𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, September 05, 2022
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Generated Tue 6 Sep 02:42:43 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
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Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/09/05/


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

QmZ7mLY8uo6YvRrfUTtX3hPHDhQgDNyt4AB4fPvzYWrcC4
QmTZezLwd5vekievmKZscKgr1hkxvuHoSSsWhkA4iTy7Tu
QmNWKKu3gEEUM8UjAb868zLoy5CP9rUmyUWSSFH78F7ZGy
Qmc1hpdpKJMrmE55WT3tg3aQBqe3inuQhnbsjTc8RVVKFq
QmZNGE6NoRBC2J66AEvKbXxsP9j48e5nLCkLncW2SuYUD5
Qmd1qRcbFUvYnekMd31x6KbniK82hv6mEweUfvuLLLU3Dn
QmPGPjyuWmmi4WH1Pm1qxX7pzZhtRC3umeb4DmdE7NfXdU
QmbvCLhKBwB76DsbrKx6Pq16KSvtb9sW8UKVXj9v1pDgCv
QmcoFCaZUJmzby8Vb2wg8PBXe6VR8hW77edQo1u3NsCJ3Q
QmT4B1hoouASzbTAnEZbb6oYbbFnicQpd6JXDB5iwP9Y91
QmZeoDeQynAEb5Yhp8urADxooTvcjp93jYM7aoGTReoxAm
QmUR5BqkVtBjeM3RbDysVaCrQyP93xoRwDKU5C1u5XZdyR
QmS9E4XW4XZrtmFNP12pX65zisQkFTw7frAgGwhna5Fz9m
Qmdj75rdsbiWjm4ms8CTMfcbYno6Pw9hH66AytZ3Hs3qV7
QmWKkufDr5sMvj78wx9nn63R5KYSQipfAGMrMawgr7i6RW
QmVy1ihFnjMRS9u243rmwceZUtn8FwSqLsbXzXsLPS8M37
QmcZN6RDP7J7Dk8c2QYXeoVfYifxDsaK62EM44gSje2HDr
QmcvJBJvcdzE6YbN5kUFP3Cqgwc9K38gcNKU3B86eL6WLr
QmUZ8Zpgu5W6CLgXAAXnvYwpAw9fCGWhqWM6MWMHcNxEwP
QmUtqYa5g8brBCgtMeneus47sgXJXCdgZvkekvW8UuYchF
QmdXKq8frFc6SxT7BErqJC3fnDsbXQfhNmEGEc1BVWprrQ


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

⦿ IRC Proceedings: Sunday, September 04, 2022 | Techrights

⦿ What the Linux Foundation (LF) Truly is: Lobbying Franchise | Techrights

⦿ What is Judenlager Zemlin? | Techrights

⦿ Survey of 3 Million Sites: Microsoft Windows Sinks to Another All-Time Low This Month, GNU/Linux Reaches Record Highs | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/09/05/irc-log-040922/#comments
		http://techrights.org/2022/09/05/lf-lobbying-franchise/#comments
		http://techrights.org/2022/09/05/on-judenlager-zemlin/#comments
		http://techrights.org/2022/09/05/statcounter-record-month/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/09/05/apache-age-1-1-0/#comments
		http://techrights.org/2022/09/05/just-work/#comments
		http://techrights.org/2022/09/05/openmandriva-rome/#comments
		http://techrights.org/2022/09/05/salix-xfce-15-0/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 59

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/05/irc-log-040922/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/05/irc-log-040922/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Sunday,_September_04,_2022⠀✐


Posted in IRC_Logs at 2:11 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-040922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-040922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-040922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-040922.gmi
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
 QmWEozbU1rMr5kATgqKvDBSUCSvUP2Ny7MqDMWWWA8EARB #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmTXJmRQCJgagSxT4LabwDN7WEaXxW89Hk2dDvXTdhf98t (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmNweXFoo4UFNTLVmKZq3RBLGi6EvitxsPL3UQqnQ1LUZX social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmPvAbPwfhcUN2wKf1aa7dtC93VDUCi7h2iHd83DG6dKzE social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmebQ7TAykGM3k9spajAAWcpT8V2Q3jnpN3uHmodemuJrr #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmQnxcfLdpHGxZgFbbHAeFZZ8UqiEfdEA9bPcQJVS7mhpc (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmXFJcnucA1uWLYwzNGGmrtXNMk6PSTTxVfkTX2Pv7agiL #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmWjxdndFgDsaU8w3VorCbixsKbi1uN3C63RopWy9thEbg (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmdXKq8frFc6SxT7BErqJC3fnDsbXQfhNmEGEc1BVWprrQ



                    ䷩ 𝚕𝚒𝚗𝚎 186

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/05/lf-lobbying-franchise/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/05/lf-lobbying-franchise/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ What_the_Linux_Foundation_(LF)_Truly_is:_Lobbying_Franchise⠀✐


Posted in Deception, GNU/Linux, Kernel at 3:24 pm by Dr. Roy Schestowitz


Video_download_link | md5sum 70778d311e7b301386104778dd087dfa
Looking Closely at IRS Form of LF
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/lf-irs-walkthrough.webm


Summary: Linux Foundation (LF) in recent years is little but a bunch of
corporate charlatans; it’s quite evident when one critically looks at their
official paperwork, which became_suppressed


THE year 2019 was quite a year. All Linux.com staff got sacked [1, 2], leaving
the site orphaned without prior warning. Some of that staff has since then quit
writing altogether! Even in other sites… truly devastating.


“It’s all about large corporations and almost all the money is spent in the US,
so it’s not international either.”We now have a copy of the relevant_form_for
2019 (i.e. before COVID-19 impact and collapse of Linux_Foundation revenues)
and the video above goes through it. Jim Zemlin — like his wife [1, 2, 3] —
seems to be defrauding a lot of people. He doesn’t use Linux, he is besieging
it in pursuit of money. He monetises the attacks_on_the_GPL, on decentralised
collaboration (he keeps shilling Microsoft’s GitHub), and he generally misuses
civil rights/good causes to confuse and deflect. The Linux Foundation is all
about greed and it has nothing to do with ethics or morality. It’s all about
large corporations and almost all the money is spent in the US, so it’s not
international either.


“Be wary of what blogs_too say about the Linux Foundation; in recent years the
Linux Foundation started bribing blogs_too (in exchange for ads and puff
pieces).”We don’t suppose any large publishers care to illuminate what’s really
happening. The corporate media protects corporations. Journalism is not
harassment. If done properly, it does bother some people, corporations,
governments, and non-profit organisations. That’s how it is when you do the job
and expose facts. But a sicker society cares so much about every person’s
feelings that humour is seen as rudeness and journalism is perceived to be
“toxic”. This is why Zemlin et al keep shaming the community. They want to dis-
empower anyone who isn’t a big sponsor. That includes Richard Stallman.
Oversensitive people are a form of censorship tool. Sometimes they’re co-opted/
used by censors, wilfully or not…


Be wary of what blogs_too say about the Linux Foundation; in recent years the
Linux Foundation started bribing blogs_too (in exchange for ads and puff
pieces).


Don’t expect the media to cover any of these issues. Wikipedia_too_spreads
lies. █


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


                   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Twitter_as_a_company⦈_
       Unfortunately, Linus Torvalds has let Linux too become a company


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

                    ䷩ 𝚕𝚒𝚗𝚎 763

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/05/on-judenlager-zemlin/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/05/on-judenlager-zemlin/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ What_is_Judenlager_Zemlin?⠀✐


Posted in Deception at 3:44 pm by Dr. Roy Schestowitz


Survivors_angered_over_rock_concert_at_neglected_WWII_Nazi_concentration_camp
in_Belgrade


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


Anger_over_Serbia’s_Nazi_Rock_Venue


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Anger_over_Serbia’s_Nazi_Rock_Venue⦈_


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


Summary: Jim Zemlin (not Judenlager Zemlin) has undermined the Linux community
through something called Linux_Foundation; can he bury the real history and
tradition of the GNU/Linux community to make $1000-per-day “LF Events” on top
of it all?


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

                    ䷩ 𝚕𝚒𝚗𝚎 1554

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/05/statcounter-record-month/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/05/statcounter-record-month/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Survey_of_3_Million_Sites:_Microsoft_Windows_Sinks_to_Another_All-Time_Low
This_Month,_GNU/Linux_Reaches_Record_Highs⠀✐


Posted in GNU/Linux, Microsoft at 10:41 am by Dr. Roy Schestowitz


                   🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Windows_all-time_low⦈_
       Windows has just 27.5%_of_the_whole and 73.5%_of_laptops/desktops


               🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇GNU/Linux_share_2009-present⦈_
GNU/Linux share over time. Chart_source and data in OpenDocument Format (ODF).


Summary: As of today, based on data aggregated by StatCounter so far in
September, Windows sinks to new lows and GNU/Linux is about the exceed 3% on
desktops/laptops worldwide


⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠷⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⠃⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢻⠁⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢸⣿⠉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢸⣿⣿⣿⠟⠻⡿⢿⠟⣿⡏⠀⠀⠈⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⣿⢿⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠹⣿⠀⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠇⠀⠀⠁⠀⠻⠇⠸⠀⠋⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠛⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⡿⠻⡟⠉⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⡏⠸⠛⠻⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 1638

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/09/2022:_Another_RC_of_Linux_6.0_and_Apache_AGE_1.1.0⠀✐


Posted in News_Roundup at 2:48 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audio_and_Video
          o Kernel_Space
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o Reviews
          o BSD
          o Arch_Family
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Mozilla
          o Programming/Development
                # Rust
    * Leftovers
          o Science
          o Hardware
          o Pseudo-Open_Source
                # Openwashing
          o Entrapment_(Microsoft_GitHub)
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o ⚓ 9to5Linux ☛ 9to5Linux_Weekly_Roundup:_September_4th,_2022⠀⇛


                 This week has been all about Ubuntu as we kicked off the
                 week with a piece of fantastic news for fans of the good
                 old Unity7 desktop environment, namely that the Ubuntu
                 Unity distribution is becoming an official Ubuntu flavor.
                 In addition, Ubuntu 20.04.5 LTS arrived with an updated
                 HWE kernel, Ubuntu 22.10 adopted the Linux 5.19 kernel,
                 and both Ubuntu 22.04 LTS and 20.04 LTS users got a new
                 kernel security update.


                 On top of that, this week brought us a new major OBS
                 Studio release, new point releases of the Nitrux, MX
                 Linux, and Armbian distributions, as well as a plethora
                 of software releases for everyone. Below, you can enjoy
                 these and much more in 9to5Linux’s Linux weekly roundup
                 for September 4th, 2022.


          o ⚓ Linux Made Simple ☛ Linux_Weekly_Roundup_#198⠀⇛


                 Welcome to this week’s Linux weekly Roundup. We had a
                 full week in the world of Linux releases with MX Linux
                 21.2, Absolute Linux 20220825, Bluestar Linux 5.19.4,
                 Nitrux OS 20220831, Garuda Linux 220903, Linuxfx
                 11.2.22.04.2, deepin 20.7, and Ubuntu 20.04.5 with all
                 it’s flavors.


          o § Audio and Video⠀➾


                # ⚓ Open Source Security (Audio Show) ☛ Episode_339_–_Is_a
                  network_problem_a_security_vulnerability_–_Open_Source
                  Security⠀⇛


                       Josh and Kurt talk about really weird networking
                       bugs. Josh tells a story about his home network
                       problems that made no sense. There was also a qt5
                       bug that affected wireless networks that made
                       virtually no sense. What should count as a security
                       vulnerability?


                # ⚓ Video ☛ Installing_Arch_Linux_Packages_Never_Been_This_Easy
                  –_Invidious⠀⇛


                       Pacman is a great package manager but some people
                       don’t want to use it directly so instead how about
                       you use a TUI such as pacseek, it’s not the feature
                       rich project out there but it does everything you
                       need


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


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


                # ⚓ Video ☛ Cinnamon_Desktop_Customization_|_Nord_Color_Theme_–
                  Invidious⠀⇛


                       Cinnamon is a Linux desktop that provides advanced
                       innovative features and a traditional user
                       experience.


                # ⚓ Video ☛ Free_Games_for_Linux_|_August_2022_–_Invidious⠀⇛


                       Best Free Linux Games are the most searched term
                       when a windows user switches from his own comfort
                       world. After switching, everyone wants to know what
                       and how to play games on Linux.


                # ⚓ Video ☛ C++_Random_Number_Generator_AKA_STOP_USING_Rand()_–
                  Invidious⠀⇛


                       The C++ random library is one of the most robust
                       and effective ways of generating random numbers in
                       C++. In this video I’ll show you how to generate
                       random numbers using both the old C style interface
                       using rand() and also the Modern C++ style using
                       random engines and distributions


                # ⚓ Video ☛ We_Are_In_Control_Of_Your_Thermostat_–_Invidious⠀⇛


                # ⚓ Video ☛ LastPass_Got_Hacked,_Time_to_Switch_to_KeePass_–
                  Invidious⠀⇛


                       In this video I discuss the recent security
                       incident where LastPass got hacked and had their
                       proprietary source code and company information
                       stolen, I also discuss a better, safer alternative
                       to LastPass called KeepassXC which gives you
                       control over your passwords as well as how you can
                       sync your keepass database with syncthing.


                # ⚓ Linux’s_Malware_Inevitability_|_LINUX_Unplugged_474 [Ed:
                  Playing along with a Microsoft-connected narrative, spreading
                  mostly by Microsoft partners and Microsoft-connected media to
                  distract from Windows' woes]⠀⇛


                       Can Linux do better? Apple is scrambling to build
                       always-on malware protection into the next macOS as
                       its market share grows. A precautionary tale for
                       Linux users.


                       Plus we take a look at Ubuntu Unity as it becomes
                       an official flavor.


          o § Kernel Space⠀➾


                # ⚓ Linux_6.0-rc4⠀⇛


                       It's Sunday afternoon, which can only mean one
                       thing - another rc
                       release. We're up to rc4, and things mostly still
                       look fairly normal.

                       Most of the fixes the past week have been drivers
                       (gpu, networking,
                       gpio, tty, usb, sound.. a little bit of everything
                       in other words).
                       But we have the usual mix of fixes elsewhere too -
                       architecture fixes
                       (arm64, loongarch, powerpc, RISC-V, s390 and x86),
                       and various other
                       areas - core networking, filesystems, io_uring,
                       LSM, selftests and
                       documentation. Some of this is reverts of things
                       that just turned out
                       to be wrong or just not quite ready.

                       Please do go test,
                                   Linus

                # ⚓ LWN ☛ Kernel_prepatch_6.0-rc4_[LWN.net]⠀⇛


                       The 6.0-rc4 kernel prepatch is out for testing.
                       “We’re up to rc4, and things mostly still look
                       fairly normal”.
                       Beyond the usual fixes, 6.0-rc4 includes one
                       feature change: a hook to allow security modules to
                       control access to the io_uring command pass-through
                       mechanism. See this article for the background
                       behind this late-arriving change


          o § Applications⠀➾


                # ⚓ Earthly ☛ 15_Essential_Linux_Terminal_Commands_–_Earthly
                  Blog⠀⇛


                       Linux, a powerful, free, stable, secure, and highly
                       customizable operating system, is essential for any
                       developer’s workflow. The Linux terminal interacts
                       with the operating system for all basic and
                       advanced tasks. Moreover, most web servers run
                       Linux, and tools like Docker work by providing an
                       additional layer of abstraction and automation on
                       top of Linux.


                       While some distributions have GUI (graphical user
                       interface), the GUI is limited with regard to
                       functionality and customization. The terminal, or
                       the shell, provides you with the power to customize
                       and carry out tasks in seconds that would have been
                       tedious, multi-click steps on a GUI. You can chain
                       commands to run multiple commands together with an
                       order of execution or simultaneously, which makes
                       your workflow optimized and efficient.


                       In this post, you’ll learn about fifteen essential
                       commands—commands that will help supercharge you as
                       a Linux user. The commands in this post have been
                       selected based on their popularity and usefulness.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Made Simple ☛ How_to_install_Ripcord_on_a
                  Chromebook⠀⇛


                       Today we are looking at how to install Ripcord 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.


                # ⚓ LinuxTechi ☛ How_to_Deploy_Docker_Swarm_on_Ubuntu_22.04
                  Step-by-Step⠀⇛


                       Docker Swarm is a container orchestration tool that
                       runs on the Docker platform. It helps users to
                       create and manage a cluster of Docker nodes.
                       Clustering in Docker is a crucial concept in
                       providing redundancy by enabling Docker Swarm to
                       fail over should one or more nodes in the cluster
                       fail.


                       Docker Swarm uses the standard Docker API to
                       communicate with other tools such as Docker Engine.
                       It intelligently assigns containers to worker nodes
                       and ensures resource optimization by scheduling
                       container workloads to run on the most suitable
                       node(s)


                # ⚓ Data Swamp ☛ How_to_host_a_local_front-end_for_Reddit_/
                  YouTube_/_Twitter_on_NixOS⠀⇛


                       I’m not a consumer of proprietary social networks,
                       but sometimes I have to access content hosted
                       there, and in that case I prefer to use a front-end
                       reimplementation of the service.


                       These front-ends are network services that acts as
                       a proxy to the proprietary service, and offer a
                       different interface (usually cleaner) and also
                       remove tracking / ads.


                       In your web browser, you can use the extension
                       Privacy Redirect to automatically be redirected to
                       such front-ends. But even better, you can host them
                       locally instead of using public instances that may
                       be unresponsive, on NixOS it’s super easy.


                # ⚓ Data Swamp ☛ Managing_a_fleet_of_NixOS_Part_1_–_Design
                  choices⠀⇛


                       I have a grand project in my mind, and I need to
                       think about it before starting any implementation.
                       The blog is a right place for me to explain what I
                       want to do and the different solutions.


                       It’s related to NixOS. I would like to ease the
                       management of a fleet of NixOS workstations that
                       could be anywhere.


                       This could be useful for companies using NixOS for
                       their employees, to manage all the workstations
                       remotely, but also for people who may manage NixOS
                       systems in various places (cloud, datacenter,
                       house, family computers).


                       In this central management, it makes sense to not
                       have your users with root access, they would have
                       to call their technical support to ask for a
                       change, and their system could be updated quickly
                       to reflect the request. This can be super useful
                       for remote family computers when they need an extra
                       program not currently installed, and that you took
                       the responsibility of handling your system…


                # ⚓ Trend Oceans ☛ Arch2appimage:_Convert_Arch_Package_into
                  Appimage_using_Python_Script_on_Linux_–_TREND_OCEANS⠀⇛


                       If you are using Arch Linux due to a specific
                       package being only available in that distribution,
                       then it’s time for you to move on with that
                       package.


                       What am I talking about? You might be thinking
                       about what I’ve just said. Look, you and I both
                       know that Arch or its derivatives like Manjaro and
                       Endeavour, are community-driven and have the
                       largest software repository.


                       It’s been a long time since I’ve used Arch or any
                       of its derivates, but as I recall, I remember there
                       were many packages that were not available for
                       other distributions and vice-versa.
                       However, if you are using an Arch-based system just
                       because your favourite package is not available for
                       another distribution like Debian, Ubuntu, RHEL,
                       Fedora, etc, then it’s time for you to move your
                       package to those distributions using Arch2appimage.


          o § Games⠀➾


                # ⚓ Batocera,_the_retro-gaming_linux_distro,_now_available_on
                  PS4_–_Wololo.net⠀⇛


                       Noob404 is offering yet another Linux distribution
                       for Jailbroken PS4 owners, this time Batocera
                       Linux.


                # ⚓ Overclocked_PS4_shows_fairly_impressive_benchmark_numbers_–
                  Wololo.net⠀⇛


                       There are plenty of guides out there on how to run
                       Linux on your PS4, but you’ll need a Jailbroken PS4
                       to install Linux.


                # ⚓ Wii_U_Emulation:_Cemu_2.0_released,_goes_open_source,_Linux
                  version_now_available_–_Wololo.net⠀⇛


                       Some big news for the small world of Wii U
                       emulation, with the announce that popular Wii U
                       emulator Cemu goes open source. This 2.0 release
                       also brings Linux support!


                       Exzap, the main developer behind Cemu, has shared
                       the news in a lengthy announce over at Reddit,
                       where he explains the reasons for going open
                       source. Mostly, trying to bring fresh blood to the
                       project as he’s been the only main developer on the
                       project for the past 8 months.


                       [...]


                       For the linux builds, some preliminary builds can
                       be found on github, but in general for now (until
                       better support is added) you are expected to build
                       the binary yourself.


          o § Desktop Environments/WMs⠀➾


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ Gingerblue_6.2.0_for_musicians_who_compose,_record,
                        and_share_original_music_in_Evolution_–_Ole_Aamot⠀⇛


                             You can try Gingerblue 6.2.0 with Evolution
                             email attaching in the Broadcast step in the
                             GTK+/GNOME wizard available from https://
                             www.gingerblue.org/ and https://
                             wiki.gnome.org/Apps/Gingerblue


                             Gingerblue 6.2.0 provides a link in the final
                             GtkAssistant Broadcast page that launch
                             Evolution or another email program that
                             supports mailto:
                             ?attachment=localOggVorbisRecording.ogg
                             application handler in GNOME 43. The syntax
                             mailto:?attachment is not yet a RFC and it is
                             only supported by Evolution 3.44 as far as I
                             have tested, the default email client on
                             GNOME 43.


                      # ⚓ Linux Links ☛ Saving_Money_with_Linux:_Power_Settings
                        in_GNOME_–_LinuxLinks⠀⇛


                             The first article in this series recommended
                             you use a power meter to establish how many
                             Wh your computer uses. In this article we’ll
                             explore a few ways you can reduce this
                             footprint without sacrificing your
                             productivity or workflow.


                             We’re testing power consumption using the
                             GNOME desktop on a Mini PC with a quad-core
                             i5-6500T processor. This is a relatively old
                             desktop processor (Intel 6th generation with
                             a 35W TDP).


                             From the GNOME desktop, there are three power
                             profiles available. To choose a power profile
                             go to the Activities overview and start
                             typing Settings. Click Power to open the
                             panel.


    * § Distributions and Operating Systems⠀➾


          o § Reviews⠀➾


                # ⚓ Distro Watch ☛ Review:_deepin_23_Preview⠀⇛


                       Hiweed GNU/Linux is an Ubuntu-based distribution
                       developed in China. Actually, that description is a
                       bit out of date, let me start over. Linux Deepin is
                       an Ubuntu-based Linux distribution featuring a
                       custom desktop environment called Deepin Desktop
                       Environment. Actually, that’s no longer accurate.
                       Deepin is a Debian-based distribution featuring the
                       custom Deepin desktop and a number of desktop
                       applications developed in-house. Wait, I’m almost
                       up to date now. deepin is a Chinese distribution
                       which claims to be independently developed. It
                       features the Deepin desktop, a custom system
                       installer, a custom application repository called
                       Linglong, and the project offers atomic updates.


                       A preview of the latest version of deepin was
                       published in mid-August and its release
                       announcement featured a few key points.
                       Specifically: the move away from Debian to be an
                       independent distribution; the use of Linglong to
                       offer a custom repository of portable applications
                       that can be run across multiple distributions; and
                       the use of atomic updates to make updates more
                       reliable.


                       The new deepin release, version 23, is currently in
                       the development phase at the time of writing and I
                       wanted to see what this departure from the
                       previous, Debian-based model would look like. I
                       downloaded the deepin ISO which is a 3.4GB build
                       for 64-bit (x86_64) computers. After confirming the
                       media’s checksum was good, I tried booting from it.


                       The live media brings up a boot menu asking if we’d
                       like to install deepin with version 5.15 of the
                       Linux kernel or 5.18. Both options also have
                       failsafe driver options, resulting in four menu
                       options. There’s a fifth menu entry for running a
                       self-check on the media. There are no options for
                       running a live desktop in the menu. I decided to
                       try the 5.18 kernel option first.


          o § BSD⠀➾


                # ⚓ DragonFly BSD Digest ☛ In_Other_BSDs_for_2022/09/03 [Ed: A
                  batch of BSD news for the week]⠀⇛


          o § Arch Family⠀➾


                # ⚓ Linux Shell Tips ☛ The_History_of_Arch_Linux_Distribution
                  and_Repositories⠀⇛


                       Most Linux distributions are renowned for their
                       ease of use. Out of the box, you get pre-installed
                       applications that will help you get working without
                       so much of a struggle.


                       Arch Linux is a Linux distribution that takes on a
                       different philosophy. It’s a pragmatic Linux flavor
                       and demands a high level of skill in setting
                       everything up.


                       Designed for Intel’s x86_64 architecture, Arch
                       Linux is a general-purpose operating system that is
                       free and open source and designed for intermediate
                       to advanced users.


                       By default, it provides a minimal base system
                       allowing the user to install and configure only
                       what is required. This is especially handy in
                       avoiding bloatware that comes with graphical
                       installations.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ MakeTech Easier ☛ 7_Easy_Ways_to_Transfer_Files_from_Your
                  Computer_to_Your_Android_–_Make_Tech_Easier⠀⇛


                # ⚓ Android Police ☛ Here_are_the_10_indie_Android_games_you’ll
                  want_to_pick_up_this_weekend⠀⇛


                # ⚓ The Sun ☛ Three_Android_security_hacks_to_must_learn_today
                  –_ignoring_them_could_cost_you_|_The_Sun⠀⇛


                # ⚓ SlashGear ☛ 5_Android_Cleaner_Apps_To_Free_Up_Space_On_Your
                  Phone⠀⇛


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


          o ⚓ PostgreSQL ☛ PostgreSQL:_Announcing_the_release_of_Apache_AGE
            1.1.0⠀⇛


                 Apache AGE is a PostgreSQL extension that provides graph
                 database functionality.


                 AGE (A Graph Extension) is inspired by AgensGraph, a
                 multi-model database Bitnine built from PostgreSQL 10.
                 The goal of the project is to apply graph processing and
                 analytics to relational databases, enabling both the
                 ANSI-SQL and openCypher.


          o § Web Browsers⠀➾


                # § Mozilla⠀➾


                      # ⚓ OMG Ubuntu ☛ Firefox_105_Includes_Gesture_Navigation,
                        PDF_Annotation_+_More_–_OMG!_Ubuntu!⠀⇛


                             Mozilla Firefox 105 is shaping up to be an
                             impressive update when the stable release
                             lands in a couple of weeks time.


                             Intrigued by what I’ve been hearing, I
                             downloaded the latest beta of the famous FOSS
                             browser to find out first-hand what Mozilla’s
                             got in store for us.


                             And spoiler: it’s set to be a real doozie.


          o § Programming/Development⠀➾


                # ⚓ uni Toronto ☛ Go_1.19_added_an_atomic.Pointer_type_that’s_a
                  generic_type⠀⇛


                       In Go 1.18, the Go developers were careful to keep
                       generic types out of the standard library, to the
                       point where they decided not to have a
                       ‘constraints’ package of generics helpers in the
                       standard library, never mind generic versions of
                       slices and maps. As the Go 1.18 release notes say,
                       all three packages were instead put under
                       golang.org/x/exp. However, Go 1.19 turns out to
                       have somewhat quietly changed that, adding the
                       standard library’s first public generic type in
                       sync/atomic’s new atomic.Pointer[T any] type.


                       The atomic.Pointer type is a type-safe atomic
                       pointer to a *T, with the type safety assured at
                       compile time. You could previously do atomic
                       pointers through atomic.Value, but that was only
                       type safe at runtime and might panic if you
                       violated type safety (and storing a nil in one was
                       complex (but possible)). The appeal of
                       atomic.Pointer as a generic type is pretty obvious
                       and it also seems unlikely that you could design a
                       better generic type or a better API than the one it
                       uses (which atomic.Value had from Go 1.4 and Go
                       1.17 (for .CompareAndSwap())). I suspect that all
                       of this adds up to why it was considered safe to
                       add to the standard library in Go 1.19, and thus
                       commit Go to having it there as part of the
                       compatibility guarantee.


                # § Rust⠀➾


                      # ⚓ Red Hat ☛ How_to_create_Python_binding_for_a_Rust
                        library_|_Red_Hat_Developer⠀⇛


                             This article continues a series about how to
                             take advantage of the recent Rust support
                             added to Linux.


                      # ⚓ Red Hat ☛ How_to_create_C_binding_for_a_Rust_library
                        |_Red_Hat_Developer⠀⇛


                             This article is the second installment of a
                             series about how to take advantage of the
                             recent Rust support added to Linux. The first
                             article in the series, 3 essentials for
                             writing a Linux system library in Rust,
                             describes special considerations that system
                             libraries require when you are writing in
                             Rust. This article demonstrates how to create
                             a C binding so that programmers in C or C++
                             can call your Rust library. Rust has not
                             conquered the Linux world yet, so our system
                             library needs to provide bindings to other
                             languages.


    * § Leftovers⠀➾


          o ⚓ Matt Rickard ☛ Why_Does_Google_Kill_So_Many_Products?⠀⇛


                 Google’s reputation for discontinuing products is
                 unmatched. There’s even a site dedicated to it
                 (KilledByGoogle). We all loved Google Reader, but it shut
                 down almost ten years ago.


          o § Science⠀➾


                # ⚓ ACM_TechBrief_Warns_of_Promise_and_Peril_of_“Sleeper”
                  Quantum_Simulation_Technology,_Highlighting_Multiple_Risks⠀⇛


                       The Association for Computing Machinery’s global
                       Technology Policy Council (ACM TPC) has just
                       released “Quantum Computing and Simulation.” It is
                       ACM’s fourth TechBrief: a series of short technical
                       bulletins by ACM TPC that present scientifically
                       grounded perspectives on the impact of specific
                       technological developments in computing and their
                       applications.


                       “Quantum Computing and Simulation” underscores how
                       quantum simulation, an offshoot of quantum
                       computing that has received relatively little
                       attention, poses profound societal and individual
                       risks as well as benefits with serious public
                       policy implications. These include that intense
                       media and policymaker focus on the theorized
                       encryption-cracking power of future quantum
                       computers has obscured the imminent viability, and
                       actual likely consequences, of quantum simulation
                       technology today.


                # ⚓ Scientists_discover_new_‘origins_of_life’_chemical
                  reactions⠀⇛


                # ⚓ BBC ☛ ‘We_talk_to_plants_–_they_tell_us_how_happy_they_are’
                  –_BBC_News⠀⇛


                       Vertical farming – growing plants indoors, on
                       stacked levels, in a highly controlled environment
                       – allows higher yields.


                       And now, the Gardin company hopes to further
                       improve productivity, using sensors and artificial
                       intelligence to assess individual leaves and
                       suggest changes to each plant’s environment.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ Telink_energy_harvesting_wireless_module_to
                  enable_batteryless_remote_controls_–_CNX_Software⠀⇛


                       The solution is based on a 48MHz RISC
                       microcontroller that supports Bluetooth 5.1 LE,
                       802.15.4 (Zigbee/RF4CE/6LoWPAN/Thread), and 2.4GHz
                       proprietary protocols. With a single module
                       integrating all main components required for
                       batteryless operation, Telink says its solutions
                       reduce BOM and size, as well as supply chain
                       complexity, and improves user-friendliness by
                       removing the need for battery swaps.


          o § Pseudo-Open Source⠀➾


                # § Openwashing⠀➾


                      # ⚓ Enterprisers Project ☛ Digital_transformation:_3
                        steps_to_enable_innovation⠀⇛


                             Everyone wants to be seen as innovative.
                             Innovation conjures images of exciting,
                             dynamic companies that move fast, generate
                             great results, and leave everyone (employees
                             and customers) happy.


                      # ⚓ OpenSource.com ☛ Saving_home_energy_using_open
                        organization_principles [Ed: Openwashing and
                        greenwashing all in one]⠀⇛


                             There are (at least) two ways to look at the
                             move to more green power generation: the
                             supply side and the demand side. The supply
                             side emphasizes a transition from fossil
                             fuels to renewable energy and carbon-free
                             energy. The demand side, however, looks at
                             how to reduce energy use, preferably without
                             hurting the current standard of living.


          o § Entrapment (Microsoft GitHub)⠀➾


                # ⚓ Its FOSS ☛ StackAid_Helps_Developers_Fund_Hundreds_of_Open-
                  Source_Project_Dependencies_in_No_Time [Ed: GitHub (Microsoft
                  proprietary prison) trap disguised as "aid"]⠀⇛


                       Free and open-source projects empower you with
                       essential tools and services without spending a
                       dime.


                       While that sounds exciting, these projects need
                       funding to keep things running and potentially
                       improve your experience with it.


          o § Security⠀➾


                # ⚓ Daniel Stenberg ☛ A_bug_that_was_23_years_old_or_not_|
                  daniel.haxx.se⠀⇛


                       The vulnerable code has been in curl versions since
                       version 4.9 which makes it exactly 8,729 days (23.9
                       years) until the shipped version 7.85.0 that fixed
                       it. It also means that we introduced the bug on
                       project day 201 and fixed it on day 8,930.


                       The code was not problematic when it shipped and it
                       was not problematic during a huge portion of the
                       time it has been used by a large amount of users.


                       It become problematic when HTTP servers started to
                       refuse HTTP requests they suspected could be
                       malicious. The way this code turned into a denial
                       of service was therefore more or less just
                       collateral damage. An unfortunate side effect.


                       Maybe the bug was born first when RFC 6265 was
                       published. Maybe it was born when the first widely
                       used HTTP server started to reject these requests.


                # ⚓ OpenSource.com ☛ 3_things_to_know_about_planning_for_OTA
                  updates_in_your_homelab_|_Opensource.com⠀⇛


                       Updates to a system used to be relatively
                       straightforward. When a developer needed to revise
                       something that they’d already distributed to the
                       public, an updater would be released for people to
                       run. Users would run the updater, allowing old
                       files to be replaced by new files and new files to
                       be added. Even with these “relatively
                       straightforward” updates, though, there was a
                       catch. What happens when a user’s installation is
                       in an unexpected state? What happens when an
                       upgrade is interrupted? These questions are just as
                       relevant now when all kinds of devices are online,
                       and sometimes in need of important security
                       updates. Many updates today are delivered
                       wirelessly, over-the-air (OTA), and the potential
                       for poor connections, sudden loss of signal, or
                       loss of power, can potentially be disastrous to
                       what should be a minor update. These are the top
                       three strategies you need to consider when planning
                       to deliver over-the-air updates.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Make Use Of ☛ Is_Wickr_Secure?_How_the_Encrypted
                        Instant_Messenger_App_Works [Ed: Wickr has been buster
                        and is not trustworthy anymore.]⠀⇛


                             You have almost certainly used an instant
                             messaging app at some point. In fact, you
                             probably use one on a daily basis, and it is
                             highly likely you use apps like Facebook
                             Messenger—which is neither secure nor
                             private.


                             Fortunately, secure alternatives that keep
                             your messages private, and don’t collect or
                             sell your personal data, exist. Wickr is
                             among their number. So, what is Wickr, and
                             how does it work? Is Wickr safe? How does it
                             compare to other encrypted messaging apps?


                      # ⚓ The Register UK ☛ China_orders_tech_companies_to_ID
                        users_who_spread_fake_news⠀⇛


          o § Defence/Aggression⠀➾


                # ⚓ New York Times ☛ China_Charges_28_People,_Months_After
                  Brutal_Beating_of_Women_–_The_New_York_Times⠀⇛


                       A group of men caught on camera violently beating
                       several women at a barbecue restaurant in June were
                       charged on Monday, part of a wider investigation
                       into the criminal activities of a local gang in the
                       Chinese city of Tangshan.


                       More than a dozen officials and police officers are
                       also under investigation for corruption, more than
                       two months after the brutal attack unleashed a
                       torrent of outrage over violence against women.


                # ⚓ Ukraine_and_the_Politics_of_Permanent_War⠀⇛


                       No one, including the most bullish supporters of
                       Ukraine, expect the nation’s war with Russia to end
                       soon. The fighting has been reduced to artillery
                       duels across hundreds of miles of front lines and
                       creeping advances and retreats. Ukraine, like
                       Afghanistan, will bleed for a very long time. This
                       is by design.


                       On August 24, the Biden administration announced
                       yet another massive military aid package to Ukraine
                       worth nearly $3 billion. It will take months, and
                       in some cases years, for this military equipment to
                       reach Ukraine. In another sign that Washington
                       assumes the conflict will be a long war of
                       attrition it will give a name to the U.S. military
                       assistance mission in Ukraine and make it a
                       separate command overseen by a two- or three-star
                       general. Since August 2021, Biden has approved more
                       than $8 billion in weapons transfers from existing
                       stockpiles, known as drawdowns, to be shipped to
                       Ukraine, which do not require Congressional
                       approval.


                # ⚓ Radioactivity_under_the_sand⠀⇛


                       The Hoggar massif is located in the west of the
                       Algerian Sahara. Prehistoric men have left stunning
                       rock carvings there. The men of the 20th century
                       left nuclear waste.


                       Between 1960 and 1996, France carried out 17
                       nuclear tests in Algeria and 193 in French
                       Polynesia. In Algeria, atmospheric and underground
                       tests were carried out at the Reggane and In Ekker
                       sites, in an atmosphere of secrecy and conflict
                       between an Algerian nation under construction and a
                       colonial power seeking strategic autonomy. A
                       majority of the tests – 11 – were carried out after
                       the Evian agreements (18 March 1962), which
                       established Algeria’s independence.


                       [...]


                       In French Polynesia, the strong mobilization of
                       many associations has enabled the environmental
                       consequences to be taken into account and the first
                       remediation steps to be put in place. For Algeria,
                       the situation is different. Due to a tumultuous
                       Franco-Algerian relationship, the absence of
                       archives, and the absence of registers of local
                       workers who participated in the tests, the data on
                       the consequences of the tests remains patchy and
                       incomplete. It was only in 2010, thanks to
                       independent expertise, that a map from the Ministry
                       of Defense was revealed, showing that the European
                       continent was also affected by fallout from the
                       nuclear tests carried out in the south of the
                       Sahara.


          o § Environment⠀➾


                # ⚓ Rlang ☛ CO2_Emissions_Comparing_and_Modeling_for_Global
                  Warming_|_R-bloggers⠀⇛


                       Recently, I watched the new Predator movie, Pray,
                       and I loved it. Hence, I’ve fallen into the
                       Predators series, especially the first two movies,
                       again. The Predators in the movie would choose warm
                       planets to hunt because their vision capabilities
                       are based on infrared thermal, which allows them to
                       see heat signatures.


                # ⚓ Jacobin Magazine ☛ The_Floods_Devastating_Pakistan_Are_More
                  Than_a_Natural_Disaster⠀⇛


                       Monsoon rains and melting glaciers have driven tens
                       of millions of Pakistanis from their homes. The
                       disaster shows that the poor Global South
                       populations who do least to cause climate change
                       are the people who pay most for its consequences.


                # § Energy⠀➾


                      # ⚓ Didier Stevens ☛ Quickpost:_Standby_Power_Consumption
                        Of_My_Bosch_18V_Chargers_|_Didier_Stevens⠀⇛


                             I have 2 Bosch 18V “power for all” chargers.
                             A normal charger (AL 1830 CV) and a fast
                             charger (AL 1880 CV).


                             Measuring the power consumption of these 2
                             chargers in standby mode (plugged into a 230V
                             outlet, but no battery connected) with a GPM-
                             8310 powermeter, I obtained the following
                             results


          o § Finance⠀➾


                # ⚓ Michael West Media ☛ Wing_crack_fears_for_A380_superjumbo
                  escalate_customer_nightmare_for_Qantas_chief_Alan_Joyce_–
                  Michael_West⠀⇛


                       Qantas international flights may become even more
                       expensive as Airbus has issued a global directive
                       concerning A380 wing cracks. Holus-bolus leasing of
                       foreign aircraft and flight crew is now being
                       considered. Michael Sainsbury with this exclusive
                       investigation.


                       Qantas is being forced into urgent maintenance on
                       two of its three double-decker A380 planes, due to
                       fears at their manufacturer Airbus that some of the
                       aircraft may have cracks in their wings due to
                       problems with critical aircraft infrastructure. The
                       superjumbos are the biggest planes in the sky and
                       can carry up to 853 passengers.


                # ⚓ Michael West Media ☛ Pensions_boost_as_cost_of_living_bites
                  –_Michael_West⠀⇛


                       More than 4.7 million Australians struggling to
                       cope with cost of living pressures are in line for
                       a helping hand. Social Services Minister Amanda
                       Rishworth says an indexation increase to welfare
                       payments set to kick in on September 20 will be the
                       largest in more than 30 years for allowances and 12
                       years for pensions.


                # ⚓ The_Past,_Present,_and_Future_of_Work_–_YES!_Magazine⠀⇛


                       Our work environment is deeply dysfunctional. But
                       making systemic change requires understanding how
                       we got here.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Reason ☛ Trump_Disregards_Democracy,_While_Biden_Ignores
                  Its_Dangers⠀⇛


                       In his speech last night about “the continued
                       battle for the soul of the nation,” President Joe
                       Biden said some things that are indisputably true.
                       He noted that democracy requires candidates to
                       accept the results of “free and fair elections” and
                       that refusing to do so threatens the rule of law as
                       well as the peaceful transfer of power.


                       Donald Trump and his followers have conspicuously
                       failed that basic test. But Biden’s emphasis on
                       preserving democracy sets the bar for good
                       government pretty low, eliding the tension between
                       majority rule and individual freedom. And his
                       related claim that Trump’s refusal to concede
                       electoral defeat amounts to an “extreme ideology”
                       gives the former president, who is anything but a
                       systematic thinker, too much credit.


                # ⚓ Scheerpost ☛ Katrina_vanden_Heuvel:_Gorbachev’s_Legacy⠀⇛


                       On March 11, 1985, Mikhail Gorbachev became leader
                       of the Soviet Union. Within a few weeks, the full-
                       scale reformation he attempted to carry out both
                       inside his country and in its Cold War relations
                       with the West, particularly the United States,
                       began to unfold. Perestroika (“restructuring”)—as
                       Gorbachev called his reforms—officially ended with
                       the Soviet Union and his leadership in 1991. The
                       historic opportunities for a better future it
                       offered Russia—and the world—have been steadily
                       undermined ever since.


                       Usually forgotten is that the wave of
                       democratization at the end of the 20th century
                       began in a place, and in a way, that few had
                       expected: in Soviet Russia, under Gorbachev’s
                       leadership as the head of the Soviet Communist
                       Party. Indeed, the extent to which his democratic
                       achievements during nearly seven years in power
                       have been forgotten or obscured is a measure of
                       historical amnesia.


                # ⚓ TwinCities Pioneer Press ☛ Serge_Schmemann:_Gorbachev_freed
                  the_Soviet_Union_but_could_not_save_it_–_Twin_Cities⠀⇛


                       Back in the old Soviet Union, the political joke
                       was the principal underground conduit of political
                       opinion. One that made the rounds soon after
                       Mikhail Gorbachev came to power in 1985 posed this
                       question: “Who supports Gorbachev in the
                       Politburo?” The answer: “Nobody has to. He can move
                       around on his own.”


          o § Censorship/Free Speech⠀➾


                # ⚓ New York Times ☛ Parler_Returns_to_Google_Play_Store⠀⇛


                       Parler, the social media service that attracted
                       fans of former President Donald J. Trump, will
                       return to Google’s Play app store on Friday, more
                       than a year after Google suspended the app for
                       content that incited violence.


                       A Google spokesman said the app had significantly
                       increased its content moderation since the
                       beginning of 2021. All apps in Google’s Play Store
                       must have practices “that prohibit objectionable
                       content, provide an in-app system for reporting
                       objectionable” content, and remove or block abusive
                       users who violate terms and policies, the spokesman
                       said in a statement.


                       The app had also been banned from Apple’s App
                       Store, but has since been reinstated.


                       Parler defended its content moderation policies on
                       Friday. “While Parler believes the best way to
                       address the problems of hate and divisiveness in
                       today’s culture is to allow more speech, not less,
                       we are still happy to do business with those who
                       think differently, on the terms on which we do
                       agree,” Christina Cravens, Parler’s chief marketing
                       officer, said in a statement. “The conversation
                       isn’t over, and those who want to see Parler as we
                       intend it may always do so in the browser at
                       Parler.com.”


                # ⚓ New York Times ☛ Opinion_|_Salman_Rushdie_and_What_It_Means
                  to_Support_Free_Speech_–_The_New_York_Times⠀⇛


                       Violence against writers was the topic I was about
                       to interview the novelist Salman Rushdie about at
                       the Chautauqua Institution on Aug. 12. We were
                       being introduced onstage when out of nowhere, like
                       a scene from Mr. Rushdie’s novel “Shalimar the
                       Clown,” a knife-wielding man rushed onto the stage
                       and began to stab him.


                       Immediately audience members ran to the stage to
                       defend him.


                       It was a remarkable response. That rush of people
                       leaping from their seats was the opposite of the
                       so-called “bystander effect,” when individuals do
                       nothing, relying on others to help. I would call it
                       “the reader effect.” Reading creates empathy, and
                       Chautauqua is an intentional community of readers.
                       The intuitive response of an empathetic community
                       is to help.


                # ⚓ RFA ☛ Shanghai_police_detain_zero-COVID_critic_who_called
                  on_local_leader_to_resign⠀⇛


                       Shanghai police have detained a prominent rights
                       activist who called on a local official to resign
                       over the citywide COVID-19 lockdown in April.


                       Ji Xiaolong has been incommunicado, believed
                       detained by the Shanghai state security police, for
                       24 hours, sources told RFA on Friday.


                       Ji, 46, lives in an expatriate district of Pudong
                       district, and has around 33,000 followers on
                       Twitter, which is banned in China.


                       His detention came after he began writing petitions
                       to Shanghai ruling Chinese Communist Party (CCP)
                       secretary Li Qiang, calling on him to resign for
                       “blindly following orders from the central
                       government [in Beijing]” when implementing weeks of
                       grueling lockdown in the city earlier this year.


                       In the petition, Ji wrote that he was fine with
                       being jailed for opposing government policies in an
                       era of widespread internet censorship and
                       surveillance of ordinary people.


                # ⚓ Reason ☛ Biden_Admin’s_‘Misinformation’_Crusade_is
                  Censorship_by_Proxy⠀⇛


                       On July 16, 2021, the day that Joe Biden accused
                       Facebook of “killing people” by failing to suppress
                       misinformation about COVID-19 vaccines, a senior
                       executive at the social media platform’s parent
                       company emailed Surgeon General Vivek Murthy in an
                       effort to assuage the president’s anger. “Reaching
                       out after what has transpired over the past few
                       days following the publication of the
                       misinformation advisory, and culminating today in
                       the President’s remarks about us,” the Meta
                       executive wrote. “I know our teams met today to
                       better understand the scope of what the White House
                       expects from us on misinformation going forward.”


                # ⚓ Hong Kong Free Press ☛ Explainer:_Hong_Kong’s_national
                  security_crackdown_–_month_26⠀⇛


                       Hong Kong’s High Court made a landmark ruling this
                       month to lift reporting restrictions on committal
                       proceedings for criminal cases, including national
                       security cases, should the defendant request the
                       limitations be removed.


                # ⚓ RFA ☛ Facebook_user_fined_for_accusing_Vietnamese_police_of
                  ‘singing_too_much_karaoke’_—_Radio_Free_Asia⠀⇛


                       A Facebook user in Vietnam has been fined VND 7.5
                       million (U.S.$ 323) by authorities in Bac Giang
                       province for “slanderous acts, distorting and
                       affecting the honor and reputation of the police
                       force.”


                       State media cited a source from the Son Dong
                       District police as saying the 35-year-old owner of
                       the Facebook account P*****R***, who had the
                       initials NVP and lived locally, posted an article
                       titled: “Crackdown on brothels hiding in the shadow
                       of Karaoke bars.”


                       NVP added the comment: “The crackdown was for show.
                       Maybe policemen go singing more [than ordinary
                       people],” with the implication that “singing” was
                       not the only activity the police were taking part
                       in.


                       NVP was fined in accordance with Point A, Clause 1,
                       Article 101, Decree 15 of the government
                       regulations on penalties for administrative
                       violations in the fields of post,
                       telecommunications, radio frequencies, information
                       technology and electronic transactions, often used
                       to punish those accused of spreading “fake news”
                       online.


                # ⚓ Vice ☛ Virginia_Court_Blocks_Republican_Attempt_To
                  Criminalize_LGBTQ_Books⠀⇛


                       A court in Virginia has thrown out a lawsuit which
                       tried to make it illegal to sell or lend two
                       popular LGBTQ-themed books to minors in the state.


                       The lawsuit—which was brought against book chain
                       Barnes & Noble by state delegate Tim Arnold on
                       behalf of Republican Congressional candidate Tommy
                       Altman—tried to use the state’s ancient “obscenity”
                       laws to have the books restricted or removed from
                       stores and library shelves. While book bans have
                       become frighteningly common in schools and public
                       libraries, the West Virginia lawsuit is notable
                       because it tried to criminalize the books entirely,
                       making them illegal to sell or loan within the
                       state.


                # ⚓ Gizmodo ☛ Taliban_Is_Upgrading_Afghanistan_to_4G_Despite
                  Censorship⠀⇛


                       The Taliban wants to expand high-speed internet
                       connectivity in Afghanistan despite a history of
                       online censorship and internet blackouts to thwart
                       protests against the militant group.


                # ⚓ RFA ☛ Chinese_police_crack_down_on_petitioners,_dissidents
                  ahead_of_20th_party_congress_—_Radio_Free_Asia⠀⇛


                       The ruling Chinese Communist Party (CCP) has
                       announced it will hold its 20th National Congress
                       on Oct. 16, amid a mounting wave of censorship and
                       curbs on the freedom of dissident voices around the
                       country.


                       A Beijing-based petitioner surnamed Ma said police
                       had already started rounding up petitioners,
                       ordinary people who pursue complaints against local
                       government wrongdoing through China’s “letters and
                       visits” system, despite frequent detention and
                       harassment from “interceptors” sent from their
                       hometowns to stop them.


                       “The Beijing police started rounding up petitioners
                       more than 10 days ago — they’ve all been taken back
                       to where they came from,” she said. “People came
                       from Heilongjiang more than 10 days ago to detain
                       people, and we got into a fight with officers from
                       the police station.”


                # ⚓ RFA ☛ Taiwan_author_hits_back_over_book_ban,_saying_she_is
                  proud_to_be_banned_in_China_—_Radio_Free_Asia⠀⇛


                       Taiwanese author Lung Yingtai has responded to the
                       banning of her books in Chinese schools, saying she
                       is honored to have been targeted by the Chinese
                       Communist Party (CCP)’s ever-widening program of
                       censorship.


                       “I am honored to have been banned by you,” the
                       former Taiwanese culture minister and long-term
                       critic of authoritarian rule wrote on her Facebook
                       page after schools in the eastern Chinese provinces
                       of Shandong and Jiangsu, among other locations,
                       issued notices to parents that all of her works
                       were no longer considered suitable reading matter
                       for children.


                       “Actually, I have been banned for a long time,” she
                       wrote, adding that “Big River, Big Sea 1949″ and
                       “Please Use Civilization to Convince Me” have been
                       banned in China for more than 10 years now.


                       Other works including “Watching You Go” and “Dear
                       Andreas” have also been targeted, Lung wrote.


                # ⚓ Off Guardian ☛ ‘The_Rise_of_the_New_Normal_Reich’_banned_in
                  Germany,_Austria,_and_The_Netherlands!_–_OffGuardian⠀⇛


                       So, the censorship of my latest book, The Rise of
                       the New Normal Reich: Consent Factory Essays, Vol.
                       III (2020-2021), continues. Amazon.com has now
                       banned the book in three countries … Germany,
                       Austria, and The Netherlands.


                       The pretext the Amazon Content Review Team has
                       cited as grounds for banning the book is the semi-
                       visible swastika on the cover. This pretext is
                       clearly a pretext, i.e., a lie, as Amazon sells a
                       number of other products displaying semi-visible
                       swastikas in these markets.


                # ⚓ Reason ☛ Engineering_Board_Penalizes_Engineer-Activist_for
                  Calling_Himself_an_Engineer⠀⇛


                       The head of an urban policy nonprofit has been
                       penalized by Minnesota’s licensing board for
                       referring to himself as a “professional engineer”
                       in speeches and articles while his license was
                       expired.


                       Last month, the state’s Board of Architecture,
                       Engineering, Land Surveying, Landscape
                       Architecture, Geoscience, and Interior Design
                       (AELSLAGID) issued an official censure of Charles
                       Marohn, founder of the Brainerd-based advocacy
                       group Strong Towns, and slapped him with a $1,500
                       fine.


          o § Civil Rights/Policing⠀➾


                # ⚓ HRW ☛ Bangladesh:_Allow_UN_to_Assist_‘Disappearance’
                  Inquiries_|_Human_Rights_Watch⠀⇛


                       Bangladesh authorities should heed international
                       calls for transparent, independent investigations
                       into enforced disappearances, Human Rights Watch
                       said today on the International Day of the Victims
                       of Enforced Disappearances.


                # ⚓ Unicorn Media ☛ Passings:_Peter_Eckersley,_a_Founder_of
                  Let’s_Encrypt,_Dies_at_43_–_FOSS_Force⠀⇛


                       FOSS Force has learned that Peter Eckersley, who
                       among other things was a founder of Let’s Encrypt,
                       has died. He was 43 years old. We first learned of
                       his death from a brief notice on LWN.net that links
                       to a post from Seth Schoen, a friend of Eckersley’s
                       who worked with him on Let’s Encrypt, a project
                       that provides short-lived SSL certificates to
                       website owners that Eckersley co-founded in 2012
                       while working at Electronic Frontiers Foundation.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Backwards_Chairs⠀⇛


                       Jackson sneered, frustrated with the seating
                       coordinators. Chairs were supposed to be positioned
                       towards the stage, at least as far as he
                       understood. Maybe cyborgs had eyes on the back of
                       their heads, or maybe they modified their necks to
                       turn around 180 degrees with ease. He had no idea.
                       Regardless, anthropes like himself needed to sit in
                       the direction they’re looking, unless they wanted
                       major neck pain.


                       He casually turned each chair around, one by one,
                       accidentally clanking them against each other at
                       times and readjusting rows when all their chairs
                       had been corrected. Working slowly prevented him
                       from getting too anxious, as it freed his mind to
                       consider other things. If only straightening out
                       this thoughts was as easy as turning chairs.


                # ⚓ Passed_by_the_Dutchy_on_the_left_hand_side⠀⇛


                       Overtaking generally happens at the end of a
                       straight. The car behind gets an aerodynamic tow,
                       and can get along side as they brake for the
                       corner. No one expected much overtaking at the
                       Dutch Grand Prix because it’s all fast corners. But
                       that’s not how it went. Tyre differences and
                       strategy differences meant speed differences, and
                       passing into turn one looked almost too easy.


          o § Technical⠀➾


                # § Internet/Gemini⠀➾


                      # ⚓ a_pub,_huh?⠀⇛


                             This led me to find Geminispace, which at
                             first I was skeptical about until I realized
                             how much better it was than the regular World
                             Wide Web, at least in terms of being more
                             user-focused, easier to work with, and the
                             absence of companies finding ways to monetize
                             everything.


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



                    ䷩ 𝚕𝚒𝚗𝚎 3201

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/09/2022:_GNU/Linux_Machines_Nowadays_Just_Work⠀✐


Posted in News_Roundup at 9:50 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Server
          o Audiocasts/Shows
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Productivity_Software/LibreOffice/Calligra
          o FSFE
          o Programming/Development
                # Perl_/_Raku
    * Leftovers
          o Security
                # Fear,_Uncertainty,
                  Doubt/Fear-mongering/Dramatisation
          o AstroTurf/Lobbying/Politics
          o Internet_Policy/Net_Neutrality
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
    * § GNU/Linux⠀➾


          o ⚓ TuxPhones ☛ Linux_machines_that_just_work⠀⇛


                 In some sense, 2022 has been resembling the long-memed
                 Year of the Linux Desktop. Although this sounds like some
                 cult’s prophetic rubbish, by looking at the success of
                 the Linux desktop in very empirical terms an improvement
                 of the last couple of years becomes clearly noticeable.


                 The Steam Deck alone has had the most merit for this.
                 Although its reviews were mixed, its power and overall
                 technical brilliance has been acknowledged by essentially
                 all (mainstream) reviewers that could get their hands on
                 it. And alongside it, a new generation of Android/Linux
                 hybrid devices is slowly growing, alongside many ex-
                 Android phones (with Qualcomm Snapdragon chipsets) that
                 are starting to “just work” on mainline Linux kernels.


                 On the desktop side, products such as the Librem 14
                 laptop which we reviewed back in April show a
                 surprisingly stable and practical Linux experience. Other
                 reviewers – finally also on mainstream tech sites –
                 acknowledged the Librem 14 perks and faults, mainly
                 agreeing on the general practicality. Furthermore, newly
                 developed machines such as the HP Dev One and Dell XPS 13
                 Plus are both heavily Linux-centric professional
                 machines, the former being developed in collaboration
                 with Pop OS, the latter officially certified by Ubuntu
                 for full hardware support.


          o § Server⠀➾


                # ⚓ Episode_38:_All_About_LearnWP_with_Special_Guest_Hauwa
                  Abashiya_–_WordPress_News⠀⇛


                       In the thirty-eighth episode of the WordPress
                       Briefing, join Josepha Haden Chomphosy and special
                       guest Hauwa Abashiya for a discussion on the
                       WordPress Training team and LearnWP initiative.


                # ⚓ Linux Hint ☛ URL_Rewriting⠀⇛


                       The URL that a client requests can be changed
                       entirely or patly using the NGINX rewrite rules. In
                       addition to directing the flow of NGINX’s executing
                       pages, the primary goal of updating a URL is to
                       alert the clients that the services they are
                       seeking have moved. URLs are rewritten using the
                       return and rewrite commands in NGINX. The same task
                       of rewriting the URLs is carried out by both
                       directives. The rewrite directive is stronger than
                       the return directive, as it can handle a
                       complicated rewriting without the need to parse the
                       URLs. We will examine in this guide on how the
                       NGINX uses the return and rewrite commands to
                       modify or rewrite the URL.
                       It is highly advised to update the current Nginx
                       instance to the higher version because this
                       instruction is optimized for NGINX version 1.0.1
                       and above. Nevertheless, some of the operations and
                       syntaxes might still apply to the versions earlier
                       than the one mentioned.


                # ⚓ Netcraft ☛ Most_Reliable_Hosting_Company_Sites_in_August
                  2022 [Ed: 90% of that is GNU/Linux]⠀⇛


                       In August 2022, Rackspace had the most reliable
                       hosting company site, securing first place on the
                       leaderboard. Rackspace offers a range of cloud
                       hosting solutions and has data centres across the
                       globe including in Frankfurt, New York, and Hong
                       Kong.


                       Second and third place were occupied by New York
                       Internet (NYI) and Bigstep respectively, resulting
                       in the top three companies all moving up one spot
                       compared to July 2022. NYI offers hybrid IT
                       solutions and Bigstep provides ‘bare metal’ cloud
                       hosting.


                       The top six companies, which in August included
                       ServerStack, Flexential, and Pair Networks,
                       responded to all of Netcraft’s requests. Linux
                       remained the most popular operating system and was
                       used by nine out of the top ten hosting companies,
                       with NYI using FreeBSD.


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Linux_User_vs_Windows_User_–_Invidious⠀⇛


                       A Discussion between a Linux and Windows User


                # ⚓ Video ☛ Definitely_Don’t_Use_GitHub_Copilot_Now_–
                  Invidious⠀⇛


                       Many of my concerns about GitHub Copilot have
                       become true and it’s still a very hard no for me on
                       this piece of technology. Hope you enjoyed the
                       video!


          o § Graphics Stack⠀➾


                # ⚓ Blender_Vulkan_–_Status_report_–_Blender_Development_–
                  Blender_Developer_Talk⠀⇛


                       Last week there was some movement on discussing
                       Vulkan Blender integration. This post will give the
                       status of the Vulkan project and updated reasoning.


                       Currently there are no active developers working on
                       Vulkan integration in Blender. Although many
                       decisions are driven by this API. If you have some
                       ideas/comments or want to participate in such a
                       project please get into contact with us by leaving
                       a reply or via #eevee-viewport-module on Blender
                       chat.


          o § Applications⠀➾


                # ⚓ Linuxiac ☛ Notesnook_Private_Notes_App_Takes_the_Open
                  Source_Route⠀⇛


                       Notesnook, an Evernote app alternative, officially
                       open-sourced all its client apps (sync server will
                       be open-sourced soon) on GitHub.


                       Open Source is a way that an increasing number of
                       apps are choosing to get greater popularity among
                       consumers. And there is a logical explanation for
                       this.


                       When an app is Open Source, users’ trust in it
                       skyrockets because there’s no way to hide malware,
                       analytics, or anything else nefarious.


                       In other words, this approach guarantees
                       transparency and that nothing remains hidden behind
                       the curtains. As a result, instead of constantly
                       questioning, for example, if it’s just another tool
                       with built-in telemetry capabilities, the end user
                       approaches it with trust.


          o § Instructionals/Technical⠀➾


                # ⚓ TechRepublic ☛ How_to_schedule_Linux_upgrades_with_Webmin_|
                  TechRepublic⠀⇛


                       I’ve been a fan of Webmin for years. Although there
                       are newer, easier web-based administration tools
                       available, Webmin happens to be one of the more
                       mature and robust on the market. With a modular
                       system that makes it easy to install new
                       capabilities, there’s very little Webmin can do.
                       And given much of its capability is already baked
                       in, you can quickly install the software and get to
                       work.


                # ⚓ How_To_Install_AngularJS_on_Ubuntu_22.04_–_LinuxTuto⠀⇛


                       AngularJS is an open-source JavaScript framework
                       developed by Google for building dynamic web
                       applications. Compared to other options such as
                       jQuery, Knockout, Handlebars, or PagerJs, Angular
                       integrates a complete solution that allows us to
                       abandon the old PHP in our developments with modern
                       technology.


                       In this tutorial you will learn to install and
                       create AngularJS Application on a Ubuntu 22.04 OS.


                # ⚓ Video ☛ Learn_the_Basics_of_the_Dired_File_Manager_(Doom
                  Emacs)_–_Invidious⠀⇛


                       This tutorial will cover some of the basic commands
                       and customization options of ‘”dired”, the file
                       manager inside Emacs. This video will focus on
                       dired within Doom Emacs, using the evil keybindings
                       (vim-like keybindings). Although this video is
                       nearly 30 minutes long, it barely scratches the
                       surface of the functionality available within this
                       excellent file manager!


                # ⚓ How_to_Install_Wine_7.16_on_Ubuntu_/_Linux_Mint⠀⇛


                       Wine is a recursive acronym for “Wine Is Not an
                       Emulator“.The project’s goal was and is to allow
                       users to run their Windows software on non-Windows
                       systems, and it has been very successful in this
                       regard.


                       WineHQ is made up of a number of different parts,
                       all of which are necessary for the successful
                       running of Windows software.


                       WineHQ Team released its new Development version
                       7.16


                # ⚓ HowTo Forge ☛ How_to_Install_Appwrite_with_Docker_on_Ubuntu
                  22.04⠀⇛


                       Appwrite is a free and open-source back-end server
                       that offers core APIs required to build any
                       application packaged together as a set of easy-to-
                       use Docker containers. It helps mobile developers
                       to build advanced apps much faster.


                # ⚓ OSTechNix ☛ How_To_Perform_Arithmetic_Operations_In_Bash_–
                  OSTechNix⠀⇛


                       In this article, we will focus on how to do
                       mathematical operations in bash scripts. We can
                       perform arithmetic operations in Bash using the
                       built-in and external tools. First, we will learn
                       about the built-in tools.


                # ⚓ Dignited ☛ How_to_install_DD-WRT_custom_firmware_on_your
                  WiFi_Router_–_Dignited⠀⇛


                       Every WiFi router comes with its own firmware. This
                       is a proprietary operating system installed by the
                       manufacturer right from the factory. This is one of
                       the reasons it’s incredibly difficult to manage and
                       use routers compared to other devices such as
                       smartphones for instance. Also these vendor router
                       firmware lack in features, are rarely updated with
                       new features and security patches. So, one option
                       you have is to install an open source custom router
                       firmware on your router. The biggest ones include
                       DD-WRT, OpenWRT and Tomato.


                # ⚓ Linux Handbook ☛ Using_ifup,_ifdown,_and_ifquery_commands
                  in_Linux⠀⇛


                       The ifup, ifdown, ifquery commands are some of the
                       basic Linux networking commands.


                       The ifup command is used to activate (up) a network
                       interface, ifdown deactivates (down) it while
                       ifquery lets you check the state of a network
                       interface.


                       To be more precise, these commands are used to
                       configure network interfaces based on interface
                       definitions in the file /etc/network/interfaces.


                       Before you see the usage of ifup, ifdown and
                       ifqury, get a few things in order first.


                # ⚓ Trend Oceans ☛ Reptyr:_Move_Working_Process_into_Another
                  Terminal_Session_without_Closing_in_Linux_–_TREND_OCEANS⠀⇛


                       If you are a Linux or cloud administrator or anyone
                       whose life revolves around a Linux terminal, then
                       you need to LEARN about Reptyr, RIGHT NOW!


                       You might be thinking, what the heck is this tool
                       and why should you use it? What void space does it
                       fill? Read the complete article and you will find
                       your answer with a great sense of relaxation that
                       you have never felt before.


                       First, let me introduce you to the Reptyr tool in
                       simple terms.


          o § Games⠀➾


                # ⚓ Linux Hint ☛ How_to_Show_FPS_Counter_in_Linux_Games⠀⇛


                       Linux gaming got a major push when Valve announced
                       Linux support for Steam client and their games in
                       2012. Since then, many AAA and indie games have
                       made their way to Linux and the number of users who
                       game on Linux have increased considerably.
                       With the growth of Linux gaming, many users started
                       to look for proper ways to display “frames per
                       second” (FPS) counter as an overlay on running
                       Linux games. An FPS counter helps in tweaking
                       performance of running games as well as in
                       benchmarking a PC’s overall ability to play games
                       at different resolutions.


                       Unfortunately there is no single unified way to
                       display FPS counter in all Linux games that is
                       independent of underlying technologies a game is
                       running upon. Different renderers and APIs have
                       different ways to display FPS counter. This guide
                       will explain various methods that can be used to
                       display an FPS counter in Linux games.


                # ⚓ Video ☛ Syncthing_can_enable_multi-device_play_for_your
                  favorite_games._–_Invidious⠀⇛


                       It’s no secret that some games (even new releases)
                       can be missing basic features like Steam Cloud
                       support. but don’t worry.


    * § Distributions and Operating Systems⠀➾


          o § Open Hardware/Modding⠀➾


                # ⚓ Arduino ☛ This_wrapping_machine_makes_wire_harness_creation
                  a_breeze_|_Arduino_Blog⠀⇛


                       Many products require the use of wire harnesses,
                       which are essentially bundles of cabling that
                       connect one subsystem to another, such as a car
                       engine’s sensors to the ECU. DIY projects can also
                       find themselves needing one, but having to manage
                       the wiring without tangles or unwanted bends can be
                       a challenge.


                       YouTuber Mr. Innovative has created a simple wire
                       harness wrapping machine that takes the user’s
                       choice of tape and quickly spins it around the
                       bundle. He started by cutting out the base and
                       fixed ring out of plywood before milling the
                       spinning ‘C’ disk from acrylic. Once these parts
                       were attached together and a set of bearings/
                       pulleys were added around the moving disk, a timing
                       belt was looped on one half to an awaiting stepper
                       motor.


                # ⚓ Arduino ☛ Automating_precise_welds_with_an_Arduino_|
                  Arduino_Blog⠀⇛


                       Welding is a skill that takes years to perfect, and
                       yet consistently placing a TIG welder in exactly
                       the right spot many times over is nearly
                       impossible. To assist with this process, a few of
                       element14 Presents host Kaleb Clark and his
                       company’s clients had constructed two rigs using
                       PLCs but needed another solution after losing the
                       accompanying laptop.


                       The first device was a repurposed lathe that was
                       driven by a stepper motor and gearbox assembly.
                       Clark was able to retrofit the circuit by
                       connecting an LCD display, rotary encoder, and a
                       motor driver to an Arduino Uno. He also attached an
                       optically-isolated relay for controlling when the
                       welder should activate to begin welding the part,
                       as well as two switches for toggling the welder’s
                       output on or off. All of these components were then
                       placed into a briefcase lined with foil to prevent
                       outside interference from the TIG welder.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ PR Newswire ☛ All_42Gears_Products_Compatible_with_Android
                  13⠀⇛


                # ⚓ PR Newswire ☛ All_42Gears_Products_Compatible_with_Android
                  13⠀⇛


                # ⚓ 9to5Google ☛ Samsung_brings_Android_12L_to_the_rest_of_its
                  foldables⠀⇛


                # ⚓ Android_12_beta_5_At_a_Glance_widget_settings_broken_issue
                  escalated⠀⇛


                # ⚓ Linux Gizmos ☛ Android_TV_boxes_feature_Amlogic_SoCs_and
                  support_Android_11.0⠀⇛


                # ⚓ Business Standard ☛ Dixon_Tech_gains_on_bagging_sub
                  licensing_rights_for_Android_–_Google_TV_|_Business_Standard
                  News⠀⇛


                # ⚓ Best_Android_Board_Games:_Top_Board_Games_on_Mobile_–_Droid
                  Gamers⠀⇛


                # ⚓ Android Police ☛ The_6_best_Android_keyboard_apps_for
                  effortless_typing⠀⇛


                # ⚓ Logitech_G_Gaming_handheld’s_leaked_photos_show_possible
                  Android-powered_content_|_Pocket_Gamer⠀⇛


                # ⚓ Hacker News ☛ Fake_Antivirus_and_Cleaner_Apps_Caught
                  Installing_SharkBot_Android_Banking_Trojan⠀⇛


                # ⚓ WCCF Tech ☛ Android_Phones_to_Start_Tracking_Cough_and
                  Snore_Through_Digital_Wellbeing⠀⇛


                # ⚓ Samsung_Galaxy_Z_Flip_and_Fold_owners_get_superb_free
                  Android_features_upgrade_|_T3⠀⇛


                # ⚓ Notebook Check ☛ Google_Pixel_Tablet_could_be_a_‘budget_or
                  mid-range’_Android_tablet_that_doubles_as_a_Nest_Hub
                  replacement_–_NotebookCheck.net_News⠀⇛


                # ⚓ Gadgets Now ☛ android:_Android_device_not_charging:_4_tips
                  to_fix_the_issue⠀⇛


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


          o § Productivity Software/LibreOffice/Calligra⠀➾


                # ⚓ Document Foundation ☛ Community_Member_Monday:_Jean-
                  Baptiste_Faure_–_The_Document_Foundation_Blog⠀⇛


                       Well, from my point of view, LibreOffice is the
                       natural continuation of the OpenOffice.org project.
                       I started with StarOffice 5.1 in 1998 because I
                       needed a word processor able to write mathematical
                       equations under Microsoft Windows, and I never
                       liked Latex.


          o § FSFE⠀➾


                # ⚓ FSFE ☛ Broad_alliance_demands:_Digitization_must_serve
                  social_and_ecological_change⠀⇛


                       A broad alliance of 13 organisations from the
                       fields of environmental protection, digital policy,
                       development cooperation and academia publishes a
                       catalog of demands to show political solutions
                       towards a more sustainable digital society. This as
                       a prelude to the upcoming conference for
                       digitization and sustainability “Bits & Bäume”.


                       A broad alliance of 13 organizations from the
                       fields of environmental protection and nature
                       conservation, digital policy, development
                       cooperation and academia demands: Digitization must
                       be at the service of society and social and
                       ecological change. This is what the organizations
                       are calling for at the forthcoming conference on
                       digitization and sustainability “Bits & Bäume”,
                       which will take place from September 30 to October
                       2, 2022 in Berlin. Today, the same organizations
                       publish a catalog of demands that show political
                       solutions towards a more sustainable digital
                       society.


          o § Programming/Development⠀➾


                # ⚓ Qt ☛ Qt_Safe_Renderer_Monitor⠀⇛


                       The Qt Safe Renderer is our solution for creating
                       user interfaces (UI) for safety-critical systems.
                       Since 2017 the Qt Safe Renderer has been used by
                       multiple customers and certified for different
                       functional safety standards. With the upcoming
                       version 2.0, we are introducing a new approach for
                       validating the correct rendering of safety-critical
                       information – the Monitor.


                       Functional safety applies to many industries, such
                       as automation, medical, railway, and automotive.
                       Safety-critical information in the digital displays
                       must be correct, even if some malfunction prevents
                       rendering the other parts of the user interface. Qt
                       Safe Renderer provides a solution for rendering the
                       safety-critical information to achieve functional
                       safety. It can be used with Qt or other user
                       interface technologies – or even for creating the
                       whole user interface in some cases.


                # ⚓ Qt ☛ In_Depth:_Custom_Shader_Effects⠀⇛


                       Qt Graphical Effects was one of the modules left
                       out from the original Qt 6.0 release, unfortunately
                       without a direct replacement at the time. There was
                       a port available as source, but it wasn’t built or
                       included in the official releases.


                       One of the reasons was that not all effects were
                       compatible with the Qt 6 approach of precompiling
                       shader code: Some shaders in Qt Graphical Effects
                       are generated at run-time from the properties, to
                       enable pregenerating tables such as Gaussian
                       weights. With the introduction of RHI in Qt 6, we
                       now compile shader code at build time. This can
                       give considerable improvements for startup times
                       and frame rate during loading, but the trade-off is
                       that it somewhat restricts our ability to generate
                       code on the fly.


                       And, in addition, we had seen over the years that
                       there was a fundamental drawback in how the
                       graphical effects were designed. Chaining effects
                       requires an additional draw call, an additional set
                       of shader passes and an additional offscreen buffer
                       for each effect you add. This causes the chained
                       effect to be both slower and more memory hungry
                       than it needs to be. The end result was that users
                       would often implement custom effects instead, in
                       order to optimize their applications. We thought we
                       could do better, and therefore we did not
                       officially include Qt Graphical Effects in the
                       first releases of Qt 6.


                # ⚓ The Register UK ☛ The_modern_OS_desktop_is_a_crime_against
                  humanity_•_The_Register⠀⇛


                       The reason for the unholy UX mess with no signs of
                       converging is, of course, marketing, and the reason
                       they get away with it is because of one of the
                       greatest con jobs in IT. We have been taught, and
                       never question, the near-abolition of customer
                       support by the OS makers. Unless you pay extra, you
                       cannot pick up the phone or email Apple, Microsoft,
                       and especially not Linux, to ask basic questions.
                       You cannot say to Apple, “Which bit of the Finder
                       actually finds things?” You cannot complain to
                       Microsoft that File Manager thinks “Share with
                       Skype” is the second most important file operation,
                       right after Open. You cannot pick up a phone to
                       Ubuntu and scream “Stop! Stop! In God’s name,
                       stop!”


                       The OS companies have insulated themselves from
                       user pain, the sort that soaks up customer service
                       resources and actually costs them money. Go to the
                       forums, thou sluggard, and try to work out which
                       version the answers you find are actually about.
                       They have created their own walled poison gardens
                       where they can mess around according to the will of
                       whatever internal faction is carrying the day,
                       sentencing billions to useless frustration,
                       cognitive load, lost work, and lost lives. It is
                       frankly criminal.


                # ⚓ Making_games_in_R-_Nara_and_eventloop_Game_Changers⠀⇛


                       Making games in R- Nara and eventloop Game
                       Changers, It’s possible that you are aware of the
                       existence of the R programming language.


                       This is a fairly understandable language that is
                       mostly utilized by data scientists as well as more
                       conventional statisticians.


                # § Perl / Raku⠀➾


                      # ⚓ Rakulang ☛ 2022.36_Coming_in_at_50_–_Rakudo_Weekly
                        News⠀⇛


                             In IEEE Spectrum’s ninth annual ranking of
                             Top Programming Languages, the Raku
                             Programming Language comes in at #50 when
                             weighted by trending (/r/rakulang comments)!
                             A good trend!


    * § Leftovers⠀➾


          o § Security⠀➾


                # ⚓ LWN ☛ Security_updates_for_Monday_[LWN.net]⠀⇛


                       Security updates have been issued by Debian (flac,
                       ghostscript, libmodbus, qemu, rails, ruby-rack, and
                       thunderbird), Fedora (kernel, kernel-headers,
                       kernel-tools, libtar, qt5-qtwebengine,
                       subscription-manager-cockpit, tcpreplay, and vim),
                       Mageia (chromium-browser-stable, webkit2, and
                       ytnef), SUSE (curl, firefox, freerdp, gdk-pixbuf,
                       ImageMagick, json-c, libgda, php-composer2, and
                       python-pyxdg), and Ubuntu (libzstd, linux-aws,
                       linux-aws-5.4, linux-azure-5.4, and linux-oem-
                       5.17).


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


                      # ⚓ South Africa ☛ Ransomware_attacks_on_Linux_up_75%
                        [Ed: Trend Micro helps Microsoft by pretending
                        ransomware is a “Linux” problem. It is not. Well,
                        ransomware_is_predominantly_a_Windows_problem, in
                        practice]⠀⇛


                      # ⚓ Gadgets Now ☛ 75%_increase_in_ransomware_attacks
                        targeting_Linux_systems_in_2022⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Michael West Media ☛ Bandt_checks_his_privilege_in_pursuit
                  of_Morrison_–_Michael_West⠀⇛


                       When he’s not abjuring the Australian flag, or
                       colonial history, or the nation itself, Greens
                       leader Adam Bandt has a canny eye on the rulebook
                       under which the nation’s legislators operate.


                       On Monday he tried to have Scott Morrison referred
                       to the privileges committee of the House of
                       Representatives over his extra portfolios jape /
                       threat to our democracy (strike out whichever does
                       not fit your point of view).
                       The move was rejected by the Speaker, Labor’s
                       Milton Dick, although the House may yet take this
                       action. Morrison’s secretive conduct is the subject
                       of an inquiry headed by former High Court judge
                       Virginia Bell.


                       Privileges committees are a feature of parliaments
                       that operate under the Westminster system or were
                       inspired by it. Malta has one, so does Malaysia.
                       ”The Committee of Privileges and Members’ Interests
                       is established under standing order 216 of the
                       House of Representatives,” the Australian
                       parliamentary website tells us.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ Internet Freedom Foundation ☛ Gauhati_HC_decision_on
                  internet_shutdown_in_Assam⠀⇛


                       On 18th August, the Government of Assam issued an
                       order directing the suspension of internet services
                       in several districts in Assam on the 21st and 28th
                       of August to prevent cheating during governmental
                       recruitment examinations. On 23rd August, Mr Raju
                       Prosad Sarma, a social worker based in Assam filed
                       a petition asking the Gauhati HC to restrain the
                       Government of Assam from suspending internet
                       services on the 28th August. On 26th August, the
                       Gauhati High Court refused to grant interim relief
                       and the Government of Assam suspended internet
                       services on the 28th. Advocate Gayatri Goswami
                       represented the Petitioner in Court and IFF
                       provided legal support.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ SpellBinding:_AXINOTD_Wordo:_CRIES⠀⇛


          o § Technical⠀➾


                # ⚓ Never_underestimate_the_bandwidth_of_a_car_full_of_disks
                  driving_down_the_highway,_regardless_of_what_kind_of_society
                  you’re_in⠀⇛


                       Assuming the semi doesn’t drive any slower than a
                       car does, an entire Snowmobile transfers data from
                       LA to SF at 3,472,222 MB/s.


                # § Internet/Gemini⠀➾


                      # ⚓ Tux_Machines_in_Gemini_(gemini.tuxmachines.org)⠀⇛


                             About a month ago Tux Machines added its
                             presence to Geminispace (new Internet
                             protocol). Everything you see in HTTP/S is
                             also available over Gemini protocol (gemini:/
                             /) at gemini.tuxmachines.org, though Gemini
                             software (or a Web proxy) is needed. For
                             those who are not familiar with what Gemini
                             is and what it’s for, here’s a detailed
                             primer from Jason McBrayer.


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



                    ䷩ 𝚕𝚒𝚗𝚎 4042

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/09/2022:_OpenMandriva_Approaches_Big_Release⠀✐


Posted in News_Roundup at 6:45 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Instructionals/Technical
    * Distributions_and_Operating_Systems
          o PCLinuxOS/Mageia/Mandriva/OpenMandriva_Family
          o Canonical/Ubuntu_Family
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Web_Browsers
                # Chromium
          o Standards/Consortia
    * Leftovers
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy
                # Wildlife/Nature
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Civil_Rights/Policing
          o Monopolies
                # Copyrights
    * Gemini*_and_Gopher
          o Personal
          o Technical
    * § GNU/Linux⠀➾


          o § Instructionals/Technical⠀➾


                # ⚓ Fedora Magazine ☛ Manage_containers_on_Fedora_Linux_with
                  Podman_Desktop_–_Fedora_Magazine_Manage_containers_on_Fedora
                  Linux_with_Podman_Desktop⠀⇛


                       Podman Desktop is an open-source GUI application
                       for managing containers on Linux, macOS, and
                       Windows.


                       Historically, developers have been using Docker
                       Desktop for graphical management of containers.
                       This worked for those who had Docker Daemon and
                       Docker CLI installed. However, for those who used
                       Podman daemon-less tool, although there were a few
                       Podman frontends like Pods, Podman desktop
                       companion, and Cockpit, there was no official
                       application. This is not the case anymore. Enter
                       Podman Desktop!


                       This article will discuss features, installation,
                       and use of Podman Desktop, which is developed by
                       developers from Red Hat and other open-source
                       contributors.


                # ⚓ LinuxConfig ☛ How_to_build_Super_Mario_64_natively_on
                  Linux⠀⇛


                       Super Mario needs no presentations: it is one of
                       the most beloved video games characters. Super
                       Mario 64 was originally released for the Nintendo64
                       console in 1996, and represented the first 3D
                       episode of the Mario franchise. Thanks to a github
                       project, which achieved the full decompilation of
                       the game, it is now possible to build a native
                       Linux port and play it without the need of a
                       Nintendo64 emulator. In order to compile the port,
                       an original, and legally obtained “.z64” rom of the
                       game is needed.


                       In this tutorial we see how to compile and launch
                       the Super Mario 64 Linux port on some of the most
                       used distributions.


                # ⚓ LinuxConfig ☛ Introduction_to_the_OverlayFS⠀⇛


                       The OverlayFS pseudo-filesystem was first included
                       in the Linux kernel 3.18 release: it allows us to
                       combine two directory trees or filesystems (an
                       “upper” and a “lower one”) in a way that is
                       completely transparent to the user, which is able
                       to access files and directories on the “merged”
                       layer just like he would do on a standard
                       filesystem.


                       In this tutorial we learn the basic concepts behind
                       OverlayFS, and we see a demonstration of its usage.


                # ⚓ Red Hat Official ☛ How_to_connect_to_a_remote_computer
                  using_VNC_in_Linux_|_Enable_Sysadmin⠀⇛


                       The Wayland protocol is the latest graphical server
                       software for Linux computers, and it has replaced
                       the X11 system in most major distributions. Old
                       tricks like X Forwarding over SSH and logging in
                       through xhost are on the way out, and remote access
                       is now provided by the remote frame buffer protocol
                       and Virtual Network Computing (VNC).


                # ⚓ LinuxConfig ☛ How_to_send_desktop_notifications_using
                  notify-send⠀⇛


                       Every desktop environment on Linux has its own
                       notification system which implements the
                       Freedesktop notifications specifications. Some of
                       them, like GNOME or KDE, use their own built-in
                       notification systems which cannot be replaced;
                       others like Xfce or Mate, use more modular
                       components (Xfce notification daemon and Mate
                       notification daemon, respectively). Desktop-
                       independent notification systems also exist (dunst,
                       for example): most of the time they are used on
                       minimal setups (e.g. when using a plain window
                       manager instead of full blown Desktop
                       environments).


                       In this tutorial we learn how to send desktop
                       notifications from the command line using the
                       notify-send utility.


                # ⚓ ID Root ☛ How_To_Install_Unrar_on_Fedora_36_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Unrar on Fedora 36. For those of you who didn’t
                       know, The GNU unrar is a freeware used to extract
                       compressed files in RAR format. In addition, it
                       offers several features for manipulating archives,
                       such as the ability to list the contents of an
                       archive or extract only specific files.


                       This article assumes you have at least basic
                       knowledge of Linux, know how to use the shell, and
                       most importantly, you host your site on your own
                       VPS. The installation is quite simple and assumes
                       you are running in the root account, if not you may
                       need to add ‘sudo‘ to the commands to get root
                       privileges. I will show you the step-by-step
                       installation of the Unrar decompress on a Fedora
                       36.


                # ⚓ TecAdmin ☛ How_to_Change_the_Default_Browser_in_Ubuntu_–
                  TecAdmin⠀⇛


                       You probably know that Chrome is the default
                       browser in Ubuntu. But did you know that you can
                       change this? There are several other browsers that
                       come pre-installed with Ubuntu, such as Firefox and
                       Midori. If you’re not a fan of Chrome or if you
                       prefer to use another browser for your browsing
                       needs, changing the default browser from Chrome to
                       Firefox, for example, is pretty straightforward.


                       This tutorial will show you how to change the
                       default web browser on Ubuntu and other versions of
                       Linux Mint.


    * § Distributions and Operating Systems⠀➾


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


                # ⚓ OpenMandriva News ☛ ROME_Silver_Candidate_–_OpenMandriva⠀⇛


                       Not yet a ROME candidate release, still
                       approaching. These ISO images now receiving updates
                       from rolling Update channel.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ CNX Software ☛ NVIDIA_Jetson_Xavier_NX_fanless_embedded_box
                  PC_features_four_HDMI_input_ports_–_CNX_Software⠀⇛


                       The BOXER-8256AI ships with two wall mount
                       brackets, a screw package, and a power connector.
                       It supports NVIDIA Jetpack 4.6.2 or above, which
                       should include the recently released Ubuntu 20.04-
                       based Jetpack 5.0.2 SDK.


                # ⚓ Ubuntu ☛ Ubuntu_Blog:_The_State_of_IoT_–_August_2022⠀⇛


                       Welcome to the August edition of the monthly State
                       of IoT series.


                       Let’s dive straight into the most prominent news
                       across the IoT landscape from the last month.


                # ⚓ Why_Ubuntu_22.04_is_so_fast_(and_how_to_make_it_faster)⠀⇛


                       If you’ve upgraded to Ubuntu 22.04 then you
                       probably noticed how smooth the GNOME experience
                       is. If you haven’t noticed then try comparing it to
                       an older Ubuntu release or even the latest Fedora.
                       The main enhancement responsible for this is the
                       introduction of triple buffering in Ubuntu.


                # ⚓ Ubuntu ☛ Best_practices_to_publish_open-source_software
                  operators_|_Ubuntu⠀⇛


                       Running or operating applications requires several
                       tasks throughout their lifecycle: scaling
                       instances, checking the health, integrating with
                       other applications, running backups, and applying
                       updates – to name a few examples. It’s a time and
                       labour-intensive process. To automate these tasks,
                       developers can implement scripts for repeated
                       execution. This is where the software operator
                       comes in. Software operators are a design pattern,
                       a proven and acknowledged approach by the software
                       community. Software operators lift automation to a
                       new level. They don’t only automate the deployment
                       of application workloads, they also encode the
                       expertise required to manage and operate them. In
                       other words, they offer a secure and reliable way
                       to operate applications.


                       [...]


                       Canonical has developed Juju and the Charmed
                       Operator SDK to develop and run operators in an
                       open-source way. Operators written to run on Juju
                       are called Charmed Operators, or Charms for short.
                       Developers can publish their operators on our app
                       store: Charmhub.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Linux Gizmos ☛ Android_TV_boxes_feature_Amlogic_SoCs_and
                  support_Android_11.0⠀⇛


                       The Tanix X4 and the TX8 Pro are two TV Box devices
                       powered by Amlogic’s SoCs recently launched in the
                       market. Both devices offer similar features
                       including 4K resolution, ethernet and Wi-Fi/
                       Bluetooth connectivity.


                       The Tanix X4 TV Box features the Amlogic S905X4 SoC
                       which combines an ARM-G31 MP2 GPU and a quad-core
                       ARM-A55 processor (up to 2.0GHz). Similarly, the
                       TX8 Pro accommodates the Amlogic S905W2 chipset
                       featuring the same GPU (Mali-G31 MP2) along with a
                       quad-core Cortex-A35 processor (up to 1.8GHz). 


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


          o § Web Browsers⠀➾


                # § Chromium⠀➾


                      # ⚓ PC World ☛ Google_removes_malicious_Chrome_extensions
                        with_1.4_million_users⠀⇛


                             Extensions hijacking browsers in order to
                             plaster the web with even more ads is nothing
                             new. It’s the fact that these extensions
                             appeared on the Chrome Web Store, ostensibly
                             with Google’s seal of approval, that allowed
                             them to affect such a wide array of users.
                             You can admonish users for being careless all
                             you want, but if Google hosts the extensions
                             and presents them directly to users, the
                             company bears some of the responsibility. But
                             initial testing and scans can only do so
                             much, especially when popular extensions can
                             be sold to less-scrupulous new owners.


          o § Standards/Consortia⠀➾


                # ⚓ PC World ☛ USB4_leaps_ahead_of_Thunderbolt_with_80Gbps
                  standard⠀⇛


                       The USB Promoter Group announced USB4 Version 2.0
                       on Thursday, a specification that will allow for up
                       to 80Gbps to be transferred over the USB-
                       C connector that is commonly in use on PCs and
                       smartphones. The standard will be backwards
                       compatible with USB4 Version 1.0, USB 3.2, USB 2.0,
                       and Thunderbolt 3 — but not USB 1.0 or Thunderbolt
                       4.


                       The USB Promoter Group said that the new standard
                       will be published in November, meaning the first
                       products should debut sometime thereafter.


    * § Leftovers⠀➾


          o ⚓ India Times ☛ Smartphone_app_accurately_detects_Covid_infection
            in_people’s_voices⠀⇛


                 Its overall accuracy was 89 per cent, its ability to
                 correctly detect positive cases was 89 per cent, and its
                 ability to correctly identify negative cases was 83 per
                 cent.


          o ⚓ Rolling Stone ☛ ‘These_Kids_Are_Dying’_—_Inside_the_Overdose
            Crisis_Sweeping_Fort_Bragg⠀⇛


                 Disney’s memorial service was in July. “We were getting
                 ready to go into the chapel,” Bowman says, and Maj. Gen.
                 Chris Donahue, the commander of the 82nd Airborne
                 Division, came into the room and personally informed her
                 that the results of a toxicology report were in. The
                 cause of death was acute fentanyl intoxication.


                 [...]


                 A staggering total of 109 soldiers assigned to Fort
                 Bragg, active and reserve, lost their lives in 2020 and
                 2021, casualty reports obtained through the Freedom of
                 Information Act show. Only four of the deaths occurred in
                 overseas combat operations. All the rest took place
                 stateside. Fewer than 20 were from natural causes. All
                 the rest were preventable. This is a seemingly
                 unprecedented wave of fatalities on a modern U.S.
                 military installation.


          o § Hardware⠀➾


                # ⚓ Hackaday ☛ GP2040:_A_Configurable_Game_Pad_Firmware⠀⇛


                       [feralAI] and fellow GitHub contributors present
                       for your viewing pleasure GP2040: an open source
                       game pad firmware for RP2040-based hardware. The
                       dual-core RP2040 is a good platform to use for
                       gaming inputs, as there is plenty of CPU grunt to
                       get sub-1 ms USB polling time, regardless of any
                       other tasks the controller may be performing.
                       Currently the firmware supports PC, Android, RPi,
                       Nintendo Switch, PS3, PS4 (legacy mode), and the
                       sweet MiSTer FPGA-based retro-gaming platform.


                # ⚓ Hackaday ☛ This_Vintage_Alphanumeric_Display_Was_Huge,_Hot,
                  Heavy,_And_Expensive⠀⇛


                       It’s easy to take display technology for granted
                       nowadays, but the ability to display data in a
                       human-readable way was not always easy. This is
                       demonstrated well by the Pinlite 30003 Alphanumeric
                       Display Module, a four-character display that was
                       pure luxury for its time.


                # ⚓ Hackaday ☛ Magnetic_Maniac_Manages_Mangled_Memory⠀⇛


                       Ahh, floppy disks. Few things carry nostalgia quite
                       like a floppy — either 3 1⁄2 or 5 1⁄4, depending on
                       which generation of hacker you happen to be. (And
                       yes, we hear you grey-beards, 8-inch floppies were
                       definitely a thing.) The real goodies aren’t the
                       floppies themselves, but what they carried, like
                       Wolfenstein 3d, Commander Keen, DOS, or any number
                       of other classics from the past. Unfortunately a
                       bunch of floppy disks these aren’t carrying
                       anything anymore, as bit rot eventually catches up
                       with them. Even worse, on some trashed floppies, a
                       format operation fails, too. Surely, these floppies
                       are destined for the trash, right?


                # ⚓ Hackaday ☛ 2022_Cyberdeck_Contest:_The_Black_Beast_Will
                  Help_You_Survive_A_Robot_Apocalypse⠀⇛


                       With AI systems getting smarter every day, one
                       might wonder if they might someday evolve into a
                       sentient Skynet-like system and try to take over
                       the world. We’re not sure how close we are to such
                       a situation, but we do know that if the robot
                       apocalypse were to happen, we would want to stay
                       close to [LordOfAllThings], who would likely be
                       carrying the Black Beast. This scary-sounding
                       machine is in essence a Raspberry Pi-based portable
                       computer built inside an outdoor carrying case,
                       with a wide range of unusual peripherals that make
                       it the digital equivalent of a Swiss army knife. In
                       other words, it’s a cyberdeck built for end times —
                       and whatever comes after.


                # ⚓ Hackaday ☛ The_7805_Is_Dead!_Long_Live_The_7805!⠀⇛


                       The 78XX series of regulators are very handy to
                       use. If you need, say, a 5V regulator, you grab a
                       7805, add a capacitor for stability, and send in
                       enough voltage for the regulator to work with.
                       Cheap and easy. However, the part is not without
                       its faults.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ TruthOut ☛ EPA_Administrator_Faces_Lawsuit_for_Exempting
                  Coal_Ash_Dumps_From_Regulation⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_Rising_Up_Down_South:_A_Strategy
                  for_Radical_Togetherness⠀⇛


                       With the overturn of Roe v. Wade, the institutional
                       tentacles of a deeper regressive and anti-
                       democratic movement are now very clear.


                # ⚓ TruthOut ☛ Focusing_on_“Learning_Loss”_Obscures_How_Much
                  We’ve_Truly_Lost_in_the_Pandemic⠀⇛


          o § Proprietary⠀➾


                # ⚓ The Verge ☛ Why_it_Matters_that_I_just_saw_a_Google_Nest
                  Hub_control_an_Apple_HomeKit_smart_plug⠀⇛


                       That’s exactly what Eve was demonstrating at IFA.
                       The Matter specification hasn’t been finalized yet,
                       so none of the devices were running their final
                       Matter-enabled firmware, but it was enough to see
                       the kinds of functionality we might be able to
                       expect when Eve’s devices get updated to support
                       it.


                # ⚓ Computer World ☛ Apple_wasn’t_fooling_when_it_said_it
                  wanted_to_make_Macs_more_secure⠀⇛


                       Federighi characterized Apple as being in an
                       enduring battle against malware on the Mac. He also
                       explained that between May 2020 and May 2021 the
                       company identified 130 types of Mac malware that
                       infected 300,000 systems.


                # ⚓ Redmond Magazine ☛ Microsoft_Blames_Ubuntu_Update_DNS
                  Problems_for_Azure_Services_Outage⠀⇛


                       The problem specifically affected customers
                       “running Ubuntu 18.04 (bionic) VMs [that were]
                       recently upgraded to systemd version 237-
                       3ubuntu10.54,” Microsoft’s alert indicated.
                       Microsoft also confirmed the problem in this Azure
                       Support Twitter post.


          o § Security⠀➾


                # ⚓ Krebs On Security ☛ Violence-as-a-Service:_Brickings,
                  Firebombings_&_Shootings_for_Hire⠀⇛


                       A 21-year-old New Jersey man has been arrested and
                       charged with stalking in connection with a federal
                       investigation into groups of cybercriminals who are
                       settling scores by hiring people to carry out
                       physical attacks on their rivals. Prosecutors say
                       the defendant recently participated in several of
                       these schemes — including firing a handgun into a
                       Pennsylvania home and torching a residence in
                       another part of the state with a Molotov Cocktail.


                # § Privacy/Surveillance⠀➾


                      # ⚓ [Old] CPO Mag ☛ Class_Action_Lawsuit_Accuses_Oracle
                        of_“Global_Surveillance,”_Creating_Detailed_Profiles_of
                        Five_Billion_People⠀⇛


                             A class action lawsuit is accusing Oracle of
                             conducting global surveillance, essentially
                             attempting to create detailed shopping and
                             spending profiles of the world’s entire
                             population.


                             The suit accuses Oracle of creating profiles
                             for five billion people worldwide, attaching
                             things like purchase records and GPS
                             locations to their name and contact
                             information. While social media platforms
                             usually dominate the conversation about
                             global surveillance, the Oracle Data
                             Marketplace and the company’s BlueKai service
                             have quietly become one of the world’s
                             largest sources of the sort of personal
                             information that “data brokers” sell for
                             targeted advertising purposes.


                      # ⚓ [Old] PC Mag ☛ Class-Action_Lawsuit_Accuses_Oracle_of
                        Tracking_5_Billion_People⠀⇛


                             This claim is backed up by a video on the
                             ICCL website(Opens in a new window) of Oracle
                             CEO Larry Ellison describing how the
                             company’s real-time machine learning system
                             collects this information and confirms the 5
                             billion profiles stored in the “Oracle Data
                             Cloud.” The profiles are referred to as a
                             “Consumers Identity Graph.”


                      # ⚓ [Old] Extreme Tech ☛ Oracle_Faces_Class-Action
                        Lawsuit_Over_Tracking_5_Billion_People⠀⇛


                             The filing claims that Oracle has created
                             “proxies” for sensitive data that other data
                             brokers and advertisers have agreed not to
                             track. Case in point, Facebook made it more
                             difficult to target users based on race in
                             certain advertising categories several years
                             ago, but Oracle’s Identity Graph helped
                             advertisers achieve the same results. It did
                             this without acquiring any user consent, and
                             even common sense measures like blocking
                             third-party cookies are not enough to stop
                             Oracle’s sophisticated data collection.


                      # ⚓ [Old] Irish Council for Civil Liberties ☛ Class
                        action_against_Oracle’s_worldwide_surveillance
                        machine⠀⇛


                             Oracle’s dossiers about people include names,
                             home addresses, emails, purchases online and
                             in the real world, physical movements in the
                             real world, income, interests and political
                             views, and a detailed account of online
                             activity: [4] for example, one Oracle
                             database included a record of a German man
                             who used a prepaid debit card to place a €10
                             bet on an esports betting site.[5]


                             Oracle also coordinates a global trade in
                             dossiers about people through the Oracle Data
                             Marketplace.


                      # ⚓ Associated Press ☛ Tech_tool_offers_police_‘mass
                        surveillance_on_a_budget’⠀⇛


                             Sold by Virginia-based Fog Data Science LLC,
                             Fog Reveal has been used since at least 2018
                             in criminal investigations ranging from the
                             murder of a nurse in Arkansas to tracing the
                             movements of a potential participant in the
                             Jan. 6 insurrection at the Capitol. The tool
                             is rarely, if ever, mentioned in court
                             records, something that defense attorneys say
                             makes it harder for them to properly defend
                             their clients in cases in which the
                             technology was used.


                             The company was developed by two former high-
                             ranking Department of Homeland Security
                             officials under former President George W.
                             Bush. It relies on advertising identification
                             numbers, which Fog officials say are culled
                             from popular cellphone apps such as Waze,
                             Starbucks and hundreds of others that target
                             ads based on a person’s movements and
                             interests, according to police emails. That
                             information is then sold to companies like
                             Fog.


          o § Defence/Aggression⠀➾


                # ⚓ JNS ☛ The_BBC’s_perfectly_sealed_thought_system⠀⇛


                       Deech, a former Oxford University law lecturer,
                       wrote that “it is absolutely unacceptable to
                       respond to comments with murder or violence,” and
                       that Atwan’s comments “could amount to glorifying
                       terrorism,” a crime under English law.


                       The BBC dismissed her complaint, insisting that
                       inviting Atwan to comment was “editorially
                       justified” and that “if extreme views are expressed
                       on the BBC we would always seek to challenge them.”


                # ⚓ The Jewish Chronicle ☛ Peer_attacks_BBC_for_‘glorifying
                  terrorism’⠀⇛


                       The BBC has refused to back down after a former
                       Governor of the corporation said its coverage of
                       the Salman Rushdie attack “could amount to
                       glorifying terrorism”, the JC can reveal.


                       Baroness Ruth Deech, a crossbench peer, wrote to
                       Director General Tim Davie after a British-
                       Palestinian commentator appeared to express
                       sympathy for the Rushdie assailant’s extremism on
                       the BBC News Channel.


                # ⚓ The Jewish Chronicle ☛ In_full:_Baroness_Deech’s_letter_to
                  the_BBC⠀⇛


                       It was wrong for the BBC to have given him this
                       airtime. His comments about Rushdie could amount to
                       “glorifying terrorism” under the Terrorism Act
                       2006. It is absolutely unacceptable to respond to
                       Sir Salman’s writing or comments, no matter how
                       offensive they might seem to some, with murder or
                       violence, and any attempt to explain or justify
                       violence committed against him should be challenged
                       vigorously, not least by the presenter. No direct
                       challenge was made on the programme when Mr Atwan
                       spoke about this topic.


                # ⚓ Frontpage Magazine ☛ Horror_of_Love_Jihad_Strikes_India
                  Again⠀⇛


                       The liberal ecosystem within India is not
                       dissimilar to the United States or other western
                       theaters which are remarkably easy to buckle under
                       cries of ‘Islamophobia’ if suspects, assailants,
                       perpetrators of any crime happen to be Muslim.


                       Despite its pluralism, and the fact that the
                       majority religion (Hinduism) lives peacefully with
                       the minority religions of Islam and Christianity,
                       there are frequently shrill cries from media,
                       academia and the chattering classes whenever any
                       aspect of Hindu culture is seen to usurp Islamic
                       hegemony.


          o § Environment⠀➾


                # ⚓ TruthOut ☛ Parent_Participation_in_Climate_Justice_Efforts
                  Is_on_the_Rise⠀⇛


                # ⚓ Common Dreams ☛ Opinion_|_How_a_‘Green_Amendment’_Can_Boost
                  Environmental_Justice⠀⇛


                       According to locals, two different types of odors
                       emanate from the 366-acre High Acres Landfill,
                       which sits just outside Rochester, New York. 


                # § Energy⠀➾


                      # ⚓ Hackaday ☛ Hackaday_Prize_2022:_Drying_Clothes_With
                        Ultrasound⠀⇛


                             Clothes dryers are great, and a key part of
                             modern life, but they do use a lot of energy.
                             [Mike Rigsby] decided to see if there was a
                             more efficient method of drying clothes that
                             could compete with resistive heating for
                             efficiency. Thus, he started work on an
                             ultrasonic clothes dryer.


                # § Wildlife/Nature⠀➾


                      # ⚓ Counter Punch ☛ Animal_Welfare_in_the_Bible⠀⇛


                             So I decided to ask some Christian activists,
                             scholars, and theologians — who are concerned
                             with animal ethics — whether they thought the
                             Old Testament had more to say on the subject
                             than the New Testament, and whether they
                             viewed this as a problem. Here’s what they
                             said.


                      # ⚓ Counter Punch ☛ How_to_Green_Our_Parched_Farmlands
                        and_Finance_Critical_Infrastructure⠀⇛


                             There are, however, other ways to finance
                             these essential projects. “A work-around,”
                             says Tucker, “is so-called off-balance sheet
                             money creation.” That was the approach taken
                             in the 1930s, when commercial banks were
                             bankrupt and the country faced its worst-ever
                             economic depression; yet the government
                             succeeded in building infrastructure as never
                             before.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The Verge ☛ Google_put_Parler’s_app_back_in_the_Play
                  Store⠀⇛


                       Parler, which advertises itself as a platform for
                       free speech, agreed to moderate posts that show up
                       in the Play Store app, according to a Bloomberg
                       report. The company previously told The Verge that
                       it has a similar deal that allows it to remain on
                       the App Store — “Anything allowed on the Parler
                       network but not in the iOS app will remain
                       accessible through our web-based and Android
                       versions.” (The Android version was, at the time,
                       available via side-loading and therefore did not
                       have to conform to Google Play policies.) The
                       company also said that its algorithm could detect
                       violent content that violates its guidelines.


                # ⚓ The Verge ☛ Twitter_had_a_new_plan_to_fight_extremism_—
                  then_Elon_arrived⠀⇛


                       Instead, researchers hoped to identify people who
                       were about to engage with harmful tweets, and nudge
                       them toward healthier content using pop-up messages
                       and interstitials. “The pilot will allow Twitter to
                       identify and leverage behavioral — rather than
                       content — signals and reach users at risk from harm
                       with redirection to supportive content and
                       services,” read an internal project brief, viewed
                       by The Verge.


                       Twitter researchers partnered with Moonshot, a
                       company that specializes in studying violent
                       extremists, and kicked off a project called
                       Redirect, modeled after work that Google and
                       Facebook had done to curb the spread of harmful
                       communities. At Google, this work had resulted in a
                       sophisticated campaign to target people searching
                       for extremist content with ads and YouTube videos
                       aimed at debunking extremist messaging. Twitter
                       planned to do the same.


                # ⚓ The Verge ☛ Twitter’s_edit_button_is_a_big_test_for_the
                  platform’s_future⠀⇛


                       Whether Twitter should have an edit button is still
                       a fun and controversial debate. Will some users
                       abuse the feature, creating (or manufacturing)
                       viral tweets and then changing them to something
                       problematic that lots of users see? You betcha. Do
                       most people want an edit button to do totally
                       valid, normal, platform-improving things? Yep. Can
                       Twitter do enough to track and mitigate the abuse,
                       so that the vast majority of users — who just want
                       to correct typos, re-phrase things that are being
                       misinterpreted, and update their tweets as things
                       change — can use it for its intended purpose?
                       That’s the real question.


                # ⚓ Counter Punch ☛ Why_Gorbachev_Was_One_of_the_Greatest
                  Failures_in_History⠀⇛


                       A myth has since grown up that the Soviet Union was
                       in a state of collapse when Gorbachev took the
                       helm, but this is not correct. It was politically
                       and economically dead in the water, but it was not
                       falling apart and the Government faced no serious
                       challenge to its authority. It might have continued
                       in this semi-moribund state for decades – like the
                       Ottoman Empire in the 19th century – if its
                       leadership had so wished.


                # ⚓ Counter Punch ☛ Gorbachev_Rode_the_Tiger_and_Ended_Up
                  Inside_It⠀⇛


                       This destructive process of sweeping away all the
                       institutions of state socialism via radical
                       privatization did not give birth to the free market
                       capitalism that the ideologues of the IMF and their
                       Russian acolytes desired. Instead, it gave way to a
                       system where privatized assets passed into a few
                       hands that had mastered the system of pirate
                       capitalism.


                # ⚓ Counter Punch ☛ Where_Does_Russia_Receive_Its_Aid_From?⠀⇛


                       Even most of Russia’s key post-Soviet allies
                       belonging to its international organizations, the
                       Eurasian Economic Union (EAEU) and the Collective
                       Security Treaty Organization (CSTO), have avoided
                       supporting Moscow. Kazakhstan, for example, a
                       member of both institutions, took steps in July to
                       begin exporting its oil across the Caspian Sea,
                       bypassing Russian-controlled oil pipelines. This
                       directly undermines the Kremlin’s strategy of
                       restricting oil to Europe to compromise the
                       region’s energy security. The key exception among
                       post-Soviet states has been Belarus. Over the last
                       decade, President Alexander Lukashenko has steered
                       Belarus further into Russia’s orbit. Enticed by
                       cheap Russian oil and gas and lucrative transit
                       fees as both these commodities continue on to
                       Europe, Lukashenko has also increasingly relied on
                       Russian security forces to enforce his rule—notably
                       evident during the 2020 Belarusian protests


                # ⚓ TruthOut ☛ Biden_Adviser’s_Lobbying_Firm_Is_Undermining
                  Democratic_Party_Priorities⠀⇛


                # ⚓ Counter Punch ☛ The_Story_of_Ted_Hall,_the_Atomic_Spay⠀⇛


                       Joseph Allbright and Marcia Kunstel, former Moscow
                       correspondents and authors of the book on Ted Hall,
                       Bombshell (1997), appear on numerous occasions in
                       the film to offer expert historical commentary on
                       the Hall narrative. Photos of Hiroshima and an
                       interview with the pilot of Enola Gay, Paul
                       Tibbets, provide historical evidence of the nuclear
                       devastation that Ted Hall helped create and wished
                       to end. Well-chosen music evokes past events.


                # ⚓ Common Dreams ☛ Trump_Calls_Biden_‘Enemy_of_the_State’_in
                  ‘Fully_Unhinged’_Speech⠀⇛


                       “What Trump did by calling Biden an ‘enemy of the
                       state’ to his poorly educated crowd is literally
                       threatening the president.”


                # ⚓ Common Dreams ☛ Washington_Post_Ripped_for_‘Neocolonial’
                  Editorial_Against_Chile’s_New_Constitution⠀⇛


                       “Green or not, energy for the North continues to
                       trump democracy in the South.”


                # ⚓ TruthOut ☛ Antiwar_Activists_Decry_Saudi_Arabia’s
                  “Sportswashing”_Golf_Tournament⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ Gannett ☛ On_Salman_Rushdie:_Reading_and_speaking_to_thwart
                  those_who_would_silence_us⠀⇛


                       Purchasing the book and using it as a prop at my
                       commencement was an act of resistance to censorship
                       and terrorism, for sure; yet it was amusing that,
                       like most of those threatening or criticizing
                       Rushdie, I had not read the book, either.


                # ⚓ The Verge ☛ Cloudflare_blocks_Kiwi_Farms_due_to_an
                  ‘immediate_threat_to_human_life’⠀⇛


                       Concerns about Kiwi Farms grew after transgender
                       YouTuber and Twitch streamer, Clara Sorrenti
                       (Keffals), had been targeted by a dangerous
                       harassment campaign by users from the site. Last
                       month, Kiwi Farms users waged a swatting attack
                       against Sorrenti, otherwise known as the act of
                       providing a false tip to police that someone’s
                       planning on carrying out a violent crime, resulting
                       in police swarming the victim’s home.


                       Sorrenti later went into hiding and started a
                       #DropKiwifarms campaign that urged Cloudflare to
                       stop serving Kiwi Farms. Users across Twitter
                       shared the hashtag, also with some revealing the
                       harassment they’ve experienced at the hand of Kiwi
                       Farms’ users.


                # ⚓ Cloudflare ☛ Blocking_Kiwifarms⠀⇛


                       We have blocked Kiwifarms. Visitors to any of the
                       Kiwifarms sites that use any of Cloudflare’s
                       services will see a Cloudflare block page and a
                       link to this post. Kiwifarms may move their sites
                       to other providers and, in doing so, come back
                       online, but we have taken steps to block their
                       content from being accessed through our
                       infrastructure.


                       This is an extraordinary decision for us to make
                       and, given Cloudflare’s role as an Internet
                       infrastructure provider, a dangerous one that we
                       are not comfortable with. However, the rhetoric on
                       the Kiwifarms site and specific, targeted threats
                       have escalated over the last 48 hours to the point
                       that we believe there is an unprecedented emergency
                       and immediate threat to human life unlike we have
                       previously seen from Kiwifarms or any other
                       customer before.


                # ⚓ Scheerpost ☛ The_Chris_Hedges_Report:_Ukraine_and_the
                  Crisis_of_Media_Censorship⠀⇛


                       Throughout the Ukraine war, Western news outlets
                       have mindlessly parroted the opinions of a ruling
                       elite and overseen a public discourse that is often
                       unhinged from the real world. 


          o § Civil Rights/Policing⠀➾


                # ⚓ NBC ☛ Saudi_Arabia_investigates_video_of_men_attacking
                  orphaned_women_and_girls⠀⇛


                       ALQST, a British-based rights group which focuses
                       on Saudi Arabia, said in a statement that the
                       attack was a retaliation against women staging a
                       sit-in and strike over living conditions inside the
                       facility.


                # ⚓ Helsinki Times ☛ Telework_still_largely_regulated_at
                  company_level_in_Europe⠀⇛


                       Access to telework and working arrangements when
                       working from home are still largely determined at
                       company level in most EU Member States, with just
                       France, Lithuania and Portugal currently enshrining
                       the right to request telework in legislation. While
                       some common ground exists, there are varying
                       standards and practices in place with regards to
                       telework in the EU, which can be regulated through
                       legislation or collective agreements.


                # ⚓ European Foundation for the Improvement of Living and
                  Working Conditions ☛ Telework_in_the_EU:_Regulatory
                  frameworks_and_recent_updates⠀⇛


                       Ten countries adopted new regulation on telework
                       since the beginning of the pandemic, underlining
                       the importance of further developing capacity
                       building for social dialogue. In Member States with
                       a relatively weak culture of social dialogue,
                       implementing national-level regulation at company
                       level and protecting employees teleworking is
                       especially challenging.


                       A significant number of collective agreements on
                       telework were introduced during the pandemic at
                       company and sectoral levels, particularly in
                       sectors with existing arrangements, such as in
                       financial services, manufacturing and information
                       and communications. New agreements were developed
                       in the public services and administration,
                       education, and health and social work activities
                       sectors, highlighting how telework is fast becoming
                       an established way of work organisation across the
                       EU.


                # ⚓ The Telegraph UK ☛ Sharia_law_returns_to_Afghanistan_as
                  Taliban_confirms_public_whippings⠀⇛


                       The Taliban has been enforcing Sharia law for a
                       while since seizing power by ousting the government
                       last summer.


                       However, although there have been unconfirmed
                       reports of similar punishments being carried out
                       elsewhere in the country, this is the first time
                       the Taliban has officially said public whippings
                       are being used.


                       It came just days after Mawlawi Hibatullah
                       Akhundzada, the Taliban’s leader, ordered all
                       existing laws to be scrapped and submitted a series
                       of six new articles for how the country should be
                       governed in accordance with Sharia law.


                # ⚓ Common Dreams ☛ Opinion_|_‘Water_Is_Dignity,’_Say_Jackson,
                  Mississippi_Activists_as_Crisis_Continues⠀⇛


                       As of September 2, the vast majority of the
                       residents of the city of Jackson, Mississippi—over
                       150,000—still have no access to safe drinking
                       water. The Jackson water crisis began on August 30
                       when flooding caused the pumps at the main water
                       treatment facility, O.B. Curtis, to fail. This left
                       most residents without clean water and many with no
                       water at all due to low water pressure. Mississippi
                       Governor Tate Reeves warned residents on August 31,
                       “Do not drink the water from the pipes if you can
                       avoid it.” 


                # ⚓ Common Dreams ☛ Opinion_|_America_Needs_a_Civic_Group_to
                  Oppose_a_Cashless_Society⠀⇛


                       The most perceptive ancient historians and
                       philosophers could not have foreseen a time when a
                       certain type of mass convenience and abundance
                       becomes a threat to democracy, justice and
                       dispersed power. Welcome to the incarcerations of
                       the credit card payment systems Gulag and the
                       corporate state’s drive to stop consumers from
                       paying with cash.


                # ⚓ Counter Punch ☛ How_About_a_Civic_Group_to_Oppose_a
                  Cashless_Society?⠀⇛


                       If you are in the lower 20% of the income scale,
                       unbanked and outside the Gulag, consumer
                       protections are really weak. Rip-off practices such
                       as pay-day loan rackets and check cashing gouges
                       proliferate.


                # ⚓ Counter Punch ☛ By_Refusing_to_Prioritize_Drivers’_Safety,
                  UPS_Risks_Major_Strike⠀⇛


                       It’s not just cookies and steaks that are baking in
                       the trucks. Drivers are collapsing and dying from
                       the extreme temperatures.


                # ⚓ Counter Punch ☛ Labor_Day:_Unions_Have_a_Stake_in_Ending
                  Minority_Rule_in_the_United_States⠀⇛


                       The assault on labor has contributed greatly to
                       soaring income inequality and stagnant living
                       standards for workers in the United States. From
                       1979 to 2019, productivity (the income generated
                       from an hour of labor) has grown by 60 percent; yet
                       the typical worker’s real (inflation-adjusted)
                       compensation rose by just 14 percent. But wages
                       used to rise with productivity: from 1948 to 1979,
                       productivity rose by 118 percent, and real
                       compensation increased by 108 percent.


                # ⚓ Counter Punch ☛ America’s_New_Moment_of_Labor
                  Mobilization⠀⇛


                       It comes on the back of a wave of successful
                       efforts to mobilize at Starbucks and Amazon. The
                       growth of unionized stores at Starbucks in
                       particular has been stunning. Since baristas in
                       Buffalo, New York, became the first at the chain to
                       unionize in December 2021, colleagues at a further
                       234 outlets have followed suit in recent months.


                # ⚓ TruthOut ☛ On_Labor_Day,_Let’s_Celebrate_2022_as_a_Pivotal
                  Year_for_Independent_Unions⠀⇛


                # ⚓ Common Dreams ☛ ‘We’ll_Come_Back_Stronger,’_Vows_Chilean
                  Left_After_Plebiscite_Loss⠀⇛


                       “We resisted for 500 years and will continue to do
                       so.”


          o § Monopolies⠀➾


                # § Copyrights⠀➾


                      # ⚓ [Old] BoingBoing ☛ How_dumb_Social_Media_rules
                        punished_me_for_a_Lovecraftian_parody_of_Billy_Joel⠀⇛


                             I never heard anything back about this. The
                             video was never restored to Twitter.


                      # ⚓ Torrent Freak ☛ Pirate_IPTV:_Couple_Sold_Illegal
                        Subscriptions_&_Laundered_Money⠀⇛


                             A man has gone on trial in Sweden accused of
                             selling pirate IPTV subscriptions and pre-
                             configured set-top boxes. A two-year
                             investigation led to the seizure of almost
                             $93,000 in cash and a Tesla. After claiming
                             she was unaware of her partner’s activities,
                             a woman faces money laundering charges.


                      # ⚓ Torrent Freak ☛ Google_Received_DMCA_Takedown_Notices
                        For_4_Million_Unique_Domains⠀⇛


                             Google has reached a new milestone. Over the
                             past several years, copyright holders have
                             asked the search engine to remove URLs from
                             four million unique domains. These include
                             some egregious pirate sites but The White
                             House, the FBI, and the Vatican have also
                             been flagged as infringers.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Summer_Retrospective⠀⇛


                       Summer is coming to an end. The temperatures are
                       dropping below 30°C. To think that when I was young
                       we expected a few days only of 30°C and more.
                       Summer is coming to an end and my summer break is
                       coming to and end at the end of September. As
                       always, the prospect of going back to work is not
                       very enticing. I’m looking forward to a future were
                       we mostly entertain each other and the basic
                       necessities of life are free.


          o § Technical⠀➾


                # ⚓ Dream_XI⠀⇛


                       I got a new computer.


                       It looked strange.


                       There was a detachable screen. And a leather seat.
                       One that you could find in a car.


                       On the left side of the leather seat, was an
                       embedded keyboard, on the right, a touchpad. They
                       had the same leather finish as the rest of the
                       seat.


                       It felt like sitting in a car. But it wasn’t a car.
                       It was a computer. The screen hovered in front of
                       me. It had no mounting point or base to rest on. It
                       moved along with my head. The keyboard was nice and
                       easy to use.


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


<



                    ䷩ 𝚕𝚒𝚗𝚎 5342

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.05.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_05/09/2022:_Salix_Xfce_15.0_and_Xubuntu_22.10_Development_Update⠀✐


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Kernel_Space
          o Instructionals/Technical
          o WINE_or_Emulation
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o New_Releases
          o Screenshots/Screencasts
          o Slackware_Family
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Content_Management_Systems_(CMS)
          o Programming/Development
                # Perl_/_Raku
                # Python
                # Java
          o Standards/Consortia
    * Leftovers
          o Security
                # Fear,_Uncertainty,
                  Doubt/Fear-mongering/Dramatisation
                # Privacy/Surveillance
          o Defence/Aggression
          o Finance
          o Censorship/Free_Speech
    * Gemini*_and_Gopher
          o Personal
          o Technical
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ KDE_Slimbook_4_/_Slimbook_Pro_X_14_(2022):_FINALLY,
                  GREAT_BATTERY_LIFE!_–_Invidious⠀⇛


          o § Kernel Space⠀➾


                # ⚓ LWN ☛ Linux_5.19.7⠀⇛


                       I'm announcing the release of the 5.19.7 kernel.

                       All users of the 5.19 kernel series must upgrade.

                       The updated 5.19.y git tree can be found at:
                       	git://git.kernel.org/pub/scm/linux/kernel/git/
                       stable/linux-stable.git linux-5.19.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
                # ⚓ LWN ☛ Linux_5.15.65⠀⇛


                # ⚓ LWN ☛ Linux_5.10.141⠀⇛


                # ⚓ LWN ☛ Linux_5.4.212⠀⇛


                # ⚓ LWN ☛ Linux_4.19.257⠀⇛


                # ⚓ LWN ☛ Linux_4.14.292⠀⇛


                # ⚓ LWN ☛ Linux_4.9.327⠀⇛


          o § Instructionals/Technical⠀➾


                # ⚓ ID Root ☛ How_To_Install_WildFly_on_Ubuntu_22.04_LTS_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       WildFly on Ubuntu 22.04 LTS. For those of you who
                       didn’t know, WildFly is a powerful, modular, and
                       lightweight application server that helps you build
                       amazing applications. It is cross-platform and
                       comes with a sophisticated interface that makes
                       changing application server settings and
                       configuration very simple and quick. As of this
                       writing, WildFly 26 is the latest release in a
                       series of JBoss opensource application server
                       offerings


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


                # ⚓ Install_Oracle_Linux_9_on_VirtualBox_–_kifarunix.com⠀⇛


                       In this tutorial, you will learn on how to simply
                       install Oracle Linux 9 on VirtualBox. With Oracle
                       Linux 9 now being available, you might want to try
                       it out and the best way out is through installing
                       it as a virtual machine.


                # ⚓ Install_dhclient_command_on_Oracle_Linux_–_kifarunix.com⠀⇛


                       This simple guide will show you how to install
                       dhclient command on Oracle Linux. Have you
                       installed Oracle Linux system and trying to
                       configure automatic IP addresses via DHCP using
                       dhclient command? Well, unlike the CentOS/RHEL/
                       Rocky Linux systems, the dhclient command is not
                       installed by default.


                # ⚓ Linux Hint ☛ How_to_Boot_Raspberry_Pi_from_USB?⠀⇛


                       On paper SD cards have a bandwidth of almost 50
                       MBps but they achieve 38 MBps which is quite low.
                       On the other hand, the USBs have relatively higher
                       bandwidth at least more than that of the SD cards,
                       so they tend to be a better choice for Raspberry
                       Pi, if you are absolute fanatic about the speed
                       then go for an SSD storage for your Pi.


                # ⚓ Linux Hint ☛ How_to_Use_AWS_CLI_to_Manage_EC2_Instance_
                  [Part_1]⠀⇛


                # ⚓ Linux Hint ☛ How_to_Use_AWS_CLI_to_Manage_EC2_Instance_
                  [Part_2]⠀⇛


                # ⚓ HowTo Forge ☛ How_to_Install_a_Kubernetes_Cluster_with
                  Kubeadm_on_Rocky_Linux⠀⇛


                       Kubernetes or k8s is an open-source platform for
                       container orchestration that automates deployments,
                       management, and scaling of containerized
                       applications. Kubernetes is a container
                       orchestration created by Google, and now become an
                       open-source project and become standard for modern
                       application deployment and computing platforms.


                       Kubernetes is the solution for the modern container
                       deployment era. It provides service discovery and
                       load-balancing, storage orchestration, automated
                       rollout and rollback, self-healing service, secret
                       and configuration management. Kubernetes enables
                       cost-effective cloud-native development.


                # ⚓ Network World ☛ Checking_exit_codes_in_bash_|_Network
                  World⠀⇛


                       There are quite a few exit codes used on Linux
                       systems, though no listing you can display when
                       you’re feeling curious. In fact, you won’t see the
                       numeric codes unless you specifically ask for them.


                # ⚓ Vitux ☛ How_to_Securely_Delete_Files_Using_Shred_Command_in
                  Debian_11_–_VITUX⠀⇛


                       If you have a file with sensitive information, it
                       may not be enough to simply delete it with the rm
                       command or press the Delete key. Deleting a file
                       with the rm command usually only removes it from
                       our directory. The deleted file remains on disk and
                       can be recovered and abused by an attacker with the
                       necessary skills.


                       In Linux, you can use the shred command to safely
                       delete the files by repeatedly overwriting the file
                       with gibberish data. This makes recovery of the
                       original data quite difficult or almost impossible,
                       even if the deleted file is recovered. The Shred
                       command not only overwrites a file but also deletes
                       it if specified. You can also use it to overwrite
                       partitions or an entire disk.
                       In this article, we explain how to use the shred
                       command in Debian 11 to safely delete files. The
                       same procedure can be used in other Debian and
                       Ubuntu versions. We also discussed some of the
                       command line options.


                # ⚓ Ubuntu Handbook ☛ How_to_Install_KDE_Plasma_5.25_in_
                  (K)Ubuntu_22.04_via_PPA_|_UbuntuHandbook⠀⇛


                       For KUbuntu 22.04 users, the KDE Plasma 5.25
                       desktop is available to install via official PPA
                       repository!


                # ⚓ TechRepublic ☛ How_to_install_the_Gitea_git_repository_on
                  Ubuntu_Server_22.04_|_TechRepublic⠀⇛


                       Gitea is one of the best self-hosted Git servers on
                       the market. This Go-based package is very user-
                       friendly, lightweight and fairly straightforward to
                       install. Once you have it up and running, your
                       development teams can enjoy a Git repository from
                       within your LAN, which means sensitive code will be
                       less likely to find its way into the hands of a
                       third party. Gitea features notifications, a built-
                       in editor, user management and more.


          o § WINE or Emulation⠀➾


                # ⚓ TechSpot ☛ Wine_7.16_improves_Windows_games_compatibility
                  on_Linux_|_TechSpot⠀⇛


                       The Wine community has released a new version of
                       the eponymous software, an essential for gamers
                       using a Linux-based OS as well as for the Steam
                       Deck console from Valve. Wine 7.16 includes a lot
                       of fixes for gaming related bugs and other issues,
                       improving compatibility with software (and not just
                       games) designed to run on Windows.


                       Wine 7.16 includes many bug fixes for software
                       designed to run on Windows. Several issues with
                       games are fixed as well, which will surely make
                       Linux users happy.
                       As the developers used to point out in the past,
                       Wine “is not an emulator” but an open-source
                       compatibility layer for users that need to run
                       Windows software on Linux and other Unix-like
                       operating systems.


          o § Games⠀➾


                # ⚓ Video ☛ Life_is_Strange_–_Episode_3:_Chaos_Theory_|_Linux
                  Game_–_Invidious⠀⇛


                       Life Is Strange is a five part episodic game that
                       sets out to revolutionize story-based choice and
                       consequence games by allowing the player to rewind
                       time and affect the past, present, and future.


                # ⚓ Video ☛ Games_for_Linux_|_August_2022⠀⇛


                       I myself did great research on this topic of Linux
                       games and came to you for fulfilling your thirst
                       for a generic list of games for Linux in August
                       2022.


                # ⚓ Linux Hint ☛ 5_Best_Solitaire_Apps_for_Android_to_Download
                  in_2022⠀⇛


                       “The Google Play Store is packed with intricate
                       RPGs, thrilling first-person and third-person
                       shooters, and high-octane racing games, but what if
                       you’re looking for something familiar that you can
                       play over and over again whenever you have a few
                       minutes of free time without ever feeling bored? In
                       that case, the top 5 best Solitaire apps listed in
                       this article may be just what you need.”


                # ⚓ Boiling Steam ☛ The_New_Odroid-Go_Ultra:_The_New_King_of
                  Linux_ARM_Handhelds?_–_Boiling_Steam⠀⇛


                       Odroid has recently announced a new portable
                       console, the ODROID-Go Ultra (aka OGU), Linux-
                       based, to hit the market later this year (early
                       october 2022). It’s similar in size to the Odroid-
                       Go Super, but the internals have been massively
                       upgraded so that you can expect to play a lot more
                       demanding games (emulation is the main point here).
                       it’s based on one of the their most powerful
                       boards, the Odroid-N2+.


                       [...]


                       That should help for PSP, Dreamcast, N64 and the
                       Gamecube. Don’t expect the Gamecube games to run
                       full speed – here’s a video below of Dolphin
                       running Gamecube games on the N2+ last year…


          o § Desktop Environments/WMs⠀➾


                # ⚓ Xubuntu_22.10_Development_Update⠀⇛


                       Xubuntu 22.10 “Kinetic Kudu” is set to arrive on
                       October 20, 2022. It will include the latest
                       updates from Xfce 4.17, GNOME 43, MATE 1.26, and
                       the family of supported applications that make up
                       Xubuntu. With the Beta freeze coming later this
                       month, it’s time to start testing to make Xubuntu
                       22.10 a stable environment for users that want the
                       latest and greatest from the Linux desktop.


                       [...]


                       As usual, I’ve grouped the updates into some common
                       categories: Appearance, GNOME Apps, Xfce Apps,
                       Other Apps, and Libraries. Unless noted otherwise,
                       each app listed just includes regular maintenance
                       updates, bug fixes, or usability tweaks. It should
                       also be noted that these apps will continue to
                       change and be updated through the 22.10 final
                       release in October.


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


                      # ⚓ Adding_Room_To_Space-_GSoC’22_post_#14⠀⇛


                             I have implemented adding room to a Space.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Linux Hint ☛ Best_Linux_Distros_for_Data_Science⠀⇛


                 “In today’s day and age, we can all agree that “data is
                 king”. About 2.5 quintillion (18 zeros) bytes of data are
                 being generated daily, which various industries use for
                 their benefit.”


                 Different industries use the data in different ways.
                 However, all of them have the same goal: to understand
                 their consumers better and produce products they believe
                 would sell the most.


                 The process of evaluating data using modern tools and
                 techniques in finding patterns and extracting useful
                 information from it is called “data science” and the
                 people who carry out these tasks are known as “data
                 scientists”.


                 After finding patterns in the data, data scientists can
                 make predictive Machine Learning models that can help the
                 industries modify their marketing plans and make well-
                 informed business decisions. The overall effect? The
                 business grows, and the customers are satisfied.


                 The importance of data science in today’s world can’t be
                 understated. Many resources are invested in data
                 extraction, warehousing, processing, and analyzing.
                 Therefore, choosing a computer system that can meet the
                 required demands is also important. A supportive and
                 compatible operating system can make a huge difference
                 among other specifications.


                 There is a trend among data scientists and programmers to
                 use or prefer Linux distributions over the generally
                 popular operating systems such as Windows and Mac. There
                 are multiple reasons behind this preference.


                 Firstly, the computational speed of Linux computers is
                 better than that of Windows. 90 percent of the world’s
                 supercomputers run on Linux. There is better hardware
                 support with Linux systems as compared to Windows. There
                 are multiple distributions and software choices available
                 with Linux. Linux is also more flexible, free, and open-
                 source.


                 As you may know and as stated above, many Linux
                 distributions are available with different advantages.
                 You are at the right place if you want to use Linux to
                 perform your data science tasks and are wondering which
                 Linux distribution would best suit you. We will look at
                 the best Linux distro choices for your specific job.


          o § New Releases⠀➾


                # ⚓ Salix_Xfce_15.0_is_released!_–_Salix_OS⠀⇛


                       It has been a long journey. Salix 15.0 is finally
                       here! With so much time since our stable release,
                       the changelog is huge and a lot of things have
                       changed!


                       On a high level, this release includes Xfce 4.16 as
                       the main environment! This is now based on GTK+3
                       and almost everything else that comes with a
                       default installation has been upgraded to use
                       GTK+3. This includes all our graphical system
                       tools, which have received significant updates and
                       a more modern look. The default software selection
                       hasn’t changed much, but of course everything has
                       been upgraded to their latest releases, including
                       Firefox 102ESR, LibreOffice 7.4, GIMP 2.10 and
                       more. Whiskermenu is used as our default panel menu
                       now. There have been extensive discussions in our
                       forums with respect to how the new release will
                       look and everything has been revamped, including a
                       new GTK theme, a new icon theme, a new window
                       manager theme and a default wallpaper, especially
                       tailored for Salix 15.0. While the “light” versions
                       of the above are used by default, “dark” versions
                       are readily available. In general, our users will
                       find themselves in a modern but familiar
                       environment.


                       One of the reasons that it took so long to make
                       this release, is that our software repositories are
                       now full of packages. We have built thousands of
                       packages in an enormous effort and these are
                       available for immediate installation through the
                       Gslapt package manager. The package repositories
                       for 15.0 are larger than those of all our previous
                       releases combined! On top of that, it is now
                       possible to install software using flatpaks! Salix
                       15.0 has Flathub as a preconfigured source of
                       software and we have also developed software for
                       better desktop integration. Users should only need
                       to browse flathub.org and install any software they
                       wish a few clicks.


                       The installer has received several updates under
                       the hood, but on the surface is the same classical
                       text dialog-driven installer we’ve always had.
                       Thanks to our wonderful translator community, it is
                       now available in several different languages,
                       including Catalan, Dutch, English (US and Great
                       Britain), French, German, Greek, Hungarian,
                       Italian, Polish, Portuguege (Brazil and Portugal),
                       Spanish (Spain and Costa Rica), Swedish, Turkish
                       and Ukrainian!


                # ⚓ Beta News ☛ Slackware-based_Salix_15_Linux_distribution
                  available_for_download⠀⇛


                       Linux distributions based on Slackware, however,
                       are far less common these days, so such distros are
                       definitely worth some attention. Today, the
                       Slackware-based Salix 15 becomes available for
                       download. This Linux-based operating system uses
                       the Xfce 4.16 desktop environment and kernel
                       5.15.63. In addition to Flatpak support, this
                       version of the distro comes with some excellent
                       software pre-installed, such as Firefox 102 ESR,
                       GIMP 2.10, and LibreOffice 7.4. Believe it or not,
                       there are even versions for both 32-bit and 64-bit
                       processors!


                       “This release includes Xfce 4.16 as the main
                       environment! This is now based on GTK+3 and almost
                       everything else that comes with a default
                       installation has been upgraded to use GTK+3. This
                       includes all our graphical system tools, which have
                       received significant updates and a more modern
                       look. Whiskermenu is used as our default panel menu
                       now. There have been extensive discussions in our
                       forums with respect to how the new release will
                       look and everything has been revamped, including a
                       new GTK theme, a new icon theme, a new window
                       manager theme and a default wallpaper,” says the
                       development team.


          o § Screenshots/Screencasts⠀➾


                # ⚓ Video ☛ BigLinux_2022.08.29_overview_|_in_search_of_the
                  perfect_system!_–_Invidious⠀⇛


                       In this video, I am going to show an overview of
                       BigLinux 2022.08.29 and some of the applications
                       pre-installed.


          o § Slackware Family⠀➾


                # ⚓ Eric Hameleers ☛ Chromium_105_update_addresses_zero-day
                  exploit_|_Alien_Pastures⠀⇛


                       Only a few days after Google released Chrome 105
                       (by means of the 105.0.5195.52 sourcecode) they
                       have pushed an update to 105.0.5195.102.
                       This update fixes a single bug, but it is a
                       critical one (CVE-2022-3075) for which a zero-day
                       exploit is actively abused by malicious third
                       parties. It’s highly recommended to upgrade your
                       Chromium (regular as well as un-googled) browser to
                       the latest version.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Make Use Of ☛ Upgrade_Your_Dumb_TV_With_the_Mecool_KA1_All-
                  in-One_Android_TV_and_Smart_Speaker⠀⇛


                # ⚓ TechRadar ☛ Dixon_Technologies_gets_rights_to_make_Android
                  –_Google_TVs_in_India_|_TechRadar⠀⇛


                # ⚓ SamMobile ☛ Samsung_Galaxy_A12_gets_Android_12_(One_UI_4)
                  update_in_the_US_–_SamMobile⠀⇛


                # ⚓ Notebook Check ☛ Xiaomi_POCO_M5_debuts_with_Android_12,_a
                  90_Hz_display_and_a_MediaTek_Helio_G99_from_€189_–
                  NotebookCheck.net_News⠀⇛


                # ⚓ Notebook Check ☛ Redmi_A1_leaks_as_Xiaomi’s_next_entry-
                  level_smartphone_running_Android_12_(Go_edition)_–
                  NotebookCheck.net_News⠀⇛


                # ⚓ Notebook Check ☛ Xiaomi_12S_Ultra’s_camera_successor_is
                  backed_to_launch_as_an_Android_smartphone_with_a_significant
                  charging_upgrade_–_NotebookCheck.net_News⠀⇛


                # ⚓ How_to_turn_on_WiFi_calling_on_Android_–_Phandroid⠀⇛


                # ⚓ Android Police ☛ Google_readies_Chromebook_keyboard
                  controls_for_Android_games⠀⇛


                # ⚓ 9to5Google ☛ EU_proposes_five_years_of_Android_updates_as
                  standard⠀⇛


                # ⚓ The Sun ☛ Warning_for_MILLIONS_of_Android_users_–_don’t
                  make_costly_mistake_|_The_Sun⠀⇛


                # ⚓ Linux On Mobile ☛ LINMOB.net_–_Weekly_GNU-like_Mobile_Linux
                  Update_(35/2022):_Phosh_0.21.0,_postmarketOS_22.06.2_and
                  progress_reports_on_Kaidan_and_Nemo_Mobile⠀⇛


                       News on GNOME Shell Mobile, a new UI for GNOME
                       Calls and a lot more.


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


          o § Content Management Systems (CMS)⠀➾


                # ⚓ The_Month_in_WordPress_–_August_2022_–_WordPress_News⠀⇛


                       August has been a busy month, with the redesign of
                       WordPress.org, new localized content on Learn
                       WordPress, and the WordPress 6.0.2 security and
                       maintenance release. But that’s not all! Read on to
                       catch up on the latest WordPress news.


          o § Programming/Development⠀➾


                # ⚓ PHP_8.2.0_RC1_available_for_testing⠀⇛


                       The PHP team is pleased to announce the first
                       release candidate of PHP 8.2.0, RC 1. This
                       continues the PHP 8.2 release cycle, the rough
                       outline of which is specified in the PHP Wiki.


                       For source downloads of PHP 8.2.0 RC1 please visit
                       the download page.


                       Please carefully test this version and report any
                       issues found in the bug reporting system.


                       Please DO NOT use this version in production, it is
                       an early test version.


                       For more information on the new features and other
                       changes, you can read the NEWS file, or the
                       UPGRADING file for a complete list of upgrading
                       notes. These files can also be found in the release
                       archive.


                       The next release will be the second release
                       candidate (RC 2), planned for Sept 15th 2022.


                       The signatures for the release can be found in the
                       manifest or on the QA site.


                       Thank you for helping us make PHP better.


                # § Perl / Raku⠀➾


                      # ⚓ Valid_temperatures_|_Playing_Perl_6␛b6xA_Raku⠀⇛


                             PWC 181 Task 2 asks for input validation of
                             dates and numbers. OK, it should ask for
                             input validation so my solution isn’t totally
                             over the top. Better safe then sorry.


                # § Python⠀➾


                      # ⚓ Linux Hint ☛ Grid_Search_CV_in_Sklearn⠀⇛


                             “The variables of a machine learning model
                             that determine how the parameters will be
                             tuned are known as hyperparameters. The
                             problem of selecting a group of ideal
                             hyperparameters for a learning algorithm is
                             known as hyperparameter tuning. The
                             hyperparameters can be configured manually or
                             automatically. There are numerous algorithms
                             available for this tweaking. One such method,
                             GridSearchCV, will be covered in this blog.”


                      # ⚓ Linux Hint ☛ Class_Method_vs_Static_Method_in
                        Python⠀⇛


                             Let’s talk about the definition and usage of
                             class and static methods in Python.


                      # ⚓ Linux Hint ☛ First_Class_Functions_in_Python⠀⇛


                             The “First Class Function” is supported by
                             several programming languages including Lisp,
                             Haskell, Scala, Julia, Python, JavaScript,
                             Ruby, Perl, as well as Go. Every Python
                             functions were the first class function, to
                             put it briefly. In just about any programming
                             language, a function is considered a first-
                             class variable and can therefore be provided
                             as well as handled in the same way as the
                             other types of objects (all objects in Python
                             are considered to be objects), like an
                             integer or a string for instance.


                      # ⚓ Linux Hint ☛ *args_and_**kwargs_in_Python⠀⇛


                             When there is а changeable number of
                             parameters, the error is raised in the code.
                             Then, would the function continue to be
                             altered to take the precise number of
                             arguments? In this case, *args and **kwargs
                             are employed.


                             Whenever we’re unclear about how many
                             arguments to send to a function, we might use
                             *args (non-keyword arguments) and **kwargs
                             (keyword arguments) for parameters.


                # § Java⠀➾


                      # ⚓ Linux Hint ☛ How_to_Check_if_a_String_Contains
                        Character_in_Java⠀⇛


                             The Java wrapper class “Character” wraps a
                             primitive data type “char“. Java utilizes the
                             “char” data type to hold a single character
                             enclosed in single quotes (‘ ‘), as opposed
                             to the “String” data type that belongs to the
                             Java wrapper class “String”, used to carry a
                             sequence of characters enclosed in double
                             quotations (” “). There are times while
                             writing Java code that you need to verify if
                             a certain character or a group of characters
                             are present in the sequence or not.


                      # ⚓ Linux Hint ☛ How_to_Check_if_an_Object_is_Null_in
                        Java⠀⇛


                             Java is a dynamic object-oriented programming
                             language that implements classes and objects.
                             A unique instance of a class defines an
                             object of the class. It is a self-contained
                             entity with a state and behavior that
                             facilitates mapping real-world entities while
                             coding. The class defines the data and
                             methods, and its object can utilize them to
                             represent a specific entity.


          o § Standards/Consortia⠀➾


                # ⚓ Liliputing ☛ Lilbits:_EU_could_mandate_longer_life-spans
                  for_phones,_Motorola_Edge_30_Ultra_and_Fusion_leaked_–
                  Liliputing⠀⇛


                       A growing number of phone makers are promising to
                       support their phones by offering as many as five
                       years of software updates. In some cases they’re
                       even making spare parts and repair manuals
                       available for folks who want to fix their own
                       hardware at home.


                       But European officials are considering regulations
                       that would make long-term support the rule rather
                       than the exception. Among other things, a new draft
                       would require device makers to offer security
                       updates and spare batteries, displays, cameras,
                       back covers, and other parts for at least five
                       years.


    * § Leftovers⠀➾


          o ⚓ Daniel Pocock ☛ Anzacs:_Lombard,_Arc-et-Senans_aviators_ceremony,
            3_September_2022⠀⇛


                 On 31 August 1944, a Stirling bomber LJ503 departed from
                 Tempsford airbase in Bedfordshire, described as the most
                 secret airfield of the second world war. The airmen
                 conducted missions for the Special Operations Executive
                 (SOE), known today as MI6, the stomping ground of James
                 Bond.


                 At about 3am on 1 September, the aircraft crashed into a
                 mountain in the German occupied region of France. The
                 crew of LJ503 was comprised of six Australians and two
                 Scots.


                 The mountain and crash site are in the municipal district
                 of Lombard. The airmen were buried in the cemetery of
                 Arc-et-Senans which is a larger town. This is a very
                 remote location. It is closer to Switzerland than to
                 Paris. It appears to be the only Anzac site in the Jura
                 mountains.


                 I previously wrote about using data science techniques to
                 find less well known Anzac sites and this was one of the
                 first sites that I found.


          o § Security⠀➾


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


                      # ⚓ IT World CA ☛ Cyber_Security_Today,_Sept._5,_2022_–
                        An_alert_to_energy_companies,_a_warning_to_Linux
                        administrators_and_more [Ed: Trying to attribute a
                        Windows epidemic to "Linux"... somehow]⠀⇛


                # § Privacy/Surveillance⠀➾


                      # ⚓ HRW ☛ China:_New_Evidence_of_Mass_DNA_Collection_in
                        Tibet_|_Human_Rights_Watch⠀⇛


                             (New York) – Chinese authorities are
                             significantly increasing policing, including
                             arbitrary collection of DNA from residents in
                             many towns and villages throughout the Tibet
                             Autonomous Region (TAR), Human Rights Watch
                             said today.


                             The available information indicates that
                             people cannot decline providing their DNA and
                             that police do not need credible evidence of
                             any criminal conduct. A report from Lhasa
                             municipality in April 2022 stated that blood
                             samples for DNA collection were being
                             systematically collected from children at
                             kindergartens and from other local residents.
                             A report from a Tibetan township in Qinghai
                             province in December 2020 stated that DNA was
                             being collected from all boys aged 5 and
                             above.


                             “The Chinese government is already subjecting
                             Tibetans to pervasive repression,” said
                             Sophie Richardson, China director at Human
                             Rights Watch. “Now the authorities are
                             literally taking blood without consent to
                             strengthen their surveillance capabilities.”


                      # ⚓ ANSPDCP_(Romania)_–_Asociația_de_Proprietari_Aviației
                        Park_–_GDPRhub⠀⇛


                             The Romanian DPA found that the controller -
                             has excessively processed the personal data
                             (first name, surname, ID series and number,
                             destination, time of arrival, time of
                             departure, comments) of the deliverers and/or
                             couriers as data subjects, without a legal
                             basis justified in relation to the purpose of
                             the processing (access control in the
                             residential complex) and without presenting
                             evidence that it ensures the correct and
                             complete information of the data subjects, as
                             well as that the processed data are adequate,
                             relevant and limited to what is necessary in
                             relation to the purpose of the processing; -
                             did not establish a storage period for the
                             personal data processed through the video
                             surveillance system (images) and stored them
                             for a period longer than that necessary to
                             fulfill the purpose for which they are
                             processed, i.e. controlling access to the
                             condominium.


                             In addition, the DPA ordered the controller
                             to: – Reviewing and updating the technical
                             and organizational measures implemented as a
                             result of the risk assessment for the rights
                             and freedoms of individuals, including the
                             procedures related to the protection of
                             personal data and the establishment of
                             deadlines for the retention of data in a form
                             that allows the identification of the data
                             subjects for a period that does not exceed
                             the period necessary to fulfill the purposes
                             for which the data are processed. –
                             Evaluation of the processing carried out
                             taking into account the principle of
                             proportionality and the reduction of data to
                             a minimum relative to the purpose and legal
                             basis of the processing and the
                             implementation of the necessary measures in
                             order to comply with the principles related
                             to the processing of personal data.


                      # ⚓ Reason ☛ Glenn_Greenwald_on_the_Deep_State,
                        Capitalism,_and_Identity_Politics⠀⇛


                             I think it’s mostly the latter. The main
                             reason Edward Snowden has said that he was
                             drawn to me wasn’t so much because of my
                             views about privacy and surveillance,
                             although those aligned with his. But he saw
                             that I looked at journalism in a radically
                             different way than most of the media.


                      # ⚓ US News And World Report ☛ Tech_Tool_Offers_Police
                        ‘Mass_Surveillance_on_a_Budget’⠀⇛


                             Local law enforcement agencies from suburban
                             Southern California to rural North Carolina
                             have been using an obscure cellphone tracking
                             tool, at times without search warrants, that
                             gives them the power to follow people’s
                             movements months back in time, according to
                             public records and internal emails obtained
                             by The Associated Press.


          o § Defence/Aggression⠀➾


                # ⚓ Deutsche Welle ☛ US_greenlights_$1.1_billion_arms_deal_with
                  Taiwan⠀⇛


                       A potential deal to supply weapons to Taiwan has
                       been approved by the US State Department. It
                       includes the sale of anti-ship and air-to-air
                       missiles as well as a radar surveillance system.


                # ⚓ teleSUR ☛ Russia_Halts_Drone_Attack_on_Zaporizhzhia_Plant
                  [Ed: Is Venezuela a mouthpiece for Putin?]⠀⇛


                       Authorities of Enerhodar City denounced constant
                       Ukrainian attacks on the Zaporizhzhia facilities
                       and power lines since Saturday morning.


                # ⚓ New York Times ☛ Iran_Seizes,_Then_Releases_Two_U.S.
                  Drones,_Officials_Say⠀⇛


                       Iran seized two American maritime drones operating
                       in the Red Sea on Thursday, three U.S. defense
                       officials said, the latest naval incident in a
                       string of late-summer spats between Washington and
                       Tehran.


                       The crew of the Iranian naval ship that captured
                       the drones, Saildrone Explorers that were operating
                       near each other, hoisted the vessels onto their
                       warship, the Jamaran, and covered them with tarp,
                       one official said.


                       On request from the U.S. Navy, the Iranian crew
                       released the drones Friday morning, the officials
                       said.


                # ⚓ CNN ☛ Iranian_Navy_seized_2_US_Navy_maritime_drones_on
                  Thursday⠀⇛


                       The drones were eventually released, but a US
                       defense official says the incident looks like an
                       escalation of Iranian hostile actions against the
                       United States.


                # ⚓ Atlantic Council ☛ How_Turkey_can_play_a_more_constructive
                  role_in_Russia’s_war_on_Ukraine⠀⇛


                       During the early days of the Kremlin’s war against
                       Ukraine, Turkey earned well-deserved praise from
                       both Kyiv and its Western allies for supporting
                       Ukrainian sovereignty and territorial integrity,
                       providing armed drones, and closing the Turkish
                       Straits for Russian warships. More recently, its
                       diplomatic efforts to ease the Black Sea grain
                       blockade have also been welcomed.


                # ⚓ Reason ☛ Whitmer_Kidnapping_Plot_Just_One_Example_of_FBI
                  Entrapment⠀⇛


                       Here’s a tip: If you have some radical political
                       views and an acquaintance reaches out, encourages
                       you to act on your convictions, and maybe offers to
                       introduce you to a guy who can sell you some bomb
                       parts, don’t take him up on it. That guy’s almost
                       definitely working for the feds.


          o § Finance⠀➾


                # ⚓ Vitalik_Buterin_Thinks_Crypto_Could_Be_the_Linux_of_Finance
                  by_2040 [Ed: Just using the brand “Linux” to legitimise a
                  fake “coin” in a site that advertises casinos (among others).
                  And by 2040 nobody will have heard of Vitalik Buterin; it’s
                  like old politicians promising climate goals/targets by some
                  distant year when they’re already long dead]⠀⇛


                       With the merge fast approaching this September, the
                       debate of Proof of Work versus Proof of Stake has
                       never been stronger, and Vitalik has shared some
                       thoughts on where crypto is going, as well as the
                       potential limitations of Bitcoin’s current
                       consensus model.


          o § Censorship/Free Speech⠀➾


                # ⚓ New York Times ☛ China_Imposes_More_Covid_Lockdowns,
                  Stoking_Anxiety_–_The_New_York_Times⠀⇛


                       In the hours before the southern Chinese city of
                       Chengdu entered a coronavirus lockdown, Matthew
                       Chen visited four vegetable markets in an attempt
                       to stock up on fresh food. But seemingly the entire
                       city had the same idea, and by the time he got to
                       each place, most of the shelves had been stripped
                       bare, except for hot peppers and fruit, he said.


                       Mr. Chen, a white-collar worker in his 30s, managed
                       to scavenge enough cherry tomatoes, meat and greens
                       for about one day, and since then has been ordering
                       grocery deliveries to tide him through the
                       lockdown, which began on Friday. But he worries
                       about whether that supply will remain stable, and
                       how much longer he will have to rely on it.


                # ⚓ Quartz ☛ China’s_internet_censors_outwitted_by_Weibo_posts
                  in_Cantonese_—_Quartz⠀⇛


                       Thanks to Beijing’s sprawling internet censorship
                       apparatus, content critical of the Chinese
                       government rarely survives on the internet for
                       long. As a result, users have become adept at using
                       code like “Martian” language, emojis, and braille
                       to evade censors.


                       Sometimes, however, even everyday language is
                       enough to confound online censorship mechanisms.


                # ⚓ New York Times ☛ Opinion_|_Student_Journalists_Reveal_a
                  Changing_World._Let_Them._–_The_New_York_Times⠀⇛


                       It wasn’t exactly news when a principal in Nebraska
                       censored a high school newspaper, canceled the
                       school’s journalism program and abruptly disbanded
                       its student newspaper. I mean, it’s news news, but
                       it’s not surprising news. Red state bureaucrats and
                       politicians have been at war with the First
                       Amendment for a while now.


                       Even school officials’ reason for shutting down The
                       Viking Saga, the award-winning 54-year-old student
                       paper at Northwest High School in Grand Island,
                       Neb., wasn’t exactly a shock. When the school
                       principal announced a new edict requiring student
                       journalists, including at least three transgender
                       staff members, to use bylines that match their
                       legal names, the Saga staff members responded in
                       its June issue with two opinion pieces on
                       L.G.B.T.Q. issues and an article explaining the
                       history of homophobia and the origins of Pride
                       Month.


                # ⚓ New Yorker ☛ The_Censorship_Machine_Erasing_China’s
                  Feminist_Movement_|_The_New_Yorker⠀⇛


                       This summer, a viral video of a group of women
                       being viciously attacked in a restaurant sparked
                       national outrage. The response has been quashed.


                # ⚓ Hong Kong Free Press ☛ China_prosecutes_28_suspects_after
                  attack_on_women_in_restaurant⠀⇛


                       Chinese prosecutors said Monday they had launched
                       criminal proceedings against 28 people suspected of
                       assaulting a group of women in a viral incident
                       that sparked outrage over gender-based violence in
                       the country.


                # ⚓ US News And World Report ☛ U.S._Concerned_About_Judicial
                  Harassment_After_Turkish_Pop_Star’s_Arrest⠀⇛


                       The United States said it remained concerned about
                       Turkey’s censorship of free speech, and women’s
                       groups protested in Istanbul on Saturday, after the
                       arrest of pop star Gulsen over a past quip she made
                       about religious schools.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Rubik’s_Cube_to_the_Rescue⠀⇛


                       For medical reasons I had to spend the latter half
                       of yesterday and the first half of today in a very
                       idle manner. No need to expand on that except to
                       say that it was planned and all is fine.


                       Two days ago I was talked into buying a Rubik’s
                       cube. I’ve had one before but never been motivated
                       to learn it, but now it was one of few things that
                       I could do with my time.


                       It took me two hours to solve it the first time,
                       following a thorough tutorial on youtube. Every
                       time I missed a step or messed something up I
                       started from the beginning. Subsequently I was
                       already very good at the first two steps after
                       solving it just that one time.


                # ⚓ Comdex’90⠀⇛


                       James is noticeably upset. His hands are shaking,
                       his voice is cracking, and his grey toupee is
                       slightly askew, but I can’t really tell him that.
                       He takes another sip of his Donald Duck juicebox
                       and looks around.


                       There are 11 computers with dark screens, the
                       newest of the IBM PS/2 line, sitting on tables on
                       an otherwise empty stage. A couple of actors are
                       running lines off the side, and my partner is
                       sleeping in the first row of chairs.


                # ⚓ Bjork_Tier_List⠀⇛


                       I’ve just finished listening to the Homogenic
                       episode of Bjork’s new podcast series Sonic
                       Symbolism.[1] Each episode of the podcast is a
                       retrospective look at a Bjork album.


                       The series as a whole (so far) is a beautiful
                       examination the way art mirrors life, the way that
                       the spirit and time of the artist is woven into the
                       artwork.


                       Having studied lots of post-structuralist
                       philosophy, I have always been a bit too cynical
                       about the extent to which the artist informs the
                       meaning of their work. I’ve read too many pieces on
                       how the names ‘author’ and ‘artist’ are just
                       products of capitalist economics, and that it is
                       always dangerous to reduce the meaning of a work to
                       its author. ‘Damien Hirsh’ or ‘Stephen King’ are
                       just names or labels, like ‘Nike’ or ‘Chanel’.
                       Furthermore, focusing too much on the artists
                       themselves can result in overly-’psychologised’
                       explanations of a work, while a critical analysis
                       of the social structures and means of production
                       surrounding the work result in a more ‘progressive’
                       view.


          o § Technical⠀➾


                # § Internet/Gemini⠀➾


                      # ⚓ Sneakernets_and_other_networks⠀⇛


                             I have moved across the country! I’m totally
                             wiped out and still have much to do, so
                             please forgive a rambling post. Several
                             things have popped up and they feel related
                             and timely to me.


                # § Programming⠀➾


                      # ⚓ Mocking/stubbing_sys_environment_variables_in_Java
                        unit_testing⠀⇛


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


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