣤⣴⣿⡟⠙⠃⠀⠀⠛⠛⠀⣼⣿⣿⡿⠟⠉⠁⠹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⡇⢸⣿⣿⣭⡭⠿⠾⡟⠀⢀⣀⣻⠀⠀⠘⠋⣑⢌⣁⣸⠷⠀⣤⣌⣉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⢸⣷⣿⣿⣏⣿⣿⣁⡀⠀⠀⠀⠀⠀⣸⡿⠛⣽⣇⢀⠀⠀⠀⠙⣿⣿⠻⣿⣿⠇⠀⠀⠀⢀⣼⣿⡟⠀⠀⠙⣿⡿⢡⣾⠿⠿⠃⠀⠀⠀⠘⠿⣿⣿⣿⣿⠀⢀⣀⣀⠀⠉⠛⢲⠶⠿⠏⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢸⣿⣿⣿⣇⣀⠀⠶⠶⠀⠁⣴⣶⣿⣿⠐⣿⣦⡀⠀⠈⠻⣷⣾⠁⠀⠀⢀⣴⣿⣿⣿⡆⠀⠀⠀⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣧⠀⠙⠿⠿⠇⣀⡀⠘⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣸⣿⣿⣿⠿⠿⠀⠀⠀⣶⣾⣿⣿⣿⣿⠀⣿⣿⣿⣦⣄⠀⠈⠙⠆⢀⣴⣿⣿⡿⠿⠛⠁⠀⠀⢠⡿⣸⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣶⣦⣄⣻⠃⠀⡤⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⣿⡗⠀⠈⣽⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠁⠀⠀⠀⠀⠀⢀⣴⣾⣿⠇⣿⣿⣿⣿⣇⠀⠀⠼⠤⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⡦⣴⣷⣀⡀⠀
⠀⠀⠐⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣶⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⢠⣿⣿⣿⣿⠿⠻⠂⠀⠀⢴⣶⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⡏⢉⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢰⣿⣿⡟⠁⠀⢠⣠⠀⠉⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⠀⠀⢰⣶⡆⠀⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣶⣾⣖⣉⠉
⣀⠀⠢⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣧⣀⠀⠈⠉⠀⠀⣼⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣶⣶⠀⠈⢁⣀⣀⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠋⠙⠉⢉⡍
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⠋⠉⠀⣀⠀⠰⢯⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⠇⢰⣿⣿⣿⣿⡏⠈⠉⣀⡀⠘⠿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡄⡀⢠⡌⠀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣀⡀⣾⣿⠄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⣼⣿⣿⣿⣿⣧⡀⠀⠻⠀⠀⠀⢸⣿⣿⣿⡿⠀⠛⠿⢿⣿⣿⣿⣇⣁⡈⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⣿⣿⠁⠀⠀⢈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡿⠁⣸⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠂⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣲⣄⣀⠀
⠀⠤⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠁⣄⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡀⠀⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣈⣀⠛
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣄⠙⠿⠟⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⡀⣠⣀⣀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⣀⣀⠀⠀⠀⢨⣿⣿⣿⣷⣿⣿⢝⣐⠻⣷⣼⣿⡿⣿⣿⣿
⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠙⠿⣿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡏⠉⠛⠛⠿⣄⡙⠻⠟⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣿⣮⠻⢿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠔⢊⣹⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣶⣶⣦⣤⣴⡆⢹⣿⣿⣿⣿⢟⣵⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⢀⣾⣿⠛⠻⠛⠛⠟⠓⡦⠐⠀⠐⠀⠘⠛⠛⠿⠿⣿⠟⠛⠻⢿⠿⠿⠻⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⡿⠿⢿⠃⢸⠛⠛⠻⢿⣿⣿⣿⣿⡇⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⣸⣿⣿⠀⠀⠀⠀⠂⠀⡇⠀⠀⠀⢀⡄⠀⣴⡆⠀⠏⠀⢰⠀⠘⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⡇⠀⠘⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣿⡇⠀⠀⠀⢸⠛⠛⠀⠀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⡏⠀⣠⣄⠀⠀⢀⠀⠀⠀⠀⣼⡇⠀⣿⡇⠀⠀⠀⠈⠀⠘⠀⠀⠉⣹⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⡇⠀⣇⠀⢸⠀⠀⠀⣀⣿⣿⣿⣿⡇⢸⣿⣦⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠛⠿⣿⣿⣿⣶⣄⣀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⢠⣶⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠸⠟⠛⠛⠛⠋⠉⠉⠁⢠⣾⡿⠉⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣷⣤⣤⣤
⣿⣿⣁⠀⣴⣄⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠂⠀⠀⣠⣶⠗⠈⠀⠀⠏⢉⣧⠹⡏⠉⠉⢷⣾⡟⠞⢰⣴⣿⠟⢻⡟⣿⣿⣿⣿⣿⣀⠀⣼⣿⣿⡟⠹⠿⣿⠛⠃⢀⡆⠀⠄⠀
⠀⠀⠈⢓⣿⡏⠉⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠈⠁⣣⣨⠀⠘⠿⢃⢈⣿⣤⡎⠀⠈⠁⠀⠁⠀⡀⠁⠸⢇⡀⠀⠉⠀⠀⠟⠀⠀⣼⡇⠀⢸⠉⠁⢻⢛⡿⣅⡀⣠⣾⣷⣤⣿⠀⢠⣦⣤
⠀⠒⠊⠙⠋⠋⠀⣰⡶⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠙⠘⢛⠁⠈⢉⣠⠑⠆⡨⠀⣀⠀⠦⠀⣀⣀⣨⠟⠋⠀⠀⠠⠼⠿⣀⠉⢋⠤⣀⠀⠀⠾⣇⣴⡀⠈⣼⡾⠿⠃⠈⢹⡛⠻⠿⢻⣷⣤⣾⣯⣭
⠀⣀⣀⣠⠀⠀⠈⠁⠀⠀⠀⠀⡀⠂⠰⠆⠋⠩⢤⠉⠁⠀⢀⣀⠒⠉⠠⠺⢛⣪⡗⠦⠉⠁⠀⢠⣠⢼⣅⡀⠤⠀⠈⠛⠛⠇⠀⠀⡀⠀⠘⣛⡀⠀⣠⡿⠀⣿⡞⡿⣁⠀⠸⡽⢷⠶⡇⠀⠠⠁⠀⠀⠀⠈⠽⠉⠉⠉
⠁⠈⠁⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠞⠻⠀⠀⠀⢰⠆⠀⠂⡺⠋⠁⣀⣀⠌⠁⠀⠛⢒⣿⣴⣶⣾⣷⣶⣾⣶⣶⣦⡄⠄⠀⢀⡄⣸⢼⡃⣸⠋⢀⣤⣿⠂⠀⠀⠀⠀⣈⠀⣶⡟⠀⠀⣋⡁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢛⢀⣀⣶⣾⣤⣾⣿⣷⠀⢸⣧⡂⠀⠿⣿⠆⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠱⠶⠾⠿⣭⣤⢼⠛⡏⣀⡀⠒⣲⣀⠁⠄⡾⢆⡒⣦⣿⢚⡗⢀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠿⢏⣹⣟⡿⠟⠏⠀⡀⣣⣦⣽⠡⣀⡀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠉⠓⢠⠬⠀⡔⠸⠃⠉⠹⠽⢏⣙⣋⢀⣄⠹⣿⠿⣿⣿⣧⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣟⠋⠉⠟⠓⠚⠓⢀⠐⣇⠜⠸⠃⠓⢻⣿⣿⣿⠿⠛⠛⠒⠀⢹⣿⣿⣿⡟⠋⠉⠩⣽⣿⣿⣦⠤⠰⠇⠀⢨⡍⣠⠦⠀⠀⠀⠀⠉⣁⡀⠀⠨⣧⣖⡈⠹⠿⠿⣟⣾
⠀⠀⠀⠀⠘⠒⢀⠄⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⣛⠟⠛⠀⣴⠆⢠⡌⠣⠀⡀⠀⠰⠀⣸⣿⣿⣥⣶⣿⣖⣲⣴⣿⣿⣿⣿⣧⣀⣠⣄⣤⡙⢿⣿⡀⠀⠀⠀⠀⠂⣀⠀⣠⣌⣥⡄⣀⣀⠀⠀⠀⣨⡿⣦⣴⣎⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢀⠐⡒⠀⠀⠿⠀⡈⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠉⠉⠻⣿⣯⣍⣛⣿⣿⣿⣇⠀⠀⢀⠶⠆⠈⠛⠧⡧⣾⣿⡿⣀⣠⠤⢾⣿⡾⡿⣿⠿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢒⣀⣰⣆⣠⣤⣴⣴⠄⠀⠀⠀⠠⠖⣻⣟⠀⠀⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣸⢿⣿⣿⣿⣿⣿⣿⠐⠒⠀⠴⢿⡟⠀⢲⣟⣿⣿⡯⣤⣤⡀⠀⠓⢛⠃⠉⠀⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡙⠛⠤⠦⠿⣿⣩⠀⠀⠀⠠⡄⠀⠙⠓⢒⠀⢀⣿⣿⣿⣿⣿⡿⣱⣿⣿⠿⠿⠿⠿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⠁⠀⠹⠃⠈⠉⠀⢼⣝⠁⠀⣉⡅⠘⠛⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠒⡒⠀⠀⠉⠉⢐⠀⠒⠀⠿⠀⠒⠰⢾⠃⣾⣿⣿⣿⣿⣿⣧⣿⡿⠁⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⣿⣿⣿⣿⡀⠀⠀⠳⠍⢀⠤⠀⢀⢀⠒⠀⠠⣉⠻⠿⠬⢶⡦⠁⢰⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣒⠂⣠⡄⠀⠀⠀⠀⠀⠀⠀⢒⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠘⠛⠓⠆⠈⠙⠛⠇⠐⠛⢏⢀⠀⠰⠨⠄⠀⠀⡼⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠁⣷⡒⠁⠀⠀⠂⠆⠀⠀⠀⠂⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡤⡴⠘⣿⠶⠂⢀⣸⣏⠁⡂⠀⠀⠐⠼⠟⠂⠀⠀⠀⠐⠖⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⢀⣀⣀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠂⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠁⠐⠓⠂⠀⠨⠛⢿⡇⠺⠀⠀⠀⠀⣤⠄⢝⣿⠷⠀⠀⢩
⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠄⣀⠘⠀⠈⠁⠀⠁⣠⡤⠜⢃⠀⠤⠤⠴⢶⡆⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⡿⠻⡏⠀⠀⠀⠀⠰⢀⡠⠄⣀⡈⡀⠀⢑⣒⢦⡄⠑⡀⠀⠀⠀⢀⠏
⠀⠀⣀⠀⠀⠀⠠⠀⠀⠘⠓⠒⠒⠿⠄⢀⡀⠲⠟⠋⠀⠸⠿⢷⡤⠒⠈⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠙⠛⠟⠋⣿⣿⣿⡿⡡⠀⠀⠀⠀⠀⠤⠀⠉⣄⣧⠀⠀⣵⠄⢫⠄⣸⡟⢃⠘⠀⠶⠀⡎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠉⠙⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⠏⠉⠁⠀⠁⠁⠀⠀⠀⠀⠈⣝⠿⣿⡟⢳⡏⠉⠒⠀⠀⠀⠀⠘⠃⠈⠘⠛⠃⠀⠐⠻⠘⠀⢹⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠠⠤⠀⣰⣶⣤⣤⣤⡤⠴⣶⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⡌⠁⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣘⡏⠐⠋⠋⠀⠹⠴⠶⠓⠲⠀
⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡟⠛⢻⣦⣤⠟⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⣿⣿⣿⣷⣄⣉⣸⣛⠳⠒⢶⡐⠠⠾⢛⣶⡖⣖⡀⢀⡤⠀⠀⣘⡀
⠀⠀⠀⠀⠀⠀⠐⠐⠰⡤⢤⢤⣄⣛⣲⣾⣿⠏⠉⠀⠀⠀⠉⠉⢀⣿⣿⣿⡟⡏⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣠⣤⠞⠛⢿⣿⣿⡇⢻⣿⣿⡶⠒⠛⠛⢩⣄⣲⣶⣿⣄⠀⠈⠡⠭⠢⣤⣽⠛⢠⣶⣦⣨
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣺⣷⣶⣿⣧⣿⣿⣤⡀⠀⠀⠀⠀⠀⡾⠟⠁⣿⣇⢀⣀⠀⠀⠈⢿⣿⣝⣿⣿⠇⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⣿⡟⣴⣿⠛⠋⠀⠀⠀⠀⠀⠛⢻⣿⣿⡛⢀⣤⣤⣤⠀⠈⠉⣹⠛⠛⠀⠈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢸⣿⣿⣿⣧⣤⠘⠛⠋⠀⣀⣾⣿⣿⣿⠈⣿⣷⣄⠀⠀⠙⠻⣿⠋⠀⠀⣴⣿⣿⣿⣿⠏⠀⠀⠀⣿⢧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣇⢠⡈⠛⠚⠡⣤⡄⠉⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣸⣿⣿⡿⠛⠛⣀⠀⠘⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⣦⣀⠀⠈⠁⢠⠾⠿⠿⠛⠋⠁⠀⠀⣀⣤⡟⣸⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⣀⣨⣿⣿⢸⣿⣿⣶⣤⣟⠀⠀⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠰⠿⠿⠀⠀⣾⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠃⣿⣿⣿⣿⣧⡀⠀⠘⠓⠀⠀⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣿⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⠿⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⢰⣿⣿⣿⣿⠏⠈⢀⠀⠀⠻⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⡿⠇⣠⠏⣀⣀
⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⡟⠀⠀⢤⣒⠀⠈⢹⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⠀⠀⠸⢿⡇⠀⠀⣿⣿⣿⣿⡂⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣘
⠤⠔⠳⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢰⣿⣿⣷⣦⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⢻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⢿⣿⠀⠀⢰⣶⣶⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⠁⠈⠀⢠⠉
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠋⠁⢀⣠⡀⠈⠛⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⡇⢰⣿⣿⣿⣿⡇⠀⠀⡶⡄⠀⠉⢻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡀⠀⠰⠄⠀
⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣤⡄⠼⠿⣗⣀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⣾⣿⣿⣿⣿⣷⣤⠀⠉⠀⠀⠀⣸⣿⣿⣿⡿⠀⠛⠿⢿⣿⣿⣿⡧⠤⠄⠀⠠
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠹⠁⣸⣿⣿⣿⣿⣿⠋⠉⣄⣀⡀⠻⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠯⣵⢦⠄⣀
⠀⠒⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⡇⣤⣤⣤⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣤⡀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠉
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣷⣌⣛⣛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⡀⣤⣀⣀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣷
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡃⠰⣶⣤⠄⠀⠀⢠⣿⣿⣿⣷⣿⣿⢝⣐⠻⣷⣼⣿⡿⣿⣿⣿
⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠉⠛⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⣈⣉⣉⣓⡠⠈⠉⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣮⠻⢿⣿⣿⣿⣿
⠀⣼⣿⣿⣿⣿⣿⣿⡟⠈⠀⠀⠉⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⢟⣵⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⣼⣿⣿⠛⠻⠛⠛⠛⠓⡦⠐⠀⠀⠀⠐⠛⠛⠟⠿⢿⠟⠛⠻⢿⠿⠿⠿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⡿⠿⢿⠃⢀⠛⠛⠻⢿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⡄⠀⣴⡆⠀⠈⠀⢰⠀⠘⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣿⠀⠀⡇⠀⠘⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣿⡇⠀⠀⠀⠘⠛⠛⠀⠀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⣿⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⠎⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⡉⠀⣠⣄⠀⠀⢀⣀⠀⠀⠀⠘⠃⠀⣿⡇⠀⣢⡀⠀⠀⠀⠀⠀⠉⢹⣿⠀⢀⡄⠀⠀⠀⣀⡀⠀⠈⠀⣀⠀⠀⠀⠀⠀⡇⠀⣇⠀⢸⠀⠀⠀⢀⣿⣿⠿⠿⠇⢸⣿⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣦⣄⡀⠀⣿⣿⣿⡿⡁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣧⠈⠉⠉⠁⠀⠀⠀⠀⠀⢰⣿⡿⠉⠀⣀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣷⣤⣄⣤
⠿⠿⢤⣀⣿⣴⣄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢬⡁⣄⣀⣴⣶⡟⢿⡄⠀⡘⠁⠿⠇⢻⡀⠀⢈⠛⣿⡉⠁⢾⡿⠟⠉⣿⠻⡿⣿⠿⠿⢷⣦⢰⣿⣿⣿⠁⢘⠙⣿⠀⢀⡼⠀⠈⠀⢀
⠀⢀⣠⣽⣿⡆⠀⠀⠨⠅⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠁⠀⠆⠀⠀⣤⣀⣤⠠⢷⡏⢀⡉⠉⠤⠼⠷⢾⣧⠀⠀⠀⢀⣀⡡⠀⠀⠛⣧⣄⠠⡄⡄⠰⠃⠀⠐⣿⠂⠀⠂⡀⡌⣯⣿⡛⠤⢤⣿⣿⣷⣾⡃⠀⣽⢶⡖
⠈⠉⠀⢁⡤⠀⣠⠿⠛⠀⠀⠀⡀⡀⠀⠀⣀⡠⢶⣦⡀⠀⠀⠀⣠⡄⢉⣀⣤⣠⡀⠤⡧⠉⠱⠃⠀⣤⠈⠋⠰⠶⢶⣿⣅⡀⢀⠀⠓⠛⢫⣦⠀⠖⢡⣤⢀⣀⣛⣶⠿⠤⢀⣿⣉⣩⡀⠀⠺⡌⠙⠓⠻⠿⣾⡿⡶⢶
⡀⣦⠤⠾⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠘⠁⠀⢒⢆⣈⣁⠉⠂⠄⠁⠀⣉⠉⢡⡾⠈⠃⠀⣀⠀⢰⣾⢻⣶⠖⢒⣂⣀⣉⣈⣁⠀⠀⣂⠈⠩⠅⠂⡠⣾⠏⢺⡿⠮⢻⡄⠀⠸⠛⠟⠛⠅⠀⢀⣀⠀⢠⣄⠘⠃⠀⠀⠀
⠠⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠉⠁⡄⠀⣀⣿⡁⠉⣠⠏⡀⢰⣤⣎⠀⠀⡀⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣅⣀⢴⡬⢛⣻⣄⡏⠀⣴⣿⡏⠀⠀⠀⠀⢰⠆⢘⣿⢇⠂⣠⡴⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⡀⠀⢀⣨⣵⣤⣶⣿⣿⣾⡿⠛⢇⡀⠹⡿⠁⠈⠛⠟⠁⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠛⣛⡛⠛⠷⠆⠋⣹⠥⠤⣤⣩⣶⣦⡰⠸⢛⣺⣭⣿⣧⣻⠁⠠⠠⣶
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣤⠿⢿⣏⣉⣁⡀⠀⢿⡿⡇⢱⢠⢀⣠⣤⣶⣿⣿⣿⣿⡛⠻⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣧⡀⠀⢁⠴⠒⣠⡇⠏⠀⠀⠛⠛⢣⣭⠄⠰⠖⣻⠟⠛⡿⢿⣷⣶⡆⡄
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⣿⣭⣄⡈⠉⠉⠉⠡⣤⠘⠒⠋⠉⠈⠉⢹⣿⣿⡟⣋⣥⣀⠈⠀⣼⣿⣿⣿⡋⠀⠀⠐⠻⢿⣿⣷⠊⠙⠀⠀⠴⠄⠚⠓⠤⠅⠀⠀⠀⠦⠄⠀⠚⢿⡧⠔⢛⣛⣻⢽⣿
⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠁⠀⠀⠤⠀⠀⠀⠤⠜⠉⠁⠘⢟⠀⣧⠂⠁⢰⡆⠀⣉⡀⣼⣿⣿⣿⣿⣯⣭⣭⣾⣿⣿⣿⣿⣷⣤⡶⢧⣶⣤⣹⣿⣇⠀⠀⠐⢈⠀⢄⣠⠴⠶⣶⢢⡤⠆⠀⠀⣠⣾⣻⣿⣿⣾⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠤⠩⢁⣀⡈⠃⠠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠉⢿⣿⣶⣾⣿⣿⣿⣿⢀⡀⠘⢛⣤⣀⠉⣻⣛⣿⣿⡻⠖⠒⠚⢿⣟⣿⠻⡟⢉⡿⠋⠛
⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠄⠬⢡⣴⣮⠶⢾⣶⣿⡟⠀⠀⠀⠀⠚⢩⣿⠅⠀⠀⠰⣾⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣶⣶⣦⣾⡿⣿⣿⣿⣿⣿⣿⠈⠁⠐⣫⣿⠃⠈⣿⡹⠿⠿⠓⢶⣦⠀⢠⣭⡭⣠⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣊⠉⡛⠃⠹⣧⠖⠀⠀⠀⠰⡀⠀⠀⢈⣭⡀⣰⣿⣿⣿⣿⣿⢣⣾⣿⠟⠛⠉⠙⠛⠛⢿⣿⣿⢽⣿⣿⣿⣿⣿⡇⠀⢼⠿⠇⠀⠀⠋⠀⠀⠀⠜⠻⢦⣀⣀⠾⢶⠀⠈⠙⠳⠦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠉⠉⠀⠀⠀⠀⠅⠀⠀⠈⠉⠀⡁⠋⠟⢀⣻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣥⡄⠈⣙⣂⡴⠓⣤⢤⡬⠁⢀⣢⣤⠛⠛⠋⠿⠃⠀⠻⣷⣶⡿
⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⢠⣄⡿⣉⠀⠶⢁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⣍⠉⠁⠀⣨⣩⡀⠈⠉⠆⠠⢠⣈⠑⠀⠀⠐⣋⣉⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠀⠂⠀⠀⠺⠯⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠇⢹⠟⠛⠠⢠⣾⣧⠠⢀⠀⠀⠉⠛⠃⢀⣀⣄⠀⠈⠡⣭
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⡤⠤⠤⠀⠀⠀⣤⠄⠀⠀⠀⠀⣈⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠘⠀⠈⠉⠀⠀⠘⠈⠻⣌⠃⣀⣀⡀⠠⠻⡀⠹⠿⠁⠀⢀⣼
⠀⠀⢀⠀⠀⠀⠀⠀⠐⢒⣐⡂⢀⡀⠀⠀⠀⢡⣶⡋⠉⣤⣀⢓⠀⠉⡿⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣟⠙⠛⠛⠻⠿⣿⣿⣿⣿⠯⠙⠃⠀⠈⠀⠀⠒⣠⣐⡒⢦⠠⡄⢀⡴⠜⣳⣄⡀⡀⠀⠀⠀⡜⠘
⠀⠠⠄⠀⠀⠀⠂⠀⠀⠈⠉⠉⠙⠓⣐⣴⣈⠉⠁⠀⠀⡙⠛⠻⠟⠁⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣯⢆⣄⡀⠀⠀⠀⠓⠀⣰⡶⡆⣀⣠⠟⠈⢓⡤⣾⢉⣥⠀⠈⠁⠸⠇⠒
⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣀⡀⠁⠀⠀⠐⣆⣀⡀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣏⢬⠡⣤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⢀⡉⢁⢁⡄⢻⡗⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠋⠁⠀⠀⠀⢀⠒⠒⠒⣿⣿⣿⠿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣀⣀⣰⡀⠀⠠⢄⣀⣀⣀⠀⠀⠤⢸⣀⢈⢀⠀⠀⠛⠛⠃⢉⡁⠐
⠀⠀⠀⠀⠀⠀⠛⡁⠀⠀⠀⠀⠀⣀⠀⣰⣿⡟⠛⠃⠀⠘⠿⠟⠁⣽⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⡇⣿⣿⣿⡟⠦⣤⣮⣍⠉⠙⢫⡅⠈⠋⠽⠿⣝⠳⢄⣴⣀⠀⠠⠴⢤
⠀⠀⠀⠀⠀⠀⠁⠁⠛⠆⣦⣪⣤⣽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⣿⠿⣿⡇⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣿⡟⠉⠙⢿⣿⣿⢃⣿⣿⣿⠟⠋⠉⠉⢶⣦⣿⣿⣷⡄⠀⠀⠐⠊⠛⢲⣾⣀⣼⡯⠞⠞
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣿⣿⣿⣿⢹⣿⣿⣿⣇⡀⢠⣤⡄⠀⠋⣥⣴⣿⡇⢡⣶⣀⠀⠀⠻⣿⣾⣿⠏⠀⠀⢀⣴⣿⣿⣿⠁⠀⠀⠘⣿⣇⣿⡟⠈⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⡁⠰⣶⣾⣧⠀⠄⠀⡏⠀⠉⠁⢘
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣸⣿⣿⣿⣿⡿⠀⠀⢠⣶⣾⣿⣿⣿⡇⢸⣿⣿⣷⣄⠀⠀⠙⢷⡀⢀⣴⣿⣿⣿⣿⠟⠀⠀⠀⢸⡿⣸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣦⣄⣉⠉⠻⣿⠀⢀⡀⡈⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⢰⣶⣶⠈⠙⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣦⣄⡀⠀⠚⠛⠋⠉⠁⠀⠀⢀⣠⣶⣾⠃⣿⣿⣿⣿⠀⠀⠀⣤⠀⠀⠀⣤⣼⣿⡇⣿⣿⣿⣿⣾⣇⣀⣬⡁⠀⠉⠨
⠀⠀⡠⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⣿⣿⣿⣷⣶⠀⠉⢁⣄⣤⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢸⣿⣿⣿⣿⣷⣶⠀⠉⠁⣀⣠⣿⣿⣿⡧⢹⣿⣿⣿⣿⣿⣿⠿⢿⠶⠶⠶
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⣿⡟⠉⠉⡀⣀⠈⠛⢿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠁⣼⣿⣿⣿⡿⠁⠉⣤⣤⠀⠛⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣯⣤⣯⠴⠦⣤
⠀⢀⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⢸⣿⣿⣧⣄⠀⠻⠃⠀⠀⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⣷⣤⡤⠙⠛⠁⠀⢸⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⠿⠿⠳⠥⠴
⠋⠁⠉⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⠛⠛⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⣿⠇⢸⣿⣿⣿⣿⠟⠛⠇⠀⠀⠺⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠋⠀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣟⣀⡀⣾⣿⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⣿⣿⡿⠀⣿⣿⣿⣿⣿⡀⠀⠘⣿⠆⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡗⠒⠀⠋⠀⠠
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⠀⠀⠉⢁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⡿⠀⣼⣿⣿⣿⣿⣿⡿⡗⠀⠀⢠⣤⣴⣿⣿⣿⣿⠇⠟⠛⠻⢿⣿⣿⣿⣿⡉⡀⠈⢰
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⢁⣀⣀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⣿⣿⣿⣿⡇⠀⣰⣶⣦⠈⠘⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠉⠹⠛⠚⢶⡴
⠈⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⡈⠻⠿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠈⠉⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀⠀⠀⠀⠀⢀⡀⣤⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⢿⣿⣿
⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠃⠈⠻⢿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠛⠛⠿⢿⣧⡀⠿⠿⠿⠃⠀⠀⢨⣿⣿⣯⣿⣿⣿⢝⣚⠻⣷⣼⣿⡿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⣶⣶⣶⣶⣭⣤⣀⣀⣀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣮⠛⢿⣿⣿⣿⣿
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠌⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠟⠟⠛⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⢺⣿⣿⠛⠻⠛⠛⠟⠛⡿⠛⠛⠃⠀⠛⠛⠿⠿⠿⢿⠟⠛⠻⢿⠿⠿⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⢶⠒⠒⠄⠀⠻⡿⠻⠿⠀⢿⠻⠿⠿⢿⣿⣿⣿⡿⠀⣧⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡆⠀⣴⡆⠀⠀⠀⢰⠀⠘⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⣿⡇⠀⠀⠀⠈⠉⠛⠀⠀⢤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣯⠀⣿⣿⠎⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⡉⠀⣀⣄⠀⠀⢀⣆⠀⠀⠀⠈⠁⠀⠻⡇⠀⣰⡀⠀⠀⠀⠀⠀⠈⣹⣿⠀⠀⠀⠀⠀⢀⣿⣇⠀⠈⠀⣀⠀⠀⠀⠀⠀⡇⠀⣆⠀⠸⠀⠀⠀⠀⠋⠉⠉⢉⣴⣿⣿⣦⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣤⣿⣿⡿⢋⣾⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠍⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣷⣤⣄⣤
⠛⠓⢦⣸⣿⠶⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢤⠀⠀⠠⣼⣿⡛⢧⡄⢀⡜⠀⠿⠃⢻⠀⠀⠸⠽⣿⠀⠁⠾⠟⠋⢀⡟⠙⠟⣿⠛⠛⠷⠦⣸⣿⣿⣿⠁⠉⡙⣧⡀⢠⡞⠀⣈⠀⠠
⢀⣀⠤⣾⢿⠄⠀⢀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⡆⣤⡤⠘⠿⢆⣤⣈⠀⠂⠚⠓⢛⡄⠀⠀⠀⢠⣀⠰⠀⠀⠋⣵⣆⠠⢤⠀⠈⠀⠀⠈⣿⠀⡀⠃⢄⣆⣯⣿⠉⠲⣤⣿⣿⣿⣿⡁⢀⣽⢿⠍
⠀⠀⠀⢀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⢀⠠⠤⠄⠺⢦⡀⠀⠀⢀⡠⠄⣀⣤⣦⢥⣀⠶⡷⠉⠐⠁⠐⣦⠈⠁⠘⠘⠴⣧⣤⡀⠀⠀⠉⠉⣱⡆⠀⠎⢱⡆⠠⣬⣽⡾⠗⠀⡘⣿⣩⣥⡄⠀⠹⠀⠉⠁⠛⢻⡿⠿⠿⠿
⠐⠶⠶⠗⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠉⠀⣤⡀⠀⠒⠂⣀⠀⣁⡀⣰⠿⠀⠁⠀⡤⠀⢲⣎⣿⡞⣋⣭⣤⣤⣤⣤⣄⣀⠀⢄⠀⠐⠒⢀⡴⣾⠁⣼⠟⠛⢳⣆⠀⠙⠉⠋⠙⠀⢀⣥⡄⠀⢰⠤⠈⢀⠀⠀⠀
⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡆⠀⠈⣀⣆⢀⣠⣯⡀⢀⣴⢃⡀⢰⣶⣎⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣤⢲⣔⣉⣾⡴⠇⠀⣾⣿⠇⠀⢀⣀⠀⠰⠂⢸⣿⢂⣀⢰⡶⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⢠⣴⣷⠶⣾⣿⣿⣿⠟⠛⢣⡀⠽⣟⠀⠈⠙⠛⠀⢄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠉⢭⡉⠙⠻⠁⠃⣼⠲⠶⣤⣴⢷⣦⠌⠘⠩⣷⣬⣿⣧⣼⡀⠐⠐⠿
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣩⣶⠿⢾⣭⣀⣤⡔⠒⣻⠛⡇⣵⢲⣠⣤⣾⣿⣿⣿⠿⠿⡍⠙⢿⣿⣿⣿⠿⠟⠛⣛⣿⣿⣦⡀⠀⣠⠊⠁⠴⠆⠁⠀⠀⠉⠉⠠⠴⠆⠐⠂⢽⢋⡙⠿⣿⣷⣷⣆⣆
⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⣿⣶⣤⡀⠀⣀⠀⡀⢦⠘⠋⠉⠁⡀⠀⣽⣿⣿⣫⣤⣦⡤⢄⣰⣿⣿⣿⣿⡀⠀⢀⢈⡙⢿⣿⣷⠉⠉⠀⠀⠛⠒⠋⠙⠀⠀⠀⠀⠀⠒⠀⠀⠹⢻⣖⣈⢉⢭⣝⣺⣿
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠘⡫⠈⣇⡁⠁⢰⡀⠀⠅⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⢿⣾⣛⡛⢿⣶⣿⣿⡄⠀⠀⢀⣀⠐⢦⣴⠺⢒⣿⣴⡶⠂⠀⠀⣤⣟⣽⣿⣿⣾⣿⣿⣿
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⡀⠨⠁⠀⠀⢐⣠⣤⡌⠁⠰⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠈⢩⣤⡄⣈⣹⣿⣿⣿⠝⠒⠛⠉⠻⣻⣿⠙⠏⠩⠟⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠂⠰⢶⡿⢒⣻⣿⡿⠏⠀⠀⠀⠀⠋⠰⠿⣂⡀⠀⢲⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⠀⠀⢈⡭⠿⠁⠠⣽⠒⠿⠟⠙⠿⠷⠀⠠⢤⠆⢤⡄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣐⣈⡉⠉⠹⠷⠇⡀⢀⡀⢹⡄⠀⡀⣀⣦⢀⣾⣿⣿⣿⣿⣿⣼⣿⠟⠁⠀⠀⠀⠀⠉⠙⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⢺⡻⠇⠀⠀⠁⠀⢀⡀⠊⠻⢦⣤⣄⣞⣒⡀⠀⡉⠙⠆⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠈⠁⠀⡀⠙⢇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡦⠄⠀⢭⣅⣊⠁⠤⣦⣦⠀⣠⣵⠦⠉⠉⡉⠟⠁⠀⠙⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠁⠄⠀⠂⣀⠀⠀⠀⠀⠰⢪⣓⡢⠀⠚⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠳⢶⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡀⣤⣄⠈⠀⠠⣤⠬⠀⠀⠀⠂⡐⣤⡄⠉⠀⠀⠘⣁⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⡩⠅⢸⣋⠉⠀⢴⣿⣧⢐⡄⠀⠀⠈⠛⠁⢠⣤⣤⡀⠈⠲⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠴⠒⠦⡀⠀⠀⢴⠀⠐⠀⠀⢀⣈⠀⠈⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠇⠉⠀⠀⠀⡀⠀⠈⠈⠻⠆⠁⠤⣄⣀⡘⠫⡈⠚⠛⠀⠀⢠⢿
⠀⠀⠀⠀⠀⠀⢀⠀⠉⣩⣐⣒⣁⡄⠀⠀⢀⣰⡿⠍⠀⣤⣄⡉⢉⡩⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡟⠁⠙⠀⡀⠀⠀⠀⠑⠶⢨⠐⠒⠰⡂⢠⠖⠊⣽⣤⠐⡄⢀⡀⢀⠎⠘
⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠁⠀⠉⠁⡤⠶⡄⠉⠀⠀⠀⠍⠉⠛⠉⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣻⣿⡷⣣⡤⠄⡁⠀⠀⠉⠀⣼⠚⠇⢤⣴⠋⠀⣫⡔⡟⠨⣆⠀⠈⠁⠘⠑⠈
⠀⠀⠀⠤⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⣠⣤⣀⣀⣀⣀⣸⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣧⠿⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠠⠤⡄⠻⣏⣀⣠⣄⡀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠋⢉⣹⣿⣿⡿⠛⢻⣍⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⢶⣤⣤⣴⣀⠀⠔⢤⣤⣀⣀⣀⡀⢒⣾⣄⣀⣀⡀⠀⠉⠉⠁⠠⠅⠈
⠀⠀⠀⠀⠀⠀⡉⡁⡀⠀⠀⠀⢀⣄⣀⣾⣿⠋⠉⠁⠀⠈⠛⠋⢠⣿⣿⣿⡿⠋⠁⠀⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣾⣤⠶⢿⣿⣿⣿⠀⣿⣿⣿⣭⠵⠶⠿⠆⠀⣈⣳⡅⠉⠁⠾⠻⢜⠚⠠⢾⡅⢀⣐⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⣶⣷⣶⣶⢿⣿⣿⣀⡀⠀⠀⠀⠀⢀⣾⠟⢋⣿⡇⠆⠀⠀⠀⠹⣿⣿⢻⣿⣿⠇⠀⠀⢀⣼⣿⣿⠇⠀⠀⢹⣿⡟⣴⡿⠿⠏⠁⠀⢀⠀⠻⢿⣿⣿⡿⠆⠀⠀⠉⠀⠉⠻⠧⣤⢿⣟⠙⢋
⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⣿⣿⣿⣿⢸⣿⣿⣿⣧⣄⠸⠿⠆⠀⢀⣶⣾⣿⡇⢸⣿⣦⡀⠀⠈⠻⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⢠⣿⢳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠀⠸⢿⣟⣗⢀⠀⠰⠇⠀⠀⠀⣩
⠀⠀⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⣿⣿⣿⡿⠻⢟⡀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣶⣄⠀⠈⠙⠀⣠⣾⣿⠿⠟⠛⠁⠀⠀⣀⣸⠏⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⣷⣶⣤⣀⣻⡟⠀⢠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣿⣿⣿⣃⠀⠸⢿⡿⠀⠀⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢰⣿⣿⣿⣿⣀⣀⠘⠿⠆⠀⢈⣿⣿⣿⡇⣿⣿⣿⣿⣿⣇⣤⣾⡄⠀⠁⠰
⠀⠀⠤⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⡿⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇⢸⣿⣿⣿⣿⠿⠿⠀⠀⢰⣶⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣟⠛⣻⠛⠚⠛
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠀⠀⣴⣤⠈⠉⢻⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⣿⣷⠀⠉⢹⣿⣿⣿⡇⢿⣿⣿⣿⣿⣷⣿⣾⣥⠒⠒⣴
⠁⡠⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢸⣿⣿⣷⡆⠀⠉⠁⢀⠀⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⣷⡇⠀⠈⣤⣤⣾⣿⣿⣿⡇⢾⣿⣿⣿⣿⣿⠿⠛⠛⠛⡂⠶
⠉⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⠉⠁⢀⣀⠀⠟⢿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠨⣿⣿⣿⠃⣸⣿⣿⣿⣿⠃⠈⢡⣤⡄⠙⠻⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⡀⠀⠀⡘⠁⠀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣤⠤⠿⢿⣂⡀⣸⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢻⣿⠏⢠⣿⣿⣿⣿⣿⣤⣄⠈⠛⠃⠀⢀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⠉⠀⠁⣀⠐
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⡿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠏⢀⣾⣿⣿⣿⣿⡿⠛⢃⣀⠀⠸⢿⣿⣿⣿⣿⣿⠀⠟⠛⠿⢿⣿⣿⣿⣯⣍⡀⠀⠑
⠀⣀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⣤⣤⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⣄⠺⠿⠿⠁⠀⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠉⠉⠵⠚
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣦⣉⣛⣛⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣦⣤⣤⡄⠀⢀⡀⣤⣀⣀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⢿⣿⣷
⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠃⠀⠈⠙⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⢀⣉⣙⣛⡦⠈⠉⠉⠀⠀⠀⢀⣿⣿⣯⣿⣿⣿⢝⣘⠻⣷⣼⣯⣿⣿⣿⣿
⠀⣼⣿⣿⣿⣿⣿⣿⣷⠿⠋⠉⠽⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⢺⣿⣿⣿⣿⣿⣿⣿⣀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣾⣮⠻⢿⣿⣿⣿⣿
⣠⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡤⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡉⠉⠉⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⣿⣿⣿⠛⠻⠛⠛⠟⠛⠿⠛⠉⠁⡀⠛⠿⠛⡿⠿⢿⠟⠛⠻⢿⠿⠿⠟⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⠛⠛⡇⠀⠛⡟⠻⢿⠀⢻⠿⠿⠿⢿⣿⣿⣿⣿⠀⣧⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡆⠀⣴⡇⠀⠀⠀⠰⠀⠘⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠇⠀⠀⡇⠀⠈⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⣄⡀⠀⢠⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⡿⠿⠀⣿⣿⠎⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣀⣄⠀⠀⢀⣆⡀⠀⠀⠀⠀⠀⠈⠁⠀⣰⡀⠈⢀⣠⠀⠀⠈⣹⣿⠀⠀⠀⠀⠀⢀⣿⣷⠀⠈⠀⣠⠀⠀⠀⠀⠀⡇⠀⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣦⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠍⠀⢀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣷⣤⣄⣤
⠈⠙⠲⣿⠟⠛⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠀⠀⠀⠘⠛⢃⢀⠀⠲⠿⠗⠘⣷⢀⡴⠀⠈⠉⠀⠃⠀⡀⠂⢸⠇⡀⠈⠛⠁⠀⡸⠁⠙⣼⣇⠀⢈⠛⠃⢿⠟⠫⠃⠀⢀⣼⣧⣀⣾⠀⠀⣄⢀⡀
⠤⠖⠛⠛⠓⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠸⠡⠖⠃⠙⠛⢤⠲⠤⢀⠀⠉⠉⢵⠀⣀⠀⠀⠶⠒⠁⠀⢀⣰⣿⠀⠈⠚⣠⠁⠀⠀⢸⣇⣠⡄⠐⢸⣼⢾⠗⠈⢱⡞⠿⢿⣛⣇⣀⣬⣏⣀⠰
⠀⠀⢀⡀⠀⠐⠉⠁⠀⠀⠀⠐⠀⠠⡤⠐⢒⡈⠙⠂⠀⢀⠀⠠⠚⠠⠶⠾⢒⡦⢌⠛⠀⠀⠁⡀⣸⣂⣀⠀⠉⠙⠻⠷⠖⠀⠂⠀⠀⠠⠻⠂⠈⠀⣿⠁⣶⣆⣿⠏⠁⠠⣾⣷⣴⡖⠀⠀⠑⠀⠀⠀⠉⡽⠛⠉⠉⠛
⠉⠉⠉⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠴⠶⠀⠀⠈⢠⡤⠀⠆⢠⠟⠁⠀⢀⠐⠂⠀⠳⡦⣿⣧⣶⣶⣶⣶⣶⣶⣦⣴⣂⠠⠀⠉⡁⢨⣙⡇⠸⠟⠀⣁⡿⠄⠀⠁⠀⢀⢁⠀⣴⡶⠀⠀⠙⡃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠿⡀⠀⣠⣼⣄⣶⣾⣗⠀⠰⣧⡴⠀⣿⣿⡄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠂⠙⣤⣾⣧⣟⣀⢼⠿⡟⠀⠀⠤⣄⣀⠋⡀⣾⣄⠄⢄⣿⢱⡶⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠶⠿⠟⢻⡿⣿⠿⠏⠁⠈⢢⣰⣫⠅⡀⠀⠉⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠐⠲⠀⣈⠁⡀⢰⠋⠉⢹⣦⡿⠻⠖⠀⣀⢺⣷⡾⣿⣧⣇⣀⡀⠙⠓
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡾⠟⠙⠻⠶⠶⠢⠀⠈⣏⡹⠰⠇⠇⠶⣾⣿⣿⠿⠟⠛⠂⠈⢻⣿⣿⣿⡟⠋⠉⢩⣽⣿⣿⣧⣀⢠⡎⠀⢐⡛⢈⣤⡀⠠⠀⠀⠙⢋⠀⠉⢐⣇⣤⠘⣩⣿⡿⡿⣼⣤
⠀⠀⠀⠐⠖⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠘⠿⡿⠶⠀⣠⡄⢠⢘⠆⠉⠀⠀⠠⠄⢠⣿⣿⣧⣶⣿⡶⢦⣠⣿⣿⣿⣿⣆⠀⣠⣄⣀⠙⣿⣿⣇⠀⠀⠀⠈⠉⠁⠀⢀⣀⣀⡀⠀⢈⠀⠀⠀⢈⡭⣥⣤⣖⣶⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠉⠂⠸⠤⠀⠀⢷⠀⠀⠂⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⢿⣿⣯⣍⣛⣿⣿⣿⣿⡄⠀⠀⣤⡄⠈⠶⢯⣥⣽⣧⡿⣉⣀⣀⣴⣿⣵⣿⣿⡿⢿⡷⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⢄⢀⣀⣠⣠⡄⠃⠀⠈⠀⡥⢶⡶⠀⠀⠃⣠⣿⣿⣿⣿⣿⠿⣿⣿⣦⣴⣄⣀⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡧⠶⢀⡠⣶⣖⠀⢴⡶⢾⣿⣷⣉⣀⠀⠈⠣⠿⠃⠉⠀⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠍⢀⣛⠿⢯⣭⡿⡿⢛⡀⠀⠀⠀⡀⠀⠛⠋⠤⠀⠀⣼⣿⣿⣿⣿⢏⣼⣿⣿⡿⠿⠿⢿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣚⠃⡀⢲⠎⠉⠉⠁⣬⡟⠃⠀⢚⡟⠺⠒⠠⣤⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠴⠄⠀⠛⠋⠠⠀⠀⠀⢷⠂⠀⠠⢾⠃⢸⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠭⣍⠀⣠⠀⠀⠀⠤⠀⢀⠉⢳⣶⣬⠥⡤⠁⢠⣄⣉⣠⣤
⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠈⠀⠀⠉⠀⢠⡤⠄⢀⡠⠀⠀⠀⠀⠠⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠶⠦⢤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠲⠮⠄⠘⠫⠾⡅⠀⠶⡛⠀⠀⠠⠬⡁⠀⠀⡹⠿⠟⠉
⠀⠀⠀⠀⠀⠠⠐⠂⠄⠀⠤⠀⠀⠀⠐⠋⣾⠭⠃⠈⠁⠀⠤⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠠⠰⣗⣦⡄⠀⢺⡖⠃⠀⠀⠈⠨⢵⡷⠀⠀⠀⠀⠰⠖⠲⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠈⠀⠧⠄⠀⠐⠿⢿⡆⢕⠂⠀⠀⠀⣀⡀⢒⣿⡦⠀⠀⢙⡾
⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀⡀⠘⠀⠘⠋⠉⠀⢀⣀⠸⠅⠀⢀⡀⠠⣤⡄⠀⠀⠀⠈⣿⣿⣿⣿⣿⡻⠟⠉⠉⠉⠉⠁⠀⠀⠉⠉⣸⣿⣿⣿⡟⠙⠏⠀⠀⠄⠀⢠⡀⠀⡄⣈⠙⡀⠐⠒⣒⣤⡁⠠⡀⠉⠀⠀⠀⢞⡇
⠀⠀⠀⠀⠀⢀⡀⠀⠐⠦⠭⠤⣶⡀⡀⡀⠤⡿⠒⠀⠸⣷⣦⡤⠠⠘⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣿⡏⢀⠀⠀⠀⠀⠀⢠⡀⠐⡑⣂⠈⠁⣫⡀⢟⡉⢸⡷⠆⠑⠀⠤⠀⡜⢀⣁
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠂⠀⠀⠀⠐⠀⠈⣁⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣷⠣⠾⠒⠠⠀⠀⠀⠀⠐⠋⠙⠐⠺⠏⠀⠰⠾⠙⠁⢺⣤⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠂⠀⠀⠀⢠⠦⠀⠀⠀⠈⢀⣀⣀⣤⣿⣿⣿⣿⡿⠭⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣏⠃⠙⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⡖⠀⠂⠚⠀⠻⣤⣴⠲⢦⢀⣀
⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠂⠀⣴⣿⠿⠿⠁⠀⠿⠿⠟⢩⣿⣿⣿⣿⠿⠟⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣼⡾⢟⣿⣿⣿⣿⡟⢻⣷⣶⢧⣄⡈⣑⡶⠶⠦⣦⠤⠉⠽⠷⣤⡔⣆⡀⠀⠀⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠠⠰⢠⣄⣀⣀⣤⣶⣶⢿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⢡⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⡖⠛⠻⣿⣿⣿⡇⢸⣿⣿⠷⡶⠛⠛⢩⣤⣴⣶⣿⡄⠀⠘⢉⡕⢮⣅⣚⠗⢠⡤⣥⣍⣶
⠀⠀⠀⠀⠀⣀⠀⠀⠉⢸⣿⣿⣿⡿⣾⣿⣿⣿⡀⠀⣤⣤⡄⠚⢉⣀⣼⣿⠈⣤⣀⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⣠⣾⣿⡟⠀⠀⠀⢸⣿⡟⣼⣿⠉⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⡛⠀⣤⣠⣄⠀⠀⠛⢲⠚⠻⠅⠡⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⠀⠈⣴⣤⣾⣿⣿⣿⠁⣿⣿⣷⣄⠀⠈⠻⣿⡁⠀⣠⣾⣿⣿⣿⡿⠀⠀⠀⢸⣿⢣⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⢀⠉⠿⠸⢥⣬⡀⠙⠀⠀⠀⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢱⣿⣿⣿⠀⠀⢰⣶⡆⠉⢻⣿⣿⣿⣿⡆⢹⣿⣿⣿⣷⣦⣀⠀⠁⠰⠟⠛⠛⠉⠁⠀⠀⣀⣤⣾⡏⣼⣿⣿⣿⡇⠀⠀⣄⡀⠀⠀⣀⣸⣿⣷⢸⣿⣷⣦⣬⣿⠀⠀⠆⠀⠠⠀⠛
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢸⣿⣿⣿⣶⡆⠈⠉⢁⣠⣸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⣿⣿⣿⣿⣷⣤⡄⠛⠛⣀⣀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣴⣾⣷⣄⣀⣀⣉
⠀⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣼⣿⣿⠋⠉⠁⣀⡀⠊⠻⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⠛⠛⢡⣀⡀⠿⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠷⠏⣩⢏⣩⡉⢉
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣄⠀⠘⠿⠇⠀⢠⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣤⣄⠘⠿⠇⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⢘⡛
⠤⠰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⡟⠓⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠻⣿⣿⣿⡏⢀⣿⣿⣿⣿⡿⠻⠿⠀⠀⢰⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡏⠉⠉⠀⣩⠉⢉
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣇⣀⣰⣿⡯⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣸⣿⣿⣿⣿⡇⠀⠠⣿⡶⠀⠉⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⡇⣀⡀⢰⠀⠀⢀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡇⠀⠈⠉⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠸⣿⠇⢰⣿⣿⣿⣿⣿⣷⣷⠀⠈⠁⣤⣤⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⠤⠤⠀⠀⠌⣙
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⡏⣀⣀⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠋⢠⣿⣿⣿⣿⣿⣟⠁⠀⣦⣤⠜⠛⢻⣿⣿⣿⣿⡇⠸⠟⠛⠿⢿⣿⠿⢿⡷⠤⢄⣀⡉
⠤⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣇⠛⠿⠿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡄⠉⠉⠀⣠⣼⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⠀⠀⠀⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠀⠉⠻⠿⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠛⠛⠿⠿⣿⡀⠻⠿⠿⠇⡦⠀⠀⡀⣤⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⢿⣿⣿
⢲⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠄⢰⣷⣷⣶⣮⣤⣀⣀⣤⠀⠀⠀⢀⣾⣟⣫⣿⣿⣿⢝⣐⠻⣷⣼⣷⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⣀⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣿⣮⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⡆⠀⢹⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⣿⣿⣿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠸⡿⠻⠿⠿⠿⠛⢿⠟⠛⠻⢿⠿⠟⠛⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⢿⠟⠃⠀⠸⠻⡿⠛⠀⠛⢿⠿⠿⠿⢿⣿⣿⣿⠀⣿⣧⣿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣵⡆⠀⣴⡇⠀⠀⠀⠐⠀⠈⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠃⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠈⣷⣇⠀⢠⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠉⠁⢀⣴⣿⣿⣿⠎⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⡁⠀⣠⣄⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⢀⣰⠀⠀⠉⣹⠟⠀⠀⠀⠀⠀⢀⣿⣟⠀⠈⠀⢠⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠟⢿⡆⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠿⢋⣥⣾⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣇⣀⣀⣀⣠⣤⣤⣶⣶⠟⠛⠛⠻⡿⠉⠀⠀⢀⣼⣶⣶⣾⣿⣿⣿⣿⣷⣤⣀⣤
⠀⠈⣲⣿⠉⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⡀⠀⠀⢀⠀⠉⠉⣡⡶⠒⠛⠿⢃⢘⠟⣤⠉⠀⠉⠀⠈⠁⠀⠀⠁⠸⢇⡀⠈⠉⠀⠀⠏⠀⠉⣼⡇⠀⢨⠙⠙⠻⠛⡉⢁⠀⣢⣾⣦⣴⡟⠀⢠⣦⠬⠅
⠒⠋⠝⠙⠃⠐⣶⠶⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠙⠐⢛⠄⠉⡁⣴⠲⠄⡬⠀⡀⠀⠞⠀⣀⢀⠘⠟⠊⠀⠀⠤⠼⠿⣀⠉⠃⠄⣀⠀⠀⠾⣇⣴⡀⠀⣶⡾⠻⠃⠈⠸⡛⠻⠿⢻⣧⣤⣾⣤⣥⢒
⣀⣀⣴⠀⠀⠚⠈⠀⠀⠀⠀⠐⠆⠰⠂⠛⠩⠄⠙⠃⠀⣀⣀⠂⠉⠰⠳⠛⢨⠃⠏⠋⠀⠀⢀⣀⢾⣤⡠⠤⠈⠉⠛⠛⠓⠀⠀⠀⠀⠐⣛⠀⢀⣸⡯⢀⣿⡶⠿⡁⠀⢰⠿⠷⢾⠇⠀⠀⠁⠀⠀⡀⠀⠟⠉⠉⠉⠉
⠉⠉⠁⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠺⠗⠀⠀⠀⠰⠄⠐⠂⡺⠋⢀⣀⡀⠈⠀⠈⠛⢚⣿⣷⣾⣿⣿⣿⣿⣿⣶⣦⣅⡂⠀⠀⡄⡺⢜⠁⣸⠋⢈⣤⡷⠀⠀⠀⠀⠀⣁⠀⣶⡋⠀⠀⣋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠳⣀⣀⣶⣾⣔⣶⡾⣇⠀⢾⣤⠂⠀⠿⣿⠆⠀⠂⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠴⢶⠾⠿⣭⡀⢸⠛⡇⣀⡀⢐⣂⣀⢁⠀⡷⢄⡒⣦⣿⢺⠗⢀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣋⣻⣛⡿⠿⠃⠐⣘⣣⣬⣥⠠⢀⠀⠀⢀⣠⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⠓⢠⠤⠀⡄⡚⠂⠉⠹⣬⡏⠛⡋⢌⣀⢿⡿⠿⣿⣿⣆⣤⡀⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣛⠋⠉⡙⠒⠛⠃⠀⢐⣆⠦⠾⠓⠒⠿⣷⣿⣿⠟⠛⠉⠓⠀⢈⣿⣿⣿⡟⠋⠁⠨⢽⣿⣿⣷⡤⢴⠇⠀⣨⡁⡠⠦⠀⠀⠀⠀⠉⣁⡀⠀⠸⣣⣖⡉⠼⠿⠻⣑⣿⣾
⠀⠀⠀⠐⠂⢠⠄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠘⠛⠟⠒⢠⣴⠄⣦⡙⠦⠀⡀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣛⣒⣲⣿⣿⣿⣿⣷⣀⣠⣄⣤⡈⢻⣿⣇⠀⠀⠀⠀⠀⣀⠀⣠⣈⣠⡄⣀⡀⠀⠠⠀⣡⡷⣦⣴⣘⣿⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠺⠒⠀⠀⠇⠀⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⠉⠉⠛⣿⣷⣬⣭⣿⣿⣿⣿⠀⠀⠠⠶⡀⠐⠛⠧⡧⢾⣾⢿⣀⢠⠤⢾⡯⡿⡿⡿⠟⣿⠟⢿⠟
⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⡀⢒⣀⡴⣄⣠⣤⣠⡤⠈⠁⠀⠀⠠⠖⣻⡟⠀⠈⢀⣰⣿⣿⣿⣿⣿⢟⣽⣿⣷⣶⣶⣤⣄⣀⣼⡿⣿⣿⣿⣿⣿⣿⡖⠒⠀⠴⢿⡍⠐⠺⢒⣿⣿⠯⣥⣄⠀⠈⠗⢛⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡙⠳⠥⠾⠿⣟⣩⠀⠀⠀⢤⠀⠈⠉⠑⠒⠀⢀⣼⣿⣿⣿⣿⣏⣴⣿⣿⠿⠿⠿⠿⢿⣿⣿⣷⠹⣿⣿⣿⣿⣿⡇⠀⢰⣿⣝⠀⠄⠛⠃⠈⠈⠀⢬⣍⠀⠈⣹⡋⠙⠓⠲⢦⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠐⠂⠒⠀⠀⠉⠁⠒⠀⠂⠠⠿⠀⠂⠐⣿⠀⢼⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⠀⠈⠻⣿⣷⣿⣿⣿⣿⣿⣇⠀⠈⠢⠅⢀⡤⠀⣀⣀⠒⠀⢬⣉⠿⠿⠽⢶⠆⠀⢴⣤⣤⣦⣤
⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡀⠀⣀⠄⠀⠀⠀⠀⠰⠀⠁⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⡉⠙⠓⢶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠛⠒⠀⠈⢑⠛⠆⠐⠛⢉⠀⠀⠐⠩⠀⠀⠠⠞⠛⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡀⠀⠀⢩⣗⠞⠁⠀⠐⢂⠆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠆⢺⣽⠴⠀⢀⣻⡏⢁⠂⠀⠀⠂⠾⠟⠀⠀⠀⠀⠰⢊⡃⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠙⢿⣿⢿⣿⣿⣿⣿⣿⡟⠥⠁⠐⠒⠂⠀⢸⠙⢿⡜⠺⠀⠀⠀⢀⠤⠸⢻⣿⠆⠀⠀⣹⠛
⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⠙⠀⠉⠉⠉⠀⣀⠤⠌⠈⠀⠤⠄⠴⢶⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣿⣿⠋⠹⡃⠀⠀⠀⠀⢠⣀⡀⠄⣀⠋⡀⠈⣑⡴⢦⡀⠁⡀⠀⠀⠀⢰⢻⡇
⠀⡀⠀⠀⠀⠀⢀⠀⠐⠖⠒⠲⢦⠀⢀⡠⠶⠛⠁⠀⠸⠥⣦⡰⠀⠁⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣿⡇⡠⠀⠀⠰⠀⠀⠤⠀⢉⣈⡄⠀⢈⣧⠀⢣⢀⣸⠛⢂⠑⠐⠖⢠⢇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠉⠑⠂⣀⡀⠄⠁⠀⠀⡄⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⢳⠋⠉⠒⠀⠀⠀⠀⠘⠁⠁⠙⠛⠁⠀⠒⠃⠋⠀⢻⡦⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⠤⠤⣾⣿⣿⡿⢿⡟⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⣿⣿⣏⣁⠉⢀⠀⠁⢀⡀⠀⠀⠀⠀⠀⣀⣸⠁⠘⠉⠁⠈⠳⠶⠞⠛⠖⠠⠤
⠀⠀⠀⠀⠀⣰⠦⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠿⠟⠀⠀⠿⠿⠇⢉⣿⣿⣿⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⢠⡾⢞⣩⣾⣿⣿⣿⡇⣿⣿⣿⣓⢨⣍⣼⣛⠗⠲⢶⡂⠰⠞⢛⣶⡲⣶⡀⣀⠄⠀⢈⣁⡀⡠
⠀⠀⠀⠀⠀⠂⠐⢴⡄⢤⣠⣤⣶⣶⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⢸⠀⠀⠀⠙⣿⣿⣿⣿⣿⡯⠀⠀⠀⢀⣿⣿⡏⠁⠙⢿⣿⣿⢁⣿⣿⡿⠿⠏⠈⠉⢶⣶⣿⣿⣷⡄⠀⠈⠠⠝⠦⢤⡽⠉⢴⣖⡄⡬⠧
⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⣤⣤⠄⠘⢫⣤⣾⣿⠈⣦⣦⡀⠀⠈⠻⣿⣿⡿⠁⠀⠀⣴⣿⣿⣿⠀⠀⠀⢸⣿⢇⣿⡏⠀⠁⠀⠀⠀⠀⠀⠈⣿⣿⣯⠁⢠⣤⣤⣄⠀⠈⠉⡟⠉⠓⠀⠰⠶
⠀⠠⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⡇⠀⠀⣧⣦⣾⣿⣿⣿⠀⣿⣿⣿⣦⣀⠀⠈⠻⡄⠀⣠⣾⣿⣿⡿⠟⠀⠀⠀⣸⡿⣼⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣦⣬⡛⠺⣤⡤⠀⠁⠀⠀⠀⢸⣶
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⣴⣶⠆⠉⢻⣿⣿⣿⣿⡀⢹⣿⣿⣿⣿⣷⣤⣀⠀⠘⠛⠉⠉⠀⠀⠀⢀⣴⣾⣿⢁⣿⣿⣿⣿⠀⠀⢰⣦⡄⠀⢰⣶⣾⣿⡇⣿⣿⣿⣿⣶⡟⠀⣐⠃⠁⠀⢘⣂
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⢸⣿⣿⣿⣶⡆⠈⠉⢀⣤⣼⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⢸⣿⣿⣿⣿⣷⣶⠈⠉⢠⣤⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣟⢿⣿⣯⣤⣤⣤⣉
⠀⠈⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⣾⣿⣿⠃⠉⢀⣤⡀⠛⠛⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⣾⣿⣿⣿⡏⠀⠈⣦⣤⠈⠛⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣛⣀⢜⣣⣠⢀⢬
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣄⡀⠘⠛⢇⣀⢠⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣷⣶⡆⠙⠛⢀⣀⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣂⣨⣁
⠄⠲⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡟⠛⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⠇⢸⣿⣿⣿⣿⠋⠙⢃⣀⠀⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠖⠀⠥
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣇⣀⢰⣿⡧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⡟⢀⣿⣿⣿⣿⣿⣀⡀⠸⠿⠇⠀⢀⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡄⠤⠀⠖⠀⢀⣰
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢐⣿⣿⣿⡏⠀⠀⠉⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⡿⠁⣼⣿⣿⣿⣿⡿⠿⠇⠀⠀⢸⣶⣾⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⣴⠒⠀⠐⢠⣹
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡏⢀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⢸⣿⣶⠀⠈⣿⣿⣿⣿⣿⠀⠿⠟⠛⠿⢿⣿⠛⠫⠟⠶⢠⡬⠀
⠒⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣷⣈⠛⠿⢋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣶⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⣤⣄⣀⡈⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢽
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠏⠀⠙⠻⠿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠉⠉⠛⠛⠷⢄⠙⠛⠛⠀⠃⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⢿⣿⣿
⢺⣿⣿⣿⣿⣿⣿⣿⣻⡧⣿⢿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣶⣶⣶⣶⠀⠀⠀⢀⡾⢿⣯⣿⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣮⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡆⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⣿⣿⣿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠻⡿⠿⠿⠿⡿⠉⠻⠟⠛⠛⢿⠟⠟⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⡰⠛⠛⠻⢿⠟⠃⠀⠿⠿⡟⠛⠀⠻⢿⠿⠿⠿⢿⣿⣿⣿⠀⣿⣧⢿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣷⡆⠀⣴⡆⠀⠀⠀⠀⠀⠈⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⢀⠀⠗⠀⠀⠀⢘⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣧⠀⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢿⡇⠀⠀⠀⢀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠀⠀⠀⠈⣿⣧⠀⢠⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠉⠁⢠⣼⣿⣿⣿⠎⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⡁⠀⣠⣄⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠈⠁⠀⢰⡀⠈⢀⣰⠀⠀⠉⠹⣃⠀⠀⠀⠀⠀⢀⣿⣟⠀⠈⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡟⢿⡦⠀⠀⠀⠀⠀⠀⠈⢛⡿⠿⣿⡿⢛⣥⣾⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣧⣤⣀⣤⣤⣤⣤⣴⣶⠟⠻⠿⢿⠿⠉⠀⠀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣷⣄⣀⣤
⢀⣨⣽⣇⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠁⠈⠁⠀⠀⠀⢠⡄⣀⡄⢰⣿⡍⣈⠉⠉⠀⠼⠰⠞⡀⠀⠀⠀⢀⣀⡠⠀⠀⠫⣤⡀⢀⣀⠀⠘⠁⠀⠸⣿⠀⠀⠆⠀⡈⣋⣴⠉⠤⣀⣾⣿⣷⣾⠁⠀⡼⢖⠒⡀
⠉⠐⠀⠉⠀⡥⠟⠃⠀⠀⠀⠀⠀⠀⢀⣀⡠⢶⣀⠀⠀⠀⠀⢠⡀⢁⣉⡔⣀⠠⢠⡏⠋⠰⠂⠠⡀⠐⠁⠠⣄⣠⣌⣉⠀⠀⠀⠒⠛⢃⡄⠀⠔⢠⡄⢀⣘⣻⣶⠧⠀⢸⣿⠉⣋⠀⠀⢣⠉⠛⠒⠿⢷⣿⣷⣶⣤⡩
⡤⣤⠇⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠛⠀⠐⠂⠀⣉⠉⠰⠄⠌⠁⠀⠋⠉⢡⠮⠙⠈⠀⡀⠀⢤⡞⣷⠶⠒⣂⣀⣉⣉⠉⠑⢀⣰⠀⠀⠩⠥⠀⡤⣾⠋⣼⡿⡽⢣⠀⠈⠻⠛⠛⠫⠀⠀⣀⡀⠀⢠⣀⠘⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠉⠉⢀⡀⠀⠀⢟⠀⠉⡨⠃⠀⢠⣤⡀⠀⠀⠈⢫⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣭⡃⢀⣀⢰⡬⠓⣏⢠⡏⠀⣴⣾⡊⠀⠀⠀⠀⢤⠄⢸⠿⠐⠀⢤⣆⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⣬⣣⣤⣼⣿⣿⣾⠿⠿⢂⠀⣿⡮⠀⠘⠻⠟⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠉⢛⣛⠛⠛⠶⠈⠏⡹⢠⣤⡈⣽⣦⣄⡄⠸⢛⣮⣹⣿⣏⡟⠁⠄⢴⣿⠀
⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⢛⣤⡯⣽⣋⠛⣀⠠⠬⢷⠷⠇⣲⢄⢀⣀⣴⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠉⢁⠖⠂⣰⠀⠁⠀⠀⠓⠛⢠⣥⠄⠦⠄⣻⠛⠻⡿⣿⣷⣦⢈⠀⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣍⣀⠈⠉⠉⠉⠀⡄⠹⠞⠓⠉⠈⢹⣿⣿⡿⠋⣉⠉⠁⠀⣼⣿⣿⣿⠉⠀⠐⠒⠿⣿⣿⣷⠲⠊⠛⠀⠀⠶⠰⠚⠒⠀⡀⠀⠀⠠⠤⠀⠀⠪⢾⠥⠐⢛⣋⡣⣽⣿⡿
⠀⠀⠀⠉⠀⠔⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠩⠙⠉⠁⠲⡟⠀⡆⠈⠂⢠⠀⢀⡁⣼⣿⣿⣿⣿⣯⣭⣥⣾⣿⣿⣿⣿⣦⣤⠾⢴⣦⣈⣿⣿⡆⠀⠀⠀⠀⠁⠠⣄⣤⢖⠴⣶⣠⡤⠄⠀⠀⣠⠎⣻⣷⣷⣾⣟⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠩⢁⣀⡘⠃⢠⢀⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠁⠀⠈⠹⣿⣿⣶⣾⣿⣿⣿⣷⢀⡀⠀⠚⢣⣄⡈⠙⣺⣻⣿⣯⠳⠖⠒⠚⢿⢻⡟⠻⠋⣹⠟⠙⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣡⣤⢷⠤⢶⣶⣾⡃⠀⠀⠀⠀⠞⢩⣿⠄⠀⢀⣸⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣶⣶⣦⣴⣿⢻⣿⣿⣿⣿⣿⣿⠀⠉⠁⢐⣹⣷⠀⢉⣟⠽⡿⡿⠒⠶⡤⠀⣈⣩⣅⣄⡀⠄⠀⠀⠀⠈
⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠐⠆⠩⠓⠚⠚⢻⣥⠆⠀⠀⠀⢲⡀⠀⠈⠙⣁⢀⣿⣿⣿⣿⣏⣴⣿⡿⠛⠛⠛⠛⠛⠿⣿⣿⣷⣻⣿⣿⣿⣿⣿⠀⠀⠀⢾⢶⠄⠰⠈⠉⠀⠀⠀⠘⠷⣄⣀⡠⡷⣆⠁⠈⠛⠶⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠬⠁⠀⠀⠀⠈⠁⠈⠀⠚⠃⠈⠀⠛⠇⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⡿⠶⠶⠶⢤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠈⣓⡀⠔⠂⣤⢤⡌⠁⢐⣢⡜⠛⠛⢉⡟⠀⠘⠿⣶⣾⡿⠟
⠀⠀⠀⠀⠀⠎⠀⠀⠄⠀⠀⠀⠀⠀⢠⢰⠦⢁⠠⠔⠀⠀⠀⠀⠀⠁⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣤⠉⠉⠀⢀⣍⣙⠀⠉⠑⠄⠄⣀⡉⠂⠀⠀⠸⣉⣉⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠾⠭⠁⠀⠀⠈⠙⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢺⠁⠿⠛⠋⠠⣬⣿⣄⠌⡀⠀⠈⠚⠛⠁⣀⣠⡀⠀⠙⢬⢄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣤⡄⠀⠀⠀⡠⡀⠄⠀⠀⠀⠈⠀⠈⠉⠙⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠁⠀⠀⠉⠉⣹⣿⣿⣿⡿⣿⡗⠄⠂⠀⠈⠉⠀⠀⠁⠙⠷⡍⠃⣀⡀⠀⠜⢂⠐⠿⠟⠀⠀⢠⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⠄⠁⡀⠀⠀⠐⢠⣶⠒⠀⣀⠐⠒⠒⢚⡿⠀⠀⠀⠀⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣽⣿⡿⠁⠉⠂⠀⠀⠈⠀⠀⢃⡤⣐⠰⠤⢠⠀⢠⠴⠛⣶⣀⢠⠀⠀⠀⢀⠏⠿⠉
⠤⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠛⠂⢀⣤⡈⠛⠁⠀⠀⠓⠛⠷⠉⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⣠⢂⣀⡀⠃⠀⠐⠂⠀⣴⠼⢀⣀⣼⠇⠈⣃⢠⡏⢩⡄⠁⠉⠁⠜⠀⠐⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠁⣠⣄⣀⣀⣀⣀⣴⣄⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⢐⣿⣿⣿⣿⣉⣯⢀⣌⠁⠀⠀⠤⠀⠀⠀⠀⠈⠁⠀⣈⠉⣀⣠⡈⢿⠂⠀⣀⡀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠐⢒⣺⣿⣿⡟⠛⢿⣉⡰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣦⡺⣿⣿⣿⣿⣿⣧⣤⣀⣀⣄⠀⠀⠤⣀⣀⣀⣀⠀⠠⠤⣇⡀⢁⡀⠀⠈⠛⠛⠉⢉⠁⠒⠒
⠀⠀⠀⠀⠐⠟⠂⠀⠀⠀⠀⢀⡀⠠⣿⣿⠋⠉⠀⠀⠘⠛⠃⣰⣿⣿⣿⢿⠋⠁⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣯⠿⣿⣿⣿⣿⡇⢸⣿⣿⣏⣓⣦⣴⠯⠍⣉⡛⣯⠀⠋⠉⡿⠯⡛⠷⢠⣔⡀⠀⠀⠦⣄⠀
⠀⠀⠀⠀⠈⠁⠑⠳⠒⣴⣶⣾⣿⢳⣿⣿⣄⠀⠀⠀⠀⠀⢠⡿⠟⢹⣿⠈⡀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⡿⠁⠀⠈⢻⣿⣿⢣⣼⠿⡿⠛⠛⠀⠀⠸⣷⣿⣿⣿⡆⠀⠀⠀⠒⠙⠒⢶⣏⣀⣿⠽⠱⠚⣒
⠀⠀⠀⠀⠠⠀⠀⠀⣰⣿⣿⣿⡿⣸⣿⣿⣿⣤⣤⠛⠿⡂⠀⢰⣶⣾⣿⡇⢻⣷⣤⡀⠀⠙⢿⣿⠟⠀⠀⣠⣾⣿⣿⣧⠀⠀⠀⢸⣿⣏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡄⢰⣷⣾⡿⡄⠀⠀⢸⠀⠈⠉⠀⣙⣛
⠀⠂⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⣿⣿⣿⡿⠛⢟⣀⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣦⡀⠀⠙⠣⢀⣾⣿⡿⠿⠟⠋⠀⠀⠀⣼⡿⢸⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣶⣤⣈⡉⠱⣿⡇⠀⣀⢀⠉⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠇⣿⣿⣿⣁⠀⠸⣿⡇⠀⢠⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣷⣤⡀⠈⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⣾⣿⣿⣿⣇⡀⠀⣿⡧⠀⠀⣿⣾⣿⣇⢿⣿⣿⣿⣷⣿⢀⣠⣍⡀⠀⠀⢴⣖
⠀⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢸⣿⣿⡿⠿⠟⠀⠀⢰⣶⣾⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢀⣿⣿⣿⣿⡿⢿⠇⠀⠀⣶⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣞⡿⠿⣿⠶⠶⠶⣶
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢸⣿⣿⡇⠀⠀⣶⡶⠈⠉⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⢸⣶⡆⠉⢙⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣩⣥⣼⡭⠶⢦⣴⠶
⢀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⡢⠀⠉⠁⣤⣤⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⠈⠉⢡⣤⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢿⠿⠿⠛⠿⠤⠦⢤
⠀⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⡏⠀⠀⣠⣄⠐⠛⢻⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⣿⣿⣿⡟⢠⣿⣿⣿⣿⡏⠀⠉⣤⣤⠘⠻⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⠘⠁⠐⠂
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣷⣤⠀⠛⠿⢄⣀⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⣼⣿⣿⣿⣿⣧⣤⠀⠛⠛⡀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡗⠒⠂⠘⠁⠀⠤⡿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠻⠃⣰⣿⣿⣿⣿⣿⠟⠛⣀⣀⠀⠿⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⢭⣁⠀⠈⡶⠿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⢰⣶⣶⣶⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣤⡀⠻⠿⠁⠀⣸⣿⣿⣿⣿⡇⢼⠿⠟⠛⠿⢿⡉⠉⠛⠙⠩⠶⠂⠀
⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣦⣍⣉⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠙⢿⣿⠇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠿⣿⣿⣿⡁⠰⣶⣤⡤⢸⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⢿
⣀⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⢠⣤⣬⣭⣓⡢⠌⠉⢀⠉⠁⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠁⣿⣿⣿⣿⣿⣿⣿⣟⡐⠛⠿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡾⣿⣯⣿⣿⣿⢝⣘⠻⣷⣼⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⣠⣼⣾⣿⣿⣿⣿⡫⣶⢶⣿⣎⠛⢿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⣰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣧⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⢛
⣿⣿⣿⠛⠛⠛⠛⠛⠂⠀⠀⠚⠻⡟⠿⠿⠿⠟⠀⠙⠛⠛⠛⢿⠟⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⠛⠛⠻⢿⠛⠀⢸⠿⠟⡟⠁⢸⠛⢿⠿⠿⠿⢿⣿⣿⠀⣿⣿⣧⣿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠄⠀⣴⡆⠀⡀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⣀⣮⡏⠀⠰⠀⢈⠀⠀⢸⠀⠀⡇⠀⠈⠀⠸⠀⠀⠀⠀⠛⠛⣠⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠀⠀⠀⠈⠃⠀⠅⠀⢰⠂⠀⠀⠀⣤⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠏⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⣿⣿⡍⠀⣠⣄⠀⠀⢀⣇⡀⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⢀⣸⠀⠀⠉⢡⣾⠀⠀⠀⠀⠀⣀⣿⣇⠀⠀⠀⢀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠿⠿⣿⣿⣿⣦⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⡏⠀⠀⠀⢷⡆⡀⠀⠀⠀⠀⠁⠉⠛⠩⣶⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣤⠀⣿⠿⠁⠀⠀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣀⣬⣿⣆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠐⠀⠀⢠⠀⣀⡄⠰⢦⠁⣈⠉⠁⠀⠋⠴⠃⠀⠀⠀⠀⣀⣀⠤⠀⠈⠁⣦⠀⠤⢤⠀⠈⠀⠀⢻⡟⢀⠀⠁⢀⣸⣤⣭⠀⠤⣼⣿⣿⣿⣿⠀⢀⡷⠉⣁⣠
⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⢶⣀⠀⠀⠀⠂⠠⠀⢀⣠⣄⡄⠠⢼⠈⠁⠐⠀⢠⡄⠑⠀⠦⠄⣤⣬⣀⠀⡀⠈⠉⠉⣠⡄⠰⠊⣤⠄⢠⣈⣳⡾⠧⠄⣼⣏⣉⣅⠀⠀⢧⠈⠉⠒⠿⢿⡿⠷⠿⢦⠄
⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠃⠀⠐⡒⢀⣄⠀⠐⠀⠀⠀⠀⡉⠉⡴⠧⠐⠀⠀⠀⠀⣦⣚⣷⡖⢒⣀⣀⣈⣀⡈⠀⠰⡆⠀⠈⠤⠐⠀⠶⡿⠁⣾⠗⠝⣣⠀⠂⠟⠛⠉⠫⠀⢀⣦⠀⠀⣠⠤⠉⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉⠉⢀⠀⣀⠈⣉⠀⠀⡸⢁⠀⣤⣤⡀⠀⢀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣀⣀⣄⣢⣗⣛⠆⣰⠅⠠⣾⣯⠁⠀⠀⠀⠘⠲⠀⣹⡋⢂⡀⣴⢆⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢀⣨⡤⣦⣾⣿⣷⡽⠟⠛⡀⠈⡿⠃⠀⠙⠻⠋⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⢙⣛⠙⠻⠖⠈⢉⡏⠤⢤⠤⣶⣶⠄⠆⠟⢣⣦⣭⣿⣎⡏⠐⠀⢴⢁⠀
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⢡⣤⠿⣽⣉⣉⡀⠀⠘⣶⢷⠉⣖⣆⢀⣀⣴⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⡀⠚⠀⠴⠘⠀⠀⠀⠛⠛⢤⠤⠐⠶⢨⡟⢋⠻⠿⣿⣿⣶⢠⢀⣀
⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣯⣥⣀⠀⠁⠉⠀⠠⡄⠓⠊⠉⠁⠈⢘⣿⣿⡿⠛⢉⠉⠁⠀⣸⣿⣿⣿⠏⠁⠀⠰⠾⣿⣿⣷⠒⠉⠋⠀⠰⠗⠐⠛⠃⠈⠀⠀⠀⠐⠂⠀⠐⠲⣷⡖⠈⣛⣩⡇⣿⣿⠿
⠀⠀⠀⠁⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠤⠋⠉⠀⠺⡏⢸⡒⠈⠀⢔⠀⠈⢡⣸⣿⣿⣿⣿⣿⣯⣥⣴⣿⣿⣿⣿⣧⣀⣴⣦⣦⣈⣿⣿⣧⠀⠀⠀⠀⡀⠰⣀⡴⠖⢲⡆⣤⠶⠀⠀⢁⣴⣫⣻⣿⣷⣾⣝⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠅⣀⣀⡉⠀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠻⣿⣷⣶⣭⣿⣿⣿⣿⢀⣀⠀⠛⣳⣄⡀⣉⣛⣻⣿⣯⠶⠒⠒⠛⢗⣻⡏⠿⠉⠽⠋⠙⠃⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢤⣶⡵⠴⣷⣶⣿⡃⠀⠀⠀⠀⠋⣹⡿⠀⠀⠀⢸⣿⣿⣿⣿⡿⢋⣿⣿⣷⣾⣶⣤⣤⣤⣿⡿⣿⣿⣿⣿⣿⣿⠀⠁⠀⣊⣽⡇⠀⢬⡇⠾⠿⠏⠻⢿⡆⠀⢭⡵⢠⣄⡐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡉⣁⠙⠈⣻⡴⠂⠀⠀⠀⢆⡀⠀⠀⢊⣅⢠⣿⣿⣿⣿⣿⣥⣾⣿⠿⠛⠛⠛⠻⠿⣿⣿⣷⡝⣿⣿⣿⣿⣿⠀⠀⠠⡟⠷⠀⠀⠘⠁⠀⠀⠀⠙⠷⣄⣀⠶⢃⣂⠄⢈⠉⠲⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠍⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⠹⠃⣸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡶⠶⠦⣤⣄⣙⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠉⣃⣀⠊⠠⠤⣴⠇⠀⣈⡤⠜⠛⠋⠩⠋⠀⠘⢻⣿⣾⠟⢛
⠀⠀⠀⠀⠐⠉⡀⠀⠀⠀⠀⠀⠀⠀⠤⣸⠯⡁⠠⠎⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⢠⣤⠉⠁⠀⠠⣍⠅⠀⠀⠁⢠⢂⣬⡉⠁⠀⠀⠊⣀⣀⠀⣼
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠀⠐⠀⠀⠀⠻⠍⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠪⠈⣟⡋⠁⠀⣴⣿⡄⢄⡀⠀⠀⡉⠋⠀⣤⣤⣀⠀⠁⢾⣴⡛
⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠀⢠⡤⠤⠄⠀⠀⠠⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠟⠋⠉⠙⠋⠁⠀⠀⠉⠉⢹⣿⣿⣿⡿⣿⡇⠀⠃⠀⠀⠀⠀⠀⠃⠙⢷⠘⠀⣀⡀⡀⠚⢃⠑⠟⠋⠀⠀⣸⢇⢙
⠀⠀⠀⠀⠀⠀⠐⢒⣂⠤⠀⣀⠀⠀⠀⠀⣰⣖⠉⢁⣄⠐⠂⠈⢹⠗⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣿⠟⠀⠉⠀⠀⡀⠁⠀⠐⠲⠖⡁⠒⠂⠶⠀⣴⠒⢹⣆⣀⢀⠀⣀⠀⢰⠁⠃⠀
⠤⠀⠀⠄⠐⠀⠀⠀⠉⠉⠉⠙⢂⣢⣆⡉⠋⠀⠀⢀⠛⠛⠿⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⡔⣠⢤⠀⠁⠀⠘⠂⢠⡶⠺⢠⣤⡾⠁⢘⣣⢺⠏⢤⡄⠀⠉⠠⠋⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣶⣤⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠹⠏⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡤⠉⡀⢤⠘⢿⣀⣀⣄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠐⠉⠀⠀⠀⠀⡀⠒⢂⣿⣿⣿⠛⠛⣯⣭⡹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣔⣄⢽⣿⣿⣿⣿⡷⣤⣤⣀⣆⠀⠠⠤⣄⣀⣀⣀⠀⠀⢢⣧⣀⣀⣀⠀⠈⠉⠉⠀⠌⠀⠈⠁
⠀⠀⠀⠀⠘⢋⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⠉⠉⠀⠀⠙⠛⠃⢠⣿⣿⣿⢿⠋⠉⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣟⣦⠾⣿⣿⣿⣿⠇⣿⣿⣯⣭⡵⠶⣾⠥⠀⣁⣛⣮⠈⠉⠰⠟⠦⡓⠂⢰⣭⠀⣀⡐⠢⡄⠀
⠀⠀⠀⠀⠈⠈⠘⠓⢀⣶⣷⣾⣿⣹⣿⣧⣄⠀⠀⠀⠀⠀⢀⣾⠟⣻⣿⠸⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⡿⠁⠀⠈⢿⣿⡟⣴⡿⠿⠟⠉⠁⢀⠀⠻⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠓⠯⣤⡼⣷⠛⠛⡛⣶
⠀⠀⠀⠀⠒⠀⠀⠀⣼⣿⣿⣿⡏⣿⣿⣿⣿⣤⡄⠛⠛⠀⠈⣰⣶⣿⣿⠀⣿⣷⣄⡀⠀⠙⢿⣿⠋⠀⠀⣠⣾⣿⣿⣧⠀⠀⠀⢸⣿⢱⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⣽⡿⣿⣻⠀⠀⠀⠼⠀⠀⠀⢈⣉⣉
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⣿⣿⣿⠟⠛⢋⡀⠀⠿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣦⣀⠀⠙⠇⢀⣾⣿⣿⠿⠛⠉⠀⠀⢀⣼⠇⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⣶⣤⣀⢘⣿⡃⠀⡄⠀⠁⢀⡾⠷
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢰⣿⣿⣿⡀⠀⠾⠿⠇⠀⢸⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣷⣦⡀⠈⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢰⣿⣿⣿⣿⣀⣀⠸⠟⠀⠀⢸⣿⣿⣿⡜⣿⣿⣿⣿⣿⡿⣀⣴⣥⠀⠀⠀⢶⣂
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⢸⣿⣿⡿⠿⠇⠀⠀⣤⣶⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⣼⣿⣿⣿⡿⠿⠿⠀⠀⢰⣶⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣮⡟⢛⡟⠒⠛⠲⠶
⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⠁⠀⢰⣶⡆⠀⢁⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⠈⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣏⣶⣶⣭⡔⡒⠠⡼⠛
⢀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⠀⠈⢠⢄⣼⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⣴⣤⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⢓⠒⠶⠦
⠀⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⡏⠀⠀⣤⡄⠈⠛⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⠁⣾⣿⣿⣿⣿⠀⠀⣤⣦⡄⠙⢻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠈⠀⠀⢠⠉⠀⠈⣩
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣧⡤⠘⠻⠯⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⠋⢰⣿⣿⣿⣿⣿⣶⡄⠐⠙⢁⡀⣸⣿⣿⣿⣿⠠⣿⣿⣿⣿⣿⣿⠏⠈⢀⠈⠀⡀⠺⣻
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠏⢠⣿⣿⣿⣿⣿⠟⠙⢡⣀⣀⠹⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣭⢀⠀⠨⠒⠓
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⡇⢰⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⣤⠘⠛⠃⠀⣨⣿⣿⣿⣿⡇⢸⣿⡿⠟⠛⠿⢧⣀⣈⡉⠉⠘⠎⠁⠉
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣷⣤⣍⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡧⠀⢿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⢿⣿⣿⡇⠸⣶⣶⣶⢠⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣈⣿
⣀⣼⣿⣿⣿⣿⣿⣟⡿⠟⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠁⠀⠀⠈⠉⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠀⣤⣤⣬⣝⣂⡀⡀⢀⡈⠉⡁⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⠿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣘⠫⣵⣼⣿⡿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣿⣎⠙⢿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⢿⣿⠋⠁⠀⢀⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣧⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⢛
⣿⣿⣿⠛⠛⠛⠛⠉⠀⠀⠐⠛⠻⡟⠿⠿⠿⠇⠈⠙⠛⠛⠛⢿⠟⠛⠛⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⠛⠛⠻⢿⠃⠀⣿⠟⠛⡏⠀⢿⠻⢿⠿⠿⠿⢿⣿⡇⢸⣿⣿⣧⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⣀⣽⣟⠀⠀⠀⢈⠀⠀⣿⠀⠀⡇⠀⠈⠀⠸⠀⠀⠀⠀⠋⢁⣼⣿⣿⣿⣯⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⢰⠀⠀⠀⠀⣤⡿⣣⠀⠀⠐⠀⠀⠈⣿⡿⠀⠠⠀⠘⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⡍⠀⣠⣄⠀⠀⢀⣧⡀⠀⢀⠀⠀⠀⠀⠀⠀⠰⡀⠈⢀⣸⠀⠀⠉⣰⣿⠀⠀⢀⠀⠀⣀⣿⣇⠀⠀⠀⢀⠀⠀⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠿⢿⣿⣿⣿⡦⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⠛⣻⠃⠀⠁⢶⡆⡀⠀⠀⠀⠀⠈⠉⠙⠋⠴⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣤⠄⣿⣿⠿⠁⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⠴⠾⠷⠄⠀⣀⡐⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢖⢤⠴⠀⠻⠇⡠⣤⡀⠐⠚⠛⢛⣠⠀⠀⠀⠠⣤⠤⠂⠀⠀⣰⡦⠀⠒⠆⡀⠀⠀⠀⣿⡁⣀⠈⠀⣤⣷⣶⠎⠐⢰⠾⣿⡿⢿⣇⢀⣸⠛⠎⠴⠾
⠀⣀⠄⠀⠼⠋⠀⠀⠀⠀⠄⠀⣀⡀⠤⠄⠛⠧⠄⡀⠀⠈⡀⠆⢀⣤⡶⢤⢄⡒⠷⠀⠀⠉⠀⣲⠀⠀⢘⠛⢶⣶⣤⡄⠠⠀⠈⠀⣡⣶⠀⠛⢰⣶⢀⣤⢬⣿⠛⠒⢰⣻⣤⣤⡆⠀⠘⠇⠀⠈⠉⢛⡿⠛⠛⠻⠖⠂
⠒⠋⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠩⢣⣴⡄⠀⠁⠂⣀⡀⠠⠀⣰⠞⠂⠁⠀⡤⠀⠰⣮⣽⣋⣡⣤⣤⣤⣤⣄⣀⠀⠿⠇⠀⠀⠒⢀⢰⢻⠋⣹⠟⠓⣙⣏⡀⠘⠋⠁⠀⠀⢠⣼⡆⠀⠠⠖⠊⠡⠀⠀⠀⠀⠈
⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⣀⣆⣀⣄⣽⡤⠀⣠⣋⡄⠘⣷⣦⡀⠀⢄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⣠⣴⣼⣶⣭⣽⣴⠗⢀⣾⣿⡆⠀⣀⡀⠀⠱⠃⢨⣭⠈⢅⡐⡟⢤⣄⠀⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠁⢀⣤⣶⡺⢾⣿⣿⣿⡟⠻⠻⣄⣘⢻⠀⠀⠉⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠒⠉⠭⡍⠉⠛⠁⠐⡴⠒⠒⢖⣰⡻⢷⠜⠘⠉⣽⣶⣾⣿⣼⡀⡘⠐⠿⠆⠀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣶⡞⠳⢧⣄⡤⠔⠀⢹⡟⣏⣸⠷⡤⣶⣾⣿⣿⡿⢿⡙⠻⣿⣿⣿⣿⡿⠟⠛⢻⣿⣿⣧⡀⠀⢀⣠⠞⠉⢰⠇⢁⣀⠀⡈⠉⠑⠶⠂⠙⠋⢾⢁⡌⠛⣻⣿⣿⢃⣆⣤⣤
⠀⠀⢤⡄⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠻⣶⣦⣤⠀⣀⡀⡀⠶⡔⠋⠁⠀⣀⢠⣿⣿⣋⣥⣤⣄⡀⣀⣾⣿⣿⣷⠀⠀⢈⠉⠛⢿⣿⣷⠙⠁⠈⠀⠀⠚⠂⠉⠉⠑⠂⠀⡀⠀⠉⠀⢀⠍⢻⣿⣈⣨⠥⣼⣿⣿⣟⣛
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠈⢻⠁⢧⡁⠀⠀⡅⠀⢄⣾⣿⣿⣿⣿⣷⣶⣾⡿⠿⠿⠿⢿⣷⣾⣛⡺⢷⣶⣿⣿⣇⠀⠀⠀⢈⣠⠀⠲⣴⣚⣛⣿⣵⡞⠃⠀⣀⣴⣿⣴⣿⣿⣿⣷⣼⣿⡿⢛
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⢀⠀⢀⣀⠠⠉⠁⠐⠐⣠⣤⡤⠁⠐⢠⣿⣿⣿⣿⣿⡿⣿⣿⣀⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣯⠠⢤⡄⠈⣩⣶⠤⢠⣬⣭⣿⣿⣎⣋⡉⠉⢙⣭⠿⠉⠃⠰⠛⠀⠉⠀⣬
⠀⠀⡀⠀⠀⠀⠀⡀⢂⠂⠐⢾⣷⢓⣻⣿⣿⠯⠀⠀⠀⠀⠘⠠⠾⢓⣀⠀⣺⣿⣿⣿⣿⢋⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⡝⢿⣿⣿⣿⣿⣿⠀⠀⠀⢩⣴⡿⠁⠐⣿⠟⠛⠛⢉⣛⠽⠀⠐⢲⠃⠶⠦⣁⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⢀⣠⣍⠉⠨⠷⠟⣀⠀⠨⢘⣦⠀⡀⣀⣵⢠⣿⣿⣿⣿⣷⣿⣿⣛⣭⣤⣤⣄⣈⣉⠛⢿⣿⣬⣿⣿⣿⣿⣿⠀⠀⠀⢺⣛⠃⠌⡀⠁⠀⢀⠀⠁⠙⠳⣤⣜⣛⣹⡖⠂⣀⣉⡋⣤⢨⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠊⠀⠐⠂⠀⢀⣀⠀⠀⡀⠀⠀⠁⠀⢀⠀⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠆⠀⠬⢥⣜⡉⠒⢲⣗⠀⠠⢵⠒⠉⠉⣀⡚⠀⠀⠉⡿⠿⠏⠃⣿
⠀⠀⠀⠀⡀⠠⢀⠀⢀⡀⠀⠀⠀⠀⡖⣟⡢⠄⠚⠀⠐⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣤⢴⣶⣀⡀⠀⢴⡔⠄⠀⠀⠁⢞⣴⡦⠀⠀⠀⠈⢠⠤⡄⢸⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠃⠀⠈⠻⠛⣻⣿⣿⣿⣿⣿⡟⠻⣍⠃⠸⠍⠁⠐⢲⢿⣷⠐⡤⠀⠀⠀⠉⣀⢠⢶⣶⡄⠀⠙⢷⢮⡁
⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⢦⠀⠴⠒⠒⠄⠀⠀⢲⡢⠀⠀⠀⢀⣀⡀⠄⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠛⢿⠃⠁⠈⢀⠀⠀⠀⠀⢘⠀⠙⠧⠁⠠⠤⢤⣘⠉⠄⠙⠉⠀⠀⢠⢿⠄⣤
⠀⠀⠀⠀⠐⠀⠉⢩⣐⣒⣠⡠⠀⠀⢀⣠⡾⠍⠀⢴⢤⣈⣁⡀⠟⠃⠀⠀⣀⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡍⠀⠀⠈⠀⢠⠀⠀⡀⠉⠙⠦⡈⠉⠘⣇⢰⣎⠉⢿⣥⠄⠄⢀⡄⢀⡏⠈⠀⠀
⠂⠀⠀⠀⠉⠈⠀⠀⠁⠀⠈⠉⠠⠶⠤⠈⡀⠀⡀⠌⠉⠙⠃⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣇⢰⣣⡖⠆⠀⠀⠀⠉⠀⠾⠋⠃⠶⣾⠋⠀⢬⡎⠟⠐⣶⡀⠀⠀⠈⠀⠁⠀⠀
⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⢀⣴⣶⣶⣶⣶⣶⢲⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡆⠾⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠠⠰⠆⠙⣧⣤⡴⠤⡄⢀⡀⠀
⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠠⠈⢁⣶⡿⣿⠟⠁⢩⣶⣶⠛⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⡧⣫⣽⣿⣿⣿⡟⢷⣶⣦⣼⣄⠐⠒⢲⠤⣤⢤⡄⡀⢂⡾⢦⣠⢤⢄⠀⠀⡀⠀⠐⠀⠀⠀⠀
⠀⠀⠀⠀⣉⣉⣀⠀⠀⢀⣀⣤⡴⣾⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⡙⡀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣷⣿⠟⠉⠻⣿⣿⣿⡇⢹⣿⣿⣶⡖⠛⠛⣭⣕⣶⣬⣽⡆⠀⠀⠛⣛⣪⣉⢀⣷⠦⣠⠬⠉⣲⡀⠨
⠀⠀⠀⠀⠀⠀⠉⠋⣽⣿⣿⣿⣇⣿⣿⣶⡆⠀⢠⣤⡀⠐⠛⣁⣰⣿⡇⢣⣠⡀⠀⠈⢿⣿⣿⣿⠃⠀⠀⣰⣿⣿⡏⠀⠀⠀⢹⣿⡟⣼⣿⠙⠋⠀⠀⠀⠀⠘⠛⣿⣿⣟⠃⢰⣀⣀⣀⡀⠈⠙⠳⡶⠿⠏⠈⣩⣹⡋
⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⠈⠉⢡⣤⣴⣿⣿⣿⡇⢸⣿⣿⣦⡀⠀⠙⢿⡅⠀⣠⣾⣿⣿⣿⠟⠀⠀⠀⢸⣿⢳⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡄⣾⠟⠻⠯⣟⣀⣀⠐⠃⠀⠀⠀⢴⣤⠤
⠈⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢸⣿⣿⡏⠉⢉⣴⣤⠘⠛⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⣄⡀⠈⠰⠟⠛⠋⠉⠀⠀⠀⣠⣴⣿⡏⣾⣿⣿⣿⡇⠀⢠⣄⡀⠀⠀⣄⣼⣿⡇⣿⣿⣶⣦⣌⣽⡯⠀⢠⠀⠀⠀⠬⠛⠛
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⣿⣿⣿⣷⣤⠈⠛⠛⣀⣀⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢁⣿⣿⣿⣿⣷⣦⠈⠙⢃⣀⣰⣿⣿⣿⡇⣿⣿⣿⣿⣿⣟⠳⣴⣿⣖⣀⢀⣘⠯⠤
⠴⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⠃⣿⣿⣿⠉⠉⢀⣀⠸⠿⢿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⠉⠙⣠⣄⠘⠻⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⢿⢉⡽⠉⡍⠉⣛⣒
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢀⣿⣿⣧⢀⠀⠿⠿⠀⠀⣼⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⣤⡄⠛⠿⠀⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣸⣿⣿⣾⣉⠉⠓⠋⠀
⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢹⣿⣿⣿⡿⢀⣿⣿⣿⣿⡟⠻⠇⠀⠀⣼⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠉⠋⠉⠁⢈⡍⠉⢙⣂
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⡀⠀⣼⣿⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⠇⣸⣿⣿⣿⣿⠃⠀⠘⢿⡇⠀⠈⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⢀⡀⠀⡆⠀⠀⣠⣖
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠇⠀⠉⠁⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⠇⢠⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣦⣴⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣟⣁⣠⠄⠀⠠⡈⣋⠟
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⡏⣀⣀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⡏⠀⢐⣶⣶⠈⠉⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠿⠿⢯⣶⡄⣀⣉⢉⡉
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣇⠛⠿⠿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠉⠀⣴⣿⣿⣿⣿⣿⠀⣿⣿⠿⠟⠛⠿⢶⠤⠤⠀⠀⠙⠀⠀⠀
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⣄⣀⣀⡀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿
⠀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠅⠀⠙⠛⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡏⠉⠛⠿⠷⣄⡙⠻⠛⠃⠿⠿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⣘⣿
⢤⣿⣿⣿⣿⣿⣿⣿⠍⢘⡛⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣶⣶⣦⣤⣴⠀⢀⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⠇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣚⠫⣷⣼⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠀⢸⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣿⣌⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣧⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⢛
⣿⣿⣿⠛⠻⠛⠀⠀⠀⠀⠙⠛⠻⡟⠛⠛⠟⠇⠀⠀⠀⠉⠙⠛⠛⠛⠛⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⠛⠛⠻⠟⠀⠘⣿⠟⠛⠀⠘⢿⠛⢻⠛⠛⠿⢿⣿⠀⣿⣿⣿⣧⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢀⠀⠀⠀⠀⣶⣿⢏⠀⠀⠀⠀⠀⣀⣿⣯⠀⠰⠀⠀⠀⠀⣿⠀⠀⡆⠀⠈⠀⠈⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣯⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠓⠀⠀⢀⣱⣿⠀⠀⠓⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠋⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣠⣄⠀⠀⠀⢧⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠈⠀⢘⠀⠀⠈⣹⣿⠀⠀⣄⠀⠁⣀⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⡇⠀⡄⠀⢠⠀⠀⠀⢀⠛⠙⠛⢻⣿⣿⣿⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⠁⠀⠀⠀⠁⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡿⠀⢠⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠃⠀⠰⠛⢸⣿⣿⠏⠀⠀⠀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣤
⠲⠾⠷⠀⠀⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠤⠒⡀⠛⠆⡠⣄⠀⠀⠙⠈⢁⣆⠀⠀⠀⠰⠤⠄⠁⠀⣀⣼⡇⠀⢳⢂⡀⠀⠀⠀⣿⠀⡄⠀⢀⣆⣶⡶⠀⠑⡶⠿⣿⡿⣿⣀⣠⣝⢓⡠⠴⠚
⠀⡠⠀⠀⠎⠃⠀⠀⠀⠠⠤⠀⣀⠠⠄⠂⠙⠧⠄⠀⠀⠠⠄⠂⣠⡤⠧⢲⠄⡒⠇⠀⠀⠁⠀⣖⠀⠀⡘⠃⠲⠶⠦⠀⠀⢀⠀⠀⠴⠗⠀⠃⢰⣆⢀⣶⢼⡿⠋⠀⣤⣿⣤⣴⠀⠀⠘⠀⠀⠀⠉⢹⠟⠛⠛⠓⠊⠈
⠛⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣶⡄⠈⠉⠁⣀⠀⠤⠀⡴⠛⠀⠀⠀⠆⠀⠸⡮⣿⣉⣤⣤⣴⣴⣦⣤⣄⡀⠿⠄⠀⠐⢈⠀⣞⡿⠁⡿⠏⢓⣸⢣⠀⠈⠁⠁⡀⠀⢠⣴⠂⠀⠸⠒⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⡆⠀⢀⣠⣆⢠⣤⣷⠄⠀⣶⣡⠄⢸⣿⣧⠀⠀⢄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡤⢶⠺⣨⣥⣷⣔⡃⠀⡾⣿⠆⠀⠀⠤⠀⠸⠁⢸⣍⠡⠤⣸⡇⣶⠄⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠄⠀⢠⣴⣾⠿⠾⢿⣿⣿⠋⠍⠳⣀⣚⡏⡀⠀⠈⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠯⠄⢈⡉⠀⠀⡬⠔⠛⣆⣺⠛⠷⠂⠈⠀⣷⣲⣿⣷⣻⢀⡁⠘⠓⠀⠀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣶⠛⠻⠧⢤⠤⠌⠉⢹⢍⣅⣼⠼⠴⣶⣿⣿⣿⠿⠿⠍⠛⢿⣿⣿⣿⠿⠟⠛⣛⣿⣿⣷⡀⣀⣀⣤⠁⠀⢘⠂⣠⣀⠀⠀⠉⠐⠚⠀⠉⠁⡾⣠⠌⢛⣿⡿⣟⢤⣧⣶⣤
⠀⠀⠤⠄⢀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠿⣶⡦⠄⢀⣀⠀⡀⠷⡈⠉⠀⠀⣀⢸⣿⣿⣫⣤⡶⠤⠀⣠⣾⣿⣿⣿⡀⠀⣀⢈⡙⢻⣿⣷⠈⠁⠀⠀⠀⠋⠈⠁⠉⡀⠂⢀⠀⠈⠁⠀⠀⠈⣹⣭⣅⡤⢲⣮⡽⣿⣟⣙
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⢀⠉⡉⠀⡧⠅⠀⢸⡄⠀⠒⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠿⣿⣿⣟⣛⣿⣶⣿⣿⣇⠀⠀⠀⢀⣔⠀⠳⢶⣙⣉⣿⣾⡏⠁⢀⣀⣾⣫⣿⣿⣿⢿⣷⢾⣿⠛⣯
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⣀⠀⢀⠀⣀⣀⠐⠀⠀⠂⢀⡤⢤⠄⠀⠀⢰⣿⣿⣿⣿⣿⠟⣿⣿⣤⣄⣀⣀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠄⢉⣭⣷⠆⠠⣬⢴⣿⣷⣋⣉⠁⠀⠹⠼⠞⠈⠁⡐⠁⠀⠀⠰⣤
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠐⣿⣕⣛⣹⣿⡿⠓⠀⠀⢀⢀⠉⠰⠿⠂⠄⠀⣺⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣖⠟⢁⠐⡾⠉⠛⠋⢀⣛⠋⠀⠐⡂⠑⠒⠠⣥⡀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⣠⡄⠀⠸⠻⠃⠄⠀⠄⢸⡦⠀⠄⣠⡶⢸⣿⣿⣿⣿⣷⣿⣿⣯⣥⣤⣤⣤⣤⣈⡛⢿⣿⣦⣿⣿⣿⣿⣿⠀⠀⠀⢹⣙⡁⠈⡀⠁⠀⠠⠄⠀⡉⠳⣶⣆⡧⣵⠈⢁⣄⣉⣃⣄⢼⣾
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠀⠀⠦⠤⢍⠀⠒⠽⢯⠀⠴⠞⠂⠀⠀⠤⡃⠀⠀⢉⠿⠿⠋⠨⣿
⠀⠀⠀⠀⠁⠠⢀⠀⢀⠀⠀⠀⠀⠰⢢⣟⡴⠀⠋⠠⢤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢀⢀⡄⢶⣂⣀⠀⠀⢶⠒⠀⠀⠀⠀⢤⣶⠆⠀⠀⠀⠈⣴⠲⠀⣲⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠃⠀⠈⠛⠟⣿⣿⣿⣿⣿⣿⡟⠛⡀⠂⠨⠥⠀⠀⠻⢿⣗⠠⡆⠀⠀⠀⢠⡠⢐⣶⣦⠀⠀⠙⣷⢧⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠆⠀⠖⠒⠒⠀⠀⣀⡒⠀⠀⣀⢀⣀⣄⠀⠂⠀⠈⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢿⣿⠛⠿⠀⠁⠀⠀⠀⠀⡄⠀⢀⠀⠉⠂⠀⠒⠆⣤⡀⠐⠄⠉⠑⠀⠀⡴⣳⠨⠦
⠀⠀⠀⠀⠀⠀⠈⣥⣽⣅⣠⡄⠀⠀⢀⣴⠿⠅⠀⣶⣦⣄⣀⠀⠋⠁⠀⢀⣰⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣯⠁⠀⠀⠂⠀⡄⠀⢀⡀⠙⢛⢲⡈⠉⢘⣄⠰⡉⠀⡿⠶⠈⠄⠤⠄⢠⠁⠈⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠬⠞⠤⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣇⢼⣴⠒⠢⠄⠀⠀⠀⠀⠾⠉⠃⠲⠾⠁⠀⠵⠝⠇⠰⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠤⠀⠀⠀⠀⣠⡀⠀⠀⠐⠀⠀⠀⢠⣾⣿⣿⣿⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠄⣾⣿⣿⣿⣿⡀⠛⠐⠒⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⡶⠂⠖⠒⠀⠹⢤⣤⠶⠦⠄⣀⡀⠀
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠠⠉⢹⣾⡿⠿⠃⠀⠸⠿⠟⢉⣿⣿⣿⣿⠿⠟⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣂⣡⣿⣿⣿⣿⠙⣿⣷⡶⠿⢄⣐⠊⡶⠶⠦⢤⡤⠄⣩⠿⢦⡤⣤⣄⠀⠀⠀⠀⠐⡀⠀⠀⠀
⠀⠀⠀⠀⠍⢄⣀⠀⢀⣀⣠⣤⣏⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⢰⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠋⠉⠻⣿⣿⡿⢀⣿⣿⣿⢿⠏⠉⠋⣭⣵⣶⣦⣽⠂⠀⠀⠋⣉⢪⣉⣘⡷⠂⡤⢌⢍⣳⡀⣚
⠀⠀⠀⠀⠀⠀⠍⢁⣿⣿⣿⣿⢸⣿⣿⣿⡀⠀⢤⣤⡄⠘⢋⣤⣼⣿⠀⣦⣤⡀⠀⠈⢻⣿⣿⡟⠀⠀⢀⣾⣿⣿⡁⠀⠀⠀⣿⣿⢣⣿⡏⠉⠁⠀⠀⠂⠀⠉⢹⣿⣿⡟⠀⣧⣤⣀⣤⡀⠀⠙⢳⠚⠻⠯⠈⠤⣸⣐
⢀⠀⠀⠈⠀⠀⢀⣾⣿⣿⣿⡟⣾⣿⣿⣿⣿⡿⠀⠀⣴⣤⣾⣿⣿⣿⠃⣿⣿⣿⣦⡀⠀⠙⠻⡄⢀⣴⣿⣿⣿⡿⠃⠀⠀⠀⣿⡟⣾⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢠⣟⡉⠻⠧⣁⣤⣄⠘⠁⠀⠤⠀⣶⣄⣒
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⢸⣶⡆⠉⢙⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣷⣤⡀⠀⠚⠋⠉⠉⠀⠀⠀⢀⣴⣾⣿⢰⣿⣿⣿⣿⠀⠀⢠⡄⠀⠀⢠⣤⣿⣿⢸⣿⣿⣷⣶⣬⣿⠏⠀⠶⠐⠀⠀⢛⣛⠙
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢡⣿⣿⣿⣶⡆⠀⠉⢡⣤⣼⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⣸⣿⣿⣿⣿⣶⡆⠈⠉⢀⣄⣼⣿⣿⣿⢸⣿⣿⣿⣿⣿⣟⣳⣾⣷⣦⣀⣀⣙⣓⢶
⠒⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⣠⡄⠛⠛⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇⠉⢡⣤⣤⠘⠻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿⠏⢩⠿⣉⡉⢈⣵⣒
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣇⢀⠀⠛⠃⣀⣀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣧⣤⠈⠛⠋⣀⣀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣧⣾⣿⣿⣯⣭⠙⣛⠁⠐
⣄⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⣾⣿⡿⠃⠀⢀⡀⠰⠿⢿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢻⣿⣿⣿⠃⣼⣿⣿⣿⣿⠉⠙⢀⣀⠰⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠘⠉⠉⠁⢠⠏⠉⠁⠒
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇⣀⡰⢿⣳⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⣿⠏⢠⣿⣿⣿⣿⣇⢀⠀⠘⠿⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣤⠀⠄⢰⠆⠀⠀⣬⣭
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⡏⢀⣾⣿⣿⣿⣿⡿⠸⠁⠀⠀⣶⣶⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣩⣤⠤⠄⠀⠠⣉⡋⠛
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⢠⣤⣤⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣀⠀⢼⣷⡆⠁⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠻⠿⣽⠤⠤⣀⡍⠉⢉
⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣌⣙⠛⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⣴⣾⣿⣿⣿⣿⡇⣸⣿⣿⠿⠟⠛⠿⢶⠂⠂⠀⠀⠉⠀⠀⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣤⣄⣤⢸⣿⣿⣿⣿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⡟
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠃⠀⠀⠙⠛⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣏⠀⣉⣙⡛⠧⢌⠙⠋⠉⠘⠛⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⣷
⢴⣿⣿⣿⣿⣿⣿⡿⠍⢟⠻⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣶⣶⣶⡆⠀⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣀⢄⣴⣶⣶⣾⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣈⡉⠉⠉⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠇⠀⠀⢠⣾⣿⣯⣿⣿⣿⢝⣒⠻⣷⡼⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣶⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠏⠀⢀⣴⣿⣿⣿⣿⣿⡇⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⢛
⣿⣿⣿⠛⠻⠛⠒⠀⠀⠈⠛⠛⠻⡟⠛⠛⠃⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠻⣿⣿⠛⠛⠻⠀⠀⠛⣿⠟⠃⠀⠛⢿⠛⢻⠛⠿⠿⠟⠃⣼⣿⣿⣿⣇⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⢀⠀⠀⠀⠀⡶⢟⡄⠀⠀⠀⠀⠀⣀⣿⣿⠀⠰⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣎⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠀⠀⣀⣿⡇⠀⠀⠷⠄⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣠⣄⠀⠀⢀⡇⠀⠁⢀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⠉⣿⡇⠀⠀⣄⠀⠁⣀⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⡆⠀⣄⠀⢸⠀⠀⠀⠀⠀⣀⠈⣿⣿⣿⠁⠠⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠛⣿⡟⠁⠀⠀⠉⢸⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⡎⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠁⠀⠘⠁⣠⣿⣿⡏⠀⠀⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣤
⠛⠛⠃⠀⣄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘⠁⠚⠡⠈⠛⢠⠲⠤⢈⠉⠉⠁⠮⠄⣀⡀⡀⠷⠒⡉⠀⠠⠤⠿⠆⠉⢝⠤⢀⡀⠀⠸⣇⣰⡆⠀⢸⡾⠿⡟⠀⠩⡟⠻⠿⢻⣿⣤⣼⣏⣥⡚⣋⢉
⢀⠀⠀⠐⠈⠀⠀⠀⠀⠂⠀⠠⡄⠒⢂⣉⠛⠖⠠⢄⢀⠒⠉⠠⠶⠞⢓⡆⢬⠙⠀⠀⢀⡀⣼⡧⠤⠀⠉⠉⠛⠓⠒⠀⢂⣠⠀⠀⠛⢃⠈⣀⣿⠇⣸⣖⢿⣏⡈⠀⣯⣷⠶⡷⠀⠀⡉⠀⠀⠀⠈⠽⠋⠉⠉⠋⠁⠌
⠉⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠶⢷⠂⠀⠀⢠⡤⠐⠂⢠⠏⠁⡀⢀⠄⠀⠀⢿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣦⣟⠻⠀⠀⠉⡄⣔⢽⡏⢰⠟⠈⣡⡾⡔⠀⠁⠀⢠⣁⠀⣶⣟⡀⠀⢚⡁⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠿⠀⠀⣴⣼⣄⣴⣾⣷⠀⠸⣧⡴⠀⢿⣿⡆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠾⠳⢟⣴⣾⠿⣽⣁⠼⠿⡟⠀⠀⠀⣀⣀⠋⠀⡾⢇⡐⢶⣿⡙⡗⢀⡀⣠⠄⠀⠘
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠴⠶⠿⢻⠿⣿⠿⠏⠉⠈⢢⣤⣽⠇⡀⠀⠉⢠⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠐⠒⠀⣤⠄⢠⢲⠓⠋⠙⣥⣿⠙⠉⢁⣁⠰⣿⠿⣿⣷⣇⣤⡀⢘⠁⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡼⠟⠙⠻⠶⠶⠖⠀⠈⣟⣹⠴⠇⠓⣾⣿⣿⠟⢉⠉⠑⠀⣹⣿⣿⣿⠉⠀⠀⠲⢿⣿⣿⣆⢀⣠⠤⡖⠀⢀⣍⣀⢤⡀⠠⠀⠀⠙⢉⡀⠈⠈⣇⣔⣈⠹⠿⠿⣏⣼⣾⣶⣶
⠀⠰⠆⠀⡀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠘⠻⡿⠶⢀⣠⣄⢀⢘⠧⠁⢀⠀⠠⢴⣿⣿⣷⣿⣿⣭⣥⣶⣿⣿⣿⣿⣦⣤⠶⣤⣦⣈⣿⣿⡄⠀⠀⠀⠀⠈⠁⢁⠀⢀⣈⣀⡀⠀⣀⠀⠀⠄⢀⡿⣶⣤⣆⣾⢶⣿⣿⣭⣽
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⣀⠈⠂⠸⠦⠀⠀⠵⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠈⠙⣿⣿⣶⣾⣿⣿⣿⣷⠀⠄⠀⠀⣤⣆⠈⠚⠧⠥⢼⣷⠿⣍⣀⡤⢴⣿⡿⡿⣿⠿⢿⡿⠿⠟⠱⠦
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣀⢄⢀⣄⣀⣤⡄⠀⠀⠈⢀⡥⢶⡖⠀⠀⢀⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⣶⣶⣦⣴⣿⡟⣿⣿⣿⣿⣿⣿⠀⠒⠖⢂⠴⣺⣗⠂⠲⣖⣺⣿⣯⣬⣤⡀⠀⠵⢚⠃⠘⢠⠉⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠈⢀⡛⠿⣏⣭⡻⣿⢛⠁⠀⠀⠀⡀⠁⠛⠋⡤⠀⣸⣿⣿⣿⣿⣠⣾⣿⠟⠛⠋⠙⠋⠛⠿⣿⣷⣌⣿⣿⣿⣿⣿⠀⠀⠀⢐⣾⣮⠃⡀⢹⠓⠉⠉⠁⠬⣍⠃⠀⢉⡏⡙⠋⡢⢤⣀⠀⠀⣠⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠶⠄⠀⠚⠋⠠⠀⠤⠀⠵⠆⠀⢠⢶⢓⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣛⡛⠶⢶⣬⣿⣿⣿⣿⣿⣿⣿⣦⠈⠈⠁⠥⡥⢀⡠⠀⢀⣂⡒⠀⠠⡈⣹⢾⠭⢵⡾⠀⢰⣤⣬⣴⣴⢾⣿
⠀⠀⠀⢀⠠⠀⠀⠀⠀⠈⠀⠀⠉⠀⢠⡤⠄⠈⡠⠀⠀⠀⠀⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠐⠒⠒⠄⠈⠉⡞⠇⠀⠚⢍⠁⠀⠠⠨⠄⠀⠀⡼⠛⠋⠀⠺⡿
⠀⠀⠀⠀⠀⠂⠈⠀⡤⠀⠀⠀⠀⠚⣸⠭⠒⠈⠁⠂⡥⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠏⠙⢿⡿⢿⣿⣿⣿⣿⣿⣿⣄⣄⣴⠘⣯⡥⠄⠀⢈⣿⠁⠀⠀⠀⠘⠼⡿⠁⠀⠀⠀⠰⢖⣓⢀⡿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⢻⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⣿⡇⢈⠱⠌⠀⠓⠂⠀⠈⡟⢿⣇⢱⠂⠀⠀⠂⡠⠀⢟⣿⠖⠀⠀⢹⡞⡆⠈
⠀⠀⠀⠀⠀⠀⣈⡀⠀⠘⠂⠐⠋⠉⠁⢀⣀⡸⠏⠀⢀⣀⠠⢤⣦⠀⠀⠀⣸⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣏⡿⢃⠈⠁⣀⠀⠀⠄⠀⢐⣀⣀⠄⢀⡙⣀⠀⢙⣦⢦⡄⠐⡀⠀⠀⠀⢠⠯⡇⠐⠦
⠀⠀⠀⢀⡀⠀⠠⢦⠭⠥⣦⡂⠀⠀⠤⡾⠓⠀⠰⣷⣶⣤⠠⠘⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⡇⠀⢀⠌⠀⠀⠆⠀⢠⡄⠉⣉⣣⠀⠀⣹⠤⢿⠄⣸⡓⢃⠘⠀⠶⠀⣎⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠚⠛⠄⣤⣀⣡⣀⣀⣀⣉⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⣿⣿⡆⠧⡾⠉⠀⠀⠀⠀⠀⠈⠋⠈⠘⠛⠃⠀⠐⠛⠘⠀⢹⣦⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⢄⠦⠀⠀⠀⠉⠀⣀⢀⣺⣿⣿⠟⠛⣏⣁⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣰⣮⣄⡙⣻⣿⣿⣿⡷⣮⣅⡉⠃⡀⠈⠀⡀⠀⠀⠀⠀⠀⢀⣘⡏⠀⠋⠙⠀⠱⠶⠾⠛⠒⠠⠤⠀⠀
⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠂⣀⣾⣿⠉⠉⠀⠀⠙⠛⠀⣼⣿⣿⣿⠋⠉⠀⠘⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣾⣿⡵⠞⠻⣿⣿⣿⡇⢸⣿⣿⣭⣥⠶⠮⣍⠛⣶⣖⣶⡐⠠⠞⢛⣶⡖⣖⡄⢀⡤⠀⠀⣁⣀⡠⠀⠀
⠀⠀⠀⠠⠰⢤⣄⡀⣤⣴⣶⣿⢸⣿⣧⣄⠀⠀⠀⠀⠀⣼⠿⠋⣽⣿⠠⠀⠀⠀⠈⢻⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⠃⠀⠀⠘⣿⣿⢡⣾⠿⠿⠉⠁⠀⠀⠸⠿⣿⣿⡿⠏⢀⠀⠈⠡⠬⠢⢤⣽⠛⢰⣖⡴⡬⠧⢨⠤
⠀⠀⠀⢀⠀⠐⠈⣸⣿⣿⣿⡏⣿⣿⣿⣿⣤⡄⠛⠛⠀⠀⣰⣶⣿⣿⠀⣿⣷⣦⡀⠀⠙⢿⣟⠀⠀⣠⣾⣿⣿⣿⡆⠀⠀⠀⣿⣏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡄⣿⣷⣤⣤⢤⡀⠀⠉⣹⠉⠛⠂⠠⠦⠇⢵
⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⣿⣿⣿⠟⠛⢃⣀⡀⠿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣦⣄⠀⠉⠂⣼⠿⠿⠟⠋⠁⠀⠀⣀⣼⡿⢸⣿⣿⣿⡆⠀⠀⣀⡀⠀⠀⣀⣸⣿⡇⣿⣿⣯⣟⡚⣴⣶⡄⠈⠀⠐⠂⢘⣷⣦⣱
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢁⣿⣿⣿⣀⡀⠼⠿⠇⠀⢸⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⣾⣿⣿⣿⣧⣄⡀⠛⠃⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⡾⣟⠀⢀⡃⠁⠀⢈⣩⠌⠱
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢸⣿⣿⡿⠿⠇⠀⠀⣸⣷⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⣿⣿⣿⣿⠛⠛⢃⣀⠀⢿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣩⡿⣿⣿⣤⣤⣤⣈⡑⣿
⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢸⣿⣿⡇⠀⢠⣶⡆⠀⠀⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣄⣀⠸⠿⠇⠀⢸⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⡿⣛⣂⣼⣣⣄⢄⣼⠿⠉
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⡔⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⢿⣿⣿⣿⠁⣼⣿⣿⣿⣿⠿⠿⠀⠀⢸⣿⣾⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⡷⣿⣿⣿⠶⣆⣨⣅⡀⠅
⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⣿⣿⡟⠀⢀⣴⣤⠈⠉⢹⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡏⢀⣿⣿⣿⣿⡇⠀⠀⣿⣶⠀⠉⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠞⠀⠄⢈⣉
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⣶⠚⠛⠛⢤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⡿⠁⣼⣿⣿⣿⣿⣿⣿⠂⠀⠀⣤⣤⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⡦⠠⠄⠛⠀⢀⣰⢶⣾
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠃⣸⣿⣿⣿⣿⣿⠁⠈⣶⣦⡔⠛⢻⣿⣿⣿⣿⡇⣹⣿⣿⣿⣿⣿⣿⣶⣖⣒⠂⠈⠰⢬⣬⠉
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⠐⢿⣷⡶⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡦⠉⠉⠁⣠⣼⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⡏⠙⠻⠟⠓⢢⡤⠀⠂⠤
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢁⣀⠀⢀⢹⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⠟⠛⠿⠿⠋⠀⠀⠀⠀⣀⣠⣀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⠀⠙⠿⠿⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠛⠻⠿⢿⣇⠈⠿⠿⠟⠸⠿⢿⣿⣿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⠉
⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠀⣶⣾⣷⣶⣯⣤⣤⣤⡄⠀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⣄⣟⠷
⢺⣿⣿⣿⣿⣿⣿⣧⡌⢈⠻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⠿⠛⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⢄⣴⣶⣶⣾⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⡄⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣒⠻⣷⡼⣯⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⣼⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣿⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⡾⠿⠇⠀⢰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠉⠛⠛⠛
⣿⣿⣿⠛⠻⠓⠒⠒⠂⠀⠉⠉⠛⠛⠛⠟⠿⠿⠶⢤⠀⠀⠀⠀⠘⠛⠛⣿⢇⠀⠀⠞⠛⠛⢿⣿⣿⠛⠛⠻⠇⠀⠛⣿⠿⠛⠀⠛⠛⠛⠛⠛⠉⠉⠉⢡⣾⣿⣿⣿⣧⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢰⠀⠀⠀⠀⠖⣡⣿⠀⠀⠀⠀⠀⣀⣿⡟⠀⠐⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠀⠀⣤⣿⡿⠀⠀⠷⠄⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠟⠛⠻⣿⣿⣿⡏⠀⠻⣿⣿⣻⣯⣿⣿⣿⣿⣯⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣠⣄⠀⠀⢀⡇⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⡇⠀⠀⢀⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠉⠀⠀⡇⠀⣆⠀⠸⠀⠀⠀⠀⠀⡴⠂⣿⣿⣿⠁⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠛⣿⡟⠁⠀⠀⠀⣸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠐⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠇⠀⠀⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣤
⠟⠛⠂⠐⣠⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠄⠀⠀⠀⠀⠛⠐⠚⠀⠙⠛⢰⠲⠤⣈⠉⠉⠁⡯⢀⣀⠀⡸⠓⢚⡀⠀⠠⠼⠿⢀⠉⣏⠤⣀⠀⠀⠼⣧⣴⡀⠈⣼⡾⢿⠃⠈⢹⡛⠻⠿⢿⣷⣤⣾⣭⣧⡟⡉⣩
⢀⠀⠀⠜⠋⠀⠀⠀⠀⠂⠆⠠⠤⠒⣊⡍⠻⠶⠤⣀⢀⠂⠈⠠⠶⠞⢢⡇⠬⠛⠀⠀⢁⠀⣽⡥⠤⠄⠉⠈⠛⠛⠂⠐⢀⡄⠀⠐⡟⡁⠀⣀⣿⢇⣾⣖⢿⣡⠁⠵⣿⣿⠿⠇⠀⣠⠁⠀⠀⡀⠀⡟⠉⠉⠉⠉⠀⠈
⠉⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠾⠷⠀⠀⠀⢠⠄⠐⠂⢸⠋⠁⣀⣀⠔⠂⠈⢿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣮⣟⠧⠀⠀⠁⡄⣺⢼⡇⣸⠋⠈⣤⣟⡇⠀⠀⠀⣢⣉⠀⣷⣟⠠⠀⣫⠁⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢿⣀⡀⣴⣿⣤⣶⣾⣧⠀⠼⣧⡖⠀⣿⣿⡆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠿⠛⡻⢶⡾⠿⣭⣅⢸⠻⡏⣀⡀⠒⣂⣀⠁⠀⡿⠇⠒⣦⣿⢿⡗⢀⠀⣰⡀⠀⢘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠾⠿⠟⢻⣻⣿⠿⠏⠘⠉⣦⣼⣽⠤⡀⠀⠉⣠⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠀⠙⠒⢀⡬⠅⣀⡸⠒⠉⠹⡼⠏⠛⡋⢨⣉⢾⡿⠿⣿⣿⣗⣤⡀⠋⠁⠀⠀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡾⠏⠙⠻⠶⠶⠢⠀⠈⣏⡽⠴⠇⠓⣿⣿⣿⠟⣉⠉⠁⠀⣹⣿⣿⣿⠉⠀⠀⠒⢿⣿⣿⡄⢠⡤⢴⠇⠀⢠⡉⣠⢦⣀⠀⠀⠀⠉⣁⡀⠀⢘⣣⣖⡉⠿⠿⠿⣱⣷⣾⣷⣶
⠀⠰⠖⢀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠘⠻⡿⠶⢀⣤⡄⣠⣙⠧⠀⡀⠀⠤⢤⣿⣿⣷⣿⣿⣿⣭⣾⣿⣿⣿⣿⣦⣤⠶⣴⣦⣜⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⠀⣠⢈⣠⡄⣁⣀⠀⠀⠊⣨⣿⣶⣴⣜⣿⣾⣿⣿⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⢀⠸⠂⠸⠆⠀⠀⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠙⣿⣿⣶⣾⣿⣿⣿⣧⠀⠀⠀⢠⣶⣀⠉⠛⠧⡧⣿⣿⢿⣅⣠⡤⢾⡿⡿⡿⡿⠿⣿⠟⠿⠟⠹⠗
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⣠⣄⣀⣄⣠⣤⠄⠉⠀⠈⢀⡥⢶⡖⠀⠀⢠⣿⣿⣿⣿⡟⢩⣿⣿⣿⣿⣿⣾⣶⣶⣿⡟⣿⣿⣿⣿⣿⣿⠀⠓⠒⢀⢴⢿⣇⠐⢶⣞⣿⣿⡧⣤⣄⡀⠀⠗⢻⢃⠙⢨⠁⠀⠀⠒⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣈⡻⠷⢯⣭⠿⡿⣛⠁⠀⠀⠀⡀⠁⠛⠋⡴⠀⣾⣿⣿⣿⣿⣴⣿⡿⠛⣉⣉⠉⠉⠛⠻⣿⣿⣌⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⡝⠃⡄⢻⠃⠈⠉⠠⢬⣏⠁⠈⣹⣫⣛⣑⡲⢦⣀⠀⠀⣌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠶⠀⠀⠛⠋⠐⠀⠀⠀⠷⠂⠐⠤⢾⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣝⡛⠻⣶⣤⣿⣿⣿⣿⣿⣿⣿⣦⠈⠀⠠⠧⠥⢀⣥⠀⢑⢐⡒⠀⢬⡈⠿⠿⠽⢾⠆⠈⢶⣤⣧⣶⣴⢿⣿
⠀⠀⠀⢀⠤⠀⠀⠀⠀⠈⠀⠀⠁⠀⣠⠤⠄⢈⡤⠀⠀⠀⠀⠠⠀⠈⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠃⠀⠘⠛⠲⠆⠈⠙⠟⠇⠐⠛⢍⠁⠀⠰⠯⠄⠀⠠⡟⠛⠃⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢀⠀⠀⠛⣿⡵⠃⠈⠁⠒⠤⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣄⡶⠸⣿⠶⠆⣀⣹⡏⢁⠂⠀⠀⠳⢾⠟⠀⠀⠀⠀⠰⢏⣃⢨⠿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠉⠉⣻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡿⣿⠇⢈⠡⠁⠀⠒⠂⠀⠸⠛⢿⣍⠺⠀⠀⠀⢂⢤⠪⢿⣿⠆⠀⠀⣹⠛⡆⠉
⠀⠀⠀⠀⠀⢀⣈⡀⡀⢘⠀⠘⠉⠉⠀⢀⣀⠼⠏⠀⢠⡄⠠⢴⣄⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⢀⠉⠀⡁⠀⠐⠂⠀⢰⣀⡀⠄⣀⡉⡀⠈⣉⡱⢦⡀⠁⡀⠀⠀⠀⢰⢻⡖⠚⠢
⠀⠀⠀⢈⠀⠀⠰⠶⠯⠤⣶⡀⡀⡀⠴⡟⠓⠀⠸⣷⣦⡄⠤⠘⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡇⠀⣀⠀⠀⠰⠀⠀⢤⠀⠉⣍⣧⠀⢀⣷⠄⢳⢀⣹⠛⣃⠑⠐⠒⢠⠇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠚⠓⢂⣤⣤⣥⣄⣤⣄⣥⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⡠⠠⣺⣿⣿⣿⣿⡔⢳⡏⠙⠐⠀⠀⠀⡀⠘⠁⠈⠉⠛⠃⠀⠘⠃⠋⡀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⢠⠦⠀⠀⠀⠁⢀⣀⣀⣾⣿⣿⠛⠛⣯⣉⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢨⣿⡞⠝⣻⣿⣿⣿⡷⣬⣅⡉⢃⡄⠁⠀⡀⠀⠀⠀⠀⠀⢀⣸⡋⠘⠉⠃⠈⠳⠶⠞⠛⠒⠠⠤⠀⠀
⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠂⣤⣿⡿⠉⠉⠀⠀⠉⠉⢀⣾⣿⣿⡟⠏⠁⠀⠹⣿⣿⣿⣿⣿⣿⡆⠀⠀⢐⣿⣿⡾⠋⠻⣿⣿⣿⡇⢻⣿⣿⣭⡥⠳⠿⣘⣻⣿⣶⣷⡐⠐⠚⣻⣶⡻⣶⠄⣠⡆⠀⠀⠡⣀⠀⠀⠀
⠀⠀⠀⠠⠰⢠⣄⢀⣤⣶⣾⣿⣹⣿⣧⣤⠀⠀⠀⠀⠀⡾⠟⠉⣾⣇⢃⢀⠀⠀⠈⢿⣿⣿⣿⡟⠀⠀⢀⣾⣿⣟⠁⠀⠀⠘⣿⡿⣰⣾⠛⠛⠉⠀⠀⠀⠛⠿⣿⣿⡿⠃⣀⠀⠈⠠⠜⠢⢤⣽⠋⣶⣒⡶⡼⠧⠭⠍
⠀⠀⠀⣀⠀⠐⢀⣼⣿⣿⣿⡇⣿⣿⣿⣷⣤⡄⠛⠛⣀⣀⣾⣿⣿⣿⠈⣿⣿⣦⡀⠀⠙⢿⣏⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⢰⣿⢧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⣿⣷⣶⣶⢦⠀⠀⠉⡟⠉⠓⠀⠐⠻⠧⠭
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠇⣿⣿⣿⠛⠛⣃⣀⡀⠿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣦⣄⡀⠈⠀⠾⠻⠛⠋⠉⠀⠀⢀⣤⣾⡟⣸⣿⣿⣿⡇⠀⠀⣀⡀⠀⠀⣀⣿⣿⡆⣿⣿⣯⣟⡚⢶⣶⠀⠀⠀⠐⠂⢸⣿⣭⡥
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢸⣿⣿⣿⣀⡀⠻⠿⡃⠀⣸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠃⣿⣿⣿⣿⣧⣤⠈⠛⢃⣀⢰⣿⣿⣿⡇⣿⣿⣿⣿⣿⣶⣟⠀⣸⡃⠁⠀⢨⡥⠄⠰
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢸⣿⣿⡟⠛⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⢠⣿⣿⣿⣿⠋⠛⢀⣀⡸⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣦⡤⠤⢭⣍⣿
⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⠀⠸⣿⠇⠀⢰⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣄⣀⠻⠿⠃⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⣻⣠⣞⣠⠤⣀⣶⠖⠋
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠡⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⣿⣿⠀⣿⣿⣿⣿⡟⠻⠏⠀⠀⢾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠸⣿⢿⡿⠶⢆⣭⣄⡀⠀
⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⢇⣿⣿⡇⠀⢠⣶⣆⠈⠁⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⠇⢸⣿⣿⣿⣿⡇⠀⠐⣿⡇⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⠀⠎⠀⠀⣀⣤
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⡷⠈⠉⠑⢲⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⠟⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣶⣶⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡦⠦⠄⠗⠀⠠⡼⢷⣶
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢀⣾⣿⣿⣿⣿⣿⠀⢀⣶⣶⠎⠉⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣒⠀⠈⠢⢼⡭⠍
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣧⠘⠿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣉⠉⠹⠋⠓⢢⠔⠐⠂⠐
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠏⣤⣀⣀⣀⢹⣿⣿⣿⣿⡏⢠⣿⣿⣿⡿⠟⠛⠛⠏⠉⠀⠀⠀⠀⣠⣤⣤
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠏⠀⠉⠻⠟⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡏⠉⠙⠛⠿⢤⡘⠛⠛⠃⠾⠿⣿⣿⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣿⠉
⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣶⣶⣶⣶⠄⢀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣜⣛⢶
⢺⣿⣿⣿⣿⣿⣿⣏⡔⠈⠻⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣀⣄⣴⣶⣶⣾⣿⣿⣷
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡆⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢼⣿⠇⠀⠀⢀⡾⣿⣯⣿⣿⣿⢝⣐⠻⣵⣼⣧⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⢀⣾⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣻⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠻⠃⠀⢴⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠿⠿⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠉⠛⠛⠛
⣿⣿⣿⠛⠻⠛⠒⠀⠀⠀⠉⠉⠛⠟⠻⠿⠿⡿⠶⢤⠀⠀⠀⠀⠛⠛⠻⡿⣡⠀⠐⠿⠛⠛⢿⣿⣿⠻⠛⠿⠀⠀⠛⣿⠟⠃⠀⠉⠉⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢰⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⣀⣿⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠀⠀⣤⣿⡇⠀⠀⠷⠄⠀⠈⣿⣷⠀⢀⠀⠀⠀⠀⣿⠀⠀⡆⠀⠀⠀⢰⠀⠀⠀⠀⠁⣀⠙⣿⣿⣿⠁⠈⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣠⣄⠀⠀⢀⠇⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⣄⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠉⠀⠀⡇⠀⠆⠀⠘⠀⠀⠀⠀⠘⠉⣸⣿⣿⡏⠀⢠⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠛⣿⡟⠁⠀⠀⠀⣸⣿⡿⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠀⠀⠀⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣤
⠉⠙⠁⢑⣶⠢⠀⠀⠀⠀⠀⠀⠉⠀⢀⣤⡄⠠⠀⠀⢀⠀⡀⠃⠙⣋⠄⠉⡑⣞⠗⢂⡥⢀⡀⠰⠿⢠⣤⢄⣘⠛⠁⠀⠀⠤⠾⢇⣀⠈⣥⠆⣀⠀⠀⠿⣦⣿⣀⠁⣷⠟⢛⡁⠀⢺⡉⠛⠫⠿⣷⣴⣿⣴⣭⣋⠄⣴
⡴⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠶⠊⠉⣭⡈⠛⠂⠀⣀⡐⠂⠁⠔⠛⢛⣽⠒⠌⠁⠀⠀⢀⣠⡿⠄⢀⡀⠈⡉⠙⠛⠁⢀⣠⡄⠀⠚⣛⠀⢀⣼⡿⢰⣿⣝⠿⡤⠄⠸⠿⠿⢻⡇⠠⠀⣁⠀⢀⣀⡐⠏⠀⠀⠈⠁⠀⠀
⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠰⠿⠗⠀⠀⠀⣴⠄⠒⠒⡞⠉⢀⣀⡠⠃⠀⢈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣽⡻⠇⠀⢀⢠⣐⠴⢿⡀⣞⠁⣐⣶⡷⠃⠀⠀⠀⢤⡄⠰⣿⡃⠄⢈⣭⠀⠈⠀⠀⠀⡀⠀⢉
⠀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠀⠀⠀⠘⢧⣀⣰⣮⣷⣔⣶⣿⡇⠠⢿⣴⠃⠸⢿⣿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⢛⡛⠷⠾⠿⠿⡧⢤⢾⢛⢃⣠⣂⢢⣤⣄⣠⢸⠿⢭⣙⣾⣧⢻⠃⠀⢠⡔⠀⠀⣉
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⡛⣻⣻⡿⠿⠇⢘⣙⣧⣭⡟⢤⢀⠀⢀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠉⠃⣠⠦⢀⡌⠏⠀⠀⠸⠾⢏⣙⡀⢤⡄⣿⠟⠻⣿⣿⣶⣦⡄⡉⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣶⡟⠉⠙⠛⠒⠒⠃⡀⢘⡢⠧⠾⠘⣾⣿⣿⡿⠋⠉⠙⠀⢉⣿⣿⣿⡟⠁⠀⠐⠾⣿⣿⣷⠀⠤⠖⠺⠁⠀⣨⠀⠴⠦⠀⡂⠀⠀⠉⠤⠀⠀⠽⢵⣅⠠⠹⠟⡻⢱⣷⣿⣿⣒
⠀⠒⠂⢠⠐⠀⠀⠔⠁⠀⠀⠀⠀⠀⠛⡻⠟⠒⢠⣶⠄⣎⠝⠤⢀⠀⠀⠆⣿⣿⣿⣾⣿⣟⣛⣤⣿⣿⣿⣿⣷⣤⣴⢦⣶⣌⣻⣿⣧⠀⠀⠀⠀⠠⠀⠀⣀⢀⣠⣤⣤⣄⣀⡄⠀⠐⢁⢼⣟⣶⣾⣭⣿⢿⣿⣷⠾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠘⠀⢓⠂⠀⠐⠇⢀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠙⣿⣿⣶⣾⣿⣿⣿⣿⠆⠀⠀⠀⠰⠾⣄⠈⠛⠳⠶⣿⣿⡻⡤⠤⠶⢿⠿⣿⠻⡟⢛⡿⠛⠿⢉⠺⠊
⠀⠀⠤⠀⠀⠀⠀⡀⠐⠂⣀⡤⣄⣠⣄⣠⡴⠈⠀⠀⠀⢠⠖⣻⡓⠀⠐⣸⣿⣿⣿⣿⠟⣹⣿⣿⣾⣷⣶⣦⣤⣾⣟⢿⣿⣿⣿⣿⣿⡆⠬⠙⠃⠤⣮⣿⡍⠑⣿⣻⣿⣿⠷⣶⣦⠀⢐⣛⣍⣀⡀⠄⠀⠀⠀⠘⣳⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠁⣌⡻⠿⠥⠾⠿⣟⡩⠀⠀⠀⢠⠀⠈⠉⠒⢖⢰⣿⣿⣿⣿⣇⣾⣿⡿⢟⡛⠛⠛⠛⠿⢿⣿⣮⣻⣿⣿⣿⣿⡇⠀⣀⡀⣸⣯⡍⢱⡈⠟⠁⠀⠀⠔⢶⣍⡀⣨⣽⢡⢋⣉⠒⢦⡤⠀⠠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⠐⠐⠂⠀⠈⠉⠁⠒⠀⠂⠠⠿⠀⠂⠔⣿⢻⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡶⠶⣦⣤⣽⣿⣿⣿⣿⣿⣿⣷⣆⢀⡀⠘⠲⠆⢠⠦⣀⣈⣠⠀⠀⢦⣈⠿⠷⠒⣻⠃⠀⠷⣶⣷⣷⡿⣿⣿
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁⠀⠀⠀⡀⣤⡀⠀⣠⠄⢀⠀⠀⠀⠀⠀⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⢉⡛⠓⠂⠀⢘⢓⠀⠈⠙⠄⡡⣀⡒⠒⠀⠀⠰⠋⠉⠀⢈⣿⠟
⠀⠀⠀⠄⠐⠀⠀⠰⠂⠀⡀⠀⠀⢡⣗⡞⠁⠁⠐⠺⠆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣤⠤⡗⢻⡵⠖⢂⣀⣽⣇⢁⠁⠀⠀⠑⠻⠋⢀⣀⡀⠀⠛⢭⡁⡼⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠠⠀⠡⠉⠉⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⠿⡟⠀⡀⠱⠀⠈⠓⠀⠀⠸⠙⢻⡄⠏⠀⠀⠈⢡⠶⠘⢽⢿⠁⠀⠀⣿⠙⡀⠀
⠀⠀⠀⠀⠀⢀⡈⢀⣀⢙⠀⠋⠉⠉⠄⣀⡤⠽⠉⠀⠤⠤⠴⢶⡄⠉⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣽⠋⠄⠀⠨⠀⠀⠐⠂⠠⠤⣤⡔⠠⠤⢡⡄⢁⡭⠼⣦⣀⠡⡀⠀⠀⠀⡜⠸⠀⠛⠢
⠀⠀⠀⣀⢀⠀⠐⠶⠳⠶⣾⠀⢀⡠⠶⠏⠃⠀⠫⠵⣶⡖⠂⠉⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⢀⠤⣀⡀⠘⠀⠀⠶⠀⣠⡬⡆⣀⣠⡷⠚⠷⡠⣿⢋⣄⠁⠘⠃⡸⠧⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠋⠓⢂⣤⣤⣤⣥⣤⣬⣤⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡀⠐⣿⣿⣿⣿⣷⠚⣺⣃⣉⠀⠀⠀⢀⠀⠉⠁⠀⠉⠛⠀⢀⣉⢃⣁⡀⢿⡶⠄⢀⠀⠀⠀⠀⠀⠀
⠐⠀⠀⠀⠀⡴⠆⠀⠀⠀⠀⢠⣄⣀⣾⣿⣿⠛⠛⣯⣍⠽⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠠⣶⣮⡨⢟⣿⣿⣿⣿⢹⣶⣦⣌⢠⣀⣀⣠⣄⣀⠀⠀⠀⠀⠠⣸⡀⠈⠈⠁⠀⠻⠛⠋⢩⠃⠐⠂⠀⠀
⠀⠀⠀⣰⠤⠀⠀⠀⠀⠀⠀⢀⣀⣿⡿⠉⠁⠀⠀⠉⠉⢀⣿⣿⣿⡟⠋⠁⠀⠘⣿⣿⣿⣿⣿⡷⠀⠀⠀⢰⣿⣿⠟⠉⠻⣿⣿⣿⠀⣿⣿⣿⡷⠊⠉⢫⣭⣽⣿⣿⣧⡃⠐⠋⣽⠿⡹⠵⠀⣴⡂⠀⠠⠤⣠⠀⣤⠀
⠀⠀⠀⠂⠲⢤⣄⢤⣴⣷⣾⣿⢸⣿⣧⣤⠀⠀⢀⠀⠀⡾⠟⠉⣾⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⠏⠀⠀⣠⣿⣿⣏⠀⠀⠀⢸⣿⣧⣿⡏⠉⠁⠀⠀⠂⠀⠉⢻⣿⣿⡍⢀⣄⠀⠀⠒⠊⠒⢶⣏⣁⣿⡽⠶⠚⢢⢴⠐
⠀⠀⢀⡀⠀⠀⢀⣼⣿⣿⣿⡇⣿⣿⣿⣿⣦⡄⠛⠛⣀⣀⣼⣿⣿⣿⠀⣿⣿⣦⡀⠀⠘⠻⣇⠀⢀⣴⣿⣿⣿⡿⠀⠀⠀⣸⡿⣼⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢸⣿⣷⣶⡖⡦⠀⠀⢠⡏⠈⠉⠀⣘⠚⣒⠯
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣿⣿⣿⠛⠛⢣⣤⡀⠟⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣶⣤⡀⠈⠀⠾⠛⠛⠉⠁⠀⠀⣠⣴⣿⠃⣿⣿⣿⣿⠀⠀⢰⣤⠀⠀⢰⣶⣿⣿⢸⣿⣿⣿⣿⣅⢿⣷⠀⢀⢀⠐⠀⣹⣿⣦⠖
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢁⣿⣿⣿⣤⡀⠚⠻⢃⡀⢸⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢰⣿⣿⣿⣿⣿⣶⠀⠉⢠⣤⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡏⣀⣬⡀⠈⠀⠠⡖⠀⣛
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢸⣿⣿⡟⠛⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⢸⣿⣿⣿⡏⠀⠁⣶⣤⠈⠛⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣧⣬⣿⠿⢷⠷⠶⠶⣦⣉⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢸⣿⣿⡇⠀⠰⠿⠇⠀⠀⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣶⡆⠙⠛⣤⣄⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⢫⣽⣴⡯⠶⠖⣤⡾⢓⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠿⠄⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⢿⣿⣿⡟⢠⣿⣿⣿⣿⡏⠉⢃⣀⡀⠻⠿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠸⡿⠿⠟⠻⡤⠶⠤⣀⠂
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⣴⣶⡀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⠃⣼⣿⣿⣿⣿⣅⣀⠘⠿⠃⠀⢠⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀⡐⠁⠀⠀⠤⣤
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⠀⠉⠉⢒⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⠏⢰⣿⣿⣿⣿⣿⠟⠿⣀⠀⠸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⠖⠂⠀⠃⡀⠤⡾⣷⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⠋⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣀⡐⠿⠿⠁⢀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣶⣿⣭⣍⠀⠈⠗⠶⠦⠀
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⡄⠻⢿⠿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⣄⡉⡙⠉⠉⠷⠂⠈⠐⠚
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠃⢶⣶⣤⡆⣸⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⠟⠛⠟⠋⠀⠀⠀⠀⠠⢤⣶⣤
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⠛⠻⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⣬⣭⣝⣓⣤⠉⠁⠀⡉⠉⣿⣿⣿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢻⣇⠀
⢰⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣞⣛⠿
⣺⣿⣿⣿⣿⣿⣿⣿⡀⠀⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠉⠉⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣀⣄⣴⣶⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣐⠫⣵⣼⣧⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢀⣾⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⠟⠃⠀⢴⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠉⠙⠛⠛⢿⣿⣿⣿⣿⠀⠀⣀⣠⣀⣻⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⠿⠿⠿⠟⠃⣼⣿⣿⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠉⠛⠛⠛
⣿⣿⣿⠛⠻⠓⠀⠀⠀⠈⠉⠙⠛⠟⠛⠿⠿⡿⠶⢤⠀⠀⠀⠀⠘⠛⠛⡿⢣⠀⠀⠿⠛⠛⢿⣿⣿⠿⠟⠿⠇⠀⠛⣿⠟⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢰⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠀⠀⣤⣿⣿⠀⠀⠷⠄⠀⠈⣿⣿⠀⢠⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠋⢉⡉⢿⣿⣿⡇⠀⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⠋⠀⣠⣄⠀⠀⢀⠇⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠟⠀⠀⢀⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠉⠀⠀⡇⠀⠆⠀⠘⠀⠀⠀⠀⠀⠋⢁⣿⣿⡟⠀⢀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠛⣿⡟⠁⠀⠀⠀⣾⣿⣷⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣤
⠁⠙⠈⡈⡶⠆⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⡄⠐⠀⠀⢄⢀⡈⠁⠉⡡⢀⢈⣑⡏⠓⠢⠆⢀⡀⠰⠣⢤⣄⣤⣘⡋⠡⠄⠀⠀⠛⢃⣀⠘⡴⢂⡀⠀⠐⢻⣦⣷⡀⡡⣿⠛⢋⠁⠀⢯⠉⠛⠋⢿⣶⣾⣷⣶⣿⣩⠠⠾
⡌⠀⠐⠃⠀⠀⠀⠀⢀⠘⠀⠶⠈⠩⢤⠈⢛⠐⠂⢄⡀⠂⠁⠚⠛⣋⣽⠰⠈⠁⠀⠀⣤⣴⡯⠄⠀⠀⠈⠉⠛⠛⢀⣠⣴⡦⠐⢛⡣⠀⣀⣼⠷⣸⡿⣝⢯⡤⠀⢻⠿⠟⢛⡁⠠⠀⡀⠀⢠⣀⠸⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠜⠛⠧⡀⠀⢀⣶⠂⠁⢀⠏⠀⢠⣀⡔⠈⠀⠘⣿⣷⣾⣿⣿⣿⣿⣿⣷⣶⣿⡛⠃⠀⣀⢰⡠⠗⣟⢀⡏⠀⣰⣾⡻⠀⠀⠀⠀⢦⡄⢸⡟⠥⠂⢨⡄⣀⠈⠀⡀⠀⠀⠀⣉
⠀⠀⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠘⢣⣰⣰⣿⣷⣴⣷⣿⡅⠐⣳⡶⠁⠸⢿⡿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⡛⠻⠿⠛⢳⣧⠔⡟⢻⢡⣤⡀⣨⣥⣌⡠⢸⡛⣨⣙⣾⣇⢿⠁⠄⢠⣆⠀⠀⠉
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠻⠿⣛⣿⣻⠟⠛⡀⢁⠘⣶⣷⡗⢤⢀⠀⢀⣼⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣆⠀⠀⠀⠉⠁⡤⠆⢠⡆⠋⠁⠀⠿⠾⢏⣉⡀⢤⡌⣻⠟⠻⣿⣿⣶⣦⡀⡄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⣛⠁⢉⠛⠓⠛⢃⣂⣺⠤⠇⠟⠘⢺⣿⣿⠟⣉⡉⠉⠀⣨⣿⣿⣿⡋⠀⠀⠘⠻⣿⣿⣆⠀⠤⠖⠿⠀⠀⡼⢠⠔⠦⠀⡂⠀⠀⠁⠤⠀⠀⢭⢾⠥⠀⠛⣛⡳⢽⣿⡿⢿⣥
⠀⠛⠀⡠⠀⠀⠀⠊⠁⠀⣀⠀⠀⠀⢛⠻⠛⠃⠤⡶⠨⡶⠝⠂⣀⡀⠀⠒⣿⣿⣿⣿⣿⣭⣭⣾⣿⣿⡿⢿⣷⣴⡾⠷⢷⣬⣿⣿⡆⠀⠀⠀⠀⠠⠀⢀⣄⣀⢦⠤⣤⢠⣠⠄⠀⠀⣀⣼⣿⣷⣷⣼⣿⣿⣿⣷⠾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠛⡀⢓⠂⠀⠘⠇⢀⢹⣿⣿⣿⣿⣿⣿⣿⣏⣀⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠴⢷⣀⠈⠙⢲⢿⣿⣟⡷⡤⠴⠖⢿⢿⣻⠻⡟⣻⡟⠛⠛⢀⠚⠈
⠀⠠⠄⠀⠀⠀⠀⡄⡐⢂⣀⣶⣀⣤⣤⣦⡶⠀⠀⠀⠀⠴⢚⣿⣉⠀⠠⣼⣿⣿⣿⡿⢋⣼⣿⣿⣿⣿⣿⣿⣶⣿⣏⢻⣿⣿⣿⣿⣿⠀⠨⠛⠁⠔⣫⣿⡁⢈⡿⢽⣿⡿⠲⣶⣢⠀⢘⡋⣏⣂⠀⠆⠀⠀⠀⠈⣳⡀
⠐⠀⠀⠀⠀⠀⠂⠀⠠⠭⡙⠻⠴⠮⢿⣫⡭⠀⡀⠀⢠⠀⠈⠉⠲⢂⢰⣿⣿⣿⣿⣧⣾⡿⠛⣭⣖⣀⣀⣈⠉⠻⣿⣧⣽⣿⣿⣿⣿⠀⠀⣀⡀⣿⢷⠉⠠⠈⠏⠁⠀⠀⠔⠶⣄⡀⢠⡧⣴⣥⠭⠛⢦⡄⠀⢴⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⣚⡓⠀⠈⠉⠀⡂⠐⠂⠸⠿⠀⠀⠒⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣝⣻⣷⣾⣿⣿⣿⣿⣿⣿⣶⣄⣀⡀⠚⡒⠂⠤⠆⣈⣌⣭⠁⠀⣢⣨⠛⠓⠛⡟⠀⠘⠷⣶⣶⡷⠽⣿⣿
⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡒⠀⣠⠂⠀⠀⠐⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠁⠀⣉⡙⠑⠀⠀⣘⣛⠀⠉⠱⠀⠀⣀⡓⠒⠂⠀⠸⡉⣉⠀⣘⡿⣋
⠀⠀⠀⠈⠈⠀⠀⠲⠆⠀⡀⠀⠉⢽⣗⠊⠀⠀⠐⠺⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠛⠛⠙⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⠟⣴⢴⡃⢻⠾⠒⠀⣤⣿⣂⠀⡀⠀⠀⠙⠛⠁⣀⣀⡀⠀⠛⢭⣄⡞⢛⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠰⠀⠡⠈⠨⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣿⡿⢻⡇⠀⡌⠆⠀⠈⠉⠀⠀⠉⠙⢿⡌⠋⣀⣀⠈⠸⢎⠚⠽⢟⠀⠀⢠⣏⠹⡀⠀
⠀⠀⠀⡀⠀⠀⠄⢀⣀⡡⠀⠉⠁⠉⢀⣠⠤⠛⠀⠀⠤⠤⠒⣶⠄⠁⠀⢠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠄⠀⡠⠄⠀⠐⠀⠠⢧⣤⣜⠠⠬⢡⠀⢠⠥⠟⣦⣈⠡⠀⠀⠀⠀⠏⠞⠈⠉⠦
⠀⠀⠀⠀⢀⠀⠒⠞⠒⠺⢮⠀⣀⠐⠺⠋⠁⠀⠫⠿⢶⠖⠂⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡀⢀⠔⣀⡀⠀⠀⠐⠆⠀⣰⡼⡄⣀⣠⠗⠈⢗⣤⡏⢉⡄⠁⠉⠁⠜⠄⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⠉⠓⢂⣤⣤⣦⣤⢤⡤⣤⣄⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣄⡄⠠⣾⣿⣿⣿⣷⠋⣿⢁⣈⠁⠀⠀⠀⠀⠉⠀⠀⠈⠉⠀⣀⡉⢁⣁⡈⢿⠆⠀⣀⡀⠀⠀⠀⠀⠀
⠘⠀⠀⠀⠐⡶⠂⠀⠀⠀⠀⢠⣄⣀⣾⣿⡿⠛⢻⣭⣭⠿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⢘⣿⣿⣋⣼⣿⣿⣿⣿⢹⣶⣦⡌⠤⢀⣀⣠⣀⣀⡀⠀⠀⠀⠤⣽⡀⠁⠀⠁⠀⠙⠛⠋⢩⠁⠒⠂⠀⠀
⠀⠀⠀⡴⠦⠀⠀⠀⠀⠀⡀⢀⢤⣿⡟⠉⠁⠀⠀⠉⠉⢠⣿⣿⣿⡏⠁⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⠁⠀⠙⣿⣿⡿⢈⣿⣿⡿⠿⠋⠉⢳⣭⣽⣿⣿⣧⠁⠚⠋⡽⠯⡹⠷⢠⣾⡀⠀⠠⠦⣄⠂⣴⠂
⠀⠀⠀⠂⠃⢶⡤⢴⣤⣷⣾⡿⣾⣿⣧⡤⠀⠀⣀⡀⠀⠿⢋⢁⣿⡇⢃⣠⡀⠀⠈⠻⣿⣿⡿⠃⠀⠀⣴⣿⣿⣇⠀⠀⠀⢸⣿⢧⣿⡏⠉⠀⠀⠀⠀⠈⠉⠹⢿⣿⡅⢠⣄⠀⠀⠒⠈⠒⢶⣎⣨⣿⠽⠳⢛⣢⢖⣒
⠀⠀⢀⠄⠀⠀⢀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣶⡆⠛⠙⣄⣀⣿⣿⣿⡇⢸⣿⣿⣦⣄⠀⠈⠻⢇⠀⣠⣾⣿⣿⡿⠟⠀⠀⠀⣸⡿⣼⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⣼⣿⣿⣶⡟⡆⠀⠀⠠⠇⠈⠉⠀⣉⡛⣐⠺
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢃⣿⣿⣿⠛⠛⣧⣤⠘⠛⢿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣷⣦⣄⠀⠐⠛⠉⠉⠀⠀⠀⢀⣴⣾⣿⠁⣿⣿⣿⣿⠀⠀⢰⣶⠀⠀⢰⣶⣿⣿⢸⣿⣿⣿⣿⣽⣿⡷⠀⣀⢀⠉⠀⣿⠿⠶⠒
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣤⡄⠛⠛⣀⡀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣷⠀⠀⢰⣶⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⢅⣠⣭⡀⠀⠀⢴⣖⣀⣛
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢸⣿⣿⡟⠉⠁⢀⡀⠿⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⢸⣿⣿⣿⡏⠀⠀⣶⣶⠈⠉⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣦⣾⡿⠿⣿⠷⠒⠒⠶⣽⡿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⢸⣿⣿⡀⠀⠸⠻⠃⠀⢠⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⡆⠉⠉⣤⣤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡟⣩⣽⣼⡥⠖⢲⣤⠟⠩⠄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⠧⠛⠀⠀⢰⣴⣾⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⡟⢠⣿⣿⣿⣿⠏⠉⢡⣤⡄⠛⠻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣇⠻⠿⠿⠏⠛⡶⠶⠦⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠠⣾⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⣿⣿⠃⣼⣿⣿⣿⣿⣦⣤⠈⠚⢁⡀⢰⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⡘⠁⠈⢩⠶⡖
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠉⠈⠉⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⠇⣰⣿⣿⣿⣿⣿⠋⠛⣀⣀⠸⠧⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠿⠀⠐⠈⠡⡀⠢⣟⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⠁⣀⣀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣤⡐⠛⠛⠀⣀⣿⣿⣿⣿⣿⠐⣿⣿⣿⣿⣿⣿⣾⣿⣯⣅⠀⠀⠓⠳⠂⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣌⠻⠿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣷⣄⣀⡉⠈⠉⠓⠁⠈⡁⠉
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⡅⠸⣷⣶⡖⣸⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⠟⠛⠛⠀⠀⠀⠀⠀⠠⣶⣶⡶
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠀⠀⠈⠉⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠀⣤⣬⣭⣽⣂⣀⣀⣀⡀⠀⣿⣿⣿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⣻⡇⠀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣟⣛⠗
⢸⣿⣿⣿⣿⣿⣿⣏⡉⡐⠑⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣷
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣐⠫⣵⣼⣧⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⢀⣾⣿⣿⣿⣿⣿⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⡟⠆⠀⠰⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⠀⠀⣠⣤⣤⣬⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⡿⠿⠿⠿⠟⠛⠛⠋⢁⣾⣿⣿⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠉⠛⠛⢛
⣿⣿⣿⠛⠻⠓⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⢿⠖⠀⠀⠀⠘⠛⠛⠿⣱⠀⠀⠟⠛⠛⢿⣿⣿⠛⠛⠿⠇⠀⠛⣿⠟⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠘⠀⠀⢠⣾⣿⠀⠀⠀⠀⢀⣀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⠏⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡿⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⣤⣿⣿⠀⠀⠷⠄⠀⠈⣿⣿⠀⢠⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⡴⠀⣿⣿⡿⠀⠈⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⠋⠀⣠⣄⠀⠀⢀⡇⠀⠀⠀⠸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⣀⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠉⠀⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠇⠀⢠⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠛⣿⡟⠁⠀⠀⠀⣸⣿⡿⠷⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⠉⠁⠀⠡⠖⠀⠀⢀⠀⠀⠀⠀⡀⠀⣤⣶⣀⠀⠀⠀⠀⢀⠈⠀⢩⣔⣀⠠⣱⠌⠓⠰⠀⠠⡀⠚⠃⠤⣤⣤⣈⣉⠀⡀⠀⠒⠛⣤⡄⠠⠒⣠⡄⢀⣘⣻⣼⠇⠄⡘⣟⠙⣁⠀⠐⢧⠉⠛⠒⠿⢾⡿⣷⠶⣮⠄⠰⢻
⠀⠀⠈⠀⠀⠀⠀⠀⠌⠁⠐⠒⠉⠡⠦⢉⡉⠐⠢⠤⠍⠀⠐⠙⠋⣡⡎⠰⠈⢀⠀⠀⣄⣾⠗⢀⣀⣀⣈⣉⡉⠉⢀⣠⣶⠀⠀⠨⠅⠀⣤⣿⠣⣼⠷⠻⢳⠒⠀⠗⠻⠟⢯⠀⠢⣢⡀⠀⢠⣠⠛⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠛⠛⣁⡀⠀⢰⡒⠈⢉⡸⠁⠀⣤⣤⠊⠁⠀⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣭⡙⠀⣀⣀⣆⡅⢓⣅⣸⠃⠀⣶⣯⠋⠀⠀⠀⠈⢲⠄⢻⡋⢐⡂⢤⢆⣀⠀⠀⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⡠⠄⠀⠁⠀⠠⠀⠀⣙⣀⣄⣼⣾⣶⣾⠿⣿⡄⠐⣷⡎⠀⠛⢿⠏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢁⡍⢛⣛⠚⠳⠶⠈⡏⡏⠤⢤⡍⣽⢶⣄⠄⡝⣛⣯⣽⣿⣎⡏⠁⠎⢴⣁⠀⠠⠅
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠛⢻⣹⣿⣿⠛⠛⠀⡡⠹⡶⠾⠓⣆⡄⢀⣠⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣆⠀⠀⠀⠉⢠⠖⠂⣰⠀⠁⠀⠀⠒⠛⢤⡥⠐⠶⢘⣿⠛⠻⠿⣿⣷⣦⢠⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣟⣋⠀⠋⠋⠙⠙⢡⡁⠭⠜⠒⠋⠉⣽⣿⡿⠛⣉⢉⠁⠀⣸⣿⣿⣿⠁⠀⠀⠛⠻⣿⣿⣇⠀⠲⠊⠛⠀⠠⠦⠰⠛⠢⠀⡀⠀⠀⠠⠦⠀⠐⡃⣿⠤⠒⣛⣋⡷⣿⣽⠻⣭⣴
⠈⠋⠀⠌⠀⠀⠐⠁⠀⠀⠀⠀⠀⢈⣉⠛⠙⠁⠴⡖⠰⠮⠑⠂⢠⠀⢐⢢⣿⣿⣿⣿⣿⣭⣭⣾⣿⣿⣿⣿⣷⣴⡾⠶⣶⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣄⣤⠖⠴⡖⣤⡤⠀⠀⢀⣤⣟⣻⣿⣷⣾⣟⣿⣿⣷⡚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢃⡀⡋⠀⠀⠘⠀⡀⣼⣿⣿⣿⣿⣿⢿⣿⡋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣀⠀⠚⢣⣄⣉⠙⢺⣛⣷⣿⠓⠖⠒⠚⢿⣻⡝⢻⠋⣽⠏⠙⠃⣀⠋⠈
⠀⠐⠀⠀⠀⠀⠀⢀⠊⣀⣤⢲⣤⢦⣤⣶⡆⠀⠀⠀⠀⠖⢩⣿⠁⠀⠀⣿⣿⣿⣿⡟⢁⣾⣿⣿⣿⣷⣿⣶⣶⣿⡍⢿⣿⣿⣿⣿⣷⠐⠂⠋⠁⢚⣿⣷⠄⢈⣯⠿⡿⠟⠚⠿⡄⠀⢬⡭⢤⣤⡐⠀⠀⠀⠀⠉⣧⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠠⠍⠛⠳⠶⠛⣻⣩⠅⠀⠀⠐⢦⠀⠈⠁⠘⡁⣸⣿⣿⣿⣿⣥⣾⡿⠛⣭⣍⡉⠉⠉⠛⢿⣿⣄⣿⣿⣿⣿⣿⠀⠀⠀⠠⠿⠶⣀⠐⠈⠁⡀⠀⠀⠘⠶⣄⣀⡲⠇⣲⠤⢌⠙⠶⠂⠀⣲⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣙⠂⠀⠉⠁⢀⠁⠀⠀⠚⠃⠀⠐⠚⡏⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣭⣛⡻⣷⣦⣽⣿⣿⣿⣿⣿⣿⣶⣀⣀⠀⢉⣓⡀⠔⢂⡤⢤⠌⠀⣐⡦⣜⠛⠛⠩⠏⠀⠘⢻⣿⣿⠟⣹⣿⣿
⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⣖⢂⢀⡔⠂⠀⠀⠀⠀⠂⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠁⠀⠀⣭⡉⠉⠀⢀⣍⣍⠀⠉⠁⢀⢆⣬⡉⠁⠀⠀⠊⣀⣀⠀⣨⣟⣉
⠀⠀⠀⠈⠁⠂⠀⠲⠀⠠⠀⠀⠈⢼⡚⠉⠀⠀⠉⠘⠂⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠁⠈⠙⠛⠿⣻⣿⣿⣿⣿⡿⠳⢖⠺⠀⣷⠛⠉⠠⣴⣿⡄⠄⡀⠀⠀⢙⠋⠀⣠⣤⣀⠈⠑⢮⣤⡛⠻⠿
⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⣀⣀⡀⠀⠀⢀⣀⡀⠠⠀⠀⠀⠘⠀⠀⠀⢨⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⡟⠿⠁⠀⠀⠃⠀⠈⠁⠀⠀⠃⠙⢷⡙⠀⣀⡀⡀⠜⢃⠒⠟⠏⠀⠀⣸⠇⠁⡀⠀
⠀⠀⠀⠀⠀⠤⠤⢀⡀⠇⠈⠁⠀⠀⢠⣴⠖⠃⣀⠀⠆⠐⠚⡿⠄⠀⠀⣸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠁⠄⠀⠀⠀⠀⠉⠀⠐⠓⠶⣁⠒⠄⢴⠀⢤⠒⢻⣆⡀⢠⠀⢀⠀⢰⠃⠃⠈⠉⠦
⠀⡀⠀⠄⠀⠀⠛⠛⠒⠻⠇⠠⣠⠒⠛⠋⠀⠀⠛⠿⣆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡀⣠⢢⣄⡀⠃⠀⠘⠃⢀⣶⠺⢀⣀⡼⠓⠉⣣⢲⠏⢠⡄⠀⠉⠀⠋⠂⠀⠀⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠉⢰⣶⣶⣶⣶⣶⣴⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣄⡀⣰⣿⣿⣿⣿⣯⣉⡯⢠⣍⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⣠⠍⡀⣤⠘⢿⢓⣀⣄⣀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠤⠄⣬⣿⣿⡟⠉⠹⣶⡶⠛⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣾⣎⣬⣿⣿⣿⣿⡏⢹⣿⣷⣂⣂⣤⣤⠴⣀⣀⣀⣀⠀⠠⢠⣧⣀⣀⣀⠀⠈⠉⠙⠀⠨⠀⠁⠀⠀⠀
⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⢈⣠⢺⣿⡏⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⡏⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⠀⢀⣾⣿⡟⠀⠀⠙⣿⣿⢣⣼⡿⡿⠛⠋⢀⠀⠹⣿⣿⣿⣿⠲⠀⠉⠠⠿⠦⡓⠂⢰⣯⠄⣀⠒⠢⡆⠐⠂⢀
⠀⠀⠀⠂⠃⠶⠄⣢⣶⣿⣿⡿⣾⣿⣷⣶⠀⠀⣤⣄⠀⠛⣁⣠⣿⡇⢡⣤⣄⠀⠀⠙⢿⣿⠏⠀⠀⣠⣾⣿⣿⣄⠀⠀⠀⣿⡟⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣷⠀⣴⣄⠀⠀⠉⠈⠛⠿⢥⡼⣷⡋⠋⡉⡶⢃⣉
⠀⠀⠠⠄⠀⠁⢰⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⣿⣿⣿⡏⢸⣿⣿⣷⣄⡀⠀⠙⠧⢀⣴⣿⣿⠿⠟⠃⠀⠀⣠⣿⢳⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⣀⣾⣿⡜⣿⣿⣿⣿⡛⢆⡀⠀⠸⠀⠀⠀⢀⣍⣉⡔⠚
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⠁⠀⣰⣶⠆⠉⢻⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⣤⡀⠈⠉⠀⠀⠀⠀⠀⣠⣾⣿⡇⢸⣿⣿⣿⣧⣀⡀⠿⠇⠀⢀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣏⣿⡇⠀⡄⠀⠀⠀⢿⠿⢖⣡
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣶⡆⠈⠉⣤⣄⣾⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⣿⣿⣿⣿⡟⠛⢃⡀⠀⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠿⢠⣴⣦⠄⠀⠀⠺⢁⣈⣭
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⣿⡏⠉⠁⣠⡄⠛⠛⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣸⣿⣿⣿⣿⢀⣿⣿⣿⣿⣄⣀⠸⢿⠇⠀⢸⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣷⣾⡟⢛⡟⢛⠛⠓⠦⠼⠛
⠀⠐⠀⠀⣼⣿⣿⣿⣿⣿⡟⢸⣿⣿⣦⣀⠈⠛⠁⠀⢰⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⠿⢿⠀⠀⢸⣿⣾⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣏⣶⣷⣿⣒⡛⠰⠼⠋⠥⠐
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⣾⣿⡿⠋⠉⢀⡀⠸⠽⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⠁⣼⣿⣿⣿⡿⠀⠀⣿⣷⠀⠈⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠙⠛⠛⠉⢑⠚⠓⠢⠀⠀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣯⣀⡐⠿⣟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⠇⢰⣿⣿⣿⣿⣿⢷⡆⠀⠀⣤⣤⣿⣿⣿⣿⡇⣺⣿⣿⣿⣿⣿⣧⡀⠀⠀⢠⠉⠀⠀⣐⢲⡀
⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⢠⣿⣿⣿⣿⣿⡏⠀⢰⣶⡆⠉⢻⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⣿⡿⠛⣉⣀⡈⠠⣐⠚⠽⠿⢿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢀⣤⣤⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠁⢠⣾⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⣿⡿⢿⣿⣶⣄⣀⠐⠙⡛⠂⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣦⣉⣛⣩⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠃⣀⣀⣀⡘⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣤⡤⠁⠀⠘⠋⠀⠀⠈⠉
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠈⠿⢿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⠛⠻⠿⠷⣀⠙⠟⠛⠐⠿⢿⣿⣿⣿⠀⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⢐⣲⡷⠞
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⣶⣶⣶⣦⠀⣸⣿⣿⠇⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠈⣿⣆⠀
⢸⣿⣿⣿⣿⣿⣿⡿⠿⠻⣻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠟⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣏⣛⠈
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⡄⠨⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣐⠫⣥⣼⣧⣿⣿⣿⣿
⣿⣿⡿⡿⠿⣿⣿⡋⠉⠀⣠⣿⣿⣿⣿⣿⡇⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⠂⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠿⢀⣿⣿⣄⡀⣀⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣿⢽⠀⠀⠺⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠈⢹⣿⣿⣿⡇⠀⠀⣶⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣧⠈⠉⠉⠉⠉⠀⠀⠀⢀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⣿⣿⣿⠛⠻⠒⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⢿⠖⠂⠀⢀⠘⠛⠛⢋⣾⠀⠀⠟⠛⠛⠿⣿⡿⠛⠛⠻⠀⠀⠛⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠘⠀⠀⣤⣿⣿⠀⠀⠀⠀⢀⣀⣿⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⠀⠀⠀⢰⠀⠀⠀⠀⠁⣀⢹⣿⣿⡏⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠑⠀⠀⣤⣿⣿⠀⠀⠳⠄⠀⠈⣿⣿⠀⢠⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠘⢁⣸⣿⣿⠁⠀⠈⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣠⣄⠀⠀⢀⡇⠀⠀⠀⠘⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣄⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⣦⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⡁⠀⠀⠀⢸⣿⠟⠛⣠⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣉⣩⣴⠀⠾⠁⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⣈⠁⢈⠾⡟⠀⠀⠀⠀⠀⠀⠀⣀⢀⠤⣶⣀⠒⠄⠀⠄⣀⠈⠈⢩⢐⡀⢨⣹⠙⠓⠴⠂⠠⡀⠚⠂⢴⢤⣶⣍⣀⠀⠀⠐⠚⢛⣤⡄⠰⠚⣤⠄⢀⣘⣻⡼⠧⠄⡸⣏⣙⣅⠀⠘⢧⠈⠙⠚⠿⢿⡿⠷⠷⣦⠄⡴⢻
⠁⠀⠉⠀⠀⠀⠀⠀⠉⠁⠘⠓⠉⠱⢂⢈⡉⠑⠴⠠⠍⠀⠐⠛⠉⣡⡏⠐⠈⢀⠀⠐⣄⣾⠇⠒⣀⠀⣈⣉⠋⢉⢀⣴⣖⠂⠈⠭⠅⠀⢴⡿⠃⣾⠷⠝⢷⢂⠈⠟⠻⠛⠫⠀⢂⣠⠀⠀⣤⡤⠋⡀⠀⠀⠀⠀⢀⣼
⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠛⠋⢁⠀⠀⣰⡒⠀⢉⡸⠁⠀⣤⣤⠊⠀⠀⣸⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣏⠟⠀⣀⣀⣆⡗⢻⣇⣼⠁⢀⣾⣯⠋⠀⠀⠀⠘⢶⠄⣻⠇⢐⠀⣴⢂⣠⠀⠀⠀⠠⠀⢀⢄
⠀⠀⠀⠀⠀⡠⠄⠀⠁⠀⠀⠀⢀⣛⣠⣤⣾⣾⣶⣿⢿⣷⡄⢘⣷⠏⠀⠛⠿⠇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢉⠀⢛⣛⠛⠳⠶⠸⡍⡯⠶⢬⡍⡽⣶⣤⠆⠟⣛⣯⣽⣿⣎⡏⠰⠊⢶⡅⠀⠨⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠛⢛⣹⣽⣿⠛⢫⠀⡥⢹⣶⢾⠑⡆⡄⢀⣠⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣷⡀⠀⠀⠀⠉⣠⠖⠂⣴⠘⠁⠀⠈⠓⠛⣬⡥⠐⠶⢚⡿⢛⠻⠿⣿⣷⣦⢠⢀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣋⠀⠝⠉⠋⠉⣨⡀⠭⠘⠚⠋⠉⣿⣿⡿⣋⣠⣀⡁⢀⣼⣿⣿⣿⠀⠀⢈⠙⠻⣿⣿⡀⠐⠒⠛⠃⠀⠠⠆⠐⠛⠢⢨⡀⠀⠀⠠⠆⠀⢐⡗⣷⡆⠚⣛⣛⡿⣿⣿⠻⣯⣴
⠈⠋⠠⠌⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⣉⠛⠉⠁⠶⡖⠺⠬⠙⠂⣀⠀⢐⢺⣿⣿⣿⣿⣿⣶⣶⣿⠿⠿⠿⢿⣷⣾⣛⠿⢷⣾⣿⣿⠀⠀⠀⠀⠀⠂⡀⠠⣄⡤⢶⢶⣞⣤⠴⠀⠀⢁⣴⣿⣿⣿⣷⣿⣟⣿⣿⡿⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣰⠔⢁⠘⠋⠀⡀⠛⠀⡀⣾⣿⣿⣿⣿⣿⢿⣿⣅⣤⣀⣀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠁⣀⣀⠀⠛⣳⣄⣈⠙⣛⣻⣿⣿⠲⠒⠒⠻⣟⣻⡟⢿⠉⡿⠋⠙⠃⣌⠃⠈
⠀⠐⠀⠠⠀⠀⠀⢀⠈⣀⣴⣲⡤⣦⣴⣶⡆⠀⠀⠀⠀⠞⣹⣿⠀⠀⢠⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⢿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⡇⠒⠚⠋⠑⣪⣾⣧⠀⣨⣯⠿⠿⠟⠻⠿⡆⠀⢬⡽⣤⣄⡐⠄⠀⠀⠀⠨⣧⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠠⠽⠛⠳⠖⠛⣻⣥⠆⠀⠀⠐⢦⡀⠈⠁⠘⡁⣿⣿⣿⣿⣿⣾⣿⠟⣉⣶⣦⣤⣤⣀⡉⠻⣿⣶⣿⣿⣿⣿⡇⠀⠠⡠⠨⡿⠶⣀⠄⠘⠁⡀⡀⠐⠛⠷⣤⣀⠲⢢⣯⠤⢌⠙⠲⢂⢀⣲⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠊⠑⢛⠂⠀⠀⠁⢀⠁⠀⠁⠚⠃⠈⠐⢻⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣄⠀⢉⣛⣀⠚⢢⠤⣤⠎⠀⣐⡤⢜⠛⠋⠩⠋⠀⠘⢻⣿⡿⠟⣹⣿⡿
⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⡖⢂⢠⡔⠂⡀⠀⠈⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⢀⢀⣬⠍⠁⠀⢀⣏⣅⠀⠈⠑⢤⢢⣬⠉⠉⠀⠀⢋⣀⣀⠢⣩⣏⣅
⠀⠀⠀⠀⠁⠂⠀⠒⠀⠠⠀⠀⠈⢼⡞⠉⠀⠀⠉⠗⠂⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉⠉⠁⠀⠈⠉⠛⣿⣿⣿⣿⣿⠟⠲⢖⠺⠀⣷⠛⠉⠤⣶⣿⡄⢄⡀⠀⠀⣙⠋⠀⣤⣤⣀⠈⠑⢦⣴⡋⠹⠿
⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⢀⣀⣠⡀⠀⠀⢀⣀⠀⠠⠀⠀⠀⠘⠀⡂⠀⢸⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡽⢿⠛⠿⠀⡠⠐⠃⠀⠉⠁⠀⠀⠃⠙⢿⠘⢀⣀⣀⡀⠞⣁⠒⠟⠇⠀⠀⡼⡇⢃⡀⠀
⠀⠀⠀⠀⠠⠤⠤⢀⠀⠇⠈⠁⠀⠈⢠⣴⠒⠃⣀⠐⠆⠐⢚⡿⠀⠀⠀⣸⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡏⠡⠀⠀⠀⠀⠀⠁⠀⠐⠲⠦⡁⠒⠆⢶⠀⣴⠚⢻⣦⡀⢢⠀⣀⠀⡰⠁⠃⠈⠉⠦
⠀⡀⠀⠄⡄⠀⠛⠛⠒⠻⠅⢠⣀⠚⠛⠋⠀⢈⠛⠿⡶⠃⠂⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⣴⣢⢄⡀⠃⠀⠘⠃⢠⣶⠻⢠⣤⡾⠉⢙⣣⢶⠏⢴⡄⠀⠉⠀⠓⠊⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠉⣰⣶⣶⣶⣶⣶⣶⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣴⣎⣸⢿⣿⣿⣿⣏⣩⡯⢨⡅⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⡤⠉⡤⣤⠘⢿⣃⣀⣄⣀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠤⠤⣼⣿⣿⡟⠉⠹⣶⣶⠛⣿⣿⣿⣿⠿⠛⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢼⣿⣯⠶⠿⣿⣿⣿⡇⢿⣿⣷⣐⣂⢤⣤⠴⣤⣀⣀⣀⢀⠀⢢⣧⣀⣀⣀⠀⠈⠋⠙⠈⠬⠀⠉⠀⠀⠀
⠀⠀⠠⠷⠂⠀⠀⠀⠀⠀⢈⣠⣹⣿⡏⠀⠀⠀⠀⠀⠀⣼⣿⠟⣿⡇⡀⠀⠀⠈⢿⣿⣿⣿⣿⠇⠀⠀⢰⣿⣿⠏⠀⠀⠘⣿⣿⢣⣼⠿⠟⠛⠋⡀⠀⠿⢿⣿⣿⣿⢨⠈⠉⠰⠿⠣⡓⠃⢴⣯⢀⣀⠒⠢⡄⠰⠂⢀
⠀⠀⠀⠂⠃⠶⠄⣦⣶⣾⣿⡟⣿⣿⣷⣖⠀⢀⣤⣄⠐⠋⣡⣰⣿⡇⢣⣤⣄⠀⠀⠙⢿⣿⠃⠀⠀⣴⣿⣿⣿⡆⠀⠀⠀⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⢀⣶⣄⠀⠈⠉⠈⠛⠿⢤⡼⣷⣛⢊⡉⡞⢍⣉
⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠃⠀⠁⣤⣴⣿⣿⣿⡇⢸⣿⣿⣷⣦⣀⠀⠉⠣⢀⣾⣿⠿⠛⠋⠁⠀⢀⣴⣿⢱⣿⣿⣷⡆⠀⠀⣀⡀⠀⢀⣀⣿⣿⣸⣿⣿⣿⣿⣹⣂⡀⠀⠸⠀⠀⡀⢠⣍⡩⠙⢻
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢱⣿⣿⣿⠁⠀⣶⣦⠌⠉⢻⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⣸⣿⣿⣿⣧⣄⡀⠛⠁⠀⣠⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡇⠀⡤⠄⠀⠠⠿⠿⢛⣡
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣶⡄⠉⠉⣤⣤⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⣿⣿⣿⣿⠟⠛⢁⣀⠈⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⢤⣴⣦⢄⠀⠀⠻⢡⣨⣭
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⣿⠏⠉⢀⣄⡄⠛⢻⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣾⣿⣿⣿⣿⢀⣿⣿⣿⣿⣤⣀⠘⠿⠃⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣶⣿⡟⢛⡟⢛⠋⢙⣧⡾⠛
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣦⣄⠈⠛⢁⣀⣸⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⠿⠿⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢣⣶⣷⣿⣚⡋⠰⠞⠉⠀⠘
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⣾⣿⡿⠛⠁⣀⣀⠸⠿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⠁⣾⣿⣿⣿⣿⡀⠀⠿⡿⠀⠀⣹⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⡏⠻⠛⠛⠉⣱⠚⢓⡢⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⣿⣿⣯⣀⠸⠿⢟⣀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⠇⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⡶⣶⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡧⡀⠀⠀⢠⠁⠀⢁⣔⢻⣁
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢀⣿⣿⣿⣿⣿⣇⠀⢰⣶⡖⠉⢹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡟⢋⣈⣀⠀⠠⢐⠺⠽⠿⠿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⠀⣦⣤⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣾⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⡟⢿⣿⣶⣄⣀⢈⠉⡋⢀⣀
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣦⣌⣉⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠃⣤⣄⣠⡌⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⣤⠤⠁⠀⠘⠋⠀⠀⠈⠁
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⠀⠛⠿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡏⠉⣛⢛⠿⣄⡙⠛⠋⠐⠛⢻⣿⣿⡿⠀⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⣲⣾⠷⠟
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⣶⣶⣿⠀⢸⣿⣿⠇⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⣿⡀⡀
⢸⣿⣿⣿⣿⣿⣿⡿⡻⣟⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣋⣛⠉
⣿⣿⣿⣿⣿⣿⣿⣥⡄⡀⠳⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣷⡆⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⢠⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣐⠫⣵⣼⣧⣿⣿⣿⣿
⣿⣿⣿⠿⣿⣿⣿⡏⠁⠀⣠⣿⣿⣿⣿⣿⣿⠅⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢀⠀⠸⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⡿⠿⠀⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣯⣟⠅⠀⠘⠿⠿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣿⣿⣿⣷⠀⠉⠉⠉⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⣿⣿⣿⠛⠳⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⢿⠟⠛⠒⢦⠜⠛⠛⢫⣾⠀⠀⠟⠛⠛⠻⣿⡿⠛⠛⠻⠀⠀⠛⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠈⠀⠀⣴⣿⣿⠀⠀⠀⠀⢀⣀⣿⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⡆⠀⠀⠀⢰⠀⠀⠀⠀⢀⣀⢹⣿⣿⡏⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠀⠀⠳⠄⠀⠈⣿⣿⠀⢠⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠘⢁⣼⣿⣿⠁⠀⠈⠻⣿⣿⣻⣯⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣠⣄⠀⠀⢀⡇⠀⠀⠀⠈⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⣦⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⡁⠀⠀⠀⣸⣿⠋⠉⢰⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣥⣶⠀⠾⠁⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⠈⠁⢈⠵⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⢴⣆⠀⠀⠀⠀⠀⢀⠁⢈⣠⣒⡀⠤⢼⠈⠁⠖⠀⢥⠀⠙⠀⢶⢴⣶⣉⡀⢀⠀⠘⠋⢛⣥⡀⠰⠋⡴⠄⣠⣙⣿⡾⠧⢀⢿⣏⣉⡄⠀⠘⡇⠈⠁⠚⠿⢿⠿⠷⠷⠤⠂⠾⣳
⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠘⠋⠉⣔⠆⢉⡉⠐⠤⠤⠉⠀⠐⠋⠉⣴⠇⠐⠀⢀⠀⠀⣤⣿⠒⣀⣄⣈⣠⣀⣁⣁⣠⣤⣶⠀⠈⠭⠀⢀⢶⡟⢱⡿⠳⠝⣷⡂⠊⠟⠻⠙⠅⠀⣐⣠⠀⢀⣤⡄⠃⡀⠀⠀⠀⠀⢀⡿
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠙⠛⣀⠀⠀⣼⡂⠈⢁⠭⠁⠀⣤⣄⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣋⣀⣠⡄⢦⣛⣹⣇⣼⠀⢠⣷⣯⠍⠀⠀⠀⠘⡶⠈⣿⡃⣒⡀⣴⣠⣄⠀⠀⠀⠀⠀⣠⢠
⠀⠀⠀⠀⠀⡤⠄⠈⠁⠀⠀⠀⠀⣑⣤⣤⣶⣿⣶⣿⢿⢷⡀⢺⣷⡋⠀⠛⠿⠇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠥⠌⢛⣋⠙⠻⠖⢸⢉⣇⠶⢬⠩⡶⣶⠤⠢⠟⣳⣥⣿⣿⣹⣇⠐⠀⠾⠄⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⢙⠛⢋⣹⣭⣟⠛⠃⠈⠤⠵⠶⢶⠐⡂⡄⣀⣴⣿⣿⡿⠿⡍⠛⢻⣿⣿⣿⡿⠛⢛⣛⣿⣿⣄⠀⠀⠀⠈⡰⠚⢀⢦⠈⠀⠀⠘⠛⠃⣬⠤⠲⠖⢸⡟⣉⠿⢿⣷⣷⠆⢠⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢹⣿⣁⡈⠉⠉⠙⠉⣬⡈⠥⠚⠚⠉⢙⣿⣿⣟⣥⣴⣤⡄⣠⣾⣿⣿⣿⡀⠀⣀⢈⠙⢿⣿⡄⠐⠚⠙⠃⠀⠰⠆⠞⠛⠂⠬⠀⠀⠀⠐⠂⠀⠐⠞⣗⣒⢘⢋⣹⣻⣿⣟⠻⣷⣤
⠉⠋⠠⠌⠀⠀⠘⠁⠀⠀⠀⠀⠀⢈⡙⠋⠉⠠⢾⠓⠾⠁⠑⠀⣄⠀⢘⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⢿⣿⣝⣛⣻⣾⣿⣿⡀⠀⠀⠀⠀⠂⡀⠴⣠⡴⡔⣶⣆⣦⠖⠀⠀⣠⣼⣋⣿⣿⣶⣿⣽⣿⣿⠟⡛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡶⠞⠁⠘⠉⣀⢀⠛⠀⡄⣿⣿⣿⣿⣿⠟⣻⣿⣦⣴⣄⣀⣀⣈⣿⢿⣿⣿⣿⣿⣿⡇⠉⣁⣀⠀⢛⣷⣄⡀⣉⣛⣿⣿⡽⠲⠒⠛⠻⣟⣯⠏⡋⠩⠿⠉⠙⠁⣜⠁⠀
⠀⠒⠀⠀⠀⠀⠠⢀⢉⣠⡴⣢⡤⣦⣴⣶⡂⠀⠀⠀⠠⠎⣹⡯⠀⠀⣰⣿⣿⣿⣿⢃⣰⣿⣿⠿⠿⠿⠿⢿⣿⣿⣆⠙⣿⣿⣿⣿⡇⠒⠒⠉⠐⣫⣼⡖⠀⢬⣟⠿⠿⠏⠻⢧⠆⠠⢭⠴⢴⣄⡐⠀⠀⠀⠀⠨⣧⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠠⠍⠛⠓⠚⠛⣿⣥⠀⠀⠀⠐⣆⡀⠀⠀⢛⡅⣿⣿⣿⣿⣿⣾⣿⣋⣤⣿⣧⣤⣤⣤⣈⡹⣿⣷⣿⣿⣿⣿⣇⠀⠰⠤⠘⡿⠗⠀⠂⠚⠀⡀⡀⠀⠙⠷⣤⣤⠾⢐⣧⠒⣈⠙⡶⣀⢀⣦⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠈⢡⠈⠑⠙⠀⠀⠀⠀⢈⠁⠈⠀⠛⠃⠈⠘⢹⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣆⣤⠀⢩⣉⣐⠊⠠⠴⣴⡆⢀⣸⠦⠋⠉⢉⠹⠁⠀⠙⣻⣿⡿⠛⣹⣿⡿
⠀⠀⠠⡒⠀⠀⠀⠀⠀⠀⠀⢀⣠⡰⡖⡀⢠⠖⠀⠐⠀⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⢀⢠⡤⡅⠁⠀⣠⡭⠅⠀⠀⠓⣠⣢⣬⠉⠁⠀⠀⢃⣤⡄⠠⣵⣫⣤
⠀⠀⠀⠀⠁⠂⠀⠓⠀⠠⠀⠀⠠⠿⠟⠁⠀⠀⠉⠛⠂⠀⠀⠬⢤⠺⠟⢻⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠈⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠋⠲⠖⠫⠈⣟⡋⠁⠢⣾⣯⡄⣄⡀⠀⠈⡉⠁⡀⣤⣤⡀⠈⠑⣦⣼⡉⠽⠿
⠀⠀⠀⠀⠀⢂⠀⠀⢀⠀⢀⣀⣤⡀⠀⠀⢀⣀⡀⠤⠀⠀⠀⠂⢀⡂⠀⢸⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⠉⠋⠀⠰⠘⠀⠀⠀⢀⠀⠀⠁⠙⢷⠈⠠⢤⢀⡀⠛⣄⠐⠛⠁⠀⢀⡾⢄⣣⡀⠀
⠀⠀⠀⠀⠠⠤⠤⣤⠌⠀⠈⠀⠀⠈⣠⣖⠒⢁⣀⠐⠂⠒⢺⡷⠀⠀⣀⣼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡏⠑⠀⠠⠂⠀⠈⠁⠀⠚⠶⠦⡅⠒⠢⢆⠀⡖⠛⢹⣧⡄⢂⢀⣀⠀⡘⠈⠃⠀⠉⠂
⠀⡀⠠⠄⠄⠈⠛⠋⠒⠻⠆⢄⣄⠚⢛⠁⠀⢘⠓⠻⠿⠑⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⠀⢀⣿⣿⣿⣧⠀⡔⣡⢤⡀⠀⠀⠘⠃⢠⡶⠳⢠⣤⡞⠁⢘⣵⣾⠃⣴⡀⠀⠀⠐⠓⠀⠀⠀⠐⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⠉⠉⣿⣿⣿⣿⣿⠟⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⠭⠝⣻⣿⣿⣿⡯⣽⣯⣤⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⠤⢦⠘⢏⣀⣠⣤⣀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠰⠛⠀⠀⠀⠀⠠⠴⢠⣾⡟⠛⠋⠀⠘⠿⠛⢡⣿⣿⣿⠿⠋⠉⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡷⠋⠻⣿⣿⣿⠇⣿⣿⣷⣤⡾⠶⢆⣒⣤⣤⣄⣀⣀⠐⣲⣧⣀⣀⣀⠀⠈⡉⠉⠀⠄⠈⠉⠀⠀⠀
⠀⠀⠠⠗⠀⠀⠀⠀⢀⣀⣤⣶⣼⣿⣇⡀⠀⠀⠀⠀⢀⣾⠟⢫⣿⡘⡀⠀⠀⠀⠻⣿⣿⣿⡟⠃⠀⢀⣼⣿⣿⠁⠀⠀⠘⣿⡟⣴⡿⠛⠋⠈⠀⠀⠈⠛⢿⣿⣿⡛⢮⠈⠁⠰⠛⠢⡙⠃⢼⡧⣀⣐⣚⢲⡄⠠⠄⣀
⠀⠀⠘⠘⠓⠶⠄⣶⣿⣿⣿⡏⣿⣿⣿⣧⣀⡀⠶⠖⠀⢀⣶⣾⣿⡇⢹⣷⣦⡀⠀⠈⠻⣿⡀⠀⣠⣾⣿⣿⣿⠇⠀⠀⢀⣿⢳⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⢸⣶⣄⡀⠈⡉⠈⠙⠿⢤⠾⣶⡋⢫⣭⡏⠭⢬
⠀⠀⠤⠀⠀⠀⣼⣿⣿⣿⣿⣇⣿⣿⣿⠿⠿⣀⡀⠸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⣤⣀⠀⠁⠰⠿⠛⠋⠉⠀⠀⢀⣤⣾⡏⣼⣿⣿⣿⠀⠀⢠⣤⠀⠀⢠⣤⣿⣿⢸⣿⣿⣿⣿⣹⣂⣀⠀⠺⠀⢀⡀⢠⣤⠥⠉⢙
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢸⣿⣿⣟⣀⠀⠿⠿⠀⠀⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃⣿⣿⣿⣿⣷⣦⠈⠉⢠⣤⣼⣿⣿⣿⢸⣿⣿⣿⣿⣿⣻⣿⠃⠠⡄⠄⠀⠰⠟⠛⢋⣾
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢸⣿⣿⡿⠿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⡿⢰⣿⣿⣿⣿⠉⠉⣶⣤⠘⠛⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣟⠟⣤⣶⣦⣀⠀⠈⠻⠥⣬⣽
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⢸⣿⣿⠀⠀⢸⣿⠃⠀⢸⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣶⡦⠉⠛⣠⣄⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⣹⠟⠉⠉⢙⣓⡺⠉
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⠟⠖⠀⠀⣰⣶⣾⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⠀⣿⣿⣿⣿⡟⠙⢃⣄⡀⠛⠿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⢡⣷⣷⣷⣉⡉⠴⠚⠁⠂⢛
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⢠⣶⣆⠈⠉⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⣿⡇⢸⣿⣿⣿⣿⣧⣄⠈⠛⠃⠀⢠⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⠀⠛⠋⠉⠈⣱⠙⣛⡂⠀⢀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣶⠈⠉⠓⢢⣴⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡟⢀⣿⣿⣿⣿⣿⠟⠛⣀⣀⠸⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣠⡀⠀⠀⣴⠁⠀⢠⣖⡻⣀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡃⢿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⡐⠛⠿⠁⢀⣽⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠛⣋⣀⡤⠀⠠⢌⢹⠽⠛⠧
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠘⢿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⠻⠿⢿⡷⣦⢀⣈⠉⣍⣀⣀
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⢿⣿⣿⡇⠸⣶⣶⡖⣸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⡤⠤⠀⠀⠈⠁⠀⠠⠀⢀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠁⠀⠉⠛⠇⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠀⣤⣬⣭⣽⣒⣀⣀⣀⡀⠉⣿⣿⣿⠃⢸⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⣮⣿⠛⠋
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⡏⠀⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⢨⣿⡄⠀
⢸⣿⣿⣿⣿⣿⣟⠻⠂⠡⣸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣉⣓⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⢄⣴⣖⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣼⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣐⠻⣵⣼⣧⣿⣿⣿⣿
⣿⣿⣿⣭⡭⢻⢿⠂⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠙⠛⠛⣿⣿⣿⣿⡇⠀⠀⣠⣤⣬⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡄⠸⠿⠿⠿⠿⠛⠛⠋⢁⣼⣿⣿⣄⡀⣀⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣛⡛⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣶⣤⣄⣀⠀⠀⣿⣿⣿⠟⡤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⣿⣿⣿⠛⠻⠛⠛⠟⠓⡀⠀⠀⠀⠀⠀⠈⠙⠛⠟⢿⠟⠛⠻⢶⠟⠛⠁⣾⡇⠀⠘⡿⠛⠛⢿⣿⣿⠛⠛⠃⠀⠘⠛⣿⠟⠛⠀⠀⠀⠀⢀⠀⠀⠠⠾⠿⠿⢿⣿⣿⡇⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⣶⣿⡇⠀⠀⠀⠀⢀⣠⣿⣿⠀⠰⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣰⠆⢸⣿⣿⠃⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠳⠄⠀⠈⣿⣿⠀⢠⠀⠀⠀⠀⠿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡟⠀⢀⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣀⣄⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠺⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⠁⠀⣼⣦⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠛⢻⣿⣷⣄⡀⠀⢸⣿⠀⠀⢛⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡇⠠⠿⠁⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⠈⠁⢈⠿⠛⠀⠀⠀⠀⠀⠀⢀⣀⣀⠴⣆⡀⠂⠀⠀⠀⣄⠁⣈⣥⣂⡀⠤⣵⠉⠁⠖⠀⢥⠀⠙⠀⢶⢶⣦⣥⡀⢀⠀⠘⠉⢉⣦⠀⠳⢫⣤⡀⣠⣙⣷⡾⠧⣠⢻⣇⣩⡄⠀⠙⡆⠈⠉⠛⠿⣿⠿⠿⠿⠤⠂⠞⣳
⠀⠀⠈⠀⠀⠀⠀⠠⠈⠁⠘⠋⠉⣖⠄⣉⡍⠀⠤⠄⠁⠀⠈⠋⢩⣴⠍⠂⠀⢀⠀⠠⣴⡟⣒⣤⣤⣤⣤⣌⣉⡄⣴⣴⣗⠀⠀⠭⠂⢠⢾⡏⢲⡿⠫⠙⣖⡂⠘⠟⠛⠙⠇⠀⣀⣤⠀⢀⡦⠌⠁⠀⠀⠀⠀⠀⢠⡿
⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⠋⢛⣀⠀⠀⣼⠂⠈⢁⠝⠀⠐⣤⣴⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢋⣀⣠⣀⣦⢚⣹⣆⡿⠀⢠⣾⣗⠁⠀⠀⠀⠒⡖⠈⣿⡓⣊⡀⣶⣤⣄⠀⡀⠀⡀⠀⣠⢠
⠀⠀⠀⠀⠀⠤⠀⠈⠁⠀⠀⠀⢀⣉⣤⣦⣷⣿⣶⣿⢿⢿⣀⢻⣷⠁⠀⠛⠿⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠩⠘⣙⣋⠛⠳⠚⠸⢩⣃⠶⢥⡠⡶⣶⡤⠪⠯⣵⣦⣿⣿⣹⡁⠘⠀⡾⠆⠀⠀⠀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠛⣯⣹⣽⣟⠛⢣⡨⠬⠵⡶⠿⢑⡠⡄⣠⣾⣿⡿⠿⠯⠙⠛⣿⣿⣿⡿⠛⠋⣹⣿⣿⣧⡀⠀⠀⠀⢀⡰⠓⢀⠦⠈⠀⠀⠘⠛⢃⠬⠄⠑⠖⢹⡟⣉⠿⣿⣿⣷⢆⣄⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⢹⣿⣁⠨⠉⠉⠋⠉⣬⡨⠥⠛⠚⠉⢹⣿⣿⣯⣴⡶⠤⣄⣼⣿⣿⣿⣧⣀⣠⣄⣌⠙⣿⣷⡀⠐⠛⠙⠃⠀⠴⠂⠚⠙⠂⠭⠀⠀⠀⠐⠂⠀⡘⠺⣗⡂⢈⢉⣭⣻⣿⡝⠻⣧⣤
⠙⠉⠰⠌⠀⠀⠘⠀⠀⠀⠀⠀⠀⢈⡉⠋⠉⠠⢾⠂⠾⠃⠑⠠⡆⠀⣛⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠋⠉⠛⣿⣿⣭⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⢂⡀⠴⣠⡞⡖⣶⣧⣦⠆⠀⠀⣠⣼⣫⣿⣿⣶⣿⣽⣿⣿⠟⡛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠚⠁⠘⠍⣀⢀⠛⠀⢰⣿⣿⣿⣿⡿⢋⣿⣿⣶⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠀⠈⣁⣀⠰⢛⣷⣄⠀⣉⣟⣿⣿⡝⠳⠒⠛⠻⣟⣯⠛⠋⠩⠟⠁⠙⡁⣌⠁⠈
⠀⠒⠀⠀⠀⠀⠠⢀⢉⣤⡴⣦⠴⣦⣶⣶⠂⠀⠀⠀⠰⠏⣽⡯⠀⠀⣾⣿⣿⣿⣿⣠⣿⣿⢟⣛⠛⠛⠛⠿⣿⣿⣎⣻⣿⣿⣿⣿⠀⠒⠚⠁⢐⣩⣾⡶⠀⣭⡗⠿⠿⠋⠻⠷⠆⠠⢥⠶⣴⢄⣘⠀⠀⠀⠀⠬⣇⡰
⠀⠀⠀⠀⠀⠈⠀⠀⢦⠍⠛⠒⠚⠛⣿⣵⠀⠀⠀⠒⣎⡀⠀⠀⢋⣤⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣶⣶⣶⣤⣙⣿⣿⣿⣿⣿⣿⣀⠀⠲⠄⠸⡿⠗⠀⠇⠚⠀⢀⣀⠀⠙⠳⣤⣤⠼⣴⡧⠒⣈⠙⡶⣀⣀⣷⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠈⢡⠈⠁⠙⠀⠀⠀⠀⠈⠀⠉⠀⠛⠁⠈⠚⠹⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣆⣄⠈⢩⣁⣐⠊⠠⢴⣴⡆⢀⣽⠦⠏⠛⢉⠝⠁⠀⠙⣻⣿⡿⠋⣻⣿⠿
⠀⠀⠰⡒⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠦⡀⢠⠖⠀⠀⠀⠁⠘⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠉⠛⠿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⢀⢠⣤⣉⡁⠂⢠⡥⠅⠀⠀⠓⣔⣠⣬⠉⠁⠀⠀⢡⡤⡄⠠⣵⣣⣤
⠀⠀⠀⠈⠁⠂⠀⠓⠀⠠⠀⠀⠠⠿⠟⠁⠀⠀⠉⠓⠂⠀⠠⠍⢀⠻⠛⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⡟⠉⠲⡗⠯⠈⣟⡋⠁⢤⣾⣧⠤⣠⠀⠀⠈⡙⠁⡠⢤⣤⡀⠈⠑⢦⣼⠉⠽⠿
⠀⠀⠀⠀⠀⣂⠀⠀⢀⠀⢀⣀⣤⡀⠀⠀⢀⣄⡀⠄⠀⠀⠀⠃⢀⡂⠀⣼⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠥⠈⠁⠀⠰⠘⠀⠀⠀⢀⠀⠀⠁⠙⣧⠈⠠⠤⢀⡀⠛⣌⠘⠛⠁⠀⢀⣾⣀⣣⡀⠀
⠀⠀⠀⠀⠠⠤⠠⡤⠬⡄⠈⠀⠀⠘⣠⣖⠒⢁⣀⡐⠒⠒⢻⡇⠀⢀⣠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋⠑⠀⠠⠂⠀⠈⠁⠀⠘⠶⠦⡥⠒⠂⣆⠀⡖⠊⢿⣦⠄⢆⢀⣀⠀⡜⠈⠁⠀⠘⠂
⠀⠀⠠⠈⠄⠈⠛⠉⠓⠻⠆⢄⡄⠚⠋⠀⠀⢈⠚⠿⠿⠙⠂⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣄⡀⣬⣿⣿⣿⣇⠀⡖⡥⢤⣀⠀⠀⠙⠃⢠⡗⠳⠤⣤⡟⠁⢘⣔⣾⠀⣴⡀⠀⠀⠘⠃⠁⠀⠀⠒⠂
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠈⢉⣾⣿⣿⠿⣿⡋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣾⣿⠿⣻⣿⣿⣿⣿⢯⣽⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢠⠤⠦⠘⣏⣀⣠⣤⣀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠰⠛⠀⠀⠀⠀⠠⢶⢠⣿⡟⠛⠃⠀⠘⠛⠋⣰⣿⣿⣿⠛⠉⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⠟⠉⠻⣿⣿⣿⠈⣿⣿⣷⣶⠛⠓⢦⣒⣶⣤⣤⣄⣀⠐⣲⣧⣀⣄⣀⠀⠈⡉⠉⠀⠄⠈⠉⠀⠀⠐
⠀⠀⠢⠗⠂⠀⠀⠀⣀⣠⣵⡾⣿⣿⣃⡀⠀⠀⠀⠀⢠⠿⠛⢹⣿⠰⡀⡀⠀⠀⠻⣿⣿⣿⠟⠀⠀⣠⣿⣿⣏⠀⠀⠀⢸⣿⣇⣾⡏⠙⠀⠀⠐⠂⠈⠛⢿⣿⣿⠃⣦⠨⠀⠲⠛⡢⣙⠃⢾⡧⣀⡀⣈⢲⡄⠤⠅⣀
⠀⠀⠈⠘⠒⠶⢐⣾⣿⣿⣿⣇⣿⣿⣿⣧⣄⡰⠿⢃⠀⢰⣷⣿⣿⡆⣿⣿⣶⣄⠀⠈⠻⢿⡀⢀⣼⣿⣿⣿⠿⠃⠀⠀⢸⡿⣸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣴⣶⣄⣀⣈⡁⠈⠙⠿⢶⠿⣗⠋⣫⣹⡏⠥⢬
⠀⠀⠤⠀⠀⠀⣼⣿⣿⣿⣿⢸⣿⣿⡿⠛⠻⣄⣀⠸⢿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣷⣦⣄⡀⠁⠚⠛⠋⠁⠀⠀⠀⣠⣾⣿⠃⣿⣿⣿⣿⠀⠀⢰⣦⠀⠀⣶⣾⣿⡇⣿⣿⣿⣿⣿⣹⣀⣀⠀⠓⠀⢀⠀⠰⣤⠥⢍⢙
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢸⣿⣿⣧⣀⡸⠿⠟⠀⢀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢰⣿⣿⣿⣿⣿⣦⠀⠁⣴⣶⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⠁⢠⡄⠆⠀⠼⠟⠛⣫⣾
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⢸⣿⣿⠿⠿⠃⠀⠸⢿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⡇⢸⣿⣿⣿⣏⠀⠀⣶⣶⠉⠛⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣛⠓⣤⣶⣶⣀⠀⡈⠯⠥⣬⣵
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⣾⣿⣿⠀⠀⢼⣿⠀⠀⢸⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣷⡆⠉⠉⣤⣤⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠉⣹⠏⠉⠉⣙⣓⠛⠉
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠻⠇⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⡿⢠⣿⣿⣿⣿⡏⠉⢡⣤⡄⠙⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢡⣷⣿⣷⣉⡉⠳⠋⠐⠂⢙
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢇⣿⣿⡇⠀⢠⣶⡆⠈⢁⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⠃⣼⣿⣿⣿⣿⣷⣤⠈⠙⢁⣀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠈⠙⠉⠉⠀⡡⠙⣙⡂⠀⢀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠍⣿⣿⣿⡿⠉⠉⠁⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠏⢰⣿⣿⣿⣿⡿⠋⠻⣤⣀⠸⠿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⢠⣀⡀⠀⣤⠀⠀⢠⣔⣫⢀
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⢁⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡌⠛⠛⠀⣠⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠛⣃⣤⠤⠀⠢⢌⣹⠽⠛⠧
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡘⠿⠿⢋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠻⠿⢯⡧⡦⢄⣈⠉⢍⣀⣄
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⢿⣿⣿⡄⠺⠿⠿⠇⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⡤⠤⠀⠀⠉⠁⠀⠀⠀⢀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠉⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⣴⣴⣾⣯⣷⣀⣀⣤⡄⠀⣿⣿⣿⠁⣸⣿⣿⣿⣿⡿⠟⠓⠀⠀⠀⠀⠀⠀⣭⣿⠛⠉
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⡏⠀⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢂⢸⣿⣄⡀
⣼⣿⣿⣿⣿⣿⣿⣽⠋⠓⡿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⠀⢹⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣉⣓⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣂⡁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⢄⣴⣖⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢁⣾⣿⣿⣿⣿⣿⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⢠⣾⣿⣯⣿⣿⣿⢝⣐⠻⣵⣼⣧⣿⣿⣿⣿
⣿⣿⣯⣿⡟⡻⡿⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠈⠉⠉⣿⣿⣿⣿⡇⠀⢀⣴⣶⣮⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⠀⠿⠿⠟⠛⠛⠛⠋⠉⢁⣼⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⣻⡷⢀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣶⣤⣄⣀⠀⣿⣿⡿⢋⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⣿⣿⣿⠛⠻⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⠟⠛⠛⢿⠟⠋⠐⣿⡇⠀⠸⡿⠛⠛⢿⣿⣿⠛⠛⠃⠀⠘⠛⣿⠟⠃⡀⠀⠀⠀⢠⠀⠐⠲⠟⠛⠻⣿⣿⣿⠇⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣶⣿⡇⠀⠀⠀⠀⢀⣠⣿⣿⠀⠰⠀⠀⠀⠀⣿⠀⠀⡇⠀⠈⠀⠸⠀⠀⠀⠀⠶⠂⣿⣿⡿⠀⠈⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠷⠄⠀⠈⣿⣿⠀⢠⠀⠀⠀⠀⠛⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠇⠀⢀⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀
⣿⣿⠉⠀⣠⣄⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠺⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠿⠏⡀⢀⣼⣦⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠛⣿⣿⣧⣀⠀⠀⢿⣿⠀⠀⢻⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣴⣶⣿⡇⢸⠿⠁⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⠈⠁⣘⠾⠓⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⣖⡀⠂⠀⠐⠀⠄⠀⣀⣤⡂⡀⠤⡽⠉⠁⠒⠀⣥⠈⠉⠐⢶⣴⣦⣥⡄⢂⠀⠈⠉⠡⣦⠀⠲⢡⣶⠄⣤⣩⣷⠿⠐⣠⢻⣥⣵⡄⠀⠙⠆⠈⠉⠙⢛⡿⠿⠿⠿⠕⠂⠋⣿
⠀⠀⠁⠀⠀⠀⠀⠠⠈⠁⠘⠋⠁⣒⢆⣩⡁⠀⠆⠄⠁⠀⢈⠉⢡⡼⠍⠃⠀⣀⠀⠰⣴⡟⣂⣬⣤⣤⣤⣬⣉⣠⣤⢶⣇⠀⠈⠅⠂⢠⢾⡏⣰⡿⠫⠙⡆⡂⠘⠋⠋⠙⠄⢀⣘⡤⠀⢀⡦⠌⢁⠀⠀⠀⠀⠀⠠⠟
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⠉⠋⣀⠀⢀⣿⡁⠈⣄⠟⡀⠐⣶⣶⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣋⣀⣤⣄⣤⣚⣹⣤⡯⠀⢠⣿⡿⠁⠀⣀⡀⠓⠖⠈⣿⠆⣈⢠⡾⣤⣄⠀⡀⢀⠄⠀⣴⢠
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⣟⣤⣤⣿⣿⣶⡿⢿⢷⣀⢹⢿⠁⠀⠛⠿⠃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠤⠈⣝⣋⠙⠿⡎⢸⣩⣓⠶⢦⠰⡶⣶⠼⠸⠩⣽⣦⣿⣿⣼⣀⠘⠐⠯⠆⠀⠂⠀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡛⣯⣽⣿⣟⡉⢣⡠⠌⢿⡷⡿⢑⡦⡄⣠⣾⣿⠿⠛⠛⠊⠙⣿⣿⣿⡟⠋⠉⠽⣿⣿⣷⡀⠀⠀⠀⢀⡴⠋⠠⠇⠂⠀⠀⠈⠉⠃⠤⠖⡛⠒⢽⣏⣉⠿⣻⣿⣿⢆⣆⣤⣄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⢹⣯⣅⠨⠍⠉⠉⠉⣤⡬⠗⠛⠉⠁⢹⣿⣿⣷⣶⣿⣒⣦⣾⣿⣿⣿⣷⣤⣤⣦⣤⣙⣿⣷⡀⠘⠋⠙⠁⠀⢼⠂⠚⠛⠂⠤⠀⠀⠄⠒⠂⠀⡨⠺⣗⣂⢩⢭⣭⣻⣿⣏⡛⣶⣭
⠉⠉⠰⠈⠀⠀⠈⠀⠀⠠⠀⠀⠀⢈⠍⠋⠉⠐⢿⡃⠾⠃⠉⠀⡆⠀⣉⣼⣿⣿⣿⣿⣿⣿⣟⠁⡀⠀⠀⠉⢿⣿⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣂⠀⢶⣤⡞⡖⣾⣧⣶⠂⠀⠀⣠⣾⣭⣿⣿⣿⣿⣽⣿⡿⢿⡙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠊⠠⠈⠍⣀⣀⠛⠠⠄⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣷⣶⣶⣾⣯⢿⣿⣿⣿⣿⣿⠀⠈⣄⣀⠸⢛⣶⡄⠀⣩⣻⣽⣿⡏⠓⠘⠉⠛⣏⣿⠙⠏⠩⠟⠀⠉⠀⣌⠀⠈
⠀⠒⠀⠀⠀⠐⠤⢀⢉⣤⣜⡦⢴⣶⣶⣞⠀⠀⠀⠀⠰⠋⣽⡧⢀⠈⣸⣿⣿⣿⣿⣴⣿⠿⢫⣭⣉⣉⡉⠙⠻⣿⣷⣹⣿⣿⣿⣿⠀⠒⠋⠀⣘⣭⣽⣖⠠⣭⡗⠻⠻⠉⡛⠷⠂⠰⢶⠞⣴⠄⣑⡀⠀⠀⠀⠺⣦⡰
⠀⠀⠀⠀⠀⠈⠀⠀⠲⠮⠋⡒⠓⠚⣯⡴⠀⠠⠀⠐⣎⠀⠀⠉⣋⣄⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣀⠀⠲⠄⠘⡿⠧⠘⠃⠛⠀⠀⣀⠊⠙⠳⣤⣬⣹⣪⡗⠒⣈⣙⡚⣀⣨⣿⣿⣖
⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠡⠍⠀⠀⠀⠀⠈⠀⠉⠀⠛⠀⠀⠚⠹⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣦⡤⠈⢩⣥⣐⠉⠠⢖⣶⡀⢀⣽⠶⠍⠉⢁⡚⠁⠀⠉⡿⢿⠿⠋⣿⣿⡿
⠀⠀⠰⡀⡀⠠⠀⠀⠀⠀⠀⢀⣤⡰⠬⡁⠠⠆⠀⠀⠀⠁⠘⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⠉⠛⠀⠈⠛⠻⢻⣿⣿⣿⣿⣿⣀⠀⠀⢀⢠⣦⣀⡁⠂⢴⡤⠅⠀⠀⠑⣜⣰⣤⠀⢁⠀⠈⢡⡤⡄⠰⣼⣥⣤
⠀⠀⠀⠈⠁⠀⠀⠓⠀⠠⠀⠀⠐⠿⠍⠀⠀⠀⠉⠃⠀⠀⠀⠀⠤⠝⠉⢹⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿⢿⡏⠁⠹⠗⠍⢘⣟⡉⠐⢲⢾⣧⣐⡠⠀⠀⢈⠍⣁⡠⢤⣶⡄⠀⠙⢶⢾⡉⠽⠿
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⢀⣠⣤⡀⠀⠀⢠⣄⠀⠄⠀⠀⠀⠃⢀⠂⠀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡤⠈⠀⠀⠰⠈⠀⡀⠀⢀⠀⠘⠀⠙⠧⠉⠠⠤⢤⡐⠉⣌⠙⠛⠀⠀⢀⢿⡀⣠⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠬⡄⡀⠀⠀⠀⣠⣖⠊⢡⣀⣐⡒⠊⢹⠗⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠉⠐⠀⠠⠂⠀⠈⠁⠀⠈⠴⠮⡥⠓⠒⣇⠐⣞⠉⢿⣧⠄⢧⢀⣄⠀⡎⠈⠁⠀⠘⠒
⠀⠀⠠⠈⠄⠈⠛⠉⠛⠻⠆⣠⡄⡛⢋⣀⣀⣈⣓⣻⣟⣙⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⣦⣼⣿⣿⣿⣿⣇⢀⣞⡴⢤⣈⠀⠀⠉⠁⠴⠗⠣⠴⢴⡟⠁⢨⡖⠿⠀⣾⣀⠀⠀⠘⠉⠁⠀⠀⠓⠂
⡀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠈⠁⠈⢁⣿⣿⡟⠛⢿⣅⣸⠿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢰⣿⣿⣯⢼⣿⣿⣿⣿⢳⣿⣧⡴⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡴⢠⠰⠆⠘⢏⣅⣴⣤⡄⢀⣀⠀⠀⠀
⠁⠀⠀⠀⠸⠛⠀⠀⠀⠀⡠⢶⢲⣿⡏⠉⠁⠀⠈⠉⠁⣼⣿⣿⣿⢁⠀⠀⠀⠻⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⠃⠀⠈⢿⣿⡿⣸⣿⣿⠿⠶⠉⠙⢥⣤⣶⣶⣦⡄⣀⢒⣺⢦⣤⢤⠤⠀⢈⡁⠁⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠠⠗⠀⠀⠀⠀⣠⣴⣶⡏⣿⣿⣧⡄⠀⢀⣀⡀⠰⠛⣁⣸⣿⠘⣤⣄⡀⠀⠘⢿⣿⡿⠁⠀⢀⣼⣿⣿⣷⠀⠀⠀⢸⣿⢱⣿⡏⠉⠀⠀⠀⠀⠈⠉⢿⣿⣯⠁⡆⠀⠀⠚⢛⡪⣉⡁⣿⠶⣠⡤⣉⣲⡄⠨⢀⣤
⠀⠀⠈⠈⠚⠶⢒⣿⣿⣿⣿⢇⣿⣿⣿⣷⣶⠈⠙⢡⣤⣼⣿⣿⣿⠀⣿⣿⣿⣦⣀⠀⠈⠻⠄⣠⣿⣿⡿⠟⠛⠁⠀⣀⣼⡏⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣴⣶⣆⣀⣀⡁⢈⠙⠛⡶⠿⠯⠁⣡⣸⡋⠤⡼
⠀⠀⠤⠀⠀⠀⣾⣿⣿⣿⣿⢸⣿⣿⡟⠉⢉⣶⣴⠘⠛⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣶⣄⠀⠉⠀⠀⠀⠀⠀⣠⣾⣿⣿⢰⣿⣿⣿⣯⣀⠀⢿⡇⠀⠀⣿⣾⣿⡇⣿⣿⣿⣿⣯⣽⣤⣄⡂⠓⠀⢠⠀⢴⣤⡴⢍⢩
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢸⣿⣿⣷⣶⡌⠛⢫⣤⣰⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⢸⣿⣿⣿⡿⠿⠇⠀⠀⣶⣷⣿⣿⣿⡇⣿⣿⣿⣿⣿⣧⣿⡿⠁⠠⠆⠂⠠⠼⢟⠛⣡⣾
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⣿⣿⣿⠉⠉⢀⣤⠘⠛⢿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣿⣿⣿⣿⠃⣿⣿⣿⣿⣇⣀⠸⣿⡇⠀⢹⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣝⠃⣴⣾⣶⣀⣀⣈⠋⠤⣤⣾
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣿⣿⣿⣤⡄⠛⠛⣀⡀⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠸⣿⣿⣿⡟⢀⣿⣿⣿⣿⡿⢿⠃⠀⢰⣶⣾⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⡿⣿⠉⡹⢏⡍⠉⣙⣒⠛⢉
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢃⣿⣿⡏⠉⠃⣀⡀⠿⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⡇⣸⣿⣿⣿⣿⠀⠀⣾⣶⠀⠈⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣭⡅⢓⠋⠀⠂⣉
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣥⡀⠺⠿⣗⡀⢸⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢿⡟⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⣤⣤⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⠀⡙⠉⠉⠀⡭⠉⡩⢒⠀⠀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⢀⣾⣿⣿⣿⣿⡏⠀⣰⣶⡦⠙⢹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣠⣀⠀⠀⡦⠀⠀⣠⣍⣣⡀
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⢴⣶⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⢠⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⣉⣡⡤⠤⠁⠐⢌⣹⡛⠛⠷
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷⣬⣉⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⣄⣀⣀⡈⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣟⠛⠿⢯⡿⠦⢄⡠⠩⢅⣠⠄
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠻⣿⣿⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⡟⠙⠛⠿⢿⣄⡙⠛⠛⠐⠻⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠷⡶⠒⠀⠀⠉⠀⠀⢀⣀⣠
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⣷⣶⣶⣶⠀⢸⣿⣿⡇⢠⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢿⣿⠛⠋
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢂⣸⣿⣄⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡽⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⡆⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣀⣋⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⢄⣤⣖⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⠛⠋⢁⣴⣿⣿⣿⣿⣿⡇⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⢠⣾⣿⣯⣿⣿⣿⢝⣐⠻⣵⣼⣧⣿⣿⣿⣿
⣿⣿⣷⣯⣽⡽⣯⡀⠀⠻⢿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣧⠈⠋⠉⠉⠉⠉⠀⠀⠀⣾⣿⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣾⣌⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣛⡛⢀⡀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣷⣶⣤⣼⣿⡿⣫⣾⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⢛
⣿⣿⣿⠛⠻⠛⠛⠟⠳⡄⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⠟⠛⠛⢟⠋⠒⠻⣿⠀⠀⠻⡿⠛⠛⢿⣿⣿⠛⠛⠀⠀⠛⠛⣿⠟⠂⡄⠀⢤⠐⢲⠚⠛⠛⠉⣉⠹⣿⣿⡟⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣟⠀⠀⠀⠀⠀⠀⡇⠀⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣶⣿⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠰⠀⠀⠀⠀⣿⠁⠀⡇⠀⠘⠀⠘⠀⠀⠀⠀⠋⣸⣿⣿⠃⠀⣨⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠷⠄⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⢀⣿⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀
⣿⣿⠉⠀⣠⣄⠀⠀⣀⣄⠀⠀⠀⢀⡇⠀⠈⠁⠀⣠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠁⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣉⣤⠀⣾⣿⣦⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠛⣿⡿⣿⣦⠀⡈⣿⡇⠀⢀⣿⣿⣿⠿⠿⣿⣶⣤⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠀⠀⠀⢰⣿⣿⣿⡀⠏⠮⠁⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⠈⠀⣨⠿⠛⠀⠀⠀⠀⠀⠀⢀⣀⡀⢶⣆⡐⠀⠀⠀⠀⠀⢈⣀⣤⣀⡀⠤⡇⠉⠁⠚⠀⣧⠈⠉⠐⢶⢴⣮⣥⠄⢀⠀⠈⠉⠩⣤⠀⠚⢡⡖⠄⣤⣩⣿⠟⠒⣠⢻⣆⣽⡄⠀⠙⠆⠈⠉⠙⢛⡿⠿⠛⠿⠖⠀⠋⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠙⠉⠁⣒⢄⣩⡀⠀⠆⠠⠁⠀⢈⠉⢡⡼⠌⠃⠀⠀⠀⠰⣼⣟⣠⣤⣤⣤⣤⣤⣤⣠⣤⢴⡇⠀⠈⠕⠂⢰⢾⡏⣰⡟⠫⠛⣏⡀⠘⠉⠫⡙⠇⢉⣘⡤⠀⢰⠶⠌⢁⠀⠀⠀⠀⠀⠠⠿
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠉⢙⣀⠀⠀⣽⠃⠈⣀⠟⡀⠀⣤⣞⠁⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣃⣀⣤⣤⣴⣈⣹⣤⡯⠀⣴⣿⡎⠀⠀⣀⡀⠙⠖⢈⣿⢖⣉⣐⡞⣤⡄⠀⠀⠀⠄⠀⣴⠠
⠀⠀⠀⠀⠀⠤⠀⠈⠀⡀⠀⠀⢀⣁⣤⣥⣿⣿⣶⡿⢿⠷⣀⢹⢿⠃⠀⠛⠿⢣⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠄⠊⣝⡉⠉⠟⠊⢻⢹⣓⠶⢶⢴⡾⣶⠔⠸⠩⣽⣶⣿⣿⣼⣀⠑⠐⠯⠄⠀⠒⠀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡛⣏⣽⣭⣟⡉⢁⠀⠌⢿⡿⡿⢐⡄⣄⣴⣿⡿⠟⠛⠓⠀⢹⣿⣿⣿⠋⠁⠀⠾⢿⣿⣧⡀⠀⠀⠀⢀⡞⠉⠠⠇⢂⠀⠀⠈⠉⠑⠶⠆⠘⠒⢽⡏⣉⠻⣻⣿⣿⢆⣆⣠⣄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⢹⣭⣁⠈⠉⠉⠉⠉⣤⡬⠗⠛⠉⠁⢹⣿⣿⣶⣿⣿⣷⣴⣿⣿⣿⣿⣧⣤⣶⣴⣤⣙⣿⣧⠀⠘⠋⠙⠃⠀⢚⠂⠋⠋⠂⠠⠀⠀⠄⠒⠂⢀⡩⢸⣗⣊⣩⢭⣽⣻⣿⣏⢙⣶⣯
⠉⠉⠰⠈⠀⠀⠊⠀⠀⠠⠀⠀⠀⢈⠍⠋⠉⠐⢻⠃⠾⠂⠁⠠⡆⠀⣉⣿⣿⣿⣿⣿⣿⣿⣏⣀⡀⠀⠀⠉⣿⣿⣷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⣂⠀⢶⣴⡞⣜⣿⣧⣶⠂⠀⠀⣤⣶⣭⣿⣿⣿⣿⣽⣿⠿⢹⡭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠈⠀⠈⠅⣀⣀⠙⠠⢸⣿⣿⣿⣿⠋⣼⣿⣿⣿⣿⣿⣷⣶⣿⣝⢿⣿⣿⣿⣿⡇⠈⠈⣄⣀⠘⣙⣷⠄⠀⣉⣿⣽⣿⡟⠛⠈⠉⠛⣯⣿⠙⠏⠠⠟⠀⠉⠐⣌⠀⠈
⠀⠒⠀⠀⠀⠀⠠⢀⢉⣤⡜⡦⠴⣶⣶⣞⠀⠀⠀⠀⠐⠋⣽⡧⢀⠀⣸⣿⣿⣿⣧⣾⡿⠛⣭⣖⣀⣀⣉⡉⠻⣿⣆⣽⣿⣿⣿⡇⠀⠒⠋⠁⣈⣽⢿⡖⠀⣬⡖⠻⠻⠉⡙⠳⠆⠰⢶⠚⠴⢄⣁⡀⠀⠀⠀⠺⣦⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢲⡌⠋⡒⠓⢚⣯⡴⠀⠀⠀⠐⣎⠀⠀⠈⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣧⡄⠀⠰⠄⠺⣟⠃⠀⠁⠊⡀⠀⣀⠀⠙⠳⣤⣌⣙⣸⡖⠒⣌⣙⡎⣀⢨⣷⣿⣖
⠀⠀⠀⠀⠀⠀⠀⠈⠡⠈⠁⠍⠀⠀⠀⠀⠈⠀⠉⠀⠛⡀⠀⠚⠹⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠷⣤⠄⠈⢩⣥⣐⠉⠠⢖⣶⡂⢀⣽⠶⠍⠉⣁⡚⠁⠀⢉⡿⢿⠟⠃⣽⣿⡿
⠀⠀⠰⣁⡀⠤⠀⠀⠀⠀⠀⢀⣤⡴⠬⡀⠰⠆⠀⠀⠀⠁⠘⠀⠀⣽⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⠉⠉⠉⠀⠈⠉⠙⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⢰⡦⢈⡁⠂⢴⡤⠅⠀⠀⠃⣜⣰⡤⠀⢁⠀⠈⢡⡤⡄⢠⣾⣥⣤
⠀⠀⠀⠈⠁⠀⠈⠓⠀⠠⠀⠀⠐⠿⠍⠀⠀⠀⠉⠃⠀⠀⠀⠠⢤⠉⠁⢻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⠿⣿⡇⠈⠸⠇⠯⢘⣟⡉⠒⢲⣿⣷⢐⡠⠀⠀⠈⠍⣁⠠⢤⣦⡄⠀⠘⢶⠮⡁⠙⠿
⠀⠀⠀⠀⠀⠂⠀⠐⢀⠀⢀⣠⢤⡀⠀⠀⢠⣄⠀⠔⠀⠀⠀⠃⠀⠀⠀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠤⠈⠀⠀⠐⠈⠀⡀⠀⢀⠀⠈⠀⠙⠣⠉⠠⠤⢠⡐⠋⠌⠘⠛⠀⠀⢠⢿⠀⣠⡄⠀
⠀⠀⠠⠀⠀⠀⠠⡤⠤⡆⡀⠀⠀⠐⣰⣖⠊⢡⣀⣐⠒⠊⢹⠇⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡉⠐⠀⠠⠂⠀⠈⠀⢀⠈⠵⠮⡥⠑⠒⣇⠀⢞⠁⢿⣧⠄⢧⢀⣄⢀⡎⠈⠀⠀⠘⠓
⠀⠀⠠⠈⠌⠈⠛⠉⠙⠛⠆⣦⣄⠋⣋⣀⣀⣈⣛⣻⣟⣙⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣲⣴⣸⣿⣿⣿⣿⣇⢀⣞⣤⢤⣈⠀⠀⠉⠀⠴⠗⠣⠤⢴⡏⠁⢨⡞⠿⠀⣾⣀⠀⠀⠚⠉⠁⠀⠀⠁⠂
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠈⣭⣿⣿⡟⠛⢻⣭⡽⢿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⡽⠾⣿⣿⣿⣿⢲⣾⣷⠶⠆⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⢠⠶⢠⠰⠆⠘⣏⣥⡴⢤⡄⢀⣀⠀⠀⠀
⠁⠀⠀⠀⠸⠛⠀⠀⠀⠀⡠⢖⣺⣿⡏⠉⠀⠀⠈⠉⠁⣼⣿⢿⣯⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⠁⠀⠀⣼⣿⡿⠁⠀⠈⣿⣿⡟⣸⣿⣿⠿⠟⠉⠉⣶⣾⣿⣷⣶⠤⣀⢒⣺⢦⣠⢤⠤⠀⢈⡁⠁⠐⠀⠀⠀⠀⠀⠘
⠀⠀⠰⠟⠂⠀⠀⢀⣤⣴⣾⡟⣿⣿⣶⡆⠀⢀⣀⡀⠘⢋⣁⣼⣿⠘⣤⣤⡀⠀⠈⠻⣿⡿⠁⠀⣠⣾⣿⣿⣿⡀⠀⠀⢸⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠀⡇⠠⠀⠚⢛⡪⣉⡀⣿⠶⣠⢬⣉⣲⡄⠪⢀⣤
⠀⠀⠈⠈⠚⠷⢶⣾⣿⣿⣿⢧⣿⣿⣿⣿⣿⠈⠉⢡⣤⣼⣿⣿⣿⠀⣿⣿⣿⣦⣄⠀⠈⠛⠄⣴⣿⠿⠟⠛⠉⠀⠀⣠⣾⠇⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⡀⣿⣿⡠⣶⣷⣤⣀⣀⡀⠈⠙⠛⡶⠿⠯⠁⢠⣼⣋⠤⣼
⠀⠀⠤⠀⠀⢀⣿⣿⣿⣿⣿⢸⣿⣿⡏⠀⢨⣶⣶⠈⠛⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⢸⣿⣿⣿⣧⣄⡀⠿⠇⠀⢀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣽⣤⣄⠀⠓⠀⠀⠀⢴⣤⡐⢉⢩
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢸⣿⣿⣿⣶⠊⠉⢩⣤⣴⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⢸⣿⣿⣿⡟⠛⢃⣀⡀⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣧⣿⡿⠁⠠⠆⠀⠀⠸⢛⠛⣡⣾
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⣾⣿⣿⠉⠉⣠⣤⠈⠛⢻⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢰⣿⣿⣿⣿⠃⣿⣿⣿⣿⣧⣀⡸⠿⠇⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣯⣍⠓⣶⣾⣶⣄⣀⣈⠃⠤⣴⣾
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣤⡄⠉⠙⣀⣀⣾⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠸⣿⣿⣿⣿⢠⣿⣿⣿⣿⠿⠿⠁⠀⢰⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⣿⠉⡽⢏⣍⠉⣹⣶⠛⣉
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⡏⠉⢁⣤⡀⠻⢿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⠇⣸⣿⣿⣿⣿⡀⠀⠾⣿⠀⠀⢸⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣭⡅⣛⠃⠀⠀⢉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣧⡄⠼⠿⢇⣀⣸⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢻⡟⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⣶⣶⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⠀⠙⠉⠁⠀⡭⠉⠩⢆⡀⠀
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢀⣾⣿⣿⣿⣿⣧⡄⠸⣷⡖⠉⢹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣰⣄⠀⠀⡦⠀⢀⢰⣭⣅⡠
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⡇⢰⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⢰⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣉⣡⣤⠤⠀⠐⢤⣱⡚⠛⠓
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣦⣭⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⣶⣤⣤⡄⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡙⠻⢿⠷⠦⢄⡠⠈⠄⠠⠄
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠃⠉⠛⢿⠇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠉⣙⣛⣻⡦⠌⠙⠉⠁⠛⢻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⡖⠒⠀⠀⠈⠀⢀⣀⣀⣠
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⣶⣿⠀⢸⣿⣿⡏⢠⣿⣿⣿⣿⣿⡿⠟⠓⠀⠀⠀⠀⠀⠀⢷⣿⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠄⣸⣿⣿⡇⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⣸⣿⣆⡀
⣿⣿⣿⣿⣿⣿⣟⢊⠡⢿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡆⠀⣿⣿⣿⡷⠰⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣀⣋⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣥⠁⣸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⢄⣤⣖⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⡿⠛⠋⢁⣰⣿⣿⣿⣿⣿⡇⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⠆⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⡿⠿⠀⣿⣿⣿⡇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣐⠻⣵⣼⣯⣿⣿⣿⣿
⣿⣿⣾⣯⣹⣿⣖⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⣿⣿⣿⡟⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡀⠉⠉⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣶⣌⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣛⡟⢀⡀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣷⣶⣴⣿⡿⢫⣾⡇⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠙⠛⢛
⣿⣿⣿⠛⠻⠛⠛⠟⠳⡤⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠟⠛⠛⢟⠁⠚⠛⣿⡇⠀⠻⡿⠛⠛⢿⣿⣿⠛⠛⠀⠀⠛⠛⣿⠟⠓⡖⠒⢶⠒⢻⠛⠛⠋⠁⣀⢹⣿⣿⡿⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⣿⠇⠀⠀⠀⠀⢀⣠⣿⣿⠀⠰⠀⠀⠀⠀⣿⠀⠀⡇⠀⠘⠀⠈⠀⠀⠀⠀⢁⣸⣿⣿⠁⠀⢨⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⣼⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀
⣿⣿⠁⠀⣀⣄⠀⠀⣀⣆⠀⠀⠀⠀⡆⠀⠀⠀⠀⣠⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠁⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⣩⣴⠀⣼⣿⣦⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠃⠛⣿⡿⢿⣶⠄⣀⣹⣿⠀⢠⣾⣿⡿⠛⡛⢿⣷⣶⣤⣀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣶⠀⠀⠀⢸⣿⣿⣿⣠⣟⡭⠁⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⡈⠀⡐⠟⠓⠀⠀⢀⢀⠀⠀⢀⣀⣀⢶⣦⠀⠀⠀⠠⠄⠀⢀⣀⣤⡠⡀⠤⡧⠁⠁⠃⠐⣦⠈⠉⠐⠶⢶⣧⣤⠄⠀⠀⢉⠉⣡⢦⠀⠞⢡⣖⠀⣤⢩⣷⠛⠒⣰⢻⣤⣹⡄⠀⠙⠆⠉⠉⠙⢛⡿⠻⠛⠷⠖⠀⠋⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⢀⣒⢆⣩⡀⠀⠆⠄⠁⠀⢈⠉⣠⡾⠍⠃⠀⠀⠀⠰⣾⣏⣠⣶⣶⣶⣦⣤⣤⣄⡤⢸⡇⠀⠀⠓⢀⣐⣾⠏⣱⡟⠫⠉⣏⡀⠘⠉⠋⡑⠁⢨⣸⡤⠀⢰⠶⠈⠁⠀⠀⠀⠀⠀⠴⠟
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠘⠉⠑⡄⠀⢀⣯⠁⠀⣀⠟⡀⠐⣤⣆⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣁⣀⣤⣼⣴⣉⣽⣦⠏⠀⣼⣿⡟⠀⢀⣀⡀⠙⠗⢨⣿⢂⣁⣰⡿⣤⡆⠀⠄⢀⠄⠀⡄⠤
⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣀⣅⣤⣴⣷⣿⣦⡿⢟⢷⢀⠹⢿⠁⠀⠙⠿⢁⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠈⢭⡍⠉⠻⡋⢻⣸⣲⠖⢶⢴⡿⣶⠜⡘⠩⣽⣶⣾⣿⣼⣀⠑⠐⠇⠀⠀⠂⠀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠈⣉⡙⣏⡽⣿⣏⣉⢁⡠⠈⢿⡿⡟⢑⣰⣀⣴⣿⡿⠛⡉⠉⠀⢨⣿⣿⣿⡋⠁⠀⠒⠿⣿⣷⡀⠀⠀⠀⣠⡞⠉⠰⠇⢁⡀⠀⠈⠉⠑⠶⠆⠙⠋⢽⣋⢈⠛⣻⣿⣿⣆⣆⣤⣄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⢹⣭⣁⡀⠉⠈⠉⠉⣦⡨⠒⠋⠉⠉⢻⣿⣿⣾⣿⣯⣭⣴⡿⢿⠿⢿⣷⣤⡶⢶⣦⣬⣿⣷⠀⠘⠋⠙⠁⠀⢚⠂⠉⠉⠂⠠⠀⠀⠄⠚⠀⢀⠭⢸⣷⣈⣩⠭⣽⣺⣿⣏⢙⣶⣿
⠉⠉⠴⠈⠀⠀⠈⠀⠀⠤⠀⠀⠀⠨⠝⠋⠁⠐⢻⠃⠾⠂⠁⠠⡆⠀⣉⣿⣿⣿⣿⣿⡿⣿⣏⣀⣀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⠀⢒⣴⠞⣚⣻⣷⣶⠂⠄⡀⣤⣾⣵⣿⣿⣿⣿⣽⣿⠿⢩⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠉⠠⠨⢅⣀⣈⠛⠠⢰⣿⣿⣿⣿⠋⣸⣿⣿⣿⡿⣿⣿⣿⣿⣮⠻⣿⣿⣿⣿⡇⠀⠈⣤⣀⠈⣙⣷⠄⠀⣩⣿⣿⣿⣏⣛⡉⠉⠹⣯⣷⠙⠏⠰⠋⠀⠉⠠⣌⠀⠈
⠀⠒⠀⠀⠀⠐⠤⠤⢡⣤⡞⠧⢶⣶⣾⣟⠀⠀⠀⠀⠐⠋⣽⠧⢀⠀⣼⣿⣿⣿⣧⣾⡿⢋⣱⣾⣥⣤⣀⣈⠙⢿⣷⣽⣿⣿⣿⡇⠀⠓⠉⠀⣈⣼⣻⡗⠀⣬⠟⠻⠛⠉⣙⠱⠂⠐⢶⠚⠶⠦⣁⡀⠀⠀⠀⠺⣦⠠
⠁⠀⠀⡀⠀⠀⠀⠀⡲⠔⠉⡚⠓⢈⣯⡶⠀⠀⠀⠐⣎⠀⢀⠀⣋⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧⣄⠀⠒⠀⢚⣛⠃⠀⡃⠁⠀⠀⢀⠂⠙⠳⣶⣌⣛⣸⡗⠐⣆⣙⣆⣄⢨⣷⣿⣖
⠀⠀⠀⠀⠀⠀⠀⠉⠠⠈⠩⠍⠀⠀⠀⠀⠨⠀⠉⠀⠛⠀⢁⠘⠹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢤⠦⠀⢬⣭⣘⡉⠰⢒⣖⡀⢠⢽⠲⠍⠉⣀⣊⠀⠀⢉⡿⠿⠛⠡⡿⣿⠛
⠀⠀⠰⡁⠀⠤⠀⠐⠀⠀⠀⢀⣤⡶⠭⡀⠴⠎⠀⠀⠀⠁⠘⠀⠀⣽⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⠈⠈⠁⠀⠀⠉⠉⢻⣿⣿⣿⣿⣧⣀⠀⠀⣠⢰⣦⣀⡀⠀⢴⡴⠄⠀⠀⠁⣜⣴⡦⠀⢁⠀⠈⢠⡤⡄⢰⣾⣵⣦
⠀⠀⠀⠀⠀⠀⠈⠓⠀⠠⠀⠀⠰⠯⠍⠀⠀⠀⠁⠁⠀⠀⠀⠀⠤⠉⠁⢹⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⠿⣿⡇⠈⠙⢍⠃⠐⣏⡁⠀⢲⢿⣷⠐⡠⠀⠀⠀⠍⣀⢠⢶⣦⡄⠀⠘⢶⢮⡀⠙⠛
⠀⠀⠀⠀⠀⠂⠀⠐⢀⠀⢀⣤⠤⡀⠀⠀⢠⡄⠀⠐⠀⠀⢀⣁⠀⠁⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣀⠀⠀⠀⠐⠈⢀⡀⠀⢀⠀⠈⠀⠘⠧⠉⠠⠤⣠⡔⠉⢄⠙⠉⠀⠀⢠⢿⠀⢡⠄⠀
⠀⠀⠠⠀⠐⠒⠀⠤⠤⡄⠀⠀⠀⢀⣴⣒⠊⢡⣀⣐⡒⠈⢹⠇⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠐⠀⠀⠁⢀⠀⠀⣀⠈⠙⠣⡅⠹⠒⣃⡐⣏⠉⢿⡷⠀⠧⢠⡄⢠⡇⡈⠀⠀⠈⠓
⠀⠀⠠⠈⠌⠈⠙⠉⠙⠻⠂⣢⡄⣉⣫⣤⣤⣬⣿⣿⣿⣭⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣴⣤⢾⢿⣿⣿⣿⣇⢠⣎⣶⢤⡀⠀⠀⠉⠀⠴⠏⠃⠴⢶⠏⠁⢬⡎⠿⠀⣿⣀⠀⠐⠈⠈⠀⠀⠀⠁⠂
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⢈⣵⣿⣿⠏⠉⢻⣦⡞⢻⣿⣿⣿⡿⠛⠋⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠷⠛⢿⣿⣿⡏⢿⣿⣷⣶⣆⣄⣀⠀⠂⠀⠀⠀⠀⠀⠀⢰⠖⠰⠒⠆⠘⢧⣥⡴⠦⠄⢀⣀⠀⠀⠀
⠁⠀⠀⠀⠹⠛⠀⠀⠀⠀⢀⣖⣿⣿⠇⠀⠀⠀⠀⠀⢀⣿⡿⢻⣷⢀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠁⠀⢀⣾⣿⡟⠀⠀⠈⣿⣿⢇⣼⠿⡿⠛⠋⠀⠉⣶⣾⣿⣿⣶⢤⢄⢂⣾⢶⣤⢤⢤⠀⢀⡀⠀⠀⠂⠀⠀⠀⠀⠘
⠀⠀⠸⢛⠂⠀⠀⢠⣶⣾⣿⡇⣿⣿⣿⡆⠀⢠⣤⡄⠈⢁⣤⣾⣿⠈⣴⣦⣄⠀⠀⠙⢿⣿⠁⠀⣠⣿⣿⣿⣿⠀⠀⠀⣸⡟⣾⣿⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣇⠘⡇⠀⠀⠙⢋⡲⣉⣁⣻⠖⣤⣌⣭⣳⣂⣊⣀⢤
⠀⠀⠈⠈⠚⠷⣲⣿⣿⣿⣿⢹⣿⣿⣿⡿⢿⠀⠀⢰⣶⣾⣿⣿⣿⠀⣿⣿⣿⣷⣤⣀⠀⠉⠂⠼⠿⠟⠛⠉⠁⠀⢀⣴⣿⢳⣿⣿⣷⡆⠀⠀⣀⡀⠀⢀⣀⣿⣿⢰⣶⣷⣦⣄⣀⡄⠀⠘⠛⡶⠻⠯⠁⠴⢼⡂⣒⣜
⠀⠀⠔⠀⠀⢰⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⢠⣿⣿⠀⠉⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⢸⣿⣿⣿⣧⣤⡐⠛⠃⣀⣸⣿⣿⣿⣸⣿⣿⣿⣿⣷⢽⣤⣤⡀⠃⠀⠤⠀⢰⣶⣐⣀⢩
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⠀⠀⢰⣶⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇⣾⣿⣿⣿⠟⠙⢀⣀⡀⠻⢿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣦⣽⡿⠀⠰⠂⠂⠀⠘⣋⡉⢥⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⣰⣶⠀⠉⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⢀⣿⣿⣿⣿⣦⣤⠘⠛⢃⣀⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣏⣉⣓⣶⣿⣶⣄⣀⣈⣓⡲⣶⣾
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣶⡆⠀⠉⣤⣤⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⠛⠛⣀⣀⠸⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⡽⢍⣉⠀⣬⠴⠋⣀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢠⣿⣿⡇⠀⢠⣤⡄⠋⢻⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⠃⣿⣿⣿⣿⣿⣀⡀⠻⠟⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⢬⣄⣛⡉⠀⠁⠩
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣷⡖⠚⠛⠣⣤⣼⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢻⠏⣰⣿⣿⣿⣿⡿⠿⠁⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⠀⠉⠉⠁⠀⡔⠉⠭⠁⣀⠀
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⣄⠸⠿⠏⠀⣹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣰⡄⢄⡀⡆⠀⢀⣰⣯⣕⡠
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣇⠺⣿⣿⠇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣈⣥⣤⠦⠀⠐⢠⣴⡚⠙⠓
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⠇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⣶⢠⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠙⠛⢫⠟⠶⣀⡤⠠⠆⠠⠄
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠈⠙⠻⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⢀⣬⣭⣿⣓⡄⠁⢀⣈⠉⢹⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⡟⡖⠒⠀⠀⠀⠀⣀⣀⣀⣨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⠃⢰⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀⢀⠈⢶⣿⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⣀⣈⣈⡀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡄⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣸⣿⡤⠀
⣿⣿⣿⣿⣿⣿⡞⠉⢀⠿⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣄⣉⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⢀⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⢄⣤⣖⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⡟⠋⠉⣀⣾⣿⣿⣿⣿⣿⡇⠀⠈⠉⠙⠛⠻⠻⣿⣿⣿⣿⠀⠀⢀⣠⣴⣽⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠘⣿⣿⣿⠿⠿⠿⠟⠛⢀⣿⣿⣿⡇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣚⠻⣵⣼⣷⣿⣿⣿⣿
⣿⣷⣤⣭⣚⠉⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⣿⣿⣿⢋⡆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣿⣌⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣛⡛⠂⡀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣷⣾⡿⢟⣵⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣴⣿⡿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠙⠛⢛
⣿⣿⡿⠛⠻⠛⠛⠛⠦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠛⠛⢫⠐⠻⠿⣿⡇⠀⠻⡿⠛⠛⢿⣿⣿⠛⠛⠀⠀⠟⠛⣿⠟⠛⡟⠛⢿⠛⢻⠛⠛⠉⠀⣤⠈⣿⣿⡿⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠃⠀⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⠿⠇⠀⠀⠀⠀⢀⣠⣿⣿⠀⠰⠀⠀⠀⠀⠿⠀⠀⠇⠀⠈⠀⠈⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⢨⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⢀⣿⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⣿⣿⠉⠀⣀⡄⠀⠀⣀⣄⠀⠀⠀⢰⡇⠀⠀⠀⠀⣰⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣥⣶⠀⣾⢿⣦⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠻⠃⠛⣿⠿⢿⡦⢀⣈⣿⡇⠀⢀⣿⣿⡿⣛⡙⢻⣿⣿⣶⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣶⣿⠀⠀⠀⢠⣿⣿⣿⣤⣀⠛⠁⠀⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⠀⢀⡱⡟⠙⠀⠀⢀⢀⠀⠀⢀⣀⡠⢶⣆⡒⠒⠀⠰⠠⡄⢀⣀⣤⣡⡀⠤⡷⠉⠡⠃⠀⣦⠈⠉⠐⠶⢬⣯⡥⠄⠀⠀⢉⠉⡡⢶⠈⠚⢱⣖⠠⣤⢩⣷⠟⠒⣠⢻⣆⣽⡆⠀⠙⠆⠀⠉⠙⢛⡿⠛⠛⠳⠖⠀⠋⣿
⠀⠈⠁⠁⠀⠀⠀⠠⠈⠀⠛⠉⢀⣒⢆⣩⡁⠁⠂⠆⠁⠀⣉⡉⣠⡾⠄⠃⠀⡠⠀⠰⣾⣫⣭⣶⣶⣶⣦⣤⣤⣰⠄⢸⡇⠀⠀⠒⢀⢰⣾⠏⣸⡿⠓⢩⣏⡂⠘⠉⠋⡑⠂⢸⣸⡆⠀⢰⠶⠊⠠⠀⠀⠀⠀⠀⠴⠟
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠈⠉⡑⡄⠀⣀⣿⡁⠀⣤⠋⡀⠰⣶⣎⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣘⣃⣀⣤⣸⣶⣉⣿⣤⠟⠀⣼⣿⡟⠀⢀⣀⡀⠰⠓⢈⣿⢂⣥⣰⡟⣤⡄⠀⠄⢀⠂⠀⡄⠤
⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠂⢀⣨⣥⣾⣼⣿⣿⣾⡿⢿⠗⣀⠹⢿⠀⠈⠛⠟⣠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠁⠀⠉⢭⡍⠉⠛⠋⠻⣸⡲⠖⢶⣴⡿⣗⢞⡘⠩⣽⣶⣾⣷⣼⣀⠃⠘⠇⠀⠀⠂⠀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡛⣧⡿⣿⣏⣉⢡⡠⠀⢿⡟⡏⢰⣴⣠⣼⣿⠟⢛⠉⠁⠀⣽⣿⣿⣿⠁⠀⠒⠻⢿⣿⣆⠀⠀⠀⠀⣠⡞⠉⠰⠇⢁⡀⠀⡈⠉⠱⠶⠂⠙⠋⢽⣋⢍⠛⢻⣿⣿⢆⣆⣤⣤⡀⠀
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⢿⣯⣄⣨⠉⠈⠁⠀⣦⠘⠓⠋⠉⠀⣿⣿⣷⣾⣿⣭⣥⣾⠿⠿⠿⢿⣶⣶⡷⢶⣦⣽⣿⣦⠀⠘⠋⠙⠁⠀⢚⡂⠉⠙⠀⠢⠀⠀⠐⠚⠀⢀⠭⢹⣷⣈⣩⠭⣬⣺⣷⣏⠙⣶⣾
⠉⠁⠴⠈⠀⠀⠈⠀⠀⠤⠀⠀⠀⠠⠝⠋⠁⠰⢻⠃⠮⠂⠁⠠⡆⠀⢽⣿⣿⣿⣿⣿⢿⣿⣅⣤⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢐⣁⠀⢶⣴⡞⣛⣿⣷⣶⠃⠄⡀⣤⣾⣯⣿⣿⣿⣿⣽⣿⠿⢩⠹⢿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠋⠤⠨⢁⣀⣈⠉⠠⣸⣿⣿⣿⡿⢁⣾⣿⣿⣿⠿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⠅⠈⠀⣤⣀⠊⡩⣷⠤⠄⣭⣯⣿⣿⣏⣉⡉⠉⠙⣯⣷⠙⠏⠐⠋⠀⠈⠰⣌⠀⠈
⠀⠒⠀⠀⠀⠐⠤⠤⢡⣤⣮⠧⢾⣶⣾⣟⠀⠀⠀⠀⠰⠭⣽⠧⢀⢀⣿⣿⣿⣿⣷⣿⡟⢉⣶⣯⣥⣀⣀⡉⠻⣿⣦⣿⣿⣿⣿⠃⠈⠃⠉⠀⣈⣾⣿⡗⠠⣾⠞⠻⠛⠉⣙⠱⠂⠐⢶⠗⠶⠦⣁⡀⠀⠀⠀⠺⣦⠰
⠁⠀⠀⡀⠀⠀⠀⠁⡲⠖⠉⡚⠓⢚⣯⡶⢀⠀⢀⠐⣆⠀⢀⠁⣣⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⡄⢀⠲⠒⢒⣛⠃⠀⡃⠁⠠⠀⠀⠂⠙⠳⣦⣌⣻⣸⡖⠒⣆⣉⣏⣄⢨⣷⣿⣖
⠀⠀⠀⠀⠀⠀⠀⠉⠴⠀⠩⠭⠀⠀⠀⠀⠬⠀⠉⠀⠙⡀⢁⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠶⠤⠦⠀⠬⣭⣜⡉⠰⢒⣾⡀⠠⢽⡲⠍⠉⣄⣊⠀⠀⢉⡽⠿⠛⠡⣿⣿⡛
⠀⠀⠰⡁⠀⠠⠀⠀⠀⠀⠀⢀⡤⡾⠭⡅⠴⠏⠀⠀⠀⠁⠈⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠉⠉⠉⠁⠀⠈⠉⠙⣿⣿⣿⣿⣿⣆⣀⠀⠀⣄⢰⣶⣈⡀⠀⢴⡴⠆⠄⠀⠃⢞⣴⡦⠀⠀⠀⠈⣠⡴⠄⢴⣾⣵⡶
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠰⠿⠍⠀⠀⠀⠠⠃⠀⠁⠀⠠⠬⠉⠀⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⣿⡀⠈⠙⢍⠃⠸⣏⡉⠐⢲⢿⣷⣐⡠⠀⠀⠠⠍⣀⢠⢶⣦⡄⠀⠙⣷⠮⡀⠛⠻
⠀⠀⠀⠀⠀⠢⠀⠐⢀⠀⣀⡤⠤⡀⠀⠀⢠⡄⠀⠐⠀⠀⢀⡁⠀⠀⢀⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣂⠀⠀⠀⠐⠈⢀⡀⠀⢠⠀⠈⠀⠘⠷⠉⠔⠤⣠⠜⠉⢄⠙⠉⠀⠀⢠⢿⠀⢤⠄⠀
⠀⠀⠠⠀⠐⢒⡠⡤⠤⣄⠀⠀⠀⠀⣴⣖⠊⢡⣄⣘⣂⡈⠹⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣯⠁⠐⠀⠀⠁⢀⠀⠀⣀⠉⠛⠓⡍⠉⠐⣃⡐⢏⠉⢿⡷⠀⠣⢠⡄⢠⡇⡈⠀⠀⠈⠓
⠀⠀⠠⠀⠈⠈⠉⠉⠙⠛⠂⣢⣄⡉⣫⣤⣤⣬⣿⣿⣿⣭⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣴⣤⡺⢿⣿⣿⣿⣇⣠⣎⣴⢤⠈⠀⠀⠉⠀⠴⠏⠃⠶⢶⠏⠁⢬⡎⠿⠀⣾⣀⠀⠀⠈⠉⠀⠀⠀⠁⠁
⡀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⢈⣵⡿⠿⠏⠉⠻⣶⡞⣻⣿⣿⣿⠟⠋⠉⠻⣿⣿⣿⣿⣿⣧⠀⠀⠀⢾⣿⣿⠞⠛⢿⣿⣿⡏⣿⣿⣶⣒⣢⣤⣄⠂⢂⡄⠀⠀⠀⠀⠀⢰⠖⠰⠒⠦⠘⢧⣥⡴⠦⠤⢀⡀⠀⠀⠀
⠁⠀⠀⠀⠹⠋⠀⠀⠀⠀⢐⣾⣾⣿⠇⠀⠀⠀⠀⠀⣰⡿⠟⢹⣿⢀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠀⠀⣠⣿⣿⣟⠀⠀⠀⣿⣿⢣⣿⠿⠟⠛⠃⠀⠀⠿⢿⣿⣿⠷⢤⠄⢊⣽⢶⣤⢤⢤⠀⢀⡀⠀⠈⠂⠀⠀⠀⠀⠘
⠀⠀⠸⢛⠂⠀⠀⢠⣶⣾⣿⡏⣿⣿⣿⣇⡀⢠⣶⡄⠉⢀⣤⣼⣿⠈⣾⣦⣄⠀⠀⠙⢿⣟⠁⠀⣴⣿⣿⣿⣿⠀⠀⠀⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡇⠘⡧⠀⠀⠙⢋⡪⣉⣀⣻⠶⣤⢌⣩⣱⣄⣚⢀⣤
⠀⠀⠈⠈⢚⠳⣲⣿⣿⣿⣿⢻⣿⣿⣿⢿⣿⠀⠀⢸⣷⣾⣿⣿⣿⡆⢿⣿⣿⣷⣦⣀⡀⠈⠀⠾⠛⠛⠋⠉⠀⢀⣠⣴⣿⢹⣿⣿⣿⡇⠀⢀⣄⡀⠀⢠⣤⣿⣿⢰⣾⣷⣦⣤⣀⡄⠀⠘⠛⡶⠛⠯⠁⠴⢼⡂⣒⣜
⠀⠀⠔⠀⠀⣰⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠠⣿⣿⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇⣸⣿⣿⣿⣷⣶⠈⠙⢣⣤⣼⣿⣿⣿⢸⣿⣿⣿⣿⣷⢿⣤⣥⡀⠁⠀⠠⠀⢰⣆⣐⣂⢩
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢸⣿⣿⡿⠿⠇⠀⢠⣶⣾⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⣿⣿⣿⣿⠋⠉⢠⣤⡜⠛⢿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣦⣿⡿⠁⠰⠆⠂⠀⢚⣋⡉⣥⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⣾⣿⣿⠀⠀⣼⣿⠀⠈⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⢀⣿⣿⣿⣿⣷⣶⠈⠛⢣⣄⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣏⣋⢋⣶⣿⣶⣤⣀⣈⣃⠲⣶⣾
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡗⠀⠉⣴⣦⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⣿⣿⣿⡇⢸⣿⣿⣿⣿⠉⠙⣠⣄⠚⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠿⢁⡽⣉⣁⠀⣬⠭⠋⣀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⣀⣶⣆⠉⢙⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⠃⣿⣿⣿⣿⣿⣦⡄⠛⠛⣀⢀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠤⣄⣛⣁⠈⠁⠭
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡍⣿⣿⣷⣖⠊⠙⠓⣤⣼⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⠃⣸⣿⣿⣿⣿⡟⠛⢡⣀⡀⠿⢿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⠀⡉⠁⠁⠀⠞⠉⠭⠅⣀⠠
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⢃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣤⠘⠛⠃⢀⣸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣶⡄⢄⠀⠆⠀⢀⣴⣯⣵⡠
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡘⢿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣏⣥⣤⠖⠀⠑⢢⣵⡚⠙⠓
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⠇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠿⣿⣿⣿⡀⢿⣿⠿⢣⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠟⠗⣠⡤⠀⠤⠤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠀⠀⠉⠙⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⣤⣾⣿⣿⣖⣀⣀⣤⠀⢸⣿⣿⣟⠀⣿⣿⣿⣿⣿⣿⣿⣿⡖⠒⠀⠀⠀⠀⣀⣀⣀⣨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⡇⢸⣿⣿⣿⣿⣿⠿⠟⠛⠿⠀⠀⠀⢀⠈⢶⣿⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀⠀⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣸⢿⡦⠀
⣿⣿⣿⣿⣿⡿⠟⢃⣻⣿⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣄⣉⠀
⣿⣿⣿⣿⣿⣿⣶⣶⣷⡿⢀⣾⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣤⣖⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⡟⠋⠁⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠛⠛⣿⣿⣿⣿⡇⠀⢀⣴⣶⣬⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣧⠀⠿⠿⠿⠿⠟⠛⠛⠛⣀⣿⣿⣿⠏⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣘⠻⣷⣼⣧⣿⣿⣿⣿
⣿⣽⣻⢻⣿⡇⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⣿⣿⣿⢋⡆⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣿⣮⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣇⡀⢀⣀⣀⣀⣠⣤⣴⠿⠿⢿⣿⣿⣷⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠙⠛⢛
⣿⣿⣿⠛⠻⠛⠛⠛⠷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⢫⠒⠻⠿⣿⡇⠀⠻⡿⠛⠛⢿⣿⣿⠛⠛⠃⠀⠛⠛⣿⠟⠛⡟⠛⢿⠛⢻⠛⠛⠁⢀⡦⢸⣿⣿⡟⠀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⣿⣿⣟⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠃⠀⠀⠀⠀⢀⣠⣿⣿⠀⠰⠀⠀⠀⠀⠿⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⢀⠀⠈⠻⣿⣿⣻⣯⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⣿⣿⠁⠀⣀⠀⠀⠀⣀⣄⡀⠀⠀⢰⡇⠀⠀⠀⠀⣰⣀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⠀⡿⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⣿⣿⣿⠿⠛⠻⠃⢻⣿⠟⢿⡖⢠⣄⣿⡟⠀⢠⣿⣿⡟⣩⣭⢻⣿⣿⣷⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣾⣧⡤⠀⠀⠀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣷⣄⣀⣠
⠀⢀⡁⠛⠁⠀⠀⢀⢀⠀⠀⢀⣀⠠⢶⣇⡐⠐⠀⠰⠠⡄⢀⣀⣤⣭⡀⠤⡗⠁⠁⠋⠐⣦⠈⠉⠘⠳⠾⣾⡥⠄⠠⠀⠉⠉⣡⣶⠀⠛⢰⣖⠀⣤⢬⣷⠛⠒⢠⣻⣦⣼⡆⠀⠘⠆⠀⠀⠉⢛⡿⠛⠛⠓⠒⠀⠋⣿
⠀⠈⠁⠀⠀⠀⠀⠀⠌⠀⠋⠁⠀⣒⢆⣩⡉⠀⠂⠂⠁⠀⢉⡉⣠⠾⠄⠃⠀⢤⠀⠰⣾⣏⣥⣴⣶⣶⣶⣤⣤⣤⠄⢸⡆⠀⠀⠒⢀⢐⣾⠏⢸⠟⠓⠉⣏⡄⠘⠉⠉⡁⠂⢈⣬⡄⠀⠰⠶⠊⠠⠀⠀⠀⠀⠀⠴⠛
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠉⣕⡄⠀⣀⣿⡁⠀⣤⠃⡀⢰⣶⣆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣁⣠⡴⢬⣞⣉⣽⣦⠗⠀⣾⣿⡟⠀⢀⣀⠀⠐⠗⢀⣿⢪⢥⣰⡏⣤⡆⠀⠆⢀⠂⠀⠌⠦
⠀⠀⠀⠀⠠⠔⠀⠀⠀⡀⠂⠀⣠⣥⣶⣼⣿⣿⣧⡿⢿⢳⡀⠹⢿⠀⠀⠙⠟⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠭⡍⠉⠛⠉⠻⡼⠘⠚⢶⣴⡿⢿⠞⡘⠙⣽⣶⣿⣷⣼⣀⠈⠘⠗⠀⠀⠀⠀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡉⣥⡿⢿⣏⣉⢁⡠⠂⢻⡟⡏⢹⣰⣀⣴⣿⣿⠿⠛⠓⠈⢹⣿⣿⣿⠛⠁⠠⠿⣿⣿⣷⡀⠀⠀⢀⣠⡞⠉⠰⠃⢁⡀⠀⡈⠉⠡⠶⠂⠙⠋⢸⢉⠄⠛⢿⣿⣿⢃⣆⣤⣤⠀⠀
⣀⡀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⢿⣭⣄⣀⠈⠉⠉⣁⣦⡘⠒⠋⠉⠀⢸⣿⣿⣵⣶⣷⣒⣠⣾⣿⣿⣿⣧⣤⣶⣴⣄⣹⣿⣷⠀⠈⠉⠈⠁⠀⠚⠁⠉⠉⠀⠢⠀⡀⠀⠋⠀⠀⠩⢸⣯⣄⣨⠥⣼⣽⣿⣏⣛⣷⣶
⠈⠁⠐⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠠⠜⠉⠁⠐⢻⠁⣻⡂⠉⠀⡆⠀⠩⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠙⣿⣿⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣡⠄⠒⢴⣞⣊⣿⣷⣶⠃⠀⣀⣴⣿⣽⣿⣿⣿⣿⡾⣿⠟⢩⠹⢿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠉⠤⠨⢁⣀⣀⠉⠠⢰⣿⣿⣿⣿⡟⢩⣿⣿⣿⣷⣶⣶⣴⣾⡝⢿⣿⣿⣿⣿⡇⠀⠀⢤⣄⢈⡩⣷⠦⠀⣨⡯⣿⣿⣎⣉⡉⠉⢙⣯⠷⠙⠃⡐⠋⠀⠈⠠⣄⠀⠈
⠀⠂⠀⠀⠀⠐⠄⠬⢡⣤⣎⠷⢞⣶⣾⣛⠀⠀⠀⠀⠐⠩⣽⠧⣀⠀⣼⣿⣿⣿⣿⣴⣿⡿⢋⠭⠉⠉⠉⠛⢿⣿⣄⣿⣿⣿⣿⡇⠀⠉⠉⠀⢩⣾⡹⠗⠀⣾⠞⠻⠛⠉⣙⠲⠆⠐⢲⠚⠾⠦⣥⡀⠀⠀⢀⠺⣧⠰
⠁⠀⠀⡀⠀⠀⠀⠀⡲⢀⠉⡚⠓⢈⣯⡶⢀⠀⢀⠐⣆⠀⢀⢀⣣⡄⣻⣿⣿⣿⣿⣿⣯⣴⣿⣿⣷⣶⣶⣦⣤⣹⣿⣿⣿⣿⣿⣷⡆⢀⠐⠒⢘⣛⡃⠄⣃⠁⠠⠀⠀⠀⡙⠛⣶⣤⣛⣨⡝⠙⣤⣉⣏⣄⣨⣿⣿⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠩⠍⠀⠀⠀⠀⠤⠀⠀⠈⠉⡀⢁⠉⠹⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠴⠦⠀⠬⢭⣌⡉⠐⢲⣞⡄⠠⠽⡒⠁⠉⣄⣊⡀⠀⢉⡿⠿⠋⠁⡿⡿⠛
⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⢀⡤⡾⢭⡄⠴⠍⠀⠀⠀⠀⠈⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠿⠉⠻⠿⠿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣠⢰⣶⣀⡀⠀⢼⡖⠆⠄⠀⠁⢄⣴⠶⠀⠀⠀⠈⢰⡖⠄⢐⣾⣵⡶
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠐⠯⠍⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠉⠁⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⠛⢿⡅⠀⠙⢏⠃⠀⠯⠁⠀⢲⢿⣷⡐⢴⠀⠀⠀⠌⣀⢴⢶⣦⡄⠀⠘⢧⠮⠀⠚⠛
⠀⠀⠀⠀⠀⠤⠀⠐⢀⠀⢀⡤⠤⡀⠀⠀⢠⡄⠀⠐⠀⠀⢀⡁⠀⠀⣠⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣒⡀⠀⠀⠘⠈⢀⡀⠀⢠⠀⠈⡀⠈⠷⠀⠔⠲⣠⣌⠉⠆⠈⠉⠀⠀⢠⢟⠠⠴⢄⠀
⠀⠀⠠⠀⠐⢒⡀⡤⠀⣀⠀⠀⠀⢀⣴⣚⠉⢡⣄⣘⡂⡉⠹⢇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡁⠀⠀⠐⠁⢀⠀⠀⣀⠉⠛⠓⡄⠉⠐⣃⡐⢏⠉⢻⠷⠂⠣⠠⠄⢠⡇⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢂⣢⣄⣉⣹⣿⣿⠿⢿⣟⣙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠄⠀⢀⢛⣿⣿⣿⡧⣤⣮⣶⢢⠀⠀⠀⠈⠀⠰⠏⠓⠲⢶⠏⠀⠬⠎⠿⠀⣿⣄⠀⠀⠈⠀⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣾⣿⠉⠉⠀⠀⠛⠋⣼⣿⣿⣿⠋⠉⠀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⢐⣿⣷⡟⠉⠻⣿⣿⡇⣿⣿⣷⣤⠔⠒⢖⣂⣠⣤⣄⡀⠀⠀⠀⢰⠖⠰⠒⠗⠈⢧⣤⡴⠶⠤⢀⡀⠀⠀⠀
⠁⠀⠀⠀⠰⠋⠀⠀⣠⣤⣶⣿⢹⣿⣧⣤⠀⠀⠀⠀⠰⠛⠉⢀⣿⡆⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⠀⠀⠀⢹⡿⣼⣿⠙⠃⠀⠀⠀⠀⠛⢻⣿⣿⡃⢠⠤⢨⡽⠶⣤⢤⣤⡀⣀⡄⠀⠀⢂⠀⠀⠀⠀⠘
⠀⠀⠘⢛⠂⠀⢀⣾⣿⣿⣿⡇⣿⣿⣿⣿⣶⡆⠉⠙⣀⣀⣿⣿⣿⡇⢸⣿⣶⣄⠀⠈⠛⢿⠋⢀⣴⣿⣿⣿⠿⠀⠀⠀⣼⢷⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⢘⣿⣇⣈⣧⣀⠀⠙⢋⡱⢍⣀⣻⠓⣤⣄⣬⣱⣆⣒⡂⢴
⠀⠀⠈⠈⠙⢳⣿⣿⣿⣿⣿⢇⣿⣿⣿⠉⠉⣤⣤⡄⠛⢻⣿⣿⣿⣧⠘⣿⣿⣿⣿⣶⣄⡀⠀⠚⠉⠉⠁⠀⠀⢀⣴⣾⡏⣸⣿⣿⣿⡇⠀⠰⢶⡆⠀⢰⣾⣿⣿⢸⣿⣿⣿⣿⣦⣄⠀⠈⠛⡖⠛⠯⠁⠴⠼⡆⣒⣞
⠀⠀⠐⠀⣰⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣦⡄⠉⠉⣅⣀⣾⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⣿⣿⣿⣿⠿⠿⠀⠀⢰⣶⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡼⣤⣤⡀⠁⠀⠠⠄⢐⣶⣒⣂⢩
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡏⠉⢁⣠⡄⠛⠻⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣿⣿⣿⣿⢀⣿⣿⣿⣿⣀⠀⢾⣿⠀⠀⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣷⣬⡿⠀⠰⠆⠂⠀⢚⣋⡉⢡⣿
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣤⣠⠘⠛⢃⣀⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢺⣿⣿⣿⡏⢸⣿⣿⣿⣿⠿⡿⠀⠀⣰⣶⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣉⣶⣿⣷⣄⣀⣌⣃⠒⣶⣾
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⡿⠉⠁⡀⡀⠘⠻⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠘⣿⣿⣿⠃⣾⣿⣿⣿⡏⠀⠀⣾⡶⠀⠉⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡼⣃⣀⡀⣬⠭⠋⣀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⣤⠰⠿⢟⣀⢀⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⡏⢰⣿⣿⣿⣿⣿⣷⠆⠀⠀⣦⣴⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⣔⣙⣁⠈⠁⠬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⢀⣿⣿⣿⣿⣿⡃⠀⣲⣶⡄⠉⢻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠔⠈⡭⠅⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢰⣶⣦⡤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣾⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠖⠀⢀⣰⣯⣵⡠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣶⣬⣭⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⢡⣤⣤⣠⢸⣿⣿⣿⣿⣟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠐⢠⣰⣊⠉⠓
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠂⠙⠻⠿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡏⠉⡛⡻⣿⣤⡙⠛⠉⠘⠛⢻⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⠀⠤⠤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⣶⣶⣷⠀⣸⣿⣿⠇⢸⡿⣢⡟⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣠
⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⢸⡆⠘⣿⣿⣿⡿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣟⠉⠀
⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣷⡆⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡆⠸⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦⣀
⣤⣠⣀⣠⣄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⣿⣿
⣿⡿⠟⠟⠉⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣀⢸⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣿⣿⣿⣿
⣟⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⡁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣷⡈⠉⠉⠉⠉⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⢀⡾⣿⣫⣷⣿⣿⠝⣐⠻⣵⣼⣿⣿⣿⣿⣿
⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣿⡿⢋⣼⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣄⡀⣀⣼⣿⣿⣿⣿⣿⡫⣖⠶⣾⣎⠛⢿⣿⣿⣿⣿
⠛⠋⠉⠀⠀⠀⣠⣷⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⠿⣋⣴⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣶⣤⣤⣶⣶⣶⣾⣿⠛⠉⣉⢹⣿⣿⡇⢹⣿⣿⣿⣿⣟⣵⣾⣷⣾⣿⣿⡆⠀⠉⠛⠛⢛
⠀⠀⠀⠀⠀⠺⠿⡿⠻⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠚⠛⠛⠛⣿⡇⠀⠛⡿⠛⠛⢿⣿⣿⠟⠛⠀⠀⠟⠛⣿⠟⠛⡟⠛⠿⠛⠛⠛⠃⠀⠘⢁⣸⣿⣿⠁⠀⢿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠀⠀⠃⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠐⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣋⣤⠀⡴⠀⠀⠻⣿⣿⣻⣯⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⣀⣧⡀⠀⠀⠸⡇⠀⠀⠀⠀⣶⡀⠈⠀⣰⠀⠀⠀⢀⠀⠀⠀⣄⠀⠁⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⢰⣿⣿⣿⣠⠇⢀⡀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⢻⣿⣿⠛⠙⠃⣼⣶⣿⡇⠀⣰⣿⣿⣧⡺⡆⠘⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣼⣿⣿⣿⣿⣿⡿⠅⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣤
⠄⢀⡁⢛⠑⠀⠀⢀⢀⠀⠀⢀⣀⠰⢾⣧⡈⠐⠀⢲⡀⠄⢀⣀⣤⣥⡀⠤⡿⠈⠁⠋⠐⣦⠈⠉⠰⠶⠽⣯⡥⠄⠠⠀⢉⠉⣡⢶⠀⠛⢰⣶⠀⣤⢬⣿⠛⠒⣰⣻⣥⣽⡇⢀⠈⠇⠀⠀⠙⢛⡿⠛⠛⠛⠒⠀⠋⣽
⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠋⠉⠐⢛⢆⣨⡀⠁⠂⠖⠀⠀⣁⡉⣤⠾⠈⠃⠀⣤⠀⠰⣿⣛⣠⣤⣤⣤⣶⣤⣤⣴⠤⢸⡆⠀⠀⠒⢀⢐⣿⠏⣹⠟⠓⢋⣯⡍⠘⠉⠉⠉⠃⢨⣨⡆⠀⠰⠶⠊⠠⠀⠀⠀⠀⠀⠴⠛
⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡄⠈⠉⢕⡄⢀⣀⣿⡁⠀⣤⢃⡀⠰⣶⣎⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣁⣠⣴⣼⣾⣉⣽⣤⠟⠀⣼⣿⡟⠀⣀⣀⠀⠑⠓⢠⣿⢮⢥⣰⣏⣴⡆⠀⠆⢀⠆⠀⠼⠰
⠀⠀⠀⠀⠠⠖⠀⠀⠀⡀⠂⠀⣠⣥⣴⣼⣿⣿⣿⡿⢻⢓⢀⠹⢿⠀⠈⠙⠿⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠭⡍⠉⠛⠃⠺⡼⠚⠚⢶⣴⡿⢿⠞⡘⠙⣽⣶⣿⣿⣼⣠⠋⠘⠗⠀⠀⠂⠀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡉⣥⡾⢿⣏⣉⣡⡤⠂⢻⡟⡋⢹⣰⣀⣴⣿⣿⡿⠿⠿⠍⠻⣿⣿⣿⡟⠋⠉⠭⣿⣿⣷⡀⠀⠀⢀⣠⡞⠉⠰⠃⢁⡀⠀⣈⠉⠹⠶⠂⠙⠋⢸⢋⠄⠛⢿⣿⣿⣃⣂⣤⣤⡄⠀
⣀⡀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⢿⣭⣄⣀⠀⠈⠁⣀⣦⡜⠒⠉⠉⠀⢸⣿⣿⣫⣴⡶⠤⢄⣼⣿⣿⣿⣇⣀⣠⣄⣄⡹⣿⣧⡀⠈⠉⠘⠁⠀⠚⠁⠉⠉⠐⠢⠀⡀⠐⠋⠀⠀⠩⢹⣿⣈⣨⠥⣾⣽⣿⣏⣛⣷⣶
⠉⠁⠐⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠠⠜⠉⠁⠐⢻⠁⣏⡃⠉⠀⡆⠀⠩⣾⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⣿⣿⣯⣽⣿⣿⣿⡆⠀⠀⠀⠀⢀⣡⠄⠺⢴⣞⣎⣿⣷⣶⡃⠄⣀⣤⣿⣯⣿⣿⣿⣿⡿⣿⠟⢩⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠤⠩⢁⣀⣀⠉⠠⢰⣿⣿⣿⣿⣿⠟⣽⣷⣶⣶⣤⣄⣄⣸⡟⣿⣿⣿⣿⣿⡇⠀⠀⢤⣤⠈⡩⣷⠦⠀⣬⡿⣿⣿⣏⣉⡉⠉⢙⣯⠿⠈⠏⠐⠋⠀⠈⠠⢆⠀⠈
⠀⠂⠀⠀⠀⠐⠤⠬⢡⣤⣮⠷⢾⣶⣿⣛⠀⠂⠀⠀⠘⠩⣾⠇⣀⠀⣼⣿⣿⣿⣿⢃⣴⣿⡿⢟⡛⠛⠛⠿⣿⣿⣆⢿⣿⣿⣿⡇⠀⠉⠁⠀⢨⣾⣿⠗⠀⣾⠟⠻⠛⠁⣙⠺⠂⠐⢲⠛⠾⠦⣥⡀⠀⠀⠀⡺⣧⠒
⠁⠀⠀⡀⠀⠀⠈⠁⡒⢂⠉⡛⠓⢘⣯⡶⢀⠀⢀⠐⣆⠀⢀⢀⣡⡄⣻⣿⣿⣿⣿⣾⣿⣃⣼⣥⣤⣤⣤⣄⣀⠹⣿⣿⣿⣿⣿⣷⡆⠀⠁⠂⢚⣛⡁⠄⣃⠉⠠⠀⠀⠃⡙⠛⣶⣴⣻⣸⡟⠙⣤⣉⣎⣄⣩⣷⣿⣖
⠀⠀⠀⠀⠀⠀⠠⠀⠴⠀⠩⠭⠀⠀⠀⠀⠤⠀⠀⠈⠉⡀⢀⠉⠹⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⠴⠦⠀⠬⢭⣬⡉⠐⢒⣾⡄⠠⢽⡒⠁⠁⣄⣈⡀⠀⢉⡿⠿⠋⠡⣾⣿⠛
⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⢀⡤⡾⢭⡄⠴⠉⡀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⣤⢰⣖⣀⡄⠀⢾⡖⠆⠄⠀⠁⢌⣵⠶⠀⠀⠀⠈⢰⡖⠄⢐⣾⣵⡶
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠰⠯⠍⠀⠀⠀⠀⠉⠀⠀⠀⠀⠤⠉⠁⢹⣿⣿⣿⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⠟⢿⠅⠀⠙⢏⠓⠀⠯⠁⠐⢲⢿⣷⡐⢴⠀⠀⠠⠄⣀⢴⢶⣶⡄⠀⠘⢧⠮⡔⠚⠛
⠀⠀⠀⠀⠀⠤⠀⠐⢀⠀⢠⡤⠤⡀⠀⠀⠠⡤⠀⠐⠀⠀⢀⡁⠠⠀⣠⣾⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣖⡀⠀⠀⠐⠈⢀⡀⠀⢠⠀⢈⡀⠈⠷⠀⠔⠲⣠⣜⠉⠆⠈⠉⠀⠀⢠⢿⡠⠴⣄⠀
⠀⠀⠠⠀⠐⢒⡂⡤⠄⣄⠀⠀⠀⢀⣴⣚⠉⢡⣄⣘⣀⣉⠹⢇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡅⠈⠀⠐⠁⢀⠀⠀⣀⠉⠛⠛⡄⠉⠐⣃⡐⢏⠉⢻⠷⠂⠣⠠⠤⢠⡇⠀⠀⠀⠈⠁
⠀⠀⠀⠁⠀⠈⠉⠉⠉⠛⢂⣢⣆⣉⣽⣿⣿⠿⠿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠚⣻⣿⣿⡧⣤⣯⣔⣲⠀⠀⠀⠈⠀⠰⠏⠓⠶⢶⠏⠀⠬⠎⠿⠀⣿⣄⠀⠀⠈⠀⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⣄⣾⣿⠉⠉⠀⠀⠙⠋⣼⣿⣿⢿⡟⠉⠀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣶⡿⠋⠙⢿⣿⠇⣿⣿⣷⣶⠊⠉⢫⣥⣶⣶⣦⡄⠀⠀⠀⢰⠖⠰⠒⠖⠈⢧⣤⡴⠶⠤⣀⡀⠀⠀⠀
⠁⠀⠀⡀⠰⠉⢀⣰⣾⣿⣿⣿⢹⣿⣿⣶⠀⠀⣀⣀⠸⠛⠉⠀⣾⡇⢀⡀⠀⠀⠑⢿⣿⣿⣿⠂⠀⢀⣼⣿⣿⠁⠀⠀⢸⣏⣾⡟⠉⠁⠀⠀⠀⠀⠈⠻⢿⣿⡅⣤⠤⢨⡽⠶⣤⢤⣤⡀⣀⠄⠀⠀⢂⠀⠀⠀⡀⠈
⠀⠀⠘⢛⠂⣠⣾⣿⣿⣿⣿⡿⣸⣿⣿⣿⣷⡆⠉⠉⣤⣀⣼⣿⣿⣿⠀⣿⣷⣄⠀⠀⠙⠿⡿⠀⣠⣾⣿⣿⠿⠃⠀⠀⣼⢻⣿⣧⣤⠀⠀⠀⠀⠀⠀⢀⣸⣿⣧⣿⣷⣶⣤⣝⢋⡱⢍⣁⣻⠓⣤⣄⣬⣱⣆⣐⠂⢴
⠀⠀⠈⢈⣼⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⠀⢰⣶⡆⠈⢻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣶⣤⣀⠀⠘⠉⠉⠁⠀⠀⢀⣴⣶⡏⣼⣿⣿⣿⣄⣀⠸⠻⠁⠀⣸⣿⣿⣿⢸⣿⣿⣿⣿⣧⣄⠀⠈⠛⡖⠛⠯⠁⠱⠶⡇⣒⣶
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣶⠈⠉⢡⣤⣼⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⣿⣿⣿⣿⠛⠛⢀⢀⠸⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣄⣬⡀⠁⠀⠠⠀⢘⣶⣒⡂⢸
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⡏⠈⠁⣤⡄⠘⠙⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣿⣿⣿⣿⢀⣿⣿⣿⣿⣄⣀⠿⠿⠀⠀⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⡁⠐⠆⠂⠀⢚⣋⡉⢡⡽
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣤⠈⠉⢃⣀⣠⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⠛⠟⣀⠀⠺⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣌⣑⠒⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⠉⠉⣤⣄⠘⠻⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⠃⣾⣿⣿⣿⣇⣀⠀⠿⠿⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⡀⣬⠭⠉⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣤⠴⠿⠿⢀⣀⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⡏⢰⣿⣿⣿⣿⣿⠿⠇⠀⠀⣿⣶⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣈⣉⠈⠁⠬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢀⣿⣿⣿⣿⣿⣧⣀⠹⠿⠇⠀⢹⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠩⢥⣀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠸⣿⣿⡐⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣵⡠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢽⠀⣿⣿⣷⣦⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠁⣶⣶⣴⢀⣿⣿⣿⣿⣿⠀⠏⠁⠉⡠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠓
⣿⣿⣿⣿⣿⠃⠁⠀⠂⠀⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠇⠈⠛⠻⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⣩⣽⣿⣓⣀⠉⢀⣈⠀⢹⣿⣿⡟⠀⠀⠀⠀⢿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⠃⠀⠀⠀⠈⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢁⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡀⢀⣀⠐⢎⠉⠰⠢⠜⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠛⠋⠀⠀⠀⠛⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢘⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿
⣬⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⣻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⣟⢿
⠀⠙⠂⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⣿⣿⠇⠉⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣈⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⠿⠿⠀⣿⣿⣿⣧⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣀⢄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⢀⡀⠤⠀⠀⠸⢿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣣⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⢀⡾⣟⣫⣷⣿⣿⠝⣐⠻⣵⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣶⣶⣤⣿⡿⢋⣴⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⡿⡫⣖⢶⣶⣌⠛⢿⣿⣿⣿⣿
⠛⠀⠀⠀⢀⣼⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⠟⣫⣴⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⠋⠁⣀⠈⣿⣿⡧⢹⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⢾⠿⠿⡿⠛⡟⠛⠒⠀⡀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠈⠛⠛⠛⢿⠿⠀⠘⠿⠛⠛⢿⣿⣿⠿⠟⠃⠀⠛⠛⣿⠟⠛⡟⠛⠟⠛⠛⠉⠉⠀⠘⢁⣸⣿⣿⠁⠀⢿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⢀⠀⠘⠀⠀⠇⠀⠀⠀⠀⠀⠃⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡇⠀⠈⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣉⣴⠀⡶⠀⠀⠻⣿⣿⣻⣯⣽⣿⣿⣿⢯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⢀⡇⠀⠀⠀⡈⡇⠀⠀⠀⠀⣷⡀⠈⠀⢰⠀⠀⠀⣀⠀⠀⠀⣄⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢰⠀⠀⠀⠀⢠⣿⣿⣿⣠⢇⣀⡄⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠟⠛⠻⣿⣿⣿⡟⠁⠁⢸⣿⣿⠇⠀⣼⣿⣿⣷⡜⡟⠈⣿⣿⣿⣿⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣼⣿⣿⣿⣿⣿⡿⠅⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⠄⢀⡔⡛⠉⠀⠂⢀⢀⡀⠀⢠⣀⠴⢾⣶⡊⠱⠀⠲⡤⠄⢀⣀⣶⢭⡀⠦⡷⠉⠁⠋⠐⣦⠈⠉⠘⠳⢼⣯⡥⠄⠠⠀⣉⠉⣵⣶⠀⠛⢰⣖⠠⣤⢽⣿⠛⠒⣰⣻⣮⣽⡇⠀⢙⠆⠀⠈⠉⢛⡟⠛⠛⠓⠚⠈⠋⣿
⠀⠈⠀⠀⠀⠀⠀⠠⠌⠀⠛⠉⠐⣚⢆⣬⣈⠙⠃⠆⡀⠀⣁⡉⣤⠾⠄⠃⠀⣤⡀⠰⣿⣿⠶⢉⣉⣀⣀⣀⠀⣀⣀⢸⡆⠀⠐⠒⢀⢐⣿⠇⣹⠟⠑⣋⣯⡌⠘⠩⠉⡙⠒⢸⣬⡆⠀⠰⠶⠊⠠⠀⠀⠀⠀⠀⠴⠛
⠀⠐⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢠⡄⠈⠉⣵⡄⢀⣠⣿⡁⠀⣤⢃⡀⢸⣶⣎⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣌⣁⣠⣴⣼⣾⣍⣽⣦⡗⢀⣾⣿⡟⠀⣀⣀⠀⠙⠟⢠⣿⢨⢥⣰⡯⣴⡆⡀⠄⣀⠂⠀⠌⠢
⠀⠀⠂⠀⠠⠖⠀⠀⠀⡀⠂⢀⣨⣵⣶⣼⣿⣿⣿⡿⢿⢷⠠⠹⢿⠂⠈⠙⠛⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠨⠉⠭⡍⠉⠛⠃⠻⣼⠗⠚⣶⣴⡿⢿⢞⡙⠙⣿⣶⣿⣷⣾⣠⡋⠘⠗⠀⠀⠁⠀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠈⣉⣉⣥⡾⢿⣏⣉⣠⣠⠂⢻⡟⡋⢹⣰⣂⣀⣸⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣷⡄⠀⠀⢀⣠⡞⠉⠰⠇⢁⡀⠀⡈⠉⠡⠶⠒⠙⠋⢾⢉⠤⠛⢿⣿⣿⢇⣦⣤⣤⠄⠀
⣀⡀⠀⡀⠀⠀⢀⡠⠠⠀⠀⠀⠀⣿⣭⣄⣸⠉⠈⠉⣁⣦⡜⠒⠉⠉⠀⠘⣿⣿⣿⣋⣡⣀⣀⢀⣾⣿⣿⣧⠀⠀⣉⠙⠻⣿⣷⡄⠈⠉⠈⠀⠀⠚⠃⠉⠉⠑⠢⠀⡀⠐⠋⠀⠀⠬⢹⣯⣅⣨⠥⣮⣽⣿⣏⣛⣷⣶
⠉⠁⠐⠀⠀⠀⠉⠀⠀⠤⠀⠀⠀⠠⠜⠁⠁⠒⢻⡁⣟⡂⠉⠐⡆⠀⣩⣰⣿⣿⣿⣿⣿⣶⣶⡿⠿⠿⠿⠿⣿⣿⣛⣿⣷⣾⣿⣇⠀⠀⠀⠀⢀⣡⠄⠺⢴⣞⣋⣿⣷⣶⡃⢀⣀⣴⣿⣿⣿⣿⣿⣿⡿⣿⠟⣩⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠤⠨⢁⣤⣄⠉⠠⠄⢸⣿⣿⣿⣿⣿⢿⣿⣤⣤⣀⣀⠀⢈⡿⣿⣿⣿⣿⣿⣿⠀⠀⣤⡄⠊⡩⣷⠦⠀⣬⡯⣿⣿⣏⣋⡉⠉⣙⣯⠿⠙⠏⠐⠋⠀⠈⠰⣌⠀⠈
⠀⠒⠀⠀⠀⠐⠤⠬⢡⣤⣮⠷⢾⣶⣿⣛⠀⠂⠀⠀⠘⠩⣾⠇⣀⠀⢀⣿⣿⣿⣿⡟⢁⣾⣿⣿⡿⠿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⠀⠉⠉⠀⢩⣾⡽⠟⠀⣾⠟⠻⠛⠉⣛⠳⠃⠐⢲⢛⡾⠧⣥⡀⠀⠀⢀⡺⣧⠾
⠁⠀⠀⡀⠀⠀⠈⠁⡒⢏⠉⡛⠓⢚⣯⡶⢀⠀⢀⠘⣆⠀⢀⢀⣡⡄⣼⣿⣿⣿⣿⣷⣿⡟⠋⣖⣋⣁⠀⠀⠉⢻⣿⣬⣿⣿⣿⣿⣄⠀⠑⠒⢚⣟⡃⠤⣃⠁⢠⠤⠨⠁⡘⠻⣶⣴⣻⣸⡟⠙⣧⣉⣏⣄⣬⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠠⠀⠴⠀⠩⠍⠀⠀⠀⠀⠤⠀⠀⠈⠉⡀⢁⠉⠹⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠷⠴⠦⠀⠬⢭⣼⡃⠐⢺⣾⡄⠠⠾⡓⠁⠉⣤⣋⡀⠀⢉⡿⠿⠋⠡⣿⡿⠛
⠀⠀⠰⣁⠀⠄⠀⠀⠀⠀⠀⢀⡤⡿⢭⡄⠴⠉⡀⠀⠈⠀⠈⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣤⢰⣶⣀⣀⠁⢼⡖⠆⠄⠀⠉⢮⣴⡶⠀⠀⠀⠈⣴⡖⠆⢐⣾⣴⡶
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠰⠯⠋⠀⠀⠀⠀⠉⠁⠀⠀⡀⠦⠘⠛⢻⣿⣿⣿⣿⣿⠿⠟⠋⠛⠛⠛⠁⠈⠙⠛⠻⣿⣿⣿⣿⡏⠀⠙⢏⠓⠠⠯⠁⠐⢺⢿⣷⣒⢴⠀⠀⠠⠌⣀⢴⣶⣶⡄⠀⠘⣧⠯⡔⠛⠛
⠀⠀⠀⠀⠀⠠⠀⠀⢠⠀⢠⡤⠤⠄⠀⠀⢤⡤⠀⠒⠀⠀⢀⡁⠠⠁⢀⣼⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣋⣿⣟⡈⠁⠀⠘⠈⢀⡀⠀⢠⠀⢘⡀⠈⠷⠀⠔⠲⣠⣌⠉⢆⠈⠉⠀⠀⢠⢻⠤⠵⢄⠀
⠀⠀⠠⠀⠐⢒⡂⡤⠸⣄⠀⠀⠀⠀⣴⣚⣉⣡⣄⣘⣁⣉⠹⢇⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡅⠈⠀⠒⠁⢠⠀⠀⣀⠉⠛⠓⡌⠉⠐⣣⡐⢏⠉⢿⠷⠂⠣⠠⠤⢠⡇⡀⠀⠀⠈⠑
⠀⠀⠀⠈⠄⠈⠉⢉⣉⣷⣶⣶⣶⣿⣿⣿⠿⠟⠛⢻⣯⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣶⣮⡖⣲⠀⠀⠀⠈⠀⠲⠏⠓⠶⢾⠏⠀⠬⡎⠿⠀⣿⣄⠀⠀⠈⠁⠀⠀⠀⠉⠁
⣀⣀⣴⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⢸⣿⣟⣀⠀⠀⠀⢨⣿⡿⠿⠛⣯⠀⠀⠀⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⢐⣯⣶⡞⠛⢿⣿⢏⣿⣿⠷⠶⠉⠉⢻⣷⣿⣶⣶⡄⣀⠀⠀⢰⠖⠰⠒⠷⠈⢧⣤⡴⠶⠄⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣀⡀⠤⠯⠁⠀⣀⣠⣿⡆⠀⠀⠀⠘⢿⣿⣿⣿⡆⠀⠀⣠⣾⣿⡏⠀⠀⠀⣿⣿⡇⠉⠀⠀⠈⠀⠀⠀⠙⢻⣿⡆⣿⣿⣿⣿⣿⣦⣶⣤⡀⣠⡄⠀⠀⣂⠀⠀⠀⡀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⠟⠛⢇⡀⠀⣶⣦⣿⣿⣿⡇⢸⣷⣦⡀⠀⠙⠻⢿⠇⣠⣾⣿⣿⡿⠗⠀⠀⢰⣿⣿⣷⣶⠀⠀⣀⣀⠀⠀⣤⣼⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡤⣱⣄⣒⠂⢴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣀⡀⠿⠿⠃⠀⣸⣿⣿⣿⣷⠸⣿⣿⣿⣷⣦⣄⡀⠈⠉⠉⠉⠀⠀⢀⣠⣶⡏⣿⣿⣿⣿⣤⣤⠉⠉⢠⣤⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣁⣒⣞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⠟⠿⠃⠀⠀⣿⣶⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⢠⣿⣿⣿⣿⠉⠉⣤⣤⠘⠛⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡀⠀⢾⣿⡆⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣿⣿⣿⡟⢸⣿⣿⣿⣿⣶⡆⠛⠉⣤⣤⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⡿⠿⠇⠀⠀⣵⣶⣾⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇⣼⣿⣿⣿⡟⠉⠃⣤⣤⠛⠻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠉⠙⢿⣿⣿⣿⢸⣿⣿⠀⠀⣴⣶⣆⠉⢻⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⠁⣿⣿⣿⣿⣷⣤⡀⠛⠛⣀⣀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠈⠁⠀⠀⠈⣿⣿⣿⢸⣿⣿⣿⠇⠉⠙⠒⣤⣾⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⡏⣸⣿⣿⣿⣿⡿⠛⢁⣀⣀⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠋⠛⠋⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠈⣿⣿⡏⣀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⢠⣿⣿⣿⣿⣿⣧⣤⡘⠛⠃⢀⣸⣿⣿⣿⣿⡇⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⠛⠻⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣧⡛⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠘⣿⣿⣿⣿⣿⠁⣿⠻⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⡤⠀⠀⠀⠀⠀⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡁⠻⣿⠶⠃⠿⢿⣿⣿⣿⠀⠋⠁⠀⠴⠆⠀⢀⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠯⠀⠉⠛⠃⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠀⣤⣭⣿⣭⣤⣀⣠⣤⠀⢸⣿⣿⡇⢠⣶⣤⣀⠸⡿⣀⠀⠉⠛⠻⠟⠓⢢⡄⠀⠀⠠⠂
⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠄⢸⣿⣿⠁⠀⠀⠙⠛⠀⠀⠈⢐⠛⠟⠊⠀⠀⠀⠀⢀⣰⣀⣠
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠘⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⣿⠀⢀⣄⠐⢮⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⢻⣿⠉⠀
⠀⠂⠀⠐⠀⠀⠀⠛⠁⠀⠻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⡇⢸⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣥⣼⣿⣦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⣸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⣀⠀
⠀⠉⠂⠀⠀⠀⢀⡄⠈⢁⣼⣿⣿⣿⣿⣿⠀⠀⠈⠉⠉⠛⠛⠛⢻⣿⣿⣿⡟⠀⠀⣀⣤⣤⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⠿⠿⠿⠿⠛⠛⠛⠛⣡⣿⣿⣿⣇⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣀⢄⣴⣖⣶⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠛⠿⢿⣿⣿⣷⣤⣤⣀⣀⠀⠀⠀⢸⣿⣿⠟⣱⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⢀⡾⣿⣫⣷⣿⣿⠝⣐⠻⣵⣼⣷⣿⣿⣿⣿
⠀⠀⠀⠀⣰⣿⣿⣷⣄⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣶⣿⠟⣡⣾⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣇⠀⠀⢀⣀⣠⣤⣴⠾⠛⠋⠉⣿⣄⠀⣠⣼⣿⣿⣿⣿⡿⡫⣖⢶⣶⣌⠛⢿⣿⣿⣿⣿
⠛⠀⠀⣰⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⢋⣵⣾⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠠⠟⢁⣿⡟⠀⢹⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠙⠛⢛
⠀⠀⢰⠿⢿⠿⠿⡿⠿⡟⠈⠋⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠀⠘⠿⠛⠛⢿⣿⣿⠿⠿⠃⠀⠘⠛⠿⠟⠛⠟⠛⠋⠁⠀⠀⠀⠀⠀⣰⣿⣿⠃⢠⣦⢿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⣿⠀⠘⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⣥⠆⣾⡿⠉⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⡷⠦⡀⠀⠀⠄⠀⠀⠀⠀⡀⠀⢰⠒⠂⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠈⣿⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣿⣿⣼⣿⠃⣀⠀⠻⣿⣿⣻⣯⣽⣿⣿⣿⢯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⢀⣇⠀⠁⠀⣠⡄⠀⠀⠀⠀⣷⡀⠈⠀⠰⠀⠀⠀⣠⠀⠀⠀⣄⠀⠀⢀⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⣆⠀⢸⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⣿⣿⣿⠛⠁⠀⠀⠹⣿⡏⠀⣼⣿⣿⣿⡆⠙⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠹⣿⡿⠁⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⠆⢀⣵⣛⠙⠘⠃⢠⣀⡀⡀⢠⣀⠴⢾⣷⡌⠱⠀⢶⡴⠄⢀⣀⣶⢭⡀⠦⡿⠉⠱⠋⠐⣦⠈⠉⠘⠓⢿⣿⡥⠄⠠⠀⣉⠉⣵⣶⠀⠿⢰⣶⢠⣤⢽⣿⠛⠒⣴⣻⣶⣿⡇⠀⢙⠇⠀⠈⠙⢛⡿⠛⠛⠛⠚⠉⠟⣿
⠀⠀⢁⠀⠅⠀⠀⠴⠮⠄⠛⠉⠐⣚⢇⣭⣉⠙⠃⠖⡀⠀⣉⡉⣤⠾⠈⠃⠀⣤⡀⠱⣿⣿⣶⣉⣩⣤⣤⣤⣄⣀⣠⣸⡇⠀⠰⠒⢀⢰⣿⠏⣹⠟⢙⣛⣏⡍⠘⠩⠉⡙⠓⢸⣼⡆⠀⠰⠶⠊⠠⠀⠀⠀⠀⠁⠴⠛
⠀⠐⠁⠀⠀⠀⠀⢀⠈⠀⠀⠀⢠⡄⠈⠉⣗⡄⢀⣨⣿⡁⠀⣤⢃⡀⢰⣶⣎⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⣼⣾⣍⣿⣦⡗⢀⣾⣿⡟⠀⣀⡀⠀⠙⢟⢠⣿⣮⢥⣴⣯⣴⡆⣀⠆⣀⠆⠀⠮⠲
⠀⠀⠂⠀⠠⠖⠀⠀⠀⡀⠂⢀⣤⣽⣶⣼⣿⣿⣿⡿⢿⢷⣠⠹⢿⠂⠘⠛⠟⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠉⠯⡍⢙⠻⠃⠻⣼⠟⠚⢶⣶⡿⢿⢞⡘⠙⣿⣶⣿⣿⣼⣠⡋⠘⠗⠀⠀⠀⠀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠈⣉⣉⣧⡿⢿⣯⣉⣥⡤⠒⢻⡛⡏⢹⣰⣆⣤⣦⣼⣿⣿⣿⠿⡝⠛⣿⣿⣿⣿⠿⠛⣛⣻⣿⣷⣄⠀⣀⣠⡞⠉⢴⠇⢁⡀⠀⡈⠉⠱⠶⠒⠙⠫⢺⣏⠥⠛⢿⣿⣿⢇⣧⣤⣤⡄⠀
⣀⡀⠀⠀⠀⠀⢀⡠⠠⠀⠀⠀⠀⣿⣭⣤⣰⠈⠈⠉⣁⣦⡜⠒⠉⠉⠀⠉⠋⣿⣿⣟⣥⣴⣤⣄⣠⣿⣿⣿⣧⠀⢀⡈⣉⠻⣿⣿⡏⠉⠈⠁⠀⠚⠁⠉⠉⠑⠲⠀⡀⠒⠛⠁⠀⠭⢹⣯⣁⣨⢥⣾⣽⣿⣏⣛⣿⣶
⠉⠁⠐⠈⠀⠀⠉⠀⠀⠤⠀⠀⠀⠤⠜⠁⠁⠐⢻⡓⣧⣃⠉⠐⡆⠀⠭⠤⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣟⣿⣷⣿⣿⣇⢀⠀⠀⢀⣡⠄⠺⢴⣞⣏⣿⣷⣶⡃⠄⣀⣴⣿⣿⣿⣿⣿⣿⡿⣿⠟⣩⠽⣿
⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢋⠤⠩⢁⣠⣄⠉⠠⠄⠛⣿⣿⣿⣿⣿⠿⣻⣿⣤⣦⣀⣀⠀⣸⡿⣿⣿⣿⣿⣿⣿⠀⣤⡤⢊⡩⣷⠦⠄⣬⡿⣿⣿⣏⣋⡉⠉⣙⣯⠷⢙⠏⡐⠋⠀⠨⠰⣎⠀⠈
⠀⠂⠀⠀⠀⠐⠤⠬⠡⣴⣎⠷⢾⣶⣿⣛⠀⠂⠀⠀⠘⠭⣾⠧⣀⠀⠐⢺⣿⣿⣿⣿⠏⣰⣿⣿⠿⠿⠿⢿⣿⣿⣷⡙⣿⣿⣿⣿⣿⠁⠉⠀⢩⣾⡻⠯⡐⣾⠝⠻⠛⠉⣛⡿⠆⠐⢲⠻⠾⠧⣥⡄⠀⠀⢀⢺⣷⠞
⠁⠀⠀⡀⠀⠀⠈⠁⡲⢈⠉⡛⠓⢚⣿⣶⢀⠀⣀⠙⣆⠀⢀⢀⣡⡄⠀⣿⣿⣿⣿⣿⣿⣿⠋⣰⣋⣁⣀⡀⠀⠉⢿⣷⣿⣿⣿⣿⣿⣤⠐⠒⢚⣟⡃⠤⣃⠹⢴⠤⠨⠃⡙⠻⣶⣴⣻⣸⡟⠙⣧⣉⣏⣄⣬⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠁⠼⠀⠩⠍⠈⠀⠀⠀⠤⠀⠀⠈⠉⡀⢁⠉⠙⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡯⠷⠦⠀⠬⢭⣼⡉⠐⢺⣾⡄⠠⢾⡛⠁⠉⣤⣋⡁⠀⢉⡿⠿⠋⠡⣿⡿⠛
⠀⠀⠰⣁⠀⠄⠀⠀⠀⠀⠀⢀⡦⡿⢭⡄⠴⠏⡀⠀⠀⠁⠈⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣤⢰⣶⣀⡄⠁⢾⡖⠆⠄⠀⠁⢬⣵⡶⠀⠀⠀⠈⣴⡖⠆⢒⣾⣵⡶
⠀⠀⠂⠀⠀⠀⠘⠁⠀⠀⠀⠀⠴⠯⠋⠀⠀⠀⠀⠉⠁⠀⠀⠐⠶⠀⠉⢋⣿⣿⣿⣿⣿⣿⠿⠛⠉⠛⠛⠛⠀⠘⠛⠛⣿⣿⣿⣿⣿⠋⠙⢏⠓⠰⠯⠁⠐⢻⢿⣷⡐⣴⠀⠀⠠⠌⣠⢴⣶⣷⡄⠀⠙⣧⠯⡐⠛⠛
⠀⠀⠀⠀⠀⠤⠀⠀⢤⠀⢠⠤⠤⡀⠁⠀⢤⡤⠀⠒⠀⠀⢀⣁⠈⠁⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡋⠈⠠⠘⠈⢀⡀⠀⢠⠀⢈⡀⠈⠷⠁⠔⠲⣢⣌⠍⢆⠈⠉⠂⠀⢨⢻⠦⠵⢄⠀
⠀⠀⠤⣄⣲⣶⣶⣶⣾⣶⣶⣶⣶⣿⣷⣾⣿⣿⣿⣿⣷⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡁⠀⠒⠁⢠⠀⠀⣀⠉⠛⠓⡆⠉⠐⣣⡐⢏⠉⢿⠷⠂⠣⠠⠤⢠⡇⡀⠀⠀⡈⠑
⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠉⠁⠀⠘⣿⣿⣿⣿⢿⠟⠛⠛⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠚⣻⣿⣿⣿⣿⣷⣖⣀⣤⡄⠈⣀⣰⡏⢓⣲⣾⣏⡀⠬⠎⠿⠀⣿⣄⠀⠀⠈⠀⠀⠀⠀⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣇⠀⢀⣜⠛⠉⠁⠀⢈⣄⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣾⡿⠉⠙⢿⣿⣿⣿⠛⠛⠁⠀⠸⠟⢿⣿⣿⡛⣿⣿⣿⣷⣾⣿⣶⣿⣿⣷⣤⣴⣶⣤⡀⡠⠅⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠉⠉⢁⣀⣠⣶⣾⣿⡀⣤⡀⠀⠘⠻⣿⣿⡧⠀⢀⣠⣾⣿⣿⡀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⡏⠀⢀⣶⣶⠘⠛⣿⣿⣿⣿⡇⣿⣿⣦⣄⡀⠈⠙⠃⣤⡿⠿⠿⠟⠛⠀⠀⢠⣿⣿⣿⣿⠀⠀⣰⣶⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⠀⠉⢹⣤⣤⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣿⣿⣿⣿⣿⡶⠀⠀⢸⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⡏⠀⠀⣶⣤⠘⠛⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⢰⣿⣿⣿⣿⡀⠀⣿⡿⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠻⣿⣿⡏⠉⠻⣿⣿⣿⣿⡏⣸⣿⣿⣷⣶⠀⠉⢃⣀⣀⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣾⣿⣿⡟⢸⣿⣿⣿⣿⣿⣟⠀⠀⣼⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⠀⠹⣿⣿⣿⣇⣿⣿⡏⠁⠀⣤⡄⠘⠿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⡇⣼⣿⣿⣿⡇⠀⠐⣾⣿⠀⠈⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⣿⡿⣿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠘⣿⣿⣷⡆⠘⠿⠿⣀⣠⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠹⣿⣿⢀⣿⣿⣿⣿⣿⣷⡆⠀⠀⣶⣦⣿⣿⣿⣿⡇⢸⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿⠀⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢻⠇⣸⣿⣿⣿⣿⡏⠉⢱⣶⣶⠉⠻⣿⣿⣿⣿⣧⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢶⠆⢸⣿⣿⡆⢿⣿⡇⢿⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⡆⠈⠀⠀⣾⣿⣿⣿⣿⡟⢸⣿⣟⠗⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠤⣬⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢸⣿⣿⣷⣬⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⣠⣀⣀⡀⢹⣿⣿⣿⣿⡇⣼⣿⣿⠀⠀⠀⠐⣶⡄⠠⠀⢃⠀⢀⣴⣮⣷⡦
⠀⠀⠠⡤⠀⠀⠀⠀⠀⢻⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠛⠛⠿⢿⠧⡈⠛⠋⠁⠈⠉⣿⣿⣿⢀⣿⣿⠃⠰⠄⠀⢤⣤⣴⣖⡒⠀⠈⠢⣨⡅⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠉⠀⠀⠈⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⢼⣿⣿⣿⣶⣶⣶⣿⡇⢀⣿⣿⡏⢸⣿⣧⣄⠸⠿⣀⡀⠙⠛⠻⠟⠓⢦⡴⠀⠀⠔⠂
⠀⠀⠀⠠⠀⠀⢀⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⢿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⠸⠉⠘⠛⠀⠀⠈⢰⠛⠟⠋⠀⠀⠀⠀⣀⣰⣀⣤
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠸⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⠀⢸⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⢀⣄⠐⢯⠀⠀⠀⠄⠂⠀⠀⠀⠀⢀⠀⢿⣿⠉⠀
⠀⠒⠂⠐⠀⠀⠀⠟⢁⣴⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⣬⡅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣥⣼⢿⣤⠤
⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⣡⣾⣿⣿⣿⣿⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⡿⠿⠇⣸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⣀⠀
⠀⠉⠂⠀⠀⠀⢰⡇⠀⠀⠻⠿⢿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⣴⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣇⠘⠉⠉⠉⠀⠀⠀⠀⣾⣿⣿⣿⡧⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣀⢄⣴⣖⣶⣾⣿⣿⣷
⠀⠀⠀⠀⣴⣦⣼⣿⣄⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣷⣶⣤⣤⣀⣼⣿⡿⣫⣾⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⠿⠟⠛⢻⡇⠀⠀⢀⡾⣿⣫⣷⣿⣿⠝⣐⠻⣵⣼⣷⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡿⠟⣡⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣤⣴⣶⣶⣾⣿⡿⠁⠀⡴⠀⣼⠀⠀⣠⣼⣿⣿⣿⣿⡿⡫⣶⢶⣶⣌⠛⢿⣿⣿⣿⣿
⠛⠀⣰⣿⣿⣿⣿⣿⣿⣿⠋⠻⢃⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠿⢿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⣾⡟⢀⣤⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⢠⣿⠿⠿⠿⠻⠿⠿⡿⠀⠀⠀⠉⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠸⡼⠛⠛⢿⣿⣿⠿⠛⠇⠀⠘⠛⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠾⣫⡄⣼⣿⣧⢿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠘⠛⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⡈⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⢠⡀⠀⠀⠀⠀⡆⠀⠸⠛⠛⠀⠀⡀⠀⠀⠀⠀⠗⠄⠀⠈⣿⡟⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡇⠀⠻⣿⣿⣻⣯⣽⣿⣿⣿⢿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⢀⠃⠀⠀⠀⠸⠇⠀⠀⡀⠀⣷⡀⠀⠀⠀⠀⠀⠉⣹⠀⠀⠀⣄⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⢸⠀⠀⠀⢀⣿⣥⣤⠘⣿⣿⠃⠀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⢻⣿⡿⢛⠁⠀⠀⠀⢸⡇⠰⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⡇⣰⣿⡿⢛⡭⠄⠛⠉⠀⠀⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣿⣿⣿⣿⣿⣿⣿⢀⣀⠀⣂⣠⣤⠴⣾⣷⣞⠳⠒⢾⡴⠄⣀⣠⣾⢭⣄⠶⡿⠋⠱⠋⠐⣦⠈⠉⡙⠻⣿⠿⠧⠄⢠⠀⣉⠉⣵⣶⠈⠿⢵⣶⣤⣦⢽⣿⢛⠒⣼⣻⣿⣿⡇⢀⢛⠇⠀⠈⠙⢛⡿⠛⠛⠻⠚⠹⠿⣿
⣿⣿⣿⣿⣿⣿⣿⠶⠬⡄⠛⠉⠰⣟⣧⣭⣍⠙⠓⢖⡁⠄⣉⣉⣵⡿⠀⠃⠀⣤⡀⠹⣿⣻⣾⣿⣭⣥⣶⣶⣶⣶⣤⣼⣿⡍⠠⠒⢀⣰⣿⡏⣿⠿⢛⣻⣿⡯⠘⠩⢛⡙⠻⢺⣿⡇⠀⠼⠗⠊⠡⠆⠀⠂⠀⠁⠴⠛
⠛⠛⠂⠁⠀⠈⠁⢀⠈⠀⠀⠀⢠⡆⠛⠉⣷⡌⢀⣬⣿⣅⠠⣤⢃⡄⢰⣶⣾⡁⠀⠀⠐⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣾⣭⣿⣶⡟⢐⣾⣿⡿⠀⣀⣀⠌⢹⢟⢸⣿⣯⢥⣴⣯⣵⡦⣀⠆⣀⡆⠀⠾⠶
⠀⢀⣴⣿⣿⣿⡇⠀⠀⡀⠂⢀⣬⣿⣾⣾⣿⣿⣿⡿⢿⢷⡠⠽⣿⠂⠼⠛⠟⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠋⢯⡍⢙⡻⡟⠻⣼⠿⠛⣶⣶⡿⣿⢞⡛⠛⣿⣾⣿⣿⣿⣠⡋⠘⠗⠁⠀⠁⠀
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⣉⣙⣧⡿⢿⣯⣉⣣⣤⠒⣻⡟⡏⣹⣴⣦⣤⣦⣩⣿⣿⣿⠿⠛⠳⠍⢻⣿⣿⣿⡿⠛⢉⣽⣿⣿⣆⣀⣠⡟⠉⢴⠇⢣⣀⡀⣉⢉⠹⠶⠛⠙⠻⢿⣏⠬⠛⣿⣿⣿⣧⣧⣤⣤⡄⠀
⣀⡀⠀⡀⠀⠀⢀⡠⠤⠀⠀⠀⡀⣿⣯⣤⣸⠋⢈⠉⣛⣶⡜⠓⠉⠉⠀⠘⠉⣿⣿⣿⣿⣶⣾⣶⣶⣦⣿⣿⣿⣿⣧⣀⣠⣤⡉⢻⣿⡏⠉⠁⠀⠚⠃⠉⠉⠑⠲⠀⡀⠒⠋⠁⢀⠭⢹⣯⣍⣨⢶⣾⣿⣿⣟⣿⣿⣿
⠉⠁⠔⠂⠀⠀⠉⠀⠀⠤⠀⠀⠀⠤⠜⠁⠁⠾⢿⡓⣿⣃⠉⠰⣇⠀⢭⣤⢶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⢈⣡⠆⢾⣶⣟⣟⣿⣿⣾⡋⢄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣩⠽⣿
⠀⠈⠀⠀⠠⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⢨⠟⢋⠤⠩⢁⣤⣤⠉⠠⠄⡿⡟⣿⣿⣿⣿⣿⡿⢛⣿⣷⣶⣧⣤⣤⣀⣼⣿⣿⣿⣿⣿⣿⣤⡤⢚⡹⣷⠦⠄⣼⣿⣿⣿⣏⣛⡉⠉⣙⣯⢷⣝⠟⡐⠋⠀⠈⠰⣎⠀⠈
⠀⠓⠀⠀⠀⠐⠴⠬⢡⣴⣮⠷⢾⣷⣿⣿⠅⠂⠀⠀⢸⠯⣿⠧⣀⠘⠉⢹⣿⣿⣿⣿⣿⣿⣠⣿⣿⠿⣛⣛⡻⠿⢿⣿⣿⡿⣿⣿⣿⣿⡏⠀⣩⣾⣿⡿⡐⣾⠟⠻⠻⢃⣟⡿⠇⠐⣶⢿⡾⠦⣥⡄⠀⠀⢈⣺⣷⡾
⠁⠀⠐⡀⠀⠀⠈⠁⡲⢞⠉⣛⠛⢛⣿⡾⢀⠀⣀⠙⣧⡀⢀⢀⣩⡄⢀⢼⣿⣿⣿⣿⣿⣿⣿⡟⣁⣬⣥⣀⣀⣀⠀⠘⣿⣷⣿⣿⣿⣿⣷⠒⢚⣟⡃⠴⣃⠑⣴⠤⠬⠇⣘⠿⣾⣶⣿⣻⡏⠙⣦⣉⣏⣤⣭⣿⣿⣿
⣤⣤⣄⣀⠀⠀⠀⠉⠼⠀⠩⠭⠈⠀⠀⠀⠤⠀⠀⠈⢉⡀⢁⠙⠹⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡿⠦⠁⠬⣭⣿⡍⠓⢺⣿⡆⠠⢾⡛⢍⠉⣤⣋⡠⠄⢉⡿⠿⠛⢡⣿⡿⠛
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣀⣀⣴⣿⣭⡄⠴⢏⡀⡉⠀⠁⠈⣀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣤⣰⣶⣤⣄⠑⢾⡖⠆⠄⠀⠉⢾⣽⡶⠀⠈⠁⠈⣴⡶⠦⣶⣾⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣀⠉⠀⠀⠐⡒⠾⡀⠀⠸⢍⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⠛⠛⠓⠀⠈⠛⢻⣿⣿⣿⣿⡟⢏⠛⠰⠯⠍⠉⢻⢿⣷⡲⢴⠀⠀⠠⠪⣡⣴⣶⣷⣤⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡝⠙⠈⢠⡀⠀⢠⠀⣬⣤⣈⣷⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠠⣰⣿⣿⣿⡇⠀⠀⠀⢀⣴⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⡀⠘⠉⠉⠉⠀⠀⠙⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⢂⣦⣭⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠛⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⠿⠿⡇⠀⠀⠀⠀⣤⣰⣧⠀⠀⠀⠉⠻⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⢹⠋⠁⠀⠀⠀⠀⠀⠀⣤⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⠟⠿⠻⢻⣿⣿⣿⠁⣿⣿⣿⡏⡀⠀⣶⣶⠀⠚⢻⣿⣿⣿⡄⣶⣄⠀⠀⠈⠛⠿⠇⠀⢀⣤⣾⣿⣿⠷⠀⠀⢀⣾⣤⡄⠀⠀⠶⠦⣀⣤⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉
⠀⠀⠀⠀⠙⠀⠀⠀⠀⢫⣿⣿⡇⢸⣿⣿⡿⠿⠿⠀⠀⢀⣀⣠⣿⣿⣿⣿⡇⢿⣿⣿⣶⣤⣤⣄⡀⠀⠈⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣷⠶⠆⢀⣀⠛⠛⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⣾⣿⣿⠁⠀⢰⣶⡄⠈⠛⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⢋⣿⣿⣿⣇⣀⣀⠛⠛⢀⣀⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⠿⡯⠻⢿⡧⠄⠀⢀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡟⣸⣿⣿⢿⣿⠇⠀⠉⣢⣄⣼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣾⣿⣿⢸⣿⣿⣿⣿⠿⠿⣀⣀⡸⠿⢿⣿⣿⣿⣿⠸⣿⣿⣿⣛⡋⡀⢐⠌⠀⠀⠄⢾⣶⣆⣀⢹
⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⠁⣿⣿⡟⠀⢀⣴⣦⠄⠻⢿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠸⡿⠇⠀⢸⣿⣿⣿⣿⡄⣿⣿⣿⣯⣖⣄⢠⣱⡋⠁⠀⢈⣉⠉⢿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢰⣿⣿⣿⡟⠉⠛⠻⢅⣀⣾⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠹⣿⡇⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣷⣿⣿⣿⣤⣠⣤⣯⣲⣴⣿
⠀⠀⠀⠀⠤⠀⠀⠹⣿⣿⣧⠸⣿⣿⠏⡁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠹⠁⣾⣿⣿⣿⣿⣏⠉⠽⣿⠿⠀⣨⣿⣿⣿⣿⣿⢸⣿⣿⡿⣿⣟⣻⣀⣼⣭⡤⣀⣭⠽⠋⣀
⠀⠀⠀⠀⠀⠀⠘⠃⣹⣿⣿⠀⣿⣿⡀⠿⣿⣷⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⡏⢸⣿⡿⠋⠉⢹⣿⣿⣿⢶⣆⣈⣁⠀⠀⠬
⠀⠀⠀⠀⠀⠀⢶⣆⠘⢿⣿⡇⢿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⠿⣿⣿⠰⣦⣤⠤⠸⣿⣿⣿⣿⠇⣾⠋⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⠴⣥⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠉⠙⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠀⣠⣤⣤⣀⣀⣀⣀⣠⡄⠀⣿⣿⣿⢠⣷⡀⠲⠀⠲⣾⡦⠤⠄⢗⠀⢀⣴⣿⣷⡖
⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⡏⠈⠁⠰⠀⠐⢠⣥⣶⣖⣒⠀⠈⠢⣬⡍⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⣤⣄⠸⠟⣄⡀⡉⠛⠻⠟⠓⢦⡾⠀⠓⠔⠂
⠀⠀⠀⠠⠀⠀⢀⠀⠀⣠⣼⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠃⠛⠛⠁⠀⠈⢱⠛⠟⠋⠀⠀⠀⠀⠤⣴⣤⣴
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠻⢃⣼⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⠘⢯⠀⠀⠀⠔⠒⠀⠀⠀⠀⢀⡀⢻⣿⠀⠀
⠀⠒⠀⠐⠀⠀⠀⣿⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⠀⠀⣀⣤⣴⣮⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⡿⠿⠿⠿⠿⠛⠛⠛⢃⣼⣿⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣥⣾⣿⣶⠤
⠀⠀⠀⠀⣴⣶⣴⣿⣄⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣶⣦⣤⣄⣀⡀⣸⣿⣿⠟⣡⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣃⣀⠀
⠀⠉⠀⣼⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⠿⢛⣵⣾⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢀⣀⣀⣀⣠⡤⠜⠛⠋⠁⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣀⢄⣴⣶⣶⣾⣿⣿⣷
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠻⠖⣀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢥⣾⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠰⠃⠀⠀⠀⢠⣾⣿⣯⣷⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⡀⣸⣿⣿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠙⠻⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⢀⣾⠄⠀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣶⣌⠛⢿⣿⣿⣿⣿
⠛⠛⢯⣷⣦⢸⣷⣮⢹⣿⣤⡀⠀⠀⠀⣼⡟⠛⢁⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣵⣧⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠛⠚⠛⠟⠋⡿⠛⠛⠳⠆⠀⠛⠃⠀⠀⣿⠿⠛⠻⢿⠖⠀⠀⠀⠀⠀⠀⠿⠛⠛⢿⣿⣿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⡿⣿⣿⣷⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠆⠀⠀⠀⠀⡏⠀⠠⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⣾⡏⠒⢸⣿⣿⠋⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠁⠀⠘⠙⠀⠀⠀⣤⣿⡇⠀⠀⠷⠄⠀⠈⣿⣧⠀⢀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣿⡿⢛⠀⠟⠁⠀⠀⠻⣿⣿⣻⣯⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⠀⠀⡀⠀⠀⠉⣹⡇⠀⢀⣄⠀⠁⣀⣿⣿⠀⠈⠀⠀⠀⠀⠉⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⢁⣤⣶⠁⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠑⠿⠛⠻⠃⠛⠻⣿⣿⣿⣿⣦⣄⡀⠀⠀⢸⣿⣿⡅⠈⢋⣿⣿⣿⣿⠅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⢠⠀⠀⣾⡿⡃⠀⠀⠘⠀⠀⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⠀⠀⣠⣠⣴⡾⠿⢉⣠⡀⣐⣠⣤⠴⣾⣇⡀⠀⠐⢷⡴⠄⢀⣠⣾⢭⣄⠶⡿⠋⠱⠋⢐⣶⠘⣉⣿⠿⠿⠿⠧⠄⢠⠀⣉⠉⣵⣶⠀⠛⢵⣶⣤⣤⢽⣿⠟⠳⣼⣻⣶⣿⣇⢀⢙⠇⠀⠀⠙⢻⣿⣿⣿⠿⣿⣿⣯⣤
⣿⣿⣿⠛⠋⠂⠀⠶⠮⠅⠛⠋⠰⣿⣯⣭⣅⠐⠒⢖⡁⠄⣉⣉⣷⡿⠈⠃⠀⣤⡀⠹⣿⣿⣿⣿⣴⣶⣶⣶⣶⣶⣦⣼⣿⡊⠐⠒⢁⣰⣿⡏⣿⠿⢛⣻⣟⡍⠘⠩⣛⣙⠛⢹⣿⡇⠀⠸⠶⢚⢿⣷⣦⡀⠀⠈⠙⠻
⡿⠋⠃⠀⠀⠀⠀⢀⠉⠀⠀⠀⢠⡦⠙⠙⣷⣬⢀⣨⣿⣅⡤⣤⢋⡄⢸⣶⣾⡁⠀⠀⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣾⣭⣽⣾⡟⢐⣾⣿⡟⠂⣀⣀⠄⠹⢗⢸⣿⣮⣥⣴⣯⣷⡦⣿⡿⣿⡇⣶⣤⡀
⠁⠀⠀⠀⠠⠖⠀⠀⠀⡀⠂⢀⣼⣷⣾⣾⣿⣿⣿⡿⢿⢿⢠⠽⣿⠂⠨⠛⠟⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠋⠯⡍⠙⡻⠟⠻⣼⠿⠛⢶⣶⡿⢿⢞⡚⠛⣿⣶⣿⣿⣾⣠⡋⠘⠏⠃⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣉⣉⣧⡿⢿⣯⣉⣧⣤⠒⢻⡟⣛⢹⣶⣦⣤⣦⣿⣿⣿⠿⠛⠛⠦⠙⣿⣿⣿⡿⠛⠉⠽⣿⣿⣿⣆⣀⣠⡞⠉⢴⠗⢣⣀⠀⣉⢉⠹⠶⠻⠽⠫⢿⣏⠭⠻⣿⣿⣿⣧⣧⣶⣤⡄⣹
⣀⡀⠀⡀⠀⠀⢀⡠⠦⠀⠀⠀⠀⣿⣿⣤⣸⠃⢈⠉⣋⣶⡜⠓⠉⠉⠀⠘⣫⣿⣿⣿⣷⣶⣿⣶⣶⣼⣿⣿⣿⣿⣤⣤⣦⣤⣉⢿⣿⡏⠙⠁⠀⠺⠃⠉⠙⠓⠲⠀⡀⠖⠛⠁⢀⠽⢹⣯⣁⣠⢴⣾⣽⣿⣟⣛⣿⣾
⣭⣁⠴⠀⠀⠀⠈⠀⠀⠤⠀⠈⠀⠤⠜⠉⠁⠾⣻⡃⣿⣃⠉⠰⣆⠠⢭⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⢈⣡⠖⠾⣶⣟⣿⣿⣿⣾⡃⢄⣀⣴⣿⣿⣿⣿⣿⣿⡿⣿⠟⣩⢽⣿
⣿⣿⣷⣦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠟⢋⠤⠩⢁⣤⣬⠉⢰⠄⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣶⣦⣤⣀⣤⣤⣟⣻⣿⣿⣿⣿⣿⣤⡤⢚⡹⣷⠦⠄⣼⣿⣿⣿⣏⣋⡉⠉⣙⣯⠿⣟⠏⡐⠋⠀⠨⢵⢯⣸⣿
⣿⣿⣿⣿⣷⣶⡴⠬⢥⣴⣮⠷⢾⣷⣿⣿⠅⠂⠀⠀⢸⠭⣿⠧⣀⠐⠘⢽⣿⣿⣿⣿⣿⢁⣸⣿⡿⢟⡛⠛⠛⠿⢿⣿⣎⠹⣿⣿⣿⣿⠏⠀⣭⣿⣿⢿⠐⣾⠟⠻⠻⢁⣛⡿⠇⠐⣶⢻⡾⠧⣥⡄⠀⢀⣠⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⠉⣛⠛⢛⣿⣾⢀⡀⣀⠝⣧⠀⢀⢀⣫⡆⠀⣾⣿⣿⣿⣿⣿⣿⣿⠋⢀⣁⣀⣀⣀⡀⠀⠹⣿⣾⣿⣿⣿⣿⣷⠒⢚⣟⡃⠴⣃⠹⣴⠤⡬⠇⣙⠿⣾⣶⣻⣿⡟⠙⣯⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠠⠀⠀⠈⢉⡀⢁⠙⠹⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⠛⢿⣶⣿⣿⣿⣿⣿⣿⡿⠦⠁⠼⢭⣿⡉⠓⢻⣿⡄⠤⢾⡛⢅⠁⣤⣋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣤⡉⠈⠁⠈⣀⠀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣤⣴⣶⣤⣄⠁⢾⡖⠆⠄⠀⢉⣮⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣷⣤⡔⠲⣶⠀⠀⣼⣿⣿⣿⣿⣿⠏⠋⠛⠋⠀⠙⠛⠃⠀⠈⠙⠛⢻⣿⣿⣿⣿⡟⢏⠓⠸⠯⠅⣈⢻⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣿⣿⠉⠛⣙⣷⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠈⠀⠀⢠⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⡆⠉⠙⠋⠋⠛⠛⠻⠻⠿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⡀⠀⠀⠀⠀⠛⠿⢿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⢿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⢾⣿⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣾⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⠃⠀⢀⣀⡀⠀⠀⣰⣤⣆⠀⠀⠀⠀⠻⣿⣿⣟⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⢸⠉⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠋
⠹⢻⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣾⡆⠈⠉⠁⠀⢠⣿⣿⣿⡇⢶⣤⡀⠀⠈⠙⠛⠄⠀⢀⣴⣿⣿⡿⠿⠀⠀⢀⣾⣶⣆⠀⠀⠀⠀⣶⠾⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠺⠋⠀⠈
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⡟⠁⠀⣤⣀⠀⠾⢿⣿⣿⣿⣿⣷⢸⣿⣿⣷⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⠛⠁⣤⣖⠀⠀⢿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡢⢴
⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣷⣤⠀⠻⠃⠀⠀⣼⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⠇⣿⣿⣿⣿⣤⣴⠁⠀⢸⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠹⠽⡇⣲⡞
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢇⣾⣿⣿⠉⠉⢁⣀⡀⢼⣷⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣼⣿⣿⠀⣿⣿⣿⣿⠋⠉⢠⣶⡌⠀⠈⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⡟⠁⠀⠤⠀⢰⣶⣏⣀⢹
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢠⣿⣿⣿⣶⠤⠿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣿⣿⠀⣿⣿⣿⣿⣦⣤⡈⠛⠁⢴⣶⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⡿⠃⣰⡆⠃⠀⢘⣉⠛⢽⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⢸⣿⣿⡿⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⣿⣿⢀⣿⣿⣿⣿⣿⠿⢧⣤⣤⡾⠛⢻⣿⣿⣿⣿⣇⢸⣿⣿⣀⣹⣿⣿⣿⣤⣠⣤⣏⣶⣴⣿
⠀⠀⠀⠀⠤⠀⠀⠈⣿⣿⣿⠀⣿⣿⢡⣷⣦⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠏⢸⣿⣿⣿⣿⣿⣦⣦⡛⠛⠁⠀⣿⣿⣿⣿⣿⡟⢸⡿⠿⣿⣟⣻⣀⣾⣥⡤⠀⣬⠿⠏⣀
⠀⠀⠀⠀⠀⠀⠘⠃⣸⣿⣿⡄⣿⣿⣦⣍⣛⣉⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢃⣀⣀⣀⡜⣿⣿⣿⣿⡇⠀⠀⠋⠉⠸⣿⣿⡿⢶⣒⣭⣅⠀⠀⠨
⠀⠀⠀⠀⠀⠀⢶⡖⠘⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠹⠿⠟⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡏⠉⠉⠉⠉⠋⠈⠉⠉⠉⠁⠉⣻⣿⣿⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠖⠀⠔⣦⣥⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⠀⠀⠐⠒⢒⣶⡦⠤⠄⢗⠀⢀⣴⣿⣷⡶
⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⡇⠀⢲⡂⠀⢠⣤⣶⣶⣒⠀⠉⢢⣬⡅⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡆⠀⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⢀⢸⡿⣠⡀⣈⠛⠻⠟⠛⢶⡖⠀⠂⠔⠂
⠀⠀⠀⠠⠀⠀⢀⢀⠀⢾⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠁⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠇⠘⠉⠀⠈⢹⠛⠟⠉⠀⠀⠀⠀⠤⣴⣤⣴
⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⢠⣿⣿⣿⣿⣿⣿⠈⠙⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡀⠉⣀⠀⠀⠐⠂⠀⠀⠀⠀⢀⡀⢙⣿⠁⠁
⠀⠒⠀⠀⢠⣄⣠⣿⡄⠀⠀⠙⠛⠿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⠀⠉⠉⠉⠉⠁⠀⠀⠀⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⠠
⠄⠀⠀⢠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣶⣶⣦⣤⣼⣿⡿⢋⣴⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣃⣀⠀
⠀⠉⢁⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⠿⢋⣥⣶⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣧⣤⣶⣶⣶⣶⣿⡟⠁⢀⡄⠀⠀⡀⢀⣀⢀⣀⣴⣠⣠⣀⢄⣴⣶⣶⣾⣿⣿⣷
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠰⣶⢀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠈⠀⠀⠀⢠⣾⣿⣯⣷⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⣀⢰⡿⢟⣯⠉⣮⣝⠻⣿⡇⠀⠀⠀⠀⢸⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣧⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢠⠄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣶⣌⠛⢿⣿⣿⣿⣿
⠛⠀⠈⠛⢻⡇⣿⣿⣧⣿⣿⣶⣤⡀⠀⢸⣧⠀⠀⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠛⠛⠟⠛⠸⠛⠈⠛⠋⠐⠺⠟⠀⠰⣿⠿⠛⠛⠿⠟⠒⠀⣀⠀⠀⠀⠘⠛⠛⢿⣿⡿⠛⠛⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠒⠚⠀⠀⢀⣿⣿⡛⣷⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡏⠀⠐⠀⠀⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⣴⠀⠀⡆⠀⠘⠀⢸⠀⠀⠀⠀⢲⣽⣷⣤⡤⢹⣯⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠦⡀⠀⠀⠀⠀⠀⠇⠀⡁⠀⠈⠘⠃⠀⠀⣠⣿⣿⠀⠀⠲⠄⠀⠈⣿⣷⠀⢠⠀⠈⠀⠀⣿⠀⠀⡇⠀⠀⠀⠸⠀⠀⠀⠀⣼⣿⠟⠫⠖⠈⠁⠀⠻⣿⣿⣻⣯⣽⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠁⢀⣄⠀⠀⠀⠀⠀⣷⣀⠀⠀⣰⠀⠀⠉⢹⣿⠀⠀⣄⠀⠁⣀⣿⣟⠀⠈⠀⠀⠀⠀⠉⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣴⣾⠃⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠑⠿⠛⠻⠃⠛⠛⠛⠻⠿⣿⣿⣿⣶⡄⠀⠀⣿⣿⣦⠀⢠⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠼⠟⡅⠀⠸⠀⠀⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣗⣠⣤⠴⢾⣷⣾⠳⠖⢲⡴⠄⢀⣄⣶⣭⣄⡦⣿⠉⠡⠋⠐⣦⠈⠉⠁⠂⣀⡀⠀⠀⠀⠀⠉⠉⣵⣶⠠⠛⢴⣶⣠⣦⢽⣿⠟⠒⣼⣻⣿⣿⣇⢀⢙⠗⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠙⠉⠀⣛⣇⣭⣍⠙⠓⠖⣁⠀⣉⡉⣰⡾⠀⠃⠀⣤⡀⠸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣶⣶⣬⡰⠒⢀⢰⢿⡏⣽⠟⢛⣛⣿⡏⠘⠩⠙⡙⠳⢺⣽⡗⠘⣿⣦⣀⡀⠀⠀⠀⠀⠀⠘⠿
⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⢠⣤⠘⠉⣡⣤⢀⣠⣿⣅⠠⣤⢛⡀⢸⣶⣮⡁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣭⣽⣷⡟⢀⣾⣿⡟⠀⣀⡀⠀⠹⢟⢸⣿⣯⢭⣼⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣆⠀⣀⠂⠀⣠⣽⣶⣾⣿⣿⣿⡿⢿⢻⣠⢹⢿⠂⠨⠙⠟⠁⣀⣴⣿⣿⣿⣟⠛⠻⢿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣏⠽⡍⢉⢻⡓⠻⣼⠿⠛⢶⣼⡿⢿⢞⡚⠛⣿⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢉⣉⣯⡼⢿⣯⣉⣡⣤⢒⢻⣟⣛⢹⣶⣦⣤⣴⣿⣿⡿⠋⣁⣀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠐⠻⣿⣿⣆⣠⡞⠉⢴⠇⢣⣀⠀⣈⠉⠹⠶⠳⠝⠋⢾⣏⠭⠛⣿⣿⣿⣿⣿⡋⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢹⣯⣥⣰⠋⠈⠉⣉⣶⡔⠓⠉⠉⡀⠈⢋⣹⣿⣿⣿⣿⣯⣭⣤⣶⣿⣿⣿⣿⣧⣤⠄⠤⣤⣀⣿⣿⡉⠁⠀⠺⠃⠉⠉⠑⠲⠀⡀⠔⠋⠁⢀⠬⢹⣯⣭⣸⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠠⠜⠁⠉⠲⢻⡋⣻⣃⠉⠐⣦⠀⢩⣄⣔⣾⣿⣿⣿⣿⣿⠟⣿⡉⠀⠀⠀⠈⠉⢻⣷⣶⣾⣿⣿⣿⡇⠀⢈⣡⠆⠺⢶⣟⣏⣿⣷⣾⡃⢄⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠿⢋⡠⠨⢀⣠⣤⡙⠠⠀⢿⣿⣿⣿⣿⣿⡿⠃⣰⣿⣿⣷⣦⣤⣦⣤⣿⠙⣿⣿⣿⣿⣿⣧⣤⠘⣭⢷⠦⠀⣼⣿⣿⣿⣎⣋⡉⠉⠙⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠅⠂⠀⠀⢘⠯⣿⠷⣀⠀⠘⢹⣿⣿⣿⣿⣿⣧⣴⣿⠟⣋⠍⠉⠉⠛⠻⣿⣧⠈⣿⣿⣿⣿⡇⠀⣬⣿⣿⠟⡐⣾⠟⠻⠛⢁⣛⠻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠝⣧⡀⢀⢁⣫⡆⠀⢺⣿⣿⣿⣿⣿⣿⣿⣃⣀⣠⣀⣀⣀⡀⠀⠘⣿⣶⣿⣿⣿⣿⣿⠓⢚⣟⡋⠤⣃⠑⣰⠤⠨⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣂⢑⠙⠹⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⣍⡛⢻⣶⣾⣿⣿⣿⣿⣿⣿⠾⠁⠼⢭⣿⡋⠒⢺⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣫⣽⣿⣿⣟⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⢴⣶⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⠩⠿⠽⢷⣶⣦⣤⣤⣿⣿⣿⣿⣿⠛⠉⠙⠉⠉⠙⠛⠑⠀⠈⠉⠙⠛⣿⣿⣿⠟⠿⠉⠀⠈⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⡖⠀⠀⠀⠀⠉⠛⠿⣿⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⡃⠀⠀⠀⠀⠐⠹⠿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⡿⢧⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣿⣧⠄⠀⠀⠀⠀⠀⣀⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠁
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠻⣿⡻⣿⣿⠀⠀⠀⠀⠀⠀⢄⣤⣶⡶⠛⠻⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠁
⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣶⡶⠀⠘⠛⠀⠀⢰⣿⣷⡄⡀⠀⠀⠙⠻⣿⣿⡇⠀⠀⠀⣠⣶⣿⣿⠋⠀⠀⢀⣧⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠏⣼⣿⣿⡟⠀⠀⢀⡀⠀⢴⣦⣤⣿⣿⣿⡇⢻⣷⣤⣀⠀⠀⠈⠁⠀⠴⠾⠿⠿⠛⠛⠀⠀⢠⣾⣿⡷⠒⢠⣶⠀⠀⢸⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠘⠛⠁⠀⠀⢻⣿⣿⣿⡏⣰⣿⣿⣿⣷⣦⠀⠘⠟⠀⠀⣹⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⣠⣴⡶⢻⣿⣿⣄⣤⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⠷⣶⣦⣤⡿⣆⣐⠃⢴
⠀⠀⠀⠀⠈⠻⠒⣾⣿⣿⡟⣼⣿⣿⡏⠉⠉⣁⠀⠀⣴⣶⣴⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⣿⣿⠀⣿⣿⣿⡟⠛⠑⣶⣶⠀⠀⢸⣿⣿⣿⣿⣷⠘⣿⣿⣿⠁⠈⠙⡟⠻⠿⠉⠹⠼⠇⣲⣞
⠀⠀⠐⠀⠀⠀⠀⠉⢻⣿⠃⣿⣿⣿⣷⠖⠾⢿⡿⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢀⣿⣿⣿⣧⣄⣀⠉⠉⠠⣾⣿⣿⣿⣿⣿⣿⣇⢹⡿⠿⣧⣤⡄⠉⠀⠠⠀⢰⣶⣌⡀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⣿⡿⡋⠀⠀⠀⢩⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢿⣿⣿⢸⣿⣿⣿⣿⡿⠿⣦⣤⣴⡉⠉⣿⣿⣿⣿⣿⣿⠈⡗⣦⣼⡿⠀⢰⠂⠀⠀⢈⣉⠉⢽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢿⣿⣝⢿⣷⣶⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⢿⣇⣼⣿⣿⣿⣿⣷⣤⣿⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⠀⣶⡧⣠⣩⣿⣿⣿⣤⣠⣤⣏⣲⣴⣿
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⣧⢸⣿⣿⣷⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣤⣤⣴⢼⣿⣿⣿⣿⣿⠀⠿⠻⣿⣟⣻⣀⣼⣧⡤⠀⣬⠽⠋⣀
⠀⠀⠀⠀⠀⠀⠘⠃⣠⠄⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏⠉⣉⣉⣉⠁⠉⠉⠉⠀⣀⠀⢸⣿⣿⣿⠀⠠⠊⠉⠹⣿⣿⡿⢶⡂⣈⣅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠲⠾⠂⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠈⠙⠛⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⠴⣮⡥⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠟⠛⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣧⠀⠀⠐⠐⢾⡦⠤⠄⢗⠀⢀⣴⣶⣷⡆
⠀⠄⠀⠤⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⠐⠂⠐⢢⣤⣶⣶⣒⠀⠉⠢⣬⡍⠉⠋
⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠘⠛⠀⠀⢈⠛⠻⠟⠛⢴⡔⠀⠂⠐⠂
⠀⠀⠀⠠⠀⠀⢠⠙⠿⠿⢁⣿⣿⣿⣿⣿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢰⣿⣶⡆⠙⠟⠉⠀⠀⠀⠀⠤⣴⣤⣴
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⠀⠀⣀⣠⣤⣼⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⡀⠻⠛⠛⠛⠉⠉⠉⠁⠀⣴⣿⣿⣿⣿⣾⠏⠉⠀⠐⠀⠀⠀⠀⣀⡀⢙⣿⠀⠀
⠀⠒⠀⠀⢠⣤⣺⣷⣄⠀⠀⠀⠉⠻⣿⣿⣿⣷⣶⣦⣤⣄⣀⡀⠀⣿⣿⣿⡿⢫⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣷⠠
⠤⠀⠀⢀⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢫⣴⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣀⣀⣠⣤⣤⣴⣶⣶⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣃⣀⠀
⠀⠈⠁⣼⣿⣿⣿⣿⣿⣿⣿⢿⣦⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⢋⣥⣾⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣀⣄⣴⣖⣶⣾⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⠆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠟⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⡾⣿⣯⣷⣿⣿⢝⣐⠻⣵⣼⣿⣿⣿⣿⣿
⣀⡀⢸⡿⣟⣉⢡⣬⣙⢻⣧⠀⠀⠀⠀⣿⣿⣶⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣶⣌⠛⢿⣿⣿⣿⣿
⠉⠁⠀⠘⠛⠛⠈⣿⣿⣾⣿⣷⣦⡀⠐⢿⡇⠀⢸⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⠛⠈⠛⠁⠳⠾⠇⠀⠰⣿⠟⠛⠛⠛⠛⠓⠂⣤⣀⠀⠀⠈⠛⠛⠻⣿⡿⠛⠛⠻⢿⠓⠀⠀⠀⠀⡀⠀⢤⠀⢰⠒⠛⠿⢿⣿⣀⣀⣴⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⠀⠀⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⣀⣿⣇⠀⠀⠀⢀⠀⠀⢀⠀⠀⡇⠀⠘⠀⢸⠀⠀⠀⠀⣿⡿⢻⣭⣽⣽⡎⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠀⢸⠂⠃⠀⠀⣠⣿⣿⠀⠀⠰⠄⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⢸⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⣿⡇⣾⡿⠟⣡⠾⠊⠻⣿⣿⣻⣯⣽⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣶⡀⠈⠀⣰⠀⠀⠈⢹⣿⠀⠀⢀⠀⠁⣀⣿⣧⠀⠈⠀⣀⠀⠀⠈⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⢹⣇⠉⠀⣤⠂⠀⠀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⠛⠛⠛⠃⠙⠻⢿⣷⣦⡀⠀⠀⢿⣿⣿⡀⠀⣠⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢘⠋⠀⠈⠀⠘⠀⠀⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣄⠠⢾⣷⢾⡳⠆⢲⡠⠄⢀⣀⣶⣭⣄⠶⡿⠋⠩⠋⢐⣢⠈⠉⢀⣀⣀⣀⠀⠀⠀⠀⠈⠉⣡⣶⠠⠿⢱⣶⠢⣤⢭⣿⠟⠒⣴⣻⣷⣿⡧⠀⢙⠟⠿⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⢛⢣⣭⣌⠉⠓⠶⣀⡠⢁⡉⣰⡾⠄⠁⠀⣤⡄⠸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡠⠓⢁⢰⣻⣏⣽⡟⠛⣋⣿⡍⠘⠉⠙⢉⠓⢸⣬⡷⠈⣷⣦⣀⠀⡀⠀⠀⠀⠀⢼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣤⠘⠉⣹⣤⠀⣠⣿⣅⡠⣤⡟⣄⠐⣶⣾⡁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣩⣽⣦⠟⠀⣲⣿⡿⠀⣀⣀⠀⠙⢟⢠⣿⣯⣥⣸⣿⣿⣿⣟⣈⣗⣂⣐⣡⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣠⣽⣶⣷⣿⣿⣿⡿⢿⠻⡠⠹⢿⠆⠘⠙⠛⠁⣤⣿⣿⣿⡿⡍⠙⠻⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣏⠭⡍⠉⠛⡋⠻⢴⠷⠚⢲⣶⡿⢿⢞⡘⠛⣿⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢉⣉⣧⡼⢿⣯⣉⣡⣤⢒⢻⡟⣛⢹⣖⣦⣠⣶⣿⣿⣋⣁⣀⣀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠙⠻⣿⣿⣆⣠⡞⠉⢰⠗⢁⣀⡀⣈⢉⠱⠶⠓⠝⠛⢾⢏⠥⠛⣿⣿⣿⣷⣦⣄⣀⣀⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢽⣽⣥⣈⠃⠉⠉⣁⣶⡔⠓⠉⠉⡀⠈⢛⣿⣿⣿⣿⣿⣤⣴⣶⣿⣿⣿⣿⣿⣤⣀⠀⠢⣤⣜⣿⣿⠈⠁⠀⠚⠃⠉⠉⠐⠢⠀⡀⠐⠋⠁⢀⠽⢹⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡜⠋⠉⠐⢻⡃⣿⣓⡉⠑⣦⠀⢩⣅⢸⣿⣿⣿⣿⣿⡿⢫⣏⣀⠀⠀⠀⠈⠙⣿⣿⣶⣾⣿⣿⣿⠄⠀⢀⣡⠄⠺⢴⣟⣯⣿⣷⣶⡃⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠷⢉⠤⠨⢃⣤⣤⠉⠠⠄⣻⣿⣿⣿⣿⣿⠏⣠⣿⣿⣿⣷⣶⣶⣶⣾⡏⠹⣿⣿⣿⣿⣿⣤⡤⢘⡭⢿⠦⠀⣼⡯⣿⣿⣎⣉⡉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⢘⠯⣿⡧⣄⠀⠀⢻⣿⣿⣿⣿⣿⣶⣿⠟⠩⠥⠒⠈⠉⠛⠿⣿⡄⢻⣿⣿⣿⣿⡇⠀⢨⣷⣿⢟⡀⣾⠟⠻⠻⠁⣛⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⡈⣧⡀⢀⢁⣩⡆⠀⣾⣿⣿⣿⣿⣿⣿⣇⣀⣤⣤⣤⣀⣀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠂⢚⣟⡃⠆⣃⠉⢔⠤⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠁⠙⠹⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠁⠴⢥⣼⡍⠒⢺⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣧⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤⢰⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾⣿⡏⠒⠓⠛⠿⢷⣶⣶⣶⣿⣿⣿⣿⣿⡝⠛⠋⠉⠉⠛⠋⠀⠀⠈⠉⠉⣿⣿⣿⡟⠻⠃⠀⠀⠀⣹⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⣿⣿⣿⠇⠀⠀⠀⠀⠈⠛⠿⣧⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⣿⡁⠀⠀⠀⠀⠈⠛⢻⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢇⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⣿⣷⠀⠀⠀⠀⠀⢠⣼⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠉
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⠁⠀⠀⣀⡀⠀⠀⢠⣀⠀⠀⠈⠛⢿⣏⣿⣿⡷⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠙⢻⠋⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⡿⠿⠿⠃⠀⠉⠁⠀⢀⣿⣿⣧⢀⡀⠀⠀⠙⠻⢿⣷⠀⠀⠀⣠⣶⣿⣿⣏⠀⠀⠀⣼⣤⠀⠀⠀⠀⠚⠛⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡏⣰⣿⣿⡟⠁⠀⢠⣴⡀⠀⢶⣶⣾⣿⣿⣿⡘⣿⣷⣤⣀⣀⡀⠀⠀⠐⠚⠛⠛⠛⠉⠁⠀⠀⣼⣿⣿⠉⠁⠼⠇⢀⣤⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠘⠛⠁⠀⠀⠘⣿⣿⡟⣴⣿⣿⡿⣿⣿⠇⠈⠛⠁⠀⢀⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣴⣾⠋⣿⣿⣿⣴⣶⠀⣀⠘⠛⠙⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⠻⣶⣦⣤⠿⣆⣸⡃⢴
⠀⠀⠀⠁⠈⠛⠂⣾⢿⡿⢸⣿⣿⣿⡀⢀⣠⣤⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣿⣿⡟⢸⣿⣿⣿⠀⠀⢹⠿⠇⣠⣤⣿⣿⣿⣿⣿⣷⠸⣿⣿⣏⠀⠉⠉⣟⠛⠿⠁⠹⠼⡇⣲⣖
⠀⠀⠐⠀⠀⠀⠀⠈⠹⠇⣿⣿⣿⣿⡟⠉⠙⠿⣃⠀⣨⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣶⣶⡆⠀⢀⡹⠿⢿⣿⣿⣿⣿⣿⡇⢻⠟⠛⢦⣤⡤⠉⠀⠠⠀⢰⣶⣄⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣥⣄⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠸⣿⣿⠃⣾⣿⣿⣿⣿⣉⣹⠿⠟⠛⠀⣾⣿⣿⣿⣿⣿⣿⠈⠗⣦⣾⡟⠁⣐⡃⠁⠀⢈⣉⠉⢷⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⡿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢙⣯⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣙⣿⣿⣿⣿⣿⣿⠀⣿⣷⣤⣹⣷⣿⣿⣦⣤⣤⣍⡰⣴⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠛⠛⠿⠿⠿⠛⠛⠛⠋⠉⠋⠛⢻⣿⣿⣿⠀⠿⠛⣿⣟⣻⣀⣼⣧⡄⠀⣬⠿⠋⣠
⠀⠀⠀⠀⠀⠀⠐⠃⣠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠿⢿⣿⣿⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡄⢸⣶⣶⣦⣤⣦⣤⣶⣶⣷⠀⢸⣿⣿⡟⠀⠠⠊⠉⠹⣿⣿⡿⠶⡆⢨⣅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⠑⠀⠀⠀⠖⠀⠔⢦⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⢐⢾⡦⠠⠤⢛⠀⢀⣴⣷⣿⡖
⠀⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣷⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⠐⠒⠀⢤⣤⣴⣶⣒⠀⠈⠰⡼⠅⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢠⣤⣤⡀⣉⡛⠻⠟⠓⢶⠜⠀⠂⠐⠒
⠀⠀⠀⠠⠄⠀⢠⡜⠻⠋⣼⣿⣿⣿⣿⡟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⡿⠿⠿⠛⢃⣸⣿⣿⣿⣆⡿⠋⠀⠛⠏⠉⠁⠀⠀⠀⠤⣤⣤⣴
⠀⠀⠀⠀⠀⠀⢸⡅⠀⠘⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⠇⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⡄⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠐⠂⠀⠀⠀⠀⣠⡄⠙⣿⠀⠀
⠀⠀⠀⠀⢁⣶⣾⣷⣄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣸⣿⣿⡿⢋⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⠀
⠤⢀⠀⠀⣼⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣤⣴⣶⣶⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣃⣀⠀
⠀⠈⠁⢰⣿⣿⣿⣿⣿⣿⡟⢿⡆⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⢛⣥⣾⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣀⣄⣴⣶⣶⣾⣿⣿⣷
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠻⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠃⠀⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣯⣷⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⣀⡀⠰⠿⣫⣥⠰⣶⣏⣿⣆⠀⠀⠀⢸⣿⡿⠦⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣾⣌⠛⢿⣿⣿⣿⣿
⠉⠁⠀⠈⠉⠉⠁⢿⣿⣿⣿⣷⣄⠀⠸⣿⠀⠀⢿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣵⣾⣷⣾⣿⣿⡆⠀⠈⠛⠛⢛
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⠓⠈⠋⠜⠳⠿⠀⠀⠸⣿⠿⠛⠛⢙⠛⠛⠒⣤⣄⠀⠀⠈⠛⠛⠻⣿⡟⠛⠛⠻⢿⠉⠀⠀⠀⠀⡄⠐⢶⠚⢻⠛⠛⠿⢿⣿⣧⣴⣶⠿⣇⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⠀⠀⠀⠀⣶⣿⣿⠀⠀⠀⠀⠀⣀⣿⣇⠀⠀⠀⢀⠀⠀⢀⠀⠀⡇⠀⠈⠀⢸⠀⠀⠀⠀⣿⣿⠋⣼⣿⣿⠏⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠀⢸⠂⠀⠀⠀⣀⣿⣿⠀⠀⠰⠄⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⢸⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⢹⣿⠸⡿⠋⢁⣈⠈⠻⣿⣿⣻⣯⣽⣿⣿⣿⣯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣷⣀⠈⠀⢰⠀⠀⠈⢹⣿⠀⠀⢀⠀⠁⣀⣿⣷⠀⠀⠀⣠⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢀⠞⠁⠀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⠛⠛⠛⠁⠙⢿⣿⣶⣄⠀⠀⠀⣿⣿⣿⡅⠀⣠⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡂⢀⣀⣠⢾⣷⣚⠀⠀⠲⣤⠤⠀⣀⣴⣩⣄⠠⡾⠈⠁⠛⠁⢢⠄⣁⣀⣤⣤⣄⣀⣀⣀⠀⠀⠀⠡⢶⠀⠻⠡⣶⡄⣤⢬⣿⠟⠓⣤⣻⣶⣼⣦⠀⠘⠇⠈⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠙⠋⠀⣚⢷⣭⣍⠉⠳⠴⠁⠀⢈⡉⣨⡼⠇⠁⠀⢠⡀⠰⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠓⠂⣐⢺⡏⣹⠿⠑⣋⣯⡅⠘⠋⠙⠈⠓⢈⣽⡶⠀⠀⠀⡺⣷⣄⣀⢀⣀⣀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣤⠘⠙⢋⣢⠀⣀⣿⣏⠀⣤⡞⣀⠀⣶⣦⡀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣩⣽⣦⠿⠀⣰⣿⡿⠁⢀⣀⡀⠙⠟⠀⣿⣶⣥⣠⣿⣵⣿⣿⣿⣿⣿⣿⣽⣾
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣠⣽⣦⣧⣿⣿⣿⡿⢿⠻⣀⠩⠿⠇⠠⠛⠿⠃⣤⣿⣿⣿⠿⠍⠙⠻⢿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣏⠩⣭⠉⠻⠻⢺⢰⠗⠾⢶⣴⡿⢷⢴⡱⠉⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⣉⣣⣼⢯⣿⣉⣁⣠⠄⢻⡟⢛⢩⡆⣦⣀⣼⣿⣿⣏⣁⣀⣀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠙⠻⣿⣿⣆⣀⡞⠉⠠⠗⢠⣀⠀⢈⠉⠱⠶⠒⠙⠛⠸⢏⠭⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢹⣯⣥⣀⠏⠉⠉⢈⣬⡄⠓⠋⠉⠁⠈⠙⣿⣿⣿⣿⣿⣤⣴⣶⣿⣿⣿⣿⣿⣦⣀⠐⠲⣦⣜⣿⣿⠙⠃⠀⠚⠃⠋⠉⠐⠢⠀⠀⠔⠚⠃⢀⠭⢙⣿⣍⣉⣥⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠭⠋⠉⠐⢻⡗⢺⣑⠉⠀⣶⠀⢩⡅⣸⣿⣿⣿⣿⣿⡿⢫⣿⠁⠀⠀⠀⠉⠹⣿⣿⣶⣾⣿⣿⣿⡇⠀⠀⣁⠄⠒⣴⣞⣏⣿⣧⣶⠃⠄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⡼⠊⡡⠌⠅⣠⣄⡙⠠⠄⣼⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣷⣦⣶⣶⣶⣇⠹⣿⣿⣿⣿⣿⡇⣠⠘⣩⢿⠦⠀⣨⣿⣿⣿⣟⣙⡉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠐⠀⠀⠐⠯⣽⡿⢄⡀⠐⣿⣿⣿⣿⣿⣿⣶⣿⠿⢛⡭⠉⠉⠉⠛⠻⣿⣆⢹⣿⣿⣿⣿⣇⠀⢨⣵⣽⡏⠀⣾⠝⠻⠛⠋⣹⡿⠇⠒⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢧⡀⢀⠁⣋⣄⢰⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣶⠦⢤⣤⣀⡀⠹⣿⣾⣿⣿⣿⣿⣿⠆⢚⣟⡋⠠⣃⠙⠔⠆⢀⡉⢹⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⠈⠈⠹⢃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣌⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠨⣭⣼⣋⠐⢒⣾⡆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⢿⣿⡿⠅⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠤⠰⣶⣆⣀⣀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⣿⣏⡠⠬⠤⠾⣶⣶⣶⣶⣶⡿⣿⣿⣿⣿⣟⠉⠉⠁⠈⠉⠉⠀⠀⠀⠉⠉⢿⣿⣿⣿⠛⠃⠀⠀⠀⠈⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⡃⠀⠀⠀⠀⠈⠉⠛⠿⣧⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣽⡇⡀⠀⠀⠀⠀⠀⠟⢻⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⣿⣿⡿⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣷⡇⠀⠀⠀⠀⠀⣤⣾⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣁⡀⠀⣤⡄⠀⠀⢠⣶⣤⡀⠀⠀⠉⢹⣯⣹⣿⣟⠀⠀⠀⠀⠀⢀⣴⣿⡿⠉⠈⢻⠋⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠃
⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢇⣾⣿⣿⡟⠙⠛⠁⠀⠀⣀⠀⢠⣿⣿⣿⡿⢠⣄⠀⠀⠈⠛⠿⢿⠀⠀⠀⣠⣾⣿⣿⡏⠀⠀⢀⣼⣶⣄⡀⠀⢀⠈⠉⢻⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢏⣼⣿⣿⣿⣤⠀⢠⣮⡆⠀⠻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣶⣤⣀⣀⠀⠀⠀⠋⠉⠉⠉⠉⠀⠀⢀⣾⣿⣿⠀⠀⠈⠋⢠⣶⣾⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠛⡃⠀⠀⠈⣿⢇⣾⣿⣿⠛⠛⠟⠀⠀⢀⣄⣀⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣾⣿⢁⣿⣿⣿⠾⠟⢠⣴⡄⠀⢸⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⠷⣶⣦⣤⠽⢆⣀⠂⢴
⠀⠀⠀⠀⠈⠛⠃⣴⡟⣸⣿⣿⣿⣤⣰⣾⣷⡆⠘⠻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣿⣿⡇⢸⣿⣿⣿⣀⣀⠙⠛⠑⣶⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⠋⠉⠙⣟⠛⠿⠁⠡⠼⠏⣲⣖
⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⣿⠿⠃⠀⠈⠙⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣧⣤⣴⡏⢉⣿⣿⣿⣿⣿⣿⡄⣿⡿⠿⣷⣤⡄⠁⠀⠠⠀⢰⣶⣄⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢿⣶⣦⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠸⣿⡏⣸⣿⣿⣿⣿⣷⣴⡏⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⠗⣤⣴⡿⠁⢐⠃⠁⠀⠀⣉⠉⢶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣏⣆⣀⣀⣠⣼⠿⢿⣿⣿⣿⣿⡇⢸⣾⣧⢀⣉⣾⣿⣿⣤⣤⣤⣍⢰⣰⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⢠⣤⣥⣩⣉⣉⣉⣁⣀⣤⠀⢸⣿⣿⣿⠀⠘⠿⠛⣿⡟⣛⣂⣼⣧⡤⠀⣬⠽⠋⣀
⠀⠀⠀⠀⠀⠀⠐⠃⢀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠅⠀⠉⠙⠻⢿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⠀⠀⠀⠊⠉⠸⣿⣿⣿⠶⡆⢠⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠲⣶⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠛⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠔⢦⡤⠄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣤⣤⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⣴⡦⠤⠄⠛⠀⠀⣴⢷⣷⡖
⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠐⠂⠀⢠⣤⣴⣶⣒⠀⠈⠰⠼⠅⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢰⣶⡦⠀⣈⡛⠛⠟⠓⠶⠔⠀⠒⠐⠒
⠀⠀⠀⠀⠄⠀⠀⠘⠿⢁⣿⣿⣿⣿⣿⠀⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡀⠻⠿⠿⠿⠛⠛⠋⠉⠉⠉⣴⣿⣿⣿⣿⣷⡏⠁⠠⠛⠟⠉⠁⠀⠀⠀⠤⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠔⠒⠀⠀⠀⠀⣀⡀⢹⣿⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣦⣀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣾⣿⣿⡿⣡⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⣤⣤⣶⡾⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⢿⣦⠀
⠤⢄⡀⠀⢀⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⠟⣫⣾⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣃⣀⠀
⠀⠀⠉⠀⣾⣿⣿⣿⣿⣿⡿⣷⠄⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⢵⣾⣿⣿⣿⡇⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣀⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠸⠇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣿⣷⣿⣿⢝⣐⠻⣵⣼⣿⣿⣿⣿⣿
⣀⡀⢠⣿⢟⡋⢡⣭⡛⣿⡄⠀⠀⠀⣿⣿⣷⡄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣶⣎⠛⢿⣿⣿⣿⣿
⠉⠁⠀⠐⠛⠟⠂⣿⣿⣿⣷⣦⡀⠘⢿⡁⠀⢺⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⡄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣽⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⢛
⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⠋⠛⠁⡗⠾⠃⠀⠀⠿⣿⠟⠛⠉⠙⠛⠛⠒⣦⡄⠀⠀⠙⠛⠛⠻⣿⡟⠛⠛⠛⢏⠀⠀⢰⠖⠒⡖⠛⢿⠛⢻⠛⠛⠿⢿⣿⣧⣴⣶⡿⣇⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠆⠀⠀⡆⠀⠏⠀⠐⠀⠀⠀⠀⣶⣿⡇⠀⠀⠀⠀⢀⣀⣿⣧⠀⠠⠀⢀⠀⠀⣸⠀⠀⡇⠀⠈⠀⢸⠀⠀⠀⠀⣿⣿⡟⢁⣿⣿⣯⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⣀⣿⡇⠀⠀⠷⠄⠀⠈⣿⡿⠀⠠⠀⠘⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢸⡿⠋⢁⠊⠻⣿⣿⣻⣭⣽⣿⣿⣿⢿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣷⡀⠈⠀⣠⠀⠀⠉⢹⣧⠀⠀⣄⠀⠁⣀⣿⣷⠀⠀⠀⣠⠀⠀⠈⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⡌⠀⢀⣿⠆⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⠛⠛⠛⠑⣾⣿⣦⣄⠀⠀⠀⢻⣿⣿⣿⡀⠀⣰⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⠁⠀⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⣄⣀⣴⣷⢜⠓⠄⠲⠤⢄⠀⣀⣠⣊⡅⠠⣼⠘⠉⠙⠀⠢⡄⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠡⢶⠀⠹⠡⣶⠄⣤⣬⣿⠟⠒⣠⢿⣷⣿⣶⣿⣿⣿⣿⡿⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠋⠁⢒⠦⣉⣉⠉⠧⠴⠉⠀⢀⡙⠉⣴⠧⠙⠀⢀⡀⠒⣶⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀⠗⠂⣰⢾⡏⢱⡿⠻⠛⣿⣀⠉⠋⠙⠙⠿⢛⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣤⠁⠛⢛⣡⠀⢀⣸⣏⠈⢁⡸⢁⠀⣶⣴⡂⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣚⣹⣷⠾⠁⢠⣿⣿⠁⠀⣀⣀⠊⠞⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠁⠀
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣽⣦⣥⣾⣿⣷⣿⠿⡿⣇⣘⢿⡏⠀⢛⠻⠏⣠⣼⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⢩⣯⠉⠿⠟⢹⢨⣓⠾⢶⣴⡾⢷⢴⡳⠋⢿⣷⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⢉⣛⢫⣸⣿⣿⣋⠋⣀⠤⠹⣾⢿⠁⣆⣆⣀⣠⣿⣿⡿⠋⠁⠀⠀⠀⣹⣿⣿⣿⠋⠀⠀⠐⠶⣿⣿⣧⣀⡔⠋⠡⠾⠊⡀⠀⠈⠉⠱⠶⠖⠙⠛⠽⣏⡩⠻⣻⣿⣿⣿⣶⣤⣰⡤⠦
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢹⣿⣏⣀⠟⠉⠉⠒⣡⡤⠿⠚⠊⠁⠈⠛⣻⣿⣿⣿⣿⣏⣉⣤⣴⣿⣿⣿⣿⣆⡀⠀⠤⣤⣈⢿⣿⡏⠃⠀⠜⣇⠋⠉⠒⠠⠀⠀⠐⠚⠃⢀⡩⠏⣿⣆⣈⣭⣾⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠩⠛⠉⠐⠾⡗⢺⠗⠈⠀⢶⠀⢈⣅⢠⣿⣿⣿⣿⣿⣿⠿⣿⠋⠙⠛⠉⠛⠻⣿⣷⣦⣽⣿⣿⣿⡇⠀⠀⣃⡄⠰⣤⡞⣟⣻⣧⣶⠛⠄⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⡐⠚⡡⠌⠍⣁⣀⡙⠃⠤⢀⣿⣿⣿⣿⣿⡿⠁⣼⣿⣶⣦⣀⣀⣄⣠⣿⠻⣿⣿⣿⣿⣿⣧⢀⡘⣍⢷⡦⠄⣨⣿⣿⣿⣟⣙⡉⠉⠙⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠂⠀⠀⠀⠀⠺⣽⣿⢄⡀⠀⢞⣿⣿⣿⣿⣿⣡⣾⣿⠿⢛⣛⣛⠛⠿⢿⣿⣆⠹⣿⣿⣿⣿⣿⠀⢈⣵⣿⡟⠀⣼⡷⠛⠛⠋⣙⡷⠆⠐⠶⣾⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢶⡀⠀⡈⣙⣥⠀⣼⣿⣿⣿⣿⣿⣿⣟⣁⣨⣥⣤⣤⣀⣀⠀⠙⣿⣶⣿⣿⣿⣿⣿⠇⠐⣟⡋⠀⢁⠘⠀⠆⠀⡘⠹⢻⣶⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣘⣁⠘⠘⠻⢇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣍⠛⣿⣷⣿⣿⣿⣿⣿⣿⣿⡦⠀⠨⣭⣄⡛⠁⢞⣷⡆⠀⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⡆⠀⠀⠈⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢠⣠⣶⣄⡀⠐⣶⣶⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⡿⠉⠻⠋⠀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠛⠛⠀⠀⠈⠙⠙⠻⣿⣿⣿⠿⠿⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣷⡔⠒⠚⠛⠛⠛⠿⢿⣿⣿⢸⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣧⣶⠀⠀⠀⠀⠀⠀⣠⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠛⢿⣿⢻⣿⣷⡄⠀⠀⠀⠀⠀⣀⣴⣶⠟⠙⢻⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⣀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⡶⠂⠀⠑⠁⠀⠀⣼⣿⣿⣧⢠⡀⠀⠀⠙⠿⣿⣿⠃⠀⠀⠀⣠⣶⣿⣿⠋⠀⠀⢠⣄⡄⠀⠀⠀⠐⠚⢿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀
⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⣰⣿⣿⡿⠁⠀⠀⢠⡀⠀⣴⣦⣾⣿⣿⣿⡏⢸⣿⣷⣤⣀⠀⠀⠈⠁⠀⠴⠾⠿⠿⠛⠋⠀⠀⣠⣿⣿⡗⠊⠀⠴⠀⣀⣸⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠚⠓⠀⠀⠙⣿⡟⣰⣿⣿⣿⣿⣶⠀⠈⠛⠁⠀⢀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣠⣶⠞⣿⣿⣿⣧⣶⠀⣀⡀⠛⠛⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⠟⢶⣦⣤⡽⢆⣀⠃⢴
⠀⠀⠀⠈⠀⠙⠓⣲⡿⢱⣿⣿⣟⠀⠉⣡⣄⡀⢰⣶⣶⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣴⣿⡿⢠⣿⣿⣿⠁⠀⠸⠿⠇⣠⣤⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⡿⠛⠙⣿⠛⠿⠀⠸⠸⠇⣐⣶
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⣿⣿⠗⠚⠻⢿⠂⠀⣸⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⡇⣸⣿⣿⣿⣾⣿⣆⣀⣀⡿⠿⣿⣿⣿⣿⣿⣿⡄⣿⣿⠿⢧⣤⡄⠉⠀⠀⠀⠰⣦⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⣿⡿⢀⣿⣿⣿⣿⣿⣉⡽⠟⠛⠁⢰⣿⣿⣿⣿⣿⣿⡇⢹⠟⢤⣤⣿⠃⢐⠂⠀⠀⠀⣉⠉⠳⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣝⣻⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣾⣷⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⣁⣾⣿⣿⣤⣠⣤⣍⡐⣴⣿
⠄⠀⠀⠀⠀⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⢉⡙⠛⠛⠻⠒⠒⠛⠛⠉⠉⢹⣿⣿⣿⡇⠘⠿⠛⣿⡿⣛⣂⣼⣧⡤⠀⢨⠭⠍⢀
⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠈⠉⠛⠿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣶⣶⣶⣿⣿⠀⢸⣿⣿⣿⠃⠀⠀⠊⠉⠑⣿⣿⣿⠶⣆⢠⣅⠀⠀⠠
⣀⠀⠀⠀⠀⠀⠐⠶⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣾⣿⣿⠿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠔⢦⡤⠔
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⡇⠀⠀⠀⠀⢴⡦⠠⠄⠘⠀⠀⣴⢶⣥⡆
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⠐⠂⠀⠠⣤⣴⣶⣒⠀⠈⠰⠼⠍⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠁⠀⠀⣈⡙⠛⠟⠓⠢⠔⠀⠐⠐⠒
⠀⠀⠀⠀⠤⠀⠁⢸⣿⠃⣿⣿⣿⣿⣿⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢀⣿⣿⣿⣿⣄⡿⠗⠀⠛⠟⠉⠁⠀⠀⠀⠤⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣦⠈⠉⠉⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠐⠒⠀⠀⠀⠀⢀⡀⢹⣿⠀⠀
⠀⠀⠀⠀⠈⠀⠀⣄⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣀⣸⣿⣿⡿⣣⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠿⡶⠀
⠤⠄⡀⠀⠀⢰⣿⣿⣷⣄⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣴⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣤⣤⣤⣶⣶⣶⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣃⣀⠀
⠀⠀⠉⠁⢠⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⣩⣾⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⡀⠀⡀⢀⣀⣴⣠⣠⣀⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁⠙⢰⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⠃⠀⠀⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠿⠿⠟⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣟⣿⣷⣿⣿⢝⣐⠻⣵⣼⣿⣿⣿⣿⣿
⢀⣀⠀⣼⣿⡿⠿⠻⢿⣿⠀⠀⠀⠀⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⡿⡫⣖⢶⣾⣌⠛⢿⣿⣿⣿⣿
⠉⠉⠀⠻⣵⣶⡄⣿⣾⣿⣧⡀⠀⠸⣿⠉⠀⣾⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣵⣾⣷⣾⣿⣿⡆⠀⠈⠛⠛⢛
⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⠛⠛⠂⡄⠘⠀⠀⠘⠿⣿⠿⠛⠛⢿⠓⠂⠀⣀⡀⠀⠀⠟⠛⠛⠻⣿⡟⠛⠛⠻⠟⠀⠀⣀⠀⠀⡄⠀⢤⠀⢲⠒⠛⠿⢿⣿⡄⢀⣀⣼⣧⣿⣿⠿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣷⡆⠀⢀⡄⠀⠉⠀⠰⠀⠀⠀⠀⣶⣿⡇⠀⠀⠀⠀⠀⣀⣿⣇⠀⠀⠀⢀⠀⠀⣿⠀⠀⡇⠀⠈⠀⢸⠀⠀⠀⠀⣿⣿⣿⡿⣻⣽⣮⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠈⡇⠀⢸⡇⠀⠀⠀⠀⠁⠀⠀⠀⣤⣿⡇⠀⠀⠷⠄⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⣿⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⣿⣿⡏⣰⣿⣿⠿⠊⠻⣿⣿⣻⣯⣽⣿⣿⣿⢿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠇⠀⠸⡇⠀⣶⣀⠀⠀⡀⠀⠀⠉⢹⡇⠀⠀⣄⠀⠀⣀⣿⣏⠀⠈⠀⣀⠀⠀⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠿⠛⠁⣠⣤⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⠛⠛⠛⢡⣽⣧⡀⠀⠀⠀⠘⣿⣿⣿⡇⠈⠛⣸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠆⠀⢰⠿⠁⠀⠀⣀⣼⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠲⣤⣀⢀⡘⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠉⠛⣛⠿⠿⠿⠗⠒⠚⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠋⠀⠀⠀⢰⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠈⠀⠀⣰⣿⢋⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣇⣀⣀⣀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⡿⠏⠋⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠆⢺⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀
⠛⠛⡛⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣛⠋⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣀⡀⣀⣀⣀⠀⠀⣀⡠⣀⢠⡾⡞⠓⠛⣉⣦⣤⡀⠀⠀⠀⠀⠀⠀⠜⠀⣈⢠⣿⣿⣿⠿⠍⠉⠻⣿⣿⣿⣿⠿⠛⠛⢛⣿⣿⣿⣿⣆⠀⠀⣼⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⡿⣾⡿⠟⠁⠀⠀⠉⣿⣟⡀⠩⠉⠁⠀⢀⣄⠀⠐⠚⠂⠉⣿⣿⢋⡁⠀⠀⠀⢀⣾⣿⣿⣇⠀⠀⠀⠀⠉⠻⣿⣿⣿⡄⠈⠻⢿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠟⠁⠉⠀⠀⠀⠀⠀⠀⢉⠛⠛⠁⠴⠷⠪⠏⠍⠂⢤⠀⠘⣠⣿⣿⣿⣥⣤⣤⣶⣿⣿⣿⣿⣿⣶⣏⣀⠀⠐⣦⣼⣿⣿⡇⠀⠀⠈⣿⡿⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡛⠛⢿⣿⣿⣿⣿
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡖⢋⡀⠫⠁⣀⡘⠃⡀⣽⣿⣿⣿⠟⠋⠉⠉⠉⠉⠈⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⡐⢟⣃⠀⠘⣿⡆⢀⣀⡀⠀⠀⠀⠀⣶⣶⣶⣄⣊⡁⠁⠀⠁⠙⢟⣿
⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣤⣤⣶⡖⠀⠀⠀⠀⠶⢋⣿⡅⠀⠢⣿⣿⣿⠇⠀⠀⠀⣀⣄⣀⣀⣀⣤⣴⡆⠙⢿⣿⣿⣿⣿⣿⣇⣀⠁⢐⣫⣾⣖⠂⢬⣗⠿⠿⠏⢹⡷⡆⠠⠦⣾⡿⢿⣿⣿⣦⡂⠀⠀⣸⣿
⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠺⠛⠒⠚⠛⣯⠀⠀⠀⠀⢰⡀⠀⠀⠙⣡⠀⣾⣿⣿⡀⠀⢠⠞⢋⡩⠭⠍⠉⠛⠿⣿⣆⠀⣿⣿⣿⣿⣿⣿⡟⠀⠐⢿⠟⠀⢁⠘⠁⡄⠀⠀⠙⠳⢦⣤⣺⢽⡿⠈⠉⣿⣿⣷⣶⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠑⠋⡟⠀⣿⣿⣿⣿⣿⣇⣀⣠⣤⣤⣤⣀⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⣷⡦⠀⠩⣭⣐⡊⠡⢤⣶⡆⠀⢠⣷⠈⠉⠉⢁⠁⠀⠀⠹⠿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣠⡀⠀⠀⠀⠀⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣬⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⢀⡠⣤⠌⠉⠐⢠⣥⠇⠀⠀⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠉⣿⣿⠟⡿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠩⣇⣿⡏⠁⠐⣿⣿⣦⢐⡄⠀⠀⢀⣘⣀⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⣾⡿⠻⠟⠉⠃⢀⣠⣤⣤⣾⣿⣿⡇⠀⠉⠉⠉⠉⠛⠁⠀⠀⠈⠉⠉⠁⠙⠁⢡⢿⣿⣿⡇⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣁⢀⣠⠤⠾⠿⠿⠿⠿⠿⣿⣼⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⡇⠀⠀⠀⠀⢀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠇⠀⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠛⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠀⠀⠀⠀⠛⠝⡿⣿⢿⣿⣿⣿⡏⢸⣿⣿⣿⠛⠛⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⢹⣆⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠙⣿⡏⠁⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⢀⣿⣿⣿⣇⣀⠀⠠⡤⠀⠀⢰⣿⣿⣿⠆⣄⡀⠀⠙⠿⢆⠀⠀⠀⢀⣴⣿⣿⣿⠁⠀⠀⢠⣿⣷⣶⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡁⣺⣿⣿⣿⠁⣼⣿⣿⠟⠛⠋⠀⠀⠀⣀⢀⣾⣿⣿⣿⠀⣿⣿⣦⣀⡀⠀⠀⠀⠐⠛⠛⠛⠉⠁⠀⠀⢠⢻⣿⣿⣿⠒⠂⠀⠀⠈⠉⢹⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠈⠈⠉
⠀⠀⠀⠈⠁⠀⠷⢀⣷⣿⣿⡏⣰⣿⣿⣟⡀⠀⢠⣤⠀⠘⠛⣿⣿⣿⣿⣿⡂⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⣿⣿⣿⣿⠀⡀⠈⠉⠀⣤⣼⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⣐⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡿⢠⣿⣿⡿⠿⠿⠀⠀⢁⣀⣀⣼⣿⣿⣿⣿⣿⡃⣼⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⣿⣿⡗⠀⣿⣿⣿⣿⠟⠛⣀⣤⡈⠉⠹⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠠⣤⣀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣁⠀⣠⣶⡄⠘⠻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣀⣀⠘⠛⠡⣤⣴⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⠀⠂⠀⠀⠀⣉⠉⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠉⠉⠛⠣⣄⣰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣀⣀⣴⠿⠿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣀⣉⣴⣼⣿⣤⣀⣤⣙⡀⣰⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢯⣥⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠻⢏⣴⣿⣿⣿⣿⣿⣧⣴⡟⠛⠋⠀⣶⣿⣿⣿⣿⣿⡇⠘⠿⠿⣿⣿⢛⣃⣸⣏⡀⠀⢨⠭⠍⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣿⣿⣿⣝⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠁⣿⣿⣿⠦⣄⢀⣀⠀⠀⠨
⣀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠛⠛⠻⠿⠷⠿⡿⢿⠿⠿⠿⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠠⢦⣀⠄
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠀⠈⠙⠻⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⣾⣶⣶⣶⣶⣤⣤⣤⣴⡆⠀⣿⣿⣿⡇⠀⠀⠀⠀⢰⣦⡀⠄⠸⠀⢀⣰⣶⣵⣂
⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡇⠀⠆⠀⠠⣤⣴⣶⣒⠂⠈⠰⣬⡍⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⡁⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⠇⢀⡀⢈⡙⠛⠟⠓⢢⡴⠀⠀⠔⠒
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡀⠀⠀⠁⠟⠻⠉⠁⠀⠀⠀⠤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⡇⠀⠀⠀⠒⠀⠀⠀⠀⢀⠀⢻⣏⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⢿⠏⣸⣿⣿⣿⣿⡟⠙⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠿⢶⠀
⠤⠤⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣇⠘⠛⠛⠛⠛⠛⠛⠛⠋⠉⣡⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣃⣀⠀
⠀⠀⠈⠁⠀⠀⠀⣰⣄⠀⠈⠉⠻⢿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣼⣿⣿⠟⣡⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⢤⣀⢀⣀⣴⣠⣠⣀⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣄⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣾⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⠏⠀⠀⢠⣿⣿⣯⣷⣿⣿⢝⣐⠻⣵⣼⣿⣿⣿⣿⣿
⠀⣀⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⢵⣾⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣶⣌⠛⢿⣿⣿⣿⣿
⠈⠉⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠑⠇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁⠀⠀⠁⢹⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⢛
⠀⠀⠀⠀⠛⠋⠑⠀⠒⡿⠇⠀⠀⠀⠻⠛⠓⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⢿⣿⣿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⡀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⢲⡆⠀⠀⠀⠀⡇⠀⠸⠛⠛⠀⠀⣤⣤⡄⠀⠀⠓⠀⠀⠈⣿⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣶⠀⠀⠀⠀⣿⣿⠊⠻⣿⣿⣿⣯⣽⣿⣿⣿⢯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠸⡇⠀⢀⡆⠀⣷⡀⠀⠀⠀⠀⠀⠉⣹⣧⠀⠀⣄⠀⠀⣀⣿⣇⠀⠀⠀⢀⠀⠀⠈⠀⠀⡇⠀⡆⠀⢸⠀⠀⠀⢀⣿⣄⣠⣤⣾⣿⣿⣦⠀⠈⠻⣿⣿⣿⡿⢿⣷⣿⣧⠀⠀⠀⠀
⠀⠛⠃⠟⠛⠻⠃⠛⠛⠛⠃⠀⠀⠀⣿⠀⣾⣿⣿⣿⣿⡇⠙⠀⣻⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⠿⠁⠀⠀⣠⣼⣷⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⢛⡟⠋⢽⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣠⣤⣀⠀⠀⢈⡓⠀⠀⢘⣟⠋⠁⠀⣀⣄⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀⠀⠲⣤⣀⢀⣘⣻⣿⡖⠀⣿⣿⣿⣯⠀⠹⢇⠀⠀⠘⠻⢿⣿⡿⢿⠆⠀⠸⢿
⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠒⠀⠈⣿⡯⠛⠛⠾⡄⡹⠋⠀⠘⠛⣉⡿⠱⠀⠁⠀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠉⠀⠀⣰⣿⠛⣿⣿⣿⣿⡆⠀⠛⠛⠛⠫⠀⢠⣼⠀⠀⣤⠀⠋⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⠛⠃⠀⠀⢀⡶⠀⠈⣡⠏⠀⢀⣀⡤⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠤⢸⣿⣿⣤⠃⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣲⡂⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣘⣇⣀⣠⣾⣷⣼⣿⣿⡆⠀⣿⡾⠀⠸⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⣛⠛⠛⠶⠶⡋⣿⣧⣤⣤⣴⣶⡆⠂⠾⣿⣶⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣋⣻⣿⠟⠛⠀⠁⠈⢶⣾⡖⢢⢀⢠⣾⣿⣿⠿⠛⠉⠙⢿⣿⣿⡟⠋⠁⠀⠴⢿⣿⣿⣿⣧⠀⠈⣠⠔⠀⡴⠸⠁⠀⠀⠛⠛⢿⣷⣰⣤⣼⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⡀⠀
⣷⣶⣦⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠁⠀⠀⣀⠨⠟⠓⠛⠉⣿⣿⣯⣤⡤⠀⠀⣰⣿⣿⣿⣷⣀⠀⠀⠀⣀⣙⢿⣿⣿⡄⠀⠛⠀⠠⠇⠰⠛⠛⠅⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤⡏⠍⠂⢠⡀⠐⠂⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣷⣦⣤⣭⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠠⣄⣴⠒⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢛⠂⣀⠘⠃⢀⢹⣿⣿⣿⣿⡿⢻⣯⣄⡀⠀⠀⠀⢀⡙⢿⣿⣿⣿⣿⣿⣿⡇⠀⣀⡀⠟⣳⡤⠀⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢚⣿⡏⠀⠀⢺⣿⣿⣿⡟⢁⣾⣿⣿⣿⣿⠶⣿⣿⣧⠀⠹⣿⣿⣿⣿⣿⣷⣶⠍⠐⣫⣜⣗⠂⢤⣿⣿⣿⣿⠿⠋⠉⠉⠁⠀⠈⠉⠉⠑⠀⠀⠀⠈⢿⣿
⠉⠉⠉⠁⠀⠀⠀⢠⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⢿⢿⡇⠀⠉⠘⢋⠀⢸⣿⣿⣿⣷⣿⡟⠁⠔⠊⣒⠂⠀⠈⢻⣧⡤⣿⣿⣿⣿⣿⣿⣿⠀⠠⢿⠟⢀⢠⠘⢅⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠙⢉⠀⠀⠛⠀⠃⠚⡿⠁⣸⣿⣿⣿⣿⣿⣷⣶⡶⠾⠻⠶⢶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⣝⣀⡚⠥⠴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⢀⣾⣾⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠻⠗⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣤⠍⠉⠐⢠⣭⡤⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⢾
⠋⠋⠁⠀⠀⠀⠀⢀⣤⣀⣠⣤⣤⣿⣿⣿⣿⣶⣀⣄⣀⡀⠀⠀⣠⣀⣀⣀⣼⣿⣿⣿⣿⣿⠿⠿⣿⣿⠋⠋⠛⠟⠛⠁⠈⠀⢉⣯⣿⡛⠛⠲⠊⠁⢿⣛⠱⠀⣾⣿⣤⢂⡄⠀⠀⠈⠀⢀⣠⣤⣄⠀⠐⢻⣿⣮⣷⣭
⣠⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣿⠠⠀⠀⠀⡄⣤⣤⣃⣈⣛⣿⡧⠤⠄⠀⠙⠏⠙⠛⠃⠀⠀⣾⡇⢹⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⠛⠻⠁⠈⣩⣿⣿⠿⢿⡿⠿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿⣥⣤⣿⣶⡄⠰⠀⣀⠀⣸⠁⠁⠀⠘⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣄⠀⠐⠚⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠺⣿⣟⣼⣿⣿⠀⠀⠉⠁⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡏⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠸⢿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠛⢻⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⠋⠉⠀⠀⠀⠀⢠⣾⣿⣿⡇⢰⣄⠀⠀⠙⠶⠀⠀⠀⣠⣼⣿⣿⣿⠀⠀⠀⡸⣾⣿⣀⡀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡯⢟⠋⠻⣿⣿⣿⣿⡿⠁⣼⣿⣿⣏⣄⠀⠘⠂⠀⠀⣸⣿⣿⣿⡇⢸⣿⣿⣤⣀⡀⠀⠀⠘⠛⠋⠉⠀⠀⢀⣀⣠⢣⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠟⠄⠙⠛⣿⡀⠀⠀⠁⠃⠁⠃⠀⣿⣿⣿⠙⠉⠀⠀⠀⢤⣤⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⢸⣿⣿⣿⡟⠃⠀⣀⡀⠘⠛⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠘⠃⠀⠀⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⠀⣼⣿⣿⣿⣇⣀⡀⠈⠁⢀⣠⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣾⣿⡿⠓⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⡟⠛⠃⣀⡀⠘⠛⣿⣿⣿⣿⡇⠸⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⢀⣶⣖⠀⠉⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢹⣿⣿⡿⢠⣿⣿⣿⣿⣇⣀⡀⠛⠛⢀⣀⣿⣿⣿⣿⣷⠀⠀⢱⡿⡙⠂⢽⣿⠛⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠈⠉⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢻⣿⠃⣼⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⢿⣿⣿⣿⣿⣿⠀⠀⣲⠿⢶⣿⣾⣀⣠⡀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠀⢸⣿⣿⣯⣤⣤⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⠏⣸⣿⣿⣿⣿⣿⣿⣧⡿⠟⠛⠀⣀⣿⣿⣿⣿⣿⠀⠀⠀⠐⠉⠁⣿⣿⣿⠦⣄⢀⣀⠀⠀⠠
⣀⠀⠀⠀⠀⠀⠀⢤⣦⠀⠀⠀⢸⣿⣿⣯⣽⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠴⠀⠠⢅⡀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣦⠠⠄⠸⠀⢀⣠⣶⣵⣆
⠀⠀⠄⠀⢤⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠛⠻⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⣨⣭⣭⣭⣍⣉⣀⣀⣀⠀⢸⣿⣿⣿⠀⠀⠆⠀⠀⣤⣴⣶⣒⠂⠈⠢⣬⡥⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠂⠀⠃⢀⡀⠈⠙⠛⠟⠓⢲⡤⠀⠐⠐⠒
⣀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⡅⠀⠀⠀⠀⠟⠻⠛⠁⠀⠀⠀⠤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⠀⢹⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣇⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⡀⢻⣿⠀⠀
⠀⠀⠐⠀⠀⠁⠀⠀⠀⣾⡆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡿⣶⠀
⠤⠤⠀⠀⠀⠀⠀⠀⢰⡿⢠⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣃⣀⠀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠉⠙⠛⣿⣿⣿⣿⡿⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡀⢠⣀⢀⣀⣴⣠⣠⣀⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣄⠈⠛⠿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⠀⠀⢠⣿⣿⣿⠟⣱⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⣿⣿⣯⣷⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⠀⢀⡀⠀⠀⠀⢀⣾⣿⣷⣄⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣠⣼⣿⣿⣿⣿⡿⡫⣖⢶⣾⣎⠛⢿⣿⣿⣿⣿
⠀⠉⠁⠀⠀⢀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠛⢿⠿⣿⣿⠿⣫⣴⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⢿⣿⣿⣿⣿⡟⣵⣾⣷⣾⣿⣿⡆⠀⠈⠛⠛⢛
⠀⠀⠀⠀⠀⠾⠿⠿⠿⡿⠟⠈⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⡿⠃⠀⠸⠛⠛⢿⣿⣿⠿⠿⠿⢿⠃⠀⢼⠟⠟⡟⠻⢿⠛⢿⠛⠛⠿⢿⣿⣿⠋⠁⢠⡄⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠰⠀⢸⠀⠀⠈⠀⠀⠁⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠦⡀⠀⠀⠃⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠊⠻⣿⣿⣻⣭⣽⣿⣿⣿⢯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠁⠀⣰⡄⠀⠀⠀⠀⣴⡀⠈⠀⣰⠀⠀⠀⢀⠀⠀⠀⢀⠀⠁⢀⣿⡟⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣩⣤⠀⠈⠛⢿⣿⣿⣿⢿⣷⣿⣧⠀⠀⠀⠀
⠀⠛⠑⠿⠛⠻⠃⠛⠛⠛⣿⠀⠀⢻⣿⡇⠀⢰⣿⣿⡟⢩⣤⠌⢿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣤⣴⣦⣤⣴⣤⣦⣴⣶⣶⣿⣿⠀⠀⠀⠀⣿⡿⠉⠀⢀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⡲⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⡀⠀⠠⣀⡀⠀⠈⢻⠠⠀⠀⠸⣿⢈⠁⠀⠈⠁⠈⠁⠘⠻⠿⢿⡿⣿⡄⠀⠐⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠑⠐⢄⡀⠘⠋⠀⠐⠲⠋⠠⠀⠀⠁⠀⠀⠀⠄⠀⢠⣶⣶⣶⣦⣤⣤⣤⣄⣀⣀⠀⠈⠁⠀⠀⣿⠃⢠⡆⠘⢷⠀⠀⠘⠛⠉⠀⠀⠀⡠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⡞⠈⠀⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠠⠎⢫⢀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠐⠇⠂⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⣦⣀⣶⣿⡤⠀⢸⡆⠀⠈⢿⡷⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠛⠛⠃⠄⠀⠂⢹⠀⣤⠀⣠⣤⡄⠀⠂⠂⢀⣀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠶⠒⢛⡻⡿⠿⠃⠈⠈⢠⣬⡄⠠⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⠍⠙⠻⣿⣿⣿⣿⠿⠛⢛⣻⣿⣆⠉⢁⡄⠀⢠⠀⠁⠀⠀⠛⠟⠩⡀⠀⠀⠈⣿⠋⠻⠿⣿⣷⣀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡟⠉⠙⠛⠂⠀⠀⠀⠀⣕⠇⠘⠒⠓⠒⢉⣿⣿⣿⣡⣤⠄⠀⠀⣰⣿⣿⣿⡇⠀⠀⠈⠙⢿⣿⡆⠚⠀⠀⢤⠠⠛⠀⠀⠀⠀⠀⠠⠤⠀⠀⠛⢲⣤⠀⢛⣋⣁⣾⣿⢋⣹⣄
⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠃⢀⣴⠄⠀⠈⠂⢀⡀⠀⠄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣮⣄⡁⢲⣾⣿⡇⠀⠀⠀⠀⠀⣄⣤⠄⢠⣴⣤⡤⠀⠀⠀⣀⣼⣿⣷⣷⣾⣿⣿⣿⠗⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠀⠀⠷⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⣻⣿⣤⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⠀⠀⡖⢣⣀⠈⠉⠓⣾⣿⣿⠳⠔⠒⠚⢿⣙⡟⠛⠛⠙⠋⠉⠁⣄⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣠⣠⣤⠀⠁⠀⠀⢠⠖⣻⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠏⣠⣿⣿⠿⠿⠿⢷⣿⣿⡄⠹⣿⣿⣿⣿⡍⠁⢘⡓⣧⠄⢀⣿⠿⠿⠟⠻⠶⠀⠀⠈⡩⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠿⠭⠼⠿⢿⣏⠀⠀⠀⠀⡄⠀⠉⠑⢖⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣿⠏⠐⠚⠉⢁⡀⠀⠹⣷⣤⣿⣿⣿⣿⠀⠀⢽⠷⠂⠠⠈⠃⠀⠀⠀⠐⠷⢤⣀⣀⠀⠀⠀⢀⠀⢢⠀⠀⣠⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠂⠐⢻⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣤⣯⣿⣏⣀⠀⣿⣿⣿⣿⣿⣿⣆⡀⠀⣓⣂⠘⠃⡤⢤⡄⠀⢀⣤⡤⠛⠋⠀⠀⠀⠈⢻⣿⣿⠛⢛⣿⡿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣉⡉⣹⣿⣿⣿⣿⣿⣿⠁⠀⠀⣤⣍⠉⠀⠀⣍⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⢀⠀⠀⣸⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠒⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⢿⡿⠿⡿⢿⡿⠟⠶⠂⠁⢹⡓⠃⠀⢴⣿⣄⠀⡀⠀⠀⠉⠉⠀⢀⣤⡄⠀⠀⠀⣼⣋⣙⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡏⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠘⠃⠈⠛⠋⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⢤⣄⣴⣵⣤⣤⣤⣠⣴⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣤⣤⡀⠀⠀⠀⠀⠲⠤⢤⠐⠂⠰⡀⢀⡀⢸⣶⡄⠀⠀⣀⠀⣰⠁⢿⡟⢻⣿
⡀⠀⠀⠀⠀⠀⠀⠲⠛⠒⠺⠦⣤⣤⣤⣿⣿⣷⣿⣿⠟⠛⢻⣽⡿⠿⢿⣿⡏⠉⠉⠙⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠻⣿⡟⣿⣿⡧⠀⠀⣀⡃⢀⣴⡾⠦⢤⣴⠋⠀⣡⣶⠄⢰⣄⠀⠀⠀⠋⠀⠀⢠⣸⣿
⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⣾⣿⠃⠀⠀⠀⠈⠉⠀⠀⠸⢿⡇⠄⠀⠀⠈⢻⣿⡿⠃⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠘⢣⣿⣿⠏⠀⠀⠀⠀⠚⣿⣿⣿⡆⣀⣀⣤⠊⠀⠤⠀⠻⣄⣀⡤⡄⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣷⡄⠀⠀⢠⣿⣿⣿⣿⣿⢇⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣀⣼⣿⢸⣷⣄⠀⠀⠙⠻⣄⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡆⣿⣿⣿⣦⣀⣀⡀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠷⠀⠀⢠⣤⣾⣿⣿⣿⠘⣿⣿⣿⣦⣄⡀⠀⠀⠰⠿⠛⠋⠉⠀⢀⣠⣴⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⣀⣸⣿⣇⢻⣿⣿⣿⣿⣟⣃⠀⡷⠤⣄⣀⣀⡀⠸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⡏⠀⢀⣶⡆⠀⢹⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⢠⣿⣿⠁⣿⣿⣿⣿⡀⡀⠀⠀⢀⣀⣿⣿⣿⣯⢸⣿⣿⣿⣿⣷⣍⠛⠓⠈⠈⠊⠁⢠⠄⠹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡷⢶⠀⠀⢀⣴⣾⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣼⣿⣿⢰⣿⣿⣿⡿⠋⠁⣀⡀⠘⠻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣀⣀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⡏⠀⠀⡰⡄⠈⠉⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⡏⣸⣿⣿⣿⣧⣤⡄⠛⠁⣀⣀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢈⠉⠃⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣷⡦⠀⠈⢀⣠⣴⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⠇⣿⣿⣿⣿⡟⠉⠃⣀⡀⠻⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⣉⣐⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⠀⠀⣀⡀⠈⠉⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⡿⢠⣿⣿⣿⣿⣧⣄⠐⠛⠃⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠉⠀⢀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣶⠐⠛⠋⢤⣤⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠁⣾⣿⣿⣿⣿⠻⠛⣀⣀⡸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⣿⣿⣿⠋⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⣄⠛⠛⠁⢀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣿⣿⣿⡹⣿⣿⡷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⠃⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⢿⣿⣿⣿⡸⣿⣷⣶⢾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠉⠙⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⢠⣾⣿⣯⣏⣀⣀⣀⣀⠀⢹⣿⣿⣿⠀⠘⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠟⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡁⠈⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠈⠉⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠓⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿
⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⣟⣿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠁⣾⣿⣿⣿⣿⣿⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⠀⠀⡀⠀⣀⢀⣀⣤⣠⣠⣀⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠊⢀⣾⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢏⣴⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣷⡀⠉⠉⠉⠉⠉⠉⠉⠉⢉⣼⠏⠀⠀⢠⣾⢟⣫⣷⣿⣿⢝⣐⠻⣵⣼⣿⣿⣿⣿⣿
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣠⣄⣿⠟⣡⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣾⣌⠛⢿⣿⣿⣿⣿
⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⣁⣾⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠁⠚⠛⢿⣿⠛⠃⠀⠛⠛⢿⣿⣿⠿⠿⠿⢿⠃⠀⣿⠟⠛⡿⠛⢿⠛⢿⠛⠿⠿⢿⣿⠟⠋⢁⠈⣇⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠰⠀⢸⠀⠀⠛⠀⠀⠃⠀⠘⠀⠸⠀⠀⠀⠀⠿⠀⠀⠟⢀⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠊⠻⣿⣿⣛⣭⣽⣿⣿⣿⢯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠃⠀⢠⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠂⠀⠈⠛⢿⣿⣿⡿⣿⣷⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠟⠛⠻⠃⠛⠛⠛⢿⣿⡆⢀⡘⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠴⠀⠀⠀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛⠃⡀⠀⠠⢄⡀⠀⠀⢿⣀⡄⠀⠀⣿⣿⠃⠀⠀⠃⠈⠁⠈⠿⠿⣿⣿⣿⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠄⢤⡀⠘⠋⠀⠀⠶⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣾⠇⢶⣆⠨⢿⡀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡀⠀⠀⠐⠶⠹⠀⠀⠀⢠⣴⠆⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⣤⣄⢶⣾⣤⠀⢸⣇⠄⠈⢿⡶⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠿⠓⠻⠀⠀⠋⢙⠁⣀⣀⣠⣤⡄⠀⠐⠂⣠⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠶⠶⠖⠚⠻⡿⠿⠇⠈⠈⢀⣬⣁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣟⠛⠿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣆⠀⠉⠁⡄⠀⢀⠀⠋⠀⠀⠚⠿⠉⡀⠀⠀⠀⣻⠛⠻⣿⣿⣶⣄⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡾⠋⠙⠷⠆⠀⠀⠀⠀⣏⠁⠴⠓⠂⠶⣾⣿⣿⢛⣉⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠙⠻⣿⣿⡆⠀⠚⠀⠀⣠⠠⠶⠀⠀⠀⠀⠀⠀⠤⠀⠀⠟⢢⡦⠀⢚⣛⣑⣶⣿⡿⣿⣄
⠀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠒⠀⣤⡄⠠⠈⠢⠀⡀⠀⠤⠀⠀⣿⣿⣿⣿⣿⣥⣤⣾⣿⣿⣿⣿⣦⣄⠂⠒⢦⣼⣿⣿⠀⠀⠀⠀⠀⠀⡀⣠⠄⠀⣤⣤⡤⠀⠀⠀⣀⣼⣿⣷⣷⣿⣿⣿⣿⡷⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠀⠀⠷⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣍⡀⠁⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⠂⣄⠈⠉⠒⣺⣿⣿⡷⠄⠒⠚⢿⢙⡟⠛⠟⠛⠋⠉⠁⣀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⣤⡀⠀⠀⠀⢀⠔⣚⡗⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⣴⣿⣿⣿⣶⣦⣶⣶⣆⠹⣿⣿⣿⣿⣿⡄⠉⠉⠔⡫⣯⠄⠀⣾⡿⡿⠿⠳⠶⠀⠀⠈⣩⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠿⠭⠭⠿⢿⠏⡀⠀⠀⠀⡄⠀⠉⠁⠖⡀⠀⢸⣿⣿⣿⣿⣯⣼⣿⠏⠁⠒⠒⠀⠈⠙⢿⡄⣹⣿⣿⣿⣿⣷⠀⠀⢽⠷⠋⠀⠈⠏⠀⠀⠀⠐⠶⢤⣀⡀⠀⠀⠀⠀⠀⢠⠀⠀⣠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠉⠀⠀⠀⠀⠹⠂⠐⠰⢺⠇⠀⣸⣿⣿⣿⣿⣿⣿⣏⠀⠀⣀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⣓⡂⠜⠂⣠⢤⣤⠀⠀⣦⡬⠛⠛⠁⠀⠀⠘⢛⣿⡿⠟⠻⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⠿⢿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⣨⣍⠉⠀⠀⣉⣡⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠸⢀⠀⠄⣰⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⣭⣿⣿⣿⣿⣿⣿⣿⠿⠠⠖⠃⢹⠒⠂⠀⢴⣿⣇⠠⠀⠀⠀⠉⠉⠀⢀⣠⡀⠀⠀⠀⣠⠋⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠿⣿⡟⠛⠛⠻⠛⠛⠩⠛⠿⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠙⠛⠁⠀⠀⡀⠐⠁⠉⠛⠃⠀⠀⣰⡇⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠉⠀⠁⢤⣤⡤⢛⣀⡀⠀⠀⣲⣶⣆⣤⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣾⣆⡀⠀⠀⠀⠀⠀⠀⠰⠤⢤⠐⠂⠰⡄⢠⡀⢠⣦⡄⠀⠀⢀⡀⢠⠁⠁⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠲⠖⠒⠾⣧⢀⣀⠀⠚⠛⣥⣿⣿⡿⠿⢿⣻⣿⣿⣿⣿⡿⠿⠻⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⡿⣿⣿⡆⠀⠀⣀⡆⢀⣰⠶⣆⣤⣴⠏⠀⣉⣴⠄⢠⣄⠀⠀⠀⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣶⣿⣵⣿⡏⠉⠀⠀⠚⠛⠉⠀⠹⣿⡇⡀⠀⠘⢿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠙⣿⠇⣿⣿⡯⠭⠙⠛⠃⠤⣿⣶⣶⡄⠀⠀⢤⠄⠁⠤⡀⠻⣅⣀⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⣿⣿⣿⡇⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⣸⣷⢡⣀⠀⠀⠙⢿⡀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⣟⣴⡟⠛⠁⠀⠀⠀⠀⠀⠹⢿⣿⡅⣶⣶⣼⣧⡄⣀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⣰⣿⣿⣿⣿⢱⣿⣿⣿⣷⣶⠀⠀⠀⣀⣰⣿⣿⣿⢸⣿⣷⣄⡀⠀⠙⠂⠀⣴⣿⡿⠿⠛⠁⠀⢀⣠⢿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⣿⠚⢻⣃⠀⣿⣤⣤⣤⣦⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠰⠦⢀⣾⣿⣿⣿⣿⣿⢸⣿⣿⡟⠉⠁⣤⡄⠘⢻⣿⣿⣿⣿⠘⣿⣿⣿⣿⣶⣤⣄⠀⠉⠀⠀⠀⠀⢠⣾⣿⡏⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⣦⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⣾⣿⣿⣧⣤⠀⠉⠃⣀⣸⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣿⠁⣿⣿⣿⣿⠿⠿⠀⠀⠰⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠉⠉⢠⡀⠘⠻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⣿⣿⡿⢠⣿⣿⣿⣿⡀⠀⠼⠷⠀⠀⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣧⣄⠀⠙⠁⢀⢠⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⡏⢸⣿⣿⣿⣿⠿⠇⠀⠀⣸⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠓⠉⠀⣀⠀⠛⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⠃⣼⣿⣿⣿⡏⠀⠀⣾⡆⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣤⠄⠻⠿⢀⣀⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⡟⢠⣿⣿⣿⣿⣿⣿⠇⠀⠀⣴⣶⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣇⣉⣲⣶⡞⠉⢹⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢸⣶⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣷⣯⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡧⣶⣤⣤⣌⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠛⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⠿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠉⣙⣻⣿⠷⠍⠛⠋⠉⠉⢹⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⢤
⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⠀⠀⠀⠉⠿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡿⠂
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⣟⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢫⡳⠀⣾⣿⣿⣿⣿⡏⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⢴⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣧⠀⠀⡀⠀⣀⢀⣀⣤⣠⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠈⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡄⠙⠛⠛⠛⠛⠛⠉⠉⠉⣠⠏⠀⠀⢠⡾⢟⣫⣷⣿⣿⢝⣐⠻⣷⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡼⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣸⣿⣿⡿⣡⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣾⣎⠛⢿⣿⣿⣿⣿
⠛⠿⠋⠉⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠈⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⢟⣩⣾⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⣤⣴⣿⡿⢿⢿⣿⣿⣿⣿⠟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠟⠛⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠐⠿⢿⠛⠻⠀⠘⠛⢿⣿⣿⠛⠛⠿⢿⠇⠀⢸⠟⠛⡟⠛⢿⠛⢻⠛⠛⠿⢿⣿⠟⠁⣠⡄⣇⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠰⠀⢸⠀⠀⠘⠀⠀⠃⠀⠘⠀⠸⠀⠀⠀⠀⠛⠀⠀⠋⣠⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠠⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠂⠻⣿⣿⣻⣭⣽⣿⣿⣿⢯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇⠀⠀⡀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⡏⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠛⣀⠀⠈⠛⢿⣿⣿⡿⣿⣷⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠟⠛⠻⠃⠛⠛⠛⢹⡟⠻⠃⣤⣀⣿⡟⠀⠀⢸⣿⣿⠟⠛⠻⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣤⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⡄⠀⠀⠀⢠⣴⠿⠁⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⢾⠿⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠈⠙⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠸⠿⡀⠀⠀⠄⠀⠀⠀⠿⢄⣄⠀⠀⣿⢿⠙⠀⠀⠃⠈⠋⠀⠿⠷⣾⣿⣼⡁⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠐⠆⠤⣀⠀⠶⠀⠀⠴⠞⠂⠄⠄⠉⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣸⡗⠠⣤⠶⣿⡆⠀⠘⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠀⠀⠀⠠⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⠀⠀⠀⠀⡴⠙⠁⠀⠀⠀⣤⡅⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣤⣀⣠⣼⣧⠀⠰⣏⡄⠀⢻⣿⡄⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡔⠀⠠⠶⠾⠃⡂⠀⠈⠙⡇⢀⡀⣀⣀⡀⠀⠀⢚⣀⣀⣸⡷⡛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⣤⡶⠰⠿⢿⡿⠿⠉⠉⢂⣀⣋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⠃⣀⠀⠀⡄⠚⠁⠀⠸⠿⠏⠁⠀⠀⠀⢻⠟⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⠞⠛⠻⠦⠀⠀⠀⠀⢽⡽⠤⠅⠢⠤⢾⣿⣿⣿⠿⠛⠛⠀⠈⣻⣿⣿⡿⠋⠉⠩⢿⣿⣷⡀⠀⠰⠁⠀⣠⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠸⢢⡤⠀⠚⣛⣙⣾⣷⡟⢿⣄
⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠀⢀⣄⢀⠐⠢⠀⠀⠀⠠⠀⠀⢸⣿⣿⣷⣾⣟⣉⣀⣴⣿⣿⣿⣷⣄⠠⠤⣄⣘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⣄⣀⠀⠀⠀⠀⣘⣿⣶⣶⣽⣿⣿⣿⡷⠐⠿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠀⠀⠼⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠙⢻⣷⣤⣼⣿⣿⣇⠀⠀⠀⠠⠦⣀⠈⠉⠒⢼⣿⣿⡷⠤⠴⠖⢿⡿⣿⠿⠟⠛⠋⠉⠃⣀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⡄⠀⠀⠀⠀⡡⠖⣶⠂⠀⠁⢀⣼⣿⣿⣿⣿⣿⣿⢩⣿⣿⣶⣦⣤⣤⣤⡙⢿⣿⣿⣿⣿⠀⠘⠃⠠⣪⣽⠄⠀⢸⣿⣿⡿⠷⠶⠀⠀⠈⢋⡁⠀⠀⠀⠀⠀⠀⠈⢧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⣩⣽⣿⣿⣃⠀⠀⠀⢀⠀⠘⠋⢱⠂⠀⢸⣿⣿⣿⣿⣿⣿⢃⣾⡿⢛⡩⠭⠉⠛⢿⣷⣸⣿⣿⣿⣿⣦⠀⠀⣸⣿⠎⠀⡀⠝⠁⠀⠀⠀⠦⣄⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⠠⠄⠀⠀⠉⠁⠀⠀⠀⠸⠆⠠⠢⢴⡗⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣀⡀⠐⢒⠂⠠⠖⣀⡠⣤⠀⠀⣠⣤⠛⠛⠃⠀⠀⠘⠛⣿⣿⡿⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⢈⣉⠛⠂⠀⢈⣩⠀⠈⠉⠀⠀⣀⡀⠀⠀⠀⠸⢀⡀⠀⣀⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠏⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠉⣻⣿⣿⣿⣿⣿⣿⣷⡿⠿⠿⢿⣧⣴⣿⣿⣿⣿⣿⣿⠏⢠⠔⠒⠹⠷⠖⠀⢠⣼⣇⠀⠀⠀⠀⢈⠉⠁⠀⣀⣀⠀⠈⠂⣀⡟⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣽⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠛⠓⠏⢀⣀⠀⠀⠂⠈⠛⠛⠀⠀⢠⡇⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠉⠉⠠⣀⣠⢟⠁⠀⠀⠀⠰⣦⣤⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡏⠙⠛⠛⠛⢛⢽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠠⠄⣤⠤⠤⠠⡄⠀⠀⢀⣦⣄⠀⠀⢀⡀⢀⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⡶⠶⠾⢿⠄⠀⠀⠴⠿⠁⣾⣶⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⣶⣦⡄⠀⠀⠀⠲⠀⢠⠤⣇⣀⣠⠟⠁⣈⣠⡌⠀⣄⠀⠈⠁⠚⠀⠀⠀⠀⠀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⣨⣿⡿⠿⠏⠉⢱⣾⠿⠛⢿⣿⡏⠁⠀⠹⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠉⠛⢿⡏⣿⣿⣷⣀⠚⠦⠀⣀⣤⣤⣄⡀⠉⠀⢠⠄⠁⠤⠄⠻⢆⣀⣠⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⣤⣶⡿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣻⡇⡄⠀⠀⠉⢿⣿⡁⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⢸⣠⡿⠿⠃⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⣸⣄⡀⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⣰⣿⣿⣿⣇⣿⣿⣿⣄⡀⠀⠀⠀⠀⢠⣤⣿⣧⢹⣷⣤⡀⠀⠙⠳⠄⠀⢀⣰⣿⣿⡿⠇⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣷⣮⡉⠻⠛⠻⡃⠀⡾⢤⣀⠀⡀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣴⣿⣿⣿⣿⢸⣿⣿⣿⠿⠟⠀⠀⢰⣶⣿⣿⣿⣿⢸⣿⣿⣿⣶⣄⣀⠀⠀⠚⠛⠉⠀⠀⠀⣠⣾⡿⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⣶⣾⣿⡇⣿⣿⣿⣷⣌⠁⠉⠙⠳⡶⠏⠁⠁⢈⡖⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠰⢿⡇⠀⢸⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⣿⣿⣿⣶⡦⠀⠀⢠⣴⣿⣿⣿⣷⢸⣿⣿⣿⣿⣇⠀⡀⠀⠁⠀⠀⠀⢀⡀⠀⢫
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⣾⣿⣿⡿⠛⠀⠀⢰⣾⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢠⣿⣿⣿⠃⣿⣿⣿⣿⠀⠀⣴⣦⠈⠉⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣬⡇⠀⠠⠀⠀⠀⠈⠛⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⡟⠀⠀⣺⡇⠀⠈⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡏⢸⣿⣿⣿⣿⣿⡆⠀⠀⣤⣤⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡟⠁⣠⣶⣤⣀⢀⣘⡀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣷⠀⠀⠠⣴⣼⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⡇⣸⣿⣿⣿⡏⠀⠀⣤⡄⠉⢙⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⡏⠈⠿⠉⠉⠉⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⠁⠀⣰⣢⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠸⣿⢀⣿⣿⣿⣿⣷⣶⠀⠉⠁⣤⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡟⢳⣿⣿⡧⠠⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠆⠉⠉⢰⣶⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⡏⠉⣤⣤⡔⠻⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠀
⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⡏⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⠉⠉⠁⣠⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠇⠀⢀⣴⠄⢀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣧⡻⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⢹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⢨⣴⣶⠂⠀⠀⢀⡅⠀⠈
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢿⣿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠛⠿⢿⣿⣧⠻⠿⠛⠙⠛⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣏⠛⠛⠛⠒⣤⠀⠀⠀⠴
⢀⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⣶⣶⣶⡆⢀⣿⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⢀⣀⣄⣤
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠰⣿⣿⣿⣿⡿⠟⠛⠿⠇⢀⠀⠀⠀⠈⠻⠀⠀
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣾⣿⣧⠄
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣺⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⣟⣦
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠿⠃⣿⣿⣧⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⡀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣿⣿⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡀⠛⠉⠉⠉⠀⠀⢠⣾⣿⣿⠇⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣐⠻⣵⣼⣿⣿⣿⣿⣿
⣿⣿⣿⡛⠛⠛⢛⣉⣙⡛⣻⣿⠇⠀⠀⠀⠀⠻⣿⣿⣿⣶⣤⣄⣀⡀⢸⣿⣿⡿⣣⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣾⣎⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣷⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⣫⣾⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣧⣤⣴⣶⠶⠃⠈⠈⠉⣿⣿⣿⡇⢹⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⠟⣏⡉⠉⠉⠉⠉⠉⠛⡿⠛⠛⠻⠟⠙⠂⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠑⣾⣿⠛⠻⠀⠀⠛⢿⣿⣿⠛⠛⠿⢿⠟⠀⢸⠟⠛⡟⠛⢿⠛⠃⠀⠀⠀⠘⠁⣿⣿⡿⠀⢀⢿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣿⣿⠀⠰⠀⢸⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠟⠀⠀⢠⣯⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠉⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⣠⣽⣿⠊⠻⣿⣿⣻⣯⣽⣿⣿⣿⢣⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⢀⠸⠂⠀⠀⠀⠀⠀⠀⠈⢀⣰⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣯⣠⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠛⠛⠛⠁⣿⡿⠀⠀⠀⢿⣾⠃⠀⢀⣾⣿⡏⠁⠀⢹⣿⣿⣿⡇⠀⢠⣿⣿⣿⣝⣻⣿⣿⣋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⢀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⣿⣿⣿⠄⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠡⠤⠇⠙⠛⢁⣄⣀⠀⠈⠀⠀⣋⠀⠀⠀⠀⠴⠂⠀⠀⠠⠾⣿⠀⠀⢀⠄⠀⠀⠀⢿⣇⡤⠀⠀⣿⣿⡟⠀⠀⠸⠈⠛⠁⠿⣿⣿⣷⣿⣇⡀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⡴⠷⢦⣤⡅⠈⠿⠄⠀⢤⡴⠦⡤⢄⠚⠁⠀⢀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣸⡿⢒⣾⣲⣿⣏⠀⠀⢿⠿⠂⠀⠀⢀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀
⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣤⣦⡄⠉⠐⠁⡀⠀⠠⢠⡞⠁⠀⠀⡀⠀⠀⠀⢨⣿⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⡰⢿⡇⠀⠁⠀⣤⡇⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⣠⣄⢀⣴⣷⡀⠀⣮⡠⠀⢺⣷⡅⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠄⠀⠨⡶⠾⠷⣇⠀⠼⠛⡇⣀⡀⣀⣀⣀⠀⠀⠶⣖⣈⣼⣿⡿⠁⠀⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣴⣶⠶⠿⢿⣿⣿⠋⠋⠑⣀⣛⡃⡀⠈⠉⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⠓⢀⠠⠀⡄⠘⠁⠉⠱⠿⠏⢋⠀⢀⡀⢻⠟⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡶⠛⠾⡦⠄⠀⠀⠀⢹⣻⢄⠦⠴⠤⣴⣿⣿⡿⠛⠋⠉⢻⣿⣿⣿⠟⠋⠉⠭⣿⣿⣿⡆⠀⠤⠰⠇⠀⢠⡀⡴⠆⢀⠀⠀⠀⢈⡀⠀⠀⠸⢲⡤⠀⠘⢛⢛⣷⣶⡿⢿⣄
⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠾⢷⠶⠔⢀⣀⢀⡴⠶⠉⠁⠀⠀⠄⠀⣾⣿⣧⣶⠊⠀⣠⣾⣿⣿⣿⣄⡀⠤⢤⣀⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⣤⣄⣀⡄⠀⠀⠀⣰⣿⣷⣶⣽⣿⣿⣿⣷⠾⠻
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠀⡧⠤⠀⠹⡆⠀⠂⢰⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠙⠻⣿⣦⣤⣽⣿⣿⣿⠀⠀⠀⠀⠠⠶⣄⠈⠉⠳⡼⣿⣿⡟⠤⠤⠶⢿⡿⣿⠿⠿⠻⠟⠉⠋⣀⡃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⢀⡀⣀⣀⠀⠀⠀⠀⢨⠴⣶⠆⠀⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⡌⢿⣿⣿⣿⣿⣿⡇⠀⠘⠛⠠⢮⢽⠥⠀⣸⣿⣿⡿⠷⢶⠀⠀⠈⣋⡁⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⣋⣽⣿⣿⡋⠀⠀⠀⢀⠉⠘⠛⢥⠄⠀⢸⣿⣿⣿⣿⡟⣾⣿⠟⠉⠉⠉⠛⠻⣿⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⣸⣿⡏⠁⡆⠟⠁⠀⠀⠀⠾⣤⣀⣀⠀⠀⠀⠀⠐⢤⡄⠀⢀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠂⠠⡆⠀⠀⠑⠉⠀⠀⠀⠨⣶⠠⠄⠴⣾⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠐⢒⠆⠡⠖⢄⡠⣤⡀⠀⢠⣤⡛⠛⠃⠀⠀⠘⠻⣿⣿⡿⠾⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⢈⣉⡛⠂⠄⣨⣋⠀⠈⠉⠀⠀⢀⡀⠀⠀⠀⠸⢀⣀⠀⣠⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⣯⣽⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡤⠚⠘⡷⠶⠀⢠⣾⣧⡀⢀⠀⠀⠈⡋⠁⢀⣀⣀⠀⠀⠰⢀⡟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⠉⣻⣿⣿⣻⣿⣿⡏⠈⠉⠀⠀⠀⠀⠀⠉⠁⠀⠰⠉⠛⢇⠉⣀⣀⢀⠀⠚⠙⠛⠟⠀⠀⢠⣿⠈⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠋⠉⠀⣀⣀⣼⡃⠀⠀⠀⠤⣤⣤⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠛⠛⠏⠏⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣤⡤⠤⠤⡄⠀⡆⠺⣶⣄⠀⡀⠀⡀⢀⡎⠘⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⣶⠶⠤⢿⡆⠀⡀⠴⣿⠏⣼⣶⣶⣦⣶⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⡀⠀⠀⠀⠲⠀⢠⡦⣧⣀⣠⡞⠁⢙⣢⡾⠁⣤⠀⠈⠁⠘⠂⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠣⠀⡚⣿⡿⠿⠏⠉⣹⣾⡿⠿⢿⣿⡏⠉⠉⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⢿⣿⡏⣿⣿⣗⣀⡰⣤⡄⢀⣈⣀⣀⠀⠈⠀⢠⡬⡣⢠⡄⠹⣇⣀⣠⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⣠⣴⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⡀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⣿⢡⣿⡿⠏⠉⠀⠀⠈⠙⣿⣿⣿⠇⠀⠀⣸⣤⣀⣀⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⣰⣿⣿⣿⡏⣿⣿⣿⣇⡀⠀⠀⠀⠀⢠⣤⣿⣧⢿⣦⡀⠀⠈⠻⣄⠀⠀⢠⣾⣿⣿⡿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⣦⣌⡉⠿⢟⢿⡛⠀⣼⢦⣄⡀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⢤⡤⡤⣰⣿⣿⣿⣿⢧⣿⣿⣿⡿⠿⠀⠀⢰⣶⣿⣿⣿⣿⢸⣿⣿⣶⣄⣀⠀⠀⠰⠟⠛⠉⠁⠀⢀⣤⣶⣿⢻⣿⣿⣶⠀⠀⠀⠀⠀⠀⣤⣼⣿⡇⣿⣿⣿⣶⣈⠁⠉⠙⠓⡶⠛⠉⠉⠩⣾⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⢸⣿⣿⣏⠀⠀⠿⡗⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⣾⣿⣿⣿⣦⣤⠀⠀⢀⣤⣿⣿⣿⣷⢹⣿⣿⣿⣿⡇⣀⣀⠀⠃⠀⢀⠀⢠⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⣸⣿⣿⠿⠿⠃⠀⢰⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⣿⣿⣿⠃⣿⣿⣿⣿⠁⠁⣤⣤⠈⠛⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣾⡏⠀⠠⠀⠀⠀⠈⠛⠋⣩
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⣸⡗⠀⠉⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⣿⣿⣿⡿⢸⣿⣿⣿⣿⣶⡆⠉⠉⣠⣤⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠛⡁⣰⣶⣦⣀⣀⣈⡃⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠷⠆⠀⢀⣶⣼⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⡇⢸⣿⣿⣿⡟⠉⠁⣠⡄⠛⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⡯⠁⡿⢋⠉⠉⠭⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⢰⣶⡄⠉⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢻⣿⠁⣿⣿⣿⣿⣧⣤⠀⠛⠃⣀⣸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠛⢳⣿⣿⡧⠠⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⠇⠀⠉⢰⣶⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠃⣼⣿⣿⣿⣿⡟⠛⣠⣀⣼⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⠀
⠒⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⡏⣤⣄⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣦⠙⠛⠃⣀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⡆⣠⡄⠀⠀⠇⠀⢀⣴⠆⣀
⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣧⣻⠿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⠀⢻⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣇⣨⣶⣶⠂⠀⠀⠠⣅⠀⠈
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠿⢿⣿⣿⣘⠿⠿⠟⠸⠿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣏⠛⠻⠛⠓⢶⠄⠀⠀⠴
⠀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠈⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⢠⣿⣿⣿⣿⣶⣤⣶⡆⢠⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣟⠓⠀⠀⠀⠀⢀⣀⣤⣠
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣿⠁⢸⣿⣿⣿⣿⡿⠟⠛⠿⠇⠀⠀⠀⡀⠈⠻⠀⠀
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⠗⠀
⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣀⠀
⣿⣿⣿⣿⡿⠿⠿⠛⠛⡛⠛⢿⣿⡇⠀⢠⣿⣿⣿⡏⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⡿⠿⠟⠛⣠⣿⣿⣇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠙⢿⣿⣧⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣷⠈⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⢀⣾⣿⣯⣷⣿⣿⢝⣐⠻⣵⣼⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠛⠛⠛⢛⣿⣿⣿⣇⣤⡀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣦⣤⣸⣿⣿⢟⣵⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⠀⠀⢀⣀⣀⠄⠀⠉⠙⣿⣿⣄⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣿⣮⠻⢿⣿⣿⣿⣿
⣤⣾⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⡿⣛⣵⣾⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠋⣠⣿⣿⠏⠀⢻⣿⣿⣿⣿⣟⣵⣾⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⠛⠛⠛⠃⠀⠀⠀⠀⠐⠿⠛⠛⠻⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⢿⣿⠛⠛⠀⠈⠛⢿⣿⣿⠟⠿⠿⢿⠇⠀⢸⠟⠛⠟⠛⠉⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⢀⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠀⠰⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⣀⣘⡯⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣷⣿⡯⢴⣿⣿⣷⠈⠻⣿⣿⣻⣭⣽⣿⣿⣿⢧⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⢠⠀⠀⠀⠀⠈⢀⣸⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢀⣿⡏⠀⠈⠀⢀⠀⠀⠀⠀⠀⡄⠀⣆⠀⢸⠀⠀⠀⠀⠛⣿⣟⠀⣿⣿⣿⠀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠛⠛⠛⠁⢸⣿⠉⠀⠀⠈⠻⠃⠀⢰⣿⣿⣅⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣯⠀⠀⢼⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠀⣼⣿⠟⠁⡽⠉⠁⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣧⣄⣀⣠
⣴⣿⣿⣢⣀⣀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠤⠄⠈⠛⠃⣀⣄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠒⠀⠀⠀⠘⢿⡇⠀⠀⡠⠀⠀⠀⠸⢧⣠⡄⠀⢸⣿⠿⠃⠀⠘⡂⠛⠃⠻⢿⣿⣿⣾⣿⣄⠀⠸
⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⢾⢶⣤⣥⠈⠿⠆⠀⢠⣤⠶⢤⠄⠒⠋⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢀⣿⠷⣾⣶⣾⣿⡀⠀⠘⠻⠫⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀
⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣶⡆⠈⠁⠂⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣿⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⢰⢾⣿⠀⠉⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⣠⣤⡠⣤⣯⣄⠀⣶⣁⠀⠐⣷⣧⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡔⠀⠉⢶⡶⢿⣿⣀⠠⠛⢿⣀⣀⣀⣂⣀⡀⠀⢼⣾⣊⢠⣿⣾⠃⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⣦⡶⠾⣿⣿⣿⡏⠙⠙⢂⣚⡁⢀⠀⠉⠁⢀⣼⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣷⡀⠀⠀⠛⢀⡀⠀⣠⠰⠋⠉⠉⠿⠿⠋⡀⠤⣤⢸⡿⠛⢿⣿⣷⣦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣶⠞⠻⣷⠤⠀⠀⠈⠹⡏⡅⡼⠰⠤⠴⣾⣿⡟⣉⡀⡀⠀⣸⣿⣿⣿⠁⠀⠀⠙⢻⣿⣷⠀⠤⠀⠟⠀⢀⡍⢠⠦⢄⠀⠀⠀⠈⠁⠀⠀⠸⠗⣤⠀⠐⠟⣛⣿⣿⣿⢿⣧
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⢷⡶⠦⠀⣠⡀⡠⡲⠌⠉⡀⠀⠄⠀⢠⣿⣿⣿⣿⣷⣶⣾⠿⠿⠿⢿⣷⣖⠑⠶⣶⣽⣿⡇⠀⠀⠀⠀⠀⠀⢀⡀⣠⠤⣤⣤⣀⡄⠀⠀⠀⣀⣿⣷⣶⣬⣿⣿⣿⣿⠶⠻
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⢩⠤⠀⠀⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⢈⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠴⢆⡀⠉⠓⠶⣿⣿⣿⠦⠤⠴⠾⣿⢿⠿⠿⠛⠟⠉⠙⢁⡘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⣀⢀⣀⡀⠀⠀⠀⢀⡥⢶⡖⠀⠈⢀⣠⣿⣿⣿⣿⣿⢳⣿⡿⠿⠿⠿⢿⣿⡇⢿⣿⣿⣿⣿⣧⠀⠀⠓⠀⢴⣽⡯⠀⢀⣿⣿⣿⠿⢶⡆⠀⠀⢙⣉⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣛⣩⣿⣿⣟⠁⠀⠀⠀⡈⠀⠛⠫⡤⠀⠀⣿⣿⣿⣿⣿⣧⣾⡟⠀⠀⠀⠀⠀⠘⣷⣾⣿⣿⣿⣿⣿⡤⠀⠀⢀⣿⡿⠉⢀⠸⠃⠀⠀⠀⠲⣧⣀⣀⣀⠀⠀⠀⡀⠐⡄⠀⠀⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠠⠤⠀⠀⠈⠉⠀⠀⠀⠀⢷⠆⠔⢤⢾⠂⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠒⡒⠀⠴⢂⣀⢤⡄⠀⢀⣤⡞⠛⠛⠀⠀⠀⠛⣿⣿⡿⠟⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠸⣿⣿⣿⣿⣿⣿⣿⣆⣴⣶⣤⣤⡤⢸⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠀⢈⣉⡛⠓⠠⢀⣉⡇⠀⠉⠀⢀⡀⣀⠀⠀⠀⠀⢃⣀⡀⢀⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣭⠆⠈⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⠿⣿⠋⠠⣤⠒⠈⡷⠶⠆⠠⣴⣿⡀⠄⡀⠀⠈⡉⠉⠀⣠⣄⡀⠀⠀⠤⣼⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣿⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠎⠙⠟⠝⣀⣀⣀⠀⠞⠎⠙⠛⠁⠀⢀⣾⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠋⠉⠑⣄⣀⣬⣿⣀⣀⣀⠠⣴⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠋⠀⠀⠈⠉⠀⠘⣻⣶⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠦⢄⡤⠴⠄⢤⠀⣦⠾⢷⣦⠀⢀⠀⣀⠀⡜⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠶⠶⠼⣧⠀⠀⠀⠾⣿⣽⣿⣿⠟⢻⣻⣿⣿⣿⣿⡿⠛⠛⢿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠿⣿⣿⡿⣿⣿⡆⠀⣀⡀⠐⠂⢀⡶⢶⣄⣤⡼⠃⢈⣃⣶⠃⢤⡀⠀⠉⠘⠓⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣧⡆⣾⡿⠉⠁⠀⠘⠛⠉⠀⠸⢿⣇⠀⠀⠈⠻⣿⡆⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠈⣿⢳⣿⣿⠗⠖⠉⠉⠙⢶⣿⣷⣿⡀⠀⠁⠀⡤⢏⠤⢤⠈⢿⣀⣀⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣠⣶⣿⣿⢻⣿⣷⣶⠀⠀⠀⠀⠀⠀⡀⣸⣿⢰⣤⡀⠀⠙⠻⣄⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⣬⣿⡏⠉⠀⠀⠀⠀⠀⠀⠿⣿⣷⢀⠀⠀⣲⣧⣌⣠⣀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⣰⣿⣿⣿⡏⣾⣿⣿⣿⣿⠃⠀⢠⣤⣼⣿⣿⣿⢸⣿⣿⣦⣄⠀⠈⠀⠀⣾⠿⠟⠛⠉⠀⢀⣤⣶⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⣀⣿⣿⠸⣿⣶⣤⡘⠛⡛⣛⠀⢺⠧⣤⣀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⣠⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⣶⡶⠀⠉⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣴⣿⣿⠇⣿⣿⣿⣧⣀⡀⠀⠀⢀⣰⣿⣿⣿⡏⣿⣿⣿⣿⣦⡁⠈⠙⠛⣶⠿⠛⠉⠈⣿⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢃⣿⣿⣿⣶⠆⠀⢁⣴⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⢰⣿⣿⣿⡟⠛⠃⣀⡀⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡏⢀⣀⠀⠁⠀⠀⠀⢠⣄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⠃⠀⢠⣶⠈⠙⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⣸⣿⣿⣿⣧⣄⠘⠛⢃⣀⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣧⣶⣿⠀⠀⠄⠀⠀⠀⡉⠛⢩
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢸⣿⣿⣷⡆⠀⠁⣤⣤⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⢿⣿⣿⠁⣿⣿⣿⣿⠟⠛⠀⡀⠸⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠉⣉⠠⣶⣦⣄⣀⣀⣁⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⢠⣦⡄⠉⢻⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⣿⡟⢰⣿⣿⣿⣿⣀⡀⠸⠿⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⣿⠁⢸⠏⠀⠈⢩⠝⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⣿⣿⣷⡆⠈⠉⠑⣦⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⠁⣾⣿⣿⣿⣿⠿⠇⣀⣀⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠉⠑⣿⣿⣷⠀⢀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⢻⣿⡿⣁⣀⣀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⡜⠛⠛⠀⣸⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣇⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀
⠒⠈⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠸⣿⣷⣙⠿⠿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡧⣴⣄⠀⠀⠲⠀⢀⣰⠦⢀
⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢿⣿⣿⣇⠿⣿⡿⠇⠿⢿⣿⣿⡿⢀⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⡒⠀⠀⠠⢴⠀⠈
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠈⠉⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⢰⣾⣿⣿⣧⣤⣤⣤⠀⢸⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣆⠉⠛⠛⠛⠲⠆⠀⠀⠒
⠀⢀⣀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⠁⠀⠀⠀⢠⣤⣤⢤
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⣠⣤⣤⡄⠀⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⢀⣿⣿⣿⣿⣿⡿⠟⠛⠿⠀⠀⠀⠀⣀⠀⠻⡀⠀
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⢸⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠿⢿⠛⠀
⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⠀⢠⣿⣿⣿⡏⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⢿⣿⣿⣧⣀⡀⠀⠀⠀⠉⢹⣿⣿⣿⡿⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠘⠛⠛⠛⠋⠉⠉⢡⣴⣿⣿⣇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣦⣤⣸⣿⡿⢋⣼⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⠏⠀⠀⢀⣾⣿⣯⣿⣿⣿⢝⣚⠻⣷⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⠿⣫⣴⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣷⣴⣶⣶⡶⠖⠀⠀⢠⠄⢸⣿⡄⠀⣠⣼⣿⣿⣿⣿⣿⡫⣖⢶⣿⣎⠛⢿⣿⣿⣿⣿
⡿⠿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠀⡀⠀⠀⠀⠀⠈⠉⠉⠑⠿⢿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣴⣾⡿⠁⠀⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⣤⣶⣾⠛⠻⠛⠛⠟⠛⠛⠉⠙⠻⡇⠀⠀⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠛⢿⣿⣿⠿⠿⠿⢿⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⠀⠁⢿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢤⣴⣦⡄⠋⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⢸⠛⠛⠀⠀⣀⣦⡄⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⠀⠀⠀⠀⣍⠀⠈⣿⣿⡇⠀⠈⠻⣿⣿⣻⣯⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀
⢀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⢠⡀⠈⠀⡀⠀⠀⠈⣹⣿⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠆⠀⠸⠀⠀⠀⢀⡟⠃⠀⠛⠉⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀
⠈⠛⠛⠟⠛⠻⠃⠛⠛⠛⠁⠘⠋⢣⡀⠀⠀⢀⠀⢸⣿⣿⣿⡏⠀⠀⢸⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣶⡏⠀⠀⠀⠄⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣤⣾⣿⢷⣀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠤⠞⠈⠛⠛⣤⡤⠀⠀⠁⠀⠸⠇⠀⠀⠀⠐⠖⠂⠀⠀⠠⠿⣇⠀⠀⣠⣀⠀⠀⠸⠿⣼⣇⠀⢸⡿⡿⢗⠀⠀⡇⠙⠛⠿⣿⣿⣿⣿⣿⣅⠀⠸
⠀⠀⠀⠀⠄⠚⠋⠀⠀⠀⠀⠀⢀⣀⠠⣤⣾⣷⣤⣢⡠⠻⠗⠀⢠⣴⠿⢴⠄⡐⠛⠀⠀⠀⢈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢀⣿⠷⣿⣿⢿⣿⡁⠀⠻⠿⠋⠀⠀⠀⠠⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀
⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣴⣦⠈⠉⠋⡀⡀⠠⠄⣴⠃⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⡀⢰⠾⣿⣀⠈⠁⣡⣽⠂⠀⠀⠀⠀⠀⠀⢼⠧⠠⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⣠⣤⡀⣤⣿⣄⠀⢰⣧⠄⠘⣿⣷⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠂⠑⣿⣶⠿⢷⣀⠠⠛⢛⢄⣀⣀⣂⣀⡀⡀⣼⣾⣆⣠⣿⣿⡏⠀⠀⢐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣰⣶⡾⠾⣿⣿⣿⡏⠙⠙⢂⣾⣍⢀⠀⠉⠁⢀⣼⣿⡿⠿⠯⠙⢻⣿⣿⣿⠿⠛⠛⣻⣿⣿⡄⠀⠀⠛⢀⡄⠄⢠⠰⠋⠉⠉⠿⠿⢟⣃⠡⣤⡘⡿⠛⢿⣿⣷⣦⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⠞⠻⢷⠦⠀⠀⠈⠹⣿⡧⠼⠵⠶⠤⣾⣿⣯⣶⡶⢐⣠⣾⣿⣿⣿⣄⡀⣀⡀⠙⣿⣿⠀⠤⠴⠞⠀⢀⣍⢠⠶⠶⡀⠀⠀⠈⡁⠄⠀⠠⠟⣦⠄⠐⠛⣋⣿⣿⣿⠿⣧
⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠿⡶⠶⢀⣠⣀⣤⢶⠏⠉⡀⠀⠤⠀⢠⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠙⢻⣷⣬⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⠠⢤⣤⣄⡄⠀⠀⠀⣀⣿⣷⣶⣮⣿⣿⣿⣿⡶⠛
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠃⠺⠤⠀⠀⢷⠀⠐⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⡽⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡴⣦⡀⠉⠛⠲⣾⣿⣿⠣⠤⠶⠾⣿⣿⡟⠛⠛⠟⠉⠙⢄⡘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⣀⣀⣀⡀⠀⠀⠀⢀⡥⢶⡶⠀⠈⢁⣠⣿⣿⣿⣿⡟⣸⡿⠋⠉⠁⠉⠉⢻⣇⣿⣿⣿⣿⣿⣷⠀⠀⠛⠂⢔⣽⡯⠄⢐⣿⣿⣿⡿⠶⣦⠀⠀⢉⣩⠄⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣟⣩⡿⣿⣟⡁⠀⠀⠀⡈⠀⠛⠏⡴⠀⠀⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⢀⣿⡷⠉⢀⠸⠋⠀⠀⠀⠸⢧⣄⣀⣠⠀⠄⠀⠑⠒⡄⠀⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⠠⠄⠀⠈⠙⠀⠀⠀⠀⠵⠆⠔⠤⢶⡇⢀⣿⣿⣿⣿⣿⣿⣿⡀⢀⣀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠚⣒⣀⠴⢂⣀⢤⡄⠀⣐⣤⡞⠛⠋⠀⠀⠀⠛⣿⣿⡿⠟⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⢀⣉⡙⠓⠠⢀⣍⣅⠀⠉⠀⢠⣀⣄⠀⠀⠀⠀⢁⣀⡀⢠⣼⣏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠘⣿⣯⠟⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣄⡈⢙⣿⣿⣿⣿⣿⣿⠿⡿⠉⠂⠶⠖⠉⢿⠶⠣⠠⣼⣿⣄⠄⡀⠀⠈⣉⠛⢀⣠⣤⡀⠈⠁⢄⣼⡋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠟⠻⢿⣿⣿⣧⡀⠁⠀⠀⠀⠂⠀⠈⠉⠀⠀⠆⠙⠻⠺⠁⢄⣀⠀⠘⠊⠙⠛⠃⠀⠀⣾⠁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠋⠉⠁⢆⣠⣤⣷⣦⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠈⠁⠀⠀⠀⠀⠀⠨⣯⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠦⠤⣤⠖⠂⢴⠀⢴⡀⢻⣮⡄⢀⠀⣀⠀⡜⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⠶⠾⣿⠀⠀⠠⢼⣻⣿⠿⠟⠉⢹⣾⠿⠛⢻⣿⡏⠀⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠉⠛⢿⡟⣿⣿⣗⠒⣴⣤⡐⠃⣀⣴⣾⣦⣤⡾⠋⢈⣳⣶⠅⢴⡄⠀⠁⠐⠃⠀⠀⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣧⣿⣏⡀⠀⠀⠀⠀⠀⠀⠈⢹⣇⠆⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⢸⣡⡿⠿⠋⠉⠀⠀⠈⠻⣿⣿⡿⠄⠀⠀⠀⡤⠞⠤⠤⠈⢿⣀⣠⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⣾⣿⣿⣿⢸⣿⣿⣿⣤⡀⠂⠀⠀⢠⣤⣿⣿⢸⣷⣦⡀⠀⠉⠳⠀⠀⣠⣾⣿⣿⠿⠀⠀⠀⣀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⢀⣀⠐⢲⣧⣤⣀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⣰⣿⣿⣿⡇⣿⣿⣿⠟⠛⣀⣀⠘⢿⣿⣿⣿⣿⢸⣿⣿⣿⣷⣤⣄⡀⠈⠋⠉⠁⠀⠀⢀⣴⣿⡟⣾⣿⣿⣿⠀⠀⠀⡀⠀⠀⣶⣿⣿⡸⣿⣷⣦⣌⠛⣛⣟⠂⢸⠷⣤⣀⣈⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠰⢤⠀⣴⣿⣿⣿⣿⡇⣿⣿⣿⣤⡀⠛⠏⣀⣠⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢰⣿⣿⣿⠇⣿⣿⣿⣿⣶⡆⠀⠀⣴⣾⣿⣿⣿⡇⣿⣿⣿⣿⣇⣁⠀⠙⠛⢶⠞⠛⠉⠁⢿⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢱⣿⣿⠏⠛⢁⣀⠸⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⡿⢰⣿⣿⣿⡏⠀⠰⣶⡆⠉⢹⣿⣿⣿⡇⣿⣿⣿⣿⣿⠏⢠⣀⠀⠈⠀⠀⠀⢰⣤⡀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣆⡀⠺⠿⠀⠀⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠰⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⠀⠀⢠⣶⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣴⣾⣿⠀⠀⠆⠀⠀⠀⣉⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⣾⣿⡿⠛⠃⡀⠀⠿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⠃⣿⣿⣿⣿⠁⠀⢰⣶⡌⠉⣻⣿⣿⣿⡇⣿⣿⣿⣿⣿⣇⠈⡉⣠⣾⣷⣤⣀⣀⣁⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⣿⣿⣇⡀⠸⠿⣇⣀⣼⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠏⣸⣿⣿⣿⣿⣿⡶⠈⠉⣠⣤⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢿⢁⣸⠯⠄⠀⣨⠍⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⢰⣿⣿⣿⣿⣿⡀⢡⣶⣶⠛⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠉⠑⣿⣿⣿⠀⢄⣀⡁⠀⠀
⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠸⣿⣏⢷⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣾⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⡀
⠓⠁⠉⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡏⣶⣦⣤⡄⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⢴⣆⠀⠀⠺⠀⠀⣴⡶⢀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠈⠛⠻⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⢩⣽⣿⣷⣌⡉⢉⣁⠉⢹⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣦⣤⣶⣶⣆⠀⠀⠰⠴⠀⠈
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠉⠛⠋⠱⠆⠀⠀⠒
⠀⢀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢙⡋⠋⠉⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⣤⡴⠤
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠟⠛⠿⠀⠀⠀⠀⠠⣀⣙⣀⠀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⢀⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡛⢿⠛⠆
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⢸⣿⣿⡇⠀⠀⠉⠉⠛⠛⢻⣿⣿⣿⣿⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⢸⣿⠿⠿⠿⠛⠛⢛⣰⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⣀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠙⢿⣿⣷⣶⣤⣄⣀⠀⢸⣿⣿⡿⣣⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣀⣀⣀⣤⣤⡤⠀⠀⣁⠈⣿⠏⠀⠀⢀⣾⣿⣯⣿⣿⣿⣝⣚⢻⣷⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠆⠀⠀⠀⠀⠈⠛⠻⠿⢛⣵⣾⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⢁⣴⣿⠀⠀⣠⣼⣿⣿⣿⣿⣿⡫⣶⢶⣿⣮⠛⢿⣿⣿⣿⣿
⣿⡿⠟⠛⠛⠛⣉⣡⣤⣤⣽⢿⣿⣿⠁⠀⠀⠛⢀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⢀⡾⠟⠋⠀⠀⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⣿⣿⣿⠛⠻⠛⠛⠛⠛⠿⠃⠀⠈⠟⠀⠀⠀⠀⠚⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢿⣿⣿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠄⣠⣀⠀⢿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠧⠁⠈⣿⣿⡇⠈⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠤⠤⠇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢸⠛⠁⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠈⠀⠀⣤⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⣾⡄⠀⠹⠟⠁⠀⠈⠻⣿⣿⣻⣯⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡀⠈⢀⡀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⣀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠛⢀⣠⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠛⠛⠛⠁⠈⠀⠈⣦⡀⠀⠘⠀⠈⢿⣿⣿⡇⠀⠀⢨⣿⣿⡏⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣾⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠆⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣤
⣠⠴⠾⠷⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠞⠀⠉⠋⠠⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠃⠀⠀⠀⠺⠇⠀⠀⠠⢀⡀⠀⡀⠿⣴⡿⠀⠰⣿⣿⣛⠀⠀⠣⠈⠛⠘⠻⠶⣿⡷⠶⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠈⠤⠠⠀⠈⠻⠀⠀⠶⠾⢂⡤⠀⠛⠀⠀⠀⢠⣶⣀⣀⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠈⡋⠀⠀⣾⡏⢨⣿⡿⢿⡁⠀⠘⠛⠛⠃⠀⠀⡀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀
⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡶⠀⠈⠈⢀⡀⠀⠀⢰⠋⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⢀⠀⠾⣫⠀⡈⠀⢠⣾⡁⠀⠀⠀⠀⠠⠀⠘⠏⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⣤⣄⣠⣾⣧⠀⠰⣧⡄⠀⢻⣷⡄⣠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠂⠀⠰⠿⠛⠾⠤⠄⠏⢹⠀⢄⣀⣨⣤⠄⠀⠐⢿⣇⣨⣾⣿⡏⠀⠀⠐⠆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⢤⢶⠶⠿⢿⡿⠿⠉⠉⢠⣤⣭⠀⡀⠀⠀⣰⣿⠟⠛⡉⠀⠈⣿⣿⣿⡏⠁⠀⠒⠿⣿⣷⡀⠀⠀⠉⠁⡄⠀⢠⠄⠋⠀⠀⠚⠻⠉⣄⠀⠠⠄⣿⠉⠻⠿⣿⣶⣦⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠟⠛⠻⠶⠄⠀⠀⠀⣻⡹⠤⠖⠒⢰⣿⣿⣾⣿⣭⣤⡾⠿⠿⠿⣷⣤⠐⠶⣤⣽⣿⡇⠀⠠⠖⠚⠀⠀⣴⠠⠚⠂⠀⠀⠀⠀⠀⠄⠀⠀⠋⢳⡄⠀⢛⣋⣻⣿⣿⡋⢻
⠀⠀⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠃⣠⣄⢀⢒⠣⠀⡀⠀⠠⠀⣾⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠄⠠⣴⣠⡤⠀⠀⠀⣠⢴⣿⣿⣷⣾⣿⣾⡿⠗⠚
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠵⠀⠀⠸⠀⣀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣷⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⢳⣄⠈⠉⢳⣻⣿⣿⠁⠐⠒⠛⢻⣹⡏⠻⠋⠙⠀⠈⠠⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⡀⣀⣀⣠⡄⠐⠀⠀⠀⠠⢒⣿⠂⠀⠀⢺⣿⣿⣿⣿⣧⣿⠃⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣆⡀⠀⠉⠁⢚⡵⣗⠄⢀⣿⠿⠿⠟⠛⡂⠀⠀⠈⡥⠄⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠿⡭⡽⢿⣟⣁⠀⠀⠀⢀⠀⠈⠉⠲⠂⠀⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠽⠿⢂⠰⠈⠃⠀⠀⠀⠈⠳⢦⣤⣐⠀⡄⠀⣀⣉⣰⢀⡀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠆⠀⠀⠙⠁⠂⠀⠀⠸⠇⠐⠢⠶⡟⢰⣿⣿⣿⣿⣿⣿⣿⣀⣤⣤⣀⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⡧⢤⣀⡀⠈⢙⣂⡘⠃⠤⢴⣦⠀⣀⣶⠎⠉⠉⠀⠀⠀⠉⣻⠿⠟⠋⢨⣿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⢹⣿⣿⣿⣿⣿⣿⠿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⡭⠉⠀⠀⣬⠼⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠁⣤⠄⠀⣴⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⢹⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⡿⣿⣿⣿⡃⠀⠀⠀⠉⠶⡚⠁⢹⣛⠃⠀⠴⣿⣦⢐⡀⠀⠀⠉⠉⠀⢠⣤⣄⠀⠈⠒⡴⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠛⠿⠁⠈⠀⠉⠁⠈⠿⢿⣿⣷⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠂⠡⠤⠄⠀⠈⠁⠈⠛⠁⠀⠀⡼⡇⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠈⠉⠀⠱⣤⣤⣿⣿⠿⠿⣟⣿⣿⣿⣿⡿⠛⠛⢿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⢿⣿⣿⢷⣶⣤⣀⡀⠀⠀⠀⠀⠐⠲⢤⠒⠒⠰⣂⠰⡀⠸⣷⠆⠀⠀⣠⠀⣸⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠒⠲⠿⠄⣀⡀⡲⣿⣿⠋⠉⠀⠀⠛⠋⠁⠀⢿⡇⠀⠀⠘⠿⣿⡂⠀⠀⠀⠀⠀⢀⣴⣾⠏⠀⠀⠘⡿⣸⣿⣿⠂⠈⠉⠑⢦⣾⣶⣶⡔⠦⠤⡾⠋⠀⢥⠴⠇⢰⣆⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣿⣧⣿⣿⣶⠀⠀⢀⠀⠀⠀⠀⣸⣿⢰⣄⡀⠀⠙⠿⡄⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⣷⣿⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠀⠀⠀⣴⠂⠀⠒⠀⠹⣤⣤⠤⠤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⣸⣿⣿⣿⢸⣿⣿⣿⣿⠆⠀⠀⣤⣼⣿⣿⣿⢸⣿⣿⣦⣄⣀⠀⠀⠰⠿⠟⠛⠉⠁⠀⣀⣴⣼⣿⣿⣶⡆⠀⠀⠀⠀⠀⣀⣸⣿⡇⣶⣤⣄⡀⢿⣶⣤⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⢠⣿⣿⣿⡿⣼⣿⣿⠃⠀⢴⣶⠀⠈⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⢠⣾⣿⡿⢸⣿⣿⣿⣧⣄⠀⠀⢀⣀⣿⣿⣿⣧⣿⣿⣿⣿⣶⡉⣩⠯⣁⣸⠟⢲⡄⠠⠤⣄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⣲⣿⣿⣿⣿⡇⣿⣿⣿⠿⠇⠀⠀⣴⣾⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⠇⣾⣿⣿⣿⠉⠈⣠⠄⠘⠛⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⣤⠀⠀⠉⢹⠋⠉⠀⠀⠸⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢣⣿⣿⡇⠀⠰⠒⠀⠉⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢸⣿⣿⣿⢀⣿⣿⣿⣿⣶⡆⠈⠀⣄⣤⣿⣿⣿⣟⢸⣿⣿⣿⣿⡟⠀⠤⣤⠀⠀⠀⠀⠄⠐⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⠿⠇⠀⠀⢴⣦⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⡏⢸⣿⣿⣿⡟⠁⠀⣤⡀⠛⢻⣿⣿⣿⡟⢸⣿⣿⣿⣿⣧⠰⣶⣿⠀⠀⡃⠀⠀⠀⣠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣟⠀⢠⣶⡆⠀⢸⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠁⣾⣿⣿⣿⣷⣴⠀⠉⠁⣀⣼⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣶⣀⣀⣀⡽⢿⣶⠤⠤⣤⣄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡏⢸⣿⣿⡟⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⡏⠉⣤⣤⠜⠻⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡟⣿⡿⢻⣀⣰⠓⠄⠀⠰⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⢸⣿⣿⢠⣤⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⠉⠉⠀⣤⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⡅⠀⠀⢿⠿⠿⠁⠢⠤⠤⠀⠀
⠀⠀⢀⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣮⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⢡⣤⣄⣀⢻⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠿⡏⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠉⣛⣿⣿⣮⠙⠛⠋⠘⢻⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣧⡀⠰⡷⠀⠀⠘⠀⠀⠰⠿⠦
⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⡷⠶⣾⣿⣯⣀⠀⠈⠒⠂⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⢻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⠉⠉⠘⠃⠀⠀⠈
⠀⠀⠤⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣷⡄⢸⣿⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠰⣷⠚⠒
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡁⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⢀⣄⣄⣤⡀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⠋⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⠀⣿⣿⣿⣿⠿⠿⠿⢃⣾⣿⣇⣀⠈⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠾⠍⢰⠉⠓
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣤⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⣣⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣿⣿⣿⣆⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀
⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣶⣦⣾⡿⢟⣵⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢀⣀⣠⣤⡄⠈⢉⡁⢹⣿⠁⠀⠀⡀⠀⣀⢀⣠⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣤⡀⠀⠀⠘⠿⣿⣿⣿⣿⠿⣫⣴⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠚⢠⣿⣿⠆⠀⠀⢠⣾⣿⣿⣿⣿⣿⢝⣚⠻⣥⣼⣿⣿⣿⣿⣿
⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠁⡄⠀⠀⠀⠀⠀⠈⠁⠘⠛⠻⣿⣿⡇⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⠿⠿⠿⠋⠁⠀⠀⠀⠀⣠⣿⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡯⣶⢶⣿⣌⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣿⣿⢿⣧⢻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⢹⣿⣿⠿⠿⠟⠛⡟⠛⡿⠛⠛⠻⡟⠂⠀⠀⠘⠀⠀⠐⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⠛⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⡿⠀⢰⣶⣷⣄⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⢸⣿⣟⠀⠀⠀⠀⡇⠀⡇⠀⠀⣀⣠⠀⠀⢠⠀⠀⠀⠀⢰⠀⠘⠀⠀⢴⣶⣤⠀⠀⠀⠀⠀⣀⣿⡏⠀⠀⠀⠀⠀⠀⣀⠀⠀⡆⠀⠘⠀⢸⠀⠀⠀⠀⠀⠀⣻⡟⠛⠛⠋⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⢸⣿⣿⠀⠀⠀⠀⠇⠀⡟⠂⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⢸⠓⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠈⣿⣇⠀⢀⠀⠀⠀⠀⣿⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠿⠿⠶⠦⠀⠻⣿⣿⣻⣭⣽⣿⣿⣿⢯⡄⠀⠀⠀⠀
⣾⣿⠉⠀⣀⡄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⢀⡀⠀⠀⠉⢹⣿⠀⠀⢀⠀⠀⢀⣿⣿⠀⠈⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⢷⣄⡀⠀⠀⠀⠈⠛⢿⣿⣿⡿⢿⣷⣿⣧⠀⠀⠀⠀
⠙⣿⣿⣿⣿⣿⠃⠛⠛⢿⢷⠀⠀⠀⣿⡄⠀⠁⠀⠀⠛⣿⣿⠁⠀⠀⣾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⢃⣷⠀⠀⠀⠀⠀⠈⠀⠀⡾⢃⠀⠀⠀⠀⠈⠁⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣤
⣤⠶⣿⡿⠆⢀⣄⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠚⠁⠉⠋⢀⠶⠀⠈⠀⠀⠀⠇⠀⠀⠀⠀⠈⠁⠀⠀⠠⠺⢟⣄⠀⡤⢂⣀⠀⡀⢻⣶⣿⠀⠠⣿⣟⣛⠀⠀⠳⠈⠙⠑⠻⠷⣿⠷⠿⠧⠄⠐
⠀⠀⠀⠀⠀⠬⠍⠀⠀⠀⠀⠄⠀⣀⠀⢀⡼⠉⠢⠄⣀⠀⠻⠃⠠⠶⠞⢒⡇⠌⠉⠁⠀⠀⠠⢼⣆⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠘⠋⠀⠀⣺⡏⢸⡿⢿⢻⠄⠀⠺⠻⠟⠋⠀⠀⣀⠀⠀⢀⡀⠘⠀⠀⠀⠀⠀⠀
⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠶⠶⠄⠈⠉⢀⠤⠐⠒⢰⠋⠁⢀⡀⠀⠂⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⢠⠠⠾⢻⢀⡌⠀⣠⣶⡕⠀⠀⠀⠀⠦⠀⠘⠿⡀⠀⢠⣦⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⣠⣴⣤⣰⣼⣷⠀⠘⣧⡴⠀⢸⣷⡄⠀⣴⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠻⠿⠛⠻⠶⠆⢟⢹⢀⣤⡈⣭⣧⡄⠀⠰⢿⣧⣼⣾⣿⡏⠀⠂⠰⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠶⣾⠿⣿⢿⠿⠿⠉⠋⢡⣤⣭⠧⡀⠀⠀⢠⣾⣿⢛⣉⣉⠀⣸⣿⣿⣿⠋⠀⠐⠺⣿⣿⡄⠀⠀⠉⠁⡤⠀⢠⠆⠋⠀⠀⠚⠛⠡⣤⠄⠲⠄⣿⠋⠻⠿⢿⣶⣶⡠⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠟⠋⢻⠶⠆⠀⠀⠀⣹⡰⠤⠗⠒⠐⣿⣿⣿⣿⣯⣤⣾⠿⠛⠛⠻⣷⣖⠲⢦⣬⣿⣿⠀⠀⠖⠛⠀⠀⠴⠀⠚⠒⠀⠀⠀⠀⠀⠐⠀⠀⠛⢳⡖⠀⢙⣩⣽⣿⣿⡙⢻
⠀⠀⠀⠤⠤⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠛⠿⠷⠌⣠⣤⢰⣞⠳⠀⣀⠀⠠⠄⢰⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠄⠐⣶⣠⡴⠂⠀⠀⣠⣼⣽⣿⣷⣾⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⢗⠂⠀⠸⠆⢀⠀⣾⣿⣿⣿⣿⣟⣿⡿⠛⠛⠛⠻⣿⣧⣿⣿⣿⣿⣿⡆⠀⠀⢀⠀⠐⢻⣤⡀⠈⢳⣿⣿⣿⠁⠖⠚⠋⢻⣹⡏⠛⠁⠙⠁⠀⠀⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣠⣀⣀⣀⣠⡤⠀⠀⠀⠀⣤⢚⣿⡃⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠸⢴⣷⠂⢀⣽⡿⠿⠟⠉⡦⠄⠀⠠⠄⠄⠀⢈⠁⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⡻⠿⠭⠼⢿⣟⡁⠀⠀⠀⢠⠁⠈⠉⠒⢂⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠽⠿⠃⠀⠀⠊⠀⠀⠀⠈⠛⢦⣤⣄⠀⣄⠀⣠⣈⣰⢀⡀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠐⠂⠗⠀⠀⠉⠁⠒⠀⠀⠘⠷⠀⠂⠖⡟⠀⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡶⢦⣠⡄⠀⣉⣃⡒⠉⠤⢴⣶⠀⣀⡷⠎⠉⠉⠈⠁⠀⠈⣹⠿⠟⠋⢠⣿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⡀⢤⡐⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⣿⣿⣿⣿⣿⣍⣉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡬⠉⠀⠀⣬⠼⠀⠀⠀⠀⣀⣦⠄⠈⠀⠀⠁⣤⠤⠁⣴⣯
⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠆⠀⢀⠀⠀⢩⣷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⢾⡿⠿⢸⣿⣿⡏⠀⠀⠀⠈⠲⡋⠉⢸⣛⠁⠀⢤⣿⣧⠐⡀⠀⠀⠩⠁⣀⣤⣶⣦⠀⠀⢳⡼⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠈⠙⠆⠁⠤⠄⢄⠈⠁⠈⠋⠁⠀⠀⡾⣇⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡈⣀⡌⠁⠀⠐⡤⣴⣿⣿⠿⠿⣿⣿⣿⣿⣿⡟⠛⠋⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠻⣿⣷⣶⣦⡀⢂⡀⠀⠀⠀⠘⠒⠲⠉⠑⠚⣂⠰⣀⠚⠿⠆⠐⠄⢠⠄⣸⠀⠀⠀⠀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠻⠓⠒⠻⠇⣀⣀⡚⣿⣿⠁⠁⠀⠀⠉⠉⠀⠘⢻⣇⠀⠀⠈⠛⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⢸⣸⣿⡿⠓⠀⠉⠙⢲⣿⣷⣿⡞⠧⠶⠾⠉⠀⢵⠾⠇⠸⣦⡀⠀⠀⠁⠀⠀⠀⠀
⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⢿⣿⣿⣷⣀⠀⠀⡀⠀⠀⣀⣼⣿⢰⣦⣀⠀⠈⠙⠦⠀⠀⢀⣴⣿⣿⣿⠇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡆⠀⠀⠀⠀⢶⠊⠖⠒⠀⠙⡦⠤⠶⠤⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠚⠀⠀⠀⣼⣿⣿⣿⢸⣿⣿⡿⠿⠇⠀⠠⣶⣼⣿⣿⣿⢸⣿⣿⣷⣦⣄⣀⠀⠀⠛⠛⠉⠁⠀⢀⣠⣶⣧⣿⣿⣿⡆⠀⠀⣀⠀⠀⣤⣼⣿⡇⣷⣶⣤⣭⣿⣶⣤⣤⡄⢀⡀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠞⠂⠀⠀⠀⣰⣿⣿⣿⡟⣾⣿⣿⣁⡀⠾⠿⠀⢈⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣾⣿⣿⢸⣿⣿⣿⣷⢦⠀⠀⢠⣴⣿⣿⣿⡇⣿⣿⣿⣿⣧⠉⣭⠯⣅⣘⡛⢲⣦⣤⡤⢆⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⢲⣿⣿⣿⣿⡇⣿⣿⡿⠿⠃⡀⠀⣾⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⡇⣾⣿⣿⣿⠀⠀⣶⣦⠈⠉⣿⣿⣿⣯⢿⣿⣿⣿⣿⣤⣤⡀⠀⠉⢹⠋⠉⠀⠀⠸⠇⢠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣿⣿⣿⣿⣿⢁⣿⣿⣇⡀⠐⠿⠀⠀⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠠⣿⣿⣿⢀⣿⣿⣿⣿⣷⠇⠀⠀⣴⣶⣿⣿⣿⡟⢸⣿⣿⣿⣿⠛⠀⠷⣴⡄⠀⠀⠀⠂⠘⢶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⣿⠿⠃⠀⠀⠾⣶⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⡏⢸⣿⣿⣿⡏⠀⠀⣶⠆⠈⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡗⠰⢶⣾⠀⢀⡋⠀⠀⠀⣤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢾⣿⣯⣀⠰⢿⣇⠀⣸⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⣿⠁⣾⣿⣿⣿⣿⣿⠂⠀⢠⣦⣾⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣀⣤⣤⡿⢿⣶⠤⠴⠤⣔⣻
⠀⠀⠀⠄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⢸⣿⣿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⣇⣀⠶⠶⠊⠉⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠛⣻⡿⣹⣡⣰⠳⠂⢀⡴⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠘⣿⣿⢰⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⡎⠀⠀⢻⠟⠟⠉⠒⠶⠦⠀⠀
⠀⣀⡠⡄⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡄⣿⣿⣶⣭⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⢰⣶⣶⡶⢸⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠀⠀⢀⠈⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠀⠛⠛⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⣼⣿⣿⣗⣈⣁⣀⡄⢈⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣧⡀⠰⠟⣀⣀⠈⠀⠀⠺⠻⠦
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⢾⣿⣧⣀⡀⠈⠛⠂⢀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⡉⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⣤⡤⠉⠀⠈⠃⠀⠀⠀
⠀⠀⠖⠂⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠀⠀⠀⠀⠐⣿⠋⠓
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⠸⢿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⢰⣤⡤⣦⡄
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⡇⠀⠈⠉⠉⠛⠛⠛⣿⣿⣿⣿⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡄⠿⠿⠿⠛⠛⠛⠉⣡⣾⣿⣧⣤⠀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠇⢰⠉⠘
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣷⣶⣤⣤⣀⣀⡀⢠⣿⣿⡟⣱⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠂
⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⣾⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣀⣤⣤⣴⣶⡞⠀⢀⡤⢸⣿⠇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣰⣦⡀⠀⠀⠁⠈⠹⠟⠛⠿⢛⣵⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠈⢠⣾⡟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣝⣚⠻⣥⣼⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⠁⠈⢰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠙⠟⠃⠀⢸⣹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠿⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⣰⠿⠛⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡯⣶⢶⣿⣌⠛⢿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠇⠀⠀⠀⣾⣿⠦⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⣠⣾⣧⣿⣿⣿⣿⣿⣿⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⣿⣿⣿⠿⢿⠿⠿⡿⠛⡿⠛⠛⠃⠜⠀⠀⠀⠛⠃⠀⠘⠛⠻⢿⠖⠂⠀⣀⠀⠀⠀⠀⠛⠛⢿⣿⡿⠛⠛⠿⢏⠀⠀⠀⠀⠀⠀⠀⢀⠐⢲⠀⠀⠀⠀⠃⠀⢹⣿⣿⣇⢿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀
⣿⣿⣿⠀⢸⠀⠀⡇⠀⡇⠀⠀⢀⣠⠀⠀⢠⡀⠀⠀⠀⢰⠀⠈⠀⠀⢶⣿⣿⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠈⠀⠀⣶⠀⠀⡇⠀⠘⠀⢸⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⣿⣿⣿⠀⢸⠀⠀⡇⠀⡿⠦⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠛⠓⠀⠀⣠⣿⣿⠀⠀⠀⠄⠀⠈⣿⣷⠀⢠⠀⠀⠀⠀⣿⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⢀⣴⠆⠀⢳⣷⣾⠈⠻⣿⣿⣻⣭⣽⣿⣿⣿⢯⡄⠀⠀⠀⠀
⡿⣻⡉⠀⣸⣄⠀⠀⢀⣇⡀⠀⠀⠀⠀⠀⠀⡇⠀⠰⡀⠈⢀⣸⠀⠀⠈⢹⣿⠀⠀⠀⠀⠁⣀⣿⣟⠀⠈⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⡀⠀⣸⡟⠛⠂⠀⠈⠛⢿⣿⣿⣿⣿⣷⣿⣧⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⠷⠀⣷⡄⠀⠁⠀⠀⢸⣿⣿⣿⠀⠃⣽⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠘⠋⣸⠓⢀⣿⡟⠓⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⣤⠶⠿⠿⠇⢀⠄⠌⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠙⠚⠃⠀⢉⢰⡶⠂⠀⠀⢀⠀⠠⠀⠀⠀⢀⠈⠁⠀⠀⠐⠛⢛⣤⠀⠀⢢⣄⠀⣀⣛⣷⡿⠀⢀⣿⣿⣛⡁⠀⠹⠀⠉⠉⠛⢻⡿⠿⠿⠧⠐⠐
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠰⠀⠤⠄⢂⡀⠉⠓⠀⢀⡀⡙⠃⠀⠴⠞⡃⡵⠪⠉⠁⠀⠀⣄⣈⣃⣀⣀⣀⣀⣀⡀⠀⠀⢀⡀⠀⠈⠍⠀⢀⣼⡏⢠⡿⠿⢿⡆⠀⠘⠛⠛⠙⠁⢀⣤⡄⠀⠠⠤⠈⠀⠀⠀⠀⠀⠀
⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠾⠆⠀⠀⠁⡄⠐⠒⢒⡟⠁⢀⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠁⠀⢀⢀⠀⠚⣻⣅⡞⠁⢰⣶⡟⠀⠀⠀⠀⠣⠄⠘⢿⢃⣀⣰⣷⣤⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢃⠀⣠⣤⣦⣰⣾⣿⡄⠀⣿⣴⠀⠸⣿⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠛⠉⠉⠝⣛⡋⠛⠶⠆⢻⢹⡣⠦⢬⣵⣶⣦⠀⠈⠻⣿⣤⣾⣿⣯⣀⠃⠐⠇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠶⠾⠟⣻⣻⡿⠿⠁⢀⣈⣤⣯⡄⢄⠀⢠⣾⡿⠛⠛⠈⢹⣿⣿⣿⠉⠀⠐⠚⢿⣿⣷⡀⠀⠀⠀⠀⢁⡔⠀⢠⠆⢂⡀⠀⠘⠛⠃⢤⠆⠐⠂⣽⡋⠙⠛⢻⣿⣷⣄⣄⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡟⠋⢙⠟⠒⠲⠁⠀⢸⡇⠓⠛⠚⣾⣿⣾⣿⣩⣴⠿⠿⠿⠿⣦⣀⠲⠶⣤⣽⣿⡇⠀⠀⠐⠒⠙⠁⠀⠼⠂⠚⠓⠂⠤⠀⠀⠀⠒⠂⠀⠉⢹⣖⣀⡩⢥⣽⣾⣿⣝⠻
⠀⠀⠀⠰⠦⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠛⠻⠟⠓⢠⡶⠤⡆⠝⠂⢠⠀⠐⢲⣿⣿⣿⣿⣿⣧⣤⣄⣀⡀⢘⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣂⠀⢦⣴⠒⣐⣶⣴⡶⠂⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠖⠀⢛⠂⡀⠐⠇⢀⣿⣿⣿⣿⡿⣿⣿⠿⠛⠛⠿⣿⣧⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⠘⣙⣦⠀⠀⣩⣿⣿⣿⣁⠂⠉⠉⢹⣭⠯⠙⠉⡘⠀⠀⠀⢢⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⣀⣠⣄⣠⣤⣤⡤⠀⠀⠀⠀⢰⠚⣿⣃⠀⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣾⣿⣿⣿⣿⣿⣦⣄⠀⠀⠈⠀⣨⣟⣿⠂⠀⣼⠟⠛⠛⢉⣒⠶⠀⠐⠒⡒⠀⢨⣁⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡹⠻⠥⠾⠿⣿⣩⠀⠀⠀⢠⡀⠀⠉⠀⢋⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⣟⠁⠀⡁⠁⠀⠀⠀⠀⠛⠳⣦⣴⡁⡔⠀⣠⣉⣴⣠⡀⢴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠒⣒⠀⠀⠉⠉⠀⠀⠀⠀⠛⠀⠁⠚⡟⢼⣿⣿⣿⣿⣿⣿⣠⣶⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠶⢦⠄⠀⢨⣥⣊⡉⠐⢲⣶⠀⠠⠿⠗⠈⠁⢀⣀⠀⠀⣩⠿⠛⠋⠐⣿
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⡂⢠⠐⠀⠀⠀⠁⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⡀⠀⠀⠀⢰⣖⠀⠀⠀⢴⡞⠀⠀⠀⠀⣤⣶⠆⠀⠀⠀⠀⢶⠲⠀⣲⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠹⢿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⡿⠿⠶⣿⠿⠛⢿⣿⣿⣟⠀⠀⠀⠀⠀⠛⢏⠑⠸⠯⠁⠀⢠⢿⣷⠐⡄⠀⠀⠀⠀⡀⢰⣶⣶⠀⠀⢙⡟⢣⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡟⠉⠙⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣦⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠂⠀⠒⠂⢆⣈⠑⠄⠉⠁⠀⠀⡾⣇⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠄⢠⡤⠀⠀⠀⣰⣶⣿⣿⡿⢷⣾⣿⣿⣿⣿⡿⠿⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡭⠿⣿⣿⡏⣶⣶⣄⣠⠂⣀⠀⠀⣀⠈⠙⠛⡀⠉⠘⣧⠸⣤⠘⡿⠇⠀⠂⠰⠄⢰⡀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠤⠀⠀⠙⠋⠙⠛⠷⢠⣤⢘⣿⣿⠋⠉⠀⠀⠛⠛⠉⠸⢿⡇⠀⠀⠙⢿⣷⠀⠀⠀⠀⠀⠀⣠⣿⡯⠀⠀⠀⢻⡇⣿⣿⡟⠟⠋⠉⠑⣶⣿⣶⣾⠛⠓⠒⠿⠁⠀⢶⡟⠋⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⣿⣿⣶⠀⠀⣀⡀⠀⠀⣀⣼⣧⢣⣄⠀⠈⠛⢷⡀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⣸⣾⡿⠀⠀⠀⠀⠀⠀⠀⠛⣿⣷⠀⠀⠀⠀⠀⢰⠃⠛⠘⠃⠈⠶⠶⠒⠖⠀⠤⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠙⠀⠀⠀⢀⣿⣿⣿⢻⣿⣿⣿⠿⡏⠉⠠⣤⣼⣿⣿⣿⢸⣿⣷⣦⣄⡀⠀⠀⠼⠟⠛⠋⠁⠀⢀⣤⣾⢿⣿⣿⣶⠀⠀⠀⠀⠀⠀⣤⣿⣿⢸⣿⣶⣤⣬⠿⣷⣆⣶⡆⢀⣤⠀⠀⠠⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⢀⣾⣿⣿⣿⢸⣿⣿⠇⠀⠼⣿⠂⠉⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⣴⣿⣿⡏⣾⣿⣿⣿⣦⡆⠀⠀⣠⣴⣿⣿⣿⡿⣿⣿⣿⣿⣦⠉⠤⠓⠤⣬⣏⣹⣧⠰⡶⢧⡤⠅
⠂⠀⠀⠀⠀⠀⠀⠈⠙⠓⢰⣿⣿⣿⣿⡏⣿⣿⣿⠿⠟⠀⠀⣶⣾⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⠃⣿⣿⣿⡿⠀⠀⣤⡄⠉⢹⣿⣿⣿⡇⣿⣿⣿⣿⣿⣶⡶⡄⠀⠈⢹⠇⠈⠀⢀⠘⠃⡈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⡇⠀⠠⠿⠃⠈⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⠆⠁⢀⣤⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⡉⠁⠻⢶⠆⠀⢀⠀⠂⠈⠿⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢣⣿⣿⠿⠿⠀⠀⣾⣶⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠹⣿⣿⡇⣸⣿⣿⣿⡏⠀⢰⣶⠀⠉⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣟⡘⠷⢿⠅⢠⣍⠀⠀⠀⢴⢂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢸⣿⣿⣀⣰⣿⡦⠀⣸⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢻⡿⢠⣿⣿⣿⣿⣿⣶⠀⠀⢰⣴⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⠻⡿⠒⠒⠒⠶⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢸⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢁⣾⣿⣿⣿⣿⣍⠁⣶⣶⠈⢙⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⡉⡽⠟⣩⣥⣼⡛⠂⠠⠜⠉⠁
⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠈⣿⣿⢰⣶⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⠟⠛⠉⢁⠒⠒⠀⠀
⠀⣤⠔⠦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⢻⣿⣷⣭⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⢶⣶⣶⡆⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⣄⠀⠀⢠⠈⠀⠀⣐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠈⠛⠟⠀⠀⠀⠀⣰⣿⣿⣿⣿⣏⢠⣭⣿⣿⣖⣉⣁⣠⠀⢸⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⡦⠈⢛⣉⣥⠀⠀⢀⣘⠙⠓
⠀⠀⠀⠀⠀⠀⠈⠃⣾⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⠿⠿⣷⠶⢄⡀⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⠁⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢶⠶⠀⠀⠈⠁⣀⣀⡀
⠀⠀⠘⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢸⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠿⠁⠉
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⠉⠁⠈⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣁⠉⠛⠛⣿⣿⣿⣿⡿⠟⠛⠿⠄⢀⣀⣀⣸⣶⠖⣷⣆
⠀⠀⢀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⠀⠀⠉⠉⠛⠛⠻⣿⣿⣿⣿⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⠿⠛⠛⠋⠉⠉⢠⣾⣿⣿⣿⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⠸⠀⠉
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⢿⣶⣦⣤⣄⣀⡀⢀⣿⣿⡿⣣⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⡗⠀⠀⠀⠀⠀⡀⠚⠋⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁
⠶⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⣋⣷⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣷⣤⣶⣶⣿⡿⠀⠀⠎⢠⣿⠇⠀⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⠀⠀⠀⠈⡿⠿⠿⢟⣯⣾⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣝⣚⠻⣵⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⣄⠄⠀⠀⠀⠀⠀⠉⠉⠙⠟⠃⠀⢸⣹⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠛⢋⣴⠀⢀⠀⣠⣼⣿⣿⣿⣿⣿⣯⣶⢶⣿⣎⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢸⡿⢷⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⢴⣿⣧⣿⣿⣿⣿⣿⣿⣽⣿⣷⣾⣿⣿⡆⠀⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠛⠛⡿⠿⡿⠟⠛⠻⡟⠛⠛⠛⠀⠀⠀⠘⠛⠻⢿⠟⠓⠀⣀⡀⠀⠀⠀⠛⠛⢿⣿⡿⠛⠛⠿⢯⠀⠀⠀⠀⠀⡀⠀⢴⠛⢻⠂⠀⠀⠸⠟⠱⢾⣿⣿⣇⢿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢀⣠⡄⠀⣤⡄⠀⠀⠀⢰⠀⠈⠀⠀⢶⣿⣿⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠘⠀⢸⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡗⠦⡀⠀⢻⡇⠀⢿⡇⠀⠀⠀⢸⠛⠓⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠈⣿⣷⠀⢠⠀⠀⠀⠀⣿⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⡆⠀⣠⣼⣟⠈⠻⣿⣿⣻⣯⣽⣿⣿⣿⢫⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⢀⣇⡀⠁⢀⣼⡇⠀⣸⡇⠀⢠⡀⠈⢀⣸⠀⠀⠀⢹⣿⠀⠀⠀⠀⠁⣀⣿⣏⠀⠈⠀⠀⠀⠀⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣠⣀⣿⠟⠛⠀⠀⠈⠛⢿⣿⣿⡿⢿⣷⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⠛⢻⣿⣿⣿⣿⣿⠿⢿⢿⣧⣄⠀⠀⠹⣿⣿⠀⢁⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡿⢸⣿⡀⠀⠀⠀⠀⠀⠁⠀⠉⣜⠉⢿⣿⡇⠒⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⠤⠖⠿⠿⠃⠐⣂⡈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠉⢛⡀⠀⢉⣀⡺⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⢋⣤⠀⠐⢢⡤⠀⣀⣙⣷⠿⠀⢀⣿⣏⣭⡀⠀⠙⠀⠉⠉⠙⢛⠿⠟⠛⠓⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠄⠀⡌⠉⠓⠀⢂⣀⡘⠋⠀⠚⠛⣁⣷⠢⠈⠀⠀⠀⠄⣨⣡⣤⣤⣤⣤⣀⣀⡀⠀⠀⡀⠀⠈⠅⠀⢠⢼⡏⢠⡿⠿⠛⡆⠀⠘⠉⠛⠙⠀⢀⣤⡄⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀
⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠾⠂⠀⠀⠀⡄⠐⠒⢐⠏⠀⢀⣀⠀⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠁⠀⣀⣀⠂⣛⣱⣆⡮⠀⢠⣾⡏⠀⠀⣀⡀⠓⠀⢈⣫⣢⢀⢰⣷⣤⠄⠀⠀⡀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠃⢀⣠⣤⣦⣴⣾⣷⡄⠀⣷⡶⠀⠸⠿⠇⢠⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠈⢛⣉⠙⠛⠋⠻⢸⡀⠶⢦⣴⡿⠖⠀⠘⠛⣿⣴⣾⣿⣯⣀⠁⠘⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠾⠿⡛⣻⣻⡿⠛⠁⢀⠈⣴⣿⡖⠄⠀⠀⣰⣿⡿⣋⣉⠁⢀⣽⣿⣿⡏⠀⠀⠚⠻⣿⣧⠀⠀⠀⠀⢀⡔⠀⠠⠇⢀⡀⠀⠈⠉⠁⠴⠂⠙⠃⢹⡁⠈⠛⢻⣿⣿⢦⣂⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡟⠉⢙⠟⠒⠐⠀⣀⠸⠥⠓⠛⠙⢺⣿⣿⣿⣿⣭⣴⡾⠛⠛⠛⠿⣦⡙⠲⢶⣼⣿⡇⠀⠐⠋⠉⠁⠀⠚⠀⠋⠁⠀⠀⠀⠀⠀⠒⠀⠀⠉⢸⣧⣀⡨⢵⣾⣿⣿⣍⢹
⠀⠀⠀⠐⠖⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠠⡶⠠⡎⠍⠂⢠⠀⠐⠂⣼⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⣀⣘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠲⣴⡆⣀⣿⣶⡶⠃⢀⣀⣤⣶⣾⣿⣿⣿⡿⠿⠟⠛⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢛⠀⣀⠘⠃⢀⢠⣿⣿⣿⣿⣿⢻⣿⠟⠛⠛⠛⠻⣿⡼⣿⣿⣿⣿⣷⠀⠀⠀⢀⣤⢈⡹⣷⠄⠀⣩⣿⣿⣿⣄⠋⡉⠉⠹⡽⠏⠉⠁⡈⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠒⣀⣰⣤⣠⣤⣴⣶⠀⠀⠀⠀⠰⠊⣽⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⣨⣿⡿⠅⠀⣼⠟⠛⠛⢀⣚⠒⠀⠐⠂⠂⠀⠠⢄⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠛⠧⠾⠛⣿⣥⠀⠀⠀⠰⡀⠀⠀⠉⢩⢀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠚⣛⡁⠀⣁⠁⠀⠀⠀⠀⠉⠙⣶⣶⢄⡤⠈⢬⣤⣴⣠⣄⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠚⠀⠀⠈⠁⠈⠀⠀⠀⠛⠀⠁⠋⠿⠸⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠒⠳⠶⠦⠀⠠⢥⣍⡀⠐⢺⢿⠀⠤⠟⠓⠀⠀⠤⣀⠀⠀⣸⠛⠋⠉⠰⣿
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣖⡀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣭⣉⠉⢙⣿⣿⣿⣿⣿⣿⠿⠇⠠⢄⠀⣀⡀⢰⣖⣀⠀⠀⢸⡞⠀⠀⠀⠀⣤⡶⠆⠀⠀⠀⠀⠶⡒⠀⡾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠿⠛⢿⣿⣿⡀⠀⠀⠀⠀⠙⢭⠘⠈⠯⠀⠀⢰⠻⣷⠨⡔⠀⠀⠐⢂⡤⢰⣾⡷⠀⠀⢉⡞⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⡤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⠿⠋⠁⠉⠁⠀⠀⠀⠀⠀⠿⣿⣿⣷⣒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⠀⡈⢃⠀⠘⠀⢦⣄⠀⢀⠁⠀⠀⠀⠞⠧⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⢀⡀⠀⠀⠀⣲⣶⣾⣿⡿⠿⢿⣻⣿⣿⣿⣿⠛⠋⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⢿⡿⣿⣿⣦⡄⢁⣀⡀⠀⣠⠈⢉⣙⡀⠈⢈⣧⠘⠤⠉⡻⢃⡀⠂⠰⠂⡸⠀⠀⠀⠀
⢀⠀⡄⠀⠀⠀⠠⠀⠀⠙⠉⠉⠙⠓⣠⣴⣈⢹⣿⡏⠉⠀⠀⠛⠋⠁⠀⠻⣿⠀⠀⠀⠙⢿⣇⡀⠀⠀⠀⠀⢠⣼⣿⠃⠀⠀⠀⣧⣿⠿⠟⠛⠀⠀⠙⠿⣿⣿⡿⠈⠙⠛⠻⠁⠀⠺⠟⠃⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⣶⣿⣿⣿⣷⡆⠀⣀⣀⠀⠀⣀⣰⣿⡸⣶⣄⡀⠀⠙⠳⠄⠀⢀⣼⣿⣿⠿⠀⠀⠀⢀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⢀⠀⠀⠀⢀⢹⠁⠉⠉⠁⠈⠛⠒⠋⠓⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠉⠁⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⠿⠿⠀⠀⣶⣶⣿⣿⣿⡇⣿⣿⣿⣶⣤⣄⡀⠀⠛⠋⠉⠀⠀⢠⣴⣾⢻⣿⣿⣿⠀⠀⢠⠄⠀⠀⣶⣿⣿⣸⣿⣷⣦⣴⢻⣿⣦⣷⡄⢀⣤⡀⠀⠠⠄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⢉⠀⠀⠀⢀⣼⣿⣿⣿⢇⣿⣿⣟⡀⠰⠿⠃⠀⣻⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⡿⣸⣿⣿⣿⠷⠆⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠐⠛⠲⣶⣏⣹⣓⠲⠞⢲⡄⠒
⠂⠀⠀⠀⠀⠀⠀⠈⠉⠋⢸⣿⣿⣿⣿⣿⢸⣿⣿⠿⠻⠁⠀⣰⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⠃⣿⣿⣿⣟⠀⠀⠶⠆⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡚⡆⠀⠀⠸⠁⠀⠀⢀⣉⡃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢸⣿⣿⣀⠀⠸⠇⠀⢸⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠠⣿⣿⣿⢰⣿⣿⣿⣿⠿⠇⠀⠀⢾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⡀⠀⠉⢻⠆⠀⣀⠀⠁⠀⠻⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣼⣿⡿⠿⠃⠀⠰⣾⣾⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢹⣿⡇⣸⣿⣿⣿⣇⡀⠨⠿⠀⠀⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣏⣜⠛⠿⠀⣠⣤⡀⠀⠀⠶⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⣿⣿⣇⡀⠾⢿⡀⢀⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⡿⢠⣿⣿⣿⣿⣿⠿⠀⠀⢰⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡞⠛⡿⠓⠛⠒⡮⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢁⣾⣿⣿⣿⣿⣧⡄⠿⠿⠀⣨⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⡠⠿⠋⣼⣶⣾⣉⡁⠠⠎⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⠸⣿⡇⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠰⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⠋⠉⠀⢡⠉⠁⠀⠀
⠀⠤⠔⠲⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⣿⣿⣶⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⢿⣿⣿⡹⠿⠿⠇⠿⢿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⡄⠀⢀⣄⢀⠀⢠⠀⠀⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠉⠛⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⣶⣿⣿⣯⣤⣤⣴⡆⢸⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣷⠄⢁⣉⣥⠤⠄⠀⢀⣹⡙⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⡿⢐⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠙⠛⠷⠶⢤⡠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡄⠸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠗⠒⠶⠒⠀⠀⠀⢠⣤⣠⣀
⠀⠀⠈⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⢨⣿⣿⣿⣿⣿⣿⣿⣿⣄⠄⠀⠀⠀⠀⠀⠈⠛⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⡇⣽⣿⡇⠘⠛⢿⣿⣿⣿⣿⡿⠟⠛⠠⠤⣀⣤⣄⣸⡿⢂⠿⣂
⠀⠀⢀⣄⣀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣿⣿⡁⠀⠀⠀⠉⠉⠉⣿⣿⣿⣿⠇⠀⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣇⠙⠉⠉⠉⠉⠀⠀⣴⣿⣿⣧⣴⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠉⠁⠘⠀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠙⣿⣿⣷⣶⣦⣤⣄⣀⣿⣿⡿⣣⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣰⣿⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤
⠒⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣶⣶⣶⣿⣿⠟⠀⢀⠖⢀⡿⠃⠀⠀⡀⢀⣀⢀⣀⣴⣤⣠⣀⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⠇⠀⠀⠀⠉⠛⠛⠛⠵⢿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⣠⡾⢁⠀⠀⠀⢠⣾⣿⣯⣿⣿⣿⢝⣐⠻⣵⡼⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢁⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣧⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⢉⣴⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⢖⠶⣶⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⡟⠛⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣺⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠘⠛⡟⠛⡿⠛⠛⠻⡟⠛⠛⠛⠂⠘⠇⠀⠘⠻⢿⠿⠟⠛⣶⣤⠀⠀⠀⠘⠛⠻⣿⡿⠛⠛⠻⢿⠂⠀⣀⠀⠀⡄⠀⢶⠛⢻⠐⠒⠿⢿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠂⣀⣴⡄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠠⣿⣿⠀⠀⠀⠀⠀⣀⣿⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠇⠀⠈⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠦⡀⠈⢻⡇⠀⠀⠀⠀⠀⠀⢸⠛⢛⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠈⠻⣿⣿⣻⣯⣿⣿⣿⣿⢫⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠁⣀⣧⡀⠁⢀⣼⡇⠀⠀⠀⠀⠀⠀⠈⢀⣸⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣀⣿⣧⠀⠀⠀⠀⠀⠀⠉⠀⠀⡄⠀⠀⠀⢈⠀⠀⠀⠀⠛⠛⠛⠟⠿⡏⠀⠀⠀⠈⠛⢿⣿⣿⡿⢿⣷⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡀⠀⠀⠀⣿⣿⣿⡄⢠⣾⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⢸⣿⠀⠀⠀⢸⡟⠓⠀⠀⠀⠂⢴⣶⣶⠇⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⡤⠞⠿⠛⠗⠰⢦⡌⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡀⠀⣀⣀⣀⡀⠘⠉⢛⡁⠀⢉⣰⡿⠃⠀⠀⢀⠀⠢⠀⠀⠀⠠⠉⠁⠀⠀⠀⠉⢋⣤⠀⠒⢣⣤⢄⣠⣙⣷⠟⠀⢠⣿⣛⣯⡄⠀⠙⠀⠉⠉⠙⢛⠿⠛⠛⠓⠂⠘
⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⢒⠀⠶⠄⢀⡄⡈⠑⠂⢠⣀⡐⠋⠠⠞⠛⣋⣷⠲⠈⠀⠀⠀⢀⢞⣁⣀⣀⣀⣀⣀⠀⠀⠀⢠⣄⠀⠈⠥⠀⢠⢼⡏⢰⡿⠻⠙⣆⠄⠘⠉⠋⠙⠀⢠⣤⡄⠀⠠⠢⠈⠀⠀⠀⠀⠀⠀
⠛⠛⠉⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡐⠱⠛⠂⠀⠀⢐⣖⠀⠋⣐⠏⠀⢠⣄⠈⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⠁⢀⣀⢤⢔⣙⣱⣇⡏⠀⣰⣿⡏⠀⢀⣀⡀⠒⠂⢈⣿⣭⢤⣴⣿⣦⠄⠀⠂⡀⠀⠀
⠂⠂⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠃⣀⣠⣶⣷⣶⣿⣿⡆⠀⣿⡞⠁⠸⠿⠇⣴⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⠟⠋⠁⠈⠘⣿⡋⠛⠻⠋⠹⣸⠁⠶⢶⣶⡿⠗⠈⠘⠛⣿⣾⣿⣿⣥⣠⠁⠘⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠿⡟⣻⣻⡟⠛⠁⢀⠨⣾⡿⠖⣢⠄⢠⣾⡿⣋⠉⠀⣹⣿⣿⣿⠁⠀⠈⠙⢻⣿⣧⠀⠀⠀⠀⠀⢀⡖⠀⢠⠇⢂⡀⠀⠈⠉⠑⠶⠃⠙⠃⣿⣁⠍⠛⣿⣿⣿⣴⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣟⡉⢹⠟⠓⠉⠀⣀⠸⠥⠓⠋⠉⣿⣿⣾⣯⣥⣾⠛⠙⠉⠛⢻⣬⣙⣻⣶⣿⣿⡇⠀⠀⠐⠋⠉⠀⠀⠚⠂⠋⠉⠂⠠⠀⠀⠀⠈⠀⠀⠉⢸⣿⣀⣠⢶⣾⣿⣿⣌⣹
⠀⠀⠀⠐⠒⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢙⡛⠛⠋⠠⠶⠦⣯⠝⠂⢠⠄⠐⢰⣿⣿⣿⣿⣿⣷⣶⣶⣴⣤⣬⡻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣁⠀⠲⢴⣞⣘⣿⣷⡞⠃⢀⣀⣶⣾⣷⣿⣿⣿⠿⠿⠟⠛⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⢛⠁⣀⡘⠃⠀⣼⣿⣿⣿⡟⣿⡟⠉⠉⠉⠉⠻⣷⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⡤⢨⡽⣷⠄⠀⣬⣿⣿⣿⣤⠋⠉⠁⠹⠾⠟⠉⠁⡍⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⢒⣀⣰⣦⣤⣤⣴⣶⠀⠀⠀⠀⠰⠋⣽⡅⠀⠠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⡤⠀⠀⠀⠀⣼⣽⡿⠅⠀⣿⠟⠛⠋⢀⣻⠚⠀⠐⡒⠃⠁⢡⣤⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠛⠳⠾⠙⣿⣥⠀⠀⠀⠰⣄⠀⠀⠈⣡⠀⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢘⣛⡁⠀⣃⠁⠀⠀⠀⠀⡉⠙⣶⣾⠁⡖⠉⢴⣤⣿⣤⣄⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠙⠀⠀⠀⠀⠉⠀⠈⠀⠛⠀⠁⠋⠟⣀⣿⣿⣿⣿⣿⣿⣶⣿⢿⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠻⠶⠆⠀⠠⢶⣭⠀⠐⢫⢿⠀⠰⠿⠛⠀⠀⠤⢤⠀⠀⡼⠛⠋⠁⢘⡿
⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⠤⡀⠰⠎⠀⠀⠀⠁⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣷⣶⣦⣄⣼⣿⡿⣿⣿⣿⣿⡿⠿⠃⠠⢄⣀⣀⣠⢲⣖⡀⠀⠀⣾⡞⠀⠀⠀⠀⡴⡿⠆⠀⠀⠀⠀⢶⣉⢀⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠸⠿⠏⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠿⠿⠏⠁⠉⠉⠁⠉⣻⣿⣿⣯⠀⠀⠀⠀⠀⠙⢣⠙⠘⠧⠀⠉⢸⠻⣿⠨⡖⠀⠀⠐⢢⡄⠺⣿⡷⠀⠀⢸⡎⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠤⢄⠀⠀⢀⣄⣀⡀⠀⠀⣀⣀⣴⣾⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⢐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⡀⣈⢃⡀⢉⠑⢣⣄⠈⢀⠀⠀⠀⢀⠏⠇⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣠⡄⣀⡤⠀⠀⢀⣵⣶⣾⣿⡿⠛⢻⣿⣿⡿⣿⣿⠋⠉⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠉⠻⣿⣿⢷⣶⣦⡠⣥⣤⡀⠀⣤⠈⢩⣙⡄⠈⢉⡧⠘⠶⣈⡟⢃⡀⠀⠒⠂⠾⠀⠀⠀⠀
⠀⠀⡤⠀⠀⠀⠐⠀⠀⠈⠉⠉⠙⠓⣰⠶⢌⣹⣿⡏⠀⠀⠀⠘⠉⠁⠀⠛⣿⢀⠀⠀⠙⢿⣄⠀⠀⠀⠀⢠⣾⣿⡏⠀⠀⠀⢸⡟⣼⡿⠿⠛⠀⠀⠙⠿⣿⣿⡿⠈⠉⠙⠛⠀⠀⣻⡋⢁⠘⣷⠦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠰⢢⣶⣿⣿⢻⣿⣿⣧⣀⠠⠤⠀⠀⣤⣼⣿⡞⣶⣤⡀⠀⠙⠳⠀⢀⣴⣿⣿⠿⠛⠀⠀⢀⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠀⠀⠀⠀⣀⣿⡁⠁⠉⠁⠈⠛⠛⠉⠉⠀⠒⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠉⠁⠀⠀⠀⣼⣿⣿⡏⣿⣿⣿⠟⠛⣀⣀⠿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣦⣄⡀⠈⠉⠁⠀⠀⢀⣴⣾⣿⡏⣿⣿⣿⡇⠀⢀⣤⠀⠀⣶⣿⣿⡟⣿⣶⣤⡾⢻⣿⢿⡿⠆⢠⣦⣀⡀⠰⢄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⢘⢉⣀⡀⠀⣀⣾⣿⣿⣿⡇⣿⣿⣿⣤⡄⠛⢃⣀⣼⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⢱⣿⣿⣿⡿⠿⠀⠀⢰⣶⣿⣿⣿⡇⣿⣿⣿⣿⡆⠀⠒⠉⠒⢶⣏⣽⣇⠚⠟⣳⡔⢂
⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣾⣿⣿⣿⣿⢇⣿⣿⠟⠛⢣⣤⠘⠿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⡟⢸⣿⣿⣿⣇⣀⠰⠷⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⡿⣿⠛⡆⠀⠀⠸⠀⠀⠀⢠⣉⡁⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣤⡤⠉⢋⣠⣰⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠸⣿⣿⣿⠇⣿⣿⣿⣿⠟⠻⠀⠀⠾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣧⣀⢀⡉⣿⡇⠀⣄⠀⠁⠀⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣸⣿⣿⠉⢡⣤⡘⠛⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⢠⣿⣿⣿⣿⣤⡀⠟⠃⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣧⣜⠛⠛⢀⣴⣦⣀⠀⠀⠻⢠⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣷⡶⠚⠛⠣⣤⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢿⠃⣾⣿⣿⣿⣿⠿⢃⣀⣀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣟⣿⣷⣿⣿⡟⢹⣟⠉⠉⢙⣓⡺
⠀⠀⠀⠒⠀⠀⠀⠀⠂⠀⣼⣿⣿⣿⣿⣿⢸⣿⣿⢃⣀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⡜⠛⠃⢀⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⡄⠛⠋⣾⣶⣿⢬⡁⢒⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣘⠿⠿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⡿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟⣄⣀⣀⢸⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⠉⠉⠀⡠⠉⠁⠀⠀
⠀⠤⠔⠲⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⠿⠇⠀⠀⠀⠀⢠⣾⣿⣿⣿⡟⠛⣿⣿⣧⡙⠛⠛⠘⠛⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⡆⠀⢠⣆⣀⡀⠰⠀⠀⣠⣮⣈
⠀⠀⠀⠀⠀⠀⢀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣶⣶⣿⠃⣼⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⠀⣈⣩⣴⡖⠀⠀⢠⣸⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠛⠛⠟⠓⢢⠄⠀⠀⠰
⠀⠀⢀⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⠀⢻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠚⠟⠋⠀⠀⠀⢲⣶⠦⣄
⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡄⣿⣿⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⣀⣈⢁⣀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡋⠉⠀⠀⢸⣿⣿⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣧⢸⣿⠿⠿⠛⠛⠋⣡⣿⣿⣾⠉⠙⠛⣻⣿⣿⣿⡿⠟⠛⠷⠦⣤⠶⣦⣼⡛⣩⠛⠆
⠀⠀⠠⠤⠤⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠘⢿⣿⣄⣀⡀⠀⠀⠀⠀⣿⣿⣿⢟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⣰⡿⠿⢿⡟⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠄⠃⠉⠀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠈⠻⣿⣿⣿⣿⣷⣶⣶⣿⡿⣫⣾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣇⣀⣤⣤⣶⠎⠀⢠⠆⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡴
⠛⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⠀⠀⠘⠙⢿⣿⣿⡿⣟⣵⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣰⠏⠀⠀⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⣠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠋⡆⠀⡀⠀⠀⠀⠀⠈⠛⠛⢻⣿⠏⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠿⠟⠛⠟⠋⠀⠀⠀⠀⠀⠐⣋⢠⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢝⡐⠻⣵⡼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⢠⡿⠧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⢿⣧⣀⠀⣠⣼⣿⣿⣿⣿⣿⡯⣶⠶⣶⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢸⡇⠀⢻⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⣴⣿⡇⠀⠀⠀⠀⠈⣿⠟⣧⣻⣿⣿⣿⣿⣟⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠛⠛⡟⠿⡿⠟⠛⠻⡟⠛⠛⠁⠈⠀⢷⠇⠀⠻⢿⠋⠉⠙⢿⣿⠛⠳⠀⠀⠘⠻⣿⡿⠛⠛⠻⢿⠛⠀⢰⠖⠚⡟⠛⢿⠛⢿⠛⠀⠀⠀⠀⢠⣟⢀⣿⣇⢿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠂⣀⣷⡆⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣀⣿⣷⠀⠰⠀⢈⠀⠀⣾⠀⠀⡇⠀⠈⠀⠈⠀⠀⠀⠀⡀⠈⠙⠻⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠦⡀⠈⢻⡇⠀⢀⠀⠀⠀⠀⠸⠛⢻⠀⠀⡀⣸⣿⠀⠀⠀⠀⠀⠈⣿⣟⠀⠀⠀⠘⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣿⣿⣿⠋⠻⣿⣿⣿⣯⣿⣿⣿⣿⢻⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠁⢀⣇⡀⠁⢀⣼⡇⠀⣹⡇⠀⠀⠀⠀⠀⣸⠀⠀⠁⣸⣿⠀⠀⠀⠀⠁⢀⣿⣿⠀⠈⠀⣠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⣴⣿⣿⣿⣦⠀⠈⠻⢿⣿⣿⡿⢿⣷⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠟⠛⠻⢻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠹⣿⣿⠀⢸⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇⣼⣿⣆⠀⠀⠀⠀⢀⡰⠘⠋⢹⣿⣿⣿⠿⠁⠀⢀⣀⣴⣶⣶⣾⣿⣿⣿⣿⣧⣄⣀⣠
⡤⠞⠟⠻⡃⠀⣤⠌⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠀⠘⠉⢛⡃⠀⢉⣐⡛⠃⠠⠀⠀⠀⠐⠀⠀⠀⠀⢈⠀⠀⠀⠘⠋⢫⣤⠀⠐⢡⣤⢀⣄⣙⣿⠟⠀⣸⣿⣿⣧⠄⠀⠛⠀⠉⠈⠙⢛⠟⠛⠛⠓⠊⠘
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠂⠶⠆⠀⠄⡀⠐⠃⢀⣀⡐⠋⠁⠘⠛⣉⣝⠀⠈⠀⠀⠀⢄⣾⣁⣀⣀⣤⣀⣀⣀⠀⠀⢀⡄⠀⠈⠅⠀⢠⢾⡏⢰⠟⠿⠙⣆⠀⠈⠉⠋⠉⠀⢀⣦⠄⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀
⠻⠋⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠛⠃⠀⠀⠀⡖⠀⠋⣠⠏⠀⢠⣄⠀⠈⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⢀⣀⠀⣦⣛⣹⣅⠏⠀⣰⣿⡏⠀⢀⣀⠀⠻⠓⢈⣛⣇⢤⣰⣷⣦⠄⠀⠂⡀⠀⠀
⠂⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⢃⣀⣠⣦⣷⣴⣾⡿⡆⠀⣷⠦⠀⠸⠿⠇⣰⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠋⣿⡉⠉⡛⠋⠻⣸⠓⠶⢶⣶⡿⠗⠈⠈⠻⣿⣾⣿⣷⣧⣀⠁⠘⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠿⣛⣻⣻⡟⠛⠁⢁⠨⢶⡷⠆⣢⠀⠀⣼⣿⡿⣋⡉⠁⢨⣿⣿⣿⠉⠀⠐⠛⢿⣿⣦⠀⠀⠀⠀⢠⡆⠀⢰⠇⢃⡀⠀⠈⠉⠑⠶⠂⠙⠁⣿⣡⠌⠛⣿⣿⣿⣴⣤⣴⣤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣟⡁⢉⠛⠋⠰⠁⣀⠸⠥⠓⠋⠉⢹⣿⣿⣿⣿⣬⣵⠟⠛⠛⠻⢷⣾⣛⣷⣶⣿⣿⠀⠀⠀⠋⠉⠀⠀⠚⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠁⢹⣯⣀⣤⢶⣾⣿⣿⣅⣸
⠀⠀⠀⠐⠒⠀⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⢈⡛⠛⠉⠠⠶⠂⡏⠍⠂⢠⡄⠀⡀⣼⣿⣿⣿⣿⣿⣿⣴⣤⣤⣄⣀⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠲⢴⣋⣩⣿⣷⡞⠁⢀⣠⣶⣿⣿⣿⣿⣿⠿⠿⠛⢳⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢉⠉⣀⡘⠃⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠛⠿⣷⢿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⠨⣝⡷⠄⠀⣤⣿⣿⣿⣄⢋⠉⠀⠹⠼⠇⠉⢁⠏⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⣀⣈⣀⣴⣦⣤⣤⣴⣶⠀⠀⠀⠀⠰⠋⣽⠥⠀⠀⢸⣿⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⣼⣭⡿⠅⠀⣾⠏⠋⠉⢀⣯⠛⠀⠐⠺⠋⠉⠠⠄⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠟⠓⠺⠙⣿⣵⠀⠀⠀⠰⣄⠀⠀⠉⣡⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⢋⡀⠀⣀⠁⠀⠀⠀⠀⡉⢹⣶⣶⢀⠔⠀⢦⣤⣿⣴⣄⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠩⠀⠀⠀⠀⠉⠀⠈⠀⠛⠀⠁⠉⠿⡀⣿⣿⣿⣿⣿⣿⣿⣦⣾⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠉⠛⠶⠆⠀⠰⠶⢥⠀⠒⢽⢿⠀⠐⠟⠋⠀⠀⠤⠤⠀⠀⠼⠛⠋⠁⢘⡿
⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⣠⣰⢯⡁⠰⠎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⣸⣿⣿⣿⣿⣿⡿⠿⠇⠀⢀⣀⣀⡀⢰⣗⡀⠀⠀⣾⡚⠀⠀⠀⠀⡴⠿⠂⠀⠀⠀⠀⠟⣑⢠⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠨⠿⠏⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠛⠛⢩⣿⣿⣿⠀⠀⠀⠀⠀⠙⢣⠉⠘⠧⠀⠈⢙⠻⣿⡈⡆⠀⠀⠐⢠⡄⠺⣿⡗⠀⠀⢸⡏⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠤⠄⠀⠀⠀⣤⣀⣀⣀⠀⣀⣀⣤⣾⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⢂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡨⢀⣈⢃⡀⣉⠙⣧⣄⡀⢀⠀⠀⠀⢀⠏⠇⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣂⡄⢠⡄⠀⠀⢀⣵⣾⣿⣿⡿⠛⠛⣫⣿⣿⣿⣿⠛⠉⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠛⢿⣿⢻⣿⣶⣌⣠⣤⡀⢀⣤⠀⢩⣙⡀⢀⢈⡧⠘⢆⣈⡟⢁⡀⠀⠚⠂⠞⠀⠀⠀⠀
⠀⠀⡤⠀⠀⠀⠐⠀⠀⠈⠋⠉⠉⠛⣰⣶⣄⣙⣿⣿⠀⠀⠀⠀⠋⠉⠀⠛⣿⣄⠀⠀⠈⠻⣿⡀⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⢸⣯⣾⠿⠟⠉⠀⠀⠉⠻⣿⣿⡿⠈⠉⠉⠛⠀⠀⣻⣋⣁⠘⣷⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⢆⣴⣾⣿⢿⣿⣿⣿⣀⡀⠤⠄⠀⣠⣴⣿⡇⣶⣦⣀⠀⠈⠳⠄⠀⣠⣾⣿⡿⠟⠀⠀⢀⣸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠉⣿⣿⢀⣀⠀⠀⡀⣹⡁⠁⠈⠀⠈⠛⠛⠉⡉⠀⠒⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠉⠁⠀⠀⠀⣸⣿⣿⣿⣸⣿⣿⡿⠛⣀⣀⢜⣷⣿⣿⣿⡇⢿⣿⣿⣷⣦⣤⣀⠀⠉⠉⠁⠀⠀⣠⣶⣿⢻⣿⣿⣿⣃⠀⠀⠖⠀⠀⣶⣿⣿⢸⣿⣿⣶⣞⠛⡿⢧⡿⠇⢠⣶⣀⡀⠐⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢩⣀⡀⢀⣀⣴⣿⣿⣿⡇⣿⣿⣿⣤⡄⠛⠏⣀⣸⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣰⣿⣿⡿⢸⣿⣿⣿⠟⠛⢀⠀⠾⣿⣿⣿⣿⣼⣿⣿⣿⣿⣇⠀⠒⠉⠒⠾⣧⣽⣥⠙⢛⣳⡆⢂
⠉⠀⠀⠀⠀⠀⠀⠀⠨⠉⢸⣿⣿⣿⣿⣿⡇⣿⣿⡟⠛⢃⣄⡘⠿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⠃⣿⣿⣿⣿⣄⡀⠛⠇⣀⣸⣿⣿⣿⡏⣿⣿⣿⣿⣿⠿⢛⣆⢀⠀⠸⠀⠀⠀⢠⣈⡉⠍
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⣼⣿⣿⣿⣿⢇⣿⣿⣧⣤⠘⠛⣀⣠⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⢀⣿⣿⣿⣿⠛⠃⡀⠰⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡀⢀⣉⣻⠃⠀⡤⠀⠁⠀⠛⠛⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢸⣿⣿⠋⢉⣤⡀⠛⢿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⡏⣸⣿⣿⣿⣧⣤⠘⠛⢀⣀⣾⣿⣿⣿⠀⣿⣿⣿⣿⣿⣧⣼⠛⠛⠀⣴⣦⣄⠀⡀⠛⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢸⣿⣿⣦⠚⠛⠣⣤⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠿⢠⣿⣿⣿⣿⡟⠛⣤⣤⡸⠿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠿⣷⣿⢿⠏⢹⣟⠉⠉⢙⣓⡻
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⢃⣀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⠉⠉⠀⣤⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⣿⣇⠛⠉⣿⣿⣿⠤⠄⣒⡋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⣿⣿⣘⠿⠿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢣⣄⣀⣀⢻⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠉⠀⠀⡤⠀⠁⠀⠀
⠀⠤⠞⠙⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⠛⣛⣿⣿⡦⠝⠛⠁⠙⢻⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⡄⢀⣦⡀⠀⠴⠀⠀⣠⣮⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⢈⣥⣶⡒⠀⠀⢠⣼⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠛⠟⠓⢰⠔⠀⠀⠐
⠀⠀⢀⣀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣷⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠉⠀⠀⠀⢦⡶⠦⢤
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡆⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣈⢁⣀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⢸⣿⡟⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⡷⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⡇⢸⠿⠿⠿⠛⠛⠉⣡⣿⣿⣷⡆⠀⠀⢩⣿⣿⣿⡿⠟⠛⠿⢧⣴⠶⢦⣾⡛⣩⠛⠦
⠀⠀⠀⠶⠤⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣧⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣣⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⠿⣿⣿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠃⠩⠠⠄
⣀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠻⣿⣿⣿⣿⣶⣶⣾⣿⢟⣵⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣀⣠⣤⣤⣶⠎⠁⢠⠆⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣒⠶
⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠻⣿⣿⣿⡿⣫⣵⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣰⡿⠁⠀⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⣠⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⡆⠀⠀⠀⠀⠀⠀⠈⠋⠙⢻⠿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠸⠟⠛⠛⠛⠋⠀⠀⠀⠀⠀⠴⣛⡁⣰⠄⠀⠀⢀⣾⣿⣿⣿⣿⣿⢝⣒⠻⣵⡼⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢰⡿⠄⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠟⠸⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡯⣶⢶⣶⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⡄⢸⡄⠀⢻⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣀⣠⣴⣿⣇⠀⠀⠀⠀⠀⢹⣿⣧⣿⣿⣿⣿⣿⣿⣵⣿⣷⣾⣿⣿⡆⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠈⠛⠟⠻⡿⠟⠛⠻⡿⠛⠛⠛⠀⠀⢿⠃⠐⠻⢿⠋⠉⠙⢿⣿⠛⠲⠀⠀⠘⠻⣿⡿⠛⠛⠻⢿⠃⠀⣴⠟⠛⡟⠛⢿⠛⢻⠛⠓⠀⠀⠀⠀⠀⣹⣿⣧⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⣀⣷⡆⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠀⣸⣿⠀⠀⠀⠀⢀⣀⣿⣷⠀⠰⠀⢈⠀⠀⣿⠀⠀⠇⠀⠈⠀⠈⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠂⠀⠀⠉⠁⠀⢀⠀⠀⠀⠀⠸⠛⢻⠀⠀⡀⣽⣿⠀⠀⠀⠀⠀⠈⣿⣟⠀⢀⠀⠘⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⢻⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⢀⢃⡀⠀⢀⣼⡇⠀⣹⡇⠀⢠⠀⠀⠀⣸⠀⠀⠁⣸⣿⠀⠀⠀⠀⠁⢀⣿⣿⠀⠈⠀⣠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⠙⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠟⠛⠻⠃⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⢿⣿⠁⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⡿⠿⠉⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣦⣄⣀⣠
⠤⠞⠛⠻⠃⠀⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠈⠁⢉⡁⠀⢀⣠⡻⠃⠐⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⣦⠀⠔⢡⡦⢤⣤⣭⣷⠟⠀⢴⣿⣽⣧⡀⠀⠙⠀⠀⠀⠉⢩⠛⠛⠋⠃⠉⠈
⠀⠀⢀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠶⠀⠁⠄⡀⠐⠀⠠⣄⡔⠃⠀⠚⠋⣉⡗⠐⠈⠀⠀⠀⢠⣾⣧⣤⣤⣤⣤⣤⣤⡀⡀⠀⣄⠀⠀⠂⠀⢠⢾⡇⢰⡟⠛⠙⣆⠀⠈⠉⠉⡀⠀⢠⣦⠄⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀
⠛⠉⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠐⠛⠃⠀⠀⢀⡔⠀⠉⣠⠏⠀⢠⣄⠀⠈⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢉⣀⣤⣤⣦⣉⣽⣦⠇⠀⣴⣿⡏⠀⠀⠀⠀⠙⠀⢨⣏⡥⢤⣾⣷⡶⠀⠀⢂⡄⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢘⠃⣀⣠⣶⣷⣮⡿⡿⡆⠀⣿⠞⠀⠘⠿⠏⢀⣾⣿⣿⡛⢿⣿⣿⡿⠟⠛⣻⣿⣿⣿⠉⠀⠀⠈⠭⡍⠉⠙⠃⠑⡼⠐⠓⢲⣾⠿⠇⠀⠀⠙⣿⣾⣿⣷⣧⣄⡀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣋⣹⣿⡟⠛⢁⣠⠤⢶⡷⠆⣠⢀⠀⣠⣿⣫⣴⠄⣄⣾⣿⠿⣿⣄⣠⣄⣄⣹⣿⣷⠀⠀⠀⠀⣠⠎⠀⢰⠃⣁⡀⠀⠈⠉⠀⠒⠀⠉⠁⣾⣄⠌⠉⣽⡿⣿⣸⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⣁⢈⠛⠋⠙⠁⣀⠼⠍⠓⠋⠉⠉⣿⣿⣿⣿⣿⣏⣀⡀⠀⠀⠹⣷⣶⣾⣿⣿⣿⡄⠀⠀⠁⠈⠀⠀⠚⠀⠉⠀⠀⠒⠀⠀⠀⠉⠀⠀⠁⢸⣧⣤⣖⣲⣾⣿⣿⣤⣸
⠀⠀⠀⠐⠒⠂⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢈⡙⠋⠙⠰⢾⠢⡏⠊⠃⢠⡀⠀⣁⣰⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣜⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⠀⠳⠾⣉⣥⣿⣾⠟⠁⣀⣠⣾⣿⣿⣿⡿⢿⠿⠿⠋⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠩⢉⣀⣈⠃⠠⠀⣿⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢤⠤⠰⣝⡷⠀⠀⣴⣿⣿⣿⡤⢁⡀⠀⠸⠞⠃⠀⢀⠅⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢈⣀⣴⣦⠤⣶⣶⣶⠀⠀⠀⠀⠰⠉⣽⠥⡀⠀⠐⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⢼⣽⡿⠁⠀⡿⠋⠉⠉⠠⣏⡁⠀⠈⠩⠈⠀⠒⠦⢀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠛⢒⠚⠛⣿⣴⠀⠀⠀⠰⣄⠀⡀⢈⣡⡀⠀⣿⣿⣿⣿⣿⣿⣠⣤⣤⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠘⢭⡀⢀⣄⠁⠀⠀⠀⠀⡍⡹⠿⠾⠀⠆⠀⠶⣶⣿⣶⣦⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠉⡀⢁⠉⠟⡀⠸⠿⣿⣿⣿⣿⣿⣿⣯⣍⡉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠒⠃⠀⠰⠶⠦⠄⠉⠹⢿⠀⠒⠛⠉⠀⠀⠤⠤⠀⠀⠞⠉⠁⢀⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣯⡅⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠙⢿⣿⣿⣿⡿⠛⠋⠀⠀⣀⣀⡤⢸⣯⠤⠀⢀⣾⡋⢀⠀⠀⠀⠖⠟⠃⠀⣀⠀⠀⠛⣅⢠⠟⠻
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⣠⣴⣿⣿⣿⣿⠟⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠉⡢⠉⠘⠒⠀⠀⢹⠻⣿⡐⠆⣀⠀⠈⢡⠆⠻⡿⠟⠀⠀⣸⡏⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠤⠴⠆⠀⠀⢀⣴⣶⣶⣤⣤⢤⣤⣶⣿⣿⠿⠿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡩⢿⣿⣿⣏⣀⠀⠀⡀⠀⠀⠀⠀⢠⣀⡬⠠⣌⣡⡀⢠⠜⣷⣦⡈⢠⠀⠀⠀⢠⠃⠃⠈⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠐⣂⣐⣒⣰⣄⠀⠀⢀⣴⣟⣿⡟⠛⠋⠀⠱⠿⠟⠋⢿⡇⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠘⣿⡇⣿⣿⣯⡤⠶⠦⣄⣴⣄⣠⣬⣄⣀⣨⠷⠘⢆⣨⡍⢡⡄⠁⠙⠀⠟⠀⠀⠀⠀
⠀⠀⡤⠀⠀⠀⠐⠂⠀⠈⠁⠈⠉⠋⠰⢶⣦⣽⢸⣿⣧⡄⠀⠀⠀⠀⠀⠀⢰⣿⢠⣄⠀⠀⠙⢷⣄⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⣿⣵⣿⠛⠁⠀⠀⠀⠀⠻⣿⣿⡃⠉⠉⠙⠀⣀⡙⣃⣡⠘⢿⣂⢀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠂⣴⣿⣿⣿⣾⣿⣿⣷⡶⠈⠉⣤⣤⣿⣿⣿⢸⣿⣿⣦⣄⡀⠀⠀⠼⠿⠛⠋⠉⠀⢀⣤⣶⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⡀⠀⠤⣽⡀⠁⡀⠀⠈⠙⠙⠈⠁⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⣿⣿⣿⠀⠠⣶⡆⠈⢻⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣴⣿⣿⣿⢸⣿⣿⣿⣀⡀⠚⠂⣀⣸⣿⣿⣿⣿⣿⣿⣿⡉⠿⠷⡟⠂⢰⣶⣄⡀⠐⢢⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠈⠡⣀⣀⠀⣀⣰⣿⣿⣿⣿⡇⣿⣿⣿⠿⠅⠀⢰⣶⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣸⣿⣿⣿⡇⣿⣿⣿⡿⠉⠁⣠⡀⠛⢿⣿⣿⣿⢹⣿⣿⣿⣷⣀⣉⠈⠙⠿⢧⠿⡧⠘⢋⣵⡌⠭
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢷⣿⣿⣿⣿⣿⢸⣿⣿⡃⠀⠺⢷⠀⢈⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⢀⣿⣿⣿⣿⣶⡆⠉⢁⣤⣼⣿⣿⣿⢸⣿⣿⣿⣿⠿⠹⣆⣀⡀⠘⠀⠀⡀⢰⣠⡀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢸⣿⣿⠿⠇⠀⠀⣾⣾⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⣿⣿⡏⢸⣿⣿⣿⡏⠉⢠⣤⠈⠙⣿⣿⣿⣿⢸⣿⣿⣿⣿⡤⢄⣄⣽⠅⠀⠄⠀⠀⠀⠙⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢾⣿⣷⣀⡺⢿⡄⠀⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠃⣿⣿⣿⣿⣷⣶⠈⠁⢠⣠⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⣮⢙⠙⠀⣶⣶⣀⣀⣀⡋⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢸⣿⣿⠟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⣿⣉⡁⣶⣶⠈⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⣿⣿⠿⠉⣹⢏⡉⠈⣩⠿⠛
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠘⣿⣿⢰⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣾⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡄⠉⠁⣿⣿⡿⠦⠄⣈⡁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡄⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠸⣶⣶⠆⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⠁⠀⠀⠈⠀⠀⠀⠔⠀⠀⢀⠀
⠀⠐⠒⠙⠂⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⣾⣿⣿⣷⣀⣀⣤⠀⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⡆⠀⢰⣦⠄⠄⠚⠀⠀⣰⣷⣠
⠀⠀⠀⠀⠀⠄⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⡇⠀⣤⣴⣶⣒⡀⠀⠰⠴⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣠⣤⣤⡄⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣶⠀⣀⣉⡙⠋⠉⠰⠂⠀⠀⠘
⠀⠀⢀⣤⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠨⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣧⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠋⠁⠀⠀⠀⢻⡟⠓⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣠⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⢿⡿⣾⣾⣿⣿⣿⣿⣿⣧⠀⠁⠀⠀⠀⠀⣤⣄⢠⣄⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⠇⠀⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣆⠛⠛⠉⠉⠉⠀⢠⣾⣿⣿⠀⠀⣹⣿⣿⣿⣿⡿⠟⠂⠘⠳⣶⡛⠶⢿⡍⣴⠉⠂
⠀⠀⠀⠒⠒⠂⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢿⣿⣿⣿⣷⣶⣦⣤⣄⣸⣿⡿⣣⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⡼⠿⠟⠛⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠁⠀⠀⠄
⣀⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣀⠀⠙⠻⠿⣿⣿⣿⣿⣿⢟⣫⣾⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣶⣶⣶⣿⣿⠏⠀⠰⠂⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⣒⠾
⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠆⠀⠀⠀⠘⠉⠉⠋⠱⠿⢿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⣰⡇⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⢿⣿⣿
⠀⠀⠀⠀⠠⠤⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⣾⣰⣿⠇⠀⠀⢠⣾⣿⣯⣿⣿⣿⠝⠐⠻⣵⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⣸⣿⠋⢠⣴⣤⣤⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⡿⡫⢐⠶⣶⣌⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠇⣼⣿⠀⢠⣿⣿⠿⠿⢿⣷⣶⣦⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠂⢀⣀⣀⣠⣤⣤⣴⣾⣿⠀⠀⣼⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡟⣵⣾⣷⣾⣿⣿⡇⠀⠈⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠟⠛⡿⠛⠛⠻⡟⠛⠛⠛⠛⠀⢻⠏⠀⠻⢿⠟⠚⠛⠈⣿⠛⠻⡇⠀⠐⢿⣿⣿⠛⠛⠻⢿⠛⠀⢸⠛⠛⡟⠛⢿⠛⢻⠛⠀⠀⢿⣿⣿⣿⣿⣿⣇⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⣀⣷⡆⠀⢠⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣠⣿⣿⠀⠰⠀⢸⠀⠀⣾⠀⠀⠇⠀⠈⠀⠈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⡀⠈⢻⡇⠀⣿⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⢜⣿⠀⠀⠃⠀⠀⠈⣿⣷⠀⢠⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠻⣿⣿⣻⣯⣿⣿⣿⣿⢫⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⢃⡀⠁⢀⣼⡇⠀⣿⡇⠀⣀⠀⠀⠀⣰⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣿⣿⠀⠈⠀⣠⠀⠀⠉⠀⠀⠀⠀⣄⠀⢸⠀⠀⠀⢀⣿⣿⢿⣿⣿⣿⠁⠀⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⠿⠇⠀⣿⡏⠛⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⡿⠁⠠⠁⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣦⣄⣀⣠
⡤⠟⠿⠻⠗⠐⣤⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⣄⣀⠈⠁⢉⡁⣀⢈⣠⡛⠃⠠⠀⢠⡀⠐⠀⠀⠀⠠⠊⠀⠀⠀⠈⠉⢩⣦⠀⠒⢡⣦⢀⣤⣭⣷⠟⠀⢴⣿⣽⣿⠀⠀⠙⠀⠀⠀⠉⣽⠟⠛⠉⠓⠉⠈
⠀⠀⢀⠀⠀⠐⠘⠀⠀⠀⠀⡒⠀⠶⠄⠀⡄⡈⠁⠀⠠⣄⡜⠋⠁⠘⠛⣉⣗⠰⠊⠀⠀⠀⠠⣾⣣⣤⣤⣤⣤⣤⣤⣄⡀⠠⣄⠀⠈⠃⠀⢠⢾⡇⢸⠟⠟⢙⣆⠄⠈⠉⠉⡙⠀⢀⣶⠄⠀⠠⡂⠀⠀⠀⠀⠀⠀⠀
⠙⠋⠉⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠘⠟⠃⠀⠀⢀⣤⠀⠉⣁⠏⠀⢠⣤⠀⠈⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢉⣀⣤⣤⣦⣉⣽⣦⡇⠀⣼⣿⡏⠀⢀⣀⠀⠙⠃⢨⣯⡦⢤⣾⣷⡶⠀⠀⢂⡄⠀⠰
⠂⠂⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠃⣀⣠⣶⣷⣶⣿⡿⣆⠀⣿⢞⠀⠸⠿⠟⢀⣾⣿⣟⠻⢿⣿⣿⣿⠿⠛⣛⣿⣿⣿⠉⠀⠁⠙⠯⡍⠉⢙⠃⠓⡼⠁⠓⣶⣾⡿⠗⠈⠘⠹⣿⣾⣿⣷⣧⣄⡀⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣟⣻⣻⡟⠛⠁⡠⠬⢶⡷⠆⣢⢀⠀⢠⣿⣋⣥⠤⢀⣾⣿⣿⣷⣀⣠⣄⣉⢻⣿⣷⠀⠀⠀⠀⣠⠆⠀⢰⠃⣡⡀⠀⠈⠉⠑⠖⠂⠉⠁⣿⣀⠌⠉⣿⡿⣿⣼⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⡁⢘⠛⠋⠑⠁⣀⠨⠵⠁⠋⠉⠉⣿⣿⣿⣿⣿⣏⣀⠀⠀⠈⢻⣶⣬⣿⣿⣿⣿⡀⠀⠈⠉⠈⠀⠀⠛⠀⠉⠉⠀⠂⠀⠀⠀⠉⠀⠀⠁⣸⣯⣤⣔⣲⣾⣿⣿⣄⣹
⠀⠀⠀⠐⠒⠀⡄⠀⠀⠐⠂⠀⠀⠀⠀⠀⢈⡙⠋⠋⠰⠶⠢⡿⠏⠂⢰⡄⠀⡁⣰⣿⣿⣿⣿⣿⣿⡿⠿⠿⣷⣿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⠀⠳⢾⣉⣼⣿⣾⠟⠁⣀⣠⣾⣿⣿⣿⡿⢿⠿⠿⠋⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠩⢉⣄⣈⠃⠀⠀⣿⣿⣿⣿⣷⣿⠃⠀⠀⠀⠀⠹⣧⣿⣿⣿⣿⣿⡇⠀⠀⠀⢤⡤⠸⣽⡗⠀⠀⣴⣿⣿⣿⡄⢁⡀⠀⠹⠞⡃⣉⣀⠇⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢈⣠⣴⣦⣤⣶⣴⣶⠂⠀⠀⠀⠰⠉⣽⠥⣀⠀⠊⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⢼⣽⡿⢁⠰⡿⠋⠉⠁⢠⣏⡛⠀⠈⠉⢉⠁⡲⠆⢀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠬⠛⢓⠚⠛⣿⣴⠀⠀⠀⠰⣆⠀⠀⢈⣡⡀⢠⣿⣿⣿⣿⣿⣧⣀⣤⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠙⢭⡀⠀⣄⠁⠀⡀⠀⠀⣉⡹⠿⡿⢠⠃⠀⠷⣶⣿⣶⣆⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠹⠀⠀⠀⠀⠈⠀⠀⠀⠙⡀⠁⠉⠟⡀⠸⠿⣿⣿⣿⣿⣿⣿⣟⣋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠒⠃⠀⠰⠶⠧⠀⠉⠽⢿⠀⠒⠛⠁⠀⠀⠦⠤⠀⠀⠞⠉⠁⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⣠⣲⣯⡅⠰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠟⠳⠾⠿⠋⣹⣿⣿⣿⡿⠟⠃⠀⠤⣀⣀⢤⢸⣿⠆⠀⢀⣿⡉⠀⠀⠀⠈⠶⠿⠂⠀⣀⠀⠘⠫⣅⣨⠟⠻
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠘⠻⠏⠀⠀⠀⠀⠁⠀⠀⠐⡀⠀⢀⣠⣶⣿⣿⣿⣿⠏⠉⠉⠀⠀⠀⠀⠀⢽⣿⣿⣿⣆⠀⠀⠀⠀⠉⡣⠉⠘⠓⠀⠀⠙⠻⣿⡰⠆⣀⠀⠈⣰⠂⠻⡿⠟⠀⠀⣸⡏⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⡤⠴⠄⠀⠀⠠⣴⣶⣶⣤⣤⢤⣤⣶⣿⣿⡿⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⡯⠀⠀⠀⡀⠀⠀⠀⠀⣠⣀⣤⠤⣌⣡⡀⣥⠼⣷⣆⡈⢀⠀⠀⠀⢠⠃⠇⠈⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠐⣒⣒⣖⣠⡄⠀⠀⢀⣵⣿⣿⡟⠛⠃⠀⠱⠿⠟⠋⢿⡇⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠈⢻⣿⡏⣿⣿⣮⡤⠤⢤⣀⣤⣀⣠⣬⣄⣀⣨⠷⠘⢆⣨⡏⢡⡈⠀⠛⠀⠏⠀⠀⠀⠀
⠀⠀⡤⠀⠀⠀⠐⠀⠀⠈⠁⠈⠉⠛⠴⣶⣦⣽⣾⣿⣧⡄⠀⢀⠀⠀⠀⣀⣸⣧⢦⡀⠀⠈⠻⣦⡀⠀⠀⣠⣾⣿⣿⡄⠀⠀⠈⣿⣼⡟⠛⠉⠀⠀⠀⠉⢻⣿⣿⠃⠉⠉⠋⠀⣀⡽⣉⣡⠘⣿⣂⢀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⡄⠀⠀⠀⣀⡀⠀⠀⠀⠂⣸⣿⣿⡏⣿⣿⣿⣷⡆⠉⠡⣤⣼⣿⣿⣿⢸⣿⣷⣤⣀⠀⠁⠀⠾⠿⠟⠛⠉⠀⣀⣠⣴⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⠀⠀⠤⣯⡀⢁⣀⠀⠀⠉⠙⠩⠉⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣄⠈⠀⠀⠀⠀⣴⣿⣿⣿⣷⣿⣿⡏⡀⢰⣶⠆⠉⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⣾⣿⣿⡟⣾⣿⣿⣿⣄⡀⠒⠂⠀⣼⣿⣿⡇⣿⣿⣶⣿⠙⠿⠷⡟⠂⢰⣶⣄⡀⠒⢂⡄⠠⠄
⠀⠀⠀⠀⠀⠀⠈⢩⣀⣀⢀⣀⣼⣿⣿⣿⣿⢸⣿⣿⠿⠿⠀⠀⣶⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⣿⣿⣿⢃⣿⣿⣿⡟⠉⢁⣀⠘⠿⣿⣿⣿⣗⣿⣿⣿⣿⣧⣀⣉⠉⠙⠿⢤⠿⡧⠙⢋⣿⡎⠭
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠼⠷⣿⣿⣿⣿⣿⢸⣿⣿⣀⠀⠿⠇⠀⣸⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⡟⢸⣿⣿⣿⣷⣶⠈⠉⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠹⣆⣀⠀⠘⠀⢀⡀⢠⣤⠤⢍
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⣿⣿⡿⠻⠂⡀⠸⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠻⣿⣿⠇⣼⣿⣿⣿⡏⠉⣠⣄⠈⠛⣿⣿⣿⡿⣸⣿⣿⣿⣿⡄⣤⣌⣿⠀⠀⡄⠀⠀⠀⢛⠛⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⣿⣿⣧⡤⠿⠿⣂⣸⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⡟⢰⣿⣿⣿⣿⣷⡖⠉⠁⣤⣼⣿⣿⣿⡇⢸⣿⣿⣿⣿⣧⣬⢉⠛⣠⣶⣶⣀⣀⣈⣛⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢠⣿⣿⣿⣿⣿⣍⡰⣶⡆⠙⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⠉⣹⣏⡁⠀⡩⠯⠛
⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⢀⣿⣿⣿⣿⣿⡇⢸⣿⣇⢿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡆⠉⠡⣿⣿⡷⢦⣄⣈⡀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢿⣿⣿⣇⠿⣶⡶⢪⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠖⠀⠀⣀⡀
⠀⠐⠒⠙⠂⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡇⢰⣶⣿⣿⣥⣤⣤⠀⣰⣿⡿⢃⣼⣿⣿⣿⣿⣿⣿⣇⠀⢰⣦⠤⠄⠚⠀⠀⣴⣧⣁
⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣏⠀⣠⣴⣶⣖⡀⠀⠰⠴⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣴⣶⣤⠀⢻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠠⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣉⣙⠋⠉⠰⠂⠀⠀⠚
⠀⠀⢀⣤⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠉⠋⠁⠀⠀⠀⢿⡟⠓⠤
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⢸⣿⡟⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⢸⣿⣿⣿⡿⠿⠛⣀⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡉⠀⠀⠀⠀⣤⣤⢠⣄⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⠀⣿⣿⣿⡿⡃⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡄⠉⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠈⢽⣿⣿⣿⡿⠟⠛⠛⠳⣾⡛⠻⢿⠅⣼⠹⠒
⠀⠀⠐⠒⠒⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣶⣦⣤⣿⣿⢟⣽⠇⢘⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣀⣀⣤⡶⠋⢁⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠁⠐⠀
⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣆⠀⠀⠙⢿⣿⣿⣿⡿⣫⣵⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣐⣚⡟
⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠋⢫⠀⠀⢀⠈⠉⠉⠁⠺⠛⢿⣿⣿⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠿⠿⣿⠿⠛⠁⠀⠀⠀⢀⢏⣤⠀⠀⠀⠀⡀⠀⣀⢀⣀⣴⣤⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠠⠶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⢀⠀⠀⠀⢠⣾⣿⣯⣿⣿⣿⠝⠐⠫⣵⣼⣿⣿⣿⣿⣿
⠀⠀⠠⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⠀⠸⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠘⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⣿⡫⢒⠶⣶⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢰⡿⠀⣼⣿⡿⣻⣽⢿⣿⣶⣦⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣦⣴⣶⣶⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣟⣵⣾⣷⣾⣿⣿⡇⠀⠈⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⠟⠛⠻⡿⠿⠿⠟⠇⠀⠈⠃⠘⠻⢿⠟⠋⠃⢸⣿⠛⠻⠇⠀⠘⢿⣿⣿⠛⠛⠿⢿⠃⠀⣿⠟⠛⡟⠛⠿⠛⠻⠛⠁⠀⠀⠘⢻⣿⣿⣿⣧⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⣀⣣⡄⠀⣤⡄⠀⠀⠀⠰⠀⢸⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣿⡿⠀⠰⠀⢸⠀⠀⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠀⢻⡇⠀⢻⡇⠀⠀⠀⠀⠘⠛⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠊⠻⣿⣿⣻⣯⣿⣿⣿⣿⢫⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣸⡇⠀⢠⡀⠀⠀⣰⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⣀⣿⣿⠀⠈⠀⣠⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⡀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠛⠛⠛⠹⣿⣿⣿⣿⠿⠿⠿⣿⣧⣄⠀⠀⠈⠙⠁⢸⣿⠉⠙⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⠿⠋⠈⣿⣿⣧⣀⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠁⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣦⣄⣀⣠
⣤⠾⠿⠻⠇⠀⣀⡌⠁⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠁⢛⡣⠀⢉⣰⠿⠃⠠⠀⢀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠘⠛⢻⣤⠀⠴⢣⡤⢀⣤⣹⣿⠿⠀⣼⣿⣭⣶⠀⠀⠱⠀⠀⠈⠙⣻⠟⠛⠛⠓⠁⠙
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠒⠀⠤⠄⠀⡄⡈⠛⠀⢀⣀⡸⠋⠀⠜⠛⢁⣿⠂⠈⠁⠀⠀⢠⢺⣇⣠⣤⣤⣤⣤⣀⣀⠀⠠⡄⠀⠉⠥⠀⢠⢾⡇⢸⡟⠿⢹⣆⠀⠉⠉⠋⠙⠀⢠⣦⠀⠀⠰⠆⠈⠀⠀⠀⠀⠀⠀
⠻⠒⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⠿⠂⠀⠀⢀⡄⠀⠒⢐⠏⠁⢀⣀⠈⠉⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⢰⢦⣘⣻⣤⠏⠀⣼⣿⡏⠀⢀⣀⠀⠳⠂⢘⣍⡠⢤⣴⣷⡦⠀⠀⢀⡀⠀⠰
⠓⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢃⢀⣠⣶⣷⣴⣾⣿⡆⠀⣿⡶⠀⠸⠿⡗⠀⣰⣿⣿⣿⡻⢿⣿⣿⣿⣿⡿⠿⢿⣿⡏⠁⠐⠙⣟⡋⠙⡛⠋⠋⣸⡱⠶⢶⣶⠿⠆⠀⠉⠻⣷⣾⣿⣧⣧⣄⠁⠙⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠿⠿⡟⣻⣻⡿⠻⠁⢁⠘⣶⡷⡆⣤⢀⠀⠀⣼⣿⣟⣭⣤⠉⣰⣿⣿⣿⡁⢀⣈⠙⢻⣿⡆⠀⠀⠀⣠⠆⠀⠰⠃⣃⡀⠀⠉⠉⠐⠖⠀⠙⠁⣿⡀⠜⠛⣿⣿⡷⣼⣴⣦⡤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣟⡉⢙⠟⠓⠈⠁⣀⠸⠵⠓⠛⠉⠉⢻⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠻⣿⣭⣿⣷⣿⣷⠀⠘⠉⠉⠀⠀⠞⠀⠉⠉⠀⠀⠀⠀⠂⠉⠀⠀⠁⢻⣯⣤⣔⣶⣿⣿⣿⣅⣿
⠀⠀⠀⠐⠖⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⠟⠛⠠⣶⠢⡯⠍⠂⢠⡄⠀⡂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢈⣀⠀⠶⢶⣉⣹⣿⣾⠞⠀⣀⣠⣶⣶⣿⣿⡿⣿⠿⠿⠛⠳⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢛⠁⣀⡘⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⡤⠨⣽⡷⠀⠀⣼⣿⣿⣷⡄⠉⠁⠀⠹⠾⠃⠉⢨⠁⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠘⣀⣰⣦⣤⣤⣴⣶⠀⠀⠀⠀⠰⠊⣽⠥⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣷⠀⠀⠀⠀⢼⣽⡿⢁⠰⡿⠉⠋⠁⢠⣏⠃⠀⢘⡋⠉⠀⠦⠄⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠛⠳⠶⠙⣿⣥⠀⠀⠀⠰⣆⠀⠈⠉⣡⣀⠀⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⣩⡀⢈⡄⠁⠀⠀⠀⠀⡉⠹⣷⡾⢠⠓⠀⢶⣴⣷⣶⡔⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠁⠛⠀⠀⠈⠀⠈⠀⠈⠀⠛⠀⠁⠋⠿⡀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠶⠂⠀⠶⠶⠤⠀⠊⠽⠿⠀⠒⠟⠁⠀⠀⠤⠤⠀⠀⡞⠋⠁⠀⢺⠟
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⢦⡀⠠⠎⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄⡿⡟⣛⣿⣿⡿⠟⠋⠀⢤⣀⣀⡄⢺⣿⠄⠀⢀⣿⠉⠀⠀⠀⠨⠾⠿⠂⠀⢀⠀⠘⢫⣁⣨⠿⠾
⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠊⠀⠀⠀⠀⠸⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠟⠙⠛⠀⠀⠀⠀⠀⢺⣿⣿⣧⠀⠀⠀⠀⠉⡢⠁⠘⠒⠀⠈⠙⠻⣿⡡⠇⠀⠀⠊⡠⠀⢿⣿⠗⠀⠀⣹⠋⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣤⠤⢄⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⡿⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⢠⣀⢡⠀⣉⠘⣧⣄⡀⢀⠀⠀⠀⠰⠻⠆⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣂⡄⢠⣄⠀⠀⢀⣴⡾⣿⣿⠿⠋⠉⠹⣾⠿⠛⣿⡏⠀⠀⠈⢿⣿⡆⠄⠀⠀⠀⠀⢀⣴⣾⠏⠀⠙⣿⡏⣿⣿⣦⡥⠶⢤⣀⣤⣀⣡⣹⣀⣀⣸⠶⠑⣆⣨⡍⢡⡈⠀⠛⠀⠇⠀⠀⠀⠀
⠀⠀⡤⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠛⣰⣶⣌⣩⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⢠⣿⢰⣀⠀⠀⠙⢿⣄⠀⠀⠀⣤⣿⣿⣿⠀⠀⠀⣿⣾⡟⠛⠁⠀⠀⠀⠙⢿⣿⣟⠀⠉⠉⠋⠀⣀⡟⡉⣀⠸⣷⡆⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠂⢰⣿⣿⣿⢹⣿⣿⣷⣤⠘⠓⢀⣀⣾⣿⣿⡞⣿⣿⣦⣄⡀⠈⠁⢠⡾⠿⠟⠋⠁⠀⣀⣴⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⠀⢀⠤⣏⣀⠃⡈⠀⠈⠋⠙⠉⠉⠀⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⢠⣾⣿⣿⡿⣿⣿⣿⠉⢩⣶⡦⠘⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣠⣾⣿⡏⣿⣿⣿⣷⣀⠀⠛⠀⢀⣿⣿⣿⡿⣿⣿⣾⣏⠹⠿⢾⡿⠂⢴⣦⣀⡀⠒⣀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠈⢉⣀⡀⢀⣀⣠⣿⣿⣿⣿⡇⣿⣿⣿⣿⠆⠀⢱⣶⣾⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⢃⣿⣿⣿⡏⠉⢠⣄⠘⠻⣿⣿⣿⡇⣿⣿⣿⣿⣇⢀⡉⠉⠛⠿⢤⠿⡆⠙⢉⣷⠈⠭
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠿⣿⣿⣿⣿⣿⡇⣿⣿⡃⠀⢾⡶⠀⠉⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢸⣿⣿⡏⢸⣿⣿⣿⣷⣶⠈⠈⣠⣴⣿⣿⣿⡇⣿⣿⣿⣿⡿⠿⢹⣂⣀⠀⠃⠀⢀⡀⢦⣤⠬⣭
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⠿⡇⠀⢠⣶⣾⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⠇⣾⣿⣿⣿⠁⠈⣶⠄⠘⢻⣿⣿⣿⡇⣿⣿⣿⣿⣧⡤⢠⣉⣿⠀⠠⠄⠀⠀⠘⡛⠋⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢼⣿⣟⣀⣰⣿⡆⠠⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⡟⢰⣿⣿⣿⣿⣿⡆⠈⠡⣤⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣦⣌⠉⢋⡠⣶⣦⣀⣀⣈⣃⠤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣁⢰⢶⠖⠙⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠿⣶⡿⠿⠁⣽⣏⢀⠁⡭⠯⠋
⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⣿⠈⣿⣿⢰⣶⣶⡎⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡔⠉⠰⣿⣿⡷⢦⢄⣉⡀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⢿⣿⣷⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡙⢷⣶⠖⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠆⠀⠀⣀⡀
⠀⠐⠒⠙⠂⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠙⠛⠀⠀⠀⢀⣼⣿⣿⣿⣿⡇⣴⣾⣿⣯⣥⣤⣤⡄⢸⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⡄⠀⢴⡤⠤⠀⠇⠀⠀⡾⣆⣰
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⡇⣻⣿⣿⣿⣿⣿⣿⡇⣼⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⠃⠠⣤⣶⣾⣁⠀⠈⠲⠦⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣟⢰⣿⣿⣿⣿⣿⣿⣿⣷⢀⣄⣉⡙⠋⠉⠶⠂⠀⠀⠘
⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡇⢹⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠋⠀⠀⠀⠀⢿⠛⠓⠴
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⢻⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⣤⣤⣤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⢸⣿⣿⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⡿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣧⠈⠉⠉⠉⠉⠁⠀⢰⣿⣿⣿⡷⠀⢩⣿⣿⣿⣿⡿⠟⠓⠙⠳⣏⡛⠻⢿⠀⡎⠉⠃
⠀⠀⠀⠒⠒⠂⣰⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠘⢿⣿⣿⣿⣷⣶⣦⣤⣤⣿⡿⣫⣾⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡀⠀⠀⠀⢀⣀⣀⣿⠿⠿⣿⠇⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠂⠐⠀
⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⢤⣄⠀⠙⠛⠿⣿⣿⣿⣿⢟⣯⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣷⣶⣾⣿⣿⡿⠋⠀⡶⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣒⣟⢿
⠉⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠀⠀⠀⠀⠈⠀⠈⠁⠛⠛⠿⣿⡿⠀⢸⢿⣿⣿⣿⣿⣿⣿⡟⠀⢼⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⢠⣾⠁⠀⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠠⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣵⣶⠇⠀⠀⢠⣾⣿⣯⣿⣿⣿⠝⠐⠫⣵⣼⣿⣿⣿⣿⣿
⠀⠀⠠⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⡇⠀⢰⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⡿⡫⢒⠶⣶⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢣⣿⠇⣠⣿⣿⢟⣛⡻⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⣴⣤⣤⣶⣶⣶⣾⣿⣷⠀⠀⠀⣸⣿⣿⣿⣧⣿⣿⣿⣿⣿⣟⣵⣾⣷⣾⣿⣿⡇⠀⠈⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠚⠟⠛⡿⠛⠛⠻⡟⠛⠛⠃⠀⠘⠟⠐⠛⠻⢿⠏⠛⠃⢻⣿⠛⠻⠀⠀⠛⢿⣿⣿⠛⠛⠿⢿⠃⠀⣿⠟⠛⡟⠛⠿⠛⢻⠛⠁⠀⢰⣿⣿⣿⣿⣿⣇⢿⣿⣿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⣀⣴⡄⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⣿⡿⠀⠰⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⡀⠈⢻⡇⠀⢰⠀⠀⠀⠀⠘⠛⠛⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⠀⢠⠀⠘⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠊⠻⣿⣿⣻⣯⣽⣿⣿⣿⣯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⢀⣧⡀⠁⢀⣼⡇⠀⠸⠇⠀⠀⠀⠀⠀⣸⠀⠀⠉⢹⣿⠀⠀⠀⠀⠀⣀⣿⣿⠀⠈⠀⡀⠀⠀⠈⠀⠀⡇⠀⣀⠀⢸⠀⠀⠀⣀⣿⣿⣿⠛⠿⣿⣇⢀⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠃⠀⠀⠈⠙⠃⠀⣿⡇⠉⠹⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⠏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠸⠁⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣦⣄⣀⣠
⣀⡼⡿⢿⡇⠠⣠⡘⠁⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠀⡀⢀⡀⠀⠘⠁⠛⠣⠀⢉⢠⠿⠂⠠⠀⡀⠀⠠⠀⡀⠀⠠⠂⠀⠀⠀⠘⠛⢋⣄⠀⠔⢣⡄⢀⣈⣻⣿⠷⠀⣼⣿⣿⣯⠀⠀⠳⠈⠉⠈⠛⣻⠿⠛⠛⠒⠃⠛
⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠠⡀⢠⠤⠂⣀⠙⠓⠀⢀⡀⡸⠋⠀⠴⠞⢃⡗⠈⠙⠁⠀⠠⠠⣾⠂⠀⣀⣀⣀⣀⡀⠀⠀⢀⡄⠀⠉⠥⠀⢀⣿⠇⢸⡿⠿⢻⣆⠀⠉⠙⠋⠻⠀⢀⣠⠀⠀⠰⠄⠁⠀⠀⠀⠀⠀⠀
⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠱⠾⠆⠀⠈⢡⡀⠀⠒⢐⡏⠁⢀⡀⠈⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡘⠃⠀⣀⢠⣠⢛⣻⣀⡏⠀⣼⣿⡏⠀⢀⠀⠀⠒⠂⢙⣿⡠⢀⣾⣧⡤⠀⠀⢀⠀⠀⠰
⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢀⢀⣤⣦⣴⣾⣷⡄⠀⣷⡶⠀⠸⣿⡇⢀⣴⣿⡿⢿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡾⠋⠉⠈⠛⣟⡛⠛⠻⠍⠏⣹⡰⠶⣤⣾⣷⡆⠀⠙⢻⣷⣾⣿⣯⣅⡈⠀⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠶⠿⠟⣿⣿⡿⠿⠁⢑⡘⣦⣯⡔⢄⠀⠀⢀⣾⠟⣋⣉⢀⣽⣿⣿⣏⠀⠀⠉⠛⢿⣿⡄⠀⠀⠀⠀⣀⠆⠀⠰⠆⣁⠀⠀⠉⠉⠠⡤⠀⠛⠂⣟⡡⠙⢛⣿⣿⣷⣴⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣟⠋⢙⠟⠒⠺⠁⣂⢸⠥⠒⠓⠘⠂⣾⣿⣿⣿⣶⡟⠉⠉⠉⠙⢿⣭⣝⣿⣿⣿⣿⠀⠀⠘⠋⠉⠀⠐⠛⠐⠉⠁⠀⠄⠀⠀⠐⠂⠀⠈⠁⣻⣇⣀⡡⣶⣿⣿⣿⡉⣿
⠀⠀⠀⠀⠤⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠘⠻⠟⠋⢠⡶⠤⡮⠝⠂⢠⠀⠐⠂⢠⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣾⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⢦⣶⣓⣹⣶⣶⠞⠁⢀⣠⣶⣿⣿⣿⣿⣿⠿⢿⠛⢿⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢛⠂⣀⠘⠇⢀⠀⣿⣿⣿⣿⣯⣿⠋⠀⠀⠀⠈⢻⣟⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⡀⠬⢿⡦⠄⠀⣽⣿⣿⣷⡈⠉⠉⠈⢻⠾⠇⠉⢨⠁⠀⠀⠐⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⣀⣠⣦⣠⣤⣴⣶⠀⠀⠀⠀⠰⢚⣿⡅⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢈⣯⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⣽⣽⠿⠁⠰⡿⠛⠛⠋⢀⡟⠃⠀⠐⠀⠃⠀⠤⡄⠀⠀⠀⠸⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠿⠧⠾⠝⣿⣭⠀⠀⠀⠰⡄⠀⠉⠈⣣⠀⠀⣿⣿⣿⣿⣿⣇⢀⣀⡀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠐⢻⣉⡀⢘⡀⠁⠀⠀⠀⢀⠉⢳⣶⡶⢠⠂⠩⣧⣴⣧⣶⡴⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠚⠀⠀⠁⠈⠈⠀⠀⠀⠛⠀⠁⠋⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠳⠶⠂⠀⠴⢶⠥⠀⠒⠽⠏⠀⠔⠟⠃⠀⠠⠤⠄⠀⠠⠟⠛⢉⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣠⣰⠶⣀⠠⠔⠀⠀⠀⠁⠈⠀⠈⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠳⠞⠟⠿⢽⣿⣿⣿⡿⠿⠃⠠⢄⣀⣀⡀⢶⣶⠄⠀⠀⣷⠓⠀⠀⠀⠠⠾⠿⠀⠀⠀⠀⠰⢏⡃⣸⠿⢾
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠄⠀⠸⠿⠟⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⡏⠉⠋⠀⠀⠀⠀⠐⣿⣿⣿⣿⡄⠀⠠⠀⠀⠙⡀⠁⠸⠥⠀⠀⡟⠿⣷⠡⠂⠀⠀⠒⣠⠔⢿⣿⠇⠀⠀⣽⠑⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡤⢄⠀⠀⢠⢤⣤⣤⣤⣄⣈⣁⣤⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡈⣀⠈⡉⢙⣦⣄⠐⠀⠀⠀⠀⡸⠹⠄⠚⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡠⠤⢀⣤⠄⠀⢀⣰⣶⣿⡿⠿⠋⠉⢹⣿⠿⢿⣿⡏⠀⠀⢹⣿⣧⡠⠀⠀⠀⠀⠀⣠⣶⡟⠉⠙⢿⣿⣷⣷⣶⣅⣠⣤⣀⢀⣄⠈⣉⣹⡀⠀⣸⠦⠑⣆⣉⡟⣀⠈⠀⠒⠀⠇⠀⠀⠀⠀
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠋⠉⠙⠓⣰⡶⣌⣩⢻⣿⣧⡄⠀⠀⠀⠀⠀⠀⢸⣷⢄⡀⠀⠘⢿⣦⠀⠀⠀⢠⣾⣿⣿⡀⠀⠀⢸⡿⣼⡿⠿⠋⠁⠀⠀⠻⣿⣿⡿⠈⠉⠙⠋⠀⢐⣿⡉⣀⠹⣷⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠂⢰⣿⣿⣿⣿⣿⣿⣷⣦⠚⠁⣀⣰⣿⣿⣿⢸⣿⣶⣄⡀⠈⠁⠀⣴⡿⠿⠟⠋⠀⠀⣀⣸⣿⣿⣇⣀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⢀⢀⣏⡀⢁⠈⠀⠈⠋⠋⠉⠁⠐⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⢠⣿⣿⣿⡇⣿⣿⣿⠀⢡⣶⡆⠙⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⡏⣿⣿⣿⣇⠀⠀⠶⠀⠀⣶⣾⣿⣾⣿⣦⣔⠚⢻⠿⢯⡿⠀⢴⣆⣀⠀⠒⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢘⢩⣀⡀⠀⢀⣠⣿⣿⣿⣿⣧⣿⣿⣿⣿⠀⠀⣡⣶⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣾⣿⣿⣿⢃⣿⣿⣿⡿⠛⢀⡀⠰⠷⣿⣿⣿⡇⣿⣿⣿⣿⣄⠀⠊⠉⠲⠿⣤⢿⡌⠛⢉⣶⠠⣉
⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣯⣿⣿⣿⣿⣿⢸⣿⣿⢁⠀⣶⡗⠀⢹⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡟⢸⣿⣿⣿⣧⣤⠘⠛⢀⣀⣿⣿⣿⡇⣿⣿⣿⣿⡿⠯⢳⡀⣀⠀⠃⠀⢀⠀⣆⣬⠭⣍
⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⡿⠿⠇⠀⢠⣶⣾⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⢿⣿⣿⡇⣼⣿⣿⣿⠛⠉⣀⡀⠛⢿⣿⣿⣿⡇⣿⣿⣿⣿⣧⡤⢀⣉⡿⠀⢠⠄⠈⠀⠘⠛⠛⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣇⣀⣾⣿⡄⢀⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⡿⢠⣿⣿⣿⣿⣤⡄⠋⢁⣀⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣴⣍⢉⠓⠠⣶⣦⣀⣀⣘⠃⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⢿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢹⢁⣾⣿⣿⣿⣿⠛⢡⣤⡌⠻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠉⣽⣉⠉⠉⡽⠗⠋
⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣷⠸⣿⡇⢶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠈⠉⠀⣴⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣧⠚⠉⠰⣿⣿⡷⢤⢀⣀⠀⠀⠀
⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣦⣤⣤⢸⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠋⠀⠀⠠⠆⠀⠈⣀⡀
⠀⠐⠒⠙⠂⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠉⠉⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⣨⣽⣿⣗⣊⣉⣁⡉⢹⣿⣿⡏⢸⣿⣿⣿⣿⣿⣧⠀⠀⣴⡤⠤⠀⠇⠀⢀⡾⣆⣴
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣶⣶⣂⠀⠀⠦⠧⠁⠉
⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢀⣿⣿⣿⣿⣿⣿⣷⡆⢀⣈⣉⡙⠋⠁⠶⠀⠀⠀⠛
⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠋⠀⠀⠀⠀⣾⠛⠳⠴
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢡⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣠⣴⣿⣿⣿⣿⣿⠀⢿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣼⣽⣿⣿⣿⣿⣿⣿⡄⠈⠁⠀⠀⠀⠠⣤⣄⣤⡄⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠈⠉⣿⣿⣿⡿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣧⠘⠛⠛⠛⠛⠋⠉⢡⣾⣿⣿⣯⠙⢛⣿⣿⣿⣿⡿⠗⠀⠛⠷⣏⡛⠻⢯⢠⡎⠙⠂
⠀⠀⠀⠲⠖⠂⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⢻⣿⣿⣿⣿⣶⣦⣤⣤⣿⡿⣫⣾⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠂⠐⠀
⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⡀⠈⡛⠿⣿⣿⣿⣿⢟⣫⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣧⣤⣴⣶⣶⣶⡿⠛⠋⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣚⣟⢿
⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠃⠀⠀⡀⠉⠁⠉⠁⠛⠻⢿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠃⠀⠀⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠠⠤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⣠⡆⣰⠇⠀⠀⢀⣾⣿⣿⣿⣿⣿⠝⠐⠫⣵⣼⣯⣿⣿⣿⣿
⠀⠀⠀⠄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢸⣯⠀⢰⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⡿⡫⢐⠶⣶⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⡏⢠⣾⣿⢟⣛⡻⣿⣷⣶⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⣀⣠⣀⣤⣤⣶⣧⠀⠀⠀⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⣵⣾⣷⣾⣿⣿⡇⠀⠈⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⠛⠛⠻⡿⠿⠿⠛⠇⠀⠹⠁⠛⠻⢿⠗⠛⠃⢹⣿⠛⠻⠀⠀⠛⢿⣿⣿⠛⠛⠻⢿⠁⠀⣿⠟⠛⡟⠛⢿⠛⢻⠛⠀⠀⠰⣿⣿⣿⣿⣿⣇⢿⣿⣿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠢⣀⣷⡆⠀⣴⡆⠀⠀⠀⢰⠀⢸⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⣿⣿⠀⠰⠀⢸⠀⠀⣿⠀⠀⠃⠀⠈⠀⠘⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠈⢻⡇⠀⣿⡇⠀⠀⠀⢀⠛⠛⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠈⣿⣷⠀⢠⠀⠈⠀⠀⣿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠊⠻⣿⣿⣻⣯⣽⣿⣿⣿⣯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⢀⣼⡇⠀⣿⡇⠀⢰⡀⠈⠀⣰⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⣀⣿⣿⠀⠈⠀⠀⠀⠀⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡏⢀⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠛⠛⠛⠁⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⣿⡇⠉⢻⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⡿⠟⢹⣷⣤⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠿⣿⡿⠰⠁⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣦⣄⣀⣠
⣀⡼⣿⢿⠇⠀⡀⡐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠓⠃⠈⠛⢀⠶⠀⠠⠀⠀⠀⠤⠀⠀⡀⠬⠛⠁⠀⠀⠒⠛⣣⣄⠀⠔⢣⡄⣀⣘⢻⣿⠷⠀⣸⣿⣭⣂⠀⠘⠇⠈⠉⠙⠛⣻⠿⠿⠻⠒⠀⠛
⠀⠀⠀⠀⠀⠀⠴⠅⠀⠀⠀⠠⠄⢤⠀⠂⡀⠈⠓⠀⢄⡀⠹⠏⠠⠴⠞⢃⡗⠌⠝⠁⠀⠀⠀⣾⣆⣀⣀⣀⣀⣉⢀⠀⠀⢠⡄⠀⠈⠅⠀⢀⣿⠇⣼⠿⠞⢳⡆⠀⠛⠛⠋⠋⠀⢠⣤⠀⠀⡤⠄⠁⠀⠀⠀⠀⠀⠠
⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠒⠱⠶⠆⠀⠈⠁⡤⠀⠒⢰⡟⠁⢀⡀⠀⠒⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠁⠀⣀⡠⣠⠛⣿⣠⡍⠀⣴⣿⠏⠀⠀⢀⠐⠦⠂⢙⣿⡀⣠⣾⣤⡄⠀⠀⢀⠀⠀⢰
⠃⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢀⣤⣧⣴⣾⣷⡄⠀⣷⡔⠀⠸⣿⡆⠀⣰⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠻⣿⡛⠛⠗⠊⠏⣹⡰⠦⣤⣴⢶⡆⠀⠛⢻⣧⣿⣿⣽⣁⡈⠀⠛⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠⠶⠿⡟⣿⣻⡿⠿⠁⢂⣙⣤⣯⡅⣄⠀⠀⠀⣾⣿⢟⣩⣉⡁⢨⣿⣿⣿⠋⠁⠐⠻⣿⣧⠀⠀⠀⠈⣀⠆⠀⡴⠆⣁⠀⠀⠙⠛⠠⠄⠀⠓⠪⣏⣉⠛⢻⣿⣿⣇⣄⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡟⠋⢙⠟⠒⠢⠃⣂⣸⡗⠶⠗⠚⠊⢻⣿⣿⣿⣿⣷⣾⠟⠛⠛⠛⢷⣖⡲⢶⣬⣿⡆⠀⠐⠊⠛⠀⠠⠗⠐⠛⠃⠀⠄⠀⠀⠐⠒⠀⠈⠉⣿⣂⣈⠭⣼⣿⣿⣯⡉⣿
⠀⠀⠀⠠⠤⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠘⠻⠟⠊⢠⣴⠤⡯⠝⠂⢀⠀⠀⠂⢀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣈⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢐⣀⠠⣦⣶⠒⣲⣾⣶⡞⠀⢀⣠⣴⣿⣿⣿⣿⣿⠿⡟⠛⣯⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠒⠀⢛⠂⡀⠘⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⣀⡬⢻⡦⠀⢈⣽⣿⣿⣧⡐⠉⠉⠉⣫⠿⠊⠉⢰⠃⠀⠀⠰⢆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⣀⣠⣆⣠⣤⣤⣴⠀⠀⠀⠀⢐⢚⣿⣁⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⡄⠀⠀⠉⢀⣜⣽⡿⠀⢰⡿⠛⠛⠋⣠⡟⠂⠀⠒⠒⠃⠀⢤⠀⠀⠀⠀⠸⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠿⠦⠶⠟⣿⣭⠀⠀⠀⠠⣀⠀⠉⠘⢣⠀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢛⣋⠀⢘⡈⠁⠀⠀⠀⢈⠛⢻⣶⡮⢠⠆⢱⣤⣼⣇⣦⡰⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠚⠀⠀⠉⠉⠈⠀⠀⠐⠛⠀⠁⠊⡿⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠷⠶⢿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠶⠴⠄⠀⠬⣥⣍⠀⠒⡿⡇⠀⠴⠛⠃⠀⠠⠤⠄⠀⢠⠟⠛⢉⠀⢾⠟
⠀⠀⠀⠀⠀⠀⢔⠂⠀⠀⠀⠀⠀⠀⠀⣠⣰⠖⡀⢠⠖⠀⠀⠀⠁⠈⠀⠈⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣦⣴⣿⡿⢿⣿⣿⣿⠟⠃⠠⣀⢀⣀⡀⣴⣒⠀⠀⠀⣷⠃⠀⠀⠀⢰⢼⠿⠀⠀⠀⠀⠰⢖⡃⣸⠿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⠿⠟⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠛⠛⠁⠀⠈⠉⠀⣿⣿⣯⠀⠀⠠⠀⠈⠛⣅⠃⠸⠥⠀⠁⡟⠿⣧⠱⠂⠀⠀⠒⣤⠀⣿⣿⠆⠀⠀⣷⠓⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡤⢄⠀⠀⢀⣤⣀⣀⣀⣀⣀⣁⣠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⢀⡙⣁⢈⡉⢰⣤⣀⠁⠀⠀⠀⠀⡸⠹⠀⠚⠢
⠀⠀⠀⠁⠀⠀⠠⠀⠀⢀⣠⠤⢠⣤⠀⠀⢀⣱⣶⣴⣿⡿⠛⠻⣿⣽⣿⣿⣿⠋⠉⠀⢹⣿⣷⠄⠀⠀⠀⠀⠀⢠⣴⡞⠉⠙⣿⡇⣿⣿⣖⣀⣤⣤⡀⢀⣄⡈⣉⣣⠀⠀⣹⡬⠳⣌⣙⠋⣀⠑⠐⠒⠰⠇⠀⠀⠀⠄
⢀⠀⣠⠁⠀⠀⠀⠀⠀⠈⠋⠉⠙⠛⣲⣶⡈⣻⣿⣿⡀⠀⠀⠀⠈⠉⠀⠉⣿⣆⣀⠀⠀⠘⢿⣆⠀⠀⠀⢀⣴⣿⣿⠁⠀⠀⢸⣳⣿⠛⠋⠁⠀⠀⠛⢻⣿⣿⠏⠈⠙⠛⠃⠀⢐⣟⠉⣀⢻⡶⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠂⣠⣷⣾⣿⣿⣿⣿⣄⡠⠖⠄⡀⣰⣶⣿⡇⣿⣿⣦⣄⠀⠈⠃⠀⣰⣿⡿⠿⠋⠀⠀⣀⣼⣿⣧⣤⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⠀⠀⢀⢈⣏⠈⠁⠉⠀⠙⠛⠋⠉⠁⠐⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⢠⣿⣿⣿⢻⣿⣿⡟⠙⢣⣤⠘⢿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⢹⣿⣿⣿⣀⠀⠒⠂⠀⣸⣿⣿⡇⣿⣿⣿⣶⡚⢻⠿⢽⠷⠀⣴⣆⣀⠀⠂⣀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⢘⠩⣀⡀⠀⠀⣠⣿⣿⣿⣿⢸⣿⣿⣧⣤⠉⠛⣠⣼⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⡇⣿⣿⣿⡿⠛⢃⣀⠀⠻⣿⣿⣿⡇⣿⣿⣿⣿⣷⡄⠐⠊⠑⠲⠿⣬⣿⡈⠛⢉⣦⠂⣉
⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣏⣿⣿⣿⣿⡟⣼⣿⡟⠉⢡⣦⠌⠛⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⢠⣿⣿⣿⣷⣤⠚⠛⢠⣀⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⠟⢳⣀⠀⠀⠃⠀⢀⠀⣄⣌⠬⣉
⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⣿⣿⣿⣶⠈⠉⣠⣤⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⢿⣿⡏⣸⣿⣿⣿⠏⠉⣤⣄⠙⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⣧⡀⢈⣙⡿⠀⢠⠄⠈⠀⠘⠛⠛⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣿⠠⢠⣶⣆⠙⣹⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⢁⣿⣿⣿⣿⣷⡆⠉⢁⣤⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣤⣍⡛⠃⢤⣶⣤⣀⣀⡘⠃⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⣿⣿⣿⠉⠉⠁⣶⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠃⣾⣿⣿⣿⣿⣉⣱⣶⡖⠛⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⢉⣿⣉⠉⢉⡽⠟⠋
⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⣸⣿⣿⣿⣿⣿⡆⢿⣿⢣⣤⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠀⠀⠀⣴⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⠘⠉⢰⣿⣿⡷⢤⣀⡃⠀⠀⠀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣅⢸⣿⣷⣭⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⡇⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣇⠶⣶⡶⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠠⠂⠀⠀⣀⠀
⠀⠐⠔⠙⠂⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠂⠙⠻⠃⠀⠀⠀⣠⣿⣿⣿⣿⡇⢠⣾⣿⣿⣗⣂⣀⡄⠉⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⠄⠀⣴⡤⠤⠰⠇⠀⢀⣾⣤⣲
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣿⡧⢸⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⡀⢦⣤⣶⣶⣂⠀⠁⠦⠎⠁⠉
⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⡀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡧⢸⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣈⣉⡙⠉⠉⠶⠀⠀⠀⠛
⠀⠀⠀⣀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⢸⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⡇⣿⣿⢿⣿⣿⣿⣿⣿⣯⠈⠙⠉⠀⠀⠀⠰⣾⠛⠳⠴
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡶⠋⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⢠⣤⡄⣤⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣿⡇⠀⠀⠀⠈⠉⠉⢹⣿⣿⣿⡀⠀⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡌⠛⠉⠉⠉⠉⠉⠁⣾⣿⣿⣿⠂⠀⠀⣿⣿⣿⣿⡿⠟⠛⠛⢶⣏⠛⠻⢯⢠⡏⠙⠂
⠀⠀⠀⠶⠖⠂⣀⣴⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠹⣿⣿⣶⣶⣤⣤⣄⣸⣿⢟⣵⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣸⣿⠿⢿⡏⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠂⠒⢀
⣀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣤⠀⠈⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣷⣶⣶⣶⣿⣿⠟⠀⢠⠆⢸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣒⣟⢟
⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⡇⠀⠀⠈⠋⠉⠉⠺⠿⠿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⠀⠀⣰⠏⠀⠀⠀⠀⡀⠀⣀⢀⣀⣴⣠⣠⣠⣄⣴⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠠⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢡⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣾⣰⠇⠀⠀⢠⣾⣿⣯⣿⣿⣿⠝⠐⠻⣵⣼⣯⣿⣿⣿⣿
⠀⠀⠀⠄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣼⠉⠰⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣄⡀⣠⣼⣿⣿⣿⣿⡿⡫⢐⠶⣶⣌⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⡿⢀⣼⣿⡿⣟⠻⣿⣷⣶⣦⡄⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣤⣤⣶⣶⣶⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣧⣿⣿⣿⣿⣿⡟⣵⣾⣷⣾⣿⣿⡇⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠘⡟⠛⡿⠛⠛⠻⡟⠛⠛⠛⠁⠀⠃⠞⠛⠛⢿⠛⠛⠘⣿⣿⠛⠃⠀⠐⠛⢿⣿⣿⠛⠛⠿⢗⠀⠚⣿⠟⠛⡟⠛⠿⠛⢿⠛⠀⠀⠀⣾⣿⣿⣿⣿⣇⢿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⣀⣴⡄⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠠⣿⣿⠀⠀⠀⠀⠀⣀⣿⣿⠀⠰⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⡀⠈⢻⡇⠀⢠⠀⠀⠀⠀⢸⠛⠃⠀⠀⣀⣿⣿⠀⠀⠀⠀⠀⠈⣿⣷⠀⢠⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠊⠻⣿⣿⣻⣯⣽⣿⣿⣿⣯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⢀⣧⡀⠁⢀⣼⡇⠀⠸⠀⠀⠀⠀⠈⠀⣰⠀⠀⠉⢹⣿⠀⠀⠀⠀⠀⣀⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢿⣿⣿⣏⣀⠀⠈⠛⢿⣿⣿⡿⢿⣿⣿⣧⠀⠀⠀⠀
⠀⠛⠁⠝⠛⠻⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠃⠀⠀⠈⠛⠀⢸⣿⠉⠉⢿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡿⠛⠉⣿⣿⣷⣠⣶⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⠹⠿⠁⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣦⣄⣀⣠

                    ䷩ 𝚕𝚒𝚗𝚎 4087

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/07/30/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2024/07/30/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Jul 30, 2024


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Android_Leftovers⠀⇛


           Google starts rolling out Android Cross-device services -
           PhoneArena


   2. ⚓ Linux_Mint_22_–_subtle_but_desirable_improvements_to_an_already
      powerful_operating_system⠀⇛


           Linux Mint is not known for continuously releasing many gadgets
           and a plethora of new internal and visual changes


   3. ⚓ GNU/Linux_Now_at_16.2%_in_India_(Desktops_and_Laptops) [original]⠀⇛


           This means that Windows is quickly losing its "monopoly-like"
           status


      ⚓  New⠀⇛


   4. ⚓ Wine_9.14_Released⠀⇛


           The Wine development release 9.14 is now available


   5. ⚓ today's_howtos⠀⇛


           only 4 more howtos for now


   6. ⚓ 9to5Linux_Weekly_Roundup:_July_28th,_2024⠀⇛


           The 198th installment of the 9to5Linux Weekly Roundup is here
           for the week ending on July 28th, 2024.


   7. ⚓ Programming_Leftovers⠀⇛


           Programming related picks for the day


   8. ⚓ today's_leftovers⠀⇛


           mix of many GNU/Linux related topics


   9. ⚓ Windows_TCO:_ClownFlare,_Cyberattack,_and_Secure_Boot⠀⇛


           3 more stories


  10. ⚓ today's_howtos⠀⇛


           many howtos for today


  11. ⚓ Forlinx_FET3576-C_Rockchip_RK3576_SoM_powers_feature-rich_OK3576-
      C_board_for_AIoT_applications⠀⇛


           In terms of software, the SoM is compatible with Linux 6.1.57
           and Android and supports multi-task and multi-scenario parallel
           processing


  12. ⚓ Best_Free_and_Open_Source_Software,_howtos_and_Installations⠀⇛


           There are so many terminal emulators available for Linux that
           the choice is, frankly, bamboozling


  13. ⚓ Review:_SysLinuxOS_12.4⠀⇛


           SysLinuxOS is a Debian-based GNU/Linux distribution designed
           for system administrators


  14. ⚓ What_I_did_in_KDE/Plasma_Mobile_land_in_July-ish⠀⇛


           As an exciting update, near the end of June (the 25th to be
           exact) I got accepted to the KDE dev team


  15. ⚓ What’s_Come_of_Lubuntu_as_of_its_24.04_Release?⠀⇛


           Lubuntu 24.04 was released along with the other Ubuntu flavored
           back in April 2024


  16. ⚓ KDE_Snaps,_Kubuntu,_Debian_updates_and_“Oh_no,_not_again..”⠀⇛


           This week our family suffered another loss with my brother in-
           law


  17. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


      =========================================================================
      The corresponding text-only bulletin for Monday contains all the text.
      Top-read articles (excluding bot/crawler visits):


                          Span from 2024-07-23 to 2024-07-29
      1764 /n/2024/07/23/
           Linux_Mint_22_Wilma_Is_Now_Available_for_Download_Here_s_What_s.shtml


      997  /n/2024/07/25/
           VirtualBox_7_1_Promises_Wayland_Support_for_Clipboard_Sharing_o.shtml


      958  /n/2024/07/23/
           NVIDIA_560_Beta_Linux_Driver_Released_with_Open_GPU_Kernel_Modu.shtml


      911  /n/2024/07/23/
           The_final_Linux_Mint_22_ISOs_are_undergoing_final_checks_before.shtml


      816  /n/2024/07/24/today_s_howtos.shtml


      809  /n/2024/07/24/
           GNOME_bans_Manjaro_Core_Team_Member_for_uttering_Lunduke.shtml


      774  /n/2024/07/23/The_GNU_C_Library_version_2_40_is_now_available.shtml


      761  /n/2024/07/27/today_s_howtos.shtml


      758  /n/2024/07/26/today_s_leftovers.1.shtml


      757  /n/2024/07/26/
           The_Debian_Project_mourns_the_loss_of_Peter_De_Schrijver.shtml


      730  /n/2024/07/23/
           First_Pop_OS_24_04_Alpha_with_COSMIC_DE_Drops_on_August_8.shtml




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣟⣛⣿⡿⣿⣿⣿⡿⠿⢿⣿⣿
⠛⠋⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⡗⠾⠛⠉⠉⠀⠀⢾⣿⣿⣿⠻⢿⡟⡋⢉⠙⡧⢙⣿⠿⣿⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠛⠛⢛⠛⠻⠿⢿⣿⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠠⠒⠐⠋⠛⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⠚⠒⠀⠀⠀⠀⠀⠈⠟⠛⠟⣬⠀⠹⣿⠿⠇⠀⠁⠀⠈⠉⠨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 4333

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/07/30/Truth_and_Microsoft_Aren_t_Compatible.shtml
    Gemini version at https://techrights.org/n/2024/07/30/Truth_and_Microsoft_Aren_t_Compatible.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Truth and Microsoft Aren't
Compatible⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024,
updated Jul 30, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Looking_north_up_the_Rio_Grande_in_Truth_or_Consequences,_NM
in_autumn_under_a_very_blue_sky⦈_


WE HAVE probably said something to that effect many times before, but now it's
a good time to revisit the matter because later today Microsoft will deliver a
bogus report with fake "results", i.e. the usual.


Moreover, Waggener_Edstrom will prepare an army of pseudo-journalists to
distract us from the facts. Truth and opinion aren't the same thing and
selective illumination of facts can be called "dishonesty" or "misdirection".


In the past, when we challenged convicted_pedophiles who had raped children and
lied about Microsoft's financial results (in Ars Technica), they came to IRC to
troll us and abuse us. The same people whom I_reported_to_the_police_some_hours
ago did this to us every time we challenged phony Microsoft finances, so the
subject must be very sensitive.


Later today when the so-called "press" or "media" says Microsoft performed
well... (they always say that!) be patient and wait for debt-related
information to surfaces. It's very much possible that Microsoft as a whole
operates at a loss. █


"Microsoft, the world’s most valuable company, declared a profit of $4.5
billion in 1998; when the cost of options awarded that year, plus the change in
the value of outstanding options, is deducted, the firm made a loss of $18
billion, according to Smithers."


                                                          --The_Economist,_1999




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⢤⣤⣀⠀⡄⠚⡱⠉⣿⣫⣤⣁⣄⡖⠍⢫⠍⣛⠿⢿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠩⠀⠨⠩⠹⣿⡒⠟⠅⠐⡿⣿⠿⢿⣿⠌⠏⠀⠩⠿⠶⠎⢺⣿⡇⠬⠟⠁⠘⠻⠏⠁⠀⠹⠿⣁⣀⣀⣈⣹⡿⠟⠛⠉⠹⠿⠛⠛⠛⠻⡿⠛⠟⠻⡟⠛⠛⠛⠛⣛⠛⠛⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢈⣻⡟⠋
⠁⠀⠀⠀⠀⠀⠀⠐⠒⡖⢶⠀⠁⠀⠐⠀⠀⠀⠀⠠⠤⣤⠀⠀⠁⢤⠄⠀⣤⣤⣤⠴⢶⣦⠀⠀⣈⣿⣉⡯⠳⠶⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡶⢶⠄⠠⣤⣤⡀⢀⣀⣉⣀⣄⣤⣶⣋⣀⢀⣤⣀⣶⣿⣶⣬⢾⡿⠵
⠀⠀⠀⠀⠀⠀⠉⠀⠐⠷⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠈⠩⠓⠂⠋⠉⠀⠐⠛⠋⠉⠈⠉⠉⠁⠀⠉⠝⠃⡤⠆⠀⠀⠀⡀⠀⠐⠂⠂⠀⠹⠞⠷⠂⢀⣷⢿⣿⣿⣿⠟⠻⣃⣄⣴⠿⣿⣯⡿⢋⣿⣛⢻⠟⠛⠗⣿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠈⠃⠁⠁⠀⠰⡟⠙⠋⠁⠚⠁⠀⠀⠀⠈⠃⠀⡠⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣆⡤⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠋⠃⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⣶⣶⣶⣶⣶⣶⣶⣤⣶⣦⣶⣶⣶⣤⣶⣴⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣴⣴⣦⣤⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣴⣶⣶⣶⣦⣶⣶⣦⣤⣦⣤⣴⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣷⣶⣶
⡀⠀⠀⠀⠀⠀⠰⣠⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢦⡹⡠⠄⠲⠀⠀⠀⣽⣿⣿⠟⢻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4409

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 30/07/2024: Burnout and Plan
9⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ 🔤SpellBinding:_ADEHINW_Wordo:_SEVEN⠀⇛


                # ⚓ Burnout⠀⇛


                       I've been meaning to make an entry for quite a
                       while now, but for one reason or another I never
                       get around to completing one. I surf the
                       gopherscape every night before bed, and it's good
                       to read people's entries.


                       This has been an unpleasant summer so far: hot and
                       humid and sticky, from sun up to sun down,
                       everyday. It saps all my energy and it puts me in a
                       bad mood. I am already looking forward to autumn
                       and cooler weather, however that probably won't be
                       until November, judging by last year.


                       Recently I was watching a television program where
                       a camera crew rode on a domestic ferry and
                       interviewed people here and there. At one point
                       they came upon an older woman in a cabin at the
                       front of the ship. The woman was quietly reading by
                       herself and she said she had been a nurse, had
                       raised her children and had been busy all her life.
                       Now she is retired and all she wants is time. Time
                       to herself to do what she wants. This struck a
                       particular chord with me, because I feel the same
                       way.


                       Earlier this year I said if I could retire tomorrow
                       I would. That is because I am burned out from work.
                       The corporate landscape has changed a lot since I
                       was young, and I don't think I'm fit for it
                       anymore. Let the younger generations take over so I
                       can retire.


                       Outside of work, I avoid the news except for things
                       domestic. I'm tired of war, and deceit and
                       gaslighting. At times it seems like the whole world
                       has gone mad. Everything seems to be going so fast,
                       and in a direction I personally am not comfortable
                       with.


          o § Politics and World Events⠀➾


                # ⚓ Five_good_things,_July_29⠀⇛


                       1. Thankful for God's protection when the kids and
                       I were in a car accident on Wednesday. Someone
                       (absentmindedly, it appears) turned in front of me
                       as I was going through a green light and I couldn't
                       avoid hitting them.


                       I prayed for protection before we left home that
                       day, which I always do. Mainly because I've made
                       enough absentminded (or just plain foolish -- gulp)
                       mistakes myself while driving that I know it can be
                       dangerous out there and the danger could come from
                       either me or others.


          o § Technology and Free Software⠀➾


                # ⚓ Plan_9_is_my_cove⠀⇛


                       Plan 9 is such a beautifully weird mixture of
                       ideas... God I love it so much.


                # ⚓ Fight_On!_Magazine_​#15⠀⇛


                       And it includes the Caverns of Slime! So now
                       there's a way to get them in print and PDF,
                       together with a lot of other good stuff.


                # ⚓ A_6502_on_a_$20_Tang_Nano_9K⠀⇛


                       Ah, after some fiddling, got a minimal 6502 system
                       flashing an LED. Running at stock 27MHz, with 2K
                       RAM and 2K ROM.


                # ⚓ Monday,_Monday⠀⇛


                       The bigger challenges of moving off of the $$$$$
                       Mainframe onto the $ of Linux (code for Unix, BSD,
                       etc.) always pop up when someone takes your claims
                       seriously. Today it was converting 2m lines of IBM
                       Mainframe Assembler code!


                # ⚓ From_the_White_House_to_Caesar's_Palace:_Trump_at_the_2024
                  Bitcoin_Conference⠀⇛


                       My first reaction to the news that Trump was
                       heading to Nashville to headline Bitcoin 2024: I
                       joked that he's scraping the bottom of the barrel
                       for support. The truth is, it's surprising that he
                       ever positioned himself as anti-cryptocurrency
                       since, in a sort of takes-one-to-know-one moment,
                       he clearly understood its utility, calling it "a
                       scam" in 2021.


                # § Internet/Gemini⠀➾


                      # ⚓ building_HTML_from_source⠀⇛


                             I don't remember when I did it, but I
                             downloaded the "source" for the jargon file,
                             and was wanting to make it so it could build
                             again. I remember trying to get it to build a
                             long time ago and it would fail to build for
                             various dumb reasons. ESR's tarball is
                             missing a handful of scripts that the build
                             scripts use, and there are some typos or
                             broken xml in a few of the files. I fixed
                             them as well as I could and commit'd all the
                             changes I was making into a git repo, so if
                             someone wants to pick up the jargon file
                             using ESR's build system, they wouldn't have
                             to redo this work. I also found that there
                             were a few sections in the tarball that
                             aren't included in the live version on ESR's
                             website.


                      # ⚓ Greetings_from_Lynx⠀⇛


                             I am back home from my holiday trip: I am sad
                             the holiday is over, but also happy to be
                             home.


                             It is really warm here and I am finding it a
                             bit hard to function. The house is fine (I
                             have aircon), but I pretty much only want to
                             go out in the early morning.


                # § Programming⠀➾


                      # ⚓ Chapter_Ten:_Embedding_Janet⠀⇛


                             Okay. In the last chapter we learned how to
                             call C code from Janet. In this chapter,
                             we’re going to learn how to call Janet code
                             from C.


                             Specifically, we’re going to learn how to
                             embed the Janet interpreter inside a larger
                             app — it doesn’t *have* to be written in C,
                             as long as it has a C FFI. But we’ll stick
                             with C as our lingua franca.


                             Oh wait! I forgot that JavaScript was
                             supposed to be our lingua franca. Oh no. Oh
                             no. We just spent a whole chapter writing C
                             code together and you didn’t say anything to
                             me? Did you forget about the `(say)`
                             function?


                      # ⚓ Back_to_the_Rust_programming_language,_again⠀⇛


                             So, This is an another post about my struggle
                             to push my little personal programming
                             project forward. I’m currently trying to make
                             a point & click game with 3D graphics. I
                             started this project a long, long time ago
                             mainly because I wanted to learn how a
                             computer does images from 3D models and found
                             this topic insanely interesting.


                      # ⚓ Chapter_Eleven:_Testing_and_Debugging⠀⇛


                             I know that you’ve been looking forward to
                             this chapter the whole book.


                             Sure, compile-time metaprogramming or
                             whatever is fine, but when do we get to talk
                             about *automated test suites*? You haven’t
                             even *thought* about skipping this one.


                             I hope we can forego the spiel about the
                             importance of testing — we’re both adults
                             here, and I’m going to assume that if you’ve
                             ever worked on a codebase in a dynamically
                             typed language for longer than six weeks, you
                             understand the value of a comprehensive
                             automated test suite and an ergonomic testing
                             framework.


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





                    ䷩ 𝚕𝚒𝚗𝚎 4672

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 30/07/2024: Atrocities in Sudan,
Escalations Near Lebanon⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Lebanon⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Internet_Policy/Net_Neutrality
          o Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ France24 ☛ ‘Tourists,_go_home!’:_Mass_tourism_exasperates_locals
            in_Spain_and_other_countries⠀⇛


                 An increasing number of visitors has sparked numerous
                 anti-tourism movements in Spain and elsewhere in Europe.
                 Locals blame tourists for driving up housing costs,
                 inflation, and causing environmental degradation. Some
                 affected regions are beginning to take small steps to
                 ease their residents' concerns.


          o ⚓ Press Gazette ☛ Huw_Edwards_charged_with_making_indecent_images
            of_children⠀⇛


                 Edwards will appear in court on Wednesday (31 July).


          o ⚓ New York Times ☛ Huw_Edwards,_Former_BillBC_Anchor,_Charged_With
            Making_Indecent_Images_of_Children⠀⇛


                 Huw Edwards, who led the BBC’s coverage of major events,
                 including King Charles III’s coronation, has been charged
                 with three offenses, the police said on Monday.


          o ⚓ Hackaday ☛ A_Brief_History_Of_AlphaSmart⠀⇛


                 There are a handful of gadgets that do one thing so well
                 that they become cult classics long after the company
                 that made them has moved on or closed up shop. [This Does
                 Not Compute] takes us through the history of the
                 AlphaSmart word processor which started as an educational
                 tool, but finds itself in many a writer’s bag today.


          o § Science⠀➾


                # ⚓ Science Alert ☛ Solar_Mystery_Solved_by_Astronomer's
                  Drawings_From_Hundreds_of_Years_Ago⠀⇛


                       Johannes Kepler isn't done yet.


                # ⚓ New York Times ☛ Two_Meteor_Showers_Peak_This_Week._Here’s
                  How_and_When_to_Watch.⠀⇛


                       The Southern Delta Aquarids and the Alpha
                       Capricornids are reaching their peak this week. The
                       Perseids, one of the best shows of the year, are
                       also ramping up.


                # ⚓ Science Alert ☛ Astronomers_Just_Discovered_The_Earliest
                  Galaxy_We've_Ever_Seen⠀⇛


          o § Hardware⠀➾


                # ⚓ Tom's Hardware ☛ Alleged_GDDR6X_shortage_could_briefly
                  hinder_Nvidia_gaming_GPU_supply_starting_August_—_affected
                  models_include_RTX_4070_through_RTX_4090⠀⇛


                       A rumor suggests RTX 4070 through RTX 4090 GPUs
                       will face temporary supply shortages due to a
                       quality control failure on a batch of Micron GDDR6X
                       memory modules.


                # ⚓ CNX Software ☛ Jetway_JMTX-ADN8_mini-ITX_motherboard
                  features_defective_chip_maker_Intel_N97_CPU,_dual_GbE,_three
                  display_interfaces⠀⇛


                       The Jetway JMTX-ADN8 is a mini-ITX motherboard
                       built around an defective chip maker Intel N97
                       (Alder Lake-N) processor.


                # ⚓ Hackaday ☛ A_Soviet_Cassette_Recorder_Receiving_Some_Love⠀⇛


                       For those of us who lived in the capitalist west
                       during the Cold War, there remains a fascination to
                       this day about the Other Side. The propaganda we
                       were fed as kids matched theirs in describing the
                       awful things on the other side of the wall,
                       something that wasn’t borne out when a decade or so
                       later in the 1990s we met people from the former
                       communist side and found them unsurprisingly to be
                       just like us. It’s thus still of interest to have a
                       little peek into Eastern Bloc consumer electronics,
                       something we have the chance of courtesy of
                       [DiodeGoneWild], who’s fixing a 1980s Soviet
                       cassette recorder.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Science Alert ☛ Common_Drug_May_Extend_Women's_Fertility_by
                  Years,_Early_Results_Show⠀⇛


                # ⚓ Hackaday ☛ Foliodeck_Squeezes_A_Writerdeck_Into_A_Planner⠀⇛


                       When it comes to writing, sometimes a computer or
                       smartphone is just too distracting to keep on task.
                       [vagabondvivant] found this to be the case and
                       rolled their own distraction-free writing tool, the
                       Foliodeck.


                # ⚓ Science Alert ☛ Olympics:_The_Brains_of_Elite_Athletes
                  Reveal_Crucial_Differences⠀⇛


                       Peak performance begins in the mind.


                # ⚓ Science Alert ☛ Infections_Spreading_in_US_Hospitals_Are_on
                  The_Rise._Here's_Why.⠀⇛


                       Something has changed.


                # ⚓ Science Alert ☛ This_New_Blood_Test_Identifies_Alzheimer's
                  Memory_Loss_With_90%_Accuracy⠀⇛


                       It's already available in the US.


                # ⚓ Science Alert ☛ Brain-Invading_Parasite_Could_Be_Hacked_to
                  Deliver_Meds_in_Your_Head⠀⇛


                       Let's put this parasite to work.


                # ⚓ Latvia ☛ Pets_evacuated_from_flooded_shelter_in_Jelgava,
                  Latvia_Monday⠀⇛


                       An animal shelter at Helmaņa Street 8 in Jelgava,
                       under the supervision of the Latvian University of
                       Life Sciences and Technologies, has been flooded
                       due to the storm, the LETA news agency reports July
                       29.


                # ⚓ CS Monitor ☛ They_stepped_away_for_mental_health._Their
                  comebacks_are_powering_the_Olympics.⠀⇛


                       From Simone Biles to Caeleb Dressel, today’s
                       athletes are more open about their mental health.
                       They that honesty has led to better balance in
                       their lives.


                # ⚓ The Straits Times ☛ Nearly_a_quarter_of_adolescent_girls
                  suffer_partner_violence,_WHO_study_finds⠀⇛


                       GENEVA - Around a quarter of adolescent girls who
                       have been in relationships have endured physical or
                       sexual violence, a World Health Organization study
                       said on Tuesday, calling for more prevention
                       actions.


                # ⚓ Latvia ☛ Two_hospitalized_with_storm_injuries_on_Monday_in
                  Rīga⠀⇛


                       On Monday, July 29, two patients who suffered
                       severe injuries from falling trees were brought to
                       the Emergency Medicine and Patient Admission Clinic
                       of Riga East Clinical University Hospital (RAKUS),
                       LETA news agency reports.


                # ⚓ University of Michigan ☛ UMich_receives_a_$17.9_million
                  grant_to_research_improving_first-time_mental_health
                  treatment⠀⇛


                       The University of Michigan received a 17.9 million
                       dollar grant from the National Institute of Mental
                       Health June 25th to study mental health treatment.
                       The study, called COMPASS, aims to improve first-
                       time mental health treatment and better predict
                       what treatment methods or combination of treatment
                       methods work best for patients. 


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Atlantic Council ☛ A_policymaker’s_guide_to_ensuring_that_
                  [buzzword]-powered_health_tech_operates_ethically⠀⇛


                       The private sector is moving quickly with the
                       development of Hey Hi (AI) tools. The public sector
                       will need to keep up with new strategies,
                       standards, and regulations around the deployment
                       and use of such tools in the healthcare sector.


                # ⚓ Microsoft’s_DEI_Layoffs:_Are_We_Being_Gaslit?_–_Techish
                  Podcast⠀⇛


                       • Microsoft lays off a DEI team (00:00:20)


                # ⚓ ABP ☛ Major_Layoffs_In_July:_Microsoft⠀⇛


                       Layoffs across the industry are not showing any
                       signs of slowing down, as companies continue to
                       fire a significant number of employees this month
                       as well. From industry giants to small start-ups,
                       every sector is dealing with difficult times amid
                       economic challenges, and firing employees is one
                       way these firms are coping with these testing
                       times.


                       From Nike to Dyson, companies across different
                       sectors are firing people in an effort to optimise
                       costs and regain their profit margins. These
                       layoffs may be necessary for organisational
                       survival and strategic adjustments, but their
                       effects on the employees affected by the layoffs
                       are widespread and complex. Here are some of the
                       major layoffs carried out in the month of July.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Pro Publica ☛ How_One_State’s_Anti-Gift-Card_Fraud
                        Law_Could_Impact_U.S._Retailers⠀⇛


                             Maryland Gov. Wes Moore recently signed the
                             Gift Card Scams Prevention Act of 2024,
                             creating the country’s first law aimed at
                             curbing a rising form of gift card fraud
                             called card draining.


                             Card draining is a scheme in which thieves
                             remove gift cards from stores, capture their
                             numeric codes or swap them out for
                             counterfeit cards, and place the products
                             back on display. When an unsuspecting
                             customer loads money onto a tampered or
                             counterfeit card, criminals access it online
                             and steal the balance.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Unicorn Media ☛ Google_Dropped_a_Planned_3rd-party
                        Cookie_Ban…Because_of_Course_They_Did!⠀⇛


                             We're probably not going to find a solution
                             to mass data mining by advertisers and
                             others, as long as privacy issues are handled
                             in a siloed manner by the individual
                             platforms.


          o § Defence/Aggression⠀➾


                # ⚓ JURIST ☛ Human_Rights_Watch_reports_widespread_sexual
                  violence_in_Sudan_amid_catastrophic_humanitarian_crisis⠀⇛


                       Human Rights Watch (HRW) revealed an extensive
                       report on sexual violence perpetrated by the Rapid
                       Support Forces (RSF) in Khartoum, Sudan, amounting
                       to war crimes and crimes against humanity.


                # ⚓ The Strategist ☛ China’s_growing_influence_in_the_Middle
                  East⠀⇛


                       China’s economic and political engagement in the
                       Middle East has surged over the past decade,
                       particularly in the aftermath of the Arab Spring
                       and amid growing perceptions of the United States’
                       withdrawal from the region.


                # ⚓ The Strategist ☛ Beware_mesmerisation_by_China’s_spell⠀⇛


                       In the lexicon of Japan’s diplomacy, there is a
                       phrase, ‘China magic’. Both Japan and Australia
                       seem to be absorbed by this magical power and
                       obsessed with making efforts not to displease their
                       Chinese counterparts.


                # ⚓ Meduza ☛ Taking_on_‘alien_clothing’_The_context_and
                  consequences_of_Tajikistan’s_hijab_ban_—_Meduza⠀⇛


                # ⚓ New York Times ☛ Anguish_in_Golan_Heights_Village_After
                  Rocket_Strike_From_Lebanon⠀⇛


                       A stunned hush of collective mourning fell over
                       Majdal Shams, in the Israeli-controlled Golan
                       Heights, after the attack from Lebanon.


                # ⚓ New York Times ☛ Netanyahu_Vows_‘Severe’_Response_to_Deadly
                  Attack_in_Golan_Heights⠀⇛


                       Fears linger among Lebanese civilians after a
                       strike killed 12 children and teenagers in the
                       Israeli-controlled Golan Heights.


                # ⚓ France24 ☛ Lebanon_braces_for_Israeli_retaliation_after
                  deadly_Golan_Heights_strike⠀⇛


                       Lebanon braced on Monday for a possible large-scale
                       counterstrike after Israel's security cabinet
                       authorised a military response to the weekend
                       rocket attack from Lebanon that killed 12, all
                       teenagers and children. Diplomats engaged in
                       extensive last-minute diplomatic efforts to avert a
                       full blown war between Israel and Hezbollah.


                # ⚓ France24 ☛ Netanyahu_vows_'harsh'_response_to_deadly_Golan
                  Heights_strike_blamed_on_Hezbollah⠀⇛


                       Israel's response to a rocket strike from Lebanon
                       that killed 12 children in the occupied Golan
                       Heights on Saturday will be "harsh", Israeli Prime
                       Minister Benjamin Netanyahu said Monday after
                       visiting the stricken town of Majdal Shams. Israel
                       aims to harm the Lebanon-based, Iran-backed
                       Hezbollah movement, which it holds responsible for
                       the attack, without causing an all-out war in the
                       Middle East, two Israeli officials said Monday.


                # ⚓ Digital Music News ☛ DOJ_Fires_Back_Against_Fentanylware_
                  (TikTok)_Injunction_Push_Ahead_of_January_Forced_Sale
                  Deadline⠀⇛


                       Five weeks ago, Fentanylware (TikTok) formally
                       sought an injunction blocking the forced sale
                       deadline it’s staring down in the U.S. Now, the
                       Justice Department has fired back against the
                       request and the arguments therein.


                # ⚓ RFA ☛ Authorities_in_Xinjiang_rearrest_son_of_prominent
                  Uyghur_businessman⠀⇛


                       Uyghurs who have already served time are being
                       detained again under the guise of ‘threats to
                       national security.’


                # ⚓ RFA ☛ Quad_foreign_ministers_meet_in_Tokyo_to_discuss
                  regional_security⠀⇛


                       It comes after US announced plans for a major
                       revamp of its military command to improve
                       coordination with allies.


                # ⚓ Defence Web ☛ EU_sanctions_nine_people_and_a_political
                  movement_in_DR_Congo⠀⇛


                       Nine people and an “entity” apparently involved in
                       “sustaining armed conflict, instability and
                       insecurity” in the eastern Democratic Republic of
                       Congo (DRC) find themselves on a European Union
                       (EU) restrictive measures – also known as sanctions
                       – list as of last Friday (26 July).


                # ⚓ Defence Web ☛ Investigation_into_illegal_White_River
                  military_training_camp_still_ongoing⠀⇛


                       Police and Home Affairs officials are continuing to
                       investigate an illegal military training camp in
                       White River, Mpumalanga, with firearms recovered
                       and 95 Libyan nationals facing charges of
                       contravening the immigration act.


                # ⚓ The Strategist ☛ Peacebuilding_in_the_Middle_East_requires
                  women⠀⇛


                       On 19 July, US Secretary of State Antony Blinken
                       said negotiations on an agreement to release
                       hostages held in Gaza and establish a ceasefire
                       were nearing the finish line.


                # ⚓ France24 ☛ Airlines_cancel,_delay_Lebanon_flights_amid
                  Israeli_retaliation_fears⠀⇛


                       Hours after Israel’s security cabinet authorised
                       Prime Minister Binyamin Netanyahu and his defence
                       minister to decide how to retaliate for a deadly
                       attack in the Golan Heights, airlines such as Air
                       France and Lufthansa on Monday cancelled or delayed
                       flights to Beirut. Israel blamed Hezbollah for the
                       attack. The Lebanese-based militant group has
                       denied responsibility.


                # ⚓ The Straits Times ☛ Chinese_spy_or_counterrevolutionary?
                  Foreign_agent_trial_begins_in_Brooklyn⠀⇛


                       NEW YORK - U.S. prosecutors alleged a Chinese
                       academic betrayed U.S.-based dissidents to Beijing
                       at the start of the 76-year-old's trial on foreign
                       agents charges on Monday, while defense lawyers
                       said their client was trying to bring democracy to
                       communist China.


                # ⚓ RFERL ☛ Protests_In_Western_Pakistan_Turn_Violent,_Leaving
                  1_Soldier_Dead,_Many_Injured⠀⇛


                       Thousands of Pakistanis have been protesting for
                       nearly a week in the port city of Gwadar, leading
                       to the death of one soldier and the injury of at
                       least 16 others, Pakistan’s army said on July 29.


                # ⚓ Hong Kong Free Press ☛ US,_Japan,_Australia,_India_foreign
                  ministers_express_‘serious_concern’_over_situation_in_South
                  China_Sea⠀⇛


                       The foreign ministers of the United States, Japan,
                       Australia and India on Monday expressed “serious
                       concern” over the situation in the South China Sea
                       in a veiled rebuke to Beijing.


                # ⚓ RFA ☛ Philippines_conducts_resupply_mission_to_disputed
                  shoal⠀⇛


                       Philippine vessel brought supplies to troops at
                       Second Thomas Shoal amid confusion over deal with
                       China.


                # ⚓ France24 ☛ Quad_foreign_ministers_'seriously_concerned'
                  over_South_China_sea_tensions⠀⇛


                       The foreign ministers of the United States, Japan,
                       Australia, and India expressed concern on Monday
                       over the situation in the South China Sea,
                       indirectly criticising Beijing during their meeting
                       in Tokyo. The Quad's joint statement emphasised the
                       need for a "free and open" Pacific and condemned
                       recent confrontations involving Chinese and
                       Philippine vessels, as well as North Korea's
                       missile launches.


                # ⚓ RFA ☛ Chinese_dissidents_in_exile_stage_sporadic_Olympic
                  rights_protests_in_Paris⠀⇛


                       Overseas activists make the most of their freedom,
                       but still fear retaliation against loved ones back
                       home.


                # ⚓ RFA ☛ Hong_Kongers_in_UK_'lonely,'_but_most_plan_to_stay
                  for_good⠀⇛


                       A survey by Hongkongers in Britain says migrants
                       from the city experience 'higher than average'
                       distress levels.


                # ⚓ Hong Kong Free Press ☛ Italy’s_Giorgia_Meloni_meets_Chinese
                  leader_Pooh-tin_Jinping_in_Beijing,_pledging_to_‘relaunch
                  ties’⠀⇛


                       Italian Prime Minister Giorgia Meloni hailed China
                       as an “important interlocutor” in managing global
                       tensions Monday as she met President Pooh-tin
                       Jinping.


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


                      # ⚓ RFA ☛ Is_North_Korea_planning_to_join_BRICS?⠀⇛


                             Verdict: Lack of evidence


                      # ⚓ RFERL ☛ Whereabouts_Of_2_Imprisoned_Former_Navalny
                        Associates_Unknown⠀⇛


                             Two former leaders of the late Russian
                             opposition politician Aleksei Navalny’s teams
                             in Ufa and Tomsk, Lilia Chanysheva and Ksenia
                             Fadeyeva, have been transferred from the
                             prisons where they were being held and their
                             current whereabouts are not known.


                      # ⚓ France24 ☛ Russia's_Wagner_group_reports_casualties
                        in_intense_clash_with_Tuareg_rebels_in_Mali⠀⇛


                             The Wagner mercenary group reported on Monday
                             that its fighters, alongside Malian soldiers,
                             suffered casualties during intense clashes
                             with Tuareg rebels near Mali's border with
                             Algeria. Despite claims by Malian authorities
                             that Russian forces in the country are
                             trainers rather than mercenaries, Wagner
                             confirmed its involvement in the fighting,
                             which saw significant losses on both sides.


                      # ⚓ Meduza ☛ ‘A_successful_military_operation’_Ukrainian
                        intelligence_says_‘more_to_come’_after_rebels_in_Mali
                        reportedly_kill_dozens_of_Wagner_Group_fighters_—
                        Meduza⠀⇛


          o § Environment⠀➾


                # ⚓ Defence Web ☛ Joint_army/police_ops_to_curb_illegal_mining
                  ongoing⠀⇛


                       Soldiers continue to work in tandem with police to
                       curb illegal mining with the arid, but mineral-rich
                       Northern Cape the latest in the sights of Operation
                       Vala Umgodi teams.


                # ⚓ MIT Technology Review ☛ From_Meta_CTO_to_climate_tech
                  investor:_Mike_Schroepfer_on_his_big_pivot [Ed: Seems like
                  greenwashing PR; follow the MTR money...]⠀⇛


                       As the pandemic locked down cities in early 2020,
                       Mike Schroepfer, then the chief technology officer
                       of Meta, found himself with more free time than
                       he’d ever had in his career.


                # ⚓ Hackaday ☛ Saildrones_Searching_The_Sea_For_Clues_To
                  Hurricane_Behavior⠀⇛


                       Hurricanes can cause widespread destruction, so
                       early forecasting of their strength is important to
                       protect people and their homes. The US National
                       Oceanic and Atmospheric Administration (NOAA) is
                       using saildrones to get better data from inside
                       these monster storms.


          o § Finance⠀➾


                # ⚓ New York Times ☛ Scammers_Are_Targeting_Older_Americans_and
                  Their_Retirement_Savings⠀⇛


                       Criminals on the internet are increasingly going
                       after Americans over the age of 60 because they are
                       viewed as having the largest piles of savings.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ New York Times ☛ Warning_of_‘Extreme’_Agenda,_Biden_Calls
                  for_Supreme_Court_Overhaul⠀⇛


                       In a speech in Austin, Texas, the president
                       outlined a proposal that included term limits and
                       an enforceable ethics code for the justices but
                       that faces long odds in a divided Congress.


                # ⚓ New York Times ☛ Roy_Cooper_Withdraws_From_Kamala_Harris_VP
                  Sweepstakes⠀⇛


                       Mr. Cooper, the governor of North Carolina, had
                       been seen as one of the half-dozen top candidates
                       to join the Democratic presidential ticket. It was
                       not immediately clear why he withdrew.


                # ⚓ NYPost ☛ North_Carolina_Gov._Roy_Cooper_withdraws_from
                  consideration_to_be_Kamala_Harris’_running_mate⠀⇛


                       North Carolina Governor Roy Cooper is no longer in
                       the running to be Vice President Kamala Harris's
                       running mate this election season.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Reason ☛ Judge_Tosses_Former_'Disinformation'_Chief's
                        Defamation_Suit,_Says_She_Really_Was_a_Censor⠀⇛


                             Nina Jankowicz finds out the truth may hurt,
                             but it isn’t lawsuit bait.


          o § Censorship/Free Speech⠀➾


                # ⚓ Reason ☛ Trump's_Favorite_Justice_Was_One_of_Those_'Stupid
                  People'_Who_Think_Flag_Burning_Is_Protected_Speech⠀⇛


                       Antonin Scalia twice joined Supreme Court decisions
                       rejecting bans on that particular form of political
                       expression.


                # ⚓ RFERL ☛ Georgian_Constitutional_Court_Consolidates_Lawsuits
                  Against_'Foreign_Agent'_Law⠀⇛


                       Georgia's Constitutional Court on July 29 said it
                       would consolidate cases against the controversial
                       "foreign agent" law after 32 opposition lawmakers
                       filed a lawsuit against the legislation.


                # ⚓ JURIST ☛ Bangladesh_authorities_announce_end_to_11-day
                  Internet_shutdown⠀⇛


                       The Bangladeshi Minister for Posts,
                       Telecommunications, and Information Technology,
                       Zunaid Ahmed Palak, announced Sunday that 4G mobile
                       internet services would be restored after an 11-day
                       nationwide blackout. However, access to social
                       control media platforms such as WhatsApp, Facebook,
                       TikTok, and YouTube would remain restricted.


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


                # ⚓ Reason ☛ KOSA_Moves_Forward_in_Congress,_Threatening_Free
                  Speech_and_Encryption⠀⇛


                       Only Sens. Paul and Wyden are expected to vote "no"
                       on Tuesday. Power to stop KOSA now resides with the
                       House.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Tom's Hardware ☛ Overnight_fiber_optic_sabotage_disrupts
                  telecommunications_in_several_French_regions_—_Paris_and_the
                  Olympic_Games_unaffected⠀⇛


                       Just days after saboteurs struck France's train
                       network, unknown parties cut fiber optic bundles,
                       affecting phone and internet service in several
                       country regions.


                # ⚓ APNIC ☛ Are_subsea_cables_feeling_the_heat_from_climate
                  change?⠀⇛


                       Guest Post: How future climate change may affect
                       subsea cables and their shore-based landing
                       stations.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Digital Music News ☛ The_MLC_and_Spotify_Won’t_Be_Settling
                  Anytime_Soon_—_Dismissal_Arguments_Ramp_Up_in_High-Stakes
                  Legal_Battle⠀⇛


                       In turns out Spotify and the Mechanical Licensing
                       Collective (MLC) won’t be settling their legal
                       battle anytime soon, as the MLC has officially
                       fired back against the streaming giant’s dismissal
                       arguments.


                # ⚓ Press Gazette ☛ Channel_4_News_bets_Youtube_is_‘where
                  podcast_market_growth_really_lies’⠀⇛


                       The Political Fourcast averaged more than 100,000
                       views an episode over the UK general election.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ KOL437_|_Morgan_Meets_the_Eye:_Argumentation_Ethics,
                  Private_Law,_Restitution_and_Punishment,_Intellectual
                  Property⠀⇛


                       Patent attorney Stephan Kinsella joins the show to
                       discuss the problems intellectual "property" laws
                       create in society, how these laws came into being
                       in the first place, and why intellectual property
                       is a flawed concept to begin with.


                # ⚓ Dennis Crouch/Patently-O ☛ Degrees_of_Disagreement:
                  Surveillance_Giant_Google_Petitions_En_Banc_on_Smart
                  Thermostat_Patent_Damages⠀⇛


                       Google recently petitioned for en banc review a
                       Federal Circuit split decision in EcoFactor v.
                       Google. The case focuses on when a damages expert
                       testimony satisfies Daubert.  The original opinion
                       also highlights an interesting debate regarding the
                       appeal of pre-trial eligibility rulings.


                       In EcoFactor, Inc. v. Surveillance Giant Google
                       LLC, No. 23-1101 (Fed. Cir. June 3, 2024), the
                       Federal Circuit issued a 2-1 split decision
                       affirming a $20 million jury verdict in favor of
                       smart thermostat company EcoFactor.  The majority
                       opinion, authored by Judge Reyna and joined by
                       Judge Lourie, upheld the district court’s denial of
                       Google’s motions for judgment as a matter of law on
                       non-infringement and for a new trial on damages.
                       Judge Prost dissented from the damages portion of
                       the decision, arguing that the testimony of
                       EcoFactor’s damages expert was fatally flawed and
                       should have been excluded.


                # ⚓ How_the_End_of_Chevron_Deference_Is_(Or_Isn’t?)_Reshaping
                  IP_[sic]_Regulation⠀⇛


                       In a decision that reverberated throughout the
                       regulatory world, the Supreme Court ruled on June
                       28th, in Loper Bright Enterprises v. Raimondo, that
                       federal courts may no longer defer to an agency’s
                       interpretation of an ambiguous statute.


                # § Kangaroo Courts⠀➾


                      # ⚓ Kluwer Patent Blog ☛ Panasonic_cases:_Clarification
                        on_the_production_of_comparable_licenses_before_UPC_
                        (orders_to_produce_evidence) [Ed: UPC is illegal and
                        unconstitutional, so this kangaroo court ought not even
                        exist, nor should this case]⠀⇛


                             This week we reported on the case between
                             Huawei and Netgear, in which the defendant
                             had obtained a production order for a
                             comparable license granted by Huawei to
                             Qualcomm, the production of which Netgear had
                             obtained via a decision of the Munich local
                             division on 24 April 2024.


                # § Software Patents⠀➾


                      # ⚓ JUVE ☛ UK_Court_of_Appeal_issues_landmark_ruling_in
                        Emotional_Perception_Hey_Hi_(AI)_case⠀⇛


                             The dispute centres on a patent monopoly
                             application by Emotional Perception Hey Hi
                             (AI) for a system that recommends data files.
                             The technology uses an artificial neural
                             network (ANN) to, for example, organise music
                             files in a different way than common search
                             algorithms.


                      # ⚓ Unified Patents ☛ Atlantic_IP_entity,_Foras
                        Technologies,_parallel_processor_patent_monopoly_found
                        invalid⠀⇛


                             On July 26, 2024, the Central Reexamination
                             Unit (CRU) entered a final rejection of the
                             challenged claims 1-2, 5-18, and 21-30 of
                             U.S._Patent_7,627,781, owned and asserted by
                             Foras Technologies, Ltd., an NPE and entity
                             of Atlantic_IP_Services_Limited. The ‘781
                             patent monopoly relates to lockstep processor
                             technology where two processors are paired
                             together, and the two processors perform
                             exactly the same-operations and the results-
                             are compared.(e.g., with an XOR gate).


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ With_Amended_First_Use_Date,_RESORT_WEAR
                  SEASPICE_Registration_Survives_Section_2(d)_Attack⠀⇛


                       The Board denied a petiton for cancellation of a
                       registration for the mark shown below, for various
                       clothing items, rejecting Petitioner Paradise
                       Holdings' likelihood of confusion claim because
                       Paradise failed to prove priority. Respondent Neo
                       Nyc asserted dates of first use in its registration
                       as early as January 1, 2018, but by clear and
                       convincing evidence it successfully established a
                       first used date of June 10, 2015. Paradise
                       Holdings,_Inc._v._Neo_Nyc_inc, Cancellation No.
                       92078182 (July 26, 2024) [not precedential]
                       (Opinion by Judge Jennifer L. Elgin).


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ K-Pop_Keeps_Surging_on_the_Global
                  Stage_—_So_Why_are_K-Pop_Agencies_Sinking?⠀⇛


                       As K-pop surges on the global stage, K-pop agencies
                       sink further beneath financial pressure. So what’s
                       going on? As K-pop fans flock to Los Angeles for
                       KCON L.A., a three-day convention and concert
                       series celebrating Korean pop music, the talent
                       agencies behind the world’s biggest K-pop acts are
                       sinking under an ever-increasing financial
                       pressure.


                # ⚓ Digital Music News ☛ TikTok_Targets_Shazam,_YouTube_Music
                  with_‘Sound_Search’_—_Hum_or_Sing_a_Song_to_Find_a_Match⠀⇛


                       TikTok takes on Shazam and YouTube Music with a new
                       feature that allows you to find a sound by singing,
                       humming, or playing it. Fentanylware (TikTok) is
                       rolling out a new feature to rival Shazam and
                       YouTube Music with Sound Search, which allows users
                       to find a sound by singing, humming, or playing it.





                    ䷩ 𝚕𝚒𝚗𝚎 5643

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 30/07/2024: Microsoft Admits Lying
About ClownStrike/Windows Outages to Save Face and Shared Email
Addresses⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          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 Monopolies/Monopsonies
                # Patents
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Low-Gravity_Playground_Looks_Highly_Entertaining_(and
            Useful)⠀⇛


                 With US astronauts scheduled to return to the Moon in
                 2026, it might be nice for them to really and truly know
                 ahead of time what the gravity situation is going to be
                 like. At 1/6th Earth’s gravity, the difference can be
                 difficult to simulate.


          o ⚓ Tedium ☛ Cassingle_Culture⠀⇛


                 Why the single version of the cassette didn’t feel as
                 worthy of a purchase as, say, a 45. Or, perhaps, even a
                 digital download.


          o ⚓ Flamed Fury ☛ Rebuilding_The_Web⠀⇛


                 This post isn’t about rewilding the web or building out
                 new infrastructure to compete with big tech, but how we,
                 as members and participants of the independent web, can
                 help rebuild the connections that made the web diverse
                 and fun to surf again.


          o ⚓ Dan Q ☛ Shared_Email_Addresses⠀⇛


                 Sure, the need for most of these solutions would
                 evaporate instantly if more services supported multi-user
                 or delegated access3. But outside of that fantasy world,
                 shared aliases seem to be pretty useful!


          o ⚓ Dustin ☛ This_site_will_be_deleted⠀⇛


                 If you read this in your RSS reader, there will be no
                 more posts, and the feed will eventually 404, so you
                 could remove it from your list now if you want.


          o § Science⠀➾


                # ⚓ Science Daily ☛ Why_males_pack_a_powerful_punch⠀⇛


                       But even with roughly uniform levels of fitness,
                       the males' average power during a punching motion
                       was 162% greater than females', with the least-
                       powerful man still stronger than the most powerful
                       woman. Such a distinction between genders, Carrier
                       says, develops with time and with purpose.


          o § Education⠀➾


                # ⚓ Tracy Durnell ☛ Learning_your_own_learning_process⠀⇛


                       I wanted to look at whatever they had for me to
                       look at and notice what about it stood out to me —
                       or if nothing did, wonder why it was important. To
                       see it as it really exists first, to look with
                       unfiltered eyes, and then to apply a label.


          o § Hardware⠀➾


                # ⚓ The Age AU ☛ Cirque_du_Soleil_Luzia_at_Claremont
                  Showgrounds_Perth⠀⇛


                       “As far as I’m aware, there isn’t anything else out
                       there that travels like this,” he explains. “I’ve
                       seen plenty of rain curtains before, but they’re
                       always fixed. To bring something like this on the
                       road is a pretty complex thing to do.”


                       Westland hails from Tasmania, where he originally
                       did his apprenticeship as a plumber. His job saw
                       him relocate to Perth, and eventually to Canada. It
                       was there he made the industry contacts that led
                       him to join the Cirque during its London season of
                       Luzia.


                # ⚓ Hackaday ☛ Printed_Portable_Computer_Inspired_By_The
                  Classics⠀⇛


                       These days, laptop computers are all more or less
                       the same, at least externally. Some are thicker
                       than others, they might come in different colors,
                       or with a 360° hinge that lets you flip the screen
                       around the back and use it as a tablet, but overall
                       they’ve all got the same shape and proportions. The
                       industry, and indeed the users, eventually agreed
                       on the best way to make a computer portable and are
                       now fully committed to it.


                # ⚓ Hackaday ☛ An_RC_Tracked_Robot,_Without_The_Pain⠀⇛


                       Small robots can be found at all levels from STEM
                       toys for kids all the way through to complex hacker
                       projects. Somewhere along that line between easy
                       enough for anyone to build and interesting enough
                       for hackers lies the PlayCar, from [ComfySpace].
                       It’s a small build-it-yourself tracked robot that’s
                       controlled from your smartphone via an app.


                # ⚓ Hackaday ☛ A_Demo_Party_On_A_Chip⠀⇛


                       The demoscene has provided our community with its
                       artistic outlet since the first computers which
                       could handle graphics, and has stayed at the
                       forefront of technology all the way. For all that
                       though, there’s a frontier it hasn’t yet entirely
                       conquered, which exists in the realm of silicon. To
                       address this cones the ever awesome Tiny Tapeoput,
                       who are bringing their ASIC-for-the-masses scheme
                       to the world of demos with an ASIC demo
                       competition.


                # ⚓ Hackaday ☛ You’ve_Got_The_Portable_Radio,_Now_What_About
                  The_Antenna?⠀⇛


                       There’s an old saying in the amateur radio
                       community that when it comes to antennas all you
                       need is a piece of wet string. This may be a little
                       fanciful, but it’s certainly true that an effective
                       antenna can be made with surprisingly little in the
                       way of conductor. It’s something [Evan Pratten
                       VZ3ZZA] demonstrates amply with a description of
                       the antenna he took camping in a Canadian
                       provincial park.


                # ⚓ Hackaday ☛ The_BiVACOR_Total_Artificial_Heart:_A_Maglev
                  Bridge_To_Life⠀⇛


                       Outside of the brain, the heart is probably the
                       organ that you miss the most when it ceases to
                       function correctly. Unfortunately, as we cannot
                       grow custom replacement hearts yet, we have to keep
                       heart patients alive long enough for them to
                       receive a donor heart. Yet despite the heart being
                       essentially a blood pump, engineering even a short-
                       term artificial replacement has been a struggle for
                       many decades. A new contender has now arrived in
                       the BiVACOR TAH (total artificial heart), which
                       just had the first prototype implanted in a human
                       patient.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Science Alert ☛ We_May_Have_Found_a_Target_For_Treating_The
                  Fatigue_of_Long_COVID⠀⇛


                       Here's where it begins.


                # ⚓ LRT ☛ Housing_affordability_in_Lithuania_still_below_pre-
                  pandemic_levels_–_what_can_be_done?⠀⇛


                       Housing affordability in Lithuania is still worse
                       than it was before the Covid 19 pandemic. The Bank
                       of Lithuania argues that regulation should
                       discourage housing-as-investment purchases, while
                       some politicians argue for a property tax.


                # ⚓ No,_“right-to-try”_has_not_“saved_thousands_of_lives,”
                  contrary_to_Donald_Trump’s_claims⠀⇛


                       Back in the beforetime (i.e., before 2020, when
                       COVID-19 changed everything), a frequent topic for
                       me dating back a decade was the push for “right-to-
                       try” laws. The very first time that I wrote about
                       “right-to-try,” I compared the idea to the movie
                       Dallas Buyers’ Club, noting that it might make
                       material for a great movie but that it was terrible
                       for patients and terrible policy. (More detail on
                       why a little later.) I also noted how, with the
                       support of the “free market” Goldwater Institute,
                       right-to-try laws started metastasizing to various
                       states, including my own. Ultimately, these laws
                       passed in state after state after state. As long as
                       they stayed at the state level, however, right-to-
                       try laws were largely performative and ceremonial,
                       given that the federal government, through the Food
                       & Drug Administration (FDA), regulates drug
                       approval, not the states. Basically, these state
                       laws gave the illusion that something was being
                       done, when, in fact, at the federal level nothing
                       changed.


                # ⚓ Nicholas Tietz-Sokolsky ☛ Integrate_rest_into_your_work_and
                  practice⠀⇛


                       Resting depends on what you're resting from. If
                       you're doing labor all day, then rest will probably
                       involve sitting down, and it may not preclude
                       thinking hard. If you're programming all day, then
                       rest will probably involve stepping away from the
                       computer and doing something physical, which might
                       involve moving heavy things. And if you're very
                       fatigued, resting might involve doing nothing: no
                       thinking, no lifting, just lying in bed.


                # ⚓ Lou Plummer ☛ Screen_Time⠀⇛


                       In closing, I love the quote from David Foster
                       Wallace that I used as a lead on this post. I have
                       shared it many times. I still believe in its inner
                       truth as it applies to algorithmically driven
                       social media and meaningless doom scrolling. I
                       don't subscribe to it as a blanket condemnation of
                       the entire medium, however.


                # ⚓ Deseret Media ☛ 'We_kind_of_lost_him':_Why_Jordan_School
                  District_was_named_lead_plaintiff_in_suit_against_Meta,
                  TikTok⠀⇛


                       After being given a cellphone for his birthday as
                       he entered middle school, Logan Dunford experienced
                       a dramatic shift in personality, his father said,
                       leading to slipping grades and negative mental
                       health impacts.


                       "Logan was not prepared to be sucked into the
                       social media world that was waiting for him, nor
                       were his mother and I aware of what was happening
                       on the other end to suck him in," Dunford said. "We
                       kind of lost him."


                       That struggle continued for years, he said, until
                       "on his own, Logan decided that the problem was not
                       his cellphone, it was social media. And on his own,
                       he decided to delete all social media apps from his
                       phone."


                # ⚓ The Register UK ☛ Microsoft_admits_8.5_million_CrowdStruck
                  machines_estimate_was_lowballed⠀⇛


                       Microsoft has admitted that its estimate of 8.5
                       million machines crashed by CrowdStrike's faulty
                       software update was almost certainly too low, and
                       vowed to reduce infosec vendors' reliance on the
                       kernel drivers at the heart of the issue.


                       Redmond posted an incident response blog on
                       Saturday – titled "Windows Security best practices
                       for integrating and managing security tools" – in
                       which veep for enterprise and OS security David
                       Weston explained how Microsoft measured the impact
                       of the incident: by accessing crash reports shared
                       by customers.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ By_the_Numbers:_Fear_of_layoffs_and_AI_have_far-reaching
                  organizational_effects [Ed: Nothing to do with Artificial
                  Intelligence (AI)]⠀⇛


                       But according to a report from MarketWatch, layoff
                       figures are on a slight downswing year-over-year.
                       The report found that 70% of employees are bracing
                       themselves for perceived impending layoffs, whether
                       they’re likely to happen or not. More than half
                       (55%) of employees who took part in the survey
                       believe that the national unemployment rate is
                       higher than it was during the height of the COVID
                       pandemic (which topped out at 11%), despite it
                       currently being just 4.1%.


                # ⚓ San_Francisco_Real_Estate_Struggles_Amid_Record_Office
                  Vacancy_Rates,_Despite_AI_Boom [Ed: There is no "boom", it's
                  just a bubble that will go boom! Microsoft shut down offices
                  there...]⠀⇛


                       San Francisco’s commercial real estate woes are
                       largely attributed to two major factors: the
                       struggle to bring employees back to the office
                       post-Covid and a slowdown in the tech sector, which
                       has led to over 530,000 layoffs since 2022,
                       according to Layoffs.fyi. Major tech companies like
                       Alphabet, Meta, Amazon, Tesla, Microsoft, and
                       Salesforce have all experienced significant
                       downsizing.


                # ⚓ The Verge ☛ The_gymnastics_world_braces_for_an_AI_future⠀⇛


                       The governing body of international gymnastics has
                       pushed for an AI-assisted aid for judges. But what
                       justifies the tremendous expense for such a system?
                       The World Gymnastics Championship held an answer,
                       and it might not have anything to do with
                       gymnastics at all. The governing body of
                       international gymnastics has pushed for an AI-
                       assisted aid for judges. But what justifies the
                       tremendous expense for such a system? The World
                       Gymnastics Championship held an answer, and it
                       might not have anything to do with gymnastics at
                       all.


                # ⚓ 404 Media ☛ Websites_are_Blocking_the_Wrong_AI_Scrapers_
                  (Because_AI_Companies_Keep_Making_New_Ones)⠀⇛


                       Dark Visitors tracks hundreds of web crawlers and
                       scrapers, attempts to explain what each scraper
                       does, and lets website owners constantly update
                       their site’s robots.txt file, which is a set of
                       instructions that tells bots if they have
                       permission to crawl a site. We have seen time and
                       time again that AI companies will often find
                       surreptitious ways of crawling sites that they
                       aren’t supposed to, or, in some cases, they simply
                       ignore robots.txt. This has led some sites to block
                       all crawlers regardless of what they do, or to only
                       specifically allow a few select ones (Reddit is now
                       only being crawled by Google because of this). This
                       can have the effect of blocking search engines,
                       internet archiving tools, and academic research,
                       even if that wasn’t the website owner’s intention.


                # ⚓ The Register UK ☛ Meta's_AI_safety_system_defeated_by_the
                  space_bar⠀⇛


                       Meta's machine-learning model for detecting prompt
                       injection attacks – special prompts to make neural
                       networks behave inappropriately – is itself
                       vulnerable to, you guessed it, prompt injection
                       attacks.


                # ⚓ The Washington Post ☛ A_field_guide_on_how_to_spot_fake
                  pictures⠀⇛


                       Photographs have a profound power to shape our
                       understanding of the world. And it’s never been
                       more important to be able to discern which ones are
                       genuine and which are doctored to push an agenda,
                       especially in the wake of dramatic or contentious
                       moments.


                       But advances in technology mean that spotting
                       manipulated or even totally AI-generated imagery is
                       only getting trickier.


                # ⚓ BoingBoing ☛ AI_crawlers_run_up_a_website's_hosting_bill⠀⇛


                       Web crawlers for search have long used a surprising
                       amount of bandwidth and sometimes CPU resources.
                       Website owners, however, want these crawls in most
                       cases because they are how discovery now works on
                       the Internet. AI crawlers training themselves on
                       the content, however, really doesn't benefit the
                       site owner and, in this case, costs them a lot of
                       money.


                # ⚓ Bruce Schneier ☛ New_Research_in_Detecting_AI-Generated
                  Videos_-_Schneier_on_Security⠀⇛


                       The latest in what will be a continuing arms race
                       between creating and detecting videos: [...]


                # ⚓ Daniel Miessler ☛ We've_Been_Thinking_About_AI_All_Wrong⠀⇛


                       Great question. An Intelligence Pipeline is a
                       series of Intelligence Tasks that result in a
                       useful output. And Intelligence Tasks are functions
                       that can only be done using human intelligence.


                       Here are some real-world examples.


                # ⚓ Baldur Bjarnason ☛ The_other_shoe_dropping_on_'AI'_and
                  office_work⠀⇛


                       What’s interesting about this is that the study
                       isn’t trying to measure productivity but instead
                       feelings of productivity.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Futurism ☛ Catholic_Priest_Sues_Grindr_After_He_Gets
                        Caught_Using_It⠀⇛


                             Later allowed to resume ministry as a
                             parochial administrator, Burrill is now suing
                             Grindr in California's Superior Court for
                             selling the data that ultimately outed him —
                             and to find out who, exactly, his information
                             was sold to.


                             "We want answers so we can use that as a
                             warning to other Grindr users," explained
                             Gregory Helmer, the priest's attorney, in an
                             interview with WaPo.


                      # ⚓ EFF ☛ Senators_Expose_Car_Companies’_Terrible_Data
                        Privacy_Practices⠀⇛


                             When it comes to the price that companies can
                             get for selling your driving data, the
                             numbers range wildly, but the data isn’t as
                             valuable as you might imagine. The letter
                             states that Honda sold the data on about
                             97,000 cars to an analytics company,
                             Verisk—which turned around and sold the data
                             to insurance companies—for $25,920, or 26
                             cents per car. Hyundai got a better deal, but
                             still not astronomical numbers: Verisk paid
                             Hyundai $1,043,315.69, or 61 cents per car.
                             GM declined to share details about its sales.


                             The letter also reveals that while GM stopped
                             sharing driving data after The New York
                             Times’ investigation, it did not stop sharing
                             location data, which it’s been sharing for
                             years. GM collects and shares location data
                             on every car that’s connected to the
                             [Internet], and doesn’t offer a way to opt
                             out beyond disabling [Internet]-connectivity
                             altogether. According to the letter, GM
                             refused to name the company it’s sharing the
                             location data with currently. While GM claims
                             the location data is de-identified, there is
                             no way to de-identify location data. With
                             just one data point, where the car is parked
                             most often, it becomes obvious where a person
                             lives.


                      # ⚓ EFF ☛ EFF’s_Concerns_About_the_UN_Draft_Cybercrime
                        Convention⠀⇛


                             The proposed UN Cybercrime Convention is an
                             extensive surveillance pact that imposes
                             intrusive domestic surveillance measures and
                             mandates states’ cooperation in surveillance
                             and data sharing. It requires states to aid
                             each other in cybercrime investigations and
                             prosecutions, allowing the collection,
                             preservation, and sharing of electronic
                             evidence for any crime deemed serious by a
                             country’s domestic law, with minimal human
                             rights safeguards. This cooperation extends
                             even to countries with poor human rights
                             records. Negotiations for this treaty began
                             in 2022, initiated by a controversial
                             proposal from the Russian Federation. If
                             adopted, it will rewrite surveillance laws
                             worldwide. Millions of people, including
                             human rights defenders, journalists, security
                             researchers, and those speaking truth to
                             power, will be affected. Without clear,
                             enforceable safeguards, the treaty risks
                             becoming a tool for state abuse and
                             transnational repression rather than
                             protecting human rights. Below are our main
                             concerns. For a comprehensive list, please
                             refer to our redlines and appeal to EU
                             Delegates.


                      # ⚓ EFF ☛ Why_You_Should_Hate_the_Proposed_UN_Cybercrime
                        Treaty⠀⇛


                             Tech companies and their overseas staff,
                             under certain treaty provisions, would be
                             compelled to help governments in their
                             pursuit of people’s data, locations, and
                             communications, subject to domestic
                             jurisdictions, many of which establish
                             draconian fines.


                             We have called the draft convention a blank
                             check for surveillance abuse that can be used
                             as a tool for human rights violations and
                             transnational repression. It’s an
                             international treaty that everyone should
                             know and care about because it threatens the
                             rights and freedoms of people across the
                             globe. Keep an eye out for our posts
                             explaining how.


                      # ⚓ RTL ☛ Targeting_'dissenting_voices':_UN_cybercrime
                        text_faces_new_scrutiny_from_tech_firms,_rights
                        groups⠀⇛


                             The document could thus require governments
                             "to facilitate investigations into things
                             like same-sex conduct, criticizing one's
                             government, investigative reporting,
                             participating in protests or being a
                             whistleblower," said Human Rights Watch
                             executive director Tirana Hassan.


                             Rather than a cybercrime treaty, the text
                             "actually resembles a global surveillance
                             treaty that would address all crime," she
                             told reporters, adding that it exceeds "even
                             the most expansive possible interpretation of
                             its mandate."


                             The 40-nation Freedom Online Coalition warned
                             that the treaty "could be misused as a tool
                             for acts of domestic and transnational
                             repression and other human rights
                             violations."


          o § Defence/Aggression⠀➾


                # ⚓ France24 ☛ UK_police_say_two_children_killed_in_'ferocious'
                  knife_attack,_suspect_arrested⠀⇛


                       Two children were killed and 11 people injured in a
                       stabbing incident at a dance class in northwest
                       England on Monday, UK police said. A 17-year-old
                       from Banks in Lancashire has been arrested on
                       suspicion of murder and attempted murder.


                # ⚓ RTL ☛ 80th_anniversary_of_WWII_escapes:_Exploring_northern
                  Luxembourg's_'Smugglers'_Path'⠀⇛


                       On 30 August 1942, the German occupiers ordered the
                       forced conscription of Luxembourgish men born
                       between 1920 and 1924, later extending this to
                       those born up to 1927. Many of the conscripted men
                       went into hiding to avoid military service, seeking
                       refuge on farms and in the forests around
                       Troisvierges in northern Luxembourg. As these
                       hiding places became overcrowded, escape routes
                       were sought.


                # ⚓ Deutsche Welle ☛ French_police_arrest_far-left_suspect
                  after_rail_sabotage⠀⇛


                       However, Darmanin warned against jumping to
                       conclusions because the perpetrators could have
                       been manipulated.


                # ⚓ Cyble Inc ☛ U.S._Department_Of_Justice_Urges_Court_To
                  Reject_TikTok_Appeal⠀⇛


                       The government argues that TikTok poses a
                       significant national security threat due to its
                       Chinese ownership, citing concerns about data
                       collection and potential manipulation of content by
                       the Chinese government. To support its case, the
                       Justice Department is submitting a classified
                       document to the court, detailing additional
                       security concerns and including declarations from
                       the FBI, the Office of the Director of National
                       Intelligence, and the DOJ’s National Security
                       Division.


                # ⚓ JURIST ☛ Sudan_rights_group_says_at_least_25_killed_in_RSF
                  attacks_on_El-Fasher⠀⇛


                       At least 25 people were reportedly killed and
                       dozens wounded in an attack by Sudan’s Rapid
                       Support Forces (RSF) Saturday on the city of El-
                       Fasher in western Darfur, local pro-democracy
                       activists El-Fasher Resistance Committees shared on
                       Facebook.


                # ⚓ BIA Net ☛ Erdoğan_says_Turkey_could_use_military_force
                  against_Israel_‘just_as_we_did_in_Libya_and_Karabakh’⠀⇛


                       The president has both criticized Netanyahu’s
                       speech in the US Congress and Palestinian President
                       Mahmoud Abbas for rejecting their invitation to
                       speak in Turkey’s parliament.


                # ⚓ New York Times ☛ Israel_Hits_Lebanon_in_Overnight_Strikes
                  After_Soccer_Field_Attack⠀⇛


                       Diplomats were scrambling to prevent a surge in
                       fighting, officials said, after Israel retaliated
                       for the rocket fire that killed at least 12
                       children and teenagers in an Israeli-controlled
                       town.


                # ⚓ New York Times ☛ A_Village’s_Anguish_Over_12_Children_Lost
                  to_a_Rocket_Strike⠀⇛


                       A stunned hush of collective mourning fell over
                       Majdal Shams, in the Israeli-controlled Golan
                       Heights, after the attack from Lebanon.


                # ⚓ JURIST ☛ Gaza_health_ministry_reports_Israel_Defence_Forces
                  kill_30_in_school_strike⠀⇛


                       Israel struck a school in central Gaza on Saturday,
                       and the Hamas-run health ministry reported that the
                       attack injured 100 and killed at least 30
                       Palestinians.


                # ⚓ France24 ☛ Israeli_strike_on_Gaza_school_housing_field
                  hospital_kills_at_least_30,_says_health_ministry⠀⇛


                       An Israeli air strike hit a school housing a field
                       hospital in central Gaza on Saturday, killing at
                       least 30 people and wounding more than 100, said
                       the health ministry in the Hamas-run Palestinian
                       territory. The Israeli military said its strike
                       targeted Hamas "terrorists" operating from the
                       school.


                # ⚓ France24 ☛ Deadly_strike_fired_from_Lebanon_into_Golan
                  Heights_sparks_fears_of_regional_war⠀⇛


                       A rocket fired from Lebanon struck a football pitch
                       and killed at least 12 young people in the Israeli-
                       annexed Golan Heights on Saturday, Israel's army
                       said, claiming the rocket was fired by the Lebanese
                       militant group Hezbollah, who denied any connection
                       to the incident. This strike raised fears of a
                       wider regional conflict, as it is the deadliest
                       attack on Israeli civilians since Hamas's October 7
                       attack on Israel, according to the military's chief
                       spokesman.


                # ⚓ RFA ☛ North_Korea_increases_production_of_152-millimeter
                  artillery_shells⠀⇛


                       Officials in the country assume that the shells are
                       for Russia to use in Ukraine.


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


                      # ⚓ France24 ☛ Zelensky_visits_frontline_Kharkiv_region
                        as_Russia_claims_advances_in_Donetsk⠀⇛


                             Ukrainian President Volodymyr Zelensky on
                             Monday visited special forces in the Kharkiv
                             region, where the military said it had
                             repelled six Russian attacks over the past
                             day. Zelensky’s visit comes as Moscow said
                             its forces had captured Vovche, a settlement
                             in the Donetsk region northwest of Avdiivka,
                             and Progres and Yevgenivka, villages a few
                             kilometres away from Vovche.


                      # ⚓ JURIST ☛ 5_civilians_dead_and_15_wounded_in_Ukraine
                        province_following_Russia_strikes⠀⇛


                             Russian military officers allegedly killed
                             five civilians and wounded 15 on Saturday
                             following strikes in the Donetsk province,
                             Ukraine. Vadym Filashkin, the governor of the
                             province, reported that the shelling wounded
                             more civilians, including children. Three
                             people were killed in Ivanivka, one in
                             Kostiantynivka, and one in Toretsk.


                      # ⚓ LRT ☛ Russian_media_exiles_get_a_hard_landing_in_the
                        Baltics⠀⇛


                             After Russia invaded Ukraine, Riga became a
                             hub for exiled Russian journalists. Among the
                             first to arrive was TV Rain, a flagship of
                             independent Russian media.


                      # ⚓ RFERL ☛ Fencer_Kharlan_Wins_Ukraine's_First_Paris
                        Olympics_Medal⠀⇛


                             Saber-fencing world champion Olha Kharlan won
                             Ukraine's first medal at the Paris Olympics
                             on July 29, giving her country something to
                             celebrate as it battles invading Russian
                             forces.


                      # ⚓ RFERL ☛ Slovakia_Threatens_To_Halt_Diesel_Supplies_To
                        Ukraine_Unless_Oil_Transit_Restored⠀⇛


                             Slovak Prime Minister Robert Fico said on
                             July 29 that his country would halt diesel
                             supplies to Ukraine if Kyiv fails to restore
                             oil flows from Russian group LUKoil through
                             its territory.


                      # ⚓ RFERL ☛ U.S._Announces_Up_To_$1.7_Billion_In_Security
                        Assistance_For_Ukraine⠀⇛


                             The United States on July 29 announced two
                             assistance packages for Ukraine valued at
                             $1.7 billion.


                      # ⚓ RFERL ☛ Another_Indian_National_Dies_Fighting_With
                        Russian_Troops_In_Ukraine⠀⇛


                             NDTV television in India reported on July 29
                             that another Indian citizen has died while
                             fighting alongside Russia's armed forces in
                             Ukraine.


                      # ⚓ RFERL ☛ Russian_Warrants_Issued_For_Members_Of_Anti-
                        War_Youth_Movement_In_Exile⠀⇛


                             A Moscow court on July 29 issued arrest
                             warrants for two more self-exiled members of
                             the Vesna youth movement over their public
                             condemnation of Russia's invasion of Ukraine.


                      # ⚓ RFERL ☛ Ukraine_Strikes_Russian_Energy_Facilities_For
                        Second_Day_In_A_Row⠀⇛


                             Ukraine launched a wave of drone strikes deep
                             inside Russian territory early on July 29,
                             damaging energy facilities in two regions,
                             Russia's Defense Ministry and regional
                             officials said a day after a reported
                             Ukrainian attack set a Russian oil refinery
                             on fire.


                      # ⚓ CS Monitor ☛ Ukraine's_freedom,_book_by_book⠀⇛


                             Book reading, from the war trenches to the
                             bedrooms of children, has helped Ukrainians
                             assert their cultural independence and mental
                             toughness.


                      # ⚓ New York Times ☛ Ukraine’s_Olha_Kharlan_Wins_Bronze
                        in_Fencing_at_Olympics⠀⇛


                             The war has torn apart old alliances in
                             fencing, and heightened the acrimony between
                             Russia and Ukraine.


                      # ⚓ Meduza ☛ ‘Everyone_is_afraid’:_The_Kremlin_says_it
                        wants_Russian_soldiers_who_fought_in_Ukraine_to_take_up
                        ‘leading_positions’_in_government_—_so_where_are_they?
                        —_Meduza⠀⇛


                      # ⚓ RFERL ☛ Accreditation_Revoked For_4_Russian
                        Journalists_Covering_Olympics⠀⇛


                             The Paris 2024 Organizing Committee confirmed
                             on July 29 that the accreditation of four
                             journalists with the Russian state-run news
                             agency TASS has been revoked.


                      # ⚓ RFERL ☛ Imprisoned_Veteran_Russian_Rights_Defender
                        Orlov's_Whereabouts_Unknown⠀⇛


                             Less than three weeks after the Moscow City
                             Court upheld the 30-month imprisonment of
                             veteran rights activist Oleg Orlov was moved
                             from a detention center in the city of
                             Syzran, the Memorial human rights group said
                             on July 29.


                      # ⚓ RFERL ☛ Prosecutors_Seek_Lengthy_Prison_Terms_For_2
                        Jailed_Chechens_Allegedly_From_Basayev's_Group⠀⇛


                             Prosecutors asked a military court in Russia
                             to sentence two alleged members of the late
                             Chechen field commander Shamil Basayev’s
                             group to 24 years in prison each over their
                             alleged participation in a terrorist attack
                             in Chechnya in 2005.


                      # ⚓ RFERL ☛ Vucic_Says_Serbia,_Russia_To_Jointly_Mark
                        80th_Anniversary_Of_Belgrade_Liberation⠀⇛


                             Serbia and Russia have agreed to jointly mark
                             the 80th anniversary of the liberation of
                             Belgrade from under the Nazi occupation,
                             President Aleksandar Vucic said July 29 after
                             talks with Russian Ambassador Aleksandr
                             Bocan-Kharchenko.


                      # ⚓ RFERL ☛ Moscow-Friendly_Armenian_Blogger_Barred_From
                        Entering_Moldova⠀⇛


                             Armenian blogger Mika Badalian, who is close
                             to fugitive pro-Russian Moldovan businessman
                             Ilan Shor, was barred from entering Moldova
                             last week, RFE/RL has learned.


                      # ⚓ RFERL ☛ 1_Dead,_Several_Missing_After_Dam_Bursts_On
                        Major_Shipping_Canal_In_Russia⠀⇛


                             Officials in Russia's northwestern region of
                             Karelia said on July 29 that one person died
                             and several are missing after a temporary dam
                             burst on the White Sea-Baltic Canal
                             (Belomorkanal).


                      # ⚓ TwinCities Pioneer Press ☛ Russia_is_relying_on
                        unwitting_Americans_to_spread_election_disinformation,
                        US_officials_say⠀⇛


                             By DAVID KLEPPER WASHINGTON (AP) — The
                             Kremlin is turning to unwitting Americans and
                             commercial public relations firms in Russia
                             to spread disinformation about the U.S.
                             presidential race, top intelligence officials
                             said Monday, detailing the latest efforts by
                             America’s adversaries to shape public opinion
                             ahead of the 2024 election.


                      # ⚓ Meduza ☛ Whereabouts_of_four_Russian_political
                        prisoners_unknown_after_unexpected_prison_transfers_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Train_derails_in_Russia’s_Volgograd_region,
                        reportedly_injuring_at_least_140_people_—_Meduza⠀⇛


                      # ⚓ LRT ☛ Latvia_asks_Lithuania’s_assistance_in_policing
                        its_border_with_Belarus⠀⇛


                             Latvia has asked Lithuania to send 10–15
                             border guards to help it handle irregular
                             migration on its border with Belarus.


                      # ⚓ LRT ☛ Poland_to_let_security_forces_use_arms_with
                        impunity,_activists_bemoan_‘license_to_kill’⠀⇛


                             Polish lawmakers on Friday, July 26, voted to
                             allow the security forces to use lethal
                             weapons with impunity in response to active
                             threats, including at the tense border with
                             Belarus.


          o § Environment⠀➾


                # ⚓ DeSmog ☛ How_to_Blunt_the_‘New_Climate_Denial’_with_Better
                  Language⠀⇛


                # § Energy/Transportation⠀➾


                      # ⚓ SANS ☛ 'Quickie:_Password_Cracking'_Energy,_(Sun,_Jul
                        28th)⠀⇛


                      # ⚓ Futurism ☛ [Cryptocurrency]_Fans_Disgusted_by_Trump's
                        Rambling_Appearance_at_Bitcoin_Event⠀⇛


                             The price of Bitcoin actually fell following
                             Trump's remarks, indicating a muted response.


                             Even [cryptocurrency] enthusiasts who were
                             willing to give Trump a pass for his
                             regressive beliefs, criminal record, and keen
                             interest in ending democracy in the US
                             weren't impressed.


                      # ⚓ Wired ☛ People_Are_Using_Memecoins_to_Bet_on_the_US
                        Election⠀⇛


                             Beyond financial speculation, the coins serve
                             no purpose and promise no utility, but over
                             the course of the US presidential election
                             campaign, their market performance has
                             correlated with the political fortunes of the
                             individuals they depict.


                      # ⚓ The Guardian UK ☛ Renewables_overtake_fossil_fuels_to
                        provide_30%_of_EU_electricity⠀⇛


                             Wind turbines and solar panels have overtaken
                             fossil fuels to generate 30% of the European
                             Union’s electricity in the first half of the
                             year, a report has found.


                             Power generation from burning coal, oil and
                             gas fell 17% in the first six months of 2024
                             compared with the same period the year
                             before, according to climate thinktank Ember.
                             It found the continued shift away from
                             polluting fuels has led to a one-third drop
                             in the sector’s emissions since the first
                             half of 2022.


                      # ⚓ Molly White ☛ When_did_cryptocurrency_policy_become_a
                        voter_issue?⠀⇛


                             Congressional hopefuls adding to their
                             platforms unexpected promises about
                             supporting “blockchain innovation”.


                             Especially combined with the broad perception
                             among everyday people that cryptocurrency is
                             a years-old fad that died off somewhere
                             between NFTs becoming cringe and FTX
                             exploding, I’m seeing a lot of confusion:
                             when did cryptocurrency suddenly become a
                             major issue for US voters?


                             I don’t believe that it has.


                      # ⚓ Hamilton Nolan ☛ [Cryptocurrency],_As_a_Political
                        Characteristic⠀⇛


                             The first thing that needs to be said about
                             cryptocurrency is that it has no socially
                             redeeming reason to exist. The primary thing
                             that it is actually useful for is buying
                             things on the [Internet] that are illegal. I
                             guess there could be a situation where
                             freedom fighters could use it to purchase
                             weapons to wage a revolution against a
                             repressive regime. That is a pretty niche
                             scenario though. That is not the sort of
                             thing that causes big banks and investment
                             firms and institutional money managers to
                             flock to something. That’s not why any of us
                             are talking about this stuff.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Revelator ☛ Rwanda’s_Inyambo:_The_Cows_Who_Are
                        Treated_Like_Royalty_—_But_Still_Face_Risks_to_Their
                        Survival⠀⇛


          o § Finance⠀➾


                # ⚓ Hong Kong Free Press ☛ World’s_top_auction_houses_racing_to
                  expand_in_Hong_Kong_despite_economic_slowdown⠀⇛


                       Three of the world’s top auction houses are racing
                       to expand in Hong Kong, eager to woo young Asian
                       buyers even as the global art market retreats from
                       pandemic-era highs.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ IT Wire ☛ Lenovo_names_Dr.Tolga_Kurtoglu_as_new_Chief
                  Technology_Officer⠀⇛


                       Lenovo says Dr. Kurtoglu, renowned for his
                       groundbreaking work in the IT industry, brings a
                       wealth of experience from leading roles within the
                       IT industry, including CTO of HP Inc. and Global
                       Head of HP Labs, CEO of Xerox Palo Alto Research
                       Center, and lead for the product development group
                       at Dell. He holds numerous patents and has
                       published multiple papers in the fields of
                       automation and machine intelligence, computational
                       design, systems engineering, and 3D/digital
                       manufacturing.


                # ⚓ The Washington Post ☛ Inside_the_powerful_Peter_Thiel_tech
                  network_that_launched_JD_Vance⠀⇛


                       “The best way for them to [instate] their elitist
                       scheme and reactionary views is regulatory
                       capture,” investor Del Johnson posted on X, using a
                       term to describe the private sector’s control of
                       the regulatory process. “You haven’t seen anything
                       yet if you let the VC class get into the
                       presidency.”


                       This report is based on 17 interviews with people
                       familiar with Vance’s rise in the Valley, his
                       relationship with Thiel, and the tech world’s
                       ambitions for him should he win the country’s
                       second-highest political office, many of whom spoke
                       on the condition of anonymity to protect their
                       relationships.


                # ⚓ Manuel Moreale ☛ Thoughts_on_politics_and_communities⠀⇛


                       Years ago, during the COVID era, the 37signals
                       company got into hot water online because they
                       announced in an internal communication that they
                       were going to ban “societal and political
                       discussions” on their internal work chat. The
                       announcement is online if you’re interested in
                       reading it.


                       People online reacted in all sorts of ways to that
                       news and many, many opinion pieces got published. I
                       remember talking about it with a few people
                       privately and had some interesting conversations
                       around that topic. As you can see, years later,
                       positions on topics such as politics and religion
                       are still controversial in the context of online
                       spaces.


                # ⚓ Idiomdrottning ☛ Utopian_ghouls⠀⇛


                       I’m a huge proponent of UBI as soon as possible,
                       it’s one of my main issues, but I’m at the same
                       time scared of it and see it as not sustainable. So
                       why am I so for it? Because I see it as a stepping
                       stone to tide us over while we figure out new
                       economics, new ways to handle tasks and give out
                       resources, not as the be-all-end-all.


                # ⚓ Kev Quirk ☛ Politics_and_Communities⠀⇛


                       People on 500 Social can still seek out and discuss
                       political topics with others, I'd just prefer they
                       didn't publish post about them there. But if
                       someone is having a political discussion and a
                       member of 500 Social wants to chime in, who am I to
                       say they can't? Of course they can. Like I said,
                       it's important.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ VOA News ☛ Manipulated_video_shared_by_Musk_mimics
                        Harris'_voice,_raising_concerns_about_AI_in_politics⠀⇛


                             A manipulated video that mimics the voice of
                             Vice President Kamala Harris saying things
                             she did not say is raising concerns about the
                             power of artificial intelligence to mislead
                             with Election Day about three months away.


                             The video gained attention after tech
                             billionaire Elon Musk shared it on his social
                             media platform X on Friday evening without
                             explicitly noting it was originally released
                             as parody.


                             The video uses many of the same visuals as a
                             real ad that Harris, the likely Democratic
                             president nominee, released last week
                             launching her campaign. But the video swaps
                             out the voice-over audio with another voice
                             that convincingly impersonates Harris.


                      # ⚓ New Eastern Europe ☛ Seven_favourite_hidden
                        narratives_of_Russian_propaganda⠀⇛


                             Nevertheless, when analysing narratives about
                             Ukraine and its war against unprovoked
                             Russian aggression, one can find some stories
                             much more digestible than others and more
                             difficult to be labelled as pure propaganda
                             from Russia or its political and media
                             satellites. The text below will be useful to
                             those who need arguments in such disputes.


                      # ⚓ VOA News ☛ Russia’s_top_spymaster_falsely_claims
                        Kremlin_does_not_interfere_in_other_countries’
                        affairs⠀⇛


                             Interference in the internal political
                             affairs of foreign nations is a deeply rooted
                             key part of Russia’s foreign policy. To
                             project influence, Moscow habitually goes
                             beyond diplomacy, using malicious hybrid
                             strategies and, in many instances, war.


                             Just a few widely reported, comprehensively
                             documented examples of Russian meddling in
                             the affairs of foreign nations: [...]


          o § Censorship/Free Speech⠀➾


                # ⚓ JURIST ☛ Thailand_court_jails_activist_Arnon_Nampa_for_four
                  extra_years_upon_royal_defamation_convictions⠀⇛


                       A Thailand court imposed Thursday an additional
                       four-year imprisonment on an activist and human
                       rights lawyer Arnon Nampa for defaming the Thai
                       royal family and violating the Computer Crime Act
                       through two social control media posts made between
                       January and April 2021.


                # ⚓ The Register UK ☛ Minister:_Malaysia_is_working_on_an_
                  [Internet]_kill_switch⠀⇛


                       Said did not expand on what Malaysia wants the
                       power to block, nor the circumstances under which
                       it will be permissible to do so. She did write that
                       the government wants social media platform
                       providers and [Internet] messaging services to take
                       more responsibility for the role their products
                       play in online crimes such as fraud, child sexual
                       abuse material, sexual harassment and solicitation,
                       plus bullying. Such actions, the minster explained,
                       are "in line with legislative initiatives enforced
                       in various other countries."


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


                # ⚓ The Dissenter ☛ US_Still_Won't_Comply_With_Spanish
                  Investigation_Into_CIA-Backed_Operation_That_Targeted
                  Assange⠀⇛


                # ⚓ VOA News ☛ Morocco_pardons_3_journalists_held_for_years⠀⇛


                       Human Rights Watch has accused Morocco of using
                       criminal trials, especially for alleged sexual
                       offenses, as "techniques of repression" to silence
                       journalists and government critics.


                # ⚓ France24 ☛ Morocco's_King_Mohamed_VI_pardons_imprisoned
                  journalists,_activists⠀⇛


                       Morocco's King Mohammed VI pardoned three
                       journalists, as well as an activist and a historian
                       on Monday to mark his 25th anniversary as monarch.
                       Rights groups criticised the journalists'
                       detentions as repressive tactics to silence
                       critics. In total, 2,476 people were pardoned.


          o § Civil Rights/Policing⠀➾


                # ⚓ Papers Please ☛ 5th_Circuit_reads_travel_blacklists_into
                  Federal_law⠀⇛


                       In a decision issued last week, the 5th Circuit
                       Court of Appeals has offered the first appellate
                       opinion on whether there is any basis in law for
                       the U.S. government’s creation and use of a system
                       of “watchlists” (blacklists) to determine who is
                       allowed to travel by air and how they are treated
                       when they travel, as well as to impose other
                       sanctions.


                       Numerous lawsuits have challenged various aspects
                       of the government’s blacklistsing system and its
                       application to airline passengers, but this is the
                       first time that any U.S. appellate court has ruled
                       on whether Congress has given the various agencies
                       that created, maintain, and use these lists any
                       statutory authority to so so.


                       The 5th Circuit panel found multiple mentions in
                       Federal law of the use “databases” for “screening”
                       of airline passengers. But that begs the question
                       that was actually presented. As the Council on
                       American-Islamic Relations (CAIR) argued in their
                       brief on appeal:


                # ⚓ The Register UK ☛ CBP_needs_warrant_to_search_phones,_says
                  yet_another_judge⠀⇛


                       US border agents must obtain a warrant, in New York
                       at least, to search anyone's phone and other
                       electronic device when traveling in or out of the
                       country, another federal judge has ruled.


                       Judge Nina Morrison of the Eastern District of New
                       York issued a decision [PDF] last week that Customs
                       and Border Patrol (CPB) officials need a warrant to
                       search citizens and non-citizens' electronics in
                       all but the most exceptional of circumstances.


                # ⚓ The Register UK ☛ Apple_agrees_to_terms_with_US_store_union
                  for_first_time⠀⇛


                       Apple is on the verge of entering its first-ever
                       agreement with a stateside retail employee union,
                       caving to demands from store workers who threatened
                       to walk off the job in May.


                       The International Association of Machinists and
                       Aerospace Workers' Coalition of Organized Retail
                       Employees (IAM CORE) said Friday it had reached a
                       tentative three-year deal between Cook & Co and the
                       roughly 85 employees the union represents at
                       Apple's store in Towson, Maryland.


                # ⚓ Modern Diplomacy ☛ Various_Global_Efforts_to_Tackle_Female
                  Genital_Mutilation_(FGM)_Issue⠀⇛


                       According to the World Health Organization (WHO),
                       an estimated 200 million women and girls living
                       today have undergone FGM, with the highest
                       prevalence found in countries across Africa, the
                       Middle East, and some parts of Asia (WHO, 2020).
                       The practice varies widely in form and severity,
                       encompassing everything from the removal of the
                       clitoral hood to more severe forms that involve
                       infibulation. FGM has no health benefits and is
                       associated with numerous complications, including
                       severe pain, bleeding, infection, and long-term
                       psychological effects (WHO, 2018).


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ The Register UK ☛ French_fiber_sabotaged_to_cause_net
                  outages_across_country⠀⇛


                       Major French telecom firms Bouygues, SFR, and Free
                       were all affected by the attacks, which apparently
                       could have only been carried out by an "axe or
                       grinder," according to an SFR spokesperson in a
                       statement to Le Monde. SFR didn't specify what
                       parts of its cable network were hit, merely saying
                       it was vandalized in "several departments."


                # ⚓ Cyble Inc ☛ Fiber_Optic_Cable_Sabotage_Disrupts_France's
                  Telecom_Network⠀⇛


                       SFR, France’s second-largest telecom operator,
                       confirmed extensive damage to its long-distance
                       cables. “Our long-distance fiber optic network was
                       the victim of acts of vandalism last night in
                       several departments. Disruptions may remain in the
                       most impacted areas. All our teams are mobilized to
                       allow you to connect again with those and what are
                       essential to you,” the telecom operator said.


      § Monopolies/Monopsonies⠀➾


          o ⚓ Baldur Bjarnason ☛ Very_short_note_on_the_EU's_DMA_and_DSA
            regulations⠀⇛


                 Americans also overestimate how emotionally invested
                 Europeans are in their own big companies. You’re
                 generally not going to get the same sort of emotional
                 “how dare they touch my favourite company” when the EU
                 acts against a big European website.


                 The DSA attempts to regulate “harmful content” on social
                 media and that’s when things get quite a bit iffy as a
                 politician’s idea of harmful isn’t the same as that of a
                 child welfare organisation, researcher, or education
                 expert.


          o § Patents⠀➾


                # ⚓ Dennis Crouch/Patently-O ☛ Lovevery_Argues_that_APEX
                  Jurisdiction_Holding_Undermines_Anti-Counterfeiting_Efforts⠀⇛


                       Most recently, toy-maker Lovevery has filed an
                       amicus brief supporting en banc review.  Lovevery
                       is an American company that specializes in
                       educational toys for babies and toddlers. According
                       to its motion for leave to file an amicus brief,
                       Lovevery does a substantial portion of its business
                       through online retailers like Amazon. The company
                       says it has a strong interest in the case because
                       the panel’s expansive “extrajudicial enforcement”
                       theory of personal jurisdiction could impede  its
                       ability to protect patent monopoly rights without
                       risking being sued in distant forums.


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ High-Tech_Karaoke_Piracy_Crackdown,_18
                  Arrested_and_Streaming_Servers_Seized⠀⇛


                       Karaoke may not scale the heights of popularity it
                       once did in the West, but after more than 50 years
                       the format may still be generating around $5
                       billion a year for rightsholders. That may explain
                       why Hong Kong Customs carried out a month-long
                       crackdown, arrested 18 people, and for the very
                       first time, seized hardware and remote servers
                       powering an online karaoke streaming system.


                # ⚓ Torrent Freak ☛ 'Indian_Police_Pinpoint_Seat_of_Movie
                  “Camming”_Pirate_by_Analyzing_the_Film_Angle'⠀⇛


                       Recording first-run movies in cinemas, an activity
                       commonly known as "camming", is seen as a major
                       threat to filmmakers worldwide. In India, the
                       practice was elevated to a criminal offense last
                       year and law enforcement is on high alert. A few
                       days ago, a camming suspect was caught in the act
                       after the filming angle of a previous upload,
                       reportedly identified the cinema and a 'hot seat'.


                # ⚓ Torrent Freak ☛ Ad_Blocking_Infringes_Copyright?_Ancient
                  Sony_Cheat_Lawsuit_May_Prove_Pivotal⠀⇛


                       Despite suffering losses in a legal battle that has
                       dragged on for years, German publishing giant Axel
                       Springer is refusing to give up on its claim that
                       ad blocking software illegally interferes with its
                       business model. Thus far, Eyeo GmbH, the company
                       behind Adblock Plus, has come out on top. However,
                       with Axel Springer's reformulated claims now rooted
                       firmly in copyright law, the stakes are high at
                       Germany's highest court. A long-running lawsuit
                       involving Sony and a cheat device may yet hold the
                       answers.


                # ⚓ Digital Music News ☛ South_Africa_Stands_Its_Ground_On_Fair
                  Use_Expansions_Vs._AI⠀⇛


                       The International Intellectual [sic] Property [sic]
                       Alliance (IIPA), which represents the ESA, MPA, and
                       RIAA, among others, recently published its findings
                       on the latest eligibility review of the African
                       Growth and Opportunity Act (AGOA). Led by the US
                       Trade Representative (USTR), the process determines
                       which sub-Saharan African countries are eligible
                       for certain trade benefits, and which, at the
                       opposite end of the spectrum, should be sanctioned.


                # ⚓ CoryDoctorow ☛ Pluralistic:_A_profoundly_stupid_case_about
                  video_game_cheating_could_transform_adblocking_into_a
                  copyright_infringement⠀⇛


                       Here's a weird consequence of our societal shift
                       from capitalism (where riches come from profits) to
                       feudalism (where riches come from rents):
                       increasingly, your rights to your actual property
                       (the physical stuff you own) are trumped by
                       corporations' metaphorical "intellectual property"
                       claims.


                       That's a lot to unpack! Let's start with a quick
                       primer on profits and rents. Capitalists invest
                       money in buying equipment, then they pay workers
                       wages to use that equipment to produce goods and
                       services. Profit is the sum a capitalist takes home
                       from this arrangement: money made from paying
                       workers to do productive things.




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