𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, June 23, 2022
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Generated Fri 24 Jun 02:39:44 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
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Gemini index for the day: gemini://gemini.techrights.org/2022/06/23/


╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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QmXFr24fsod4hN7dFFg3cke2MTRCdpmXGmrzBy4E9SuDmx


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

⦿ [Meme] Council Says... | Techrights

⦿ EPO Management Behaves As If the Goal is to Shut Down and Outsource the Patent Office, Making a ’Monopolies Bank’ Instead... or Having Rubber-Stamping With Kangaroo Courts Override the European Patent Convention (EPC) | Techrights

⦿ IRC Proceedings: Wednesday, June 22, 2022 | Techrights

⦿ The EPO is Ceasing to Be a Patent Office | Techrights

⦿ [Meme] Granting Patents Like Mad is Not Productivity (It’s Also Illegal) | Techrights

⦿ EPO Staff Survey’s Preliminary Results Published (Almost 2,000 Staff Surveyed), António Campinos Less Trustworthy Than Benoît Battistelli at Similar Points in Their Terms | Techrights

⦿ Selected Slides From Technologia’s EPO Staff Survey (2022 Compared to Prior Years) | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/06/23/epo-admin-council-says/#comments
		http://techrights.org/2022/06/23/epo-hot-desking/#comments
		http://techrights.org/2022/06/23/irc-log-220622/#comments
		http://techrights.org/2022/06/23/not-a-patent-office-anymore/#comments
		http://techrights.org/2022/06/23/sobbing-tony/#comments
		http://techrights.org/2022/06/23/staff-survey-of-the-epo-is-out/#comments
		http://techrights.org/2022/06/23/technologia-slides/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/06/23/beta-for-krita-5-1/#comments
		http://techrights.org/2022/06/23/easyos-update-process/#comments
		http://techrights.org/2022/06/23/gemini-on-esp32/#comments
		http://techrights.org/2022/06/23/lf-fluff/#comments
		http://techrights.org/2022/06/23/tails-5-1-1/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 69

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/23/epo-admin-council-says/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/23/epo-admin-council-says/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Council_Says…⠀✐


Posted in Europe, Patents at 8:29 pm by Dr. Roy Schestowitz


  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Steve Harvey: We changed the face, but all the same EPO
                               issues remained⦈
 “Insanity is doing the same thing over and over again and expecting different
                 results.” — not patent clerk Albert Einstein


Summary: The Administrative_Council of the EPO must be kidding itself if it
thought replacing Benoît_Battistelli with his friend António_Campinos (and his
unqualified or unsuitably unqualified friends_from_Alicante) would set the EPO
on a route to improvement


⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣯⣽⣯⣽⣿⣿⡯⠉⣭⣿⣭⢹⡏⣿⡍⣿⣯⢹⣯⣽⣏⣽⢿⡝⣿⣿⢹⣿⣭⣉⣹⣿⣿⣽⡯⣿⣯⣿⣯⣿⣿⣿⣍⣿⣯⢫⣿⣯⣩⣿⣿⠉⠉⠉⠉⠉⠉⠉⣩⡉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢻⣿⠆⠀⣿⣟⣛⢸⡷⣿⣿⣿⣿⣸⣿⣿⣿⣿⢬⡅⣿⡷⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠶⡟⣿⡷⢸⣟⣿⢸⣿⣛⣻⣿⠶⠀⠀⠀⠀⠀⢀⣈⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠻⠿⠸⠿⠶⠀⠻⠿⠟⠸⠇⠿⠿⠟⠿⠿⠏⠿⠏⠿⠾⢇⠿⠷⡾⠿⢿⣻⣿⣿⣇⡸⠿⠿⠿⠿⠶⣁⠿⠇⠼⠏⠿⢞⠿⠿⠻⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣟⣭⣭⣽⣿⣿⣿⣛⡛⠻⢥⢍⢻⣿⣦⣴⣶⣾⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣠⣤⣤⣾⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⣿⠿⣷⣨⣿⣷⣌⣿⣿⣿⣿⣦⣀⢀⣀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⣉⣩⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠏⠛⠛⠛⣻⣿⣿⣿⡟⠁⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠰⣶⣶⣦⠄⠈⠹⡏⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣄⣠⣼⣿⡿⢿⣿⣏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⣷⣿⣿⣿⣿⣿⠶⠀⠃⣾⠁⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⠛⣿⣿⣿⣿⣦⣤⣄⠘⠃⠀⢀
⣤⡄⠀⠀⠀⣤⣶⣶⣦⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢿⣿⣿⣯⣭⣤⠆⠀⠀⠁⠀⡀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠻⠿⣿⣿⣿⣿⣿⣦⣀⣀⠘
⢿⣇⠀⠀⠀⠙⢿⣿⡇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣮⡉⠛⠉⠁⠀⠀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡛⣻⣿⣿⡟⠀
⠈⠻⢆⠀⠀⠀⠈⢿⣿⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⣷⣦⣴⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⣤⣶⣾⣧⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦⡀⠘⣿⣤⣶⡶⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠠⣿⣤⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⠘⣿⣷⣤⣿⡟⠟⠁⠀⠘⠛⠿⠿⠿⠿⠟
⠀⠀⠘⢿⣿⣧⡀⣀⡀⠀⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠈⣿⡿⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠐⢸⣿⣦⡀⠈⠻⣿⣷⣾⣇⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣷⣬⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢿⣿⣦⣤⣾⣟⠋⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠤⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⣻⠿⠏⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⡀⣀⢀⣀⣀⣈⢿⣏⡀⣿⣿⣿⣿⣿⣿⣋⣀⢀⣀⣀⡀⠀⣀⡀⢀⣀⢀⣀⣀⡀⣀⡀⢀⣀⡀⣀⡀⢀⣿⣿⣿⣿⣿⣇⠀⣀⡀⣀⢀⣀⣀⡀⣀⡀⠀⣀⣀⢀⣘⣆⣀⢀⣀⢀⣀⢀⡱⣀⢀⢀⣀⢀⣀⡀⠀
⠀⢸⣿⡗⣿⢸⡏⣿⢩⡄⣿⣷⣿⡟⣿⢸⣯⣿⡏⣿⣿⣿⣿⡅⠸⣿⡃⣿⣿⢸⣿⣿⡇⣿⡅⢸⣿⣭⣿⣿⣿⢹⣿⣿⣇⣿⣟⠺⣿⡃⣿⣿⣿⣿⡽⣯⣛⠀⣿⣿⢿⣯⣽⣿⣾⣿⣿⣿⢸⡇⣿⣿⢸⣯⢸⡟⣿⠀
⠀⠸⠿⠟⠻⠼⢧⠿⢸⡻⠿⠿⠿⠷⠿⠾⣿⠿⠇⠿⠿⠿⠿⠆⠸⠿⠿⠿⠿⠾⠿⠿⠇⠿⠆⠸⠿⠾⠿⠀⠻⠼⣿⣿⣯⡿⠿⠻⠿⠟⠿⠿⠻⠿⠾⠯⠿⠀⠿⠿⠿⠷⠾⠿⠟⢿⠿⠿⠿⠇⠿⠿⠸⠷⠼⠿⠿⠀
⠀⠀⠀⠀⢰⣤⣠⣿⣿⣿⣿⡿⡇⢀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 123

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/23/epo-hot-desking/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/23/epo-hot-desking/

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✐ EPO_Management_Behaves_As_If_the_Goal_is_to_Shut_Down_and_Outsource_the
Patent_Office,_Making_a_‘Monopolies_Bank’_Instead…_or_Having_Rubber-Stamping
With_Kangaroo_Courts_Override_the_European_Patent_Convention_(EPC)⠀✐


Posted in Europe, Patents at 10:48 am by Dr. Roy Schestowitz


Video_download_link | md5sum 7337ee218b827f2a1121a0103fb4f979
EPO Hates Its Workers
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/hot-desks-epo.webm


Summary: Flabbergasting strategy in Europe’s second-largest institution makes
one wonder if the goal is to drive out the workers or simply shut down the
workplace


The Central Staff Committee (CSC) of the EPO, or elected staff representatives
to put it all in more generic terms, is rightly concerned. For a little bit of
background see “Hot_desking_was_meant_to_save_us_all_time_and_money._It_hasn’t”
(Wired) and “The_hidden_hell_of_hot-desking_is_much_worse_than_you_think” (FT
behind paywall; EPO-bribed_publisher). There are more references in the
publication below, but one can get the gist of the issue…


Last night we published “At_the_EPO,_“Bringing_Teams_Together”_or_“New
Management_of_Office_Space”_is_Another_Step_Towards_EPO_Outsourcing“ and we
showed two internal publications. “According to our estimates, 33% of staff (at
best) may have a permanently allocated desk,” the LSCMN committee wrote this
week.


What on Earth is going on???


“Can’t examiners in Europe’s largest patent office expect and receive the very
basics?”So workers with 6-figure salaries… cannot have their own PC and chair?


People with several degrees and decades of experience in difficult disciplines?
They are hard to recruit and retain.


As explained in the video above, I’m speechless. I lack the words to express
how baffling this is. It just doesn’t. Make. Any. Sense. At all!


I’ve asked some people around for their thoughts about “hot-desking” or
“hoteling” (being a temporary guest in one’s ‘own’ compartment). In my personal
experience, when they dynamically allocate a desk at work it’s done for
practical reasons under very particular circumstances (like computer labs with
special equipment that’s scarce and very experience). Think about the sharing
of a 3-D printer for example… I don’t have experience with this except in
Computer Science labs, where engineering/programmable boards are made available
to students. In other situations it can be helpful for experiments and
simulations on computer clusters, e.g. overnight utilisation of untapped
computing resources. Otherwise idling…


“In my own experience, as a postgraduate student and then as a postdoc, we all
got individual desks.”But this is not what’s happening at the EPO. So again,
this does not make any sense at all. Not even remotely practical…


Can’t examiners in Europe’s largest patent office expect and receive the very
basics? In my own experience, as a postgraduate student and then as a postdoc,
we all got individual desks. The annunal payment was a lot lower (zero as a
student!) and back then the typical computers were a lot more expensive.


A Techrights associate told me that “it has been proven through multiple
studies to be both inefficient and demoralizing” to share desks. He said “it
really is intended to limit the employee’s ability to get work done and to mess
with their status…”


This whole arranagement “makes *everything* more difficult,” the associate
concluded, and “that is a primary goal.”


And “after desksharing of course comes mandatory carpooling,” said someone in
our IRC channel moments ago. “And that’s not the worst of it, they’re also
assigning seats in the cafeteria…”


“…at today’s EPO the staff got cynical about the so-called “New Ways of
Working” (or not getting work done; getting worked, instead).”Those who have
experience working on shared desks at work will never claim that it boosted
productivity. That’s not what it’s done for. When you get dynamically allocated
a desk you need to do a lot of adjustment each and every time (like chair) and
if the EPO’s management wants to implement this madness, that should make one
wonder what the true motivations are.


“I had that at one job, I was assigned a different desk and chair every 2
months,” one person recalls. “I think they do it so you get to know your
colleagues better but it could also be so you don’t form too strong a team or
clique… it’s definitely weird.”


Well, some cities do this (even Manchester does this), e.g. with council
housing, and they do this for that reason. But the EPO isn’t trying to reduce
crime, maybe it just hopes to make it harder to organise (as workers, as
colleagues). Both Benoît_Battistelli and António_Campinos are renowned or
notorious for union-busting ambitions.


In any event, at today’s EPO the staff got cynical about the so-called “New
Ways of Working” (or not getting work done; getting worked, instead).


Here is what the CSC told colleagues this week:


     Munich, 21/06/2022
     sc22080cp


     § What_is_wrong_with_hot-desking?⠀➾


     Dear Colleagues,


     Many staff members are now used to a certain amount of teleworking.
     Nevertheless, they also chose to work on the Office’s premises, which
     is a statutory right1 and remains the default. It is not a favour
     management would do you depending on “special circumstances”, as it
     sometimes would like you to believe.


     Therefore, staff are entitled to adequate working conditions on site.


     On the 1st of September 2022, the New Ways of Working will kick off
     with the management’s intention to introduce a feature that deeply
     changes work life: hot-desking2. Your staff representatives have not
     been involved at any stage so far and we have asked for urgent
     discussions (see the CSC open letter).


     The reflections below are based on what we have understood from
     meetings management held with some of you, putting the cart before
     the horse and making announcements before any discussions with the
     Staff Committee(s).


     What is hot-desking?
     Interestingly, the Cambridge dictionary defines it this way: a way of
     saving office space in which workers do not have their own desk and
     are only given a desk when they need it. Indeed, the idea behind this
     is not efficiency, well-being or sense of belonging as advertised to
     staff, but rather a means for the employer to make savings, and not
     only on office space. The New Ways of Working foresee that only
     employees working at leas t three days on site will be eligible for
     an assigned workplace.


     When will it enter into force?
     Staff is required to make up their mind concerning their preferred
     working pattern by the end of September and the final floor plans
     will be made immediately after. This is at least what management
     currently contemplates.


     ______
     1 See Article 55a(1) ServRegs: “Permanent employees in active
     employment shall normally perform their work on the Office’s
     premises.”
     2 Bookable hot-desking is sometimes referred to as hoteling.


     =====================================================================
     What is wrong with hot-desking?
     First of all, it is hard to think that hot-desking and reinforcement
     of the sense of belonging combine well together. With hot-desking,
     you basically belong nowhere. Every time you will need to come to the
     Office, you will have to book a workplace for the day via a booking
     tool. Departments and directorates will be allocated a number of
     floors that will form working “neighbourhoods”. This way, making the
     booking options limited.


     All personal belongings must be removed from your current office, No
     plants, family photos, no items displaying your individuality. Your
     allotted locker will soon be the last homely place on offer. You
     might quickly end up thinking you would rather stay at home since
     there is no point in finding yourself in this sterile co-working
     environment where you are never sure where and with whom you sit.
     Hot-desking simply sends the message that employees don’t matter.


     Inefficiency and waste of productive time:
     UK_statistics3 teach that a hot-desking organisation can spend the
     equivalent of two weeks each year looking for a desk, or an average
     of 18 minutes each day thrown into finding an appropriate workspace.
     We can therefore be sure that a lot of precious working time is going
     to go into desk chasing and this is totally counterproductive, to say
     the least. While a small company might find some benefit in hot-
     desking, for an organisation the size of the Office the
     disorganisation it provokes can rapidly turn into chaos. There is a
     major risk that the musical chair exercise may be quickly proven
     totally inefficient, and the conclusion be a waste of time, energy,
     and money, before we go back to square one. We can expect that
     instead of facilitating an agile workforce, to paraphrase management,
     this is going to seriously impact the productivity and further damage
     the trust in management.


     Has the EPO done any benchmarking on hot-desking? (How_Hot-Desking
     Will_Kill_Your_Company, Forbes, 2019)


     Previous negative experience with open space:
     As soon as the New Main in The Hague and its open spaces started to
     be occupied, complaints about noise pollution started pouring in.
     Many Team Managers (TMs) had a hard time mitigating and accommodating
     the needs of their team members. Ultimately, doors were placed at the
     entrance of these areas which is pretty ironic for an open space. It
     should serve as an indication of how the hot desking is likely to be
     welcome. EPO core tasks, along with many other jobs in the Office,
     require peace and quiet. When working less than three days per week
     on premises, you may have to sit in an open space or shared office,
     at least according to the current intention of management. The nature
     of many jobs forbids them to be carried out in open space. If your
     job requires confidentiality, high concentration or simply spending a
     lot of time in online meetings, it is not possible for you to sit in
     an open space.


     Absence of consideration for colleagues with special needs:
     So far, there is no confirmation that colleagues with special health
     conditions will receive a different treatment than the rest of staff.
     It often takes a very long time for these colleagues to find a
     balance and be able to work at the best of their capacity. It is not
     acceptable that they would all of a sudden be asked to blend into the
     crowd.


     The two points above alone indicate how the desk lottery is going to
     carry problematic situations which de facto will require extensive
     “exception” handling.
     ______
     3 See the publication UK office workers waste ‘almost two weeks’ a
     year finding somewhere to sit (bmmagazine.co.uk)


     =====================================================================
     Hindering collaboration instead of facilitating it:
     Each day, if you are a coach, a trainee or simply someone who needs
     to speak to a specific colleague or seek for a quick work tip, after
     you found your own spot, you are going to have to find your
     interlocutor’s. Playing hide and seek might be fun for a day, but
     people will quickly get tired. They are less likely to engage in in-
     person exchanges and keep it to phone, email or chat contact. They
     will have no interest in exchanging with the people around them as
     they will likely change regularly, making it more difficult to create
     social bonds. The result is a permanent situation of teleworking even
     for those who are on site. Leave a lone brief impromptu meetings that
     a TM would like to have with his team. This practice simply won’t
     happen anymore.


     Asking staff to massively come back to the Office VS proposing
     unattractive and hostile work conditions:
     On one hand, management would like that you observe the new ways of
     working and are currently asking all managers to promote coming back
     to the office. But on the other, after the 19 degrees maximum office
     temperature (see our publication), and reduced service of canteens,
     management tries even harder to “attract” staff back to the Office
     with poor work environment such as hot-desking. In French one would
     say: “on attrape pas les mouches avec du vinaigre”4. What management
     really wants is pretty unclear, should you stay home or come back?
     They seem to be talking both ways at once.


     You can safely assume that the Presidential floor will be spared from
     hot-desking as they do not have that kind of time to waste. After two
     reorganisations in four years, now a relocation with hot-desking on
     the way, management’s creativity is endless when it comes to the art
     of making us run like headless chicken. After all, what better way to
     prevent people from thinking about what is really important?


     Previous failed trial with hot-desking:
     Finally, it is interesting to mention that there is already an
     example of failed hot-desking in the EPO’s history. In 2002, upon
     opening of the Hinge in The Hague, this work model was imposed on the
     11 colleagues housed in the building and working for epoline customer
     services. After a couple of weeks of turn-over, the colleagues who
     never found any advantage in this practice, began to pick every day
     the same desk. End of the experiment.


     Your Central Staff Committee


     _____________
     4 “You can catch more flies with honey than with vinegar.”


One can conclude that the EPO either wants no staff or desires to get rid of
its premises. Either possibility or both possibilities would be in violation of
the EPC. They’ve even set up a_fake_case to make it seem like imposing
“webchat” as access to justice is somehow compatible with the law. █



                    ䷩ 𝚕𝚒𝚗𝚎 448

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

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✐ IRC_Proceedings:_Wednesday,_June_22,_2022⠀✐


Posted in IRC_Logs at 2:18 am by Needs Sunlight


Also available via the Gemini protocol at:


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                          Enter_the_IRC_channels_now


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                    ䷩ 𝚕𝚒𝚗𝚎 575

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✐ The_EPO_is_Ceasing_to_Be_a_Patent_Office⠀✐


Posted in Europe, Patents at 12:01 am by Dr. Roy Schestowitz


Video_download_link | md5sum f33e598381ee0bf0d85c4a80d06da3d1
EPO Rubberstamping
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/epo-race-to-zero.webm


Summary: Patent offices are meant to carry out patent examination, but today’s
EPO is so focused on money (by granting a ton of legally-invalid monopolies)
that it is willing to enlist incapable and inexperienced workers as ‘machine
operators’; this is done in violation of many EPC provisions


THE latest EPO post discussed António_Campinos attacking EPO workers even more
than Benoît_Battistelli had done, in effect abolishing a lot of rights and
lowering the salary by a factor of 2-3 during massive inflation. There’s no
doubt that the objective of today’s management is to replace competent
examiners with rubberstampters, common patent courts with kangaroo courts, and
high-quality patents with a sea of junk like in INPI and CNIPA (imagine
millions of European_software_patents whose examination_process_involved_little
but_Google_Search).


“By the time the EPC turns 50 it will have been so thoroughly violated that one
can wonder if the EPO even deserves to exist anymore.”Everything that EPO was
supposed to stand for gets dismantled one step at a time. By the time the EPC
turns 50 it will have been so thoroughly violated that one can wonder if the
EPO even deserves to exist anymore. █


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇So_you_are_saying_EPO_gave_you_a_patent_because_Google
search_for_'closest_prior_art'_found_no_plagiarism?⦈_


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣛⢿⣷⡀⣿⡇⣿⡇⣿⣧⢿⣿⢹⢸⣿⢸⣿⢸⣿⣿⣿⡇⡿⢸⣿⣻⣧⢸⣿⢻⣯⢸⣿⡿⢇⣷⢈⣻⣿⣦⢸⣿⣸⣷⠀⣿⣿⢱⣿⣿⢸⣿⣿⣿⠀⣿⡷⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣼⣿⠇⢿⣧⣿⢇⣿⣿⢸⣿⣿⡸⣿⣼⡿⣘⣿⣿⣿⢃⡇⣿⣿⢻⣿⢸⣿⢸⣿⢸⣿⣷⡏⠏⠸⣿⣼⡿⣼⣿⢻⣿⠈⣿⣿⠾⣿⣿⢸⣿⢹⣿⠀⢿⣧⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣷⣶⣶⣿⣿⣿⣷⣶⣿⣿⣶⣶⣿⣿⣷⣶⣶⣿⣷⣶⣶⣶⣶⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣦⣶⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣦⣴⣤⣤⣤⣿⣶⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⡤⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⡀⠀⠀⠀⠀⣸⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡦⢀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠳⠳⣿⣧⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⣅⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠟⠉⠘⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠤⢼⣿⣿⣿⣿⣿⣿⣯⡏⠉⠉⠉⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣭⣥⣈⣻⣿⣿⣿⣿⣯⣶⣟⣿⣯⠍⢀⠉⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⣿⣿⣿⣿⣴⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⡟⠛⣩⣿⠩⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⣿⣿⣟⣋⣀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⣴⣼⣷⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣾⡯⠀⠈⢁⣽⣿⣿⣿⣿⣿⣿⡈⠋⠹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣸⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠋⠻⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠉⠀⠀⠀⣠⠀⣿⣿⣿⣿⣿⠟⠁⠈⠀⠙⢿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⡟⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠘⣿⣿⣻⣿⣱⣿⠀⣠⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠈⠩⢿⣿⣿⡿⣿⣆⠹⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣤⠀⠀⣧⣿⣿⣿⣿⣿⡿⠿⠿⣿⣟⣛⣉⣅⣠⣤⣶⣿⣿⣿⡗⡿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⡿⡟⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⣿⡎⢻⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣿⣧⡄⠀⠀⠀⠑⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣿⠃⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡻⠟⠛⠛⠉⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣤⣤⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡇⣿⡯⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⣛⣿⠶⢯⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣼⢟⣉⣠⣶⣿⣿⣿⡆⠛⠀⠄⢯⣿⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⣾⣿⣿⣿⣶⣤⣄⣀⣸⠻⣿⣿⣿⡏⠋⢀⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⣻⣿⣿⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠹⣿⣿⣿⣿⣿⣿⠏⣰⡇⠈⢠⣴⣶⣶⠚⢚⣉⡟⣿⣿⣿⣿⡿⠀⠀⢐⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠋⠀⣶⠆⣶⢶⢰⣶⣦⠀⣶⢶⡄⣶⡆⣶⢰⡶⣶⠆⠰⣦⡖⣶⢲⣴⡆⣶⢸⢰⣶⠹⢱⡖⣮⣴⣶⠰⣶⠖⣶⠆⣶⣰⠲⣶⠆⠀⠀⣾⠸⣿⣿⠙⣬⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⣿⠋⢸⣿⡿⠀⣿⣺⣾⣯⣿⢹⣿⢿⣿⡃⠀⣿⠁⣿⣸⣿⣇⣿⠘⣿⣽⡇⢸⡟⡏⣿⣿⡄⣿⠀⣿⡃⣿⣿⠀⣿⠀⠀⢴⣿⣿⣿⡇⠨⣿⣷⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠉⠁⠀⠈⠉⠉⠁⠉⠈⠉⠈⠉⠁⠀⠉⠀⠈⠽⠶⠭⠵⠃⠉⠈⠡⠮⠵⠧⢩⠮⠷⠭⠾⠭⠥⠽⣯⠶⠉⠀⠀⠀⠛⠻⠍⠂⠘⠿⠷⠟⠀⠀⠀⠀⠀⠀
⠀⢸⣏⡿⢸⣏⢸⡿⠧⣾⣿⢸⡇⣿⢾⣝⠃⣿⡁⢰⣟⣿⢸⣿⣧⣾⢹⡇⣿⣿⢸⡇⢸⣏⠀⢾⣝⠃⣿⡁⣿⣿⢸⣿⡇⣿⠹⢿⣿⣿⢰⢸⣏⣸⣿⡇⣿⣽⠆⠘⢸⡿⠷⣿⠀⣿⢹⡾⣯⡛⣿⣏⢾⣝⠋⣿⡏⠀
⠀⢸⣧⡿⢸⣧⠸⣷⡇⣿⢺⡾⣧⡿⢲⣽⠇⣿⡄⠸⣯⢿⠸⣿⡟⢿⣼⠇⣿⣿⢸⣧⢸⣧⠀⢲⣽⠇⣿⣤⡿⣿⣸⣿⡇⢿⣼⢿⣿⣿⠘⢸⡇⢸⣿⠇⣿⢸⡇⣿⠸⣷⡗⣿⣤⢿⣼⠷⣮⡿⢿⣧⢲⣽⠇⢿⡇⠀
⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⣀⢀⣠⡀⣀⣀⡀⠀⣀⡀⣀⣀⣀⣀⣀⣀⠀⢀⣀⡀⣠⣀⢀⣀⡀⣀⢀⣀⣀⣀⠀⢀⣀⡀⣀⣄⠀⢙⣀⡀⣀⠀⣛⡂⢖⣿⡛⣗⢈⣉⡐⣄⣚⢃⡀⣡⣄⢈⣀⢀⣀⢒⣅⡀⠉⢄⠀⠀
⠀⠀⠀⠀⠀⣿⠼⢸⣿⡇⣿⢸⡇⣿⣿⢾⡇⢠⣟⣧⣿⢾⡇⢸⡇⠁⠀⢸⣿⢼⡇⣿⢸⣿⡇⣿⣿⣿⣿⣿⠀⢸⣿⡇⣿⢸⡇⢸⡧⠟⣿⠀⣿⣿⢸⣿⣇⣿⢸⣿⡇⣿⢾⣻⡇⠻⣮⣹⣿⣾⣿⣭⣸⡇⣤⣤⠠⠀
⠀⠀⠀⠀⠀⠿⠀⠸⠟⠗⠻⠘⠷⠋⠻⠸⠇⠸⠏⠿⠻⠸⠇⠸⠃⠀⠀⠘⠟⠈⠳⠟⠘⠿⠃⠿⠹⠟⠿⠟⠀⠸⠘⠇⠻⠞⠁⠸⠇⠀⠿⠾⠟⠿⣘⠟⠟⠿⠺⠛⠗⠿⠸⡻⢇⣻⣾⣻⠏⡇⢟⣺⣠⣼⡿⢿⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢉⠩⠅⢀⣠⣄⣰⣶⣿⣷⣦⡰⢾⣾⣯⣽⣿⣿⡈⣿⣿⣿⣷⣾⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 670

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

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    Gemini version at gemini://gemini.techrights.org/2022/06/23/sobbing-tony/

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Gemini_version_available_♊︎


✐ [Meme]_Granting_Patents_Like_Mad_is_Not_Productivity_(It’s_Also_Illegal)⠀✐


Posted in Europe, Patents at 11:00 am by Dr. Roy Schestowitz


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇'Productivity' down? But I am the f***ing president⦈
 What will EPO President ‘Monopoly Tony’ tell the Council next week? Which lie
                                 will he try?


Summary: Patent granting is down_by_a_quarter at the EPO, so António_Campinos —
like Benoît_Battistelli before him — resorts_to_terrorising_staff


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

                    ䷩ 𝚕𝚒𝚗𝚎 1939

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/23/staff-survey-of-the-epo-is-out/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/23/staff-survey-of-the-epo-is-out/

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Gemini_version_available_♊︎


✐ EPO_Staff_Survey’s_Preliminary_Results_Published_(Almost_2,000_Staff
Surveyed),_António_Campinos_Less_Trustworthy_Than_Benoît_Battistelli_at_Similar
Points_in_Their_Terms⠀✐


Posted in Europe, Patents at 8:12 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 64f6fc42cc6308937682078b9765e6cf
EPO Staff Survey for 2022
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/staff-survey-epo.webm


Summary: At long last, after a couple of months in the making, the staff survey
of the EPO is out (not the one controlled by EPO_management with push-polling
and ‘trick questions’)


THE situation at the EPO has worsened to the point where only 1% of surveyed
staff trusts the Administrative Council (national representatives) and only 3%
trust António_Campinos (for comparison, Benoît_Battistelli was polled at 4%
after 3 years at the Office).


There’s growing recognition that nothing has improved, e.g. in this new_article
(blog post with 3 good comments in there, at least those appearing already;
many more will come). “Translations are available in German, French and Dutch,”
SUEPO_notes, having already produced 3. The English title is “Demonstration EPO
staff during meeting about re-election president Campinos” and that comes on
the same day as the release of the 2022 (“Fifth Edition”) results of the
Technologia Staff Survey. Here is what SUEPO Central wrote to staff some hours
ago:


     Dear SUEPO Members,
     Dear colleagues,


     SUEPO mandated the company Technologia to run its fifth edition of
     the EPO Staff Survey in 2022. The survey asks the same questions as
     the previous survey conducted in 2010, 2013, 2016 and 2020 in order
     to be able to reliably compare the results. Contrary to the standard
     practice among other international organisations, the President of
     the Office did not authorise the dispatch of individual survey access
     codes to all EPO staff members at their @epo.org email address. SUEPO
     could therefore only rely on the private emails of its members and
     those among EPO staff who actively opted in.


     Technologia contacted 2.915 EPO staff members among which 1.766
     answered representing a 60,6% response rate. The results are
     available in the Frequency Tables and Presentation of the results (in
     French only for now) and show that dissatisfaction about the 2015 New
     Career System (NCS) increases, quality and staff’s perception of EPO
     quality decrease, mistrust in management persists, the atmosphere and
     social dialogue deteriorate and there is a historical worsening of
     staff’s engagement and staff’s mental/physical health.


     In this letter sent to the Heads of Delegations, SUEPO urges the
     Council to take due account of the Technologia survey results and
     give the proper mandate to EPO management to repair the situation.


As shown in the video above, Heads of Delegations were contacted_in_English
[PDF] and presented with preliminary analysis/overview, supported by the
presentation_in_French [PDF] and results_in_English [PDF]. There will be lots
more to come, for sure… █


               🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇technologia_5_results_054148⦈_
           This is the fifth time (after 2010, 2013, 2016 and 2020)


⣿⣿⣿⡿⠿⠇⠀⠀⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠇⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⢿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⢾⣽⣷⣦⠨⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⡸⢟⣫⣭⡄⣭⣷⣌⠻⣿⣶⡆⣶⠿⠿⢿⣿⡿⢿⠿⡇⠿⠿⣿⡿⠿⠿⢿⣿⠿⡿⢿⣿⢸⡿⢿⠿⣿⣿⠿⡿⢿⢿⢾⣿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢋⣴⡻⢿⣿⢧⣿⣿⡹⠀⣿⣿⡇⡇⣛⣛⣃⣻⢸⣿⣿⡇⣿⣿⡞⡇⣿⣿⡎⡇⣾⣿⣷⣹⢸⢰⣿⣿⣎⡇⣾⣿⣷⢸⢸⢱⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢈⢿⣿⣷⢌⣈⠛⣁⣁⣴⣿⣿⣧⣷⣬⣭⣵⣿⣮⣭⣭⣧⣿⣿⣧⣧⣿⣿⣧⣿⣬⣭⣵⣿⣼⣷⣭⣭⣾⣿⣬⣭⣵⣸⣼⣷⣭⣭⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⠒⢚⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡿⡟⢻⠻⣿⡟⢻⠿⡿⢻⠿⡿⡿⢿⡿⢿⢻⡟⡟⢿⠿⣿⡟⡻⢿⠿⠻⢿⠿⡿⢿⡿⣿⠿⠿⡿⢿⡟⢻⢻⠿⡟⢟⣿⢛⡿⣿⢿⠿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣧⣿⣮⣼⣿⣯⣽⣬⣧⣮⣴⣵⣿⣼⣷⣵⣼⣧⣷⣿⣬⣿⣧⣧⣽⣽⣾⣼⣧⣯⣾⣷⣵⣌⣤⣯⣼⣷⣵⣾⣤⣿⣿⣿⣥⣧⣽⣼⣶⣯⣿⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣯⢹⢩⣿⠢⡷⡸⠢⠖⢾⣯⡫⣭⢹⡹⠁⡯⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⠿⠟⠉⠉⠛⠛⠛⠛⠛⠻⠟⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠿⠿⠿⠏⠉⠙⠿⠿⠿⠿⠿⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⡿⠛⠋⠙⣿⠃⠀⠀⣿⡄⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣽⣿⣿⢸⡄⠀⠀⣤⣿⣿⣿⡇⠀⠐⡇⣿⣿⣿⣿⣿⠿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⣿⣿⣿⣿⣿⣿⠿⠿⢿
⣇⠀⠀⠀⢹⠀⠀⠀⣿⠃⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠀⠀⠈⠛⠟⢸⣇⠀⠀⣿⣿⡿⠏⠀⠀⠀⠀⣿⣿⣿⠟⠃⠀⠐⠁⠉⢻⣿⡿⠏⠛⠋⠉⢼⣿⣿⣿⡟⠓⠀⠘⠻⣿⣿⣿⣿⣟⠀⠀⠀
⠉⠀⠀⠀⠉⠀⠀⠀⡟⠀⠀⠀⠀⠈⠛⢻⣿⣟⠀⠀⠀⠀⠀⣤⠉⠛⠻⠀⠀⠀⠀⠀⢀⣘⡇⠀⠀⠿⣿⣇⠀⠀⠀⠀⢀⣿⣟⣁⡀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣿⡿⠟⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠑⠻⠿⠟⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⣠⣶⣾⡟⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣨⡆⠀⠀⠀⠀⢀⣹⣷⣦⠀⠀⠀⢠⡟⠁⡀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⣰⣿⣧⠀⠀⢀⡆⠀⠀⢸⣿⣿⣇⠀⠀⠀⠘⠇⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡖⠀⠀⣶⣿⣿⣿⡏⠀⠀⠀⠈⣷⡞⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠇⠀⠀⠿⠋⠀⠀⠘⠷⢄⣠⣾⣿⡿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⠀⠀⣹⠿⠿⠿⠧⠀⠀⢀⣼⣿⣧⣤⡄⢀⠀⠀⠀⢘⠣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠁⠀⠀⠸⠟⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2064

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/06/23/technologia-slides/#comments
    Gemini version at gemini://gemini.techrights.org/2022/06/23/technologia-slides/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Selected_Slides_From_Technologia’s_EPO_Staff_Survey_(2022_Compared_to_Prior
Years)⠀✐


Posted in Europe, Patents at 8:16 pm by Dr. Roy Schestowitz


From the just-released preliminary_file/draft (contains some typos, still):


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_mission⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_illusion⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_seniority⦈_


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_reps'_views⦈_


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


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


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_quality⦈_


Summary: In spite of the lack of media coverage, EPO insiders (mostly people
who have worked at the EPO for quite a while) see the downward spiral in patent
quality and they do not trust the management


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

                    ䷩ 𝚕𝚒𝚗𝚎 2322

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_23/06/2022:_Pango_1.90,_First_Beta_for_Krita_5.1_and_Microsoft_Bricks/
Breaks_Windows_Server_Again⠀✐


Posted in News_Roundup at 4:47 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Server
          o Audiocasts/Shows
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Red_Hat_/_IBM
          o Devices/Embedded
    * Free,_Libre,_and_Open_Source_Software
          o SaaS/Back_End/Databases
          o Programming/Development
                # Java
                # Rust
    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Linux_Foundation
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Chrome Uboxed ☛ Chromebooks_have_become_the_Swiss_Army
                  Knife_of_computing [Ed: No, proper GNU/Linux did this and
                  still does this. ChromeOS is spyware.]⠀⇛


                       11 years. 11 short years since the Chromebook was
                       first released to the public. (ChromeOS was
                       introduced in 2009 but the first consumer
                       Chromebook actually launched in May of 2011.) In
                       just over a decade, ChromeOS has evolved into a
                       massive ecosystem the like so of which, not even
                       Sundar himself could have predicted. You may have
                       heard someone say “a Chromebook is nothing more
                       than a browser” and once upon a time, that would
                       have been fairly accurate. Problem is, that
                       synopsis has stuck around entirely too long and has
                       created a stigma around ChromeOS that prevents many
                       from even giving a Chromebook a chance.


          o § Server⠀➾


                # ⚓ OpenSource.com ☛ How_to_use_a_circuit_breaker_pattern_for
                  site_reliability_engineering_|_Opensource.com⠀⇛


                       Distributed systems have unique requirements for
                       the site reliability engineer (SRE). One of the
                       best ways to maintain site reliability is to
                       enforce a certain set of best practices. These act
                       as guidelines for configuring infrastructure and
                       policies.


          o § Audiocasts/Shows⠀➾


                # ⚓ The BSD Now Podcast ☛ BSD_Now_460:_OpenBSD_airport
                  folklore⠀⇛


                       Containerd gains support for launching Linux
                       containers on FreeBSD, OpenBSD 7.1 on PINE64
                       RockPro64, true minimalistic window manager does
                       not exist, OpenBSD folklore, HardenedBSD May 2022
                       Status Report, DragonFlyBSD 6.2.2 out, and more


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ /dev/userfaultfd⠀⇛


                       The userfaultfd() system call allows one thread to
                       handle page faults for another in user space. It
                       has a number of interesting use cases, including
                       the live migration of virtual machines. There are
                       also some less appealing use cases, though, most of
                       which are appreciated by attackers trying to take
                       control of a machine. Attempts have been made over
                       the years to make userfaultfd() less useful as an
                       exploit tool, but this patch set from Axel
                       Rasmussen takes a different approach by
                       circumventing the system call entirely.


                       A call to userfaultfd() returns a special file
                       descriptor attached to the current process. Among
                       other things, this descriptor can be used (with
                       ioctl()) to register regions of memory. When any
                       thread in the current process encounters a page
                       fault in a registered area, it will be blocked and
                       an event will be sent to the userfaultfd() file
                       descriptor. The managing thread, on reading that
                       event, has several options for how to resolve the
                       fault; these include copying data into a new page,
                       creating a zero-filled page, or mapping in a page
                       that exists elsewhere in the address space. Once
                       the fault has been dealt with, the faulting thread
                       will continue its execution.


                       A thread will normally encounter a page fault while
                       running in user space; it may have dereferenced a
                       pointer to a not-present page, for example. But
                       there are times that page faults can happen within
                       the kernel. As a simple example, consider a read()
                       call; if the buffer provided to read() is not
                       resident in RAM, a page fault will result when the
                       kernel tries to access it. At that point, execution
                       will be blocked as usual, but it will be blocked in
                       the kernel rather than in user space.


                # ⚓ LWN ☛ Zoned_storage⠀⇛


                       Zoned storage is a form of storage that offers
                       higher capacities by making tradeoffs in the kinds
                       of writes that are allowed to the device. It was
                       the topic of a storage and filesystem session led
                       by Luis Chamberlain at the 2022 Linux Storage,
                       Filesystem, Memory-management and BPF Summit
                       (LSFMM). Over the years, zoned storage has been a
                       frequent topic at LSFMM, going back to LSFMM 2013,
                       where support for shingled magnetic recording (SMR)
                       devices, which were the starting point for zoned
                       storage, was discussed.


                       Chamberlain began with the news that a zoned
                       storage microconference had been accepted for this
                       year’s Linux Plumbers Conference (LPC). He
                       encouraged attendees to submit topics and hoped it
                       was an opportunity to introduce more user-space
                       developers to zoned-storage concepts. LPC will be
                       held September 12-14 in Dublin, Ireland.


                # ⚓ LWN ☛ Retrieving_kernel_attributes⠀⇛


                       At the 2022 Linux Storage, Filesystem, Memory-
                       management and BPF Summit (LSFMM), Amir Goldstein
                       and Miklos Szeredi led a discussion on a new
                       interface for extracting information from kernel
                       objects using the filesystem extended-attributes
                       (xattr) interface. Since Szeredi was not present in
                       Palm Springs, he co-led the session virtually over
                       Zoom audio, which was the only filesystem session
                       with a virtual leader at LSFMM this year. Szeredi’s
                       proposal for an interface of that sort had been
                       posted just the day before the session.


                       Goldstein started things off by noting that there
                       are several use cases where there is a need for a
                       new API to obtain bits of information from the
                       kernel, so it seems like a good idea to create a
                       common API that can meet those needs. Szeredi
                       proposed the getfattr mechanism, which builds on
                       the xattr interface; Goldstein said that he was
                       happy with the idea, as were Szeredi and Dave
                       Chinner, who suggested the idea a year or so ago.
                       In addition, other than an objection to binary
                       data, Greg Kroah-Hartman was “not unhappy” with the
                       idea.


                       Szeredi took over to describe the proposal in more
                       detail. The intent is to be able to get attributes
                       from some kernel objects; those could be mounts or
                       inodes, but processes or other objects are possible
                       as well. There are several existing interfaces for
                       getting this kind of information, but each has a
                       different way to access the attributes, so it would
                       be nice to have a unified interface, he said.


                       The xattr API was repurposed for his proposal. It
                       uses a different namespace for the new attributes,
                       however, in order to ensure that legacy code will
                       not break due to unexpected new attributes. For
                       example, listxattr() would not return attributes
                       from the new namespace. One objection to the
                       interface is that it is not efficient enough if
                       there is a need to retrieve multiple attributes.
                       Szeredi said that would need to be tested to see if
                       it is truly a problem, but if so, the API could be
                       extended with a bulk-retrieval mechanism.


                # ⚓ LWN ☛ A_discussion_on_readahead⠀⇛


                       Readahead is an I/O optimization that causes the
                       system to read more data than has been requested by
                       an application—in the belief that the extra data
                       will be requested soon thereafter. At the 2022
                       Linux Storage, Filesystem, Memory-management and
                       BPF Summit (LSFMM), Matthew Wilcox led a session to
                       discuss readahead, especially as it relates to
                       network filesystems, with assistance from Steve
                       French and David Howells. The latency of the
                       underlying storage needs to factor into the
                       calculation of how much data to read in advance,
                       but it is not entirely clear how to do so.


                       Wilcox began by describing readahead a bit. If user
                       space is reading a file one byte at a time, Linux
                       does not actually read the data that way; instead,
                       it issues reads for a bigger chunk, say 64KB, which
                       gets stored in the page cache. There is a certain
                       amount of latency between the time a page is
                       requested from the storage and when it appears in
                       the page cache; that latency varies greatly over
                       the wide variety of storage types that Linux
                       supports. For network storage, those types can
                       range from locally stored data on multi-gigabit
                       Ethernet to data stored halfway around the world
                       over decidedly slower links. Similarly, for local
                       storage it can range from a 5GB-per-second NVMe SSD
                       to some “crappy USB key picked up from a vendor at
                       a trade show”. There is “a lot of stuff to contend
                       with there”.


                # ⚓ LWN ☛ Remote_participation_at_LSFMM⠀⇛


                       As with many conferences these days, the 2022 Linux
                       Storage, Filesystem, Memory-management and BPF
                       Summit (LSFMM) had a virtual component. The main
                       rooms were equipped with a camera trained on the
                       podium, thus the session leader, so that remote
                       participants could watch; this camera connected
                       into a Zoom conference that allowed participation
                       from afar. In a session near the end of the
                       conference, led by conference organizer Josef
                       Bacik, remote participants were invited to share
                       their experiences—on camera—with those who were
                       there in person. It was an opportunity to discuss
                       what went right—and wrong—with an eye toward
                       improving the experience for future events.


                       Ric Wheeler was first up; he said that aside from
                       the first few minutes where he could not hear
                       anyone, “it was a good virtual experience”. Mel
                       Gorman echoed that and noted that it “was
                       infinitely superior to not being able to
                       participate at all”. One thing he noted is that the
                       “raised hands” in the Zoom interface were not
                       monitored in some sessions. There were two sessions
                       that he remembered where the speaker asked for
                       objections or other comments and he was left
                       “screaming at the mic”. It is difficult to keep an
                       eye on that when leading a session, he said; it was
                       only a minor detraction from the overall great
                       experience.


          o § Applications⠀➾


                # ⚓ Libre_Arts_–_LSP_Plugins_1.2.2⠀⇛


                       Vladimir Sadovnikov released a new version of his
                       free/libre LSP PLugins pack, this time featuring a
                       multiband dynamics plugin in four variations: left/
                       right, midside, mono, and stereo. Basically it’s an
                       8-band compressor (only 4 enabled by default to
                       start small probably).


          o § Instructionals/Technical⠀➾


                # ⚓ Trend Oceans ☛ Where_Do_Files_Go_When_the_rm_Command_Is
                  Issued?⠀⇛


                       The data itself is not destroyed or shredded; it is
                       only unlinked from the filesystem that references
                       the data and indicates the block as free when you
                       remove it using the rm command.


                       In this scenario, recovering the files becomes too
                       complex, and it’s a good choice not to rewrite
                       something on your system (ex: copying, moving,
                       installing), which overwrites the unlinked block


                # ⚓ H2S Media ☛ How_to_Install_Jenkins_on_Ubuntu_22.04_or_20.04
                  Linux_–_Linux_Shout⠀⇛


                       Learn the steps and commands to install Jenkins
                       software on Ubuntu 22.04 LTS Jammy JellyFish or
                       20.04 Focal Fossa Linux.


                       Jenkins is a software common in the field of
                       professional software development. When more than
                       one developer is working on a software project, it
                       becomes confusing when all of their changes are put
                       together. To solve this Jenkins comes in to
                       picture. Jenkins is a Continuous Integration System
                       (CI system) programmed in Java, which is used in
                       agile software development: It ensures that small
                       code changes are always immediately tested and
                       imported into the software. Jenkins was first known
                       as Hudson but after some dispute, all developers
                       involved in this (open source) project decided to
                       rename it to Jenkins.


                       Hence, in a few words, Jenkins is an open-source
                       project that helps software developers in
                       development by automating various aspects of
                       software app coding such as building, testing, and
                       deploying…


                # ⚓ TecMint ☛ How_to_Install_SUSE_Linux_Enterprise_Server_15
                  SP4⠀⇛


                       SUSE Enterprise Linux Server (SLES) is a modern and
                       modular Linux distribution that was developed
                       mainly for servers and mainframes. It focuses on
                       supporting production workloads and is typically
                       used by large organizations to host and run
                       applications.


                       SUSE also supports traditional IT environments and
                       is also available for desktop/workstation lovers as
                       SUSE Enterprise Linux Desktop (SLED). Check out the
                       release notes for more information about SLES 15
                       SP4.


                       SUSE Enterprise Linux Server provides a 60-day
                       Evaluation that allows you to get patches and
                       updates.


                       In this guide, we will demonstrate how to install
                       SUSE Enterprise Linux Server 15 SP4.


                # ⚓ Linux Shell Tips ☛ How_to_Use_Grep_to_Extract_Emails_from_a
                  File_in_Linux⠀⇛


                       If you have once crossed paths with data entry and
                       extraction tasks either as a freelancing virtual
                       assistant or for a personal/work project, you have
                       understood the importance of data organization and
                       management. The Linux operating system always
                       transforms its users into data specialists.


                       An important piece of data that is irreplaceable in
                       both personal and work projects is the email
                       address. It uniquely identifies and links specific
                       user information within a data management system.


                       Using an email address as a primary data reference
                       point meets the following objectives.


                # ⚓ Linux Shell Tips ☛ How_to_Watch_a_Growing_Size_of_a_File_in
                  Linux⠀⇛


                       Linux operating system distributions are masters at
                       solving computing riddles. These operating system
                       distributions do not entertain computing myths.
                       Therefore, its open-source attribute makes all
                       Linux OS activities transparent to its users.


                       This article guide will try to uncover the
                       possibility of monitoring the growing size of a
                       file in a Linux operating system environment.


                # ⚓ DebugPoint ☛ 5_Useful_Linux_Command_Line_Tools_that
                  Everyone_Should_Use⠀⇛


                       A set of five useful Linux command(s) which gives
                       you ultimate productivity boost in your day to day
                       workflow.


                # ⚓ Error_messages⠀⇛


                       There’s no shortage of dire error messages produced
                       by software. There’s an old joke referencing Ken
                       Thompson[a], one of the creators of Unix, as well
                       as the creator of the programming language ‘B’ (the
                       predecessor to ‘C’) and the video game ‘Space
                       Travel’…


          o § Games⠀➾


                # ⚓ Inscryption_Mac_and_Linux_ports_now_available⠀⇛


                       Bonkers card game Inscryption can now be enjoyed by
                       more people thanks to a new launch on Mac and
                       Linux.


                # ⚓ Linux Hint ☛ 10_Best_Linux_Games_for_Free_2022⠀⇛


                       Gaming on Linux has become very popular and gained
                       the trust of hardcore gamers in very short period
                       of time. Thanks to digital video game distribution
                       services like Steam and PlayOnLinux, it has been
                       possible for gamers like me to enjoy my favourite
                       video games from Windows on Linux and its
                       distributions.


                       Now that we’re in mid-2022, there are many games
                       from popular developers and publishers available
                       for Linux and its distributions like Ubuntu. But
                       games from popular publishers guarantees one thing
                       and that is price tag and some games are very
                       expensive too. So, today I’m going to introduce you
                       to the 10 free games for Linux.


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ MiTubo_comes_to_macOS_|_Mardy⠀⇛


                             While bringing in the macOS version, I
                             updated the QScreenSaver library to support
                             inhibiting the screensaver on macOS too.


                      # ⚓ Krita ☛ First_Beta_for_Krita_5.1.0_Released_|_Krita⠀⇛


                             We’re releasing the first beta for Krita
                             5.1.0 today. Krita 5.1.0 is packed with new
                             features! For the full list, check out the
                             work-in-progress full release notes!


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Pango_1.90_|_Goings_on⠀⇛


                             I’ve finally convinced myself that I need to
                             make a Pango 2.0 release to clean up the API,
                             and introduce some new APIs without breaking
                             users that expect Pango to be very stable.


                             So, here it is… well not quite. What I am
                             presenting today is not Pango 2.0 yet, but
                             1.90 – an unstable preview of the coming
                             changes, to gather feedback and give some
                             heads-up about whats coming.


    * § Distributions and Operating Systems⠀➾


          o § Red Hat / IBM⠀➾


                # ⚓ OpenSource.com ☛ Applying_smart_thinking_to_open
                  organization_principles [Ed: What "open org"? IBM is not an
                  open organisation but a proprietary and patent bully
                  corporation whose own president (the author of the "open
                  org") quit abruptly]⠀⇛


                       Habits have an unfair reputation of being bad
                       things that need to be stopped. But consider this:
                       Automation and habits have many things in common.
                       First, they’re both repetitive. They’re done over
                       and over, the exact same way. More importantly,
                       they reduce costs (both cost per piece and cost of
                       energy used).


                # ⚓ Enterprisers Project ☛ IT_leadership:_3_ways_CIOs_prevent
                  burnout⠀⇛


                       Fighting employee burnout is a key priority for
                       CIOs, especially as teams deal with the ongoing
                       impact of the pandemic and embrace new hybrid ways
                       of working. But IT leaders are not immune to the
                       impacts of burnout. In order to truly help their
                       employees manage work stress and find work-life
                       balance, leaders have to start with themselves.


                       We asked CIOs who recently won the 2022 Houston CIO
                       of the Year ORBIE Awards how they personally
                       protect themselves from burnout. Read their
                       responses for advice on how to maintain a healthy
                       work-life blend while continually finding
                       inspiration at work.


                # ⚓ Enterprisers Project ☛ 3_E’s_of_effective_leadership⠀⇛


                       Almost two years ago, I shared what I learned about
                       leadership from my experience in a leadership
                       development program. The takeaway? In order to be a
                       strong leader, especially in times of crisis, it’s
                       imperative to be vulnerable and create a
                       psychologically safe environment for your team.


                       I was reflecting recently on my leadership style
                       and how it may have changed over the past two
                       years. In some ways, I am the same person, the same
                       colleague, and the same leader. In other ways, I
                       have evolved and adjusted my style to fit the new
                       ways that we engage and work together.


                       Three distinct words came to me during this
                       reflection time (and I do love alliteration!).
                       These three words represent what I think is most
                       important in effective leadership today, maybe more
                       so than ever.


                # ⚓ Red Hat ☛ Multi-cloud_storage_strategies_for_SaaS
                  applications⠀⇛


                       The SaaS architecture checklist is a series of
                       articles that cover the software and deployment
                       considerations for Software as a Service (SaaS)
                       applications. In this fourth article in the series,
                       you’ll learn about software SaaS providers can use
                       to simplify their storage architecture while still
                       accommodating a multi-cloud strategy.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ MaaXBoard_8ULP_SBC_leverages_NXP_i.MX_8ULP
                  Cortex-A35/M33_SoC_for_Edge_audio_and_HMI_applications_–_CNX
                  Software⠀⇛


                       Avnet MaaxBoard 8ULP will be one of the first
                       single board computers (SBC) based on the new NXP
                       i.MX 8ULP Cortex-A35/M33 processor designed for
                       Edge audio and HMI applications, and featuring
                       NXP’s EdgeLock for device-to-cloud security.


                       The board will come with 2GB RAM, 32GB eMMC flash,
                       a MIPI DSI display connector, a MIPI CSI camera
                       connector, Fast Ethernet and WiFi 5 connectivity, a
                       digital microphone, and a 3.5mm stereo audio jack,
                       and provide expansion capabilities via a 40-pin
                       header for Raspberry Pi HATs and a 16-pin Shuttle
                       Click header for MikroE Click add-on boards.


                # ⚓ CNX Software ☛ DevTerm_portable_Linux_terminal_now_supports
                  Raspberry_Pi_CM4_via_a_$19_adapter⠀⇛


                       DevTerm modular, portable Linux terminal initially
                       designed for modules based on Raspberry Pi CM3 form
                       factor, can now work with Raspberry Pi CM4 for
                       extra performance and memory thanks to a $19
                       adapter.


                       The Devterm was initially launched in 2020 with a
                       6.8-inch IPS screen, a keyboard with 67 keys, and a
                       battery module, all connected through the
                       ClockworkPi v3.14 carrier board taking a choice of
                       core modules based on Allwinner H6 or Rockchip
                       RK3399 (now supported in Armbian), besides the
                       Raspberry Pi Compute Module 3 mentioned above. More
                       recently, it also got an Allwinner D1 RISC-
                       V module.


                # ⚓ Linux Gizmos ☛ Orbbec_introduces_Femto_Time-of-Flight_3D
                  Camera_line⠀⇛


                       Following the introduction of the Persee+ 3D
                       embedded camera in April 2022, Orbbec has released
                       a complete new line of 3D cameras optimized to
                       capture static or moving objects and scenes with
                       superior accuracy. The company ensured the Femto
                       ToF 3D cameras are enabled to be used in
                       applications including healthcare, robotics,
                       augmented reality and more.


                       Orbbec’s new Femto line consists of three models,
                       the Femto (standard), the Femto W and the Femto
                       Live. All models share a similar design as seen in
                       the image below.


    * § Free, Libre, and Open Source Software⠀➾


          o § SaaS/Back End/Databases⠀➾


                # ⚓ Mariuz’s_Blog:_Firebird_3.0.10_sub-release_is_available⠀⇛


                       Firebird Project is happy to announce general
                       availability of Firebird 3.0.10 — the latest point
                       release in the Firebird 3.0 series.This sub-release
                       offers a few important bugfixes, please refer to
                       the Release Notes for the full list of changes.


                # ⚓ PostgreSQL ☛ PostgreSQL:_InfluxDB_FDW_1.2.0_released⠀⇛


                       We have just released version 1.2.0 of the Foreign
                       Data Wrapper for InfluxDB.
                       This release can work with PostgreSQL 10, 11, 12,
                       13 and 14.


                # ⚓ PostgreSQL ☛ PostgreSQL:_PGSpider_extension_1.0.0_is
                  released⠀⇛


                       We have released PGSpider extension v1.0.0.


                       This is an extension to construct data
                       virtualization engine by PostgreSQL.
                       As compared to the first release of 10 months ago,
                       the quality and connectivity of FDWs were improved.
                       Please refer README.md for supporting FDWs.


                # ⚓ PostgreSQL ☛ PostgreSQL:_JDBC_FDW_0.2.0_release⠀⇛


                       We have just newly released Foreign Data Wrapper
                       for databases with JDBC interface.


                       This release can work with PostgreSQL 13 and 14.


                # ⚓ PostgreSQL ☛ Parquet_S3_FDW_0.3.0_released⠀⇛


                       We have just released version 0.3.0 of the Foreign
                       Data Wrapper for Parquet file on Amazon S3.
                       This release can work with PostgreSQL 13 and 14.


          o § Programming/Development⠀➾


                # ⚓ LWN ☛ Wielaard:_Sourceware_–_GNU_Toolchain_Infrastructure
                  roadmap⠀⇛


                       Mark Wielaard writes about improvements at
                       Sourceware, the site that holds the repository for
                       many projects in the GNU toolchain and beyond.


                # § Java⠀➾


                      # ⚓ LWN ☛ Rethinking_Fedora’s_Java_packaging⠀⇛


                             Linux distributors are famously averse to
                             shipping packages with bundled libraries;
                             they would rather ship a single version of
                             each library to be shared by all packages
                             that need it. Many upstream projects,
                             instead, are fond of bundling (or
                             “vendoring”) libraries; this leads to tension
                             that has been covered here numerous times in
                             the past (examples: 1, 2 3, 4, 5, …). The
                             recent Fedora discussion on bundling
                             libraries with its Java implementation would
                             look like just another in a long series, but
                             it also shines a light on the unique
                             challenges of shipping Java in a fast-moving
                             community distribution.


                             As is often the case with Fedora, the
                             conversation started with the announcement of
                             a Fedora change proposal; this one is
                             authored by Jiri Vanek. The proposal is aimed
                             at the Fedora 37 release, which is currently
                             planned for late October. Vanek proposes to
                             change Fedora’s builds of the OpenJDK Java
                             development kit (JDK) to link against several
                             of that project’s bundled libraries
                             (including zlib, FreeType, libjpeg, and
                             HarfBuzz) rather than the versions packaged
                             separately in Fedora. The JDK would also be
                             statically linked against Fedora’s build of
                             the libstdc++ library.


                             This proposal, however, is only the first
                             step in a longer project to change how the
                             JDK is built. In short, once the JDK (along
                             with the Java runtime environment, or JRE)
                             has been made to use its own libraries, the
                             way these components are packaged will
                             change. The RPM for a given JDK release will
                             contain a single tarball that will be
                             unpacked on the target system. Notably, this
                             tarball will be the same for all Fedora
                             releases, from the oldest supported release
                             through Rawhide; the use of bundled libraries
                             will help to ensure that this package will
                             work the same way on all target
                             distributions.


                # § Rust⠀➾


                      # ⚓ Rust Blog ☛ The_Rust_Programming_Language_Blog:_Call
                        for_testing:_Cargo_sparse-registry⠀⇛


                             The Cargo nightly sparse-registry feature is
                             ready for testing. The feature causes Cargo
                             to access the crates.io index over HTTP,
                             rather than git. It can provide a significant
                             performance improvement, especially if the
                             local copy of the git index is out-of-date or
                             not yet cloned.


                      # ⚓ Rust Weekly Updates ☛ This_Week_In_Rust:_This_Week_in
                        Rust_448⠀⇛


                      # ⚓ LWN ☛ Vetting_the_cargo⠀⇛


                             Modern language environments make it easy to
                             discover and incorporate externally written
                             libraries into a program. These same
                             mechanisms can also make it easy to
                             inadvertently incorporate security
                             vulnerabilities or overtly malicious code,
                             which is rather less gratifying. The stream
                             of resulting vulnerabilities seems like it
                             will never end, and it afflicts relatively
                             safe languages like Rust just as much as any
                             other language. In an effort to avoid the
                             embarrassment that comes with shipping
                             vulnerabilities (or worse) by way of its
                             dependencies, the Mozilla project has come up
                             with a new supply-chain management tool known
                             as “cargo vet”.


    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ The_beauty_of_equations_in_Physics⠀⇛


                       I have been stereotyped by many I know (and
                       understandably so) as a quintessential computer
                       geek, probably someone who dabbled in computers
                       since his childhood and is his first love. That is
                       however far from the truth because I first
                       programmed a computer at the age of 20 and started
                       my career soon after as a lowly back office
                       outsourced engineer that a lot of the geek
                       community looks down upon. What I did grow up with
                       was something related but still different –
                       mathematics and physics.


                       Around the age of 15 my mother enrolled me for IIT
                       coaching classes (a huge financial struggle and a
                       social shock for me, but that’s another story) and
                       I found teachers that ignited a love for these
                       subjects. I was always technically inclined thanks
                       to my father who was an engineer. After his early
                       death everyone around me wanted me to be his
                       ‘successor’ as an engineer and I happily (almost
                       proudly then, what does a 9 year old know!)
                       obliged. Whatever technical inclination I had was
                       due to watching my father as a 6-9 year old
                       (another interesting story) and it was enough to
                       make me an above average math and science student.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ Kontron_D3723-R_–_An_AMD_Ryzen_Embedded
                  R2000_motherboard_in_mini-ITX_form_factor⠀⇛


                       Kontron D3723-R is an industrial mini-ITX
                       motherboard equipped with the just-announced AMD
                       Ryzen Embedded R2000 processor family that delivers
                       higher performance than Ryzen R1000 Series while
                       keeping the costs lower than AMD Ryzen Embedded
                       V2000 solutions, and enabling Windows 11 support.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Getting_rid_of_obesogens_and_endocrine-disruptors_by_
                  (usefully)_bleeding⠀⇛


                       One of the things that people are starting to worry
                       about, at least a little bit, are endocrine
                       disruptors. In a nutshell, endocrine disruptors
                       mess with your hormones. Since your hormones get
                       your body to do all sorts of different things,
                       endocrine disruptors can have wide-ranging, if
                       subtle, effects.


                       There are also obesogens — things that make you
                       fat. When I say “make you fat” here, I’m
                       specifically claiming that they’ll get your body to
                       generate fat with the food you eat instead of doing
                       something useful with it, like making your
                       mitochondria generate more energy for you to use.


          o § Proprietary⠀➾


                # ⚓ Bleeping Computer ☛ Recent_Windows_Server_updates_break
                  VPN,_RDP,_RRAS_connections⠀⇛


                       This month’s Windows Server updates are causing a
                       wide range of issues, including VPN and RDP
                       connectivity problems on servers with Routing and
                       Remote Access Service (RRAS) enabled.


          o § Linux Foundation⠀➾


                # ⚓ TechRepublic ☛ Employers_to_increase_hiring_of_IT_pros_with
                  open_source_skills [Ed: Lance Whitney has been reduced to
                  puff pieces (Sponsored Trash) writer, even for the 'Linux'
                  Foundation that pays his employer to do this. Journalism is
                  dead. It's PR now.]⠀⇛


                # ⚓ ZDNet ☛ Blind_trust_in_open_source_security_is_hurting_us:
                  Report [Ed: Steven Vaughan-Nichols now running anti-FOSS FUD
                  pieces for Microsoft proxies because 'Linux' Foundation pays
                  him to do this]⠀⇛


                # ⚓ Cardano_Foundation_Becomes_Gold_Member_In_The_Linux
                  Foundation [Ed: They basically signed a marketing contract
                  and will misappropriate the "Linux" mark in exchange for
                  money]⠀⇛


                # ⚓ Cardano,_Linux_Foundations_To_Drive_Blockchain_Innovation
                  [Ed: Any crank can pay the 'Linux' Foundation to promote its
                  crap; the "Linux" brand is being reduced to rubble]⠀⇛


                       The Cardano Foundation has joined the Linux
                       Foundation. In an announcement released by the
                       Cardano Foundation yesterday, Cardano stated that
                       they have joined the Linux Foundation as a gold
                       member. The announcement added that this makes the
                       Cardano Foundation the only non-profit active at
                       this level.



                    ䷩ 𝚕𝚒𝚗𝚎 3285

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Gemini_version_available_♊︎


✐ Links_23/06/2022:_EasyOS_Improves_Update_Process⠀✐


Posted in News_Roundup at 5:47 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Debian_Family
          o Canonical/Ubuntu_Family
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Events
          o Web_Browsers
                # Chromium
          o Programming/Development
                # Perl_/_Raku
                # Rust
    * Leftovers
          o Linux_Foundation
          o Security
          o Monopolies
                # Patents
                # Copyrights
    * § GNU/Linux⠀➾


          o ⚓ Linux Links ☛ Linux_Around_The_World:_USA_–_Kentucky_–
            LinuxLinks⠀⇛


                 Kentucky is a state in the Southeastern region of the
                 United States and one of the states of the Upper South,
                 bordered by Illinois, Indiana, and Ohio to the north. It
                 borders West Virginia and Virginia to the east, Tennessee
                 to the south, and Missouri to the west.


          o ⚓ Liliputing ☛ Lilbits:_Linux_on_iPhones_and_iPads,_Brave_Search
            emerges_from_beta,_and_a_DIY_retro_audio_player_made_with_modern
            tech⠀⇛


                 The developers who disclosed a new way to boot Linux on
                 jailbroken Apple devices this month initially explained
                 that their method worked on devices with Apple A7, A8,
                 and A8X chips. But they later added support for A9 and
                 A10 series chips… and now you can boot Linux on an iPhone
                 or iPad with an Apple A11 chip as well.


                 But there’s a difference between booting and operating
                 system and having everything run smoothly. Case in point:
                 so far it looks like the touchscreen isn’t functional on
                 Apple devices running Linux. Neither are cameras,
                 speakers, or a bunch of other things. But that could
                 change over time. And if you’re curious to know what
                 hardware is working on devices with specific chips, now
                 there’s a resource that will let you know.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ KaOS_2022.06_Run_Through_–_Invidious⠀⇛


                       In this video, we are looking at KaOS 2022.06.


                # ⚓ Video ☛ People_Know_Gates_&_Jobs_But_Why_Not_Linus_Torvalds
                  –_Invidious [Ed: Well, people do not 'know' them, either.
                  They're being spoonfed lies and propaganda.]⠀⇛


                       Ask the average person who is important in
                       computing, they’ll know the names Bill Gates and
                       Steve Jobs but if you ask them about Linus Torvalds
                       they will probably have no idea who that is but
                       why, isn’t he core the state of modern computing.


                # ⚓ Video ☛ Valve’s_new_VR_headset,_Brave_Search_anti-bias
                  tool,_Microsoft_vs_FOSS_copycat_apps_–_Linux_news_–
                  Invidious⠀⇛


          o § Instructionals/Technical⠀➾


                # ⚓ ID Root ☛ How_To_Install_Apache_CouchDB_on_Debian_11_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Apache CouchDB on Debian 11. For those of you who
                       didn’t know, Apache CouchDB is an open-source NoSQL
                       database developed by the Apache Software
                       Foundation. CouchDB uses multiple formats and
                       protocols to store, transfer and process data.
                       CouchDB uses JSON to store data, JavaScript as its
                       query language, and HTTP as an API.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the Apache CouchDB NoSQL database
                       server on a Debian 11 (Bullseye).


                # ⚓ Ubuntu Handbook ☛ How_to_Move_Clock_to_the_Left_or_Right
                  Corner_in_Ubuntu_22.04_|_UbuntuHandbook⠀⇛


                       For those don’t like to have the ‘date and time’
                       menu in the center of top panel, here’s how to move
                       it to either left or right in Ubuntu 22.04 LTS.


                       Ubuntu, definitely the GNOME desktop, does not have
                       option to configure the clock menu position. But,
                       there are a few extensions can do the job. And,
                       here I’m going to show you how to install and use
                       them.


                # ⚓ Linux Made Simple ☛ How_to_install_the_PokeMMO_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install the PokeMMO
                       on a Chromebook. Please follow the video/audio
                       guide as a tutorial where we explain the process
                       step by step and use the commands below.


                # ⚓ Purism ☛ How_to_Enable_Hot_Spot_and_Tethering_in_PureOS_on
                  Your_Librem_5⠀⇛


                # ⚓ Make Use Of ☛ How_to_Install_and_Play_Rocket_League_on
                  Linux⠀⇛


                       Learn how to install and run Rocket League on Linux
                       to enjoy the unmatched vehicular soccer experience
                       on your desktop.


                       Linux is making great strides when it comes to
                       desktop gaming. The ongoing development of software
                       like Wine, Proton, and Lutris makes it evident that
                       gamers have now started considering Linux distros
                       for their gaming needs. Valve is also at the
                       forefront of developing gaming-related software and
                       hardware compatible with Linux.


                       Thanks to the rapid advancements made in the Linux
                       gaming industry, you can now enjoy Rocket League on
                       your Linux desktop, with minimum hassles out of the
                       box. Here’s how to install Rocket League and “kick-
                       start” your soccer journey on Linux.


                # ⚓ LinuxOpSys ☛ Linux_Package_Manager_–_What_it_is_used_for⠀⇛


                       There are numerous Linux flavors are available to
                       use. Each distribution uses different tools and
                       utilities to handle software installation, upgrade,
                       and removal. Different Linux operating systems use
                       different software package archives in remote
                       repositories. Linux package managers act as the
                       middle man who fetches these software packages from
                       repositories and manipulates them on behalf of the
                       end-users.


                # ⚓ OSTechNix ☛ Limit_The_Number_Of_SSH_Logins_Per_User,_Group,
                  System_–_OSTechNix⠀⇛


                       As you probably know, we can SSH into a remote
                       Linux system by the same user multiple times. There
                       is no limit! You could simply open multiple
                       Terminal windows (or multiple tabs in the Terminal)
                       and initiate multiple SSH sessions from each tab by
                       the same user account. What if you want to change
                       this behavior? For example, you might want to allow
                       only one active SSH session for an user. That’s
                       what we are going to see now. This brief tutorial
                       explains how to limit the number of SSH logins per
                       user or group or system on Linux.


                # ⚓ Make Use Of ☛ How_to_View_Hidden_Files_and_Folders_on
                  Linux⠀⇛


                       The concept of hidden files is simple yet very
                       important in Linux. They are mainly used for
                       storing configuration files or user settings.
                       Usually, these files are used by your system
                       services, scripts, or other programs. For example,
                       the .bash_logout script is executed whenever you
                       log out of your Bash sessions. Another great
                       example is the .gitignore file used by Git to
                       exclude certain files from being pushed to your
                       remote repository.


                       Sometimes the concept of hidden files can be used
                       to hide certain files from the prying eyes of
                       mostly non-advanced users.


          o § Games⠀➾


                # ⚓ The Verge ☛ Inscryption,_the_delightfully_unsettling_card-
                  battling_roguelike,_comes_to_Mac_and_Linux⠀⇛


          o § Desktop Environments/WMs⠀➾


                # ⚓ OMG Ubuntu ☛ Chertan_is_a_Cool_Circular_Conky_Theme_for
                  Linux_Desktops_–_OMG!_Ubuntu!⠀⇛


                       Conky is a great way to personalise your Linux
                       desktop regardless of which distro or DE you’re
                       using.


                       There are hundreds if not thousands of Conky themes
                       available, ranging from simple stat tables to Lua-
                       laden masterpieces. I recently came across a new
                       Conky config I like. It shows the date, current
                       weather conditions, an average CPU and RAM load,
                       and the currently playing song in MPD.


                       I figured I’d share the theme on here and add a bit
                       info on how to customise this Conky to work with
                       your location and any MPRIS-compatible music
                       player, rather than MPD. It requires a fair bit of
                       directory swapping and file editing, but the end
                       result is a setup that’s mostly usable.


                       Note: this is not an article on why you should or
                       shouldn’t use Conky versus anything else. Some
                       people don’t see the point of conky (it’s on the
                       desktop, which is mostly hidden) whilst others,
                       myself included, don’t mind a bit of eye-candy for
                       eye-candy’s sake.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Barry Kauler ☛ EasyOS_Update_delta_files_for_smaller_downloads⠀⇛


                 When you click the “update” icon on the desktop, Easy
                 looks online to see if there is a later version. If so,
                 it downloads it. Say that you are running 4.0 and the new
                 version is ‘easy-4.1-amd64.img’; the update script will
                 download this to /mnt/wkg/easy-4.1-amd64.img (or, if you
                 want the full path; /mnt/${WKG_DEV}/${WKG_DIR}easy-4.1-
                 amd64.img).


                 In earlier versions of Easy, prior to 4.1, the update
                 script used to use ‘rsync’. If you had, say /mnt/wkg/
                 easy-4.0-amd64.img’ from the previous update, the ‘rsync’
                 utility is able to compare that with the online ‘easy-
                 4.1-amd64.img’ and only download differences, then
                 construct the full ‘easy-4.1-amd64.img’.


                 The download size saving is enormous; unfortunately, the
                 rsync server at ibiblio.org has been unreliable,
                 disconnecting seemingly randomly, causing download
                 failure.


          o § Fedora Family / IBM⠀➾


                # ⚓ Business Today ☛ EXCLUSIVE:_Edge_computing_can_provide
                  enterprises_better_control_over_sensitive_data,_says_Red
                  Hat’s_Ben_Panic_–_BusinessToday⠀⇛


                       Ben Panic, Vice President and Head Of Telco, Media
                       & Entertainment – APAC in an exclusive conversation
                       with Business Today talks about how enterprises can
                       benefit from edge computing and the associated
                       costs.


                # ⚓ Navigating_global_supply_chain_disruption_–_ERP_Today⠀⇛


                       Open source is crucial for common, industry-wide
                       standards that enable companies to future-proof
                       solutions – Ishu Verma / Red Hat


                # ⚓ SDx Central ☛ IBM,_Red_Hat_Expand_Telefónica’s_Cloud_Push⠀⇛


                       Telefónica Tech signed a deal with IBM and Red Hat
                       to integrate Red Hat’s OpenShift platform into a
                       new cloud service marketed at enterprises across
                       Telefónica’s footprint in Europe and Latin America.


                       The integration will be marketed as the Telefónica
                       Red Hat OpenShift Service (TROS), which will tap
                       into the use of containers to help organizations
                       modernize their cloud applications and drive their
                       digital transformation. It will allow those
                       organizations to migrate applications to hybrid
                       cloud or multi-cloud environments using either
                       private or public clouds from hyperscalers like
                       Amazon Web Services (AWS), Microsoft Azure, or
                       Google Cloud Platform (GCP).


                       “It is going to be the way forward and what many
                       customers who want to evolve their business
                       models,” explained Santiago Madruga, VP for
                       ecosystem success in EMEA at Red Hat, in an
                       interview with SDxCentral. “When going digital,
                       it’s not just putting workloads on the cloud but
                       really transforming businesses.”


                # ⚓ Adam_Young:_Intro_to_libvirt_based_virtualization_on
                  Linux⠀⇛


                       The processes of development, installation,
                       testing, and debugging of software all benefit from
                       the use of a virtual machines. If you are working
                       in a Linux based infrastructure, you have access to
                       the virtual machine management on your system.
                       There are a handful of related technologies that
                       all work together to help you get your work done.


                # ⚓ Fedora Project ☛ Fedora_Community_Blog:_Fedora_Job_Opening:
                  Community_Action_and_Impact_Coordinator_(FCAIC)⠀⇛


                       It is bittersweet to announce that I have decided
                       to move on from my role as the Fedora Community
                       Action and Impact Coordinator (FCAIC). For me, this
                       role has been full of growth, unexpected
                       challenges, and so much joy. It has been a
                       privilege to help guide our wonderful community
                       through challenges of the last three years. I’m
                       excited to see what the next FCAIC can do for
                       Fedora. If you’re interested in applying, see the
                       FCAIC job posting on Red Hat Jobs and read more
                       about the role below.


                # ⚓ Fedora Project ☛ Changes/fno-omit-frame-pointer⠀⇛


                # ⚓ F37_proposal:_Add_-fno-omit-frame-pointer_to_default
                  compilation_flags_(System-Wide_Change_proposal)⠀⇛


                       Fedora will add -fno-omit-frame-pointer to the
                       default C/C++ compilation flags, which will improve
                       the effectiveness of profiling and debugging tools.


                # ⚓ Video ☛ EuroLinux_9.0_overview_|_ENTERPRISE_LINUX
                  DISTRIBUTION_–_Invidious⠀⇛


                       In this video, I am going to show an overview of
                       EuroLinux 9.0 and some of the applications pre-
                       installed.


                # ⚓ Red Hat Official ☛ Introducing_Red_Hat_Insights_integration
                  with_Splunk⠀⇛


                       Businesses want to make data driven decisions using
                       data platforms and artificial intelligence (AI) to
                       extract valuable knowledge to apply to the products
                       and services they use and offer. Most of them rely
                       on specialized data platforms to ingest and analyze
                       all business sources of data in a continuous
                       fashion.


          o § Debian Family⠀➾


                # ⚓ WineZGUI⠀⇛


                       There is a new application available for Sparkers:
                       WineZGUI


                       WineZGUI (pronounced Wine-Zee-Goo-Eee) is a wine
                       frontend for playing windows games with wine
                       easily. It is a collection of Bash scripts for Wine
                       Prefix Management and Linux Desktop Integration for
                       easier wine gaming experience using Zenity. It
                       allows quick launching of Direct play (not
                       installed) EXE application or game from File
                       Manager like Nautilus and allow creating separate
                       wine prefix for each Windows’ EXE binary.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ The Register UK ☛ UBports_OTA-23_is_coming:_Here’s_a_list
                  of_models_to_test_on_•_The_Register⠀⇛


                       The UBPorts community is in the final stages of
                       preparing its next release and it’s calling for
                       testers.


                       OTA-23 is getting close – the project’s Github
                       kanban looks quite good to us – and if you’re lucky
                       enough to have one of the project’s supported
                       devices lying around, then you can help.


                       Many of them are a few years old now, so there’s a
                       good chance that you’ve already replaced them and
                       they sit unloved and neglected in a drawer. The
                       starred entries in the list of devices are the best
                       supported and should have no show-stopping
                       problems. In order of seniority, that means: the
                       LG-made Google Nexus 5 (2013); the original Oneplus
                       One (2014); two models of Sony Xperia X, the F5121
                       and F5122 (2016); and Google’s Pixel 3a and 3a XL
                       (2019).


                       (The Reg FOSS desk suspects that if you have one of
                       those lying around somewhere and aren’t tempted,
                       you can probably sell it to some open-sourcy
                       enthusiast who would love to give it a go.)


                       Not starred but still high on the list are several
                       devices which are listed as “functioning well.”
                       This means that they get green ticks across almost
                       all of the feature-list apart from one or two
                       items, such as lacking support for wireless
                       external monitors. To us, this doesn’t sound like a
                       deal-breaker. These models include the Xiaomi Mi A2
                       (2018) and Poco X3 NFC (2020), and the Asus Zenfone
                       Max Pro M1 (2018).


          o § Open Hardware/Modding⠀➾


                # ⚓ Linux Gizmos ☛ Core-V_development_kit_packs_32-bit_RISC-
                  V_core⠀⇛


                       This week, the non-profit global organization
                       OpenHW presented a RISC-V based development board
                       at Embedded World 2022. The Core-V MCU dev kit
                       integrates a 32-bit CV32E40P open source RISC-
                       V core and the ArticPro eFPGA from QuickLogic.


                       OpenHW specified that the Core-V MCU features the
                       CV32E40P processor (previously known as the RI5CY)
                       which is a 32 RISC-V core with four-stage pipeline
                       that implements the RV32IM[F]C RISC-V instruction
                       extensions. To accelerate AI/ML applications, the
                       Core-V also features the low-cost QuickLogic’s
                       ArticPro eFPGA.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ MakeTech Easier ☛ AirDroid_Cast_Review:_Screen_Mirroring
                  Made_Easy⠀⇛


    * § Free, Libre, and Open Source Software⠀➾


          o § Events⠀➾


                # ⚓ The_Freedom_of_Internet_at_OSCAL_2022⠀⇛


                       How old is the Internet? Are we aware of the
                       technologies that are behind this concept? What
                       does it mean to be secure while accessing the
                       Internet? How many antivirus programs have been
                       developed to protect GNU/Linux systems? These were
                       some of the questions I had in mind when I decided
                       to attend OSCAL 2022. To my surprise, this event
                       exceeded my expectations. I discovered really
                       interesting topics and workshops, young tech
                       developers, experienced speakers, hardworking
                       organizers, and a very enthusiastic FLOSS community
                       in Tirana, Albania.


          o § Web Browsers⠀➾


                # § Chromium⠀➾


                      # ⚓ Google ☛ Chrome_104_Beta:_New_Media_Query_Syntax,
                        Region_Capture,_and_More⠀⇛


                             Unless otherwise noted, changes described
                             below apply to the newest Chrome beta channel
                             release for Android, Chrome OS, Linux, macOS,
                             and Windows. Learn more about the features
                             listed here through the provided links or
                             from the list on ChromeStatus.com. Chrome 104
                             is beta as of June 23, 2022. You can download
                             the latest on Google.com for desktop or on
                             Google Play Store on Android.


          o § Programming/Development⠀➾


                # ⚓ Adam_Young:_copy_in_for-each_loops_in_C++⠀⇛


                       The bug was that the o.calculate_position(); call
                       was supposed to update the internal state of the
                       Orbitor structure, but was called on a copy of the
                       instance in the original structure, and not on the
                       original structure itself. Thus, when a later call
                       tried to show the position, it was working with the
                       version that had not updated the position first,
                       and thus was showing the orbitors in the wrong
                       position.


                # ⚓ Conan-izing_an_OpenGL_project.⠀⇛


                       Now that I can build my app with Autotools, I want
                       to make it work with conan. In my head, I have
                       conan mapped to projects like cargo in rust and pip
                       in Python. However, C++ has a far less homogenized
                       toolchain, and I expect things are going to be more
                       “how to make it work for you.” I started with
                       Autotools to minimize that.


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ Perl_Weekly_Challenge_170:_Primorial_Numbers
                        and_Kronecker_Product⠀⇛


                # § Rust⠀➾


                      # ⚓ Slashdot ☛ Linus_Torvalds_Says_Rust_For_The_Kernel
                        Could_Possibly_Be_Merged_For_Linux_5.20_–_Slashdot⠀⇛


                             Speaking this week at the Linux Foundation’s
                             Open-Source Summit, Linus Torvalds talked up
                             the possibilities of Rust within the Linux
                             kernel and that it could be landing quite
                             soon — possibly even for the next kernel
                             cycle


                      # ⚓ The New Stack ☛ Rust_in_the_Linux_Kernel_by_2023,
                        Linus_Torvalds_Predicts [Ed: "The Linux Foundation is a
                        sponsor of The New Stack" so they get to tell the media
                        what to say or 'report' for LF sponsors' agenda;
                        Torvalds says he only worked on Git for 6 months. It
                        took off because Linux used it and Linux was a high-
                        profile project with strong reputation (before LF came,
                        attacking it reputation for money... from Linux foes
                        and GPL haters).]⠀⇛


                             Rust, the fast-growing systems programming
                             language, may be merged into the Linux kernel
                             next year, or “maybe the next release,”
                             according to Linux creator Linus Torvalds.


                             The creator of Linux made the statement
                             Tuesday during an on-stage interview at the
                             Linux Foundation‘s Open Source Summit North
                             America.


                      # ⚓ Mozilla ☛ Fuzzing_rust-minidump_for_Embarrassment_and
                        Crashes_–_Part_2_–_Mozilla_Hacks_–_the_Web_developer
                        blog⠀⇛


                             This is part 2 of a series of articles on
                             rust-minidump. For part 1, see here.


                             So to recap, we rewrote breakpad’s minidump
                             processor in Rust, wrote a ton of tests, and
                             deployed to production without any issues. We
                             killed it, perfect job.


                             And we still got massively dunked on by the
                             fuzzer. Just absolutely destroyed.


                             I was starting to pivot off of rust-minidump
                             work because I needed a bit of palette
                             cleanser before tackling round 2 (handling
                             native debuginfo, filling in features for
                             other groups who were interested in rust-
                             minidump, adding extra analyses that we’d
                             always wanted but were too much work to do in
                             Breakpad, etc etc etc).


                             I was still getting some PRs from people
                             filling in the corners they needed, but
                             nothing that needed too much attention, and
                             then @5225225 smashed through the windows and
                             released a bunch of exploding fuzzy rabbits
                             into my office.


    * § Leftovers⠀➾


          o ⚓ Posthumous_Remorse⠀⇛


          o ⚓ The_Community⠀⇛


                 Have you ever wanted a perfect community? Well search no
                 more, since it’s here! Located in cities, The Community
                 is always growing with new members! Every single day,
                 millions are becoming like us!


          o § Linux Foundation⠀➾


                # ⚓ Linux Foundation’s Site/Blog ☛ Sharing_Health_Data_while
                  Preserving_Privacy:_The_Cardea_Project [Ed: Linux Foundation
                  again paints mass surveillance as "privacy"; there's no
                  connection to Linux, it's a liability to the "Linux" brand]⠀⇛


                # ⚓ Linux Foundation’s Site/Blog ☛ Ensuring_Patents_Foster
                  Innovation_in_Open_Source [Ed: No, Linux Foundation. We need
                  to abolish software patents, not “Ensur[e] Patents Foster
                  Innovation in Open Source”; they literally repeat lies IBM
                  told in Europe]⠀⇛


                       So, I am old enough to remember when the U.S.
                       Congress temporarily intervened in a patent dispute
                       over the technology that powered BlackBerries. A
                       U.S. Federal judge ordered the BlackBerry service
                       to shutdown until the matter was resolved, and
                       Congress determined that BlackBerry service was too
                       integral to commerce to be allowed to be turned
                       off. Eventually, RIM settled the patent dispute and
                       the BlackBerry rode off into technology oblivion.


                       I am not here to argue the merits of this nearly
                       20-year-old case (in fact, I coincidentally had
                       friends on both legal teams), but it was when I was
                       introduced to the idea of companies that purchase
                       patents with the goal of using this purchased right
                       to extract money from other companies.


                       [...]


                       They added an Open Source Zone in 2019 with the
                       help of the Linux Foundation, Open Invention
                       Network, and Microsoft.


          o § Security⠀➾


                # ⚓ Google ☛ The_curious_tale_of_a_fake_Carrier.app⠀⇛


                       Although this looks like the real My Vodafone
                       carrier app available in the App Store, it didn’t
                       come from the App Store and is not the real
                       application from Vodafone. TAG suspects that a
                       target receives a link to this app in an SMS, after
                       the attacker asks the carrier to disable the
                       target’s mobile data connection. The SMS claims
                       that in order to restore mobile data connectivity,
                       the target must install the carrier app and
                       includes a link to download and install this fake
                       app.


                       This sideloading works because the app is signed
                       with an enterprise certificate, which can be
                       purchased for $299 via the Apple Enterprise
                       developer program. This program allows an eligible
                       enterprise to obtain an Apple-signed
                       embedded.mobileprovision file with the
                       ProvisionsAllDevices key set. An app signed with
                       the developer certificate embedded within that
                       mobileprovision file can be sideloaded on any
                       iPhone, bypassing Apple’s App Store review process.
                       While we understand that the Enterprise developer
                       program is designed for companies to push “trusted
                       apps” to their staff’s iOS devices, in this case,
                       it appears that it was being used to sideload this
                       fake carrier app.


                # ⚓ USCERT ☛ Malicious_Cyber_Actors_Continue_to_Exploit
                  Log4Shell_in_VMware_Horizon_Systems [Ed: VMware is failing to
                  patch its proprietary stuff that's violating the GPL]⠀⇛


                       CISA and the United States Coast Guard Cyber
                       Command (CGCYBER) have released a joint
                       Cybersecurity Advisory (CSA) to warn network
                       defenders that cyber threat actors, including
                       state-sponsored advanced persistent threat (APT)
                       actors, have continued to exploit CVE-2021-44228
                       (Log4Shell) in VMware Horizon® and Unified Access
                       Gateway (UAG) servers to obtain initial access to
                       organizations that did not apply available patches.
                       The CSA provides information—including tactics,
                       techniques, and procedures and indicators of
                       compromise—derived from two related incident
                       response engagements and malware analysis of
                       samples discovered on the victims’ networks.


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Kluwer Patent Blog ☛ UPC_–_the_great_paradox:_why_the
                        CJEU_could_bring_in_“uniform_protection”_and_“equal
                        effect”_when_interpreting_the_EU’s_“external”_patent
                        law_(e.g._TRIPS),_notwithstanding_the_futile_efforts_at
                        keeping_its_grubby_little_hands_off_“internal”_patent
                        law⠀⇛


                      # ⚓ Kluwer Patent Blog ☛ Demonstration_EPO_staff_during
                        meeting_about_re-election_president_Campinos⠀⇛


                             Staff members of the European Patent Office
                             will demonstrate in front of the Isar
                             building in Munich during the meeting of the
                             Administrative Council on 29 June 2022, where
                             re-election of president António Campinos
                             will be discussed.


                             The demonstration has been organised by trade
                             union Suepo. According to an announcement
                             distributed among Suepo members, Campinos was
                             elected and mandated by the Administrative
                             Council in 2018 to restore social dialogue at
                             the EPO after the harsh years of president
                             Benoit Battistelli, but failed to do so. ‘EPO
                             staff hoped the new President elect would put
                             an end to the breaches of fundamental
                             rights’, but is instead ‘protecting Mr
                             Battistelli’s inheritance as long as possible
                             and at all costs’.


                             ‘Mr Campinos continues the attacks against
                             staff representation and trade unions by
                             banning them from freely using mass-emails on
                             EPO lines and disbanded in 2021 any
                             secretarial support for staff representation.
                             There are also warning signs that staff
                             representation and unions will be hidden
                             further clicks away in the new Intranet.


                             Since 2012, the EPO is consistently testing
                             the limits of Employment Law and feels only
                             governed by the Tribunal. In this respect, Mr
                             Campinos continues to act along the line of
                             his predecessor.’


                # § Copyrights⠀➾


                      # ⚓ Public Domain Review ☛ Precedents_of_the
                        Unprecedented:_Black_Squares_Before_Malevich_–_The
                        Public_Domain_Review⠀⇛


                             Described by Kasimir Malevich as the “first
                             step of pure creation in art”, his Black
                             Square of 1915 has been cast as a total break
                             from all that came before it. Yet searching
                             across more than five hundred years of images
                             related to mourning, humour, politics, and
                             philosophy, Andrew Spira uncovers a slew of
                             unlikely foreshadows to Malevich’s radical
                             abstraction.



                    ䷩ 𝚕𝚒𝚗𝚎 4163

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Gemini_version_available_♊︎


✐ Links_23/06/2022:_3,500_Games_on_Steam_Deck_Verified_or_Playable,_Gemini_on
ESP32⠀✐


Posted in News_Roundup at 12:47 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o New_Releases
          o Devices/Embedded
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Chromium
          o SaaS/Back_End/Databases
          o Programming/Development
                # Shell/Bash/Zsh/Ksh
          o Standards/Consortia
    * Leftovers
          o Hardware
          o Proprietary
          o Politics
          o Linux_Foundation
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Overpopulation
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ FLOSS_Weekly_686:_Authentic_Data_–_David_Huseby,_Authentic
                  Data⠀⇛


                       Cryptography expert Dave Huseby tells Doc Searls
                       and Katherine Druckman how to build infinitely
                       scalable layer two solutions that unbind the
                       Internet from time and space without changing
                       existing systems. All with authentic data.


          o § Instructionals/Technical⠀➾


                # ⚓ uni Toronto ☛ Some_network_speeds_and_network_related
                  speeds_we_see_in_mid_2022⠀⇛


                       On 1G connections, anything can get wire bandwidth
                       for streaming TCP traffic (or should be able to; if
                       it can’t, you have some sort of problem). On 10G
                       connections, a path between Linux machines without
                       a firewall in the middle should readily run over
                       900 Mbytes/sec for a TCP connection without any
                       specific tuning (and without Ethernet jumbo
                       frames). We haven’t tried to measure our OpenBSD
                       firewalls recently but I don’t think they can move
                       traffic this fast yet. SSH connections aren’t this
                       fast; we can count on hitting 1G wire bandwidth but
                       generally not anywhere near close to 10G TCP
                       bandwidth with a single SSH connection.


                # ⚓ [Old] Rohan Kumar ☛ A_look_at_search_engines_with_their_own
                  indexes⠀⇛


                       This is a cursory review of all the indexing search
                       engines I have been able to find.


                       The three dominant English search engines with
                       their own indexesnote 1 are Google, Bing, and
                       Yandex (GBY). Many alternatives to GBY exist, but
                       almost none of them have their own results;
                       instead, they just source their results from GBY.


                       With that in mind, I decided to test and catalog
                       all the different indexing search engines I could
                       find. I prioritized breadth over depth, and
                       encourage readers to try the engines out themselves
                       if they’d like more information.


                # ⚓ Learning_Vim,_what_am_i_doing?⠀⇛


                       I’ve been using Linux and the Linux terminal for a
                       long time. I dabble in programming, web
                       development, server management, and all sorts of
                       fun open-source stuff. I’ve always got by with
                       using nano for everything. I think I used to do
                       stuff before nano, but I can’t for the life of me
                       remember what I used then. Maybe just a bunch of
                       ‘cat’ and gui text editors? Anyway, I’ve always
                       heard that Vi/Vim is “powerful” and can speed up
                       your coding. I’ve heard that wars have been fought
                       over emacs vs vi (I’ve used neither very much). But
                       I’ve decided to take the plunge. I’m working my way
                       through vimtutor, taking notes, working on
                       mnemonics.


          o § Games⠀➾


                # ⚓ Its FOSS ☛ Minetest,_an_Open_Source_Minecraft_Alternative⠀⇛


                       Back in 2009, Minecraft was introduced to the
                       world. Since then, it has become a cultural
                       phenomenon. In that time period, several developers
                       have released open-source games with similar ideas
                       and mechanics. Today, we will look at one of the
                       biggest ones: Minetest.


                # ⚓ GamingOnLinux ☛ Meet_me_at_NooN_is_a_sweet_new_puzzler_with
                  time-loop_mechanics⠀⇛


                       Meet me at NooN is the first game from the duo at
                       Pandaroo Interactive and quite an impressive entry
                       to the puzzle genre.


                # ⚓ GamingOnLinux ☛ Rail_Route:_The_Story_of_Jozic_is_a_great
                  free_intro_to_the_tycoon_&_management_game⠀⇛


                       Rail Route: The Story of Jozic is a standalone free
                       expansion and introduction to the main Rail Route
                       game. Giving you an interesting way to try out this
                       pretty great tycoon & management game.


                # ⚓ GamingOnLinux ☛ RTS_game_TFC:_The_Fertile_Crescent_gets_a
                  great_looking_roadmap⠀⇛


                       TFC: The Fertile Crescent is a pixel-art RTS that
                       resembles some of the classics like Age of Empires.
                       It’s currently in Early Access with Native Linux
                       support and their new roadmap looks great.


                # ⚓ GamingOnLinux ☛ GZDoom_powered_dark-fantasy_FPS_‘Hands_of
                  Necromancy’_is_out_now⠀⇛


                       Powered by the awesome GZDoom game engine, Hands of
                       Necromancy looks like another solid choice for
                       those of you (like me!) who absolutely love retro
                       shooters. Made in the spirit of the classics like
                       Heretic, Hexen, Doom and Quake it does look pretty
                       good.


                # ⚓ GamingOnLinux ☛ 3,500_games_now_Steam_Deck_Verified_or
                  Playable⠀⇛


                       Another great milestone has been hit for the Steam
                       Deck, with Valve’s popular Linux-powered handheld
                       now having 3,500 games rated as either Verified or
                       Playable.


    * § Distributions and Operating Systems⠀➾


          o § New Releases⠀➾


                # ⚓ 9to5Linux ☛ KaOS_Linux_2022.06_Released_with_KDE_Plasma
                  5.25_Desktop_and_Calamares_3.3_Installer⠀⇛


                       
                       Coming two months after KaOS Linux 2022.04, the
                       KaOS Linux 2022.06 released is here with the latest
                       and greatest KDE Plasma 5.25.1 desktop environment,
                       which is accompanied by the latest KDE Frameworks
                       5.95 and KDE Gear 22.04.2 software suites, all
                       built against the Qt 5.15.5 framework.


                       So there you have it! If you want to enjoy the most
                       recent KDE technologies, you can download and
                       install KaOS Linux right now on your personal
                       computer. To top that, KaOS’s Plasma theme Midna
                       has been updated for the KDE Plasma 5.25 desktop
                       environment changes with the addition of a well-
                       integrated virtual keyboard in the login and lock
                       screens.


          o § Devices/Embedded⠀➾


                # ⚓ Gemini_on_ESP32⠀⇛


                       I received my ESP32 dev board about two weeks ago I
                       think, but I haven’t found the time to do this with
                       all the renovation/MA/work/orchestra craziness
                       going on.


                       It’s slow and I don’t know if it can handle
                       multiple requests at the same time. But it seems
                       pretty stable, after I increased the thread stack
                       size from 4K to something more reasonable.


    * § Free, Libre, and Open Source Software⠀➾


          o § Web Browsers⠀➾


                # § Chromium⠀➾


                      # ⚓ Mark Nottingham ☛ What_willwould_a_Chromium-only_Web
                        look_like?⠀⇛


                             On the face of it, there is some sense to it
                             – after all, most W3C and WHATWG
                             specifications have been written
                             algorithmically (rather than declaratively)
                             for a while now. Why not just converge on a
                             single actual codebase? That way, interop on
                             things like HTML parsing is perfect, but
                             people can still choose the browser with the
                             features (e.g., privacy protections) that
                             they want.


                             It’s also not that far-fetched. Microsoft has
                             already ditched their engine for Chromium;
                             we’re all worried about Mozilla’s health and
                             long-term (or even medium-term) viability,
                             and Apple is only one competition judgement
                             away from having to open up iOS to other
                             engines.


                             After all, the code is what determines what
                             browsers are capable of and therefore it
                             defines the shape of the Web. Chromium
                             already has a high market share of browser
                             engines; why not just formalise it?


                             Putting aside the many arguments one might
                             raise about diversity, risk management,
                             innovation, and so on, I want to focus on one
                             aspect of this potential change – governance.


          o § SaaS/Back End/Databases⠀➾


                # ⚓ TecMint ☛ 8_Best_MySQL/MariaDB_GUI_Tools_for_Linux
                  Administrators⠀⇛


                       MySQL is one of the most widely-used open-source
                       relational database management systems (RDBMS),
                       that has been around for a long time. It is an
                       advanced, fast, reliable, scalable, and easy-to-use
                       RDBMS intended for mission-critical, heavy-load
                       production systems and packaged software.


                       In this guide, we will share a list of the best
                       MySQL graphical user interface (GUI) tools for
                       Linux systems.


                # ⚓ Rlang ☛ Bind_together_two_data_frames_by_their_rows_or
                  columns_in_R⠀⇛


                       Bind together two data frames by their rows or
                       columns in R, To join two data frames by their
                       rows, use the bind_rows() function from the dplyr
                       package in R.


          o § Programming/Development⠀➾


                # ⚓ Geeks For Geeks ☛ Why_Every_Developer_Should_Learn_Data
                  Structures_and_Algorithms?⠀⇛


                       Having proper knowledge of Data Structure and
                       Algorithms makes a good identity for a Software
                       Developer. The main reason behind this is that it
                       improves developers’ problem-solving ability to a
                       great extent. So tech giants like Google, Meta,
                       Adobe, Amazon, Netflix, etc. hire software
                       developers with in-depth knowledge of Data
                       Structure and Algorithms as they are more capable
                       of making the right decisions when it comes to
                       problem-solving.


                # ⚓ Ben Congdon ☛ [Reposted]_You_Need_to_be_Wrong_(Sometimes)⠀⇛


                       “Well-calibrated” means that if you predict
                       something occurs with X% probability, then that
                       event actually occurs X% of the time. Since
                       predictions are often made on one-off events,
                       another way of expressing calibration is that X% of
                       predictions that you made with X% confidence should
                       resolve in your favor. For example, if you make 100
                       predictions of 100 independent events, each with
                       probability 75%, then you’d expect that (roughly)
                       75 of your predictions would be “correct”.


                # § Shell/Bash/Zsh/Ksh⠀➾


                      # ⚓ Python_CLI_encrypted_chat_program.⠀⇛


                             This CLI program written in Python allows you
                             to chat securely with encryption (Fernet).


          o § Standards/Consortia⠀➾


                # ⚓ Preaching_to_the_choir:_the_web_sucks⠀⇛


                       I know, I know, you guys wouldn’t be reading this
                       unless you somewhat already have come to this
                       conclusion but a little bit of circle-jerking isn’t
                       too bad.


                       About a month ago I switched back to Firefox. I had
                       been running falkon for a few months and then
                       waterfox-g3 before that. I don’t remember why I
                       switched away from Firefox, sometimes you just get
                       that itch to try something new, but I enjoyed my
                       journey through alternative browsers.


    * § Leftovers⠀➾


          o ⚓ car_troubles⠀⇛


                 So one of the spark plugs managed to shoot it’s way out
                 of the top of my engine, destroying a coil with it and
                 then only having 3 cylinders while going 80 on the
                 highway.


          o ⚓ Wash_Your_Steering_Wheel⠀⇛


                 If you own a vehicle, this is a reminder to wash the
                 steering wheel.


                 It’s a spot that people often forget about. The weel is
                 usually a dark color, making it a difficult to spot the
                 grime building up. With hands touching it all the time,
                 it’s as dirty as a doorknob.


          o § Hardware⠀➾


                # ⚓ Stacy on IoT ☛ They_call_it_a_security_drone,_but_this_is_a
                  flying_multisensor⠀⇛


                       The Tando drone has a camera for visually scanning
                       a facility after an alarm has been raised or for
                       general airborne patrol, but I’m most interested in
                       its other features, such as temperature monitoring
                       and air quality sensors that might be more useful
                       in industrial settings. The ability to track the
                       release of dangerous chemicals in a refinery or
                       chemicals plant could be very helpful, for example.


          o § Proprietary⠀➾


                # ⚓ YLE ☛ Google_is_buying_more_land_from_the_city_of_Hamina⠀⇛


                       Google employs roughly 400 people directly and
                       indirectly in various industries in Hamina.


                       In 2020, Google opened its sixth data centre in
                       Hamina in an old paper mill that was formerly
                       operated by Stora Enso. The data centre uses
                       seawater to cool the massive complex and is powered
                       by electricity from three new wind farms.


          o § Politics⠀➾


                # ⚓ The Hill ☛ Tech_executives_urge_government_to_share_cyber
                  threat_intel⠀⇛


                       Tech leaders testifying on Wednesday before a House
                       subcommittee on cyber told lawmakers that more
                       coordination is needed between the public and the
                       private sector to identify security threats,
                       including cyber, that stem from emerging
                       technologies like quantum computing and artificial
                       intelligence.


                       Ron Green, executive vice president and chief
                       security officer at Mastercard, said that
                       partnership should incentivize the government to
                       share threat intelligence to the private sector so
                       that both sectors are able to mitigate
                       cybersecurity risks posed by U.S. adversaries both
                       at home and abroad.


                # ⚓ Broadband Breakfast ☛ FTC_Commissioner_Says_Agency_Report
                  on_AI_for_Online_Harms_Did_Not_Consult_Outside_Experts⠀⇛


                       The one dissenting opinion on the report was from
                       Phillips, who said the FTC did not do the study
                       that was required by Congress. As part of the 2021
                       Consolidated Appropriations Act, Congress asked the
                       FTC to conduct a study on how artificial
                       intelligence could address online harms such as
                       fake reviews, hate crimes and harassment and child
                       sexual abuse.


                       “I do not believe we conducted the requisite study,
                       and I do not think the report on AI issued by the
                       Commission takes sufficient care to answer the
                       questions Congress asked,” Phillips said in his
                       dissenting statement.


                # ⚓ New York Times ☛ Saudi_Leader_Expected_in_Turkey_for_First
                  Visit_Since_Khashoggi_Murder⠀⇛


                       The rapprochement follows similar moves by other
                       countries to rebuild ties with Saudi Arabia, which
                       drew global outrage over Mr. Khashoggi’s killing
                       and dismemberment inside the Saudi consulate in
                       Istanbul on Oct. 2, 2018.


                # ⚓ JURIST ☛ Russia_court_upholds_Meta_ban_for_‘extremist
                  activity’⠀⇛


                       State news agency TASS reported that the court
                       called the ban “lawful and justified” after
                       Russia’s media regulator, Roskomnadzor, and Federal
                       Security Service (FSB) intervened in support of it.
                       Meta’s lawyers argued that the “extremist” label
                       and the resulting ban were inappropriate as Meta
                       did not promote extremist content and that
                       “refusing to block access to content and labeling
                       state-controlled media were not activities that
                       qualified as extremist.”


                       The court’s ruling means that Meta platforms
                       Facebook and Instagram will continue to be largely
                       inaccessible within Russia.


          o § Linux Foundation⠀➾


                # ⚓ Cardano_Foundation_joins_The_Linux_Foundation_as_a_Gold
                  Member⠀⇛


                       We are delighted to announce our membership with
                       The Linux Foundation, the nonprofit organization
                       enabling mass innovation through open source. The
                       Cardano Foundation has joined as a Gold member,
                       becoming the only nonprofit active at this level.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Site36 ☛ Border_Security_Partnership:_EU_states
                        consider_unprecedented_biometrics_agreement_with_U.S.⠀⇛


                             In a letter to several EU member states and
                             the Commission, the U.S. government threatens
                             a new condition for visa-free entry. There is
                             confusion in Brussels over a response.
                             Parliament was the last to be informed about
                             the initiative, although it concerns
                             fingerprints and facial images.


                      # ⚓ Business Insider ☛ Inside_ID.me’s_torrid_pandemic
                        growth_spurt,_which_led_to_frantic_hiring,_ill-equipped
                        staff,_and_data-security_lapses_as_the_company_closed
                        lucrative_deals_with_unemployment_agencies_and_the
                        IRS⠀⇛


                             As it grew rapidly, so did errors, technical
                             hurdles, and strain on its relatively new
                             staff of customer service representatives,
                             nine former ID.me employees told Insider.
                             Helpline queues for the millions of Americans
                             who relied on unemployment benefits in 2020
                             and 2021 would sometimes number in the
                             thousands because of these strains, they
                             said.


                             ID.me’s rush to hire and train nearly 1,500
                             new workers at this time also led to lax
                             verification practices and poor user privacy
                             protections, these people said. Information
                             like passports and social security numbers
                             were often posted in internal Slack channels,
                             and some employees were hired and given
                             access to confidential data without completed
                             background checks. Some chattered about how
                             easy it would be to steal users’ information.
                             Most of the former employees who spoke with
                             Insider did so under condition of anonymity
                             for fear of professional repercussions


                      # ⚓ The Verge ☛ Brave’s_search_engine_lets_you_customize
                        your_results⠀⇛


                             Brave Search has launched a new feature that
                             gives you a way to create or apply custom
                             filters that change the way its results are
                             ranked. It’s called “Goggles,” and it could
                             potentially help uncover sources you might
                             not find right away on traditional search
                             engines like Google.


                             Brave has some demos ready for users to try
                             today, including ones that prioritize posts
                             from smaller tech blogs and filter out posts
                             from the 1,000 most-viewed sites on the web.
                             There’s even a Goggle to exclude posts from
                             Pinterest — because Brave clearly knows the
                             frustration of trying to find an image and
                             getting a Pinterest post with no source.
                             Brave says these Goggles are just for
                             demonstrative purposes, and developers can
                             expand on or fork them. It will start
                             deleting these Goggles once users start
                             coming up with their own, but I’m hoping the
                             Pinterest one sticks around.


                      # ⚓ The Verge ☛ Zuckerberg_details_his_plan_to_move_your
                        digital_items_across_the_metaverse⠀⇛


                             Mark Zuckerberg announced on Wednesday that
                             Facebook Pay has officially become Meta Pay,
                             but his post is mainly focused on what the
                             company hopes to build in the future — “a
                             wallet for the metaverse.” While Meta Pay is
                             essentially the same tool as it was before,
                             just with Meta branding, Zuckerberg says the
                             company is working on something that will let
                             users manage their identities, items, and
                             payment methods while making their way
                             through the digital world that Meta bets will
                             be the future.


                             The company has hinted at these plans before
                             — its May announcement of the Meta Pay
                             rebranded also mentioned that it was “scoping
                             out what a single wallet experience might
                             look like” with regards to making payments
                             and storing your identity and digital items.
                             Zuckerberg’s post, though, focuses mostly on
                             how the company’s metaverse wallet will
                             enable proof of digital ownership; he
                             mentions how it could be used to create and
                             buy “digital clothing, art, videos, music,
                             experiences, virtual events, and more.”


          o § Defence/Aggression⠀➾


                # ⚓ CNN ☛ Amid_high-profile_hearings,_some_January_6_committee
                  members_beef_up_security⠀⇛


                       When Rep. Adam Kinzinger recently received a letter
                       at his home threatening to execute him, his wife
                       and his baby, the Illinois Republican immediately
                       flagged it for the United States Capitol Police.


                       But Kinzinger — whose high-profile role on the
                       House select committee investigating the January 6,
                       2021, insurrection has made him a reviled figure on
                       the right and who is no stranger to such violent
                       threats — was advised by some of his GOP
                       colleagues, who also voted to impeach Donald Trump,
                       to elevate the issue to the FBI as an added
                       precaution, sources said.


                       It’s just the latest sign of how seriously the
                       threat of political violence is being taken by
                       lawmakers in the Capitol as the select committee
                       publicly reveals the findings of its nearly
                       yearlong investigation into the January 6
                       [insurrection]. Committee members say they are
                       taking extra security steps — including requesting
                       security details, which several lawmakers have
                       already been assigned — amid the heightened
                       concerns over their safety as the public hearings
                       play out.


                # ⚓ The Hill ☛ Kinzinger:_Execution_threats_over_Jan._6_panel
                  show_‘depravity_of_what’s_existing_out_there’⠀⇛


                       Rep. Adam Kinzinger (R-Ill.) said the “constant”
                       death threats he’s received over the course of the
                       Jan. 6 House panel’s hearings reveal the “depravity
                       of what’s existing out there.”


                       Kinzinger told host Wolf Blitzer on CNN’s
                       “Situation Room” that threats against him have only
                       increased as the House committee prepares for its
                       fifth hearing on Thursday about the events leading
                       up to a pro-Trump mob storming the U.S. Capitol
                       last year.


                       “I even heard a voicemail just this morning that we
                       got last night threatening execution. That kind of
                       seems to be the normal thing nowadays is just
                       threaten execution,” the congressman said.


                # ⚓ The Atlantic ☛ What_Are_Trump_Supporters_So_Afraid_Of?⠀⇛


                       Such conversations are just part of life in divided
                       America now. We live in a democracy, and there’s no
                       law (nor should there be) against the willing
                       suffocation of one’s own brain cells with
                       television and the internet. But living in an
                       alternate reality is unhealthy—and dangerous, as I
                       realized yet again while watching the January 6
                       committee hearings and listening to the stories of
                       Republicans, such as Arizona House Speaker Rusty
                       Bowers and others, describing the threats and
                       harassment they have received for doing their duty
                       to the Constitution.


                       And the threats don’t stop with political figures;
                       families are now in the crosshairs. Representative
                       Adam Kinzinger, for example, tweeted Monday about a
                       letter he received in which the writer threatened
                       not only to kill him, but to kill his wife and
                       infant son.


          o § Environment⠀➾


                # § Overpopulation⠀➾


                      # ⚓ CS Monitor ☛ ‘Pray_for_a_miracle’:_Taps_run_dry_as
                        drought_hits_Mexican_city⠀⇛


                             A combination of an intense drought, poor
                             planning, and high water use has left
                             residents of Mexico’s industrial powerhouse
                             to resort to extreme measures that call up
                             images of isolated, poorer areas: storing
                             water in buckets to use a scoopful at a time.


          o § Censorship/Free Speech⠀➾


                # ⚓ Medium ☛ The_Fall_Of_Reddit:_Why_It’s_Quickly_Declining
                  into_Chaos⠀⇛


                       I only recently found out that Ghislaine Maxwell,
                       wife to Jeffery Epstein, ran one of the most
                       powerful Reddit accounts on the website. In fact,
                       it was the eighth-most popular account by karma on
                       Reddit.


                       I won’t get into the implications of that — as it
                       could be an article on its own — but it’s only one
                       case of elites having massive power on Reddit.


                       The bigger issue is that Reddit has several
                       competing corporate interests.


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


                # ⚓ Mexico News Daily ☛ AMLO_to_bring_up_case_of_Wikileaks
                  founder_Assange_during_meeting_with_Biden⠀⇛


                       “His crime, in quotation marks, was to report
                       serious human rights violations in the world as
                       well as interference of the United States
                       government in the internal affairs of other
                       countries – that’s what Assange did,” he said.


                       “He’s the best journalist of our time in the world
                       and, I repeat, he’s been very unfairly treated,
                       worse than a criminal. This is a disgrace for the
                       world,” said López Obrador, known more for
                       attacking journalists rather than trying to protect
                       them.


                       “A lot of people don’t know that what he did, with
                       an unorthodox investigation, was to gather
                       [diplomatic] cables, reports from United States
                       embassies, that spoke about acts of interventionism
                       and about crimes committed – flagrant violations of
                       human rights, [exposed] not just [in] texts, but
                       [in] images too.”


                # ⚓ Reason ☛ Julian_Assange’s_Case_Is_a_Frightening_Omen_for
                  Press_Freedom⠀⇛


                       While the ordeal of Wikileaks founder Julian
                       Assange elicits grudging reactions from many
                       American journalists who find him distasteful, his
                       pending extradition to the United States, just
                       approved by the British government, spurs protests
                       around the world. In countries not blessed with a
                       First Amendment, advocates of free speech rightly
                       see Assange’s years-long persecution for exposing
                       U.S. government secrets as an attack on
                       transparency and a threat to anybody who
                       embarrasses powerful officials. Comfortable seat-
                       warmers who are cozy with the powers-that-be may
                       hesitate, but real journalists battling censorious
                       politicians recognize Assange as one of them.


                # ⚓ VOA News ☛ Journalists_Demand_Assange_Be_Released_From_UK
                  Jail⠀⇛


                       Fifteen representatives of journalist and
                       publishers’ unions and organizations from six
                       countries gathered in Geneva for the ‘call to free
                       Julian Assange in the name of press freedom’


                       The petitioners also called on Swiss authorities,
                       who have said they have worked to protect Assange,
                       to facilitate his release by offering him a safe
                       haven from further prosecution in Switzerland.


          o § Civil Rights/Policing⠀➾


                # ⚓ KSAT TV ☛ Officer_husband_of_slain_Uvalde_teacher_was
                  detained,_had_gun_taken_away_after_trying_to_save_wife⠀⇛


                       McCraw said Mireles called Ruiz and told him that
                       “she had been shot and was dying.”


                       “And what happened to him, is he tried to move
                       forward into the hallway,” McCraw said. “He was
                       detained and they took his gun away from him and
                       escorted him off the scene.”


                # ⚓ The Hill ☛ Police_use_social_media_to_search_for_teens_who
                  broke_into_Florida_mansion,_threw_party⠀⇛


                       The office said just because videos were posted on
                       Snapchat, where posts disappear after a certain
                       amount of time, does not mean they will stay
                       private, as word can spread and people can tag
                       others in Instagram posts, which do not disappear.
                       It added that the office can subpoena Snapchat for
                       videos.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Simpler_Times⠀⇛


                       The Internet was not nearly as heavily populated or
                       restricted as it is today, nor was it as filled
                       with bots, spam, tracking, and harmful content of
                       one kind or another. I lived in a very small
                       farming town in those days, and the tight-knit,
                       trusting culture of that town was similar to
                       culture of the early Internet.


          o § Monopolies⠀➾


                # ⚓ Computer World ☛ What_the_EU_Qualcomm_ruling_means_for_big
                  tech_antitrust_efforts⠀⇛


                       This week, Qualcomm successfully appealed against a
                       €997 million ($1 billion) fine imposed by European
                       Union regulators in 2019. The fine was originally
                       given after the European Commission ruled that
                       between 2011 and 2016, the chipmaker had paid
                       billions of dollars to Apple to exclusively use its
                       chips in all of its iPhones and iPads, an act that
                       breaks EU antitrust laws.


                       The decision to nullify the fine came after the
                       second highest court in Europe, The General Court,
                       found that “a number of procedural irregularities
                       affected Qualcomm’s rights of defense”, ultimately
                       invalidating the Commission’s analysis.


                       The judgement was also very critical of basic
                       aspects of the Commission legal service’s process,
                       including the fact that meetings with third parties
                       had not been recorded, or that the notes of
                       meetings were too general for Qualcomm to properly
                       understand the complaints made against it.



                    ䷩ 𝚕𝚒𝚗𝚎 5083

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Gemini_version_available_♊︎


✐ Links_23/06/2022:_Open_Hardware_and_More_LF_‘Fluff’⠀✐


Posted in News_Roundup at 2:04 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o Open_Hardware/Modding
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Linux_Foundation
          o Security
          o Defence/Aggression
          o Environment
                # Energy
                # 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 Monopolies
                # Patents
                # Copyrights
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ I_Can’t_Stop_Tinkering_With_Xmonad!_(NamedActions
                  and_GridSelect)_–_Invidious⠀⇛


                       I have an addiction. I’m addicted to configuring my
                       window managers. There was nothing wrong with my
                       Xmonad config. But I just couldn’t stop myself from
                       thinking that it could be better. So I decided to
                       play around with two Xmonad libraries (NamedActions
                       and GridSelect) and see if I could get them to do
                       what I wanted.


                # ⚓ Video ☛ The_Worst_Linux_Advice_You_Will_Ever_Hear_–
                  Invidious⠀⇛


                       I’ve seen some pretty terrible pieces of linux
                       advice out there but this is without a doubt the
                       worst thing that I have ever heard.


                # ⚓ mintCast Pocast ☛ 389.5_–_The_Martial_Arts_of_Podcasting_–
                  mintCast⠀⇛


                       1:04 Linux Innards
                       55:23 Vibrations from the Ether
                       58:20 Housekeeping and Announcements


                       In our Innards section, we interview Steve Seguin,
                       creator of VDO.Ninja


                # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_959⠀⇛


                       Joel scans when he shops.


          o § Applications⠀➾


                # ⚓ OMG Ubuntu ☛ Flameshot_Screenshot_Tool_Just_Added_Even_More
                  Features⠀⇛


                       When it comes to Linux screenshot tools nothing
                       comes close to Flameshot.


                       It’s quite the statement to make, I know. But this
                       Qt-based screen-snipping utility richly earns its
                       place on our list of the best Ubuntu apps because
                       it is that good.


                       Today, a new version of Flameshot arrived that adds
                       even more features to its already feature-crammed
                       toolset.


                       In this post I tell you a bit more about what’s
                       new, and point you in the direction of official
                       downloads so you can try it for yourself,
                       regardless of what Linux distribution or packaging
                       perforce you have.


          o § Instructionals/Technical⠀➾


                # ⚓ Hackaday ☛ Linux_Fu:_Roll_With_The_Checksums⠀⇛


                       We are often struck by how often we spend time
                       trying to optimize something when we would be
                       better off just picking a better algorithm. There
                       is the old story about the mathematician Gauss who,
                       when in school, was given busy work to add the
                       integers from 1 to 100. While the other students
                       laboriously added each number, Gauss realized that
                       100+1 is 101 and 99 + 2 is also 101. Guess what 98
                       + 3 is? Of course, 101. So you can easily find that
                       there are 50 pairs that add up to 101 and know the
                       answer is 5,050. No matter how fast you can add,
                       you aren’t likely to beat someone who knows that
                       algorithm. So here’s a question: You have a large
                       body of text and you want to search for it. What’s
                       the best way?


                # ⚓ UNIX Cop ☛ How_to_Install_Apache_Maven_on_Ubuntu_22.04⠀⇛


                       Hello, friends. In this post, you will learn how to
                       install Apache Maven on Ubuntu 22.04 This post, is
                       quite short, but it is useful for users who are
                       just starting with Java.


                # ⚓ Video ☛ How_to_install_Sublime_Text_on_Pop!_OS_22.04_–
                  Invidious⠀⇛


                       In this video, we are looking at how to install
                       Sublime Text on Pop!_OS 22.04.


                # ⚓ Linux Made Simple ☛ How_to_install_Unity_2022.1.5_on_a
                  Chromebook [Ed: But this is a Microsoft Mono trap]⠀⇛


                       Today we are looking at how to install Unity
                       2022.1.5 on a Chromebook. Please follow the video/
                       audio guide as a tutorial where we explain the
                       process step by step and use the commands below.


          o § Games⠀➾


                # ⚓ Techdirt ☛ KOTOR_2_Released_On_Nintendo_Switch_In_A_State
                  That_Makes_It_Un-Finishable⠀⇛


                       Video games have always had bugs at the time of
                       their release, though there has been a trend
                       coinciding with the uptick in digital game sales in
                       which games seem to be published in broken states
                       far too often and are then “fixed” with a day-one
                       patch or something of the like. Some of these bugs
                       are on the more minor side, while some involve game
                       releases that were very clearly pushed for way too
                       early.


    * § Distributions and Operating Systems⠀➾


          o § Open Hardware/Modding⠀➾


                # ⚓ The Register UK ☛ RISC-V_International_reveals_latest_spec
                  approvals_•_The_Register⠀⇛


                       RISC-V International has grown its pile of royalty-
                       free, open specifications, with additional
                       documents covering firmware, hypervisors, and more.


                       RISC-V – pronounced “risk five”, and not to be
                       confused with the other architecture of that name,
                       RISC-5 – essentially sets out how a CPU core should
                       work from a software point of view. Chip designers
                       can implement these instruction set specifications
                       in silicon, and there are a good number of big
                       industry players backing it.


                       The latest specs lay out four features that
                       compatible processors should adhere to. Two of
                       them, E-Trace and Zmmul, will be useful for
                       organizations building RISC-V hardware and
                       software, and the other two could prove important
                       in future, aiding the development of OSes to run on
                       RISC-V computers.


                # ⚓ Raspberry Pi ☛ The_names_of_the_new_Astro_Pi_computers_get
                  revealed⠀⇛


                       We and our collaborators at ESA Education are
                       excited to announce that 17,168 programs written by
                       young people from 26 countries have been
                       successfully deployed on board the International
                       Space Station (ISS) for the European Astro Pi
                       Challenge 2021/22. And we can finally reveal the
                       names of the two new and upgraded Astro Pi
                       computers that Astro Pi participants have chosen.


                # ⚓ Hackaday ☛ Putting_A_Little_More_Juice_In_Your_Emulation
                  Station⠀⇛


                       After you’ve built a snazzy Raspberry Pi-powered
                       retro gaming console, you might be wondering if you
                       could have just a wee bit more power and run some
                       of those other games you might remember, such as
                       Xbox, Wii, or PS3. Perhaps in the future, a later
                       revision of an RPi could handle it but currently,
                       to emulate the 6th/7th generation of consoles, you
                       need something a little beefier. Luckily, [Zac] got
                       his hands on an old gaming laptop and turned it
                       into his own game console.


    * § Free, Libre, and Open Source Software⠀➾


          o § Programming/Development⠀➾


                # ⚓ DEV Community ☛ Afshan_Ahmed_Khan:_Outreachy_Week-3:
                  Everybody_struggles [Ed: "Everybody struggles" became a
                  chorus for "cannot complete my assignment" and "it's OK", as
                  if nobody is supposed to accomplish it but that's not a
                  failure of Outreachy]⠀⇛


    * § Leftovers⠀➾


          o ⚓ Common Dreams ☛ ‘Villages_Have_Been_Completely_Destroyed’:
            Earthquake_Kills_900+_in_Afghanistan⠀⇛


                 A powerful earthquake in Afghanistan killed more than 900
                 people and injured hundreds more on Wednesday, flattening
                 homes and devastating entire villages in a nation already
                 ravaged by decades of U.S.-led war and an ongoing
                 economic collapse.


                 The earthquake, which hit overnight, had an estimated
                 magnitude of 6.1 with an epicenter near the nation’s
                 border with Pakistan.


          o ⚓ Counter Punch ☛ Slavoj_Zizek_Does_His_Christopher_Hitchens
            Impression⠀⇛


                 But, yeah.  Zizek has been out of the left-leaning
                 limelight for a while.  Maybe this inattention to his ego
                 from the media, his fans and detractors is why he penned
                 a piece attacking pacifists and calling for a stronger
                 NATO in the June 21, 2022 edition of the mainstream
                 liberal publication British publication the Guardian. 
                 Yes, like a few others mostly in the US/western European
                 Left, Zizek has decided that the only response to the
                 Russia-Ukraine conflict is full-on support for the Kyiv
                 government, no matter what.  Going beyond others on the
                 Left who have voiced similar sentiments, but kept their
                 opposition to NATO/US troops and air involvement intact,
                 Zizek has jumped full on board with the “fight to the
                 last Ukrainian” crowd; the liberals, nazis, church
                 patriarchs and every other segment of the pro-war crowd.


                 In his column, he lumps Noam Chomsky and Henry Kissinger
                 together, solely because they both support negotiations
                 instead of a wider war.  In making this comparison
                 conveniently ignores the differences in each man’s
                 statements on the subject.  Of course, that is truly the
                 only approach he can take—by removing context from the
                 equation.  After attacking pacifism and its advocates
                 throughout the piece, Zizek makes a claim that only
                 someone with his ego and arrogance would be okay with
                 making, at least seriously.  He writes, “Today, one
                 cannot be a leftist if one does not unequivocally stand
                 behind Ukraine.”  in other words, Zizek’s test of left
                 moral purity is whether or not they support every and any
                 version of the Kyiv government and its war.  In a
                 sentence, Zizek goes from just someone stating his
                 argument against negotiated settlement for an expanded
                 NATO, and against rational alternatives to a long, deadly
                 and potentially wider war to purging a fairly large
                 segment of the international left from the debate.  As
                 far as I know, no other leftist who supports Ukraine has
                 dismissed those who don’t from the ranks, such as they
                 are.  No other leftist has written out those they
                 disagree with over the Ukraine-Russia conflict.  Slavoj
                 Zizek, on the other hand, makes this the core of his
                 argument.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ How_Far_Can_You_Push_A_£500_Small_Electric_Car;
                  Four_Years_Of_The_Hacky_Racer⠀⇛


                       Four years ago when the idea of a pandemic was
                       something which only worried a few epidemiologists,
                       a group of British hardware hackers and robotic
                       combat enthusiasts came up with an idea. They would
                       take inspiration from the American Power Racing
                       Series to create their own small electric racing
                       formula. Hacky Racers became a rougher version of
                       its transatlantic cousin racing on mixed surfaces
                       rather than tarmac, and as an inaugural meeting
                       that first group of racers convened on a cider farm
                       in Somerset to give it a try. Last weekend they
                       were back at the same farm after four years of
                       Hacky Racer development with racing having been
                       interrupted by the pandemic, and Hackaday came
                       along once more to see how the cars had evolved.


                # ⚓ Hackaday ☛ An_Impressively_Functional_Tacobot⠀⇛


                       We’re big fans of useless machines here at
                       Hackaday, there’s something undeniably entertaining
                       about watching a gadget flail about dramatically
                       without actually making any progress towards a
                       defined goal. But what happens when one of these
                       meme machines ends up working too well? We think
                       that’s just what we might be witnessing here with
                       the Tacobot from [Vije Miller].


                # ⚓ Hackaday ☛ The_Little_Lightgun_That_Could:_Sinden_Makes
                  Good⠀⇛


                       Back in 2018, we covered the work being done by
                       [Andrew Sinden] to create a lightgun that could
                       work on modern televisions. The project was looking
                       for funding via Kickstarter, but due at least in
                       part to skepticism about the technology involved,
                       the campaign fell well short of its goal. It
                       seemed, at the time, like the story would end
                       there.


                # ⚓ Hackaday ☛ Extruded_Resin_FDM_Printing_(With_Lasers!)⠀⇛


                       At this point, 3D printers are nearly everywhere.
                       Schools, hackerspaces, home workshops, you name it.
                       Most of these machines are of the extruded-filament
                       variety, better known as FDM or Fused Deposition
                       Modelling. Over the last few years, cheap LCD
                       printers have brought resin printing to many shops
                       as well. LCD printers, like their DLP and SLA
                       counterparts, use ultraviolet light to cure liquid
                       resin. These machines are often praised for the
                       super-high detail they can achieve, but are
                       realllly slow. And messy —  liquid resin gets
                       everywhere and sticks to everything.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Orac ☛ Nazis._With_the_Brownstone_Institute_it’s_always
                  Nazis.⠀⇛


                       Nazis. It’s always Nazis. At least, with
                       antivaxxers it is.


          o § Linux Foundation⠀➾


                # ⚓ Network World ☛ Linux_Foundation_works_toward_improved
                  data-center_efficiency⠀⇛


                       Organizations exploring the use of data-processing
                       units (DPU) and infrastructure processing units
                       (IPU) got a boost this week as the Linux Foundation
                       announced a project to make them integral to future
                       data-center and cloud-based infrastructures.


                       DPUs, IPUs, and smartNICs are programmable
                       networking devices designed to free-up CPUs for
                       better performance in software-defined cloud,
                       compute, networking, storage and security services.


                # ⚓ Linux Foundation’s Site/Blog ☛ Open_Source_Brings_Good
                  Things_to_Life [Ed: The author of this fluff, Dan Whiting,
                  chooses_proprietary_software]⠀⇛


                # ⚓ Its FOSS ☛ 500_Individuals_Received_Training_&
                  Certification_Scholarships_by_The_Linux_Foundation [Ed:
                  Ankush Das continues to post marketing spam for the so-called
                  'Linux' Foundation; they almost certainly pay for this
                  spam]⠀⇛


          o § Security⠀➾


                # ⚓ Krebs On Security ☛ Meet_the_Administrators_of_the_RSOCKS
                  Proxy_Botnet⠀⇛


                       Authorities in the United States, Germany, the
                       Netherlands and the U.K. last week said they
                       dismantled the “RSOCKS” botnet, a collection of
                       millions of hacked devices that were sold as
                       “proxies” to cybercriminals looking for ways to
                       route their malicious traffic through someone
                       else’s computer. While the coordinated action did
                       not name the Russian hackers allegedly behind
                       RSOCKS, KrebsOnSecurity has identified its owner as
                       a 35-year-old Russian man living abroad who also
                       runs the world’s top spam forum.


                # ⚓ Hackaday ☛ HDMI_Is_An_Attack_Surface,_So_Here’s_An_HDMI
                  Firewall⠀⇛


                       Many years of using televisions, monitors, and
                       projectors have conditioned us into treating them
                       as simple peripherals whose cables carry only
                       video. A VGA cable may have an i2c interface for
                       monitor detection, but otherwise it presents little
                       security risk. An HDMI interface on the other hand
                       can carry an increasing number of far more capable
                       ports, meaning that it has made the leap from
                       merely a signal cable to being a connector stuffed
                       with interesting attack vectors for a miscreant. Is
                       it time for an HDMI firewall? [King Kévin] thinks
                       so, because he’s made one.


          o § Defence/Aggression⠀➾


                # ⚓ Techdirt ☛ Uvalde_PD_Continues_Stonewalling,_Hires_Private
                  Law_Firm_To_Block_Release_Of_School_Shooting_Recordings⠀⇛


                       The Uvalde Police Department — recipient of 40% of
                       the city’s budget — botched its response to a mass
                       shooting at Robb Elementary School. Rather than
                       rush to the sound of gunfire, the officers stopped
                       making forward progress once they were adjacent to
                       the gunfire. It took another law enforcement agency
                       (a Border Patrol tactical team) to end the killing,
                       which at that point numbered 19 students and two
                       teachers.


                # ⚓ TruthOut ☛ Cori_Bush_Shares_Her_Experience_With_Gun
                  Violence_From_an_Abusive_Partner⠀⇛


                # ⚓ The Nation ☛ A_Peace_Settlement_in_Ukraine⠀⇛


                       It is becoming more and more urgently necessary to
                       achieve a stable cease-fire in Ukraine, leading to
                       a lasting peace; and unfortunately, the initiative
                       for this will probably have to come from
                       Washington. The Europeans are too divided among
                       themselves and too subservient to the United States
                       to adopt any effective independent strategy for
                       peace. With the East Europeans opposed to any
                       compromise, the European Union is paralyzed.


                # ⚓ Scheerpost ☛ Joseph_E._Stiglitz:_How_the_U.S._Could_Lose
                  the_New_Cold_War⠀⇛


                       Jospeh E. Stiglitz warns that other countries will
                       not want to ally themselves with a U.S. whose power
                       rests on increasingly uncertain economic, social,
                       and political foundations.


                # ⚓ Common Dreams ☛ Demanding_Global_Ban,_UN_Chief_Calls
                  Nuclear_Weapons_a_‘Recipe_for_Annihilation’⠀⇛


                       Warning of the heightened threat of nuclear war in
                       a “world rife with geopolitical tensions and
                       mistrust,” United Nations Secretary-General António
                       Guterres on Wednesday called upon nuclear nations
                       to join the scores of countries that have adopted a
                       landmark treaty banning atomic weapons.


                       “The once-unthinkable prospect of nuclear conflict
                       is now back within the realm of possibility.”


                # ⚓ Counter Punch ☛ What_is_Westinghouse_Doing_in_Ukraine?⠀⇛


                       Earlier this month, Energoatom inked a new
                       agreement with Westinghouse of all companies, the
                       American corporation that went bankrupt trying to
                       build four of its AP1000 reactors in South Carolina
                       and Georgia. The two in South Carolina were
                       canceled mid-construction, while the pair in
                       Georgia are years behind schedule and billions of
                       dollars over-budget.


                       But like a good corporate vulture, Westinghouse has
                       swooped into Ukraine, to grab a golden opportunity.
                       Already the supplier of nuclear fuel to almost half
                       of Ukraine’s reactors, the company now plans to
                       increase that commitment to all 15, replacing
                       Russia’s Rosatom; to establish a Westinghouse
                       Engineering and Technical Center; and, craziest of
                       all, build nine new AP1000 reactors there.


                # ⚓ Common Dreams ☛ Opinion_|_Children_Have_the_Right_to_Be
                  Safe_From_Gun_Violence_Made_Possible_by_the_GOP’s_Political
                  Lunacy⠀⇛


                       A deadly epidemic is hitting the US and ordinary
                       citizens are unable to stop it. The reason is
                       simple: the laws protect the killers. And those
                       responsible for making the laws have abdicated
                       their responsibility. They do so even when the
                       victims could be their children or grandchildren,
                       engulfed in a wave of violence and death that is
                       increasingly targeting schools. The Gun Violence
                       Archive reports that mass shootings have increased
                       from 269 in 2014 to 693 in 2021.


                # ⚓ Scheerpost ☛ America’s_Second_Civil_War_is_Underway⠀⇛


                       The frightening epidemic of gun violence in the US
                       has become a commonplace reality. Easy access to
                       firearms is an obstacle that national politicians
                       have not been able to overcome with more than lip
                       service. But gun violence is only one ominous
                       symptom of a growing social collapse that directly
                       threatens our nearly 250-year old system of
                       democratic capitalism. 


                # ⚓ Scheerpost ☛ The_Pentagon_Gets_More_Money_and_Americans_Pay
                  the_Price⠀⇛


                       What’s all this new defense spending for?


                # ⚓ Common Dreams ☛ ‘Unconscionable’:_House_Committee_Adds_$37
                  Billion_to_Biden’s_$813_Billion_Military_Budget⠀⇛


                       Progressives expressed outrage after a House panel
                       voted Wednesday to tack an additional $37 billion
                       on top of President Joe Biden’s already gargantuan
                       military spending request.


                       “Members of the House Armed Services Committee put
                       the demands of the military-industrial complex over
                       the needs of the American people yet again.”


                # ⚓ Common Dreams ☛ Opinion_|_Remembering_Operation_Bagration:
                  When_the_Red_Army_Decapitated_the_Nazi_Front⠀⇛


                       Eighty-one years ago, in the early summer of 1941,
                       Nazi Germany launched Operation Barbarossa,
                       attacking the Soviet Union along a massive front at
                       the height of World War II. 


                # ⚓ Common Dreams ☛ Citing_‘Deluge_of_New_Evidence,’_House_Jan.
                  6_Committee_Delays_Hearings⠀⇛


                       Citing a “mountain of new information” requiring
                       analysis, the congressional committee investigating
                       the January 6, 2021 attack on the United States
                       Capitol announced Wednesday that it will delay the
                       hearings into the deadly insurrection until next
                       month.


                       “We’ve taken in some additional information that’s
                       going to require additional work. So rather than
                       present hearings that have not been the quality of
                       the hearings in the past we made a decision to just
                       move into sometime in July,” committee chair Rep.
                       Bennie Thompson (D-Miss.) told reporters, according
                       to The Hill.


                # ⚓ Common Dreams ☛ Opinion_|_The_Second_Amendment_Is_a
                  Palladium_of_Death._It_Should_Be_Repealed⠀⇛


                       It is shameful and unconscionable that this country
                       has allowed gun violence to become the leading
                       cause of death among children in the United
                       States—but that is the reality. The legislation,
                       including gun measures, recently proposed by a
                       bipartisan group of senators represents a step in
                       the right direction: it does some good things, such
                       as provide money to encourage states to pass and
                       implement “red flag” laws to remove guns from
                       potentially dangerous people, as well as money for
                       school safety and mental health resources; it
                       expands background checks for gun purchases for
                       people between the ages of 18 and 21 and penalties
                       for illegal straw purchases by convicted criminals.


                # ⚓ Common Dreams ☛ Far-Too-Weak_Senate_Gun_Control_Bill
                  Slammed_as_‘Crumbs’⠀⇛


                       While Democratic lawmakers lauded the gun control
                       package unveiled in the U.S. Senate after weeks of
                       negotiations late Tuesday and national advocacy
                       groups called the bill a “step in the right
                       direction,” educators, parents, and local civil
                       rights organizations in Arizona rebuked their
                       senators for standing in the way of farther-
                       reaching reforms.


                       In a 64-34 vote, the Senate agreed to take up the
                       Bipartisan Safer Communities Act hours after the
                       group of 10 Democrats and 10 Republicans released
                       the 80-page bill, with senators hoping to pass the
                       legislation by this weekend.


          o § Environment⠀➾


                # ⚓ Pro Publica ☛ Utah_Officials_Called_It_the_“Year_of_Water.”
                  Special_Interests_Still_Resist_Conservation.⠀⇛


                       Utah policymakers billed the 2022 legislative
                       session as the “year of water.” Gov. Spencer Cox
                       signed into law more than 15 measures related to
                       water conservation, heralding “generational”
                       progress as the West’s megadrought continues well
                       into its third decade.


                       Those pieces of legislation allow farmers to earn
                       money by sending their water downstream to
                       shrinking lakes, require water meters for
                       landscaping, appropriate $40 million to protect the
                       Great Salt Lake and more. But perhaps more telling
                       were proposals that lawmakers carved up or voted
                       down.


                # ⚓ DeSmog ☛ Climate_Denial_Group_Criticised_For_Ties_to_Pro-
                  Putin_Millionaire⠀⇛


                       A climate science denial group campaigning against
                       the UK’s green policies has close ties to a right-
                       wing businessman who backed Vladimir Putin’s
                       invasion of Ukraine, DeSmog can reveal. 


                       CAR26, which launched in October with a call for a
                       referendum on the UK’s net zero target, is run by
                       Lois Perry, a regular guest on GB News and
                       talkRADIO who has used Russia’s war to argue that
                       the UK should extract more fossil fuels. 


                # ⚓ DeSmog ☛ Rep._Grijalva_Tours_Cancer_Alley_Communities
                  Plagued_by_Racial_Discrimination_and_Environmental
                  Injustice⠀⇛


                       Temperatures soared into the high nineties on
                       Saturday, June 18, as Chair of the House Natural
                       Resources Committee Rep. Raúl Grijalva spoke about
                       the moral imperative to achieve environmental
                       justice at a press conference on the grounds of the
                       Whitney Plantation, a converted historical museum
                       about slavery, in St. John the Baptist Parish,
                       Louisiana.


                       After delivering an update on the bill that he
                       spearheaded, known as the Environmental Justice For
                       All Act, Grijalva and his team were taken on a tour
                       of Cancer Alley where they could learn firsthand
                       the challenging circumstances some fenceline
                       communities face. The visit coincided with
                       Juneteenth weekend and the start of a heat dome
                       stretching from the Gulf Coast to Canada, serving
                       as a reminder of the urgent need to simultaneously
                       address the climate crisis and racial injustice.


                # ⚓ Counter Punch ☛ Climate_Change:_The_New_Abnormal⠀⇛


                # ⚓ Counter Punch ☛ Mining_Resistance_From_Alberta_to
                  Argentina⠀⇛


                       At one of the many frontiers of mineral extraction
                       in the Patagonian province of Chubut, Argentina,
                       Indigenous Mapuche-Tehuelche communities and
                       citizens groups flooded the streets for days just
                       before Christmas 2021.


                       A U.S.-Canadian mining company, Pan American
                       Silver, had been pressuring legislators there to
                       overturn a nearly 20-year prohibition on open-pit
                       metal mining and the use of cyanide in mineral
                       processing, which threatens precious water
                       supplies. When lawmakers obliged and zoned for
                       mining where the company wants to operate on the
                       province’s plateau, people went to the streets by
                       the thousands and faced violent police repression.


                # § Energy⠀➾


                      # ⚓ Torrent Freak ☛ Tarantino_Asks_Court_to_Dismiss
                        Miramax’s_‘Pulp_Fiction’_NFT_Lawsuit⠀⇛


                             Quentin Tarantino has asked a California
                             court to dismiss a copyright lawsuit filed by
                             Miramax against his “Pulp Fiction” NFT
                             project. The director’s legal team submitted
                             a motion for judgment, arguing that the movie
                             company’s claims fall flat. The Pulp Fiction
                             film is a derivative of the screenplay, not
                             the other way around, they stress.


                      # ⚓ Scheerpost ☛ ‘Moral_Failure’:_California_Dem_Pulls
                        Plug_on_Fossil_Fuel_Divestment_Legislation⠀⇛


                             “This defeat is just a temporary setback,”
                             said one campaigner. “We will organize to
                             come back stronger to make our demand for
                             fossil fuel divestment heard because fossil
                             fuel com…


                      # ⚓ Scheerpost ☛ Progressives_Say_Windfall_Profits_Tax_a
                        ‘Better_Solution’_Than_Biden’s_Gas_Tax_Holiday⠀⇛


                             “A windfall tax would get more relief to more
                             people by penalizing the Big Oil profiteering
                             that’s driving up prices,” said one
                             campaigner.


                # § Wildlife/Nature⠀➾


                      # ⚓ Common Dreams ☛ Conservationists_Warn_the_‘Save_Our
                        Sequoias_Act’_Would_Do_the_Opposite⠀⇛


                             A coalition of more than 80 environmental
                             organizations representing millions of
                             Americans has sent a letter urging members of
                             Congress to vote against the so-called “Save
                             Our Sequoias Act”—legislation the groups warn
                             would do the very opposite of what its name
                             suggests.


                             Smart planning and public engagement as
                             required by NEPA are integral to success, not
                             a barrier to success.


                      # ⚓ Counter Punch ☛ Tribal_Waters_Trailer⠀⇛


                      # ⚓ The Revelator ☛ An_Earth_Activist_Talks_to_the
                        Trees⠀⇛


                      # ⚓ Counter Punch ☛ Targeted_Grazing:_the_Latest_Magical
                        Solution_To_Improve_Rangeland_Health⠀⇛


                             I have previously warned almost all the
                             “evidence” for the value of grazing to reduce
                             wildfires comes from university range
                             departments or government apologists with
                             connections to the livestock industry. And
                             this is the case with the recent action to
                             implement “targeted grazing” on public lands.


                             As is the case across the West, range
                             department researchers’ primary mission is to
                             find excuses to continue livestock grazing on
                             public lands. Our tax dollars support these
                             efforts on behalf of private businesses.


                # § Overpopulation⠀➾


                      # ⚓ Common Dreams ☛ Children_‘Dying_Before_Our_Eyes’:_Aid
                        Workers_Plea_for_Help_as_Famine_Unfolds_in_Somalia⠀⇛


                             International aid workers are issuing
                             desperate pleas for help this week as severe
                             climate-driven drought coupled with
                             critically depleted global food supplies due
                             to Russia’s invasion of Ukraine are fueling a
                             slide into “catastrophic famine” in Somalia
                             that could claim the lives of hundreds of
                             thousands of children by summer’s end.


                             “If an intervention does not happen as
                             expected, and quickly, we will inevitably
                             witness the mass death of children in the
                             coming months.”


          o § Finance⠀➾


                # ⚓ Counter Punch ☛ Private_Equity_Funds’_Claims_of_Strong
                  Performance_are_Based_on_a_Mirage⠀⇛


                # ⚓ TruthOut ☛ Bipartisan_Group’s_School_Meal_Plan_Axes_Funds
                  That_Have_Fed_Millions_of_Kids⠀⇛


                # ⚓ TruthOut ☛ Mexican_GM_Workers_Win_an_8.5_Percent_Wage_Hike
                  in_First_Union_Contract⠀⇛


                # ⚓ Scheerpost ☛ UK_Railway_Workers_Begin_Largest_Strike_in_30
                  Years⠀⇛


                       Amid high inflation, tens of thousands of railway
                       and subway workers across the United Kingdom have
                       declared at least three days of work stoppages to
                       demand wage increases and other protections. Tr…


                # ⚓ Common Dreams ☛ Opinion_|_Who_Is_to_Blame_for_Inflation?
                  The_Power_Brokers_of_Capitalism⠀⇛


                       The blame game over surging prices is on. Was it
                       too much central-bank money being pumped out for
                       too long that caused inflation to take off? Was it
                       China, where most physical production had moved
                       before the pandemic locked down the country and
                       disrupted global supply chains? Was it Russia,
                       whose invasion of Ukraine took a large chunk out of
                       the global supply of gas, oil, grains, and
                       fertilizers? Was it some surreptitious shift from
                       pre-pandemic austerity to unrestricted fiscal
                       largesse?


                # ⚓ The Nation ☛ Billionaire_Bash⠀⇛


                       Forbes started compiling an annual list of the
                       world’s billionaires in 1987. That year, 141 people
                       made the cut. The number crossed the four-figure
                       threshold for the first time in 2008; a brief
                       market correction brought it down to 793 the
                       following year, but the group has expanded at a
                       fairly steady rate since then, until a recent and
                       unprecedented surge. From the spring of 2020 to the
                       spring of 2021, the number of billionaires jumped
                       from 2,095 to 2,755, with a collective net worth of
                       over $13 trillion, up from $8 trillion the year
                       before. This increase, which roughly coincides with
                       year one of life under the Covid-19 pandemic, is
                       just one of the more dramatic indicators of a
                       longer period of socialized risk and privatized
                       reward.


                # ⚓ Counter Punch ☛ The_Fed’s_Austerity_Program_to_Reduce
                  Wages⠀⇛


                       So in practice, one of the Fed’s two directives has
                       to give. And hardly by surprise, the “full
                       employment” aim is thrown overboard – if indeed it
                       ever was taken seriously by the Fed’s managers. In
                       the Carter Administration (1777-80) leading up to
                       the great price inflation of 1980, Fed Chairman
                       Paul Volcker expressed his economic philosophy in a
                       note card that he kept in his pocket, to whip out
                       and demonstrate where his priority lay. The card
                       charted the weekly wage of the average U.S.
                       construction worker.


                       Chairman Volcker wanted wages to go down, blaming
                       the inflation on too much employment – meaning too
                       full. He pushed the U.S. bank rate to an
                       unprecedented 20 percent – the highest normal rate
                       since Babylonian times back in the first millennium
                       BC. This did indeed crash the economy, and with it
                       employment and prosperity. Volcker called this
                       “harsh monetary medicine,” as if the crash of
                       financial markets and economic growth showed that
                       his “cure” for inflation was working.


                # ⚓ Counter Punch ☛ The_People_vs._Petrocracy⠀⇛


                       Now, freaked out by high fuel prices, the
                       Democratic majority in Congress is pushing to
                       accelerate this fossil fuel rush while President
                       Biden rushes, hat in hand, to Saudi Arabia,
                       forgetting that the kingdom is supposed to be a
                       pariah. Furthermore, as Robinson Meyer recently
                       wrote in The Atlantic, the party’s leadership seems
                       blissfully unbothered by the fact that Congress has
                       failed to pass even the weakest of laws to curb
                       climate catastrophe. And if the Democrats—having
                       been unable to defend either voters’ rights or life
                       on Earth over the past year and a half—lose their
                       congressional majority to the oily authoritarians
                       in November, our already dim hopes for the federal
                       government to reverse course and start phasing out
                       fossil fuels could fade away altogether.


                       If that nightmare scenario unfolds, local and
                       regional activism will not only become more
                       essential than ever; it could be the nation’s only
                       route to climate mitigation and adaptation. As the
                       republic teeters on a knife edge in coming months,
                       “In Real Time” will be recognizing grassroots
                       movements across the country that stand as
                       exemplars for collective climate action. Climate is
                       not always the chief focus of such struggles, but
                       the movements’ strategies and methods are deeply
                       relevant.


                # ⚓ Common Dreams ☛ Progressives_Say_Windfall_Profits_Tax_a
                  ‘Better_Solution’_Than_Biden’s_Gas_Tax_Holiday⠀⇛


                       As President Joe Biden on Wednesday prepares to
                       urge Congress to temporarily suspend federal
                       gasoline and diesel taxes in a bid to ease pain at
                       the pump, progressives are calling instead for the
                       passage of Democratic lawmakers’ overwhelmingly
                       popular bill to impose a windfall profits tax on
                       Big Oil.


                       “Congress should take the president’s call and
                       answer it with the windfall profits tax legislation
                       already proposed in the House and Senate,” Jamie
                       Henn, a spokesperson for the Stop the Oil
                       Profiteering (STOP) campaign, wrote on social
                       media. “A windfall tax would get more relief to
                       more people by penalizing the Big Oil profiteering
                       that’s driving up prices.”


                # ⚓ Meduza ☛ ‘Borjomi_is_for_Borjomians,_not_for_Russian
                  oligarchs!’_When_the_Russian_owner_of_a_Georgian_bottling
                  plant_came_under_sanctions,_workers_stopped_getting_paid._Now
                  they’re_fighting_back.⠀⇛


                       In late April, the Georgian company IDS Borjomi,
                       which sells mineral water under the brand name
                       Borjomi, announced it was temporarily suspending
                       operations at both of its bottling plants in
                       Georgia due to financial difficulties resulting
                       from the war in Ukraine. Oligarch Mikhail Fridman,
                       owner of the Alfa Group, which owns a majority
                       stake in the company, had come under sanctions. Now
                       Alfa Group plans to donate its shares to Georgia
                       — but this hasn’t helped the plants’ employees, who
                       haven’t been paid in two months. Meduza takes a
                       closer look at the town of Borjomi, where protests
                       are ongoing.


                # ⚓ Scheerpost ☛ VIDEO:_Senator_Elizabeth_Warren_Challenges_Fed
                  Chair_Jerome_Powell_in_Senate_Banking_Committee_Hearing⠀⇛


                       Senator Elizabeth Warren challenges and urges
                       caution to Federal Reserve Chair Jerome Powell.
                       During a Senate Banking Committee hearing, Sen.
                       Warren warned about what a recession could me…


                # ⚓ Common Dreams ☛ Warren_Warns_Powell_That_Fed’s_Rate_Hikes
                  Could_Drive_US_Economy_‘Off_a_Cliff’⠀⇛


                       Sen. Elizabeth Warren on Wednesday told Federal
                       Reserve Chair Jerome Powell directly that the
                       central bank’s recent decision to enact more
                       aggressive interest rate hikes in an effort to
                       combat inflation could push the U.S. economy “off a
                       cliff”—and throw millions of people out of
                       work—without reining in soaring prices.


                       “Inflation is like an illness and the medicine
                       needs to be tailored to the specific problem,
                       otherwise you could make things a lot worse,”
                       Warren (D-Mass.) said during her remarks at a
                       Senate Banking Committee hearing. “Right now, the
                       Fed has no control over the main drivers of rising
                       prices.”


                # ⚓ Common Dreams ☛ Civil_Rights_Groups_Demand_Biden_Cancel_at
                  Least_$50K_in_Student_Debt_Per_Borrower⠀⇛


                       Marking one year since the Biden administration
                       announced its intention to narrow the racial wealth
                       gap and “reinvest in communities that have been
                       left behind by failed policies,” 60 civil rights
                       groups on Tuesday wrote to the White House
                       demanding the cancellation of at least $50,000 in
                       student debt per borrower—a step, they said, that
                       would help “alleviate the financial suffering of
                       millions of Americans.”


                       Noting that 45 million Americans carry a total of
                       more than $1.6 trillion in student debt, the groups
                       called the federal student loan payment
                       moratorium—which has been extended multiple times
                       since the coronavirus pandemic began and is
                       currently set to expire at the end of August—”only
                       a band-aid solution.”


                # ⚓ Common Dreams ☛ Opinion_|_In_Praise_of_the_15-Hour_Work
                  Week⠀⇛


                       Back in 1930, renowned economist John Maynard
                       Keynes predicted that technological advances,
                       slowed population growth, increasing capital (or
                       “material things”) and changing economic priorities
                       would make three-hour shifts or a 15-hour workweek
                       possible and desirable within 100 years.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Counter Punch ☛ Putin_Attempts_to_Justify_the
                  Unjustifiable⠀⇛


                       Although, in defending the Russian invasion,
                       Russian President Vladimir Putin’s primary emphasis
                       has been on the threat of Ukraine joining NATO,
                       that action, had it occurred, would have been
                       perfectly legitimate under international law. The
                       UN Charter, which is an instrument of international
                       law, does not ban membership in military alliances.
                       And, in fact, a great many such alliances are in
                       existence. Russia currently heads up the Collective
                       Security Treaty Organization, a military alliance
                       composed of six nations in Eastern Europe and
                       Central Asia.


                       Of course, Putin’s focus upon NATO is based on the
                       notion that Russia’s national security would be
                       endangered by the existence of a NATO nation on its
                       border. But why are Russia’s national security
                       concerns more valid than the national security
                       concerns of nations on Russia’s
                       borders―particularly nations that, in the past,
                       have been invaded and gobbled up as territory by
                       Russia or the Soviet Union? Moreover, if a feared
                       threat to national security provides valid grounds
                       for a military invasion, this would also justify
                       military attacks by many nations. Finally, the
                       degree of danger to Russia posed by NATO might well
                       be questioned, as the Western alliance has never
                       attacked Russia during the 73 years of NATO’s
                       existence.


                # ⚓ The Nation ☛ The_Supreme_Court_Strikes_Another_Blow_to_the
                  Separation_of_Church_and_State⠀⇛


                       I do not know what most people think “separation of
                       church and state” means, but I can tell you that
                       the six conservative justices on the Supreme Court
                       think it means nothing. There is no meaningful
                       check anymore on whether conservatives will allow
                       religious concerns to supersede secular laws. Can
                       businesses run by religious people deny health care
                       to women? Yes, according to Burwell v. Hobby Lobby
                       Stores. Can religious schools use public funds to
                       upgrade their school playgrounds? Yes, according to
                       Trinity Lutheran v. Comer. Can the state be forced
                       to give scholarship aid to students attending
                       religious education? Yes, according to Espinoza v.
                       Montana Department Of Revenue. Can religious
                       organizations or institutions get state funds to
                       discriminate against LGBTQ couples in adoption
                       services? Yes, according to Fulton v. City of
                       Philadelphia. Can houses of worship ignore
                       occupancy restrictions during a pandemic? Yes,
                       according to Roman Catholic Diocese of Brooklyn v.
                       Cuomo.


                # ⚓ The Nation ☛ The_Perils_of_Shaping_a_Recalcitrant_World⠀⇛


                       Whenever you hear senior US officials tout
                       Washington’s determination to “shape” the world
                       order pursuant to America’s vision of all that is
                       right and good, make sure you have your flak jacket
                       handy. In practice, “shaping” typically culminates
                       in exchanges of gunfire.


                # ⚓ TruthOut ☛ Trump_Ranks_Near_Very_Bottom_in_Survey_of_Best
                  Presidents_in_US_History⠀⇛


                # ⚓ The Nation ☛ The_Democrats_Have_a_Winning_Message:_“Stop
                  Dangerous_Extremists”⠀⇛


                       “Trump and his allies are a clear and present
                       danger to American democracy.”—the Honorable J.
                       Michael Luttig


                # ⚓ Counter Punch ☛ Trump_“A_Clear_and_Present_Danger”⠀⇛


                # ⚓ TruthOut ☛ Ron_Johnson_Fakes_Call_to_Avoid_Discussing_His
                  Involvement_in_Electors_Plot⠀⇛


                # ⚓ TruthOut ☛ Trump’s_Election_Lies_Unleashed_Racist_Death
                  Threats_Against_Poll_Workers⠀⇛


                # ⚓ TruthOut ☛ 70_Percent_of_Voters_Want_to_Ban_Congress_From
                  Trading_Stocks⠀⇛


                # ⚓ Scheerpost ☛ The_Tragic_Absurdity_of_Qatar’s_World_Cup
                  Sportswashing⠀⇛


                       Labor abuses, homophobia, corruption? Qatar and
                       FIFA will use the men’s World Cup to put a happy
                       gloss on it all.


                # ⚓ Scheerpost ☛ Electoral_Victory_of_Colombians_Petro_and
                  Marquez_is_Unprecedented⠀⇛


                # ⚓ Scheerpost ☛ Ecuadorians_Continue_To_Resist_as_National
                  Strike_Enters_Second_Week⠀⇛


                       Defying the state of emergency, enduring brutal
                       police and military repression, hundreds of
                       thousands of Ecuadorians continue to remain on the
                       streets against neoliberalism.


                # ⚓ TruthOut ☛ Democrats_Are_Recklessly_Promoting_Far_Right_GOP
                  Candidates_in_Midterm_Ploy⠀⇛


                # ⚓ The Nation ☛ Hate_Is_Not_Welcome_Here⠀⇛


                # ⚓ The Nation ☛ For_Once,_a_Republican_Tells_the_Truth_About
                  Trump⠀⇛


                # ⚓ Scheerpost ☛ The_Federal_Bureau_of_Tweets:_Twitter_is
                  Hiring_an_Alarming_Number_of_FBI_Agents⠀⇛


                # ⚓ Common Dreams ☛ Democratic_Groups_Panned_Over_‘Dangerous’
                  Midterm_Ploy_to_Boost_GOP_Extremists⠀⇛


                       In several midterm primary races across the United
                       States, political organizations affiliated with the
                       Democratic Party—including Speaker Nancy Pelosi’s
                       House Majority PAC—are spending big to boost far-
                       right Republican candidates in the hopes of
                       securing more favorable general election matchups
                       for Democrats.


                       What could possibly go wrong?


                # ⚓ TruthOut ☛ January_6_Hearings_Remind_Us_of_the_Lives
                  Threatened_by_“Big_Lie”_Proponents⠀⇛


                # ⚓ Common Dreams ☛ Amid_Jan._6_Hearings,_Watchdogs_Warn_GOP
                  Efforts_to_Steal_Elections_Are_‘Still_Underway’⠀⇛


                       As the ongoing January 6 congressional hearings
                       further confirm the threat posed by former
                       President Donald Trump’s coup attempt last year,
                       watchdog groups emphasized following Tuesday’s
                       testimony that the GOP’s election subversion
                       efforts across the United States are continuing—and
                       intensifying—in the present.


                       “Long before January 6, attempts were underway to
                       illegally steal our votes,” said Lisa Gilbert,
                       executive vice president of Public Citizen,
                       referring to the Trump campaign’s coordinated push
                       to overturn the results of the 2020 presidential
                       election—an effort that has been a central focus of
                       the House select committee’s public hearings thus
                       far.


                # ⚓ Telex (Hungary) ☛ Hungarian_counties_may_be_given
                  centuries-old_archaic_names,_and_government_commissioners
                  will_be_named_after_officials_representing_Hungarian_kings_of
                  the_past⠀⇛


                # ⚓ FAIR ☛ ‘The_Times_Is_Telling_You_to_Choose_Between_Rights
                  and_Safety’⠀⇛


                       Janine Jackson interviewed Alec Karakatsanis about
                       the recall of Chesa Boudin for the June 17, 2022,
                       episode of CounterSpin. This is a lightly edited
                       transcript.


                # ⚓ Pro Publica ☛ DOJ_Settlement:_Facebook_to_Eliminate_Tool
                  that_Let_Advertisers_Discriminate⠀⇛


                       In a settlement announced by the Department of
                       Justice on Tuesday, Meta Platforms — formerly known
                       as Facebook — has agreed to eliminate features in
                       its advertising business that allow landlords,
                       employers and credit agencies to discriminate
                       against groups of people protected by federal civil
                       rights laws.


                       The deal comes nearly six years after ProPublica
                       first revealed that Facebook let housing marketers
                       exclude African Americans and others from seeing
                       some of their advertisements. Federal law prohibits
                       housing, employment and credit discrimination based
                       on race, religion, gender, family status and
                       disability.


                # ⚓ Democracy Now ☛ Top_Arizona_Republican_Testifies_He
                  Rejected_Trump_Plot_to_Overturn_Vote,_Then_Faced_Violent
                  Threats⠀⇛


                       The House select committee investigating the
                       January 6 insurrection held its fourth public
                       hearing Tuesday with testimony that included a
                       series of Republican state officials detailing
                       pressure they faced from President Donald Trump and
                       his staff to overturn the results of the 2020
                       election. Republican Speaker of the Arizona House
                       “Rusty” Bowers described how he was pushed by
                       Trump, John Eastman and Rudy Giuliani to call the
                       Arizona Legislature back into session to
                       investigate what Trump’s team claimed were hundreds
                       of thousands of illegal votes cast by dead people
                       and undocumented immigrants in a greater effort to
                       undo Joe Biden’s win in the state. Bowers refused
                       after Trump’s team wasn’t able to provide evidence
                       of a rigged election — and consequently Bowers and
                       his family became the target of death threats by
                       white supremacist groups and other Trump
                       supporters. “I didn’t want to be used as a pawn,”
                       said Bowers during his live testimony.


                # ⚓ Democracy Now ☛ Georgia_Poll_Workers_Falsely_Targeted_by
                  Trump_as_“Scammers”_Faced_Racist_Harassment,_Lived_in_Fear⠀⇛


                       In some of the most dramatic testimony from the
                       fourth hearing of the House Select Committee to
                       Investigate the January 6th Attack on the U.S.
                       Capitol, Shaye Moss, a Black election worker in
                       Georgia, and her mother Ruby Freeman described how
                       their lives were forever changed in December of
                       2020 when Trump’s top campaign lawyer Rudy Giuliani
                       claimed they manipulated ballots to rig the
                       election outcome in the state, which was among
                       those he had lost. They faced severe harassment,
                       racism and death threats from Trump supporters and
                       had to be relocated by the FBI for safety. “I don’t
                       want anyone knowing my name. … I don’t want to go
                       anywhere. I second-guess everything that I do,”
                       said Moss, who, like her former colleagues, is no
                       longer an election worker in Fulton County. “Do you
                       know how it feels to have the president of the
                       United States to target you?” said Freeman in taped
                       testimony. “The president of the United States is
                       supposed to represent every American — not to
                       target one.”


                # ⚓ Democracy Now ☛ “Whatever_You_Can_Do”:_Jan._6_Hearing_Lays
                  Out_“Fake_Electors”_Scheme_to_Rig_2020_Election_for_Trump⠀⇛


                       Tuesday’s hearing of the House committee
                       investigating the January 6 attack included
                       evidence of how then-President Trump and his
                       campaign “were directly involved” in a plot to
                       replace Biden electors with fake electors for Trump
                       in states where he had lost. Investigators
                       displayed fake certifications manufactured by the
                       Trump campaign and said that one group of fake
                       electors even asked for a promise that the campaign
                       would pay their legal fees if they got sued or
                       charged with a crime. The committee also revealed
                       that just minutes before the joint session on
                       January 6, a staffer for Wisconsin Senator Ron
                       Johnson told Mike Pence he wished to hand deliver
                       to the vice president the fake electors’ votes from
                       Michigan and Wisconsin — which Pence’s aide
                       unambiguously refused. We feature a video presented
                       to the January 6 committee as evidence that
                       features Casey Lucier, an investigative counsel,
                       describing the plan to organize fake electors for
                       Trump in states where he had lost, with testimony
                       of former Trump staffers, lawyers and other
                       Republican officials.


                # ⚓ Meduza ☛ ‘Taira_is_already_home’:_Release_of_famous
                  Ukrainian_paramedic_Yulia_Paevska_leaves_pro-Kremlin
                  blogosphere_confused⠀⇛


                       On the evening of June 17, President Volodymyr
                       Zelensky announced that Ukrainian paramedic Yulia
                       “Taira” Paevska had been released from Russian
                       captivity. Paevska has long been hailed as a hero
                       in Ukraine, known for saving hundreds of lives as a
                       volunteer medic in the Donbas. At the beginning of
                       Russia’s full-scale invasion of Ukraine, Paevska
                       spent more than two weeks evacuating the wounded in
                       besieged Mariupol (the harrowing footage from her
                       body camera was later published by the Associated
                       Press). After Russian troops captured Paevska on
                       March 16, pro-Kremlin media began smearing her as a
                       “Nazi” and accusing her of terrible crimes. As a
                       result, news of Paevska’s release sent the rumor
                       churning once again as pro-Kremlin bloggers
                       wondered how it was even possible for Russia to let
                       her go.


                # ⚓ Meduza ☛ ‘In_Moscow_everything’s_fine’:_In_Russia’s
                  capital,_Mayor_Sergey_Sobyanin_tries_to_distance_himself_—
                  and_his_city_—_from_the_war_against_Ukraine⠀⇛


                       Moscow Mayor Sergey Sobyanin has precious little to
                       say about Russia’s war against Ukraine. Over the
                       past four months of the full-scale invasion, he has
                       hardly made any public statements about the
                       progress and consequences of the so-called “special
                       operation.” Meanwhile, his counterparts in other
                       regions (like St. Petersburg Governor Alexander
                       Beglov, for example) have been toeing the line and
                       parroting Kremlin propaganda narratives about
                       “fighting Nazis” in Ukraine. As Meduza special
                       correspondent Andrey Pertsev learned, Sobyanin has
                       instead “buried himself” in work in the Russian
                       capital and is deliberately trying to distance
                       himself from the war. Here’s why. 


                # § Misinformation/Disinformation⠀➾


                      # ⚓ Techdirt ☛ White_House_Launches_Yet_Another_Task
                        Force_To_Try_To_Curb_Online_Abuse;_But_So_Far_It_Seems
                        Extremely_One-Sided⠀⇛


                             Apparently missing the entire controversy the
                             White House faced just a few weeks ago
                             regarding Homeland Security’s poorly
                             explained Disinformation Governance Board
                             (which has since been put on hold), the White
                             House is trying yet again, with its new White
                             House Task Force to Address Online Harassment
                             and Abuse. At least this time, they didn’t
                             launch it without any details at all. This
                             time, there’s an official document explaining
                             the taskforce, and the announcement came
                             complete with a speech from VP Kamala Harris
                             and a meeting with a strikingly one-sided
                             group of “experts.”


          o § Censorship/Free Speech⠀➾


                # ⚓ Scheerpost ☛ Criminalizing_Palestine_Solidarity_Activism_in
                  the_UK⠀⇛


                       In January, British Education Secretary Nadhim
                       Zahawi claimed that the popular phrase, “From the
                       river to the sea, Palestine will be free” is anti-
                       Semitic and implied that chanting it should be
                       considered a criminal offense.


                # ⚓ AccessNow ☛ Internet_shutdowns_hide_atrocities:_people_in
                  Myanmar_need_global_action_–_Access_Now⠀⇛


                       Content note: this statement contains references to
                       violence, murder, and war crimes.


                       Since the February 2021 coup, the Myanmar military
                       has systematically imposed internet shutdowns
                       across regions where it faces the most intense
                       resistance, while implementing an aggressive
                       scorched-earth campaign across the nation. In one
                       of the regions most heavily hit by the military
                       invasion, Sagaing, the junta has shut down
                       internet, mobile, and landline connections since
                       late 2021, with access only available
                       intermittently for a few hours every few days. When
                       connections are cut, it can be a sign of an
                       impending military attack.


                       “The situation on the ground in Myanmar is
                       deteriorating at a tremendous rate,” said Wai Phyo
                       Mint, Asia Pacific Policy Analyst at Access Now.
                       “The military is targeting these communication
                       blackouts to bury the atrocities of its campaign
                       and crush the resistance. Homes and religious
                       buildings are regularly burned. Houses are raided,
                       and people are dying. The flickering attention from
                       the international community is further intensifying
                       suffering. It’s time for immediate global action.”


                # ⚓ AccessNow ☛ How_internet_shutdowns_affect_women_in_Iran⠀⇛


                       Women in Iran face an incredible array of legal and
                       social obstacles to gaining financial independence.
                       The worsening economic situation across Iran —
                       owing to a barrage of economic sanctions and
                       domestic corruption and mismanagement, among other
                       things — has only made matters worse. Women are
                       disproportionately affected by the crisis, and some
                       have turned to selling goods online to earn income
                       and support their families. But what happens when
                       the internet goes dark?


                       As a new report from the United Nations confirms,
                       internet shutdowns, by their very nature, restrict
                       human rights, and there are almost no circumstances
                       under which they can be justified according to
                       international human rights law. Yet Iran’s regime
                       systematically imposes internet shutdowns to
                       silence dissent and simultaneously repress the
                       right to peaceful assembly and association. Often,
                       these shutdowns entail cutting off mobile phone
                       networks, slowing down broadband speeds, or
                       completely cutting internet access across regions
                       or on a national scale, affecting both national and
                       international networks.


                # ⚓ AccessNow ☛ Open_call_to_all_international_actors:_Do_more
                  to_stop_internet_shutdowns_shrouding_torchings_and_killings
                  in_Myanmar_–_Access_Now⠀⇛


                       For months, the Myanmar military has systematically
                       imposed internet shutdowns to facilitate an
                       aggressive scorched-earth campaign across the
                       nation. Internet, mobile, and landline connections
                       are cut in an impending sign of a military attack —
                       and as shutdowns reign for days on end, entire
                       villages, schools, places of worship, and personal
                       property are torched, villagers killed, and food
                       and other necessary supplies destroyed. Internet
                       shutdowns have fortified the military’s oppressive
                       “Four Cuts” strategy — a military campaign to
                       indiscriminately destroy anything or anyone deemed
                       to support the raging popular resistance movement
                       on the ground. As places continue to be wiped out
                       amidst communications blackouts, the international
                       community and companies tasked to enforce the
                       junta’s orders have remained largely silent. This
                       must change.


                       Internet shutdowns have been imposed across regions
                       where resistance against the military has been most
                       intense, and where arson attacks by the junta have
                       been most widespread as both punishment, and cover
                       for atrocities. In one of the worst-hit regions of
                       Sagaing, internet, mobile and landline connections
                       have been shut down since late 2021, with access
                       only available intermittently for a few hours every
                       few days. Out of 34 townships in Sagaing, eight are
                       facing regular internet blackouts, while the other
                       townships have access only to 2G connections.
                       Reports indicate that more than 22,000 sites
                       including residential and religious buildings have
                       been burned down between February 1 to May 2022.
                       Homes have been raided by soldiers, property
                       destroyed, and burned bodies reportedly found “shot
                       in the head” and “tied with cables.” Regional
                       shutdowns have been reported and continue across
                       the regions of Magway and Mandalay, and states of
                       Chin, Kayah (Karenni) and Kachin, where intense
                       fighting between military and resistance forces is
                       ongoing. This is all being perpetrated with
                       impunity amidst recurring internet shutdowns, now
                       in place in at least 54 townships across the
                       country.


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


                # ⚓ Common Dreams ☛ Opinion_|_The_Assange_Case_Still_Matters—A
                  Lot⠀⇛


                       The announcement by UK Home Secretary, Priti Patel,
                       that WikiLeaks founder Julian Assange would be
                       extradited to the US to face espionage charges may
                       be news that many consider to be of lesser
                       importance. We are, after all, in the midst of both
                       a war inside of European borders and an economic
                       crisis. The seemingly endless Assange saga has been
                       going on for 12 years, and there is undoubtedly
                       fatigue on the part of news consumers who have lost
                       interest in the story.


                # ⚓ TruthOut ☛ Extraditing_Assange_Would_Be_a_“Legalized”
                  Rendition_to_US_Torture⠀⇛


                # ⚓ Scheerpost ☛ Assange_Put_on_Suicide_Watch_After_Patel
                  Decision,_Father_Says⠀⇛


                       John Shipton said Julian Assange was stripped naked
                       and put in an empty cell to prevent him from
                       killing himself over the home secretary’s decision
                       to sign his extradition order, Joe Lauria reports…


                # ⚓ Scheerpost ☛ Free_Assange?_Yes,_But_That’s_Not_Nearly
                  Enough⠀⇛


                # ⚓ Counter Punch ☛ Assange_Should_Put_the_Pentagon_and_the_CIA
                  on_Trial⠀⇛


                       Let’s hope that he uses the opportunity to put the
                       Pentagon and the CIA on trial. Yes, I know that
                       whichever federal judge is appointed to preside
                       over the trial will do his best to not permit that
                       to happen, but what’s wrong with a little civil
                       disobedience in what will inevitably be a rigged
                       kangaroo court whose outcome of guilt will be
                       preordained?


                       Let’s not forget, after all, that Assange isn’t the
                       criminal here. He’s the guy who disclosed the
                       criminal conduct to the world through his
                       organization WikiLeaks. That criminal conduct was
                       committed by the Pentagon and the CIA, supported by
                       their enablers in the executive and legislative
                       branches of the federal government. 


          o § Civil Rights/Policing⠀➾


                # ⚓ Pro Publica ☛ Louisiana_Limits_Solitary_Confinement_for
                  Youth⠀⇛


                       Lawmakers in Louisiana passed new restrictions on
                       the use of solitary confinement in juvenile
                       facilities following an investigation by The
                       Marshall Project, ProPublica and NBC News into
                       harsh conditions in a youth lockup.


                       The law, which will go into effect Aug. 1, marks
                       the first time that lawmakers in a state known as
                       the world’s incarceration capital have put limits
                       on solitary confinement for youth, advocates say.


                # ⚓ The Nation ☛ Abortion_Involves_Killing–and_That’s_OK!⠀⇛


                       In 2019, I published a kind of manifesto—Full
                       Surrogacy Now—whose opening line is “It is a wonder
                       we let fetuses inside us.” The opening pages are
                       entirely given over to my extended paean to the
                       process of gestating in all its shockingly grisly
                       biology, its everyday sublimity. Whereas, in other
                       species, a female can often discard or expel a
                       pregnancy at will, in our species, a hyper-invasive
                       placenta puts the gestator at risk of lethal
                       hemorrhage. Locked down, our body becomes a
                       daredevil participant in a wrestling match (or
                       similar extreme sport) we cannot easily quit. From
                       this starting point, I make a case for rethinking
                       human gestation as real and, currently, often
                       deadly dangerous labor, deserving of maximal
                       support. The controversial part is that a key
                       correlate of viewing gestating as labor is that
                       forcing someone to gestate against their will is
                       forced labor.


                # ⚓ The Nation ☛ Labor’s_Coachella⠀⇛


                       Reading about an event you didn’t attend isn’t
                       always fun. After all, now it’s over, and you
                       missed it. And unless you were there and could feel
                       the passion, why would you care who attended and
                       what was said?


          o § Monopolies⠀➾


                # ⚓ Techdirt ☛ Roku,_Netflix,_Start_Behaving_More_Like_The
                  Annoying_Cable_Giants_They_Once_Disrupted⠀⇛


                       It’s always interesting to watch one-time
                       disruptors shift toward turf protection, apparently
                       remembering none of the annoyances that drove their
                       passion for disruption (and ultimate success) in
                       the first place.


                # ⚓ EFF ☛ Westlaw_Must_Face_Antitrust_Claims_in_a_Case_That
                  Could_Boost_Competitive_Compatibility⠀⇛


                       The ruling is a significant step in an antitrust
                       case about Westlaw’s conduct as an entrenched
                       incumbent. The company controls 80 percent of the
                       market for legal research tools and maintains a
                       massive, impossible-to-duplicate database of public
                       case law built over decades. It faces few major
                       competitors. Westlaw doesn’t license access to its
                       database, which means that it’s difficult for
                       another company to offer new and innovative online
                       tools for searching case law or other follow-on
                       products and services. 


                       The potential ramifications of this case are huge.
                       The outcome could boost the case for competitive
                       compatibility (comcom), the ability of challengers
                       to build on the work of entrenched players like
                       Westlaw to create innovative and useful new
                       products. More prosaically, it could improve public
                       access to court records.


                       The U.S. District Court for the District of
                       Delaware in April refused to dismiss an antitrust
                       claim against Westlaw by the now-defunct legal
                       research company ROSS Intelligence. ROSS developed
                       a new online legal research tool using artificial
                       intelligence (AI), contracting with an outside
                       company for a database of legal cases sourced from
                       Westlaw. Westlaw sued ROSS for copyright
                       infringement, accusing it of using AI to mine the
                       Westlaw database as source material for its new
                       tool. Though the database is mainly composed of
                       judicial opinions, which can’t be copyrighted,
                       Westlaw long maintained that it holds copyrights to
                       the page numbers and other organizational features.
                       ROSS went out of business less than a year after
                       Westlaw filed suit. 


                # ⚓ Techdirt ☛ Techdirt_Podcast_Episode_324:_Revisiting_The
                  Question_Of_Proprietary_Platforms_For_Media_Companies⠀⇛


                       We’ve got some great new discussions for the
                       Techdirt Podcast… coming in a few weeks. But at the
                       moment, amidst a very busy schedule on a variety of
                       fronts, we’re taking a short break to look back on
                       a very old conversation: our 14th episode ever,
                       from 2015, about media companies rolling out
                       proprietary content management systems. Since we
                       recently completed our own migration to WordPress
                       (the popular platform that was also a major
                       component of that seven-year-old discussion) we
                       thought it might be fun to revisit the question. So
                       on this week’s episode, Mike and I open with a bit
                       of a retrospective followed by a replay of the
                       original conversation in full.


                # ⚓ Techdirt ☛ Another_Issue_With_Internet_Antitrust_Bills:
                  Sloppy_Drafting_Could_Lead_To_Problems_For_Encryption⠀⇛


                       As the big push is on to approve two internet-
                       focused antitrust bills, the American Innovation
                       and Choice Online Act (AICOA) and the Open App
                       Markets Act, we’ve been calling out that while the
                       overall intentions of both may be good, there are
                       real concerns with the language of both and how it
                       could impact content moderation debates. Indeed, it
                       seems pretty clear that the only reason these bills
                       have strong support from Republicans is because
                       they know the bills can be abused to attack
                       editorial discretion.


                # ⚓ Counter Punch ☛ Neoliberals_Don’t_Like_Free_Markets,_But
                  They_Want_You_to_Think_They_Do⠀⇛


                # § Patents⠀➾


                      # ⚓ Techdirt ☛ Too_Little,_Too_Late,_WTO_Finally_Eases
                        Patent_Rights_On_COVID_Vaccines⠀⇛


                             In what definitely feels like a case of way
                             too little, way too late, the WTO last week
                             finally decided to grant the TRIPS waiver on
                             COVID vaccines, allowing others to make more
                             of the vaccine without violating patent
                             rights. The WTO has long had this ability to
                             issue a patent waiver as part of its Trade-
                             Related Aspects of Intellectual Property
                             Rights (TRIPS) agreement. The idea is that in
                             an emergency, when patents or copyrights are
                             getting in the way of real harm, the WTO can
                             say “hey, let’s grant a waiver to save
                             people.”


                # § Copyrights⠀➾


                      # ⚓ Creative Commons ☛ Open_Minds_Podcast:_*Special
                        Episode*_CC_Roundtable_on_EU_DATA_ACT⠀⇛


                             Hi Creative Commoners! We are back with a
                             brand new episode of CC’s Open Minds … from
                             Creative Commons podcast. 


                      # ⚓ Creative Commons ☛ Here_are_four_key_takeaways_from
                        evaluating_the_CC_Certificate⠀⇛


                             The CC Certificate program is an investment
                             in the global community of open creators and
                             advocates. It is a tool to support people as
                             proactive participants in our shared digital
                             commons, and strengthen the diversity of
                             creative thought and expression to improve
                             open access to open knowledge and culture. 


                      # ⚓ Torrent Freak ☛ Megaupload_Pair_Plead_Guilty,_Kim
                        Dotcom_Turns_Anger_on_Former_Friends⠀⇛


                             In May, former Megaupload executives Mathias
                             Ortmann and Bram van der Kolk revealed a deal
                             to avoid extradition to the US by being
                             charged with crimes in New Zealand. Today the
                             men pleaded guilty and both face up to 10
                             years in prison. Kim Dotcom – who is not part
                             of the deal – congratulated his former
                             friends last month but now accuses them of
                             facilitating Chinese spying.



                    ䷩ 𝚕𝚒𝚗𝚎 6999

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 06.23.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_23/06/2022:_digiKam_7.7_and_Tails_5.1.1⠀✐


Posted in News_Roundup at 11:53 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Debian_Family
          o Canonical/Ubuntu_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o GNU_Projects
          o Licensing_/_Legal
          o Programming/Development
                # Perl_/_Raku
          o Standards/Consortia
    * Leftovers
          o Science
          o Linux_Foundation
          o Security
                # Privacy/Surveillance
          o Environment
                # Energy
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Patents
                # Copyrights
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Jupiter Broadcasting ☛ Linux_Action_News_246⠀⇛


                       Some highlights from Linus’ recent fireside chat,
                       Qt gets a new leader and a Linux botnet we should
                       probably take seriously.


          o § Applications⠀➾


                # ⚓ Trend Oceans ☛ Lorien:_Infinite_canvas_drawing/
                  whiteboarding_tool_for_Linux⠀⇛


                       
                       Lorien is a simple and open-source infinite canvas
                       drawing/whiteboarding brainstorming tool written in
                       the open-source Godot Game Engine.


                       This tool is not like a standard tool that works on
                       bitmap images like Photoshop, Krita, and Gimp;
                       instead, it saves your drawn brushes as a
                       collection of points and renders them at the
                       runtime (kind of SVG), making it more performance-
                       focused.


          o § Instructionals/Technical⠀➾


                # ⚓ ID Root ☛ How_To_Install_VNC_Server_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install a
                       VNC server on Ubuntu 22.04 LTS. For those of you
                       who didn’t know, Virtual Network Computing, or VNC,
                       is a connection system that allows you to use your
                       keyboard and mouse to interact with a graphical
                       desktop environment on a remote server. VNC is
                       working on GUI (Graphical User Interface)
                       environments, it transmits movements of your mouse
                       and keyboard input over the network using the
                       Remote Frame Buffer (RFB) protocol.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the VNC server on Ubuntu 22.04
                       (Jammy Jellyfish). You can follow the same
                       instructions for Ubuntu 22.04 and any other Debian-
                       based distribution like Linux Mint, Elementary OS,
                       Pop!_OS, and more as well.


                # ⚓ Linux Capable ☛ How_to_Install_Krita_on_Ubuntu_22.04_LTS_–
                  LinuxCapable⠀⇛


                       Krita is a free and open-source graphics editing
                       program for digital painting, 2D animation, or
                       general image manipulation. It runs on Windows,
                       macOS (both Intel 64bit), Linux hits, Android &
                       Chrome OS and is one of the more popular paint
                       applications for users with digital photos.


                       The following tutorial will teach you how to
                       install Krita on Ubuntu 22.04 LTS Jammy Jellyfish
                       using the official PPA to install the command
                       terminal’s digital editor.


                # ⚓ Linux Capable ☛ How_to_Install_Wireshark_on_Ubuntu_22.04
                  LTS_–_LinuxCapable⠀⇛


                       Wireshark is a powerful and popular network
                       communication tool that allows viewing individual
                       recorded data packets or sorting them according to
                       specific content. This networking software lets you
                       see what’s going on on your computer, and it helps
                       take apart any encrypted messages being sent around
                       it through analysis of their contents with ease!


                       Some of the most common tasks Wireshark is used for
                       amongst software users include troubleshooting
                       networks with performance issues and cybersecurity
                       tracing connecting, viewing contents of suspect
                       network transactions, and identifying bursts of
                       network traffic for further analysis.


                       The following tutorial will teach you how to
                       install WireShark on Ubuntu 22.04 LTS Jammy
                       Jellyfish Linux using the command line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Insomnia_on_Ubuntu_22.04_LTS
                  –_LinuxCapable⠀⇛


                       Insomnia is a free, open-source, cross-platform
                       desktop application that makes interacting with
                       GraphQL servers more straightforward than ever
                       before. It provides you with gRPC and REST
                       endpoints, so there’s no need to worry about which
                       one will work best for your needs! One of the most
                       common uses is to test GraphQL APIs and HTTP-based
                       RESTful APIs.


                       The following tutorial will teach you how to
                       install Insomnia on Ubuntu 22.04 LTS Jammy
                       Jellyfish. The tutorial will import the official
                       repository and gpg key and update and remove
                       software using the command line terminal.


                # ⚓ Linux Capable ☛ How_to_Install_Google_Chrome_on_MX_Linux_21
                  –_LinuxCapable⠀⇛


                       Google Chrome is the most used Internet Explorer
                       software on the earth, with a recent update in 2021
                       that Chrome is currently the primary browser of
                       more than 2.65 billion internet users; as you would
                       know, installing MX Linux, like most Linux
                       distributions, only install Mozilla Firefox.
                       However, installing Google Chrome on Chrome is a
                       straightforward task.


                       In the following tutorial, you will learn how to
                       install Google Chrome on MX Linux 21 release series
                       in three alternative ways: stable, beta, or
                       unstable versions, along with some essential
                       command tips for users.


                # ⚓ OSNote ☛ How_to_Install_the_Latest_Python_Version_on_Debian
                  11_–_OSNote⠀⇛


                       Python is an interpreted, interactive, object-
                       oriented programming language. It was created by
                       Guido van Rossum in 1991.


                       Python runs on Windows, Linux/Unix, Mac OS. Python
                       can be used to develop desktop GUI applications and
                       CGI scripts for the web. Also, it’s used for
                       server-side scripting for Apache HTTP Server sites.
                       Python is most popular for its elegance and
                       simplicity.


                       The major advantage of using Python is that there
                       are very few keywords to learn and easy to
                       understand. It’s a general-purpose programming
                       language, which means it can be used in any field
                       of software development with ease and adaptability.


                # ⚓ Video ☛ Linux_Crash_Course_–_The_df_and_du_Commands_–
                  Invidious⠀⇛


                       In the Linux Crash Course series, we’ll go over one
                       important foundational Linux topic each episode.
                       This series includes tutorials, demonstrations, and
                       more!


                # ⚓ Linux Handbook ☛ Search_for_Available_Linux_Commands_With
                  apropos⠀⇛


                       So you used a certain command but cannot remember
                       its exact name anymore?


                       You can use the ctrl+r keyboard shortcut in the
                       terminal and reverse search through the shell
                       history.


                       This could work if you had used the command on the
                       same system. But what if you used it on some other
                       Linux system or just came across it in some forum
                       or website?


                       The good thing here is that there is a dedicated
                       Linux command that lets you search with a string in
                       the available commands on your system.


                # ⚓ Make Use Of ☛ How_to_Create_a_Data_Backup_and_Recovery
                  Strategy_for_Linux⠀⇛


                       As the saying goes “Failing to prepare is preparing
                       to fail,” you should always be prepared with a data
                       backup to avoid losing valuable data on your Linux
                       PC or server.


                       A backup strategy is a simple plan that prepares
                       you to quickly and easily recover your important
                       data in the shortest amount of time possible. Let’s
                       look at how you can devise a backup and recovery
                       plan for Linux that best suits your needs.


                # ⚓ H2S Media ☛ Install_LAMP_on_Ubuntu_20.04_|_22.04_with_a
                  single_command_–_Linux_Shout⠀⇛


                       To run some popular web applications we need a
                       lightweight LAMP server installation, here we learn
                       how to do that on Ubuntu 20.04 focal or 22.04 Jammy
                       Jellyfish using a single command.


                       LAMP sounds may be familiar but it is not for our
                       table, instead, it is an acronym composed of the
                       initial letters of the software Linux, Apache,
                       MySQL, and PHP. This stack is quite common when it
                       comes to creating a web server environment for
                       installing popular PHP-based web applications such
                       as WordPress. We can use LAMP to provide static or
                       dynamic web content.


                # ⚓ LinuxTechi ☛ How_to_Install_Rancher_on_Ubuntu_22.04_(Step
                  by_Step)⠀⇛


                       In this guide, we explore how you can install and
                       set up Rancher on Ubuntu 22.04 (Jammy Jellyfish).


                # ⚓ Linux Capable ☛ How_to_Install_Draw.io_on_Ubuntu_22.04_LTS
                  –_LinuxCapable⠀⇛


                       Draw.io is a free and open-source cross-platform
                       drawing software that can easily create various
                       types of diagrams such as flowcharts or UML
                       drawings for organizational structure analysis!


                       In the following tutorial, you will learn how to
                       install Draw.io on Ubuntu 22.04 LTS Jammy Jellyfish
                       using the command line terminal using the default
                       Ubuntu APT repository or installing the Flatpak
                       third-party package manager to get a newer version
                       binary.


                # ⚓ How_to_install_Insomnia_on_Ubuntu_22.04_–_NextGenTips⠀⇛


                       Insomnia is an open-source, cross-platform API
                       client for GraphQL, REST, and gRPC. It’s a free
                       cross-platform desktop application that takes the
                       pain out of interacting with the designing HTTP-
                       based APIs.


                       Insomnia is an API client that allows you to send
                       requests outside your terminal without writing
                       code. What you need to know in the API world are
                       the requests and endpoints.


                       An Endpoint is a requestable URL. Think of it like
                       this, you have a domain name and inside that domain
                       name, there are a few routes pointers taking you to
                       a certain page. For example, for nextgentips.com,
                       we have an endpoint like category/monitoring.


                # ⚓ H2S Media ☛ How_to_install_Wireshark_on_Ubuntu_22.04_or
                  20.04_LTS_–_Linux_Shout⠀⇛


                       Use the default system repository to install
                       Wireshark of Ubuntu 22.04 LTS Jammy Jellyfish or
                       20.04 focal fossa Linux distros.


                       The Sniffer Wireshark is available in all Linux
                       distributions to easily install. Apart from it, the
                       executable can be downloaded for Windows and Mac
                       OS. This open-source application is very useful for
                       network administrators. IT can record the traffic,
                       where you can look at the contents of a data
                       packet. The IP address of the target system is
                       always logged. Wireshark, for example, can be used
                       to expose notoriously programs using networks to
                       perform some unusual tasks. You can also
                       statistically evaluate the collected data traffic,
                       for example by searching for particularly large
                       packets or picking out addresses that are
                       frequently accessed. A counter-test of who owns
                       such an IP address may then put you on the trail of
                       an attack.


                       Wireshark logs the network traffic of the
                       interfaces of the system on which it is installed.
                       It can therefore examine all incoming and outgoing
                       connections of the respective computer. At the same
                       time, it also receives all data packets that are
                       sent to all systems in the network (broadcasts).


                # ⚓ SUSE’s Corporate Blog ☛ Let_it_fly_–_SAP_HANA_on_SUSE
                  cluster_and_systemd_native_integration⠀⇛


                       The good news first: The cluster configuration
                       stays unchanged. SUSE updated the resource agents
                       for SAP HANA to get the native systemd integration
                       transparent for the cluster administration.


                # ⚓ ID Root ☛ How_To_Install_Magento_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Magento on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, Magento is a highly popular open-
                       source e-commerce platform written in PHP and
                       managed by Adobe Inc. The platform is flexible and
                       has a large variety of features to build an online
                       store. Magento offers a community and a commercial
                       version of its platform the community version is
                       free and is designed primarily for individuals and
                       or small businesses. On the other hand, the
                       enterprise version is mainly aimed at medium to
                       large businesses and more of an enterprise
                       environment.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the Magento open-source e-commerce
                       platform on Ubuntu 22.04 (Jammy Jellyfish). You can
                       follow the same instructions for Ubuntu 22.04 and
                       any other Debian-based distribution like Linux
                       Mint, Elementary OS, Pop!_OS, and more as well.


                # ⚓ Barry Kauler ☛ Ask_ext4_encrypt_and_simplified_boot_menu⠀⇛


                       Whether on a flash-stick or internal drive, EasyOS
                       is now laid out in the drive in the same way, in
                       what we call a “frugal” install. Easy no longer
                       knows what boot-manager or bootloader was used to
                       boot it. In the case of the image file that you
                       write to a flash-stick, the bootloader is now
                       Limine, in a 7MiB fat12 esp partition, and Easy is
                       in a 816MiB ext4 partition.


                # ⚓ Red Hat Official ☛ How_to_use_Linux_shell_command_exit
                  codes_|_Enable_Sysadmin⠀⇛


                       When you execute a command in Linux, it generates a
                       numeric return code. This happens whether you’re
                       running the command directly from the shell, from a
                       script, or even from an Ansible playbook. You can
                       use those return codes to handle the result of that
                       command properly.


                # ⚓ Linux Capable ☛ How_to_Install_PHP_Composer_on_Ubuntu_22.04
                  LTS_–_LinuxCapable⠀⇛


                       Composer is an application-level package manager
                       for the PHP programming language similar to NPM for
                       Node.Js or PIP for Python. Composer provides a
                       standard format for managing all dependencies of
                       PHP software and the required libraries by
                       downloading all the required PHP packages for your
                       project and managing them for you. It is used by
                       most modern PHP frameworks such as Laravel, Drupal,
                       Magento, and Symfony.


                       The following tutorial will teach you how to
                       install Composer on Ubuntu 22.04 LTS Jammy
                       Jellyfish using the command line terminal, along
                       with some basic usage examples working with
                       composer.


                # ⚓ Linux Capable ☛ How_to_Install_Apache_(HTTPD)_on_AlmaLinux
                  9_–_LinuxCapable⠀⇛


                       Apache, also known as Apache HTTP server, has been
                       one of the most widely used web server applications
                       globally for the past few decades. It is a free,
                       open-source web application software maintained by
                       the Apache Software Foundation. Apache provides
                       some powerful features with dynamically loadable
                       modules, easy integration with other software, and
                       handling of static files, among other popular
                       features.


                       In the following tutorial, you will learn how to
                       install Apache Web Server on AlmaLinux 9 using the
                       command line terminal for desktop or server and
                       basic configuration and creating a TLS/SSL
                       certificate with Let’s Encrypt.


          o § Games⠀➾


                # ⚓ Boiling Steam ☛ New_Steam_Games_with_Native_Linux_Clients_–
                  2022-06-23_Edition_–_Boiling_Steam⠀⇛


                       Between 2022-06-16 and 2022-06-23 there were 25 New
                       Steam games released with Native Linux clients. For
                       reference, during the same time, there were 298
                       games released for Windows on Steam, so the Linux
                       versions represent about 8.4 % of total released
                       titles. Here’s a quick pick of the most interesting
                       ones…


                # ⚓ Linux Links ☛ 10_Fun_Free_and_Open_Source_Board_Games⠀⇛


                       
                       We have always had a fascination with board games,
                       in part because they are a device of social
                       interaction, they challenge the mind and, most
                       importantly, they are great fun to play. Many
                       students gather together to escape the horrors of
                       the classroom, and indulge in a little escapism.
                       The time provides an outlet for tension and
                       rivalry.


                       Board games help teach diplomacy, how to make and
                       break alliances, bring families and friends
                       together, and learn valuable lessons.


                       Let’s explore the 10 games. For each game we have
                       compiled its own portal page, a full description
                       with an in-depth analysis of its features, a screen
                       shot of the game in action, together with links to
                       relevant resources.


          o § Desktop Environments/WMs⠀➾


                # § K Desktop Environment/KDE SC/Qt⠀➾


                      # ⚓ KDE Official ☛ Submit_a_Goal_and_Help_Shape_the
                        Future_of_KDE_|_KDE.news⠀⇛


                             I’m super excited to finally announce the
                             start of the submission process for the brand
                             new KDE Goals!


                             KDE sets goals that help the community focus
                             on important things that need to get done in
                             collaboration across many teams. Over the
                             years, the community has set goals to tackle
                             issues with usability, made it easier for new
                             contributors to start working on KDE
                             projects, implemented new tech that will
                             serve us for years to come, and much more.


                             KDE Goals set a direction for the community
                             and help concentrate efforts in areas deemed
                             important by the KDE community itself. Every
                             couple of years, new goals are selected to
                             reflect the communities current priorities.


                      # ⚓ 9to5Linux ☛ Krita_5.1_Promises_JPEG-XL_Support,
                        Improved_Support_for_WebP_and_Photoshop_Files⠀⇛


                             
                             Krita 5.1 promises to introduce lots of
                             goodies for digital artists using this
                             powerful software to create art. Highlights
                             include support for the JPEG-XL file format,
                             improved support for the WebP, OpenEXR,
                             Photoshop layered TIFF, and Photoshop files,
                             support for PSD fill layers and color labels,
                             support for ASE and ACB color palettes, as
                             well as improved painting performance through
                             the use of XSIMD


                      # ⚓ 9to5Linux ☛ digiKam_7.7_Photo_Manager_App_Released
                        with_AVIF_Image_and_Olympus_OM-1_Support⠀⇛


                             
                             Coming about three and a half months after
                             digiKam 7.6, the digiKam 7.7 release is here
                             with support for the AOM AV1 Image File
                             Format (AVIF) open, royalty-free video coding
                             format, which is support for reading and
                             writing in all bundles (AppImage, macOS, and
                             Windows).


                             digiKam 7.7 also appears to add read/write
                             support for the JPEG-XL image format in all
                             supported bundles, though JPEG-XL support was
                             initially introduced in the digiKam 7.6
                             release, but there were some issues in
                             handling animated JPEG-XL files which are now
                             fixed.


    * § Distributions and Operating Systems⠀➾


          o ⚓ The Register UK ☛ How_RISC_OS_happened,_as_told_by_original_Acorn
            Arthur_lead_•_The_Register⠀⇛


                 One of the longest-lived GUI operating systems in the
                 world has its origins as an emergency project –
                 specifically the means by which Acorn planned to rescue
                 the original Archimedes operating system.


                 This is according to the original Acorn Arthur project
                 lead, Paul Fellows, who spoke about the creation of RISC
                 OS at the RISC OS User Group Of London, ROUGOL [after
                 some helpful arrangements made by Liam Proven – Ed].


                 On Monday, your correspondent hosted and moderated a
                 reunion of four of the original developers of Acorn’s
                 RISC OS.


                 Fellows explained that participating were “Paul Fellows
                 (VidC controller, Palette, I2C interface, Real Time Clock
                 and EEPROM), Tim Dobson (Fonts, Audio and Utilities),
                 Richard Manby (Graphics and Desktop), and Stuart Swales
                 (Fileswitch and Heap Manager).”


                 Today, RISC OS is still rumbling along, and version 5 is
                 now open source. But it wasn’t the original, planned
                 operating system for Acorn’s Archimedes computer. That
                 was going to be ARX, of which almost no trace exists
                 today apart from a few Usenet posts. What information
                 survives has been compiled into the Wikipedia article.


          o § Fedora Family / IBM⠀➾


                # ⚓ Remi_Collet:_PHP_version_8.0.21RC1_and_8.1.8RC1⠀⇛


                       Release Candidate versions are available in testing
                       repository for Fedora and Enterprise Linux (RHEL /
                       CentOS / Alma / Rocky and other clones) to allow
                       more people to test them. They are available as
                       Software Collections, for a parallel installation,
                       perfect solution for such tests, and also as base
                       packages.


                # ⚓ Cockpit_Project:_Cockpit_272⠀⇛


                       Cockpit is the modern Linux admin interface. We
                       release regularly.


                # ⚓ Linuxiac ☛ ALBS,_the_AlmaLinux_Build_System_Becomes
                  Publicly_Open_to_All [Ed: AlmaLinux is again outsourcing to
                  Microsoft proprietary software. Use RockyLinus instead.]⠀⇛


                       The AlmaLinux Build System (ALBS) opening aims to
                       increase project transparency and encourage
                       collaboration and community contributions.


                       After CentOS left the enterprise Linux scene as a
                       free Red Hat replacement, various distributions
                       attempted to fill in the gap. As a result,
                       AlmaLinux and Rocky Linux have managed to break
                       through and become the most popular Red Hat
                       replacements.


                # ⚓ Red Hat ☛ GPU_enablement_on_MicroShift⠀⇛


                       MicroShift, a small footprint Kubernetes/Red Hat
                       OpenShift Container Platform implementation, can be
                       configured with NVIDIA Container Runtime and
                       provide containerized jobs with access to your
                       system’s GPUs in order to use the CUDA API. The
                       NVIDIA-GPU Operator can be used in the cluster to
                       enforce the GPU as a requestable resource, just
                       like memory and CPU. In this article, we will
                       demonstrate this by running a few sample CUDA
                       programs that are provided by NVIDIA within a
                       MicroShift implementation.


                       By the end of this article, you will know how to
                       configure MicroShift with your NVIDIA drivers using
                       the all-in-one image, and will have deployed
                       several CUDA programs provided as containers.


          o § Debian Family⠀➾


                # ⚓ Tails ☛ Tails_–_Tails_5.1.1_is_out⠀⇛


                       This release fixes a high severity security issue
                       in tor, that affects performance and possibly
                       anonymity.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Current_status_of_LightDM⠀⇛


                       LightDM is a cross-desktop display manager that was
                       developed by Canonical. It was used as the default
                       display manager in Ubuntu from 11.10 to 17.04 after
                       which it was replaced with GDM. It continues to be
                       part of Ubuntu and other distributions and is used
                       by the smaller desktops as a display manager.


                       Since it was no longer the default display manager
                       in Ubuntu development resources have reduced, but
                       it continues to work. There is some bit rot that
                       has occurred as things change around it.


                       All development is done in GitHub. You are welcome
                       to file issues and pull requests there. Discussion
                       is done here on discourse.ubuntu.com. Note that
                       even though this is the Ubuntu discourse, LightDM
                       is still expected to work on other distributions
                       and this is not an indication that this project
                       only relates to Ubuntu.


                       LightDM used to follow a release cycle that matches
                       the Ubuntu release cycle. Currently no releases are
                       being made, you can either use the most recent
                       release or use the main git branch. The main branch
                       should always be usable.


          o § Devices/Embedded⠀➾


                # ⚓ Tom’s Hardware ☛ Raspberry_Pi_‘Slimshader’_Adds_Real-Time
                  Visual_Effects_to_Your_Music_|_Tom’s_Hardware⠀⇛


                       Custom synth projects are nothing new in the
                       Raspberry Pi community but this open-source shader
                       PCB known as Slimshader is definitely a breath of
                       fresh air in the DIY synth world! Created by maker
                       and developer Erik Oostveen, this project aims to
                       provide custom visual effects to music in real-
                       time.


                       According to Oostveen, Slimshader is a GlslViewer-
                       based, open-source PCB designed to display shader
                       files with a Eurorack design. It offers both analog
                       and HDMI output for video, allowing users to add
                       visual effects to music in real-time. If you’re new
                       to shaders, these are graphic simulations that
                       respond to audio input.


                       The Slimshader PCB was designed from scratch by
                       Oostveen and features a graphics design printed
                       across the top. It has a series of inputs available
                       that can be used to program custom visual effects.
                       On the reverse is a Raspberry Pi which powers the
                       project. Slimshader has been tested and confirmed
                       to operate with a Raspberry Pi Zero W, Raspberry Pi
                       Zero 2 W, and a Raspberry Pi 3B.


                       A custom image file was created just for the
                       Slimshader which, can be downloaded from a Google
                       Drive link available on Oostveen’s website. Shaders
                       can be displayed and modulated using audio input,
                       potentiometers, low-frequency oscillators, voltage
                       control and even via MIDI. Oostveen recommends
                       glslsandbox for finding shaders to experiment with
                       created by various artists who share their work
                       online.


                # ⚓ CNX Software ☛ Mekotronics_R58_review_–_Part_1:_Rockchip
                  RK3588_mini_PC_unboxing_&_teardown_–_CNX_Software⠀⇛


                       Mekotronics R58 is a cost-optimized Rockchip RK3588
                       mini PC and SBC that sells for as little as $169
                       with 4GB and 32GB eMMC flash. The company has now
                       sent me a model with 8GB RAM and 64GB flash for
                       evaluation, and in the first part of the review,
                       I’ll do an unboxing, check out the hardware more
                       closely, and boot it up for a quick check.


                       There’s no retail package so to speak with just a
                       white box and a sticker reading “MINI 8+64G”
                       indicating the RAM and storage capacity for the
                       device.


                       The mini PC ships with a 12V/3A power adapter and
                       cord, an IR remote control with two AAA batteries,
                       two WiFi antennas, an HDMI cable, and a USB-A to
                       USB-C cable probably to flash the firmware if
                       needed.


                       [...]


                       That would be Android operating system and more
                       specifically Android 12 TV OS with support for
                       Google Play.


                # ⚓ The DIY Life ☛ I_Made_A_Home_Assistant_Hub_Using_The
                  Atomstack_X20_Pro_–_The_DIY_Life⠀⇛


                       I’ve been slowly adding more and more devices and
                       sensors to my home automation setup and it’s gotten
                       to a stage where I now have a pretty significant
                       number of apps to control them on my phone and
                       iPad. I’ve also wanted to set up automations and
                       routines between devices, but the interfacing
                       across platforms and between brands isn’t usually
                       available or is buggy at best.


                       If you’ve done anything home automation related on
                       a Raspberry Pi then you’ve probably heard of Home
                       Assistant. It a free and open-source software
                       package that is designed to be a central hub or
                       control system for all of your smart home devices
                       and it’s got a pretty substantial online community
                       working on integration. So, for example, it allows
                       you to do things you wouldn’t normally be able to
                       do like use an Ikea motion sensor to turn on a
                       Philips hue light. Something that isn’t supported
                       by either ecosystem individually.


                       So today I’m going to be installing Home Assistant
                       onto a Raspberry Pi and I’m going to use a new
                       laser cutter, the Atomstack X20 Pro, to laser cut a
                       housing for it so that I can put it somewhere
                       convenient in my house without it looking like a
                       jumble of wires, dongles and PCBs.


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ This_project_lets_you_experience_life_with_a
                  cybernetic_tail_|_Arduino_Blog⠀⇛


                       Modern humans have forgone their tails in favor of
                       walking upright, and this fact left maker Pengfei
                       Zhang wondering what it would be like to have such
                       an appendage. From this idea, she along with
                       Sarvenaz Sardari and Xi Peng created the Cyber
                       Tail, which integrates embedded electronics into a
                       small device that moves with its wearer.


                       The Cyber Tail’s design revolves around a central
                       base that houses a set of four servo motors. In
                       order to move the tail in various directions, each
                       servo motor can either pull or release a single
                       string, which causes the tail itself to bend, akin
                       to how a finger works except in four possible
                       directions. The Arduino Uno controlling these
                       motions relies on an external IR sensor within a
                       pair of glasses that detects whenever the user
                       blinks.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Tech Times ☛ [Gadget_Battle]_Best_Android_Phones_of_2022_|
                  Tech_Times⠀⇛


                # ⚓ Make Use Of ☛ Make_New_Pen_Pals_With_These_5_Android_Apps⠀⇛


                # ⚓ XDA ☛ OnePlus_10_Pro_vs_Xiaomi_12_Pro:_Which_Android
                  flagship_is_better?⠀⇛


                # ⚓ I_welcome_Samsung_Galaxy’s_‘Dream_Team’_as_Android_phones
                  need_shaking_up_|_T3⠀⇛


                # ⚓ 9to5Google ☛ Samsung_Android_13_beta_is_right_around_the
                  corner_–_9to5Google⠀⇛


                # ⚓ Android Authority ☛ Wallpaper_Wednesday:_Android_wallpapers
                  2022-06-22_–_Android_Authority⠀⇛


                # ⚓ Android Police ☛ The_most_interesting_Android_phone_of_2022
                  won’t_be_sold_in_the_US⠀⇛


                # ⚓ Android Headlines ☛ Top_10_Sports_Live_Score_Apps_For
                  Android_(2022)⠀⇛


                # ⚓ SamMobile ☛ Samsung_could_open_the_Galaxy_S22_Android_13
                  beta_program_soon_–_SamMobile⠀⇛


                # ⚓ Android Police ☛ Samsung_looks_nearly_ready_for_beta
                  testers_to_try_Android_13-based_One_UI_5_on_Galaxy_S22
                  phones⠀⇛


                # ⚓ Android Central ☛ Android_13′s_clipboard_overlay_could_add
                  a_handy_button_for_Nearby_Share_|_Android_Central⠀⇛


                # ⚓ Hindustan Times ☛ Google_has_iPhone-like_features_on
                  Android_12!_Tap_the_back_of_your_phone_and_see_what_happens_|
                  Mobile_News⠀⇛


                # ⚓ MIUI_13_review:_The_Android_12_skin_that_balances_tradition
                  and_modernity_|_NextPit⠀⇛


                # ⚓ TechRadar ☛ Oppo_Find_X5_Lite_review:_a_cheap_and_easy-
                  going_Android_phone_|_TechRadar⠀⇛


                # ⚓ Good E Reader ☛ First_Look_at_the_Hanvon_N10_E-Note_with
                  English_and_Android_11_–_Good_e-Reader⠀⇛


                # ⚓ The Sun ☛ Warning_for_MILLIONS_of_Android_phone_owners_–
                  these_alerts_mean_someone_may_be_watching_you_|_The_US_Sun⠀⇛


                # ⚓ SlashGear ☛ The_Reason_Your_Android_Phone_Is_Charging
                  Slowly_And_How_You_Can_Fix_It⠀⇛


                # ⚓ CNET ☛ Clear_Your_Android_Phone’s_Cookies_and_Cache_To_Get
                  Rid_of_Excess_Junk_Files_–_CNET⠀⇛


                # ⚓ Indian Express ☛ Considering_an_older_Android_flagship
                  smartphone?_Here’s_what_to_keep_in_mind _|_Technology
                  News,The_Indian_Express⠀⇛


    * § Free, Libre, and Open Source Software⠀➾


          o § GNU Projects⠀➾


                # ⚓ GNU ☛ GNU_Parallel_20220622_(‘Bongbong’)_released⠀⇛


                       GNU Parallel 20220622 (‘Bongbong’) has been
                       released.


          o § Licensing / Legal⠀➾


                # ⚓ Drew DeVault ☛ GitHub_Copilot_and_open_source_laundering⠀⇛


                       We have seen an explosion in machine learning in
                       the past decade, alongside an explosion in the
                       popularity of free software. At the same time as
                       FOSS has come to dominate software and found its
                       place in almost all new software products, machine
                       learning has increased dramatically in
                       sophistication, facilitating more natural
                       interactions between humans and computers. However,
                       despite their parallel rise in computing, these two
                       domains remain philosophically distant.


                       Though some audaciously-named companies might
                       suggest otherwise, the machine learning space has
                       enjoyed almost none of the freedoms forwarded by
                       the free and open source software movement. Much of
                       the actual code related to machine learning is
                       publicly available, and there are many public
                       access research papers available for anyone to
                       read. However, the key to machine learning is
                       access to a high-quality dataset and heaps of
                       computing power to process that data, and these two
                       resources are still kept under lock and key by
                       almost all participants in the space.1


                       The essential barrier to entry for machine learning
                       projects is overcoming these two problems, which
                       are often very costly to secure. A high-quality,
                       well tagged data set generally requires thousands
                       of hours of labor to produce,2 a task which can
                       potentially cost millions of dollars. Any approach
                       which lowers this figure is thus very desirable,
                       even if the cost is making ethical compromises.
                       With Amazon, it takes the form of gig economy
                       exploitation. With GitHub, it takes the form of
                       disregarding the terms of free software licenses.
                       In the process, they built a tool which facilitates
                       the large-scale laundering of free software into
                       non-free software by their customers, who GitHub
                       offers plausible deniability through an inscrutable
                       algorithm.


                # ⚓ LWN ☛ DeVault:_GitHub_Copilot_and_open_source_laundering⠀⇛


                       Drew DeVault takes issue with GitHub’s “Copilot”
                       offering and the licensing issues that it raises…


          o § Programming/Development⠀➾


                # ⚓ Understanding_explicit_OpenCL_memory_migration_between
                  device⠀⇛


                       Lately someone emailed me asking how OpenCL memory
                       migration works. To be specific, when and how to
                       use the `clEnqueueMigrateMemObjects` API when using
                       more then one device.


                       Yeah, the description of it in Khronos’s
                       documentation[1] is very unhelpful. Nor is this API
                       used often. I also spent quite some time to
                       understand what the documentation is talking about.
                       But first, let’s read the documentation.


                # ⚓ CER ☛ Programming_in_blocks_lets_far_more_people_code_—_but
                  not_like_software_engineers:_Response_to_the_Ofsted_Report⠀⇛


                       I completely agree with the first sentence — there
                       are benefits to using block-based programming in
                       terms of reducing the need to memorize syntax and
                       increasing usability. There is also evidence that
                       secondary school students learn computing better in
                       block-based programming than in text-based
                       programming (see blog post). Blanchard, Gardner-
                       McCune, and Anthony found (a Best Paper awardee
                       from SIGCSE 2020) that university students learned
                       better when they used both blocks and text than
                       when they used blocks alone.


                # § Perl / Raku⠀➾


                      # ⚓ A_toy_language_using_Raku_and_QBE⠀⇛


                             You probably already know that Raku is a
                             language intended to replace Perl 5.
                             QBE is a compiler backend in the same vein as
                             llvm, but much simpler.
                             The Hare programming language uses QBE as an
                             IR (intermediate representation).


          o § Standards/Consortia⠀➾


                # ⚓ Fun_with_Anchor_Text_Keywords⠀⇛


                       Anchor texts are a very useful source of keywords
                       for a search engine, and in an older version of the
                       search engine, it used the text of such hyperlinks
                       as a supplemental source for keywords, but due to a
                       few redesigns, this feature has fallen off.


                       Last few days has been spent working on trying to
                       re-implement it in a new and more powerful fashion.
                       This has largely been enabled by a crawler re-
                       design from a few months ago, which offers the
                       crawled data in a lot more useful fashion and
                       allows a lot more flexible post-processing.


                       It is easy enough to grab hyperlinks within the
                       same domain that is being crawled and process them
                       on the spot and assign the keywords to each
                       document.


    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ AAAS ☛ Japan_tries—again—to_revitalize_its_research_|
                  Science_|_AAAS⠀⇛


                       Latest effort would spend billions on a few
                       universities, but skeptics give it long odds


                # ⚓ Let_Machines_Do_the_Work:_Automating_Semiconductor_Research
                  with_Machine_Learning⠀⇛


                       The development of new thin semiconductor materials
                       requires a quantitative analysis of a large amount
                       of reflection high-energy electron diffraction
                       (RHEED) data, which is time consuming and requires
                       expertise. To tackle this issue, scientists from
                       Tokyo University of Science identify machine
                       learning techniques that can help automate RHEED
                       data analysis. Their findings could greatly
                       accelerate semiconductor research and pave the way
                       for faster, energy efficient electronic devices.


          o § Linux Foundation⠀➾


                # ⚓ ZDNet ☛ The_open_source_jobs_are_out_there [Ed: Steven
                  Vaughan-Nichols,found himself as a job as a marketer of Jim
                  Zemlin, sub-contracted via ZDNet and working on Microsoft's
                  payroll. LF-funded fluff instead of news. When "journalism"
                  is just a sub-branch of the Public Relations industry.]⠀⇛


                       The tech unemployment rate reached 2.1% in May.
                       That was a slight drop from April, but with 623,627
                       tech job openings, that’s still a year-over-year
                       increase of 52%. As good as that is, The Linux
                       Foundation and the trusted learning platform edX’s
                       10th Annual Open Source Jobs Report have found that
                       for open source savvy job seekers, the market is
                       even better than that.


                # ⚓ Cardano_Joins_Linux_Foundation_as_Gold_Member⠀⇛


                       Cardano has announced that it is now a member of
                       the Linux Foundation. According to a blog post, the
                       Cardano Foundation has joined as a gold member,
                       becoming the only nonprofit active at this level.


          o § Security⠀➾


                # ⚓ USCERT ☛ CISA_Releases_Cloud_Security_Technical_Reference
                  Architecture [Ed: This is absurd because "the clown" means a
                  security breach, unless it's the government itself running
                  and controlling that "clown computing"]⠀⇛


                       CISA has released its Cloud Security (CS) Technical
                       Reference Architecture (TRA) to guide federal
                       civilian departments and agencies in securely
                       migrating to the cloud.


                # ⚓ ACM ☛ Closing_the_Cybersecurity_Talent_Gap_With_New
                  Candidate_Pools [Ed: Decades of back doors have meant
                  security failures and a lack of people traintd to understand
                  real security]⠀⇛


                       HR and security leaders must deploy new strategies
                       to attract, hire, and retain cyber professionals
                       while looking for ways to leverage the transferable
                       skills and potential of untapped talent.


                       Demand for cybersecurity talent has reached an
                       historic high: 63% of businesses say they have
                       unfilled security positions, and 60% experienced
                       difficulties retaining qualified cybersecurity
                       professionals in 2021, according to the ISACA State
                       of Cybersecurity 2022 report. And information
                       security analyst jobs are expected to grow faster
                       than the average for all other occupations.


                # ⚓ Diffoscope ☛ Reproducible_Builds_(diffoscope):_diffoscope
                  217_released⠀⇛


                       The diffoscope maintainers are pleased to announce
                       the release of diffoscope version 217. This version
                       includes the following changes:


                       * Update test fixtures for GNU readelf 2.38 (now in
                       Debian unstable).


                       * Be more specific about the minimum required
                       version of readelf (ie.


                       binutils) as it appears that this “patch” level
                       version change resulted in


                       a change of output, not the “minor” version.
                       (Closes: #1013348)


                       * Don’t leak the (likely-temporary) pathname when
                       comparing PDF documents.


                # ⚓ Bruce Schneier ☛ On_the_Subversion_of_NIST_by_the_NSA⠀⇛


                # ⚓ LWN ☛ Security_updates_for_Thursday⠀⇛


                       Security updates have been issued by Debian
                       (chromium, firejail, and request-tracker4), Fedora
                       (ghex, golang-github-emicklei-restful, and
                       openssl1.1), Oracle (postgresql), Scientific Linux
                       (postgresql), Slackware (openssl), SUSE (salt and
                       tor), and Ubuntu (apache2 and squid, squid3).


                # ⚓ Raphaël Hertzog ☛ Raphaël_Hertzog:_Freexian’s_report_about
                  Debian_Long_Term_Support,_May_2022⠀⇛


                       Like each month, have a look at the work funded by
                       Freexian’s Debian LTS offering.


                       Debian project funding


                       Two [1, 2] projects are in the pipeline now. Tryton
                       project is in a final phase. Gradle projects is
                       fighting with technical difficulties.


                       In May, we put aside 2233 EUR to fund Debian
                       projects.


                       We’re looking forward to receive more projects from
                       various Debian teams! Learn more about the
                       rationale behind this initiative in this article.


                # ⚓ Video ☛ Enterprise_Linux_Security_Episode_33_–_Patch_your
                  Confluence_Server!_–_Invidious⠀⇛


                       Atlassian software is constantly under attack, and
                       often the source of many lost weekends for IT
                       admins. Recently, a brand-new vulnerability has
                       been discovered – CVE-2022-26134. This particular
                       vulnerability is remotely exploitable, and has been
                       listed as critical. In this episode, Jay and Joao
                       discuss this vulnerability, as well as some of the
                       struggles around Atlassian software in general.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Public Knowledge ☛ Public_Knowledge_Applauds
                        Bipartisan_Privacy_Efforts,_Cautions_Congress_Must_Fix
                        FCC_Authority_Concerns_Before_Full_Committee_Markup_–
                        Public_Knowledge⠀⇛


                             Today, the House Energy and Commerce
                             Committee’s Subcommittee on Consumer
                             Protection and Commerce marked up the
                             “American Data Privacy and Protection Act,” a
                             bipartisan, bicameral bill introduced by
                             Frank Pallone, Jr., (D-NJ), Cathy McMorris
                             Rodgers (R-WA), Jan Schakowsky (D-IL), and
                             Gus Bilirakis (R-FL) to establish a national
                             standard to protect consumer data privacy.


                             The bill would also impose restrictions on
                             how businesses (like Facebook and Google) can
                             collect, use, and share consumer data, as
                             well as allow for federal, state, and
                             individual enforcement to protect consumers’
                             rights. Public Knowledge urges the committee
                             to continue strengthening this bill to ensure
                             individuals’ privacy is protected.


                             The following can be attributed to Sara
                             Collins, Senior Policy Counsel at Public
                             Knowledge:


                             “We are pleased to see the committee make
                             such great strides in improving this
                             bipartisan bill. Since the draft text was
                             released, the bill’s data minimization
                             provisions have been tightened and there is
                             more clarity around what businesses can and
                             cannot do with consumers’ data. This means
                             that internet users don’t have to rely on a
                             failed notice and consent regime for
                             protection.


          o § Environment⠀➾


                # ⚓ Michael West Media ☛ Ransom_Notes:_pay_us_to_keep_our_old
                  power_plants_running_or_else,_say_fossil_fuel_majors_–
                  Michael_West⠀⇛


                       Prepare to subsidise fossil fuel plants
                       indefinitely. That is the message this morning as,
                       in the wake of Coalition dithering, the new
                       government grooms Australian energy customers for
                       more of the same energy policy. It’s the Richard
                       Wilkins solution. Callum Foote and Michael West
                       report.


                       Nine years of Coalition dithering on climate and
                       energy have surely taken their toll. Way behind the
                       eight-ball on transition to renewable energy, the
                       new government is now grooming Australians to
                       subsidise multinational fossil fuel corporations to
                       keep their polluting coal and gas power stations
                       running way into the future.


                       The public grooming comes via Murdoch and Nine
                       media this morning to extend the life of fossil
                       fuel plants and entrench the power of the very same
                       corporations which have just extorted the energy
                       market operator AEMO by threatening to pull supply
                       out of the grid unless richly compensated.


                # § Energy⠀➾


                      # ⚓ Extreme Tech ☛ Japan_Successfully_Produces
                        Electricity_With_Kairyu_Deep_Sea_Turbine⠀⇛


                             A deep sea turbine off the coast of eastern
                             Japan has proven capable of producing almost
                             as much energy as a coal plant.


                             Kairyu, a massive turbine prototype produced
                             by Japanese machinery manufacturer IHI Corp,
                             sits at least 100 feet underwater. Its anchor
                             line allows it to flex its position to most
                             effectively harness energy from the Kuroshio
                             Current—one of the strongest ocean currents
                             in the world.


                             At first glance, Kairyu looks like an
                             underwater jet. Its middle consists of a 66-
                             foot fuselage, each side of which has a
                             similarly-sized turbine cylinder attached.
                             Both turbine cylinders contain power
                             generators, control mechanisms, and measuring
                             systems which correspond with their
                             respective 36-foot turbine blades. The
                             machine sends all generated energy up a
                             series of cables for use on the country’s
                             power grid.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ AccessNow ☛ #KeepItOn:_U.N._spotlights_global_impacts_of
                  internet_shutdowns_with_new_report_–_Access_Now⠀⇛


                       Today, the Office of the U.N. High Commissioner for
                       Human Rights (OHCHR) joined civil society’s wave of
                       pressure to elevate the devastating impacts of
                       internet shutdowns and highlight the need for their
                       urgent global attention with the official launch of
                       its highly anticipated Human Rights Council report,
                       Internet shutdowns: trends, causes, legal
                       implications and impacts on a range of human
                       rights.


                       “The dramatic real-life effects of shutdowns on the
                       lives and human rights of millions of people are
                       vastly underappreciated and deserve much greater
                       attention from States, international organizations,
                       businesses and civil society,” the report states,
                       shining notable attention on economic, social, and
                       cultural rights.


                       Access Now welcomes the final report, and strongly
                       supports the call for a new “collaborative
                       mechanism for the systematic collection of
                       information on mandated disruptions,” into which
                       “States, civil society and companies all
                       contribute.”


                       “Initiating internet shutdowns are a choice that an
                       increasing number of authorities make to suppress
                       and oppress,” said Felicia Anthonio, #KeepItOn
                       Campaign Manager at Access Now. “These choices must
                       be met with equal resistance. The new Human Rights
                       Council report on internet shutdowns will help
                       amplify the fight to #KeepItOn.”


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ ACM ☛ Artificial_Intelligence_Is_Breaking_Patent_Law
                        [Ed: No, overzealous patent maximalists and their
                        lobbyists break patent law and the patent system]⠀⇛


                             Within a few years, numerous inventions could
                             involve artificial intelligence (AI), which
                             could create one of the biggest threats
                             patent systems have faced. Patent law is
                             based on the assumption that inventors are
                             human; it currently struggles to deal with an
                             inventor that is a machine.


                             Courts around the world are wrestling with
                             this problem as patent applications naming an
                             AI system as the inventor have been lodged in
                             more than 100 countries. If courts and
                             governments decide that AI-made inventions
                             cannot be patented, the implications could be
                             huge. Rather than forcing old patent laws to
                             accommodate new technology, we propose that
                             national governments design bespoke IP
                             law—AI-IP—that protects AI-generated
                             inventions.


                # § Copyrights⠀➾


                      # ⚓ Michael Geist ☛ The_Law_Bytes_Podcast,_Episode_131:
                        The_Bill_C-11_Clause-by-Clause_Review_–_What_“An
                        Affront_to_Democracy”_Sounds_Like⠀⇛


                             Last week, the Standing Committee on Canadian
                             Heritage rushed through the clause-by-clause
                             review of Bill C-11 in a manner that should
                             not be forgotten or normalized. Despite the
                             absence of any actual deadline, the
                             government insisted that just three two hour
                             sessions be allocated to full clause-by-
                             clause review of the bill. Once the
                             government-imposed deadline arrived at 9:00
                             pm, the committee moved to voting on the
                             remaining proposed amendments without any
                             debate, discussion, questions for department
                             officials, or public disclosure of what was
                             being voted on. This week’s Law Bytes podcast
                             features clips from a hearing that one Member
                             of Parliament described as “an affront to
                             democracy”.


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