𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, December 07, 2023
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Generated Fri 8 Dec 02:49:32 GMT 2023
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
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Gemini index for the day: gemini://gemini.techrights.org/2023/12/07/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕

⦿ Techrights  -  A Googlebombing Campaign Targeting "Gemini" Takes on E-mail, Too

⦿ Techrights  -  Google is Googlebombing the Term "Gemini"

⦿ Techrights  -  IRC Proceedings: Wednesday, December 06, 2023

⦿ Techrights  -  Lennart Poettering and Fellow Microsofters Turn GNU/Linux Into Windows, Expect Poor Reliability With systemd-bsod

⦿ Techrights  -  Rumour: Major Finance Layoffs at Microsoft Next Week

⦿ Techrights  -  Still Not 'Canceled'

⦿ Techrights  -  The Effort to Silence (Squash) GNU/Linux Advocates and Press Coverage

⦿ Techrights  -  [Video] Microsoft Without a So-called 'Common Carrier' (Windows Monoculture)

⦿ Techrights  -  [Video] To Combat Efforts to Cancel or Kill the Career (and Reputation) of the People Who Made GNU/Linux We Must Rally the Community

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://news.techrights.org/n/2023/12/07/A_Googlebombing_Campaign_Targeting_Gemini_Takes_on_E_mail_Too.shtml
https://news.techrights.org/n/2023/12/07/Google_is_Googlebombing_the_Term_Gemini.shtml
https://news.techrights.org/n/2023/12/07/irc-log-061223.shtml
https://news.techrights.org/n/2023/12/07/Lennart_Poettering_and_Fellow_Microsofters_Turn_GNU_Linux_Into_.shtml
https://news.techrights.org/n/2023/12/07/Rumour_Major_Finance_Layoffs_at_Microsoft_Next_Week.shtml
https://news.techrights.org/n/2023/12/07/Still_Not_Canceled.shtml
https://news.techrights.org/n/2023/12/07/The_Effort_to_Silence_Squash_GNU_Linux_Advocates_and_Press_Cove.shtml
https://news.techrights.org/n/2023/12/07/_Video_Microsoft_Without_a_So_called_Common_Carrier_Windows_Mon.shtml
https://news.techrights.org/n/2023/12/07/_Video_To_Combat_Efforts_to_Cancel_or_Kill_the_Career_and_Reput.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://news.techrights.org/n/2023/12/07/Links_07_12_2023_Climate_Events_Occupied_by_Their_Enemy_Workers.shtml
https://news.techrights.org/n/2023/12/07/Links_07_12_2023_More_EPO_Patents_Squashed_More_Pfizer_COVID_19.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 72

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/12/07/A_Googlebombing_Campaign_Targeting_Gemini_Takes_on_E_mail_Too.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/12/07/A_Googlebombing_Campaign_Targeting_Gemini_Takes_on_E_mail_Too.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ A Googlebombing Campaign Targeting "Gemini"
Takes on E-mail, Too⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


Google can do Googlebombing too (the term is even named after it)


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


THE "gemini" name is not trademarked in the area of technology (at least not in
a way that would be easily enforced in a court), as there are computer devices
(running Linux) among other things that already use the name. It's not new, it
has gone on for decades and after all it's also a Zodiac Sign. But over the
past half a decade Gemini Protocol has become increasingly used and widely
recognised in several contexts, including GemText syntax.


As noted_this_morning, after some delays, Google-centric (sometimes Google-
funded or Google-reliant) sites began bombarding the word (name, term,
whatever!) "gemini" in relation to something else completely, obscuring any
mentions of the thing that threatens Google's Net dominance (by essentially
bypassing the Web). My wife complained to me that her RSS feeds were getting
filled up by this 'fake' (new) "Gemini" thing that was not in fact the Gemini
thousands of capsules and millions of people speak about.


Sent to me only hours ago by E-mail:


     § Google launches AI model challenging OpenAI? Copyleaks Insights on
     Gemini⠀➾


     Hey Roy,


     Google has introduced Gemini, its latest large language model,
     marking a significant step in the AI landscape to rival OpenAI's GPT-
     4. Gemini, available in three versions, distinguishes itself with
     advanced capabilities in understanding and interacting with video and
     audio, positioning it for integration into various Google products
     and services worldwide.


So how many millions of people get those sorts of spammy E-mail messages
(unsolicited marketing spam)?


We'll say more about Gemini and the Web in our next video. Google is being very
evil and the tactic of hijacking names is very Microsoft-inspired. Remember
that_Google_hires_from_Microsoft_more_than_any_other_company. █




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                    ䷩ 𝚕𝚒𝚗𝚎 156

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/12/07/Google_is_Googlebombing_the_Term_Gemini.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/12/07/Google_is_Googlebombing_the_Term_Gemini.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Google is Googlebombing the Term
"Gemini"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


Days ago: Web_Monopolist,_Google,_'Pulls_a_Microsoft'_by_Hijacking/Overriding
the_Name_of_Competitor_and_Alternative_to_the_Web


Now: (Source)


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Google launches Gemini, upping the stakes in the global AI
                                    race⦈


Could Google not pick a name that's already "taken"?




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢩⢹⢻⠟⡟⢻⢻⠙⣟⣿⠹⡟⢻⢻⢻⠛⣿⢹⢻⢛⣟⢿⡏⡏⡟⣻⢻⢻⠛⡟⡟⢻⣿⢻⢻⢻⠛⡟⡟⢻⢻⢻⢻⣿⡏⡟⢻⣻⣿⠏⡿⡟⡏⢻⢻⣛⢿⡟⡟⡟⣿⣽⢹⠛⣟⣿⣛⡏⢟⣻⢹⠻⡟⣿⣿⣿
⣿⣿⡷⡾⢶⣿⣾⣥⣼⣾⣶⣿⣶⣶⣷⣾⣾⣾⣶⣾⣾⣶⣷⣾⣿⣶⣷⣾⣾⣾⣶⣷⣷⣾⣿⣷⣾⣴⣧⣶⣷⣾⣾⣤⣾⣷⣷⣷⣷⣾⣷⣿⣾⣶⣷⣷⣷⣶⣾⣷⣷⣷⣿⣾⣾⣾⣶⣿⣤⣷⣷⣾⣶⣷⣶⣿⣿⣿
⣿⣿⣨⣙⣸⣇⣆⣀⣐⣂⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣄⢠⡀⣄⢠⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣿
⣿⣿⣿⢸⣇⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⢽⣟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣙⡀⢀⣀⠀⣀⡀⢀⣀⢰⢀⣀⠀⠀⠒⠲⣀⡀⡀⡀⢀⢀⢀⣰⢆⢀⢶⡂⡀⣀⢀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣸⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡭⠏⠧⠼⠺⠤⠇⠧⢼⠸⠻⠬⠀⠀⠤⠴⠹⠤⠅⠧⠌⡧⠤⠻⠈⠊⠸⠇⠇⠸⠣⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣹⡟⣿⣿⣿⣿⢀⠀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣄⣠⣤⣀⣤⣠⣤⣤⣤⣽⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣿⣿⣿⣿
⣿⣿⣿⣼⣿⣿⣻⣿⣿⣺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⡟⣿⢿⣿⣿⠒⠙⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⣿⣿⣼⣿⣿⠀⠀⠐⠘⠚⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠉⠛⠋⠟⠻⠟⠻⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢻⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠙⠉⠙⠛⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢸⡟⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡯⣿
⣿⣿⣿⢸⡇⣿⢸⡇⣿⠀⠀⠀⢀⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿
⣿⣿⣿⢸⡇⣿⢸⡇⣿⢠⡀⠀⢰⠜⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⣤⣤⣤⣴⣶⣯⣭⣽⣿⣿⣿⡿⣿⣿⢿⡿⣿⣿⣿⣿⡟⣿⣿⣿⡏⠀⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⢿⣿⣿⠿⣿⣿⣿⡿⣿⢿⣿⢿⢿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 213

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/12/07/irc-log-061223.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/12/07/irc-log-061223.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Wednesday, December 06,
2023⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


                          Enter_the_IRC_channels_now





                    ䷩ 𝚕𝚒𝚗𝚎 245

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/12/07/Lennart_Poettering_and_Fellow_Microsofters_Turn_GNU_Linux_Into_.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/12/07/Lennart_Poettering_and_Fellow_Microsofters_Turn_GNU_Linux_Into_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Lennart Poettering and Fellow Microsofters
Turn GNU/Linux Into Windows, Expect Poor Reliability With systemd-
bsod⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


Recent: IBM:_EMBRACE,_EXTEND,_and_Microsoft_Proprietary_GitHub_(With_Project
Leader_on_Microsoft's_Payroll)


Reminder:


             🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Lennart Poettering at Microsoft⦈


Pushing Microsoft's restrictions onto Free software users:


                      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Microsoft key⦈


Made_by_Microsoft_employees, turning Linux into Microsoft Windows:


"Ahead of the holidays systemd 255 has debuted as stable and comes with
systemd-bsod as a "Blue Screen of Death" service capable of displaying full-
screen error messages on Linux." --Phoronix in article systemd 255 Released
With A "Blue Screen of Death" For GNU/Linux Systems (discussion_here)


To quote one comment: "Yet another proof that Microsoft destroys everything it
touches! But I wonder, Lennart couldn't really find another employer than
Microsoft or Microsoft really has thrown a lot of money in his direction that
he could not refuse?"




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣼⣧⣥⣼⣾⣤⣴⣼⣧⣮⣾⣬⣴⣬⣼⣴⣷⣤⣸⣟⣤⣴⣴⣮⣿⣷⣿⣿⣬⣦⣷⣷⣵⣧⣿⣼⣷⣦⣤⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⡿⠿⠿⢿⢟⠿⢿⠿⠿⠿⠿⡿⢻⠿⠿⢿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 320

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/12/07/Rumour_Major_Finance_Layoffs_at_Microsoft_Next_Week.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/12/07/Rumour_Major_Finance_Layoffs_at_Microsoft_Next_Week.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Rumour: Major Finance Layoffs at Microsoft
Next Week⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


Posted 9_hours_ago_by_CampbellSoup:


 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Major finance layoffs coming before December 15. AH direct
               reports amongst others on the team. Good luck.⦈


THE Microsoft_layoffs carry on, according to this new rumour. Workers are
fearful and Microsoft_cuts_all_sorts_of_things. The_debt_at_Microsoft_is
surging.


If the rumour is true, we'll be hearing barely anything from the mainstream
media next week, even if those are real people - perhaps a lot of people - let
go just before Christmas. Maybe some compromised_media will try to pretend that
this is still part of the layoffs announced back in January.


By our estimate, Microsoft got rid of about 30,000 workers this year, including
in_areas_of_hype_like_"AI"_and_"Clown_Computing". The company struggles to find
a new future for itself as Windows revenue goes down at alarming rates, as does
the_price_of_Windows. █




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⣿⢸⣿⣿⣀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⢿⣿⢿⣿⡇⣿⣙⣋⢉⣍⣽⣡⣩⣋⣩⣫⣩⣇⣉⢉⣍⣀⣙⣯⣫⣩⣍⣉⡉⢹⣉⣩⣈⣉⣭⣿⣏⣩⣩⣩⣉⣁⣉⣍⣭⣯⣺⣏⣋⣿⣫⣩⣍⣍⣭⣏⣭⣭⣫⣩⣩⣹⣉⣉⣙⣭⣝⣉⣉⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣷⣵⣾⣿⡇⣿⡛⡋⠛⠛⡛⡿⡛⣻⣛⠙⠛⡟⠛⠛⠛⢻⡟⡿⡻⡻⡋⣟⡟⢛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⡇⣿⣾⣶⣾⣶⣷⣿⣶⣾⣷⣶⣶⣷⣷⣶⣶⣶⣷⣾⣾⣾⣶⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢸⣿⣿⣿⣿⣿⡇⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣘⣛⣛⣛⣛⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

                    ䷩ 𝚕𝚒𝚗𝚎 371

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/12/07/Still_Not_Canceled.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/12/07/Still_Not_Canceled.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Still Not
'Canceled'⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


Ted Ts'o, Jan Kara, Linus Torvalds last month: [via]


      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Ted Ts'o, Jan Kara, Linus Torvalds last month⦈




⣿⣙⣂⣿⣗⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀
⣿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀
⠬⢡⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⠀⠀⠰⠣⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣾⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣐⣸⣿⣷⣣⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡅⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠀⣠⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣤⣶
⠭⢽⡯⠀⠀⠀⠀⠀⠀⠀⣰⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣠⣾⣿⣿
⣶⣾⣷⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⣽⣿⣽⣿⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠀⣠⣾⣿⣿⣿⠟
⠀⠀⠃⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣧⣾⣿⣿⠟⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡀⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣽⣿⣿⢧⠀⠀⠐⣯⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣻⣿⣿⡟⠀⠀⠀⠀⠐⠦⣄⢀⣰⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣷⡡⠐⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⠻⣿⣿⣿⣿⣿⣿⣾⣧⣤⣐⡿⢿⡿⡿⠟⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⡫⠉⠁⠀⠀⠀⠀⠀⠀⣠⣤⣾⠸⣿⣟⣋⣻⣿⡿⠫⣱⣿⣶⣦⣤⣀⡀⠀
⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⡿⠟⠌⠦⠉⠉⠉⠠⠀⣈⣩⣼⣿⣿⣿⡿⣿⣆
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣞⣽⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠯⡾⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⣰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡽⢫⣫⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⣰⢿⣿⣯⠘⠟⣻⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣷⣾⣿⣿⡧⣭⢟⣯⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⣿⡀⣰⡩⡿⡛⠞⠂⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⡛⠛⠿⡇⢵⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⢌⢕⠳⠳⠂⠀⡈⣁⣒⠾⣾⣿⣿⣿⣿⣿⣿⣶⣤⣶⣶⣂⠀⠩⢹⢵⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢐⠓⠤⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⡥⢩⣾⣲⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢟⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠠⣿⣷⡄⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⣴⣾⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡿⣿⣯⣾⣯⠀⠀⠀⠀⠀⢤⠀⠄⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣹⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣾⣿⣿⣿⢟⡋
⣿⣿⣿⣿⡽⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣃⠀⠀⢠⠞⠈⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⡀⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⢟⡍⠉⠀

                    ䷩ 𝚕𝚒𝚗𝚎 415

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/12/07/The_Effort_to_Silence_Squash_GNU_Linux_Advocates_and_Press_Cove.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/12/07/The_Effort_to_Silence_Squash_GNU_Linux_Advocates_and_Press_Cove.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Effort to Silence (Squash) GNU/Linux
Advocates and Press Coverage⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


If nobody even mentions it anymore, does it still exist and is_it_considered
potent?


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


THE Google 'News' (Gulag Noise [1, 2]) mentions of "Linux" diminish again,
partly because sites_that_used_to_cover_GNU/Linux_every_day_suddenly_stopped_a
few_weeks_ago (our coverage of it had struck a nerve, attracting about 3,000
readers). No need to shame the publisher or anything (it had done a great job
until it stopped almost a month ago). I wrote to the editors:


     § Linux coverage⠀➾


     Hi,


     Regular reader here.


     I want to thank you for several years of good coverage regarding FOSS
     and GNU/Linux, with splendidly detailed reviews, HowTos, commentary,
     and relevant news items. It has helped raise awareness and is widely
     appreciated by us users. I can humbly say that your did a good job.


     I am concerned that over the past fortnight or so the coverage of
     these topics/themes quite suddenly stopped. I can see that David
     Delony, Ummara Mushtaq, Bertel King, Hannah Knight, Sharqa Hameed,
     Chioma Ibeakanma and others who write in this technical domain,
     either habitually or regularly, are not actively publishing or barely
     active anymore.


     It is starting to look like the site may have divested and perhaps
     laid off ~5 people who covered GNU/Linux, 3 of them regularly. Can
     you please consider assigning more budget/people to coverage (as
     before) or is there an unknown factor here?


It has been a few days and I got no reply (I've just checked my inbox again
very carefully).


What's going on? We don't want to guess aloud, but there are many
possibilities.


Remember that Microsoft_still_bribes_to_the_tune_of_billions_of_dollars (we
gave_the_essential_context_the_other_day) to approve multi-billion-dollar
acquisitions that were otherwise denied (then Microsoft blackmailed an entire
nation, the UK). One associate of ours called it "bribery to distract from the
anti-trust action starting now" in the UK (and we suppose it's also possible
that they reward CMA for its Activision reversal).


To repeat a couple of links from the_latest_News_Roundup:


   1. ⚓ Amazon_slams_Microsoft’s_business_practices_in_UK_cloud_market_probe⠀⇛


           Amazon’s concerns regarding Microsoft follow similar criticisms
           made by Google to the CMA in October. In the letter published
           on Tuesday, Google claims Microsoft’s licensing practices were
           harmful to UK customers because they leave them with “no
           economically reasonable alternative but to use Azure as their
           cloud services provider, even if they prefer the prices,
           quality, security, innovations, and features of rivals.” Google
           said these licensing practices were the biggest issue
           preventing competition in the UK cloud-computing market.


   2. ⚓ AWS_accuses_Microsoft_of_clipping_customers'_cloud_freedoms⠀⇛


           AWS has publicly called out Microsoft's software licensing
           terms, claiming they "restrict choice" and make it "financially
           unviable" for customers to choose anyone other than Microsoft –
           something Google and other rivals have complained of.


           This was one among the many points addressed by Amazon in its
           submission [PDF] to Competition Markets Authority, the
           regulator charged with inspecting the health of the UK cloud
           sector with special attention to be given to egress fees;
           committed special discounts; interoperability; and cloud
           software policies.


           Amazon reckons that the first of these four "hypotheses" are
           "based on fundamental misconceptions about the IT sector,
           global networking technology, the actual interoperability of IT
           services, and discounts on offer."


Is it possible that Microsoft also interferes with publications about GNU/
Linux? Using threats or some pseudo-legal agreement with an odious NDA? Don't
rule that out, as that happened before. And we also saw how GNU/Linux OEMs
stopped promoting GNU/Linux (or lessened that) after Microsoft has paid them to
become "partners". In Canonical's case, they even began marketing Windows
(WSL).


The latest_major_Windows_news_is_this: (from British publisher)


     Microsoft on Tuesday warned that full security support for Windows 10
     will end on October 14, 2025, but offered a lifeline for customers
     unable or unwilling to upgrade two years hence.


Where's the UK-based Canonical? Why does it not use this to promote Ubuntu?


We've checked their blog meticulously. It's not even mentioned there! The
Ubuntu blog is barely about Ubuntu anymore, or barely about "the desktop". It
often promotes Microsoft's proprietary software and back doors, even_TPM.


We should politely (if at all possible; truth hurts!) note that Microsoft has
its share of British moles (who later move to the US to better serve GAFAM,
even Microsoft) inside GNU/Linux distros, notably Debian and Ubuntu, or both.
They promote Mono/.NET and TPM, even in spite of a lack of relevant
qualifications.


What's wrong with all this? Look at the big(ger) picture. Look at the long-term
agenda, not just the stepping stones.


It's also about pushing DRM deeper into the market via TPM requirements, an
associate reminds us. First, TPM is:


1) optional


Then:


2) required but off by default


3) required and on by default


4) required and no choice but on


We're at step 2 there, especially with Vista 11. And Canonical helps Microsoft
get to 4, as_does_IBM.


The impending doom of Vista 10 is something that Canonical ought to make hay
with, according to an associate. It's not acceptable that they continue to pass
up such opportunities for increasing Ubuntu market share. It's a repeat of an
old problem that started once they got infiltrated by Jo Shields and co.


Prior to Microsoft's Jo getting MoU access, the associate explains, Canonical
was keeping Microsoft on the defensive. Then Canonical hired a worker from
Microsoft to manage Ubuntu on the desktop (Spencer).


Microsoft took advantage and Canonical never_recovered.


Does any or all this stuff sound familiar? To us it most certainly does.


Remember that in Novell, in late 2006, workers censored the site. Novell
basically censored its own site to avoid "disparaging" Microsoft after it had
signed the notorious patent "deal" (collusion).


Here we go again...


Microsoft's Jo of Team_Mono went on to become a direct Microsoft employee (not
just their mole or/and shill/shell gamer) and now he's openly friends with
Matthew_J_Garrett, who is also a friend of other Microsoft moles (like the_one
inside_the_OSI's_Board).


They're still scheming_to_take_down_our_site_based_on_vicious_lies_or_a_false
narrative, wherein the saboteur gets misframed as the helpless victim. █




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠠⠠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣦⣀⣶⣶⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠁⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⢘⣿⡿⠃⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 663

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/12/07/_Video_Microsoft_Without_a_So_called_Common_Carrier_Windows_Mon.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/12/07/_Video_Microsoft_Without_a_So_called_Common_Carrier_Windows_Mon.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] Microsoft Without a So-called
'Common Carrier' (Windows Monoculture)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


Video_download_link | md5sum e6ef25e60e258668001a374208d000a4
Windows_Has_Fallen
Creative Commons Attribution-No Derivative Works 4.0


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


TODAY'S second video hopefully reminds readers that a lot has changed over the
past 20 years. Long gone are the "Windows XP" days. Many people carry
functional computers inside their pockets and not even 1% of those runs Windows
(apparently_0%_in_China).


Times have changed, but those devices in people's pockets don't respect freedom
and not even basic dignity, including privacy. Yes, many run Linux, but the
users aren't aware of it and that "Linux" is wrapped up in a ton of spyware, so
plenty_of_work_remains_to_be_done over the coming decade (more on that in our
next video).


The principal point of this current video is that, according to statCounter at
least, GNU/Linux_surged_to_nearly_4%_of_desktops/laptops and Microsoft_now
gives_Vista_10_licences_for_as_little_as_28_US_dollars. It cannot compete with
GNU/Linux like it did back in 2006 via Vista (charging hundreds of dollars for
some "editions" of Vista).


I honestly dislike over-relying on statCounter, but many other metrics and
surveys went extinct, except perhaps W3Schools. It_too_puts_GNU/Linux_at_4%_of
the_market. GNU/Linux_performance_is_far_better_than_Windows'_even_for_games
(drivers improved a lot, both for graphics and peripherals), so one cannot call
a freedom-respecting operating system user merely principled but non-pragmatic.
It's perfectly rational and practical to abandon Windows already.


Speaking of W3Schools, the "Open Web" seems to be dying fast and Mozilla
probably won't last much longer.


"I am personally unaware of any serious reason to believe that Firefox’s
numbers will improve soon. Indeed, for the web as a whole, they’ve been
declining consistently for years," Bryce_Wray_wrote_a_week_ago regarding
Firefox, citing statCounter as a reference (statCounter's numbers are derived
from Web statistics from 3 million sites, according to the company). Wray is_a
Web_person, so if he deems statCounter worth citing, then it's probably not
pure nonsense in his assessment. █




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⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠈⠀⠘⠉⠉⠉⠁⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⣆⢂⡄⡅⡄⡄⠄⡇⠄⡄⣠⣠⠀⡀⠀⡦⢴⢀⣠⢀⡀⠀⡦⠄⣠⡄⢸⢠⣠⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠾⠻⠿⠿⠿⠿⠿⠟⠛⠉⠉⠙⠛⠿⠿⠿⠿⠿⠻⠿⠿⠝⠹⠙⠑⠀⠀⠀
⠀⠀⠀⠈⠈⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠁⠀⠁⠈⠈⠈⠀⠁⠀⠁⢠⣭⣥⡌⠈⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠀⣄⣤⠰⣠⣴⣾⣿⣿⣿⣷⡄⠠⣤⣤⣤⣤⣤⠀⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⣶⣶⣶⣶⣦⣲⠢⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠀⠉⠉⠉⠉⠋⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠈⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠠⠿⠇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣄⠀⠀⣀⣄⠀⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠀⠀⠴⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠴⠿⠀⠀⠀⣘⣟⣋⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠷⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠘⠙⠉⠁⠸⠥⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡆⢂⡄⡄⡤⡄⠤⡆⠤⡄⣠⣠⢠⡄⠀⡆⢰⢠⣤⢠⡄⠀⡆⠀⣤⡀⢰⢠⣤⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠺⠿⠿⠿⠿⠿⠿⠿⠿⠛⠉⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠻⠝⠹⠁⠐⠀⠀⠀
⠀⠀⠀⠈⠈⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠁⢠⣤⣥⡌⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⢠⢠⣤⠰⣠⣴⣾⣿⣿⣿⣷⡄⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣾⣿⣿⣿⣿⣿⣿⣷⠀⣶⣶⣶⣶⣶⣶⢆⣰⡢⠖⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠁⠀⠉⠉⠁⠀⠉⠉⠉⠛⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡀⠲⠿⠂⠀⠀⠉⠉⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣆⠀⠀⣀⣄⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠲⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⣸⣏⣋⣀⣀⣀⣩⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠘⠙⠁⠁⠸⠷⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡄⢂⡄⡆⡤⡄⠤⡆⠤⡀⢠⣠⢠⠄⠀⡆⢰⢠⣄⢠⠄⠀⡖⠂⣤⡀⢰⢠⣤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠙⠻⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠻⠽⠙⠙⠐⠁⠀⠀
⠀⠀⠀⠘⠈⠁⠃⠁⠃⠐⠃⠑⠁⠃⠉⠐⠂⠀⠃⠘⠀⠘⠐⠀⠀⠃⢀⣶⣧⡜⠈⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⢠⢄⣤⠠⣠⣴⣶⣿⣿⣿⣶⡀⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣧⠀⣶⣶⣶⣶⣶⣶⣶⡶⠂⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠈⠉⠉⠉⡋⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠚⠓⠀⠀⠀⠉⠁⠀⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⣀⡄⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠲⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⣸⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠘⠉⠁⠁⠸⠵⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡄⠆⡀⡆⡠⡀⠠⡆⠠⡀⢀⢀⠠⠄⠀⣆⣰⠀⢄⠠⠄⠀⣖⡂⠤⡀⢰⠀⢄⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠻⠿⠿⠿⠿⠿⠻⠟⠿⠙⠙⠑⠐⠀⠀⠀
⠀⠀⠀⠙⠘⠁⠃⠃⠃⠒⠃⠒⠁⠃⠋⠐⠃⠀⠃⠘⠘⠚⠐⠃⠀⠃⢀⣓⣃⡘⠐⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠠⢄⡠⠠⣠⣤⣶⣶⣶⣷⣶⡀⢠⣤⣤⣤⣤⣄⠀⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣧⠀⣶⣶⣶⣶⣶⣶⣶⢰⠂⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠉⠀⠉⠉⠁⠈⠉⠉⠛⠏⠋⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠿⠐⠀⠀⡉⠁⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣆⠀⠀⣀⣄⠀⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢈⡤⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⣸⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡄⠆⡀⡂⡀⡀⡀⡆⡀⡀⢀⢀⠀⠀⠀⣆⣰⠀⢀⠀⠀⠀⣖⡂⠩⡉⢱⢀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠕⠙⠙⠐⠀⠀⠀
⠀⠀⠀⠙⠘⠃⠃⠃⠃⠒⠃⠒⠃⠋⠋⠐⠃⠀⠃⠘⠘⠛⠐⠃⠀⠃⢀⣛⣃⡘⠘⠛⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠀⠀⣤⠰⣠⣴⣶⣶⣿⣿⣦⡀⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢲⣶⣶⣶⣶⣶⣶⣶⣶⣰⣾⣿⣿⣿⣿⣿⣿⣧⠀⣶⣶⣶⣶⣶⣶⣦⣲⠂⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠉⠀⠉⠉⠁⠈⠉⠉⠛⠏⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠇⠐⠀⠀⡉⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣆⠀⠀⣀⣄⠀⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢈⡤⠀⠀⠀⠀⡀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠸⠿⠂⠀⠀⣸⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠘⠉⠁⠁⠸⠵⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡄⠄⡀⡂⡀⡀⡀⡆⡀⡀⢀⢀⢀⠀⠀⡄⣠⢀⢀⠀⠀⠀⣄⠈⣉⠉⢱⢀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠿⠟⠿⠻⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠙⠹⠘⠑⠀⠀⠀
⠀⠀⠀⠙⠘⠃⠃⠃⠃⠂⠃⠂⠃⠋⠋⠈⠁⠀⠃⠘⠘⠙⠈⠁⠀⠃⢀⣛⣃⡘⠘⠙⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠀⣤⣤⠠⣠⣤⣶⣶⣶⣿⣶⡀⢠⣤⣤⣤⣤⣄⠀⠀⠤⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣧⠀⣶⣶⣶⣶⣶⣶⡦⢲⠂⠖⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠈⠉⠙⠛⡟⠋⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠐⢦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠯⠐⠀⠀⡉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣆⠀⠀⣀⣄⠀⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢈⡦⠀⠀⠀⠀⡀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠸⠿⠄⠀⠀⣸⣏⣀⣀⣀⣀⣩⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡀⠄⡀⡀⣀⡀⣀⡄⣀⠀⢀⢀⢀⡀⠀⡄⢠⢀⡀⢀⡀⠀⡤⠌⣉⠉⢡⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠝⠙⠙⠐⠀⠀⠀
⠀⠀⠀⠑⠘⠃⠇⠃⠇⠂⠇⠢⠃⠊⠛⠈⠀⠀⠇⠸⠈⠹⠈⠀⠀⠇⢀⣍⣇⡸⠘⠍⠀⠸⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⢠⢠⣤⠀⣠⣤⣶⣿⣿⣿⣶⡀⢠⣤⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⢶⣶⣶⣶⣶⣶⣶⣶⣶⡠⣿⣿⣿⣿⣿⣿⣿⣷⠀⣶⣶⣶⣶⣶⣶⡶⢶⠦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠈⠉⠉⠙⠟⠋⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠿⠀⠀⠀⠉⠉⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣄⠀⠀⣀⡄⠐⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⣺⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠘⠉⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡀⠄⠀⡄⢀⠀⣀⡄⢀⠀⠀⠀⢀⡀⠀⡄⢠⢀⡀⢀⡀⠀⡤⠌⣉⠉⢡⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉⠙⠛⠿⠿⠿⠿⠿⠻⠟⠿⠙⠙⠕⠑⠁⠀⠀
⠀⠀⠀⠳⠰⠃⠇⠇⠇⠤⠇⠤⠃⠎⠞⠠⠄⠀⠏⠹⠰⠼⠠⠆⠀⠏⠁⠤⠇⠸⠠⠬⠀⠸⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠀⣄⣤⢠⠆⣤⣶⣿⣿⣿⣿⣦⠀⣤⣤⣤⣤⣄⠀⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡇⣰⣶⣶⣶⣶⣖⡆⢲⠄⠔⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠀⠈⠉⠍⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⡳⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢽⠃⠀⠀⠀⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⠀⢀⣤⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂⠀⠀⠀⠀⢈⡂⠀⠀⠀⠀⣀⣀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠠⠿⠆⠀⠀⣐⣟⣋⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡀⡄⠀⡄⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⡤⠌⢉⠋⢡⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉⠙⠻⠿⠿⠿⠿⠿⠿⠟⠿⠙⠙⠑⠑⠀⠀⠀
⠀⠀⠀⠳⠰⠃⠇⠇⠇⠥⠇⠥⠇⠞⠞⠠⠆⠀⠏⠹⠰⠼⠠⠆⠀⠏⠁⠦⠇⠸⠸⠬⠈⠸⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⢀⣄⣤⢰⢀⣴⣶⣿⣿⣿⣷⡄⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣾⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⣶⣶⣶⣶⡶⣰⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠁⠉⠉⠉⠉⠋⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠐⢦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⡀⠈⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠿⠃⠀⠀⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣆⠀⠀⢀⣤⠀⠶⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⡀⢀⠀⠀⢀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠰⠿⠆⠀⠀⣘⣟⣁⣀⣀⣀⣩⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠘⠉⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡀⡀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⠈⠛⠛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉⠙⠻⠿⠿⠿⠿⠿⠿⠟⠻⠝⠙⠙⠐⠀⠀⠀
⠀⠀⠀⠳⠰⠇⠇⠇⠇⠅⠇⠅⠇⠞⠞⠐⠆⠀⠏⠹⠰⠺⠐⠆⠀⠏⠀⠶⠆⠸⠸⠺⠈⠸⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠠⢠⣤⢠⢂⣤⣶⣿⣿⣿⣷⡄⠀⣤⣤⣤⣤⣄⠀⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣿⣿⣿⣿⣿⣿⣷⠀⣲⣶⣶⣶⣶⣶⣶⣶⠂⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠀⠉⠉⠉⠋⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠈⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠿⠇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⡀⠀⢀⣠⠀⠶⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⣠⡀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠠⠿⠆⠀⠀⣘⣟⣋⣀⣀⣀⣨⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠈⠉⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⠘⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠿⠿⠿⠿⠿⠿⠻⠟⠻⠙⠙⠙⠙⠉⠀⠀
⠀⠀⠀⠣⠰⠇⠇⠏⠇⠍⠇⠍⠇⠞⠞⠘⠃⠀⠇⠸⠘⠳⠘⠃⠀⠇⠀⡛⠆⠸⠸⠛⠈⠹⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠠⢤⣤⠀⣠⣤⣶⣿⣿⣿⣶⡀⢠⣤⣤⣤⣤⣄⠀⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢠⣾⣿⣿⣿⣿⣿⣿⣷⠀⣶⣶⣶⣶⣶⣶⡶⢲⢆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠈⠉⠀⠉⠉⠁⠈⠉⠉⠉⠛⠋⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀
⠀⠀⠀⠀⠐⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠺⠿⠄⠀⠀⡉⠉⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣄⠀⠀⣀⡄⠐⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠠⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⡄⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠸⠿⠄⠀⠀⣸⣇⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠈⠉⠉⠀⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⣀⡘⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠿⠾⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠝⠙⠙⠑⠀⠀⠀
⠀⠀⠀⢣⢰⠇⡇⡏⡆⣉⡇⣉⠆⡜⡼⢘⡁⠀⡗⢺⢈⣱⢈⡁⠀⡗⠂⣙⡆⢸⢐⣑⠈⢱⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠠⢄⡠⠐⣠⣴⣶⣿⣿⣿⣦⡀⢠⣤⣤⣤⣤⣄⠀⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⣶⣶⣶⣶⣶⣶⣆⢰⠢⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠁⠀⠉⠉⠁⠈⠉⠉⠛⠏⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀
⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠧⠐⠀⠀⡉⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⠀⠀⣀⣄⠐⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⡄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠸⠿⠆⠀⠀⣘⣇⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠘⠘⠙⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⣀⡘⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠻⠿⠿⠿⠿⠿⠻⠿⠛⠝⠹⠙⠐⠀⠀⠀
⠀⠀⠀⢧⢡⠆⡇⡎⡆⣀⡇⣊⠆⡴⡴⢀⡄⠀⡗⢺⢠⣱⢀⡄⠀⡗⠂⣌⡆⢸⢀⣑⠐⢱⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠀⠀⣤⠠⣠⣤⣶⣾⣿⣿⣶⡀⢠⣴⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣢⣾⣿⣿⣿⣿⣿⣿⣧⠀⣶⣶⣶⣶⣶⣶⣖⢲⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠁⠀⠉⠉⠁⠈⠉⠉⠛⡟⠋⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀
⠀⠀⠀⠀⠐⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠀⠺⠯⠐⠀⠀⡉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣆⠀⠀⢀⣄⠀⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠨⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠠⠿⠆⠀⠀⣘⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠷⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠘⠘⠙⠉⠁⠸⠥⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠻⠿⠿⠿⠿⠿⠻⠿⠛⠙⠹⠑⠑⠀⠀⠀
⠀⠀⠀⢧⢡⡆⡆⡆⡆⣂⡇⡂⡆⡴⡴⢀⡄⠀⡗⢺⢠⣴⢀⡄⠀⡗⠂⣤⡆⢸⢰⢴⠐⢰⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠀⣤⣤⠠⣠⣴⣶⣾⣿⣿⣶⡀⢠⣤⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆⣲⣶⣶⣶⣶⣶⣶⣶⣶⣲⣾⣿⣿⣿⣿⣿⣿⣧⠀⣶⣶⣶⣶⣶⣶⣆⢰⢂⠆⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠈⠉⠉⠋⠟⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠐⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠿⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⣀⣤⠀⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢈⡂⠀⠀⠀⠀⡀⠀⠀⠀⢠⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠠⠿⠆⠀⠀⣘⣏⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠛⠻⠿⠿⠿⠿⠿⠻⠟⠻⠝⠙⠑⠙⠁⠀⠀
⠀⠀⠀⢦⢡⡆⡆⡆⡆⡂⡇⡂⡆⡴⡴⠰⠄⠀⡇⢸⢰⢴⠰⠄⠀⡇⠀⣶⡄⢸⢰⢴⠐⢰⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⢄⢠⣤⢠⢀⣤⣶⣶⣶⣿⣶⡄⢠⣤⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣿⣿⣿⣿⣿⣿⣷⠀⣶⣶⣶⣶⣶⣶⣖⢰⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠁⠈⠉⠉⠁⠀⠉⠉⠙⠟⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠺⠿⠀⠀⠀⡉⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣆⠀⠀⣀⣄⠀⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠠⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⡀⠀⠀⡀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠠⠿⠆⠀⠀⣸⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠘⠉⠉⠉⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠛⠋⠉⠙⠻⠿⠿⠿⠿⠿⠻⠿⠻⠝⠹⠙⠘⠀⠀⠀
⠀⠀⠀⢆⢡⡆⡇⡖⡄⠒⡇⠒⡄⡰⣠⠰⠂⠀⡧⢼⠐⢦⠰⠂⠀⡯⠅⠶⡄⢸⠰⠦⠐⢢⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠀⣄⣤⢰⢠⣴⣶⣿⣿⣿⣷⡄⢀⣤⣤⣤⣤⣄⠀⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠈⠀⠁⠁⠁⠉⠁⠈⠀⠁⠁⠈⠁⠀⠁⠈⠈⠉⠈⠁⠀⠁⢠⣿⣷⡎⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣿⣿⣿⣿⣿⣿⣷⠀⣲⣶⣶⣶⣶⣶⣶⣰⢲⠖⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠀⠉⠉⠉⠛⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠺⠿⠄⠀⠀⠉⠍⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⣀⡄⠐⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠙⠀⠀⠀⠀⠀⠀⠀⠀⢠⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⡄⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠰⠿⠄⠀⠀⣸⣇⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠷⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠘⠘⠙⠉⠁⠸⠿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠉⠉⠉⠛⠿⠿⠿⠿⠿⠻⠿⠿⠝⠹⠙⠐⠀⠀⠀
⠀⠀⠀⣆⢃⡄⡇⡔⡄⠐⡇⠐⡄⡠⣠⠐⡂⠀⡧⢼⢐⢢⠐⡂⠀⡯⠅⡒⡄⢸⠀⠢⠀⢢⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠀⣄⣤⢠⢀⣴⣶⣿⣿⣿⣷⣦⠀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠈⠀⠁⠁⠁⠉⠁⠉⠀⠁⠁⠈⠁⠀⠁⠈⠈⠉⠈⠁⠀⠁⢠⣭⣥⡌⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣿⣿⣿⣿⣿⣿⣿⡆⢰⣶⣶⣶⣶⣶⣶⢲⣆⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠉⠁⠀⠉⠉⠁⠀⠉⠉⠉⠛⠋⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠈⠀⣠⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡀⠺⠿⠇⠀⠀⠉⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⢀⣄⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⣶⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠠⠿⠆⠀⠀⣸⣗⣂⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠘⠘⠙⠉⠉⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠙⠻⠿⠿⠿⠿⠿⠻⠟⠻⠙⠙⠙⠙⠀⠀⠀
⠀⠀⠀⣆⢃⡄⡅⡄⡄⠄⡇⠄⡄⣠⣠⠀⡀⠀⡦⢼⢀⢠⠀⡀⠀⡯⠅⣐⡄⢸⢠⠠⠠⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⢠⢠⣤⠠⢠⣤⣶⣿⣿⣿⣷⡄⢠⣤⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠈⠀⠁⠁⠁⠉⠁⠉⠁⠁⠁⠈⠁⠀⠁⠈⠈⠉⠈⠁⠀⠁⢠⣭⣥⡌⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣾⣿⣿⣿⣿⣿⣿⣷⠀⣲⣶⣶⣶⣶⣶⣖⣲⠢⠄⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠁⠀⠉⠉⠁⠀⠉⠉⠉⠛⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠈⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠺⠿⠄⠀⠀⡉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣄⠀⠀⣀⣄⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢨⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡾⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⡀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⣸⣇⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠘⠘⠉⠉⠈⠸⠯⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠿⠾⠟⠿⠿⠿⠿⠿⠿⠛⠋⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠻⠝⠹⠘⠙⠁⠀⠀
⠀⠀⠀⣆⢂⡄⡄⡄⡄⠄⡇⠄⡄⣠⣠⢀⡀⠀⡦⢴⢀⣠⢀⡀⠀⡦⠀⣤⡄⢰⢠⣠⠠⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⢠⢤⣤⠰⣠⣴⣶⣿⣿⣿⣶⡄⢠⣤⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠈⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠀⠀⠀⠁⠈⠈⠈⠀⠁⠀⠁⢠⣭⣥⡌⠈⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡖⢶⣶⣶⣶⣶⣶⣶⣶⣶⡀⣾⣿⣿⣿⣿⣿⣿⣷⠀⣶⣶⣶⣶⣶⡶⣶⢰⠂⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠀⠉⠉⠉⠛⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠲⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠿⠇⠀⠀⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡄⠀⠀⣠⡄⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠾⠿⠀⠀⠀⣾⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠁⠀⠸⠵⠂⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠙⠻⠿⠿⠿⠟⠿⠻⠟⠻⠕⠹⠉⠑⠀⠀⠀
⠀⠀⠀⡄⢂⡀⡆⡤⡀⠤⡆⠤⡀⢠⣠⢠⠄⠀⡆⢰⢠⣄⢠⠄⠀⡖⠂⣤⡀⢰⢠⣄⠠⢄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠠⢄⡠⠠⣠⣴⣶⣿⣿⣿⣷⡄⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠈⠁⠃⠁⠃⠐⠃⠐⠁⠃⠉⠐⢂⠀⠃⠘⠐⠚⠐⠂⠀⠃⢀⣶⣧⡜⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡖⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⣾⣿⣿⣿⣿⣿⣿⣷⠀⣶⣶⣶⣶⣶⡶⡶⢲⢂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠁⠀⠉⠉⠁⠀⠉⠉⠉⠛⠋⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠈⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠢⠿⠇⠀⠀⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⣀⡄⠐⠶⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠀⠀⠀⠀⢑⠂⠀⠀⠀⠀⡀⠀⢀⠀⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⠀⣺⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠻⠙⠙⠘⠑⠁⠀⠀
⠀⠀⠀⡄⢂⡄⡆⡤⡀⠤⡆⠤⡀⢠⢠⢠⠄⠀⣆⣰⠠⢄⠠⠄⠀⣖⡂⣤⡀⢰⢀⢄⠀⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠀⠀⣤⠀⣠⣴⣶⣿⣿⣿⣶⡀⢠⣤⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠘⠁⠃⠃⠃⠒⠃⠒⠁⠃⠋⠐⢂⠀⠃⠘⠐⠚⠐⠂⠀⠃⢀⣒⣃⡘⠐⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢠⣿⣿⣿⣿⣿⣿⣿⣷⢀⣶⣶⣶⣶⣶⣶⣖⣰⠆⠖⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠁⠀⠉⠉⠁⠈⠉⠉⠉⠛⠋⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠘⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠺⠿⠇⠀⠀⠉⠉⠁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⣠⡄⠰⠶⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠲⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⡰⠄⠀⠀⠀⠀⡀⠀⠀⠀⢀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⣾⣏⣀⣀⣀⣀⣩⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⣿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠘⠘⠙⠉⠁⠸⠿⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠞⠾⠻⠿⠿⠿⠿⠿⠿⠛⠛⠙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠝⠙⠕⠑⠁⠀⠀
⠀⠀⠀⡄⠆⡀⡆⡠⡀⠀⡆⡠⡀⢀⢀⠀⠀⠀⣆⣰⠀⢄⠀⠄⠀⣖⡂⠤⡀⢰⢀⢄⢀⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠀⣤⣤⠠⣠⣤⣶⣾⣿⣿⣶⡀⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠘⠁⠃⠃⠃⠒⠃⠒⠁⠋⠋⠐⠃⠀⠃⠘⠘⠚⠐⠃⠀⠃⢀⣓⣃⡘⠐⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣶⣶⣶⣶⣶⣶⣶⣶⣶⠠⣾⣿⣿⣿⣿⣿⣿⣷⠀⣶⣶⣶⣶⣶⣶⣖⣰⢂⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠈⠉⠉⠙⠟⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠈⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠿⠇⠀⠀⠉⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠀⣠⡀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠲⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠿⠶⠀⠀⠀⣼⣏⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠉⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠻⠝⠙⠘⠙⠁⠀⠀
⠀⠀⠀⡄⠄⡀⡂⡀⡀⡀⡆⡀⡀⢀⢀⠀⠀⠀⣄⣠⠀⢀⠀⠀⠀⣄⡀⡀⡀⢰⢀⢀⢀⢀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⢠⢠⣤⢀⣤⣴⣶⣿⣿⣷⣆⠀⣤⣤⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠘⠃⠃⠃⠃⠂⠃⠂⠃⠋⠋⠐⣃⠀⠃⠘⠘⠛⠀⠃⠀⠃⢀⣛⣃⡘⠘⠙⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⡆⢰⣶⣶⣶⣶⣶⣶⣖⣲⢂⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠉⠀⠉⠉⠁⠉⠉⠙⢿⠋⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠈⠲⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠺⢁⠇⠀⠊⡉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⢀⣠⡀⠰⠖⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠒⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⣻⣏⣂⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⣿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠉⠈⠙⠉⠁⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉⠛⠻⠿⠿⠿⠿⠿⠻⠿⠻⠙⠙⠑⠙⠉⠀⠀
⠀⠀⠀⡀⠄⡀⡄⣀⡀⣀⡄⣀⠀⢀⢀⢀⡀⠀⡄⢠⢀⡀⢀⡀⠀⡤⠄⣉⠉⢡⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⢀⣄⣤⠀⣠⣴⣶⣾⣿⣿⣦⠀⢤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠑⠐⠃⠃⠃⠇⠂⠃⠢⠃⠊⠛⠨⠀⠀⠇⠸⠈⠹⠈⠀⠀⠇⠀⣍⣇⡘⠘⠍⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⢶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡆⢰⣶⣶⣶⣶⣶⣶⡶⢐⠂⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠈⠉⠙⢻⡏⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠉⢦⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠺⠧⠓⠀⠀⡉⠁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⣠⡄⠰⠶⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠲⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠅⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⣺⣏⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣷⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠉⠈⠉⠉⠁⠸⠵⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠻⠾⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠻⠝⠹⠝⠐⠉⠀⠀
⠀⠀⠀⡀⠄⡀⡄⣀⠀⣀⡄⣀⠀⢀⢀⢀⡀⠀⡄⢠⢀⡀⢀⡀⠀⡤⠄⣉⠉⢡⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠀⣄⣤⠀⣠⣴⣶⣾⣿⣿⣦⠀⢤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠱⠸⠃⠇⠇⠇⠤⠇⠠⠃⠎⠞⠨⠄⠀⠏⠹⠠⠽⠨⠄⠀⠏⠀⠭⠇⠸⠈⠭⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡆⢰⣶⣶⣶⣶⣶⣶⣶⣰⣂⡒⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠁⠈⠉⠉⠁⠈⠉⠙⢻⡏⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀
⠀⠀⠀⠀⠙⢦⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⡺⠧⠓⠀⠀⡉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⡄⠀⠀⣠⡄⠰⠶⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠲⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⢀⡀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⣺⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⣿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢟⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠉⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠻⠙⠙⠑⠐⠀⠀⠀
⠀⠀⠀⡀⡄⠀⡄⢀⠀⢀⡄⢀⠀⠀⠀⢀⡀⠀⡄⢠⠀⡀⢀⡀⠀⡤⠄⣉⠉⢡⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠠⢠⣤⠀⣠⣴⣶⣾⣿⣿⣦⠀⢠⣤⣤⣤⣤⣄⠀⠀⠄⠀⠄⠀⠀⠀
⠀⠀⠀⠳⠰⠃⠇⠇⠇⠤⠇⠤⠃⠞⠞⠠⠆⠀⠏⠹⠰⠼⠠⠆⠀⠏⠁⠦⠇⠸⠠⠬⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡆⢀⣶⣶⣶⣶⣶⣶⣖⢲⣂⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠉⠀⠉⠉⠁⠈⠉⠉⢻⡏⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠧⠓⠀⠀⣉⠁⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⣠⡄⠰⠶⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠲⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠇⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⢀⡀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⣺⣏⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⣿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠁⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠾⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠝⠹⠙⠙⠀⠀⠀
⠀⠀⠀⡀⡄⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⡤⠄⣉⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠀⢤⣤⠀⣠⣴⣾⣿⣿⣿⣦⠀⢠⣤⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⠳⠰⠃⠇⠇⠇⠥⠇⠥⠇⠞⠞⠠⠆⠀⠏⠹⠰⠼⠠⠆⠀⠏⠁⠶⠇⠸⠸⠬⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡆⢀⣶⣶⣶⣶⣶⣶⣶⢲⣦⠔⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠁⠈⠉⠉⠁⠈⠉⠉⢛⠏⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠺⢇⠀⠀⠀⡉⠁⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⡀⠀⠀⣠⡄⠐⠶⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠠⠲⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⡀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠿⠗⠀⠀⠀⣻⣏⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⣿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠙⠉⠉⠉⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠺⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠛⠿⠿⠿⠿⠿⠿⠿⠟⠻⠕⠹⠉⠘⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⠐⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠠⢄⡠⠀⣠⣴⣿⣿⣿⣷⣦⠀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠣⠰⠇⠇⠏⠇⠍⠇⠍⠇⠞⠾⠘⠃⠀⠇⠸⠘⠳⠘⠃⠀⠇⠀⡛⠆⠸⠸⠛⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡆⢰⣶⣶⣶⣶⣶⣶⣖⢲⣆⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠁⠈⠉⠉⠁⠈⠉⠉⢛⠏⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠑⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠺⠃⠅⠀⠂⡉⠁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀
⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⡀⠀⠀⣠⡄⠰⠶⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠠⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⣻⣏⣃⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠉⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠻⠝⠹⠙⠙⠀⠀⠀
⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⣀⡐⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠀⠀⣤⠀⣤⣴⣶⣾⣿⣷⣆⠀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠄⠀⠀⠀
⠀⠀⠀⢣⠰⠇⡇⠏⡆⢉⡇⢉⠆⡜⠾⢘⡁⠀⡇⢸⢈⣳⢘⡁⠀⡇⠀⣛⡆⢸⠸⡓⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡄⢰⣶⣶⣶⣶⣶⣶⣶⣒⡂⠐⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠈⠉⠙⢿⠋⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀
⠀⠀⠀⠀⠑⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⢀⠗⠀⠊⡉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⠀⣠⡄⠐⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢀⡀⠀⠀⠀⢠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⣺⣇⣀⣀⣀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠙⠁⠁⠸⠷⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠛⠻⠿⠿⠿⠿⠿⠻⠟⠿⠙⠹⠝⠐⠀⠀⠀
⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⣀⡐⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠀⣤⣤⠀⣠⣴⣶⣶⣿⣷⣦⠀⢤⣤⣤⣤⣤⣄⠀⠀⠄⠀⠀⠀⠀⠀
⠀⠀⠀⢧⢰⠇⡇⡏⡆⣉⡇⣉⠆⡜⡼⢈⡁⠀⡗⢺⢈⣱⢈⡁⠀⡗⠂⣙⡆⢸⢐⣑⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡖⢶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡆⢐⣶⣶⣶⣶⣶⣶⣶⢲⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠁⠈⠉⠉⠁⠈⠉⠙⢛⡋⠋⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀
⠀⠀⠀⠀⠑⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠺⠧⠓⠀⠂⡉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⡀⠀⠀⣠⡄⠐⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠠⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠿⠗⠀⠀⠀⣻⣏⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⡿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠙⠉⠉⠉⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠻⠿⠿⠿⠿⠿⠟⠛⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠟⠻⠝⠙⠙⠙⠀⠀⠀
⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⣀⡐⠛⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⡄⠄⢠⣤⠀⣠⣴⣶⣾⣿⣿⣦⠀⢤⣤⣤⣤⣤⣄⠀⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⢧⢡⠆⡇⡎⡆⣂⡇⣊⠆⡴⡴⢀⡅⠀⡗⢺⢠⣱⢀⡄⠀⡗⠂⣍⡆⢸⢀⣑⠐⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡆⢐⣶⣶⣶⣶⣶⣶⣶⢰⠆⡔⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠉⠀⠉⠉⠁⠈⠉⠙⢻⡏⠋⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀
⠀⠀⠀⠀⠑⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠺⠧⠒⠀⠀⡉⠁⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⣠⡄⠐⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠠⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠏⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⢀⡀⠀⢀⠀⢠⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⣺⣏⣀⣀⣀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⣿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠘⠘⠙⠉⠉⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠙⠛⠻⠿⠿⠿⠿⠿⠻⠿⠿⠝⠹⠙⠙⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠀⣄⣤⢀⣤⣴⣶⣶⣿⣷⣆⠀⣤⣤⣤⣤⣤⣄⠀⠀⠤⠀⠀⠀⠀⠀
⠀⠀⠀⢇⢡⡆⡆⡆⡆⡂⡇⡒⡆⡴⡴⠰⠆⠀⡇⢸⢰⢴⠰⠆⠀⡇⠀⢶⡄⢸⢰⠴⠐⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⡄⢰⣶⣶⣶⣶⣶⣶⣶⣰⡂⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠙⣿⠛⠋⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠑⢦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠺⠅⠗⠀⠈⡉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⣀⡄⠐⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⡀⠀⢀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠿⠶⠀⠀⠀⣺⣏⣀⣀⣀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⣿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢿⣿⣿⢿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠈⠙⠙⠁⠁⠸⠵⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣟⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣶⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠺⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠙⠛⠿⠿⠿⠿⠿⠿⠻⠟⠻⠙⠙⠐⠙⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⢠⣠⡄⠀⠀⠀⣄⣤⠀⣠⣴⣶⣶⣶⣶⣦⠀⢤⣤⣤⣤⣤⣄⠀⠀⠄⠀⠄⠀⠀⠀
⠀⠀⠀⢆⢡⡆⡆⡖⡆⡒⡇⡒⡄⡰⣴⠰⠂⠀⡇⢸⠰⢦⠰⠂⠀⡏⠁⠶⡄⢸⢰⠶⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⡖⢶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣿⣿⣿⣿⣿⣿⣿⡆⢰⣶⣶⣶⣶⣶⣶⡶⠰⠢⠔⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠈⠀⠈⠈⠀⠀⠁⠀⠉⠁⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠉⠉⠀⠉⠉⠁⠈⠉⠙⢿⠏⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠑⢦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠺⡗⠓⠀⠀⣉⠁⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣀⡄⠐⠲⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⡀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀
⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠿⠦⠀⠀⠀⣺⣇⣀⣀⣀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢸⣿⡿⡿⢿⡿⣿⣿⡿⢿⣿⢿⡿⣿⢿⡿⣿⣿⢿⢿⡿⠿⡿⡿⣿⣿⡿⢿⡿⣿⡿⣿⣿⢿⣿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣷⣶⣿⣶⣶⣶⣾⣶⣾⣿⣿⣾⣾⣿⣿⣾⣶⣶⣶⣷⣿⣶⣷⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢟⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⣽⣋⣚⣿⣟⣛⣛⣛⣛⣛⣚⣙⣻⠿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠋⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠈⠈⠘⠉⠉⠉⠸⠷⠄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⢿⡟⡿⣿⢟⣛⣿⢟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⣶⣷⣾⣾⣾⣾⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1477

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

(ℹ) Images, hyperlinks and comments at https://news.techrights.org/n/2023/12/07/_Video_To_Combat_Efforts_to_Cancel_or_Kill_the_Career_and_Reput.shtml
    Gemini version at gemini://gemini.techrights.org/n/2023/12/07/_Video_To_Combat_Efforts_to_Cancel_or_Kill_the_Career_and_Reput.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] To Combat Efforts to Cancel or Kill
the Career (and Reputation) of the People Who Made GNU/Linux We Must Rally the
Community⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


Video_download_link | md5sum a6d2eee3c4642e11f2efa3a855e82e8e
Killing_the_Founders
Creative Commons Attribution-No Derivative Works 4.0


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


THE previous post entitled Still_Not_'Canceled' (as in so-called 'cancel
culture') celebrated the fact that some of the earlier if not earliest
developers_of_Linux are still around. Ted Ts'o, who had become obese, seems
like he lost weight (he looks better now) and the same is true for Linus
Torvalds, who looks younger again:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linus_Torvalds⦈_


This is how LWN captured him a few weeks ago. Ted Ts'o is on the left of this
photo.


The video (been_a_while) shown above focuses on GNU and the GPL, whose main
people have comes under another wave of attacks from Microsofters who go to
Linux_Foundation events (part of the Corporate Cabal). It reminds people of the
vital role both GNU and the GPL played in the adoption of Linux, not just among
developers but users too. Nowadays the vast majority of servers and most mobile
devices use Linux. Few users are aware that they use Linux and many never heard
of this thing called "GNU" (except the animal).


The bottom line is, nobody speaks better for projects and for licences than
their own founders, who are far_from_dead and are very eager to keep leading
their "babies". █




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

                    ䷩ 𝚕𝚒𝚗𝚎 2328

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 07/12/2023: Climate Events Occupied
by Their Enemy, Workers Going on Strike⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o ⚓ James G ☛ Advent_of_Technical_Writing:_Clarity⠀⇛


                 Good technical writing is clear. I could make that
                 statement and say "that's all you need to know!" But that
                 wouldn't be clear! Herein lies a question: what does it
                 mean to communicate technical concepts with clarity?
                 Let's talk through a few tips that will help make your
                 writing more comprehensible and intuitive to your
                 audience.


          o ⚓ [Repeat] Kev Quirk ☛ PenPals⠀⇛


                 I read this post and thought it was chock full of lovely
                 stories from Brandons past (and present) with his
                 PenPals.


          o ⚓ Brandon ☛ Pen_Pals_✍️⠀⇛


                 Over the past couple of months, I've seen pen pals pop up
                 on several of the blogs I follow, and I love it. A one-
                 on-one connection with someone else done in private is
                 sort of the opposite of what we've been doing all these
                 years with social media. It's something that takes more
                 time than a "like" or a one liner, it's a real commitment
                 to building something. In my opinion, that is what the
                 internet should be all about.


                 I thought it might be fun to look back on my pen pals
                 from over the years, since I hold these relationships
                 just as a close as any IRL relationship that I have.
                 Heck, in some cases, even closer.


          o § Science⠀➾


                # ⚓ Computers Are Bad ☛ vhf_omnidirectional_range⠀⇛


                       The term "VHF omnidirectional range" can at first
                       be confusing, because it includes "range"---
                       a measurement that the technology does not provide.
                       The answer to this conundrum is, as is so often the
                       case, history. The "range" refers not to the radio
                       equipment but to the space around it, the area in
                       which the signal can be received. VOR is an
                       inherently spatial technology; the signal is
                       useless except as it relates to the physical world
                       around it.


          o § Education⠀➾


                # ⚓ New York Times ☛ Math_Scores_Dropped_Globally,_but_the_U.S.
                  Still_Trails_Other_Countries⠀⇛


                       The results are the latest indicator of an American
                       education system that struggles to prepare all
                       students from an early age, with proficiency in
                       math dropping the longer students remain in the
                       system. National test results last year also
                       reported greater declines in math compared with
                       reading, a subject that can be more influenced by
                       what happens at home and was less affected by
                       school closures.


                # ⚓ Hillel Wayne ☛ Notes_on_Every_Strangeloop_2023_Talk_I
                  Attended⠀⇛


                       This is my writeup of all the talks I saw at
                       Strangeloop, written on the train ride back, while
                       the talks were still fresh in my mind. Now that all
                       the talks are online I can share it. This should
                       have gone up like a month ago but I was busy and
                       then sick. Enjoy!


                # ⚓ The Conversation ☛ Rural_communities_are_being_left_behind
                  because_of_poor_digital_infrastructure,_research_shows⠀⇛


                       In an era where businesses and households depend on
                       the [Internet] for everything from marketing to
                       banking and shopping, the lack of adequate digital
                       access can be a significant hurdle. And our recent
                       research shows that many homes and businesses in
                       the UK are being left stranded in the digital age.


                       Our two studies focused on a rural county in Wales,
                       Ceredigion, where the lack of reliable digital
                       infrastructure worsened the impacts of the pandemic
                       on families and businesses. Poor digital
                       accessibility and connectivity exacerbated the
                       stress levels of families who were already having
                       to juggle home schooling and working from home.


                # ⚓ Bridge Michigan ☛ Michigan_spread_word_on_free_college._But
                  are_residents_listening?⠀⇛


                       Michigan is making a big push to increase the
                       number of college graduates in the state, investing
                       $70 million this year to expand the Michigan
                       Reconnect program that pays for community college,
                       lowering the minimum age from 25 to 21 years old.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_students’_performance
                  drops_in_global_study_amid_general_decline_over_Covid-19
                  pandemic⠀⇛


                       Hong Kong secondary school students’ performance in
                       maths and reading has fallen in a global assessment
                       amid a general decline internationally over the
                       Covid-19 pandemic. The Programme for International
                       Student Assessment (PISA), a global study that
                       evaluates the maths, science, and the mother-tongue
                       reading literacy of 15-year-old students [...]


          o § Hardware⠀➾


                # ⚓ SparkFun Electronics ☛ Pete's_Headphones_Featured_on_IEEE⠀⇛


                       This project gives musicians a way to block out
                       unwanted sound while still being able to hear what
                       they're playing. Complete with some really great
                       graphics and a full project writeup from Pete, this
                       is an article you won't want to miss!


                # ⚓ IEEE ☛ Build_Your_Own_Hi-fi_Ear_Defenders:_An_inexpensive
                  solution_to_hearing_well_in_loud_environments⠀⇛


                       The microphone’s breakout board applies a gain of
                       64x, using two stages. My first thought was to
                       reduce this gain. Maybe the clipping was happening
                       at only the first gain stage. Unfortunately, even
                       with this gain eliminated, the clipping remained. I
                       then tested the raw MEMS microphone output by
                       feeding it into some “pro grade” mic preamps. With
                       this setup, I was able to see that the problem
                       wasn’t the amplification stages but that the mics
                       themselves were producing the clipping. Through
                       this test, I learned a valuable lesson: A mic’s
                       listed AOP is the point at which the microphone
                       will produce a 10 percent total harmonic
                       distortion, and so noticeable clipping can actually
                       start to happen well below this level.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ The Conversation ☛ Technology_is_stealing_your_time_in_ways
                  you_may_not_realise_–_here’s_what_you_can_do_about_it⠀⇛


                       On the face of it some of these tasks may seem like
                       examples of tech saving us time. In theory, online
                       banking should mean I have more time because I no
                       longer need to go to the bank in my lunch break.
                       However, our research suggests that this is not the
                       case. Technology is contributing to a denser form
                       of life.


                # ⚓ University of Arizona ☛ New_wearable_communication_system
                  offers_potential_to_reduce_digital_health_divide⠀⇛


                       A group of University of Arizona researchers has
                       set out to change that with a wearable monitoring
                       device system that can send health data up to 15
                       miles – much farther than Wi-Fi or Bluetooth
                       systems can – without any significant
                       infrastructure. Their device, they hope, will help
                       make digital health access more equitable.


                # ⚓ teleSUR ☛ Flu_and_COVID-19_Infections_Tick_Up_in_the_United
                  States⠀⇛


                       New COVID-9 strains have caused 15,000
                       hospitalizations and around 1,000 deaths every
                       week.


                # ⚓ Latvia ☛ 23_Covid_deaths_in_Latvia_last_week⠀⇛


                       The incidence of Covid-19 continued to rise in
                       Latvia last week. The number of both inpatient and
                       deceased patients increased, according to
                       monitoring data from the Disease Prevention and
                       Control Center (SPKC) published December 6.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ The Verge ☛ Ex-Twitter_security_head_claims_the_company
                  fired_him_to_flout_regulations⠀⇛


                       The lawsuit alleged that Musk hired Steve Davis as
                       an adviser and gave him broad authority, with which
                       he immediately “began cutting Twitter’s products
                       and services that supported and complied with the
                       Twitter FTC Consent Decree.” Twitter had settled
                       with the FTC over its inappropriate use of users’
                       personal information only a few months before,
                       prompting the decree. Rosa’s suit complains that
                       Davis and Musk were both “dismissive” of the
                       decree.


                       In November, around the time Davis was hired, a
                       lawyer for Twitter posted a message to Slack saying
                       that anyone feeling uncomfortable about things
                       Twitter was asking them to do should seek
                       whistleblower protection.


                # ⚓ Scoop News Group ☛ GAO_preparing_report_on_agency
                  artificial_intelligence_use_case_inventories⠀⇛


                       Federal agencies’ annual AI use case inventories,
                       which were initially required under a Trump-era
                       executive order, have so far lacked consistency and
                       received criticism from academics and advocates as
                       a result. A major 2022 report by several Stanford
                       researchers analyzed progress on the existing AI
                       requirements under statute and existing executive
                       orders, detailing compliance issues with the
                       inventories in the first year they were required.
                       FedScoop has continued to report on issues with
                       those public postings in recent months.


                # ⚓ Futurism ☛ Former_Tesla_Employee_Offers_Grim_Warning_About
                  Vehicles'_Safety⠀⇛


                       A former Tesla employee and whistleblower has come
                       forward, telling the BBC in a damning interview
                       that the car company's controversial Autopilot
                       system is not safe for use on public roads, arguing
                       that other drivers, passengers, and pedestrians
                       could be put at risk.


                # ⚓ Jamie Zawinski ☛ Gmail_sucks,_water_is_wet⠀⇛


                       One for the annals of Apple / Google
                       interoperability.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Futurism ☛ Oops!_23andMe_Admits_Hackers_Stole_7
                        Million_Customers'_Genetic_Data⠀⇛


                             But the problem goes beyond this relatively
                             small number of people. Because the website
                             allows users to share DNA information with
                             other users in order to find relatives, the
                             true number impacted is orders of magnitude
                             larger — with about 6.9 million customers
                             having their personal information
                             compromised, according to TechCrunch. Big
                             yikes on that figure, because it affects
                             something like half of the 14 million users
                             at 23andMe.


                             Personal information included users' names,
                             birthdays, location, relationships, ancestry
                             background, and shared DNA percentages with
                             relatives, according to the news outlet.


                      # ⚓ CPJ ☛ CPJ_to_EU:_The_time_to_act_on_spyware_is_now⠀⇛


                             Negotiations on the European Media Freedom
                             Act (EMFA), a draft EU law seeking to
                             strengthen media freedom and pluralism in EU
                             member states, are likely to conclude during
                             a meeting scheduled for December 15.


                             CPJ is concerned that Article 4 of the EMFA
                             on the protection of journalists and their
                             sources could be problematic, despite its
                             well-intended purpose, because EU member
                             states have requested that a “national
                             security” exemption be included to justify
                             spyware against journalists.


                      # ⚓ [Old] CPJ ☛ Special_report:_When_spyware_turns_phones
                        into_weapons⠀⇛


                             There’s nothing new about governments or
                             criminal gangs spying on journalists or
                             activists they fear might expose or discredit
                             them. But the development of high-tech “zero-
                             click” spyware – the kind that takes over a
                             phone without a user’s knowledge or
                             interaction – poses an existential crisis for
                             journalism and the future of press freedom
                             around the world.


                      # ⚓ Tech Central (South Africa) ☛ US_senator_claims
                        governments_spying_on_Apple,_Android_users⠀⇛


                             Wyden’s letter cited a “tip” as the source of
                             the information about the surveillance. His
                             staff did not elaborate on the tip, but a
                             source familiar with the matter confirmed
                             that both foreign and US government agencies
                             have been asking Apple and Google for
                             metadata related to push notifications to,
                             for example, help tie anonymous users of
                             messaging apps to specific Apple or Google
                             accounts.


                      # ⚓ Vice Media Group ☛ Apple_Just_Confirmed_Governments
                        Are_Spying_on_People’s_Phones_With_Push_Notifications⠀⇛


                             Wyden wrote that the federal government had
                             restricted Apple and other companies’ ability
                             to share information about this process. The
                             Senator’s office “received a tip” last year
                             that “government agencies in foreign
                             countries were demanding smartphone ‘push’
                             notification records from Google and Apple,”
                             Wyden, a Democratic senator from Oregon,
                             wrote in the letter to Attorney General
                             Merrick Garland. “My staff have been
                             investigating this tip for the past year,
                             which included contacting Apple and Google.
                             In response to that query, the companies told
                             my staff that information about this practice
                             is restricted from public release by the
                             government.”


                      # ⚓ Federal News Network ☛ Congress_should_reauthorize
                        Section_702⠀⇛


                             Letitia A. Long is chairwoman of the
                             Intelligence and National Security Alliance.


                      # ⚓ ABC ☛ FBI_chief_makes_fresh_pitch_for_spy_program
                        renewal_and_says_it'd_be_'devastating'_if_it_lapsed⠀⇛


                             The thorny path to reauthorization was laid
                             bare during Tuesday's hearing, when lawmakers
                             from both parties questioned Wray, at times
                             aggressively, over periodic misuse of the
                             program by FBI employees seeking out
                             information about Americans. Though the
                             program enables surveillance only of
                             foreigners located outside the U.S, it also
                             can capture the communications of American
                             citizens and others in the U.S. when those
                             people are in contact with those targeted
                             foreigners.


                      # ⚓ CoryDoctorow ☛ Privacy_first⠀⇛


                             The internet is embroiled in a vicious
                             polycrisis: child safety, surveillance,
                             discrimination, disinformation, polarization,
                             monopoly, journalism collapse – not only have
                             we failed to agree on what to do about these,
                             there's not even a consensus that all of
                             these are problems.


                             But in a new whitepaper, my EFF colleagues
                             Corynne McSherry, Mario Trujillo, Cindy Cohn
                             and Thorin Klosowski advance an exciting
                             proposal that slices cleanly through this
                             Gordian knot, which they call "Privacy
                             First": [...]


          o § Defence/Aggression⠀➾


                # ⚓ Futurism ☛ Head_of_Climate_Conference_Who_Happens_to_Be_an
                  Oil_Exec_Says_Actually_Fossil_Fuels_Are_Fine⠀⇛


                       The conflict of interest is palpable. Al Jaber is
                       CEO of Adnoc, the largest drilling company in the
                       Middle East that's gearing up to expand its
                       drilling ventures considerably.


                       According to the Global Oil and Gas Exit List, a
                       public database that keeps track of the activities
                       of oil and gas ventures, the Al Jaber-led state oil
                       company has far and away the biggest plans to
                       expand oil and gas production in the world.


                # ⚓ Ruben Schade ☛ Human-induced_climate_change⠀⇛


                       The COP28 summit reminds me that some people need a
                       primer: [...]


                # ⚓ Democracy Now ☛ COP28:_Amy_Goodman_Attempts_to_Question_UAE
                  Oil_CEO_Serving_as_President_of_U.N._Climate_Talks_in_Dubai⠀⇛


                       As Democracy Now! broadcasts from the U.N. climate
                       summit, Amy Goodman attempts to question the oil
                       CEO presiding over the talks. COP28 president and
                       United Arab Emirates oil CEO Sultan Al Jaber is
                       facing criticism over the record number of fossil
                       fuel lobbyists in attendance at the summit, and
                       recently claimed there is “no science” to back up
                       calls to phase out fossil fuels in order to limit
                       global warming to 1.5 degrees Celsius above pre-
                       industrial levels.


                # ⚓ Democracy Now ☛ Big_Oil’s_Takeover_of_U.N._Climate_Summit
                  Decried_by_Activists_Fighting_for_Fossil_Fuel_Phaseout⠀⇛


                       Climate activist Harjeet Singh joins us for an
                       update on the U.N. climate summit in Dubai, where
                       fossil fuel lobbyists outnumber many countries’
                       delegations. “It is deeply, deeply problematic to
                       see how fossil fuel lobbyists are taking over these
                       climate talks,” he says, noting that climate
                       activists’ fears of an industry takeover of the
                       world’s foremost gathering for climate governance
                       appear to have come true. “We can’t just allow
                       fossil fuel industry to define what is going to
                       happen here,” Singh warns, as financial interests
                       continue to divert political energy away from
                       decarbonization. Singh is the head of global
                       political strategy with Climate Action Network and
                       works on the Fossil Fuel Non-Proliferation Treaty,
                       a global initiative to phase out fossil fuels and
                       support a just transition.


                # ⚓ Democracy Now ☛ Carbon_Colonialism:_Oil-Rich_UAE_Buys_Up
                  Large_Swaths_of_Africa_for_Carbon_Credits_to_Keep_Polluting⠀⇛


                       As Democracy Now! broadcasts from COP28 in Dubai,
                       we look at how the United Arab Emirates is using
                       its vast oil money to buy up the rights to land in
                       many African countries in order to sell carbon
                       credits to major polluters, a plan that critics
                       characterize as a new form of colonialism. “After
                       failing to mitigate at the source,” wealthy
                       polluters now “want to, basically, buy, on the
                       cheap, African land,” says Power Shift Africa’s
                       Mohamed Adow about wealthy nations’ failure to
                       deliver on climate finance and turn to a “land
                       grab” on the African continent. “What they’re doing
                       is actually commodifying nature,” says Adow, who
                       describes carbon credits as an “imaginary concept”
                       amounting to “permits to pollute.”


                # ⚓ Democracy Now ☛ Why_Are_Russia_&_U.S._Promoting_Nuclear
                  Power_at_U.N._Climate_Talks?_Russian_Environmentalist_Speaks
                  Out⠀⇛


                       As Vladimir Putin arrives in Abu Dhabi but does not
                       plan to attend the COP28 summit in Dubai, we speak
                       with Vladimir Slivyak, co-chair for the leading
                       Russian environmental organization Ecodefense,
                       about the climate impact of Russia’s war on Ukraine
                       and the renewed push at the summit to expand
                       nuclear power. “When you promote nuclear power, you
                       have to understand it’s diverting resources from
                       renewable energy, and renewable energy is the real,
                       most efficient answer to climate change,” says
                       Slivyak. He also discusses how the collapse of
                       civil society in Russia has pushed him and other
                       social activists to leave the country.


                # ⚓ Truthdig ☛ Reuters_Tops_List_of_Fossil_Fuel_Industry_Media
                  Enablers⠀⇛


                # ⚓ Axios ☛ GOP's_"dictator"_test⠀⇛


                       Why it matters: This isn't 2016. Trump is well
                       aware that the softball question lobbed last night
                       by Fox News' Sean Hannity — "Do you in any way have
                       any plans whatsoever, if re-elected president, to
                       abuse power?" — is rife with alarming context.


                # ⚓ The Nation ☛ A_Trump_Dictatorship_Is_Not_“Inevitable”—as
                  Long_as_We_Step_Up_Now⠀⇛


                       But that’s if Trump wins. I don’t expect him to win
                       11 months from now. And I’m starting to worry that
                       some of the alarm might be counterproductive.


                       You don’t need investigative reporters or well-
                       placed sources to know that Trump plans to end
                       democracy. He’s told us, repeatedly, and as Maya
                       Angelou famously warned, we ought to believe him.
                       In his first campaign speech of the 2024 election,
                       in Waco, Tex., he promised his followers, [...]


                # ⚓ The Atlantic ☛ Trump_Says_He’ll_Be_a_Dictator_on_‘Day
                  One’⠀⇛


                       It’s not unusual for political candidates to accuse
                       their opponents of being would-be fascists or
                       authoritarians. Rivals of Franklin Roosevelt, Barry
                       Goldwater, Richard Nixon, and Barack Obama, among
                       many others, warned about these men’s supposed
                       dictatorial ambitions. (Of course, none of those
                       presidents mounted a months-long effort to steal an
                       election, capped by inciting a violent assault on
                       the Capitol.)


                       What is unusual, and in fact crazy, is for the
                       rival to respond: Yeah, you bet I will.


                # ⚓ The Atlantic ☛ Donald_Trump_vs._American_History⠀⇛


                       A central part of Trump’s project is to depict the
                       presentation of empirical evidence as an attempt at
                       ideological indoctrination. The claim that this
                       country has prevented millions from achieving
                       upward mobility should not be a controversial one;
                       it reflects actual policies such as convict
                       leasing, school segregation, and housing covenants.
                       To Trump and his allies, however, anyone making
                       such a claim has fallen prey to a “radical
                       movement” that sees America as an inherently and
                       irredeemably evil country. A professor stating that
                       the Confederacy seceded from the Union because of
                       slavery and racism is a member of the “woke mob,”
                       never mind the fact that the seceding states said
                       this directly in their declarations of secession.
                       (Mississippi in 1861: “Our position is thoroughly
                       identified with the institution of slavery—the
                       greatest material interest in the world.”) An
                       elementary-school teacher highlighting the
                       importance of LGBTQ figures in the history of
                       American activism is reprimanded for being part of
                       an effort to force sexuality onto students, never
                       mind the fact that Bayard Rustin, Harvey Milk, and
                       Marsha P. Johnson played an indisputable role in
                       shaping political life.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ El País ☛ ‘A_colossal_jerk_has_died’:_when_celebrity
                  obituaries_are_not_kind⠀⇛


                       In his poem Obituary with cheers, the Uruguayan
                       writer Mario Benedetti invited “the innocent” and
                       “the victims” to celebrate the death of a “piece of
                       shit” with “a black soul.” It was widely circulated
                       on social media in 2004 when former US President
                       Ronald Reagan died and it was misinterpreted that
                       the author had just composed the verses for the
                       occasion. It would happen again two years later
                       with the death of former Chilean dictator Augusto
                       Pinochet, but, in fact, it had been published in
                       1963 (although, in an interview in El Clarín in
                       2007, Benedetti gave his approval for the Chileans
                       to appropriate it to use against Pinochet). The
                       poem does not state who the deceased in question
                       is; moreover, it specifically recreates the need to
                       enjoy the departure for good of someone who was
                       presumably horrible and whose death has made the
                       world a better place: “it’s time to celebrate / not
                       to tone it down / remember, not just anyone has
                       died [...] don’t forget this dead man / was a real
                       S.O.B.”


                # ⚓ [Old] Rolling Stone ☛ Henry_Kissinger,_War_Criminal_Beloved
                  by_America’s_Ruling_Class,_Finally_Dies⠀⇛


                       Henry Kissinger died on Wednesday at his home in
                       Connecticut, his consulting firm said in a
                       statement. The notorious war criminal was 100.


                       Measuring purely by confirmed kills, the worst mass
                       murderer ever executed by the United States was the
                       white-supremacist terrorist Timothy McVeigh. On
                       April 19, 1995, McVeigh detonated a massive bomb at
                       the Murrah federal building in Oklahoma City,
                       killing 168 people, including 19 children. The
                       government killed McVeigh by lethal injection in
                       June 2001. Whatever hesitation a state execution
                       provokes, even over a man such as McVeigh —
                       necessary questions about the legitimacy of killing
                       even an unrepentant soldier of white supremacy —
                       his death provided a measure of closure to the
                       mother of one of his victims. “It’s a period at the
                       end of a sentence,” said Kathleen Treanor, whose
                       four-year-old McVeigh killed.


                       McVeigh, who in his own psychotic way thought he
                       was saving America, never remotely killed on the
                       scale of Kissinger, the most revered American grand
                       strategist of the second half of the 20th century.


          o § Environment⠀➾


                # ⚓ [Old] National World Publishing Ltd ☛ Edinburgh_Tyre
                  Extinguishers_hit_‘posh’_New_Town_area_and_boast_about
                  deflating_tyres_of_32_SUVs⠀⇛


                       Climate activist group Tyre Extinguishers claim to
                       have deflated the tyres of another 32 SUVs in
                       Edinburgh.


                # ⚓ [Old] Auto Evolution ☛ Apparently,_the_Annoying_"Tire
                  Extinguishers"_Were_Right_About_SUVs⠀⇛


                       A new report confirms that the activists are right
                       about at least one thing – polluting the world. The
                       Global Fuel Economy Initiative says that heavier
                       and bigger vehicles considerably slowed down
                       automakers' efforts to bring more fuel-efficient
                       and cleaner vehicles to market.


                # ⚓ [Old] National World Publishing Ltd ☛ Edinburgh_Tyre
                  Extinguishers_‘on_a_roll’_as_they_hit_New_Town_area_again_and
                  deflate_tyres_of_another_15_SUVs⠀⇛


                       Since 2022, hundreds of SUVs have been deflated in
                       the Leith, Portobello, Hillside, Marchmont,
                       Bruntsfield and New Town areas by the group.


                       A global organisation, Tyre Extinguishers want to
                       make it “impossible” to own an SUV. It describes
                       them as “a climate disaster”, “dangerous” and
                       “unnecessary”.


                # ⚓ [Old] The Herald ☛ Tyre_Extinguishers_Edinburgh:_Group
                  targets_New_Town_SUVs⠀⇛


                       It is part of a protest against the pollution
                       produced by these vehicles and the impact on
                       climate change and clean air in cities.


                # ⚓ [Old] Reach PLC ☛ Edinburgh_climate_protest_group_deflate
                  tyres_of_32_SUV's_in_city_centre⠀⇛


                       "Why do you own a tank in the middle of the city?!"


                # § Energy/Transportation⠀➾


                      # ⚓ Futurism ☛ You'll_Be_Astonished_How_Much_Power_It
                        Takes_to_Generate_a_Single_AI_Image⠀⇛


                             As first spotted by The Register, a team of
                             researchers from AI developer Hugging Face
                             and Carnegie Mellon University recently
                             shared a yet-to-be-peer-reviewed paper on how
                             much power AI tools need to perform a variety
                             of tasks.


                             Their results are — and highlight the very
                             real carbon footprint of turning to AI
                             instead of a human artist for imagery needs.


                      # ⚓ Positech Games ☛ Solar_farm_4th_site_visit:
                        Substations!⠀⇛


                             Its been a long time since my last visit to
                             the site, and work stalled for ages due to
                             arguments and analysis regarding earthing.
                             Finally at LONG LAST, that was agreed upon,
                             and we could recommence work. I went up there
                             with a friend yesterday in pretty bad wet
                             weather to see what progress there had been.
                             Hopefully this is the start of the final leg
                             of getting the farm finished and connected.
                             When I was last there, most (85%?) of the
                             panels and frames were installed, and most of
                             the inverters, but that was it. This time
                             there was some more stuff done.


                      # ⚓ New York Times ☛ Renewable_Energy_Could_Be_a_Casualty
                        in_the_War_on_Inflation._Here’s_Why.⠀⇛


                             High interest rates make green start-up costs
                             soar. Officials at the U.N. climate summit
                             fear the world could miss an opportunity to
                             avert future greenhouse gas emissions.


                      # ⚓ The Verge ☛ Climate_groups_say_Biden_AI_order_doesn’t
                        address_AI’s_climate_impact⠀⇛


                             The groups sent a letter to the White House
                             urging the Biden administration, including
                             national climate advisor Ali Zaidi, to add
                             more climate-centered policies in its AI
                             executive order released earlier in October.
                             Seventeen groups signed the letter, including
                             Accountable Tech, Amazon Employees for
                             Climate Justice, Climate Action Against
                             Disinformation, Greenpeace USA, and the Tech
                             Oversight Project.


                             The letter accuses the administration of
                             neglecting AI’s impact on spreading
                             disinformation on climate and the huge energy
                             cost of training large language models.


                      # ⚓ Tech Central (South Africa) ☛ The_case_against
                        bitcoin⠀⇛


                             The bull case preached by the laser-eyed and
                             luna-tattooed crowd is, as before, driven by
                             sentiment and speculation rather than
                             utility. Bitcoin may be a glorified pet rock
                             in terms of money-ness, but people like to
                             hoard it and trade it as a risky hybrid of
                             gold and Nasdaq start-up in the hope of
                             outsized gains. The optimistic view is that
                             any news will be good news as bad actors like
                             Sam Bankman-Fried or Changpeng Zhao get
                             flushed out, mass-market spot ETFs get
                             closer, and potential interest-rate cuts lift
                             risk appetite. With a rising price providing
                             a positive feedback loop, who wouldn’t want
                             to take a punt?


                      # ⚓ APNIC ☛ A_carbon-aware_Internet_with_the_Green_Web
                        Foundation⠀⇛


                             At the Green Web Foundation, we seek to
                             increase the Internet’s energy efficiency and
                             speed the Internet’s transition away from
                             fossil fuels by 2030. As part of this vision,
                             we conducted the project ‘A Carbon-Aware
                             Internet’ with support from the RIPE NCC
                             Community Projects Fund in 2022.


                             Using real-time data about electricity around
                             the world, we annotated network connections
                             with carbon intensity. With this information,
                             any digital infrastructure provider can move
                             their compute workloads to greener regions.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Bruce Schneier ☛ Security_Analysis_of_a_Thirteenth-Century
                  Venetian_Election_Protocol⠀⇛


                       I like that this paper has been accepted at a
                       cybersecurity conference.


                       And, for the record, I have written about the
                       positive aspects of security theater.


                # ⚓ [Old] HP ☛ Electing_the_Doge_of_Venice:_analysis_of_a_13th
                  Century_protocol⠀⇛


                       Abstract: This paper discusses the protocol used
                       for electing the Doge of Venice between 1268 and
                       the end of the Republic in 1797. We will show that
                       it has some useful properties that in addition to
                       being interesting in themselves, also suggest that
                       its fundamental design principle is worth
                       investigating for application to leader election
                       protocols in computer science. For example it gives
                       some opportunities to minorities while ensuring
                       that more popular candidates are more likely to
                       win, and offers some resistance to corruption of
                       voters. The most obvious feature of this protocol
                       is that it is complicated and would have taken a
                       long time to carry out. We will advance a
                       hypothesis as to why it is so complicated, and
                       describe a simplified protocol with very similar
                       features. Publication Info: IEEE Computer Security
                       Foundations Symposium, Venice, Italy, July 6-8,
                       2007


                # ⚓ Scoop News Group ☛ DHS_seeks_information_for_CISA_analytics
                  and_machine_learning_project⠀⇛


                       The Department of Homeland Security is seeking
                       cloud-related information to support an analytics
                       and machine learning research and development
                       project that’s in the works for the Cybersecurity
                       and Infrastructure Security Agency.


                       The Advanced Analytics Platform for Machine
                       Learning (CAP-M) project, which is being developed
                       by DHS’s Science and Technology Directorate for
                       CISA, is “envisioned to be a multicloud, multi-
                       tenant environment for testing new software and
                       tools, and developing complex machine learning
                       capabilities,” per DHS’s request for information,
                       posted Tuesday.


                # ⚓ Silicon Angle ☛ Microsoft_announces_major_security
                  leadership_reshuffle,_appoints_new_CISO⠀⇛


                       Igor Tsyganskiy, who joined Microsoft four months
                       ago in the role of chief strategy officer, has been
                       appointed the new CISO, replacing Bret Arsenault,
                       who had held the role for 14 years.


                # ⚓ Security Week ☛ Microsoft_Hires_New_CISO_in_Major_Security
                  Shakeup⠀⇛


                       Microsoft security boss Charlie Bell has quietly
                       executed a major shakeup of the software giant’s
                       security hierarchy, removing the CISO and Deputy
                       CISO and handing the reins to Igor Tsyganskiy, a
                       recent hire who previously served as CTO and
                       President at asset management giant Bridgewater
                       Associates. d


                # ⚓ Michael Geist ☛ My_CRTC_Appearance_on_Bill_C-11:_Why_Isn’t
                  the_Commission_Concerned_with_Competition,_Consumer_Choice,
                  and_Affordability?⠀⇛


                       The CRTC’s Bill C-11 hearings are in their third
                       and final week as a steady stream of broadcasters
                       and producers make their way to Gatineau to urge
                       the Commission to force Internet streamers to hand
                       over cash in a giant cross-industry subsidy scheme
                       designed to support everyone from small producers
                       to Bell’s news division. As the witnesses take
                       turns seeking the mantle that they are facing the
                       biggest crisis (even as there is record film and
                       television production in Canada and broadcasters
                       stand to be the biggest beneficiary of the Online
                       News Act), there has been practically no interest
                       or discussion of the risks to consumers and
                       competition that could come from significant new
                       regulatory costs.


                # ⚓ Vox ☛ The_Israel-Hamas_war_is_tearing_American_cultural
                  institutions_apart⠀⇛


                       Balancing the need to be current, especially in the
                       midst of major political moments, is tricky, says
                       Mary Elizabeth Williams, a former museum
                       professional who’s written about how museums should
                       approach political activism and protest art. “As
                       people become more divided in the United States,
                       there’s voices calling for action, but museums need
                       to balance that and find a way to engage in their
                       communities but not alienate certain members of the
                       population.” Cultural organizations risk losing
                       funders and even their nonprofit status if they
                       make the wrong move, she says.


                # ⚓ CS Monitor ☛ EU_leaders_in_a_race_against_time_to_agree_on
                  first_AI_regulations⠀⇛


                       Some 85% of the technical wording in the bill
                       already has been agreed on, Carme Artigas, AI and
                       digitalization minister for Spain, which holds the
                       rotating EU presidency, said at a press briefing
                       Dec. 5 in Brussels.


                       If a deal isn’t reached in the latest round of
                       talks, starting the afternoon of Dec. 6 and
                       expected to run late into the night, negotiators
                       will be forced to pick it up next year. That raises
                       the odds the legislation could get delayed until
                       after EU-wide elections in June – or go in a
                       different direction as new leaders take office.


                       One of the major sticking points is foundation
                       models, the advanced systems that underpin general
                       purpose AI services like OpenAI’s ChatGPT and
                       Google’s Bard chatbot.


                       Also known as large language models, these systems
                       are trained on vast troves of written works and
                       images scraped off the [Internet]. They give
                       generative AI systems the ability to create
                       something new, unlike traditional AI, which
                       processes data and completes tasks using
                       predetermined rules.


                # ⚓ University of Michigan ☛ Sam_Altman’s_return_sparks_fears
                  of_the_AI_apocalypse⠀⇛


                       However, just four days later, OpenAI announced
                       that Altman would be reinstated in his previous
                       role as CEO. The news came as a shock to many,
                       considering a letter was signed by nearly 600
                       OpenAI employees threatening to resign if Altman
                       was not brought back as CEO. Left with no other
                       choice than to backtrack on their original
                       decision, OpenAI quickly rehired Altman, stirring
                       up a media frenzy. Altman “now has more power—and
                       fewer constraints—than ever,” one article warned.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ New York Times ☛ Russia’s_Latest_Disinformation
                        Tactic_Exploits_American_Celebrities⠀⇛


                             “Russian cyber and influence operators have
                             demonstrated adaptability throughout the war
                             on Ukraine, trying new ways to gain
                             battlefield advantage and sap Kyiv’s sources
                             of domestic and external support,” Microsoft
                             wrote in its report, referring to Ukraine’s
                             capital.


                      # ⚓ Marcy Wheeler ☛ DOJ_Will_Show_that_Trump’s_Campaign
                        Intended_to_Cause_a_Riot_at_TCF_Center_in_Detroit⠀⇛


                             According to the Election Integrity Project,
                             Roman was also one of the most efficient
                             spreaders of disinformation during the post-
                             election period, wildly out of proportion to
                             his number of Twitter followers (suggesting
                             he had offline ways to help make things go
                             viral).


                      # ⚓ Quartz ☛ A_disinformation_scholar_claims_Meta_is_the
                        reason_her_time_at_Harvard_was_cut_short⠀⇛


                             Donovan’s lawyers at Whistleblower Aid allege
                             that the school “began to target Dr.
                             Donovan’s team, their work, and her
                             personally in an effort to diminish—if not
                             destroy—their research and public engagement”
                             after receiving funding from the Chan
                             Zuckerberg Initiative (CZI), the foundation
                             that Meta founder Mark Zuckerberg and his
                             wife, Priscilla Chan, run together.


                             Donovan’s alleged gagging and eventual firing
                             violated her civil rights, including her
                             freedom of speech and freedom of association,
                             her lawyers argue.


                      # ⚓ The Atlantic ☛ The_Truth_Won’t_Matter⠀⇛


                             Facts are work. They require study; they
                             require curiosity; they require patience;
                             they require humility. Democracy requires the
                             same. The demands of both become greater in
                             an information environment teeming with
                             stories that are ever more suspect—a place
                             where truth has plausible deniability. Trump
                             will ease the burden, he suggests: You can
                             outsource your mind to his gut. You would be
                             foolish not to. Science lies to you.
                             Hollywood lies to you. The media lie to you.
                             Books lie to you. Courts lie to you. Teachers
                             lie to you. Other people lie to you.
                             Democracy lies to you. The only thing you can
                             trust, in this dizzying world, is the
                             inveterate liar who would never lie to you.


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


                # ⚓ The Dissenter ☛ Whistleblowers_and_Journalists_Under
                  Attack⠀⇛


                # ⚓ EFF ☛ The_Latest_EU_Media_Freedom_Act_Agreement_Is_a_Bad
                  Deal_for_Users⠀⇛


                       Last year, the EU Commission presented the EMFA as
                       a way to bolster media pluralism in the EU. It
                       promised increased transparency about media
                       ownership and safeguards against government
                       surveillance and the use of spyware against
                       journalists—real dangers that EFF has warned
                       against for years. Some of these aspects are still
                       in flux and remain up for negotiation, but the
                       political agreement on EMFA’s content moderation
                       provisions could erode public trust in media and
                       jeopardize the integrity of information channels. 


                       Millions of EU users trust that online platforms
                       will take care of content that violates community
                       standards. But contrary to concerns raised by EFF
                       and other civil society groups, Article 17 of the
                       EMFA enforces a 24-hour content moderation
                       exemption for media, effectively making platforms
                       host content by force.  


                       This “must carry” rule prevents large online
                       platforms like X or Meta, owner of Facebook,
                       Instagram, and WhatsApp, from removing or flagging
                       media content that breaches community guidelines.
                       If the deal becomes law, it could undermine
                       equality of speech, fuel disinformation, and
                       threaten marginalized groups. It also poses
                       important concerns about government interference in
                       editorial decisions.Imagine signing up to a social
                       media platform committed to removing hate speech,
                       only to find that EU regulations prevent platforms
                       from taking any action against it. Platforms must
                       instead create a special communication channel to
                       discuss content restrictions with news providers
                       before any action is taken. This approach not only
                       undermines platforms’ autonomy in enforcing their
                       terms of use but also jeopardizes the safety of
                       marginalized groups, who are often targeted by hate
                       speech and propaganda. This policy could also allow
                       orchestrated disinformation to remain online,
                       undermining one of the core goals of EMFA to
                       provide more “reliable sources of information to
                       citizens”.  


                # ⚓ Press Gazette ☛ Barclays_take_back_control_of_Telegraph_and
                  Specator,_for_now⠀⇛


                       Telegraph readers today woke up to the news that
                       the Barclay family is back in control of the
                       publisher, some six months after Lloyds bank
                       repossessed it.


                       The full outstanding debt has been repaid by Abu
                       Dhabi-backed investment fund Redbird IMI.


                       But the future ownership of both the Telegraph and
                       Spectator titles is still far from certain.


          o § Civil Rights/Policing⠀➾


                # ⚓ Deutsche Welle ☛ German_train_drivers_to_strike_from
                  Thursday⠀⇛


                       The strike is the fourth to hit Deutsche Bahn this
                       year and comes on the heels of a 20-hour GDL work
                       disruption that forced the cancellation of nearly
                       80% of all long-distance and regional trains in
                       Germany on November 15-16.


                # ⚓ Axios ☛ Fully_remote_work_is_on_the_decline_in_the_U.S.⠀⇛


                       Why it matters: While far more Americans work
                       remotely now than before the pandemic, the share of
                       those who are fully remote has been steadily
                       declining.


                # ⚓ CS Monitor ☛ Malala_Yousafzai_demands_action_against
                  Taliban’s_‘gender_apartheid’⠀⇛


                       Since their takeover, the Taliban have banned
                       education for girls beyond the sixth grade and
                       imposed severe restrictions on women, barring them
                       from work and most public spaces and seeking to
                       implement their strict interpretation of Islamic
                       law, or Sharia.


                       “Afghanistan has only seen dark days after it fell
                       to the Taliban,” Ms. Yousafzai said in the AP
                       interview. “It has been two and half years and most
                       girls have not seen school again.”


                       Ms. Yousafzai appealed to the United Nations to
                       “recognize the current state of Afghanistan as a
                       gender apartheid” and cited recent reports of
                       “women being detained, put into prisons and beaten
                       and even put into forced marriages.”


                # ⚓ University of Michigan ☛ Exonerated:_Freeing_the_wrongly
                  accused_from_prison⠀⇛


                       What makes the clinic different is that it
                       exclusively handles non-DNA cases whereas other
                       innocence projects typically deal with DNA cases.


                       Moran said if the case appears to turn entirely on
                       DNA, they will refer it to the Cooley Innocence
                       Project, which handles DNA cases. With a non-DNA
                       case, the lawyers are looking for new evidence to
                       determine their clients’ innocence, he explained.


                # ⚓ US News And World Report ☛ Taliban’s_Abusive_Education
                  Policies_Harm_Boys_as_Well_as_Girls_in_Afghanistan,_Rights
                  Group_Says⠀⇛


                       Because the Taliban have dismissed all female
                       teachers from boys’ schools, many boys are taught
                       by unqualified people or sit in classrooms with no
                       teachers at all.


                # ⚓ New York Times ☛ Tesla_Is_Fighting_With_Sweden’s_Unions.
                  Here’s_What_to_Know.⠀⇛


                       Unions say Tesla is flouting Sweden’s tradition of
                       collective agreements. About 90 percent of Swedish
                       workers are covered by these agreements, which
                       apply to nonunion employees and set work conditions
                       across industries. They have a long history in
                       Nordic countries and are widely seen as crucial to
                       maintaining social cohesion and a high standard of
                       living.


                # ⚓ BIA Net ☛ 'Ban_all_aid_that_would_contribute_to_the
                  maintenance_of_the_Taliban_regime'⠀⇛


                       In the letter, women from EŞİK addressed UN
                       officials, drawing attention to the report's
                       alleged disregard for "the gender-based apartheid
                       regime of the Taliban."


                       The letter expressed the following: [...]


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Gizmodo ☛ Apple_Will_Reportedly_[Ship]_New_M3-Powered_iPads
                  and_MacBook_Airs_in_2024⠀⇛


                       All those devices will get access to the latest M3
                       silicon. The MacBook Air will also receive the M3
                       upgrade. All of these devices could launch in March
                       at the earliest. Apple’s iPadOS will see the jump
                       to version 17.4, while the new MacBooks will get
                       upgraded to macOS 14.3. Both those software patches
                       should arrive within the first few months of 2024.


                # ⚓ Chris Hannah ☛ Sony_Playstation_Removes_Access_to_Already
                  Purchased_Content⠀⇛


                       I’m so glad this didn’t affect me. Because
                       something like this would annoy me so much I’d stop
                       buying things digitally. And I’m not quite ready
                       for that yet.


                # ⚓ Sony ☛ Legal_update_notice⠀⇛


                       As of 31 December 2023, due to our content
                       licensing arrangements with content providers, you
                       will no longer be able to watch any of your
                       previously purchased Discovery content and the
                       content will be removed from your video library.


      § Monopolies/Monopsonies⠀➾


          o ⚓ The Verge ☛ Amazon_slams_Microsoft’s_business_practices_in_UK
            cloud_market_probe⠀⇛


                 Amazon’s concerns regarding Microsoft follow similar
                 criticisms made by Google to the CMA in October. In the
                 letter published on Tuesday, Google claims Microsoft’s
                 licensing practices were harmful to UK customers because
                 they leave them with “no economically reasonable
                 alternative but to use Azure as their cloud services
                 provider, even if they prefer the prices, quality,
                 security, innovations, and features of rivals.” Google
                 said these licensing practices were the biggest issue
                 preventing competition in the UK cloud-computing market.


          o ⚓ AWS_accuses_Microsoft_of_clipping_customers'_cloud_freedoms⠀⇛


                 AWS has publicly called out Microsoft's software
                 licensing terms, claiming they "restrict choice" and make
                 it "financially unviable" for customers to choose anyone
                 other than Microsoft – something Google and other rivals
                 have complained of.


                 This was one among the many points addressed by Amazon in
                 its submission [PDF] to Competition Markets Authority,
                 the regulator charged with inspecting the health of the
                 UK cloud sector with special attention to be given to
                 egress fees; committed special discounts;
                 interoperability; and cloud software policies.


                 Amazon reckons that the first of these four "hypotheses"
                 are "based on fundamental misconceptions about the IT
                 sector, global networking technology, the actual
                 interoperability of IT services, and discounts on offer."


          o § Copyrights⠀➾


                # ⚓ Torrent Freak ☛ Pirate_IPTV_Operation_Dismantled,_9
                  Arrested,_43_Customers_Investigated⠀⇛


                       Greek police say they have dismantled a pirate IPTV
                       operation after carrying out coordinated raids in
                       five areas of the country. A criminal case was
                       filed against 12 members of the illegal
                       organization, of which 9 were arrested during the
                       raids. A reported 43 customers of the IPTV service
                       are reportedly under investigation for viewing
                       illegal streams.


                # ⚓ Torrent Freak ☛ EU_Mulls_Expansion_of_Geo-Blocking_'Bans'
                  to_Video_Streaming_Platforms⠀⇛


                       A recent report from the European Parliament's
                       Committee on Internal Market and Consumer
                       Protection urges the EU Commission to review its
                       current geo-blocking policies. One suggestion is to
                       expand geo-blocking restrictions to the audiovisual
                       sector, including streaming platforms. This has
                       spooked some stakeholders who warn that a ban on
                       geo-blocking would put the entire industry at risk.


                # ⚓ git_setup-email⠀⇛


                       Here’s a li’l three line shell script that tries to
                       help you guess and set format.subjectPrefix and
                       sendemail.to in a git repo.


                       Normally it uses completing-read and all its
                       dependencies, but you can edit the script to
                       instead use gum choose or whatever you want.


                # ⚓ OpenBSD_in_a_CI_environment_with_sourcehut/a>⠀⇛


                       If you ever required continuous integration
                       pipelines to do some actions in an OpenBSD
                       environment, you certainly figured that most Git
                       "forge" didn't provide OpenBSD as a host
                       environment for the CI.


                       It turns out that sourcehut is offering many
                       environments, and OpenBSD is one among them, but
                       you can also find Guix, NixOS, NetBSD, FreeBSD or
                       even 9front!


                       Let's see how this works.


          o § Gemini* and Gopher⠀➾


                # § Personal/Opinions⠀➾


                      # ⚓ 🔤SpellBinding_—_ACLNUTP_Wordo:_HAVES⠀⇛


                      # ⚓ [Old]_Lost_a_Bike,_Made_a_Bag,_Bought_Trousers⠀⇛


                             Yesterday we had some colleagues from
                             Stockholm visit the local office. It was
                             great fun; there was a lot of socialising and
                             pizza involved. Anecdotally a pizza place
                             owner becomes very very happy if you order 20
                             pizzas on an otherwise slow Tuesday night.


                             When I was to go home at around 22:00 I
                             couldn't find my bike. Anywhere within a 500
                             metre radius. Even though I'd parked it just
                             outside. Oh, well.


                             Now I'm using an old commuter bike that we
                             had in storage. It's not bad. Definitely a
                             lot slower than the 27 gear hybrid I had, but
                             I do need to practice slowing down in general
                             for my well-being so that's not necessarily a
                             bad thing. I just hope it holds up better
                             than my last commuter bike which eventually
                             just couldn't handle the, uhm, urban
                             terrain...


                      # ⚓ I_Have_a_Lot_To_Write_Here⠀⇛


                             Just haven't had the time. I mean I've
                             prioritized other things, obviously. But
                             there are a lot of topics I'd like to share,
                             for fun and (absolutely no) profit.


                # § Technology and Free Software⠀➾


                      # ⚓ Make_a_StealthBox_with_Devuan_and_Libre_Computer
                        Renegade⠀⇛


                             This allows you to browser on internet
                             privately and if for some reason the board is
                             lost or stolen your data is encrypted thus
                             inacessible. It is important to mention than
                             usually the images provided for those SBC do
                             not support installation over any encrypted
                             the filesystem.


                      # ⚓ Home-built_Tech⠀⇛


                             Many low-tech and small-tech movements have a
                             focus on stewardship. They embrace old
                             technology because they argue that throwing
                             away a tool before its useful life is over is
                             wasteful. Similarly, keeping a small
                             technological footprint and replacing
                             inefficient electrical systems with
                             mechanical or human-powered ones reduces out
                             impact on the planet.


                             There are other sides of low tech that
                             interest me more. I'm fascinated with old,
                             small, and alternative tech because of its
                             DIY potential. Instead of needing to rely on
                             a massive supply chain and an intricate
                             global logistics network to get the things we
                             use, we might be able to make other tools
                             ourselves that can do just fine.


                      # § Internet/Gemini⠀➾


                            # ⚓ The_Gemtext_Print_Hurdle⠀⇛


                                   The oldest pages on my website date
                                   back to about 1997. I was in school, my
                                   ISP provided webspace for me as part of
                                   their service, so I learned to write
                                   HTML to take advantage of that. The
                                   School of Business at this university
                                   had recently decided that the ability
                                   to work well with others in group
                                   setting was a very important skill for
                                   their graduates to acquire. Nearly
                                   every course included a group project
                                   of some sort, and having a place to
                                   easily share files with group members
                                   proved to be very helpful.


                                   HTML soon became my primary document
                                   format. I used word processor software
                                   for documents that required more than
                                   what HTML offered, but nearly
                                   everything else I wrote was done as
                                   HTML; in fact I soon started writing
                                   drafts of papers in HTML and then
                                   imported the HTML into a word processor
                                   for the final edit.


                            # ⚓ The_past_is_in_the_past_except_on_the_web⠀⇛


                                   Over on the HTTP/HTML/CSS/JS web, there
                                   used to be well-designed pages and
                                   badly designed pages.


                                   There used to be some really poorly
                                   designed pages that were just one big
                                   pixmap or Flash file.


                                   And some that were nice and gentle and
                                   straight-forward; your good old “body,
                                   h1 hi, p hello how are you” type sites.
                                   Nothing fancy, just set up the way the
                                   web was meant to work.


                      # § Programming⠀➾


                            # ⚓ cozify-window⠀⇛


                                   Here’s a li’l mini function for Emacs
                                   that when called sets the window width
                                   to one space wider than the current
                                   cursor position: [...]


                            # ⚓ Audio_Programming⠀⇛


                                   I've been privileged enough to have the
                                   time to try learn a few musical
                                   instruments, but never got any good at
                                   them. But there's another way to play
                                   music, by writing programs, that is
                                   like my day job? I've just started
                                   looking into this so I'm sure I've
                                   missed quite a bit. I recommend the
                                   interactive manual to start: [...]


                            # ⚓ My_mind_is_on_the_blink⠀⇛


                                   Last night I wrote some C for the first
                                   time in ages. The impetus was some post
                                   I read, which had me wondering how much
                                   I remembered. I was able to bang out a
                                   simple "hello world", getting spacing
                                   and naming of things the way I settled
                                   on back in the days of prowess.


                            # ⚓ Unit_testing_from_inside_an_assembler,_part
                              III⠀⇛


                                   I'm done with the “unit testing”
                                   backend for my 6809 assembler [1]. The
                                   mini-Forth engine [2] is working out
                                   fine, although the number of words
                                   increased from 41 to 47 to support some
                                   conveniences (like indexing and string
                                   comparison). It took some work to
                                   support, but the number of assertions
                                   one can make in the code is extensive.


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





                    ䷩ 𝚕𝚒𝚗𝚎 3979

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 07/12/2023: More EPO Patents
Squashed, More Pfizer COVID-19 Vaccine "Glitches"
Found⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Dec 07, 2023


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
          o Finance
          o AstroTurf/Lobbying/Politics
          o Civil_Rights/Policing
          o Digital_Restrictions_(DRM)
          o Monopolies
                # Patents
                # Software_Patents
                # Copyrights
    * Gemini*_and_Gopher
          o Personal/Opinions
          o Technology_and_Free_Software
                # Internet/Gemini
                # Programming
    * § Leftovers⠀➾


          o ⚓ Ruben Schade ☛ Singular_or_plural_follow-up⠀⇛


                 Yesterday I posted about the difference between how
                 British and other English speakers use_plurals_for
                 certain_singular_nouns. I’m used to reading a group are
                 doing something, but most say the group is doing
                 something.


                 I started doubting that what I remembered about British
                 English was true. Not to get all Malcom Gladwell on you,
                 but turns out it’s even less clear cut than I thought!


          o ⚓ Ruben Schade ☛ Bardinet_VSOP_brandy⠀⇛


                 A friend recommended this as an introductory brandy for
                 someone who loves less-peaty Scotch and Japanese whisky.
                 I’d never had brandy (or cognac) before, besides
                 drizzling it into Xmas puddings.


                 It’s lovely! It’s fruity and light, but has that subtly
                 matured taste of a younger whiskey.


          o § Science⠀➾


                # ⚓ Pete_Zaitcev:_Suvorov_vs_Zubrin⠀⇛


                       When they discussed his "engine on salt of Uranium"
                       [NSWR — zaitcev] I wrote that the engine will not
                       work in principle, because a reactor can only work
                       in case of effective deceleration of neutrons, but
                       already at the temperature of the moderator of 3000
                       degrees (like in KIWI), the cross-section of
                       fission decreases 10 times, and the critical mass
                       increases proportionally. But nobody paid attention
                       — who am I, who is Zubrin!


          o § Education⠀➾


                # ⚓ CS Monitor ☛ Cal_State_University_faculty_are_striking.
                  What_are_their_demands?⠀⇛


                       A series of one-day strikes, held by the California
                       Faculty Association, have begun across California
                       State University campuses, pushing for a 12% salary
                       increase and other benefits. The university
                       chancellor’s office says the pay increase is not
                       feasible.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ AMD_Ryzen_Embedded_V3000_COM_Express_Type_7
                  module_supports_up_to_64GB_DDR5_memory⠀⇛


                       ADLINK Express VR7 is a COM Express Basic size Type
                       7 computer-on-module powered by the eight-core AMD
                       Ryzen Embedded V3000 processor with two 10GbE
                       interfaces, fourteen PCIe Gen 4 lanes, and optional
                       support for the “extreme temperature range” between
                       -40°C and 85°C. The COM Express module supports up
                       to 64GB dual-channel DDR5 SO-DIMM  (ECC/non-ECC)
                       memory and targets headless embedded applications
                       such as edge networking equipment, 5G
                       infrastructure at the edge, video storage
                       analytics, intelligent surveillance, industrial
                       automation and control, and rugged edge servers.


                # ⚓ Hackaday ☛ Affordable_Networking_For_Your_Classic_Mac⠀⇛


                       The Mac SE and in particular the Mac SE/30 number
                       among the more sought-after of the classic all-in-
                       one Apple computers, and consequently their
                       peripherals including network cards are also hard
                       to find and pricey. Even attempts at re-creating
                       them can be expensive, usually because the chips
                       used back in the day are now nearly unobtainable.
                       But if the search is widened to other silicon it
                       becomes possible to create substitutes, as [Richard
                       Halkyard] is doing with a modern version of the SE
                       Ethernet card.


                # ⚓ Hackaday ☛ Retrotechtacular:_The_Gunsmith_Of_Williamsburg⠀⇛


                       A modern firearm is likely to be mass-produced
                       using high-precision machine tools, and with a
                       uniformity to the extent that parts from one can be
                       interchanged with those from another. This marks a
                       progression of centuries of innovation, in
                       gunsmithing, in machine tooling, and in metallurgy.
                       In the 18th century there was little of the
                       innovations found in a modern weapon, and a rifle
                       would have been made entirely by hand through the
                       work of a master gunsmith. The video below the
                       break is a fascinating 1969 film following Wallace
                       Gusler, the gunsmith at the museum town of
                       Williamsburg, Virginia, as he makes an 18th-century
                       muzzle-loading flintlock rifle from raw materials.
                       It’s a long video, but it leaves nothing out and
                       has a really informative commentary we’re told from
                       the gunsmith himself.


                # ⚓ Hackaday ☛ This_Pogo_Pin_Test_Fixture_Keep_Your_SMDs_From
                  Taking_Flight⠀⇛


                       There’s no denying how useful surface mount
                       technology is, and how enabling the ability to make
                       really small circuits has become. It comes at a
                       price, though; most of us probably know what it’s
                       like for the slightest wrong move to send a part
                       the size of a grain of sand into another dimension.


                # ⚓ Hackaday ☛ Inside_A_Rubidium_Frequency_Standard⠀⇛


                       We think of crystals as the gold standard of
                       frequency generation. However, if you want real
                       precision, you need something either better than a
                       crystal or something that will correct for tiny
                       errors — often called disciplining the oscillator.
                       [W3AXL] picked up a rubidium reference oscillator
                       on eBay at a low cost, and he shows us how it works
                       in the video you can see below. He started with a
                       GPS-disciplined oscillator he had built earlier and
                       planned to convert it to discipline from the
                       rubidium clock.


                # ⚓ Hackaday ☛ Directional_Antenna_Stands_Tall⠀⇛


                       When you think of directional ham radio antennas,
                       you probably think of a Yagi, cubical quad, or a
                       log-periodic antenna. These antennas usually are in
                       a horizontal configuration up on a high tower.
                       However, it is possible to build beams with a
                       vertical orientation and, for some lower
                       frequencies, it is far more practical than mounting
                       the elements on a boom. [DXCommander] shows us his
                       40 meter two-element vertical antenna build in the
                       video below.


                # ⚓ Hackaday ☛ Dry_Ice_From_Seashells,_The_Hard_(But_Cheap)
                  Way⠀⇛


                       [Hyperspace Pirate] wants to make his own dry ice,
                       but he wants it to be really, really cheap. So
                       naturally, his first stop is… the beach?


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ teleSUR ☛ UK_Resident_Doctors_Prepare_New_Strikes⠀⇛


                       "It is evident that the government is still
                       unwilling to address the real salary cuts that
                       doctors have endured since 2008," the BMA said.


                # ⚓ Yahoo News ☛ One_in_four_who_had_Pfizer_Covid_jabs
                  experienced_unintended_immune_response⠀⇛


                       More than a quarter of people injected with mRNA
                       Covid jabs suffered an unintended immune response
                       created by a glitch in the way the vaccine was read
                       by the body, a study has found.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ [Repeat] Silicon Angle ☛ Tesla_whistleblower_says_Autopilot
                  not_ready,_contradicting_Elon_Musk’s_‘best’_Hey_Hi_(AI)
                  remark⠀⇛


                       A former Tesla Inc. employee said in an interview
                       with the BillBC published today that the software
                       powering the company’s self-driving cars is not
                       ready and should not be used on public roads.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ EDRI ☛ New_educational_videos_about_Hey_Hi_(AI)_in
                        media,_privacy_&_digital_exclusion._Here_is_what_they
                        show⠀⇛


                             You can now watch all ten videos about
                             artificial intelligence (AI) in the media,
                             cybersecurity for journalists, but also about
                             digital exclusion and the impact of
                             digitalisation on people with disabilities.


          o § Defence/Aggression⠀➾


                # ⚓ New York Times ☛ Nigeria’s_President_Calls_for_Inquiry
                  After_Military_Strike_Kills_at_Least_85_Civilians⠀⇛


                       Many of the victims were women and children
                       gathered for a religious celebration. President
                       Bola Ahmed Tinubu described the attack as a
                       “bombing mishap.”


                # ⚓ teleSUR ☛ Nigeria:_85_Civilians_Killed_in_Military’s
                  Airstrike_Accident⠀⇛


                       In a separate statement signed by defense spokesman
                       Edward Buba, the Nigerian military said the drone
                       strike was based on information about suspected
                       terrorist activity in the area.


          o § Environment⠀➾


                # ⚓ European Commission ☛ Speech_by_Commissioner_Simson_at_the
                  COP28_Ministerial_on_Renewables_and_Energy_Efficiency⠀⇛


                       European Commission Speech Dubai, 05 Dec 2023 Your
                       Excellencies, dear colleagues, and friends,


                       Three days ago, at the World Climate Action Summit,
                       our leaders set a clear goal for our energy
                       transition.


                # ⚓ Science Alert ☛ Real_or_Fake:_Scientist_Explains_How_to
                  Choose_The_Most_Sustainable_Christmas_Tree⠀⇛


                       The dilemma is real.


          o § Finance⠀➾


                # ⚓ France24 ☛ Hollywood_actors_ratify_new_contract_deal_to
                  formally_end_strike⠀⇛


                       Hollywood actors overwhelmingly ratified a new,
                       hard-fought deal with studios on Tuesday that paves
                       the way for a rebound of an entertainment industry
                       that had seen film and television production come
                       to a halt during a months-long strike.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Common Dreams ☛ Texas_GOP:_We_Are_the_(White_Supremacist)
                  Storm⠀⇛


                       Slithering ever further down a timeworn slippery
                       slope into fascism, Texas Republicans just took one
                       small step for white supremacy by rejecting a
                       resolution to ban members from consorting with
                       anti-Semites, Nazi-sympathizers or plain ole Nazis
                       in a state already crawling with them. Critics
                       claimed the move - born of furor over a meeting
                       between a big-wig GOP fundraiser and Hitler-fanboy
                       Nick Fuentes - was "too vague" and akin to a
                       "Marxist" decree, evidently in that it seeks to
                       differentiate between "good" and "bad" guys.


          o § Civil Rights/Policing⠀➾


                # ⚓ RFERL ☛ Nobel_Laureate_Malala_Calls_Out_Taliban_For_Making
                  'Girlhood_Illegal'_In_Afghanistan⠀⇛


                       Nobel Peace Prize laureate Malala Yousafzai decried
                       Afghanistan's Taliban rulers in a speech on
                       December 5 and called on the international
                       community to make gender apartheid a crime against
                       humanity.


                # ⚓ ACLU ☛ Preserving_the_History_of_Civil_Rights_in_New
                  Orleans⠀⇛


                       On the same morning that 6-year-old Ruby Bridges
                       became the first Black student to integrate an
                       elementary school in the South, three young girls
                       completed the same historic act just a mile away.
                       On November 14, 1960, Leona Tate, Gail Etienne, and
                       Tessie Prevost were escorted by Federal Marshals
                       past angry protestors into McDonogh 19 Elementary
                       School in New Orleans.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ New York Times ☛ Spotify_Cancels_Two_Acclaimed_Podcasts:
                  ‘Heavyweight’_and_‘Stolen’⠀⇛


                       The shows will finish out their seasons on Spotify
                       and then have the option to shop their shows
                       somewhere else.


                # ⚓ Digital Music News ☛ Spotify_Cancels_‘Heavyweight’_and
                  ‘Stolen’_Podcasts_Following_Massive_Layoffs_—_Stock-Price
                  Surge_Continues⠀⇛


                       Yesterday, Spotify stock spiked after the streaming
                       company announced plans to lay off 17 percent of
                       its team. Now, amid news of additional cutbacks
                       yet, affecting two podcasts, shares have hit $200
                       apiece.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Unified Patents ☛ Fortress_IP_entity_Entropic
                        Communications_cable_packet_transmission_patent
                        monopoly_found_invalid_in_reexam⠀⇛


                             On November 22, 2023, the Central
                             Reexamination Unit (CRU) entered a final
                             rejection of the challenged claims of U.S.
                             Patent_8,228,910, owned by Entropic
                             Communications, LLC, an NPE and a Fortress_IP
                             entity. The '910 patent monopoly relates to
                             aggregating packets for transmission to a
                             destination node and has been asserted
                             against Comcast, Cox_Communications, Charter
                             Communications, and Dish.


                             View district_court_litigations_by_Entropic
                             Communications.


                      # ⚓ JUVE ☛ EPO_Boards_of_Appeal_revoke_Edwards
                        Lifesciences’_heart-valve_patent [Ed: EPO once again
                        admits to have granted fake monopolies, and there must
                        be hundreds of thousands of fake patents (they profit
                        from giving those)]⠀⇛


                             The dispute concerns Edwards Lifesciences’ EP
                             3 583 920, which protects a prosthetic valve
                             frame. The Examining Division of the EPO
                             granted the patent monopoly in 2020.


                      # ⚓ JUVE ☛ Video:_Inside_the_JUVE_Patent_team [Ed: A
                        group of propagandists who chose spamfarming as their
                        business model, plus taking bribes to lie for firms and
                        lobby for illegal and unconstitutional policies, in
                        effect associating "journalism" with crime]⠀⇛


                             In JUVE Patent’s latest video, our editors
                             Amy Sandys, Konstanze Richter, Laura King,
                             Mathieu Klos and Christina Schulze explain
                             how they came to JUVE Patent, what role they
                             play in the team and what they have found to
                             be important over the past five years.


                # § Software Patents⠀➾


                      # ⚓ Unified Patents ☛ Dolby_VVC_patent_monopoly_revoked
                        in_EPO [Ed: Good luck revoking those endless software
                        patents that criminals who took over the EPO have let
                        be granted]⠀⇛


                             On November 30, 2023, the European Patent
                             Office revoked all claims of EP_3675491,
                             owned by Dolby_International_AB.


                # § Copyrights⠀➾


                      # ⚓ Techdirt ☛ Google_Caves_In_Canada:_Agrees_To_Pay
                        $100m_News_Bribe_To_Avoid_Direct_Link_Tax⠀⇛


                             It seems that every other day or so we get
                             another story of big tech companies tossing
                             principles out the window and caving to
                             ridiculous government demands. The latest is
                             Google, yet again, which has cut a deal with
                             the Canadian government to bribe news orgs
                             with $100 million to pay them off to avoid a
                             more specific link tax. It’s the worst kind
                             of corruption.


    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ 🔤SpellBinding_—_UGHLOTF_Wordo:_SINEW⠀⇛


                # ⚓ Self-nuts_roasting_on_an_open_mire⠀⇛


                # ⚓ Drilling_down⠀⇛


                # ⚓ Christmas⠀⇛


                       Christmas is right around the corner and I for one
                       am really excited! I love this time of the year and
                       spend time with my friends and family, i'm really
                       in a holly jolly mood right now. The only thing I
                       don't like is the weather, everyday looks so gray
                       and ugly so I hope they change that sometime
                       soon...


          o § Technology and Free Software⠀➾


                # ⚓ On_the_Shoulders_of_Giants⠀⇛


                       The work we do suggests the form of what can be
                       built on top of it. If we are careful, a larger
                       whole can be extrapolated from the simple pieces we
                       present.


                       This is a relatively simple tessellation compared
                       with previous ones I have done, with the twist of
                       it being animated. A looping animation can be
                       thought of as a tessellation of its own kind,
                       making this work 3 dimensional.


                       On the technical side the work is bulit on SVG and
                       (what I hope to be) well supported CSS animations
                       which should take advantage of the GPU when
                       present.


                       I hope to mint this at some point soon, but my
                       preferred marketplace has nuked my account and
                       previous collections on it, so I might have to find
                       another. If that falls through I can just mint
                       myself and accept offers off-chain. I'll keep this
                       page updated, for any interested.


                # ⚓ Dystopia_et_Documentation⠀⇛


                       They'll probably end up moving some of the docs yet
                       again when the next great thing comes along.
                       Obviously what documentation needs is a nice Cloud-
                       Integrated ECMAScript Application (CIEA) to make it
                       even more difficult, expensive, and dangerous (DED)
                       to access.


                # ⚓ Make_a_StealthBox_with_Devuan_and_Libre_Computer_Renegade⠀⇛


                       Finally I was able to complete this gemlog series.
                       🎇


                       For this idea rather than doing a big endless
                       gemlog I preferred split it into several gemlog
                       that can be read also as indivul log, as a matter
                       of fact some of them were already published!


                # ⚓ OpenBSD_in_a_CI_environment_with_sourcehut⠀⇛


                       If you ever required continuous integration
                       pipelines to do some actions in an OpenBSD
                       environment, you certainly figured that most Git
                       "forge" didn't provide OpenBSD as a host
                       environment for the CI.


                       It turns out that sourcehut is offering many
                       environments, and OpenBSD is one among them, but
                       you can also find Guix, NixOS, NetBSD, FreeBSD or
                       even 9front!


                # § Internet/Gemini⠀➾


                      # ⚓ The_success_of_the_QA_format⠀⇛


                             I think the Emacs Wiki was great or is great
                             especially for that usecase which Alex’
                             defense admits the most concern: randos
                             searching the web and stumbling on a half-
                             working, probably-deprecated elisp snippet
                             that they manage to cobble together into
                             something that works for them. If the purpose
                             of the Emacs Wiki was to save people from a
                             trip to IRC or a mailing list, then it has
                             had many wins in that regard over the years.


                             Further down in the text, he isn’t too happy
                             about the culture on Stack Exchange, and
                             there is some merit to that. Just like on
                             Wikipedia, you can run into some rando
                             småpåve who thinks they’re the king of the
                             world and tries to put you in your place
                             while they’re the one who’s being all wrong
                             about something.


                      # ⚓ Back_to_the,_smol,_web⠀⇛


                             And there are two reasons for it. First,
                             Adële's smol website and the links therein
                             have got me inspired. There's a plethora of
                             indy, light-bloat sites with interesting
                             content and resources to reach them: a true
                             alternative web. And given that, neither
                             gemini nor gopher nor any other protocol I
                             know is meant to replace the web, I think
                             it's important to fight the Big Bad Web in
                             its own turf.


                             Secondly, there's an opportunity to show what
                             a corner of the web can be. More accessible,
                             more friendly to people, better designed,
                             faster and even easier to manage. And that in
                             a humble, unpretentious way, a celebration of
                             “good enough”, a sane haven. This is, in
                             part, with a style taken from gemini, as it
                             should be pretty evident in my site. Well, I
                             hope.


                      # ⚓ Your_momma_don't_grep_and_your_daddy_don't_pipe_and
                        cURL⠀⇛


                             It seems our nature is to graze on cheap
                             promises, the very first of a very long chain
                             being our seeming individuality. It makes
                             sense so mythical a beast would graze on more
                             of the same.


                      # ⚓ RE:_The_end_of_Good_Enough⠀⇛


                             I wish you were wrong. Not only because
                             Gemini is good enough, (lagom?) and so are
                             many of the things we like. Not only because
                             the world's rejection of “good enough”
                             rejects us gemininauts too, and the more
                             serious issues you refer in your article.


                # § Programming⠀➾


                      # ⚓ On_C_popularity_vs_python,_size_of_stdlib,_package
                        managers_in_langs⠀⇛


                             I have a friend who is a ridiculously
                             advanced programmer and he half-jokingly said
                             that in C, there's an implicit slogan that
                             'You want a function? write it yourself!'.
                             This is very much in the spirit of 'C',
                             there's very little in the standard library
                             and that's by design (when compared with
                             other languages).


                      # ⚓ Tabs_in_Emacs_code⠀⇛


                             Somewhen down the line, my tab-width
                             accidentally got set to 2.


                             That meant that indent-region in Lisp code
                             inserted a ton of extra tabs.


                             And when I pasted that code into other
                             formats, like Markdown, it’d look weird so
                             I’d run untabify on it.


                             I didn’t know what was going on but when I
                             finally got around to finding the issue and
                             fixing it, I was really surprised.


                             I set the tab-width back to the default
                             (which is 8) and reverted the lisp buffers.
                             They suddenly looked massively borked. Even
                             though I had run indent-region on them
                             earlier!


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




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