𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, November 18, 2023
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Generated Sun 19 Nov 02:49:43 GMT 2023
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/2023/11/18/


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

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

⦿ Techrights  -  Internet Relay Chat (IRC) Turns 35

⦿ Techrights  -  IRC Proceedings: Friday, November 17, 2023

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  The World Wide Web - and the Net as a Whole - Drowns in Bot Traffic, Partly Due to Computer-generated (CG) Hype - and Generating/Generative  Harvesting Farms (Also: Sam Altman Just Ousted! The Microsoft Chatbot Bubble is Imploding, Just Wasting Power and Bandwidth!)

⦿ Techrights  -  [Video] Bill's and Satya Nadella’s Whitewashing Campaigns?

⦿ Techrights  -  [Video] Corporate/Mainstream Media Still Failing to Call Out Windows (and Microsoft)

⦿ Techrights  -  [Video] No, Phoronix, Microsoft is Not an Acceptable Participant But a Snake (But Microsoft Gives Phoronix 'Gifts') and Heather Meeker Acts Like a Microsoft 'Asset', Professional Revisionist

⦿ Techrights  -  [Video] "Washington's Worsening Debt Problem" Includes Microsoft's Massive Corporate Debt (Over 105 Billion in Debt)

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://news.techrights.org/n/2023/11/18/Internet_Relay_Chat_IRC_Turns_35.shtml
https://news.techrights.org/n/2023/11/18/irc-log-171123.shtml
https://news.techrights.org/n/2023/11/18/Over_at_Tux_Machines.shtml
https://news.techrights.org/n/2023/11/18/The_World_Wide_Web_and_the_Net_as_a_Whole_Drowns_in_Bot_Traffic.shtml
https://news.techrights.org/n/2023/11/18/_Video_Bill_s_and_Satya_Nadella_s_Whitewashing_Campaigns.shtml
https://news.techrights.org/n/2023/11/18/_Video_Corporate_Mainstream_Media_Still_Failing_to_Call_Out_Win.shtml
https://news.techrights.org/n/2023/11/18/_Video_No_Phoronix_Microsoft_is_Not_an_Acceptable_Participant_B.shtml
https://news.techrights.org/n/2023/11/18/_Video_Washington_s_Worsening_Debt_Problem_Includes_Microsoft_s.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://news.techrights.org/n/2023/11/18/Links_18_11_2023_Amazon_Alexa_Layoffs_Arguments_Over_Hong_Kong_.shtml
https://news.techrights.org/n/2023/11/18/Links_18_11_2023_OpenAI_s_Management_in_Disarray_and_Twitter_X_.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 69

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/11/18/Internet_Relay_Chat_IRC_Turns_35.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/11/18/Internet_Relay_Chat_IRC_Turns_35.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Internet Relay Chat (IRC) Turns
35⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 18, 2023


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Jarkko_Oikarinen⦈_


In August 1988 (35 years ago) IRC was "invented"_by_Jarkko_Oikarinen, who was
21 at the time. He was working at the University of Oulu. He has since then
earned his Ph.D. (11 years later) at the Department of Information Processing
Science, University of Oulu. I myself started using IRC around 1994 and I'm
still using it today, almost 30 years later.


Right now we work to rectify a certificate authority-related issue in our IRC
network and we're glad to see that IRC, unlike so many other protocols, is
still kicking. Matrix ([matrix]) barely survived a decade. Introduced in
September 2014, it already has serious problems [1, 2], particularly
Matrix.org.


My Jabber days were over the moment my last employer decided to cease its use
for no good reason; too many of the "clown computing" cargo cults decided to
trade in their sensitive data (workers' privacy and customers' dignity
abandoned) in favour of state/spy-connected harvesting disservices.


With IRC, anyone can roll out one's own network. Let's hope IRC can still be
around in 35 years from now, even as a niche ("retro") thing.


Gopher is still used, but it is only a niche and it is younger than IRC (3
years younger). USENET goes back to 1979. To most people, USENET is just
"Google Groups" (and Google will probably abandon this too, having already
turned it into a highly bloated "webapp", rendering it obsolete for many
people). █




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠁⠀⠀⠀⠿⠿⠿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣷⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 174

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/11/18/irc-log-171123.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/11/18/irc-log-171123.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Friday, November 17,
2023⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 18, 2023


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


                          Enter_the_IRC_channels_now





                    ䷩ 𝚕𝚒𝚗𝚎 206

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/11/18/Over_at_Tux_Machines.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/11/18/Over_at_Tux_Machines.gmi

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


posted by Roy Schestowitz on Nov 18, 2023


⚓  Updated This Past Day⠀⇛


   1. ⚓ EasyOS_Kirkstone-series_version_5.6.1_released⠀⇛


           We were discussing Firefox versus Chromium on the forum


   2. ⚓ Calibre_7.0_E-Book_Manager_Introduces_New_Notes_Feature,_Support_for
      Audio_EPUBs⠀⇛


           Calibre developer Kovid Goyal announced today the release and
           general availability of Calibre 7.0 as the latest stable
           version and a major update to this powerful, free, open-source,
           and cross-platform e-book management software.


   3. ⚓ Wireshark_4.2_Packet_Analyzer_Adds_Support_For_HTTP/3⠀⇛


           Wireshark 4.2 introduces smarter display filter autocomplete,
           avoiding invalid syntax for more efficient network analysis


   4. ⚓ FFmpeg_6.1_“Heaviside”_Released_with_VAAPI_AV1_Encoder,_HW_Vulkan
      Decoding⠀⇛


           FFmpeg 6.1 open-source multimedia framework has been released
           today as a major update that brings new features, new decoders,
           new filters, and many other changes.


   5. ⚓ New_Horizons_for_EL:_OpenELA_Publishes_Package_Sources⠀⇛


           Bright future for Enterprise Linux with OpenELA’s RHEL-
           compatible sources for packages now available. More is on the
           way


   6. ⚓ HandBrake_1.7_Released_with_AMD_VCN_AV1_and_NVIDIA_NVENC_AV1_Encoders⠀⇛


           HandBrake 1.7 has been released today as a major update to this
           open-source, free, and cross-platform video transcoder
           application for GNU/Linux.


      ⚓  New⠀⇛


   7. ⚓ Today_in_Techrights⠀⇛


           one day's articles


   8. ⚓ today's_howtos⠀⇛


           some howtos for Friday


   9. ⚓ today's_leftovers⠀⇛


           a few assorted links and video


  10. ⚓ Windows_TCO_(Security_Issues)⠀⇛


           incidentrs and high costs of ownership (TCO), not even
           ownership


  11. ⚓ Audiocasts/Shows:_Linux_in_the_Ham_Shack_and_BSDNow⠀⇛


           2 new episodes


  12. ⚓ Unveiling_the_Life_Stories_of_Linux_Innovators⠀⇛


           Linux, the open-source operating system that powers millions of
           devices worldwide


  13. ⚓ Oppo_starts_rolling_out_ColorOS_based_on_Android_14⠀⇛


           Chinese smartphone vendor Oppo says it has begun rolling out
           ColorOS 14, its variant based on Android 14, to its 600 million
           active users


  14. ⚓ Tuning_the_Linux_kernel_with_AI,_according_to_ByteDance⠀⇛


           ByteDance has a proposal to make this easier


  15. ⚓ It’s_Official:_Linux_Kernel_6.6_Will_Be_LTS,_Supported_Until_December
      2026⠀⇛


           In another unexpected turn of events, the latest Linux 6.6
           kernel series has been officially marked as LTS (Long Term
           Support) on the kernel.org website with a predicted life
           expectancy of at least three years.


  16. ⚓ Allwinner_VPU_gets_open-source_H264_hardware_video_encoder_Linux
      driver⠀⇛


           Bootlin’s Linux kernel support for H.264 video encoding with
           the Allwinner V3/V3s/S3 platforms consists of patchsets on top
           of the mainline Linux Cedrus driver


  17. ⚓ mesa_23.3.0-rc4⠀⇛


           As always, if you find any issues please report them


  18. ⚓ Software_doing_what_you_want,_not_what_you_say⠀⇛


           The KDE launcher also isn’t doing anything fancy; it’s matching
           on metadata associated with the launcher


  19. ⚓ BSD:_OpenSMTPD,_FreeBSD_packages_routine,_and_more⠀⇛


           BSD news


  20. ⚓ Open_Hardware/Modding_and_Linux_Devices⠀⇛


           Raspberry Pi 5, MIKROE, and more


  21. ⚓ Programming_Leftovers⠀⇛


           R, Java, Shell...


  22. ⚓ Rust_1.74.0⠀⇛


           New release


  23. ⚓ The_Web_and_Free,_Libre_Software⠀⇛


           Some FOSS in relation to the WWW


  24. ⚓ Free,_Libre,_and_Open_Source_Software_Leftovers⠀⇛


           FOSS news, misc.


  25. ⚓ Events:_libcurl,_WordPress,_and_Capitole_du_Libre_2023⠀⇛


           Some FOSS highlights


  26. ⚓ Linux_Kernel_6.6_Officially_Confirmed_as_an_LTS⠀⇛


           Last month saw the release of the Linux 6.6 kernel, a big
           update jam-packed with new features, hardware support, security
           enhancements, and performance improvements


  27. ⚓ Gear,_Frameworks,_Kernel_updates_in_Tumbleweed⠀⇛


           A large amount of software updates made it into openSUSE
           Tumbleweed snapshots this week


  28. ⚓ 6_Best_Free_and_Open_Source_Linux_Electronic_Medical_Records_Software⠀⇛


           Open source EMR software has an important role to play


  29. ⚓ Games:_Core_Keeper,_Bzzzt,_art_of_rally,_and_More⠀⇛


           half a dozen new stories from Liam Dawe


  30. ⚓ Kubernetes_and_Servers⠀⇛


           5 related stories


  31. ⚓ today's_howtos⠀⇛


           only 5 for now


  32. ⚓ Is_Bing_Dead?⠀⇛


           ChatGPT not doing anything for Bing


  33. ⚓ More_Security_Leftovers_and_Microsoft_Problems⠀⇛


           Security links, part II


  34. ⚓ How_to_Install_LXQt_1.4_on_Lubuntu_22.04_LTS⠀⇛


           Learn how to install the latest LXQt 1.4 desktop environment
           using backport PPA in Lubuntu 22.04.


  35. ⚓ Security_Leftovers_and_Windows_TCO⠀⇛


           also some FUD


  36. ⚓ today's_leftovers⠀⇛


           3 more links


  37. ⚓ Free,_Libre,_and_Open_Source_Software_Leftovers⠀⇛


           FSF, Tor, and more


  38. ⚓ 12_Best_Time_Tracking_Software_for_Linux_Desktop⠀⇛


           Time tracking software can be an effective solution to enhance
           productivity and control time expenses


  39. ⚓ Programming_Leftovers⠀⇛


           R, Rust, and more


  40. ⚓ Red_Hat:_Proprietary_(Secretive)_Hardware_as_'Security',_Flathub,_Red
      Hat_Working_With_Lockheed_Martin,_Pagure_Exporter⠀⇛


           Some IBM news


  41. ⚓ Scientists_use_Raspberry_Pi_and_Raspberry_Pi_Now_in_Google's_Pocket,
      Too⠀⇛


           A pair of reports about Raspberry Pi


  42. ⚓ New_Steam_Games_with_Native_GNU/Linux_Clients_and_13_Best_Distributions
      for_Gaming_on_Linux⠀⇛


           2 new articles about games


  43. ⚓ Windows_TCO⠀⇛


           Cost of Microsoft mindset


  44. ⚓ Barry_Kauler_on_EasyOS_Development⠀⇛


           3 new updates


  45. ⚓ LXQt_1.4_Desktop_Arrives_for_Lubuntu_23.10_Users,_Here’s_How_to_Install
      It⠀⇛


           The Lubuntu developers have decided to backport the LXQt 1.4
           desktop environment to the latest Lubuntu 23.10 (Mantic
           Minotaur) release.


  46. ⚓ Kernel:_Torvalds,_Bootlin,_CMRR_Variable_Refresh_Rate_Feature⠀⇛


           3 new stories


  47. ⚓ Release_of_Red_Hat_Enterprise_Linux_9.3⠀⇛


           RHEL release


  48. ⚓ Steam_Deck_OLED_Is_Now_Available_to_Order_with_HDR_Display_and_Bigger
      Battery⠀⇛


           Valve today officially released the Steam Deck OLED Linux-
           powered gaming handheld that brings a bigger screen with high
           dynamic range (HDR) support, a bigger battery, and more.


  49. ⚓ Android_Leftovers⠀⇛


           Android's new Private Space feature could let you hide apps and
           data on your phone


  50. ⚓ Five_things_to_consider_when_switching_to_Linux_Mint⠀⇛


           A guide to what you'll need to think about if you switch your
           old laptops to Linux Mint


  51. ⚓ today's_howtos⠀⇛


           many howtos for the day


  52. ⚓ Canonical_releases_new_low-touch,_open-source_cloud_solution⠀⇛


           Canonical, the company behind Ubuntu, has released MicroCloud,
           which is a low-touch private cloud any business can use


  53. ⚓ What_makes_a_Linux_distro_light?⠀⇛


           It's a Swiss Army knife that can do anything and that's part of
           its definition


  54. ⚓ today's_leftovers⠀⇛


           GNU/Linux, BSD, and more


  55. ⚓ Applications_for_GNU/Linux⠀⇛


           5 assorted FOSS stories


  56. ⚓ CodeWeavers_CrossOver_23.6_and_Black_Friday_Bundle⠀⇛


           New release


  57. ⚓ Peter_Czanik_and_syslog-ng_News⠀⇛


           3 links


  58. ⚓ Cautionary_Tale_About_Microsoft_and_VSCode⠀⇛


           proprietary junk


  59. ⚓ Security_Leftovers⠀⇛


           Security-related stories


  60. ⚓ Hands-On_with_MX_Linux_23_on_Raspberry_Pi_5⠀⇛


           MX Linux 23 is coming to the Raspberry Pi as the team announced
           today the first alpha version of an updated MX Linux respin
           image for the tiny single-board computer.


  61. ⚓ Windows_Total_Cost_of_Ownership_(Data/System_Breaches)⠀⇛


           Microsoft breaking things


  62. ⚓ Kubernetes_Resource_Limits_and_Major_Changes_in_Kubernetes_1.29⠀⇛


           Some Kubernetes news from the official blog


  63. ⚓ Games:_Steam_Deck,_SteamOS,_Anima_Flux,_and_More⠀⇛


           7 posts by Liam Dawe


  64. ⚓ Android_Leftovers⠀⇛


           My favourite affordable Android phone is even cheaper in
           Google's Black Friday sale


  65. ⚓ Kernel:_New_in_LWN_(Outside_the_Paywall)_and_Rust_Burden⠀⇛


           Some kernel news


  66. ⚓ Lubuntu_22.04_LTS_Users_Can_Now_Install_the_LXQt_1.4_Desktop,_Here’s
      How⠀⇛


           Lubuntu developer Simon Quigley informs us today about the
           availability of the latest LXQt 1.4 desktop environment for
           users of the long-term supported Lubuntu 22.04 LTS (Jammy
           Jellyfish) operating system series.


  67. ⚓ Kdenlive_Sprint_Recap_–_November_2023⠀⇛


           The Kdenlive team met last weekend in Zürich for a sprint. Many
           topics were discussed, here is a quick overview of what we did


  68. ⚓ Programming_Leftovers⠀⇛


           Python and more


  69. ⚓ Linux_Foundation_Openwashing_Subgroups⠀⇛


           some new ones


  70. ⚓ Red_Hat/Servers:_F39_Elections,_Fedora_Magazine,_Kubernetes,_and
      Qubes⠀⇛


           mostly IBM and derivatives


  71. ⚓ Nordic_introduces_nRF7002_EK_WiFi_6_Arduino_Shield,_nRF7000_SSID-based
      Wi-Fi_locationing_chip⠀⇛


           But as noted by Hackster.io, Nordic also just released a Linux
           driver for nRF70 chips and tested with a Raspberry Pi 4 running
           Ubuntu 22.04 64-bit connected to the nRF7002 EK through an
           interposer board


  72. ⚓ Open_Hardware/Modding:_Raspberry_Pi_and_Arduino⠀⇛


           3 stories/projects


  73. ⚓ today's_howtos⠀⇛


           morning batch of howtos


  74. ⚓ How_to_Emulate_macOS_Interface_on_your_Linux_System⠀⇛


           This guide compiles various methods to give your preferred
           Linux distribution a makeover with a macOS theme


  75. ⚓ The_Linux_Scheduler_And_How_It_Handles_More_Cores⠀⇛


           Did the Linux developers make an egregious error more than a
           decade ago that has crippled Linux performance to this day


  76. ⚓ OBS_Studio_30_Released_with_Support_for_Intel_QSV_H264,_HEVC,_and_AV1
      on_Linux⠀⇛


           OBS Studio 30 is now available for download coming with
           exciting new features, as well as numerous other changes and
           bug fixes for this popular free and open-source screencasting
           and streaming app.


  77. ⚓ Banana_Pi_teases_RK3588-powered_Single_Board_Computer_with_dual
      2.5GbE⠀⇛


           The product announcement indicates that the Banana Pi BPI-M7
           board will support Debian Buster, Android 12 and Linux Kernel
           5.10


  78. ⚓ Haiku_Activity_&_Contract_Report,_October_2023⠀⇛


           his report covers hrev57309 through hrev57363 (again a bit of a
           shorter month than average.)





                    ䷩ 𝚕𝚒𝚗𝚎 762

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/11/18/The_World_Wide_Web_and_the_Net_as_a_Whole_Drowns_in_Bot_Traffic.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/11/18/The_World_Wide_Web_and_the_Net_as_a_Whole_Drowns_in_Bot_Traffic.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The World Wide Web - and the Net as a Whole
- Drowns in Bot Traffic, Partly Due to Computer-generated (CG) Hype - and
Generating/Generative Harvesting Farms (Also: Sam Altman Just Ousted! The
Microsoft Chatbot Bubble is Imploding, Just Wasting Power and
Bandwidth!)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 18, 2023


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Bad Bots Account for 73% of Internet Traffic: Analysis⦈


YESTERDAY in Daily Links we included this_story, which says it's a lot worse
than we stated only a couple of months ago, citing one new - at least at the
time - survey. A previous survey said that things improved a little this year
and that 'only' about half of Web/Net traffic is now bots/junk, down from the
prior year. But this one says 73% is bad (undesirable) bots. So it must be
getting worse. Either way, trends aside, this is objectively bad.


As a reminder, some sites and companies took action or threatened to take
action against OpenAI and Microsoft for scraping a lot of "content" at the
expense of those companies' back end, causing all sort of technical issues.


Well, first of all, Sam Altman has just been kicked out. He got the boot (see
Sam_Altman_ousted_as_OpenAI’s_CEO). They are losing_money_like_crazy -
bankruptcy seems like only a matter of time - and OpenAI will go out of
business if Microsoft stops funding them or offering 'free' hosting to fake
Azure 'demand'. Microsoft has its own financial woes*, as we'll explain in a
later article some time on Saturday. We recorded a video about it last night,
just need to finalise the text now. Going back to the subject of bot traffic,
we too have witnessed this for years and we're deeply concerned. The sorts of
requests that come from mindless bots generate heavy loads... and who for? For
sure some companies stand to gain from the open Web becoming a vortex of
energy-wasting activity, but those companies are themselves not profiting
(Clownflare for example**). As somebody put it, that's "73% [of] electricity
wasted shifting those packets around on the Net" (also costing in hosting bills
to the targeted sites).


We're generally glad SecurityWeek points out bots took over the Net, maybe the
Web too. This merit more widespread discussion because many sites and companies
fake their "reach", citing traffic that's basically fake, making their
overambitious claims bunk and merely increasing their "clown computing" bills.
It's a big problem and it has been getting a lot worse in recent years. "Bots
== Wasted Electricity / Wasted Bandwidth" as someone put it, but it's seen as
an externality to bot operators. To them, it is "cheap"; they send one or two
TCP/IP packets, causing churn (wear and tear) at the other end and they might
discard the packets sent in response. They just don't care....


This whole bot issue on the Net means that going static is good proactive
practice, as it lowers operational costs and churn. It leads to better speeds
and reduced complexity. The speed does matter; I sometimes navigate Gemini and
the Web with keyboard only, as the latency for both is so low that it's like
navigating pages locally.


If the Web continues to get this bad, sites should at least prevent requests
for pages from invoking programs (like PHP). On the Net, restricting access can
help, but then we undermine the notion of openness and accessibility. Cui bono?
█


___
* Microsoft no longer sells or licences software. It's trying serfdom instead.
With Microsoft, ownership does not exist. You're not even renting. With all
this "clown_computing"_nonsense you're not even licensing or deploying
anything. You are a slave and you pay the master, let alone remain unpaid. It
makes no sense at all.


** See this_month-old_video for more on Clownflare and other such companies.
Their business model is a ticking time bomb. Avoid them for your own sake.




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠄⣻⠿⢿⠿⠇⣿⣿⠀⠄⣹⠿⢿⠏⢿⠿⢿⣿⡟⠀⢿⠿⠿⡿⠿⢿⠿⢿⠿⡿⠿⠿⠿⠏⢹⣿⠏⢽⠿⠿⠿⠿⣿⣦⠀⣎⣰⢈⠁⡆⡏⣾⣿⣿⡿⠿⢿⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠆⠑⠨⢸⠀⡇⣿⣿⠀⠆⠁⢸⠀⡇⢿⢌⠸⣿⠇⣀⢸⠀⠗⡇⠗⠂⢸⠀⠀⡇⠀⢸⠀⡇⢸⣿⡇⣿⢸⠀⠀⣾⣿⡟⢰⡟⠳⠈⣷⣶⢱⠰⠈⣿⡇⠸⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣾⣿⣾⣾⣷⣶⣿⣿⣶⣶⣿⣶⣾⣷⣾⣷⣾⣿⣶⣿⣶⣷⣾⣿⣶⣿⣶⣾⣷⣷⣶⣾⣶⣷⣾⣿⣷⣿⣶⣾⣷⣿⣿⣷⣾⣿⣶⣾⣿⣷⣿⣷⣾⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠟⠟⠟⠉⡿⠛⢿⠻⢻⠻⠻⡿⠛⠟⠙⣿⣷⠀⡞⠻⠿⠛⠟⠀⠁⠰⢺⠟⠻⡟⣿⣿⠇⠈⡿⠻⠻⠿⠻⡇⢸⢻⠛⠟⢻⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⡇⢸⠀⡇⠐⢺⢰⣿⢸⠀⡇⠗⣺⠸⣿⣿⠀⡇⢸⡏⠅⢸⢸⠀⡇⢸⠀⠒⡟⣿⣿⢀⡁⠃⢸⠀⠋⠅⡇⢸⡈⢸⠦⠛⣿⡟⠌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣛⣒⡀⠓⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡯⠄⠂⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⡀⣀⡀⡀⣀⣀⣀⡀⣀⢀⢀⡀⣀⢀⢀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣂⢧⣄⠉⣙⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⡇⣿⣺⣯⣽⣿⡇⡗⡇⡇⢸⠀⣿⠀⠛⠘⠐⠂⠒⠘⠊⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣤⡄⠱⠙⡇⢙⣦⣝⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠁⠭⠁⠩⠀⠉⠀⠥⠡⠁⠈⠤⠉⠀⠄⠠⠀⠀⠄⠀⠀⠄⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⢀⠁⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⠀⠀⠀⠀⠴⠄⠈⠐⣿⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⡀⣤⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢰⣀⢂⣡⠀⠀⠐⠀⠈⠹⡉⠐⠢⡀⠀⢏⣽⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣸⣿⣸⡐⣴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⡇⡿⣿⡇⡻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠘⡇⡰⠹⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣷⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡄⠀⠀⢿⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠠⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠌⠀⠀⠀⠈⠴⣶⣶⣶⣶⣶⣶⣶⡶⢶⣯⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿

                    ䷩ 𝚕𝚒𝚗𝚎 881

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/11/18/_Video_Bill_s_and_Satya_Nadella_s_Whitewashing_Campaigns.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/11/18/_Video_Bill_s_and_Satya_Nadella_s_Whitewashing_Campaigns.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] Bill's and Satya Nadella’s
Whitewashing Campaigns?⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 18, 2023


Video_download_link | md5sum e350f781f0c398ad3908113da27dfa58
The_Nadella_Perception
Creative Commons Attribution-No Derivative Works 4.0


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


THE VIDEO we publish today takes note - but not full stock - of sponsored and/
or spoon-fed puff pieces posted this past summer to hail Mr. Nadella,
portraying him as some modest and poor guy who is underpaid compared to
Google's CEO. Is Nadella some sort of charitable marvel or a professional
fraud?


Remember that while the media rushes to paint him as a genius and a saviour of
Microsoft, under his leadership - especially this year - tens of thousands of
workers were laid off, so embellishing his image was important to Microsoft as
it sought to quell dissent from within. A few days ago a Microsoft-bribed
propaganda_site_MTR was posting_Microsoft_spam_for_this_fraud. Around the same
time off-guardian spoke of yet_another_fraud. As one reader put it, Microsoft
(and thus Bill Gates) is antithetical to "interoperability".


The attempts to soften the image of Nadella and his_handler are likely a
response to growing "pushback" from the public. People are tired of being
dictated by frauds and criminals. █




⣿⣿⠈⢹⠁⡗⡄⣔⡄⠀⣧⡂⣔⡄⡔⡇⣔⡄⡇⣧⣢⠀⢸⠽⢠⣢⢰⣿⣿⣧⣢⢰⢢⢺⢺⣰⢢⠰⢢⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣩⠀
⣻⣋⣀⠈⡀⠁⠁⠉⠁⠀⠁⠁⠉⠁⠉⠁⢉⣁⣁⡉⣉⣀⣈⣀⢈⣉⣸⣿⣿⣏⣉⣘⣉⣈⣉⣈⣉⣀⣈⣸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣽⣉⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀
⠀⠠⠠⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⢹⣿⣿⣿⣧⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣹⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡯⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠿⣿⣿⣻⡟⢿⡝⣿⣿⣿⣿⣿⡷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣏⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⡀⠹⣿⠟⠁⠘⠒⠻⢻⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠿⠟⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⢒⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⡗⢺⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠀⠐⠃⠐⠀⠘⡇⢃⣾⣿⣻⣿⣿⣄⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠃⠘⠗⠺⠛⣹⠩⠟⠛⠛⠛⠛⠛⠛⠛⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⠀⠀⠔⠂⢐⠲⣾⣿⣿⢿⡟⢻⣏⣳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢺⣿⣿⣿⣿⠒⣿⣟⣿⠉⠓⢨⡁⢀⡄⠀⠀⠀⠀⠻⠛⡟⢛⠁⠙⠃⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢹⡂⢛⠃⠉⠀⠉⠘⡣⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢉⣳⣄⠀⣼⣿⣿⡇⡁⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⣀⡂⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣵⣽⣾⣿⣿⣇⣄⣠⣄⣴⣄⣠⣁⣤⣤⣤⣀⣄⣠⣤⣴⣯⣼⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣥⣉⡩⠛⠻⠿⡏⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠈⢹⠁⡇⡄⣄⡄⠀⣧⡂⣄⡄⡄⡇⣄⡄⡇⣦⣠⠀⢸⡱⢠⣠⢰⣿⣿⣧⣠⢠⢠⢰⢨⡠⢤⠠⢤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⠀
⣻⣋⠀⠈⠀⠁⠁⠉⠁⠀⠁⠁⠉⠁⠉⠁⠉⠁⡁⡉⢉⣀⣈⣀⠈⡉⣸⣿⣿⣏⣉⣸⣉⣈⣉⣈⣉⣀⣈⣸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡉⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀
⠀⠀⠠⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⢹⣿⣿⣿⣧⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠥⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡯⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⠔⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠿⣿⣿⣻⡟⢿⡝⣿⣿⣿⣿⣿⣷⣗⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⡀⠹⣿⠝⠁⠘⠒⠻⢻⣿⣿⣿⡿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠿⠏⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⢒⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⡟⢻⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠈⠐⠃⠐⠀⠘⡇⢫⣾⣿⢻⣿⣿⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠋⠙⠟⠺⢛⣽⠍⠟⠛⠻⠙⠛⠛⠛⠛⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠠⠀⠀⠀⠔⠂⢐⠢⣿⣿⣿⢻⡟⣻⣏⣱⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢺⣿⣿⣿⣿⠳⣿⣿⣿⠉⠓⢨⡁⣀⡄⠀⠀⠀⠀⠻⡛⡫⢹⠉⠙⠁⠙⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⡏⢹⡊⢟⠃⠉⠀⠉⠀⡡⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢉⣳⣄⠀⣼⣿⣿⡇⡁⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⣈⡆⢘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣵⣽⣾⣿⣿⣇⣄⣠⣄⣴⣌⣠⣡⣤⣤⣤⣀⣄⣠⣤⣴⣯⣼⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣥⣤⣉⡉⠛⠻⠿⠏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠐⢲⠂⡧⡄⣤⡄⠀⣦⠆⣤⡄⡤⡇⣤⡄⡇⣦⣤⠀⢰⣲⢠⣤⢰⣿⣿⣧⣤⢠⢤⢴⢼⡠⢤⠠⢤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⠀
⣋⢉⠀⠘⠀⠃⠃⠑⠁⠀⠁⠃⠑⠃⠑⠃⠑⠁⠃⠉⠚⠀⡘⡀⠈⠊⢸⣿⣿⡏⠊⠸⠊⠘⠚⢘⠋⡀⠘⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡉⣩⣩⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠀
⠀⠀⡢⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⡸⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡯⢷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠴⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⠸⣿⡝⠀⠐⠚⠻⢽⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠻⠛⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⢑⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⣟⢺⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠀⠐⠂⠐⠀⠘⡇⢇⣾⣿⣻⣿⣷⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠃⠘⠗⠺⢋⡽⠍⠟⠛⠻⠛⠟⠛⠛⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠠⠀⠀⠀⠔⠂⢐⠒⣿⣿⣿⢿⡿⣻⡏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢿⣿⣿⣟⣿⠲⣿⣿⣿⠉⠃⢨⣁⢀⡄⠀⠀⠀⠀⠻⠛⡋⢙⠁⠙⠁⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠏⢹⡆⢝⠂⠁⠀⠉⠀⡡⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢉⣣⣄⠀⣼⣿⣿⡇⡁⢀⡀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⡀⣉⡂⢘⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣵⣽⣿⣿⣿⣇⣄⣠⣄⣴⣄⣳⣡⣤⣤⣤⣀⣄⣠⣤⣼⣇⣼⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣬⣉⡩⠛⠻⢿⠏⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠛⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠐⢲⠂⡦⡄⣤⡄⠀⣦⠆⣤⡄⡤⡆⣤⡄⡆⣦⣤⠀⢰⣲⢠⣤⢰⣿⣿⣧⣤⢠⢤⢴⢴⡠⢤⢠⢤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⠀
⣻⣉⠀⠘⠀⠃⠃⠓⠂⠀⠃⠃⠓⠃⠑⠃⠑⠂⠃⠙⠚⠀⠘⠀⠈⠒⢸⣿⣿⡟⠒⠸⠊⠘⠚⠙⠊⠀⠘⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⣉⣩⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠀
⠀⠠⡀⠉⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣧⢸⣿⣿⣿⣿⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀
⠀⠀⠈⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣽⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠖⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠿⣿⣿⣻⡿⠿⢿⣿⣿⣿⣿⣿⣧⢿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠺⣿⡝⠀⠐⠊⠻⢽⣿⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠿⠟⠸⠟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠪⢰⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⣟⢿⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠷⠟⠉⠐⠃⠘⠀⠘⡇⢷⣾⣿⣿⡿⣿⣄⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠇⠀⠀⠀⠀⠐⠀⢸⣿⣿⡇⠋⠙⠛⠻⠯⠹⠏⠛⠛⠛⠙⠛⠛⠛⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⠀⠀⠀⠔⠂⢐⠲⣿⣿⣿⣻⡗⣿⡏⣱⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⣿⣿⣟⣿⠲⣿⣻⣿⠉⡃⢈⡁⣀⡄⠀⠀⠀⠀⠻⠛⡿⢛⠉⠙⠃⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⢂⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⡏⢹⠃⢟⠂⠉⠀⠉⠀⡡⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣩⣷⣄⠀⣹⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⣉⡂⢈⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣿⣿⣿⣿⣿⣇⣄⣠⣄⣴⣄⣳⣡⣤⣤⣤⣀⣄⣠⣤⣼⣏⣼⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣈⡉⠛⠻⢿⠏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠛⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠐⢲⠒⡦⡀⡤⡀⠀⣦⠄⠠⡄⡠⡆⡠⡄⡆⡦⢤⠀⢰⣲⢠⢤⢰⣿⣿⣧⢄⢠⢄⢴⢴⢠⢄⢠⢄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⠀
⣋⣉⠀⠘⠀⠃⠃⠓⠂⠀⠋⠃⠓⠃⠓⠃⠓⠂⠃⠙⠚⠀⠘⠀⠘⠒⢸⣿⣿⡟⠒⠸⠚⠘⠚⠙⠚⠀⠘⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⣉⡩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀
⠀⠠⡈⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣧⢸⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣸⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⢯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡯⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠴⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠾⣿⣿⣻⡿⢿⢟⣿⣿⣿⣿⣿⣷⢷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣏⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠸⣿⡙⠁⠐⠂⠻⣽⣿⣿⣿⡿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⠻⡏⠸⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠐⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⡟⢺⡻⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠷⠟⠁⠐⠃⠐⠀⠘⡇⢋⣾⣿⣿⣿⣿⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠇⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠃⠘⠗⢺⠋⠽⠭⠛⠛⠻⠛⠛⠛⠛⠛⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⠀⠀⠀⠔⠂⢐⠢⣾⣿⣿⣿⡿⣿⡏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⢿⣿⣿⣿⠒⣿⣿⣿⠉⠃⢨⡁⣀⡄⠀⠀⠀⠀⠻⠟⡏⢻⠉⠙⠁⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⡏⢹⠄⢟⠂⠉⠀⠉⠀⡱⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣩⣷⣌⠀⣹⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣈⡆⢘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣿⣿⣿⣿⣇⣄⣠⣄⣴⣄⣲⣠⣤⣤⣤⣀⣄⣠⣤⣴⣏⣾⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣄⣉⡭⠛⠛⢿⠏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠐⢲⠒⡦⡀⡠⡀⠀⣆⡄⡠⡀⡠⡏⡩⡁⡆⣆⢄⠀⢰⢲⢀⢄⢸⣿⣿⣇⢄⢠⢄⢤⢴⢠⢌⢀⢄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⠀
⣻⣉⠀⠘⠀⠃⠃⠛⠃⠀⠋⠃⠛⠃⠓⠃⠛⠃⠃⠛⠛⠀⠘⠀⠘⠛⢸⣿⣿⡟⠛⠸⠚⠘⠚⠑⠚⠀⠘⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⣉⣩⢩⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠀
⠀⠠⠠⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣷⣸⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡧⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠻⣿⣿⣻⡿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣾⣇⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡂⠸⣿⡝⠀⠀⠘⠻⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠿⠏⠸⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⢑⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⣟⢺⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠁⠘⠂⠘⠀⠘⡇⢟⣾⣿⣻⡿⣿⣆⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠋⠹⠟⠻⢏⣽⠭⠟⠛⠻⠛⠛⠛⠛⠛⢛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠀⠀⠀⠔⠂⠐⠒⣿⣿⣿⢿⡟⢿⡏⢳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢈⠉⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⣿⡿⠺⣿⣿⣿⠉⠃⢨⡁⢀⡆⠀⠀⠀⠀⠻⠿⡟⢛⠁⠙⠃⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡏⢹⠎⢟⠃⠉⠀⠉⠀⡹⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣙⣷⣆⠀⣸⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣉⡂⢘⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣯⣿⣿⣿⣿⣇⣄⣠⣄⣤⣄⣱⣠⣤⣤⣤⣀⣄⣠⣤⣼⣗⣼⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡙⠟⠻⢿⡏⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠁⢠⠀⣆⡀⣀⡀⠀⣄⠀⣀⡉⣀⡏⣉⡉⡆⣆⣀⠀⢠⢠⢀⣀⢸⣿⣿⣇⣁⢈⣉⣩⣙⢉⣉⢉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⣱⠀
⣻⣉⠀⠘⠀⠃⠃⠋⠃⠀⠋⠂⠋⠃⠃⠃⠋⠃⠃⠛⠙⠀⠘⠁⠘⠙⢸⣿⣿⡟⠙⢸⠚⠘⠘⠑⠚⠀⠘⢸⣿⣿⣿⣿⡏⢉⣍⣭⣩⣭⣭⣉⣩⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⠀
⠀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⣸⣿⣿⣿⣷⣀⢺⣿⣿⣷⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣿⣿⣿⣇⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠭⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡯⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠖⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠿⣿⣿⣾⡿⠿⢽⣿⣿⣿⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣇⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⡟⠁⠐⠛⠻⠽⣿⣿⣿⡿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⡟⠿⠟⠘⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢋⠑⡟⠀⠀⠀⠀⠀⠀⣻⣿⣿⡗⡟⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠋⠐⠃⠐⠀⠘⡇⢟⣾⣿⣻⣿⣿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠋⠙⡟⠺⢋⡹⠍⠛⠛⠛⠙⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⠀⠔⠂⢐⠂⣿⣿⣿⢻⡟⢻⡏⣳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⢸⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⡧⢻⣿⣿⣿⡿⠲⣿⣿⣿⠙⡃⢨⡁⣀⡄⠀⠀⠀⠀⠻⠿⡯⢋⠁⠐⠅⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⢈⡏⢹⠂⢏⠂⠁⠀⠉⠁⡁⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣙⣵⣄⠀⣹⣿⣿⡇⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣗⣄⣠⣄⣴⣄⣰⣡⣤⣤⣤⣀⣄⣠⣤⣴⣟⣼⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣄⣉⡩⠛⠻⢿⠏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠩⢭⠍⣍⡁⣀⡀⠀⣅⠌⣈⡉⣉⡍⣉⡉⡌⣍⣉⠁⢡⢬⢉⣉⢹⣿⣿⣏⣉⢉⣉⣩⣩⢉⣉⢉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣭⠀
⣋⣉⠀⠸⠀⠇⠇⠫⠃⠀⠏⠇⠫⠇⠣⠇⠫⠅⠇⠛⠽⠀⠸⠉⠘⠍⠸⣿⣿⡟⠝⢸⠜⠸⠼⠹⠜⠘⠸⢸⣿⣿⣿⣿⡏⢉⢍⣭⣭⣭⣭⣉⣭⣭⣽⣹⣿⣿⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀
⠀⠠⡢⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣦⣰⣶⣶⣶⣶⣀⣺⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢘⣾⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣿⣿⣯⢽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠔⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠿⣿⣿⣾⡿⠿⢽⣿⣿⣿⣿⣿⡷⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠸⣿⡟⠀⠀⠚⠻⢽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠿⠏⠹⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⢑⡝⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⣟⢺⡻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠊⠐⠃⠘⠀⠘⡇⢛⣾⣿⣻⡿⣿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠀⠀⠀⠀⠐⠀⢹⣿⣿⡇⠋⠙⠟⠺⠯⣽⠭⠛⠛⠻⠛⠛⠛⠛⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠨⠀⠀⠀⠔⠂⢐⠒⣿⣿⣿⢿⡿⢻⠏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢺⣿⣿⣿⣿⠚⣿⣟⣿⠙⠓⢸⡁⢀⡆⠀⠀⠀⠀⠻⠛⡿⢛⠃⠙⠁⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠀⠀⢘⡏⢹⠆⢻⠂⠉⠀⠉⠐⡣⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣌⠀⣼⣿⣿⡇⡀⢀⡀⢀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡁⢈⡂⢈⣀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣼⣿⣿⣿⣿⣿⣇⣄⣠⣄⣴⣄⣰⣠⣤⣤⣤⣀⣄⣠⣤⣼⣇⣴⣦⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡉⠛⠻⢿⠏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⠩⢭⠭⣍⡁⣀⠁⠀⣅⡌⣉⡉⣉⡍⢉⡉⡍⣍⣉⠁⢡⢤⢈⣉⢹⣿⣿⣏⣉⢉⡉⣩⣩⢉⡉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣹⠀
⣋⣩⠀⠸⠀⠇⠇⠯⠅⠀⠟⠇⠮⠇⠧⠇⠯⠅⠇⠵⠽⠀⠸⠉⠸⠭⢸⣿⣿⡿⠭⢸⠼⠸⠼⠺⠼⠸⠸⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡉⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⠀
⠀⠠⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⣶⡀⣶⣶⣶⣶⣄⢺⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣨⣿⣿⣟⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡯⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠖⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠺⣿⣿⣿⡿⠿⠽⣿⣿⣿⣿⣿⣿⢿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠘⣿⡟⠀⠐⠐⠻⢽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⠿⠏⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠐⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⣏⢻⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠷⠟⠂⠐⠃⠐⠀⠘⣏⢏⣾⣿⣿⣿⣿⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠋⠀⠀⠀⠀⠈⠀⢹⣿⣿⡇⠋⠙⠟⢻⢋⠽⠙⠟⠛⠛⠛⠛⠛⠛⠛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⣿⡿⢻⡏⣱⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢿⣿⣿⣟⣿⠺⣿⣟⣿⠉⡃⢸⡁⣀⡄⠀⠀⠀⠀⠻⠻⡯⢛⠃⠙⠃⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢘⠏⢹⠊⢛⠂⠉⠀⠉⠀⡱⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣩⣳⣄⠀⣸⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡂⢘⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣾⣿⣿⣿⣇⣄⣠⣄⣴⣄⣰⣠⣤⣤⣤⣀⣄⣠⣤⣼⣇⣴⣦⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡉⠛⠻⢿⠟⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠩⢭⠭⣍⠁⢀⠀⠀⡅⡀⢉⠉⢉⡍⢉⠉⡍⡍⡉⠉⢡⢬⠈⡉⢹⣿⣿⡏⡉⢉⡉⣩⣩⢉⡉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣹⠀
⣫⣉⠀⠸⠀⠇⠇⠷⠇⠀⠟⠆⠷⠇⠧⠇⠷⠇⠇⠹⠾⠀⠸⠉⠸⠾⢸⣿⣿⡿⠾⢸⠼⠸⠼⠺⠼⠸⠸⢸⣿⣿⣿⣿⡏⢉⢍⣭⣭⣭⣭⣉⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣰⣶⣶⣶⣶⡀⢲⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣾⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠿⣿⣿⣿⡿⠿⢟⣿⣿⣿⣿⣿⣯⣟⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣇⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠸⣿⡟⠀⠐⠐⠿⠹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⡟⠿⠟⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠑⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⡟⢺⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡃⠿⠛⠀⠘⠃⠐⠀⠘⡏⠛⣾⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠇⠀⠀⠀⠀⠀⠀⢺⣿⣿⡇⠋⠙⠟⠚⢫⠽⠑⠟⠛⠻⠛⠛⠛⠛⠛⠟⢹⣿⣿⢿⣿⣿⣿⣿⣿⣷⣏⠠⠀⠀⠀⠔⠂⢐⠂⣾⣿⣿⢿⡷⣻⡯⣳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⣿⣿⣿⣿⠺⣟⣛⣿⠁⠃⢨⡁⢀⡄⠀⠀⠀⠀⠻⠛⡏⢙⠋⠙⠁⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⠂⢿⠂⠉⠀⠉⠀⡁⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢉⣷⣄⠀⣸⣿⣿⡇⡀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡆⢘⢉⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣿⣿⣿⣇⣄⣠⣄⣴⣄⣤⣡⣤⣤⣤⣀⣄⣠⣤⣴⣏⣼⣦⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣅⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡭⣻⠞⣻⠈⡇⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠻⡟⢺⠀⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⣻⡿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣄⣉⡉⠛⠻⢿⡏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⠩⢭⠍⡍⠁⠀⠀⠀⡅⡀⠉⠉⠉⡝⠙⠉⡍⡍⠉⠁⢩⢌⠉⠉⠹⣿⣿⡏⠉⠉⠉⢉⠩⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣸⠀
⣙⢉⠀⠸⠀⠇⠇⠷⠇⠀⠟⠇⠷⠇⠧⠇⠷⠇⠇⠽⠾⠀⠸⠊⠸⠾⠸⣿⣿⡿⠾⢸⠼⠸⠼⠪⠽⠨⠹⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡉⣭⣩⣭⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⠀
⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣦⢰⣶⣶⣦⣶⡀⣸⣿⣿⣷⣶⣾⣶⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢘⣼⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡫⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⣿⡯⢿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⣿⣷⣺⡿⢿⢟⣿⣿⣿⣿⣿⣗⣷⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣾⣇⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⣿⡟⠀⠘⠊⠻⢻⣿⣿⣿⡯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡟⠿⠋⠸⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠊⢐⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠝⠺⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡃⠗⠛⠁⠐⠁⠈⠀⠘⡇⢇⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠊⠐⠉⠺⠋⠙⠭⠛⠛⠛⠙⠛⠛⠛⠛⠛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣏⠠⠀⠀⠀⠔⠂⠐⠒⣾⣿⣿⢻⣟⣻⡏⢱⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢺⢿⣿⣟⡿⠨⣿⣿⣿⠁⡃⢀⡁⠀⡀⠀⠀⠀⠀⠻⠛⡏⢉⠉⠙⠃⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⢹⠀⢻⠀⠈⠀⠈⠀⡡⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡙⣧⢄⠀⣸⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣮⣿⣿⣿⣇⣄⣠⣀⣀⣄⣠⣦⣤⣤⣠⣀⣄⣠⣤⣔⣇⣸⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣧⢤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣄⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠥⣻⠞⢱⠀⡂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣍⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⣿⢿⣻⠿⡗⢺⡫⠛⡗⢺⠀⡍⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⠏⠹⠟⢻⠻⠿⠫⢿⠟⡿⢻⢟⠻⡟⢿⡿⡽⡏⢿⠟⡿⢙⠯⠻⡟⠻⠏⠹⣿⢻⢾⡟⡟⣾⣶⣷⣶⢗⡖⠃⠚⠂⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣩⡩⠛⠛⢿⠏⢁⣠⣨⣭⣤⣥⣼⣌⣽⣥⣼⣤⣭⣭⣬⣤⣥⣬⣭⣭⣥⣼⣄⣭⣭⣼⠀⠕⠈⢋⠐⡃⢘⠛⠚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⢛⣛⡛⡟⠃⠀⠀⠀⡁⡀⠘⠛⠛⡟⠛⠛⡝⡛⠛⠛⢛⣀⠛⠃⢻⣿⣿⡟⠛⠛⠛⢛⢻⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠀
⣋⣩⠀⢸⠀⡏⡇⢟⠇⠀⡟⡅⢟⡇⢏⡇⢟⠇⡇⠹⣻⠀⢸⠚⠸⡻⢸⣿⣿⡿⡻⢸⡹⢹⣹⢺⡹⠸⢹⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⣉⣯⣭⣭⢹⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣜⠀
⠀⠀⡠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣦⣴⣤⣶⣄⣸⣿⣿⣧⣤⣬⣤⣴⣤⣴⣦⣴⣤⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣼⣿⣿⣷⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢴⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⢽⢾⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠺⣿⣿⣿⡿⢿⡟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠘⣿⡿⠃⠘⠂⠻⢽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢟⠿⠟⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠙⡝⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⡟⢻⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠷⠛⠃⠐⠂⠐⠀⠘⣏⠟⣼⣿⣿⣿⣿⣆⠀⠁⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠏⠀⠀⠀⠀⠐⠀⢹⣿⣿⡇⠋⠙⠟⢺⢋⠹⠍⠛⠛⠻⠛⠛⠛⠛⠛⠟⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⡏⠠⠀⠀⠀⠔⠂⢐⠂⣾⣿⣿⢿⡗⢻⡏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⢀⡇⢺⣿⣿⣿⡿⠲⣿⣿⣿⠓⡃⢸⡁⣀⡄⠀⠀⠀⠀⠻⠻⡿⢛⠇⠙⠃⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢆⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢈⡏⢹⠌⢟⠂⠉⠀⠉⠀⡡⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⣩⣷⣄⠀⣼⣿⣿⡇⡁⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⢈⡄⢘⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣷⣿⣿⣿⣇⣄⣠⣄⣴⣄⣰⣧⣤⣤⣤⣀⣄⣠⣤⣴⣏⣼⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣅⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡭⣻⠞⣻⠈⡇⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠻⡟⢺⠀⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣥⣤⣩⡩⠛⠻⢿⡟⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⢛⣛⣛⡛⠋⠀⠂⠀⡁⡊⠙⠛⠛⡛⠛⠋⡘⡛⠛⠓⢃⣘⠛⠈⢻⣿⣿⡟⠛⠛⠛⢛⢛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣱⠀
⣫⢉⠀⢸⠀⡏⡇⣟⡂⠀⡟⡅⣝⡇⣏⡇⣟⡃⡇⣯⣻⠀⢸⠚⢸⣛⢸⣿⣿⣿⣛⢸⣹⢹⣹⢸⡱⠘⢱⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡉⠩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠀
⠀⠠⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣠⣤⣤⣤⣤⡄⢰⣿⣿⣧⣤⣬⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢘⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢸⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡲⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠾⣿⣿⣻⡏⢿⢿⣿⣿⣿⣿⣿⣷⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⣿⡝⠁⠐⠀⠻⢽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⠿⠏⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⡟⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠷⠟⠊⠘⠃⠘⠀⠘⡇⢓⣾⣿⣻⣿⣿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠇⠀⠀⠀⠀⠈⠀⢹⣿⣿⡇⠋⠙⠗⠺⠋⠹⠭⠛⠛⠻⠛⠛⠛⠛⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⢿⡿⣿⡏⣳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠁⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢻⣿⣿⣿⡿⠲⣿⣿⣿⠉⠓⢨⡁⣀⡆⠀⠀⠀⠀⠻⠛⡏⢛⠃⠙⠁⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢨⡏⢹⠄⢟⠂⠉⠀⠉⠐⡹⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢩⡧⣄⠀⣹⣿⣿⡇⡁⢈⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡆⢈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣶⣿⣿⣿⣇⣄⣠⣄⣴⣄⣰⣦⣦⣤⣴⣀⣄⣠⣤⣴⣯⣼⣷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣥⣤⣉⡉⠛⠻⠿⠏⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢛⣛⣛⡛⠃⠀⠂⠀⡁⠈⠘⠛⠛⡛⠛⠙⡛⡛⠛⠛⢋⣘⠛⠙⢻⣿⣿⡟⠛⠛⠛⢛⢛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⠀
⣋⣉⠀⢸⠀⡏⡆⣏⡂⠀⡷⡄⣌⡇⣎⡇⣎⡃⡇⣿⣽⠀⢸⠚⢸⣑⢸⣿⣿⣿⣑⢸⣱⢹⣹⢼⣱⠸⢱⢸⣿⣿⣿⣿⡏⢉⢍⣭⣭⣭⣭⡉⣭⢩⣭⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⠀
⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣠⣤⣤⣤⣤⡀⣼⣿⣿⣧⣤⣬⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢘⣾⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠾⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣷⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣏⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡒⠸⣿⡟⠁⠐⠘⠻⢽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⡟⠿⠏⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢰⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⡟⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠃⠐⠃⠘⠀⠘⡏⢏⣾⣿⣿⣿⣿⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠇⠀⠀⠀⠀⠈⠀⢺⣿⣿⡇⠋⠙⠟⢺⠯⡽⠭⠟⠛⠻⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⢿⡿⢻⡟⣳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⢾⣿⣿⣟⡿⠻⣿⣛⡿⠉⡃⢀⡁⢀⡆⠀⠀⠀⠀⠻⠛⡟⢛⠃⠙⠁⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⣄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⡏⢹⡊⢿⠂⠉⠀⠉⠀⡡⠀⠀⠀⠁⠈⠃⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣹⣷⣄⠀⣼⣿⣿⡇⡁⢀⡀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⡁⣈⡄⢘⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣇⣄⣠⣄⣴⣄⣰⣥⣤⣤⣤⣀⣄⣠⣤⣼⣏⣼⣦⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣥⣤⣉⡉⠛⠻⢿⠏⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⢛⣛⣛⡛⠃⠀⠀⠀⡁⠊⠙⠛⠛⡛⠛⠋⡛⡛⠻⠓⢃⣙⠙⠙⢻⣿⣿⡟⠟⠻⠟⠻⢟⠻⠛⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣱⠀
⣋⢋⠀⢸⠀⡏⡆⣮⡆⠀⡷⡇⣮⡆⣎⡇⣮⡆⡇⣷⣵⠀⢸⠘⢰⣵⢸⣿⣿⣷⣵⢰⣱⢹⣹⢼⣳⠐⢱⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡉⣭⣭⣭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀
⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣤⣄⢠⣤⣤⣤⣤⣀⢼⣿⣿⣧⣤⣼⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡭⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠿⣿⣿⣻⡿⠿⢟⣿⣿⣿⣿⣿⣧⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠸⣿⡟⠁⠐⠊⠻⢽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡟⠿⠏⠸⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠑⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣟⢺⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡃⠿⠟⠀⠘⠃⠘⠀⠘⡟⢳⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠋⠙⠟⢻⢋⠽⡏⠛⠛⠻⠙⠛⠛⠛⠛⠏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⠀⠀⠀⠔⠂⠘⠢⣿⣿⣿⣿⡟⢻⡏⣱⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢹⣿⣿⡇⠀⢈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⢿⣿⣿⣿⣿⠚⣿⣿⣿⠙⠃⢨⡁⣐⡄⠀⠀⠀⠀⠻⠻⡏⣋⠉⠙⠁⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⣀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢈⡏⢹⡈⢿⠂⠁⠀⠉⠐⡳⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠀⣩⣥⣄⠀⣹⣿⣿⡇⡁⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣉⡅⢘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣿⣿⣿⣿⣇⣄⣠⣄⣴⣄⣤⣦⣦⣤⣤⣀⣄⣠⣤⣼⣗⣸⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣩⡹⠛⠻⢿⠏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠟⠿⡛⠁⠀⠂⠀⠁⠊⠘⠛⠛⡛⠛⠙⡽⠿⠿⠗⠃⠙⠚⠙⢿⣿⣿⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣫⠀
⣫⣉⠀⢸⠀⡗⡆⡶⡆⠀⡷⡃⡶⡆⡖⡇⡶⡆⡇⣷⢶⠀⢸⠼⢰⢶⢸⣿⣿⣷⢶⢰⢲⢺⢲⢔⣲⠰⢲⢸⣿⣿⣿⣿⡏⢉⢉⣭⣭⣭⣭⣉⣭⣭⣭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⠀
⠀⠠⡀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣠⣬⣤⣤⡀⣸⣿⣿⣇⣅⣸⣁⣄⣍⣠⣠⣄⣬⣼⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⣯⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠔⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠿⣿⣿⣾⡿⢿⡟⣿⣿⣿⣿⣿⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠆⠸⣿⡿⠁⠐⠛⢻⢽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡟⠿⠛⠹⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠊⠐⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⣟⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠿⠛⠋⠐⠂⠐⠀⠘⡗⢻⣾⣿⢿⣿⣷⡄⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠛⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠋⠹⠗⠺⠫⡽⠭⠛⠛⠻⠙⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠠⠀⠀⠀⠔⠂⢘⠲⣾⣿⣿⢿⡿⣻⡏⣰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⢺⣿⣿⣿⡿⠒⣿⣟⣿⠉⡃⢨⡁⢀⡆⠀⠀⠀⠀⠻⠛⡯⢛⠉⠙⠓⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢹⠀⢿⠂⠁⠀⠉⠀⡡⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⣉⣳⣆⠀⣹⣿⣿⡇⡁⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⡀⢘⠉⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣇⣄⣠⣄⣴⣄⣴⣧⣤⣤⣤⣀⣄⣠⣤⣴⣟⣸⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣩⡩⠛⠻⢿⠟⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢿⠿⠿⠿⠿⠃⠀⠂⠀⠁⠀⠘⠻⠛⠛⠛⠛⠼⠿⠿⠷⠷⠸⠽⠈⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⠀
⣫⣉⠈⢹⠉⡗⡆⡶⠆⠀⡷⡇⡲⡆⡖⡇⡶⠆⡇⣑⢶⠀⢸⠽⢰⠶⢸⣿⣿⣷⠶⢰⢲⢺⢺⣴⢲⠰⢲⢸⣿⣿⣿⣿⡏⢉⢍⣭⣭⣭⣭⣍⣭⣯⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⠀
⠀⠀⡀⠈⡀⠁⠁⠉⠁⠀⠁⠁⠉⠁⠉⠁⠈⣁⣁⣉⣉⣀⣈⣀⣈⡉⣸⣿⣿⣏⣉⣘⣁⣈⣉⣈⣁⣀⣈⣸⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⠀
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣽⣿⣿⣷⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⢽⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠔⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠸⣿⣿⣿⡿⢿⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠘⣿⡿⠁⠘⠂⠻⢽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣟⠿⠟⠘⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠳⣟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⡟⢻⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠊⠘⠃⠐⠀⠘⡏⢛⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠋⠙⠛⠻⠋⡹⠭⠛⠛⠻⠙⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⣻⡟⢿⡟⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⢿⣿⣿⣟⣿⠲⣿⣟⣿⠙⡃⢨⡁⢀⡆⠀⠀⠀⠀⠻⠿⡏⢛⠃⠙⠁⠘⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⢂⠀⠀⠀⢸⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⢹⠍⢿⠂⠉⠀⠉⠀⡩⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⣩⣳⣆⠀⣼⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣁⣈⡅⢘⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣾⣿⣿⣿⣇⣄⣠⣄⣴⣄⣥⣦⣦⣤⣤⣀⣄⣠⣤⣼⣟⣰⣧⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡩⠛⠻⢿⠏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⠿⠿⠿⠿⠋⠀⠂⠀⠁⠀⠙⠛⠛⠛⠛⠋⠯⠿⠿⠿⠇⠸⠽⠟⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣡⠀
⡙⢩⠈⢹⠉⡗⡆⡶⠄⠀⣷⡅⡲⡆⡖⡇⡴⠆⡇⣗⢶⠀⢸⠽⢰⠶⢸⣿⣿⣷⠶⢰⢢⢺⢺⣴⢢⠰⢢⢸⣿⣿⣿⣿⡏⢉⣉⣭⣭⣭⣭⡍⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⠀
⠀⠀⠀⠈⡀⠁⠁⠉⠁⠀⠁⠁⠉⠁⠉⠁⠉⣁⣁⣈⣉⣀⣈⣀⣈⡉⣸⣿⣿⣏⣉⣘⣉⣈⣉⣈⣉⣀⣈⣸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣾⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢰⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣯⢽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣷⣺⡿⠿⢿⣿⣿⣿⣿⣿⣗⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣾⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠸⣿⡟⠁⠀⠈⠹⢿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢿⣿⣿⡟⠟⠃⠙⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠐⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⡝⢾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⠟⠋⠀⠐⠀⠀⠀⠘⡏⢿⣾⣿⡿⣿⣿⡄⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠊⠙⠉⠚⠋⠙⠩⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠠⠀⠀⠀⠔⠂⢐⠂⣾⣿⣿⣿⡿⢿⡏⣳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡧⢻⣿⣿⣿⣿⠉⣿⣝⣿⠐⠇⢨⡁⢀⡂⠀⠀⠀⠀⠙⠛⡗⠉⠁⠑⠁⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠐⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢹⠈⢛⠂⠈⠀⠉⠀⡁⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠩⣳⢄⠀⣼⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣯⣼⣿⣿⣿⣏⣄⣠⣀⣀⣄⣤⣦⣤⣤⣠⣀⣄⣠⣠⣔⣆⣼⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣧⢤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣄⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠥⣻⠞⢱⠀⡂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣍⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⠿⡗⢺⡫⠛⡗⢺⠀⡍⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⠏⠹⠟⢻⠻⠿⠫⢿⠟⡿⢻⢟⠻⡟⢿⡿⡽⡏⢿⠟⡿⢙⠯⠻⡟⠻⠏⠹⣿⢻⢾⡟⡟⣾⣶⣷⣶⢗⡖⠃⠚⠂⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣩⡉⠛⠛⢿⠏⢁⣠⣨⣭⣤⣥⣼⣌⣽⣥⣼⣤⣭⣭⣬⣤⣥⣬⣭⣭⣥⣼⣄⣭⣭⣼⠀⠕⠈⢋⠐⡃⢘⠛⠚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⠿⠿⠁⠀⠂⠀⠁⠈⠊⠻⠛⠛⠛⠛⠻⠿⠿⠿⠯⠸⠿⠩⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣡⠀
⣋⣩⠈⢹⠁⡗⡄⣔⡄⠀⣧⡀⣔⡄⡔⡇⣔⡄⡇⣧⣢⠀⢸⠽⢠⣢⢸⣿⣿⣧⣢⢰⢢⢲⢺⣰⢢⠠⢢⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⣍⢩⣩⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀
⡀⠀⡀⠈⡀⠁⠁⠉⠁⠀⠁⠁⠉⠁⠉⠁⠉⣁⣁⣉⡉⣀⣈⣀⣈⡉⣸⣿⣿⣏⣉⣘⣉⣈⣉⣈⣉⣀⣈⣸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⣸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡷⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡯⢽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠺⣿⣿⣺⡿⢿⢟⣿⣿⣿⣿⣿⣷⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠸⣿⡟⠁⠀⠒⢻⢽⣿⣿⣿⡯⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡟⠿⠏⠙⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠐⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⡟⢺⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠛⠊⠘⠃⠐⠀⠘⡏⢓⣾⣿⣿⣿⣷⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢘⠃⠀⠀⠀⠀⠐⠀⢻⣿⣿⡇⠋⠙⠗⢺⠋⡽⠝⠟⠛⠻⠛⠛⠛⠛⠛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⠀⠀⠔⠂⢐⠃⣾⣿⣿⢿⡟⣻⡏⢳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢻⣿⣿⣿⣿⠺⣿⣿⣟⠙⡓⢈⡁⢀⡆⠀⠀⠀⠀⠻⠛⡏⢛⠉⠙⠃⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢹⡍⢟⠂⠁⠀⠉⠀⡩⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣩⣷⣄⠀⣺⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⣈⡁⢘⡁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣾⣿⣿⣿⣇⣄⣠⣄⣴⣄⣶⣦⣤⣤⣤⣀⣄⣠⣤⣶⣏⣼⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣩⡩⠛⠻⢿⡏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠿⠿⠿⠿⠃⠀⠂⠀⠁⠈⠘⠻⠛⠛⠻⠛⠽⠿⠿⡿⠷⠈⠿⠉⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⠀
⣫⣉⠈⢹⠁⡇⡄⣄⡄⠀⣧⠆⣄⡄⡄⡇⣄⡄⡇⣦⣠⠀⢸⡱⢠⣠⢸⣿⣿⣧⣤⢠⢤⢰⢨⡠⢤⠠⢤⢸⣿⣿⣿⣿⣏⢉⢍⣭⣭⣭⣭⣍⢩⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣋⠀
⠀⠀⠀⠈⠀⠁⠁⠁⠁⠀⠁⠁⠉⠁⠉⠁⠉⠁⠁⡉⠉⣀⣈⡀⣈⡉⢸⣿⣿⡏⣉⢸⣉⣈⣉⣈⡉⣈⣈⣸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢰⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⢹⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐⡂⠸⣿⡿⠃⠚⠒⢿⢽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⠟⠿⠋⠙⠿⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠐⡟⠁⠀⠀⠀⠀⠀⢿⣿⣿⡗⡟⢻⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠂⠐⠃⠐⠀⠘⡏⢟⣾⣿⢿⡿⣷⣄⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠇⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠋⠘⠷⠺⠋⠽⠍⠟⠛⠻⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠔⠂⢐⠃⣾⣿⣿⢿⡟⣻⡏⢱⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⣟⡿⠺⣿⣿⣿⠙⡃⢨⡁⢀⡆⠀⠀⠀⠀⠻⠛⡏⢛⠉⠙⠃⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠀⢀⠀⠀⠀⢸⣿⣿⡇⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⢹⠉⢿⠃⠉⠀⠉⠀⡡⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣩⣣⣌⠀⣼⣿⣿⡇⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢈⡃⢈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣇⣄⣠⣄⣴⣄⣦⣦⣤⣤⣤⣀⣄⣠⣤⣼⣗⣼⣦⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣩⡹⠛⠻⢿⡟⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣻⣿⣿⣿⠃⠀⠂⠀⠁⠈⠘⠻⠛⠛⠻⡋⢩⣿⣿⣿⣷⠈⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣹⠀
⣉⢩⠐⢲⠂⡦⡄⣤⡄⠀⣦⠀⣤⡄⡤⡆⣤⡄⡆⣦⣤⠀⢰⣲⢠⣤⢸⣿⣿⣧⣤⢠⢤⢴⢴⡠⢤⢠⢤⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡍⡩⣭⣭⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠀
⠀⠀⠀⠘⠀⠃⠃⠓⠂⠀⠃⠃⠓⠃⠑⠃⠑⠂⠃⠛⠚⠀⠘⠀⠘⠒⠸⣿⣿⡟⠒⠸⠊⠘⠚⠘⠊⠀⠘⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣾⣿⣿⣧⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠖⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠺⣿⣿⣻⡿⠿⠿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⡿⠁⠐⠐⢻⢻⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣼⡟⠿⠏⠙⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠑⡝⠁⠀⠀⠀⠀⠀⢿⣿⣿⡟⡟⢺⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⡿⠟⠂⠐⠁⠐⠀⠘⡏⠛⣾⣿⣻⣿⣿⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠇⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠋⠙⠗⢺⠏⢽⠝⠟⠛⠻⠛⠛⠛⠛⠛⡟⣹⣿⣿⢿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠔⠂⠐⠃⣾⣿⣿⢻⡿⣻⣟⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢾⣿⣿⣻⢿⠲⣿⣟⣿⠙⡓⢈⡁⣀⡆⠀⠀⠀⠀⠹⠻⡏⢋⠋⠙⠃⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠘⠀⢀⠀⠀⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢘⡟⢹⠈⢿⠃⠉⠀⠉⠀⡡⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣉⣳⡄⠀⣸⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣁⣈⡀⢘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣷⣿⣿⣿⣇⣄⣠⣄⣤⣄⣦⣦⣤⣤⣤⣀⣄⣠⣤⣶⣇⣼⣧⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣩⡩⠛⠻⢿⠟⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⠈⠘⠻⠛⠛⠛⡋⢽⣿⣿⣿⣯⠘⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⠀
⣫⢉⠐⢲⠒⡦⡄⣤⡄⠀⣦⠂⢤⡄⡤⡆⣤⡄⡆⡢⣤⠀⢰⣲⢠⣤⢸⣿⣿⣧⣤⢠⢄⢴⢴⣠⢄⢠⢄⢸⣿⣿⣿⣿⡏⢉⣉⣭⣭⣭⣭⡍⣩⢩⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀
⠀⠀⠀⠘⠀⠃⠃⠓⠂⠀⠃⠃⠓⠃⠓⠃⠓⠂⠃⠚⠚⠀⠘⠀⠘⠒⢸⣿⣿⡟⠒⠸⠚⠘⠚⠙⠚⠐⠘⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠥⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡯⢿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠻⣿⣿⣺⡿⣿⡿⣿⣿⣿⣿⣿⣷⣟⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡐⠸⣿⡿⠃⠘⠒⠻⢽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⠟⠿⠏⠹⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠑⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⡟⢻⢻⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠛⠂⠘⠃⠘⠀⠘⡏⢛⣾⣿⣿⣿⣿⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠋⠙⠟⢻⡫⡽⠝⠟⠛⠛⠋⠛⠛⠛⠛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠔⠂⢐⠃⣾⣿⣿⢿⡿⣿⡏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⢺⣿⣿⣿⡿⠚⣿⣿⣿⠛⠓⢨⡁⢀⡆⠀⠀⠀⠀⠹⠛⡿⢛⠃⠙⠃⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⡀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⢹⠍⢿⠂⠉⠀⠉⠀⡁⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⣹⣷⣄⠀⣺⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣈⡅⢘⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣿⣿⣿⣿⣇⣄⣠⣄⣴⣄⣶⣦⣤⣤⣤⣀⣄⣠⣤⣾⣇⣼⣦⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡩⠛⠻⢿⠏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠁⠊⠈⠛⠛⠛⠛⠛⢽⣿⣿⣿⣯⠈⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢞⣹⠀
⣻⣉⠐⢲⠒⡦⡀⡠⡀⠀⣆⠄⠠⡄⡠⡆⡠⡄⡆⡂⢤⠀⢰⣲⢀⢄⢰⣿⣿⣧⢄⢠⢄⢴⢴⢠⢄⢠⢄⢸⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡍⣩⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⠀
⠀⠠⠀⠘⠀⠃⠃⠓⠃⠀⠋⠃⠛⠃⠓⠃⠛⠃⠃⠛⠛⠀⠘⠀⠘⠛⢸⣿⣿⡟⠛⠸⠚⠘⠚⠙⠚⠐⠘⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣾⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⡼⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡯⢹⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠺⣿⣿⣿⣿⢿⣝⣿⣿⣿⣿⣿⣷⢗⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣇⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠸⣿⡽⠁⠚⠊⢻⢽⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠿⠇⠘⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠊⢐⡟⠁⠀⠀⠀⠀⠀⢻⣿⣿⡟⡟⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠛⠉⠐⠂⠐⠀⠘⣏⢟⣾⣿⣿⡿⣿⣄⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠋⠹⠛⢻⠫⡽⠉⠛⠛⠻⠙⠛⠛⠛⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⢻⡗⣻⡟⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⣿⣯⣿⠺⣿⣟⣿⠙⡃⢨⡁⣀⡆⠀⠀⠀⠀⠹⠛⡏⢛⠋⠙⠁⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢆⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢨⡇⢹⠌⢻⠂⠁⠀⠉⠀⡁⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣉⣷⣄⠀⣸⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣈⡅⢘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣿⣿⣿⣿⣇⣄⣠⣄⣤⣄⣽⣷⣤⣤⣤⣀⣄⣠⣤⣾⣎⣼⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣥⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠞⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡩⠛⠻⢿⠏⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣯⣿⣿⣿⣿⡿⠁⠀⠀⠀⠁⠀⠛⠛⠛⠛⠛⠛⢹⣿⣿⣿⣿⠀⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠀
⢹⢉⠐⢲⠂⡦⡀⡠⡀⠀⣆⠀⡠⡀⡠⡆⡠⡀⡆⣀⢄⠀⢰⢲⢀⢄⢸⣿⣿⣇⢄⢀⢄⢠⢴⢀⣄⢀⣌⢸⣿⣿⣿⣿⡏⢉⢍⣭⣭⣭⣭⡍⣩⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠀
⠀⠀⠀⠘⠀⠃⠃⠛⠃⠀⠋⠃⠛⠃⠓⠃⠛⠃⠃⠛⠛⠀⠘⠁⠘⠛⢘⣿⣿⡟⠛⢸⠚⠘⠚⠑⠚⠐⠘⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣿⣿⣷⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡥⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⢹⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠸⣿⣷⣾⡿⠿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣇⢹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⣿⡿⠁⠈⠚⠙⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡟⠟⠃⠸⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢐⡝⠁⠀⠀⠀⠀⠀⢻⣿⣿⡗⣝⢺⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡃⠟⠋⠁⠐⠀⠈⠀⠘⣏⠏⣾⣿⡻⡿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢺⣿⣿⡇⠊⠙⠁⠚⠋⠙⠉⠛⠛⠛⠋⠛⠛⠛⠛⡛⢽⣿⣿⢿⣿⣿⣿⣿⣿⣿⡏⠠⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⢻⡿⢻⡏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢾⢿⣿⣿⣿⠩⣿⣟⣿⠑⡗⢨⡁⢀⡀⠀⠀⠀⠀⠻⠛⡏⢹⠋⠑⠁⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢩⠈⢿⠂⠈⠀⠉⠀⡁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡩⡷⢄⠀⣸⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⢘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣧⣾⣿⣿⣿⣇⣄⣠⣀⣀⣄⣤⣀⣤⣄⣤⣀⣄⣠⣀⣰⣧⣼⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣧⢤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣄⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠥⣻⠚⢱⠀⡂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣍⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⣿⢿⣻⠿⡗⢺⡫⠛⡗⢺⠀⡍⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⠏⠹⠟⢻⠻⠿⠫⢿⠟⡿⢻⢟⠻⡟⢿⡿⡽⡏⢿⠟⡿⢙⠯⠻⡟⠻⠏⠹⣿⢻⢾⡟⡟⣾⣶⣷⣶⢗⡖⠃⠚⠂⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡍⠛⠻⠿⠏⢁⣠⣨⣭⣤⣥⣼⣌⣽⣥⣼⣤⣭⣭⣬⣤⣥⣬⣭⣭⣥⣼⣄⣭⣭⣼⠀⠕⠈⢋⠐⡃⢘⠛⠚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⠀⠘⠻⠛⠛⠻⡋⢽⣿⣿⣷⣟⠈⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⠀
⣻⣉⠩⢭⠅⣌⡀⣀⡀⠀⣄⠄⣀⡀⣀⡄⣀⡈⡍⣍⣉⠉⢩⢥⢈⣁⢹⣿⣿⣏⣉⢉⣉⣩⣩⢉⣉⢉⣉⢹⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡍⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀
⠀⠀⠀⠸⠀⠇⠇⠫⠁⠀⠏⠇⠫⠇⠣⠇⠫⠅⠇⠛⠽⠀⠸⠉⠘⠭⢸⣿⣿⡟⠽⢸⠜⠸⠼⠻⠜⠘⠸⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣴⣶⣶⣶⢶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣨⣿⣿⣟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⣽⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠾⣿⣿⣻⡿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣇⢹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠸⣿⡿⠃⠐⠒⠻⠹⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⠿⠏⠹⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠑⡟⠁⠀⠀⠀⠀⠀⢻⣿⣿⡗⡗⢺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠛⠃⠘⠃⠐⠀⠘⣏⠏⣾⣿⣿⣿⣿⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠋⠙⠗⢻⢋⠹⠏⠛⠛⠛⠙⠛⠛⠛⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⣿⡗⢻⣏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⢈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢾⣿⣿⣿⡿⠚⣿⣿⣿⠋⡃⢨⡁⣀⡄⠀⠀⠀⠀⠻⠛⡏⢛⠋⠙⠃⠘⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⡏⢹⡈⢿⠂⠉⠀⠉⠀⡁⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣉⣱⣄⠀⣸⣿⣿⡇⡀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⣈⡀⢘⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣇⣄⣠⣀⣴⣄⣴⣁⣤⣤⣤⣀⣄⣠⣤⣴⣟⣾⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣡⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠚⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣥⣤⣩⡩⠛⠻⢿⠏⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠁⠈⠂⠀⠁⠈⠘⠻⠛⠛⠛⡻⢽⣿⣿⣿⣿⠈⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⠀
⢋⣉⠩⢭⠥⣌⡀⣀⡀⠀⣄⡀⣀⡀⣀⡄⣀⡁⡍⣍⣉⠉⢩⢥⢉⣁⢹⣿⣿⣏⣉⢉⣉⣩⣩⢉⣉⢉⡉⢹⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡍⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣜⠀
⠀⠀⠀⠸⠀⠇⠇⠯⠅⠀⠏⠇⠮⠇⠧⠇⠫⠅⠇⠷⠽⠀⠸⠉⠸⠭⢸⣿⣿⡿⠭⢸⠼⠸⠼⠹⠜⠘⠸⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣶⣶⣶⣶⢶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣨⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢿⣿⣿⢽⣼⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⣿⣿⣻⡿⢿⢿⣿⣿⣿⣿⣿⣿⣷⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣇⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠸⣿⡿⠁⠐⠚⠻⢽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⠿⠏⠸⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢘⡝⠁⠀⠀⠀⠀⠀⢻⣿⣿⡇⡟⢻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠙⠂⠐⠀⠐⠀⠘⣏⠟⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠋⠙⠟⠻⠛⠹⠍⠛⠛⠻⠛⠛⠛⠛⠛⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠔⠂⢐⠓⣾⣿⣿⢻⡟⣻⣏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢈⠉⠙⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢻⣿⣿⣿⡿⠚⣿⣿⣿⠛⡃⢸⡁⢀⡄⠀⠀⠀⠀⠻⠛⡋⠛⠋⠉⠁⠘⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢈⡏⢹⠉⢿⠂⠉⠀⠉⠀⡁⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣙⣱⣄⠀⣽⣿⣿⡇⡀⢀⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⣁⡄⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣿⣷⣿⣿⣿⣇⣄⣠⣀⣴⣄⣵⣀⣤⣤⣤⣀⣄⣠⣤⣼⣇⣾⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣡⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠚⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣥⣤⣩⡩⠛⠻⠿⡏⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⠀⠘⠛⠛⠛⠻⡛⢻⣿⣿⣷⣧⠀⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⠀
⣩⣉⠩⢭⠥⣄⠀⣀⠀⠀⣄⠀⢀⡀⣀⡄⢀⡈⡍⣍⣉⠉⢩⢥⢉⣉⢹⣿⣿⣏⡉⢉⡉⣩⣩⢉⡉⢉⡉⢹⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⣍⣭⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀
⠀⠠⠀⠸⠀⠇⠇⠧⠅⠀⠟⠇⠦⠇⠧⠇⠯⠅⠇⠷⠽⠀⠸⠉⠸⠬⢸⣿⣿⡿⠭⢸⠼⠸⠼⠻⠼⠘⠸⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⣿⣯⢽⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠺⣿⣿⣿⡟⣿⠿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠆⠘⣿⡽⠃⠘⠘⠻⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⠿⠏⠸⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠙⣟⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⡗⢺⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠛⠂⠐⠃⠐⠀⠘⣏⠟⣾⣿⣿⣿⣿⣄⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠀⠀⠀⠀⠈⠀⢸⣿⣿⡇⠋⠙⠟⢺⢋⡽⠍⠟⠛⠻⠙⠛⠛⠛⠛⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⢿⡷⢿⡏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⢀⡇⢺⣿⣿⣿⡿⠖⣿⣿⣿⠙⡇⢈⡁⢀⡄⠀⠀⠀⠀⠻⠛⡏⢙⠏⠑⠃⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢺⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠏⢹⠆⢿⠂⠁⠀⠉⠀⡡⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣩⣷⣄⠀⣸⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣈⡂⢈⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣿⣿⣿⣿⣇⣄⣠⣀⣴⣄⣶⣄⣤⣤⣤⣀⣄⣠⣤⣴⣇⣼⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣡⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠚⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣥⣤⣉⡹⠛⠛⢿⠏⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠀⠃⠀⠁⠊⠘⠻⠛⢛⠛⡛⣽⣿⣿⣷⣧⠘⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠀
⣋⣩⠩⢭⠅⣄⠀⢀⠀⠀⡄⡀⢀⠀⢀⡅⢀⠉⡍⡍⡉⠉⢩⢥⠉⡁⢹⣿⣿⡏⡉⢉⡉⣉⣩⢉⡉⠉⡉⢹⣿⣿⣿⣿⡏⢉⢍⣭⣭⣭⣭⣍⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀
⠀⠀⠀⠸⠀⠇⠇⠷⠇⠀⠟⠆⠷⠇⠧⠇⠷⠇⠇⠿⠾⠀⠸⠉⠸⠾⢸⣿⣿⡿⠾⢸⠼⠸⠼⠺⠼⠘⠸⢸⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣯⢽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠾⣿⣿⣿⡿⠿⢟⣿⣿⣿⣿⣿⣿⣟⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠸⣿⡝⠁⠘⠊⠻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⡟⠿⠏⠸⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢊⢹⣟⠀⠀⠀⠀⠀⠀⢿⣿⣿⡗⡟⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠟⠁⠐⠃⠘⠀⠘⣏⠟⣾⣿⣿⣿⣿⣄⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠍⠀⠀⠀⠀⠀⠀⢺⣿⣿⡇⠃⠸⠟⢺⠋⣽⠉⠛⠛⠻⠛⠛⠛⠛⠛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠔⠂⢐⠂⣾⣿⣿⢻⡿⢿⡏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢻⣿⣿⣿⡿⠒⣿⣟⣿⠋⡃⢈⡁⢀⡄⠀⠀⠀⠀⠻⠛⡏⢛⠋⠙⠁⠈⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⢄⠀⠀⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⢹⡂⢽⠃⠁⠀⠉⠀⡱⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⣙⣳⣄⠀⣸⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⣈⡂⢈⡀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣷⣿⣿⣿⣿⣇⣄⣠⣀⣴⣄⣶⣄⣤⣤⣤⣀⣄⣠⣤⣴⣏⣼⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠚⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⡯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣥⣤⣉⡹⠛⠛⢿⠟⢉⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠂⠀⠁⠈⠈⠛⠛⠛⠻⠛⢻⣿⣿⣿⣟⠈⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⣻⠀
⣫⣉⢛⣛⡓⡈⠀⠀⠀⠀⡀⡀⠀⠀⠀⡁⠀⠈⡏⡙⠛⠛⢛⣃⠙⠛⠻⣿⣿⡟⠛⠛⠛⢛⢻⠛⠛⠛⠛⢻⣿⣿⣿⣿⡏⢉⢍⣭⣭⣭⣭⣭⡩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⠀
⠀⠠⠀⢸⠀⡏⡇⢟⠇⠀⡟⡅⢟⡇⢏⡇⢟⡃⡇⠿⣻⠀⢸⠚⠸⡻⢸⣿⣿⡿⡻⢸⡹⢹⣹⢺⡹⠘⢹⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⣤⣤⢤⣤⣤⣤⣤⣼⣿⣿⣧⣤⣬⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢿⣿⣯⢽⢾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠸⣿⣿⣾⣿⢿⠿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠸⣿⡿⠃⠘⠒⢻⢿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡟⠿⠏⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠙⡏⠁⠀⠀⠀⠀⠀⢿⣿⣿⡗⡗⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠛⠀⠘⠂⠘⠀⠘⣏⠟⣼⣿⣿⣿⣿⣆⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠋⠙⠓⠺⢛⠽⠝⠛⠛⠻⠙⠛⠛⠛⠛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⠀⠀⠀⠔⠂⢐⠒⣾⣿⣟⢻⡷⢿⡏⣹⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⢈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⢻⣿⣿⣯⣿⠺⣿⣟⣿⠉⡇⢨⡁⢀⡄⠀⠀⠀⠀⠹⠛⡿⢛⡏⠙⠁⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢄⠀⠀⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢹⠄⢿⠃⠁⠀⠉⠐⠡⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡈⣹⣷⣄⠀⣼⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡆⢘⡈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣶⣿⣿⣿⣇⣄⣠⣀⣴⣄⣶⣆⣤⣤⣤⣀⣄⣠⣤⣼⣇⣼⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠚⣻⠈⡗⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⠯⠿⡟⢺⠈⡟⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡭⠛⠛⢿⠯⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣭⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢘⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠁⠀⠘⠛⠛⠛⠻⠛⠻⣿⣿⣿⣷⠂⣷⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⠀
⣡⢈⢛⣚⡓⡈⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⡓⡙⠛⠛⢛⣓⠘⠓⠻⣿⣿⡟⠛⠛⠛⢛⢛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡍⣭⢩⣭⢹⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣜⠀
⠀⠀⠀⢸⠀⡏⡇⣟⡃⠀⡟⡇⣟⡇⣏⡇⢟⡃⡇⢿⣻⠀⢸⠚⢸⣛⢸⣿⣿⣿⣛⢸⡹⢹⣹⢾⡹⠘⢹⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣺⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⢠⣤⣤⣤⣤⣼⣿⣿⣧⣤⣬⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⢽⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠨⢿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣗⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⣇⢺⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣿⡿⠁⠈⠊⠹⠽⣿⣿⣿⡯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⠟⠃⠘⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢐⡞⠁⠀⠀⠀⠀⠀⢻⣿⣿⡗⠟⢻⠛⡿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠿⠛⠀⠐⠁⠐⠀⠘⣏⠟⣶⣿⣿⡟⣿⣄⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠊⠐⠁⢺⠋⣝⠉⠻⠛⠛⠋⠋⠙⠛⠛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⢿⡗⣻⡏⢱⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢺⢿⣿⡿⡿⠸⣿⣟⣿⠐⡃⢈⡁⢀⡀⠀⠀⠀⠀⠹⠟⡏⢙⠏⠁⠁⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⢹⠀⢛⠀⠀⠀⠈⠀⡱⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡹⣳⢄⠀⣸⣿⣿⡇⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣽⣿⣿⣿⣇⣄⣠⣀⣀⣄⣤⣄⣤⣄⣤⣀⣄⣠⣀⣠⣇⣴⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣧⢤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣄⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠥⣻⠚⢱⠀⡂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣍⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⠻⡗⢺⠫⠛⡗⢺⠀⡍⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⠏⠹⠟⢻⠻⠿⠫⢿⠟⡿⢻⢟⠻⡟⢿⡿⡽⡏⢿⠟⡿⢙⠯⠻⡟⠻⠏⠹⣿⢻⢾⡟⡟⣾⣶⣷⣶⢗⡖⠃⠚⠂⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡉⠛⠛⢿⠏⢉⣠⣨⣭⣤⣥⣼⣌⣽⣥⣼⣤⣭⣭⣬⣠⣥⣬⣭⣭⣥⣼⣄⣭⣭⣼⠀⠕⠈⢋⠐⡃⢘⠛⠚⠛⠓⠓⠓⠚⠓⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠁⠈⠙⠻⠛⠛⠻⠋⣽⣿⣿⣿⣯⠈⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀
⣋⣩⢙⣙⣓⡀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠈⠉⡉⡙⠛⠛⢛⣓⠙⠓⢻⣿⣿⡟⠛⠛⠛⢛⢛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⣍⣭⣭⣭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⠀
⠀⠀⠀⢸⠀⡏⡇⣟⡂⠀⡟⡇⣝⡇⣏⡇⣟⡃⡇⣯⣻⠀⢸⠚⢸⣛⢸⣿⣿⣿⣛⢸⣱⢹⣹⢾⣱⠘⢱⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣠⣤⣤⣤⣤⣼⣿⣿⣧⣤⣬⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⢹⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠴⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠮⢿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣇⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠸⣿⣿⠃⠘⠚⠻⢽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣟⠻⠟⠙⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠹⡞⠃⠀⠀⠀⠀⠀⢻⣿⣿⡇⡇⢿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠿⠙⠂⠘⠃⠐⠀⠘⣏⠛⣾⣿⣿⡿⣿⣄⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠉⠁⠀⠀⠀⠐⠀⢹⣿⣿⡇⠋⠙⠟⢻⠋⡽⠍⠟⠛⠻⠙⠛⠛⠛⠛⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⢿⡗⣿⡏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⢾⣿⣿⣿⣿⠺⣿⣿⣿⠛⡃⢨⡁⣀⡄⠀⠀⠀⠀⠻⠿⡯⣛⠇⠙⠃⠸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⢀⠀⠀⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢘⡟⢹⠉⢟⠂⠉⠀⠉⠀⡩⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣉⢱⣞⠀⣽⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⢈⡅⢘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣇⣄⣠⣀⣴⣄⣴⣁⣤⣤⣤⣀⣄⣠⣤⣼⣇⣼⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠚⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⠯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣩⡭⠛⠛⢿⠿⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⠈⠘⠻⠛⠛⠻⠛⢽⣿⣾⣷⣯⢐⣽⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⠀
⣫⣉⢛⣙⡓⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡁⠀⠈⡋⡛⠛⠛⢛⣒⠙⠛⢻⣿⣿⡟⠛⠛⠛⢛⢛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡏⢉⢍⣭⣭⣭⣭⡍⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀
⠀⠀⠀⢸⠀⡏⡆⣮⡆⠀⡷⡄⣬⡆⣎⡇⣮⡇⡇⣷⣽⠀⢸⠚⢰⣵⢸⣿⣿⣿⣵⢸⣱⢹⣹⢼⣱⠘⢱⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⢤⣤⣤⣤⣤⣼⣿⣿⣧⣤⣬⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠵⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢿⣿⣯⢽⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠄⠺⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠸⣿⣿⠃⠘⠊⢿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⠟⠿⠟⠙⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢰⡟⠃⠀⠀⠀⠀⠀⢻⣿⣿⡗⡗⢺⢟⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡃⠿⠛⠊⠐⠂⠐⠀⠘⣏⠟⣼⣿⣿⣿⣿⣄⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠋⠀⠀⠀⠀⠘⠀⢸⣿⣿⡏⠋⠹⡟⠺⠫⣽⠍⠛⠛⠛⠙⠛⠛⠛⠛⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠔⠂⢐⠒⣾⣿⣿⢻⡟⢻⡏⣳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡕⢾⣿⣿⣿⣿⠻⣿⣟⣿⠛⡃⢨⡁⣀⡄⠀⠀⠀⠀⠻⠛⡿⢛⠃⠑⠀⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⠀⢠⠀⠀⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⡏⢹⠍⢟⠃⠁⠀⠉⠐⡁⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣩⡫⣮⠀⣹⣿⣿⡇⡀⢀⡀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⡀⣉⡁⢈⡀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣿⣿⣿⣇⣄⣠⣅⣴⣄⣼⣀⣤⣤⣤⣀⣄⣠⣤⣼⣇⣼⣦⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⢤⣅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣕⣡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣾⠐⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡽⣻⠚⣻⠈⡗⠂⠒⠠⠀⠀⠀⠀⠀⠀⠀
⣟⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡗⢺⠯⠿⡟⢺⠈⡟⠁⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠛⢻⡏⣹⠟⢿⠻⢿⡫⣿⠟⣿⢻⣿⢻⡟⢿⣿⣿⡟⢿⠟⣿⢙⡿⠻⡟⠻⣏⢹⣿⢻⣾⡟⡟⣿⣶⣿⣷⢗⡞⠓⠚⠇⠘⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣩⡭⠛⠛⢿⠿⢁⣠⣬⣭⣭⣧⣼⣭⣽⣭⣽⣤⣭⣭⣯⣤⣧⣼⣭⣽⣧⣼⣤⣭⣭⣽⠀⠟⠉⢋⠙⡃⢚⠛⢚⠛⠓⠓⠓⠚⠛⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⡿⠃⠀⠂⠀⠁⠀⠘⠛⠛⠛⠻⠛⢻⣿⣿⣧⣧⠘⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢐⠀
⣙⢉⠟⠙⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⡀⠙⠿⠿⠿⠃⠙⠲⢿⣿⣿⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡏⢉⣍⣭⣭⣭⣭⡉⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢜⠀
⠀⠀⠀⢹⠁⡗⡆⡶⡆⠀⡷⡅⡶⡆⡖⡇⡶⡆⡇⣶⢶⠀⢸⠽⢰⢶⢸⣿⣿⣷⢶⢰⢲⢺⢺⢔⣲⠐⢲⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀
⠀⠀⠀⠈⠀⠀⠁⠈⠀⠀⠀⠁⠈⠀⠈⠁⢈⣀⣁⣀⣁⢀⣬⣀⣀⣅⣼⣿⣿⣇⣁⣘⣁⣈⣉⣠⣥⣤⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡥⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⢽⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠸⣿⣿⣺⣿⢿⣽⣿⣿⣿⣿⣿⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣾⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣿⣿⠃⠚⠂⠽⣿⣿⣿⣿⡯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢿⣿⣿⡟⠿⠃⠙⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢑⡟⠃⠀⠀⠀⠀⠀⢻⣿⣿⡗⠇⢺⠻⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⡟⠛⠁⠐⠀⠀⠀⠘⣏⢏⣾⣿⣻⣿⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠋⠀⠀⠀⠀⠈⠀⢸⣿⣿⡏⠊⠐⠐⠺⠋⢽⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠔⠂⢐⠂⣾⣿⣿⣿⡟⢻⡏⢳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⢿⢿⣿⣫⢿⠸⣿⣿⣿⠓⡃⢀⡁⢀⡀⠀⠀⠀⠀⠹⠻⡟⢙⠉⠙⠃⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⣹⠌⢏⠀⠈⠀⠉⠀⡁⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⡱⢆⠀⣸⣿⣿⡇⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣵⣿⣿⣿⣇⣄⣠⣀⣀⣄⣤⣀⣤⣤⣠⣀⣄⣠⣠⣴⣇⣼⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⠏⠻⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣧⢤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣄⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡴⣾⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠥⣻⠚⢱⠀⡂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀
⣍⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⠻⡗⢺⠫⠛⡗⢺⠀⡍⠁⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡖⢈⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠛⢻⠏⠹⠟⢻⠻⠿⠫⢿⠟⡿⢻⢟⠻⡟⢿⡿⡽⡏⢿⠟⡿⢙⠯⠻⡟⠻⠏⠹⣿⢻⢾⡟⡟⣾⣶⣷⣶⢗⡖⠃⠚⠂⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣰⣿⣿⣿⣷⣶⣤⣤⣉⡉⠛⠻⢿⠏⢁⣠⣨⣭⣤⣥⣼⣌⣽⣥⣼⣤⣭⣭⣬⣠⣥⣬⣭⣭⣥⣼⣄⣭⣭⣼⠀⠕⠈⢋⠐⡃⢘⠛⠚⠛⠓⠓⠓⠚⠓⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⠀⠘⠻⠛⠛⠻⠛⢿⣿⣿⣿⣶⢨⣽⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣿⠀
⣋⣉⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠨⠛⠿⠿⠿⠄⠹⠦⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡏⢉⢍⣭⣭⣭⣭⡉⣭⣭⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣞⠀
⠀⠀⠈⢹⠁⡗⡆⡶⠆⠀⡷⡁⡶⡆⡖⡇⡶⠆⡇⣷⢶⠀⢸⠽⢰⠶⢸⣿⣿⣷⢶⢰⢲⢺⢺⢴⢲⠐⢲⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠀
⠀⠀⠀⠈⡀⠁⠁⠉⠀⠀⠁⠁⠈⠁⠈⠁⢈⣁⣁⣈⣉⢀⣈⣀⣈⣉⣘⣿⣿⣏⣉⣘⣁⣈⣉⣈⣁⣀⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠺⢿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⣿⡿⠁⠘⠘⠻⠿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢿⣿⣿⣟⠿⠏⠹⠟⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠰⡝⠂⠀⠀⠀⠀⠀⢻⣿⣿⡗⡟⢿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⣿⠟⠂⠐⠃⠐⠀⠈⡏⢓⣾⣿⣿⣿⣿⣄⠀⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠋⠙⡟⠻⢋⠹⠽⠛⠛⠻⠛⠛⠛⠛⠛⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠠⠀⠀⠀⠔⠂⢘⠃⣾⣿⣿⢻⡿⢻⣏⣳⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠈⠉⠈⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⢐⡇⢺⣿⣿⣛⣿⠺⣿⣻⣿⠛⡃⢈⡁⢀⡄⠀⠀⠀⠀⠻⠻⡯⢛⠉⠙⠁⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠸⠀⢀⡀⠀⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢈⡏⢹⡉⢿⠂⠉⠀⠉⠀⡁⠀⠀⠈⠁⠈⠁⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 1675

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/11/18/_Video_Corporate_Mainstream_Media_Still_Failing_to_Call_Out_Win.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/11/18/_Video_Corporate_Mainstream_Media_Still_Failing_to_Call_Out_Win.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] Corporate/Mainstream Media Still
Failing to Call Out Windows (and Microsoft)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 18, 2023


Video_download_link | md5sum ec6bd91d56d0f81f8dd7d66e7f4ddc50
Security_Slant_in_Mainstream_Media
Creative Commons Attribution-No Derivative Works 4.0


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


TODAY'S POST (and video) deals primarily with security and how the media fails
to_properly_cover_the_issues, possibly due to sponsors and ads (which are also
a form of sponsorship). Too many Windows issues are being blamed on generic
computer problems rather than Microsoft Windows, especially in Microsoft-
sponsored sites.


The issue isn't limited to security coverage. For instance, in Finland if one
writes an address on a paper letter by hand, the system finds the right address
if you use the Finnish names but if you use the Swedish place names, then the
system fails. Both languages are official. However, this is being blamed 'on
the computer'.


It hardly says anything meaningful.


We saw other examples of institutions blaming "Internet" or "network" or
"computers" instead of Microsoft or Windows. One more example is Sampo Pankki
responding to inquiries by saying "IBM takes care of the network" when
SharePoint falls flat on its face for several consecutive months without
respite. That 1) prevented people from accessing their own accounts, 2)
prevented accounts from receiving money, 3) allowed access to accounts which
weren't yours, 4) all of the above.


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


This happened around 2007 and Sampo Pankki is still failing.


Sompi, from Finland, told he "had an account in Sampo Pankki, currently known
as Danske Bank. I could not access my money because their online bank only
showed me a page that read "Internal error. Try again later." I contacted their
customer service and they just said "Use Chrome, we don't support Firefox or
other browsers." Also they recommended me to use their Android app. It was this
year."


"Eventually they fixed their stuff but a lot of damage was already done." This
went on for months.


The mainstream press is is moreover conscientious in avoiding mention of the
role of Microsoft in the shutting down of shipping in Australia, as the video
above notes, even after what Microsoft did to Denmark a short while back.


The video then mentions this_potential_way (subject change) to distract from
Exchange and Azure giving away like trillions of E-mails to every hostile
nation. It mentions "government emails", but that's what Microsoft is
vulnerable and notorious for, having giving mail of the US government to
Chinese spies. Microsoft only admitted this after being forced to (by the
government) and then it turned out to be a widespread problem. They hide their
breaches. That's not even ledal.


Also see "Google_reveals_details_of_Zimbra_vulnerability_used_to_target
government_organizations" (a legitimate problem but being spun as FOSS being
insecure, and thus Microsoft being acceptable). This one says "Google LLC’s
Threat Analysis Group today revealed details of how it identified and responded
to a new exploit in the Zimbra Collaboration Suite that was used to target
international government organizations. [...] noticed it being actively
exploited in targeted attacks [...]"


So what's the solution, GMail? Either way, Webmail is a bad idea (chaining more
vulnerabilities in a fatter stack) and Microsoft's products have back doors by
intention. Owing to Edward Snowden's NSA leaks, we already know Outlook was
intentionally made not secure. But nobody ever mentions this anymore. █




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

                    ䷩ 𝚕𝚒𝚗𝚎 2549

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/11/18/_Video_No_Phoronix_Microsoft_is_Not_an_Acceptable_Participant_B.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/11/18/_Video_No_Phoronix_Microsoft_is_Not_an_Acceptable_Participant_B.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] No, Phoronix, Microsoft is Not an
Acceptable Participant But a Snake (But Microsoft Gives Phoronix 'Gifts') and
Heather Meeker Acts Like a Microsoft 'Asset', Professional
Revisionist⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 18, 2023


Video_download_link | md5sum ffb194d0eaf6f5ab2b28028b0decc9ec
Question_of_Interests
Creative Commons Attribution-No Derivative Works 4.0


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


The Microsoft-loving Phoronix is not a new subject here. As noted_the_other
night_in_a_quick_post_about_Mr._Larabel (of Phoronix), he is doing a disservice
by being so soft. I say this as someone who used to be the #1 source of traffic
to his site, according to Alexa.com. Things have only changed in the
attitudinal (virtual) sense and eventually Microsoft apologists - including Mr.
Larabel - will all eat crow because Microsoft has not changed and more people
recognise what the company is really doing, not what it merely claims to do.
The fraud Nadella may have fooled (or paid) the media for the whole "Microsoft
loves Linux" lie, but people aren't buying it.


Here's a pair of examples of what Phoronix published in recent days:


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Windows, Not Linux: Microsoft Gets OpenGL 4.4 Running Atop
                 Direct3D 12 Using Mesa, OpenGL 4.5 Inbound⦈


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Microsoft Achieves OpenGL 4.5 Atop Direct3D 12 With Mesa⦈


Our regular readers probably need no explanation of what's wrong with this, but
Microsoft attacking Mesa with WSL E.E.E. is a longstanding problem. However,
Nr. Larabel is in the pockets of the x86 camp, hence he cannot cover this
properly and objectively, for fear of severing some business connections. The
second of the two says: "Hours after writing about Microsoft's Direct3D 12
back-end for Mesa seeing OpenGL 4.4 support, the in-review OpenGL 4.5 code
mentioned in that article happened to land in Mesa..."


Covering this even once is too much. Twice in a row is... worrisome and
troublesome. Mr. Larabel holds wooden horse on a leash, bringing it past the
gate for traffic and ad clicks... and we're meant to be joyful? Only about a
day ago he said we can "enjoy hardware acceleration of various crypto and
compression algorithms". Yes, enjoy back doors using proprietary hardware you
can neither audit nor change. Joy!


The majority of the above video, however, speaks of Heather Meeker, whom we
mentioned_in_passing_yesterday. Due to a lack of time we failed at explaining
what she is and does (we did this before). She is mostly a revisionist and her
supposed relation to FOSS is rather weak.


One reader presumed she is some random MBA working for Microsoft in Redmond
"but cannot be sure."


As noted in the video above, she seems to be trying to hide past connections to
Microsoft or GAFAM. The headline is wordplay because her latest book, which is
looking at Free software from a greedy person's perspective, not a community
angle. As an invited guest (by Microsoft), according to our reader, it seems
she's "say-for-pay" and involved in "open-washing as a service, I presume."


To me, as somewhat who has closely watched and covered these issues for over 2
decades, what's most conspicuous is how she seemingly came almost out of
nowhere as "authority" and is now entrusted to to write the history of "Open
Source". I say a lot more in the video and would rather not do it as text
(people like to quote out of context with gender-baiting).


Imagine Microsoft trying to lecture us on its competition, claiming to be
speaking for it. █




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

                    ䷩ 𝚕𝚒𝚗𝚎 3416

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/11/18/_Video_Washington_s_Worsening_Debt_Problem_Includes_Microsoft_s.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/11/18/_Video_Washington_s_Worsening_Debt_Problem_Includes_Microsoft_s.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] "Washington's Worsening Debt
Problem" Includes Microsoft's Massive Corporate Debt (Over 105 Billion in
Debt)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 18, 2023,
updated Nov 18, 2023


Video_download_link | md5sum 0d49c3ba2afe5fc5f492903394654923
Microsoft_Debt_Exceeds_100_Billion_Dollars
Creative Commons Attribution-No Derivative Works 4.0


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Preview_for_Microsoft_Debt_Exceeds_100_Billion_Dollars⦈_


Recent: Microsoft's_Total_Debt_Has_Just_Surged_to_an_All-Time_High_of_106
Billion_Dollar_(26_Billion_Increase_in_Just_3_Months_Despite_Mass_Layoffs)


THE abusive monopoly (or monopolist) from Redmond has a little secret. The
people there aren't just greedy/lusting for money. They need money for the
company's survival. They need bailouts.


"So if Nat Friedman still works for Microsoft and is hoarding Nvidia Chips,"
one reader told us yesterday, and "Microsoft wants to compete with Nvidia,"
what is the company's future? Chatbots? Hardware? Chips sold using chatbots as
a gimmick? Mr. Friedman is hiding_in_the_shadows, investing in all sorts of
things (his family is a financial family, not technical), having long attacked
the Free software community both from inside and outside. He always worked for
Microsoft.


That's just a symptom of what happened to the 'tech' industry. It's ruled by
marketers and bankers/lawyers, not technical people.


Either way, GitHub continues losing loads of money (the video talks about this)
and Microsoft has loads of layoffs in Washington, its home state. According to
a new article (Washington's_Worsening_Debt_Problem), Washington now ranks 5th
highest in the US for consumer debt. To quote: "Are you in debt? Seems like
many are and, unfortunately, many in Washington are and it's getting worse."


How about national debt, corporate debt, state debt, set aside consumer and
mortgage debt?


Consumer debt in the US is well over $17 trillion* (this figure is almost a
year out of date already). That's "not the national debt," someone told folks
in the media, "that's just us random folks who might get a little spend-crazy
with a credit card, those with student loans and those who needed financial
support and are having trouble zeroing it out."


So we're looking at 17+ trillion (US dollars) for working families, well over
33 trillion in national debt (almost_34_trillion_now). That's 50+ trillion
totalled without yet adding any of the other components.


One might even say that Microsoft isn't the exception here, as a president who
filed for bankruptcy six times can attest to**, but that does not change the
fact that Microsoft may be in trouble. This cannot carry on for much longer. █


____
* Greedy reckless people and fantasists, to use the labels crudely, wrongly
believe it's normal for an average family to rack up a million bucks in debt
and somehow, miraculously, pay that back some day. What happens in practice is
pure agony, stress, sleepless nights, poor health, and loss of one's (not
really, the bank's) home. Lenders like it when people borrow money. Don't trust
lenders. They are not thinking like most people, they are reckless hoarders who
lack empathy. Not just bankers, who like to tell you the government will back
and bail them out no matter what. Then comes the day it does not happen. People
lose all their savings.


** A lot of US billionaires (not all of them but a lot) are like Donald Trump -
swimming in debt and many lies. The economy has become a Jenga_tower of
speculations, loans, and promises that cannot be fulfilled, i.e. deliberate or
unintended Ponzi scheme where the deficits are passed to "credit" cards,
mortgages, national debt etc.




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

                    ䷩ 𝚕𝚒𝚗𝚎 4260

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 18/11/2023: Amazon Alexa Layoffs,
Arguments Over Hong Kong and Taiwan⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 18, 2023


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Patents
                # Copyrights
    * Gemini*_and_Gopher
          o Personal/Opinions
          o Games
          o Technology_and_Free_Software
                # Internet/Gemini
    * § Leftovers⠀➾


          o ⚓ Federal News Network ☛ After_years_of_delays,_the_TSP’s_I_fund
            will_track_a_new_index_starting_in_2024⠀⇛


                 After several years of delays and controversy, the TSP’s
                 I fund will transition to tracking a new, broadened
                 benchmark index, but will exclude investments in China
                 and Hong Kong.


          o ⚓ Hackaday ☛ After_MEMS_Microphones,_MEMS_Speakers_Enter_The
            Market⠀⇛


                 These days it’s hard to not come across solid-state
                 (micro-electromechanical systems, MEMS) microphones, as
                 they are now displacing electret microphones almost
                 everywhere due to their small size and low cost. Although
                 MEMS speakers are not impossible, creating a miniature
                 speaker that can both displace a lot of air (‘volume’)
                 and accurately reproduce a wide range of frequencies –
                 unlike simple piezo buzzers – is a lot tougher. Here a
                 startup called xMEMS figures that they have at least
                 partially cracked the code with their piezoMEMS speakers,
                 with Creative using the Cowell version in their brand-new
                 Aurvana Ace in-ear monitors.


          o ⚓ Hackaday ☛ Robots:_How_The_Pros_Keep_Them_Safe⠀⇛


                 Robotic safety standards are designed for commercial
                 bots, but amateur robot builders should also consider
                 ideas like the keepout zone where a mobile robot isn’t
                 permitted to go or how to draw out the safety perimeter
                 space for your experimental robot arm. After all, that
                 robot arm won’t stop crushing your fingers because you
                 built it yourself. So, it is worth looking at the
                 standards for industrial robots, even if your aim is fun
                 rather than profit.


          o ⚓ Hackaday ☛ Robot_Hand_Has_Good_Bones⠀⇛


                 What do you get when you mix rigid and elastic polymers
                 with a laser-scanning 3D printing technique? If you are
                 researchers at ETH Zurich, you get robot hands with
                 bones, ligaments, and tendons. In conjunction with a
                 startup company, the process uses both fast-curing and
                 slow-curing plastics, allowing parts with different
                 structural properties to print. Of course, you could
                 always assemble things from multiple kinds of plastics,
                 but this new technique — vision-controlled jetting —
                 allows the hands to print as one part. You can read the
                 full paper from Nature or see the video below.


          o ⚓ Hackaday ☛ ColorReplica_Is_A_Rainbow_At_Your_Fingertips⠀⇛


                 Have you ever wanted to match paint to the color of a
                 pillow, or make a website where the primary color matches
                 your favorite shade of electrolytic capacitor? Then
                 ColorReplica is the project for you.


          o ⚓ Hackaday ☛ Umbrella_Antenna_Protects_You_From_Rain,_But_Not_The
            Way_You_Think⠀⇛


                 You never know when you’ll be called upon to [MacGyver]
                 your way out of an emergency. We can’t imagine what kind
                 of situation would call for whipping up a satellite
                 ground station for NOAA weather satellites from junk, but
                 hey, it could happen.


          o ⚓ Hackaday ☛ A_3D_Printed_Grinder_For_Printed_Lens_Blanks⠀⇛


                 When one thinks of applications for 3D printing, optical
                 components don’t seem to be a good fit. With the possible
                 exception of Fresnel lenses, FDM printing doesn’t seem up
                 to the job of getting the smooth surfaces and precision
                 dimensions needed to focus light. Resin printing might be
                 a little closer to the mark, but there’s still a long way
                 to go between a printed blank and a finished lens.


          o ⚓ Kev Quirk ☛ Fat_Boy_at_40_-_Update_02⠀⇛


                 I just realised that I forgot to give the update for this
                 month's Fat Boy at 40. I'll keep this brief as I don't
                 have much time...


                 Things are still going well. I'm continuing to lose
                 weight and feel good. What's more, friends and family are
                 starting to notice now too.


                 Here's the number as they stood as of Mon 13th Nov 2023:
                 [...]


          o § Science⠀➾


                # ⚓ Science Alert ☛ Physicists_Uncover_a_New_State_of_Matter
                  Hidden_in_The_Quantum_World⠀⇛


                       A new secret is revealed.


          o § Hardware⠀➾


                # ⚓ Tedium ☛ When_Tools_Unlock_New_Paths⠀⇛


                       Don’t just keep doing the same thing hoping that
                       something is going to change. If you want to truly
                       be creative, try a different tool sometime. You’ll
                       thank yourself.


                       Case in point: Have you ever tried to remove a
                       hydraulic lift from an office chair? It is the most
                       painful process, one that seems designed to wear
                       down anyone that tries to do it. I do not recommend
                       it.


                # ⚓ CNX Software ☛ AMD_Ryzen_Embedded_7000_Zen_4_SoC_integrates
                  Radeon_RDNA_2_graphics,_up_to_28_lanes_of_PCIe_5
                  connectivity⠀⇛


                       AMD Ryzen Embedded 7000 Series is a new “Zen 4”
                       processor with integrated Radeon RDNA 2 graphics
                       designed for high-performance embedded systems
                       targetting industrial automation, machine vision,
                       robotics, and edge servers. The last two Ryzen
                       Embedded families from AMD, namely the Ryzen
                       Embedded V3000 and Ryzen Embedded 5000, mostly
                       targeted headless networking and storage
                       applications since the processors lacked any 3D
                       GPU. But the new Ryzen Embedded 7000 processors
                       bring back graphics with a Radeon RDNA 2 GPU
                       clocked at up to 2.2 GHz and also come with up to
                       12 Zen4 cores clocked at up to 5.4 GHz, and feature
                       up to 28 lanes of PCIe 5 connectivity. >


                # ⚓ Tom's Hardware ☛ Apple-Scented_Thermal_Paste_Launches_in
                  Japan⠀⇛


                       An apple-scented thermal paste has been launched in
                       Japan. One explanation provided is that the light
                       green color helps DIYers check for an even
                       application.


                # ⚓ Tom's Hardware ☛ Cerebras_Boss_Calls_Nvidia_‘Un-American’
                  for_Sanctions-Swerving_GPUs⠀⇛


                       The CEO of Cerebras has accused Nvidia of following
                       the letter of the law regarding US-China sanctions,
                       but limboing under the GPU restrictions in an
                       unpatriotic manner.


                # ⚓ Tom's Hardware ☛ China's_YMTC_Preps_Next-Gen_Xtacking_4.0
                  NAND_Tech⠀⇛


                       Yangtze Memory proceeds to Xtacking 4.0
                       architecture, but without increasing the number of
                       layers.


                # ⚓ Hackaday ☛ Underwater_Kites_Buoying_The_Prospect_Of_More
                  Tidal_Power_Generation⠀⇛


                       Swedish start-up Minesto has been for years trying
                       to float the idea of having underwater turbines
                       that generate power for use on-shore. These would
                       be anchored to the seafloor by a long tether and
                       move around in figure-of-eight patterns like a
                       kite, which would increase the flow over the
                       turbine’s blades. After a few years of trials, its
                       1.2 MW Dragon 12 kite will now be installed off the
                       coast of the Faroe Islands.


                # ⚓ Hackaday ☛ Don’t_Look_Up,_Or_You’ll_See_The_Time_From_This
                  VFD_Projection_Clock⠀⇛


                       Ceiling clocks were a bit of a thing back in the
                       days when clock radios were a fixture of
                       nightstands. The idea was to project the time onto
                       the ceiling so you’d only have to roll over onto
                       your back and open your eyes to check the time,
                       instead of potentially disturbing your slumber by
                       craning your neck around to see the front of the
                       clock.


                # ⚓ Hackaday ☛ Backyard_UFO_Is_Out_Of_This_World⠀⇛


                       Halloween may be over for another year, but UFOs in
                       your yard are cool year-round. This one might take
                       the cake. [frydom.john]’s excellent UFO is fully
                       programmable and contains about 2000 addressable
                       RGB LEDs, smoke, a laser-lit ramp, and of course,
                       an alien crew.


                # ⚓ Hackaday ☛ Probably_The_Largest_Selfie_Camera_In_The
                  World⠀⇛


                       Most readers will have some idea of how a camera
                       works, with a lens placed in front of a piece of
                       film or an electronic sensor, and the distance
                       between the two adjusted until the images is in
                       focus. The word “camera” is a shortening of “camera
                       obscura”, the Latin for “dark room”, as some early
                       such devices were darkened rooms in which the image
                       was projected onto a rear wall. [David White], a
                       lecturer at Falmouth University in the UK has
                       created a modern-day portable camera obscura using
                       a garden gazebo frame, and uniquely for a camera
                       obscura, it can be used to take selfies.


                # ⚓ Silicon Angle ☛ Report:_Applied_Materials_under
                  investigation_for_sending_chipmaking_gear_to_China_in_breach
                  of_export_rules⠀⇛


                       Shares of the semiconductor manufacturing
                       technology provider Applied Materials Inc. traded
                       lower after-hours today in the wake of a report
                       that it’s being investigated by the U.S. Justice
                       Department for violating export restrictions by
                       shipping products to a leading Chinese chipmaker.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ A_Federal_Report_Shows_“Climate-Sensitive”
                  Diseases_Are_Spreading_Through_the_US⠀⇛


                # ⚓ Science Alert ☛ Common_Pill_Slashes_Risk_of_Deadly_Drug-
                  Resistant_Tuberculosis_Strain⠀⇛


                # ⚓ Science Alert ☛ Experts_Explain_FDA_Warning_to_Stop_Using
                  Suspect_Eye_Drops_Immediately⠀⇛


                       Alarming findings.


                # ⚓ Science Alert ☛ Is_Ketchup_Really_a_Sports_Supplement?_A
                  Nutritionist_Reveals_The_Truth.⠀⇛


                       We have questions.


                # ⚓ Science Alert ☛ Extreme_Drop_in_Oxygen_Will_One_Day
                  Suffocate_Most_Life_on_Earth⠀⇛


                       The end of the road.


                # ⚓ Federal News Network ☛ A_decade_after_its_creation,_DHA
                  thinks_it_has_building_blocks_in_place_for_an_integrated
                  military_health_system⠀⇛


                       After a decade of constant change, DHA's new
                       director says it's time to focus on delivering a
                       truly integrated military health system.


                # ⚓ Federal News Network ☛ Protected:_Open_Season_Exchange
                  2023:_UnitedHealthcare’s_Dr._Rhonda_Randall_on_getting_mental
                  health_care_when_you_need_it⠀⇛


                       There is no excerpt because this is a protected
                       post.


                # ⚓ Federal News Network ☛ Protected:_Open_Season_Exchange
                  2023:_UnitedHealthcare_Dental’s_Haley_Landherr_on_picking_a
                  dental_plan_that_adapts_with_you⠀⇛


                       There is no excerpt because this is a protected
                       post.


                # ⚓ The Straits Times ☛ Italy_arrests_six_in_crackdown_on
                  fentanyl_smuggling_from_China_to_US⠀⇛


                       Italian police have arrested six people in a
                       crackdown on a network that allegedly played go-
                       between for fentanyl trafficking from China to the
                       United States, Guardia di Finanza police and
                       prosecutors in the northern city of Piacenza said
                       on Wednesday.


                # ⚓ teleSUR ☛ Africa:_WHO_Warns_of_Growing_Diabetes_Amid
                  Lifestyle_Changes⠀⇛


                       Diabetes was responsible for 416,000 deaths in
                       Africa in 2021 and is expected to be one of the
                       leading causes of death on the continent by 2030
                       unless communities adopt healthier lifestyles, such
                       as regular exercise.


                # ⚓ YLE ☛ Police_warn_of_deadly_designer_drug_circulating_in
                  Kuopio⠀⇛


                       Metonitazene is estimated to be 10 times as potent
                       than fentanyl. Police say it has been sold on the
                       street in tablets that look like Subutex.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ GeekWire ☛ Internal_memo:_Amazon_will_cut_‘several_hundred’
                  Alexa_jobs_as_it_ends_unspecified_initiatives⠀⇛


                       Amazon will eliminate several hundred roles in its
                       Alexa division as part of a broader shift in
                       priorities and a focus on developing new forms of
                       artificial intelligence, according to an internal
                       memo sent to employees Friday morning.


                # ⚓ Pro Publica ☛ DOJ_Backs_Tenants_in_Price-Fixing_Case
                  Against_Big_Landlords_and_Real_Estate_Tech_Company⠀⇛


                       The U.S. Department of Justice late Wednesday
                       stepped into a massive antitrust lawsuit filed by
                       dozens of tenants who are accusing a tech company’s
                       apartment software of helping landlords collude to
                       inflate rents.


                       The DOJ action comes after a ProPublica
                       investigation last year found that Texas-based
                       software provider RealPage used algorithms to
                       recommend rents to landlords across the country to
                       maximize profits — a practice that experts said may
                       violate antitrust laws.


                # ⚓ Reason ☛ From_Judge_Michael_J._Newman_(S.D._Ohio)_on_Use_of
                  Hey_Hi_(AI)_to_Prepare_Filings⠀⇛


                       From today's order in Whaley v. Experian Info.
                       Solutions, Inc., which dismisses the case on the
                       merits but also adds: Plaintiff admits that he used
                       Artificial Intelligence ("AI") to prepare case
                       filings. [This yielded hallucinated citations to
                       nonexistent cases. -EV] The Court reminds all
                       parties that they are not allowed to use AI—for any
                       purpose—to prepare…


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Pro Publica ☛ Mother_Suing_NYC_Child_Welfare_Agency
                        for_Its_Warrantless_Searches_of_Her_Home_and_Son⠀⇛


                             It was 5:30 a.m. Flashlights beamed in
                             through the windows of the ground-floor
                             apartment in East Flatbush, Brooklyn. Police
                             officers and child welfare caseworkers were
                             ordering a woman to open her front door.


                             When she did, the first thing she saw was
                             that the police had their guns drawn. Her
                             hands flew up into the “don’t shoot”
                             position; she was well aware of the recent
                             stories of cops “shooting first and asking
                             later.” She prayed that her 7-year-old son
                             was still asleep in his room.


                      # ⚓ Security Week ☛ Threat_Intel:_To_Share_or_Not_to
                        Share_is_Not_the_Question⠀⇛


                             To share or not to share threat intelligence
                             isn’t the question. It’s how to share, what
                             to share, where and with whom.


                      # ⚓ Techdirt ☛ UK_Law_Enforcement_Continues_To_Expand_Use
                        Of_Facial_Recognition_Tech⠀⇛


                             UK law enforcement seems incapable of
                             recognizing warning signs. Officials seem
                             willing to compete with China in terms of
                             Most Cameras Per Capita. And it’s not enough
                             to just have cameras covering every bit of
                             open space. Those cameras must contain
                             questionable tech that is notoriously
                             inaccurate, at least when deployed by UK law
                             enforcement.


          o § Defence/Aggression⠀➾


                # ⚓ New York Times ☛ International_Court_Orders_Syria_to_Stop
                  Torture_of_Political_Opponents⠀⇛


                       Human rights experts have estimated that some
                       14,000 people died from torture or were killed in
                       the prisons run by military intelligence and
                       security forces during Syria’s long civil war.


                # ⚓ Federal News Network ☛ Cyber_Solarium_leader_pushes_to
                  ensure_continuity_in_national_cyber_director_job [Ed: Hiring
                  another poser]⠀⇛


                       "The worst thing would be if we suffered a serious
                       cyber attack, and this position was vacant."


                # ⚓ Hong Kong Free Press ☛ China’s_leader_Pooh-tin_Jinping_and
                  US_President_Joe_Biden_agree_to_restore_military_ties_at
                  ‘productive’_summit⠀⇛


                       United States US President Joe Biden hailed his
                       “most constructive” talks with Chinese President
                       Pooh-tin Jinping Wednesday, as they agreed at their
                       first summit in a year to restore military-to-
                       military communications and ease tensions.


                # ⚓ Atlantic Council ☛ Global_China_Newsletter:_Pooh-tin_and
                  Biden_dazzle,_but_don’t_be_blinded_to_action_elsewhere⠀⇛


                       The November 2023 edition of the Global China
                       newsletter.


                # ⚓ Federal News Network ☛ Federal_cybersecurity_strategy_faces
                  a_crucial_test._Will_it_pass?⠀⇛


                       More often than not, legacy contracts and programs
                       with existing providers and solutions are routinely
                       extended. That may save time, but it also prevents
                       the innovation and collaboration needed to address
                       modern threats.


                # ⚓ Federal News Network ☛ One_of_the_EPA’s_most_sacred
                  databases_could_be_at_risk⠀⇛


                       The Environmental Protection Agency's (EPA)
                       Integrated Risk Information System (IRIS), is one
                       of the main tools the agency relies on for
                       environmental regulations, containing information
                       on human health effects that may result from
                       exposure to various chemicals in the environment. A
                       new report from the EPA's inspector general, said
                       the agency needs to do a better job of who has
                       access to it. For more on the report, the Federal
                       Drive with Tom Temin's Executive Producer Eric
                       White talked with Jeremy Sigel, the IG office's
                       Supervisory Audit Manager in the Information
                       Resources Management Directorate.


                # ⚓ Security Week ☛ State-Sponsored_Online_Spies_Likely_to
                  Target_Australian_Submarine_Program,_Spy_Agency_Says⠀⇛


                       Australia’s cooperation with the U.S. and Britain
                       to develop an Australian fleet of submarines
                       powered by U.S. nuclear technology is a likely
                       target of state-sponsored cyberespionage, the
                       nation’s digital spy agency said.


                # ⚓ The Straits Times ☛ South_Korea’s_Yoon,_Japan’s_Kishida_vow
                  to_deepen_ties⠀⇛


                       They made the pledge during a meeting on the
                       sidelines of the Apec summit in San Francisco.


                # ⚓ RFA ☛ Yoon,_Kishida_aim_for_better_ties;_island_issues_may
                  constrain⠀⇛


                       Ongoing territorial disputes could hamper full
                       security cooperation, says an expert.


                # ⚓ RFA ☛ Biden:_US-China_ties_‘not_all_kumbaya’_after_Pooh-tin
                  talks⠀⇛


                       He also told world leaders that their main focus
                       should be building resilience, ‘not about how much
                       we trade.’


                # ⚓ RFA ☛ Xi_and_Biden_hold_talks_outside_San_Francisco⠀⇛


                       Despite progress after an hourslong meeting, Biden
                       also said that he still thinks Pooh-tin is a
                       ‘dictator.’


                # ⚓ Meduza ☛ Police_raid_Voronezh_restaurant,_hand_out_50
                  military_summonses_to_immigrants_from_Azerbaijan_—_Meduza⠀⇛


                # ⚓ RFA ☛ Has_North_Korea_shut_down_all_diplomatic_missions?⠀⇛


                       Verdict: False


                # ⚓ The Straits Times ☛ Philippines_calls_on_China_to_remove
                  illegal_structures,_cease_reclamations_in_South_China_Sea⠀⇛


                       It also called on China to be accountable for
                       environmental damage in the South China Sea.


                # ⚓ The Straits Times ☛ Philippines’_Marcos,_China’s_Pooh-tin
                  to_discuss_tensions,_way_forward_in_South_China_Sea⠀⇛


                       The Permanent Court of Arbitration in 2016 said the
                       line on China’s maps had no legal basis.


                # ⚓ The Straits Times ☛ 26_dead,_dozens_hospitalised_in_China
                  building_fire:_State_media⠀⇛


                       The fire started at a four-storey building
                       belonging to a coal company in Shanxi province.


                # ⚓ RFA ☛ Thailand_backs_away_from_Chinese_police_patrol_plan
                  amid_furor⠀⇛


                       Prime minister says there is no plan to station
                       Chinese police in Thailand for joint patrols.


                # ⚓ YLE ☛ Finland_closes_southeastern_border⠀⇛


                       Prime Minister Petteri Orpo said that all four
                       southeastern border crossing points will be shut on
                       Friday night.


                # ⚓ New York Times ☛ ‘Erase_Gaza’:_War_Unleashes_Incendiary
                  Rhetoric_in_Israel⠀⇛


                       Experts say that inflammatory statements by
                       prominent Israelis are normalizing ideas like the
                       killing of civilians and mass deportations.


                # ⚓ New York Times ☛ How_International_Law_Views_Israel’s
                  Military_Action_at_Al-Shifa_Hospital⠀⇛


                       Human rights laws prohibit harming or interfering
                       with a hospital like Gaza’s Al-Shifa, with very
                       narrow exceptions, or using it as a human shield.
                       Attacking one can be a war crime.


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


                      # ⚓ Meduza ☛ St._Petersburg_artist_Sasha_Skochilenko
                        sentenced_to_seven_years_in_prison_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘When_you_imprison_pacifists,_you_delay
                        peace’:_Key_excerpts_from_St._Petersburg_artist_Sasha
                        Skochilenko’s_final_statement_in_court_—_Meduza⠀⇛


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ RFERL ☛ Prosecution_Seeks_Seven_Years_For_Kyrgyz_Blogger
                  Who_Wrote_About_Issues_At_Mining_Complex⠀⇛


                       The prosecutor in the trial of Kyrgyz blogger
                       Yryskeldi Jekshenaliev, who was arrested in August
                       on charges of making public calls for mass disorder
                       and violence, asked a Bishkek court on November 16
                       to convict and sentence the defendant to seven
                       years in prison.


                # ⚓ Marcy Wheeler ☛ The_Suspected_2019_Exposure_of_Jonathan
                  Buma’s_Source⠀⇛


                       The reasons I'm cautious about Jonathan Buma's
                       whistleblower complaint go beyond the fact that he
                       thought Chuck Johnson would make a good informant.


          o § Environment⠀➾


                # ⚓ Reason ☛ New_U.S.-China_Climate_Deal:_Same_as_the_Old
                  Deals⠀⇛


                       China pledges again to do exactly what it was going
                       to do anyway.


                # ⚓ Hackaday ☛ A_Brief_History_Of_Weather_Control⠀⇛


                       It used to be a common expression to say that
                       something would happen when “people walked on the
                       moon.” That is, something that was never going to
                       happen. Of course, by 1960, it was clear that
                       someone was going to walk on the moon eventually.
                       There were many other things everyone “knew” would
                       happen in the future. Some of them came true, but
                       many of them didn’t. Some, like video phones and
                       robot factory workers, came true in a way, but not
                       as people imagined. For example, people were
                       confident that computers would easily translate
                       between human languages, something we still have
                       trouble doing entirely reliably. Another standard
                       prediction is that people would control the
                       weather.


                # ⚓ YLE ☛ Finland_leads_'Freezing_Winds_23'_drills_in_Baltic
                  Sea⠀⇛


                       Sixteen allied aircraft will also take part, with
                       drills planned over areas of southern Finland and
                       the northern Baltic Sea.


                # § Energy/Transportation⠀➾


                      # ⚓ European Commission ☛ Security_of_gas_supply:_the
                        European_Commission_decides_to_refer_POLAND_to_the
                        Court_of_Justice_of_the_European_Union_for_measures
                        imposing_additional_costs_on_cross-border_gas_trade⠀⇛


                             European Commission Press release Brussels,
                             16 Nov 2023 Today, the Europen Commission
                             decided to refer Poland to the Court of
                             Justice of the European Union for imposing
                             restrictive requirements on companies engaged
                             in the cross-border trade of natural gas
                             under its national gas storage legislation.


                      # ⚓ RFA ☛ China’s_renewable_energy_boom_powers_global_job
                        surge,_report_says⠀⇛


                             Investment in renewables in Asia reached
                             US$345 billion at the end of 2022.


                # § Overpopulation⠀➾


                      # ⚓ Science Alert ☛ Doomsday_Clock_Warns_We're_Alarmingly
                        Close_to_an_Uninhabitable_Earth⠀⇛


                             The nearest we've ever been to midnight.


          o § Finance⠀➾


                # ⚓ Atlantic Council ☛ CBDCs_will_further_fragment_the_global
                  economy—and_could_threaten_the_dollar⠀⇛


                       By the end of 2023, over 130 central banks
                       representing 98 percent of global GDP will have
                       initiated programs to develop central bank digital
                       currencies (CBDCs). In the next five to seven
                       years, it is reasonable to expect that quite a few
                       of those countries will have issued CBDCs either in
                       wholesale or retail formats.


                # ⚓ Reuters ☛ Amazon.com_to_cut_'several_hundred'_Alexa_jobs⠀⇛


                       The cuts affect several hundred employees working
                       on Alexa, according to the email. A spokeswoman
                       declined to elaborate on exactly how many were
                       affected.


                # ⚓ CNBC ☛ Amazon_cuts_‘several_hundred’_jobs_in_Alexa
                  division⠀⇛


                       on Friday began laying off “several hundred” people
                       in its Alexa division as part of broader belt-
                       tightening that’s been underway since last year,
                       the company confirmed.


                       Daniel Rausch, Amazon’s vice president of Alexa and
                       Fire TV, sent a note to staffers informing them of
                       the job cuts, according to a copy of the memo
                       shared by an Amazon spokesperson.


                       “As we continue to invent, we’re shifting some of
                       our efforts to better align with our business
                       priorities, and what we know matters most to
                       customers — which includes maximizing our resources
                       and efforts focused on generative AI,” Rausch wrote
                       in the memo, which was reported earlier by
                       GeekWire. “These shifts are leading us to
                       discontinue some initiatives, which is resulting in
                       several hundred roles being eliminated.”


                       Amazon didn’t specify which Alexa initiatives it’s
                       winding down as a result of the move.


                # ⚓ TechCrunch ☛ Sam_Altman_ousted_as_OpenAI’s_CEO⠀⇛


                       Sam Altman has been fired from OpenAI, Inc., the
                       501(c)(3) nonprofit that acts as the governing body
                       for OpenAI, the AI startup behind ChatGPT, DALL-
                       E 3, GPT-4 and other highly capable generative AI
                       systems. He’ll both leave the company’s board of
                       directors and step down as CEO.


                       In a post on OpenAI’s official blog, the company
                       writes that Altman’s departure follows a
                       “deliberative review process by the board” that
                       concluded that Altman “wasn’t consistently candid
                       in his communications” with other board members,
                       “hindering its ability to exercise its
                       responsibilities.”


                # ⚓ CS Monitor ☛ Starbucks_to_face_biggest_strike_on_one_of_its
                  busiest_days⠀⇛


                       The Workers United union says its expecting more
                       than 5,000 Starbucks workers to take part in its
                       one-day “Red Cup Rebellion” on Nov. 16. It’s the
                       largest strike yet in the effort to unionize the
                       company’s stores.


                # ⚓ Vice Media Group ☛ 'No_Contract,_No_Coffee':_Starbucks
                  Workers_Hold_Largest_Strike_in_Company_History⠀⇛


                       Workers participating in the "Red Cup Rebellion"
                       told Motherboard that all they were asking was that
                       the company come to the table with them.


                # ⚓ The Kent Stater ☛ ‘Red_Cup_Day’_protest_will_be_the_largest
                  strike_in_Starbucks_history⠀⇛


                       Thousands of Starbucks workers at hundreds of
                       stores will be on strike, as they protest the lack
                       of their first contract despite a nearly two-years
                       long organizing drive at the coffee chain.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong’s_unemployment_rate_edges
                  up_to_2.9%_from_four-year_low⠀⇛


                       Hong Kong’s jobless rate has edged up to 2.9 per
                       cent from a four-year low, following an increase in
                       unemployment in manufacturing and trade. The
                       seasonally adjusted unemployment rate rose from 2.8
                       per cent during July to September to 2.9 per cent
                       between August and October, according to figures
                       released Thursday by the Census and […]


                # ⚓ RFA ☛ US_Congress_pushes_sanctions_on_HK_pension,_judicial
                  issues⠀⇛


                       The moves would further batter the city’s
                       reputation, deal a blow to Beijing's credibility,
                       experts say.


                # ⚓ YLE ☛ Exploitation_of_foreign_workers_an_"open_secret"_in
                  Lapland_tourism_sector⠀⇛


                       Tourism is booming in Finnish Lapland, but the
                       industry faces growing questions over its treatment
                       of foreign workers.


                # ⚓ YLE ☛ Survey:_Half_of_recent_retirees_want_to_keep
                  working⠀⇛


                       Many of Finland's retirees remain keen to work even
                       after they start claiming their pensions, according
                       to a new survey.


                # ⚓ CS Monitor ☛ Inflation_is_falling_for_the_first_time_in_a
                  year._Why_now?⠀⇛


                       Inflation didn’t rise from September to October,
                       the first time that consumer prices haven’t moved
                       from one month to another in over a year. A new
                       report shows prices are down for just about
                       everything – from gas to airfares to home
                       appliances.


                # ⚓ WhichUK ☛ Inflation_plummets_to_4.6%_in_October_2023_–_and
                  half_of_all_savings_accounts_now_beat_it⠀⇛


                       Lower energy prices helped slow the rate at which
                       prices are rising


                # ⚓ France24 ☛ ‘Feminisation_of_poverty’:_France’s_cost-of-
                  living_crisis_is_hitting_women_hardest⠀⇛


                       Poverty is worsening in France and women and
                       children are the main victims, the charity Secours
                       Catholique has warned in its annual report,
                       highlighting the burden of inflation, childcare and
                       entrenched gender inequality on single women and
                       mothers.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Silicon Angle ☛ Meta_calls_for_new_legislation_around_how
                  teens_download_apps_from_app_stores [Ed: Way to spin the
                  troublemaker as solution seeker]⠀⇛


                       In what might be construed as a passing of the
                       buck, Meta Platforms Inc. today said the U.S. needs
                       new legislation that will require app stores to
                       receive parental approval before their kids can
                       download an app.


                # ⚓ Marcy Wheeler ☛ Election_Interference:_Aileen_Cannon_Denies
                  Republicans_Speedy_Trial_in_Stolen_Document_Case⠀⇛


                       Aileen Cannon has all but ensured that Republican
                       voters won't learn whether Donald Trump sold out
                       America's security before they choose to make him
                       their party's nominee.


                # ⚓ The Straits Times ☛ Old_photo,_birthday_wish,_ravioli
                  lunch:_Personal_diplomacy_on_display_during_Xi-Biden
                  meeting⠀⇛


                       Both presidents also pledged to pick up the phone
                       should the other call.


                # ⚓ CS Monitor ☛ At_Biden-Xi_summit,_the_voices_of_Taiwan⠀⇛


                       The summit’s reach for stability between the U.S.
                       and China relies on respect for Taiwan’s embrace of
                       democracy and independence.


                # ⚓ RFA ☛ Taiwan’s_opposition_parties_join_forces_in
                  presidential_race⠀⇛


                       Kuomintang, Taiwan People’s Party to offer a joint
                       ticket based on a controversial opinion poll.


                # ⚓ The Strategist ☛ Australia_should_be_clear_that_‘disagree
                  where_we_must’_means_disagreeing_with_Beijing_on_Taiwan⠀⇛


                       Prime Minister Anthony Albanese’s visit last week
                       to the People’s Republic of China was a reminder
                       that beyond the metrics of trade and the mechanics
                       of statecraft, the Australia–China relationship
                       carries deep meaning [...]


                # ⚓ New York Times ☛ Panda_Diplomacy_Might_Not_Be_Dead_Just
                  Yet⠀⇛


                       President Pooh-tin Jinping of China said his
                       country may keep sending giant pandas to the United
                       States. The National Zoo in Washington sent three
                       of them back to China last week.


                # ⚓ New York Times ☛ In_Talks_With_Biden,_Pooh-tin_Defends
                  China’s_Rise,_While_Seeking_to_Reassure⠀⇛


                       China’s depiction of Pooh-tin Jinping’s U.S. visit
                       reflected his sometimes-contradictory priorities:
                       to project both strength and a willingness to
                       engage with Washington.


                # ⚓ New York Times ☛ Day_After_Pooh-tin_Meeting,_Biden_Says
                  U.S._Has_‘Real_Differences’_With_China⠀⇛


                       Mr. Biden won applause when he noted that he and
                       Mr. Pooh-tin had agreed to resume military-to-
                       military communication to “reduce the risk of
                       miscalculation.”


                # ⚓ New York Times ☛ Biden_and_Pooh-tin_Make_Nice_Despite_U.S.-
                  China_Tensions⠀⇛


                       Despite simmering tensions, President Biden and
                       President Pooh-tin Jinping exchanged the kind of
                       pleasantries that adversarial leaders deploy when
                       they are trying to make nice.


                # ⚓ New York Times ☛ For_Biden,_a_Subtle_Shift_in_the_Power
                  Balance_With_China’s_Pooh-tin_Jinping⠀⇛


                       For the first time in years, a Chinese leader
                       desperately needed a few things from the United
                       States.


                # ⚓ CS Monitor ☛ From_anti-narcotics_to_US-China_military
                  contacts,_Biden-Xi_talks_make_headway⠀⇛


                       At their first face-to-face meeting since last
                       year, Pooh-tin Jinping and Joe Biden made several
                       small steps forward on repairing U.S.-China
                       relations. Perhaps the most important
                       accomplishment was laying groundwork for future
                       cooperation.


                # ⚓ The Straits Times ☛ Peru_President_Boluarte_talks_trade
                  boost_after_meeting_China's_Xi⠀⇛


                       Peruvian President Dina Boluarte met with Chinese
                       counterpart Pooh-tin Jinping on Thursday,
                       discussing major infrastructure projects and
                       possible investments, her office said on social
                       control media.


                # ⚓ New York Times ☛ China’s_Pooh-tin_Jinping_Draws_Elon_Musk,
                  Tim_Cook_and_Other_U.S._CEOs_to_Gala_in_San_Francisco⠀⇛


                       Amid frosty U.S.-China relations, Pooh-tin Jinping
                       emphasized friendship in an address to executives
                       from Apple, Boeing, Nike and others.


                # ⚓ TruthOut ☛ Poll_Shows_More_Than_Half_of_Americans_Want_More
                  Choices_for_President_in_2024⠀⇛


                # ⚓ TruthOut ☛ Joe_Manchin_Considers_2024_Run_—_Even_as_Polls
                  Show_Voters_Don’t_Like_Him_Much⠀⇛


                # ⚓ TruthOut ☛ George_Santos_Is_Not_Running_for_Reelection
                  After_Scathing_House_Ethics_Report⠀⇛


                # ⚓ The Straits Times ☛ Voter_support_for_Japan_PM_Kishida
                  slides_to_record_low:_Poll⠀⇛


                       Public support for Japanese Prime Minister Fumio
                       Kishida's government slid to a record low, a poll
                       conducted by Jiji news agency showed on Thursday,
                       as Kishida's tax cut plans to help cushion the blow
                       of rising inflation left voters unimpressed.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Bruce Schneier ☛ FTC’s_Voice_Cloning_Challenge⠀⇛


                             The Federal Trade Commission is running a
                             competition “to foster breakthrough ideas on
                             preventing, monitoring, and evaluating
                             malicious voice cloning.”


                      # ⚓ Meduza ☛ ’Teachers,_sales,_family_—_no_hot-button
                        issues’:_The_Kremlin’s_favorite_fake_news_factory
                        launches_its_own_polling_company_—_Meduza⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ Reason ☛ Academic_Freedom_Alliance_Protests_USC_Prof's_Ban
                  from_Campus⠀⇛


                       University of Southern California appears to ignore
                       its own policy to remove professor from campus over
                       alleged speech


                # ⚓ teleSUR ☛ Censorship_is_Out_of_Control:_Stella_Assange⠀⇛


                       Misinformation problems will not be resolved
                       because there are "revolving doors" between major
                       corporations and intelligence agencies.


                # ⚓ Reason ☛ Bans_on_Approaching_or_Videorecording_Hunters
                  Struck_Down_by_Seventh_Circuit⠀⇛


                       From Brown v. Kemp, decided Monday in an opinion by
                       Judge David Hamilton, joined by Judge Ilana Rovner:
                       [A Wisconsin law] makes it a crime to interfere
                       intentionally with a hunter by [two or more acts
                       of] "maintaining a visual or physical proximity" to
                       the hunter, by "approaching or confronting" the
                       hunter, or by photographing,…


                # ⚓ RFA ☛ China's_official_silence_on_Li_Keqiang's_death_hides
                  shock_and_fear⠀⇛


                       Li's fate as sidekick to Pooh-tin Jinping's
                       protracted power grab resonates deeply with many
                       officials.


                # ⚓ Project Censored ☛ Dark_Money,_Leonard_Leo,_and_the
                  Anachronistic_Supreme_Court⠀⇛


                       In How to Interpret the Constitution (2023),
                       Harvard law professor Cass Sunstein argues that any
                       theory of constitutional interpretation used by
                       Supreme Court justices must be defensible in terms
                       of beneficial outcomes, to make democracy “better.”
                       Better is subjective, though. Considering the
                       current Supreme Court, “better” begs the obvious
                       question, “Better for whom?”


                # ⚓ LRT ☛ Lithuanian_MP_Gražulis_stripped_of_immunity_over
                  homophobic_statements⠀⇛


                       The Lithuanian parliament on Thursday stripped MP
                       Petras Gražulis of his legal immunity so that he
                       can be investigated over suspected hate speech
                       towards LGBTQ+ people.


                # ⚓ New York Times ☛ Supreme_Court_Refuses_to_Revive_Florida
                  Law_Restricting_Drag_Shows⠀⇛


                       A federal judge in Orlando ruled that the law
                       violated the First Amendment, saying it was
                       “specifically designed to suppress the speech of
                       drag queen performers.”


                # ⚓ Meduza ☛ ‘I’m_behind_bars,_but_I’m_more_free_than_you’:
                  Chronicling_antiwar_activist_Sasha_Skochilenko’s_19-month
                  trial,_from_her_arrest_to_her_seven-year_prison_sentence,_in
                  photos_—_Meduza⠀⇛


                # ⚓ RFA ☛ Chinese_police_put_Tiananmen_artist,_film_director
                  under_travel_ban⠀⇛


                       Guo Zhenming won't be able to attend the Singapore
                       screening of his film about post-1989 dissident
                       malaise.


                # ⚓ Techdirt ☛ Indiana:_Another_Age_Verification_Bill
                  Criminalizing_Legal_Pornography⠀⇛


                       Another state lawmaker has introduced an age
                       verification bill looking to block minors’ access
                       to porn websites.


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


                # ⚓ RFERL ☛ Kyrgyz_Journalist_Guljan_Sheripbaeva_Detained_For
                  At_Least_48_Hours⠀⇛


                       The Kyrgyz State Committee of National Security has
                       detained journalist Guljan Sheripbaeva for at least
                       48 hours on unspecified charges.


          o § Civil Rights/Policing⠀➾


                # ⚓ RFERL ☛ Kazakh_Opposition_Leader_Continues_Hunger_Strike_In
                  Jail_To_Demand_Open_Trial⠀⇛


                       The lawyer for the chairman of the unregistered
                       Algha Kazakhstan party, Marat Zhylanbaev, said on
                       November 16 that his client had lost 13 kilograms
                       while on a hunger strike launched on October 30 to
                       protest against a court decision to hold his trial
                       behind closed doors.


                # ⚓ France24 ☛ Indonesia:_Rare_video_of_indigenous_tribe_facing
                  down_bulldozer_shows_‘uncontacted_peoples_do_exist’⠀⇛


                       On the Indonesian island of Halmahera, two members
                       of an “uncontacted” indigenous tribe were filmed
                       facing down a logging company’s bulldozer. The rare
                       encounter caught on camera testifies to the growing
                       threat that industrial activities – particularly
                       nickel mining managed in part by a French company –
                       pose to indigenous tribes. For members of an
                       indigenous rights NGO, the video serves as a
                       reminder to the government and companies that
                       uncontacted populations exist.


                # ⚓ TruthOut ☛ From_Death_Row,_Keith_LaMar_Has_Built_a_Movement
                  for_Love,_Art_and_Abolition⠀⇛


                # ⚓ RFA ☛ What_did_the_protesters_want_with_Pooh-tin_Jinping?⠀⇛


                       Xi's visit unites dissidents, Hong Kongers,
                       Tibetans, Uyghurs in 'tsunami' of protest, clashes
                       with Pooh-tin supporters.


                # ⚓ Hong Kong Free Press ☛ After_US_report_calls_Hong_Kong_a
                  ‘Chinese_rather_than_international_city,’_gov’t_slams
                  ‘slanders_and_smears’⠀⇛


                       Hong Kong’s government has “firmly rejected” a
                       report by a US Congressional commission, which said
                       the city now lives under the mainland’s control
                       after Beijing interfered with the judicial system
                       and weakened civil society. The US-China Economic
                       and Security Review Commission (USCC) submitted its
                       annual report to Congress on Tuesday.


                # ⚓ Hong Kong Free Press ☛ Tibet_activists_and_pro-China
                  supporters_stage_opposing_demos_in_San_Francisco_as_Pooh-tin
                  Jinping_joins_APEC_summit⠀⇛


                       San Francisco, United States Groups of Tibet
                       activists and pro-China supporters staged opposing
                       demonstrations in San Francisco on Wednesday as
                       Chinese President Pooh-tin Jinping visited the city
                       for an APEC summit.


                # ⚓ Techdirt ☛ Indiana’s_Top_Court_Adds_More_Due_Process_To
                  Forfeiture,_Says_A_Jury_Needs_To_Be_Part_Of_The_Process⠀⇛


                       The courts in Indiana have made significant moves
                       in recent years to do what the legislature won’t:
                       limit asset forfeiture abuse.


                # ⚓ RFA ☛ 12_men_in_tea_shop_massacred_by_junta_troops_for_no
                  apparent_reason⠀⇛


                       As Myanmar’s civil war rages on, 10 civilians are
                       killed in airstrikes in southern Chin state.


                # ⚓ Pro Publica ☛ A_Knoxville_Detention_Center_Illegally_Locks
                  Kids_Up_Alone⠀⇛


                       With a glint in his eye, Richard L. Bean reminisces
                       about the days when children in his detention
                       center could be paddled.


                       “We didn’t have any problems then,” Bean says. “I’d
                       whip about six or eight a year and it run pretty
                       smooth. They’d say, ‘You don’t want him to get hold
                       of you.’” Once, he chuckles, a kid had to be held
                       down by four guards to be spanked.


                # ⚓ Pro Publica ☛ This_Louisiana_Village_Brought_in_$1_Million
                  Through_a_Court_Where_the_Mayor_Is_the_Judge⠀⇛


                       The village of Fenton, outside the oil and gas town
                       of Lake Charles, covers only about 20 blocks.
                       There’s City Hall. The library. One gas station. A
                       small public housing complex. A Dollar General. A
                       grain elevator. A Baptist church. Drivers headed to
                       east Texas from central Louisiana go right through
                       town, passing it all in under a minute.


                       In many ways, Fenton is like other small towns in
                       Louisiana. But it is remarkable in one way: This
                       village of 226 people collected more money in a
                       single year through fines and forfeitures,
                       primarily traffic tickets, than almost any other
                       municipality in Louisiana, according to audits.


                # ⚓ Pro Publica ☛ When_Health_Insurers_Break_State_Laws⠀⇛


                       In North Carolina, lawmakers outraged that breast
                       cancer patients were being denied reconstructive
                       surgeries passed a measure forcing health insurers
                       to pay for them. In Arizona, legislators intervened
                       to protect patients with diabetes, requiring health
                       plans to cover their supplies. Elected officials in
                       more than a dozen states, from Oklahoma to
                       California, wrote laws demanding that insurance
                       companies pay for emergency services.


                       Over the last four decades, states have enacted
                       hundreds of laws dictating precisely what insurers
                       must cover so that consumers aren’t driven into
                       debt or forced to go without medicines or
                       procedures. But health plans have violated these
                       mandates at least dozens of times in the last five
                       years, ProPublica found.


                # ⚓ JURIST ☛ UK_Prime_Minister_promises_emergency_legislation
                  to_circumvent_ruling_against_controversial_asylum_plan⠀⇛


                       UK Prime Minister Rishi Sunak promised emergency
                       legislation and a new treaty with Rwanda Wednesday
                       to ensure his flagship asylum policy of sending UK
                       asylum-seekers to Rwanda is not blocked again after
                       the Supreme Court ruled it unlawful Tuesday.


                # ⚓ TruthOut ☛ New_Policy_Will_Ban_Chicago_Police_From_Joining
                  Hate_and_Extremist_Groups⠀⇛


                # ⚓ The Nation ☛ War,_What_Is_It_Good_For?⠀⇛


                # ⚓ RFA ☛ Former_lawmaker_dies_in_police_custody_after_arrest
                  for_Myanmar_scams⠀⇛


                       China issued warrants for Ming Xuechang and his
                       family members earlier this week.


                # ⚓ Atlantic Council ☛ Joseph_Nguramo_testifies_before_Congress
                  on_child_labor_in_Congo⠀⇛


                       Joseph Mulala Nguramo, nonresident fellow with the
                       Freedom and Prosperity Center, testified to the
                       Congressional Executive Commission on China on
                       November 14, 2023. He discussed China’s mining
                       practices in the Democratic Republic of Congo,
                       drawing attention to how China’s mining industry is
                       rampant with corruption and forced child labor of
                       Congolese citizens.


                # ⚓ Meduza ☛ Court_sentences_Navalny_associate_Vladimir_Milov
                  to_eight_years_in_absentia_—_Meduza⠀⇛


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ IPv6,_the_DNS_and_Happy_Eyeballs⠀⇛


                       Why mandating IPv6 DNS transport requires careful
                       thinking in specifications.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ The Kent Stater ☛ OPINION:_Are_movie_theaters_going
                  extinct?⠀⇛


                       Streaming services have been America’s number one
                       source for television and movies for quite some
                       time now. DRM spreader Netflix started streaming in
                       January of 2007 and ever since then, more and more
                       apps have popped up, easily replacing cable as the
                       go-to place to watch new television shows.


                # ⚓ Techdirt ☛ Apple’s_‘180_On_Right_To_Repair’_Was_Widely
                  Overstated⠀⇛


                       The consumer quest to be able to affordably repair
                       your own tech is going well, if you hadn’t noticed.
                       Maine just became the fourth state to implement
                       right to repair protections in the wake of laws
                       passed in New York, California, and Minnesota. As
                       that vote (84 percent of Maine voters approved)
                       illustrates, support for the movement is
                       significant and bipartisan.


                # ⚓ Techdirt ☛ Maine_Voters_Once_Again_Show_‘Right_To_Repair’
                  Reforms_Are_Overwhelmingly_Popular⠀⇛


                       Maine residents have made it very clear: the
                       overwhelming majority of Americans want to be able
                       to easily and affordably repair the stuff they own.
                       83 percent of Maine voters last week responded yes
                       to “Question 4,” asking whether automakers should
                       be required to provide car owners (and independent
                       repair shops) access to on-board diagnostic
                       systems:


          o § Monopolies⠀➾


                # ⚓ Mexico News Daily ☛ Google_faces_allegations_of_anti-
                  competitive_practices_in_Mexico⠀⇛


                       Google is again accused of monopolistic practices -
                       this time by Mexico's antitrust agency, for abusing
                       its market position in digital advertising.


                # ⚓ Silicon Angle ☛ Apple_moves_to_make_RCS_messaging_available
                  on_iPhones_amid_regulatory_scrutiny⠀⇛


                       Apple Inc. will finally enable iPhone and Android
                       users to exchange messages via the RCS
                       communications protocol. A company spokesperson
                       told 9to5Mac today that the feature is scheduled to
                       roll out next year.


                # ⚓ Silicon Angle ☛ Amazon_is_about_to_get_into_the_business_of
                  selling_cars⠀⇛


                       Amazon.com Inc. announced today that next year, it
                       will allow automakers to sell cars on its e-
                       commerce platform, starting with South Korean firm
                       Hyundai Motor Co.


                # § Patents⠀➾


                      # ⚓ JUVE ☛ Bayer_and_Simmons_&_Simmons_repel_Sandoz
                        nullity_suit_over_Xarelto [Ed: EPO kangaroo courts,
                        favouring low-quality and invalid patents to raise
                        money]⠀⇛


                             The current dispute between Bayer and Sandoz
                             revolves around EP 1 845 961, which describes
                             a dosage for Bayer’s thrombosis drug Xarelto
                             using the active ingredient rivaroxaban.
                             While the European Patent Office revoked EP
                             961 in the first instance in 2018 due to lack
                             of inventive step, the EPO Boards of Appeal
                             reinstated the patent monopoly...


                      # ⚓ Unified Patents ☛ 2023_Corporate_IP_Strategy
                        Conference_was_a_success!⠀⇛


                             The 2023 Corporate IP Strategy Conference
                             (CIPSC) was attended by over 200 IP
                             professionals, attorneys, and consultants
                             with several presentations and discussions on
                             the most thought-provoking IP issues of our
                             current times.


                      # ⚓ Dennis Crouch/Patently-O ☛ Predicting_Eligibility
                        [Ed: Patent maximalists upset to accept that patent
                        bubbles implode]⠀⇛


                             I have really enjoyed reading the new article
                             by Professors Rantanen and Datzov providing
                             empirical evidence that eligibility outcomes
                             are now quite predictable.  When the Supreme
                             Court decided Bilski back in 2010, I was
                             quite concerned about predictability and co-
                             authored a BTLJ article with Prof. Rob Merges
                             on the topic.  If you recall though, in
                             Bilski the Supreme Court offered no decision
                             making framework beyond suggesting a case by
                             case approach.  At the time, there were only
                             a sparse few prior cases to guide future
                             decisions.  But a more complete legal
                             framework was developed fairly quickly in the
                             subsequent cases of Alice Corp and Mayo, and
                             the lower courts decided several hundred
                             eligibility cases that provided substantial
                             guideposts that so often seek in our common
                             law system.


                      # ⚓ Hackaday ☛ Tech_In_Plain_Sight:_What_Does_A_Yellow
                        Light_Mean?⠀⇛


                             The traffic light is a ubiquitous feature of
                             modern life and is quite old — dating back to
                             1868 London, although that device was a
                             modified railroad semaphore operated by a
                             policeman, but it was the same idea. The
                             initial test of the signal proved disastrous.
                             The semaphore had gas lamps to illuminate the
                             signs in the dark. A gas leak caused one of
                             the lamps to explode, badly burning the
                             operator and ending the nascent invention for
                             a while. In 1910, American inventor Ernest
                             Sirrine worked out an automatically
                             controlled traffic signal. Two years later,
                             Lester Wire, a police officer, developed a
                             different version powered by overhead trolley
                             wires to light the signal. A 1917 patent by
                             William Ghiglieri also had two lights — red
                             and green. But where was the yellow light?


                # § Copyrights⠀➾


                      # ⚓ Public Domain Review ☛ Modernity_in_the_Rainforest:
                        Man_and_his_Desire_(1917)⠀⇛


                             Handmade book showing Paul Claudel's
                             scenario, with illustrations by Audrey Parr
                             and Hélène Hoppenot, for Darius Milhaud's
                             ballet *L'homme et son desir*.


                      # ⚓ Techdirt ☛ Error_402:_Searching_For_Ways_To_Pay_For
                        Content⠀⇛


                             Last week in our Error 402 series on the
                             history of web monetization, we wrote about
                             the earliest forms of web advertising: banner
                             ads. As we noted, this “simple” way of making
                             money seemed to derail other forms of
                             monetization, including early attempts at
                             paywalls (which had many other problems and
                             were destined to fail). Either way, though,
                             the success of ads as a way of funding
                             content online in the mid to late 90s of the
                             original dot com boom certainly meant that
                             much less attention was paid to other ways to
                             monetize content on the web.


    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ hello!⠀⇛


                       i could have sworn it was morning here but the
                       moment i stepped into the pub it seems like it
                       quickly became midnight somehow. imagine that!
                       either way, i think i'll have some green tea for
                       now.


                # ⚓ A_High_Probability_that_I_Believed_It⠀⇛


                       On the drive up to Lubbock from Seminole today for
                       my father's surgery, I was suddenly gripped by the
                       memory of lying on my back on the floor of Jenn
                       DuBois's apartment in Galveston. Dave was also
                       present, and later that same evening he
                       appropriated my truck. And luckily, my SHOVEL,
                       which incidentally was one of my brilliant gifts
                       for the beginning of the 23rd year of my life, was
                       in the "toolbox" that stretched from side to side
                       in the bed of the truck. More about that later.


                # ⚓ Urney.xyz_-_1974⠀⇛


                       Dear outsider, I'm happy to announce you that I'm
                       alive; hope you care. I'm writing you from the
                       post-apocalypse, the country formerly known as
                       Rhedesia. In the good times, before we all went
                       zombi and had the obese daddy of a civil war, mommy
                       took me to the mall and we ate ice-cream. I can't
                       remember the taste of vanilla, but the dance and
                       the music of that day, I haven't forgotten. That's
                       all gone when we started killing each other and
                       you, the rest-of-the-world locked us in and threw
                       the key. I can't blame you, really, I can't; you
                       owe it to your own children, I suppose.


          o § Games⠀➾


                # ⚓ 1974_starting_a_new_gamebook⠀⇛


                       Just started a gamebook called 1974, about a family
                       living in a local post-apocalypse. The idea is that
                       some fictional country, Redhesia, got into a civil
                       war bad enough to lead to a local collapse in
                       civilization. The outside world has done little but
                       locked them in, patrolling every border so that the
                       "dangerous" refugees cannot come into
                       "civilization".


          o § Technology and Free Software⠀➾


                # ⚓ Adless_Kineto⠀⇛


                       Here is a branch of Kineto that doesn’t have the
                       “details” at the bottom, making the pages look more
                       like they belong on the web and less like an ad for
                       Kineto.


                # ⚓ Re:_I_gave_emacs_a_serious_look_back_in_the_day⠀⇛


                       So, something that changed my life as an Emacs user
                       was Helm-Mode fuzzy completion. How it works on my
                       setup is I press a key-chord (META-SHIFT-3) and
                       then I can type two or three characters from ANY
                       available emacs command, and it will fetch the
                       command that it thought I meant. I can either press
                       ENTER to use that command, or press down arrow (or
                       CTRL-n) to get to one of the other likely matches.
                       It is fuzzy search, so I can type characters from
                       any part of the command (e.g., "v l i" will bring
                       up the "visual-line-mode" command). It keeps track
                       of my history, so 99% of the time it guesses
                       correctly, and the rest of the time the command I
                       want is one or two entries down. I can also keep
                       typing more letters to clarify.


                # ⚓ Defaults⠀⇛


                # ⚓ Re:_Defaults⠀⇛


                # ⚓ This,_that,_and_Re:_Defaults⠀⇛


                       It was fun to come across a gemlog post speaking to
                       "org-mode" after recent emacs remembrances.


                       Pride cometh before a fall because that's what
                       individuality is.


                # § Internet/Gemini⠀➾


                      # ⚓ Sustainability_doubts⠀⇛


                             Gemini is feeling like /dev/null again.


                             Don't get me wrong. We're talking lots of
                             really interesting people writing fairly
                             interesting things. And I can't tell you how
                             impressed I am with @skyjake for creating
                             gemini://bbs.geminispace.org/ and the
                             Lagrange browser.


                      # ⚓ [Old]_Will_this_content_will_be_lost⠀⇛


                             I remember I was new to internet world, I
                             created a site, started writing articles
                             thinking all will be live forever. But I
                             change few sites playing with domain names,
                             ideas etc.


                             Then I discovered thoughts.com and I started
                             writing poetry, blogs and was engaging with
                             audience.


                             It greed my post views and comments. This was
                             new to me, I thought this content will be
                             forever, I can show this to my grandchildren
                             what their grandfather was writing in his
                             teenage. Later due to study i left platform
                             for some time, And after a while when I
                             opened my site, it was 404. The platform was
                             discontinued.


                      # ⚓ Sustainability_doubts⠀⇛


                             But back to Gemini: the sense of content
                             getting lost starts about half an instant
                             after a post publishing.


                             You'd think this would be easy to solve. But
                             such thinking wouldn't take into account the
                             stultifying physical/conceptual isolation of
                             individuals.


                      # ⚓ Sending_plain_text,_would_like_to_send_gemtext⠀⇛


                             So I have my first gamebook running... a very
                             little thing, but I'm encountering a problem,
                             the client is interpreting the result as
                             plain text, as per the default, but I'd like
                             to show it as gemtext and I don't know how to
                             do that.


                      # ⚓ Urney.xyz_-_First_Story⠀⇛


                             This is a short and simple gamebook,
                             comprising 4 sections. Its main purpose is to
                             teach myself how to do interactive fiction on
                             Gemini.


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





                    ䷩ 𝚕𝚒𝚗𝚎 6108

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 18/11/2023: OpenAI’s Management in
Disarray and Twitter (X) in More Trouble⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Nov 18, 2023


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Patents
                # Copyrights
    * Gemini*_and_Gopher
          o Personal/Opinions
          o Politics_and_World_Events
          o Misc
          o Technology_and_Free_Software
                # Internet/Gemini
                # Programming
    * § Leftovers⠀➾


          o ⚓ Dedoimedo ☛ Greatest_sites_on_the_Internet⠀⇛


                 The title of this page is one of the most inaccurate
                 statements in the world. This is because my view of the
                 World Wide Web might not be your view of the World Wide
                 Web. Over the year, there has been a small, select number
                 of websites that have really impressed me with their
                 overall feel, functionality and usefulness, the
                 uniqueness of design and the quality of content that I
                 felt I should spare them their own special corner on
                 Dedoimedo.


                 There is no particular order to the listed sites - you
                 should really invest a little bit of time and check them
                 all. Moreover, I assigned categories, which roughly
                 denote the spirit and/or nature of these domains, e.g.
                 humor, science, art, unique, games, etc. Since the
                 Dedoimedo theme revamp in early 2018, new entries will be
                 added to the top of the list. If you have website
                 suggestions that you feel like might be worthy of
                 inclusion, don't hesitate to contact me, but please make
                 sure to clearly state your affiliation. Enjoy!


          o ⚓ Dhole Moments ☛ This_Would_Be_More_Professionally_Useful_If_Not
            For_the_Furry_Art⠀⇛


                 Even some old school hackers conveniently forget that
                 alt.fan.furry was a thing before the Internet.


                 As frustratingly incompetent as these hot takes are, they
                 pale in comparison to, by far, the biggest source of bad
                 opinions about the furry fandom.


          o ⚓ Ruben Schade ☛ “That’s_not_how_that_works!”⠀⇛


                 The challenge with such requests isn’t that they’re
                 merely impossible (how inconvenient!), but that they’re
                 often coming from a place of misunderstanding. This means
                 that to grok why something can’t or shouldn’t be done,
                 preconceived ideas and prior learning need to be
                 unravelled. But people making such demands are generally
                 not as receptive to this; they just want the damned
                 feature added, and the boffins are standing in the way.


          o § Hardware⠀➾


                # ⚓ The Drone Girl ☛ Detroit:_from_Motor_City_to_Drone_City?⠀⇛


                       The Michigan Department of Transportation (MDOT) in
                       partnership with a tech project called Michigan
                       Central announced the launch of the “Advanced
                       Aerial Innovation Region” (AAIR). The initiative
                       was established to position Detroit and the broader
                       state of Michigan as a leader in next-generation
                       aerial mobility and drone technology. Its goal? To
                       attract startups, to catalyze new high-skill jobs,
                       to advance policy and ultimately to drive
                       commercialization and adoption of drone technology.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ NBC ☛ Global_decline_in_male_fertility_linked_to_common
                  pesticides⠀⇛


                       The new analysis focuses on two groups of chemicals
                       — organophosphates and some carbamates — that are
                       commonly used in insecticides. The researchers
                       looked at data collected from groups of people with
                       exposures to pesticides and others who were not.
                       Most, but not all, of the research centered on
                       exposures in the workplace. The researchers
                       controlled for outside factors that could
                       contribute to lower sperm counts like smoking and
                       age.


                       “It was very well done, very carefully done, very
                       comprehensive,” Meeker said.


                # ⚓ Shot_Dead:_A_particularly_disgusting_piece_of_antivax
                  propaganda⠀⇛


                       A couple of days ago, I wrote about how a new study
                       published recently is yet another compelling piece
                       of evidence arguing that the antivax “died
                       suddenly” conspiracy theory in which COVID-19
                       vaccines are supposedly causing a wave of sudden
                       death among younger people is not a real thing.
                       Basically, the study showed that sudden cardiac
                       deaths among college athletes, contrary to what
                       antivaxxers claim about such deaths among young
                       people in general and athletes in particular, are
                       not skyrocketing. Quite the contrary. They’re
                       slowly declining, most likely because of better
                       protocols for resuscitation, required screening of
                       student athletes for the gene mutations and
                       congenital heart anomalies that most frequently
                       lead to sudden cardiac death, as well as the
                       increased availability of automated external
                       defibrillators (AEDs). Ironically, almost at the
                       same time, a group called We The Patriots USA
                       released a movie very much in the “died suddenly”
                       vein, but of an older type than, for instance, Died
                       Suddenly, the movie that pulled together all the
                       conspiracy mongering about COVID-19 vaccines
                       supposedly causing mass death. Never mind that
                       several of the deaths shown happened before the
                       pandemic. After all, what’s stretching the truth a
                       bit among conspiracy theorists?


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ India Times ☛ France's_Macron_warns_against_'punitive'_AI
                  regulation⠀⇛


                       The European Union must avoid overly restrictive
                       regulation of artificial intelligence technologies,
                       French President Emmanuel Macron said Friday.
                       "Regulation must be controlled, not punitive, to
                       preserve innovation," Macron said of the EU's
                       efforts.


                # ⚓ Rachel ☛ My_rants_about_TP-Link_Omada_networking_products⠀⇛


                       But no, this isn't about that. This is about TP-
                       Link. I was pointed at this ecosystem as a possible
                       escape from the clowntown that is Ubiquiti, so
                       that's what I bought this time around: one of their
                       gateway boxes (calling it a router would be too
                       kind), a switch, and a hardware controller for
                       local control - none of that cloud crap here,
                       thanks.


                       It's been a new bit of stupid every week with this
                       stuff. First of all, the switch is really best
                       suited for a closet at a business, not anywhere in
                       someone's home. It has dinky little fans that run
                       pretty hard all the time, with all the noise that
                       entails. People who replace them invariably get fan
                       errors and then the thing eats itself within a
                       year. (Maybe the switches fail by themselves either
                       way - the jury is still out on that.)


                # ⚓ Insight Hungary ☛ Hungarian_journalists_and_activists_were
                  targeted_by_spy_firm,_Linkedin_says⠀⇛


                       Black Cube, an Israeli private intelligence firm,
                       orchestrated a video campaign using LinkedIn to
                       target Hungarian activists and journalists in the
                       lead-up to last year's election, according to the
                       professional networking site. LinkedIn researcher,
                       Mona Damian, revealed that Black Cube established a
                       network of fake personas utilizing deceptive job
                       postings to connect with targets on the platform.
                       Subsequent off-platform video conversations were
                       recorded, and clips from these interactions were
                       employed in a campaign to discredit NGOs in
                       Hungary. The LinkedIn researcher reported the
                       removal of a network of fake Black Cube-run
                       accounts and the deletion of Black Cube's LinkedIn
                       company page due to a "high volume of abuse and a
                       clear violation of our terms of service."


                       LinkedIn did not disclose the party Black Cube may
                       have been working for and did not provide details
                       on the number of fake accounts removed. The
                       Hungarian government spokesperson did not respond
                       to inquiries.


                # ⚓ The Telegraph UK ☛ ‘Being_deepfaked_showed_me_how_easy_it
                  is_to_hack_a_bank_account’⠀⇛


                       I’ve been deepfaked, a process that technology has
                       made easy. A picture was taken of me on a
                       smartphone and seconds later, anyone in the lab
                       could become me – at least online.


                       Deepfaking sees one person take on the face or even
                       the voice of another digitally, meaning they can
                       take pictures and videos as if they were the person
                       they’ve copied. It’s essentially a filter.


                # ⚓ India Times ☛ How_Walmart_is_using_AI_and_Gen_AI⠀⇛


                       Beginning this holiday season, the systems will
                       also use predictive analytics to optimize
                       catchments and connect with driver availability, so
                       that drivers can complete more deliveries, with
                       less driving, delivering multiple items in one
                       trip. Today, the catchments are of equal size, but
                       AI will now begin optimizing the size based on
                       local demand and need.


                # ⚓ IT Wire ☛ 77%_of_organisations_are_investing_in_artificial
                  intelligence_solutions_to_bolster_their_Quality_Engineering:
                  report⠀⇛


                       According to Capgemini and OpenText, the use of AI
                       is on the rise in quality engineering, but an
                       incremental approach is key - and trends in the use
                       of AI to deliver quality outcomes are moving fast -
                       while organisations cite for the first time, higher
                       productivity as the primary outcome driven by AI
                       (65%), with Generative AI making it possible
                       increased productivity and velocity, leading to
                       more frequent deployments with a higher quality
                       customer experience.


                # ⚓ Computer World ☛ Dell_cuddles_up_to_Hugging_Face_to_offer
                  genAI_to_customers⠀⇛


                       The service means Dell will consult with a client
                       who uses Hugging Face to pick an open-source AI
                       model that best fits its needs. Dell then takes the
                       model, optimizes it for the Dell PowerEdge server,
                       and provides it to the customer as a “container” it
                       can run on its on-prem server — either a new one
                       they buy from Dell or one they already have,
                       according to Gold.


                # ⚓ IEEE ☛ Just_Calm_Down_About_GPT-4_Already:_And_stop
                  confusing_performance_with_competence,_says_Rodney_Brooks⠀⇛


                       It’s a textbook example of the mixture of amazement
                       and, especially, anxiety that often accompanies a
                       tech triumph. And we’ve been here many times, says
                       Rodney Brooks. Best known as a robotics researcher,
                       academic, and entrepreneur, Brooks is also an
                       authority on AI: he directed the Computer Science
                       and Artificial Intelligence Laboratory at MIT until
                       2007, and held faculty positions at Carnegie Mellon
                       and Stanford before that. Brooks, who is now
                       working on his third robotics startup, Robust.AI,
                       has written hundreds of articles and half a dozen
                       books and was featured in the motion picture Fast,
                       Cheap & Out of Control. He is a rare technical
                       leader who has had a stellar career in business and
                       in academia and has still found time to engage with
                       the popular culture through books, popular
                       articles, TED Talks, and other venues.


                       IEEE Spectrum caught up with Brooks at the recent
                       Vision, Innovation, and Challenges Summit, where he
                       was being honored with the 2023 IEEE Founders
                       Medal. He spoke about this moment in AI, which he
                       doesn’t regard with as much apprehension as some of
                       his peers, and about his latest startup, which is
                       working on robots for medium-size warehouses.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Federal Trade Commission ☛ The_FTC_Voice_Cloning
                        Challenge⠀⇛


                             Voice cloning technology is becoming
                             increasing sophisticated due to improving
                             text-to-speech AI. The technology offers
                             promise, including medical assistance for
                             people who may have lost their voices due to
                             accident or illness. It also poses
                             significant risk: families and small
                             businesses can be targeted with fraudulent
                             extortion scams; creative professionals, such
                             as voice artists, can have their voices
                             appropriated in ways that threaten their
                             livelihoods and deceive the public.


                             The FTC is running an exploratory challenge
                             to encourage the development of
                             multidisciplinary approaches—from products to
                             policies to procedures—aimed at protecting
                             consumers from AI-enabled voice cloning
                             harms, such as fraud and the broader misuse
                             of biometric data and creative content. The
                             goal of the Challenge is to foster
                             breakthrough ideas on preventing, monitoring,
                             and evaluating malicious voice cloning.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Torrent Freak ☛ Dozens_of_VPNs_&_Shadowsocks_Named_in
                        Leaked_Russian_Blocking_Document⠀⇛


                             A document originating from Russia's Ministry
                             of Transport shines more light on the
                             government's plans to crack down on
                             encryption tools that help people to evade
                             monitoring and censorship. The leaked
                             document lists dozens of VPN service targets
                             and, for the first time, open source
                             encryption protocol Shadowsocks, best known
                             for its ability to evade firewalls, one in
                             China especially.


                      # ⚓ [Old] Sundial Services International LLC ☛ Why_Your
                        Web_Site_Should_Be_"Advertisement_Free"⠀⇛


                             The trouble is that this very-identifiable
                             information is sent, first to the broker,
                             then to every advertiser who is bidding. This
                             is a tremendous amount of personal
                             information to be "spewing," and you have no
                             idea where it goes. Neither does your
                             unsuspecting site visitor. Many advertisers
                             bid only enough to keep the advertising-
                             broker interested: the data that they really
                             want to "harvest" is the bid requests
                             themselves.


                      # ⚓ Chris ☛ How_Not_To_Collect_Data⠀⇛


                             Asking customer service representatives to
                             record every single interaction might be a
                             bit excessive on the bureaucracy.2 This is
                             typical of what anthropologist Marilyn
                             Strathern calls audit cultures. We don’t want
                             to micro-manage, but we also don’t trust
                             people to self-monitor, so we impose
                             bureaucracy that ensure mechanised self-
                             monitoring processes are followed – and in
                             the end, this bureaucracy becomes micro-
                             managing. Making matters worse, people start
                             to rest against the bureaucracy instead of
                             self-monitoring, which lowers quality
                             further.3


                      # ⚓ Latvia ☛ Security_service_to_publish_job_vacancies
                        online⠀⇛


                             One of Latvia's three security services, the
                             Constitution Protection Bureau (Satversmes
                             aizsardzības birojs, SAB), may necessarily
                             rely upon a certain amount of secrecy in
                             performing its tasks, but is becoming more
                             open in at least one respect: recruitment.


          o § Defence/Aggression⠀➾


                # ⚓ Axios ☛ Where_efforts_to_disqualify_Trump_from_2024_ballot
                  stand⠀⇛


                       The big picture: At least 31 cases filed across the
                       U.S. that have argued the Republican presidential
                       front-runner should be disqualified over his
                       actions surrounding the U.S. Capitol riot through
                       the 14th Amendment's insurrection clause.


                       More than a dozen cases remain pending before the
                       courts.


                       Context: Section 3 of the 14th Amendment states
                       that no one should hold office in the U.S. if they
                       "have engaged in insurrection or rebellion against
                       the [U.S.], or given aid or comfort to the enemies
                       thereof."


                # ⚓ Hindustan Times ☛ US_house_speaker_to_release_over_40,000
                  hours_of_Capitol_[insurrection]_video⠀⇛


                       The thousands of hours of surveillance footage have
                       already been reviewed by a congressional committee
                       that investigated the attack on Congress


                       More than 40,000 hours of security video from the
                       January 6, 2021 attack on the US Capitol is to be
                       released to the public, the new Republican speaker
                       of the House of Representatives said Friday.


                # ⚓ teleSUR ☛ Over_1,200_Migrants_Reach_Italy's_Island_in_26
                  Hours⠀⇛


                       The Western African migration route to Europe has
                       seen "the biggest rise in the number of irregular
                       crossings, which nearly doubled so far this year to
                       over 27,700," the European Border and Coast Guard
                       Agency (Frontex) said, adding that the number of
                       arrivals registered in October -- some 13, 000 -
                       - was the highest monthly figure on record.


                # ⚓ The Economist ☛ Donald_Trump_poses_the_biggest_danger_to
                  the_world_in_2024⠀⇛


                       But knowing that America would abandon Europe, Mr
                       Putin would have an incentive to fight on in
                       Ukraine and to pick off former Soviet countries
                       such as Moldova or the Baltic states. Without
                       American pressure, Israel is unlikely to generate
                       an internal consensus for peace talks with the
                       Palestinians. Calculating that Mr Trump does not
                       stand by his allies, Japan and South Korea could
                       acquire nuclear weapons. By asserting that America
                       has no global responsibility to help deal with
                       climate change, Mr Trump would crush efforts to
                       slow it. And he is surrounded by China hawks who
                       believe confrontation is the only way to preserve
                       American dominance. Caught between a dealmaking
                       president and his warmongering officials, China
                       could easily miscalculate over Taiwan, with
                       catastrophic consequences.


                # ⚓ Media Matters ☛ Elon_Musk_praises_antisemitic_replacement
                  theory_that_motivated_a_mass_shooting_as_“the_actual_truth”⠀⇛


                       Musk’s platform, ostensibly run by CEO Linda
                       Yaccarino, has said that posts claiming “Hitler was
                       right” and that there needs to be a “final
                       solution” regarding Jewish people don’t violate the
                       platform’s “safety policies”; run ads for major
                       brands on Holocaust denial accounts; and apparently
                       paid a pro-Hitler Holocaust denial a share of its
                       ad revenue.


                       Indeed, Musk and Yaccarino have reinstated known
                       white nationalists and antisemites on the platform.
                       Musk has directly engaged with some of the
                       reinstated antisemitic accounts and amplified
                       conspiracy theories that were used to push
                       antisemitism. Musk’s posts earlier this year earned
                       the praise of a leading neo-Nazi.


                # ⚓ NBC ☛ Antisemites_are_saying_Elon_Musk_is_on_their_side
                  after_his_latest_tweets_about_Jews⠀⇛


                       “At a time when antisemitism is exploding in
                       America and surging around the world, it is
                       indisputably dangerous to use one’s influence to
                       validate and promote antisemitic theories,” he
                       wrote on X, with a screenshot of Musk’s six-word
                       tweet.


                # ⚓ The Hill ☛ Haley_cites_viral_bin_Laden_letter_in_call_for
                  social_media_reform⠀⇛


                       “[W]hen you look at social media, I have long said
                       that we have to ban TikTok,” Haley, a 2024 GOP
                       presidential primary candidate, said on Fox News
                       Radio’s “The Guy Benson Show.” “And if you didn’t
                       know why, there’s another example today.”


                       “They are posting letters of Osama bin Laden’s
                       letter, the week after the 9/11 attack, and it is
                       the justification for why he did it,” Haley
                       continued. “And so you have a lot of our kids
                       sitting there siding with that, that ‘Oh, America
                       deserved it at that time.’”


                # ⚓ Computer World ☛ Meta_and_ByteDance_dispute_gatekeeper
                  status_of_platforms_under_EU’s_DMA⠀⇛


                       Meta and ByteDance, the parent company of TikTok,
                       have launched a challenge against the gatekeeper
                       status designated to them by the European
                       Commission under the EU's Digital Markets Act.


                       The DMA came into force in September 2023 and is
                       designed to rein in the power of large tech
                       corporations, requiring them to change how they
                       integrate digital services and handle customer data
                       while also addressing issues including the right to
                       uninstall software on devices, greater personal
                       data access controls, enhanced advertising
                       transparency, an end to vendors self-preferencing
                       their own services, and a stop to certain
                       restrictive app store requirements for developers.


                # ⚓ NPR ☛ The_election_interference_case_against_Trump_is
                  taking_shape⠀⇛


                       The case set for trial in Washington, D.C., in
                       March accuses Trump of leading a conspiracy to
                       obstruct the certification of the 2020 election and
                       deprive millions of voters from having their
                       ballots count. More than 140 law enforcement
                       officers suffered injuries after a mob stormed the
                       U.S. Capitol on Jan. 6, disrupting the peaceful
                       transfer of power.


                # ⚓ Kansas Reflector ☛ Colorado_judge_rejects_attempt_to_bar
                  Trump_from_2024_ballot_under_‘insurrection’_clause⠀⇛


                       In a 102-page ruling, Wallace accepted many of the
                       plaintiffs’ core claims about Trump’s actions on
                       Jan. 6, and rejected arguments from Trump’s legal
                       team that his messages to his supporters, including
                       incendiary social media posts and a speech at the
                       White House Ellipse just prior to the violence at
                       the Capitol, was protected speech under the First
                       Amendment.


                       “The Court concludes … that Trump incited an
                       insurrection on Jan. 6, 2021 and therefore
                       ‘engaged’ in insurrection within the meaning of
                       Section 3 of the 14th Amendment,” Wallace wrote.


                # ⚓ RFERL ☛ Kyrgyzstan_Mulls_Banning_Women's_Islamic_Niqab,
                  Men's_Bushy_Beards_Over_'Security_Fears'⠀⇛


                       The parliament of the former Soviet republic of
                       some 7 million has unveiled a bill that would ban
                       women from putting on the all-covering niqab and
                       prohibit men from growing long beards to preserve
                       “public security.”


                       The bill, released for public discussion on
                       November 14, says the measures are needed so that
                       people’s faces can be seen and individuals
                       identified.


                # ⚓ TruthOut ☛ Sanders_Doubles_Down_Against_Gaza_Ceasefire_in
                  the_Face_of_Progressive_Backlash⠀⇛


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ The Dissenter ☛ Australian_Whistleblower_Who_Exposed_War
                  Crimes_In_Afghanistan_Forced_To_Plead_Guilty⠀⇛


          o § Environment⠀➾


                # ⚓ Security Week ☛ 2_Environmentalists_Who_Were_Targeted_by_a
                  Hacking_Network_Say_the_Public_Is_the_Real_Victim⠀⇛


                       Two environmentalists told a federal judge Thursday
                       that the public was the real victim of a global
                       computer hacking campaign that targeted those
                       fighting big oil companies to get the truth out
                       about global warming.


                # ⚓ Teen Vogue ☛ The_EPA_Launches_Youth_Council_of_Gen_Z_and
                  Millennials⠀⇛


                       Sixteen young people will launch a new program with
                       Environmental Protection Agency (EPA) administrator
                       Michael S. Regan, beginning November 16. In an
                       exclusive report with Teen Vogue, the National
                       Environmental Youth Advisory Council (NEYAC) has
                       announced it will provide independent advice and
                       recommendations on behalf of youth communities
                       regarding EPA efforts.


                # ⚓ NPR ☛ "It_feels_like_I'm_not_crazy."_Gardeners_aren't
                  surprised_as_USDA_updates_key_map.⠀⇛


                       This week the map got its first update in more than
                       a decade, and the outlook for many gardens looks
                       warmer. The 2023 map is about 2.5 degrees
                       Fahrenheit warmer than the 2012 map across the
                       contiguous U.S., says Chris Daly, director of the
                       PRISM Climate Group at Oregon State University that
                       jointly developed the map with the USDA.


                       Daly says the new map means about half the country
                       has shifted into a new half zone and half hasn't.
                       In some locations, people may find they can grow
                       new types of flowers, fruits, vegetables and
                       plants.


                       Many of the nation's gardeners are not surprised by
                       the change.


                # ⚓ International Business Times ☛ Microplastics_Found_In
                  Clouds_Could_Affect_Weather_Pattern:_Study⠀⇛


                       A study published in the journal "Environmental
                       Science & Technology Letters" has claimed that
                       these could affect cloud formation and, as a
                       result, weather.


                       The research found that microplastics are being
                       carried along by clouds to different places.


                # ⚓ DeSmog ☛ Nigel_Farage’s_Reform_Party_Took_£135,000_from
                  Climate_Science_Deniers_and_Fossil_Fuel_Interests⠀⇛


                       Donors registered this year include: a firm owned
                       by Terence Mordaunt, a director of the Global
                       Warming Policy Foundation (GWPF), the UK’s leading
                       climate science denial group; political donor
                       Jeremy Hosking, who has millions invested in fossil
                       fuels; and a property investment firm whose
                       chairman has defended those who question whether
                       “global warming is happening”.


                       The revelations come after DeSmog reported that
                       hedge fund founder Paul Marshall, co-owner of GB
                       News – which has both Farage and Tice on its
                       payroll – has £1.8 billion invested in fossil
                       fuels.


                # ⚓ Deutsche Welle ☛ Who_pays_for_climate_damage_and_where_does
                  the_money_go?⠀⇛


                       Fossil fuels powered the industrial revolution and
                       the economic success of many countries. But burning
                       oil, gas and coal produces greenhouse gases that
                       warm the atmosphere and warp the climate.


                       Advanced industrialized nations have historically
                       contributed most to the human-induced climate
                       crisis because they've burned fossil fuels for so
                       long to grow their economies.


                       And many analysts, activists and heads of state in
                       low-income countries argue big historical emitters
                       like the United States and Europe should largely
                       foot the bill for climate change.


                # ⚓ LRT ☛ Protesters_in_Vilnius_call_for_stop_to
                  deforestation⠀⇛


                       Around 100 people gathered in the square by the
                       Lithuanian parliament in Vilnius to protest against
                       clear-cutting of forests in protected areas.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ CoryDoctorow ☛ Red-teaming_the_SCOTUS_code_of_conduct⠀⇛


                       This string of scandals and outrages naturally
                       prompted public curiosity about the Supreme Court's
                       ethical standards, and that triggered fresh waves
                       of incredulous outrage when we all found out that
                       the Supreme Court doesn't have any: [...]


                # ⚓ New York Times ☛ X_Races_to_Contain_Damage_After_Elon_Musk
                  Endorses_Antisemitic_Post⠀⇛


                       X employees said on Thursday that they had gotten
                       calls from advertisers wondering why Mr. Musk was
                       making comments seen as antisemitic and why their
                       ads were showing up next to white nationalist and
                       Nazi content, according to internal messages that
                       were viewed by The New York Times. IBM cut off
                       about $1 million in advertising spending that it
                       had committed to the platform for the last three
                       months of the year, the messages said.


                # ⚓ Futurism ☛ Apple_Drops_Ads_on_Twitter_After_Elon_Musk’s
                  Antisemitic_Outburst⠀⇛


                       Although Musk's hired punching bag CEO Linda
                       Yaccarino issued a milquetoast statement saying the
                       social network is against "discrimination by
                       everyone," the X owner's latest unmasked act of
                       bigotry has, along with the advertiser exodus,
                       earned him condemnation from the White House as
                       well.


                # ⚓ Variety ☛ IBM_Immediately_Suspends_Advertising_From_X/
                  Twitter_After_Discovering_Its_Ads_Appeared_Next_to_Pro-Nazi
                  Content⠀⇛


                       IBM was among five major brands that progressive
                       watchdog group Media Matters said it had found ads
                       for adjacent to posts that “tout Hitler and his
                       Nazi Party” on X. The others were Apple,
                       NBCUniversal’s Bravo, Oracle and Comcast’s Xfinity.


                # ⚓ BBC ☛ IBM_suspends_ads_on_X_after_they_appeared_next_to
                  Nazi_posts⠀⇛


                       The left-leaning watchdog Media Matters for America
                       said it found ads bought by IBM and other companies
                       next to posts including Hitler quotes, praise of
                       Nazis and Holocaust denial.


                       One pro-Nazi post that was shown next to an IBM ad
                       was seen about 8,000 times, X said in a statement
                       to the BBC.


                       The other firms listed include Apple, Oracle,
                       television network Bravo and telecoms company
                       Xfinity. The BBC has approached the companies for
                       comment.


                # ⚓ BW Businessworld Media Pvt Ltd ☛ Amazon_To_Cut_Jobs_In
                  Alexa_Unit⠀⇛


                       While exact numbers remain undisclosed, the
                       decision is said to align with Amazon's increased
                       focus on generative artificial intelligence (AI)
                       and the optimisation of resources.


                       The job cuts are not confined to the Alexa unit
                       alone, as Amazon undertakes a broader restructuring
                       across various divisions. Recent reductions have
                       been witnessed in the music and gaming sectors,
                       along with adjustments in specific human resources
                       roles. The restructuring signals a company-wide
                       realignment, showcasing Amazon's adaptability to
                       evolving market dynamics.


                # ⚓ India Times ☛ Amazon_to_cut_'several_hundred'_Alexa_jobs⠀⇛


                       The cuts affect "several hundred" employees working
                       on Alexa, according to the email. A spokeswoman
                       declined to elaborate on exactly how many were
                       affected.


                # ⚓ The Nation ☛ Mike_Johnson,_Undoing_the_Constitution⠀⇛


                # ⚓ TruthOut ☛ Advocates_in_Nebraska_Want_the_Right_to_an
                  Abortion_on_the_2024_Ballot⠀⇛


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Quillette ☛ Hamas_Cheerleaders_Are_All_Over
                        Instagram⠀⇛


                             Even mainstream media outlets trying to act
                             in good faith have been caught repeating fake
                             news that’s been fed to them, directly or
                             indirectly, by Hamas. In other cases, online
                             opportunists, some of them with purely
                             financial motives, have exploited the 10/
                             7 attacks for personal gain, using AI-
                             generated imagery and pro-Hamas bots to flood
                             the [Internet] with clickbait.


                             [...]


                             Israel may have the upper hand in the
                             unfolding military conflict within Gaza. But
                             it is evident that Hamas and its allies are
                             winning over many youth by weaponizing the
                             pre-existing idioms of social-justice
                             advocacy. Since 2020, Instagram, like all
                             social-media platforms, has been awash with
                             dubious slideshows purporting to educate
                             users about “systemic racism,”
                             “decolonization,” and the need for non-white
                             people to rise up and “disrupt” our
                             supposedly white-supremacist western
                             societies. The formula worked as a means to
                             promote Black Lives Matter protests. And
                             anti-Israel groups are now seeking to copy
                             this formula in their campaign to support
                             Hamas.


          o § Censorship/Free Speech⠀➾


                # ⚓ TruthOut ☛ Pro-Palestine_Student_Group_Sues_Ron_DeSantis
                  for_Violating_Free_Speech_Rights⠀⇛


                # ⚓ Meduza ☛ Russian_government_authorizes_federal_censor_to
                  block_websites_with_instructions_for_bypassing_website
                  blocks⠀⇛


                       The Russian government has granted the country’s
                       federal censorship agency, Roskomnadzor, permission
                       to restrict access to websites that contain
                       information about circumventing Internet
                       censorship.


                # ⚓ [Repeat] teleSUR ☛ Censorship_is_Out_of_Control:_Stella
                  Assange⠀⇛


                       During the Portugal Web Summit on Thursday, lawyer
                       and human rights activist Stella Assange, the wife
                       of WikiLeaks founder Julian Assange, asserted that
                       the European Union (EU) imposes Internet
                       regulations under the pretext of controlling
                       misinformation.


                       "The EU loves this new era of misinformation
                       because it allows them to regulate the Internet
                       extensively," she said, adding that the institutes
                       and programs created to combat misinformation are
                       not genuinely effective.


                       "If there were any truth to their eagerness to stop
                       false information, then they would be the biggest
                       supporters of WikiLeaks and would promote the
                       WikiLeaks model as the best possible journalism.
                       But usually, those involved in all of this are the
                       staunchest critics of WikiLeaks because they see it
                       as a real threat," Stella pointed out.


                # ⚓ New York Times ☛ Russia_Sentences_Activist_to_Penal_Colony
                  for_Antiwar_Notes_on_Price_Tags⠀⇛


                       The artist, Aleksandra Y. Skochilenko, 33, was
                       found guilty on Thursday of spreading false
                       information about the Russian Army — a criminal
                       offense introduced shortly after Russia’s full-
                       scale invasion of Ukraine last year — for placing
                       the messages at her local supermarket in St.
                       Petersburg.


                # ⚓ RFA ☛ Protest_book_authors_'can't_return'_to_Hong_Kong_amid
                  crackdown⠀⇛


                       The authors of a new book on the Hong Kong protest
                       movement say they won't be able to return to the
                       city now, for fear of reprisals under a draconian
                       security law.


                       Shibani Mahtani and Timothy McLaughlin, whose in-
                       depth portrait of the 2019 protest movement "Among
                       the Braves" was published recently in New York,
                       said they had realized while researching the book
                       that there would likely be a trade-off between ease
                       of access to the city they once called home and
                       their ability to write freely about the movement.


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


                # ⚓ CPJ ☛ Russian_journalists_Aleksandr_Dorogov_and_Yan
                  Katelevskiy_sentenced_to_lengthy_prison_terms⠀⇛


                       The journalists repeatedly denied the charges and
                       claimed that their persecution stems from their
                       investigative work, in particular their joint
                       investigation into alleged corruption between
                       funeral businesses and senior police officials,
                       published on the YouTube account Dvizhenie, which
                       investigates corruption and irregularities by the
                       road police and has about 613,000 subscribers.


                # ⚓ Variety ☛ Gawker_Sold_to_Founder_of_Singapore’s_Caldecott
                  Music_Group:_‘It_Has_the_Opportunity_for_Reinvention’_
                  (EXCLUSIVE)⠀⇛


                       Meng Ru Kuok, CEO and founder of Singapore-based
                       Caldecott Music Group, acquired the assets of
                       Gawker from Bustle Digital Group. In an email to
                       Variety, Kuok confirmed that he has closed the deal
                       buying the Gawker trademarks and domain name but
                       not its article archives. He said the deal for
                       Gawker is unrelated to his existing operating
                       businesses.


                # ⚓ Hollywood Reporter ☛ On_Rupert_Murdoch’s_Last_Day_as_News
                  Corp_Chair,_Mogul_Says_He_Hopes_to_Keep_“Active_Role”_at
                  Company⠀⇛


                       Wednesday marks Rupert Murdoch‘s last day as
                       chairman of News Corp., the publishing company that
                       formed his initial entry into the U.S. market
                       nearly 50 years ago. His son Lachlan Murdoch, the
                       CEO of Fox Corp., will assume the role of chairman
                       in his place.


                       But he told shareholders of the company that he
                       does not intend to ride off into the sunset.


          o § Civil Rights/Policing⠀➾


                # ⚓ New York Times ☛ How_Bad_Is_Antisemitism_Online?_It’s
                  Increasingly_Hard_to_Know.⠀⇛


                       Where the truth lies, however, is hard to glean,
                       according to academic researchers and advocacy
                       groups. They said the debates over content related
                       to the Israel-Hamas war have highlighted the
                       roadblocks complicating independent analysis of
                       what appears on the major online services. Instead
                       of being able to conduct methodical studies of
                       online discourse, they must try to grasp its scope
                       and effects using inefficient and incomplete
                       methods.


                # ⚓ Hollywood Reporter ☛ Actors’_AI_Protections_Are_a_Step
                  Forward,_But_There’s_Reason_to_Worry⠀⇛


                       But SAG-AFTRA members may still have plenty to
                       worry about on AI restrictions — especially on the
                       issue of the creation and deployment of digital
                       replicas in performances that could allow studios
                       to circumvent what were intended to be enhanced
                       protections for actors. Though the deal requires
                       advance notice and a specific description for the
                       intended use, it allows members of the Alliance of
                       Motion Pictures and Television Producers (the
                       studios) to negotiate directly with performers for
                       approval instead of requiring them to go through
                       the union, which sought a veto on certain uses of
                       AI. In practice, this could result in studios
                       strongarming actors into accepting terms that
                       enable them to utilize digital doubles as a
                       condition of employment, according to agents and
                       lawyers consulted by The Hollywood Reporter.


                       [...]


                       But consider Schedule F performers who fall short
                       of making the A-list and are presented with offers
                       that are tied with blanket licenses to use digital
                       clones over the duration of a franchise. Over time,
                       if enough studios arrange deals in this manner, the
                       term will become normalized in contravention of the
                       tentative deal’s aim to empower performers with the
                       ability to control future uses of their AI doubles.


                # ⚓ Variety ☛ End_of_the_Strikes_Is_Just_the_Beginning_for_a
                  New_Era_in_Hollywood⠀⇛


                       Meanwhile, more and more disgruntled workers,
                       particularly in the visual effects and animation
                       sectors, have been voting to unionize with IATSE
                       this year, bringing their own concerns to an
                       already crowded table.


                # ⚓ RTL ☛ Fear_mounts_for_Saudi's_youngest_death-row
                  detainees⠀⇛


                       Because Saudi Arabia does not typically notify
                       lawyers and relatives before carrying out
                       executions, "we will receive news of his (death) at
                       any moment", said one relative who spoke to AFP on
                       condition of anonymity for fear of reprisal.


                       Saudi authorities did not respond to AFP's request
                       for comment.


                # ⚓ Kansas Reflector ☛ After_Kansas_school_district_forces
                  Native_American_boy_to_cut_his_hair,_ACLU_sends_warning⠀⇛


                       “The present-day harms of school policies that
                       restrict Native American boys from wearing long
                       hair must be understood in the historical context
                       of multifaceted efforts to separate Native American
                       children from their families and tribes and to deny
                       them their rights of cultural and religious
                       expression,” the ACLU letter reads. “Haderlein’s
                       policy impacts Native American students
                       disproportionately and perpetuates a legacy of
                       cultural, psychological, and spiritual trauma and
                       discrimination.”


                # ⚓ [Repeat] New York Times ☛ Jewish_Celebrities_and
                  Influencers_Confront_TikTok_Executives_in_Private_Call⠀⇛


                       The celebrities and creators described, sometimes
                       with fiery rhetoric, how TikTok’s tools did not
                       prevent a flood of comments like “Hitler was right”
                       or “I hope you end up like Anne Frank” under videos
                       posted by them and other Jewish users.


                       “What is happening at TikTok is it is creating the
                       biggest antisemitic movement since the Nazis,” Mr.
                       Cohen, who does not appear to have an official
                       TikTok account, said early in the call. He
                       criticized violent imagery and disinformation on
                       the platform, telling Mr. Presser, “Shame on you,”
                       and claiming that TikTok could “flip a switch” to
                       fix antisemitism on its platform.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Zimbabwe ☛ Min_of_ICT_says_Starlink_still_has_not_applied
                  for_licence_in_Zim,_what_could_be_the_hold_up?⠀⇛


                       Here is the latest in the Starlink saga. The
                       Minister of ICT, Mavetera, gave a statement on
                       where we are with the satellite internet service
                       provider. Spoiler: she repeated herself, we are
                       where we were a few months ago.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Greece ☛ Greeks_fall_into_the_subscription_trap⠀⇛


                       Greek consumers appear trapped in online
                       subscriptions, as subscribing via mobile phone to
                       various services, from TV content to video game
                       platforms, but also marketplaces for purchasing
                       goods or ordering food at the push of a button can
                       be easy. However, at the end of the month the bills
                       come, emptying bank accounts.


                       According to claims management company Intrum’s
                       annual report on consumer payments, Kathimerini
                       reveals 67% of consumers in Greece – the highest
                       among the 20 European countries examined – are
                       affected by the phenomenon of so-called
                       “subscription creep,” the difficulty of managing
                       their many subscriptions in terms of financial
                       costs.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ India Times ☛ Finnish_wearables_startup_Oura_sues
                        Indian_rival_Ultrahuman_for_patent_violations⠀⇛


                             In the lawsuit filed in the US District Court
                             for the Eastern District of Texas, Marshall
                             Division, the Finnish company has sought the
                             award of damages for the alleged
                             infringements, including no less than all the
                             profits realised by Ultrahuman as a result of
                             the alleged infringements.


                      # ⚓ The Next Web ☛ The_two_rings:_Finland’s_Oura_sues
                        Ultrahuman_over_rival_wearable⠀⇛


                             In the filing, Oura sets out several details
                             and features in Ultrahuman’s ring that it
                             claims the rival company has copied.


                             This includes the titanium used in the
                             device, skin sensors and PPG sensors, which
                             measure various health metrics for the
                             wearer, and the fact that the device uses
                             similar batteries from the same suppliers.


                # § Copyrights⠀➾


                      # ⚓ Hollywood Reporter ☛ ‘South_Park’_Streaming_Rights
                        Standoff:_Judge_Rules_Against_Warners_on_Some_Claims_in
                        Licensing_Battle⠀⇛


                             The agreement provided for two types of
                             content: longform episodes over 20 minutes
                             that first appear on a non-streaming
                             platform, and episodes from seasons 24 to 26
                             that do not fall into the first category.
                             Among of the long list of disputes is the
                             number of episodes WBD was entitled to for
                             those seasons. WBD insisted it’s owed 10 for
                             each season, but Paramount countered there
                             was no minimum commitment and that it’s
                             delivered 16 episodes over those three
                             seasons.


                      # ⚓ Torrent Freak ☛ MPA_&_IPR_Center_Tackle_'Holiday'
                        Piracy_With_New_PSA_Campaign⠀⇛


                             The U.S. Government's Intellectual Property
                             Rights Coordination Center (IPRCenter) has
                             teamed up with the MPA to launch a new anti-
                             piracy campaign. Through public service
                             announcements, they hope to deter the
                             seasonal holiday piracy spike by highlighting
                             malware threats and other harms.


                      # ⚓ Digital Music News ☛ WIPO_&_Music_Rights_Awareness
                        Foundation_Launches_New_Online_Platform_to_Raise
                        Creators’_Awareness_of_Their_IP_[sic]_Rights⠀⇛


                             CLIP — Creators Learn Intellectual [sic]
                             Property [sic] — is an innovative, user-
                             friendly, and free-to-use online learning
                             platform that will be filled with curated
                             content from experienced musicians and
                             mentors to help creators make better business
                             decisions.


                             Though the creator industry is soaring at
                             record levels, creators often lack crucial
                             information for managing their intellectual
                             property rights, and miss out on receiving
                             proper credit and reward for their work —
                             especially when it comes to online
                             consumption. CLIP aims to improve this
                             situation with a wealth of free resources,
                             supporting creators with the knowledge and
                             skills needed to transform their passion into
                             a viable profession.


    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ Vacation!⠀⇛


                       I have no plans, except for not traveling. I have
                       been screwing around with my Gemini PDA and my
                       phone all day. Wrote scripts to put battery
                       percentage in the tmux status line, with a battery
                       or plug emoji depending on whether or not the
                       device is plugged in.


                # ⚓ An_Affront_to_Queenie⠀⇛


                       I just found myself typing this story out, and kept
                       going. It is anything but serious :) This story is
                       a mashup of characters from a couple of different
                       D&D campaigns. Some names have been changed to
                       protect the guilty!


                # ⚓ Still_here⠀⇛


                       The capsule still lives and is still relevant. it's
                       not abandoned. I know there haven't been any
                       postings as of late. I am personally disappointed
                       that I've discoverd how much self-discipline I lack
                       to be able to write consistently as I have desired
                       to or imagined in my mind that I would write. Much
                       has happened since my last update. There have been
                       many periods of mental struggle and feeling
                       disconnected from the projects that I want to
                       complete. I struggle to get into the mindset of
                       writing because I end up feeling mentally exhausted
                       most days. If Cal Newport and other profilic
                       authors have anything to say about this, it's due
                       to the fact that I'm doing things that don't
                       benefit me mentally and I'm doing too much context
                       switching between tasks or taking on too much at
                       one time causing fractured focus.


                # ⚓ 🔤SpellBinding:_DEFXSUI_Wordo:_CROAK⠀⇛


                # ⚓ The_Fair-Weather_Friend⠀⇛


                       A fair-weather friend is someone who's there for
                       you when things are going well in your life, when
                       it's convenient for them, or when they benefit, but
                       whenever you need a favor or you're not doing well,
                       this 'friend' is nowhere to be found. Needless to
                       say, fair-weather friends aren't really your
                       friends. Real friends care about your well being.


          o § Politics and World Events⠀➾


                # ⚓ F04_LiveFromFrance_S1E04⠀⇛


                       This new month in France was very dark, between the
                       war in Palestine/Israel, the Ciaran Tempest (far
                       from the dramatic Otis Hurricane in Mexico) and
                       french politics.


                # ⚓ Peace_is_a_choice.⠀⇛


                       Peace is a choice.


                       This is something that I've been reflecting on over
                       the course of the last few months.


                       Years ago, I was generally very angry. Ready to
                       argue, ready to fight to solve problems.


                       Life has a way of smoothing those rough edges. It's
                       hard to burn at both ends all the time, as a
                       candle, per se, if the time is more common than not
                       that you just want to take a nap. I've watched
                       those pieces of me chip and fall off bit by bit.
                       I'm not quite there, and unsure if I'll ever be,
                       but I do have a point to make.


          o § Misc⠀➾


                # ⚓ Re:_Atomic_Habits⠀⇛


                       I recently finished reading Atomic Habits¹. It's a
                       decent self-help book about forming good habits and
                       quitting bad habits. It touches on some of the same
                       concepts in my journal entry "The Power of
                       Convenience²", just in more depth. I've learned
                       quite a bit from it and I've even started
                       implementing some of the strategies in the book
                       with success. I'm glad I read it and I would
                       recommend it to anybody.


                       One big idea that was mentioned in the book but not
                       expanded on is that we need our leaders to organize
                       society such that it's easier to form good habits
                       and quit bad ones. To a limited extent, we can
                       build a controlled environment inside our homes
                       which promotes good habits, but we can't
                       individually control the environment outside of our
                       homes.


                # ⚓ Nation_Books⠀⇛


                       I was reading a book which invited me to visit the
                       publisher: Nation Books. Searching online, I did
                       not immediately find what I was looking for.
                       However, if you visit the web address directly, you
                       are redirected to Type Media Center's Bold Type
                       Books imprint. My book is listed there. And Bold
                       Type Books appears to be the successor to Nation
                       Books. I'm leaving this breadcrumb to help others
                       find the current publisher.


          o § Technology and Free Software⠀➾


                # ⚓ Hole-y_Tao_bells!⠀⇛


                       Maybe it's just lack of participants. But I've
                       occasionally wondered if there's a bit of a fear of
                       "Gemini becoming too much like The Web" or "Bubble
                       becoming too much like a corporate social network"
                       subconsciously driving activity down, as though
                       suspecting activity itself might have played a
                       significant role in the arguable downfall of those:
                       "Maybe it'll stay more pristine if I don't add to -
                       or otherwise sully - it" kind of thing.


                # ⚓ Setup_Dropbear_to_unlock_Debian_on_the_Libre_Computer
                  "Renegade"_over_your_Local_Network⠀⇛


                       In a previous gemlog I illustrated how to installed
                       Debian over an encrypted file-system, perhaps you
                       want to connect to this board remotely and
                       therefore you need to unlock it from your terminal
                       otherwise you need at least a keyboard plugged
                       into, and this is not very handy.


                # ⚓ Postgres_Quick_Notes,_take_two⠀⇛


                       What follows is some quick notes to remind me of
                       the things I do when I setup a new instance of
                       PostgreSQL on the various machines I work with.


                # ⚓ Re:_I_gave_emacs_a_serious_look_back_in_the_day⠀⇛


                       But I also remember concluding the vi[m] command to
                       pipe some or all lines to a script's stdin and
                       receive its stdout in its stead (:%!<command>) was
                       plenty sufficient to accomplish mass editing things
                       I was enamored of at the time, and it's definitely
                       served me well in that capacity over the years.


                # ⚓ Setup_Dropbear_to_unlock_Debian_on_the_Libre_Computer
                  "Renegade"_over_your_Local_Network⠀⇛


                       In a previous gemlog I illustrated how to installed
                       Debian over an encrypted file-system, perhaps you
                       want to connect to this board remotely and
                       therefore you need to unlock it from your terminal
                       otherwise you need at least a keyboard plugged
                       into, and this is not very handy.


                # ⚓ Emacs_Basics⠀⇛


                       Emacs is a Lisp machine. Lisp is a programming
                       language from the 1950s but it’s good. It looks
                       different from C or JavaScript or shell scripts but
                       just like them, you can make functions, and
                       functions can be marked as interactive so they can
                       be called as commands. Don’t worry, it comes with a
                       huge amount of ready-made commands.


                # ⚓ AGE_for_email⠀⇛


                       I’ve had a couple of different people ask to use
                       AGE for email, and Emacs can handle that just fine,
                       so I’ve acquiesced


                # § Internet/Gemini⠀➾


                      # ⚓ I_read_Gemini_and_I_care⠀⇛


                             I do. I cannot say I read everything it's
                             posted on Gemini; I'm not that dedicated, but
                             I do read most that's posted on Antenna or
                             Cosmos, and some of what's available on the
                             BBS. And I read because I often like what I
                             find there, even if I don't always agree with
                             what said.


                # § Programming⠀➾


                      # ⚓ show-trailing-whitespace_is_my_friend⠀⇛


                             When I am writing prose in Emacs and I have
                             sprawlbrain, I usually type one or more
                             spaces at the end of all the places I know I
                             need to continue writing or editing, and
                             they’ll show up because of how show-trailing-
                             whitespace is on.


                             So I can write a few words about things I
                             need to remember to address without losing my
                             place. It helps me “bookmark” what I’m doing.


                             Sprawlbraininess can differ from day to day
                             because sometimes I have zero and other times
                             I have like five or six such bookmarks in a
                             given post, even a super short one.


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




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