𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, July 30, 2025
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Generated Thu 31 Jul 02:49:23 BST 2025
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
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Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2025/07/30/


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

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


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

⦿ Techrights  -  Corruption is the Standard Operating Procedure at the European Patent Office (EPO)

⦿ Techrights  -  Dealing With Sociopaths, Liars, and Cranks

⦿ Techrights  -  GAFAM 'Revolving Doors' at The Register and a "Bribe Price List"

⦿ Techrights  -  Google 'Search' is Fast Becoming No Better Than Social Control Media Infested With Bots

⦿ Techrights  -  How to Report Apple Layoffs Without Saying the "L" Word

⦿ Techrights  -  IRC Proceedings: Tuesday, July 29, 2025

⦿ Techrights  -  Last Month Our IRC Community Turned 17

⦿ Techrights  -  Local Staff Committee Munich (LSCMN) at the European Patent Office (EPO) Requests an Urgent Meeting to Avoid Abolishing the Office

⦿ Techrights  -  Microsoft Rapidly Shrinking (No, It's Not About Efficiency, It's About Unbearable Debt)

⦿ Techrights  -  Microsoft Will Continue Resorting to Crimes in Order to Keep GNU/Linux Usage Down

⦿ Techrights  -  My Experience With Judges Has been Positive, But We Must Still Pursue SLAPP Reform in the United Kingdom

⦿ Techrights  -  Not Owning Mobile Phones

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  PCLinuxOS Had Functional Backups Before the House Fire, the Site Will be Restored in New Webhost

⦿ Techrights  -  Riot for peace & Love: Catholic Influencers and Digital Missionaries welcome Jubilee of Youth

⦿ Techrights  -  Slopwatch: Fake 'Linux' 'Articles' and Spamfarms/Slopfarms

⦿ Techrights  -  Slopwatch: Google News is Pumping in Lots of Web Traffic Into Fake Sites That Say "Linux"

⦿ Techrights  -  Slopwatch Makes the Web Better

⦿ Techrights  -  Some People See What Others See... But Only 40 Years Later

⦿ Techrights  -  The Register Relays Microsoft Marketing, Dubs That Marketing "Research"

⦿ Techrights  -  "The Unix Kernel"

⦿ Techrights  -  Wall Street Does Not Care About Microsoft's Impending (August) Layoffs, It Believes Lies From Microsoft, Whose Debt Grows Rapidly

⦿ Techrights  -  Wayland Considered Harmful (to GNU/Linux Adoption)

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2025/07/30/Corruption_is_the_Standard_Operating_Procedure_at_the_European_.shtml
https://techrights.org/n/2025/07/30/Dealing_With_Sociopaths_Liars_and_Cranks.shtml
https://techrights.org/n/2025/07/30/GAFAM_Revolving_Doors_at_The_Register_and_a_Bribe_Price_List.shtml
https://techrights.org/n/2025/07/30/Google_Search_is_Fast_Becoming_No_Better_Than_Social_Control_Me.shtml
https://techrights.org/n/2025/07/30/How_to_Report_Apple_Layoffs_Without_Saying_the_L_Word.shtml
https://techrights.org/n/2025/07/30/IRC_Proceedings_Tuesday_July_29_2025.shtml
https://techrights.org/n/2025/07/30/Last_Month_Our_IRC_Community_Turned_17.shtml
https://techrights.org/n/2025/07/30/Local_Staff_Committee_Munich_LSCMN_at_the_European_Patent_Offic.shtml
https://techrights.org/n/2025/07/30/Microsoft_Rapidly_Shrinking_No_It_s_Not_About_Efficiency_It_s_A.shtml
https://techrights.org/n/2025/07/30/Microsoft_Will_Continue_Resorting_to_Crimes_in_Order_to_Keep_GN.shtml
https://techrights.org/n/2025/07/30/My_Experience_With_Judges_Has_been_Positive_But_We_Must_Still_P.shtml
https://techrights.org/n/2025/07/30/Not_Owning_Mobile_Phones.shtml
https://techrights.org/n/2025/07/30/Over_at_Tux_Machines.shtml
https://techrights.org/n/2025/07/30/PCLinuxOS_Had_Functional_Backups_Before_the_House_Fire_the_Site.shtml
https://techrights.org/n/2025/07/30/Riot_for_peace_Love_Catholic_Influencers_and_Digital_Missionari.shtml
https://techrights.org/n/2025/07/30/Slopwatch_Fake_Linux_Articles_and_Spamfarms_Slopfarms.shtml
https://techrights.org/n/2025/07/30/Slopwatch_Google_News_is_Pumping_in_Lots_of_Web_Traffic_Into_Fa.shtml
https://techrights.org/n/2025/07/30/Slopwatch_Makes_the_Web_Better.shtml
https://techrights.org/n/2025/07/30/Some_People_See_What_Others_See_But_Only_40_Years_Later.shtml
https://techrights.org/n/2025/07/30/The_Register_Relays_Microsoft_Marketing_Dubs_That_Marketing_Res.shtml
https://techrights.org/n/2025/07/30/The_Unix_Kernel.shtml
https://techrights.org/n/2025/07/30/Wall_Street_Does_Not_Care_About_Microsoft_s_Impending_August_La.shtml
https://techrights.org/n/2025/07/30/Wayland_Considered_Harmful_to_GNU_Linux_Adoption.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2025/07/30/Gemini_Links_30_07_2025_Two_Sides_of_Me_and_Hooked_on_Cosmic_Vo.shtml
https://techrights.org/n/2025/07/30/Gemini_Links_30_07_2025_Watson_s_List_of_Limits_Lysenko_2000.shtml
https://techrights.org/n/2025/07/30/Links_30_07_2025_Climate_Calamities_Highlighted_Kyrgyzstan_Crac.shtml
https://techrights.org/n/2025/07/30/Links_30_07_2025_Tea_Class_Action_and_Google_Killing_the_Web_Wi.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 116

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Corruption_is_the_Standard_Operating_Procedure_at_the_European_.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Corruption_is_the_Standard_Operating_Procedure_at_the_European_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Corruption is the Standard Operating
Procedure at the European Patent Office (EPO)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Jul 30, 2025


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇I_am_here_to_'protect'_the_nation;_I_am_here_to_'protect'
                      American_companies,_Microsoft_ICE⦈_


Ten years ago the European_Patent_Office_(EPO) decided to embark on a SLAPP
campaign against me. It took several law firms in London - including one very
large and notorious one - and tried to crush me for no reason other than me
helping to expose crimes of Benoît_Battistelli. I wrote more than a dozen
articles about what they did to me back then. I also shared the details of how
my solicitor, David Allen Green (Preiskel & Co.), responded to them and stopped
their abuse against me. As a general rule, it's important to make people who
SLAPP pay for their SLAPPs.


Since 2018 the EPO has been run by Battistelli's friend, António_Campinos, who
is not less corrupt. He continues_to_crush_the_workers. He even tries to
replace them with slop, i.e. he looks forward to outsourcing_to_Microsoft_the
decision-making_processes in addition to passing_all_the_data_there.


This is no laughing matter. 10 years ago I wrote about how the EPO decided to
give Microsoft preferential treatment (jumping the line/queue). Now we see a
corrupt EPO already experimenting with externalising the processes to a foreign
company's algorithms, under the false guise of "intelligence".


The EPO is a dictatorship that stains Europe. █


    * Local_Staff_Committee_Munich_(LSCMN)_at_the_European_Patent_Office_(EPO)
      Requests_an_Urgent_Meeting_to_Avoid_Abolishing_the_Office
    * IRC_Proceedings:_Tuesday,_July_29,_2025


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⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣎⠘⢛⢠⠈⠙⠍⢿⣿⣿⡟⠻⢶⣿⡶⠘⣿⣿⣻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡠⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀
⣿⡿⢀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠗⣿⣻⣷⠂⠁⠤⣷⢦⣤⣿⣿⣷⣶⣦⣍⣷⣶⣿⡟⣿⣏⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠒⠧⣐⠂⠀⠀⠀⠀⠀⠀⠒⠐⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⡀⣴⡶⠟
⣿⢷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⠃⠸⠛⣚⣋⣽⣿⣿⣿⣀⣙⣻⣿⣿⣽⡇⣿⡿⣬⣿⠅⠀⠀⠀⢀⡀⡀⢀⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠀⠀
⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠭⠙⢻⣤⠀⢬⣿⣿⣿⣿⢿⣿⡉⢙⢿⣿⣿⣿⣿⣿⣿⣿⣇⠄⠀⠀⠄⠐⠁⠀⠁⠉⠈⠉⠁⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠑⢦⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣾⡟⣷⢴⢰⢌⣵⣿⣧⣿⣿⣿⣾⣧⣟⣿⣿⣷⣿⣿⣾⣷⣀⠀⡀⣀⣈⢀⣀⡀⣀⡀⢀⣀⡁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⢹⠻⠏⣿⣯⢹⣽⠙⢹⢉⢙⣽⠉⠫⢩⡏⠟⢫⠉⢯⠟⠉⣯⢫⠙⢉⠹⠋⢩⣹⣿⡿⠿⣛⣿⡿⣿⠗⠈⠋⠀⠀⠀⡀⠉⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣭⣿⣿⣛⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠟⣛⡻⡏⠉⠙⣶⣿⣟⡰⠗⠃⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡲⢰⣿⠟⡷⠴⠩⡛⠿⣿⠀⠻⡈⠁⠀⠀⠑⣊⡌⠀⢀⠀⠀⠀⠀⠄⠪⠀⠀⠀⠀⠀⠀
⣙⣛⠛⠿⠿⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠄⢚⠄⠀⠀⢠⣵⠟⢒⡄⠀⠁⠀⠀⠀⠈⠐⠈⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣮⢩⣭⣝⣛⣛⣻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠙⣿⡿⠁⠀⠹⠿⡿⠻⢿⣿⣿⣿⣟⡿⠩⠵⢛⠊⠁⠠⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢚⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠿⠻⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣭⣿⣿⣾⠐⢛⠻⣦⣄⣁⠀⠀⠀⠀⠈⠉⠙⠛⠉⠛⠷⢶⣤⣦⣀⣀⣴⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀
⠛⣫⣭⣽⣿⣿⣿⣿⡿⢿⡏⡟⠓⢀⠒⢂⣿⠟⢋⢉⠩⠙⣿⣿⣿⣿⣿⣯⣿⠀⠀⠀⠸⣿⣿⣿⣶⣶⣆⢄⢄⣤⢀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠛⠹⠟⢲⠹⠿⠚⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣇⠀⠐⠀⠀⠈⠀⠀
⠒⠐⠚⠒⠟⠻⠉⠁⢻⣀⣠⣀⣟⣛⣃⡬⠍⠀⠘⠀⠠⢿⣿⢿⣹⠿⡟⡟⡟⠀⠀⠀⠀⠈⢻⢿⣿⣿⠏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢶⣌⣟⡂⣀⠸⠠⠠⢾⡟⡛⣿⠁⠀⠀⠀⠀⠀⠐⠘⠪⡍⠻⡿⣧⡇⠀⠀⠀⠀⠀⠀⠁⢻⠏⠀⠄⠐⡒⡒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣀⣀⢀⡀
⠀⠀⠐⠀⠌⠀⢁⡘⢂⠃⠄⠼⣷⣤⣽⣿⢀⡰⠀⠀⠀⠀⠀⢠⠈⢀⡅⡇⡃⠀⠀⠀⣀⡀⠄⣤⣽⣿⣿⣿⣿⣿⣽⣿⡦⢤⣤⠤⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣰⣡⣴⣶⣶⣒⣶⡾⠛⠛⠙⠁⠀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠖⠀⠀⡇⣟⣋⣛⣿⣿⣿⡭⠽⢿⣿⢿⣿⣿⣟⣿⡿⣿⣿⢻⣿⡿⠿⢿⣟⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⡿⢿⡊⠁⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠁⣿⣷⣾⣷⣿⠏⠀⣾⠟⠯⡖⣿⡾⡗⠟⠿⠿⢨⠾⢟⡟⢃⣗⣟⣵⣟⢾⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣌⢳⣄⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠉⠉⡉⠉⠉⠀⠠⠶⠶⠈⠠⠾⠭⠤⠤⠤⠀⠀⠀⠀⠀⠑⣻⣼⠿⣡⣤⣥⣔⠛⠻⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠊⠴⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡤⡦⡀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⢰⠀⢀⣀⢠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡌⠰⠀⢇⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⣿⢖⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⡀⣀⢀⠀⠁⠄⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢀⣀⢀⣀⡀⢀⣠⣴⣷⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⢰⢰⡶⢶⡶⣶⢲⢰⣒⢰⢲⣼⡇⣿⠀⣿⣾⢙⢺⡯⠉⠉⠉⠉⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠛⠛⠛⠘⢘⢛⣛⡇⠛⠚⠘⠚⠘⠚⠙⠃⠛⠀⠛⠙⠚⠙⠓⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿
⠀⠀⠀⠀⠠⠘⠛⠛⠛⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣵⣶⣶⣶⣶⣦⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⣛⣻⣭⣶

                    ䷩ 𝚕𝚒𝚗𝚎 204

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Dealing_With_Sociopaths_Liars_and_Cranks.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Dealing_With_Sociopaths_Liars_and_Cranks.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Dealing With Sociopaths, Liars, and
Cranks⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Horoscope⦈_


Since 2022 I've had to routinely deal with online bullying. By 2023 that
bullying already started targeting family members (like my wife, my mother, and
others). I reported the matter to the police only after it had become an actual
crime and the police acknowledged it as such. On several occasions I invited
them to my home to collect relevant evidence.


For 18 months (since February 2024) I also had to deal with another kind of
bullying. I reported this to the relevant British authorities.


I quite like what Andy from the_Cybershow says about authorities; we're not
against authorities, we're against authoritarians. The authorities can provide
many valuable services and those who abhor authorities aren't always
anarchists, some just like to do illegal things and get all angry that
authorities get in their way.


In some sense I grew to believe that authorities do serve many legitimate
purposes; without authorities, things would get worse.


We live in an age of lies and superstition. We are surrounded by people who for
medical reasons or due to trauma are detached from reality and some totally
lack empathy. Some are literally sick for or addicted to money. For instance,
I've had to deal with journalists who would defend bad behaviour because some
company - unlike me - pays them to act that way.


Regarding lies, I've seen them all. Some people lie to shareholders, many
people lie about their wealth (it's obscene how far these lies would go!), and
some who commit crimes would outright deny those crimes ever happened (even if
they did).


I worry about a society that's facilitating and actively entertaining such
people; they're a yoke, since they defraud people, steal from people, viciously
attack innocent people, and it's typically done for personal gain, emboldened
by psychological problems. A dysfunctional society such as this would never
develop.


This episode_that_I_listened_to_yesterday said that British universities now
openly and knowingly accept cyber criminals and fraudsters from other countries
in exchange for tuition fees; both Helen and Andy give several examples that
they saw firsthand; the administrators at universities don't seem to care at
all; they try to brush it all under a rug while taking the money (to train
cyber criminals and fraudsters). Andy posits that there is some kind of
societal or systemic collapse in the making and, unlike back in "his days"
(when he studied and became a lecturer), access to education is nowadays based
on finances, not potential or underlying skills. It's all about money, no
matter the means (like committing serious crimes with many real victims). █


    * Not_Owning_Mobile_Phones
    * The_Register_Relays_Microsoft_Marketing,_Dubs_That_Marketing_"Research"


⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠀⠂⠀⠀⠐⠂⠀⠠⠐⠠⠀⠢⠂⠀⠀⠀⠖⠀⢈⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣾⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣽⠟⠁⢠⠀⠀⠀⢀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⣿⢳⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠀⠢⣘⢀⡆⡌⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠏⠀⠦⠀⠀⠀⠀⠀⠀⠀⠘⣾⡻⣿⣿⣿⠿⣛⣿⣽⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠁⠁⠒⠦⣼⣁⡀⢀⡀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣷⣾⣿⣿⣶⣤⡂⠰⠀⠀⠟⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣿⣿⠿⠿⠟⢁⣀⣀⣀⣐⣀⣠⣤⡥⢄⣌⠀⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣄⢻⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣾⣿⣿⣿⠿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣻⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡆⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡇⠀⠀⠀⢻⣿⣿
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀⣀⡀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠙⠻⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿
⠀⠀⢀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⢻⣿⣶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣸⣿
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠃⠉⠉⠁⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡏⢉⣿⡆⣽⣿⣿⣿⣿⡟⣿⣿⢻⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢃⣾⣿⣿⣿⣿⣭⣷⡶⣾⣿⣯⣯⣍⣻⣿⣷⣿⡟⣼⣿⣿⣽⣿
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣀⣠⣤⣈⡀⠀⠀⠀⣘⣿⣿⣿⡷⠾⠟⠛⠛⠻⢿⣿⣻⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿⣿⣿⣿⡏⢨⡉⣸⣿⢛⣿⠿⠈⠻⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣇⢠⣼⡿⠗⠚⢻⣿⣦⡐⡏⣿⣿⣿⣽⡏⠋⣩⣿⣍⠛⠻⢻⢹⣿⣿⣿⣷⣿⣿⣿⡟⢛⣛⣩⣭⣭⣭⣭⣽⣞⣁⢙⠷⢻⣿⡎⡁⢾⣷⠷⠌⠛⠛⠛
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣧⠀⠀⠸⣿⠿⡅⡇⢹⣿⣿⠈⣇⣀⠙⠛⠋⣀⣤⣼⣾⣿⣿⣿⠉⢩⣽⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠿⡷⣥⡸⣿⣶⣍⠓⢶⣤⠀⠀
⢛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢯⣿⣷⣶⣾⣿⣿⣾⣿⢸⣿⣿⠀⠀⠀⠈⠉⠉⠉⠘⢻⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⡀⢻⣿⣌⡻⣿⣷⣌⠻⡇⠀
⢿⢸⣿⣿⣷⣿⣭⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⡌⠻⠛⠁⠈⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⡆⠀⡠⠔⠢⠄⠀⠀⠎⠛⠿⠿⠁⡰⢊⠹⣿⡛⣻⣿⡻⣿⣿⣿⣿⣿⣿⣿⡇⡾⣹⡈⣿⣿⣿⣌⠻⣽⠇⡰⠀
⣾⡧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠄⠀⠐⠾⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠐⢆⠀⠀⡸⠀⠀⠀⠀⠐⢄⠀⣐⣤⠸⡿⢃⢻⣿⣾⣿⣷⣾⣿⣿⣽⣿⣿⡇⣿⣷⣼⣿⢸⣿⡀⢶⣶⠇⠀
⣿⣁⡾⠶⣭⣛⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⠀⣀⠀⠈⠐⠊⠁⢀⣦⠀⠀⠀⠀⠀⢈⢛⣃⢺⣟⣼⣿⣥⣿⣿⣿⠿⣿⣿⣿⣿⣷⣭⣍⣛⡻⢿⣿⣍⣿⠟⡀⠀
⣿⣿⣷⣾⣿⣭⣽⣩⣿⣗⣶⡶⢶⣶⣶⣭⡛⠿⣿⣿⣿⣿⣄⡀⠀⠀⢀⣳⣽⢿⣿⣿⣿⣿⣟⢛⣻⠟⠋⠀⠀⠀⣠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣾⡇⠀
⣇⡔⢻⠟⣛⡣⣼⣿⣉⣿⠿⣿⣮⣶⢿⡿⠓⠈⠈⠙⠿⣿⣿⣿⣿⣶⡾⣷⣶⣷⣾⣿⣿⣿⣿⣶⣦⠀⠀⠀⢀⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣵⢿⣿⣿⡇⠀
⣿⣇⣃⠺⣿⠗⣹⡿⢿⣿⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣀⣠⣾⡿⠛⠛⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣶⣶⣿⡇⠀
⣯⣤⣿⣿⣶⣾⠛⣷⣿⡿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣻⣿⣿⣿⣿⡄⠀⠠⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⢩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⡇⠀
⡿⣤⣷⣾⣿⢷⠼⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠐⠀⠀⠈⠛⠛⠉⢻⣿⡍⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⡇⠀
⣴⣿⣿⡉⢻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠒⠂⠀⠀⠀⠀⢘⣿⣷⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⢀⠀
⣿⡛⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠶⠶⠶⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣹⣷⣭⣛⣻⣿⡿⢿⠿⡿⣿⣟⣫⣾⠇⣼⠀
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡄⠀⠀⠀⠀⠀⠠⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⠀
⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠑⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⣼⡽⠂⡄⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⡟⣠⣿⣿⠀
⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⡀⢤⠄⣀⣀⡆⠀⠀⠀⠀⠀⠋⠛⠀⠻⠃⠘⢡⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⠀
⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢷⡟⠐⠋⢋⣼⠳⣵⠋⡇⠀⠀⠀⠀⠀⣏⠀⠐⢖⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀
⣿⣛⣃⠀⠀⣀⣀⠀⣐⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠿⣦⡀⠀⠉⡐⠁⠀⠇⠀⠀⠀⠀⠘⠢⠋⠐⠚⠀⢠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣟⠀⠉⠐⠒⠲⠶⠒⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢿⠀⠀⠀⠀⠛⠁⠀⠀⣰⡆⠈⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣷⣶⣶⣶⣤⣬⣭⣭⣉⣛⣛⡛⠂
⣿⣿⣿⡇⣿⣶⣶⣦⣦⢠⣴⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⡁⠀⠀⠀⠀⠀⣿⠃⠀⡇⠀⠀⠀⠀⠀⢰⣯⠀⢨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⢿⣫
⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⠿⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⡛⠛⠷⠴⠗⢶⠄⠀⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⢰⢸⣿⣿⣿⣿⣿⣿⣷⣾⣭⠿⣟⣯⣿⣾⣿⣿
⣿⣯⣿⠃⣿⣿⣿⣿⣿⣠⣾⡏⣠⣿⣿⣶⡂⠀⠀⠀⠀⣀⡀⠀⠈⠉⠃⠑⠓⠘⠚⠳⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠿⠿⠿⠿⠆⢿⡟⠛⣿⢫⡝⣿⣿⣟⢟⣿⣿⣿⣿⣿⣿⣿
⡿⠇⢐⣄⡙⠻⠿⠿⠿⠿⠿⠇⠻⣿⣿⣿⡇⠂⠀⠄⠀⠈⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣼⣿⣿⣇⣒⣂⣻⢻⣿⣿⣇⣐⣈⠷⣂⣬⣑⣦⣭⣭⠹⣿⣿⣿⣿⣿⣿⣿
⣷⣤⠭⠭⠁⠀⠤⠤⣔⢒⣀⣲⣿⣿⡿⠉⠓⠂⠐⢀⣠⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡍⡊⢿⣯⣿⣿⠿⢿
⣿⣿⣶⣶⣾⣿⣶⣾⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣷⡦⠤⣄⣈⣛⣾⣿⣷⣖⠒⣤⣴⣶⣶⣶⡀⢀⠀⠠⣤⣤⣄⣀⠀⠀⡀⢀⣼⣟⣿⣿⣿⡿⢛⡭⠉⣦⠤⠉⣭⡛⢛⡛⢛⡛⠹⢍⡉⠛⢤⣶⣲⡝⣫⡶⠛⢾
⣿⣿⣿⠟⡛⢿⣿⣏⣹⣿⠏⣭⡉⢻⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠿⢿⣷⣦⣴⣤⣤⣤⣶⣿⣶⣶⣾⣿⣿⣿⣯⣉⣩⣥⣤⣾⣶⣴⣿⣿⣿⣿⣶⣶⣾⣶⣿⣿⣟⣛⣷⣘⣃⣉⣿⣿⣿⢿⣷⠘⣋⣉⠰⡏⣰⣿⡦
⢿⣿⡇⢸⣿⣦⡙⣿⣿⢛⠀⣿⣿⣆⠻⢛⠻⡏⢰⣷⣦⠙⣉⡙⠇⢾⣦⡙⢿⣿⡏⢰⣶⡌⠋⣴⣦⡙⣿⣿⢡⣶⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⡉⢻⣿⣿⡿⠿⠿⠟⠩⠟⣩⣴⡆⢁⣾⣿⣿⠀⢀⣿⣿⡇
⣆⠙⠛⠈⣿⣿⣷⠘⠛⠘⣧⠸⣿⣿⠀⣿⣷⡀⢸⣿⣿⡀⣿⣿⣄⠘⣿⣿⡆⢻⣷⠸⣿⣿⡄⢿⣿⣧⢸⣿⠘⣿⣿⢂⣉⡛⢿⣿⣿⣿⣿⣿⡿⢃⣾⣿⡿⠸⢋⣥⣶⣷⢀⣿⣷⠀⣿⡿⢠⣿⣿⣿⠏⡌⢸⣿⣿⠀
⡟⢸⣿⣆⠘⣿⣿⠀⣿⣷⡘⢦⠹⣿⡇⢻⣿⣷⠀⢿⣿⡇⢻⣿⣿⡄⢸⣿⠏⣠⣦⡀⢿⣿⣷⠘⣿⣿⠈⢩⡄⢿⣿⠸⣿⣿⡈⣿⣿⣿⣿⣿⢃⣾⣿⣿⠃⣴⣿⣿⡿⢃⣾⣿⣿⢠⣿⠁⣿⣿⣿⡟⢰⡇⣾⣿⣿⢠
⣇⢸⣿⣿⣇⠸⣿⡆⢻⣿⣷⠘⣇⢹⣿⠘⣿⣿⡇⠸⣿⣿⡈⣿⣿⣷⠸⣿⠀⣿⣿⣿⡈⣛⣭⣤⣝⢿⡇⠸⣇⢸⣿⡄⢿⣿⣧⢸⣿⡿⣿⡇⣼⣿⣿⠃⣼⣿⣿⠋⣴⣿⣿⣿⠃⣾⡏⢸⣿⣿⣿⢁⣿⠇⣿⣿⣿⢸
⣿⡈⣿⣿⣿⡄⢿⣿⡈⣿⣿⣇⢹⡄⣿⣇⢹⣿⣿⠀⣿⣿⣧⢸⣿⣿⣀⣿⡄⢻⣿⣿⡇⢿⣿⣿⣿⢫⡇⠀⣿⠸⣿⣷⠸⣿⣿⠈⣿⣿⣿⢀⣿⣿⡏⣸⣿⣿⢃⣾⣿⣿⣿⠃⣼⣿⠇⣿⣿⣿⡏⣸⣿⠀⣿⣿⣿⢸
⡘⢇⢹⣿⣿⣧⢸⣿⣷⠘⣿⣿⡈⣧⢸⣿⡈⣿⣿⡇⣿⣿⣿⠀⣿⣿⡇⣿⣷⠈⣿⣿⣷⢰⣮⣍⢱⣿⡇⢸⣿⢠⣿⣿⡄⣿⣿⡇⣿⠷⡋⣸⣿⣿⢠⣿⣿⠃⣾⣟⠉⣻⠇⣼⣿⣿⢠⣿⣿⣿⠁⣿⣿⠀⣿⣿⣿⢸
⣿⣄⠀⣿⣿⣿⡄⣷⣿⣇⢹⣿⡇⢿⠀⣿⡇⠻⢿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡄⣿⣿⣿⢸⣿⣿⠀⣿⡇⢸⡏⢹⣿⣿⡇⣿⣿⠃⡏⣾⡇⣿⣿⡇⣸⣿⡿⢰⣿⣿⣿⣿⢰⣿⣿⡏⢸⣿⣿⣿⠠⣿⣿⢀⣿⣿⣿⢸
⣿⣿⣆⠸⣿⣾⣇⢸⣿⣿⠘⣿⡇⢸⡇⣿⣇⢸⣿⣇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡇⡿⣨⣿⢰⣿⣿⠀⣿⡇⡸⢡⣿⣿⣿⠇⣿⣿⠀⣷⣝⢣⣿⣿⠃⣿⣿⡇⢸⣿⣿⣿⡇⢸⣿⣿⡇⣾⣿⣿⣿⠰⣿⣿⢀⣿⣿⣿⢸

                    ䷩ 𝚕𝚒𝚗𝚎 332

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/GAFAM_Revolving_Doors_at_The_Register_and_a_Bribe_Price_List.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/GAFAM_Revolving_Doors_at_The_Register_and_a_Bribe_Price_List.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ GAFAM 'Revolving Doors' at The Register and
a "Bribe Price List"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Matt_Rosoff_is_an_analyst_with_Directions_on_Microsoft,
      where_he_covers_Microsoft's_consumer_products_and_corporate_news.⦈_


I recently got an opportunity to discover what had happened to The Register MS.
After I repeatedly criticised it (not before giving an opportunity to respond)
I learned that the new Editor in Chief "spent_a_decade_as_an_analyst_at
Directions_on_Microsoft" or "spent_10_years_as_an_IT_industry_analyst_for
Directions_on_Microsoft."


This_one_says "he was an analyst at Microsoft for 10 years" (The Atlantic's
official page about him).


Yes, it says "an analyst at Microsoft"!


Was it just pretending to be an independent company (otherwise, does trademark
violation not became a problem)? Sort of like Waggener_Edstrom?


Notice where he was based. To quote_CRN: "Matt Rosoff, an analyst with
Kirkland, Wash.-based Directions on Microsoft, antitrust litigation has become
the norm for Microsoft."


Well, "the norm"... he tried to trivialise it. He was paid to write prose to
sell Microsoft products. The BillBC quoted_him on Microsoft and even almost a
decade after he 'left' he still shilled Microsoft. In fact, he_continued_his
focus_on_Microsoft_pieces_even_more_than_7_years_later. As editor in a number
of online publications he imported his Microsoft bias. Now... The Register MS.
And he's bringing in more_Microsofters_as_editors.


We're meant to think he was some Microsoft expert (he's not even technical);
the media would quote a Microsoft operative... about Microsoft. Very clever PR
trick.


I tried to understand how that happened and I got an answer 2 days ago.


"Your output is good," I told one of the writers there (a long timer). "I don't
write to you in bad faith. I can assure you that. The previous editor in chief
and I discussed your good work months ago."


It turns out that the previous editor quit; he didn't get the boot apparently.


"So, what, you didn't know Chris had quit?" I was told. "I knew him socially
before I ever even freelanced for the Reg. He's gone to Google; it's on
Linkedin."


So he went to GAFAM, eating from the palm he was supposed to "bite".


"He hired Matt," I was told, then "Matt hired Aaron. There is no skullduggery,
no covert subliminal message."


Well, I see an influx of Microsofters as editors and, accordingly, the
publication is being flooded with Microsoft brands.


The interesting part is this: they make jokes about taking bribes.


To quote: "Hell, 13Y ago I wrote _The Register Guide to Windows Server 2012_
and made a few £K from it and that was MS ad money. The Reg is very open about
accepting anyone's money. It used to have a bribe price list!"


How is that a good thing?


I had a lengthy chat with the previous editor about how they had taken IBM
money, which can compromise their coverage of IBM layoffs and offshoring. He
tried to assure me this was not a problem. I didn't agree with him back then
and I still disagree on that. Now he works for Google.


This publisher is going_downhill and sinking_in_debt. █


    * Microsoft_Rapidly_Shrinking_(No,_It's_Not_About_Efficiency,_It's_About
      Unbearable_Debt)
    * Microsoft_Will_Continue_Resorting_to_Crimes_in_Order_to_Keep_GNU/Linux
      Usage_Down


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⠄⠤⠀⣄⠀⠤⢠⡄⠀⢤⠠⢠⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠀⠀⠀⠈⢳⣄⢸⡇⠒⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠈⠀⠁⠀⠉⠈⠁⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠤⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠤⢤⡤⠄⠤⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⠤⡤⢠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡶⣀⢶⢀⣀⣠⢠⡀⢰⠒⡄⣀⡀⣀⡀⣀⣀⣔⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠇⠿⠸⠪⠹⠸⠘⠄⠸⠉⠇⠣⠇⠯⠎⠧⠃⠇⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠀⠀⠓⠀⠀⠒⠐⠀⠂⠀⠂⠐⠂⠒⠐⠐⠂⠀⠂⠐⠀⠒⠐⠀⠐⠀⠀⠀⠀⠂⠐⠀⠂⠂⠐⠂⠐⠂⠂⠐⠐⠒⠐⠀⠂⠀⠒⠂⠐⠐⠀⠒⠐⠀⠒⠀⠖⠀⠒⠐⠀⠂⠐⠂⠐⠀⠲⠂⠂⠀⠂⠀⠂⠂⠀

                    ䷩ 𝚕𝚒𝚗𝚎 456

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Google_Search_is_Fast_Becoming_No_Better_Than_Social_Control_Me.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Google_Search_is_Fast_Becoming_No_Better_Than_Social_Control_Me.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Google 'Search' is Fast Becoming No Better
Than Social Control Media Infested With Bots⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025,
updated Jul 30, 2025


Related: Google_Spreading_Misinformation_and_Lies | Google_"AI_Overview"_is_Not
AI_and_Not_Overview


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


Today I tried using "Google" (Alphabet) "Search" to look for a very specific
and very precise quote. Instead, Google spewed out a bunch of totally
irrelevant, totally wrong LLM slop at me. Its "word/s salad" was placed at the
top of the page, distracting from anything that could in fact be useful.


There are reports this week about Google increasing this sort of thing. Decades
ago people accused Google of being US government propaganda in the form of
search results pages (SERPs) and now we see Google acting like an "agent"
(slop, not intelligence) trying to direct people to think/act a certain way.


To me, personally, Google is in many ways dead. I don't use Android, I don't
use Google disservices (I very much loathe how many people use Gmail, which
means their mail to and from me gets scanned by Google for commercial gain and
spy agencies), and the main impact the 'Google things' seem to have comes in
the form of invisible trackers in many billions of Web pages. We don't even use
YouTube here anymore; we use Invidious. YouTube became an obnoxious ad-spewing
machine, trying to fake a "growth" in revenue by just spewing out more and more
ads (even_if_YouTube_still_loses_money).


Google emerged almost 30 years ago as a company looking to organise the Web and
direct people towards informative pages. That Google is dead. █


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


    * PCLinuxOS_Had_Functional_Backups_Before_the_House_Fire,_the_Site_Will_be
      Restored_in_New_Webhost
    * Not_Owning_Mobile_Phones


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡌⠉⠢⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⣤⡀⠀⠀⢀⣤⡀⠀⠀⢠⣤⡀⠀⠀⠀⠀⣶⣷⡿⢉⣾⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⣄⣤⡹⢷⣄⣀⠀⠀⠀⣿⣿⡀⠀⠀⣿⣿⢄⣀⣼⣿⣿⠀⠀⠀⣸⣄⠀⠀⠀⢸⣿⣿⣄⡀⢸⣿⣧⣤⣤⣿⣿⠃⠀⣀⣿⣿⡇⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡀⢻⣷⣾⣿⣿⣶⣤⣤⣿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣾⡇⣼⣿⣿⣿⣶⡀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⣏⠛⠿⣿⣿⣿⣿⣿⣿⢻⡟⠒⠺⠿⢿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⣿⡟⠛⠛⢻⣿⣿⡟⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣠⢻⣿⣿⣿⣿⣿⣿⣷⡄⡄⣖⣺⣿⣷⠀⠀⠀⣿⣿⣿⠏⠉⢻⣿⡇⠀⠀⠀⢰⣿⠂⠀⠀⢸⣿⣿⣧⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⡙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⣻⣿⡄⣀⡀⢹⣿⣿⠀⠀⠸⣿⡃⠀⠀⠀⣾⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣳⣿⣿⣿⣷⡿⠓⠏⠹⠛⣇⣴⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡆⣛⢻⣿⣿⣿⣿⣿⣦⣀⠀⠹⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠉⠋⢁⢀⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠛⠁⢠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⣤⠀⠀⠁⠀⠠⢍⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣤⠇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⢀⣀⣉⣃⣀⣀⣀⣀⣈⣹⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣷⣶⣦⣤⣄⣸⣷⣦⣶⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠛⠋⠹⠿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠻⠿⠿⠻⠉⠙⢿⠟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠉⠉⠻⠏⠉⠻⠋⠁⠀⠀⠉⠛⠛⠛⠛⠉⠻⣿⢻⣿⡿⠛⠛⠛⠛⠛⠁⠈⣿⣟⠛⠋⠉⠉⠉⠉⠈⠟⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣿⣿⣿⣷⠀⠀⣿⡿⣿⣿⣿⣿⢻⣷⡀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠻⣿⣷⣄⣿⣿⣶⢸⣿⣿⣿⣸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢻⣿⣿⠇⣿⣿⣤⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣧⣿⣿⢻⣿⣸⣿⠇⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⢀⣉⣙⣋⣁⣀⢀⣉⡉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠳⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠈⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡌⠉⠢⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣤⡀⠀⠀⢀⣤⡀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣶⣷⡿⢉⣼⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢄⣤⠹⢷⣄⣀⠀⠀⠀⣿⣿⡆⠀⠀⣿⣿⢀⣀⣼⣿⣿⠀⠀⠀⣸⣄⠀⠀⠀⢸⣿⣿⣄⡀⢸⣿⣧⣤⣤⣿⣿⠃⠀⣀⣿⣿⡇⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡀⢻⣷⣾⣿⣿⣷⣤⣠⣿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣼⡇⣼⣿⣿⣿⣶⡀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⣏⠛⢿⣿⣿⣿⣿⣿⣿⢻⡟⠒⠾⠿⢿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⣿⡟⠛⠛⢻⣿⣿⡛⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣠⢻⣿⣿⣿⣿⣿⣿⣷⡆⡄⣒⣺⣿⣷⠀⠀⠀⣿⣿⣿⠋⠉⢻⣿⡇⠀⠀⠀⢰⣿⠀⠀⠀⢸⣿⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⡙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⣛⣿⡀⣀⡀⢻⣿⣿⠀⠀⠸⣿⣃⡀⠀⠀⣽⠿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡿⢿⣿⣿⡿⠓⠟⠙⠓⣇⣼⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣯⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⣛⢻⣿⣿⣿⣿⣿⣦⣀⠀⠉⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡇⠉⠟⢁⣀⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⢛⠁⢠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠠⢍⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⠇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⣀⣉⣁⣀⣀⣀⣀⣈⣹⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣷⣶⣦⣤⣀⣸⣷⣦⣶⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠛⠋⠹⠿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠻⠿⠿⠻⠉⠙⢿⠟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠉⠉⠻⠏⠉⠹⠋⠁⠀⠀⠉⠛⠛⠛⠛⠋⠻⣿⢻⣿⡿⠛⠛⠛⠛⠛⠁⠈⣿⣟⠛⠉⠉⠉⠉⠉⠈⠟⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣿⣿⣿⣷⠀⠀⣿⡿⣿⣿⣿⣿⢻⣷⡀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⣸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢻⣿⣿⠇⣿⣿⣴⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢻⣿⣸⣿⠇⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⢀⣉⣙⣋⣁⣀⢀⣉⡉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠳⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠈⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡌⠉⠢⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⣤⡀⠀⠀⢠⣤⡀⠀⠀⢠⣤⡀⠀⠀⠀⠀⣶⣶⡿⢉⣾⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢄⣤⡹⢷⣄⣀⠀⠀⠀⣿⣿⡄⠀⠀⣿⣿⢄⣀⣼⣿⣿⠀⠀⠀⣸⣄⠀⠀⠀⢸⣿⣿⣄⡀⢸⣿⣧⣤⣤⣿⣿⠃⠀⣀⣿⣿⡇⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡀⢻⣷⣾⣿⣿⣷⣤⣠⣿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣼⡇⣼⣿⣿⣿⣶⣀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⣏⠛⢿⣿⣿⣿⣿⣿⣿⢻⡟⠒⠾⠿⢿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠿⣿⡟⠛⠛⢻⣿⣿⡛⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⢻⣿⣿⣿⣿⣿⣿⣷⡆⡄⣒⣺⣿⣿⠀⠀⠀⣿⣿⣿⠋⠉⢻⣿⡇⠀⠀⠀⢰⣿⠁⠀⠀⢸⣿⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣻⣿⡄⣀⡀⢻⣿⣿⠀⠀⠰⣿⢃⠀⠀⠀⣾⠿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣳⡿⢿⣿⣿⡿⠓⠟⠙⠓⣇⣴⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⣛⢻⣿⣿⣿⣿⣿⣦⣀⠀⠙⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠈⠛⠁⣀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠛⠁⢠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⣤⠀⠈⠀⠀⠠⢍⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣤⠇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⢀⣀⣉⣁⣀⣀⣀⣀⣘⣹⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣷⣶⣦⣤⣄⣸⣷⣦⣶⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠛⠋⠹⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠻⠿⠿⠻⠍⠙⢿⠟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠉⠉⠻⠏⠉⠻⠏⠁⠀⠀⠉⠛⠛⠛⠛⠋⠻⣿⢻⣿⡿⠛⠛⠛⠛⠛⠀⠈⣿⣟⠛⠉⠉⠉⠉⠉⠈⠟⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣿⣿⣿⣷⠀⠀⣿⡿⣿⣿⣿⣿⢻⣷⡀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠻⣿⣷⣄⣿⣿⣶⢸⣿⣿⣿⣸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢻⣿⣿⠇⣿⣿⣤⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣧⣿⣿⢻⣿⣸⣿⠇⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⢀⣉⣙⣋⣁⣀⢀⣉⡉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠈⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡈⠉⠢⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣤⡀⠀⠀⢠⣤⡀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣼⣿⡿⠉⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⢤⣤⠙⢿⣄⣀⠀⠀⠀⣿⣿⡂⠀⠀⣿⣿⢀⣀⣼⣿⣿⠀⠀⠀⣸⣄⠀⠀⠀⢸⣿⣿⣄⡀⢸⣿⣧⣤⣤⣿⣿⡇⠀⣀⣿⣿⡇⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⢻⣷⣶⣿⣿⣷⣤⣤⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣼⡇⣼⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⣏⠛⢿⣿⣿⣿⣿⣿⡟⢻⡟⠒⠺⠷⢿⣿⡿⠿⠿⠿⣿⡿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠿⣿⠟⠛⠛⢻⣿⣿⡛⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣠⠻⣿⣿⣿⣿⣿⣿⣗⡄⡄⣖⣾⣿⣷⠀⠀⠀⣿⣷⣿⠋⠉⢹⣿⡇⠀⠀⠀⢰⣿⠃⠀⠀⢸⣿⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣆⡘⣻⣿⣿⣿⣿⣿⣷⣷⣦⣊⣛⣿⡀⣀⡀⢹⣿⣿⠀⠀⠸⣿⠇⠀⠀⠀⡚⠟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣓⠾⢿⣿⣿⡿⠃⠟⠙⠛⢇⣬⣿⣦⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣶⣿⣿⣿⣧⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡄⣓⠹⣿⣿⣿⣿⣿⣦⣄⠈⢛⣿⣿⣿⣿⣿⣿⣦⣄⣠⣾⣿⣿⣿⣿⣿⠋⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠈⠉⠁⣀⣽⣿⣿⣿⣿⣿⣿⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⢠⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣄⠀⠀⠁⠀⠠⢉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⡇⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⢀⣀⣉⣁⣀⣀⣀⠀⠈⣡⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣽⣿⣷⣶⣮⣤⣀⣰⣶⢦⣴⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠙⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠟⠛⠿⠿⠿⠏⠉⠙⠿⠟⠚⠙⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠉⠘⠿⠉⠉⠙⠋⠀⠐⠒⠛⠛⠛⠛⠛⠉⠣⠥⢻⣿⡿⠛⠛⠛⠛⠛⠃⠀⠿⣿⠉⠉⠉⠉⠉⠉⠉⠛⠉⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣿⣿⣿⣷⠀⠀⣿⡿⣿⣦⣽⣿⢻⣷⡀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⣸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢻⣿⣿⠇⣿⣿⣠⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣧⣿⣿⢻⣿⣸⣿⠃⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠈⣀⢉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠠⠤⠀⠲⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣒⣒⣒⡶⠋⠁⠀⠈⠉⠛⠲⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⡀⠉⢠⣤⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⣤⡄⠀⠀⢀⣤⡀⠀⠀⢠⣤⡄⠀⠀⠀⢀⣼⣿⣿⡁⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠘⢤⣦⡙⢻⣤⣄⠀⠀⠀⣿⣿⡀⠀⠘⣿⣿⣀⣀⣼⣿⡿⠀⠀⠀⣾⣄⠀⠀⠀⢸⣿⣿⣄⣀⢸⣿⣧⣤⣤⣼⣿⡇⠀⣀⣾⣿⣯⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⣹⣿⣶⣿⣿⣷⣦⣴⣿⣿⣿⠃⣰⣿⣿⣿⣿⣿⣿⣿⣼⡇⣼⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⣟⠛⢿⣿⣿⣿⣿⣿⡟⢿⡟⠒⠿⠳⢿⣿⠿⠿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠷⣿⡟⠛⠛⠻⣿⣿⡟⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣴⡻⣿⣿⣿⣿⣿⣿⣗⡄⡆⣖⣚⢿⣇⠀⠀⠀⣿⣿⣿⠋⠉⢹⣿⡇⠀⠀⠀⢠⣿⠃⠀⠀⢰⣿⣿⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣀⣻⣿⣿⣿⣿⣿⣦⣃⠀⡚⣟⣿⡀⣀⡀⢻⣿⣧⠀⠀⢸⣿⣇⡀⠀⠀⣽⣿⠀⠀⠀⢸⣿⡧⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣯⠿⠷⢿⣿⣿⠿⡿⠓⠋⠙⠓⢇⣶⡽⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡿⣿⣓⠙⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠈⠿⣿⣿⡆⠀⠀⠀⠀⣸⣿⣗⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠈⠙⣓⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⢠⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⡉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣠⡶⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠍⣩⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣥⣷⡼⣿⣿⣦⢬⣥⣀⣀⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠛⠃⠺⠿⠿⢿⣿⣿⣿⢿⣿⣿⣿⠿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠉⠻⠿⠿⠉⠙⠻⢿⠗⠹⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⠈⠻⠯⠁⠀⠀⠀⠀⠀⠙⠛⠛⠙⠛⠋⠈⢋⠛⢸⣿⡿⠏⠉⠙⠛⠛⠛⠃⠀⣨⡅⠀⠀⢀⠉⠉⠉⡉⠷⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣿⣿⣿⣷⠀⠀⣿⡿⣿⣦⣸⣿⢻⣷⡀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠄⣿⡇⣿⣿⣿⣿⢸⣿⡟⠛⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⣸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢻⣿⣿⠇⣿⣿⣀⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢻⣿⣸⣿⠃⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠒⠄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢦⡀⠈⢠⣤⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⢀⣤⣄⠀⠀⢠⣤⡄⠀⠀⢠⣤⣄⠀⠀⠀⢀⣼⣿⣿⣁⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠘⠶⣆⠙⢻⣦⣄⠀⠀⢸⣿⣿⠀⠀⠘⣿⣿⣀⣠⣼⣿⡿⠀⡀⠀⣾⣄⠀⠀⠀⢸⣿⣿⣄⣀⢸⣿⣧⣤⣤⣾⣿⡇⠀⣀⣸⣿⣿⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⣀⣹⣷⣾⣿⣿⣷⣦⣼⣿⣿⣿⠃⣴⣿⣿⣿⣿⣿⣿⣿⣼⡇⣼⣿⣿⣿⣷⣀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⣿⡀⢹⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠟⠳⢿⣿⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⢿⡟⠛⠛⠛⣿⣿⡟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡻⣿⣿⣿⣿⣿⣿⣗⡄⡆⣖⣚⢿⡇⠀⠀⠀⣿⣿⡿⠁⠈⢹⣿⡏⠀⠀⠀⢠⣿⠃⠀⠀⢰⣿⣿⠇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣳⣇⣻⣿⣿⣿⣿⣿⣷⣗⠒⡛⣛⣟⣀⣀⡀⣺⣿⣗⠀⠀⢸⣿⠇⠀⠀⠀⣾⡷⠀⠀⠀⢰⣿⡛⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣯⠿⠷⢿⣿⣿⠿⡿⠓⠟⠛⠓⢇⣴⡌⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠛⠻⢿⠚⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢽⣿⣿⡆⠀⠀⠀⠀⣼⣿⡏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠘⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣿⣏⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣠⡀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⣤⣀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⡉⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣀⣴⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣟⣀⡀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠍⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣭⣵⣼⢣⣿⣧⣌⢥⣀⡀⣰⣦⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠋⠈⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠛⠉⠻⠿⠿⠏⠉⠻⠿⠇⠙⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠈⠻⠏⠁⠀⠀⠀⠀⠀⠙⠛⠙⠛⠛⡛⢁⡙⡛⢸⡿⠟⠁⠉⠉⠛⠛⠛⠆⠀⢠⣼⠀⠀⠀⠉⠉⠉⢉⠹⠆⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⣴⣿⢻⣷⡀⠀⣾⡿⣿⣷⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣿⣿⢸⣿⡗⠛⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢻⣿⣿⠁⣿⣿⣀⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢻⣿⣸⣿⠃⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠉⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⠿⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠧⡀⠈⢢⣤⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢀⣤⣄⠀⠀⢀⣤⣄⠀⠀⢀⣤⣄⠀⠀⠀⢀⣼⣿⣿⣃⣴⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠈⢶⣆⠉⠻⣦⣄⠀⠀⢸⣿⣷⠀⠀⠘⣿⣿⣀⣠⣼⣿⡿⠀⡀⢀⣾⣄⡀⠀⠀⢘⣿⣿⣄⣀⠸⣿⣧⣤⣤⣾⣿⡏⠀⣀⣼⣿⣿⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⣄⣽⣷⣾⣿⣿⣷⣦⣼⣿⣿⡿⠁⣼⡿⣿⣿⣿⣿⣿⣿⣼⡇⣾⣿⣿⣿⣷⣀⣼⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠯⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠿⠳⢿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⡟⠛⠛⠛⣿⣿⡟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡆⣖⣚⢿⠄⠀⠀⠀⣿⣿⡟⠁⠉⢹⣿⡇⠀⠀⠀⢀⣼⠇⠀⠀⠀⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⡛⣛⣇⡀⣀⡀⣻⣿⣇⠀⠀⢸⣿⠇⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡯⠿⠿⣿⣿⣿⠿⡿⠓⠟⠛⠓⢇⣠⡌⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⢺⣿⣮⠀⠀⠀⠀⠀⢺⣿⣇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⠀⠀⠘⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⢀⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢺⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣠⡀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠀⣄⣠⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣛⣻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡈⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⠿⢄⣴⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠉⡍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣼⢣⣽⣦⣄⢡⣀⣀⢰⣦⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠩⠁⠶⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⡿⢿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠿⠟⡇⠙⠿⠿⠏⠉⠹⠿⠁⠻⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠋⠉⠉⠀⠀⠈⠀⠀⠉⠋⠙⠓⣛⣻⡇⠞⠻⢹⡿⣏⠛⠈⠉⠛⠛⠛⠦⠀⠀⢤⠄⠀⢀⠉⠉⠉⠉⢹⠄⠀⠀⢀⣴⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢹⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⢰⣿⢻⣷⡀⠀⣾⡿⣿⣷⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣿⣿⢸⣿⡗⠂⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢹⣿⣸⣿⠁⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠉⠁⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠿⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠧⡀⠈⢠⣤⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⡀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢀⣤⣄⠀⠀⢀⣤⣄⠀⠀⢠⣤⣄⠀⠀⠀⢀⣼⣿⣿⣇⣴⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠘⢶⣆⠉⢻⣦⣄⠀⠀⢸⣿⣷⠀⠀⠘⣿⣿⣀⣠⣼⣿⡟⠀⡀⢀⣾⣄⡀⠀⠀⢘⣿⣿⣄⣀⢸⣿⣧⣤⣤⣾⣿⡏⠀⣀⣼⣿⣿⠀⣀⣼⣿⣿⣽⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⣄⣽⣷⣾⣯⣿⣷⣦⣼⣿⣿⡿⠁⣼⡿⣿⣿⣿⣿⣿⣿⣼⡇⣾⣿⣿⣿⣷⣀⣼⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⡿⣿⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠯⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠟⠳⢿⣿⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⡟⠛⠛⠛⣿⣿⡟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡆⣖⣚⢻⡀⠀⠀⠀⣿⣿⡟⠁⠈⢹⣿⡇⠀⠀⠀⢀⣼⠇⠀⠀⢀⣿⣿⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡙⣛⣃⡀⣀⡀⣺⣿⣇⠀⠀⢸⣿⠃⠀⠀⠀⢸⡿⠀⠀⠀⠀⣿⣻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡯⠿⠷⣿⣿⣿⠿⡿⠓⠟⠙⠓⢇⣠⠅⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠒⠚⣿⣧⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⠀⠀⠘⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢀⣿⣏⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⡀⢼⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠀⣄⣠⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡉⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡟⢿⣿⣿⠿⢄⣴⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣝⣀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠉⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣼⣬⢻⣿⣶⣄⢡⣀⣀⢰⣦⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠩⠁⠶⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⡿⢿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠿⠛⡏⠙⠿⠿⠏⠉⠹⠿⠁⠺⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠋⠉⠉⠀⠀⠘⠃⠀⠉⠋⠙⠛⣛⣻⡇⠞⠻⢹⡟⣯⠛⠈⠉⠛⠛⠛⠧⠀⠀⢬⠆⠀⢀⠀⠉⠉⠉⠹⠄⠀⠀⢀⣴⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢹⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⣰⣿⢻⣷⡀⠀⣾⡿⣿⣷⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢿⣿⢸⣿⡗⠂⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢹⣿⣸⣿⠁⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡏⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠌⠀⠘⠁⠛⠛⠙⠁⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠟⢋⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠦⡀⠀⣶⣦⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢀⣤⣄⠀⠀⢀⣴⣤⠀⠀⢀⣶⣦⠀⠀⠀⣀⣴⣿⣿⣧⣴⣿⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢤⣶⡀⠘⠿⣦⡈⢻⣶⣦⠀⠀⢸⣿⣧⡀⠀⢸⣿⣇⣀⣠⣾⣿⡇⢀⠀⢀⣾⣄⡀⠀⠀⠘⣿⣿⣤⣀⠈⣿⣯⣶⣦⣼⣿⣏⠀⢀⣼⣿⣿⣄⣠⣾⣿⣿⣿⣿⣿⣿⣽⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣤⣌⣿⣿⣿⣿⣿⣶⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣧⣼⣇⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⡿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⣷⣼⣿⣿⣿⣿⣿⣿⣿⠒⠒⠛⠺⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣴⠿⠿⢿⠿⠿⡿⠛⠛⠛⣿⣿⣿⠛⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣾⡇⠀⠀⠀⢿⣿⣽⢿⠉⢹⣿⣅⡀⠀⠀⠀⠀⠠⡇⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⡀⣀⣸⣿⣿⣇⡀⠈⢩⣿⡃⠀⠀⠀⠀⠀⡁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣟⡿⠿⠿⠓⣿⡻⠓⠇⠀⠀⠀⣤⡀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡇⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣽⣿⠆⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠈⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡐⢄⣠⣀⣄⢸⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠁⢠⣤⣤⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡡⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠓⠒⣿⣿⣿⣿⡟⢿⣿⣿⡿⠃⣲⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣂⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⢸⠋⡖⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣸⣧⣼⣧⣄⣉⣀⡀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠽⠶⠶⢲⣿⣿⡁⠶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢻⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⡻⣿⣿⠿⠟⠛⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠁⠀⠛⣻⡏⠛⠿⣿⡟⡁⠤⠄⠿⠿⢿⣿⣿⣿⡛⠻⠿⡉⣼⣝⡻⠏⠈⠉⠛⠻⠿⣄⠛⠉⢿⠅⠀⠀⠈⠙⠋⠉⠉⠩⢤⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢹⣿⣿⣿⡏⠉⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⣰⣿⢻⣷⠀⠀⣾⡿⣿⣯⣿⣿⠿⠉⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣿⣿⢸⣿⡇⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠇⣿⣿⣀⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢻⣿⣸⣿⠁⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⢉⡀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠄⠀⠘⠃⠋⠛⠛⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠛⢛⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠚⠙⠀⡀⠀⣷⣦⡀⠀⠀⠀⠀⢀⣄⡀⠀⠀⢀⣤⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢀⣤⣄⠀⠀⢀⣴⣤⠀⠀⠀⣶⣦⠀⠀⠀⣠⣶⣿⣿⣯⣴⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠴⣦⡄⠘⠻⣦⡈⠻⣷⣦⡀⠀⣻⣿⣇⡀⠀⢸⣿⣇⣀⣠⣼⣿⠇⢀⠀⢀⣿⣄⣀⡀⠀⠘⣿⣿⣤⣀⠈⣿⣯⣦⣤⣬⣿⣿⠀⢀⣼⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣯⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⣌⠿⣿⣾⣿⣿⣶⣿⣿⣿⡟⠀⣾⣿⣿⣿⣿⣿⣿⣇⣾⣇⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠻⣷⣼⣿⣿⣿⣿⣿⣿⣿⠒⠒⠛⢿⣿⡿⠿⠿⠿⢿⣿⢿⣿⣿⣿⣿⠿⠴⠿⠿⠿⠿⠿⡿⠛⠛⠛⠻⣿⣿⠋⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣟⠀⠀⠀⠀⣿⣯⢀⡟⠉⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⡀⣀⣸⢿⣟⣿⣀⡉⡈⣶⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⠓⣿⠻⠓⠇⠀⠀⢀⣦⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡝⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⡯⢡⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡇⠀⠀⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⣀⣉⣭⣧⠴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠁⢠⣤⣤⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣟⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂⠂⠀⢈⠡⣝⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠒⠒⣾⣿⣽⣿⣿⢿⣿⣿⡿⠇⣉⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠹⠋⡇⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⣁⣸⣿⣼⣷⣄⣉⣁⡀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠥⠴⠶⣶⣶⣾⣷⡀⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⡿⡟⠛⠛⣿⠿⠅⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⢛⣻⡛⠿⣿⣿⡟⡁⠽⠅⠀⠸⢿⣿⣿⣿⠿⠿⠯⠉⣿⣟⡻⠟⠉⠙⠛⠿⠷⣬⡿⠋⢻⡇⠀⠀⠉⠛⠛⠋⠉⠉⠭⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣿⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡆⠈⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⣹⣿⢻⣷⠀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣸⣿⢸⣿⠀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠿⣿⣿⣀⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢻⣿⣸⣿⠃⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⢁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠁⠘⠃⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⢋⣵⡶⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡠⢿⣦⣀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢠⣤⡀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⢀⣴⣤⠀⠀⠀⣴⣦⠀⠀⠀⣴⣶⡀⠀⠀⣠⣴⣿⢿⣿⣴⣿⡟⣥⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠾⣦⡀⠛⠿⣦⣈⠿⣷⣦⡀⠀⣿⣿⣇⡀⠀⢹⣿⣇⣀⣠⣾⣿⠇⢀⠀⢀⣿⣄⣀⡀⠀⠈⣿⣿⣦⣀⠀⣿⣿⣦⣤⣤⣿⣿⠀⢀⣤⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣯⣶⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣤⣘⠿⣿⣾⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⢿⣿⣿⣿⣆⣼⣁⣿⣿⣿⣿⣿⠄⢰⣿⣿⡿⣿⡀⣿⣿⣿⣿⣿⣿⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⣦⣼⣿⣿⣿⣿⣿⣿⣿⠒⠚⠛⢿⡿⠾⠿⠿⠿⣿⣿⠿⣿⣿⣿⡿⠿⠶⢾⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⣿⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣇⠀⠀⠀⠀⠄⠀⠀⡉⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⣀⣀⠠⣂⣆⣙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⠓⠿⠻⠓⠇⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡝⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠐⠿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠘⢽⣿⣿⢣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠀⠀⠀⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣀⣽⣿⡾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⢠⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣶⣾⣿⣿⣿⣿⣿⢻⣃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡉⢉⡂⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠓⠒⢺⣯⣿⣿⣿⣿⣿⣿⣿⡟⢁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⠻⢻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣿⣿⣻⣏⣉⣈⣿⣿⣿⣀⣈⣋⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠤⠤⣰⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⢿⠛⠻⠿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠘⠋⢙⣟⠛⢿⣿⣿⢋⠸⠿⠿⠿⠛⠿⢿⣿⡿⠿⠿⠯⠉⢙⡻⠿⠿⠿⠛⠻⠟⠿⢿⣿⡟⠹⣏⠁⠀⠹⠻⠿⠿⠉⠉⠫⠍⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣿⡟⣿⡟⣿⣿⠿⢸⣿⣿⣿⡆⠘⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⢹⣿⢻⣷⠀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⠀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢻⣿⣿⠁⣿⣿⣀⠀⢸⣿⣯⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢻⣿⣸⣿⠓⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⢁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠃⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡘⠛⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠟⢉⣴⡶⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠠⡀⡠⣿⣦⡀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢠⣤⡀⠀⠀⢠⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⣴⣤⠀⠀⠀⣴⣦⠀⠀⠀⣴⣶⡄⠀⠀⣠⣴⣿⣿⣿⣴⣿⡟⣥⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠾⣦⡀⠛⠻⣦⣈⠿⣿⣦⡀⠀⣿⣿⣆⡀⠀⢸⣿⣇⣠⣤⣾⣿⠇⢀⠀⢀⣿⣄⣀⡀⠀⠈⣿⣿⣦⣀⠀⣿⣿⣦⣦⣴⣿⣿⠀⢀⣤⣿⣿⣧⣰⣾⣿⣿⣿⣿⣿⣿⣴⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⣘⠻⣿⣮⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⢿⣿⣿⣿⣆⣾⣁⣿⣿⣿⣿⣿⠄⢰⣿⣿⣟⣿⡀⣿⣿⣿⣿⣿⣿⣿⡄⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⣦⣼⣿⣿⣿⣿⣿⣿⣿⡒⠚⠛⢿⡿⠿⠿⠿⠿⢿⣿⠿⣿⣿⣿⣿⠿⠶⠾⠿⠿⠟⠻⠟⠛⠛⠛⠛⢛⣿⡋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣃⠀⠀⠀⠀⢤⠀⠀⠙⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⣀⣀⠀⡀⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⠿⠓⠿⠻⠓⠇⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡟⠟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠐⠿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢼⣿⣿⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⢽⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⡀⢠⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣶⣾⣿⣿⣿⣿⣿⣛⣃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡉⢭⡖⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠒⢺⣯⣿⣿⣿⣿⣿⣿⣿⡟⢁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠻⢛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣻⣏⣉⣙⣿⣿⣿⣀⣈⣁⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠤⠤⣰⣶⣶⣶⣶⣶⣶⣾⣷⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⢿⠛⠻⠿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠐⠋⢙⣟⠛⣿⣿⣿⢋⠩⠿⠿⠿⠛⠿⢿⣿⡿⠿⠿⠏⠉⠙⡻⠿⠿⠿⠛⠻⠟⠿⢿⣿⡟⠹⡏⠁⠀⠽⠻⠿⠿⠉⠉⠯⠍⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣿⡟⣿⡟⣿⣿⠿⢸⣿⣿⣿⡆⠐⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⣹⣿⢻⣷⠀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢹⣿⢸⣿⠀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢹⣿⣸⣿⠗⠂⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⢁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠛⠀⠄⠀⠘⠃⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣄⠋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡾⠉⣱⣿⠗⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠺⠿⣦⡀⠀⠀⠀⠀⣤⣄⠀⠀⠀⣠⣤⡀⠀⠀⣠⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⣶⣦⠀⠀⠀⣴⣶⡄⠀⠀⣰⣶⡄⠀⠀⣠⣴⣿⣿⣿⣷⣾⢿⣣⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢷⣆⡈⠙⢷⣄⣘⠿⣷⣄⡀⢠⣿⣿⣄⡀⠀⣻⣿⣀⣠⣤⣿⣿⠇⢀⠀⣀⣿⣄⣄⡀⠀⠈⣿⣿⣦⣄⠀⢻⣿⣴⣤⣤⣿⣿⡀⠀⣤⣾⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣷⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣦⡝⠻⣿⣾⣿⣿⣿⣿⣿⣿⠉⢠⣿⣿⣿⢻⣿⣿⣿⠀⣾⣠⣿⣿⣿⣿⣿⠆⢠⣿⣿⣟⣿⡀⣸⣿⣿⣿⢿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢷⣦⣿⡿⣿⣿⣿⣿⣿⣿⡒⠺⣿⡿⠟⠺⠿⣿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠶⠾⣿⠿⠛⠻⠗⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣃⠀⠐⠃⠀⠀⠀⢨⣿⣿⡟⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⣀⣀⢀⣻⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⢿⡿⡿⠓⠟⠹⠓⠇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣾⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠘⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⡀⣈⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠋⠀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠉⠉⣱⠉⣴⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠒⠒⣿⣉⣛⣻⡿⣿⣿⣿⣿⡟⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠀⠀⠀⠀⠘⡂⡟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣶⣶⣶⣶⣿⣿⣻⣋⢁⣸⣿⣿⣿⣎⣛⡁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠶⢶⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠐⠛⠻⠿⠿⠻⠻⠿⠟⠋⠉⠿⠽⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠿⢿⡿⢿⣿⠿⠿⠿⣿⣿⣿⣿⣿⠛⣿⠟⠉⠉⠻⠿⠿⣿⠉⠛⣉⡉⠉⠈⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣿⡟⣿⡇⢻⣿⠿⢸⣿⣿⣿⡆⠂⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣿⢻⣿⢻⣿⠄⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣼⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⢠⡄⣿⡇⣿⣿⢸⣿⢸⣿⡀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣯⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢹⣿⣸⣿⠛⠛⣿⣟⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣎⠉⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⣠⣾⠟⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣄⠻⠿⣤⣀⠀⠀⠀⢀⣤⣄⠀⠀⠀⣤⣤⠀⠀⠀⣴⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⣶⣶⠀⠀⠀⣴⣶⡄⠀⠀⢰⣶⣆⠀⠀⣠⣴⣿⣟⣿⣿⣿⠟⣉⣶⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠶⣆⠉⠙⢷⣤⣝⣿⣷⣤⣀⣸⣿⣿⣀⡀⠀⣿⡿⣀⣠⣤⣿⡿⠂⢀⠀⣠⣿⣤⣤⡀⠀⠀⣿⣿⣦⣤⠀⢺⣿⣴⣶⣤⣼⣿⡅⠀⣤⣼⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣥⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⣶⣦⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁⢰⣿⣷⣿⢻⣿⣿⡇⢀⣿⣠⣿⣿⣿⣿⣿⠆⠀⣿⣿⣟⣿⡆⢸⣿⣿⣿⢻⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣷⣴⣿⡻⣿⣿⣿⣿⣿⣷⣒⣿⡿⠿⠟⠺⠿⡿⠷⠾⠿⣿⣿⣿⣿⠿⠿⠖⠒⢿⡿⠟⠛⠓⠚⠻⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣒⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣙⣿⣿⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠓⠟⠙⠓⠇⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠚⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⣽⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠈⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⢽⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠃⢀⣀⣀⣐⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠀⠈⠉⠹⡇⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠒⠒⢺⣟⣈⣛⣿⣿⣿⣿⣿⣿⢇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠄⠀⠀⠀⠀⠓⢸⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣷⣶⣶⣶⣿⣿⣏⣯⠉⠛⣹⣿⣿⣔⡟⠛⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⡴⣶⣶⣶⣶⣶⣤⣤⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠒⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠿⠿⠿⠿⠿⠿⠿⡿⠛⠉⠹⠿⠿⠿⠿⠛⢿⣿⣿⠿⠿⠿⠿⠿⣿⡿⢿⠿⠟⠿⠿⣿⣿⣿⣿⣿⠟⣿⡟⠉⠉⠉⠹⠿⢿⢿⡯⠉⠉⠉⠈⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡿⣿⡇⣿⡿⣿⡇⢹⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣿⢻⣿⢻⣿⡇⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣇⣿⡇⠻⣿⣶⡄⣼⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⣻⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠛⠛⣿⣟⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠿⠿⣣⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡇⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣽⠛⠳⣦⣄⠀⠀⠀⣠⣶⡄⠀⠀⢠⣴⣦⠀⠀⠀⣴⣦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣶⣦⠀⠀⠀⣶⣶⡄⠀⠀⢰⣿⡆⠀⠀⢠⣿⣷⠀⠀⣀⣴⣿⣿⣽⣿⣿⠟⢣⣴⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⢧⣀⠈⠙⢷⣦⣟⢿⣷⣤⣀⣾⣿⣧⣀⡀⢀⣿⣟⣤⣤⣴⣿⡿⠀⣀⠀⣠⣿⣶⣶⣄⠀⠀⣿⣿⣶⣤⠀⢸⣿⣴⣶⣦⣼⣿⡇⠀⣤⣼⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣙⣷⣶⣄⠙⢿⣷⣿⣿⣿⣿⣿⣿⡟⠁⣸⣿⣿⣿⣿⣿⣿⡇⢠⣿⣰⣿⣿⣿⣿⣿⠂⠀⣿⣿⣟⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣶⣾⣝⠻⣿⣿⣿⣿⣿⣷⣚⣿⣿⠿⠛⠿⢿⡿⠗⠾⣿⣿⣿⣿⡿⠿⠿⠖⠒⢿⣿⠟⠛⠟⠚⠻⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⠀⠆⠀⠀⠀⠀⣹⣿⣿⠇⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣹⣿⣿⡅⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠟⠙⠓⠇⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠛⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢈⣹⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⡿⠟⠀⢀⣀⣀⣂⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠉⠉⣱⠊⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠗⠒⠂⣿⣘⣛⣻⣿⣿⣿⣿⣿⣿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⢿⣦⠀⠀⠀⠀⠘⠂⡞⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡖⣶⣶⣿⣿⣿⣿⡏⠛⠙⢻⣿⡿⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣬⣦⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠦⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠛⢿⣿⠿⠿⠟⠋⠛⠉⠋⠈⠻⠿⠿⠿⠿⠿⠿⠿⢿⠟⠛⠛⢻⣿⣿⡿⠟⠛⠻⠿⠿⠿⣿⡿⠆⠀⢈⣹⠉⠀⠀⠈⠙⠿⠿⠿⡟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡟⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡿⣿⡷⢿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⣸⣿⢻⣿⠟⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡿⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢾⣿⣸⣿⠇⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣧⣿⡇⣿⣏⣿⣿⣼⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠁⠊⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠿⠿⣡⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡇⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣽⠛⠳⣤⣄⠀⠀⠀⣠⣶⡄⠀⠀⢠⣴⣦⠀⠀⠀⣴⣦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⣶⣶⡄⠀⠀⢰⣷⡆⠀⠀⢠⣾⣷⠀⠀⣀⣴⣿⣿⣽⣿⣿⠟⢡⣰⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⢧⣄⠈⠙⢷⣦⣟⢿⣷⣤⣀⣼⣿⣧⣀⡀⢀⣿⣟⣤⣤⣴⣿⡿⠀⣀⠀⣠⣿⣶⣶⣄⠀⠀⣿⣿⣦⣤⠀⢸⣿⣶⣶⣦⣼⣿⡇⠀⣤⣼⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣙⣷⣶⣌⠙⢿⣷⣿⣿⣿⣿⣿⣿⡟⠁⣸⣿⣿⣿⣿⣿⣿⡇⢠⣿⣰⣿⣿⣿⣿⣿⠂⠀⣿⣿⣟⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣶⣾⣝⠻⣿⣿⣿⣿⣿⣷⣚⣿⣿⡟⠛⠿⣿⡿⠗⠿⣿⣿⣿⣿⡿⠿⠷⠖⠒⢿⣿⠟⠛⠛⠚⠻⠛⠛⠛⡻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠆⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣸⣿⣿⡅⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠟⠙⠓⠇⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠛⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠁⠀⠀⠈⢹⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠿⠀⢀⣀⣀⣂⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣶⣿⣷⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⠈⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠗⠒⠂⣿⣘⣛⣻⣿⣿⣿⣿⣿⣿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⢿⡦⠀⠀⠀⠀⠘⠂⡚⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡖⣶⣶⣿⣿⣿⣿⡏⠛⠛⢹⣿⡿⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣦⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠦⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⢿⡿⠿⠿⠟⠋⠛⠉⠋⠉⠻⠿⠿⠿⠿⠿⠿⠿⢿⠟⠛⠛⢻⣿⣿⡿⠟⠛⠻⠿⠿⠿⣿⡿⠆⠀⢈⣹⠉⠀⠀⠈⠘⠿⠿⠿⡟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡟⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡿⣿⡷⢿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⢸⣿⢻⣿⠟⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⣸⣿⠆⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⣼⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠿⠟⢣⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣏⣀⣾⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣝⠛⢳⣦⣄⠀⠀⠀⣴⣶⡄⠀⠀⢠⣶⣦⠀⠀⠀⣶⣦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣾⣶⠀⠀⠀⣶⣶⡆⠀⠀⢰⣿⡆⠀⠀⠀⣿⣷⠀⠀⣀⣴⣿⣿⣽⣿⣿⠿⢋⣴⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢧⣀⠈⠙⢷⣦⣟⣿⣷⣤⣀⣿⣿⣧⣀⠀⢈⣿⣟⣤⣤⣶⣿⡿⠀⣀⠀⣰⣿⣶⣦⣄⠂⠀⣿⣿⣷⣤⡀⢸⣿⣶⣶⣦⣼⣿⣇⠀⣤⣴⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣧⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⣿⣿⡟⣿⣿⣿⡇⢠⣿⣠⣿⣿⣿⣿⣿⠂⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠥⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣶⣾⣟⠻⣿⣿⣿⣿⣿⣷⣚⣿⣿⡟⠛⠿⠿⡿⠗⠾⡿⣿⣿⣿⡿⠿⠿⠒⠒⢿⣿⠟⠛⠛⠚⢻⠛⢻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⠀⠗⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣀⣀⣼⣿⣿⣇⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠟⠙⠓⠇⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⢠⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢛⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠀⣀⣀⣀⣢⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢶⣾⣿⣿⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⣡⢈⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠗⠒⠂⣾⣙⣛⣻⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠨⢿⣄⠀⠀⠀⠈⠒⠚⠼⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡖⣶⣶⣶⣿⣿⣿⡟⠻⠟⢻⣿⣿⠻⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢦⣼⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠹⠿⠿⠿⠋⠀⠙⠉⠙⠉⠈⠿⠿⠿⠿⠿⠿⠿⠛⠿⠛⠃⠀⢩⣿⣿⡏⠙⠛⠻⠿⠿⠛⠛⠿⠆⠀⢈⣹⠉⠁⠀⠉⠙⠻⠿⠿⡿⠛⠁⠉⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡟⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡿⣿⡧⣿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⢰⣿⢻⣿⠉⠀⣾⡿⣿⣧⣿⣿⠿⠁⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣏⣿⡇⠻⣿⣶⡄⢽⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢾⣿⣸⣿⠆⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣯⣿⡇⣿⣏⣿⣿⣼⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠀⠚⠛⠉⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠿⠙⣡⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢐⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣝⠛⢷⣦⣄⠀⠀⠀⣴⣶⡄⠀⠀⢠⣶⣦⠀⠀⠀⣶⣦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣾⣶⠀⠀⠀⣾⣷⡆⠀⠀⢰⣿⡆⠀⠀⠀⣿⣷⠄⠀⣀⣴⣿⣿⣿⣿⣿⡟⢋⣤⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣦⣀⠈⠙⣷⣾⣟⣿⣷⣤⣠⣿⣿⣧⣀⠀⢨⣿⣟⣤⣴⣾⣿⡟⠀⣀⠀⣠⣿⣶⣦⣄⠀⠀⣿⣿⣷⣤⠀⢸⣿⣾⣶⣦⣬⣿⣇⠀⣤⣤⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣧⡌⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⣿⣿⡿⣿⣿⣿⡇⢠⣿⣰⣿⣿⣿⣿⣿⠂⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣾⣟⠻⣿⣿⣿⣿⣿⣷⣚⣿⣿⣿⠟⠟⠻⢿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠒⠒⢿⡿⠟⠛⠛⠚⢻⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣸⣿⣿⣏⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⣸⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠟⠹⠓⠇⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⢰⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⠀⠐⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠉⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢹⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠀⣀⣀⣀⣢⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢳⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠦⠀⠈⠉⠉⠱⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠒⠒⢸⣍⣛⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠒⠉⠒⢀⠶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣶⣶⣶⣿⣿⣿⣟⠛⢿⡽⣿⣿⠋⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡠⣤⣤⣤⣤⣤⣤⡤⠀⣤⣼⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⠉⠙⠷⣦⣼⣶⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠁⠸⠿⠋⠉⠉⠈⠁⠀⠈⠋⠉⠋⠀⠘⠿⠟⠻⠿⠿⠿⠿⠋⠛⠻⠿⠦⠀⠀⣿⠟⠛⠛⠿⠿⠿⠋⠀⠙⠃⠀⠈⣹⠉⠉⠀⠉⠉⠻⠿⠿⣿⠃⠀⠉⠉⠁⠀⠀⠁⠈⠉⠸⠅⠂⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⢰⣿⢻⣷⡌⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⣿⣿⡇⠻⣿⣶⡄⣿⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⣧⣤⣿⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣯⣿⡇⣿⣏⣿⣿⣿⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣹⣿⠀⠀⣿⣏⣿⣿⣿⣿⣒⣺⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠉⠉⡉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠁⠚⠛⠉⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡜⠁⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⣶⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣉⢹⣿⣶⣄⠀⠀⠀⣶⣶⠀⠀⠀⢴⣿⡆⠀⠀⠀⣾⣷⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⢺⣿⡆⠀⠀⠰⣿⡷⠀⠀⠀⣿⣿⡇⠀⣀⣴⣿⣿⣿⣿⣿⡿⠋⣠⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣤⣀⠈⢹⣿⣿⣟⣿⣷⣄⣠⣿⣿⣦⣄⠀⠈⣿⣧⣤⣶⣦⣿⣟⠀⣄⠀⣴⣿⣿⣷⣦⠀⠀⣿⣿⣷⣤⡄⢸⣿⣴⣶⣶⣮⣿⡇⠀⢠⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣦⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⡟⣿⠛⣿⣿⣴⣿⣸⣿⣿⣿⣿⡿⠃⢰⣿⣿⣿⣹⣇⣿⣿⡉⣿⣯⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣯⡙⠻⣿⣿⣿⣿⣿⣟⠒⠛⣿⣿⡟⠛⠒⠿⣿⣿⣿⠿⠿⣿⣿⡿⠓⠒⣿⠟⠛⠛⠚⢿⣿⠟⠓⠛⢛⣿⣿⣏⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣗⠀⠀⠀⣿⣿⣇⠀⠀⢻⣿⡇⠀⠀⡿⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣿⣿⡇⠀⠀⢀⣹⡃⣀⢀⠀⠀⠀⠀⢰⣿⣿⠄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⠿⡿⣳⣟⡹⠛⠇⠀⠀⢸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠺⠎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣤⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡙⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠀⠀⢀⢰⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠟⠛⠀⢀⣀⣀⣰⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⠛⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢲⠖⠂⣇⣘⣻⣿⣿⢿⣷⣴⣶⡾⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠒⠀⠐⠒⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣿⣿⣛⡟⠛⠈⢿⣤⡿⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣶⣦⣀⣀⣀⣀⠈⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⡰⠶⢶⣾⣿⠁⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠿⠋⠀⢿⣿⣿⣿⠷⠀⠀⢀⣿⠿⢿⣿⣿⡿⠿⠟⢻⡿⠻⣿⣿⣿⠟⠛⠿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠃⠀⠀⠉⠀⢠⠿⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡟⣿⣿⠿⠀⢸⣿⡿⣿⡇⣾⣿⣿⡧⢿⣿⠿⢹⣿⣿⣿⡆⠈⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⢰⣿⢻⣷⡀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⡇⢀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠋⠛⣿⣟⣿⣿⣿⣿⣉⣹⣿⢿⣿⣾⣿⣷⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⣛⣋⡀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠀⠋⠛⠙⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡞⠁⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⣶⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡉⢹⣿⣶⣄⠀⠀⠀⣶⣶⠀⠀⠀⢴⣿⡆⠀⠀⠠⣾⣷⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⢾⣿⡆⠀⠀⠰⣿⡷⠀⠀⠀⣿⣿⡇⠀⣀⣶⣿⣿⣿⣿⣿⡟⠋⣠⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣤⣀⠈⢻⣿⣿⣿⣿⣷⣄⣀⣿⣿⣦⣄⠀⠈⣿⣧⣤⣶⣦⣿⣟⠀⣄⠀⣴⣿⣿⣷⣦⠀⠀⣿⣿⣷⣤⡄⢸⣿⣴⣶⣶⣮⣿⡇⠀⢠⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣦⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣿⣿⡏⣿⠛⣿⣿⣼⣿⣸⣿⣿⣿⣿⡿⠃⢸⣿⣿⣿⢻⣇⣿⣿⡉⢿⣯⣿⣿⡄⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣯⡙⠻⣿⣿⣿⣿⣿⣿⡒⠛⣿⣿⡛⠛⠒⠿⣿⣿⡿⠿⠿⣿⣿⡿⠛⠒⣿⡟⠛⠛⠛⢿⣿⠟⠓⠛⠛⣿⣿⣏⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⣿⣿⣇⠀⠀⢻⣿⣷⠀⠀⡿⠀⠀⠀⠀⣾⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣐⣿⣿⡇⠀⠀⢀⣙⡋⣀⣀⠀⠀⠀⠀⢰⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⠿⡿⣳⣟⡹⠛⠇⠀⠀⣸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠺⠄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡙⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠀⠀⢀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠺⠟⠛⠀⢀⣀⣀⣰⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⠛⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣲⣲⠂⣇⣘⣛⣿⣿⣿⣷⣶⣶⡾⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠒⠀⠐⠒⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣿⣿⣛⡟⠛⠈⢿⣥⡿⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣶⣦⣀⣀⣀⡀⠈⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡰⠶⢶⣾⣿⠁⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠿⠋⠀⢿⣿⣿⣿⠷⠀⠀⢀⣿⠿⡿⣿⣿⡿⠿⠟⢻⡿⠻⣿⣿⣿⠟⠛⠿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠃⠀⠀⠉⠀⢠⠿⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡟⣿⣿⠿⠀⢸⣿⡿⣿⡇⣾⣿⣿⡧⢿⣿⠿⢹⣿⣿⣿⡆⠈⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⢰⣿⢻⣷⡀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⡇⢀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠋⠛⣿⣟⣿⣿⣿⣿⣉⣹⣿⢿⣿⣾⣿⣷⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⢛⣋⡀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡾⠁⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣷⣶⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣉⢹⣿⣶⣄⠀⠀⢀⣾⣷⠀⠀⠀⢴⣿⡆⠀⠀⠀⣾⣷⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⢺⣿⡆⠀⠀⠰⣿⡿⠀⠀⠀⣾⣿⡇⠀⣀⣼⣿⣿⣿⣿⣿⡿⠋⣠⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣄⣀⡈⠿⣿⣿⣿⣿⣷⣄⣀⣿⣿⣦⣄⠀⠈⣿⣧⣤⣶⣦⣿⣯⠀⣄⠀⣴⣿⣿⣷⣦⠀⠀⣿⣿⣷⣤⡄⢸⡟⢰⣶⣶⣶⣿⠁⠀⢠⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣈⣿⣷⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⣿⣿⣟⣿⠛⣿⣿⣾⣿⣸⣿⣿⣿⣿⡿⠃⣸⣿⢻⣿⢹⣷⣿⣿⠈⢿⣯⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠟⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣯⡙⢿⣿⣿⣿⣿⣿⣟⠒⠛⣿⣿⡟⠛⠒⠛⢿⣿⣿⠿⠿⣿⣿⡿⠗⠐⣿⠟⠚⠛⠚⣿⣿⠛⠒⠉⢻⣿⣿⡏⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⢸⣿⣷⠀⠀⠘⣿⣷⠀⠀⠇⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣛⣿⡏⠀⠀⠀⠙⣟⣀⣠⠀⠀⠀⠀⢸⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⠿⣳⣿⣹⠛⠃⠀⠀⢸⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣽⣿⣿⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠺⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣷⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⢀⣀⣀⣀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢻⣿⣿⣿⣷⣾⠛⠋⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠈⢁⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠒⠒⠀⣬⣐⣛⣿⣿⢸⣷⢤⣶⣶⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠀⠀⠐⠒⠀⠀⢰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⡿⣿⠿⡟⠛⠀⢹⣅⠹⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣤⣾⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣴⣄⣤⣤⣾⡟⠰⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠃⠐⠛⠿⡿⠿⠛⢿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠾⠿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠙⣿⡿⠿⡿⠿⠿⠿⠟⠟⠛⠛⠛⠟⠛⠛⠛⠛⠋⠁⢀⡀⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⢹⣿⠿⢸⣿⣿⣿⡟⠛⠿⣿⣿⡿⣿⣿⣿⣷⠀⠀⣿⡿⣿⣦⢰⣿⢻⣷⡀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⣿⣿⡎⣿⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡏⣿⡇⠻⣿⣶⡄⣸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣿⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠃⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠛⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠙⠛⠛⠛⠛⠓⠋⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠐⠀⠛⠛⠛⠷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣤⣾⡿⣿⣿⣶⡾⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣯⣀⣸⣿⣶⡀⠀⠀⢠⣾⣷⠀⠀⠀⣾⣿⡆⠀⠀⠀⣿⣷⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⢸⣿⠆⠀⠀⠀⣿⡿⠀⠀⠀⣺⣿⡇⠀⣀⣼⣿⣿⣿⣿⣿⡿⠋⣡⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣤⣀⡈⠿⣿⣿⣻⣿⣷⣄⣀⣿⣿⣦⣄⠀⠈⣿⣧⣴⣶⣦⣿⣯⠀⣔⠀⣴⣿⣿⣿⣦⠀⢀⣿⣿⣷⣤⡄⢸⣟⢰⣶⣶⣶⣿⠁⠀⢠⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣙⣿⣷⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⡿⠋⢻⣿⣾⣿⢸⣿⣿⣿⣿⡿⠁⣼⣿⠹⣿⢸⣷⣿⣇⠀⢻⣯⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠛⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣯⡙⢿⣿⣿⣿⣿⣿⣟⠛⠒⣻⣿⣿⠓⠒⠚⢿⣿⡿⠿⠿⢿⣿⣿⠓⠒⣿⠛⠒⠛⠚⣿⡟⠛⠂⠘⢿⣿⣿⡍⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠀⠀⠀⢸⣿⣿⡀⠀⠀⢿⣿⡀⠀⠁⠀⠀⠀⢰⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⡀⣸⣿⣿⠀⠀⠀⢘⣿⣿⣧⠀⠀⠀⠀⣼⣿⠆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⠿⣿⣟⣽⠛⠃⠀⠀⢽⣿⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⡆⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣿⣿⣿⣧⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⢀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣾⡟⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠻⠈⢁⡐⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠒⠀⣸⣀⣘⣿⣻⠻⠵⢤⣤⣶⠄⣐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠈⠁⠀⠐⠒⠀⠀⠸⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⡿⢻⠛⡟⠛⠀⢸⡍⠹⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣴⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣤⣄⣤⣤⣴⣷⠶⢤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠃⠠⠾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠛⠋⠉⠙⠿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⣿⡿⠿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠿⠛⠛⠛⠛⠛⠋⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⣿⣿⡇⣾⡟⣿⡇⢸⣿⠿⢸⣿⣿⣿⡏⠛⠿⣿⣿⡿⣿⣿⣿⣷⠉⠁⣿⡿⣿⣦⢰⣿⢻⣷⡀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⣆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡏⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⠇⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⣸⣿⣿⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⣸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠾⠍⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠄⠀⠘⠀⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣴⣾⣿⢻⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⠿⣦⣼⣿⣿⣦⡀⠀⠀⢸⣿⣧⠀⠀⠐⣿⣿⠀⠀⠀⠰⣿⡷⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⡿⠁⠀⠀⢸⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⠛⣁⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣤⣀⠹⢿⣿⣯⣿⣿⣶⣄⣼⣿⣿⣤⡄⠀⠈⣿⣥⣴⣶⣦⣿⣯⢀⡄⢀⣴⣿⣿⣿⣦⡀⢀⣿⣿⣷⣶⡆⣸⡟⢰⣿⣷⣶⣿⡇⠀⠀⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣯⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡟⠁⢸⣿⣿⣷⣼⣿⣿⣿⣿⡟⠀⣼⡟⠈⣿⢸⣷⣿⡇⠀⠹⣿⣿⣿⣄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠟⠓⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⣍⠻⣿⣿⣿⣿⣿⣿⣟⠛⠚⣿⣿⣿⠓⠒⠚⢻⣿⣿⠿⠛⠻⣿⣿⠓⠺⡿⠓⠒⠛⠚⣿⡿⠛⠀⠘⣻⣿⣿⣏⢉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣗⠀⠀⠀⣸⣿⣷⠀⠀⠀⢻⣿⣦⡠⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⡀⣹⣿⣗⠀⠀⠀⠀⣻⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠿⠿⡿⣻⣿⣽⡛⠃⠀⠀⢈⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠒⠀⢀⣀⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣶⣶⣶⣾⣷⡶⠿⠯⠴⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠋⠻⠉⠁⣀⡓⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠄⠀⡯⢀⣾⡿⣿⠛⣣⣤⣤⣤⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⠀⠐⡦⢄⠀⠠⢿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣭⣭⢤⣤⣤⠷⡟⠛⠟⠛⠈⢻⠉⠽⠁⢼⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀⣀⣀⣣⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣤⣥⣤⡀⣤⣤⣬⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⣿⣿⠿⠿⣿⣷⠟⠛⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⡿⠿⠿⠿⠿⠛⠉⠋⠻⠿⠿⢿⡿⠿⠟⠛⠛⠛⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡏⣿⡇⣾⡟⣿⡇⢹⣿⠿⢹⣿⣿⣿⡎⢻⠿⣿⣿⣿⣿⣿⣿⣿⠀⠉⣿⡿⣿⣧⢰⣿⢻⣿⡇⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⡿⠆⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠇⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⢿⣿⠿⠧⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠄⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣤⣾⣿⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⠿⣦⣼⣿⣿⣧⡀⠀⠀⢼⣿⡇⠀⠀⠐⣿⣿⠂⠀⠀⢰⣿⡷⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⡿⠁⠀⠀⢸⣿⣿⠀⣀⣴⣿⣿⣿⣿⣿⣿⠛⣁⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣤⣀⠹⢿⣿⣯⣿⣿⣷⣤⣼⣿⣿⣤⡄⠀⠈⣿⣥⣴⣶⣦⣿⣯⢀⡄⢀⣴⣿⣿⣿⣦⠀⢀⣿⣿⣷⣶⡆⣸⡟⢰⣾⣷⣶⣿⡇⠀⠀⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡟⠁⢸⣿⣿⣧⣼⣿⣿⣿⣿⡟⠀⣼⣯⠈⣿⢸⣷⣿⡇⠀⠸⣿⣿⣿⣦⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠟⠓⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣍⠻⣿⣿⣿⣿⣿⣿⣟⠛⠛⣿⣿⣿⠓⠒⠛⢿⣿⡿⠿⠛⠻⣿⣿⠓⠺⠿⠛⠒⠛⠚⣿⡿⠓⠀⠈⣿⣿⣿⣏⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣗⠀⠀⠀⣸⣿⣧⠀⠀⠀⢻⣿⣦⡄⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⡀⣹⣿⣗⠀⠀⠀⠀⣿⣿⡧⠀⠀⠀⠀⠼⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⡿⣻⣟⣽⠛⠃⠀⠀⢨⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣿⣿⣿⣧⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⢀⣀⣀⡀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣶⣶⣶⣾⣷⢶⠷⠦⠔⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠋⠻⠉⠃⣀⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠄⠀⡯⢀⣾⡿⣿⠛⣣⣤⣤⣤⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⠀⠐⡦⢄⠀⠠⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡭⣭⢤⣤⣤⠷⡟⠛⠟⠛⠈⢻⠉⡽⠁⢬⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡀⡀⢀⣀⣣⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣤⡥⣤⡀⣤⣤⣬⣤⣴⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⣿⣿⠿⠿⣿⣷⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⠿⠿⠿⠿⠟⠋⠙⠻⠿⠿⢿⡿⠿⠟⠛⠛⠛⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡏⣿⡇⣾⡟⣿⡇⢹⣿⠿⢹⣿⣿⣿⡎⢻⠿⣿⣿⣿⣿⣿⣿⣿⠈⠉⣿⡿⣿⣧⢰⣿⢻⣿⡇⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⣿⠆⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠇⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠥⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠄⠀⠀⠀⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣴⣾⣿⣛⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣼⣿⣿⣆⡀⠀⠀⢾⣿⡇⠀⠀⠐⣿⣿⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⡿⠃⠀⠀⢸⣿⣿⠀⣀⣴⣿⣿⣿⣿⣿⣿⣋⣁⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣤⣄⠻⠿⣿⣭⣿⣿⣷⣤⣼⣿⣿⣤⡄⠀⠈⣿⣤⣶⣶⣦⣿⣧⢀⡄⢀⣴⣿⣿⣿⣦⠀⢀⣿⣿⣷⣶⡆⣸⡟⠰⣾⣷⣶⣿⡇⠀⠀⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡟⠁⢸⣿⣿⣷⣬⣿⣿⣿⣿⡟⠀⣼⣟⠈⣿⢸⣷⣿⡇⠀⠹⣿⣿⣿⣆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣍⠻⣿⣿⣿⣿⣿⣿⣏⠙⠛⣿⣿⣿⠓⠒⠛⢿⣿⡿⠿⠛⠻⣿⣿⠓⠺⠿⠓⠒⠛⠚⣿⡟⠓⠀⠈⢿⣿⣿⡏⢉⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠻⣿⣦⠄⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⡀⣸⣿⣗⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⡄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠿⠿⡿⢻⣿⣽⠛⠃⠀⠀⢸⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠁⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⢀⣀⣀⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢳⣶⣾⣿⣿⡶⠷⠦⠵⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠋⠫⠉⠃⣀⡒⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠨⢄⣸⣿⢻⡟⢣⣤⣤⣤⠄⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢐⣂⠀⠀⠀⠀⠀⠰⠤⠀⠀⢨⢿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡭⣭⢤⣤⣤⠷⡾⠛⡟⠛⠃⢹⠈⢹⠁⢴⠅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢈⣀⣱⣴⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣤⡀⣤⣤⣬⣤⣠⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⢿⣿⡿⠿⠿⠿⠋⠹⣿⣿⣿⣿⠿⠿⣿⣿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⠿⠻⠿⠿⠟⠋⠉⠙⠿⠟⠿⣿⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡏⣿⡇⣾⡟⣿⡇⢹⣿⠿⢸⣿⣿⣿⡎⠧⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡿⣿⣧⢰⣿⢻⣿⡏⠀⣾⡟⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⡇⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠇⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠍⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⣧⣤⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣴⣾⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⣿⣿⣦⣀⠀⠀⣿⣿⡇⠀⠀⠸⣿⣿⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣆⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⠟⠀⠀⠀⣻⣿⠃⠀⠀⢨⣿⣿⠇⣀⣤⣿⣿⣿⣿⣿⣿⡟⣁⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣤⡌⠿⢿⣿⣿⣿⣿⣷⣤⣾⣿⣷⣤⠀⠀⢸⣿⣴⣶⣷⡦⣿⣧⢠⡆⢠⣾⣿⣿⣿⣷⡀⢀⣿⣿⣿⣶⡆⣸⣿⠠⣾⣿⣶⣿⡇⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⠟⠁⢺⣿⣿⣷⣼⣿⣿⣿⣿⡏⠀⣼⣿⠈⣿⠈⣷⣿⡇⠀⠘⣿⣿⣿⣧⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⡉⠻⣿⣿⣿⣿⣿⣿⣟⠛⢻⣿⣿⣿⠓⠒⠛⢿⣿⡿⠛⠛⢻⣿⣿⠓⠚⠿⠛⠒⠛⠛⣿⡿⠛⠂⠙⣿⣿⣿⣏⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣗⠀⠀⠀⣿⣿⣧⠀⠀⠀⢻⣿⣦⣔⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣹⣿⣷⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⢰⣿⣧⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠿⡿⣿⣿⣿⠛⠃⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣴⣿⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠒⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⠀⣀⣀⣀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠙⣶⣾⣿⣿⣷⠾⠿⠭⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠙⠉⠋⠉⢁⠼⢳⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠂⠂⢰⠥⢀⣿⣿⣿⠿⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⢶⠤⡀⠀⢸⣿⣷⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣦⣼⣤⠿⢿⠿⠋⠁⡇⠉⡏⢡⣍⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⣤⣄⢠⣤⣤⣅⣀⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠂⠀⠐⠿⠿⠿⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣟⠛⠻⢿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⡿⠟⠿⠿⢿⣿⡟⠛⠛⠛⠉⠉⠉⠀⠀⠛⠿⠿⠿⠿⠿⠟⠛⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡏⣿⡇⣾⡟⣿⡇⢸⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⡿⣿⣧⢰⣿⢻⣿⣿⠀⣾⡟⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⣇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⡿⠃⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣿⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⣀⠀⣿⣇⣿⣿⢻⣿⣸⣿⠀⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠱⠋⠀⠉⠉⠉⠁⠈⠙⠛⠉⠰⢶⣾⣿⣿⣷⣿⣿⣿⣿⣿⡾⠿⠿⡿⠿⠿⠗⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠀⠀⠐⠀⠂⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠟⢻⣦⣤⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⢠⣤⡀⠀⠀⠀⣠⣤⡀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⣤⣀⠀⠸⣿⣿⡆⠀⠀⠸⣿⣿⠀⠀⠀⢺⣿⡇⠀⠀⠀⢀⣦⣀⣀⠀⠀⠀⣿⣿⡀⠀⠀⢸⣿⡟⠀⠀⠀⢹⣿⠋⠀⠀⢀⣿⣿⣗⣀⣴⣾⣿⣿⣿⣿⣿⣿⣁⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣦⣘⠻⢿⣿⣿⣿⣿⣧⣠⣿⣿⣷⣦⠀⠀⢸⣿⣶⣾⣿⣦⣿⣧⣠⡆⢠⣾⣿⣿⣿⣿⡄⢀⣿⣿⣿⣶⡆⣰⣿⠀⣾⣿⣷⣿⡯⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣿⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⣸⣿⣿⣿⠋⠈⣿⣿⣿⣷⣾⣽⣿⣿⣿⡏⠀⣾⣿⠈⣿⣘⣷⣿⣯⠀⠘⣿⣿⣿⣿⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣏⠛⢿⣿⣿⣟⠓⠒⠛⣿⣿⡟⠛⠛⢿⣿⣿⠓⠚⡿⠛⠒⠛⠓⣿⣿⠛⠃⠉⢿⣿⣿⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⠀⠀⠀⣿⣿⣧⠀⠀⠀⢿⣿⣦⣾⠇⠀⠀⠀⠀⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣛⣿⣿⡀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⣿⣿⣿⣿⡛⠃⠀⠀⣸⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣼⣿⣿⣿⣷⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠓⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠁⠀⠀⠀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠾⠀⠀⣀⣀⣀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⢻⣿⣿⣿⣿⣶⣿⠯⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠐⠒⠂⡌⠔⠈⣿⣻⣷⣷⣤⣠⣤⡼⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠰⠤⠠⠄⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣶⣿⣿⠿⡿⠿⠛⢻⡋⢹⡏⣬⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⡟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡟⢀⡁⣀⣀⣈⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠃⠘⠛⠀⠀⠀⠉⠻⣿⣿⡿⠿⠿⠿⢃⣤⣴⣿⡿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠏⠉⠻⣿⣿⠿⠿⠿⠇⠀⠈⠙⠋⠉⠉⠁⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⡇⣿⡏⣿⣿⠿⠀⢸⣿⡿⣿⡇⣾⡟⣿⡇⢻⣿⠿⢸⣿⣿⣿⡟⠃⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⡿⣿⣧⣰⣿⢻⣷⠀⠀⣾⣿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠉⣿⣿⣿⣿⡰⠀⣿⡇⣿⣿⣿⣿⢸⣿⡀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠃⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠀⠊⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠟⢻⣦⣤⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⢠⣤⡀⠀⠀⠀⣠⣤⡀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣤⡀⠀⠸⣿⣿⡆⠀⠀⠸⣿⣿⠀⠀⠀⢺⣿⡇⠀⠀⠀⢀⣦⣀⣀⠀⠀⠀⣿⣿⡀⠀⠀⢸⣿⡟⠀⠀⠀⢹⣿⠋⠀⠀⢀⣿⣿⣗⢀⣴⣿⣿⣿⣿⣿⣿⣿⣁⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣦⣘⠻⢿⣿⣿⣿⣿⣧⣠⣿⣿⣷⣦⠀⠀⢹⣿⣶⣾⣿⣦⣿⣧⣠⡆⢰⣾⣿⣿⣿⣿⡄⢀⣿⣿⣿⣶⡆⣰⣿⠀⣾⣿⣷⣾⡯⠀⠀⣴⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣿⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣸⣿⣿⣿⠋⠀⣿⣿⣿⣷⣾⣿⣿⣿⣿⡏⠀⣼⣿⠈⣿⢘⣷⣿⣯⠀⠘⣿⣿⣿⣷⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣏⠛⢿⣿⣿⣟⠓⠒⠛⣿⣿⡟⠛⠛⢿⣿⣿⠓⠚⡿⠛⠒⠛⠓⣿⣿⠛⠃⠉⢿⣿⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠀⠀⠀⣿⣿⣧⠀⠀⠀⢿⣿⣦⣼⠇⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣛⣿⣿⡀⠀⠀⢘⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⣿⣿⣿⣿⡛⠃⠀⠀⣸⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣼⣿⣿⣿⣧⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠓⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡿⠂⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠁⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠀⠀⣀⣀⣀⡄⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⢻⣿⣿⣿⣿⣶⢿⠯⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠈⠁⠀⠹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠒⠒⠂⡌⠔⠈⣿⣻⣿⣷⣤⣠⣤⡼⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠰⠤⠠⠄⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣶⣿⣿⠿⡿⠿⠛⢻⡋⢹⣏⣭⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡟⢀⡁⣀⣀⣈⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠃⠘⠛⠀⠀⠀⠉⠻⣿⣿⡿⠿⠿⠿⢃⣤⣼⣿⡿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠏⠉⠻⢿⣿⠿⠿⠿⠇⠀⠈⠉⠛⠉⠉⠁⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⡇⣿⡏⣿⣿⠿⠀⢸⣿⡟⣿⡇⣾⡟⣿⡇⢻⣿⠿⢸⣿⣿⣿⡟⠃⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⡿⣿⣧⣰⣿⢻⣷⠀⠀⣾⣿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠉⣿⣿⣿⣿⡰⠀⣿⡇⣿⣿⣿⣿⢸⣿⡀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠃⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠘⠀⠁⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣦⣤⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⣄⠀⠀⠀⢀⣤⣄⠀⠀⠀⣠⣤⣄⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣤⡀⠀⠸⣿⣿⠀⠀⠀⠹⣿⣟⠀⠀⠀⢻⣿⡇⠀⠀⠀⢠⣧⣀⣀⠀⠀⠀⣿⣿⡀⠀⠀⠘⣿⡟⠀⠀⠀⢸⣿⠋⠀⠀⠀⣿⣿⡟⢀⣴⣾⣿⣿⣿⣿⣿⣿⣁⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣦⡉⠿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣷⡦⠀⠀⢹⣷⣶⣿⣿⣆⣿⣧⣰⡆⢰⣾⣿⣿⣿⣿⠄⢠⣿⣿⣿⣶⡆⢰⣿⠀⣾⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣿⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣼⣿⣯⣿⠏⠀⣿⣿⣿⣇⣾⣿⣿⣿⣿⠇⠀⣾⣿⠈⣿⠀⣿⣿⣯⠀⢈⣿⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⡏⠙⢿⣿⣿⣟⠓⠚⠛⣿⣿⡟⠛⠛⢻⣿⣿⠒⠚⠿⠛⠚⠛⠛⢻⣿⠟⠋⠉⢻⣿⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣗⠀⠀⠀⣿⣿⣷⠀⠀⠠⣿⣿⣦⣴⠇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣛⣿⣿⡀⠀⠀⢘⣹⣿⣿⡀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⠿⡿⣻⣿⣿⡛⠃⠀⠀⢸⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⣠⣿⣿⣿⣿⣄⡀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣷⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠓⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠀⠁⠀⠀⠀⠭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠸⠀⢀⣀⣀⣀⠄⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢙⣿⣿⣿⣿⣿⣿⡟⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠒⠒⢸⠃⢉⣹⣛⡟⢋⣧⡀⣠⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠦⠀⠄⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⡧⣤⣤⣤⣤⣾⣿⡿⢻⠟⠃⠈⡏⠉⣿⣭⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡏⠀⠀⠈⣿⣿⣿⠿⠿⠿⣿⣿⠃⡀⢀⣀⡀⠁⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠈⠿⠿⠂⠀⠀⠘⠿⣿⣿⡿⠿⠻⣿⣿⠿⠿⠟⠛⢿⡿⣿⣿⡿⠿⠟⠀⠀⠋⠉⠻⠿⣿⣿⠿⠿⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡿⣿⡇⣾⡿⣿⡇⢻⣿⠿⢻⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⣰⣿⢻⣷⡄⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⠃⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠐⠀⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣟⠛⣷⣶⣦⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⣄⠀⠀⠀⢠⣤⣄⠀⠀⠀⣠⣤⡄⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣤⡀⠀⠸⣿⣿⠀⠀⠀⠹⣿⣟⠀⠀⠀⢻⣿⡃⠀⠀⠀⢰⣧⣀⣀⡀⠀⠀⣿⣿⡀⠀⠀⠘⣿⡟⠀⠀⠀⢸⣿⠋⠀⠀⠀⣿⣿⣟⢀⣴⣾⣿⣿⣿⣿⣿⣿⣁⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣦⡉⠟⣿⣿⣿⣿⣿⣦⣴⣿⣿⣷⡦⠀⠀⣹⣷⣶⣿⣿⡆⣿⣇⣰⡆⢰⣾⣿⣿⣿⣿⠄⢠⣿⣿⣿⣶⡆⢰⣿⠀⣾⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣼⣿⣯⣿⠏⠀⣿⣿⣿⣧⣾⣿⣿⣿⣿⠇⠀⣼⣿⠈⣿⢘⣿⣾⣯⡀⠈⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⡍⠙⢿⣿⣿⡟⠓⠒⠛⣿⣿⡟⠛⠛⢻⣿⣿⠒⠚⠿⠛⠒⠛⠚⢻⣿⠟⠋⠉⢻⣿⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣗⠀⠀⠀⣿⣿⣿⠀⠀⠘⢿⣿⣦⣴⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣛⣿⣿⡄⠀⠀⢘⣻⣿⣿⡀⠀⠀⠀⢰⣿⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⡿⣿⣿⣿⡛⠃⠀⠀⢿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢠⣿⣿⣿⣿⣀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⡀⠀⠁⠀⠀⠀⠤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠠⠀⢀⣀⣀⣀⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣿⡟⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠒⠒⢸⠃⢉⣻⣛⡟⢋⣧⡀⣤⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠦⠀⠄⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⡧⣤⣤⣤⣤⣾⣿⡿⢿⠟⠃⠈⡏⠉⢿⣭⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡏⠀⠀⠈⣿⣿⣿⢿⠿⠿⣿⣿⠃⡀⢀⣀⡀⠁⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠈⠿⠿⠂⠀⠀⠘⠿⣿⣿⡿⠿⠿⢿⣿⠿⠿⠟⠻⢿⣿⣿⣿⡿⠟⠛⠀⠀⠉⠉⠻⠿⣿⣿⠿⠿⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠿⠿⠿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡿⣿⡇⣾⡿⣿⡇⢻⣿⠿⢻⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⣰⣿⢻⣷⡄⠀⣾⡟⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣹⣿⢸⣿⠃⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠈⠀⠃⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣟⢻⣤⣶⣦⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢀⣤⣄⠀⠀⠀⢀⣤⣄⠀⠀⠀⣠⣦⣄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣤⡀⠀⢻⣿⣿⠀⠀⠀⠻⣿⡟⠀⠀⠀⢻⣿⡃⠀⠠⠀⢰⣧⣤⣄⡀⠀⠀⣿⣿⡀⠀⠀⠘⣿⡟⠀⡀⠀⢸⣿⠟⠀⠀⠀⣿⣿⡿⠀⣠⣾⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣦⡛⠻⣿⣿⣿⣿⣿⣦⣴⣿⣿⣷⡦⠀⠀⣽⣷⣶⣿⣿⡖⣿⡇⣰⡆⢰⣾⣿⣿⣿⣿⠄⢠⣿⣿⣿⣷⡖⢰⣿⠀⢾⣿⣿⣿⣿⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣽⣿⣿⣿⠏⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠋⠀⣼⣿⠈⣿⠀⣿⣾⣿⡀⠈⣿⣿⣿⣿⣇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣮⡙⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⡟⠓⠒⢛⣿⣿⡛⠛⠛⢻⣿⣿⠒⠚⣿⠛⠒⠛⠛⢿⣿⡟⠉⠉⢹⣿⣿⣿⣍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⢸⣿⣿⡷⠀⠀⠘⣿⣿⣦⣄⡅⠀⠀⠀⢀⣿⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣗⣀⣸⣿⣿⣷⡀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⢘⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⡿⣿⣿⣿⡻⠃⠀⠀⣼⣿⣿⡇⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢠⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠐⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣧⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠓⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⠀⠁⠀⠀⠀⢨⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠿⠇⠀⣀⣀⣀⡤⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⣽⣿⡿⣿⣿⣟⣟⠓⠚⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢐⣶⣄⣿⢋⣘⣛⣻⠛⢻⣄⣤⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣤⣤⢼⣿⣿⡿⢿⠛⡛⠛⠀⠸⡏⠹⣭⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⡟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢻⣿⣿⣟⠉⠀⠀⢸⣿⠿⠿⢿⣿⣤⣈⣀⢁⣀⣀⣀⣃⣠⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠷⠶⠶⠶⠆⠀⢺⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠙⡋⠀⠲⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣶⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡿⣿⡏⣿⡿⣿⡟⢿⣿⠿⢿⣿⣿⣿⡏⠉⠿⣿⣿⠿⣿⣿⣿⣿⠁⠀⣿⡿⣿⣦⢰⣿⢻⣿⡍⠁⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⠁⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣟⢿⣴⣦⣦⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢀⣤⣄⠀⠀⠀⢠⣤⣄⠀⠀⠀⣠⣶⣄⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣤⡀⠀⢻⣿⣿⠀⠀⠀⠻⣿⡟⠀⠀⠀⢻⣿⡃⠀⠠⠀⢰⣷⣤⣀⡀⠀⠀⣿⣿⡀⠀⠀⠘⣿⡟⠀⡀⠀⢸⣿⠋⠀⠀⠀⣿⣿⡿⠀⣠⣾⣿⣿⣿⣿⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣦⡙⠻⣿⣿⣿⣿⣿⣦⣴⣿⣿⣷⡦⠀⠀⣽⣷⣶⣿⣿⠶⣿⣇⣰⡆⢰⣾⣿⣿⣿⣿⠆⢠⣿⣿⣿⣷⡖⢰⣿⠀⢾⣿⣿⣿⣿⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣼⣿⣿⣿⠏⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⠋⠀⣼⣿⠈⣻⠀⣿⣾⣿⠀⠈⣿⣿⣿⣿⣇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣮⡙⣿⣿⣿⣿⣿⣿⣿⡉⠉⣿⣿⣿⡟⠓⠒⠛⣿⣿⡛⠛⠛⢻⣿⣿⠒⠚⣿⠛⠒⠛⠚⢿⣿⡟⠉⠉⢹⣿⣿⣿⣍⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⢸⣿⣿⡷⠀⠀⠘⣿⣿⣦⣄⠋⠀⠀⠀⠀⣿⣿⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣗⣀⣸⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⢿⣿⣿⣿⡟⠃⠀⠀⢸⣿⣿⣷⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢠⣿⣿⣿⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠐⠂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣶⣾⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠓⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⠀⠁⠀⠀⠀⢰⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠶⠇⠀⣀⣀⣀⡤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⣽⣿⣿⣿⣿⣟⣟⠓⠚⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢐⣶⣄⣿⢋⣈⣛⣻⠛⢻⣄⡤⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣤⣤⢼⣿⣿⡿⢿⠛⡛⠛⠀⠸⡏⠹⣭⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⡟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢻⣿⣿⣟⠉⠀⠀⢸⣿⠿⠿⢿⣿⣦⣌⣀⢁⣀⣀⣀⣇⣠⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠷⠶⠶⠶⠆⠀⢺⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⡛⠐⠲⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣶⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡿⣿⡏⣿⡿⣿⡟⢿⣿⠿⢿⣿⣿⣿⡏⠉⠿⣿⣿⠿⣿⣿⣿⣿⠁⠀⣿⡿⣿⣦⢰⣿⢻⣿⡍⠃⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣶⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⠁⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠂⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡉⣣⣶⣶⣆⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣠⣤⡄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⢀⣴⣦⠀⠀⠀⢀⣴⣦⠀⠀⠀⢠⣶⣦⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⣤⡀⠘⢿⣿⣗⠀⠀⠀⠻⣿⡇⠀⠀⠀⢻⣿⡃⠀⢀⠀⢰⣷⣤⣤⣀⠀⠀⣿⣿⣀⠀⠀⠀⣿⡟⠀⣀⠀⢨⣿⡏⠀⠀⠀⣸⣿⣿⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣬⠛⢻⣿⣿⣿⣿⣿⣤⣼⣿⣿⣷⠆⠀⠀⣿⣷⣾⣿⣿⠾⣿⡆⣰⡆⢰⣿⣿⣿⣿⣿⠂⢀⣿⣿⣿⣿⣷⢠⣿⠃⢾⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣯⣿⠁⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠉⠀⣸⣿⠁⢿⠀⣿⣾⣿⡇⠀⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⡍⠉⠉⣿⣿⣿⠋⠁⠚⢻⣿⣿⠛⠛⠛⢿⣿⡟⠒⠒⠻⠟⠒⠛⠛⢻⣿⡟⠉⠉⠉⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣇⠀⠀⣿⣿⣿⡄⠀⠀⢿⣿⡇⠀⠀⠈⠀⠀⠀⠀⢸⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣓⣀⣿⣿⣿⣇⠀⠀⣸⣿⣅⣠⣄⡀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⣿⣿⣿⣿⡛⠃⠀⠀⣐⣿⣿⣇⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢀⣰⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⡀⠉⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠃⢀⣀⣀⣠⡤⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠿⠿⣿⣿⣿⣿⠛⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠑⠒⠂⢠⣀⣀⣛⠛⣿⡟⣧⣠⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⠠⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢤⣤⣤⣤⠽⠛⢿⢻⠛⠛⠉⠸⢯⢭⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠋⠀⠘⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⣁⣀⣀⣤⢋⣾⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣾⠿⠿⠿⠷⠶⠶⠋⠀⠀⠀⠀⠉⠻⣿⡿⠿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠙⠛⠿⢿⣿⣿⡿⠋⠛⠻⠿⠟⠛⠛⠿⣿⣿⡿⠟⠛⠻⠿⠟⠋⠀⠀⠈⠽⡿⠿⠿⢿⣿⡿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡇⣿⡇⣾⡟⣿⡇⢻⣿⠿⢹⣿⣿⣿⡆⡀⠿⣿⣿⠿⣿⣿⣿⣿⠉⠁⣿⡿⣿⣦⢰⣿⢻⣿⡟⠀⣾⡟⣿⣧⣿⣿⠿⠀⣿⣿⣿⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⣸⣿⢸⣿⠀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠁⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠈⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⡇⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⣹⡿⠋⠙⠋⠁⠀⠀⠉⢉⡉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⣩⣍⠉⠁⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⡉⣰⣶⣶⣆⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣴⣦⠀⠀⠀⢠⣶⣦⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⣤⡀⠘⢿⣿⣇⠀⠀⠀⠻⣿⡇⠀⠀⠀⢻⣿⠁⠀⠀⠀⢸⣷⣤⣤⣀⠀⠀⣿⣿⣀⠀⠀⠀⣿⡟⠀⡀⠀⢨⣿⡏⠀⠀⠀⣸⣿⣟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣬⠙⢻⣿⣿⣿⣿⣷⣤⣼⣿⣿⣶⠆⠀⠀⣿⣷⣶⣿⣿⠾⣿⡆⣰⡆⢰⣿⣿⣿⣿⣿⠂⢀⣿⣿⣿⢿⣷⢀⣿⠀⢾⣿⣿⣿⣿⡇⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣦⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢀⣿⣿⣯⡿⠁⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⠁⠀⣼⣿⠀⢻⠀⢹⣾⣿⡇⠀⢻⣿⣿⣿⣅⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⡉⠉⠉⣿⣿⣿⠋⠀⠘⢻⣿⣟⠛⠛⠛⢻⣿⡟⠒⠒⠻⠛⠒⠛⠛⢻⣿⡟⠉⠉⠉⣿⣿⣿⣧⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣆⠀⠀⣺⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣓⣀⣼⣿⣿⣇⠀⠀⢐⣾⠄⢀⣀⡀⠀⠀⠀⠀⣸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⣿⣿⣿⣿⡛⠃⠀⠀⠀⣿⣿⡇⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡎⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆⠀⢀⣻⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠃⠀⣀⣀⣠⡄⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⡿⠿⣿⣿⣿⣿⡛⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠷⠁⠒⠀⢀⣄⣀⡛⠛⣿⡿⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢤⣤⣤⡤⠼⣿⣿⠿⠟⠋⠇⠸⢯⣢⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠈⣉⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⢀⡀⠁⠁⢀⠀⣠⠞⣰⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⡿⠿⠿⠷⠶⠶⠒⠒⠀⠀⠒⠛⠛⠻⢿⡿⠻⣿⣿⣿⠿⣿⣿⡿⠟⠛⠛⠿⠿⠿⣿⣿⣿⡟⠉⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠟⠋⠀⠀⠈⠙⠿⠿⠿⣿⣿⣿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⣇⣿⡏⣿⣿⠿⠀⢸⣿⡇⣿⡇⣾⡟⣿⡇⢹⣿⠿⢹⣿⣿⣿⡏⠁⠿⣿⣿⠿⣾⣿⣿⣿⠉⠀⣿⡿⣿⣦⢰⣿⢻⣷⡌⠉⣿⡟⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⠀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⠸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⣀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⢉⣴⡾⠙⠋⠙⠋⠀⠉⠉⣭⡁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⢽⠏⠉⠁⠈⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠄⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠠⣶⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⢈⣶⣾⣷⣆⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⣠⣤⡄⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣴⣦⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⡀⠘⢿⣿⣇⠀⠀⠀⠻⣿⡇⠀⠀⠀⢻⣿⠁⠀⠀⠀⢸⣷⣦⣤⣄⠀⠀⣽⣿⣁⠀⠀⠀⣿⡟⠀⣀⠀⠀⣿⡏⠀⠀⠀⣸⣿⣿⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡌⠛⢻⣿⣿⣿⣿⣷⣄⣿⣿⣿⣷⠆⠀⠀⣿⣿⣾⣿⣿⠺⣿⡆⣴⡆⢸⣿⣿⣿⣿⣿⠂⢀⣿⣿⣿⣿⣷⢀⣿⠃⢾⣿⣿⣿⣿⡇⠀⠐⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣧⡿⠀⢠⣿⣿⣿⣷⣿⣿⣿⣿⣿⠁⠀⣸⣿⠀⢻⠀⣽⣾⣿⡆⠀⢿⣿⣿⣿⣇⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣍⢻⣿⣿⣿⣿⣿⣿⡉⠉⠉⣿⣿⣿⠉⠁⠙⢻⣿⡟⠛⠛⠛⣿⣿⡟⠒⠒⠻⠟⠒⠛⠛⢻⣿⡟⠉⠉⠉⣿⣿⣿⣯⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣆⠀⠀⣿⣿⣿⠀⠀⠀⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣓⣀⣿⣿⣿⣇⠀⠀⢀⣟⣀⣀⣀⡀⠀⠀⠀⠀⣾⣿⣧⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡟⠿⠿⣿⣻⣿⣿⡿⠃⠀⠀⠀⣾⣿⣿⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣃⣀⡀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⣀⣠⡄⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⢹⠿⣿⣿⣿⣿⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⠁⠀⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠒⠂⠀⣆⡀⠙⠛⢻⣿⡅⢀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣿⣿⡿⡿⠿⠹⡹⣖⠲⡂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢈⣛⡦⠁⠀⠀⢁⡊⣠⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⠷⠶⠖⠒⠒⠀⠀⠒⠂⠐⠚⠛⠻⠿⠿⠟⠿⠿⠿⠛⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠻⠿⢿⣿⣿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⡇⣿⡏⣿⣿⠿⠀⢸⣿⡇⣿⡇⣾⡟⣿⡇⢸⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣿⠉⠁⣿⡿⣿⣦⢸⣿⢻⣿⡟⠛⣿⡟⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⠀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⠸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⣾⣶⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⣇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⢉⣠⣬⠟⠛⠛⠛⠋⠉⠉⣭⣥⣈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠙⠛⠛⠉⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⢈⣶⣾⣶⣆⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⣤⣤⡄⠀⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣶⣦⠀⠀⠀⢠⣶⣦⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⡀⠘⢿⣿⣇⠀⠀⠀⠻⣿⡇⠀⠀⠀⢻⣿⠁⠀⠀⠀⢸⣷⣦⣤⣄⠀⠀⣽⣿⡀⠀⠀⠀⣿⡟⠀⣀⠀⠀⣿⡏⠀⠀⠀⣸⣿⣿⠁⢠⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡌⠙⢻⣿⣿⣿⣿⣷⣄⣾⣿⣿⣶⠆⠀⠀⣿⣿⣾⣿⣿⠺⣿⡆⣴⡆⢸⣿⣿⣿⣿⣿⠂⢀⣿⣿⣿⡿⣷⢀⣿⠇⢾⣿⣿⣿⣿⡇⠀⠐⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣯⡿⠀⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⠁⠀⣸⣿⠀⢻⠀⣽⣾⣿⡅⠀⢿⣿⣿⣿⣇⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣍⢻⣿⣿⣿⣿⣿⣿⡉⠉⢉⣿⣿⣿⠋⠁⠙⢻⣿⣟⠛⠛⠛⣿⣿⡟⠒⠒⠻⠛⠒⠛⠛⢻⣿⡟⠉⠉⠉⣿⣿⣿⣯⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣆⠀⠀⣿⣿⣿⠀⠀⠀⢿⢿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣓⣀⣿⣿⣿⣇⠀⠀⢀⣙⢀⣀⣀⡀⠀⠀⠀⠀⣾⣿⣧⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠿⠿⣿⣻⣿⣿⡟⠃⠀⠀⠀⣿⣿⣿⣇⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡷⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⣀⡀⠈⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⣠⡄⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⢹⢿⣿⣿⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⠁⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠃⠒⠂⠀⣆⡀⠙⠛⢻⣿⡅⢀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣿⣿⡿⡿⠿⢹⡹⣖⠲⡂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢈⣛⡦⠁⠀⠀⢁⡈⣠⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⠿⠶⠖⠒⠒⠀⠀⠒⠂⠐⠚⠛⠻⠿⠿⠟⠻⠿⠿⠛⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠻⠿⢿⣿⣿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⡇⣿⡏⣿⣿⠿⠀⢸⣿⡇⣿⡇⣾⡟⣿⡇⢸⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣿⠉⠁⣿⡿⣿⣦⢸⣿⢻⣿⡟⠛⣿⡟⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⠀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⠸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣶⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⣇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⢉⣠⣬⠝⠛⠛⠛⠃⠉⠉⣭⣥⣈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠉⠉⠉⠙⠛⠛⠉⠙⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⣰⣶⣿⣿⡆⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⣴⣶⡀⠀⠀⠀⣴⣦⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣴⣦⡄⠀⠀⠀⣶⣦⡀⠀⠀⢀⣶⣶⡀⠀⠀⢠⣶⣶⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⡀⠘⣿⣿⣇⠀⠀⠀⢻⣿⡅⠀⢀⠀⢿⣿⠁⠀⠀⠀⣸⣷⣶⣦⣤⠀⠀⣽⣿⣁⠀⠀⠀⣿⡟⢀⣀⡀⠀⣿⡏⠀⠀⠀⣸⣿⣿⡏⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡌⠙⢿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣷⠆⠀⢐⣿⣿⣿⣿⡿⢾⣿⡆⣼⡆⣾⣿⣿⣿⣿⣿⠂⢀⣿⣿⣿⡿⣷⠀⣿⡇⢺⣿⣿⣿⣿⡇⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⢸⣿⡃⢹⡀⢻⣿⣿⡇⠀⢻⣿⣿⣿⣇⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣏⠉⠉⢹⣿⣿⣿⠉⠁⠙⣿⣿⣟⠛⠛⠛⣿⣿⡟⠒⠒⠛⡟⠛⠛⠛⠻⣿⡟⠉⠉⠉⣿⣿⣿⣿⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣆⠀⠀⣿⣿⣿⡄⠀⠀⢹⡿⡇⠀⠀⠨⠁⠀⠀⠀⢰⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣓⣀⣿⣿⣿⣇⠀⠀⣈⣿⠁⣠⣄⡀⠀⠀⠀⠀⣼⣿⣷⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠟⢿⣿⣿⣳⣿⣿⡻⠃⠀⠀⠀⣿⣿⣿⣷⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⡧⠀⢀⣽⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⣸⣿⣿⣿⣿⣿⣿⣇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣈⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⣀⣀⣤⡄⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⢹⠿⢿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠁⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠋⠒⠒⠂⢠⣀⣘⣛⣻⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣿⣿⠿⡿⠿⠏⢺⡗⠺⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠘⢚⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣷⣀⠀⢀⡉⣠⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁⠐⠿⠟⠛⠿⠿⠛⠛⠿⠿⢿⣿⣿⣿⣿⠇⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠏⠁⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⡇⣿⡏⣿⣿⠿⠀⢸⣿⡏⣿⡇⣾⡟⣿⡇⢸⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣼⣿⣿⣿⠉⠀⣿⡿⣿⣦⢰⣿⢻⣷⠀⠀⣾⡟⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡧⣿⣿⢸⣿⢸⣿⡀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⣿⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠚⠀⣿⣇⣿⣿⢸⣿⣸⣿⠇⠆⣿⣇⣿⣿⣿⣿⣀⣸⣿⢿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⣹⡿⠋⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠛⠋⠁⠉⠉⠉⠉⠉⠈⠉⣽⣿⣿⣿⣿⣿⠿⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠀⠀⠐⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⢀⣴⣦⡄⠀⠀⢀⣴⣶⡀⠀⠀⢀⣶⣶⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⣶⣶⡄⠀⠀⠀⣶⣶⡄⠀⠀⢀⣶⣷⡄⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⠀⠘⣿⣿⣇⠀⠀⠈⢻⣿⠁⠀⣀⡀⢻⣿⠁⠀⠀⠀⣸⣷⣶⣶⣤⠀⠀⣽⣿⣁⠀⠀⠀⣿⡿⢀⣀⡀⠀⣿⡟⠀⠀⠀⣸⣿⣿⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡟⠛⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⢾⣿⣀⣼⣆⣾⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⢀⣿⡇⢺⣿⣿⣿⣿⣿⠀⠰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⣻⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣸⣿⠅⣿⡄⣿⣿⣿⣇⠀⢻⣷⣿⣿⣿⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⣹⣿⣿⣿⠉⠉⠙⣿⣿⡟⠛⠛⠻⣿⣿⡟⠒⠒⢻⡿⠛⠛⠛⠛⣿⣿⠉⠉⠉⣽⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡂⠀⠀⣿⣿⣿⡀⠀⠀⢹⣿⠇⠀⠀⠸⠅⠀⠀⠀⢀⣿⣿⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢓⣀⣿⣿⣿⡀⠀⡀⣸⣟⡁⣀⢀⡀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⣿⣿⣿⣿⠏⣿⡿⣿⣷⣿⣿⣻⠃⠀⠀⢨⣿⣿⣿⣷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⢿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣁⡀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⣀⣀⣴⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⢉⠿⢿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠁⠈⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠓⠒⠒⢸⢀⣘⣻⣻⣿⢃⣶⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢆⢀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⡿⠿⠟⢹⡿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠘⣻⣿⣿⣿⠟⠻⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠛⠻⣦⡀⠈⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠛⠛⠛⠛⠁⠀⠀⠀⠀⡤⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠿⠧⢀⠀⠉⠛⠛⠛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⡇⣿⡏⣿⣿⠿⠀⢸⣿⡇⣿⡇⣾⡟⣿⡇⢹⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⢰⣿⢻⣿⠀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢿⣿⢸⣿⠀⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⢸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⢸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠇⠀⣿⣏⣿⣿⣿⣿⣀⣸⣿⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⡈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⣽⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠋⠀⠄⠀⠐⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡿⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⢀⣴⣦⡀⠀⠀⢀⣴⣶⡀⠀⠀⢀⣶⣶⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⣶⣶⡄⠀⠀⠀⣶⣶⡄⠀⠀⢠⣶⣷⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣶⣦⠀⠘⢿⣿⡇⠀⠀⠈⢻⣿⠀⠀⣀⡀⢻⣿⠀⠀⠀⠀⣼⣿⣶⣶⣦⠀⠀⣼⣿⣁⠀⠀⠀⣿⡟⢁⣀⡀⠀⣿⡟⠀⠀⠀⣠⣿⣿⡗⢀⣾⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡟⠛⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⡂⠀⣸⣿⣿⣿⣿⣿⣿⣿⡀⣾⡆⣾⣿⣿⣿⣿⡿⠁⠀⣿⣿⣿⡿⣿⠀⣿⡇⢾⣿⣿⣿⣿⣿⠀⠠⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁⠀⣻⣿⣿⣽⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⡇⣿⡀⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⣿⣿⣿⣟⠉⠉⠙⣿⣿⡛⠛⠛⢻⣿⣿⡛⠒⠒⢻⡿⠛⠛⠛⠛⣿⣿⠉⠉⠉⢹⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡂⠀⢸⣿⣿⣿⠀⠀⠀⢿⣿⡄⠀⠀⢨⡅⠀⠀⠀⢠⣿⣿⡆⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣓⣸⣿⣿⣿⡄⠀⠀⣸⣿⡁⢀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣳⣿⣿⡻⠁⠀⠀⢀⣿⣿⣿⣷⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠐⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣯⣄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠓⡀⠀⠀⢠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣰⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⡁⠀⠀⠀⢰⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠄⢀⣀⣀⣠⣴⢦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠈⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠓⠒⢰⣠⣼⣻⣿⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣄⡀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⠿⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⡿⠻⠛⠁⠀⣀⣉⣿⣯⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄⠀⠁⠀⠀⠀⠸⠿⠿⠿⠛⠛⠛⠻⠿⠛⠀⣀⠈⣁⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣾⣿⣿⡮⠍⠁⠀⠀⠀⠘⠻⠟⠛⠋⠀⠀⠀⠀⠘⢿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢸⣿⡇⣿⡏⣿⣿⠿⠀⢸⣿⡟⣿⡇⣿⡟⣿⡇⢹⣿⠿⢸⣿⣿⣿⡆⠀⠿⣿⣿⠿⣾⣿⣿⣷⠀⠀⣿⡿⣿⣦⢰⣿⢻⣷⠀⠀⣾⡿⣿⣧⣿⣿⠿⠀⣿⣿⣷⢸⣿⡿⣿⡆⣾⣿⣿⣷⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣦⠀⢸⣿⡇⣿⡇⠻⣿⣶⡄⢸⣿⣶⢸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⠇⠀⠻⣿⣶⣄⣿⣿⣶⢸⣿⣿⣿⣸⣿⣷⣿⡃⣿⣿⠛⠛⢸⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⢹⣿⣿⠀⣿⣿⣀⠀⠸⣿⣇⣿⡇⣿⣏⣿⣿⢸⣿⣀⣸⣿⣿⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⣿⠀⠀⣿⣇⣿⣿⢸⣿⣸⣿⠀⠀⣿⣇⣿⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣏⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠈⠉⡉⠈⠉⠉⠀⠉⠉⠉⠀⠀⠉⠛⠋⠀⠈⠙⠋⠁⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠀⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠈⠙⠛⠉⠀⠀⠈⠙⠋⠁⠉⠉⠉⠉⠉⠈⠭⣽⣽⣿⣭⣵⣮⠛⠋⠁⠈⠉⠉⠉⠁⠀⠀
⠀⠉⠀⠄⠀⠀⠀⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣧⡀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⡄⣤⣶⣶⡄⠀⠀⢠⣶⣶⡄⠀⠀⢠⣾⣷⡆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣶⣷⡆⠀⠀⢠⣾⣷⡆⠀⠀⢠⣾⣿⡆⠀⠀⢠⣾⣿⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣦⢿⣿⣿⣇⠀⠀⠈⢻⣿⢇⢀⣀⣘⣿⣿⠁⠀⠀⢀⣾⣿⣿⣷⣦⡀⠀⣿⣿⣇⡀⠀⠀⣿⣿⢁⣤⣀⣀⣿⣿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣇⣾⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣾⣿⣯⣿⣯⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢉⣿⣿⣿⣿⡛⠙⢻⣿⣿⣿⠛⠿⣿⣿⣿⡟⠛⠛⣿⣿⠟⠛⠛⢻⣿⣿⡏⠉⠉⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢾⣿⣿⣿⡄⠀⢻⣿⣿⣧⡀⢀⣿⣿⠀⠀⠀⣼⣿⣿⣷⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⣽⣿⡇⠀⠀⢰⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠸⠷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠃⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠀⠀⠀⠐⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣛⣀⠀⠀⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⣿⣿⣿⣿⣿⣿⣿⡓⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠈⠙⠛⠙⠚⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣸⣤⣿⣻⣿⣿⣿⠋⠙⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⢼⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢈⣉⣹⣿⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣤⠈⠉⠀⠀⠀⠸⠿⠿⠿⠟⠛⠛⠿⠿⠿⣷⣦⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠂⠀⢀⣼⣾⣿⣿⣿⣿⣿⣿⡋⢁⣄⠈⢻⣿⣿⡿⠿⠛⠋⢨⣷⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠻⣿⣿⡆⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⢠⣦⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠁⠀⠙⠋⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠲⣦⡄⠀⠀⢀⣤⣤⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⣠⣾⣿⣿⣿⣭⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠃⠛⠃⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠹⡿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣧⡀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣮⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⣄⣀⣤⣶⣶⡄⠀⠀⢠⣾⣶⡄⠀⠀⢠⣾⣷⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣾⣷⡆⠀⠀⢠⣾⣿⡆⠀⠀⢠⣾⣿⡦⠀⠀⢠⣾⣿⣦⣤⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⠀⠀⠘⢿⣿⣇⣀⣀⣘⣿⣿⠃⠀⠀⢀⣾⣿⣿⣷⣶⡀⠀⣿⣿⣇⣀⠀⠀⣿⣿⣁⣤⣀⣀⣿⣿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣇⣾⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⢹⣿⣿⣿⣿⡋⠙⢻⣿⣿⣿⠿⢻⣿⣿⣿⡟⠛⠛⣿⣿⠟⠻⠛⢻⣿⣿⣟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⡅⠈⢿⣿⣿⣿⡀⠀⣿⣿⠀⠀⠀⣾⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷⣀⣜⣿⣿⣿⣇⣰⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠃⠀⠀⠸⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠀⠀⠀⠐⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣀⣀⠀⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⣿⣿⣿⣿⣿⣿⣿⡓⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠛⠹⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣒⣛⣿⣿⣿⡟⠻⣷⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣧⣿⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢹⣿⣿⣿⠁⠀⠀⠀⢻⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⣸⡿⠿⠟⠛⠛⢿⣿⣿⢗⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠶⠿⠳⠂⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⠿⠻⡏⠀⠈⢿⣿⡿⠛⠋⠉⠁⠀⠀⠉⣿⡿⠛⠛⠛⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⣬⠀⠈⠉⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣴⣿⣿⣿⣟⡛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠘⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠙⠘⠃⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠻⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⣀⣀⣤⣶⣶⡄⠀⠀⢠⣾⣶⡄⠀⠀⢠⣾⣷⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⢠⣾⣿⡆⠀⠀⢠⣾⣿⡆⠀⠀⢠⣾⣿⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⠀⠀⠈⣿⣿⢃⣀⣀⣸⣿⣿⠁⠀⠀⢀⣾⣿⣿⣷⣶⡄⠀⣽⣿⣧⡀⠀⠀⣿⣿⣁⣤⣀⣀⣿⣿⠁⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣇⣾⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣯⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⢹⣿⣿⣿⣿⠉⠙⣻⣿⣿⣿⡿⢻⣿⣿⣿⣟⠛⠛⣿⣿⠟⠛⠛⢻⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⣸⣿⠀⠀⠀⣾⣿⣿⣿⡆⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣆⣠⣿⣿⠆⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣚⣿⣿⡟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡵⣿⣿⣿⠁⠀⠀⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠐⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣃⣀⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⡗⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠑⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⡿⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠙⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⣀⣸⣿⣿⣿⣿⣿⠛⠉⢻⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⣿⣇⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠙⢃⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠾⢿⡿⠿⠿⠟⠓⢿⡿⠿⠻⠿⠿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡋⠁⠀⠀⠈⠛⠛⠛⠿⠿⠀⠀⠻⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢺⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠛⠃⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣇⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⠀⢀⣠⣴⣶⣶⡄⠀⠀⢠⣾⣶⡄⠀⠀⢰⣾⣷⡄⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⣾⣿⡆⠀⠀⢠⣾⣿⡆⠀⠀⢠⣾⣿⣷⣠⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⣿⣿⢃⣀⣀⣘⣿⣿⠁⠀⠀⢀⣿⣿⣿⣿⣶⡀⠀⣽⣿⣧⣀⡀⠀⣿⣿⣃⣤⣄⣀⣿⣿⠁⠀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣇⣾⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⠟⣿⣿⣿⣿⡟⠛⠛⢻⣿⡟⠛⠛⠛⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⠠⣿⣿⣿⣿⣇⠀⠀⢸⣿⡇⠀⠀⣼⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣀⣀⣾⣿⡧⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣛⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡇⠀⢴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠀⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣏⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⢿⣿⣿⠿⠲⣾⣿⡅⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠁⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠃⠟⠀⠀⢨⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣍⠀⠉⢁⣀⡹⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⣿⣿⠿⠿⠿⠿⠿⠇⠀⠀⠘⠻⠿⠟⠛⣿⣿⣿⣿⣿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⢰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠄⠁⠚⠃⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⡀⠀⠀⠀⢠⣶⣦⡀⠀⠀⢠⣶⣦⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⣶⣶⡄⠀⠀⠀⣶⣷⡄⠀⠀⠀⣶⣿⡦⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣷⣶⣄⠀⠘⣿⣿⡄⠀⠀⠈⢻⣿⠀⠀⣀⡀⢻⣿⠀⠀⠀⠀⣼⣿⣿⣷⣦⠀⠀⢹⣿⣁⡀⠀⠀⢽⡟⢀⣀⣀⠀⣿⡟⠁⠀⠀⣠⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡉⠙⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⡿⣿⣿⠀⣾⣆⣼⣿⣿⣿⣿⡿⠁⠀⣿⣿⣿⡿⣿⠀⣸⣷⠾⣿⣿⣿⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⢸⣿⣿⣿⣼⠏⠀⣿⣿⣷⣿⣼⣿⣿⣿⣿⡏⠀⠀⢀⣿⡇⢹⡄⢿⣦⣿⣿⠀⢻⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉⢩⣿⣿⡏⠉⠉⠉⣻⣿⣿⠛⠛⠛⢿⣿⣿⠓⠒⠒⠚⡿⠛⠛⠛⠋⢛⣿⡏⠉⠉⢹⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠐⠚⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣲⣶⣾⣿⣿⣿⣖⡂⠀⣿⣿⣿⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠈⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡃⣓⣼⣿⣿⣇⡀⠈⡻⣟⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⠏⢿⣿⣿⢳⢿⣿⡻⡃⠀⠀⠀⢸⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠛⠛⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⣸⣿⣿⣿⡟⠀⠀⢨⣿⣷⣯⣾⣷⣾⣿⣆⡀⢀⢸⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠺⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⡃⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠂⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⢀⣜⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⡶⡦⠀⢀⣀⡀⣤⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿⣿⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠉⠉⠅⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠓⢰⣿⣿⣙⣛⣻⠿⠻⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⣶⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠛⢿⡛⡟⠛⠀⠐⣯⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⠉⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠘⠿⣿⡿⠿⠛⠉⠉⠉⠙⢛⣻⡿⠿⠛⠛⠛⠟⠀⠀⠀⠀⠙⠛⠉⠉⢻⣿⡿⠛⠛⠛⠋⠉⣉⡉⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⢿⣷⢰⣿⣿⣿⣧⠀⠀⢸⣿⣿⡇⢸⣿⣷⢸⣿⣿⣿⣿⢿⣿⡆⠀⢰⣿⡟⣿⣧⢸⣿⡇⠀⣾⣿⢿⣷⡄⣿⣿⢿⣷⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣼⣿⠘⢿⣷⣿⡇⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⠉⣿⣿⢸⣿⡇⠀⠘⢿⣷⣦⡀⢸⣿⡇⠀⣿⣿⢸⣿⡇⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⡇⣿⣿⡏⠉⠀⣿⣿⠉⠁⢰⣶⡏⣿⣿⠀⢀⣿⣿⣿⣿⣼⣿⡿⣿⣿⠀⣿⣿⢸⣿⡇⠀⢰⣶⡏⣿⣿⢸⣿⣇⡀⣿⣿⢸⣿⡇⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠿⠸⡿⠇⠙⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠻⠿⠇⠀⠀⠿⠿⠀⠀⠈⠻⠿⠿⠋⠀⠸⠿⠇⠸⠿⠟⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠇⠙⠿⠿⠛⠀⠿⠿⠀⠀⠀⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⡀⠀⠀⠀⢠⣶⣦⠀⠀⠀⢠⣶⣦⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⠀⣶⣶⡄⠀⠀⠀⣶⣷⡄⠀⠀⠀⣶⣿⣦⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣷⣶⣄⠀⠘⣿⣿⡄⠀⠀⠈⢻⣿⠀⠀⣀⡀⢻⣿⠀⠀⠀⠀⣼⣿⣿⣶⣦⠀⠀⣹⣿⣁⡀⠀⠀⢽⡿⢁⣀⣀⠀⣿⡟⠁⠀⠀⣠⣿⣿⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡋⠙⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⡿⣿⣿⠀⣾⣆⣾⣿⣿⣿⣿⡿⠁⠀⣿⣿⣿⡿⣿⠀⣼⣧⠾⣿⣿⣿⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⢸⣿⣿⣿⣾⠏⢀⣿⣿⣾⣿⣼⣿⣿⣿⣿⡏⠀⠀⢀⣿⣧⢹⡄⣿⣤⣿⣿⡇⢹⣿⣿⣿⣿⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉⢩⣿⣿⣯⠉⠉⠉⣿⣿⣿⡛⠛⠛⢻⣿⣿⠓⠒⠒⠚⡿⠛⠛⠛⠋⢛⣿⡏⠉⠉⢹⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠐⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣗⡂⠠⣿⣿⣷⡄⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⢘⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡃⣒⣼⣿⣿⣧⣀⠘⡻⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⡏⣿⣿⡿⢳⡿⣿⣻⣃⠀⠀⠀⢸⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⠋⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⣼⣿⣿⣿⠀⠀⢸⣿⣿⣿⣧⣤⣦⣿⣧⣇⡀⠀⢸⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠺⣇⢙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢤⡄⠤⠀⢀⣀⡀⣤⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⣿⣿⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠙⠉⡅⠈⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⣢⣿⣿⣛⣛⣻⡷⠿⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢴⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⠿⢿⣿⡟⠛⠀⠀⠿⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠘⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⠿⢿⣿⣿⣿⣿⡟⠋⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠋⠉⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠿⠛⠁⠀⠀⢀⣀⡀⠀⠈⣿⣿⠿⣿⠆⠀⠀⠀⠉⠉⠉⢻⣿⡿⠛⠛⠛⠉⠉⣉⡁⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡇⠈⠉⣿⣿⣿⠙⣿⣿⣿⣿⡇⣿⣿⢿⣷⢰⣿⡟⣿⣧⠀⢸⣿⣿⣿⡇⢸⣿⣷⢸⣿⠉⣿⣿⣿⣿⡆⠀⢰⣿⡟⣿⣧⢸⣿⡇⠀⣾⣿⢿⣿⡄⣿⣿⢿⣷⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣼⣿⠘⢿⣷⣦⡀⠀⠈⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⣿⣿⢸⣿⡇⠀⠘⢿⣷⣦⡁⢸⣿⡇⠀⣿⣿⢸⣿⡇⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣸⣿⣿⣿⡇⣿⣿⡏⠉⠀⣿⣿⠉⠁⢰⣶⡏⣿⣿⠀⢀⣿⣿⣾⣿⣼⣿⡿⣿⣿⠀⣿⣿⢸⣿⡇⠀⢰⣶⡏⣿⣿⢸⣿⣇⡀⣿⣿⢸⣿⡇⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠿⠸⡿⠇⠙⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠻⠿⠇⠀⠀⠿⠿⠀⠀⠈⠻⠿⠿⠋⠀⠸⠿⠇⠸⠿⠟⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠇⠙⠿⠿⠛⠀⠿⠿⠀⠀⠀⠀⠀
⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣄⣻⣿⣿⣿⣿⣧⣤⣼⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⣃⣀⣿⣿⣿⣿⣟⣼⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣟⡉⢹⢿⣿⣿⣿⡿⠿⠗⠶⠆⠠⣿⣿⣿⣿⢿⣿⣷⣰⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠧⣾⣿⣷⣇⠈⠘⠿⣿⠟⢀⠀⠀⢀⠀⢰⣿⣿⠿⠿⢤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠏⢻⣿⠇⠀⠀⠀⠀⠀⠂⠀⠻⠀⠀⠉⠀⠀⠀⠀⡀⠀⡻⠿⠛⠛⠉⠙⠿⠿⠿⠟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⡿⡖⠀⠀⠘⣿⡿⠿⠛⠛⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⡦⣖⣂⠀⡶⠆⡔⡄⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠨⣽⣿⢿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡁⡀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢂⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣧⠀⠘⠁⠀⠀⠀⠀⠀⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢩⣞⠀⠳⠓⣗⡒⠀⠊⠕⠚⠛⠏⠛⠓⠿⠏⠾⠻⠟⠃⠛⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⣀⣦⣔⣯⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣠⡄⢀⣼⣿⡷⠀⠀⠀⣀⢀⣾⣿⣿⣯⣾⡆⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣾⣿⣿⣟⣿⣘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣯⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢊⣁⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠛⠓⠈⠈⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡏⠁⢰⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣸⣿⣿⣿⣧⣿⣿⡏⠹⠟⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠁⠿⠿⠿⠿⠇⠀⠀⠿⠿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⢷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⣠⣿⣿⣿⣿⣧⣤⣀⣧⠟⣿⣿⣿⣧⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣤⣿⣀⣀⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⡛⠉⠀⡿⣿⣿⣿⣿⠿⠟⠓⠂⠀⠴⣿⣿⣿⢿⣿⣷⣦⣶⣿⣿⣷⣶⣦⣦⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠸⣾⣿⡗⠀⠀⠀⠙⠿⠿⠏⣄⠀⠀⡄⠀⣾⣿⡿⠦⠀⣄⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠇⠀⠀⠁⠀⠀⠀⠠⠈⢉⠛⠛⠛⠉⠛⠻⠿⠿⠿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⣿⢺⡆⠀⢨⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣂⠀⡶⠆⡔⡄⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣆⠀⠨⠢⠁⠀⠀⠀⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡁⠀⢀⠀⣈⣀⣀⣀⠁⠀⡀⢂⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢹⡞⠀⠳⠒⣗⣒⠀⠪⠕⠚⠛⠏⠛⠃⠿⠏⠾⠻⠟⠃⠛⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⢻⣿⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡀⠀⠀⣀⣀⠀⢀⣼⣿⣿⣦⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⡐⢐⣿⣿⣇⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣦⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⠀⣀⣀⣀⣀⠀⠀⠀⠀⠛⠃⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣇⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠼⠙⠛⠓⠈⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣍⡛⠻⠷⠶⠶⠄⠀⢀⣾⣿⣿⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡏⠁⢡⣿⣿⣿⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣸⣿⣿⣿⣧⣿⣿⡏⢉⣠⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⣿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠉⠿⠿⠿⠿⠗⠿⣿⣿⠿⠘⠟⠛⠻⢿⣿⣛⣛⣻⣿⣿⣽⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⣠⣿⣿⣿⣿⣧⣤⣀⣧⠟⣿⣿⣿⣧⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣤⣿⣠⣀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⣛⠉⠀⡿⣿⣿⣿⣿⠿⠟⠓⠂⠀⢴⣿⣿⣿⢿⣿⣷⣦⣾⣿⣿⣷⣶⣶⣦⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠸⣾⣿⡟⠀⠀⠀⠙⠿⠿⠏⣄⠀⠀⡄⠀⣾⣿⡿⠦⠀⣀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠇⠀⠀⠁⠀⠀⠀⠠⠈⢉⠛⠟⠛⠋⠛⠻⠿⠿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⢸⣿⢹⡆⠀⢉⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣂⠀⡶⠆⡔⡆⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⡇⠀⠈⠉⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡁⠀⢀⠀⣈⣀⣀⣀⠁⠀⡀⢂⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢹⡞⠀⠳⠒⣗⡒⠀⠪⠕⠚⠛⠏⠛⠃⠿⠏⠾⠻⠟⠃⠛⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣟⢿⢿⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣀⠀⢀⣼⣿⣿⣤⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣇⣁⣁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⡀⠀⣿⣿⣇⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣶⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣦⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⠀⣀⣀⣀⣀⠀⠀⠀⠀⠛⠃⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣇⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠼⠙⠛⠓⠈⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⡛⠻⠷⠶⠶⠄⠀⢀⣾⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡏⠉⢡⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣼⣿⣿⣿⣧⣿⣿⡏⢉⣠⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠉⠿⠿⠿⠿⠗⠿⣿⡿⠿⠘⠟⠛⠿⢿⣿⣛⣟⣻⣿⣿⣽⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣆⣤⣽⣿⣿⣷⣤⣄⢀⣷⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⣴⣶⣤⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣤⣟⣠⣤⣌⣿⣿⣿⣧⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⢿⣟⠁⠀⠀⡿⣿⣿⣿⡿⠿⠛⠂⠂⠀⢼⣿⣿⡿⢿⣿⣷⣦⣾⣿⣿⣶⣶⣶⣤⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⡤⢛⣿⣿⡇⠀⠀⠀⠻⠿⠿⠃⡄⠀⢠⠀⠀⣿⣿⠿⠦⠀⡄⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠂⠛⠀⠀⠆⠀⠀⠀⠀⠀⠀⠤⠉⢘⠛⠟⠉⠙⠛⠻⠿⠿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⣿⢻⠆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⡦⣖⣂⠀⡶⠆⡔⡄⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡄⠀⠘⠋⠁⠈⠈⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡁⠀⢀⠀⣈⣀⣀⣀⠁⠀⡀⢂⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢹⡞⠀⠳⠚⣗⡒⠀⠪⠵⠚⠚⠏⠛⠓⠿⠏⠾⠻⠟⠓⠛⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏⠻⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣠⣤⡀⢀⣼⣿⣿⣄⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡆⠀⣽⣿⣧⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣲⣿⣿⣿⣿⣿⣾⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⣠⣶⣀⣀⣀⣀⠀⠀⠀⠈⠛⢀⣀⣥⣤⣶⣶⣾⣿⣿⣿⣿⣅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣛⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣍⠙⠛⠓⠈⠀⠀⢀⣠⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⠛⠿⠿⠶⠦⠄⠀⢀⣾⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡏⠉⢡⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣼⣿⣿⣿⣧⣿⣿⡏⣉⣴⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠉⠿⠿⠿⠿⠿⠿⢿⣿⠿⢈⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣣⣤⣿⣿⣿⣦⠤⠤⢸⣞⣹⣿⣿⣿⡄⠀⠀⠀⠀⢀⣶⣶⣤⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣧⣤⣤⣤⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⡟⡀⢀⠀⠀⠸⢻⣿⣿⣿⡟⠛⠛⠓⠀⠀⣾⣿⣿⠿⣿⣷⣦⣠⣾⣿⣿⣶⣤⣄⣨⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠦⣿⣿⣿⠆⠀⠀⠀⠻⠿⠋⠠⡀⠀⢠⠀⠰⣿⡿⠿⠆⠠⡄⠀⣸⣿⣿⣿⣍⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠒⠂⠃⠰⠜⠂⠀⠀⠀⠀⠀⠀⠇⠈⠘⠛⠉⠉⠙⠛⠻⠿⠿⠟⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢙⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⡦⣖⣂⠀⡶⠆⡔⡄⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠛⠿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡁⠀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢂⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠗⢹⡞⠀⠳⠃⣟⡒⠀⠊⠑⠚⠚⠯⠿⠧⠿⠏⠿⠺⠟⠓⠛⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣗⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣝⡀⠀⠀⢀⣼⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡀⢀⣤⣦⣄⠀⣸⣿⣿⣿⣄⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡟⡬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⣰⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⠿⣀⣀⣀⣀⠀⠀⠀⠘⣠⣄⣀⣥⣤⣶⣶⣾⣾⣿⣿⣏⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣠⣄⣈⠉⠋⠙⠉⠀⠀⢠⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣍⣉⣉⣉⣉⣭⣴⡂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠿⢿⣿⣶⡦⠤⠀⠀⠉⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡏⠁⢂⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡏⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⣷⣿⣿⡏⣩⣴⣿⣿⠙⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠉⠿⠿⠿⠿⣷⣿⣿⣿⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢧⣶⣾⣿⡿⢿⠶⠤⠄⣿⠁⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣾⣷⣄⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣤⣤⣤⣴⣾⣿⣇⣴⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⠛⢻⣁⡀⠀⠀⠀⠏⢿⣿⣿⡿⠋⠉⠀⠀⠀⢀⣿⣿⡿⠿⣷⣶⣄⣴⣿⣿⣿⣦⣦⣄⣽⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⢾⣿⣿⡿⠀⠀⠀⠈⠛⠛⠁⢠⠀⠀⡆⠀⢸⣿⠿⠗⠀⢠⠀⢀⣿⣿⣿⣿⣽⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠛⠋⠀⠒⠛⠀⠀⠀⠀⠀⠀⠈⠄⠹⠟⠋⠉⠉⠙⠛⠻⠿⠻⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣂⠀⡶⠆⣔⡆⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⡟⢉⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡁⡀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢂⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⠃⠀⠹⠟⠋⠀⠸⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢹⣼⠀⠳⠇⣗⡒⠀⠊⠑⠚⠚⠯⠿⠧⠿⠇⠿⠺⠟⠃⠛⠟⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣑⣄⢀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠅⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⣤⣠⣰⣶⣶⣤⣀⣴⣿⣿⣿⣤⣀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⣀⣨⣤⣴⣶⣾⣿⣾⣿⣿⠛⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣤⣤⣼⣱⡶⠁⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢛⠻⠿⠿⠿⠿⠿⠿⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠻⠋⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡏⠋⢀⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣾⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣸⣿⣿⣿⣇⣿⣿⡏⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠿⠿⠇⠀⢠⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⠿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢧⣶⣾⣿⡿⠷⠶⠦⠄⣿⠃⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣾⣷⣄⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣤⣤⣤⣴⣾⣿⣇⣴⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⠛⢻⣁⡀⢀⠀⠀⠏⣿⣿⣿⡿⠉⠉⠀⠀⠀⢀⣿⣿⡿⠿⢿⣶⣄⣴⣿⣿⣿⣦⣦⣄⣽⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⢾⣿⣿⡟⠀⠀⠀⠈⠛⠋⠀⢠⠀⠀⡆⠀⢸⣿⠿⠧⠀⢠⠀⢀⣿⣿⣿⣯⣩⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠛⠋⠀⠒⠛⠀⠀⠀⠀⠀⠀⠘⠆⠸⠟⠋⠉⠉⠙⠛⠻⠿⠻⠫⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣂⠀⡶⠆⣔⡆⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⣿⣿⣿⠟⢋⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡁⡀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢂⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠅⠀⠹⠟⠉⠀⠸⢫⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠗⢹⣜⠀⠷⠇⣗⡒⠀⠊⠑⠒⠚⠯⠿⠧⠿⠇⠾⠺⠟⠃⠙⠟⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣀⡀⠀⠀⠀⠀⢀⣿⣟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠙⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⣤⣴⣰⣶⣶⣤⣀⣴⣿⣿⣿⣤⣀⡀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⣀⣨⣤⣴⣶⣾⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣤⣤⣼⣱⡶⠁⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⢛⠻⠿⠿⠿⠿⠿⠿⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠻⠋⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡏⠋⢀⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣾⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⣇⣿⣿⡏⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠿⠿⠇⠀⢠⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⣶⣿⢿⠻⠷⠖⠀⠠⣿⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⣶⣿⣷⡄⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣤⣴⣶⣶⣾⣿⣯⣤⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣛⣻⣧⣤⣀⠀⠀⠀⠛⣿⣿⣿⡏⠀⠈⠀⠀⠀⢸⣿⣿⠿⠿⢷⣦⣠⣴⣿⣿⣷⣶⣤⣄⣽⣿⣶⣶⣶⠖⣶⣏⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠉⣀⣆⠀⠀⡄⠀⢿⡿⠟⠂⠀⣦⢈⢹⣿⣿⣿⣏⡉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠋⠁⠐⠛⠁⠀⠀⠀⠀⠀⢀⡻⠀⠘⠛⠉⠉⠛⠛⠻⠻⠿⠛⠉⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣒⠀⡶⠆⣔⡆⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛⣾⣿⣿⠟⣉⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡁⡀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢂⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡠⣛⠏⠉⠀⠛⠉⢈⡻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢩⢼⠀⠷⠇⣟⡛⠀⠊⠑⠚⠛⠏⠛⠃⠿⠏⠾⠻⠟⠃⠛⠟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣏⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⣰⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣴⣿⣿⣿⣶⣄⡀⠀⣿⣿⣿⣯⣄⡀⠶⢷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣾⣿⣿⠛⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠠⣤⣄⣼⡟⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡛⠿⠿⠿⣿⣿⠿⠿⠟⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢻⠼⠿⢿⣿⣍⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⡏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠃⡀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⡇⣿⣿⡏⠉⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠛⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣟⡻⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣿⣿⡻⠿⠓⠀⠀⠸⣏⣈⣿⣿⣟⠀⠀⠀⠀⠀⢀⣾⣿⣷⡄⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣶⣶⣶⣶⣾⣿⣷⣴⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣿⣿⣧⣤⣠⠀⠀⠘⠙⣿⣿⣿⠇⠀⠁⠀⠀⠀⣸⣿⡿⠛⠿⠷⣦⣠⣼⣿⣿⣿⣶⣤⣤⣽⣷⣶⣶⣶⢶⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⢁⣀⣄⠀⢰⡀⠀⢿⠿⠛⠀⠀⣆⢀⢹⣿⣿⣿⣯⡉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⠋⠁⠀⠀⠀⠀⠀⢀⡻⠀⠘⠉⠉⠉⠛⠛⠻⠿⠟⠛⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⡦⣖⣒⠀⡶⠆⣔⡆⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢻⣿⣿⣿⠏⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡁⡀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢂⡀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⢰⣿⠟⠋⠀⠛⠉⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢩⢼⠀⠳⠧⣟⡛⠀⠊⠑⠚⠛⠏⠛⠓⠿⠏⠾⠻⠟⠃⠛⠟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢹⣿⣿⣿⣿⡛⠀⠀⠀⠀⣀⣤⣬⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣴⣿⣿⣿⣧⣄⡀⢀⣿⣿⣿⣧⣄⡀⠶⣮⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡷⣽⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⣀⣴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⡀⠁⠀⠀⠀⡠⠉⠁⠀⠀⠀⢀⣀⣤⣴⣶⣾⣽⣿⣿⣿⣿⡛⠻⠿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠾⢟⣀⣡⡆⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡟⡻⠿⠿⠿⠿⠿⠿⢛⡋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⣮⠿⣿⣷⣤⠒⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⣷⣾⡯⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡇⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠁⣸⣿⣿⣿⡇⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠿⠿⠇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⡤⣭⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⡻⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⡏⠉⠉⠀⠀⠀⡿⣄⣼⣿⣿⡀⠀⠀⠀⠀⠀⣸⣿⣿⣦⡀⠀⠀⠀⢀⣴⣆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣿⡿⣿⣷⣿⣅⣰⣷⣠⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣦⣤⡀⠀⠀⠁⢻⣿⣿⠇⠀⠀⠀⠀⠀⢀⣽⣿⡟⠻⣿⣷⡀⣤⣿⣿⣿⣧⡤⠄⢰⣿⣶⣶⡶⠶⣾⣿⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⢿⣿⣿⠇⠀⠀⠀⠀⠈⢀⣤⣴⠄⣀⣦⠀⠘⠿⠛⠃⠀⢸⠈⠀⣿⣿⣿⣄⠀⠀⠀⣽⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠠⣬⠇⢀⠋⠉⠉⠙⠛⠂⠈⠟⠋⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣶⠀⢤⡴⡦⡠⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣴⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣒⢀⡶⠆⣔⡆⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠄⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡁⡀⢀⠀⣈⣀⣀⣀⠁⠀⡀⢂⡀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣅⢀⢿⠟⠃⠙⠛⠉⠁⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢹⡜⠀⠳⠛⣟⣒⠀⠎⠵⠚⠛⠏⠛⠃⠿⠋⠾⠻⠗⠃⠛⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⡍⠀⠘⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣴⣿⣿⣿⣶⣤⠀⢠⣿⣿⣿⣯⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣟⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⠂⠀⠀⣠⣤⢤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄⢀⡠⠤⠂⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡶⠶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣰⡶⠿⠋⠀⠀⠀⣀⣡⣤⣶⣾⣿⣿⣿⣿⣿⣯⣭⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⢀⣉⣛⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣯⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⢳⣽⣿⣿⣦⡤⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠇⠁⢸⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⡇⣿⣿⣯⣿⣿⣿⣿⣿⣿⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⠿⠿⠿⠿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸⣿⣿⣿⣿⡟⠉⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⡟⠉⠉⠀⠀⠀⡿⣄⣼⣿⣿⡀⠀⠀⠀⠀⠀⣸⣿⣿⣦⡀⠀⠀⠀⢀⣴⣆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣿⢿⣏⣷⣿⡅⣰⣷⣠⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣤⣤⡀⠀⠀⠁⢻⣿⣿⠗⠀⠀⠀⠀⠀⢀⣽⣿⡟⠻⣿⣷⡄⣤⣿⣿⣿⣧⣤⠄⢠⣿⣶⣶⣶⠶⣾⣿⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⢿⣿⡿⠇⠀⠀⠀⠀⠈⢁⣤⣴⠄⣀⣦⠀⠘⠿⠛⠃⠀⢸⠈⠠⣿⣿⣿⣄⠀⠀⠀⣽⣿⣿⣧⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠠⣬⠇⢀⠋⠁⠉⠙⠛⠂⠈⠛⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣶⠀⢤⡤⢦⢄⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣴⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣒⠀⡶⠆⡔⡆⡆⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡀⠀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡁⠀⢀⠀⣈⣀⣀⣀⠁⠀⡀⢂⡀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣄⢠⡿⠛⠃⠙⠛⠉⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢹⡜⠀⠳⠛⣗⣒⠀⠎⠵⠚⠛⠏⠛⠓⠿⠋⠾⠻⠗⠃⠛⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡋⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⠁⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣴⣿⣿⣷⣶⣤⠀⢠⣿⣿⣿⣯⣤⣴⣧⣶⣶⣾⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣝⣿⣇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⠃⠀⠀⣠⣤⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡄⢀⡠⠤⠂⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⠶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣰⡶⠿⠋⠀⠀⠀⣀⣡⣤⣶⣾⣿⣿⣿⣿⣿⣯⣭⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⣩⣛⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠙⢳⣽⣿⣿⣦⡤⠲⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠃⡁⢸⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⠿⠿⠿⠿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠺⢿⣿⣿⣿⡟⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠉⠁⠀⠀⠀⠀⡿⣤⣾⣿⡏⣀⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀⠀⠀⠀⣠⣴⣆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠻⣛⣿⣿⣄⣰⣿⢠⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⣤⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⠟⠻⣿⣷⠀⣴⣿⣿⡿⡧⠤⠄⢰⣿⣶⣶⣶⣶⣾⣧⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⢿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣴⣷⢀⣀⣤⠀⠘⠟⠛⠁⠀⢰⠁⠤⣿⣿⣧⣀⠀⠀⢠⣿⣿⣿⣧⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠠⣼⠂⣀⠋⠁⠉⠙⠃⠀⠈⠛⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⡶⠀⣤⡴⢶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣒⠀⡶⠆⣔⡄⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡁⠀⢀⠀⣈⣀⣀⣀⠁⠀⡀⢀⡀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡦⣿⡿⠟⠁⠉⠙⠈⠉⠉⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠗⢹⡜⠀⠳⠛⣗⣒⠀⠎⠵⠚⠚⠏⠛⠃⠿⠏⠾⠻⠗⠃⠛⠛⠚⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠋⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣾⣿⣿⢷⣶⣤⠀⣠⣿⣿⣿⣯⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣟⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠤⠔⠂⠀⠀⣠⠶⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⠶⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡰⠞⠋⠀⠀⠀⠀⠀⣀⣥⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⡿⢿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣬⣍⣀⡸⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣽⣿⣿⣶⡊⣙⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡇⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⡀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⡇⣿⣿⡏⣿⣿⣿⣿⢿⣋⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠿⠿⠇⢿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⠿⠟⠿⠿⢿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠹⣿⣿⣤⣤⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⣇⠀⠀⠀⠀⠀⠘⢧⣤⣼⣿⡁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⡀⠀⠀⠀⣠⣴⣆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠛⣛⣿⣿⣄⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣦⣴⠀⠀⠈⠈⢿⣿⡿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠛⠿⣿⣶⠀⣴⣿⣿⡿⣦⡤⠀⣰⣿⣶⣶⣶⣶⣦⣤⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠛⢿⣿⠿⠀⠀⠀⠀⠀⠀⣤⣶⣷⣀⣀⡆⠀⠙⠟⠋⠀⠀⢠⠀⢴⣿⣿⣧⡀⠀⠀⢠⣿⣿⣿⣥⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⢠⡼⠂⠈⠋⠁⠉⠉⠀⠀⠈⠋⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣶⢠⣤⠴⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠋⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣒⠀⡶⠆⡔⡆⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡁⡀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢂⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⢿⣿⣿⣿⣿⡿⠟⠁⠉⠉⠛⠉⠉⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠗⢹⡞⠀⠳⠛⣟⡓⠀⠊⠵⠒⠚⠏⠛⠃⠿⠏⠾⠻⠗⠃⠙⠛⠚⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡿⠃⠀⠀⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⣿⣿⣿⣶⣶⣦⠀⣠⣿⣿⣿⣿⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠀⠸⣿⣿⣿⣿⣿⣿⣧⣼⣟⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠂⠀⠀⠠⠖⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⠶⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣡⣄⠀⠀⠀⠀⠀⢀⣀⣥⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣼⣟⣻⡠⢶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠿⣿⣿⣦⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⣿⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⣇⣿⣿⡏⢽⣿⣿⣿⣭⡿⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠘⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠿⠿⠇⠈⠻⢿⣿⣀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⠿⠞⠿⠿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣿⡄⠀⠀⠀⠀⠀⡟⣦⣴⣷⡄⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⢠⣴⣿⡄⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠿⣋⣁⣬⣿⣿⣠⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠹⠿⠿⣏⡀⠀⠀⠀⠀⢀⣾⣿⡟⠛⠻⠦⠄⢰⣿⣿⡿⠿⠦⡄⢀⣾⣿⣷⠶⠄⢠⣤⣄⠀⣠⣾⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠻⠿⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣶⠀⠈⠛⠉⠁⠀⠸⡇⠲⣿⣿⣿⣀⠀⠀⠀⣼⣿⣿⣅⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠐⢶⡏⠠⡝⠛⠛⠛⠀⣀⡀⠉⠉⠈⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠟⠀⠀⠀⠀⢹⡇⠰⠆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣒⠀⡶⠆⡔⡄⡆⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡁⡀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⣿⣿⡏⠉⠋⠀⠁⠙⠉⠉⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠗⢹⣾⠠⠷⠣⣟⡓⠀⠊⠑⠒⠚⠯⠛⠃⠿⠇⠾⠺⠗⠃⠘⠛⠚⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠋⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠠⣿⣿⣿⣿⠀⠀⠀⠀⠐⣀⣀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣨⣿⡳⣶⣿⣿⣿⣿⣿⣿⣆⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⣠⣾⡶⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣢⣄⠀⠀⠀⠀⠀⣀⣨⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣈⣝⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣼⠿⠉⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣶⣄⣠⣿⣿⣿⡿⠿⢋⣼⣿⢟⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⣿⣿⣿⣩⣿⣿⣿⣿⡶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⣧⣿⣿⡏⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢷⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠉⠿⠿⠿⠿⠇⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠿⠶⠿⠿⢿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣿⡄⠀⠀⠀⠀⠀⡟⣦⣴⣶⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⢠⣴⣯⡄⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠿⣋⣁⣤⣿⣿⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠹⠿⠿⣇⡀⠀⠀⠀⠀⢀⣾⣿⡟⠛⠻⠦⠄⢰⣿⣿⡿⠿⠦⠄⠀⣾⣿⣷⠶⢄⣠⣤⣄⡀⣠⣾⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣷⠀⠈⠛⠉⠁⠀⠸⡇⠲⣿⣿⣿⣄⠀⠀⠀⣼⣿⣿⣥⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠐⢶⡏⠠⡝⠛⠛⠛⠃⢀⡀⠉⠉⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠻⠀⠀⠀⠀⢹⡇⠰⡄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡢⡦⣖⣒⠀⡶⠆⡔⡆⡆⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡁⡀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢂⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⠉⠉⠉⠉⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠗⢹⣾⠠⠷⠧⣟⡓⠀⠊⠑⠒⠚⠯⠛⠃⠿⠇⠾⠺⠗⠃⠘⠛⠚⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⠋⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠠⣿⣿⣿⣿⠀⠀⠀⠀⢒⣀⣀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣨⣿⡳⣶⣿⣿⣿⣿⣿⣿⣆⣀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⣠⣶⠶⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣢⡄⠀⠀⠀⠀⠀⣀⣨⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣽⣟⣈⣝⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣼⡿⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣶⣤⣠⣿⣿⣿⡿⠿⢋⣼⣿⢟⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⣿⣿⣿⡨⣿⣿⣿⣿⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⣧⣿⣿⡏⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢾⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠉⠿⠿⠿⠿⠇⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠿⠓⠿⠿⢿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣧⡄⠀⠀⠀⠀⠀⡏⣦⣶⣶⡄⠀⠀⣀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⣠⣶⣯⡀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠿⣋⣡⣴⣿⣿⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⠿⠿⣃⡀⠀⠀⠀⠀⢠⣾⣿⡛⠛⢿⢦⡄⢰⣿⣿⠿⠷⠦⠄⢀⣿⣿⣷⡶⢤⣀⣤⣄⡀⣠⣾⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠛⠿⠛⠀⠀⠀⠀⠀⠀⢼⣿⣿⣷⣶⡷⠀⠈⠋⠉⠀⠀⢸⡆⠲⣿⣿⣷⡀⠀⠀⠀⣾⣿⣿⣅⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠐⢾⡏⠤⡟⠛⠋⠀⠀⣀⡀⠉⠉⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣠⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠟⠀⠀⠀⠀⢹⡇⢸⡆⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡦⣖⣒⢀⡶⠆⣔⡆⡆⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡁⡀⢀⠀⣈⡀⣀⣀⠁⠀⡀⢂⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠙⠛⠛⠛⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⢹⣾⠠⠷⠷⣟⡓⠀⠊⠑⠒⠚⠯⠛⠃⠿⠇⠾⠺⠗⠃⠘⠛⠚⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢠⣼⣿⣿⣿⠏⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠐⠂⣀⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⣻⣛⢶⣾⣿⣿⣿⣿⣿⣿⣄⣀⣮⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣄⠀⠀⠀⠀⣰⣾⠆⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣴⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢀⣀⣄⠀⠀⠀⠈⢀⣀⣬⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣼⠿⠉⠀⠀⢠⣴⣿⣿⣿⢟⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣷⣶⣤⣰⣿⣿⣿⠛⣡⣾⣿⣿⢏⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡇⠀⠀⣿⣿⣿⣀⣿⣿⣿⣿⡟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡏⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⣷⣿⣿⡏⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢾⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠉⠿⠿⠿⠿⠇⣼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠿⠟⠿⠿⠿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠻⠿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣦⣤⣿⣿⣶⣤⣤⣴⣿⠋⣴⣶⣾⣿⣿⣷⣶⣶⣰⣿⣿⣿⣿⣿⣿⡖⢾⣿⣷⣦⣤⠀⠸⣿⣶⣦⣤⡄⠹⣧⣀⣤⣤⣶⣿⣶⣿⣦⣴⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⠈⣿⣿⠛⡟⠀⠀⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⠿⠛⠿⠿⠿⠿⢿⣿⣿⠿⠭⠿⠿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣽⣿⠤⡰⠄⠀⠽⠿⣿⣿⡶⠷⠾⠿⠿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣷⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⢿⡟⣻⣿⣛⣛⣛⣹⣛⣿⣛⣿⢿⣟⠻⣿⣿⣿⣟⣛⣛⣻⣿⡟⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣭⣾⣧⣿⣿⣯⣭⣭⣿⣿⣿⣿⣛⣻⣯⣩⣾⣿⣷⣭⣭⣭⣽⣿⡏⢿⣿⣿⣿⡿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣿⣿⣷⣾⣿⣿⣾⣿⣶⣷⣶⣾⣿⣿⣿⣶⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠒⠻⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠋⠉⢿⣿⣿⣿⣷⠀⠀⠀⠀⢀⢥⣾⠩⠦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⣒⣈⣛⢉⡙⣉⣛⢿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠉⠉⠛⠛⠶⠄⢊⣉⡑⠀⠉⠉⣽⣷⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⢂⡉⡽⠥⣼⣿⣿⡟⢻⠛⣏⠀⠀⠀⣀⣠⣴⣾⣿⣿⠞⣷⣼⣿⣿⣿⣿⣿⣿⠀⠀⠠⠤⠴⡟⠛⠛⠛⠁⠀⠀⠈⠙⠻⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣤⣤⣤⣤⣄⣶⣶⡀⣴⣶⣦⢻⣿⣿⣿⡟⣿⣿⣦⣶⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⠹⣟⣿⣿⣄⣰⣶⣶⣦⣰⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣯⢻⣷⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⢻⣿⣿⡿⠓⢻⣿⣿⣿⣾⡿⠿⠿⣿⣿⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣉⣉⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⠃⠀⠀⣼⣿⣿⣿⣿⣋⣀⡾⣿⣿⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⣀⡈⠉⠻⠿⠿⠿⠿⣛⣛⠿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡿⣿⣿⢸⣿⣿⢹⣿⡏⢻⢷⣿⣿⣿⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⡟⣿⣧⢸⣿⡇⠀⣾⣿⢿⣿⡌⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣾⣿⣿⣿⣿⠁⡈⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⢿⣷⣦⡀⢸⣿⡇⠀⣿⣿⢸⣿⡇⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⣰⡇⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⠀⢰⣶⣏⣿⣿⢸⣿⣇⠀⣿⣿⢸⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠘⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⢿⣿⣷⠿⠿⠁⢿⣿⠿⠿⠟⠛⠛⠿⠿⠀⠀⠈⠻⠿⠿⠋⠀⠸⠿⠇⠸⠿⠟⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠇⠙⠿⠿⠛⢻⡿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠋⠁⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⣶⣶⣿⣷⣦⣤⣴⣶⣷⣤⣤⣶⣿⣿⣶⣶⣦⠀⢿⣿⣿⣿⣿⣿⡥⠰⣿⣦⣤⣄⠀⢘⣿⣶⣤⣤⡄⣿⣧⣤⣶⣶⣾⣿⣿⣿⣤⣴⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢻⣿⣿⣿⡿⠿⠛⠀⠀⢿⣿⠛⣿⠀⠀⣿⣿⣿⣿⡿⠻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣮⡿⠛⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠀⢀⣴⣿⣿⣿⣀⣀⣀⣀⣀⣿⣿⣴⣿⣇⠤⠽⢿⡿⠿⠧⠤⠽⠷⠲⠿⣿⣿⣿⣿⡟⠿⠛⠁⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠁⠀⠀⠀⠀⠀⣸⡟⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣤⣶⣤⣤⡀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣦⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣻⣿⡿⣻⣿⢛⣛⣛⣻⣛⣛⣛⣻⢿⡿⠛⣿⣿⣿⣟⣛⣛⣻⣿⡟⣿⣿⣾⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣭⣾⣧⣿⣿⣭⣭⣭⣽⣿⣛⣟⣛⣻⣮⣉⣼⣿⣷⣭⣭⣭⣽⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣾⣷⣶⣶⣶⣿⣷⣶⣷⣶⣾⣿⣿⣿⣶⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠤⣾⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢻⣿⣷⣶⣿⡄⠀⠦⠀⠄⣴⣦⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⠽⠾⠛⠿⠟⢿⣿⣿⣫⣝⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠛⠛⠒⠂⢉⠉⠀⠉⣽⣿⡿⠿⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠀⠒⣛⣂⣹⣿⣿⣿⣿⣯⡍⠉⠉⠉⠉⠉⣩⣽⣾⡿⠿⣦⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⢴⠶⠾⠿⠛⠀⠀⡰⠛⠻⡇⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣴⣶⣔⢰⣶⣶⡸⡟⣿⣿⣟⢿⣿⢃⡝⢉⣧⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⢻⣏⣿⣿⡄⣶⣷⣷⣄⣴⣶⣶⣶⣶⣽⣶⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣾⡇⢿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣷⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⣁⣀⣤⣴⣿⣿⣷⠆⠀⠐⠛⠚⠻⣿⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣃⣀⡶⠶⢶⡆⠀⢰⣶⣶⣶⣶⣴⣔⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⣛⡛⠛⠀⠀⠉⠉⠉⢉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡏⣿⣿⢿⣿⣿⢻⣿⡇⠀⢠⣿⣿⣿⡀⣿⣿⣿⣿⡏⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣿⡟⣿⣧⢸⣿⡇⠀⣾⣿⣿⣿⡄⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣼⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣧⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢿⣷⣦⡀⢸⣿⡇⢰⣿⣿⣾⣿⣷⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢹⣿⣿⡏⣿⣿⣿⠀⠶⣾⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⢰⣶⡏⣿⣿⠀⠀⣿⣿⣿⣿⡌⣿⡟⣿⣿⠉⣿⣿⢻⣿⡇⠀⢰⣶⡏⣿⣿⢸⣿⣇⡘⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠇⠿⠿⠿⠀⠀⠿⠿⠁⠿⢿⣿⡿⠇⠙⠛⠿⠿⠛⠃⠈⠻⠿⠿⠋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠛⠹⠿⠿⠇⠙⠿⠿⠟⢿⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⣶⣶⣿⣷⣦⣤⣴⣶⣷⣤⣴⣴⣿⣿⣶⣶⣦⠀⢿⣿⣿⣿⣿⣿⡥⠰⣿⣦⣤⣄⠀⠘⣿⣶⣤⣠⡄⣻⣦⣄⣶⣶⣾⣿⣿⣿⣤⣴⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⣿⡿⠿⠛⠀⠀⣿⣿⠛⣿⠀⠀⣿⣿⣿⣿⡏⠻⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣦⡿⠛⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⢻⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⠿⠯⠀⢀⣸⣿⣿⣟⣀⢀⣀⣀⣀⣽⣿⣴⣿⣧⠄⠽⢿⡿⠿⠧⠤⠽⠶⠲⠿⣿⣿⣿⣿⣿⠿⠛⠁⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠀⠠⠀⠀⠀⠀⢼⡗⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣤⣶⣤⣤⡀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣦⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣟⣻⣿⡿⣻⣿⢛⣛⣛⣻⣛⣛⣛⣻⢿⡿⠛⣿⣿⣿⣟⣛⣛⣻⣿⡟⣿⣿⣾⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣯⣭⣾⣧⣿⣿⣭⣭⣭⣽⣟⣛⣟⣛⣻⣮⣉⣼⣿⣷⣭⣭⣭⣽⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣾⣷⣶⣶⣶⣿⣷⣶⣷⣶⣾⣿⣿⣿⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠤⣾⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⣷⣶⣿⡄⠀⠦⠀⠀⣴⣦⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⠽⠾⠛⠻⠟⣿⣿⣿⣫⣍⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠛⠛⠛⠂⢉⠉⠀⠁⣽⣿⡿⠿⡃⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠀⠒⣛⣂⣹⣿⣿⣿⣿⣯⡍⠉⠉⠉⠉⠉⣩⣿⣾⡿⠿⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⢴⠶⠾⠿⠛⠀⠀⡰⠛⠻⡇⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣴⣶⣔⢰⣾⣶⡸⡟⣿⣿⣟⢿⣿⢃⡝⢉⣧⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⢻⣏⣿⣿⡄⣶⣿⣶⣄⣴⣶⣶⣶⣦⣽⣦⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⡇⢿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣧⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⣀⣤⣴⣾⣿⣷⠆⠀⠀⠛⠚⠛⣿⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣃⣀⡴⠶⢶⡆⠀⢰⣶⣶⣶⣦⣴⣶⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⣙⡛⠛⠀⠀⠉⠉⠉⢉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡏⣿⣿⢿⣿⣿⢻⣿⡇⠀⢠⣿⣿⣿⡀⣿⣿⣿⣿⡏⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣿⡟⣿⣧⢸⣿⡇⠀⣾⣿⣿⣿⡄⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣼⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣧⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢿⣷⣦⡀⢸⣿⡇⢰⣿⣿⣾⣿⣷⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢹⣿⣿⡏⣿⣿⣿⠀⠶⣾⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⢰⣶⡏⣿⣿⠀⠀⣿⣿⣿⣿⡼⣿⡟⣿⣿⠉⣿⣿⢻⣿⡇⠀⢰⣶⡏⣿⣿⢸⣿⣇⡘⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠘⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠇⠿⠿⠿⠀⠀⠿⠿⠁⠿⢿⣿⠿⠇⠘⠛⠿⠿⠛⠃⠈⠻⠿⠿⠋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠹⠿⠿⠇⠙⠿⠿⠟⢿⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣾⣿⣶⣿⣷⣦⣤⣶⣷⣷⣦⣦⣶⣿⣿⣷⣶⣦⠠⢿⣿⣿⣿⣿⣿⡥⢸⣿⣦⣤⣄⠀⢸⣿⣿⣤⣀⡀⣿⣧⠀⣰⣶⣾⣿⣿⣿⣦⣴⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⠉⢻⣿⣿⣿⣿⠿⠛⠀⠀⣿⣿⠟⣿⡀⠀⢿⣿⣿⣿⡿⢻⣿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⢀⣠⣿⣿⣅⣀⣀⣀⣀⣀⣹⣏⣀⣿⣇⠀⠸⣿⣿⠿⡧⠄⠽⠷⠶⠿⢿⣿⣿⣿⣟⣿⡟⠣⠴⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠧⣀⡀⠀⠀⠀⢸⡟⠀⠀⠺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣡⣶⣿⣿⣿⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣶⣦⣄⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣟⣻⣿⣿⣻⣿⣛⣛⣛⣻⣛⣛⣛⣻⢿⡿⠛⣿⣿⣿⣟⣛⣛⣻⣿⡟⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣯⣾⣯⣿⣿⣭⣭⣭⣽⣿⣛⣟⣛⣻⣮⣉⣼⣿⣷⣭⣭⣭⣽⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣾⣷⣶⣶⣶⣾⣷⣾⣷⣶⣾⣿⣿⣿⣶⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣤⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢿⣿⣷⣶⣾⡄⠀⠦⠀⠠⣼⣦⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠡⠖⠢⠭⠽⠿⠟⠿⢟⣿⣿⣿⢫⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠛⠛⠻⠽⠋⣉⠉⢉⡉⣭⣿⡿⠿⡧⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠊⢓⣒⣆⣙⣿⣿⣷⣿⣿⡟⠉⠉⠉⠉⠉⣉⣽⣾⡿⢿⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣴⠶⠾⢿⠛⠀⠈⡿⠛⠿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣴⣄⢰⣾⣷⡸⡟⣿⣿⣿⢿⣿⢏⡹⠉⣧⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⢻⣿⣿⣿⡍⣶⣿⣷⣄⣴⣶⣶⣶⣶⣿⣦⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣷⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣏⢿⣷⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠟⠛⠛⠛⠋⠛⢋⣹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣶⡶⠶⠿⠿⣷⠀⠀⠈⣿⣿⡿⠿⣿⣿⣿⣃⣀⡴⠶⠶⠶⠀⠀⣶⣶⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡉⠁⠀⠀⠉⠉⠉⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡎⣿⣿⢸⣿⣿⢸⣿⡇⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣿⡟⣿⣧⢸⣿⡇⠀⣾⣿⢿⣿⡄⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣼⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢿⣿⣯⡉⠙⠃⣿⣿⣿⣿⢻⣿⣿⣿⣿⢿⣿⣿⢿⣿⡇⠀⠘⢿⣷⣦⡀⢸⣿⡇⢸⣿⣿⣿⣿⣷⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢹⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣷⣶⡏⣿⣿⠀⠀⣿⣿⣾⣿⡈⣿⡟⣿⣿⠀⣿⣿⢸⣿⡇⠀⢰⣶⡏⣿⣿⣸⣿⣇⡸⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠇⠿⠿⠿⠀⠀⠿⠿⠛⢿⣿⣿⡿⠇⠈⠙⠿⠿⠙⣿⠉⠻⠿⠿⠋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠹⠿⠿⠇⠙⠿⠿⠛⠉⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣸⣷⣄⣠⣾⣶⣿⣧⣤⣀⣤⣿⣷⣶⣿⣿⣿⣿⣿⣿⣆⠨⢿⣿⣿⣿⣿⣿⡅⢸⣿⣷⣤⣀⠀⢹⣿⣿⣦⣀⡀⣿⡄⠀⣀⣠⣶⣿⣿⣿⣦⣼⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠈⠉⣯⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣗⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠁⠀⣀⣀⣿⣿⣿⣿⣟⣉⣉⣀⣀⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣯⣤⣿⣷⡾⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⠃⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠃⠀⣾⣿⣟⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣥⠘⠿⠟⠀⠀⠈⢿⣿⣦⣧⣴⠏⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣽⣿⡿⠿⣷⣾⣟⠉⠉⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠉⠉⠉⠀⠀⣿⣿⣿⣿⣶⣶⣶⣦⣤⣠⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣶⣶⣦⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣶⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠆⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢹⣿⣿⣿⣻⣿⣿⣻⣿⢿⣛⣛⣻⣛⣿⣛⣻⣿⣿⠿⣿⣿⣿⣿⣻⣿⣿⣿⡟⣿⣿⣾⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣯⣼⣿⣿⣿⣯⣭⣭⣽⣟⣛⣛⣓⣻⣯⣩⣿⣿⣿⣭⣭⣭⣽⣿⡍⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣷⣶⣾⣷⣾⣿⣿⣷⣶⣾⣿⣿⣿⣾⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⣀⣤⣼⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣷⣶⣾⡄⠰⠶⠇⢠⣴⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠼⢭⣝⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠒⠒⠶⣿⣭⠻⠟⣛⢯⣭⣿⣿⣿⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠷⠦⣒⣲⣲⣞⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⣻⣿⡟⠛⣏⣹⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣶⠾⠿⣿⠛⠈⢫⡿⣛⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣄⢰⣾⣿⡝⡟⣿⣿⣿⣿⣿⣿⣿⣿⣳⣄⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢻⣻⣿⣏⡍⣿⣿⣷⣄⣿⣶⣾⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⡋⢛⣿⣿⣷⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⠿⠛⠛⠛⠛⠋⢿⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠟⠿⠟⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⣀⣤⣼⣶⣤⣤⣤⠤⠤⠶⣦⠀⠀⠀⣿⣿⣿⠿⣿⣿⣇⣀⡆⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡁⠀⠀⠈⠉⠉⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢻⣿⣿⡿⢻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠺⠿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⢿⣿⡄⠀⢰⣿⡟⣿⣧⢸⣿⡇⠀⣾⣿⢿⣿⡄⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣾⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⠿⣿⣿⣯⡛⠃⠀⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⠘⢿⣷⣦⡀⢸⣿⡇⠀⣿⣿⣾⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣼⣿⣿⣿⣧⣿⣿⡏⠉⢾⣿⣿⣿⠏⢰⣶⡟⣿⣿⠀⠀⣿⣿⣾⣿⡀⣿⡟⣿⣿⠈⣿⣿⢹⣿⡇⠛⢲⣶⡟⣿⣿⣼⣿⣇⡘⣿⣿⣿⣿⡿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠇⠿⠿⠟⠀⠀⠿⠿⠛⠿⠿⠿⢿⠇⠀⠈⠿⠿⠁⠀⠈⠻⠿⠿⠋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠹⠿⠿⠇⠛⠿⠿⠛⠁⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⢰⣤⡄⢠⣼⣶⣿⣧⣄⣀⢸⣷⣶⣾⣿⣿⣿⣿⣿⣿⣆⠀⢺⣿⣿⣿⣿⣟⡆⢸⣿⣦⣄⡀⠀⢹⣿⣿⣤⣀⠀⣿⡄⠀⣀⣤⣶⣦⣿⣿⣦⣼⣧⣄⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⠿⠻⡿⠛⠙⢹⣿⣿⠿⣿⣿⡏⠀⠈⠙⣾⣿⣿⣿⣿⣿⣿⡅⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡗⢿⣷⠀⢿⣿⣿⣿⡟⠛⣿⣿⣿⣿⡖⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠓⠒⠲⠖⠠⠤⢼⠧⠀⠀⠽⠉⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣟⣀⣼⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣧⣬⣿⡦⠬⠿⣿⣿⡿⠾⢿⣿⣿⣿⣿⠂⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠙⠉⠉⠻⠃⠀⠀⠀⠀⢩⠯⠀⠽⠁⠀⠀⠘⢿⠆⠀⠺⠃⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣂⡀⠀⠀⡠⠌⠂⠀⠐⣿⡏⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣤⣀⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣤⣤⣤⣼⣿⣿⣶⣶⣦⣬⣤⠀⠀⡬⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣶⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠄⠀⠅⠀⠀⢠⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢹⣿⣿⣿⢻⣿⣿⣿⣿⢿⣿⣟⣻⣟⣿⣟⣻⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠠⣤⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣵⣟⣿⣿⣿⣿⣯⣽⣟⣛⣛⣒⣻⣯⣉⣽⣿⣿⣽⣭⣭⣿⣯⡍⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⢧⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣾⣷⣶⣷⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⢤⡄⠀⠀⠀⠀⠀⢀⠤⠤⠤⣤⣤⡼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣽⣷⣶⣾⡮⡿⡿⠁⣴⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⣩⣷⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠒⠶⠤⣤⣍⡙⠿⢿⣿⣿⣶⣶⣶⣶⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠯⠵⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⢛⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⢿⠿⠿⣿⠟⠙⢯⡟⣛⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣷⣀⣠⣤⣤⣤⣤⣤⣤⣤⣠⣦⣆⡀⣶⣶⡌⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡤⠀⠀⠀⠾⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⢟⣿⣿⣿⢿⣻⣿⣯⣍⣿⣿⣷⣬⣿⣷⣿⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣁⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⢩⣭⣍⣿⢠⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠛⠛⠻⠏⢿⣾⣿⣿⣿⣼⣿⣿⣿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠟⠛⠛⠛⠛⠛⠿⠟⠛⠿⠛⠛⠛⠿⠟⠛⠛⠛⠿⠻⣾⣿⣿⣿⣿⡇⠀⠀⣀⠀⡤⠾⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣷⡀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣤⣤⣤⣤⣤⠤⡤⠀⠀⠀⠙⠻⠿⢿⡿⢃⣀⡈⢿⡿⠿⠄⠈⠁⠀⢸⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⡀⠀⠀⠀⠀⠀⠀⢀⣀⠚⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡿⢿⢿⣿⣿⣿⠀⣿⣿⣿⣿⡆⣿⣿⢿⣿⢸⣿⡟⣿⣿⠄⠀⢸⣿⣿⡗⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣿⡟⣿⣧⢸⣿⡇⠀⣾⣿⣿⣿⣄⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣼⣿⠙⢿⣷⣦⡙⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠛⣿⣿⢿⣿⣧⣠⡘⢿⣷⣦⡀⢸⣿⡇⢠⣿⣿⢿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⣇⣿⣿⣿⡍⠀⣿⣿⣭⣥⣴⣶⣿⣿⣿⠀⠀⣿⣿⣾⣿⡀⣿⡟⣿⣿⠀⣿⣿⢸⣿⡇⠉⢻⣶⡿⣿⣿⣼⣿⣧⣿⣿⣿⣸⣿⡏⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠻⠿⠏⠁⠀⠿⠿⣩⣿⣽⣿⣿⡿⠋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠹⠿⠿⣿⠻⠿⢿⣟⠀⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠚⠛⠛⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⢰⣤⡄⢠⣼⣶⣿⣧⣄⣀⣼⣷⣶⣾⣿⣿⣿⣿⣿⣿⣆⠀⢺⣿⣿⣿⣿⣟⡆⢸⣿⣦⣀⡀⠀⢹⣿⣷⣄⣀⠀⣿⡄⠀⣀⣤⣶⣦⣿⣿⣤⣼⣧⣄⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⠟⠛⢹⣿⡿⠿⣿⣿⡋⠀⠈⠉⣺⣿⣿⣿⣿⣿⣿⡁⢘⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡗⢻⣷⠀⢿⣿⣿⣿⡏⠛⢿⣿⣿⣿⡖⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⠓⠒⠶⠖⠀⠤⢼⠯⠀⠀⠽⠉⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣫⣀⣸⣿⣿⣿⣿⣇⣀⣽⣿⣿⣿⣧⣬⣿⡦⠬⠿⣿⣿⠿⠿⢿⣿⣿⣿⣿⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠈⠀⠀⠀⠙⠉⠈⢻⠁⠀⠀⠀⠀⢩⠇⠀⠿⠀⠀⠀⠘⢿⠂⠀⠜⠃⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠸⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠁⠀⠀⠐⣿⡏⠀⠀⢐⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣤⣀⣠⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣤⣤⣼⣿⣿⣶⣶⣦⣤⣄⡀⠀⡅⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠠⡆⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢹⣿⣿⣿⢻⣿⣿⣿⣿⢿⣿⣟⣻⣟⣿⣟⣻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠠⡴⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣿⣯⣵⣟⣿⣿⣿⣿⣭⣽⣟⣛⣛⣒⣻⣯⣉⣽⣿⣿⣭⣭⣭⣿⣯⡍⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣾⣷⣷⣷⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢎⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⢀⠤⠤⠤⣤⣤⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣽⣷⣶⣾⣾⡿⡿⠁⣴⣶⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⣨⣷⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠶⠤⣤⣍⡙⠿⢿⣿⣿⣶⣶⣶⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠯⠵⣔⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⢛⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⢿⠿⠿⣿⠟⠙⢯⡟⣻⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⣤⣤⣤⣤⣤⣤⣤⣠⣤⣆⡀⣶⣷⡌⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡤⠀⠀⠀⠺⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⢟⣿⣿⣿⢿⣻⣿⣯⣍⣿⣿⣷⣬⣿⣶⣷⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣁⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⢩⣭⣍⣯⢀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠛⠛⠻⠋⢿⣾⣿⣿⣿⣼⣿⣿⣿⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠟⠛⠛⠛⠛⠻⠻⠟⠛⠿⠻⠛⠛⠿⠟⠛⠛⠛⠿⠻⣾⣿⣿⣿⣿⡇⠀⠀⣀⢀⡤⠾⢿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣷⡀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣤⣤⣤⠤⡤⠤⣄⠀⠀⠀⠛⠿⠿⢿⡿⢃⣀⡈⢿⡿⠿⠄⠈⠁⠀⢸⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⡀⠀⠀⠀⠀⠀⠀⢀⣐⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡿⢿⢿⣿⣿⣿⠀⣿⣿⣿⣿⡆⣿⣿⢿⣿⣸⣿⡟⣿⣿⠄⠀⢸⣿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⣿⡟⣿⣧⢸⣿⡇⠀⣾⣿⣿⣿⣄⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⢿⣿⣼⣿⣿⣾⣿⠁⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣼⣿⠙⢿⣷⣦⡙⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⠛⣿⣿⢿⣿⣧⣠⡘⢿⣷⣦⡀⢸⣿⡇⢠⣿⣿⢿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⣇⣿⣿⣿⡍⠀⣿⣿⣭⣥⣴⣶⣿⣿⣿⠀⠀⣿⣿⣾⣿⡀⣿⡟⣿⣿⠀⣿⣿⢸⣿⡇⠉⢳⣶⡿⣿⣿⣼⣿⣧⣿⣿⣿⣸⣿⡏⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠻⠿⠏⠁⠀⠿⠿⣩⣿⣿⣿⣿⡿⠋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⣿⠻⠿⢿⣟⠀⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠚⠛⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⣀⣠⣿⣧⣀⡀⠀⠀⡄⣠⣄⠀⠀⡿⠿⢿⣄⢀⣰⣿⣿⣿⣿⣧⡀⢰⣿⣦⣀⡀⠀⢺⣇⣤⣄⠀⠀⣶⠀⠀⣀⣠⣤⡄⠈⢻⣤⣤⣄⠀⠀⠀⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣶⣦⣿⣀⣰⣿⡿⠛⠛⢿⡏⢼⣿⣿⡿⠋⠉⠃⠀⠀⠀⠉⠲⣾⣿⣿⣿⣿⠷⠁⠀⣿⠟⢻⣷⠀⠀⣿⣿⣿⣿⡄⣻⣧⠀⣿⣿⣿⣿⡄⠀⠉⣿⣿⣿⣷⣠⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⣿⣿⣿⠻⠛⠂⠀⠠⠦⠤⠦⠽⠿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣹⣿⣟⡉⠁⠀⠀⢀⣿⣆⢘⣿⣀⠀⣻⣿⣿⣿⣧⣿⣿⡤⠼⢿⣿⣿⡿⣶⣾⣿⣿⣿⣿⣿⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠈⢿⣆⠀⠀⣿⣟⠋⠙⠻⣿⣿⣿⡏⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠀⠀⣼⣿⠖⠀⠀⢼⣿⣿⡇⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⣿⣶⣶⣿⣯⡄⠀⢀⣿⣿⠟⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⢿⡿⣿⢟⣿⠿⡿⠿⣻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣻⣵⣿⣿⣿⣿⣯⣭⣽⣟⣛⣛⣓⣻⣯⣫⣽⣿⣯⣽⣿⣿⣿⣭⡍⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢼⣿⣟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣿⣿⣯⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠈⣈⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣷⣾⣶⣶⡚⣿⣿⣿⣽⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠦⢬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠦⠤⢤⣀⡘⠛⠿⢿⣿⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠯⠽⣶⣻⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⠿⠿⠿⠟⣻⡟⠿⠿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡈⢿⠿⢿⡿⠟⠛⣿⠟⡻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣷⣦⣠⣤⣀⣶⣦⡂⠰⠒⠀⠙⢻⣿⣿⣿⣿⣿⣫⣽⣷⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⡟⣿⣿⣿⣯⢹⣿⣿⣯⣹⣷⣿⣶⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡀⠘⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢻⣿⣷⣿⠡⠿⠿⠿⣬⣿⣿⣿⣿⣿⣿⣿⣍⣩⣽⢿⡿⠟⠻⠟⣿⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡄⠘⠿⣿⡟⠉⠉⠉⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠸⢿⣿⣿⠆⠀⠀⠀⠘⠻⠿⠿⣿⣿⡿⠿⢿⣿⣿⣿⠇⣤⣶⣶⣶⣬⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣟⡀⠀⢿⠃⠀⢸⠛⠛⠛⠻⣏⣀⣠⣤⣴⣶⠀⠀⢤⣤⠀⠀⠀⠀⠀⢠⢤⣀⣸⣿⣿⣿⠀⠈⠙⠻⠇⢾⣿⣿⣿⣿⣿⣿⣿⣿⡈⠉⠙⠻⣿⡿⠟⠿⠿⠿⢿⣿⣿⣿⠟⠿⠁⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⣿⣿⣧⣿⣿⣸⣿⣿⢸⣿⡇⠈⢻⣿⣿⣿⡁⣿⣿⣿⣿⡆⣿⣿⣿⣷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣷⣄⢰⣿⡟⣿⣧⢸⣿⡇⢀⣿⣿⣿⣿⣾⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⠀⣿⣿⢹⣿⡿⢿⣿⣿⣷⣦⡀⢸⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢹⣿⣿⡟⣿⣿⣿⠹⡷⣾⣿⣿⣿⣇⣿⣿⡏⠉⠂⣿⣿⣭⣿⣿⣿⣿⣿⣿⠙⠃⣿⣿⣾⣿⡄⣿⡟⣿⣿⠀⣿⣿⢸⣿⡇⠀⢰⣶⡟⣿⣿⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠇⠿⠿⠿⠀⠀⠿⠿⠉⠿⠿⠻⠿⠇⡀⠀⠿⠿⠹⣿⣿⣿⣿⣿⣯⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠇⠙⠿⠿⠛⠉⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡏⠀⠀⠀⠀⠉⠓⠿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣄⠀⠀⠀⣠⣿⣧⣀⡀⠀⠀⠠⢀⣀⠀⠀⢿⠿⣿⣆⠀⣴⣿⣿⣿⣿⣧⡀⢰⣷⣤⣀⡀⠀⢺⣇⣤⣤⠀⠠⣶⠀⠀⢀⣀⣤⡄⠀⠀⣀⣀⣀⠀⢰⡿⣮⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⣛⢀⣀⣾⡿⠛⠛⢿⠛⣸⣶⣿⠟⠋⠙⠃⠀⠀⠀⠉⢐⣾⣿⣿⣿⣿⡿⠁⠀⣿⠟⠻⡇⠀⠀⣿⣿⣿⣿⠀⣿⡀⠀⣿⣿⣿⣷⠀⠀⠈⣹⣿⣿⣿⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⣿⣿⣿⡟⠻⠛⠀⠠⠤⠦⠤⠬⠽⠯⠀⠀⢀⣀⣀⠀⠀⡀⠀⣹⣿⣏⠉⠁⠀⠀⢀⣿⡄⠀⣃⠀⠀⣙⣋⣈⣿⣧⣼⣧⠤⠬⢿⣿⣿⣿⣷⣶⢿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡄⠀⠈⣿⣿⣿⠿⠟⠴⣿⣿⣿⢟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⠇⠀⠀⣸⣿⣿⣧⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣷⣶⣶⣾⣯⡀⠀⢀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠴⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢼⣿⣿⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⡿⣿⢟⣿⠿⡿⠿⢻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⢸⢛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣻⣥⣿⣿⣿⣿⣿⣭⣽⣟⣛⣛⣓⣻⣯⣫⣽⣿⣯⣽⣿⣿⣿⣭⡝⣯⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣿⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣷⣶⣶⣦⠐⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠽⣭⣽⣽⣻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠤⠤⣄⣀⡘⠻⠿⠿⣷⣶⣾⣿⣿⣿⠇⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠯⠽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢛⡏⠿⡿⣿⣿⣿⣿⣿⣇⣁⣀⣀⣈⢽⠿⢿⡿⠏⠘⣯⢟⡛⢟⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣦⣤⡀⣴⣶⣦⣿⣿⣿⡟⠿⣿⣿⣫⣿⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⢟⣿⣿⡟⣿⣿⣿⣯⢹⣿⣿⣯⣹⣿⣾⣦⣤⣤⣤⣼⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠃⠁⠀⢀⣿⢃⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⢿⣿⣿⢿⣿⣿⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢰⣿⣿⡏⠉⢉⣛⣛⣛⣿⣿⣿⣷⣶⣶⣦⠄⠀⣾⠟⠚⠛⢿⣿⣷⣿⣿⣿⣿⣿⡿⠳⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢟⣉⣴⣿⡿⠿⡏⠀⣾⡟⠛⠿⢿⣿⣿⣿⣿⣿⣷⠆⠀⣤⠀⠀⠀⠀⠉⠛⢿⣿⡟⠹⣿⣿⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⣿⣿⣿⣿⣿⣸⣿⣿⢸⣿⣧⠀⢹⣿⣿⣿⡛⣿⣿⣿⣿⡆⣿⣿⢿⣷⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣧⢸⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣷⣿⣿⣿⣿⡇⣿⣿⣾⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⣿⣿⢻⣿⡟⠉⠙⢿⣿⣿⣥⣸⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢹⣿⡇⢹⣿⣿⡟⣿⣿⣿⠙⠋⣿⣿⣿⣿⡏⣿⣿⣿⣿⡟⣿⣿⠉⣡⣶⣶⣯⣿⣿⠙⢻⣿⣿⣾⣿⣼⣿⡟⣿⣿⠀⣿⣿⢸⣿⡇⠀⢰⣶⡏⣿⣿⢸⣿⣇⡀⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠇⠿⠿⠿⠀⠀⠿⠿⠉⠿⠿⠿⠿⠟⢿⠇⠿⠿⠈⣯⣝⣿⣿⣿⣯⡄⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠏⠛⠿⠿⠿⠟⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠁⠚⠝⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣦⡀⠀⠀⠀⠠⢀⣀⠀⠀⢻⠿⢿⣆⠀⣼⣿⣿⣿⣿⡦⠀⢰⣷⣤⣄⠀⠀⢲⡆⣠⣄⠀⠠⣶⠀⠀⢀⢀⣤⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡄⠀⢀⢀⣠⠖⠛⠛⢻⠟⢰⣦⡶⠘⠋⠘⠂⠀⠀⠀⠙⠐⣿⣿⣿⣿⣿⡿⠂⠀⠿⠛⠛⡇⠀⠀⣿⠟⠿⣷⠀⣿⡆⠀⢿⣿⣿⣇⠀⠀⠀⠀⡇⣠⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⢰⣾⣇⠐⠚⠚⠓⠀⠠⠤⠤⠤⠤⠤⠅⠀⠀⢀⣀⣄⡀⠀⠀⠀⣻⣿⡛⠉⠁⠀⠀⢀⣷⠀⠀⠀⠀⠀⢁⣀⠀⣟⡠⢼⣧⠀⠨⣿⣿⡶⠤⠤⠀⠒⢃⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣤⣤⣤⣤⣇⡀⠒⣶⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣄⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⡿⣿⢟⣿⠿⠿⠿⢻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠀⠀⣠⡈⠀⠉⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣥⣟⣸⣿⣿⣟⣋⣽⣟⣛⣛⣓⣺⣏⣋⣽⣿⣯⣽⣿⣿⣿⣭⡉⣯⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣷⣥⣾⣿⣿⣿⣼⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⡿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣶⣶⣶⣦⠐⠗⠀⣴⣂⡖⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠯⠤⣬⣙⣇⠿⠻⠿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢄⣀⣀⣀⡘⠭⠥⠿⣟⣠⣤⠤⢵⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠽⢆⣈⣙⣿⣿⣿⣿⣿⣿⣿⡿⣟⠻⠿⠿⠿⠿⠿⠿⢿⢻⣿⣿⣿⣿⣿⣿⣁⣀⣀⣀⣉⣿⠿⢿⡿⠂⠀⠈⠄⠛⠟⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣀⢰⣶⣦⢰⡞⣿⣿⣿⣿⣿⢻⣶⣿⣽⣿⣿⣶⣶⣶⣶⣶⣾⣿⣷⣶⣼⣿⣿⣿⣿⢗⣾⣿⡞⡿⣽⣿⣯⢹⣶⣿⣧⣸⣶⣶⣶⣿⡿⢿⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠆⢀⣤⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⠙⠻⠏⢀⣼⣿⣷⣿⠻⠿⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣋⣡⣶⣿⣿⣿⡿⠋⠙⠛⠛⠉⠛⢻⣿⣿⣿⣿⣿⣿⡅⠀⠀⠙⠛⢻⣿⣏⣀⡰⠂⢈⠛⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣟⠿⠿⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡇⢈⣿⣿⣿⣿⣶⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣼⣿⠻⢿⣿⣿⡛⢻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠉⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⣻⣿⡏⢻⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⡏⣿⣿⣯⣿⣿⣿⣿⠉⠁⢰⣶⡏⣿⣿⠛⠻⣿⣿⣿⣿⣼⣿⡿⣿⣿⠀⣿⣿⢸⣿⡏⠙⢻⣿⣿⣿⣿⣿⣿⣇⡀⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠘⠿⠇⠘⣿⡿⠟⠁⠸⠿⠿⠇⠿⠿⠿⠀⠀⠿⢿⠛⠿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠘⠻⠿⢿⣯⣄⡸⠿⠇⠸⠿⠏⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠛⠻⠿⠿⠇⣻⡿⠿⠟⠁⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣦⡀⠀⠀⠀⠠⢀⣀⠀⠀⢻⠿⢿⣄⠀⣼⣿⣿⣿⣿⡦⠀⢰⣷⣤⣄⠀⠀⢲⡆⣠⣄⠀⠠⣶⠀⠀⢀⢀⣤⠀⠀⠀⠀⠀⡀⠀⢐⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⢤⡄⠀⢀⠀⣠⠖⠛⠛⠻⠟⣰⣦⡶⠚⠋⠘⠂⠀⠀⠀⠙⠐⣽⣿⣿⣿⣿⡿⠂⠀⠿⠛⠛⡇⠀⠀⣿⠟⠿⣶⠀⣻⡄⠀⣿⣿⣿⣇⠀⠀⠀⠀⡇⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢰⣿⣇⠐⠚⠚⠛⠀⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⣀⣂⡀⠀⠀⠀⣹⣿⣋⠉⠁⠀⠀⢀⣖⠀⠀⠀⠀⠀⢁⣀⠀⣻⡄⢽⣧⠀⠨⣿⣿⣶⠤⠤⠀⠒⢃⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣭⣆⡀⠒⢶⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡛⢿⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⡿⣿⢟⣿⠿⠿⠿⢻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏⠀⠀⣠⡌⠁⠉⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣥⣿⣸⣿⣿⣟⣫⣽⣟⣛⣛⣓⣺⣏⣋⣽⣿⣯⣽⣿⣿⣿⣭⡉⣯⣽⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣷⣷⣧⣾⣿⣿⣿⣼⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣷⣶⣶⣦⠐⠗⠀⣤⣒⡔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠯⠥⣭⣙⣇⠿⠻⠿⢟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢄⣀⣀⣀⡘⠭⠭⠿⣟⣠⣤⠤⠽⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠽⢆⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠿⠿⠿⠿⠿⢿⢻⣿⣿⣿⣿⣿⣿⣁⣀⣀⣀⣉⢿⠿⢿⡿⠂⠀⠈⠄⠛⠟⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣀⢰⣶⣦⢸⠟⣿⣿⣟⣿⣿⢻⣶⣿⣽⣿⣿⣶⣶⣶⣶⣶⣾⣿⣷⣶⣼⣿⣿⣿⣿⢗⣾⣿⡟⡿⣽⣿⣯⢱⣾⣿⣧⣸⣶⣶⣶⣿⡿⢿⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠆⢀⣤⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⠉⠻⠋⢀⣼⣿⣷⣿⠻⠿⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣋⣡⣶⣿⣿⣿⡿⠋⠘⠛⠛⠉⠙⢻⣿⣿⣿⣿⣿⣿⡅⠀⠀⠙⠛⢻⣿⣏⣀⡰⠂⠈⠙⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣟⠛⠿⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡇⢀⣿⣿⣿⣿⣶⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⡇⣿⣿⣼⣿⠻⢿⣿⣿⡛⢻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠉⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢿⣿⡏⢹⣿⣿⡏⣿⣿⣿⠀⠀⣸⣿⣿⣿⡏⣿⣿⣯⣿⣿⣿⣿⠉⠁⢰⣶⡏⣿⣿⠛⠻⣿⣿⣾⣿⣼⣿⡿⣿⣿⠀⣿⣿⢸⣿⡏⠙⢻⣿⣿⣿⣿⣿⣿⣇⡀⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠘⠿⠇⠘⣿⡿⠟⠁⠸⠿⠿⠇⠿⠿⠿⠀⠀⠿⢿⠛⠿⣿⣿⣿⣿⣿⡿⠿⠿⠀⠀⠘⠻⠿⠿⣯⣄⡸⠿⠇⠸⠿⠗⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠛⠻⠿⠿⠇⣻⡿⠿⠟⠁⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠀⠀⠀⠀⠠⢀⣀⠀⠀⢻⠿⢿⣆⠀⢼⣿⣿⣿⣿⡦⠀⢰⣷⣤⣄⠀⠀⢶⡆⣠⣄⠀⠠⣶⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡀⠀⠀⣿⣷⣿⣧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⢀⡀⠀⠀⠀⣀⠄⠛⠛⢻⡟⢤⣤⡶⠘⠋⠐⠂⠀⠀⠀⠛⢐⣽⣿⣿⣿⣿⡿⠂⠀⠿⠟⠛⡇⠀⠀⢿⠟⠿⣶⠀⣿⡆⠀⣿⣿⣿⡇⠀⠀⠀⠀⡇⣠⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢰⣿⣇⠐⠚⠺⠗⠀⠤⠤⠤⠤⠤⠄⠁⠀⠀⢀⣀⣆⠀⠀⠀⠀⣻⣿⡛⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⣋⡀⣽⣧⠀⠨⣿⣿⠥⠤⠄⠀⠀⠃⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣥⡐⠒⢲⣿⠋⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣦⣄⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢿⣿⣿⡿⣿⠿⠿⠿⢻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⠋⠀⠀⣤⡌⠀⠀⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣚⣣⣿⣸⣿⣿⣛⣋⣽⣟⣛⣛⣛⣺⣏⣊⣽⣿⣯⣝⣿⣿⣿⣭⡙⣯⣽⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠁⠁⠈⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣷⣧⣾⣥⣾⣿⣿⣿⣼⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣶⣦⣶⣤⠀⠶⠀⣄⡠⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠭⠭⣝⣓⣃⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣀⣀⣀⠘⠭⠭⠿⣟⢠⣤⠤⠬⣤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠶⢆⣈⣙⣻⣿⣿⣿⣿⣿⣿⡿⣟⡛⠿⠿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣀⣉⣿⠿⢿⡿⠂⠀⠀⠄⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣄⣤⣤⣐⢰⣶⣶⢰⡞⣿⣶⣾⣿⣿⢯⣷⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣿⣶⣦⣼⣿⣿⣿⣿⢗⣾⣿⡞⡿⣽⣿⣯⢱⣶⣿⣆⣸⣶⣶⣶⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⠀⢀⣀⣴⣿⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⣿⣾⣇⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⢿⡟⠉⢸⣿⣷⣿⠻⠿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⠋⣠⣾⣿⣿⣿⡿⠛⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠿⠿⣿⣏⣀⡈⠛⠛⠉⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣟⠻⠿⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡟⠛⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⢿⣷⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⡟⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⢸⣿⡇⢀⣿⣿⣿⣿⣶⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣗⣿⣿⣿⣿⡟⣿⣿⣼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢻⣿⡇⢹⣿⣿⡟⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣏⣥⣄⣿⣿⠉⠁⢹⣶⡏⣿⣿⠀⢿⣿⣿⣿⣿⣼⣿⡿⣿⣿⠀⣿⣿⢸⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣇⡈⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠘⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠇⠿⠿⠿⠀⠀⠿⢿⡟⠿⢿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠈⠿⠿⠿⣋⣀⡸⠿⠇⠸⠿⠟⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠻⠻⠿⠿⠇⣹⠿⠿⠟⠁⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⢀⣀⠀⠀⢹⠿⢿⡄⠀⢠⣾⣿⣿⣷⡄⠀⢰⣷⣤⡄⠀⠀⢶⡆⣀⣀⠀⠠⡆⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⢨⠀⠀⠀⠀⠀⢀⠀⣀⡤⠛⠿⢿⡿⢀⢤⣾⠛⠛⠐⠂⠀⠀⠈⠛⢐⣼⣿⣿⣿⣿⣿⠃⠈⡿⠛⠛⡇⠀⠈⠳⠟⠿⣶⣤⣿⡄⠐⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢰⣾⣇⠐⠘⢶⡿⠤⠤⠤⠬⠥⠀⠀⣀⠀⠀⢀⣀⣀⠀⠀⠀⠘⣿⣿⡛⠋⠉⠀⠀⠀⣇⠀⠀⠃⠀⠀⢀⠀⠀⣙⢉⣿⣧⡀⢹⣿⣿⡿⠿⠦⠤⠀⢀⣴⡶⢸⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⢀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⢀⣼⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⠀⠀⠀⣼⣿⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣬⣏⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠁⠁⠀⠀⠠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⣄⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⢰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⠉⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠭⢟⣿⢩⣿⣖⣒⣒⣺⣟⣛⣛⣛⣺⣍⣚⣽⣿⣯⣛⣛⣛⣿⣭⡹⣭⣽⣿⣿⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⠏⠉⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣷⣧⣾⣭⣽⣿⣿⣿⣼⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣦⣤⣤⣤⡰⠗⠀⣀⣤⡔⠋⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠬⠭⢘⣛⣻⡸⠿⠿⡿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⢙⣛⣿⣿⢥⣤⠤⠯⣷⠒⠝⠓⠚⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⢶⣈⣙⣿⣓⣻⣿⣿⣿⠿⣿⣿⣟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣈⠉⠉⢉⡿⠿⢶⡾⠀⠀⣉⠜⠛⡟⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⡄⠀⠠⣤⣄⣠⣤⣐⢠⣶⣶⡰⡖⣷⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣶⣤⣤⣤⣤⣴⣦⣝⣙⣿⣿⣿⣿⢃⣿⣿⡟⣟⣿⣿⡏⣿⣿⣿⣅⣿⣶⣶⣶⣶⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡋⠁⠀⠀⢀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣾⢏⣾⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣷⣿⠿⠿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠃⣼⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡈⠉⠁⠰⠿⢿⣿⣟⣀⡸⠿⠿⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠿⢻⣿⣛⠓⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⣦⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⢿⣷⣿⣿⣿⣿⣧⣤⣀⣸⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣧⢸⣿⡇⠀⣿⣿⣿⣿⣤⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢸⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⢿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠙⠁⣾⣿⣿⣿⣿⣿⣿⡏⠉⠈⣿⣿⠉⠙⢻⣿⡟⣿⣿⠀⢸⣿⣿⣿⣿⣼⣿⡿⣿⣿⡂⣿⣿⢸⣿⡟⠻⣿⣿⣿⣿⣿⢼⣿⣇⠙⣿⣿⣿⣿⡏⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠘⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠇⠿⠿⠟⠀⠀⠿⠿⢁⡿⠿⠻⢿⣧⣤⣤⠿⠿⠀⠀⠈⠻⠿⠿⠋⠀⠸⠿⠇⠸⠿⠏⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠟⠻⠿⠿⠟⠁⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⡀⠀⠀⠀⢀⢀⣀⠀⠀⢸⡿⣷⡄⠀⣀⣾⣷⣿⣷⣂⡀⢠⣷⣤⡀⠀⠀⢶⡆⣀⣀⠀⢠⡤⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣴⣄⠀⠀⠀⠀⠀⢀⠀⣠⣿⠿⠿⢿⡿⢤⣤⣾⠛⠛⢰⠖⠺⠃⠈⣿⣤⣼⣿⣿⣿⣿⣿⠆⠘⣿⠿⢻⡇⠀⠘⣷⠿⣿⣶⣰⣿⣶⣶⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁⢠⣾⣇⠀⠾⣿⣿⡥⠤⠤⢼⠡⢈⠁⣙⡀⡀⣸⣀⣰⡀⢀⣀⢻⣿⣿⣟⠿⠋⠁⠀⠀⣿⠀⠀⠁⠀⠀⢈⡀⠀⣛⢉⣻⣯⣁⣿⣿⣿⡿⠿⠷⠤⠄⢀⣾⡦⢐⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣷⣴⣾⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠁⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡀⠀⠀⠀⠀⡞⠉⣿⣿⠋⢨⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠠⣿⣿⣧⣾⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣤⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠛⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣠⣤⣀⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⢿⣿⠿⢽⣟⣚⣽⣿⣯⣛⣛⣛⣿⣭⢹⣭⣿⣟⣿⢽⣿⣿⣿⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣯⣭⣭⣭⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠠⡄⣀⣼⣿⣿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⠿⠃⠀⠀⠀⠀⠘⠀⠀⠄⠀⠀⢁⡠⠤⠬⠟⣃⣶⣾⠿⢿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡗⠀⠈⠉⠉⠃⠀⠉⠉⣃⣀⣩⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠾⠿⠿⢿⣉⣐⣲⣿⢺⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⠋⠒⠒⠲⠢⣶⣶⣿⡍⠒⠈⣻⣿⢿⣿⡟⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣷⡖⠀⠀⠀⣤⣤⣤⣤⣤⣤⣠⣤⣄⢠⣶⣶⡄⡶⣿⣿⣿⢿⣿⣿⣿⣷⣻⣿⣿⣷⣦⣀⣀⣈⣉⣉⣏⠻⠿⣿⣿⣿⣿⢳⣿⣿⢿⣿⣿⣿⡏⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⢏⣾⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠈⣿⣿⣾⣿⣿⣿⣷⣿⠿⠿⣿⠿⠛⣿⣿⣿⣿⠁⠀⠉⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡀⢿⣿⣿⢿⣿⡖⠀⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣽⣿⠛⠛⠛⢿⣿⣯⣁⡶⠓⠐⠒⠀⣸⡿⠃⢀⣾⣿⣿⣶⣶⡄⠉⠙⠻⠿⣿⡏⠉⣉⡛⠛⠛⠉⠉⠋⠛⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⣿⣿⡇⣿⣿⢿⣿⣿⢸⣿⡿⠿⢹⣿⣿⣿⣴⣿⣿⣿⣿⡆⣿⣿⢻⣿⣿⣿⡿⣿⣧⢀⣤⣸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢱⣿⡟⣿⣧⢸⣿⡇⢀⣾⣿⣿⣿⣤⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣾⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣧⣿⣿⣿⣿⣧⣿⣿⣼⣿⠻⢿⣿⣯⣿⣿⡟⣿⣿⣿⣿⢸⣿⣿⣿⣿⠛⣿⣿⢿⣿⣿⣷⣾⣿⣷⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣏⠉⣿⣿⣿⠙⠃⢰⣶⡏⣿⣿⠿⢃⣿⣿⣾⣿⣼⣿⡿⣿⣿⠀⣿⣿⢸⣿⡏⠙⢻⣷⡏⣿⣿⢸⣿⣟⡻⣿⣿⣿⣿⡇⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠻⣿⡿⠿⠿⠏⣀⣾⠿⠿⠀⡴⠾⣿⣿⣿⡋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠟⠛⠿⠿⠛⠀⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡟⠀⢀⡀⠀⠀⠀⠘⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⡀⠀⠀⠀⢀⢀⣀⠀⠀⢸⡿⣿⡄⠀⣀⣾⣿⣿⣷⣂⠀⢠⣷⣤⡀⠀⠀⢶⡆⣀⡀⠀⢠⡤⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣤⣄⠀⠀⠀⠀⠀⢀⠀⣠⣿⡿⠿⢿⡟⣦⣶⣾⠟⠛⢰⡖⠾⠂⠐⢿⣤⣼⣿⣿⣿⣿⣿⠆⠘⣿⠿⢻⡇⠀⠘⣷⠿⣿⣶⣴⣿⣿⣶⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁⢠⣾⣇⠀⠸⣿⣿⡧⠤⠤⢼⠥⢈⠉⣉⣀⡀⣸⣄⣺⡀⠀⣘⢻⣿⣿⣟⠿⠋⠁⠀⠀⣿⠀⠀⠁⠀⠀⢁⡀⠀⣟⢉⣻⣿⣵⣿⣿⣿⣿⠿⠷⠤⠤⢀⣾⡦⢐⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣾⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⡀⠀⠀⠀⠀⡞⠉⣷⣿⠋⢸⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⣿⣿⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣦⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠛⠁⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣠⣤⣀⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⢿⣿⠿⢽⣟⣚⣽⣿⣯⣛⣛⣛⣿⣭⢹⣭⣿⣟⣿⢽⣿⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣯⣭⣭⣭⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⠀⡄⣀⣼⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠘⠂⠀⠄⠀⠀⢁⡠⠤⠬⠟⡃⣶⣾⠿⢿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⡻⣿⡗⠀⠈⠉⠉⠃⠀⠈⠉⣃⣈⣩⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠾⠿⠿⢾⣉⣑⣲⣿⢾⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠏⠒⠒⠢⠢⣶⡾⣿⡥⠂⢈⣻⢿⢿⣿⡟⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣵⡖⠀⠀⢀⣤⣤⣤⣤⣤⣤⣠⣤⣄⢠⣶⣶⡄⡶⣿⣿⣿⢿⣿⣿⣿⣷⣻⣿⣿⣷⣦⣀⣀⣈⣉⣉⣏⠻⠿⣿⣿⣿⣿⢳⣿⣿⢻⣿⣿⣿⡟⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⢏⣾⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠟⠉⠈⠀⠈⣿⣿⣾⣿⣿⣿⣿⣿⠿⠿⣿⠿⠛⣿⣿⣿⣿⠁⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡀⢻⣿⣿⣿⣷⡖⠀⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣼⣿⠛⠛⠛⢿⣿⣯⣁⡶⠓⠐⠖⠀⣸⡿⠃⢀⣾⣿⣷⣷⣶⡀⠉⠙⠻⠿⣿⡏⠉⣉⡛⠛⠛⠋⠉⠉⠋⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⣿⣿⡇⣿⣿⢿⣿⣿⢸⣿⡿⠿⢹⣿⣿⣿⣴⣿⣿⣿⣿⡆⣿⣿⢻⣿⣿⣿⡿⣿⣧⢀⣠⣸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢱⣿⡟⣿⣧⢸⣿⡇⢀⣾⣿⣿⣿⣤⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣾⣿⣿⣿⣿⡇⠘⢸⣿⣿⣿⣇⣿⣿⣿⣿⣧⣿⣿⣼⣿⠻⢿⣿⣯⣿⣿⡟⣿⣿⣿⣿⠸⣿⣿⣿⣿⠛⣿⣿⢿⣿⣿⣷⣾⣿⣷⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣏⠉⣿⣿⣿⠙⠃⢰⣶⡟⣿⣿⠿⢃⣿⣿⣾⣿⣼⣿⡿⣿⣿⡀⣿⣿⢸⣿⡏⠉⢻⣷⡏⣿⣿⢸⣿⣏⣻⣿⣿⣿⣿⡇⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠻⣿⡿⠿⠿⠏⣀⣾⠿⠿⠀⠔⢾⢿⢿⣿⡋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠏⠛⠿⠿⠛⠀⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡟⠀⢀⡀⠀⠁⠀⠈⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣦⡀⠀⠀⠀⢀⠀⣀⠀⠀⢸⣿⣷⡄⠀⣀⣾⣿⣿⣿⣆⠀⢠⣧⣤⡀⠀⠀⣴⡆⣀⣀⠀⢠⣤⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣤⣄⠀⠀⠀⠀⠀⢀⠀⣠⣿⡿⠿⢿⣿⣶⣶⣿⡿⠟⢰⡖⢾⠇⠀⢻⣤⣼⣿⣿⣿⣿⣿⠖⠘⣿⠿⢿⡇⠀⠈⣷⣿⣿⣶⣴⣿⣷⣶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁⢠⣾⣇⠀⠺⣷⣿⡯⠤⠤⣼⠧⣬⣯⣽⣀⣀⣸⣇⣼⡆⢀⣽⣻⣿⣿⣿⣿⠿⠉⠀⠀⣿⡂⢈⠃⠀⠀⢻⡀⢀⣿⣙⣿⣿⣿⣿⣿⣿⣿⠿⠷⠦⠤⢠⣿⡦⢰⡿⠿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣼⠿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡿⠋⣿⣿⠁⢰⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣄⣸⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢰⡄⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠘⠃⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣄⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⢿⣿⣯⣿⣿⣿⡿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣛⣛⣛⣻⣟⣒⣻⣿⣯⣛⣛⣛⣿⣭⢹⣭⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿⣯⣽⣿⣿⣿⣿⣯⣯⣿⣭⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣄⣠⣀⠀⣀⣠⣿⣷⣿⣾⡆⠀⢹⠅⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⣈⠨⠭⠽⡏⣶⣿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠉⠉⠙⠃⠉⠉⠻⣃⣉⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠿⠾⣖⣛⣑⣲⣿⣾⣿⣿⣷⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠒⠢⠤⣤⣶⣾⣾⡖⠂⢻⣻⣿⣻⡿⠛⠪⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣄⢠⣶⣶⡆⡶⣿⣿⣿⢿⣿⣿⣿⣯⣾⣿⣿⣷⣦⣀⠀⢉⣉⣉⡏⢿⢿⣿⣿⣿⣿⣻⣿⣿⢿⣿⣿⣿⡟⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣶⣦⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⢏⣾⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣯⣛⡙⠻⣿⣿⣿⡿⠛⠋⠁⠙⢿⣿⣿⠿⠾⠿⣿⣿⣿⣿⡿⢿⣿⣥⣴⣿⣿⣿⠁⠀⠈⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠻⣿⣿⣿⢿⣿⠇⢠⣿⣿⣿⡇⠀⠀⠀⠀⠠⣿⡅⠀⠀⠀⠈⢈⣽⣟⣡⣶⡇⠈⠷⠀⠹⠃⠀⣶⣷⣦⣤⣀⡀⠀⠈⠉⠛⠿⢿⡏⠉⣉⡛⠛⠛⠛⠛⠛⠛⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢿⣿⡆⣿⣿⢿⣿⣿⢸⣿⡟⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⣿⣿⣷⣶⠆⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⣿⡟⣿⣧⢸⣿⡇⣀⣾⣿⣿⣿⣤⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣾⣿⣿⣿⣿⡏⠿⢽⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣼⣿⠙⢿⣿⣿⣿⡿⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⠛⣿⣿⢿⣿⡇⠀⠘⢿⣷⣦⣙⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⠉⠁⣰⣶⡟⣿⣿⠃⢀⣿⣿⣾⣿⣼⣿⡿⣿⣿⡐⣿⣿⢸⣿⡇⠀⢰⣶⡏⣿⣿⢹⣿⣟⣿⣿⣿⣿⣿⡇⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠉⠿⠿⠿⠿⠇⢀⣿⠿⠿⠨⣿⣿⣿⣿⣿⠋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠏⠛⠿⠿⠛⠀⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⠀⣀⡀⠈⠈⠙⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⡀⠀⠀⠀⢀⡀⣀⠀⠀⢸⠿⢷⡄⠀⣠⣾⣾⣿⣷⣄⠀⢠⣧⣤⠀⠀⠀⣴⡄⣀⡀⠀⢠⣥⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣤⣤⠀⠀⢀⠀⠀⢀⠀⢀⣾⣿⣿⣿⣿⣶⣶⣿⡿⠿⠿⡷⢺⠁⠀⣿⣦⣻⣿⣿⣿⣿⣿⠆⠸⣿⡿⢿⡆⠀⠸⣷⣿⢿⣷⢸⣿⡄⢰⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⡟⠓⢲⣾⣇⠀⠨⢷⣿⣯⠥⣀⣼⣏⣹⣟⣿⣇⡀⢀⣇⣼⣇⣠⣿⣿⣿⣿⣿⣿⠟⠉⠀⢸⣿⠀⢈⡇⠀⠀⣿⣇⠀⣃⢈⣿⣯⣈⣿⣿⣿⡿⠿⠷⠤⠤⣠⣿⣆⣶⡿⠛⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣿⣷⣴⡞⠉⠙⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢹⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠉⢀⣠⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⠇⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣼⡗⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠽⣿⣿⣟⣳⣖⣒⣿⣭⢹⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣟⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣤⣠⣄⣀⢰⣆⣠⣴⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣺⠮⠯⠿⡛⣶⣾⠿⢿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠆⠈⠉⠉⠙⠁⢉⢛⡟⣈⣩⣿⣿⣿⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⢿⣿⣛⣑⣲⣿⣾⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠢⠤⣄⣰⣶⣿⣿⡿⠈⢛⡿⡻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⣄⢂⣶⣶⡆⡾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣉⣩⡛⣿⣿⣿⣿⣿⡿⣻⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣼⣷⣶⣤⣶⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣾⣿⣿⢿⣵⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣀⢀⣿⠿⣿⣿⣿⡿⠋⠉⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢿⣿⣿⡿⣿⣿⡏⠀⠸⠿⠟⠛⠂⠀⠻⠿⠉⠉⠀⢠⣤⠀⠀⠀⠹⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠃⠀⠀⣀⡉⠙⠛⠉⠹⠛⠋⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡎⣿⣿⢸⣿⣿⢸⣿⡏⠀⢀⣿⣿⣿⡀⣿⣿⣿⣿⡟⣿⣿⣿⣷⢻⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⢻⣿⣷⢸⣿⣯⣿⣿⢿⣿⡆⠀⢰⣿⡟⣿⣧⢸⣿⣇⣀⣾⣿⣿⣿⣶⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣾⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⠘⢿⣿⣿⡁⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⠙⣿⣿⢸⣿⡇⠀⠘⢿⣷⣦⡀⢸⣿⣿⣿⣿⣿⢹⣿⡇⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢸⣿⡇⢸⣿⣿⡟⣿⣿⣿⠀⠀⣸⣿⣿⣿⣇⣿⣿⡏⠻⣿⣿⣿⣽⣿⣷⣶⡟⣿⣿⠀⠀⣿⣿⣾⣿⣼⣿⡿⣿⣿⡐⣿⣿⢸⣿⡇⠀⢰⣶⡟⣿⣿⢸⣿⡇⠹⣿⣿⢸⣿⠇⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠃⠿⠿⠟⠀⠀⠿⠿⠙⠿⠿⠿⠿⠇⠀⠈⠿⠿⢟⣿⣿⣿⡿⠿⠋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⠋⠸⠿⠿⠇⠙⠿⠿⠛⠀⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡇⠀⢤⣀⡀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣧⡀⠀⠀⢀⣏⡀⣀⣀⡾⣿⣿⢿⡄⠀⠠⣴⣾⣾⣦⡀⠀⢨⣿⣤⠀⠀⠀⣤⠄⣀⡀⠀⢠⣅⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢘⣿⣾⠄⠀⠀⠀⠀⢀⠀⢀⣼⣿⣿⣿⣿⣶⣾⣿⡿⠿⢿⡿⠿⡁⠀⠻⣄⣹⣿⣿⣿⣿⣟⠆⢸⣿⡿⢷⡆⠀⠸⣿⣿⢿⣷⢼⣿⡂⢸⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⡿⠓⢲⣾⣷⠠⠬⢷⣿⣿⣏⣠⣽⣿⣿⣿⣿⡇⠀⢀⡇⢸⡇⢀⣺⣿⣿⣿⣿⣿⠿⠛⠀⢸⣿⠀⠈⡇⠀⠰⣿⡆⠀⡃⢘⣿⣇⣘⣿⣿⣿⣿⠿⠷⠤⠤⣰⣿⣤⣾⠟⠛⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣶⡞⠉⠙⣧⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠛⠛⠋⠉⠁⠁⠉⠉⠉⠉⠈⠉⠀⠈⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢻⣿⣯⣀⣠⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣛⣿⣭⢺⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣽⣯⣯⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⣼⣯⣭⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣤⣀⡠⠾⢇⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣻⣻⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢈⣻⣿⣿⣿⣇⣀⣬⣿⣧⠘⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⠛⠛⣿⣿⣿⣷⠆⠉⢋⡝⠛⢟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⡂⣶⣶⡆⣿⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣶⣤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣼⣶⣦⣤⣦⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⣿⣿⣿⣿⡟⣽⣿⣿⡿⠋⠀⠀⠙⣿⣿⣿⣏⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⣶⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⡇⠀⠀⠀⠀⠙⠟⠋⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⠻⡿⠁⠀⠀⠀⠀⣀⣠⡤⠎⠀⠀⠀⠠⣄⠀⠀⠉⠿⠿⠁⠀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠙⠀⠀⣀⡀⠈⠙⠟⠛⠋⠉⣉⣈⣩⣿⡇⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡀⣿⡇⣼⣿⢻⣿⡆⣿⣿⢸⣿⣿⢸⣿⡇⠀⢨⣿⣿⣿⠀⣿⣿⣿⣿⡆⣿⣿⢿⣿⢰⣿⣿⣿⣿⣿⠆⣸⣿⣿⣷⢸⣿⣷⢸⣿⣀⣿⣿⢿⣿⡆⠀⢰⣿⡟⣿⣧⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⢻⣷⠀⠀⠀
⠀⣿⣿⣷⣿⡇⣿⣿⢸⣿⡇⣿⣿⣾⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣼⣿⠘⢿⣷⣯⡁⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⠻⣿⣿⣸⣿⡇⠀⠘⢿⣿⣧⡀⢹⣿⣿⣿⣿⣿⢿⣿⡟⣿⣿⣼⣿⠀⠀⠀
⠀⣿⣿⣿⣿⡇⣿⣿⢹⣿⡇⢹⣿⣿⡟⣿⣿⣿⠀⠀⣸⣿⣿⣿⣧⣿⣿⡿⠿⡖⣿⣿⣿⣷⣶⣶⡟⣿⣿⠀⢀⣿⣿⣾⣿⣼⣿⡿⣿⣿⡒⣿⣿⢹⣿⡇⠀⢰⣶⡟⣿⣿⢸⣿⣟⡈⣿⣿⢸⣿⡇⣿⣿⠉⠁⠀⠀⠀
⠀⠿⠟⠸⠿⠇⠘⠿⠿⠟⠁⠸⠿⠿⠇⠿⠿⠟⠀⠀⠿⠿⠀⠿⠿⠿⠿⠇⠀⠀⠿⠿⠹⢿⡏⠻⠿⠿⠋⠀⠸⠿⠇⠸⠿⠇⠿⠇⠻⠿⠀⠿⠿⠿⠟⠁⠀⠈⠻⠿⠿⢛⡸⠿⠿⠇⠙⠿⠿⠛⠀⠿⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣗⠀⠀⠀⠠⠤⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⣷⡒⠸⢿⣿⣿⣦⠶⠚⣻⠛⢓⣾⣿⣿⣿⣿⣿⣶⡀⠠⣼⣿⣿⡯⠉⠛⠳⢤⣴⡿⡀⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣈⣴⠀⠅⢻⠏⠙⣿⣷⣿⣿⣿⣿⣥⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣄⣼⣿⣷⣿⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⠖⠟⠋⠀⡀⠀⠀⡈⠚⢽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣶⣶⣶⢦⡀⠀⠀⠀⠀⠀⠠⠴⠶⠆⠱⠷⠟⠺⠁⠀⢀⠧⠀⢈⠺⢁⡟⠙⢿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠌⠡⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠄⠀⠀⠀⠀⠀⠤⡆⢹⡐⠀⢿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠀⠀⡀⠀⢾⣿⣥⡴⠧⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⣿⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⢠⣶⠂⠆⢠⣿⣧⣄⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⣻⣿⡇⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⡦⠁⠁⣿⣿⣷⢻⣻⣻⣩⢿⣷⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⣀⢀⣨⣤⡴⠛⠹⡍⠡⠀⢸⠟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⣿⠙⠛⣋⣙⣊⣛⠁⠀⠀⠀⣇⢌⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⢀⠇⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣥⣬⣍⡉⠁⠈⠉⠓⠀⠀⢏⠈⠀⢑⡀⠸⠿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣮⣤⠀⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠛⠛⠛⠛⢿⣿⠖⠀⠀⠀⠘⠂⠀⡰⠀⠀⠈⣒⣪⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠠⠔⠀⣶⣿⣿⣿⠇⠀⢻⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⠀⣿⣿⡟⠛⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠘⣯⡙⠀⣿⢰⡏⢹⡇⣇⣹⠟⠛⢸⡏⢹⣀⢸⡇⡃⡇⠀⣿⢸⣧⢹⢸⡏⠙⠀⠀⣿⣀⣿⢸⣿⣿⣿⣿⢻⣿⣿⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⠛⠃⣿⠀⣇⣈⣇⣿⣼⣧⢼⣼⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠠⣆⣹⠀⣿⠈⣇⣸⠇⡇⠀⠀⠀⢸⡇⢸⣀⣸⣇⡃⣇⣀⣿⢸⡏⢿⠸⣍⣹⠀⠀⡇⣿⢸⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿⣀⡿⠀⠀⣿⠀⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2274

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ How to Report Apple Layoffs Without Saying
the "L" Word⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Apple_Is_Shutting_a_Store_in_China,_Its_First_Closure_in_the
                                   Country⦈_


Back in 2020 Microsoft shut down all of its "Stores". Back then the media kept
parroting the Microsoft lie about such outlets "going online". But there were
loads of layoffs. The media failed to do its job.


Now it's happening in Apple as well. However, don't look for the "L" word.


See, the media is toothless and in many ways useless. Microsoft had a ton of
layoffs in China this year, but what little media that covered it called it
"exit" or some similar euphemism. All the GAFAM companies have layoffs this
year. Lots of layoffs. It has nothing to do with buzzwords and catchphrases
like "hey hi". They just have cashflow woes. █


Last week: Apple_Vision_Pro_Failed_So_Badly_That_Its_Sales_Are_About_2,000
Times_Smaller_Than_iPhone_Sales (Apple_is_about_100_billion_dollars_in_debt)


    * Wall_Street_Does_Not_Care_About_Microsoft's_Impending_(August)_Layoffs,
      It_Believes_Lies_From_Microsoft,_Whose_Debt_Grows_Rapidly
    * next


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⣿⣿⣿⣿⣿⢏⠘⡟⢛⢛⢛⢻⢡⢟⢻⣿⢠⠛⣻⣯⡘⠾⢘⢻⢻⢻⢋⡋⡛⡚⢛⢻⢛⢛⡿⣛⢻⣿⣘⢳⢋⠟⡻⡛⡻⡛⢿⡟⡚⠛⢻⡟⢰⣿⡆⡚⡟⡚⢛⢻⢛⢻⣿⣿⠇⡞⡹⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣷⣦⡸⠿⠿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⡿⢿⣧⢀⣾⣿⣿⣷⣶⣄⡀⠀⠀⣴⣿⣿⣷⡄⠀⠀⣀⣤⣶⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⢹⣿⣿⣿⣿⣿⡟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠛⣿⣿⣿⡇⠀⠀⣿⣿⣿⠉⡭⠭⠭⡭⠀⣉⣉⣩⣭⣍⣉⣉⣭⣭⣭⣭⣿⣿⣋⡉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣯⡿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⣿⡇⠀⠀⢻⣿⣿⡇⡇⠘⠈⠀⢸⡛⠛⢻⣿⣟⣯⣝⠯⢿⡿⢯⢟⣿⣿⣛⣛⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠿⣿⠃⠁⠀⣐⠀⢘⠭⠡⠬⠩⠅⠩⠬⠉⠻⠓⠚⠊⠏⠛⠑⠂⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠛⠃⠀⠿⠿⠿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⣰⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⢀⣀⠀⠀⡀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⢰⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⡿⣿⢦⣴⣷⣶⡆⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠛⠻⡉⢤⣤⣐⢡⢰⠖⠀⠀⠀⢀⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣴⣵⡀⠀⠀⢀⣀⣀⣀⣘⣑⣀⣀⡀⢀⠀⣠⣔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠘⢑⣯⠁⠀⠀⠀⠀⠸⠃⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣄⠀⠀⠀⠀⢀⠉⢨⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠜⣤⣸⢿⣿⣿⣿⣿⣷⣶⣶⣶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠈⠢⠀⠀⠀⡀⠀⡐⠄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢠⣿⡏⠀⠀⠀⠀⠉⠉⠉⠘⢁⢨⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2352

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/IRC_Proceedings_Tuesday_July_29_2025.shtml
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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Tuesday, July 29,
2025⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GPS_location⦈_


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now


    * Corruption_is_the_Standard_Operating_Procedure_at_the_European_Patent
      Office_(EPO)
    * Over_at_Tux_Machines...


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣯⣵⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⠉⠉⠀⠉⠉⠙⠻⠟⣿⢿⣿⣿⣿⣿⡟⣾⣯⢹⣿⠹⠉⣹⡍⣿⣿⢙⢉⢴⣏⣄⣼⣯⣸⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⢿⣿⣿⣿⢿⡾⢾⠿⠻⣿⡿⢻⡟⢻⣙⣽⣉⣫⣟⣻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣎⣿⣿⣿⣓⣽⣾⣶⣾⣿⠿⢿⢿⠿⢟⠟⣻⣻⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⢙⣻⣿⣿⣇⢟⣭⣟⢿⣷⣓⣤⣦⣿⣿⣽⣶⣶⣿⣿⣿⢟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠀⠹⢂⠀⠀⢹⣿⣿⣫⣴⣿⣿⣿⣷⣯⣛⡿⣿⢿⠿⠿⣿⣟⣻⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⠭⢁⠘⡆⠀⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⢠⡴⠄⢉⣠⠂⣶⣿⣿⣿⣿⢟⣯⣶⣿⣿⢻⢻⣿⣷⣯⣽⣿⣛⣿⣯⣽⣶⢻⣿⣿⣾⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⢘⣛⣿⠿⠏⣠⣿⣿⣿⣿⣯⣿⣟⠍⢿⣹⣿⣾⣿⣿⣯⢋⣯⣩⣋⣿⣿⣟⣭⣟⣏⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⢠⡠⠙⠛⠂⢰⣿⣿⣿⣿⣿⣿⣮⡟⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣁⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡏⣿⣷⢻⠿⢻⣯⣻⣿⡻⢛⣛⣿⣿⡛⣯⣙⣋⣟⣽⣷⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡻⣷⣄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⡻⣿⣾⢿⣿⠻⢿⣿⣿⢿⣿⣿⣷⡿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣾⣧⣼⣧⣿⣿⣼⣩⣕⣧⣤⣦⣥⣤⣼⣿⣮⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡟⣿⡿⠏⣿⣿⡟⠟⣿⢿⡿⣿⡟⣿⣿⢿⣿⣿⣿⡿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣯⣿⣿⣿⣿⣿⣮⡳⢤⣯⣼⣿⣿⣷⣷⣾⣥⣶⣿⣷⣿⣷⣷⣾⣶⣾⣷⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣙⣛⣻
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣾⣿⣷⣿⡿⣿⣿⣿⣿⣷⣶⣽⣿⢟⣽⣶⣿⣿⢲⡴⢾⣯⣽⣿⣿⣭⣽⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢃⣤⣿⣿⣷⣾
⣿⣿⢡⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣽⢿⣿⣿⣿⣿⢿⣿⡿⢋⣺⣵⣿⣿⣿⣿⣿⠸⠿⢘⣛⠻⠿⢿⣿⡏⠻⣿⣿⣏⣧⡌⢿⣿⠟⢋⣴⡝⣼⣿⣿⢿⣻
⣛⣏⣻⠴⠹⢿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠝⢿⣿⣿⣿⣿⠋⡿⢛⣿⣿⣷⣾⣻⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡞⣾⣿⡄⡁⣴⣻⡿⣧⣿⢵⣟⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⡿⠏⠁⢀⣴⠃⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⣨⣽⣿⣿⣿⣽⣻⡿⣿⣿⣿⣰⣿⣵⣾⣿⡝⣾⣿⣏
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠯⢿⠰⠿⣿⣿⡷⠘⢿⣿⣿⣿⣿⣿⣻⣿⣷⣾⣿⣻⣿⣿⢿⣟⣿⣿⣟⣺⢿⣟⣿⣿⣿⣿⣸⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠁⠀⠀⠀⠀⢲⠏⣩⣄⡀⠀⣉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣙⠿⣾⣯⣿⡷⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣗⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣷⣀⡈⠙⠛⠿⣷⣭⣟⣻⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣥⢹⡉⣩⣥⡲⣄⠈⢿⣿⣿⢿⡅⢆⣤⣤⡀⠈⠉⠙⠛⠳⢾
⣿⣿⣿⢩⠛⢿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⣯⢋⣾⣿⣿⣿⣌⠣⡈⢻⡋⠘⠙⠻⣟⣛⢧⡀⠀⢦⣄⡀⠀
⣿⣿⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣷⡑⠄⠁⠐⠶⢄⡉⠻⢧⣻⠀⠀⠈⠛⠷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⡀⠀⠀⠉⠳⢤⡙⠀⠀⣀⣤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡋⢟⣩⠉⢶⣧⣿⠟⢚⢿⣿⣿⣿⣿⣿⣿⣿⠂⣀⠀⠙⢦⡀⠀⠀⠀⠸⠷⢆⠉⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣤⣥⢿⣏⣐⠢⡄⠀⠐⢾⢆⣫⠻⢿⡽⡛⣿⠏⣰⡿⠷⠍⠀⠙⢤⡀⠀⣸⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2584

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Last_Month_Our_IRC_Community_Turned_17.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Last_Month_Our_IRC_Community_Turned_17.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Last Month Our IRC Community Turned
17⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇It_is_fine⦈_


Two years ago, a few months before we_dumped_WordPress (which we had used since
2006), we mentioned the history_of_our_IRC_community, dating_back_to_June_2008
in_Freenode. Funnily enough we never missed a single day when it comes to
logging and likewise we never missed a message. Our records are very complete.


Freenode_perished_in_2021 and perhaps this was a blessing in disguise; we
finally had a good reason to form our own IRC network, not be a tenant in
someone else's. This way we're better off and in greater control over our
destiny. Over time our_reach_grew and we didn't need to depend on some "big
network" or Social Control Media. This makes us a lot more robust to
censorship. █


    * "The_Unix_Kernel"
    * Links_30/07/2025:_Tea_Class_Action_and_Google_Killing_the_Web_With_Slop


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣳⣿⡇⣴⣶⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⠭⠙⠛⣛⢃⣿⣿⣿⣿⡗⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⢀⠀⠛⢿⣿⣿⣿⣿⠇⣰⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣰⢨⣐⠂⣀⠉⠻⣿⣿⣸⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣉⡘⣻⢿⣮⠓⠢⣄⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣮⣗⠀⢹⣿⣿⣿⣿⣿⡛⠈⢉⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠝⡻⠯⠻⠿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⢿⠛⠉⣁⣀⣉⣙⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣤⢨⢀⣙⣚⣛⡁⠀⢀⣼⣿⣿⣿⣿⠀⢬⣭⣿⣛⡛⠉⢻⢸⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣋⢜⣴⣶⣤⣴⣶⠿⣿⣿⣿⣿⣿⣿⡆⠘⢾⣿⣿⣋⣛⠳⠆⣿⣘⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⡐⣺⣵⣿⣿⣷⣿⣿⣿⣷⣮⣙⠿⡿⠿⠟⣛⣎⠢⣍⡛⠿⢭⣉⣧⢹⡇⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⡜⢿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣧⣴⣾⣿⣿⣿⣷⣌⠋⢠⣄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⠳⠦⣴⣦⣽⣿⣿⣿⡟⠃⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⡟⠻⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡿⣿⣿⣿⣿⣿⣶⣍⡉⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣷⣬⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⣴⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠂⠀⠀⢀⡀⠀⠀⠀⠈⣿⣧⢻⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠻⠀⠀⢈⡟⠀⠀⠀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠿⠟⠀⠀⠀⢀⣿⣿⣏⢿⣿⣿⣦⣻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⣤⣶⣄⡀⣿⠉⠙⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⡀⠀⢸⣿⣿⣿⣎⢿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⣴⣼⢿⣿⣿⣿⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⡗⠀⢸⣿⣿⣿⣿⡞⣿⣿⣿⡿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀
⠀⠀⢰⣾⣯⣉⣉⠳⣆⠀⢸⣿⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⡿⠁⠉⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀
⢠⣾⣿⣿⡿⠋⣩⣥⣽⣷⣚⠉⠉⠉⠻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡏⠀⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣈⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⡿⠃⠀⠘⠻⢿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⡁⠀⠀⠀⠀⠀⠀⠉⠙⠃⠂⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀
⠘⢷⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣨⣿⣿⣄⣴⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⡟⢠⣤⣤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠏⢀⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⣤⣤⢠⣶⣴⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⢰⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡀⠀⣛⠻⠌⣷⣯⣭⣯⢍⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 2672

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Local Staff Committee Munich (LSCMN) at the
European Patent Office (EPO) Requests an Urgent Meeting to Avoid Abolishing the
Office⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


                🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Richard_M._Stallman_(2005)⦈_


Exactly a week ago a letter was sent by the EPO's Local Staff Committee Munich
and it was later circulated among staff. The latest communication says:


     Dear Colleagues,


     Following our_recent_publication_of_10_July_2025 regarding the ISAR
     building renovation and in response to the Office’s announcement
     “Two-year renovation of the ISAR building starting in 2025”, the
     Local Staff Committee Munich (LSCMN) kindly requests an urgent
     meeting with Social Dialogue.


     The decision to abolish all allocated offices for more than two years
     raises serious concerns about staff working conditions and undermines
     the commitments made under "Bringing Teams Together." Since the
     announcement, numerous concerned colleagues have reached out to us,
     urging the staff representation to engage with the administration and
     explore alternative solutions.


     In this open letter, we request that the decision is suspended, to
     have a discussion on the concerns outlined in our communication and
     to identify practical alternatives as soon as possible.


Here's the open letter in its entirety:


     European Patent Office
     80298 Munich
     Germany


     Local Staff Committee Munich
     Comité local du personnel de Munich
     Örtlicher Personalausschuss München


     Email: mnstcom@epo.org


     Date: 23.07.2025


     sc25007ml


     European Patent Office | LSC Munich | GERMANY


     To: Social Dialogue


     By_email:
     socialdialogue@epo.org


     OPEN LETTER


     Request for urgent meeting on abolition of allocated offices


     Dear Social Dialogue,


     Following our recent publication of 10 July 2025 regarding the ISAR
     building renovation and in response to the Office’s announcement
     “Two- year renovation of the ISAR building starting in 2025”, we
     kindly request an urgent meeting with Social Dialogue.


     The decision to abolish all allocated offices for more than two years
     raises serious concerns about staff working conditions and undermines
     the commitments made under "Bringing Teams Together." Since the
     announcement, numerous concerned colleagues have reached out to us,
     urging the staff representation to engage with the administration and
     explore alternative solutions.


     We request that the decision is suspended, to have a discussion on
     the concerns outlined in our communication and to identify practical
     alternatives as soon as possible.


     Please let us know your earliest availability.


     Sincerely yours


     Ingrid Peller
     Chair of the Local Staff Committee Munich City, Haar und Brussels


Tolerating the abuses of the EPO means that - as noted and emphasised by the
author of this open letter - management can get away with all sorts of things,
including European_software_patents - i.e. patents which are both illegal and
undesirable. We need to push back, both outsiders and insiders of the EPO. This
is dictatorship led by the most corrupt. █


    * Slopwatch:_Fake_'Linux'_'Articles'_and_Spamfarms/Slopfarms
    * Corruption_is_the_Standard_Operating_Procedure_at_the_European_Patent
      Office_(EPO)


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡿⢿⡿⢿⣿⣿⠈⡸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⠿⢿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠅⠃⢹⢰⡆⣸⠀⠁⠈⢠⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⡆⢰⠈⠐⢀⠐⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣯⣴⣶⣾⣶⣶⣶⡆⠀⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣸⣥⣧⣬⣼⣼⣿⣼⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡛⢛⢛⡛⠏⡉⡏⡁⠈⣉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢙⡇⣼⠸⠃⠀⣴⡇⡄⠀⠾⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2828

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Microsoft_Rapidly_Shrinking_No_It_s_Not_About_Efficiency_It_s_A.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Microsoft_Rapidly_Shrinking_No_It_s_Not_About_Efficiency_It_s_A.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Rapidly Shrinking (No, It's Not
About Efficiency, It's About Unbearable Debt)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Jul 30, 2025


Yesterday: Expect_More_Microsoft_Layoffs | Microsoft_Behaving_Like_It's_Running
Out_of_Money_to_Pay_Salaries


Today:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_feels_like_the_new_Sega_-_why_the_recent_studio
            closures_feel_like_the_collapse_of_the_Xbox_ecosystem⦈_


Proprietary software giants that suck the veins of government budgets (i.e.
taxpayers) aren't success stories. They are - to put it bluntly - leeches. They
go out of their way to portray themselves as tolerant, even while they profit
from bombing_people, from_racism etc.


1_hour_ago_somebody_wrote:


     Microsoft also requires all employees to write up how they have
     contributed to and will contribute to D&I. (D&I is Microsoft's brand
     for DEI and includes all components of DEI ideology including
     equity).


     Managers are then required to provide feedback and guidance on their
     employee's D&I performance and plans.


     D&I is the first required "Core Priority" (and remained so for years)
     in annual performance reviews. Then Microsoft started failing in
     security to the point that there were several government agency hacks
     and foreign actors attained access to government systems in Azure.
     (coincidence?) So Microsoft added "Security" as the second required
     core priority as a reaction. This is how it still today. Any employee
     (including managers) are familiar with these requirements and go to
     msconnects to see.


     Google says "Microsoft connects Diversity & Inclusion (D&I) with
     performance reviews by integrating D&I considerations into the
     performance evaluation process. This includes setting D&I goals ...
     Microsoft incorporates D&I goals into performance plans, encouraging
     managers and employees to actively contribute ... Performance reviews
     assess not only what employees achieve but also how they achieve it,
     specifically evaluating their inclusive behaviors, such as
     collaboration, communication, and alignment with core values ...
     Ensuring Equitable Outcomes: Microsoft strives for pay equity and
     equitable performance outcomes"


     Microsoft's own diversity report publicly says: "Annual performance
     and development goal related to Diversity & Inclusion (D&ICore
     Priority) introduced for all employees" [2018-2022] and "Every
     employee sets an annual D&I Core Priority goal, informed by the One
     Microsoft D&I Plan, to enable individual accountability" [2024].


     https://fortune.com/2023/11/08/microsoft-diversity-performance-
     reviews-inclusion-managers/


     All employees are required to take D&I training and given that D&I is
     part of everyone's performance evaluations it has become embedded in
     ALL projects including Microsoft's required annual security and
     compliance training.


     Even employees working directly and indirectly under federal contract
     are required to take D&I training and write a D&I core priority in
     their annual performance reviews.


This is about one thing: optics. It can also help keep wages down.


There are meanwhile new stories about how Microsoft rips apart the workforce
[1] and shutting things down [2].


The company is going to fake its financial performance, as usual, in effect
defrauding_shareholders_again. We'll soon see how_much_debt_grew_in_the_past
quarter. █


Related/contextual items from the news:


   1. ⚓ ‘Like_Second-Hand_Office_Chairs’:_Ex-Microsoft_Employee_Slams_Deal_With
      Cognizant_Which_Resulted_In_Layoff⠀⇛


           A Reddit user called out Microsoft and Cognizant for a sudden
           sale of the entire business division without intimating the
           staff, calling it a betrayal that cost employees their futures.


   2. ⚓ Microsoft_feels_like_the_new_Sega_-_why_the_recent_studio_closures_feel
      like_the_collapse_of_the_Xbox_ecosystem⠀⇛


           Gaming is in a weird place right now. There are layoffs
           happening everywhere, games are getting delayed even as the
           Switch 2 proves to be a bigger hit than even Nintendo could
           imagine, and a group of studio executives have accused their
           publisher of sabotaging the release of a game to avoid a $250
           million bill. But none of that is going to impact the industry
           quite as much as what is happening with the Microsoft Xbox.
           I’ve been following video games for a long time, and the
           closest analogy I have is remembering Sega in the wake of the
           Saturn.


           In case you weren’t around, that isn’t good news for Microsoft.


    * Over_at_Tux_Machines...
    * GAFAM_'Revolving_Doors'_at_The_Register_and_a_"Bribe_Price_List"


⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣏⣉⣍⣹⣍⣏⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⠀⣿⣿⣿⠻⢻⠻⠿⠿⠿⡿⠿⢿⠛⠻⡟⠻⠿⠿⡟⠿⣿⠛⠛⠿⠿⡿⠻⠻⡿⢿⡿⠿⠿⠿⠿⢿⠛⡿⢿⠿⠿⢿⣿⡿⡿⠿⠻⠿⠿⡟⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣟⣀⣸⣀⣒⣰⣀⣂⣀⣂⣰⣐⣇⣀⣀⣀⣀⣀⣻⣀⣀⣘⣀⣿⣘⣀⣇⣸⣇⣀⣀⣆⣀⣸⣂⣀⣀⠀⣀⣸⣭⣧⣀⣸⣀⣇⢰⣇⣃⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⡿⢿⠿⡿⡿⠿⠿⠟⣿⠿⠻⢿⠿⠟⢻⠿⣿⠿⢻⠿⡿⠿⡿⠿⡿⡿⢿⠟⡿⢿⢿⢻⡟⢻⠻⠿⢿⠖⠟⢿⠿⣿⠿⠿⡟⡟⠾⡿⢿⠿⡿⣿⡿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⡇⣆⠀⡐⡂⠀⠀⡆⡗⠀⠐⠘⠀⠂⢀⠀⣿⠐⢀⠀⡀⠀⠃⢰⠀⠀⢸⡆⡀⢀⠀⢸⡇⢸⠀⠂⢸⡆⠂⢸⠀⣿⠐⠐⡀⡇⠀⠀⠀⠀⡀⢸⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⢿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣷⠰⠀⠁⢸⠇⠀⠀⡁⠀⠀⡇⠂⠰⠁⠠⠀⠀⡄⠀⠆⢈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⠿⣿⣿⡿⣿⣥⣿⣿⢿⣿⣿⣿⣿⡿⡿⣿⡿⣿⠿⡿⡿⣿⡿⣿⢿⣿⠿⢿⣿⡿⣿⣿⢿⣿⡿⢿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⡧⠤⠧⠤⠼⡦⡤⠼⠤⡤⠤⠦⠤⠤⠼⠤⠧⠤⣦⣤⣤⣼⣤⣤⣼⣤⣤⣤⣤⣤⣦⣧⣤⣤⣤⣼⣤⣤⣥⣤⣤⣧⣼⣦⣤⣤⣤⣤⣤⣷⣤⣤⣤⣧⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣷⣷⣶⣶⣦⣷⣷⣶⣶⣿⣶⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2977

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Microsoft_Will_Continue_Resorting_to_Crimes_in_Order_to_Keep_GN.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Microsoft_Will_Continue_Resorting_to_Crimes_in_Order_to_Keep_GN.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Microsoft Will Continue Resorting to Crimes
in Order to Keep GNU/Linux Usage Down⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


Last August: Good_Reason_to_Delete_Windows,_Not_Dual-Boot,_and_Call_Out_the
Microsofters_Who_Worked_to_Impose_'Secure'_Boot,_Undermining_Antitrust
Complaints (when/if_you_serve_Microsoft,_crimes_are_"OK")


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_loves_Linux_as_long_as_it_doesn't_take_share_from
                                  Microsoft⦈_


Throughout the month we saw lots of articles (maybe a couple dozen) about how
GNU/Linux had managed to exceed 5% market share in the US, based on
statCounter. Some said it had exceeded 6%, citing US government data.


Regardless, looking at statCounter right now (almost end of July), it_is_fast
approaching_5.5%:


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


Many sites correctly argued this might be attributable to "the end of [Vista]
10"; But Microsoft has a "time bomb payload" via UEFI: see Linux_and_Secure
Boot_certificate_expiration


It's very revealing that 'secure' boot pushers said_nothing_to_refute_this_or
defend_this. Some_Microsoft_staff_bought_LWN_subscriptions_to_'troll'_the
comments. It is a real problem and we'll revisit it later this week. █


    * GAFAM_'Revolving_Doors'_at_The_Register_and_a_"Bribe_Price_List"
    * Gemini_Links_30/07/2025:_Two_Sides_of_Me_and_"Hooked_on_Cosmic_Voyage"


⠀⠐⠀⠀⠀⣠⣶⣶⣶⣶⣶⣤⣀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⡆⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⢐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⣀⡀⢀⣠⣤⡀⢀⣀⣀⣀⠀⣀⣤⣄⡀⢀⣤⣤⡀⢀⣠⣤⣀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀
⠀⣿⣿⣿⣯⣭⣉⠛⣿⣿⣿⡟⠉⣀⣼⣷⣽⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⡇⣿⡇⣿⣿⢹⣿⢸⣿⣿⣿⡇⣿⡏⣿⣧⣿⣿⡿⠿⢸⣿⢹⣿⢸⣿⡏⠉⢹⣿⡏⠁⠀⠀⠀
⠀⣿⣿⠿⠿⠿⢿⣇⡸⣿⣿⠃⠉⠭⠿⠛⠿⣿⠄⢾⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⡇⣿⡇⣿⣿⢠⣤⢸⣿⣿⣿⡄⣿⡇⣿⣿⣈⣻⣿⣧⢸⣿⢸⣿⢸⣿⡟⠃⢸⣿⡇⠀⠀⠀⠀
⠀⣿⣷⣾⣷⣶⣶⣶⣦⣾⣷⠶⣾⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣯⣀⠃⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⠿⣿⠇⣿⡇⠻⣿⣾⠟⢸⣿⠿⣿⠇⠿⣷⡿⠇⠻⣿⣾⠟⠸⢿⣾⠿⠸⣿⡇⠀⢸⣿⠇⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠟⠋⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⠀⣀⣀⢀⣀⣀⣀⣀⡀⢀⣀⣀⠀⠀⢀⣀⡀⢀⣀⡀⣀⡀⣀⡀⣀⣀⢀⣀⢀⣀⢀⣀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⣿⢻⣿⢹⣿⢸⣿⣿⣿⡟⠃⣿⣏⠿⠇⠀⢸⣿⡇⢸⣿⡇⣿⣷⣿⡇⣿⣿⢸⣿⢸⣿⣾⡟⠀⠀⠀
⠀⣿⣿⢟⣿⣿⣿⣿⣿⣯⣋⣹⣿⣿⣿⠷⢹⣿⣿⣿⡿⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢸⣿⠸⣿⣿⣿⢸⣿⡿⠇⣙⡿⣷⡄⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢠⣿⣿⣇⠀⠀⠀
⠀⣿⣿⣼⣟⠛⢛⣛⣛⣛⢛⣋⣍⡍⠀⣴⣾⣿⣿⡏⠀⠀⣴⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⢻⣿⣼⡿⠀⣿⣿⣿⢸⣿⣧⡄⢿⣧⣿⡟⠀⢸⣿⣧⣼⣿⡇⣿⡟⣿⡇⢻⣿⣼⡿⢸⣿⢹⣿⡀⠀⠀
⠀⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣁⣾⣿⣿⣿⣿⣧⠀⠈⣿⣴⣿⣷⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣶⣄⠉⠻⢿⡿⠿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⣨⣿⢇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣻⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡹⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⠆⠖⢠⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣦⣀⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠚⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣾⣻⡆⠀⣶⠆⣴⣶⣄⣤⡄⣤⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠻⠿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⣧⣽⣿⡆⢀⣿⠀⣿⢹⡏⣿⣿⡿⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣷⣦⣄⠀⠈⠙⣿⣿⡏⠀⠀⠀⢠⣶⣶⣦⣜⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠉⠈⠋⠛⠛⠁⠘⠛⠋⠻⠾⠃⠿⠹⠇⢿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⡟⡛⠀⢸⣿⣿⣿⠀⠀⣀⣩⠿⠭⠽⠿⣿⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢼⣿⠷⠀⢸⡗⢷⡶⠆⢰⣶⣶⡄⣤⣦⡄⣤⣤⢀⣤⣀⢀⡀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣁⡁⢠⡀⠀⣀⣀⣬⡍⣭⣭⣭⢩⣥⣤⣶⠀⠀⠀⣠⣿⣇⡀⣻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣬⣽⣷⠀⣿⡇⢸⡇⠀⢸⡿⣿⣷⣿⣾⡇⣿⣤⠻⣯⡛⣾⣷⣿⠸⠙⣿⠛⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠙⠁⠀⠛⠃⠛⠃⠀⠸⠷⠿⠙⠿⠿⠳⣿⣤⢿⣿⡿⣿⢻⣿⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢣⣿⣶⢰⣶⣶⢲⣶⡆⠀⣤⣤⡄⣤⢠⣄⢀⣀⡀⣀⣀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣯⣿⢸⣿⣯⢸⡿⠆⠀⠿⣮⣁⣿⣾⡇⣾⢿⡇⣿⣿⡇⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣙⠛⠟⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠔⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠃⠛⠃⠛⠚⠋⠛⠸⠷⠆⠘⠿⠿⢿⣿⣾⣧⣿⢾⣇⣿⢹⡇⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣼⣟⣷⣰⣟⣷⢰⣶⣰⣶⠀⢰⣦⣤⣤⣤⣤⢀⣤⣄⢀⣀⣀⠀⣀⡀⠈⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⡇⠀⣠⣄⠀⠀⢰⣿⠉⣿⣿⣷⣿⣿⣿⣸⣿⡿⣿⠀⢸⣿⣿⣿⢿⣿⣾⡇⠿⢸⣿⣿⢸⣿⣿⣷⣿⡿⢦⣿⣿⡆⣶⠶⢶⣶⠆⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢿⣧⣾⣿⣿⣷⠀⠈⠉⠀⠉⠉⠉⠙⠛⠋⠛⠛⠃⠛⠀⠸⠿⠟⠿⠸⡏⢿⣷⡿⣼⡇⣿⢸⣇⣿⢳⣝⣿⢸⣿⣿⣿⣿⠓⢸⡿⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣭⣤⣄⣀⣀⣀⣀⠤⠖⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡰⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠈⠉⠉⠈⠛⠋⠘⠛⠀⠸⠇⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠉⠉⠉⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⡛⠻⠿⣿⣿⣿⣷⣶⣆⠠⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣷⣄⠀⠉⠛⠿⠿⠿⠀⠀⢩⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡿⣿⣶⣶⣾⣿⣧⡙⠿⠿⢿⠟⡛⠿⠿⠿⢡⣷⣦⣍⡙⣿⣿⣿⣿⡟⣍⣥⣙⡙⣋⣼⣦⣦⣥⣿⣿⣿⣿⣿
⣶⣶⣶⣶⠀⠀⠀⠀⣶⣶⣶⡆⠀⠀⠀⢰⣶⣆⠀⢴⠀⣴⠤⠀⣦⢠⡔⢠⣤⠂⣤⠀⡆⣶⢰⠀⣤⢰⡄⣤⠂⢀⣰⢠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡲⣶⢠⣐⢂⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡄⠀⠀⠀⠙⠿⠟⠁⠀⠀⣠⣼⣿⣧⣥⣼⣦⣼⣤⣤⣼⣤⣼⣤⣥⣧⣬⣴⣧⣤⣬⣤⣿⣼⣧⣤⣦⣤⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣬⣭⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣴⣦⣤⣶⣿⣿⣶⣶⣦⣴⣴⣦⡙⢛⢛⣭⣡⣿⣿⣿⣿⣇⣛⠿⠛⣋⣙⢻⡿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⠿⢀⡻⠿⠟⢿⣿⣿⡿⢋⣙⣋⣉⣋⣭⣭⣌⠛⣉⡛⢛⡛⠻⢛⠻⠿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⣦⢻⣿⣿⡿⣿⣿⣿
⣭⣭⠹⢩⡙⠟⣰⣷⣦⣭⣴⣆⣰⣾⣿⣷⣶⣾⣨⣭⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠈⠬⠿⠇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠘⢐⠁⠛⣈⣐⢘⣃⣈⣃⣀⡘⠛⣛⡀⣿⣿⣿
⣿⣿⡿⠿⢿⣿⡿⣿⠿⡿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠍⠛⠛⠛⠻⠟⠛⠛⡛⠉⠻⠋⢠⣤⠀⠀⠉⠰⠶⠶⠜⠛⠋⠴⠤⠶⠖⠈⠰⠿⠲⠿⠢⠙⠡⠶⠶⠋⠙⠶⠾⠗⠀⡐⢂⢉⠀⠉⠉⢈⠩⣿⡇⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣭⣭⣭⣤⣭⣭⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣥⣭⣭⣿⡇⣿⣿⣿
⣿⣉⣏⣉⣉⣉⣉⣿⣯⣫⣙⣙⣹⣿⣝⣍⣫⣉⣉⣉⣉⣹⣿⣙⣏⣩⣉⣹⣯⣫⣟⣉⣩⣉⣉⣿⣯⣫⣏⣉⣿⣯⣭⣉⣉⣉⣏⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3082

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/My_Experience_With_Judges_Has_been_Positive_But_We_Must_Still_P.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/My_Experience_With_Judges_Has_been_Positive_But_We_Must_Still_P.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ My Experience With Judges Has been
Positive, But We Must Still Pursue SLAPP Reform in the United
Kingdom⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


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


Growing up in the 90s, I used to watch "Judge Judy" quite a lot. Yes, I know
that turning courts into "showbiz" is in bad taste and all, but it does give
one an insight into processes, procedures, pleading approaches and so on.


I think the first time I went to court to watch random cases (not related to me
in any way) was in the early 90s. I was a kid. Some person, I assume a lawyer,
displayed footage of an old lady doing housework (filmed from afar, maybe from
a distant building). Lacking context, I assumed he was trying to prove that she
had falsely alleged disability or something to that effect. I found that
interesting. I still remember that very well.


I come from a fairly small family because my parents have barely any siblings
(0+1). My aunt is married to a judge, who is basically my only uncle.


On occasions, or very occasionally, to some people's misfortune, he gave me
advice. I'm reasonably well protected from bullies (including those who wear a
suit and exploit a lawyer's licence).


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇1993,_Roy_Schestowitz⦈_


Techrights, as I explained this morning, isn't anti-authority. I explained why.
On many occasions I encountered authorities that were very helpful and
courteous. Those include regulators (my barrister comes from one). I also spoke
to judges and usually, at the end, they can relate to what I say and side with
me. Maybe I'm just lucky, who knows?


In any event, society where profit-related motives control almost everything
(both at a personal and commercial level) we must at least strive to have
something that can look above and beyond money. We need to have people who can
look at the issues and objectively assess them, based on the underlying facts.
This is where judges come in.


At the moment we have a long-term plan to explain what Techrights was subjected
to, how it tackled the challenges (we deem this an educational endeavour; we
want to help others, especially in predicaments), then spend years pursuing
SLAPP reform with the help of politicians. I have many useful contacts. There
are also NGOs which show genuine interest in helping.


We believe it'll be a "feather_in_the_cap" if we can help change laws in the UK
to better protect investigative reporters; nations are better off with media
freedom. Society is guarded from crooks and violent thugs when the media is
functional and unafraid by default. █


    * Slopwatch_Makes_the_Web_Better
    * Wayland_Considered_Harmful_(to_GNU/Linux_Adoption)


⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣽⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⣶⣴⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣴⣿⡿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⢤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠉⣿⣿⣿⣿⣿⣯⣥⣽⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣤⣽⣿⣿⣷⣽⣿⣿⣿⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⢻⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣴⣿⣿⣿⣿⣿⠿⣿⡻⠿⣤⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠄⣰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠘⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣻⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡆⢹⣻⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⣿⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣬⡅⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠆⡏⣸⠃⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣷⡇⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡱⣠⣇⡃⠞⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⣸⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⡿⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣴⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣾⣿⡟⠁⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢡⡀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠲⣶⣴⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡏⠀⠀⢀⣠⣤⣶⠾⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠁⠀⠈⠉⠛⠻⠿⣿⣷⣦⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠤⢄⠀⠀⠀⠀⢸⡇⢠⠀⡷⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⣸⣿⣿⣿⣦⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠠⠴⣦⣤⠄⠀⣶⡄⠀⠀⠀⢸⣧⡆⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⣿⠁⠀⠀⢰⣿⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣿⣥⣾⣶⣶⣦⠀⠀⢀⣴⣿⣿⡇⠀
⢹⡀⠀⠀⠘⠃⠀⠀⠺⠟⠛⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢺⣿⣿⠿⠃⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠞⠀⠀⢀⣤⠞⠁⠀
⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠿⠛⢿⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⡠⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⡿⠋⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠙⠛⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠼⠧⠤⠤⠀⠊⠀⠀⠀⠀⠤⠤⠒⠁⠠⠀⠀⠀⠀⠜⠀⠀⠠⠃⠀⠀⠀⠀⠉⠉⠟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣏⣀⣀⡀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀
⠛⠛⠛⠛⠛⠛⡛⣛⠛⠛⣿⣿⣻⣛⣛⣛⠛⢻⠛⠛⠛⠛⠛⠛⢛⡛⠛⣻⣿⠛⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠟⠛⠛⠛⠛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠺⢿⣯⣀⣿⡟⣿⣼⣿⣿⣯⣴⣾⡄⠀⠀⠀⠀⠀⠀⢠⠀⠈⠉⢰⡏⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠛⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡀⠀⠀⡀⠀⡄⠀⡀⣾⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢧⠆⣀⣀⡀⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⢀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣧⣿⣿⣿⣿⣟⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿⣿⠟⢁⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⠟⠂⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣄⣾⠀⣼⡿⣿⣿⣿⣿⣿⣿⣴⠟⢁⡴⠋⠀⠀⠰⣿⣿⠛⠏⣿⡿⢻⣿⣿⢿⣉⡝⡿⢏⡀⣭⣿⣿⣿⣿⣿⣿⡿⠐⠛⠐⠾⣿
⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⢡⣤⢈⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢠⣿⢿⣿⣿⣿⣿⣿⡟⢁⡴⠛⠁⣀⠀⠀⠀⠀⠀⠛⠛⠋⠱⠆⠀⡀⠀⠈⠃⠀⠰⣿⠟⢹⣿⣏⠈⠛⣿⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣨⣿⡿⢿⣿⣿⡀⣥⠀⣰⢿⣿⣏⣽⡿⣿⣿⡇⣿⢻⣿⣿⣿⣿⣿⣻⣿⡿⢿⣼⡶⢾⣿⣿⣿⣿⣿⣿⠋⣠⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠛⣿⣧⢶⣿⡿⠛⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢬⣿⣷⣿⣿⣿⡁⣟⣲⡞⠒⠛⠻⠿⠭⢿⣿⠓⢛⣿⡏⠛⡿⣾⣿⣽⣿⣿⣦⣿⣛⣿⣿⣿⣿⣿⣿⣿⣎⠛⠀⣽⡟⠀⠀⡀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣟⠃⠀⠀⠃⠀⣿
⠀⠀⠀⠀⢺⣿⡏⣿⣿⣿⠁⠟⠁⠀⠀⠀⠀⠀⠀⡈⢻⠀⣾⠹⡇⠀⠁⢿⣿⠙⣏⣿⡿⣯⡝⣿⣿⣿⣿⡟⢿⣿⣿⡀⠀⠈⠀⠀⢠⣿⣿⣿⣿⣷⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⢀⠀⠘⢻⣿⣿⡙⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⣿⡷⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⡿⢈⡄⠻⡦⠁⠀⠀⢸⣿⡄⠉⣿⣧⣿⣿⣿⣿⣿⣿⣧⣄⣿⠧⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⠾⠛⠃⠉⠉⠉⢙⠀⢹⣻⣷⣦⡄⠀⠀⠀⠀⣿
⠉⠀⠀⣸⣿⡏⠁⢺⣇⣿⢀⡀⠃⠀⠀⠀⠀⠀⢰⣾⣾⣿⣾⣿⣦⣤⣤⣿⣿⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣤⣿⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⣷⣿⣿⣿⣿⣀⣀⣀⣀⣿
⣷⣶⣶⣼⣿⣿⣆⣾⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣀⡀⠈⣿
⢿⣏⠳⡙⢻⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠉⠁⠀⣿
⣿⣿⣿⣮⣿⡶⣾⣿⡿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡄⢀⣠⣶⣤⣄⣤⣀⣀⣿
⣿⣿⣿⣿⣿⣿⣿⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣛⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣬⠁⢾⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⣀⣬⣿⣿⣧⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠈⢈⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⣽⣿⣽⣿⣿⣿⣇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣭⣿⣿⣷⣾⣷⣿⡿⠖⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣿⣿⣿⣿⣿⡓⣿⣿⡏⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣟⠿⣤⣤⣤⠼⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⠙⠻⣿⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣿⣿⣦⣍⠻⣿⣷⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣍⣀⣤⣤⣞⣋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣙⣛⠿⢿⣿⣿⠿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢿⣿⣿⣿⣿⣿⣿
⠛⠌⠉⠉⠛⠛⠛⠛⠳⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⢤⣴⡶⡶⠶⠀⠀⢾⣿⣿⣿⠛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠛⢓⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠀⢻⣿⣷⣾⣿⣿⣿⣿⣿
⡉⠻⣦⣀⠀⠀⠀⠀⠙⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠄⠀⠀⠰⢶⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⣠⣠⢿⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣦⣤⡉⠳⠦⡀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠶⠀⣘⣛⠷⠐⠦⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⠀⠘⠿⢿⣿⡃⠀⠀⠀⠀⠀⠀⢠⣀⣁⣀⡀⠚⠩⣿⣿⣿⣿⣿⣿⣿
⢤⡈⠻⡿⣧⡀⠘⣆⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣟⣿⣿⣿⣿⣿⣿⢋⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠠⠤⣤⣈⠉⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿
⠀⠉⢂⡁⠈⢿⣓⣿⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠶⢤⣤⠠⠀⠀⠀⠈⠁⢸⣿⣿⣿⣿
⣠⣴⠉⠛⢣⣼⡟⠃⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⣋⢻⡛⠉⡉⠉⣙⡋⣉⣩⡉⠉⣈⠉⠉⠉⠁⠀⢀⡴⢻⠁⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⢒⣲⣦⠂⢀⠀⠀⠀⠀⣼⡋⠉⣁⣿
⣛⠿⣷⡄⠘⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡇⢹⣏⣹⢿⣿⢀⣿⠸⢿⣅⢹⡏⢀⡼⠃⣶⣶⣰⣦⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣧⡈⢿⣄⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠻⠀⢻⢾⡟⠛⠟⠋⠘⠃⣚⣁⡀⠛⣋⣭⢿⡟⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿
⠀⡙⠀⠈⣿⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣶⣤⣀⣤⣬⠁⠀⢤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠠⢄⠀⢀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⢴⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣭⠛⣿⣏⣄⣀⠀⠀⠀⠀⠀⠀⣸
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                    ䷩ 𝚕𝚒𝚗𝚎 3250

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Not_Owning_Mobile_Phones.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Not_Owning_Mobile_Phones.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Not Owning Mobile
Phones⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Mom⦈_


It's not about resistance for resistance's sake; it's common sense


According to statistics that I recently heard and read, over a million people
in England do not have a "mobile phone" (in the US they're commonly called
"cellphones"). One of the reasons I quit Sirius in 2022 was their demand that
all staff gets an Android phone (I never_had_such_a_thing; I did_my_research).
It wasn't the main reason but the last straw - that and the fact the company
quietly registered itself using a bogus address - a fact that I confronted the
CEO about (over the phone, it lasted about 40 minutes) only a day after I had
noticed that (I routinely checked my employer for any dodgy activity and had
good_reasons_to_do_so). I basically demanded to talk about this after they had
made fictional, false excuses to avoid that sort of conservation (the typical
"I'm busy" and variants thereof).


Some years ago we shared correspondence related to that. At one point I told
them I'd not sign any agreement related to a "phone" and also said that if they
sent me something to sign, then I'd need time to go check through the whole
thing with a lawyer. The lack of "blind faith" in the management was a "rub",
but there was nothing they could do about it. So they left me alone. They'd
stop trying to force me to get a 'free' Android phone.


After all those years I still don't have a mobile phone. My wife bought one in
2012, but it's one of those "Galaxy" phones; she hasn't bothered since. In
life, concentration requires not having those sorts of things. But the main
benefit has nothing to do with concentration; for one thing, it's about dignity
and human rights.


Any time someone says to me that he or she got a new "smartphone" my immediate
gut feeling is, not only does this person inhibit prospects of focus/
concentration; it's a mindless act of consumerism.


To place a phonecall you do not need anything new.


I fully recognise that many employers demand some sort of "mobile" so they can
contact you any time. That's hardly a selling point to you, maybe it is for
them. But there are many employers where no such requirement exists, not even
tacitly or implicitly. For accessibility reasons - set aside the statistics
above - there are always fallbacks.


They say that sometimes not having something is harder than just having
something. The other day Andy_wrote about his mother: "It is not because she is
a "Luddite" that my mother passionately hates the "cashless society" which
means she cannot park her car, or the inability to book a doctors appointment
while standing right in front of the doctor… it's because these are patently
stupid and regressive ideas. Our inability to reflect and challenge the
failures of technological society is one of many modern threats."


"We've lost a generation," Andy explained, "perhaps two, of people capable of
making decisions about technology because they've learned to completely defer
thinking about anything at all (other than perhaps money). We endure a default
and arbitrary course set by whims of those interests served by gratuitous over-
manufacture of hardware, software and attendant policy."


The closing paragraph has reluctant hope: "The cynical hope of neophyte
cultists, technofascists and proponents of faux "progress" is that change will
happen one funeral at a time. The hope is that resistance to insanity will
simply die out. Based on what I've seen of the youngest Gen-Alpha I've some bad
news for those hoping that. Radical revision and re-examination of the
technological project is alive and vibrant within the youth. It is conspicuous
how those voices are being muted. This time it is clear that reluctance is not
coming from just the older generation. Once again we are united across ages in
a shared interest in technology. This time it is not excitement, but a visceral
unease around so-called "AI". Perhaps it is time for the older generation to
once again step-up to help the younger ones to understand and navigate the
technological world so that wisdom as well as enthusiasm will have some say in
human development."


There's a_podcast_episode_related_to_this_on_its_way. █


    * Google_'Search'_is_Fast_Becoming_No_Better_Than_Social_Control_Media
      Infested_With_Bots
    * Dealing_With_Sociopaths,_Liars,_and_Cranks


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⠀⣠⡄⣤⢠⣤⣤⢠⣤⣤⣄⣄⡤⢠⡤⢠⡄⣤⣤⣤⣠⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢾⣿⠿⡿⣿⡿⣿⠻⣿⣿⣿⣿⣻⢿⢿⢛⡻⡟⡟⠟⡍⡍⠟⣿⠙⢹⣯⡿⣷⣦⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣧⣿⣾⣿⣷⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣻⣿⣝⣧⣭⣦⣧⣧⣻⣬⣼⣻⣿⣿⣾⣧⣼⣬⣷⣤⣽⣼⣧⣷⣷⣿⣴⣼⣷⣷⣾⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠻⢿⡏⣶⣇⡏⣞⡸⢿⣘⣜⣿⣯⣿⡿⠟⠁⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⡋⢛⠟⡍⣽⣿⣿⢹⣇⡃⠋⣻⣿⡏⣿⡇⣪⡸⢹⣿⣿⡹⡙⢸⢡⣻⡤⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠒⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠙⠓⠚⠛⠛⠋⠉⠉⠉⠉⠙⠛⠿⣿⣿⡿⢿⡿⣿⣿⠿⡿⠿⣿⣿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣀⣠⣤⣤⣤⡤⡀⠀⠀⠀⠀⠈⢿⣇⣷⣇⣼⣠⣳⣇⣣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣯⣶⡄⠀⠀⠀⠀⠉⠉⣩⣭⣭⣽⣿⣿⣯⣥⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡀⡂⠍⡻⣿⣿⣛⠅⣞⣹⡉⠀⠀⠀⠀⢸⢹⣧⣧⣯⡛⣿⣿⣷⢥⡧⢺⣘⡅⠡⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⢝⢣⡻⣿⡿⣿⡷⠟⠛⠽⣆⠄⠀⠀⢀⣾⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢶⢲⣦⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣮⣤⣶⣿⣿⣷⣷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⢡⡟⣼⣿⠂⠁⠀⡈⠀⠸⠁⠀⢀⣎⢭⢹⢼⡇⢝⣿⣿⣏⣙⢸⢱⢹⡰⣇⡅⣠⢘⣸⣐⡟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠬⠍⢉⣻⣿⣿⡿⠖⣂⣭⣶⣶⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⢻⡿⣁⣿⠁⣿⡟⡖⠀⠀⠁⢀⡀⠀⠀⢸⣿⡿⣿⣶⣿⣿⣿⣿⣿⡿⡿⢿⢿⣿⡿⣿⢿⣿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⠛⣷⠖⣽⣿⣧⠘⠿⠿⠿⠌⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣨⢄⣟⣾⢸⣿⣿⣇⠂⣦⣬⡖⠊⠀⠀⠸⣿⠨⠘⣇⢏⣆⣾⣿⣷⣀⣝⣺⣘⣷⣟⣿⣻⣿⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⣤⣡⣾⠿⠿⠿⣻⣷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠈⠺⢸⣿⡗⣿⡿⡝⣿⡆⠀⢀⢄⠀⠙⠛⠿⠿⣿⣿⡿⠟⡟⠛⠿⣯⣽⣿⣯⢭⡫⢽⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠟⣛⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⣿⡇⡿⠡⠿⡿⡁⣀⠨⢭⠀⡙⠀⠀⠀⠀⢻⠷⢷⣷⣿⣾⡷⣾⣿⣿⣿⣿⠿⢿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣿⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠃⠀⠀⡀⡄⣯⢧⣸⢘⣀⠀⢱⡜⣴⢸⣏⡘⣧⣸⣼⣆⣹⣉⣿⣿⣧⣧⣾⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣦⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣘⠀⠀⠀⠀⠀⠀⠀⡀⣷⢱⢳⡕⣧⡆⡂⣘⢨⣇⡚⢸⣿⡛⡿⡻⢿⢛⢿⢻⠛⡇⣿⣿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡦⠀⠀⠀⠀⠀⠀⣼⣌⣸⢸⠸⣷⡿⢃⣴⣼⢰⡟⠣⠘⣧⣷⣴⣾⣾⣼⣾⣾⣾⣶⣯⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⢎⢢⣶⣦⡀⢹⡿⠻⢺⢸⢸⣕⡂⢟⢟⡕⢸⡇⡀⢖⣎⣙⡻⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠂⠀⠀⠀⠘⠘⠽⢛⠳⣫⠞⢸⡇⡏⠎⠚⣭⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠊⡄⢾⣌⡣⠃⠀⢀⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⣴⣤⣀⣒⣒⣲⣦⣬⣭⣭⣭⣭⣥⡄⠀⠀⢠⣶⣶⣦⣤⣄⣀⠀⠈⠀⠩⠚⠊⠀⠀⠰⢻⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⡇⠀⠀⣿⣨⡅⢫⢽⠛⠿⡿⠷⣄⠈⠀⠀⠀⠀⢀⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⠿⢿⣿⣿⣷⣿⢧⣷⢋⣾⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣷⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠙⠛⠿⠿⠯⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿⡿⡿⠛⢻⣿⣿⣶⣿⣷⣶⣶⣶⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠛⠁⠄⠀⠹⣿⣿⣿⣻⡿⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠒⠚⠛⢳⣿⡿⠻⣝⣬⣦⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣗⣀⣀⢀⣀⣈⣿⣿⣭⣧⣶⣶⣶⣶⠖⢀⢂⠴⢤⠄⡀⠉⠀⠛⢿⣿⣿⣿⣿⣿⣽⣿⣿⠟⠉⣿⣿⣿⣿⣟⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣛⠛⣻⣿⣷⣶⣾⣿⣿⡛⡹⡋⡿⣫⠀⡀⠔⣀⡀⢴⡶⣐⣥⡎⡀⡇⠈⢫⡛⣿⣿⣿⣶⡿⠃⢠⣲⣿⣾⣻⣟⡻⠽⣟⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣭⣭⢽⡻⣿⣶⣬⣅⠨⠶⢃⣬⡛⠿⠁⢲⣿⡕⠻⡑⡑⣠⢳⣬⣑⣿⣿⣽⣿⣤⣲⣼⠾⣯⣓⣣⣿⣳⣿⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⣯⣽⡿⠿⠟⣹⣿⣿⣿⣷⠶⣿⣿⣧⢀⠀⠈⣿⡇⣦⣮⠐⣵⣿⣟⣿⠿⠿⠿⠿⢿⣿⣿⡿⣿⣿⠿⣿⣿⡿⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣿⢿⡖⢒⣶⣶⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⠀⣾⣷⣶⣿⣿⣿⠀⢉⣿⣿⣷⣾⣿⣟⣛⣿⣿⣿⣿⣽⠾⠭⠉⠉⠉⠀⠸⣷⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣻⠛⠛⢙⣓⣩⣥⣶⣶⣾⣿⡿⢿⣛⣻⢿⣿⣿⣾⡁⠄⢢⣟⡓⢀⣀⡒⢻⣶⣿⣛⣻⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣯⣽⣾⣷⣾⣻⣿⣿⡿⢿⣻⡭⢗⣺⣽⣿⡷⠽⣿⣿⣿⠿⣿⣿⣤⣤⣀⣀⣠⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠾⣿⣿⣯⡿⠛⠋⠉⠨⣶⣿⣽⡶⠿⢛⣋⣥⣷⣚⣾⣻⣟⣻⣦⣭⣩⣭⣭⣭⣭⣤⣤⣶⣶⣶⣶⣾⣿⣿⡿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣭⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3388

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

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


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Planetary⦈_


⚓  Updated This Past Day⠀⇛


   1. ⚓ Linuxiac_is_Not_a_Slopfarm,_But_at_Least_Some_of_Its_Articles_Are
      Machine-Generated_Fakes [original]⠀⇛


           Crossposted from Techrights


      ⚓  New⠀⇛


   2. ⚓ Security_Leftovers⠀⇛


           with Linux focus


   3. ⚓ Free,_Libre,_and_Open_Source_Software_and_Programming⠀⇛


           FOSS and more


   4. ⚓ GNU/Linux_and_BSD_Leftovers⠀⇛


           today's picks that are orphaned


   5. ⚓ Open_Hardware/Modding:_Arduino,_Snagboot,_and_More⠀⇛


           Hardware picks for today


   6. ⚓ today's_howtos⠀⇛


           3 howtos for now


   7. ⚓ Audiocasts/Shows:_LINUX_Unplugged,_Late_Night_Linux,_and_Destination
      Linux⠀⇛


           3 new episodes


   8. ⚓ today's_leftovers⠀⇛


           GNU/Linux and more


   9. ⚓ Programming_Leftovers⠀⇛


           Development news


  10. ⚓ Mozilla_Leftovers⠀⇛


           Mozilla picks for today


  11. ⚓ Kernel_Space:_Linux_Kernel_Should_Stick_With_C_and_a_Look_at
      OpenLinkHub⠀⇛


           a couple of Linux picks


  12. ⚓ today's_howtos⠀⇛


           howtos for today


  13. ⚓ Android_Leftovers⠀⇛


           Google Messages gets Material 3 Expressive on Wear OS before
           Android


  14. ⚓ My_5_favorite_Linux_distros_for_home_office_desktops_-_and_I've_tried
      them_all⠀⇛


           If you work remote or run your own business out of your house


  15. ⚓ Testing_New_Linux_Kernels_on_Ubuntu_is_About_to_Get_Easier⠀⇛


           Canonical has announced a change in its kernel strategy for
           Ubuntu development builds


  16. ⚓ Firefox_Add-Ons_Website_Revamps_Listing_Pages⠀⇛


           If you go visit the Firefox Add-Ons website today you’re sure
           of a slight surprise


  17. ⚓ Boardcon_Compact3576_–_A_feature-rich_Rockchip_RK3576_SBC_with_Android
      14_and_Debian_12_support⠀⇛


           The company mentions that the RK3576 module and SBC support
           Android 14 and Debian 12


  18. ⚓ Free_and_Open_Source_Software⠀⇛


           This is free and open source software


  19. ⚓ Wayland_Will_Never_Be_Ready_For_Every_X11_User⠀⇛


           Some users also simply say that they do not care about Wayland
           either way as it offers no new features they want


  20. ⚓ Games:_The_Crazy_Hyper-Dungeon_Chronicles_(TCHDC),_Cattle_Country,_and
      More⠀⇛


           8 stories from GamingOnLinux


  21. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


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


                         Span from 2025-07-23 to 2025-07-29
      1018 /n/2025/07/20/Clear_Linux_In_Memoriam.shtml


      994  /n/2025/07/25/This_Laptop_Has_a_Raspberry_Pi_inside.shtml


      933  /n/2025/07/23/
           This_Core_Ultra_Tiny_PC_Is_Built_for_Kubuntu_Linux.shtml


      899  /n/2025/07/24/
           _Wayback_Keeps_Old_Linux_Desktop_Environments_Alive_on_Wayland.shtml


    * IRC_Proceedings:_Tuesday,_July_29,_2025
    * Microsoft_Rapidly_Shrinking_(No,_It's_Not_About_Efficiency,_It's_About
      Unbearable_Debt)


⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻
⠀⢠⡦⠦⡤⠀⠰⢤⡴⠦⠤⠤⠴⠤⠀⠂⡄⠀⠀⢠⢤⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣾
⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⣿⣿
⠉⠉⠛⠉⠁⠀⠸⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠐⠊⠀⡀⣘⠀⠀⠀⠀⠀⠀⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠓⠛⠒⠀⡄⣤⠀⡿⣵⣢⠀⠙⠻⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁⠃⠀⠉⠙⠛⠖⠂⠤⣄⣀⠀⠀⠉⠉⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠹⠿⠿⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠉⠉⠈⠉⠉⠉⠉⠛⠻⠿⠿⢿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠀⠶⠄⠀⠀⠀⠀⠀⠑⠂⢀⣰⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠤⠤⠔⠒⠒⠀⠀⠀⠀⢸⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⣤⣄⣤⣤⣴⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⣿⡻⢿⣿⣟⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⠀⠘⡀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⢁⠀⡜⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡻⣿⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣻⣿⣿⠟⠀⠀⠀⣆⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⢄⡹⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⢻⣧⠉⠙⢣⠐⠲⠀⠀⠀⠤⣀⠀⠀⠉⠛⠛⠻⢿⣿⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠿⠿⠛⠛⠛⠿⠿⢿⣿⣷⡀⠀⠀⠀⠀⠱⡠⠊⠁⠀⠐⡀⠀⠀⠀⠀⢀⢻⣿⣶⣾⡿⠀⠀⠀⠱⡀⠀⠀⠀⠀⢸⡀⠄⠐⡄⠀⠀⠀⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⠋⠀⡀⠠⠀⠤⠤⠤⢀⠀⠈⢿⡇⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠁⡀⠀⠀⠀⠸⡀⠉⠋⠉⠀⠀⠀⠀⠀⢱⣀⠀⠀⡠⠇⠒⡏⡇⢠⡀⠀⢠⠿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠟⠛⠉⠀⢀⠴⢁⠄⠒⠀⠀⠀⠀⠀⠑⢄⠈⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠐⣄⠀⠀⢴⠘⠦⡀⠀⠀⠀⣀⣤⡠⠎⡀⠀⣰⡃⣀⠀⠥⠄⢸⢷⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠁⣀⠀⠀⠀⢀⣠⣤⣄⣀⢃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠢⡀⢘⠂⠀⠀⠀⠠⠄⠈⣧⠐⠉⠀⠀⡯⠤⣐⣂⢬⠿⠋⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠌⣄⠥⠚⣛⣧⣎⠀⢿⡿⢻⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡄⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠐⠛⠉⠀⡀⠜⠀⠀⢸⠳⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠘⡸⠁⠀⠐⣿⣿⡏⢣⠔⠒⢚⡆⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⣀⡙⣤⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⠀⢸⢘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⣇⠀⠀⠀⠈⠁⣠⣿⡀⠠⢳⠧⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠉⣀⣠⣼⣄⠀⠀⠉⠀⢹⠀⠀⡠⢀⠐⠀⠀⠀⠀⠀⠀⡌⡁⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠁⠘⣯⣔⣒⣒⣪⣴⢿⣿⣿⣏⡆⢷⣄⠀⣪⢭⡤⠤⡤⣧⡀⠀⠀⡠⡌⠁⠀⢡⣿⣿⣦⣀⠀⠀⢘⣇⣴⡊⠁⠀⠀⠀⠀⠀⠀⠰⠡⠁⠀⠘⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠄⠀⠀⠀⠀⠀⢀⠴⠁⠈⡀⠀⠪⡛⠾⠾⠯⣁⠀⢿⣿⣿⣷⢸⡀⢲⣷⡭⠥⠊⠀⠈⠣⡔⠻⠀⠨⣠⣶⣿⣿⣛⠻⢿⣿⣿⣿⣿⣧⣱⡀⠀⠀⠀⠀⠀⡠⡡⠁⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡐⠂⢤⣧⣤⣔⡄⠀⠀⠀⠠⢌⡘⠿⢿⠇⠀⠁⠀⡎⣧⠀⠀⠀⠀⠀⠈⠦⡀⠀⠻⣿⣿⠃⠀⠉⠁⠀⣿⣿⣿⡈⠛⢕⣂⡀⠀⢒⡨⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⣿⠉⠙⠻⣦⣄⠀⠀⠀⠈⣉⠀⠀⠸⠀⢰⠱⡸⡆⠀⠀⠀⠀⠀⠀⠸⠾⣆⠈⠃⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣿⣄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⡤⠠⠂⡠⢻⠀⢡⡟⡄⢀⣠⡤⠶⠿⠁⠀⠘⢣⡉⠲⢤⡀⠀⠀⣿⣿⣿⠁⡀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠒⠒⠒⠒⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠚⠻⠄⠀⠠⡴⠀⠀⠀⠉⡠⡏⡄⠘⣷⠉⠉⢀⣀⠀⠀⠀⠀⠀⠠⣛⣖⣂⠀⠈⠁⠁⠀⢸⠀⡹⢰⠀⡐⡆⢠⠀⠄⠤⠀⢠⠀⢀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⣠⠞⢇⠟⠃⢀⣿⠭⠒⠚⣳⣦⡄⠀⠀⡖⠁⠈⠛⣻⠁⠀⠀⠀⠀⢸⠠⠀⣘⠀⠓⡇⠘⣤⠀⠆⠀⠘⠀⣆⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⡀⠀⠀⢨⠉⠉⠈⠉⠀⣀⣠⣤⣆⣫⡠⠓⠁⠀⢸⠘⡧⣀⠀⠀⣈⠝⠁⠀⠀⠈⠂⠄⣚⠏⠀⠀⠀⠀⠀⢈⠀⠀⠈⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠇⠀⢰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠠⠀⠀⡄⠸⢦⢍⠉⠀⠀⡴⠫⣉⠑⣄⡈⡇⠀⠀⠀⠀⠁⠀⠘⠛⢷⢶⠶⣤⣄⣤⣀⣤⣤⠔⠒⠀⠐⠒⠠⣀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⢁⣇⠀⢸⠘⠀⢀⢸⠥⠤⡿⣤⢴⢁⢰⠶⡄⠀⠀⠀⠀⠀⠀⢀⠸⠀⢡⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⢀⠼⠒⣃⠠⠸⣂⣀⡼⡁⢘⡸⠘⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡄⠰⢁⣾⣿⣷⡄⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣧⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢊⠞⡧⠔⠉⠸⡀⡄⠏⠉⢀⢰⠉⡃⠀⡂⢣⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⡃⠄⠸⣿⣿⣿⠇⠀⠀⣾⣿⣦
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡐⠈⠑⢧⠀⠀⠘⢇⠀⢸⠶⢌⡨⠶⢇⠀⠻⣼⠀⠀⠀⠀⠀⠀⠈⠀⡇⢀⡇⠐⠤⢌⠉⠁⢀⡀⠠⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠛⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠃⠀⠀⠀⠀⠠⢣⠘⡄⠀⢂⠀⠈⠄⠀⣦⢀⠩⢦⡀⠠⠀⠀⠀⠀⠀⡇⠈⠡⠀⠀⠀⢁⣀⠛⠻⠀⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠗⠉⢳⡌⠂⠤⢇⠀⠀⠀⢸⠘⣄⠀⠁⠀⠀⠀⠀⠀⠀⡅⠀⠀⡇⠀⠀⠘⠛⠛⠷⠊⠣⣨⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢒⠊⠰⠠⠀⠘⠀⠀⠀⢸⠀⠚⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⢀⣀⢀⠀⠀⡴⣒⢿⠈

                    ䷩ 𝚕𝚒𝚗𝚎 3626

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/PCLinuxOS_Had_Functional_Backups_Before_the_House_Fire_the_Site.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/PCLinuxOS_Had_Functional_Backups_Before_the_House_Fire_the_Site.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ PCLinuxOS Had Functional Backups Before the
House Fire, the Site Will be Restored in New
Webhost⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Monday⦈_


The Chief Editor of PCLOS (PCLinuxOS) magazine sent me mail about this_latest
issue_of_PCLOS_magazine, which includes this detailed_editorial about the
status of PCLOS infrastructure:


     In late June, 2025, YouCanToo/The CrankyZombie experienced a fire at
     his place of residence. Inside his residence were the servers that
     ran all of the “services” that PCLinuxOS users came to rely on. That
     included the forum, PCLOS-Mail, PCLOS-Talk, PCLOS-Cloud, this
     magazine’s website, and the PCLinuxOS Knowledgebase Wiki.


     Even though his residence experienced significant smoke and water
     damage from the fire, YCT/TCZ found that the backups he had made of
     the magazine, wiki, and cloud site were intact. That meant that it
     was only a matter of finding a new webhost for these sites. Texstar
     had already started a new forum. He is still figuring out a format
     for the main PCLinuxOS page.


     We found a new webhost, and with the help of YCT/TCZ, we managed to
     move the domain to the new webhost fairly quickly (same address …
     https://pclosmag.com). YCT/TCZ, TerryN, and I worked tirelessly to
     find a new webhost for the PCLinuxOS Knowledgebase Wiki (note the new
     URL).


There are more details in that page. Last week we_published "PCLinuxOS is
Raising Money to Support Development After Fire Incident at the Host" and 10
days ago we said, "Nice_Recovery_(From_Actual_Fire)_by_PCLinuxOS,_New_Version
of_PCLinuxOS_Released,_Now_Top_of_DistoWatch".


Remember that PCLinuxOS is an actual community distro. My dad used it about 15
years ago. It was good. Even the hosting was done by the PCLinuxOS community or
by volunteers. This is the direction we want for GNU/Linux, not some IBM sales
strategy. █


    * Gemini_Links_30/07/2025:_Two_Sides_of_Me_and_"Hooked_on_Cosmic_Voyage"
    * Google_'Search'_is_Fast_Becoming_No_Better_Than_Social_Control_Media
      Infested_With_Bots


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⡀⠄⠀⠀⣀⠄⡤⠀⢀⢀⠠⢀⠀⡤⣠⠄⠀⡤⣠⣤⣤⠀⢸⣿⣞⣿⣿⣇⠺⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢸⡇⣿⣿⣿⣿⡏⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠁⠈⠁⠁⠈⠈⠁⠈⠈⠈⠈⠈⠈⠀⠀⠉⠀⠀⠉⠙⠉⠉⢀⣸⣿⣿⣾⣿⡿⢎⣛⣀⣛⣛⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣼⣧⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡙⠿⣿⣿⣿⣿⡌⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⢿⣎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡭⠬⠿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⡀⢠⠤⠀⠀⠀⣿⣿⣿⣦⣉⣠⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⢸⠄⡇⡇⡇⠇⠸⠀⡥⡄⠋⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠈⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣛⣛⣛⣫⣼⣿⣿⡿⠿⣛⣛⣛⠻⠿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣛⠿⢿⣿⣿⣿⡿⣫⣶⣿⢫⡝⣿⣿⢣⡾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠤⡀⢀⣒⡄⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⢿⣟⣿⣿⡞⣿⣿⣷⣽⣛⠿⠿⢟⣻⣵⡟⣱⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢰⠀⢇⡸⠘⠤⠌⠈⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣷⡷⠿⣛⣼⣿⣿⣿⣿⣿⣿⣿⠿⢛⣡⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢄⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠡⡨⠧⠆⠈⠉⠀⠂⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⡀⢠⡆⢰⠆⣤⢰⠰⠒⢄⡪⢯⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠂⠐⠸⠌⠃⠉⠀⠒⠁⠀⠈⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 3728

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Riot_for_peace_Love_Catholic_Influencers_and_Digital_Missionari.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Riot_for_peace_Love_Catholic_Influencers_and_Digital_Missionari.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Riot for peace & Love: Catholic Influencers
and Digital Missionaries welcome Jubilee of
Youth⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025,
updated Jul 30, 2025


Reprinted with permission from Daniel_Pocock.


11:30 Wed, 30 Jul 2025


Throughout the Jubilee_of_Digital_Missionaries, people asked how can we make
the Jubilee go viral on social_control_media?


I pointed out there are a number of surefire ways to go viral:


    * Use an insider at one of the tech companies, this happens_all_the_time,
    * Leak a scandal of some kind about yourself or your opponent, or
    * Use a Pope. The Catholic_Church happens to have one of these but with all
      the problems in the world today, he is a busy man.
On Tuesday, we had a bit of all that. A tech insider waiting with a camera as a
well-intentioned riot got underway amongst pilgrims anxious to catch a glimpse
of the Pope. The Jubilee of Digital Missionaries closed with an evening concert
in Piazza del Risorgimento. My camera captured the moment of joy as Catholic
influencers passed the baton to pilgrims arriving for the much bigger Jubilee
of Youth.


I just happened to be in the right place at the right time. My birthday is the
day the Berlin Wall came down and by coincidence, my camera was running at the
very moment the wall came down in Rome last night.


People asked about my Debian lanyard and it became part of a sermon_by_the_Pope
himself:


     There is a second challenge in this mission: always look for the
     “suffering flesh of Christ” in every brother and sister you encounter
     online. Today we find ourselves in a new culture, deeply
     characterized and formed by technology. It is up to us – it is up to
     each one of you – to ensure that this culture remains human.


It is a culture that I have been documenting carefully for some time, with an
emphasis on the harassment and abuse in the Debian group. The_story_shocks
people. The church has given a lot of thought to the issues involved,
especially euthanasia. In Debian, Mark_Shuttleworth became filthy rich while
Joel_"Espy"_Klecker, an underage youth in the group, was tricked to work for
free. Klecker's neighbors in the state of Oregon were voting to allow him to
take his own life. They never formally confirmed if he chose euthanasia. Leaked
emails reveal the final weeks of his life were planned in some detail, even to
the point where his final messages forecast the day he would die. When_you_put
all_the_facts_in_order,_it_is_an_extremely_uncomfortable_situation. Some time
after Klecker died, we clearly had a suicide cluster but due to the intense
secrecy, nobody had dared to speculate that the first death may have been a
case of euthanasia. The church has expressed some concern about the risks of
euthanasia. Debian has a server named after Klecker. Other developers interact
with the Klecker server on a daily basis.


The deaths continued. After the Debian Day suicide, Shuttleworth told us in_a
secret_debian-private_email:


     None of us should judge Frans' choices: there are many valid reasons
     to choose one's end. But we should be careful not to put others at
     risk.


Was there a valid reason for Adrian_von_Bidder_to_die_a_few_months_later,_on
Palm_Sunday,_which_was_the_very_same_day_that_Carla_and_I_got_married? If
Shuttleworth had anticipated a risk, why hadn't it been studied and mitigated?
If von Bidder's death was both anticipated and avoidable then somebody could be
held responsible for it. What could be a more relevant story in Rome as we
confront the relationship between technology and the church?


Over_$120,000_has_been_spent_on_legal_fees_to_try_and_censor_evidence_about
this_culture_and_the_suicides_in_particular. Yet invalid_judgments created by
extraordinarily_corrupt_lawyers_who_have_not_one_ethical_bone_in_their_body can
not bring somebody back after they die.


The Pope explicitly denounced the_culture_of_humiliating_people_that_grips
groups_like_Debian. The words of the Pope himself:


     Science and technology influence the way we live in the world, even
     affecting how we understand ourselves and how we relate to God, how
     we relate to one another. But nothing that comes from man and his
     creativity should be used to undermine the dignity of others. Our
     mission – your mission – is to nurture a culture of Christian
     humanism, and to do so together. This is the beauty of the “network”
     for all of us.


In those few words, did the Pope capture the link between Debian culture and
Debian deaths? When people are tricked to work evenings and weekends without
pay based on totally false promises of a social agenda and public recognition,
that is clearly an attack on our dignity.


During my time at Catholic College Bendigo, I had also been an alter boy at St
Joesph's church in Quarry Hill. It is an odd coincidence that in Rome this week
I was able to meet up with rock star priest Fr_Rob_Galea from the neighboring
parish of St Kilian's. I showed Fr Galea the_picture_of_Fr_Sean_O'Connell_on
the_front_of_The_Age_in_1977.


An old newspaper article from 1 February 1951 recounts the rebirth_of_St
Kilian's_parish and the appointment of Fr Timothy (Tim) Scott at Pyramid Hill.
Fr Scott's final posting was at St Joseph's where he gave us responsibility for
lighting the candles and organizing small processions during the mass. None of
our processions ever ended up like this ...


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Daniel_Pocock⦈_


 


Pope Leo's speech also expressed concerns about the challenges of artificial
intelligence for society:


     the widespread adoption of artificial intelligence will mark a new
     era in the lives of individuals and society as a whole


A 2004 article on the Pentagon web site claims the first autonomous drone was
tested_at_Graytown,_which_is_also_in_the_Diocese_of_Sandhurst. Can that be
linked to a former alter boy?


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Pentagon,_artificial_intelligence,_Graytown⦈_


 


Please follow_the_Catholic.Community_web_site. █


§ Related blogs about the church⠀➾


    * Eulogy_for_Father_John_Brosnan_by_Peter_Norden_AO
    * Prison_gate_backdrop_to_baptism_by_Fr_Sean_O'Connell,_St_Paul's,_Coburg
    * Polygamy,_from_Catholic_Synod_on_Synodality_to_Social_Control_Media_&
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      Outreachy
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§ Related blogs about social control media⠀➾


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    * Framed_by_social_control_media:_Alex_Belfield,_Voice_of_Reason
    * Riot_for_peace_&_Love:_Catholic_Influencers_and_Digital_Missionaries
      welcome_Jubilee_of_Youth
§ Related blogs about the death of Adrian von Bidder on Palm Sunday, our
wedding day⠀➾


    * Adrian_von_Bidder,_homeworking_&_Debian_unexplained_deaths
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      wedding_day
    * Some_People_See_What_Others_See..._But_Only_40_Years_Later
    * Gemini_Links_30/07/2025:_Watson’s_List_of_Limits,_Lysenko_2000


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⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣸
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣯⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠋⢿⣿⣿⣿⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⣤⣤⣤⣤⡀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⣿⡏⢺⣿⢸⠀⠀⡗⠀⠄⠀⡈⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠊⢺⣼⡟⠁⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⠿⠿⡓⣠⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⣿⡟⠹⢿⣿⠿⠹⣿⣿⡟⠋⢽⣿⠟⠻⣿⡏⡷⠛⠿⣿⣿⠿⣿⣿⠛⢿⣿⡿⠻⢿⡿⣿⣿⢿⢿⡿⢿⢿⠿⢿⡿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣇⣰⣼⣿⣵⣄⣿⣿⡧⣠⣼⣿⣀⣀⣿⣿⣧⣀⣠⣿⣄⣄⣠⣠⣤⣠⣅⣦⣤⣤⣤⣠⣬⣄⣤⣦⣥⣬⣤⣤⣄⣤⣄⣅⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠿⢿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⢶⣿⡿⢿⠿⣿⣿⣿⣿⡿⠿⠿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3967

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Slopwatch_Fake_Linux_Articles_and_Spamfarms_Slopfarms.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Slopwatch_Fake_Linux_Articles_and_Spamfarms_Slopfarms.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Slopwatch: Fake 'Linux' 'Articles' and
Spamfarms/Slopfarms⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


Today's "Slopwatch" will be relatively short. So we start with the slopfarm
that was mentioned_yesterday_because_it_flooded_Google_News. Hours later it
published the following fake article with a slop image:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Kernel_6.17_VFS_Patch_Boosts_Disk_Failure_Handling_for
                               Btrfs,_Bcachefs⦈_


A pair/'sisters' of slopfarms did the same yesterday. Two fake articles with
slop images:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_6.16_Released_–_Optimized_for_Better_Performance_and
                                 Networking⦈_


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_6.16_Released_with_Performance_and_Networking
                                Enhancements⦈_


Google News promotes all the above 3 as "news" about "Linux"; neither the
images nor the texts are real, they're mindless slop.


Those same slopfarms about "Linux":


   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Apple’s_New_Containerization_Feature_Allows_Kali_Linux
                            Integration_on_macOS⦈_


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


Google News also promotes the above. So that's at least 5 fake articles in one
day.


Since Google is itself a pusher of slop, it's hard to believe Google News sees
a problem with that. █


    * Gemini_Links_29/07/2025:_Wayland_Unfit_for_Use_and_LLM_Slop_Faking_One's
      Language_Skills_With_Robot_Communications
    * Local_Staff_Committee_Munich_(LSCMN)_at_the_European_Patent_Office_(EPO)
      Requests_an_Urgent_Meeting_to_Avoid_Abolishing_the_Office


⣿⣿⣿⣿⣿⣿⣿⡌⠟⠏⡄⣶⡁⡙⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣧⣿⡧⡿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠓⠚⠚⠙⠛⠐⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣾⣿⣿⣿⣷⣷⣿⣿⣿⣿⣷⣶⣾⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⠿⢿⢿⠿⣿⠻⣻⠿⡿⡿⢿⠿⡟⣿⠟⣿⣟⢻⣛⢻⡟⡟⡟⣻⢛⣻⡟⡛⠿⠿⠿⠿⠻⢿⡟⡛⡿⢿⠿⡿⢿⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣤⣧⣮⣼⣤⣿⣴⣴⣤⣷⣧⣼⣤⣧⣿⣬⣮⣿⣼⣧⣿⣿⣴⣧⣿⣭⣼⣧⣾⣤⣼⣵⣭⣼⣼⣧⣥⣮⣼⣬⣧⣼⣼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡍⢻⡻⡇⢻⡏⣛⢿⠛⡇⢻⢻⣻⢛⣿⢙⡋⢿⠛⡟⢻⢸⡇⣟⢻⢛⢻⡅⢿⢻⢻⡏⡋⡏⡟⡏⣞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣷⣿⡷⣿⣿⣶⢷⣷⣾⣿⣷⣿⣾⣿⣿⣶⣷⣷⣾⣷⣿⣾⣥⣾⣿⣷⣿⣿⣷⣾⣿⣷⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣕⣱⣙⣎⣱⣁⣏⣱⣵⣨⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣿⣻⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠟⠻⠛⠛⠟⠻⠟⠻⠻⠻⠛⡿⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣤⣄⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠐⠀⣠⠴⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀⢀⢄⠪⠀⠂⢁⢠⠐⠈⠁⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠠⠂⠈⢁⡤⠂⠘⠈⡀⠤⠐⠉⠀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⣀⠂⠔⠋⢁⢠⠠⠖⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠺⠛⠛⠛⠋⠘⠚⠛⠃⠚⠃⠘⠱⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠐⠊⠑⠀⠀⠘⠈⠓⠘⠃⠀⠀⠘⠐⠓⠈⠋⠀⠓⠓⠛⠂⠁⠂⠀⠈⠑⠓⠚⠒⠚⠛⠈⠂⠀⠀⠑⠂⠂⠘⠒⠂⠀⠀⠓⠚⠃⠁⠀⠓⠈⠂⠃⠀⠘⠐⠓⠓⠘⠀⠀⠀⠒⠓⠛⠀⠂⠀⠀⠘⠗⠓⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⡿⢿⣿⢿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣰⣸⣸⣸⣂⣿⣇⣆⣿⣿⣸⣇⣎⣿⣨⣵⣅⣬⣸⣠⣸⣀⣗⣔⣇⣤⣱⣸⣿⣿⣿⣿⣸⣣⣗⣎⣖⣇⣷⣶⣾⣸⣢⣮⣠⣇⣆⣿⣇⣇⣆⣇⣾⣇⣇⣋⣤⣇⣷⣾⣠⣅⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢻⡿⣿⠿⠟⡿⢿⡿⡿⢿⢿⡿⢿⢿⢿⡿⣿⠿⣿⣿⢿⡿⢿⡿⢿⣿⠻⡟⡿⢿⠿⢿⢿⢿⠿⡿⢿⢻⢿⡿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣾⣜⣺⣸⣿⣗⣣⣿⣇⣇⣇⣏⣃⣸⣸⣜⣾⣚⣾⣏⣃⣇⣇⣜⣸⣿⣸⣅⣇⣳⣟⣏⣎⣦⣛⣄⣿⣠⣻⣇⣇⡧⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠆⠲⠢⠀⠒⠂⠴⠖⠲⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⣬⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣉⣴⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠐⡀⠀⠀⠀⠀⣿⣯⣟⣏⣿⣻⣟⣙⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⣷⣿⣿⣿⣽⣯⣿⣯
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣜⠻⣿⣿⣿⣿⣿⣿⣄⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠈⠿⠿⠟⠁⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠁⠹⢿⣿⣿⣽⣿⣻⣿⣽⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠩⠐⠁⠀⠉⣱⣿⡿⣷⣿⠾⢶⣷⣿⢷⢿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⣠⢀⠀⢄⠀⡄⡀⠠⢠⢀⠀⣠⢠⡀⢀⣄⢠⢀⢄⣄⡠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠈⠁⠉⠀⠁⠉⠀⠈⠈⠀⠈⠈⠀⠈⠀⠉⠀⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠄⠀⠅⠀⠀⠀⠀⣿⣿⡿⣿⣿⣯⣽⣯⣽⣿
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣷⣯⣿⣟⣟⣿⣽⣿⣻⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⣭⣭⣭⣽⣽⣿⣯⣯⣭⣭⣭⣯⣭⣭⣿⣿⣭⣭⣭⣭⣽⣭⣭⣿⣿⣭⣽⣭⣭⣭⣭⣿⣯⣿⣿⣭⣭⣭⣭⣿⣿⣭⣭⣽⣿⣯
⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛⣻⣿⡇⠀⣀⠀⠀⣀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣉⠁⠀⢸⣿⣟⡉⠁⠀⠈⢁⡀⠀⠀⠹⣿⣟⣉⠀⠀⢸⣿⣏⡉⠀⠀⣿⣧⣄⠀⠀⠠⣽⣧⠀⢀⣤⣾⣶⣾⣿⡇⠈⠀⠇⠀⠁⢀⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⡆⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣧⡀⠀⠙⠁⣠⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⠻⠕⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠿⢿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⡷⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠏⢀⡀⠀⠀⣀⣴⣦⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⡇⠀⢸⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠘⠿⠿⠇⠀⠀⣿⣿⣿⠏⢀⣼⣧⡀⠀⠙⣿⣿⣿⡿⠁⢠⣾⣿⣶⣾⣿⣿⣿⣇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣿⣿⣦⣄⣀⣠⣤⣦⣤⣤⣤⣧⣤⣤⣤⣽⣿⣤⣤⣤⣤⣼⡿⠁⢀⣴⣿⣿⣿⣿⣿⣿⣶⣬⣂⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣛⣛⣛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣿⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣯⣭⣭⣭⣿⣶⣶⣶⣆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣛⣛⣭⣭⣿⣾⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠙⠀⠁⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣿⣛⣛⣻⣿⣯⣭⣽⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠉⠀⡀⡀⠤⠀⡄⠀⠀⠘⢟⣻⣿⣭⣿⣷⣾⣿⣿⣿⣿⣿⣿⠋⣡⣶⣿⣿⣿⡍⠀⣿⡿⠋⣴⣶⣿⣿⣿⡿⠛⠋⠁⠀⠀⠍⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⢈⠄⠏⠈⠎⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣦⠈⣿⣿⣿⡇⠀⣿⡇⢰⡆⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠄⠀⠒⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣛⣠⣏⣈⣿⣃⣀⣻⣧⣀⣃⣴⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⡂⠀⠀⡀⠀⠀⠀⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣦⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡛⡟⢻⢻⠛⠿⢻⢛⣻⢿⠛⠛⣿⢻⣿⣟⠛⢻⣿⠛⣿⢻⠛⣻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⢸⢉⠋⠹⢉⠋⣿⠀⢹⡄⡇⡈⡏⠉⡛⠙⠸⠋⠛⡉⠙⠙⠋⠛⢙⢸⡹⠙⠁⡈⡁⡉⣿⠉⡙⠉⠏⡁⡘⡙⠏⡉⡉⡋⠛⡉⡏⡙⠋⠙⠋⢻⠋⠉⢙⠙⢋⢸⣿⣿⣿⣿⣿⣿⣿⡿⠧⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⢾⣾⡾⣶⣶⣷⣿⣶⣷⢷⡷⢾⣷⣷⣷⣶⠾⣶⣶⠶⣶⣶⣶⣾⣶⣾⣷⣷⣶⣷⣶⣷⣿⣾⣿⢶⣷⣷⣷⣶⣷⣷⣷⣷⣶⣶⣷⣷⣷⣾⣶⣾⣷⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⢈⠀⣁⢦⢃⢁⡱⢈⢠⢈⠀⠀⡆⡁⠆⣿⠠⡇⡆⠀⡌⡱⢸⢰⢈⠰⣉⠄⡅⡆⡆⡁⢈⢰⢰⠰⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢭⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣗⡚⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⢀⢀⠀⠀⢀⣄⣀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠀⠈⠈⠈⠈⠀⠉⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠒⠒⠀⠀⠠⠂⠀⠀⠀⠐⠒⠂⠂⠀⠀⠂⠐⠒⠒⠐⠐⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠒⠐⠒⠒⠂⠀⠀⠐⠐⠒⠂⠀⠀⠐⠐⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⠏⠝⠩⢹⡏⢹⠏⢽⡇⡁⡏⢹⢋⢻⣏⠶⡏⢝⢩⠃⡍⢹⢸⡍⡏⢹⣽⠨⢹⠉⡇⡇⠫⢹⡍⣿⢐⡎⢙⠉⡇⡏⢿⢩⠉⣻⢇⡸⢸⡏⠝⡙⢋⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⡟⢟⡿⢿⠛⣿⢻⡟⡿⢿⣿⡿⢿⡟⡿⢿⢻⠿⡿⢿⠿⠿⡟⡟⡿⡿⠿⣿⠿⡿⢿⣿⠿⠿⡿⢿⢿⢟⣻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣮⣧⣼⣤⣿⣼⣧⣿⣼⣭⣧⣼⣧⣧⣼⣼⣤⣇⣹⣼⣤⣧⣧⣼⣤⣧⣿⣬⣦⣧⣿⣧⣧⣵⣤⣭⣮⣽⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣈⣀⣀⣀⣂⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⠛⠛⢻⡿⣿⣿⣿⣿⢿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⣟⣿⣟⣻⣛⣯⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠭⠭⠭⠭⢭⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣤⣤⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠃⠀⠙⢿⣿⣶⣗⣗⣾⣶⣿⣾⢿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣤⣤⣤⣤⣤⣼⣯⣯⣽⣽⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⣿⣿⣿⠀⢀⠄⠀⠀⠀⢸⣿⡿⣽⣿⡭⣭⣭⡯⣽⢭⣭⣯⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⣿⣿⣿⣶⣶⣶⣶⣶⣂⣸⣿⣿⣛⣟⣛⣿⣟⣛⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠊⠉⠉⠀⠀⠀⣀⡷⠶⠦⢤⣌⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⢤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
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⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⠿⢿⠿⢿⠻⠿⣿⠻⠿⡟⢿⢿⠿⢿⠿⠻⣿⡿⠿⡿⢿⠿⣿⢟⣻⡿⢿⠿⢿⠻⠿⢿⢽⠿⢿⠿⡿⠿⡿⢿⠿⠿⢻⠽⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣼⣼⣨⣼⣨⣼⣴⣤⣿⣤⣿⣴⣽⣿⣬⣴⣭⣴⣭⣧⣭⣦⣼⣥⣿⣮⣭⣮⣵⣼⣿⣬⣬⣼⣼⣼⣴⣤⣧⣧⣧⣽⣭⣼⣼⣴⣭⣧⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢩⡟⣟⢛⡛⢙⢻⡟⢛⠟⣻⡏⡟⡛⡟⣻⣩⢽⢛⡛⡛⡟⡟⣛⠏⡟⣛⡻⢛⠟⣿⠙⡽⣛⠋⡗⣿⢹⢺⢻⢻⢻⢻⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣷⣶⣷⣷⣶⣾⣷⣾⡷⣿⣶⣷⣿⣷⣾⣶⣷⣶⣷⣷⣿⣶⣷⣾⣶⣾⣶⣿⣾⣾⣶⣶⣷⣿⣶⣾⣾⣾⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠈⣭⢃⢝⠉⡏⠍⡏⡍⠍⡇⠍⡏⠍⢩⡝⣏⠭⡏⡍⣿⢩⢩⢹⠩⢹⠩⣏⠶⢹⠔⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Slopwatch_Google_News_is_Pumping_in_Lots_of_Web_Traffic_Into_Fa.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Slopwatch: Google News is Pumping in Lots
of Web Traffic Into Fake Sites That Say
"Linux"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


This morning we published_a_"Slopwatch", but here we are again with yet more
(newer) examples, starting with LinuxSecurity, which became a slopfarm last
year or the year before that. These are fakes:


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Debian_13_“Trixie”:_RISC-V_Support,_Security_Upgrades⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Hidden_in_Plain_Sight:_Koske_Linux_Malware’s_Stealthy_Panda
                               Image_Delivery⦈_


Notice the SEO around "Debian", "Linux", "security".... classic spamfarm
tactics, albeit in slopfarm form (constructed with LLMs).


There's also the webpronews slopfarm, propped up by Google News. Today Google
had the results for "Linux" stacked/stuffed with the following fake 'articles':


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Desktop_Share_Hits_6%_Amid_Windows,_macOS_Privacy
                                    Woes⦈_


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


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Kernel_6.17_Boosts_SSD_Zeroing_with_NVMe_and_SCSI
                                   Support⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_Kernel_6.16:_Btrfs_Boosts,_Rust_Integration,_Intel_TDX
                                  Security⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_6.17_Staging:_WiFi_Driver_Removals,_Enhancements,_and
                                10K_Line_Cut⦈_


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


The above (most but not all) are lots of Phoronix junk with slop images. Those
are just bot versions of Phoronix pages. For sure a lot of the above are just
Phoronix articles rewritten by LLMs; webpronews is publishing using a worrisome
form of "state-of-the-art" plagiarism. webpronews is a parasite.


Also propped up by Google News today was this family of slopfarms: (a network
of at least 3 fake news sites, operated by the same people and made to look
real)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linux_6.16_Released_–_Optimized_for_Enhanced_Performance_and
                                 Networking⦈_


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Apple’s_New_Containerization_Feature_Seamlessly_Integrates
                             Kali_Linux_on_macOS⦈_


Blaming Windows and SAP issues on "Linux": (see Linux_Fear,_Uncertainty,_Doubt_
(FUD):_Blaming_the_Wrong_Things_on_"Linux")


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇New_Gunra_Ransomware_Linux_Variant_Launches_100_Encryption
                   Threads_with_Partial_Encryption_Feature⦈_


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Hackers_Exploiting_SAP_NetWeaver_Vulnerability_to_Deploy
                          Auto-Color_Linux_Malware⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Hackers_Target_SAP_NetWeaver_to_Deploy_New_Auto-Color_Linux
                                   Malware⦈_


So basically, I estimate that somewhere between 30% and 40% of today's "news"
about "Linux", as seen by Google News, is LLM slop. That's really appalling. █


    * Links_30/07/2025:_Climate_Calamities_Highlighted,_Kyrgyzstan_Crackdown_on
      Expression/Freedoms
    * Slopwatch_Makes_the_Web_Better


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

                    ䷩ 𝚕𝚒𝚗𝚎 4648

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Slopwatch_Makes_the_Web_Better.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Slopwatch_Makes_the_Web_Better.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Slopwatch Makes the Web
Better⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Latest_Linux_and_Open_Source_News_(Original)⦈_


Ever since we called out LinuxIac [1, 2, 3] on the LLM slop (I had also
contacted the editor, who did not deny this) the site has improved; I manually
check its output (both manually and with tools, but the eye can typically catch
slop if one is familiar with its patterns and originality; I became quite good
at it) every day, sometimes several times per day. There's a real improvement.


Remember what happened to BetaNews?


See, calling out the culprits can help. Sometimes they decide to rethink their
approach, knowing they're being watched and would likely get caught (and called
out) if they cheat with LLMs.


I've meanwhile noticed this new_article_in_French. The image looks like slop,
but the text seems original, even if I cannot comprehend French:


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


Richard Stallman calls LLMs "bullshit generators". I agree but would rather not
use a word like "bullshit".


If we can convince people to be original and creative, not "bullshit artists",
society will be better off and honest_people_will_gain. █


    * Slopwatch:_Google_News_is_Pumping_in_Lots_of_Web_Traffic_Into_Fake_Sites
      That_Say_"Linux"
    * My_Experience_With_Judges_Has_been_Positive,_But_We_Must_Still_Pursue
      SLAPP_Reform_in_the_United_Kingdom


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡿⠿⡿⣿⣿⠿⣿⠿⡿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⢀⢿⡿⡼⣑⠇⡸⣿⢾⢾⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣶⣦⣿⣿⣿⣿⣯⣶⣮⣶⣷⣷⣴⣷⣶⣼⣴⣷⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣳⣁⣆⣼⢔⣰⡇⢿⣀⣎⣸⣇⣸⣗⣸⣀⡵⣸⣗⣇⠰⣁⣼⣀⣿⣎⣗⣸⢇⣰⡱⡱⣽⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣀⣤⣤⣀⣀⣀⡀⠀⣀⣀⢀⣄⠀⣀⣿⣿⣿⣿⣶⣾⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡟⠛⣿⣿⣶⣿⣿⠛⠛⠛⣿⣿⣇⣸⣿⣿⣸⣟⣆⣿⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⣿⣿⢿⣿⣟⢹⣿⣿⢀⣠⣄⣿⣿⣿⣿⣿⣿⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣾⣿⣿⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣷⣿⣟⢿⣿⣿⣿⣿⣿⣷⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣒⣒⣚⣚⣳⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⠟⠃⠒⠚⠛⠛⠛⠛⣿⡟⢿⣿⣷⡙⠛⠛⠒⠒⠒⠒⠚⢿⣿⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠙⢛⠗⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⡿⠞⠖⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⠀⠀⠀⢠⡄⠀⠄⠀⠀⠀⢀⠀⠀⢠⡄⡄⠀⢤⡄⠀⣤⣤⠀⣩⢽⠋⢩⢿⡁⠀⢠⣠⡄⠀⠀⣭⢭⡖⠢⠀⡀⠀⠀⠀⠀⠄⡀⢠⠀⠀⢠⠀⡄⠤⡀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⢰⠽⡄⡏⣏⣹⡏⡇⡇⡏⡇⣫⢸⣡⣝⣿⡇⣇⠀⣘⡧⣀⣧⣸⣀⢙⡺⠀⢸⢺⣸⣹⢾⣸⡃⣫⠀⢸⣀⡟⣇⡏⣏⠀⢳⢿⡏⡇⣏⢸⢹⠀⢸⣀⠇⣼⡁⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠠⢤⢠⢤⢠⢼⠀⢸⣹⢺⠀⡄⡄⡤⡤⡦⡠⢄⡠⢤⣴⢼⢤⡀⠰⣍⢠⢠⣤⠤⣠⡤⣄⡤⡄⡤⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠸⠙⠘⠘⠘⠜⠀⠸⠔⠛⠆⠗⠃⠣⠀⠗⠳⠞⠳⠞⠸⠘⠘⠃⠐⠞⠙⠞⢻⠶⢻⠶⠋⠳⠃⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣻⢿⠛⡟⣿⠛⣟⣿⣿⣿⢿⠛⣿⣿⣟⢿⣿⢻⢛⣿⢛⣿⣿⣿⣿⣿⣿⡿⣿⣿⢟⢿⡿⣻⢟⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣞⣻⣠⣠⣃⣿⣐⣇⣸⣀⣃⣘⣀⣓⣽⣏⣚⣷⣸⣂⣿⣐⣇⣸⣂⣝⣀⣇⣘⣗⣽⣰⣸⣗⣺⣘⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠤⠄⠀⠀⠀⠠⠄⡀⠀⢀⣤⣤⢠⣄⢠⣤⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⢀⡶⠶⠔⠲⢆⠀⢸⠀⢸⣇⣶⢸⡟⣾⡿⣇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣗⣁⣃⢘⡄⣺⣀⣇⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠈⠓⠃⢀⠁⠂⠘⡆⠹⠋⠀⢰⡶⣦⢰⣆⡀⣀⢀⡀⣀⣠⣄⣶⣶⠀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⡆⡁⠀⠀⠂⠀⠂⠀⠀⢸⣯⣽⢼⣿⡏⣿⢸⡧⣿⢸⣇⣿⢿⣌⣿⡶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢀⠀⠨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠑⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠍⠀⠀⠈⠀⠁⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⠿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⡿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣞⣻⣀⣇⣨⣻⣟⣸⣫⣅⣏⣺⣇⣛⣁⣸⣀⣻⣈⣷⣁⣄⣇⣸⣸⣷⣅⣘⣇⣎⣿⣰⣍⣊⣹⣸⣀
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢾⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⡿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣶⣶⣴⣶⢸⣿⡇⣶⣶⢸⣿⣧⣶⣶⡄⣠⣶⣶⡖⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣳⣱⣐⣿⣸⣇⣫⣂⣸⣘⢻⣇⣀⣆⣐⣸⣨⣆⣸⣸⣨⣂⣰⣰⣆⣃⣇⣾⣐⣀⣿⣘⣁⣸⣀⣆
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣤⣽⣿⢸⣿⡇⣿⣿⢸⣿⣧⣤⣿⡟⢿⣿⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢈⣭⣋⣽⣿⠈⢭⡅⣭⡍⡨⡉⡍⣽⠍⣤⢠⢩⡿⡩⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⡈⠙⠛⢋⣁⠘⠼⠟⠻⠇⠣⠂⠧⠿⠕⣿⠖⠾⠇⠇⠀⠀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣦⠂⠀⠀⠂⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣏⠉⢹⡇⠙⢽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠀⠘⡀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠻⠀⠸⠇⠀⠉⠙⠛⠻⠿⠛⣩⣿⣿⣿⣿⢿⣿⡄⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⠿⣦⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡆⠀⠀⠀⠀⠀⠀⠈⠁⠈⠷⠈⢿⣿⣿⡌⡀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⢢⣤⣤⣄⢙⣾⣿⣿⣿⠄⠀⠀⠀⠀⠀⠐⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠦⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⢸⣿⠉⡇⢫⡇⡝⢏⠋⡟⡅⣿⠙⡯⡏⢻⠁⡟⣽⢻⠙⡟⣹⣿⣿⢹⡿⢹⡏⡟⡙⡹⡝⠝⢸⠟⡏⡇⡯⢻⡋⣿⢫⠘⡏⣿⠘⡝⠫⢹⡟⣽⠛⣙⢸⡇⣿⢨⠋⡝⡙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣩⣇⣿⣸⣹⣎⣸⣸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢒⣄⠀⠀⢸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣻⣿⣿⣟⣟⣻⣿⣻⣿⣛⣟⣻⣿⣿⣟⣿⣿⣻⣿⣿⣟⣿⣻⣟⣿⣿⣟⣿⣻⣻⣿⣿⣻⣻⣟⣟⣿⣻⣿⣻⣻⣿⣛⣟⣛⣿⣛⣿⣻⣟⣿⣿⣻⣟⣟⣻⣟⣿⣻⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣽⣽⣭⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣽⣯⣯⣽⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣭⣭⣿⣿⣽⣭⣿⣿⣯⣍⣿⣿⣿⣽⣿⣿⣿⣯⣯⣿⣿⣯⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣟⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣽⣿⣿⣿⢿⣯⡯⢿⣿⣿⣭⣿⣿⣽⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⡿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⣟⣟⣿⣿⣻⣿⣿⣟⣻⣿⣟⣻⣟⣿⣿⣻⣛⣿⣟⣻⣿⣟⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣽⣿⣿⣽⡿⣿⣿⣽⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣾⣿⣷⡶⣿⣾⢿⣿⣿⣿⣷⣾⣿⡿⡷⣿⣿⣷⡿⣿⢿⡿⣿⣿⣿⣿⢿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣿⣻⣻⣿⣟⣟⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⣿⣻⣿⣿⣻⣟⣿⣿⣟⣻⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4784

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Some_People_See_What_Others_See_But_Only_40_Years_Later.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Some_People_See_What_Others_See_But_Only_40_Years_Later.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Some People See What Others See... But Only
40 Years Later⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Stallman_was_right_from_the_beginning,_and_big_tech_have
  proven_over_and_over_again_that_they_are_incapable_of_being_good_citizens⦈_


In science fiction (sci-fi) literature, authors make predictions either about
something that they envision or consider strictly fictional; sometimes it is
something they want, or something they definitely do not want (i.e. it can be a
cautionary tale). The work known as "1984" envisioned that year in some certain
way and even 40+ years after the real 1984 people still refer to current,
contemporary events as "1984" (some commentary on what skinnerboxes,
surveillance and censorship would potentially look like).


The above screenshot shows hours-old comments about RMS (Dr. Stallman). Ignore
the context of the nasty comments (it's a generally unsavoury site controlled
by the rich). To me, personally, some time around 2004 was the year I became
better aware of the warnings that Stallman et al had issued for decades prior.
Before 2004 I was just barely exposed to these ideas. Not many people talked
about them. For instance, not many people believed that the locations of their
mobile_phones were not just tracked all the time but this data was also sold.
Up until 2003 I had carried around (with the battery removed) a 1990s Motorola
'dumb phone'. That then... abruptly ended. The benefit of being able to place
calls was outweighed by all those other factors.


When people deviate from "the norm" they typically get ridiculed and dismissed
as "crazy". That's the first step. █


    * Links_30/07/2025:_Tea_Class_Action_and_Google_Killing_the_Web_With_Slop
    * Riot_for_peace_&_Love:_Catholic_Influencers_and_Digital_Missionaries
      welcome_Jubilee_of_Youth


⣿⣛⣏⣛⣋⣏⣹⣟⣛⣻⣛⣛⣙⣛⣻⣟⣛⣛⣻⣙⣛⣻⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⣉⣹⣉⣉⡹⣉⣉⣩⣉⢹⢍⡉⣹⢉⡉⣉⣹⣉⡹⣙⣉⣉⣉⣉⣉⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⣏⡉⡉⢹⣹⡉⣉⣉⡋⣉⣹⣉⡉⣉⢉⣉⣍⣉⡉⣉⢩⣉⣉⣹⣉⣉⣉⣉⣉⣉⡉⣹⣉⣉⣉⣉⣉⣍⣿⣿
⣿⣿⡇⠦⠴⢤⠴⠦⢢⠠⡤⠇⠄⢴⡦⠦⣴⣷⣦⣦⣧⣦⣮⣤⣴⣤⣧⣴⣴⣥⣼⣴⣴⣥⣦⣤⣦⣼⣴⣦⣤⣴⣦⣮⣴⣤⣧⣶⣥⣴⣦⣦⣦⣤⣴⣴⣤⣴⣤⣦⣧⣧⣤⣦⣤⣴⣥⣦⣧⣦⣤⣤⣧⣴⣧⣼⣿⣿
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⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⠿⡿⡿⢿⠿⠿⢿⠿⢿⠿⠿⢿⡿⡿⠿⢿⠿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣾⠶⡞⠶⠾⠶⠶⢷⡾⠷⠶⠾⢶⠾⠶⢶⠿⠷⠶⢶⠾⢶⠶⠶⠶⠾⠿⠿⡟⠿⠿⠿⢿⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠷⡾⠾⠾⠶⢾⠷⠷⢶⠶⠾⠶⠶⠾⠷⠶⠾⠾⢾⠾⠶⡿⠾⠾⠾⠶⠷⠶⢶⠶⢾⠶⠶⠾⡶⠶⠿⠿⠿⡿⠿⡿⠿⠿⠿⠿⢿⠿⢿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣓⣂⣓⣲⢖⣲⣈⣒⣒⣚⣖⣶⢐⣋⣖⣚⣂⣖⣒⡘⣖⣒⣗⣒⣒⢒⣐⣚⢲⣒⣰⣘⣒⡆⣒⣇⣲⣐⣒⣖⣓⣒⣑⣖⣲⣒⢺⣈⡲⣞⣒⣀⣒⢐⣒⡖⣒⣒⣒⣒⣒⣲⣲⢞⣒⣒⣒⣒⣓⣲⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4843

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/The_Register_Relays_Microsoft_Marketing_Dubs_That_Marketing_Res.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/The_Register_Relays_Microsoft_Marketing_Dubs_That_Marketing_Res.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Register Relays Microsoft Marketing,
Dubs That Marketing "Research"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


Last month: What_Linux_Foundation_'Research'_is:_Paid_Marketing (they want to
confuse people by calling their PR or marketing spam "research", pretending
that it is a separate thing)


Hours ago they did a "Microsoft sez" piece, linking to microsoft.com and saying
there's a "project, described in a pre-print paper..."


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Microsoft_researchers:_To_fend_off_AI,_consider_a_job_as_a
                                 pile_driver⦈_


"I analysed the finances of The Register last week (its parent company)," I
told somebody a few days ago, "and I worry it'll drift towards another goal,
maybe new ownership structure. There is more information in http://
techrights.org - I think the new EIC [Editor in Chief] already reads it." (The
previous one told me that he did)


"I really doubt it," an insider replied. "But so long as they keep paying me,
and remain as editorially independent as they are now, I don't vastly care.
It's a good place to work. By next year, this will have been the longest job of
my life and I hope it continues for years to come."


See, whether he gets paid by them or not isn't relevant. That's fine for him.
They, unlike me, pay him. So he'd defend them from critics.


"You need to choose your targets much MUCH more carefully. Most of what little
I have seen from you is way off beam," he said. That's funny given that his old
boss told me that he regularly reads this site. So words like "what little" are
just defensive; he read a lot and he's trying to pretend it is "little". I was
told they read us every day. The EIC told me so.


But here's the most troubling part. There's now this insinuation that the
threat to Linux isn't Microsoft. To quote: "There are plenty of more nefarious
subtle trends. Go look at XLibre for instance. Look at who Poettering works
for. Look at the people behind Wayland and GNOME. Or who is behind Btrfs and
Bcachefs."


Reading between the lines, the dismissive tone suggests we need to look away
from Microsoft and instead scapegoat people who still use X or something to
that effect.


My trust in The Register, whose new EIC is a Microsofter, is rapidly waning. As
shown at the top, now it's shamelessly relaying Microsoft marketing as
'articles'. It moreover puts Microsoft-related logos right next to its logo/top
banner. I predict that over time it'll get worse, more so due_to_financial
pressures. █


    * Dealing_With_Sociopaths,_Liars,_and_Cranks
    * "The_Unix_Kernel"


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⢸⡘⣰⢸⢸⡁⡶⢾⢰⣎⢰⠆⡧⢌⠒⡁⣶⢸⡇⣿⢸⣿⡇⢰⡇⢬⢼⠤⡑⢊⢨⠤⡗⡤⢸⠀⣾⠰⡶⡇⣴⠀⡇⢤⢼⠀⣾⢌⡐⣿⢾⣿⣿⠀⣿⠰⡇⢸⣿⡇⣏⢨⠤⡇⣶⠈⡁⡶⢸⣿⡇⢾⠀⡇⢸⠀
⣿⣿⣾⣷⣿⣾⣾⣿⣶⣿⣾⣿⣷⣾⣿⣶⣾⣿⣶⣿⣷⣿⣶⣿⣷⣾⣿⣶⣿⣷⣶⣿⣷⣾⣷⣾⣶⣶⣿⣷⣾⣷⣿⣶⣿⣶⣿⣶⣿⣷⣾⣿⣾⣿⣿⣷⣿⣷⣶⣿⣿⣷⣿⣷⣾⣷⣿⣶⣷⣾⣾⣿⣿⣶⣾⣷⣾⣶
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠛⣿⣿⣿⣿⣿⣿⢻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢒⡂⣿⣿⢸⡁⣶⢘⠀⣶⢸⣿⠗⡒⢸⣔⡒⣿⣿⢒⡂⣿⣿⠠⡆⢹⢸⠀⡇⣒⣸⣿⡇⣶⢸⡇⣶⠀⣇⠛⣸⠁⣂⣹⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣾⣟⣸⣷⣶⣾⣶⣶⣾⣿⣷⣶⣶⣶⣶⣿⣿⣶⣶⣾⣿⣰⣶⣿⣾⣶⣷⣶⣾⣿⣷⣶⣶⣷⣿⣶⣿⣶⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢈⠏⡏⡹⣉⡙⡅⠙⡍⠇⠹⡏⢻⣯⢋⣉⠏⢹⢈⡟⢹⡭⠫⣯⢋⡉⣿⣿⠸⢉⠋⣿⡍⡏⠹⡩⢻⢿⡟⢹⡇⡟⢙⠯⢘⠋⡻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣯⣯⣿⣭⣿⣺⣯⣯⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⣿⣨⣽⣬⣽⣛⣾⣰⣽⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4935

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/The_Unix_Kernel.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/The_Unix_Kernel.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ "The Unix
Kernel"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


               🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNU_Linux-Libre_6.15_kernel⦈_


"Linux is a clone of the Unix kernel," says this_announcement_of_GNU_Linux-
Libre_6.15_kernel, posted by Freedo (pseudonym; mascot) on Monday in linux-
libre.


A day earlier we published: Pushers_of_systemd_Rewrite_History_(Richard
Stallman_Said_UNIX_"Was_Portable_and_Seemed_Fairly_Clean")


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


The gist of it was, Richard Stallman said: "I never used Unix (not even for a
minute) until after I decided to develop a free replacement for it (the GNU
system). I chose that design to follow because it was portable and seemed
fairly clean. I was never a fan of Unix; I had some criticisms of it too. But
it was ok overall as a model."


"Unix" - or "POSIX" as he might call it - was not just a kernel and GNU didn't
develop a kernel (Hurd) until much later. It would be misleading to call Unix
or UNIX a kernel, even if Apple borrowed [sic] one.


Linux was inspired by MINIX and did so poorly, according to the creator or
MINIX. Later Linux_got_plugged_into_GNU, which had a Unix-like design. █


    * The_Register_Relays_Microsoft_Marketing,_Dubs_That_Marketing_"Research"
    * Last_Month_Our_IRC_Community_Turned_17


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣽⡟⣿⣿⣕⣷⣏⣿⣿⣿⣿⣿⢏⣀⡀⢀⣀⣈⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣹⡏⣭⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢏⣀⡀⢀⣀⡈⢿⣿⣿⣿⣿⣿⣿⣿⢜⣿⣿⡿⣿⣜⣿⣿⣿
⣿⣿⢛⣾⣿⣿⡑⣽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡾⡿⣿⣿⣷⡟⣿⡇⣏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣿⢻⣶⣿⣿⣿⣿
⣿⣿⣟⣙⣿⣟⡷⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣤⣿⣿⢯⣺⣿⣿⣿⡿⣤⢿⢿⣼⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣻⣏⣶⣿⣯⢦⣿⣿⣿⣿⣿
⣿⠽⣢⣷⣿⣷⣏⣝⢿⣿⣟⣵⣿⣿⣿⣿⢿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣛⢺⣿⣽⣺⣿⡿⠿⠿⠷⠭⠶⠭⠾⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠆⠘⠛⠉⠉⠛⠙⠻⢥⡄⠈⢿⣿
⣿⣿⡯⢿⣭⣿⢱⣿⢸⣿⣦⣿⣿⣿⣿⣿⢸⣿⠀⢠⣤⣤⣤⣤⣤⢠⢠⢸⣿⣿⢻⣿⡇⢠⣤⣤⣤⣤⣤⣤⡄⠀⣿⣿⡟⢟⣿⣿⡇⠀⣤⣤⣤⣤⣤⣤⣤⠀⢸⣿⣿⣿⣿⣿⢩⣭⡥⠀⠐⠀⠀⠀⠀⠈⢁⣠⣾⣿
⣿⣿⣹⣋⣻⣯⡃⣿⢸⣿⡍⠛⠟⠃⣿⣻⢸⣿⠀⢸⢸⣿⣿⡇⣿⠨⡞⣻⣮⢳⣯⣿⡇⢸⡇⣽⡞⣿⢷⢸⡇⠀⣟⢉⡺⣕⡻⣿⡇⠀⣿⢸⣿⣿⣿⡇⣿⠀⢸⣿⣿⣿⣿⣿⢸⣿⠖⠂⠀⠈⠀⠀⠀⠸⢿⣿⣿⣿
⣿⡏⣯⢾⠴⠮⠁⣿⣜⣛⣒⣛⣂⣐⣚⣚⣸⣿⠀⢸⢸⣿⣿⠇⣿⢨⣽⣛⢎⣬⢿⣿⡇⢸⡇⣯⣟⣒⣺⢸⡇⠀⣿⣧⡄⢚⣾⣿⡇⠀⣿⢸⣿⣿⣿⡇⣿⠀⢸⣿⣿⣿⣿⣿⢲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿
⡿⣹⣿⣿⣥⣤⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣮⣭⣬⣥⣿⠠⣦⡥⢞⣼⢾⣿⡇⢸⣧⣭⣭⣭⣭⣼⡇⠀⣿⣿⢸⡇⣿⣿⡇⠀⣿⣬⣭⣭⣭⣥⣿⠀⢸⣿⣿⣿⣿⣿⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⢳⣿⢿⣷⡿⢿⣾⠇⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠉⠨⣯⢇⢟⣵⣿⣿⡇⢸⡇⠀⠀⠀⠀⠈⠁⠀⣿⣛⠊⢃⣛⣿⡇⠀⣿⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⣿⣿⣿⣮⣭⣍⡀⢠⣾⣿⣷⠀⠀⠀⢰⣿⣿
⣿⣟⣽⢝⣾⣿⣞⣷⣜⢿⣍⠉⠍⠉⠉⠉⠙⣿⠀⢸⠀⠀⠀⠀⣤⢨⣫⢲⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⢠⡄⠀⣿⡿⢰⡀⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⣴⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⣬⣟⠟⠁⠀⠀⠀⢸⣿⣿
⢻⣼⣳⣿⣿⣿⣿⣷⣻⠷⠌⢀⠀⠀⠀⠀⢠⣿⠀⢸⠀⠀⠀⠀⣿⢸⠏⢸⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⢸⡇⠀⣿⡇⣾⣧⢹⣿⡇⠀⣿⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣯⠅⠀⠀⠀⠀⢻⣿⣿
⣷⢿⣿⣟⣿⢿⣟⣿⢿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣀⣀⣀⣀⣿⠨⠀⢸⣿⣿⣿⣿⡇⢸⣇⣀⣀⣀⣀⣸⡇⠀⣿⢸⣿⣿⡜⣿⡇⠀⣿⣀⣀⣀⣀⣀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣾⠘⢿⣿
⡫⠾⠷⠾⣱⠙⠯⠶⠾⡦⣀⣀⣀⣀⣀⣀⣘⣛⣀⣘⣛⣛⣛⣛⣛⣘⣃⣘⣛⣛⣛⣛⣃⣘⣛⣛⣛⣛⣛⣛⣃⣀⣛⣛⣛⣛⣃⣛⣃⣀⣛⣛⣛⣛⣛⣛⣛⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⠛⣛⠛⠀⠐⠂⠀⠛⠃⣀⣛
⣿⣶⣶⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣶⣶⣧⣤⣤⣥⣾⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⣾⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠁⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⣤⣤⣿⣧⣤⣤⣤⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠸⣿⡟⠛⠂⠀⠀⠀⠀⠀⣀⣀⣀⠀⡀⣀⣀⣄⣄⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣀⣤⣀
⣀⠀⢀⠀⠂⠒⠻⡿⡿⢿⣷⣶⠀⠆⠀⠀⠀⠁⠩⠄⠀⠙⢻⣿⣿⣅⣨⣍⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢄⠀⠒⠒⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠻⠿⣿⢿⣿⣿⣿⡿⠻⢛⢰⣿⠀⠀⠀⢒⣚⣓⣾⣷⣿⣿⣿⣿⠿⣿⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠙⠑⠶⣿⠀⣛⣣⠀⠀⠐⠞⠂⡋⠉⠙⠙⠛⠋⢀⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠇⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⠯⠙⠛⠉⠉⠉⠉
⠉⠉⠉⠀⢉⠁⠉⢿⠌⣳⣦⠌⠁⣭⡿⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡴⣻⣇⣤⣤⣤⣄⠀⣀⡀⠀⠻⠿⠿⠿⠿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣄⠀⠀⠀⣀
⣤⡄⠠⢀⣿⡁⠉⠀⢨⣧⣄⣰⡒⠀⠀⠀⠀⠀⠀⠘⠀⠒⠖⠖⠒⠒⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠿⢿⣻⣛⣛⣻⣻
⣤⡷⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠿⠿⠿⠿⠿⣛⣛⣻⣉⣉⣹⣿
⣿⣿⣿⣿⣿⣿⣠⣭⣥⣤⣶⣷⣿⠀⠁⠠⠓⣒⢂⢐⣞⡛⠓⣚⣑⣄⠉⠁⠈⢿⣿⣿⣿⣿⣉⣉⣉⣹⣿⣿⣿⣿⣿⡿⠿⠿⢿⡿⠿⠿⢿⡧⢤⣽⣿⣿⣿⠤⠄⣤⣤⣤⣦⣾⣶⣶⣶⣶⢶⡶⡶⠿⣿⣿⠉⠉⢹⣿
⠟⠳⣿⠿⠿⠷⠀⢾⣿⣭⣽⣿⣿⠀⠄⢰⠂⣤⣀⣭⣭⡯⡭⢽⠍⠉⠉⣉⣿⡡⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⠶⠶⢷⠶⠦⢾⠤⠀⠋⠉⢉⣿⠄⠀⣬⣽⣿⡿⢿⢿⣿⣷⣺⣿⣧⣯⡤⠸⣿⠀⠀⣾⣿
⠀⣀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣿⣿⠀⡇⠸⠏⠹⡟⠹⠽⢭⣭⣽⡉⠉⢹⣿⣻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⡀⣀⣀⢀⣀⣴⣾⠻⢾⣿⡀⠀⣩⣽⣿⠒⠀⣿⣿⣿⣿⣿⣿⡇⠛⣿⣿⠶⠾⣿⣿
⢛⡛⣿⣷⡟⢻⣿⣛⣛⣛⣻⣿⣿⣶⣷⣾⣿⡯⢱⣁⣘⣯⣽⣿⣷⣶⣶⢿⡿⠃⣸⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠻⠿⠿⠿⠿⠿⢿⣿⣾⣿⡏⠈⠁⣿⣿⠀⢨⠿⠛⠉⠻⢾⣿⡧⠶⠾⢿⠷⡿⣿⣿
⠙⣛⣿⣿⣷⡟⣭⣍⣉⠉⣛⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣟⣿⡿⠛⠁⠀⠀⠉⠀⢹⣿⣿⣿⣿⡙⠉⣹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠿⣿⣿⠇⠀⠀⣆⣿⣶⣿⣷⣶⣶⣴⣼⣿⣗⠄⣀⣽⠀⠁⣿⣿
⡧⠤⣿⣿⠿⣧⣿⣿⡿⠻⠿⣿⣷⣾⣿⣿⣿⡛⢫⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡟⠛⠓⠀⠛⣻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣻⣿⣷⢸⣿⣿
⣷⠄⣿⣿⣶⣼⡯⠈⢠⡤⢀⣈⠙⢾⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣾⣿⣿
⣿⣶⣾⣿⣿⣿⣷⡖⣰⣨⣿⣧⡄⣺⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠏⠉⢹⣛⣿
⣿⣿⣿⣿⡿⢷⣿⣧⣻⣿⣿⡵⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⣿⡿⠿⣿⠏⢠⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⠘⢛⣁⠀⠰⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣀⣾⣷⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⢀⣀⢀⣤⡤⢀⣀⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠉⠉⣽⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣌⠛⣥⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡤⣄⣿⠟⠏⠙⠄⠈⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⢱⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠈⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁⠈⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿
⠛⠛⠛⣿⣿⡿⢿⣷⣷⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧⡸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢸⣷⣾⣿⠿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠐⠆⠀⠐⠢⠉⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠁⠀⠙⠛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠈⠉⠁⠈⠙⠛⠀⠛⠿⠿⢿⠿⢿
⢀⣀⢰⡇⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣆⢸⣿⣿⢻⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⣾
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠸⠿⠿⢸⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣾⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⡟⣿⣿⣇⣻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⣶⠒⠒⠒⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠓⠛⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠋⠛⠛⣾⢿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠿⢿⣧⡖⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣶⣶⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠸⣿⡟⠛⠃⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣀⣀⣀⡤⣤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⣀⡀⢀⢀⣀⣀⡀⣀⣄⣤⣄
⣀⠀⢀⠀⠂⠐⠻⣿⠿⢿⣷⣖⠀⠆⠀⠀⠀⠉⠩⠄⠀⠉⢹⣿⣿⣍⣩⣭⣻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡇⠒⠒⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠻⠿⣿⢿⣿⣿⣿⡿⠛⢛⢰⣿⠀⠀⠀⢒⣺⣳⣾⣿⣿⣿⣿⣿⠿⣿⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠑⠶⣿⢀⣛⣣⠀⠀⠀⠔⠂⠏⠉⠙⠙⠛⠋⢀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠛⠉⠉⠉⠉
⠉⠉⠉⠀⢉⠁⠉⣿⠌⣻⣦⠄⠁⣭⡿⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣇⣤⣤⣤⣄⠀⣀⡀⠀⠿⠿⠿⠿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⡿⠿⠀⢄⠀⠀⠀⣀
⣤⡄⠀⢀⣿⡁⠉⠀⢨⣧⣄⣰⡒⠀⠀⠀⠀⠀⠀⠘⠀⠲⠖⠒⠒⠒⠀⠀⠈⢿⣿⣿⣿⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⡀⠀⣾⣿⣗⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⠿⢿⣻⣛⣛⣻⣻
⣤⡵⣷⣿⣿⣿⣶⣿⣿⣿⣿⣿⣗⠀⠂⠀⡀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠿⠿⠿⠿⠿⣛⣛⣻⣉⣉⣹⣿
⣿⣿⣿⣿⣿⣯⣠⣭⣥⣤⣶⣷⣿⠀⠁⠠⠛⣒⢂⢐⣞⠓⢒⣋⢐⡁⠩⠅⢌⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠿⠿⢿⡿⠿⠿⢿⡧⢤⣽⣿⣿⣿⠤⠄⣤⣤⣤⣤⣾⣶⣶⣶⣶⢶⣶⡶⠿⢿⣿⠉⠉⢹⣿
⠟⠳⣿⡿⠿⠷⠀⢾⣿⣭⣽⣿⣿⠀⠄⠰⠀⣠⣀⣭⣭⡯⡭⠽⠍⠉⠉⣋⢥⠄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⠶⠶⣷⠶⠤⢾⠤⠀⠛⠋⢩⣿⠄⠠⣬⣽⣿⡿⢿⢿⣿⣷⣺⣿⣧⣧⡄⠨⣿⠀⠀⣾⣿
⠀⣀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣿⣿⡀⡇⠨⠏⠽⡭⠩⠽⢭⣭⣭⢍⠈⠻⠏⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠻⢾⣿⡄⠀⣩⣽⣿⠒⠀⣾⣿⣿⣿⣿⣿⡇⠻⣿⣿⠶⠶⣿⣿
⢻⡛⣿⣷⡟⢿⣿⣛⣛⣛⣻⣿⣿⣷⣷⣾⣿⣍⣁⣤⣴⡿⠧⠽⠃⠀⢀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠦⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠀⠉⠉⠙⠟⠿⣼⣿⡋⠈⠁⣿⣿⠀⢸⠿⠛⠉⠻⢾⣿⡧⠶⠶⢿⠶⡿⣿⣿
⠙⢛⣿⣿⣷⡟⣭⣍⣉⠉⣛⣿⣿⣿⣿⣿⡟⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣫⣯⡀⠀⠀⢠⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣦⣿⣴⣿⣿⣾⣶⣦⣼⣿⡗⡄⢄⣽⠀⠁⣿⣿
⡦⠤⣿⣿⠿⣷⣿⣿⡿⠻⠿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣻⣿⣧⢹⣿⣿
⣷⠄⣿⣿⣷⣼⡯⠈⢠⡤⠀⣈⠛⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣴⣆⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣾⣿⣿
⣿⣶⣾⣿⣿⣿⣷⡖⣠⣨⣿⣧⡄⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⢁⣙⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠏⠉⢹⣟⣿
⣿⣿⣿⣿⡿⢷⣿⣧⣿⣿⣿⣭⢼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⠶⣾⠯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢿⡿⠿⢿⠏⢠⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⠘⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡗⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⣀⢀⣤⡤⣀⣀⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠉⠉⣽⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣃⣸⡋⡷⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡤⣄⣿⠟⠟⠙⠄⠈⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢛⣿⢷⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢨⡉⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁⠈⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠛⠛⠛⣿⣿⡿⢿⣷⣷⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠈⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⢸⣷⣾⣿⠿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠐⠖⠀⠐⠾⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠉⠁⠈⠙⠛⠀⠙⠿⠿⢿⠿⠿
⢀⡀⢸⡗⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣷⣆⢸⣿⣿⢻⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡤⣴
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠸⠿⠿⢸⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⣧⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⡟⣿⣿⣇⣿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠒⠒⠒⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀
⠐⠛⠻⠿⠛⠻⠓⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⣸⣿⣿⣿⣿⡟⠋⠛⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣡⣤⣿⣷⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠸⣿⡟⠛⠂⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣀⣀⡀⠀⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⢀⠀⣀⣀⣠⣀
⣀⠀⠀⠀⠂⠐⠺⠿⠿⢿⣷⣖⠀⠆⠀⠀⠀⠀⠩⠄⠀⠈⢹⣿⣿⣍⣠⣥⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠖⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠻⠿⠿⢿⣿⣿⣿⡟⠛⢓⠰⣿⠀⠀⠀⢒⣚⣓⣾⣷⣾⣿⣿⣿⠿⣿⠛⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠶⣿⠀⣛⣡⠀⠀⠀⠀⠀⠋⠉⠙⠙⠛⠋⢀⡄⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠏⠘⠛⠉⠉⠉⠉
⠉⠉⠉⠀⢉⠁⠉⢿⠄⣲⣦⠄⠀⣬⡿⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢻⣇⣤⣤⣤⣄⠀⣀⡀⠀⠛⠿⠿⠾⠟⠛⠛⢱⣿⣿⣿⣿⣿⣿⡿⠏⠀⢄⠀⠀⠀⠀
⣤⡄⠀⠀⣿⠁⠀⠀⢨⣧⣀⣰⡐⠀⠀⠀⠀⠀⠀⠈⠀⠒⠖⠒⠒⠒⠀⠀⠸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⡀⠀⣼⣿⡗⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣛⣛⣛⣻
⡄⠴⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⡗⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⠟⠛⠛⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠿⠿⠿⠿⣛⣛⣻⣉⣉⣹⣿
⣿⣟⣿⣿⣽⣯⣠⣭⣥⣤⣴⣰⣿⠀⠀⠀⠓⣒⠂⢐⣒⠙⠂⢀⢀⡀⠉⠁⢈⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠿⠿⢿⡿⠿⠿⢿⡧⢤⣽⣿⣿⣿⠤⠄⣤⣤⣤⣤⣾⣶⣶⣶⣶⢶⡶⡶⠿⢿⣿⠉⠉⢹⣿
⠗⠲⣿⠿⠿⠷⠀⠾⢿⣬⣽⣿⣿⠀⠀⢠⠀⣤⣀⣨⣥⠭⠍⠽⠍⠉⠉⣻⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠠⠶⠶⢷⠶⠤⢾⠤⠀⠋⠉⠉⣿⠀⠀⣬⣽⣿⡿⢿⢿⣿⣷⣺⣾⣧⣧⠄⢈⣿⠀⠀⣼⣿
⠀⣀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣿⣿⠀⡇⠠⠏⠩⡍⠉⠭⢩⣬⣭⠉⠀⠹⠏⠚⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠛⢺⣿⡀⠀⡩⣭⣿⠒⠀⣸⣿⣿⣿⣿⣿⡇⠛⢷⣿⠶⠶⣿⣿
⠛⠛⣿⣷⡟⢻⣿⣛⣛⣛⣻⣿⣿⣶⣷⣶⣶⣅⣁⢤⡬⡼⠧⠿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣍⣽⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠙⠟⠻⣼⣿⡃⠈⠀⣿⣿⠀⢠⠿⠛⠉⠻⢾⣿⡧⠶⠶⢿⠶⠾⣿⣿
⠙⠛⣿⣿⣷⡟⣭⣍⡉⠉⣛⣻⣿⣿⣿⣿⡟⠉⠉⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣟⣋⠉⠁⠀⢉⣭⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠃⠀⠀⣠⣿⣴⣿⣷⣶⣶⣤⣤⣿⡗⠄⢀⣽⠀⠀⣿⣿
⡦⠠⣿⣿⠻⣧⣿⣿⣿⢺⣿⣿⣧⢼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢋⣻⣿⣧⢸⣿⣿
⣦⠀⣾⣿⣶⣼⣿⣿⣿⣼⣿⣿⠋⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⣰⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠁⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣿⣿⣼⣿⣿
⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠉⠋⠻⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣯⣿⠏⠉⢹⣋⠿
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠖⣶⡿⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⠿⢿⠿⠿⢿⠏⢠⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⣠⣬⡿⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⢀⢀⣤⠄⢀⣀⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⠈⠛⣯⢾⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠙⢿⣿⣧⡄⡀⣽⠛⠋⠉⠀⠀⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡿⣿⣿⢾⣿⡇⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢪⠂⠨⢿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⣿⡿⢻⣿⣿⣷⠀⠀⠀⠀⠀⠙⠻⠁⠈⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿
⠛⠛⠛⣿⣿⡿⠷⠾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣿⠿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠐⠂⠀⠀⠀⢿⣿⡿⠁⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠛⠀⠙⠿⠿⠿⠿⠿
⢀⡀⢸⡇⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣷⣆⢸⣿⣿⢸⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⢶
⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠸⠿⠿⢸⣿⣿⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⠄⠀⠀⠀⠀⠀⠀⢠⡶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣼⣿⣿⢸⣿⡟⣿⣿⡇⢻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣶⠒⠒⠒⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠋⠛⠛⠘⠛⣿⣿⠛⠃⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣗⡠⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣋⣠⣼⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⣀⣀⣀⠤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⣾⣿⣷⣦⣀⣀⢀⣀⣀⠀⠀⠀⣀⣀⡀⣀⣀⣤⣀
⣀⡀⠀⠀⠂⠒⠻⠿⢿⣿⣿⣿⠛⠆⠀⠀⠀⠉⠩⠄⠀⠉⢹⣿⣿⣅⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀⠀⠒⠖⢶⠆⠀⠄⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠻⠿⣿⢿⣿⣿⣿⣿⣿⣿⢰⣿⡆⠀⠀⢒⣺⣳⣾⣷⣿⣿⣿⣿⠿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣰⣿⣧⠀⠀⠐⠔⠒⡏⠉⠛⠙⠛⠋⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠛⠛⠉⠉⠉⠉
⠉⠉⠉⠁⢉⠁⠀⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⢻⣇⣤⣤⣤⣄⠀⣀⡀⠀⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠠⣄⠀⠀⠀⣀
⣤⡄⠀⠀⣿⡉⠁⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠀⠒⠖⠒⠒⠒⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⡷⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣻⣛⣛⣛⣻
⣤⡾⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣶⣶⣿⣿⣿⣿⣿⣿⡧⠛⠛⠛⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣛⣛⣻⣉⣉⣹⣿
⣿⣿⣿⣿⣿⣯⣤⣭⣿⣿⣿⣿⣿⣿⡇⢠⠻⣒⣂⢐⣞⡛⢒⢋⢀⡈⠩⡄⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠿⠿⢿⡿⠿⠿⢿⡧⢤⣽⣿⣿⣿⣼⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⢶⣶⡶⠿⢿⣿⠉⠉⢹⣿
⠗⠳⣿⠿⠿⠿⢤⣿⣿⣿⣿⣿⣿⠋⡅⢸⠂⣬⣈⣭⣭⡯⡭⠽⠭⠉⠉⣏⣁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠠⠶⠶⣷⠶⠤⢾⠤⠀⠉⠋⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣧⣧⡄⢸⣿⠀⠀⣿⣿
⠀⣂⠀⠀⣠⣄⣿⣿⣿⣿⣿⣿⣿⡀⡇⠸⠏⠽⡭⠹⠽⢭⣭⣭⢍⠀⢿⣯⠆⣼⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡾⠛⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠻⣿⣿⠶⠶⣿⣿
⢻⡛⣿⡿⠛⣹⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣥⣤⣤⣿⡧⠿⠀⠀⢀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠻⢾⣿⡧⠶⠾⢿⠷⡿⣿⣿
⠙⡛⣯⠀⠰⣿⣿⣿⡿⠿⠋⠉⠽⣿⣿⠟⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⡉⠉⠀⢉⣭⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠹⠿⣿⣿⣿⣿⣿⡇⢰⣶⣼⣿⡗⠄⢄⣽⠀⠀⣿⣿
⡦⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠁⢸⣿⣿⣿⣧⣛⣻⣿⣷⢸⣿⣿
⣷⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣰⣆⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣻⣿⣿⣾⣿⣿
⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⢉⣹⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏⠉⢹⣛⢿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡾⣦⡿⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⢠⠙⠿⠀⠀⣸⣿⣿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠶⣿⣿⢯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡄⢀⣀⣤⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣀⣍⣹⣆⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠄⠈⢹⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡯⠌⠃⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠉⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠁⠰⠆⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠈⠁⠉⠛⠛⠀⠙⠿⠿⠿⠿⢿
⢀⣀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣷⣆⢸⣿⣿⢿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡤⣾
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠸⠿⠿⢸⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⣟⣿⣿⣧⢻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⣶⠒⠒⠒⠖⠒⠒⠂⠂⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠓⠛⠛⠛⠃⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡛⠋⠛⠛⠘⠛⣿⣿⣿⣿⡆⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠛⠉⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⣀⣨⣰⣤⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠹⣿⡟⠛⠂⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⡀⣀⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⣀⠀⠀⠀⠂⠒⠻⠿⠿⢿⣷⣦⣠⣦⣀⡀⠀⠀⠩⠄⠀⠉⢻⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠟⠉⠀⠀⠒⠖⢶⠆⠀⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⠻⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢒⣚⣓⣾⣶⣾⣿⣿⡏⢿⣯⣭⣝⣻⣿⣛⣋⣭⣿⣿⣿⢟⡃⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⠟⠐⠔⠂⠋⠉⠉⠙⠛⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣾⣻⣿⡯⠘⠛⠉⠉⠉⠉
⠉⠉⠉⠁⢉⠁⠀⣷⢿⣿⣿⣿⣏⣿⣿⡿⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠛⠓⢻⣇⣤⣤⣤⣄⠀⣀⡀⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⣿⠧⠠⢄⠀⠀⠀⠀
⣤⡄⠀⢀⣿⠉⠁⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠀⠲⠖⠒⠒⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣻⡛⣛⣛⣻
⣄⡶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣙⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠚⠛⠛⣿⣿⣿⣿⠀⠀⠀⣸⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣛⣛⣻⣉⣉⣹⣿
⣿⣟⣿⣿⣽⣏⣤⣭⣿⣿⣿⣿⣿⣿⠟⠠⠶⣒⠂⢐⡚⠙⠒⠐⢀⡀⠁⠘⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠠⠿⠿⢿⡿⠿⠿⢿⡧⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡶⡶⠿⢿⣿⠉⠉⢹⢿
⠗⠳⣿⠿⠿⠿⢠⣿⣿⣿⣿⣿⣿⡇⡄⠠⠀⣄⣀⣨⣭⡭⡭⠽⠭⠉⠉⣉⠹⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠤⠶⣧⢶⡤⢾⡤⠀⠉⠋⢩⣿⡿⣿⣿⣿⣿⣿⣿⣇⠉⠙⢾⢿⣧⣧⡄⢨⣿⠀⠀⣾⣿
⠀⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡅⡇⠸⠏⢭⡍⠩⠯⢭⡭⣿⠁⠀⢻⣯⠂⣿⣿⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠉⠉⠙⠛⠛⠛⠋⠀⠀⢻⣻⣿⡇⡛⣷⣿⠶⠶⣿⣿
⢻⡛⣿⡆⠀⠀⠉⠉⠙⠛⠛⠉⢹⣶⣷⠏⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢰⣿⡿⣟⠋⠁⠀⠉⣩⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⡧⠶⠶⢿⠷⡿⣿⣿
⠘⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡗⠄⠀⣽⠀⠀⣿⣿
⡦⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣀⢀⡈⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣛⣻⣿⣧⢸⣿⣿
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⠁⠛⠲⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣭⣹⣿⣿⣾⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡴⣾⡿⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣿⠏⠉⢹⣋⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡶⣖⣷⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠿⠀⠀⣸⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⡀⠟⣿⡗⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣡⡶⣧⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⡇⣨⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣐⡅⠉⠛⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⡿⠿⠿⠿⠿⠿
⠒⠀⠀⢀⡀⠀⠀⢀⣤⣶⣶⠿⠿⠿⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡖⠀⠀⢰⣶⣾⣿⠿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠘⠻⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠉⠉⠹⠿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠉⠛⠛⠀⠙⠻⠿⠿⠿⠿
⢀⡀⢰⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣆⢸⣿⣿⢿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⢾
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⣟⣿⣿⣿⢿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣶⠒⠒⠒⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠓⠻⠛⠟⠃⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠛⠛⠘⢻⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠞⠃⠈⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣤⣤⣤⡄⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠸⣿⡟⠛⠂⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡀⣀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⣀⠀⠀⠀⠂⠐⠻⠷⠿⢿⣷⡦⠀⠆⠀⠀⠀⠀⠩⠄⠀⠉⢹⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢷⠀⠀⠀⠀⠒⠖⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣷⣿⣿
⠋⠛⠻⠿⢿⢿⣿⣿⣿⡿⠿⢧⢐⣾⠀⠀⠀⢒⣚⡒⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠱⠦⣿⠀⡙⢀⠀⠀⠀⠄⠀⠋⠉⠉⠉⠛⣯⣬⡍⢿⢿⣋⣉⣭⣿⠿⠿⣿⣃⡀⣠⣴⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣛⢿⣿⣿⠛⣻⡟⠣⠘⠛⠉⠉⠁⠉
⠉⠉⠉⠀⢉⠁⠀⠷⠀⢠⣤⠀⠀⣽⣿⠀⠀⠀⠀⣠⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡏⠐⠛⠓⢻⣗⣤⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠻⠿⡿⣿⣯⣿⣿⣿⣟⡿⠇⠀⢄⠀⠀⠀⠀
⣤⡄⠀⠀⣿⠉⠀⠀⢨⣇⣨⣶⣾⣇⣤⡄⠀⠀⠀⠈⠀⠒⠶⠂⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⠿⢿⣻⠛⡛⢛⣻
⣄⡤⣾⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠚⠛⠛⣿⣟⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢿⡿⣿⠿⠿⠿⠿⠿⣛⣛⣻⣉⣉⣹⣿
⣿⣟⣿⣿⣽⣭⣤⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣒⠂⢐⣚⠁⠂⠀⢀⡀⠹⣟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠠⠿⠯⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⣤⣤⣤⣿⣶⣶⣶⣶⢲⡶⡶⠿⢿⣿⠉⠉⢹⢿
⠗⠳⣿⠿⠿⠧⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣨⣭⠥⠭⠽⠨⠉⠉⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠠⠤⢤⡧⢤⡤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⡿⠿⢿⣿⣿⢾⢼⣇⣧⡄⠨⣿⠀⠀⣾⣿
⠀⣀⠀⠀⢠⡄⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⡨⠍⠉⠭⣍⡬⡭⠉⠈⠹⠉⢻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⢸⣿⡿⣿⢿⣿⡇⠓⢿⣿⠶⠶⣿⣿
⢻⡛⣷⣶⡿⢿⣿⢛⡿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⣷⣭⡭⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠀⠿⠛⠉⠙⢹⣿⡧⠶⠶⢿⠶⡶⣿⣿
⠘⠙⣻⣽⣓⠊⣍⣉⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⠀⠀⠀⣠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣿⣷⣶⣦⣄⣼⣿⡗⠄⠀⣽⠀⠀⣿⣿
⡦⢠⣾⡋⠛⣃⣿⠟⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠛⠛⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣇⢋⣛⣿⣦⢸⣿⣿
⣷⠀⣾⣿⣦⣼⠀⠀⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⢄⡰⡀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣍⣹⣿⣿⣞⣿⣿
⣿⣶⣾⣿⣿⡿⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣀⢡⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠿⠿⣿⣿⣿⣯⣿⠏⠉⢹⣙⢻
⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠙⢛⡫⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠿⣿⠏⢠⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢓⣶⡟⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢀⣀⣠⣽⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠄⠀⡲⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠀⠈⢹⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣦⠈⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣉⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠠⠟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⠿⠿⠿⠿⠿⠿
⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⢀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡗⠀⠑⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠙⠻⠿⠿⠿⠿
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⢿⣷⣆⢸⣿⣿⢿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠶
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠸⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⡟⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⣟⣿⣿⣇⣿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⡶⠒⠒⠒⠖⠒⠂⠂⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠓⠛⠛⠛⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡝⠛⠋⠛⠛⠘⣿⣿⣿⣿⣿⣿⣟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠹⣿⡟⠛⠣⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡤⠶⠖⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⣀⠀⢀⣀⣀⡀⣀⡀⣤⣀
⣀⠀⠀⠀⠂⠒⠻⣿⠿⢿⣷⣶⠀⠆⠀⠀⠀⠉⠩⠄⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠛⠻⠿⣿⢿⣿⣿⣿⡿⠿⢏⢐⣿⠀⠀⠀⢒⣺⣓⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠱⠶⣿⢀⡛⣤⠀⠀⠐⠔⠊⡏⠉⢛⣻⣍⡙⣿⡟⢛⣻⣿⣿⣿⣿⣿⡟⠛⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠛⠉⠉⠉⠉
⠉⠉⠉⠁⢉⠁⠁⣿⠔⢠⣤⠄⠁⣽⡿⠀⠀⠀⠀⣠⠀⠀⣿⣼⣿⣷⣿⣿⣿⣿⣯⣽⣭⣽⣿⣅⣀⣀⣩⣭⣷⡀⠀⠐⠛⠓⢻⣗⣤⣄⣠⡀⠀⢀⠀⠀⠧⠿⠿⣿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⣄⠀⠀⠀⣀
⣤⡄⠠⢀⣿⠋⠁⠀⢸⣇⣀⣵⡆⠀⠀⠀⠀⠀⠀⠘⠀⠲⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣻⡛⣛⢻⣻
⣄⠿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⡷⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⠶⠚⠛⠛⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⠿⠿⢛⣛⣻⣉⣉⣹⣿
⣿⣟⣿⣿⣿⣭⣤⣍⣉⣀⣀⣽⣿⠀⠀⢀⢚⣒⠂⣒⣾⠛⠂⣢⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⠟⠠⣿⡯⢿⣿⠿⠿⣿⣧⣤⣼⣿⣷⣿⢤⡄⣤⣤⣤⣤⣿⣶⣶⣶⣶⢶⣶⡶⠿⣿⣿⠉⠉⢹⣿
⠟⠲⣿⠿⠿⠿⠀⢼⣯⣭⣭⣿⣿⠀⡀⢸⣀⣤⣀⣬⣭⠭⡭⢽⡕⣦⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠧⠀⠠⠦⠶⣧⢤⡤⢼⡤⠀⠛⠉⢉⣿⠀⢤⣭⣽⣿⡿⢿⣿⣿⣿⣿⣿⣯⣧⡄⢸⣿⠀⠀⣾⣿
⠀⣂⠀⠀⢠⡄⠀⠀⠀⡀⠀⣿⣿⠀⡇⢰⠭⣩⡯⠭⡽⣭⡭⢭⡍⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣾⠿⢾⣿⡂⠀⢩⣿⣿⠒⠀⣹⣿⣿⣿⣻⣿⡇⡻⣿⣿⡶⠶⣿⣿
⢻⡛⣷⣶⡿⢿⣿⢻⡟⢛⣿⣿⣿⣶⣷⣾⡿⣯⢬⢭⣽⠉⠁⠉⠁⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⣿⣼⣿⠇⠀⠈⣿⣿⠀⢰⠿⠛⠉⠙⣿⣿⡷⠶⠾⢿⠶⡷⣿⣿
⠙⢛⣻⣽⣷⠊⣍⣉⡉⠛⣛⣻⣿⣿⣿⣿⠟⠛⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣍⡉⠽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠃⠂⠀⣧⣿⣴⣿⣷⣾⣦⣄⣼⣿⡗⡌⠀⣽⠀⠁⣿⣿
⡦⢠⣾⡋⢻⣃⣿⣿⡿⠿⠿⣿⣿⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣅⠀⠀⠀⢨⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣻⣿⣷⢸⣿⣿
⣷⠀⣾⣿⣦⣼⣇⠀⢠⡤⠀⣛⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿
⣿⣶⣾⣿⣿⣿⣷⡖⣠⣠⣿⣼⣲⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠠⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣯⣿⠏⠉⢹⣟⣿
⣿⣿⣿⣿⡿⣷⣿⣧⣿⣿⣿⣭⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⣀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⠏⢠⠙⠿⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡛⠘⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠶⣾⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⠤⣀⣀⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠁⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢶⣼⣾⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡤⠈⣯⠙⠋⠙⠄⠈⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⡀⠙⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣠⠟⢺⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠉⠉⢿⡿⠿⠿⢿⡿⠿⠿⠿⠿⣿
⠿⠛⠻⣿⣿⡿⠿⣶⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢥⡔⣱⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⢺⣿⣾⣿⠿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠆⠀⠀⠦⠼⠿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠐⠉⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠉⠉⠛⠛⠀⠙⠿⠿⢿⠿⠿
⠀⡀⢰⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣾⣿⢿⣷⣿⣿⣿⣧⢸⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⣼
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠸⠿⢿⣿⣿⣿⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡟⣿⣿⣧⣻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⣶⠒⠒⠒⠖⠒⠒⠒⠐⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠓⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⠀⠈⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⢀⣀⣀⣀⣦⣆⣀⣀⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠸⣿⡟⠛⠢⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⡀⣀⣄⣤⣀
⣀⠀⠀⠀⠂⠒⠻⠿⠿⢿⣷⣶⠀⠆⠀⠀⠀⠉⠩⠄⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠛⠻⠿⢿⢿⣿⣿⣿⡿⠿⢯⢐⣶⠀⠀⠀⢒⣚⣓⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠳⠶⣿⢆⡙⣤⠀⠀⠐⠖⠂⡏⣩⣛⠈⣹⣿⡉⣭⡿⠿⣿⣿⣿⣿⠁⠙⠙⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠛⠉⠉⠉⠉
⠉⠉⠉⠁⢉⠁⠁⢿⠘⢠⣤⠀⠁⣽⡿⠀⠀⠀⠀⣠⠀⢿⣯⣿⣿⣿⣿⣾⣷⣿⣷⣶⣿⣿⣦⢤⣤⣾⣿⣷⡀⠀⠀⠐⠛⠓⢻⣗⣤⣄⣀⡀⠀⢀⠀⠀⠿⠿⢿⡿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠯⠀⢄⠀⠀⠀⣀
⣤⡄⠀⠀⣿⠉⠁⠀⢸⣇⣀⣴⡆⠀⠀⠀⠀⠀⠀⠘⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠛⡛⢻⣻
⣄⡷⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡗⠀⠂⠀⠀⠐⠂⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣰⡶⠚⠛⠛⣿⣿⣿⣿⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⠿⠿⢛⣛⣻⣉⣉⣹⣿
⣿⣟⣿⣿⣿⣭⣤⣍⣅⣀⣀⣽⣿⠀⠀⢀⢚⡓⠂⣒⣺⠛⡒⣙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠠⣿⡯⢿⣿⠿⠿⣿⣧⣤⣼⣿⣷⣿⢤⡄⣤⣤⣤⣤⣿⣶⣶⣶⣶⢶⡶⡶⠿⢿⣿⠉⠉⢹⣿
⠗⠳⣿⠿⠿⠷⠀⢼⣯⣭⣭⣿⣿⠀⡀⢸⣀⣤⣀⣬⣭⢭⣭⣭⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠏⠀⠠⠦⢴⣧⢤⡤⢼⡤⠀⠛⠉⢉⣿⠀⢠⣭⣭⣿⡿⢿⣿⣿⣿⣿⣽⣧⣧⡔⣸⣿⠀⠀⣼⣿
⠀⣀⠀⠀⢠⡄⠀⠀⠀⡀⠀⣿⣿⠀⡇⠰⠯⢩⡏⠭⡿⣩⣽⣿⠿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡾⠿⢾⣿⡂⠀⢩⣿⣿⠒⠀⣹⣿⣿⣿⣿⣿⡇⠻⣿⣿⡶⠶⣿⣿
⢻⡛⣷⣶⡿⢿⣿⣛⡟⠛⣿⣿⣿⣶⣷⣾⣾⣧⠁⣙⣹⣯⡼⠈⠁⠀⠉⠉⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠙⠻⠿⠿⢿⣿⣿⣼⣿⠃⠀⠉⠿⣿⠀⢸⠿⠛⠉⠙⢻⣿⡧⠶⠾⢿⠶⡿⣿⣿
⠙⠛⣻⣽⣷⠊⣉⣉⡉⠛⣛⣻⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⣷⣶⠿⠿⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠃⠀⠀⣦⣿⣴⣿⣷⣷⣦⣄⣼⣿⡗⡄⠀⣼⠀⠁⣿⣿
⡦⢠⣾⡋⢛⣇⣿⣿⡿⠿⠿⣿⣯⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣭⡄⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣛⣿⣷⢸⣿⣿
⣷⠀⣾⣿⣦⣼⣦⠀⢀⡄⠀⣙⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠔⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣾⣿⣿
⣿⣶⣾⣿⣿⣿⣷⡆⣠⣠⣿⣼⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣾⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⣿⠏⠉⢹⣛⢿
⣿⣿⣿⣿⡿⣷⣿⣧⣿⣿⣿⣭⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢀⡀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⠏⢠⠙⠿⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡛⠘⠛⡋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠸⠷⠙⣺⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⢀⢀⣠⠄⢀⣀⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠁⣭⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣦⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡤⠈⣯⠙⠋⠙⠄⠈⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠉⣹⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢰⠄⢰⡎⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠉⠉⢿⡿⠿⠿⢿⡿⠿⠿⠿⠿⢿
⠟⠛⠻⣿⣿⡿⠿⣶⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠈⠁⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⢸⣿⣿⣿⠿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠤⠀⠀⠮⠌⠿⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠉⠙⠛⠛⠀⠛⠿⠿⠿⠿⠿
⠀⠀⢰⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣾⣿⢿⣷⣿⣿⣿⣧⢸⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⣾
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢸⣿⣿⠸⠿⢿⣿⣿⣿⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣶⣦⣄⡀⢼⣿⣿⣿⣿⢸⣿⣿⣼⣿⣿⣿⣿⡟⣿⣿⡇⢻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣶⠒⠒⠒⠖⠒⠒⠒⠒⠀⠀⠀⠀⠀
⠐⠛⠳⠿⠛⠻⠓⠻⠛⠛⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⢀⡀⠀⢀⢀⣉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠹⣿⡟⠛⠢⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⣠⣾⣿⣾⣿⣿⣿⣿⣷⣷⣶⣤⡤⠴⠶⠦⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⢀⢀⠀⢀⣀⢀⡀⣠⡄⣤⣄
⣀⠀⠀⠀⠂⠒⠿⣿⠿⢿⣷⣶⠀⠆⠀⠀⠀⠈⠩⠅⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⢿⣿⣿⣿⡿⠿⢷⢰⣿⠈⠀⠀⢒⣺⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠱⠶⣿⢆⡛⣄⠀⠀⠐⠝⠚⠋⣹⡟⠻⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⠿⠛⠛⠉⠉⠉⠉
⠉⠉⠉⠀⢉⠁⠁⢿⠐⢠⣤⠀⠀⣽⡿⠀⠀⠀⠀⣀⠀⣿⣦⣶⣿⣷⣦⣭⣭⣭⣿⣿⣿⣇⣀⣀⣈⣿⣿⣧⠀⠀⠀⠐⠛⠓⢻⣗⣤⣄⣀⡀⠀⢀⠀⠀⠿⠿⢿⡿⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⡠⣄⠀⠀⠀⣀
⣤⣄⠠⢀⣿⠉⠁⠀⢨⣧⣀⣵⡆⠀⠀⠀⠀⠀⠀⠘⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠷⠿⣿⠛⡛⢻⣻
⣤⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⡗⠀⠂⠀⠀⠐⠆⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⡦⠚⠛⠛⣿⣟⣻⣷⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⠿⠿⢛⣛⣻⣉⣙⣹⣿
⣿⣻⣿⣿⣿⣭⣤⣍⣉⣀⣀⣿⣿⠀⠀⢀⢛⣒⢂⣒⣞⠛⣒⣚⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠿⠟⠠⣿⡯⢿⣿⢿⡿⣿⣧⣤⣼⣿⣷⣿⢤⡄⣤⣤⣤⣤⣿⣶⣶⣶⣶⢶⣶⡶⠿⣿⣿⠉⠉⢹⣿
⠟⠺⣿⠿⠿⠷⠄⢼⣯⣭⣭⣿⣿⠀⡄⢸⣀⣤⣀⣭⣭⠥⣭⣿⢧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⠯⠀⠠⠤⢴⣧⢤⡤⣼⡤⠀⠛⠉⢉⣿⠀⢤⣭⣽⣿⡿⠿⣿⣿⣿⣿⣿⣧⣧⣄⢾⣿⠀⠀⣾⣿
⠀⣂⠀⠀⢠⡄⠀⠀⠀⡀⠀⣿⣿⠀⡇⢰⠯⢩⡍⠭⡿⣭⣽⣿⠿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣤⣾⠻⢾⣿⠂⠀⣩⣿⣿⠒⠀⣹⣿⣿⣿⣿⣿⡇⡻⣿⣿⡶⠶⣿⣿
⢻⡛⣿⣶⡿⢿⣿⣻⡟⢛⣿⣿⣿⣶⣷⣾⣾⣭⢀⣹⣿⡭⡝⠋⠀⠙⠻⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠁⠹⠻⠿⢿⢿⣿⣿⣼⣿⠃⠀⠁⣿⣿⠀⢰⠿⠛⠉⠙⣻⣿⡷⠶⠶⢿⠶⡿⣿⣿
⠙⢛⣿⣽⣷⡊⣍⣉⡉⠙⣛⣻⣿⣿⣿⣿⡟⠟⠻⠛⠙⠁⠀⠀⠀⠀⠀⢰⣶⣭⣉⠙⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⠃⠂⢀⣧⣿⣴⣿⣷⣷⣦⣄⣼⣿⡗⡬⢄⣽⠀⠁⣿⣿
⡧⢠⣾⡛⢻⣇⣿⣿⡿⠿⠿⣿⣿⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣩⡀⠀⠀⢀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣻⣿⣶⢸⣿⣿
⣷⠀⣾⣿⣦⣼⣦⠀⢀⡄⠀⣛⠁⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣼⣿⣿
⣿⣶⣾⣿⣿⣿⣷⡖⣠⣠⣿⣽⣲⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣾⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⣿⠟⠉⢽⣟⣿
⣿⣿⣿⣿⡿⣷⣿⣧⣿⣿⣿⣥⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠏⢡⠙⠿⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡛⠙⠛⣋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠐⣼⠛⢼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⢀⢀⣤⠦⣀⣀⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠁⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠷⣦⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡤⠀⣯⠙⠋⠙⠀⠈⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠙⣿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢀⠀⢠⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠉⢿⠿⠿⠿⢿⡿⠿⠿⠿⡿⡿
⠟⠛⠻⣿⣿⡿⠿⣶⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⢸⣿⣾⣿⠾⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠦⠀⠀⠾⠬⠿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠈⠙⠛⠛⠀⠹⠿⠿⠿⠿⠿
⠀⡀⢰⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⣿⣧⢸⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⣼
⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⠸⠿⣿⣿⣿⣿⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣿⣿⣿⣿⣇⢸⣿⣿⣼⣿⣿⣿⣿⣟⣿⣿⡇⢻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠲⣶⠒⠒⠒⠖⠒⠒⠒⠒⠀⠀⠀⠀⠀
⠀⠛⠻⠿⠛⠻⠓⠻⠟⠛⠃⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠁⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⢀⠀⠀⣈⣉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠹⣿⡟⠟⠃⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⡀⣠⣾⣷⣾⣿⣿⣿⣿⣾⣶⣦⣄⣠⣤⣦⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⠀⢀⣀⣀⡀⡀⣀⣤⣀
⣀⠀⠀⠀⠂⠒⠿⢿⠿⢿⣷⣶⠀⠆⠀⠀⠀⠉⠩⠅⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⣿⣿⣿⣿⡿⠿⢯⢰⣾⠀⠀⠀⢒⣺⣳⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠳⠶⣿⢆⡙⣴⠀⠀⠐⠞⠒⠋⢙⣿⡟⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠛⠉⠉⠁⠉
⠉⠉⠉⠉⢉⠁⠀⢿⠐⢰⣤⠀⠁⣽⣿⠀⠀⠀⠀⣀⠀⢸⣿⣤⣶⣿⣷⣬⣯⣭⣭⣿⣿⣿⣀⢉⣉⣛⣿⣿⡄⠀⠀⠐⠛⠒⣻⣖⣤⣄⣀⡀⠀⢀⠀⠀⠿⠿⢿⡿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢤⣄⠀⠀⠀⣀
⣤⣄⠠⠀⣿⠉⠁⠀⣨⣧⣠⣴⡆⠀⠀⠀⠀⠀⠀⠘⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠷⢿⣿⠛⠛⢻⣻
⣅⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⡷⠀⠂⠀⠀⠐⠂⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠚⠛⠛⣿⣟⣻⣷⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠿⠿⠿⠿⢛⣻⣻⣛⣛⣻⣻
⣿⣻⣿⣿⣿⣭⣤⣍⣍⣀⣀⣿⣿⠀⠀⢀⢛⣓⣂⣒⣛⡛⠀⣺⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡾⢿⠠⣿⡯⢿⣿⢿⡿⣿⣧⣤⣼⣿⣷⣿⢤⡄⣤⣤⣤⣤⣿⣶⣶⣶⣶⢶⡶⡶⡿⣿⣿⠉⠉⢹⣿
⠗⠲⣿⠿⠿⠯⠀⢼⣯⣭⣭⣿⣿⠀⡀⢸⣄⣄⣀⣈⣭⣯⡨⣽⠹⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠯⠀⠠⠤⢴⣧⢤⡤⣼⡤⠀⠛⠉⢉⣿⠀⢤⣭⣽⣿⡿⢿⣿⣿⣿⣿⣿⣧⣧⡄⢨⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣿⣿⠀⡇⢰⠯⠨⡍⠍⡽⣭⣽⣿⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⠀⢀⠀⢀⡀⣤⣾⠿⢾⣿⠂⠀⢩⣿⣿⠂⠀⣹⣿⣿⣿⣿⣿⡇⡛⢿⣿⡶⠶⣿⣿
⢻⡛⣿⣶⡿⢿⣿⢻⡟⢛⣿⣿⣿⣶⣷⣾⡼⡧⠀⣈⣹⣍⣽⣿⣇⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠉⠻⠿⡿⣿⠿⠿⣿⣿⣼⣿⡅⠐⠉⣿⣿⠀⢸⠿⠛⠉⠙⢻⣿⡧⠶⠶⢿⠶⠿⣿⣿
⠙⢛⣻⣿⣷⡊⣭⣉⡉⠙⣛⣻⣿⣿⣿⣿⣿⣿⡿⠻⠛⠿⠛⠉⠁⠀⠀⠀⣤⣽⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠃⠂⠀⣯⣿⣴⣿⣷⣿⣶⣄⣼⣿⡗⡤⡤⣼⠀⠁⣿⣿
⡧⢠⣿⡋⢻⣇⣿⣿⡿⠿⠿⣿⣿⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡋⠁⠀⠈⢉⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣻⣿⣶⢸⣿⣿
⣷⠀⣾⣿⣦⣼⣧⠀⢀⡄⠀⣙⠈⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣾⣿⣿
⣿⣶⣾⣿⣿⣿⣷⡆⣠⣠⣿⣼⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣾⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⣿⠟⠋⢹⣛⡿
⣿⣿⣿⣿⡿⣷⣿⣧⣿⣿⣿⡭⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⠏⢡⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡛⠙⠛⡋⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⣤⡷⢆⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣤⠦⢀⣀⣤⣽⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠁⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡣⣌⣑⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡤⠀⣯⠙⠋⠙⠀⠈⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠻⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⣀⠈⡹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠉⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⢿
⠿⠛⠻⣿⣿⡿⠿⣶⣶⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠁⠀⠉⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⢸⣿⣷⣿⠾⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠤⠀⠀⠾⠌⠯⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠈⠉⠻⠛⠀⠛⠿⠿⡿⠿⠿
⠀⡀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢣⣾⣿⢿⣷⣿⣿⣿⣧⢸⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⢾
⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠸⠿⢿⣿⣿⣿⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣟⣿⣿⡇⢻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣶⠒⠒⠒⠖⠒⠒⠂⠂⠀⠀⠀⠀⠀
⠐⠛⠻⠿⠛⠻⠓⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⣤⣀⣀⣠⣤⣄⣰⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⠸⣿⡟⠟⠂⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⣀⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖⠒⠛⠒⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⢀⣀⠀⢀⣀⣀⡀⡀⣀⣤⣄
⣀⠀⠀⠀⠂⠒⠿⠷⠿⢿⣷⡶⠀⠆⠀⠀⠀⠉⠩⠄⠐⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⣿⣿⣿⣿⡿⠿⢯⢰⣾⠀⠀⠀⢒⣚⡲⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠳⠶⣿⢂⡛⣠⠀⠀⠐⠝⠒⠋⠉⢩⣿⠋⠙⣿⡛⢛⡿⠿⢿⣿⣿⣿⠛⠻⠟⣿⣿⡇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠉
⠉⠉⠉⠁⢉⠁⠀⢾⠀⢢⣤⠀⠀⣽⡿⠀⠀⠀⠀⣀⠀⠀⠸⣿⣾⣿⣿⣿⣶⣷⣾⣷⣶⣶⣾⣦⣤⣤⣤⣶⣿⡆⠀⠀⠚⠒⢻⣖⣤⣄⣀⡀⠀⢀⠀⠀⠿⠿⢿⡿⠟⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠧⠄⢄⠀⠀⠀⢀
⣤⣄⠀⠀⣿⠉⠀⠀⢠⣇⣀⣰⡄⠀⠀⠀⠀⠀⠀⠸⠀⠶⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠷⠿⣿⠛⠛⢛⣻
⣄⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡗⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠚⠛⠛⣿⣟⣻⣷⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠿⠿⠿⢟⣛⣻⣛⣛⣻⣻
⣿⣟⣿⣿⣿⣭⣤⣍⣅⣀⣀⣾⣿⠀⠀⢀⢚⡒⣂⣒⣚⠛⠂⣒⣢⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠠⣿⡯⢿⣿⢿⠿⣿⣧⣤⣼⣿⣷⣿⢤⡄⣤⣤⣤⣤⣿⣶⣶⣶⣶⢶⡶⡶⡿⢿⣿⠉⠉⢹⣿
⠗⠲⣿⠿⠿⠿⠀⢼⣯⣭⣭⣿⣿⠀⡀⢸⣀⣄⣀⣀⣭⣯⡈⣬⠉⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠀⠠⠤⢴⣧⢤⡤⢴⡤⠀⠛⠉⢉⣿⠀⢠⣭⣭⣿⡿⢿⣿⣿⣿⣿⣿⣧⣧⡀⢹⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣿⣿⠀⡇⢰⠯⠨⠍⠍⠽⣭⣭⣯⠁⠛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⣤⡾⠛⢾⣿⠀⠀⢩⣿⣿⠂⠀⣸⣿⣿⣿⣿⣿⡇⡛⣿⣿⡶⠶⣿⣿
⢻⡛⣷⣶⡿⢿⣿⢛⡟⠛⣿⣿⣿⣶⣷⣾⡼⡇⠀⢀⢹⣭⣭⣿⠧⠀⠁⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠹⠿⠿⣿⠿⠿⣿⣿⣼⣿⠁⠐⠀⡿⣿⠀⢰⠿⠛⠉⠙⣻⣿⡧⠶⠶⢿⠶⡿⣿⣿
⠙⠛⣻⣽⣷⡊⣍⣉⡉⠙⣛⣻⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⠃⠀⢀⣧⣿⣴⣿⣷⣾⣦⣄⣼⣿⡗⡤⢄⣽⠀⠁⣻⣿
⡦⢠⣿⡏⠛⣇⣿⣿⡿⠿⠿⣿⣯⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣭⡄⠀⠀⢀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣻⣿⣶⢸⣿⣿
⣶⠀⣾⣿⣦⣼⡦⠀⢠⡄⠀⠘⠀⣾⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠰⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⣿⣬⣿⣿
⣷⣶⣾⣿⣿⣿⣷⡆⣠⣠⣿⣾⢤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣯⣿⠟⠉⣹⣛⣿
⣿⣿⣿⣿⡿⣷⣿⣧⣿⣿⣿⣥⡼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⠏⢡⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡛⠘⠛⡋⠀⠸⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠒⠔⠙⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⠄⢀⣀⣠⣽⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠁⣭⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠰⣆⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡤⠀⣧⠉⠉⠙⠄⠈⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠈⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢠⠀⣸⡛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠈⠻⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠟⠛⠻⣿⣿⡿⠿⣶⣶⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠐⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⢸⣷⣶⣾⠾⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠤⠀⠀⠶⠬⠻⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠈⠉⠛⠛⠀⠛⠻⠾⢿⠿⠿
⠀⡀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣾⣿⢿⣷⣾⣿⣿⣧⢸⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⣾
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠸⠿⠿⣿⣿⣿⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣼⣿⡟⣿⣿⡇⢻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠲⣶⠒⠒⠒⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀
⠐⠛⠳⠿⠛⠻⠓⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⢰⣆⣀⣢⣤⣤⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠹⣿⡟⠟⠃⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠶⠶⠦⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣠⣄⣤⣤
⣀⠀⠀⠀⠂⠒⠿⠿⠿⢿⣶⣶⠠⠆⠀⠀⠀⠉⠩⠅⠈⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⣿⣿⣿⣿⡿⠿⢧⢰⣿⠀⠀⠀⢒⣺⡶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠳⠶⣿⢂⡛⣤⠀⠀⠐⠝⠒⠛⠛⠉⣿⡟⠙⢿⣟⠛⣿⠿⢿⣿⣿⣿⡟⢿⡿⢿⣿⣗⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⠉⠉
⠉⠉⠉⠉⢉⠁⠁⢿⠀⢲⣤⠀⠁⣽⡿⠀⠀⠀⠀⣀⠀⠀⠘⣿⣷⣿⣿⣿⣷⣾⣶⣶⣶⣾⣿⣧⣤⣤⣬⣽⣿⣦⠀⠀⠐⠒⣻⣖⣤⣄⣠⡀⠀⢀⠀⠀⠽⠿⢿⡿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢄⠀⠀⠀⣀
⣤⣄⠀⠀⣿⠋⠁⠀⣨⣧⣀⣴⡆⠀⠀⠀⠀⠀⠀⠸⠀⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠶⠿⣿⠛⠛⢛⣻
⣅⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡗⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠚⠛⠛⣿⣟⣿⣷⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⡿⠿⠿⠿⠿⢟⣛⣻⣛⣛⣻⣻
⣿⣿⣿⣿⣿⣭⣤⣍⣏⣀⣀⣿⣿⠀⠀⢀⢛⡓⣂⣒⣺⣛⠒⣒⢂⣍⣹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡶⠠⣿⡯⢿⣿⢿⡿⣿⣧⣤⣼⣿⣷⣿⢤⡄⣤⣤⣤⣤⣿⣶⣶⣶⣶⢶⡶⡶⡿⢿⣿⠉⠉⢹⣿
⠟⠲⣿⠿⠿⠷⠀⢼⣯⣭⣭⣿⣿⠀⡀⢸⣄⣤⣀⣈⣭⣯⡉⣭⠩⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⠤⢴⣧⢤⡤⣼⡤⠀⠛⠉⢉⣿⠀⢠⣭⣭⣿⡿⢿⣿⣿⣿⣿⣿⣧⣧⡄⣻⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡄⠀⠀⠀⡀⠀⣿⣿⠀⡇⢰⠯⠩⡍⠭⠽⣭⣭⣿⠯⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⠀⢀⠀⢀⡀⣤⣾⠻⢾⣿⡀⠀⢩⣿⣿⠒⠀⣹⣿⣿⣿⣿⣿⡇⡛⢿⣿⡶⠶⣿⣿
⢻⡛⣷⣶⡿⢿⣿⢛⡟⢛⣿⣿⣿⣶⣷⣾⡼⡧⠀⢀⣹⣭⣤⣿⣷⠌⠉⠁⠈⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠹⠿⣿⣿⠿⠿⣿⣿⣼⣿⠁⠀⠉⣿⣿⠀⢸⠿⠛⠉⠹⣻⣿⡷⠶⠶⢿⠶⡿⣿⣿
⠙⢛⣿⣿⣷⡊⣍⣉⡉⠙⣛⣻⣿⣿⣿⣿⣿⣿⣿⠿⡛⠿⠛⠋⠁⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠻⠿⢿⠃⠂⠀⣧⣿⣴⣿⣷⣾⣦⣄⣼⣿⡗⡤⣄⣽⠀⠁⣻⣿
⡦⢠⣿⡋⢻⣇⣿⣿⡿⠿⠿⣿⣿⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣋⡉⠀⠀⠈⣩⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣻⣿⣶⢸⣿⣿
⣶⠀⣾⣿⣦⣼⣦⠀⢀⡄⠀⠘⠁⣾⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣼⣿⣿
⣿⣶⣾⣿⣿⣿⣷⡆⣠⣠⣿⣿⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⣿⠟⠉⢹⣛⣿
⣿⣿⣿⣿⡿⣷⣿⣷⣿⣿⣯⣥⠈⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⣿⠿⠿⣿⠏⢡⠙⠿⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡛⠘⠛⡋⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠰⠀⠛⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⢀⢀⣠⠤⢀⣀⣤⣽⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠀⣭⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠲⣄⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡤⠈⣯⠙⠋⠉⠄⠈⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠛⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢠⡄⢨⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠉⠿⡿⠿⠿⢿⡿⠿⠿⠿⠿⣿
⠿⠛⠻⣿⣿⡿⠿⣶⣶⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⢸⣿⣶⣾⠾⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠆⠀⠀⠶⠼⠿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠉⠉⠛⠛⠀⠙⠻⠿⢿⠿⢿
⠀⡀⢰⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⢿⣷⣞⣿⣿⣧⢸⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⣾
⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠸⠿⠿⣿⣿⣿⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⢹⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣸⣿⡟⣿⣿⡇⢻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠲⣶⠒⠒⠒⠖⠒⠒⠒⠀⠀⠀⠀⠀⠀
⠐⠛⠳⠿⠛⠻⠓⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⣀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡥⢽⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣤⣷⣶⣾⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡿⠟⠣⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⡀⣀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠦⠶⠦⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⡀⠀⠀⢀⣀⠀⠀⣀⣤⣀
⣀⠀⠀⠀⠂⠒⠾⢷⠿⢿⣷⣦⠀⠄⠀⠀⠀⠉⠩⠅⠈⠙⢻⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⠆⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⣿⣿⣿⣿⡿⠿⢯⢰⣿⠀⠀⠀⢒⣺⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠣⠤⣿⢈⡛⣦⠀⠀⠀⠭⠂⠛⠉⠉⠉⣿⣿⣣⣼⣿⣤⣾⣾⣹⣻⠿⣿⣿⠛⠿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⠙⠛⠉⠉⠉⠉
⠉⠉⠁⠀⢉⠁⠀⣿⠀⢱⣤⠀⠀⣽⡿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣬⣽⣿⣇⠀⠀⠐⢻⣗⣤⣄⣀⡀⠀⢀⠀⠀⠷⠿⠿⡿⠿⠿⠿⢿⣿⣿⣾⣿⣿⣿⡿⠷⢔⣄⠀⠀⠀⣀
⣤⣄⠀⢀⣿⡏⠀⠀⢱⣧⣀⣱⡆⠀⠀⠀⠀⠀⠀⠹⠀⠶⠶⠦⠒⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠛⠛⢻⣻
⣏⣷⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠘⠛⣿⡟⣿⣷⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⠿⠿⠿⢟⣛⣛⣋⣛⣻⣻
⣿⣏⣿⣿⣿⣭⣤⣍⣍⣀⣀⣸⣿⠀⠀⢀⢚⡒⡂⢐⣞⡛⢐⣒⢒⡀⣦⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣦⣄⠠⣿⡯⢿⣿⢿⠿⣿⣧⣤⣼⣿⣷⣿⢤⡄⣤⣤⣤⣤⣾⣷⣴⣶⣶⢶⡶⣶⣿⣿⣿⠉⠉⢹⣿
⠗⠲⣿⠿⠿⠿⠀⢽⣯⣭⣭⣿⣿⠀⡀⢸⣄⣀⣂⣈⣿⣯⠉⣯⣨⠉⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⢴⣧⢤⡤⣼⡤⠀⠛⠉⢉⣿⠀⢠⣥⣭⣿⡿⢿⣿⣿⣿⣿⣾⣧⣧⠄⣹⣿⠀⠀⣾⣿
⠀⡀⠀⠀⣠⡄⠀⠀⠠⡀⠀⣿⣿⠀⡇⢰⠯⣭⡍⠭⠽⣭⡽⣿⠯⠠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣾⠛⢾⣿⠀⠀⠹⣿⣿⠒⠀⣸⣿⣿⣿⣿⣿⡏⡛⣿⣿⡶⡶⣿⣿
⢿⡟⣿⣶⡿⢿⣿⣛⡟⢛⣻⣿⣿⣶⣷⣿⣾⡯⠀⢈⣹⣯⣭⣿⣿⠍⠋⠉⠈⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⠛⠿⡿⠿⠿⣿⣿⣼⣿⡃⠀⠀⣿⣿⠀⢀⠿⠛⠉⠻⢿⣿⡧⠶⠶⢿⠶⠶⣿⣿
⠙⢛⣻⣿⣷⠈⣉⣍⡉⠙⣛⣻⣿⣿⣿⣿⣟⣿⣿⠿⢿⠿⠯⠝⠁⠀⠀⠀⠀⢸⣿⣦⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠛⠻⡿⠃⠀⠰⣦⣿⣴⣿⣷⣾⣦⣄⣴⣿⡗⣤⣀⣼⡀⠀⣿⣿
⡧⢠⣿⡏⢛⣇⣿⣿⡿⠿⠿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣋⣭⡄⠀⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢛⣻⣿⣦⢸⣿⣿
⣦⠀⣾⣿⣦⣽⣷⠀⢀⡄⠀⠀⠓⣾⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣾⣿⣿
⣿⣶⣾⣿⣿⣿⣷⡆⣠⣠⣿⣾⡶⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣾⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣯⣿⠟⠛⢩⣛⣿
⣿⣿⣿⣿⡿⣷⣿⣧⣿⣿⣯⣧⣖⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⣀⢼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣿⡿⠿⣿⡏⢡⠙⠿⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡛⠙⠛⡋⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠘⠦⠻⢺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣤⣽⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠁⣭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠐⣠⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡤⠀⣯⠋⠏⠙⠀⠈⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⠄⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁⠉⢿⡿⠿⠿⢿⡿⠿⠿⠿⠿⣿
⠿⠛⠻⣿⣿⡿⢿⣶⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⢸⣷⣷⣾⠾⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠄⠀⠀⠶⠬⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠈⠉⠛⠛⠀⠛⠿⠿⠿⠿⢿
⠀⡀⢰⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢿⣷⣆⢸⣿⣿⢸⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣶
⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠸⠿⠿⢸⣿⣿⣾⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⡶⠶⠶⣶⡶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀⢼⣿⣿⣿⣿⣿⣿⣼⣿⣿⣸⣿⣟⣿⣿⡇⢻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⣶⠒⠒⠒⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀
⠐⠛⠳⠿⠛⠻⠓⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣪⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠆⢛⣛⡻⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠖⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⢸⣿⡿⠟⠣⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⢀⣀⣀⣀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⣀⠀⣀⣀⣀⣀⢀⠀⣀⣤⣀
⣀⠀⠀⠀⠂⠐⠾⠶⠿⢿⣷⣦⠀⠄⠀⠀⠀⠉⠩⠄⠀⠉⢻⣿⣿⣲⣉⣹⣙⣿⣿⣿⡛⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⢶⠆⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⣿⣿⣿⣿⡿⠿⢿⢰⣶⠀⠀⠀⢒⣚⡶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠙⢿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠣⠤⣿⢀⡛⣠⠀⠀⠀⠝⠂⠛⠋⠙⠙⠛⠃⢀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠙⠛⠉⠉⠉⠉
⠉⠉⠁⠀⢉⠁⠀⣿⠀⢠⣤⠀⠀⣽⡿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣀⣤⣄⣀⡀⠀⢀⠀⠀⠤⠿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠄⣄⠀⠀⠀⠀
⣤⡄⠀⠀⢿⠋⠀⠀⢸⣇⣀⣰⡄⠀⠀⠀⠀⠀⠀⠘⠀⠶⠶⠦⠀⠀⠀⠀⢸⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢈⡀⠀⣾⣿⡗⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⠿⣟⠛⠛⢻⣿
⣍⢵⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠀⣿⡟⣿⣷⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣋⣋⣻⣻
⡝⢀⣿⣭⣿⣭⣤⣍⣁⣀⣀⣸⣿⠀⠀⠀⠘⠒⠂⢐⣚⠋⠀⢒⢒⡀⠀⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡯⢿⣿⠿⠿⣿⣧⣤⣼⣿⣷⣿⢤⡄⣤⣤⣤⣤⣶⣶⣴⡶⣶⢶⡶⡶⡿⢿⣿⠉⠉⢹⢿
⠗⠲⣿⠿⠿⠿⠀⢽⣯⣭⣭⣿⣿⠀⡀⢰⣀⣀⣂⣘⣹⣏⠈⣤⡨⠉⠠⡿⠝⠻⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠤⢤⡧⢤⡤⢼⡤⠀⠛⠉⢉⣿⠀⠀⣥⣭⣿⡿⢿⢿⣿⣿⣿⣾⣧⣧⠀⢸⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡄⠀⠀⠀⡀⠀⣿⣿⠀⡇⠰⠭⢩⡍⠭⠭⣭⡬⣿⠏⠀⠽⠉⠉⠁⠀⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠳⢾⣿⠀⠀⠩⣿⣿⠒⠀⢸⣿⣿⣿⣿⣿⡇⠋⣿⣿⡶⠶⣿⣿
⢿⡛⣷⣶⡾⢻⣿⣛⡟⠛⣻⣿⣿⣶⣷⣾⡼⡇⠀⠠⠭⠿⠌⠋⠁⠁⠀⠀⠀⠀⠀⣿⡿⠿⠟⠛⠛⠛⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⠛⠁⠀⠀⢻⣿⠀⢀⠿⠛⠉⠹⢻⣿⡧⠶⠶⢿⠶⠶⣿⣿
⠙⠛⣻⣽⣳⠈⣉⣉⡉⠙⣛⣻⣿⣿⣿⣿⣟⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣶⡇⠀⠀⣠⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣤⣿⣷⣾⣦⣄⣴⣿⡇⣤⡀⣼⠀⠁⣻⣿
⡧⢠⣾⡋⢛⣅⣿⣿⡿⠿⠿⣿⡟⢻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡃⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⣺⣿⣦⢸⣿⣿
⣦⠀⣾⣿⣦⣼⡧⠀⠀⡀⠀⠀⠉⣾⣿⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣼⣿⣿
⣷⣶⣾⣿⣿⣿⣷⡆⣠⣠⣿⣿⠶⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢠⡶⠲⢾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣯⣿⠟⠉⢩⣛⣿
⣿⣿⣿⣿⡿⣷⣿⣧⣿⣿⣯⣥⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢈⡁⢠⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⠿⠿⣿⡏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡛⠘⠛⡋⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⠻⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⢀⣠⢄⣀⣀⣠⣽⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠁⣭⠉⠀⠀⢀⣶⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠤⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡤⠀⣯⠋⠏⠙⠀⠀⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣶⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⢫⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠈⢿⡿⠿⠿⢿⡿⠿⠿⠿⠿⢿
⠟⠛⠻⣿⣿⡿⢿⣶⣶⣿⡿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⠀⠀⢸⣷⣶⣶⠾⣷⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠄⠀⠀⠶⠈⠋⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠐⢂⣾⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠉⠛⠛⠀⠹⠿⠿⠿⠿⢿
⠀⠀⢰⣗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢻⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⣶
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣿⣿⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⡟⣿⣿⡇⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⠒⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠓⠛⠛⠛⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠛⠋⠛⠛⣼⣿⣿⣿⠛⠃⣾⣿⣟⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠖⠈⣯⣭⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠸⣿⡿⠟⠃⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⡀⣀⣀⠀⣀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⣀⠀⠀⠀⠂⠒⠾⠶⠿⢿⣷⣦⠀⠄⠀⠀⠀⠈⠩⠄⠀⠉⢻⣿⣾⣄⣀⣁⣤⣀⣽⣿⣟⣿⣉⣽⣿⣛⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⡿⣿⣿⣿⣿⡿⠻⢯⢰⣷⠀⠀⠀⢒⣺⡲⣾⣷⣿⣿⣿⣿⠿⣿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣅⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠣⠤⣿⢀⡛⢀⠀⠀⠀⠙⠀⠋⠉⠙⠙⠛⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣽⣟⣿⡺⢪⠙⠛⠉⠉⠉⠉
⠉⠉⠁⠀⢉⠁⠀⣿⠀⢠⣤⠀⠀⣽⡿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣤⣄⣀⡀⠀⢀⠀⠀⠌⠺⠿⠿⠟⠟⠿⢿⣿⣿⣯⣿⣿⣿⡿⠧⠄⣄⠀⠀⠀⠀
⣤⣄⠀⠀⣿⠃⠀⠀⢰⣇⣀⣐⣆⣠⣤⣤⣾⣿⣷⢸⠀⠶⠶⠦⠀⠀⠀⠀⠀⠈⣯⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠋⠀⠀⠀⠀⢈⡀⠀⣾⣿⡗⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠾⠿⣿⠛⠛⢻⣿
⣏⢷⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣟⣿⣷⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣋⣋⣻⣻
⣿⢅⣿⣿⣿⣭⣤⣍⣇⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⢒⢒⡀⠀⣄⢰⠈⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣧⣤⣼⣿⣷⣿⢤⡄⣤⣤⣤⣤⣾⣶⣴⣶⣶⢶⡶⣶⡿⢿⣿⠉⠉⢹⢿
⠗⠲⣿⠿⠿⠿⠀⢿⣯⡭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠩⣮⠈⠉⠠⡿⡝⠒⠉⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣤⣴⡤⠀⠛⠉⢉⣿⠀⠀⣥⣭⣿⡿⢿⢿⣿⣿⣿⣾⣧⣧⠀⢨⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡄⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠥⡿⣯⠯⠀⠭⠉⠀⠀⠀⠀⣾⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠠⠾⠻⠾⣿⠀⠀⠉⣿⣿⠂⠀⢸⣿⣿⣿⣿⣿⡇⠋⣿⣿⡶⡶⣿⣿
⢿⡛⣷⣶⡿⢿⣿⣛⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣛⡉⠁⠀⠀⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠠⠿⠛⠉⠻⢿⣿⡧⠶⠶⢿⠶⠶⣿⣿
⠙⠛⣻⣝⣇⠈⣉⣉⡉⢙⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⣤⣿⣷⣾⣦⣄⣤⣿⡗⡤⠀⣼⠀⠁⣻⣿
⡧⢠⣾⡋⢛⣇⣿⣿⡗⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣤⢰⡀⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠋⣸⣿⣦⢸⣿⣿
⣦⠀⣾⣿⣦⣼⡧⠀⠠⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⡀⣄⢸⣿⣿⣿⡏⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣼⣿⣿
⣷⣶⣾⣿⣿⣿⣷⠀⠀⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠾⠯⠛⣼⣿⣿⣿⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣭⣿⠟⠙⢹⣛⣻
⣿⣿⣿⣿⡿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠦⣴⣾⢼⣿⣿⡿⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⠿⠿⣿⡏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⢷⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠸⢿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⢀⣠⠄⢀⣀⣤⣽⣿⣿
⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠖⠄⠈⣾⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⡤⠀⣮⠋⠏⠉⠀⠀⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠈⠀⠀⢘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣯⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠁⠈⠿⡿⠿⠿⢿⡿⠿⠿⠿⠿⢿
⠟⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⣷⣶⣶⠶⣷⣶⣶⣶⣿⣿
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠛⠻⠻⠿⠿⢿
⢀⡀⣰⣗⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣷⣆⢸⣿⣿⢻⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⣶
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠸⠿⠿⢸⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⡶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⡟⣿⣿⡇⢻⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⣶⠒⠒⠒⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠓⠛⠛⠛⠃⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⠋⠛⠛⠘⢻⣿⣿⣿⡃⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠾⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⠁⠀⠀⠨⠈⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡿⠟⠣⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⣀⣀⠀⡀⡄⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⣀⠀⠀⣀⣀⣀⡀⢀⣀⣤⣀
⣀⠀⠀⠀⠂⠒⠾⢷⠿⢿⣷⣦⠀⠄⠀⣠⣤⣿⣿⣷⣾⣿⣾⣿⣿⣞⣀⣃⡉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⣿⣿⣿⣿⡿⠿⢿⢤⣷⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠁⠘⣿⣿⣟⡿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣀⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠣⠦⣿⢀⡛⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⠀⡀⠀⠀⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣮⣭⣭⣧⣀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠉⠉⠉⠉
⠉⠉⠉⠀⢉⠁⠁⣿⡀⢲⣤⠀⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠀⠀⠿⠿⠿⠟⠛⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠄⣄⠀⠀⠀⣀
⣤⣄⠀⢀⣿⡇⠀⠀⢹⣧⣀⣑⡖⢀⣾⣿⣿⣿⣿⡿⠟⠷⠶⠦⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠛⠛⢻⣻
⣏⣷⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⢿⠿⠿⠿⢟⣛⣻⣋⣋⣻⣻
⣿⣏⣿⣿⣿⣭⣀⣭⣅⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣒⣖⣒⢂⢒⢒⡀⠀⣤⠠⠿⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢤⡄⣤⣤⣤⣤⣾⣷⣴⣶⣶⢶⡶⡶⣿⣿⣿⠉⠉⢹⢿
⠟⠳⣿⡿⠿⠯⠀⢹⡇⠀⠐⠿⠿⠿⠟⠛⠛⢛⣀⣘⣽⣏⢙⣦⣨⡍⠡⠯⠿⠇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⠉⢿⠀⠀⣭⣽⣿⡿⢿⣿⣿⣿⣿⣿⣧⣧⡄⣹⣿⠀⠀⣾⣿
⠀⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠭⠉⠻⠨⠭⠩⢭⡌⠉⠁⠀⠀⠀⠘⢰⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠻⠿⣿⣿⣿⠟⠀⠀⠀⠀⠉⣿⣿⠒⠀⣸⣿⣿⣿⣿⣿⡇⠛⣿⣿⡶⠶⣿⣿
⢿⡟⣿⣶⡿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣋⡅⠀⠀⠀⣨⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⣰⠿⠛⠉⠻⢿⣿⡷⠶⠶⢿⠶⠿⣿⣿
⠙⢛⣿⣿⣷⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⡀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣿⣿⣿⣦⣄⣴⣿⡗⣤⠀⣼⡀⠁⣿⣿
⡧⢤⣿⡟⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⣤⣰⡀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⣺⣿⣦⢸⣿⣿
⣧⠀⣾⣿⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⢀⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣼⣿⣿
⣿⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⣿⡔⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⢿⣿⣿⣿⣿⣿⠟⠛⢹⣟⣿
⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢾⣿⣿⠇⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠿⣿⠏⢩⠙⠿⠀⠀⣹⣿⣿
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠈⠁⡽⣆⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⣠⣽⣿⣿
⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠙⠂⢿⣏⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠟⠙⠉⠉⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀⢹⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⣤⠀⠈⠛⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠉⠈⢿⡿⠿⠿⢿⡿⠿⠿⠿⠿⣿
⠟⠛⠻⣿⣿⡿⢿⣶⣾⣿⣿⠿⣿⠿⠿⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⡧⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⢸⣿⣷⣾⠾⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠯⠿⠿⠦⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠈⠿⢁⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠈⠙⠛⠛⠀⠻⠿⠿⠿⢿⢿
⢀⡀⢰⡗⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⣶
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣄⠂⠀⢂⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⡶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠐⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠲⣶⠒⠒⠒⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀
⠐⠛⠳⠿⠛⠻⠓⠛⠛⠛⠃⠀⢺⡧⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠘⢬⢄⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠾⢿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⡁⠀⠀⠨⠈⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡿⠟⠃⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⣀⣀⠀⣠⡠⡀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⣀⠀⠀⣀⣀⣀⠀⡀⣀⣤⣀
⣀⠀⠀⠀⠂⠒⠾⢷⠿⣿⣷⣦⠠⠄⠀⣠⣤⣿⣿⣷⣾⣿⣾⣿⣿⣞⣀⣉⡉⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⣿⣿⣿⣿⡿⠿⣯⢴⣷⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠁⠘⣿⣿⣟⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣄⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠣⠤⣿⢀⡛⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⠀⡄⠀⠀⣼⣿⣿⣿⣾⣿⣷⣿⣿⣿⣮⣭⣭⣧⢀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠹⠛⠉⠉⠉⠉
⠉⠉⠉⠀⢉⠁⠉⣿⠀⢱⣤⠀⢈⣭⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠀⠀⠿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠄⣄⠀⠀⠀⣀
⣤⡄⠀⢀⣿⡋⠀⠀⢰⣧⣀⣵⡆⢀⣾⣿⣿⣿⣿⡿⠟⠷⠶⠦⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠛⠛⢻⣻
⣏⣷⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⠿⠿⠿⢟⣛⣻⣋⣛⣻⣻
⣿⣯⣿⣯⣿⣭⣀⣍⣍⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣒⣖⣒⢒⣚⢓⡀⠀⣦⠤⠿⠀⠻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⢤⡄⣤⣤⣤⣤⣾⣶⣴⣶⣶⢶⡶⡶⣿⣿⣿⠉⠉⢹⣿
⠟⠳⣿⡿⠿⠯⠀⢸⡧⠀⠐⠿⠿⠿⠟⠛⠛⢛⣂⣉⣽⢏⠩⣮⣨⡉⠡⠿⠾⠇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⠉⢿⠀⢠⣭⣭⣿⡿⢿⣿⣿⣿⣿⣿⣧⣧⡄⣹⣿⠀⠀⣿⣿
⠀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠭⠉⠻⠈⠌⠻⢯⠭⠉⠁⠀⠀⠐⠙⢰⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠻⠿⣿⣿⣿⠟⠀⠀⠀⠀⠉⣿⣿⠒⠀⣸⣿⣿⣿⣿⣿⡇⠛⣿⣿⡶⡶⣿⣿
⢿⡟⣷⣶⡿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣋⡁⠀⠀⠀⣨⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⣸⠿⠛⠉⠻⢿⣿⡧⠶⠶⢿⠶⠾⣿⣿
⠙⠛⣻⣽⣷⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⡀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣿⣶⣷⣦⣤⣼⣿⡗⣤⣀⣽⠀⠁⣿⣿
⡧⢠⣿⡏⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⣤⣰⡀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⣻⣿⣦⢹⣿⣿
⣧⠀⣾⣿⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣾⣿⣿
⣿⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⣷⡀⠿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⢿⣿⣿⣿⣯⣿⠟⠛⢻⣛⣿
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢾⣿⡽⠃⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠿⣿⡏⢩⠙⡿⠀⠀⣹⣿⣿
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠉⠀⡸⣆⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣤⣽⣿⣿
⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠙⢡⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠋⠏⠙⠈⠈⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣦⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⡀⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⣤⠀⠀⠛⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠉⠉⢿⡿⠿⠿⢿⡿⠿⠿⠿⠿⣿
⠿⠛⠻⣿⣿⡿⢿⣶⣾⣿⣿⠿⢿⠿⠿⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⣿⡆⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⢸⣿⣷⣿⠾⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠏⠿⠿⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠟⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠈⠉⠛⠛⠀⠻⠿⠿⠿⠿⢿
⢀⡀⢰⣗⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⣶
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠂⠀⢀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⡶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⠒⠒⠒⠖⠒⠐⠀⠀⠀⠀⠀⠀⠀
⠐⠛⠳⠿⠛⠻⠓⠛⠛⠛⠃⠀⢺⡧⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠘⢸⣆⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣀⠀⠀⠀⠀⢀⠄⠀⠈⠑⠀⠀⠀⠀⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡿⠿⠣⠀⠀⠀⠀⠀⣀⣀⣀⢀⢀⣀⣀⣠⣀⢀⣤⣤⣀⣤⣀⣈⠀⠀⠀⢀⣈⢉⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⡀⣀⠀⢀⢀⢀⣀⣀⢀⣀⣤⣤
⣀⠀⠀⠀⠂⠒⠿⢷⠿⢿⣷⣦⠠⠆⡀⠀⠀⠉⣩⣍⣈⣿⣿⣿⣿⣿⣩⣿⡛⢁⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⠐⢠⣶⣶⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⡀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⠿⣿⢼⣿⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠣⠤⣿⣏⡛⣷⠄⠀⣺⣿⣿⣿⣿⣿⣿⣿⡏⢀⡌⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠉⠉⠉⠉
⠉⠋⠉⠁⢋⠉⠙⣿⠘⢳⣤⠌⠁⣽⣿⠅⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠁⠀⠀⠘⣿⣯⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⡿⡂⣰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠿⠿⢿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣴⣤⠀⠀⠀⣀
⣤⣄⠀⢀⣿⡏⠀⠀⢹⣧⣀⣷⡦⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠀⠤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣷⣦⣿⣿⣿⣽⣾⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠛⡛⢻⣿
⣏⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⡗⠀⠂⣰⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⠿⠿⠿⢿⣛⣿⣛⣛⣻⣻
⣿⣯⣿⣿⣿⣭⣤⣭⣏⣠⣌⣽⡿⢀⣿⣿⣿⣿⣿⣿⣿⡿⣐⣺⣒⡒⢀⣿⠼⡿⠆⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⣤⣤⣤⣤⣾⣷⣴⣶⣶⢶⣶⣶⣿⣿⣿⠉⠉⢹⣿
⠟⠳⣿⡿⢿⠿⠄⢽⣯⣭⣽⡟⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣨⡍⠡⣿⠿⠗⠀⠸⣿⣿⣛⠛⠞⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⢤⣭⣽⣿⡿⣿⣿⣿⣿⣿⣿⣧⣧⡄⣻⣿⠀⢀⣿⣿
⡀⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠼⠍⢻⢯⡼⡟⠁⠀⠀⠰⠅⢹⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠀⠀⠀⠹⣿⣿⠒⠀⣹⣿⣿⣿⣿⣿⡇⣻⣿⣿⡶⡶⣿⣿
⢿⣟⣿⣾⡿⢿⣿⠟⡿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⣸⠿⠛⠙⠻⣿⣿⡷⠶⢶⢿⠶⠿⣿⣿
⠙⣛⣿⣿⣷⠚⣭⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡄⠀⠀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⣿⣷⣿⣶⣄⣼⣿⣗⣤⣄⣿⡀⠁⣿⣿
⡧⢤⣿⣏⢻⣯⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠁⠑⠸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⢛⣻⣿⣶⢸⣿⣿
⣧⠀⣾⣿⣦⣽⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠂⣿⡄⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣾⣿⣿
⣿⣶⣾⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢂⠀⢠⡅⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⢿⣿⣿⣿⣿⣿⠟⠛⢿⣟⣿
⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣾⣧⠆⡉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⣿⡟⢩⠙⡿⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣷⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⠁⡄⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣠⣤⣽⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣾⣿⣼⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠟⠹⠏⠉⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⣀⣀⣀⣀⣠⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠐⡿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⡧⠭⢿⣽⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠉⠉⣿⡿⠿⠿⣿⡿⠿⠿⠿⣿⣿
⠿⠛⠻⣿⣿⡿⢿⣶⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⣸⣼⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⣼⣿⣷⣾⠾⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠤⠀⠀⠯⠿⠿⠧⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡯⠿⢿⡧⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠉⠛⠻⠿⠀⠻⠿⠿⠿⢿⣿
⢀⡀⣰⣗⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣅⠠⠀⠰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣶
⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⠀⣖⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠏⠀⠀⠘⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢶⡶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠲⣶⠒⠒⠒⠖⠒⠒⠒⠒⠀⠀⠀⠀⠀
⠐⠛⠳⠿⠛⠻⠓⠛⠻⡿⠧⠄⣾⣧⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣀⠀⠀⠀⢀⠠⠤⠀⠀⠙⠀⠀⠀⠀⠙⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡿⠿⠳⠀⠀⠀⠀⢀⣀⣀⣁⢀⣀⣤⣤⣠⣄⣠⣴⣤⡀⠀⢀⠛⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣤⣴⣤
⣀⠀⠀⠐⠒⠒⠿⢷⠿⢿⣷⣧⠰⠆⣀⠀⠀⠉⢩⡍⠘⢿⣿⣿⣿⣿⣽⣿⣩⣧⣎⣋⠀⠀⠀⣀⣉⣉⣀⣤⣦⣶⣶⡄⠀⠀⠰⠶⢶⠆⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⣿⣿⣿⣿⣿⣿⡿⠿⣿⢼⣿⠟⠀⠀⢶⣶⣶⣿⣯⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⣠⣾⣾⣿⣿⣷⣦⣀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⠦⣿⣎⡛⣷⠂⣴⣿⣿⣿⣿⣿⣿⣿⡿⠇⢀⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉
⠉⠉⠉⠁⣋⠉⡙⣿⡜⢳⣤⠌⠁⣽⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣼⣦⠀⠀⠀⣀
⣤⣄⢠⢠⣿⡏⠁⠀⢹⣧⣀⣷⡶⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠂⠤⠀⠀⠀⠚⣿⣿⣽⡻⢿⣿⡟⠛⣻⣯⣿⣿⣿⣷⣾⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠛⡛⢻⣿
⣏⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣗⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣾⣷⣿⣿⣿⣾⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⣿⣛⣿⣛⣛⣻⣻
⣿⣯⣿⣿⣿⣭⣤⣭⣏⣠⣌⣹⣿⠀⠂⣰⣿⣿⣿⣿⣿⣿⣛⣾⢒⡂⣲⣿⣟⠛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⣤⣤⣤⣤⣿⣷⣶⣶⣶⢶⣶⣶⣿⣿⣿⠙⠉⢹⣿
⠟⠻⣿⡿⢿⠿⠄⢿⣯⣭⣽⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣭⠽⣿⣿⡇⠹⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢤⣭⣽⣿⡿⣿⣿⣿⣿⣿⣿⣯⣧⡄⣿⣿⠀⢂⣿⣿
⡁⡂⠀⠀⣠⡄⠀⠀⠠⠀⠀⣿⡟⢠⣿⣿⣿⣿⣿⣿⣟⣹⡿⢻⣿⡿⡟⠁⠀⠈⠺⢻⣿⣯⣍⣙⣛⣻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⣿⣿⠒⠀⣻⣿⣿⣿⣿⣿⡏⣻⣿⣿⡶⣶⣿⣿
⢿⣟⣿⣾⡿⢿⣿⠟⡿⢻⢻⡇⠀⢸⣿⣿⣿⠿⠿⠋⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣭⣭⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠀⠀⠈⣿⣿⠀⣸⣿⠛⠉⠻⣿⣿⡷⢶⢶⣿⠶⣿⣿⣿
⡛⣛⣿⣿⣷⠚⣭⣹⣉⠙⠛⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣟⠉⠁⠉⠉⢉⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠃⠀⠀⠀⠈⣿⣴⣿⣿⣿⣦⣤⣼⣿⣷⣤⣄⣿⡀⢁⣿⣿
⡧⢤⣿⣯⢿⣯⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧⠠⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣻⣿⣷⢻⣿⣿
⣧⠄⣿⣿⣦⣽⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄⢀⡀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣿
⣿⣶⣾⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⡘⣱⣮⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣰⢀⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠿⣿⡿⢩⠙⡿⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⡟⠛⠿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣠⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣷⣾⣄⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠿⠻⠝⠉⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣉⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣗⢸⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⢿⣿⡿⠿⠿⠿⣿⣿
⠿⠻⠻⣿⣿⣿⢿⣶⣶⣴⡤⠀⠀⠀⠶⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠞⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⣿⣿⣿⣿⠾⣿⣷⣶⣾⣿⣿
⠀⠀⠀⢠⠥⠀⠀⠿⠿⠿⠿⠤⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣄⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠉⠛⠻⠿⠀⠻⠿⠿⢿⣿⣿
⢀⣀⣸⣷⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣶
⠉⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠟⠻⠟⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠉⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣶⠲⠒⠒⠶⠒⠒⠒⠂⠒⠂⠀⠀⠀
⠐⢛⠻⠿⠛⠻⠓⢿⢿⣿⠷⠶⣾⣷⠶⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠸⣿⡟⠟⠃⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⣀⣀⠀⠀⣀⠀⠀⡀⣠⣶⣶⣶⣤⣶⣶⣶⣶⣶⣦⣤⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⣀⠀⠀⠀⠂⠐⠾⠶⠿⢿⣷⣄⠀⠄⠀⠀⠀⠉⢩⠅⠀⠰⢾⣿⣾⣂⣀⣀⠀⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⡿⢿⣿⣿⣿⡿⠿⢯⢰⣶⠈⠀⠀⠒⣶⡶⣶⣶⣾⣿⣿⣿⢿⣿⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣾⢀⡛⢢⠀⠀⠒⠙⠋⠋⠉⠙⠛⠛⠇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡙⣿⣿⠿⣿⢿⠿⣾⠾⣯⢛⢪⠙⠛⠉⠉⠁⠉
⠉⠉⠁⠀⢉⠁⠀⣿⠀⢠⣤⠀⠀⣩⡿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣤⣽⣿⣥⢶⣾⣿⣟⣛⣛⠀⢀⣴⣆⣤⣄⣀⣀⠀⢀⠀⠀⠀⠙⠿⠟⠛⠛⠿⢾⣿⣼⣾⣿⣿⣿⡿⠧⠀⢀⠀⠀⠀⠀
⣤⡄⠀⠀⣯⠁⠀⠀⢠⣇⣀⣠⠄⠀⠀⠀⠀⠀⠀⠸⠀⠲⠶⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠶⠾⢟⠛⠛⢛⣻
⣍⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣗⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣋⣋⣻⣻
⡤⢀⣯⣭⣯⣭⣀⣍⣅⣀⣀⣈⣿⠀⠀⢀⣃⡒⠂⠀⠒⠂⠀⢐⢒⡀⠀⡄⠐⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢿⣿⣿⡿⣿⣧⣤⣼⣿⣿⣿⢠⡄⣤⣤⣤⣤⣶⣶⣴⡶⢶⢶⡶⡶⡿⣿⣿⠉⠉⢹⠿
⠗⠲⣿⠿⠿⠥⠀⢸⣯⣭⣽⣿⣿⠀⠀⢰⠄⢐⣀⡀⣀⠄⠉⢌⠈⠉⠠⠮⠽⠆⠘⣿⣿⣯⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⠠⠤⢤⡧⢤⡤⠴⡤⠀⠛⠋⢉⣿⠀⢠⣤⣭⣿⡯⢿⢿⣿⣿⣼⢼⣧⣧⠀⠈⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢼⣿⠀⡀⠀⠀⠈⠉⠉⠩⠁⢬⠈⠉⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⠺⢾⣿⡀⠀⠉⣽⣿⠂⠀⢸⣿⣿⣿⢺⣿⡇⠃⣾⣿⡶⠶⣿⣿
⢿⠛⣷⣶⡿⢻⣷⠛⠟⠛⢛⣾⣿⣶⣷⣾⣥⣅⠄⠠⠌⠋⡤⠇⠠⠄⠀⠁⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣿⣟⣽⣿⡇⠀⠀⠀⠀⠈⠉⠻⠿⢿⣿⣿⣼⣿⠃⠀⠀⠻⣿⠀⠀⠻⠛⠉⠙⢺⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠙⠛⣻⣝⣃⠊⣉⣉⡉⠉⢛⣛⣿⣿⣿⣿⣿⡿⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡌⠁⠀⢙⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⡀⣿⣴⣿⣶⣶⣦⣄⣤⣷⡇⡤⠀⣼⠀⠀⣺⣿
⡦⢠⣾⡋⠙⣥⣿⣿⡟⠾⠿⠿⠃⢨⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣋⠁⠀⠀⠈⣛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⣘⣿⣦⢸⣿⣿
⣦⠀⣾⣿⣦⣸⡇⠀⢀⡀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣀⡿⡌⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡯⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣿⠟⠉⠩⣛⣿
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣧⡀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢿⣿⠿⠿⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣿⡛⠘⠛⡋⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠄⠀⠤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⣽⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠁⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⡄⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠄⠀⢭⠋⠋⠉⠀⠈⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡓⠈⠂⡀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠍⠀⡆⡠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠉⠉⢿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿
⠟⠛⠻⣿⣿⡿⠿⣶⣶⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⢢⡻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢸⣷⣶⣶⠾⣷⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⢯⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠈⠉⠛⠛⠀⠙⠛⠻⠿⠿⢿
⠀⠀⢐⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡄⣾⣿⣿⣣⣶⣶⣶⣄⢿⣿⣿⣶⣶⣆⡄⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣶⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⣴
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣧⣿⣿⢿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣩⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠘⠿⣿⣿⣦⣻⣶⡀⣿⣿⣿⣿⣿⣸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⢾⣿⡏⣻⣿⣯⣿⡇⣿⣿⢻⣿⣿⡿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⢿⣿⣼⣿⣿⣿⣿⣿⣿⣧⠿⠿⢸⣿⣿⡧⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⠸⣿⡟⠗⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠐⠶⠶⠿⢿⣶⣄⠀⠄⠀⠀⠀⠈⠉⠀⠀⠀⢘⣷⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠐⠖⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⣶⢶⡖⣶⣤⣴⣷⣶⣶⣦⣦⣿⣶
⠛⠛⠻⠿⠿⢿⣿⣿⣿⡟⠛⠇⠀⣶⠀⠀⠀⠒⣒⠂⣴⣶⣾⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠴⠗⢆⢤⠽⠏⠫⠉⣉⠉⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠡⠤⣾⠀⡙⠠⠀⠀⠀⠘⠀⠋⠉⠉⠙⠛⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⡿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀
⠉⠉⠁⠀⠀⠁⠀⠴⠀⢠⣄⠀⠀⣩⡠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣭⠛⢿⣿⡿⠟⣛⣿⣿⣿⣿⡇⠀⠀⠀⠀⢲⣆⣠⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⠨⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠰⠀⠀⠀⠀⠀⣼⣿⣷⣷⣾⣿⣶⣼⣿⣿⣿⣽⣿⣧⢀⣶⣿⡂⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⢨⣷⣶⣷⣿⣷⣶⣶⠶⠾⠛⠛⠛⢛⣻
⠀⠀⣶⣾⣾⣷⣶⣷⣾⣿⣿⣿⡓⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⡗⣻⣗⠀⠀⠀⢸⣿⣗⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠿⠿⠿⠿⠛⣛⣛⣋⡉⣙⣛
⡄⠀⣤⣭⣬⣥⣀⣈⣁⣀⣀⡀⡿⠀⠀⠀⠂⠀⠀⠀⠐⠂⠀⠀⢀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠧⢾⣷⠿⡟⣿⣧⣤⣬⣿⣷⣷⢠⠀⣠⡤⣤⣄⣴⣦⣤⡶⢶⠶⡖⡖⠿⠿⣭⠉⠉⢹⠙
⠆⠀⣶⠷⠤⠤⠀⢸⣧⡭⣭⣿⣿⠀⠀⢰⠀⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠎⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣽⠀⠠⠤⠤⠦⢤⡤⠴⡤⠀⠉⠉⠉⣿⠀⠀⣄⣤⣿⡯⠸⢿⣿⡇⢰⢨⡇⡅⠀⠈⣿⠀⠀⣸⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢼⣿⠀⡀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠚⢺⣿⠀⠀⠉⣀⣿⠂⠀⢸⣿⡷⣴⢸⣇⡄⠂⢶⣿⠶⠶⣿⣿
⠛⠙⣶⣶⡞⠻⣷⠛⠛⠛⢒⡶⢼⣤⣧⣼⣤⡄⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠹⠿⢿⣿⣿⣼⣿⠁⠀⠀⠻⣿⠀⠀⠛⠛⠉⠘⠸⡟⡇⠶⠶⢿⠶⠶⣾⣿
⠘⠙⣻⣍⣁⠈⣉⣉⡉⠉⢛⣛⠹⢿⣿⣿⡿⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣍⡉⠉⠉⠁⢘⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠀⠀⠀⠀⢺⣤⣷⣦⣤⣄⡀⢤⣧⡇⡀⠀⣸⠀⠀⢺⣿
⡆⢠⣾⠋⠉⣁⣿⣿⡗⠲⠿⠟⠀⢠⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠇⠀⠀⠀⠘⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⡆⠀⣿⣿
⣦⠀⣾⣿⣦⢨⡅⠀⠀⠀⠀⠀⠀⢨⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⡆⠀⢀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣬⣿⣿
⣷⣤⣾⣿⣿⡿⣦⡄⣀⣀⠻⠈⠀⠈⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⡇⠀⣠⣾⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣥⣽⠟⠉⠉⠉⠛
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣦⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⠷⠶⢾⠏⠀⠙⠟⠀⠀⢸⣾⣿
⣿⣿⣿⣿⠷⣾⣟⠋⠈⠛⡉⠀⠰⠆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣤⠄⠀⢡⠉⠈⠉⠀⠀⢸⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣦⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⠉⣭⣩⣭⣽⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠁⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠛⠛⠛⣿⣿⡿⠷⠶⣶⣾⡿⠇⠀⠀⢸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⢰⣶⣶⣶⠶⣶⡶⢶⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠸⣿⣿⡇⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠈⠙⠛⠀⠙⠛⠺⠿⠿⠷
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢫⣴⣶⣶⣤⡀⠀⠀⣶⣶⡄⣿⣿⡿⣠⣶⣶⣶⣄⣿⣿⣷⣶⣶⡆⠀⢰⣾⣿⢻⣿⣿⢻⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣧⣿⣿⢡⣿⣿⢹⣿⣿⣿⣽⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣸⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⠶⠶⠶⣶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⡸⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠃⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠇⠘⠿⠿⠿⠿⠃⠀⠀⠿⠿⣼⣿⣿⡇⠻⠿⡿⠿⠋⣿⣿⣿⡿⠀⠀⠀⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⠸⣿⡟⠓⠂⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⡀⠀⠀⠀⠂⠐⠺⠶⠿⢿⣶⣄⠀⠄⠀⠀⠀⠉⢉⠄⠀⠀⢼⣿⣠⣂⣀⣀⢀⣠⣀⣀⣀⣀⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠒⠖⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣷⣿⣷
⠛⠛⠻⠿⠿⢿⣿⣿⣿⡿⠻⢇⠐⣶⠀⠀⠀⠒⣲⠲⣶⣶⣾⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡰⣾⡿⣳⣥⣟⡿⣿⣛⣻⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣾⠀⡙⢠⠀⠀⠀⠙⠀⠋⠉⠙⠙⠛⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣷⣿⡛⠈⠉⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠁⠉
⠉⠉⠁⠀⢈⠁⠀⢾⠀⢠⣤⠀⠀⣩⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠩⠊⠀⠀⢺⣖⣠⣄⣀⡀⠀⢀⠀⠀⠀⠀⠒⠛⠀⠈⠀⠀⣀⠈⠀⠀⠀⢀⡠⠦⠀⢀⠀⠀⠀⠀
⣤⡄⠀⠀⢫⠁⠀⠀⢠⣇⣀⣀⠄⠀⠀⠀⠀⠀⠀⠘⠀⠰⠲⠄⠀⠀⠀⣿⣿⣏⠛⣿⡿⠟⢛⣿⣿⣿⣿⣿⠇⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣷⠶⠾⢟⠛⠛⢛⣻
⡁⠰⣶⣾⣿⣷⣶⣷⣾⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧⣰⣿⣿⡟⠛⣿⣗⣿⣗⠀⠀⠀⢸⣿⣗⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠿⠿⠿⠛⣛⣛⣋⣉⣹⣛
⡄⠀⣯⣭⣯⣭⣀⣍⣁⣀⣀⣈⣿⠀⠀⠀⠓⠒⠂⠀⠒⠂⠀⠐⢀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡧⢾⣿⢿⡟⣿⣧⣤⣼⣿⣿⣷⢠⠀⣤⡤⣤⣤⣶⣦⣤⡶⢶⢶⡶⡶⡿⢿⣿⠉⠉⢹⠻
⠇⠒⣾⠷⠤⠤⠀⢸⣧⣭⣭⣿⣿⠀⠀⢰⠀⢀⣀⠀⡀⠄⠁⠄⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠠⠤⠤⠧⢤⡤⠴⡤⠀⠋⠉⠉⣿⠀⠠⣤⣥⣿⡯⢼⢿⣿⣷⢸⢸⡧⡇⠀⠈⣿⠀⠀⣼⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢼⣿⠀⡀⠀⠀⠈⠉⠉⠉⠍⠈⠠⠀⠈⢉⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⡀⣤⣶⠲⢺⣿⠀⠀⠉⣝⣿⠂⠀⢸⣿⡿⣿⢸⣧⡇⠃⢶⣿⠶⠶⣿⣿
⢻⠛⣶⣶⡾⢻⣷⠛⠟⠛⢛⣾⢿⣤⣷⣾⣤⠄⠀⣀⣸⣋⣁⣿⡀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠻⠷⠿⠿⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⠻⣿⠀⠀⠛⠛⠉⠙⢸⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⠛⣻⣍⣃⠈⣉⣉⡉⠉⢛⣛⠿⢿⣿⣿⣿⠟⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⣟⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⠀⠀⠀⠀⢺⣤⣿⣶⣶⣤⡀⣤⣧⡇⠀⠀⣸⠀⠀⢺⣿
⡆⢠⣾⠋⠉⣣⣿⣿⡗⠾⠿⠿⠁⢨⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣘⣿⣆⠰⣿⣿
⣦⠀⣾⣿⣦⢨⡇⠀⢀⡀⠀⠀⠀⢨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⣋⣀⠀⠀⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣀⠿⡌⠀⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣿⠟⠉⢉⠛⠻
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⠏⢀⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⢷⣾⣟⡛⠘⠛⡉⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠛⠁⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠁⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣤⠄⠀⢭⠉⠋⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣽⣽⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⡂⠀⢀⢆⢹⣿⣿⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠁⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠷⣶⣶⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⠇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠀⠀⢰⣶⣶⣶⠶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠈⠉⠙⠛⠀⠙⠛⠻⠿⠿⢿
⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⢯⣿⣿⣿⣿⣿⣿⠟⣷⣶⡼⣿⣿⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠿⠿⠿⠛⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡞⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⠿⠿⠿⠃⠀⠀⠿⢿⣾⣿⣿⠀⠻⠿⠿⠿⢿⣿⣿⠿⠿⠀⣿⣿⣿⡿⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⠸⣿⡿⠟⠂⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⡀⣀⢀⠀⢀⣤⣤⣤⣤⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣀⠀⠀⠀⠂⠐⠾⢶⠿⢿⣶⣄⠀⠄⠀⠀⠀⠉⢩⠄⠀⠐⢿⣿⣵⣺⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠒⠖⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⡿⣿⣿⣿⣿⡿⠻⢏⢰⣶⠈⠀⠀⠒⣲⠶⣶⣶⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣿⢀⡛⢠⠀⠀⠐⠙⠈⠋⠉⠙⠛⠛⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡹⣿⡿⡿⠿⢿⣿⡺⠿⠟⣏⠊⠙⠛⠉⠉⠁⠉
⠉⠉⠁⠀⢈⠁⠀⣾⠀⢠⣤⠀⠀⣩⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣩⣤⣽⣿⣍⡉⢿⣿⠟⠿⢿⣿⠁⠀⠁⠀⠀⠀⠒⢻⣖⣤⣄⣀⣀⠀⢀⠀⠀⠀⠑⠿⠟⠛⠚⠓⢟⣿⣼⣿⣿⣿⡽⡿⠦⠀⢀⠀⠀⠀⠀
⣤⡄⠀⠀⢭⠁⠀⠀⢠⣇⣀⣠⠄⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣤⣴⣾⣆⠀⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣷⠶⠾⢟⠛⠛⢻⣻
⡉⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣿⣟⣿⣗⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣛
⡄⢂⣧⣭⣭⣭⣀⣍⣅⣀⣀⣈⣿⠀⠀⠐⡓⡒⠂⠀⠐⠂⠀⠐⢂⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠠⣿⡧⣿⣿⣿⡟⣿⣧⣤⣼⣿⣿⣿⢠⡄⣤⡤⣤⣤⣶⣶⣤⡶⢶⢶⡶⡶⡿⢿⣿⠉⠉⢹⢿
⠇⠲⣶⠿⠮⠬⠀⢸⣯⣭⣽⣿⣿⠀⠀⢰⠀⢀⣀⢀⡀⠄⠀⠄⠈⠁⢹⣿⣏⣉⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠠⠤⢤⡧⢤⡤⠶⡤⠀⠛⠉⢉⣿⠀⠠⣤⣭⣿⡯⢿⢿⣿⣿⢸⢸⣧⣧⠀⠈⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢾⣿⠀⡀⠀⠀⠈⠉⠉⠩⢅⠌⠤⠀⠈⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⢀⠀⠀⠀⢀⡀⣤⣶⠲⢾⣿⠀⠀⠉⣟⣿⠂⠀⢸⣿⣿⣿⢸⣧⡇⠃⢾⣿⠶⠶⣿⣿
⢟⠛⣶⣶⡿⢻⣷⠛⠟⠛⢛⣶⢿⣶⣷⣾⣤⡤⠀⢀⣼⣋⣤⠿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠙⠷⠿⠯⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⠻⣿⠀⠀⠛⠛⠉⠙⢸⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠙⠛⣻⣝⣃⠈⣉⣉⡉⠉⢛⣛⡿⣿⣿⣿⠿⡿⣟⠛⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⣛⠋⠉⠛⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⣿⣿⠀⠀⠀⠀⣾⣴⣿⣶⣶⣦⣄⣤⣷⡇⡠⠀⣸⠀⠀⣻⣿
⡦⢠⣾⠋⠙⣧⣿⣿⡟⠾⠿⠿⠃⢨⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠗⠀⠀⠀⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠓⣘⣿⣆⠸⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣾⡇⠀⠀⣴⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣀⡿⡄⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠉⠩⢛⡻
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠏⢀⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣟⡛⠘⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⢀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠋⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣤⡄⠀⢭⠉⠋⠉⠀⠀⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠐⠊⢢⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⢐⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠉⠈⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠟⠛⠻⣿⣿⡿⠷⣶⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⢸⣶⣶⣶⠶⣷⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠈⠉⠙⠛⠀⠙⠛⠺⠿⠿⢿
⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⣿⣿⣿⠀⣠⣶⣶⣾⣿⣿⣿⣶⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⣴
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣽⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢺⣿⡏⣿⣿⣇⣶⡀⣿⣿⢿⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⣼⣿⣦⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⢀⣤⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠻⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⠸⣿⡟⠗⠂⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡀⣀⠀⢠⣤⣶⣤⣤⣤⣦⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⡀⠀⠀⠀⠂⠐⠾⠶⠿⢿⣶⣄⠀⠄⠀⠀⠀⠉⢉⠄⠀⠀⢼⣿⣴⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠐⠉⠀⠀⠀⠀⠀⠒⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣶⣶⣶⣦⣾⣿⣾⣶⣿⣷⣿⣿
⠛⠛⠻⠿⡿⢿⣿⣿⣿⡿⠻⢇⢰⣶⠀⠀⠀⠒⣒⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠔⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣾⠀⡙⢠⠀⠀⠀⠙⠊⠋⠉⠙⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣾⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⡟⠋⠉⡗⠉⠍⠉⠁⠀⠉⠄⠀⠨⠘⠛⠉⠉⠀⠉
⠉⠉⠁⠀⢈⠁⠀⢾⠀⢠⣤⠀⠀⣭⡾⠀⠀⠀⠀⣀⠀⠀⠀⢀⣸⣥⣤⣽⣿⣍⡰⣿⡟⣛⠿⢿⣿⠁⠀⠉⠁⠀⠀⠀⠘⠒⢻⣖⣠⣄⣀⡀⠀⢀⠀⠀⠀⠁⠛⠛⠃⠋⠁⢀⡀⠀⠀⢀⣄⢎⡷⠦⠀⢀⠀⠀⠀⠀
⣤⡄⠀⠀⢯⠁⠀⠀⢠⣆⣀⣠⠄⠀⠀⠀⠀⠀⠀⠘⠀⠰⠆⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣠⣤⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠶⠿⢟⠛⠛⢛⣻
⡉⠰⣶⣾⣿⣷⣶⣷⣾⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠚⠛⠛⣿⣟⣿⣗⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣛
⡄⠀⣯⣭⣯⣥⣀⣍⣁⣀⣀⣈⣿⠀⠀⠐⡃⡒⠀⠀⠐⠂⠀⢐⠈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠗⠠⣿⡧⣿⣿⣿⡟⣿⣧⣤⣼⣿⣿⣷⢠⠄⣤⡤⣤⣤⣴⣶⣤⡶⢶⢶⡶⡶⠿⢿⣿⠉⠉⢹⠿
⠇⠒⣷⠷⠮⠤⠀⢸⣯⣭⣭⣿⣿⠀⠀⢠⠀⢀⣀⠀⡀⠀⠀⠀⠈⢹⣧⣉⡉⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⢶⠇⠀⠠⠤⢤⡧⢤⡤⠴⡤⠀⠋⠉⢉⣿⠀⠠⣤⣬⣿⡯⢾⢿⣿⣿⢸⢸⡧⣇⠀⠈⣿⠀⠀⣸⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢼⣿⠀⡀⠀⠀⠈⠉⠉⠉⠄⠨⠅⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀⠀⣤⣶⠲⢾⣿⠀⠀⠉⣜⣿⠂⠀⢸⣿⣿⣿⢸⣇⡇⠂⢶⣿⠶⠶⣿⣿
⢟⠛⣶⣶⡾⢻⣷⠛⠟⠛⢓⣶⣿⣤⣷⣼⣤⡄⠄⢀⣼⣋⣡⠷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠻⠷⠿⠿⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⠻⣿⠀⢀⠛⠛⠉⠙⢸⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⠛⣻⣍⣁⠈⣉⣉⡉⠉⢛⣛⠿⢿⣿⣿⠿⡟⡿⠛⠛⠋⠁⠀⠀⠀⠀⠈⣿⡛⠛⠻⠿⢿⡿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⣿⣿⠀⠀⠀⠀⢺⣴⣿⣶⣶⣤⡀⣤⣷⡇⡀⠀⣼⠀⠀⣿⣿
⡦⢠⣾⠋⠙⣧⣿⣿⡟⠾⠿⠟⠁⢨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠘⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠑⣘⣿⣆⠐⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣴⣶⡆⠀⠀⣠⣾⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣧⡄⣠⣀⠿⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠉⠉⢛⡻
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⠏⢀⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⢷⣾⣟⡛⠘⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣥⠄⠀⢭⠉⠉⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠔⠂⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣯⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠁⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠿⢶⣶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣷⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⢰⣶⣶⣶⠶⣷⣶⢶⣶⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠈⠉⠛⠛⠀⠙⠛⠺⠿⠿⠿
⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣿⣿⣿⣿⣶⣾⣿⣿⣶⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣇⣿⣿⣏⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠓⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠻⠿⣿⢿⣿⣿⣿⡿⠿⠘⠛⣿⣿⣿⣿⣿⡿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⢸⣿⡿⠟⠂⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀⣀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣀⠀⠀⠀⠂⠐⠾⠷⠿⢿⣶⡄⠀⠄⠀⠀⠀⠉⢩⠀⠀⠃⢿⣿⣭⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠒⠉⠀⠀⠀⠀⠀⠐⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⡿⢿⣿⣿⣿⡿⠿⢇⢰⣶⠀⠀⠀⢖⣒⡲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣿⠀⡛⢠⠀⠀⠀⠙⠚⠋⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣶⣿⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⠋⣯⣷⣿⣿⣾⣾⣾⡷⠆⡑⢨⠙⠛⠉⠉⠀⠉
⠉⠉⠁⠀⢁⠁⠀⣾⠀⢠⣤⠀⠀⣹⡾⠀⠀⠀⠀⣀⠀⠀⠀⣠⣙⣁⣈⣽⣫⡉⢭⣝⠻⠿⢿⣿⡏⠀⠈⠋⠃⠀⠀⠀⠚⠒⢻⣖⣤⣄⣀⣀⠀⢀⠀⠀⠄⠪⠿⠿⠟⠻⠿⢟⣾⣿⣶⣿⡾⡿⠻⠧⠀⢀⠀⠀⠀⠀
⣤⡄⠀⠀⢿⠁⠀⠀⢠⣇⣀⣠⠄⠀⠀⠀⠀⠀⠀⠘⠀⠰⠢⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣾⣷⡀⣤⣤⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣷⠶⠿⣟⠛⠛⢻⣻
⡁⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠚⠛⠛⣿⡗⣿⣗⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣻
⡄⠄⣧⣭⣭⣭⣀⣍⣁⣀⣀⣈⣿⠀⠀⠀⠓⡒⠀⠀⠒⠂⠀⣒⢘⡟⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠗⠠⣿⡷⣿⣿⣿⡟⣿⣦⣤⣼⣿⣿⣯⢠⡄⣤⡤⣤⣤⣶⣶⣤⡶⢶⢶⡶⡶⡿⢿⣿⠉⠉⢹⢿
⠇⠒⣾⠿⠿⠥⠀⢸⣯⣭⣽⣿⣿⠀⠀⢰⠀⣀⣀⣀⡀⠄⠁⠀⠈⢻⣄⣙⣋⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⠇⠀⠠⠤⢴⡧⢤⡤⢴⡤⠀⠋⠉⢉⣿⠀⠠⣬⣥⣿⡯⢿⢿⣿⣿⢸⢽⣧⣧⠀⢈⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢿⣿⠀⡀⠀⠀⠈⠉⠉⠩⠅⠉⠅⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡀⢀⡀⠀⠀⢀⡀⣤⣶⠲⢾⣿⠀⠀⠉⣝⣿⠂⠀⢸⣿⣿⣿⢸⣧⡇⠂⢾⣿⠶⠶⣿⣿
⢟⠛⣷⣶⡿⢻⣷⠛⠟⠛⢺⣿⣿⣶⣷⣾⣥⡤⡀⢠⢼⣈⣀⣿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠿⠷⠿⠿⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⠿⣿⠀⠀⠛⠛⠉⠹⢺⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⢛⣻⣍⣃⠈⣉⣉⡉⠉⢛⣛⡿⢿⣿⣿⠿⡿⠿⠻⠛⠛⠋⠀⠀⠀⠀⠈⣯⡉⠉⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⠃⠀⠀⠀⣾⣴⣾⣶⣶⣦⡀⣤⣷⡇⡤⠀⣼⠀⠀⣻⣿
⡦⢠⣾⡋⢙⣥⣿⣿⡟⠾⠿⠿⠃⢨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠶⠂⠀⠀⠘⠻⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠓⣘⣿⣆⠘⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⣾⣷⠀⠀⣀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣀⡿⡄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠉⠩⣛⡻
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣿⡛⠘⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⠄⢀⢀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠋⠁⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⡄⠀⢥⠉⠊⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠆⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠉⠈⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠿⣶⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡗⠀⠀⢸⣶⣶⣶⠶⣷⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠈⠉⠙⠛⠀⠙⠻⠺⠿⠿⢿
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣤⡀⠀⠀⣶⣾⣿⣿⣶⠀⣠⣶⣶⣿⣿⣿⣶⣶⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⢹⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣼⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⣿⣿⣇⢺⣿⡏⣿⣿⡇⣤⣄⣿⣿⢿⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣤⣻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡿⠟⠂⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡀⣀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⣀⠀⠀⠀⠂⠐⠶⠶⠿⢿⣶⡄⠀⠄⠀⠀⠀⠉⢩⠁⠀⠈⢿⣿⣴⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⡿⢿⣿⣿⣿⡿⠿⢇⢠⣶⠀⠀⠀⠲⣶⢲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⢬⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠙⠡⠤⣿⠀⡛⢠⠀⠀⠂⠙⠈⠋⠉⠉⠉⠩⢭⠛⢻⣿⠿⠿⠿⣿⣿⣿⣿⣿⠟⠻⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣿⣿⣿⢛⣿⣿⣿⠿⢿⢷⣿⣿⢆⢑⠈⠙⠛⠉⠉⠁⠉
⠉⠉⠁⠀⢈⠁⠀⣿⠀⢠⣤⠀⠀⣩⡿⠀⠀⠀⠀⣀⠀⠀⠀⠸⣷⣴⣶⣿⣿⣷⣬⣿⣠⣭⣙⣛⣟⡀⠀⠈⠙⣀⡀⠀⠀⠀⢺⣖⣠⣄⣀⣀⠀⢀⠀⠀⠀⠫⠿⠟⠛⠋⠛⢳⣿⡟⣓⡾⣶⣷⡿⠦⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⢯⠁⠀⠀⢠⣇⣀⣠⠄⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠶⠿⣟⠛⠛⢻⣻
⡍⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠛⠛⣿⡟⣿⣗⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣻
⡄⠀⣯⣭⣭⣭⣀⣭⣁⣀⣀⣈⣿⠀⠀⠀⠒⠒⠂⠀⠒⠂⠐⠒⠂⢸⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠠⣿⡿⣿⣿⣿⡟⣿⣧⣤⣼⣿⣿⣧⢠⡄⣤⡤⣤⣤⣶⣶⣤⡶⢶⢶⡶⡶⡿⢿⣿⠉⠉⢹⢿
⠇⠒⣿⠿⠯⠴⠀⢸⣯⣭⣭⣿⣿⠀⠀⢰⠀⢀⣀⢀⣀⠄⠁⠈⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠠⠤⢴⡧⣤⡤⢴⡤⠀⠋⠉⢉⣿⠀⢠⣬⣭⣿⡯⢿⢿⣿⣿⣸⢼⣧⣧⠀⠈⣿⠀⠀⣼⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢿⣿⠀⡀⠀⠀⠈⠍⠉⠩⠅⠨⠭⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⣤⣶⠲⢾⣿⠀⠀⠉⣝⣿⠂⠀⢸⣿⣿⣿⢸⣿⡇⠃⣶⣿⠶⠶⣿⣿
⢟⡛⣷⣶⡿⢻⣷⠛⠟⠛⢳⣿⣿⣴⣷⣾⣥⣥⡀⠀⣼⣏⣁⣿⠦⠀⠀⠀⢉⡉⠉⣛⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠉⠙⠿⠿⠿⠿⠿⠿⣿⣿⣼⣿⠃⠀⠀⢿⣿⠀⢀⠛⠛⠉⠹⢺⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⠛⣻⣍⣃⠈⣉⣉⡉⠉⢛⣛⡿⢿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠿⣿⣿⠃⠀⠀⠀⣿⣴⣿⣶⣶⣤⡀⣤⣷⡇⡠⠀⣼⠀⠀⣻⣿
⡦⢠⣾⡋⠙⣧⣿⣿⡟⠾⠿⠿⠁⢨⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣛⡉⠉⠀⠈⠉⣛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠑⣸⣿⣆⠰⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣀⡿⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠉⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣿⠟⠉⠩⣛⡻
⣿⣿⣿⣿⡿⣷⣿⣇⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⣿⠿⠾⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣿⡛⠘⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⠀⢀⢀⣠⣽⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠁⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⡄⠀⢥⠉⠊⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠃⢀⢾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣭⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠉⠈⠻⡿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠿⣶⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡗⠀⠀⢸⣶⣶⣶⠶⣷⣶⣶⣶⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠢⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠈⠉⠛⠛⠀⠙⠛⠻⠿⠿⢿
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣾⣿⣿⣶⠀⣠⣶⣶⣿⣿⣿⣶⣶⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢴
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣹⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⣿⣿⣇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢿⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿⠿⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⠸⣿⡿⠟⠂⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⢀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⣀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣀⠀⠀⠀⠂⠐⠶⠶⠿⢿⣷⣄⠀⠄⠀⠀⠀⠉⢩⠁⠀⠈⢛⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⡿⢿⣿⣿⣿⡿⠻⢇⢠⣶⠀⠀⠀⢖⣶⢲⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠣⠤⣿⠀⡛⢠⠀⠀⠂⠙⠚⠋⠉⠙⠉⠉⠭⠍⠛⠿⠿⠟⣻⠿⣿⣿⣿⣿⡿⠛⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣿⣿⣿⢛⣻⣿⢿⠿⠿⢾⣿⣿⣀⡙⢘⠙⠛⠉⠉⠀⠉
⠉⠉⠁⠀⢈⠁⠀⣿⠀⢠⣤⠀⠀⣩⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠿⣦⣶⣾⣿⣿⣦⣭⣧⣴⣭⣭⣿⣇⠀⠀⠉⣀⣀⠀⠀⠀⢺⣆⣠⣄⣀⣀⠀⢀⠀⠀⠄⠫⠿⠟⠛⠛⠓⢻⣿⡗⣳⣖⣳⣾⡿⠦⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⢿⠁⠀⠀⢠⣆⣀⣠⠄⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠶⠿⢟⠛⠛⢻⣻
⡉⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⠛⣿⡟⣿⣷⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣋⣋⣻⣛
⡄⢀⣯⣭⣭⣭⣀⣍⣁⣀⣀⣈⣿⠀⠀⠀⠒⡂⠀⠀⠐⠂⡐⢒⢂⡀⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡋⠀⠀⣿⡯⣿⣿⣿⡟⣿⣧⣤⣼⣿⣿⣿⢠⡄⣠⡤⣤⣄⣶⣶⣤⡶⢶⢶⡶⡶⡿⢿⣿⠉⠉⢹⢻
⠇⠒⣾⠷⠿⠵⠀⢸⣯⣭⣽⣿⣿⠀⠀⢰⠀⢀⣄⢀⣀⠄⠁⠈⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠠⠤⢴⡧⣤⡤⢴⡤⠀⠋⠉⢉⣿⠀⢠⣤⣭⣿⡯⢿⢿⣿⣿⢼⢽⣧⣧⠀⠈⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣼⣿⠀⡀⠀⠀⠈⠍⠉⠩⠅⢉⠭⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⠀⠀⠀⢀⡀⣤⣶⠲⢾⣿⠀⠀⠉⣟⣿⠂⠀⢸⣿⣿⣿⢸⣯⡇⠃⣾⣿⠶⠶⣿⣿
⢿⡛⣷⣶⡿⢻⣷⠛⠟⠛⢳⣿⢿⣶⣷⣾⣥⣥⠀⠀⣼⣋⣁⣿⠦⠄⠀⠀⠉⠉⠉⢹⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠙⠷⠿⠿⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⠿⣿⠀⢀⠛⠛⠉⠙⢺⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⠛⣻⣝⣃⠈⣉⣉⡉⠉⢛⣛⡽⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⠃⠀⠀⠀⣿⣴⣿⣶⣶⣦⡀⣤⣷⡇⡤⠀⣼⠀⠀⣿⣿
⡦⢠⣾⡋⢙⣧⣿⣿⡟⠾⠿⠿⠃⢨⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣛⡉⠉⠁⠉⢙⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⣘⣿⣆⠐⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣁⡿⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠉⠉⢛⡻
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣿⠛⠘⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠠⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⠄⢀⣀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠛⠁⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⡄⠀⢥⠉⠊⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠘⠃⠁⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣭⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠱⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠉⠈⠻⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠷⣶⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡗⠀⠀⢸⣶⣶⣶⠶⣷⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠈⠉⠛⠛⠀⠙⠛⠻⠿⠿⢿
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⣿⣿⣷⠀⣠⣶⣶⣾⣿⣿⣷⣶⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣴
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣽⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⣿⣿⡇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢿⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠓⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⣿⣿⣿⣃⣾⣿⣿⣿⣿⣿⡿⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡿⠗⠂⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢀⣀⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⣀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⣀⠀⠀⠀⠂⠐⠶⠷⠿⢿⣶⣤⠀⠄⠀⠀⠀⠉⢩⠁⠀⠀⢽⣿⣶⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠐⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⡿⣿⣿⣿⣿⡿⠻⢇⢠⣶⠀⠀⠀⢒⣖⣲⣶⣾⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣿⠀⡛⢠⠀⠀⠂⠘⠙⠋⠉⠙⠙⠋⡁⠤⠉⠻⡿⠟⢛⣻⢿⣿⣿⣿⣿⡿⠻⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⢏⢿⣿⠿⣿⠿⣿⣿⣟⡆⡘⢈⠘⠛⠉⠉⠁⠉
⠉⠉⠁⠀⢉⠁⠀⣿⠀⢠⣤⠀⠀⣹⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢿⣴⣶⣿⣿⣿⣬⣽⣤⣬⣭⣽⣛⡁⠀⠀⠀⢁⡀⠀⠀⢰⣖⣠⣄⣀⣀⠀⢀⠀⠀⠃⠻⠿⠿⠛⠛⠛⢻⣟⡾⣿⣷⣾⣿⡿⠦⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⢿⠁⠀⠀⢠⣇⣀⣠⠆⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠦⠆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣷⠶⠿⣟⠛⠛⢻⣻
⡉⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠛⣿⣟⣿⣷⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣻
⡄⢀⣯⣭⣭⣭⣀⣉⣁⣀⣀⣈⣿⠀⠀⠀⠒⡒⠀⠀⠒⠂⡐⢒⠒⡀⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠁⠀⣾⡿⣿⣿⣿⡟⣿⣧⣤⣼⣿⣿⣯⢠⠄⣠⡤⣤⣤⣶⣶⣤⡶⢶⢶⡶⡶⡿⢿⣿⠉⠉⢹⢿
⠇⠲⣾⠿⠮⠥⠀⢸⣯⣭⣭⣿⣿⠀⠀⢰⠀⣀⣔⢀⣀⠀⠉⠄⠈⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⢴⡧⢤⡤⢴⡤⠀⠛⠉⢉⣿⠀⢠⣨⣭⣿⡯⢿⢿⣿⣿⢼⢹⣧⣧⠀⠨⣿⠀⠀⣼⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢿⣿⠀⡀⠀⠀⠈⠍⠉⠩⢍⢩⡭⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀⠀⡀⢀⡀⣤⣶⠲⢾⣿⠀⠀⠉⣝⣿⠂⠀⢸⣿⣿⣾⢸⣷⡇⠃⣾⣿⠶⠶⣿⣿
⢟⠛⣶⣶⡿⢿⣷⠛⠟⠛⢻⣿⣿⣶⣷⣾⣥⣄⡀⠄⢸⣉⣡⣿⣦⠄⠄⠉⠁⠀⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠙⠿⠿⠿⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⠻⣿⠀⠀⠛⠛⠉⠙⢺⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⢛⣻⣍⣃⠈⣉⣉⡉⠉⢛⣛⡽⢿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⣿⣦⣬⣏⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⠃⠀⠀⠀⣿⣴⣿⣶⣶⣤⡀⣤⣷⡇⡤⠀⣼⠀⠀⣿⣿
⡦⢠⣾⡋⠉⣇⣿⣿⡟⠾⠿⠟⠃⢨⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠓⣘⣿⣆⠸⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⡆⠀⢀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣁⡿⡄⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠉⠩⣛⡿
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⣿⠿⠿⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣿⡛⠘⠛⡋⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⠄⢀⢀⣠⣽⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠁⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⡄⠀⢥⠉⠊⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠰⠘⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡟⠉⠈⠻⡿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠷⣶⣶⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠀⠀⢸⣶⣶⣶⠶⣷⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠈⠉⠙⠛⠀⠙⠛⠻⠿⠿⢿
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡼⣿⣿⠁⣠⣶⣶⣶⣽⣿⣿⣶⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⣿⣿⣇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢿⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⢿⣿⣿⣃⣴⣿⣿⣿⣿⣿⣿⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⠸⣿⡿⠟⠂⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⢀⣠⡀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣀⠀⠀⠀⠂⠐⠶⠷⠿⢿⣶⡤⠀⠄⠀⠀⠀⠉⢩⠁⠀⠀⢾⣿⣯⣈⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⡿⢿⣿⣿⣿⡿⠻⢇⢠⣶⠀⠀⠀⢖⣖⣲⣶⣷⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣴⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣿⠀⡛⢠⠀⠀⠐⠙⠈⠋⠉⠙⠋⠛⢡⡲⠆⢉⣻⣟⠉⣩⡛⠿⣿⣿⣿⡟⠙⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⢛⣿⣷⣿⣿⣿⣮⣶⣻⡁⡍⠘⠘⠛⠉⠉⠀⠁
⠉⠉⠁⠀⠁⠁⠀⣾⠀⢠⣤⠀⠀⣩⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣷⣶⣧⣶⣶⣭⣭⣅⡀⠀⢀⣒⣆⠀⠀⠐⣖⣠⣄⣀⣀⠀⢀⠀⠀⠄⠱⠿⠟⠛⠛⠟⢖⣶⡶⣞⣲⣞⢮⡷⠧⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⢯⠁⠀⠀⢠⣇⣀⣠⠄⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠦⠂⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣷⠶⠿⢟⠛⠛⢻⣻
⡁⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠘⣿⡟⣿⣷⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣻
⡄⠀⣯⣭⣭⣭⣀⣍⣁⣀⣀⣈⣿⠀⠀⠐⠒⠒⠀⢀⠐⠂⡐⢒⠒⡂⢘⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠋⠀⢼⡧⢿⣿⣿⡟⣿⣧⣤⣼⣿⣿⣯⢠⡄⣠⡤⣤⣤⣶⣶⣴⡶⢶⢶⡶⡶⡿⢿⣿⠉⠉⢹⢿
⠇⠲⣶⠿⠾⠥⠀⢸⣯⣭⣭⣿⣿⠀⠀⢰⠀⣄⣀⣀⣀⠄⠉⠌⠈⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠤⢴⡧⢤⡤⣴⡤⠀⠛⠉⢉⣿⠀⢠⣬⣭⣿⡯⢿⢿⣿⣿⣸⢸⣧⣧⠀⠈⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣿⣿⠀⡀⠀⠀⠈⠍⠉⠩⠅⢨⣭⠀⠀⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⡀⠀⡀⢀⡀⣤⣶⠺⢾⣿⠀⠀⠉⣝⣿⠂⠀⢸⣿⣿⣿⢸⣧⡇⠂⢶⣿⠶⠶⣿⣿
⢟⡛⣷⣶⡿⢿⣷⠛⠟⠛⢻⣿⢿⣴⣷⣾⣥⣄⡀⠀⢸⣋⣁⣿⣦⠄⠄⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠙⠷⠿⠿⠿⠿⠿⣿⣿⣼⣿⠃⠀⠀⠻⣿⠀⠀⠛⠛⠉⠘⢸⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⠛⣻⣍⣃⠈⣉⣉⡉⠉⢛⣛⡽⢿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⠁⠀⠀⠀⢿⣴⣾⣶⣶⣤⣀⣤⣷⡇⡀⠀⣼⠀⠀⣻⣿
⡆⢠⣾⡋⠙⣧⣿⣿⡿⠾⠿⠟⠃⢨⣿⢿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠛⠛⠛⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠓⣘⣿⣆⠐⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⡨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡧⠀⠀⣠⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣶⡄⣠⣀⡿⡄⠀⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣿⠟⠉⠩⣋⡻
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⠿⠾⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣿⠛⠘⠛⡋⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⠀⢀⢀⣠⣽⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠛⠁⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⡄⠀⢥⠉⠊⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠈⢳⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠐⢂⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠉⠈⠻⡿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠷⣶⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠁⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠀⠀⢸⣶⣶⣶⠶⣷⣶⢶⣶⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠢⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠈⠈⠛⠛⠀⠙⠛⠻⠿⠿⢿
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡼⣿⣿⠃⣠⣶⣶⣶⣽⣿⣿⣷⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⣿⣿⡇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⢿⣿⣿⣃⣼⣿⣿⣿⣾⣿⣿⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣈⣠⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡿⠟⠂⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⢤⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣀⠀⠀⠀⠂⠐⠶⠶⠿⢿⣶⣤⠀⠄⠀⠀⠀⠉⢩⠁⠀⠀⢻⣿⣧⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠶⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⢿⣿⣿⣿⡿⠿⢇⢠⣶⠀⠀⠀⢖⣖⣢⣶⣶⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣿⠀⡛⢠⠀⠀⠀⠙⠉⠋⠉⠙⠛⠻⢡⡖⠆⢀⣙⣻⣉⢭⡝⠻⢿⣿⣿⣿⠉⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢛⣿⣿⠿⠿⠿⣾⣷⣾⠆⣓⢈⠙⠛⠉⠉⠉⠉
⠉⠉⠁⠀⢉⠁⠀⣽⠀⢠⣤⠀⠀⣩⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠿⣾⣿⣿⣿⣿⣶⣶⣾⣷⣶⣯⣭⣀⠀⣈⣙⣢⡀⠀⠀⣖⣠⣄⣀⣀⠀⢀⠀⠀⠀⠺⠿⠟⠛⠛⠛⢿⣿⡟⢻⡿⣗⡋⡻⠧⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⢯⠁⠀⠀⢠⣇⣀⣠⠄⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠶⠦⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠶⠿⢟⠛⠛⢻⣻
⡉⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣿⣟⣿⣗⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣛
⡄⠀⣯⣭⣭⣭⣀⣍⣁⣀⣀⣈⣿⠀⠀⠀⠒⠐⠀⢀⠐⠂⠐⠒⢒⡂⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡋⠀⢴⡧⢾⣿⣿⡟⣿⣧⣤⣼⣿⣿⣯⢤⠄⣤⡤⣤⣤⣶⣶⣴⡶⢶⢶⡶⡶⠿⢿⣿⠉⠉⢹⢿
⠗⠲⣾⠷⠮⠥⠀⢸⣯⣭⣭⣿⣿⠀⠀⢰⠀⢆⣐⣀⣀⠄⠁⠌⠈⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⠤⠴⡧⣤⡤⢴⡤⠀⠛⠉⢉⣿⠀⢠⣬⣭⣿⡯⢿⢿⣿⣿⢸⢽⣧⣧⠀⠈⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢼⣿⠀⡀⠀⠀⠈⠍⠉⠉⠅⢩⡭⠁⠀⢽⡝⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⡀⢀⡀⣤⣶⠺⢺⣿⠀⠀⠉⣝⣿⠂⠀⢸⣿⣿⣿⢻⣧⡇⠂⢾⣿⠶⠶⣿⣿
⢟⠛⣶⣶⡿⢻⣷⠛⠟⠛⢻⣿⢿⣶⣷⣾⣥⣅⠀⠀⣘⣉⣡⣿⡤⠄⠈⠉⠀⠀⠀⡈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠫⠿⠿⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⠿⣿⠀⠀⠛⠛⠉⠹⢺⡿⡧⠶⠶⢿⠶⠶⣾⣿
⠘⠛⣻⣍⣃⠈⣉⣉⡉⠉⢛⣛⡽⣿⣿⣿⣿⡿⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⠃⠀⠀⠀⢾⣴⣿⣶⣶⣤⡀⣤⣷⡇⡤⠀⣼⠀⠀⣿⣿
⡆⢠⣾⡋⠙⣇⣿⣿⡟⠾⠿⠟⠃⢨⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢟⡛⠛⠉⠙⠛⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠃⣰⣿⣆⠰⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⢘⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣶⡄⣠⣁⡿⢄⠀⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠉⠩⣛⡿
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⠿⠿⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣟⠛⠘⠛⡋⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠄⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⠀⢀⢀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠁⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⡄⠀⢥⠉⠊⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠐⠀⠱⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣯⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢢⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠉⠈⠿⡿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠿⣶⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠁⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⠀⢸⣶⣶⣶⠶⣷⣶⣶⣶⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠈⠉⠛⠛⠀⠙⠛⠻⠿⠿⢿
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡼⣿⣿⡏⣠⣶⣶⣶⣜⣿⣿⣷⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠴
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⣿⣿⡇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢿⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠓⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⢿⣿⣿⣃⣴⣿⣿⣿⣾⣿⣿⡆⠻⠿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣥⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⢸⣿⡿⠗⠂⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⡀⣀⠠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠤⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣀⠀⠀⠀⠂⠐⠶⠶⠿⢿⣶⣄⠀⠄⠀⠀⠀⠉⢩⠀⠀⠀⢿⣿⣧⣀⣁⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠻⠿⣿⢿⣿⣿⣿⡿⠻⢏⢰⣶⠀⠀⠀⢒⣖⣒⣶⣶⣾⣿⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣿⠀⡛⢠⠀⠀⠘⠙⠑⠋⠉⠙⠛⠛⢃⣖⢒⣀⣬⣻⣅⠬⣍⠛⠿⣿⣿⣿⠇⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣿⣿⣿⢫⣹⣿⠿⣿⠿⢾⣗⡿⢀⢙⠈⠙⠛⠉⠉⠉⠉
⠉⠉⠁⠀⢈⠁⠀⢾⠀⢠⣤⠀⠀⣹⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣿⣿⣷⣿⣾⣿⣶⣶⣶⣄⣀⣈⣐⣶⣄⠀⠀⣀⣠⣄⣀⣀⠀⢀⠀⠀⠀⠫⠿⠟⠛⠛⠛⢿⣿⣾⣻⡷⣾⣻⡯⠧⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⢿⠁⠀⠀⢠⣇⣀⣠⠄⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠶⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠶⠿⣟⠛⠛⢻⣻
⣍⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣿⣟⣿⣗⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣛
⡄⠀⣯⣭⣭⣭⣀⣉⣁⣀⣀⣨⣿⠀⠀⠐⠂⠒⠂⠀⠒⠂⠐⠒⠒⡀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡍⠀⢰⡧⢿⣿⣿⡟⣿⣧⣤⣼⣿⣷⣿⢤⠄⣤⡤⣤⣄⣶⣶⣤⡶⣶⢶⡶⡶⡿⢿⣿⠉⠉⢹⢻
⠗⠲⣿⠿⠧⠴⠀⢸⣯⣭⣭⣿⣿⠀⠀⢰⠀⣄⣀⠀⣀⠀⠁⠌⠈⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠤⢤⡧⢤⡤⢴⡤⠀⠛⠉⢉⣿⠀⢠⣤⣭⣿⡿⢿⢿⣿⣿⣼⢽⣇⣧⠀⠈⣿⠀⠀⣼⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢿⣿⠀⡀⠀⠀⠈⠉⠉⠩⠅⠈⣭⠁⠀⢹⡝⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⡀⢀⡀⣤⣶⠲⢾⣿⠀⠀⠉⣟⣿⠂⠀⢸⣿⣿⣿⢹⣧⡇⠂⣶⣿⠶⠶⣿⣿
⢟⠛⣷⣶⡿⢻⣷⠛⠟⠛⢻⣿⢿⣶⣷⣾⣥⡄⠀⠀⠘⣉⣀⡾⢤⠀⠀⠉⠀⠀⠀⣀⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠫⠽⠿⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⠿⣿⠀⢀⠛⠛⠉⠹⢻⡿⡧⠶⠶⢿⠶⠶⣾⣿
⠘⠛⣻⣽⣃⠈⣉⣉⡉⠉⢛⣛⠽⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⠃⠀⠀⠀⢿⣴⣿⣶⣶⣤⡀⣤⣷⡇⡠⠀⣼⠀⠀⣻⣿
⡦⢠⣾⡋⢙⣧⣿⣿⡟⠾⠿⠟⠁⢨⣿⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢛⣉⠉⠉⠉⠉⣛⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣰⣿⣆⠘⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⢐⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣀⡿⡄⠀⠉⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠉⠉⠋⠻
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⠿⠿⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣟⡛⠘⠛⡋⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠄⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠁⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂⠀⠀⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⡄⠀⢥⠉⠊⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠘⠀⠱⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣯⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡱⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡟⠉⠈⠻⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠿⣶⣶⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⠀⢸⣶⣶⣶⠾⣷⣶⣶⣶⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠈⠉⠛⠛⠀⠙⠛⠿⠿⠿⢿
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡼⣿⣿⡏⣠⣶⣶⣶⣜⣿⣿⣷⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⣿⣿⣗⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠓⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⢿⣿⣿⣧⣠⣾⣿⣿⣾⣿⣿⡆⠻⢿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣥⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡿⠗⠂⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⡀⣀⣀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠄⠤⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⣀⠀⠀⠀⠂⠐⠶⠶⠿⢿⣶⡄⠀⠄⠀⠀⠀⠉⢩⠁⠀⠀⢸⣿⣧⣂⣁⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣦⣿⣿⣿⣷⣿⣿⣿⣿
⠛⠛⠻⠿⡿⣿⣿⣿⣿⡿⠿⢇⢠⣶⠀⠀⠀⢖⣶⣢⣶⣶⣾⣿⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣿⠀⡛⢠⠀⠀⠚⠙⠊⠋⠉⠙⠙⠛⢧⣆⢒⣀⣽⣻⣍⠭⡝⠛⠿⣿⣿⣿⠋⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠋⠛⠻⠇⠈⠘⠀⠱⠈⠎⠀⠀⢈⠘⠛⠉⠉⠉⠉
⠉⠉⠁⠀⢈⠁⠀⣿⠀⢠⣤⠀⠀⣹⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣶⣷⣾⣷⣶⣶⣧⣀⣀⣈⣐⣶⡀⠀⠀⣀⣠⣄⣀⣀⠀⢀⠀⠀⠁⠺⠻⠟⠂⠀⠅⢠⣤⡤⠀⡠⣄⣸⠦⠦⠀⠀⠀⠀⠀⠀
⣤⡄⠀⢀⣯⠁⠀⠀⢠⣇⣀⣠⠆⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠶⠖⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠶⠾⣟⠛⠛⢻⣻
⡍⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣿⣟⣿⣷⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣛
⡅⠀⣯⣭⣭⣭⣀⣉⣁⣀⣀⣨⣿⠀⠀⠐⠒⠒⠂⢀⠒⠂⠐⠒⠒⡀⠀⢿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡏⠀⢰⡧⢿⣿⣿⡟⣿⣧⣤⣼⣿⣯⣯⢠⡄⣠⡤⣤⣤⣶⣶⣴⡶⢶⢶⡶⡶⡿⢿⣿⠉⠉⢹⠿
⠇⠲⣿⠿⠿⠥⠀⢸⣯⣭⣭⣿⣿⠀⠀⢰⠀⢄⣐⣀⣀⠀⠁⠈⠀⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠤⢴⡧⢤⡤⢴⡤⠀⠛⠉⢉⣿⠀⢠⣤⣭⣿⡯⢿⢿⣿⣿⣼⢸⣧⣧⠀⠈⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢿⣿⠀⡄⠀⠀⠈⠍⠉⠩⢍⠨⣭⠁⠀⢹⡍⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⡀⢀⡀⣤⣶⠲⢾⣿⠀⠀⠉⣝⣿⠂⠀⢸⣿⣿⣿⢼⣷⡇⠂⢾⣿⠶⠶⣿⣿
⢿⠛⣶⣶⡿⢻⣷⠛⠟⠛⢻⣿⢿⣴⣷⣾⣤⡥⠀⠀⢼⣈⣀⡿⣤⠀⠀⠉⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠫⠽⠿⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⢿⣿⠀⠀⠿⠛⠉⠹⢺⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⠛⣻⣭⣃⠈⣉⣉⡉⠉⢛⣛⠽⢿⣿⣿⣿⡿⠟⠻⠯⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⠃⠀⠀⠀⣿⣤⣾⣶⣶⣤⡀⣤⣷⡇⡄⠀⣼⠀⠀⣿⣿
⡦⢠⣾⡋⢙⣧⣿⣿⡟⠾⠿⠿⠃⢨⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣛⡉⠉⠉⠉⠉⣻⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠃⣸⣿⣦⠐⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⣤⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣀⡿⣄⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠙⠩⣛⡿
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⠿⠿⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣟⠛⠘⠛⡋⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠄⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⠄⢀⣀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠁⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠈⠀⠀⡄⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡄⠀⢥⠉⠋⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡡⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣯⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡱⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠉⠈⠿⡿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠿⣶⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⠀⢸⣶⣶⣶⠶⣶⣶⣶⣶⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠈⠉⠛⠛⠀⠙⠛⠻⠿⠿⢿
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡼⣿⣿⡏⣠⣶⣶⣶⣜⣿⣿⣷⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢴
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⡶⠶⠶⣶⡶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⣿⣿⣇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⢿⣿⣿⣧⣠⣾⣿⣿⣾⣿⣿⡆⠻⢿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠉⠀⠀⠀⢸⣿⡟⠗⠂⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⢀⠀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡀⠀⠀⠀⠂⠐⠶⠶⠿⢿⣶⣤⠀⠄⠀⠀⠀⠈⢩⠀⠀⠀⢹⣿⣧⣤⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣷⣶⣷⣶⣿⣿⣿⣷⣿⣷⣿⣿
⠛⠛⠻⠿⡿⢿⣿⣿⣿⡿⠻⢇⢀⣶⠀⠀⠀⢖⣶⡲⣶⣶⣾⣿⣿⡿⠛⠟⡛⠿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡴⣾⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠙⠡⠤⣿⠀⡛⢠⠀⠀⠂⠙⠊⠋⠉⠙⠙⠛⢳⣿⢻⣿⣿⣷⣷⣾⣿⣧⣭⣝⣻⣿⠏⠀⠟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣿⣿⠛⠙⠻⠏⠩⠠⠀⠂⠂⠉⠀⠀⠀⠘⠛⠉⠉⠁⠉
⠉⠉⠁⠀⠀⠁⠀⣽⠀⢠⣤⠀⠀⣩⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣬⣽⡦⠀⠀⣂⣠⣄⣀⣀⠀⢀⠀⠀⠄⠉⠻⠗⠐⠀⠍⢢⡄⣄⢄⢀⢐⠼⡖⠦⠀⠄⠀⠀⠀⠀
⣤⡄⠀⠀⢫⠁⠀⠀⢠⣇⣀⣠⠆⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠶⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠶⠿⣗⠛⠛⢛⣻
⡁⠰⣶⣾⣿⣷⣶⣷⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⡗⣿⣗⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣛
⡄⠀⣧⣭⣭⣭⣀⣍⣁⣀⣀⣀⣿⠀⠀⠀⠂⠀⠂⠀⠐⠂⠀⠀⠂⡀⠀⢺⣷⣴⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢼⡧⢿⣿⣿⡟⣿⣧⣤⣼⣿⣷⣯⢠⠄⣠⡤⣤⣤⣶⣶⣤⡶⢶⢶⡶⡶⠿⢿⣿⠉⠉⢹⢻
⠇⠒⣶⠷⠿⠤⠀⢸⣯⣭⣭⣿⣿⠀⠀⢰⠀⢄⣀⠀⣀⠀⠈⠀⠀⠉⠀⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠠⠤⢴⡧⢤⡤⠴⡤⠀⠛⠉⢉⣿⠀⢠⣬⣭⣿⡯⢿⢿⣿⣿⢸⢹⡇⣥⠀⠈⣿⠀⠀⣼⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢾⣿⠀⡀⠀⠀⠈⠉⠉⠉⠅⠈⠭⠀⠀⢽⣤⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⢀⡀⣤⣶⠲⢾⣿⠀⠀⠉⣝⣿⠂⠀⢸⣿⣿⣷⢸⣇⡇⠃⢶⣿⡶⠶⣿⣿
⢛⠛⣶⣶⡿⢻⣷⠛⠟⠛⢳⣷⢿⣶⣷⣾⣤⡄⠀⠀⢘⣈⣀⠿⠄⠀⠀⠁⠀⠀⢉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠙⠯⠿⠿⠿⣿⣿⣼⣿⠁⠀⠀⠻⣿⠀⠀⠟⠛⠉⠘⢸⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⠛⣻⣭⣁⠈⣉⣉⡉⠉⢛⣛⠹⢿⣿⣿⣿⡟⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣷⣥⡽⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠿⠻⠁⠀⠀⠀⢾⣤⣾⣶⣴⣤⡀⣤⣷⡇⡤⠀⣼⠀⠀⣺⣿
⡦⢠⣾⡋⠉⣇⣿⣿⡟⠾⠿⠟⠁⢨⣿⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣩⣴⡄⠀⠀⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣐⣿⣆⠐⣿⣿
⡦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣬⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣨⣀⡿⠄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠋⠩⠛⠻
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⠿⠿⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣿⡛⠈⠛⡋⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠈⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣃⠀⠀⠀⠀⠀⢀⣀⠀⢀⢀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠀⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠰⣮⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡄⠀⢥⠉⠊⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠌⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣩⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠉⠈⠻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠷⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⠀⢰⣶⣶⣶⠶⣶⣶⢶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠈⠉⠛⠛⠀⠙⠛⠺⠿⠿⠿
⠀⠀⢐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡼⣿⣿⠃⣠⣶⣶⣶⣼⣿⣿⣶⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⣿⣿⣇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠷⠘⠿⢿⣿⣿⣳⣿⣿⣿⣿⣾⣿⣿⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⠻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣷⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⠸⣿⡿⠗⠂⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⡀⣀⢀⣤⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⡀⠀⠀⠀⠀⠐⠶⠶⠿⢿⣶⣄⠀⠄⠀⠀⠀⠈⢩⠁⠀⠈⢿⣿⣧⣔⣁⣀⠄⠸⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠦⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿
⠛⠛⠻⠿⡿⣿⣿⣿⣿⡿⠻⢇⢠⣶⠀⠀⠀⢒⣶⣂⣶⣶⣾⣿⣿⣿⢿⣿⠛⢚⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⣿⠀⡛⢠⠀⠀⠀⠘⠘⠋⠉⠙⠙⠛⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡟⡻⣿⣿⣿⣿⣿⣶⣶⣶⠄⣛⠨⠙⠛⠉⠉⠉⠉
⠉⠉⠁⠀⢀⠁⠀⣾⠀⢠⣤⠀⠀⣩⡾⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣄⣀⣀⠀⢀⠀⠀⠀⠳⠿⠿⠛⠛⠿⢷⣶⣖⣺⠶⣚⣹⠿⠦⠀⠄⠀⠀⠀⠀
⣤⡄⠀⠀⢯⠀⠀⠀⢠⣇⣀⣠⠆⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠶⠤⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠶⠿⣟⠛⠛⢻⣻
⡁⠰⣶⣾⣿⣷⣶⣷⣾⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⡟⣿⣗⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⣋⣉⣹⣛
⡄⠀⣮⣭⣭⣭⣀⣍⣁⣀⣀⣀⣿⠀⠀⠐⠂⠀⠀⠀⠐⠂⠀⠐⠂⡀⠀⠒⠒⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢾⣿⣿⡟⣿⣧⣤⣼⣿⣯⣧⢠⡄⣠⡤⣤⣤⣶⣶⣤⡶⢶⢶⡶⡶⠿⢿⣿⠉⠉⢹⢿
⠇⠲⣶⠷⠦⠤⠀⢸⣯⣭⣭⣿⣿⠀⠀⢰⠀⣄⣀⢀⣀⠄⠁⠀⠈⠉⠀⠡⠴⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠤⠴⡧⢤⡤⠴⡤⠀⠛⠉⢉⣿⠀⢠⣬⣭⣿⡯⢿⢿⣿⣿⢸⢹⣧⣧⠀⠈⣿⠀⠀⣾⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢿⣿⠀⡀⠀⠀⠈⠍⠉⠉⠅⠈⢭⠀⠀⠘⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠲⢺⣿⠀⠀⠉⣝⣿⠂⠀⢸⣿⣿⣿⢽⣇⡇⠂⣶⣿⡶⠶⣿⣿
⢟⠛⣶⣶⡿⢻⣷⠛⠟⠛⢻⣿⢿⣴⣷⣼⣥⠤⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠗⠀⠀⠸⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠙⠁⠀⠀⢻⣿⠀⠀⠻⠛⠉⠙⢸⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⠛⣻⣍⣃⠈⣉⣉⡉⠉⢛⣛⡹⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣭⣾⣶⠀⠀⢀⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⣶⣶⣤⡀⣤⣧⡇⡤⠀⣼⠀⠀⣻⣿
⡦⢠⣾⡋⢙⣇⣿⣿⡟⠾⠿⠟⠁⢨⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣘⣿⣆⠐⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⢀⡀⠀⠀⠀⢈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠷⠿⣦⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣼⣿⣿
⣷⣦⣾⣿⣿⣿⣷⡄⣠⣀⡿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⠠⡼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣭⣽⠟⠋⠩⢋⡻
⣿⣿⣿⣿⡿⢷⣿⣇⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠁⠀⣁⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⣿⠿⠿⣿⠏⢁⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⣷⣾⣿⡛⠘⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠰⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣃⠀⠀⠀⠀⠀⢀⣀⠀⢀⢀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠀⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡄⠀⢥⠉⠊⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡸⠇⡀⡃⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢉⣭⣭⣽⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠳⠄⠀⢤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠉⠈⠻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡿⠷⣶⣶⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡆⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⠀⢰⣶⣶⣶⠶⣶⣶⣶⣶⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠁⠓⠀⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠛⠛⠀⠙⠛⠻⠿⠿⢿
⠀⠀⢐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣿⣿⣶⣧⡀⠀⠀⣶⣶⡜⣿⣿⣿⣧⣶⣶⣶⣄⢸⣿⣷⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢴
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠿⣿⡇⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⢹⣿⣿⣸⣿⣿⣿⢉⣁⡀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⡗⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⡿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠳⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⢘⠿⣿⡿⠿⠃⠀⠀⠿⢿⣾⣿⣿⣇⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠉⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⠸⣿⡟⠖⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠶⠶⠿⢿⣶⣄⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⢘⣿⣤⡀⣀⣀⠄⠸⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢳⠲⠦⢶⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡶⢶⠶⣆⣀⣤⣶⣶⣶⣶⣦⣿⣧
⠛⠛⠻⠿⠿⢿⣿⣿⣿⡿⠻⠇⢀⣶⠀⠀⠀⢒⣒⠂⣴⣶⣾⣿⣿⡿⠿⣿⠓⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡜⠂⠠⠛⠁⠊⠉⡉⠉⡿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠙⠡⠤⣾⠀⡛⠀⠀⠀⠀⠘⠀⠉⠉⠙⠙⠛⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠉
⠉⠉⠁⠀⠀⠁⠀⠼⠀⢠⣄⠀⠀⣩⡾⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⣆⣠⣄⣀⣀⠀⢀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡄⠀⠀⠩⠁⠀⠀⢠⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠶⠶⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠋⣉⣉⠛⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⡀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣶⣶⣶⣶⠶⠾⢷⠛⠛⢛⣻
⠀⠠⣶⣾⣿⣷⣶⣷⣾⣿⣿⣿⡃⠀⠀⠀⣠⣶⣶⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣻⡗⣻⣗⠀⠀⠀⢸⣿⣗⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⠿⠿⠿⠟⣛⣛⠛⡋⣻⣛
⡄⠀⣤⣭⣭⣥⣀⣈⣀⣀⣀⡀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⡧⣾⣷⣿⡟⣿⣦⣤⣼⣿⣧⣥⢠⠄⢠⡄⣤⣤⣴⣦⣤⡶⠶⢶⡶⡶⠿⠿⣭⠉⠉⢹⠹
⠆⠒⣶⠷⠤⠤⠀⢸⣧⣭⣭⣿⣿⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⠀⠡⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣶⣶⣤⡀⠉⠉⢉⣿⠀⠀⣀⣭⣿⡯⢸⢿⣿⡇⢸⢸⡇⣅⠀⠀⣿⠀⠀⣸⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢼⣿⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠛⠛⠛⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⠐⠲⠺⣿⠀⠀⠉⣉⣿⠂⠀⢸⣿⡿⣴⢸⡇⡆⠃⣶⣿⠶⠦⣿⣿
⠓⠙⣶⣶⡾⢻⣷⠛⠟⠛⢳⣷⣿⣤⣧⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣻⣥⠀⠀⠀⢀⣤⣿⣿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠈⠁⠀⠀⠻⣿⠀⠀⠛⠛⠉⠘⠸⡿⡧⠶⠶⢿⠶⠶⣾⣿
⠘⠛⣻⣍⣁⠈⣉⣉⡉⠉⢛⣋⠿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠐⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢺⣤⣾⣦⣤⣄⡀⢤⣧⡇⠄⠀⣸⠀⠀⢻⣿
⡆⢠⣾⠋⠉⣃⣿⣿⡗⠾⠿⠟⢀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠶⣠⣄⢹⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⢯⡀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣐⣿⡆⠀⣿⣿
⡦⠀⣾⣿⣦⣨⡆⠀⢀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣈⢼⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣾⣿⣦⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⣿⣿⣤⣿⣿
⣷⣦⣾⣿⣿⣿⣦⡄⣀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠁⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⡿⠿⢿⣿⣿⣍⣹⠟⠉⠉⠉⠹
⣿⣿⣿⣿⡿⢷⣿⣇⠁⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠄⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⣿⠿⠾⣾⠏⠀⠙⠟⠀⠀⣸⣿⣿
⣿⣿⣿⣿⠷⣾⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠰⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣼⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡃⠄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣧⡄⠀⢡⠉⠊⠁⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⠉⣭⣹⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠟⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠎⠀⠂⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡶⠶⣶⡶⢶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⠀⠄⠃⠠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠙⠛⠚⠿⠿⠷
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡄⣿⣿⣿⣧⣶⣶⣶⣄⢰⣿⣿⣷⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣦⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢾⣿⣏⠿⠿⠇⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⢹⣿⣿⠈⣽⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠶⠶⠶⣶⡶⠤⠤⠤⠤⠤⠤⢶⣶⠦⠀⣿⣿⡇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣸⣿⣿⠀⣿⣿⣿⡀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠒⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⠛⠛⠛⠁⠀⢸⡇⠀⠀⠿⠿⠧⠘⠿⠿⠿⠿⠃⠀⠀⠿⠿⣸⣿⣿⣿⠻⠿⣿⠿⠏⠀⣿⣿⣿⣧⠀⠀⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠉⠀⠀⠀⢰⣿⡶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠶⣶⠿⢿⣦⡤⠀⠄⠀⠀⠀⠈⠉⠁⠀⠀⢘⣷⣄⡀⢀⣀⠀⠟⢉⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠻⣷⠠⠤⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣶⡶⠶⢂⣀⣀⣶⣶⣶⣦⣦⣿⣧
⠛⠛⠻⣿⣿⣿⣿⣿⣶⡿⠿⢏⢀⣶⠀⠀⠀⠤⢔⠂⣴⣴⣾⣿⣿⣿⢿⣿⠒⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⢠⣬⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡞⠐⠄⠋⠁⠉⠉⠉⠉⢿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠛⠛⠃⢤⣽⠀⡛⠀⠀⠀⢈⣭⣥⣿⣿⣿⠛⠛⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠖⠶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠁⠉
⠚⠒⠀⠀⠐⠂⠀⣶⠀⢠⣄⠀⠀⣱⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⣤⡀⠀⠀⢨⠀⠀⠀⢀⣇⣁⣀⠄⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⠿⢹⣿⣿⣿⣿⣿⣿⡟⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⣦⠶⠾⠷⠒⠚⢚⣻
⠉⠠⣶⣾⣿⣷⣴⣶⣾⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⠁⢸⣿⣗⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠿⠿⠿⠾⢛⠛⠛⡛⣛⣛
⡄⠀⣥⣭⣭⣉⣀⣉⣉⣉⡉⢉⣿⠀⠀⠀⣺⣿⣿⣿⣿⣿⠟⢑⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⡷⣿⣿⣿⣿⣿⣿⣦⣸⣿⣧⣵⢠⡄⣀⣄⣤⣄⣴⢦⣤⡤⠤⢶⡶⡶⡿⢿⣿⠉⠉⢹⠛
⠇⠐⣥⠯⠭⠥⠀⢹⣯⣍⣭⣿⡿⠀⣀⣾⣿⣿⣿⣿⡟⠂⠀⠈⠈⠁⠀⠆⠀⠀⢸⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡉⠉⣿⠀⢀⣀⣩⣿⡯⢼⢾⣿⡇⢸⢸⡇⣅⠀⠀⣿⠀⠀⣸⣿
⠀⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠽⠷⣰⣿⣿⣿⣿⣿⣿⠓⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠛⠛⢻⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡀⠻⠀⠀⠉⣈⣿⠂⠀⢸⣿⡿⣼⢸⡇⡇⠂⣶⣿⣤⡦⣿⣿
⢗⠛⣶⣶⡾⢻⣶⠶⠿⠿⢶⡗⢀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣻⣿⣄⠀⠀⠀⣠⣶⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠁⠀⠀⠻⣿⠀⠀⠟⠛⠁⠹⢸⡿⡧⠶⠶⢿⠶⠶⣿⣿
⠘⠛⢻⣉⣁⠈⣉⣉⡉⠛⠛⠀⠸⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢾⣤⣾⣦⣦⣄⡀⣀⣧⡇⡠⠀⣸⠀⠀⣺⣿
⡄⢠⣼⠋⠙⣇⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡧⠂⠔⡄⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⢐⣿⣆⠐⣿⣿
⣦⠀⣾⣿⣦⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢹⣿⣿⣈⣿⣿
⣷⣤⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠿⢿⣿⣿⣍⣽⠟⠛⠉⠛⠻
⣿⣿⣿⣿⡿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⠿⢾⣾⠏⠁⠙⡟⠀⠀⢸⣷⣿
⣿⣿⣿⣿⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣽⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢰⠀⠀⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢣⠉⠈⠉⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠐⠀⠁⠁⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿
⣍⠉⣭⣹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⡿⠿⠿⢿⡿⠿⠿⠿⣿⣿
⠿⠟⠿⣿⣿⣷⣦⠄⣀⣀⠀⠀⠠⡶⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡗⢆⠈⠂⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡖⠀⠀⢰⣶⣶⣶⠶⣶⣶⢶⣶⣶⣶
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⠁⠀⠀⠈⠈⠙⠟⠀⠹⠟⠾⠿⠿⢷
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⣼⣿⣿⣿⣣⣶⣶⣶⣄⢸⣿⣿⣿⣿⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢾⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⢹⣿⣿⠈⣿⣿⣿⣽⡅⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣿⣇⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⢤⣤⠄⠀⣿⣿⡇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢿⣿⣿⡻⣿⣿⣸⣿⣿⠀⣿⣿⣿⣿⣿⡀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠿⠛⠻⠃⠛⠛⠛⠁⠀⢸⡇⠀⠀⠿⠿⠧⠘⠿⠿⠿⠿⠃⠀⠀⠿⢿⣿⣿⣿⣇⠻⠿⣿⠿⠏⢸⣿⣿⣿⣿⣿⣇⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡈⢀⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠃⠘⠀⠀⠀⢰⣿⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣦⣄⠀⠄⠀⠀⠀⠉⠩⠁⠀⠀⢸⣿⣤⣀⣀⡀⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⠃⠠⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡾⣶⣶⡿⣶⣤⣾⣶⣷⣷⣷⣦⣿⣿
⠛⠛⢻⣿⣷⣿⣿⣿⣶⡾⠿⢏⢀⣶⠀⠀⠀⠤⢴⠦⣤⣶⣾⣿⣿⣿⢿⣿⣂⢸⣿⣿⣽⡛⠿⣿⠟⠛⣻⣿⣿⡿⠏⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢰⣾⣿⣷⡴⣿⠿⢍⣭⢭⠉⣿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠛⠛⠣⣤⣽⠀⡛⠀⠀⠀⢈⣩⣥⣿⣿⣿⠛⠿⠏⠀⡁⢹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⡶⢿⣿⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠉⠉⠉
⠒⠒⠀⠀⠒⠂⠀⣶⠀⢀⣄⠀⠀⣹⣾⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠛⠀⠀⠀⢀⡀⡀⠀⠀⣀⣰⠄⠀⠀⠀⠀⠀⠀⠀
⣤⡀⠀⠀⠩⠀⠀⠀⢠⣆⣁⣀⡄⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⡧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣼⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣶⣿⣿⣿⣶⣶⠶⠿⠶⠶⢺⢷
⡉⠠⣶⣾⣿⣶⣴⣶⣾⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡟⠀⠀⢹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠶⠾⢟⠛⠛⣛⣛
⡁⠀⣫⣹⣽⣉⣈⣙⣉⣉⣉⠉⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⢃⢂⠀⠀⠂⠂⢸⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣷⣆⣀⣼⣿⣷⣿⢠⡀⣀⣄⣤⣄⣶⣦⣤⣤⣤⠤⡤⡴⣿⣿⣿⠙⠛⢻⢻
⠧⠤⣭⠯⢭⣥⠉⢹⣯⣍⣽⣿⣿⠀⣀⣾⣿⣿⣿⣿⣟⠃⠐⣚⠊⠁⡐⠆⠰⢘⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣎⠋⠉⢙⣿⠀⢀⣈⣉⣿⣯⣾⣿⣿⣷⢸⢸⡇⣅⠀⠘⣿⠀⠀⣸⣿
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣽⠷⣰⣿⣿⣿⣿⣿⣿⠛⠀⠒⠒⠒⠀⠀⠀⠀⠀⣿⣿⣿⡿⠶⠶⠾⠿⣿⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⠀⠸⣿⠀⠀⠉⣙⣿⠂⠀⢸⣿⡿⣼⢸⡇⡇⠃⣶⣿⣤⣤⣾⣿
⠶⠛⣶⣶⡾⢿⡶⠶⠾⠿⢶⡗⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣋⠀⠀⠀⢀⣩⣝⣿⡇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠈⠁⠀⠀⢿⣿⠀⠀⠿⠛⠉⠹⢸⣿⣧⣶⡶⢿⠶⢶⣿⣿
⠘⠳⢛⣛⣃⠌⣛⣙⠛⠛⠟⠀⠘⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣾⣿⣿⠂⠀⠰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣤⣾⣶⣶⣦⡀⣈⣧⡇⡀⠀⣼⠀⠀⣻⣿
⡆⢠⣼⡟⢙⣣⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣤⣀⡀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⢸⣿⣄⢠⣿⣿
⣆⠀⣾⣷⣤⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠘⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⣿⣿⣘⣿⣿
⣷⣤⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣍⣹⡟⠛⢛⠛⣿
⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣾⣿⠏⠉⠙⡿⠀⠀⢰⣾⣿
⣿⣿⣿⣿⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣽⣿⣿
⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠄⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣣⠛⠚⠋⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠉⠖⢰⠎⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿
⣝⠉⣭⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣀⡁⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⢻⡿⠿⣿⣿⣿⣿⢿⣿⣿⣿
⠿⠿⠿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⡴⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⡝⠿⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⡶⠀⠀⢰⣶⣶⣶⠶⣶⣦⢶⣶⣶⣶
⠀⠀⠀⠀⠉⠀⠀⠀⠹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠁⠂⠚⠃⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⠟⠁⠀⠀⠈⠘⠛⠿⠀⠻⠿⠾⠿⡿⣿
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⣿⣿⣿⡿⣠⣶⣶⣶⣄⢸⣿⣿⣿⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣾⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⣿⣧⣿⣿⢹⣿⣿⢸⣿⣿⣿⡉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⢸⣿⣿⢸⣿⣿⣿⣷⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣿⣿⡇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢿⣿⣿⠸⣿⣿⣸⣿⣿⢸⣿⣿⣿⣿⡄⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠓⠿⠛⠻⠃⠛⠛⠛⠃⠀⢸⡇⠀⠀⠿⠿⠷⠘⠿⠿⠿⠿⠃⠀⠀⠿⣿⣿⣿⣿⡇⠻⠿⣿⠿⠏⢸⣿⣿⣿⣿⣷⠀⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⣀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣶⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠶⣶⣿⣷⣤⡄⠀⠄⠀⠀⠀⠈⠉⠀⠀⠀⢰⣿⣀⡀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⠀⡀⠀⠠⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⡒⣀⢠⣤⣶⣶⣶⣦⣤⣾⣶
⠛⠒⢺⣷⣶⣶⣶⣷⣶⡾⠿⡇⠀⣶⠀⠀⠀⠤⠴⠤⣠⣤⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢄⠞⠁⠂⠚⠈⠀⠉⠈⠉⣿⢿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠛⠛⠃⣀⣼⠀⠻⠀⠀⠀⠈⠹⠅⠟⠋⠻⠛⠿⠇⠀⢻⣯⠍⠙⠿⡿⠟⠛⢛⣻⡿⡿⢿⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠉⠉⠙
⠒⠒⠂⠀⠒⠀⠀⣶⠀⢀⣀⠀⠀⣑⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣾⣿⣶⣶⣶⣾⣷⣶⣶⣶⣴⣿⣯⡶⠄⠴⡆⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠠⠀⠀⠀⢠⣆⠁⢀⡄⠉⠁⠀⠀⠀⣀⣹⣤⡤⠤⠤⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣭⣍⡉⠉⠁⠀⣼⣷⡆⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣷⣷⣶⣶⣶⣶⡶⠶⠶⠶⠶⢷
⡉⠠⣤⣴⣿⣶⣤⣶⣾⣿⣿⣿⡇⠀⠀⢠⣶⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⢸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠶⠶⠿⠚⠓⢛⢛
⡁⠀⣢⣘⣿⣉⣉⡙⠉⠉⡉⠉⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡗⠀⠐⠀⠸⣿⣿⡟⠛⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣸⣿⣥⣷⣠⡀⣀⣀⣀⣀⢦⣤⣤⣤⣤⣤⡤⡤⣿⣿⣛⠙⠛⢻⠿
⠇⠤⣭⢭⣍⣥⠉⢹⣏⣙⣻⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⢿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣁⠈⠛⠉⠛⣿⠀⢀⣈⣉⣿⡟⢼⣿⣿⡇⢸⢸⡇⣇⠀⠀⣿⠀⠀⣸⣿
⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠉⣽⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣀⣒⠀⠀⠀⠈⢻⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⠈⠀⣀⣠⠶⢼⣿⠀⠀⠙⣙⣿⠄⠀⢸⣿⡿⣼⢸⡇⡃⠂⣤⣿⣤⣤⣿⣿
⢆⠓⣦⣤⡾⢷⡶⠶⠶⠶⢶⣾⣿⣤⣦⣾⣿⣿⣿⣿⣿⣿⠟⠒⠀⠀⠀⠀⠀⢹⣷⣦⡀⠀⠰⠿⢿⣿⣿⣿⣿⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠈⠻⠀⠀⠀⢻⣿⠀⠀⠻⠟⠋⠹⢸⣷⡇⣤⣤⣿⡤⣶⣿⣿
⠘⠲⢟⣛⣀⠘⣛⡐⠓⠒⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⡿⢟⣇⠀⠀⠀⢈⣭⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⣶⣤⣄⣀⠀⢀⣇⡇⠀⠀⣸⠀⠀⢻⣿
⡆⢀⣼⠟⢙⣧⣿⣿⡧⢴⣾⠿⠈⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠰⣿⣿⣿⣿⡇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠃⠐⣿⣄⢠⣾⣿
⣄⠀⣽⣷⣄⣹⡏⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣄⣠⡄⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣷⣘⣿⣿
⣷⣤⣾⣿⣿⣿⣧⡄⢈⡀⠶⠀⠘⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠙⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣉⣹⡟⠛⢛⠛⣿
⣿⣿⣿⣿⣿⣧⣿⡇⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣿⠟⠉⠙⡿⠀⠀⢰⣾⣿
⣿⣿⣿⣿⣧⣾⣟⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣹⣿⣿
⣿⣿⣿⣿⣾⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣀⣀⠀⢒⠚⠚⠛⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⡈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣴⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⣟⠛⣛⣛⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⡘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠋⠉⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠶⠀⠀⢰⣦⣶⣶⢶⣶⣤⣤⣴⣶⣶
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠈⠠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠈⠙⠻⠿⠀⠻⠿⠾⠿⠿⢿
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⣿⣿⣿⠁⣠⣶⣶⣶⣽⣿⣿⣷⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣾⣿⣏⠿⠿⠇⠀⠀⣿⣿⣿⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣿⣿⡇⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠑⠿⠛⠻⠃⠛⠛⠛⠁⠀⢸⡇⠀⠀⠿⠿⠷⠘⠿⠿⠿⠿⠃⠀⠀⠿⢿⣾⣿⣿⠀⠻⠿⣿⠿⠏⣿⣿⣿⣿⡄⠀⠀⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣶⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠄⠤⢴⣶⣿⣷⣤⡄⠀⠄⠀⠀⠀⠉⠁⠀⠀⠀⢰⣿⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣶⣶⣿⣶⣤⣴⣶⣶⣶⣶⣦⣿⣶
⠛⠒⢲⣶⣶⣶⣶⣶⣶⡾⠿⠇⠀⣶⠀⠀⠀⠤⠴⠤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⣶⡞⡳⠆⠻⠋⠊⠋⢩⠉⣿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠁⠛⠛⠃⣄⣼⠀⠻⠀⠀⠀⠨⠹⠅⠟⠛⠻⠻⠏⡉⣩⣯⠛⢿⡿⠟⢛⣿⣿⣿⣿⣿⣿⠉⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠉⠙
⠒⠒⠂⠀⠒⠂⠀⣶⠀⢀⣀⠈⠀⣁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⠀⠀⠁⣀⡀⠀⠤⢶⠆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⢠⠀⠀⠀⢠⡎⠉⠀⡄⠉⠁⠀⠀⠀⠀⠙⠀⢠⠤⠄⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⡗⠀⠀⠉⠉⠉⠉⠉⠁⠀⣼⣶⡆⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣾⣷⣿⣷⣶⣶⠶⠶⠶⠶⠶⢶
⡉⠠⣦⣴⣿⣶⣤⣦⣼⣿⣟⣿⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⠶⠶⢶⡶⢶⡦⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠶⠶⠷⠒⠓⢚⠛
⣁⠀⣊⣙⣻⡉⠉⠙⠉⠉⠉⠩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⢀⣶⣆⣿⣗⣿⣿⣶⣆⣀⣸⣿⣵⣶⣠⡀⣀⡀⣀⣀⣰⣥⣠⣤⣤⣤⡤⡤⣿⣿⣛⠙⠛⢻⢻
⠧⠤⣭⣯⣍⣡⠉⢹⣏⣙⣛⣿⣿⠀⠀⠨⠁⠀⠀⠀⠀⠀⠈⠈⠀⠁⠸⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣀⣨⣅⣀⣀⣩⣁⠈⠛⠉⢛⣿⠀⢀⣈⣁⣿⣏⣾⣿⣿⣷⢸⢸⡇⣇⠀⠀⣿⠀⠀⣸⣿
⠀⠀⠈⠀⢀⡀⠀⠀⠈⠁⠉⣽⣿⠀⡀⠀⠀⣰⣚⣛⣓⣀⡀⢒⡀⠀⠀⢻⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠴⢼⣿⠀⠀⠙⣋⣿⠄⠀⢸⣿⡿⣼⢸⡇⡃⠀⣬⣿⣤⣤⣾⣿
⢆⠓⣤⣤⡾⢷⡶⠶⠶⠶⢶⣾⣿⣀⣧⣴⡀⠐⠀⠀⠀⠇⡀⡈⠀⠀⠀⠀⠻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠐⠚⠆⣶⣶⣾⣿⣿⣿⣶⣨⣿⠀⠀⠀⢿⣿⠀⠀⠿⠟⠃⠹⢸⣿⣇⣤⣤⣿⡤⣶⣿⣿
⠸⠲⢟⣛⣃⠜⢛⡐⠓⠒⠿⠿⢻⣿⣿⣿⣿⢶⡶⠾⠿⠟⠃⠀⠀⠀⠀⠀⠀⣿⣿⣛⠛⠋⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⢿⣠⣶⣤⣂⣄⠀⠀⣇⡇⠀⠀⣸⠀⠀⢻⣿
⡄⢀⣼⠟⢙⣇⣿⣿⡧⢴⣾⠿⠂⢘⣿⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣋⠀⠀⠀⠉⣙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠁⠀⣿⣄⢠⣿⣿
⣅⠀⣽⣶⣄⢙⡏⠉⠀⡀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚⢻⣿⣷⣘⣿⣿
⣧⣤⣼⣿⣿⣿⣧⡄⢈⠀⢶⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⢠⡄⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣹⡟⠛⢛⠛⢿
⣿⣿⣿⣿⣿⣧⣿⡇⢿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠉⠹⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠉⠙⡿⠀⠀⢰⣶⣿
⣿⣿⣿⣿⣧⣼⣟⠿⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠐⠀⠐⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣹⣿⣿
⣿⣿⣿⣿⣷⣿⡿⠓⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠠⢘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣀⣀⠀⢂⠚⠚⠛⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣥⣤⣤⣬⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣿⣿⡇⠀⢀⠐⠞⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣾⣴⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⣟⠛⣛⢻⣟⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⢨⣠⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠋⠉⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⣿⣿⣿⣯⣭⣭⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠆⠀⠀⢰⣦⣶⣶⢶⣶⣤⣤⣴⣶⣶
⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠀⠀⠐⠚⠙⠻⠿⠀⠻⠿⠺⢿⣿⣯
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⢠⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⣿⣶⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣽⣿⣿⢩⣵⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣮⡻⢿⠃⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠩⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠧⠘⠿⢿⠿⠿⠃⠀⠀⠿⣿⣼⣿⠿⠀⠻⠿⣿⠿⣿⣿⣿⠿⠿⠀⢻⣿⣯⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣶⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⢴⣦⣿⣷⣤⡄⠀⠄⠀⠀⠀⠈⢉⠀⠀⠀⠐⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣴⣶⠲⣦⣤⣴⣶⣶⣶⣶⣤⣿⣾
⠛⠒⢶⣶⣶⣶⣶⣶⣶⡾⡿⡏⠀⣤⠀⠀⠀⠤⠴⠤⣤⣤⣼⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢵⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠴⠌⠑⠒⠋⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠈⠁⠿⠿⠃⣀⣾⠀⠻⠀⠀⠀⠈⠹⠅⠟⠋⠛⢠⠒⣚⣠⣼⣭⣤⠘⣿⣍⣝⣻⠿⡯⠀⠉⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⠉⠉
⠒⠒⠂⠀⠒⠂⠀⣴⠀⢀⣀⠉⠀⣃⣶⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣤⣴⣶⡀⠀⠤⠤⢶⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠠⠀⠀⠀⢀⡎⠉⠀⠄⠉⠁⠀⠀⠀⠀⠙⠀⢠⢤⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⣼⣶⡆⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣷⣿⣷⣶⣦⣶⡶⠶⠶⠶⢶
⠉⠀⣤⣴⣾⣶⣤⣤⣼⣿⣿⣿⡃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠰⠶⠶⣶⡶⢶⡦⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠶⠶⠶⠒⠒⢚⢛
⡁⠀⣛⣙⣿⡉⠉⠙⠉⠉⠉⠉⣷⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⢾⣭⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⢰⡆⢀⣶⣖⣿⣷⣿⣿⣶⣆⣀⣸⣿⣥⣶⣀⡀⣀⡀⣀⣀⢰⣥⣠⣤⣤⣤⡤⣤⣾⣿⣿⠙⠛⢻⠻
⠧⠤⣭⣯⣍⣡⠉⢹⣟⣛⣛⣿⣿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⡄⠀⢈⣀⣈⣅⣀⣀⣩⣉⠈⠛⠛⠛⣿⠀⠀⣈⣉⣿⣏⣼⣾⣿⡗⢸⢸⡇⡇⠀⠈⣿⠀⠀⢸⣿
⠀⠀⠉⠀⢀⠀⠀⠀⠉⠉⠉⣽⣷⠀⠀⠀⠀⣐⣚⢛⣓⣀⡀⢒⡀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⠤⢴⣿⠀⠀⠙⣉⣿⠅⠀⢸⣿⡿⣼⢸⡇⡃⠀⣤⣿⣤⣤⣿⣿
⠆⠓⣤⣤⡾⢷⡶⠶⠶⠶⢶⣶⣿⣀⣧⣴⠀⠐⠀⠀⠀⠀⡀⠜⠀⠀⠀⠀⢠⣤⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠚⠦⢲⣖⣾⣷⣿⣿⣶⣨⣿⠀⠀⠀⢿⣿⠀⠀⠿⠟⠃⠙⢸⡿⣇⣤⣤⣿⡤⣴⣽⣿
⠰⠲⢟⣛⣁⠜⢛⡐⠓⠒⠿⠿⢽⣿⣿⣿⣿⢶⡶⠾⠻⠛⠁⠀⠀⠀⠀⠀⢸⣿⣷⣾⡿⠿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠂⠀⠀⠀⢿⣠⣶⣤⣀⣀⠀⠈⣇⡇⠀⠀⣸⠀⠀⣻⣿
⡄⢀⣼⠟⢙⣃⣿⣿⡧⢴⣾⠿⠁⢘⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣋⣥⡄⠀⠀⢀⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣾⣿⡇⠃⠀⣿⣄⢀⣿⣿
⣅⠀⣽⣷⣄⢙⡏⠉⠁⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢻⣿⣷⣘⣿⣿
⣯⣤⣼⣿⣿⣿⣧⡄⢈⠀⢶⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣸⡟⠛⢛⠛⢿
⣿⣿⣿⣿⣿⣧⣿⡇⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡟⠋⠙⡿⠀⠀⢰⣶⣾
⣿⣿⣿⣿⣧⣼⣿⠟⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠋⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣶⣿⡿⠓⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠂⣿⣿⣿⣿⠃⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⣀⠀⢲⠚⠚⠛⠀⠀⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣥⣤⣤⣬⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠁⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣾⣴⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⣛⠛⣛⠻⣿⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢄⡼⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠉⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠶⠿⣿⣿⣿⣯⣥⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠢⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⢰⣦⣤⣴⣴⣦⣤⣤⣤⣶⣶
⠀⠀⠀⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣷⡆⠀⠀⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠐⠚⠙⠻⠷⠀⠻⠿⠾⢿⡿⣯
⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣼⣿⣿⣿⣿⣿⡄⣶⣿⣿⣿⣶⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢱⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣏⠿⣿⣿⣿⡇⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣽⣿⣿⠉⠱⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠘⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⣿⢿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⡟⣿⣿⣿⣿⡇⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠩⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⡜⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠿⠀⠻⠿⣿⠿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣶⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⢴⣦⣿⣷⣤⡀⠀⡄⠀⠀⠀⠉⠁⠁⠀⠀⢀⣶⣤⢰⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣤⡀⠀⠠⠄⠀⠀⠀⠀⠀⠠⡤⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢶⠴⠂⢠⣤⣶⣶⣶⣦⣦⣾⣷
⠚⠶⢶⣶⣶⣶⣶⣶⣶⡾⣿⡇⠀⣤⠀⠀⠀⠤⠴⠤⣄⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⢷⠠⢎⠑⠉⠉⢙⠉⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠈⠉⠿⠿⠃⣀⣼⠀⠻⠀⠀⠀⠨⠹⠅⠟⠋⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⠉⠙
⠒⠒⠀⠀⠒⠂⠀⣤⠀⢀⣀⠉⠀⣓⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠉⠝⠟⡀⠀⠀⠀⠀⠤⠤⢴⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠢⠀⠀⠀⢀⡎⠉⢀⠄⠉⠁⠀⠀⠀⠀⠘⠀⠠⢴⡄⣵⣶⣾⣷⣶⣈⣽⣠⣭⣉⣻⣋⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⣼⣶⡆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣾⣶⣷⣷⣦⣦⣶⡶⠶⠶⠶⠶
⠋⠠⣤⣴⣶⣶⣤⣤⣼⣿⣿⣿⡃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡇⠀⠰⠶⠶⢶⡶⢶⡦⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠶⠶⠶⠒⠒⢚⢛
⡁⠀⣇⣙⣹⡉⠉⠙⠉⠉⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡦⢀⣶⣆⣽⣗⣿⡿⣶⣆⣀⣸⣿⣥⣦⣀⡀⣀⡀⣀⣀⢠⣅⣉⣤⣤⣤⡤⣤⣾⣿⣿⠘⠛⢻⠿
⠧⠤⣭⣯⣍⣡⠉⢹⣟⣛⣛⣿⣟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣀⣤⡄⠀⢈⣀⣈⣍⣈⣀⣩⡉⠉⠛⠛⠛⣿⠀⠀⣈⢉⣿⡟⣸⣾⣿⡧⢸⢰⡇⡅⠀⠈⣿⠀⠀⢨⣾
⠀⠀⠉⠀⢀⠀⠀⠀⠉⠉⠉⣽⣿⠀⠀⠀⠀⣐⣚⢛⣒⣀⠀⣀⠀⢷⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⠤⢴⣿⠀⠀⠙⣉⣿⠅⠀⢸⣿⡿⣼⢸⡇⡁⠀⣤⣿⣤⣤⣾⣿
⠆⠓⣤⣤⡾⢷⡦⠶⠶⠶⢶⣾⣿⣀⣧⣴⠀⠐⠀⠀⠂⠀⠀⢐⠀⠘⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⠒⣾⣆⣲⣖⣾⣶⣿⣿⣶⣸⣿⠀⠀⠀⢿⣿⠀⠀⠿⠟⠃⠙⢸⣿⣇⣤⣤⣿⡤⣴⣿⣿
⠰⠶⢿⣛⣁⠜⠛⡘⠓⠒⠿⠿⢻⣿⣿⣿⣿⣶⡶⢾⡿⢿⠿⠟⠀⠀⠘⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠂⠀⠀⠀⢿⣠⣦⣄⣀⣀⠀⠀⣇⡇⠀⠀⣸⠀⠀⣻⣿
⡄⢀⣼⠟⢙⣃⣿⣿⡧⢴⣾⠿⠁⢘⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡌⠉⠉⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⣿⣄⢀⣿⣿
⣅⠈⣽⣷⣄⢙⡏⠉⠁⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣥⣶⡀⠀⠀⢀⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⢻⣿⣷⣐⣿⣿
⣧⣤⣼⣿⣿⣿⣥⡄⢈⠀⠶⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠐⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣸⡟⠛⢛⠛⢿
⣿⣿⣿⣿⣿⣧⣿⡇⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣧⠀⠀⢸⣿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠉⠙⡿⠀⠀⢰⣴⣿
⣿⣿⣿⣿⣧⣼⣟⠟⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⡇⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⠇⠀⠈⠀⠀⠈⠀⣀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⣾⣿⡿⠓⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡇⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣀⣀⠀⢲⠒⠚⠋⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣥⣤⣤⣬⣤⣄⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠟⢸⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣤⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⣛⠛⣛⠛⣟⣻⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⡇⠀⠀⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠶⠿⣿⣿⣿⣯⣥⣭⣿⣿⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢠⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤
⠀⠀⠀⠉⠉⠁⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠀⠀⠚⠙⠻⠷⠀⠻⠷⠾⣿⡿⣿
⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⢻⣿⣶⣶⣤⡀⠀⠀⣶⣾⡟⣶⣶⠀⣠⣶⣿⣿⣟⢱⣶⣶⣾⣿⣿⣿⣿⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣧⣿⣿⢠⣿⣿⢻⣿⣿⡈⢹⣿⣿⢩⣿⣿⢻⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣇⢸⣿⣿⢸⣿⠟⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⢸⣿⣿⠈⠉⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠩⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠇⠘⠿⠿⠿⠿⠃⠀⠀⣿⣿⣼⠿⠿⠀⠻⠿⣿⣿⣿⣿⡾⠿⠿⠀⠀⠀⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠒⠀⠀⠀⢰⣶⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⣦⣿⣷⣤⡄⠀⡄⠀⠀⠀⠙⠒⠂⠀⠀⢰⣶⣦⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣾⣶⣷⣶⣤⣤⣤⣴⣶⣶⣧⣿⣿
⠶⠶⢶⣶⣶⣶⣶⣶⣶⣾⣿⡏⠀⣤⠀⠀⠀⠤⢴⠤⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢴⣶⣾⣿⣶⣿⠽⢋⡛⣻⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠿⠿⠃⣀⣼⠀⠻⢀⠀⠀⠨⠹⠅⠟⠛⠻⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⠿⠃⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠿⠛⠋⠉⠛
⠒⠒⠀⠀⠐⠂⠀⣤⠀⢀⡀⠉⠀⣓⣾⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⠏⣹⣿⣿⡉⢿⡿⢻⣿⣿⣿⡏⠈⠚⠻⠆⠀⠀⠀⠠⠤⢤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⢀⣄⣀⠀⠀⢀⣢⠁⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠲⠀⠀⠀⢀⡎⠉⢀⡄⠉⠁⠀⠀⠀⠀⠙⠀⢠⣄⡿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣠⣤⣶⣶⡄⠀⠀⠀⠈⠉⠉⠉⠙⠁⠀⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣿⣿⣦⣴⣶⣶⠶⠶⠶⢶
⠋⢡⣤⣴⣾⣦⣠⣤⣼⣿⣿⣿⡃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠠⠶⠶⣶⡦⢶⡦⠀⠀⠀⢹⣿⡧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡶⠶⠶⠶⠶⢾⠿
⡁⠀⣏⣙⣻⡉⠉⠛⠉⠉⠉⠩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢀⣶⣆⣽⣷⣿⡿⣶⣆⣀⣸⣿⣥⣦⣀⡀⣀⡀⣀⣀⣰⣅⣉⣤⣤⣤⣤⣤⣾⣿⣿⠒⠓⢻⢿
⠧⠤⣭⣯⣍⣩⠉⣻⣟⣛⣛⣿⣿⠀⠀⠨⠁⠀⠀⠀⠁⡀⠀⠠⠈⢫⡉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡤⠀⢉⣁⣉⣉⣉⣁⣩⡉⠉⠛⠛⢛⣿⠀⢀⣉⣛⣿⣟⣼⣿⣿⣷⢸⢰⡇⡇⠀⠈⣿⠀⠀⢸⣿
⠀⠀⠉⠀⢀⠀⠀⠈⠉⠉⠉⣽⣿⠀⠀⠀⠀⣘⠛⠛⢓⣀⡀⢒⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠁⠈⠁⠁⠁⣀⣤⠤⢼⣿⠀⠀⠛⣛⣿⠅⠀⢸⣿⣷⣼⢸⡇⡃⠀⣤⣿⣤⣤⣿⣿
⠆⠳⣤⣤⡾⢷⡦⠶⠶⠶⣴⣾⣿⣀⣧⣴⣄⠐⠂⠀⠚⢢⠀⠉⡆⠀⠻⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠒⠒⣿⣆⣲⣖⣾⣶⣿⣿⣶⣨⣿⠀⠀⠀⢿⣿⠀⠀⠿⠟⠓⠹⢸⣿⣇⣤⣤⣿⣥⣤⣿⣿
⠸⠦⢿⣛⣃⠜⠛⡐⠒⠒⠾⠿⣹⣿⣿⣿⣿⣶⡶⢶⣾⢿⠿⠿⠃⠀⠀⠙⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠂⠀⠀⠀⢿⣠⣶⣦⣀⣀⠀⠀⣧⡇⠀⠀⣸⠀⠀⣻⣿
⡄⢀⣼⠟⢛⣆⣿⣿⡧⢴⣾⡿⠂⣸⣿⠟⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠈⠉⠉⠻⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⠃⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣾⣿⣇⠀⠀⣿⣄⢀⣾⣿
⣅⠈⣽⣷⣄⢹⡏⠉⠁⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⣴⣆⠀⠀⢀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⢻⣿⣷⣐⣿⣿
⣯⣤⣼⣿⣿⣿⣧⡄⢈⠁⢶⢀⠀⡉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣸⡿⠛⢛⠛⣿
⣿⣿⣿⣿⣿⣧⣿⡇⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡟⠉⠛⡿⠀⠀⢰⣴⣿
⣿⣿⣿⣿⣧⣼⣿⠿⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢠⢨⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡇⠀⠈⠀⠀⠈⠀⣀⠀⠀⠀⢀⣹⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠓⠂⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣀⣀⠀⣲⠚⠚⠛⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣇⣤⣤⣭⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⡘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣶⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⣛⠛⣛⢛⣟⣟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠐⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠶⢿⣿⣿⣿⣿⣭⣭⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠘⠇⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧⠀⠀⢠⣤⣤⣴⣤⣦⣤⣤⣤⣤⣶
⠀⠀⠀⢉⠉⠁⠀⢄⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣶⣶⣶⡄⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠀⠀⠀⠚⠙⠻⠷⠀⠻⡿⠾⣿⣿⣿
⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⢠⣴⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣿⣿⣿⣿⣽⡅⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠛⠩⠿⠛⠻⠃⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⢿⣿⣿⠿⢿⣿⢿⣿⣿⡇⣿⣿⣿⡿⠿⠀⠻⠿⣿⣿⣿⣿⣿⣿⠿⠸⣿⣿⣿⣿⡿⠿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠒⠀⠀⠀⢰⣶⡶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⣴⣦⣿⣷⣤⡀⠀⡄⠀⠀⠀⠙⠒⠂⠀⠀⠀⣦⡄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠤⠄⠀⠀⠀⠀⢠⣤⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⣶⠲⢦⣤⣤⣤⣤⣦⣴⣤⣿⣦
⠶⠶⢶⣶⣶⣶⣶⣶⣶⣾⣿⡇⠀⣤⠀⠀⠀⠤⠴⠤⣤⣤⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡌⠁⠐⠲⠙⠀⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠈⠉⠿⠿⠃⣀⣼⠀⠻⠀⠀⠀⠨⠹⠁⠟⠛⠛⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠋⠉⠙
⠒⠒⠀⠀⠐⠂⠀⣤⠀⢀⡀⠉⠀⢃⣴⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⣎⣀⣿⣿⡉⠽⡿⢻⢿⣿⣿⡏⠀⠉⠛⠄⠀⠀⠀⠀⠤⢤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠲⠀⠀⠀⢀⡎⠉⢀⠄⠉⠁⠀⠀⠀⠀⠘⠀⢠⣄⡸⠳⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⡀⢀⣀⣤⣤⡀⠀⠀⠀⠈⠉⠉⠉⠙⠁⠀⣸⣶⡆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣷⣤⣤⣶⡶⠶⠶⠶⢶
⠋⢀⣤⣴⣶⣦⣠⣤⣼⣿⣿⣿⡂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠰⠶⣶⡦⢶⡦⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡶⠶⠶⠶⠶⢺⠛
⡁⠀⣏⣙⣫⡉⠉⠙⠉⠉⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣶⣆⣽⣷⣿⡿⣶⣆⣀⣸⣿⣡⣦⣀⡀⢀⡀⣀⣀⢠⣄⣉⣤⣤⣤⣤⣤⣾⣿⣿⠒⠓⢻⠿
⠧⠄⣭⢏⣍⣉⠉⢹⣟⣛⣛⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣍⠉⠙⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣀⡀⠀⠉⣁⣉⣉⣈⣁⣩⡉⠉⠛⠛⢛⣿⠀⠀⣈⣛⣿⡟⣸⣾⣿⣇⢸⠐⡇⡇⠀⠈⣿⠀⠀⢸⣾
⠀⠀⠉⠀⢀⠀⠀⠈⠉⠉⠉⣽⣿⠀⠀⠀⠀⣘⠋⠛⢒⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠁⠈⠁⠁⠁⣀⣤⠤⢼⣿⠀⠀⠙⣉⣯⠅⠀⢸⣿⡷⣸⢰⡇⡃⠀⣤⣿⣤⣤⣾⣿
⠆⠲⣤⣤⡾⢷⡦⠶⠶⠶⢴⣾⣿⣀⣧⣴⡀⠀⠀⠀⠊⠀⠀⠐⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠒⠒⣾⣆⣲⣖⣾⣶⣿⣿⣶⣸⣿⠀⠀⠀⢿⣿⠀⠀⠿⠟⠃⠙⢸⣿⡇⣤⣤⣿⣤⣤⣽⣿
⠰⠶⢿⣛⣁⠜⠛⠐⠒⠒⠾⠿⢹⣿⣿⣿⣷⣶⡶⢶⣶⠿⡿⠿⠛⠀⠀⠙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠂⠀⠀⠀⢿⣠⣴⣤⣀⣀⠀⠈⣇⡇⠀⠀⣘⠀⠀⢿⣿
⡄⢀⣼⠟⢛⣂⣿⣿⡧⢴⣾⡿⠀⢘⣿⢽⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠍⠉⠉⠹⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠃⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠐⣿⣄⢠⣾⣿
⣅⠈⣽⣷⣄⢙⡏⠉⠁⠀⠀⠀⠀⢸⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣥⣦⠀⠀⠀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⢻⣿⣷⣘⣿⣿
⣧⣄⣼⣿⣿⣿⣧⡄⢈⠀⠶⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⢺⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⢸⡟⠛⢛⠛⢻
⣿⣿⣿⣿⣿⣧⣿⡇⢿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠈⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠟⠉⠙⡿⠀⠀⢰⣤⣾
⣿⣿⣿⣿⣧⣼⣟⠟⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣼⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠈⠀⠀⠈⠀⣀⠀⠀⠀⢀⣹⣿⣿
⣿⣿⣿⣿⣾⣿⡿⠓⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣀⣀⠀⢒⠒⠘⠛⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣅⣤⣤⣭⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣾⣿⣿⣶⣶⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⣛⠛⣛⠛⣛⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣻⣿⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠶⢿⣿⣿⣿⣯⣭⣭⣽⣿⡏⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⢁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢠⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤
⠀⠀⠀⠉⠉⠁⠀⢈⠉⠙⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠀⠀⠘⠙⠻⠷⠀⠻⠷⠾⣿⠿⣿
⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠉⣶⣶⣿⣿⣶⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⣯⢹⣿⣿⠉⣽⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣸⣿⣿⠀⢻⣿⢿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣄⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠁⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠛⠩⠿⠛⠻⠃⠛⠛⠛⠀⠀⠀⠀⠀⠀⠿⠿⠇⠘⠿⠿⠿⠿⠃⠀⠀⠿⣿⣾⣿⠿⠀⠻⠿⣿⢿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣶⡶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⣤⣤⣿⣷⣄⡀⠀⡀⠀⠀⠀⠚⠓⠂⠀⠀⠐⣶⡄⠀⠀⣰⣿⣶⣶⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣖⢶⣦⣤⣤⣤⣤⣴⣤⣤⣿⣶
⠶⠶⢶⣶⣶⣶⣶⣾⣷⣾⣿⡏⠀⣤⠀⠀⠀⠤⢴⠤⣠⣤⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡶⢷⡓⠿⠆⠉⠉⣛⣉⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠋⠿⠿⠇⣀⣼⠀⠻⠀⠀⠀⠨⠹⠅⠟⠛⠻⠻⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡷⡯⠂⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠟⠛⠉⠛
⠒⠒⠀⠀⠀⠀⠀⣤⠀⢀⡀⠉⠀⢓⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣇⠀⠀⠀⠀⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⢲⠀⠀⠈⢀⡎⠉⢀⠀⠋⠁⠀⠀⠀⠀⠘⠀⢠⣀⡀⣿⢬⣴⣾⣿⣦⣀⣿⣋⣟⣻⣿⣿⠀⠀⠁⠙⢂⡀⠀⠀⠀⠈⠉⠙⠉⠙⠃⠀⣺⣶⡆⠀⠀⠀⠀⠀⠀⠀⢰⣾⣾⣷⣷⣶⣷⣷⣤⣶⣶⠶⠶⠶⢶
⠋⢡⣤⣴⣶⣦⣤⣤⣼⣿⣿⣿⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣶⣿⣿⣿⠀⠀⠶⢶⡦⢴⡦⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⠶⠶⠶⠶⠾⠿
⡁⠀⣟⣙⣻⡉⠉⠙⠉⠉⠙⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣶⣆⣽⣧⣿⡿⣴⣆⣀⣸⣿⣁⣦⣀⠀⢀⡀⣀⣀⣤⣍⣉⣠⣤⣤⣤⣤⣶⣾⣿⠐⠓⢻⠿
⡧⠤⣽⣯⣍⣩⠉⢻⣟⣛⣛⣿⣟⠀⠀⠨⠀⠀⠀⠈⠀⡀⠀⠀⠐⠃⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠉⣁⣉⣋⣉⣁⣩⡉⠉⠛⠛⢋⣿⠈⠁⣉⢋⣿⣟⣹⣾⣿⡇⢸⢸⡇⡇⠀⠀⣿⠀⠀⢸⣾
⠀⠀⠉⠀⢀⠀⠀⠈⠉⠉⠉⣽⣿⠀⠀⠀⠀⡐⠒⠓⢓⣀⠀⣀⡀⠀⢸⣦⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⠉⠉⠁⠉⠁⣀⣤⠤⢼⣿⠀⠀⠛⡋⣿⠅⠀⢸⣿⣿⣼⢸⡇⡃⠂⣠⣿⣤⣤⣿⣿
⠆⠷⣤⣤⡼⣷⣦⠶⡶⠶⣤⣾⢿⣀⣇⣰⡀⠀⠀⠀⠀⠠⠀⠐⠀⡀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠒⣶⣆⣲⣖⣾⣶⣿⣿⣶⣸⣿⠂⠀⠀⢿⣿⠀⠀⠻⠟⠃⠹⢸⡿⣇⣤⣬⣿⣤⣤⣽⣿
⠸⠶⢿⣛⣃⠜⠛⠐⠒⠲⠾⠿⢺⣿⣿⣿⣿⣶⡶⢶⣶⢿⡿⠿⠿⠂⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠂⠀⠀⠀⢿⣠⣶⣤⣀⣀⠀⠈⣇⡇⠀⠀⣸⠀⠀⢿⣿
⡄⢀⣼⠟⢙⣆⣿⣿⡧⣤⣾⡿⠄⢘⣿⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⣉⠛⠻⠿⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠁⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⣿⣄⠀⣿⣿
⣅⠈⣽⣿⣄⢙⡏⠉⠁⠀⠀⠀⠀⢸⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣃⡀⠀⠀⠀⣩⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⢻⣿⣷⣈⣿⣿
⣧⣄⣼⣿⣿⣿⣧⡄⢈⠀⢶⢀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠠⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣺⡿⠛⢛⠛⣿
⣿⣿⣿⣿⣿⣧⣿⡇⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠉⠻⡿⠀⠀⢰⣴⣾
⣿⣿⣿⣿⣧⣼⣟⠟⠘⠿⠏⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠏⠀⠈⠀⠀⠉⠀⢀⠀⠀⠀⠀⣻⣿⣿
⣿⣿⣿⣿⢿⣿⡿⠓⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣀⣀⠀⢲⠒⠐⠃⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣅⣤⣤⣬⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⡆⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣾⣿⣿⣶⣤⣿⣶⣶⣶⣦⣶⣾⣿⣿⣿⣿
⣛⠛⣛⢛⣟⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠶⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢠⣤⣤⣤⣤⣥⣤⣤⣤⣼⣬
⠀⠀⠀⠉⠉⠁⠀⢉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠀⠀⠚⠙⠻⡷⠀⠻⠷⠾⣿⡿⣿
⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣷⣾⣿⣿⣿⣿⡟⣿⣶⣿⣿⣷⠀⣠⣶⣶⣿⣿⢷⣶⣶⣿⣿⣿⣿⣿⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠿⠿⠟⠿⠁⣿⣿⣷⣿⣿⢠⣿⣿⢹⣿⣿⡌⢹⣿⣿⢩⣿⣿⢿⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠾⠿⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⡇⢸⣿⣿⢸⣿⠿⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠘⣿⣿⣸⣿⣿⣿⢸⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠩⠿⠛⠻⠋⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠇⠘⠿⠿⠿⠿⠃⠀⠀⠿⢿⣾⣿⡿⠀⠻⠿⣿⠿⣿⣿⡾⠿⠿⠀⠀⠀⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢠⣶⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣤⣿⣷⣀⡀⠀⡀⠀⠀⠀⠒⠒⠀⠀⠀⠠⣶⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⠀⣀⡀⠀⠀⠀⣀⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢦⡂⢠⣤⣀⣀⣤⣤⣤⣤⣤⣿⣦
⠶⠶⢶⣶⣶⣶⣶⣾⣧⣾⣿⡇⠀⣤⠀⠀⠀⠀⣤⢀⣀⣤⣼⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠷⠄⠋⠀⠉⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠉⠉⠋⠿⠿⠃⣀⣼⠀⠻⠀⠀⠀⠀⠲⠄⠟⠛⠻⠻⣿⠏⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠋⠉⠛
⠐⠀⠀⠀⠀⠀⠀⣤⠀⢀⡀⠉⠀⢓⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡾⠛⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠒⠀⠀⠈⢀⡎⠉⢀⠀⠋⠁⠀⠀⠀⠀⠘⠀⢠⣀⣀⣀⢸⣗⣶⣾⣿⣿⣦⣽⣇⣬⣭⣿⣿⣇⠀⠈⠈⠃⣀⠀⠀⠀⠀⠙⠋⠛⠃⠀⣲⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣮⣶⣶⣤⣤⣴⣶⠤⠤⠴⢶
⠋⢁⣄⣴⣶⣤⣠⣤⣼⣿⣿⣿⡂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⡇⠀⠠⡦⢴⡤⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣤⠶⠶⠶⠶⠾⠾
⡁⠀⣋⠙⣋⡉⠉⠙⠉⠉⠙⠋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣼⣯⣿⡿⣤⡄⠀⣸⣿⣃⣤⢀⠀⢀⡀⣀⣀⢤⣍⣉⣉⣤⣤⣤⣤⣶⣾⣾⠒⠒⢻⠿
⡧⠄⣹⣏⣍⣉⠉⢻⣟⣛⣛⣿⣿⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⣾⡛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣀⣉⣉⣉⣉⣩⡉⠉⠿⠛⠋⣿⠈⠁⠈⢋⣿⡟⣸⣼⣿⡇⢸⢘⡇⡆⠁⠉⣿⠀⠀⢨⢾
⠀⠀⠉⠀⢀⠀⠀⠈⠉⠉⠉⣽⣿⠀⠀⠀⠀⠐⠒⠛⠚⢀⠀⣀⠀⠀⢀⣾⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠁⠉⠉⠉⠉⠉⠉⣀⣠⢤⢼⣿⠀⠀⠛⡉⣯⠅⠀⢸⣿⡷⣼⢨⡇⡇⠀⣀⣿⣀⣀⣿⣿
⢆⠦⣤⣤⡼⣷⣤⢤⣶⣦⣤⣼⢿⣀⣇⣰⠀⠐⠂⠀⠀⣀⠀⢁⠀⠀⠐⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⢲⣆⣲⣖⣶⣶⣿⣿⣦⣘⣿⠀⠀⠀⢿⣿⠀⠀⠾⠟⠃⠙⢸⡗⡇⣤⣬⣿⣭⣤⣽⣿
⠸⠦⣿⡛⢃⠜⠛⠐⠖⠶⠶⠿⢺⣿⣿⣿⣷⢶⢶⢶⣶⣾⡿⢾⣿⠿⠟⠁⠈⠻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠁⠀⠁⠈⣹⣿⣿⣿⠂⠀⠀⠀⢿⣀⣦⣄⣀⡀⠀⠈⣇⡇⠁⠀⣸⠀⠀⢻⣿
⡄⠀⣸⠟⠛⣂⣿⣿⡧⣤⣾⣿⠂⢘⣿⣿⡷⢶⡆⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠉⠛⠟⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⣿⣄⠀⣿⣿
⣁⠈⣽⣷⣌⢙⡏⠉⠁⠀⠀⠀⠀⢸⣿⣨⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣉⡀⠀⠀⠀⢉⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⢺⣿⣷⣐⣿⣿
⣧⣄⣽⣿⣿⣿⣥⡀⠈⠀⣶⢀⠀⠉⡿⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢺⡿⠟⢛⠛⢿
⣿⣿⣿⣿⣿⣯⣿⡇⢿⣿⡆⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣶⣿⡟⠉⠻⡿⠀⠀⢰⣤⣾
⣿⣿⣿⣿⣧⣼⣿⠿⠘⠿⠟⠀⢡⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠋⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⣹⣿⣿
⣿⣿⣿⣿⢾⣿⡿⠓⠂⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⠀⠀⠀⠄⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣀⣀⠀⢒⠒⠐⠃⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣁⣄⣤⣬⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣼⣦⣶⣶⣤⣶⣾⣿⣿⣿⣿
⣛⠛⣛⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣯⣩⣭⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡧⠀⠀⢠⣤⣤⣤⣤⣥⣄⣠⣤⣭⣬
⠀⠀⠀⢉⠉⠁⠀⠉⠉⠙⠉⠀⠀⠀⠀⢀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠚⠙⠻⡷⠀⠻⠿⠼⣿⣿⣿
⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⣷⣶⡄⣾⣿⡿⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠿⠿⠏⠛⠁⣿⣿⣧⣿⣿⢡⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⣽⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⢼⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⠸⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠘⣿⢿⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠩⠿⠛⠻⠋⠛⠛⠛⠀⠀⠀⠀⠀⠀⠿⠿⠇⠘⠿⠿⠿⠿⠃⠀⠀⠿⠿⣸⣿⣿⡇⠻⠿⣿⠿⠋⣿⣿⣿⠿⠀⠀⠀⠈⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠙⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⣴⣬⣿⣷⣄⡀⠀⡀⠀⠀⠀⠒⠒⠂⠀⠀⠸⣶⡂⠀⠀⠀⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠰⠖⠀⠀⠀⢀⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣶⣶⡶⣦⣤⣤⣤⣤⣦⣶⣯⣿⣿
⠶⠶⢶⣶⣶⣶⣶⣾⣷⣾⣿⡇⠀⣤⠀⠀⠀⠀⣴⢄⣄⣤⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⢶⣾⣿⡷⣿⡯⢻⢏⣟⣻⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠉⠉⠋⠿⠿⢃⣀⣼⠀⠿⠀⠀⠀⠀⢻⠅⠟⠛⠻⠻⣿⠏⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡿⠈⠐⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠉⠛
⠐⠀⠀⠀⠀⠀⠀⣤⠠⢀⡀⠉⠀⢓⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⢉⣹⣟⡋⣩⣟⠿⢿⣿⣿⣿⠙⠻⣿⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⡀⣀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⢒⠀⠀⠈⢠⡎⠉⢀⡄⠋⠁⠀⠀⠀⠀⠸⠀⣠⣀⣀⡀⠀⠟⢾⣿⣿⣿⣿⣶⣷⣾⣷⣶⣾⣷⡄⢀⣠⣬⣴⣆⠀⠀⠀⠛⠋⠛⠃⠀⣲⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣾⣿⣧⣤⣴⣶⠤⠴⠴⢶
⠋⢁⣄⣴⣶⣤⣤⣤⣼⣿⣿⣿⡂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⡦⢴⡤⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣤⡶⠷⠶⠶⠾⠿
⡁⠀⣟⣙⣋⡉⠉⠛⠋⠙⠛⠫⣷⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣼⣯⣿⡿⣤⡆⠀⣸⣿⣣⣤⣀⠀⢀⡀⣀⣀⣤⣍⣉⣉⣥⣤⣤⣤⣶⣾⣿⠒⠒⢻⠿
⡧⠤⣽⣏⣝⣉⠉⢻⣟⣛⣛⣿⣿⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠈⠐⠃⠀⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣄⣀⣀⣉⣋⣉⣉⣩⡉⠉⠿⠛⠛⣿⠈⠁⠉⢛⣿⣟⣸⣾⣿⣷⢸⢸⡇⣇⠉⠉⣿⠀⠀⣸⣾
⠀⠀⠉⠀⢀⠀⠀⠈⠉⠉⠉⣿⣿⠀⠀⠀⠀⡐⠒⠛⠚⣀⠀⣀⠀⠀⣀⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠁⠉⠉⠉⠉⠉⠉⣀⣠⢤⢼⣿⠀⠀⠛⡉⣿⠅⠀⢸⣿⣷⣸⢸⡇⡃⠂⣤⣿⣀⣠⣿⣿
⣖⠶⣤⣤⡾⣷⣤⣤⣶⣶⣤⣾⢿⣀⣇⣰⣀⠐⠀⠀⠀⣁⡀⢉⡀⠀⠘⣿⡿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢲⣖⣾⣶⣿⣿⣦⣸⣿⠀⠀⠀⢿⣿⠀⠀⠾⠟⠃⠹⢸⡟⣇⣤⣭⣿⣭⣤⣽⣿
⠸⠶⣿⣛⣃⡜⠛⠐⠶⠶⠾⠿⣺⣿⣿⣿⣷⣶⣶⢶⣶⣿⡿⢿⣷⠶⠂⠁⠀⠀⠀⣤⡐⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠁⠈⢹⢿⣿⣿⠂⠀⠀⠀⣿⣠⣶⣤⣀⡀⠀⠈⣇⡇⠁⠈⣸⠀⠀⢻⣿
⡄⢀⣼⠿⠛⣆⣿⣿⡧⣤⣾⣿⠆⢘⣿⣿⡷⣶⡆⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠟⠻⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠀⠘⣿⣄⢀⣿⣿
⣅⠈⣽⣷⣌⢙⡏⠉⠁⠀⠀⠀⠀⢸⣿⢸⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣴⣶⡀⠀⠀⣠⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⢾⣿⣿⣸⣿⣿
⣯⣄⣽⣿⣿⣿⣧⡄⠈⠃⣶⢀⠀⠉⣿⠹⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣾⡿⠟⢛⠛⢿
⣿⣿⣿⣿⣿⣯⣿⡇⣿⣿⣷⠈⠀⠂⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣶⣿⡟⠉⠻⡿⠀⠀⢸⣤⣾
⣿⣿⣿⣿⣧⣽⣿⠿⠸⠿⠟⠁⢡⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠈⠀⠀⠉⠀⢀⠀⠀⠀⠀⣻⣿⣿
⣿⣿⣿⣿⢿⣿⡿⠓⠀⢐⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠂⠀⠀⣸⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣀⣀⠀⢲⠒⠐⠃⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣃⣤⣤⣭⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣽⣶⣶⣶⣦⣶⣾⣿⣿⣿⣿
⣛⠛⣛⠛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡄⠀⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣯⣩⣭⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡧⠀⠀⢠⣤⣤⣤⣤⣥⣄⣠⣤⣭⣬
⠀⠀⠀⠉⠉⠁⠈⣉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀⠀⠀⠚⠙⠻⣷⠀⠻⡿⢿⣿⣿⣿
⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣠⣶⣶⣶⣄⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣾⣿⣯⠿⠿⣿⣿⣿⣿⣿⣧⣿⣿⢡⣿⣿⢹⣿⣿⣿⣽⣿⣿⠉⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠘⣿⣿⣿⣦⡻⠿⠇⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⢻⣿⢿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⡼⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⢰⠁⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠠⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠩⠿⠛⠻⠋⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠇⠘⠿⢿⡿⠿⠃⠀⠀⠿⠿⢘⣿⣿⣿⠻⠿⣿⠿⠋⣼⣿⣿⠿⠀⠀⠀⠀⠻⠿⠿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣶⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣐⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣴⣬⣿⣷⣆⡀⠀⡀⠀⠀⠀⠓⠒⠂⠀⠀⢸⣷⡶⠈⠀⠠⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠄⠴⠶⠀⠀⠀⢀⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣿⣿⣿
⠶⠶⢶⣶⣶⣶⣶⣾⣷⣾⣿⡯⠀⣤⠀⠀⠀⢄⣴⢤⣤⣴⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠉⠉⠋⠿⠿⢇⣀⣾⠈⠿⠀⠀⠀⠘⢻⠅⡟⠛⠻⠻⣿⡏⠀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠿⠃⠙⡇⠚⡰⠂⠩⠁⠀⠀⠀⠀⠸⠿⠟⠛⠋⠛
⠒⠀⠀⠀⠀⠀⠀⣤⠠⢄⡈⠉⠀⢓⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠉⣹⣟⡛⣩⣟⠻⢿⣿⣿⣿⠋⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠗⠀⠘⠆⢔⣬⣀⡀⠀⡠⡙⣕⠀⠀⡀⠀⠀⠀⠀
⣀⡀⠀⠀⢲⠀⠀⠉⢠⡎⠉⢀⠄⠋⠉⠀⠀⠀⠀⠸⠀⣠⣀⣀⣀⠀⠻⢷⣿⣿⣿⣿⣶⣷⣾⣷⣶⣶⣷⣄⣀⣠⣤⣵⣦⡀⠀⠀⠛⠋⠛⠃⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣴⣴⣶⠤⠴⢴⣶
⠛⢁⣤⣴⣿⣦⣤⣤⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡤⣴⣤⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣶⠶⡶⠶⠶⢾⠿
⡁⠐⣿⣙⣛⡋⠉⠛⠋⠙⠛⠻⣷⠀⠀⠀⠠⠠⠀⠀⠠⠄⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣼⣿⣿⡿⣤⡆⠀⣸⣿⣣⣦⣀⡀⢀⡀⣀⣀⣴⣍⣉⣩⣥⣤⣤⣤⣶⣾⣿⠒⠒⢿⢿
⣧⢴⣽⣯⣍⣉⠉⢻⣟⣛⣛⣿⣿⠀⠀⠨⠀⠀⠀⠀⠉⠄⠀⠉⠐⠃⠀⣽⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣀⣀⣉⣋⣉⣉⣩⡉⠉⠿⠛⠛⣿⠈⠁⠉⢛⣿⣟⣿⣾⣿⣿⢹⢸⣇⡇⠉⠉⣿⠀⠀⣼⣾
⠀⠀⠉⠀⢀⠀⠀⠈⠉⠉⠉⣿⣿⠀⠀⠀⠀⢐⠒⠛⢚⢀⠀⣀⠀⠀⢀⣗⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⣀⣠⢤⢼⣿⠀⠀⠛⣻⣿⠅⠀⢸⣿⣿⣾⢸⣇⡇⠂⣤⣿⣠⣠⣿⣿
⣶⡶⣤⣤⡾⣷⣤⢤⣶⣦⣤⣾⢿⣀⣧⣰⣄⠐⠂⠀⠒⣁⣉⢉⣀⡀⠺⣷⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠲⠆⣲⣶⣾⣶⣿⣿⣶⣸⣿⠂⠀⠀⢿⣿⠀⠀⠿⠿⠋⠹⢸⡿⣇⣤⣭⣿⣭⣤⣿⣿
⠸⠶⣿⣛⣃⠜⠛⠐⠶⠶⠾⠿⣿⣿⣿⣿⣿⣾⣶⢶⣶⣿⣿⣾⣷⣶⡾⠿⠋⠀⠀⢀⡀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠁⠉⠁⠈⣽⣿⣿⣿⠆⠀⠀⠄⣿⣠⣶⣦⣀⡀⠀⠈⣇⡇⠉⠈⣸⠀⠉⣻⣿
⡄⢀⣼⡿⢛⣆⣿⣿⣧⣤⣾⣿⡆⢘⣿⣿⡷⣾⣦⡾⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠈⠘⣿⣄⢠⣿⣿
⣅⠈⣽⣿⣌⢹⡏⠉⠁⠀⠀⠀⠀⢸⣿⢺⡏⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣩⣴⡀⠀⠀⢀⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢾⣿⣿⣸⣿⣿
⣯⣄⣽⣿⣿⣿⣧⡄⠘⠃⣶⢀⠀⠙⣿⢹⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠐⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣾⡿⠟⢛⠻⢿
⣿⣿⣿⣿⣿⣯⣿⡇⣿⣿⡟⠈⠀⠀⣿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣶⣿⡟⠋⠻⡿⠀⠀⢸⣦⣾
⣿⣿⣿⣿⣧⣽⣿⠿⠸⠿⠟⠉⢡⣤⣿⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠈⠀⠀⠉⠀⢀⠀⠀⠀⠀⣻⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠓⠂⢲⠃⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠘⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⣀⠀⢲⠖⠚⠛⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣇⣤⣤⣭⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣤⣿⣶⣶⣶⣦⣶⣾⣿⣿⣿⣿
⣛⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⢨⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣯⣩⣽⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠨⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡧⠀⠀⢠⣤⣤⣤⣬⣥⣤⣤⣤⣭⣭
⠀⠀⠀⢉⠉⠁⠈⣉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠚⠙⢻⣿⠀⠿⡿⢽⣿⣿⣿
⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡄⣶⣿⣿⣠⣶⣶⣶⣄⣿⣿⣿⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣬
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣧⣿⣿⢡⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⣀⣀⣀⣿⣿⣿⣿⣿⢸⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣇⢺⣿⡏⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡾⣿⣿⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠩⠿⠛⠻⠋⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣷⠻⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣷⣦⡻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣶⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣴⣶⣶⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⣴⣬⣿⣷⣄⡀⠀⡀⠀⠀⠀⠓⠒⠂⠀⠂⢸⣷⡦⠈⢀⠀⠶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠀⠒⠒⠀⠀⠀⣠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿
⠶⠶⢶⣶⣶⣶⣶⣾⣷⣾⣿⡯⠀⣤⠀⠀⠀⢄⣴⣤⣤⣴⣼⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠉⠙⠋⠿⠿⢇⣀⣾⠈⠿⠀⠀⠀⠸⢻⠇⡟⠛⠿⠿⣿⠏⠀⠙⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠟⠀⠹⡇⣹⠉⠉⠉⠄⠎⡑⠁⠉⠹⠿⠟⠛⠛⠛
⠒⠂⠀⠀⠀⠀⠀⣤⠀⢀⡀⠉⠀⢓⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢃⣠⣭⣥⡴⢶⢉⣛⠿⠿⣿⡏⠘⠿⢿⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠘⠟⠀⠀⠆⢺⣆⣄⣐⡆⣴⡝⣣⠀⠀⡀⠀⠀⠀⠀
⣀⡀⠀⠀⢲⠂⠀⠉⢠⡎⠉⢀⠄⠋⠉⠀⠀⠀⠀⠸⠀⣠⣄⣀⣀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣤⣤⣴⣶⡄⠀⠀⠛⠋⠛⠃⠀⣺⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣤⣴⡶⠤⠴⠴⢶
⡛⢁⣤⣴⣿⣦⣤⣤⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡤⣴⣤⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣴⠶⡷⠶⠶⢾⠿
⡁⠀⣟⣙⣫⣉⠉⠛⠛⠙⠛⠻⣷⠀⠀⠀⠠⠀⠄⠀⠤⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣰⣯⣿⡿⣴⡄⠀⣸⣿⣣⣦⣀⡀⢀⡀⣀⣀⣼⣍⣉⣩⣥⣤⣤⣤⣶⣾⣿⠒⠒⢿⢿
⣯⣤⣿⣿⣟⣩⠉⣻⣟⣛⣛⣿⣿⠀⠀⢸⠁⠀⠀⠠⠁⠆⠐⠉⠐⠃⠀⣔⣿⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣄⣀⣉⣋⣉⣉⣩⡉⠉⠟⠛⠛⣿⠈⠁⠉⢛⣿⣟⣿⣾⣿⣷⢸⣸⣇⣇⠉⠉⣿⠀⠀⣼⣿
⠀⠀⠉⠀⢀⠀⠀⠈⠉⠉⠉⣿⣿⠀⠀⠀⠀⣘⠓⠛⢛⢀⠀⣀⡀⠀⣀⣂⣻⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⠉⠉⠉⠉⣀⣠⣤⢼⣿⠀⠀⠛⣻⣿⠅⠀⢸⣿⣿⣾⢸⣇⡇⠂⣤⣿⣠⣠⣿⣿
⣶⠶⣤⣤⣾⣷⣤⣤⣶⣦⣤⣼⣿⣀⣧⣰⣄⡘⠂⠀⠞⣁⣈⣫⣀⠐⢺⣷⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠲⠆⢲⣶⣾⣶⣿⣿⣶⣸⣿⠂⠀⠈⢿⣿⠀⠀⣿⠿⠓⠹⢸⡿⣇⣤⣭⣿⣭⣤⣿⣿
⠸⠦⣿⣛⣃⠜⠛⠒⠶⠶⠶⠿⣾⣿⣿⣿⣿⣾⣶⣶⣶⣿⣿⣶⣷⣶⠿⠟⠉⠀⠀⠀⣐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠁⠉⠁⠈⣽⣿⣿⣿⠆⠀⠀⠊⣿⣠⣶⣦⣀⡀⠀⠘⣷⡇⠉⠉⣹⠀⠉⣿⣿
⡄⢀⣼⡿⢛⣆⣿⣿⣧⣤⣾⣿⡆⢘⣿⣿⡷⣶⣶⡾⠛⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠀⠹⣿⣄⢀⣿⣿
⣁⠈⣽⣷⣌⢹⡟⠙⠁⠀⠀⠀⠁⢸⣿⣹⡟⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣩⡄⠀⠀⠀⢨⣽⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢾⣿⣿⣸⣿⣿
⣯⣄⣽⣿⣿⣿⣧⡄⢘⠃⣶⣀⡀⠿⣿⢻⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣾⡿⠿⢻⠿⢿
⣿⣿⣿⣿⣿⣯⣿⡇⣿⣿⣿⡉⠱⠄⣷⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⡟⠛⠻⡿⠁⠀⢸⣤⣾
⣿⣿⣿⣿⣧⣽⣿⠿⠹⠿⠟⠉⢡⣴⣿⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⠉⠁⠈⠉⠀⢀⠀⠀⠀⠀⣻⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠳⠂⢲⠃⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠘⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣀⣀⠀⣲⠖⠒⠟⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣃⣤⣤⣭⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣿⣶⣶⣴⣤⣶⣾⣿⣿⣿⣿
⣻⠛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⢠⠚⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣯⣩⣽⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠈⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⢨⣤⣤⣬⣬⣥⣤⣤⣤⣭⣭
⠀⠀⠀⢉⠉⠁⠈⣉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠚⠙⢿⣿⠀⠿⡿⢿⣿⣿⣿
⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡄⣶⣿⣿⣡⣶⣶⣶⣄⣿⣿⣷⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬
⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣧⣿⣿⢹⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣧⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⡼⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠩⠿⠛⠻⠋⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⢿⡿⢿⢃⣴⣶⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠻⠿⡿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣭⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⠀⣤⣬⣿⣷⣄⣀⠀⡀⠀⠀⠀⠒⠒⠂⠀⠀⢾⣷⣦⠀⢘⣀⠖⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠠⠶⠂⠀⠀⠀⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⣤⣄⣤⣤⣤⣴⣶⣷⣿⣿
⠶⠶⢶⣶⣶⣶⣶⣾⣷⣿⣿⡏⢀⣤⠀⠀⠀⠀⣴⣤⣤⣴⣼⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠉⠙⠋⠿⠿⢇⣀⣾⠌⠿⠤⠀⠀⠰⢻⠇⡟⠛⠿⠻⣿⠏⠈⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡛⠒⢿⡿⣷⣤⡟⢛⠛⢿⠊⠗⢉⠹⠿⠟⠛⠋⠛
⠒⠐⠀⠀⠠⠀⠀⣤⠠⢄⡈⠉⠈⢓⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⢃⣨⣟⣥⡩⣭⠛⠿⢿⣿⣿⡏⠹⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠣⢼⠿⠃⠘⠷⢏⣏⣿⣖⣢⠷⢧⣿⠂⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⢲⠀⠀⠉⢀⡎⠋⢀⡀⠋⠉⠀⠀⠀⠀⢸⠀⣠⣄⣀⣀⠀⠻⢳⣿⣿⣿⣿⣷⣿⣾⣿⣶⣶⣶⣦⣄⣤⣤⣥⣷⡀⠀⠀⠛⠋⠛⠋⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣤⣶⣦⠤⠴⠶⢶
⡛⢡⣤⣴⣷⣦⣤⣤⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡠⣴⣤⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣶⡷⠶⠶⢾⢿
⣁⡌⣟⢙⣻⣋⠉⠻⠋⠛⠛⠋⣷⠀⠀⠀⠠⠠⠄⠀⠤⠄⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣠⣯⣿⡿⣤⣄⠀⣸⣿⣯⣖⣀⡀⢀⡀⣀⣀⣨⣍⣉⣭⣥⣤⣤⣤⣶⣾⣿⠒⠓⢻⢿
⣯⠤⣿⣿⣟⣛⠉⣻⣟⣛⣻⣿⣟⠀⠀⢸⠁⠀⠄⠠⠨⠅⠒⠈⠐⠃⠀⣎⣿⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣄⣀⣉⣋⣉⣉⣩⡉⠉⠟⠛⠋⣿⠈⠁⠉⢛⣿⣟⣿⣿⣿⣷⢸⣸⣇⡇⠉⠉⣿⠀⠀⣼⣿
⠀⠀⠉⠀⠉⠀⠀⠈⠉⠉⠙⣿⣿⠀⠀⠀⠀⠒⠛⠛⢛⣁⠀⣄⡀⠀⣀⣖⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠉⠉⣀⣠⣤⣼⣿⠀⠀⠛⡫⣿⠅⠁⢸⣿⣿⣿⢻⣧⡇⠆⣀⣿⣠⣠⣿⣿
⢶⡶⣤⣤⣾⣷⣤⣤⣶⣦⣤⣼⢿⣀⣧⣰⡀⡘⠂⠀⠞⣃⢘⣿⣀⡀⢲⣷⣿⡿⠿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠒⠆⢲⣖⣶⣶⣿⣿⣦⣸⣿⠂⠀⠀⢿⣿⠀⠀⠿⠿⠛⠹⢸⡿⡇⣤⣭⣿⣭⣥⣿⣿
⠺⠧⣿⣛⣃⡸⠛⠲⠶⠶⠶⠿⢾⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣷⣶⡿⠛⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠁⠉⠁⠉⣽⣿⣿⣿⠆⠀⠀⠈⣿⣀⣦⣤⣀⠀⠀⠘⣗⡇⠉⠉⣹⠀⠉⣿⣿
⡄⢀⣽⡿⢛⣆⣿⣿⣧⣤⣾⣿⡄⢘⣿⣿⣷⣾⣶⡾⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠂⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠐⠹⣿⣄⢠⣿⣿
⣁⠈⣽⣷⣌⢻⡟⠉⠁⠀⠀⠀⠁⢸⣿⢹⡏⣻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣩⡉⠉⠀⠈⢉⣽⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⢾⣿⣿⣸⣿⣿
⣧⣄⣽⣿⣿⣿⣧⡀⠈⠂⣶⣀⡀⠹⣿⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⡿⠿⢿⠿⢿
⣿⣿⣿⣿⣿⣯⣿⡇⣿⣿⣗⡉⠁⠂⣿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⡟⠛⠻⡿⠁⠀⢸⣤⣼
⣿⣿⣿⣿⣧⣽⣿⠿⠹⠿⠟⠉⢡⣶⣿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⠈⠉⠁⠈⠉⠀⢀⡀⠁⠀⠀⣻⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠷⠂⢲⠇⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠐⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⣀⠀⢲⠶⠒⠟⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣃⣤⣠⣭⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣦⣿⣶⣶⣶⣤⣶⣾⣿⣿⣿⣿
⣛⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⢺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠺⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡯⠀⠀⢸⣥⣤⣭⣬⣥⣤⣤⣭⣭⣭
⠀⠀⠀⢉⠉⠁⠈⣉⠉⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠚⠛⢿⣿⠀⠻⡿⣹⣿⣿⣿
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡄⣾⣿⣿⣣⣶⣶⣶⣄⣿⣿⣿⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣧⣿⣿⢹⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣧⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⣸⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⠤⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠩⠿⠛⠻⠋⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⢿⡿⠿⢣⣴⣦⣿⣿⣼⣿⣿⣿⣻⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⠻⠿⡿⠿⠋⠸⠿⠧⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠒⠀⠀⠀⢰⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣤⣼⣶⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠄⠀⣴⣬⣿⣷⣄⣀⠀⡀⠀⠀⠀⠒⠒⠂⠀⠀⢸⣷⡴⠁⢈⢀⠶⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠖⠂⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣦⣤⣴⣶⣷⣿⣿
⠶⠶⢶⣦⣶⣶⣶⣯⣷⣿⣿⡯⢀⣤⠀⠀⠀⢀⣸⣤⣤⣤⣼⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠙⠋⠿⠿⢇⣀⣾⠌⠿⠠⠀⠀⠐⢳⠂⡿⠛⠿⠿⣿⠏⠀⠙⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠗⠟⣻⣟⣷⣾⡛⠟⠿⡿⠋⠺⠋⠹⠿⠟⠛⠛⠛
⠠⠀⠀⠀⠤⠀⠀⣤⠠⠀⡈⠙⠀⢒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢃⣠⣽⣧⣤⢶⠍⠛⠿⠿⣿⣿⠉⠽⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⣾⠿⠖⠿⠗⢿⣻⣷⣞⣤⣴⢷⣿⠂⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠒⠀⠀⠉⢠⡜⠋⢀⡀⠋⠉⠀⠀⠀⠀⢸⠀⣀⣀⣀⣀⠀⠈⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣠⣤⣬⣾⡄⠀⠀⠘⠋⠛⠃⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣴⣦⠤⠴⠦⢶
⠛⢡⣄⣴⣷⣦⣠⣤⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⣤⣤⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣴⣶⡷⠶⠶⢾⢾
⡁⠈⣟⢛⣻⠉⠉⠻⠛⠙⠛⠛⣷⠀⠀⠀⠀⠀⠄⠀⠤⠄⠀⠀⠀⠀⠠⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⣿⣿⡿⣤⣄⠀⣸⣿⣋⣆⢀⠀⢀⡀⣀⣀⣨⣍⣉⣉⣡⣤⣤⣤⣶⣾⣿⠒⠒⢿⢿
⣧⠤⣿⣿⣟⣛⠛⣻⣟⣛⣻⣿⣟⠀⠀⢸⠀⠁⠀⠈⠩⠄⠐⠀⠐⠂⠐⡏⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣀⣀⣉⣋⣉⣉⣩⡉⠉⠟⠛⢛⣿⠉⠁⠛⠛⣿⣟⣾⣿⣿⣷⢹⣸⣇⡇⠉⠉⣿⠀⠀⣼⣾
⠀⠀⠉⠀⠈⠀⠀⠈⠉⠉⠛⣿⣿⠀⠀⠀⠀⠘⠛⠛⢗⠀⢀⣄⠀⠀⣐⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⣁⣠⣤⣼⣿⠀⠀⠛⠻⣿⡍⠉⢹⣿⣿⣼⢸⣇⡇⠆⣀⣿⣀⣀⣿⣿
⣦⡶⣤⣄⣼⣷⣤⣤⣶⣶⣤⣼⢿⣀⣇⣰⣀⡘⠀⠀⢜⣁⡙⡽⣀⠀⣺⣷⣶⡟⠿⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠂⢲⣶⣶⣶⣿⣿⣦⣸⣿⠂⠈⠀⣿⣿⠀⠀⢿⠿⠛⠹⢸⡿⡇⣄⣭⣿⣭⣭⣿⣿
⠸⠧⣿⡿⢃⡸⠿⠲⠶⠶⠾⠿⣾⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣷⣶⣶⠟⠓⠀⠀⠀⠀⢐⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠁⠉⠁⠉⣽⣿⣿⣿⡆⠀⠀⠀⣿⢀⣶⣤⣀⡀⠀⠘⣿⡇⠉⠉⣹⠀⠁⣿⣿
⡄⢀⣼⡿⠻⣆⣿⣿⣧⣤⣾⣿⡀⢹⣿⣿⣷⣶⣶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠃⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠈⠘⣿⣄⢠⣿⣿
⣁⠈⣽⣷⣌⢻⡟⠉⠁⠈⠀⠈⠉⢹⣿⢸⡏⣻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣩⣄⠀⠀⠀⢈⣭⣿⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⢾⣿⣿⣸⣿⣿
⣯⣄⣽⣿⣿⣿⣧⡀⠘⠃⣶⣀⡀⠽⣿⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⡿⠿⢻⠿⢿
⣿⣿⣿⣿⣿⣯⣿⡇⣿⣿⣿⡉⠑⠆⣿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⡟⠛⠻⡿⠁⠀⢸⣤⣼
⣿⣿⣿⣿⣯⣽⣿⠿⠹⠿⠟⠉⢡⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢨⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠉⠉⠁⠈⠉⠀⢀⡀⠁⠀⠀⣻⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠷⠂⢲⠇⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠘⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣀⣀⠀⢲⠶⠲⠟⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣃⣤⣠⣭⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣤⣽⣦⣤⣴⣤⣶⣾⣿⣿⣿⣿
⡻⠛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⢀⢺⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣯⣩⣭⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠈⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡥⠀⠀⢠⣥⣬⣭⣭⣭⣥⣤⣭⣭⣭
⠀⠀⠀⢉⠛⠁⠈⣉⠉⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠘⠛⢻⣿⠈⠿⡿⣼⣿⣿⣿
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡦⢠⣴⣶⣶⣤⡀⠀⠀⣶⣶⡄⣾⣿⣿⣣⣶⣶⣶⣄⣿⣿⣿⣶⣶⡆⠀⢠⣶⣶⢰⣶⣶⢰⣶⣦⢠⣶⣦⢰⣶⣶⢴⣶⡆⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣏⠿⠿⠇⠀⠀⣿⣿⣧⣿⣿⢹⣿⣿⢹⣿⣿⣿⣿⣿⣿⠉⠁⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠻⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣷⢺⣿⡏⣿⣿⡇⠀⠀⣿⣿⢻⣿⣿⡼⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⡟⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⡄⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠉⠿⠛⠻⠋⠛⠛⠛⠁⠀⠀⠀⠀⠀⠿⠿⠿⠘⠿⢿⡿⠿⢃⣴⣦⣿⣿⣼⣿⣿⣿⣻⣿⣿⣿⣯⣾⣿⣿⡿⠀⠀⠀⠀⠻⠿⡿⠿⠋⠸⠿⠇⠹⠿⠿⠸⠿⠿⠾⠿⠇⠻⠿⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 6556

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Wall_Street_Does_Not_Care_About_Microsoft_s_Impending_August_La.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Wall_Street_Does_Not_Care_About_Microsoft_s_Impending_August_La.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Wall Street Does Not Care About Microsoft's
Impending (August) Layoffs, It Believes Lies From Microsoft, Whose Debt Grows
Rapidly⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025,
updated Jul 30, 2025


4 weeks ago: Microsoft's_August_Layoffs_Wave:_"August_is_Confirmed_for
Additional_Performance_Based_Cuts"


3 months ago: Microsoft's_Debt_Grew_2.1_Billion_Dollars_in_the_Past_3_Months
Alone_or_8.2_Billion_in_the_Past_Half_a_Year


If Microsoft rebrands everything as "hey hi" (AI), there will be growth in that
area. It_did_the_same_with_"cloud"_and_lied_to_shareholders. It's just
cannibalisation (one buzzword devours the prior one). It is not real, genuine
growth.


In the past few days we saw several reports in the mainstream media in India
about rumours of more Microsoft layoffs on the way. If Microsoft is doing so
well and swimming in money, why so many cuts (about 29,000 layoffs so far this
year)? There were almost 10 waves of layoffs since January, not two. We covered
them all (the verifiable ones).


As they say in programming, "check your inputs". █


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


                                                           -The_Economist,_1999


    * Wayland_Considered_Harmful_(to_GNU/Linux_Adoption)
    * How_to_Report_Apple_Layoffs_Without_Saying_the_"L"_Word



                    ䷩ 𝚕𝚒𝚗𝚎 6610

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2025/07/30/Wayland_Considered_Harmful_to_GNU_Linux_Adoption.shtml
    Gemini version at gemini://gemini.techrights.org/n/2025/07/30/Wayland_Considered_Harmful_to_GNU_Linux_Adoption.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Wayland Considered Harmful (to GNU/Linux
Adoption)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


In case it's not already obvious, many people are either not interested in
Wayland or don't even know what that is. If they use X, it's not a political
statement. If they wish to stay with what works for them, it's not a political
statement either.


Only yesterday:


     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇AMD_Streaming_SDK_Updated_With_Linux_Support_-_But
                       Recommending_X.Org_Over_Wayland⦈_


There are almost_100_comments_about_it, starting with "wAylANd worKs for mE
guYs, EverYthiNg wORks FiNe iT doEs not LaCk aNYThinG!!!!!!!!!!!!!!!!!! Where's
all the other stupid clowns who said Wayland is feature complete and has no
design imposed limitations? I'm sick of providing links every single time when
the same clowns will always ask again in the next topic."


A later comment said: "Could this be the end of Wayland?"


Probably not, as it refuses to die for nearly 2 decades already. In page 2:
"Targeting X11 is fine for the time being. WINE/Proton isn't fully ready to
support Wayland aswell, so most games have to run through some X11
implementation anyways."


Indeed, and it's not limited to games.


Apropos games, Connor McLaughlin yesterday (shunning a distro because of
Wayland):


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


Maybe next year will be the "year of Wayland". If not, maybe the year after
that... or after that.


Wayland would not work for any of our machines at home. We rely on features and
tools that Wayland lacks, set aside compatibility.


As Hackaday_put_it_this_week: "After more than forty years, everyone knows that
it’s time to retire the X Window System – X11 for short – on account of it
being old and decrepit. Or at least that’s what the common narrative is,
because if you dig into the chatter surrounding the ongoing transition there
are some real issues that people have with the 16-year old spring chicken –
called Wayland – that’s supposed to replace it. [...] Even if Wayland does end
up succeeding X11, the one point that many people seem to agree on is that just
because X11 is pretty terrible right now, this doesn’t automatically make
Wayland the better option. Maybe in hindsight Mir was the better choice we had
before it pivoted to Wayland."


A few days ago in our_Geminispace_links, but in Gopher protocol, someone_wrote:


     Anyway, when you don't do sandboxing to begin with, it hardly matters
     if you're using Wayland or X11. `ping` can read my SSH keys. My
     terminal can. `ls` can. `jq` can.


     If Wayland gave me a huge boost in terms of security, it would be
     worth the sacrifices. We're not there yet.


     This whole situation reminds me a lot about my efforts to switch from
     Windows to Linux some 20 years ago. I tried to switch to 100% Linux
     many times because it was interesting and supposedly better, but it
     just wasn't what I *wanted*. There were too many things that caused
     pain.


     Only when I eventually got sold on the philosophical/political/moral
     idea of Free Software, I was able to think: "Okay, this is worth it,
     I'm gonna push through. This is what I want now."


Maybe Wayland will be functional for everyone one day. Or maybe not. For now,
however, many people have pragmatic reasons to avoid/skip it. Don't try to
insult them. It won't work. █


    * My_Experience_With_Judges_Has_been_Positive,_But_We_Must_Still_Pursue
      SLAPP_Reform_in_the_United_Kingdom
    * Wall_Street_Does_Not_Care_About_Microsoft's_Impending_(August)_Layoffs,
      It_Believes_Lies_From_Microsoft,_Whose_Debt_Grows_Rapidly


⠀⠀⡤⠤⢄⡦⠤⠤⢀⠤⠤⡀⡠⢀⠤⠤⡀⡤⠤⡄⡆⢄⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡧⠤⠘⠃⠀⠀⠘⠠⠤⠃⠃⠘⠤⠄⠃⠃⠀⠃⠇⠔⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠃⠃⠗⠪⠢⠿⠖⠰⠆⠞⠺⠳⠒⠟⠲⠸⠀⠀⠀⠷⠺⠓⠆⠇⠖⠚⠪⠐⠒⠞⠇⠀⠀⠀⠓⠕⠷⠳⠗⠶⠀⠀⠀⠘⠘⠼⠘⠂⠠⠘⠂⠀⠀⠐⠕⠕⠲⠋⠣⠄⠇⠀⠀⠐⠗⠰⠐⠾⠸⠪⠪⠺⠾⠿⠖
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣹⡽⣽⢹⢽⣯⡻⣿⢻⢻⡻⡟⢻⢻⡟⣿⢻⡟⣿⣝⢿⣯⡋⣿⣿⢹⢹⡟⣻⢹⡟⣯⣿⣻⡏⣿⡹⡽⡝⣽⢹⢻⡏⣿⡟⣿⢻⣿⢻⣿⣛⣿⣿⢻⡟⡟⢻⠛⡏⣿⣿⣿⢙⠝⡟⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⡿⣿⢿⣿⣿⣿⢿⣿⡿⣿⣿⣷⣿⣿⢿⡿⣿⣿⢿⣿⣿⢿⢿⣿⡿⣿⣿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣼⣶⣿⣧⣧⣿⣼⣧⣧⣿⣼⣧⣿⣼⣧⣿⣼⣇⣿⣷⣽⣧⣿⣦⣧⣿⣿⣿⣼⣵⣼⣦⣿⣧⣴⣬⣦⣏⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⢿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣛⣟⣻⣸⣸⣸⣿⣿⣇⣟⣿⣿⣫⣟⣿⣛⣿⣸⣟⣘⣜⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 6759

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 30/07/2025: Two Sides of Me
and "Hooked on Cosmic Voyage"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇On_Gopher⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ Two_Sides_of_Me⠀⇛


                       Chasing that vibrant coloured sunset, My two halves
                       stare into its enticing aura Walking down that one
                       way track


                       My right hand, who speaks much, yet knows little
                       With acoustic guitar on his back, and book in hand,
                       He longs to understand the world,


                       He who looks to the towering trees And longs to
                       attain serenity Taking solace in solitude of
                       nature’s grace Bathed in sunlight and lakewater


                # ⚓ Nepa_Cinerea⠀⇛


                       I spotted a strange creature trying his damnedest
                       to enter the Baltic Sea on a beach in the Swedish
                       archipelago yesterday. ObsIdentify came to the
                       rescue as I had never seen nor heard of a Nepa
                       cinerea or "water scorpion".


          o § Technology and Free Software⠀➾


                # ⚓ You're_making_me_crazy⠀⇛


                       Every year the Stack Exchange corporation publishes
                       their annual Stack Overflow Developer Survey—one of
                       if not the most comprehensive surveys of software
                       developers available—and I read it as a sort of
                       self-flagellation ritual. If you don't partake you
                       probably won't be surprised to learn that over the
                       last few years AI and AI-driven software
                       development has taken center stage.


                # § Internet/Gemini⠀➾


                      # ⚓ Hooked_on_Cosmic_Voyage⠀⇛


                             Seems I got really hooked on gemini://
                             cosmic.voyage, the basis for communication
                             between outposts (or space ships or
                             collonies) is Quantum Entanglement
                             Communicator (QEC). There are some very
                             interesting interconnections happening there.
                             Take a look with me at some of the exchanges
                             - I'm only attaching small fragments.


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


    * Microsoft_Will_Continue_Resorting_to_Crimes_in_Order_to_Keep_GNU/Linux
      Usage_Down
    * PCLinuxOS_Had_Functional_Backups_Before_the_House_Fire,_the_Site_Will_be
      Restored_in_New_Webhost



                    ䷩ 𝚕𝚒𝚗𝚎 6861

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 30/07/2025: Watson’s List of
Limits, Lysenko 2000⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇OpenBSD_pump⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal/Opinions
          o Politics_and_World_Events
    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ 🔤SpellBinding:_ACINOTX_Wordo:_ARISE⠀⇛


                # ⚓ Watson’s_List_of_Limits⠀⇛


                # ⚓ rose_quartz_singing_bowl⠀⇛


                       listening to someone play a rose quartz singing
                       bowl this morning -- it's a nice way to wake up
                       although it's interpreted through an evil streamer
                       (spotify). if i lived alone, I'd just start
                       collecting singing bowls, rollout of bed, and play
                       them for a bit before starting my day. I read this
                       story about david geffen's spicy divorce, which was
                       partially about how he met his ex on seeking. for
                       context, david geffen was one of the wealthiest and
                       perhaps most overtly abusive guys in the music
                       industry. the fact that he used seeking was kind of
                       astonishing to me. i tried to use it before in the
                       converse situation, but always chickened out. but i
                       think as I near having to pay a towering amount of
                       debt, it seems tempting to try again. mostly i'd
                       like to find someone whose fetish is treating me
                       like a high-end therapist and then paying me like a
                       high-end therapis† who doesn't take insurance. he'd
                       just tell me his ails over zoom & i'd be like, "how
                       does that make you feel?"... my last therapist
                       seemed to get off on talking to me & then I soft
                       ghosted him after he said, "I think next time we
                       should talk about OUR relationship." nobody thought
                       this was funny except me. there's a lot more to say
                       about that but i'll keep it offline.


                # ⚓ The_woman_who_pledged_zero⠀⇛


                # ⚓ a_home_beneath_the_florals⠀⇛


                       I dress in florals


                       a lush meadow for you to dive into


                       and disappear


          o § Politics and World Events⠀➾


                # ⚓ Lysenko_2000⠀⇛


                       Trofim Lysenko was a guy many years ago with very
                       wrong-headed ideas on how nature worked; would’ve
                       been fine if he had done smaller trial runs but
                       unfortunately he had the ear of the men in power
                       and created mass starvation and ecological
                       disaster.


                       I was talking to someone the other week who was a
                       staunch believer in capitalism to the point that
                       rather than see any change, any regulation of
                       fossil fuels, he said “I’d rather take my chances
                       with climate change”. Few things are so harrowing
                       and distressing to me as people understimating the
                       problem. I know that people getting overwhelmed by
                       hopelessness is a real phenomenom but I run in to
                       way more often people who have the opposite
                       problem; they don't see how serious and * the
                       stakes are.


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


    * Riot_for_peace_&_Love:_Catholic_Influencers_and_Digital_Missionaries
      welcome_Jubilee_of_Youth
    * Links_30/07/2025:_Climate_Calamities_Highlighted,_Kyrgyzstan_Crackdown_on
      Expression/Freedoms



                    ䷩ 𝚕𝚒𝚗𝚎 6980

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 30/07/2025: Climate Calamities
Highlighted, Kyrgyzstan Crackdown on Expression/
Freedoms⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Crypto_bots⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Career/Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
                # Social_Control_Media
          o Security
                # Integrity/Availability/Authenticity
                # Confidentiality
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
                # Misinformation/Disinformation/Propaganda
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Adam_Young:_Memorizing_Chord_Changes⠀⇛


                 I have been working on memorizing chords for a bunch of
                 Standards and originals. It helps tremendously. A couple
                 things that have worked for me: [...]


          o § Science⠀➾


                # ⚓ Science Alert ☛ 4,000-Year-Old_Handprint_Discovered_on
                  Ancient_Egyptian_Artifact⠀⇛


                       "You can see all the fingers, and also where the
                       heel of the hand rested."


                # ⚓ Science Alert ☛ Gold_Does_Something_Unexpected_When
                  Superheated_Past_Its_Melting_Point⠀⇛


                       Pushing the limits.


          o § Career/Education⠀➾


                # ⚓ The Straits Times ☛ South_Korea_to_grant_all_pre-schoolers
                  universal_access_to_education_by_2027⠀⇛


                       The new plan aims to significantly reduce the
                       financial burden on families.


                # ⚓ New York Times ☛ University_of_California_Settles_With
                  Jewish_Students_Over_U.C.L.A._Protests⠀⇛


                       Jewish students and a professor said the university
                       had allowed a hostile protest. After the settlement
                       was announced, the Department of Justice separately
                       said it had found the university violated civil
                       rights laws.


          o § Hardware⠀➾


                # ⚓ Tom's Hardware ☛ ‘World’s_smallest_defective_chip_maker
                  Intel_Core_Ultra-powered_Mini_PC’_crown_claimed_by_fanless
                  Aaeon_PICO-MTU4-SEMI_—_just_43mm_high_and_0.44_liters_in
                  size⠀⇛


                       The tiny new Aaeon PICO-MTU4-SEMI is claimed to be
                       the “world’s smallest defective chip maker Intel
                       Core Ultra-powered Mini PC.”


                # ⚓ Tom's Hardware ☛ U.S._semiconductor_design_company_fined
                  $140_million_over_China_dealings_—_sold_software_to_a
                  military_institution_thought_to_be_conducting_nuclear
                  explosion_simulations⠀⇛


                       Cadence admits to selling EDA tools to sanctioned
                       entities from 2015 to 2020.


                # ⚓ Hackaday ☛ 2025_One-Hertz_Challenge:_Fixing_The_Clock_That
                  Once_Synced_The_World⠀⇛


                       The HP 115BR is not one of the most well-known
                       products from Hewlett-Packard. And yet, it was
                       remarkably important nonetheless. This hardware
                       once synced time around the world. Now, for our
                       2025 One-Hertz Challenge, [curiousmarc] has taken
                       on the job of restoring it. 


                # ⚓ Hackaday ☛ ATtiny-Powered_Business_Card_Plays_Cracktro
                  Hits⠀⇛


                # ⚓ Hackaday ☛ Power_Line_Patrols:_The_Grid’s_Eye_In_The_Sky⠀⇛


                       Those of us who like to monitor air traffic with
                       ADS-B aggregators such as FlightAware and ADS-
                       B Exchange tend to see some interesting flight
                       paths. I’m not talking about the truly ambitious
                       pictures drawn by pilots, or even the more ribald
                       ones, but rather flights that follow paths that
                       seem to make little sense from either a commercial
                       or leisure standpoint.


                # ⚓ Hackaday ☛ 2025_One_Hertz_Challenge:_Precise_Time_Ref_Via_1
                  Pulse-Per-Second_GPS_Signal⠀⇛


                       Our hacker [Wil Carver] has sent in his submission
                       for the One Hertz Challenge: Precise Time Ref via 1
                       Pulse-Per-Second GPS Signal.


                # ⚓ Hackaday ☛ Casting_Meteorite-like_Materials⠀⇛


                       From the outside, iron meteorites tend to look like
                       formless, rusted lumps of metal, which is why
                       museums often polish and etch sections to show
                       their interior structure. This reveals their
                       Widmanstätten patterns, a latticework structure of
                       parallel iron-nickel intermetallic crystals which
                       forms over millions of years of very slow
                       solidification. Inspired by this, [Electron
                       Impressions] created his own metal composition
                       which forms similar patterns on a much-faster-than-
                       geological time scale.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Pro Publica ☛ Investigation_Underway_After_Two_Women_Fell
                  Ill_at_RAADFest,_a_Las_Vegas_Anti-Aging_Conference⠀⇛


                       They went to a Las Vegas conference this month that
                       promised pathways to an “unlimited lifespan.” But
                       at least two attendees left in ambulances and were
                       hospitalized in critical condition, requiring
                       ventilators to breathe.


                       The two women, who are recovering, fell ill after
                       receiving peptide injections at a conference booth.
                       The doctor who ran the booth was a Los Angeles
                       physician specializing in “age reversal” therapies
                       who did not have permission to practice medicine or
                       dispense prescriptions in Nevada. Public health
                       investigators are trying to determine if anyone
                       else who attended the Revolution Against Aging and
                       Death Festival experienced a similar illness.


                # ⚓ Science Alert ☛ Sleepiness_Could_Be_Triggered_by_a_Power
                  Overload_in_Our_Brain⠀⇛


                       Lights out.


                # ⚓ Federal News Network ☛ The_director_of_the_NIH_on_growing
                  controversy_over_grant_terminations,_the_Bethesda
                  Declaration,_and_what_it_will_take_to_make_America_healthy⠀⇛


                       "We haven't yet achieved the mission of the NIH,
                       which is research that improves the health and
                       longevity of the American people," Jay Bhattacharya
                       said.


                # ⚓ The Straits Times ☛ South_Koreans_live_longer_but_suicide
                  rate_remains_highest_among_OECD_countries⠀⇛


                       Since 2003, South Korea has topped OECD's list in
                       suicide mortality.


                # ⚓ Latvia ☛ Daugavpils_hospital_to_stop_funding_drunk_tank⠀⇛


                       Daugavpils City Council has stopped funding the 24-
                       hour sobering-up service at the city hospital
                       because it has become too expensive, Latvian Radio
                       reported on 30 July.


                # ⚓ New York Times ☛ Top_F.D.A._Official_Resigns_Under
                  Pressure⠀⇛


                       After turning down several new drugs and
                       restricting use of another, Dr. Vinay Prasad drew
                       the ire of the right-wing influencer Laura Loomer
                       and others.


                # ⚓ The Straits Times ☛ ‘Putting_food_on_table’_outweighs
                  health_risks_for_Philippine_e-waste_dismantlers⠀⇛


                       Work frequently involves burning away rubber wire
                       casings, releasing a toxic brew of chemicals.


                # ⚓ The Straits Times ☛ Australia_widens_teen_social_control
                  media_ban_to_YouTube,_scraps_exemption⠀⇛


                       Research found 37 per cent of children aged 10 to
                       15 reported seeing harmful content on the platform.


                # ⚓ Digital Music News ☛ Dihydroxyacetone_Man_Refers_FireAid
                  ‘Scam’_to_DOJ_Prosecutors_as_Questions_Continue_Over_$100
                  Million_Fund_Distributions⠀⇛


                       Hell Toupée has referred the FireAid charity drive
                       to the Department of Justice (DOJ) for
                       investigation amid public concern that the funds
                       raised have not reached their intended recipients.
                       This referral follows a formal request from
                       California Rep. Kevin Kiley, who confirmed the
                       referral on Ex-Twitter yesterday.


                # ⚓ Latvia ☛ Strawberry_season_grinds_to_a_halt_in_Latvia⠀⇛


                       This year, the strawberry season is almost over,
                       but raspberries and other berries are filling the
                       market. The strawberry season has not been easy,
                       with some growers admitting that the excessive
                       humidity has also affected the harvest, as well as
                       the seasonal lack of workforce, Latvian Radio
                       reported on 30 July.


                # ⚓ The Straits Times ☛ HPV-linked_throat_cancer_on_the_rise
                  among_South_Korean_men⠀⇛


                       Medical experts have warned that HPV can also cause
                       a type of cancer which especially affects men.


                # ⚓ The Straits Times ☛ Malaysia_may_bar_those_under_13_from
                  having_social_control_media_accounts,_says_minister⠀⇛


                       He says protecting children must be a shared
                       responsibility of the govt, social control media
                       platforms and parents.


                # ⚓ The Straits Times ☛ Malaysia_says_study_needed_before
                  classifying_etomidate_as_a_dangerous_drug⠀⇛


                       The move follows reports of deaths caused by
                       etomidate in Singapore.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_steps_up_border_measures
                  against_mosquito-borne_chikungunya_fever_as_Guangdong_faces
                  outbreak⠀⇛


                       Hong Kong health authorities have announced
                       tightened border control measures to prepare for
                       imported cases of chikungunya fever, as mainland
                       China is battling an outbreak of the mosquito-borne
                       disease.


          o § Proprietary⠀➾


                # § Social Control Media⠀➾


                      # ⚓ The Straits Times ☛ Outrage_in_China_after
                        exploitative_images_of_Chinese_women_shared_in_Telegram
                        groups⠀⇛


                             Sexually exploitative images of Chinese women
                             were shared in encrypted Telegram chat groups
                             with hundreds of thousands of users, Chinese
                             media reported, triggering widespread outrage
                             online.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ The Straits Times ☛ 139_Malaysians_stranded_abroad
                        due_to_job_scams,_Parliament_told⠀⇛


                             Of the 533 Malaysians rescued, 431 were male
                             while 102 were female.


                # § Confidentiality⠀➾


                      # ⚓ Security Week ☛ Tea_App_Takes_Messaging_System
                        Offline_After_Second_Security_Issue_Reported⠀⇛


                             Tea has said about 72,000 images were leaked
                             online in the initial incident, and another
                             59,000 images publicly viewable in the app
                             from posts, comments and direct messages were
                             also accessed.


          o § Defence/Aggression⠀➾


                # ⚓ Pro Publica ☛ Albert_Jesús_Rodríguez_Parra_Was_Sent_to
                  CECOT_Days_After_Appearing_in_a_Chicago_Immigration_Court⠀⇛


                       In the early days of President Donald Trump’s
                       second term, I spent a few weeks observing
                       Chicago’s immigration court to get a sense of how
                       things were changing. One afternoon in March, the
                       case of a 27-year-old Venezuelan asylum-seeker
                       caught my attention.


                       Albert Jesús Rodríguez Parra stared into the camera
                       at his virtual bond hearing. He wore the orange
                       shirt given to inmates at a jail in Laredo, Texas,
                       and headphones to listen to the proceedings through
                       an interpreter.


                # ⚓ The Revelator ☛ 50_Years_Later:_The_Vietnam_War’s_Enduring
                  Effect_on_the_Tiger_Trade⠀⇛


                # ⚓ New York Times ☛ The_Familiar_Suicide_and_Final_Wish_of_the
                  N.Y.C._Gunman⠀⇛


                       Shane Tamura is not the first former football
                       player to shoot himself in the chest and request
                       that his brain be examined.


                # ⚓ The Strategist ☛ Friends_to_all:_Papua_New_Guinea_seeks
                  equal_status_in_partnerships⠀⇛


                       Amid rising strategic competition, the pursuit of a
                       security treaty and a long-standing shared history
                       have made Australia the security partner of choice
                       for Papua New Guinea.


                # ⚓ The Straits Times ☛ Thailand_accuses_Cambodia_of_second
                  ceasefire_violation_in_two_days⠀⇛


                       The allegations come less than two days after both
                       governments agreed to a ceasefire brokered in
                       Malaysia.


                # ⚓ The Straits Times ☛ China_accuses_Taiwan_of_forcing_its
                  people_to_be_‘cannon_fodder’⠀⇛


                       China described Taiwan's recent “Han Kuang”
                       military drills as “merely a show”.


                # ⚓ Hong Kong Free Press ☛ US_says_Hell_Toupée_has_‘final_call’
                  on_China_trade_truce⠀⇛


                       China and the United States agreed Tuesday to hold
                       further talks on extending their tariff truce, but
                       a top US trade official stressed that President The
                       Insurrectionist would make any “final call.”


                # ⚓ Marcy Wheeler ☛ A_Dossier_Steal:_HPSCI_Expertly_Discloses
                  Their_Own_Shoddy_Cover-Up⠀⇛


                       Most of the HPSCI Report complaints about the
                       Steele dossier object that the Intelligence
                       Community Assessment did not include details the
                       committee itself discovered much later. But as with
                       the main part of the report, their OWN silences -
                       - about Paul Manafort, about Oleg Deripaska -- are
                       the real story.


                # ⚓ Tom's Hardware ☛ China_forms_Hey_Hi_(AI)_alliances_to_cut
                  U.S._tech_reliance_—_Huawei_among_companies_seeking_to_create
                  unified_tech_stack_with_domestic-powered_standardization⠀⇛


                       Chinese Hey Hi (AI) hardware and software
                       developers form alliances to develop Hey Hi (AI)
                       standards to compete against American Hey Hi (AI)
                       technologies and deploy Hey Hi (AI) across a broad
                       set of applications.


                # ⚓ New York Times ☛ North_Korea_Says_Kim’s_Relations_With
                  Convicted_Felon_‘Not_Bad,’_but_Stands_Firm_on_Nukes⠀⇛


                       The country appeared to signal an openness to
                       talks, but said it must be recognized as a nuclear
                       power and would not discuss abandoning its arsenal.


                # ⚓ The Straits Times ☛ South_Korean_prosecutors_seek_new
                  warrant_to_question_ex-president_Yoon⠀⇛


                       This comes after he refused to appear at his
                       summons multiple times.


                # ⚓ The Straits Times ☛ ‘Will_Taiwanese_be_ready?’:_Taiwan_TV
                  drama_confronts_fear_of_a_Chinese_invasion⠀⇛


                       Zero Day Attack is the first Taiwanese drama to
                       portray China’s invasion of the territory.


                # ⚓ RFERL ☛ Serbia-China_Military_Drills_End_Amid_EU,_US
                  Objections⠀⇛


                       A Serbian military special operations brigade has
                       completed joint training with a Chinese brigade in
                       China despite strong objections from the European
                       Union and the United States.


                # ⚓ France24 ☛ US-China_trade_talks_in_Sweden_end_without_truce
                  extension⠀⇛


                       Two days of talks between delegations from Beijing
                       and Washington ended without an extension of the
                       tariff truce set to expire on August 12. US
                       Treasury Secretary Scott Bessent said that The
                       Insurrectionist still needs to be briefed on the
                       discussions. Also, the International Monetary Fund
                       has revised its global growth outlook upward, as
                       Convicted Felon’s tariff policies are scaled back.
                       And, Lesotho's textile industry remains on edge
                       ahead of the August 1 tariff deadline.


                # ⚓ Atlantic Council ☛ Safeguarding_Uyghur_human_rights:_The_US
                  should_leverage_economic_statecraft_tools_to_end_Uyghur
                  forced_labor⠀⇛


                       Through sanctions and the adoption of anti-forced
                       labor legislation, the United States has led the
                       global effort to combat China’s forced labor
                       practices. While these measures have moved the
                       needle in the fight against forced labor,
                       widespread tariffs and the absence of new punitive
                       measures targeting forced labor may cause progress
                       to stagnate.


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


                      # ⚓ Meduza ☛ Kremlin_has_‘taken_note’_of_Trump’s_decision
                        to_shorten_ceasefire_deadline,_spokesperson_says_—
                        Meduza⠀⇛


                      # ⚓ Latvia ☛ Rīga's_Eastern_Hospital_launches_new
                        catering_tender⠀⇛


                             The caterer of Riga East Clinical University
                             Hospital (RAKUS) has corrected most of the
                             hygiene violations but the hospital has
                             launched a new catering tender worth €25
                             million, Latvian Radio reports on 29 July.


                      # ⚓ Latvia ☛ Defence_industry:_Latvia_still_leads_in
                        drone_production⠀⇛


                             Competition in the drone industry in Europe
                             is growing - other Member States have also
                             stepped up, Elīna Egle, head of the Latvian
                             Security and Defence Industry Federation,
                             told Latvian Radio's ‘Labrīt’ programme on
                             Tuesday, 29 July.


                      # ⚓ Meduza ☛ Putin’s_security_team_spotted_carrying
                        handheld_interceptor_drones_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_strike_hits_prison_in_Zaporizhzhia
                        region,_killing_at_least_16,_Ukrainian_official_says_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Cyberattack_may_have_cost_Russia’s_Aeroflot
                        millions_of_dollars_in_a_single_day,_experts_say_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Assessing_Aeroflot’s_aftermath_Ukrainian_and
                        Belarusian_hackers_claim_a_‘strategic_blow’_to_Russia’s
                        flagship_airline,_but_the_dust_has_yet_to_settle_—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ Trump_says_Ukrainian_refugees_can_stay_in
                        U.S._until_the_end_of_the_war_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_airstrike_hits_Ukrainian_training
                        facility,_killing_3_soldiers_and_injuring_18_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_couple_convicted_of_treason_for
                        photographing_military_sites_near_Moscow,_sentenced_to
                        17_and_15_years_in_prison_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ First_tsunami_wave_strikes_Russia’s_Pacific
                        Coast_following_8.8-magnitude_earthquake_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_government_stops_publishing_data_on
                        crime-related_deaths_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ His_days_are_numbered_—_we’ve_been_saying_it
                        for_years_In_press_releases_since_2023,_Russia’s
                        Foreign_Intelligence_Service_has_predicted_a_Western
                        coup_against_Zelensky._Meduza_reviews_the_timeline._—
                        Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘Appeasement_of_the_aggressor’:_Sanctioned
                        Russian_Federation_Council_speaker_attends_global
                        summit_in_Switzerland,_uses_platform_to_repeat_Kremlin
                        war_narrative_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ ‘Too_much_is_slipping_through’:_Russia’s
                        crackdown_on_leaked_data_complicates_life_for
                        criminals,_anti‑corruption_activists,_and_private
                        snoops_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Russian_governor_asks_for_‘understanding’_as
                        Krasnoyarsk_region_enters_fourth_day_without_mobile
                        Internet_—_Meduza⠀⇛


                      # ⚓ Meduza ☛ Head_of_Russia’s_space_agency_travels_to
                        U.S._for_first_meeting_with_NASA_leadership_in_seven
                        years_—_Meduza⠀⇛


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ CS Monitor ☛ What_20_years_of_investigations_tell_us_about
                  the_Epstein_files⠀⇛


                       The Forrest Dump administration faces pressure to
                       release additional files from investigations of
                       sex-offender Jeffrey Epstein. Here’s what’s known
                       from two decades of lawsuits and what could come
                       from efforts to reveal more.


          o § Environment⠀➾


                # ⚓ The Straits Times ☛ Taiwan's_President_Lai_postpones
                  Americas_visit_after_typhoon⠀⇛


                       Taiwan's President Lai Ching-te will delay an
                       expected trip to remaining allies in the Americas
                       that would have taken place next month, embassy
                       officials told Reuters on Tuesday, due to damages
                       from a typhoon and as the island faces more
                       torrential rains.


                # ⚓ Hong Kong Free Press ☛ 30_dead_as_northern_China_hit_by
                  heavy_rain,_landslides⠀⇛


                       By Peter Catterall Heavy rain in Beijing killed 30
                       people and forced authorities to evacuate tens of
                       thousands as swathes of northern China were lashed
                       by torrential downpours that sparked deadly
                       landslides, state media said Tuesday.


                # ⚓ France24 ☛ China:_Deadly_floods_hit_the_north_of_the
                  country⠀⇛


                       Heavy rain killed more than 30 people and forced
                       authorities to evacuate tens of thousands as swaths
                       of northern China were lashed by torrential
                       downpours that sparked landslides and flooding,
                       state media said on July 29.


                # ⚓ The Straits Times ☛ Extreme_weather_turns_Beijing_into_rain
                  trap;_30_killed,_over_80,000_evacuated⠀⇛


                       The highest death toll was reported in Miyun, a
                       suburban district north-east of the city centre.


                # ⚓ The Straits Times ☛ ‘Once_in_a_hundred_years’:_Villagers
                  clean_up_after_deadly_China_floods⠀⇛


                       Weary locals worked desperately to retrieve what
                       belongings they could find.


                # ⚓ Science Alert ☛ 90_Billion_Liters_of_Water_Punched_Through
                  Greenland's_Ice_Sheet_–_And_Nobody_Noticed⠀⇛


                       The power of water.


                # ⚓ Science Alert ☛ Incredible_Ice_Core_Captures_12,000_Years
                  Of_European_Climate_History⠀⇛


                       All the way back to the last Ice Age.


                # § Energy/Transportation⠀➾


                      # ⚓ France24 ☛ US_proposes_revoking_law_regulating_gas
                        emissions⠀⇛


                             The Forrest Dump administration said on
                             Tuesday it will rescind the long-standing
                             finding that greenhouse gas emissions
                             endanger human health, removing the legal
                             foundation for all U.S. greenhouse gas
                             regulations. If finalized, the repeal would
                             end current limits on greenhouse gas
                             pollution from vehicle tailpipes, power plant
                             smokestacks and other sources, and hamper
                             future U.S. efforts to combat global warming.


                      # ⚓ The Straits Times ☛ South_Korea_launches_joint_probe
                        to_revisit_deadly_2022_Halloween_crowd_crush_in
                        Itaewon⠀⇛


                             The joint investigation team is set to
                             revisit the overall circumstances regarding
                             the incident.


                      # ⚓ The Straits Times ☛ Malaysia_moving_closer_to
                        adopting_nuclear_energy,_says_minister⠀⇛


                             A study found that it has strong potential to
                             serve as a stable, clean and reliable power
                             source.


                # § Wildlife/Nature⠀➾


                      # ⚓ Defence Web ☛ SANDF_soldier_on_border_patrol_trampled
                        to_death_by_elephants⠀⇛


                             A member of the South African National
                             Defence Force (SANDF) deployed on Operation
                             Corona border patrol duties along the border
                             with Zimbabwe has been killed by elephants.


                      # ⚓ Science Alert ☛ Stunning_Dinosaur_Tracks_Appear_to
                        Show_Something_Never_Seen_Before⠀⇛


                             The first evidence of its kind?


                      # ⚓ Science Alert ☛ Yellowstone's_Aspen_Forests_Are
                        Already_Responding_to_The_Return_of_Wolves⠀⇛


                             A success story.


                      # ⚓ Science Alert ☛ Researchers_Identified_New_Blood
                        Group_After_50_Year_Mystery⠀⇛


                             A medical breakthrough that could save lives.


                      # ⚓ Science Alert ☛ World's_Smallest_Snake_Rediscovered
                        After_Vanishing_For_Decades⠀⇛


                             Small enough to be mistaken for a worm.


                # § Overpopulation⠀➾


                      # ⚓ The Straits Times ☛ South_Korea’s_population
                        stagnates_despite_number_of_foreign_residents_topping_2
                        million⠀⇛


                             The South Korean national population has now
                             decreased for four consecutive years since
                             2021.


                      # ⚓ The Straits Times ☛ China_earmarks_$12.5_billion
                        budget_for_2025_childcare_subsidies⠀⇛


                             China's finance ministry on Wednesday said it
                             had earmarked 90 billion yuan ($12.54
                             billion) as an initial budget for childcare
                             subsidy payments this year, an amount that
                             experts said would probably be insufficient
                             to boost a flagging birth rate.


          o § Finance⠀➾


                # ⚓ The Straits Times ☛ Malaysia_scraps_plan_to_impose_luxury
                  goods_tax⠀⇛


                       But the underlying principle behind it has been
                       incorporated into the revised sales tax framework.


                # ⚓ The Straits Times ☛ China_and_US_still_key_trade_partners,
                  commerce_minister_says⠀⇛


                       US and Chinese officials agreed to seek an
                       extension of their 90-day tariff truce on July 29.


                # ⚓ The Straits Times ☛ China_social_spending_hits_highest
                  level_in_nearly_two_decades⠀⇛


                       China runs a record budget deficit with a focus on
                       boosting consumption to cushion the blow from US
                       tariffs.


                # ⚓ The Straits Times ☛ China’s_top_leaders_vow_support_for
                  economy,_crackdown_on_disorderly_competition⠀⇛


                       In the second half of the year, China will keep
                       policy stable while boosting flexibility.


                # ⚓ CS Monitor ☛ Inflation_has_improved_in_Argentina._Why
                  consumers_don’t_feel_a_difference.⠀⇛


                       Inflation in Argentina hit a five year low in May.
                       But Argentines say they don't feel that reflected
                       in their day-to-day consumption.


          o § AstroTurf/Lobbying/Politics⠀➾


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ New York Times ☛ After_Park_Avenue_Shooting,_Anti-
                        Muslim_Disinformation_Spread_Rapidly⠀⇛


                             Once it became clear that the only Muslim
                             involved in the attack was one of the
                             victims, right-wing commentators sought to
                             shift the focus to Zohran Mamdani.


          o § Censorship/Free Speech⠀➾


                # ⚓ The Straits Times ☛ Kyrgyzstan_bans_online_porn_in
                  crackdown_on_internet_freedoms⠀⇛


                       Kyrgyzstan has banned access to online pornography
                       and imposed state control over internet traffic
                       under new laws signed by President Sadyr Japarov,
                       his office said on Tuesday.


                # ⚓ AccessNow ☛ #KeepItOn:_Nepal’s_Telegram_ban_is_a_dangerous
                  escalation_of_digital_censorship⠀⇛


                       Access Now and the #KeepItOn coalition are alarmed
                       by the Government of Nepal’s decision to ban the
                       popular messaging application Telegram.


                # ⚓ AccessNow ☛ #KeepItOn:_Nepal_authorities_must_reverse
                  nationwide_Telegram_ban_and_uphold_human_rights⠀⇛


                       Access Now and the #KeepItOn coalition urgently
                       demand that the Government of Nepal immediately
                       reverse its decision to block messaging platform
                       Telegram across the country.


          o § Civil Rights/Policing⠀➾


                # ⚓ Citizen Lab ☛ Targeted_Across_Borders:_Digital
                  Transnational_Repression,_Gender_Dimensions,_and_the_Role_of
                  Host_States⠀⇛


                       In a new article published in the Georgetown
                       Journal of International Affairs, the Citizen Lab’s
                       Noura Aljizawi, Siena Anstis, and Gözde Böcü
                       investigate the practice of transnational
                       repression in its physical and digital forms.


                # ⚓ Michael Geist ☛ The_Law_Bytes_Podcast_Law_Society_of
                  Ontario_CPD_Professionalism_Pack⠀⇛


                       Regular listeners know that my Law Bytes podcast
                       addresses a wide range of digital policy issues.
                       Some of the episodes venture into issues related to
                       technology and the practice of law, notably
                       including the impact of artificial intelligence,
                       new technologies, and open access to law. I
                       recently sought accreditation for Professionalism
                       Hours credit from the Law Society of Ontario for
                       those episodes.


                # ⚓ The Straits Times ☛ Don’t_call_them_‘hey’:_South_Korea
                  widens_campaign_to_address_migrant_workers_by_name⠀⇛


                       The campaign is part of broader efforts to promote
                       a culture of respect toward various ethnic groups.


                # ⚓ JURIST ☛ Rights_group_calls_on_Pakistan_to_end
                  discrimination_against_sanitation_workers⠀⇛


                       Amnesty International called on Pakistan’s
                       authorities on Tuesday to end the systemic
                       discrimination and human rights violations against
                       sanitation workers in the country, following the
                       release of a new report. The organization
                       emphasized how these abuses violate Pakistan’s
                       obligations under international law and urged
                       authorities to amend existing laws to align with
                       international norms.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Unicorn Media ☛ Power_Outage_at_Newark_Data_Center_Disrupts
                  Linode,_Took_LWN_Offline⠀⇛


                       When one of open source’s favorite cloud hosts went
                       dark, even LWN.net blinked. Here’s what
                       happened—and why it matters.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ Patent_Troll_Fumbles_Cases_Against_NFL_Teams⠀⇛


                       Earlier this month, a particularly aggressive non-
                       practicing entity (NPE) – TicketMatrix LLC –
                       quietly dropped a pair of patent monopoly
                       infringement lawsuits against two National Football
                       League teams, the Kansas City Chiefs and the Dallas
                       Cowboys.


                # ⚓ JUVE ☛ Showdown_in_Munich:_Federal_Patent_Court_revokes
                  Xarelto_patent [Ed: EPO gave fake patents again]⠀⇛


                       The patent monopoly court’s ruling deviates from
                       its qualified opinion given in 2024, where the
                       judges had assumed the patent’s validity. The
                       Federal Patent Court now revoked EP 1 845 961 due
                       to lack of inventive step (case ID: 3Ni 11/22).


                # ⚓ Dennis Crouch/Patently-O ☛ The_New_Convicted_Felon-Lutnick
                  Patent_Tax:_Trading_Innovation_Policy_for_Deficit_Reduction⠀⇛


                       The Forrest Dump administration is reportedly
                       considering a radical transformation of the US
                       patent monopoly system that would replace the
                       current flat-fee maintenance structure with a
                       percentage-based "property tax" on patent monopoly
                       value, according to a recent Wall Street Journal
                       report. Howard Lutnick and his Commerce Department
                       team are discussing a tax of between 1% and 5% of
                       overall patent monopoly value annually, a shift
                       that could dramatically increase costs for certain
                       patent monopoly holders while making the US an
                       international anomaly among major patent monopoly
                       systems.


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ Casalonga_opens_in_Düsseldorf_with_Fieldfisher
                        litigation_team [Ed: UPC is illegal and Fieldfisher is
                        a malicious mafia that sent Techrights baseless threats
                        on behalf of actual criminals at the EPO.]⠀⇛


                             Benjamin Grzimek (53) from Fieldfisher’s
                             Düsseldorf office is now launching a
                             Düsseldorf office on behalf of Casalonga. The
                             litigator will be joined by his two existing
                             associates. Grzimek complements Casalonga’s
                             mixed team with his proven experience in
                             electronics patent monopoly litigation,
                             particularly SEP actions for NPEs.


                      # ⚓ JUVE ☛ Edwards_Lifesciences_prevails_in_heart_valve
                        dispute_at_the_UPC [Ed: Totally illegal and
                        unconstitutional court, propped up in exchange for
                        money by this Web site]⠀⇛


                             Edwards Lifesciences filed UPC infringement
                             proceedings against Meril before the Nordic-
                             Baltic division in Stockholm concerning EP 3
                             769 722 and EP 2 628 464. The US medical
                             device company claims Meril infringes these
                             patents with its Myval Navigator range of
                             heart valves.


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ TTAB_Allows_Amendment_of_Admission_Responses
                  but_Grants_Motion_for_Summary_Judgment_for_Lack_of_Bona_Fide
                  Intent⠀⇛


                       The Board granted Opposer Champion's motion for
                       summary judgment, finding that Applicant Derek
                       Buzak lacked a bona fide intent to use the proposed
                       mark I FEEL LIKE A CHAMPION "Sports shirts" as of
                       his filing date. Buzak provided no documentation
                       showing "any concrete steps taken or plans made to
                       actually use his mark contemporaneous with filing
                       his involved application," and there was no
                       explanation as to how he had the capacity to
                       produce the identified goods. ABG-Champion_LLC_v.
                       Derek_Buzak, Opposition No. 91288945 (July 23,
                       2025) [not precedential].


                # ⚓ TTAB Blog ☛ On_Remand,_TTAB_Sustains_Cognac_Institute's
                  Section_2(d)_Opposition_to_COLOGNE_&_COGNAC_ENTERTAINMENT⠀⇛


                       On remand from the CAFC, the Board sustained this
                       opposition to registration of the mark shown below,
                       for musical recordings and production services,
                       finding confusion likely with Opposer's common-law
                       certification mark COGNAC for brandy. The Federal
                       Circuit found error in the Board’s likelihood of
                       confusion analysis as to the first, second, third
                       and fifth DuPont factors, and so it vacated the
                       Board's original decision and sent the case back to
                       the Board. [TTABlogged here]. Following the CAFC's
                       directives, the Board found the COGNAC mark to be
                       well-known and strong, the marks more similar than
                       dissimilar [a bit hard to swallow for me - ed.],
                       and the channels of trade and classes of consumers
                       related. Bureau_National_Interprofessionel_du
                       Cognac,_Institute_National_de_Appellations
                       d'Origine_v._Cologne_&_Cognac_Entertainment,
                       Opposition No. 91250532 (July 28, 2025) [not
                       precedential] (Opinion by Judge Thomas W.
                       Wellington).


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Cosynd_Pushes_Into_the_Streaming
                  Platform_Space_with_SoundCloud_Copyright_Tie-Up⠀⇛


                       Cosynd is making moves into the streaming space
                       with a copyright monopoly registration deal for
                       SoundCloud users. Cosynd, a platform for copyright
                       monopoly protection, has announced an expanded
                       collaboration with SoundCloud. The partnership
                       provides SoundCloud users with access to Cosynd’s
                       copyright monopoly registration and ownership
                       tools.


    * Gemini_Links_30/07/2025:_Watson’s_List_of_Limits,_Lysenko_2000
    * Slopwatch:_Google_News_is_Pumping_in_Lots_of_Web_Traffic_Into_Fake_Sites
      That_Say_"Linux"



                    ䷩ 𝚕𝚒𝚗𝚎 8110

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 30/07/2025: Tea Class Action and
Google Killing the Web With Slop⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Jul 30, 2025


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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Career/Education
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
                # Confidentiality
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Overpopulation
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Old VCR ☛ prior-art-dept.:_The_hierarchical_hypermedia_world_of
            Hyper-G⠀⇛


                 Because Hyper-G is a stateful protocol, enveloping the
                 backend is a process providing the session layer called
                 hgserver (no relation to Mercurial). This talks directly
                 to other Hyper-G servers (using TCP port 418), and also
                 directly to clients with port 418 as a control connection
                 and a dynamically assigned port number for document
                 transfer (not unlike FTP). Since links are bidirectional,
                 Hyper-G servers contact other Hyper-G servers to let them
                 know a link has been made (or, possibly, removed), and
                 then those servers will send them updates.


          o ⚓ Howard Oakley ☛ Paintings_of_Dante’s_Inferno:_1_To_the_gates_of
            Hell⠀⇛


                 Dante’s Inferno opens just before dawn on Good Friday in
                 1300, when the author is in mid-life, and wandering lost
                 in a dark wood.


          o § Career/Education⠀➾


                # ⚓ CS Monitor ☛ Social_media_self-control_among_students⠀⇛


                       With a new academic year due to start in the United
                       States, states and districts are seeking to manage
                       students’ cellphone use during the school day.
                       Proposals range from developing usage guidelines to
                       implementing outright bans.


                # ⚓ Ben Werdmuller ☛ If_I_ran_my_life⠀⇛


                       For the final post in the series, I want to turn
                       inward and ask a more personal question. Knowing
                       what I know now, with all the experiences I have,
                       how would I run my own life?


                       The question might seem absurd, but here’s what I
                       mean. Our lives are a product of a combination of
                       our experiences, our context, decisions we make for
                       ourselves, and decisions that are made for us: they
                       evolve naturally as we live. We have the ability to
                       design aspects of how we live, but others fall into
                       place in ways that aren’t fully in our control.
                       That’s not bad: it’s how life works, no matter how
                       intentionally we travel through it.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ [Old] US National Library of Medicine ☛ Effect_of_forest
                  bathing_trips_on_human_immune_function⠀⇛


                       These findings indicate that forest bathing trips
                       increase NK activity, which was mediated by
                       increases in the number of NK cells and the levels
                       of intracellular anti-cancer proteins (Fig. 10).
                       Phytoncides released from trees and the decreased
                       production of stress hormones may partially
                       contribute to the increased NK activity.


          o § Proprietary⠀➾


                # ⚓ The Register UK ☛ CISA_to_release_long-buried_US_telco
                  security_report⠀⇛


                       The release of an unclassified, three-year-old
                       document sounds like a minor deal. But this report
                       has been the bane of US Senator Ron Wyden's (D-OR)
                       existence for years, and has put the nomination of
                       would-be CISA boss Sean Plankey in limbo for
                       months.


                # ⚓ Terence Eden ☛ I’m_never_going_back_to_Matrix⠀⇛


                       It was dead. Even among the most seasoned geeks on
                       the planet, most people preferred to use other
                       services like Signal, Telegram, and Slack. Why?
                       Because those other tools actually work.


                # § Artificial Intelligence (AI) / LLM Slop / Plagiarism⠀➾


                      # ⚓ Tech Central (South Africa) ☛ Google's_new_AI_trick
                        is_killing_the_web⠀⇛


                             Then again, to describe those billions as
                             “users”, as parent company Alphabet did when
                             announcing its quarterly earnings last week,
                             is perhaps disingenuous. No one consciously
                             uses AI Overviews — it’s just there when
                             users perform a regular search on Google,
                             something billions of them have done several
                             times a day for two decades.


                             That’s one key advantage Google has over its
                             competitors: people already associate the
                             service with finding things out. The company
                             has every right to capitalise on that
                             reputation, one it built off the back of
                             genuine innovation and quality (though,
                             admittedly, it was later solidified with
                             illegal multibillion-dollar deals to prevent
                             competition).


                      # ⚓ India Times ☛ With_AI_plan,_Trump_keeps_chipping_away
                        at_a_foundational_environmental_law⠀⇛


                             And that meant taking aim at the National
                             Environmental Policy Act - a 55-year-old,
                             bedrock law aimed at protecting the
                             environment though a process that requires
                             agencies to consider a project's possible
                             impacts and allows the public to be heard
                             before a project is approved. Data centers,
                             demanding vast amounts of energy and water,
                             have aroused strong opposition in some
                             communities.


                # § Social Control Media⠀➾


                      # ⚓ Omicron Limited ☛ Women_politicians_receive_more
                        identity-based_attacks_on_social_media_than_men,_study
                        finds⠀⇛


                             This study used a machine learning approach
                             to analyze over 23 million tweets addressed
                             to politicians in Germany, Spain, the United
                             Kingdom, and the United States, to determine
                             the degree of incivility that female
                             politicians face. Women in politics
                             frequently report serious online harassment,
                             yet the extent of this harassment and how it
                             compares to harassment experienced by men
                             remains understudied, or has been assessed in
                             surveys with varying response rates. This new
                             research aims to address this gap.


                # § Windows TCO / Windows Bot Nets⠀➾


                      # ⚓ The Record ☛ Minnesota_governor_activates_National
                        Guard_after_cyberattack_on_state_capital⠀⇛


                             Saint Paul, the state’s capital, is home to
                             more than 300,000 people — making it one of
                             the largest U.S. cities to face a cyberattack
                             in 2025.


                             Mayor Melvin Carter said during a press
                             conference on Tuesday that the city is most
                             concerned about the data it holds on
                             government employees, arguing that the city
                             does not carry much information on city
                             residents.


                      # ⚓ SANS ☛ Parasitic_Sharepoint_Exploits⠀⇛


                             Last week, newly exploited SharePoint
                             vulnerabilities took a lot of our attention.
                             It is fair to assume that last Monday (July
                             21st), all exposed vulnerable SharePoint
                             installs were exploited. Of course, there is
                             nothing to prevent multiple exploitation of
                             the same instance, and a lot of that
                             certainly happened. But why exploit it
                             yourself if you can just take advantage of
                             backdoors left behind by prior exploits? A
                             number of these backdoors were widely
                             publicised. The initial backdoor
                             "spinstall0.aspx", was frequently observed
                             and Microsoft listed various variations of
                             this filename [1].


                             Since then, we have observed attempts to
                             access these backdoors. The scans started a
                             week ago, just as the exploits (and the name
                             of the backdoors) became better known.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ The Washington Post ☛ How_to_opt_out_of_TSA_facial
                        recognition_at_the_airport⠀⇛


                             I’ll explain your rights with facial
                             recognition scans at security and other
                             airport locations. Two years after a U.S.
                             senator said he got pushback for opting out
                             of TSA facial recognition, there remains
                             evidence that the airport scans are optional
                             on paper but not in practice.


                             The TSA didn’t respond to my questions.


                      # ⚓ 404 Media ☛ UK_Users_Need_to_Post_Selfie_or_Photo_ID
                        to_View_Reddit's_r/IsraelCrimes,_r/UkraineWarFootage⠀⇛


                             Several Reddit communities dedicated to
                             sharing news and media from conflicts around
                             the world now require users in the UK to
                             submit a photo ID or selfie in order to prove
                             they are old enough to view “mature” content.
                             The new age verification system is a result
                             of the recently enacted Online Safety Act in
                             the UK, which aims to protect children from
                             certain types of content and hold platforms
                             like Reddit accountable if they don’t.


                      # ⚓ The Record ☛ Wyden_asks_White_House_to_scrutinize_UK
                        surveillance_laws_|_The_Record_from_Recorded_Future
                        News⠀⇛


                             Wyden’s letter makes clear that his concerns
                             extend beyond the specific request to Apple.


                             U.K. surveillance laws could be used to
                             “secretly force U.S. companies to store the
                             data of U.S. users in the U.K., where it
                             could then be seized by the U.K. government,”
                             according to Wyden’s letter.


                             The British government has not denied Wyden’s
                             concerns about whether under its
                             Investigatory Powers Act 2016 (IPA) it can
                             require such U.K.-based storage for newly
                             created data belonging to U.S. users, the
                             letter says.


                      # ⚓ Pivot to AI ☛ Copilot_Vision_AI_sends_your_data_to
                        Microsoft⠀⇛


                             Microsoft swears the data won’t be kept “long
                             term.” However long that is.


                             Copilot Recall is on all the time, but
                             Copilot Vision only switches on when you tell
                             it. Or when you accidentally click on the
                             glasses button.


                      # ⚓ TechRadar ☛ Europol_doesn't_only_want_an_encryption
                        backdoor,_but_also_your_metadata⠀⇛


                             Europol’s 2025 Internet Organized Crime
                             Threat Assessment (IOCTA) indicates E2EE
                             (end-to-end encrypted) apps as an obstacle to
                             investigations
                             The report also calls for better rules on
                             metadata collection and tracking


                      # ⚓ Michael Tsai ☛ UK_Online_Safety_Act⠀⇛


                             “Scope” seems to mean the scope of the Act
                             itself, which is very broad. I guess Ofcom
                             gets to decide what the truth is.


                      # ⚓ BoingBoing ☛ VPN_use_surging_in_UK_after_online
                        censorship_laws_kick_in⠀⇛


                             The so-called "Online Safety Act" does
                             prohibit VPN companies from disclosing that
                             their services can be used to circumvent
                             censorship, but did not otherwise regulate
                             their use. The omnishambles at hand–nothing
                             successfully blocked and everyday Britons
                             learning en masse how to browse more
                             privately–has already got local media vaguely
                             suggesting a VPN ban is now on the table.


                      # ⚓ Wired ☛ Age_Verification_Laws_Send_VPN_Use
                        Soaring—and_Threaten_the_Open_Internet⠀⇛


                             Experts had expected the surge, given that
                             similar trends have been visible in other
                             countries that have implemented age check
                             laws. But as a new wave of age check
                             regulations debuts, open [Internet] advocates
                             warn that the uptick in use of circumvention
                             tools in the UK is the latest example of how
                             an escalating cat-and-mouse game can develop
                             between people looking to anonymously access
                             services online and governments seeking to
                             enforce content restrictions.


                      # ⚓ The Register UK ☛ Publishers_oppose_W3C_plan_to_kill
                        third-party_cookies⠀⇛


                             Third-party cookies (3PCs) have long posed a
                             privacy problem because they allow
                             organizations with no relationship to web
                             users to track their online browsing
                             activities, often without legitimately
                             obtained consent. While cookie-based tracking
                             of this sort may not involve personally
                             identifiable information (PII), it can be
                             combined with other data sets to identify and
                             profile people.


                # § Confidentiality⠀➾


                      # ⚓ 404 Media ☛ Tea_User_Files_Class_Action_After_Women’s
                        Safety_App_Exposes_Data⠀⇛


                             A user of women’s dating safety app Tea has
                             filed a class action lawsuit after the app
                             repeatedly exposed users’ sensitive data,
                             including selfies, photographs of IDs, and
                             more than a million direct messages sent by
                             users. Both data breaches were first revealed
                             by 404 Media.


          o § Defence/Aggression⠀➾


                # ⚓ CoryDoctorow ☛ Pluralistic:_Boss-politics_antitrust_and_the
                  MAGA_crackup⠀⇛


                       Victory is deadly to any coalition that agrees on
                       what they want to destroy, and violently disagree
                       on what they want to build. Once victory is
                       attained, some of those groups are going to get
                       what they want, which means other groups are going
                       to absolutely eat shit. Worse (for Trumpism) is
                       that his coalition's affect is purely libidinal, a
                       roaring mob of ragged tribes of swivel-eyed loons
                       who believe they are doing battle with the "deep
                       state," "Jewish space-lasers" and "antifa super-
                       soldiers," and are primed to see shadowy cabals
                       everywhere: [...]


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Jacobin Magazine ☛ A_Judge’s_Conflict_of_Interest_Over
                  Jeffrey_Epstein_Documents⠀⇛


                       Preska’s role in the saga is colored by the fact
                       that her spouse is a partner at one of New York’s
                       preeminent Wall Street law firms. Thomas Kavaler is
                       a fifty-year veteran of Cahill Gordon & Reindel, a
                       firm that, by its own description, “has thrived for
                       a century by focusing on the most significant
                       opportunities and complex challenges facing the top
                       financial services firms and other multinational
                       corporations.”


                # ⚓ CS Monitor ☛ What_20_years_of_investigations_tell_us_about
                  the_Epstein_files⠀⇛


                       Here are details about the investigations, and the
                       ambiguities that have only grown more glaring over
                       time.


          o § Environment⠀➾


                # ⚓ Common Dreams ☛ EU_Bowing_to_Trump_Pressure⠀⇛


                       The EU and the U.S. have announced a new trade
                       deal, ending months of a stand-off over tariffs.
                       Under the new deal, the EU has given in to pressure
                       from the Trump Administration to buy $750 billion
                       worth of oil, gas and other energy products from
                       the U.S. over the next three years in exchange for
                       tariff relief.


                # ⚓ Hamilton Nolan ☛ Cheap_Tricks_for_Hard_Problems⠀⇛


                       Fast forward a little further, and there is the
                       looming and very real possibility of a national or
                       global financial crisis precipitated by a rapid
                       devaluation of hundreds of billions or trillions of
                       dollars worth of real estate values. Basically: The
                       insurance crisis, and the associated unwillingness
                       of banks to write mortgages on homes that are
                       effectively uninsurable, reaches a tipping point
                       which causes there to be many more sellers of
                       coastal and other exposed real estate than there
                       are buyers; this causes rapid price drops; this
                       results in both bankrupt homeowners and also in
                       enormous financial losses for the banks holding the
                       loans on all of that property; voila, financial
                       crisis. The number of potential contributing
                       factors to this process are beyond calculation, but
                       the contours of it—and the fact that we are heading
                       towards it—are easy to see. The scariest thing
                       about this particular scenario, to me, is that the
                       tipping point could be reached very fast, and it is
                       impossible to predict what will precipitate it, and
                       when. One big disaster could cause enough of a
                       mental shift in enough homeowners to cause a
                       stampede for the exits, the real estate equivalent
                       of a bank run. Seen from this perspective, owning a
                       home that is highly exposed to climate disaster
                       risk is like holding a speculative asset that could
                       blow up at any moment. Bitcoins and beach houses
                       have more in common than you think.


                # ⚓ YLE ☛ Heatwave_warms_inland_waters_to_record-high
                  temperatures⠀⇛


                       The temperatures of North Savo's Lake Pielavesi and
                       the Pielisjoki River reached record highs last
                       week. On Sunday, the lake's surface temperature
                       measured 26.3 degrees Celsius while the river's
                       water reached 25.2 degrees.


                # § Energy/Transportation⠀➾


                      # ⚓ YLE ☛ Helsinki_goes_a_full_year_without_a_traffic
                        death⠀⇛


                             Helsinki has not recorded a single traffic
                             fatality in the past 12 months, city and
                             police officials confirmed this week.


                # § Overpopulation⠀➾


                      # ⚓ IranWire ☛ Iran’s_Capital_Faces_‘Day_Zero’_Water
                        Crisis_as_Dams_Run_Dry⠀⇛


                             He said, “Although Iranians had managed to
                             survive for thousands of years through
                             groundwater management, modern development -
                             accompanied by social structural changes,
                             marked by growing public distrust toward
                             rulers and various sectors of society - has
                             brought the situation to a point where even
                             if responsible officials give people the most
                             realistic reasons and best suggestions for
                             water conservation, most people have no
                             interest in cooperation.”


                      # ⚓ NBC ☛ Iran_shuts_down_in_the_face_of_blistering
                        heat⠀⇛


                             Officials are now warning that water supplies
                             are dwindling in Tehran, which is estimated
                             to have a population of over 9.5 million
                             people.


                             Water shortages and severe heat have led to
                             unrest in Iran in the past. In 2021, street
                             protests broke out in cities in the Khuzestan
                             province in southwest Iran, as well as a
                             handful of other cities, which were met with
                             a violent crackdown by government security
                             forces.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Silicon Angle ☛ Report:_Palo_Alto_Networks_could_acquire
                  CyberArk_for_$20B+⠀⇛


                       Palo Alto Networks Inc. is reportedly close to
                       buying fellow cybersecurity provider CyberArk
                       Software Ltd.


                # ⚓ Nick Heer ☛ That_Pew_Report_Is_Sure_Looking_Like_a
                  Foundational_Text,_Unfortunately⠀⇛


                       I will continue to harp on this report. I think it
                       is going to be foundational, yet I do not think it
                       is robust enough to sustain the number of articles
                       and conclusions that will be derived from it. The
                       same is also true of a lot of third-party research
                       into Google’s search engine. A decline of 30% in
                       click-through rates is significant, but 70% is
                       catastrophic. It is hard to see how these are both
                       valid results.


                # ⚓ The Telegraph UK ☛ Tom_Lehrer_shut_up_far_too_early⠀⇛


                       So even by the time that I, aged 12, had become an
                       ardent fan of his work, Lehrer was already a thing
                       of the past. He had won a place to study
                       mathematics at Harvard aged only 15. After less
                       than a decade of showbiz fame, he became a teacher
                       at that great university. A few years after that,
                       he forsook composing and performing satirical
                       songs; he stayed on at Harvard for ever. I notice
                       that none of his obituaries had anything to say
                       about his maths classes. It is hard to imagine they
                       were not funny.


                # ⚓ Jacobin Magazine ☛ Big_Tech_Is_Under_Legal_Fire_in_Trump’s
                  Second_Term⠀⇛


                       After Donald Trump’s return to the White House, the
                       Big Tech firms continue to be battered by antitrust
                       lawsuits stemming from prior administrations. The
                       cases could even lead to the forced breakup of some
                       of the tech giants.


          o § Censorship/Free Speech⠀➾


                # ⚓ The Verge ☛ YouTube_tells_creators_they_can_drop_more_F-
                  bombs⠀⇛


                       YouTube will continue to limit monetization if you
                       use moderate or strong profanity in titles or
                       thumbnails. Videos with a “high frequency” of
                       strong profanity are also still a “violation” of
                       YouTube’s advertiser-friendly content guidelines,
                       Kavanagh says. “You have to pick and choose your
                       fucks carefully.”


                # ⚓ Nick Heer ☛ Subreddits_with_War_Media_Are_Caught_in_the
                  U.K._Age_Verification_Law⠀⇛


                       Contrary to the beliefs of one moderator of one of
                       these subreddits, this does not seem to be
                       motivated by burying evidence of the atrocities of
                       war. This is the predictable overreach of Reddit
                       choosing to require age verification to view any
                       “not safe for work” subreddit, because of course
                       Reddit is not going to be sensitive to context. It
                       is not right; it is what is least expensive because
                       it requires little additional moderation or
                       underlying technical changes. Reddit could
                       implement different types of NSFW labelling, but
                       that also increases its risk of legal liability if
                       something is improperly labelled.


                # ⚓ ANF News ☛ 20_people_executed_in_Iran_in_one_week⠀⇛


                       According to the statement, 20 people were executed
                       last week in prisons in Eastern Kurdistan and Iran.


                       The Campaign reported that a total of 1,477 people
                       have been executed during Masoud Pezeshkian’s
                       presidency so far.


                # ⚓ Techdirt ☛ FCC_To_Install_A_‘Bias_Monitor’_At_New_CBS_To
                  Ensure_Network_Kisses_Trump’s_Ass⠀⇛


                       Last week Trump’s FCC lackey, Brendan Carr, quickly
                       set about rubber stamping approval for the $8
                       billion CBS Skyance merger, now that CBS execs paid
                       their $16 million bribe to the king.


                       One of the key merger conditions to net approval
                       was the installation of a sort of FCC “bias
                       ombudsman,” who’ll be installed at CBS to ensure
                       that the new network is appropriately feckless when
                       it comes to criticizing our buffoonish orange king.
                       Making the rounds on right wing propaganda networks
                       last week, Carr ironically insisted this was
                       necessary in order to restore trust in U.S.
                       journalism: [...]


                # ⚓ US News And World Report ☛ Harvard_to_Comply_With_Trump
                  Administration_Demand_to_Turn_Over_Employment_Forms⠀⇛


                       Rights advocates have raised concerns over free
                       speech, due process and academic freedom.


                       Harvard said that, for now, it was not sharing
                       records with the government for people employed in
                       roles only available to students as it was
                       determining if such a request complied with privacy
                       protection requirements.


                # ⚓ Techdirt ☛ Oh_My_God,_TAKE_IT_DOWN_Kills_Parody⠀⇛


                       Despite this well-established pattern of silencing
                       dissent, lawmakers handed him the Take It Down Act:
                       a sweeping censorship weapon he has openly vowed to
                       wield against his critics.


                       Recently, South Park fired back in its first new
                       episode in years, with a bold, refreshing, and
                       unapologetically crude parody of the Christian “He
                       Gets Us” campaign—featuring a deepfaked, fully nude
                       Donald Trump wandering the desert as a solemn
                       narrator asks, “When things heat up, who will
                       deliver us from temptation?” The “public service
                       announcement” ends with a glowing political
                       endorsement from Trump’s wide-eyed, “teeny tiny
                       penis.”


                       It’s brilliant satire that cuts right to the heart
                       of American political delusion. It’s also
                       potentially criminal under the law Trump
                       championed. Welcome to the new reality: mocking the
                       President with AI could now land you in prison.


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


                # ⚓ Axios ☛ Which_public_TV_and_radio_stations_most_rely_on
                  federal_funds⠀⇛


                       Driving the news: For hundreds of stations with
                       available data, CPB grants made up about 10.3% of
                       U.S. public TV stations' overall funding as of
                       fiscal 2023, and 4.1% for radio stations.


                       That share is much greater for some specific
                       stations.


                # ⚓ ANF News ☛ Release_of_journalist_Umed_Beroşkî_postponed_for
                  six_months⠀⇛


                       Beroşkî had posted on Facebook on July 23, 2024,
                       reporting that Mela Nezîr had been detained by
                       officials at Zîrkan Prison but was never taken to
                       the facility. Following this post, prison
                       authorities filed a complaint against Beroşkî,
                       accusing him of “defamation.”


                # ⚓ American Oversight ☛ American_Oversight_Launches_Epstein
                  Records_Investigation,_Seeks_Details_on_DOJ_and_FBI_Review_of
                  Investigative_Holdings⠀⇛


                       We’re seeking records following reports that FBI
                       personnel were instructed to flag Epstein files for
                       Trump references.


          o § Civil Rights/Policing⠀➾


                # ⚓ Futurism ☛ Man_in_Prison_Gets_Hired_as_Software_Engineer_at
                  Silicon_Valley_Startup,_Works_Every_Day_From_Cell⠀⇛


                       In case you're wondering how a currently
                       incarcerated inmate scored a cushy Silicon Valley
                       job, you're not alone. Thorpe is allowed to work
                       the job remotely from custody through an
                       experimental program in Maine, the ultimate
                       instance of remote work that transcends 30-foot
                       barbed wire fences and a criminal record.


                       Depending on how you look at it, it's either an
                       optimistic story of redemption and meaningful
                       rehabilitation or the ultimate captive employee.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Techdirt ☛ Two_Michigan_Men_Hated_Comcast._So_They_Built
                  Their_Own_Broadband_Alternative.⠀⇛


                       Now locals can get much faster broadband at much
                       lower prices, which is almost always the case when
                       it comes to locally-owned broadband alternatives.
                       Herman and Baciu’s new provider, PrimeOne, offers
                       locals symmetrical 500Mbps for $75, 1 Gbps for $80,
                       2Gbps for $95, and 5Gbps for $110. Prices well
                       ahead of what most Americans pay even in major
                       tech-centric cities like Seattle.


                # ⚓ IT Wire ☛ Europe-North_Africa_Medusa_subsea_cable_to_be
                  powered_by_Nokia⠀⇛


                       Designed as an open access system, the Medusa
                       subsea cable will connect countries such as
                       Morocco, Tunisia, Libya, Algeria, and Egypt with
                       high-capacity fibre-optic links, providing telecom
                       providers to advanced connectivity services,
                       enabling 5G, cloud infrastructure, and AI
                       technologies.


      § Monopolies/Monopsonies⠀➾


          o ⚓ India Times ☛ Uber_loses_UK_Supreme_Court_appeal_over_tax_on
            rival_apps⠀⇛


                 Uber's rival taxi operators in England and Wales will not
                 face a 20% VAT charge on their profit margins outside of
                 London after the ride-hailing firm lost its appeal on
                 Tuesday against a previous ruling.


          o ⚓ India Times ☛ Uber_loses_UK_Supreme_Court_appeal_over_tax_on
            rival_apps⠀⇛


                 Uber's rival taxi operators will not face a 20% tax
                 charge on their profit margins outside of London after
                 the United Kingdom's Supreme Court on Tuesday ruled that
                 private-hire operators do not enter into a contract with
                 passengers.


          o § Copyrights⠀➾


                # ⚓ Wired ☛ The_Real_Demon_Inside_ChatGPT⠀⇛


                       But ChatGPT and similar programs weren’t just
                       trained on the [Internet]—they were trained on
                       specific pieces of information presented in
                       specific contexts. AI companies have been accused
                       of trying to downplay this reality to avoid
                       copyright lawsuits and promote the utility of their
                       products, but traces of the original sources are
                       often still lurking just beneath the surface. When
                       the setting and backdrop are removed, however, the
                       same language can appear more sinister than
                       originally intended.


                # ⚓ Torrent Freak ☛ The_Risks_of_Pirate_Site_Blocking,_Who
                  Benefits,_Who_Pays,_And_at_What_Cost?⠀⇛


                       With site-blocking legislation currently under
                       discussion in the United States, a new report
                       examines site blocking measures elsewhere in the
                       world. Commissioned by Cloudflare, the report warns
                       that a patchwork of measures risks disruption to
                       the [Internet]'s global technical infrastructure.
                       It also questions whether the claimed benefits are
                       worth the risk in the bigger picture.


                # ⚓ Torrent Freak ☛ 'Fair_Use'_Prevails_as_Library_of_Congress
                  Wins_DMCA_Anti-Circumvention_Battle⠀⇛


                       Medical device associations behind a lawsuit
                       challenging a Library of Congress exemption to the
                       DMCA's anti-circumvention provisions, have failed
                       to have the exemption ruled illegal. Motions for
                       summary judgment from both sides went in favor of
                       the defendants after a district court judge found
                       that the exemption, granted for the maintenance and
                       repair of medical devices, permits a non-
                       infringing, transformative fair use.


                # ⚓ BoingBoing ☛ Spotify_using_AI_to_make_new_music_from_dead
                  artists_without_permission⠀⇛


                       Trying to spoof the public with musical slurry
                       created using a computer is one thing. Generating
                       said slurry and flogging it as the work of a dead
                       artist is some next-level fuckery. Spotify is
                       treating its listeners like it thinks that they're
                       stupid. If you must stream, consider moving to a
                       company that doesn't abuse its clients. Better
                       still, buy your music and download it to your
                       devices. Your favourite artists will get a bigger
                       chunk of the payout, and you won't be funding
                       bullshit like this.


                # ⚓ RFERL ☛ Armenia_Is_About_To_Put_Its_Ancient_Manuscripts
                  Online_For_Free⠀⇛


                       Among columns of exhausted ethnic Armenians fleeing
                       the mass killings carried out by Ottoman Turks
                       beginning in 1915, some hid books or ancient
                       documents inside their clothing. For many
                       survivors, the easily hidden manuscripts were the
                       only remnant of their nation that they were able to
                       smuggle to safety.


                       Thousands of those books and documents eventually
                       arrived in modern Armenia where today they are held
                       in the purpose-built Matenadaran, a storehouse for
                       the country’s historic manuscripts. Many, however,
                       remain in museums and private collections scattered
                       throughout the world.


    * Last_Month_Our_IRC_Community_Turned_17
    * Some_People_See_What_Others_See..._But_Only_40_Years_Later


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