𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Thursday, October 14, 2021
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Generated Fri 15 Oct 02:40:22 BST 2021
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2021/10/14/


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

QmP3ZqUhWLtsoNk9e1XZbKMU4hB7Z4XET8rdm3utr2x9y9
QmRJGaosMaTsLMaPkXt42c3eUm2cmGbMQsiWbqwfSj4rFV
QmVpm9hDw5gu77p5GNGaG5DU2W7uzy83mFBbqknJREAU3w
QmV3rmUZyHKRZr4HLVsZHXH3SyMh5Xz6dwshz5vRFuVMAD
QmSoYJzJX4ejm4LRdPXhN6F7YBjLvbCRnrxdhaDSj8iaNC
QmbpQyjzfhZNaWnZ1L6GHyRzDA6B5RojnHgAGKGeJKMiyn
QmZjNRnDnEWPhNuhKXBvuyovU32qnjESR1UG1T8emS6oy2
QmSjHyfej3iKcBfRyB2EGPkqcfwQ3z51X2Qz89CbQ1D5GX
QmRXKRPosZ7Bz2MggcSzikrb6U91AxeDNghC3nQk4eD4fh
QmXTYTLpzWBYZ5xwWzbbZJAw6K15tUSpUQPiKiZLEsKUUq
QmUeuLZQ99vnV24pVDJ9uvHk32tda8NgQW3EpyMCrA9AuB
QmZmZwDEJRgqxWPLUg1yQVpFv4YB6HxbHmBdDJg9X68QK2
QmeLhW4oLVWzxpCUCDkA1dFjjenb5EnMwdtSi35sDbQZgd
QmajCNJF85CQYXyosFsER5Yo2XiPM6BUZkHYzeqXkCfiv3
QmScBUgZwyXW8e6VTQ7hn4TPr2dPrqRq4mBq4A6SJD33QU
QmNq798z2Jmsd7aRXgNnfjRvXzECKPp7piDVUnWvgsGMmw
QmRVquEDfjUxjZohz6NpGuYae1hJY5sYhcGTzygC15t1qe
QmS8QHtXh2RotXbWpZsvGPyWGq3WgJPQrsFc5JaTmqKcxD
QmYzF6VmHg31fxPQwnB9o6yJM36EqoqsYXvNMqVE941LM6
QmXCdRHxnSMKmGrnRzrnSPCDWQmdjzEejArfYqZsaBy35Z
Qmf9EcBFemckbJcR5iWC3PVGJxQ5xe3ZqCGKzz681rKMmD


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

⦿ Splitting the Time to Cover More Leaks and Exposés | Techrights

⦿ [Meme] Destroying the Workplace | Techrights

⦿ Links 14/10/2021: DragonFly 6.0.1 Released and Red Hat Loses Another Top Executive | Techrights

⦿ The EPO’s Overseer/Overseen Collusion — Part XII: The French Connection | Techrights

⦿ [Meme] Another Maladministration Meeting Comes to an End | Techrights

⦿ Microsoft GitHub Exposé — Part I — Inside a Den of Corruption and Misogynists | Techrights

⦿ IRC Proceedings: Wednesday, October 13, 2021 | Techrights

⦿ [Teaser] What Miguel de Icaza Really Thinks of the CEO of Microsoft GitHub | Techrights

⦿ EPO Management Tricks EPO Staff Into Taking More Paycuts | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2021/10/14/covering-more-leaks/#comments
		http://techrights.org/2021/10/14/destroying-epo-workplace/#comments
		http://techrights.org/2021/10/14/dragonfly-6-0-1/#comments
		http://techrights.org/2021/10/14/epo-french-connection/#comments
		http://techrights.org/2021/10/14/epo-maladministration/#comments
		http://techrights.org/2021/10/14/github-expose-commences/#comments
		http://techrights.org/2021/10/14/irc-log-131021/#comments
		http://techrights.org/2021/10/14/miguel-de-icaza-on-nat/#comments
		http://techrights.org/2021/10/14/so-called-reforms/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2021/10/14/libreoffice-7-2-2/#comments
		http://techrights.org/2021/10/14/whisker-menu-2-6-1/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 72

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/14/covering-more-leaks/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/14/covering-more-leaks/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Splitting_the_Time_to_Cover_More_Leaks_and_Exposés⠀✐


Posted in Europe, Patents at 9:54 am by Dr. Roy Schestowitz


Video_download_link | md5sum 1e7df6305daaed83cf134276fb2a02b4


http://techrights.org/videos/epo-and-github-series.webm


Summary: We take stock of Part 11 of the ongoing EPO series (“EPO’s Overseer/
Overseen Collusion”) and explain what caused various delays yesterday; we may
have to up our pace a little in order to keep up with an influx of leaks and
whistleblowers


THE LASTEST three articles [1, 2, 3] serve to remind us that EPO abuses
implicate staff everywhere in Europe, states everywhere in Europe, and media in
Europe (and beyond Europe). When labour rights get crushed with impunity, the
media takes bribes to do marketing instead of journalism and when we’re meant
to think this is perfectly “normal” everybody loses.


“At this current pace we should have a part published each day until the last
day of this month.”Having just started a new GitHub_exposé (can be anywhere
between a dozen parts and two dozen parts), we hope to still manage to post a
part of the EPO series every midnight, then prepare a video to discuss it. At
this current pace we should have a part published each day until the last day
of this month. █



                    ䷩ 𝚕𝚒𝚗𝚎 119

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/14/destroying-epo-workplace/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/14/destroying-epo-workplace/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Destroying_the_Workplace⠀✐


Posted in Europe, Patents at 9:40 am by Dr. Roy Schestowitz


Chinese labour standards, one stage at a time…


                      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Team Campinos⦈


Summary: The working conditions at the EPO continue_to_worsen under the António
Campinos regime, perpetuating the decade-long_'demolition_project' of Benoît
Battistelli and his cohorts in the_complicit_Administrative_Council


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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣼⣶⢠⣴⣧⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⠿⡿⢿⣇⢡⡄⠀⣤⣿⣿⣏⣹⣿⡟⠛⠛⠛⢋⣉⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠇⢸⣿⠉⠁⠀⠀⠀⠀⠀⣿⣆⣷⡎⠈⣿⣿⣿⣿⣿⡇⠀⠀⣠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⣟⣃⣴⣤⣶⣾⣿⣦⣤⣤⣤⣶⣶⡆⠛⢻⣟⠻⢿⣿⣿⣿⣿⣿⡇⠀⠛⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⢀⡚⢷⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢣⣁⡄⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢇⡏⠢⣿⣈⠂⣿⠛⣿⡿⢸⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣯⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣏⢵⢫⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠧⠸⠿⠿⠿⠿⣾⣿⡟⠀⠀⠉⠉⠻⡻⠿⠿⠿⠿⠿⠿⠛⢗⢽⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣖⣒⢒⣶⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠊⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠘⣻⣿⣻⣗⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣶⣤⣀⠘⠙⣛⣛⣛⣛⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢲⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢠⣴⣼⢿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣠⣿⣿⣿⣏⠀⠘⠛⠉⠉⠉⠻⠀⠀⠀⠘⢙⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣷⣿⣟⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣇⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠀⡀⠀⠀⠀⠀⣷⡀⠀⣀⣀⣤⣶⣶⡶⢆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡆⠀⠀⠀⠀⣤⣤⣼⣷⣾⣿⣧⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣷⠄⣵⣶⣶⣶⣾⢿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⠀⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣷⣶⣾⣯⣴⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⣷⣶⣦⣄⡀
⣤⣤⣠⣤⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣛⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠗⠒⠶⠒⢒⣒⣒⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⣭⣿⣶⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠛⠛⠛⠛⢋⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣼⣶⢠⣴⣧⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡇⢸⣿⣿⣿⣿⠿⢿⠿⢿⣄⢡⡀⠀⣤⣿⣿⣏⣛⣿⡟⠛⠛⠛⢋⣉⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠇⢸⣿⠉⠁⠀⠀⠀⠀⠀⣿⣆⣷⡎⠈⣿⣿⣿⣿⣿⡇⠀⠀⣀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⣟⣃⣶⣤⣶⣾⣿⣦⣤⣤⣤⣶⣶⡖⠛⢻⣟⠛⢿⣿⣿⣿⣿⣿⡇⠀⠛⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢀⡛⢶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢭⣨⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢇⡏⠢⣿⣈⠂⣿⠛⣿⡿⢸⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡋⠒⣳⢪⣞⢄⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠇⠼⠿⠿⠿⠿⣾⣿⡗⠀⠀⠉⠉⠻⠿⠟⠿⠿⠿⠿⠿⠛⢗⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡶⣶⣶⣒⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠑⠾⣿⣿⣿⣗⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⣾⣿⣶⣶⣶⣤⣌⡛⠛⢛⣛⣛⣛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠐⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢋⣴⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠴⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⡏⢀⣾⣿⣿⣿⠋⠈⠉⠉⠻⢿⡇⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣧⣿⣿⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠘⠿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⣇⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡄⢀⠀⠀⠀⠀⣷⡀⢀⣀⣀⣤⣀⣀⠀⢶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡄⠀⠀⠀⠀⢠⣴⣶⣽⣷⣿⣿⡄⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⠄⣵⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣵⣶⣾⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⣷⣶⣶⣄⡀
⣤⣤⣤⣤⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣛⣻⡿⠿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠗⠒⠶⠒⠒⣒⣒⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣟⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⣭⣿⣶⡀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠛⠛⠛⠛⢋⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣼⣶⣀⣴⣧⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡇⢸⣿⣿⣿⡿⢿⣿⡿⢷⣄⢡⡄⠀⣤⣿⣿⣏⣙⣿⡟⠛⠛⠛⢋⣉⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠇⢸⣿⠉⠁⠀⠀⠀⠀⠀⣿⣆⣷⡎⠈⣿⣿⣿⣿⣿⡇⠀⠀⣀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⣿⣫⣶⣦⣶⣾⣿⣦⣤⣤⣤⣶⣶⡆⠛⢻⣟⠛⢿⣿⣿⣿⣿⣿⡇⠀⠛⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢀⡛⢶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⡈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣾⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠒⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡹⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⣿⡟⠀⣨⣿⠟⠉⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⣿⣇⣰⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣾⡿⠿⠶⠖⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣠⣀⣀⣀⣠⣤⣠⣄⡀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡆⢸⡄⠀⠀⠀⠀⠀⠀⣤⣿⣶⣿⣷⣾⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣀⣴⣿⣿⣄⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⢿⣷⠀⢀⣴⣶⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⢸⣿⣶⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⢭⣥⣶⣆⣥⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⠛⠿⠿⠿⠿⠿⠿⠳⣺⣿⣿⣿⣿⣶⣶⣄
⡀⠀⠀⠀⠀⠀⢰⣦⣤⣄⡠⣄⣤⡄⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣍⣛⣛⠿⠿⢟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠒⠒⠒⠒⠀⢀⣀⣀⣨⣭⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣷⣬⣿⣿⣛⣛⠻⡿⠿⠿⠿⠿⠿⠿⠛⠛⠒⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⡀⠰⣾⣿⣿⣿⡇⠉⠛⠛⠛⠉⠉⠉
⠄⡄⣤⢦⣤⢤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⡘⣆⠀⢀⣇⣀⣀⣀⣠⣤⣤⣤⣤⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⣿⠿⠿⢷⡄⠀⠀⠀⡄⡼⣿⣇⣈⣿⡟⠛⠛⠋⠉⠁⣀⣀
⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⠀⠀⠀⠀⠀⣿⣆⣶⡆⠀⣭⣭⡟⣟⡿⡇⠀⠀⠀⢤⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣤⣤⣤⣤⣤⡄⠙⢛⣛⠛⢾⠾⠿⣠⣽⣿⡇⠀⠉⠁⣸⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣵⣾⣿⣿⣿⡇⠀⠚⠢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠓⠒⠛⠒⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠐⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣶⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⣿⣿⣿⡟⠀⠈⠁⠀⠀⠀⠀⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣾⡿⠿⠶⠖⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠈⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡆⠸⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣴⣧⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣤⣾⣿⣿⣯⠄⠀⠀⠀⢀⣴⣾⣿⣿⠗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⢿⣷⠀⢠⣴⣶⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠾⠿⢿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣷⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⢭⣥⣲⣆⣥⣀⣶⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠙⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⢰⣦⣤⣠⣀⣠⣤⣄⠀⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣍⣛⣛⠿⠿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠒⠒⠀⣀⣀⣀⠀⠈⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣷⣬⣿⣿⣛⣛⠻⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠰⣼⣿⣿⣿⣇⣀⡀⠈⠙⠛⠛⠉
⣶⣤⣤⣤⣠⢠⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣤⡘⣆⠀⢀⣇⣀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠿⢿⣿⠿⠿⢷⡄⠀⠀⠀⡄⡼⣿⣇⣈⣿⡏⠛⠛⠛⠉⢁⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣿⣄⣶⡆⠀⣭⣩⠟⣟⡿⡇⠀⠀⠀⢤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣤⣤⣤⣤⣤⡄⠙⢛⣛⠛⢿⠿⠿⣠⣽⣿⡇⠀⠉⠁⣸⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⡧⠀⠚⢠⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢇⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠲⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠒⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡹⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣹⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⣰⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⢰⣿⣿⣿⣿⠋⠀⠀⠀⠀⠙⢅⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣦⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣾⡿⠿⠶⠶⠒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠈⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⣴⣄⣀⣀⣤⣦⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⡄⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠠⢼⣿⣿⣿⣿⡇⠀⠀⢀⣠⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡽⢿⣷⠀⣠⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣤⠦⠿⢿⣿⣿⣿⣷⡆⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⢭⣥⣲⣆⣭⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣁⣀⠀⠀⠈⠻⢿⣿⢷⣤⣶⣿⣿⣿⣿⣿
⣀⣀⣀⠀⡀⠀⣸⣷⣴⣤⣤⣤⣤⡤⢤⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣭⣛⣛⠿⠿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠿⠟⠓⠒⠒⠀⠀⣀⠀⠀⠀⠀⠈⠙⢿⣿
⠁⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣛⣛⢻⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⢰⣾⣿⣿⣿⣷⣶⣒⡂⠀⠀⠀⠉
⣶⣴⣶⣖⣦⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣤⡘⣆⠀⢠⣇⣀⣀⣄⣤⣤⣤⣴⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⣿⠿⠿⢷⡄⠀⠀⠀⣄⡼⣿⣇⣈⣿⡟⠛⠛⠛⠛⠉⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣆⣶⡆⠀⣭⣻⡿⣟⡿⡇⠀⠀⠀⢤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣤⣤⣤⣤⣤⡄⠛⢛⣛⠛⢿⢿⣿⣹⣽⣿⡇⠀⠉⠁⣸⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⡧⠀⠚⢢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠒⠛⠳⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡹⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⠀⣾⣿⣿⣿⣿⡿⠿⢿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠘⢿⡀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣾⡿⠿⠶⠶⠒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣻⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄⠀⡄⡀⣴⣤⣀⣀⣤⣶⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀⠈⠀⣹⣿⣿⡇⠀⠀⠀⢠⣴⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⡽⢿⣷⠀⣠⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⡇⠀⠀⣠⠄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣥⣶⣖⣭⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣶⣤⣤⣤⠄⠉⠛⠿⠇⠀⠈⠁⠀⢰⣿⣿
⣀⡀⣀⠀⠀⠀⢸⣷⣤⣦⣦⣤⣤⣄⣂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣛⣛⠿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠒⠂⢀⣀⡀⠀⠀⢀⠈⠻⠿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⣿⣻⣛⢻⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⠃⠘⠛⠛⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⡀⠀
⣶⣶⣶⣶⣶⣀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡘⣆⠀⢀⣇⣀⣀⣀⣤⣤⣤⣤⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢿⡿⠿⠿⢷⡄⠀⠀⠀⣄⡼⣿⣇⣈⣿⣿⣿⣿⣿⣿⣿⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣿⣆⣶⡆⠀⣭⣽⡟⣟⣿⡿⠿⠛⠛⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣤⣤⣤⣤⣦⡄⠙⢛⣛⠛⢿⢿⡿⣰⣽⣿⡇⠀⠉⠁⣸⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⡇⠀⠚⢢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢇⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠒⠛⠒⠖⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠐⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡹⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⠀⣼⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⢀⣼⣿⣿⣿⠟⠉⠀⠀⠀⠈⢿⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢷⣄⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⡿⠿⠶⠶⠒⣶⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠉⠻⠿⠄⠀⠀⠀⠀⠀⢸⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣠⣆⣦⡄⣸⣤⣄⣤⣠⣴⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣇⠘⣇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⠉⢁⣢⡇⠀⠀⠀⠀⢀⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⡆⣠⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣥⣶⣆⣭⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣠⣶⣾⡿⠿⠿⠇⠀⠀⠀⠀⠀⢀⣴
⣀⢀⣀⡀⠀⠀⢠⣷⣴⣦⣶⣤⣠⣤⣄⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⣛⡿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡒⡂⠀⠀⢠⣤⣤⣿⣿
⠁⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣻⣟⠻⡿⠿⠿⠿⠿⠿⠿⠿⠛⠓⠂⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⡿
⣶⣶⣶⣶⣶⣦⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣦⡌⢦⠀⢀⣇⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⠿⣿⠿⠿⠿⢷⣄⠸⠛⠻⡏⣽⣿⣇⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣿⣆⣶⡆⠀⣭⣽⡟⣟⡿⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣤⣤⣤⣤⣴⡆⠙⢛⣛⠛⢿⢿⣿⣨⣽⣿⣿⣶⣟⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣿⣿⣿⣿⣯⠈⠛⢠⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢇⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠚⠛⠓⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠒⢒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡹⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⣤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⡀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣽⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⢠⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⢠⣾⣿⣿⣿⡟⠋⠀⠀⠀⠈⠛⠉⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠓⢲⡆⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠙⠿⠿⠇⠀⠀⠀⠀⠀⠠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣀⢀⣀⠀⢠⣦⣤⣤⣤⣴⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣿⠈⣇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⡆⢠⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣀⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡭⣭⣴⣶⣨⣅⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣤⣤⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⡀⠀⠀⣠⣿⣦⣶⣶⣤⣦⣦⣤⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣬⣙⣛⡿⠿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⣛⣛⡃⠀⠀⠀⠀⣶⣾⣿
⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣻⣟⣻⣿⠿⠿⠿⠿⠿⠿⠿⠟⠓⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡀⢴⣶⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣟
⣿⣿⣶⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣦⡌⢧⠀⢀⣇⣀⣀⣤⣤⣤⣤⣤⣴⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⠿⠿⠯⢿⣍⠀⠀⠀⡄⡼⣿⣇⣙⣿⡿⠿⠛⠛⠛⠛⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣆⣶⡆⠀⣭⣽⡿⣟⡿⡇⠀⠀⠀⣤⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣤⣤⣤⣤⣴⡆⠙⢛⣛⠛⢿⣿⡿⣹⣽⣿⡇⠀⠘⠀⣻⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣿⣾⣿⣿⣿⣇⠀⠚⢠⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠟⠒⠚⠒⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡹⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⣿⣿⣿⣿⠟⠉⠛⠉⠁⠈⠉⠉⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⢶⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠻⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⠛⠛⠿⢿⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡀⠀⠀⠀⠀⠀⢘⣦⣀⣠⣠⣤⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣇⠀⢿⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣿⡆⢠⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⣶⣖⣨⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣴⣶⡇⠀⠀⠀⠀⠀⠀⣤
⣀⢀⡀⠀⠀⠀⢠⣷⣶⣦⣶⣦⣴⣦⣤⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣭⣛⣛⠿⠿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠋⣉⣻⣀⣀⣠⣤⣤⣄⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⣿⣛⣛⠻⡿⠿⠿⠿⠿⠿⠿⠿⠛⠓⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣴⣶⣦⣤⣢⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⡌⢧⠀⢀⣇⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠿⠿⢿⡿⠛⠛⠻⡅⡼⣿⣇⣉⣿⣿⣿⣿⠛⠋⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⣿⣆⣶⡆⠀⣭⣵⡟⣟⡿⣿⣿⣿⣷⣴⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣤⣤⣤⣤⣤⡆⠙⢛⣛⠛⢿⠿⡿⣠⣽⣿⣿⣿⣿⠛⣻⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣿⣿⣿⣿⣿⠁⠛⢢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⡈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣾⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⣿⣿⣿⡟⠁⠉⢻⠛⠉⠉⠉⠹⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⣿⣿⣿⡆⠀⣠⠁⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠈⠻⣿⣿⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠉⠙⠛⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣇⠀⢿⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣿⡆⢠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡀⠀⠀⠀⡀⣸⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⣴⣖⣨⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣜⠛⣻⣿⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⣠⣶⣦⣦⣴⣤⣴⣤⣤⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⠿⠿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢛⣛⣿⣿⣿⣿⣶⣦⣀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣬⣽⣿⣛⣛⠻⡿⠿⠿⠿⠿⠿⠿⠿⠛⠓⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣶⣤⣴⣴⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣦⡌⢧⠀⢀⣇⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⠿⢿⣿⠻⠟⠻⣏⣽⣿⣇⣈⣿⣿⣿⣿⣿⠉⠉⢉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠉⠉⠁⠀⠀⠀⠀⣿⣆⣶⡆⠀⣭⣵⡿⣟⡿⣿⣿⣿⣿⣧⣤⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣤⣤⣤⣤⣤⡄⠙⢛⣛⠛⢿⠿⡿⣰⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⡿⠀⠛⠢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠂⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣾⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠓⠒⠒⠒⠒⠒⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢠⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣣⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⣿⣿⠃⠀⢀⣼⣿⣿⡟⠉⠙⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⣿⣿⣦⣤⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠒⢶⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠈⠛⠿⣿⣿⣿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠙⠛⠓⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣸⡇⠀⡀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣇⠀⣧⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣿⡆⢀⣶⣶⣶⣶⣶⣿⣿⣿⣿⡇⢠⣴⣶⣶⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⣿⣿⣿⣿⡷⠀⠀⠀⢀⣀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉⣩⣔⣆⣨⣽⣿⣿⣿⣿⣿⣟⣴⣴⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢴⣤⣀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣦⣀⣀⣀⣠⡀⠀⠀⠸⣿⣿⣿⣿⣮⣿⣿⣿⣿⣶⣬⣛⣛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡋⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣷⣾⣶⣖⢻⣿⣬⣽⣿⣛⣛⠻⡯⠿⠾⠿⠿⠿⠿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⢀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣦⡌⢧⠀⢀⣇⣀⣀⣀⣀⣀⣀⣠⣀⡀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⠛⣇⠽⣿⣇⣈⣿⣿⣿⣿⣿⣿⣿⣿⠉
⣿⣿⣶⣿⣿⣧⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣿⠛⠉⠉⠀⠀⠀⠀⣽⣄⣶⡆⠀⣩⣭⡟⣟⡿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣤⣤⣤⣠⣤⡄⠙⢛⣛⠛⢾⠻⠿⣠⣽⣿⣿⣿⣟⠙⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣾⣶⣾⣿⣿⣿⡟⠀⠛⠠⣭⣿⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣾⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠓⠒⠒⠒⠒⠒⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢠⣤⢀⣤⣶⣦⡄⢠⣴⣶⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣻⣿⣿⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⣿⡇⠀⢀⣼⣿⣿⣿⠉⠈⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⣿⣷⣶⣿⣿⠿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠒⢶⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠛⠻⣿⣿⣟⡒⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣸⡇⢀⡀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⣻⣇⠘⣇⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⡆⢀⢶⣶⣶⡶⣶⣿⣿⣿⣇⠀⢀⣴⣶⣾⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣤⣀⠀⣼⣧⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡩⣩⣔⣖⣨⣄⣶⣾⣵⣳⣴⣲⣶⣷⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⣀⠀⠀⣰⣿⣧
⡀⠀⠀⠀⠀⠀⠠⣦⣠⣄⠠⣠⡀⠀⡀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢸⣿⣿⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣷⣆⢻⣿⣬⣽⣿⣛⣛⠻⡯⠿⠾⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⡌⢧⠀⢀⣇⣀⣀⣀⣀⣀⣠⢀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠛⣇⡽⣿⣇⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠋⠉⠉⠉⠉⣿⣆⣶⡆⠀⣩⣭⡟⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣤⣤⣄⣤⣤⡄⠙⢛⣛⠛⢾⠿⠿⣠⣽⣿⣿⣿⣟⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣶⣾⣿⣿⣿⡿⠀⠛⠢⣭⣿⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠓⠓⠚⠓⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡹⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣻⠟⠁⠈⣿⣿⣿⣿⠿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡎⡀⣠⣾⣿⣿⣿⣇⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⣿⣿⣿⣉⣙⣿⣿⣄⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⣭⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⡇⢸⡀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⣿⣿⣷⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⡄⢠⣶⣶⣶⣶⣾⣿⡇⠀⠀⠀⢀⣴⣶⣿⣆⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣤⣀⠀⠀⢀⣾⣤⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣭⣶⣖⣬⣄⣶⣼⣯⣧⣭⣿⣤⣯⣵⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣷⣤⣀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⠠⣦⣤⣤⣤⣤⣄⠀⢄⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⡿⠿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣻⣿⣿⣿⣿⣿⣿⣶⣄⣀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣬⣽⣿⣛⣛⠻⡯⠿⠿⠿⠿⠿⠟⠻⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣆⣆⣦⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣤⣄⣀⣤⣹⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⣇⡽⣿⣏⣉⣿⣿⣿⣿⣿⣿⡛⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠛⠉⠉⠛⠛⣿⣄⣿⡆⠀⣭⣽⡟⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣤⣤⣤⣤⣤⡄⠛⢛⣛⠛⢿⠿⠿⣠⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣿⣾⣿⣿⣿⣿⠉⠛⠢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠓⠚⠓⠒⠒⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡹⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣴⣶⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠁⠀⣹⣿⣿⣿⠿⢿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⣠⣾⣿⣿⣿⣧⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣿⣿⣍⣩⣿⣿⣧⣠⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠶⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⡇⢹⡀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⡄⢰⣶⣶⣶⡶⣿⣏⠀⠀⠀⠀⢀⣴⣶⣿⣆⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣤⣀⡀⠀⠀⣰⣆⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⣶⣖⣬⣄⢶⣾⣿⣦⣿⣿⣬⣵⣦⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀
⡀⣀⠀⠀⠀⢀⠰⣦⣤⣤⣤⣤⡤⢰⣠⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⣿⣶⣤⣀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣛⣛⡻⡿⠿⠿⠿⠿⠿⠿⠟⠻⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⣶⣏⣔⣼⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣦⡌⢧⠀⢀⣇⣀⣀⣄⣀⣤⣤⣤⣚⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⣇⡽⣿⣏⣙⣿⣿⣿⣿⣿⣿⠛⠋⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⣿⣄⣿⡆⠀⣭⣽⡟⣿⡿⣿⣿⣿⣿⣿⣷⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣤⣤⣤⣤⣤⡄⠛⢛⣛⠛⢿⠿⡿⣡⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣿⣾⣿⣿⣿⣿⠉⠛⠢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠒⠚⠓⠲⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡱⠋⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣼⣿⣭⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⣠⣿⣿⣿⠟⠛⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⣿⣿⣿⣿⣆⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⡷⢤⣾⣿⣿⣦⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠿⠿⡿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⡇⢳⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⢀⣿⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣷⠄⢰⣶⣶⡶⢮⡍⠀⠀⠀⠀⠀⢀⣴⣾⣿⣇⣀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⣴⣖⣬⣄⢶⣼⣿⣷⣾⣿⣶⣄⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣸⣿⣷⣄⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⣦⣤⣤⣤⣤⣄⢢⣠⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⠿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢛⣿⣿⣿⣿⣷⣶⣤⣀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣛⣛⠻⡿⠿⠿⠿⠿⠿⠿⠟⠛⠻⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣀⣀⣅⡰⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣤⣤⣠⣤⣤⣭⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠿⣇⡽⣿⣏⣻⣿⣿⣿⣿⣿⣿⠋⢉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⣿⣄⣿⡆⠀⣭⣥⡟⣿⡿⣿⣿⣿⣿⣿⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣠⣤⣤⣤⣤⡄⠛⢛⣛⠛⢿⢿⡿⣱⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠋⠛⠢⣯⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠓⠚⠚⠓⠒⠒⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢊⡹⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢠⣽⣿⣭⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⢃⣼⣿⣿⡿⠋⠙⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⠿⠿⣿⣷⡀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⡲⢶⣿⣿⣷⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⡇⢳⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⣿⣷⣾⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⠄⢰⣶⣶⢶⠮⡅⠀⠀⠀⢀⡀⢀⣴⣾⣿⣇⣀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⣴⣖⣬⣄⢶⣼⣿⣷⣿⣧⣦⣄⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣸⣿⣤⣀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠸⣦⣤⣤⣄⣤⡄⡀⢤⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣭⣛⣛⡿⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢛⢛⣻⣿⣿⣿⣿⣶⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⣿⣛⣛⠻⡯⠿⠿⠿⠿⠿⠿⠿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣖⣈⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣦⡌⢧⠀⢠⣇⣠⣀⣤⣄⣠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠿⣇⣽⣿⣇⣻⣿⣿⣿⣿⣿⣿⡋⢉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠛⠙⠛⠛⠛⣿⣄⣿⡆⠀⣭⣭⡟⣿⡿⣿⣿⣿⣿⣿⣷⣼⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣤⣄⣤⣤⣤⡄⠛⢛⣛⠛⢾⢿⡿⣱⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⠋⠛⠢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠓⠲⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢊⡹⠋⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢪⣽⣿⣭⡙⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣣⣿⣿⣿⡋⠀⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⠛⢻⣿⣷⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣛⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠇⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⡇⢳⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠿⠇⠀⠀⠀⠀⣸⣿⣾⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣷⡄⢰⣶⢶⣶⡬⠀⠀⠀⠀⠀⡀⢀⣴⣾⣿⣇⣠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣭⣶⣖⣬⣦⣿⣿⣿⣶⣶⣯⣥⣀⣀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⣷⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣦⣤⣤⣤⣤⣤⣤⡤⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣛⣿⣿⣿⣿⣶⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣛⣛⠻⡯⠿⠿⠿⠿⠿⠿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣼⣶⣖⣀⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣦⡌⢧⠀⢀⣇⣄⣤⣀⣀⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠿⣇⡽⣿⣇⣻⣿⣿⣿⣿⣿⣿⡏⢉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠛⠙⠛⠛⠛⣿⣄⣿⡆⠀⣭⣭⡟⣿⡿⣿⣿⣿⣿⣿⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣀⣄⣤⣤⣤⡄⠛⢛⣛⠛⢾⠿⡿⣰⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠛⠛⠢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢄⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣾⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠓⠒⠚⠳⠲⠒⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢂⡹⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢫⣽⣿⣭⡙⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣣⣿⣿⣿⡋⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⠛⢻⣿⣷⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣙⣻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠗⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠇⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣇⢹⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠿⠇⠀⠀⠀⠀⢸⣿⣾⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⣦⣴⣶⣶⠶⠬⠀⠀⠀⠀⢀⡀⢀⣴⣾⣿⣇⣠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣍⣭⣶⣖⣬⣼⣿⣿⣿⣶⣿⣦⣦⣔⣀⣤⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⣷⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⣦⣤⣤⣤⣤⡤⣤⣠⢼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⠿⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣛⣿⣿⣿⣿⣶⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣮⣽⣿⣛⣛⠻⡯⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣆⣖⢒⣠⣔⣔⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣠⣠⣄⣤⣤⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠿⣇⡽⣿⣇⣻⣿⣿⣿⣿⣿⣿⡏⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠛⠙⠛⠛⠛⣿⣄⣿⡆⠀⣭⣭⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣤⣄⣤⣤⣤⡄⠛⢛⣛⠛⢾⠿⡿⣰⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠛⠛⠢⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠒⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠒⡹⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢫⣽⣿⣭⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣣⣿⣿⣿⡋⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⠛⠻⣿⣿⡀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣙⣻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⠇⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣇⢸⣶⣠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⠟⠀⠀⠀⠀⢸⣿⣶⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣿⡜⣿⣿⣷⣶⡬⠀⠀⠀⠀⠀⡀⢀⣴⣾⣿⣧⣠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣭⣶⣖⣬⣄⢿⣿⣿⣿⣿⣯⣀⣀⣀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣿⣷⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣧⣤⣤⣤⣦⣠⡀⣰⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⠿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣶⣤⡀⠀
⠀⠀⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣶⣿⣿⣷⣿⣿⣮⣽⣿⣛⣛⡻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣔⣶⡂⣴⣴⣗⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣦⡌⢧⠀⢀⣇⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⣇⡽⣿⣇⣻⣿⣿⣿⣿⣿⣿⣏⣉⣉
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⣿⣄⣿⡆⠀⣭⣵⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣠⣤⣄⢠⣤⡄⠛⢛⣛⠛⢾⢻⣿⣰⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠛⠛⠧⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠓⠒⠒⠒⠲⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⢒⡹⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡄⢫⣽⣿⣭⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣣⣿⣿⣿⡏⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⠛⠻⣿⣿⡀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣙⣻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠟⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣇⢀⣷⣠⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⢸⣿⣶⣿⣷⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣿⡆⣿⣿⣷⣶⣭⠀⠀⠀⠀⣀⡀⣀⣴⣾⣿⣧⣠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⣶⣖⣬⣄⢿⣾⣿⣿⣿⣿⣄⣀⣀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣰⣿⣷⣤⣀⠀⠀⠀⠀⠀
⣀⡀⠀⢀⢀⠀⢰⣧⣤⣤⣤⣴⣢⣴⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⠿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣶⣤⡀⠀
⠀⠀⠀⠀⡀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣛⣛⡻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣦⣔⣤⢮⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣠⣠⣄⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⣇⡽⣿⣇⣻⣿⣿⣿⣿⣿⣿⣏⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⣿⣄⣿⡆⠀⣭⣭⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣠⣤⣤⢤⣤⡄⠛⢛⣛⠛⢾⢿⣿⣰⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠛⠛⠧⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠟⠒⠒⠒⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⢂⡹⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡔⢫⣽⣿⣭⡙⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣷⣿⣿⣿⡁⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡎⠛⢻⣿⣷⡀⣠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣝⣻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠗⠀⠀⠀⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⡇⢀⣧⢀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⢸⣿⣶⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣷⣾⣿⣾⣧⣤⣍⡄⠀⠀⠀⠀⠀⠀⣴⣾⣿⣧⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⣶⣖⣬⣈⢷⣿⣿⣿⣿⣇⣁⣀⣀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣸⣿⣿⣤⣀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠸⣷⣦⣤⣤⣦⣤⣸⣶⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣭⣛⣛⠿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣛⣿⣿⣿⣿⣿⣶⣤⡀⠀
⠀⠀⠀⠀⠀⣀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣮⣽⣿⣛⣛⡻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣰⣀⣠⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣀⣤⣤⣤⣤⣤⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⣇⡽⣿⣇⣻⣿⣿⣿⣿⣿⣿⣏⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⣿⣄⣿⡆⠀⣭⣭⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣠⣤⣤⢠⣤⡄⠛⢛⣛⠛⢶⠿⣿⣠⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠛⠛⠧⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣾⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠓⠒⠒⠒⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⢂⡹⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣦⡼⢫⣽⣷⣬⣹⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣿⣿⣿⣯⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡎⢙⣻⣿⣧⣀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣭⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⣇⠀⡇⡀⠀⢀⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠿⠿⠷⠀⠀⠀⠀⣸⣿⣶⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⣶⣿⣿⣤⣈⡉⠁⠀⠀⠀⠀⠀⠀⣴⣾⣿⣧⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣭⣶⣖⣬⣵⢾⣿⣿⣿⣿⣏⣅⣀⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿⣿⣤⣄⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⣴⡠⣐⣢⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣭⣛⣛⠿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣿⣿⣿⣿⣿⣦⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣬⣽⣿⣛⣛⠻⡿⠿⠾⠿⠿⠿⠿⠿⠟⠒⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣤⣰⣤⣄⡆⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⣇⡽⣿⣇⣻⣿⣿⣿⣿⣿⣿⣏⣉⣉
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⣿⣄⣿⡆⠀⣭⣭⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣠⣀⣄⠤⣤⡄⠛⢛⣛⠛⢶⢿⣿⣰⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠛⠛⠣⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠗⠒⠒⠒⠲⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣒⡹⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⠀⢠⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣶⣮⡟⢫⣵⣶⣬⣻⣿⣿⠛⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠻⢿⣿⡄⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⢾⣿⣿⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣸⡇⢀⠀⠀⠀⢠⣤⣤⣀⣀⡀⠀⠀⠀⢠⣿⣿⡷⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣻⡇⢸⡆⠀⠀⣾⣿⣿⣿⣿⣿⣶⡾⠿⠿⠿⠿⠅⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣷⣼⣿⣆⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣧⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣠⣀⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣭⣶⣖⣼⣤⣿⣿⣿⣴⣷⣆⣀⣀⣀⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀
⡀⡀⠀⠀⠀⠀⠰⣧⣤⣤⣤⣄⣠⢠⣶⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣭⣛⣛⡿⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣻⣿⣿⣿⣿⣿⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣮⣽⣿⣛⣛⠻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠒⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣔⣦⢄⣄⢢⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣀⣠⣤⣤⣀⣄⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⡿⣇⡽⣿⣇⣻⣿⣿⣿⣿⣿⣿⡏⣉⣉
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⣿⣆⣿⡆⠀⣭⣭⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣠⣄⣤⢤⣤⡄⠛⢛⣛⠛⢶⢿⣿⣸⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠛⠛⠧⣭⣿⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠒⠒⠒⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢂⡹⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⠀⠀⢀⣾⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣤⢀⣤⣾⣯⡟⢡⣴⣶⣭⣻⣿⡏⠀⢹⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⢋⣿⣷⡀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡎⣿⣿⣷⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠶⠖⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣸⡇⢀⠀⠀⠀⣼⣿⣷⣦⣀⣤⣤⣀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⣻⡇⠸⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⠀⠠⠤⠄⠀⠀⠀⣼⣿⣿⣿⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣷⣹⣽⡄⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣧⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣀⢠⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣭⣶⣆⣤⣄⣿⣿⣿⣴⣦⣀⣀⣀⣀⡀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀
⡀⡀⠀⠀⠀⠀⠨⣧⣄⣤⣤⡀⡀⣔⢠⡸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⠿⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣦⣤⡀⢰
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⣮⣽⣿⣛⣛⠻⡯⠿⠾⠿⠿⠿⠿⠿⠟⠚⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⣀⣤⡤⢽⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣦⡌⢧⠀⢀⣇⣀⣀⣀⣠⣤⣤⣀⣠⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⣇⠽⣿⣇⣻⣿⣿⣿⣿⣿⣿⡏⣉⣉
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⣿⣆⣿⡆⠀⣭⣭⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣠⣠⣀⠠⣤⡄⠛⢛⣛⠛⢶⣿⣿⣰⣽⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠛⠛⠣⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠲⠲⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⢀⣠⣤⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡻⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⣠⣿⣿⡟⠁⣨⣿⣿⣿⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣴⢛⣭⣿⣦⡜⢫⣽⣿⣭⡂⠀⢻⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣻⣄⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⣿⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⣻⡇⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢶⣶⣤⣄⣀⡀⠀⣼⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣧⣳⣷⡌⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣤⣶⣾⣿⣯⣭⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣀⢰⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣭⣶⣆⣤⣈⢿⣿⣿⣴⣶⣀⣀⣄⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀
⣀⡀⢀⠀⡀⠀⠰⣷⣦⣤⣤⣴⣨⣴⣲⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣬⣛⣛⡿⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣶⣤⡀⣸
⠀⠀⠀⠀⠀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣛⣛⡻⡿⠿⠿⠿⠿⠿⠿⠿⠟⠚⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣶⣰⣞⢿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣀⣠⣤⣤⣤⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⣇⡽⣿⣇⣻⣿⣿⣿⣿⣿⣿⡏⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⠛⠻⠟⠛⠛⠛⠛⣿⣆⣿⡆⠀⣭⣿⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣠⣠⣤⣠⣤⡄⠛⢛⣛⠛⢾⢿⣿⣹⣽⣿⣿⣿⣿⠛⣿⣿⣿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣾⣷⣿⣿⣿⣿⣿⠛⠛⠣⣭⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠖⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⢀⣠⣤⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡻⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⠈⠉⠈⠉⣠⣿⣿⡟⠁⣨⣿⣿⣿⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣤⡄⢤⣴⢛⣭⣿⣦⡼⢫⣽⣿⣭⡂⠀⢻⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣼⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣻⣄⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡞⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣀⣀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⠿⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⣻⡇⠀⠀⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢶⣶⣤⣄⣀⡀⠀⣼⣿⣶⣶⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠿⣧⣳⣷⡌⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣤⣶⣾⣿⣯⣭⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣀⢰⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣭⣶⣆⣤⣈⢿⣿⣿⣴⣶⣀⣀⣄⣀⣄⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣤⣠⣴⣰⣴⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣭⣛⣛⡿⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣶⣤⣀⣸
⠀⠀⠀⠀⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣮⣽⣿⣛⣛⡻⡿⠿⠿⠿⠿⠿⠿⠿⠟⠚⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣷⣶⣶⣨⡞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⣀⣇⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣇⡽⣿⣇⣻⣿⣿⣿⣿⣿⣿⡏⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⠛⠻⠟⠛⠛⠛⠛⣿⣆⣿⡆⠀⣭⣽⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣠⣤⣤⡤⣤⡄⠛⢛⣛⠛⢶⢿⣿⣸⣽⣿⣿⣿⣿⠛⣿⣿⣿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠛⠛⠣⣭⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠒⠚⠓⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⢀⣤⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡻⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⠈⠉⢨⣭⣬⣩⣴⣿⣿⣿⡿⠛⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣤⢠⣼⡟⣿⣿⢛⣤⣾⣯⡟⢠⣴⣿⣭⣻⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣽⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣠⣄⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣾⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠀⠀⠀⢸⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⠰⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠤⣴⣶⣿⣷⣀⣀⣀⡀⣀⢠⣿⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⣬⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣤⣥⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⣠⣄⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⡅⣒⣀⣄⣠⣀⠠⣬⣿⣿⣿⣷⣶⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⢀⣀⣀
⠀⣀⠀⠀⠀⠀⠸⣷⣤⣴⣴⣤⣕⣤⣴⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣭⣛⣛⠿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿
⠀⠀⠀⠀⢄⠄⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣮⣽⣿⣛⣛⡻⡿⠿⠿⠿⠿⠿⠿⠟⠛⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣧⣾⣿⣳⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣀⣠⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣧⡽⣿⣏⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠛⠿⠿⠛⠛⠛⠿⣿⣆⣿⡆⠀⣭⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣀⣀⣠⢠⣤⡄⠛⢛⣛⠛⢾⣿⣿⣱⣿⣿⣿⣿⣿⠛⣿⣿⣿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣿⣾⣿⣿⣿⣿⠟⠛⠧⣭⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠒⠚⠓⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⢰⣶⣶⣦⣤⣄⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢛⡻⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⠁⠉⠉⢈⣭⣬⣭⣬⣭⣿⡟⠛⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣤⡄⣤⣼⢹⣯⡟⣽⣿⢛⣥⣶⣮⡝⢫⣽⣿⣤⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣽⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⣤⣄⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣷⣶⣾⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⠀⠰⣿⣧⣀⣀⡀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣾⣷⣶⣦⣤⣤⡀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠈⠉⠉⣽⣿⣷⡄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠀⣀⣀⣄⣠⣀⠠⣄⣠⣴⣿⣿⣿⣷⣾⣆⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣦⣄⣠⣠⣿⣿⣿
⡀⣀⣀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣦⣶⣶⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣭⣛⣛⡿⠿⢿⣛⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⡀⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣻⣛⡻⡿⠿⠿⠿⠿⠿⠿⠟⠛⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣷⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⢠⣧⣀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣧⢽⣿⣯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢨⣿⠛⠿⠿⠛⠛⠻⠿⣿⣆⣿⡆⠀⣭⣽⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣀⣀⣀⢠⣤⡄⠛⢛⣛⠛⢾⣿⣿⣱⣿⣿⣿⣿⣿⠛⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣿⣾⣿⣿⣿⣿⠟⠛⠧⣭⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢇⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠳⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⢠⣄⡀⠀⠀⠐⠒⠂⠂⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⣛⡹⠍⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⢸⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠉⢁⣭⣭⣬⣭⠬⣭⣬⣭⣿⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣤⣭⡝⣿⣿⢡⣤⡌⣿⣿⢛⣭⣷⣦⡄⢫⣵⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⠀⠀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣷⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⣀⣀⣠⣠⣴⣿⣦⣤⣤⣤⣄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠒⠒⣶⣦⣿⣿⣿⣿⣿⣿⣭⡀⠀⠀⣀⡀⣄⣤⣀⠠⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣤⣾⣿⣿⣦⡄⠀⠀⠀
⣀⣀⢀⣀⠀⠠⡤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣭⣛⣛⡿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣛⣿⣿⣿⣿⣷⣦⣄⠀
⣀⢀⣄⣒⣠⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣻⣛⡻⡿⠿⠿⠿⠿⠿⠿⠿⠛⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⣠⣧⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⡿⣧⢽⣿⣇⣉⣿⣿⣿⣿⣿⣿⣿⣉⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢨⣿⠻⠿⠿⠛⠛⠿⠿⣿⣆⣿⡆⠀⣭⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣄⣀⣀⣀⣤⣤⡄⠛⢛⣛⠛⢾⣿⣿⣱⣿⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⠻⢧⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢇⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠳⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠐⠒⠀⠀⠀⠀⠀⠀⠀⣛⡻⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⢉⣡⣭⣭⣬⣭⣬⣭⣬⣭⡟⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣭⣭⡟⣥⣼⢹⣿⡟⣿⣿⢉⣤⣶⣯⡿⢣⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⠛⠃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣴⣆⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⠀⠀⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⣀⣀⣀⣤⣤⣿⣧⣤⣤⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠠⠶⠶⠆⠀⠀⠀⠉⠙⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠐⠒⠒⣾⣿⣿⣿⣿⣿⣿⣷⣤⡀⣀⡀⢀⡀⢤⣤⣄⠀⣤⣄⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡤⣶⣶⣄⡀⠀⠀⠀⠀
⣀⣀⣀⡀⡀⠠⠤⣴⣦⣴⣴⣾⣶⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣛⠿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣛⣿⣿⣿⣿⣶⣤⣀⠀
⠀⠀⣄⡀⣐⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣻⣛⡻⡿⠿⠿⠿⠿⠿⠿⠿⠛⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⢠⣧⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣧⡽⣿⣇⣋⣿⣿⣿⣿⣿⣿⣿⡏⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠻⠿⠿⠛⠛⠿⠿⣿⣆⣿⡆⠀⣭⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣆⣀⣀⣀⣤⣤⡄⠛⢛⣛⠛⢾⣿⣿⣱⣿⣿⣿⣿⣿⠛⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⠻⢧⣽⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠓⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡻⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⢉⣵⣭⣭⣬⣭⣬⡭⢨⣭⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣤⣭⣭⡍⣯⣽⢹⣯⡄⢤⣽⢛⣭⣿⣯⡟⢠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣤⣤⣤⣤⡄⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡇⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⢛⡃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⠈⠃⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣶⣾⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣠⣄⣾⣧⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⠿⢛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣤⠤⠀⠀⠀⠈⠉⣹⣵⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠙⢶⣶⣿⣿⣿⣿⣿⣷⣦⣶⣆⡀⢀⠐⣴⣦⣄⠰⣶⣦⣤⣤⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠄⣴⣤⣀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⣿⣗⣤⣤⡄⣀⡄⣤⣀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣭⣛⣛⠿⠿⢿⣛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣛⣛⣻⣿⣿⣿⣶⣤⣀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣽⣿⣻⣛⡻⡿⠿⠿⠿⠿⠿⠿⠟⠛⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣀⣀⣶⡖⣒⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⢧⠀⢀⣇⣀⣀⣤⣤⣤⣤⣤⣤⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣇⡽⣿⣇⣉⣿⣿⣿⣿⣿⣿⣿⣏⢉
⣿⣿⣿⣿⣿⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠛⠻⠟⠛⠛⠻⠿⣿⣆⣿⡆⠀⣭⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣀⣀⣀⢤⣤⡄⠛⢛⣛⠓⢾⢿⡿⣠⣽⣿⣿⣿⣿⠛⣿⣿⣿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣿⣿⣿⣿⣿⠟⠻⢇⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢆⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣾⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠐⠓⠒⠒⠒⠒⠒⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡱⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⣉⣵⣭⣭⣬⣭⣬⠉⣬⣭⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣮⣭⣭⡝⣯⣽⢹⣧⡄⢤⣽⢛⣭⣿⣯⡕⢠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣸⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⢛⡃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⠈⠃⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⣠⣶⣾⣷⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣀⣀⣀⣀⣠⣄⣼⣿⣤⣤⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⡿⠋⠀⢀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠄⠀⠀⠀⠀⠀⠀⢉⣩⣵⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠰⢶⣴⣿⣿⣿⣿⣿⣿⣦⣄⢠⠀⢀⠒⣶⣤⣄⠲⣶⣤⣤⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠄⢼⣦⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢿⣣⣤⠀⣀⣰⡀⣠⣤⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣭⣛⣛⠿⠿⢿⣛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣛⣛⣹⣿⣿⣿⣦⣤⡀⠀
⠀⠀⠀⠀⠀⠀⠉⢻⣴⣿⣿⣿⣿⣿⣿⣿⣻⣿⣮⣽⣿⣛⣛⠻⡿⠿⠿⠿⠿⠿⠟⠟⠛⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣷
⣄⣠⣤⣶⣲⣴⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣦⡌⢇⠀⢀⣇⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣇⡽⣿⣇⣉⣿⣿⣿⣿⣿⣿⣿⣏⠉
⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠛⠻⠟⠛⠛⠻⠿⣿⣆⣿⡆⠀⣭⣽⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⣤⣴⣾⣿⣀⣀⣀⡀⣀⣤⡀⠛⢛⣛⠓⢶⠿⠿⣀⣽⣿⣿⣿⣿⠛⣿⣿⣿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣾⣷⣾⣿⣿⣿⣿⠟⠻⢇⣭⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠉⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢇⡏⠢⣿⣈⠀⣿⠛⢿⡿⢸⡟⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⠀⢀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠚⡿⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⣿⣿⠛⠃⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠳⠲⠒⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠿⠆⣿⡏⣿⣇⢸⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠐⡒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣛⣻⠏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣤⣴⣿⡿⣿⣿⢸⣿⢸⣿⢹⣿⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⣩⣵⣭⣭⣬⣭⣬⢭⣮⣭⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⣠⣤⣤⠀⢠⣤⣤⢠⣤⣤⢠⣾⣯⣭⡝⣿⣿⢹⣧⡄⣽⣿⢛⣭⣿⣧⡄⢠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⡿⣿⡇⢸⣿⣿⣼⣿⣿⢸⣿⡇⣿⡇⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⢿⣿⣜⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣤⣤⣿⣇⣿⣧⢸⣿⢿⣿⢻⣿⢸⣿⡟⢛⡃⣿⣿⢸⣿⣿⣿⣿⢸⣿⡇⣿⣿⣈⣙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡿⢹⣿⡏⣿⣿⣸⣿⢸⣿⢸⣿⢸⣿⡇⠘⠇⣿⣿⢸⣿⡏⣿⣿⠘⣿⣧⣿⠟⠹⣿⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⣀⣀⣀⣤⣤⣤⣼⣿⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⢸⡛⢉⣧⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⣀⢀⠀⢀⣤⣄⡤⠤⠤⢄⡀⠀⠀⠀⠀⠀⢉⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣻⡀⠀⠀⠀⠀⠀⠸⡇⣨⣿⣷⣴⠤⠾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⡛⣿⣶⣄⠾⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⣦⢶⣤⣀⡀⠀⠀⠀⠀
⣿⣷⠀⢀⣀⣀⣴⣿⣧⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣛⡿⠿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣾⣿⣿⣿⣷⣦⣄⠀
⣿⣿⣷⣯⣅⣈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣻⣛⡻⡿⠿⠿⠿⠿⠿⠿⠿⠛⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⡌⣧⠀⣠⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠂⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⡽⣿⣏⣉⣿⣿⣿⣿⣿⣿⣿⣯⣉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠛⠻⠿⠛⠛⠛⠿⣿⣆⣿⡇⠀⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣠⣤⣴⣾⣿⣀⣄⣀⣀⣤⣤⡄⠛⢛⣛⠓⢾⣿⣿⣱⣿⣿⣿⣿⣿⠛⣿⣿⣿⡛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⠻⢧⣽⣿⣿⣷
⠀⠀⠀⠀⡃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠀⠈⡄⡀⠉⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣧⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠀⢃⡇⠀⠸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣶⡇⣿⠀⣷⢀⣀⣀⣢⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⣿⣿⣿⣿⣸⣗⣢⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡇⠀⣀⣿⢹⡍⡶⠀⠀⣸⠃⢠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠻⠟⢿⠀⠀⣌⠁⠐⠛⠿⣿⡇⠀⠀⠰⡄⠀⣗⠒⠒⠂⠀⠀⠀⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠟⡛⢿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣇⣶⣶⣿⠀⡀⠀⠀⠉⠄⠠⠀⢠⡇⢀⠀⢀⠀⠀⠀⠀⠀⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⣿⣿⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⣿⣾⢸⣧⣽⣿⣿⣿⣿⣦⣌⣀⣁⣀⣤⣿⣿⣿⣏⣉⣻⣶⣾⣷⣄⠀⠀⠀⠀⢰⣢⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢋⣿⡿⠛⠛⠉⣇⢤⣰⣾⣿⣿⣏⣿⡿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣿⣿⣿⡯⢾⣿⣿⣿⣿⣿⣧⡀⠀⣠⣾⣿⣶⣤⣼⣿⣬⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠾⠛⣿⣿⠀⠀⠙⢿⢻⣿⣿⣿⡿⣠⣭⣻⣍⣈⣿⣿⣿⣿⣟⣿⣿⣮⡛⣶⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣀⣀⣸⣿⣿⠿⣿⣶⡾⠾⢿⢶⣿⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠛⠻⠿⠏⢡⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠻⠹⠿⠿⡿⠛⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠏⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣾⣶⣦⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⡀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠁⠀⠀⣿⣿⣿⡿⠋⠁⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⠿⠿⠿⢿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡿⠻⠟⢿⣿⣿⣿⣷⣶⣶⣧⣥⣀⣀⠀⣀⣼⣶⣷⣶⣶⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣄⣤⣤⣾⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢺⡆⠀⢸⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣯⡉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣠⣴⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡧⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⠀⠀⠉⠁⠘⠛⠛⠿⠶⢶⣦⣴⣯⣀⠘⠻⠿⠿⢿⠇⢉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠀⠀⡄⡀⠉⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣦⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠀⢣⡇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⡿⣿⣿⣿⢸⣷⣠⣀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠃⠀⣀⣾⢹⡍⡄⠀⠀⣼⠃⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠛⢿⠀⠀⣄⠀⠀⠛⠻⣿⡇⠀⠀⠰⡄⠀⣗⠒⠒⠂⠀⠀⠀⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⣿⠄⣀⠀⠀⠉⡁⠀⠀⢠⡇⡀⠁⢀⠀⠀⠀⠀⠀⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⣿⣿⣀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠼⣿⣾⢸⣧⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣏⣈⣿⣷⣾⣷⣤⠀⠀⠀⠀⢰⣦⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠹⣿⣿⣇⣿⡿⠛⠛⠉⣇⢤⣰⣾⣿⣿⣏⣿⡿⣿⣿⣿⣿⣿⣷⣾⡿⢿⣿⣿⣿⡯⢾⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣶⣤⣼⣿⣬⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⠛⠉⠉⣿⡿⠀⠀⠘⢿⢛⣿⣿⣿⡿⣠⣯⣫⣍⣈⣻⣿⣿⣿⣟⣿⣿⣮⣙⣶⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣴⣦⣤⣿⣿⣿⠿⣿⣶⡾⠾⠿⢷⣼⣃⣀⣤⣶⣤⣬⣭⣥⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣄⠀⠀⠀⢿⡏⠛⠻⠿⠏⢡⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠻⠹⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠏⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⣸⣿⢰⣷⣿⣿⣾⣶⣤⣤⣭⣉⡙⠙⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⡀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠁⠀⠀⣿⣿⣿⡿⠋⠁⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⠿⠟⠿⢿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⠻⠟⢿⣿⣿⣿⣷⣶⣶⣧⣥⣀⡀⢀⣀⣼⣶⣷⣶⣶⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣠⣤⣾⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣯⡉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⣀⣄⣀⣤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣏⣁⡂⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠘⠻⠿⠿⣿⠇⢉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡝⠎⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⡆⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣒⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢀⣘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠃⠀⡄⡀⠉⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢨⣧⣾⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠀⢣⡇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⡿⣿⣿⣿⢸⣇⣠⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣾⢹⡍⡄⠀⠀⣼⠃⢀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠙⠿⠀⠀⣄⡀⠀⠛⠛⣿⡇⠀⠀⠰⡄⠀⣗⠒⠒⠂⠀⠀⠁⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⣙⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⣿⡇⣀⠀⠀⠉⡀⠀⠀⢠⡇⠀⠁⢀⠀⢀⠀⠀⠀⠀⣸⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠼⣿⣾⢸⣧⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣟⣈⣹⣷⣿⣷⣤⠀⠀⠈⠀⢰⣢⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠻⣿⣿⠿⡿⠛⠛⠉⣇⠤⣰⣶⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣷⣾⡿⢿⣿⣿⣿⡯⢾⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣶⣤⣼⣿⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠉⠀⣿⡿⠀⠀⠙⢿⢛⡿⣿⣿⣿⣠⣭⣫⣍⣈⣻⣿⣿⣿⣟⣽⣿⣮⣝⣶⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⣤⣴⣿⣿⣿⠿⣿⣶⡾⠾⠿⢷⣼⣋⣀⣤⣶⣤⣬⣭⣥⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣄⣀⠀⠈⠛⠻⠿⠏⠡⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠻⠹⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠏⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣀⢰⣶⣶⣶⣶⣶⣤⣤⣭⣉⡙⠙⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⡀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠛⠁⠀⠀⣿⣿⣿⡿⠋⠁⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠿⠻⠿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣿⠏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡿⠻⠟⢿⣿⣿⣿⣷⣶⣶⣧⣥⣀⣀⠀⣀⣼⣶⣷⣶⣶⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣰⣗⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣯⠉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⣀⣄⣤⣠⣦⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣏⣀⢠⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠘⠻⠿⠿⣿⠇⢉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡎⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣿⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣒⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠃⠀⡄⡀⠉⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢐⣇⣿⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠀⢣⡇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⡿⣿⣿⣿⢸⣷⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣾⢹⡍⡄⠀⠀⣼⠃⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠛⠿⠀⠀⣈⡄⠐⠛⠻⣿⡇⠀⠁⠰⡄⠀⣗⠒⠒⠂⠀⠀⠉⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⡟⠁⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⣯⡥⢀⡀⠀⠉⢁⠀⠀⢠⡇⠀⠁⢀⠀⢀⠀⠀⠀⠀⣸⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠛⠛⢿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠽⢿⣶⢘⣣⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣋⣈⣹⣿⣿⣷⣥⠀⠀⠈⠀⢰⣢⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠙⣿⠿⡿⠛⠛⠉⣇⠤⣠⣲⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣿⣿⣿⡯⢾⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣶⣤⣼⣿⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠘⢿⢿⡿⣿⣿⣿⣠⣭⣫⣍⣈⣻⣿⣿⣿⣟⣹⣿⣮⣍⣶⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⣿⣿⠿⣿⣶⡾⠾⠿⠷⣭⣛⣀⣤⣶⣤⣬⣭⣥⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡗⠒⠀⠸⠏⠡⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠻⠹⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠏⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣷⣶⣶⣶⣤⣤⣍⣉⡙⠙⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡀⡀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠛⠁⠀⠀⣿⣿⣿⡿⠋⠁⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⡿⠿⠛⠿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⣥⣀⡀⢀⣀⣼⣶⣷⣶⣶⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣔⣶⡿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠛⠛⠛⠿⠿⢿⣷⣿⣯⠉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣀⣤⣤⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠄⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠻⠿⠿⢿⠇⢉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣒⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠛⠿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣦⣶⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠃⠀⡄⡀⠉⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢨⣇⣾⣦⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠀⢣⡇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⡿⣿⣿⣿⢸⣷⣠⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣿⢹⡍⡄⠀⠀⣼⠃⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠛⠟⠀⠀⣀⡄⠀⠛⠛⣿⡆⠀⠁⢰⡄⠀⣗⠒⠒⠂⠀⠀⠉⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⣯⣵⢀⡀⠀⠉⢀⠀⠀⢠⡇⠀⠁⢀⠀⢀⠀⠀⠀⠀⣸⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠯⢿⣶⠘⣧⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣋⣉⣹⣿⣿⣷⣥⠀⠀⠈⠀⢰⣢⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⣿⠿⡿⠛⠛⠉⣃⠤⣠⣲⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣿⣿⣿⡯⢾⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣶⣤⣼⣿⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠘⢿⢿⣟⢿⣿⣿⣠⣯⣫⣍⣈⣻⣿⣿⣿⣟⣹⣿⣮⣙⣶⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⢹⣿⠿⣿⣶⡾⠾⠿⠷⣭⣟⣀⣤⣶⣤⣬⣭⣥⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⠃⠼⠏⢁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠛⠹⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠏⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣶⣶⣶⣤⣤⣭⣉⡙⠙⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⡀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠛⠁⠀⠀⣿⣿⣿⡿⠋⠁⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠿⠛⠛⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡟⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⣥⣀⡀⠀⣀⣼⣶⣷⣶⣶⣶⣉⣸⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⡿⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣟⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣯⠉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⣀⣀⣠⣴⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣇⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣼⡇⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠘⠻⠿⠿⣿⠇⢉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣒⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⡀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠃⠀⡄⡀⠉⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠀⢣⡇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⡿⣿⣿⣿⢸⣷⣠⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠂⣀⣾⢹⡍⡄⠀⠀⣼⠇⠀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠙⠯⠀⠀⣌⣤⠀⠛⠛⣿⡇⠀⠁⠰⡄⠀⣗⠒⠒⠂⠀⠀⠉⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⡁⢠⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⣿⣽⣄⣴⠀⠉⢁⠀⠀⢠⡇⠀⠁⢀⠀⢀⠀⠀⠀⠀⣸⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠯⣿⣶⢘⣧⣼⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣃⣉⣹⣿⣿⣷⣧⠀⠀⠈⠀⢰⣢⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠹⠿⡿⠛⠛⠉⣃⠤⣠⣲⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣷⣾⡿⠿⣿⣿⣿⡯⢾⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣶⣤⣸⣿⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠘⢿⢟⣏⢿⣿⣿⣠⣭⣫⣍⣈⣻⣿⣿⣿⣟⣹⣿⣯⣓⣶⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⢸⣿⠿⣿⣶⡾⠾⠿⢿⣮⣝⣁⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠏⠁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠛⠹⠿⠿⠿⠋⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠇⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣶⣶⣶⣤⣤⣍⣉⡙⠙⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⡀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠛⠁⠀⠀⣿⣿⣿⡿⠋⠁⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠟⠋⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡟⠿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⣀⡀⠀⣀⣼⣶⣷⣶⣶⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⡿⣿⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠛⠛⠛⠿⠿⠿⣷⣿⣏⠉⣹⠙⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣠⣠⣴⣶⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣯⣤⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠈⠻⠿⠿⣿⠇⢉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣒⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⢿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣄⡀⠙⠛⠋⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠓⠀⡄⡀⠉⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠀⢣⡇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⡿⣿⣿⣿⢸⣧⣠⣀⠀⠀⠀⢀⠀⣀⣀⣀⠀⠀⡈⠁⠂⣀⣾⢩⡍⡄⠀⠀⣼⠇⠀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠛⢿⠀⠀⣀⣤⠀⠛⠛⣿⡇⠀⠁⢰⡄⠀⣗⠒⠒⠂⠀⠀⠉⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⡁⢠⣿⣿⣿⣿⣿⣿⣿⡿⢛⠻⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣌⣶⣶⣿⣽⣆⣤⠀⠉⢀⠀⠀⢀⡇⠀⠁⢀⠀⠀⠀⠀⠀⠀⣸⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠯⢿⣶⠸⣧⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣏⣉⣹⣿⣿⣷⣧⠀⠀⠈⠀⢰⣢⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠹⠿⡿⠛⠋⠉⣃⠤⣠⣲⣿⣿⣯⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⣿⣿⣿⡯⢾⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣶⣤⣸⣿⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠘⢿⢟⣿⢿⣿⣿⣠⣭⣫⣍⣈⣻⣿⣿⣿⣟⣽⣿⣯⣳⣶⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⣸⣿⠿⣿⣶⡾⠾⠿⢿⣮⣝⣁⣤⣶⣤⣬⣭⣥⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⠏⠁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠛⠙⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠇⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣶⣶⣶⣤⣤⣭⣉⡙⠙⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⡀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠛⠁⠀⠀⣿⣿⣿⡿⠋⠁⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠟⠋⠙⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡟⠻⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⣀⡀⠀⣀⣼⣶⣷⣶⣶⣶⣈⣸⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣠⣴⣶⡿⡿⠿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣯⠉⣹⠙⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣀⣤⣠⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠘⠻⠿⠿⣿⠇⢉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣤⣄⣀⣀⠀⠀⠀⢨⢤⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣒⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠛⠀⡄⡀⠉⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⠨⣇⣾⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠀⢣⡇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⡿⣿⣿⣿⢸⣷⣀⠀⠀⠀⠀⠀⠀⡀⢀⣄⠀⠀⠀⠁⠂⣀⣾⢩⡍⡄⠀⠀⣼⠇⠀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡺⢻⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠙⠳⠀⠀⣂⣤⡄⠛⠛⣿⡇⠀⠀⢰⡄⠀⣗⠒⠒⠂⠀⠀⠉⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⡟⢛⠻⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⣿⣬⣇⣤⠀⠉⣀⠀⠀⢠⡇⠀⠇⢀⠀⠀⠀⠀⠀⠀⣸⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠯⢿⢶⡘⣇⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣛⣉⣹⣿⣿⣷⣧⠀⠀⠈⠀⢐⣢⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠘⠿⡿⠛⠋⠉⣃⠤⣠⣲⣿⣿⣧⣿⡿⣿⣿⣿⣿⣿⣷⣾⡿⠿⢿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣴⣤⣸⣿⣬⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣿⡿⠀⠀⠘⢿⢟⣿⢻⣿⣿⣠⣭⣩⣍⣈⣛⣿⣿⣿⣟⣿⣿⣟⣶⣶⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣹⣿⠿⣿⣶⡾⠾⠿⠿⣮⣝⣁⣤⣶⣤⣬⣭⣤⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣖⠚⠂⠿⠏⠁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠛⠙⠿⠿⠟⠋⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣶⣶⣶⣤⣤⣍⣉⡙⠙⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡀⡀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠛⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠋⠉⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡎⠙⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⣀⡀⠀⣀⣼⣶⣷⣶⣶⣶⣁⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣲⡾⠛⠿⠫⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣟⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⠉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⡠⣠⢠⣦⣆⣻⣦⣦⣽⣿⣿⣿⣻⣯⣆⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠈⠻⠿⠿⢿⠇⢉⣿
⣾⣿⣷⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⣀⣴⣤⣤⣤⣄⣀⣀⠀⠀⠀⢨⢤⠀⠀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠛⠀⡄⡀⠉⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢈⣧⣾⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠀⢣⡇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣶⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⡀⣀⠀⠀⠀⠀⠀⡀⣀⣄⡀⠀⠐⠀⠂⡀⣾⢩⡍⡄⠀⠀⣼⠃⠀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠛⠿⠀⠀⣀⣤⡄⠻⠛⣿⡇⠀⠀⠰⡄⠀⣗⠒⠒⠂⠀⠀⠉⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⢙⣿⣷⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⡟⢛⠻⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⣿⣬⣇⣤⠀⠈⣠⠀⠀⢠⡇⠀⠁⢀⠀⠀⠀⠀⠀⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠯⢿⣶⡘⣧⣼⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣟⣉⣹⣿⣿⣷⣧⠀⠀⠈⠀⢰⣢⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠘⠿⡿⠛⠛⠙⣃⠤⣠⣲⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣷⣾⡿⠿⢿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣶⣤⣸⣿⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⣿⡿⠀⠀⠘⢿⢟⣿⢻⣿⣿⣠⣭⣫⣍⣈⣻⣿⣿⣿⣟⣿⣿⣿⢦⣶⣾⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢻⣿⠿⣿⣶⡾⠾⠿⠿⣮⣝⣁⣤⣶⣤⣬⣭⣤⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣖⠒⠂⠿⠏⠁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠻⠙⠿⠿⠿⠛⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣷⣶⣶⣤⣤⣭⣉⡙⠙⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⡀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠛⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠛⠋⠉⠉⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡆⠉⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⢀⡀⠀⣀⣼⣶⣷⣶⣶⣶⣀⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣤⣐⣸⠿⠿⢻⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣟⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⠉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⡀⣤⢠⣴⣴⣦⣦⣺⣿⣾⣿⣿⣿⣿⣤⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠈⠻⠿⠿⢿⠇⢉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣤⣄⣀⣀⠀⠀⠀⢨⢤⠀⠀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠋⠁⡄⡀⠙⢺⠵
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢀⣧⣾⣦⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠸⢻⡇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣶⡇⣿⠀⣷⢀⣀⣀⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⢶⠀⢸⠿⣿⣿⣿⢸⣿⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢀⠠⠂⣀⣾⢩⡍⡄⠀⠀⣼⠀⠀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢻⣻⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠉⠛⠿⠀⠀⣆⣤⡄⠓⠛⣿⡇⠀⠀⠰⡄⠀⣗⠒⠒⠂⠀⠀⠉⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⣿⣿⣾⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⡟⢛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⣿⣬⣇⣤⠀⠈⠠⠀⠀⢠⠇⠀⠅⢀⠀⠀⠀⠀⠀⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⡿⠯⢿⣶⡘⣃⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣛⣉⣹⣿⣿⣷⣄⠀⠀⠈⠀⢰⣢⠀⠀⢸⣆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠈⠻⡿⠛⠛⠙⡃⠤⣠⣲⣿⣿⣯⣿⡿⣷⣾⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢞⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣶⣤⣸⣿⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⡿⠀⠀⠘⢿⢟⣿⢻⣿⣿⣠⣭⣫⣍⣈⣛⣿⣿⣿⣟⣙⣿⣿⣦⣶⣸⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⠿⣿⣶⡾⠾⢿⠿⣯⣝⣁⣤⣶⣤⣬⣭⣥⠀⣀⣠⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡖⠒⠂⠸⠏⠁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠻⠻⠿⢿⡿⠟⣻⣿⣿⣿⣿⣿⠀⣛⣛⣛⡛⢻⣿⣿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣶⣶⣶⣤⣤⣍⣉⡙⠋⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠟⠛⠋⠉⠋⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡆⠙⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⣀⣼⣶⣷⣶⣶⣶⣈⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣴⡶⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣯⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣏⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⢠⣄⣠⣤⣶⣦⣶⣾⣿⣷⣿⣿⣿⣿⣤⣄⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠈⠻⠿⠿⢿⠇⢨⣿
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀⣀⡀⠀⠀⢀⣀⣴⣦⣤⣤⣀⣀⣀⠀⠀⠀⢨⢦⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠉⠉⠹⢿⣶⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⣉⠁⠋⢁⡄⡀⠙⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣦⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠸⢹⠇⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣶⡇⣿⠀⣷⢀⣀⣀⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣿⣦⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢠⠠⠂⣀⣾⢩⡍⡄⠀⣀⣾⠀⣀⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡺⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠉⠛⠷⠀⠀⣆⣤⡄⠛⠛⣿⡆⠀⠀⡴⡆⠀⣗⠒⠒⠂⠀⠀⠉⠀⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠉⣿⣿⣷⣿⣿⣿⠁⢨⣿⣿⣿⣿⣿⣿⡟⢛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⣿⣬⣇⣤⠀⡉⠠⠀⠀⢰⠇⠀⠅⢀⠀⠀⠀⠀⠀⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠛⢷⣾⣿⣿⣿⣿⣿⡿⠯⢿⣶⡘⣇⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣛⣉⣹⣿⣿⣷⣄⠀⠀⠉⠀⢰⣢⠀⠀⢸⡆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠻⡿⠛⠛⠙⡣⠤⣠⣲⣿⣿⣯⣿⡿⣷⣾⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢞⣿⣿⣿⣿⣿⣷⡀⠀⣠⣮⣿⣶⣤⣼⣿⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⢹⡿⠀⠀⠘⢿⢟⣿⢻⣿⣿⣠⣭⣫⣍⣈⣻⣿⣿⣿⣟⡙⣽⣿⣦⣶⢸⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢿⠿⣿⣶⡾⠾⠿⠿⣯⣝⣁⣤⣶⣤⣭⣭⣥⠀⣀⣤⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⠒⠒⠀⠏⠁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠻⠻⠿⢿⣿⡟⣻⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⣿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣷⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠟⠛⠛⠉⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡇⠙⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⣀⣼⣶⣷⣶⣶⣶⣍⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⡞⠽⠽⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣿⣿⣯⡉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣀⣠⣤⣤⣷⣶⣦⣶⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠈⠻⠿⠿⢿⠇⢨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣀⡀⠀⠀⢀⣀⣴⣶⣤⣤⣀⣀⣀⡀⠀⠀⢨⢦⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠉⢱⣀⠀⠙⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢀⣧⣿⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠸⣸⠀⠀⢸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣠⣖⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⡿⣿⣿⣿⢸⣿⣦⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣠⠵⠀⣀⣾⢩⡍⡄⠀⣀⣿⠠⡄⠸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠙⠙⢿⠀⠀⣊⣠⡀⠷⠛⣿⡇⠀⠀⡇⡆⠀⣗⠒⠒⠂⠀⠈⠁⠀⠰⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⢿⣿⣿⣾⣿⣿⡟⠁⢹⣿⣿⣿⣿⣿⡟⢛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⣿⣹⣇⣴⠀⡋⠐⠂⠀⣸⠁⡀⠅⢀⠀⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠻⠿⣶⣿⣿⣿⣿⣿⡿⠿⢿⣦⡸⣇⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣛⣙⣻⣿⣿⣷⣄⠀⠀⠉⠀⢰⣦⠀⠀⢸⡆⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⠀⠀⠀⠀⠘⠿⠛⠋⢹⡁⠤⣠⣲⣿⣿⣯⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⠞⣿⣿⣿⣿⣿⣧⡀⠀⣠⣬⣿⣶⣤⣼⣿⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠉⠀⠀⠙⢾⢟⣿⢿⣿⣿⣠⣯⣫⣍⣈⣻⣿⣿⣿⣟⡙⣽⣿⣦⣶⢸⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⡀⠠⣶⣶⡾⠾⠿⢷⣭⣹⣃⣤⣶⣤⣭⣭⣥⠀⣀⣤⣾⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠿⠏⠀⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠻⠿⡿⣿⣿⣿⠟⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣷⣶⣶⣤⣤⣭⣉⡙⠋⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠟⠛⠙⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡎⠙⠃⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⣀⣼⣶⣷⣶⣶⣶⣍⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⡟⠝⠝⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣏⡉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣄⣤⣠⣤⣷⣿⣦⣾⣾⣿⣿⣿⣿⣿⣥⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠘⠻⠿⠿⢿⠇⢨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⠀⠀⠀⢀⣀⣴⣶⣤⣤⢀⣀⣀⡀⠀⠀⢨⢦⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠉⢰⢀⠀⠘⢻⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢠⣧⣿⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠸⣼⠀⠀⢰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣂⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣷⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢠⠔⠀⢀⣾⢩⡍⡄⠀⣀⡿⠰⠀⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠛⠲⠀⠀⣀⣠⠐⠖⠻⣿⡇⠀⠀⣇⡆⠀⣗⠒⠒⠂⠀⠈⠁⠀⠰⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣷⣿⣿⣿⠋⢹⣿⣿⣿⣿⣿⡟⢛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⣯⣹⣆⣴⠀⡏⠁⠂⠀⣸⢠⠀⠟⢀⠀⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⣦⣾⣿⣿⣿⣿⡿⠿⢿⢦⡘⣇⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣋⣙⣻⣿⣿⣷⣄⠀⠀⠉⠀⢰⣂⠀⠀⢸⡄⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠈⠛⠛⠛⠻⠁⠤⣠⣲⣿⣿⣯⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⠞⣿⣿⣿⣿⣿⣧⠀⠀⣠⣬⣿⣶⣤⣸⣿⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢟⣿⢿⣿⣿⣠⣯⣫⣍⣈⣻⣿⣿⣿⣟⡙⣽⣿⣦⣶⢸⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⡤⠰⡿⣶⠾⠾⠿⢶⣝⣹⣃⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠿⠏⠀⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠻⢯⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣶⣶⣶⣤⣤⣍⣉⡙⠋⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠟⠟⠛⠙⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡄⠙⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⣀⣼⣶⣷⣶⣶⣶⣉⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣲⡐⠙⠞⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣏⡉⣸⠙⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⣠⣤⣑⣮⣆⣶⣾⣿⣿⣿⣿⣯⣤⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠈⠻⠿⠿⢿⠇⢨⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⠀⠀⠀⢀⣀⣴⣦⣤⣤⣄⣀⣀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠉⢠⢀⠀⠀⣹⠵
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢐⣧⣿⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠟⡿⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⢶⠀⢸⢿⣿⣿⣿⢸⣿⣦⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣠⠔⠀⠀⣼⢩⡍⡄⠀⣀⡇⠉⠀⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠙⠻⠯⠀⢠⣀⣀⠐⠞⢻⣿⡇⠀⠀⣦⠀⠘⣷⡒⠒⠂⠀⠉⠀⠀⢰⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠩⠿⣿⣿⣿⣵⣿⣿⣿⠋⢻⣿⣿⣿⣿⡟⢛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⣏⣹⣄⡔⠀⡏⠀⠄⢀⡸⠐⠀⠿⢇⠀⠀⠀⠀⠀⠀⢨⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣤⣾⣿⣿⣿⡿⠿⢿⢧⡘⣇⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣋⣛⣻⣿⣿⣷⣄⠀⠈⠁⠀⢰⣆⠀⠀⢸⡄⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡋⠁⠀⠀⠈⠛⠛⠉⠁⠀⣰⣲⣿⣿⣯⣿⡿⣷⣾⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⠏⣿⣿⣿⣿⣿⣧⠀⠀⣠⣬⣿⣶⣤⣼⣿⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠰⢾⢟⣿⣿⣿⣿⣤⣯⣫⣍⣈⣻⣿⣿⣿⣟⡙⣽⣿⣦⣶⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠶⡿⣶⠾⠾⢿⢼⣟⣻⣃⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠏⠁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠛⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠀⣛⣛⣛⣛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣷⣶⣶⣤⣤⣭⣉⡙⠋⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣀⡀⠀⠀⠀⠀⠁⠲⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠟⠛⠛⠉⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡄⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡅⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣍⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⡐⠐⠋⠛⠍⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣏⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⢀⣀⣀⣤⣐⣢⣴⣾⣿⣿⣿⣿⣯⣿⣤⣤⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠈⠻⠿⠿⢿⠇⢨⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⡀⠀⠀⠀⢀⣀⣴⣦⣤⣤⣄⣄⣀⠀⠀⠀⢨⢦⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠉⣤⢀⠐⠀⣜⣡
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢰⣧⣿⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠏⡟⡀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣔⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⡿⣿⣿⣿⢸⣷⣤⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡰⠔⠀⠀⣸⢩⡍⡄⠀⣀⠇⠀⢀⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠛⠫⠀⢰⢀⣀⠸⠞⢻⣿⡇⠀⠀⣦⠀⠰⣷⡖⠒⠂⠀⠉⠀⠀⢱⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠩⢿⣿⣿⣿⣩⣾⣿⣿⠏⢻⣿⣿⣿⣿⡟⢛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⣏⣻⣄⡄⠈⡏⠀⡄⢀⡸⠁⢠⠿⢇⠀⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣿⡿⠿⢿⢧⣘⣇⣝⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣋⣛⣻⣿⣿⣷⣄⠀⠈⠀⠀⢱⣆⠀⠀⢰⡄⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠋⠁⠀⠉⠻⠿⠉⠁⠀⣰⣲⣿⣿⣯⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⠏⣿⣿⣿⣿⣿⣧⠀⠀⣠⣬⣿⣶⣤⣼⣿⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⢶⢟⣿⣿⣿⣿⣤⣯⣫⣍⣈⣛⣿⣿⣿⣟⡙⣽⣿⣦⣶⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⡤⠤⡶⢖⠾⠾⢿⢽⣛⣻⣃⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⣿⡏⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠿⠏⠀⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡿⠿⠿⣿⣻⣿⣿⣿⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣷⣶⣶⣤⣤⣍⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡀⡀⠀⠁⠀⠀⠑⠲⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⠛⠛⠉⠛⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡄⠈⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣉⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⣴⣖⠿⠟⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⢿⣷⣿⣏⡉⣸⠙⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⢤⣤⣠⣤⣾⣿⣦⣾⣿⣿⣿⣿⣿⣿⣷⣤⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠘⠻⠿⠿⢿⠇⢨⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⠀⠀⠀⢀⣀⣴⣶⣤⣤⣄⣀⣀⠀⠀⠀⢨⢦⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠉⣦⡀⠐⠂⣴⣠
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢰⣧⣾⣦⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠏⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣶⡇⣿⠀⣷⢀⣀⣐⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣷⣦⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡰⠖⢀⠀⢸⢹⡍⡄⢀⣠⠁⠀⢠⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠻⠿⠀⢰⢀⣀⠰⠾⢿⣿⡇⠀⠀⢶⠀⢠⣷⣶⠒⠂⠀⠁⠀⠀⢱⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠉⠿⣿⣿⣿⠏⣽⣿⣿⡿⠻⣿⣿⣿⣿⡟⢛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⣏⣻⣀⡄⠘⡏⠀⡀⢀⡀⠀⢸⠿⢿⠀⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⡿⠿⢿⣧⣘⣇⣼⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣋⡛⣻⣿⣿⣷⣄⠀⠈⠀⠀⢱⣆⠀⠀⢰⡄⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠋⠉⠙⠻⢏⠉⠁⠤⣰⣲⣿⣿⣯⣿⡿⣷⣾⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢏⣿⣿⣿⣿⣿⣦⠀⠀⣠⣬⣿⣶⣤⣼⣷⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢈⢙⣿⣿⣿⣿⣠⣯⣫⣍⣈⣛⣿⣿⣿⣟⡙⣽⣿⣦⣶⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡄⠀⠀⠒⠾⠾⠯⢿⣛⣻⣃⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⣿⡏⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠍⠀⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿⣷⣶⣶⣤⣤⣍⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⡀⠀⠈⠉⠁⠉⠉⠰⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠛⠛⠋⠛⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡄⠈⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡅⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣉⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢄⣴⣖⠋⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣏⡉⣸⠙⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⢄⣀⣀⣦⣼⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠈⠻⠿⠿⢿⠇⢨⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⠀⠀⠀⢀⣀⣴⣦⣤⣤⣤⣀⣀⠀⠀⠀⢨⢦⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠉⡆⡀⠑⠲⢠⣴
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠀⠇⠚⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣲⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣯⣦⡀⠀⠀⠀⡀⢀⣀⣀⣀⠀⠀⡴⠖⢀⠀⠀⢹⡍⡄⢀⣰⠀⠀⢠⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡺⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠛⠿⠀⠐⢋⡀⠸⡿⢿⣿⡇⠀⢠⠲⠀⠁⣶⣶⠒⠂⠈⠀⠀⠀⢰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠩⢿⣿⣿⣿⣿⠟⣿⣿⣿⠿⣿⣿⣿⣿⡟⢛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣾⣏⣻⢀⡄⢘⡏⠀⠀⢀⡄⠀⢠⠿⢿⡇⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⣾⣿⣿⣯⠀⣼⣿⣿⡿⠯⢿⢷⣘⣧⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣛⡛⣻⣿⣿⣧⡈⠃⠈⠀⠀⢰⣆⠀⠀⢰⡄⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠿⠻⠟⠿⣿⠋⠁⢤⣴⣲⣿⣿⣯⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢏⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣼⣷⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⠒⠥⣼⢟⣿⣿⣿⣿⣠⣯⣫⣍⣈⣻⣿⣿⣿⣟⡙⣽⣿⣦⣶⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠨⠼⠿⢿⣿⣿⣠⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⣿⡏⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠄⠀⣼⣾⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡿⢿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⡿⠐⣛⣛⣛⣛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⣶⣶⣤⣤⣍⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡈⡀⠈⠉⠉⠉⠉⠰⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⠛⠛⠋⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡆⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡅⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣍⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⣴⣖⢿⡿⠏⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠙⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣤⣤⣄⣦⣼⣯⣦⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣴⣯⡀⠈⠻⠿⠿⣿⠇⢨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⠀⠀⠀⢀⣀⣴⣦⣤⣤⣄⣀⣀⠀⠀⠀⢨⢦⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣶⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⠁⡦⡄⠛⣿⢂⣴
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢨⣧⣿⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⡴⠀⠀⠃⠁⠀⠈⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣂⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⡴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣠⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣰⠆⣀⡀⠀⠨⡍⡆⢀⡄⠀⠀⠀⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠻⢟⠀⠐⢉⡁⢴⡿⣿⣿⠇⠀⢸⠲⠈⠟⣼⣿⡖⠂⠈⠁⠀⠀⢰⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣾⡟⣧⢀⡆⢸⡏⠀⠀⣀⠀⠀⢀⠿⢿⡇⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠟⢻⣿⣿⣾⣿⣿⡇⢠⣿⣿⡿⠯⢿⣧⣸⣧⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣛⠛⣿⣿⣿⣧⡰⠆⠈⠀⠀⢰⣆⠀⠀⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣿⣿⣿⠿⠛⠛⠻⣿⡏⠁⢤⣴⣲⣿⣿⣯⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢏⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣼⣷⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠥⣠⣼⢟⣿⣿⣿⣿⣠⣯⣩⣍⣈⣛⣿⣿⣿⣟⡙⣽⣿⣦⡶⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠨⠼⠿⢿⣿⣿⣠⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡏⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠄⠀⣴⣾⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⣿⣿⣿⣾⢷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⡐⠈⠉⠙⠉⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠛⠛⠋⠙⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣶⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡄⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣈⣸⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣾⣿⡿⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⡿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⠉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⣠⣠⣴⣦⣶⣶⣧⣾⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠻⠿⠿⣿⠇⢨⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⡀⠀⠀⢀⣀⣴⣶⣤⣤⣄⣀⡀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⢱⣦⡌⠛⣿⡇⣶
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢨⣧⣿⣶⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠸⠈⠁⠀⠛⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⢿⣿⣿⣿⢸⣯⣠⡀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⣰⠆⣀⣀⠀⢰⡍⡆⠀⡄⠀⠠⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠻⢯⠀⠈⢃⡁⢼⡟⣿⣿⠇⠀⠸⠒⠈⡟⣸⣿⣖⠂⠈⠁⠀⠀⢰⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⡿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣿⡿⠿⠿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣾⡛⣧⢀⠆⢸⡏⠀⠀⣀⠀⠀⠀⠿⢿⡇⠀⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠏⣻⣿⣷⣿⣿⣿⡅⢠⣿⣿⡿⠿⢿⣧⢸⣣⣝⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣛⠿⣿⣿⣿⣧⡰⠀⠈⠀⠀⢐⣆⠀⠁⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣿⣿⡿⠛⠋⠙⠻⣿⡏⠀⢤⣴⣶⣿⣿⣯⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢿⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣼⣷⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⢶⣠⣾⢟⣿⣿⣿⣿⣠⣭⣫⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡖⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢼⣼⢿⣿⣿⣿⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠄⠀⢼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡰⠉⠉⠛⠋⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠛⠛⠋⠙⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣈⣸⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣄⣴⣺⣿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣟⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⢿⣷⣿⣯⡉⣸⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⡀⣀⣤⣤⣶⣵⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣯⣤⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠻⠿⠿⣿⠇⢈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⡀⠀⠀⢀⣀⣴⣶⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⢱⢦⡌⠛⣿⡇⣴
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠸⠈⠀⠀⠿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣴⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣗⣢⡀⠀⠀⠀⣀⢀⣀⣀⣀⠀⠀⡰⠆⣀⣀⠀⢰⡍⡄⠀⡄⠀⢠⠃⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠛⢯⠀⠈⢉⡀⢼⡟⣿⣿⡇⠀⠸⠖⠈⡿⢸⣿⣶⠂⠈⠁⠀⠀⢰⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⡿⠟⠿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣾⡛⣧⢀⠄⢹⡏⠀⠀⢀⠀⢀⠁⠿⢿⡟⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠙⣻⣿⣿⣿⣿⣿⣀⣾⣿⣿⡿⠿⣿⣦⢸⣧⣜⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣛⠿⣿⣿⣿⣧⡠⠀⠈⠀⠀⢐⣆⠀⠁⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡟⠋⠉⠉⠻⣿⡏⠀⢤⣴⣶⣿⣿⣯⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠙⢶⣴⣿⢟⣿⣿⣿⣿⣠⣯⣫⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡖⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠠⣼⣼⣛⣿⣿⣏⣀⣤⣶⣤⣭⣭⣥⠀⣀⣤⣼⣿⣿⢿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠄⠀⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⡿⣿⣿⣿⣿⡿⠐⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⣶⣶⣤⣤⣭⣉⡙⠙⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡠⠌⠉⠛⠉⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠟⠛⠋⠙⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣈⣹⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣴⣿⣿⡟⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⠉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⡀⣄⣠⣤⣤⣶⣾⣦⣾⣿⣿⣿⣿⣿⣿⣿⣯⣤⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠛⠿⠿⣿⠇⢈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀⡀⠀⠀⢀⣀⣴⣶⣤⣤⣄⣀⣀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣛⣛⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⢹⣦⡌⠚⣿⡇⣴
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠸⠈⠀⠀⣿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣢⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣟⣀⣀⠀⠀⠀⡀⢀⣀⡀⣀⠀⠀⡴⠂⣀⣀⠀⢠⡍⡆⠀⠀⠀⠀⡏⠠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠻⢿⠀⠒⢋⠀⢴⡿⣿⣿⠃⠀⠸⠖⠈⣿⢹⣿⣶⠂⠈⠀⠀⠀⢱⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⡟⠿⢿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣾⡛⣇⣀⠀⢻⡏⠀⠀⢀⠀⠀⡇⠸⢿⣿⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣻⣿⣿⣿⡿⣿⣤⣿⣿⣿⣿⡿⢿⣿⣄⢸⣃⣝⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣛⠿⣿⣿⣿⣧⡀⠀⠈⠀⠀⢐⣆⠀⠁⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣿⡏⠁⠀⠀⠈⢿⡟⠉⢀⣴⡶⣶⣿⣿⣭⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢿⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣧⡀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⣿⣿⠇⣠⣯⣫⣍⣈⣟⣿⣿⣿⣟⡙⣽⣿⣦⡖⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣉⣿⣿⣝⢶⣽⣿⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣷⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⡿⣿⣿⣿⣿⡿⠐⣛⣛⣛⣛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣷⣶⣶⣤⣤⣭⣉⡙⠙⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⡀⡍⠉⠛⠉⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠛⠛⠋⠙⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⠀⠉⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣌⣹⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⣀⣤⣤⣤⣤⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠻⠿⠿⣿⠇⢈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀⡀⠀⠀⢀⣀⣴⣶⣤⣤⣤⣄⣀⠀⠀⠀⢨⢦⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⢹⣦⡈⠛⣿⡇⣴
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠘⠈⠀⠀⣿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣠⣴⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣗⣤⡀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⡶⠂⣠⣀⠀⢠⡍⡆⢀⠀⠀⠀⡿⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠻⢿⠀⠐⢋⠀⢬⠿⣿⣿⠃⠀⠘⠆⠈⣿⢹⣿⣶⠂⠈⠀⠀⠀⢱⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⡟⢈⣿⣿⣿⣿⣿⠟⠿⢿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣾⡛⣇⣠⠀⢿⡏⠀⠀⢀⠀⠀⡏⠸⢿⣿⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⣿⣿⣿⡿⠿⢷⣾⣿⣿⣿⣿⡿⢿⣷⡼⢸⣃⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⡛⠿⣿⣿⣿⣧⡀⠀⠈⠀⠀⢑⣆⠀⠁⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠘⠿⠛⠉⣠⣶⡷⣾⣿⣿⣭⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⠆⣠⣭⣫⣍⣈⣛⣿⣿⣿⣟⡙⣽⣿⣦⡖⢸⣿⣿⣿⣿⣿⣿⣇⣺⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⣩⣿⣯⣹⢿⣿⣇⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡆⣾⣿⣷⣶⣶⣤⣤⣭⣉⡙⠙⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⡐⡉⠉⠛⠉⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠛⠛⠋⠙⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣵⠈⠉⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣍⣹⣿⣿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣤⣠⣤⣴⣿⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠻⠿⠿⢿⠇⢈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀⡀⠀⠀⢀⣀⣴⣶⣤⣤⣄⣀⣀⡀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⢹⣤⠈⠚⣿⡇⣴
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠘⠈⠀⠀⣿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣐⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣷⢤⣀⠀⠀⠀⣀⠀⡀⣀⣀⠀⠀⡴⠂⣄⣀⠀⢠⡍⡆⢠⠀⠠⠠⡿⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠻⢷⠀⠒⠉⠁⣼⠾⣿⣿⠃⠀⡟⠆⠈⣿⢸⣿⣶⠂⠈⠀⠀⠈⢱⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⡿⣿⣿⣿⣿⣿⡏⢨⣿⣿⣿⣿⣿⡿⠛⢿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣾⠻⡇⣠⠀⢿⡏⠀⠀⢀⠀⢀⡏⠸⢿⣿⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⠿⠻⠿⣾⣿⣿⣿⣿⣿⣿⣿⣄⠼⢸⣣⣼⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⡛⠿⣿⣾⣿⣧⡄⠀⠈⠀⠀⢑⣆⠀⠁⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⠀⠀⠀⠀⠈⡿⠛⠛⠉⣴⣾⢶⣿⣿⣮⣍⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣆⠀⠀⠀⠀⠙⣿⢀⣾⢿⣿⣿⣿⣿⡟⠆⣠⣯⣫⣍⣈⣛⣿⣿⣿⣟⡙⣽⣿⣦⡖⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠐⠿⡿⣿⣷⣛⣛⢿⣿⣇⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠤⠌⠁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣛⣛⣛⣛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣿⣷⣶⣶⣤⣬⣭⣉⡙⠙⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⡠⡉⠋⠛⠋⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⠻⠛⠋⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⠈⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣍⣸⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⡿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣠⣠⣤⣦⣯⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠻⠿⠿⢿⠇⢨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⣀⡀⠀⠀⢀⣀⣴⣦⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⢹⣤⠈⠺⣿⡇⣴
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠞⠈⠀⠀⣿⢱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣶⡇⣿⠀⣷⢀⣀⣀⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣷⣤⣀⠀⠀⠀⣀⠀⡀⢀⣀⡀⠀⡴⢀⣄⣀⠀⢠⡍⡆⢠⠀⠠⠠⣿⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠻⢷⠀⠖⠈⠡⣼⠿⣿⣿⠃⠀⡟⠆⠈⣿⢸⣿⣾⠂⠈⠀⠀⠈⢱⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠙⡿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⡿⠿⢿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⠻⡆⣠⠀⢿⡏⠀⠀⢀⠀⠀⡏⠸⢿⣿⠀⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠿⠟⠿⢷⣿⣿⣿⣿⣿⣿⣲⣷⡄⢾⢸⣣⣼⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⡛⠿⣿⣾⣿⣧⡀⠀⠈⠀⠀⢑⡆⠀⠁⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⢹⡟⠛⠋⢉⣴⣶⣵⣿⣷⣬⣭⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⣠⣾⡿⣷⣿⣿⣿⡟⠆⣠⣯⣫⣍⣈⣛⣿⣿⣿⣟⡙⣽⣿⣦⡖⢸⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⠀⠀⠘⠿⣿⣿⣿⣾⣛⣛⢿⣿⣇⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡀⠠⢤⠄⠍⠁⣼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣾⣿⣿⡿⣿⣿⣿⣿⡿⠐⣛⣛⣛⣛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⣰⣶⣶⣶⣶⣤⣬⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⡠⡋⠛⠛⠋⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠟⠛⠉⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡤⠙⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣍⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣾⣿⣿⡿⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣟⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⡀⣤⣠⣤⣤⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠻⠿⠿⣿⠇⢈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⣀⡀⠀⠀⢀⣀⣴⣶⣤⣤⣤⣄⣀⡀⠀⠀⢨⢦⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣒⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⣷⣤⠙⢻⣿⣆⣴
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣧⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠇⠉⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣶⡇⣿⠀⣷⢀⣀⣀⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⢿⣿⣿⣿⣸⣿⣢⡀⠀⠀⠀⣀⠀⣀⣀⣀⠀⠀⡴⢀⣄⣀⠀⠸⡍⡆⢠⠀⠠⢠⡿⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠛⠿⠀⠚⠈⠡⣼⠿⣿⣿⠁⠀⡗⠆⠈⣿⣼⣿⣞⠂⠈⠀⠀⠈⢱⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠹⣿⣿⣷⣿⣿⠃⢹⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⢻⡄⣠⠀⢿⡏⠀⠀⢀⠀⠀⡏⠻⢿⣇⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠿⠿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣆⠀⠾⢸⣣⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⡻⠿⣿⣾⣿⣧⡀⠀⠀⠀⠀⢑⣆⠀⠁⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠈⣿⡿⡿⠛⠋⢉⣵⣌⣽⣷⣦⣬⣭⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⣽⣿⣴⣿⠿⢷⣿⣿⣿⡟⠆⣠⣭⣫⣍⣈⣟⣿⣿⣿⣟⡙⣽⣿⣦⡖⢸⣿⣿⣿⣿⣿⣿⣇⣺⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠈⢻⣿⣿⣿⢿⡶⣟⣋⢻⣿⣇⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣤⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣤⣤⣤⣀⠀⠭⠍⠁⢼⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⣿⣿⣿⣼⣧⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⢋⣴⣶⣶⣶⣶⣤⣬⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣏⡨⠋⠟⠛⠋⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠿⠛⠋⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡏⠙⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣈⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠿⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣟⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⡀⣤⣠⣤⣴⣷⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣀⠀⠀⠀⢀⣀⣴⣶⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⣧⣠⠙⢻⣿⣦⣴
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠇⠙⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣆⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⡀⠀⣀⣀⣀⠀⠀⡴⢀⣤⣄⠀⠸⡍⡆⢠⠀⠠⢠⡟⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠙⠿⢿⠀⠘⠊⠡⣽⠿⣿⣿⠃⠀⡷⠆⠈⣿⣼⣿⣞⠂⠈⠀⠀⠈⢳⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠉⠉⠹⣿⣿⣾⣿⡟⠘⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⢻⡄⣠⠀⣿⡏⠀⠀⢀⠀⢀⡏⠿⢿⣇⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣾⣆⠀⢾⢸⣧⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣻⠿⣿⣾⣿⣧⡀⠀⠀⠀⠈⢑⣆⠀⠁⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠁⠀⠀⠈⢻⣿⡿⡿⠛⠋⢉⣵⣍⣽⣷⣦⣬⣭⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠠⣽⣿⣴⣿⢿⢱⣿⣿⣿⠟⠆⣠⣭⣫⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡖⢸⣿⣿⣿⣿⣿⣿⣆⣺⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡶⢾⣛⢻⣿⣆⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣤⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠭⠍⠉⣠⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣧⣾⣿⣯⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⣛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢀⣶⣶⣶⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣏⡨⠋⠟⠛⠋⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠟⠛⠛⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣿⣷⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡏⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣉⣹⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⣀⣠⣤⣤⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣀⠀⠀⠀⠀⣀⣰⣶⣤⣤⣤⣀⣀⡀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠙⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⣇⣀⠑⢻⣿⣦⣴
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠶⠀⠏⠹⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣦⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡴⢀⣠⣀⠀⠸⡍⡆⢠⠀⠀⢠⡏⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡺⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠙⠻⢿⠀⠚⠊⠡⣼⠿⣿⣿⠀⠀⡷⡆⠘⣿⣾⣿⣞⠂⠈⠀⠀⠈⢱⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⠹⣿⣿⣿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣆⣶⣶⢻⡄⣠⠈⣿⡏⠀⠀⠀⠀⢀⡏⠿⢿⣇⠀⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⠀⠾⢘⣣⣜⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢻⠿⣿⣾⣿⣧⡀⠀⠀⠀⠈⢑⡆⠀⠁⢰⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠀⠀⠉⢻⣿⣿⠿⡿⠛⠋⢩⣴⣍⣽⣶⣦⣬⣭⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠩⠀⠀⣽⣿⣴⣿⢿⢹⣿⣿⣿⠟⠆⣠⣯⣫⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⢸⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⠶⢞⣛⢙⣿⣆⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠭⠿⠉⣁⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣧⣾⣿⣯⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣴⣶⣶⣶⣶⣦⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡬⠋⠟⠛⠋⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠟⠛⠛⢻⠇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣷⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣈⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣴⣟⢿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣹⠙⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⢀⣀⣠⣤⣾⣶⣾⣷⣤⣾⣿⣿⣿⣿⣧⢥⣤⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⣇⡀⠙⢻⣿⣦⣴
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠀⠏⠻⠀⠈⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⢀⠀⣀⣀⣀⠀⠀⡴⢀⣠⣀⠀⠸⡍⡆⢠⠀⠀⢠⡟⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠿⢿⠀⠚⠉⠩⣽⢾⣿⣿⠁⠀⡷⡄⠙⣿⣼⣿⣖⠂⠈⠀⠀⠈⢰⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⢹⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⢻⡀⣠⠈⣿⡏⠀⠀⠀⠀⢀⡯⠿⢿⣇⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⠀⠞⢘⣧⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢿⠿⣿⣾⣿⣧⡀⠀⠀⠀⠈⢐⡆⠀⠃⢠⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⠀⠈⠙⣿⣿⣿⠿⡿⠛⠋⢩⣴⣍⣽⣶⣦⣬⣭⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠈⠡⠀⠀⣽⣿⣴⣿⢿⢹⣿⣿⣿⠟⠆⣠⣯⣫⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣸⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣷⢞⣛⢹⣿⣆⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠨⠿⠉⣉⣿⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣾⣾⣿⣿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣴⣶⣶⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡤⠋⠛⠛⠋⠉⠉⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠟⠛⠛⠻⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣷⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠇⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣈⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣤⣦⢭⡿⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠙⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⣀⣠⣠⣤⣴⣶⣾⣦⣶⣾⣿⣿⣿⣿⣿⣀⣄⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⡀⠈⠛⠿⠿⢿⠇⢨⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⣇⡀⠙⢻⣿⡇⣴
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣶⣧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠶⠀⠷⢷⠀⠈⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣠⣠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⢀⠀⠀⡀⣀⠀⠀⡶⢀⣠⣄⠀⢸⡍⡆⢰⠀⠀⢠⠯⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠻⠿⠀⠚⠂⢡⣼⢿⣿⣿⠁⠀⣷⡀⠙⣿⣼⣿⣖⠂⠈⠀⠀⠈⢰⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⣿⣿⠁⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣶⢿⡀⣡⠈⣿⡏⠀⠀⠀⠁⢀⡿⠿⣿⣿⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⠀⠾⢘⣣⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢿⠿⣿⣾⣿⣧⡀⠀⠀⠀⠈⢸⡆⠀⠋⢠⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠃⠀⠀⠈⠙⣿⠛⠿⢿⣿⣿⣿⣿⣿⣍⣽⣶⣦⣬⣍⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢾⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠤⠟⠻⣿⣿⡿⠿⣹⣿⣿⣿⠗⠆⣠⣭⣫⣍⣈⣛⣿⣿⣿⣟⡙⣽⣿⣦⡆⣸⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣵⡴⠶⣟⢛⣻⣆⣀⣀⣤⣶⣤⣭⣭⣤⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣖⠀⠒⠚⠿⠿⠛⢛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣾⣾⣿⣿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⣶⣶⣶⣶⣦⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⠤⠚⠛⠛⠋⠉⠋⠰⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣷⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡍⠀⠀⠀⠀⠀⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣈⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣖⡏⠿⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⢀⢀⣠⣴⣽⣷⣦⣶⣾⣿⣯⣭⣺⣋⣓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠉⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⣿⠇⢨⣿
⣿⣿⣿⡿⠼⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⡇⡀⠙⢻⣿⡇⣴
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢨⣧⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠐⢷⢧⡀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡶⢀⣀⣄⠀⢠⡍⡆⢰⠀⠀⢠⠟⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡾⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠟⠿⠀⠚⠊⠡⣽⢿⣿⣿⠁⠀⣷⡀⠙⣿⣼⣿⣶⠂⠈⠀⠀⠈⢰⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⢹⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⡶⢷⡀⣡⠈⣿⡏⠀⠀⠈⠁⢀⡿⠿⢿⣿⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⠀⠾⢘⣣⣜⣿⣿⣿⣿⡦⣈⣀⣁⣀⣤⣿⣿⣿⢿⠿⣿⣾⣿⣧⡀⠀⠀⠀⠈⢰⣆⠀⠏⢠⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠉⠛⠉⢁⠿⢿⣿⠟⣫⣷⣍⣽⣶⣦⣬⣭⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡿⠿⣹⣿⣿⣿⡟⠆⣠⣯⣩⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣸⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣀⠀⢀⡀⠀⠀⢠⣿⣿⣿⣵⡶⠾⠿⠛⣛⣇⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠘⠒⠛⠿⠿⠛⢛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣶⣾⣽⣿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⣾⣿⣶⣶⣶⣦⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⠤⠚⠛⠛⠋⠉⠋⠸⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⢿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣷⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡏⠀⠀⠀⠀⠀⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣉⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠊⠛⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣶⣿⣏⡉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⡀⢄⣤⣶⣿⣦⣦⣺⣿⣮⣏⣑⡱⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢈⣿
⣤⣤⣴⣶⣮⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕⠀⠀⠀⠀⡀⠀⠀⢀⣤⣤⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⢨⢤⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⡇⡄⠙⢺⣿⣷⣤
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠰⢗⣇⠀⠈⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⢿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⡶⢠⣤⣠⠐⢀⡍⡆⢸⠀⠁⢀⢿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠐⣺⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠿⢿⠀⠚⠋⢡⣼⢾⣿⣿⠁⠀⣷⠀⠙⣿⢳⣿⣶⠂⠈⠀⠀⠈⢰⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⢨⣿⡀⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⡶⢷⡀⣡⠈⣿⡏⠀⠀⠘⠑⢀⡿⠿⣿⣿⠀⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠻⠿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠾⢘⣧⣜⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢿⠿⣿⣾⣿⣧⡄⠀⠀⠀⠈⢐⣆⠀⠟⢠⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⡿⠛⢋⣩⣶⣶⣼⣿⣶⣬⣭⣿⡿⣷⣾⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣀⠀⠀⠀⠀⠀⣠⠀⡠⢿⣿⡿⠿⠿⣧⣿⣿⣿⣿⣦⣠⣭⣩⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣼⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣿⡾⢷⣾⡄⠘⣿⣿⣴⣶⣤⣿⢿⣩⣇⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠘⠛⠛⠿⠿⠛⢛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣶⣿⣽⣿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⣶⣶⣶⣦⣬⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⡤⠜⠛⠛⠋⠉⠊⠸⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠻⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣷⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡇⠀⠀⠀⠀⠈⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣈⣹⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⠬⠟⠩⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣏⡉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⢀⢄⢀⣰⣷⣦⣖⣴⣼⣸⣮⡏⠓⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⣿⠇⢨⣿
⠀⣠⣭⣶⠄⣐⣾⣿⣿⣿⣿⣿⣿⣶⣶⣯⣯⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⢨⢤⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣾⣿⣿⣾⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⡇⡄⠙⢻⣿⣷⢠
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠰⢓⢇⠀⠀⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣄⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣯⣀⣀⠀⠀⠀⢀⠀⣀⣀⣀⡀⠀⡶⢠⣠⣠⡀⠀⡍⡆⢸⠈⠃⠀⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⡚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠿⠿⠀⠒⠊⢡⣽⢿⣿⣿⠁⠀⣷⠀⠙⣿⢷⣿⣷⠂⠈⠀⠀⠈⢰⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⢸⣇⣸⣿⣿⣧⣻⡟⠉⠙⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⡶⢷⡀⣡⠈⣿⡏⠀⠀⠘⠂⠀⡿⠿⢿⣿⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠛⠻⠿⠿⠟⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣄⣾⢸⣣⣽⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢿⠿⣿⣾⣿⣧⡄⠀⠀⠀⠈⢰⣆⠀⠟⢠⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣛⣋⣉⣶⣶⢴⣿⣿⣦⣭⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣼⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣄⡀⠀⠀⠀⠀⣤⠀⣠⣿⣿⠿⠛⠻⡯⣿⣿⣿⡟⠛⣠⣭⣫⣍⣈⣛⣿⣿⣿⣟⡙⣽⣿⣦⡆⣼⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⡶⢶⣿⣏⠈⢛⣷⣴⣶⣤⣿⣿⣿⣇⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠘⠛⠛⠷⠿⠛⢛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣶⣿⣽⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣶⣶⣶⣦⣬⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡠⠝⠛⠛⠋⠉⠊⠸⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠟⠿⢿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣷⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠀⠀⠀⠀⠀⠙⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣈⣹⣿⡿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣶⠿⠟⠿⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣶⣿⣯⣉⣹⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⢀⣀⣠⣴⣿⣶⣤⣤⣶⣠⣾⡙⡓⣋⠨⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠉⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⣀⣤⣭⣧⣠⣿⣭⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣤⣤⣄⣀⣀⡀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣂⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⡇⡄⠙⢻⣿⣿⢦
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢨⣧⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠰⢳⠃⠀⠀⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣙⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⣀⠀⣀⣀⣀⠀⠀⠶⢠⣆⣠⡆⠂⡌⡆⢸⠐⠂⠀⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⢘⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠿⢿⠀⠚⠊⢡⣽⢿⣿⣿⠀⠀⣶⠀⠙⣿⣯⣿⣿⡂⠈⠀⠀⠈⢹⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⢠⣸⣿⣿⣧⣸⠁⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⢛⠻⣿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⡶⢷⡀⡡⠘⣿⡏⠀⠀⠸⠀⠀⣿⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠛⠿⠿⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⢿⣧⣾⣿⣧⣜⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢿⠿⣷⣾⣿⣧⡀⠀⠀⠀⠀⢹⣆⠀⠹⢡⠀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠟⢿⣭⣥⣶⣷⣾⣿⣿⣯⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣦⣀⡀⠀⠀⠀⠀⣤⣀⣤⣿⣿⠀⠛⠛⡿⢿⣿⣿⡿⠃⣣⣭⣩⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣼⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠺⣵⣶⣷⣾⢿⣿⣧⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠘⠛⠻⠿⡿⠒⢛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣶⣿⣿⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠰⣿⣿⣿⣷⣶⣶⣦⣬⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⡠⠝⠛⠛⠋⠉⠊⠸⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠻⠿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⣿⣧⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠀⠀⠀⠀⠈⠟⠁⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⢏⠿⠝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⡀⣠⢦⢿⣷⣤⣰⣶⣢⣨⡉⢛⡃⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠉⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⡤⣔⣻⣮⡈⣿⣟⣿⣿⣿⣿⣿⣷⣵⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣾⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⣀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠁⡅⡈⠙⢻⣿⣿⡇
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠶⠰⢳⠃⠀⠐⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠶⢠⣤⣀⣿⠐⡈⡆⢸⠀⠒⠀⣼⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠉⠻⢿⠀⠒⠊⢩⣾⢷⣿⣿⠀⠀⣶⠀⠉⣿⣿⣾⣿⡆⠈⠀⠀⠀⢙⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⢰⣀⣿⣿⣿⠙⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⡶⢷⠀⣁⠘⣿⡇⠀⠀⢸⠠⠀⣾⠿⣿⣿⡇⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠻⢿⣿⣿⡿⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⣿⡴⣿⣧⣝⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢾⠿⣷⣾⣿⣧⡀⠀⠁⠀⠀⢹⣆⠀⢹⢧⠀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠻⡿⠛⠛⢿⣀⣤⣶⣴⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⠀⠘⠛⣿⠿⣿⣿⣿⠿⣩⣭⣩⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣼⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣶⣦⣤⡤⢿⣿⣿⣿⣿⣶⣵⣶⣽⣾⣿⣿⣿⣀⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠛⠛⠻⠿⢧⣼⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣦⣤⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣠⠭⠛⠛⠋⠉⠋⠸⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣿⣿⡇⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣧⣦⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠀⠀⠀⠀⠙⣿⠏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡶⠎⠻⠏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣶⣿⣯⡉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⢄⠀⣺⣳⣦⠠⣂⣐⣢⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣼⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠉⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢈⣿
⠀⢐⢀⠈⠁⠪⣚⣿⣿⣿⣿⣿⣿⣾⣥⣾⣮⣏⠂⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣴⣽⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⠡⡅⡌⠙⢻⣾⣿⣷
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠶⠰⢳⠃⠀⢸⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⢿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠶⢠⣤⣠⣿⠐⠀⡆⢸⠀⠒⡀⣸⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⠺⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠻⠿⠀⠒⠈⢩⣽⢿⣿⣿⠀⠀⣶⠀⠙⢿⣿⣼⣿⡆⠈⠀⠀⠁⢙⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⣼⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⡶⢷⡀⣡⠈⣿⡇⠀⠀⢸⠠⢀⣼⠿⣿⣿⡇⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣦⢼⣿⣝⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢿⠿⣿⣾⣿⣧⡀⠀⠀⠀⠁⢹⣆⠀⠉⣷⠀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⣿⣿⣿⡟⣧⣤⣴⣶⣿⣷⣿⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣄⡀⠀⠀⠀⠀⠀⢀⣤⠀⣼⣿⣿⣿⡗⠛⣿⡿⣿⣿⣿⡿⣿⣯⣩⣍⣈⣝⣿⣿⣿⣟⡙⣽⣿⣦⡆⣼⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣵⣶⣿⣷⣿⣿⣿⣁⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣆⠀⠑⠛⠛⠿⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⣛⣛⣛⣛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣶⣶⣶⣦⣤⣤⣤⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣠⡬⠛⠛⠋⠉⠋⠸⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣦⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⠉⠁⠀⠈⠉⠻⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⡴⠙⠻⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢺⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠠⠄⡤⣲⣿⣄⣀⢠⣔⣒⡦⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣼⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠉⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠛⠿⠿⢿⠇⢈⣿
⠀⠀⢜⠐⠞⡈⣙⣿⣿⣿⣿⣶⣷⣶⣶⣶⣾⡎⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣦⣦⣤⣤⣠⣤⣀⡀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣽⣶⣦⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢡⡅⡈⠙⢻⣿⣿⣿
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠶⠸⢳⠃⠀⢸⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠶⢠⣤⣤⣿⠐⠀⡆⢸⠀⠖⣠⢸⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⠺⢻⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠙⠻⢟⠀⠚⠈⢩⣽⢿⣿⣿⠁⠀⣶⠀⠙⢿⣿⣽⣿⡆⠈⠀⠀⠁⢹⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⢩⣿⣟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⡖⢿⡀⣡⠈⣿⡇⠀⠀⢸⠠⢀⣼⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣧⢼⣿⣼⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢿⠿⣿⣾⣿⣧⡀⠀⠀⠀⠁⢹⣆⠀⠉⣷⠀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⡿⠛⠋⠉⣧⣤⣴⣶⣿⣷⣾⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⠈⢀⣤⠀⣀⣽⣿⠀⠀⠛⣿⡟⣿⣿⣿⡿⣿⣯⣩⣅⣈⣝⣿⣿⣿⣟⡙⣽⣿⣦⡆⣾⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣾⣵⣶⣿⣿⣿⣿⣿⣁⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣄⠀⠀⠀⠘⠛⠛⠻⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⣿⣿⣿⣼⣷⣿⣿⣽⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣴⣶⣶⣶⠶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣠⡬⠛⠛⠉⠉⠉⠸⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣵⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣽⠋⠉⠁⠉⠉⠛⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣠⠶⠾⠟⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣏⡉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⠀⣄⣲⣷⣤⠀⣂⣠⣢⡇⣄⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢈⣿
⠀⣀⢁⡘⡚⣉⣅⣿⣿⣿⣿⣷⣵⣶⣶⣷⣶⠆⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣦⣤⣤⣤⣤⣀⣀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣧⣵⣵⣬⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡅⡌⠙⢻⣿⣿⣿
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠶⠸⢳⠃⠀⢸⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣐⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣯⣤⣀⠀⠀⠀⢀⠀⡀⣀⣀⠀⠀⠶⢠⣤⣄⣿⠁⠂⡆⢸⠀⠴⣸⣺⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⠺⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠙⠿⢿⠀⠚⠊⠩⣽⢿⣿⣿⠀⠀⣶⠀⠙⣿⣿⣷⣿⡆⠈⠀⠀⠁⢙⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⢉⣿⣿⡿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⢻⡀⣠⠈⣿⡇⠀⠀⣸⠠⢀⣾⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⢿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣧⡸⣿⣿⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢿⠿⣿⣾⣿⣧⡀⠀⠀⠀⠀⢹⣆⠀⠉⣷⠀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠈⠻⣿⣿⣟⣿⠿⡿⠛⠋⠉⣧⣤⣴⣶⣿⣷⣾⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⠀⠀⠀⠀⠀⠙⠛⣥⠀⣀⣿⣿⠀⠐⠛⣿⠟⣿⣿⣿⡿⣿⣯⣩⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣾⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠘⢿⣿⣟⣻⠛⣾⣵⣶⣿⣿⣿⣿⣿⣁⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠈⠉⠉⠿⠿⠛⢛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡿⣿⣿⡾⣷⣿⣿⣽⡿⣿⣿⣿⣿⡿⠀⣛⣛⣛⣛⢻⣿⡿⠃⠐⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣶⣶⣶⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣠⡬⠛⠛⠉⠉⠉⠸⠿⠿⠿⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⡿⠛⠉⠁⠉⠙⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⡦⠞⢋⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢺⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⢤⣄⣪⣮⣆⢀⡤⢐⣐⠒⠂⠄⠂⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣼⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠉⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠛⠿⠿⣿⠇⢈⣿
⠀⡐⣀⡘⠇⠚⠞⣿⣾⣿⣶⣽⣶⣶⣦⣤⣴⠆⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣦⣤⣤⣤⣤⣀⡀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣯⣴⣶⣤⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡅⡈⠙⢻⣿⣿⣿
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠸⢳⠃⠀⢸⣏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣂⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣯⣤⣀⠀⠀⠀⡀⠀⣀⣀⣀⠀⠀⠦⢰⣦⣄⣿⠁⠂⡄⢸⠀⠰⣸⣻⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⠺⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠛⠻⠿⠀⠚⠈⠩⣼⢿⣿⡟⠁⠐⣶⠀⠙⣿⣿⣷⣿⡆⠈⠀⠀⠁⢘⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⣨⣿⣿⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣤⣶⣶⢻⡀⣠⠀⢿⡇⠀⠀⣸⠠⢠⣿⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠿⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣧⡸⣿⣿⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⢻⠿⣿⣾⣿⣧⡀⠀⠈⠀⠀⢸⣆⠀⠉⣷⠀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠈⢻⣿⣿⣏⣿⠿⡿⠛⠋⠉⣧⣤⣴⣶⣿⣷⣾⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠉⠉⣦⠀⣀⣿⣿⠀⠐⠙⣿⠟⣿⣿⣿⡿⣿⣯⣩⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣾⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣵⣶⣿⣿⣿⣿⣿⣁⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠛⠛⠩⠿⠛⢛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⠿⣿⣿⡾⣷⣿⣿⣽⣿⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠐⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣶⣶⣶⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣠⡬⠛⠋⠉⠉⠉⠸⠿⠿⠟⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡟⠋⠉⠈⠉⠙⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣉⣸⣿⣿⣿⣧⠄⢀⣀⣀⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⠯⠟⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢺⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠠⠄⣠⣿⣿⣤⣀⣀⣰⣦⡅⠀⠩⠲⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠉⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠛⠿⠿⢿⠇⢈⣿
⠀⢀⣐⡆⣶⡭⠓⣿⣿⣾⣿⣷⣷⣶⣥⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⣶⣦⣤⣤⣤⣤⣄⡀⠀⠀⠀⢨⢤⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣿⣾⣲⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡅⡈⠙⢻⣿⣾⣿
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠸⢳⠃⠀⢈⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⢿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⡀⠀⠀⣀⣀⠀⠀⠦⣰⣦⣄⣿⡡⠂⡄⢸⠀⠰⢸⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⢺⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠻⢿⠀⠒⠀⠩⣴⠿⣿⡿⠁⠘⣶⠀⠹⣿⣿⣷⣿⡆⠈⠀⠀⠈⢘⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⣨⣿⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣤⣶⣖⢻⡀⣠⠀⢿⡇⠀⠀⣸⠀⢠⣿⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠻⣿⣿⣾⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣦⣸⣿⣟⣿⣿⣿⣿⣦⣈⣀⣁⣀⣤⣿⣿⣿⣻⠿⣿⣾⣿⣧⡀⠀⠈⠀⠈⢸⣆⠀⠉⣳⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠿⡿⠛⠋⠉⣧⣤⣴⣶⣿⣷⣾⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣄⠀⠀⣠⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠙⣿⠟⣿⣿⣿⡿⣿⣯⣩⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣾⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣿⣿⡀⡠⣴⣿⣷⡼⠉⣽⣵⣶⣿⣾⣿⣿⣿⣁⣀⣤⣶⣤⣭⣭⣤⠀⣀⣠⣼⣿⣿⢿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⠛⠛⠻⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⢫⣽⣿⣿⢸⣿⣿⡿⢿⣿⣾⣿⣿⣿⣽⢟⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠐⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣷⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣠⡬⠛⠋⠉⠉⠀⠸⠿⠿⠟⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣴⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡏⠀⠀⠀⠀⠻⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠥⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠎⠹⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣶⣿⣯⡉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⠄⣀⢯⡼⡄⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠛⠿⠿⢿⠇⢈⣿
⠀⠀⠀⠀⠁⢀⢠⣾⣶⣾⣷⣦⣦⣤⣤⣀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣴⣤⣤⣤⣤⢀⠀⠀⠀⠀⢨⢤⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣤⣴⡢⣔⢄⡐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣀⣹⣿⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡄⡈⠙⢿⣿⣾⣿
⠀⠀⡠⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠶⠸⢳⠃⠀⢈⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠦⣰⣦⣤⣿⡡⠂⡄⢸⠀⠠⢸⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠙⠛⠿⠀⠚⠀⠉⣼⠷⣿⡿⠀⠘⣶⠀⠙⣿⣿⣷⣿⡆⠈⠀⠀⠈⢘⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⢀⣼⣾⣿⣿⣿⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣶⢻⡄⣠⠀⢿⡇⠀⠀⣸⠀⢠⣿⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠁⠀⠉⠛⠛⠛⠋⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠿⣿⣦⢼⣿⣿⣿⣿⣿⣿⣦⣈⣀⣁⣠⣤⣿⣿⣿⣻⠿⣿⣶⣿⣧⡀⠀⠈⠀⠈⢸⣆⠀⠉⣳⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠛⠋⠉⣧⣤⣴⣶⣿⣿⣾⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡧⢺⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠙⣿⠟⣿⣿⣿⡿⣿⣯⣩⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣾⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⡤⡤⢾⣿⣿⡬⠉⢹⣵⣶⣿⣾⣿⣿⣿⣁⣀⣤⣶⣤⣭⣭⣥⠀⣀⣠⣼⣿⣿⢿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⠉⠙⠛⠛⠿⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡿⢿⣿⣾⣿⣿⣿⣿⢟⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠐⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣷⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣠⡬⠛⠋⠉⠉⠀⠸⠿⠿⠟⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡅⠀⠀⠀⠈⠻⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⠅⠀⠀⠀⢀⣼⣶⣷⣶⣴⣶⣉⣹⣿⣿⣿⣧⠄⢀⣀⣀⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠆⠎⠉⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣏⡉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⠀⡀⠰⡦⠀⠀⠀⣀⢀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣼⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⠉⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢈⣿
⠀⠀⠀⠐⠀⠙⠣⣿⣷⣾⣷⣄⣴⣤⣠⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣴⣤⣤⣤⣤⣤⢀⠀⠀⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣤⣬⣶⡀⣀⠀⡊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠚⠀⣾⣷⣤⣈⣂⣠⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡄⡈⠛⢻⣿⣾⣿
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⢴⣶⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢐⣧⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠸⢻⠃⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⣀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠦⣸⣦⡀⣿⡡⠂⡄⢸⠀⢠⢸⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠀⢀⣾⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠛⠿⠀⠘⢈⠉⢴⡶⣿⡿⠀⢸⢶⠀⠙⣿⣿⣧⣿⡇⠈⠀⠀⠈⢘⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⢐⣾⣿⣿⣷⣾⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠻⢿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣾⢛⡇⣀⠀⢻⡇⠀⠀⣸⠀⣰⣿⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠈⠙⠛⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠧⢿⢷⣿⣧⣼⣿⣿⣿⣿⠦⣈⣀⣁⣀⣤⣿⣿⣿⣻⠟⣿⣾⣿⣧⡀⠀⠀⠀⠈⢸⣆⠀⠙⣳⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠛⠋⠉⣷⣤⣴⣶⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣆⠀⠀⣠⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣀⣀⡀⠀⠀⠀⠀⡤⠀⢀⣿⣿⠀⠀⠙⣿⢏⣿⣿⣿⡿⣿⣯⣩⣍⣈⣝⣿⣿⣿⣟⡙⣽⣿⣧⡆⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⣿⣿⡬⠉⢓⣵⣶⣿⣿⢿⣿⣿⣁⣀⣤⣶⣤⣭⣭⣤⠀⣀⣠⣼⣿⣿⢿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠛⠿⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣽⣿⣿⢸⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠐⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣷⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣠⡤⠛⠉⠉⠉⠀⠺⠿⠿⠟⠋⠀⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠿⣿⣿⣿⣿⡟⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠙⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣉⣹⣿⣿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣶⣿⣯⡉⣸⠛⠛⠿⠿⢿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠘⠛⠿⠿⢿⠇⢈⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⣷⣽⣄⣄⡠⣠⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣦⣤⣤⣤⠤⠤⠄⠀⠀⢨⢤⠀⢀⣾⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⡀⡄⠤⠄⡠⡄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣷⣤⣈⣂⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣷⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⣛⣛⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡄⡈⠛⢿⢿⣾⣿
⠀⠀⡀⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣶⣧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠶⠸⢻⠃⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣶⡇⣿⠀⣷⢀⣈⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣿⣠⣀⠀⠀⠀⡀⠀⣀⣀⣀⠀⠀⠦⣸⣦⡤⣿⡡⠂⡄⢸⠀⢠⢸⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠀⢀⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠉⠻⠿⠀⠀⢉⠉⠨⡱⣿⡿⠀⢸⢶⠀⠙⣿⣿⣷⣾⡇⠈⠀⠈⠈⢘⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⣾⣿⣿⣦⣼⡏⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⡛⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣤⣷⣾⡙⣇⣠⠀⢹⡇⠀⠀⣸⠀⣰⣿⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠈⠙⠻⠿⠟⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠧⢿⢷⣿⣧⣽⣿⣿⣿⣿⡦⣈⣀⣁⣀⣤⣿⣿⣿⣻⠟⣿⣿⣿⣷⡀⠀⠈⠀⠈⢸⣆⠀⠛⣱⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠛⠋⠉⣷⣤⣴⣾⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣆⠀⠀⣤⣬⣿⣶⣤⣸⣧⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⡀⠀⠀⠀⠀⠀⣤⠀⢀⣿⣿⠀⠀⠙⣻⢏⣿⣿⣿⡿⣩⣭⣩⣅⣈⣙⣿⣿⣿⣟⡙⣽⣿⣦⡆⣿⣿⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡴⢿⣿⣿⣽⣛⢚⣵⣶⣿⣿⢿⣿⣿⣁⣀⣤⣶⣤⣬⣭⣤⠀⣀⣤⣼⣿⣿⢿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠛⠿⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⡟⠿⣿⣻⣿⣿⣿⣿⢻⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣷⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⡤⠛⠉⠉⠉⠀⠻⠿⠿⠟⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⢿⣿⣿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠙⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡻⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣈⣸⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣶⣿⣯⡉⣹⠙⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣶⣧⣬⣤⣀⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⡤⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⡐⣂⡀⠰⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⣷⣤⣈⣒⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣶⣾⣿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⣛⣛⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡄⡈⠛⢿⣿⣾⣿
⠀⠀⠀⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢀⣧⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠸⢻⠃⠀⢘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣶⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣷⠄⣀⠀⠀⠀⣀⠀⡀⢀⣀⠀⠀⠦⣸⣦⡄⣾⡡⠂⡄⢸⠀⢠⢸⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠉⠻⠿⠀⠀⢉⡈⠰⡻⢿⡟⠀⢸⢶⠀⠙⣿⣿⣷⣾⡇⠈⠀⠈⠈⢘⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⢀⣼⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠻⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣤⣶⣾⡙⣇⢀⠄⠸⡇⠀⠀⣸⠀⣰⣿⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⢿⢷⢿⣧⣼⣿⣿⣿⣿⡦⣈⣀⣁⣀⣤⣿⣿⣿⣛⡛⣻⣷⣿⣷⡄⠀⠀⠀⠈⢸⣆⠀⠛⢱⡀⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠙⠛⠿⠋⠉⠛⠻⡿⠛⠛⠉⣷⣤⣴⣾⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣦⠀⠀⣤⣬⣿⣶⣤⣸⣷⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠙⣿⢏⣿⣿⣿⡿⣩⣭⣩⣅⣈⣹⣿⣿⣿⣟⡙⣽⣿⣦⡖⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣄⣀⣀⡀⠀⢼⣿⣿⣿⣿⣾⣵⣶⣿⣿⢿⣿⣿⣁⣀⣤⣶⣤⣬⣭⣤⠀⣠⣤⣼⣿⣿⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⠛⠛⠿⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⡝⠻⢿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣷⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣀⡤⠛⠀⠈⠁⠀⠻⠿⠿⠟⠋⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡄⠀⠀⠀⠙⢿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡻⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣉⣸⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠻⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⠉⣸⠙⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣶⣴⣌⣲⣂⣀⡠⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣄⣤⣄⢀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠑⣤⣈⣒⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣼⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⣛⣛⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡄⡈⠛⢿⣿⣾⣿
⠀⠀⡠⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠸⢻⠃⠀⢘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣲⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣧⣤⡀⠀⠀⠀⣀⠀⡀⣀⣀⠀⠀⠦⣸⣦⡄⣿⡡⠒⡄⢸⠀⢠⢸⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⢀⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠁⠻⡿⠀⠀⢉⡈⠰⡻⢿⡿⠀⢸⢶⠀⠙⣿⣿⣿⣾⡇⠈⠀⠈⠈⢘⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⣄⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠻⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣤⣶⣾⣉⣧⢀⡄⠸⡇⠀⠀⣸⠀⣠⣿⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠻⢿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⢿⣷⣿⣧⣼⣿⣿⣿⣿⡦⣈⣀⣁⣀⣤⣿⣿⣿⣚⡛⣻⣷⣿⣷⣄⠀⠁⠀⠈⢸⣆⠀⠛⢹⡄⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠙⠻⣿⣿⣿⠿⣿⠿⣿⣿⣿⡋⣧⣤⣴⣾⣿⣿⣿⣿⡿⣷⣾⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣦⠀⠀⣤⣬⣿⣶⣤⣸⣷⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠈⠀⠤⢠⣾⣿⣿⣿⡇⠙⣿⢏⣿⣿⣿⡿⣩⣭⣩⣍⣈⣙⣿⣿⣿⣟⡙⣽⣿⣧⡖⣾⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣵⣶⣿⣿⢿⣿⣿⣁⣀⣤⣶⣤⣭⣭⣤⠀⣠⣤⣼⣿⣿⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣶⡀⠀⠀⠚⠛⠿⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⡝⠻⢿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣶⣶⣶⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣀⡤⠛⠀⠈⠁⠀⠻⠿⠿⠟⠋⠀⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡭⠀⠀⠁⠙⢿⡿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡻⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡅⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣍⣸⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣷⣿⣯⡉⣸⠙⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣿⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⠀⠀⠀⠀⠂⠀⠀⢰⣶⣥⣤⣦⣮⣴⣅⢀⠤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣠⡌⣀⢠⣠⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⣤⣈⣒⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣷⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⣛⣛⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡄⡈⠛⢿⣿⣾⣿
⠀⠀⡀⢄⡏⠀⣿⡈⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣶⣦⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠸⢻⠃⠀⢘⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣶⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⢿⣿⣿⣿⢸⣷⣤⡀⠀⠀⠀⣀⠀⣀⣀⣀⠀⠀⠦⣸⣆⡄⣾⡩⠖⡀⢸⠀⢠⢸⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⢀⡚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠁⠿⡟⠀⠀⣈⡀⠀⠞⢿⡿⠀⢸⢶⠀⠹⣿⣿⣿⣾⡇⠈⠀⠈⠈⢘⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠉⣭⡗⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⠻⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⢀⣄⣶⣾⣍⣧⢀⡄⠈⡇⠀⠀⣸⠀⣠⣿⠿⢿⣿⡇⠀⠀⠀⠀⢸⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⣷⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯⣿⣶⣿⣦⣼⣿⣿⣿⣿⡦⣈⣀⣁⣀⣤⣿⣿⣿⣚⣛⣻⣷⣿⣷⣄⠀⠈⠀⠈⢸⣆⠀⠛⢹⡄⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠈⠻⣿⣷⣿⡿⣿⠿⡿⠛⠋⠉⣧⣤⣴⣾⣿⣿⣿⣿⡿⣷⣾⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣦⠀⠀⣤⣬⣿⣶⣤⣸⣷⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠘⠛⠋⣥⠀⣀⣿⣿⠀⠀⠙⣿⢋⣿⣿⣿⡿⣣⣯⣩⣅⣈⣹⣿⣿⣿⣟⡙⣽⣿⣧⡶⣾⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣵⣦⣿⣿⢿⣿⣿⣁⣀⣤⣶⣤⣭⣭⣤⠀⣰⣶⣾⣿⣿⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀⠈⠙⠟⠛⠛⠿⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⡍⠛⢿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⢰⣶⣶⣶⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣿⣿⣿⣿⣿⢸⣿⣿⣇⣀⡤⠚⠀⠈⠁⠀⠻⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣯⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣭⠉⠀⠉⠉⢻⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣉⣸⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣶⣿⣯⠉⣹⠛⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣤⣤⣤⣄⣠⡔⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣦⣤⣤⣄⡀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣂⢀⣉⠀⢀⡀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⣈⣒⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⣛⣛⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠃⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣉⢱⡄⡈⠛⢿⣿⣾⣿
⠀⠀⡀⢄⡏⠀⣿⡀⠀⣿⠋⢿⡿⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⢸⣧⣿⣦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠴⠸⢻⠃⠀⢘⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠆⣴⡇⣿⠀⣷⢀⣀⣀⣾⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⠀⢸⠿⣿⣿⣿⢸⣷⣤⣀⠀⠀⠀⢀⠀⣀⢀⣀⠀⠀⠦⣸⣆⣠⣾⣩⠖⡀⢸⠀⢠⢸⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢤⡬⠁⢙⠄⢀⡚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣿⣿⣿⠅⣶⣾⣿⠉⠉⠀⠈⠋⠺⡻⠀⠀⣈⡁⠀⠟⠻⡟⠀⢸⢶⠀⠙⣿⣿⣿⣾⡇⠈⠀⠘⠈⢘⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠈⠀⠈⠁⣭⣿⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣶⣛⣀⣿⣿⣟⢀⣀⡀⠀⠀⠀⣄⣶⣾⣍⣳⢀⡄⠀⠇⠀⠀⣸⠀⣠⣿⠿⢿⣿⡇⠀⠀⠀⠀⣸⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠿⢿⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣾⣿⣧⣼⣿⣿⣿⣿⡦⣈⣀⣁⣀⣤⣿⣿⣿⣋⣛⣻⣷⣿⣷⣄⠀⠈⠀⠈⢸⣆⠀⠛⢻⡄⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠙⣿⣿⣾⡿⣿⠿⡿⠛⠛⠉⣧⣤⣴⣾⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣷⣾⡿⠿⠿⠿⣿⡯⢾⣿⣿⣿⣿⣿⣦⠀⠀⣤⣬⣿⣶⣤⣸⣷⣨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠈⠛⠛⣧⠀⣀⣿⣿⠀⠀⠙⣿⢋⣿⣿⣿⡿⣡⣭⣩⣅⣈⣹⣿⣿⣿⣟⡙⣽⣿⣦⡶⣾⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣛⣛⣱⣶⣿⣿⢿⣿⣿⣁⣠⣤⣶⣤⣭⣭⣤⠀⣐⣶⣾⣿⣿⢿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣶⣼⣿⣿⡟⠛⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠈⠛⠛⠛⠿⠿⠛⠛⣻⣿⣿⣾⣿⣿⣿⣯⡿⠝⣫⣿⣿⣿⢸⣿⣿⡏⠛⢿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠀⣛⣛⣛⡛⢻⣿⡿⠃⠀⠒⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣶⣶⣶⣶⣶⣶⣤⣤⣭⣉⡙⠛⣉⣤⣶⣾⣿⣿⣿⣿⢸⣿⣿⣇⣀⡤⠚⠀⠈⠁⠀⠻⠿⠿⠿⠋⠁⠀⠀⣿⣿⣿⡟⠋⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣭⣿⣿⣿⣿⡿⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣭⠉⠀⠉⠉⢻⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡻⠻⠟⢻⣿⣿⣿⣷⣶⣶⣧⡥⠀⠀⠀⢀⣼⣶⣷⣶⣶⣶⣍⣸⣿⡿⣿⣧⠤⢀⣀⣀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⢸⣿⠿⠛⡇⢸⡆⠀⢸⠉⠉⠙⠛⠛⠿⠿⠿⣶⣿⣯⡉⣹⠙⠛⠿⠿⣿⠏⣻⣾⠙⢺⣿⣿⣷⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀⢡⣾⡇⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠈⠁⠘⠛⠛⠿⠶⢶⣦⣤⣯⣀⠈⠛⠿⠿⢿⠇⢨⣿
⠀⠀⠀⠀⠀⠀⠀⣶⣤⣴⣶⣧⣅⣷⡦⣨⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣴⣶⣴⣤⣤⣤⣀⡀⠀⠀⠀⢨⢦⠀⢀⣼⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠉⠉⠹⢿⣷⣶⣶⣤⣤⣼
⣀⢀⢈⢀⣀⡀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⣒⣤⣼⣿⣗⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⠀⠀⠀⠉⠉⠉⠛
⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣿⣿⣿⣿⣿⣿⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣛⣛⣛⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1910

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/14/dragonfly-6-0-1/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/14/dragonfly-6-0-1/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_14/10/2021:_DragonFly_6.0.1_Released_and_Red_Hat_Loses_Another_Top
Executive⠀✐


Posted in Site_News at 3:55 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ What_is_the_Linux_Operating_System?⠀⇛


                       The Linux kernel is the main component of the Linux
                       operating system. In general terms, the kernel is a
                       software code that serves as a layer between the
                       hardware and main programs that run on a computer.
                       It was created by Linus Torvalds back in the early
                       1990s in Finland and licensed under the GNU General
                       Public License (GPL). In other words, Torvalds was
                       made the Linux kernel available to the world for
                       free. There is an official website for the Linux
                       kernel.


                       The rest of the system consists of other programs,
                       many of which were written by or for the GNU
                       Project. These utilities were then added to the
                       Linux kernel to create a complete system. The
                       kernel is an essential part of an operating system,
                       but useless by itself, because the Linux kernel
                       alone does not form a working operating system. It
                       can only function in the context of a complete
                       operating system.


                       The Linux kernel is used by Linux distributions
                       alongside GNU tools and libraries that interact
                       with it. This combination is sometimes referred to
                       as GNU/Linux.


                       So Linux is just a kernel, but the term Linux is
                       far more commonly used by the public and media and
                       that it serves as a generic term for systems that
                       combine that kernel with software from multiple
                       other sources. Therefore when most people say
                       Linux, they’re really talking about a combination
                       of the Linux kernel plus a lot of tools and
                       libraries from the GNU Project.


                       To put it more clearly, Linux and GNU/Linux refer
                       to the same operating system and software. There is
                       still a controversy over which term is more
                       appropriate.


          o § Audiocasts/Shows⠀➾


                # ⚓ DeskPi_Pro_v2_Review_–_Turn_your_Raspberry_Pi_into_a
                  Desktop!_–_Invidious⠀⇛


                       Raspberry Pi is an awesome platform, the only limit
                       is your imagination. If you want to turn your Pi
                       into a desktop, the DeskPi aims to help you do
                       exactly that. In this video, I’ll review the DeskPi
                       Pro v2 and give you my thoughts.


                # ⚓ How_to_install_MEGAsync_on_Linux_Lite_5.4_–_Invidious⠀⇛


                       In this video, we are looking at how to install
                       MEGAsync on Linux Lite 5.4.


                # ⚓ The_L4E_Show:_Gross_Invasion_of_Privacy_–_Invidious⠀⇛


                       The brand new L4E Show is here! Jason, Jerry and
                       Schykle talk about their recent passion projects,
                       then get into a somewhat disturbing conversation
                       about the creeping invasion of our online privacy.
                       Plus, a Software Spotlight and a proper
                       introduction of our new co-hosts!


                # ⚓ How_To_Handle_A_Data_Leak_feat_Twitch_–_Invidious⠀⇛


                       Recently Twitch had a massive data leak of source
                       code, creator payouts, and information about a
                       steam competitor but I thought I’d be good to talk
                       about the follow up that Twitch did which I
                       honestly don’t think was that bad.


                # ⚓ Building_the_Perfect_Linux_Desktop_for_Gaming_and_Daily
                  Driving_–_Invidious⠀⇛


                # ⚓ FLOSS_Weekly_651:_Open_Source_and_Construction⠀⇛


                       Silicon Valley technology veteran, Mary Hodder,
                       joins Doc Searls and Aaron Newcomb on FLOSS Weekly
                       to talk open source in construction. Home
                       construction is the original open-source field, and
                       nobody knows more about making it work than Hodder.
                       Where does open source fit in the world of
                       construction and building codes? Hodder details it
                       all on FLOSS Weekly.


                # ⚓ Ask_Alice_|_Coder_Radio_435⠀⇛


                       Mike just launched the secret project he’s been
                       working on for months and shares all the details.


                       And Chris has a surprise for the end of the show.


                # ⚓ The_Linux_Link_Tech_Show_Episode_926⠀⇛


                       support falters, standardNotes, tomato powder,
                       smokers


                # ⚓ Linux,_Scripting_and_Virtual_Machines_–_DT_LIVE!_–
                  Invidious⠀⇛


          o § Kernel Space⠀➾


                # ⚓ Linux_5.14.12⠀⇛


                       I'm announcing the release of the 5.14.12 kernel.

                       All users of the 5.14 kernel series must upgrade.

                       The updated 5.14.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.14.y
                       and can be browsed at the normal kernel.org git web
                       browser:

                       https://git.kernel.org/?p=linux/kernel/git/stable/
                       linux-s...

                       thanks,

                       greg k-h
                # ⚓ Linux_5.10.73⠀⇛


                # ⚓ Linux_5.4.153⠀⇛


                # ⚓ Linux_4.19.211⠀⇛


                # ⚓ Moving_Google_toward_the_mainline_[LWN.net]⠀⇛


                       Two Google engineers came to Open Source Summit
                       North America 2021 to talk about a project to
                       change the way the company creates and maintains
                       the kernel it runs in its data centers on its
                       production systems. Andrew Delgadillo and Dylan
                       Hatch described the current production kernel
                       (Prodkernel) and the problems that occur because it
                       is so far from the mainline. Project Icebreaker is
                       an effort to change that and to provide a near-
                       mainline kernel for development and testing within
                       Google; the talk looked at the project, its risks,
                       its current status, and its plans.


                # ⚓ User-space_interrupts_[LWN.net]⠀⇛


                       The term “interrupt” brings to mind a signal that
                       originates in the hardware and which is handled in
                       the kernel; even software interrupts are a kernel
                       concept. But there is, it seems, a use case for
                       enabling user-space processes to send interrupts
                       directly to each other. An upcoming Intel processor
                       generation includes support for this capability; at
                       the 2021 Linux Plumbers Conference, Sohil Mehta ran
                       a Kernel-Summit session on how Linux might support
                       that feature.


                # ⚓ How_Red_Hat_uses_GitLab_for_kernel_development_[LWN.net]⠀⇛


                       Much of the free-software development world has
                       adopted Git forges (such as GitHub, GitLab, or
                       sourcehut) with enthusiasm. The kernel community
                       has not. Reasons for that reticence vary, but one
                       that is often heard is that these forges simply
                       don’t work well at the scale needed for the kernel
                       project. At a Kernel-Summit session during the 2021
                       Linux Plumbers conference, Donald Zickus and Prarit
                       Bhargava sought to show how Red Hat has put GitLab
                       to good use to support its kernel team. Not only
                       can these forges work for kernel development, they
                       said, but moving to a forge can bring a number of
                       advantages.


                # ⚓ How_Windows_NTFS_finally_made_it_into_Linux_•_The
                  Register⠀⇛


                       Love it or hate it, Linux users in a Windows world
                       must deal with Microsoft’s New Technology File
                       System (NTFS). This has always been a pain in the
                       rump. Even after Microsoft finally gave up on its
                       anti-Linux rhetoric and released its patents to the
                       open-source community and expressively opened up
                       its exFAT patents, we still couldn’t get into NTFS.


                       Things have changed. Starting with the Linux 5.15
                       kernel, NTFS is finally being fully supported in
                       Linux. This journey hasn’t been easy.


                       Microsoft introduced NTFS, a proprietary –
                       naturally – journaling file system in Windows NT
                       3.1 in 1993. From there, it replaced 1977′s File
                       Allocation Table (FAT) file system across Windows.


                # ⚓ Rolling_stable_kernels [Ed: Microsoft wants Linux to become
                  unstable like Windows]
                  ⠀⇛


                       [Microsoft's] Sasha Levin, one of the maintainers
                       of the stable kernels, gave a presentation at Open
                       Source Summit North America 2021 on a proposal for
                       a different way to handle the stable tree. He noted
                       that throughout most of the kernel’s history,
                       version numbers did not really mean anything, but
                       that the versioning scheme suggests that they do,
                       which leads to a disconnect between how the kernels
                       are seen versus how they are actually maintained.
                       He proposed making a “rolling stable” release that
                       provides users what they need—timely fixes to their
                       kernel—without forcing them to choose to switch to
                       a new version number.


                # § Graphics Stack⠀➾


                      # ⚓ mesa-21.3.0-rc1_·_Tags_·_Mesa_/_mesa_·_GitLab⠀⇛


                      # ⚓ Mesa_21.3-rc1_Released_With_Improved_Zink,_Radeon
                        Ray-Tracing,_RADV_NGG_Culling_–_Phoronix⠀⇛


                             Mesa 21.3 feature development is now over
                             with the code having been branched and the
                             first release candidate issued.


                             Mesa 21.3 will be the last major feature
                             release to this collection of open-source GPU
                             drivers for 2021. Mesa 21.3 should debut in
                             November if all goes well but until then will
                             be weekly release candidates to help test out
                             the new code that has accumulated over the
                             past three months.


          o § Applications⠀➾


                # ⚓ 5_markdown_editors_I_recommend_trying⠀⇛


                       You can use markdown for anything—formatting
                       websites, authoring books, and writing technical
                       documentation are just some of its uses. I love how
                       easy it is to create rich documents. Everyone has
                       their favorite markdown editor. I have used several
                       on my markdown journey. Here are five markdown
                       editors I have considered.


          o § Instructionals/Technical⠀➾


                # ⚓ Reasons_to_limit_your_stack_size_even_in_non-threaded
                  environments⠀⇛


                       One reaction to learning that 4BSD is where Unix
                       started to have a stack size limit is to ask why
                       you would bother with a stack size limit at all in
                       an environment without threads (where a process
                       will thus only ever have one stack). There are a
                       number of reasons that operating systems have
                       generally done this, and probably why it starts in
                       Unix in the 4BSD line, which ran on 32-bit VAX
                       systems instead of the 16-bit PDP-11s that V7 did.


                # ⚓ An_UPDATE_without_a_WHERE,_or_something_close_to_it⠀⇛


                       Imagine what happens when you forget the WHERE.
                       It’s the last thing on the line as shown, so you
                       could send off the command early and it would
                       totally work. It would look like this: [...]


                # ⚓ How_to_Clone_a_Git_Repository_Into_a_Specific_Folder_–
                  TecAdmin⠀⇛


                       The process of git repository cloning is initiated
                       on a daily basis in the DevOps world. But, if you
                       simply issue a git clone command, the cloning
                       process will create a new directory for the
                       repository. In this tutorial, we will help you
                       learn how to clone a git repository into a specific
                       folder.


                # ⚓ How_to_Download_and_Upload_Remote_Directory_in_sFTP⠀⇛


                       sFTP or Secure File Transfer Protocol is a
                       convenient upgrade from the traditional FTP (File
                       Transfer Protocol). The sFTP program boasts of
                       improved security layers since it mirrors encrypted
                       SSH transport protocols in its file transfer
                       operations.


                # ⚓ How_to_Install_Redis_&_Configure_on_AlmaLinux_8_–
                  LinuxCapable⠀⇛


                       Redis is an open-source (BSD licensed), in-memory
                       key-value data structure store used as a database,
                       cache, and message broker. Redis supports data
                       structures such as strings, hashes, lists, sets,
                       sorted sets with range queries, bitmaps, hyperlog
                       logs, geospatial indexes, and streams. Redis also
                       provides high availability with Redis Sentinel
                       software logic, creating automatic partitioning
                       across Redis nodes with Redis Cluster.


                       At the end of the guide, you will know how to
                       install and configure Redis on your AlmaLinux
                       operating system.


                # ⚓ How_to_Install_Redis_on_Rocky_Linux_8_or_AlmaLinux_8⠀⇛


                       Redis is a popular in-memory key-value store that
                       can be used as a NoSQL key-value database, message
                       broker as well as a caching solution. It is
                       renowned for its flexibility, scalability, seamless
                       replication, simplicity, and ease of use. Redis is
                       widely used in various fields such as machine
                       learning, real-time analytics, chat, messaging, and
                       gaming leaderboards.


                       On its own, Redis has no robust features, however,
                       you can still tweak Redis to provide added security
                       and ward off unauthorized users.


                # ⚓ GNU_Linux_–_network_config_madness_–_the_(ever_changing)
                  basics_–_how_to_(try_to)_set_fixed_&_dynamic_ip_&_dns_per
                  interface⠀⇛


                # ⚓ How_to_Install_Telegram_on_Linux_Mint_20⠀⇛


                       Telegram is a popular free cross-platform, cloud-
                       based instant messaging system. Telegram is famous
                       for providing end-to-end encrypted video calling,
                       VoIP, file sharing, amongst many other features.
                       One of the main attractions of Telegram, it is
                       unique in having no ties or shared interests with
                       the big social media giants such as Facebook or
                       Twitter. The application is also cross-platform,
                       with versions of the app available for most
                       operating systems for desktops and mobile/tablet
                       devices.


                       In the following tutorial, you will learn how to
                       install the Telegram client on Linux Mint.


                # ⚓ Toggle_Light_&_Dark_Mode_for_Flatpak_Apps_in_Ubuntu_20.04+
                  /_Linux_Mint_|_UbuntuHandbook⠀⇛


                       Using Flatpak apps in Linux? You may found that
                       Flatpak app appearance does not change when
                       toggling light & dark mode or switching to another
                       app theme.


                       As more and more apps publish Linux packages via
                       Flatpak, I have a few of them installed in my
                       Ubuntu laptop. However, the apps stick to the light
                       theme whenever I switches to dark mode in
                       Appearance settings.


                       Since Flatpak runs in sandbox and does not have
                       permission to access the “/usr” directory, it does
                       not use system theme according to the document. So,
                       some popular GTK themes are packaged as Flatpaks.
                       And, it detects the current system app theme and
                       tries to install the Flatpak version of the theme
                       if available during app installation or update.


                       I’m working with default Yaru theme in the most
                       time, so it automatically installs Yaru theme
                       flatpak package but leaves Yaru Dark not installed.
                       When I switching to Yaru Dark, it can’t find the
                       match theme so falls back to the default Adwaita.


                # ⚓ How_to_connect_Rocky_Linux_8_via_Windows_RDP_protocol_–
                  Linux_Shout⠀⇛


                       f you have Rocky Linux 8 desktop and Windows 7/10/
                       11 in a local environment and want to access using
                       the RDP- Remote desktop protocol, then here is the
                       way.


                       To connect Linux operating systems such as Rocky
                       Linux, AlmaLinux 8, or CentOS, we can use the open-
                       source implementation of Remote desktop protocol
                       called XRDP. RDP is developed by Microsoft and has
                       been an integral part of Windows operating systems.
                       It allows the users to remotely control and use the
                       GUI desktop systems just like a local one.
                       Although, Windows can be operated over this
                       protocol out of the box, for Linux we need to
                       install some additional packages. Here we learn how
                       to set up a remote desktop connect to Rocky Linux
                       8.


                # ⚓ Automatically_reassign_your_default_printer_–_Fedora
                  Magazine⠀⇛


                       I run Linux,…or does it run me? Some computing
                       paradigms are so ubiquitous, so ingrained, we
                       rarely stop to think that things could work another
                       way. When such a realization comes, we can exercise
                       our freedom – one of Fedora’s four foundations – to
                       improve the user experience. For that sentiment to
                       be more than cliché, I needed to re-imagine the
                       idea of the default printer and how it gets set.
                       This article presents that implementation.


                # ⚓ How_to_install_Ubuntu_on_VirtualBox_(Windows) [Ed: A lot
                  better than WSL]⠀⇛


                # ⚓ Proxmox_VE_Full_Course:_Class_12_–_The_Command-Line
                  Interface_–_Invidious⠀⇛


                       LearnLinuxTV’s Proxmox full course aims to get you
                       up to speed with all the finer points of Proxmox
                       Virtual Environment. In video #12, we take a look
                       at the Command-Line interface.


                # ⚓ [Older]_Permanently_add_a_directory_to_shell_PATH⠀⇛


                       When you type a command into a Linux terminal,
                       what’s really happening is that a program is being
                       executed. Normally, to execute a custom program or
                       script, we need to use its full path, such as /
                       path/to/script.sh or just ./script.sh if we’re
                       already in its residing directory. Alternatively,
                       we can execute a lot of commands without specifying
                       paths, like uptime or date, etc.


                # ⚓ 15_Super_Useful_Examples_of_Find_Command_in_Linux⠀⇛


                       The find command is used for searching for files
                       and directories in the Linux command line.


                       Find is one of the most powerful and frequently
                       used commands. It is also one of the most extensive
                       commands with over 50 options and this makes it a
                       bit confusing, specially when it is paired with the
                       exec or xargs command.


                       It is impossible for a sysadmin or software
                       developer to avoid the find command while working
                       in the command line. Instead of being afraid of it,
                       you should embrace its power.


                       I am going to discuss some of the most common
                       examples of the find command that you are likely to
                       use. But before that, let me show you its syntax
                       and how to use it.


                # ⚓ Sending_logs_to_Panther_using_syslog-ng_–_Blog_–_syslog-ng
                  Community_–_syslog-ng_Community⠀⇛


                       Panther is an open-source log management system,
                       which is also available as a service for a time-
                       limited trial. It is still in beta phase, but it
                       looks promising. You can see the “beta” sign on its
                       opening page: https://app.panther.support/ I tested
                       the time-limited cloud service version, but you can
                       also install it locally, either from Dockerhub, or
                       you can build the containers locally from the
                       source.


                       Even if it is still in beta phase, Panther comes
                       with detailed documentation. There is a notable
                       exception: while syslog-ng is shown on some of the
                       figures, documenting it is still to be done. This
                       blog helps you to get started with sending logs to
                       Panther, using syslog-ng. You can use either legacy
                       syslog with TLS encryption (still a bit
                       problematic) or the http() destination to send logs
                       to the Panther HTTP API.


                # ⚓ 7_Important_Linux_Commands_for_Every_Linux_User⠀⇛


                       Linux might sound scary for first-time Linux users,
                       but actually, it isn’t. Linux is a bunch of open-
                       source Unix operating systems based on Linux
                       Kernel. These operating systems are called Linux
                       distributions, such as Fedora, Debian, Ubuntu, and
                       Mint.


                       Since its inception in 1991, Linux has garnered
                       popularity for being open-source. People can modify
                       and redistribute Linux under their own brand. When
                       using a Linux OS, you need a shell to access the
                       services provided. Also, it’s recommended to run
                       your Linux OS through a CLI or command-line
                       interface. CLI makes time-consuming processes
                       quicker.


                       This article presents a guide to 7 important Linux
                       commands for every Linux user to know. So, let’s
                       begin.


                # ⚓ How_to_Install_Ubuntu_MATE_Desktop_on_Ubuntu_20.04⠀⇛


                       For those not familiar with Ubuntu MATE, it is a
                       free, open-source community-driven lightweight
                       desktop environment and an official derivative of
                       Ubuntu. One of the main differentiation from Ubuntu
                       is that it uses the MATE desktop environment as its
                       default user interface instead of the GNOME desktop
                       environment that is the default user interface for
                       Ubuntu.


                       Ubuntu MATE is famous for being lightweight, fast,
                       and stable, a community-driven project, and a great
                       alternative to Ubuntu’s stock Gnome. At the end of
                       the tutorial, you will have learned how to install
                       Ubuntu MATE on your Ubuntu 20.04 system.


                # ⚓ How_to_Install_Vanila_Forum_on_CentOS_8_–_Unixcop⠀⇛


                       Vanilla is a Canadian software company founded in
                       2009 in Montreal, Quebec, Canada. It is both a
                       cloud-based (SaaS) community forum software and an
                       open source community supported software. The
                       company’s main product is Vanilla Cloud.


                       Its open source product, Vanilla OSS, is a
                       lightweight Internet forum package written in the
                       PHP scripting language using the Garden framework.
                       The software is released under the GNU GPL. Vanilla
                       Forums is free software, standards-compliant,
                       customizable discussion forums. Since 2009 there is
                       also a cloud-hosted version (offered by Vanilla).


                # ⚓ How_to_Set_Environment_Variables_in_Docker_|_RoseHosting⠀⇛


                       Docker is an open-source application that provides
                       lightweight operating-system-level virtualization
                       through the use of containers. It is a kind of
                       virtualization technology that is specially
                       designed to easily develop and deploy applications
                       inside of neatly packaged virtual containerized
                       environments. Docker containers are in essence a
                       set of software packages that run as one
                       application that’s isolated from others. We can
                       deploy it to any machine without any compatibility
                       issues. By using this, the software stays system
                       agnostic, simpler to use, less work to develop, and
                       easy to maintain.


                # ⚓ How_to_connect_Rocky_Linux_8_via_Windows_RDP_protocol_–
                  Linux_Shout⠀⇛


                       If you have Rocky Linux 8 desktop and Windows 7/10/
                       11 in a local environment and want to access using
                       the RDP- Remote desktop protocol, then here is the
                       way.


                       To connect Linux operating systems such as Rocky
                       Linux, AlmaLinux 8, or CentOS, we can use the open-
                       source implementation of Remote desktop protocol
                       called XRDP. RDP is developed by Microsoft and has
                       been an integral part of Windows operating systems.
                       It allows the users to remotely control and use the
                       GUI desktop systems just like a local one.
                       Although, Windows can be operated over this
                       protocol out of the box, for Linux we need to
                       install some additional packages. Here we learn how
                       to set up a remote desktop connect to Rocky Linux
                       8.


                # ⚓ How_to_install_UTAU_on_a_Chromebook⠀⇛


                       Today we are looking at how to install UTAU 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.


                # ⚓ How_to_install_Unreal_Engine_4_on_Ubuntu⠀⇛


                       Are you looking to develop video games on your
                       Ubuntu PC using the Unreal Engine? If so, you will
                       need to install the latest Unreal Engine toolkit to
                       your system. This guide will show how to set up the
                       newest release of Unreal Engine 4 on your Ubuntu
                       computer.


                # ⚓ Install_Gitlab_CE_on_Debian_11_–_kifarunix.com⠀⇛


                       In this tutorial, you will learn how to install
                       Gitlab CE on Debian 11. GitLab is an open source
                       end-to-end software development platform with
                       built-in version control, issue tracking, code
                       review, CI/CD, etc. It is is a complete DevOps
                       platform, delivered as a single application.


                # ⚓ FreeIPA_Server_on_Alma_Linux_8/CentOS_8_–_Unixcop⠀⇛


                       We have 3 users, Jhon, Doe, Mike. Suppose you are
                       at the IT department for a Software Company. You
                       have to manage the identity of those 3 users. Easy
                       right? You can easily manage their Identity Access.
                       But how about 3 users become 300 or 3000? How can
                       you manage them?


                       Well things get pretty hard I guess, How about if
                       we can have a system that has a central identity
                       info, maybe that would be easier to solve our
                       stated problem.No worries, FreeIPA is here to help
                       you by solving the problem.


                # ⚓ Add_Client_to_the_FreeIPA_Server_on_CentOS_8_–_Unixcop⠀⇛


                       Hi Everyone ! In the previous article, we have seen
                       how to set up freeIPA Server on centOS 8.


                       In this write up, we will show how to add a client
                       host to the freeIPA Domain. We will be configuring
                       a CentOS 8 machine to authenticate against an
                       existing FreeIPA server.


                # ⚓ How_to_Install_KDE_Plasma_Desktop_Environment_on_Ubuntu
                  20.04_–_LinuxCapable⠀⇛


                       The name KDE comes from “K Desktop Environment”.
                       For those not familiar with KDE Desktop, it is a
                       free, open-source desktop environment. It provides
                       Linux users on various distributions an alternative
                       graphical interface to customize their desktop
                       environment and applications for everyday use
                       enhancement.


                       Besides the graphical enhancements and changes, it
                       is also a lightweight, fast, smooth environment
                       with superior performance compared to native
                       shipped desktops with some Linux Distributions. In
                       Ubuntu’s case, this is Gnome.


                       At the end of the tutorial, you will have learned
                       how to install KDE Desktop Environment on your
                       Ubuntu 20.04 system.


                # ⚓ How_to_fix_“Got_permission_denied_while_trying_to_connect
                  to_the_Docker_daemon_socket_at_unix:///var/run/docker.sock
                  error_–_blackMORE_Ops⠀⇛


                       Quickest way to fix How to fix “Got permission
                       denied while trying to connect to the Docker daemon
                       socket at unix:///var/run/docker.sock: Post “http:/
                       /%2Fvar%2Frun%2Fdocker.sock/v1.24/auth”: dial unix
                       /var/run/docker.sock: connect: permission denied”
                       error.


                # ⚓ How_To_Install_NVIDIA_Drivers_on_Fedora_–_TecAdmin⠀⇛


                       Fedora, the operating system of RHEL(Red Hat
                       Enterprise Linux) does not have pre-installed
                       exclusive Nvidia drivers in it for the users.
                       Although it does have default Nouveau drivers which
                       work in most conditions, you may face some problems
                       while using them. If you encounter issues while
                       using the Nouveau drivers you will have to install
                       the official proprietary Nvidia drivers.


                       The official Nvidia drivers can help you get the
                       most out of your GPU by enhancing its performance.
                       In this article, we will learn to install the
                       official Nvidia drivers on Fedora


                       However, before we start with the installation
                       process, we need to do system configuration. The
                       first configuration we need to do is stop the GUI
                       from running and the second step is to disable the
                       default nouveau drivers. From the GRUB boot menu,
                       it is really easy and doable.


                # ⚓ Securing_your_Kubernetes_cluster_with_Kubewarden⠀⇛


                       Kubernetes is fast becoming the operating system of
                       the cloud. Every major cloud provider has a
                       supported Kubernetes platform, Kubernetes can be
                       run on-premises, and Kubernetes even has a package
                       manager with Helm. And thanks to the operator
                       pattern, Kubernetes has built-in support to
                       describe and manage almost any kind of workload.


          o § Games⠀➾


                # ⚓ DOOM_Played_By_Tweet⠀⇛


                       Getting DOOM to run on hardware it was never
                       intended to run on is a tradition as old as time.
                       Old cell phones, embedded systems, and ancient
                       televisions have all been converted to play this
                       classic first-person shooter. This style of playing
                       games on old hardware might be passé now as the new
                       trend seems to be the ability to play this game on
                       more ethereal platforms instead. This project
                       brings DOOM to Twitter.


                # ⚓ Post-apocalyptic_4x_strategy_game_Punk_Wars_releases
                  November_11_|_GamingOnLinux⠀⇛


                       Strategy Forge S.A. and Jujubee S.A. have announced
                       that their 4x strategy game Punk Wars will be
                       releasing with Linux support on November 11.


                       “Punk Wars tells the story of four new powers
                       emerging from the ashes of a global cataclysm and
                       fighting for domination of the ruins of a once
                       magnificent megacity. Become the powerful leader of
                       the messianic steampunk, tenebrous dieselpunk,
                       militaristic steelpunk, or technocratic atompunk,
                       with each faction holding the key to a different
                       branch of industrial science, with a different set
                       of unique skills. Explore the ruins of a bygone
                       civilization, where resources are scarce and the
                       dangers way too common. Develop your infrastructure
                       and technology that will secure your triumph.
                       Create a winning strategy and a playstyle for each
                       faction, utilising their distinctive skills and
                       units. Become the messiah of the new age and lead
                       humanity towards the era of prosperity and
                       happiness… as you see it.”


                # ⚓ Fallout_3_removes_Games_for_Windows_Live,_works_well_on
                  Linux_with_Proton_|_GamingOnLinux⠀⇛


                       Fallout 3 from Bethesda Game Studios received a
                       surprise update recently where the developer
                       finally removed Games for Windows Live which is
                       great news.


                       Released back in 2008, Fallout 3 is something of a
                       classic and a game I thoroughly enjoyed before
                       making the switch fully to Linux. Thanks to Steam
                       Play Proton, you can play Fallout 3 easily on Linux
                       and with this update no workarounds are needed – at
                       all.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ KDE’s_25th_Anniversary⠀⇛


                             You’ll find on the website − https://
                             25years.kde.org/ − the full celebration of
                             the event: videos, meeting, activities, old
                             KDE distro ready to run on virtual machine,
                             merch (Tee-Shirt/Stickers).


                             But if you still wonder what is KDE; I’ll try
                             to give you an overview: KDE is an
                             international free software community that
                             develops free and open-source software. KDE
                             helps these projects to get common tools: bug
                             trackers, software development forge,
                             distributing the software, organizing in real
                             life events like sprints,conferences, etc… Y


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ More_GNOME_Software_FAIL._Useless_software_reviews._–
                        BaronHK’s_Rants⠀⇛


                             It’s come to my attention several times now
                             that if you want information about a program
                             for GNU/Linux, don’t bother reading the
                             reviews that people put in GNOME Software.


                             Some of it isn’t in English, which is the
                             language that I speak, and GNOME Software
                             doesn’t sort them out based on your preferred
                             language.


                             The GNOME Software application doesn’t
                             collect basic information about what
                             distribution of GNU/Linux. (Or if it even is
                             GNU/Linux, as GNOME actually still does run
                             on other *nix systems, but I can’t imagine
                             there’s too many non-GNU/Linux users left).


                             It doesn’t consider what package manager you
                             installed the program from.


                             It could be from Fedora, it could be from
                             Debian, or Ubuntu, or Arch. It could be a
                             Snap. It could be a Flatpak.


          o § Distributions⠀➾


                # § BSD⠀➾


                      # ⚓ DragonFly_6.0.1_released⠀⇛


                             DragonFly version 6.0 has been released.
                             DragonFly version 6.0 brings a revamped VFS
                             caching system, significant dsynth updates,
                             various filesystem updates including HAMMER2,
                             and a long list of userland updates. 6.0.1
                             brings a Let’s Encrypt certificate fix for
                             dport installation, plus other minor fixes


                      # ⚓ DragonFlyBSD_6.0.1_Released_With_AMD_Zen_3
                        Temperature_Monitoring,_Fixes_–_Phoronix⠀⇛


                             Released back in May was the shiny
                             DragonFlyBSD 6.0 release while today a point
                             release for it has been issued.


                             The DragonFlyBSD 6.0.1 release appears to be
                             primarily driven by the need to address a
                             certificate issue for downloading dpkg
                             binaries. Due to an expired Let’s Encrypt
                             certificate, downloading dpkg binaries began
                             failing. With DragonFlyBSD 6.0.1 that
                             certificate has been renewed.


                # § Screenshots/Screencasts⠀➾


                      # ⚓ Linux_overview_|_Ubuntu_21.10_–_Invidious⠀⇛


                             In this video, I am going to show an overview
                             of Ubuntu 21.10 and some of the applications
                             pre-installed.


                # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾


                      # ⚓ Filezilla_»_PCLinuxOS⠀⇛


                             Filezilla updated to 3.56.0. FileZilla is a
                             fast and reliable FTP, FTPS and SFTP client
                             with lots of useful features and an intuitive
                             graphical user interface.


                      # ⚓ Chromium_Browser_»_PCLinuxOS⠀⇛


                             The Chromium Browser has been updated to
                             94.0.4606.81 and shipped to the PCLinuxOS
                             Software Repository.


                      # ⚓ Dino_»_PCLinuxOS⠀⇛


                             Dino 0.2.2 is a modern XMPP (“Jabber”) chat
                             client using GTK+/Vala.


                      # ⚓ Blender_»_PCLinuxOS⠀⇛


                             Blender 2.93.5 is the essential software
                             solution you need for 3D, from modeling,
                             animation, rendering and post-production to
                             interactive creation and playback.
                             Professionals and novices can easily and
                             inexpensively publish stand-alone, secure,
                             multi-platform content to the web, CD-ROMs,
                             and other media.


                # § SUSE/OpenSUSE⠀➾


                      # ⚓ SUSE_Announces_Integration_Of_SUSE_Rancher_With
                        Harvester⠀⇛


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ ModelMesh_and_KServe_bring_eXtreme_scale_standardized
                        model_inferencing_on_Kubernetes⠀⇛


                             One of the most fundamental parts of an AI
                             application is model serving, which is
                             responding to a user request with an
                             inference from an AI model. With machine
                             learning approaches becoming more widely
                             adopted in organizations, there is a trend to
                             deploy a large number of models. For
                             internet-scale AI applications like IBM
                             Watson Assistant and IBM Watson Natural
                             Language Understanding, there isn’t just one
                             AI model, there are literally hundreds or
                             thousands that are running concurrently.
                             Because AI models are computationally
                             expensive, it’s cost prohibitive to load them
                             all at once or to create a dedicated
                             container to serve every trained model. Also,
                             many are rarely used or are effectively
                             abandoned.


                             When dealing with a large number of models,
                             the ‘one model, one server’ paradigm presents
                             challenges on a Kubernetes cluster to deploy
                             hundreds of thousands of models.


                      # ⚓ The_Application_Hierarchy_of_Needs_for_SREs_and_IT
                        Operators_–_IBM_Developer⠀⇛


                             The Hierarchy of Needs was defined by the
                             psychologist Abraham Maslow in his paper “A
                             Theory of Human Motivation.” The base of the
                             pyramid contains the most fundamental and
                             most critical needs, with each subsequent
                             layer representing needs that become
                             important once those of the preceding layer
                             have been satisfied.
                             Maslow’s “Hierarchy of Needs” was used to
                             represent the needs and behavioral motivation
                             drivers for humans. This pyramid represented
                             a series of basic psychological and self-
                             fulfillment needs.


                             Maslow’s hierarchy of needs has been adapted
                             and adopted to represent the needs and
                             motivations in other domains, including the
                             needs of applications and services being
                             managed by SREs and IT Operations teams.


                      # ⚓ A_Red_Hat_validated_pattern_for_Industrial_Edge⠀⇛


                             We’ve improved on the technology of our AI/ML
                             Industrial Edge solution, designed to boost
                             manufacturing efficiency and product quality
                             with AI/ML, edge computing and Kubernetes.
                             Let’s see what’s new!


                      # ⚓ Meet_single_node_OpenShift:_Our_newest_small
                        OpenShift_footprint_for_edge_architectures⠀⇛


                             Single node OpenShift is here, putting both
                             control and worker capabilities into a single
                             server to help fit into space-constrained
                             environments.


                      # ⚓ Single_node_OpenShift_at_the_manufacturing_edge⠀⇛


                             Where does it make sense to utilize single
                             node OpenShift? Learn how it can help at the
                             manufacturing edge!


                      # ⚓ Transitioning_Red_Hat’s_Marketing_leadership⠀⇛


                             Today, we are sharing news that Tim Yeaton,
                             Red Hat’s executive vice president and chief
                             marketing officer (CMO) will retire in 2022.
                             We’ve had the benefit of planning for Tim’s
                             retirement for some time and using Red Hat’s
                             succession planning process to identify and
                             develop our next CMO. Long time Red Hat
                             marketing communications and brand leader
                             Leigh Day has been promoted to senior vice
                             president (SVP) of Marketing and in January,
                             she will assume the role of CMO. Until his
                             retirement in mid-2022, Tim will become a
                             senior advisor at Red Hat, helping with a
                             smooth transition.


                      # ⚓ Customer_experience_(CX)_plans:_5_questions_to_ask_|
                        The_Enterprisers_Project⠀⇛


                             The pressure is on for companies to deliver a
                             top-notch customer experience (CX). But to
                             deliver a high-quality and holistic CX, you
                             need to invest in the right data and
                             technology. For IT leaders facing an
                             abundance of options, investing in technology
                             to enhance CX can feel like a gamble.


                      # ⚓ IBM_Cheese_Cutter_Restoration_|_Hackaday⠀⇛


                             For a while now, Mac Pro towers have had the
                             nickname “cheese grater” because of their
                             superficial resemblance to this kitchen
                             appliance. Apple has only been a company
                             since the 70s, though, and is much newer than
                             one of its historic rivals, IBM. In fact, IBM
                             is old enough to have made actual cheese-
                             related computers as far back as the 1910s,
                             and [Hand Tool Rescue] recently obtained one
                             of these antique machines for a complete
                             restoration.


                      # ⚓ Going_to_market_with_an_open_source_product⠀⇛


                             Many people with a long career in
                             engineering, including me, have had
                             misconceptions about sales and marketing. As
                             an engineering community, we’ve viewed it as
                             things like ordering swag, naming things,
                             running ad campaigns, and creating white
                             papers. There’s a joke in the marketing
                             community about how engineers are always
                             willing to provide their “opinions” on
                             marketing decisions without fully
                             comprehending the discipline, but marketers
                             rarely—like never—make suggestions on code
                             improvements. To work together, engineers and
                             marketers must share a common definition.


                             While product marketers do help drive those
                             commonly recognized tasks, the role is so
                             much richer. Product marketers, technical
                             marketers, and evangelists have outbound
                             responsibilities like creating content (e.g.,
                             blogs, press releases, white papers, demos),
                             delivering roadmap sessions to customers (as
                             well as analysts and journalists), building
                             content for sales teams, and much more.
                             Combined, these outbound functions are often
                             referred to as getting a product to market,
                             but just as importantly, product marketing
                             also has inbound functions. They serve as
                             another set of eyes and ears to listen for
                             customer needs and provide input to the
                             product strategy. There’s a saying in product
                             management: nothing interesting happens
                             within these four walls. Businesses must go
                             out into the world, talk to customers, and
                             more importantly, listen to them.


          o § Devices/Embedded⠀➾


                # ⚓ Dev_kit_debuts_RISC-V_XuanTie_C910_SoC_with_a_3D_GPU_and
                  Android_and_Linux_support⠀⇛


                       Sipeed and Alibaba T-Head have opened $399 pre-
                       orders on an “RVB-ICE” dev kit featuring a RISC-
                       V compatible, dual-core, 1.2GHz XuanTie C910 ICE
                       SoC with a Vivante 3D GPU, an NPU, 4GB RAM, and
                       support for Android 10 and Debian 11.


                       Sipeed and Alibaba’s T-Head Semiconductors unit
                       (AKA Pintouge) are launching a development kit for
                       a XuanTie C910 ICE SoC, featuring the first 3D GPU
                       we have seen on a commercially available RISC-
                       V SoC. The RVB-ICE dev kit is available for pre-
                       order in limited quantities at $399, including a 7-
                       inch touchscreen, with shipments expected in
                       November.


                # § Open Hardware/Modding⠀➾


                      # ⚓ Inspiring_learners_about_computing_through_health_and
                        well-being_projects_|_Hello_World_#17⠀⇛


    * § Leftovers⠀➾


          o § Health/Nutrition⠀➾


                # ⚓ Deputy_health_minister_proposes_ban_on_all_tobacco
                  marketing⠀⇛


                       Separately, he called on senators to reject a bill
                       on the legalization of vapers and electronic
                       cigarettes, and claimed that tobacco companies were
                       deliberately obfuscating the issue. “If we go with
                       this fallacy that the tobacco industry has put to
                       us, that vapers are the alternative solution to the
                       tobacco problem, we will once again be making a
                       mistake because vapers and heated tobacco products
                       are not an alternative to harm reduction,” he said.


                # ⚓ COVID-19_could_nudge_minds_and_societies_towards
                  authoritarianism⠀⇛


                       It is a little-known fact that humans have not one
                       but two immune systems. The first, the biophysical
                       immune system – the one we’ve all heard much about
                       – responds to infections as they enter the body,
                       detecting and eliminating intruders such as the
                       coronavirus.


                       The second is the behavioural immune system, which
                       adapts our behaviour to preemptively avoid
                       potentially infectious people, places and things.
                       The behavioural immune system is the first line of
                       defence against infectious disease. It prompts
                       people to socially conform with known traditions
                       and to avoid foreign, dissimilar and potentially
                       infectious groups.


                       In a recently published study, my colleagues and I
                       at the University of Cambridge examined the impact
                       of the behavioural immune system on our attitudes
                       towards obedience and authority. We found that high
                       rates of infectious diseases – and the disease-
                       avoidance they promote – may fundamentally shape
                       political opinions and social institutions.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # ⚓ After_Spike_in_Ransomware_Attacks,_U.S._Looks_to_Go
                        on_the_Offensive [iophk: Windows TCO]⠀⇛


                             The Biden administration has sought to rally
                             its allies to help fight cyberthreats and
                             ransomware attacks, pushing NATO to adopt a
                             new cyber defense policy and launching talks
                             on cyberthreats among G-7 nations. It also
                             launched a series of initiatives in recent
                             months to target cybercriminals and boost
                             protection against ransomware attacks
                             following several high-profile ransomware
                             attacks against a major oil pipeline company
                             and a meat-processing company earlier this
                             year. The attacks laid bare how vulnerable
                             elements of U.S. critical infrastructure,
                             including its food and energy sectors, were
                             to cyber incursions.


                      # ⚓ VirusTotal_study_finds_95%_of_80m_ransomware_samples
                        analysed_aimed_at_Windows⠀⇛


                             About 2% were Android-based, while one set,
                             known as EvilQuest, targeted OSX, the study,
                             titled Ransomware Activity Report, said. It
                             took into account samples submitted all the
                             way back to January 2020.


                             Vicente Diaz of VirusTotal said in a short
                             blog post accompanying the 14-page study that
                             of the 140 countries which submitted
                             ransomware samples, Israel was far and away
                             an outlier with the highest number of
                             submissions and nearly 600% rise in
                             submissions compared to its baseline.


                      # ⚓ Insulin_dump⠀⇛


                             The student is allowed to keep a small purse
                             with her at all times, as it contains a
                             smartphone that runs an app that talks to,
                             and controls her insulin pump. The teachers
                             at the school were briefed about the
                             smartphone. However, there’s one part of the
                             setup that caused problems: the pump would
                             occasionally issue a beeping noise.


                             This beeping makes for a disastrous
                             experience for a sixth grade girl. She’s at
                             the age where social pressures really start
                             to manifest. The pump gives something other
                             students can latch onto to make fun of.


                      # ⚓ White_House_to_host_virtual_ransomware_summit_with_30
                        countries_—_but_not_Russia [iophk: Windows TCO]⠀⇛


                             The White House plans for at least 30
                             countries to attend a series of meetings to
                             be held over Zoom. The summit will be the
                             most concrete step it has taken so far to
                             build an international coalition to address
                             ransomware, an epidemic of cybercrime where
                             hackers remotely lock victims’ computers and
                             demand an extortion payment to fix them.


                      # ⚓ End_of_Life_Google_Chrome_devices_should_be
                        repurposed_with_GNU/Linux._–_BaronHK’s_Rants⠀⇛


                             Of all companies, Lenovo gave me an idea.


                             They mentioned GalliumOS as a potential
                             Chrome OS replacement on some of their own
                             Chrome devices.


                             These are considered low end by PC standards,
                             but they run Chrome OS fine because it’s a
                             stripped down GNU/Linux system. Not some
                             bloated 100 GB+ Windows horror that has to
                             trap every file system call in case it’s a
                             virus.


                             The Intel-based ones, mostly, should run a
                             normal GNU/Linux distro, but they
                             occasionally have odd hardware in them that’s
                             not well supported by the vanilla Linux
                             kernel, and GalliumOS steps in to add those.


                             Many years ago, there was a guy running a
                             charity in Texas that took old computers that
                             were not able to run Windows anymore, and re-
                             imaged them with a minimum GNU/Linux
                             distribution, which they were able to run
                             okay.


                             Somewhere, out of the blue, Texas sent the
                             police in to enforce “environmental
                             standards”.


                      # ⚓ macOS_11.6_makes_the_theme_worse_then_ever._Free
                        Software_GUIs_are_whatever_you_want_them_to_be._–
                        BaronHK’s_Rants⠀⇛


                             Jamie Zawinski commented that his perfect Mac
                             experience continues with light grey text on
                             light grey backgrounds.


                             These have been a problem for years, and it’s
                             only getting worse.


                             It’s why I use the Adwaita-Dark theme and
                             Solarized Dark for Gedit and GNOME Terminal.


                             I think they’re all making the default theme
                             so unusable unless you jack up the display
                             backlight to “IT BURNS US! IT BURNS US
                             PRECIOUS!” so they can market “Dark Mode” as
                             if it was a special feature, when I’ve always
                             used them in one form or another.


                             When I started using Solaris, I got hooked on
                             one that Sun wrote for GTK2 called Nimbus.
                             The icon pack was pretty sharp too. And even
                             the light version was quite lovely.


                      # § Pseudo-Open Source⠀➾


                            # § Openwashing⠀➾


                                  # ⚓ .NET_Foundation_admits_it_‘violated_the
                                    trust_of_project_maintainers’ [Ed: Simon
                                    Sharwood at it again, relaying Microsoft
                                    talking points and face-saving
                                    statements]⠀⇛


                                         The beleaguered .NET Foundation
                                         has apologised, again, and
                                         reversed one of the policies that
                                         saw its members revolt.


                                         The Foundation’s had a tricky few
                                         weeks, after a board member
                                         resigned and complained the
                                         reasons for doing so were
                                         misrepresented. Members have also
                                         complained the organisation had
                                         made unauthorised changes to
                                         projects, and about the decision
                                         to move projects to a GitHub
                                         account the Foundation controlled
                                         without advance notice.
                                         Foundation executive director
                                         Claire Novotny stepped down as
                                         the controversies swirled.


                      # § Security⠀➾


                            # ⚓ Russia_excluded_from_virtual_White_House
                              meeting_on_ransomware⠀⇛


                                   The White House on Wednesday will
                                   convene a virtual meeting on countering
                                   ransomware with senior officials
                                   representing 30 countries and the
                                   European Union, Biden administration
                                   officials said, as part of President
                                   Biden’s effort to work with global
                                   partners to address cyber threats.


                                   Ministers and senior officials from a
                                   range of countries will take part in
                                   the virtual meeting, though the
                                   attendees do not include
                                   representatives from Russia, which has
                                   been a key focus of the Biden
                                   administration in trying to root out
                                   criminal ransomware groups.


                            # ⚓ How_does_HTTPS_protect_you_(and_how_doesn’t
                              it?)_–_The_Mozilla_Blog⠀⇛


                                   It’s true that looking for the lock
                                   icon and HTTPS will help you prevent
                                   attackers from seeing any information
                                   you submit to a website. HTTPS also
                                   prevents your internet service provider
                                   (ISP) from seeing what pages you visit
                                   beyond the top level of a website. That
                                   means they can see that you regularly
                                   visit https://www.reddit.com, for
                                   example, but they won’t see that you
                                   spend most of your time at https://
                                   www.reddit.com/r/CatGifs/. But while
                                   HTTPS does guarantee that your
                                   communication is private and encrypted,
                                   it doesn’t guarantee that the site
                                   won’t try to scam you.


                                   Because here’s the thing: Any website
                                   can use HTTPS and encryption. This
                                   includes the good, trusted websites as
                                   well as the ones that are up to no good
                                   — the scammers, the phishers, the
                                   malware makers.


                                   You might be scratching your head right
                                   now, wondering how a nefarious website
                                   can use HTTPS. You’ll be forgiven if
                                   you wonder in all caps HOW CAN THIS BE?


                                   The answer is that the security of your
                                   connection to a website — which HTTPS
                                   provides — knows nothing about the
                                   information being relayed or the
                                   motivations of the entities relaying
                                   it. It’s a lot like having a phone. The
                                   phone company isn’t responsible for
                                   scammers calling you and trying to get
                                   your credit card. You have to be savvy
                                   about who you’re talking to. The job of
                                   HTTPS is to provide a secure line, not
                                   guarantee that you won’t be talking to
                                   crooks on it.


                                   That’s your job. Tough love, I know.
                                   But think about it. Scammers go to
                                   great lengths to trick you, and their
                                   motives largely boil down to one: to
                                   separate you from your money. This
                                   applies everywhere in life, online and
                                   offline. Your job is to not get
                                   scammed.


                            # ⚓ Security_updates_for_Wednesday_[LWN.net]⠀⇛


                                   Security updates have been issued by
                                   Debian (flatpak and ruby2.3), Fedora
                                   (flatpak, httpd, mediawiki, redis, and
                                   xstream), openSUSE (kernel, libaom,
                                   libqt5-qtsvg, systemd, and
                                   webkit2gtk3), Red Hat (.NET 5.0, 389-
                                   ds-base, httpd:2.4, kernel, kernel-rt,
                                   libxml2, openssl, and thunderbird),
                                   Scientific Linux (389-ds-base, kernel,
                                   libxml2, and openssl), SUSE (apache2-
                                   mod_auth_openidc, curl, glibc, kernel,
                                   libaom, libqt5-qtsvg, systemd, and
                                   webkit2gtk3), and Ubuntu (squashfs-
                                   tools).


                            # ⚓ Linux_Foundation_Raises_$10M_To_Expand_And
                              Support_Open_Source_Security_Foundation⠀⇛


                            # ⚓ Open_Source_Security_Foundation_Raises_$10
                              Million_in_New_Commitments_to_Secure_Software
                              Supply_Chains⠀⇛


                            # ⚓ Linux_Foundation_raises_$10M_to_support_open-
                              source_security_project_–_SiliconANGLE⠀⇛


                                   The funding came from members of the
                                   foundation. The long lineup: Dell
                                   Technologies Inc., Telefonaktiebolaget
                                   LM Ericsson, Facebook Inc., Fidelity
                                   Investments Inc., GitHub Inc., Google
                                   LLC, International Business Machines
                                   Corp., Intel Inc., JPMorgan Chase &
                                   Co., Microsoft Corp., Morgan Stanley,
                                   Oracle Corp., Red Hat Inc., Snyk Inc.,
                                   VMware Inc., Anchore Inc., Apiiro LLC,
                                   AuriStar Technologies Inc., Deepfence
                                   Inc., Devgistics, GitLab Inc., Nutanix
                                   Inc., Tidelift Inc. and Wind River
                                   Systems Inc.


                            # ⚓ The_World’s_Major_Technology_Providers_and
                              Converge_to_Improve_the_Security_of_Software
                              Supply_Chains⠀⇛


                                   Imagine you have created an open source
                                   project that has become incredibly
                                   popular. Thousands, if not millions, of
                                   developers worldwide, rely on the lines
                                   of code that you wrote. You have become
                                   an accidental hero of that community —
                                   people love your code, contribute to
                                   improving it, requesting new features,
                                   and encouraging others to use it. Life
                                   is amazing, but with great power and
                                   influence comes great responsibility.


                                   When code is buggy, people complain.
                                   When performance issues crop up in
                                   large scale implementations, it needs
                                   to be addressed. When security
                                   vulnerabilities are discovered —
                                   because no code or its dependencies are
                                   always perfect — they need to be
                                   remediated quickly to keep your
                                   community safe.


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ I_Lived_Through_the_US_Military’s_Culture
                                    of_Surveillance⠀⇛


                                         I know what it means to be
                                         watched all too carefully, a
                                         phenomenon that’s only grown
                                         worse in the war-on-terror years.
                                         I’m a strange combination, I
                                         suspect, being both a military
                                         spouse and an anti-war-on-terror
                                         activist. As I’ve discovered, the
                                         two sit uncomfortably in what
                                         still passes for one life. In
                                         this country in these years,
                                         having eyes on you has, sadly
                                         enough, become a common and
                                         widespread phenomenon. When it’s
                                         the government doing it, it’s
                                         called “surveillance.” When it’s
                                         your peers or those above you in
                                         the world of the military spouse,
                                         there’s no word for it at all.


                                  # ⚓ Who_should_police_the_web?⠀⇛


                                         For an example of how private
                                         firms have become the digital
                                         police, consider the rules on
                                         [Internet] pornography being
                                         introduced by Mastercard on
                                         October 15th. In a bid to weed
                                         out illegal material, the card
                                         firm is demanding that porn sites
                                         take steps that go beyond what
                                         the law requires, including
                                         reviewing footage before
                                         publication and checking the
                                         identity of those who upload or
                                         feature in it. Sites that think
                                         these sorts of rules too onerous
                                         are under no obligation to work
                                         with Mastercard. But Visa is also
                                         cracking down, and the two firms
                                         handle 90% of card payments
                                         outside China, meaning that they
                                         are becoming the industry’s de
                                         facto regulators.


                                  # ⚓ Microsoft_Agrees_to_Human_Rights_Review
                                    in_Deals_With_Law_Enforcement,_Government⠀⇛


                                         The move came in response to a
                                         June filing of a shareholder
                                         proposal asking the company to
                                         evaluate how well it sticks to
                                         its human rights statement and
                                         related policies. Microsoft
                                         committed to a review of any
                                         human rights impacts that its
                                         products have on those including
                                         communities of Black, Indigenous
                                         and People of Color in contracts
                                         for police, immigration
                                         enforcement and unspecified other
                                         government agencies, according to
                                         correspondence from the company
                                         viewed by Bloomberg.


                                  # ⚓ Samsung_is_the_worst_phone_for_privacy_in
                                    the_Android_market,_and_if_you_try_to_fix
                                    it,_they_will_punish_you._–_BaronHK’s
                                    Rants⠀⇛


                                         A new report shows that Samsung
                                         is the worst Android vendor for
                                         invasions of privacy.


                                         Among the problems unique to
                                         Samsung is that they’ve foisted
                                         Microsoft spyware and Clown
                                         Computing that phones home to
                                         Microsoft into the stock ROM as
                                         system apps.


                                         Also, LineageOS could fix it, if
                                         you could get it to run. But
                                         Samsung’s “security system” will
                                         break your camera for no reason
                                         whatsoever if you do, in their
                                         newer phones. This isn’t “Oh, the
                                         other firmware has no driver.”.
                                         It’s Samsung Knox preventing the
                                         camera from ever working again.


          o § Defence/Aggression⠀➾


                # ⚓ Kashmir:_Minority_killings_increase_amid_violent
                  demographic_tensions⠀⇛


                       The slew of killings has instilled fears in
                       thousands of migrants from minority Hindu and Sikh
                       communities. Many are refusing to leave their homes
                       or go to work this week. Others are fleeing Kashmir
                       for safety in India.


          o § Environment⠀➾


                # ⚓ Environmental_Justice_Advocates_Respond_to_Oil_Spill:_End
                  Neighborhood_and_Offshore_Oil_Drilling_Now⠀⇛


                       Governor Newsom’s oil and gas regulators have
                       continued granting offshore oil well permits also.
                       As of October 1, 2021, there have been a total of
                       150 reported permits issued for offshore wells
                       since January 1, 2019, according to a new analysis
                       of permits approved through October 1, 2021 and
                       posted at www.NewsomWellWatch.org by Consumer
                       Watchdog and FracTracker Alliance.


                       In the wake of another disastrous oil spill, CEJA
                       and VISION provided the following statements:


                # ⚓ Degrees_of_danger:_What_will_the_world_look_like_if_we_miss
                  our_climate_targets?⠀⇛


                       In 2015, almost all of the world’s nations agreed
                       to limit the temperature increase to 2 degrees
                       Celsius (3.6 F) above preindustrial levels, and to
                       aim for a limit of 1.5 C under the Paris
                       Agreement.  So far, the actual commitments made to
                       cut fossil fuel use and other measures to reduce
                       emissions of greenhouse gases into the atmosphere —
                       if carried through — will only get us down to 2.7 C
                       of warming, the UN has warned.


                # ⚓ EU_Commission:_Climate_change_‘most_comprehensive_threat’
                  facing_Arctic⠀⇛


                       The Arctic region has reached an “unprecedented
                       crisis point” due to climate change, a problem
                       which is the “most comprehensive threat” facing the
                       region, the EU Commission said in a joint statement
                       on Wednesday.


                # § Energy⠀➾


                      # ⚓ [Old] Will_PayPal’s_adoption_of_bitcoin_make
                        cryptocurrency_more_mainstream?⠀⇛


                             Cryptocurrencies are decentralised systems
                             with no official oversight, so regulation is
                             difficult. Registered companies that deal in
                             them are finding themselves under increasing
                             scrutiny. In June, the UK’s Financial Conduct
                             Authority ruled that Binance Markets Limited,
                             one of the world’s largest cryptocurrency
                             exchanges, had to cease regulated trading in
                             the UK.


                      # ⚓ Bitcoin_Uses_More_Electricity_Than_Many_Countries.
                        How_Is_That_Possible?⠀⇛


                             We’ll explain how that works in a minute. But
                             first, consider this: The process of creating
                             Bitcoin to spend or trade consumes around 91
                             terawatt-hours of electricity annually, more
                             than is used by Finland, a nation of about
                             5.5 million.


                             That usage, which is close to half-a-percent
                             of all the electricity consumed in the world,
                             has increased about tenfold in just the past
                             five years.


                      # ⚓ Anti-money_laundering_chief:_Cryptocurrency_licenses
                        should_be_revoked⠀⇛


                             Cryptocurrency operating licenses in Estonia
                             should be revoked, and the system rebuilt
                             from scratch, chief of the money laundering
                             bureau (RAB) Matis Mäeker told investigative
                             weekly Eesti Ekspress. Failure to do so may
                             result in another Danske-style financial
                             scandal. The news comes amid revelations that
                             despite a cull of license-holders in 2020,
                             over 400 cryptocurreny operators are still
                             active in Estonia.


                      # ⚓ EU_Pushing_for_Oil,_Coal_and_Gas_to_Stay_in_the
                        Ground⠀⇛


                             The European Commission argues that oil, gas,
                             and coal should not be extracted in the
                             Arctic if the climate goals are to be met, in
                             addition to its representing a risk for
                             environmental pollution in vulnerable areas,
                             and calls for an international moratorium on
                             hydrocarbon extraction in the Arctic.


                      # ⚓ EU_to_push_for_an_end_to_exploitation_of_Arctic_gas,
                        oil_and_coal⠀⇛


                             The document has been drawn up by the
                             European Commission and the bloc’s diplomatic
                             service. It is due to be finalized and
                             published this week. The strategy says Arctic
                             fossil fuel extraction needs to stop so EU
                             countries can meet targets in the 2015 Paris
                             Agreement to limit temperature rises from
                             global warming. It calls for a widening of
                             the scope of existing curbs on Arctic fossil
                             fuel exploration in the Arctic in areas of
                             the U.S., Canada, and Greenland.


                             EU member states would have to change their
                             behavior sharply under the new policy, since
                             they import Arctic fossil fuels including an
                             estimated 87% of liquefied natural gas
                             produced in the Russian Arctic. The new
                             strategy would not have legal force, but it
                             would create political pressure for member
                             states to comply.


                # § Wildlife/Nature⠀➾


                      # ⚓ Wall_Street’s_Takeover_of_Nature_Advances_with_Launch
                        of_New_Asset_Class⠀⇛


                             Last month, the New York Stock Exchange
                             (NYSE) announced it had developed a new asset
                             class and accompanying listing vehicle meant
                             “to preserve and restore the natural assets
                             that ultimately underpin the ability for
                             there to be life on Earth.” Called a natural
                             asset company, or NAC, the vehicle will allow
                             for the formation of specialized corporations
                             “that hold the rights to the ecosystem
                             services produced on a given chunk of land,
                             services like carbon sequestration or clean
                             water.” These NACs will then maintain, manage
                             and grow the natural assets they commodify,
                             with the end of goal of maximizing the
                             aspects of that natural asset that are deemed
                             by the company to be profitable.


                             Though described as acting like “any other
                             entity” on the NYSE, it is alleged that NACs
                             “will use the funds to help preserve a rain
                             forest or undertake other conservation
                             efforts, like changing a farm’s conventional
                             agricultural production practices.” Yet, as
                             explained towards the end of this article,
                             even the creators of NACs admit that the
                             ultimate goal is to extract near-infinite
                             profits from the natural processes they seek
                             to quantify and then monetize.


                             NYSE COO Michael Blaugrund alluded to this
                             when he said the following regarding the
                             launch of NACs: “Our hope is that owning a
                             natural asset company is going to be a way
                             that an increasingly broad range of investors
                             have the ability to invest in something
                             that’s intrinsically valuable, but, up to
                             this point, was really excluded from the
                             financial markets.”


          o § Finance⠀➾


                # ⚓ Hampster_Economics⠀⇛


                       Something about the obnoxious, carefree version of
                       the internet from my youth has always appealed to
                       me. I remember exactly where I was when the
                       Heaven’s Gate mass suicide went down and
                       periodically check the cult’s still-functioning
                       website. Even for a mass suicide cult, there’s
                       something innocuous and joyful in the way the
                       site’s displayed. The rainbow coloring, the dreamy
                       night sky background, the welcoming tone. I love
                       it. My love affair with the cutesy, silly part of
                       the internet started there, but never seemed to
                       end. In my teenage years, I must’ve watched every
                       Homestar Runner episode at least ten times. More
                       than anything though, Hampsterdance left an
                       indelible mark on the way I see the internet. The
                       focus of my own writing each week is branding and
                       it’s impossible not to compare the notoriety of
                       Heaven’s Gate and Homestar Runner against that of
                       the dancing Hampsters. Today’s Tedium ponders the
                       commercial viability of the Hampsterdance. — Jared
                       @ Tedium


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Bullying_Standard_Practice_for_Right-wing_Republicans⠀⇛


                # ⚓ The_View_From_Here:_Rethinking_What_Local_News_Can_and
                  Should_Be⠀⇛


                       Local news organizations are rethinking their
                       relationships with the communities they serve, from
                       deploying new messaging platforms that deliver news
                       to overhauling their reporting practices, editors
                       told ProPublica in a series of recent
                       conversations.


                       Amid increased polarization and a pandemic in which
                       misinformation has spread as fast as the virus,
                       editors in Atlanta, Phoenix and Detroit told us in
                       live virtual events that the notion of local news
                       as a public good is more relevant than ever.


                # ⚓ Facebook_increasing_protections_for_activists,_journalists
                  against_harassment⠀⇛


                       The platform’s policies surrounding how public
                       figures are treated include generally allowing
                       users to call for the death of a public figure so
                       long as they are not tagged in the post. Users are
                       not permitted to call for the death of private
                       users, a policy that will now extend to
                       journalists, Reuters reported.


                # ⚓ Does_This_Ring_A_Bell?⠀⇛


                       No matter your ultimate lean on politics, you have
                       to admit it’s pretty strange to sit with the
                       knowledge that OAN, a conservative news network,
                       was effectively funded by AT∓T, right? This is a
                       strange headline that kind of shakes through
                       people’s heads in part because of what AT∓T used
                       to represent, as the phone company that we all had
                       to use. (Now, at least with the dust settled, we
                       have something of a choice.) The irony of the
                       company that currently owns CNN bankrolling
                       something that is literally the opposite of CNN in
                       every way that matters is too bizarre to ignore.
                       Now combine this with the effect of Facebook’s many
                       negative headlines this week (including its
                       downtime), creating the real possibility that
                       Facebook is the AT∓T of social media (down to
                       the permissive approach around controversial
                       content) and might need to be broken up, and you
                       have some real knotty fodder to think about.
                       Today’s Tedium considers the messy effects of
                       AT∓T’s breakup with the Baby Bells in a modern
                       context.


                # ⚓ A_second_Facebook_whistleblower_says_she’s_willing_to
                  testify_before_Congress_and_that_she’s_shared_documents_with
                  a_US_law_agency⠀⇛


                       Zhang also said on Twitter on Sunday that she had
                       provided a US law-enforcement agency with “detailed
                       documentation regarding potential criminal
                       violations.”


                       When asked by CNN, Zhang did not say which agency
                       she gave documents to. An FBI spokesperson declined
                       to comment when contacted by CNN.


                # ⚓ Another_Facebook_whistleblower_says_she_is_willing_to
                  testify_before_Congress⠀⇛


                       Central to Zhang’s allegations about Facebook is
                       that it doesn’t do enough to tackle abuse of its
                       platform in countries outside of the United States.
                       Roughly 90% of Facebook’s monthly active users are
                       outside the US and Canada, according to its most
                       recent quarterly filing.


                # ⚓ Sophie_Zhang:_Second_Facebook_whistleblower_reports
                  ‘potential_criminal_violations’_to_authorities⠀⇛


                       “I’ve found multiple blatant attempts by foreign
                       national governments to abuse our platform on vast
                       scales to mislead their own citizenry, and caused
                       international news on multiple occasions. I have
                       personally made decisions that affected national
                       presidents without oversight, and taken action to
                       enforce against so many prominent politicians
                       globally that I’ve lost count.”


                # ⚓ Facebook_says_it_will_ban_content_that_sexually_harasses
                  celebrities⠀⇛


                       As part of this new policy update, Facebook said
                       that it would remove any profiles, pages, groups,
                       or events dedicated to sexualizing public figures,
                       including celebrities, politicians, and content
                       creators. The new policy bans sexualized photoshops
                       and drawings and any degrading content “in the
                       process of bodily functions,” Antigone Davis,
                       global head of safety at Facebook, said in a blog
                       post on Wednesday.


                       Facebook also said that it would remove “unwanted
                       sexualized commentary” and repetitive attacks
                       harassing an individual sexually.


          o § Censorship/Free Speech⠀➾


                # ⚓ LinkedIn_Caves_Again,_Blocks_US_Journalists’_Accounts_In
                  China⠀⇛


                       LinkedIn — the business-oriented social media
                       platform owned by Microsoft — has spent the last
                       few years increasing its compliance with the
                       Chinese government’s demands for censorship. A
                       couple of years back, the network drew heat for not
                       only blocking accounts of Chinese pro-democracy
                       activists but also critics of the government
                       located elsewhere in the world.


                # ⚓ Oppose_the_right-wing,_racialist_attack_on_composer_Bright
                  Sheng_at_University_of_Michigan⠀⇛


                       Sheng, the Chinese-born Leonard Bernstein
                       Distinguished University Professor of Composition,
                       is a world-class composer, who has been teaching at
                       the University of Michigan since 1995. He was a
                       Pulitzer Prize finalist and was given a MacArthur
                       “genius” fellowship in 2001. The Foundation
                       described him as “an innovative composer whose
                       skillful orchestrations bridge East and West,
                       lyrical and dissonant styles, and historical and
                       contemporary themes to create compositions that
                       resonate with audiences around the world.”


                       The “crime” for which Sheng has been forced out of
                       teaching the class has only been made possible by
                       the whipping up of racialist frenzy on the
                       university campuses and in the media. No honest or
                       fair-minded individual could find anything remotely
                       offensive about Olivier’s performance or the film
                       as a whole.


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


                # ⚓ Lee_Camp:_Julian_Assange’s_Father,_John_Shipton,_on_the
                  U.S._Government’s_‘Scandalous’_Plan_to_‘Murder’_His_Son⠀⇛


                # ⚓ [Old] 3_arrested_can_challenge_Louisiana_pipeline_trespass
                  law⠀⇛


                       The law “is part of a national effort to crack down
                       on environmental activists across the U.S.,” the
                       Center for Constitutional Rights, which represents
                       White Hat, Savage and Mejia, said in Thursday’s
                       news release. It said the first was passed in
                       Oklahoma in 2017, and said similar bills have been
                       introduced 23 times in 18 states since 2017,
                       including 14 in 2019.


                # ⚓ Covering_Myanmar_is_Becoming_Impossible,_Say_Local
                  Journalists⠀⇛


                       Access to social media and the [Internet] was
                       blocked, at least five local media outlets had
                       licenses revoked, and authorities detained dozens
                       of journalists covering nationwide protests against
                       the junta.


                       In the months that followed, media outlets have
                       been forced to restructure their operations by
                       working online or from self-imposed exile.


                       Win Zaw Naing, a journalist at the Yangon-based Red
                       News Agency, says he has been stuck inside his
                       house for seven months, having to work almost
                       entirely online.


                       “It is almost impossible to report on the ground
                       now. I did not leave the house and I did not see
                       anyone. I do it online, I make phone calls,” he
                       told VOA.


          o § Civil Rights/Policing⠀➾


                # ⚓ Minneapolis_Police_Caught_on_Video_‘Hunting’_Activists⠀⇛


                       The extraordinary footage was released last week by
                       the lawyer of a man who was caught up in an
                       exchange of fire with police that night. (That man,
                       Army veteran Jaleel Stallings, was exonerated by a
                       jury in September for acting in self defense.) The
                       footage, which was part of the evidence used in
                       Stallings’ trial, also shows Minneapolis cops
                       making racist comments, cursing protesters and
                       journalists, slashing the tires of parked cars — in
                       short, acting more lawless than the crowds they
                       were supposed to be controlling that night.


                # ⚓ Election_workers_accused_of_shredding_voter_applications⠀⇛


                       Preliminary information indicates that the
                       employees checked out batches of applications for
                       processing, and they are alleged to have shredded
                       some of the forms, the Fulton County statement
                       says. Fellow employees reported the alleged actions
                       to their supervisor Friday morning, and the two
                       employees were fired that day.


                # ⚓ The_Government’s_Secret_‘Google_Search’_Warrant_Trap⠀⇛


                       Keyword warrants are not new, but they are rare,
                       and they are little known by the broader public.
                       The Forbes documents provide hard proof of the
                       government’s judicial exercise of keyword warrant
                       in a 2019 Wisconsin case tracking down men
                       suspected of kidnapping and abusing a minor.
                       Investigators asked Google for data on anyone who
                       had searched for the victim’s name, her mother’s
                       name, and her address over a period of 16 days.


                       Other known uses of keyword warrants include
                       demands for information on Google searches for the
                       address of an arson victim who was a witness in the
                       racketeering case against crooner R. Kelly in 2020
                       and Google searches for a fraud victim in Minnesota
                       in 2017. It’s not just Google. Jennifer Lynch of
                       the Electronic Frontier Foundation points out that
                       keyword warrants were served to Microsoft and Yahoo
                       for searches on things like “pipe bomb” and “low
                       explosives” in the course of tracking down the 2018
                       Austin bombings. Additionally, Forbes was able to
                       track down the existence of a fifth keyword warrant
                       request in California in late 2020, but it was only
                       noted in a court docket, so we don’t know the
                       extent of the order.


                # ⚓ The_Boston_Marathon_bomber_case_reaches_the_Supreme_Court⠀⇛


                       “This case is the first case where the court is
                       confronted with an almost unlimited amount of
                       information through social media,” says George
                       Kendall, a capital defense lawyer. “So it was
                       really sort of surprising, to say the least, that
                       when the judge decided, ‘OK, we can do this in
                       Boston,’ that kind of question was not asked of
                       everyone.”


                # ⚓ Outrage_Grows_Over_Jailing_of_Children_as_Tennessee
                  University_Cuts_Ties_With_Judge_Involved⠀⇛


                       In the days after ProPublica’s investigation of the
                       juvenile justice system in Rutherford County,
                       Tennessee, one state lawmaker wrote that she was
                       “horrified.” Another called it a “nightmare.” A
                       third labeled it “unchecked barbarism.” A former
                       Tennessee congressman posted the story about the
                       unlawful jailing of kids and tweeted, “The most
                       sickening and unAmerican thing I’ve read about in
                       some time.” The NAACP Legal Defense and Educational
                       Fund called for a federal civil rights
                       investigation. A pastor, in his Sunday sermon in
                       Nashville, said: “We can’t allow this madness to
                       continue. These are our babies.”


                       And on Tuesday evening, four days after the story
                       published, the president of Middle Tennessee State
                       University notified faculty and staff that Donna
                       Scott Davenport, a juvenile court judge at the
                       heart of the investigation, “is no longer
                       affiliated with the University.” Davenport had been
                       an adjunct instructor at the school, which is based
                       in Murfreesboro, Tennessee. For many years, she
                       taught a course on juvenile justice. In 2015, she
                       was one of the university’s commencement speakers.


                # ⚓ The_General_Strike_of_2021⠀⇛


                # ⚓ Origin_and_Meaning_of_Critical_Race_Theory⠀⇛


                       In August 2021, the Brookings Institute reported
                       that at least eight states had passed legislation
                       banning the teaching of Critical Race Theory,
                       although only Idaho actually uses the phrase.


                       The modern iteration of Critical Race Theory begins
                       in the 1980s when legal scholars followed by social
                       scientists and educational researchers began to
                       employ CRT as a way of understanding the
                       persistence of race and racism in the United
                       States. Kimberlé Crenshaw, who teaches law at UCLA
                       and Columbia University and was an early proponent
                       of critical race theory, described it as “an
                       approach to grappling with a history of white
                       supremacy that rejects the belief that what’s in
                       the past is in the past, and that the laws and
                       systems that grow from that past are detached from
                       it.” Basically, Critical Race Theory rejects the
                       idea of colorblindness or legal neutrality and
                       argues that race and racism have always played a
                       major role in the formulation of American laws and
                       the practices of American institutions. It is a
                       study of laws and institutions that sifts through
                       the surface cover to look for underlying meaning
                       and motivation. As an academic discipline it does
                       not claim that everything about the United States
                       is racist or that all white people are racist. The
                       CRT lens examines laws and institutions, not
                       people, certainly not individual people.


                # ⚓ Ronald_Deibert_Provides_Statement_on_behalf_of_Chelsea
                  Manning_–_The_Citizen_Lab⠀⇛


                       Citizen Lab founder and director, Dr. Ronald
                       Deibert, recently provided a statement in the
                       context of Chelsea Manning’s inadmissibility
                       proceeding before the Immigration and Refugee Board
                       of Canada.


                       The statement proceeds in four parts. In the first
                       section, Deibert provides background context
                       regarding his professional experience and the
                       Citizen Lab’s work. In the second section, he
                       describes the Citizen Lab’s research activities in
                       detail and the academic and public interest impacts
                       of those activities. In the third section, he
                       summarizes certain events that have threatened or
                       aimed to chill the Citizen Lab’s research
                       activities in the past. In the fourth section, he
                       explains the chilling effects that a broad
                       interpretation of section 342.1 of the Criminal
                       Code and/or of subsection 16(2) of the Security of
                       Information Act (“SOIA”) could have on the Citizen
                       Lab’s scholarship and on related initiatives.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Facebook’s_Nick_Clegg_Makes_It_Clear:_If_You’re_Looking_To
                  Undermine_Section_230,_That’s_EXACTLY_What_Facebook_Wants⠀⇛


                       Facebook policy dude/failed UK politician Nick
                       Clegg has written an op-ed for USA Today confirming
                       what has been obvious to everyone who understands
                       Section 230, but (for reasons I don’t quite
                       understand) seems obscured from basically every
                       politician out there: >Facebook wants to destroy
                       Section 230. And it’s practically giddy that
                       politicians are so eager to grant it its wish,
                       while pretending that doing so will somehow hurt
                       Facebook.


          o § Monopolies⠀➾


                # ⚓ Amazon_copied_products_and_rigged_search_results_to_promote
                  its_own_brands,_documents_show⠀⇛


                       Amazon.com Inc has been repeatedly accused of
                       knocking off products it sells on its website and
                       of exploiting its vast trove of internal data to
                       promote its own merchandise at the expense of other
                       sellers. The company has denied the accusations.


                       But thousands of pages of internal Amazon documents
                       examined by Reuters – including emails, strategy
                       papers and business plans – show the company ran a
                       systematic campaign of creating knockoffs and
                       manipulating search results to boost its own
                       product lines in India, one of the company’s
                       largest growth markets.


                # § Patents⠀➾


                      # ⚓ Corner_office_podcast:_Managing_Salesforce’s_diverse
                        IP_needs [Ed: Software patents propaganda and other
                        nefarious agenda from Salesforce disguised as
                        'journalism' from the voice of patent trolls, Patrick
                        Wingrove]⠀⇛


                             David Simon, senior vice president of IP at
                             Salesforce, shares his views on Section 101,
                             Fintiv, the DMCA, and more


                      # ⚓ Europe’s_IPR_rules_need_to_be_strengthened_to_ensure
                        they_meet_current_and_future_challenges,_explains
                        Marion_Walsmann [Ed: Europe does not have "IPR rules";
                        it has laws for patents, copyrights, etc. and they're
                        not "rights; what we have here is lobbying that
                        namedrops "SMEs" and shameless (massive) lies about UPC
                        in the text below; What we basically have here is a
                        German EPP MEP frontally attacking small businesses by
                        lying about them while claiming to speak for them.]⠀⇛


                             Filing a single application, rather than
                             numerous national procedures, and obtaining a
                             single patent that is valid throughout Europe
                             will dramatically simplify the patent
                             application process and greatly reduce
                             corresponding costs. Pricey parallel lawsuits
                             would also be prevented [sic] by the Unified
                             Patent Court, while legal certainty would be
                             increased. [sic]


                      # ⚓ Patent_case:_In_re_Juniper_Networks_Inc.,_USA [Ed:
                        Texas run by corrupt judges who treat their courts like
                        for-profit corporations; the higher patent courts
                        belatedly tackle this corruption from the whackos of
                        Waco]⠀⇛


                             The federal district court in Waco, Texas
                             abused its discretion in denying Juniper
                             Networks’ motion to transfer six patent
                             infringement actions filed by a Texas-based
                             patent assertion entity to the Northern
                             District of California, the U.S. Court of
                             Appeals for the Federal Circuit has decided
                             in granting Juniper’s motion for a writ of
                             mandamus. The district court erred in its
                             analysis of the relevant public and private
                             public interest factors used for determining
                             whether the transferor or the transferee
                             district is the more convenient forum. For
                             example, concerning the most important
                             factor, the relative convenience of the
                             transferee forum for the potential witnesses,
                             Juniper identified 11 witness located in the
                             Northern District of California, while the
                             plaintiff—a company’s whose presence in Texas
                             appeared to be both recent and
                             ephemeral—identified only one witness (In re
                             Juniper Networks, Inc., September 24, 2021,
                             per curiam).


                      # ⚓ Opinion:_Tired_of_Brexit?_The_exhaustion_is_still_to
                        come! [Ed: Misusing the words "IP" (which are both
                        inappropriate for the subject at hand]⠀⇛


                             The UKIPO has still to decide on a path
                             forward for exhaustion after Brexit – but
                             with IP taking a back seat in government
                             circles, don’t hold your breath


                      # ⚓ Hanwha_Q-Cells_and_Hoyng_ROKH_Monegier_win_cross-
                        border_injunction_against_Longi [Ed: Instead of
                        journalism JUVE is now doing ads for law firms, puff
                        pieces thinly disguised as nothing but "case studies";
                        JUVE is just a PR agency now]⠀⇛


                             The ruling from Rotterdam District Court is
                             interesting because the Hanwha patent is
                             valid in 16 European countries, but not in
                             the Netherlands. Nevertheless, the court
                             issued a cross-border injunction for 9
                             countries. The court also ordered a penalty
                             sum capped at €5 million.


                             The Rotterdam court did have doubts as to
                             whether the Dutch Longi company directly
                             infringed EP 2220689 B1. It nevertheless
                             ruled that the distribution and sale of the
                             solar panels in Belgium, Bulgaria, Germany,
                             France, Liechtenstein, Portugal, Spain, the
                             UK and Switzerland is an unlawful act against
                             Hanwha Q-Cells. Therefore, the judges granted
                             the cross-border injunction for nine
                             countries (case ID: C/10/621252 / KG ZA 21-
                             563).


                      # ⚓ Restoring_the_America_Invents_Act:_legislative
                        measure_to_defend_post-grant_review_of_U.S._patents
                        welcomed_by_tech_industry,_patent_experts⠀⇛


                             About a year ago I described a complaint by
                             Apple, Google, Intel, and Cisco over then-
                             USPTO Director Iancu’s PTAB rulemaking as
                             “litigation to the rescue of legislation”
                             because the case was brought in defense of
                             the ideas underlying the Leahy-Smith America
                             Invents Act (AIA). Essentially, Mr. Iancu had
                             gutted the PTAB IPR (inter partes review)
                             part of the AIA by establishing a
                             discretionary-denial regime.


                             By now there is also hope for the PTAB IPR
                             process because of developments on other
                             fronts. The next USPTO Director may undo some
                             of Mr. Iancu’s rulemaking, and now there’s a
                             proposal in the United Senate that amounts to
                             “legislation to the rescue of (earlier)
                             legislation”: the Leahy-Cornyn Restore AIA
                             bill (“RAIA”). Sen. Patrick Leahy (D-Vt.),
                             one of the sponsors of the original AIA, is
                             now the President pro tempore of the Senate.
                             Sen. John Cornyn (R-Tex.) has also taken an
                             interest in patent policy for some time. Both
                             have a reputation for balanced positions on
                             patent enforcement: neither are they in the
                             “Coons camp” (which favors ever stronger
                             enforcement even of weak patents) nor could
                             they be reasonably accused of seeking to
                             weaken patent protection.


                             Litigation, executive action,
                             legislation–three ways to reverse Mr. Iancu’s
                             PTAB rules, any single one of which could do
                             the job. Executive action would potentially
                             be quickest (as it won’t take that much
                             longer until the new USPTO Director has been
                             named). Durability is the most important
                             quality of new legislation: the Restore AIA
                             would not only solve the problem at hand but
                             would also prevent it from reoccurring,
                             unless and until Congress would decide
                             otherwise.


                      # ⚓ Koenig_&_Bauer_wins_infringement_case_against
                        Hebenstreit [Ed: This is framed as a shameless
                        advertisement instead of actual reporting about a
                        patent case. JUVE is a marketing company now, which
                        occasionally lies for lobbyists.]⠀⇛


                             Koenig & Bauer has won the second instance of
                             the patent infringement case. However the
                             breach of trade secrets dispute is still
                             ongoing. The founders of Hebenstreit, based
                             in Ludwigsburg, are former employees of the
                             patent holder. Koenig & Bauer accuses them of
                             having used the company’s technical drawings
                             for their own business.


                             Koenig & Bauer, based in Würzburg, sued
                             Hebenstreit for patent infringement. Its EP 1
                             266 852 B1 protects a device for feeding and
                             stacking tabular goods. The technology is
                             used in metal pressing, where it stacks the
                             pressed metal plates on top of each other at
                             the end of the line. The speed of the
                             stacking process in particular, as well as
                             its precise coordination with the speed of
                             the press, plays an essential role. The
                             original patent applicant was LTG Mailänder,
                             which was acquired by Bauer + Kunzi (later
                             Koenig & Bauer-MetalPrint) in 2006.


                      # § Software Patents⠀➾


                            # ⚓ Prior_art_found_on_Heritage_IP_patent⠀⇛


                                   Unified is pleased to announce prior
                                   art has been found on U.S. Patent
                                   6,854,067, owned by Heritage IP, LLC,
                                   an NPE and subsidiary of IP Edge. The
                                   ’067 patent generally relates to a
                                   method and system for interaction
                                   between a processor and a power on
                                   reset circuit to dynamically control
                                   power states in a microcontroller. This
                                   patent has been asserted in district
                                   court against NXP, Resideo
                                   Technologies, Maytronics, Insulet
                                   Corp., August Home, and others.


                # § Trademarks⠀➾


                      # ⚓ Public_Backlash_Leads_Tusla_Park_To_Stop_Bullying
                        Coffee_Shop_Over_Trademark⠀⇛


                             A good public outcry and backlash can lead to
                             many, many good things. We see it here at
                             Techdirt all the time, particularly when it
                             comes to aggressive bullying episodes over
                             intellectual property. Some person or company
                             will try to play IP bully against some
                             victim, the public gets wind of it and throws
                             a fit, and suddenly the necessity over the IP
                             action goes away. Retailers, manufacturers,
                             breweries: public outcry is a great way to
                             end ridiculous legal actions.



                    ䷩ 𝚕𝚒𝚗𝚎 4586

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/14/epo-french-connection/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/14/epo-french-connection/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_EPO’s_Overseer/Overseen_Collusion_—_Part_XII:_The_French_Connection⠀✐


Posted in Europe, Patents at 5:48 pm by Dr. Roy Schestowitz


Series parts:


   1. The_EPO’s_Overseer/Overseen_Collusion_—_Part_I:_Let_the_Sunshine_In!
   2. The_EPO’s_Overseer/Overseen_Collusion_—_Part_II:_A_“Unanimous”
      Endorsement?
   3. The_EPO’s_Overseer/Overseen_Collusion_—_Part_III:_Three_Missing_Votes
   4. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IV:_The_Founding_States
   5. The_EPO’s_Overseer/Overseen_Collusion_—_Part_V:_Germany_Says_“Ja”
   6. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VI:_A_Distinct_Lack_of_Dutch
      Courage
   7. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VII:_Luxembourgish_Laxity
   8. The_EPO’s_Overseer/Overseen_Collusion_—_Part_VIII:_Perfidious_Albion_and
      Pusillanimous_Hibernia
   9. The_EPO’s_Overseer/Overseen_Collusion_—_Part_IX:_More_Holes_Than_Swiss
      Cheese
  10. The_EPO’s_Overseer/Overseen_Collusion_—_Part_X:_Introducing_the
      Controversial_Christian_Bock
  11. The_EPO’s_Overseer/Overseen_Collusion_—_Part_XI:_“General_Bock”_–
      Battistelli’s_Swiss_Apprentice?
  12. YOU ARE HERE ☞ The French Connection
                       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇French_INPI⦈_
 Exploring the role of the French delegation in the adoption of Battistelli’s
                        Vichyite “Strike Regulations”.


Summary: The EPO‘s presidency (led by Frenchmen for nearly_15_years_out_of_the
past_18_years; Benoît_Battistelli and António_Campinos are both French despite
their somewhat misleading surnames) is extremely unlikely to even be mildly
scrutinised by the French delegates because of a web of nepotism and
protectionism


At the 136th meeting of the EPO’s Administrative Council in June 2013, the
French delegation was headed by Yves_Lapierre who was assisted by his deputy
Fabrice Claireau.


Lapierre took over at the helm of the French INPI in August 2010 following
Battistelli’s appointment as EPO President.


“From this it would appear that Lapierre did not have much prior experience in
“IP” matters before taking over the top job at the INPI.”Before becoming head
of the INPI, Lapierre had worked at the French Atomic Energy Commission
(Commissariat à l’énergie atomique – CEA). Between 2003_and_2010 he was
employed at AREVA, a French multinational group headquartered in Paris and
specializing in nuclear power and renewable energy.


From this it would appear that Lapierre did not have much prior experience in
“IP” matters before taking over the top job at the INPI. Same as Battistelli
for that matter. It seems that he was mostly reliant on the guidance and
counsel of his subordinates for the purpose of running the national “IP”
office.


            🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Yves_Lapierre_and_Fabrice_Claireau⦈_
  The French representatives: head of delegation Yves Lapierre and his deputy
                               Fabrice Claireau.


In particular, when it came to EPO affairs, Lapierre was more or less dependent
on the “advice” provided to him by his deputy Fabrice Claireau.


Claireau was the INPI’s longtime Director of Legal and International Affairs.
Of particular significance here is that Claireau had already served in this
capacity under Battistelli during the latter’s tenure as head of the INPI
between 2004 and 2010.


                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Fabrice_Claireau⦈_
   Fabrice Claireau served as the INPI’s Director of Legal and International
Affairs under Benoît Battistelli from 2004 onwards. Source: INPI Annual Report
                                     2006.


Given Claireau’s key “advisory” role in relation to EPO affairs, it’s hardly
surprising that the French delegation under Lapierre gave its unquestioning
support to Battistelli and voted in favour of his Vichyite_"Strike_Regulations"
in June 2013.


“Of particular significance here is that Claireau had already served in this
capacity under Battistelli during the latter’s tenure as head of the INPI
between 2004 and 2010.”Some time later in April 2016 – after the Administrative
Council had passed_a_resolution trying to reign in Battistelli and curb his
abusive actions toward EPO staff – Lapierre made a statement to the French
press in which he confirmed the official French view that the “reforms” being
pursued by Battistelli were necessary and that it was important to implement
them.


On that occasion he did manage to express some disquiet about the manner in
which these “reforms” were being implemented: «les réformes sont nécessaires,
il est important de les mettre en place, mais ce qui m’interroge, c’est la
manière».


“Given Claireau’s key “advisory” role in relation to EPO affairs, it’s hardly
surprising that the French delegation under Lapierre gave its unquestioning
support to Battistelli and voted in favour of his Vichyite “Strike Regulations”
in June 2013.”It’s not quite clear what exactly Lapierre intended to convey
here, apart from trying to salve his own guilty conscience.


If you are prepared to advocate and rubber-stamp “reforms” which abrogate
fundamental rights – which is exactly what Lapierre and his peers on the
Administrative Council did in June 2013 – then you are essentially paving the
way for abuses of authority and a deleterious social climate. It makes no sense
whatsoever to call such measures “necessary” while at the same time purporting
to deplore their inevitable consequences.


Lapierre’s term at the head of the French INPI ended when he retired in
November_2016.


As for Claireau, he had departed from the INPI sometime earlier, towards the
end of 2014.


By a strange “coincidence” Claireau resurfaced shortly afterwards at the EU
trademark agency OHIM/EUIPO in Alicante where he was appointed [PDF] as chef-
de-cabinet to the agency’s Executive Director, António Campinos. The chef-de-
cabinet is responsible for the “cabinet” which assists and advises the
Executive Director in the general running of the agency and the implementation
of its strategy.


“…it’s difficult to avoid the impression that Claireau received his new
position in Alicante as a reward for his services as Battistelli’s faithful
“mole” on the French EPO delegation from 2010 onwards.”It’s not clear how
exactly Claireau managed to get this job because no vacancy notice can be
found. It thus remains unclear whether the position was filled by means of an
open competition or whether Claireau was simply parachuted into it by his
cronies in the “European IP Network”.


In any event, it’s difficult to avoid the impression that Claireau received his
new position in Alicante as a reward for his services as Battistelli’s faithful
“mole” on the French EPO delegation from 2010 onwards.


Claireau’s appointment to such a senior position in Alicante indicates that is
part of the inner “circle of trust” of the Battistelli-Campinos clique which
has come to dominate both the EPO and EUIPO to the detriment of their good
governance.


               🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Claireau_and_Martti_Enäjärvi⦈_
Claireau (left) with EUIPO “Special Advisor” Martti Enäjärvi (right) at a WIPO
                          Symposium in Krakow (2011).


Claireau’s soujourn in Alicante ended sometime in 2018 when he returned to
France to take up a position as legal advisor to the Secrétariat général des
affaires européennes (SGAE). His position as Campinos’ chef-de-cabinet in
Alicante was “inherited” by his deputy, Niloofar_“Nellie”_Simon. Simon later
joined Campinos at the EPO in Munich as predicted by Techrights in October
2018.


The SGAE where Claireau now works is a French government body under the
direction of the Prime Minister. It is responsible for inter-ministerial
coordination in European affairs and its function is to ensure the coherence
and unity of France’s position in relation to the EU and OECD.


“The SGAE where Claireau now works is a French government body under the
direction of the Prime Minister. It is responsible for inter-ministerial
coordination in European affairs and its function is to ensure the coherence
and unity of France’s position in relation to the EU and OECD.”More recently,
Claireau was spotted with Richard_Yung, a former Principal Director in the
EPO’s International and Legal Affairs Directorate who now heads the French
National Anti-Counterfeiting Committee (CNAC).


During the Battistelli era at the EPO, Yung was openly_critical of his
compatriot’s excesses. More recently, he seems to have become a rather
uncritical cheerleader for the French branch of Team UPC.


In May 2021, together with Max Brunner, an official from the French Ministry of
Justice, Claireau and Yung conducted an inspection of premises which have been
earmarked for the French division of the Unified Patent Court (UPC).


                   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Fabrice-Claireau-UPC⦈_
 Fabrice Claireau (left) inspecting premises earmarked for the UPC in Paris in
 the company of Richard Yung (right) and Max Brunner (centre) from the French
                             Ministry of Justice.


That more or less wraps up our look at the French representatives who gave
their unqualified endorsement to Battistelli’s Vichyite_"Strike_Regulations" in
June 2013.


“In May 2021, together with Max Brunner, an official from the French Ministry
of Justice, Claireau and Yung conducted an inspection of premises which have
been earmarked for the French division of the Unified Patent Court (UPC).”As
far as Lapierre and Claireau are concerned, one thing which can be said without
fear of contradiction is that during their time on the EPO’s Administrative
Council neither of them showed any particular concern for their duty of care to
EPO staff.


The inimitable duo were more at home rubbing shoulders with high-ranking
representatives of French industry such as Yves_Carcelle, CEO of Louis Vuitton,
which forms part of the luxury goods conglomerate LVMH controlled by the
prominent French plutocrat Bernard_Arnault.


              🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Claireau-and-Louis-Vuitton-CEO⦈_
 Claireau (left) and Lapierre (right) posing for a photo-op with Louis Vuitton
                      CEO Yves Carcelle (centre) in 2010.


Before concluding, it is worth noting that the position adopted by the French
delegation on the EPO’s Administrative Council is often followed by the
representatives from France’s traditional "Club_Med" allies, the Iberian
nations Spain and Portugal, as well as Italy.


“As far as Lapierre and Claireau are concerned, one thing which can be said
without fear of contradiction is that during their time on the EPO’s
Administrative Council neither of them showed any particular concern for their
duty of care to EPO staff.”In the case of Battistelli’s “Strike Regulations”,
Spain and Portugal followed the lead give by France and voted in favour.
However, as we shall see in due course, Italy decided to withhold its support
by abstaining.


In the upcoming parts we will take a look at the Spanish and Portuguese
delegations and we will return to the Italian delegation in a later part of the
series. █


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

                    ䷩ 𝚕𝚒𝚗𝚎 5007

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/14/epo-maladministration/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/14/epo-maladministration/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Another_Maladministration_Meeting_Comes_to_an_End⠀✐


Posted in Europe, Patents at 4:41 pm by Dr. Roy Schestowitz


Virtual ‘oversight’


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Lisa_Block_Tower:_EPO_Oversight,_EPO_Out_of_Sight⦈_


Summary: Did the EPO‘s overseeing body properly tackle Benoît_Battistelli‘s
illegal acts, authorised by that very same overseeing body? Don’t hold your
breath as António_Campinos continues to crack down on staff (maybe ILOAT will
rule on it in 2030)


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡋⣀⣰⠂⠀⠸⠶⠶⠀⠀⢀⠩⠝⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠻⡷⠔⠃⠀⠀⠀⠀⠀⣘⠻⠰⠓⢂⣛⣛⠛⠟⣑⡒⠒⠈⠛⢋⡩⠟⢻⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⢿⣇⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡆⠄⠀⠈⣥⣐⠂⡀⠸⢶⠀⠀⢰⣶⣶⢨⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣄⢸⣶⡇⣶⣎⡃⡛⠿⠘⠃⠘⠂⠀⠀⢸⣿⣿⠀⣿⡇⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⣃⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠉⡀⠀⣀⢀⣀⣀⣀⣀⢀⡀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢳⣶⣬⣛⣿⣿⣿⣎⣛⣭⡍⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣛⡃⠀⠀⠀⠀⠀⠀⠀⢛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣍⣡⣉⣙⡉⡉⣉⣁⠉⠉⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿
⣶⣶⡆⣒⣚⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡒⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠿⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⠁⠈⠁⠈⠈⠀⠀⠀⠀⠀⢸⣷⣦⣍⡻⢿⣿
⣿⣿⣇⢻⣿⣿⣿⣿⣿⢟⣛⣛⢿⡿⢿⣛⠟⣾⣿⡿⠿⠿⢿⣿⡟⠉⠉⠙⣿⣿⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⣐⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡛⢃⠛⠺⠚⢛⣛⣀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣶⣭
⣿⣿⢋⣼⣿⣿⣿⣿⣷⣿⣿⣿⡏⣳⣿⣿⡇⣿⣿⢠⣬⣿⣷⡖⠃⠀⠀⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠛⠛⠛⠓⠐⠛⠁⠘⠛⠀⠀⠀⢀⣀⣰⠖⢋⣭⠉
⣿⣿⣶⡍⣿⣿⣿⣿⣿⣟⣛⣛⣵⣷⣭⣛⢱⣿⢟⣈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣲⡖⠦⣦⡄⡤⡠⢦⢤⢴⢴⢴⠀⢸⣿⣿⣿⣿⡖⠀
⣿⣿⣿⣘⠻⢏⡾⣿⣿⣿⣿⣿⣿⣿⣷⣿⠇⡏⣼⣿⠿⠇⣶⣶⣤⡄⠀⢀⡀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⣶⡅⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠶⠖⠆⠷⠶⠶⠶⠂⠆⠀⠀⠀⠀⢰⣶⣯⣭⣿⣁⣀
⣿⣿⣿⣿⣿⣈⢉⢻⣿⣿⣿⡷⣯⣷⣶⣶⣿⢡⣿⣿⡶⢸⣿⣇⣿⡏⣾⣿⢻⣷⠀⣿⠆⣀⣀⡀⠀⠀⠀⠿⠿⢘⠻⣿⣿⣿⣿⣿⡟⢿⣿⢻⣿⣿⣿⣿⣧⣤⣤⡄⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⢠⣭⡍⠛⠛⠿⢿
⣿⣿⣿⣿⡿⣃⡀⠈⢙⣿⣹⡁⢸⣿⣿⣿⡏⣼⣿⣁⡂⣿⣿⠛⠛⢹⣿⡇⣿⣿⢰⡇⣼⣿⢹⣿⡆⣷⡶⢩⣥⡄⣀⠛⠿⠸⣿⣿⡇⢸⣏⠘⣿⣿⣿⣿⣾⣿⡿⠇⢀⣀⣠⣤⣶⣬⣁⣠⣴⣶⣤⣌⣛⡃⠀⠀⠀⣿
⣿⣿⣿⣿⣰⣿⣷⠀⠈⠛⠛⠃⠈⣿⣿⣿⣷⣭⣭⣛⡘⠿⠇⠀⠀⢿⣿⣸⣿⠇⢸⢰⣿⡏⣾⣿⢸⣿⣇⣿⡿⢹⣿⠿⠏⣴⣶⣬⣅⠠⠖⠒⠿⣿⢙⣫⣥⣶⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣇⢿⣿⣿⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠙⠛⣫⣾⢠⢸⣿⣱⣿⠇⢸⣿⣿⣿⠃⣿⣿⣶⢠⣿⣟⣽⣿⢰⣿⢿⣿⡆⣰⣭⠙⢛⣛⠠⢬⢡⡄⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠘⢿⣿⡟⣤⣶⡀⠀⠀⠀⠐⠌⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⠹⢷⣬⣭⣭⣆⠸⠿⢿⠃⣸⣿⣇⡀⣼⣿⢹⣿⡅⠘⢿⣧⡉⢁⣿⡟⣰⣿⢟⣿⡆⢰⣦⡄⣀⡉⠀⠿⣿⣿⣿⣿⣿⠿⠟⣋⣭⣴
⣿⣿⣿⡇⠀⠀⠉⠁⠻⠿⠃⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⠀⠀⢠⣤⡄⠀⠀⠻⢿⠀⠀⠀⠙⠛⠿⠀⠀⠀⣷⡍⣉⠛⡃⠿⠏⣾⣿⢸⣿⣎⣿⡏⣸⣿⢃⣿⡿⣬⣙⠃⣿⣿⣸⣿⠇⢿⣿⣶⣶⢉⣍⡐⠚⠋⣡⣼⣿
⣿⣿⣿⣿⣤⣀⣀⡀⡀⠀⠀⣀⣀⣠⣤⣝⢿⣿⣿⣿⣿⣶⣦⣍⡛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡅⣿⣷⠀⠀⠀⠀⠙⠛⠛⠡⢿⡟⢸⣿⣇⣿⡿⢸⣿⡟⣿⡿⠀⣸⣿⠇⢀⡀⢰⣶⣶⠸⠛⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣛⣋⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣦⠀⠀⠀⣰⣤⣄⠀⠀⠀⣿⡇⣫⡤⣿⣟⠀⠀⠀⠀⠀⠀⠀⣶⣦⠄⠂⣙⣋⠛⠃⠿⡿⣸⣿⠇⢃⣿⡟⠀⠿⠃⢈⣭⣶⢸⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡻⠿⡿⠀⠀⠀⠿⠇⠿⠋⣿⣿⣿⣶⣦⣄⣀⣤⡄⣛⠻⠀⠀⣿⣿⣶⣮⣥⠀⣀⠉⣼⡘⠛⠃⠀⣼⡇⢸⡿⠏⠈⠉⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣶⣿⡇⣿⣿⣿⣿⢿⣿⣿⣿⠇⣿⣿⡗⠀⣿⡿⠽⣿⣯⠨⣯⠀⢿⡇⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⢻⣿⣿⡗⢁⣶⠀⣬⣽⠀⠀⣿⣿⢶⣶⡯⠀⢄⡀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣙⠻⠗⠸⠛⣀⠻⢿⡆⠀⠿⠿⢻⣿⡏⢀⣿⠀⣿⡇⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣶⣦⡄⠀⠀⢠⣬⣅⣨⣥⣴⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓⠠⠄⠸⣿⡿⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣶⣤⣤⣴⣤⣌⢻⣻⣿⣽⣶⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣽⣿⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡙⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠠⣿⣿⣟⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢩⣭⣭⡍⣩⣍⣙⡛⠿⢛⣛⣃⠿⣿⣿⡿⠿⠿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⢿⣿⣿⣿⣿⣿⡇⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡏⠁⣿⣿⢹⣿⢰⣿⡏⣿⣧⢻⡏⣾⣿⢻⣷⢀⣿⡇⣶⣶⢰⣶⣶⣶⡎⣿⢋⣭⣭⣭⠛⣯⣭⣛⡻⣿⢟⣛⣛⡓⠝⠓⠿⡿⠿⠟⠳⠏⠏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢿⡟⢸⣿⠛⠃⣿⣿⠿⠟⢸⣿⣇⣿⡏⣾⢇⣿⡇⣿⣿⢸⣿⡇⣿⣿⢰⢸⣿⢃⣾⡇⣾⣿⢸⣿⡇⣿⣿⠛⣵⡇⣿⣿⢻⣿⢠⣿⡇⣴⣿⢻⣷⡄⣶⣶⢰⣶⣆⣶⣶⣶⣮⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠏⣿⣷⣆⣿⣿⣶⡆⣿⡿⢸⣷⢸⣿⣸⣿⡇⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠿⣸⡧⠙⢿⣷⣄⢸⣿⡇⣿⣿⣈⣉⡃⣿⣿⣼⣿⡇⢰⣿⡇⣐⣛⣛⣛⠿⢿⣿⣿⣿⣿
⣶⣦⣤⣤⣼⣿⣿⣿⣶⣶⣶⣶⣯⡅⣶⣶⣦⣭⣻⣭⣾⣿⣧⣝⣛⣛⣣⣌⡻⠿⠿⣣⣇⠿⠿⢸⣿⣇⠻⣿⣾⡿⢀⣿⡏⣾⣿⡇⣿⣇⣿⣿⢸⣿⡇⣿⣿⢹⣿⠇⣿⣿⣽⣿⢰⢸⣿⡇⣿⣿⣿⣿⣿⣷⣮⣍⣛⠿
⣿⠷⣻⣿⣿⣿⡿⣟⣟⣭⣿⣿⣿⡧⠭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⢰⣾⣷⣭⣵⣿⣿⣷⣬⣝⡋⣁⣘⠛⣃⠙⠛⠛⠛⣀⠿⠇⠿⠿⠘⠸⠿⠇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡱⣾⣿⣿⣿⣧⣾⣿⣿⣿⣾⣿⣿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣼⣿⣿⣿⣿⠟⠋⠉⠙⢻⡇⢟⣯⠀⡀⣀⣬⠩⢀⣿⣿⣿⣿⡿⠃⣷⠶⠾⣦⣍⠙⣿⣿⣿⣿⣿⣿⣿
⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣿⣿⣿⢀⣒⣀⠉⣿⡟⣉⡩⠍⠛⣿⣿⣄⣀⡀⣀⣼⣿⣶⣶⣴⣿⣶⢰⣾⡞⣿⣿⣿⣿⡇⢶⢯⠷⢒⣛⣛⣁⣿⡿⠿⢿⣿⣿⣿
⣧⣝⡛⣿⣿⣿⣿⣿⣽⣶⡾⡣⢊⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⣍⣥⣼⣿⣧⣙⣛⣛⣃⣿⣿⣿⣿⣿⣿⣿⠏⠙⠛⢸⣿⣿⡏⠻⠓⢹⣿⣿⣿⣿⣷⣶⡾⠿⠿⠿⣿⡏⠀⠀⠀⠀⢸⣿
⣿⣿⣷⣙⠅⠾⣿⣿⣿⣾⢟⣼⣿⣿⣿⣿⠿⢿⣛⣻⠟⣿⣿⣷⣤⣤⣤⣀⣀⣀⡼⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⣿⣷⣤⣤⣀⣤⣾⣿
⣿⡿⢟⣣⣤⠀⠁⢹⣿⣟⠉⣿⣿⣿⣶⣾⣿⢿⠿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣒⣤⣾⣿⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⠿⠇
⠫⢾⣿⡿⠛⠃⠀⠀⠛⠛⠀⢸⣿⣟⣛⣭⣵⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠏⠉⠉⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠿⢿⠿⢿⣿⡏⢀⣒⣂⠉⣿⠿⠿⠿⣿⣿⣿⣿⡟⠉⠀⠈⠉⢁⣤⣥
⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡏⠱⢾⡑⠶⣯⣶⠆⣿⣿⣌⣩⣭⣼⠁⣶⡆⠄⣸⣿⡟⠉⠁⠀⠀⠀⠀⣬⠴⢒
⢙⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣀⡲⠌⠙⢿⣿⣿⣉⣒⡒⠉⣿⣿⣿⡇⣤⡀⠙⠸⠟⢛⣀⠀⠀⣀⣀⠀⢀⣰⣶⣍⢰⡾⢱⡖⠈⠉⠙⢻⣿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣇⣀⠀⠀⢀⣘⠻⠗⣟⣸
⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣈⠛⢛⣃⣾⣿⣿⣏⣛⣛⣠⣿⣿⣿⣷⣬⣁⠘⠛⠰⣶⣶⠶⢂⡇⣤⣍⣨⡛⣛⡋⠀⠀⠉⠃⠀⠀⢀⣼⣿⣿⢁⣔⣖⡀⢹⣿⣿⣿⣿⠟⢛⡻⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣤⣤⣀⣀⣤⣤⣴⣶⣶⡿⣿⣿⣿⣿⣿⣿⡿⢛⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢉⠀⢰⣾⠏⠁⠀⠁⠈⣴⣿⡇⠀⠲⢒⣠⡍⠙⣿⣿⣿⣿⣦⣭⣭⣥⣾⣿⣿⣿⣿⠰⡾⣯⣥⡄⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣮⣭⣽⣭⣭⣶⣷⣶⣿⣿⣿⣿⣿⣿⡇⠶⣾⡥⢰⣿⣿⣿⣿⡇⠠⣶⡈⣿⣿⣷⣤⣤⣤⡾⠋⢀⡀⠀⣀⣀⣛⠿⣿⣿⣆⢾⣿⡿⠇⣿⣿⠿⠛⠻⠿⣿⣿⠀⠀⠀⠈⢻⣷⣤⣭⣭⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣇⡘⠿⢂⣿⣿⣿⣿⣿⣿⡇⠓⠶⠦⣴⣾⡍⡵⢆⣿⣿⣿⣷⣶⣶⣿⣿⣏⢠⣭⡇⠀⣿⣿⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠬⠥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣠⣿⣿⣿⣿⡿⠁⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⠉⠉⠉⠛⠻⣿⡏⣁⣒⢛⣥⢸⣿⣿⣿⣿⡏⠉⠀⠀⠉⠛⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠰⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠈⠉⠙⢿⣿⣿⠉⠡⣀⠘⠁⢀⡀⠛⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣿⣇⣛⣛⣈⣡⣾⣿⣿⣿⣿⣇⠐⠂⠰⠀⢀⣿⣿⡆⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿

                    ䷩ 𝚕𝚒𝚗𝚎 5091

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/14/github-expose-commences/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/14/github-expose-commences/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Microsoft_GitHub_Exposé_—_Part_I_—_Inside_a_Den_of_Corruption_and
Misogynists⠀✐


Posted in Microsoft at 9:01 am by Dr. Roy Schestowitz


Series parts:


   1. YOU ARE HERE ☞ Inside a Den of Corruption and Misogynists
          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GitHub: Where everything comes to die⦈
                                Et tu, GitHub?


Summary: Today we commence a new series that implicates Microsoft, GitHub,
Copilot, and Team Mono


LAST SUMMER we_mentioned_in_passing_the_story_of_Preston-Werner, who became
extremely rich by selling the_loss-making_GitHub to Microsoft. For Microsoft,
it was all about taking control over the rivals, so even a losing business was
worth it to them. The partner of Preston-Werner was abusive to staff; this is a
matter of public record.


But what has happened since Microsoft took over GitHub, besides_the_ICE
controversy?


“We’re outlining the series and we shall present things in a tidy, easy-to-
digest fashion over the coming weeks.”As we are going to show in the long
series (expected to last over a dozen parts) is that GitHub is now controlled
by hugely dodgy people, even predators. No sane project would accept
sovereignty or supremacy by such people; so far this week Microsoft boosters
have been trying_to_'soften'_an_ongoing_GitHub_scandal. But what we’re going to
show involves fraud, sexual abuse, and even theft. We’re outlining the series
and we shall present things in a tidy, easy-to-digest fashion over the coming
weeks. █


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣀⡀⠀⠀⠀⠘⠛⠓⠐⠿⠿⣿⣷⣶⣦⣤⣤⣤⠀⠀⣤⣄⠤⢄⣀⡄⠈⢻⣿⣿⠋⢁⣀⣀⣽⡏⢙⣿⠛⢻⣿⠉⢹⣯⡄⠀⣠⣤⣤⣤⣤⡄⠀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣿⣿⣿⣿⣿⣷⠀⠈⣿⡇⠀⣾⡟⠛⢻⡏⠉⣏⠀⢈⣹⡀⠘⠛⠃⠀⡏⠉⣿⡏⠉⡇⠀⣉⡉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⣿⣿⣿⣿⠟⠀⢰⣿⣧⠀⢿⣷⡆⢸⡇⠀⣿⠀⢸⣿⠂⢸⣿⡇⠀⡗⠀⣿⡇⠀⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠦⢼⣿⣿⠀⠀⣠⣿⣿⣿⣶⣤⣤⣤⣼⣧⣤⣿⣦⣤⣼⣤⣼⣿⣧⣤⣿⣤⣤⣤⣤⣧⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡿⠿⡿
⠷⣿⣷⣷⣯⣄⣍⠻⣿⣿⣿⣯⣽⡽⢿⣿⣿⣿⣿⡿⡿⢿⣿⣟⠛⠻⢿⢿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣿⣷⣶⢶⣿⣿⣿⣷⣷⣬⣵⣶⣷⣴⣲⣆⣌
⠞⢅⣵⣒⣾⣬⠺⡟⣿⣾⣿⡯⣷⣽⣗⣿⣗⣝⣿⣯⣮⣿⡞⣿⢭⣓⣿⣏⡿⡈⣿⢿⢷⣿⠏⣿⢿⣿⣻⡿⣽⣿⣿⢯⣿⣿⣫⣿⣟⣯⣿⣿⢻⡿⢷⣿⣿⣿⣟⢹⣟⢻⢿⡯⣿⣿⢻⣯⣻⣿⣿⢿⠿⠙⠯⠿⠿⠛
⠋⠃⠀⠈⠚⡁⠓⠱⠿⠆⠘⠛⠑⠮⠿⠡⠿⠹⣿⡧⣪⠿⠡⠿⣭⣏⣿⣭⣿⣤⣿⣤⣆⣼⣠⠿⣬⣆⠫⠿⠷⠸⢿⣶⣶⣿⣌⠷⣯⠿⢿⠖⠼⢧⠶⣿⡄⣼⣧⣼⣧⡼⣴⡿⢇⡝⢧⠼⠫⠏⠍⠛⢻⡂⠄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⣀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⣴⠒⣲⢨⡖⠺⣍⢻⣿⠩⣵⡟⢻⡟⡻⣻⣷⡺⡙⠲⠖⢺⣞⢏⡷⠒⣮⢳⣄⣲⡞⢲⡌⣲⣖⢲⡖⣲⣄⠉⠌⠉⠁⠁⠒⣁⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⠀⠐⠀⠀⠈⢿⣩⡢⡸⣇⣢⡟⣸⡘⠟⣸⣇⣸⣏⣅⣠⣉⣻⠆⠈⠐⣸⡟⢘⣯⣖⡿⠀⠋⣹⣏⣹⠇⣸⡏⣸⣏⣫⠀⠀⠀⠈⠀⠉⠁⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 5168

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/14/irc-log-131021/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/14/irc-log-131021/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Wednesday,_October_13,_2021⠀✐


Posted in IRC_Logs at 2:27 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/tr_text_version/irc-log-techrights-
      131021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-131021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-social-131021.txt
    * gemini://gemini.techrights.org/tr_text_version/irc-log-techbytes-
      131021.txt
Over HTTP:


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


                                      🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H                                     🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


===============================================================================
§ IPFS Mirrors⠀➾


CID                                              Description     Object type


                                                 IRC log for
 QmUeYCgMagUagLWBByAn7PjrXxzhPp6UUa7W7yzGAB6dJG #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmbJE3fKYNak14Ci68SdXNF7gsKJnrFTgL3y5vf3YDju7r (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmQ3NNNsSe9LNwBGPwiCH4yqYTuhoi23AqDWPxdarJMT4d social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmU8RuGwsgZ91KYRbMenVb66o41n8izMg5BXXFL8GoKU6X social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmWjpUZyzdmNu62BB9PxaQCXrwGZyEUsfFDcuhgYFP4dmV #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmWMWzDG3xMKgLxQjsxKKrepduryw3sKcevjzs69yChVrF (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmYXpRDf5sjz4ADhxWx6DMcoii9KQ2H735wmJC5q3Zpj32 #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmTjWgiJpK1GzzzBq1ANeTuNXJgW44tnMmKpmiAvXot82G (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmdjD3F5X1T9xbTPMY2Wrk5YUS8tfKUD5inGbqQ8rnJrpo



                    ䷩ 𝚕𝚒𝚗𝚎 5297

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/14/miguel-de-icaza-on-nat/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/14/miguel-de-icaza-on-nat/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Teaser]_What_Miguel_de_Icaza_Really_Thinks_of_the_CEO_of_Microsoft_GitHub⠀✐


Posted in Microsoft at 2:52 pm by Dr. Roy Schestowitz


                  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Miguel_de_Icaza_on_Nat⦈_
   Miguel_de_Icaza was speaking about Nat Friedman (both work at Microsoft)


Summary: Following the opening_of_a_new_series_about_Microsoft_GitHub we drop a
little teaser today; we expect dozens of parts to be released in the coming
weeks/months as facts are being validated and organised


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⢸⣿⣤⣼⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣩⣟⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠛⠻⠿⠛⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠒⡤⢰⢲⠰⢢⠀⣴⣠⠆⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 5342

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2021/10/14/so-called-reforms/#comments
    Gemini version at gemini://gemini.techrights.org/2021/10/14/so-called-reforms/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ EPO_Management_Tricks_EPO_Staff_Into_Taking_More_Paycuts⠀✐


Posted in Europe, Patents at 7:29 am by Dr. Roy Schestowitz


Summary: “Education and childcare reform” [sic] is an António_Campinos “reform”
in the same sense regressive salary reductions are just “adjustments”
(euphemism); Electronic opt-in gaffes, according to staff representatives, show
that the tradition of Benoît_Battistelli carries on at the Office, taking away
from staff for a few corrupt officials to milk the institution to death


“We sent a letter to the [EPO] President,” the Central Staff Committee of the
EPO writes, “to inform him that several colleagues who are opting into the New
Education Allowance System later realised that they are losing other benefits
such as the expatriation allowance supplement. It is only after seeing their
September payslip that they became aware of the disadvantageous situation.”


“The letter was sent the day before yesterday and someone has leaked it to
us.”Central Staff Committee (CSC) representatives aren’t the same as the union,
so the language is more diplomatic. The letter was sent the day before
yesterday and someone has leaked it to us. “The number of staff affected is not
merely accidental,” says the CSC. “The change of regulation and the information
provided are so extensive and cumbersome that many staff were unable to
identify accurately their own present and/or future situation and perform
complex calculations to compare the new scheme to the old scheme. We are
concerned that the Office considers the opt-in as immediately irrevocable
following a one-click on a webpage. We suggest that the administration provides
a grace period for staff wishing to reconsider their opt-in. It would show that
our Office strives to be a caring organisation.”


For the general public to better understand the situation at the EPO (or why
the EPO can no longer recruit suitable workers who can obstruct abstract
patents that lack novelty and/or merit), here’s the full letter as HTML:


     Reference: sc21122cl
     Date: 12/10/2021


     European Patent Office | 80298 MUNICH | GERMANY
     Mr António Campinos
     President of the EPO


     By email


     OPEN LETTER


     New Education Allowance System
     Electronic opt-in


     Dear Mr President,


     Several colleagues who are opting into the New Education Allowance
     System later realised that they are losing other benefits such as the
     expatriation allowance supplement. It is only after seeing their
     September payslip that they became aware of the disadvantageous
     situation.


     The number of staff affected is not merely accidental. The change of
     regulation and the information provided are so extensive and
     cumbersome that many staff were unable to identify accurately their
     own present and/or future situation and perform complex calculations
     to compare the new scheme to the old scheme.


     We are concerned that the Office considers the opt-in as immediately
     irrevocable following a one-click on a webpage.


     It is common practice, especially when an agreement affects the
     employment conditions and the employee might incur a financial loss,
     as it is the case here, to provide beforehand the agreement specified
     to the individual for confirmation with signature. The digital form
     should state explicitly and exhaustively the terms to which the
     individual agrees, to ensure that the transmission of information is
     voluntary and informed. Following receipt by the administration of
     the confirmation, the general rule is to set a retraction period
     before the agreement becomes final.


     For these reasons, we suggest that the administration provides a
     grace period for staff wishing to reconsider their opt-in. It would
     show that our Office strives to be a caring organisation.


     Finally, we would like to point at the importance of this matter as
     the EPO administration transitions towards a fully digitalised
     interaction with staff. Surely, other agreements will be made
     electronically in the future.


     Yours sincerely,
     Alain Dumont


     Chairman of the Central Staff Committee


Don’t worry about the Office. It already sits_on_a_big_mountain_of_money_it's
not_supposed_to_even_have! The authoritarian Frenchman still has the nerve to
moan about a “gap”… █


http://techrights.org/videos/campinos-gap.webm



                    ䷩ 𝚕𝚒𝚗𝚎 5472

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 10.14.21⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_14/10/2021:_LibreOffice_7.2.2,_Happy_Birthday_to_Jolla,_Ubuntu_21.10,
Devuan_GNU+Linux_4.0,_OpenBSD_7.0⠀✐


Posted in News_Roundup at 4:22 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Kubuntu_Focus_M2_is_renewed_with_Intel_Tiger_Lake_and
                  NVIDIA_RTX_30_–_itsfoss.net⠀⇛


                       Recently we have among us the third generation of
                       the Kubuntu Focus M2 , the renewal of the
                       professional laptop that stands out for its high
                       performance and for using the Ubuntu family member
                       as a pre-installed operating system, more
                       specifically the 20.04 LTS version.


                       The processor incorporated in the renewed Kubuntu
                       Focus M2 is the Intel Core i7-11800H ,
                       corresponding to the Tiger Lake generation and
                       incorporating 8 physical cores, 16 threads (2
                       threads per core), 24MB of Intel Smart Cache,
                       integrated Gen12 graphics ( Xe) and is capable of
                       working at a maximum frequency of 4.6GHz. It is
                       important to bear in mind that this component is
                       fixed and cannot be modified in the purchase
                       process.


                       The notebook also includes the latest generation of
                       NVIDIA graphics technology, offering a in the base
                       configuration 6GB RTX 3060 that can be replaced by
                       an 8GB RTX 3070 or a 16GB RTX 3080 . Here we find
                       one of the great buts of the product, since NVIDIA
                       does not care much about complying with the
                       standards , despite the many efforts that there are
                       to make them swallow them by force . Added to this
                       are the problems tearing that are usually present
                       when combining KDE Plasma with the official NVIDIA
                       driver, which is easy to solve as long as you are
                       willing to use the console. Hopefully with Wayland
                       the dynamics begin to change.


          o § Audiocasts/Shows⠀➾


                # ⚓ Building_the_New_Steam_OS_with_One_Script_–_Invidious⠀⇛


                       Let’s build out the perfect Linux Desktop and
                       document it as we go, so you can use Linux faster,
                       better, and more efficiently.


                # ⚓ Review:_The_EVICIV_Raspberry_Pi_All-In-One_Touchscreen_–
                  Invidious⠀⇛


                       EVICIV was awesome and sent me over a brand new
                       Raspberry Pi display so that I could review it, and
                       that’s exactly what I did. In this video, I’ll give
                       you my thoughts on this display and whether or not
                       I can recommend it.


                # ⚓ Review:_The_19″_Raspberry_Pi_Rack_Mount_from_52pi_–
                  Invidious⠀⇛


                       52pi sent their 19″ Raspberry Pi rack mount over to
                       the studio, so as always I gave it a full review.
                       In this video, I’ll talk about the pros and the
                       cons so you can make a decision for yourself as far
                       as if this product will fit your Pi-server use-
                       case.


                # ⚓ Behind_the_Distro_–_benny_Vasquez,_AlmaLinux_OS_Chair_of
                  the_Board_–_Invidious⠀⇛


                       I recently had a chance to chat with Benny Vasquez,
                       who was recently named the Chair of the Board of
                       Directors for AlmaLinux OS. In this conversation,
                       we chat about some of the things that led to the
                       creation of AlmaLinux itself, the community-focused
                       and inclusive nature of the project, the new board
                       position, and more!


                # ⚓ Bad_Voltage_3×37:_I_Will_See_Them_In_The_Fire⠀⇛


                       Stuart Langridge, Jono Bacon, and Jeremy Garcia
                       present Bad Voltage, in which whistles are blown,
                       audio is twitched…


                # ⚓ BSDNow_424:_Unveiling_OpenBSD’s_pledge⠀⇛


                       J language working on OpenBSD, Comparing FreeBSD
                       GELI and OpenZFS encrypted pools, What is FreeBSD,
                       actually?, OpenBSD’s pledge and unveil from Python,
                       and more.


          o § Kernel Space⠀➾


                # § Graphics Stack⠀➾


                      # ⚓ NVIDIA_495_Linux_Beta_Driver_Released_With_GBM
                        Support_–_Phoronix⠀⇛


                             NVIDIA 495.29.05 is out today as the first
                             public Linux driver in the 495 series.


                             Most exciting with the NVIDIA 495.29.05 beta
                             release is GBM API support! After years of
                             waiting and NVIDIA wanting to pursue an
                             alternative API instead after years of
                             pushing EGLStreams, NVIDIA’s proprietary
                             driver has finally adopted the Generic Buffer
                             Manager (GBM) API. This greatly enhances the
                             Wayland support for NVIDIA’s proprietary
                             driver stack and makes it compatible with a
                             lot more Wayland software. For example, the
                             likes of Sway should now run fine with this
                             new driver.


                      # ⚓ NVIDIA_Beta_495.29.05_rolls_out_with_GBM_for_expanded
                        Wayland_support_|_GamingOnLinux⠀⇛


                             NVIDIA has today released the 495.29.05
                             driver as a Beta in their New Feature Branch
                             and it’s a relatively big one.


                             The main highlight feature is that NVIDIA has
                             finally added support for the GBM API making
                             it more compatible with Wayland, this is
                             instead of EGLStreams that they were
                             previously pushing. Just another tick in the
                             box for running a Wayland system with NVIDIA
                             with it now using the same API as Mesa with
                             GBM.


          o § Benchmarks⠀➾


                # ⚓ 9-Way_H2’2021_Linux_OS_Performance_Comparison_On_Intel_Xeon
                  Scalable_Ice_Lake⠀⇛


                       While we recently looked at autumn 2021 Linux
                       distributions on Intel Tiger Lake for seeing how
                       these various latest distributions are competing on
                       client platforms, in today’s article is a look at
                       how well the latest Linux distributions perform
                       when using the latest-generation Intel Xeon
                       Scalable 3rd Gen “Ice Lake” server hardware with
                       two Xeon Platinum 8380 processors. AlmaLinux, Arch
                       Linux, CentOS Stream, Clear Linux, Debian, Fedora,
                       openSUSE, and Ubuntu were battling it out on this
                       Intel reference server.


                       The Linux distribution releases being compared for
                       today’s performance comparison included…


          o § Applications⠀➾


                # ⚓ Hashbrown_–_Simple_Tool_to_Verify_Your_Downloads_By
                  Checking_File_Hash⠀⇛


                       To verify downloaded packages, we do hash checks.
                       And Hashbrown is a simple graphical tool to
                       generate or verify file hash in Linux Desktop.


                       Software developers often provide cryptographic
                       hashes along with downloads, for users to ensure
                       the file or program matches the source. Usually,
                       they are MD5, SHA-1, and SHA-256 hashes.


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_Steam_with_Ubuntu_21.04_–_Unixcop⠀⇛


                       Today we will see how to install Steam with Ubuntu
                       21.04. This is the ultimate destination for
                       playing, discussing, and creating games. This is
                       the official statement of the Steam website. A
                       cross-platform where users can play or purchase
                       games. While surfing across the official site, I
                       was able to see more than five million gamers
                       online. Now. you can imagine of polarity level of
                       the platform.


                # ⚓ Get_the_colour_of_any_screen_pixel⠀⇛


                       I am currently investigating how to manage the
                       situation when bootup results in a black screen.


                # ⚓ How_To_Install_XFCE_Desktop_Environment_on_Debian_11_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       XFCE Desktop Environment on Debian 11. For those of
                       you who didn’t know, Xfce is a lightweight desktop
                       environment for UNIX-like operating systems. It
                       aims to be quick and light on system resources,
                       while still being visually appealing and user
                       friendly. Unlike GNOME and KDE desktops which are
                       heavier, but XFCE uses fewer system resources.


                       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 through the step-by-
                       step installation of XFCE on a Debian 11
                       (Bullseye).


                # ⚓ How_to_Access_Remote_Desktop_from_Browser_Using_TightVNC⠀⇛


                       VNC stands for (Virtual Network Computing) is an
                       open-source graphical desktop sharing tool for
                       managing and control machines remotely using a VNC
                       client called VNC Viewer.


                # ⚓ How_to_Add_a_User_to_Sudoers_on_Fedora_–_LinuxCapable⠀⇛


                       When installing Fedora, the user account created
                       during the initial setup should have access to sudo
                       rights. However, there may be a need to add
                       additional sudo users or make the default user have
                       sudo rights. This is a straightforward process with
                       a few commands.


                       In the following tutorial, you will learn to add a
                       user to the sudoers group on any Fedora system.


                # ⚓ How_to_Find_and_Kill_Zombie_Process_on_Linux⠀⇛


                       Brief: This is a quick tip on finding zombie
                       processes in Linux and then killing them. You also
                       learn a thing or two about processes and zombie
                       processes.


                       Before you learn about Zombie process, let me
                       recall what is a process in Linux.


                       In a few words, a process is a running instance of
                       a program in performance. It can be foreground
                       (interactive process) or background (not
                       interactive or automatic process). It can be a
                       parent (creator of other processes during run-time)
                       or child (process created by others) process.


                       In Linux, except for the first init (or systemd)
                       process with PID 0, every other process has a
                       parent process. Processes also have their own child
                       processes.


                       Don’t believe me? Use the pstree command in
                       terminal to look at the process tree to see the
                       ‘family tree’ of your system’s processes.


                # ⚓ How_to_Install_Cockpit_on_Debian_11⠀⇛


                       The Cockpit is a free and open-source server
                       management application sponsored by Red Hat. It
                       comes with a simple web-based admin interface to
                       manage the server through the web browser instead
                       of cli. It also provides information on CPU load,
                       filesystem statistics, processes, and further
                       information. It allows you to perform day-to-day
                       system administrative tasks including, creating and
                       managing users, troubleshoots network issues,
                       upload and download files, and more.


                       In this post, we will show you how to install and
                       use Cockpit on Debian 11.


                # ⚓ How_to_Install_Jenkins_on_Rocky_Linux_8⠀⇛


                       Jenkins is an open-source continuous build system.
                       It is a server-based application written in Java,
                       and it typically runs as a background service on
                       Windows or Unix machines. We use Jenkins to
                       automatically monitor the repository for changes of
                       our source code. As soon as someone pushes his/her
                       changes to the central source code repository,
                       Jenkins analyzes the new source files for changes.
                       If it finds that the source file has changed since
                       our last compilation, then Jenkins initiates a new
                       build on our Continuous Integration Server.


                # ⚓ How_to_Install_MongoDB_Compass_on_CentOS_8_–_Unixcop⠀⇛


                       MongoDB compass is the official GUI tool for
                       MongoDB. You can add, delete, update, create
                       Databases from GUI. It is specifically for someone
                       who finds querying data using commands difficult.


                       In this tutorial we will install mongoDB compass.


                # ⚓ How_to_Install_PHP_Composer_on_Debian_11⠀⇛


                       PHP Composer is a dependency manager for PHP. It
                       uses a composer.json file placed in your project
                       root which contains a description of the project,
                       including its dependencies and other information
                       such as author, license, and so on. With PHP
                       Composer, you can install all necessary libraries
                       to build a PHP application with just one command
                       from your terminal.


                       PHP Composer easily manages dependencies, libraries
                       of your project. It also allows you to make a
                       release of your application to other people or for
                       yourself. You can think about PHP Composer as npm,
                       bower, and bundler on JavaScript.


                       In this tutorial, we will show you how to install
                       Composer on Debian 11. All the steps should work on
                       other Debian-based distributions as well.


                # ⚓ How_to_Install_Zirkula_CMS_on_Ubuntu_20.04_–_VITUX⠀⇛


                       ZIkula means “plus” in Swahili language, so it
                       translates as “more than” or “something more”. The
                       name embodies what this project provides – an
                       extension beyond common web technologies with tools
                       like templates that help you create simple one-page
                       websites all the way up to complex applications
                       powered by Node JS modules & MVC architecture. You
                       can create anything from basic one-page websites to
                       sophisticated and powerful online apps with
                       Zikula’s user-friendly interface. It is very simple
                       to set up, so you will have no trouble making your
                       vision come alive.


                       In this guide, we’ll guide you through how to
                       install Zikula and all of its requirements on an
                       Ubuntu 20.04 system.


                # ⚓ How_to_Install_and_Configure_Postgres_14_Ubuntu_20.04⠀⇛


                       In this guide we are going to install Postgresql 14
                       in Ubuntu 20.04.


                       Postgresql is an open source object-relational
                       database system with over 30 years of active
                       development that has earned it a strong reputation
                       for reliability, feature robustness, and
                       performance. Postgres, is a free and open-source
                       relational database management system emphasizing
                       extensibility and SQL compliance. It was originally
                       named POSTGRES, referring to its origins as a
                       successor to the Ingres database developed at the
                       University of California, Berkeley. PostgreSQL is
                       used as the primary data store or data warehouse
                       for many web, mobile, geospatial, and analytics
                       applications. PostgreSQL can store structured and
                       unstructured data in a single product.


                # ⚓ How_to_check_your_CPU_in_a_Linux_system⠀⇛


                       To troubleshoot or build a software stack, you must
                       not only know what type of architecture you work
                       with, but also the details about your hardware and
                       its performance. When it comes to Linux, you can
                       gather that information via the command-line
                       interface. The Linux CLI can provide you with
                       detailed CPU information, such as the number of CPU
                       cores, CPU architecture and CPU usage.


                       You can use several specific commands to pull CPU
                       information from your hardware, regardless of
                       whether you use bare metal or virtualized hardware.
                       These commands should work on any Linux
                       distribution and should come preinstalled on your
                       systems.


                # ⚓ How_to_create_Bootable_USB_using_Ventoy_on_Ubuntu_21_–
                  Unixcop⠀⇛


                       Ventoy is a free and open source software to create
                       bootable USB drives in Linux and Windows
                       environment.


                       You don’t need to format your USB device everytime
                       you want it make bootable with another OS. you just
                       have to create a bootable USB drive once and add as
                       many as ISOs you want in future.


                       Ventoy will automatically create entries for the
                       newly added ISOs and add them to the boot menu.


                       Once you created the multiboot USB, boot your
                       system with the USB drive, select the ISO you want
                       to load and start using it.


                # ⚓ How_to_install_Chromium_Browser_on_Debian_11_(Bullseye)_–
                  VITUX⠀⇛


                       Google’s Chromium browser is a Google project. It
                       is an open-source web browser whose major objective
                       is to make online browsing safer and quicker for
                       all users. This browser is not designed for end-
                       users, but rather for developers or programmers,
                       because Google makes changes to its source code
                       practically every day. As a result, it is critical
                       to obtain the most recent version of this web
                       program. The Chromium browser is available for
                       nearly every Linux distribution, including Ubuntu,
                       Debian, CentOS, and Fedora, as well as Windows,
                       Android, and macOS.


                       In this tutorial, we will demonstrate how to
                       install the Chromium browser on the Debian 11
                       bullseye distribution. The instructions for
                       installing the Chromium browser will also work for
                       other Linux distributions such as Debian 10 buster,
                       Ubuntu, LinuxMint, and others.


                # ⚓ How_to_install_Chromium_Browser_on_Debian_11_(Bullseye)_–
                  VITUX⠀⇛


                       First of all, we need to know what is the openfire
                       which is one of Ignite open Realtime projects.


                       Open Realtime:


                       So Ignite Realtime is the community site for the
                       users and developers of Jive Software’s open source
                       Real Time Communications projects.Your involvement
                       is helping to change the open RTC landscape.


                # ⚓ How_to_install_Ubuntu_21.10_–_Invidious⠀⇛


                       In this video, I am going to show how to install
                       Ubuntu 21.10.


                # ⚓ How_to_manage_users_and_groups_in_Linux_|_Enable_Sysadmin⠀⇛


                       “What skills must Linux administrators have?” is
                       way too broad a question for any single article.
                       But there are plenty of general must-have sysadmin
                       skills—and user and group administration are chief
                       among them. Proper user account management enables
                       Linux to enforce access controls (permissions) and
                       audit who does what on the system.


                       The commands below are written for Red Hat
                       Enterprise Linux (RHEL) and RHEL-like
                       distributions, but the concepts apply to any
                       distribution of Linux. Knowing the skills and
                       commands outlined in this article (and its two
                       follow-up pieces, which dive deeper into user admin
                       and group admin) helps ensure you’re ready for the
                       day-to-day user and group administration tasks a
                       sysadmin is called on to do.


                # ⚓ How_to_use_PS_command_–_Unixcop⠀⇛


                       Using a system without monitoring what’s happening
                       in the background is not a good thing to do -
                       especially in Linux- because as a result, you may
                       be consuming resources in the wrong side of the
                       city, or your system may be not properly utilized
                       in the manner way.


                       There are some systems depend almost exclusively on
                       the GUI screens to monitor the system, and some
                       people may prefer this method, but we will talk
                       about one of the traditional, essential and
                       effective ways to monitor our Linux system which is
                       the PS command


                # ⚓ File_timestamps_in_Linux_–_atime,_mtime_and_ctime⠀⇛


                       In the Linux system, the system provides a file
                       with three timestamps, namely access timestamp
                       (atime), change timestamp (mtime), and change
                       timestamp (ctime). Linux stores the timestamp in
                       the Unix epoch instead of the actual date and time.
                       The Unix epoch is the number of seconds from 00:00:
                       00 on January 1, 1970.


                       This article will help you understand Linux file
                       timestamps and how file timestamps work. I have
                       used for all the examples in this article an Ubuntu
                       20.04 system. Let’s first discuss the definition
                       and how we can display it in our Linux system.


                # ⚓ How_to_Upgrade_to_KDE_Plasma_5.23_from_5.22⠀⇛


                       The KDE team announced the stable release of KDE
                       Plasma 5.23 with new features, improvements, and
                       bug fixes. Here, in this quick guide, we give you
                       the steps to upgrade to KDE Plasma 5.23 from 5.22.


          o § Games⠀➾


                # ⚓ Proton_Experimental_fixes_up_Satisfactory_networking_making
                  it_easier_to_join_others_|_GamingOnLinux⠀⇛


                       Satisfactory is a first-person open-world factory
                       building sim from Coffee Stain Studios and while it
                       works well on Linux with Steam Play Proton the
                       online networking had a big issue.


                       For people with multiple network connections,
                       trying to join others online would be problematic
                       and most of the time just not work at all with an
                       error message. There were workarounds like
                       disabling other connections but it obviously wasn’t
                       ideal and just another barrier. Thankfully the
                       Proton Experimental release from October 13 notes a
                       single change as “Fix connection issues in
                       Satisfactory on systems with multiple network
                       interfaces”.


                # ⚓ Lutris_0.5.9_Released_for_Easier_Access_to_Linux_Games_–
                  itsfoss.net⠀⇛


                       After almost a year of development , the gaming
                       platform has Lutris 0.5.9 been released , providing
                       tools to simplify the installation, configuration
                       and management of games on Linux. The project code
                       is written in Python and is distributed under the
                       GPLv3 license.


                       The project maintains a directory for quickly
                       finding and installing game applications, which
                       allows you to launch games in Linux with one click
                       through a single interface, without worrying about
                       installing dependencies and settings. Runtime
                       components for running games are supplied by the
                       project and are not tied to the distribution kit
                       used. Runtime is a distribution-independent set of
                       libraries that includes components from SteamOS and
                       Ubuntu, as well as various additional libraries.


                       Provides the ability to install games distributed
                       through the services GOG, Steam, Epic Games Store,
                       Battle.net, Origin and Uplay. At the same time,
                       Lutris itself acts only as an intermediary and does
                       not sell games, therefore, for commercial games,
                       the user must independently purchase the game in
                       the appropriate service (free games can be launched
                       with one click from the Lutris graphical
                       interface).


                # ⚓ Hacking_tactical_narrative-driven_RPG_Midnight_Protocol_is
                  out_now_|_GamingOnLinux⠀⇛


                       Developed by LuGus Studios who are known for
                       Liftoff: FPV Drone Racing, Midnight Protocol is all
                       about becoming a hacker who recently got doxxed and
                       has been targeted for blackmail by a shadowy branch
                       of government.


                       Played entirely with your keyboard, Midnight
                       Protocol is pretty much a game about revenge. You
                       were arrested after your details got leaked, let go
                       due to a lack of solid evidence and now you’re
                       jumping right back into the hacking game which is
                       against your parole but that’s not going to stop
                       you. It’s a game that blends together a turn-based
                       hacking feature, style-wise that part looks like
                       something out of the modern two Deus Ex titles with
                       a bunch of narrative drip-fed to you through emails
                       and other sources.


                # ⚓ Interplay_updating_many_classic_titles_on_Steam_to_add
                  support_for_Linux⠀⇛


                       Interplay Entertainment announced today they’re
                       updating many of their classic titles to support
                       Linux. A lot of it of course is thanks to the
                       excellent free and open source DOSBox, which allows
                       thousands of classic to play on modern systems
                       without much hassle.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ KDE_Plasma_5.23_Release_Brings_a_Fresh_Look_with
                        Performance_Updates⠀⇛


                             The 25th-anniversary edition – KDE Plasma
                             5.23 is released with brand-new features and
                             performance updates. Here’s what’s new.


                      # ⚓ KDE_celebrates_25_years_with_a_big_new_Plasma_desktop
                        release⠀⇛


                             Has it really been 25 years? That’s absolute
                             madness. I still remember trying out the
                             first released version of KDE. Plasma – 25th
                             Anniversary Edition is available now.


                             For this release a big user-facing change is
                             the new Breeze — Blue Ocean theme that has an
                             aim to make everything much more clear. Lots
                             of little enhancements like active elements
                             lighting up when a window gets focus,
                             scrollbars are bigger and more accessible but
                             redesigned to still look good. There’s some
                             more “glossiness and style to the desktop”
                             with lots of subtle added details. You can
                             also choose accent colours now in the system
                             settings (for highlighted items), allowing
                             you to adjust it without switching your
                             theme.


                      # ⚓ KDE_Plasma_5.23_Released_In_Marking_25_Years_Of_KDE⠀⇛


                             KDE Plasma 5.23 is officially out this
                             morning as the newest major open-source
                             desktop release and is known now as the KDE
                             25th Anniversary Edition.


                             The KDE community is celebrating the 25th
                             birthday of what started as the “Kool Desktop
                             Environment” and they now have this new
                             Plasma release that is in very good shape to
                             mark the occasion. KDE Plasma 5.23 / 25th
                             Anniversary Edition is very exciting with
                             countless improvements, much better Wayland
                             support that is good enough for day-to-day
                             use for most individuals, and a number of
                             other noticeable refinements throughout.


                      # ⚓ Plasma_–_25th_Anniversary_Edition⠀⇛


                             25 years ago today, Matthias Ettrich sent an
                             email to the de.comp.os.linux.misc newsgroup
                             explaining a project he was working on. The
                             latest and direct result of that email (plus
                             a quarter of a century of relentless
                             experimentation, development and innovation)
                             has just landed in KDE’s repositories.


                             This time around, Plasma renews its looks
                             and, not only do you get a new wallpaper, but
                             also a gust of fresh air from an updated
                             theme: Breeze – Blue Ocean. The new Breeze
                             theme makes KDE apps and tools not only more
                             attractive, but also easier to use both on
                             the desktop and your phone and tablet.


                             Of course, looks are not the only you can
                             expect from Plasma 25AE: extra speed,
                             increased reliability and new features have
                             also found their way into the app launcher,
                             the software manager, the Wayland
                             implementation, and most other Plasma tools
                             and utilities.


                      # ⚓ Happy_25th_KDE_|_Kdenlive⠀⇛


                             Happy 25th birthday KDE. We love being part
                             of this wonderful community! Join the party
                             at: https://25years.kde.org/


                      # ⚓ KDE_Plasma_5.23_Release_Marks_its_25th_Anniversary
                        With_Exciting_Improvements_–_It’s_FOSS_News⠀⇛


                             For years, KDE Plasma has been among the
                             most-used desktop environments. This is due
                             to its seemingly endless customization
                             options, flashy looks, and feature-filled
                             updates.


                             With KDE Plasma 5.23, the desktop environment
                             marks 25 years of work. Hence, this release
                             is also known as Plasma 25th Anniversary
                             Edition.


                      # ⚓ Plasma_25th_Anniversary_Edition_released⠀⇛


                             The KDE project is celebrating its 25th
                             anniversary with a special release of the
                             Plasma desktop.


          o § Distributions⠀➾


                # § New Releases⠀➾


                      # ⚓ KaOS_2021.10⠀⇛


                             Today KDE is celebrating its 25th
                             anniversary, to commemorate that event, KaOS
                             is releasing the 2021.10 ISO, including the
                             latest Plasma 5.23.0.


                             For installer Calamares there are three major
                             changes. Biggest one is the addition of a
                             bootloader selection module. For UEFI
                             installs it is now possible to select between
                             systemd-boot, rEFInd or no bootloader, all
                             presented in a nice, QML based GUI. Second
                             change is the addition of an interactive
                             keyboard preview in the keyboard setup page.
                             And third is the porting of the License page
                             to QML.


                      # ⚓ KaOS_2021.10_Is_Here_as_One_of_the_First_Linux
                        Distros_to_Ship_with_KDE_Plasma_5.23_Desktop⠀⇛


                             In celebration of KDE’s 25th anniversary, the
                             KaOS developers release KaOS 2021.10 with the
                             latest and greatest KDE Plasma 5.23 desktop
                             environment series, which also landed today.
                             This makes KaOS one of the first GNU/Linux
                             distributions to ship with KDE Plasma 5.23,
                             following close on the heels of KDE neon.


                             Therefore, if you want to install and use the
                             KDE Plasma 5.23 desktop environment on your
                             personal computer right now, you can either
                             download the KDE neon 20211014 release if you
                             like Ubuntu-based distributions, or KaOS
                             2021.10 if you want an Arch Linux-inspired
                             but independent distro. Both offer a rolling-
                             release model where you install once and
                             receive updates forever, including new KDE
                             Plasma versions.


                # § BSD⠀➾


                      # ⚓ OpenBSD_7.0⠀⇛


                             This is a partial list of new features and
                             systems included in OpenBSD 7.0. For a
                             comprehensive list, see the changelog leading
                             to 7.0.


                      # ⚓ OpenBSD_7.0_Released_With_RISC-V_64-bit_Port,_Better
                        Apple_Silicon_Support⠀⇛


                             Not only is Ubuntu 21.10 releasing today but
                             over on the BSD side of the table is the
                             debut this morning of OpenBSD 7.0.


                             OpenBSD 7.0 brings many improvements to this
                             security-minded BSD operating system. Some of
                             the many OpenBSD 7.0 changes include:


                             - RISC-V 64-bit system support with the
                             initial “riscv64″ platform added.


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ Red_Hat_Shares_―_Special_edition:_Red_Hat_Summit_2021
                        Virtual_Experience_recap⠀⇛


                             After a successful first run as a virtual
                             event last year, Red Hat Summit Virtual
                             Experience garnered more than 43,712* session
                             views globally in 2021. Spread out over a
                             couple of two-day events in April and June,
                             this year’s Summit was all about offering
                             attendees a way to “open your perspective.”


                             The two-part event included 177 keynotes,
                             breakouts, demos, and featured sessions, and
                             76 “Ask the Experts” sessions—all of which
                             are available on demand for one year after
                             their air dates. We also had five special
                             guests—actors Joseph Gordon-Levitt and Kumail
                             Nanjiani, musicians Ben Folds and Ahmir
                             “Questlove” Thompson, and philanthropist Mick
                             Ebeling—the Open Source Arcade, the #RHSummit
                             photo maker, the “Code is open” challenge,
                             the Open Neighborhood digital expo hall, and
                             lots of news. And it wouldn’t be Red Hat
                             Summit without a ton of Red Hat swag
                             available from the Cool Stuff Store.


                             In this special edition of Red Hat Shares,
                             check out highlights from the virtual event,
                             including featured keynotes, the top 10
                             sessions, our Red Hat Innovation Awards
                             winners, and more.


                      # ⚓ AlmaLinux_Foundation_chair_says_he_stepped_down_to
                        highlight_value_of_community_status⠀⇛


                             Igor Seletskiy, the founder of the AlmaLinux
                             distro created in December 2020 as an
                             alternative to CentOS, has explained that he
                             stepped down as chair of the AlmaLinux
                             Foundation in an effort to strengthen its
                             community status – though his company still
                             dominates the board.


                             AlmaLinux is one of several distros to have
                             sprung up, or demanded renewed attention, in
                             the aftermath of Red Hat’s decision to make
                             CentOS a late preview of what will become Red
                             Hat Enterprise Linux (RHEL) rather than a
                             binary-compatible rebuild. Other contenders
                             include Rocky Linux, founded by an original
                             co-founder of CentOS, and Oracle Linux.
                             AlmaLinux originated as a project of
                             CloudLinux, a company and commercial distro
                             which already tracked RHEL, and of which
                             Seletskiy is CEO.


                      # ⚓ Embracing_open_culture:_Fostering_innovation_and
                        resilience_through_organizational_change⠀⇛


                             The increasing popularity of hybrid work
                             arrangements has many organizations looking
                             for new organizational and cultural
                             strategies.


                             On top of this, the ability to quickly adapt
                             and innovate is increasingly critical to many
                             organizations’ survival, but innovation is
                             unpredictable and something you can neither
                             plan for nor control.


                             So what are leaders to do? How can you help
                             new hybrid teams work together productively?
                             How can you retain existing talent and
                             attract new people to your organization? How
                             can you encourage more rapid innovations and
                             harness them more effectively?


                             By deliberately reshaping your organizational
                             culture to a more open model, you can create
                             the conditions that enable more effective
                             hybrid teams and increase individual
                             engagement while also encouraging innovation,
                             flexibility and growth.


                      # ⚓ Emotional_intelligence:_6_powerful_phrases_of_future
                        CIOs_|_The_Enterprisers_Project⠀⇛


                             The events of the last year and a half have
                             proven how essential emotional intelligence
                             is for CIOs leading their technology
                             organizations through challenging times. “The
                             requirements to lead through complexity and
                             ambiguity, while using more influence rather
                             than formal roles of position and authority,
                             continue to grow,” says Noelle Akins,
                             leadership coach and founder of Akins &
                             Associates. High-EQ leadership is no longer
                             an option; it’s mandatory for success.


                             Emotional intelligence is evidenced in the
                             way individuals behave and – just as
                             importantly – the way they speak. “Quite
                             simply, words matter,” says Patrick Malone,
                             director of American University’s Key
                             Executive Leadership Programs and author of
                             “Leading with Love and Laughter: Letting Go
                             and Getting Real at Work.” “The way we
                             communicate is the most impactful tool for
                             building trust and bonds with our
                             colleagues.”


                             Earlier this year, we shared some simple yet
                             effective phrases that CIOs and IT leaders
                             use to practice and demonstrate their
                             emotional intelligence. “A key aspect of
                             emotional intelligence is relationship
                             management,” says Dr. Sunni Lampasso,
                             consulting psychologist, executive coach, and
                             founder of Shaping Success. “The ability to
                             communicate clearly and openly helps to
                             establish credibility and build trust.”


                # § Devuan Family⠀➾


                      # ⚓ Devuan_4_Chimaera_Release_Notes⠀⇛


                      # ⚓ Devuan_4.0_(Chimaera)_released⠀⇛


                             Devuan Developers are pleased to announce the
                             release of Devuan Chimaera
                             4.0 as the project's newest stable release.
                             This is the result of lots of
                             painstaking work by the team and extensive
                             testing by the wider Devuan
                             community.

                             We wish to thank all of you for the
                             incredible support given to Devuan.
                             Without your help and feedback, Devuan could
                             not be the reliable and
                             versatile distribution that it is.
                      # ⚓ Devuan_GNU+Linux_4.0_“Chimaera”_Released_for_Software
                        Freedom_Lovers,_Based_on_Debian_Bullseye⠀⇛


                             Dubbed “Chimaera” and based on the recently
                             released Debian GNU/Linux 11.1 “Bullseye”,
                             Devuan GNU+Linux 4.0 comes with Linux kernel
                             5.10 LTS by default and a choice of three
                             init systems, including sysvinit, runit, and
                             OpenRC.


                             Devuan is the GNU/Linux distribution you must
                             download and use if you want to have a Debian
                             GNU/Linux operating system installation
                             without the systemd init system. Devuan is
                             here for software freedom lovers!


                # § Canonical/Ubuntu Family⠀➾


                      # ⚓ Ubuntu_Linux_21.10_arrives,_bringing_developer-
                        focused_features_and_GNOME_40⠀⇛


                             Ubuntu is one of the most popular desktop
                             Linux distributions, and it serves as the
                             base for countless other desktop operating
                             systems, like Linux Mint and Elementary OS.
                             There are two major releases of Ubuntu each
                             year, and right on schedule, Ubuntu 21.10
                             “Impish Indri” has just been released. The
                             last major Ubuntu release was 21.04, dubbed
                             “Hirsute Hippo”.


                             Ubuntu 21.10 is not a Long-Term Support (LTS)
                             release, so it will only be updated for the
                             next nine months. If you don’t want to
                             upgrade regularly or prefer stability over
                             new features, Ubuntu 20.04 is the current LTS
                             release and will receive updates until April
                             2025. Impish Indri is the final interim
                             release before the next LTS release,
                             scheduled for April 2022. Developers can use
                             Ubuntu 21.10 to future-proof their work for
                             the next LTS, which will be supported until
                             at least 2032.


                             “As open source becomes the new default, we
                             aim to bring Ubuntu to all the corners of the
                             enterprise and all the places developers want
                             to innovate,” said Canonical CEO Mark
                             Shuttleworth. “From the biggest public clouds
                             to the tiniest devices, from DGX servers to
                             Windows WSL workstations, open source is the
                             springboard for new ideas and Ubuntu makes
                             that springboard safe, secure and
                             consistent.”


                      # ⚓ Ubuntu_21.10_Arrives_With_a_Customized_GNOME_40
                        Desktop⠀⇛


                             There’s a lot of new stuff in Ubuntu 21.10,
                             and our Linux expert Dave McKay broke it all
                             down in a post explaining what’s new in
                             Impish Indri. The prominent feature that
                             stands out is the customized GNOME 40
                             desktop, but there’s a lot to be intrigued
                             by.


                             With Ubuntu 21.10’s version of GNOME 40,
                             instead of seeing the Activities View when
                             you log in, you’ll see your usual desktop,
                             just like previous versions of Ubuntu, which
                             should create a more comfortable experience.


                             Of course, you can still access the
                             Activities View, which is a critical part of
                             the GNOME 40 experience.


                      # ⚓ Ubuntu_21.10_wants_to_mae_cloud-native_app
                        development_easier_for_all_|_TechRadar⠀⇛


                             Canonical, the corporate sponsor of the
                             popular Ubuntu distribution, has announced
                             the launch of their latest Ubuntu 21.10,
                             which they claim is “made for Ubuntu
                             developers.”


                             Code name Impish Indri, Canonical hails
                             Ubuntu 21.10 as the most productive
                             environment for cloud-native developers.


                             “From the biggest public clouds to the
                             tiniest devices, from DGX servers to Windows
                             WSL workstations, open source is the
                             springboard for new ideas and Ubuntu makes
                             that springboard safe, secure and
                             consistent,” remarked Canonical’s CEO, Mark
                             Shuttleworth.


                      # ⚓ Canonical_releases_Ubuntu_21.10_with_kernel_5.13_and
                        GNOME_40_–_Neowin⠀⇛


                             Canonical has announced the release of Ubuntu
                             21.10 Impish Indri with plenty of big changes
                             namely the Linux 5.13 kernel and GNOME 40.
                             This update also fixes a really annoying
                             Firefox issue, in previous Ubuntu releases it
                             took days for Firefox to receive the latest
                             updates but now the browser is packaged as a
                             snap managed directly by Mozilla and
                             Canonical so it’ll be updated quickly.


                             The new Linux 5.13 kernel introduces support
                             for more hardware. Notable in this update is
                             support for newer Intel and AMD chips such as
                             Intel Alder Lake S or AMD Aldebaran, support
                             for Microsoft Surface devices has been
                             improved and rudimentary support for Apple M1
                             is available. If you had hardware issues with
                             Ubuntu in the past, trying Ubuntu 21.10 may
                             see your issue resolved.


                      # ⚓ Canonical_unveils_Ubuntu_21.10⠀⇛


                             Ubuntu 21.10 adds GCC 11, PHP 8, Gnome 40,
                             WSLg, and a range of Ubuntu Docker container
                             images, according to Rob Gibbon, product
                             manager at Canonical. Additionally, “there’s
                             Apache Cassandra, packaged both as a Docker
                             container image and as a snap, giving DataOps
                             teams a new option for building and running
                             data-intensive Cassandra clusters.”


                             Another feature is the new GCC 11, which
                             Canonical called the de facto C/C++ compiler.
                             Improved static code analysis capabilities
                             have been added to automatically detect
                             vulnerabilities and help developers gain
                             better code security insights earlier in the
                             development cycle, the company said.


                      # ⚓ Ubuntu_21.10_wants_to_make_cloud-native_app
                        development_easier_for_all⠀⇛


                      # ⚓ Ubuntu_21.10_is_Available_Now!_Finally_Brings_the
                        Much_Awaited_GNOME_40_With_Ubuntu_Twist_–_It’s_FOSS
                        News⠀⇛


                             Ubuntu 21.10 is the last non-LTS release
                             before the next big LTS update. Codenamed,
                             Impish Indri, Ubuntu 21.10 will be supported
                             for nine months until July 2022.


                             Unless you want to try the latest and
                             greatest features, you should stick to Ubuntu
                             20.04 LTS and wait for Ubuntu 22.04 LTS.


                             Now that you can download and install Ubuntu
                             21.10 on your systems, let me highlight a few
                             things about this update.


                      # ⚓ Ubuntu_21.10_‘Impish_Indri’_is_Available_for
                        Download,_Here’s_What’s_New⠀⇛


                             The wait is over. The brand new release of
                             Ubuntu 21.10 ‘Impish Indri’ has hit the
                             download mirrors. Let’s check out what’s new!


                             Ubuntu 21.10 is a regular short term release
                             that will be supported for nine months. It
                             doesn’t sound like a lot but remember you
                             will be able to upgrade to Ubuntu 22.04 next
                             April and that is supported for at least 5
                             years.


                      # ⚓ Ubuntu_21.10_Releases_Impish_Indris_On_Desktops
                        Everywhere⠀⇛


                             Ubuntu is a popular choice for both new and
                             seasoned Linux users and with Ubuntu 21.10 we
                             see a new shell, Gnome 40, which starts up
                             with a new Activities view rather than a
                             blank desktop. The favorites bar is now at
                             the bottom of the screen, and looks more like
                             a Mac OS dock than ever. The app launcher
                             slides in from the left of the screen (but
                             this can be tweaked), with the workspaces –
                             virtual desktops – turned into thumbnails
                             while you’re using it. Rounded corners are
                             also noticeable on windows, Gnome apps, and
                             the workspace switcher.


                             Workspaces themselves have moved from a
                             vertical to a horizontal design, and there
                             are new touchpad gestures and keyboard
                             shortcuts for navigating them. Security is
                             enhanced by a clever new randomisation of the
                             kernel stack in memory at each system-call
                             entry on both the amd64 and arm64
                             architectures with, it is claimed, a minimal
                             impact on performance. Kernel Electric Fence,
                             a runtime memory error detector, is also
                             supported.


                      # ⚓ Ubuntu_21.10_brings_GNOME_40_debut_and_a_focus_on
                        devs⠀⇛


                             Ubuntu 21.10 comes out today, an interim
                             release with nine months of support, and the
                             first to use GNOME 40 for the desktop.


                             The Ubuntu release cycle delivers a new LTS
                             (Long Term Support) version every two years,
                             the next one being 22.04 in April. This means
                             that 21.10 is a handy preview of features
                             that may not get production use until 22.04.


                      # ⚓ Ubuntu_21.10_is_Now_Available_to_Download⠀⇛


                             Ubuntu 21.10 comes crammed with six months
                             worth of changes including the GNOME 40
                             desktop, a new GTK theme, a Firefox Snap app
                             by default, PulseAudio 15, and Linux 5.13 to
                             name but a few.


                             This release — the 35th Ubuntu release for
                             those keeping count — is backed by 9 months
                             of security updates, critical fixes, and
                             select software updates. If you install 21.10
                             (or upgrade to it from Ubuntu 21.04) you can
                             upgrade to Ubuntu 22.04 LTS next April — a
                             release supported for at least five years.


                      # ⚓ How_to_Upgrade_to_Ubuntu_21.10_Right_Now⠀⇛


                             Ubuntu 21.10 ‘Impish Indri’ has just been
                             released. If you are using Ubuntu 21.04, you
                             should be provided the option to upgrade to
                             Ubuntu 21.10.
                             However, this roll out will be gradual. This
                             means not everyone will be notified about the
                             availability of the new version immediately.
                             It may take a couple of weeks before you see
                             the upgrade option.


                             But what if you are itching to get your hands
                             on Ubuntu 21.10 that comes with GNOME 40 and
                             other new features? Do you really have to
                             wait? The answer is no.


                      # ⚓ Ubuntu_21.10_‘Impish_Indri’_is_out_now_with_GNOME_40,
                        Kernel_5.13_|_GamingOnLinux⠀⇛


                             After another 6 months of hard work following
                             the Ubuntu 21.04 release, Ubuntu 21.10 is out
                             now with it being supported until July 2022.
                             If you want long-term support (LTS), you’re
                             best sticking with Ubuntu 20.04.3 LTS but
                             there will be another LTS release in April
                             2022.


                      # ⚓ Ubuntu_21.10_Official_Flavors_Released,_Here’s_What’s
                        New⠀⇛


                             The official Ubuntu flavors released as part
                             of Ubuntu 21.10 include Kubuntu 21.10,
                             Xubuntu 21.10, Lubuntu 21.10, Ubuntu Studio
                             21.10, Ubuntu MATE 21.10, Ubuntu Budgie
                             21.10, and Ubuntu Kylin 21.10. As expected,
                             they come with all the internal changes of
                             Ubuntu 21.10, such as the Linux 5.13 kernel
                             and updated toolchain, as well as…


                             Kubuntu 21.10 features the latest KDE Plasma
                             5.22 desktop environment by default, namely
                             Plasma 5.22.5, which is accompanied by the
                             KDE Gear 21.08.1 and KDE Frameworks 5.86
                             software suites, Latte Dock 0.10, and Qt
                             5.15.2. Ubuntu Studio 21.10 also features the
                             KDE Plasma 5.22 desktop environment, but with
                             a different layout and a more darkish theme
                             by default.


                      # ⚓ Ubuntu_21.10_Impish_Indri_Now_Available_for_Download.
                        This_is_What’s_new⠀⇛


                             The final release of 2021 for Ubuntu – Ubuntu
                             21.10 Impish Indri is here, and we round up
                             the release in this page.


                      # ⚓ Ubuntu_21.10_Released_With_GNOME_40_Desktop,_Many
                        Underlying_Improvements⠀⇛


                             Ubuntu 21.10 “Impish Indri” is now officially
                             available as the latest six-month update to
                             Ubuntu Linux and also serving as the last
                             release prior to the next long-term support
                             cycle, Ubuntu 22.04 LTS.


                             Ubuntu 21.10 brings a wide variety of
                             improvements, most notably on the desktop
                             side switching to GNOME Shell 40 and offering
                             many improvements there including some theme
                             refinements. There are also many underlying
                             improvements to enjoy with Ubuntu 21.10, like
                             what gets us excited about kernel and
                             compiler upgrades along with other notable
                             package version bumps.


                      # ⚓ Ubuntu_Unity_21.10_Released_to_Keep_the_Unity7
                        Desktop_Alive_in_2021⠀⇛


                             Ubuntu Unity 21.10 is here today as part of
                             the upcoming Ubuntu 21.10 “Impish Indri”
                             release, but Ubuntu Unity still doesn’t have
                             the “official flavor” status. However, that
                             shouldn’t stop you from using this great
                             distribution on your personal computer if you
                             still want to use the Unity desktop
                             environment in 2021.


                             This release still uses the old Unity7
                             interface rather than the upcoming UnityX 10
                             desktop that the Ubuntu Unity team is
                             developing for some time now as the successor
                             of Unity7, which received new and updated
                             indicators, and saw the migration of the
                             glib-2.0 schemas to gsettings-ubuntu-schemas.


                      # ⚓ Ubuntu_21.10_brings_GNOME_40,_Linux_5.13,_and_more⠀⇛


                             The latest version of Ubuntu is here, and
                             Ubuntu 21.10 “Impish Indri” brings a number
                             of updates to the core of the popular Linux
                             distribution including a newer kernel, an
                             updated desktop environment, and many other
                             improvements.


                             While Ubuntu 21.10 will only be officially
                             supported for 9 months, it paves the way
                             Ubuntu 22.04 LTS, which is arriving in April.
                             As a long term support release, Ubuntu 22.04
                             will be supported at least until 2032.


                      # ⚓ Canonical_Launches_Ubuntu_21.10_With_Few_Surprises⠀⇛


                             Canonical on Thursday released Ubuntu 21.10,
                             Impish Indri. The new version of its flagship
                             OS has a heavy focus on cloud-native, AI/ML,
                             and Ubuntu developers on Windows.


                             This is not a major distro upgrade. Rather,
                             it is a holding action that is not a long-
                             term release either. Nonetheless, Ubuntu
                             21.10 does play catch up with the latest
                             Wayland improvements and GNOME 40 — finally.


                             The cloud-native and underbelly improvements
                             add considerable zest to Ubuntu 21.10’s
                             productivity and performance ratings,
                             however. That is not a bad assessment for an
                             otherwise minor upgrade release.


                      # ⚓ Download_Ubuntu_Linux_21.10_Impish_Indri⠀⇛


                             Is Ubuntu the best Linux-based operating
                             system? That is a matter of opinion, but I
                             would say no. While it is a great OS, there
                             are other distributions that are arguably
                             better. Is Ubuntu the most popular Linux
                             distro? Not likely. These days, it isn’t even
                             in top five on DistroWatch.


                             With all of that said, new Ubuntu releases
                             still seem to generate the most excitement in
                             the Linux community. This is partly due to
                             Ubuntu’s name recognition, but also, there
                             are many great distributions based on Ubuntu,
                             such as Linux Mint, Pop!_OS, and elementary
                             OS to name a few. Let us not forget the
                             excellent official flavors of Ubuntu, such as
                             the KDE Plasma-focused Kubuntu.


                      # ⚓ Ubuntu_21.10_“Impish_Indri”_Is_Now_Available_for
                        Download,_This_Is_What’s_New⠀⇛


                             Dubbed as the “Impish Indri,” Ubuntu 21.10
                             has been in development for the past six
                             months and comes as an upgrade to the Ubuntu
                             21.04 “Hiruste Hippo” release, which will
                             reach end of life on January 2022. Ubuntu
                             21.10 is supported for the next nine months,
                             until July 2022, so it’s the obvious upgrade
                             choice.


                             The biggest new feature of Ubuntu 21.10
                             “Impish Indri” is the GNOME 40 desktop
                             environment. This is the first Ubuntu release
                             to ship with a complete GNOME 40 desktop, as
                             the Ubuntu 21.04 release only offered GNOME
                             40 apps on top of the GNOME 3.38 desktop
                             environment.


                      # ⚓ Ubuntu_MATE_21.10_Release_Notes⠀⇛


                             The significant change in Ubuntu MATE 21.10
                             is the introduction of MATE Desktop 1.26.0 ✨
                             which was 18 months in the making. Thanks to
                             the optimisations in MATE Desktop 1.26,
                             Ubuntu MATE 21.10 is faster and leaner.


                             Here are the highlights of what’s changed
                             since the release of Hirsute Hippo.


                      # ⚓ You_Can_Now_Upgrade_Ubuntu_21.04_to_Ubuntu_21.10,
                        Here’s_How⠀⇛


                             Dubbed Impish Indri, Ubuntu 21.10 introduces
                             several new features and improvements, such
                             as Linux kernel 5.13 for better hardware
                             support, GNOME 40 desktop environment,
                             Wayland session enabled for NVIDIA GPU users,
                             as well as updated apps and internals with
                             the most recent GNU/Linux technologies.


                             Ubuntu 21.04 “Hirsute Hippo” is supported for
                             only nine months, until January 2022, so you
                             might want to upgrade to a new release,
                             Ubuntu 21.10 in this case, which is supported
                             for another nine months, until July 2022.


          o § Devices/Embedded⠀➾


                # ⚓ Using_Raspberry_Pi_400_keyboard_PC_as_a_USB_keyboard_for
                  your_PC⠀⇛


                       Let’s try not to get confused, but you can now use
                       Raspberry Pi 400 keyboard PC as a standard USB
                       keyboard, optionally with a mouse attached to it,
                       for your computer, or twisted minds may even
                       connect it to a Raspberry Pi SBC… “But why?” you
                       may ask. Because we can.


                       That’s now possible thanks to work from Phil Howard
                       (Gadgetoid), software lead of Pimoroni, and his
                       Pi400kb project which implements a raw HID keyboard
                       forwarder that turns the Raspberry Pi 400 into a
                       standard USB keyboard.


                # ⚓ Wooting_announced_the_new_analog_60%_Wooting_60HE_keyboard
                  |_GamingOnLinux⠀⇛


                       Over here we’re a fan of Wooting, since they fully
                       support Linux with their products. It’s still
                       pretty rare since other vendors don’t but their
                       Wootility application is cross-platform and appears
                       to work quite well and they have a bunch of what’s
                       used up on GitHub too.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ Samsung_Galaxy_S21_range_will_probably_get_Android_12
                        by_December_|_TechRadar⠀⇛


                      # ⚓ Android_12_review:_The_Pixel-exclusive_feature_fest⠀⇛


                      # ⚓ Get_Android_12_on_your_Exynos_Galaxy_S10_with_this
                        LineageOS_19.0_ROM⠀⇛


                      # ⚓ Google_Maps_Getting_New_Widget_to_Let_Android_Users
                        Start_Navigation_Right_From_the_Home_Screen:_Report_|
                        Technology_News⠀⇛


                      # ⚓ Happy_Birthday_Jolla!⠀⇛


                             Ten years back from today, our super excited
                             founding crew including myself (Sami
                             Pienimäki), Marc Dillon, Stefano Mosconi,
                             Jussi Hurmola, and Antti Saarnio, took the
                             founding papers of Jolla Ltd to the Finnish
                             Patent and Registration Office, and the story
                             of Jolla started officially. Soon after this,
                             many individuals from the former MeeGo team
                             joined the Jolla company to give birth to
                             Sailfish OS.
                             I say ‘officially’ for Jolla, since as most
                             of you know, the story had already begun
                             years before this in the vibrant and
                             enthusiastic MeeGo team at Nokia, and the
                             passionate community around it. Back in 2010,
                             Nokia was on full speed to make MeeGo its
                             primary smartphone operating system, but
                             after a change in strategy, MeeGo was
                             discontinued in February 2011.


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


                # § Productivity Software/LibreOffice/Calligra⠀➾


                      # ⚓ LibreOffice_7.2.2_Community_Released_with_68_Bug
                        Fixes,_Update_Now⠀⇛


                             The LibreOffice 7.2 office suite was released
                             in mid-August 2021 with many new features and
                             improvements for all of its core components,
                             including Writer, Calc, Impress & Draw, Math,
                             and Chart, native support for Apple M1
                             machines, as well as improved
                             interoperability with the MS Office document
                             formats.


                             LibreOffice 7.2.2 is here about a month after
                             the LibreOffice 7.2.1 point release to fix
                             even more bugs and security issues. According
                             to the RC1 and RC2 changelogs, there are a
                             total of 68 bug fixes, so you should update
                             your installations as soon as possible.


                      # ⚓ The_Document_Foundation_announces_LibreOffice_7.2.2
                        Community⠀⇛


                             The Document Foundation announces LibreOffice
                             7.2.2 Community, the second minor release of
                             the LibreOffice 7.2 family targeted at
                             technology enthusiasts and power users, which
                             is available for download from https://
                             www.libreoffice.org/download/. This version
                             includes 68 bug fixes and improvements to
                             document compatibility.


                             LibreOffice 7.2.1 Community is also available
                             for Apple Silicon from this link: https://
                             download.documentfoundation.org/libreoffice/
                             stable/7.2.2/mac/aarch64/.


                             For enterprise-class deployments, TDF
                             strongly recommends the LibreOffice
                             Enterprise family of applications from
                             ecosystem partners, with long-term support
                             options, professional assistance, custom
                             features and Service Level Agreements: https:
                             //www.libreoffice.org/download/libreoffice-
                             in-business/.


                             LibreOffice Community and the LibreOffice
                             Enterprise family of products are based on
                             the LibreOffice Technology platform, the
                             result of years of development efforts with
                             the objective of providing a state of the art
                             office suite not only for the desktop but
                             also for mobile and the cloud.


                # § Programming/Development⠀➾


                      # ⚓ Qt_Creator_6_Beta_Released_With_Updated_C++_Code
                        Model,_Binaries_Built_Against_Qt_6.2_–_Phoronix⠀⇛


                             With Qt 6.2 LTS having shipped at the end of
                             September, The Qt Company is now turning
                             their attention to Qt Creator 6 as the next
                             version of their Qt/C++ focused integrated
                             development environment.


                             Qt Creator 6.0 Beta is out this morning as
                             the first public test release of this Qt/C++
                             IDE. Qt Creator 6 Beta has moved launching of
                             external processes to a separate server
                             process for better handling on Linux and the
                             C++ code model is re-based to that from LLVM
                             13.


                      # ⚓ Qt_Creator_6_Beta_released⠀⇛


                      # ⚓ 5_common_bugs_in_C_programming_and_how_to_fix_them_|
                        Opensource.com⠀⇛


                             Even the best programmers can create
                             programming bugs. Depending on what your
                             program does, these bugs could introduce
                             security vulnerabilities, cause the program
                             to crash, or create unexpected behavior.


                             The C programming language sometimes gets a
                             bad reputation because it is not memory safe
                             like more recent programming languages,
                             including Rust. But with a little extra code,
                             you can avoid the most common and most
                             serious C programming bugs.


                      # ⚓ Steinar_H._Gunderson:_Apache_bug_with_mpm-itk⠀⇛


                             It seems there’s a bug in Apache 2.4.49 (or
                             newer) and mpm-itk; any forked child will
                             segfault instead of exiting cleanly. This is,
                             well, aesthetically not nice, and also causes
                             problems with exit hooks for certain modules
                             not being run.


                      # § Python⠀➾


                            # ⚓ [Older]_Creating_a_Python_Makefile_–_Earthly
                              Blog⠀⇛


                                   Even though Python is regarded as an
                                   interpreted language and the files need
                                   not be compiled separately, many
                                   developers are unaware that you can
                                   still use make to automate different
                                   parts of developing a Python project,
                                   like running tests, cleaning builds,
                                   and installing dependencies. It’s
                                   honestly an underutilized function, and
                                   by integrating it into your routine,
                                   you can save time and avoid errors.


                                   make is a commonplace tool in the world
                                   of software development, especially
                                   compiled languages like C or C++. It is
                                   a tool which controls the generation of
                                   executable and other non-source files
                                   from a program’s source file. It can
                                   automate the process of building
                                   software by tracking its dependencies
                                   and compiling the program only when the
                                   dependencies change.


                      # § Rust⠀➾


                            # ⚓ This_Week_In_Rust:_This_Week_in_Rust_412⠀⇛


    * § Leftovers⠀➾


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Security⠀➾


                            # ⚓ Security_updates_for_Thursday⠀⇛


                                   Security updates have been issued by
                                   Mageia (golang, grilo, mediawiki, plib,
                                   python-flask-restx, python-mpmath,
                                   thunderbird, and xstream/xmlpull/
                                   mxparser), Oracle (389-ds-base,
                                   grafana, httpd:2.4, kernel, libxml2,
                                   and openssl), Red Hat (httpd), and SUSE
                                   (kernel).


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ The_Dust_That_Measures_All_Our_Time_–_The_Public
                        Domain_Review⠀⇛


                             From the mythical Sandman, who participates
                             in dream and vision, to an irritating grain
                             lodged in the beachgoer’s eye, sand harbours
                             unappreciated power, however mundane. Steven
                             Connor celebrates this “most untrustworthy”
                             type of matter.


                      # ⚓ Cloudflare_Isn’t_Liable_for_Sites_That_Hawk
                        Counterfeits_|_WIRED⠀⇛


                             Cloudflare was sued in November 2018 by Mon
                             Cheri Bridals and Maggie Sottero Designs, two
                             wedding dress manufacturers and sellers that
                             alleged Cloudflare was guilty of contributory
                             copyright infringement because it didn’t
                             terminate services for websites that
                             infringed on the dressmakers’ copyrighted
                             designs….


                             [Judge] Chhabria noted that the dressmakers
                             have been harmed “by the proliferation of
                             counterfeit retailers that sell knock-off
                             dresses using the plaintiffs’ copyrighted
                             images” and that they have “gone after the
                             infringers in a range of actions, but to no
                             avail — every time a website is successfully
                             shut down, a new one takes its place.”
                             Chhabria continued, “In an effort to more
                             effectively stamp out infringement, the
                             plaintiffs now go after a service common to
                             many of the infringers: Cloudflare. The
                             plaintiffs claim that Cloudflare contributes
                             to the underlying copyright infringement by
                             providing infringers with caching, content
                             delivery, and security services. Because a
                             reasonable jury could not — at least on this
                             record — conclude that Cloudflare materially
                             contributes to the underlying copyright
                             infringement, the plaintiffs’ motion for
                             summary judgment is denied and Cloudflare’s
                             motion for summary judgment is granted.”



                    ䷩ 𝚕𝚒𝚗𝚎 7373

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Gemini_version_available_♊︎


✐ Links_14/10/2021:_Whisker_Menu_2.6.1_and_KDE’s_Birthday⠀✐


Posted in News_Roundup at 6:44 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distributions
          o Devices/Embedded
    * Free_Software/Open_Source
    * Leftovers
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Why_I_only_have_one_computer⠀⇛


                       Assuming you’re more than just a consumer of online
                       content, you probably have local files for things
                       that are important to you: school work; in-progress
                       projects; creative pursuits; family photos; a
                       personal music collection; source code repos; saved
                       memes–you name it. With more than one computer, you
                       need to figure out a way to keep these files in
                       sync, and good solutions are elusive.


                       Cloud services are expensive and may compromise
                       your privacy. Free non-cloud local sync services
                       only work when both machines are on the same
                       network. Any FOSS versions of these are
                       unfortunately buggy and a chore to set up and
                       maintain. Even if your chosen sync solution works
                       perfectly (which it never does), you have to deal
                       with the headaches of…


          o § Audiocasts/Shows⠀➾


                # ⚓ On_KDE’s_25th_Anniversary_–_Kockatoo_Tube⠀⇛


          o § Kernel Space⠀➾


                # ⚓ Intel_Linux_Driver_Lands_Tessellation/Geometry_Distribution
                  Feature_For_Xe-HPG_–_Phoronix⠀⇛


                       A new feature for upcoming XeHPG graphics that was
                       merged into Intel’s open-source Linux OpenGL and
                       Vulkan drivers today was for tessellation
                       distribution and geometry distribution across the
                       graphics hardware.


                       A two-month-old merge request landed this evening
                       for enabling the tessellation/geometry distribution
                       functionality as found with upcoming XeHPG hardware
                       in the form of the Intel ARC “Alchemist” (DG2)
                       graphics cards.


                # ⚓ Linux_Patches_Rewrite_The_Retpoline_Rewrite_Code_–_Possible
                  Performance_Benefit_–_Phoronix⠀⇛


                       The Linux kernel has supported Retpolines for over
                       three years now as part of their Spectre Variant
                       Two mitigations while now a patch series is
                       proposed that rewrites Retpoline’s rewrite logic.


          o § Applications⠀➾


                # ⚓ Best_Spotify_Alternatives_For_Linux⠀⇛


                       Spotify is the most popular music streaming
                       service. A Spotify free account grants access to a
                       massive catalogue of songs, podcasts, and internet
                       radio. But, if you’re a big fan of open-source
                       software like me, you’ll want to check out these
                       free and premium Spotify alternatives for Linux.


                       These Spotify alternatives not only give us access
                       to a large collection of free music resources, but
                       we can also use some of them to host our own
                       streaming server.
                       Spotify does not enable you to host the software on
                       your own server. Furthermore, the Spotify client
                       for Linux is not developed by a dedicated team, so
                       expect bugs and glitches with the official Spotify
                       Linux client. In this case, you can look through
                       the following list to see which music application
                       you prefer for your Linux distribution.


                # ⚓ Whisker_Menu_2.6.1_released⠀⇛


                       Fix menu not toggling (Issue #61)
                       Fix small icon in multi-row panels (Issue #37)
                       Fix missing minimize and maximize buttons in
                       settings dialog
                       Replace deprecated code for grab check
                       Translation updates: Greek, Slovak, Spanish


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Twenty-Five_Years_of_KDE⠀⇛


                             It’s KDE’s birthday today. Twenty-five years
                             ago Matthias Ettrich called for programmers
                             to create a GUI for end users of Linux. They
                             came and did. I wrote about the first Twenty
                             Years of KDE five years ago. What I wrote
                             there is still true, but there is more.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Check_File_Integrity_on_Linux_the_Easy_Way_With
                        GtkHash⠀⇛


                             GtkHash is a simple and lightweight tool for
                             generating checksums on Linux. You can also
                             check for the validity of a given checksum
                             using this tool. Comparing checksums is an
                             excellent way of ensuring data integrity as
                             it can help you be sure whether you’re
                             downloading files from a safe site.


                             Let’s see how you can check the integrity of
                             your files on Linux using GtkHash.


                      # ⚓ GtkSourceStyleSchemePreview⠀⇛


                             In the past, we had a style scheme chooser
                             widget to help people find style schemes that
                             look useful. It was fairly rudimentary and
                             doesn’t fit how we’d like style scheme
                             selection to work going forward. So in what
                             will become GtkSourceView 5.4, I’ve added the
                             GtkSourceStyleSchemePreview widget which you
                             can use to preview a specific style scheme.


          o § Distributions⠀➾


                # § IBM/Red Hat/Fedora⠀➾


                      # ⚓ What_New_Features_to_Expect_in_the_Coming_Release_of
                        Fedora_35⠀⇛


                             Twice each year, in April and October, the
                             community behind Fedora releases a new major
                             version of the extremely popular Linux
                             distribution. Currently scheduled for October
                             19, 2021, the release of Fedora 35 is quickly
                             approaching. Let’s take a look at what you
                             can expect when you install or upgrade to the
                             35th incarnation of the world’s most popular
                             bleeding edge Linux distribution.


                             [...]


                             Fedora 35 is tentatively scheduled to be
                             released on October 19 with a fallback date
                             of October 26 in case of any release-blocking
                             problems. While we’d love to see Fedora 35
                             released as soon as possible, history shows
                             that it’s more likely that the release will
                             come on the later date.


                             You can currently download Fedora 34 or the
                             Fedora 35 Beta release from the Fedora
                             Project’s website. You’ll also find links to
                             both current and beta versions of the many
                             Fedora spins.


                # § Debian Family⠀➾


                      # ⚓ Sparky_Linux_2021.10_Semi-Rolling_Comes_with_Updated
                        Packages⠀⇛


                             Sparky Linux have just released an update to
                             their rolling release version. Sparky 2021.10
                             features a new kernel of 5.14 as well as some
                             other changes.


                             Sparky Linux is a lightweight desktop-based
                             Linux distribution based on Debian. It aims
                             to be easy on system resources and can
                             breathe new life into aging computers.


                             Sparky is a unique distribution in the sense
                             that it provides both Debian stable and
                             testing editions. In general, Sparky is not
                             targeted to Linux beginners, but rather users
                             with some amount of Linux knowledge.


          o § Devices/Embedded⠀➾


                # ⚓ Sitara-based_LoRa_gateway_launches_with_serial-to-LoRa
                  adapter_node⠀⇛


                       Embux’s “ELA-MG” LoRa gateway runs Linux on TI’s
                       AM335x and offers a Semtech SX1272 LoRa module with
                       -137dBm sensitivity plus GbE, USB, RS232, and RS485
                       ports. There is also an NB-IoT model and an “ELA-
                       MA” serial-to-LoRa adapter for endpoints.


                       Nexcom announced a LoRa wireless gateway from its
                       Embux subsidiary, which has previously manufactured
                       products such as its i.MX6-based 3.5-inch EBC3A1-1G
                       Y0 SBC. Like the SBC, the new ELA-MG gateway runs
                       Linux on the aging Cortex-A8 architecture, this
                       time in the form of a Texas Instruments Sitara
                       AM335x SoC.


                       The ELA-MG incorporates Semtech’s SX1272 LoRa
                       transceiver, which enables the gateway to transmit
                       over 862 ~ 932MHz frequencies with up to 20dBm
                       output power at rates of up to 18.2Kbps.
                       Transmissions can achieve up to a 2 Km range,
                       according to most citations, although the specs
                       also say 2-5 Km.


                # ⚓ Updating_Librem-EC_on_your_Librem_14⠀⇛


                       With this (E)mbedded (C)ontroler update, your
                       Librem 14 will have better temperature management;
                       fans will gradually ramp up earlier. You’ll also
                       get improved keyboard mapping and better switching
                       between battery and external power supplies.


                # ⚓ Vintage_Radio_Gets_Internet_Upgrade⠀⇛


                       There’s nothing quite like vintage hardware, and
                       the way it looks and works is something that can be
                       worth celebrating. [Old Tech. New Spec] did that
                       with his loving modification of a 1964 Dansette
                       portable radio, bringing it into the modern era by
                       giving it the ability to play Internet radio
                       stations while keeping all the original controls
                       and appearance. As he says, you’d hardly know it
                       has been modified unless you turned it on.


                # ⚓ Tiger_Lake_signage_player_ships_with_Quividi_analytics
                  software⠀⇛


                       Axiomtek’s Linux-ready “DSP511” signage player is
                       equipped with an 11th Gen CPU plus 4x HDMI, 3x M.2,
                       2.5GbE, and optional Quividi audience measurement
                       software. Quividi is also available on the Whiskey
                       Lake based “DSP501-527.”


                       Axiomtek announced a partnership with signage
                       analytics software company Quividi to offer
                       Quividi’s audience and campaign intelligence
                       software on two of its Intel-based signage players.
                       One is the Whiskey Lake based DSP501-527, which we
                       covered in June 2020. The second player — a DSP511
                       system based on Intel’s 11th Gen Tiger Lake-
                       U processors — has not been previously announced
                       and is listed as “coming soon.” We cover it farther
                       below.


                # § Open Hardware/Modding⠀➾


                      # ⚓ Tiny_TV_Tells_The_Temperature_Tale_|_Hackaday⠀⇛


                             Once upon a time, we would run home from the
                             bus stop to watch Gargoyles and Brady Bunch
                             reruns on the family TV, a late-1970s console
                             Magnavox number that sat on the floor and was
                             about 50% more cabinet than CRT. The old TV,
                             a streamlined white Zenith at least ten years
                             older, had been relegated to the man cave in
                             the basement. It looked so mod compared to
                             the “new” TV, but that’s not the aesthetic my
                             folks were after. They wanted their
                             electronics to double as furniture.


                             This little TV is a happy medium between the
                             two styles, and for us, it’s all about those
                             feet. But instead of cartoons, it switches
                             between showing the current weather and the
                             top news headlines. Inside that classy oak
                             cabinet is an LCD, an ESP32, and an SD card
                             module. The TV uses OpenWeatherMap and pulls
                             the corresponding weather image from the SD
                             card based on time of day — light images for
                             day, and dark images for night.


                # § Mobile Systems/Mobile Applications⠀➾


                      # ⚓ You_might_be_unlocking_your_car_with_Android_12
                        sooner_than_you’d_think⠀⇛


                      # ⚓ Android_12-based_RealmeUI_3.0_debuts:_first_beta_to
                        come_to_Realme_GT_in_October_–_GSMArena.com_news⠀⇛


                      # ⚓ Samsung_Android_12_release_will_come_before_2021′s
                        end_–_9to5Google⠀⇛


                      # ⚓ Android_12_CDD_released:_‘Performance_class’
                        requirements_–_9to5Google⠀⇛


                      # ⚓ Samsung_One_UI_4.0_(Android_12)_update_tracker:
                        Eligible_devices_&_more⠀⇛


                      # ⚓ Android_12_Material_You:_you_will_get_six_shapes_to
                        choose_from_for_the_Google_Photos_widget_–_PhoneArena⠀⇛


                      # ⚓ Samsung_wants_to_release_Android_12_and_OneUI_4_very
                        soon⠀⇛


                      # ⚓ Teclast_T50:_Budget_Android_11_tablet_revealed_with
                        4G_connectivity_and_a_large_2K_display_–
                        NotebookCheck.net_News⠀⇛


                      # ⚓ Motorola_Android_11_update:_List_of_eligible_devices
                        &_release_date⠀⇛


                      # ⚓ The_best_way_to_play_retro_games_on_Android
                        smartphones_or_modern_PCs:_ScummVM_turns_20_–
                        NotebookCheck.net_News⠀⇛


                      # ⚓ Best_stock_widgets_for_Android_–_Phandroid⠀⇛


                      # ⚓ Top_10_Best_Arcade_Games_For_Android⠀⇛


                      # ⚓ Assistant_Driving_Mode_adds_Bluetooth_auto-launch_–
                        9to5Google⠀⇛


                      # ⚓ Google_Chrome_adds_a_new_‘Follow’_feature_for_RSS
                        updates_on_Android_–_Good_e-Reader⠀⇛


                      # ⚓ Google’s_Pixel_6_reveal_event_is_Oct._19:_How_to
                        watch_the_Android_phone_reveal_–_CNET⠀⇛


                      # ⚓ Google_Pixel_6_rumor_says_it_will_get_4_years_of
                        Android_updates_|_TechRadar⠀⇛


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


                # ⚓ 10_Best_Free_and_Open_Source_Linux_Comic_Book_Viewers⠀⇛


                       A comic book is a magazine which consists of
                       narrative artwork in the form of sequential images
                       with text that represent individual scenes. Panels
                       are often accompanied by brief descriptive prose
                       and written narrative, usually dialog contained in
                       word balloons emblematic of the comics art form.
                       Comics are used to tell a story, and are published
                       in a number of different formats including comic
                       strips, comic books, webcomics, Manga, and graphic
                       novels. Some comics have been published in a
                       tabloid form. The largest comic book market is
                       Japan.


                       Many users associate desktop Linux with their daily
                       repetitive grind. However, we are always on the
                       look out for applications that help make Linux fun
                       to use. It really is a great platform for
                       entertainment.


                # § Programming/Development⠀➾


                      # ⚓ New_features_coming_in_Julia_1.7⠀⇛


                             Julia is an open-source programming language
                             and ecosystem for high-performance scientific
                             computing; its development team has made the
                             first release candidate for version 1.7
                             available for testing on Linux, BSD, macOS,
                             and Windows. Back in May, we looked at the
                             increased performance that arrived with Julia
                             1.6, its last major release. In this article
                             we describe some of the changes and new
                             features in the language and its libraries
                             that are coming in 1.7.


                             Historically, Julia’s release candidates have
                             been close to the finished product, and most
                             users who would like to work with the new
                             features can safely download binaries of
                             version 1.7rc1 from Julia headquarters in the
                             “upcoming release” section. Officially,
                             however, the current version is not
                             “production ready”; the developers welcome
                             bug reports to the GitHub issue tracker.


                      # ⚓ Rust_and_GCC,_two_different_ways⠀⇛


                             Developers working in languages like C or C++
                             have access to two competing compilers — GCC
                             and LLVM — either of which can usually get
                             the job done. Rust developers, though, are
                             currently limited to the LLVM-based rustc
                             compiler. While rustc works well, there are
                             legitimate reasons for developers to wish for
                             an alternative. As it turns out, there are
                             two different ways to compile Rust using GCC
                             under development, though neither is ready at
                             the moment. Developers of both approaches
                             came to the 2021 Linux Plumbers Conference to
                             present the status of their work.


          o § Standards/Consortia⠀➾


                # ⚓ Showdown_Time_For_Non-Standard_Chargers_In_Europe_|
                  Hackaday⠀⇛


                       It seems that few features of a consumer electronic
                       product will generate as much rancour as a mobile
                       phone charger socket. For those of us with Android
                       phones, the world has slowly been moving over the
                       last few years from micro-USB to USB-C, while
                       iPhone users regard their Lightning connector as
                       the ultimate in connectivity. Get a set of
                       different phone owners together and this can become
                       a full-on feud, as micro-USB owners complain that
                       nobody has a handy charging cable any more, USB-
                       C owners become smug bores, and Apple owners do
                       what they’ve always done and pretend that Steve
                       Jobs invented USB. Throwing a flaming torch into
                       this incendiary mix is the European Union, which is
                       proposing to mandate the use of USB-C on all phones
                       sold in its 27 member nations with the aim of
                       reducing considerably the quantity of e-waste
                       generated.


    * § Leftovers⠀➾


          o ⚓ Progressive_Dems_Offer_Simple,_Brilliant_Path_Forward_for_Build
            Back_Better_Act⠀⇛


          o ⚓ “No_First_Use”:_An_Empty_Gesture_That_Would_Cost_Nothing⠀⇛


                 Is it really a big deal for the US government to affirm
                 that it will not use nuclear weapons first in any future
                 conflict?


                 US Senator Jim Risch (R-ID) says it would signal
                 prospective enemies  “that they can plan an attack and do
                 whatever they want to and not worry.”


          o § Health/Nutrition⠀➾


                # ⚓ Study_Cited_by_Antivaxxers_Is_Retracted_After_Authors_Admit
                  Mathematical_Error⠀⇛


                # ⚓ Opinion_|_Pandemic_Politics:_5_Reasons_Why_Medicare_for_All
                  Must_Be_Part_of_a_Workers’_Recovery⠀⇛


                       The Covid-19 pandemic has ravaged the nation for
                       nearly 20 months now and America’s workers have
                       borne the brunt of the crisis. While the wealth of
                       the country’s 614 billionaires increased by 62%,
                       tens of millions of workers deemed essential have
                       been forced to work under Dickensian conditions
                       while disproportionately exposed to Covid-19
                       infection. Over 20 million workers lost their jobs
                       at some point during the pandemic. The economy is
                       still experiencing a net job loss and 11 million
                       households face the threat of eviction.


                # ⚓ Health_Expert_Urges_Congress_to_‘Transform_People’s_Lives’
                  as_Millions_Face_Persistent_Financial_Hardship⠀⇛


                       “The notion of America being a land of opportunity
                       is a fantasy for millions of people, reserved only
                       for those of privilege.”


                # ⚓ 2_Airlines_Plan_to_Defy_Greg_Abbott’s_Ban_on_Vaccine
                  Mandates_in_Texas⠀⇛


                # ⚓ Prescription_Drug_Safety_Risks_Hidden,_Hypochondria_Created
                  by_Marketing⠀⇛


                       Humira marketing is a case study in how drug makers
                       promote expensive, dangerous and often unnecessary
                       prescription drugs risking public safety and at
                       taxpayer expense.


                       Before creating AbbVie, Abbott had already lobbied
                       Congress successfully to get Humira covered by
                       Medicare and seeded seniors with “free samples” to
                       create “demand.” Today Humira costs $2,984 per one
                       syringe, pricing which the U.S. Congress is
                       investigating. The cost of the Medicare-reimbursed
                       Humira has been raised 27 times since the drug’s
                       launch.


                # ⚓ Social_Medicine_and_the_Coming_Transformation:_a_Manual_for
                  Career_Path_2.0⠀⇛


                       With Social Medicine and the Coming Transformation,
                       Howard Waitzkin, Alina Pérez, and Matthew Anderson,
                       give us a how-to manual on how to become a social
                       medicine practitioner. They invite all of us
                       involved in health work to re-invent ourselves and
                       adopt social medicine as career path 2.0. It should
                       become, as the British say, the primer on the
                       subject.


                       The clinician sees patients one by one, assigns
                       diagnoses, and chooses appropriate therapies (which
                       might be medications, surgical procedures, talk
                       therapy, or rehabilitation). This is the essence of
                       a medical education, refined further during
                       postgraduate training. The focus is on the
                       individual patient, on the biological aspects of
                       the individual human organism. The more
                       reductionist and mechanistic, the better. Simply
                       follow the “best practice” algorithms, approved by
                       the insurance corporation. Blood pressure too high?
                       Reduce the afterload! Or, tamp down the sympathetic
                       nervous system! Even psychiatry has fallen prey to
                       mechanistic paradigms. Feeling sad? Ramp up the
                       synaptic re-uptake of serotonin!


                # ⚓ Ecological_fallacy:_When_a_scientist_(inadvertently,_I
                  hope)_uses_a_favorite_antivax_form_of_study⠀⇛


                       Longtime regular readers might remember the various
                       times over the years that I discussed bad
                       epidemiology papers by antivaxxers that claimed to
                       have found associations between various vaccines
                       and bad outcomes. You know the studies, for
                       example, the study ten years ago by Neil Z. Miller
                       and Gary S. Goldman that claimed to find an
                       association between the vaccination schedules of
                       various countries and infant mortality rates. (Yes,
                       they incorrectly claimed that schedules with more
                       vaccines were associated with higher infant
                       mortality rates.) A couple of years before that,
                       antivaccine activist J.B. Handley had published a
                       report that used a cherry picked group of
                       nations to try to argue not only that nations that
                       require more vaccines have higher rates of infant
                       mortality but higher prevalence of autism in
                       children under five. A year before even that, in
                       2008, the father-son duo of antivaccine quack
                       activists Mark and David Geier had tried to use a
                       similar technique to “show” (incorrectly) that
                       increased vaccine uptake was associated with and
                       increased prevalence of autism. The flaw at the
                       heart of all of these studies was the ecological
                       fallacy. Sure, there were, as you might imagine,
                       many other problems with these studies, such as
                       failure to control for confounders and cherry
                       picking nations used in the analysis (they were
                       done by antivaxxers after all), but the main
                       problem always came back to the ecological fallacy.


          o § Integrity/Availability⠀➾


                # § Proprietary⠀➾


                      # § Pseudo-Open Source⠀➾


                            # § Privatisation/Privateering⠀➾


                                  # § Linux Foundation⠀➾


                                        # ⚓ Linux_Foundation_announces_$10
                                          million_cross-industry_investment_in
                                          Open_Source_Security_Foundation⠀⇛


                                        # ⚓ The_Linux_Foundation_raises_$10
                                          million_to_expand_and_support_the
                                          OpenSSF⠀⇛


                                        # ⚓ Open_To_New_Opportunities,_Linux
                                          Foundation’s_LF_Edge_Expands_Open
                                          Source_Edge_Project⠀⇛


                                               In a few short years, LF
                                               Edge, which is an umbrella
                                               organization within the
                                               constantly expanding Linux
                                               Foundation, has made
                                               significant strides in
                                               addressing challenges
                                               associated with edge
                                               computing in the real
                                               world.


                                               Established in January
                                               2019, LF Edge comprises
                                               existing Linux Foundation
                                               projects Akraino Edge
                                               Stack, EdgeX Foundry, and
                                               the Open Glossary of Edge
                                               Computing, as well as
                                               Project EVE led by ZEDEDA
                                               and Home Edge Project led
                                               by Samsung Electronics.


                                        # ⚓ CNCF_and_Linux_Foundation_launch
                                          entry-level_Kubernetes_certification
                                          [Ed: Lots of paid-for SPAM from LF
                                          about some silly “certification” — a
                                          reminder that this media will only
                                          cover what it gets paid to cover. LF
                                          as_‘diploma_mill’.]⠀⇛


                            # § Entrapment (Microsoft GitHub)⠀➾


                                  # ⚓ GitHub_Pulls_Site_and_Repo_of_Pirate
                                    Proxy_Service_‘Unblockit’_Offline⠀⇛


                                         GitHub has removed the repository
                                         and the mirror website of
                                         Unblockit, a proxy service that
                                         allows people to access blocked
                                         sites. The developer platform
                                         says that the content in question
                                         was removed for violating its
                                         terms of service, which was
                                         confirmed by a follow-up
                                         investigation. Unblockit,
                                         meanwhile, remains available
                                         through its regular website.


                      # § Security⠀➾


                            # § Fear, Uncertainty, Doubt/Fear-mongering/
                              Dramatisation⠀➾


                                  # ⚓ FontOnLake_Malware_Can_Target_Linux
                                    Systems [Ed: This isn't really about Linux
                                    any more than a security hole in Adobe
                                    Photoshop is about Windows]⠀⇛


                                         Documentation released by
                                         internet security company, ESET,
                                         on October 7th, has given details
                                         to what was lesser known malware
                                         family that emerged this past
                                         May, including details that are
                                         very relevant to the Linux world,
                                         especially those using older
                                         RedHat Enterprice Linux systems
                                         for production servers.


                                         The malware family given the name
                                         FontOnLake, uses custom modules
                                         providing remote access to
                                         infected systems, using a rootkit
                                         to conceal the infection. The
                                         malware is able to collect
                                         credentials, and also acts as a
                                         proxy server by the use of
                                         advanced designed components that
                                         can be placed into three
                                         categories, according to the ESET
                                         release:


                            # § Privacy/Surveillance⠀➾


                                  # ⚓ New_‘Stop_Facebook’_Campaign_Demands_Ban
                                    on_Data_Harvesting_and_Corporate
                                    Surveillance⠀⇛


                                         A new campaign is calling for
                                         federal action to “shut down
                                         Facebook’s surveillance machine”
                                         including passing legislation to
                                         ensure strong data privacy
                                         protections.


                                         “The best way to stop Facebook’s
                                         harms for the whole world is to
                                         cut off the fuel supply for its
                                         dangerous machine,” says the How
                                         to Stop Facebook campaign,
                                         launched Wednesday by a diverse
                                         coalition of over 40
                                         organizations.


                                  # ⚓ Meet_the_Alliance_for_Encryption_in_Latin
                                    America_and_the_Caribbean⠀⇛


                                         The virtual launch event is
                                         October 21, with the
                                         participation of member
                                         organizations. It is open to the
                                         public.


                                         This regional Alliance seeks to
                                         advance a proactive agenda to
                                         promote and defend encryption in
                                         Latin America and the Caribbean.
                                         It aims to strengthen the use of
                                         encryption and generate an
                                         ecosystem of trust, security and
                                         stability within information and
                                         communications technologies
                                         (ICTs), particularly the critical
                                         infrastructure of the internet
                                         and its applications and
                                         services.


                                  # ⚓ In_Latest_Black_Eye_For_NSO_Group,
                                    Dubai’s_King_Found_To_Have_Used_NSO_Spyware
                                    To_Hack_His_Ex-Wife’s_Phone⠀⇛


                                         NSO Group has endured some
                                         particularly bad press lately,
                                         what with leaked data pointing to
                                         its customers’ targeting of
                                         journalists, political figures,
                                         religious leaders, and
                                         dissidents. That its powerful
                                         spyware would be abused by its
                                         customers was not surprising.
                                         Neither were the findings from
                                         the leaked data, which only
                                         confirmed what was already known.


                                  # ⚓ Big_Opportunity!_CCI_accepts_IFF’s_expert
                                    information_in_its_investigation_of
                                    WhatsApp’s_2021_Privacy_Policy⠀⇛


                                         In the Competition Commission of
                                         India’s (CCI) suo moto
                                         investigation into potential
                                         anti-competitive practices, we
                                         have submitted expert information
                                         before the Director-General in
                                         charge of the investigation. In
                                         our information, we have
                                         highlighted how WhatsApp has a
                                         dominant position in its relevant
                                         market, and how WhatsApp’s 2021
                                         Privacy Policy abuses such
                                         dominant position. On October 12,
                                         2021, the CCI issued an order
                                         tagging the information with the
                                         ongoing investigation. As a
                                         result, we are now a formal party
                                         before the Director-General and
                                         will participate as such in the
                                         investigation proceedings. This
                                         is a huge opportunity to present
                                         the user’s point of view to the
                                         Commission!


                                  # ⚓ Google_Analytics:_the_gold_standard?⠀⇛


                                         Ever since I started this
                                         personal blog site, I was curious
                                         if people actually read what I
                                         write. Luckily, based on the
                                         responses I received on Twitter,
                                         LinkedIn and in private, there is
                                         no problem with that. Next I
                                         wanted to see numbers. I was
                                         told, that Google Analytics is
                                         the gold standard of measurement.
                                         Well…


                                         [...]


                                         Last week I asked around what
                                         should I use to replace Google
                                         Analytics. Quite a few people
                                         suggested that I keep using GA,
                                         as even if it is not much use, it
                                         is still the gold standard.
                                         However it is a personal blog
                                         without any ads. It is not a
                                         business site and I am more
                                         curious about real usage than how
                                         many ads I can serve.


          o § Defence/Aggression⠀➾


                # ⚓ ‘No_Tech_for_Apartheid’:_40+_Groups_Demand_Amazon_and
                  Google_Ditch_Israeli_Military⠀⇛


                       A day after hundreds of Amazon and Google workers
                       condemned their employers for complicity in
                       Israel’s human rights violations against
                       Palestinians, over 40 grassroots groups on
                       Wednesday announced a campaign to amplify the
                       efforts of activists around the world working to
                       stop apartheid profiteers.


                       “As the Israeli military bombed homes, clinics, and
                       schools in Gaza and threatened to push Palestinian
                       families from their homes in Jerusalem this past
                       May, Amazon Web Services and Google Cloud
                       executives signed a $1.22 billion contract to
                       provide cloud technology to the Israeli government
                       and military,” the campaign noted. “By doing
                       business with Israeli apartheid, Amazon and Google
                       will make it easier for the Israeli government to
                       surveil Palestinians and force them off their
                       land.”


                # ⚓ CIA_Creates_a_Mission_Center_to_Counter_China⠀⇛


                       President Joe Biden has been slow getting out of
                       the blocks on various foreign policy and national
                       security issues, particularly when it comes to
                       China. He has continued the bombastic policies of
                       Donald Trump, leaving tariffs in place over the
                       opposition of American business leaders and
                       concluding a treaty with Australia to provide
                       nuclear submarine technology. The United States
                       hasn’t provided such technology to any nation since
                       the late 1950s, and the Australian treaty violates
                       the spirit of the Non-Proliferation Treaty of the
                       late 1960s.  Meanwhile, there are bipartisan
                       majorities in the Congress supporting increased
                       defense spending and modernization of nuclear
                       weapons in order to counter Brennan’s description
                       of the Chinese threat to “international order,”


                       China’s response to the surprising submarine deal
                       was quick and forceful. Last week, nearly 150
                       Chinese warplanes were flown into Taiwan’s air
                       defense identification zone, placing military
                       tensions between China and Taiwan at their worst
                       level in four decades. China’s President Xi Jinping
                       didn’t mention the flights in his speech
                       commemorating the 1911 revolution that overthrew
                       China’s last imperial dynasty. But he did vow to
                       achieve a peaceful “unification” with Taiwan.


          o § Environment⠀➾


                # ⚓ Fossil_Fuel_CEOs_Will_Testify_About_Role_in_Climate_Denial
                  Before_Congress⠀⇛


                # ⚓ 90_More_Arrested_as_Victims_of_Climate_Chaos_Descend_on
                  White_House⠀⇛


                       Another 90 people were arrested outside the White
                       House on Wednesday as residents and supporters of
                       communities on the frontlines of climate chaos
                       joined a week of action ramping up pressure on
                       President Joe Biden to deliver on his campaign
                       promises.


                       “How much longer will the future of our communities
                       be on the shoulders of citizens without the backing
                       of our elected officials?”


                # ⚓ Opinion_|_Why_Nature-Based_Solutions_Won’t_Solve_the
                  Climate_Crisis—They’ll_Just_Make_Rich_People_Even_Richer⠀⇛


                       Imagine you’re a Baka, a hunter gatherer in the
                       Congo Basin forest. That land has been your home
                       for generations. You know every stone and every
                       tree there. Your grandparents are buried on that
                       land. You and your people have nourished it, taken
                       care of it and loved it. Now imagine that you’re
                       evicted and your house destroyed because, as
                       someone explains to you, a white man living very
                       far away, thinks that your forest has to become a
                       Protected Area where only elephants are allowed to
                       live. He likes elephants, they tell you. White men
                       like elephants. Apparently he went up to space and
                       realized that he likes your forest, and he is
                       worried about climate change. That man created a
                       company that produced 60.64 million metric tons of
                       carbon dioxide last year—the equivalent of burning
                       through 140 million barrels of oil. But, they tell
                       you, if your forest is protected, he can feel
                       better about his emissions of CO2. You might wonder
                       why he doesn’t stop his emissions instead of
                       destroying your life. The answer to that is money.
                       You might also wonder how anyone can believe he’s
                       doing good. And the answer to that is the topic of
                       this article.


                # ⚓ Nature_Defenders_Warn_Global_Biodiversity_‘Kunming
                  Declaration’_Lacks_Urgency⠀⇛


                       More than 100 countries on Wednesday concluded a
                       round of negotiations on global efforts to restore
                       and protect the variety of life on Earth by
                       pledging “urgent and integrated action” to achieve
                       “transformative change, across all sectors of the
                       economy and all parts of society.”


                       “Ambition urgently needs to ramp up from here
                       before the spring 2022 session.”


                # ⚓ Opinion_|_Climate_Movement_Vs._the_Industry⠀⇛


                       Global movements see young people utilising their
                       power by voicing their grievances, organising in
                       different youth-run climate change
                       organisations, and using all available platforms to
                       make their demands heard and spread.


                # § Energy⠀➾


                      # ⚓ IEA_Sends_Clear_Message_to_World_Leaders:_Stop
                        Investing_in_New_Oil_and_Gas⠀⇛


                             Just over two weeks out from the COP26
                             climate summit in Glasgow, the International
                             Energy Agency on Wednesday delivered a
                             straightforward and urgent message to world
                             leaders: Fossil fuels must stay in the ground
                             if planetary warming is to be limited to
                             1.5°C by the end of the century.


                             “The social and economic benefits of
                             accelerating clean energy transitions are
                             huge, and the costs of inaction are immense.”


                      # ⚓ Drax’s_‘Carbon_Negative’_Bioenergy_Claims_‘Wildly
                        Exaggerated’,_Study_Argues⠀⇛


                             The current supply chain of biomass giant
                             Drax “makes the impacts of climate change
                             worse”, a new study has claimed.


                             Analysis by US environmental advocacy group,
                             the National Resources Defense Council
                             (NRDC), studied the emissions from wood
                             pellets transported from pine plantations in
                             the southeastern United States to be used in
                             a bioenergy, carbon capture and storage
                             (BECCS) operation by Drax in Yorkshire.


                      # ⚓ IEA_Urges_World_Leaders_to_Stop_Investing_in_New_Oil
                        and_Gas⠀⇛


                # § Wildlife/Nature⠀➾


                      # ⚓ ‘We’re_Taking_Action_Into_Our_Own_Hands’_—_A
                        Community_Stands_Against_a_Landfill⠀⇛


          o § Finance⠀➾


                # ⚓ ‘Historic_Showdown’_Coming_as_Fossil_Fuel_CEOs_Agree_to
                  Testify_on_Climate_Deception⠀⇛


                       Proponents of holding the fossil fuel industry to
                       account for its role in climate deception welcomed
                       confirmation Wednesday that top oil and gas CEOs
                       will testify before House lawmakers later this
                       month.


                       News that the executives of BP, Chevron,
                       ExxonMobil, and Shell Oil—as well as the American
                       Petroleum Institute and the U.S. Chamber of
                       Commerce—would testify was reported by the
                       Washington Post.


                # ⚓ US_Intervention_and_Capitalism_Have_Created_a_Monster_in
                  Honduras⠀⇛


                       The Honduran government headed by president Juan
                       Orlando Hernández does have excellent relations
                       with the United States. The alliance is toxic,
                       however, what with the continued hold of capitalism
                       on an already unjust, dysfunctional society.
                       Hondurans will choose a new president on November
                       28.


                       Honduras, a dependent nation, is subject to U.S.
                       expectations. These center on free rein for
                       businesses and multi-national corporations, large
                       foreign investment, low-cost export goods, low
                       wages, foreigners’ access to land holdings and sub-
                       soil resources, and a weakened popular resistance.


                # ⚓ Top_1_Percent_in_US_Now_Have_More_Wealth_Than_Entire_Middle
                  Class_Combined⠀⇛


                # ⚓ ‘There’s_a_Lot_the_Postal_Service_Can_Do_to_Be_Present_in
                  the_21st_Century’⠀⇛


                       Janine Jackson interviewed Lisa Graves about the
                       fight for the Postal Service for the October 8,
                       2021, episode of CounterSpin. This is a lightly
                       edited transcript.


                # ⚓ Charter_Spectrum_Threatens_To_Ruin_Potential_Customers_Over
                  Debt_They_Don’t_Owe⠀⇛


                       There’s a reason U.S. cable and broadband companies
                       have some of the worst customer satisfaction
                       ratings of any companies, in any industry in
                       America. The one/two punch of lagging broadband
                       competition and captured regulators generally mean
                       there’s little to no meaningful penalty for
                       overcharging users, providing lackluster services
                       and support, and generally just being an obnoxious
                       ass.


                # ⚓ How_Coinbase_Phishers_Steal_One-Time_Passwords⠀⇛


                       A recent phishing campaign targeting Coinbase users
                       shows thieves are getting smarter about phishing
                       one-time passwords (OTPs) needed to complete the
                       login process. It also shows that phishers are
                       attempting to sign up for new Coinbase accounts by
                       the millions as part of an effort to identify email
                       addresses that are already associated with active
                       accounts.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Opinion_|_We_Must_Force_Politicians_to_Recognize_the_Stakes
                  of_This_Moment⠀⇛


                       In Washington, the big debate over President
                       Biden’s Building Back Better program is coming to a
                       head. It will soon be settled—one way or another.


                # ⚓ Opinion_|_Means_Testing_Is_Inhumane,_Divisive,_and_Very_Bad
                  Politics⠀⇛


                       It’s ‘popularism’ week in the commentariat, as
                       pundits across the ideological spectrum discuss
                       recent remarks by pollster David Shor. This
                       problematic and imprecise term reflects a way of
                       thinking about politics that is poised to reshape
                       the Build Back Better debate, and other debates yet
                       to come. That’s potentially disastrous. Shor has
                       written and spoken extensively on the need for
                       Democrats to back away from talking about unpopular
                       ideas and listen more to pollsters like… well, like
                       David Shor. Ezra Klein covered his ideas well, but
                       the headline for his piece gets it wrong. Shor
                       isn’t “telling Democrats what they don’t want to
                       hear.” Shor’s words are music to the ears of
                       Democratic centrists. Shor seems like an engaging,
                       bright guy. His ‘popularism’ concept is
                       interesting, if not very well defined, and his
                       framework makes the most sense when he’s talking
                       about phrases that poll badly in core Democratic
                       demographics. “Defund the police” performs poorly
                       among communities of color, for example, and it’s
                       easy to see why it’s a problem. The problem arises,
                       as it always does, when Democrats craft tomorrow’s
                       policies on today’s poll readings. That’s like
                       prescribing medication today based on what your
                       temperature was last week. Poll results are
                       transient and reflect the biases of the pollster.
                       Most importantly, they fail to consider the
                       political impact of policies that sound convincing
                       when asked by a pollster, but which are infuriating
                       and unfair once they’re enacted. Shor emphasized
                       his own leftism in interviews and, to be fair, he
                       doesn’t say politicians should shape their policies
                       on what polls well. He says they should talk about
                       things that poll well and play down the things that
                       don’t. In the real world, however, there’s not much
                       difference between the two. You can’t pass a law in
                       Congress without talking about it. Even if you try,
                       if it’s unpopular you can bet your opponents will.


                # ⚓ Broken_Britannia’s_Conservative_Party_Conference⠀⇛


                       Unlike the fairly contentious Labour party
                       conference the week before, where its leader Keir
                       Starmer left behind him a slew of broken promises
                       and betrayals of ordinary members and the unions as
                       he pushed the party rightwards into the arms of a
                       played-out Blairism, Boris “BoJo” Johnson
                       encountered nothing to threaten his childhood dream
                       of becoming “king of the world” (or the Tory party
                       at any rate).


                       This Tory conference was stage-managed in the
                       manner of the meaningless jamborees held by the US
                       Republicans and Democrats every 4 years in which a
                       candidate from each party is anointed to contest
                       the forthcoming presidential election.


                # ⚓ Manchin_and_Sinema_Obstruct_Reconciliation_With_No_Proposal
                  of_Their_Own⠀⇛


                # ⚓ In_Dead_of_Night,_Texas_House_Approves_GOP’s_Gerrymandered
                  Map⠀⇛


                       In the early hours of Wednesday morning, while much
                       of the country slept, the Republican-dominated
                       Texas House approved a heavily gerrymandered
                       district map that critics have denounced as part of
                       an anti-democratic and racist GOP power grab—one
                       that right-wing lawmakers could try to replicate
                       across the United States.


                       “Democrats… could soon be powerless to stop the
                       GOP’s takeover of the U.S. House and state capitols
                       for the next decade.”


                # ⚓ Opinion_|_Heroes_or_Parasites:_Europe’s_Self-Serving
                  Politics_on_Refugees⠀⇛


                       Language is politics and politics is power. This is
                       why the misuse of language is particularly
                       disturbing, especially when the innocent and
                       vulnerable pay the price. 


                # ⚓ Opinion_|_Manchin’s_Means-Testing_and_Work_Requirements_Are
                  a_Recipe_for_Building_Back_Worse⠀⇛


                       President Joe Biden’s Build Back Better legislation
                       would bring the United States into the 21st
                       century, finally enacting programs that other
                       industrialized nations have had for a very long
                       time. These include children’s allowances in the
                       form of tax credits, paid family and medical leave,
                       free post-secondary education, expanded Medicare,
                       home and community-based services, and so much
                       more.


                # ⚓ Chomsky,_Pollin_and_Lapavitsas:_Are_We_Witnessing_the
                  Demise_of_Neoliberalism?⠀⇛


                # ⚓ Progressives_Push_Democrats_to_Reject_‘Outdated_Austerity
                  Policies’_and_Pass_Bold_Agenda⠀⇛


                       The leaders of dozens of grassroots progressive
                       advocacy groups joined their congressional allies
                       late Tuesday in calling on Democrats to reject
                       “false choices” posed by right-wing lawmakers and
                       ensure that all of the party’s key priorities—from
                       child care to Medicare expansion to climate
                       action—remain in the final budget reconciliation
                       package.


                       “What we are talking about is not simply a laundry
                       list, a wish list. It is the needs of the American
                       people.”


                # ⚓ Governors_Can_Run_Away_to_Texas,_But_They_Can’t_Hide_From
                  the_Problems_Back_Home⠀⇛


                # ⚓ Cheney_Says_Trump_Aides_That_Ignore_Subpoena_Orders_Could
                  Face_Criminal_Charges⠀⇛


                # ⚓ Come_Back_with_a_Warrant:_Congress_Should_Pass_the
                  Protecting_Data_at_the_Border_Act⠀⇛


                       CBP as well as U.S. Immigration and Customs
                       Enforcement (ICE) have been conducting intrusive
                       warrantless border device searches since at least
                       2009, when CBP and ICE first published their device
                       search policies (CBP’s currently operative policy
                       was published in 2018). The number of device
                       searches at the border has been steadily
                       increasing, affecting tens of thousands of
                       international travelers each year. Our electronic
                       devices contain intimate information about our
                       personal preferences and daily routines, as well as
                       private communications with friends and family.
                       They contain data revealing health conditions,
                       financial standing, and religious and political
                       beliefs. A search that reveals this information to
                       anyone, let alone law enforcement, is a gross
                       violation of our privacy and free speech rights. 


                       EFF and the American Civil Liberties Union
                       (ACLU)—believing that any warrantless search of
                       electronic devices at the border violates
                       travelers’ rights to privacy under the Fourth
                       Amendment, and freedom of speech and press, private
                       association, and anonymity under the First
                       Amendment—filed suit in 2017 on behalf of 11
                       individuals whose devices were searched without a
                       warrant at the border. Where the U.S. Supreme Court
                       in Riley v. California (2014) acknowledged
                       electronic devices contain “the sum of an
                       individual’s private life” and thus ruled that a
                       warrant must be obtained before searching the cell
                       phone of an arrestee, EFF/ACLU’s suit sought to
                       extend this warrant requirement to border searches
                       of electronic devices. Unfortunately, our path in
                       the courts is currently stalled. The Supreme Court
                       this summer declined to take our case, and despite
                       making some progress in the appellate courts, no
                       circuit court has required a warrant for border
                       device searches in all circumstances.


                       The Protecting Data at the Border Act takes the
                       fight to Congress (Rep. Ted Lieu (D-CA) is expected
                       to introduce the House bill). Along with requiring
                       government officials to obtain a probable cause
                       warrant before accessing the contents of an
                       electronic device, the bill would also protect our
                       digital privacy and free speech rights in the
                       following ways: 


                # ⚓ The_Unsure_State_of_Asian_America⠀⇛


                       People have strong feelings about Jay Caspian Kang.
                       He is one of the few writers currently working in
                       America who filters many disparate subjects through
                       a singular intelligence—sometimes brusque, but
                       always thoughtful. His most recent endeavor, a
                       newsletter for the New York Times Opinion section,
                       has tackled an incredibly wide range of subjects:
                       NFTs, YIMBYs in California, and Chinese immigrants
                       in the Mississippi Delta. He began his career
                       writing about basketball, gambling, high school
                       debating and identity politics, and, memorably, a
                       highly controversial ranking of pop divas. He is
                       also the cohost of a podcast, Time to Say Goodbye
                       (with journalist E. Tammy Kim and historian Andrew
                       Liu), that discusses current events and politics in
                       Asia and Asian America with a distinctively left-
                       internationalist lens.


                # ⚓ Democrats_Are_Ready_to_Abandon_Black_Voters,_Again⠀⇛


                       We have come to a familiar crossroads of American
                       politics. Democrats, who cannot win national office
                       without the overwhelming support of Black people,
                       are facing rejection from perpetually aggrieved,
                       poorly educated whites. These whites are poised to
                       vote to defeat Democrats in upcoming elections. In
                       response, a chorus of powerful Democrats has risen
                       up inside the Beltway to tell Democrats that
                       abandoning Black people—the very people who put
                       them in power in the first place—and making
                       performative efforts to win the support of racists,
                       is the only way to stay in power.


                # ⚓ Indigenous_Peoples,_Like_Mine,_Are_Fighting_for_Their
                  Homelands⠀⇛


                       Latin American and Caribbean communities like ours
                       are rarely noticed in U.S. media — except when we
                       migrate.


                       In summer 2021, U.S. Vice President Kamala Harris
                       came to Central America and told would-be migrants:
                       “Do not come.” More recently, photos of U.S. Border
                       Patrol agents whipping Haitian refugees in the
                       Texas desertbrutally drove that message home.


                # ⚓ Primary_Kyrsten_Sinema⠀⇛


                       In light of Arizona Senator Kyrsten Sinema’s
                       actions repeatedly obstructing progress on policies
                       that would foster greater economic, and racial
                       justice, momentum is gathering for an effort to
                       back a Democratic challenge to her in the 2024
                       primary when she comes up for reelection. Key state
                       leaders and groups including Living United for
                       Change in Arizona (LUCHA) have launched
                       PrimarySinema, an effort to lay the foundation now
                       for defeating her in 2024. Such an effort makes
                       eminent sense for several political, policy, and
                       moral reasons.


          o § Censorship/Free Speech⠀➾


                # ⚓ Prudish_Mastercard_About_To_Make_Life_Difficult_For_Tons_Of
                  Websites⠀⇛


                       For all the attention that OnlyFans got for its
                       shortlived plan to ban sexually explicit content in
                       response to “pressures” from financial partners, as
                       we’ve discussed, it was hardly the only website to
                       face such moderation pressures from financial
                       intermediaries. You can easily find articles from
                       years back highlighting how payment processors were
                       getting deeply involved in forcing website to
                       moderate content.


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


                # ⚓ Progressives_to_Put_US_War_Crimes_on_Trial_and_Demand
                  Freedom_for_Julian_Assange⠀⇛


                       A group of prominent global progressives on
                       Wednesday announced a return of the Belmarsh
                       Tribunal, where participants will put the United
                       States government on informal trial for war crimes
                       and demand freedom for jailed WikiLeaks founder
                       Julian Assange.


                       “At the Belmarsh Tribunal, we will turn the world
                       the right way up, placing crimes of war, torture,
                       kidnapping, and a litany of other gross human
                       rights abuses on trial.”


          o § Civil Rights/Policing⠀➾


                # ⚓ Family_Searches_for_Father_Missing_in_Texas_Desert_as
                  Border_Deaths_Peak⠀⇛


                # ⚓ Opinion_|_Collapse,_Fascism,_or_Progressive_Renewal?⠀⇛


                       While there’s apparently “nothing to see here” when
                       it comes to conservative media outlets and even, in
                       many ways, mainstream media, it’s worth asking the
                       question: “How far down the road toward
                       authoritarian oligarchy, or even outright fascism,
                       have we gone?”


                # ⚓ ‘Striketober’_in_Full_Swing_as_Nearly_100,000_Workers
                  Authorize_Work_Stoppages⠀⇛


                       “The so-called ‘labor shortage’—which we know is
                       really just a shortage of jobs that pay us enough
                       to live on—is a powerful bit of leverage workers
                       have over employers right now.”


                # ⚓ Why_Is_Stalking_Legal?⠀⇛


                       Now that they’re beleaguered, this may be the
                       perfect time to convince lawmakers to act to
                       protect Americans’ most personal information: their
                       home address and phone number.


                       Type your name into a search engine. Odds are, a
                       few of the results will include private companies
                       that reveal your home address or part thereof, your
                       phone number or part thereof, employment and
                       education history, along with information about
                       “known associates” like your friends and family
                       members. For a fee, these personal search services
                       offer to fill in the gaps with data culled from
                       public records such as those of the Department of
                       Motor Vehicles, marriage records, voter
                       registration rolls and consumer credit reports.


                # ⚓ Women_Activists_to_World_Bank:_‘Unfreeze’_Funds_to_Pay
                  Afghan_Teachers,_Health_Workers⠀⇛


                       As the World Bank held its annual meeting on
                       Wednesday, women’s rights advocates gathered
                       outside the powerful institution’s headquarters in
                       Washington, D.C., to demand the release of frozen
                       Afghan funds so that teachers and healthcare
                       workers trying to rebuild war-torn Afghanistan can
                       be paid.


                       “After 20 years of military operations that killed
                       tens of thousands of Afghans, the U.S. should not
                       retaliate against the people of Afghanistan.”


                # ⚓ Family_Searching_for_Migrant_Father_Who_Went_Missing_in
                  Texas_Desert_as_Border_Deaths_Hit_Record⠀⇛


                       Armando Alejo Hernández went missing in the desert
                       after crossing the U.S.-Mexico border in May of
                       2021, but not before sending several last audio
                       messages to his eldest son describing the difficult
                       terrain and asking for help. “He wasn’t feeling so
                       good, and he was out of water and food,” says
                       Hernández’s 17-year-old son Derek. “The group got
                       ahead, and then he lost the group.” Hernández was
                       an undocumented worker in the United States for
                       more than a decade before being deported in 2016.
                       His wife and two sons, who are U.S citizens by
                       birth, have pleaded with Border Patrol and the
                       Mexican Consulate for help, without any luck so
                       far. “This year we are going to break the record of
                       migrants dying at the border,” warns Fernando
                       García of the El Paso-based Border Network for
                       Human Rights, one of many organizations demanding
                       that the Biden administration “fulfill their
                       promise to change the inhumane policies at the
                       border.”


                # ⚓ “Missing_in_Brooks_County”:_Thousands_of_Migrants_Denied
                  Due_Process_at_Border_Have_Died_in_Desert⠀⇛


                       We continue to look at the humanitarian crisis
                       along the border, where more people are dying
                       trying to cross the U.S.-Mexico border than ever
                       before, as President Biden has increased funding
                       for border enforcement and militarization even as
                       he vowed not to expand Trump’s border wall. We go
                       to Brooks County in South Texas, which has recorded
                       at least 98 migrant deaths so far this year, nearly
                       triple the number from 2020. “People are being
                       expelled without any due process regarding their
                       asylum claim,” says Eddie Canales, director of the
                       South Texas Human Rights Center. “There really
                       hasn’t been a change in policy,” said Canales, when
                       asked about Biden’s approach to asylum seekers. We
                       also speak with filmmaker Lisa Molomot, co-director
                       of the new documentary “Missing in Brooks County,”
                       which follows the story of two families searching
                       for lost loved ones who went missing there after
                       crossing the border, driven further into the desert
                       by inland checkpoints and the policy in place since
                       1994 called “prevention through deterrence.”


                # ⚓ Protest_Song_Of_The_Week:_‘No_Jesus_Piece’_By_Snotty_Nose
                  Rez_Kids⠀⇛


                       The following was originally published at Ongoing
                       History of Protest Music.The Canadian Indigenous
                       hip-hop duo Snotty Nose Rez Kids recently released
                       “No Jesus Piece,”the fourth single off their
                       upcoming album “Life After,” which will drop on
                       October 22. It is the follow-up to their excellent
                       2019 album, “Trapline” (one of the best protest
                       albums of 2019).


                       The duo says of the track: “‘No Jesus Piece’ is a
                       reference to embracing our own spiritual symbols.
                       The Catholic church and the government of Canada
                       used Catholicism as a tool of annihilation of
                       Indigenous culture, practice, teachings and ways of
                       being.”“We want to identify the connections between
                       the importance of putting our faith in a sacred
                       metal. While we respect people for having their own
                       religions and religious symbols, we’d rather rock
                       our copper shield.”


                # ⚓ The_Great_Strike_of_2021⠀⇛


                       We are witnessing the ‘Great Strike of 2021’ and
                       it’s composed mostly of millions low paid non-
                       unionized workers!


                       Workers returned to jobs at a rate of 889,000 a
                       month during the 2nd quarter 2021 (April-June) as
                       the economy reopened. That average fell to only
                       280,000 per month in the just completed 3rd quarter
                       2021 (July-Sept), according to the Economic Policy
                       Institute.


                # ⚓ George_Floyd,_Born_This_Day_in_1973⠀⇛


                # ⚓ Breaking_Glass:_Curriculum_“Diversity”_and_Its
                  Discontents⠀⇛


                       Between the first time I read Tennessee Williams’s
                       play The Glass Menagerie and my current round of
                       teaching it in Hungary, some 40 years and scores of
                       readings have gone by, but I still look forward to
                       its language and atmosphere. This dreamlike memory-
                       play has no heroes or villains; its four characters
                       weave through bravery and folly, through obsession
                       and practicality.


                # ⚓ Indigenous_Leaders_Deliver_Petitions_to_Army_Corps_DC
                  Headquarters,_After_155_Activists_Arrested_at_The_White
                  House⠀⇛


                       On the second day of ‘People vs. Fossil Fuels’
                       demonstrations in Washington, D.C., hundreds
                       marched to the White House, again calling on
                       President Biden to recognize  the world is in a
                       climate emergency and to halt approvals of new
                       fossil fuel projects. More than 150 people were
                       arrested for refusing to clear the sidewalk in
                       front of the White House, just a day after similar
                       arrests of 136 people. After the U.S. Park Police
                       escorted the last protesters away, a second rally
                       was held in front of the U.S. Army Corps of
                       Engineers headquarters. There, over a hundred
                       environmental activists showed their ongoing
                       resistance to the recently completed construction
                       of Enbridge’s expanded Line 3 tar sands pipeline.


                       Pipeline opponents have been battling against the
                       Line 3 project in northern Minnesota since it was
                       first proposed in 2014. Enbridge, the project
                       owner, described the pipeline as a replacement of
                       an older, corroding pipe built in the 1960s, but
                       opponents dismiss the company’s claim. They argue
                       it is a new pipeline rather than a replacement,
                       saying Line 3 is larger and has portions that
                       traverse a different area than the older pipeline,
                       including traditional Anishinaabe lands.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ ‘Unacceptable’:_Congressional_Democrats_Slam_Biden’s
                  Refusal_to_Round_Out_FCC⠀⇛


                       Congressional Democrats are reiterating their
                       warning that President Joe Biden’s glaring failure
                       to fully staff the five-person board of the Federal
                       Communications Commission could result in a 2-
                       1 Republican majority on the panel by year’s end,
                       jeopardizing efforts to secure high-speed internet
                       for all and restore net neutrality.


                       “The fact that the Biden administration hasn’t done
                       this, when broadband is such a massive priority for
                       them, is vexing.”


          o § Monopolies⠀➾


                # ⚓ Google,_Amazon,_And_Microsoft_Are_Using_Third_Party
                  Companies_To_Sell_Surveillance_Tech_To_ICE,_CBP⠀⇛


                       A few years ago, tech companies stood up to the US
                       government, issuing statements objecting to
                       immigration policies instituted by the Trump
                       Administration and, in some cases, threatening to
                       pull contracts with ICE (Immigration and Customs
                       Enforcement) and the CBP (Customs and Border
                       Protection).


                # ⚓ After_Docs_‘Show_What_We_Feared’_About_Amazon’s_Monopoly
                  Power,_Warren_Says_‘Break_It_Up’⠀⇛


                       U.S. Sen. Elizabeth Warren on Wednesday renewed her
                       call to break up Amazon after internal documents
                       obtained by Reuters revealed that the e-commerce
                       giant engaged in anti-competitive behavior in India
                       that it has long denied, including in testimonies
                       from company leaders to Congress.


                       “This is not shocking. But it is appalling.”


                # § Copyrights⠀➾


                      # ⚓ ESA_Reports_Game_Piracy,_File-Hosting_and_Cheating
                        Sites_To_US_Government⠀⇛


                             The Entertainment Software Alliance, which
                             counts Nintendo, EA, Activision, Epic, and
                             Ubisoft among its members, has filed a
                             response to the United States Trade
                             Representative’s call for comment on
                             ‘Notorious Markets’. The trade association
                             calls out various piracy-focused platforms
                             including torrent and linking sites, file-
                             hosting services, plus cheating and digital
                             asset platforms.


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