𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, September 13, 2024
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Generated Sat 14 Sep 02:49:20 BST 2024
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2024/09/13/


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

⦿ Techrights  -  Dr. Richard M. Stallman (RMS) Explains That a Free/Libre Program Running on Somebody Else's Server (e.g. Clown Computing) Leads to Freedom Deficit

⦿ Techrights  -  EPO Staff Representatives Explain the Latest Corruption at the EPO in a New Paper

⦿ Techrights  -  ircII Has Turned 35

⦿ Techrights  -  IRC Proceedings: Thursday, September 12, 2024

⦿ Techrights  -  [Meme] Code of Conduct in WINE

⦿ Techrights  -  [Meme] From Checked by Three Examiners to Gone (Granted) in 3 Seconds!

⦿ Techrights  -  Mono as a Double-Purpose Trojan Horse Inside Wine

⦿ Techrights  -  Number of Gemini Capsules Rising Closer to 4,100, Certificate Authority "Let's Encrypt" Down to 1.1%

⦿ Techrights  -  Once Again, Mass Layoffs at Microsoft (Just Like Every Month This Year)

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  RedMonk: September the Month of the Mouth of Redmond (Still)

⦿ Techrights  -  Richard M. Stallman Explains Why the Web Becoming a Pile of Proprietary JavaScript Programs (Not Pages to Render) Does Harm to Web Users

⦿ Techrights  -  Rumour: Layoffs in IBM Consulting Today

⦿ Techrights  -  This is How Bad Things Have Become at Microsoft

⦿ Techrights  -  [Video] Why Hurd and MINIX (or BSD) Didn't Get Ahead of Linux?

⦿ Techrights  -  Wine Took the Bait (Mono), Soon Starts the Microsoft Circus With the Banhammer

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/09/13/Dr_Richard_M_Stallman_RMS_Explains_That_a_Free_Libre_Program_Ru.shtml
https://techrights.org/n/2024/09/13/EPO_Staff_Representatives_Explain_the_Latest_Corruption_at_the_.shtml
https://techrights.org/n/2024/09/13/ircII_Has_Turned_35.shtml
https://techrights.org/n/2024/09/13/IRC_Proceedings_Thursday_September_12_2024.shtml
https://techrights.org/n/2024/09/13/Meme_Code_of_Conduct_in_WINE.shtml
https://techrights.org/n/2024/09/13/Meme_From_Checked_by_Three_Examiners_to_Gone_Granted_in_3_Secon.shtml
https://techrights.org/n/2024/09/13/Mono_as_a_Double_Purpose_Trojan_Horse_Inside_Wine.shtml
https://techrights.org/n/2024/09/13/Number_of_Gemini_Capsules_Rising_Closer_to_4_100_Certificate_Au.shtml
https://techrights.org/n/2024/09/13/Once_Again_Mass_Layoffs_at_Microsoft_Just_Like_Every_Month_This.shtml
https://techrights.org/n/2024/09/13/Over_at_Tux_Machines.shtml
https://techrights.org/n/2024/09/13/RedMonk_September_the_Month_of_the_Mouth_of_Redmond_Still.shtml
https://techrights.org/n/2024/09/13/Richard_M_Stallman_Explains_Why_the_Web_Becoming_a_Pile_of_Prop.shtml
https://techrights.org/n/2024/09/13/Rumour_Layoffs_in_IBM_Consulting_Today.shtml
https://techrights.org/n/2024/09/13/This_is_How_Bad_Things_Have_Become_at_Microsoft.shtml
https://techrights.org/n/2024/09/13/Video_Why_Hurd_and_MINIX_or_BSD_Didn_t_Get_Ahead_of_Linux.shtml
https://techrights.org/n/2024/09/13/Wine_Took_the_Bait_Mono_Soon_Starts_the_Microsoft_Circus_With_t.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/09/13/Gemini_Links_13_09_2024_Towards_Aristocratic_Personal_Computing.shtml
https://techrights.org/n/2024/09/13/Links_13_09_2024_Crackdowns_on_Bloggers_Deepfakes_Internet_Arch.shtml
https://techrights.org/n/2024/09/13/Links_13_09_2024_Disinformation_in_Focus_End_of_Presidential_De.shtml
https://techrights.org/n/2024/09/13/Links_13_09_2024_Recorded_Future_Bought_by_MasterCard_Bits_of_F.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 95

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/Dr_Richard_M_Stallman_RMS_Explains_That_a_Free_Libre_Program_Ru.shtml
    Gemini version at https://techrights.org/n/2024/09/13/Dr_Richard_M_Stallman_RMS_Explains_That_a_Free_Libre_Program_Ru.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Dr. Richard M. Stallman (RMS) Explains That
a Free/Libre Program Running on Somebody Else's Server (e.g. Clown Computing)
Leads to Freedom Deficit⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


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


From the talk he gave a_few_weeks_ago:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Closing_Keynote_Day_3_-_Dr._Richard_Stallman_-_Web3_Summit
                                 2024_Berlin⦈_


THE "Clown_Computing" delusion is a very harmful one. In his public talks
months ago RMS refused to use the word "cloud" or to respond to questions that
use this misleading/nebulous term... and - to his credit - he clearly explained
why.


Weeks ago he coherently explained his views on the subject, based on his
handwritten notes (pointers) rather than a spontaneous response to the Czech
audience:


     Now when you are doing your computing you must not entrust that to
     somebody else's server because users including you should have
     control over their own computing but you can never have control over
     what somebody else's server does because somebody else installs
     software in that computer and configures it and thus decides what
     computing it is going to do. So it may be useful to talk with
     somebody else's server as a way of communicating with her with
     somebody else. Servers are fine for that. If I want to publish
     something that I say and you want to see what I said connecting to my
     server stallman.org is a fine way to do it. And running a server for
     that purpose is a fine way of conveying the information to those who
     are interested. The GNU Project has its own things to say different
     to my personal views so it has a different server gnu.org and again
     it is fine for the GNU Project to use a server as a way of enabling
     you to see what the GNU Project has to say if you're interested. And
     the Free Software Foundation has another server fsf.org which gives
     other information about a related part of the issue of Free Software.
     But when it comes to doing your computer you shouldn't entrust anyone
     else's server, not stallman.org, not gnu.org, not fsf.org, not
     google.com, or apple.com, or basically any one else that sets up a
     server that is not you. And that person or organization's server is
     not your computer, it's not under your control, and so you shouldn't
     depend on that server to do your computing. Which means that a very
     wide spread architecture that is quite commonly recommended by the
     people who don't think about this issue is a bad way to do computing.


     It might be perfectly fine to use a certain Free program by running
     it on your computer. That way you can change it if you want. But to
     have the same program running on somebody else's server, and you just
     connect to that server, well, you can't change the version of that
     program that's running on that server because that server is not
     yours. So it's not just which program you're talking to, it's who's
     running it that matters in terms of your freedom. For your freedom it
     should be you running that free program, so you can modify it. If
     it's running in my server, well, that's my copy and I can modify it
     but you can't. At least you can't put the modifications into the copy
     running on my server. That's not good for your freedom.


The above starts about 08:30 (mm:ss) from the start of this_video. █




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠉⠉⠛⠙⠛⠋⢻⠉⡿⢈⠙⠛⠛⠋⡉⢛⡿⠙⠙⠙⠛⠉⡙⠋⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠶⣷⣾⡶⢶⠶⡾⢶⡶⣶⡴⢶⡶⣶⡆⣼⣧⣶⣶⢶⡶⠶⣶⣶⢶⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⣿⡿⣿⣿⣿⡿⠿⢿⠿⠿⠿⡿⠿⣿⣿⣿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠂⠁⢹⡇⠠⢄⡀⢈⠂⠻⡇⠀⠈⠁⠀⠈⠁⠉⠁⠀⡇⠀⠀⠊⠀⠈⠁⠌⠀⠉⠉⠃⠑⠁⠉⠀⠉⠄⠈⠁⡉⠀⡇⠂⠈⠈⣅⠰⠁⠀⠀⠐⢀⡷⠀⠄⠀⠈⠉⠈⠉⠀⠗⢈⠈⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢛⣿⠛⣿⣿⣿⣿⢻⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡿⣿⣿⠛⠛⠛⠟⠛⠛⠛⢻⡟⣟⢻⣿⣿⣶⣾⣿⡿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣠⠄⣀⣀⣀⠀⣠⣀⣈⣄⣰⣄⣀⣘⣆⣀⣀⣄⣄⣀⣀⡀⠀⣀⣂⡀⠀⣺⣀⣸⣀⣀⣀⣀⡀⠀⣄⣀⣀⣀⣸⣇⣃⣀⣦⣀⣈⣀⣩⣅⣀⣀⣀⣠⣇⣀⠐⣀⣀⣀⣀⣐⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠛⠛⠛⠛⠻⠛⠛⠿⠋⠙⠟⠟⢻⠛⠛⠟⠛⠛⠉⠋⣹⠛⠉⠹⠛⠛⠛⢻⠉⠙⠟⣻⠋⠙⠟⠟⠻⡟⠻⠻⠉⠙⠛⠛⠛⢛⠛⢿⠛⠛⠻⠻⣿⡍⠉⠉⢙⠟⠛⢻⠉⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣂⣤⣴⣴⣤⣤⣤⣴⣤⣤⣤⣤⣾⣦⣴⣤⣦⣴⣤⣤⣶⣤⣤⣤⣤⣤⣦⣿⣤⣤⣤⣽⣤⣤⣦⣤⣴⣧⣴⣴⣤⣴⣴⣴⣤⣤⣦⣾⣤⣤⣴⣤⣼⣷⣴⣴⣤⣤⣴⣼⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢃⠈⡉⠉⠉⠁⠈⢉⠉⠋⠙⠀⣏⠉⠉⠉⠉⢿⠁⠈⠋⢹⠁⠆⠀⠁⠀⠆⢸⠋⠉⠉⠉⠉⠍⠉⠀⠈⠙⢉⡟⠉⠙⠉⠉⠉⠉⠉⠉⢿⠁⠀⠆⠀⠀⠀⢶⢸⡇⠉⠿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣾⣷⣷⣶⣶⠦⣴⣷⣾⣶⣿⣾⣾⣶⣶⣾⣶⣶⣷⣿⡷⠲⣷⣿⡾⠶⠿⠷⢧⠴⠶⠶⢷⣾⠶⡶⢦⣤⢾⠶⠵⠷⡶⠶⠶⠶⢶⠾⢧⣵⣶⣷⡟⣿⠲⢿⠷⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⡀⣀⣀⠀⠀⡀⣀⣀⣀⣀⣃⣀⠀⢀⡀⡀⢀⠀⡄⢀⢸⣆⣀⢀⢐⣶⣄⣸⣀⢆⢀⡸⢠⡀⣸⡇⣀⡀⣀⢸⣇⢇⡁⣄⡀⡖⡀⠛⢶⣞⡀⠀⢈⠀⣳⠀⢸⡀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢛⡿⠿⠿⠛⠾⣟⠛⠛⠉⠙⠋⠛⢻⣟⢙⡟⠻⠿⠿⠿⠿⡟⠛⢿⠿⢿⠿⠿⠿⠿⠻⠿⠿⠟⢿⠿⠟⢛⠛⠻⠿⢿⠟⡛⠋⠛⠋⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣄⣤⣠⣠⣠⣠⣠⣄⣠⣨⣄⣄⣠⡃⣀⣀⣄⣀⣤⣰⣤⣈⣸⣤⣤⣏⣯⣈⣁⣀⣀⣠⣄⣨⣇⣄⣼⣄⣬⣦⣦⣤⣠⣠⣄⣀⣀⣽⣀⣄⣽⣤⣀⣄⣼⣦⣁⣄⣦⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠛⠛⠛⡛⠛⠋⡁⠛⠛⠛⡛⠛⠛⠛⠋⠛⠛⠛⠛⣯⢹⡅⢠⠈⠋⠛⢻⠈⠋⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⡏⠙⠛⠛⡛⠛⠛⣻⠉⠙⠛⢻⠛⠛⠛⠛⠃⠙⢛⠉⠛⠛⠛⡿⠛⠋⣨⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣆⣴⣶⢶⢶⣶⣶⣶⣦⣠⣷⣦⣤⣶⣶⣶⣶⣶⣶⣦⡼⣷⣾⣶⣶⣶⣾⣶⣶⣶⣦⣠⢴⣶⣆⣴⣶⣤⣼⢷⡶⣶⣶⣶⣶⣶⡾⣶⢶⣶⡾⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠈⠁⠀⠀⠈⠈⠉⠀⢠⠈⣋⠈⠉⠉⠈⠉⠉⠁⠉⠉⠉⣻⠉⠉⠈⠁⠁⠈⠉⢹⠄⠀⠉⠉⠉⠈⡏⠉⠈⠀⠈⠉⠁⢿⠉⠁⠈⠀⠀⠐⡇⠈⠈⡇⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡾⣿⠿⡿⣿⡿⡿⢿⠿⡿⣿⡿⡿⢿⣿⢿⣻⣿⣿⢿⣿⠿⢿⣦⣾⡿⢿⣿⢿⣿⡟⠻⢿⣿⡟⠻⣿⣶⡴⢻⣿⣿⢿⣿⢿⢿⠟⠻⠿⡿⡿⣿⡿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣈⣀⣀⣈⣀⣈⣀⣀⣻⣈⣀⣼⠀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣺⣃⣁⣀⣰⣇⣁⣀⣀⣀⣇⣀⣀⣂⣀⣄⣠⣀⣀⣄⣈⣿⣃⣡⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡫⠙⠻⡟⠉⠹⠟⠿⡿⠿⢿⣿⠩⠿⠿⠿⢿⢿⠿⠻⠉⠻⠿⠿⠿⠿⠿⡿⠽⢿⡿⠿⠿⠿⠿⠿⠋⠉⠿⢿⠿⠯⠝⢿⠏⣽⡿⡿⠿⠿⠉⡟⠉⠿⠿⡟⠋⠿⠿⠿⠿⠿⠿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣌⣽⣤⣴⣤⣤⣾⣤⣤⣤⣤⣴⣤⣦⣬⣴⣤⣧⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣀⣿⣧⣦⣤⣤⣤⣉⣧⣤⣤⣤⣤⣧⣤⣤⣤⣷⣤⣤⣤⣞⣀⣦⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠉⠉⠉⠉⢻⠋⠀⠙⠉⠋⠙⠀⠉⠋⢹⠨⠙⠙⡇⠝⠉⠋⢹⠃⠘⠉⠉⠉⠉⠉⠙⠁⣿⠈⠃⠊⢹⠀⠈⠀⠙⡏⠙⠙⡟⠙⠉⠉⠃⠀⠈⠙⠙⠉⠈⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣷⣾⣷⣾⣷⡾⢾⡷⣷⣾⣶⣶⣶⣿⣶⣾⣾⣷⣶⣶⣶⣾⣷⣾⡶⢷⣷⣾⡾⢾⣶⣿⣶⣶⣶⠾⣶⣶⣶⣾⣿⣾⣶⠿⠶⢾⣶⠷⢶⣶⣾⣶⣶⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⢀⣀⠀⠀⢀⣀⢀⢀⢀⣀⣠⢠⣏⢀⡀⡀⣀⡀⢂⣀⣹⡐⡀⠀⢀⡀⣀⢸⣆⣀⡀⢀⣀⣈⣇⣀⣀⣀⣳⣀⣀⡀⣀⣀⠀⣘⣿⡀⠀⣀⣀⣄⣠⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠶⠾⠿⠿⠶⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⢿⠛⠛⠻⠿⠛⠻⠿⠿⠿⠿⠿⢿⠛⠛⠙⠙⣿⠛⡙⠿⠟⠿⠿⠿⠿⠿⠿⠿⢛⠹⠾⠿⡟⠻⠏⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⣤⣤⣀⠠⣠⣄⣤⣠⣠⣤⣤⣄⣤⣤⣼⣤⣠⣤⣤⣄⣤⣄⣼⣥⣠⣠⣠⣴⣠⣧⣄⣤⣤⣌⣿⣤⣤⣤⣤⣿⣬⣢⣤⣤⣄⣠⣨⣄⣤⣤⣤⣬⣤⣀⣄⣯⣤⣦⣴⣄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 241

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/EPO_Staff_Representatives_Explain_the_Latest_Corruption_at_the_.shtml
    Gemini version at https://techrights.org/n/2024/09/13/EPO_Staff_Representatives_Explain_the_Latest_Corruption_at_the_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ EPO Staff Representatives Explain the
Latest Corruption at the EPO in a New Paper⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024,
updated Sep 13, 2024


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


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


THE Central Staff Committee at the EPO has contacted colleagues to say that
following its letter_about_clear_misconduct (corruption) by EPO managers it has
received no response. It was like this under Benoît_Battistelli and António
Campinos runs an equally corrupt office that bribes people, organisations,
media etc. They just don't talk about it and nobody gets prosecuted. To quote
the Staff Committee (CSC): "Dear Colleagues,


"DG1 Operations is currently arbitrarily reallocating files to new Examining
Divisions without explanation and without disclosing the criteria. The focus is
put on patent applications from signatories of the IPQC charter.


"The Central Staff Committee (CSC) addressed Mr Campinos by letter but no reply
is available until now.


"This paper provides further details on the evolution of events."


Many of these applications are for European_software_patents - i.e. patents
which are both illegal and undesirable - and the process is in clear violation
of the protocols. The EPO has once again turned legal processes into white-
collar crimes. Here is the full publication shared with staff and dated
yesterday:


     Zentraler Personalausschuss
     Central Staff Committee
     Le Comité Central du Personnel


     Munich, 12.09.2024
     sc24056cp


     § Arbitrary reallocation of patent applications and
     cancellation of oral proceedings⠀➾


     DG1 Operations is currently arbitrarily reallocating files to new
     Examining Divisions without explanation and without disclosing the
     criteria. The focus is put on patent applications from signatories of
     the IPQC charter. The Central Staff Committee (CSC) addressed Mr
     Campinos by letter but no reply is available until now. This paper
     provides further details on the evolution of events.


     ⚓  Reallocation of files of specific applicants⠀⇛


     In August 2024, DG1 Operations put in place a specific unit in charge
     of scrutinizing patent applications filed by Siemens AG. For a number
     of these patent applications, the Examining Division in charge had
     already sent summons to oral proceedings which had successfully
     passed all the EPO statutory “quality” checks. The specific unit
     nevertheless took the decision to allocate new Examining Divisions
     working in another Directorate and in another field. The new
     Examining Divisions cancelled the oral proceedings that may have led
     to refusals but instead directly sent intentions to grant.


     In a letter1 of 29 August 2024, the Central Staff Committee (CSC)
     noted the lack of legal basis for this course of action, which can be
     considered to be against the principle of neutrality in the treatment
     of patent applications. At the time of drafting this paper, our
     letter remains unanswered.


     Since then, DG1 Directors explained to their teams that DG1
     Operations indeed put in place specific units for checking summons to
     oral proceedings and put the focus on patent applications from
     Siemens AG, Ericsson and Bayer. The latter are members of the IPQC,
     which is publicly critical about the substantive quality of EPO
     patents.


     ⚓  No prior notification and no information given to Examiners⠀⇛


     The Examining Divisions which had originally sent the summons to oral
     proceedings were not consulted on the intention to reallocate and not
     given an opportunity to bring corrections or to comment. They were
     not even informed in advance of the reallocation, were not provided
     with any reason for the change and just got informed of the
     cancellation by an automatic Outlook notification in their calendar.
     Team Managers and Examiners are currently analysing the files which
     were silently taken away from them and allocated to a new Examining
     Division and trying to guess which criteria these summons to oral
     proceedings were not fulfilling.


     In the absence of clear criteria from DG1 Operations, some Directors
     have decided to proactively check themselves summons to oral
     proceedings from IPQC members including as well Nokia and Qualcomm.
     In some Directorates, a set of new “Golden Rules” was presented in
     team meetings, but not handed out. There is the explicit mention that
     these shall remain confidential.


     __________


     1 “High-level user meetings and special treatment of patent
     applications”, CSC paper of 29-08-2024 (sc24050cl)


     =====================================================================
     This week, the staff representation became aware that examination
     actions other than summons are now also checked and, in case,
     reallocated to another Examining Division. Examiners saw their
     dossier list shrink even further without any notification. Even when
     colleagues explicitly asked their Team Manager or Director, they did
     not receive written feedback about what was allegedly wrong with
     their work.


     ⚓  Examiners left facing arbitrariness and speculation⠀⇛


     Examiners are left alone, are still waiting for explanations, and can
     only speculate as to the reasons why their examination actions could
     have been flagged by the special unit(s). In the absence of clarity
     on the matter, the feeling is now growing that if examiners send
     summons for oral proceedings or examination actions with critical
     objections against patentability, specific unit(s) might intercept
     their application and allocate it to another examiner who will get
     the reward for bringing the procedure to an end. Therefore, examiners
     currently find themselves in a safer position if they directly send
     an intention to grant.


     The Central Staff Committee (CSC) considers the current situation,
     with covert reallocation of files and questionable confidential
     instructions, intolerable. We recommend that the concerned colleagues
     keep written track of relevant incidents, question dubious verbal
     instructions, ask about the legal basis and, if necessary, ask for
     written confirmation.


     There is good reason for the provision that Article 18(2) EPC
     stipulates that an Examining Division shall consist of three
     technically qualified examiners. This number of members is a further
     safeguard that decisions be not influenced by external influence and
     arbitrary considerations. If an Examining Division has become
     responsible for the examination of a European patent application
     under Rule 10(2) EPC, an arbitrary replacement of its members
     according to a non-documented procedure or secret criteria does not
     appear to be in line with this objective.


     ⚓  Conclusion⠀⇛


     At a time when the increased number of patents granted by the EPO and
     their quality have become a major concern among users of the patent
     system. DG1 Operations is taking the wrong course of action by
     interfering in the Examining Divisions and creating wrong incentives
     for shortening the procedure towards an intention to grant.


     Sincerely yours,


     The Central Staff Committee


About a year has passed since the EU and EPO started fake_new_patent_courts
(both illegal and unconstitutional) to assess those phony patents, often
granted illegally owing to a crooked_process_designed_to_hide_the_bubble_or
delay_its_implosion.


Owing to corrupt management the EPO has resorted to corporate crime or
organised crime designed to benefit large corporations. Who will pay the price?
Everybody else in Europe. This_corruption_also_spreads_to_the_EU. █




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣈⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⠀⠄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠉⠉⠍⠉⠉⠉⠉⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠓⠓⠛⠓⡒⠒⠒⠚⡛⠛⠻⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡷⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣿⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣾⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⡀⡀⢸⣏⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠟⠿⠿⠿⠿⠿⠟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢰⣶⣶⡖⠒⠐⢶⣶⢰⠀⠒⠐⠒⠀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣉⣉⣉⣉⣉⣩⣏⣉⣋⣉⣉⣍⣉⣋⣉⣉⣉⣍⣝⣋⣉⣹⣿⣿⣿⣿
⣿⣿⣿⢸⣿⣿⠟⠀⠀⠀⣿⢸⠤⠤⠤⠤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⣉⣩⣉⣍⣹⣁⣉⣉⣤⣗⣉⣩⣽⣍⣉⣉⣉⣹⣿⣿⣿⣿
⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⣿⢸⣄⣀⣠⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣉⣗⣊⣉⣉⣀⣉⣗⣊⣩⣙⣉⣁⣏⣟⣿⣬⣩⣍⣉⣩⣩⣉⣸⣿⣿⣿⣿
⣿⣿⣿⢸⡃⠀⠀⢀⣤⣼⣿⠸⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⡛⠛⡻⡟⠟⠿⠻⠿⠻⠛⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣉⣉⣍⣩⣋⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⡟⡋⡛⢙⢹⡛⠛⢛⡻⢻⡟⡛⠻⠛⡏⢹⣛⠟⣻⠛⡋⣿⢛⠛⡛⣿⢛⠋⣹⣟⠻⠛⡋⠛⠛⡛⣛⣿⠛⡟⣻⢛⠏⢹⢛⡟⢛⢹⡟⡛⢛⢻⠛⣿⠛⡟⣻⢛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣷⣶⣾⣾⣷⣶⣾⣥⣿⣷⣷⣶⣶⣶⣾⡶⣷⣶⡶⣶⣾⣶⣶⣷⣿⠶⣶⣿⣷⣾⡶⣶⣶⣶⣷⣷⣷⣶⣶⣾⣴⡷⡾⣶⣶⣶⣶⣷⣶⣾⣶⣶⣿⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣒⣀⣃⣨⣐⣇⣀⣇⣁⣐⣂⣇⣪⣰⣸⣇⣲⣰⣇⣂⣰⣀⣀⣿⢐⣸⣦⣂⣅⣲⣀⣅⣸⣂⣇⣰⣨⠂⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⣝⣯⣏⣏⣍⣉⣉⣉⣝⣝⣹⣉⣽⣍⣏⣉⣉⣉⢝⣟⣙⣩⣩⣍⣩⡉⣽⣉⣉⣉⣍⣍⣉⣉⡩⣿⣍⣉⣹⣏⣽⣯⣉⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣐⣉⣩⣍⣉⣩⠉⣿⣂⣜⣉⣉⣩⣉⣿⣉⣈⣍⣉⣁⣏⣉⢉⣉⣩⣋⣉⣉⣽⣏⣉⣉⣏⣉⣀⣉⣙⣹⣏⣈⣉⣉⣉⣉⡉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⣉⣿⣙⣇⣉⣁⣉⣿⣷⣦⣍⣿⣧⣫⣋⣉⣿⣇⣹⣏⣋⣑⣿⣋⣿⣿⣋⣁⣉⣉⣾⣏⣙⣙⣁⣋⣁⣜⣹⣉⣿⣠⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 494

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/ircII_Has_Turned_35.shtml
    Gemini version at https://techrights.org/n/2024/09/13/ircII_Has_Turned_35.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ircII Has Turned
35⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Daniel_Stenberg⦈_


Daniel Stenberg (wolfSSL) wrote a decent history of IRC, collaboratively


"ircII was released 1989 by Michael Sandrof," says Daniel_Stenberg_of_Curl
fame. Wikipedia states "it is the oldest IRC client still maintained." It's
written in C, it predates the Web, and its_Web_site_is_still_online:


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


The software was built as_recently_as_this_month, or its files were touched by
a script:


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


Here is the_news_file: (file last touched but not modified early today)


     Changes in ircII 20240603:


       o  fix some issues in choosing the window a message belongs to


     Changes in ircII 20240326:


       o  fix hang in /window create
       o  fix problem in dcc_chatpeers_func() with no peers
       o  fix problems with new_realloc(0)
       o  updates for the manual
Don't listen to people who say IRC is "dead" or Discord_is_a_replacement (or
Slack for that matter). IRC is lean, easy to deploy, and generally works with
hundreds of client software. It's simpler and faster to interact over IRC than
over bloated, clunky stuff like Mastodon.


IRC is for practical people, not "neckbeards". Its pragmatism is measured not
in clicks or "engagement". A lot of important work still gets done over
hundreds_of_IRC_networks. IRC is not controlled by a company, so nobody pays
the media for hype or "buzz" about it. That's better that way - same as Gemini
Protocol. █




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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣽⠏⠋⠁⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠋⠀⢹⣿⣿⣿⣿⣿⣿⣿⣟⡉⣰⠀⠀⢠⡄⠉⠙⠛⣿⣿⣿⣿⣿⣿⠡⣶⡆⠐⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⡿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣷⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡁⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣦⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠛⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠀⠆⢤⡁⠆⠇⠸⠀⣿⣷⠰⢈⠆⢦⠰⢈⡆⡇⠢⢉⠰⢰⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⠀⣿⠿⢿⢿⠿⢿⠿⢿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣴⣮⣥⣬⣽⣤⣼⣤⣯⣦⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠻⠿⣟⢻⠻⢿⠿⠿⣿⠛⠻⣛⣿⠿⠿⢿⡟⢟⠛⢻⡿⣿⡿⠿⠟⡿⠟⠿⠟⣿⠿⠿⢿⢿⡿⡿⠿⠻⠿⢿⠿⠿⠿⠟⢿⢛⡛⣛⣛⢻⠿⠟⠿⠻⠻⠿⠿⠿⢿⣿⡛⡿⠿⠿⠿⡿⠿⣿⠻⢿⠿⠿⠿⠿⠿⠿
⠀⣿⠲⠶⠶⠾⡶⠾⢶⢲⣿⢶⡷⠶⠷⠶⠶⠲⠷⠶⠶⠾⡗⠲⠶⠶⡶⠿⣲⢶⠶⠾⡶⠖⠶⠾⠷⠶⠶⢶⠶⠿⡖⠶⠶⠶⣾⣒⡳⠾⣶⠺⠥⣒⢲⠶⠶⠶⠲⠶⠞⢿⡶⣷⢶⡶⠶⠶⠶⠿⢶⠾⠖⣶⣶⣾⣶⣶
⠀⣿⠶⠶⠿⠶⢳⢶⠿⠾⢿⢾⡷⠾⠾⠲⠴⠶⠞⠶⡾⠜⠷⢿⠶⠶⠷⠾⠿⠾⡷⠼⠷⠲⢶⡶⠧⡴⡶⠾⠶⠾⠿⠶⠶⠲⠾⢿⡟⠾⠿⠶⣷⢿⠾⠔⡾⢶⠴⠶⢷⠺⠷⠟⢾⡧⠴⠿⣶⣦⣾⣾⣿⣿⣿⣿⣿⣿
⠀⣿⣴⣶⣶⣼⣶⣾⣷⣾⣷⣷⣷⣶⣶⣾⣿⣶⣶⣶⣿⣷⣶⣾⣶⣶⣶⣿⣶⣶⣷⣶⣶⣶⣮⣿⣿⣷⣾⣶⣭⣾⣾⣶⣿⣶⣦⣼⣿⣶⣷⣶⣿⣾⣶⣶⣿⣿⣶⣶⣿⣷⣶⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣛⠻⠿⣿⣿⣿⠿⠿⠿⠟⣿⠿⠟⠿⠿⠿⠿⣿⠿⣿⡿⠿⢛⣻⡛⢛⡛⠟⡟⢛⣟⢻⢻⡿⢿⠿⠻⠟⢿⡻⢿⠿⠿⠿⣛⡿⡿⠟⠿⡿⠟⣿⡟⠿⢿⣿⠿⠟⣛⡿⠿⠿⠻⡿⠿⠿⠿⠿⠿⣿⡿⠿⠿⣿⣿⣿
⠀⣿⠲⠶⠲⠿⠾⣲⣶⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣶⣾⣶⣶⣶⣷⣶⣶⣶⣾⣾⣷⣾⣶⣶⣶⣾⣶⣾⣶⣷⣶⣶⣶⣶⣶⣶⣷⣶⣿⣶⣶⣾⣶⣶⣶⣶⣷⣾⣶⣶⣷⣶⣶⣷⣶⣶⣿⣷⣶⣶⣿⣿⣿
⠀⣿⣶⣶⣶⣾⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠛⡿⣻⢿⡛⢿⡿⠿⡿⡻⢿⡿⠿⢻⠿⠿⠿⢿⠿⣻⣿⢿⡿⢿⣻⡟⠿⢿⣿⡿⡟⣛⡟⣿⠿⠿⡟⠿⡿⠟⠿⠿⡿⠿⠿⢟⡻⢿⡿⠻⢿⠿⠿⡟⠿⣿⠛⠿⡿⣿⠿⡿⠿⢿⣿⠻⢿⣿⠿⢿⢛⡿⠿⢿⠛⣿
⠀⣷⠷⢷⠶⠶⠶⠜⡷⠦⣶⢲⠶⠶⢶⠾⢲⣶⠶⢔⣒⠶⠶⢶⠷⠶⠾⠖⣶⡞⠲⠶⢶⢲⢷⠾⡖⢖⠷⠶⠷⣶⠶⠶⠷⡞⠶⠶⡖⠶⠶⡶⠾⠶⡖⠷⠾⡶⠶⠿⠶⠶⡶⠳⠶⡶⡖⠲⢶⣶⣶⣶⣶⣷⣶⣿⣶⣶
⠀⣿⣶⣶⣴⣶⣶⣶⣶⣶⣾⣶⣷⣶⣾⣶⣾⣧⣤⣤⣤⣥⣤⣤⣥⣥⣤⣤⣾⣷⣶⣶⣾⣶⣶⣶⣷⣾⣶⣶⣷⣿⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣷⣶⣾⣷⣶⣶⣾⣶⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⢛⡻⠛⡟⠛⠛⣻⣛⠛⠻⡛⣻⡛⡛⡛⣿⡟⢛⠻⠛⢻⣛⠛⠛⡟⢛⢿⣟⠛⢟⠛⠛⢻⣛⡟⢻⡻⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣶⣾⣶⣷⣶⣶⣾⣶⣾⣾⣶⣾⣶⣶⣶⣶⣷⣾⣾⣶⣾⣷⣶⣶⣷⣶⣶⣶⣷⣾⣶⣶⣾⣷⣷⣶⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⡟⣿⡟⢙⣛⠛⡛⡛⠛⢻⣯⠛⡛⠋⣛⣿⠛⡛⠛⣽⣯⠉⠛⣛⣿⠙⠛⠛⠻⡟⡍⠛⣽⡏⠋⠛⠛⠛⢏⣛⠛⠉⢟⠛⠛⣛⠛⠛⠋⡿⠛⡛⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠭⠙⠛⡿⠟⠛⠩⢽⠙⠛⠹⢻⡯⠋⠛⠛⡟⠛⡛⣻⠛⢛⠛⠉⠛⠙⠽⢻⡟⠛⠋⠹⠛⢻⡟⠛⠛⡛⣿⡏⡍⠛⢻⡛⠛⠟⠛⡛⠟⡻⠛⢻⠯⢛⠛⠛⢿⠙⡻⠯⢹⠝⠛⠽⠛⡏⠛⣿⠻⠹⠛⢽⡏⢻⣿⣿
⠀⣿⢻⠏⠉⡿⠟⢿⠋⠛⣛⠛⠑⠛⠛⠛⠛⠛⠋⡿⠻⠻⠋⡏⠝⠛⢻⠙⠛⡛⠛⠛⠹⠏⠛⠛⣿⢻⠯⠉⡏⠛⠛⠙⠛⡟⠛⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠩⢝⠉⡏⠉⠉⢽⠭⠍⠉⢹⡫⡹⠭⡏⠉⢉⡉⠉⡏⠉⢝⢝⠯⢹⠭⡍⠉⠿⡏⢉⠍⠉⢹⠩⠋⠫⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣷⣤⣍⣉⣏⣉⣉⣽⣥⣭⣉⣸⣉⣙⣍⣏⣁⣉⣉⣫⣹⣩⣉⢉⣉⣩⣀⣩⡉⣽⣈⣉⠉⣉⣏⣩⣍⣹⣏⣅⣉⣉⣁⣉⡉⣿⣩⣩⣩⣍⣉⣭⣹⣈⣉⠉⣉⣯⣭⣹⣈⣭⣱⣸⣥⣍⣉⣭⣿⠈⠉⠩⠹⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣒⣈⣋⣹⣈⣹⣘⣉⣉⣇⣺⣩⢉⢩⣉⡙⣇⣁⣻⣙⣉⣁⣗⣛⣙⣉⣋⣉⣉⣿⣀⣙⣙⣻⣈⣝⣓⣸⣙⣍⣉⣙⣉⣹⣏⣹⣛⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣻⣀⣂⣸⣐⣄⣓⣄⣽⣀⣀⣀⣇⣠⣠⣐⣚⣆⣰⣈⣂⣀⣀⣁⣄⣔⣿⣀⣀⣔⣟⣀⣐⣀⣚⣀⣀⣇⣀⣒⣑⣆⣀⣀⣠⣸⣓⣄⣾⣨⣇⣂⣀⣐⣄⣿⣐⣸⣜⣜⣀⣸⣡⣃⣆⣇⣓⣰⣸⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⠀⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⢿⡿⣿⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⢿⣿⣿⡿⢿⣿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣭⣤⣥⣼⣠⣤⣅⣤⣾⣤⣤⣤⣧⣤⣤⣬⣬⣯⣴⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣬⣟⣀⣀⣉⣁⣁⣹⣤⣤⣤⣸⣥⣤⣀⣤⣧⣔⣼⣥⣤⣬⣬⣼⣧⣤⣤⣤⣤⣭⣬⣴⣴⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⠀⣿⠿⡿⡿⡿⠿⡿⠿⠿⠿⠿⡿⡿⠿⢿⣿⠿⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣬⣮⣯⣥⣤⣦⣬⣧⣤⣤⣯⣭⣬⣬⣭⣤⣬⣥⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⢸⣿⢿⣽⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⢝⣿⢿⡏⣿⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⠯⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⢸⣿⣿⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣼⣿⣿⣦⣿⣷⣿⣿⣾⣽⣿⣾⣿⣷⣿⣷⣿⣿⣾⣿⣽⣿⣾⣷⣷⣮⣿⣿⣷⣬⣿⣷⣯⣿⣧⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 664

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/IRC_Proceedings_Thursday_September_12_2024.shtml
    Gemini version at https://techrights.org/n/2024/09/13/IRC_Proceedings_Thursday_September_12_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Thursday, September 12,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


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


                          Enter_the_IRC_channels_now




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⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠋⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣚⣺⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⠿⣿⣿⣝⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠤⠄⢙⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣿⣿⣿
⠀⠀⣀⣀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣸⣿⣿⣷⣦⣩⣿⡟⣻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡶⠶⠿⠿⣿⣿⣿⣿⣿⠺⣿⣇⣿⣿⣿⣷⣷⣾⣟⣛⢉⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣢⣀⣀⣿⣿⣿⣿⣿⣿⣯⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣽⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣙⣭⣍⠽⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣿⣯⣽⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆⣿⣏⢿⣛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡄⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢋⣉⣡⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⡈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⡿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⢻⣯⣹⣧⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣟⣛⣿⣤⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠛⠛⡿⠿⣷⣤⣿⣶⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 893

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/Meme_Code_of_Conduct_in_WINE.shtml
    Gemini version at https://techrights.org/n/2024/09/13/Meme_Code_of_Conduct_in_WINE.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Code of Conduct in
WINE⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇A_big_wine_glass⦈_ Context: Wine_Took_the_Bait_(Mono),_Soon
Starts_the_Microsoft_Circus_With_the_Banhammer


Step_one: irritate productive developers.


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


Step_two: forcibly interject very divisive politics (as someone is bound to not
fully agree).


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇he/him_and_she/her;_NixOS_now_discusses_RESERVING_a_board
seat_to_non-binary._If_you_express_dissatisfaction_about_it,_you_are_a_'nazi'⦈_


Step_three: fill up the gaps (or vacuum left after resignations, suspensions,
oustings) with obedient, passive operatives or employees of Microsoft.


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


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


Been there, done that, seem that. The modus operandi does not vary much.




⣿⣿⡇⠀⠀⠀⢰⣿⠁⠀⠍⠉⠉⠛⢛⠛⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣇⡀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠒⠄⠀⠀⠁⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣧⢭⣽⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣷⣾⣿⣤⣦⣴⣶⣇⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣻⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈
⣿⣿⡁⠀⠉⠉⣻⡟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⣿⣿⣿⣿⣿⣶⣿⣷⣶⣦⣤⣠⣀⣀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀
⣿⣿⣿⣿⣿⣟⣿⣟⣻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿
⣿⡟⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣯⢸⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀
⣿⣿⣧⣀⣤⣤⣿⡀⠀⠈⠉⠉⠉⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⠉
⣿⣿⣿⣿⣿⢿⡛⠻⢿⠿⣿⣿⠟⢒⣶⣶⣶⣶⣦⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠉⠀⠀⠈⠁⠭⠇⠀⠀⠉⠁⠀⠀⠈⠉⠉⠉⠉⢉⠻⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⠙⢢⣼⣿⡿⠛⢛⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⠿⠯⣭
⣿⣿⣿⣿⠄⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠄⣀⠀⣀⣀⠀⢀⣾⣿⡿⠋⠩⢀⢻⡅⠀⠀⠈⠙⠃⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀
⣿⣿⢻⣿⠆⠀⠈⠁⠀⠄⠻⣿⣿⣿⠿⠶⠿⠷⠶⣶⡖⠲⣶⣦⣤⣤⣤⣿⣿⣿⣿⣿⣷⢾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⢓⠿⢧⣀⣀⣀⡀⠀⠀⣀⣀⡀⠀⢀⣀⣀⣤⡄⠀
⣿⣿⣄⢿⠘⠀⠀⠀⠀⠀⠀⠀⠙⠛⢓⠿⢿⣶⣶⣶⠀⡀⢢⡄⠀⠉⠉⢉⡽⠿⡟⣿⣿⣸⣿⣿⣿⣿⣿⠋⠡⣾⣿⣟⠿⠿⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣈⣿⣿⣿⣿⡟⣉⠁⠈⠁⠙⠉⡉⠀⠀
⣿⣿⡿⢿⣧⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠸⠟⠿⠿⠲⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⡀⠈⠉⠁⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣧⠀⠀⠀⣴⣿⣲⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠈⠀⠒⣒⣿⣷⣶⣶⣶⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣀⡔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣰⣿⣿⣿⣷⠀⠀⠀⠈⠈⠓⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣶⣾⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿⡏⠉⠉⠉⠉⠈⠁⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢻⣿⣿⣿⣿⣿⣿⣷⡈⠛⠛⠻⠿⠿⠟⠁⣰⣿⣿⣽⣿⣿⠃⣼⣿⣿⡇⠀⢀⣩⣿⣿⣿⡋⠁⠚⢺⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣧⠀⠊⠉⣿⣿⡏⠀⠀⠈⢸⣿⡿⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣿⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠃⠀⠀⢀⣼⣿⠗⢀⡀⠀⡀⠀⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⡿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⠸⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣷⠀⠀⠀⠀⠀⢀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠟⣦⣸⣿⣿⡟⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⡟⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⣿⣷⢠⣿⣷⡄⠀⠈⠓⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⢃⠟⢛⣵⣿⣿⣽⣿⣿⣷⠀⠀⠘⠙⣿⣿⣿⣿⣿⡿⠃⠁⠐⠀⠀⠉⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⢸⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⡿⡿⠁⠄⠂⠚⠻⠸⠯⣿⣿⠿⠟⠀⠀⢠⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⡿⢸⣿⣿⣿⣄⢸⣿⣦⣄⠀⢻⣿⣿⣿⣇⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⣿⣿⢃⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⡇⣼⣿⣿⣿⣿⣿⡿⣿⣿⣷⡌⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⡇⣿⣿⣿⣿⣿⣿⣙⢹⣿⣿⢳⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠌⣿⡏⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢷⡿⢠⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢹⣿⣿⣿⣿⡏⣼⠇⠚⠋⠀⠉⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⠀⠉⠉⢿⣿⣿⡿⠀⠀⠀⠀⣀⣤⣶⠆⢀⣴⣿⣿⣂⠀⠀⣠⡘⢉⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⢠⣿⣿⣿⣯⠈⠀⠀⠀⣴⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣦⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣯⠉⢰⠾⠟⠛⠛⠿⠿⠿⠏⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⡙⠛⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⡁⠈⢹⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠛⠉⠉⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠋⠁⠀⠲⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣾⣿⣿⣷⣦⣄⣀⣠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠟⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣾⣿⣶⣶⣿⣷⣶⣿⣷⣶⣾⣿⣶⣶⣿⣿⣶⣿⣷⣶⣾⣷⣶⣶⣶⣶⣶⡶⣶⡶⢶⡶⢶⣶⢶⣶⠶⣶⠶⣶⡶⣶⣶⣶⣶⣶⢖⡒⣶⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⢿⡧⠀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⣿⣷⣤⢤⢀⠁⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣾⠔⡆⠄⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣹⣿⡥⠃⠀⠀⠥
⣿⣿⡿⣿⣿⡿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⢿⣟⡣⢩⣬⣐⠂
⠿⠟⠻⠟⠛⠀⠀⠀⠀⠀⠉⠉⠋⠛⠛⠻⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠋⢋⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣻⠛⣟⣿⣽⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣺⣯⣯⣟⣿⣭⣝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⢿⢿⣿⡿⣽⣿⣿⣿⣿⣿⣷⠿⡿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠛⠓⠐⠓⠈⠈⠈⢹⣧⣿⡿⣏⢯⣯⣷⣯⢾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠨⢙⡛⣿⣷⣿⣿⣿⣿⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢠⢀⠀⠨⡁⢜⡉⢋⡎⣷⣾⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠤⠘⣀⠂⠁⣟⣟⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡔⠈⠁⢲⠻⣿⡷⢲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢈⠀⣀⣀⣀⠀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣫⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣿⣿⣿⣿⣿⣿⣠⡈⠘⣿⣧⣿⣽⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⢫⣼⠟⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⣻⣄⣤⣿⣟⣿⢿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⡟⠁⠀⠀⠁⢰⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠿⢿⣿⠟⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠟⢇⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣃⠀⠀⠀⠀⢀⣄⢀⠀⠀⠀⠐⢐⣷⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠀⠀⠀⢠⣿⣿⣿⣿⣷⣵⣻⣿⣿⣿⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣇⠀⠀⢠⠟⣸⣿⡻⡿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣀⣀⣀⣀⣀⣀⡀⢠⣶⠒⠀⠀⠀⠀⠀⡏⠀⢠⡏⠀⠿⠃⠀⠀⠸⣿⣿⣿⣿⣭⣿⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⠒⣾⣿⣇⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡿⢿⣿⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢮⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣧⡉⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠀⠨⠼⡿⣻⢿⢿⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠛⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢲⣆⡀⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⣀⠀⠀⠁⢿⣾⣿⣷⠾⢧⡄⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⠟⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢀⢀⡀⣠⡾⠿⠟⠀⠀⡀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣷⣯⢰⣶⡖⢻⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⣿⢡⣿⣿⣿⣿⠏⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⣀⣹⡏⠁⠈⢠⡀⠀⠀⠀⠂⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠻⢿⣿⣿⣿⣿⡟⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠀⣄⢀⣀⠲⠄⠀⠈⠀⠀⡆⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⣻⣤⣛⣛⣠⡿⠿⠿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⠟⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣷⠀⣿⣿⣿⡿⣿⣿⡇⣰⣶⡶⣾⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣽⣛⢿⢿⣛⡻⠿⢿⣿⠿⠿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⣿⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡙⣩⣵⣶⣤⣌⠹⣿⣿⣿⡇⠀⠛⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡉⣿⣿⠀⣿⣿⠘⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣾⣿⡇⠂⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⠃⢠⠂⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣈⠉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⡇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⢀⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠙⠻⠿⣈⠻⢿⣿⠿⠋⠀⠀⠎⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀
⠀⠛⠁⠜⠙⠛⠃⠛⠛⠛⠁⠀⢸⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣶⣶⣶⣶⣶⠶⣶⡶⣶⡶⣶⡶⢶⡶⢶⣶⢶⣶⠶⣶⠶⣒⣶⣶⡖⣶⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⡻⣿⣿⣟⡔⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣬⣷⣄⡀⠈⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣳⢿⡄⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⡿⣯⡅⡞⠅⠢⠀⠆
⣿⣿⣿⣿⣿⣿⡿⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⡏⣍⣰⡄⣍
⠿⠟⠛⠛⠻⠁⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠉⠁⠋⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⣷⣜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠊⣿⣻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⡿⣿⣻⣿⣷⣙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⢿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣷⠿⡟⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠊⠋⠛⡛⠊⠈⠉⠈⣟⣺⣿⣿⣾⢭⣶⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠻⣿⣿⣿⣿⣿⣿⡄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠙⡍⠉⣍⣶⣺⣼⣺⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠠⠬⠴⣯⣿⣋⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠁⠍⢀⠸⢮⣘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣟⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣿⣿⣿⣿⣿⣿⣠⡈⠸⣿⣧⣿⣿⣾⣿⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢓⣱⠟⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣻⣤⣤⣛⣏⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡟⠁⠀⠀⠀⢰⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠻⠟⢃⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣃⠀⠀⠀⠀⢀⣄⢀⠀⠀⠀⢀⢘⣽⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⠟⠛⠛⠛⠛⠋⠙⠉⠉⠉⠉⠉⣉⠉⠉⠉⠀⠀⠀⢠⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣇⠀⠀⢠⠟⣸⣿⡛⠿⣿⣾⣿⣿⣿⣿⣿⠁⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣀⣀⣀⣀⣀⣀⡀⢀⣴⠐⠀⠀⠀⠀⠀⡏⠀⢠⡏⠀⠿⠃⠀⠀⠹⣿⣿⣿⣿⣽⣿⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⠒⣼⣿⣇⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠙⠟⣿⠯⣿⣿⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢜⣽⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣧⡉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⠙⡏⢯⡿⣿⣧⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠛⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢲⣆⡀⠀⠀⠀⠠⠀⣤⣀⡀⢀⣀⣀⠀⠈⠁⢽⣾⣿⣷⠾⢧⡄⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⠟⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⡀⣠⡾⠿⠛⠀⠀⡀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣷⣯⢰⣶⡖⢻⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⣿⢡⣿⣿⣿⣿⠏⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⣀⣹⡏⠀⠈⢠⡀⠀⠀⠐⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠻⢿⣿⣿⣿⣿⡟⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠆⣄⢀⣀⠲⠄⠀⠊⠀⠀⡆⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣯⣽⣥⣟⣻⣤⣛⣛⣠⡿⠿⠿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⢿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡶⣾⣿⣿⣿⢻⣯⣭⢿⡿⣛⣯⣽⣛⢿⢿⣛⡻⠿⢿⣿⠿⠿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⣿⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡙⣫⣵⣶⣤⣌⠻⣿⣿⢿⡇⠀⠜⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡉⣿⣿⠀⣿⣿⠘⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣾⣿⡇⠂⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⠃⢀⠂⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣈⠉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⡇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⢀⡎⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣭⣿⣿⣿⣭⣉⡛⠛⠃⠛⠛⠙⠻⠿⣈⠻⢿⣿⠿⠋⠀⠀⠎⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⢸⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣶⣶⣶⣶⣶⠶⣶⡶⣶⡶⣶⡶⢶⡶⢶⣶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣐⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⢿⡧⡀⠀⠀⠀⠀⠀⢬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⠶⣶⣤⡀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⢤⠠⢄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣫⣷⡖⡂⠂⠀⡀
⣿⣿⣿⣿⣿⣿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡷⢾⣏⠁⢬⣩⢥
⠿⠿⠻⠻⠻⠅⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠋⢋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣛⣿⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠨⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⢻⣿⢿⣭⣿⡿⣿⣿⣿⣿⣷⢻⡿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠛⠛⠛⠋⢈⠉⢨⣽⣭⡟⣿⣟⣯⡹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⣻⣿⣿⣿⣿⣿⣿⡁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠄⠀⠨⢉⠫⣝⢢⡑⣿⣿⣷⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠄⣘⢁⣑⢩⣝⣿⣭⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠘⣍⠁⢱⣃⢹⡫⡾⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣿⣿⢿⣿⣿⣿⣿⣟⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣈⡉⠁⠈⡩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠽⣻⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣿⣿⣿⣿⣿⣿⣠⡈⠛⣿⣧⣷⣯⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢍⢹⣽⠟⠁⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣻⣤⣤⣿⣧⣿⢿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠁⠀⠀⠁⢰⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠿⠿⢿⠟⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠻⠻⢇⠀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣃⠀⠀⠀⠀⢀⣄⢀⠀⠀⠀⠀⠛⣷⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠀⠀⠀⢠⣿⣿⣿⣿⣇⣷⣿⣿⣿⣿⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣇⠀⠀⢠⠟⣸⣿⡻⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣀⣀⣀⣀⣀⣀⡀⢀⣶⠐⠀⠀⠀⠀⠀⡏⠀⢠⡏⠀⠿⠃⠀⠀⢸⣿⣿⣿⣿⢯⣿⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⠒⣾⣿⣇⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠈⠉⢟⣿⢿⣿⣿⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢾⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣧⡉⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠁⠈⠝⣛⣿⡿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠛⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢲⣆⡀⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⣀⠁⠀⠁⢽⣾⣿⣷⠾⢧⡄⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⡏⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⢀⡀⣠⡾⠿⠟⠀⠀⡀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣷⣯⢰⣶⡖⢻⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⣿⢡⣿⣿⣿⣿⠟⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⣀⣹⡏⠁⠈⢡⡀⠀⠀⠐⠂⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠻⢿⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠀⣄⢀⣀⠲⠄⠁⠈⠀⠀⡂⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⣻⣤⣛⣛⣠⡿⠿⠿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣷⠀⣿⣿⣿⡿⣿⣿⡇⣰⣶⡶⣾⣿⣿⣿⢻⣯⣭⢿⡿⣛⣯⣽⣛⢿⢿⣛⡻⠿⢿⣿⠿⠿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⣿⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡙⣩⣵⣶⣤⣌⠻⣿⣿⣿⡇⠀⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡇⣼⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⠘⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣾⣿⡇⠂⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⠃⢠⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣈⡉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⡇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⢀⡎⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠙⠻⠿⣈⠻⢿⣿⠿⠋⠀⠀⠎⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⠛⠁⠀⢸⣿⣿⣿⣿⣿⡅⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣾⣿⣷⣶⣶⣶⣶⠶⣶⡶⣖⢖⣒⣶⢖⡲⢶⡖⡒⣲⠶⣖⢲⣶⣶⣲⣲⠶⣖⣶⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⣳⣿⣿⣿⣿⣿⣛⣿⣯⣻⣿⣿⢿⣿⣿⣿⣏⣩⣌⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⢷⣷⣯⣿⣿⡿⡿⣿⣿⣿⣿⣞⠀⠂⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⡿⣿⣿⣿⣷⣻⣾⣿⣿⠿⣿⣿⣿⣿⣿⢿⣧⣤⠤⠀⠀⠀⠀⢘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⣾⣯⣻⣟⡿⣿⣿⣿⣿⢿⣻⣿⣷⣻⣻⣿⣻⣔⠀⠤⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣫⣿⣭⣿⣭⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣽⣍⣻⡦⡄⠀⠄⡰
⣿⣿⣿⣿⣿⣿⢿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⠿⣿⢮⣿⣽⣿⣿⣿⠿⣿⣿⣿⣿⢽⡿⡿⣯⡿⣽⣿⠧⣷⣽⠽⠂⡐⣚⢖
⠿⠷⠟⠿⠾⠆⠀⠀⠀⠀⠈⠉⠉⠛⠛⠹⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠛⠋⠉⠉⠀⠁⠀⠀⠀⠀⠀⠐⠂⠅⢷⢿⣿⣳⣿⣿⡿⣿⣻⡿⣿⢹⣻⣻⣟⣿⣿⣫⣷⢹⣟⣎⣓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣯⣯⣷⣿⣿⣾⣿⣟⣿⣿⣯⣿⣿⣷⣿⣽⣿⣿⣽⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⠹⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢿⡿⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠃⠋⠉⠕⠒⠀⡘⣿⣿⣥⡟⣿⢽⠿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⡠⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡅⡁⠱⡴⣓⡮⢺⣿⢿⣽⢻⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣕⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⠀⠀⠦⠞⠏⢉⣿⣻⣿⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠐⠹⢁⡰⢴⣠⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⢯⣿⣿⣟⣿⣛⢅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⠀⠀⠈⠁⠀⠈⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣤⡀⠹⣿⣷⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⣩⡾⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣻⣄⣤⣿⣯⣿⣻⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⠋⠀⠀⠀⠠⣶⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠏⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠻⠿⢃⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣇⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠸⠋⣧⣿⣷⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⢻⠛⠛⠛⠛⠛⠋⠙⠉⠉⠉⠉⠉⣉⠉⠉⠉⠀⠀⠀⢀⣾⣟⣿⣿⣿⢶⣷⣷⣿⣻⣇⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣥⠀⠀⢠⣿⣿⣿⢇⠿⣧⣿⣿⣿⣿⣿⣭⡟⠒⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣀⣀⣀⣀⣀⣀⡀⢀⣶⠐⠀⠀⠀⠀⠀⡏⠀⢀⣿⣿⣿⣧⡄⠀⢸⣿⣿⣿⣿⣿⣻⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⠒⣼⣿⣇⠀⡇⠀⣼⠁⠀⠉⠉⠀⠀⠰⠈⠹⠿⠟⣿⣿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡿⠿⠂⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠺⣿⡟⣷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡆⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠀⠉⠻⣿⣿⢿⣶⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀
⠛⠟⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⢲⣯⣄⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⣀⠀⠈⠁⢨⣿⣿⣿⡶⠾⣇⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⢿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⡟⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⣠⡀⢰⡿⠛⠋⠀⠀⠆⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣦⢱⣶⡖⢸⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣇⣿⣿⣿⣿⠏⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⠃⢀⣠⡸⠇⠀⠀⢰⠄⠀⠀⠐⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⢹⣿⣿⣿⡟⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠁⠦⢀⡤⠓⠂⠀⠉⠀⠀⡕⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠟⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣽⣧⣟⣻⣤⣛⣛⣠⡿⠿⠿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⠟⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡿⣿⣿⡇⣰⣶⡶⣶⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣽⣛⢿⢿⣛⡻⠿⢿⣿⠿⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠈⣿⠏⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢠⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⣿⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡉⣩⣵⣶⣤⣌⠻⣿⣿⡿⠇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡉⣿⣿⠀⣿⡿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣾⣿⡇⠂⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⡿⠃⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣈⡉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡟⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣭⣿⣿⣿⣯⣉⣛⠛⠃⠛⠛⠙⠻⠿⠈⠻⢿⣿⠿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠛⠁⠜⠙⠛⠃⠛⠛⠛⠁⠀⢸⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠠⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣾⣿⣷⣶⣶⣶⣦⣲⣶⣶⣖⣖⢶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣰⣶⣰⡒⡖⢀⡤⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣯⣖⣿⣿⣟⣾⣽⣮⣻⢶⣯⡶⣿⣞⣿⣿⢿⣿⡇⣷⣰⠐⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⡿⢻⡯⡾⣯⣿⣿⣿⣕⣽⠿⡾⣿⣿⢿⣿⣟⢸⣟⠃⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣟⣿⣽⢿⡿⣿⣗⣽⣾⣯⣿⣿⣶⢿⣴⢿⣇⣤⠤⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣝⡮⣟⣏⣿⣼⣷⣽⣮⣻⣿⣿⣿⣾⢿⣻⣺⣩⡻⡦⠠⠤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⢿⣺⣵⣯⣿⣿⣿⣿⣾⣿⣾⢯⣝⣽⢿⡿⢬⢻⡅⠁⠀⠀⢀
⣿⡿⣿⣿⣿⡿⠟⠻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠻⣿⣿⣿⣟⣾⢿⣿⣿⡻⡿⣿⣿⣿⣻⣿⡳⣿⣿⡭⣿⣣⡟⣉⢩⡂⢀⡔⢐
⠯⠟⠛⠳⠓⠁⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠙⠛⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⡜⣹⢼⢿⠛⠿⢽⡛⣎⡾⣌⣿⣾⣻⣻⣷⣏⣿⡙⡿⣟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢟⡵⢮⣇⣼⣽⣎⡏⢶⣎⢷⣧⣛⣷⡯⣤⣅⠴⣇⣾⣓
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠿⢻⣽⣯⣿⣿⢿⣿⣿⣿⣿⡿⡿⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠉⠙⠂⠙⠉⠙⢉⡻⣟⡛⠿⣽⠸⣹⣼⢯⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢚⣿⣿⣿⣿⣿⣿⡀⢤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⣠⣭⣷⡩⣿⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡯⣿⣯⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠍⠈⣘⡓⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠁⠑⠑⢯⡈⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣿⣿⣿⢯⣿⣿⣟⣿⠟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣛⣿⢾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣤⡀⠘⣿⣆⣾⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⢩⡟⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⣹⣠⣄⣛⣏⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠋⠀⠀⠀⢀⣶⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠯⠻⠿⠏⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣚⢇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠟⢃⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣇⠀⠀⠀⠀⢀⣤⣀⣀⡀⠀⠀⡊⡏⣾⡗⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⢻⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠀⠀⠀⢀⣾⣏⣿⣿⣿⢪⣦⣿⣿⣻⣇⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣅⠀⠀⢠⣾⣿⣿⠁⠿⣻⣿⣿⣿⣿⣟⣭⡜⠒⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣀⣀⣀⣀⣀⣀⡀⢀⣶⠒⠀⠀⠀⠀⠀⡏⠀⢀⡿⣿⣿⣧⡄⠀⠨⣿⣿⣿⣿⣣⣻⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⠒⣼⣿⣇⠀⡇⠀⣼⠁⠀⠉⠉⠀⠀⠐⠈⠙⠿⠟⣿⣿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡿⠿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⡾⡿⣷⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠈⠜⣿⢿⢿⢦⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀
⠛⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⢳⣯⣄⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⣀⠀⠁⠉⢨⣾⣿⣿⡶⠾⣃⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⢿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠟⠁⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⣀⡀⢰⡿⠛⠛⠀⠀⠆⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣦⢱⣶⡖⢸⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣧⣿⣿⣿⣿⠏⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠃⢀⣠⡸⠇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⢹⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠁⠤⢀⡤⠓⠂⠀⠉⠀⠀⡰⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠟⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣽⣧⣟⣻⣄⣛⣛⣠⡿⠿⠿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⠟⢀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡿⣿⣿⡇⣰⣶⡶⣶⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣽⣛⢿⢿⣛⡻⠿⢿⣿⠿⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠈⣿⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢠⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⣿⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡉⣩⣵⣶⣤⣌⠹⣿⣿⡟⠇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⡿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣾⣿⡇⠂⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠸⡿⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣈⡉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡟⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣭⣿⣿⣿⣭⣉⣛⡛⠃⠛⠛⠙⠻⠿⠈⠻⢿⣿⠿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠛⠁⠜⠑⠛⠃⠛⠛⠛⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠟⠂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣾⣷⣾⣷⣾⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠂⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⡄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠔⠄⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡂⢀⠐⠂
⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣪⣪⣮⣫
⠿⠿⠛⠟⠛⠁⠁⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠏⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠛⠟⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠆⠉⠹⡟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣩⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⣿⡰⠹⣿⣿⣿⡹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠁⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣤⡈⠸⣿⡇⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣫⣿⠟⠁⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⣻⣤⣄⣿⣯⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠁⠀⠀⠀⠀⢿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠟⠿⠿⠟⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣧⣄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⢃⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣇⠀⠀⠀⠀⠀⣠⣦⣤⣄⣀⢠⣾⣷⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⠛⠛⠋⠉⠙⠋⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠀⠀⠀⠀⣴⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣆⣥⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠈⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣀⣀⣀⣀⣀⣀⡀⢀⣶⠒⠀⠀⠀⠀⠀⡏⠀⠀⣼⢿⣿⡿⠲⠀⠐⣿⡿⣿⣿⣿⣿⡄⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⠂⣼⣿⣇⠀⡇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⢙⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣿⢿⡿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣺⣽⣿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⡻⡿⢿⠿⡷⣦⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠛⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠀⣿⣷⡀⠀⠀⠀⠀⣨⣀⡀⢀⣀⣀⠀⠉⠉⣵⣿⣿⣿⣿⢿⡶⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢠⣤⠤⠀⠿⠋⠉⠁⠀⡰⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢰⣶⡖⢹⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⢇⣾⣿⣿⣿⡿⠁⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⢀⣤⠤⠛⠀⠀⠘⡆⠀⠀⠀⠁⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⢿⣿⣿⣿⣿⡿⠁⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠁⠒⠠⠶⠉⠉⠀⠀⠀⠀⢸⠀⢸⣿⣿⡟⢸⣿⣿⣿⣀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⡿⠁⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣽⣥⣛⣛⣤⣛⣛⣠⡿⠿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣾⣿⣿⠟⠁⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣿⣿⢿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡶⣾⣿⣯⣿⢻⣯⣭⢿⡿⣛⣯⣽⣛⢿⢿⣛⡻⠿⢿⣿⠿⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⢻⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⣿⢸⣿⣿⠈⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡙⣩⣵⣶⣤⣌⠻⣿⣿⣟⣿⠀⠈⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡇⣼⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⡇⢨⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣾⣿⡏⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⡟⠀⠈⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣌⡉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡷⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠟⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣭⣉⣛⠛⠃⠛⠛⠙⠻⠿⣈⠻⢿⣿⠿⠋⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀
⠀⠛⠁⠜⠙⠛⠃⠛⠛⠛⠁⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡆⠀⡤⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣠⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣛⣻⡇⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣾⡿⣿⣽⢿⣿⣿⣿⣿⣿⣵⣤⡂⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡰⡠⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠳⠀⠀⡄
⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⢿⣿⣷⣿⣿⡗⠄⣠⣨⣐
⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠃⠻⠶⠈⡋⣿⢯⣻⣟⣿⢟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣬⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⠨⢙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡥⠉⠏⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠚⣿⣿⡻⡻⡿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣽⣿⣿⡿⠯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢈⠀⠀⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣾⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣤⡈⠘⣿⣧⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⠟⠁⢀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣻⣤⣄⣟⣏⣿⣟⣻⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠁⠀⠀⠀⠀⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠟⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣧⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⢣⡀⣰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣇⠀⠀⠀⠀⠀⣠⣦⣤⣄⡀⣈⣬⡿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⠛⠛⠋⠉⠛⠋⠙⠉⠉⠉⠉⠉⣉⠉⠉⠉⠀⠀⠀⠀⣴⣿⣹⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠈⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣀⣀⣀⣀⣀⣀⡀⢀⣶⠒⠀⠀⠀⠀⠀⡏⠀⠀⣼⢿⣿⡿⠲⠆⠺⢿⡿⣿⣿⣿⣿⡄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⠂⣼⣿⣇⠀⡇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⢙⣿⣿⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣿⢿⡿⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⢾⡿⢿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⡆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢻⡿⡿⡿⡷⣶⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠛⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠀⣿⣷⡀⠀⠀⠀⠀⣬⣁⡀⢀⣀⣀⠈⠉⠈⣵⣿⣿⣿⡿⢿⡶⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢠⣤⠤⠀⠿⠋⠉⠁⠀⡰⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢰⣶⡖⢻⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⢃⣾⣿⣿⣿⡿⠁⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⢀⣤⠴⠛⠀⠀⠘⡆⠀⠀⠐⠁⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⢿⣿⣿⣿⣿⡿⠁⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠁⠒⠠⠶⠉⠉⠀⠁⠀⠀⢸⠀⢸⣿⣿⡟⢸⣿⣿⣟⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⡿⠁⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣽⣥⣟⣛⣤⣛⣛⣠⡿⠿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣿⣿⠟⠁⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⣿⢿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡶⣾⣿⣿⣿⢻⣯⣭⢿⡿⣛⣯⣽⣛⢿⢿⣛⡻⠿⢿⣿⠿⠿⠿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⢻⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢠⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⣿⢸⣿⣿⠈⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡙⣩⣵⣶⣤⣌⠹⣿⣿⡿⣿⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡉⣿⣿⠀⣿⣿⡇⠨⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣾⣿⡏⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⡟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣈⣉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⣗⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠟⠁⢠⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿⣿⣭⣉⣛⠛⠃⠛⠛⠙⠻⠿⣈⠻⢿⣿⠿⠋⠀⠀⠀⠃⠀⠀⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀
⠀⠛⠁⠜⠙⠛⠃⠛⠛⠛⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡆⠀⣤⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣾⣷⣶⣶⣶⣷⡶⣶⡶⣖⣾⣿⣶⣶⣿⣷⣷⣖⣒⣲⣖⣶⡶⣶⡆⣶⣄⡐⠀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⡑⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣯⢿⢏⣛⣿⣯⡁⣂⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⣟⣿⣿⣷⢿⣿⣿⣾⣿⡿⣿⣗⣿⣷⢿⣶⣿⣿⡗⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣽⣿⡿⣿⣯⣟⢿⡯⣿⢿⣿⣿⣿⣟⣯⡅⠠⠠⠠⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣯⣿⣿⣿⣻⣮⣵⣢⣖⡯
⣿⡿⣿⣿⣿⢿⢿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣷⢿⣿⣿⣷⣷⣿⣿⣿⢷⣿⣿⡯⡹⡬
⠟⠟⠛⠻⠏⠀⠀⠀⠀⠀⠉⠙⠛⠋⠛⠻⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⢟⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣟⣿⡻⣟⡻⢻⣿⢿⢿⣾⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⣿⣿⣿⣿⣯⣿⢿⣯⣿⣿⣯⣿⣿⣷⣽⣿⣭⣿⣿⣍
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠑⠮⠂⠘⣺⡽⡿⢼⣴⡷⠿⡾⢷⡷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠏⠽⠙⣚⣿⣾⣿⣿⣿⣇⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠠⣴⢮⣷⡺⣪⠿⣳⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣱⣿⣿⣿⣯⣿⣿⣿⣿⣿⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠊⠀⠡⠋⠁⣿⡟⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣷⣿⣿⣿⣯⣿⣿⣿⣿⡏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡔⠀⢻⣮⢶⢊⢷⡟⣯⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⢿⣯⣿⣿⣿⡿⠏⢝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⠀⠈⠀⠀⠁⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢙⣿⠿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣾⣿⣿⣿⣿⣷⣶⣶
⣿⣿⣿⣿⣿⣿⣤⡈⠸⣿⣇⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚⡋⡒⣻⠞⠁⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣻⣤⣄⣿⣯⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⢲⣾⠃⠀⠀⠀⠀⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣽
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠟⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢺⣧⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣿⠛⠟⢓⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣇⠀⠀⠀⠀⢀⣴⣦⣤⣤⣈⣈⢵⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⢻⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠀⠀⠀⢀⣾⣏⣿⣿⣿⣿⣿⣿⣷⣞⣇⣄⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣥⠀⠀⢠⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⡍⠉⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣀⣀⣀⣀⣀⣀⡀⢀⣶⠒⠀⠀⠀⠀⠀⡏⠀⢀⡿⠿⣿⠟⠿⠀⠙⣿⢿⣿⣿⣿⢾⣇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡇⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡆⠀⣼⣿⣇⠀⡇⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠿⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢓⢉⣯⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡖⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⢀⡹⢑⡿⣿⣿⠷⣶⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣴
⠛⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⢹⣿⣶⠀⠀⠀⠀⠈⣥⣀⡀⢀⣀⣀⠉⠁⠉⢽⣿⣿⣿⣿⢿⣧⠄⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⢿⣿⣿⣿⣿⡟⣼⣿⣿⣿⡿⠃⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢠⡴⠆⠘⠏⠉⠁⠀⠀⡆⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡖⢻⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣷⣿⣿⣿⣿⠃⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⣠⡶⠚⠓⠀⠀⠸⠂⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⠏⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢃⣄⠀⠀⠀⡀⠀⠄⣤⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠓⠐⠂⠈⠁⠀⠀⠀⠀⡿⠀⢸⣿⣿⡟⢸⣿⣿⣿⣀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⡟⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣽⣧⣟⣻⣤⣛⣛⣠⡿⠿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣷⠀⣿⣿⣿⡿⣿⣿⡇⣰⣶⡶⣾⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣽⣛⢿⢿⣛⡻⠿⠿⣿⠿⠿⠿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠈⢿⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⣿⢸⣿⣿⠈⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡉⣩⣵⣶⣤⣌⠹⣿⣿⡿⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡉⣿⣿⠀⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡯⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡂⣾⣿⡏⠓⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠸⡿⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣈⣉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⡇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⣛⡛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⠛⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠿⠂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⣖⣒⣲⣶⣶⣶⣖⣂⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣻⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣖⣯⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢟⣿⣾⢽⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣯⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣀⢀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣿⣿⣿⣷⡯⡾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⡠⢬⡀
⣿⣿⣿⣿⣿⡿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⡿⠙⠛⠿⣿⣿⡿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢿⣿⣧⢭⣿
⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠉⠙⠋⠛⠛⠻⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⣷⢿⣯⣿⣷⣭
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡟⣻⣙⡧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⡋⠈⠉⠁⠙⠳⡺⡟⣻⣽⣟⣽⡝⣵⣟⣝⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠴⡇⠎⠻⣿⢞⠏⣾⡷⣯⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣷⠻⣯⢷⣗⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠛⡂⠫⠯⠶⣫⣖⣚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣛⠿⢿⣿⡿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣠⡈⠸⣿⡇⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠩⣨⡼⠋⠀⠀⠀⢀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣯⣻⣤⣤⣟⣧⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠻⠿⠿⠿⠿⠿⠿⠿⠻⠿⠏⠈⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠸⣹⣢⣤⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠛⢓⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⠀⠀⠀⠀⢀⣾⣻⣾⣷⣤⣐⣚⣽⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⢻⠛⠛⠋⠙⠛⠋⠉⠉⠉⠉⠉⠉⣉⠉⠉⡋⠀⠀⠀⢠⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⡷⣦⣀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣅⠀⠀⣠⣿⣿⣿⣻⠻⢟⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣀⣀⣀⣀⣀⣀⡀⢀⣶⠒⠀⠀⠀⠀⠀⡏⠀⢀⠟⠉⠙⠁⠉⠀⠸⣿⢿⣿⣿⣷⣽⡇⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⠀⣠⣿⣇⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠀⠿⠯⡾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⢿⡿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠁⣸⢞⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⠄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣖⡀⠀⠀⠀⠀⢀⠠⠖⠁⠀⠂⠃⠘⠱⣙⢟⣟⣮⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠛⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⠿⢻⡾⠿⠿⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠸⣾⣿⣿⣿⣿⣿⡶⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⡿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⣀⣹⡏⠁⠈⣥⠠⠀⠀⠀⠁⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢰⣶⡞⢹⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⢠⣿⣿⣿⣿⡟⠁⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠃⣿⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠴⠂⡄⢀⡐⠦⠄⠀⠃⠀⠀⡄⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⢻⣿⣿⣿⣿⡟⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣼⣿⣿⣿⠟⠀⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣯⣽⣧⣟⣛⣄⣛⣛⣠⡿⠿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⠋⢀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣷⠀⣿⣿⣿⡿⣿⣿⡇⣰⣶⡶⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣽⣛⢿⢿⣛⡻⠿⢿⣿⠿⠿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⠘⣿⡿⠃⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠈⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡙⣩⣴⣶⣤⣌⠹⣿⣿⡟⠇⠀⠘⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⡀⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⡿⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡆⣼⣿⡏⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⢸⣿⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣈⠉⠉⠙⠁⠘⠛⢛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⡇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠋⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣯⣿⣿⣿⣭⣉⡛⠛⠃⠛⠛⠛⠻⠿⡈⠻⢿⣿⠿⠋⠀⠀⠈⠀⠀⢨⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⠀⠛⠁⠜⠉⠛⠃⠛⠛⠛⠀⠨⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠠⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀
⣷⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣶⣖⣲⣤⣤⣴⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⠻⠉⠋⠉⠁⠀⠀⠉⠀⠈⠉⠉⠋⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠛⡿⠿⡾⠿⠿⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠦⠈⢿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠉⠛⠿⠟⡿⠿⠿⠿⠿⠿⠿⠛⠛⣿⣟⡻⣻⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⣿⣿⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⢿⣿⣷⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿
⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⠿⠞⡟⠁⢠⣷⣦⣤⣶⠀⠠⣄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣶⣿⣿⣿⣛⠻⠿⠿⢿⣿⣿⣿⣿⠀⠀⣴⠟⢁⠀⠐⡇⠀⢈⡿⣿⣿⡟⢶⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣯⣍⠀⢰⠃⠀⠈⠀⠀⠀⠀⣸⠉⣻⣿⠣⢺⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⡿
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡘⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠈⠛⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣶⠆⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⢠
⣿⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⣉⣶⣄⣀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠙⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣠⣿
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⠿⠿⣿⣿⠟⢻⡿⠛⠓⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠴⣿⢿⣿⣿⣿⣿⡶⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⢿⣿⣿⣿⣿⢃⣿⣿⣿⣿⠋⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⢀⣀⡹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢰⣶⡞⢹⣿⣷⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢻⣿⣿⣿⣼⣿⣿⣿⠏⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⢿⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⠠⠄⢀⠐⠢⠀⠀⠃⠀⠀⡀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⠃⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣭⣽⣦⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡟⠁⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣭⣭⢻⡿⣛⣭⣭⣛⠿⢿⣛⡛⠿⠿⡿⠿⠿⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡇⠈⠻⠁⢰⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢘⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡉⣩⣴⣶⣤⣄⠙⣿⣿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣸⠏⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡆⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⡈⠉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⡇⣿⡟⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣯⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠋⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣴⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡒⠖⠄⠀⢄⡤⢤⢤⣴⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡽⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣫⣿⣿⣽⣿⣿⣿⣿⣿⣾⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢦⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠋⠙⠈⠀⠀⠀⠀⠀⠀⠋⠉⠁⠘⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢭⠛⢿⠻⠯⠛⠛⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠘⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠻⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⣿⣃⡘⢹⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⣿⣿⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⢿⣿⡷⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⠿⠟⡿⠁⠠⣶⣦⣤⣶⠈⠰⣄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣷⣿⣿⣿⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⣴⠟⢁⠀⠐⡇⠀⢐⣿⣿⣿⡟⢶⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⢰⠃⠀⠈⠀⠀⠀⠀⣘⠙⢻⣿⠃⢸⡧⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⡟
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡘⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠛⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣶⠆⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⢠
⣿⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⣁⣶⣄⣀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠹⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣠⣿
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⠿⣿⣿⠟⢿⡿⠛⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠴⣿⣿⣿⣿⣿⣿⡶⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⢿⣿⣿⣿⣿⢃⣿⣿⣿⣿⠋⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⢀⣀⡹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢰⣶⡞⢹⣷⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢿⣿⣿⣿⣸⣿⣿⣿⠏⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠛⢻⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠐⠠⠄⢀⠐⠢⠀⠀⠃⠀⠀⠄⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⡿⠁⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣭⣽⣦⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⠁⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣭⣭⢻⡿⣛⣭⣭⣛⠿⢿⣛⡛⠿⠿⡿⠿⠿⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⣿⡇⠈⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⠀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠈⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣩⣴⣶⣤⣄⠘⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣻⠇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡆⣾⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⠏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣈⠉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡟⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣯⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠋⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⠦⠤⡤⠐⠤⣴⣶⣶⣶⡶⢶⢶⣶⠔⢀⢐⣦⣦⣶⡴⣴⡤⢦⣦⢦⣔⢦⢶⣴⢴⠠⠆⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣿⣿⣿⡯⡂⠂⣈⡊⣿⣿⣿⣿⣿⣟⣿⣿⡇⣛⣺⠂⢀⡢⠄⠰⠖⡢⠤⡂⠐⢁⣁⢊⠔⠄⠂⠰⠳⢉⡁⠁⠢⠀⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡷⠴⠄⣀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣼⣃⢀⠀⠄⡣⢢⠃⢌⠋⡀⠄⠊⢀⠀⠈⢀⠛⠁⢠⠐⠀⠀⣼⠔⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠻⣏⠊⡄⢲⠷⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣧⣄⠠⢁⣐⡫⠀⠂⠌⠄⠨⣤⠠⠅⠖⠉⣒⣛⠠⠴⠈⠉⣠⠄⠔⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢫⣶⡹⠱⠮⡎⢽⣆⠉⡿⠛⡟⣿⣿⣿⣿⣿⣿⣻⣷⣿⣿⣿⣧⡩⣌⣒⣦⠴⠀⠇⠌⠽⠤⠄⠠⢠⢜⡬⠬⠴⢙⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣽⡗⣗⢒⠛⠆⣷⠭⢄⡴⣝⢋⣭⠽⡯⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣖⣩⡠⠅⠒⠁⠀⠤⠠⠑⡂⠐⠒⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠛⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⡫⢚⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣷⣷⣍⡟⣃⣀⣐⡉⠄⠠⠁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠀⠰⠵⡝⢿⠿⣿⣿⡿⡿⠿⠿⣿⠋⣛⡓⠙⢁⣬⠙⡒⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠑⠂⠓⠪⠛⠘⠊⠉⠀⠈⠉⠱⣤⣤⡀⢸⡷⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣣⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣴⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⢻⣶⣶⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿
⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⡾⢻⡇⠀⢀⣀⣀⣄⡀⢄⡀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⣺⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⢠⠟⠛⠛⠀⠀⠀⠀⠀⠘⢻⣿⢇⣿⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⠿⠇⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠙⠧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣶⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣴⣂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢉⣲⣄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⠿⢿⣿⡿⠻⣧⠞⠟⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠰⢾⢿⣿⣿⣿⢿⣷⠂⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⡿⠁⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⢀⣠⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢰⣶⡆⢰⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠻⣿⣿⣿⡏⣾⣿⣿⣿⠟⠀⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣼⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⢿⣿⣵⣿⣿⣿⡟⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠀⠤⠀⡀⠂⠄⠀⠐⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⡟⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡟⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣭⣭⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠏⠀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⠿⢟⣛⡛⠿⠿⡿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠽⣿⣿⣿⣿⣿⡗⠀⢻⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠈⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠘⣿⣿⡟⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣸⣿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⡮⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄⡈⠉⠉⠉⠁⠘⠛⢛⣛⣣⣼⣻⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡷⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠅⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠉⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣶⣶⠶⣦⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⠦⠤⠀⠒⠄⣴⣶⣶⢶⠶⣶⣶⣦⠐⠄⢐⣦⣦⣶⡰⣴⣤⣆⢦⣦⣴⡢⠶⢴⣴⣤⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣟⣿⣿⣿⡯⠣⠁⠒⢆⣿⣿⣿⣿⣿⣟⣿⣿⡏⡻⡟⠐⠴⢤⡈⠧⠔⠈⡚⡄⢀⢕⠗⣔⠐⠀⢋⠠⠦⠂⠩⠂⠂⠀⠷⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣗⠄⠀⠢⢁⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣙⠂⡅⡌⠐⠈⠩⢤⡚⢅⢤⢐⠒⠀⠀⡦⠐⠀⠻⠄⠶⠐⣞⡠⠀⢻⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢻⣇⡭⡀⣠⡶⢿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣷⣦⢶⡭⢁⠁⠔⠄⠠⠌⠐⢀⠂⠁⣢⠁⠆⣈⢠⡄⠔⣄⠰⠠⠐⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣕⡥⡊⡍⢣⠨⡙⣋⠃⡯⢽⣻⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣵⣦⣇⣔⣄⡠⡭⡄⠇⠎⠢⠐⠆⠑⡖⠦⠤⡤⡤⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣽⣟⣭⠅⣊⠨⡊⠜⢓⠆⣀⡠⡍⢉⣫⠭⡝⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣯⡬⠂⣀⢰⠏⠀⠀⠢⠀⠔⢛⠀⣂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢶⣙⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣧⣗⠩⠀⢄⣔⢱⠂⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠀⠨⠑⣗⠻⡿⣿⣻⢿⣿⠿⡿⠿⠛⣛⢛⡛⣈⡀⡹⠏⢄⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠋⠐⠛⠪⠈⠚⠈⠋⠎⠀⠉⠉⠤⣤⣄⠈⣿⠲⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⢻⣶⣶⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⡿⣺⠟⠏⠀⢀⡄⢀⣄⡀⢄⡀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣽⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⡟⢃⠀⠀⢀⠈⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⢀⡿⠻⢿⣇⠘⠀⠀⠀⠀⠀⠰⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⢧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣿⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡂⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠈⢉⣠⣤⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⡿⡿⠟⢣⠼⠿⠃⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠰⢾⢿⣿⣿⣿⣻⡷⠂⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢻⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⠏⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⣀⡀⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢰⣶⡆⢰⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠻⣿⣿⣿⣿⢁⣿⣿⣿⣿⠃⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣼⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠹⣿⣿⣟⣼⣿⣿⣿⠇⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠠⠀⣀⠲⠤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⡟⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣭⣽⣤⣛⣛⣀⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⣾⣿⣿⠏⠀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⠿⢿⣛⡛⠿⠿⡿⠿⠿⠿⢿⡿⠿⠿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡇⠀⢹⣿⠇⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣷⡖⢰⣶⣶⣶⣦⡉⣡⣴⣶⣤⣄⠘⣿⣿⡿⠃⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣸⣿⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣼⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⣿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⡈⠉⠉⠉⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣯⣭⣿⣿⣿⣍⣉⠛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠉⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⠶⢶⣶⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣦⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠒⠒⡂⠀⢀⣀⣀⡠⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡝⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢧⣫⣞⢿⢧⣿⣿⣿⣿⡯⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⡿⢯⣻⡿⣿⣍⣽⣽⣝⣫⢷⣮⢯⣆⣾⣿⡿⡟⣖⣭⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣽⢽⠺⣿⣏⣧⢽⣿⣿⣿⣌⣼⡮⡿⣿⡿⣌⢎⣛⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⡾⣿⣿⣽⣙⡜⣼⡿⡽⣿⡿⡜⣿⣿⡇⡇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⡷⢿⣷⣿⣷⣯⣮⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣦⣣⢻⣛⢻⡿⣿⣷⡜⣿⠋⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠇⣾⠛⠛⠩⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠛⠟⠛⠛⠻⠿⠿⠿⠛⠛⠻⢿⣧⠘⢹⡿⠟⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣂⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡞⣷⣶⡄⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿
⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⢳⡿⠛⠁⠀⠂⠀⠀⡐⠀⣀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣽⣿⣿⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⡿⠟⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣭⣍⠀⠀⠀⣼⠟⠿⣏⠀⠁⠀⠀⠀⠀⠀⣾⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿
⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣶⡤⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⣑⣶⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⡿⣿⠟⢣⡜⠿⠑⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⢶⠿⣿⣿⣿⣿⣿⡖⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢻⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠏⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⣀⡀⡹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⣿⣿⣿⡇⣾⣿⣿⣿⠃⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣸⣿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠿⢿⣿⣿⣿⣿⠏⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠊⠠⠀⣀⠐⠤⠀⠀⠂⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⡏⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⠟⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣯⣭⣤⣟⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠏⢀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡶⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⠿⢿⣛⠛⠿⠿⣿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠋⢻⣿⣿⣿⣿⣿⠀⠹⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠈⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡀⣡⣴⣶⣤⣄⠈⢻⣿⡿⠉⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⢸⣿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣼⣿⡇⠂⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⢿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⡈⠉⠉⠉⠁⠘⠛⠛⣛⣣⣸⣻⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠉⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣠⣶⣶⠂⠒⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣦⣤⠠⢐⢦⣤⣤⣶⣶⣶⣶⣶⣐⣤⣶⢦⣴⣦⣤⣤⣶⣦⣴⣶⣦⣖⣴⣶⣦⣦⢔⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣿⡰⡿⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠾⣟⡿⡿⢏⢷⠍⢾⣻⠷⠷⣟⠯⡣⢱⠸⣂⣄⠬⠠⣸⡷⡺⢔⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡷⣻⣗⠿⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⢓⡴⣫⠕⢫⢐⡙⡚⠕⡚⠨⠅⣱⢟⠤⢐⢏⢗⠡⡗⢚⠂⢾⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢫⢽⣫⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣝⣇⣅⡛⡫⣢⡻⠆⠇⣙⡇⢖⣽⣊⠕⠴⢌⣚⢏⡩⠓⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢲⡯⣿⡷⣿⣿⣿⡯⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡧⢌⣪⠥⡬⠔⡽⢲⢵⢩⢦⡅⣮⢥⢮⡿⣿⠤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⣻⢿⣿⠿⢟⠿⡿⣾⡤⣜⢿⣏⣻⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣧⣿⣷⣿⡏⢥⡨⡱⡡⢩⠉⢽⢵⢍⠠⠻⡛⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠈⠁⠙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⢼⠻⣾⢩⡊⡌⠀⠈⠜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡦⠐⠿⠾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⢫⡹⡾⢱⣅⡆⣹⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠛⠓⠓⠛⠚⠊⠪⠒⠓⠋⠉⠛⢼⣧⡀⢸⠟⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣶⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⠋⣾⣿⠆⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣲⠟⠁⠀⢀⣰⠀⣀⡄⠀⠄⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣧⡊⠀⠀⠀⠘⠃⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⣾⠟⠻⠯⠀⠀⠀⠀⠀⠀⠸⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣿⣿⠿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⡄⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣆⣀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⢉⣠⣤⣀⣤⡄⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⢿⢿⡟⠁⡴⠻⠃⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⢶⠿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⣿⣿⣿⣿⣿⡿⢀⣾⣿⣿⣿⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⢀⣀⠨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡆⢰⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠹⣿⣿⣿⣿⠃⣾⣿⣿⣿⡟⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⢿⣿⣿⣼⣿⣿⣿⡟⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠁⠄⢀⠀⠂⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⡆⠀⠉⣿⣿⣿⣿⡟⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⡟⢸⣿⣿⣟⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⡟⠁⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣭⣩⣤⣛⣛⣀⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠟⠀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡶⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⠿⢿⣛⡛⠿⠿⡿⠿⠿⠿⢿⣿⠿⠿⠿⢿⣿⣿⣿⡿⠼⢼⣻⣽⣿⣿⣿⠀⠘⣿⠇⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣷⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⢛⣿⡿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⢿⣿⠀⢨⣿⠃⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⢻⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡈⠉⠉⠙⠁⠘⠛⠛⢛⣃⣸⣻⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠉⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣶⣶⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⡦⣤⢠⢀⢦⣠⣤⣶⣶⣶⣶⣶⣐⡤⣶⢴⣤⣤⣤⣤⣴⣦⣴⣦⣦⣶⢔⢴⣦⣆⡐⠀⣀⠀⠀⢀⡀⢀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡷⡾⠁⣲⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢕⣿⡫⠻⡵⠧⡟⣿⢺⠟⣿⡥⢖⠷⠫⡹⠀⡐⠠⡂⢡⠘⡿⡾⡈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⣺⡉⡔⡢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣞⣿⢩⡒⠠⢒⠣⣀⡉⡐⠀⡃⠩⡛⢤⡨⣈⠚⢛⠦⡑⠄⣀⠜⣜⣗⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢳⣭⣆⣥⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡭⣏⣆⡈⡐⠠⠁⢬⠃⡞⢨⢆⡔⠩⣊⠐⡑⢓⢈⠄⠬⣉⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⣽⣮⣿⣮⣿⢷⣾⡬⠙⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣌⠢⠅⡧⠄⢅⣅⠦⠰⡄⢦⠂⡦⢜⠵⡱⡺⡯⡦⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⢿⡏⠟⢾⠿⣿⣖⣅⣍⠂⣛⣻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣷⡠⢐⠘⡈⠒⠖⠒⠵⡑⠼⣚⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠁⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠘⠀⢛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡭⣎⢮⢠⡂⡎⠁⠈⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠦⠀⠗⠽⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣹⣟⢒⢤⣅⣢⡟⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠊⠋⠪⠦⠎⠉⠙⠓⢽⣧⡀⠸⠟⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣶⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⢛⣾⣿⠆⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⡺⠟⠉⠀⢀⣴⠀⣀⡄⠀⠄⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣧⡀⠀⠀⠀⠈⠁⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⣾⠟⠻⠯⠀⠀⠀⠀⠀⠀⠸⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣿⣿⠿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⡄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣦⡀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⢁⣀⣤⣀⣤⡄⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⢿⢿⠟⠁⡴⠻⠃⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⢾⠿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠹⣿⣿⣿⣿⣿⡿⢀⣾⣿⣿⣿⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⢀⣀⠨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡆⢰⣾⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠹⣿⣿⣿⣿⠃⣾⣿⣿⣿⡟⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣼⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⢿⣿⣿⣼⣿⣿⣿⡟⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠁⠄⢀⠀⠂⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⡆⠀⠉⣿⣿⣿⣿⡟⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣷⠀⢰⣿⣿⣿⡟⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣭⣩⣤⣛⣛⣀⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠟⠀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡶⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⠿⢿⣛⡛⠻⠿⡿⠿⠿⠿⢿⡿⠿⠿⠿⠿⣿⣿⣿⡿⠝⢝⡻⢿⣿⣿⣿⠀⠘⣿⠇⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣷⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⢻⣿⡿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⢰⣿⠇⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⢾⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠈⠉⠉⠉⠁⠘⠛⠛⢛⣃⣸⣻⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣷⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠉⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣠⣶⡶⣶⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣦⣤⣶⣆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢤⣶⠆⠀⢀⠤⣠⠤⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣿⢿⣿⠿⣿⠿⢿⠿⢿⡿⣱⣟⣲⣾⡻⣿⡳⣷⣿⠿⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⡍⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣹⣡⢽⣷⢵⢰⠳⢺⣻⣲⡚⢷⣗⣺⣙⣏⣟⣏⠧⡿⣟⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣝⣽⣳⢾⣥⡳⢾⣿⢟⣗⡻⣗⣹⡵⣔⣧⠣⣽⢷⡓⣉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣻⣿⣿⣿⢛⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡯⣙⡟⡾⡞⣭⣿⢶⣏⡏⣿⣿⢷⣏⣿⡿⡪⣣⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠿⢿⡷⣿⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣋⡐⣴⢦⣜⢗⡯⡵⡧⡸⣻⡹⢦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠋⠋⠛⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠛⠙⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⡷⣧⡰⠉⠐⠫⠽⠲⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡦⠘⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⢊⡧⢃⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠛⠿⠻⠿⠿⠋⠛⢿⣷⡀⠺⡿⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣷⣷⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣶⠆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⠛⣷⣷⡆⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⢸⡟⠋⠀⣀⣦⠄⢀⡤⠀⡀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣯⠘⠀⠀⠀⠺⠻⣢⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣭⣍⠀⠀⠀⣾⠟⢿⡋⠁⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿
⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠛⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡦⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣆⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⢉⣠⣤⣀⣠⣤⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⣿⣿⠟⢡⡼⠿⠖⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⢾⢿⣿⣿⣿⣿⣿⠇⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠿⣿⣿⣿⣿⡏⣸⣿⣿⣿⡟⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⢀⣀⡹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡖⢸⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣿⣿⣿⢷⣿⣿⣿⡿⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⠻⣿⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠚⠠⠀⢀⠐⠤⠀⠀⠂⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⢸⣿⣿⡟⢸⣿⣿⣟⠀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⠏⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣭⣽⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠋⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡶⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⠿⢿⣛⡛⠿⠿⡿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠯⢿⢿⣿⣿⣿⣷⠀⠹⠋⠀⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⣿⣿⡿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⢸⣿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⡿⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡈⠉⠉⠙⠁⠘⠛⠛⢛⣣⣸⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡟⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠋⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⠶⣲⡴⣴⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⢀⣒⠂⠀⢀⣤⣤⡤⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣯⣾⡭⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣟⣏⣹⣽⣻⢹⣽⢿⣫⣿⡿⡦⣊⢻⢻⠳⢯⣾⣿⣻⣝⣊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣡⠧⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⢭⣿⡳⠝⣗⣿⢵⣯⣏⡼⢳⢏⣟⣿⣭⢫⣿⣭⣿⢸⡟⢺⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣿⣽⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣭⣙⢺⣷⠛⢃⣦⣫⠿⢶⣻⣭⣙⣺⣷⢲⣺⡗⣻⡦⢙⣊⠙⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣫⡿⢼⣞⢷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⣞⣿⣗⡭⢵⣟⣡⣎⡑⠯⠿⡮⢭⡿⢿⠧⣟⣟⡦⡦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⢲⢽⣟⣿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢳⣞⢏⣓⡭⢗⢎⣁⡷⡿⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠙⠋⠈⠀⠀⠀⠀⠈⠉⠛⠀⠉⠈⠉⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡧⣳⢧⡴⠋⠘⠻⠞⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡦⠉⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣪⡬⣷⣜⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠋⠓⠻⠿⠿⠟⠻⠻⠿⠋⠙⢿⣧⡈⠺⡿⠟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣷⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣶⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⠛⣷⣶⡆⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⢸⡿⠋⠀⣠⣶⠀⢀⡤⠀⡀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣯⠈⠀⠀⠀⣾⠻⣆⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣭⣍⠀⠀⠀⣾⠟⢿⡋⠁⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿
⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠛⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⡦⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣆⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⢉⣠⣤⣀⣠⣤⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣼
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⣿⣿⠛⢡⠼⠿⠖⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⢾⠿⣿⣿⣿⣿⣿⠇⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠿⣿⣿⣿⣿⡏⣸⣿⣿⣿⡟⠁⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⢀⣀⡹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡖⢸⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣿⣿⣿⢧⣿⣿⣿⡿⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣼⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⠻⣿⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠚⠠⠀⣀⠐⠤⠀⠀⠂⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⠅⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⢸⣿⣿⡟⢸⣿⣿⣟⠀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⠏⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣭⣽⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡶⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⠿⢿⣛⡛⠻⠿⡿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⠀⠹⠃⠀⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠈⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⣟⣿⡿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡉⣿⣿⠀⢼⣿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⡽⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠈⠉⠉⠙⠁⠘⠛⠛⢛⣃⣸⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣦⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠉⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠄⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⣾⣽⣾⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡆⠰⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠉⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠉⠉⢻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠦⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠛⠯⠛⠛⠻⠿⠿⠿⠛⠛⠛⣿⣧⡈⢿⠟⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡏⣾⣿⠆⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣻⠟⠋⠀⢀⣴⠄⢀⣄⠂⢠⠀⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣤⣿⣿⣝⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠊⣿⣯⠈⡴⠀⠀⠘⠋⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⡀⠀⠘⠷⠎⠀⠀⢠⠄⢤⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿
⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢿⠿⠿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⡆⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⣧⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢈⣩⣤⣀⣤⣤⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⣿⡏⠛⠳⠊⠛⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⢶⠿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢻⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⠋⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⣤⠄⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡆⢰⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣸⣿⣿⣿⡿⠁⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠘⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣼⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⠿⣿⣿⣿⣿⣿⣿⠁⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⠐⠀⠄⠉⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢈⣿⣿⣿⡿⠃⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⡿⠁⢀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣭⣽⣤⣟⣛⣀⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡟⠁⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡶⣿⣿⣯⣽⢻⣯⣭⢻⡿⣛⣭⣭⣛⠿⢟⣛⡛⠻⠿⣿⠿⠿⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⡿⠭⢏⠽⣿⣿⣿⣿⠀⠙⠟⠀⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠿⢸⣿⣿⠀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⢱⣿⣿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⡿⠀⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡉⢿⣿⠀⢸⣿⠇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡀⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⢾⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⡈⠉⠉⠙⠁⠘⠛⠛⢛⣣⣸⣻⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠉⠀⠸⣿⣿⣯⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠯⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣐⡢⢄⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⣀⡄⣄⣀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣦⢄⣺⠞⠂⡆⠥⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣽⣻⣿⣽⣯⣿⣿⣿⣿⣿⣿⣶⣠⢶⣓⣶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣝⣿⣿⣮⡽⣷⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡦⢠⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⡿⣻⣿⣿⣿⣟⢿⣿⣿⡆⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠋⠈⠈⠀⠀⠀⠈⠀⠀⠁⠀⠁⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⣿⡜⡏⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠀⠧⠆⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡿⢿⣿⣿⢿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠁⠋⠖⠛⠛⠻⠛⠻⠛⠛⠛⠛⠋⠛⣿⣷⡄⠸⠟⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣖⣤⣄⠀⠀⠀⣾⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣇⣾⣿⠟⠀⠀⠀⠛⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣶⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⠿⢋⠀⠀⠰⣿⣆⣰⣶⠁⠠⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣤⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡇⠀⠞⠀⠀⠺⠓⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⠠⠎⠀⠈⠛⠂⠀⠀⠀⠀⠀⢸⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠈⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⣶⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⠼⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣦⣤⣶⡆⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣧⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⠿⣿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⢶⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠹⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢹⣶⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣿⣿⣿⣿⢣⣿⣿⣿⣿⠃⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠸⡔⠁⠄⢀⡀⠦⠀⠀⠄⠀⠀⠀⢸⣿⣧⣿⣿⣿⣼⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢿⣿⣿⣾⣿⣿⣿⠇⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⣿⣿⣿⣿⠏⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⠏⠀⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣭⣽⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠋⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⠿⢿⣛⡛⠿⠿⣿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⡇⠘⠿⠃⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢘⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⠀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⣿⣿⣿⠏⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⡄⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣨⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⣧⡿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⡈⠉⠉⠙⠁⠘⠛⠛⢛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠽⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣯⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠉⠀⢸⣿⣿⣧⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠀⣶⠖⠲⢶⡦⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣲⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣷⣾⣆⣻⡿⣿⣿⣻⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⢿⣯⣿⡿⣾⡿⣿⣿⢦⣽⡿⢳⣼⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣰⣿⢿⣿⣾⡱⣿⣿⣽⡿⢾⣟⠿⣶⣿⣼⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠏⣿⣿⡻⣼⣿⣻⣿⢮⣟⠿⣿⣿⣿⡧⢰⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣵⡙⣟⣿⡯⣻⣶⣿⣿⣿⣷⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠋⠁⠉⠉⠉⠀⠀⠀⠀⠈⠈⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣳⠿⣿⣼⡿⣷⡛⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡶⠀⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠷⠝⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠙⠻⣿⣦⡀⠼⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢟⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣩⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣶⣤⠀⠀⢰⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠿⣿⣿⡿⠛⢻⣽⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣿⣿⠏⠀⣀⠈⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣳⠆⠀⢾⣿⢧⣴⣯⠀⠐⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣤⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⠿⣿⡇⠀⠁⠀⠀⠛⠋⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣭⣍⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿
⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣮⡀⠀⠀⠀⠀⠀⠀⡀⠄⠉⠀⠀⠀⠈⠙⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣷⣦⠄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠠⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣤⣤⣶⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⠾⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⣿⣿⡏⣼⣿⣿⣿⡟⠁⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢹⣶⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣽⣿⣿⣿⡟⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⣇⠀⠉⠀⠂⠑⠂⠀⠒⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⠿⢿⣿⣿⣿⡿⠁⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠃⢀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠻⠆⠀⠀⠀⠀⠀⠐⠚⠁⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣭⣩⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⡿⠃⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⢿⢿⣟⡛⠿⠿⣿⠿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠀⠻⠁⢠⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢘⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢈⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡀⣠⣴⣶⣤⣄⠉⣿⣿⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⢸⣿⡟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠏⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣾⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⣿⡟⠀⠀⠠⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣄⡈⠉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡗⣿⡟⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠌⠁⠘⠃⠛⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠀⣶⠾⠲⢶⣶⣶⡴⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⣄⡀⢠⣀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⢏⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠿⠛⠛⠋⠉⠉⠉⠉⠉⠁⠘⠉⠉⠉⠋⠉⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠅⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡶⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠿⣿⣦⡄⠸⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢟⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣩⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣶⣤⠀⠀⢰⣿⠅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠿⣿⣿⡿⠛⢻⣭⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣿⣿⠟⠐⢀⠈⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⡿⡿⣹⠆⠀⣼⣿⣿⣼⣮⠀⠐⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣤⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⠿⣿⡇⠀⠃⠀⠀⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣭⣍⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿
⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣮⡀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠙⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣷⣦⠄⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠠⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣽⣦⣤⣶⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣼
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⠿⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⠾⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⣿⣿⡏⣼⣿⣿⣿⡟⠁⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢹⣶⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⣇⠀⠉⠀⠆⠑⠂⠀⠒⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠟⢿⣿⣿⣿⡿⠁⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠃⢀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠻⠆⠀⠀⠀⠀⠀⠐⠚⠁⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣭⣩⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⡿⠃⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⢿⣿⣟⡛⠿⠿⣿⠿⠿⠿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⠻⠁⢠⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢘⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢈⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡀⣠⣴⣶⣤⣄⠙⣿⣿⣿⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣸⣿⡏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣾⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⣿⡟⠀⠀⠠⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⡈⠉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡟⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠀⣶⠷⠶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣶⠶⠶⠶⢶⣶⢶⡶⣶⣶⣶⣦⣤⣄⣀⣀⡀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣛⣿⣟⣟⣿⡿⣭⢿⣿⣿⣿⣫⢯⣿⣟⣿⣛⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣯⣿⢞⣿⣫⣟⣾⣫⡷⣾⣛⣼⡾⣯⡿⢻⢷⣷⢺⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣷⣿⣟⣿⢻⣿⢿⣯⣟⣫⡿⣯⢿⣛⣯⣿⣻⣫⣿⣾⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢭⣽⠿⡿⣽⣽⢿⣽⢽⣭⡿⢽⣿⣿⡧⠤⣄⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣿⢗⣳⡿⣾⢗⣯⠿⣿⣿⣿⣷⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣳⣫⡿⣟⡱⠛⠻⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠦⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡻⣛⡥⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠛⠛⠻⠿⠿⠿⠿⠿⠻⠻⠛⠛⠛⠛⠛⢿⣷⣤⠀⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣥⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣞⣿⣿⡦⠀⠀⠰⣿⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⢠⡀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⠛⠁⠊⠀⠠⣾⠉⠀⢸⠇⠀⠤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣤⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⣰⡿⠟⢿⡀⠀⠀⠀⠀⠉⠀⠀⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿
⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣦⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣥⣴⣄⣠⣤⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⠿⢿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠠⠶⠿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠹⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⢸⡥⠂⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢹⣶⡆⢰⣶⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⢿⣿⣿⣿⣰⣿⣿⣿⣿⠃⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡇⠀⠀⠀⠀⢈⠁⠀⠁⠀⠀⠀⢸⣿⣧⣿⣿⣿⣼⣿⡇⣼⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠙⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⠃⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⠃⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⠃⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠿⠂⠀⠀⠀⠀⠀⠒⠋⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣍⣹⣤⣛⣛⣀⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⡟⠁⢀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣽⢻⣯⣭⢻⡿⣛⣭⣭⣛⢿⣿⣟⡻⠿⢿⣿⠿⠿⠿⢿⡿⠿⠿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⢹⡟⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠛⢸⣿⣿⠀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣷⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⢿⣿⡿⠋⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⡾⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⢸⣿⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡂⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⣿⠃⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⣀⣈⠉⠉⠙⠁⠘⠛⠛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⠛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠉⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣧⣶⣿⣶⣶⣶⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⠶⢆⣰⣶⣶⣶⣶⣶⣶⣶⣶⡶⠲⣴⣢⣶⣶⡶⣶⡶⠦⣦⢴⢶⣶⡦⡶⣴⣶⣢⣤⣄⣤⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣫⣿⣻⣮⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣭⣯⣽⣓⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⠗⢶⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣻⣿⣿⡿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣯⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠋⠁⠁⠁⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠁⢊⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠁⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡶⠐⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⠺⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠉⠿⠟⠻⠿⠿⠿⠿⠿⠋⠉⠙⠙⠙⢿⣿⡆⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⡭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢀⡄⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⠿⢻⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⡅⢀⣤⡾⠂⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣿⣿⡏⣷⣶⣿⣿⣿⣿⣿⣿⣿
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⡏⠁⡘⠛⠁⢙⡿⠃⠀⡟⠐⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⢰⡿⠟⢻⡅⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⠏
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⠄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠐⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣶⣶⣷⡀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠈⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇⣰⣿
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⠿⠿⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠀⠴⢿⠿⣿⣿⣿⣿⣿⡿⠃⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢿⣿⣿⣿⣿⡇⣼⣿⣿⣿⠇⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⡧⠆⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢹⣶⡖⢸⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠹⣿⣿⣿⣿⣿⣿⣿⠏⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⢧⠀⠀⠀⠃⢀⡁⠀⠁⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⠿⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⠁⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠇⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠻⠇⠀⠀⠀⠀⠀⠛⠋⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣯⣭⣹⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⠋⢠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⢿⣿⣿⡛⠿⠿⣿⠿⠿⠿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠀⠻⠃⢀⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢘⣿⣿⠀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢨⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡀⣡⣴⣶⣤⣄⠈⡿⣿⣿⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣏⣟⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⢼⣿⡏⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣐⡗⣼⣿⡇⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⣈⡉⠉⠙⠁⠘⠛⠛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⡇⣿⡏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣯⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠉⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⢶⣆⡒⣶⣶⣶⣶⣶⣶⣶⣶⡲⣶⣶⣶⣶⣶⣶⠶⠶⠶⡴⢶⢶⡶⠶⢶⣴⡶⣆⣤⣄⣀⣀⣀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣯⣿⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣛⣿⣋⣝⣿⣿⢷⣣⣷⣿⣵⣼⣿⢿⡯⣳⣿⣿⣽⣛⣿⣬⡽⣽⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡷⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⢟⡮⢁⣷⡟⣱⣿⡿⠿⣻⢿⣿⣿⣿⣔⣗⣻⢿⣞⢿⢏⣝⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⡿⠛⡼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣞⣵⡷⠾⡿⢾⣶⣾⣿⡷⡮⢾⣿⣿⣷⣲⣿⣯⣿⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣹⣿⠷⢾⣿⢏⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢷⣛⣷⣏⡟⣿⢭⠛⣆⢭⣿⣩⣿⣿⢯⣿⣏⡆⣜⡔⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⢷⡿⣿⣯⣷⣭⣭⢽⣭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣿⢻⡁⣸⣿⣗⡈⡎⠵⠟⠳⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠁⠉⠀⠈⠀⠀⠀⠀⠁⠀⠁⠉⠋⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢗⣧⠷⣿⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡶⠀⢿⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣆⡁⢿⡾⠊⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠻⠛⠿⠿⠻⠿⠟⠟⠋⠉⠉⠋⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢰⣿⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣩⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠗⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠟⣿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⡿⠟⢫⡀⠀⢠⣦⠀⠀⠀⠀⣠⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⠿⣿⣄⠀⠉⠀⢌⣾⠉⠀⢟⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣤⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⡟⠀⠀⠁⠀⠀⠀⠠⠞⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠈⠃⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣌⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣢⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⢠⠾⠿⠿⢿⣿⣿⣿⣿⣿⠇⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⣿⣿⣿⡿⣸⣿⣿⣿⡿⠃⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⡖⠁⡄⠀⠠⢄⠀⠀⡀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡟⢹⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⢿⣿⣿⣷⣿⣿⣿⡿⠁⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⣇⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⡀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⢿⣿⣿⣿⣿⠁⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣼⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠋⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣛⠃⠀⠀⠀⠀⠀⠙⠁⠀⠀⣠⣾⣶⣶⣿⣿⣿⣿⣿⣿⣍⣩⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠁⢠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣭⣭⢻⡿⣛⣭⣭⣛⢿⣿⣟⡻⠿⢿⡿⠿⠿⠿⢿⡿⠿⠿⠿⢿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡇⠀⠻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⠀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢨⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⣿⣿⡏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⡾⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣺⡟⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣐⡗⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⡟⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⣀⢈⠉⠉⠉⠁⠘⠛⢛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡟⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⠛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠛⠁⠌⠁⠘⠃⠛⠛⠉⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⢿⣿⣿⣿⣿⣷⣶⣿⣟⣲⣶⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⠶⣆⡒⣶⣶⣶⣶⣶⣶⣶⢶⠶⡖⣶⣶⣶⣶⣶⠶⣶⣶⢶⢶⣶⠶⡶⣶⣴⣶⣂⣄⣄⣀⣄⠀⠠⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣟⡾⣾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣭⣞⣿⣧⣟⣾⣷⣱⣻⣖⡶⠍⠲⣧⣛⣿⣧⣺⡟⢻⣿⣯⡝⢟⣢⣽⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡏⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣭⣿⣿⡮⣵⣲⣏⢯⣍⡬⣿⣽⢽⣻⡟⣵⣽⠮⣿⣶⣷⡿⡍⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⡿⣿⡿⡻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⢮⣶⣥⢟⣭⣛⠋⣿⢻⣏⢷⢩⣎⢸⢿⣗⠲⣾⣿⢗⠝⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣟⣻⡟⢯⣯⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣾⠍⢭⡽⣶⣿⣽⣏⣭⡻⡻⠿⣟⣿⣻⣿⣟⡄⢸⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢿⢞⡟⣿⣟⣷⡿⡟⣩⣁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡷⣎⢧⣿⣡⣭⡏⠍⠿⠟⠳⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠃⠁⠉⠁⠀⠀⠀⠁⠁⠀⠐⠉⠁⠉⠁⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣝⣗⢲⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡶⠀⢿⡗⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣆⡁⢿⡿⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠙⠿⠻⠿⠿⠻⠿⠿⠿⠋⠉⠉⠃⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢠⣿⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣩⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡗⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠟⣻⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⠟⢻⠁⠀⢠⣴⠀⠀⠀⠀⣠⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⠿⣿⣄⠀⠋⠀⢌⣾⠉⠀⢟⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣤⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⡿⠀⠀⠁⠀⠀⠀⠠⠞⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠈⠃⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣌⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣢⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⢠⠾⠿⠿⢿⣿⣿⣿⣿⣿⠃⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⣿⣿⣿⡿⣸⣿⣿⣿⡿⠃⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⡖⠁⡄⠀⠠⢄⠀⠀⡀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡟⢹⣷⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⢿⣿⣿⣷⣿⣿⣿⡿⠁⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⣇⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⡀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠻⢿⣿⣿⣿⣿⠃⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣼⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠃⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣛⠃⠀⠀⠀⠀⠀⠙⠁⠀⠀⣠⣾⣶⣶⣿⣿⣿⣿⣿⣯⣍⣹⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡿⠃⢠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣿⣿⣯⣿⢻⣭⣭⢻⡿⣛⣭⣭⣛⢿⣿⣟⡻⠿⢿⡿⠿⠿⠿⢿⡿⠿⠿⢿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡇⠀⠻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⠀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢨⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⣿⣿⡏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⢸⡟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣐⡗⣾⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⡟⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⣀⣈⠉⠉⠉⠁⠘⠛⢛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⡇⣿⡟⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⠛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠉⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⢿⣿⣿⣿⣿⣧⣶⣿⢿⣶⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⡤⡄⠄⠐⠀⠀⠀⡢⠠⣶⣶⣶⠖⠒⡆⠀⠀⠀⠒⠒⠒⠂⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣯⣿⣟⡫⠧⠐⠀⠀⠀⣰⣷⣿⣿⣗⣎⣧⣿⢃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⢟⠨⠈⡄⠠⢀⣹⣿⣿⣿⣿⣿⣿⣿⣴⡬⣽⣬⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣾⠞⠰⣰⡀⠀⠀⠘⢦⣿⣿⣿⣿⣿⣿⣶⣷⢺⢾⠮⡈⡀⠀⣠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡓⡀⠂⠂⠀⠀⠠⡼⠛⠫⠛⣿⣏⣿⣿⣿⣯⣿⣟⣵⣤⡬⡭⣦⣥⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡟⠃⠀⠀⠈⠠⠄⠊⠀⠢⣢⢁⠚⢼⠟⠸⣩⣿⣽⡥⢿⣿⡇⣿⣽⣿⣶⣧⢔⣶⡆⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠙⣨⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⡾⢬⠑⠁⠀⠀⠀⢰⡶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡦⠀⠀⠈⢀⠾⠳⠿⠿⠿⠿⠟⠻⠟⠛⠽⡕⢀⢀⣀⠀⠀⣀⡔⠒⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠂⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⡗⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⠵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⢀⣤⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠃⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⡿⠛⢩⠅⠀⠀⣴⠄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿
⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠃⠈⠿⠀⠀⠀⠀⢀⣾⢯⣿⣿⠄⠀⠉⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣝⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢠⣿⠿⢻⣿⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣸⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿
⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠸⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡈⠛⠛⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠖⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⡶⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⢿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠴⠿⠿⠿⣿⡿⣿⣿⣿⠟⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠙⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⢸⠀⠉⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡖⢸⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⢽⣿⣿⣿⡿⠃⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠸⡆⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣼⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠛⠻⣿⣿⣿⣿⣿⠃⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⣿⣿⣿⡿⠃⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⡿⠃⢀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣿⣿⣿⣿⣿⣿⣍⣉⣤⣛⣛⣄⣛⣛⣀⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣺⣿⣿⣿⣿⣿⡇⢾⣿⡟⠀⢠⣾⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣹⣶⡾⣷⣿⣯⣿⢻⣯⣭⢻⡿⣛⣭⣭⣛⢿⣿⣟⡻⠿⢿⣿⠿⠿⠿⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⠾⢿⣿⣿⣿⣿⣿⡇⠈⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣡⣴⣶⣤⣄⠈⣿⣿⣿⠏⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⡾⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⢿⣿⠀⢘⣿⠏⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⢘⠏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⣀⣄⣈⠉⠉⠉⠁⠘⠛⠛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⡟⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣽⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀
⠀⠛⠀⠌⠁⠘⠃⠛⠛⠉⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⠶⣖⣖⣖⣶⣶⣶⣶⣶⡶⣶⡖⡰⠒⢶⣶⣶⠶⣲⠒⠆⢢⠲⡲⠒⢖⠲⠶⡶⣢⣦⠶⠲⣴⣤⢄⣠⠄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣻⣿⣿⣿⣿⣿⣟⣿⣿⣺⣝⣖⣞⣹⣾⣿⢷⡶⣽⠾⣽⣧⣟⣮⡽⣋⡽⣟⣛⣿⢾⣿⣿⣿⢷⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣖⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣟⣟⣻⡥⣿⢴⣹⡻⣝⠷⢿⡿⢿⣟⣍⣸⣯⣹⣷⣱⣗⣲⣽⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣻⣧⢫⣿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣷⡿⡭⡟⢳⢖⣷⢿⠾⣽⠯⣟⣜⣟⠽⣾⣫⣾⠍⣿⡿⡿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣏⣿⣿⣳⣾⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣭⠿⣗⡿⠯⢼⣧⡮⢭⣳⣿⣶⡥⢾⡣⣭⣙⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣯⠽⣍⣿⢶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣯⢽⢆⠪⣬⣱⢳⣿⢺⣷⠿⣝⠾⣷⣶⣾⣴⣰⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠊⠁⠉⠀⠈⠀⠀⠁⠀⠉⠁⠁⠉⠉⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣷⢶⠽⣛⣸⣿⣾⢆⠀⠀⠀⠈⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡶⠐⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠈⣯⣥⠿⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠙⠙⠛⠋⠛⠛⠛⠛⠉⠋⠉⠋⠛⠛⣿⣿⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⢏⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⡄⠀⠀⣾⡆⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣉⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠃⠀⡀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠛⣥⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠞⠁⣰⠿⠫⠷⠂⢨⣾⣿⣦⡐⠀⢀⡀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⡟⣷⣶⣾⣿⣿⣿⣿⣿⣿
⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡾⠁⠐⠂⠀⠀⠀⢀⣼⣿⣿⣿⡗⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠸⠛⠋⣽⢏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠁⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⡟
⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠛⢅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣤⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇⢠⣿
⠟⠃⠀⠙⠿⠿⠿⠛⠿⠿⠿⢿⡞⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠴⠿⠿⠿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⡇⣼⣿⣿⣿⠏⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⡇⠀⠀⠉⠀⡌⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡖⢹⣿⣿⣭⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⢸⣿⣿⣿⡏⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⢧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⠿⣷⣾⣿⣿⡿⠀⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣸⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⣴⠎⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⠃⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣋⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⣶⣿⣶⣶⣿⣿⣿⣿⣿⣯⣍⣙⣤⠛⣛⣄⣛⣛⣠⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⠋⢠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣱⣶⡾⣷⣿⣯⣿⢻⣯⣭⢻⡿⣋⣭⣭⣛⢿⣿⣿⡟⠿⠿⣿⠿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠀⢹⠃⢀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢠⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣠⣴⣶⣤⣄⠙⣿⣿⣿⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⡞⣿⣿⡇⣿⣿⡇⣼⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⢹⣿⡟⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣐⡗⣼⣿⡇⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⣿⡟⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣀⣀⣀⢈⠉⠉⠙⠁⠘⠛⠛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡗⣿⡟⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠛⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣖⣒⢶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⢃⠲⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠋⠁⠉⠈⠈⠉⠀⠉⠉⠉⠉⠉⠋⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡶⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡜⠄⣷⣿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠘⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠁⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡯⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⡆⠀⢀⣶⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣠⣾⣿⣵⣿⣿⡏⡁⢀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⢿⢿⣿⣿⣿⠟⢉⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⠘⠋⢀⣼⣿⡇⠀⠀⠀⢀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⠟⠋⠻⠟⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣽⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣭⣍⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿
⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠤⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠛⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣤⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⢿⡀⠀⠀⠂⠉⠂⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠠⠾⣿⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠻⣿⣿⣿⣿⡟⣰⣿⣿⣿⡿⠁⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣯⢹⣶⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⣿⣿⣿⢧⣿⣿⣿⡿⠁⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠿⢿⣾⣿⣿⣿⠁⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⠀⠀⠀⠀⠠⠾⠁⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡏⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣶⣿⣿⣿⣿⣿⣿⣭⣹⣤⡛⣛⣄⣛⣛⣠⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣸⣶⡾⣷⣾⣯⣿⢻⣯⣭⢻⡿⣛⣭⣬⣛⢿⣿⣿⡟⠿⢿⣿⠿⠿⠿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⠸⠋⢀⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⠀⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⠀⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣷⡖⢰⣶⣶⣶⣦⡈⣠⣴⣶⣤⣄⠹⣿⣿⣿⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⡦⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣻⣿⡟⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣼⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠀⣾⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⡀⣀⣀⣈⠉⠉⠉⠁⠘⠛⢛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡁⣿⣿⡇⣿⣏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠛⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢖⣲⣦⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠋⠉⠁⠈⠉⠀⠁⠀⠉⠉⠉⠙⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡶⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠈⡸⣽⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡯⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⡆⠀⢀⣶⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣡⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣠⣶⣿⣵⣿⣿⡟⠁⢀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⡿⢿⣿⣿⣿⠟⢉⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⠈⠋⢀⣼⣿⡧⠀⠀⠀⢀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿
⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⠿⠋⠻⠟⠀⠀⠀⠸⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⢠⣿⣦⣿⣿⣿⣛⠛⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣭⣍⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿
⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠠⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠛⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣇⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣤⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼
⠟⠃⠀⠙⠿⠿⠿⠟⠿⠿⠿⢿⡀⠀⠀⠂⠉⠂⠀⠐⠀⠀⠀⠀⠀⣠⣀⡀⢀⣀⣀⠀⠠⠾⣿⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠻⣿⣿⣿⣿⡿⣰⣿⣿⣿⡿⠁⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣯⢹⣶⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣧⣿⣿⣿⡿⠁⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡇⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠿⣿⣾⣿⣿⣿⠁⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠁⣿⣿⣇⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡏⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣶⣿⣿⣿⣿⣿⣿⣭⣹⣤⡛⣛⣄⣛⣛⣠⠿⠿⠿⠿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣷⠀⣿⣿⣿⡟⣿⣿⡇⣰⣶⡾⣷⣾⣯⣿⢻⣯⣭⢻⡿⣛⣭⣬⣛⢿⣿⣿⡟⠿⢿⣿⠿⠿⠿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⠹⠋⢀⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢠⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⠈⢸⣿⡿⢻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡈⣠⣴⣶⣤⣄⠙⣿⣿⣿⠏⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⡆⣿⣿⡇⣿⣿⡇⣸⣿⣇⣾⣿⢻⣿⣿⣀⡀⣾⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⢹⣿⡟⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡏⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣼⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⡋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠐⣿⡟⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⣀⣀⣄⣈⠉⠉⠉⠁⠘⠛⢛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⠻⣿⣷⣿⡿⡁⣿⣿⡇⣿⣏⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠙⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣯⣭⣿⣿⣿⣍⣉⡛⠛⠃⠛⠛⠘⠻⠿⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⠀⠛⠀⠜⠁⠘⠃⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣶⠂⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣶⣾⣿⣾⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣷⣶⣶⣶⡀⠀⡀⠀⠄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣠⠀⠀⠀⠀⠀⢴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣁⠒⠠⠂⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡬⣡⢐⠂⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠿⡿⠿⢿⣿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠟⠟⠛⠁⠉⠙⠻⠛⠛⠻⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠥⠀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⡓⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⠹⠾⣛⣯⣭⡿⠿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡽⢿⣿⣿⣿⣿⣿⡟⠁⠀⠘⠶⢆⣠⣠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⣿⣿⣿⣿⣿⣿⣿⣷⣵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠏⠁⠀⣨⣿⣿⣿⣿⢟⠟⠉⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⢰⣿⣿⣿⣿⣿⣷⣴⡄⠀⠀⠒⠀⠘⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣳⣿⣿⣿⢿⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⢀⣴⠾⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⡟⠀⠀⠀⠀⠀⣴⣯⣿⣷⠛⣽⡝⠁⠀⠀⠀⠀⠀⠀⢀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣷⣶⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⢸⡟⠿⠟⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿
⠀⠀⢰⣿⢿⣿⣿⣿⣧⠻⠿⠋⢀⣀⣸⣿⡆⢀⣖⠚⠟⠃⠀⢀⣀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠸⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠠⣿⡿⠈⢻⠀⠈⣿⠂⠀⠀⣠⠋⠠⠈⢭⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣦⣤⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⠁⠀⠸⣿⣿⣿⣿⠀⠀⣿⢛⡄⠐⢀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⡧⠀⠀⠉⠁⣙⠀⠘⠃⠀⠀⡀⠀⣤⣀⡀⢀⣈⣁⠙⠹⠿⣿⠿⣿⣿⣿⣿⣿⡿⠓⠒⠐⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⡿⠁⢠⣾
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⢿⠀⠀⠀⠀⠛⠀⠀⠀⠀⣰⠇⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢹⣶⡆⢰⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⠇⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⠀⠀⢀⣠⣶⣾⠟⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠛⣿⣿⣿⣿⠏⠀⣼⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣖⣶⣶⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⣀⣈⣛⣋⠉⠉⡛⠋⠉⠁⠀⠊⠀⢢⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣭⣽⣥⣛⣛⣤⣛⣛⣤⣿⡿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿
⢳⠚⠃⣱⣀⡘⠑⠐⠆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⡿⣿⣿⡇⣿⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣽⣻⣿⣿⣿⡿⠿⢿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠹⠈⠉⠁⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢸⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡉⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⠂⠘⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⡿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢨⣿⣿⣐⡟⣿⣿⡏⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⢸⣿⣿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⠛⣛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⣿⣁⣿⣿⣇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⡤⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣯⣭⣿⣿⣿⣭⣉⣛⡛⠃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⡰⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣤⣤⣤⠞⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣿⣶⣾⣿⣾⣿⣶⣿⣶⣿⣶⣿⣿⣿⣿⣿⣷⣾⣶⣷⣶⣶⣶⣀⡀⡠⠠⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢆⡀⡀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡃⠂⠀⡬⡙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣔⠀⠌⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠲⠈⡀⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣵⢠⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⢿⡿⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠟⠛⠋⠈⠈⠙⠻⠿⠟⠿⠻⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠩⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠨⢰⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠶⢀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣂⡿⠮⣙⣭⣽⡿⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢿⣿⣿⣿⣿⣿⡟⠉⠀⠘⠶⢆⣠⣠⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠅⠄⣻⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣼⠿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠏⠁⠀⣨⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⢰⣿⣿⣿⣿⣿⣦⣄⡄⠀⠀⠆⠀⠘⣿⠀⠀⠀⠀⠀⠀⣤⣾⣿⣳⣿⣿⣿⢿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡤⠾⢿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣦⣄⣀⡟⠀⠀⠀⠀⠀⣴⣿⣽⣷⠛⡯⠏⠁⠀⠀⠀⠀⠀⠀⢀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣷⣶⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⢸⡟⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿
⠀⠀⢰⣿⣿⣿⣿⣿⣧⠻⠿⠫⢀⣀⣼⣿⡖⢀⣖⠚⠟⠃⠀⢀⡀⠀⢀⣀⣶⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠸⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠠⣿⡿⠈⢻⠀⠘⣿⠆⠀⠀⡠⠋⠁⠈⠭⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣦⣄⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⠁⠀⠘⣿⣿⣿⡯⠀⠀⣿⢛⡄⠈⢀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠑⠫⢹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⡧⠀⠀⠉⠁⣙⠈⠘⠂⠀⠀⠀⠀⣤⣀⡀⢀⣈⣀⠙⠹⠿⣿⢿⣿⣿⣿⣿⣿⡿⠓⠒⠐⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢻⣿⣿⣿⣿⣿⡏⣸⣿⣿⣿⡿⠁⢠⣾
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⢿⠀⠀⠀⠀⠛⠀⠀⠀⠀⣠⠇⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢹⣶⡆⢰⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣤⡏⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⠇⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⠀⠀⢀⣤⣶⣿⠟⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠋⠛⣿⣿⣿⣿⠏⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣴⣖⣶⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣟⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠒⠂⢠⠀⠀⠀⠀⣀⣈⣛⣋⠉⠉⡛⠋⠉⠁⠀⠈⠀⢠⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣭⣽⣥⣛⣛⣤⣛⣛⣤⣿⡿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣾⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿
⢄⢀⠠⡀⠒⠚⠓⠰⠄⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⡿⣿⣿⡇⣻⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣽⣻⣿⣿⣿⡿⠿⢿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⠋⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢸⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡉⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⠇⠘⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣟⡿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⣿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣐⡟⣿⣿⡟⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⢸⣿⣿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⠛⣛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⣿⣁⣿⣿⣇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⡤⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣯⣭⣿⣿⣿⣿⣉⣛⡛⠃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⡸⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣦⣤⣦⠖⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⣿⣷⣾⣷⣾⣿⣾⣿⣶⣿⣶⣿⣷⣷⣶⣾⣷⣶⣶⣶⣤⠄⢄⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⡀⡀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡎⠀⠒⢀⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣔⢈⠊⠑
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⠀⡒⢢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⠛⠛⠻⠟⠻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠛⠛⠋⠉⠉⠙⠻⠛⠛⠟⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠉⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣏⠀⢀⣀⠀⠀⢀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠐⢔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣳⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠐⠩⠨⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡓⡚⣪⣩⣿⣽⣟⣿⡻⢿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⣻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⣵⣶⠾⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣬⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⠏⠉⠀⣠⣼⣿⣿⣿⠿⠟⠉⠈⠁⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢀⣨⣿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣇⣠⡀⠀⠀⢀⠀⠀⠿⠀⠀⠀⠀⠀⣠⠿⢛⣣⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⢀⡤⠾⠿⠿⢿⣿⣿⣿⣿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⢰⣿⣾⠿⡏⠈⠘⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⠏⠉⠉⠉⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣶⡄⠀⡠⠼⡿⠇⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⢸⣿⡿⠛⢿⠃⠈⣿⠄⠀⠀⢀⠖⠁⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⡀⠸⠀⠀⠿⠀⠀⠀⠉⠀⠀⠀⠉⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣦⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⡇⠉⠁⠲⠘⠢⠀⠠⠆⠀⠀⠀⠀⠀⠐⠳⣺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⣿⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⡆⠀⣤⣀⡀⢀⣈⣉⣹⠿⠿⢿⢿⣿⣿⣿⣿⣿⡿⠀⣃⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢿⣿⣿⣿⣿⣿⣸⣿⣿⣿⡿⠁⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢱⣶⡞⢻⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⢸⣇⠀⠀⠀⠀⢀⣀⣤⡿⠁⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⡀⠀⢀⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢹⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⢳⣿⣿⣿⠋⠀⠀⠀⠀⣠⣸⣿⣿⡟⢸⣿⣿⣟⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⡿⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣀⣙⣛⣁⠀⠈⠉⠉⠁⠀⠀⢀⣴⣿⣿⣿⣶⣾⣿⣿⣿⣿⣷⣿⣭⣽⣥⣛⣻⣤⣛⣛⣤⣿⡿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⡟⢁⣾⣿⣿⣿⣿⣿⣿
⢋⠀⡀⡬⡌⢚⠢⢔⠆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣹⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣿⣻⣿⣿⣿⡿⠿⢿⣿⠿⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⡟⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠅⠀⠀⠐⠀⠐⠂⢸⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢸⢹⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡉⣩⣴⣶⣤⣌⠻⣿⣿⣿⢟⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣟⣿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⡏⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢨⣿⣿⣐⡟⣿⣿⡟⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⢸⣿⡟⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⠛⣛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⣿⣁⣿⣿⣇⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⠟⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣯⡬⠁⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣯⣭⣿⣿⣿⣽⣉⣛⠛⠃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀
⠀⠛⠁⠜⠙⠛⠃⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⠂⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣶⣾⣿⣾⣿⣶⣿⣶⣿⣷⣿⣷⣾⣷⣾⣿⣶⣶⣾⣶⣶⣦⣤⡄⠠⠀⠀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣔⣄⣀⠀⠀⠄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⡀⠀⢒⢒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠌⡀⠃⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣁⡂⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠻⠟⠛⠿⠿⠟⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠋⠙⠉⠉⠙⠛⠻⠟⠛⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠋⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠀⠉⢻⡇⠀⠀⠀⠀⠀⠈⢭⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⣐⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣶⣦⣬⡉⠀⠀⠀⠀⠀⠨⠿⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢗⣿⣿⣟⣿⣿⣿⡿⠿⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠑⢻⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⢳⣿⣾⣿⣿⣿⣿⣧⣀⠀⠀⢀⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠉⠉⠁⣠⣿⣿⣿⡿⠟⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⢟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣽⣿
⠀⠀⢀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣛⣭⣾⣿⢿⣿⣿⣿⣿⡅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⣿⣿⣿⣿⣿⠿⣿⣶⣿⣿⣿⣿
⢠⡴⠿⠿⠟⠛⣿⣿⣿⣿⣾⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠛⠂⠓⣚⣿⣿⣿⣿⠿⠗⠀⠀⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⡍⠉⠉⠉⠉⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⣠⣤⣿⣿⠃⢠⡖⠙⠟⠀⠀⠀⢀⠀⠀⣠⣤⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡅⠀⡇⠀⢸⡟⠀⠀⢀⠠⠋⠀⣦⣼⣿⣿⣿⣿⣿⣿⡟⠻⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⠁⢸⡿⢵⠀⠀⡀⠸⠃⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⣿⣤⡀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⡤⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⢸⡇⠀⠈⠁⢈⡂⠀⠚⠀⠀⠀⠀⠀⠂⢘⢩⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⢸⡇⠀⠀⠀⠙⠃⠀⠀⠀⢀⡶⠀⣤⣀⡀⢀⣈⣈⢨⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⠟⠐⠂⣂⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣰⣿⣿⣿⡿⠁⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⣧⠀⠀⠀⠈⠀⠀⠀⢠⣾⠁⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢻⣶⡖⢰⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠇⠀⢠⣿⣆⠀⠀⠀⣤⣴⣶⡟⠃⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢻⣿⣿⣿⣿⣿⠏⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣲⠤⢜⣿⣿⠛⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢩⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠃⠀⢿⢿⣟⠇⠀⠀⠀⠀⣠⣼⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⡿⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠠⠄⠀⠠⠀⠀⠁⠀⣀⣙⣋⣀⠀⠀⠀⠀⠀⠀⢀⣪⣶⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣭⣽⣥⣛⣛⣤⣛⣛⣤⡿⠿⠿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡟⢁⣾⣿⣿⣿⣿⣿⣿
⡏⠰⠶⣒⠜⢓⢂⡴⠆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡟⢀⣾⣿⣿⣿⣿⣿⣿⣿
⠉⠈⠀⠂⠀⠡⠀⠀⠂⢸⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢸⢸⣿⡿⣻⣿⡏⢸⣿⡿⢿⣷⡅⣿⣿⣿⡖⢸⣶⣶⣶⣮⡉⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡏⢸⣿⣿⣐⡟⣿⣿⡏⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣏⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⢺⣿⣿⠏⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠅⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⠛⣛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⣟⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠈⣿⠋⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠤⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣽⣿⣿⣿⣽⣉⣛⣛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⣸⠃⠀⠀⠀⣺⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣤⣶⣾⠃⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣴⣦⣄⠤⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⡅⠀⠀⠰⢑
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣴⡂⣰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠝⢋⠩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣰⠠⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠿⣿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠻⠿⠛⠓⠒⠀⠉⠛⠛⠛⠛⠛⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠋⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠰⠡⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣾⣿⣶⣦⣬⡉⠀⠀⠀⠀⠀⠈⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠐⢛⣤⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡂⢻⣻⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⢰⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠉⠉⠉⢀⣨⣿⣿⡿⠿⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣯⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⣹⡿⠋⠿⠿⣿⣿⣿⣿⣀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢿⣿⣏⣉⡉⣽⣿⣿⣿⣿
⣠⣴⠿⠿⠟⠛⢿⣿⣿⣿⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠉⠀⠀⠀⠀⠸⠿⣿⣿⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡭⠉⠉⠉⢉⣀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⣠⣤⣾⣿⡇⢀⣖⠈⠛⠃⠀⠀⡀⣀⢀⣤⣴⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⠀⢹⠁⠘⣿⠃⠀⠀⡠⠊⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⠇⢸⡿⠽⠄⡀⢠⠀⡏⠀⠀⠀⠀⠀⠅⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣤⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⢸⡇⠀⠀⠉⢀⣕⠀⠘⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠘⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰⠀⣤⣀⡀⢀⣀⣈⠉⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⡿⠇⠐⢃⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⠟⠀⣰
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⣷⠀⠀⠀⠀⠀⠐⠀⢀⣿⠃⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢹⣷⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⢠⣿⣦⠀⠀⠀⢠⣴⣶⠿⠃⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣻⣿⣿⣿⣿⣿⣿⡟⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢒⣤⣰⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣽⣿⣿⣿⡟⠁⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠈⠰⠺⢾⠷⠋⠀⠀⠀⢀⣠⣸⣿⣿⡟⢸⣿⣿⣟⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⡿⠁⣰⣿⣿⣿⣿
⠀⠀⠐⠄⠠⣠⠀⠀⠁⠀⣀⣛⣋⣀⠀⠀⠀⠀⠀⠀⣠⣦⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⣛⣤⣛⣻⣠⡿⠿⠿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿
⡏⠽⢱⣯⡪⡿⠳⠐⠆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠠⠎⠄⠀⠡⠁⠈⠀⢸⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡅⣿⣿⣿⡖⢸⣶⣶⣶⣮⡉⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⡿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⡿⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣿⣿⡏⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⣿⡿⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⠛⣛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⣿⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⢿⣿⡔⠀
⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⢠⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣤⣤⣶⡟⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⡶⣾⣶⣷⣶⣶⣶⣷⣶⣶⣶⣶⣴⣶⣤⡤⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⠀⠀⠠⠲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢄⣴⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠛⢩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣻⣴⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠿⣿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠛⠛⠛⠛⠛⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠋⠉⠉⠙⠃⠀⠀⠀⠀⠀⠈⡉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠠⠑⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣼⣿⣿⣿⣿⣿⣿⣤⣤⣤⣾⣿⣶⣦⣬⡉⠀⠀⠀⠀⠀⠀⠄⠨⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⢻⣠⣴⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠂⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢰⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠙⠋⠉⢀⣨⣿⣿⣿⡟⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⣹⡿⠋⠿⠿⣿⣿⣿⣿⣀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢿⣿⣯⣉⡉⣽⣿⣿⣿⣿
⣠⣴⠿⠿⠟⠛⢿⣿⣿⣿⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠉⠀⠀⠀⠀⠸⠿⣿⣿⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣯⠉⠉⠉⢉⣀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⣠⣤⣾⣿⡇⢀⣆⠈⠛⠃⠀⠀⡀⣀⢀⣤⣴⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⠀⢹⠁⠘⣿⠃⠀⠀⠠⠊⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⡇⢸⡿⠵⠄⡀⢠⠀⠏⠀⠀⠀⠀⠠⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣦⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⢸⡇⠀⠀⠉⢀⣕⠀⠘⠀⠀⠀⠀⠀⠙⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠘⡇⠀⠀⠀⠀⠉⠀⠀⠀⢀⣰⠀⣤⣀⡀⢁⣈⣈⠉⠽⠿⣿⠿⢿⣿⣿⣿⣿⣿⠿⠗⠐⢇⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⠟⠀⣰
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⣷⠀⠀⠀⠀⠀⠐⠀⢠⣾⠁⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢹⣷⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⢠⣿⣆⠀⠀⠀⢠⣤⣶⠟⠃⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣻⣿⣿⣿⣿⣿⣿⡟⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⠐⣄⣲⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣻⣿⣿⣿⡟⠁⣰⣿⣿⣿
⠀⠀⡀⠀⡀⡀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠰⣙⢿⡿⠋⠀⠀⠀⢀⣠⣸⣿⣿⡟⢸⣿⣿⣟⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⡿⠁⣰⣿⣿⣿⣿
⠀⢀⡐⠀⠳⣤⠀⠀⠀⠀⣀⣛⣋⣀⠀⠀⠀⠀⠀⠀⣠⣦⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣯⣽⣥⣟⣛⣄⣛⣻⣤⡿⠿⠿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿
⣏⠲⣯⣏⣶⣿⣷⠐⠆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿
⠉⠉⠽⠄⠋⠫⠈⠄⠀⢸⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⣄⣿⣿⣿⡗⢸⣶⣶⣶⣮⡉⣩⣴⣶⣤⣍⠻⣿⣿⣿⣿⡿⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⡿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣿⣿⡏⠃⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠸⣿⣿⡿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⠛⣛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⣿⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀
⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⣠⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⡟⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣿⣷⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣶⣶⣶⣶⣦⠀⡀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣖⠂⠀⠀⠀⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⢒⣠⣺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠍⡉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣊⢶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿
⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠛⠛⠈⠒⠙⠙⠛⠛⠿⠿⠻⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠈⠈⠁⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡑⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⢹⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣿⣿⣷⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⢀⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠋⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠄⠠⡬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠃⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⣿⡿⣿⢿⣿⡻⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠨⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢱⣤⣶⠮⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⠟⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠂⠰⢾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠀⠈⣉⠉⠀⣙⣿⣿⡿⠋⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣿⡿⣿⠿⠛⠛⠛⠻⣿⣿⠃⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠀⠀⠀⠀⠀⠀⢠⣾⡓⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣋⡀⠀⣸⣿⣿⣿⣿
⣠⣴⣿⡿⠿⠛⣿⣿⣿⣿⣦⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣩⠃⠀⠉⠀⠀⠀⢀⣴⣶⣾⡟⣅⡟⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠍⠉⠉⣁⣀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣴⣶⠾⢿⡟⠀⣾⡀⠈⠁⠀⠀⣀⣤⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⣿⡿⡀⠸⠁⠀⣿⠀⠀⠀⠀⠊⣀⢠⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⡆⡟⠓⠃⠤⠰⢄⠩⠀⡄⠀⠀⠀⠁⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣦⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡿⠀⣿⠀⠀⠀⠠⣮⠀⠈⠀⠀⠀⠀⠀⢈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⣤⣀⡀⢀⣀⣉⠉⠹⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠂⢂⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡟⠀⣰
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣽⠃⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢹⣿⣯⢹⣿⡆⢰⣶⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠃⠀⠀⣿⣷⠀⠀⠀⢠⣶⣾⡿⠃⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⡿⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢽⢶⣸⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠛⢹⣿⣿⣿⣿⠁⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠈⠶⡻⡿⠃⠀⠀⠀⠀⣠⣼⣿⣿⡟⢸⣿⣿⣟⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⠇⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠈⠉⠀⣀⣛⣋⣀⠀⠀⠀⠀⠀⠀⢀⣰⣴⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣯⣭⣽⣥⣟⣛⣀⣛⣛⣠⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿
⣟⠀⠅⠓⢠⣓⢣⡴⠆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣯⣭⣻⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠁⣰⣿⣿⣿⣿⣿⣿
⠁⠀⠁⠀⠀⠀⠐⠀⠀⢸⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢘⢸⣿⡿⣻⣿⡏⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣮⡉⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⣿⠀⠘⠁⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣿⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⡟⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣿⣿⡟⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⣿⡟⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⠛⣛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⠻⣿⣷⣿⡿⣁⣿⣿⡏⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⡟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣭⣿⣿⣿⣿⣉⣛⣛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⣰⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣦⣤⣶⣶⠋⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⡆⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠆⠤⡀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢎⡟⣾
⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠟⠛⠂⠀⠈⠁⠙⠛⠛⠿⠻⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠠⠔⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣿⣿⣿⣿⣿⣟⣀⣀⣠⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣊⣻⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠋⢤⣤⠶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⡟⠛⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠀⠀⣉⡉⢁⣈⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣻⣽⣿⠿⠟⠛⠋⣿⣿⡟⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿
⣀⣴⡿⠿⠿⠛⣿⣿⣿⣿⣷⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⠃⠀⠀⠀⠀⠠⣶⡿⠛⢀⡀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⣀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣍⠉⠉⠁⠀⠀⠀⠀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⣄⣀⣿⣿⠀⢠⡂⠙⠛⠀⠀⠀⢀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣻⣿⡇⠈⡿⠀⢸⡏⠀⠀⠀⠀⢋⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠀⠁⡄⢸⠃⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣦⣤⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⣿⠀⠀⠈⠁⣈⠂⠑⠃⠀⠀⠀⠀⠀⠌⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⢹⡀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣤⣀⡀⢀⣉⣉⠉⠉⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠃⠄⠂⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⠏⠀⣰
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠂⠀⢀⡄⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣧⢹⣿⡏⢰⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠃⠀⠀⢰⣿⡀⠀⠀⠀⢀⣤⣤⡟⠁⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⣿⣿⣿⣿⣿⠇⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢗⠀⠀⣶⣿⡿⠋⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⡏⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠡⠠⣶⡿⠷⠃⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⣟⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⠟⢀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⣀⣀⣛⣋⠀⠀⠀⠀⠀⠀⠀⠐⢐⣴⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⣛⣀⣛⣛⣠⣿⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡀⠠⡢⠴⠆⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣹⣶⡶⣿⣿⣿⣿⢻⣯⣥⢿⡿⣛⣯⣭⣹⣿⣿⣿⡿⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⠃⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢸⣶⣶⣶⣮⡉⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⣿⠃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢨⣿⣿⣀⡶⣿⣿⡏⠛⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣶⡄⠸⣿⣿⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣤⣤⣌⣉⡉⠙⠁⠘⠛⢛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⣿⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⢰⡿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀
⠀⠛⠁⠜⠙⠛⠃⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣤⣶⣶⡟⠁⠀⠀⣰⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⣶⣿⣶⣿⣿⣶⣿⣶⣿⣷⣿⣷⣾⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⢀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣇⡀⣺⣦
⣿⣿⣿⣿⣿⣿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⠿⠿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠟⠛⠛⠒⠒⠀⠈⠛⠛⠛⠛⠛⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠑⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣫⣿⣿⣿⣿⣿⣿⡟⠀⢀⣀⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⡟⣻⣟⣿⣻⣿⠛⠯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢉⣤⣶⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⡟⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠁⠀⣸⣿⣍⣀⣀⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣟⣳⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠿⣿⣿⣿⣟⣛⣿⣿⣿⣿
⢀⣴⣿⢿⠿⠿⣿⣿⠿⢿⣿⣷⣴⣤⣤⣄⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠈⠝⠻⠛⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡏⣻⣿⣿⣿⣯⣉⠉⠉⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣾⣶⡦⠀⣠⠼⢿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡛⢻⡗⠀⣿⡦⠀⠀⠀⣠⢖⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⡅⠘⠁⠀⡿⠇⠀⠀⠀⠀⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⡤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣏⠉⠃⠒⠈⢢⠘⠠⠄⠀⠀⠀⠐⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣿⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⢈⣈⣉⠉⠹⠿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠛⠺⢚⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⡿⠁⢠
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⢻⠀⠀⠀⠀⠤⠀⠀⠀⠀⡰⠁⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢹⣿⣿⢹⣷⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⢸⣇⠀⠀⠀⠀⠀⣀⣤⣿⠃⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢻⣿⣿⣿⣿⣿⣿⡏⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡆⡀⣀⡨⣿⣿⠟⠁⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⡟⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠫⠙⣶⣿⣿⠛⠀⠀⠀⠀⠀⣸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠟⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣛⣁⠀⠘⠉⠉⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⢛⣄⣛⣛⣠⡿⠿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠋⢠⣾⣿⣿⣿⣿⣿
⠀⠰⢄⢸⡸⠞⠡⢴⡆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⢿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡿⠃⢠⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠈⠀⠀⠁⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡏⠛⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡄⣿⣿⣿⡖⢰⣶⣶⣶⣮⡙⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⠏⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣾⣿⡟⠛⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣏⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠰⣿⣿⠏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⠛⢛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⣿⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣭⣉⣛⣛⠃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⢀⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⡶⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⢀⠀⠀⠀⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣀⠀⣰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠞⠘⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣡⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠿⠿⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠟⠛⠋⠛⠀⠈⠙⠛⠛⠛⠛⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠔⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣀⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠐⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢽⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⢙⣦⡶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⡿⠿⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠁⠀⣸⣿⣍⣀⣠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣟⣳⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠿⣿⣿⣿⣟⣛⣟⣿⣿⣿
⢀⣴⣿⢿⠿⠿⣿⣿⡿⢿⣿⣷⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠈⠝⠿⠛⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⢸⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡏⣽⣿⣿⣿⣯⣍⠉⠉⠁⠀⠀⢀⣤⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⣠⠼⢿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣶⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡛⢻⡇⠀⣿⡄⠀⠀⠀⣠⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡅⠘⠁⠀⠿⠃⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⡤⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣏⠉⠃⠒⠈⢢⠐⠰⠄⠀⠀⠀⠐⠑⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠙⣿⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⡀⠀⣤⣀⡀⢈⣉⣉⠉⠹⠿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠋⠒⢉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⡿⠁⢠
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⢹⠀⠀⠀⠀⠤⠀⠀⠀⠀⡴⠁⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢹⣿⣿⢹⣷⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠃⠀⢸⣇⠀⠀⠀⠀⢀⣀⣤⣾⠃⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢻⣿⣿⣿⣿⣿⣿⡏⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⡀⢀⣨⣿⣿⠟⠁⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⡟⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠏⣹⣾⣿⣿⠛⠀⠀⠀⠀⠀⣸⣿⣿⡟⢸⣿⣿⣿⠀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠟⠀⣴⣿⣿⣿⣿
⢀⡀⠄⠀⠀⠀⠀⠀⠁⠀⣀⣘⣛⣁⠈⠉⠉⠉⠁⠀⠀⠈⢠⣴⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⣛⣤⣛⣛⣠⡿⠿⠿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠋⢠⣾⣿⣿⣿⣿⣿
⡧⢕⡢⡺⢻⣛⣷⣴⡆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⢿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡿⠃⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠈⠈⠈⠈⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡏⠛⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡄⣿⣿⣿⡖⢰⣶⣶⣶⣦⡙⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⠟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣟⣾⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⠇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣾⣿⡟⠛⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣏⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⠛⣛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⣿⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣽⣉⣛⣛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⢠⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⡶⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣿⣷⣶⣶⣷⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣷⣶⣶⣶⡦⡀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣛⠀⠀⠀⠀⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⡀⡢⡤⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡈⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢂⢄⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣛⣿
⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠻⠛⠛⠿⠿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠟⠛⠚⠃⠒⠋⠙⠛⠿⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠠⠩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢉⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⢿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢎⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠛⢥⣤⡶⣵⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢡⣼⣿⣿⣿⠛⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢴⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠁⠀⣹⣿⣿⣥⣤⣾⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⣭⠵⣿⣿⣿⠋⠀⠙⣿⡣⢄⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣴⡿⣿⠿⠿⣿⣿⡿⢻⣿⣿⣷⣶⣶⣶⣄⠀⠀⠀⠀⢀⣿⢿⣿⡿⠂⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣶⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⠏⠁⢘⣿⣷⠌⠉⠁⣁⡀⠀⠀⢰⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣤⣼⣿⡇⠀⣖⠈⠛⠃⠀⠀⠀⣀⡀⢀⣤⣶⣿⣿⣿⣿⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢿⠇⠸⣿⠇⠀⠀⠠⠊⢠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡐⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠆⣈⢠⠀⡏⠀⠀⠀⠀⠀⠰⢙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⢀⣟⠀⠚⠀⠀⠀⠀⠀⠂⠀⠖⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠂⠀⣤⣀⡀⢀⣀⣉⠉⠹⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠈⣣⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⢹⠀⠀⠀⠀⠁⠀⠀⢀⣠⠈⠀⠀⢹⣿⡇⣾⣿⣿⢸⣿⣿⢸⣿⣿⢹⣿⣯⢹⣿⡖⢰⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⣸⣧⠀⠀⠀⠀⣠⣴⣾⠏⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢹⣿⣿⣿⣿⣿⣿⡿⠁⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⡤⠠⢴⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⢹⣿⣿⣿⣿⠃⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠷⠌⣈⢽⣿⡟⠂⠀⠀⠀⠀⢀⣸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡿⠃⢠⣾⣿⣿⣿
⠀⠠⠀⢀⣀⠀⠀⠀⠁⠀⣀⣛⣋⣀⠀⠀⠈⠉⠀⠀⠀⠒⣢⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⣛⣤⣛⣛⣠⣿⡿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡟⠁⣴⣿⣿⣿⣿⣿
⠃⢀⠌⠠⢷⠷⠒⡶⡆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⢿⣿⠿⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⠏⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠤⠀⠁⠀⢸⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⠸⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡄⣿⣿⣿⡖⢸⣶⣶⣶⣮⡉⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⡟⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣿⣿⡟⠛⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⠛⢛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⣿⣁⣿⣿⣇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⠋⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣽⣉⣛⡛⠃⡛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⢍⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⠖⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠿⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣾⣿⣶⣶⣶⣶⣶⣶⣶⡄⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣃⢬⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⠀⠠⡀⠼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠠⠀⠴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣏⡻⣯
⣿⣿⣿⣿⣿⡿⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠟⠛⠿⠿⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠛⠃⠀⠂⠂⠈⠙⠛⠛⠛⠛⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠱⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⠁⠀⠀⣹⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡍⣛⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢐⣶⡦⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠃⣤⣿⣿⣿⠟⠋⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠰⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠁⠀⣸⣿⣿⣷⣤⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠟⣋⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠋⣁⣼⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⢀⣾⣿⠿⠿⢿⣷⣶⣿⣿⡄⣀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠋⠀⣠⣴⣾⣿⣿⣿
⢀⣴⡿⢿⡿⠿⣿⣿⡟⢻⣿⣿⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⣠⠂⠀⠉⠀⠀⠀⠀⠀⢻⣿⡿⠏⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡻⢿⣿⣿⣿⡿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⠏⠁⢈⡽⠋⠀⠀⠀⢠⣴⡄⠀⣀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⡀⠀⣶⣟⠛⢿⡗⠀⣿⡄⠀⠀⠀⢀⠄⢠⣤⣠⣤⣶⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡿⠛⣿⣻⡄⠸⠁⠀⡿⠀⠀⠀⠀⠈⣨⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣼⣏⠉⠀⠒⠘⡄⠂⣠⠀⠀⠀⠀⠀⠦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣶⡦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⣤⣀⡀⢀⣀⣉⠉⠩⠾⣿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⠁⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢹⣿⣿⢹⣿⡖⢲⣾⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣿⣿⣿⣿⣿⣿⣿⠁⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⠀⣿⣧⠀⠀⠀⢠⣾⣶⠟⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⡿⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡞⠃⠀⡀⠫⡛⠅⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠣⠋⠀⠀⠀⠀⠀⢀⣸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣠⡀⠀⠀⠀⠀⣀⣘⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣭⣽⣥⡛⣛⣤⣛⣛⣠⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⡟⢁⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠪⠕⠙⠂⠶⡆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣿⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠟⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢸⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣮⡙⣩⣴⣶⣤⣍⠻⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣷⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⣿⡿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡟⣿⣿⡟⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣏⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⢰⣿⣿⡿⠁⠀⣰⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⠛⢛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⣿⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⡟⠁⠀⢰⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣭⣉⣛⣛⡃⠛⠛⡛⠻⠿⠈⠻⢿⣿⠿⠋⢀⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⢔⠋⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣾⣿⣿⣶⣿⣷⣿⣿⣶⣿⣷⣿⣷⣿⣿⣾⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣰⣖⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠲⠢⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⠒⠢⢀⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣏⣅⣆⣞⡻
⣿⣿⣿⣿⣿⣿⡟⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠿⠿⠿⠿⠋⠀⠉⠁⠀⠀⠙⠙⠛⠛⠛⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠈⠀⠈⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠟⠛⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⣿⣘⣿⡛⢇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢡⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠟⢠⣤⣿⣿⡿⠁⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⣿⣿⣿⣿⣿⠿⠛⠛⠿⠛⠒⠀⠀⠸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠉⠀⣹⣿⣿⣿⣿⣶⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡿⢋⠹⠟⠋⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⣋⣤
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⠛⠀⠀⠀⠀⠀⠀⣠⣮⡄⢀⣄⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠁⢀⣴⣾⣿⣿
⢀⣴⣿⣿⡿⠿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⡴⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠀⢸⣿⡇⢰⣿⠟⠛⠿⠿⣿⡿⠀⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣯⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⠏⠁⡼⠃⠀⣰⣶⠒⣿⡇⢠⣿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣹⡆⠿⠁⢸⡿⠀⠀⠀⠀⠚⠈⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⡇⠸⠑⠂⢣⡐⠄⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣾⣷⠀⠀⠀⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣦⣄⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⣿⡏⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣧⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⣤⣀⡀⢀⣀⣈⠉⠉⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠠⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⠁⢠⣾
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⣾⣆⠀⠀⠀⠀⣤⣤⠾⠁⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣧⢹⣿⡟⢰⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠇⢠⣿⣿⡆⢒⠄⠼⢿⠏⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠌⢭⢀⢁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣹⣿⣿⣿⠃⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣿⣿⣿⠃⢠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⣆⠀⠀⠀⠀⠈⣟⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣍⣽⣥⣟⣛⣀⣛⣛⣠⣿⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠃⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠁⠀⢶⢦⡆⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣯⣿⢻⣯⣭⢿⡿⣛⣯⣭⣙⣿⣿⣿⡿⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡿⠃⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⣿⠆⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣟⣴⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⣿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣾⣿⡏⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⢸⣿⣿⡿⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⣤⣤⣌⠉⠉⠙⠁⠘⢛⣛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⣿⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⡿⠧⠄⠂⠀
⠀⠀⠀⠀⣀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣭⣉⣛⣛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⢠⡏⠁⠀⠀⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣦⣤⣴⣶⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠐⠆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢅⢯⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡷⣶⣖⣺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣾
⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠏⠀⠘⠁⠈⠈⠙⠛⠟⠻⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠁⠈⠉⠉⠙⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠁⢉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣋⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠈⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠿⠿⠏⠟⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠙⣷⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣶⣷
⣿⣿⣿⣿⣿⣿⣿⣿⠛⢠⣤⣽⣿⡿⠏⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠉⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⢿⢟⣻⣿⣿⣿⣿⠿⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠛⠙⢋⣵⣾⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠀⠀⢀⣴⣿⣿⣿⣿
⢀⣴⣿⣿⡿⠿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⢠⡄⠀⡤⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠀⢸⣿⡇⢠⣿⠏⠙⠛⠛⠛⣛⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡏⠁⣼⠃⠀⠀⣠⡄⣼⣿⠁⢰⡆⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢸⣿⡗⢸⡟⠀⣿⡇⠀⠀⠀⠠⠀⠲⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⠿⡇⣈⢡⡀⣛⠁⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⡆⠀⠀⢠⡟⠈⠐⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠘⣿⡇⠀⠀⠈⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⡁⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⣉⠉⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠄⠂⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃⢀⣾
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⢸⣇⠀⠀⠀⠀⣀⣀⣠⡏⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢹⣿⣯⢹⣿⡏⢰⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠇⠀⣾⣿⣦⣀⣀⣠⣿⣿⠃⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢹⣿⣿⣿⣿⣿⣿⡟⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⢊⠛⠋⠑⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⢹⣿⣿⣿⡿⠁⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⠃⣠⣿⣿⣿⣿
⠀⠀⠀⡤⣦⠀⠀⠈⠁⠀⣸⣋⣁⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣍⣽⣥⣟⣛⣀⣛⣛⣠⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⠃⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠏⠿⠧⠴⡆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡾⣿⣿⣯⣿⢻⣿⣭⢿⡿⣛⣯⣭⣹⢿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⠁⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠂⢸⣿⣿⢨⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡅⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣤⣌⢻⣿⣿⣿⣿⣿⠀⠘⠁⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⣿⢿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢰⣿⣿⣀⡖⣾⣿⡟⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⢸⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⠛⣛⣛⣷⣼⣿⣿⣿⣇⡿⠿⠿⣿⠻⣿⣷⣿⣿⣁⣿⣿⣇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠈⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⡢⠂
⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣽⣿⣿⣿⣭⣉⣛⣛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⢰⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣤⣴⣶⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⠖⠢⡒⢲⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡱⠐⢃⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⣦⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠒⡋⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠟⠛⠋⠉⠈⠉⠙⠛⠻⠻⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⠉⠀⠉⠉⠙⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠨⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⢐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢋⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⣵⣶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣤⣽⣿⡿⠏⠙⠁⠀⠀⠀⠀⠀⠀⠀⠱⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠉⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠟⣻⣿⣿⣿⣿⠟⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠛⠙⢋⣽⣾⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⠿⠿⠛⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠀⠀⢀⣴⣿⣿⣿⣿
⢀⣴⣿⣿⡿⠿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⣠⡄⠀⡦⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠀⢸⣿⡇⢠⡿⠋⠙⠛⠛⠛⣛⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡏⠁⣼⠇⠀⠀⣠⣄⣼⣿⠁⢠⡆⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢸⣿⡷⢸⡟⠀⣿⡇⠀⠀⠀⢠⠐⢶⣶⣶⣤⣶⣿⣿⣿⣿⣿⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⠿⡇⣈⢡⡀⣋⠁⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⡆⠀⠀⢠⡟⠈⠐⠀⠀⠀⠀⠰⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠘⣿⡇⠀⠀⠈⠛⡀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⡀⠀⠀⠀⠚⠃⠀⠀⢀⠀⠀⠀⣤⣀⡈⢉⣉⣉⠉⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠤⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣾
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⢸⣇⠀⠀⠀⠀⣀⣀⣠⡇⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢹⣿⣯⢹⣿⡏⢰⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⣼⣿⣦⢀⡀⣠⣿⣿⠃⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠙⢀⠈⣉⠑⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⢻⣿⣿⣿⣿⠁⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⠃⣠⣿⣿⣿⣿
⣶⣂⣠⣦⣶⢤⠀⠈⠁⠀⣸⣛⣁⣀⠀⠀⡀⠀⠀⠀⠀⢚⣧⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣍⣽⣥⣟⣛⣀⣛⣛⣠⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⠃⣰⣿⣿⣿⣿⣿
⠛⣻⣿⢿⡿⣿⣷⣴⡆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣱⣶⡶⣿⣿⣯⣿⢻⣿⣭⢿⡿⣛⣯⣭⣹⢿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⡿⠁⣰⣿⣿⣿⣿⣿⣿
⠁⠻⠿⠗⠄⠺⠟⡀⠂⣸⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠛⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡅⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⣿⠀⠘⠁⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⣿⣿⠿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢰⣿⣿⣀⡖⣾⣿⡏⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⢸⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⠛⣛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⣿⣁⣿⣿⣇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⡿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀
⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣽⣿⣿⣿⣯⣉⣛⣛⡃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⣠⡟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠁⠁⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣤⣴⣾⠏⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⣷⣶⣿⣷⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡤⡄⠀⠀⠀⠀⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⡢⠄⡀⡄⢵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⠤⠁⢁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡭⢈⣁⢭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣷⠇⣶⢣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠟⠉⠽⠀⠀⠀⠘⠻⠛⠻⠻⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠉⢉⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠐⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢟⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⠈⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣻⣿⢿⠻⡟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡰⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⢀⣼⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣄⣈⣿⣿⠯⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠏⠉⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠋⠛⣩⣤⣾⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⡀⠀⠀⠀⠀⠀⢀⣾⣯⣶⡶⠿⠿⢿⠛⠋⠀⠹⣿⠀⠰⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠀⠀⣰⣾⣿⣿⣿⣿
⢀⣴⣿⣿⡿⠿⣿⢿⠛⠋⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣸⡿⠿⣿⣇⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⠉⠉⠁⠀⠀⠀⣰⣿⡆⢠⣿⠟⠉⠛⠛⠛⠉⠀⠀⠀⢀⣀⡈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⠏⠁⣼⡟⠀⠀⠀⠀⣠⣤⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣺⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⢠⣶⠖⢿⣿⠀⣾⡆⠈⠀⠀⢀⡀⢄⣤⣤⣀⣤⣴⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠀⣸⣿⡇⠸⡏⠀⣿⡇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠉⠃⠤⠔⢦⠰⠀⠀⠀⠀⠀⠀⠄⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⣀⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⡇⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⣉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⣤⣀⡀⢈⣀⣈⠉⠉⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠢⠆⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠃⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠘⡇⠀⠀⠀⠈⠀⠀⠀⣰⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢹⣿⣯⢹⣷⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⢸⣿⣄⠀⠀⠀⢢⣾⡟⠁⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⣻⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠨⢀⠄⠮⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠙⣿⣿⣿⣿⠁⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠠⠀⠡⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿
⠘⢒⣄⠀⡄⠀⠀⠈⠀⠀⣀⣛⣋⣀⠀⠀⠀⠀⠀⠀⠀⠂⢣⣴⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⣛⣤⣛⣛⣠⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿
⠑⢸⠿⣿⡿⢿⠶⡴⡆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣹⣶⡶⣿⣿⣯⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⡿⠃⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠀⠄⠅⠈⠙⠄⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢸⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡄⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⣿⠟⠇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣿⣿⡏⠛⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⢸⣿⣿⡿⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣏⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⠛⢛⣛⣧⣾⣿⣿⣿⣇⣿⠿⠿⣿⠻⣿⣷⣿⡿⣁⣿⣿⣟⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡤⠅⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣯⣉⣛⡛⠃⠛⠛⠛⠻⠿⡈⠻⢿⣿⠿⠋⢠⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣴⠏⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣶⣶⣶⣿⣶⣷⣿⣷⣾⣿⣾⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⣄⠀⠀⡀⠐⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⢻⡀⠀⡀⠀⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠆⠤⠮⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡍⢀⡁⢱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢱⣞⢨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢎⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠏⠉⠉⠀⠈⠁⠚⠻⠛⠿⠻⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠁⢹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿
⢫⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠⢤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣟⣿⣿⠛⠻⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠮⣹⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⢀⣼⣿⠟⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣄⣈⣿⣿⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⢺⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠏⠉⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢫⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠋⠛⣩⣤⣾⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⡀⠀⠀⠀⠀⠀⢀⣾⣯⣶⡶⢿⡿⠻⠙⠋⠉⠻⣿⠀⠰⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⣰⣿⣿⣿⣿⣿
⢀⣴⣿⣿⡿⠿⣿⢿⠛⠋⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣼⡿⠿⣿⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿
⠉⠉⠁⠀⠀⠀⣰⣿⡆⢠⣿⠟⠉⠛⠛⠛⠉⠀⠀⠀⢀⣀⡈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⠏⠁⣼⡟⠀⠀⠀⠀⣠⣤⠀⠀⡀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣾⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⢠⣶⠦⢿⣿⠀⣾⡆⠈⠀⠀⢀⠠⢤⣤⣄⣀⣠⣴⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠀⣸⣿⡇⠸⠏⠀⣿⠅⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠉⠃⠠⠔⢦⠰⠀⠀⠀⠀⠀⠀⠴⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⣿⡇⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⡄⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⣤⣀⡀⢀⣈⣈⠉⠉⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠳⠆⣢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠃⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠘⡇⠀⠀⠀⠉⠁⠀⠀⣰⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢹⣿⣯⢹⣷⡆⢰⣶⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⢸⣿⣄⠀⠀⠀⢲⣾⡟⠁⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠐⠀⢲⠿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠉⣿⣿⣿⣿⠁⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⡇⠀⠘⡥⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿
⠀⢠⣂⠀⣴⠲⠀⠈⠁⠀⣀⣛⣋⣀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣴⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⢛⣤⣛⣛⣠⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿
⠊⠰⠖⡚⠗⠿⠶⡴⡆⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣹⣶⡶⣿⣿⣯⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⠃⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠲⠒⠈⠁⡘⠘⠂⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢸⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣷⡄⣿⣿⣿⡖⢰⣶⣶⣶⣮⡙⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⡇⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⣿⠟⠆⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢰⣿⣿⣀⡖⣿⣿⡟⠛⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠸⣿⣿⡿⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⠛⢛⣛⣧⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⣿⣁⣿⣿⣟⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⡿⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡡⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣽⣉⣛⡛⡃⠛⠛⠛⠻⠿⡈⠻⢿⣿⠿⠋⢠⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣦⣴⠏⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣿⣷⣾⣿⣾⣿⣶⣿⣶⣿⣷⣿⣷⣾⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⢄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣘⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⡄⠂⠀⡰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⡾⡗⡤⣤⢲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣳⣿⣇⣸
⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠋⠛⠛⠛⠛⠻⠟⠛⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠋⠁⠉⠀⠀⠀⠙⠛⠛⠛⠛⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠁⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⠿⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⣻⣿⣿⣿⡟⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⡀⠈⢿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠘⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠈⣽⣿⣿⣿⣿⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠟⣡⣾⡟⠁⠈⠁⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⢋⣡⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⡀⠀⠀⠀⠀⠀⣰⣿⣷⣿⡟⢿⣯⣅⠀⠀⠀⠻⠃⠀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⠏⢉⣴⣶⣿⣿⣿
⢀⣼⣿⣿⡿⠿⣿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⠛⠻⠿⠃⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⠍⠉⠉⠁⠀⠀⣀⣴⡄⢀⣿⣿⠋⠛⠛⠛⠋⠀⠀⣠⣤⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣻⠏⠁⣸⣿⣏⣀⡀⣼⣿⠀⣠⡄⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡧⣿⡟⠀⣿⠇⠀⠀⠀⠀⠒⠒⠠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣧⣈⢡⠀⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣇⠉⠀⢠⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣠⣶⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣦⡤⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢸⡇⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣇⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⣉⠉⠉⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠂⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡟⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⣿⡀⠀⠀⠀⠀⢀⣀⣴⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢹⣿⣧⢹⣿⡇⢰⣶⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⣿⣷⡄⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠃⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣸⣿⣿⣿⠃⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡟⢸⣿⣿⣟⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⠇⢠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⣘⣋⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⣛⣠⣛⣛⣠⣿⠿⠿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⠋⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠉⠛⠙⠠⢴⡒⠀⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡏⣹⣶⡾⣿⣿⣯⣿⢻⣯⣭⢿⡿⣛⣯⣭⣹⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠃⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡄⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⢿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣾⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡖⣿⣿⡟⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠠⣿⣿⠏⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⠛⢛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⣿⣁⣿⣿⣇⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢯⠬⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⡃⠛⠛⠙⠻⠿⠈⠻⢿⣿⠿⠋⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⢤⠔⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣾⣿⣾⣿⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢠⡦⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣙⡙⠄⠀⠀⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⣠⠷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⢂⠀⠈⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⢺⣶⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾
⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠟⠈⠩⠀⠀⠀⠛⠛⠟⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⡦⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣿⣿⣛⣻⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣼⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⡀⠀⢻⣿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣤⠀⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠈⣽⣿⣿⣿⣿⣶⣶⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⡿⠿⠻⡿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠛⠛⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢹⡿⠟⠛⠅⠀⠀⣼⣿⣿⣷⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣯⣀⣀⠀⣴⣿⣿⣿
⣀⣼⣿⣿⡿⢿⣿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿
⠍⠉⠉⠁⠀⠀⢀⣴⠄⢀⣿⣿⡟⠛⠛⠛⠛⣀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠏⠀⢸⣿⣿⠀⢀⣤⣤⣾⣿⡃⣰⣆⠙⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⢸⣿⡏⢹⡟⠀⣿⡇⠀⠀⡀⠀⠂⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⠿⠗⡀⠠⡀⣋⠁⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⣿⠄⠀⠀⢠⣾⠀⠒⠀⠀⠀⠀⠀⠘⢿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣦⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⣿⠀⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⣉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠳⢶⣢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠁⢠
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⣼⣇⠀⠀⠀⢀⣠⣤⣴⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢹⣿⡟⢱⣶⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠇⠀⠀⣿⣿⣷⠄⠀⣤⡽⠟⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢿⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⣈⡉⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣿⣿⣿⣿⠃⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⡏⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⢸⣿⣿⣿⣀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠃⢀⣾⣿⣿⣿
⠀⠀⠀⠀⣀⠀⠀⠈⠉⠀⣀⣛⣋⣁⠀⠀⠀⠀⠀⠀⠀⢀⣦⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣭⣽⣥⣟⣛⣠⣛⣻⣤⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⡿⠃⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠽⠛⠙⠧⢶⡆⠀⣿⣿⢿⣿⣷⠀⣿⣿⣿⡿⣿⣿⡏⣹⣶⡾⣿⣿⣯⣿⢻⣯⣭⢿⡿⣛⣭⣭⣻⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠟⠁⣰⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠀⠐⠂⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢸⢸⣿⡿⣻⣿⡏⢸⣿⡿⢿⣿⡅⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣤⣌⢻⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⣿⣿⡿⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡾⣿⣿⡟⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣋⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⣿⣿⠏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⠛⠛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⣁⣿⣿⣇⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⣿⠏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⡃⠛⠛⠛⠻⠿⣈⠻⢿⣿⠿⠋⢠⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⢤⣶⠟⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⠖⠐⠒⣒⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣱⢾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠍⠉⠉⠋⠉⠻⠛⠛⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠟⠁⠀⠀⠹⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⠿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⠃⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠁⠠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠤⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⡤⠀⠀⢀⣴⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢹⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢂⣶⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠉⠉⢉⣽⣿⣿⣿⣿⣭⣤⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠨⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣽⣿
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠗⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿
⣀⣼⣿⣿⡿⠿⣿⡿⠛⠋⣻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣤⡀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣆⣶⣾⣿⣶⣶⣿⣿⣿⣿
⠏⠉⠉⠉⠀⠀⣸⣷⠀⢀⣿⣿⡏⠛⣿⣿⢿⣿⡇⢀⣤⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠏⠀⠸⣿⣿⠁⢰⣿⣿⠘⣿⠇⢸⣿⠀⠀⠀⠀⣠⣤⣄⣀⣀⣀⣠⣾⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⠀⢸⡏⠿⠀⠁⡄⢘⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⡆⠀⠀⢠⣞⠈⠡⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣿⠀⠀⠀⠈⠛⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⣿⠀⠀⠀⣼⠿⠃⠀⠀⡀⠀⠰⠖⢹⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⡄⠀⠀⠀⠀⣀⣠⣰⠄⡀⠀⣤⣀⡈⢉⣉⣉⠛⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠶⣂⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⢠⣿⣷⣠⠀⠀⣨⣿⡟⠁⠀⠄⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡟⢱⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⢠⣾⡿⠯⢻⣳⡴⠚⠋⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⣿⣿⣿⣿⣿⣿⣿⠃⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠟⣿⣿⣿⣿⠏⠀⣼⣿⣿
⡀⢀⢀⠀⡀⠀⠀⠀⠀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣸⣿⣿⡟⢸⣿⣿⣿⣀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⠟⠀⣼⣿⣿⣿
⡿⢱⠷⣈⣔⣲⠀⠈⠀⢸⣟⣉⣁⣀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣍⣹⣥⣟⣛⣀⣛⣻⣠⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⠟⢀⣾⣿⣿⣿⣿
⠯⣻⣿⣿⣿⣿⣷⣶⣶⡆⣿⣿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⣰⣶⡶⣶⣶⣯⣿⢻⣯⣽⢻⡿⣛⣯⣭⣻⣿⣿⣿⡿⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠏⢠⣿⣿⣿⣿⣿⣿
⠙⠛⠿⡿⠿⠋⠸⠍⣿⣿⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢸⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡄⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣬⣍⢻⣿⣿⣿⣿⣿⡇⠈⠁⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⣿⣿⣿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢰⣿⣿⣀⡖⣿⣿⡟⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣶⡄⠸⣿⣿⣿⡿⠘⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⣤⣤⣌⣉⠉⠙⠁⠘⢛⣛⣛⣷⣾⣿⣿⣿⣇⣿⠿⠿⣿⠻⣿⣷⣿⣿⣁⣿⣿⣿⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⣿⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠆
⠀⠀⠀⠀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⣃⠛⠛⠛⠻⠿⣈⠻⢿⣿⠿⠋⣠⡿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⠟⠁⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⣿⠖⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⡄⠀⠀⠀⠀⢲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⡀⠀⠀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕⢀⣀⣅⣨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢌⡙⢻⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣾⡯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠟⠿⠉⠀⠀⠁⠀⠛⠛⠛⠛⠛⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠟⠁⠀⠀⠘⠛⠟⠿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠁⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢙⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⠃⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠠⠤⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⡤⠀⠀⢀⣼⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢹⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⢿⣿
⠉⠉⢉⣽⣿⣿⣿⣿⣥⣤⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣼⣾
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠗⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⣀⣼⣿⣿⡿⠿⣿⡿⠟⠋⣻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣤⡄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣆⣶⣾⣿⣶⣶⣿⣿⣿⣿
⠏⠉⠉⠉⠀⠀⣸⣶⠀⢀⣿⣿⡉⠛⣿⣿⣿⣿⡇⢀⣤⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠋⠀⠘⣿⣿⠁⢰⣿⣿⠸⣿⠇⢸⣿⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣠⣾⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⠀⢸⡏⠿⠀⠁⡀⢘⠁⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣆⠀⠀⢠⣞⠈⠡⠀⠀⠀⠀⢠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⣿⠀⠀⠀⠈⠛⡀⠀⠀⠀⠀⠀⠈⢉⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⣿⠀⠀⠀⣴⠿⠃⠀⠀⢠⠀⠀⠄⠀⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡄⠀⠀⠀⠀⣀⣀⣤⠎⠀⠀⣤⣀⡀⢀⣀⣉⠉⠉⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠶⢂⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⢠⣿⣷⣠⣀⠀⢸⣿⡟⠁⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢹⣾⡟⢱⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⢠⣾⡿⠏⢛⣶⡔⢚⠉⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⣿⣿⣿⣿⣿⣿⣿⠃⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠐⠈⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠛⣿⣿⣿⣿⠏⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣸⣿⣿⡟⢸⣿⣿⣿⣀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⠟⢀⣼⣿⣿⣿
⠀⠀⠄⢀⢐⡀⠀⠈⠀⢸⣟⣉⣁⣀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣍⣹⣥⣟⣛⣀⣛⣻⣠⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⠏⢀⣾⣿⣿⣿⣿
⠀⠀⠀⡌⡜⠘⠣⣶⣶⡆⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⣿⣿⡇⣰⣶⡶⣶⣶⣯⣿⢻⣭⣭⢻⡿⣛⣯⣭⣻⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠏⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡄⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣬⣍⠻⣿⣿⣿⣿⣿⡇⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⣿⣿⠿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡏⢸⣿⣿⣀⡖⣿⣿⡟⠛⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⣿⣿⠏⠘⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⢛⣛⣛⣷⣾⣿⣿⣿⣇⡿⠿⠿⣿⠻⣿⣷⣿⣿⣁⣿⣿⣿⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀
⠀⠀⠀⠀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⣃⠛⠛⠛⠻⠿⢈⠻⢿⣿⠿⠋⢀⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀
⠀⠛⠁⠜⠛⠛⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠄⢰⠝⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣶⣿⣶⣿⣿⣿⣿⣾⣿⣾⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠐⢆⠀⠀⠀⢀⢒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⠀⠀⠀⠀⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡇⢀⢀⢀⡸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡢⠜⢂⡸⢂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⡯⣶⢜
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠟⠻⠁⠀⠀⠀⠀⠙⠛⠛⠛⠛⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠛⠁⠀⠈⠉⠉⠉⠙⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿
⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠁⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠋⠉⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠚⢛⠿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠁⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢹⣿⡿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⠿⠗⠀⠀⠀⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿
⠉⠉⢉⣽⣿⣿⣿⣿⣭⣁⣠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⣯
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⢉⣸⣿⣿
⣀⣼⣿⣿⡿⠿⣿⡿⠛⠋⣻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⡄⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣦⣾⣿⣿⣶⣶⣾⣿⣿⣿
⠍⠉⠉⠉⠀⠀⣽⣶⠀⢀⣿⣿⠁⣹⣿⢿⣿⡃⢀⣤⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠉⠀⠘⣿⣿⠀⣿⣿⢸⣿⠃⢸⡿⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⡿⠀⡏⠈⠤⠠⡄⣛⠁⠀⠀⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⢿⠇⢸⣧⠈⠀⢰⡟⠈⠡⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⡇⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸⡇⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣤⣀⡀⢈⣁⣉⠉⠉⠹⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣧⣾⣿⣿⣿⠏⠀⣠
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⢸⣿⣆⣀⠀⠠⣽⣿⠋⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢱⣶⡟⢻⣷⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣿⣿⣿⡏⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠇⢠⣾⡿⠛⠷⠑⠀⠚⠁⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠻⣿⣿⣿⣿⣿⡟⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠁⣿⣿⣿⡿⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⡟⢸⣿⣿⡿⣀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⡿⠃⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣟⣉⣁⣀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣶⣶⣿⣿⣿⣭⣿⣿⣯⣉⣥⣟⣻⣄⠛⣛⣠⡿⠿⠿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⠁⣼⣿⣿⣿⣿⣿
⠀⠀⠀⡐⠀⠐⠡⡶⠶⡆⣿⣿⢿⣿⣿⠀⣿⣿⣿⡿⣿⣿⡏⣱⣶⡶⣶⣶⣾⣿⢻⣯⣿⢿⡿⣛⣯⣽⣛⢻⣿⣿⡿⠿⢿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡿⠁⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⠀⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡄⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣬⣍⠻⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⡿⣤⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⣿⡟⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡂⣾⣿⡏⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣶⡄⢸⣿⣿⣿⡟⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⢛⣛⣛⣧⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⣿⣁⣿⣿⣷⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⣿⠏⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠅⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⣃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⢠⣿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀
⠀⠛⠁⠜⠙⠛⠃⠛⢻⣿⣿⣿⣿⣿⣿⣿⣇⣠⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⡄⠴⡿⠃⠀⠀⢀⣾⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⣒⠀⠀⠀⡀⣒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡯⢀⢰⣠⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡴⡟⢷⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠿⠿⠿⠿⠃⠁⠉⠀⠀⠛⠟⠛⠛⠻⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠉⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠟⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⣿⣿⣿⠀⠀⢀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣙⣋⣛⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢈⢴⠶⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠀⢸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿
⠉⠉⢉⣿⣿⣿⣿⣿⣟⠁⢀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢿⣿
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣿⣿⣿⡿⣿⣿⣿⠿⠉⣴⣾⡟⠉⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠛⠉⠀⣠⣿⣿
⣠⣾⣿⣿⡿⢿⣿⡿⠟⠋⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⡀⣿⡿⣿⣿⡇⠹⠛⠙⠀⠀⠛⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣆⣶⣿⣿⣷⣶⣾⣿⣿⣿
⠍⠉⠉⠉⠀⠀⣿⣿⠀⠀⣾⣿⡏⠈⠛⠛⠛⠀⠀⠀⠀⠀⢠⣤⡀⠉⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠉⠀⠸⣿⣿⠀⠀⢠⣤⡄⢰⣿⠃⢠⡄⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡟⠀⠀⢸⣿⡇⢸⡟⠀⣿⡏⠀⠀⠀⠀⣤⣤⣤⣤⣀⣠⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠿⠇⠀⠀⣾⠹⣇⣈⢡⠀⡛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⠂⠀⠀⣠⡇⠈⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣷⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⠀⠀⠀⠾⠿⠃⠀⠀⠀⠀⣤⣀⡀⢀⣈⣉⠉⠉⠙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠄⠠⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠁⢠
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⣿⡄⠀⠀⠀⣀⣀⣠⡤⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢹⣶⡟⢻⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇⠀⠀⢰⣿⣿⣤⡖⢀⣾⣿⠋⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⣸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⣿⣿⣿⣿⣿⡿⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠉⠉⡌⢉⠙⠁⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣽⣿⣿⣿⠁⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢸⣿⣿⡿⣀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⠃⣠⣿⣿⣿⣿
⠀⠀⠀⢀⣐⣐⠀⠀⠉⠀⣀⣘⣛⣉⠀⠀⠀⠀⠀⠀⠀⠊⣳⣴⣶⣿⣶⣶⣿⣿⣿⣽⣿⣿⣯⣙⣥⣟⣻⡄⣛⣛⣠⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿⣿
⠀⠀⠀⡶⢿⠖⠷⠶⠆⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⡿⣿⣿⡏⣱⣶⡶⣿⣿⣿⣿⢻⣯⣿⢿⠿⣛⣯⣭⣛⣿⣿⣿⡿⠿⢿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠁⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⢿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⢈⢸⣿⡿⣻⣿⡏⢸⣿⡿⢿⣿⡅⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣤⣍⠻⣿⣿⣿⣿⣿⣿⠇⠀⣠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡩⣿⣿⠀⣿⣿⣿⣿⣿⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡂⣾⣿⡟⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠙⢿⣿⣦⡄⠸⣿⣿⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣤⣤⣌⣉⣉⠙⠃⠘⠛⠛⣛⣧⣾⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⡿⡀⣿⣿⣷⣿⣿⢸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⣿⣿⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⠷⠄⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣛⣃⠛⠛⠛⠻⠿⠈⠻⢿⣿⠿⠋⣀⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠛⠁⠜⠙⠛⠃⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⡿⠁⠀⢀⣾⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣠⡔⠀⠀⠀⠀⣰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⠄⢀⣠⡾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡤⣟⡺⣨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣺⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠉⠀⠁⠀⠀⠙⠛⠛⠛⠛⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠏⠁⠀⠀⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⠁⠀⢀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠙⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣆⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢛⣉⣟⣹⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣴⠞⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠀⠸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠉⠉⢉⣿⣿⣿⣿⣿⡟⠋⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣯⣭⣰⣿⣿⣿⡿⠿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣧⠀⠈⠉⠙⣠⣾⣿⣿⠏⢹⣦⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⠋⠉⣉⣵⣿
⣠⣾⣿⣿⣿⣿⣿⡿⠟⠋⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣄⠀⠛⠛⠿⢿⡿⠀⠀⠀⠀⠘⠛⠋⠁⠀⠘⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣆⣶⣿⣿⣿⣷⣶⣿⣿⣿
⠍⠉⠉⠉⠀⠈⣿⣷⠀⠀⣠⣿⣿⣿⡟⣿⣿⠀⣠⡄⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⣿⣿⣿⣿⡇⣿⡏⠀⣿⠇⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⢀⢧⠈⢄⢐⡋⠀⠀⠀⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣾⡇⣿⠀⠀⢠⣾⠃⠁⠄⠀⠀⠀⠀⠀⢼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠀⣿⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⣿⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⡇⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⢀⣀⣉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⣿⣷⣄⣀⡀⢈⣿⡟⠀⠀⠀⠀⠀⢹⣿⡇⣾⣿⣿⢰⣿⣿⢸⣿⣿⢸⣿⣯⢹⣾⡟⢱⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢇⣼⣿⠛⠉⠛⠀⠛⠋⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣾⣿⡏⣾⣿⡇⢸⣿⣿⣼⣿⡇⣼⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⡏⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⣿⠁⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠛⣿⣿⣿⣿⠏⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⡟⢸⣿⣿⣿⡀⣿⣿⡇⣿⣿⢸⣿⣿⠃⣿⣿⣇⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⠟⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⡠⠀⠈⠁⣿⣏⣉⣀⣀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣾⣿⣿⣯⣽⣿⣿⣏⣹⣥⣟⣛⣀⣛⣛⣠⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠏⢀⣾⣿⣿⣿⣿
⠀⠀⠀⣀⠆⠎⠣⣶⣾⡇⣿⣿⢿⣿⣿⠀⣿⣿⣿⡿⣿⣿⡏⣱⣶⡶⣶⣶⣯⣽⢻⣯⣿⢻⡿⣛⣭⣭⣙⣿⣿⣿⡿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠃⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣿⢻⣿⣿⢸⣿⣿⢰⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡏⠙⢸⣿⣿⠘⢸⣿⡿⣻⣿⡇⢸⣿⡿⢿⣿⡄⣿⣿⣿⡖⢸⣶⣶⣶⣮⡙⣩⣴⣶⣤⣌⠻⣿⣿⣿⣿⣿⠀⠈⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⠃⢸⣿⣿⣿⣿⢀⣿⣿⣿⡇⢸⣿⣿⣴⣿⣿⡇⣿⣿⡇⣾⣿⣇⣾⣿⢻⣿⣿⣀⡀⣿⣿⡇⣿⣿⡇⣿⣿⡹⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣾⣿⡟⢸⣿⣿⣤⡄⢸⣿⣿⣿⡇⢸⣿⣿⣀⡂⣾⣿⡏⠋⣿⣿⡇⣿⣿⡇⣿⣿⡟⣛⣯⢸⣿⣿⠿⠇⣿⣿⡿⣿⣯⠀⠹⢿⣿⣦⡄⠸⣿⣿⡿⠆⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⣤⣤⣌⡉⠉⠙⠁⠘⠛⣛⣛⣣⣼⣿⣿⣿⣇⡿⠿⠿⣿⡻⣿⣷⣿⣿⣁⣿⣿⣿⣿⣿⣸⣿⣿⣤⡄⣿⣿⡇⣿⣿⢰⣷⣶⢹⣿⣿⠀⣿⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄
⠀⠀⠀⠀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣍⣛⣛⡃⠛⠛⠛⠻⠿⣈⠻⢿⣿⠿⠋⢠⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀
⠀⠛⠁⠜⠙⠛⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⠿⠛⠻⠟⠛⣿⠿⢿⠿⢿⢿⢿⢿⡿⠟⡟⠻⠿⡿⠿⡿⡿⡿⠿⡿⠿⡿⠿⡿⠿⣿⢛⢻⠛⡻⠛⠛⢛⡟⡛⡟⠛⠛⢻⢻⢻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠇⠸⠀⠀⠂⠈⣿⢸⠀⠀⢀⠈⡈⢸⡇⠇⡇⠀⠀⡇⠐⡇⠇⡇⠅⡇⠐⡀⠄⡆⠐⣿⢠⢸⠀⠔⠀⠁⠠⡇⠄⠇⠀⡄⢸⠀⢸⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢸⡇⡆⡇⠀⠁⡂⠁⢰⢰⠀⡧⠐⠂⠀⠀⠀⠀⢸⡇⠈⠀⢸⡇⠀⠀⠀⠀⠀⢘⣻⢰⢸⠀⠀⠀⠀⠀⠀⣄⠁⡷⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣷⣶⣷⣶⣶⣾⣶⣶⣿⣶⣾⣶⣷⣶⣶⣾⣷⣾⣶⣾⣷⣶⣶⣶⣷⣶⣾⣿⣶⣾⣶⣶⣶⣶⣶⣶⣯⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⠉⢻⠉⠉⣿⡿⠉⡏⠉⠋⢹⠉⢹⠉⠉⡏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⠉⢿⠉⡏⠉⡏⠉⣉⣿⡏⢩⠉⢹⠉⢹⠉⢉⣹⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⢸⠀⠚⣿⠇⢸⡇⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠙⢿⠀⡁⠀⡇⠀⣉⣿⠁⣾⠀⢈⠀⢸⠀⢈⣹⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⢸⠀⠙⠻⢀⣿⡇⠀⠀⢸⠀⢸⠀⢠⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⠀⣸⠀⡇⠀⡇⠀⠛⡇⢰⣿⠀⢸⠀⢸⠀⠘⢻⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⡟⢻⢻⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⡟⢻⡟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⡇⢸⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣻⣿⣿⣿⣿⣿⣿⣿⣋⣉⠁⠀⣤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡇⢸⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⡇⢸⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣄⠀⠀⠙⢹⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⢠⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡇⢸⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⡇⢸⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠘⣿⣿⣿⣿⣿⣿⡏⠁⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢻⡇⡇⢸⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⡇⢸⢸⣿⠆⠀⠀⠀⠀⠀⣶⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣸⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢳⣇⢸⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⡇⢸⢸⣿⠀⠀⠀⠀⠀⢀⢀⣲⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⣿⣿⣿⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⡇⢸⢸⣿⠀⠀⠀⠀⠀⠈⠲⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣄⠀⠀⠀⣾⣿⣿⠀⠀⠀⣠⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢺⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢀⡇⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⡄⠀⠀⠙⣿⣿⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⡇⢸⠈⡿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠲⠤⢾⡿⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⡇⠀⠀⣶⣿⣿⠀⠀⢾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠟⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⡇⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠁⠀⢸⣿⣿⣿⠀⠀⠈⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⣿⣿⣿⡇⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠉⠙⡁⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⡿⠃⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠰⠿⢖⡀⠈⠁⠀⠀⠈⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⡿⣿⠄⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣽
⣇⠀⠀⠀⠀⣤⣤⡐⠂⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠘⠁⢹
⡇⠀⠀⠠⣤⣄⡉⠛⠀⠐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠈⠉⣀⣤⠄⠀⠀⠀⢸
⡇⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠃⠀⣀⣤⣴⣤⣤⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠷⠀⠀⢴⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⢸⣿⠀⠀⢾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠂⠀⠀⠀⠉⢉⣛⣿⠟⠛⠀⠀⠀⠀⢸⣿⠀⠀⠀⠟⠻⣏⣋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⢗⡠⠋⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣀⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⠉⠠⢟⣱⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⡿⣿⣷⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⡟⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣈⠏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣎⣟⣀⣼⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⢹
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⢻⣯⠿⣯⡷⣝⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠦⡜⠜⠻⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠲⠀⣿⣿⢰⣴⡖⡆⣶⡆⡶⡖⣴⣶⡆⡶⡶⡦⣖⢰⡂⢰⢺⣿⢶⡲⣖⣶⡆⡇⡷⣖⢺⢰⡆⡖⢼⢺⢰⣶⣶⡆⢰⣶⡟⡆⣶⣴⢰⣿⠀⣿⡇⠀⣶⢰⣦⡆⡆⢰⣦⡶⣴⡆⢰⣶⠘⠉⡖⣶⣶⢰⢺⠘⠃⠀⢸
⣇⣈⣀⣉⣉⣐⣋⣉⣁⣉⣁⣉⣉⣉⣛⣁⣁⣉⣁⣉⣈⣁⣈⣉⣉⣉⣉⣉⣉⣁⣁⣉⣉⣈⣉⣁⣉⣉⣩⣌⣉⣉⣁⣈⣉⣉⣁⣉⣈⣉⣉⣀⣉⣙⣀⣛⣈⣉⣉⣁⣈⣉⣁⣉⣁⣈⣉⣀⣀⣁⣉⣉⣉⣉⣀⣀⣀⣸
⠺⠿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⣉⣩⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣉⡙⠻⢿⣷⣆⠀⠀
⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠛⢿⣶
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹
⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃
⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣠⣾
⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣉⣴⣾⣿⣿
⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⡄⠀⠀⢠⣿⣿⠿⢋⣡⣬⣍⣉⣉⣛⣛⣋⣉⣉⣭⣤⣶⣾⣿⣿⣧⠀⠀⠈
⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠤⠤⠤⠤⠤⠤⣾⣿⣿⣿⣿⣿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⢿⣿⣿⡿⠿⣿⣿⣿⡆⢀⡀⠀⠀⠟⠉⠀⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣶⣿⣧⣤⣤⣤⣾⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠛⠂⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣄⠀⠰⢶⣶⠶⠶⠦⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠛⣿⣿⣿⡝⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠘⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⠅⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⡂⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠉⠉⠉⠻⡿⠛⠛⠛⠛⠛⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡋⠀⠴⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣷⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠿⠿⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣉⠉⠉⠉
⢀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣆⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠻
⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠹⠿⠿⢿⣿⣿⠋⠀⠐⠐⠐⠀⠀⠀⠒⠀⠀⠀⠀⢹⣟⠉⠙⣿⣿⠿⠟⠛⠻⣿⡆⠀⡀⠀⠀⠀⠀⠉⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠸⠿⢿⣿⣿⣿⣆⣀⣠⣤⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣃⣀⣀⣀⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠟⠂⠹⣿⣯⣧⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡀⡀⠆⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⡄⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠙⠛⠛⠻⠿⢿⣿⣿⢿⣿⣿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⢤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⢀⡀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢆⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⠈⠀⠀⡀⠀⠀⠤⠀⠀⠀⠀⠀⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣶⣶⣶⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⣩⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣴⣿⣿⣿⣿⡿⠹⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣤⣤⣭⣠⣄⣀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣷⣶⣶⣶⣶⣶⡖⡲⢶⣶⣶⣦⣴
⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠿⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀
⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⣭⣭⣭⣙⣛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣏⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣶⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠉⠙⣿⣿⡟⠛⠻⣿⣿⣎⠛⢿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⡞⣸⣿⣿⠿⠿⠿⠿⣿⣿⡿⠿⠿⢟⣛⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⠙
⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⢯⣿⣿⣿⣿⡟⢰⠟⠋⠀⠀⠀⠀⠐⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠒⠁⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠰⠖⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⢟⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣶⣶⣦⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠇⠀⠉⠉⠉⠛⣿⠻⠟⠛⠿⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠁⠀⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢁⣆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣀⢠⠄⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠈⠈⢰⡆⢔⠄⠀⠈⠂⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦⣀⠄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⢸⣏⠀⢀⠀⠀⠁⠀⠰⠤⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⢀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣴⣀⣀⣴⣄⣈⣇⣀⣨⡄⠀⠀⠀⠀⠠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣯⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⡿⣿⡟⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠠⠤⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣶⣶⣴⣤⣴⣤⣤⣤⣀⣀⡀⢀⣀⠀⢀⢀⣀⡀⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣀⣀⣀⠀⠿⠗⠄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢭⢻⢿⣝⢿⢫⠽⠿⠿⠿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠿⣿⡿⠿⡇⠀⠀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡸⡇⣼⢹⡀⡟⢸⡇⣿⣉⣷⢱⣏⣙⡎⣿⡇⣿⠏⣿⠰⣏⣙⢢⣟⣉⣷⢸⡏⡇⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠻⢇⣎⠿⣣⣸⣇⣿⣿⣿⣘⡧⠴⣶⣿⣧⡿⠤⠿⣰⠤⠼⣋⡷⠤⢖⡸⣇⡇⠀⠀⡿⣿⣿⣿⣿⣟⣻⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣶⣯⣿⣿⣿⣿⣶⣾⡆⠀⠈⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠙⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠙⣿⡿⠏⢫⣼⡿⢿⣇⠘⠃⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠋⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⠀⠀⠹⠧⣶⣿⢿⣿⣿⠯⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣧⣤⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡟⢿⣿⠟⢀⣴⣿⡄⡀⠀⠀⠙⠛⠛⠉⠁⢀⣶⠀⠀⠈⡉⢩⢿⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⡘⢿⣿⡞⣿⣿⣿⣿⣿
⣿⣿⣷⡄⠀⠀⣼⣿⣿⣿⣿⣿⡇⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠸⠃⢠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⡴⢻⡇⠀⠀⠀⣷⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⣿⣧⣀⣰⣶⣴⣿⣿⡡⢿⢿⡿⢿⡧
⣿⡿⠟⠉⠉⠈⠛⠿⠛⣩⣬⣿⠃⠀⣀⡍⢻⣿⣿⣿⣿⣿⣿⣧⣶⣶⣦⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢐⡀⣿⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⠏⠁⠀⠀⠀⠀⢠
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⣧⠁⣈⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠁⠗⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠋⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢨⢸⣿⡿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣤⣄⣷⣾⣦
⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⠈⡇⠀⢠⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠔⠚⣿⠀⠀⠀⣿⠘⠞⠇⠏⠟⠏⠘⠎⠿⠏⠿⠿⠝⠟⠽⠇⠿⠿⠿⠿⠏⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠛⠀⢰⣶⣆⠀⣿⠀⣠⣤⢱⣰⢠⣤⡄⣤⠄⣤⢤⢲⢠⡄⣴⡄⢤⢄⣤⠤⣤⡆⡤⣤⢨⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿
⣿⣿⣟⠉⢁⠈⠙⣿⣿⣿⣴⠖⠀⠸⠿⢿⠄⣿⠀⢹⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⣿⣿⣟⠋⠀⣿⣿⣿⣿
⣿⣿⡿⠶⠾⠤⠤⠿⣿⣿⡗⢲⠀⣶⣾⣿⡇⣿⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠁⠙⣿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠄⠀⢀⠂⡹⢿⡏⠀⠀⠈⢹⠛⠻⠷⠄⠉⠿⣿
⣿⣿⡆⠀⢰⣦⣤⣿⣧⢹⣷⠈⡆⢹⣿⢿⡇⣿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠘⠉⠉⠉⠉⠉⠀⠀⠉⠻⢿⣿⡿⠃⠀⠀⠀⠐⠶⣾⣿⣿⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠛
⣿⠛⠁⠀⠘⣿⠛⣿⣿⠀⣿⠀⡇⠀⠈⠈⠀⠃⣀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠄⢀⡐⡲⡆⠀⠀⠀⠀⠀⠀
⡟⠀⠀⠀⠀⣿⡄⢾⡇⠀⣿⠃⢀⠀⠀⠀⢀⣼⢿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡇⢿⡇⠀⠀⠀⠀⠀⠀
⣷⣄⡀⠀⢀⣿⣿⡆⠁⢀⣿⣇⣸⣀⣀⣀⣸⣿⣎⠻⣿⡿⠿⢿⣯⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠈⣇⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡻⠳⠛⠁⠀⠘⠿⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣆⣁⣀⣀⣀⣀⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣈⠂⠤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠤⣤⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣅⣈⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣠⣤⣤⣤⣤⣤⣤⣠⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣈⣤⣤⣤⣭⣷⣶⣥⣤⣀⣀⣀⣀⣠⣤⣤⣴⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠉⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢛⠢⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣶⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣚⠛⣿⣿⣿⡿⢟⣩⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⠀⠀⠀⣿⣻⣿⣿⣿⡿⢿⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣋⣤⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠃⢠⣾⣿⡀⠀⠀⠹⣿⣿⣿⣿⣾⣿⣿⣿⡀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣴⣾⡟⣿⣿⣿⣿⣿
⠀⢰⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⠃⣿⠟⠁⣰⣿⣿⣿⠷⠂⠀⢰⣿⠿⣿⣿⠿⠿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⢶⣹⣿⡷⢸⣿⣿⣿⣿
⣀⣾⣿⣿⣿⠉⣿⡟⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⢀⣼⣿⠿⠋⠁⠀⠀⠀⠈⣿⣂⣹⣿⣀⡀⠁⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣻⣿⣧⣤⣴⣯⣾⣿⣿⡇⠚⠛⠛⠛⠛
⠀⠉⠛⠉⠰⣶⣿⡇⠀⢠⢰⡌⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣀⡸⡆⢁⣸⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⣀⣿⢹⡿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣤⣤⣰⣿⣿
⣤⣤⣤⣤⣤⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⠉⠉⢹⣿⠉⠏⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠴⠾⣿⠀⠈⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠻⣿⠟⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣿⣿⣿⡿⠹⠇⠀⣤⣴⠀⠀⣿⠀⢀⣀⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⠁⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢹⣶⣿⣿
⠛⠻⣿⣿⣿⣇⣤⠄⠀⣿⣿⣧⠀⣿⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣽⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⢿⠀⢸⣿⣿⣿
⡀⢀⣿⣧⣿⣿⢩⡀⢀⣤⣭⣿⡄⣿⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢿⣿⠟⠁⠁⠙⢿⠿⢶⣤⡈⠛⠿⣿
⡀⠉⣭⣟⢻⣿⠀⡇⠸⣿⣿⣿⡇⡿⠀⢠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣴⣎⣚⣁⣀⣀⣀⡘⠀⠀⠀⠀⠀⠀⢹
⣿⣿⣿⣿⠀⣿⡄⢸⠀⠻⠟⠻⠃⡏⠀⣾⣅⣤⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⡛⠛⠛⠛⠛⣁⣀⠀⠀⠀⠀⠀⠀
⣿⠀⢻⡿⠀⢸⡇⠸⠀⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣠⣆⣬⣿⠀⠀⠀⠀⠀⠀
⣿⣆⠻⡯⠀⢸⡇⠀⡄⠀⠀⠀⣤⣏⢻⣿⣿⣿⣿⣿⣿⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⣀⢀⣤⣾⣿⣿⣯⠙⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣇⡁⠀⣿⣷⣤⣧⣤⣤⣤⣿⣿⣯⡹⣿⡟⠛⢹⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣼⣷⢳⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠈⠛⠋⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⣠⣴⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⣀⠀⠀⠀⠡⠿⠿⠾⠿⠿⢿⣿⣿⣿⣿⣿⣧⣼⣤⣀⣀⣀⣴⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3190

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/Meme_From_Checked_by_Three_Examiners_to_Gone_Granted_in_3_Secon.shtml
    Gemini version at https://techrights.org/n/2024/09/13/Meme_From_Checked_by_Three_Examiners_to_Gone_Granted_in_3_Secon.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] From Checked by Three Examiners to
Gone (Granted) in 3 Seconds!⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024,
updated Sep 13, 2024


Context: EPO_Staff_Representatives_Explain_the_Latest_Corruption_at_the_EPO_in
a_New_Paper


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Going_once,_going_twice..._Granted!⦈_ EPO defines "success"
    as granting twice as many monopolies with 10% less staff (many of these
   monopolies are software_patents - i.e. patents_which_are_both_illegal_and
                                 undesirable)




⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠚⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣰⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣔⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢙⠻⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡶⠧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⢿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿
⢀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⣶⠠⡆⠀⠂⠀⠀
⠈⢃⠀⣤⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⣾⠰⠀⠀⠃⠀⢰
⠀⠈⡆⠈⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠞⠉⠁⠀⠀⠀⠘⠻⣿⡿⠻⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⡷⡿⠀⠀⠈⠁⠀⣾
⠤⠀⠁⠀⠀⠀⠀⣠⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠈⡟⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣲⣏⢸⣇⢘⡃⣛⣘⣿⡃⠁⢿⣿
⠀⠀⠀⠀⠀⣤⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⣈⠉⠈⠁⠙⣿⣿⠁⢾⣿⣿
⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢤⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠰⠶⠖⠀⠄⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⣼⣿⣿⣿⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣶⣦⣴⣦⣄⠀⠀⠀⠀⢀⣤⣴⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠷⣿⣿⣶⣦⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⠃⠉⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠛⠃⠀⠀⠀⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣼⡿⠃⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⠿⣿⣿⠟⣿⣿⣿⣿⢏⣿⣿⣿
⣺⡿⠃⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣾⣿⠻⢻⢯⣾⣿⣿⣿
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣄⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢍⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⢺⠘⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣿⣿⣾⣿⣿⣾⡇⣿⢿⡆⢰⣿⣿⢺⣿⣿⣾⣿⣇⣿⣻⣿⣷⣿⢿⢿⣿⣿⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣽⣿⣿⣟⣀⣀⣀⠀⠈⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⢿⡇⣿⣿⡇⢸⣿⣿⣽⣿⣿⣿⣷⡖⣿⣹⣿⢾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣏⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠟⠛⢛⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠈⠉⠉⠈⠁⠈⠉⠁⠀⠉⠁⡈⠁⠉⠈⠉⠼⠉⠭⠗⠷⠭⠿⠷⠿⠷⠾⠷⠿⠿⠷⠿⠿⠿⠛⠉⠠⠟⠻⠿⠷⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠻⠟⣿⡛⠟⠁⠀⠀⠀⠀
⠀⠀⠀⢀⣖⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣶⣶⣀⣀⣤⣴⣶⣶⡆⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⣾⣿⣿⡟⢻⣿⣿⣟⠛⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶
⠀⠀⠀⠈⠻⢿⣿⣿⡿⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠆⠀⠀⠀⡀⠀⠛⣿⣿⠄⡠⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠉⠀⠀⠠⠰⡇⠶⠀⠀⢠⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠱⡀⢶⣿⣿⠗⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣤⡄⢰⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⠀⢰⣺⡟⠃⠀⡁⣾⣿⣿⣿⣿⣿
⠘⡄⠀⠀⠀⢷⠀⠓⠀⠚⠀⠀⠀⠀⢀⣠⡴⠾⠋⠉⠙⠛⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢈⣄⢸⣿⣏⣠⡄⣤⣿⣿⣿⣿⣿⣿
⠀⠙⠒⠒⠀⠈⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠇⢀⠀⠀⠀⠀⠀⠀⠙⣿⠏⠙⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡾⡧⠼⠉⣥⢿⠇⣾⣿⣿⣿⣿⣿⣿
⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠈⠛⢰⣿⣿⣿⣿⣿⣿⣿
⠁⠁⡇⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠁⠀⠀⠀⠀⠻⠿⣶⣤⣄⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⢀⣄⣤⡄⠀⠀⠀⠀⠀⠀⠉⠁⠄⠀⢰⣷⣶⣆⣠⠀⠀⠀⢠⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠇⠂⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⣶⣶⣤⠀⠀⠀⣀⣄⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⣿⣿⣿⢿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣽⣆⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣤⣤⣼⣿⣝⢯⣾⣿⣿⣿⣿⣿⣿⣿⢟
⠀⣴⣿⡦⠀⠀⠀⠀⠀⠀⣿⣿⣆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣀⣤⣤⣤⣤⣶⣶⣶⣦⣴⣶⣤⣄⣀⣀⢀⡏⠸⣿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣧⣀⣈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠛⠻⠃⠀⠀⠀⠀⠀⠀⠸⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⠁⠀⠀⠀⠈⠉⠙⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣶⣶⢰⣶⣯⣻⣏⣿⢾⣿⡿⣿⡿⢸⣿⣷⣹⣷⣴⡊⠁⠀⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⣼⣿⣿⣿⣿⣿⣶⣿⡇⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣬⣽⣿⣿⣿⣿⣿⡆⡓⢚⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⣿⣿⣿⣯⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⠟⢁⣿⠟⠀⢠⣤⣭⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3260

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/Mono_as_a_Double_Purpose_Trojan_Horse_Inside_Wine.shtml
    Gemini version at https://techrights.org/n/2024/09/13/Mono_as_a_Double_Purpose_Trojan_Horse_Inside_Wine.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Mono as a Double-Purpose Trojan Horse
Inside Wine⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


And now they can oust founders and top contributor with a CoC:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Wine_team_now_hosting_Mono,_looking_to_adopt_the_Contributor
                          Covenant_Code_of_Conduct⦈_


How is that any better than before Microsoft offloaded its patent-encumbered
Trojan horse for others to maintain like a white elephant? It seems like an
extra burden, not a gift. It's also more risk.


"I saw that internally inside Microsoft many times when I was told to stay away
from supporting Mono in public. They reserve the right to sue"


                                    -Robert Scoble, former Microsoft evangelist




⡟⠟⠟⡿⠿⢿⡿⠿⡿⠿⠿⢿⠿⡿⠿⡿⢿⠻⡿⠿⠿⢿⠿⡿⢿⢻⢿⠿⡿⠿⢿⣿⠻⢿⠿⡿⣿⠿⠿⢿⠿⠿⡿⢿⠟⠿⠿⠿⢿⢻⠿⠿⣿⢛⡿⠿⠿⠿⠟⠻⡿⠿⠿⢿⢿⢟⡻⠿⠿⠿⡿⠿⢿⠿⢻⣿⣿⣿
⣿⠴⣦⣿⢴⣽⣯⣮⢮⡤⢾⣼⣼⣧⢴⣦⣿⣼⣯⣮⣴⣽⣼⣅⣽⣴⣾⣮⣿⣴⣽⣽⣴⣵⣤⣷⣿⣿⣀⣽⣴⣵⣧⣾⣥⣮⣦⣼⣽⣾⣧⣮⣿⣮⣯⣦⣿⣬⣧⣬⣧⣼⣵⣽⣿⣯⣵⣵⣶⣮⣿⣤⣼⣧⣮⣿⣿⣿
⣧⣛⣔⣕⣨⣸⣇⣲⣾⣜⣃⣸⣆⣐⣜⣩⣲⣺⣿⡟⠛⠛⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣙⣿⣛⣛⣏⣛⣛⣛⣿⣹⣙⢛⣟⣛⣛⣻⣉⣉⣹⣃⣄⡀⠀⣀⠀⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠶⠶⠶⠶⣶⠶⡶⢶⠶⠶⠶⠶⠶⠶⡶⠶⡶⡶⠶⢤⣤⠀⡀⠀⠀⠠⠶⠶⠶⡶⡶⠶⡶⢶⠶⠶⡶⠶⠶⢶⠶⠶⠶⢶⠶⡶⡶⢶⢶⠶⠶⠶⢶⠶⣶⠶⠶⡶⠶⡶⢶⠶⠶⠶⡶⠶⢶
⡷⠶⠶⠾⠶⡶⢷⠷⢶⠶⢿⠶⡶⠶⠮⠾⡾⠶⠾⠶⠶⢶⠶⠶⡶⠧⢾⢶⠷⠾⠾⠷⠶⠾⠶⠿⡶⢶⢶⡿⠶⡶⠾⠷⠾⠶⣶⠷⠿⣾⢾⠶⠶⢶⢾⠶⠿⡶⠾⣶⠶⠾⠶⠶⢶⣾⣾⣶⣶⣶⣷⣶⣶⣿⣶⣷⣶⣾
⣿⣿⣾⣶⣶⣶⣶⣶⣶⣾⣾⣶⣷⣶⣶⣶⣷⣾⣶⣧⣴⣾⣶⣾⣷⣾⣶⣾⣶⣾⣾⣷⣶⣶⣶⣷⣿⣷⣦⣷⣶⣷⣶⣿⣶⣦⣷⣶⣶⣷⣾⣷⣶⣾⣶⣶⣶⣷⣮⣍⠀⠀⠀⠀⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⢻⠛⠟⠛⠙⡟⢻⠋⠛⢛⠛⠛⡟⠛⠛⠛⠛⡛⡛⠛⣟⠛⠛⢹⠛⢻⢛⠛⡟⠛⠛⢻⠟⢛⠛⡟⠛⠛⢻⣛⠛⠛⠛⢻⠙⠛⡋⡛⠛⠻⡋⠛⠛⢛⠋⡛⡟⢻⠙⠓⠀⠀⠀⠀⠀⠀⠈⠉⠙⡟⠛⡟⠛⢛⢻⣿⣿
⡟⠛⠛⠛⢛⡛⠻⠛⠛⢛⣏⠒⣛⠙⢻⡟⡛⠻⠛⠻⡟⢙⢻⣛⣻⢻⡛⠛⢻⠛⠛⡛⠛⢹⢛⠛⣟⠛⢛⢛⠟⢛⡻⠟⠺⠋⠻⠋⠻⠛⠛⢛⠋⢻⠛⠛⠟⠑⣟⡛⠋⠟⢻⠛⡛⢙⠛⠓⢒⠒⠛⠛⣟⠛⣟⠛⠟⡛
⡟⠛⠛⢻⠛⠛⣻⣛⣻⢻⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣉⣏⣍⣩⣉⣏⣭⣩⣉⣉⣏⣹⣍⣉⣹⣍⣉⣉⣉⣿⣈⣍⣉⣩⣹⣩⣭⣨⣹⣭⣽⣍⣩⣉⣉⣭⣏⣩⣏⣍⣉⣹⣋⣉⣋⣉⣻⣁⣋⣹⣩⣉⣫⣉⣹⣋⣉⣩⣉⣈⣉⣏⣍⣹⣉⣩⣋⣭⣯⣉⣍⣍⣉⣩⣹⣌
⣏⣈⣉⣹⣉⣉⣋⣉⣏⣁⣉⣁⣿⣹⣍⣉⣍⣹⣍⣉⣉⣙⣉⡩⣭⣈⣉⣉⣭⣏⣩⣉⣩⣏⣉⣸⣍⣉⣉⣡⣃⣍⣏⣏⣿⣈⣉⣩⣉⢉⣭⣉⣍⣏⣉⣽⣁⣯⣨⣹⣉⣉⣉⣉⣉⣋⣉⣍⣇⣉⡍⣉⣉⣉⣏⣈⣹⣿
⣏⣉⣹⣫⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣥⣤⣮⣧⣦⣄⣦⢤⣷⣤⣼⣤⣧⣤⣧⣼⣼⣤⣤⣴⣾⡠⣦⣤⣤⣶⣾⣤⣤⣤⣾⣤⡧⣤⢬⣧⣤⣬⣤⣼⣤⣤⣤⣧⣤⣤⣤⣤⣄⠀⠀⠀⠘⠀⠤⢤⠀⠤⡽⣤⣥⣧⣦⣄⣦⣤⣇⣤⣷⣠⣦⣼⣤⣼⣦⣿⣿
⣧⣴⣥⣤⣤⣼⣦⣤⣤⣷⣤⣾⣤⣤⣤⣤⣼⣥⣤⣼⣥⣴⣴⣧⣤⣤⣴⣧⣤⣤⣽⣴⣤⣤⣤⣤⣧⣧⣤⣴⣄⣧⣦⣼⣤⣤⣤⣤⣬⣴⣼⣥⣤⣤⣤⣀⡀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⡿⠿⠿⢿⠿⠿⠿⢿⠿⠿⢿⠟⠿⡿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠻⡿⠿⠿⠿⠿⡿⠿⠿⡟⠿⠿⢿⠿⢿⢿⠿⠿⠤⠤⢶⡲⠶⠾⡿⠟⢟⠿⠿⠻⠿⢿⠿⡿⠿⠿⠿⡿⢿⢿
⡷⠶⠶⠾⠿⠶⠶⠷⠾⢶⣶⠿⠶⠶⠷⡶⡶⠷⠶⠾⢷⡶⠶⠶⠶⠶⡶⠶⠷⣿⠶⠷⠶⠶⠾⠿⠶⠶⠶⠳⠶⢶⠾⠶⠷⠳⡶⠿⢶⢿⠾⠷⠾⠾⠶⡷⠶⠶⠿⢶⠶⠶⢷⠿⠶⠶⠷⠶⢶⠾⠶⠿⠶⠶⠲⠷⠲⢿
⡷⠶⠶⠶⡶⠶⡶⠾⢶⠿⠿⠷⠦⠷⠶⠷⠶⢿⣶⠷⢷⣷⠶⠶⠶⠦⠷⠷⢶⡷⢶⠾⠴⠶⠶⡶⡶⠷⠶⠶⢾⠶⠶⡷⠾⡶⢾⡶⠾⠶⠾⠷⠶⠶⢷⡾⠶⠗⡶⡿⠶⡶⢾⠶⡶⡆⠾⠶⠾⢲⠶⢶⣶⠶⢮⣷⣶⣿
⡷⠶⠶⠶⠷⠶⠶⢷⠾⠶⠾⠷⠿⠶⠷⡶⠶⠾⠿⠷⢾⠶⡶⠶⠷⠶⠶⠶⠿⡖⠶⠷⢷⠲⠒⠷⠧⠾⠾⠶⡾⠶⢿⢷⠶⠷⡾⠷⠶⢶⠺⠶⡶⠷⢶⠳⠶⠶⣶⠷⠶⠷⠾⠶⠷⠷⡶⠶⠶⠾⠶⠿⠷⠶⢾⠿⠿⢻
⡷⠶⠾⠶⠶⣶⣶⣼⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣶⣾⣷⣶⣶⣴⣶⣷⣶⣶⣶⣯⣿⣶⣿⣶⣷⣷⣶⣶⣷⣷⣾⣷⣶⣶⣿⣷⣶⣾⣶⣾⣶⣾⣾⣶⣾⣶⣿⣾⣶⣶⣶⣶⣼⣶⣶⣷⣶⣾⣾⣶⣶⣶⣾⣶⣷⣾
⣷⣶⣷⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3320

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/Number_of_Gemini_Capsules_Rising_Closer_to_4_100_Certificate_Au.shtml
    Gemini version at https://techrights.org/n/2024/09/13/Number_of_Gemini_Capsules_Rising_Closer_to_4_100_Certificate_Au.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Number of Gemini Capsules Rising Closer to
4,100, Certificate Authority "Let's Encrypt" Down to
1.1%⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


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


"So, one thing you've gotta do for a world like this that everyone can
participate in is to make sure your web sites are accessible without running
non-Free Javascript." -Richard_M._Stallman (weeks_ago)


LAST month we celebrated_Lupa's_capsules_count_reaching_and_exceeding_4,000 for
the first time. Less than a month has passed and now it's past 4,050 (i.e.
rounded up to 4.1k):


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇There_are_4052_capsules._We_successfully_connected_recently
                              to_2872_of_them.⦈_


A lot has also changed since then when it comes to the Linux_Foundation's
Certificate Authority (CA), which was found on 2% of capsules. Now it's down to
1.1%. It was 1.2% just 2_days_ago.


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇2575_(89.7_%)_capsules_are_self-signed,_33_(1.1_%)_use_the
Certificate_Authority_Let's_Encrypt,_264_(9.2_%)_are_signed_by_another_CA_(may
                           be_not_a_trusted_one).⦈_


Some time soon the Certificate Authority "Let's Encrypt" will probably fall
below 1%. It was about 12% only a couple of years ago.


The way today's Web is "done" may seem "modern", but that means nothing for the
user. Over time the Web gravitates towards corporate interests at the users'
expense. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡇⡸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡛⠻⠿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⡏⠹⢿⠿⣿⠿⢹⣿⢿⢿⢿⠿⢿⠿⠯⠹⢿⠿⠿⢿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣰⣀⣿⣇⣃⣌⣂⣇⣋⣸⣿⣀⣄⣦⣘⣼⣸⣇⣄⣏⣈⣈⣨⣀⣸⣸⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⡿⢻⠿⣿⠿⠿⢿⡿⢿⡿⢿⣿⠛⢿⡟⡿⢿⣿⠟⣿⠿⣿⠿⣿⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣇⣄⣌⣀⣘⣘⣸⣰⣀⣰⣈⣸⣟⣸⣸⣀⣣⣱⣿⣀⣇⣆⣄⣞⣘⣸⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⡶⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠿⠿⠆⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⠿⠿⢿⣿⣛⣛⡛⣉⣩⣉⣩⡥⠤⠤⠴⢶⣶⣞⣿⣛⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⣿⣿⣿⣿⣟⣻⣭⡀⠀⠰⢶⣶⣶⣛⣿⣻⣭⣭⣭⠭⠥⠶⠶⢶⣖⣞⣿⣿⣿⣯⣭⡿⢿⠟
⣿⣿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢘⣟⣚⣛⣿⣭⣿⣿⣿⠶⠶⠅⠀⢘⣛⣋⣽⣿⡭⠿⢿⣶⣶⣒⣚⣋⣉⣭⣽⣿⣿⣿⣾⠿⣿⣟⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⡇⢸⣿⠭⠿⠷⣾⣾⣞⣿⣯⣭⠅⠀⢸⣿⡷⠶⠿⠟⠛⢛⣻⣛⣻⣭⣭⣭⣿⣿⣿⣿⣿⠿⠿⠿⢟⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠉⠍⠉⠁⠤⠒⠀⠀⢀⠀⠀⠀⠀⢠⡽⣿⣶⡆⠰⠿⠟⣛⣛⣛⣻⣿⣭⣉⣽⡁⠀⢰⣶⣶⣾⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⠷⠟⠛⢛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠐⠒⠒⠛⡛⢚⣛⣋⣁⣈⣉⣭⣁⣤⣶⣶⣼⣿⡇⢸⣿⣿⣿⣟⣛⣻⣟⣛⣭⡇⠀⡀⠈⠑⠒⢾⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣯⣿⣿⣿⣿⣷⡿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠒⠂⠒⠒⠐⠒⠛⢛⣛⣛⣋⣭⣭⣭⣭⣿⣶⣶⣶⣿⣥⣬⣍⣛⠛⠻⠿⠿⢿⣿⣟⣶⣶⣤⣴⣶⣤⣤⣄⣀⣀⣉⡉⠛⠛⠛⠛⠛⠛⠋⠉⠉⣁⣀⣤⣤⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠴⠿⠿⣿⣿⠿⠷⢄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⡏⣩⡹⠛⢿⠛⠻⠛⠻⢻⢻⢹⠟⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡆⢰⠀⢰⢀⠰⠀⢰⡄⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣧⣉⣥⣠⣼⢈⣬⣄⣤⣨⣸⣈⣤⣰⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⣬⣉⣥⣾⣦⣍⣉⣴⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣀⠹⣿⣦⡍⡉⡉⣥⣼⡿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢵⣾⡧⠶⠒⠒⠒⠚⠛⠉⠉⢉⣉⣁⡈⠙⠻⠶⠾⠛⠉⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣷⢰⡉⡋⣫⡉⣿⠉⢩⠉⣟⣘⠆⡧⡲⢰⡤⠄⠁⢄⢀⠎⡘⠉⠉⢿⡜⡜⡈⢹⠉⡰⡠⠤⠄⠀⠀⠉⡼⢁⠸⢋⡏⠍⢝⡍⢩⡉⠉⠅⠉⡋⢸⣯⠉⡩⠉⣫⢁⠽⣙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⡟⠿⢿⣟⠛⢛⡛⣛⣿⠿⠟⡟⠿⠿⢿⠿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣷⣥⣼⣧⣥⣼⣼⡥⣩⣬⣆⣁⠙⠤⠤⠷⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡙⠃⣉⣉⣉⠉⠛⠓⠒⠒⠂⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣇⠛⠘⡉⣏⢭⢽⡟⣭⢩⠋⡍⡝⢩⢩⠛⡍⡏⣽⡟⣭⠉⠉⣍⡏⢽⣿⡇⡏⢙⠩⣿⢨⢩⠟⣿⢩⢹⡏⡏⡍⣽⢨⠛⠉⣏⣿⢫⢩⣼⡟⠋⢻⢩⠋⡅⢫⢸⣩⠋⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣾⣶⣷⣾⣶⣿⣶⣷⣷⣷⣷⣾⣾⣾⣶⣷⣿⣿⣶⣶⣦⣶⣷⣾⣶⣷⣶⣾⣶⣿⣶⣾⣼⣿⣾⣾⣶⣷⣷⣿⣶⣿⣶⣿⣿⣷⣿⣿⣿⣾⣾⣶⣷⣷⣷⣾⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⡿⡿⡇⡂⡇⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣷⣶⣷⣷⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣾⡿⢋⣉⠻⣿⡟⢋⡙⢻⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⡿⠿⢿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⡅⢿⠏⡈⡇⣤⢸⢠⢠⠈⢤⠅⠈⡄⡌⡀⡏⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⡇⠠⠭⠭⠭⠭⠭⠥⠀⣿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
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⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠉⠉⠛⠋⠉⠀⢀⣤⠢⢿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
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⠀⠀⠀⠀⣿⣿⣿⣿⡗⠸⠬⡻⣴⠬⣹⡇⠠⠠⢆⣿⢣⣿⡤⡡⡳⣿⠩⡋⠉⠍⠍⡏⢏⠈⠉⠉⣿⠉⡏⡉⢹⡏⢉⠉⠨⢘⣻⢉⢈⠍⢩⢉⠉⠩⠸⣿⠦⡷⢄⣟⠶⠸⢿⠾⣿⡄⡨⡃⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
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⠀⠀⠀⠀⣿⣿⣿⣿⡛⠛⢻⠻⡻⠛⠻⠟⢹⡟⠻⠛⡟⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣧⣼⣮⣬⣴⣤⣭⣮⣼⣧⣵⣼⣧⣍⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
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⠀⠀⠀⠀⣿⣿⣿⣿⡟⣼⣀⣸⡐⡃⡀⣀⡁⣂⣻⣈⢀⡀⣺⢸⣋⣟⣏⣟⢁⣿⣄⡀⣇⣿⣰⣇⣠⣡⡀⣹⣂⠁⣎⣏⢀⢊⡇⢪⠀⣆⢈⣀⣸⡐⡁⣀⣶⢂⣶⢈⣒⢀⡖⡀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 3442

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Once Again, Mass Layoffs at Microsoft (Just
Like Every Month This Year)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


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


Reporting and articles trickling in (in recent hours):


    * ⚓ Microsoft_Gaming_to_Lay_Off_3%_of_Global_Workforce,_About_650
      Employees,_in_Additional_Post-Activision_Blizzard_Cuts⠀⇛


           The cuts will primarily impact staffers in “corporate and
           supporting functions,” per Microsoft Gaming CEO Phil Spencer.


           “For the past year, our goal has been to minimize disruption
           while welcoming new teams and enabling them to do their best
           work,” Spencer said in an email to staff Thursday, which was
           obtained by Variety. “As part of aligning our post-acquisition
           team structure and managing our business, we have made the
           decision to eliminate approximately 650 roles across Microsoft
           Gaming—mostly corporate and supporting functions—to organize
           our business for long term success.”


           U.S. employees will receive exit packages that include
           severance, extended healthcare and outplacement services, while
           international employees will receive different packages
           dependent on their location, per Spencer.


    * ⚓ Microsoft_Lays_Off_Another_650_Staff_From_Its_Video_Game_Workforce,
      Xbox_Boss_Phil_Spencer_Sends_Memo_to_Staff⠀⇛


           Microsoft is laying off a further 650 staff from its gaming
           business, according to a memo sent by Xbox chief Phil Spencer
           to staff today, September 12, and obtained by IGN.


           In the memo, Spencer said the roles affect mostly corporate and
           support functions, and were made “to organize our business for
           long term success.” He clarified that no games, devices or
           experiences are being canceled and no studios are being closed
           as part of these cuts.


           These latest layoffs mean Microsoft has let go of 2,550 staff
           from its gaming business since acquiring Activision Blizzard
           for $69 billion in 2023. In his memo, below, Spencer makes it
           clear that the cuts are related to the acquisition.


    * ⚓ Microsoft_Announces_Additional_Layoffs_to_Its_Gaming_Division⠀⇛


           Microsoft recently announced another round of layoffs impacting
           its Xbox gaming division, resulting in about 650 people being
           let go. Layoffs have become more common in the video game
           industry over the past few years, with companies like
           Microsoft, Sega, and EA cutting down their workforces
           throughout 2024. Not even smaller developers are immune, as
           Life is Strange: True Colors studio Deck Nine and Lords of the
           Fallen dev CI Games announced their own layoffs at the
           beginning of the year.


    * ⚓ Microsoft_to_cut_650_jobs_at_its_Xbox_gaming_unit_—_read_the_full_memo
      from_top_exec_Phil_Spencer⠀⇛


           Microsoft on Thursday said it is cutting 650 roles at its Xbox
           gaming division, in the latest major round of layoffs to hit
           the video game industry.


    * ⚓ Microsoft_Gaming_makes_another_650_job_cuts_in_third_round_of_Xbox
      layoffs_this_year⠀⇛


           Microsoft continued the cost-cutting in its Xbox and video
           games division Thursday morning following its $68.7 billion
           Activision-Blizzard acquisition, laying off another 650
           employees.


           Phil Spencer, the Microsoft Gaming CEO, told employees that the
           latest cutbacks do not signal the cancelation of any additional
           games, devices, or experiences. He said no further Microsoft
           games studios are being closed.


    * ⚓ Microsoft_lays_off_another_650_in_gaming_division,_bringing_the_total
      to_2,550⠀⇛


           Microsoft is making even more cuts to the staff roster of its
           Xbox gaming division.


           The company on Thursday announced plans to lay off 650
           employees, which will bring the total number of job losses
           since its October 2023 acquisition of Activision Blizzard to
           2,550.


           The latest round of cuts will largely impact corporate and
           support roles. No studios are being closed and no games or game
           systems will be cancelled as a result of the belt-tightening.
           (Microsoft closed Tango Gameworks, makers of Hi-Fi Rush, and
           Redfall developer Arkane Austin in previous layoff rounds,
           which did impact its upcoming titles.)


    * ⚓ Microsoft_will_cut_another_650_gaming_jobs,_mostly_at_Activision
      Blizzard⠀⇛


           Microsoft’s gaming chief Phil Spencer told employees in an
           email on September 12, 2024, that the company will lay off
           around 650 people from its video games division, as has been
           reported by Stephen Totilo, who gained access to the full memo
           announcing the bad news.


           It’s the second round of cuts following Microsoft’s acquisition
           of Activision Blizzard after layoffs conducted in January 2024
           already eliminated around 1,900 jobs. Whereas that wave of
           layoffs included top personnel such as former Blizzard
           president Mike Ybarra, no executives will leave the company
           this time around. According to Spencer’s memo, the brunt of
           these cuts will be borne by corporate and support roles.




⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⡏⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠶⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠒⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⣿⣿⣿⣿⠿⠡⠁⠀⠁⠀⢴⡄⠀⠀⠀⠀⠀⣟⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⠒⠠⠀⠀⢘⠅⠀⠀⠀⠀⠀⠟⠷⠶⠻⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠰⢖⣖⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠈⠉⠁⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠖⠂⢘⣧⡀⠀⠀⡀⠀⠀⠀⠀⡆⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢈⣴⣾⣾⣿⣿⡴⢶⣤⢄⣟⣋⣠⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠐⢯⢁⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⣿⣿⣿⣿⣿⡿⠿⢆⣿⣿⣿⡿⠛⠁⣫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣸⡟⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠺⣏⣛⣷⣶⠶⠿⠿⠿⠟⢩⣿⣧⣠⠞⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠫⠥⢱⣭⣭⣕⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡸⣷⡄⣤⣀⣺⣣⣼⣿⣟⣥⡶⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠲⠾⠦⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣷⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣤⣴⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠌⡉⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⣿⡿⠃⢰⣿⣿⣿⣿⣿⣿⠿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⠻⠿⠿⠿⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡄⣴⣿⣿⣿⣿⠛⠃⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⡻⢶⣬⣝⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⢛⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣓⡀⢪⣝⡛⣿⢶⣶⣤⣤⣤⠔⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠀⠀⠠⣟⣐⠟⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣄⣙⡿⠟⢻⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀⠀⠀⠀⠶⣾⡿⣿⠛⡻⠟⢱⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣶⣶⣴⠶⠚⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⣿⣿⣿⡷⠀⠀⠀⢼⣻⠿⣷⢟⣁⠴⠿⠛⢹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣀⡀⢀⣀⣠⣿⣿⣿⠏⠀⠀⠀⣀⣘⣿⣿⢟⠛⠯⠂⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⣾⣿⣿⣿⡏⠘⠀⠀⠀⠀⠀⠀⠀⠄⣸⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢚⣋⢹⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣾⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⢁⣰⣿⣿⣷⣶⡆⠀⠀⠀⣠⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⣷⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠉⠉⠉⣠⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠋⠟⢻⣿⣿⠃⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣤⣄⣠⣶⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡀⠀⠀⠀
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⢿⠅⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3631

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


posted by Roy Schestowitz on Sep 13, 2024


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Cinnamon_6.4_to_Debut_with_Revamped_Default_Theme⠀⇛


           LMDE 5 reaches End-of-Life, Cinnamon 6.4 desktop environment to
           feature an improved default theme, addressing the aesthetic gap


   2. ⚓ LibreOffice_24.8.1_Office_Suite_Is_Now_Available_for_Download_with_89
      Bug_Fixes⠀⇛


           The Document Foundation announced today the general
           availability of LibreOffice 24.8.1 as the first maintenance
           update to the latest LibreOffice 24.8 office suite series
           fixing more than 85 bugs.


   3. ⚓ KDE_Gear_24.08.1_Brings_More_Improvements_to_Your_Favorite_KDE_Apps⠀⇛


           The KDE Project released today KDE Gear 24.08.1 as the first
           point release to the latest KDE Gear 24.08 software suite with
           more bug fixes and improvements for your favorite KDE
           applications.


      ⚓  New⠀⇛


   4. ⚓ Ubuntu_22.04.5_LTS_(Jammy_Jellyfish)_Is_Now_Available_Powered_by_Linux
      Kernel_6.8⠀⇛


           Canonical released today Ubuntu 22.04.5 LTS as the fifth and
           last planned point release to the Ubuntu 22.04 LTS (Jammy
           Jellyfish) long-term supported operating system series.


   5. ⚓ Ardour_8.7_DAW_Released_with_Track_Dragging,_Combined_Rulers,_MIDI
      Scene_Markers⠀⇛


           Ardour 8.7 open-source, free, and cross-platform DAW (Digital
           Audio Workstation) has been released today as a hefty update
           that introduces new features and many improvements.


   6. ⚓ Stable_kernels:_Linux_6.10.10,_Linux_6.6.51,_Linux_6.1.110,_Linux
      5.15.167,_Linux_5.10.226,_Linux_5.4.284,_and_Linux_4.19.322⠀⇛


           I'm announcing the release of the 6.10.10 kernel


   7. ⚓ Slimbook_Titan_report_4_-_The_good_mojo_is_gone⠀⇛


           In my previous report, I remarked on how I'm finally happy with
           the Slimbook Titan


   8. ⚓ KDE_Plasma_6.2_Is_Now_Available_for_Public_Beta_Testing,_Here’s_What’s
      New⠀⇛


           The KDE Project released today the beta version of the upcoming
           KDE Plasma 6.2 desktop environment series, a major update that
           promises numerous new features and improvements.


   9. ⚓ today's_leftovers⠀⇛


           IBM, SUSE, and more


  10. ⚓ Programming_and_Hackable_Hardware⠀⇛


           some gadgets and coding


  11. ⚓ Security_Leftovers_and_Windows_TCO⠀⇛


           two examples of Windows TCO


  12. ⚓ today's_howtos⠀⇛


           many howtos for the afternoon


  13. ⚓ Why_I_Use_NixOS_(And_Why_You_Should_Too)⠀⇛


           NixOS is a Linux distribution that focuses on reproducibility,
           declarative configuration, and robust package management


  14. ⚓ New_Steam_Client_Update_Improves_Compatibility_with_More_Linux
      Desktops⠀⇛


           Valve released a new stable Steam Client update that brings
           numerous improvements and some new functionality to further
           enhance your gaming experience on Steam and bring compatibility
           for more Linux desktops.


  15. ⚓ Ubuntu_Prompting_Client_is_Here_to_Make_Snap_Apps_Safer⠀⇛


           Prompting Client is the latest security effort for snap
           software, and acts as a companion to the new desktop Security
           Center app


  16. ⚓ Free_and_Open_Source_Software⠀⇛


           OutGuess is a universal steganographic tool that allows the
           insertion of hidden information into the redundant bits of data
           sources


  17. ⚓ eLxr_–_community–hardened_Debian_distro⠀⇛


           eLxr is a community–hardened Debian-based distribution
           optimized for performance, and security. It’s tailored for
           edge-to-cloud use cases


  18. ⚓ Deepin_23_GNU/Linux_Released_with_Download_Links,_Mirrors_and
      Torrents⠀⇛


           Congratulations to Deepin Developers for the official release
           of Deepin OS 23


  19. ⚓ Announcing_the_AlmaLinux_Certification_SIG⠀⇛


           After months of work, we are happy to announce the AlmaLinux
           Certification Special Interest Group (SIG), along with our
           Hardware Certification Program!


  20. ⚓ 10_Linux_apps_I_can't_do_without_-_and_why⠀⇛


           If you've ever wondered which apps a long-time Linux user
           depends on, you might be surprised at what's included


  21. ⚓ Solus_is_a_no-frills_desktop_distribution_that_makes_using_Linux_a_no-
      brainer⠀⇛


           If you're looking for a Linux desktop distribution that puts
           function over form and gets the job done with ease


  22. ⚓ Plasma_Mobile_for_highly_configurable_Linux_phones⠀⇛


           Plasma Mobile is an open-source user interface for mobile
           devices, developed by the KDE community


  23. ⚓ Advances_in_font_technology_and_GTK_text_rendering_[LWN.net]⠀⇛


           Behdad Esfahbod and Matthias Clasen presented a two-part talk
           on a topic that's deeply important to desktop environments:
           font


  24. ⚓ Games:_Fanatical_Bundle_Fest,_Devil's_Hideout,_and_Stellaris:_Cosmic
      Storms⠀⇛


           latest 8 from GamingOnLinux


  25. ⚓ Arduino_Plug_and_Make_Kit_and_Strandbeest-style_coffee_table⠀⇛


           some Arduino projects


  26. ⚓ Security_and_Windows_TCO⠀⇛


           10 security related stories


  27. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


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


                         Span from 2024-09-06 to 2024-09-12
      963 /n/2024/09/02/
          Rhino_Linux_2024_2_horns_in_on_Microsoft_Windows_11.shtml


      886 /n/2024/09/07/
          KDE_Slimbook_Plasma_VI_Linux_Ultrabook_Launches_with_AMD_Ryzen_.shtml


      872 /n/2024/09/05/Ubuntu_24_10_Default_Wallpaper_Mascot_Revealed.shtml


      748 /n/2024/09/07/Fedora_Red_Hat_IBM_Leftovers.shtml


      687 /n/2024/09/09/Linux_6_11_rc7.shtml


      605 /n/2024/09/07/GNU_Linux_Leftoverss.shtml


      594 /n/2024/09/07/Ubuntu_Pig.shtml


      587 /n/2024/09/10/Geminispace.shtml


      578 /n/2024/09/07/Wine_9_17_Debuts_with_Enhanced_High_DPI_Support.shtml


      577 /n/2024/09/11/
          Juno_Tab_3_Tablet_Announced_Available_with_Ubuntu_24_04_LTS.shtml


      574 /n/2024/09/07/
          NGINX_Has_Chosen_Proprietary_Entrapment_Microsoft_GitHub.shtml


      558 /n/2024/09/08/This_week_in_Plasma_Stabilization_for_6_2.shtml


      557 /n/2024/09/06/today_s_howtos.shtml


      557 /n/2024/09/05/Barry_Kauler_on_His_Distro_Development_Work.shtml


      551 /n/2024/09/07/today_s_howtos.shtml


      547 /n/2024/09/07/This_Week_in_GNOME_164_Updated_Translations.shtml


      534 /n/2024/09/08/today_s_howtos.shtml


      533 /n/2024/09/07/Programming_Leftovers.shtml


      531 /n/2024/09/09/Programming_Leftovers.shtml


      531 /n/2024/09/09/
          NanoPi_R3S_is_a_30_Router_Board_with_Dual_GbE_and_FriendlyWrt_O.shtml


      531 /n/2024/09/07/Getting_Debianized.shtml


      530 /n/2024/09/09/today_s_howtos.shtml




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3967

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/RedMonk_September_the_Month_of_the_Mouth_of_Redmond_Still.shtml
    Gemini version at https://techrights.org/n/2024/09/13/RedMonk_September_the_Month_of_the_Mouth_of_Redmond_Still.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ RedMonk: September the Month of the Mouth
of Redmond (Still)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


Published yesterday: (the usual storyline, i.e. what's not controlled by
Microsoft's proprietary GitHub simply does_not_exist)


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇The_RedMonk_Programming_Language_Rankings:_June_2024:_Based
         on_projects_controlled_by_our_longtime_paymaster,_Microsoft⦈_


Old: Microsoft:_Bribing_[RedMonk]_With_Both_Hands


They're pay-to-say basically:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇RedMonk:_As_a_developer-focused_analyst_firm,_we_typically
   interact_with_folks_in_the_tech_industry_through_Briefings,_Consults,_and
                       Projects_and_Media_engagements.⦈_


Further down the page:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇We_don’t_do_PR,_but_we_complement_and_support_PR_perfectly.⦈


“Analysts sell out - that’s their business model… But they are very concerned
that they never look like they are selling out, so that makes them very prickly
to work with.”


                                            -Microsoft,_internal_document [PDF]




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣰⣄⡀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠋⠭⠽⠉⠭⠙⠏⠩⠍⠫⠁⠭⠏⠩⠝⠩⠍⠹⠇⠿⠸⠏⠭⠉⠟⠩⠍⠸⠿⠿⠈⠭⠙⠍⠿⠋⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⢀⡀⣀⢀⣀⣀⢀⣀⢀⣀⢀⡀⣀⡀⠀⣀⢀⣀⣀⠀⣀⣀⠀⢀⣀⡀⢀⣀⡀⣀⣀⠀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⣉⣿⣃⣉⣹⣻⣉⣉⣉⣉⣙⣈⣉⣙⣿⣇⣉⣩⣙⣉⣍⣉⣩⢻⣉⣉⣏⣹⣏⣉⣉⣹⣈⣉⣊⣋⡙⣿⣃⣁⣉⣿⣉⣝⣉⣈⣿⣈⣹⣉⣏⣉⣉⣙⣃⣉⣟⣛⣁⣘⣫⣉⣏⣙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠙⠛⣿⠛⡻⠟⠙⣿⢿⠻⠿⠏⠛⠟⠿⠟⣻⠻⠛⠿⠙⠟⠛⠿⠛⠻⢹⠙⡛⡯⠍⠻⠛⠛⣻⠩⠻⠻⠛⢻⠟⢛⡿⠛⠛⢿⡏⠛⠻⠟⢻⠉⠹⢻⠙⠛⢿⢉⠩⠟⠉⠿⣿⠹⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣟⢻⣻⠻⡻⣿⠛⠛⣿⡗⠿⡟⣿⠿⢷⠿⠾⠿⢿⢻⡿⢿⡿⠿⠿⡿⣿⠾⣿⠿⢻⣿⢿⣿⠻⠿⡟⢿⣿⠿⣾⣿⠿⢿⣿⣿⡿⠿⠿⠿⠿⣿⣾⢻⡿⠿⡟⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠶⡶⡷⡾⡾⡾⠾⡿⠾⠷⠶⠶⠶⠷⢶⡶⠾⡶⣶⢶⢶⠶⠶⠶⡷⠶⠷⣶⠶⠶⠿⠶⠾⠷⣷⡶⡶⠶⠶⢾⢾⠶⢷⡶⡶⠾⡷⠶⠶⡶⠶⣾⠾⠾⠾⠶⣶⠶⠷⠶⡶⠶⠶⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣾⣾⣾⢶⣷⣶⣷⣷⣾⠶⣶⣿⣷⣾⣷⣾⡶⣾⣶⣾⣷⡶⡾⣿⣶⣶⡿⣾⣾⣶⣷⡶⣷⣿⣷⣿⣦⣴⣶⢮⢮⣶⣷⣷⢿⣷⣷⣶⣵⣵⣿⣶⣿⣶⣾⣿⣶⣾⣷⣷⣶⠾⣿⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣼⣶⣤⣴⣤⣧⣧⣴⣤⣴⣦⣴⣦⣼⣿⣴⣦⣤⣯⣮⣦⣦⣤⣤⣶⣧⣾⣤⣮⣴⣤⣼⣶⣤⣴⣧⣼⣴⣴⣤⣤⣶⣮⣔⣧⣶⣤⣤⣿⣴⣦⣦⣶⣤⣠⣴⣼⣧⣴⣿⣦⡀⠀⠀⠐⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣨⣩⣉⣨⣿⣩⣉⣁⣩⣏⢎⣃⣏⣹⣉⣁⣙⡙⠉⠩⠣⠿⠁⠌⠉⣍⣉⣉⣁⣉⣩⣻⢈⣍⣉⣉⣅⣹⣹⣉⣍⣍⣥⣈⣩⣉⢎⣏⣭⣉⣩⣩⣈⣉⣙⣯⣩⣈⣩⣯⣯⣏⣄⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠟⠋⣿⠟⢻⣻⠋⢩⢛⢻⠛⡿⠻⠟⠋⠝⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⠛⠛⠛⡛⠛⠛⠛⠋⢿⠿⠙⢻⡻⡟⠋⣽⠛⠛⢛⠛⠛⢻⢿⠻⠛⠛⢛⠛⣿⡏⠛⢻⣿⣿⣿⣦⡀⠀⢀⣀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⡿⢻⠿⠿⢿⡟⠿⣿⡿⡿⠿⡿⠟⡿⢻⡿⡟⡿⠿⠿⣶⣄⠀⠀⠀⠀⠸⠿⡿⡷⡿⡟⠿⣿⣿⡿⠿⢿⣿⠿⢿⡿⠿⠿⡟⣿⣿⡿⠿⣿⠿⡛⢿⡿⢲⡟⠿⣿⡿⢿⠻⣿⠿⢿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⢶⡶⣾⣷⣶⢿⣶⢶⣶⣶⣶⡶⣶⣾⣷⢶⣶⣤⢷⣶⣦⣤⣴⣶⣶⡶⣶⣶⡶⢶⣶⣶⡾⣶⣶⣶⣾⣶⣶⣶⣤⣶⣷⣶⣾⣶⣶⣿⣶⣶⣶⣶⣶⣷⣶⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣭⣥⣤⣤⣤⣭⣥⣼⣬⣭⣤⣼⣯⣦⣤⣧⣬⣭⣭⣬⣽⣼⣭⣥⣬⣥⣼⣤⣤⣮⣮⣦⣴⣽⣥⣧⣥⣦⣬⣬⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⣾⠆⠹⢿⣏⣽⡇⢾⠶⢹⢹⢩⡏⡝⢉⠋⡍⢯⣽⣿⢘⣸⢩⠫⡍⠫⡽⢉⢙⠉⠏⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣿⣷⣶⣿⣿⣿⣶⣾⣷⣾⣾⣷⣿⣶⣷⣷⣿⣾⣿⣾⣿⣾⣷⣾⣷⣾⣷⣾⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⡿⣿⣿⣿⠿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣧⣤⢼⡬⣭⣥⣥⣧⣥⣴⣭⣤⣤⣼⡬⠨⢤⣬⣿⣤⡤⠽⠬⠁⠀⠃⠨⣤⣥⣤⡥⣵⣇⣤⣤⣥⣭⣤⣤⣧⣭⣽⣬⣤⣤⣯⣤⣬⣬⣄⣦⣥⢼⣧⡬⢧⣥⣤⣼⣤⣬⢬⣦⣮⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣥⣶⣷⣧⣤⣤⣿⣮⣽⣬⣧⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣰⣆⣤⣤⣿⣧⣥⣵⣶⣥⣤⣴⣧⣶⣿⣤⣧⣶⣥⣧⣤⣮⣴⣾⣤⣤⣶⣧⣤⣴⣾⣼⣮⣧⣶⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣫⣭⣉⣽⣹⣃⣹⣏⣭⣎⣩⣁⣀⣀⡀⠀⠀⢰⣀⣀⣈⣩⣉⣵⣽⣏⣽⣁⣝⣩⣯⣉⣉⣩⣩⣏⣩⣼⣁⣝⣹⣏⣉⣍⣍⣉⣉⣍⣍⣫⣿⣿⣉⣉⣽⣉⣉⣫⣍⢍⣯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢫⠛⡛⣿⢛⠛⢛⠋⣿⠟⢻⢙⢛⣿⠛⣻⡗⢺⠛⠛⠛⠟⣟⠛⠙⣽⢿⡿⠛⣿⠛⠛⠛⠻⠉⠋⢛⣿⠟⢻⢻⠙⢛⡟⣛⡛⡛⠋⢻⡿⢟⢿⠛⢛⠛⠛⠛⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠄⡍⠉⠛⢛⠏⠉⠙⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣿⣿⣤⣤⣴⣤⣿⣿⣤⣤⣤⣿⣧⣥⣤⣼⣿⣦⣤⣼⣿⣿⡿⠿⠿⠛⠛⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⠿⡿⠿⣿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣊⣇⣁⣎⣀⣑⣅⣉⣸⣿⣿⣿⣷⣶⣦⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣶⣶⣶⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠻⢻⢻⠛⢛⠛⠛⠟⡻⠛⠟⠛⠿⢻⠛⠟⡛⠛⣟⠟⠻⡟⠛⡟⢛⠻⠛⠛⢻⠛⠛⠛⠟⢛⠛⠛⠟⠻⠛⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢶⡶⢶⣶⡶⢶⣶⡶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣹⣛⣟⣻⣿⣹⣃⣛⣛⢟⣏⣻⣛⡛⣹⣏⣋⣋⣹⠻⣻⣯⣟⣛⣢⣙⣻⣛⣋⣏⣛⣛⣻⣛⣟⣛⣹⣉⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠒⠒⡖⠒⠛⡶⠞⢲⠛⠒⢰⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣭⣍⣝⣩⣭⣭⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠻⠟⠿⠿⣟⠻⢿⠿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣉⣉⣏⣉⣋⣟⣋⣻⣉⣉⣸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣮⣦⣼⣶⣼⣿⣤⣧⣧⣦⣷⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣝⣻⣙⣋⣛⣛⣻⣙⡛⣛⣛⣋⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠥⠤⣤⣥⣼⣤⣤⣤⣤⣬⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠿⢿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⠞⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣟⡚⣒⠒⣲⣐⣊⣙⢒⣓⣒⣒⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠭⠱⠿⠿⢿⣿⠿⠿⠎⠯⠽⠿⢿⣷⣄⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠂⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⡠⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⡺⡿⣿⣿⣿⡿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣮⣯⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣟⣒⢖⣶⣶⣶⡶⣖⣛⣿⣿⣿⣿⣿⣾⣴⣒⣦⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠙⡏⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠈⠙⠻⣿⣿⠿⢿⡦⣀⣀⣀⣀⣀⣀⣠⣧⠀⣀⢀⣀⣀⡀⣀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠚⠛⢿⣿⣿⡟⠛⠛⠛⠒⠑⠛⠻⡿⠛⠊⠓⠚⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⢷⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠭⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡀⣴⢮⣿⢟⣿⣿⣿⣿⣿⣛⣉⣋⣙⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣙⣛⣟⣛⣛⣛⣟⣛⣟⣻⣉⣙⣫⣻⢛⣻⣏⣝⣻⣟⣏⣛⣛⣛⣛⣟⣏⣛⣉⣙⣛⣹⣋⣙⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣿⠛⡛⠛⡋⣻⠯⣻⡏⣉⠟⠙⢋⠙⢻⣏⠙⠛⠙⠛⢋⠛⢟⠛⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⠛⠛⠛⠛⠛⠛⠻⡏⠙⠛⠛⠛⡟⠻⣽⠛⠟⢻⡝⠛⠛⢹⡯⠛⠙⠛⠛⠙⣿⠝⢻⠻⠛⠙⣿⠛⠛⠻⠙⠛⠛⠛⣿⠻⠛⢻⢉⠉⢿⠛⠛⠛⠻⡏⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⢛⠛⡏⠛⢛⠛⡟⢙⣋⠉⠛⠛⣝⢻⠙⡿⠛⢛⣻⡝⠛⣟⠛⢻⢋⣛⠛⢹⠙⠛⠛⣟⠋⠛⢻⢛⠙⡋⠛⡿⢛⠛⠛⠛⢻⠋⠛⣻⠚⡛⢛⣟⠛⣛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⠿⠿⠛⠻⠿⢿⠿⠿⣿⡟⠿⢿⣿⡿⠿⣿⢿⣿⡿⠿⠿⠟⠿⠿⣾⠿⠟⠿⢿⠿⠟⣿⣷⡾⠟⡿⢾⢻⣿⢿⣿⠻⠿⠿⡟⣿⢿⡷⠟⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠷⠶⠶⠶⠶⠾⠾⣶⠖⠿⠶⠾⢿⠶⠶⠶⠶⡶⠾⢷⠶⠿⠶⢶⡷⢲⠶⠶⠾⠲⢾⠿⠷⠶⠞⠿⠷⠖⢺⢶⠶⡶⠾⢶⠒⠾⡗⣶⢶⡶⠷⢶⠿⠶⠖⢲⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢾⣬⣶⢿⣶⣷⣷⢾⣶⣶⡾⣾⣾⣵⣶⣶⣿⣷⣶⢿⣼⣶⣶⠾⡶⣾⢶⣾⣷⢷⣾⡵⣾⣶⣶⣶⡶⣶⣿⣶⣾⣷⣾⢾⣶⣾⣶⣿⣾⣷⢾⣶⣶⡶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⡭⡤⣼⣯⣦⣭⣼⣼⡧⣤⣥⢽⣯⣤⣬⣿⣥⢬⣤⣼⣶⣤⣤⣤⡥⣬⣼⣯⣤⣤⣧⢬⢭⡵⣽⣥⣥⢭⣬⣤⣷⣭⣽⣶⢤⣤⣼⡷⣤⣤⣷⣾⡧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⣼⣮⣾⣢⣤⣤⣶⣦⣤⣤⣤⣾⣐⣧⣶⣤⣼⣴⣮⣦⣤⣤⣐⣢⣤⣐⣿⣿⣧⣤⣤⣴⣿⣤⣬⣤⣦⣤⣤⣥⣤⣤⣧⣴⣥⣶⣧⣤⣤⣦⣶⣴⣴⣇⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣉⣙⣋⣉⣻⣟⣉⣏⣉⣉⣉⣏⣙⣛⣉⣋⣹⣀⣷⣷⣐⣛⣉⣳⣉⣏⣉⣙⣧⣤⣌⣯⣋⣛⣛⣆⣿⣫⣻⣇⣄⣘⣿⣫⣛⣻⣍⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⣉⢉⣈⣍⣉⣫⣩⣭⣏⣉⣉⣸⣉⣉⢩⢩⣩⣭⣹⣟⣍⣹⢉⣩⣩⣈⣍⣭⡈⢹⣿⣿⣿⣿⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⡅⡯⢩⢋⣹⡇⡭⢹⣏⡙⡍⢍⢩⠈⣿⢉⢻⢨⠅⣽⣏⠏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣾⣷⣦⣀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⣉⠛⡟⠛⠛⠛⠛⠟⠿⠟⣿⠛⡻⠻⠙⣟⡛⠽⠏⢻⠛⠉⠛⠛⠹⢻⡻⠿⣿⠻⡟⡛⠹⠫⠿⠛⠻⢿⢟⢻⠟⡿⠿⠛⠛⠻⠿⡋⠙⠿⢿⡿⡟⠟⠦⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⠛⠋⠛⠛⣛⠙⠛⢫⠛⠛⠻⡟⠛⠛⡻⠛⠋⣝⢻⣛⡻⢫⡛⠛⠙⢻⠛⡏⠋⠛⠛⠙⡟⠋⡟⠛⠛⡛⠛⢫⡛⠙⣛⣻⣝⠛⠛⠛⡛⢻⡛⠙⠛⡟⠛⠛⠛⠀⢀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⡟⢹⠛⢻⢟⢓⠛⡿⡛⠛⢛⡛⠚⢞⠛⢻⢛⠛⠚⢻⢛⠛⠛⡟⡻⢻⠛⠛⠛⠋⡟⢛⣟⡟⠋⣿⣛⣻⢛⡻⠛⠟⢓⣞⠛⡟⠻⠻⠛⠛⢻⡟⢛⢟⣟⡻⣚⡛⠛⢻⣶⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠻⢟⢿⡛⠿⡿⠿⣿⠿⠿⠿⡿⠿⣻⡿⡟⡿⠿⠻⠟⠿⠿⠿⢿⡿⠿⠿⢿⠿⠿⠿⣿⡿⠿⣿⠿⠿⠟⠿⠿⠿⣟⠿⠿⠿⠿⢿⡿⠿⠿⠳⠿⢿⠿⡿⠿⠿⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡷⠶⠶⠶⠶⢶⡦⠶⠼⠶⠶⠶⠶⢶⠶⠶⠾⣷⣶⣾⣷⣶⣶⣮⣼⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣾⣶⣶⣶⣶⣶⣷⣶⣶⣤⣶⣾⣥⣶⣶⣴⣶⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⡟⠟⠿⠿⢻⠿⠿⠻⠿⢿⠟⠿⣿⠻⠿⠿⢿⠿⠻⠿⢿⠻⠿⠟⣿⠟⠿⣿⠿⠿⠿⣿⠿⠿⢿⠿⠿⠿⠛⠿⠻⠻⢿⠿⠿⠿⠻⠿⠟⠿⠿⡿⢿⠻⢿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4137

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/Richard_M_Stallman_Explains_Why_the_Web_Becoming_a_Pile_of_Prop.shtml
    Gemini version at https://techrights.org/n/2024/09/13/Richard_M_Stallman_Explains_Why_the_Web_Becoming_a_Pile_of_Prop.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Richard M. Stallman Explains Why the Web
Becoming a Pile of Proprietary JavaScript Programs (Not Pages to Render) Does
Harm to Web Users⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Richard_M._Stallman,_shown_in_an_old_file_photo.⦈_


From last month's talk_by_Dr._Richard_M._Stallman_(RMS):


     Now, another problem we have with the Web as it is today is that it
     has become common for web sites to send software to run in users'
     browsers. The World Wide Web originally operated by transmitting
     declarative data to a browser and the browser would then, I can't
     remember the word, render that data as some sort of picture on the
     screen. And the browser would do this according to code that runs in
     the users' machines so once there was a free browser users could
     control how that data would be rendered. The web was designed to let
     users control how that data would be rendered but businesses didn't
     like that. Businesses wanted to be able to control how their pages
     would look to users. And they redesigned things to give the business
     more and more say in how its pages would look when rendered by a
     user. Well to some extent it's optional, as long as it was only CSS
     you could turn it off, you could delete it, various things ultimately
     you were not under the business' control. But with Javascript it's
     much worse. Javascript as it's normally used is a program sent by a
     business or other organization to your computer to run there and
     practically speaking it is very hard to be able to change it. There
     are ways. It's a kludge though. And you could hardly ever have the
     time to study the sometimes very large programs that so many
     different web sites send you. You may look at that site only for a
     few minutes and then you're looking at something else no one can
     feasibly look at these and there's no easy way to distribute to
     people recommended changes and you don't normally get the real source
     code either. You get obfuscated code or you get compiled code in the
     form of assembler language or just numbers. This is no good. We need
     to go back to a system more like the original web where what you get
     sent is declarative data, which is then realized as standard kinds of
     behavior so that normally web sites can work without any specific
     Javascript code. This means we have to come up with general
     constructs that can be combined to get a lot of useful results,
     something like the 1990s windowing toolkits. You combine those, you
     can get the behavior you want, and it will display reasonably fast
     but always using code that is part of the system you installed and so
     we can build up a suitable library of general constructs with various
     parameters to be set for each one each time it is used and out of
     those you could build your web page.


     It would do the specific things it is supposed to do but the
     thousands of web pages you would look at would be using a finite list
     of general constructs that can be developed and maintained as Free
     Software. And who's community verification and maintenance would give
     you a reason to trust it. In this way, we would have much less
     malware in the world's web sites.


     Now the decentralized web, if it is to be for everyone, must make web
     pages accessible to everyone. Including stalwarts like me who don't
     run non-Free Javascript code. So, one thing you've gotta do for a
     world like this that everyone can participate in is to make sure your
     web sites are accessible without running non-Free Javascript. And
     ideally accessible without running non-standard constructs so that
     your system could include implementations of it.


     When I first looked at your web site for this event, I couldn't see
     most of it because it wouldn't display much without running non-Free
     Javascript. I think that that was fixed because later on I could see
     most of the site. This should be a criterion we make sure we fully
     follow and you have to watch out for making a web site use another
     web site to do part of the job because you could make all of your
     Javascript code Free and forget to check whether the other web site's
     code is Free and the solution for this is to try browsing the site
     LibreJS enabled. Which will tell you about and block non-Free
     Javascript. That way you can make sure you've made your web site
     fully accessible to stallwarts, freedom defending stallwarts.


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇On_getting_billed_for_tokens_I'm_not_even_allowed_to_see⦈_




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠂⠂⡀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⡿⢿⡃⠀⠤⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⠯⢤⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⡟⢛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⢃⠐⠀⠌⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠍⠁⠀⠠⠤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣀⣤⣶⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⠀⠀⠀⠉⠁⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠟⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡆⠀⣀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠴⠂⣰⣿⣿⡏⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⡾⠏⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣁⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⣥⣤⣬⣥⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣱⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⢟⡽⢿⢹⢿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⢱⣿⡭⡀⠠⣭⣿⣯⣿⣿⣩⣹⣝⣿⣹⡹⣯⣻⣻⣹⣏⣘⣸⣿⡧⣿⢹⡍⣇⢿⣽⣏⣿⢹⡭⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣷⡽⣾⣥⡷⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢈⢻⣿⣿⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣮⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠀⠀⠀⠁⢐⣿⣿⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠙⠛⠋⠙⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 4284

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Rumour: Layoffs in IBM Consulting
Today⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


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


Published 5_hours_ago:


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


There's also a report, "IBM_to_take_$2.7_bln_charge_related_to_transfer_of
pension_obligations" (Reuters). One can see_the_comments which include: "My
condolences to the tens of thousands of hard-working IBMers who (back in the
day) built this once-great company into the biggest and best, and the best
place to work."


IBM has had many layoffs lately.




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣉⣉⠆⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠒⣲⡖⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⡀⣠⣤⣴⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣩⣭⣿⡧⣴⣬⣾⣿⣿⣿⣿⣿⣿⡿⡟⡋⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣻⣿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣦⣾⣧⡧⠤⠤⠼⠶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠈⠈⠉⠉⠉
⣿⣿⣿⣿⣿⣿⠛⠙⠛⡏⠙⠁⠉⠉⠉⠁⠥⠅⠒⠒⠛⠃⠀⠉⠉⢉⣭⣿⣿⣿⣿⡿⠿⠿⠛⠉⠉⠉⠉⠉⠉⠙⠿⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠛⠁⠉⠁⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠉⠙⠉⣹⣿⣶⣶⣷⣶⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⣿⡮⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣼⣶⣶⣶⣀⣠⣤⣶⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠀⠀⠃⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⣤⣷⣖⣒⣒⣒⠲⠶⠶⠦⠤⣦⣤⣤⣴⣶⣶⣾⣿⡖⠀⣐⣴⣤⣤⠤⠠⠤⠤⠤⣄⣐⣂⣀⣀⠐⠺⠗⠀⠀⠛⢛⣂⣤⣂⣐⣲⠄⠂⢀⠐⠖⠆⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠜⢋⣝⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣩⣏⠽⠟⠛⠛⢛⣉⣃⣲⣿⣾⡉⠙⠻⠿⢣⣶⡶⠶⠷⠤⠤⠠⠩⠩⠉⠩⠍⠀⣒⣢⣀⠀⠀⠀⠂⠈⠁⠙⠀⢰⣾⣶⣟⣙⣟⡛⠂⠘⠛⠉⠉⠁⠀⠰⠋⠉⠉⡱⣀
⠀⠀⠒⠛⠛⠛⠀⠈⠉⠉⡛⢛⣻⣿⣿⣿⣿⣿⡿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣽⣾⣾⣿⣿⣿⣿⣭⣶⣷⣶⣶⣶⡿⣷⣶⠷⣶⣖⣒⣒⣒⣒⠒⠈⠉⠑
⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⣿⣿⣏⣉⣉⣉⣉⣉⣏⣹⣇⣈⣉⡉⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⢟⡻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣖⠒⢶⣿⣿⣿
⣿⣿⣆⣳⣾⣿⣿⣏⣌⣲⣰⢠⣱⣐⣆⣁⣸⣇⣈⣂⣑⣸⣇⣆⣺⣰⣐⣳⣈⣀⣰⣿⣐⣕⣺⣒⣇⣞⣰⣲⣰⣃⣸⣰⣃⣆⣲⣸⣗⣺⣰⣻⣛⣻⣘⣞⣞⣯⣒⣱⣐⣆⣡⣇⣚⣰⣲⣃⣎⢐⢼⡿⠯⠥⠾⣿⣿⣿
⣿⣿⣋⡍⣿⣿⣿⡟⡿⡿⡿⠿⡟⠛⡻⣿⠿⡿⣿⠿⢿⡿⡿⢿⢿⠿⠿⢿⢿⢿⠛⣿⣟⢿⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠏⡽⢿⣿⣿⣇⣟⡰⣹⣘⣄⣇⣀⣽⣜⣜⣜⣇⣟⣜⣄⣟⣻⣓⣇⣮⣿⣸⣂⢏⣾⣛⣑⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣮⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣆⣙⣩⣏⣉⡙⣍⣇⣹⣋⣀⣻⣸⣉⣩⣡⣩⣭⣉⣉⣯⣫⣿⣭⡉⢭⣏⣭⣙⣯⣇⣉⠩⣿⣹⣩⣫⣏⣭⣭⣝⣩⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣀⡀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4361

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ This is How Bad Things Have Become at
Microsoft⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


Amid mass_layoffs again:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Is_Microsoft_Officially_Running_Out_of_Money?_Phil_Spencer’s
  Xbox_Layoff_Right_after_a_Stupendous_Game_Pass_Price_Hike_Spells_Trouble⦈_


This is quite telling:


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇_Xbox_social_media_has_reportedly_gone_dark_to_avoid_drawing
               ire_over_Microsoft's_latest_round_of_layoffs._⦈_


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Xbox_layoffs:_Why_Microsoft_has_told_its_gaming_unit_to
               cancel_posting_on_social_media_-_Times_of_India⦈_


We're seeing nearly 80 reports in English about those layoffs (so far).




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢻⠷⢶⢠⣆⣰⣰⠶⣶⣠⠶⡶⡤⣶⣶⣠⠆⣿⢰⡏⢴⡶⢀⠤⢤⢠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠚⠉⠛⠛⠘⠛⠛⠒⠋⠛⠒⠓⠃⠃⠋⠿⠶⠿⠞⠃⠚⠒⠚⠘⠏⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⣿⣯⣭⣽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣻⡟⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⡟⢿⡿⣿⣿⣿⡟⢿⣿⡿⣿⣿⣿
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡷⠠⠀⢸⣿⣿⣿⣿⣿⡧⠠⠀⢾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⢀⣀⠀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡶⡆⠈⢻⣼⡗⣧⡖⣲⡖⡖⣶⢶⣴⢲⣿⢺⡂⢸⡁⡷⣿⣿⢻⣴⢒⡇⣶⡆⡇⡗⣶⠂⢸⢼⣳⣶⣶⣶⣶⣶⣾⣷⡖⣶⣶⡆⢸⡇⣿⣶⣶⣿⡀⣴⣲⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠁⠈⠉⠁⠈⠈⠁⠈⠀⠉⠀⠁⠉⠈⠁⠀⠉⠀⠉⠉⠉⠀⠁⠉⠁⠉⠉⠑⠃⠀⠉⠁⠁⠁⠉⠉⠉⠉⠉⠉⠉⠁⠛⠁⠀⠈⠀⠈⠉⠈⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡿⡴⣿⣴⣦⡶⣦⡖⠖⣖⢊⠟⠀⣿⠿⣿⣦⣿⣿⠀⡯⣅⡖⣦⡖⣶⡖⣦⡖⣶⢲⣶⠒⢳⣶⠀⢹⣎⢹⢲⣴⣦⢶⡆⠈⡏⢐⢶⢲⡰⡖⣶⡟⣿⠁⣿⢽⢸⣴⢲⢺⢲⢺⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠈⠁⠉⠉⠉⠑⠋⠈⠁⠈⠉⠀⠉⠉⠉⠉⠀⠉⠁⠛⠁⠉⠉⠉⠁⠉⠈⠉⠉⠀⠈⠉⠀⠉⠉⠉⠉⠈⠁⠉⠉⠈⠉⠉⠉⠑⠁⠉⠉⠉⠉⠀⠉⠈⠉⠙⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⡟⣿⠻⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣑⣘⣠⣘⣰⣄⣀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣭⣥⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠻⢻⠙⠿⠻⡛⢻⡟⡟⠛⠻⠟⢻⡟⡛⠟⢻⠛⠿⠛⡟⠛⢻⠛⠿⠋⠉⢻⢻⡟⡛⡟⠻⠟⠟⠛⣿⡛⡻⠛⡏⡟⠉⣟⢛⠟⢿⣏⡟⢛⡟⠻⣿⢛⠻⠛⡟⠋⠟⣏⣿⡛⡻⠛⡟⠋⠟⢿⠻⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣡⣹⣀⣀⣃⣃⣸⣇⣆⣈⣂⣒⣹⣇⣄⣄⣺⢘⣀⣀⣇⣇⣸⣐⣆⣃⣀⡆⣸⣇⣂⣇⣒⣐⣂⣀⣿⣇⣧⣀⣇⣇⣀⣿⣘⣘⣸⣿⣇⣀⣇⣀⣿⣘⣈⣀⣇⣇⣄⣿⣿⣇⣇⣀⣇⣀⣁⣸⡀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣽
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⣤
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠈⠉⠻⢿⡿⠟⠉⠁⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⡄
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢰⡇
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣠⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⠀⠀⢀⣴⣾⣿⣿⣷⣤⡀⠀⠀⠻⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⠉⣉⠙
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠠⡟⣡
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠰⢿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠚⠃⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣄⣠⣷⣿⣶⣶⣶⣶⣷⣷⣶⣶⣾⣿⣷⣿⣷⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣷⣶⣶⣿⣿⣤⣷⣶⣶⣾⣿⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⡟⠛⣿⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⢿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡝⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⡶⡾⠶⢶⢶⣾⣾⣶⣷⣾⣶⣶⣷⣶⣷⣾⣷⣶⣷⣧⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣾⣷⣶⣾⣶⣽⣾⣾⣷⣶⣾⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣾⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⠛⠛⠓⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⠿⣿⠿⡿⠿⠿⢿⢿⣿⢿⢿⠿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣻⣽⣹⣛⣤⣛⣅⣛⣇⣗⣫⣿⣮⣸⣛⣼⣱⣳⣿⣿⣿⣿⣿⣿⣿⠉⢩⢭⠭⢭⣭⡍⡭⠍
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠠⠠⠀⠀⠤⠀⣹⣿⣏⣟⣛⣛⣟⣿⣯⣿⣟⣏⣿⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣹⣻⣻⣻⣿⣽⣛⣻⣿⣝⣿⣿⣛⣻⣿⣿⣿⣿⣟⣿⣿⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣄⣀⣀⣉⣀⣁⣀⣀⣠⣾⣿⣷⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
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                    ䷩ 𝚕𝚒𝚗𝚎 4483

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/09/13/Video_Why_Hurd_and_MINIX_or_BSD_Didn_t_Get_Ahead_of_Linux.shtml
    Gemini version at https://techrights.org/n/2024/09/13/Video_Why_Hurd_and_MINIX_or_BSD_Didn_t_Get_Ahead_of_Linux.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Video] Why Hurd and MINIX (or BSD) Didn't
Get Ahead of Linux?⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Linus_Torvalds'_intellectual_training_in_creating_an
            operating_system_kernel_owes_much_to_Prof._Tanenbaum⦈_


             🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LinuxCon_+_CloudOpen_Europe_2014⦈_


"One of the reasons why GNU/Hurd didn't come out on time is that Richard
Stallman and the Hurd developers set themselves a too-ambitious goal,"
cusdeb_com wrote. "Linus Torvalds, in turn, was very cautious in setting his
goals. Now we all use GNU/Linux."


We've converted_the_video_into_WebM to make it more accessible (outside
Facebook too). █


Credit: cusdeb_com




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣷⣄⠀⠀⠀⠀⠀⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣔⠠⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣴⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣽⡟⣴⡹⣿⣶⡼⡸⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⡂⠀⠀⠀⠚⢛⣛⣻⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⣭⣽⢂⣿⣿⣿⣿⣿⡗⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸⡄⢐⣶⣴⣶⣿⢻⡿⣷⣤⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣿⡟⠿⠿⡿⠿⢻⣿⣇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⣿⣿⣿⢣⢾⡯⢿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣬⣿⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⡓⣒⣶⣖⢂⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡹⣻⣿⣿⣿⣿⣿⣧⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡻⣿⣷⣾⣿⣷⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠶⠿⣿⣿⣿⣷⣄⡙⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠳⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⠀⠀⠀⡲⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣤⠴⠷⡤⠶⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⣿⣷⣤⡘⣿⠟⠙⠀⡟⢧⢡⡄⠴⠀⠀⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢻⣿⣍⠃⣿⠇⠳⢀⢇⢀⣸⣬⣀⣀⠿⠼⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣦⣿⣖⡄⣣⣳⣭⣁⡍⢻⣿⡒⠀⠀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⠛⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⢁⣽⡌⠉⣴⠟⣿⣿⣿⣿⠈⣿⡃⢠⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⡟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿
⣿⣶⣤⠄⠀⠀⠀⠀⠀⠀⢿⣿⠟⡠⢁⣯⣩⠀⠨⢺⡿⡿⣿⣟⣴⣿⣷⢸⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡛⢄⢴⣾⣷⣷⣫⡿⠟⠈⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⡏⠻⠛⠙⠟⠛⠀⠀⠀⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢨⡷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡤⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⢠⣤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠡⣶⣷⠀⠀⠘⠿⣶⣦⡀⠀⠤⠂⢠⣿⣿⡆⠉⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠙⠿⠂⠀⠀⠀⠀⠉⠁⣶⣶⣦⣌⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⣛⡛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⡀⠀⠀⠀⠀⣤⣄⠀⣩⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠭⠟⠾⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣤⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⣿
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣦⣤⣤⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣮⣭⣅⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⡄⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⣿⡿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⣿⣤⢠⢦⣼⡧⠀⢤⣤⣤⣤⣤⢠⣤⣼⡇⣤⣿⠀⢤⣠⣠⢦⣠⣤⡄⠀⣿⢤⣤⡟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣟⡿⡅⡤⣯⢿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣇⣿⢿⢰⣽⠿⣧⠀⠸⠿⡏⢿⡿⢸⣿⠿⡇⢧⡿⠀⠸⡟⠹⡼⠻⡿⡇⠀⢿⠼⣿⣇⡇⣿⣿⣿⣿⣿⣿⣽⣿⣿⢿⢼⣸⣿⣿⣯⠇⡇⠿⢺⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠇⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡙⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠉⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣠⣤⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢷⣭⣍⣉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⢻⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4618

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

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    Gemini version at https://techrights.org/n/2024/09/13/Wine_Took_the_Bait_Mono_Soon_Starts_the_Microsoft_Circus_With_t.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Wine Took the Bait (Mono), Soon Starts the
Microsoft Circus With the Banhammer⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024,
updated Sep 13, 2024


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


Intentional or not, the move seems deeply misguided


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇I_am_offended_by_a_core_dev;_So_talk_to_him_like_a_grown-up;
        Can_you_not_just_ban_him?_Son,_he_started_the_whole_project!⦈_


It's not a controversial thing to say: large companies are exercising more
control over the thing/s they claim to "donate" to, whether it's a project or
an organisation and whether the "donation" is money, code, or whatever. The
invisible strings get attached to developers, projects, companies etc. It's not
even a "computer" or "FOSS" thing; it happens all the time in other areas,
including politics. Putting aside the loss of direction at the Linux_Foundation
or LF (whose budget is about 97% non-Linux), in an upcoming video we might
comment on what happened to Electronic_Frontier_Foundation, European_Digital
Rights_(EDRi), Southern_Poverty_Law_Center, and many others. There's some
political angle to some of it, hence we'd rather not elaborate too much in
text. It would potentially seem off-topic, maybe off-putting.


Today's main focus will be Wine (or WINE), the CoC, Mono, and Microsoft.
There's a lot to be learned about (or from) what happened to Southeast
Linuxfest or SELF [1, 2], which cautioned about doom by CoC. It's presented as
beneficial or at least benign, but then, put in the wrong hands, it's a weapon
against the "host"; it's like a Trojan horse designed to benefit large
corporations_as_enforcers. I saw that destroying events, projects, companies,
and even news sites (gamingonlinux.com nearly fell for it; it's an easy target
because anyone can comment on stories, even Unabomber proponents).


The issue was first introduced_this_morning, albeit with very few words because
words are better done after we have concrete answers, not speculations or mere
assertions.


When one person in IRC learned of the "CoC for Wine" (hours ago) he was very
alarmed. "Well," he said, "the Mono thing sort of leads me to believe Microsoft
is taking control. Probably the usual. Proxies."


Mono has long been a proxy (via Ximian, Novell, Xamarin and so on), so why
assume this time it's different? It's a form of social engineering and speaking
of which, there's_a_new_rant_about_the_likes_of_Jono_Bacon, a longtime pusher
of Mono, Microsoft etc. inside Canonical (he's still_at_it). The basic premise
it, Microsoft uses human operatives or turns innocuous people into shills and
moles inside companies, projects etc. Sometimes it rewards them later and
sometimes it only gives them promises of reciprocation (promises are a lot
cheaper; they may cost nothing).


"I'd say the enraged mob is not the real community," an associate recalls from
experience, "but Microsofters and 'outside' agitators pushing for closed
source, proprietary alternatives. Bacon was only ever a corporate spinmeister
lording it over the real community and trying to impose corporate will down
from on high. One of, perhaps the single worst, bad decisions made at Canonical
was to let him onto the payroll."


"Apropos Lunduke, recall also that Guido van Rossum was kicked out of his own
project by the creeps Lunduke is ranting about."


It's with that in mind that we sadly have to deal with WINE, seeing nonchalant
posts about a CoC on its way. "Instead of reinventing the wheel," the project's
head said, "I propose that we adopt the Contributor Covenant [5] that many
other projects (including Mono) are already using."


It looks like Microsoft has just exported a CoC to WINE and Alexandre Julliard
does not recognise the danger (which is, as usual, disguised as manners).


Here's his full message: (pay careful attention to point 5)




     Folks,


     As you may have noticed, now that the ARM64 support is done (just
     kidding), I've picked up the work on the Gitlab migration:


     1. The Wiki has been moved to Gitlab, it's now at [1].  Existing URLs
        to the previous Wiki are redirected to the appropriate page. There
        are also separate Wikis for appdb, vkd3d and wine-staging, under
        their respective project pages.


        As part of the migration I've done some minor edits, but most of
        the Wiki is badly out-of-date, and could use some love. Help is
        welcome!  Check the Writers page [2] for details on how to
        contribute.


     2. We are now hosting the Mono project on the WineHQ Gitlab [3].
        Please join me in welcoming the Mono developers to our community!


     3. We have new hardware for the Gitlab server, which is now
     noticeably
        faster. Thanks to Jeremy Newman for setting this up!  This also
        made it possible to enable robots.txt again so that our content is
        indexed. The next step will be to install new hardware for the
        Gitlab runners to offer more CI bandwidth.


     4. The Gitlab issue tracker is currently disabled because it was
        attracting too much spam. I'm going to re-enable it, first for use
        by Mono, and then ultimately also for Wine itself. To fight the
        spam I'm planning to add an explicit user verification step,
        modelled along the procedure used by Freedesktop.org [4].


     5. As part of the new sign-up process, I think it would be a good
     idea
        to have an explicit Code of Conduct to spell out our expectations.


        Instead of reinventing the wheel, I propose that we adopt the
        Contributor Covenant [5] that many other projects (including Mono)
        are already using.


     Thoughts? Questions? Comments?


     [1]: https://gitlab.winehq.org/wine/wine/-/wikis
     [2]: https://gitlab.winehq.org/wine/wine/-/wikis/Writers
     [3]: https://gitlab.winehq.org/mono
     [4]: https://gitlab.freedesktop.org/freedesktop/freedesktop/-/wikis/
     home
     [5]: https://www.contributor-covenant.org/


     --
     Alexandre Julliard
     julliard@winehq.org
"Next step then is that they expel all the senior contributors and other key
people from the project," our associate predicts.


"There's a lot more that could have been said explicitly about the dangers," he
said earlier (before seeing the above message), suggesting a more in-depth
follow-up. "It's obvious to us but maybe not to most readers, especially casual
readers, about the maintenance burden and how once Microsoft uses its
ovipositor to push a CoC into the innards of the project it will consume the
project from the inside."


"The CoC waving can be used as an opportunity to review the way those have been
used against other very prominent projects."


SELF, LF, etc. are named at the top; "but perhaps even more important than
noting the harm being inflicted upon the WINE project by Microsofters" is the
why and why now? "There's no obligation for WINE to absorb either the
Microsofters or their code, so so something is certainly amiss."


We spent the morning looking for further information under the assumption that
forums online might have the key pointers (links, summaries and so on).


"I am on the look out," the associate said as well, but we can only see what is
publicly published. "There are some pubic-facing mailing lists, with archives
[1, 2, 3]; that last one would be difficult to sift through, due to volume. At
least they_use_GitLab. Not the best, but very far from the worst."


There are mailing_lists. Nothing in WINE-Announce however. "Mono was in
Microsoft GitHub and is moved into GitLab," the associate noted, but not_much
can_be_found_about_it._"No_hint_in_the_forum. Not_much_in_bugs. The_agitators
can_be_found_here." So we're left with just the message from Alexandre Julliard
and it sounds like the CoC is being inherited for the entire project just
because of Microsoft (Mono).


The associate wondered: "Maybe the attack was the result of intrigue via a
private list?" Assuming that something instigated it, it was almost definitely
Mono and - inter alia - Microsofters. Some are now actively involved in WINE as
a project, which means it's the_same_agitation_as_Rust_inside_Linux.


Maybe this weekend we'll find time to record videos and deal with more
political aspects of it. These are inherently political tricks and stunts,
exploiting social engineering to oust the principal people and replace them
with stooges (or just leave the project to rot). We've seen this many times
before. Why expect different outcomes this time? █




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⠉⠀⠀⠀⠀⠀⠀⠑⠲⠂⠸⣿⣶⣾⡶⣠⣤⣼⣾⣿⣿⣿⠵⠾⠿⠖⠍⣻⣷⠦⠄⢀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠒⠚⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⢿⣿⢟⣓⣶⡦⠬⣽⣿⣶⢞⣁⢴⣶⡾⠿⠋⠀⠘⠁⠙⠃⠀⠒⠆⢤⣴⣶⡶⣟⣯⣽⣶⢀⡇⠸⠿⢟⣛⡤⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣿⣿⣶⣶⣶⣿⣿⣿⣾⣿⣤⣤⣶⣶⣿⣚⣲⣿⣿⣿⣿⣿⣿⣾⣭⣭⣭⣭⣶⣶⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⢛⠛⣿⢻⣻⣿⢻⣿⣿⣶⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣸⣡⣧⣼⣿⣿⣿⣿⣿⣿⣿⡇⢰⢸⣿⣿⣿⣷⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⣀⣤⣤⣶⣶⣶⡶⣶⢶⢶⣤⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠉⡏⣟⣟⡏⠉⡏⢿⣟⢏⣽⣿⣿⣿⡇⢸⢸⣿⣇⣿⣸⣨⣿⣈⣿⣻⣧⣃⣿⣿⣿⠀⠀⠀⠀⡇⢠⣾⣿⣿⡿⡂⣡⣅⣷⣠⣇⣘⣿⣿⣷⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⠿⡿⣿⡿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣧⢸⢸⣿⢹⣯⠍⢽⡍⢉⢻⢻⠏⣿⢍⣿⡟⠀⠀⠀⠀⡇⢸⣿⣿⣿⡿⠛⣿⢹⡏⢹⣏⢭⣽⣿⣿⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣤⣧⣽⣥⣤⣼⣧⣽⣾⣼⣿⣿⣿⣿⡿⢸⠘⢿⣷⣷⣶⣿⣶⣿⣾⣿⣿⣾⡿⠋⠀⠀⠀⠀⠠⡇⠈⢿⣿⣿⣿⣴⣽⣾⣷⠾⣷⢾⠿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣵⡆⢸⠀⠀⠈⠉⠛⠛⠛⠛⠛⠻⣿⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠻⣿⠠⣇⣃⣸⣯⣀⣯⣼⣱⣿⣿⢟⣴⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠶⠹⢰⣾⣿⣶⣶⣾⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⡿⢟⣛⣭⣴⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⡇⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⡠⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢐⠩⠌⠢⠹⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣙⣭⡕⣌⢿⣿⣿⡇⣿⠀⠀⠀⠀⠀⣴⣶⢲⢢⡶⣔⣶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣝⣛⣾⣶⣼⡟⠹⣹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⡽⣸⢱⣿⣈⡸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠉⣝⡾⣿⣭⣵⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠋⢀⣀⣈⣿⠉⠀⣼⣿⢸⢀⣀⠀⠀⠀⣀⠄⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣿⣾⣿⣩⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠲⠽⠿⠃⠀⢸⣿⣿⢸⢸⣛⣛⣲⣸⠎⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠽⠿⠟⠁⢻⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠐⣟⡷⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢸⢸⣟⣿⣿⡅⡤⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⢈⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⢸⢸⣿⣴⣾⡇⣰⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⡇⣿⢀⠀⡀⣠⢐⠄⣴⣿⢁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣬⣥⣾⣬⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣿⣬⣭⣭⣬⣭⣤⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤
⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⡟⡟⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡌⡇⡇⡇⣎⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⠿⢾⠿⣿⢿⡟⡻⣟⢛⡟⣻⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⢘⡃⡇⣻⣿⣜⢺⡇⡟⠄⡇⡅⣿⢸⡇⣽⢸⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣯⣧⣧⣭⣿⣮⣼⣧⣧⣿⣶⣿⣾⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⠘⡇⡇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣇⣧⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⢻⢻⢻⢻⢻⢫⡝⡏⣿⢩⣿⡏⡍⡏⡍⡏⣮⢻⢸⠰⡏⣶⣵⢰⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⢆⠀⠱⣌⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⡈⡎⣼⢸⠘⡸⠇⡇⢿⠰⢿⡇⣾⣇⣇⣇⣛⣼⣸⣘⣣⣛⣼⣸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠑⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢻⢹⣿⣷⣦⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣶⡌⢿⣿⣿⣿⠋⣡⣶⣶⣦⣤⡐⢶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠙⢿⣿⣿⣿⡿⠛⢁⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⢋⣽⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠄⠀⣰⣿⣿⣿⣿⣿⡿⠋⡠⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢚⣩⣵⠋⢀⣾⣿⣿⣿⣿⣿⣋⡤⠊⢐⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⡶⠶⠶⢤⣤⡀⠀⣤⣾⣟⠡⣊⣥⣿⠃⣰⣿⣿⣿⣿⣿⣿⡿⠋⣠⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠷⠤⠤⠿⠿⠿⠆⠘⠿⠷⠾⠯⠴⠇⠰⠿⠿⠿⠿⠿⠻⠿⠿⠿⠛⠿⠻⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 4903

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 13/09/2024: Towards
Aristocratic Personal Computing, Technology and
Privac⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Britain's_Day_Vintage_Poster⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


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


          o § Personal/Opinions⠀➾


                # ⚓ 🔤SpellBinding:_DILNPYS_Wordo:_SAKES⠀⇛


                # ⚓ A_Treacherous_Road⠀⇛


                       If you ride one of the busses around here to the
                       end of the line it will take you to a nice little
                       island connected to the shore by a bridge. It's a
                       nice place to hang out in a cafe, and there's some
                       interesting shops. I found myself there after not
                       having been for a long time, and I wondered why I
                       had stopped going; it was lovely.


          o § Technology and Free Software⠀➾


                # ⚓ Towards_Aristocratic_Personal_Computing_(ROOPHLOCH_2024)⠀⇛


                       What if the problem with personal computing
                       nowadays is that it's not aristocratic enough, or
                       at least, it lacks that Old Money sensibility?


                # ⚓ Change_the_color_of_hl-line_in_Emacs_in_the_terminal⠀⇛


                       During the last edition of the Old Computer
                       Challenge I used an old Acer Aspire One 522 POVE6,
                       which I ran without X11 or Xorg.


                       The small form factor and the low weight make this
                       laptop fine to use, as long as the workload is not
                       to high, to keep the performance within reasonable
                       limits.


                       After the challenge I installed Xorg and run it
                       together with the ratpoison window manager, Urxvt
                       terminal emulator and Tmux.


                # ⚓ Technology_and_Privacy⠀⇛


                       The above quote is a famous philosophical riddle.
                       It is intended to prompt discussion around the
                       nature of perception and reality.


                # § Internet/Gemini⠀➾


                      # ⚓ Self-hosting_at_home_and_privacy⠀⇛


                             You may self-host services at home, but you
                             need to think about the potential drawbacks
                             for your privacy.


                             Let's explore what kind of information could
                             be extracted from self-hosting, especially
                             when you use a domain name.


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





                    ䷩ 𝚕𝚒𝚗𝚎 5011

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 13/09/2024: Crackdowns on Bloggers,
Deepfakes, Internet Archive‘s Wayback Machine Now in Google
Search⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Cat_Three_Victorian_Die_Cut_Cats_from_1870-1880_in_Public
Domain⦈_


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
    * § Leftovers⠀➾


          o ⚓ MWL ☛ 60:_Free_Probing_from_the_Greys⠀⇛


                 My brain is tired after the email book, and needs the
                 concrete beaten out of it. The more experienced
                 GalactiCop is on his fifth life, old enough to actually
                 be grey. His people came from the sunny side of a
                 tidelocked inner planet, like Mercury with ice machines.


          o ⚓ New York Times ☛ A_Famous_Winston_Churchill_Portrait,_Stolen_in
            Canada_and_Found_in_Italy⠀⇛


                 A forgery delayed the discovery of the theft of the
                 photograph long enough for it to be sold at an auction in
                 London.


          o § Science⠀➾


                # ⚓ CS Monitor ☛ One_small_walk_for_a_tech_billionaire,_one
                  giant_leap_for_ultra_wealthy_space_tourists⠀⇛


                       Emerging from the hatch into the cold vacuum of
                       space, tech billionaire Jared Isaacman joined an
                       elite group of professional astronauts from a dozen
                       countries. He tested SpaceX’s new spacesuits,
                       clinging to a spacecraft going farther than any
                       since 1972.


                # ⚓ University of Michigan ☛ Elena_Gallo_to_direct_Women_in
                  Science_and_Engineering_program⠀⇛


                       Elena Gallo, professor of astronomy, has been
                       appointed the new director of U-M's Women in
                       Science and Engineering program, effective Sept.
                       15.


                # ⚓ Hackaday ☛ How_Photomultipliers_Detect_Single_Photons⠀⇛


                       If you need to measure the presence of photons down
                       to a very small number of them, you are looking at
                       the use of a photomultiplier, as explained in a
                       recent video by [Huygens Optics] on YouTube. The
                       only way to realistically measure at such a
                       sensitivity level is to amplify them with a
                       photomultiplier tube (PMT). Although solid-state
                       alternatives exist, this is still a field where
                       vacuum tube-based technology is highly relevant.


          o § Education⠀➾


                # ⚓ Latvia ☛ Latvia's_school_principals_often_think_about
                  leaving_job,_survey_suggests⠀⇛


                       More than half of the heads of educational
                       institutions have considered changing their
                       occupation several times in the last year,
                       according to a survey by the Latvian Education and
                       Science Workers' Association (LIZDA), which was
                       presented at the LIZDA Council meeting on
                       Wednesday, September 11, LETA reports.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ Building_A_Subwoofer_Box_Out_Of_Decking
                  Material⠀⇛


                       When you go to build a subwoofer box, wood is the
                       most common choice. When it came to his project,
                       though, [Startup Chuck] decided to go a different
                       route entirely. Rather than the usual plywood or
                       MDF, he decided to try Trex decking instead. Why?
                       He had some lying around, and he suspected it might
                       just sound good.


                # ⚓ CNX Software ☛ 11.6-inch_touchscreen_display_with_In-Cell
                  technology_packs_IPS_panel_and_10-point_touch_into_a_single
                  layer⠀⇛


                       Waveshare has introduced an 11.6-inch touchscreen
                       LCD with in-cell technology and 1768 × 828
                       resolution. The display comes with an IPS panel, a
                       10-point capacitive touchscreen, and supports HDMI
                       and Type-C interfaces. It includes brightness
                       control through the OSD menu and DDC/CI software.
                       The screen offers a 178° viewing angle and 72% NTSC
                       color gamut, delivering 300cd/m² brightness. While
                       we haven’t yet covered such a large screen with in-
                       cell technology, we previously reviewed the Elecrow
                       CrowVi VF156T, a 15.6-inch ultra-thin IPS
                       touchscreen display.


                # ⚓ CNX Software ☛ DeepRad_is_a_cheap,_modular_SDR_receiver
                  based_on_the_RTL-SDR_(Crowdfunding)⠀⇛


                       DeepRad is a software-defined radio (SDR) receiver
                       built in the RTL-SDR form factor. The modular SDR
                       receiver offers advantages over other RTL-SDR-based
                       devices which make it easier to integrate with
                       other components and build custom solutions for
                       your specific applications. The DeepRad SDR
                       receiver is based on the RTL-SDR dongle and
                       features the same Realtek RTL2832U demodulator chip
                       with an R860T tuner.


                # ⚓ Hackaday ☛ Review:_IFixit’s_FixHub_May_Be_The_Last
                  Soldering_Iron_You_Ever_Buy⠀⇛


                       Like many people who solder regularly, I decided
                       years ago to upgrade from a basic iron and invest
                       in a soldering station. My RadioShack digital
                       station has served me well for the better part of
                       20 years. It heats up fast, tips are readily
                       available, and it’s a breeze to dial in whatever
                       temperature I need. It’s older than both of my
                       children, has moved with me to three different
                       homes, and has outlived two cars and one marriage
                       (so far, anyway).


                # ⚓ Hackaday ☛ Back_Up_Your_Data_On_Paper_With_Lots_Of_QR
                  Codes⠀⇛


                       QR codes are used just about everywhere now, for
                       checking into venues, ordering food, or just plain
                       old advertising. But what about data storage? It’s
                       hardly efficient, but if you want to store your
                       files in a ridiculous paper format—there’s a way to
                       do that, too!


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ New York Times ☛ U.N._Says_Gaza’s_Anti-Polio_Campaign_Is
                  Ending_With_High_Hopes⠀⇛


                       Health workers have reached many vulnerable
                       children. But for the effort to be considered a
                       success, they must also be able to administer a
                       booster round of vaccinations in a few weeks.


                # ⚓ Hong Kong Free Press ☛ Complaints_about_Physical_Fitness
                  surge_as_shuttered_Hong_Kong_gym_chain’s_Wan_Chai_branch
                  rebrands_as_Healthy⠀⇛


                       A banner for wellness brand Healthy has been
                       erected outside what was until a week ago the Wan
                       Chai branch of gym chain Physical Fitness, as
                       complaints surged following the arrests of the
                       Physical’s two directors after its abrupt closure.


                # ⚓ RFA ☛ South_Korea,_Interpol_confiscate_drugs_worth_$1bn_in
                  Golden_Triangle⠀⇛


                       South Korean police said the Golden Triangle region
                       is the main origin of the drug ketamine.


                # ⚓ New York Times ☛ WADA_Report_Concludes_China_Broke_Rules_in
                  Doping_Case⠀⇛


                       An investigator hired by the global antidoping
                       regulator found no bias toward China in a case that
                       has outraged Olympic athletes and led to an F.B.I.
                       investigation.


                # ⚓ England_and_Wales_Deaths_in_Week_34_2019:_8,994._In_Week_34
                  2024:_9,819.⠀⇛


                       Does the Labour Party plan to investigate the
                       cause/s for this sharp rise in deaths?


                # ⚓ Science Alert ☛ Your_Eyesight_Could_Be_Putting_You_at_Risk
                  of_Developing_Alzheimer's⠀⇛


                       Windows into our brain health.


                # ⚓ Science Alert ☛ 5_Ways_You_Can_Resist_Food_Cravings_And
                  Stick_to_Healthy_Eating⠀⇛


                       Your brain doesn't make it easy.


                # ⚓ Science Alert ☛ Weight-Loss_Drugs_Safe_And_Effective_in
                  Children_as_Young_as_6,_Study_Finds⠀⇛


                       At least in the short term.


                # ⚓ Science Alert ☛ Your_Eyes_Can_Shed_Light_on_Underlying
                  Health_Problems⠀⇛


                       A window to early disease detection.


                # ⚓ Science Alert ☛ Exercising_Regularly_Appears_to_Make_Your
                  Belly_Fat_'Healthier'⠀⇛


                       Another reason to get moving.


                # ⚓ Science Alert ☛ These_Tiny,_Overlooked_Bones_Could_Tell_Us
                  Why_Our_Knees_Hurt⠀⇛


                       Thanks evolution!


                # ⚓ Science Alert ☛ Cannabis_Use_Is_Rising_Across_The_US_–
                  Except_in_One_Key_Group⠀⇛


                       It's the adults driving the trend.


                # ⚓ The Kent Stater ☛ COVID-19_cases_rise_as_fall_semester
                  starts⠀⇛


                       COVID-19 cases are rising in Kent, and the Kent
                       City Health Commissioner is urging residents to
                       practice safety measures to prevent further spread.
                       With the return of Kent State students, Kent City
                       Health Commissioners are reminding them of simple
                       precautions to help keep the Flashes community
                       safe.


                # ⚓ Hong Kong Free Press ☛ 1_in_3_Hong_Kong_upper_primary
                  students_have_been_bullied_at_school,_survey_finds⠀⇛


                       About one in three upper primary pupils in Hong
                       Kong have been bullied at school, a survey has
                       found, as an NGO launched a campaign calling for
                       “zero tolerance” of bullying.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Bryan Lunduke ☛ The_Register_Runs_Cover_for_CIA-
                        Backed_Smartphone_Game⠀⇛


                             Yes. Pokemon Go has ties to the CIA and other
                             intelligence agencies. The facts of this were
                             well documented roughly 8 years ago. The
                             Register (one of the more prominent Tech News
                             outlets) is seeking to discredit that
                             story... many years later. Why?


                      # ⚓ Data Swamp ☛ Self-hosting_at_home_and_privacy⠀⇛


                             You may self-host services at home, but you
                             need to think about the potential drawbacks
                             for your privacy.


                             Let's explore what kind of information could
                             be extracted from self-hosting, especially
                             when you use a domain name.

                      # ⚓ Silicon Angle ☛ Ireland_opens_privacy_probe_into
                        Google’s_PaLM_2_language_model⠀⇛


                             Ireland’s privacy regulator has opened a
                             probe into Surveillance Giant Google LLC over
                             its PaLM 2 large language model. The Data
                             Protection Commission, or DPC, announced the
                             move today. Officials will review whether
                             PaLM 2 was built in a manner compliant with
                             the European Union’s GDPR data privacy
                             regulation.


                      # ⚓ JURIST ☛ Canada_appeal_court_finds_Facebook_
                        (Farcebook)_infringed_privacy_law⠀⇛


                             The Canadian Federal Court of Appeal found
                             that social control media platform Facebook
                             (Farcebook) violated statutory obligations
                             for data protection and meaningful consent
                             created by Canada’s primary legislation on
                             the use of personal information by
                             corporations, the Personal Information
                             Protection and Electronic Documents Act
                             (PIPEDA).


                      # ⚓ Hackaday ☛ Digital_Bumper_Sticker_Tells_Everyone_What
                        You’re_Listening_To⠀⇛


                             Bumper stickers are usually political, crude,
                             or otherwise inflammatory. Rather a more fun
                             example is this digital creation from [Guy
                             Dupont], who made a bumper sticker that
                             broadcasts what he’s listening to on the
                             stereo.


          o § Defence/Aggression⠀➾


                # ⚓ The Strategist ☛ AUKUS_needs_seamless_data_sharing._Here’s
                  how_to_get_it⠀⇛


                       AUKUS won’t work without seamless information
                       sharing and data exchange between the partner
                       nations and their private sectors.


                # ⚓ France24 ☛ Alberto_Fujimori,_former_Peruvian_president
                  convicted_of_crimes_against_humanity,_dies_at_86⠀⇛


                       Peru's Alberto Fujimori, a deeply divisive
                       strongman who revamped Peru's economy, muzzled
                       political opponents, and oversaw deadly atrocities,
                       died on Wednesday after years of struggling with
                       multiple health issues.


                # ⚓ The Straits Times ☛ North_Korea_leader_Kim_calls_for
                  boosting_nuclear_might⠀⇛


                       Kim’s regime has staged dozens of launches in 2024.


                # ⚓ RFA ☛ North_Korea_fires_multiple_short-range_ballistic
                  missiles:_Seoul⠀⇛


                       The missiles flew about 360 kilometers, meaning the
                       South Korean capital would be in their range.


                # ⚓ France24 ☛ North_Korea_launches_ballistic_missiles_off
                  Korean_peninsula,_Seoul_says⠀⇛


                       After months of trading provocations with South
                       Korea and a recently renewed vow to keep growing
                       its nuclear arsenal, North Korea sent its most
                       aggressive message yet when it fired multiple
                       ballistic missiles into the Sea of Japan on
                       Wednesday, as reported by Seoul's military.


                # ⚓ The Straits Times ☛ Child_sex_abuse_allegations_in_Malaysia
                  welfare_homes:_171_suspects_to_be_remanded_for_7_days⠀⇛


                       All 20 premises raided on Sept 11 have been closed.


                # ⚓ RFERL ☛ U.S._Imposes_Sanctions_On_Chinese_Suppliers_To
                  Pakistan's_Ballistic_Missile_Program⠀⇛


                       The U.S. State Department on September 12 imposed
                       sanctions on a Chinese research institute and
                       several companies it said have been involved in
                       supplying Pakistan's ballistic missile program.


                # ⚓ RFA ☛ China_in_delicate_dance_with_Myanmar’s_rebel_groups⠀⇛


                       The junta ally is likely trying to end conflict
                       along its borders, but its assets are under rebel
                       control.


                # ⚓ Hong Kong Free Press ☛ Taiwan_will_‘never_succumb,’
                  official_says_amid_intensifying_pressure_from_Beijing⠀⇛


                       The head of Taiwan’s top China policy body said
                       Thursday that the democratic island will never
                       surrender in the face of intensifying pressure from
                       a “more aggressive” Beijing. China claims Taiwan as
                       part of its territory and has said it would never
                       renounce the use of force to bring the self-ruled
                       island under its control.


                # ⚓ France24 ☛ China_will_‘crush_hostile_encroachment’_in_South
                  China_Sea,_senior_military_official_says⠀⇛


                       A senior Chinese military official on Thursday said
                       Beijing will “crush” any foreign incursion into the
                       South China Sea, which it considers its territory
                       despite an international court ruling the assertion
                       has no legal basis. Chinese vessels have recently
                       engaged in a series of high-profile confrontations
                       with Philippine ships in the disputed waters.


                # ⚓ Atlantic Council ☛ Dispatch_from_Manila:_On_the_frontlines
                  of_the_‘gray_zone’_conflict_with_China⠀⇛


                       In the Philippines, China’s aggression is not in
                       some shadowy, ill-defined “gray zone.” It’s a real
                       and constant series of attacks on the country’s
                       people and sovereignty.


                # ⚓ The Strategist ☛ Which_countries_challenge_China’s_claim_to
                  the_Taiwan_Strait?⠀⇛


                       Spiegel magazine has reported that two German
                       warships are set to sail through the Taiwan Strait
                       in the coming weeks, becoming the first German
                       naval vessels to do so in 22 years. Germany will
                       join ...


                # ⚓ New York Times ☛ Israeli_Strike_in_Gaza_Kills_18,_Officials
                  Say,_Including_6_U.N._Workers⠀⇛


                       While resuming its offensive against militants in
                       the West Bank, Israel also kept up its bombardment
                       of the Gaza Strip, striking a school building used
                       as a shelter for displaced people.


                # ⚓ New York Times ☛ Israeli_Commandos_Carried_Out_Raid_on
                  Secret_Weapons_Site_in_Syria⠀⇛


                       The missile production facility was destroyed in
                       the attack, according to Western officials. Syrian
                       state media reported that 18 people were killed in
                       the strike.


                # ⚓ New York Times ☛ Students_at_Apalachee_High_School_Grapple
                  With_a_Mass_Shooting⠀⇛


                       The 1,900 students at Apalachee High School in
                       Winder, Ga., were just settling into the rhythms of
                       a new year before a freshman killed two teachers
                       and two students.


                # ⚓ New York Times ☛ U.S._Supports_Africa’s_Bid_for_U.N.
                  Security_Council_Seats,_With_a_Catch⠀⇛


                       The announcement provides U.S. support to permanent
                       council seats for African nations, though not new
                       veto powers. But the path to adding members
                       requires far more than White House approval.


                # ⚓ New Yorker ☛ The_Latest_“Poison_Pill”_in_the_Israel-Hamas
                  Ceasefire_Negotiations⠀⇛


                       What is the Philadelphi Corridor, and why is
                       Netanyahu at odds with his own security
                       establishment over whether I.D.F. troops should
                       remain there?


                # ⚓ The Strategist ☛ The_strategic_logic_of_Home_Affairs⠀⇛


                       There is a common idea that is contained in many of
                       the written constitutions that derive from British
                       constitutional theory and practice.


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


                      # ⚓ RFERL ☛ Closed-Door_Trial_For_Navalny_Lawyers_Facing
                        Extremism_Charges_Begins_Near_Moscow⠀⇛


                             A court in Russia's Vladimir region on
                             September 12 began the trial of three former
                             lawyers for late opposition politician
                             Aleksei Navalny on extremism charges over
                             their association with the Kremlin critic and
                             his Anti-Corruption Foundation.


                      # ⚓ RFA ☛ Putin_admires_Kim_Jong_Un,_unlike_other_world
                        leaders,_North_Koreans_are_told⠀⇛


                             Lectures cite Russian president’s punctuality
                             to 2019 meeting and expensive gifts to Kim


                      # ⚓ Latvia ☛ Belarus-registered_cars_banned_from_Latvia
                        as_of_October_31⠀⇛


                             Cars registered in Belarus must be re-
                             registered for use in Latvia by October 31 or
                             leave the country, the Saeima decided in its
                             final reading on Thursday, September 12.


                      # ⚓ RFERL ☛ Ukraine_Expected_Russian_Forces_To_Fight_Back
                        In_Kursk,_Zelenskiy_Says⠀⇛


                             Ukrainian President Volodymyr Zelenskiy said
                             on September 12 that Ukraine anticipated the
                             recent Russian military attacks that have
                             taken place in the Kursk region.


                      # ⚓ RFERL ☛ Civilian_Cargo_Ship_Carrying_Ukrainian_Grain
                        Hit_By_Russian_Strike_In_Black_Sea⠀⇛


                             Ukraine accused Russia on September 12 of
                             using strategic bombers to fire missiles at a
                             civilian ship carrying Ukrainian grain in the
                             Black Sea.


                      # ⚓ RFERL ☛ Russian_Soldier_Gets_8_Years_In_Prison_For
                        Beating_Wife_To_Death⠀⇛


                             A military court in the Siberian city of
                             Krasnoyarsk said on September 12 that it
                             sentenced Private Oleg Gorbachyov of the
                             Russian armed forces to 8 years in prison for
                             beating his wife to death.


                      # ⚓ RFERL ☛ Zelenskiy_Calls_Chinese-Brazilian_Peace_Plan
                        Proposal_'Destructive'⠀⇛


                             Ukrainian President Volodymyr Zelenskiy has
                             called a Chinese-Brazilian peace proposal
                             "destructive" that was created without the
                             input of Kyiv.


                      # ⚓ RFERL ☛ Nikolai_Svanidze,_Veteran_Russian_Journalist
                        And_Ukraine_War_Critic,_Dead_At_69⠀⇛


                             Russian TV journalist Nikolai Svanidze, who
                             is credited as one of founders of Russian
                             television, died in Moscow on September 12


                      # ⚓ RFERL ☛ Interactive_Map:_Ukraine's_Surprise_Invasion
                        Of_Russia's_Kursk Region⠀⇛


                             As fighting continues to rage in Kursk, RFE/
                             RL’s Russian Service has been keeping track
                             of Ukraine’s incursion with an interactive
                             map of events that uses information compiled
                             and verified from open sources, such as Ex-
                             Twitter and Telegram.


                      # ⚓ MIT Technology Review ☛ Meet_the_radio-obsessed
                        civilian_shaping_Ukraine’s_drone_defense⠀⇛


                             Serhii “Flash” Beskrestnov hates going to the
                             front line. The risks terrify him. “I’m
                             really not happy to do it at all,” he says.
                             But to perform his particular self-appointed
                             role in the Russia-Ukraine war, he believes
                             it’s critical to exchange the relative safety
                             of his suburban home north of the capital for
                             places where…


                      # ⚓ New York Times ☛ Russian_Forces_Are_Stepping_Up
                        Attacks_on_Pokrovsk,_Ukraine_Says⠀⇛


                             Bombardments are increasing in and around
                             Pokrovsk in eastern Ukraine, with water
                             supplies now cut, while Russian troops
                             simultaneously press a new counterattack in
                             the Kursk region.


                      # ⚓ New York Times ☛ Biden_Poised_to_Approve_Ukraine’s
                        Use_of_Long-Range_Western_Weapons_in_Russia⠀⇛


                             The topic will be on the agenda Friday with
                             the first official visit to Washington by
                             Britain’s new prime minister, Keir Starmer.


                      # ⚓ CS Monitor ☛ Moscow_gets_Iranian_missiles:_Might_that
                        actually_help_Kyiv?⠀⇛


                             Iran’s dispatch of missiles to Russia could
                             backfire if the shipment provokes Washington
                             into letting Ukraine aim U.S.-made missiles
                             deep into Russia.


                      # ⚓ New York Times ☛ Red_Cross_Workers_Killed_in_Ukraine
                        in_Shelling_Attack⠀⇛


                             The aid workers lost their lives as they were
                             preparing to distribute heating supplies in
                             preparation for winter in the region of
                             Donetsk.


                      # ⚓ New York Times ☛ Ukraine_Says_Russian_Missile_Hit
                        Grain_Ship_in_Black_Sea⠀⇛


                             If confirmed, the attack would be the first
                             on a commercial vessel in open waters since
                             the 2022 invasion, and a sharp escalation of
                             hostilities in the Black Sea.


                      # ⚓ New York Times ☛ Friday_Briefing:_U.S._May_Let
                        Ukraine_Use_Long-range_Weapons⠀⇛


                             Plus, will Taylor Swift’s endorsement affect
                             the U.S. election?


                      # ⚓ New York Times ☛ Should_Ukraine_Launch_Western
                        Weapons_Deep_Into_Russia?⠀⇛


                             President Biden has refused to allow Ukraine
                             to use long-range Western missiles on Russian
                             military targets, but he appears to be
                             wavering.


                      # ⚓ Latvia ☛ Statue_in_Rīga_daubed_with_paint⠀⇛


                             The statue of a Russian general of the
                             imperial era has been daubed with red paint,
                             reports the LETA newswire.


                      # ⚓ Latvia ☛ Girl_illegally_taken_to_Russia_returned
                        home⠀⇛


                             Monika Bukaine, who was illegally taken to
                             Russia by her father while crossing the
                             Zilupe River with a SUP board in late July,
                             has returned to her mother in Latvia,
                             Minister of Foreign Affairs Baiba Braže said
                             on X.


                      # ⚓ Latvia ☛ Daugavpils_in_Latvia_becoming_a_popular
                        place_to_learn_the_Russian_language⠀⇛


                             At Daugavpils University in the south-east of
                             Latvia, close to the border with Russia, the
                             study of the Russian language has become a
                             strong pull factor to attract foreign
                             students, reports Latvian Radio.


                      # ⚓ JURIST ☛ European_rights_court_rules_Russia_violated
                        freedom_of_assembly_and_expression⠀⇛


                             The European Court of Human Rights (ECtHR)
                             ruled that Russia had violated an official’s
                             and a group of filmmakers’ right to freedom
                             of assembly and free speech on Tuesday. The
                             applicants in the case were subject to
                             administrative sanctions for violating the
                             Public Events Act.


                      # ⚓ LRT ☛ Ship_with_Russian_chemicals_will_not_be_allowed
                        into_Klaipėda_port_–_PM⠀⇛


                             The Maltese-flagged ship Ruby carrying a
                             cargo of ammonium nitrate from Russia will
                             not be allowed to enter the port of Klaipėda
                             for repairs, Prime Minister Ingrida Šimonytė
                             says.


                      # ⚓ LRT ☛ Lithuanian_FM_warns_EU_against_China_deals_amid
                        Beijing-Moscow_rapprochement⠀⇛


                             Lithuania’s Foreign Minister Gabrielius
                             Landsbergis has castigated fellow EU member
                             states that do business with China, saying
                             his own country is an example of surviving
                             “without Russian gas and Chinese contracts”.


                      # ⚓ RFERL ☛ U.S._Black_Rights_Activists_Convicted_On
                        Charges_Linking_Them_To_Promoting_Russian_Views⠀⇛


                             Four Black rights activists were convicted in
                             the United States on September 12 on charges
                             of conspiring to act as unregistered Russian
                             agents, the Justice Department said.


                      # ⚓ The Straits Times ☛ Japan_says_scrambled_jets_after
                        Russia_aircraft_circled_country⠀⇛


                             The last time Russian military aircraft
                             circled Japan was in 2019.


                      # ⚓ New York Times ☛ Justice_Dept._Official_Calls
                        Election_Meddling_a_‘Clear_and_Present_Danger’⠀⇛


                             The head of the department’s national
                             security division amplified warnings that
                             other countries were seeking to sway the
                             outcome in November, including Russia’s
                             efforts to help Donald Trump.


                      # ⚓ CS Monitor ☛ Ukraine’s_nationalist_Azov_fighters,
                        once_sanctioned_by_US,_strive_to_clear_name⠀⇛


                             Ukraine’s Azov Brigade has been much maligned
                             for a Nazi-tainted past. But today its
                             renowned fighters proudly and emphatically
                             assert their modern self-definition as
                             nationalists with a broad appeal.


                      # ⚓ RFERL ☛ Red_Cross_Condemns_Attack_On_Aid_Truck_That
                        Killed_3_Workers_In_Donetsk_Region⠀⇛


                             The International Committee of the Red Cross
                             (ICRC) said on September 12 that three of its
                             workers in the frontline Donetsk region of
                             Ukraine had been killed and condemned the
                             attack.


                      # ⚓ RFERL ☛ Polish_Leaders_Urge_Blinken_To_Lift_Limits_On
                        Ukraine's_Use_Of_Long-Range_Weapons⠀⇛


                             U.S. Secretary of State Antony Blinken on
                             September 12 concluded a European tour in
                             Poland, where he heard more appeals for a
                             change in Washington's policy restricting the
                             use of Western-supplied weaponry for long-
                             range strikes inside Russia.


                      # ⚓ RFERL ☛ U.S._Army_Already_Implementing_Key_Lessons
                        From_Ukraine_War,_Chief_Says⠀⇛


                             The U.S. Army has reduced the footprint of
                             its command posts and increased the speed
                             with which they can be set up and taken down
                             as it implements key lessons learned from the
                             war in Ukraine, its chief said.


                      # ⚓ RFERL ☛ Orthodox_Church_Leaders_In_North_Macedonia
                        Express_Support_For_Ukrainian_Orthodox_Church⠀⇛


                             The leadership of the Orthodox Church in
                             North Macedonia on September 12 expressed
                             support for the Ukrainian Orthodox Church
                             (UOC), which has been banned in Ukraine under
                             a law signed last month by President
                             Volodymyr Zelenskiy.


                      # ⚓ France24 ☛ Moscow_claims_it_has_recaptured_10
                        settlements_in_Kursk_region⠀⇛


                             Russia said Thursday its army had recaptured
                             10 settlements in its Kursk border region,
                             where Ukraine last month launched a major
                             incursion, seizing dozens of settlements. 
                             Ukrainian President Volodymyr Zelensky
                             conceded Russia had launched its own
                             counterattack in the region but insisted that
                             the shock Ukrainian assault was still going
                             to plan. Read our liveblog to see how the
                             day's events unfolded.


                      # ⚓ France24 ☛ Toronto_festival_suspends_screening_of
                        Russian_war_film_over_threats⠀⇛


                             The Toronto International Film Festival
                             announced Thursday it is cancelling all
                             screenings of the documentary Russians at
                             War due to "significant threats" to public
                             safety. Organizers cited reports of potential
                             risks to festival operations. Directed by
                             Anastasia Trofimova, the film follows a
                             Russian battalion during the 2022 invasion of
                             Ukraine. TIFF described the decision as
                             unprecedented.


                      # ⚓ Atlantic Council ☛ Concerns_grow_over_possible
                        Russian_sabotage_of_undersea_cables⠀⇛


                             The United States has recently detected
                             indications of increased Russian military
                             activity around key undersea cables, fueling
                             concerns over a possible escalation in the
                             Kremlin's hybrid war against the west, writes
                             Aleksander Cwalina.


                      # ⚓ NYPost ☛ Even_Democrats_want_Harris-Biden_to_end
                        their_cowardice_and_remove_Ukraine’s_handcuffs⠀⇛


                             Despite Moscow’s escalations and now even
                             demands from fellow Democrats, Kamala Harris
                             and Joe Biden continue to twiddle their
                             thumbs on lifting restrictions on Ukraine's
                             use of US weapons against Russia.


                      # ⚓ Latvia ☛ Recently_acquired_education_in_Russia_might
                        not_be_recognized_in_Latvia⠀⇛


                             Amendments to the Law on Education, which
                             provide for non-recognition of education
                             documents obtained in the Russian Federation
                             after February 24, 2022, the date on which
                             Russia launched a full-scale invasion of
                             Ukraine, will be viewed in the responsible
                             parliamentary committee, LSM.lv reports
                             September 12.


                      # ⚓ Latvia ☛ Riga_film_festival_reveals_movies_competing
                        for_main_award⠀⇛


                             Riga International Film Festival (RIGA IFF,
                             17–27 October) has announced the contestants
                             in its main competition section this year.
                             Ten feature films from Denmark, Estonia,
                             Germany, Latvia, Lithuania, Norway, Sweden
                             and Ukraine will compete for the festival’s
                             main award – 10 000 EUR and a bronze
                             statuette.


                      # ⚓ New York Times ☛ Debate_Puts_Trump’s_Affinity_for
                        Putin_Back_in_the_Spotlight⠀⇛


                             The former president’s refusal to back
                             Ukraine’s war effort showed the likely limits
                             of U.S. support for Kyiv if he returns to the
                             White House.


          o § Environment⠀➾


                # ⚓ MIT Technology Review ☛ Meet_2024’s_climate_innovators
                  under_35⠀⇛


                       This article is from The Spark, MIT Technology
                       Review’s weekly climate newsletter. To receive it
                       in your inbox every Wednesday, sign up here. One
                       way to know where a field is going? Take a look at
                       what the sharpest new innovators are working on.
                       Good news for all of us: MIT Technology Review’s
                       list of…


                # ⚓ France24 ☛ Nearly_100_dead_as_floods_from_seasonal_rains
                  devastate_war-torn_Yemen⠀⇛


                       Heavy downpours in war-torn Yemen over the past
                       weeks have triggered flash flooding and landslides,
                       killing nearly 100 people and forcing hundreds to
                       seek shelter. The seasonal rains, which experts say
                       has been made worse by climate change, could lead
                       to an increase in malnutrition and cholera cases
                       among Yemen's population, according to the World
                       Health Organization.


                # § Energy/Transportation⠀➾


                      # ⚓ New York Times ☛ G.M._and_Hyundai_Plan_to_Work
                        Together_on_New_Vehicles⠀⇛


                             General Motors and the South Korean automaker
                             say they will collaborate on new vehicles,
                             buying parts and clean energy technologies.


                # § Wildlife/Nature⠀➾


                      # ⚓ Federal News Network ☛ Scientists_are_fighting
                        wildfires_with_Hey_Hi_(AI)_in_the_lab⠀⇛


                             "There is concern where we're scientists and
                             we talk data, and that data in its raw form
                             isn't particularly helpful to a first
                             responder," Norman Spiecher said.


                # § Overpopulation⠀➾


                      # ⚓ RFA ☛ How_a_cash-strapped_Chinese_woman_sold_her_eggs
                        to_a_surrogacy_agency⠀⇛


                             Activists say surrogacy is poorly regulated,
                             and can fuel human trafficking and baby-
                             selling.


          o § Finance⠀➾


                # ⚓ Federal News Network ☛ Social_Security_Administration
                  urging_budget_anomaly_to_avoid_‘devastating’_impacts⠀⇛


                       Without a 2025 budget increase for the Social
                       Security Administration, Commissioner Martin
                       O’Malley warned a hiring freeze and worsening
                       services will come.


                # ⚓ Hong Kong Free Press ☛ Optimism,_profitability_of_US
                  companies_in_China_at_record_lows,_report_says⠀⇛


                       American firms in China are grappling with an
                       unprecedented web of challenges, a business group
                       said Thursday, as economic woes and geopolitical
                       tensions drag optimism and profitability to all-
                       time lows.


                # ⚓ France24 ☛ US_government_faces_shutdown_as_Congress
                  grapples_with_spending_bill⠀⇛


                       The US federal government is on the verge of a
                       shutdown as Republicans in the House of
                       Representatives struggle to agree on a spending
                       bill. A new hurdle has emerged with former
                       President Donald Trump pushing for voter ID
                       requirements to be linked to any funding deal,
                       further complicating negotiations ahead of a
                       Sept.30  deadline.


                # ⚓ TwinCities Pioneer Press ☛ Amazon_boosts_pay_for
                  subcontracted_delivery_drivers_amid_union_pressure⠀⇛


                       Amazon is giving another pay boost to its
                       subcontracted delivery drivers in the U.S. amid
                       growing union pressure.


                # ⚓ New York Times ☛ To_Put_It_Bluntly⠀⇛


                       Much ado has been made of euphemism inflation.
                       While it’s easy to make fun of it, it’s worth
                       examining its logic.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ New Yorker ☛ Eric_Adams_Stays_Focussed,_Avoids
                  Distractions,_and_Grinds⠀⇛


                       As members of his inner circle get investigated by
                       the F.B.I., the Mayor of New York City,
                       quarantining with COVID, tries to play it cool.


                # ⚓ New York Times ☛ US_Sanctions_Venezuelan_Officials_in
                  Response_to_Disputed_Election⠀⇛


                       The sanctions against 16 government officials
                       appointed by the authoritarian president of
                       Venezuela were seen as unlikely to be effective by
                       observers and analysts.


                # ⚓ France24 ☛ US_imposes_new_sanctions_on_Venezuelan_officials
                  over_'election_fraud'⠀⇛


                       The US Treasury Department has imposed sanctions on
                       16 senior Venezuelan officials allied to President
                       Nicolas Maduro for preventing "a transparent
                       electoral process" in the July 28 presidential
                       election and for the "brutal crackdown on free
                       expression" as protesters took to the streets after
                       the poll. Those sanctioned included military,
                       intelligence and government officials.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ New York Times ☛ This_Chatbot_Pulls_People_Away_From
                        Conspiracy_Theories [Ed: But chatbots are the source of
                        the problem sometimes, they spread and create
                        "Conspiracy Theories"]⠀⇛


                             In a new study, many people doubted or
                             abandoned false beliefs after a short
                             conversation with the DebunkBot.


                      # ⚓ MIT Technology Review ☛ Chatbots_can_persuade_people
                        to_stop_believing_in_conspiracy_theories⠀⇛


                             The internet has made it easier than ever
                             before to encounter and spread conspiracy
                             theories. And while some are harmless, others
                             can be deeply damaging, sowing discord and
                             even leading to unnecessary deaths. Now,
                             researchers believe they’ve uncovered a new
                             tool for combating false conspiracy theories:
                             Hey Hi (AI) chatbots.


                      # ⚓ New York Times ☛ Deepfake_Sex_Videos_in_South_Korea
                        Seen_as_Old_Misogyny_With_New_Tech⠀⇛


                             Men in chat rooms have been victimizing women
                             they know by putting their faces on
                             pornographic clips. Some Korean women say the
                             only thing new about it is the technology.


                      # ⚓ Silicon Angle ☛ White_House_secures_commitment_from
                        Hey_Hi_(AI)_firms_to_curb_deepfake_porn⠀⇛


                             The White House today announced voluntary
                             commitments from several leading artificial
                             intelligence companies to rein in the
                             creation and distribution of image-based
                             sexual abuse, IBSA, including “deepfake”
                             content generated by AI.


          o § Censorship/Free Speech⠀➾


                # ⚓ RFA ☛ Lao_blogger_who_criticized_failed_response_to_flood
                  freed_from_prison⠀⇛


                       ‘Where is the helicopter for rescuing people?’
                       Houayheuang Xayabouly pleaded in a 2019 Facebook
                       (Farcebook) video.


                # ⚓ RFERL ☛ Kyrgyz_Opposition_Politician_Azimbek_Beknazarov
                  Detained_After_Questioning⠀⇛


                       Kyrgyz opposition politician Azimbek Beknazarov was
                       detained on September 12 after the State Committee
                       for National Security (UKMK) summoned him for
                       questioning, his son told RFE/RL.


                # ⚓ New Yorker ☛ How_a_Scientific_Dispute_Spiralled_Into_a
                  Defamation_Lawsuit⠀⇛


                       What does a Harvard Business School professor’s
                       decision to sue the professors who raised questions
                       about her research bode for academic autonomy?


                # ⚓ JURIST ☛ Amnesty_International_condemns_Libya_Arab_Armed
                  Forces_for_allowing_the_suppression_of_dissidents⠀⇛


                       Amnesty International has condemned the Libyan Arab
                       Armed Forces (LAAF) in a news report for
                       authorizing the Internal Security Agency (ISA) to
                       increase crackdown on dissidents, on Tuesday.


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


                # ⚓ Public Knowledge ☛ Now_That_Its_California_Twin_Has_Failed,
                  Is_the_JCPA_Poised_for_a_Next_Act?⠀⇛


                       A bill that would have created a new “link tax” in
                       California failed in part due to threats by Meta
                       and Surveillance Giant Google to block links to
                       news. Proponents of the Journalism Competition and
                       Preservation Act want to bring back their bill,
                       potentially with a bad, new twist.


                # ⚓ Press Gazette ☛ Future_of_Media_Awards_2024:_FT,_Telegraph
                  and_Sky_News_are_big_winners [Ed: Some of them take bribes to
                  whitewash the reputation of people who commit crimes; is that
                  something that merits an award?]⠀⇛


                       Financial Times was the big winner followed by The
                       Telegraph and Sky News.


                # ⚓ Press Gazette ☛ Mill_Media_says_goodbye_to_Substack_and
                  moves_onto_competitor_Ghost⠀⇛


                       The local news start-up says it's ready to use
                       purpose-built websites rather than the newsletter
                       platform.


          o § Civil Rights/Policing⠀➾


                # ⚓ Off Guardian ☛ The_New_Normal_Right⠀⇛


                       OK, this will be one of my non-satirical essays …
                       or mostly non-satirical essays. It will serve as a
                       companion piece to The New Normal Left, another
                       non-satirical essay that I published in April 2023,
                       which was basically just a reiteration of a speech
                       I gave at a conference in London.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ Congratulations_to_the_2024_ISIF_Asia_Award
                  winners⠀⇛


                       The APNIC Foundation congratulates the 2024 award
                       winners.


                # ⚓ Silicon Angle ☛ Google_Search_now_links_to_ancient_websites
                  via_the_Internet_Archive’s_Wayback_Machine⠀⇛


                       Starting today, Surveillance Giant Google LLC’s
                       search engine platform will provide direct links to
                       cached articles within The Internet Archive‘s
                       Wayback Machine, adding historical context to
                       user’s search results.


                # ⚓ AccessNow ☛ Access_Now_condemns_the_suspension_of_X_in
                  Brazil⠀⇛


                       Access Now opposes the suspension of X in Brazil
                       and is concerned by the growing trend of blocking
                       of entire online platforms and applications as a
                       response to systemic non-compliance.


                # ⚓ Tedium ☛ Can_Weird_Creatures_Survive?⠀⇛


                       Unfortunately for all of us, the internet doesn’t
                       reward noble ideas just because they’re noble.
                       Hence, what happened to cohost.


                # ⚓ Public Knowledge ☛ Public_Knowledge,_Allies_File_To_Defend
                  Net_Neutrality,_Consumer_Protections_in_Sixth_Circuit⠀⇛


                       Brief defends the FCC's reclassification of
                       broadband as a Title II service.


      § Monopolies/Monopsonies⠀➾


          o ⚓ The_Significant_Mistakes_in_the_DOJ’s_Definition_of_the_Ad_Tech
            Market⠀⇛


                 Google and the Justice Department (DOJ) have made their
                 opening statements in the latest monopolization case
                 against the internet company.


          o § Patents⠀➾


                # ⚓ Dennis Crouch/Patently-O ☛ If_the_Barcode_Doesn’t_Fit:
                  Reconsidering_‘Bodily_Incorporation’_in_Patent_Law⠀⇛


                       Many of us feel the daily pull toward coffee, and
                       perhaps likewise toward PTAB decisions about coffee
                       makers.


                       I found interesting a recent pair of IPR decisions
                       successfully brought by the Swiss Nespresso against
                       German competitor K-Fee.  This post delves into
                       these cases and what I call the 'glove doesn't fit'
                       fallacy in patent monopoly law obviousness
                       doctrine; it also provides a discussion of how
                       written description continues to be a risk, even in
                       inter partes review (IPR) proceedings.


                # ⚓ Dennis Crouch/Patently-O ☛ Federal_Circuit’s_New_Hands-Off
                  Approach:_Recent_Mandamus_Denials_Signal_Shift_in_Venue
                  Transfer_Landscape⠀⇛


                       by Dennis Crouch


                       On September 11, 2024, the Federal Circuit issued
                       three separate orders denying petitions for writs
                       of mandamus related to venue transfer decisions.
                       These cases highlight a trend that I previously
                       recognized of the court stepping-back from its
                       prior aggressive mandamus docket.  The cases here
                       all include the similar procedural posture where
                       the district court ordered transfer under the
                       convenient venue statute 1404(a), and the patentee
                       unsuccessfully petitioned the Federal Circuit to
                       reverse the transfer.


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ Ericsson_begins_UPC_experiment_against
                        AsusTech_at_local_division_Lisbon [Ed: UPC is not legal
                        and not constitutional, so they're just leveraging EPO
                        corruption and EU complicity to pretend this is about
                        the law when in fact this is an attack on the law]⠀⇛


                             No patent monopoly expert would have
                             questioned a mobile communications action at
                             the local division in Munich, Mannheim or
                             Düsseldorf. Nor would they have been
                             surprised if Ericsson had filed an action
                             with the local divisions in Paris or The
                             Hague.


                      # ⚓ Kluwer Patent Blog ☛ Scanning_for_signs_of
                        infringement_at_the_UPC:_First_PI_granted_on_the_basis
                        of_indirect_infringement_by_Munich_Local_Division [Ed:
                        This is a fake court [sic] that operates outside the
                        rule of law; it needs to be scuttled ASAP to salvage
                        legitimacy at the EU ]⠀⇛


                             On 27 August 2024, the Munich Local Division
                             awarded a preliminary injunction (‘PI’) in an
                             action brought by Hand Held Products against
                             Scandit for infringement of EP3866051
                             (“Mobile computer configured to read multiple
                             decodable indicia”) in relation to Scandit’s
                             ‘Data Capture SDK’ software (Order
                             UPC_CFI_74/2024).


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ Precedential_No._22:_Failure_to_Respond_to
                  Requests_for_Admissions_Leads_to_Cancelled_Registration⠀⇛


                       Tip from the TTABlog: never fail to respond to
                       admission requests. Respondent Hua Yungfu did just
                       that, and it led to summary judgment and an order
                       to cancel his registration for the mark LEARN
                       JOURNEY for various products in Class 16.
                       Petitioner pleaded several grounds for
                       cancellation, including abandonment. When
                       Respondent failed to respond to its admission
                       requests, Petitioner moved for summary judgment and
                       the Board granted the motion. The_Learning_Journey
                       International,_L.L.C._v._Hua_Yongfu, Cancellation
                       No. 92082654 (September 6, 2024) [precedential].


                       FRCP 36(a)(3) provides that “[a] matter is admitted
                       unless, within 30 days after being served, the
                       party to whom the request is directed serves on the
                       requesting party a written answer or objection
                       addressed to the matter and signed by the party or
                       its attorney.” Respondent did not respond to
                       petitioner’s requests for admission in any manner,
                       and so the requests were deemed admitted by
                       operation of law.





                    ䷩ 𝚕𝚒𝚗𝚎 6477

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 13/09/2024: Disinformation in Focus,
End of Presidential Debates (Trump Accepts It Hurts
Him)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
                # Confidentiality
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ Using_A_Potato_As_Photographic_Recording_Surface⠀⇛


                 Following in the tracks of unconventional science
                 projects, [The Thought Emporium] seeks to answer the
                 question of whether you can use a potato as a photograph
                 recording medium. This is less crazy than it sounds, as
                 ultimately analog photographs (and photograms) is about
                 inducing a light-based change in some kind of medium,
                 which raises the question of whether there is anything
                 about potatoes that is light-sensitive enough to be used
                 for capturing an image, or what we can add to make it
                 suitable.


          o ⚓ Jake Bauer ☛ An_Update_About_This_Very_Webbed_Site_-
            paritybit.ca⠀⇛


                 I don’t know why 10kbclub.com died or when it happened,
                 but what I do know is that I no longer have to care about
                 keeping the transmitted bandwidth of my front page under
                 10kB. I can stop with the stupid page size measuring
                 contest and have nice things again!


                 Besides, I’m really not interested in website asceticism
                 anymore. I want my site to feel like it’s my site; to
                 have a kind of personality rather than just being a plain
                 slab with words.


          o § Science⠀➾


                # ⚓ Science Alert ☛ Supermassive_Merger:_Sgr_A*_Formed_by_Black
                  Hole_Collision_9_Billion_Years_Ago⠀⇛


                       The Milky Way's black hole has a violent past.


                # ⚓ Science Alert ☛ Common_Weight-Loss_Diet_May_Come_With_a
                  Serious_Downside,_Long-Term_Study_Finds⠀⇛


                       Creating a whole other problem.


                # ⚓ Science Alert ☛ Rock_Used_as_Doorstop_For_Decades_Turns_Out
                  to_Be_Worth_Over_$1_Million⠀⇛


                       A value missed even by jewel thieves!


                # ⚓ Science Alert ☛ Weight_Loss_Involves_More_Than_Calories_In,
                  Calories_Out._Here's_How.⠀⇛


                       You can optimize your metabolism.


                # ⚓ Science Alert ☛ Supermassive_Black_Holes_in_Nearby_Galaxy
                  Caught_on_The_Brink_of_Collision⠀⇛


                       It'll literally shake the Universe.


                # ⚓ Science Alert ☛ Genetic_Evidence_Overrules_Ecocide_Theory
                  of_Easter_Island_Once_And_For_All⠀⇛


                       This isn't a cautionary tale.


          o § Education⠀➾


                # ⚓ Harvard University ☛ Speech_is_never_totally_free⠀⇛


                       But universities should strive to keep a balanced
                       approach to free speech while protecting their
                       educational mission, said Sunstein.


                       “The idea of the educational mission being a
                       permission slip for universities to regulate speech
                       seems to me both essential and rightly evocative of
                       the phrase ‘That way lies madness,’” said Sunstein.
                       “Suppose there is a faculty member who thinks
                       America is rotten to the core, there may be
                       students who think, ‘America is the opposite of
                       rotten to the core’ and ‘How can I learn from
                       someone who despises my nation?’ The idea that
                       leading to discomfort or feeling of something like
                       exclusion as a basis for regulating speech is like
                       the heckler’s veto, and that is not consistent with
                       the kind of pluralism educational institutions
                       prize.”


                # ⚓ Molly White ☛ Big_publishers_think_libraries_are_the
                  enemy⠀⇛


                       My beliefs are simple, and hardly radical:
                       Libraries are critical infrastructure. Access to
                       information is a human right. When you buy a book
                       you should truly own it. When a library buys a
                       book, they should be able to lend it. Readers
                       should be able to read without any third parties
                       spying over their shoulders, or preventing them
                       from accessing the materials they have legally
                       obtained.


                # ⚓ Lou Plummer ☛ Freelancing_in_the_Old_Days⠀⇛


                       I continued the business for about five years,
                       doing everything from building custom computers to
                       clearing viruses, setting up printers, tutoring a
                       millionaire's six kids to setting up the first
                       satellite-connected computer in the area. People
                       thought nothing of calling me on a Saturday night
                       in the middle of a movie to ask me random computer
                       questions because I'd been to their house one time
                       months before. Others would have a floppy drive
                       fail sometime after I'd installed AOL for them and
                       insist the problem was my fault because I was the
                       last one who touched it. By this time, I'd started
                       working professionally in IT support, making decent
                       pay, and I decided that the hassle was no longer
                       worth it. For a long time, I wouldn't even disclose
                       to people what I did for a living for fear that
                       they'd hit me up for free computer help.


          o § Hardware⠀➾


                # ⚓ Tom's Hardware ☛ Intel_partner_offers_refund_for_faulty
                  Core_i9-14900K_CPU_due_to_lack_of_stock_—_affected_user_sells
                  off_defective_chip_maker_Intel_hardware_and_switches_to_AMD⠀⇛


                       One of Intel's partners in Hong Kong is reportedly
                       refunding Core i9-14900K processors instead of
                       replacing them because it is running out of CPUs.


                # ⚓ Hackaday ☛ Supercon_2023:_Aleksa_Bjelogrlic_Dives_Into
                  Circuits_That_Measure_Circuits⠀⇛


                       Oscilloscopes are one of our favorite tools for
                       electronics development. They make the hidden
                       dances of electrons visually obvious to us, and
                       give us a clear understanding of what’s actually
                       going on in a circuit.


                # ⚓ Hackaday ☛ 2024_Tiny_Games_Contest:_Micro_One-Armed_Bandit
                  Hits_The_Cuteness_Jackpot⠀⇛


                       They don’t call slot machines one-armed bandits for
                       nothing. And although it’s getting harder and
                       harder to find slot machines with actual pull-able
                       handles instead of just big buttons, you can easily
                       simulate the handle at home with the right kind of
                       limit switch, as [Andrew Smith] did with their
                       micro slot machine.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ RFA ☛ Opium_replaces_meth_as_North_Korea’s_drug_of_choice⠀⇛


                       Decline in methamphetamine supplies from China
                       prompt farmers to grow and sell poppies.


                # ⚓ NYPost ☛ Bizarre_treatment_may_be_better_for_dry_eyes_than
                  eye_drops:_study⠀⇛


                       More than 360 million people around the world
                       suffer from chronically red, scratchy or irritated
                       eyes, a condition that can worsen with stress.


                # ⚓ Silicon Angle ☛ Coalition_of_US_attorneys_general_calls_for
                  warning_labels_on_social_control_media⠀⇛


                       A bipartisan group of 42 attorneys general today
                       called for Congress to require Surgeon General
                       warning labels on social control media apps to
                       attend to the growing mental health crisis among
                       young adults in the U.S.


                # ⚓ El País ☛ How_a_pioneering_movement_of_Basque_families
                  managed_a_‘digital_delay’_for_their_teenage_kids⠀⇛


                       “When we started in 2019, 99% of 12-year-old kids
                       going into their first year of secondary school had
                       a cell phone; today 90% of those starting their
                       second year don’t have one. We’ve turned it
                       around,” says Miren Ros, an educator and promoter
                       of a pioneering group in Spain that is working to
                       delay the age of the first cell phone in
                       adolescence. Those percentages represent “only 60-
                       65 children, but it’s already an achievement,” she
                       adds.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Bruce Schneier ☛ Evaluating_the_Effectiveness_of_Reward
                  Modeling_of_Generative_Hey_Hi_(AI)_Systems⠀⇛


                       New research evaluating the effectiveness of reward
                       modeling during Reinforcement Learning from Human
                       Feedback (RLHF): “SEAL:_Systematic_Error_Analysis
                       for_Value_ALignment.”


                # ⚓ India Times ☛ AI:_Humans_not_AI_should_control_nuclear
                  weapons:_Seoul_summit⠀⇛


                       Officials at the Responsible AI in the Military
                       Domain (REAIM) summit in Seoul, which involved
                       nearly 100 countries including the United States,
                       China and Ukraine, adopted the "Blueprint for
                       Action" after two days of talks.


                       The agreement -- which is not legally binding, and
                       was not signed by China -- said it was essential to
                       "maintain human control and involvement for all
                       actions... concerning nuclear weapons employment".


                # ⚓ Yury Molodtsov ☛ Social_Media_Platforms_Have_Killed_Links⠀⇛


                       Platforms dislike links because they are, by
                       definition, links to other websites. You click a
                       link, and your attention goes elsewhere. But that’s
                       how the internet works. Links are the foundation,
                       and people use links for all kinds of reasons. A
                       desire to start a discussion about an article or a
                       video is one of the incentives to post on social in
                       the first place.


                       Meta and Twitter imagine a future where all content
                       is directly syndicated through their properties.
                       Even if they don’t support this kind of content
                       natively. Have you tried using Twitter Articles?
                       They’re primitive, can take 10 seconds to load, and
                       in the end, the engagement figures are not too
                       different from an ordinary post with a link.
                       Twitter videos can’t replace YouTube in their
                       dreams. Most importantly, as an ordinary user, you
                       can’t just reupload someone else’s video or a news
                       article to Twitter to share it natively.


                       So you paste a link, and nobody sees it because
                       social platforms push users towards the algorithmic
                       feeds they control. As a result, people post less
                       or nothing at all.


                # ⚓ EDRI ☛ What_the_arrest_of_Telegram’s_CEO_means_for_digital
                  rights⠀⇛


                       The occasion of Durov’s arrest also presents an
                       opportunity for the French government to review its
                       overly-broad Internal Security Law, and in
                       particular to withdraw the antiquated encryption
                       registration obligation in its Trust in the Digital
                       Economy Law. The Internal Security Law was last
                       modified this summer but still fails to provide
                       meaningful human rights safeguards for law
                       enforcement requests to personal communications
                       data. The Trust in the Digital Economy Law, under
                       which Durov is also charged for having failed to
                       register Telegram in France, contains a 20th
                       century obligation for services to notify the
                       government of any encryption service they might
                       offer. In 2024 that could even be interpreted as
                       including practically any online service in
                       existence, because TLS/SSL-based transport
                       encryption (i.e. basic website security!) has
                       become ubiquitous. As a result, the obligation
                       constitutes an infringement of the freedom to
                       provide digital services in France (and hence in
                       the EU) and, in particular, a threat to smaller
                       providers and the free and open source software
                       community.


                # ⚓ India Times ☛ Adobe_to_launch_generative_AI_video_creation
                  tool_later_this_year⠀⇛


                       Dubbed Adobe Firefly Video Model, the artificial
                       intelligence tool will be released in beta and will
                       join the Photoshop maker's existing line of Firefly
                       image-generating applications that allow users to
                       produce still images, designs and vector graphics.


                # ⚓ Tech Central (South Africa) ☛ Cyberattackers_have_a_new
                  target:_your_car⠀⇛


                       In the connected cars of today, virtually all
                       communication between a driver’s smartphone and
                       their vehicle takes place over the internet via the
                       cloud for functions as basic as starting the engine
                       remotely and turning on the air conditioning.
                       Sometimes it’s a user sending a command to the car,
                       and sometimes it’s the manufacturer sending a
                       request for the car’s software to be updated.


                       There have been several instances where
                       cybersecurity experts successfully sent commands to
                       a vehicle remotely over the internet using an
                       unauthorised account, according to Liz James, a
                       consultant at IT security firm NCC Group, whose
                       clients include some European car makers.


                # ⚓ Terence Eden ☛ Why_does_no-one_discuss_negative_dynamic
                  pricing?⠀⇛


                       But that's not the only way dynamic pricing works.
                       Some shows don't sell out. Even the biggest names
                       can sometimes fail to fill a massive venue on a wet
                       Tuesday. When an event doesn't have the numbers
                       expected, negative dynamic pricing kicks in.


                       I'm subscribed a number of "Seat Filler" mailing
                       lists. They offer cut-price tickets to events which
                       haven't sold enough tickets.


                # ⚓ Andrea Contino ☛ Is_the_PlayStation_5_Pro_price_a_problem?
                  -_Go_With_The_Flow⠀⇛


                       The PS5 Pro's price increase over the original PS5
                       is significantly larger than the jump from the PS4
                       to the PS4 Pro, while it was the opposite in terms
                       of technology (PS4 didn’t have 4K support
                       originally while PS4 Pro was equipped with that).
                       This has led many to question whether the
                       performance enhancements justify the higher cost.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Tripwire ☛ WordPress_Plugin_and_Theme_Developers_Told
                        They_Must_Use_2FA⠀⇛


                             Developers of plugins and themes for
                             WordPress.org have been told they are
                             required to enable two-factor authentication
                             (2FA) from October 1st.


                # § Privacy/Surveillance⠀➾


                      # ⚓ The Register UK ☛ Google's_AI_model_faces_down_data
                        use_inquiry_in_EU⠀⇛


                             The DPC is concerned about whether Google
                             fully complied with its Data Protection
                             Impact Assessment (DPIA), an evaluation that
                             EU regulators ask data controllers to perform
                             before they ingest large amounts of personal
                             data in a systemic way. A DPIA defines the
                             scope, context, and purposes of data
                             processing and assesses whether that
                             processing might result in a high risk to the
                             freedoms and rights of individuals.


                      # ⚓ University of Michigan ☛ UMich_students_launch_app
                        RushLink_to_anonymously_rank_FSL⠀⇛


                             Arceo also expressed interest in expanding
                             the app across the University, but voiced
                             concerns about the anonymity aspect if the
                             app were to grow.


                      # ⚓ Six Colors ☛ FDA_approves_AirPods_hearing_aid
                        functionality⠀⇛


                             No surprise: a multibillion dollar company is
                             not going to announce a feature like this
                             unless it’s really confident that it’s
                             essentially all signed off on.


                      # ⚓ India Times ☛ Top_EU_privacy_regulator_opens_probe
                        into_Google's_AI_compliance⠀⇛


                             Ireland's Data Protection Commission has
                             launched an inquiry into Google's handling of
                             EU users' personal data in developing its AI
                             model, PaLM 2. This investigation is part of
                             broader efforts to regulate data processing
                             in AI development. Recently, social media
                             platform X agreed not to use EU users' data
                             for AI training without consent.


                      # ⚓ Press Gazette ☛ 'Consent_or_pay':_Why_UK_news_sites
                        are_getting_tough_over_data⠀⇛


                             The “consent or pay” model arrived in the UK
                             this summer after first being introduced by
                             European news titles including Bild and Der
                             Spiegel in Germany. At others, such as El
                             Pais in Spain, only paying subscribers to the
                             site’s overall offering can opt out of
                             personalised advertising, adding an extra
                             subscription incentive.


                # § Confidentiality⠀➾


                      # ⚓ PC World ☛ Your_VPN's_'kill_switch':_What_it_is_and
                        why_it_matters⠀⇛


                             A VPN’s kill switch is one of the first
                             features I recommend people enable with their
                             VPN and something I always have on whenever I
                             connect. It’s a simple, fail-safe way to
                             guarantee your data is never accidentally
                             exposed if your VPN disconnects. It’s so
                             important that a service must include a
                             robust and trustworthy kill switch in order
                             to make it onto my list of best VPNs.


          o § Defence/Aggression⠀➾


                # ⚓ Hong Kong Free Press ☛ Taiwan_president_Lai_Ching-te_calls
                  for_full_support_of_troops_after_fighter_jet_crash⠀⇛


                       Taiwan’s President Lai Ching-te on Wednesday
                       rallied residents to support the island’s troops
                       after a fighter jet crashed during a night training
                       flight.


                # ⚓ New York Times ☛ Violence_Resurges_in_Manipur,_Indian_State
                  Locked_in_Bloody_Conflict_for_16_Months⠀⇛


                       Ethnic tensions have turned Manipur into an open
                       war zone. Struggling to contain the unrest, the
                       authorities have reimposed a curfew and internet
                       blackout.


                # ⚓ Defence Web ☛ Sudan_conflict_“a_perfect_storm_of_crises”_–
                  WHO_Director-General⠀⇛


                       Sudan – where fighting rages on between the
                       Sudanese Armed Forces (SAF) and its opposing Rapid
                       Support Forces (RSF) – has drawn widespread
                       criticism with the latest coming from the World
                       Health Organisation (WHO).


                # ⚓ Atlantic Council ☛ A_next-generation_agenda:_Bridging_Indo-
                  Pacific_and_European_perspectives_on_security⠀⇛


                       This next generation agenda proposes policy
                       recommendations designed to improve security
                       cooperation among the United States, South Korea,
                       and European NATO countries in the context of
                       current global security threats, diverging national
                       security perspectives, and imminent leadership
                       changes.


                # ⚓ Defence Web ☛ Concerning_crime_figures_revealed_in_key
                  Stats_SA_report⠀⇛


                       Statistics South Africa (Stats SA) conducted the
                       Governance, Public Safety, and Justice Survey
                       (GPSJS) from April 2023 to March 2024. The GPSJS is
                       a countrywide household-based survey that aims to
                       bridge the statistical information gap in the field
                       of governance statistics.


                # ⚓ Atlantic Council ☛ North_America’s_moment:_The_case_for
                  energy_cooperation⠀⇛


                       Cultivating a United States, Canada, and Mexico
                       energy strategy will bolster the competitiveness
                       and security of North America in an increasingly
                       multipolar market.


                # ⚓ Defence Web ☛ Lack_of_security_at_DoD_ammunition_depot
                  worrying_AfriForum⠀⇛


                       Apparent security breaches and shortcomings at 93
                       Ammunition Depot are reasons for concern when the
                       presence of what AfriForum calls “foreign militias”
                       in South Africa is taken into account.


                # ⚓ Latvia ☛ Man_suspected_of_planning_terrorist_attacks_in
                  Latvia⠀⇛


                       On September 2 this year, the State Security
                       Service (VDD) urged the Prosecutor's Office to
                       prosecute a Latvian non-citizen for obtaining
                       instructions and knowledge for terrorist attacks,
                       as well as acquiring and possessing explosives and
                       firearms ammunition.


                # ⚓ Atlantic Council ☛ Why_Ukraine_will_remain_central_to_the
                  future_of_European_security⠀⇛


                       Russia’s war against Ukraine has thrown into stark
                       relief what has long been obvious to many
                       international relations scholars, namely that the
                       Cold War ended more than three decades ago but left
                       Europe with a security architecture that has
                       gradually decayed in subsequent years and is now
                       outdated. Mechanisms such as the OSCE and multiple
                       arms treaties are clearly no longer effective. The
                       sole exception here is NATO, but the alliance has
                       been unable to put an end to Russian aggression in
                       Ukraine.


                       It is therefore misleading to regard the invasion
                       of Ukraine as an isolated problem within the
                       framework of an otherwise stable European security
                       environment. Instead, the current war is at least
                       partially a consequence of the absence of effective
                       alternative mechanisms for maintaining European
                       security. These mechanisms are highly unlikely to
                       emerge if Russia continues to achieve its goals in
                       Ukraine.


                # ⚓ Deccan Chronicle ☛ Sanjauli_Mosque_Row:_As_protests
                  intensify,_police_use_water_canons,_lathicharge_protestors⠀⇛


                       The protests have been called by Hindu
                       organizations over the alleged illegal construction
                       of Sanjauli mosque.


                # ⚓ Truthdig ☛ Did_Saudi_Officials_Deliberately_Assist_the_9/11
                  Hijackers?⠀⇛


                       The court files also raise questions about whether
                       the FBI and CIA, which repeatedly dismissed the
                       significance of Saudi links to the hijackers,
                       mishandled or deliberately downplayed evidence of
                       the kingdom’s possible complicity in the attacks
                       that killed 2,977 people and injured thousands
                       more.


                # ⚓ The Atlantic ☛ Trump’s_Repetitive_Speech_Is_a_Bad_Sign⠀⇛


                       If the debate was a cognitive test, the former
                       president failed.


                # ⚓ The Washington Post ☛ Iran_turns_to_Hells_Angels_and_other
                  criminal_gangs_to_target_critics⠀⇛


                       Instead, officials said, Iran hired criminals in
                       Eastern Europe who encountered few obstacles as
                       they cleared security checks at Heathrow Airport,
                       spent days tracking Zeraati and then caught
                       departing flights just hours after carrying out an
                       ambush that their victim survived — perhaps
                       intentionally, investigators said, to serve as a
                       warning but not trigger the fallout that would come
                       with the murder of a British citizen.


                       Iran’s alleged reliance on criminals rather than
                       covert operatives underscored an alarming evolution
                       in tactics by a nation that U.S. and Western
                       security officials consider one of the world’s most
                       determined and dangerous practitioners of
                       “transnational repression,” a term for governments’
                       use of violence and intimidation in others’
                       sovereign territory to silence dissidents,
                       journalists and others deemed disloyal.


                # ⚓ Deutsche Welle ☛ Jordan:_Islamists_win_big_in_parliamentary
                  elections⠀⇛


                       Jordan's main Islamist opposition party made
                       significant gains and won 31 out of 138 seats in
                       parliament, according to official results.


                       The election outcome is the best yet for the
                       Islamic Action Front (IAF) — who were able to
                       capitalize on people's anger over Israel's war
                       against Hamas.


                       The IAF is the political arm of Jordan's Muslim
                       Brotherhood.


                # ⚓ Modern Diplomacy ☛ The_Taliban’s_Role_in_Al_Qaeda_and_TTP's
                  Afghan_Resurgence⠀⇛


                       An article published in Foreign Policy recently
                       disclosed that Al Qaeda and other terrorist
                       organizations are rapidly gaining a foothold in
                       Afghanistan. Contrary to this revelation, the IAG
                       has persistently denied the presence of these
                       groups, particularly the TTP. The international
                       community, however, has presented compelling
                       evidence to the contrary. Reports from multiple
                       intelligence agencies suggest that Al Qaeda has
                       established new terrorist camps across Afghanistan,
                       with at least 21 distinct terrorist organizations
                       now believed to be operating within the country.
                       This proliferation of extremist groups undermines
                       the IAG’s assertions and has alarmed nations around
                       the world, highlighting a potential disconnect
                       between the Taliban’s public messaging and the on-
                       ground realities.


                # ⚓ The Guardian UK ☛ Donald_Trump_a_de_facto_Russian_asset,
                  FBI_official_he_fired_suggests⠀⇛


                       He added: “I don’t know that I would characterize
                       it as [an] active, recruited, knowing asset in the
                       way that people in the intelligence community think
                       of that term. But I do think that Donald Trump has
                       given us many reasons to question his approach to
                       the Russia problem in the United States, and I
                       think his approach to interacting with Vladimir
                       Putin, be it phone calls, face-to-face meetings,
                       the things that he has said in public about Putin,
                       all raise significant questions.”


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ The Dissenter ☛ FBI_Sued_For_Withholding_Files_On_Assange
                  And_WikiLeaks⠀⇛


                # ⚓ Los Angeles Times ☛ Trump_refuses_second_debate_with
                  Harris,_claims_he_won_first_one⠀⇛


                       Trump did not specify which polls he was referring
                       to, and the claim strained credulity, since the
                       best known national polls all showed the opposite —
                       that a wide majority of viewers said Harris won the
                       105-minute debate on ABC News.


                       Polls taken by CNN, YouGov and a consortium
                       including SoCal Strategies all showed a majority
                       favoring Harris’ performance, by a roughly 20-
                       percentage-point margin in each.


          o § Environment⠀➾


                # ⚓ Omicron Limited ☛ Scientists_discover_crude_oil_decimates
                  sea_otter_buoyancy⠀⇛


                       Sure enough, the fur's buoyancy plummeted by almost
                       55% to 0.145 N, making it much more difficult for
                       the animals to remain afloat. The reduction in
                       buoyancy coupled with the loss of insulation would
                       almost certainly prove fatal in the wild.


                # ⚓ France24 ☛ Libya:_One_year_after_deadly_floods,
                  reconstruction_in_full_swing_in_Derna⠀⇛


                       Exactly one year ago, on September 11, 2023, the
                       eastern Libyan coastal town of Derna was hit by
                       deadly floods. Cyclone Daniel left around 5,000
                       people dead, as many missing and 45,000 displaced.
                       Today, the city is undergoing a full
                       reconstruction. Belgacem Haftar, the son of
                       powerful Libyan military and political leader
                       Khalifa Haftar, has assumed a lead role in the
                       reconstruction process. He has plans for several
                       cities in Libya's east as a way to make amends to a
                       population traumatised by more than a decade of
                       civil war. Our correspondents Lilia Blaise and
                       Hamdi Tlili sent us this exclusive report from
                       Derna over the summer, with Fadil Aliriza.


                # § Energy/Transportation⠀➾


                      # ⚓ Hackaday ☛ Train_Speed_Signaling_Adapted_For_Car⠀⇛


                             One major flaw of designing societies around
                             cars is the sheer amount of signage that
                             drivers are expected to recognize, read, and
                             react to. It’s a highly complex system that
                             requires constant vigilance to a relatively
                             boring task with high stakes, which is not
                             something humans are particularly well
                             adapted for. Modern GPS equipment can solve a
                             few of these attention problems, with some
                             able to at least show the current speed limit
                             and perhaps an ongoing information feed of
                             the current driving conditions., Trains, on
                             the other hand, solved a lot of these
                             problems long ago. [Philo] and [Tris], two
                             train aficionados, were recently able to get
                             an old speed indicator from a train and get
                             it working in a similar way in their own car.


                      # ⚓ France24 ☛ Amsterdam_to_Berlin_in_90_minutes?_Europe
                        tests_hyperloop_vehicles⠀⇛


                             The first successful test of a hyperloop
                             vehicle in Europe has been carried out at the
                             European Hyperloop Center in the Netherlands,
                             bringing the dream of passengers hurtling
                             between the continent’s cities at more than
                             700kph one step closer to reality.


                      # ⚓ DeSmog ☛ Conservatives_Accepted_£5,000_From_Laurence
                        Fox’s_Media_Company⠀⇛


                      # ⚓ The Register UK ☛ Domo_arigato,_Mr_Roboto:_Japan's
                        bullet_trains_ditch_drivers⠀⇛


                             JR East highlighted [PDF] several benefits of
                             autonomous operation – including enhanced
                             safety and transport stability, energy
                             savings from efficient operations, increased
                             flexibility to meet demand, and the ability
                             to reallocate employees to other tasks.


                             The Shinkansen, Japan's high-speed rail
                             vehicles often described as "bullet trains,"
                             connect Japan's major cities at speeds of up
                             to 320km/h (199 mph).


                      # ⚓ VOA News ☛ Electric_vehicle_sales_in_China_transform
                        auto_market⠀⇛


                             Foreign brands that used to dominate the
                             Chinese automotive industry have taken a back
                             seat to cars made domestically in China,
                             particularly “new energy vehicles,” or NEVs.


                      # ⚓ Axios ☛ Bitcoin_price_fell_as_the_presidential_debate
                        began⠀⇛


                             Why it matters: Bitcoin has been seen as a
                             proxy bet on the election, with traders
                             assuming a win for Former President Donald
                             Trump would boost the price of the oldest
                             cryptocurrency.


                             Zoom in: The price started falling almost as
                             soon as the debate began.


                      # ⚓ LRT ☛ Dutch_bicycle_maker_opens_factory_in
                        Lithuania’s_Kėdainiai⠀⇛


                             Pon.Bike, the world’s largest bicycle maker
                             owned by the Dutch holding Pon Holdings, has
                             opened its new production facility in
                             Lithuania’s central town of Kėdainiai, having
                             invested 57 million euros.


                # § Overpopulation⠀➾


                      # ⚓ Kansas Reflector ☛ U.S._senators_from_Kansas,
                        Colorado,_Arizona_introduce_bill_to_unlock_funds_for
                        water_preservation⠀⇛


                             Kansas and Colorado — along with Ciscomani’s
                             home state of Arizona — struggle with
                             continual drought and limited access to
                             water. As of last week, according to the U.S.
                             Drought Monitor, more than 51% of Kansas is
                             in some level of drought, mostly moderate or
                             severe. Almost 5% of Arizona is in extreme
                             drought. Colorado is currently the least
                             affected with about 12% of the state in some
                             level of drought.


          o § Finance⠀➾


                # ⚓ RFA ☛ US_lawmakers_ask_Biden_to_end_China_trade
                  ‘loophole’⠀⇛


                       Critics say the ‘de minimis’ exception lets
                       retailers sell clothes made with Uyghur slave labor
                       to Americans.


                # ⚓ Hong Kong Free Press ☛ EU_firms_weigh_mounting_risks,
                  declining_rewards_of_doing_business_in_China,_report_says⠀⇛


                       European firms are considering a “substantial”
                       rethink of their operations in China in the face of
                       lacklustre demand and a lack of action by Beijing
                       to mitigate economic woes, a business lobby warned
                       Wednesday.


                # ⚓ New York Times ☛ Inflation_Cooled_in_August,_Keeping_the
                  Fed_Poised_to_Cut_Rates⠀⇛


                       Consumer Price Index inflation continued to cool,
                       reaching a new three-year low. But signs of
                       stubbornness lingered under the surface.


                # ⚓ Federal News Network ☛ Lawmakers_tee_up_federal_fraud
                  scorecard_to_measure_agency_programs⠀⇛


                       Social Security’s SSI program and the IRS’s Earned
                       Income Tax Credit program are among those subject
                       to the new federal fraud scorecard.


                # ⚓ Pro Publica ☛ Exeter_Finance’s_Offers_to_Help_Cost_Car
                  Owners_More⠀⇛


                       Jessica Patterson tensed as she tore open the
                       letter from Exeter Finance. “This notice is being
                       sent to you concerning your default,” the company
                       wrote.


                       She didn’t need to keep reading to know she was in
                       trouble.


                # ⚓ Pro Publica ☛ Auto_Loan_Calculator_with_Extensions/
                  Deferments⠀⇛


                       On this page, you can find out how much a car loan
                       deferment might cost by using our free Car Loan
                       Deferment Calculator, explore frequently asked
                       questions about car loan deferments, read our
                       glossary of car loan terms or get in touch with
                       ProPublica reporters.


                       Have you taken out a car loan and struggled to pay
                       it back? You’re not alone. Borrowers like you owe
                       more than $1.6 trillion in auto debt, and many are
                       falling behind. Your lender might have given you
                       the option to move payments to a later date, also
                       known as a “deferment” or “extension.”


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Tech Central (South Africa) ☛ More_jobs_cuts_hit
                  Microsoft's_Xbox_unit⠀⇛


                       Microsoft said it is cutting 650 jobs in its Xbox
                       unit, the third such layoff this year as the
                       company tries to rein in costs and integrate its
                       US$69-billion acquisition of Activision Blizzard,
                       Bloomberg News reported on Thursday.


                # ⚓ India Times ☛ Microsoft_to_cut_650_support_jobs_in_Xbox
                  Games_unit⠀⇛


                       Microsoft Corp. said it is cutting 650 jobs in its
                       Xbox unit, the third such layoffs this year as the
                       company tries to rein in costs and integrate its
                       massive $69 billion acquisition of Activision
                       Blizzard Inc.


                       The roles to be eliminated are in “mostly corporate
                       and supporting functions,” according to a memo sent
                       to staff by Xbox chief Phil Spencer on Thursday.
                       “No games, devices or experiences are being
                       cancelled and no studios are being closed as part
                       of these adjustments today.”


                # ⚓ The Register UK ☛ Dell_announces_further_layoff_plans_in
                  SEC_filing⠀⇛


                       In its latest 10-Q filing with the US Securities
                       and Exchange Commission, published in the wake of
                       its fiscal Q2 2025 earnings report, the systems
                       maker admitted that those sparkling sales numbers
                       don't change the fact that AI means "business
                       transformation" will continue.


                # ⚓ VOA News ☛ Samsung_Electronics_plans_global_job_cuts_of_up
                  to_30%,_sources_say⠀⇛


                       The plan will be implemented by the end of this
                       year and would impact jobs across the Americas,
                       Europe, Asia and Africa, one person said. Six other
                       people familiar with the matter also confirmed
                       Samsung's planned global headcount reduction.


                       It is not clear how many people would be let go and
                       which countries and business units would be most
                       affected.


                # ⚓ Atlantic Council ☛ Experts_react:_What_the_presidential
                  debate_revealed_about_how_Trump_and_Harris_would_conduct
                  foreign_policy⠀⇛


                       On Tuesday night in Philadelphia, the two
                       candidates often presented sharply contrasting
                       visions on a range of foreign policy issues, from
                       tariffs to energy and immigration, and from China
                       to the Middle East.


                # ⚓ New Yorker ☛ Will_Kamala_Harris’s_Debate_Win_Be_Enough_to
                  Move_the_Needle?⠀⇛


                       Vinson Cunningham and Clare Malone break down the
                       first, and perhaps only, Trump-Harris debate.


                # ⚓ Craig Murray ☛ That_Harris/Trump_Debate⠀⇛


                       I just sat through a recording of the Trump/Harris
                       debate. Ignoring the merits of their political
                       stances, I agree with the general consensus that
                       Kamala Harris “won” in performance terms, but only
                       because Trump was awful.


                # ⚓ Digital Music News ☛ Nova_H1_Audio_Earrings_Promise
                  ‘Special_Edition’_for_Presidential_Debates_After_Kamala
                  Harris_Accusations⠀⇛


                       Following a conspiracy theory circling online that
                       Vice President Kamala Harris was ‘fed’ debate
                       questions through audio earrings—the company that
                       makes them is leaning into the rumor.


                # ⚓ Pro Publica ☛ Why_Did_Trump_Media_CEO_Devin_Nunes_Meet_With
                  North_Macedonia’s_New_Prime_Minister?⠀⇛


                       Earlier this summer, Devin Nunes, the CEO of Trump
                       Media and a former California congressman, touched
                       down just outside Skopje, the capital of North
                       Macedonia.


                       He and a small group of other North American
                       executives were there to talk business. But they
                       weren’t there to meet with representatives from
                       another company. A high-ranking official from the
                       Macedonian government greeted them on the tarmac
                       outside their private jet. Then a police escort
                       ferried them from the airport. They were there to
                       meet with the Balkan nation’s newly elected prime
                       minister.


                # ⚓ The Gray Zone ☛ VIDEO:_Ecuador’s_exiled_ex-president_Correa
                  discusses_the_US_lawfare_agenda_with_The_Grayzone⠀⇛


                # ⚓ New Yorker ☛ The_Desperation_of_the_Instagram_Photo_Dump⠀⇛


                       On today’s social control media, the only way to
                       counteract the overflow of online content is to put
                       out an overflow of your own.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Scoop News Group ☛ Cybersecurity,_disinformation
                        dominates_hearing_on_elections⠀⇛


                             Cybersecurity was once considered a side
                             issue in election administration. Eight years
                             after the Russian government waged a multi-
                             pronged effort to interfere in the 2016
                             elections and four years after former
                             President Donald Trump left office spewing a
                             flurry of falsehoods in a scorched-earth
                             campaign to undermine the integrity of U.S.
                             voting, things look a little different.


                             When six secretaries of state descended upon
                             Washington to testify in front of Congress
                             this week on the state of U.S. election
                             readiness, virtually every topic discussed
                             related to cybersecurity or false and
                             misleading claims around election fraud
                             driven by foreign or domestic disinformation.


                      # ⚓ The Verge ☛ Right-wingers_continue_their_anti-Haitian
                        AI_disinformation_campaign⠀⇛


                             One of the most recent examples comes from
                             Tyler Oliveira, a YouTuber and MrBeast
                             associate, who posted a misleading video
                             about Springfield on Wednesday. Oliveira’s
                             video intersperses interviews with locals —
                             including some Haitians — with AI-generated
                             images and memes. Just five seconds in, the
                             video shows a clearly AI-generated clip of a
                             Black man driving a white van surrounded by
                             cats. The video also features clips totally
                             unrelated to Springfield, including footage
                             of a woman being arrested for eating a cat in
                             Canton, Ohio, and a clip of gang members
                             marching on a street in Haiti. It’s a
                             textbook example of disinformation.


                      # ⚓ MIT Technology Review ☛ Google’s_new_tool_lets_large
                        language_models_fact-check_their_responses⠀⇛


                             Google is releasing a tool today to address
                             the issue. Called DataGemma, it uses two
                             methods to help large language models fact-
                             check their responses against reliable data
                             and cite their sources more transparently to
                             users.


                      # ⚓ Axios ☛ Anatomy_of_a_Trump_conspiracy_theory⠀⇛


                             • The result — on display as he falsely
                             claimed immigrants are eating people's pets
                             in Springfield, Ohio — is a candidate who's
                             become a walking liability for his own
                             campaign.


                             The big picture: Today, the 78-year-old Trump
                             routinely feasts on a stream of
                             misinformation on Truth Social and X, where a
                             cottage industry of MAGA influencers has
                             flourished since Elon Musk acquired and
                             renamed Twitter.


                      # ⚓ Meduza ☛ A_year_after_Yevgeny_Prigozhin’s_death,
                        Russia’s_influence_campaign_in_Africa_continues_apace_—
                        but_it_may_have_new_competition⠀⇛


                             Shortly after Prigozhin’s death, Moscow
                             created a new tool to help it expand its
                             influence in African countries: a media
                             agency called African Initiative. The
                             organization publishes articles promoting
                             pro-Kremlin narratives and disinformation
                             about Western countries, especially the
                             United States. According to BBC News Russia,
                             experts have linked it to Russian
                             intelligence services.


                      # ⚓ France24 ☛ Musk_brands_Australia_'fascists'_over
                        fines_for_tech_giants_spreading_misinformation⠀⇛


                             Australia introduced a "combating
                             misinformation" bill on Thursday, which
                             includes sweeping powers to fine tech giants
                             up to five percent of their yearly turnover
                             for breaching online safety obligations.


                      # ⚓ The Atlantic ☛ The_Americans_Who_Yearn_for_Anti-
                        American_Propaganda⠀⇛


                             But the real question is not whether the
                             talking heads of Tenet Media—the founders,
                             Lauren Chen and Liam Donovan, who were the
                             main interlocutors with the Russians, but
                             also Tim Pool, Lauren Southern, Dave Rubin,
                             and Benny Johnson—had guessed the true
                             identity of their “investor.” Nor does it
                             matter whether they knew who was really
                             paying them to make videos that backed up
                             absurd pro-Moscow narratives (that a
                             terrorist attack at a Moscow shopping mall,
                             loudly claimed by the Islamic State, was
                             really carried out by Ukrainians, for
                             example). More important is whether the
                             audience knew, and I think we can safely say
                             that it did not. And now that Tenet Media
                             fans do know who funds their favorite
                             influencers, it’s entirely possible that they
                             won’t care.


          o § Censorship/Free Speech⠀➾


                # ⚓ EFF ☛ We_Called_on_the_Oversight_Board_to_Stop_Censoring
                  “From_the_River_to_the_Sea”_—_And_They_Listened⠀⇛


                       We’re happy to see that the Oversight Board agreed.
                       In last week’s decision, the Board found that the
                       three pieces of examined content did not break
                       Meta’s rules on “Hate Speech, Violence and
                       Incitement or Dangerous Organizations and
                       Individuals.” Instead, use of the phrase “From the
                       River to the Sea” was found to be an expression of
                       solidarity with Palestinians and not an inherent
                       call for violence, exclusion, or glorification of
                       designated terrorist group Hamas. 


                       The Oversight Board decision follows Meta’s
                       original action to keep the content online. In each
                       of the three cases, users appealed to Meta to
                       remove the content but the company’s automated
                       tools dismissed the appeals for human review and
                       kept the content on Facebook. Users subsequently
                       appealed to the Board and called for the content to
                       be removed. The material included a comment that
                       used the hashtag #fromtherivertothesea, a video
                       depicting floating watermelon slices forming the
                       phrases “From the River to the Sea” and “Palestine
                       will be free,” and a reshared post declaring
                       support for the Palestinian people.


                       As we’ve said many times, content moderation at
                       scale does not work. Nowhere is this truer than on
                       Meta services like Facebook and Instagram where the
                       vast amount of material posted has incentivized the
                       corporation to rely on flawed automated decision-
                       making tools and inadequate human review. But this
                       is a rare occasion where Meta’s original decision
                       to carry the content and the Oversight Board’s
                       subsequent decision supporting this upholds our
                       fundamental right to free speech online. 


                # ⚓ Meduza ☛ The_Russian_authorities_slowed_YouTube_speeds_to
                  near_unusable_levels_—_so_why_are_Kremlin_critics_getting
                  more_views?⠀⇛


                       Curiously, journalist Dmitry Kolezev, who tracks
                       the audiences of Russian socio-political media,
                       activists, and vloggers on YouTube, noted that in
                       early August, viewership for these channels
                       continued to grow, despite the slowdown. Data from
                       Mediascope also indicated an increase in traffic in
                       Russia to both YouTube’s web and mobile app
                       versions.


                # ⚓ Techdirt ☛ California_Politicians_Embarrass_Themselves_By
                  Calling_For_‘Warning_Labels’_On_Social_Media⠀⇛


                       Just the fact that he flat out lied to the public
                       and declared victory in one of the cases he lost
                       should give you a sense of Bonta’s priorities in
                       spitting on the First Amendment. But now he’s
                       doubling down.


                # ⚓ CPJ ☛ Civil_Society_Demands_Attention_to_Human_Rights_and
                  Climate_Justice_Ahead_of_COP29_in_Azerbaijan [PDF]⠀⇛


                       Azerbaijan’s government has a longstanding and
                       well-documented pattern of repressing independent
                       civil society and silencing critical voices.
                       Hosting an international gathering such as COP29 in
                       this context raises grave concerns about the
                       ability of civil society, including environmental
                       activists, human rights defenders and journalists,
                       to participate freely and safely before, during and
                       after the conference.


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


                # ⚓ Press Gazette ☛ DPG_Media’s_investment_in_print_technology
                  helped_it_focus_on_digital⠀⇛


                       Leading Dutch/Belgium newspaper and magazine
                       publisher invested in modular print/digital
                       platform.


                # ⚓ 404 Media ☛ Historic_Newspaper_Uses_Janky_AI_Newscasters
                  Instead_of_Human_Journalists⠀⇛


                       A company that owns several newspapers in Hawaii is
                       using AI-generated newscasters to create video news
                       segments against the wishes of its unionized
                       journalists, who say the newspaper’s owners are
                       replacing journalists with AI and described the
                       practice as “digital colonialism.”


                # ⚓ JURIST ☛ Journalists_file_complaint_with_Germany
                  constitutional_court_over_phone_wiretapping⠀⇛


                       The three associations that filed the complaint are
                       the Bavarian Journalists Association (BJV),
                       Reporters Without Borders (RSF) and the Society for
                       Civil Rights (GFF). They claimed that investigators
                       illegally listened to phone conversations between
                       journalists and members of the group the Last
                       Generation (Letzte Generation). They argued that
                       this measure constituted a violation of press
                       freedom and a threat to democracy. The Last
                       Generation is a group of climate activists who use
                       direct action methods such as traffic blockades and
                       vandalism of buildings, private boats and planes to
                       protest against and raise awareness of climate
                       change.


                # ⚓ Hong Kong Free Press ☛ 23_countries_express_concern_over
                  sedition_ruling_against_HK_journalists⠀⇛


                       Members of the Media Freedom Coalition (MFC) in a
                       statement on Monday said they were “gravely
                       concerned” about the court verdict and “the wider
                       suppression of media freedom” in Hong Kong. Among
                       the 23 signatories were the UK, the US, Australia,
                       Canada, Japan, and Ireland.


                # ⚓ The Guardian UK ☛ UK_counter-terror_police_drafted_in_after
                  Telegraph_journalist_dies_in_Gibraltar⠀⇛


                       David Knowles died while on holiday on Sunday after
                       what his employers said was believed to be a
                       cardiac arrest.


                       The audio journalist, 32, had joined the Telegraph
                       in 2020 and was behind its Ukraine: The Latest
                       podcast.


                # ⚓ Press Gazette ☛ Police_probe_sudden_death_of_Telegraph's
                  David_Knowles⠀⇛


                       Royal Gibraltar Police said on Thursday it is
                       “investigating the circumstances surrounding the
                       sudden death” of Knowles although it added that
                       “there are no specific concerns at this time with
                       regard to the death”.


                # ⚓ The Telegraph UK ☛ David_Knowles,_broadcaster_who_helped
                  make_Telegraph’s_Ukraine_podcast_a_runaway_success_–
                  obituary⠀⇛


                       He ‘asked relevant and sensible questions, never
                       seeking a performative edge to his journalism. The
                       story and the guest took centre stage’


                # ⚓ CPJ ☛ Turkmen_journalist_Ruslan_Myatiev_banned_from
                  entering_Turkey⠀⇛


                       “Journalist Ruslan Myatiev’s account that Turkey
                       acceded to Turkmenistan’s request to ban him is a
                       startling suggestion of Turkey’s complicity in
                       transnational repression with one of the world’s
                       worst press freedom violators,” said Gulnoza Said,
                       CPJ’s Europe and Central Asia program coordinator.
                       “Turkish authorities should revoke the travel ban
                       against Myatiev, and Turkmenistan must stop
                       retaliating against exile-based journalists.”


                # ⚓ teleSUR ☛ Journalists_Seek_Asylum_in_Canada_After_Threats
                  to_Their_Lives_in_Ecuador⠀⇛


                       Journalists Andersson Boscan and Monica Velasquez,
                       who work for the digital media outlet La Posta,
                       have sought asylum in Canada, claiming their lives
                       are in danger in Ecuador due to death threats and
                       plans to murder them orchestrated by “corrupt
                       police officers.”


          o § Civil Rights/Policing⠀➾


                # ⚓ New York Times ☛ Guards_Say_Top_Adams_Aide,_Timothy
                  Pearson,_Threatened_Them_After_Having_Them_Arrested⠀⇛


                       Two security guards said the aide, Timothy Pearson,
                       attacked them then had them arrested. Federal
                       agents seized his cellphone last week as part of a
                       separate investigation.


                # ⚓ Site36 ☛ Demand_for_EU_directive_for_refugees:_15_German
                  organisations_criticise_persecution_as_“smugglers”⠀⇛


                       Human rights organisations are calling on the
                       German government to take a stand against the
                       criminalisation of refugees and solidarity in
                       Europe.


                # ⚓ Site36 ☛ Government_plans:_German_police_should_get_green
                  light_for_facial_and_voice_recognition_on_the_internet⠀⇛


                       The German coalition government wants to extend the
                       surveillance rights of the police to include facial
                       and voice recognition on the internet in a fast-
                       track procedure. This should enable networks of
                       suspects to be revealed more quickly. The planned
                       expansion of police surveillance powers in Germany
                       goes far beyond the facial recognition discussed so
                       far.


                # ⚓ ACM ☛ The_Moral_Implications_of_Being_a_Moderately
                  Successful_Computer_Scientist_and_a_Woman⠀⇛


                       It is difficult to even discuss these issues
                       because both sides are not using the same framework
                       of what is acceptable “moral” behavior and what is
                       not. Just like in distributed systems, we can’t
                       make progress on this topic when there is
                       disagreement on the underlying system model. These
                       beliefs are so deeply held that, consciously or
                       not, when people meet someone who challenges their
                       beliefs, the cognitive dissonance can cause them to
                       do something truly harmful. For example, my very
                       existence as a moderately young, moderately
                       successful computer scientist threatens some men’s
                       sense of identity, thus making them uncomfortable
                       and/or lash out. But if a successful woman in
                       computer science makes men in our community
                       uncomfortable, then we are not likely to have too
                       many successful women in the community.


                       In this blog post, I will attempt to describe the
                       system within which I exist as a moderately
                       successful computer scientist and woman. I will
                       highlight the fallacies that lead to women (1)
                       leaving tech, (2) generally being anxious in our
                       society, and (3) experiencing horrific harassment
                       and misogyny.


                # ⚓ US Navy Times ☛ Navy_to_commission_first_sub_designed_for
                  both_men_and_women_sailors⠀⇛


                       Female officers did not join the submarine force
                       until 2011, and such roles only opened up to
                       enlisted sailors in 2015.


                # ⚓ Hamilton Nolan ☛ Listen:_Republicans_Do_Not_Want_Unions_to
                  Exist⠀⇛


                       If there were a button that you could push that
                       would eliminate the existence of every labor union
                       in America, the Republican Party would push that
                       button. If it were possible to pass a bill that
                       outlawed labor union membership in America, and if
                       it were possible to pass that bill without a
                       political backlash that might cause them to lose
                       their next election, virtually every state and
                       federal Republican politician of note would vote
                       for it. I feel the need to make sure that anyone
                       who reads this publication understands this fact.
                       It’s hard to get a good grasp on “labor and
                       politics in America” without this baseline
                       understanding.


                # ⚓ The Washington Post ☛ Afghan_women_continue_medical_school
                  in_Scotland_after_Taliban_ban⠀⇛


                       The Linda Norgrove Foundation was founded by Lorna
                       and John Norgrove and named after their daughter,
                       an aid worker who was kidnapped in Afghanistan and
                       killed in a rescue attempt in 2010. The
                       organization had previously sponsored roughly 100
                       scholarships for women studying in Afghan
                       universities, including Hussaini, when the Taliban
                       took over the country.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ IODA:_Internet_Outage_Detection_and_Analysis⠀⇛


                       Guest Post: A scalable and reliable system for
                       detecting Internet outages in as near to real-time
                       as possible.


      § Monopolies/Monopsonies⠀➾


          o ⚓ JURIST ☛ ECJ_ruling_upholds_€2.4B_fine_against_Surveillance_Giant
            Google_and_orders_Fashion_Company_Apple_to_pay_€13B_in_tax⠀⇛


                 The European Court of Justice (ECJ) issued two rulings on
                 Tuesday, imposing a €2.4 billion fine on Surveillance
                 Giant Google for abuse of its dominant market position
                 and ordering Fashion Company Apple to repay Ireland €13
                 billion in tax.


          o ⚓ The Register UK ☛ Musk's_Starlink_dominance_sparks_FCC
            competition_concerns⠀⇛


                 When Elon Musk's Starlink hit its 7,000th broadband
                 satellite milestone, it's unlikely he expected the FCC
                 chair to suggest his space dominance might be stifling
                 competition—but here we are.


                 Speaking at the US Chamber of Commerce's annual Global
                 Aerospace Summit, FCC chair Jessica Rosenworcel expressed
                 a desire to encourage competition in the burgeoning
                 commercial space industry. She didn't name any names, but
                 her message was clear.


          o ⚓ India Times ☛ Ex-Google_executive_said_goal_was_to_'crush'
            competition,_trial_evidence_shows⠀⇛


                 A Google executive told colleagues the goal for the
                 company's then-nascent online advertising business in
                 2009 was to "crush" rival advertising networks, according
                 to evidence prosecutors presented at the tech titan's
                 antitrust trial on Wednesday.


                 The statements underscored the US Department of Justice's
                 claim that Google has sought to monopolize markets for
                 publisher ad servers and advertiser ad networks, and
                 tried to dominate the market for ad exchanges which sit
                 in the middle.


          o ⚓ Jacobin Magazine ☛ Big_Tech_Is_Lobbying_to_Keep_Its_Stranglehold
            on_Local_News⠀⇛


                 California legislators were considering bills that would
                 have forced Google, Meta, and other tech firms to pay
                 ongoing fees for earning billions from using news
                 outlets’ content. Big Tech’s lobbying and strong-arm
                 tactics helped kill the legislation.


          o § Patents⠀➾


                # ⚓ JUVE ☛ What_associates_earn_in_German_patent_monopoly
                  litigation_practices [Ed: Parasites preying on actual
                  scientists]⠀⇛


                       In the battle for the most talented lawyers with an
                       interest in patent monopoly litigation, the
                       absolute top offer comes from Quinn Emmanuel with a
                       starting salary of €175,000 plus bonus.


                # ⚓ Atlantic Council ☛ Mexico’s_new_judicial_reforms_could_put
                  the_USMCA_on_shaky_ground⠀⇛


                       All eyes were on Mexico’s Senate as it voted early
                       on Wednesday on an eighteen-point judicial reform
                       package, which passed 86-41. While the last major
                       legislative hurdle has been cleared, the
                       constitutional changes that come next will likely
                       be front and center for US legislators, who will
                       soon begin their review of the United States-
                       Mexico-Canada Agreement (USMCA) ahead of the trade
                       deal’s six-year mark on July 1, 2026.


          o § Trademarks⠀➾


                # ⚓ The Register UK ☛ Google_sued_for_using_trademarked_Gemini
                  name_for_AI_service⠀⇛


                       Google renamed its generative AI service from Bard
                       to Gemini in February, after introducing its Gemini
                       model family in December 2023. But the Chocolate
                       Factory did so without evident concern that the
                       name was already in use as an AI brand.


                # § Right of Publicity⠀➾


                      # ⚓ Scoop News Group ☛ Taylor_Swift_calls_out_AI
                        deepfakes_in_Harris_endorsement⠀⇛


                             “Recently I was made aware that AI of ‘me’
                             falsely endorsing Donald Trump’s presidential
                             run was posted to his site,” Swift wrote in
                             an Instagram post officially endorsing
                             Harris. “It really conjured up my fears
                             around AI, and the dangers of spreading
                             misinformation.”


                      # ⚓ Techdirt ☛ Taylor_Swift_Responded_To_Trump’s_AI
                        Driven_Nonsense_With_An_Endorsement_Rather_Than_A
                        Lawsuit⠀⇛


                             Now, the focus of this post is not that Trump
                             is the Big Bad, or to suggest that anyone
                             view Swift’s endorsement as a gospel they
                             themselves must follow. Instead, the point is
                             the one we made originally: no lawsuit was
                             needed for Swift to address this. As we said:
                             “she can solve [this] with more speech: her
                             own.” That lines up fairly well with Swift’s
                             statement: “The simplest way to combat
                             misinformation is with the truth.”


          o § Copyrights⠀➾


                # ⚓ The Guardian UK ☛ Wikipedia_is_facing_an_existential
                  crisis._Can_gen_Z_save_it?⠀⇛


                       And therein lies the problem: as Wikipedia’s
                       visibility diminishes, reduced to mere training
                       data for AI applications, it also loses prominence
                       in the minds of readers and potential contributors.
                       When someone notices a topic that is poorly
                       described on Wikipedia, they might feel motivated
                       to correct it. But this can-do spirit goes away
                       when the error comes through an AI summary, where
                       the source of the information isn’t clear.


                # ⚓ MIT Technology Review ☛ Why_a_ruling_against_the_Internet
                  Archive_threatens_the_future_of_America’s_libraries⠀⇛


                       I was raised in the 1980s and ’90s, and for my
                       generation and generations before us, the public
                       library was an equalizing force in every town,
                       helping anyone move toward the American dream.


                # ⚓ Public Domain Review ☛ Gottfried_Mind,_The_Raphael_of
                  Cats⠀⇛


                       Labelled a “cretin” and “imbecile” in his lifetime,
                       the Swiss artist Gottfried Mind had profound
                       talents when it came to drafting the feline form.
                       Kirsten Tambling reconstructs the biography of this
                       elusive figure, whose savant-like qualities
                       inspired later French Realists, early psychiatric
                       theorists, and Romantic visions of the artist as
                       outsider.


                # ⚓ Torrent Freak ☛ ACE_Helps_Egypt_to_Dismantle_the_Region's
                  Largest_Piracy_Site⠀⇛


                       Anti-piracy coalition ACE reports that Egyptian law
                       enforcement authorities have shut down Laroza, the
                       'largest' pirate site in the Middle East and North
                       Africa. Two of the alleged operators were arrested.
                       The piracy ring operated dozens of domains and
                       generated millions of pageviews per month.


                # ⚓ Torrent Freak ☛ 'Parasitic'_IPTV_Piracy_is_Killing
                  Football,_"It's_Them_or_Us"_Says_Serie_A_CEO⠀⇛


                       Serie A CEO Luigi De Siervo's dramatic take on
                       Italian football's piracy problems isn't new,
                       likewise his insistence that only coercive action
                       will produce results. "Football is being killed,"
                       he said in a recent interview. "However, at the end
                       of this battle we will win. Because it's either
                       them or us." How this will be achieved isn't clear.
                       Pirates keep jumping to new servers and if promises
                       are kept, fans are getting sued next.





                    ䷩ 𝚕𝚒𝚗𝚎 8287

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 13/09/2024: Recorded Future Bought by
MasterCard, Bits of Freedom Turns 25⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Sep 13, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Monopolies/Monopsonies
                # Trademarks
                # Copyrights
    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ University of Michigan ☛ $3.1M_grant_to_aid_research_on
                  high_school_career_development⠀⇛


                       With a new $3. 1 million grant from the Institute
                       of Education Sciences, a U-M researcher and his
                       colleagues are exploring approaches to career
                       development.


                # ⚓ New York Times ☛ Polaris_Dawn_Astronauts_in_SpaceX_Dragon
                  Reach_Record_Orbit_Above_Earth⠀⇛


                       After launching early on Tuesday, the billionaire
                       Jared Isaacman and his crew traveled to altitudes
                       not visited by any astronaut since the Apollo moon
                       missions of the 1960s and ’70s.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ IBM’s_1969_Educational_Computing⠀⇛


                       IBM got their PCs and PS/2 computers into schools
                       in the 1980s and 1990s. We fondly remember
                       educational games like Super Solvers: Treasure
                       Mountain. However, IBM had been trying to get into
                       the educational market long before the PC. In 1969,
                       the IBM Schools Computer System Unit was developed.
                       Though it never reached commercial release, ten
                       were made, and they were deployed to pilot schools.
                       One remained in use for almost a decade! And now,
                       there’s a new one — well, a replica of IBM’s
                       experimental school computer by [Menadue], at
                       least. You can check it out in the video below.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ BIA Net ☛ Sixty-six_children_killed_while_working_in_a
                  school_year_in_Turkey⠀⇛


                       As the new school year begins, the Health and
                       Safety Labor Watch released statistics on child
                       labor fatalities from the previous school year.


                # ⚓ New York Times ☛ Cholera_Deaths_Soar_Worldwide_Despite
                  Being_Easily_Preventable⠀⇛


                       Fatalities spiked 71 percent last year, far
                       outpacing the 13 percent rise in cases, the World
                       Health Organization said.


                # ⚓ New York Times ☛ U.K.’s_Revered_NHS_Is_in_Deep_Trouble,
                  Darzi_Report_Finds⠀⇛


                       A government-commissioned review into the National
                       Health Service laid bare the challenge Prime
                       Minister Keir Starmer faces after years of
                       underinvestment.


                # ⚓ TwinCities Pioneer Press ☛ US_uninsured_rate_was_stable_in
                  2023,_even_as_states’_Medicaid_purge_began⠀⇛


                       Enrollment in Medicaid, the government health
                       program for people with low incomes and
                       disabilities, reached its highest level in April
                       2023.


                # ⚓ Hong Kong Free Press ☛ Hong_Kong_customs_arrest_2_directors
                  of_gym_chain_Physical_after_authorities_receive_more_than
                  2,600_complaints⠀⇛


                       Hong Kong customs officers have arrested two
                       directors of the gym chain Physical Fitness after
                       the company abruptly closed last week, as law
                       enforcement authorities and the city’s consumer
                       watchdog racked up some 2,600 reports.


                # ⚓ France24 ☛ Frenchman_in_mass_rape_trial_again_excused_from
                  testifying_due_to_ill_health⠀⇛


                       Dominique Pelicot, the Frenchman on trial for
                       enlisting dozens of strangers to rape his wife
                       Gisele after he drugged her into unconsciousness
                       over a period, was on Wednesday excused a second
                       time from attending a hearing due to ill health,
                       the presiding judge said. If his condition
                       improves, Pelicot could be summoned to speak on
                       Thursday afternoon in connection with the case of
                       one of his co-defendants, identified as Jean-Pierre
                       M.


                # ⚓ Hong Kong Free Press ☛ Sharp_rise_in_suicide_rates_among
                  teen_girls_in_Hong_Kong,_study_finds⠀⇛


                       Hong Kong has seen a sharp rise in suicide rates
                       among teen girls, a study has found, with
                       researchers citing the Covid-19 pandemic’s effect
                       on mental health.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ AccessNow ☛ Why_we_need_tailored_identity_systems_for
                        our_digital_world⠀⇛


                             Digital identity systems are no silver bullet
                             for social challenges.


                      # ⚓ AccessNow ☛ Encryption_FAQ:_encrypted_messaging,_AI,
                        content_moderation,_and_more⠀⇛


                             Encryption is increasingly in the news,
                             whether it’s governments seeking access to
                             encrypted messages, or the CEO of an
                             encrypted messaging platform getting
                             arrested.


                      # ⚓ Silicon Angle ☛ Meta_confirms_it_scrapes_Australian
                        users’_posts_for_Hey_Hi_(AI)_training_without_opt-out
                        option⠀⇛


                             Meta Platforms Inc. is scraping Australian
                             users’ Facebook (Farcebook) and Instagram
                             posts without providing an opt-out option,
                             the company acknowledged today. Melinda
                             Claybaugh, Meta’s global privacy director,
                             detailed the practice during a hearing before
                             the Australian Senate.


          o § Defence/Aggression⠀➾


                # ⚓ Off Guardian ☛ Remember_when_Matt_Taibbi_Called_9/11
                  Truthers_“Hopelessly_Stupid”?⠀⇛


                       I came out as a truther in 2015 with my 9/11
                       novel, Locus Amoenus. It wasn’t an easy decision. I
                       anticipated being called “clinically insane,” a
                       “dickwad,” promoting “rank steaming bullshit” by
                       the likes of Matt Taibbi. Among other notable left-
                       leaning 9/11 truth debunkers, such as Chris Hayes
                       and Noam Chomsky, Taibbi stands out...


                # ⚓ New York Times ☛ Family_of_American_Woman_Held_in_China_for
                  10_Years_Asks_for_Help⠀⇛


                       Dawn Michelle Hunt, who is serving a life sentence,
                       says she was duped into carrying drugs. Her family
                       says she is seriously ill and should be sent home.


                # ⚓ The Straits Times ☛ China's_Li,_Saudi_crown_prince_discuss
                  cooperation_in_Riyadh,_meeting⠀⇛


                       BEIJING/DUBAI - Chinese Premier Li Qiang and Saudi
                       Crown Prince Mohammed Bin Salman discussed
                       cooperation in several sectors including energy,
                       investment and trade in a meeting in Riyadh on
                       Wednesday, the Saudi state news agency SPA
                       reported.


                # ⚓ RFA ☛ US_ELECTIONS_2024:_Trump,_Harris_trade_barbs_over
                  China_in_presidential_debate⠀⇛


                       Trump insisted dictators saw him as a strongman,
                       while Harris said U.S. military leaders called him
                       a ‘disgrace.’


                # ⚓ France24 ☛ Israeli_airstrikes_hit_UN_school_and_homes_in
                  Gaza,_killing_dozens⠀⇛


                       Israeli airstrikes across Gaza on Wednesday hit a
                       UN school sheltering displaced Palestinian families
                       as well as two homes, killing at least 34 people,
                       including 19 women and children, hospital officials
                       said. In the occupied West Bank, an Israeli soldier
                       was killed Wednesday when the driver of "a
                       Palestinian truck" rammed into "forces conducting
                       operational activity", said the Israeli soldier.


                # ⚓ France24 ☛ Israeli_air_strikes_on_occupied_West_Bank_kill
                  at_least_five_Palestinians⠀⇛


                       At least five Palestinians were killed in Israeli
                       strikes in the occupied West Bank on Wednesday,
                       according to the Palestinian Red Crescent Society.
                       The Israeli military, which did not provide a death
                       toll, said that its forces were "currently
                       conducting counterterrorism activity in the area of
                       Tubas and Tamun" and that one of its aircraft
                       "struck an armed terrorist cell" during an
                       operation in Tubas in the northern West Bank.


                # ⚓ New York Times ☛ Middle_East_Crisis:_Israeli_Airstrikes_Hit
                  School_Complex_Housing_Displaced_in_Gaza,_Killing_18⠀⇛


                       Six U.N. employees were among those killed in the
                       strikes at a school turned shelter in Nuseirat,
                       U.N. officials said. The Israeli military said
                       Hamas fighters were using the school to carry out
                       attacks.


                # ⚓ New York Times ☛ 2,000-Pound_Bombs_Likely_Used_in_Al-Mawasi
                  Strike⠀⇛


                       The large size of the two craters left in the
                       aftermath of the attack suggest that Israel used
                       the powerful bombs, according to experts and a New
                       York Times analysis.


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


                      # ⚓ RFERL ☛ More_Belarusians_Go_On_Trial_Over_2020_Anti-
                        Lukashenka_Rallies⠀⇛


                             A court in the Belarusian city of Brest on
                             September 11 began the trial of seven men
                             charged with "taking part in mass unrest" for
                             their participation in rallies in 2020 over
                             the official results of the presidential poll
                             that pronounced authoritarian ruler
                             Alyaksandr Lukashenka as the winner.


                      # ⚓ RFERL ☛ Jailed_Belarusian_Activist_Charged_With
                        Disobeying_Prison_Guards⠀⇛


                             The Vyasna human rights center said on
                             September 11 that political prisoner Andrey
                             Buday, who is serving a 15-year prison term
                             on terrorism charges that he and his
                             supporters reject, has been charged with
                             "blatantly disobeying prison guards' orders."


                      # ⚓ RFERL ☛ Belgrade_Court_Annuls_Decision_To_Extradite
                        Belarusian_Activist,_But_Orders_Case_To_Be_Retried⠀⇛


                             An appeals court in Belgrade has annulled the
                             decision to extradite Belarusian journalist
                             and political activist Andrey Hnyot to
                             Belarus, but the court said the case must be
                             retried.


                      # ⚓ RFERL ☛ Bashkir_Activist_Flees_To_U.S._Via_Mexico
                        Fearing_Arrest⠀⇛


                             Bashkir activist Zagir Mukhamedyarov has fled
                             Russia and entered the United States via
                             Mexico fearing arrest.


                      # ⚓ RFERL ☛ Soyuz_Craft_Heads_To_ISS_With_2_Russians,_1
                        American⠀⇛


                             A Soyuz spacecraft carrying two Russians and
                             an American blasted off on September 11 for
                             an express trip to the International Space
                             Station.


                      # ⚓ RFA ☛ Does_a_video_show_a_US_F-16_fighter_jet_being
                        shot_down_by_Russians?⠀⇛


                             Verdict: False


                      # ⚓ LRT ☛ Lithuania_calls_for_swifter_air_policing
                        response_after_Russia_drone_crash_in_Latvia⠀⇛


                             Lithuanian Defence Minister Laurynas
                             Kasčiūnas has called for a change in the
                             algorithm of NATO’s Air Policing mission in
                             the Baltic states following the recent crash
                             of a Russian military drone in Latvia.


                      # ⚓ LRT ☛ Cargo_ship_carrying_chemicals_from_Russia_seeks
                        repairs_in_Lithuania’s_Klaipėda⠀⇛


                             The captain of Ruby, currently moored off the
                             coast of Norway and carrying about 20,000
                             tonnes of ammonium nitrate, would like to
                             carry out repairs on his cargo ship in
                             Lithuania’s Klaipėda Port.


                      # ⚓ Latvia ☛ Latvian_Saeima_plans_stricter_rules_on
                        workplace_language_requirements⠀⇛


                             The Social and Labor Affairs Committee of the
                             Saeima has finalized amendments to the Labor
                             Law and will direct them to the Saeima. The
                             amendments aim to strengthen the role of
                             Latvian language and minimize requirements
                             for Russian in employment, Latvian Television
                             reported on September 10.


                      # ⚓ Latvia ☛ Russian_stand-up_gets_mic_drop_from_Latvia⠀⇛


                             Latvia's list of people deemed personae non
                             grata got slightly longer September 11 with
                             the inclusion of a Russian stand-up comedian.


                      # ⚓ Latvia ☛ Town_twinning_with_Russia,_Belarus_could_be
                        banned_by_law_in_Latvia⠀⇛


                             At present, there is no information that any
                             municipality in Latvia still has a twinning
                             agreement with a local authority in Russia or
                             Belarus, but to avoid issues in the future, a
                             law could be passed, Latvian Radio reported
                             on September 11.


                      # ⚓ New York Times ☛ North_Korean_Missiles_Rain_Down_on
                        Ukraine_Despite_Sanctions⠀⇛


                             Russia has received new shipments of Hwasong-
                             11 short-range ballistic missiles, according
                             to a new report.


                      # ⚓ New York Times ☛ Blinken_Visits_Kyiv_During
                        Precarious_Moment_in_Ukraine_War_and_U.S._Politics⠀⇛


                             Secretary of State Antony J. Blinken and his
                             British counterpart, David Lammy, made a rare
                             joint trip to Ukraine to show allied
                             solidarity as the American presidential
                             election looms.


                      # ⚓ RFERL ☛ Russian_Freight_Train_Derails_In_Region_Near
                        Ukraine_Border⠀⇛


                             A freight train derailed in Russia’s Belgorod
                             region, near the border with Ukraine, due to
                             what the rail operator said was an
                             “interference in operations.”


                      # ⚓ Latvia ☛ Just_under_50,000_Ukrainians_have_found
                        protection_in_Latvia⠀⇛


                             Latest figures from Eurostat show that there
                             were 46,000 Ukrainian refugees registered in
                             Latvia in July, finding protection here from
                             Russia's war of aggression.


                      # ⚓ Latvia ☛ Latvian_PM_announces_40_million_euro_aid
                        package_in_Kyiv⠀⇛


                             Latvia's third military aid package to
                             Ukraine this year will be worth around EUR 40
                             million, Prime Minister Evika
                             Siliņa announced during her visit to the
                             capital of Ukraine, Kyiv, on September 11.


                      # ⚓ European Commission ☛ Statement_by_President_von_der
                        Leyen_on_the_occasion_of_the_4th_Crimea_platform
                        Summit,_via_video_message⠀⇛


                             European Commission Statement Brussels, 11
                             Sep 2024 Dear President Zelenskyy, dear
                             Volodymyr,


                             It has been ten years since Russia began its
                             aggression against Ukraine.


                      # ⚓ RFERL ☛ Another_Ex-Wagner_Mercenary_Recruited_From
                        Russian_Prison_Sentenced_For_Murder⠀⇛


                             A court in Russia's southwestern region of
                             Volgograd on September 11 sentenced a former
                             Wagner mercenary group fighter to eight years
                             in prison for beating his wife to death.


          o § Environment⠀➾


                # § Wildlife/Nature⠀➾


                      # ⚓ Mexico News Daily ☛ ‘Tony’_the_tiger_captured_5_days
                        after_escape_from_Reynosa_zoo⠀⇛


                             The tiger was found in good health and will
                             be transferred to the Tamatán Zoo in Ciudad
                             Victoria, Tamaulipas.


                      # ⚓ New York Times ☛ 4_Climbers_Are_Found_Dead_on_Mont
                        Blanc_in_the_French_Alps⠀⇛


                             The climbers from Italy and South Korea were
                             found on Tuesday after they went missing
                             three days earlier during a period of bad
                             weather on the peak.


          o § Finance⠀➾


                # ⚓ Boston Globe ☛ Recorded_Future_bought_by_MasterCard_for
                  $2.65_billion⠀⇛


                       Recorded Future specializes in real-time tracking
                       of cybersecurity threats and hazards worldwide. It
                       will now have a particular eye on financial
                       institutions and transactions.


                # ⚓ The Business Journals ☛ Mastercard_to_acquire_Somerville
                  cybersecurity_firm_for_$2.65B⠀⇛


                       Credit-card company Mastercard Inc. (NYSE: MA)
                       signed a deal Thursday to buy Somerville-based
                       Recorded Future from New York-based Insight
                       Partners. The deal is expected to close by the
                       first quarter of 2025.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ RFA ☛ EXPLAINED:_Why_are_there_questions_about_foreign
                  judges_in_Hong_Kong’s_high_court?⠀⇛


                       Debate persists whether judges uphold rule of law
                       or legitimize a regime that no longer respects
                       rights.


                # ⚓ RFA ☛ INTERVIEW:_Hong_Kong_pro-democracy_councilor_finds
                  renewed_purpose_in_exile.⠀⇛


                       'We have to learn how to master that fear,' says
                       Carmen Lau.


          o § Censorship/Free Speech⠀➾


                # ⚓ EDRI ☛ Denmark_will_issue_removal_orders_without_court
                  approval:_Impacts_on_free_speech_and_pro-Palestinian_voices⠀⇛


                       Removal orders in the Terrorist Content Online
                       (TCO) Regulation currently require prior court
                       authorisation in Denmark, but this will soon change
                       as a consequence of a political agreement to
                       strengthen the fight against antisemitism. Together
                       with a broadened definition of antisemitism
                       focusing on the State of Israel, the already highly
                       problematic TCO Regulation could be further
                       leveraged by Danish authorities for arbitrary
                       censorship of pro-Palestinian voices on social
                       control media.


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


                # ⚓ France24 ☛ Mali_junta_suspends_French-language_channel_TV5
                  Monde_for_lack_of_'balance'⠀⇛


                       Mali's junta leaders suspended the French-language
                       channel TV5 Monde for three, allegedly for a lack
                       of "balance" in covering civilian drone strike
                       deaths without providing the Malian army's version
                       of events.


          o § Civil Rights/Policing⠀➾


                # ⚓ JURIST ☛ South_Korea_Truth_Commission_releases_further
                  findings_on_1980s_shelter_abuses_and_‘forced_adoptions’⠀⇛


                       South Korea’s truth commission announced further
                       findings this Monday on human rights violations in
                       the country’s adult homeless detention facilities,
                       including the Seoul Metropolitan Rehabilitation
                       Center in the 1980s.


                # ⚓ EDRI ☛ Mass_hacking_and_fundamental_rights:_a_missed
                  opportunity_for_the_Court_of_Justice_of_the_Euorpean_Union?⠀⇛


                       On 30 April 2024, the Court of Justice of the
                       European Union (CJEU) published its decision in the
                       ‘EncroChat’ case. The case emerged from recent
                       European police cooperation operations against
                       organised crime, involving the mass interception of
                       encrypted communications by means of spyware
                       (‘hacking’).


                # ⚓ New York Times ☛ Defying_Protests,_Mexico’s_Senate_Approves
                  Judicial_Overhaul⠀⇛


                       The chamber’s approval clears away the last major
                       hindrance to the sweeping proposals championed by
                       the president, which have prompted nationwide
                       strikes.


                # ⚓ EDRI ☛ EDRi-gram,_11_September_2024⠀⇛


                       With the post-election shake-up and the upcoming
                       appointment of new European Commissioners, both
                       governments and tech giants are making moves that
                       could threaten our rights.


                       In Denmark, efforts to broaden the definition of
                       antisemitism, including criticism of the Israeli
                       state, may lead to the misuse of the Terrorist
                       Content Online Regulation to silence pro-
                       Palestinian voices. In France, legal action against
                       Telegram’s co-founder has intensified calls for
                       stricter enforcement of the Digital Services Act.
                       At the EU level, we’ve seen a troubling decision by
                       the European Commission to cut funding for free
                       software projects.


                # ⚓ EDRI ☛ Prioritising_planet_care:_A_vision_for_our_digital
                  future⠀⇛


                       Together, we can protect human rights, strengthen
                       democracy, and reshape societal systems. Read about
                       our commitment to empowering people to flourish and
                       thrive, as part of our Vision for 2024 and beyond.


                # ⚓ EDRI ☛ Celebrating_25_years_of_Bits_of_Freedom!⠀⇛


                       In 2024, EDRi member Bits of Freedom celebrates its
                       25th anniversary. For a quarter of a century it has
                       been their mission to shape internet policy in
                       support of an open and just society. One in which
                       people can hold those in power accountable and
                       effectively question the status quo. Bits of
                       Freedom does this through advocacy, campaigning and
                       litigation, in the Netherlands and Brussels. Time
                       to look back: what are the highlights of the past
                       25 years?


      § Monopolies/Monopsonies⠀➾


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ TTABlog_Test:_Is_LEATHER_MAN_LTD_&_Design
                  Deceptive_for_Belts_Not_Made_of_Leather?⠀⇛


                       Invoking Section 2(a) of the Trademark Act, the
                       USPTO refused to register the mark shown below,
                       finding it deceptive for the following goods not
                       comprised of leather: Belts; Belts for clothing;
                       Belts made out of cloth; Belts of textile; Fabric
                       belts; Waist belts. Applicant argued that the words
                       "LEATHER_MAN" would be perceived as referring to
                       the “old Leather [M]an, … a vagabond [who] was
                       famous for the leather suit of clothes he wore.” At
                       the end of the 19th Century, the Leather Man
                       meandered around the Essex, Connecticut area,
                       "where he would have food and necessities ready for
                       him upon his arrival." How do you think this appeal
                       came out? In_re_Brockway_Ferry_Corp_DBA_Leather_Man
                       Ltd., Serial No. 90127025 (September 3, 2024) [not
                       precedential] (Opinion by Judge Angela Lykos).


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ Bad_Bunny_Secures_Latest_Role_in
                  Netflix-Led_Happy_Gilmore_Sequel⠀⇛


                       Bad Bunny secures his latest acting role, joining
                       Adam Sandler in the Netflix-led ‘Happy Gilmore’
                       sequel. Benito Antonio Martinez Ocasió, better
                       known by his stage name, Bad Bunny, has landed his
                       latest acting role as he joins the cast of Adam
                       Sandler’s ‘Happy Gilmore’ sequel.




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