𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, September 03, 2022
┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅
Generated Sun 4 Sep 02:42:10 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕
Gemini index for the day: gemini://gemini.techrights.org/2022/09/03/


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

QmXt1BammAJUuBrf4QPcungjNg2ePnbbrjoTfCoibP7XTL
QmdDSQKaZJPnyDHFjeXTz7ZrVGb39ksdMdmtNhpx75EgdH
QmZ7mLY8uo6YvRrfUTtX3hPHDhQgDNyt4AB4fPvzYWrcC4
QmTZezLwd5vekievmKZscKgr1hkxvuHoSSsWhkA4iTy7Tu
QmNWKKu3gEEUM8UjAb868zLoy5CP9rUmyUWSSFH78F7ZGy
Qmc1hpdpKJMrmE55WT3tg3aQBqe3inuQhnbsjTc8RVVKFq
QmZNGE6NoRBC2J66AEvKbXxsP9j48e5nLCkLncW2SuYUD5
Qmd1qRcbFUvYnekMd31x6KbniK82hv6mEweUfvuLLLU3Dn
QmPGPjyuWmmi4WH1Pm1qxX7pzZhtRC3umeb4DmdE7NfXdU
QmbvCLhKBwB76DsbrKx6Pq16KSvtb9sW8UKVXj9v1pDgCv
QmcoFCaZUJmzby8Vb2wg8PBXe6VR8hW77edQo1u3NsCJ3Q
QmT4B1hoouASzbTAnEZbb6oYbbFnicQpd6JXDB5iwP9Y91
QmZeoDeQynAEb5Yhp8urADxooTvcjp93jYM7aoGTReoxAm
QmUR5BqkVtBjeM3RbDysVaCrQyP93xoRwDKU5C1u5XZdyR
QmS9E4XW4XZrtmFNP12pX65zisQkFTw7frAgGwhna5Fz9m
Qmdj75rdsbiWjm4ms8CTMfcbYno6Pw9hH66AytZ3Hs3qV7
QmWKkufDr5sMvj78wx9nn63R5KYSQipfAGMrMawgr7i6RW
QmVy1ihFnjMRS9u243rmwceZUtn8FwSqLsbXzXsLPS8M37
QmcZN6RDP7J7Dk8c2QYXeoVfYifxDsaK62EM44gSje2HDr
QmcvJBJvcdzE6YbN5kUFP3Cqgwc9K38gcNKU3B86eL6WLr
QmUZ8Zpgu5W6CLgXAAXnvYwpAw9fCGWhqWM6MWMHcNxEwP


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

⦿ Edward Snowden on Mass Surveillance in the Mobile Era | Techrights

⦿ IRC Proceedings: Friday, September 02, 2022 | Techrights

⦿ The Privacy Problem Associated With All Mobile Phones (Even ’Dumb’ Ones) is Worse Than Snowden Put It | Techrights

⦿ Jim Zemlin’s Salary More Than Doubled in Just 5 Years (From $500,000 to $1,150,000 in Six Years), Unlike Linus Torvalds’ | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2022/09/03/edward-snowden-2019/#comments
		http://techrights.org/2022/09/03/irc-log-020922/#comments
		http://techrights.org/2022/09/03/privacy-of-mobile-phones/#comments
		http://techrights.org/2022/09/03/zemlin-rewards-himself/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2022/09/03/arti-1-0-0/#comments
		http://techrights.org/2022/09/03/grep-3-8/#comments
		http://techrights.org/2022/09/03/kaidan/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 58

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/03/edward-snowden-2019/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/03/edward-snowden-2019/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Edward_Snowden_on_Mass_Surveillance_in_the_Mobile_Era⠀✐


Posted in Apple, Google, Videos at 3:33 am by Dr. Roy Schestowitz


Video_download_link | md5sum 3cd922855afa2541fdcb540e1a08653a
Snowden on Mobile
Credit: Edward_Snowden:_How_Your_Cell_Phone_Spies_on_You


http://techrights.org/videos/snowden-mobile.webm


Summary: This_2019_chat is worth reproducing here as WebM; it is still very
much relevant and explains that bulk surveillance has only gotten worse since
2013


If more people understood how “smart” phones work and what they actually do,
would they still pay for them?



                    ䷩ 𝚕𝚒𝚗𝚎 95

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/03/irc-log-020922/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/03/irc-log-020922/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Friday,_September_02,_2022⠀✐


Posted in IRC_Logs at 2:34 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-020922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-020922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-020922.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-020922.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
 QmetPsDzfWpiZddPSunXcFCWavzsHYvSKxPy5rAUW9Zicm #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmURXXkwwRfGfuhGW8qiBxRJcyhGTfgcpdZ4wBuRuKGBbs (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmcHMhhzMRMeTbFnSsEQb66P2NG8MMT5Br7vBHebvZSxjK social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell-
 QmWFp2JapSFAJTLXyqzeTcUDL6yRdG1F35X5JyJgfLUsaW social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 (full IRC log
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 QmXEKj8wihrxEKj25o9UtRwz7fAKYKR4Ewe1g3pxB371h3 #techbytes      🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techbytes
 QmXQeD3kBQhVr6tKaVbXLhnHE3hyGUyY3yBMFgrobtihWi (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
 Qmd4ZTZv5xzyq7fmqx3BAAwtQz1EMafo427WngZcavWoKS #techrights     🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #techrights
 QmVGN735kGhfsHeGWevnrSofBgnX295uRqBvQGAYttKj4H (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈


§ Bulletin for Yesterday⠀➾


Local_copy | CID (IPFS): QmUZ8Zpgu5W6CLgXAAXnvYwpAw9fCGWhqWM6MWMHcNxEwP



                    ䷩ 𝚕𝚒𝚗𝚎 222

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/03/privacy-of-mobile-phones/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/03/privacy-of-mobile-phones/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ The_Privacy_Problem_Associated_With_All_Mobile_Phones_(Even_‘Dumb’_Ones)_is
Worse_Than_Snowden_Put_It⠀✐


Posted in Deception, Videos at 10:52 am by Dr. Roy Schestowitz


Video_download_link | md5sum ffeb8228626c617dc460346bbdfcd48c
Worse Than Snowden Put It
Creative Commons Attribution-No Derivative Works 4.0


http://techrights.org/videos/mobile-phones-and-privacy.webm


Summary: Edward Snowden’s sensational impact turns 10 next year (in summer);
for some reason many people still think privacy and ownership [sic] of a mobile
phone aren’t inherently incompatible


THE fantasy of mobile phones that respect freedom is nothing short of fantasy.
They do a lot more harm, at the very least to privacy, than whatever “good”. As
long as they’re connected to a network (carrier), they’re beyond redemption and
it doesn’t matter what network carriers say. You simply cannot trust them.


The video goes through about half of this_old_video (about 3 years old). It’s
Snowden at the Rogan show. Snowden is far too polite; he’s trying not to
admonish or offend the many listeners/viewers the vast majority of whom have a
mobile phone, sometimes even a “smart” (a lot more sensors and signals) so-
called ‘phone’ — i.e. one in which benefits are asymmetrically in favour of
surveillance companies, not the person who bought the darn thing.


“Well, an encrypted device should not be carried around, certainly not while
connected to a network. Under the guise of “Librem” or “Purism” or “Freedom
(Phone)” a lot of ambitious (or dishonest) people have pushed false
promises.”Quit listening to companies that claim to have resolved this issue;
it’s infeasible. I’ve given a thought to this issue for 2 decades already. It
cannot be done and hasn’t been doable for decades. Yesterday TechDirt published
“Encrypted_Phone_Provider_Calls_It_Quits_After_Failing_To_Persuade_Middlemen_To
Roll_Their_Own_Device_Management_Systems“; this is related to the topic, but
not quite the same. There are many aspects which imperil the prospects,
including physical access to the device, back doors in the baseband OS, and so
on. “Over the past few years,” it says, “international law enforcement has been
cracking down on encrypted device purveyors. We’re not just talking about
regular device encryption, which has been mainstream for several years now.
These would be specialized manufacturers that appear to cater to those seeking
more protection than the major providers offer — services that ensure almost no
communications/data originating from these phones can be obtained from third-
party services.”


Well, an encrypted device should not be carried around, certainly not while
connected to a network. Under the guise of “Librem” or “Purism” or “Freedom
(Phone)” a lot of ambitious (or dishonest) people have pushed false promises.
In the wake of Snowden’s NSA leaks several companies made proclamations and
announcements (e.g. Blackphone) and where are they now? There are ways to
communicate securely and anonymously. Mobile devices like “smart” phones aren’t
among the options. █



                    ䷩ 𝚕𝚒𝚗𝚎 298

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/03/zemlin-rewards-himself/#comments
    Gemini version at gemini://gemini.techrights.org/2022/09/03/zemlin-rewards-himself/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Jim_Zemlin’s_Salary_More_Than_Doubled_in_Just_5_Years_(From_$500,000_to
$1,150,000_in_Six_Years),_Unlike_Linus_Torvalds’⠀✐


Posted in Finance, Kernel at 4:05 pm by Dr. Roy Schestowitz


⚓  2014:⠀⇛


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Disclosures_of_the_Linux_Foundation_in_2014⦈_


         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Salaries_of_the_Linux_Foundation_in_2014⦈_


===============================================================================
⚓  2015:⠀⇛


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Disclosures_of_the_Linux_Foundation_in_2015⦈_


         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Salaries_of_the_Linux_Foundation_in_2015⦈_


===============================================================================
⚓  2016:⠀⇛


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Disclosures_of_the_Linux_Foundation_in_2016⦈_


         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Salaries_of_the_Linux_Foundation_in_2016⦈_


===============================================================================
⚓  2017:⠀⇛


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Disclosures_of_the_Linux_Foundation_in_2017⦈_


         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Salaries_of_the_Linux_Foundation_in_2017⦈_


===============================================================================
⚓  2018:⠀⇛


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Disclosures_of_the_Linux_Foundation_in_2018⦈_


         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Salaries_of_the_Linux_Foundation_in_2018⦈_


===============================================================================
⚓  2019:⠀⇛


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Disclosures_of_the_Linux_Foundation_in_2019⦈_


         🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Salaries_of_the_Linux_Foundation_in_2019⦈_


Summary: In_2019 Jim_Zemlin gave himself a salary of $1,150,000 (bonus
included) compared to $500,000 6 years earlier (before kicking the community
out of the Board and Directors and enlisting several board members who are
full-time Microsoft employees, instead); is the real goal of the Linux
Foundation mostly lining the pockets of executives who don’t even use Linux and
abuse_Linus (creator of Linux)?


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


⣿⠶⠀⠐⠂⠂⠒⠆⠲⠀⠀⠒⠒⠲⠒⠂⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⣿⣿⣿
⣿⣯⣼⣿⣯⣭⣥⣭⣥⣭⣭⣽⣭⣭⣯⣬⣥⣯⣯⣭⣭⣯⣦⣭⣽⣮⣭⣭⣥⣽⣯⣿⣭⣭⣭⣽⣭⣯⣽⣤⣭⣬⣘⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿
⣿⣯⣼⣿⡐⠒⡔⠒⠖⡴⠖⠗⠄⠐⡦⢼⠰⡧⠆⡶⠦⠒⢦⠖⢦⡗⠂⠖⠖⢤⠳⠴⡶⠻⡌⠃⠧⠔⠻⠬⢳⠳⠣⠠⠒⢠⠐⠠⢵⢦⠞⡇⠖⢳⡇⠘⢷⣯⣤⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣏⣏⣹⣉⣉⣉⣉⣿⣶⣯⣏⣉⣉⣯⣹⣉⣍⣉⣉⣿⣤⣟⣏⣩⣯⣉⣩⣉⣹⣇⣾⣩⣉⣉⣿⣉⣉⣉⣹⣹⣹⣩⣉⣍⣹⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣾⣿⠵⠶⡒⠒⡼⠒⢶⣶⠒⠆⢲⠓⠳⡖⣶⠒⠚⠓⠒⠓⢷⢪⡗⠖⠺⢶⠘⡖⡐⡗⠔⠶⢲⠳⠲⠒⡶⠒⡧⠶⡾⠚⣷⣴⣶⣴⣶⣶⣶⣾⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣹⣿⣉⣋⣻⣉⣻⣛⣛⣛⣟⣛⣙⣛⣛⣟⣋⣟⣛⣛⣙⣛⣻⣛⣛⣙⣻⣋⣍⣻⣛⣻⣛⣻⣋⣛⣟⣛⣛⣛⣛⣛⣉⣻⣛⣟⣛⣛⣋⣛⣻⣻⣛⣋⣻⣛⣋⣟⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣿⣶⣿⣶⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠬⠧⡯⠭⢼⠼⡴⠧⡵⢼⢽⢤⡿⢿⡿⡿⢿⡿⡿⣿⠿⢿⠿⣿⢿⢿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠭⠭⠭⠬⠭⠭⠭⠭⠭⠥⠬⠬⠭⠬⠭⠭⠭⠤⠭⠬⠥⠭⠭⠭⠬⠥⠭⠬⠭⠭⠭⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠍⠉⠉⠍⠉⠍⠉⠍⠩⠿⠿⠿⠿
⡇⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠩⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢩⣭⣭⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣭⣭⣭⣭⣭⣭⣭⡭⠭⢭⣭⣭⣭⢩⣭⣭⣭⠩⣩⣭⣭⣭⣽
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣋⣛⣚⣁⣏⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣛⣒⣚⣉⣿⣿⣿⣿⣹⣋⣛⣛⣻⣋⣲⣋⣹⣉⣛⣟⣿⣿⣿⣏⣛⣃⣀⣉⣉⣿⣿⣿⣏⣛⣑⣣⣘⣛⣻⣿⢸⣿⣹⣋⣂⣊⣛⣹⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠧⠤⠤⡇⠦⢾⣿⣿⡦⠤⡼⠤⡤⢤⠦⠘⡤⢤⠯⠠⡴⢤⣿⣧⣴⠠⠤⢤⠣⢼⣤⣿⣷⡧⠤⢤⠤⠠⠤⢤⣿⢸⣿⣤⡤⠤⠤⣧⣼⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢹⣉⣯⣉⣩⣹⣿⣿⣷⣉⣋⣻⣋⣉⣋⣉⣩⣉⣉⣉⣹⣿⣿⣿⣉⣉⣋⣋⣉⣉⣽⣿⣿⢉⣉⣏⣉⣉⣙⣉⣿⢸⣉⡋⣉⣉⣙⣉⣋⣽⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢄⠚⠲⠒⠢⠸⠟⣷⣰⠀⣶⡖⢲⣶⠀⡆⢀⡆⢰⠂⣶⠀⣾⣿⣶⡞⠘⠛⠑⣧⣾⣿⣿⣤⣶⠃⠂⢳⢴⣶⣿⢸⡟⠗⡦⠲⠓⠣⠟⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⠏⣉⡉⣹⡿⣿⣿⢸⠀⣿⡇⢸⣿⠀⡇⢹⡇⢨⠀⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣁⣹⣉⡉⣉⣹⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣶⣶⣷⣶⣦⣿⣿⢨⣀⣿⡇⢸⣿⣿⡇⢘⡇⣸⠂⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣦⣶⣶⣶⣶⣶⣾⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡧⢼⣿⣿⡇⢸⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⡇⢸⣿⣿⡇⣿⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡇⣿⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⡏⠉⣍⢍⣩⠭⣉⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡏⠉⠉⠉⠉⣉⣽⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⢨⣭⣭⣭⣽⣭⣭⣯⣿⣿⣾⣿⣿⣿⣿⣧⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼
⡇⣇⣀⣆⣠⣀⣆⣤⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣶⣶⣶⢶⣶⣶⣶⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢰⣶⣶⣶⣶⣶⣶⣶⣶⢾
⡇⡇⠀⠀⠠⠀⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠰⠶⠶⠶⠾⠶⠶⠶⠿⠿⠾⠿⠿⠿⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⢾
⡇⡧⠤⠧⠤⠦⠶⠤⠤⠼⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠸⠿⠿⠿⠿⠧⠼⠿⣿⣿⢻⣿⣿⣿⣿⡟⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻
⡇⡇⠀⡀⠘⠛⠛⡛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻
⡇⡗⢒⠛⢒⢒⠒⣒⣒⣒⣚⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⢘⣛⣛⣛⣻⣓⣚⣛⣿⣿⣹⣿⣿⣿⣿⣏⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣹
⡇⡏⠀⡄⠀⠀⠀⡉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡏⠍⠭⣍⡉⣭⣭⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⢨⣭⣭⣭⣽⣭⣭⣭⣿⣿⣼⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼
⡇⣇⣀⣖⣂⣀⣆⣀⣄⣀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢰⣶⣶⣶⣶⣶⣶⣶⣶⢾
⡇⡗⠒⠒⠖⠖⠶⠾⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠰⠶⠶⠶⠾⠶⠶⠷⠿⠿⠾⠿⠿⠿⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⢾
⡇⣯⣄⣯⣥⣬⣧⣭⣬⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⣼⣿⣾⣿⢿⣷⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿
⡇⡏⠍⣩⠩⡉⡿⡿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⡿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⡧⡦⡷⡶⣶⢾⢶⢶⢶⡶⣶⡿⡿⡿⢿⢿⢿⢿⢿⠿⡿⡿⡿⡿⣿⢸⢿⢿⣿⢿⡷⡾⡿⣿⣿⣻⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻
⡇⡇⠀⡐⢐⠀⠛⠛⠛⠛⠛⡛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻
⡇⡗⠓⠛⠛⠛⣛⣛⣛⣛⣛⣛⣚⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⢘⣛⣛⣛⣻⣛⣛⣛⣿⣿⣹⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣹
⡇⡇⠀⢠⡈⠄⠈⠍⠉⡍⠉⠉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡏⠉⠉⢉⠉⢭⣭⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⢨⣭⣭⣭⣭⣭⣭⣭⣿⣿⣼⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼
⡇⣇⣀⣰⣄⣀⣠⣂⣆⣀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣶⣶⣶⢶⣶⣶⣶⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢰⣶⣶⣶⣶⣶⣶⣶⣶⢾
⡇⡇⠀⠐⠠⠀⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠰⠶⠶⠶⠶⠶⠶⠶⠿⠿⠾⠿⠿⠿⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⢾
⡇⡧⠤⠼⠦⠤⠤⠼⠤⠼⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠸⠿⠿⠿⢿⠧⠼⠿⣿⣿⢻⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻
⡇⡇⠁⢉⣒⠀⢛⠛⢛⡛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⠛⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻
⡇⣗⣒⣞⣒⣒⣚⣲⣚⣒⣛⣛⣟⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⢸⣛⣛⣛⣲⣓⣚⣟⣿⣿⣻⣿⣿⣿⣿⣏⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣙⣋⣋⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣏⣹⣛⣹
⡇⡇⠠⢨⠀⠀⠨⠀⠀⠁⢀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡯⠯⠿⡯⡿⣿⣽⣽⣽⣿⣿⣯⣯⣿⣿⣿⣽⣽⣿⣯⣯⣿⣿⣯⣿⢸⣽⣽⣿⣽⣯⣯⣯⣿⣿⣽⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽
⡇⣧⣥⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣬⣭⣭⣥⣭⣭⣭⣭⣥⣭⣥⣭⣭⣭⣭⣥⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣌⠉⠉⡍⠉⠉⢩⠉⡍⢹
⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡇⡗⠀⠂⠃⠂⠘⣀⡃⣘⡀⢛⣛⡛⣛⠛⠛⣛⣛⣛⡛⠛⣛⣛⣛⣛⣛⠛⣛⡛⣛⣛⣛⠛⣛⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⢛⡛⡛⣛⣛⣛⢛⣛⣛⣛⣛⣛⢛⡛⡛⣛⣛⢛⣛⣛⣛⡛⣛⣛⣛⣛⣛⢛⣃⣃⣈⣃⣸
⡇⣇⣀⣀⣀⣀⣀⣿⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣾⣶⣦⣶⣶⣶⣶⣶⣾⣶⣴⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⠿⣿⣿⣿⡟⣿⣿⣿⡿⠿⣿⣿⣿⣿⣻⣿⣿⣿⠿⢿⣿⣿⣿⣻
⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢻⠒⠝⣛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢣⠒⠘⢻⣿⣿⣿⡟⡛⢻⠻⠛⣟⠑⡜⠛⡟⠻⠛⢻⣿⢸⣿⠻⠛⠴⡂⠟⠛⣿⡇⣿⡟⠟⠃⠊⠛⠛⣿⣿⣿⣿⠻⠛⠑⠙⠻⢻⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣍⢍⢏⠩⣿⣿⣏⣍⠭⢯⣩⡩⡏⣍⢏⣭⣙⡽⠩⣉⣹⢸⣏⣉⢍⣭⡉⢩⣉⣩⡇⣯⠍⠭⢉⣽⣉⣉⢩⣿⣏⢩⡽⣩⠹⣡⡩⣉⢩⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢒⣲⢚⠒⠒⣿⣿⣿⡗⡒⢲⢲⠓⡓⠒⠒⠒⡚⠒⠒⣶⣿⢸⣿⢛⠒⠓⠓⡒⠛⢻⡇⣿⢚⠒⠛⠒⠓⠒⠚⣿⣿⣶⣖⡒⠒⡒⠒⣶⣾⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠭⢯⠥⠭⠭⠿⢿⡆⢲⢰⣶⡶⣶⡖⢴⠀⢰⠀⠢⢰⢰⢒⢸⣇⣥⡽⣌⠬⡤⣥⣽⡇⣿⣦⡼⠼⢮⢬⣤⣽⣿⣿⣯⠍⢭⠭⠭⠽⢭⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢒⡒⣒⣶⣶⣾⡇⢹⢰⣿⡇⣿⡇⢸⠐⢺⠀⠐⢸⢸⢸⢸⣿⣿⣿⣿⣶⣷⣿⣿⡇⣿⣿⣷⣶⣾⣾⣿⣿⣿⣿⣛⢲⢚⡓⢒⡒⣚⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣬⣥⣬⣤⣾⣿⡇⢸⠰⣿⡇⣿⣿⣿⠀⢸⠀⠀⢸⢸⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢹⣿⡧⢿⣿⣿⠀⢸⢸⡇⢸⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣾⣿⣿⢰⣾⢸⡇⢸⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⢸⣿⢸⡇⢸⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⡯⠍⢩⠉⠉⢭⠉⠍⠍⠉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣭⣭⣭⡭⠭⢭⣭⣩⣭⣭⣍⣭⣭⣩⣭⢨⣭⢨⣥⣬⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡷⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⡇⡇⣁⢨⣀⣠⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⣭⣭⣭⣭⣉⣩⣭⣬⣭⣭⣭⣭⣭⣬⣭⢨⣭⢨⣭⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡏⠉⢋⠉⠉⣭⣽⣽⣭⣭⣭⣯⣭⣯⣭⣽⣭⣽⣭⣭⣯⣭⣯⣭⡿⣭⣽⣭⣭⣭⣭⣯⣽⢿⣷⣿⣿⣿⣿⢿⣿⢸⣿⢸⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼
⡇⣇⣀⣰⣤⣴⣆⣠⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣤⣴⣶⣶⡶⣶⣶⣶⣶⣶⣶⢰⣶⢰⣶⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⠆⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢾
⡇⡇⠀⠀⠠⠀⠲⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠾⠿⠷⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠆⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⢾
⡇⡧⠤⠼⠦⠤⠤⠬⠤⠤⠦⠤⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠷⠦⠴⠾⢿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⢸⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⠛⠻⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⠻⠛⢻
⡇⡇⠀⢀⠂⠀⠀⢀⠀⠘⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻
⡇⡗⢒⢚⠚⠒⠒⠚⠓⡚⠒⠒⡒⠚⢟⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣛⣛⣛⣛⣒⣒⣚⣻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣹⢸⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣉⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣏⣹⣉⣹
⡇⣧⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⣭⣬⣭⣭⣬⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽
⢸⣭⠉⠩⠉⠉⠍⡍⠩⡍⠩⠉⠩⠉⠭⠩⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⣭⣭⣥⣭⣭⣭⣭⣽⡇
⢸⣖⣰⣶⣲⣒⣶⣒⣖⣒⣒⣒⣖⣲⣲⣒⣲⣲⣲⣒⣒⢲⣒⣒⣒⣆⣒⣒⣖⣖⣲⣒⣖⣒⣲⣒⣲⣒⣖⣲⣒⣒⣒⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⡿⢿⣿⢿⠿⢿⠿⡿⣿⢿⣿⣿⢿⢿⠿⡿⢿⢿⢿⡿⠿⠿⣿⢿⣿⡿⣿⠿⣿⣿⢿⠿⢿⣿⢿⡿⡿⠿⣿⢿⠿⡿⠷⢷⢿⣿⡿⠿⢿⢿⠿⣿⠿⡿⠿⠿⢿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⣾⣿⢺⣖⣖⣚⣓⣛⣚⣚⣺⣒⣚⣒⣗⣚⣒⣲⣚⡒⣒⣗⣛⣳⣓⣒⣲⣛⣺⣚⣚⣖⣛⣖⣓⣓⣒⣓⣚⣺⣓⣓⣒⣚⣒⣖⣖⣚⣚⣖⣻⣒⣒⣟⡒⡛⣾⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣙⣛⣛⣛⣙⣏⣻⣿⣿⣿⣙⣛⣛⣛⣝⣟⣛⣛⣛⣻⣿⣛⣟⣟⣛⣟⣛⣛⣛⣻⣿⣹⣿⣉⣙⣻⣛⣿⣋⣻⣛⣻⣙⣟⣛⣙⣛⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣧⣼⣿⠤⠭⠽⢧⡭⠭⠧⢽⡭⠥⠭⠭⠼⢥⢭⡤⠽⠧⠭⠥⠵⢭⠽⢬⠭⠼⢬⠽⡽⠬⡭⡭⠯⢭⠯⠯⠥⡽⠬⡯⠭⡭⠭⠽⣽⣭⣭⣭⣭⣭⣯⣯⣭⣧⣭⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡟⢻⣿⠻⠶⡷⡟⠷⡿⠷⡾⣷⠟⢿⠿⠾⠿⠿⢷⠳⠻⠟⠿⡿⡾⠾⠾⠷⢾⢞⠒⢿⠷⢷⠶⢿⠾⠶⡿⠷⡷⠿⢷⠾⡷⡿⡾⠿⠿⠿⡿⠿⡿⡿⡿⠿⢻⢿⠿⢿⠿⠿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⠿⠿⠭⠽⠯⠭⠽⠭⠭⠽⠭⠭⠽⠽⠯⠯⠯⠽⠯⠯⠭⠽⠽⠯⠭⠭⠽⠽⠯⠿⠽⠽⠽⠯⠽⠿⠭⠯⠯⠭⠽⠭⠯⠭⠯⠝⠿⠭⠯⠽⠽⠯⠿⠭⠯⠟⠭⠯⠹⠝⠯⠭⠯⠽⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠐⠒⠂⠀⠃⠀⠃⠘⠛⠃
⢸⠖⠒⠒⡖⢒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀⣀⣰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀
⢸⠉⠉⠩⠉⠍⡍⠉⠉⣉⠙⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣶⣶⣶⣶⣶⣶⣾⣿⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣧⣬⣤⡄⠀
⢸⠭⠭⠭⠭⡭⠭⠭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⣉⣩⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⡅⠀
⢸⢟⠟⠻⠻⠟⠿⠻⠻⢟⠿⠻⠛⢟⣿⣻⣛⣟⣿⣻⣟⣟⣿⣻⣟⣿⣋⣭⣭⣭⣭⣭⣭⣽⣿⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣋⣍⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣏⣝⣉⡁⠀
⢸⠷⠷⢾⠷⠷⠶⢾⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡿⠟⠿⢿⣿⢸⣿⣿⣽⣿⣿⣿⣿⣹⣿⢸⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣒⡒⠚⣒⢒⢒⣚⢛⡛⢻⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣟⣉⣋⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣟⣙⣉⡁⠀
⢸⣚⣒⣒⣒⣒⣒⣒⣒⣒⣒⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⢛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀
⢸⠤⠤⠤⠤⠷⠶⠤⠬⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣛⣛⣛⣛⣒⣒⣺⣿⢸⣿⣿⣿⣿⣿⣿⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⡟⠻⠛⠃⠀
⢸⣦⣦⣴⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀
⢸⣿⣟⠛⠛⠛⡟⡛⠛⢿⢛⠛⡛⡟⠻⢻⣻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⢛⠛⠛⡛⠛⢛⠻⡟⠛⠛⠛⠛⠛⡛⠟⣛⠛⠛⠛⠛⠻⡟⠛⡛⡟⠛⠛⠛⠛⢛⠛⠛⢿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣕⣉⣉⣉⣉⣉⣉⣉⣉⣹⣅⣉⣉⣭⣉⣍⣍⣉⣻⣉⣉⣸⣈⣉⣍⣉⣉⣍⣈⣉⣍⣕⣉⢉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⡠⠅⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠤⠼⠿⢿⣿⢸⡿⡿⠿⠿⠿⡿⠧⡸⠿⡿⠿⠿⢿⣿⣿⡿⡿⠇⠤⠼⠿⢿⣿⣿⡿⠿⠇⠴⠿⡿⣿⡇⣿⡿⣿⠗⠄⠿⠿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣷⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣚⣓⣳⣒⣺⣿⢸⣷⣗⣒⣒⣗⣓⣒⣛⣒⣇⣒⣲⣾⣿⣟⣓⣓⣒⣒⣒⣘⣚⣿⣟⣛⣚⣒⣒⣒⣑⣛⡇⣿⣗⣟⣒⣒⣱⣂⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠧⡤⢼⣿⢸⣥⣤⣭⡼⠠⠤⢥⠼⠬⡤⣤⣼⣴⣿⣿⠿⠦⠤⠼⠤⠼⠿⣿⡿⠴⠤⠾⠤⠥⠤⠼⡇⡿⠿⠿⠤⠦⡼⠿⠿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣉⣉⣉⣋⣿⢸⣿⣿⣋⣉⣻⣚⣏⣚⣛⣉⣩⣿⣿⣿⣿⣍⣱⣋⣁⣉⣡⣙⣿⣿⣍⣼⣹⣜⣹⣉⣿⡇⣷⣿⣑⣋⣋⣙⣻⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡔⠴⠤⢴⣴⣼⢀⣰⢠⣶⡖⣶⡆⢰⠆⣴⠀⡆⢰⡆⣰⣿⣿⣧⣦⣤⣼⣿⣿⣿⣿⣿⣷⣤⣴⣽⣿⣿⡇⣿⠴⠤⡶⠄⠄⠶⣾⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣙⣹⣉⣹⣿⠀⢸⠰⣿⠀⣿⡇⢸⡆⣿⠀⡅⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣏⣉⣉⣍⣉⣉⣉⣙⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣘⣿⠢⣿⣿⣿⡄⣻⢀⡗⢺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢰⣿⡤⣿⣿⣿⡆⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣰⣿⡀⣿⣿⣿⣿⣿⢸⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣭⣿⣿⣿⣿⣿⢸⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⠉⢉⠍⠉⡍⠩⠍⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⣩⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⡅⠀
⢸⠿⢿⠿⠿⢿⠿⢿⠿⡿⠿⡿⠿⠿⢿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣏⣭⣭⣯⣭⣭⣭⣽⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣅⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣝⣭⡅⠀
⢸⠭⠭⢬⠭⡭⠥⠭⠬⢥⣭⣭⣥⣤⣬⣭⣬⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠉⠩⢩⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⡅⠀
⢸⠒⠒⢒⠒⡓⡒⠒⠒⠚⠻⣛⠛⠛⢛⡛⡛⠛⢛⡛⠛⠛⠛⣛⣛⣛⣛⣭⣭⣯⣽⣭⣭⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣋⣙⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣏⣛⣉⡁⠀
⢸⣒⣒⣓⣒⣒⣓⣒⣒⣛⣒⣓⣒⣒⣒⣚⣓⣒⣚⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⢛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀
⢸⠾⡷⢦⠷⠤⡦⢶⠶⡾⢿⢿⠿⡿⠿⠿⠿⡿⠿⢿⠿⡿⢿⠿⠿⠿⠿⣛⣛⣛⣛⣒⣒⣺⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⡟⡿⠛⡃⠀
⢸⠤⠤⠤⠥⠥⠤⠤⠤⠤⠧⠬⠤⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠻⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀
⢸⠤⡤⢤⠤⠤⡥⢤⠬⡿⢿⢿⠿⡿⠿⠿⠿⡿⠿⢿⠿⡿⢿⠿⠿⠿⠿⣿⣿⡿⣷⢶⡶⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠟⡟⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⠛⣿⠛⠇⠀
⢸⠭⠽⠭⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀
⢸⣉⣉⣉⣏⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠤⠤⢼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⡿⢿⠿⠇⠀
⢸⣀⣀⣐⣀⣂⣆⣀⣀⣤⣈⣂⣐⣐⣐⣀⣀⣀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣷⣶⣶⡆⠀
⢸⣒⣒⣶⣒⣲⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⣤⣴⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀
⢸⡉⠋⠙⠝⢏⠛⢙⠉⠋⣟⢝⡉⡋⢙⡙⣩⣯⣽⣽⣯⣯⣽⣽⣯⣯⣥⣶⣶⣶⣶⣶⣶⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣵⣦⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣧⣯⣤⡄⠀
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀
⠸⠿⠙⠛⠉⠛⠻⠩⠟⠉⠛⠟⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿
⢸⣽⣼⣿⣯⣽⣭⣽⣬⣭⣭⣯⣭⣽⣭⣭⣯⣯⣭⣭⣹⣥⣯⣭⣧⣭⣭⣧⣭⣭⣽⣭⣭⣽⣭⣯⣽⣭⣯⣭⣭⣽⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢻⢻⣿⠛⡛⡛⣻⠛⡟⢻⡛⠛⣛⠛⡟⣻⢛⠛⡛⠛⠛⢛⡟⢻⡛⢛⢻⡛⣟⣛⣛⡟⣛⠛⡟⢛⡟⠻⣛⣟⢟⠛⡛⠛⠛⡿⡟⢛⣻⢛⡛⣛⠛⣿⡟⢛⡛⠛⠻⠛⢻⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⠭⢭⣬⣭⣥⣭⣯⣥⣭⣽⠭⢭⣭⣬⣭⣧⣭⣬⣥⣽⣬⣭⡯⠭⣭⣭⣥⣽⣬⣭⣽⣭⣭⠭⢭⣽⣤⣭⣥⣯⣼⣼⣥⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢿⢿⣿⢮⣽⠧⢥⡾⢤⠤⢤⡼⡿⢬⢽⠥⠦⠴⠤⡦⠧⢤⡤⠦⣿⠧⢤⢧⠤⢤⠧⠤⢬⠤⠼⠿⡭⠼⠴⣬⢴⢤⢤⠬⢥⠿⡼⢤⠬⠥⠥⠼⣤⡿⠿⡿⢿⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣾⣾⣿⣒⣑⣶⣖⣓⣙⣒⣒⣲⣂⣞⣚⣚⣒⣚⣐⣗⣒⣚⣚⣲⣚⣗⣓⣞⣂⣚⣾⣐⣒⣒⣖⣚⣟⣒⣖⣓⣲⣶⣶⣶⣷⣷⣷⣶⣶⣷⣾⣶⣾⣶⣿⣶⣶⣾⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣬⣼⣿⠬⠭⠽⠭⢽⠭⢭⠭⠯⠭⢭⢭⠽⣭⠥⠯⠭⠭⡭⠭⠭⢭⠭⠭⠽⡥⠭⠭⠭⣭⠭⠽⡭⠭⡯⢭⠭⡭⢭⡽⡭⠽⢽⠩⡭⠭⠭⢭⡯⢯⠭⣭⠯⠭⠼⣭⣭⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠨⠭⠭⠭⠭⠬⠬⠭⠥⠤⠬⠬⠤⠤⠭⠬⠤⠭⠥⠥⠥⠭⠥⠥⠤⠬⠬⠤⠥⠥⠭⠥⠭⠭⠬⠥⠭⠭⠤⠬⠬⠤⠭⠬⠥⠭⠤⠭⠬⠬⠥⠭⠤⠬⠥⠬⠭⠥⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠉⠉⠩⠉⠉⠭⠩⠉⠉⠿
⠐⡒⠒⠲⠒⡒⢒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣀⣀⢰⣶⣶⣶⣶⣶⡆⣶⡆⣶⡆⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠈⠉⠉⠍⠩⢩⠉⠉⢉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣼⣿⣿⣿⡇⣧⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣧⣤⣥⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿
⠈⠭⠍⢩⠉⠉⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢉⢨⣭⣭⣭⣭⣭⡅⣭⡅⣭⡅⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⠨⠯⠽⡽⡽⣿⣯⣿⣽⣽⣭⣯⣯⣿⣽⣽⣭⣯⣯⣽⣽⣽⣯⣯⣯⣽⣿⣽⣭⣭⣭⣭⣭⢸⣿⣽⣿⣿⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠠⠭⠭⠬⠬⠭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⢨⣭⣭⣭⣭⣭⡅⣭⡅⣭⡅⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽
⠐⠒⠒⠚⠒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣹⣿⣿⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⢐⣒⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢘⣛⣛⣛⣛⣛⡃⣛⡃⣛⡃⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻
⢰⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣒⢸⣿⣻⣿⣿⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⢀⣀⣀⣐⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢘⣛⣛⣛⣛⣛⡃⣛⡃⣛⡃⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⠠⠤⠤⠬⠤⠤⠼⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣻⣻⣛⣟⣛⣒⢸⣿⢻⣿⣿⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠠⠥⠤⠦⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⢸⣏⢌⣩⣉⣇⣅⣉⡻⣌⢩⢹⣩⣁⣯⣇⣉⣉⣉⣉⣉⡉⣁⡉⣹⣉⣬⡨⣁⣉⡉⣉⣇⢁⣉⣉⣉⣩⣙⣨⣍⣉⣉⣉⣙⣏⣉⣩⡇⣉⣉⣈⣍⣉⣉⣻⣉⣈⢉⣉⣉⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣷⣥⣶⣤⣤⣤⣤⣤⠴⠼⠤⡀⢀⠦⠴⠤⣤⣵⣤⣤⣧⣤⣤⣤⣤⣤⡴⣄⡀⡠⢦⣴⢰⠴⢤⠤⣤⢿⠿⡉⠉⡿⠿⠿⡿⠿⠿⡇⣿⡿⠿⠏⡩⠹⠿⣿⣿⢸⣿⠿⠿⢉⠹⠿⢿⣿⡇⣿⣿⠿⢏⢩⣹⡿⣿⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢓⡒⡒⠒⢚⣿⢸⣶⣖⠒⢒⡖⡒⡗⣒⢲⠒⢒⠓⢲⣶⡇⣿⠓⡒⠒⡒⠒⢒⣛⣿⢸⡟⢒⡒⢒⠒⠒⣚⣻⡇⡟⣛⠒⡒⡒⣲⠒⡛⣻⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⠸⠤⠤⣿⢸⣿⠤⠤⡤⡏⠼⠤⠤⠇⠼⠤⠤⠤⣿⡇⣿⠿⠦⠤⠼⠤⠼⢿⣿⢸⡿⠤⠤⠧⠤⠤⠤⢿⡇⣿⣤⠴⠤⢤⠤⢬⣤⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⣍⣉⣁⣁⣿⢨⠍⡍⣡⣥⠥⡍⡍⠍⠈⡍⠩⠉⡅⡭⡅⣿⣉⣱⡎⠁⠈⣉⣿⣿⢸⣿⣅⣿⠙⠉⢉⣹⣿⡇⣉⣉⣩⡉⡉⣉⣹⣉⣹⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠐⠒⡖⠒⠒⠒⢸⠃⡇⣽⣿⢸⡇⡇⡆⠤⡇⠀⠄⡇⠀⡇⣿⣿⣿⣶⣶⣧⣿⣿⣿⢸⣿⣿⣷⣶⣾⣼⣿⣿⡇⣿⠛⠓⠒⠒⠒⠛⠛⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣺⣿⣿⢸⠄⡇⣽⣿⢸⡇⣷⡇⠀⡇⢐⠦⡇⣤⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣥⡇⣼⣿⣸⡇⣿⡇⠠⡇⣾⠁⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣽⣿⢰⡇⣿⡇⣦⡇⣿⠆⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⣿⣿⢰⡇⣿⡇⣿⡇⣿⠀⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠥⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸
⢨⣭⣭⣭⣽⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠶⠤⢸⣿⣿⣿⣿⣿⡇⡿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿
⠀⠵⠈⠯⠈⠭⠕⠹⠾⠾⠾⠷⠷⠿⠾⠾⠷⠷⠷⠿⠿⠾⠷⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠶⠾⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⠆⠿⠿⠿⠿⠿⠿⠾⠶⠶⢿
⢈⣉⣉⣉⣉⣭⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⡯⠬⠤⢸⣿⣿⣿⣿⣿⡇⡿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿
⢀⣀⣀⣄⣀⣄⣂⣰⣀⣀⣀⣐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣷⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿
⢐⣒⣒⡒⢲⠒⡒⡒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣠⣀⢰⣶⣶⣶⣶⣶⡆⣶⡆⣶⡆⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠈⢫⠉⡍⠉⠉⡉⠉⢩⡉⠉⠉⡉⠋⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⡇⣿⡇⣷⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣧⣤⣭⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿
⠘⠛⠛⠛⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣙⢸⣿⣿⣿⣼⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠨⢭⠩⡍⠍⠭⠉⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⡇⣯⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣧⣤⣧⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣴⣧⣤⣿
⠨⠭⠭⠭⠭⠭⠭⠭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠉⠉⢨⣭⣭⣭⣭⣭⡅⣭⡅⣭⡅⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽
⠐⠚⠒⠚⣒⣒⣒⣚⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⡇⣿⡇⣏⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣏⣉⣛⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣏⣋⣉⣋⣉⣿
⠐⡒⠒⢒⠛⣛⣛⠛⡛⡛⢛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢘⣛⣛⣛⣛⣛⡃⣛⡃⣛⡃⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⢐⣖⣲⣲⣒⣓⣖⣖⣒⣲⣒⣒⣟⣟⣛⣻⣛⣟⣟⣻⣻⣛⣛⣟⣟⣻⣿⣻⣻⣛⣟⣟⣛⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⣻⡇⣿⡇⣿⣿⣿⣿⣿⣟⣙⣏⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣙⢏⣛⣿
⢐⣒⣒⣓⣐⣒⣒⣒⣂⣚⣑⣂⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⢘⣛⣛⣛⣛⣛⡃⣛⡃⣛⡃⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻
⠠⠤⠤⠬⠤⠤⠤⠴⠦⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣛⣛⣛⣓⣒⣒⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⢻⡇⣿⡇⣿⣿⣿⣿⣿⡟⠛⠟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⠟⠛⣿
⠠⠼⠤⠧⠤⠤⠥⠤⠼⠤⠬⠴⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⢨⣭⣤⣭⣭⣭⣵⣭⣭⣭⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠶⠤⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⢿⡇⣿⡇⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿
⠨⠉⠉⠭⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠷⠾⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠾⠿⢿
⢈⣋⣉⣹⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠯⠭⠤⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⢿⡇⣿⡇⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿
⢀⣀⣀⣂⣐⣰⣀⣀⣠⣀⣰⣀⣂⣂⣆⣀⣀⣀⣠⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⣾⡇⣿⡇⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿
⢐⣒⣒⢖⢲⣒⠖⣒⢒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⣀⢰⣶⣶⣶⣶⣶⡆⣶⡆⣶⡆⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠈⠉⠉⠍⠉⢩⠉⠉⢉⠉⢩⠉⡉⠋⠉⡩⠉⡉⣭⣭⣭⣭⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⣾⡇⣿⡇⣿⣿⣿⣿⣿⣧⣤⣵⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠾⠿⠷⠿⠷⠿⠷⠿⠿⠷⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠸⠿⠙⠛⠉⠛⠻⠹⠏⠉⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⡇
⢸⣼⣼⣿⣯⣽⣭⣽⣬⣭⣭⣯⣭⣿⣭⣭⣭⣭⣭⣭⣽⣵⣭⣭⣧⣭⣭⣯⣤⣯⣭⣭⣭⣭⣭⣭⣧⣭⣬⣭⣭⣿⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢛⣻⣿⣛⣛⣛⣻⣛⣛⣛⣛⢻⣛⣛⣟⣻⣛⢛⣛⢛⣛⣛⣟⣻⣛⣛⣻⣛⣟⣛⣛⣿⣻⣟⣟⣻⣛⡛⣻⣻⡛⣛⣛⣛⣛⢻⣛⣻⢿⣛⣻⣛⣛⣟⣿⣻⣛⡻⢻⣟⣟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢬⢬⣥⣭⣧⣤⣧⣥⣬⣭⢦⢬⣥⣥⣼⣧⣦⣥⣤⣼⣦⣭⡯⡬⣷⣦⣬⣧⣬⣭⣽⣭⡬⣤⣥⣿⣤⣭⣭⣯⣼⣬⣤⣭⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⢿⣿⡮⠼⠶⠶⡶⢶⠶⠶⠼⠿⠬⢼⠶⠶⠶⠴⣷⠶⢦⢶⠦⣿⠧⠴⠧⠴⠶⠷⠤⠶⠶⠿⠷⠭⠷⠶⡶⢾⠥⠦⠦⠶⠷⡷⠶⡦⠴⠶⢷⡾⠿⠿⠿⡿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣉⣉⣙⣏⣙⣉⣉⣩⣉⣉⣉⣉⣉⣍⣏⣙⣹⣍⣉⣉⣹⣈⣏⣋⣏⣋⣙⣇⣋⣍⣋⣩⣻⣉⣹⣛⣋⣽⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣤⣼⣿⠤⠀⠘⠬⠘⢠⢰⢨⠇⠄⣭⢩⡝⣀⡁⠂⠀⠠⡅⢢⡷⢩⠠⢅⡚⡕⢴⡘⢨⡭⠍⢸⠁⠍⠩⡀⠠⣄⡭⡅⡌⢧⡭⠉⠮⠉⣥⠈⢸⣄⣭⠡⠉⠤⢳⣤⣬⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠛⠛⠏⠋⠹⠉⠙⠋⠹⠇
⢨⠭⠭⡭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⠉⣭⣭⣭⡅⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⠀
⢸⠓⠒⢓⠓⠒⠒⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢸⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⡇⣿⣿⢸⣹⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣋⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⠀
⢸⠾⠶⢾⠶⠶⡶⢶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⢻⠟⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⢖⠒⠚⠒⠲⢒⠚⡛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢸⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⡇⣿⣿⢸⣹⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣏⣉⣋⣉⣿⠀
⢸⣒⣒⣒⣓⣒⣒⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⣶⣶⣶⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣛⣛⣛⣛⣚⣳⣿⣿⣿⡇⣿⣿⢸⣻⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣛⢟⣛⣿⠀
⢸⠚⠒⢒⠚⢒⠒⡒⣒⣒⣚⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⢛⣛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⠒⠒⠚⢒⡒⠒⡒⠒⡛⠛⠛⢛⠛⠛⢛⠛⢛⣛⣛⣛⣛⣛⣛⣛⢸⣿⣿⣟⣿⣗⣾⣶⣿⣿⣿⡇⣿⣿⢸⣿⢸⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⠟⠛⣿⠀
⠸⠀⠂⠀⠀⠑⠄⠐⠲⠷⠾⠷⠶⠶⠶⠾⠶⠶⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀
⢸⣋⣉⣹⣍⣭⣍⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠿⠿⠧⠼⢤⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⠀
⢸⣄⣒⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⠀
⢸⣉⣉⣹⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⡿⡿⡧⢼⢥⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿⠀
⢸⣂⣆⣀⣀⣀⣀⣄⣀⣰⣀⣂⣀⣀⣀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⠀
⢸⣒⣒⣲⣒⣒⣒⣒⣒⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣦⣰⣤⣶⣶⣶⡆⣶⣶⢰⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀
⢸⣛⣛⣛⣟⣛⣛⣛⣻⣛⡻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣵⣶⣿⠀
⠸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠀
⢰⡒⢒⠒⡖⡂⠒⠖⡒⢒⢒⠒⠖⣒⡢⠒⠒⢒⠒⠒⠒⠒⠒⡖⠂⡂⡒⠒⠒⠒⢲⠒⢒⢒⠒⠒⡒⠖⠒⠒⠒⠒⠒⡖⠒⠒⡖⠒⠒⠒⠒⠒⠒⢲⠒⠒⠒⠒⠒⡆⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⠒⠒⠒⢶⣶⠀
⢸⣉⣍⣇⣍⣩⣉⣍⣍⣩⣩⣭⣕⣩⣥⣩⣉⣬⣭⣹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡬⠤⢛⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠷⠤⠿⢿⣿⡟⠿⠟⠿⢿⠟⢧⠤⢸⠿⠿⢻⠿⠿⢿⣿⣿⠻⠿⠦⠼⠟⢿⣿⢸⣿⡟⠿⠤⠠⠻⠿⣿⡇⣿⣿⠻⠣⠴⠼⠟⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣍⡩⣹⢈⢹⣿⣿⡿⣏⢍⣽⡩⡭⠩⢍⠏⡍⠍⢩⣿⣿⣿⣭⡩⠉⢉⠉⣍⣉⣿⢸⣏⢩⡁⣍⠍⠉⠉⣽⡇⣏⠭⠉⢍⣏⠽⢉⣍⣽⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣒⢲⣚⣓⣺⣿⣿⣷⣒⣲⣲⣒⣓⣒⡛⣒⣓⣚⣒⣺⣿⣿⣟⣓⣓⣒⣒⣒⣻⣿⢸⣟⣒⢒⣒⣒⣒⣒⣻⡇⣿⣶⣒⣒⣲⣒⣲⣶⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠧⠤⠧⠤⠠⠤⢿⣶⣰⠀⡆⡖⣲⢰⠐⠀⢴⠀⠆⢰⡦⢰⣿⣧⣤⠛⠐⢀⣴⣼⣿⢸⣿⣦⡞⠀⠚⣠⣴⣿⡇⣥⣦⡴⠄⠄⠤⣬⣤⣼⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣉⣈⢉⣏⢉⣉⣹⣿⢸⠀⡇⡏⣹⢸⢸⠐⢺⠀⡄⢸⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣉⣉⣉⣉⣉⣩⣩⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⣶⣾⣿⣿⣿⢸⣀⡇⡇⣾⢸⣿⠀⢸⢀⡗⢺⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⡧⢽⢸⣿⠈⢺⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡇⡇⣿⢸⣿⢸⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⣿⢸⣿⢸⣿⢸⡗⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢨⠭⠭⢭⠭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⠉⣭⣭⣭⡅⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⠀
⢸⠟⡛⠒⠒⢲⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⢸⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⡇⣿⣿⢸⣿⢸⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣉⣛⣉⣿⠀
⢸⠶⠷⣶⢿⢾⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⢻⠛⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⠒⡒⠒⡒⠒⠒⡒⢛⠛⢛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⢸⣿⣭⣯⣯⣭⣭⣽⣿⣿⣿⡇⣿⣿⢸⣿⢸⣹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⠀
⢸⣒⣓⣒⣒⣒⣒⣓⣚⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⣷⣶⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣛⣛⣛⣛⣚⣳⣿⣿⣿⡇⣿⣿⢸⣿⢸⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣛⢟⣛⣿⠀
⢘⣒⣒⣒⣚⣓⣒⣒⣒⣊⣒⣒⣒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⠤⠤⠤⠧⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣛⣛⣛⣓⣚⣲⣿⣿⣿⡇⣿⣿⢸⣿⢸⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⠿⠛⣿⠀
⢸⣤⣤⣤⣶⣤⣤⣤⣤⣦⣬⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⡤⠤⠤⠧⢤⠤⠬⠿⡿⡿⠿⠿⢿⠿⠿⠿⡿⡿⠿⠿⢿⠿⠿⠿⢸⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⡟⠛⣿⠀
⠸⠤⠬⠥⠬⠧⠤⠭⠤⠼⠭⠤⠤⠥⠤⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀
⢸⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠿⠿⠧⠼⢤⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿⠀
⢸⠩⠯⠝⠩⠝⠽⠍⠉⠩⠭⠍⠽⠨⠬⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠾⠾⠿⣿⠀
⢸⣉⣉⣉⣩⣏⣉⣉⣽⣏⣉⣍⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠿⠿⠧⠼⢤⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿⠀
⢸⣄⣒⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⠀
⢸⣆⣂⣒⣂⣀⣐⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣦⣴⣤⣶⣶⣶⡆⣶⣶⢰⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⠆⣶⣶⣶⣶⣶⣶⠶⡶⠶⣿⠀
⢸⣃⣦⣔⣒⣊⣒⣒⣔⣓⣱⣶⣶⣾⣶⣶⣶⣷⣷⣶⣶⣾⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣷⣶⣿⠀
⢸⡒⠒⡒⢲⡒⣒⣒⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣀⣶⣶⣶⡆⣶⣶⢰⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀
⢸⢋⠋⢉⣙⡙⠉⠉⡉⡋⠫⡉⠍⠝⡉⢉⠉⠋⣋⣯⣭⣽⣽⣽⣭⢸⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣥⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿⠀
⢸⣲⠲⢒⠒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣂⣶⣶⣶⡆⣶⣶⢰⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀
⢸⠍⡍⠉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢸⣿⣶⣷⣷⣶⣶⣾⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣥⣬⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿⠀
⠸⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠭⠭⠬⠭⠬⠭⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠬⠭⠭⠭⠭⠭⠭⠭⠭⠥⠭⠭⠭⠭⠭⠭⠭⠭⠭⠿⠀
⢰⠒⢖⠒⡖⠒⠒⠖⠒⢖⢒⠒⠒⣶⠒⠲⠒⠲⠒⠒⠒⠲⠒⡖⠒⡖⠒⠒⠒⠒⢶⠒⢒⠲⠒⠒⡒⠖⠒⠒⠒⠒⠒⡖⠒⠒⡖⠒⠒⠒⠲⠒⠒⢶⠒⠒⠒⠲⠒⡖⠒⠒⠒⠒⠒⠒⠒⠖⡖⠒⠒⠒⠶⠲⠒⢶⣶⠀
⢸⣉⣉⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣈⣩⣹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡬⠄⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠗⠔⠿⢿⣿⡿⠿⠿⠿⢿⠿⢧⠤⢸⠿⠿⢿⠿⠿⢿⣿⣿⠿⠿⠦⠺⠿⢿⣿⢸⣿⡿⠿⠥⠄⠿⠿⣿⡇⣿⣿⠿⠇⠴⠽⠿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣷⣾⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣀⣐⣱⢈⣹⣿⣿⣾⣇⣋⣽⣁⣚⣑⣚⣎⣂⠛⣛⣶⣾⣿⣛⡨⣂⣈⡐⣘⣈⣿⢸⣏⢙⣀⣃⣅⣀⣊⣹⡇⣏⣉⣐⣈⣇⣸⣀⣉⣹⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠒⢲⡚⠓⢺⣿⣿⣧⢒⢲⢲⠂⡓⠐⠚⡒⠓⠒⠒⢺⣿⣿⡟⠓⠒⠒⠒⠒⢻⣿⢸⡟⠒⠒⡒⠒⠒⠐⢻⡇⣿⣤⡒⠐⢲⠒⢲⣶⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠧⠭⠯⠭⠭⠥⢿⣿⢹⠛⡏⡿⢿⢹⠝⠹⢹⠉⠯⢹⡟⢻⣿⣇⣬⠽⠤⢤⣬⣬⣿⢸⣿⣢⡼⠬⠾⢤⣬⣿⡇⣭⣍⡭⠭⠭⠭⣭⣭⣽⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣘⣀⣒⣆⣀⣚⣸⣿⢸⠀⡇⡇⢿⢸⢰⠐⢺⠀⠑⢸⡇⣹⣿⣿⣿⣾⣶⣶⣿⣿⣿⢸⣿⣿⣿⣶⣶⣾⣿⣿⡇⣿⣉⣑⣂⣒⣂⣉⣛⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⣶⣼⣿⣿⣿⢺⠀⡇⡇⣿⢸⣿⠀⢸⠀⣇⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⠠⡇⡧⢿⢸⣿⠈⢺⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡇⡇⢿⢸⣿⢸⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⣿⢸⣿⢸⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⠿⠿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⢻⠿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣒⣒⠒⠓⣒⠒⢒⠛⢛⣛⠛⡛⠛⡛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢸⣿⣯⣯⣯⣯⣽⣽⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣏⣟⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣉⣏⣉⣿⠀
⢘⣒⣒⣒⣒⣚⣓⣒⣒⣒⣚⣒⣒⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⣶⣶⣾⣷⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣛⣛⣛⣛⣚⣳⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣛⢟⣛⣿⠀
⢸⣑⣂⣛⣃⣒⣒⣒⣒⣐⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⠤⠴⠧⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣛⣛⣛⣓⣚⣲⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⠟⠛⣿⠀
⢸⣤⣤⣤⣶⣤⣤⣤⣤⣦⣬⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣸⣿⣸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢰⠶⠀⠀⠀⠀⠐⠀⠲⠠⠀⠀⠀⠐⠠⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾
⢸⣮⣼⣿⣬⣽⣤⣽⣬⣭⣭⣽⣭⣬⣯⣬⣤⣧⣧⣬⣿⣭⣧⣮⣥⣮⣧⣵⣦⣼⣽⣭⣭⣭⣭⣤⣽⣬⣥⣬⣥⣼⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣹⣿⣙⣻⣛⣻⣛⣏⣻⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣛⣟⣻⣝⣛⣻⣋⣹⣹⣛⣟⣋⣙⣟⣛⣝⣓⣂⣒⣒⣲⣶⣀⣒⣖⣒⣰⣀⣰⣤⣢⣂⣀⣂⣀⣔⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⢸⣿⣿⣿⣴⣦⡽⣴⣶⣦⣴⣴⣶⣧⣶⣴⣼⣶⣦⣤⣴⣶⣿⣶⣴⣶⣶⡷⢴⣶⣶⣽⣶⣤⣼⣴⣴⢶⣶⡦⣦⣴⣼⣯⣶⣶⣾⣼⣷⣦⣼⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢻⣿⠻⠿⡿⠶⢾⢶⠶⠶⠶⠿⢿⠿⠷⠶⠶⠶⡶⠷⠶⡶⡶⢾⠿⠶⣾⠧⢶⠾⠶⠶⡶⢾⠿⠾⠿⠾⢶⠶⡯⠶⠴⡶⠾⢶⠷⠷⠶⠶⠶⢶⠾⠿⠻⣿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣩⣭⣍⣏⣭⣹⣭⣩⣍⣏⣏⣉⣉⣭⣩⣍⣏⣽⣭⣉⣍⣯⣭⣭⣍⣍⣉⣽⣨⣩⣍⣩⣭⣭⣩⣏⣭⣩⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣥⣼⣿⠠⢀⠘⠰⠼⠌⢱⠧⠃⢥⢰⣤⢬⠃⠂⠃⠀⠀⠌⠁⠸⡂⡔⠌⡐⢡⠣⣂⠃⣤⠨⠁⡇⠨⠈⢀⠀⢄⣨⢍⢠⠹⣭⠀⣴⠀⢠⠩⣬⠣⣍⠀⠜⢄⠁⣤⣭⣵⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠛⠛⠏⠙⠹⠏⠹⠋⠻
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠠⡦⠀⠀⠀⣶⢠⢀⡄⣤⡤⢤⣤⠀⣤⢀⡄⢠⠀⣤⠀⢰⣶⣂⡴⠂⠖⢀⣠⣶⡆⣶⣶⣤⠖⠰⠆⣀⣴⣶⢠⣠⣀⠄⠀⠀⢠⣆⣄⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣐⣒⣖⣒⣒⣲⢸⢉⡇⣿⡇⢸⣿⠀⣯⢸⡏⢰⢨⣿⢸⢸⣿⣿⣷⣶⣶⣿⣿⣿⡇⣿⣿⣿⣶⣶⣶⣿⣿⣿⢸⣟⡛⢒⣒⣒⣚⣛⣻⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⢸⡀⠀⣿⡧⢸⣿⣶⣟⠸⡟⢺⢬⣿⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⠍⣿⣇⣸⣿⣿⣯⢸⣿⡿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⡇⢸⣿⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⢨⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢛⠛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⢸⠦⠤⠼⠦⠬⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣛⣛⣛⣛⣚⣒⢸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇
⠸⠤⠤⠤⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢰⢦⠤⠬⠥⠤⠧⠤⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣾⣶⢸⣿⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇
⠸⠮⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣉⣽⣉⣍⣩⣩⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠼⠤⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⢸⣀⣀⣀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣾⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⢸⣛⣉⣹⣉⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣼⣤⢸⣿⣿⣷⣿⣿⣷⠿⣷⣿⣷⣿⣿⣾⣿⢸⣿⣿⣿⣿⣿⢿⣿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⠿⢿⠿⢿⡇
⢸⣐⣠⣢⣐⣰⣀⣀⣢⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣾⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣶⣾⣶⣾⡇
⢰⠒⠒⡖⢒⠒⢒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣰⣀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⢉⠉⡉⠉⠉⡉⠉⠉⣉⠉⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣤⣬⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⣬⣤⣼⡇
⢰⠒⠒⢒⢲⠒⠲⠖⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣰⣀⢰⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⠩⠉⠉⠉⠭⠉⢩⠉⠩⠩⠉⠉⠉⠍⠍⠉⠉⠉⢭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣤⣬⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⣬⣤⣼⡇
⢨⢭⠭⠭⢭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠳⠒⠞⠞⠟⠛⠳⠚⠛⠛⢟⣛⣛⣛⣛⣛⣛⣟⣛⣛⣻⣛⣛⣟⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣉⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣯⣝⣩⣹⡇
⢨⠥⠭⠤⠬⠭⠬⠥⢬⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠒⣒⠚⣒⣒⣒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣭⣭⣽⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣉⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣉⣙⣉⣹⡇
⢘⠒⠒⠒⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢛⠛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⢸⠒⠓⠓⣒⠒⠚⠚⠚⢛⠛⠛⠛⠛⠛⠛⡛⠛⢛⣛⣛⣛⣛⣛⣛⣻⣿⣛⣛⣛⣓⣚⣒⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠛⠻⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⡟⠻⠛⢻⡇
⠸⠀⠀⠀⠀⠀⠄⠀⠰⠶⠶⠾⠶⠶⠶⠶⠷⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣯⣭⣽⣭⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠼⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⢿⠿⢿⡇
⠸⠭⠩⠍⠍⠉⠉⠯⠌⠌⠅⠉⠋⠍⠬⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠶⠷⠾⠇⠿⠿⠿⠿⠿⠿⠿⠿⠷⠸⠿⠿⠿⠿⠿⠷⠶⠷⢿⡇
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⢈⣍⡩⣉⣏⣉⣙⣏⣍⣩⣩⣉⣉⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣏⣉⣉⣉⣉⣙⣏⣉⣉⣉⣉⣍⣋⣭⣉⣉⣉⣉⣻⣉⣉⣍⣉⣉⣉⣉⣉⣉⣙⣏⣉⣉⣉⣉⣩⣉⣉⣉⣉⣉⣉⣉⣉⣹⣉⣉⣉⣉⣉⣉⣉⣿⡇
⢠⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣼⢤⠤⣤⣤⣤⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠿⠿⣿⣿⣿⡟⣿⣿⣿⡿⠿⢿⣿⣿⣿⢻⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡛⡖⣂⢹⡝⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⡒⠚⢻⣿⢸⡛⢛⠛⣻⠛⢻⣐⣹⢛⣛⡛⣛⣛⣛⢸⣿⣏⠛⣒⡂⡛⣛⣿⡇⣿⣿⡛⢓⣒⢚⡛⣻⣿⢸⣿⡏⠛⣒⡓⡛⢻⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⢬⡨⠴⣿⢸⡿⠧⠤⠼⡤⡄⠧⠠⠽⢥⠄⠤⠿⣿⢸⣧⣤⠠⠤⡤⠤⢤⣼⡇⣿⡄⠤⢬⠤⠠⠤⢤⣿⢸⡤⠤⠤⠬⠤⠧⠤⢤⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣉⣹⣉⣈⣍⣿⢸⣷⣉⣉⣋⣉⣉⣉⣉⣉⣍⣉⣉⣹⣿⢸⣿⠉⢉⢉⢉⠉⢉⣿⡇⣿⡉⠉⡉⣉⡉⠉⣉⣿⢸⣿⣯⣁⣉⢏⣉⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠒⠓⠒⠒⠒⢛⢸⢈⠏⣷⡟⢻⣿⠀⡿⢰⡯⠸⢠⣾⢩⢸⣿⣵⡖⠂⠛⢶⣶⣿⡇⣿⣿⣶⡓⠚⠒⣶⣾⣿⢰⣶⣴⠒⠒⠒⢲⣷⣶⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⡭⠧⢤⣤⣼⢸⢰⠇⣿⡇⢸⣿⢀⣿⢹⣗⢸⢰⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣯⣍⣭⣬⣭⣬⣭⣽⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⢸⢡⣀⣿⡇⢸⣿⣿⣷⢘⣟⣸⢰⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠅⣿⣗⢺⣿⣿⣷⢸⣿⣟⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣂⣿⡇⣸⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠰⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢨⠭⠭⢭⠍⠭⠭⠭⡭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠿⢿⡿⠿⢿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣭⣝⣭⡅⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⣯⣙⣭⣽⡇
⢨⠬⠤⠬⡭⠬⠤⣥⣭⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠒⠒⡒⠓⢒⠒⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣉⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣏⣙⣉⣹⡇
⢘⣒⣒⣚⣒⣚⣒⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢛⠛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⢸⣶⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣛⡻⣛⡃⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⣿⣿⣿⣿⣿⣟⡻⣛⣻⡇
⢘⣒⣒⣒⣚⣒⣒⣒⣒⣚⣒⣒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢛⠛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⢸⠤⠴⠤⠬⠤⠬⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣛⣛⣛⣓⣚⣒⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠛⠻⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⡟⠻⠛⢻⡇
⠸⠴⠤⠦⠶⠤⠤⠤⠼⠤⠤⠤⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣾⣥⣼⡤⣤⣤⣭⢥⢿⡿⣿⣿⢿⢿⢿⣿⣿⡿⣿⣿⢿⣿⣿⡿⣿⣿⠿⠿⢿⠷⠾⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠛⢻⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⡟⢿⠛⢻⡇
⠸⠭⠭⠭⠽⠭⠭⠭⠭⠽⠭⠭⠭⠭⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠷⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣩⣍⣉⣏⣝⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠧⠼⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⢿⠿⢿⡇
⢸⣀⣀⣢⣀⣰⣀⣀⣠⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣷⣶⣶⣾⡇
⢸⣉⣉⣋⣙⣟⣉⣛⣛⣋⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣼⣤⢸⣿⣿⣷⣿⣿⣷⣿⣷⣿⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⢿⠿⢿⡇
⢸⣚⣒⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣾⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣷⣾⣶⣾⡇
⢰⢒⠖⠒⠒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣰⣀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⣉⠉⡉⠉⠉⠉⢉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣴⣬⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⣬⣤⣼⡇
⢸⠟⠛⠛⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣉⢸⣿⣿⣧⣿⣿⣿⣿⣷⣿⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠩⢉⢍⠩⢩⠉⠉⢍⡩⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⣤⣼⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⣼⣤⣼⡇
⢨⠭⠭⠭⠭⢭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠲⢒⠛⠚⠒⡒⠓⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣟⣛⣛⣻⣛⣛⣛⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣍⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣏⣙⣉⣹⡇
⢸⣾⣶⣶⣶⣶⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣯⣿⣿⣯⣿⣯⣿⣯⣿⣿⣽⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⠤⠤⠤⡤⠤⢤⡤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⣤⡄
⠐⠓⠊⡆⠓⠒⠒⡓⠓⠚⠚⢲⠢⠛⠒⠒⠒⠒⢒⢲⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣷⣶⣿⣶⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⢉⢽⣿⣿⣿⣿⣿⣿⢸⣿⡿⣿⣉⡉⣿⣿⣿⡇⣿⣿⢿⣏⣉⣹⣿⣿⣿⢸⣿⡿⣿⣉⣍⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⣧⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠒⠂⠀⢘⣿⢸⣶⡔⠂⢺⠀⠘⡖⠚⢴⠒⠒⠒⣶⣶⢸⡟⠓⠀⠒⠒⠒⠒⢻⡇⣿⠛⠂⠐⠒⠒⠒⠚⣿⢸⠛⠃⠐⠒⠒⡖⠘⠛⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⢭⠽⠪⠭⣿⢸⣏⠭⠭⡭⠯⠧⠭⠬⠭⠽⠥⠭⢭⣿⢸⣿⠿⠬⠭⠯⠭⠽⣿⡇⣿⠧⠭⠽⠭⠬⠭⠽⣿⢸⣯⡭⠍⠭⡭⠭⣭⣽⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣒⣞⣂⣒⣃⣿⢸⠻⡶⣶⣶⣶⣶⠒⣶⢒⡷⢲⠒⣾⠿⢸⣿⢄⣰⣐⣴⣀⣐⣿⡇⣿⣦⣠⣆⣢⣂⣀⣲⣿⢘⣛⢛⣒⣒⣑⣒⣟⣛⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠤⡄⠀⠀⢰⢸⢘⡅⣿⡗⢸⣿⠀⣯⢼⣏⢨⢘⣿⢸⢸⣿⣿⣧⣤⣤⣽⣿⣿⡇⣿⣿⣿⣦⣤⣥⣿⣿⣿⢸⡿⠿⠤⡠⠠⠘⠿⢿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣹⣿⣿⢸⠜⠁⣿⡇⢸⣿⣶⣟⢸⣷⢸⢘⣿⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣼⠆⣿⣇⣸⣿⣿⣟⢰⣷⣾⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡁⣿⡗⢸⣿⣿⣿⣼⣿⣷⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣶⣿⣇⣺⣿⣿⣿⣿⣿⣿⢘⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠬⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣭⣽⣼⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠷⠼⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⢿⠿⢿⡇
⠸⠭⠭⠭⠫⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠷⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠷⠿⢿⡇
⢸⣉⣩⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠧⠼⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⢿⠿⢿⡇
⢸⣀⣀⣢⣀⣰⣀⣀⣠⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣷⣶⣶⣾⡇
⢰⣒⣒⣒⣒⣲⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣤⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⣟⣚⣛⣓⣛⣻⣞⣚⣚⣓⣻⣓⣾⣾⣾⣷⣷⣷⣿⣿⣾⣿⣷⣷⣿⣿⣶⣶⣾⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣮⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣮⣶⣾⡇
⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃
⡿⠿⠙⠋⠙⠋⠏⠻⠉⠙⠙⠋⠋⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿
⣿⣤⣿⣿⣭⣼⣬⣯⣭⣭⣯⣤⣯⣬⣵⣯⣭⣭⣭⣬⣦⣥⣭⣽⣦⣤⣬⣭⣭⣬⣥⣬⣯⣥⣬⣥⣽⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣿⣿⣙⣛⣛⣋⣟⣛⣛⣛⣛⣻⣛⣟⡛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣏⣛⣻⣉⣛⡋⣻⣙⣛⣛⣛⣟⣛⣙⣋⣙⣻⣁⣰⣒⣒⣀⣒⣴⢐⣀⢐⣂⣒⣒⡒⣒⣒⣐⣂⣂⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⣿⣿⣿⣿⡶⢶⡾⣶⣴⣶⣶⣾⣶⡶⢶⡾⣶⣾⣴⣾⣶⢶⣶⣶⣶⠷⡶⢶⣶⣾⣷⣶⣶⣶⠷⢶⢷⢶⣴⣿⣿⣿⣿⣿⢿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⣿⣿⠳⠾⠖⠶⢲⡖⠶⠶⠟⢷⢺⠗⠖⠶⠶⠾⢶⢲⠶⡾⠿⢲⠳⠶⠶⠷⠲⠖⢾⡿⠶⠺⠲⡶⠾⠶⠖⠶⠶⠾⠶⠶⠶⠶⠶⠞⠟⠟⠻⠿⠿⢿⠿⠻⢿⠿⢿⠻⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⢭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣯⣭⣩⣭⣭⣭⣭⣍⣭⣽⣭⣏⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣒⢒⢒⣒⣓⣒⢲⣓⣒⠖⣶⣓⢲⣓⣒⣐⣒⣖⣲⣒⡒⣞⡚⣒⣦⣖⣒⣲⣒⣒⣐⣖⡲⣒⡶⣒⣚⣒⣐⢒⣒⡖⡒⠓⣶⣒⣓⣒⣳⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣦⣤⣤⣴⣤⣿
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⡖⠒⣶⣶⡆⣶⣶⣶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⠒⢲⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⣭⣥⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠧⠭⢭⠩⢿⡇⡿⠤⠭⠬⢽⠤⢭⠭⠯⠭⠥⠯⠭⡽⢿⡿⠿⠧⠭⠭⠭⠤⡽⠿⢿⡿⠿⠧⠭⠭⠯⠤⠽⠿⣿⣿⣬⣬⡭⡬⠬⢭⣭⣭⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣉⢉⣹⣈⢹⡇⣿⣿⣿⣉⢹⣉⢏⡉⣉⢏⡈⣏⣿⣿⣿⣿⠏⠁⡉⠉⢉⠉⠉⠹⣿⣿⣿⣷⡯⣉⢉⣹⡿⢿⣿⣏⡉⣉⣉⣉⡉⣩⢍⣉⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣖⣒⣒⣚⣶⡇⠛⡛⢛⣛⣒⣒⠒⢒⠒⢒⠒⡛⢛⡛⢛⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣰⣓⣒⣒⣂⡳⣶⣿⣿⣷⣖⣒⣔⣒⣒⣲⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⠤⡄⠄⠀⡄⠒⡇⣸⣿⡇⢾⠀⢸⢀⣸⠀⠇⢸⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣦⣤⣤⣦⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣯⣭⣿⣿⡇⠀⡇⢸⣿⡇⣺⢠⣼⠀⢸⠀⣇⣸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣤⡗⢺⣿⡇⢿⢸⣿⠀⢸⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⡇⢸⣿⡏⣼⢸⣿⢠⣼⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣧⣾⣿⡇⣿⢸⣿⢸⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⡧⠤⠤⠤⠬⠧⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣉⡁⣿⡟⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⡇⠀⠀⠀⠀⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠓⠒⠓⣒⣒⣒⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠿⠤⠄⣿⣯⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣇⡀⣀⣁⣀⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡿⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠷⠿⠿⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣿
⡧⠤⠤⠴⠬⠧⠬⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣉⡁⣿⡟⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⡇⠀⠀⠀⠀⠛⢛⠛⢛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠓⠒⠚⣒⣚⣓⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠿⠤⠄⣿⣯⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣧⡀⣀⣁⣀⣉⣉⣉⣉⣉⣉⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡿⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠷⠿⠿⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣿
⡧⠥⠤⠤⠤⠯⠤⠤⠤⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣉⡁⣿⡟⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⡇⠀⠀⠀⠀⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠒⠒⠚⣒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠿⠤⠄⣿⣯⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣧⡀⣄⣡⣄⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡿⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠷⠿⠿⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣿
⡧⠦⠭⠤⠤⠧⠬⠤⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⢻⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⣿
⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠒⠒⢚⣓⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣹⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣏⣋⣩⣿
⣧⡀⣀⣀⣈⣉⣉⣉⣍⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⡭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡟⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠾⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⣿
⡧⠤⠭⠤⠶⠤⠤⠤⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣿
⡇⠀⠀⠀⠘⡁⠈⠁⣀⣁⣀⣂⣀⣀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠒⠚⠒⠒⠒⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣿⢸⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣏⣋⣉⣿
⣧⡀⣀⣠⣉⣀⣈⣀⣬⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⡭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡟⠻⠛⠟⠛⠛⠻⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠾⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠷⠷⠶⣿
⡧⠤⠭⠤⠤⠭⠤⠤⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⣿
⡇⠀⠀⠀⠘⠁⡈⠁⠀⢁⣀⣈⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⢓⠒⡒⠚⠒⠓⠒⡒⠚⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣿⢸⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣟⣋⣉⣿
⣧⡉⣈⣅⣁⣅⣀⣀⣉⣁⣤⣥⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⡭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡟⠛⠛⠛⠻⠛⠛⠛⠛⠿⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠾⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⣿
⡧⠤⠭⠤⠬⠤⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿
⡇⠀⡀⠃⠀⢀⠐⠈⠈⢀⣀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠓⠒⠒⠒⠚⠒⠓⠒⠚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣯⣏⣉⣿
⣧⡀⣀⣀⣉⣀⣈⣄⣈⣈⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⡭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡟⠛⠛⠛⠛⠛⠛⠛⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⣿
⡧⠤⠤⠬⠤⠥⠭⠤⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿
⡇⠁⠉⠁⠀⠀⠁⠈⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⢒⠓⠚⠒⠒⢒⠒⠒⠚⠛⢛⠛⠛⢛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣿
⣧⠉⡄⠁⢀⠀⠈⣥⣤⣤⣬⣤⣬⡤⣬⡭⣭⡭⣭⣭⣭⣭⣭⣭⣥⢭⣭⢭⣭⢭⣭⢥⣭⣭⣭⣭⣭⣭⣬⣭⣬⣭⡌⡉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⣿⣏⣏⣋⣋⣙⣛⣛⣛⣋⣛⣛⣙⣛⣋⣛⣛⣏⣻⣉⣉⣉⣹⣙⣛⣙⣻⣹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡅⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿
⣟⣃⣃⣀⣀⣀⣈⣀⣈⣁⣀⣁⣈⣀⣁⣛⣛⣛⣛⣛⣛⣋⣛⣋⣛⣋⣛⣋⣛⣛⣛⣛⣛⣙⣛⣙⣛⣛⣛⣛⣛⣛⣃⣃⣛⣛⣛⣛⣛⣛⣛⣐⣀⣓⣂⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣛⣛⣛⣛⣛⣛⣛⣈⣐⣃⣀⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⣿⡸⣷⣉⣿⣿⡿⢿⣿⣿⣿⡇⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⡟⢿⡿⡿⣿⣿⣿⡶⠶⣾⣿⣿⡄⣾⣿⣿⣿⡢⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⠀⠠⠀⢀⣀⣠⣤⣀⣘⣿⠀⡇⣿⠻⣿⣿⣿⣼⣿⢻⡿⣷⢸⣿⡿⣿⢧⣀⣿⣿⣿⣿⠇⠀⠈⠁⠀⣿⣿⣿⣷⠀⢸⣿⣿⡇⣿⣿⣿⣿⡋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠩⣌⡀⣼⣿⣿⣿⣿⣿⣿⣤⣷⢿⡿⣿⣿⣿⣿⣿⣾⣟⣿⠸⣿⣿⣿⣿⡇⠠⠟⠁⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣧⠀⠀⠀⠀⠈⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠋⠉⢉⣉⠉⢩⣤⣤⣤⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡄⣿⣿⣿⣟⠛⡖⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠻⢿⣿⣿⣿⣿⡇⠀⣹⣟⡃⠄⠀⣨⣀⠀⢰⣿⣿⣿⣿⡿⡿⣿⢿⣿⡿⢿⠿⣀⠀⢰⠿⢿⣟⣿⣿⣿
⣤⣤⣬⣽⠿⠀⣸⣿⣿⣿⡸⣿⣿⡆⠀⠸⢿⣿⣿⣿⣿⣿⣾⡇⠉⠉⢉⣿⠿⠛⣶⡀⢀⣠⣤⣄⣀⡄⠀⠀⠤⠼⠿⢿⣿⣿⡇⢸⠇⠀⠀⠀⠀⣿⣿⣿⢩⣵⣷⣦⣿⣅⠀⠀⢠⢸⣿⣎⣸⣁⣀⣧⣶⣾⣿⣿⣿⡿
⢳⣾⣿⣿⣾⣿⣯⣿⠿⣿⡛⢿⣿⣇⢤⣼⣯⣭⣽⣿⣶⣶⣿⣇⢸⠟⠋⠀⠀⠀⣿⣿⣿⣿⣉⣙⡛⠁⠀⠀⠀⠀⢶⡾⠿⣛⣧⣼⣥⣆⡀⠀⠀⢿⡟⠋⡜⣿⣿⣿⣀⣻⣿⣷⣙⣿⣿⣿⡿⠛⣿⡏⣿⣿⣿⢻⠃⠁
⠛⠋⠉⠉⢍⣀⣰⣿⣿⣿⣿⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⡿⠆⠀⠀⠀⠈⠃⠰⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⡠⡗⢻⡇⣿⠿⠿⡻⣻⣿⣿⣿⡿⠁⠁⣿⣿⣟⡃⣀⣙⣿⣏⡸⠟
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣯⢴⣿⢿⣿⣿⣿⣿⣿⡶⣶⣷⣿⣿⣿⣿⣿⣾⣿⣞⣛⣻⣿⣿⣿⣿⠟⠛⠉⠀
⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⢏⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⣿⣿⢸⣟⠩⢠⣿⣿⣿⣿⣿⡇⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀
⣛⡻⠭⣽⣉⣀⣤⣤⠤⠒⠒⠩⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⢛⠛⠓⠀⢀⣴⣿⣿⠂⠀⠀⠀⣰⣿⣿⣿⣿⣌⣹⠟⠙⣿⣿⣿⣥⣶⣿⣶⣼⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠚⣒⣿⡇⣡⣤⡴⣏⡭⠥⠀⠀⠀⠈⠈⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠀⣴⣿⣿⣿⣿⣤⢀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣿⡼⣷⣚⣻⣭⣽⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣁⣀⣼⣿⣿⣿⣿⣿⣿⠛⠀⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⠟⠭⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⡞⠬⠙⠤⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⠀⠀⠀⠀⠈⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡯⢁⡁⠀⠀⠠⠀⠀⢸⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠻⢿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣏⣗⣌⣤⡡⢦⡈⠀⠀⣸⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⣷⠈⠁⠀⠐⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠿⠟⢸⡥⠀⠀⠁⠀⣿⣿⡿⠛⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⣄⣀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⡁⢁⡉⠁⠈⠀⠀⠀⠿⠋⠀⠀⠀⠀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡹⣟⣻⡖⢦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⣿⡸⣷⣉⣿⣿⡿⢿⣿⣿⣿⡇⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠟⢿⡿⡿⣿⣿⣿⡶⠶⣾⣿⣿⡄⣾⣿⣿⣿⡧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⠀⠠⠀⢀⣀⣠⣤⣀⣘⣿⠁⡇⣿⡻⣿⣿⣿⣼⣿⢻⣿⣷⢸⣿⡿⣿⢧⣀⣿⣿⣿⣿⠇⠀⠈⠁⠀⣿⣿⣿⣷⠀⢸⣿⣿⡇⣿⣿⣿⣿⠿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠩⣌⡀⣼⣿⣿⣿⣿⣿⣿⣤⣷⢿⡿⣿⣿⣿⣿⣿⣼⣟⣿⠸⣿⣿⣿⣿⡇⠠⠟⠁⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⡇⠀⠀⠀⠀⠈⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⠉⣉⣉⠉⢩⣤⣤⣤⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⡄⣿⣿⣿⣟⠻⡆⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠻⢿⣿⣿⣿⣿⡇⠀⣹⣟⡃⠅⠀⣰⣀⠀⢰⣿⣻⣿⣿⡿⡿⠿⢿⣿⡿⢿⠿⣀⠀⢰⠿⢿⣟⣿⣿⣿
⣤⣤⣬⡽⠿⠃⢸⣿⣿⣿⡾⣿⣿⡆⠀⠸⢿⣿⣿⣿⣿⣿⣾⡇⠉⠉⢉⣿⠿⠛⣶⡀⢀⣰⣤⣄⣀⡄⠀⠀⠤⠼⠿⣿⣿⣿⡇⢸⠇⠀⠀⠀⠀⣿⣿⣿⢩⣵⣷⣦⣿⣅⠒⠀⢠⢸⣿⣎⣸⣁⣀⣧⣶⣾⣿⣿⣿⡿
⢳⣾⣿⣿⣾⣿⣯⣿⠿⣿⡛⢿⣿⣇⢤⣼⣯⣭⣽⣿⣶⣶⣾⣧⠸⠟⠋⠀⠀⠀⣿⣿⣿⣯⣉⣙⡛⠁⠀⠀⡀⠀⢶⡾⠿⣛⣧⣼⣤⣆⡀⠀⠀⢿⡟⠋⡘⣿⣿⣿⣀⣿⣿⣷⣙⣿⣿⣿⡿⠻⣿⡏⣿⣿⣿⢻⠃⠁
⠛⢋⠉⠉⢍⣀⢰⣿⣿⣿⣿⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⡿⠆⠀⠀⠀⠈⠃⢴⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⡠⡗⢻⡇⣿⠿⠿⡻⣻⣿⣿⣿⡿⠁⠁⣿⣿⣟⡇⣈⣙⣿⣏⣸⠟
⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⡟⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣯⢴⣿⢿⣿⣿⣿⣿⣿⡶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣞⣛⣻⣿⣿⣿⣿⠟⠛⠉⠀
⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⢟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⣿⣿⢸⣟⠩⢠⣿⣿⣿⣿⣿⡇⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀
⣛⡻⠭⣽⣉⣀⣤⣤⠤⠒⠒⠩⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⢛⠛⠓⠀⢀⣴⣿⣿⠂⠀⠀⠀⣰⣿⣿⣿⣿⣌⣹⠟⠙⣿⣿⣿⣥⣶⣿⣶⣼⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠒⢒⣿⡇⣡⣤⡴⣏⣭⠥⠀⠀⠀⠈⠈⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠈⠀⣴⣿⣿⣿⣿⣤⢀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⢿⡼⣷⣚⣻⣭⣽⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣁⣀⣼⣿⣿⣿⣿⣿⣿⠓⠀⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡄⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⢟⣉⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣛⡟⠖⠹⠁⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⠀⠀⠀⠀⠈⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡩⠇⠨⠀⠀⠀⠀⠀⢸⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠻⢿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣏⢽⣚⢏⡢⠠⠀⠀⠀⣸⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠤⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠂⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠅⠈⠀⣿⣿⡿⠟⠀⠀⠀⢀⣀⣤⣤⣶⣦⣦⣄⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣛⠉⠂⠍⠃⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠑⠞⠗⢙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠆⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣇⣿⣜⣿⣿⣿⣿⣿⢹⡏⣿⢸⣿⡿⣿⣿⠀⣿⣿⣿⣿⣿⢸⢿⣿⢿⣿⣿⣿⣯⡽⢶⣿⣿⡇⢰⣾⣿⣿⡿⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠄⠀⠄⠀⢀⠀⣀⣀⣀⣿⡇⢹⢹⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣽⣧⠀⣿⣿⣿⣿⣿⠀⠀⠋⠀⢻⣿⣿⣿⡀⠸⣿⣿⣧⢸⣿⣿⣿⡿⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠉⠁⣁⢨⣷⣿⣿⣿⣿⣿⣇⣾⣼⣷⣿⣿⣿⣛⣿⣿⣿⣽⡇⣿⣿⣼⣷⣯⢁⡸⠋⠁⠀⠀⠀⠀⣠⣼⣿⣿⣿⣷⣾⣿⣿⣿⠘⢻⣿⣿⣿⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠒⠛⠛⢋⡉⠉⣩⣡⣤⠈⣿⢿⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢛⡒⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠿⣿⣿⣿⣿⣿⠀⠘⣿⣛⢐⠀⠀⣀⠀⠀⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⡟⠛⠛⣿⣿⣿⣿⣿⣿
⢀⣤⣄⣡⡽⠧⠀⣿⣿⣿⡇⣿⣿⣧⠀⠈⣬⣿⣿⣿⣿⣼⣿⣿⠘⠛⠋⢻⣿⠿⣤⡀⠀⠀⣄⣀⢀⡀⠀⠀⠀⠠⠿⢿⣿⣿⣿⠀⡏⠉⠀⠀⠀⢸⣿⣷⠚⣭⣭⣷⣿⡟⠀⠀⠀⡋⣶⣾⡁⡏⠁⣰⣤⣴⣿⣾⣿⣿
⡿⣾⣿⣿⣷⣶⣿⣿⣿⡿⠿⢿⣿⣿⢠⣤⣛⣿⣭⣭⣽⣿⣶⣿⠐⣿⠏⠉⠀⠀⢹⣷⣾⣿⡛⠛⠿⠃⠀⠀⠀⠀⢠⣼⢿⡿⣿⣠⣧⣤⠀⠀⠀⢸⣿⠟⠄⣿⣿⣿⡇⢸⣿⣷⢘⣿⣿⣿⣿⡿⣿⣟⢹⣿⣿⡿⡿⠑
⠛⠛⠛⠋⠉⢉⠁⣼⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠁⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠣⢨⣶⣾⣿⣿⣿⣿⣿⣿⣄⣀⡤⣽⢴⡷⢹⣿⣿⠿⢿⣿⣿⣿⣿⡯⠙⢻⣿⣿⣻⠈⠉⣿⣿⠃⣶
⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣩⣾⣿⣿⣿⣾⣾⣿⣾⣤⣶⣿⣿⣿⣿⣽⣷⣶⣶⣖⣻⣶⣾⣿⣿⡿⠟⠛⠃
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢺⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡝⡿⢛⡁⣿⣿⣿⣿⣿⣯⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⠀⠀⠀⠀⠀
⣟⣛⠛⢯⡏⣉⣀⣤⡤⠤⠒⠒⠏⣿⣿⡜⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⡛⠛⠗⡀⠀⣠⣾⣿⡆⠀⠀⠀⢠⣿⣿⣶⣿⡗⢲⡿⠛⢿⣿⣿⣧⣤⣶⣦⣬⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⢗⢺⣿⢉⣥⣤⢶⢈⣉⠀⠀⠈⠉⠁⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣴⣿⣿⣿⣥⣀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠯⣭⣿⣼⣟⣻⣭⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⣀⣠⣿⣿⣿⣿⣿⣿⡟⠁⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⡄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣇⠈⢼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣶⠆⠀⠀⠀⠀⠉⠀⠉⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣻⠩⠁⠪⠈⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡽⣫⠿⣪⡂⠀⠀⢸⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⡀⣂⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⠠⠊⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠇⠆⢁⠁⢸⣿⣿⠿⠃⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⣿⣿⣿⣿⣟⡮⠞⡐⠁⠄⠀⢸⠟⠋⠀⠀⠀⢀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢟⠯⣺⠴⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⣫⡫⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸⣿⣿⡸⣷⣹⣿⣿⣿⣿⣇⢿⣿⡇⢻⣿⢿⣿⡇⢸⣿⣿⣿⣿⡇⡿⣿⡿⡿⣿⣿⣿⣬⢭⣼⣿⣿⡇⣼⣾⣿⣯⡣⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⠀⠠⠄⠀⠀⢀⣀⣀⣈⣿⠀⡇⣿⠹⣿⣿⣿⣿⣿⣿⣯⣷⢸⣿⣧⣽⡄⢀⣿⣿⣿⣿⡇⠀⠘⠃⠀⣿⣿⣿⣷⠀⢻⣿⣿⡇⣿⣿⣿⣧⠭⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠜⠊⠉⢜⡀⢸⣿⣿⣿⣿⣿⣿⣄⣷⢿⡿⣿⣿⣟⣻⣿⣿⣿⣿⢸⣿⣧⣿⣾⡏⣁⠛⠉⠁⠁⠀⠀⣀⣀⣿⣿⣿⣿⣶⣿⣿⣿⡇⠻⣿⣿⣿⡇⠀⠀⠀⠀⠘⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠒⠛⠛⠋⣉⠉⢉⣭⣤⣄⢸⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠓⠂⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⢻⡿⡏⠀⠀⢀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⢩⣿⣿⣿⣿⣿
⠀⣠⣤⣄⣬⠿⠃⢸⣿⣿⣿⣼⣿⣿⡆⠀⢠⡼⣿⣿⣿⣧⣿⣿⡇⠛⠛⠙⣿⡿⢧⡄⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⣸⠿⣿⣿⣿⡇⢸⠉⠉⠁⠀⠀⣿⣿⣖⢚⣩⣭⣝⣿⠃⠁⠈⢈⢹⣷⡜⢰⠏⠀⣎⣡⣼⣿⣿⣿
⣾⢳⣾⣿⣿⣶⣾⣯⣿⡿⠿⡟⣿⣿⡇⣤⣜⣛⣿⣭⣽⣿⣶⣾⡇⢺⡿⠉⠁⠀⢸⣿⣶⣶⡟⠛⠿⠟⠀⠀⠀⠀⠠⣤⣾⣿⠿⣇⣸⣠⡄⠀⠀⠀⣿⡿⠇⢸⣿⣿⣿⠈⣿⣶⣦⠺⣾⣿⣿⣿⠿⣿⡟⣿⣿⣿⢿⡟
⠛⠛⠛⠋⠉⠉⡁⢠⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠱⠀⢩⣶⣶⣿⣿⣿⣿⣿⣧⢀⣀⣌⡧⣶⠜⣿⣿⣿⠿⣿⣿⣿⣿⣿⡋⠋⣿⣶⡿⠇⠙⠛⣟⡾⠠
⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⣿⣋⣽⣿⣿⣿⣶⣷⣿⣧⣭⣠⣶⣷⣿⣿⣯⣿⣴⣦⡴⠽⢿⣿⣷⣾⣿⣿⠿⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣏⢿⠾⣛⢸⣿⣿⣿⣿⣿⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠀⠀⠀
⣟⣛⡛⠯⣽⢉⣁⣤⣤⠤⠐⠒⢺⢻⣿⣷⢹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣟⠛⠻⢀⠀⢀⣰⣷⣶⠀⠀⠀⠀⣾⣿⣷⣾⣗⠐⣾⠟⠿⣿⣿⣿⣀⣴⣦⣭⣹⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀
⣤⠤⠔⡒⣿⡏⣡⣤⡴⡇⣉⡅⠀⠀⠉⠉⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⣾⣿⣿⣏⣄⠀⠀⢰⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣯⠽⣷⣟⣻⣯⣽⣶⣶⡆⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣂⣀⣼⣿⣿⣿⣿⣿⣿⠏⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠏⠀⠍⠌⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣟⣃⠀⠀⠀⠀⠈⠁⠈⠻⣿⣿⣿⣿⣿⡿⣛⢟⡛⠅⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣝⠉⠐⠀⠔⠂⠀⠀⠀⠀⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣷⣶⣶⡶⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⣻⠡⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡯⠛⠂⡒⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⢿⡽⡭⢎⠆⠀⠄⠀⠀⠀⠀⢨⣿⠟⠁⠀⠀⠀⢀⣴⣾⣾⣿⣿⣿⣿⣷⣶⡶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠞⡒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣠⡤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢿⣿⣧⢸⡏⣽⣿⣿⡿⣿⣿⣿⣿⡀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠸⢿⣿⠿⢸⣿⣿⣷⡶⠶⣾⣿⣿⠀⣷⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡠⣤⠀⢰⠀⡀⣀⣤⣤⣄⣸⣏⠼⣼⣿⢿⣿⣿⣧⣿⡏⣿⢿⡇⣿⣿⢾⣿⢆⣸⣿⣿⣿⣿⡄⠀⠘⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⣧⢅⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡊⠉⠩⣉⣀⣿⣿⣿⣿⣿⡟⣿⣐⡇⡿⠸⣿⣿⣿⣿⣿⣹⣿⡇⢹⣿⣾⣿⡿⠀⠜⠋⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⣿⣿⡀⠀⠀⠀⠀⢘⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⣉⣍⠁⣤⣤⣤⡄⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣾⣿⣷⢸⣿⣿⣿⠛⡗⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡟⠿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠋⠀⣘⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠋⠛⢹⣿⣿⣿⣿
⠀⢠⣴⣶⣄⡿⠟⢀⢹⣿⣿⣷⣻⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⠈⠉⠉⣹⡿⠟⣤⠀⠀⢠⣀⡀⠀⣀⠀⡀⠀⠠⠿⠿⣿⣿⣿⠀⠟⠉⠀⠀⠀⢸⣿⣗⡖⣭⣭⣥⣹⣟⠁⠀⠃⠈⣽⣷⡏⢸⠉⢰⣊⣤⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⣿⣿⡄⣤⣽⣭⣭⣿⣷⣶⣿⣿⡄⠿⠋⠁⠀⠀⣿⣷⣾⣿⠛⠻⠿⠃⠀⠀⠀⠀⢤⣴⣿⡿⣿⣠⣥⣤⠀⠀⠀⢸⣿⠟⠂⣿⣿⣿⡇⠈⣿⣶⡄⢿⣿⣿⣿⣿⡿⣿⢛⣿⣿⣿⣿
⠛⠋⣉⢉⡍⣁⣀⡀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⠿⠇⠀⠀⠀⠈⠇⣨⣶⣾⣿⣿⣿⣿⣿⣿⡄⣀⣠⣹⠴⡶⢸⣿⣿⡿⡿⣿⣿⣿⣿⣟⡙⠸⣷⣷⠿⠊⠙⢻⣷⡞
⣤⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣟⣩⣿⣿⣿⣷⣾⣾⣿⣬⣅⣶⣼⣾⣿⣿⣿⣯⣶⣦⠦⠽⣿⣿⣷⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⣹⣿⣿⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠝⡿⢛⡁⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀
⣛⡻⠯⠭⢹⣧⣠⣤⡴⠶⠒⡒⠉⠇⣿⣿⡇⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢻⡛⡛⠄⡀⠀⣠⣿⣿⡆⠀⠀⠀⣸⣿⣿⣶⣿⡒⢺⡿⠻⢿⣿⣿⣇⣠⣶⣬⣍⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀
⣤⣔⡒⢺⣩⣿⠠⣴⣶⢺⡩⠤⠀⠀⠀⠉⠁⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣠⣾⣿⣿⣿⣤⣄⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠟⢳⣦⣿⣷⣿⣭⣿⣷⣾⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣋⣄⣴⣿⣿⣿⣿⣿⣿⡟⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣻⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠉⠉⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⠟⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠁⠍⢮⠉⣺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠉⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣽⠽⡍⢋⠘⠂⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠿⢿⣿⡿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡪⣫⣂⡘⠖⠠⠀⢸⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣶⣿⣿⣇⠀⡁⠀⢀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⡷⠠⠑⠀⠀⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢁⡀⠂⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⠿⠛⠙⡑⠨⠁⠀⠀⣿⠿⠋⠀⠀⠀⢀⣀⣴⣷⣿⣿⣿⣿⣷⣶⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣗⠝⠣⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⠂⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣇⣿⣰⣿⣿⣿⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣧⠘⠻⣿⢳⣿⣿⣿⣿⠛⢻⣿⣿⡇⢸⣿⣿⣿⣯⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⢿⣿⣿⣿⣿⣿⣿⣿
⢠⢴⣴⣧⡀⡇⢠⣤⣴⣶⣶⣤⣿⡖⢹⢻⡏⣿⣿⣿⣷⣿⡿⣿⣿⠘⣿⣿⣿⣟⡤⠿⣿⣿⠿⠿⠀⠀⠁⠀⣿⣿⣿⣿⣀⣸⣿⣿⡇⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣀⣀⣢⣤⣼⣿⠿⠿⠿⠿⢹⣷⣾⡸⠓⣻⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣇⠠⠉⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⣿⠀⠀⠀⠀⠀⢉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠠⢄⣤⡄⢰⣶⣶⣶⡸⣿⣿⡇⠀⢺⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣉⡏⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠙⠻⣿⣿⣿⣿⣿⠀⣘⣿⠯⠨⠂⢠⣄⡀⢀⣿⣿⣿⣿⣿⢿⢻⠿⣿⣿⠿⡟⢿⡀⠀⣼⠿⣿⣛
⣠⣀⣴⣿⣷⣾⣋⣁⣌⣿⣿⣿⣧⣿⣿⣇⠀⠈⣿⣿⣿⣿⠿⢿⣿⣇⢀⣁⣠⠟⠛⢱⣦⡀⣀⣰⣤⣀⣀⡄⠀⠀⠀⠒⠛⢻⣿⣿⣿⠀⠃⠀⠀⠀⠀⣿⣿⣿⢩⣵⣷⣶⣿⣏⡰⠀⢀⣄⣿⣿⣁⣟⣀⣸⣤⣶⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠷⣿⣿⣿⣭⣹⣿⣿⢰⣶⣶⣶⣾⣿⣿⣿⣿⣿⠘⠋⠁⠀⠀⠀⣿⣿⣿⣏⣉⣙⠋⠀⠀⠀⡀⠰⣾⠾⢿⣛⣿⣤⣶⣆⡀⠀⠀⢿⡟⠉⡼⣿⣿⣿⣄⣸⣿⣷⣘⣿⣿⣿⣿⢛⢻⣿⢹⣿⣿⡿
⠉⢉⣠⣤⣤⢀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⠟⠿⠀⠀⠀⠀⠙⠀⢼⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⠰⡟⢻⡇⣿⠿⠿⡻⣻⣿⣿⣿⣿⠭⠁⢹⣿⣿⣛⠀⣉⣻⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣟⣥⢶⣿⢿⣿⣿⣿⣿⣷⡶⣴⣷⣿⣿⣿⣿⣿⣷⣾⣖⣒⣻⣶⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⢛⣫⢻⣿⣧⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⡇⢻⡛⠭⣸⣿⣿⣿⣿⣿⠑⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀
⠭⠭⠙⠒⣂⣿⡦⠶⠶⠚⣋⡩⠁⠰⠸⢿⣿⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⣟⠛⠐⠠⠀⣠⣾⣿⡯⠀⠀⠀⢠⣿⣿⣿⣿⡏⠀⣿⠏⢟⣿⣿⣿⣤⣶⣶⣶⣼⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀
⣶⣶⣭⣍⡥⢾⣇⢲⣾⣿⣷⠒⣀⠀⠀⠀⠀⠘⠻⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢠⣾⣿⣿⣿⣷⣖⡄⠀⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠛⠛⠉⢹⣾⣿⣿⣷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⠰⣫⣴⣴⣿⣿⣿⣿⣿⣿⣿⠁⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠎⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡠⠑⡰⢠⠎⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣯⡯⠚⠂⠁⠁⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢖⠵⢻⠑⠀⠀⠀⠀⢀⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⡀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢿⠌⠁⠨⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⡙⠀⠁⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⢿⡿⠩⠫⠒⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣷⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡳⡽⠯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠚⠈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡞⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠃⠻⠏⢻⣿⣿⣿⣟⠉⢿⣿⣿⡇⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢻⣿⣿⣿⣿⣿⣿
⣐⣶⡳⠿⠧⠸⠀⢲⣶⣿⣿⣿⣿⣿⢠⣇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣯⣿⣵⠚⠛⡿⠟⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣤⣼⣿⣿⡇⢽⣿⣿⣿⡭⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠿⠷⠶⠤⠤⠷⠶⠿⠛⠛⠛⠛⠉⢿⣿⣿⠉⠉⣽⣿⣿⣿⣿⣿⣟⣿⢸⣿⣿⣿⣿⣆⡂⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⡿⠧⠀⠀⠄⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿
⠀⠀⠀⢀⣀⡒⡲⣾⠀⢼⣿⣿⣷⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡈⠿⠿⢿⣧⣤⢄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⢹⣿⣿⣿⣿⡇⢠⠼⠯⠃⠀⠀⣼⣤⢀⣸⢿⠿⢿⣿⡿⠟⠻⠻⡿⠿⢛⠛⣳⠄⢀⠾⠛⣿
⣶⣦⣴⣿⣿⣿⣿⣭⣴⣾⣿⣿⣿⣾⣿⣿⡇⠀⠨⠿⠿⣿⣟⣛⣿⣿⡇⢤⡤⠚⠉⠀⢸⣧⣠⣤⣿⣶⣦⡶⠀⠀⠐⠀⠉⠉⣿⣿⣿⡇⢸⠀⠀⠀⠀⢸⣿⣿⡇⢶⣾⣿⣿⠻⣄⣉⡀⢠⣸⣯⣿⣤⣧⣄⣾⣶⣾⣿
⣿⣿⡿⠾⠿⠿⠟⠛⠛⢻⣿⣿⣶⣦⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣤⡌⠀⠀⠀⢠⡄⠻⢟⣛⣫⣽⣷⣾⣿⣤⠀⠀⠘⢻⣏⣱⢸⣿⣿⣿⣤⣿⣿⣟⣬⣿⣿⡿⣯⣩⣽⣏⢾⣿⣿
⠀⠀⢰⣶⣶⣾⣰⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠁⠰⢿⣿⣿⣿⣿⣿⡿⢿⣧⣴⣆⣲⢉⣿⠸⠿⢟⢛⣛⣿⣿⣿⣿⠿⠒⠀⢿⣿⡿⣏⣀⣁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⢵⣾⣿⡿⣿⣿⣿⣿⣿⣿⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⠿⠿
⣿⣿⣿⠿⠿⣿⣿⠛⠛⢉⣉⣉⣉⠥⠆⣿⣿⡇⣿⣿⣿⣿⣿⣿⢧⣐⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠀⠀⣤⣄⡀⠀⠀⠀⢸⣿⣿⣊⣯⡡⢆⣿⣿⣿⣿⣿⡟⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⠀⠀⠀
⣒⠒⢊⣉⡹⠴⣿⡚⢛⣉⣩⡴⠂⠀⠋⠻⠿⠧⣿⣿⣿⣿⣿⡟⣼⣿⣿⣷⡀⠛⠛⠛⠛⠛⢻⠟⠂⠁⠂⣠⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣉⠹⡟⢙⣿⣿⣿⣷⣴⣾⣷⣷⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣛⣻⡇⣿⠿⣷⣏⣥⡄⠀⠀⠀⠀⠉⠙⠛⠿⠟⠁⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⡤⠀⢀⣾⣿⣿⣿⣿⣿⣵⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⢉⣀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⠿⠿⠀⠀⠀⠀⠀⠀⣨⣶⣿⣿⣿⣿⣿⣿⣿⣿⡧⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⠿⠿⠊⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡻⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣠⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣃⠚⠿⢍⢾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⠀⠀⠆⠀⢸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣝⣿⣽⣯⡲⡡⠀⠀⣸⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣰⣤⠠⡄⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡭⡌⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠼⡫⢍⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣤⣀⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠛⣛⡉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⡿⣟⣻⡿⠴⠀⠀⠀⠀⡿⠛⠁⠀⠀⠀⣂⣶⣾⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡿⣯⢿⠿⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡿⣛⡿⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⢀⣀⣀⠀⣠⠀⠀⠀⣀⣀⠀⢻⡟⣹⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⡄⣿⣿⢹⣿⡀⢸⣿⣿⣿⣿⠈⠈⠻⠀⢹⣿⣿⣿⡏⠈⣿⣿⣿⠀⣿⣿⣿⣿⣟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⣿⣿⣿⣿⣿⣿
⣤⣼⣯⠟⠛⢓⠚⢀⣿⣿⣿⣿⣿⣿⣗⣺⣿⣿⣾⣿⣿⣿⣿⣿⣿⢺⡇⣿⣿⣼⣿⣶⠛⠿⠋⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣿⣿⣿⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠓⠒⠒⠛⠛⡛⠛⣉⣉⣉⡉⣿⣿⡇⠉⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠿⠬⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠟⠷⡀⢀⡀⠀⢀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⢀⣠⣰⣙⣻⡷⠐⣿⣿⣿⡧⣿⣿⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⠟⣿⡾⠧⣄⠀⠀⢀⡀⠀⠀⠀⠈⠉⠁⠉⣿⣿⣿⣿⣿⠀⡴⠛⠓⠂⠁⢠⣾⣆⣠⠼⠿⢟⣿⣿⠟⠏⠛⠻⢿⣟⣫⢍⡧⠄⡀⠟⠛
⣿⣿⣷⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿⠿⢿⣿⣿⢀⣀⣶⣛⣛⣿⣯⣽⣿⣿⠠⠶⠂⠀⠀⠐⣿⣷⣶⡾⠿⠿⡿⠃⠐⠀⠉⠉⠉⣩⣿⣿⣿⠀⠂⠀⠀⠀⠀⣸⣿⣿⠀⣿⣿⣿⡏⠻⣤⣆⠀⣼⣼⣿⣯⣬⣧⣤⣷⣾⣿
⠿⠿⠿⠟⠛⠛⠛⠋⣉⠉⣿⣿⣿⣿⣾⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣾⠀⠀⠀⠀⢤⠈⢛⣯⣥⣼⣿⣷⣿⣧⣄⠀⠀⠙⢿⣁⡇⣿⣿⣿⣧⣮⣿⣿⣧⣽⣿⣿⣿⣿⣩⣿⡇⣿⣿
⣀⣀⣈⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣶⣶⣶⣶⣾⣿⣿⢛⡀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⣿⣿⣿⡿⢟⣿⣴⣾⣜⣏⣹⣇⠹⠟⣛⣯⣻⣿⣿⣿⣿⠓⡂⠈⠿⣿⢿⣇⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡷⣞⣿⡿⢻⣿⣿⣿⣿⣿⡟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⡿⠿
⣿⠿⠿⢿⣟⣛⣿⡏⣉⣁⣠⡤⠤⠄⠚⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢈⠀⠀⢀⣰⣤⡄⠀⠀⠀⢸⣿⣿⣇⣺⣅⣒⣼⣿⣿⣿⣿⣿⠇⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠈⠀⠀
⣮⣍⣉⡤⠥⢔⢻⣯⢉⣩⣤⢶⢒⠀⠈⠉⠛⠛⢶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠛⠛⠛⠛⠛⡟⠀⠀⠈⣠⣾⣿⣿⢇⡀⠀⠀⣼⣿⣿⣿⣿⣦⣀⣟⣃⣻⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⢯⣭⣿⣼⣿⣻⣿⣤⣦⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢀⣼⣿⣿⣿⣿⣿⣿⡂⠀⢻⣿⡿⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣉⢉⣀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⠟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠟⠛⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⠭⡹⠶⡝⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠇⠠⠅⢛⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡣⡡⢂⣬⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢝⣽⢰⢽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣞⢮⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡬⡾⠣⠐⣹⣿⣿⡿⠋⠀⠀⠀⠀⢀⡀⢀⣄⣠⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⣉⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣿⡾⡜⠌⠱⠀⠺⠟⠋⠀⠀⠀⠄⣠⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣈⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡿⠡⠊⠂⠀⠂⠀⠀⠀⠀⣐⣦⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣿⢿⢿⡞⠛⠙⡁⠁⠀⠀⠀⠀⠀⣂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⣀⣀⣠⡄⠀⡄⠀⢀⢀⣀⣀⣀⣿⠡⣧⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠈⠏⠈⣿⣿⣿⣿⠀⢸⣿⣿⣧⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢉⣿⣿⣿⣿⣿
⣷⣤⣿⣿⠋⠉⢥⣁⢸⣿⣿⣿⣿⣿⣿⣇⣾⢹⣇⣿⣿⣿⣟⣿⣿⣿⣿⠈⣿⣿⣿⣷⡏⡉⠋⠁⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣶⣾⣿⣿⣿⠸⢿⣿⣿⣯⠁⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠓⠛⠛⣋⣉⡉⢉⣭⣤⣤⢸⣿⣿⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡿⢶⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠛⡖⠀⡜⠀⠀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣻
⣀⣄⠀⠀⣠⣤⣥⣭⠿⠇⠸⣿⣿⣿⣾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣻⡇⠛⠛⠛⠿⠾⣰⣄⠀⠀⣤⣄⡀⣀⠀⠈⠉⠀⢈⣿⣿⣿⣿⣿⠀⠒⠛⠚⠈⠁⣼⣷⣤⠤⠿⣟⡛⣿⡿⠛⠙⠛⠿⣟⣛⡭⢩⠥⠀⡠⠛
⣿⣿⣿⣿⣿⣾⣿⣿⣶⣾⣯⣿⡿⢿⡟⣿⣿⣇⣠⣜⣛⣿⣯⣭⣽⣿⣿⡇⠰⠂⠀⠀⠀⢸⣿⣾⣿⡛⠛⠻⠛⠀⠀⠈⠉⢁⣀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡆⢸⣿⣿⣿⠛⢣⣤⡀⢠⣦⣿⣾⣧⣼⣤⣴⣷⣿
⠟⠛⠛⠛⠛⠛⢉⠉⠩⣍⣠⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⡇⠀⠀⠀⠲⡄⠙⣫⣭⣵⣾⣿⣾⣿⣤⡀⠀⠀⠹⣏⣹⢸⣿⣿⣿⣶⣼⣿⣿⣴⣿⣿⣿⢿⣏⣽⣿⡤⢿
⣀⣠⣤⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣶⣶⣶⣶⣶⣿⣞⠋⣀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣽⣿⡿⠿⣻⣷⣶⣧⣹⣉⣿⡌⠟⢛⡛⣝⣽⣿⣿⣿⡟⣓⠀⠸⠿⡿⢯⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⡟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠊⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢾⣻⣿⠟⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⠿
⡿⠿⣟⣛⣻⠿⠭⣽⣉⣠⣤⣤⠤⠒⠒⣣⣿⣿⣧⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡁⠀⠄⠀⠀⣰⣶⣤⠀⠀⠀⠀⣿⣿⣿⣰⣯⣐⣢⣿⣿⣿⣿⣿⡟⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠁⠀
⣿⣭⣥⣤⡜⡒⢟⣿⡇⣤⣤⡴⣏⡁⠀⠁⠈⠛⠻⣾⣿⣿⣿⣿⣿⡧⣰⣦⣿⣿⣟⠛⠛⠛⠛⢻⠁⠀⠀⣠⣶⣿⣿⣏⣀⠀⠀⣼⣿⣿⣿⣿⣧⣄⣹⣋⣘⣿⣿⣿⣷⣾⣿⣷⣷⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠿⠿⣷⢼⣷⣛⣿⣭⣷⣶⡆⠀⠀⠀⠀⠀⠈⠉⠛⠻⠟⠁⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⠆⢀⣠⣿⣿⣿⣿⣿⣷⠓⠀⠘⣿⡿⠿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢭⣄⣠⣤⣴⡆⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠛⠛⠛⠉⠁⠹⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡷⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡽⡪⣿⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⢏⡩⡏⡘⠀⣸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠂⠀⠀⣾⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡴⣠⡌⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢟⡥⢅⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡱⠂⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⢀⣠⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠉⢭⢥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣏⡛⠤⠠⠀⢺⡿⠛⠁⠀⠀⡠⣢⣶⣶⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⡿⠹⠀⠈⠀⠀⠀⠀⠀⠐⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡻⣽⣿⣿⠁⠋⣀⡀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⣀⣄⣤⡄⢠⠄⠀⣀⣠⣤⣀⣸⣿⢼⡿⣿⠿⢿⣿⣿⣿⣿⣾⣾⡇⢿⣿⣿⣿⡄⢸⣿⣿⣿⣿⡇⠁⠙⠃⠹⣿⣿⣿⣿⠀⢹⣿⣿⡇⢸⣿⣿⣿⣷⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢁⣿⣿⣿⣿
⣿⣷⣶⣿⣞⠉⠩⣍⡀⣽⣿⣿⣿⣿⣟⣿⣨⡇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣷⣿⣿⢉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣶⣾⣿⣿⡇⠺⣿⣿⣿⣄⠁⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠋⠉⣉⣉⠉⣭⣤⣤⡄⣿⣿⣷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⡟⠃⠆⠀⡂⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡋
⣤⣤⡄⡀⠀⣤⣤⣭⡮⠻⢀⢹⣿⣿⣷⣻⣿⣿⠀⠀⢭⣿⣿⣿⣿⣇⣻⣿⠘⠛⠛⠻⠿⢃⣦⡀⠀⣠⣤⣀⣀⡀⠀⠉⠁⠀⣸⣿⣿⣿⣿⡇⠐⠒⠓⠁⠀⢠⣶⣦⠤⠴⢿⣛⣻⣿⡿⠛⠙⠋⡿⣛⣫⡍⣩⠅⢀⠈
⣻⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⢿⣿⠻⣿⣿⡆⣤⣿⣿⣯⣭⣽⣿⣿⣿⡄⠚⠁⠀⠀⠸⣿⣿⣿⣟⠛⣛⠟⠁⠀⠈⠈⢀⣀⣤⣿⣿⣿⡇⠀⡀⠀⠀⠀⢸⣿⣷⠀⣿⣿⣿⡟⠙⣦⣤⡀⢠⣽⣷⣿⣤⣿⣤⣼⣶
⠛⠛⠛⠛⠛⠋⣉⡉⠉⢥⡀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⠀⠀⠀⠐⢦⠈⢻⣭⣭⣶⣿⣿⣿⣧⣆⠀⠀⠈⢿⣉⡅⣿⣿⣿⣷⣦⣿⣿⣿⣼⣿⡿⡟⣿⣟⣹⣿⠰
⣇⣠⣤⣤⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⠏⠀⠀⣶⣶⣶⣶⣶⣾⣷⠙⢡⡀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⠿⢛⣿⣶⣾⣌⣏⣹⣧⠸⠛⣛⢩⣩⣿⣿⣿⣿⢟⡒⢀⠽⢿⡿⣭⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⡷⣟⣿⡿⢿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿
⣿⡿⣛⣛⡛⠿⠭⢽⣧⣠⣤⡤⠤⠒⠒⣊⡝⣿⣿⡎⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠠⠀⠀⣠⣶⣦⠀⠀⠀⠀⢸⣿⣿⣇⣾⣅⣂⣼⣿⣿⣿⣿⣿⠂⢛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀
⣿⣷⣶⣤⣔⣒⢺⣩⣿⢠⣤⣴⢺⡁⠀⠀⠀⠙⠛⢷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⠛⠛⠛⠛⠛⢻⡿⠀⠀⢀⣴⣿⣿⣿⣀⠀⠀⢠⣿⣿⣿⣿⣿⣄⣈⣛⣁⣻⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠿⠟⢓⣦⣿⣿⣿⣭⣽⣶⣦⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⣠⣾⣿⣿⣿⣿⣿⠞⠀⠈⢿⣿⠿⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠥⣶⣄⣤⣴⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠛⠋⠉⠉⠀⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠻⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣉⠝⠥⣿⠇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⠻⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣫⣟⢌⠢⠅⢀⢰⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣽⣿⣿⣷⢯⣗⢬⣒⠁⢸⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣽⡽⢧⢀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡏⠟⣜⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢲⠀⡀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠩⣀⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣝⣿⣿⣽⡟⠎⠠⠀⠀⣿⠟⠋⠀⠀⠀⠠⣦⣵⣿⣾⣷⣿⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡯⣯⣿⣽⠯⡹⠐⠁⠈⠀⠀⠀⠀⠀⠀⢀⣔⣲⣾⣿⣿⣿⣿⣿⣿⣿⡗
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣻⡿⠇⠁⠂⠁⠀⠀⠀⠀⠀⠀⢄⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⢀⣠⣄⣤⠀⢤⠀⢀⣀⣄⣄⣀⣿⡧⢻⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⠀⠈⠙⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⣿⡋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⣿⣿⣦⣾⣿⡟⠉⠩⣉⠠⣿⣿⣿⣿⣿⣻⣇⣾⢸⣧⣿⣿⣿⣟⣿⣿⣿⣿⡄⣿⣿⣾⣷⡏⠉⠉⠁⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣷⣶⣿⣿⣿⠀⠿⣿⣿⣷⡂⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠋⠉⣉⡉⠉⣭⣤⣤⢸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠛⠕⠅⠀⠀⠀⢠⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛
⢀⣤⣤⡀⠀⢀⣤⣤⣥⡼⠇⠀⣿⣿⣿⡎⣿⣿⡇⠀⠨⣭⣿⣿⣿⣿⣝⣻⡇⠙⠛⠛⡿⠶⣰⡄⠀⠀⣤⣀⡀⢀⠀⠈⠉⠁⢀⣿⣿⣿⣿⣿⠀⠒⠚⠒⠀⠀⣼⣶⡄⠤⠾⠟⣛⣿⣿⠟⠋⡟⠹⢟⣟⣩⠍⡭⠀⢀
⣿⣿⣿⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⡿⢿⣟⢿⣿⣷⢠⣬⣿⣿⣭⣭⣽⣷⣿⣷⠐⠞⠀⠀⠀⣿⣿⣾⣿⡛⠛⠿⠇⠀⠀⠈⠀⣀⣀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡖⢸⣿⣿⣿⡏⢻⣤⢄⠀⣼⣼⣷⣿⣤⣧⣤⣾
⡿⠛⠛⠛⠛⠛⠉⣉⠉⠉⣄⢀⣿⣿⣿⣿⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⡇⠀⠀⠀⢲⡄⠙⣯⣭⣵⣾⣿⣾⣿⣤⡀⠀⠀⠙⡏⣩⠸⣿⣿⣿⣶⣼⣿⣿⣧⣿⣿⢿⢿⣿⣉⣿⡇
⣿⣀⣤⣤⣤⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡿⠃⠀⣶⣶⣶⣶⣶⣶⣷⡌⠋⡀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣯⣿⣿⡿⠟⣻⣷⣶⣧⣹⣉⣿⡄⠿⠛⡛⣝⣽⣿⣿⢿⡿⠓⡂⠀⠿⡿⠏⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠿⢟⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⢘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⢾⣻⣿⠿⣿⣿⣿⣿⣿⡿⢳⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿
⣿⣿⠿⣛⣛⠻⠯⠭⣿⣅⣤⣤⠤⠔⠒⢒⣩⢹⣿⣿⢸⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⡇⢳⡁⠀⠄⠀⢀⣴⣶⡄⠀⠀⠀⠀⣿⣿⣿⣸⣭⢐⣠⣿⣿⣿⣿⣿⡇⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈
⣿⣿⣷⣦⣤⣖⠒⣋⣹⣇⢤⣤⡖⣏⠀⠀⠈⠈⠛⢻⣾⣿⣿⣿⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢸⡧⠀⠀⣠⣾⣿⣿⣃⡀⠀⠀⣼⣿⣿⣿⣿⣧⣀⣹⣃⣘⣿⣿⣿⣷⣾⣿⣷⣷⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀
⣿⣿⣿⣿⠿⠿⠛⣲⣼⣿⣾⣯⣭⣿⣶⡄⠀⠀⠀⠀⠁⠈⠉⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢂⣀⣴⣿⣿⣿⣿⣿⡷⡃⠀⠹⣿⡿⠿⢿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢤⣦⣤⣤⣶⡆⣽⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡗⠦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠚⠿⠙⠛⠉⠉⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣝⣽⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣍⡀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⣕⢫⡪⢅⠁⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠹⢿⣿⣿⣿⣻⣿⣿⣿⡿⢛⠛⠃⠀⠈⠀⠀⣻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣯⡶⠢⢀⠀⠀⠀⣿⣿⣿⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡅⠡⣐⠀⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⢼⡎⠄⢤⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⢿⣿⡀⢀⠄⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣻⣽⠏⢜⠂⠃⠀⠀⠀⢸⡿⠟⠁⠀⠀⠀⠀⢀⣤⣤⣶⣦⢠⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡏⠿⣿⡟⢇⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣾⣿⣿⣿⣿⣿⣿⡆
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⢵⣓⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⡀⠀⠀⠀⠀⣀⣀⡄⠠⡄⠀⠀⢀⣀⣀⣸⣿⠻⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠃⠙⠇⠀⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣾⣿⣿
⣿⣿⣧⣤⣿⠿⠛⠛⠑⡁⢸⣿⣿⣿⣿⣿⣿⣠⣧⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢸⣿⣷⣿⣾⠉⠉⠋⠉⠉⠁⠀⠀⢀⣀⣿⣿⣿⣿⣤⣾⣿⣿⡇⠸⢿⣿⣿⣧⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠒⠛⠛⠛⣉⠉⢉⣍⣁⡀⢿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣯⣿⣿⢸⣿⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⠻⠂⠀⢀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛
⡆⣠⣤⣤⠄⠀⣠⣤⣭⣠⠿⠂⢸⣿⣿⣿⢸⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠛⢻⣷⢂⡄⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⠈⢸⣿⣿⣿⣿⡇⠐⠒⠓⠒⠈⢀⣶⣦⢠⠤⠿⢟⣻⣿⡿⠛⠹⠛⠿⣿⣛⡭⢉⡭⠀
⣿⡾⣿⣿⣿⣿⣻⣾⣿⣿⣶⣿⣿⣿⡿⢿⠿⣿⣿⡇⣠⣘⣛⣿⣯⣭⣿⣿⣿⡇⠲⠒⠀⠀⢸⣿⣦⣶⡾⠿⠿⡿⠂⠂⠀⠈⠉⣁⣀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡂⣿⣿⣿⣿⠙⣧⣄⡀⢠⣧⣿⣾⣧⢼⣤⣤
⣿⡿⠿⠟⠛⠛⠛⢛⠉⠉⢉⣁⣸⣿⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣶⠀⠀⠀⠰⣄⠘⢛⣭⣭⣾⣿⣷⣿⣧⡄⠀⠀⠈⢿⢍⡁⢿⣿⣿⣿⣤⣿⣿⣿⣬⣿⣿⣿⣿⣯⣩⣿
⣿⣷⣀⣤⣤⡸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡟⠀⣶⣶⣶⣶⣶⣶⣷⡝⠛⡉⠁⠈⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⡿⢟⣿⣴⣾⣘⣎⣹⣧⠸⠟⢛⢫⣋⣿⣿⣿⣿⠿⠒⠀⠸⣿⡿⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⡿⠿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡟⣧⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡷⣞⣿⡿⢿⣿⣿⣿⣿⣿⠟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣿⣿
⣿⣿⡿⠿⣛⣛⣻⠯⠭⣿⣁⣤⣤⡤⠔⠒⣒⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⡀⠁⡀⠀⠀⣠⣶⣤⠀⠀⠀⠀⣽⣿⣿⣇⢯⡅⢂⣾⣿⣿⣿⣿⣿⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉
⢿⣿⣿⣵⣤⣤⡚⠒⣟⣿⡄⣤⣤⢾⡀⠀⠁⠀⠛⠛⣷⣿⣿⣿⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⣷⠀⠀⢀⣤⣿⣿⡟⣀⠀⠀⢠⣿⣿⣿⣿⣿⣀⠸⣝⢉⣻⣿⣿⣿⣴⣾⣿⣶⣼⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀
⣾⣿⣿⣿⣿⠿⠿⠟⣦⢿⣗⣻⣯⣽⣷⣆⠀⠀⠀⠀⠉⠈⠉⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⣠⣾⣿⣿⣿⣿⣷⢗⠀⠘⣿⣿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠩⣤⣄⣤⣤⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡿⠿⠛⠛⠋⠉⠀⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣝⣷⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⡇⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣿⣿⣯⣍⡉⠉⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⠻⠟⢙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⡙⠛⠃⠐⠀⢰⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣺⣮⠦⠀⠂⠂⠀⢸⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢐⢀⠂⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠕⠂⠔⠀⠂⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡋⠼⠅⠁⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠭⢥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡻⠿⣓⠉⠁⠠⠐⠀⠀⣿⡿⠛⠁⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣟⢿⡿⠗⠈⠁⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⡾⠄
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣿⡳⠭⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⡀⠀⠀⢀⣀⠀⢸⣿⠉⡟⣿⢿⣿⣿⣿⣶⣾⣸⣹⡇⢻⣿⡆⣿⡆⢸⣿⣿⣿⣿⡇⠁⠙⠇⠁⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⣷⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿
⣿⣷⣶⣶⣀⣿⣿⠟⠛⡂⠃⢰⣾⣾⣿⣿⡿⣿⠠⡇⣿⣴⣾⣿⣿⣿⣿⣿⣿⣧⢸⣿⣇⣿⣴⠈⠙⠛⠛⠛⠇⠀⠀⠀⢀⣿⣿⣿⣿⣤⣼⣿⣿⡇⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠦⠖⠚⠓⠚⠛⢛⣉⣉⡉⣿⣿⣷⠉⠙⣿⣿⣿⣻⣿⣯⣯⣿⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⠛⠀⠀⡀⠀⠀⣐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣀⣀⣀⠀⠀⢀⣀⣀⣀⣹⠀⢸⣿⣿⣷⢹⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠘⠿⠟⢻⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢹⣿⣿⣿⣿⡇⠀⠐⠛⠒⠀⢀⣶⣧⣀⠤⠿⠿⢻⣿⡿⠛⠹⠛⠿⣿⣛⡭⢉⡭
⣿⣿⡾⣿⣿⣾⣶⣾⣽⣿⣿⣶⣶⣾⣿⣿⡿⠾⣿⣿⡆⣀⣰⣞⣛⣛⣿⣭⣭⣿⡄⠖⠀⠀⢰⣿⣄⣠⣤⣶⣦⣤⠆⠀⠐⠀⠀⠉⠈⢉⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⣾⣿⣿⡿⠻⣦⣐⡀⢠⣆⣿⣿⣧⢼⣥
⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⢹⣷⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣬⠉⠀⠀⠠⢤⡄⠻⣛⣙⣮⣽⣿⣷⣿⣦⡀⠀⠀⠘⢿⢁⡆⣿⣿⣿⣷⣤⣿⣿⣿⣬⣽⣿⣿⢿⡉⡉
⣿⣿⣷⢀⣀⣀⣰⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⠋⠀⣶⣶⣶⣶⣶⣶⣿⡛⢿⠛⠋⠛⠀⠀⠀⠀⠈⠁⠰⣿⣿⣿⣻⣿⣿⡿⢿⣿⣤⣶⡐⡎⣹⠇⠻⠿⢛⢛⣋⣿⣿⡿⣿⠿⠶⠀⠸⣿⡿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⢸⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡟⡇⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⢵⣖⣿⡿⣿⣿⣿⣿⣿⣿⢷⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣛⣛⣿
⣄⣿⣿⣿⠿⠿⢿⣛⡛⠿⣿⢉⣉⣠⣤⠤⠤⠒⡏⣿⣿⡎⣿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⠀⠂⠁⠀⠀⠀⣦⣤⡄⠀⠀⠀⠀⣿⣿⣿⣬⣯⡡⢆⣿⣿⣿⣿⣿⣿⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠉⢻⣿⣿⣭⣭⣥⠤⠔⣒⣿⡉⣩⣤⢴⠀⠀⠉⠑⠻⠟⣷⣿⣿⣿⠇⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢸⡇⠀⠁⠂⣀⣼⣿⣿⠃⠀⠀⠀⣴⣿⣿⣿⣿⣯⣍⡹⠟⠙⣻⣿⣿⣧⣤⣾⣷⣦⣼⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀
⣶⣼⣿⣿⣿⣿⡿⠿⠿⣭⢿⣗⣟⣻⣭⣧⡄⠀⠀⠀⠀⠋⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣴⣿⣿⣿⣿⣿⣧⡀⠀⢿⣿⡿⠿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⡟⢉⢭⣅⣀⣤⣴⣘⣻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣶⣤⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡧⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⡇⣶⠎⠝⠛⠛⠋⠁⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠛⢰⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀
⢹⡇⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⠻⠿⣿⣿⠿⠿⠟⠙⠛⠋⠉⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⠫⠁⠉⠀⠄⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣻⣽⠞⢔⢈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣻⣿⣖⠈⠁⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠠⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⣟⡄⠅⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣷⠲⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠉⠩⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠛⡗⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⡻⠱⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠦⡬⣿⡜⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠠⢓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣽⣿⣿⣿⠄⠀⠀
⣇⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⡀⡀⠀⣿⣏⢹⢻⡿⣿⣿⣿⣧⣾⡇⡇⣿⢸⣿⣷⢹⣧⠀⣿⣿⣿⣿⣿⠀⠈⠟⠈⢸⣿⣿⣿⡇⠈⣿⣿⣿⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿
⣿⣿⣶⣶⣆⣐⣿⡿⠛⢓⠘⠀⣶⣷⣿⣿⣿⢿⡇⣼⢸⣇⣶⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣸⣷⡖⠋⠉⠙⠛⠿⠀⠀⠀⠀⣸⣿⣿⣿⣧⣤⣿⣿⣿⠀⣿⣿⣿⣯⡅⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⠿⠷⠴⠖⠛⠒⠛⠛⣋⣉⣉⢹⣿⣿⡎⠁⢻⣿⣿⣟⣿⣿⣽⣽⡆⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠟⠇⠀⠀⠀⠀⢀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣀⣀⣀⡀⠀⠀⣀⣀⡀⣘⡇⠀⣿⣿⣿⡜⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠛⢇⡀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠈⠉⠉⠉⣿⣿⣿⣿⣿⠀⠐⠚⠒⠂⠀⣴⣶⡄⡤⠼⠿⠛⣿⣿⠟⠋⠟⠻⢟⣟⣫⠍⣩
⣿⣿⣷⢿⣿⣷⣶⣶⣯⣿⣿⣷⣶⣶⣿⣿⣿⠷⣿⣿⣧⢀⣐⣶⣛⣛⣿⣭⣭⣽⡇⠀⠀⠀⣸⣿⣄⣤⣼⣶⣦⣤⠂⠀⠐⠀⠀⠉⠉⠉⣹⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⡇⢸⣿⣿⣿⠏⢳⣤⣀⠀⣼⣼⣷⣿⡤⣭
⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⢋⠉⠉⣿⣿⣿⣿⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢹⣿⣿⣿⣧⣤⣬⠁⠀⠀⠠⠤⣤⠘⢟⣋⣧⣽⣿⣿⣾⣧⣄⠀⠀⠘⠻⡏⣰⢸⣟⣿⣿⣤⣼⣿⣿⣣⣬⣿⣿⡿⣿⣉
⠸⣿⣿⡆⣀⣀⣀⣶⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⡿⠁⠀⣶⣶⣶⣶⣶⣶⣿⡛⠻⠉⠈⠛⠀⠀⠀⠀⠀⠉⠀⢿⣿⣿⣻⣿⣿⡿⠿⣿⣤⣶⣖⢲⣉⣿⠸⠿⠟⡛⣛⣹⣿⣿⢿⡿⠗⠆⠀⢿⡿
⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⡇⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⡿⡇⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⣶⣿⣿⢿⣿⣿⣿⣿⣿⡟⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻
⣷⣸⣿⣿⡿⠿⠿⣛⣛⠻⢿⡏⣉⣀⣤⡤⠤⠒⢺⢻⣿⣷⢹⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢠⠂⠀⠃⠀⠀⢀⣷⣶⡄⠀⠀⠀⢀⣿⣿⣿⣧⣽⡍⠰⣸⣿⣿⣿⣿⣿⠇⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠉⠉⣿⣿⣯⣭⣭⡤⠄⠒⣻⣏⣩⣥⡤⡆⠀⠉⠉⠺⠟⢿⣾⣿⡟⠀⠀⢰⣷⣿⡛⠛⠛⠛⠛⠃⠈⠂⠀⠁⠂⣠⣿⣿⣿⢁⡀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡽⠟⠉⣻⣿⣿⣿⣤⣶⣿⣶⣤⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀
⣶⣶⣿⣿⣿⣿⣿⠿⠿⢿⡭⣿⣺⣛⣯⣽⣄⠀⠀⠀⠀⠘⠉⠙⠁⠀⢠⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⡆⠀⠀⣸⣿⣿⣿⣿⣿⡷⡆⠀⠻⠿⠟⢙⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⠋⢩⣭⣀⣠⣤⣆⣹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⡥⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣡⣤⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⡶⡮⠽⠛⠛⠋⠉⠸⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠙⠆⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀
⡃⣿⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠛⠍⠌⠊⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢿⣻⣽⣏⢜⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠠⣢⢁⡀⡀⠀⠀⠀⠀⠀⣿⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⡯⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣻⣽⣿⣻⢝⣃⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣟⣭⢷⠯⡾⠄⠂⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢉⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣓⣿⡷⠹⠰⡍⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢏⠯⢁⢎⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣐⣶⣔⡖⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠃⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣴⣿⣿⣾⡍⠀⠀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢸⣿⠹⡾⣿⣿⣿⣿⣿⣶⣿⣸⢸⡇⣿⣿⡘⣿⡀⢸⣿⣿⣿⣿⡇⠀⢹⠃⢹⣿⣿⣿⡏⠀⣻⣿⣿⡇⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸
⣿⣿⣷⣶⣶⣀⣺⣿⠿⠛⡢⠃⢰⣾⣾⣿⣿⡿⣿⢰⡇⣿⣰⣾⣿⣿⣿⣿⣿⣿⡇⢻⣿⣟⣯⠖⠈⠉⠙⠻⢿⡇⠀⠀⠀⢈⣿⣿⣿⣿⣤⣾⣿⣿⡇⢼⣿⣿⣿⣥⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⠿⠿⠤⠶⠾⠓⠚⠛⢛⣋⣉⡉⣿⣿⣧⠉⠙⣿⣿⣿⣻⣿⣿⣿⣷⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⠛⠀⡀⡠⠀⠀⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣐⢈⣻⠀⢸⣿⣿⣧⢻⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠸⠿⠟⣀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠄⠀⠉⠁⠉⢹⣿⣿⣿⣿⡇⠠⠘⠓⠂⠀⢠⣶⣦⣀⠤⠿⠟⢻⣿⡿⠛⠹⠛⠿⣿⣛⡭⢉
⢻⣿⣿⡾⣿⣿⣶⣶⣿⣽⣿⣷⣶⣶⣾⣿⣿⡿⢾⣿⣿⡀⣀⣶⣾⣛⣻⣿⣭⣭⠟⠀⠀⠀⣿⣧⣠⣤⣾⣶⣤⡖⠀⠀⠀⠀⠂⠀⠉⠉⢉⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣷⢰⣿⣿⣿⡞⠻⣦⣀⡀⢠⣦⣿⣿⣧⢬
⣸⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⡛⠋⠉⢹⣿⣾⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⢿⣿⣿⣿⣦⣤⡎⠀⠀⠈⠡⠤⣤⠀⠻⣛⣛⣯⣿⣿⣷⣿⣤⠀⠀⠀⠛⢿⣁⡎⣿⣿⣿⣧⣤⣿⣿⣟⣬⣽⣿⣿⢿⡏
⡀⢿⣿⣷⢀⣀⣀⣰⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⠟⠀⠀⣶⣶⣶⣶⣶⣾⣿⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⣼⣿⣟⣻⣿⣿⣿⡿⢿⣧⣴⣆⠲⡋⡹⡇⠿⠿⢛⣛⣋⣿⣿⡿⣿⠿⠶⠀⠘⣿
⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠴⢿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⢦⣶⣿⣿⣿⣿⣿⣷⣷⣿⣿⣟⣛⣛
⣿⣆⣿⣿⣿⠿⠿⢿⣛⡛⢿⣯⢉⣉⣠⣤⠤⠄⠚⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⡇⢃⠊⠀⡀⠀⠀⣸⣿⣶⠀⠀⠀⠀⣸⣿⣿⣿⣿⣼⣏⠥⢰⣿⣿⣿⣿⣿⡧⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⢹⣿⣿⣭⣫⣥⠤⠜⣚⣿⢉⣭⣤⢴⠀⠈⠉⠃⢿⢻⣿⣿⣿⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠃⢘⠀⠀⠀⢁⣴⣿⣿⣿⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⠿⠋⢛⣿⣿⣿⣧⣴⣿⣶⣦⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀
⣶⣶⣾⣿⣿⣿⣿⡿⠿⠿⣯⢿⣷⣟⣿⣽⣧⠀⠀⠀⠀⠈⠋⠙⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⣸⣿⣿⣿⣿⣿⡿⠁⡄⠙⣿⣿⡿⢿⣿⣿⣷⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀
⣿⣿⡏⠉⣭⣅⣀⣤⣴⣘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⣾⣴⣈⠉⣿⣟⣳⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣾⠿⠟⠛⠛⠉⠉⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⠷⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣸⡇⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠙⠹⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢭⠟⣬⣅⠡⠉⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣠⣴⡡⠂⠐⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣇⢺⣛⣟⣇⣀⡐⣠⠀⠀⣿⣿⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡳⣉⡔⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠗⣡⡆⠔⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⡟⡨⣊⡀⠈⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⡭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⡿⣻⣝⡻⡥⠔⠐⡢⠀⠀⢲⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⡿⡷⣽⠐⠹⣽⠀⠊⠀⠁⠁⠀⠈⠋⠀⠀⠀⠀⠀⢠⣠⣤⠠⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢿⣂⠫⠅⠈⠐⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣬⣿⣷⢭⠀⠀⠀
⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠟⣇⣿⣼⣿⣿⣿⣿⣿⣷⣿⣷⢸⣿⣿⣿⡆⠀⣿⣿⣿⣿⡇⠀⠘⠏⠀⣿⣿⣿⣿⠉⢹⣿⣿⣿⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣶⣶⣄⣰⣶⡿⠿⠦⠜⠀⣦⣶⣿⣿⣿⣿⡆⢼⢸⡇⣾⣿⣿⠿⣿⣿⣿⣿⢸⣿⣯⠟⠁⠀⠉⠙⠻⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣤⣼⣿⣿⡿⢸⣿⣿⣿⣭⡍⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾
⣿⣿⣿⣿⣿⣿⠿⠷⠦⠤⠬⠾⠒⠛⠛⣛⣋⡉⢹⣿⣿⠈⠁⠻⣿⣿⣿⣿⣿⣿⣿⠈⣿⡟⠀⠀⠀⠀⠀⠀⠘⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣿⣿⠿⠰⠀⠐⠀⠀⢀⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⡀⢀⣀⣀⠀⠀⣀⣀⠀⡚⡆⠈⣿⣿⣿⣼⣿⣿⡆⠀⢹⣽⣿⣿⣿⣿⡹⣿⡄⠿⢇⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠙⠛⠈⢹⣿⣿⣿⣿⣿⠀⠤⠝⠙⠀⠀⣴⣤⣀⣀⢼⠿⠿⣿⣿⡿⠛⠟⢻⠿⠿⢛⡋
⠘⣿⣿⣧⢿⣿⣧⣶⡾⣭⣿⣿⣦⣶⣖⣿⣿⣿⡷⣿⣿⡇⣀⡸⠿⣿⣛⣛⣿⡯⠉⠁⠀⢸⣿⣤⣶⡾⠿⠶⡾⠁⠁⠀⠠⠀⠒⠀⠀⠉⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⣶⣾⣿⣷⠻⢧⣈⡀⠀⣀⣸⣿⣿⣀
⣅⣿⣿⣿⣾⠿⠿⠿⠿⠿⠛⠛⢛⠋⠉⣿⣷⣾⣷⣿⣿⣷⢹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⢿⣿⣿⣷⢶⣶⠀⠀⠀⠀⠣⠤⢤⡀⠺⢟⣛⣫⣽⣿⣿⣾⣦⡀⠀⠀⠘⢿⡟⡂⣿⣿⣿⣿⣠⣸⣿⣾⣢⣽⣿⣿⣿⡿
⣉⠸⣿⣿⡄⢀⣀⡀⣶⣿⣿⣤⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠏⠀⠀⣶⣶⣶⣶⣶⣶⣿⠉⠁⡀⠈⠀⠀⠀⠀⠀⠈⠙⢳⣿⣟⣻⣿⣿⣿⣿⣿⢿⣷⣤⣶⠐⡞⢻⣇⢸⠿⠿⢛⣚⣻⣿⣿⣿⡿⠧⠌⠀⣻
⣿⡄⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠘⢧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢽⢶⣿⡿⣿⣿⣿⣿⣿⣿⢶⣴⣾⣿⣿⣿⣻⣿⣾⣷⣾⣶⣒⣒
⣿⣧⣹⣿⣿⡿⠿⠿⣿⣛⡛⣿⡉⣉⣁⣠⡤⠤⢽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣇⠀⢈⠀⠀⠀⣼⣶⡦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⣟⡫⠄⣿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠙⣿⣿⣯⣍⣩⡤⠤⠒⣻⡏⣉⣥⡴⡂⠀⠉⠙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢹⠀⠀⠀⢀⣼⣿⣿⣇⡤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢻⠛⠹⣻⣿⣿⣧⣴⣶⣦⣤⣼⣿⣿⣿⣿⣿⡿⠟⠋⠉
⣴⣶⣦⣿⣿⣿⣿⣿⠿⠿⣭⡽⣷⣿⣛⣿⣧⡄⠀⠀⠀⠉⠛⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⢀⣼⣿⣿⣿⣿⣿⡻⠀⠎⣹⣿⣿⣿⢿⣿⣿⣧⡜⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀
⣿⣿⣿⠉⣩⣭⣀⣀⣤⡔⣹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠢⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⢲⣿⣿⣿⣿⣿⣿⣿⡟⣺⣾⡟⠛⠿⢿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⡾⠯⠛⠛⠋⠁⠹⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠯⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣋⣿⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠉⠡⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢿⣟⣿⡏⠋⠂⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣏⠩⢁⠁⠠⠂⠀⠀⠀⠀⠀⢸⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⢫⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡧⢑⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⠉⠩⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⡨⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⡏⡒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠨⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢔⣭⣓⡉⠀⠀⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢻⢸⣧⣿⣿⣿⡿⠿⣿⣿⣿⠈⣿⣿⣻⣿⠀⢿⣿⣿⣿⣿⠀⠀⢻⠀⢸⣿⣿⣿⡏⠉⣿⣿⣿⠀⣿⣿⣿⡇⡠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣷⣶⣴⣆⣀⣶⣿⠿⠧⠬⠁⣰⣶⣿⣿⣷⢾⡇⠸⡸⣧⣿⣿⣿⣿⣿⣿⢹⢿⡄⣿⡿⠈⠉⠀⠉⠙⢿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣇⣠⣿⣿⣿⠀⣿⣿⣿⣇⡉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⢻⣿⣿⣿⣿⣿⣿⡿⠷⠤⠤⠵⠶⠟⠛⠛⠛⠋⠙⣿⣯⡇⠉⠉⣿⣿⣿⣿⣿⣺⣻⡇⣿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡿⠃⠄⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⡆⠀⣀⣀⡀⠀⢀⣀⠀⠀⠣⠀⢿⣿⣿⡇⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣽⡇⠹⢀⠀⠀⠀⣀⠀⠀⢀⣿⣿⣿⢃⠈⠙⠛⠋⠋⣿⣿⣿⣿⣿⠀⠠⠭⠍⠀⠀⣠⣤⡀⣀⣠⡿⠿⣿⣿⡿⠟⠻⠟⡿⠿⢟⡛
⠀⢿⣿⣷⣽⣿⣷⣶⣶⢯⣽⣿⣧⣤⣶⣸⣿⣿⣷⢿⣿⣿⠀⡀⠿⠿⢿⣛⣛⡛⠋⠁⠀⣿⣷⣴⣶⠟⠛⠾⠏⠁⠉⠉⠄⠠⠀⠀⠀⠀⠉⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡅⣰⣶⣶⣷⡝⠿⣀⠀⠀⢀⢲⣿⣽⣇
⣭⣸⣿⣿⣷⡿⠿⠿⠿⠾⠟⠛⠛⠛⠉⣹⣿⣶⣶⣼⣿⣿⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣶⢾⡇⠀⠀⠀⠀⠶⣄⣀⡀⠰⠶⣛⣋⣭⣿⣿⣶⣆⡀⠀⠀⠨⢿⡏⢡⢸⡿⣿⣿⣄⣠⣿⣿⣆⣉⣿⣿⡿⣷
⣉⡀⣿⣿⣇⠀⢀⡀⢰⣶⣶⣦⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⠏⠀⠀⣶⣶⣶⣶⣶⣶⣷⠉⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⡠⢄⠓⣿⢸⣿⠿⠿⡻⢻⣿⣿⣿⢿⡯⡍⠁⢻
⣿⣇⢹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠻⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⣿⣯⣿⣿⣿⣯⡵⣾⣿⣿⣿⣿⣿⣿⣾⡶⣠⣤⣷⣿⣿⣿⣿⣾⣵⣶⣶⡶⠖
⣿⣿⣘⣿⣿⣿⠿⠿⠿⣟⣛⢻⡏⢉⣉⣀⣨⠤⠤⢘⢻⣿⣷⢹⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⢈⠀⠀⢀⣷⣶⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⣟⡋⡅⣼⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⠉⢿⣿⣧⣭⣉⡥⠤⢔⢺⣯⢉⣉⣥⡆⠀⠈⠉⠸⣿⣿⣾⣿⣿⣷⣤⡀⠛⠛⠛⠛⠛⠛⠋⠇⠀⠀⠈⢠⣾⣿⣿⣣⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢰⡿⠛⢛⣿⣿⣿⣀⣤⣶⣬⣈⣿⣿⣿⣿⣿⣿⠿⠛⠋
⣤⣶⣶⣼⣿⣿⣿⣿⡿⠷⢯⡭⣿⢸⣟⣓⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢰⡀⠀⢀⣿⣿⣿⣿⣿⣿⠃⢀⠊⣹⣿⣿⣿⠿⣿⣿⣧⡴⢲⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀
⣿⣿⣿⡋⠉⣭⢁⣀⣤⣤⢘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢘⡤⣴⣿⣿⣿⣿⣿⣿⣿⡗⣪⣾⡿⠛⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣧⡴⠏⠟⠛⠉⠉⠸⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠉⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣇⣿⠀⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠡⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢍⠀⠓⠨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⠋⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⡂⡉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢆⠀⡗⡐⠀⡡⠂⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠁⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⡆⣿⣼⣾⣿⣿⠉⢻⠹⢸⡇⣿⣿⠉⢿⠅⢸⣿⣿⣿⣿⡇⠀⠿⠇⠁⣿⣿⣿⣿⠛⢻⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⢹⣿⣿⣶⣦⣶⣀⣰⣾⡿⠿⠤⠏⠠⣶⣾⣿⣷⡶⣿⠀⡇⣿⠨⣿⣿⣿⣿⣿⡆⣾⡇⢸⣿⠇⠉⠁⠈⠛⢿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣀⣸⣿⣿⡇⢸⣿⣿⣿⣘⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀
⡘⣿⣿⣿⣿⣿⣿⣿⠿⠦⠤⠬⠶⠼⠛⠛⠛⠛⠋⣿⣿⣧⠉⠉⣭⣿⣿⣿⣿⣟⣟⣇⢸⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⠟⠀⠀⠀⠀⠀⠨⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣷⠀⠀⣀⡀⠀⠀⣀⡀⠀⠠⠄⢸⣿⣿⣧⢹⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⠀⣀⠀⠀⠀⣀⡀⠀⣠⣿⣿⣿⡏⡈⠉⠛⠋⠛⢻⣿⣿⣿⣿⡇⢀⡘⠿⠍⠀⢀⣤⡀⠀⢀⣿⣿⣿⣿⣿⢿⢻⡿⣿⣿⡿⠟
⠤⢸⣿⣿⣮⣿⣿⣶⣶⣾⣽⣿⣾⣤⣴⣞⣿⣿⣿⣾⣿⣿⡀⠀⠼⠿⠿⠿⣚⣛⡓⠋⠀⣿⣦⣴⣶⠟⠛⠾⠟⠛⠉⠉⠁⠀⠀⠀⠀⠒⠚⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⡏⢩⣥⣶⣶⡼⢿⡉⠀⠈⠀⠄⣶⣲⡏
⣿⣅⣿⣿⣿⣿⠿⠿⠿⠷⠿⠛⠛⠛⠋⢩⣿⣷⣶⣦⣿⣿⡇⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢹⣿⣿⣿⣷⣶⡇⠀⠀⠀⠠⣴⣤⣄⡀⠰⣶⠖⠶⣛⣿⣿⣧⣦⡀⠀⠀⠀⢿⣿⠧⢸⣿⣿⣿⡇⡀⣿⣯⡧⢘⣻⣿⣿⣿
⣉⡁⢹⣿⣿⠀⢀⣀⢰⣶⣶⣶⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⠏⠀⣶⣶⣶⣶⣶⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⡄⢤⠿⣿⠀⣿⣿⡿⠯⠿⣿⣿⣿⣿⣿⣋⠉⠸
⣿⣿⠘⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢻⣿⣿⢸⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠸⡆⠀⠀⠀⡀⠀⠀⠀⠀⠁⢢⣽⣏⣿⣿⣿⣟⣭⣴⣿⣿⣿⣷⣾⣶⣿⣧⣅⣀⣴⣿⣾⠿⢿⣯⣯⣤⣤⡤⠤
⣿⣿⣇⣿⣿⣿⡿⠿⠿⣿⣛⣛⣿⠉⣉⣁⣀⠥⠤⠔⣸⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢈⠀⠀⢀⣷⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣿⠟⣋⢰⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⠉⢹⣿⣿⣬⣉⣡⠤⠔⠚⣿⢉⣉⣡⠄⠀⠀⠉⠋⣿⢿⣶⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠋⣿⠐⠀⠀⢀⣼⣿⣿⣃⣄⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡇⢰⡿⠛⢟⣿⣿⣿⣁⣤⣭⣉⡉⣿⣿⣿⣿⣿⣿⣿⠿⠟
⣤⣶⣶⣼⣿⣿⣿⣿⣿⠿⠯⣍⣿⣦⣿⣛⣾⣄⠀⠀⠀⠀⠘⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⠇⠀⠈⣹⣿⣿⣿⣿⣿⣿⣶⣴⢲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀
⣿⣿⣿⡟⠉⠩⡅⢀⣠⣤⢈⣻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣤⣴⣿⣿⣿⣿⣿⣿⣿⡷⢎⣴⡿⠿⢿⣿⠯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣧⡶⠂⠙⠛⠊⠉⠈⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣿⣟⢸⡇⠀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠀⠀⠀⠈⠉⢍⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⢻⣿⡏⠩⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠟⠁⠀⠀⠀⠀⠀⠸⣿⠐⠐⢀⠂⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⡆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢔⡐⠄⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠑⠁⠠⠂⢅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠌⠡⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⡇⣿⢰⣿⣿⣿⣏⣿⡆⣾⡇⢸⣿⡟⢿⠃⠸⣿⣿⣿⣿⡇⠃⠻⡏⠁⣿⣿⣿⣿⠛⢻⣿⣿⡇⢸⣿⣿⣿⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣶⣦⣶⣄⣰⣶⡷⠿⠤⠝⠀⣦⣾⣿⣷⣶⣿⠀⢃⢿⡌⣽⣿⣿⣿⣿⣇⡟⣧⢸⣿⡇⠛⠃⠀⠛⢿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣀⣸⣿⣿⡇⢸⣿⣿⣿⠨⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀
⣀⣿⣿⣿⣿⣿⣿⣿⠿⠧⠤⠬⠶⠼⠟⠛⠛⠛⠛⢻⣷⣼⠘⠁⣭⣿⣿⣿⣿⣿⣗⣿⢸⡏⠀⠀⠀⠀⠀⠀⠹⣿⣧⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⠿⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⠀⠀⣀⣀⠀⠀⣀⡀⠀⢂⡄⠸⣿⣿⣿⢸⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠈⠉⠛⠏⠛⢻⣿⣿⣿⣿⡇⢀⣘⡿⠋⠀⠀⣄⡀⠀⠀⣼⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⠿
⠠⠸⣿⣿⣦⣿⣿⣷⣶⡾⣭⣿⣿⣤⣴⡆⣿⣿⣿⣾⣿⣿⡆⠀⠨⠿⠿⠿⣞⣛⣛⠟⠀⢸⣦⣀⣴⡾⠿⠿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠚⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣟⢩⣭⣭⣶⣼⢿⡋⠀⠀⠀⠉⣶⣖⡟
⣿⣅⣿⣿⣿⣾⠿⠿⠿⠷⠿⠛⠛⠛⠛⢉⣿⣷⣶⣦⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠸⣿⣿⣿⣷⣶⣶⠀⠀⠀⢠⣴⣦⣀⡀⠠⣶⠶⠶⣟⣻⣿⣧⣤⠀⠀⠀⠀⣿⣿⠷⠸⣿⣿⣿⡇⠀⣾⣧⣦⠘⢳⣿⣿⣿
⣉⣁⢸⣿⣿⡀⢀⣀⠀⣶⣶⣷⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⡿⠁⣶⣶⣶⣶⣶⣿⣿⠙⠋⠁⠈⠀⠀⠀⠀⠈⠛⢷⡟⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡄⢀⠽⢶⠆⣿⣿⣿⡯⡿⣿⣿⣿⣿⣿⣛⠋⠸
⣿⣿⡀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢾⣿⣿⢸⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣽⣏⣿⣿⣿⣟⣫⣵⣿⣿⣿⣷⣾⣶⣾⡧⣉⣀⣴⣶⣶⣿⣿⣯⣗⣭⣤⣤⣤
⣿⣿⣇⣻⣿⣿⡿⠿⠿⣿⣛⣛⣿⠉⣉⣁⣀⡡⠤⠄⡺⣿⣿⡘⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⡿⣇⠀⠈⠀⠀⠀⣥⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣳⠟⣛⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠛⠉⠉⢹⣿⣿⣬⣍⣡⠤⠤⠒⣿⠉⣉⣩⢄⠀⠀⠉⠁⣿⢿⣧⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢹⡆⠀⠁⢂⣰⣿⣿⣇⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠰⣾⠻⣿⣿⣿⣿⠁⣈⣭⣉⡉⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣤⣶⣶⣶⣿⣿⣿⣿⡿⠿⠿⣭⢿⡧⣿⣛⣺⣄⠀⠀⠀⠀⠘⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⣿⣿⣿⣿⣷⠦⠀⠈⣻⣿⣿⣿⣿⣿⣿⣷⣬⢷⣴⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀
⣿⣿⣿⣟⠉⢩⣅⣀⣠⣤⢈⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣥⣴⣿⣿⣿⣿⣿⣿⣿⡷⢔⣴⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢶⠮⠝⠛⠛⠉⠁⠿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣸⡇⠀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⣉⡉⠉⠉⠀⠀⠈⠙⢋⣉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠦⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠿⠿⠋⠑⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠈⢻⣿⣋⡛⡀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⠗⠈⣐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⡀⡈⠀⠄⡀⠠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡊⡀⠊⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠨⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠇⣿⣠⣷⣿⣿⣿⣿⡇⡗⡇⢸⣿⡟⣿⠇⠀⣿⣿⣿⣿⡇⠀⠸⡟⠁⣿⣿⣿⣿⠛⢻⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠘⣿⣿⣶⣦⣴⣄⣀⣶⡿⠿⠦⠸⠀⣤⣦⣿⣷⣶⣿⡄⢸⢹⡏⣭⣿⣿⣿⣿⣿⣇⣿⢸⣿⣟⠛⠃⠀⠛⢿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡀⣸⣿⣿⡇⢸⣿⣿⣿⠐⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀
⣄⣿⣿⣿⣿⣿⣿⣿⡿⠧⠤⠬⠶⠴⠿⠛⠛⠛⠛⢹⣷⣼⠘⠃⣿⣿⣿⣿⣿⣿⣿⣿⠘⡿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢻⣿⣿⡿⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡀⠀⠀⢀⠀⠀⢀⣀⠀⠀⡄⠠⣿⣿⣿⢸⣿⣿⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠉⠉⠻⠿⠙⢻⣿⣿⣿⣿⡇⠀⢈⣻⡛⠀⠀⣀⡀⠀⠀⢰⣾⣿⣿⣿⣿⠿⣿⢿⣿⣿⡿
⣠⠈⣿⣿⣧⢿⣿⣧⣦⡾⣭⣿⣿⣤⣤⡆⣿⣿⣿⣾⣿⣿⡇⠀⢠⠭⠿⠿⢿⣚⣛⡻⠂⢀⣷⡄⣠⣴⡷⢶⢶⠿⠉⠋⢁⠁⠀⠀⠀⠀⠘⠛⢻⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣟⢈⣭⣭⣥⣸⣿⡏⠀⠀⠀⠈⢽⣦⣴
⣿⣥⣻⣿⣿⣾⡿⠿⠿⠿⠿⠟⠛⠛⠛⢋⣽⣿⣶⣦⣿⣿⡇⢿⣷⣿⣿⣿⣿⡟⠉⠀⠀⠀⣿⣿⣿⣷⣤⣴⡄⠀⠀⢠⣤⣄⣀⠀⠠⣶⡴⠶⢞⣻⣿⣧⣤⠀⠀⠀⠀⣾⣿⠛⠘⣿⣿⣿⡏⠈⣸⣶⣆⠐⢷⣿⣿⣿
⣉⣁⠸⣿⣿⡄⠀⣀⡀⣶⣶⣶⣤⣶⣷⣾⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⡿⠋⣶⣶⣶⣶⣶⣷⣿⠙⠛⠋⠉⠁⠀⠀⠀⠈⠳⢾⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⡀⢀⠹⢴⠇⣿⣾⣿⡿⡿⣿⣿⣿⣿⣿⣛⠛⠹
⣿⣿⡄⣿⣿⣯⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢸⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣸⣏⣿⣿⣿⡿⣋⣭⣾⣿⣿⣷⣾⣶⣮⣧⡉⣉⣤⣴⣶⣿⣿⣏⣯⣋⣭⣀⣄
⣿⣿⣧⣹⣿⣿⡿⠿⠿⢿⣛⣛⣿⠉⢉⣉⣀⡩⠥⠤⡎⣿⣿⡆⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⣇⠄⠈⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣿⠾⢛⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣶
⠛⠉⠉⠹⣿⣿⣮⣍⣩⠤⠤⠒⢻⡉⣉⣉⡔⠀⠐⠈⠁⣿⢿⣧⣿⣿⠃⠀⠀⠛⠛⠛⠛⠛⠛⠃⢸⡆⠄⠁⠀⣠⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡷⠨⣾⠿⡿⣿⣿⣿⠃⢈⣍⣙⠋⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣤⣶⣶⣶⣿⣿⣿⣿⣿⠿⠾⣭⣽⡇⣿⣛⣺⣆⠀⠀⠀⠈⠘⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⣿⣿⣿⣿⣿⣵⠀⢈⣿⣿⣿⣿⣿⣿⣿⣷⣌⢭⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀
⣿⣿⣿⣟⠉⢩⠅⢀⣀⣤⡄⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⣤⣾⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⠿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⢿⣿⠶⠄⠘⠉⠚⠋⠁⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣸⡇⠀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣛⣛⠛⠛⠛⠉⠉⠉⠉⠛⢛⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣠⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢅⠀⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⡁⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢧⢿⣦⣿⣿⣿⣿⣿⣷⣇⣷⢸⣿⣿⣿⡟⠀⣿⣿⣿⣿⡇⠈⠹⡿⠻⣿⣿⣿⣷⠖⢻⣿⣿⣿⠀⣿⣿⣿⡇⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠈⣿⣿⣷⣦⣤⣄⠀⣶⣾⠾⠧⠨⠁⣤⣦⣶⣶⣶⣿⡇⢸⢸⡏⣭⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡻⠓⠀⠿⢿⣿⣿⣿⠀⠀⠁⠀⣿⣿⣿⣿⡀⢐⣿⣿⣿⢀⣿⣿⣿⡇⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀
⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⠬⠷⠤⠿⠿⠟⠛⠛⢺⣷⣾⠘⠃⢿⣿⣿⣿⣿⣿⣻⣿⠀⣿⠏⠀⠀⠀⠀⠀⠙⢿⣿⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⣿⣿⠅⠀⠀⠀⠀⠘⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⡂⠀⣿⣿⣿⣸⣿⣿⡇⠀⠘⣻⣿⣿⣿⣿⢹⣻⡀⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠛⠻⠿⠻⠿⣿⣿⣿⣿⡿⠀⠀⣿⣛⠀⠀⣄⡠⠀⠀⢰⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿
⠐⡀⣿⣿⣧⣼⣿⣷⣦⣤⣯⣿⣷⣧⣥⣤⣿⣿⣿⣧⣿⣿⡇⠀⢨⣬⡽⠿⠿⢿⣖⡻⠃⠀⣶⣄⢀⣤⣶⣶⣶⡾⠛⠛⠋⡉⠀⠀⠀⠀⠐⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⠐⣊⣩⣭⣽⣿⡟⠈⠀⠁⠈⢩⡭⣴
⣷⣧⣹⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⣿⣿⣿⣦⣿⣿⣧⢹⣿⣾⣿⣿⣿⡿⠋⠀⠀⠀⣿⣿⣿⣿⣦⣤⡄⠀⠀⠠⣤⣀⠀⠀⠀⣤⡴⠤⠚⣿⣿⣧⣤⠀⠀⠀⠀⢸⣿⠿⡀⣿⣿⣿⡟⠈⣹⣶⣢⠀⢦⣾⣿⣿
⣉⣉⠙⣿⣿⡆⠀⢀⠀⣶⣶⣶⣄⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠋⣶⣶⣶⣶⣶⣿⣿⠟⡻⠛⠉⠃⠀⠀⠀⠈⠳⢿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⢀⡹⢰⡇⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠛⠹
⣿⣿⡆⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠘⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⣟⣿⣿⣿⡿⣛⣩⣿⣿⣿⣷⣤⣦⣮⣧⡉⢉⣡⣰⣴⣿⣿⣟⣯⣋⣁⣀⣀
⣿⣿⣷⢸⣿⣿⣿⡿⠿⠿⣿⣛⣻⠛⠉⣉⣉⣉⠩⠤⠆⣿⣿⡇⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡏⢇⠀⠈⠆⠀⠀⠀⣄⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇⣿⠾⢟⢹⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶
⠛⠛⠉⠉⣿⣿⣧⣍⣉⠡⠤⠴⢻⡏⣉⣉⡽⠀⠐⠒⠡⣿⣿⣧⣿⡟⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢸⡆⠄⠂⠄⢀⣼⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠩⣼⠿⡿⣿⣿⣿⠃⢈⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣤⣴⣶⣦⣿⣿⣿⣿⣿⡿⠶⣭⣹⡇⠿⣟⣛⣆⠀⠀⠀⠈⠙⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⣿⣿⣿⣿⣿⣧⡆⠀⠻⢿⣿⠟⢻⣿⣿⣿⣄⡥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀
⣿⣿⣿⣿⠋⠉⡍⢁⣀⣠⡄⣺⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⣀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠄⢀⣀⣤⣴⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⠜⠝⠛⠛⠋⠁⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣴⣶⣶⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣉⣏⠀⢀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⣜⠛⠛⠛⠛⠛⠋⠉⠉⠛⢿⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠿⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⡿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠱⢄⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣁⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢷⢸⣇⣾⣿⣿⡿⢿⣿⣇⣿⢸⣿⣿⢿⣿⠀⣿⣿⣿⣿⣿⠈⠹⣿⠛⢸⣿⣿⣷⡶⠶⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⣿⣿⣷⣦⣤⣄⠀⢤⣶⡶⡧⢀⠀⢤⣠⣶⣶⣶⣾⡇⢸⢸⡇⣿⣿⣿⣗⣶⣿⢻⣿⠈⣿⣿⠺⠟⠀⠻⢿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⣿⣿⣿⠀⣿⣿⣿⡇⠿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀
⣆⢹⣿⣿⣿⣿⣿⣿⣿⣭⣀⣤⡵⠦⠿⠿⠿⠟⠛⢻⣷⣞⡜⠛⠛⣿⣿⣿⣿⣿⢸⣿⡀⣿⡟⠀⠀⠀⠀⠀⠈⢿⣿⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⣿⣿⠆⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⡘⣿⣽⡇⠀⢰⣿⣿⣿⣿⣿⣺⢹⡇⣿⠁⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠋⠛⠻⠿⠻⠿⣿⣿⣿⣿⣿⠀⠀⣻⣟⠁⠀⢀⡀⠀⠀⢰⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠄⡀⢿⣿⣧⣸⣿⣷⣤⣤⣞⣿⣶⣦⣤⣤⢿⣿⣿⣧⣿⣿⡇⠀⢘⣿⣿⠭⠿⠿⢷⡺⠃⠀⢰⣤⠀⣤⣴⣶⣴⣲⠟⠛⠛⠈⠀⠀⠀⠠⠴⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⠒⣂⣩⣭⣝⣿⡟⠊⠀⠃⢈⢩⡭⣴
⣯⣖⢸⣿⣿⣷⣿⣿⣿⡿⠼⠿⠿⠿⠛⠛⣻⣯⣿⣧⣹⣿⣿⢸⣷⣶⣾⣿⣿⡿⠋⠀⠀⠀⢾⣿⣿⣿⣦⣤⣬⠀⠀⠀⣀⣄⠀⠀⠀⣤⣤⢤⠺⣿⣿⣿⣤⠀⠀⠀⠀⢸⣿⡿⡀⣿⣿⣿⣿⠈⢹⣶⣢⡀⢶⣾⣿⣿
⢉⣉⠉⣿⣿⡇⠀⠀⠀⣰⣦⣶⣆⣶⣶⣶⣿⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿⡟⠋⣶⣶⣶⣶⣶⣾⣿⠛⠛⠛⠉⠛⠀⠀⠀⠈⠛⢿⣿⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⠀⡹⢴⡇⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⡿⠛⠙
⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡆⣿⣿⡟⠁⠀⣿⣿⣿⣿⣿⣿⡿⣇⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣟⣩⣽⣿⣿⣿⣤⣧⣮⣧⡉⢉⣁⣰⣴⣿⣿⣿⣯⣋⣉⣁⣀
⣿⣿⣿⢸⣿⣿⣿⣿⡿⠿⢿⣟⣻⡛⠛⢉⣉⣉⣉⠡⠇⣿⣿⡇⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠸⠠⠈⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣯⢻⠾⠟⢛⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶
⠛⠛⠋⠉⣿⣿⣗⣀⣉⡉⠥⠤⢿⡟⢋⣉⣩⠀⠀⠒⠺⢻⣿⣧⣿⠏⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⡇⠀⠐⠠⠀⣰⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡭⣼⡿⡿⢿⣿⣿⠇⢈⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣤⣤⣴⣦⣽⣿⣿⣾⣿⣷⡶⣾⣩⣧⠽⢿⣗⣧⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⣾⣿⣿⣿⣿⣯⡆⠀⠙⠿⣿⡿⠿⢿⣿⣿⣅⡭⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀
⣿⣿⣿⣿⠛⢋⣉⢉⣀⣠⡄⡹⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⢟⣡⣤⣾⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣰⡊⠺⠈⠛⠛⠃⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀
⣿⣿⡃⣿⠀⠀⣀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠉⠉⠛⠻⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⡋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠃⢁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠐⠐⠀⢀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣄⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⢀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⢸⣇⣾⣿⣿⡿⢿⣿⣿⣿⠸⣿⣿⢿⣿⠀⣿⣿⣿⣿⣿⠈⠻⢿⠛⢸⣿⣿⣷⡶⠶⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢿⣿⣷⣶⣤⣤⠀⢤⡴⣶⣇⣀⠇⢠⣠⣶⣶⣶⣼⡇⠸⢸⣧⣿⣿⣿⣟⣶⣿⢸⣿⠀⣿⣿⢰⠟⠀⠙⠻⢿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⡇⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⣦⢸⣿⣿⣿⣿⣿⣿⣿⣭⣀⣀⣦⡦⠿⠿⠿⠿⠛⠻⣷⣆⡏⠛⠙⣿⣿⣿⣿⣿⢸⢺⡆⣿⣿⠆⠀⠀⠀⠀⠀⠘⢿⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⣿⡿⠆⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣾⣷⣶⡆⣿⣽⡇⠀⢰⣾⣿⣿⣿⣿⣟⢹⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠛⠻⠿⠻⠿⣿⣿⣿⣿⣿⠀⠀⣻⣟⠃⠀⢀⡀⠀⠀⢰⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠄⡂⢻⣿⣿⣵⣿⣿⣥⣤⣞⣻⣷⣮⣤⣤⢸⣿⣿⣧⣿⣿⣧⠀⠈⣿⣿⡽⠿⠿⠿⡾⠃⠀⠀⣿⣆⣠⣴⠿⢷⣶⠟⠛⠛⠈⠀⠀⠀⠄⠤⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⠒⣂⣩⣭⣝⣿⡟⠀⠀⠁⠈⢩⡭⣴
⣷⣶⡸⣿⣿⣷⣿⣿⣿⣿⠾⠿⠿⠿⠛⠛⣻⣯⣽⣷⣸⣿⣿⢸⣷⣶⣶⣿⣿⠿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣤⣴⡆⠀⠀⠠⣄⠀⠀⠀⣤⣤⢤⠺⢿⣿⣿⣤⠀⠀⠀⠀⢸⣿⣿⡀⣿⣿⣿⣿⠈⢹⣶⣲⡀⢶⣾⣿⣿
⠛⢉⡉⣿⣿⣇⠀⠀⠀⢀⣤⣴⣆⣴⣶⣶⣿⣿⣿⣿⡿⣿⣿⣸⣿⣿⣿⡿⠁⣶⣶⣶⣶⣶⣶⡾⣟⠉⠟⠉⠉⠁⠀⠀⠀⠈⠻⢿⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⢀⡸⢷⡆⢿⣿⣿⣿⣻⣿⣯⣿⣾⣿⡟⡛⠋
⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡇⢹⡅⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣿⣿⣿⣟⣩⣽⣿⣿⣿⣤⣧⣮⣥⡈⢉⣁⣴⣶⣿⣿⣿⣹⣏⣉⣅⣀
⣿⣿⣿⠘⣿⣿⣿⣿⡿⠿⠿⢿⣛⡛⠛⠉⣉⣉⣉⡩⠽⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⡇⠈⡇⠐⠈⠆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠹⣿⡿⠿⡟⠻⠾⠛⠛⠿⢿⣿⠿⠻⠏⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣶
⠟⠛⠛⠉⣿⣿⣗⣒⣈⣉⠥⠤⢾⡗⢛⣉⣉⠀⠀⠒⠺⢹⡿⣿⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⢛⠀⠈⠀⠀⢀⣾⣿⣿⠀⠀⠀⢸⣿⠀⣿⣿⣿⣷⣸⡇⣿⡇⣿⣷⣿⣻⣷⠈⣉⡛⠋⢿⣿⣿⣿⣿⣿⣿⣿⡿
⣤⣤⣴⣦⣼⣿⣿⣿⣿⣿⣶⣾⣉⣷⠼⠿⣗⣣⠀⠀⠀⠀⢃⣠⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣴⣿⣿⣿⣿⣿⣵⠀⢸⣿⠀⣿⣿⣿⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢺⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀
⣿⣿⣿⣿⠛⠋⣉⠉⣀⣠⣄⢺⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣤⣤⣾⣿⣿⣿⣿⣿⣿⣧⡀⠸⠿⠶⠿⠿⠿⠏⠿⠇⠿⣷⡿⠛⢿⣾⠿⣰⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣵⣔⠛⠿⠟⠛⠋⠹⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣛⣛⡛⢉⣐⡲⢶⣿⣓⠚⣙⡛⣗⣛⢓⣒⡾⢿⣳⠖⣚⣛⡛⠛⢛⣉⡛⢿⡟⠀⠀⠀⠀⠀
⣿⣿⣇⣿⠀⠀⢀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠘⣿⣿⢣⣿⣿⣿⣸⣿⣻⣷⢿⣷⣿⡏⣿⣿⣇⢸⣿⠀⣿⡟⣿⡧⣿⣿⠿⠀⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⢿⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠀⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠻⠿⠹⠿⠾⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠠⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣆⣤⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠼⠔⠠⠈⠠⠀⡁⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠄⠒⠄⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢉⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⢸⡙⠀⢻⡇⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠤⠼⣿⣿⣿⣿⣿⡿⠟⠒⣺⠒⢐⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⡇⠀⠀⡇⠀⢸⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⣶⣾⡟⢻⣿⣿⣿⠋⠉⣉⣩⡉⠉⢩⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣹⠟⠋⠁⠀⠀⠠⠤⠤⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠭⠭⠤⠤⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠾⣿⣯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠄⠐⢠⣤⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡿⠋⠁⠉⠛⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣿⣿⣶⡆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣧⣤⣤⣤⣤⣼⣿⣶⣌⣻
⣩⣭⠛⠛⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠄⠀⠀⢸⡿⠛⠿⠟⠋⠛⠛⠉⠉⠉⠀
⠿⠿⠂⠀⠀⢻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⠶⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⡄⣴⣿⢷⠀⠀⠸⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣄⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⡀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⣦⣤⣤⡀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣄⠀⠈⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⢀⢀⡀⡀⣰⣾⠀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⢿⣾⠿⠀⠀⣀⣿⣇⡀⠀⠀⠀⠀⠀⠀⢸
⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠶⣴⣾⣿⣿⣿⣿⣿⣿⠿⠀⠀⢀⣀⣠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡛⢃⣀⡀⢀⣀⣀⠀⣀⡀⣀⣀⢀⣀⡚⢛⣒⠶⣚⣛⡛⠛⢛⣛⡙⢿⣀⣤⣦⣤⣤⣀
⠀⠀⠙⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠁⠀⠔⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣾⣧⣿⣟⠀⠀⠀⠀⠁⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠀⢀⠀⣿⣿⠸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⢀⣿⣿⣿⣿⣛⣻
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠈⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⣃⡻⠿⠟⣸⡿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⢷⣶⣤⣀⣤⣠⠼⣤⠙⡻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢲⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣤⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣺⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡤⠉⠀⢹⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣷⣶⣶⣶⣬⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⡄⠀⠈⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⠟⠛⣭⣬⣭⣿⣿⠛⣻⠿⢿⣿⣿⣿⣿⡿⡿⣭⣷⣿⣿⡟⢛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⠦⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣦⣷⣒⠈⠉⣭⣿⣿⣿⣯⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣛⣉⣉⣙⣿⣿⣿⣏⣉⠉⠍⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⣭⡉⠁⢸⠟⠁⣿⢻⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣭⣭⡤⠿⠥⠤⣿⣿⠿⠤⡶⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⡇⠀⢸⡆⠀⢿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣷⣶⡖⢺⣿⡒⠚⢛⣟⣛⣋⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡂⠀⠹⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣍⣉⣉⡥⠤⠤⠬⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣋⣉⣉⡩⠭⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣴⣶⣶⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠄⢀⣀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠛⠉⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⣾⣸⣿⣤⡄⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣅⣀⣀⣀⣀⣴⣶⣭⡛
⢟⣛⣛⠿⠿⠟⠛⠙⠛⠀⠀⠐⢾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⠿⣿⡿⠻⠿⠟⠛⠛⠋
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡂⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⡄⠀⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠀⠀⢻⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣴⣤⣄⣀⡀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀
⣿⣭⣥⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣠⣴⣶⡀⠀⠀⡀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠏⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⠄⠀⠀⠀⣤⡆⠀⠀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⢿⣾⠿⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣴⣷⣾⣿⣿⣧⡬⣴⣾⣿⣿⣿⣿⣿⣿⡏⠁⠁⠉⣀⡘⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡛⢋⣁⡀⢀⣀⣀⠀⣀⡀⣀⣀⢀⣀⡺⢟⣓⠶⣆⣒⡲⠶⢛⣛⡛⠲⡖⠀⣀⣀⣀⡀
⠈⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⡿⠛⠁⢀⠴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⣿⣿⠸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠀⣽⣿⣿⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⢿⣃⡻⠿⠟⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢳⣦⣤⣀⣀⡀⢭⣯⣉⠻⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠄⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣄⣀⡘⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣠⣤⣤⣶⣿⣿⠿⣿⣿⣿⣾⢷⣾⣧⡍⠋⠙⣿⣿⣿⣿⣷⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣯⣤⣤⣤⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⡉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠛⣛⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣷⣾⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⡀⣼⣿⣿⣿⣿⣷⣾⣥⣬⠭⠍⠛⠛⢿⣶⣿⣿⡿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣿⡿⣶⢖⡚⠛⠛⠛⢿⣿⣿⣟⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⣛⣋⡉⠁⢸⡿⠃⣿⡿⣤⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣙⣿⣟⣉⣉⣉⣛⣋⣀⣿⣿⡯⠤⣤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡇⠀⢸⡦⠀⣿⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⣤⢤⣤⣴⠤⠤⠤⢼⣿⠶⠖⠒⠟⠒⠒⢒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠄⠀⢼⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣴⣾⣿⣿⠒⠒⠒⣺⣿⣏⣉⣉⣉⣉⣉⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⣛⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣚⣛⣻⣿⣿⣯⣭⣭⣿⣿⣭⣤⣤⣤⣤⣤⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡉⠁⢀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⠿⠛⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡀⣶⢸⣿⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡋⠀⠀⠀⠀⢩⣭⣝
⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡿⠿⣿⡿⠿⠿
⣿⣿⣿⣧⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀
⠉⣉⣁⣤⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠁⠸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⣾⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣀⣠⣄⡀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀
⣔⣒⣒⣠⣤⣴⣿⣿⣿⣽⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⠖⠀⠀⠀⠀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⢿⣾⠿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣯⣿⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠏⠁⠀⠃⢀⣸⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡛⢋⣀⡀⢀⣀⣀⠀⣀⡀⣀⣀⢀⣀⡸⢟⣳⠶⣒⣃⡀⠤⢄⣈⡙⢷⣤⡄⠀⠀⠀⠀
⠛⠻⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠟⠋⢀⢤⣶⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⣟⣗⣶⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣬⡿⣿⣿⣿⡿⠋⠀⠀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣿⣿⠸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢙⣻⣿⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢰⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⣃⠻⠿⠟⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⣦⣤⣀⠉⠉⢉⣛⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣀⣠⣤⣤⣀⣀⣀⣀⣀⠀⠀⠻⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣶⣿⣧⣶⣛⠻⠛⢿⣿⣿⣿⣿⣆⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⡗⢿⣿⣃⣀⣀⣸⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣭⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢈⠉⠙⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠉⠁⣰⣶⣿⣿⣿⣯⣝⣉⡛⣛⡿⠿⢿⣿⣭⣾⣿⣿⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠋⠀⣀⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣤⣶⣿⣿⣿⣶⣿⣿⣿
⠾⢾⣿⣿⣶⡶⠶⠚⠓⠺⢿⣿⣿⡿⠛⠛⠛⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠛⠛⠛⠋⠸⣿⠛⢿⡿⣯⣽⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠒⠚⢿⣟⣛⣛⣋⣻⣏⣉⣽⣿⣿⣉⣩⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⡇⠀⢸⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣉⣉⣉⣩⣭⣭⡧⠤⠤⢤⣿⡥⠤⠶⠾⠶⠶⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠛⠇⠀⠀⡇⠀⢸⡅⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠤⠤⢤⣴⣿⣿⡗⠒⠒⢺⣿⡗⠒⠒⣋⣉⣉⣙⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠿⠿⠟⠛⠛⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⣿⣿⣿⣿⣟⣋⣉⣿⣿⣋⣉⣉⣩⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡂⠀⠉⠉⠉⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⣬⣴⣿⡂⡀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡟⠁⠀⠀⠈⢙⣛
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣟⠛⣿⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣶⣶⣶⣶⣾⣿
⣶⣶⣶⣿⣇⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠙⠉⠈⠉⠁⠀
⠉⠉⠉⢉⣁⡀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡏⠀⠀⠀⢀⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⢀⡀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢐⣒⣂⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⡀⠐⠀⠀⣀⠄⠁⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⢿⣾⠿⣰⣿⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣛⡋⢉⢉⣭⣿⣷⣞⠛⣛⣿⣿⡿⠀⠀⠀⠀⠘⠀⠀⠂⠀⢸⣿⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡻⢛⣉⡀⢀⣀⣀⠀⣀⡀⣀⣀⢀⣀⡀⢘⣳⠶⣞⣛⡛⠀⢀⣀⡀⢻⣧⣀⣀⠀⠀⠀
⠿⠿⠿⠿⠟⠛⠛⠃⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠈⣿⡽⣯⢤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣰⣛⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢹⣿⢿⣿⣿⣿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢠⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⣠⣾⣷⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣤⣀⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⢿⣿⣛⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣻⣿⣿⣾⣷⣾⣭⣿⣶⡭⠿⠿⠿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠭⣿⡿⠏⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣯⣭⣿⣿⣿⣟⣛⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠋⣭⣤⣶⣿⣿⡟⠻⠻⠿⢿⣿⣿⣿⣿⣟⣭⣴⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⠗⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣂⡀⢉⣽⣿⣿⣿⣭⣿⣿
⣉⣉⣉⣿⣿⣿⣿⣭⣥⣤⠿⠧⢼⣿⣿⣿⣷⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣤⣬⢿⠿⠿⠿⠟⢻⣿⡿⣿⣿⠗⣿⣻⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⠤⠤⠤⠤⠾⣿⣿⠿⠷⠗⢶⡖⠒⣺⣿⡿⠓⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡆⠀⢸⡍⠀⣿⠏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⠒⠒⠒⠒⠒⠛⣛⣛⣻⣋⣉⣉⣩⣿⣛⣉⣍⣯⣁⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⡇⠀⢈⣷⠀⢿⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⣉⣉⣉⣉⣉⣉⣹⣿⣿⡭⠥⠤⣽⣿⡧⠤⠤⠧⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠘⠀⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⣩⣭⣥⣤⣴⣿⣾⣿⣿⠶⠶⠶⣾⣿⠗⠒⠒⠒⢒⣋⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⣶⢶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⠀⢐⢠⣤⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠋⠉⠉
⣗⣒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⣿⣿⠿⣶⡆⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣧⣀⣀⣀
⣿⣿⣭⣭⣭⣵⣶⡎⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⠿⠟⠿
⣿⠙⠛⠛⠛⠛⠛⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⠤⠶⠶⠶⠿⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠁⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⡷⠀⠀⠀⢀⡠⠤⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣶⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢹⣿⣿⣿⣿⠀⠀⠀⠀⣤⣄⠀⠀
⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⣸⣿⣿⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⣟⣿⣿⣟⠁⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⡄⠐⣀⠀⢀⣶⡏⢀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣛⣛⡿⢟⣛⡻⢗⣀⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣘⣛⡻⠿⢛⣛⡀⠀⠀⢰⣿⠃⠀⠀
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣼⣿⣿⣿⣴⣄⠀⠀⢀⣼⣿⣿⣿⣿⠇⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢰⣶⣿⣿⡷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠟⠋⠁⠠⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣰⣿⢿⣿⣿⣿
⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠛⣛⣿⡿⠁⠀⠀⠀⠈⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠾⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⢸⡇⣰⣿⣁⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⡃⠀⠹⠿⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣷⣾⢃⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣤⣤⣔⡲⣯⠌⣛⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣤⣤⣶⣦⣴⣶⣶⣤⣤⣤⣤⣤⣀⣀⣘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⣤⣶⣶⣶⣾⣿⣟⡻⢿⣿⣿⢿⣿⣿⣴⠈⠀⢻⣿⣿⣿⣿⣧⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣥⣤⣤⣼⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣴⣉⣩⠝⡛⠻⠿⣿⣯⣽⣿⡿
⣉⣉⣉⣉⣹⣿⣿⣿⣏⣭⣍⣽⣿⣬⣿⣿⣿⣿⡤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣃⣘⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⡿⢾⡿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣭⣤⡤⠤⠤⠬⣿⣿⡿⠿⠾⢦⣤⠤⢨⣿⣿⠿⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣶⡦⠀⠀⡿⠁⢸⡏⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⠤⠶⠶⠶⠖⠒⠚⠛⡓⠒⡖⠒⠒⢒⣿⣟⣛⣋⣹⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⠀⠀⣏⠀⢸⡇⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⡒⠒⠚⢛⠛⠋⣉⣉⣿⣿⣏⣉⣉⣩⣿⣯⠭⠭⠭⠤⠤⢤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠋⠀⠘⠇⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣉⣉⣉⣩⣭⣿⣿⣿⣿⡧⠤⠤⢼⣿⡿⠶⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠩⠭⠭⠤⠤⠄⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣥⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡄⠰⠀⣤⡄⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡟⠛
⣶⣞⡒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⢹⣿⣿⣧⣄⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣏⣀⣀
⣿⣿⣿⣿⣭⣭⣭⣭⣿⡿⡿⠛⠻⠿⡟⠛⠛⠛⠋⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠿⠿
⣿⣿⠿⠿⠿⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣤⡤⠤⠤⠶⠶⠿⠆⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⢀⣀⣀⠀⠀⠀⣿⡶⠶⠶⣶⣶⣶⣦⣤⣶⣶⣴⣾⣷⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⠀
⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⡿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣛⣻⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⡀⡀⡠⢀⠀⠀⣴⡞⠁⣀⣀⣤⣤⣶⣶⣶⣿⣿⣛⣛⡿⢟⣛⡻⢿⣛⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣘⡻⠿⢟⣛⡛⠇⠀⠀⠀⣿⡇⠀
⣿⣿⣿⣿⠿⠿⠶⠶⠷⢿⣿⡇⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢠⣴⣶⣾⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠈⣭⣥⣿⣿⣿⣟
⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⠛⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⠀⡾⢻⡟⢀⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠀⠹⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣶⣿⠗⠀⣀⣠⣤⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣤⣤⣀⠼⣥⡬⣻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠠⢄⣠⣤⣤⣤⣴⣶⣤⣤⣀⣀⣀⣀⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡛⠀⠀⠀⠀⢠⣤⣴⣶⣾⣿⣿⠿⣿⣿⣿⠿⣿⣿⣥⡉⠉⢻⣿⣿⣿⣿⣧⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣭⣤⣤⣘⣻⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣷⣶⣾⣿⣿⣯⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠉⠁⣰⣶⣿⣿⣿⣯⣹⣙⢛⣛⠿⠿⣿⣿⣟⣝⣶
⢈⣉⣉⣉⣉⣹⣿⣿⣿⣿⣭⣭⣹⣿⣧⣿⣿⣿⣿⣤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⣨⣸⣿⣿⣿⣿⠛⣿⣿⢿⣿⣿⢾⡿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿
⢠⣬⣭⡤⠤⠤⠬⣿⣿⣿⣿⣷⣧⣤⠤⢬⣿⣿⡿⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣦⠀⠀⡟⠃⢸⡏⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿
⠰⡦⠴⠶⠶⠶⠒⠺⣿⣿⣿⣿⣿⡒⠒⣺⣟⣛⣋⣹⣏⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⠀⠀⣿⠀⢸⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿
⠐⣗⠒⠚⠛⡛⠋⣛⣛⣿⣿⣿⠟⣽⢉⣿⣿⠭⠭⠭⠤⠤⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠈⠇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿
⠈⣿⣏⣉⣉⣉⣭⣽⣷⣿⠟⠋⠀⠘⠀⠉⠀⠐⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠩⠭⠥⠤⠤⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿
⠀⣿⣯⣤⣶⣶⣶⣶⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡄⠠⠀⣤⡄⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⡿
⣤⣶⣶⡒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⢸⣷⣿⣧⣤⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⣏⣀
⠻⣿⣿⣿⣿⣭⣭⣭⣬⣭⠛⠛⢻⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠘⠛⣢⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡿
⠀⣿⣿⠿⠿⠿⠿⠿⠟⠛⠀⠀⣉⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⡆⠀⠀⠀⠀⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⣿⣿⣦⡤⠤⠤⠶⠶⠿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⢿⣿⠀⠀⠀⠀⣀⡀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⠈⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀
⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⢿⣛⣻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣤⡀⡀⣀⠀⢀⣶⡏⢀⣀⣤⣤⣶⣾⣿⣿⢿⣛⣛⡿⢟⣛⡻⢿⣛⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡻⢿⡇⠀⠀⠀⣿⡇
⣿⡿⠿⠿⠯⠽⠷⠶⠶⣾⣿⣿⡧⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⣸⣧⣤⣤⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⣿⣭⣽⣿⣿⣶
⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⠟⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⣀⣽⡿⢿⡏⠨⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⡒⠀⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢶⣾⣶⣿⠖⠂⢉⣀⣤⣴⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣤⣤⣠⠿⣧⣌⡻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣠⣤⣤⣤⣤⣶⣤⣤⣀⣀⣀⣀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠋⠀⠀⠀⠀⣤⣤⣴⣶⣾⣿⣿⢿⣿⣿⣿⠿⣿⣿⣥⠉⠁⢻⣿⣿⣿⣿⣇⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣭⣤⣤⣘⣻⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣶⣾⣿⣿⣭⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢰⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠉⠉⠉⣰⣶⣾⣿⣿⣏⣩⡛⠛⡻⠿⢿⣿⣿⢛⣙
⠀⢈⣉⣉⣉⣉⣹⣿⣿⣯⣿⣿⣿⡿⢻⡦⣿⣿⣿⣿⡤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⣼⣿⣿⣿⣿⢻⣿⣿⢿⣿⡿⢺⡿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠠⠦⠤⠤⠤⠤⠬⢿⣿⣿⡿⠿⠧⠿⠀⠈⣿⣿⠟⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣶⡆⠈⠈⡟⠁⢸⡏⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠰⡶⠶⠖⠒⠒⠒⠚⠛⣿⣛⠀⠀⠀⠀⠀⠈⠉⢉⣹⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⡇⠀⠀⣟⠀⢸⡇⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸
⠀⠐⣟⡛⣛⣛⣉⣉⣉⣉⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠘⠇⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿
⠀⢈⣿⣍⣍⣭⣭⣤⣾⣷⣿⣿⡷⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠩⠭⠤⠤⠤⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣻
⠀⠠⣿⢯⡴⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⡄⠠⠀⣤⡄⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⣤⣤⣶⣾⣒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢻⣷⣿⣧⡆⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣃
⡏⢻⣿⣿⢿⣯⣭⣭⣭⣶⡞⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠘⠛⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠿
⡇⠀⣿⣿⠙⠛⠛⠛⠛⠛⠋⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⡇⠀⣿⣿⣤⠤⠤⠶⠶⠾⠿⠃⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⡇⠀⢿⡿⠀⠀⠀⠀⡠⠤⠄⢀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀
⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣟⣛⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣧⠀⠂⡄⠀⢰⣾⢀⣠⣤⣶⣶⣿⣿⣿⢟⣛⣛⡿⢟⣛⡻⢿⣛⣂⠒⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠘⢟⣛⡻⣿⣿⡇⠀⠀⢰⣿
⠿⠛⠛⠛⠉⠛⠒⠒⠲⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⣸⣿⣧⣤⣶⣾⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠠⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠈⣿⣯⣭⣷⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠛⢛⣿⡿⠋⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⢃⠻⠿⠟⢀⣯⣿⡯⢿⠅⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢐⡃⠈⠛⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠐⣶⣿⣶⡷⠚⢉⣁⣢⣤⣾⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣶⣦⣖⣿⡧⢌⣻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠤⣠⣤⣤⣤⣤⣶⣦⣤⣤⣀⣀⣀⣀⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠉⠀⠀⠀⠀⣤⣶⣶⣶⣿⣿⣟⠿⣿⣿⡿⣿⣿⣿⡶⠉⠈⣿⣿⣿⣿⣿⣄⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣭⣤⣤⣤⣝⣛⣛⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣶⣾⣿⣿⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠉⢠⣶⣶⣿⣿⣿⣍⡍⠛⣛⡿⠿⣿⣿⡿⣉
⠀⠀⣉⣁⣀⣀⣤⣽⣿⣿⣯⣿⣬⣯⠝⠛⠁⠀⠀⢻⣷⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⣷⠿⠿⠿⠿⠟⢻⣿⡿⣿⣿⡗⣿⢿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠴⠧⠴⠦⠦⠤⠾⢿⣿⣿⠛⠒⠂⠀⠀⠀⠀⠈⠑⠒⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⣶⣶⡆⠀⢸⡙⠀⢿⠋⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⢲⠒⠒⠒⠒⠒⠒⢛⣻⣟⣉⣟⣉⣁⡀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⢸⡀⠀⢹⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⢸⣏⣉⣉⣉⣉⣉⣉⣩⣿⣿⡯⠤⠤⢴⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠘⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⢸⣿⣥⣤⣤⣤⣴⠿⢿⣿⣿⡷⠒⠒⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠸⠿⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣦⠀⠀⢠⣤⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣶⣶⣾⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⣿⣾⣿⣶⡆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⠉⢻⣿⣟⣿⣭⣭⣽⣶⣶⡎⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠛⢃⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⠀⢸⣿⡟⠛⠛⠛⠛⠛⠛⠁⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⠀⢸⣿⡷⠶⠶⠒⠒⠛⠛⠛⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⡿⠀⠘⠿⠇⠀⠀⠀⠠⠤⠄⢀⣀⣐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⡀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀
⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⣛⣻⣟⣿⣯⠿⠿⢿⣿⣿⣿⣿⣿⡿⠄⠄⠤⠠⠠⣿⣇⣠⣴⣶⣾⣿⣿⣿⢟⣛⣛⡻⢟⣛⡻⢷⣚⣒⠐⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢙⣛⡻⣿⣿⣿⡇⠀⠀⣾
⠛⠋⠉⠉⠉⠀⠀⠚⠻⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣀⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⣿⣷⣶⣾⣿
⠀⣀⣀⣀⣀⣀⣤⣤⣤⣽⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠈⣿⣿⣧⣶⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣛⣛⣻⣿⠏⠀⠀⠀⠀⠀⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢀⣿⣽⡿⢹⣇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣇⡀⠙⠛⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⢲⣾⣷⣶⠒⢉⣀⣤⣤⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣶⣶⣚⣿⣦⣝⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢥⣴⣦⣤⣤⣶⣶⣶⣤⣤⣤⣄⣀⣀⣀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡍⠁⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣻⢿⣿⣿⣟⣿⣿⣶⠂⠀⢹⣿⣿⣿⣿⣧⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣶⣤⣦⣬⣽⣛⣛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣼⣿⣿⣿⣿⣯⣜⣋⠙⣛⡻⠿⢿⣿⣋
⠀⠀⠀⠠⠤⠤⠤⠴⠾⠿⣿⣿⣾⣿⡾⠷⠛⠛⠋⠁⠈⢿⠓⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠾⠟⠛⠛⠛⠛⢸⣿⠿⢿⡿⣏⣹⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⢘⠓⠒⠒⠓⠒⠚⢻⣿⣿⣛⣉⣉⣁⠀⠀⠀⠀⠀⢩⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠿⣿⣿⣿⡇⠀⠸⡏⠀⢸⠇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⢘⣋⣉⣉⣉⣉⣉⣉⣉⣿⣧⣬⠤⠤⠤⠀⠀⠀⠀⠀⠠⠴⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⡧⠀⢸⡅⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⢠⣯⣤⣤⠤⠤⠤⢤⣤⣾⣿⣿⠒⠒⢲⡆⠀⠀⠀⠀⠀⠈⠙⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠿⠿⠿⠿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠠⣿⠶⢶⣶⣶⣶⣟⣛⣿⣿⣿⣋⣩⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠉⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠘⣛⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⠂⣠⣰⣾⡆⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀
⣿⣿⣿⣿⣿⣿⣭⣼⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢹⣟⠿⣿⡇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⡇⠸⣿⣿⣽⣷⣶⣾⣿⣿⣇⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠁⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠹⣿⡇⠀⣿⣿⠉⠉⠉⠉⢉⣉⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⢠⣿⡇⠀⣿⣿⠛⠛⠋⠉⠉⠉⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣹⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⢸⣿⠀⣿⣿⢻⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠸⠿⠃⠀⠛⠛⠀⠀⠀⢀⣒⣒⣀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀
⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣟⣛⣛⣛⣩⡉⣩⣽⣿⣶⣾⣛⣛⣻⣿⣿⣿⣿⣿⡏⠃⠀⠚⠀⡐⣿⣤⣶⣾⣿⣿⣿⣿⣟⣛⣛⡻⢟⣛⡻⢗⣚⣒⠂⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣘⡻⣿⣿⣿⣿⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡿⠿⣿
⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠀⣿⣿⢿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⡿⠁⠀⠀⠀⠀⠀⡌⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢀⣿⠷⠚⠛⠸⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣧⣄⣈⠉⠙⠛⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⣁⣤⣤⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣷⣯⣿⣴⣮⡟⠿⠿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣾⣿⣿⣷⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⣿⢿⣿⠿⠁⠀⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣟⣿⣿⡿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠿⠿⢛⣉⣙⣛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣧⠀⠀⢠⣾⣿⣿⣿⣿⣷⣮⣥⣜⠭⠭⠛⠻⠟
⠄⠀⠀⠀⠤⠤⠤⠤⠤⠿⢿⣿⣿⣾⢷⣿⣿⣿⣿⣿⣿⣿⡿⠓⠓⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠒⠟⠛⠛⣛⠛⠃⢿⡿⠟⣿⣿⣍⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠂⠀⠀⠀⠒⠒⠒⠒⠒⠒⠛⣻⣿⣿⣛⣉⣿⣿⣿⠿⢿⣿⣉⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⠁⠀⢸⠁⠀⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀
⠂⠀⠀⠀⣹⣋⣉⣉⣉⣉⣉⣉⣩⣿⣥⣬⠍⠉⠀⠀⠀⠠⠴⠿⠦⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⢸⠀⠀⣿⠈⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣁⠀⠀⠀⢸⣥⣤⣤⠤⠤⠤⣤⣤⣿⣾⣿⠂⠀⠀⠀⠀⠀⠈⠋⢉⣁⣙⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠸⠿⠿⠿⠿⠛⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⡤⠀⠀⠀⢸⣿⠶⢶⣶⣶⣾⣿⣻⣿⣿⣿⣋⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣒⠒⠂⠀⠉⠉⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀
⣶⠀⠀⠀⠘⣛⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣗⠀⣥⢸⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⣿⣿⢻⣿⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⠀⢹⣿⣏⣿⣶⣶⣾⣿⣿⡀⠀⠨⢿⣿⣿⣿⣿⣄⡀⠀⢀⣀⣤⣤⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⢹⣿⠀⢸⣿⡏⠉⠉⠉⠉⣉⣁⣀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠙⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⢸⣿⠀⢸⣿⡟⠛⠛⠉⠉⠉⠉⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀
⠿⠸⠟⠀⠈⠛⠃⠀⠀⠀⣐⣒⣂⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠈⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣛⣛⣛⣛⣉⢉⣽⣿⣷⣶⣿⣛⣛⣿⣿⣿⣿⣿⣿⠛⠀⠀⠃⢀⢸⣿⣴⣶⣿⣿⣿⣿⢟⣛⣛⡛⢟⣛⡻⢷⣛⣓⠒⣐⡂⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣀⡹⣿⣿⣿⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣤⣴⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡿⠿⠟
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠈⣿⣿⡿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⡟⠁⠀⠀⠀⠀⢠⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⣠⣿⠿⠿⠛⠋⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣦⣄⡈⠉⠙⢛⣿⢛⢿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣤⣴⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣿⣿⣿⣾⣽⣯⣴⣿⠛⠿⢻⣿⣿⣿⣿⣇⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣥⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⠽⣿⡿⠏⠀⠸⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⣛⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠿⠟⣋⣉⣽⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⡆⠠⠠⣴⣿⣿⣿⣿⣿⣷⣷⣦⣶⠯⠍⠛⠛
⠤⠀⠀⠀⠠⠤⠤⠤⠤⠴⠿⣿⣿⣿⣿⣿⣿⣿⠓⠺⢿⣿⣿⠟⠚⢛⠉⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠛⠓⢛⡛⠛⠘⣿⠟⢹⡿⣯⣽⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀
⠒⠀⠀⠀⠐⡚⠒⠒⠒⠒⠒⢻⣿⣿⣿⣿⣿⣿⣏⣉⣿⣿⣏⣩⡅⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⡟⠀⠀⣧⠀⢸⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀
⠒⠀⠀⠀⠈⣟⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⠤⢼⣿⠵⠴⠾⠷⠖⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠀⠀⡇⠀⢼⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀
⣉⡁⠀⠀⠀⣽⣤⣤⣤⠤⠤⠤⣤⣾⣿⣿⣿⣿⣷⣿⣿⡒⠀⣛⣉⣉⣉⣋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠽⠿⠿⠟⠛⠛⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀
⣥⠄⠀⠀⠀⣿⣷⠶⢶⣶⣶⣿⣛⣿⣿⣿⣿⣿⣿⠟⣋⣉⣉⣩⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣒⡒⠀⠈⠉⠉⠉⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⣶⡆⠀⠀⠀⠛⣛⣟⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠙⣻⣿⣿⣿⣿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡃⢨⡄⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀
⢿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠉⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⢸⣷⡛⣻⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀
⢰⡿⣿⡇⠈⣿⣿⣿⣷⣶⣾⣿⣿⣷⠀⠠⠤⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀
⢘⡇⢿⡇⠀⣿⣿⡏⠉⠉⠉⢉⣉⣀⡀⠀⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡏⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⢸⡇⣼⡇⠀⢹⣿⡟⠛⠋⠉⠉⠉⠉⠁⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣰⡀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢻⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⠸⠇⠟⠇⠀⠘⠛⠁⠀⠀⢀⣒⣒⣀⣤⣤⣬⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠄⠀⠀⣀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀
⠿⠿⠿⠻⠻⠿⠿⠿⠿⢿⣿⣿⣛⣛⣛⣭⡉⢩⣽⣷⣶⣾⣟⣛⣻⣿⣿⣿⣿⣿⡟⠃⠂⠚⠀⡀⣿⣤⣶⣾⣿⣿⣿⢿⣛⣛⡛⢛⣛⡻⢷⣚⣛⠒⣂⡒⣂⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣀⡀⢿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⠉⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⢠⣤⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⣿⠟⠛
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠘⣿⣿⣿⢿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⣭⣵⣿⠋⠀⠀⠀⠀⠀⡼⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣄⡻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢰⣿⠿⠟⠛⠉⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢷⣤⣀⡉⡉⢙⣻⣟⠻⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣴⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⣀⣘⣿⣿⣿⣿⣿⣮⣿⣥⣶⣟⠻⠟⣿⣿⣿⣿⣿⡀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡭⢿⡿⠏⠁⠀⠿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡛⠛⠿⠛⢫⣥⣭⣭⣿⡿⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⠷⠀⠄⢠⣾⣿⣿⣿⣿⣿⣷⣶⣦⣒⠊⠉⠙
⠤⠄⠀⠀⠀⠤⠤⠤⠤⠤⠿⢿⣿⣿⣿⡿⡿⠳⠒⠚⢿⣿⣿⡟⠒⠚⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠚⠛⠛⡛⠛⠀⣿⡟⠹⡿⢿⣭⣯⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠒⠂⠀⠀⠀⡚⠒⠒⠒⠒⠒⠛⣿⣿⣿⣋⣉⣉⣉⣉⣽⣿⣏⢉⡥⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⣃⡀⠀⡏⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠒⠂⠀⠀⠀⣛⣉⣉⣉⣉⣉⣉⣉⣩⣽⣷⣤⠤⠤⢴⣿⠥⠤⠶⠷⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⠀⠀⠰⠀⠀⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⣉⡁⠀⠀⠀⣸⣥⣤⣤⠤⠤⠤⣤⠤⣿⣶⣿⠒⠒⢺⣿⣓⠂⢚⣉⣉⣉⣋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠸⠿⠟⠛⠛⢛⢃⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⣭⡤⠀⠀⠀⢼⣿⠶⢶⡶⢶⣾⣛⣻⣿⣿⣿⣍⣉⣿⣿⣉⣉⣨⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣒⡂⠀⠈⠉⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡇
⣶⣶⠀⠀⠀⠘⣛⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣃⢠⣥⣿⡇⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠄
⠿⣿⣿⣿⣿⣿⣿⣯⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠘⣿⠛⢻⣿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⢠⣿⣿⣿⠀⢻⣿⣏⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⠈⣿⢻⣿⠀⢸⣿⡏⠉⠉⠉⠉⣉⣭⣿⣿⣿⣿⣿⣿⠛⠿⠿⠿⣿⣿⣿⠋⠁⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⠀⡗⢸⣿⠀⢸⣿⡟⠛⠋⠉⠉⠉⠉⠉⠚⡿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⠀⡇⠻⠛⠀⠘⠛⠃⠀⠀⢀⣐⣒⣂⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀
⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢀⡀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀
⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣛⣛⣛⣭⡍⢩⣽⣶⣶⣶⣆⣒⣃⣴⣤⣴⣤⣴⡟⠃⠀⠐⠀⢀⢿⣧⣶⣾⣿⣿⣿⢿⣛⣛⡛⢛⣛⡻⢗⣚⣛⠒⣂⡐⣂⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣀⡀⢿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⢀⣀⣀⣀⣈⡉⢩⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢨⣿⡿⣿⣿⣟⣛
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠅⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⣿⣿⣿⢻⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣭⣥⣾⠋⠀⠀⠀⠀⠀⢰⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣄⡻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢠⡿⠟⠛⠛⠉⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣦⣄⡀⣉⠉⣛⣿⠻⢿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣀⣀⣈⣿⣿⣿⣿⣿⣶⣿⣯⣶⣞⡛⠟⣿⣿⣿⣿⣿⡄⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⡿⢿⣿⠟⠁⠀⠸⢿⣿⣿⣿⡿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣯⣽⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡉⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡟⠛⠛⠛⢫⣥⣤⣭⣿⣿⢛⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⠷⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣦⣶⣒⠒⠈⠉
⣉⣁⠀⠀⠀⢉⣉⣉⣭⣉⣽⣿⣿⣿⣿⣿⣿⠿⠤⠤⣿⣿⣿⡷⠦⠶⠖⠲⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠧⠼⠼⠧⠿⠿⠛⠹⣿⠟⢻⣿⣟⣻⣋⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠤⠤⠀⠀⠀⠠⠦⠤⠦⠤⠤⠾⢿⣿⡿⡿⠒⠒⠒⠒⣺⣿⣟⢓⣃⣈⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣶⣶⣶⣾⡇⠀⠀⡇⠀⢸⠆⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀
⠶⠦⠀⠀⠀⠐⠖⠒⠒⠒⠒⠚⢛⣛⣙⣿⣯⣍⣉⣉⣿⣯⣥⣤⡧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⢿⣿⡧⠀⠀⡃⠀⢸⡁⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⠒⡒⠀⠀⠀⢈⣏⣉⣉⣉⣉⣉⣩⣭⣼⣯⣿⡧⠤⢴⣿⡗⠀⠒⠓⠒⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⠁⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣉⣭⡀⠀⠀⠀⣿⣤⠤⢤⠤⠶⠿⢿⣾⣿⣿⣗⣒⣺⣿⣛⣉⣉⣉⣉⡉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠉⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⣷⣶⡄⠀⠀⠀⠿⢶⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠂⣈⣀⣶⡆⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣶⣶⣶⣿⣯⣍⣹⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⢹⡟⠟⣿⡇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⡗⣸⣿⣿⡇⠙⣿⣿⣻⣷⣶⣶⣶⣿⡇⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠁⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀
⡇⢸⡟⣿⡇⠀⣿⣿⠈⠉⠉⠉⠉⣉⣁⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⡄⢸⡇⣿⡇⠀⣿⣿⠖⠚⠛⠛⠛⠋⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⡇⢸⠛⠿⠇⠀⠛⠛⠀⠀⠀⢀⣒⣒⣀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀
⠛⠙⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣛⣛⣛⣻⣭⠉⡩⣽⣷⣾⣿⡛⡆⠀⠀⠀⠀⠀⠀⠒⠐⠐⠂⢀⢿⣧⣶⣾⣿⣿⣿⢟⣛⣛⡛⢛⣛⡻⢗⣚⣓⠒⣀⡂⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣀⡸⣿⣿⣿⣿⣿⣇⣠
⠀⢀⣀⣀⣀⣀⣀⣀⣬⣏⣉⣽⣿⣿⣿⣿⣿⡇⣯⣿⣿⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣽⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⡿⣿⣿⣟⢛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣿⣿⣛⣿⢟⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣄⡻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠟⠛⠉⢀⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢱⣦⣤⣀⣈⡉⣹⣏⡙⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠄⢀⣀⣀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣷⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣀⣀⣠⣬⣿⣿⣿⣿⣿⣷⣿⣶⣶⣋⡛⠛⣿⣿⣿⣿⣷⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣯⣿⣿⡖⢻⣿⣓⣀⡀⠻⠿⠿⡿⠿⠿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣯⣭⣭⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⡉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⠛⠋⠉⣤⣴⣶⣾⣿⣙⠿⠻⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠿⠁⠀⣀⡾⠿⣿⣿⣿⣿⣿⣿⣶⣬⣉⡀⠈⠉
⣋⣙⣛⠀⠀⠀⢈⣹⣿⣿⣝⣙⣿⣿⣿⣿⣿⣿⣿⣍⣉⣿⣿⡯⠭⠅⠅⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣯⣭⣿⣿⣷⡶⢶⣷⣿⢆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠃⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⣉⣉⣭⠀⠀⠀⠨⢭⣥⡤⠤⠼⢿⣿⣿⣿⣿⡿⠿⠶⠾⣿⣿⣿⠖⠒⠒⠒⠂⠀⠀⠀⠀⠀⠈⠻⣿⠿⠴⠷⠟⠺⠛⠛⠉⣿⡿⢹⣿⣋⣹⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠶⠶⠦⠄⠀⠀⠀⠛⠒⠒⠒⠒⠚⣻⣿⣟⣿⣛⣉⣉⣉⣿⣿⣋⣩⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣾⣿⣿⣿⣿⠀⠀⠇⠀⢸⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠
⣛⣛⣛⡃⠀⠀⠀⣏⣉⣉⣩⣉⣉⣭⣭⣭⣿⣿⣧⠤⢴⣿⠷⠶⠾⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠛⠻⣿⣿⠀⠀⠂⠀⠸⡆⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⣭⣭⣭⡅⠀⠀⠀⣽⡤⠤⠤⠦⠶⣶⣖⢲⣿⣾⣟⢒⣿⣿⣉⣉⣉⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠁⠛⠛⠛⢛⣛⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⣿⣶⡶⠆⠀⠀⠀⣾⣟⣒⣺⣻⣛⣛⣿⣿⣿⣿⣯⣭⣿⣯⣥⣤⣤⣴⣖⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣍⠉⢉⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸
⣿⣿⣿⣿⣀⣀⣀⣩⣯⣯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡅⣶⣼⣿⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⡛⣿⣿⣿⠿⣿⣿⣷⣖⣛⣛⣋⣭⠻⠿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠸⠏⣉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸
⡟⢻⠀⣿⣿⣿⠀⣿⣿⠾⠿⠿⠿⠿⠿⠂⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠈⠀⡟⢸⣿⠀⣿⣿⣤⣤⠤⠤⠴⠶⠖⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⣿⠃⡇⣾⣿⠀⢸⣿⠀⠀⠀⢀⡀⠤⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢠⣤
⣿⣏⣠⣥⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣼⡏
⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⠿⠿⠿⢟⡛⢛⣛⣿⣯⣿⣿⣄⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⣶⣇⣠⣤⣶⣶⣿⢟⣛⣛⡻⢟⣛⡻⢿⣛⣛⠀⣒⡒⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢙⣛⡻⣿⣿⣿⠀⣀⣿⠃
⠀⠀⣀⣀⣀⣀⣄⣤⣴⣶⣛⢛⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢀⡾⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⠿⠿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⠁⠀⠔⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢿⡷⣿⡟⠛⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣇⣄⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⣃⠻⠿⠟⠀⠋⠁⣀⣬⣴⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⢷⣦⣄⣀⣈⢹⣿⣉⠻⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⣿⣿⣿⡿⡿⠇⠀⠀⢀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣷⣿⣟⡙⠋⢿⣿⣿⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⠻⣿⣛⣀⣀⡸⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣯⣭⣽⣿⣿⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠿⠟⠛⠀⠀⠀⠀⡉⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠉⠉⠉⠉⣶⣶⣶⣾⣿⣩⠟⠛⠿⠿⣿⣿⡿⣋⣵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠃⠀⣀⣒⣻⡿⢿⣿⣿⣿⣿⣷⣬⣅⣀⣀⣮⣯⣭
⠤⠤⠤⠤⠀⠀⠀⠠⣼⣿⡿⠦⢿⣿⣿⣷⣶⣶⣶⡤⠝⢿⣿⣷⠴⠒⠒⠒⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣾⣇⣀⣀⣤⣤⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⡿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠶⠶⠖⠒⠀⠀⠀⠸⠛⠛⠛⠓⣾⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣍⣉⣉⣀⡀⠀⠀⠀⠀⠉⠙⢻⣿⣯⣉⣏⣿⣿⣿⣿⠻⣿⣿⣿⣿⡧⣿⢿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣧
⣋⣉⣉⣉⡀⠀⠀⢈⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⠭⠥⠤⢽⣿⠿⠧⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣭⣤⣤⣤⣤⣤⠀⠀⡏⠁⢸⡀⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿
⣯⡭⠤⠤⠄⠀⠀⠰⡦⠶⠶⠖⠒⠒⠛⠛⢺⣷⣖⣒⣀⣿⣛⣋⣹⣏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⢿⣿⣿⠀⠀⡇⠀⢸⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿
⣿⠖⡒⠒⠂⠀⠀⠈⣛⣉⣛⣉⣉⣉⣉⣭⣽⣯⣿⡯⢼⣿⡧⠄⠼⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠻⠀⠀⠀⠀⠘⠀⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿
⣿⣿⣽⣯⡁⠀⠀⠠⣽⡯⠥⡤⣴⠶⠿⣶⣿⣿⣿⣗⣺⣿⣛⣋⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠐⠒⠒⠒⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡃⠀⠀⢸⣿
⣽⣿⣿⣶⡆⠀⠀⠀⣻⣲⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⣥⢰⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠅⠀⠀⠈⠀
⣿⣿⣿⠿⣿⣿⡿⣿⣿⣿⣭⡽⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⣿⡜⢻⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣶
⣳⡿⡿⢰⡿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⡾⠀⠱⢈⡇⣿⡇⠀⣿⣿⣀⣀⣀⣠⣤⣤⠄⣴⣾⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⡇⢠⣾⢸⡇⣿⡇⠀⣿⣏⠉⠀⠀⢀⣀⡀⠀⠘⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⠀
⣿⣞⣋⣈⣃⣉⣁⣀⣨⣥⣤⣤⣤⣶⣶⣶⣿⣿⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⡟⠀
⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠆⠀⠀⠀⠀⠀⠠⢤⣶⣿⣿⣿⡇⠀⠀⢀⠠⢠⣴⢀⣀⣤⣴⣶⣾⢟⣛⣛⡿⢟⣛⡻⢿⣛⣃⠐⣒⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠘⢟⣛⡻⣿⣿⠀⠀⣿⡇⠀
⠀⠀⢀⣀⣀⣀⣀⣠⣈⣭⠿⠿⠶⣷⣶⣿⣿⣿⡆⣿⣤⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⠁⠀⠈⣀⣼⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⠾⢿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠰⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢲⣾⡿⠿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣯⣉⣉⣿⠏⠀⠀⠀⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⠀⠈⢘⣃⣸⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢶⣤⣄⢉⡉⣛⣿⡛⢿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣀⣀⣀⣼⣿⣿⣿⣿⣷⣾⣷⣶⣋⡛⠛⣿⣿⣿⣿⣧⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⡌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⢻⣿⣛⣀⣀⠿⠿⢿⣿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣯⣭⣿⣿⣿⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠛⠛⠛⠀⠀⠀⠀⡉⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡮⠉⠉⠉⣰⣶⣶⣾⣿⣉⠝⠛⠻⠿⢿⣿⡿⣋⣱⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠀⢠⣔⣻⣿⡿⢿⣿⣿⣿⣾⣶⣬⣀⣠⣾⣿⣭⣭
⠛⠛⡛⣛⠓⠀⠀⠀⣛⣿⣾⣷⣛⣿⣿⣿⣟⣻⣭⣉⣛⣿⣿⣯⣉⣉⣉⡁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀
⣭⣩⣭⣭⣍⠀⠀⠀⣭⡿⠿⠯⢭⣿⣿⣿⣿⣿⣿⣿⡧⢤⣿⣿⡗⠃⠐⠂⠀⠀⠀⠈⠉⠉⠛⢿⣿⣿⠛⡿⣿⢿⣿⣿⣷⣾⣿⣿⣷⣖⣿⣿⣟⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⠁⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⡟
⠶⠶⠶⠶⠒⠀⠀⠀⢲⡶⢲⠒⠒⠛⣿⣿⣿⣿⣟⣛⣛⣛⣿⣿⣟⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⣟⣓⣛⣛⣛⣉⠉⠀⡿⠛⢻⡛⣥⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿
⣿⣟⣟⣛⣛⠀⠀⠀⢨⣉⣩⣍⣩⡭⠽⠿⠯⢽⣯⡤⠤⢴⡿⡿⠐⡖⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⠀⠀⡇⠀⢸⠃⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿
⣿⣿⣭⡥⠥⠄⠀⠀⠸⠶⠶⠶⠒⠒⠒⠒⢒⣾⣟⣿⣛⣿⣟⣉⣉⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠇⠀⠸⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿
⢿⣿⣾⣷⣖⠂⠀⠀⢘⣿⣛⣛⣩⣭⣿⣿⣭⣿⣿⣿⢤⣿⡿⠶⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠭⠭⠭⠭⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿
⣙⣻⣿⣿⣯⡅⠀⠀⢸⠿⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡦⠀⡂⣤⡄⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠁
⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣚⣿⣿⠟⠿⠿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⣿⠿⢷⣦⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⣤
⠹⢻⡿⡟⢰⣿⣿⡇⢹⣿⣿⣿⣶⣶⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠉⠐⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉
⠀⡿⠀⠃⢸⡟⣿⡇⢸⣿⡏⠉⠉⢉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣠⡇⢠⣶⢸⣇⣿⡇⢸⣿⡟⠉⠉⠉⠉⠉⠁⠀⢀⣴⣶⣶⣶⣶⣤⣤⣶⣿⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣷⣼⠏⠘⠉⣋⣁⣀⣉⣁⣠⣤⣬⣭⣥⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⣿⣿⣿⣿⣿⡇⠀⢠⣿⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣟⣛⣿⣿⣿⣿⣿⣇⠀⠀⢀⠀⠀⢠⣴⢀⣀⣤⣤⣶⣾⢟⣛⣛⡿⢟⣛⡻⢷⣛⣃⠐⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠻⢟⣛⡻⢿⡇⠀⢸⡟⠀⠀
⠀⢀⣀⣀⣀⣀⣠⣤⣬⣭⣭⡽⠿⠿⣶⣶⣶⣾⣷⢸⣷⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⠉⠈⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣷⣾⣿⡷⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣴⣿⠿⣿⡿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣛⣛⣿⠟⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠈⣿⢀⣷⣥⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣤⣈⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⣨⣿⣿⣿⣿⣷⣽⣧⣿⣟⠿⢿⣿⣿⣿⣿⡄⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣺⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⢻⣿⣛⣀⣀⠿⣿⣿⡿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣭⣽⣿⣿⣟⣛⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠛⠛⠛⠂⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣌⠉⠉⠁⣶⣶⣾⣿⣏⣉⡛⢛⡿⠿⢿⣿⣋⣱⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠁⠀⣤⣾⣟⣿⡿⢿⣿⣿⣿⣷⣦⣤⣀⣶⣿⣿⣿⣧
⠤⣤⣤⣤⣤⡤⠀⠀⠀⠯⣭⣭⡭⢿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⡴⠦⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀
⠒⠶⠒⠖⠒⠒⠀⠀⠀⣲⣿⣿⣛⣺⣿⣿⣿⣻⣿⣿⣿⣋⣹⣿⣿⣸⡉⡉⠉⠁⠀⠀⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⣴⣶⡦⣰⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠻⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿
⣉⣭⣭⣍⣉⣉⠀⠀⠀⢭⣭⣭⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⢿⣿⣿⡶⠔⠒⠂⠀⠀⠀⠀⠀⠀⠈⢻⡿⠧⠼⠾⠿⠿⠟⠋⣿⡿⢿⠿⣓⣿⣻⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⣶⣶⡶⠶⠤⠦⠀⠀⠀⢒⠒⠺⣿⣿⣿⣿⣿⣟⣿⣛⣋⣁⣸⣿⣏⣩⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣶⣶⣾⣿⣿⠀⠀⡇⠀⢸⠃⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⣿⣿⣿⣛⣛⣛⠀⠀⠀⢹⣍⣭⣽⣿⣿⣿⢿⣷⣽⢿⣶⢤⣿⡷⠶⢾⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠇⠀⢸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣽⣿⣿⣽⣭⣥⠄⠀⠀⠸⡶⠶⠶⠒⡻⠁⠈⠃⠀⠘⠟⢹⣿⣯⡉⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⣛⣛⣛⣋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⠒⠺⣿⣿⣿⣟⡂⠀⠀⢸⣟⣫⣿⣯⣭⣤⣄⠀⠀⠀⠀⠈⠀⠐⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣭⣄⠀⠄⣀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠘⠛⠛
⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣷⣓⢺⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⣷⣿⣧⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀
⡟⠻⢿⣿⡿⢹⣿⣿⠋⢿⣿⣿⣯⣭⣭⣷⣶⠉⠙⣻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠛⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠚⠛⠋
⡇⠀⣼⠁⠇⢸⡿⣿⠀⢸⣿⡟⠛⠛⠉⢉⣉⡀⠀⣼⣿⣿⣿⣶⣶⣶⣶⣆⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣧⢀⡇⢠⣴⢸⣇⣿⠀⢸⣿⡟⠛⠋⠉⠉⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣧⡸⠏⠸⠘⠛⠀⢈⣛⣁⣀⣀⣀⣬⣥⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⡀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⣿⠀⠀⣾⡇⠀⠀
⠛⠟⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢀⠀⠀⠀⣤⠂⣀⣀⣤⣴⣶⢟⣛⣛⡿⢟⣛⡻⢷⣛⣃⠒⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡻⢿⠀⠀⣿⠁⠀⠀
⠀⠀⣀⣀⣀⣀⣀⣠⣤⣝⣛⢻⢯⡽⢿⣿⣷⣶⣶⡆⣿⣾⣿⣿⣧⣴⣾⣿⣿⣿⣿⠘⠈⠈⢀⣨⣿⣿⣿⣿⣿⣿⣿⡚⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢰⣶⣾⣿⢤⡤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣶⣿⣿⣟⣟⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣛⣻⠟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⢸⣂⣼⣽⣀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣤⣀⠉⠙⢻⡿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣤⣴⣶⣾⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⣀⣿⡿⣿⣿⣷⣼⣧⣿⣟⠿⢿⣿⣿⣿⣿⡄⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣞⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⡷⠻⣿⣛⣀⣀⠿⣿⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣯⣭⣿⣿⣿⣛⣛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⠿⠛⠛⠙⠂⠀⠀⠀⢠⠈⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⡄⠉⠁⢰⣶⣿⣿⣿⣭⣋⣛⢛⡿⠿⣿⣟⣽⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢠⣬⣿⣿⣿⣿⡿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣷⣾
⠒⡒⢒⠒⠒⠒⠒⠀⠀⠀⡷⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣒⡒⡒⠒⠒⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀
⣉⣉⣉⣉⣉⣉⣉⠀⠀⠀⣍⣿⣿⣯⣹⣿⣿⣿⣿⣿⣯⣭⠿⣿⣿⡤⠤⠤⠤⠤⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣉⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⣷
⡤⠴⠶⠶⠶⠶⠦⠀⠀⠀⠾⠟⠛⠓⢺⣿⣿⡿⢿⣿⣿⣿⣒⣿⣿⣯⣁⣀⣁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣹⣹⣿⣿⣿⡿⣿⣿⣿⣿⡯⣿⢿⣏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣟⣻⣿⣛⣛⣛⣋⠀⠀⠀⢩⣭⣭⣭⠭⢽⣿⣷⡿⠋⠩⠭⠭⣽⣿⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣭⣬⣬⣥⣤⡄⠀⠟⠉⢸⡅⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⠽⠶⠤⠀⠀⠀⢲⠶⠖⠒⠒⠒⠚⠉⠀⠀⠀⠀⢠⣿⣻⣩⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡇⠀⠁⠀⢸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣿⣻⣿⣿⣻⣛⣛⡀⠀⠀⢨⣭⣩⣭⠭⢭⣭⠤⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠀⠀⠀⠈⠀⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿
⣿⣭⣭⣿⣿⣯⡿⠄⠀⠀⢸⡷⠖⣶⣲⣞⣛⣻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⡒⠀⡀⠉⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠸⡿⠿⣿
⠿⢶⣶⣾⣿⣿⣿⣆⣀⣀⣨⣭⡯⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠀⣦⣿⣇⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⠿⡿⣿⣿⢛⣿⣿⠟⣿⣿⣿⣖⣛⣛⣯⣝⠛⠻⢿⣿⣷⣤⣤⣤⣀⡀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠟⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠸⠿⠿⠿
⣿⣧⠀⣲⠋⠇⢸⡿⣿⠀⢸⣿⠟⠻⠛⠛⠛⠛⠀⢈⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣇⠀⡏⢀⣠⢸⡇⣿⠀⢸⣿⠶⠖⠒⠒⠛⠛⠁⠸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣧⣸⡟⠸⠛⠟⠀⠘⠛⠀⠀⣀⣐⣒⣂⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⣿⣿⣿⣿⣿⡇⠀⢰⣶⠀⠀⠀
⠿⠟⠻⠿⠷⠶⠶⠒⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣀⠄⠀⢀⣀⣤⣴⢒⣛⣛⡿⢟⣛⡻⢷⣚⣁⠲⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡸⠿⢟⣛⡛⠇⠀⢸⡏⠀⠀⠀
⠀⠀⠀⢀⢀⣀⣀⣀⣀⣈⣛⣛⣛⣻⣯⣭⣭⣭⣷⣶⠀⣶⣾⣿⣿⣭⣭⣿⣿⣿⣿⡗⠀⠐⠂⢀⣿⣷⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢠⣴⣿⣧⣤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢿⣿⣷⢿⢆⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣿⣿⣿⣿⠛⢛⡻⠁⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⢨⢀⣏⣁⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣤⣀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠀⠀⣿⣿⣾⣠⣤⣴⣶⣾⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⣀⣀⣻⣿⣿⣿⣷⣭⣯⣬⣟⠿⢿⣿⣿⣿⣿⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣿⣿⠚⣿⣟⣀⣀⡿⣿⢿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣽⣿⣿⣟⣛⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⠟⠛⠉⠁⠀⠀⠀⠀⡀⠉⠉⠉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠁⣴⣶⣿⣿⣯⣝⣙⠛⡻⠿⢿⣿⣯⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢠⣼⣿⣛⣻⣿⠿⣿⣿⣿⣦⣤⣤⣶⣿⣿⣷⣶⣿
⣉⣛⣛⣛⣛⣛⣓⣒⡂⠀⠀⢘⣛⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀
⠤⠤⠤⠤⠦⠤⠤⠤⠄⠀⠀⠠⢭⣭⣭⠽⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡟⡿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣮⣦
⣗⡒⠒⣒⣛⣛⣓⣒⡂⠀⠀⢐⣺⣿⣿⣛⣻⣿⣿⣿⣿⣻⣿⣏⣹⣿⡯⠍⠉⠉⠉⠀⠀⠈⠙⠻⢿⣿⣿⡿⠿⢿⣿⣷⣿⣿⣿⣿⣧⡤⢴⣶⣶⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⠘⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣿
⣽⣿⡧⠭⠭⡭⠭⠤⠤⠀⠀⠨⢥⠤⠤⠤⠿⣿⣿⣿⡿⠟⠙⠓⢿⣿⣷⣒⡒⠂⠀⠀⠀⠀⠀⠀⠈⣿⡿⠇⠒⠛⠚⠛⠛⢹⡿⠛⡿⣏⣹⣽⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣓⣿⣷⣾⣿⣗⣓⣒⣂⠀⠀⠀⣉⣉⣉⣉⣉⣹⣿⠁⠀⠀⠀⠀⣾⡿⠭⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⠀⠸⠀⠀⡇⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣭⠤⠤⠀⠀⠀⠷⠖⠲⠒⠒⠒⠒⠒⠀⠀⠀⠀⠈⠛⢋⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣿⣿⣷⢚⣻⣿⣿⣛⣓⠀⠀⠀⣻⣭⣭⣭⣭⡿⣯⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠭⠭⠭⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⣭⣭⣽⣿⣿⣧⠀⠀⠀⠿⣶⢾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠄⣐⢰⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠻
⣿⣿⣦⣾⣿⣿⣿⡿⢿⣿⣿⢿⣿⣿⡭⠿⠿⢟⣻⠿⢿⣿⣿⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠙⠚⠛⠓⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⣴⣤
⣿⣿⣿⣇⠘⣹⠛⡇⢾⢻⡇⠀⣿⡗⠿⠿⠿⠿⠿⠀⠀⢺⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁
⣿⣿⣿⠋⠀⠏⠀⡁⣼⢸⡇⠀⣿⣧⡤⠤⠤⠴⠶⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡸⣄⢸⠇⢿⠸⠇⠀⠿⠇⠀⠀⠠⠤⠄⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⣿⣿⣿⣿⣿⡇⠀⣠⡄⠀⠀⠀
⠿⠿⠿⠻⠟⠯⠤⠤⠴⠶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⡀⠀⠀⢀⣀⣤⢄⣒⣛⡿⢟⣛⡻⢷⣛⣀⠖⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡻⠿⢟⣛⡛⠁⠀⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⠿⠿⣿⣛⣛⣛⣿⣯⣭⣭⠅⣥⣶⣶⣾⣍⣩⣿⣿⣿⣿⠁⠀⠀⢀⣸⣷⣶⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣤⣿⣀⡀⠀⠀
⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣤⣼⣿⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢿⣿⡿⡧⣤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⢛⠋⠀⠀⠀⠀⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⢹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⣈⡙⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢨⣄⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⣾⣷⣗⣀⣤⣤⣶⣾⣿⣿⣿⣿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣈⣿⣿⣿⣿⣮⣽⣦⣽⡻⠿⣿⣿⣿⣿⡆⠀⠀⢲⣿⣿⣿⣾⣿⣷⣶⣶⣶⣶⣤⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣾⣿⣿⡿⢻⣿⣋⣀⣸⠿⢿⡿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣛⣛⣻⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣧⠈⠉⢁⣶⣶⣿⣿⣯⣉⠛⢛⡿⠿⣿⣏⣽⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⠉⠉⠀⢠⣬⣽⣟⣻⣿⡿⣿⣿⣷⣦⣤⣴⣾⣿⣿⣶⣿⣿
⢒⣒⣒⣚⣛⣒⠒⠒⠒⠀⠀⠀⣗⣲⣺⣗⣒⣺⣿⣷⣿⣿⣿⣿⣿⣿⡟⢛⡛⡛⠻⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠤⠤⢤⣬⣭⡥⠬⠤⠤⠀⠀⠀⠭⣭⣭⡭⢿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠤⠤⠤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⣿⠿⠿⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⡦
⣶⡒⠒⠒⢒⣒⣒⠒⡒⠀⠀⠀⣒⣟⣿⣓⣺⣿⣿⣿⣿⣿⣿⣗⣹⣿⣿⢘⠉⠉⠉⠀⠀⠈⠛⠛⢿⣿⣿⡿⢿⣿⣿⣿⣿⣛⣛⣿⣿⣤⢤⣴⣶⢀⡆⠀⠀⠀⠀⠀⠀⠀⠸⡈⠟⢻⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣷
⣯⣿⣿⠭⣭⣭⣭⡭⠭⠀⠀⠀⠭⠥⠤⠤⠽⢿⣿⣿⣿⣿⠿⠟⠾⣿⣿⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⢹⣿⠧⠼⠼⠿⠟⠛⠙⣿⠟⣟⢿⣺⣋⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⠿⢺⣿⣶⣿⣷⣒⡒⣒⠂⠀⠀⣘⣓⣛⣃⣈⣙⣿⣿⣿⡿⠉⠩⢹⣿⠯⢭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⠀⠀⡀⠀⡟⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣭⣭⠭⠄⠀⠀⢨⠤⠴⠦⠔⠒⠚⠛⠋⠁⠀⠒⣿⣟⣒⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠂⠀⠏⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⠖⢟⣿⣾⣗⣒⡂⠀⠀⢘⣟⣉⣉⣭⣽⣯⡄⠀⠀⠀⠀⠙⠷⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠉⠩⠭⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⣯⣭⣭⣿⣿⣭⡄⠀⠀⠸⠷⡶⣶⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠄⢐⣠⣤⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠻
⣼⣿⣧⣴⣿⣿⣿⣿⠿⣿⣷⠶⣾⣿⣯⠽⠿⠿⢿⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠘⠛⠛⠒⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⢠⣤⣤⣤
⣿⣿⣿⣿⠀⢏⡟⠏⢸⣿⣿⠀⢹⣿⠺⣿⡿⠿⠿⠇⠀⠐⣿⣦⡀⠀⠀⢀⣀⡀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⠉
⣿⣿⣿⡟⠀⡾⠀⢘⢰⡇⣿⠀⢸⣿⣤⠤⠤⠤⠶⠶⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣀⢇⠀⡿⢸⠳⠿⠀⠸⠿⠀⠀⠀⠤⠤⢀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⣿⣿⣿⣿⣿⡇⠀⢠⡄⠀⠀⠀
⠻⠿⠟⠛⠟⠾⠥⠤⠤⠶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⢄⣐⣒⡿⢟⣛⡻⢷⣛⣁⠒⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡹⠿⢟⣛⡛⠃⠀⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⠿⠿⢿⣟⣛⣛⣛⣏⣭⣭⡍⢭⣥⣶⣶⣏⣩⣽⣿⣿⣿⠁⠀⠀⠀⣸⣧⣶⣾⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣤⣿⣀⡀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣤⣤⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠰⢶⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢿⣿⡽⡧⢤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⢐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⢈⠁⠹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣄⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⣾⣷⣞⣀⣠⣤⣴⣾⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⣈⣿⣿⣷⣿⣾⣽⣧⣭⠟⠿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣾⣿⣷⣶⣶⣶⣶⣤⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⡿⢿⣿⣛⣀⣸⠿⠿⡿⠿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣟⣛⣛⣻⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠸⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣧⠈⠉⠁⣶⣶⣿⣿⣯⣍⠛⢛⡻⠿⣿⣟⣽⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠉⠉⠉⠀⢠⣬⣽⣟⣿⣿⡿⢿⣿⣷⣦⣤⣤⣶⣿⣿⣶⣿⣿
⠒⠒⢒⣒⣒⡒⢒⠒⠒⠂⠀⠀⢲⣶⣶⣿⣖⣶⣿⣷⣾⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣭⣭⣭⣭⣭⣭⣬⣥⣤⠄⠀⠀⠹⣭⣭⡭⢿⣿⣿⣿⢽⡿⠿⠿⣿⣿⡭⠭⠭⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢈⣦
⣶⡖⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢒⣿⣻⣛⣚⣿⣿⣿⣛⣾⣿⣷⣚⣿⣷⣀⡉⢉⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣛⣿⣿⣤⣤⣤⣴⠄⣶⠀⠀⠀⠀⠀⠀⠀⠸⡆⠻⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣴⣿⣿
⣛⣻⣿⣍⣭⣭⣭⣭⠭⠅⠀⠀⠨⠭⠭⠭⠭⢿⣿⣿⢽⣿⡿⠿⠶⣿⣿⡖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠤⠼⠿⠿⠟⠋⣿⠿⣿⣟⣒⣟⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠿⠷⣿⣷⣶⣷⣖⡒⠒⠂⠀⠀⢐⣓⣚⣒⣖⣛⣿⣿⣙⣹⡏⢉⢩⣿⡯⠭⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢶⣶⣿⣿⠂⠀⠃⠀⢸⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣯⠀⠀⠀⣿⣿⣿
⣩⣿⣿⣿⣿⣿⣯⣯⠭⠅⠀⠀⠸⠥⠤⠾⣿⣿⣾⣿⡗⣾⣻⣷⣾⣗⣒⣚⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡀⠀⠀⠀⠸⢨⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡗⠀⠀⢸⣿⣿⣿
⢾⣿⣿⡶⠾⢿⣷⣶⣒⡂⠀⠀⢘⣟⣋⣙⣿⣿⣿⣿⣿⣿⣿⣧⣿⠷⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡀⠈⠉⠩⠭⠭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⣯⣩⣭⣿⣿⣯⡥⠀⠀⠸⠿⡶⢶⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡤⢀⡀⣤⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠻
⣴⣿⣧⣵⣿⣿⣿⣿⡿⣿⣿⡶⣾⣿⣯⡭⠿⠿⠛⠀⠀⠀⠀⠀⠙⠿⢯⡝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠘⠃⠛⠒⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢠⣤⣤⣤
⣿⣿⣿⣿⡀⠈⡼⢻⠁⡟⣿⡇⢸⣿⡿⢿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠀⠉
⣿⣿⣿⣿⠃⢸⠃⠈⠀⡇⣻⡇⢸⣿⣧⡤⠤⠤⠶⠶⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⣼⡀⣿⠁⡇⡿⠇⠘⠿⠀⠀⠀⠠⠤⠀⣀⣈⣻⣿⣷⣄⣀⡀⣠⣤⣦⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢿⣿⣿⣿⣿⡇⠀⢠⡄⠀⠀⠀
⠻⠿⠿⠿⠿⠮⠥⠤⠤⠴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⢀⣀⣒⡻⢟⣛⡻⢷⣛⣃⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠇⠀⣼⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣘⠿⠿⢿⣿⣛⣻⣿⣿⣭⣭⣍⢩⣵⣶⣾⣏⣉⣽⣿⣿⣿⠉⠀⠀⢀⢸⣧⣶⣾⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣠⣿⣀⡀⠀⠀
⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣴⣿⣿⣿⣿⣇⢸⣹⣿⣿⣿⣿⣿⡿⠛⠁⠰⢲⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢿⣿⡽⠧⢄⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣿⡿⠛⠋⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⢈⡋⠁⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢢⣄⡉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣶⣿⣾⣀⣠⣤⣴⣶⣷⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⣀⣿⣿⣷⣷⣾⣽⣮⣽⠟⠿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣾⣿⣷⣶⣶⣶⣶⣤⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⠽⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⡿⠛⣿⣛⣀⡸⠿⠿⣿⠿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣟⣛⣛⣿⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣷⡀⠉⠁⣰⣶⣿⣿⣯⣍⡛⢛⡻⠿⢿⣟⣝⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠉⠉⠉⠀⢠⣬⣽⣟⣛⣿⡿⢿⣿⣷⣦⣤⣴⣶⣿⣿⣶⣾⣿
⠒⠒⠒⠒⢒⡒⠒⠒⠒⠂⠀⠀⢸⣲⣶⣿⣒⣲⣿⣿⢺⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⢬⣭⣭⣭⣭⣭⡭⠥⠭⠄⠀⠀⠸⢭⣭⡭⢽⣿⣿⣿⢽⡿⠿⠿⣿⣿⡥⠭⠥⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣻⣿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⡄
⣶⣖⠒⠒⠒⠓⠒⠒⠒⠂⠀⠀⢐⣺⣻⣛⣒⣿⣿⣿⣛⣾⣿⣷⣚⣿⣿⣀⡉⢈⠁⠀⠀⠀⠛⠻⢿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣛⣿⣿⣤⡤⣤⣴⡆⣴⠀⠀⠀⠀⠀⠀⠀⠀⡆⠻⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣄⣶⣿
⣛⣻⣿⣏⣩⣭⣭⣭⡭⠅⠀⠀⠨⠭⠭⠭⠭⢿⣿⣿⢽⣿⡿⠿⠶⣿⣿⡖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠹⣿⠷⠤⠾⠧⠿⠛⠋⢻⠿⢻⡟⣓⣟⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠿⣷⣿⣷⣶⣶⡖⡒⠒⠂⠀⠀⢐⣒⣒⣓⣀⣈⣻⣿⣛⣹⣏⠉⢭⣿⡯⠭⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣶⣾⣿⣿⡇⠀⠁⠀⢸⠡⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣉⣿⣿⣿⣿⣿⣯⣭⠭⠅⠀⠀⠨⠥⠤⠤⠤⠀⠐⠒⠒⢺⣟⣷⣺⣗⣒⣚⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⠀⠸⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⢾⣿⣿⡖⠾⣻⣷⣗⣒⡒⠀⠀⢀⣻⣋⣉⣩⣭⣿⣭⣭⣿⣿⣿⣿⠷⠄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡀⠀⠉⠩⠭⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⢿⣿⣿⣯⣩⣭⣿⢿⣯⣥⠀⠀⠐⠿⣶⢶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡤⢀⡀⣤⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠛
⣤⣿⣿⣥⣿⣿⣿⣿⡿⢿⣿⡶⣾⣿⣯⡭⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣯⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠘⠃⠛⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⢠⣤⣤⣤
⣿⣿⣿⣿⠃⠨⣼⢻⠁⣿⣿⡇⢸⣿⡿⢿⣿⡿⠿⠷⠀⠀⢺⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠈
⣿⣿⣿⣿⠁⢰⠃⠀⡀⡇⢹⡇⠈⣿⣧⡤⠤⠤⠴⠶⠢⢿⣿⣿⣿⣿⣿⠿⠿⠁⠀⠀⠀⣼⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡀⡸⡀⣾⠃⡇⡿⠇⠀⠿⠃⠀⠀⠠⠤⠄⠀⠘⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⡇⠀⢠⣄⠀⠀⠀
⠛⠿⠿⠿⠿⠣⠥⠤⠤⠴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⢀⣀⢀⣀⣒⡻⢟⣛⡻⢷⣚⣋⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠇⠀⣸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣘⠿⠿⢿⣿⣛⣛⣟⣯⣩⣭⣤⠀⠀⠀⠀⡀⣀⣀⣤⣤⣶⠈⠀⠈⣀⣸⣧⣶⣾⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣠⣿⣁⡀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⠰⢮⣟⣯⣿⣿⣿⡿⠋⠁⠐⠺⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢿⣿⡽⠯⢤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣥⣾⣿⣿⠛⠋⠀⠀⠀⠀⢈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⢈⠁⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢠⣄⡉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣾⣁⣠⣤⣴⣶⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⣀⣿⣿⣷⣿⣾⣽⣦⣽⠟⠿⣿⣿⣿⣿⡇⠀⠀⠐⣾⣿⣿⣶⣿⣿⣶⣶⣶⣶⣤⣤⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣷⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⡿⠛⣿⣋⣀⡸⠿⠿⡿⠿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣽⣿⣿⣟⣛⣛⣿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣷⠀⠉⠁⣰⣶⣿⣿⣯⣍⡙⠛⡛⠿⢿⣟⣽⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠉⠉⠉⠀⢰⣬⣽⣿⣛⣻⣿⠿⣿⣷⣶⣤⣤⣶⣿⣿⣶⣾⣿
⣒⣒⣚⣛⣛⣟⣒⡒⢒⡂⠀⠀⢸⣒⣾⣿⣒⣲⣿⣿⣺⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⡃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠤⠤⠤⣤⣤⡤⠤⠤⠤⠄⠀⠀⠸⢭⣭⣭⠽⣿⣿⣿⢽⡿⠿⠿⢿⣿⡦⠄⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⡿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡤
⣿⣖⠒⠒⢒⣛⣒⣒⣒⡂⠀⠀⢐⣺⣻⣿⣚⣿⣿⣿⣟⣿⣿⣿⡋⣿⣿⠍⠉⠉⠉⠁⠀⠀⠛⠿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣛⣿⣿⣥⠤⣴⣶⡆⣴⠀⠀⠀⠀⠀⠀⠀⠀⡃⠻⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣷⣿
⣿⣿⣿⡯⢭⢭⡭⠭⠭⠅⠀⠀⠨⠭⠤⠤⠬⠿⣿⣿⣾⣿⡿⠟⠓⢿⣿⡗⡒⢒⠒⠀⠀⠀⠀⠀⠈⢻⣿⠷⠔⠛⠓⠛⠛⠋⢿⡟⢻⡿⣋⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠟⢿⣿⣷⣾⣿⣖⣒⣒⡂⠀⠀⢀⣉⣉⣉⣉⣉⣻⣿⡯⢭⡯⠭⢤⣿⠯⠥⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⡇⠀⠀⠄⢸⠁⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣉⣿⣿⣿⣿⣿⣿⡭⠤⠤⠀⠀⠀⠧⠒⠒⠒⠒⠒⠒⠒⣲⣟⣿⣺⣟⣛⢙⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠾⣿⣿⣗⢺⣻⣿⣷⣚⣓⠀⠀⠀⣻⣍⣭⣭⣭⠿⢦⣤⣿⣿⣿⣿⠷⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠩⠭⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠿⢿⣿⣿⣭⣭⡽⣿⣯⣧⠀⠀⠀⠿⣶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡦⢀⡂⣴⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠉⠈⠛
⣴⣿⣿⣦⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⣿⡬⠿⠿⢛⣛⠿⢿⣿⣿⣿⣿⣯⣭⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠈⠗⠛⠛⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⣴⣦
⣿⣿⣿⣿⡇⠸⣸⠻⠁⣿⣿⡇⠘⣿⡟⠿⠿⠿⠿⠿⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠁⢰⠇⠀⡁⡿⢸⡇⠀⣿⣧⠤⠤⠤⠶⠶⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣀⡸⡄⢸⠇⡇⠿⠇⠀⠿⠃⠀⠀⠠⠄⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⡿⠀⢠⣤⠀⠀⠀
⠛⠿⠿⠛⠛⠃⠤⠤⠶⠶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⢀⣀⣒⡺⢟⣛⡻⢷⣛⣛⠁⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠇⠀⣸⡇⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣝⠻⢿⣿⣛⣛⣻⣿⣭⣭⣭⣭⢠⣴⣶⣶⣮⡉⠀⠀⠀⠀⠈⠀⢈⣀⣜⣷⣶⣾⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣤⣿⣁⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⢸⣾⣿⣿⣿⣿⣤⠀⠀⠀⠐⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢽⣿⡟⡿⢤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⡏⠀⠀⠀⠀⢠⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠄⢀⣝⣀⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣤⣈⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣞⣀⣤⣴⣶⣶⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⠇⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣶⣭⣧⣭⣟⠿⢿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣿⣿⣷⠺⣿⣋⣀⣸⣿⠿⣿⣿⣻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣭⣿⣿⣿⣛⣛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⡄⠀⠀⣸⣿⣿⣿⣯⣼⡉⠙⢛⠻⠿⢟⣥⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠁⠀⢰⣾⣭⣽⣿⣛⣿⡿⢿⣿⣶⣤⣤⣿⣿⣶⣶⣾⣿
⠭⠭⢭⣭⣭⣭⠍⡍⠉⠁⠀⠀⢸⣭⣽⣿⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⡯⠉⠭⠭⠉⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⡒⠒⠲⠶⠶⡶⠖⠖⠒⠂⠀⠀⠐⢲⣶⣶⠚⣿⣿⣿⣾⣟⣛⣛⢻⣿⣗⡒⣒⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣹⡟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠐⣄
⣿⣯⣉⣉⣉⣩⣍⣭⣉⡉⠀⠀⢨⣽⠽⠯⠭⣽⣿⣿⣯⣿⣿⣿⡧⣿⣿⡄⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⠛⡟⣿⣿⣿⣯⣭⣿⣿⣷⡒⣾⣿⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⠙⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣿⣿
⣬⣽⣿⡷⠰⣶⠶⠖⠒⠂⠀⠀⠐⣒⣒⣒⣒⣛⣿⣿⣟⣿⣟⣛⣉⣻⣿⣏⡉⠉⠉⠁⠀⠀⠀⠀⠈⢻⣿⣛⣒⣛⣛⣉⡉⠁⢹⡟⢹⡟⣥⣯⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣟⣙⣛⣿⣿⣿⣯⣭⣭⡍⠀⠀⠀⡭⠭⠭⠤⠤⠽⠿⠧⠤⣷⡀⢲⡿⡓⣒⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⡇⠀⠰⠀⢸⠃⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠤⢶⣿⠿⢿⣿⣿⠶⠒⠒⠀⠀⠀⣗⣒⣚⣋⣉⣉⣉⣉⣹⣯⣿⣽⡯⠭⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡇⠀⠘⠀⠘⠀⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣛⣿⣿⣏⣙⣹⣿⣿⣭⡭⠀⠀⠀⣽⠤⢤⢶⣶⣿⣷⣶⣿⣿⣿⣿⣟⣋⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠐⠒⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠛⣻⣿⠿⣶⣶⣿⣻⣷⣶⣀⣀⢀⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⠀⣅⣶⡆⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉
⢶⣿⣿⣶⡿⢿⣿⣿⡟⣻⣿⡟⢻⣿⡿⣖⣛⣛⣫⣿⠛⠿⢿⣿⣿⣿⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠿⠉⠙⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠶⠶⠶
⣿⣿⣿⣿⣧⠀⣸⠙⡇⢿⢻⡇⠀⣿⡏⠛⠛⠛⠛⠛⠀⠀⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠁⢀⠃⢀⡅⣼⢸⡇⠀⣿⡷⠖⠒⠒⠛⠛⠃⠸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⡜⠦⠸⠃⠛⠚⠃⠀⠛⢃⣀⣀⣐⣒⣀⣤⣤⣽⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⣿⠀⢰⣶⠀⠀⠀
⠛⠛⠛⠛⠉⠁⠐⠒⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣤⠀⠀⣀⣀⣤⢄⣐⣒⡿⢟⣛⡻⢷⣛⣛⠛⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡈⠿⢟⣛⡻⠏⠀⢸⡇⠀⠀⠀
⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣝⡛⣛⣿⣯⣭⠽⢿⣷⣶⣶⣿⣲⡔⠋⠁⠀⠀⠀⢀⣾⣿⡇⠀⢀⣀⣤⣿⣾⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢠⣴⣿⣧⣤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠸⣿⢀⠀⠀⠀⣰⡿⠛⠁⢀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠺⠿⣿⠛⡲⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣾⣿⣿⣿⣉⠉⠀⠀⠀⠀⠀⠝⢿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⠀⣀⣠⣥⣄⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣶⣤⣈⣉⢙⣛⡿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⢟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠃⠀⠀⠀⢠⣤⣤⣽⣿⢿⣿⣿⣶⣷⣶⣋⠛⢻⣿⣿⣿⣧⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣟⣉⣿⣥⣤⣼⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠁⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠟⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⠿⢿⣿⣿⠆⠀⢀⣼⣿⣿⣿⣷⣾⣥⣉⠭⠛⠛⣫⣶⢿⠿⢿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⢐⣿⣶⣾⣯⣽⣿⡛⠿⠿⢿⣶⣶⣿⣿⣿⣿⣿⣿
⠤⠤⠤⠤⠭⠯⠥⠥⠤⠄⠀⠀⢸⣭⠿⢿⣭⣽⣿⣿⢽⣿⣿⣿⣿⣿⠯⠤⠥⠤⠭⠅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣒⣒⣒⣛⣒⣗⣒⣒⣒⡂⠀⠀⢘⣲⣶⣶⣚⣿⣿⣿⣻⣛⣋⣛⣻⣿⣇⣁⣁⣀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟⠛⠛⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣔⣀
⣿⣿⣭⠭⠭⡭⠭⠭⠭⠅⠀⠀⠸⠼⠿⠿⠤⣽⣿⣿⢧⣿⣿⣿⡃⣿⣿⡒⠒⠒⠀⠀⠀⠀⠛⠛⢿⣿⣿⣟⠛⡟⣿⣿⣿⡿⣶⣿⣿⣷⣖⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿
⣶⣿⣿⡗⢒⣒⣒⣒⣒⡂⠀⠀⢀⣒⣒⣒⣈⣙⣿⣿⣿⣿⣟⠋⠉⣿⣿⠯⠭⠭⠉⠀⠀⠀⠀⠀⠀⠙⣿⣏⣉⣉⣉⣩⡍⠁⠛⠏⢸⡝⣧⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣽⣍⣿⣿⣿⣿⣯⡭⠭⠅⠀⠀⠠⡤⠤⠤⠤⠀⠚⠛⠓⢲⣗⣒⣺⣟⣓⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⡇⠀⠐⠀⢸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⡶⢶⣿⠛⢿⣿⣿⣓⣒⣒⠀⠀⢀⣏⣉⣉⣉⣉⡭⠭⠭⣽⣿⣿⣿⡷⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠐⠀⠈⠀⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣛⣻⣿⣯⢭⢽⣿⣯⡭⠦⠀⠀⠀⣿⠶⣲⣶⣒⣛⣻⣾⣿⣿⣿⣿⣏⣉⣩⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠒⠒⠀⠀⠀⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⡿⠿⣿
⠛⣛⣿⠿⣖⣶⣿⣿⣿⣿⣀⣀⣀⣯⡭⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠠⡤⣿⣆⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⡿⢻⢿⣿⡏⣿⣿⡟⢻⣿⡿⣿⣛⣿⣭⣍⠛⠛⣿⣿⣿⣿⣿⡷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠟⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠿⠿⠟
⣿⣿⣿⣿⡧⠘⡾⠙⡁⣿⢿⡇⠀⣿⡏⠛⠛⠛⠛⠛⣤⡀⠉⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠁⢨⠃⢠⡆⣿⣸⡇⠀⣿⡗⠒⠚⠛⠁⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⡞⠦⠸⠁⠃⠛⠃⣀⣛⣁⣀⣀⣠⣬⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⡿⠀⢰⡶⠀⠀⠀
⠙⠛⠙⠉⠉⠑⠒⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⢤⢴⣶⣿⣿⣿⣿⣿⣧⢀⠀⢀⡀⠀⣤⠀⣀⣠⣤⣴⢟⣛⣛⡿⢟⣛⡻⢷⣚⣛⠒⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡈⠿⢟⣛⡻⠇⠀⣼⡇⠀⠀⠀
⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣝⣛⣿⣯⣭⡽⠿⢿⣷⣶⣿⣶⢀⣾⣿⣿⣷⣶⣾⣿⣿⣿⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢠⣶⣿⣦⣤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠠⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠿⠿⣿⠛⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣭⡍⠀⠀⠀⠀⠀⡎⠿⣿⣿⣿⣿⣿⣿⣿⣧⡿⢟⡀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⢀⣤⣤⣧⣤⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣶⣤⣄⣉⠹⣟⡿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⢀⣀⣀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⢱⣿⣶⣴⣶⣶⣿⣿⣿⡿⢿⣿⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⣿⣿⣿⣿⠃⠀⠀⠀⣤⣤⣶⣿⣟⡿⣿⣿⡾⣷⣿⡭⠛⢿⣿⣿⣿⣧⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣟⣙⣿⣷⣦⣼⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣶⣶⣿⣿⣿⣭⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⠿⢛⣋⣛⣻⣿⢿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣯⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⠆⠀⠀⣼⣿⣿⣿⣿⣶⣦⣌⡉⠉⠛⣻⣶⣿⣟⢿⣿
⣿⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣯⣽⠟⠛⠻⡿⣿⣾⣿⣿⣿⣿⣿⣿
⠲⠶⠶⠶⠶⠶⠰⠤⠤⠀⠀⠀⢸⡶⠿⠿⣶⣿⣿⣿⢾⣿⣿⣿⣿⣿⠃⠐⠒⠐⠘⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀
⣛⣛⣛⣛⣛⣟⣛⣛⣛⡁⠀⠀⢈⣹⣿⣿⣉⣿⣿⣿⣽⣩⣭⣝⢿⣿⡍⠩⠭⠭⠤⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣼⠋⠉⢉⣉⡁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣾⣧
⣿⣷⣤⡤⠤⠤⠤⠦⠤⠄⠀⠀⠰⠾⠞⠓⠲⣿⣿⣿⢶⣿⣿⣿⣒⣿⣿⣒⣒⣐⣀⠀⠀⠀⠈⠉⠻⢿⣿⣟⢙⣻⣟⣿⣿⡿⣷⣿⣿⣿⣍⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣾⣿⣿⣗⣺⣿⣿⣛⣋⡁⠀⠀⢨⣝⣩⣭⠉⠹⣿⣿⣽⢿⡯⠭⢭⣿⡿⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣭⣭⣭⣭⣥⡄⠀⡟⠉⢸⠃⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠽⠭⣿⣿⣿⣿⡷⠦⠤⠄⠀⠀⢰⣶⣶⣶⠒⠒⣚⣛⣒⣺⣧⣀⣽⣿⣩⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠛⠻⢿⣿⡇⠀⠁⠀⢸⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣒⣲⣿⣛⣿⣿⣟⣟⣋⣃⠀⠀⠸⣿⣿⣿⣭⣭⣤⠤⢤⣿⣾⡟⣿⣗⠒⢚⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠐⠿⠿⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡯⠥⢿⣷⣿⢷⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠉⡉⢉⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠿⠿⣿
⠙⣿⡿⢿⣿⣿⣿⣿⣿⣿⣤⣀⣠⣭⡿⠽⡿⠃⠉⠃⠉⠛⠿⠟⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢰⡆⣿⣤⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⡀
⣿⣿⣿⣿⠟⠻⢻⣿⠏⣿⣿⡏⢻⣿⣿⣯⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠛⠁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠀⠀⠘⠛⠛⠟
⣿⣿⣿⣿⡆⢘⡟⠘⠀⡏⢿⡇⢸⣿⡟⠛⠛⠉⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣏⣿⠀⢸⠀⣤⡆⡇⣼⡇⠈⣿⡟⠋⠉⠉⠉⠉⠀⢸⣿⣿⣶⣶⣤⣶⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⠊⠆⠻⠀⣃⣋⣁⣀⣉⣀⣠⣤⣬⣭⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀
⠋⠙⠉⠉⠉⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣟⣛⣿⠿⢿⣿⡇⠀⠠⠀⠠⠀⢠⣦⣀⣤⣴⣶⣿⢟⣛⣛⡛⢛⣛⡻⢷⣒⣒⠒⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠇⠀⣿⠇⠀⠀⠀
⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣍⣉⣭⣿⣿⡿⢛⣻⣿⣿⣿⣷⢸⣿⣿⣿⣿⣶⣿⣿⣿⣷⠄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠰⢿⣿⣶⣖⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⠋⠁⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠻⠻⣯⡯⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣭⠄⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⣬⣴⣿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣷⣦⣤⣈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⢻⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⠃⠀⠀⠀⣴⣶⣶⣿⣟⣿⣿⣿⢿⣾⣯⡝⢿⣿⣿⣿⣿⣷⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⡿⠿⠿⣿⠀⠀⠀⠀⠛⠛⠿⠿⠿⣿⣿⣯⣋⣛⣿⣶⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⠛⢋⣭⣽⣿⡿⢿⠿⣿⣿⣿⣿⣿⢟⣛⣯⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⠂⢀⡠⠿⣿⣿⣿⣿⣷⣶⣤⣒⠉⢉⣵⣿⣿⣛⣻⣿
⠿⢿⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣤⣄⡀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⠭⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠒⣒⣒⣺⣒⢒⠒⠒⠀⠀⠀⣻⠟⢛⡛⣿⣿⣿⣗⣿⣿⣿⣿⣿⣟⣒⣒⣒⡂⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀
⣭⣭⠭⢭⣭⣭⣭⠭⠭⠀⠀⠀⠭⣽⣿⣿⣽⣿⣿⣿⢯⣥⣦⡭⢿⣿⡤⠠⠀⠂⠐⠆⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣉⣀⣠⣠⡀⡄⠀⠀⠀⠀⠀⠀⠀⢰⠌⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣿⣆
⢿⣷⣖⠒⠒⣒⢒⡒⠒⠀⠀⠀⢒⣛⣻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣹⣿⣯⣉⠈⠍⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣸⣹⣿⣿⡿⠿⣿⡿⣿⣿⢼⡿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠐⢣⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠰⣿⣿⣿
⣿⣿⣿⣍⣭⣭⣽⡭⠭⠀⠀⠀⠤⠯⢿⣿⣿⣿⣿⣿⠾⢿⠖⠒⢺⣿⡛⢒⡒⠂⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣦⣶⣶⣶⠀⠀⡟⠀⣿⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⠞⠒⣿⣿⣿⣿⣖⣒⣒⠂⠀⠀⢸⣒⣛⣿⣿⣿⣿⡏⠉⣿⣯⡭⣿⡯⠤⢼⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⠀⠀⡇⠀⢹⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣏⣽⣯⣽⣿⣿⣿⣭⣭⡅⠀⠀⢸⡦⠴⠶⠚⠛⠛⠁⠀⠙⢿⣿⣿⣏⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠛⠛⣛⣛⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣿⣿⣿⡖⠒⢿⣿⣟⣿⡃⠀⠀⢸⣟⣭⣽⣭⣤⣄⠀⠀⠀⠀⠈⠙⢶⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣩⣭⡀⠠⢀⣀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇⠀⠀⠘⠛⠻⢿
⣩⣿⣟⣻⣿⣿⣿⣿⣿⣷⣤⣤⣴⣶⣓⣻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⢸⡿⣿⣤⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⣀
⣿⣿⣿⣿⠉⠿⣿⣿⢠⣿⣿⠋⢻⣿⣻⣿⣷⣶⣶⡎⠉⠁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠈⠁⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠘⠋⠉⠛
⣿⣿⣿⣿⠆⢰⠇⠸⠈⡇⣿⡆⢸⣿⡉⢉⣉⣉⣩⣤⠀⣰⣿⣿⣷⣶⣶⣶⣆⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣟⡏⠀⣼⠀⣶⠰⡇⣿⠇⢸⣿⠉⠉⠉⠉⣁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⣿⣿⣿⣿⣿⡇⠀⢀⡀⠀⠀⠀
⣿⣿⣿⣿⣶⠙⣂⣛⣀⣁⣉⣠⣤⣥⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢹⣿⣿⣿⣿⡇⠀⣾⡇⠀⠀⠀
⠉⠉⠉⠉⠀⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣟⡛⢛⣻⣿⣿⡿⠿⢿⣷⣤⣀⠀⠀⠐⠀⣰⣦⣴⣶⣿⣿⣿⢟⣛⣛⡛⢛⣛⡛⢓⣀⣒⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠁⣀⣿⠀⠀⠀⠀
⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣍⣹⣿⣶⣶⣛⣛⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠘⣿⣿⣿⣇⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠛⢻⠷⢳⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⡘⠙⠻⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⢟⣠⣶⣾⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣷⣦⣄⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢤⣴⣦⣦⣴⣶⣦⣤⣤⣤⣄⣀⣀⠻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠁⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⠻⣿⣿⣿⣿⣧⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠿⠿⠿⢿⠀⠀⠀⠀⡍⠛⠛⠻⠿⠿⠿⢍⣋⣩⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠛⠋⣥⣤⣿⣿⣟⠟⠿⠿⣿⣿⣿⡟⣻⣭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠃⢀⣐⣿⣿⣿⣿⣿⣿⣿⣮⣅⣀⣩⣭⣿⣿⣭⣿⣿
⠿⡿⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡋⠉⢹⣿⣟⣿⣿⣿⣿⣿⣿⣿
⣉⣉⣉⣉⣭⣉⣉⣉⣉⠀⠀⠈⣟⣋⣉⣛⣿⣿⣿⣯⣿⣿⣿⣿⣿⡏⠍⠭⠍⠍⠩⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⡄
⣶⠤⠤⠶⠶⠶⠶⠶⠶⠀⠀⠀⡖⣿⣿⣷⣿⣿⣿⣿⣷⣶⣶⡞⣻⣿⣖⣖⣂⣂⣘⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣤⣤⣤⣤⢠⡆⠀⠀⠀⠀⠀⠀⠀⠸⠘⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣼⣿⣧
⣿⣿⣦⣉⣛⣛⣛⣉⣉⠀⠀⠀⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⡿⠧⢿⣿⣧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠈⣿⡿⠦⠼⠿⠿⠿⢿⢹⣿⠿⣿⣟⣺⣛⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⣤⣶⣶⠴⠦⠶⠀⠀⠀⡚⠒⠒⠒⠚⣻⣷⣾⠟⠳⣂⣀⣼⣿⡉⣩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⣶⣿⣿⣿⠀⠐⣍⠀⡯⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣒⣛⣿⣿⣿⣿⣛⣋⣉⡀⠀⠀⣭⡭⠭⠭⠥⠭⠉⠁⠀⠀⠀⢶⣿⠒⢒⣛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣭⣿⣿⢿⢿⣿⢾⣶⡶⠀⠀⠀⢺⣖⣒⣒⣒⣲⣤⣀⠀⠀⠀⠀⠉⠡⠤⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣘⠉⠉⠭⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣾⣟⣿⣚⣛⣿⣿⣿⣿⡁⠀⠀⠽⡯⡽⣿⣿⣶⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠄⢰⢠⣄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠿
⣴⣿⣯⣻⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣍⣻⣿⡿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⡼⢿⣶⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢠⣤⣤⣤
⣿⣿⣿⣿⠉⣋⡿⡟⢰⣿⣿⠀⢿⣿⢿⣶⣶⣿⣿⠇⠀⠸⣿⣿⣶⣤⣤⣤⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠈⠁⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠈⠁
⣿⣿⣿⡟⠀⡾⠁⠁⢸⠏⣿⠀⢸⣿⣀⣀⣀⣤⣤⡤⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⣇⠰⡿⢸⢰⣿⠀⢸⡿⠁⠀⠀⣀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⣿⣿⣿⣿⣿⡇⠀⣤⡀⠀⠀⠀
⣿⣿⣿⣿⣎⣈⣀⣥⣬⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⣾⣿⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢿⣿⣿⣿⣿⠁⠀⣿⠁⠀⠀⠀
⠉⠉⠀⠀⠀⠈⠀⠀⠉⢿⣿⣿⣿⡿⠿⢿⣿⣟⣻⣿⣿⡋⢭⣭⣿⣿⣛⣛⣿⣿⣿⡖⠂⠀⣢⣴⣿⣾⣿⣿⣿⣿⣿⢟⣛⣛⡛⢛⣛⡛⢂⣀⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡸⠿⢟⣛⡛⣀⣼⣟⣀⠀⠀⠀
⣤⣤⣤⣶⣶⣶⣶⣶⣶⣷⣤⣾⣿⣿⣿⣍⣭⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠈⣿⣿⣿⡧⣠⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠃⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠉⣹⡗⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⡙⠻⣿⣿⣿⣿⣿⣿⣶⣤⣄⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⢟⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣶⣌⠻⠿⣿⣿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣷⣶⣶⣶⣤⣤⣤⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣭⢿⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢺⣿⣿⣿⡿⠀⠀⠀⠐⣿⣿⣿⣿⣿⡿⣷⣦⣄⣀⠉⢻⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⣛⣟⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠛⠛⠻⠇⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠋⠁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣧⠉⠉⠁⣶⣶⣾⣿⣏⣙⡛⣻⠿⠿⣿⣫⣝⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⣤⣽⣿⣛⣿⣿⣿⣿⣿⣶⣦⣤⣴⣿⣿⣿⣶⣿⣿
⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⣿⣿⣶⣦⣤⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣁⣀⣽⣯⣽⣿⣿⣿⣿⢿⣿⣿
⠤⠤⠤⠴⠶⠴⠤⠤⠄⠀⠀⠸⠭⣤⣤⡼⢿⣿⣿⣿⣿⠿⠿⣿⣿⡘⠒⠒⢒⠀⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣿⣭
⣗⡒⢛⣛⣛⣛⣛⣛⡃⠀⠀⢸⣹⣿⣿⣉⣹⣿⣿⣿⣿⣿⣯⢭⣿⣿⠼⠥⠬⠄⠅⠀⠀⠙⠛⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣿⣿⣷⡖⣾⣿⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠉⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿
⣿⣿⡧⠭⠭⠭⠥⠤⠄⠀⠀⠨⡤⠤⠦⠐⢻⣿⣿⣟⣿⣿⣛⡚⣿⣿⣖⣒⡘⠀⠀⠀⠀⠀⠀⠀⢻⣿⣛⡒⣛⣛⣛⡛⠇⢻⡟⢹⡟⣭⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣷⣾⣿⣟⣛⣛⡃⠀⠀⢨⣉⣉⣉⣉⠩⠽⢿⡿⠛⠀⠠⢴⡿⠏⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⣿⣿⡇⠀⢸⠄⢸⠃⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⣭⣽⣿⣿⣿⣿⡧⠤⠤⠀⠀⠀⡷⠒⠒⠒⠒⣒⣂⠀⠀⠀⠀⠙⠯⠉⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠘⠀⠘⠂⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⣾⣿⡞⣟⣿⣟⣿⣿⣃⠀⠀⠈⣿⣭⣭⣭⡭⡷⢶⣶⡄⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⠿⣿⣿⣭⣽⣿⣿⣿⣷⠀⠀⠀⣟⣶⣻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⠀⣅⣶⡆⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⢛
⣿⣿⣮⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⣷⡮⠿⢿⣛⣛⠿⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠿⢙⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⡶⠶⢿⠿
⣿⣿⣿⡇⠸⣽⠻⠇⣿⣿⡇⠈⣿⡗⠿⠿⠿⠿⠟⠀⠀⣻⣿⣿⣶⣶⣶⡄⠀⠀⠀⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⢐⠇⢀⡃⣿⢸⡇⠀⣿⣧⠤⠤⠴⠶⠾⠂⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡀⡸⣄⢸⠇⠿⠾⠇⠀⠿⠃⠀⠀⠠⣄⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠘⣿⣿⣿⣿⣿⠀⢠⣶⠀⠀⠀⠀
⣿⣿⣿⣿⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⣿⣿⣿⣿⡟⠀⢸⡏⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣛⣛⣿⣿⣭⣭⣭⣿⢠⣶⣶⣿⣿⣭⣽⣿⣿⣿⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡻⢟⣛⡛⢂⣚⣒⠂⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡻⠿⢟⣛⡣⢴⣾⣧⣤⠀⠀⠀
⣤⣤⣶⣶⣶⣶⣾⣿⣿⣷⣬⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡺⣿⣿⣿⣿⣿⣿⣿⡿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⢿⣿⣻⡲⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣛⣛⠋⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠃⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠀⢰⣿⣮⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠀⢳⣦⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⢟⣴⣿⣿⣿⢟⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡟⠀⠀⠀⢀⣈⣻⣯⣹⢿⣿⠛⢿⣿⣿⣿⣿⡃⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣶⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣭⣄⠀⢀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠛⠛⠛⠀⠀⠀⠀⢰⠀⠀⠀⠈⠙⠋⠁⠐⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣻⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣧⠀⢀⣸⣿⣿⣿⣿⣶⣭⣍⠭⠟⠛⢿⣶⣿⡿⢿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣶⣷⣿⣯⣿⣿⣻⡿⠿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿
⠿⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⢿⣿⠛⠿
⠲⠶⠶⠶⠶⠶⠲⠖⠀⠀⠀⡟⢲⣶⣶⠚⣿⣿⣷⣟⣛⣛⣻⣿⣷⣃⣀⣀⣀⣠⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⢠⡐⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣷
⣍⣉⣉⣉⣩⣩⣉⣉⠀⠀⠀⣭⡿⠿⠯⢭⣿⣿⣿⣿⣿⣿⡤⢼⣿⡗⠂⠀⠂⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⢻⢻⣿⣿⣿⣿⣶⣿⣿⣿⣻⣿⣿⣳⡇⠀⠀⠀⠀⠀⠀⠀⠨⢇⠉⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿
⣿⣿⠤⣶⣶⠶⠶⠒⠀⠀⠀⢒⣖⣒⣒⣚⣿⣿⣿⣿⣿⣛⣉⢙⣿⣿⠩⠉⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣉⣉⣉⣩⣭⠉⠀⡿⠉⣿⢻⣾⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿
⣛⣿⣿⣿⣿⣽⣭⣭⠁⠀⠀⢬⡭⠭⠥⠤⠽⣿⣿⣿⡗⠒⠒⣾⣿⣒⣲⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⠀⠀⡇⠀⢿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿
⢤⡿⢿⣿⣿⣾⠶⠶⠂⠀⠀⢸⣒⣒⣛⣉⣉⣹⣿⠟⠉⠹⢩⣿⡯⠭⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠄⠀⠁⠀⠘⢸⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣛⣻⣿⣿⣿⣭⡅⠀⠀⢨⣿⢤⢴⣶⠾⣿⠀⠀⠀⠀⠘⢛⣛⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠒⠂⠀⠈⠉⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇⠀⠀⠸⠿⠿⣿⣿
⣿⣿⣦⣴⣿⣿⣿⣿⣇⡀⠀⢘⣛⣟⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢨⣶⣿⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣩
⣿⣷⣾⠿⣿⣿⣿⠛⣿⣿⠿⣿⣿⣷⣞⣛⣛⣻⡟⠻⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠸⠏⣝⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠸⠟⠛⠿⠟
⣿⣿⣿⡄⢁⡟⢻⠸⡟⣿⡀⢸⣿⠾⠿⠿⠟⠛⠃⠀⢈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠁⢸⠁⣈⠀⡇⣿⡇⢸⣿⠶⠖⠒⠒⠛⠛⠀⢺⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⢇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣁⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⣀⠾⡀⣿⠀⠇⠟⠃⠘⠛⠀⢀⣀⣐⣒⣠⣤⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢸⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠈⠀⣀⠀⠀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⢸⣿⣿⣿⣿⡇⠀⣿⠇⠀⠀⠀⠀
⠁⠁⠀⠀⠀⠀⠀⠀⠙⢿⣟⣛⣻⣿⢭⠭⢭⣿⣷⣶⣶⢸⣿⣿⣿⣷⣶⣾⣿⣿⡏⠁⢀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡻⢟⣛⡛⢒⣒⣂⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣘⡻⠿⢟⣛⡲⢾⣿⣶⡦⠀⢀⣀
⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣮⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⠻⣯⡯⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣉⡝⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣸⣷⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢴⡿⢿⣿⣋⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠃⠀⠀⠀⣀⣭⣿⣧⣽⣻⣿⠟⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⡷⢀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠃⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠁⠀⠘⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢟⣋⣛⣻⣿⠿⣿⣿⣿⣿⣿⣿⠿⣛⣻⣿⣾⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⡿⠧⠀⠠⣾⣿⣿⣿⣿⣷⣶⣖⣋⠉⢛⣛⣿⣿⣟⣻⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣶⣤⣀⣸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⢯⡟⠛⠛
⠒⠒⠚⣓⣚⣓⣒⠂⠀⠀⣚⣳⣶⣶⣞⣿⣿⣿⣛⣛⣛⣛⣿⣿⣍⢉⠭⠩⠤⡧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣉⣁⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⣗
⣉⠩⣭⢭⠭⠭⠭⠅⠀⠀⠼⠾⠿⠷⠦⣼⣿⣿⣿⣿⣿⡖⣲⣿⣿⡚⣒⣒⠀⠂⠀⠀⠈⠙⠻⣿⣿⣿⢙⣟⣿⣿⣿⡿⣿⣿⢿⣿⡯⣿⢿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⡖⣒⣒⣒⣒⣒⡂⠀⠀⢐⣖⣚⣛⣛⣿⣿⣿⣿⣿⠯⠭⠭⣿⡿⠯⠥⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣭⣭⣭⣵⡄⠀⢹⡏⢸⡏⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣭⠭⠅⠀⠀⢰⠤⠤⣾⣿⣿⣿⣿⣟⣗⣒⣒⣺⣟⣋⣉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⡇⠀⢸⠀⢸⠁⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣖⣒⡂⠀⠀⢘⣏⣉⣹⣿⣿⣿⣿⣿⣯⣿⡧⣿⡷⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠀⠈⠁⠿⠿⠿⠟⠛⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣍⣿⣿⣿⣿⣭⡥⠀⠀⠠⣿⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣀⣈⠉⡉⢉⡁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⢟⠛⠿⣿⣿
⣿⣷⣶⣾⣿⣿⣿⣷⣀⣀⣈⣽⡿⢽⣿⣿⣿⣿⠿⠋⠛⠿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⣶⣿⣧⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⣨⣭
⣿⣿⡿⢿⣿⣿⡟⣻⣿⡟⢻⣿⡿⣗⣛⣻⣯⡅⠀⠀⠀⠀⠈⠛⠻⠗⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠛⢲⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠛⠋⠛⠛⠋
⣿⣿⡇⠘⡾⠙⡇⣿⢿⡇⠀⣿⡏⠛⠛⠛⠛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠃⢸⠃⢀⡅⣿⢸⡇⠀⣿⡷⠒⠒⠚⠛⠛⠁⠐⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣬⣤⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣄⠜⠦⠸⠃⠻⠛⠃⠀⢛⣃⣀⣀⣐⣦⣤⣤⣴⣿⣿⣿⣶⣤⣀⣴⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢹⣿⣿⣿⣿⠀⢠⣿⠀⠀⠀⠀⠀
⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⢠⡄⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⠶⠿⠿⠾⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⣸⣿⣿⣿⡿⠀⢸⡟⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠈⢛⣿⣻⣿⣿⣿⠿⢿⣷⣶⣶⣿⡆⣿⣿⣿⣿⣶⣶⣿⣿⣶⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡛⢛⣛⡓⢒⣂⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠤⣀⣛⡻⠿⢛⣛⡛⢿⣿⣶⡂⢀⣤⣀
⣤⣶⣶⣶⣶⣶⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣷⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⢿⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣯⡭⠉⠀⠀⢀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠀⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠿⠟⠀⠻⠿⠟⠸⠿⠸⢿⡘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⢃⠻⠿⠟⣐⣿⣿⣯⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⡟⠀⠀⠀⢠⣤⣽⣿⣷⣿⣽⣟⣋⠻⣿⣿⣿⣿⣿⣂⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠁⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⠿⠛⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⢉⠉⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⠛⣭⣭⣭⣿⡟⡿⠿⣿⣿⣿⣿⡿⢻⣭⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠟⠂⣀⣴⣿⣿⣿⣿⣿⣷⣯⣭⣆⣉⣩⣿⣿⣿⣭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠉⠝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⠉⠉⠉

                    ䷩ 𝚕𝚒𝚗𝚎 1988

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_03/09/2022:_digiKam_7.8.0,_Deepin_20.7,_and_Arti_1.0.0_Released⠀✐


Posted in News_Roundup at 2:29 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Distro_Videos
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
                # GNOME_Desktop/GTK
    * Distributions_and_Operating_Systems
          o New_Releases
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
                # Perl_/_Raku
                # Python
                # Java
          o Standards/Consortia
    * Leftovers
          o Hardware
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy
          o Finance
          o AstroTurf/Lobbying/Politics
    * Gemini*_and_Gopher
          o Personal
          o Technical
    * § GNU/Linux⠀➾


          o § Distro Videos⠀➾


                # ⚓ Video ☛ PeppermintOS_Based_on_Devuan_–_Invidious⠀⇛


                       In this video I’ll be taking a look at PeppermintOS
                       based on Devuan, It looks to be be an exact copy of
                       the Debian Based PeppermintOS minus the ability to
                       install Snap Packages which I believe need SystemD
                       to work. During this look around I take a closer
                       look at the Peppermint tools which you will find in
                       both builds and the choices made by the community
                       for their purpose. Hope you enjoy the video.


                # ⚓ Makulu_Max,_Weekend_Update_on_The_Theming_series_–
                  MakuluLinux⠀⇛


          o § Graphics Stack⠀➾


                # ⚓ Ricardo García ☛ Geek_Blight_–_VK_EXT_mesh_shader_finally
                  released⠀⇛


                       Vulkan 1.3.226 was released yesterday and it
                       finally includes the cross-vendor
                       VK_EXT_mesh_shader extension. This has definitely
                       been an important moment for me. As part of my job
                       at Igalia and our collaboration with Valve, I had
                       the chance to work reviewing this extension in
                       depth and writing thousands of CTS tests for it.
                       You’ll notice I’m listed as one of the extension
                       contributors. Hopefully, the new tests will be
                       released to the public soon as part of the open
                       source VK-GL-CTS Khronos project.


                       [...]


                       Both Timur and myself have submitted a couple of
                       talks to XDC 2022 which have been accepted and will
                       give you a primer on mesh shading as well as some
                       more information on the RADV implementation. Do not
                       miss the event at Minneapolis or enjoy it remotely
                       while it’s being livestreamed in October.


          o § Applications⠀➾


                # ⚓ Tor ☛ Arti_1.0.0_is_released:_Our_Rust_Tor_implementation
                  is_ready_for_production_use._|_The_Tor_Project⠀⇛


                       Back in 2020, we started work on a new
                       implementation of the Tor protocols in the Rust
                       programming language. Now we believe it’s ready for
                       wider use.


                       In this blog post, we’ll tell you more about the
                       history of the Arti project, where it is now, and
                       where it will go next.


                # ⚓ LWN ☛ Arti_1.0.0_released_[LWN.net]⠀⇛


                       Arti is a reimplementation of the Tor server in
                       Rust; version 1.0.0 has just been released and
                       proclaimed ready for production use.


          o § Instructionals/Technical⠀➾


                # ⚓ LinuxOpSys ☛ Dig_Command_in_Linux_–_Usage_+_Examples⠀⇛


                       Domain Name System (DNS) is a hierarchical naming
                       system that stores critical domain name
                       information. The DNS resource records also contain
                       other information related to the records. If you
                       have configuration or connectivity issues with a
                       DNS server, then use the dig command to query DNS
                       records.


                # ⚓ UNIX Cop ☛ How_to_get_and_change_PDF_metadata_on_Linux
                  using_the_terminal⠀⇛


                       Hello, friends. In this post, I will show you How
                       to get and change PDF metadata on Linux using the
                       terminal. So, you can quickly use it for a specific
                       case or several files. You can even include it in
                       scripts.


                # ⚓ uni Toronto ☛ Using_systemd_timers_to_run_things_frequently
                  (some_early_notes)⠀⇛


                       If you’re satisfied with running something no more
                       often than once a minute, /etc/cron.d entries are
                       the easiest approach and what I use. But today I
                       wound up wanting to run something more frequently.
                       While there are various ways to do this with
                       various degrees of hackery, it seemed like a good
                       time to try out systemd timer units.


                # ⚓ Linux Capable ☛ How_to_Install_mpv_Media_Player_on_Linux
                  Mint_21_LTS⠀⇛


                       MPV is a highly versatile media player that
                       supports various video and audio codecs. It has
                       comprehensive playback, audio, and video control
                       options, as well as support for different input URL
                       types for reading input from a variety of sources
                       other than disk files. MPV is available on
                       Microsoft Windows, macOS, Linux, and BSD operating
                       systems and is often used to play YouTube videos or
                       be a client for streaming services such as
                       Twitch.tv. Thanks to its wide range of features and
                       compatibility with many different operating
                       systems, MPV has become one of the most popular
                       media players available today.


                       In the following tutorial, you will learn how to
                       install mpv Media Player on Linux Mint 21 LTS using
                       three different methods using the command line
                       terminal.


                # ⚓ Linuxiac ☛ How_to_Set_Up_Nginx,_MariaDB,_and_PHP_with
                  Docker_Compose⠀⇛


                       This guide shows you how to set up your LEMP
                       (Nginx, MariaDB, PHP) stack easily and quickly
                       using Docker Compose.


                       When it comes to application development,
                       containers are now the standard approach. They are
                       popular among software developers due to their
                       flexibility and portability.


                       The LEMP stack is an open-source solution used to
                       develop web applications. It is an acronym
                       representing Linux, Nginx, MySQL/MariaDB, and PHP.
                       In addition, it is widely popular and well-
                       supported among the Open Source community.


                # ⚓ Linux Made Simple ☛ How_to_install_J-Stars_Victory_Vs_Mugen
                  on_a_Chromebook⠀⇛


                       Today we are looking at how to install J-Stars
                       Victory Vs Mugen 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.


                # ⚓ ID Root ☛ How_To_Install_Thunderbird_on_Linux_Mint_21_–
                  idroot⠀⇛


                       In this tutorial, we will show you how to install
                       Thunderbird on Linux Mint 21. For those of you who
                       didn’t know, Thunderbird is a free and open-source
                       email client developed by Mozilla Foundation. It
                       offers support for multiple email accounts, a
                       personal address book, and built-in search tools to
                       help you find messages quickly. This application
                       can also be used as a chat client, RSS, and news
                       client app.


                       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 a Thunderbird on Linux Mint 21
                       (Vanessa).


                # ⚓ PXE_boot_netboot.xyz_on_a_Mikrotik_router_–_Major_Hayden⠀⇛


                       The first RFCs for PXE, or preboot execution
                       environment, showed up in June 1981 and it’s still
                       a popular tool today. It enables computers to boot
                       up and download some software that runs early in
                       the boot process.


          o § Desktop Environments/WMs⠀➾


                # ⚓ Bryan Lunduke ☛ Make_Linux_look_like_IRIX_from_an_SGI
                  workstation⠀⇛


                       From the late 1980s through the early 2000s,
                       Silicon Graphics, inc. (or just SGI as they were
                       typically called) produced the IRIX operating
                       system for their line of high performance, multi-
                       media workstations.


                       IRIX was (really is) pretty darn cool. Based on
                       UNIX System V (plus BSD extensions), IRIX is where
                       OpenGL was created. Along with the XFS file system.
                       High performance, and highly scalable (up to 1024
                       processors).


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


                      # ⚓ Its FOSS ☛ 8_Exciting_New_Features_in_the_Upcoming
                        KDE_5.26_Release⠀⇛


                             KDE Plasma, the popular desktop environment,
                             has been receiving some major updates and
                             tons of fixes over the last five months.


                             The previous release—Plasma 5.25—saw many new
                             features and improvements, especially to the
                             user interface and experience, and the next
                             release sounds even more exciting.


                             [...]


                             Just like the last release, Plasma 5.26
                             brings in numerous refinements and how you
                             interact with the UI. You will find subtle
                             changes, and tweaks to give more information
                             to the users while interacting/searching for
                             things on KDE Plasma 5.26.


                             For instance, the Settings pages for “Format”
                             and “Language” pages have now been merged to
                             give you a cleaner look and get rid of some
                             usual bugs associated with it.


                      # ⚓ Nate Graham ☛ This_week_in_KDE:_day_color_–
                        Adventures_in_Linux_and_KDE⠀⇛


                             We’re getting close to the Plasma 5.26 beta
                             and plenty of features have landed before the
                             soft feature freeze–the point at which new
                             features need discussion before being merge-
                             able. Many are mentioned below! But now, the
                             idea is to focus on bugfixing and UI polish
                             for the next six weeks before the final
                             release of Plasma 5.26, and assistance is
                             greatly appreciated. If you’re a developer
                             who’s excited about Plasma, the time to fix
                             bugs is now! Which bugs? These bugs! Pick a
                             bug and fix it!


                             [...]


                             On System Settings’ Night Color page, you can
                             now set a day color in addition to a night
                             color for maximum flexibility…


                      # ⚓ digiKam_–_digiKam_7.8.0_is_released⠀⇛


                             After three months of active maintenance and
                             another bug triage, the digiKam team is proud
                             to present version 7.8.0 of its open source
                             digital photo manager. See below the list of
                             most important features coming with this
                             release.


                             [...]


                             Rendez-vous in a few months for the new major
                             digiKam 8.0.0 release.


                # § GNOME Desktop/GTK⠀➾


                      # ⚓ DebugPoint ☛ GNOME_Web_43_Looks_Beautiful_with
                        Adwaita_Tab_View⠀⇛


                             GNOME Web 43 Tab View looks awesome and its
                             going to change your workflow.


                             Our beloved GNOME Web (Epiphany) becoming
                             more and more intuitive in every passing day
                             – thanks to the developers.


                             Recently, it has been ported to GTK4,
                             libadwaita which brings the nice looks
                             overall and some cool new features. All of
                             these changes arriving on GNOME 43 release
                             due in a few weeks.


                             [...]


                             In my opinion, the most cool feature of GNOME
                             Web 43 is the Tab view.


    * § Distributions and Operating Systems⠀➾


          o ⚓ T2_22.9_“TOP_SECRET”_–_The_Open_System_Development_Environment⠀⇛


                 Today T2 SDE Linux 22.9 was released. Another major
                 milestone update with latest and greatest GCC, LLVM /
                 Clang, X.org, Mesa3D, Glibc and more. Improved security,
                 as well as SMART and whole-program LTO optimizations.


                 As technology snapshot a pre-built binary ISO is relased
                 for high-performance x86-64-v3, and of course all other
                 architectures, including: alpha, arc, arm, arm64, avr32,
                 hppa, ia64, m68k, mipsel, mips64, nios2, ppc, ppc64-32,
                 ppc64le, riscv, riscv64, s390x, sparc, sparc64, superh
                 x86, x86-64 and x32 can be rolling release updated thru
                 the scripted build system from source – optimized for the
                 native system.


                 There were 1450 changesets with 2378 lines of commit
                 messages. Approximately 1918 packages got updates, 122
                 issues fixed, 1918 packages or features added and 47
                 removed. Around 15 improvements have been committed.


          o § New Releases⠀➾


                # ⚓ Deepin_20.7_Released_–_Deepin_Technology_Community⠀⇛


                       Deepin is the top Linux distribution from China,
                       devoted to providing a beautiful, easy-to-use,
                       safe, and reliable operating system for global
                       users. (Global Ranking)


                       In deepin 20.7, we have developed and integrated a
                       great number of practical functions based on the
                       community users’ feedback, synchronized with the
                       upstream kernel version, fixed underlying
                       vulnerabilities, upgraded the Stable kernel to
                       V5.15.45, added the HWE 5.18 kernel to be
                       compatible with more devices, and further improved
                       system compatibility and security. Welcome to try
                       it!


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ John Gruber ☛ What_Explains_Android_vs._iPhone_Usage_Share
                  Discrepancies_Between_Countries?⠀⇛


                       Today’s earlier item about iPhone usage share
                       overtaking Android in the U.S. led to an
                       interesting thread on Twitter regarding the
                       seemingly curious large differences in iPhone/
                       Android share between different countries. The
                       iPhone is particularly popular in the U.S. and
                       Japan, and in English-speaking countries (Canada,
                       United Kingdom, Australia) in general. Android, for
                       obvious reasons, is overwhelmingly popular in
                       poorer countries. But there are wealthy countries
                       like Germany and France where Android is more
                       popular by roughly 3 to 1 margins. I suspect there
                       is no simple answer to this, and that it comes down
                       to nuanced but significant nation-by-nation
                       cultural differences.


                # ⚓ Android Police ☛ Google_and_Qualcomm_tease_satellite
                  connectivity_for_Android_phones⠀⇛


                # ⚓ TechRadar ☛ Redmi_A1_with_clean_Android_launching_on
                  September_6_|_TechRadar⠀⇛


                # ⚓ Lifewire ☛ How_to_Clear_a_YouTube_Queue_With_Chromecast_on
                  Android⠀⇛


                # ⚓ Giz China ☛ AnTuTu:_Here_are_the_TOP_10_most_powerful
                  Android_smartphones⠀⇛


                # ⚓ Gmail_Notifications_Not_Working_Android?_Here’s_9_Ways_To
                  Fix_It⠀⇛


                # ⚓ Forbes ☛ Android_Circuit:_Stunning_Honor_70_Launches,_Nokia
                  Circular_Subscription_Service,_Pixel_7_Pro_Specs_Leak⠀⇛


                # ⚓ GSM Arena ☛ Android_app_developers_can_sign_up_for_Google
                  Play_Store’s_User_Choice_Billing_–_GSMArena.com_news⠀⇛


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


          o § Programming/Development⠀➾


                # ⚓ Rlang ☛ A_proposal_for_capping_exploding_electricity_spot
                  market_prices_without_subsidies_or_supply_reduction_|_R-
                  bloggers⠀⇛


                       At the EEX, German baseload electricity futures for
                       the year 2023 trade at a price of 950 Euro / MWh
                       and peak load futures at 1275 Euro / MWh. Future
                       prices for France are even higher. (Prices were
                       looked up on 2022-08-28).


                # ⚓ Harshvardhan ☛ Up_and_Running_with_R_Markdown⠀⇛


                # ⚓ Rlang ☛ 23_New_books_added_to_Big_Book_of_R_|_R-bloggers⠀⇛


                       Today we have another huge addition of books to the
                       library, now consisting at 350 R programming books!
                       Thanks to Gary and Abraham for the additions!


                # ⚓ Stacey on IoT ☛ When_is_TinyML_too_much?⠀⇛


                       When it comes to machine learning (ML), sometimes
                       every problem looks like it needs a neural net,
                       when in fact it just needs some statistics. This is
                       especially true when it comes to running algorithms
                       on microcontrollers and for industrial use cases
                       such as predictive maintenance, according to
                       Bernard Burg, director of AI and data science at
                       Infineon.


                       I focus a lot on using machine learning at the edge
                       — specifically the idea of running machine learning
                       models on microcontrollers, known as TinyML —
                       because there are clear benefits for the IoT. By
                       analyzing incoming data where that data is created,
                       engineers can reduce latency, lower bandwidth
                       costs, and increase privacy while also saving on
                       energy consumption. But one doesn’t always need
                       TinyML. Sometimes using linear regression or
                       anomaly detection will do.


                # ⚓ Rlang ☛ pkgdown_and_GDPR_–_How_to_host_a_pkgdown_site_in
                  Germany_|_R-bloggers⠀⇛


                       pkgdown is a great tool for generating a website
                       with documentation for an R package.


                       Unfortunately, pkgdown uses CDNs (content delivery
                       networks) like Cloudflare to embed often used
                       JavaScript libraries into the generated website.


                # ⚓ Rlang ☛ How_a_Local_Community_Produced_the_First_Nation-
                  wide_R_useR_Group_|_R-bloggers⠀⇛


                       The R Consortium recently interviewed Szilard Pafka
                       with the Real Data Science USA R Group (formerly
                       known as the Los Angeles R User Group). The former
                       Los Angeles R useR Group had been based in Los
                       Angeles for more than 10 years, but after organizer
                       Szilard moved to Texas, he kept the group going and
                       even expanded!


                # ⚓ PowerDNS ☛ Sharing_data_between_threads_in_PowerDNS
                  Recursor_|_PowerDNS_Blog⠀⇛


                       This is the third part of a series of blog posts we
                       are publishing, mostly around recent developments
                       with respect to PowerDNS Recursor. The first blog
                       post was Refreshing Of Almost Expired Records:
                       Keeping The Cache Hot, the second Probing DoT
                       Support of Authoritative Servers: Just Try It.


                       In PowerDNS Recursor the actual resolving is done
                       using mthreads: a lightweight cooperative thread
                       switching mechanism. This allows us to write the
                       resolving code in a straightforward manner, we can
                       program it as if we are resolving in a synchronous
                       way. The mthreads abstraction takes care of running
                       another mthread when the resolving process for a
                       particular query has to wait for incoming data from
                       the network. Mthreads are mapped to Posix threads,
                       the thread abstraction the C++ runtime provides.
                       Typically a handful of Posix threads run many
                       mthreads, one for each query in-progress. Mthread
                       switching happens only at specific points in the
                       resolving process, basically whenever I/O is done.


                # ⚓ Lee Yingtong Li ☛ Gamma_regression_in_Stata_and
                  statsmodels⠀⇛


                       Generalised linear models with a gamma distribution
                       and log link are frequently used to model non-
                       negative right-skewed continuous data, such as
                       costs [1].


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ On_interpolating_stuff_into_pattern_matches_|
                        Aristotle_[blogs.perl.org]⠀⇛


                             Ironically, it’s qr objects which don’t get
                             that benefit. On the machine I’m typing on,
                             the following benchmark…


                # § Python⠀➾


                      # ⚓ How_to_Use_the_String_join()_Method_in_Python_–_Pi_My
                        Life_Up⠀⇛


                             The join method makes it easy to combine
                             multiple strings stored within an iterable
                             such as tuples, lists, sets, and
                             dictionaries. In addition, you can set
                             characters to be used as a separator, such as
                             a space or a dash.


                             There are many more methods that you can use
                             to manipulate strings within Python. For
                             example, you can use the split method to
                             split a string based on a specified
                             separator.


                             The tutorial below will touch on the syntax
                             of the join method and the various iterables
                             you can use with join. For example, we will
                             touch on using a join with a list,
                             dictionary, set, or tuple.


                      # ⚓ Didier Stevens ☛ Update:_jpegdump.py_Version_0.0.10_|
                        Didier_Stevens⠀⇛


                             This update to jpegdump.py, my tool to
                             analyze JPEG images, brings 2 small changes:


                             Data between segments can be selected with
                             suffix d. Like this: -s 10d


                             This means: select the data between segments
                             9 and 10.


                # § Java⠀➾


                      # ⚓ OpenSource.com ☛ Infuse_your_awk_scripts_with_Groovy
                        |_Opensource.com⠀⇛


                             Recently I wrote a series on using Groovy
                             scripts to clean up the tags in my music
                             files. I developed a framework that
                             recognized the structure of my music
                             directory and used it to iterate over the
                             content files. In the final article of that
                             series, I separated this framework into a
                             utility class that my scripts could use to
                             process the content files.


                             This separate framework reminded me a lot of
                             the way awk works. For those of you
                             unfamiliar with awk, you might benefit from
                             Opensource.com’s eBook, A practical guide to
                             learning awk.


                             I have used awk extensively since 1984, when
                             our little company bought its first “real”
                             computer, which ran System V Unix. For me,
                             awk was a revelation: It had associative
                             memory— think arrays indexed by strings
                             instead of numbers. It had regular
                             expressions built in, seemed designed to deal
                             with data, especially in columns, and was
                             compact and easy to learn. Finally, it was
                             designed to work in Unix pipelines, reading
                             its data from standard input or files and
                             writing to output, with no ceremony required
                             to do so—data just appeared in the input
                             stream.


                             To say that awk has been an essential part of
                             my day-to-day computing toolkit is an
                             understatement. And yet there are a few
                             things about how I use awk that leave me
                             unsatisfied.


                             Probably the main issue is that awk is good
                             at dealing with data presented in delimited
                             fields but curiously not good at handling
                             comma-separated-value files, which can have
                             field delimiters embedded within a field,
                             provided that the field is quoted. Also,
                             regular expressions have moved on since awk
                             was invented, and needing to remember two
                             sets of regular expression syntax rules is
                             not conducive to bug-free code. One set of
                             such rules is bad enough.


          o § Standards/Consortia⠀➾


                # ⚓ Visit_for_a_surprise_–_Eric_Bailey⠀⇛


                       Could spoiling a joke be an accessibility issue?
                       You better believe it.


    * § Leftovers⠀➾


          o ⚓ Tedium ☛ Star_Trek,_Free_Willy:_Animatronic_Whales_in_Movies⠀⇛


                 Since the day I visited the Denver Museum of Natural
                 History and saw a giant whale skeleton, I’ve been
                 fascinated by whales. There’s just something inherently
                 fascinating about whales that captures the imagination.
                 There’s also a natural beauty to them that is hard to
                 define. Similarly, robots and animatronics have always
                 been a subject of fascination for me as well. When I read
                 an article in an old art magazine from the 90s
                 highlighting depicting whales in art, it got me thinking
                 about animatronic whales and how they might change the
                 world for the better–not to mention having a fascinating
                 history. In today’s Tedium, we’re bringing you one whale
                 of a tale about animatronics and art in the cerulean
                 world.


          o ⚓ Fantasy,_J.R.R._Tolkein_–_Experiences_in_the_community⠀⇛


                 Now unless you have been living under a rock cave, I am
                 sure you know who Mr. Tolkein is. Apparently, the
                 gentleman passed away on 2nd September 1973 at the
                 sprightly age of 80. And this gives fans like me to talk
                 about fantasy, fantasy authors, and the love-hate
                 relationship we have with them. For a matter of record, I
                 am currently reading Babylon Steel by Gaie Sebold. Now
                 while I won’t go into many details (I never like to, if I
                 enjoy a book, I would want the book to be mysterious
                 rather than give praise, simply so that the next person
                 enjoys it as much as I did without having any
                 expectations.) Now this book has plenty of sex so
                 wouldn’t recommend it for teenagers but more perhaps to
                 mature audiences, although for the life of me couldn’t
                 find any rating on the book.


          o ⚓ Jim Nielsen ☛ Stats_Page⠀⇛


                 I came across Brian Baking’s “Cool Things People Do With
                 Their Blogs” which led me to Luke Harris’ stats page
                 which motivated me to finally make something similar of
                 my own.


                 I’ve written previously about enumerating the external
                 and internal links on my blog. I’ve also written
                 previously about graphing my blogging goals. All of these
                 are different forms of representing stats about my blog,
                 so really this was an exercise in making all these
                 disparate statistical representations accessible in one
                 central place: my /about page.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ Intel_Loihi_2_high-efficiency_neuromorphic
                  chip_works_with_the_Lava_open-source_framework_–_CNX
                  Software⠀⇛


                       Loihi is said to consume far less than 1 watt of
                       power compared to the tens to hundreds of watts
                       that standard CPU and GPU solutions consume, so
                       this type of neuromorphic AI accelerator may
                       eventually bring the power of datacenter hardware
                       to robots, autonomous vehicles, and so on, and
                       deliver similar performance at much lower power
                       consumption and latency since the processing can be
                       done on the device itself. Lower-end neuromorphic
                       chips will leverage SNN’s efficiency in battery-
                       powered sensors with built-in AI instead.


                # ⚓ uni Toronto ☛ We_now_have_some_1U_servers_with_U.2_NVMe
                  SSDs_and_they’re_okay⠀⇛


                       Back in early 2021 I wrote about my impressions of
                       NVMe versus SATA (or SAS) SSDs for basic servers.
                       At that point I didn’t expect us to get NVMe based
                       servers any time soon, especially for servers not
                       focused on fast storage. Well, times change, and we
                       now have a number of 1U servers with U.2 NVMe
                       drives. These aren’t really “basic” servers in our
                       usual sense; instead they tend to be pretty
                       powerful compute servers. But they’re still 1U
                       servers and in theory there’s nothing to stop
                       people from having lower end ones with NVMe SSDs.
                       Our experiences with these servers have been
                       positive, in that everything works as we expect and
                       basically how things would be if these were SATA
                       SSDs instead.


                       (Obviously the U.2 NVMe drives are a lot faster and
                       have lower latency, but these servers mostly don’t
                       put any real stress on their storage.)


                       We didn’t get these servers with NVMe disks instead
                       of SATA (or SAS) disks because we had some
                       attraction to NVMe; if anything, we prefer SATA
                       SSDs to U.2 NVMe SSDs because it’s much easier to
                       get spares and replacements (SATA SSDs are
                       commodity items; U.2 NVMe SSDs are more expensive
                       and harder to find). Instead, we got these servers
                       with U.2 NVMe drives because that’s the
                       configuration they really wanted to come in. All of
                       these servers have four hot swap drive bays (taking
                       their own proprietary drive carriers), although we
                       normally only use two (for a mirrored pair of
                       system disks), and we opted to get them with four
                       U.2 NVMe drives each in order to build up a pool of
                       spares.


                # ⚓ uni Toronto ☛ ZFS_DVA_offsets_are_in_512-byte_blocks_on
                  disk_but_zdb_misleads_you_about_them⠀⇛


                       That is to say, when zdb prints ZFS DVAs it is not
                       showing you the actual on-disk representation, or a
                       lightly decoded version of it; instead the offset
                       is silently converted from its on-disk form of 512-
                       byte blocks to a version in bytes. I think that
                       this is also true of other pieces of ZFS code that
                       print DVAs as part of diagnostics, kernel messages,
                       and so on. Based on lightly reading the code, I
                       believe that the size of the DVA is also recorded
                       on disk in 512-byte blocks, because zdb and other
                       things use a similar C macro (DVA_GET_ASIZE()) when
                       printing it.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Patrick Breyer ☛ Clear_lines_against_chat_control:
                        Liberals’_paper_puts_German_Interior_Minister_Faeser_on
                        the_spot_–_Patrick_Breyer⠀⇛


                             Screening chat messages, scanning private
                             photos: For the German ministries led by the
                             liberal FDP, the plans for chat control by
                             the EU Commission crosses “red lines” in many
                             places. An internal document shows that the
                             federal government is not united on the
                             issue.


                             The FDP-led federal ministries are apparently
                             putting internal pressure on the federal
                             government, because the EU Commission’s plans
                             for chat control go too far for them. This
                             becomes clear from a list of “red lines” that
                             the Ministry of Justice and the Ministry of
                             Digital Affairs have sent to the SPD-led
                             Ministry of the Interior, according to
                             Tagesspiegel Background. (We publish the list
                             in full text.)


                             Chat control refers to plans by the EU
                             Commission to combat the spread of recordings
                             of sexualised violence against children. The
                             Commission presented a draft in May which
                             demands far-reaching obligations for tech
                             companies. Among other things, they are to
                             automatically recognise known and previously
                             unknown depictions of sexualised violence
                             against children, even in private chats. The
                             plans have been met with scathing criticism,
                             including warnings from the EU data
                             protection authorities of unnecessary mass
                             surveillance.


                             The German government also criticised the
                             planned measures. In a letter, it badgered
                             the EU Commission with more than 60
                             questions, some of them very pointed,
                             including the importance of encrypted
                             communication or the error rates to be
                             expected when recognising such images. Now a
                             letter shows that the critical attitude
                             within the German government is apparently
                             not consistent. As Tagesspiegel Background
                             reports, in the letter the ministries of
                             justice and digital affairs address the
                             ministry of the interior (BMI) led by SPD
                             minister Nancy Faeser, the ministry in charge
                             of the matter.


                      # ⚓ Stacey on IoT ☛ IoT_news_of_the_week_for_Sept._2,
                        2022_–_Stacey_on_IoT_|_Internet_of_Things_news_and
                        analysis⠀⇛


                             Carriers aren’t the only source of location
                             data: While cell phone carriers do track a
                             users location and will share it with law
                             enforcement when presented with a warrant,
                             not every cop needs to get one. The
                             Electronic Frontier Foundation has discovered
                             that police agencies across the country have
                             contracted with a company called Fog Data
                             Sciences to buy location information gathered
                             from 250 million devices. The location data
                             is often gathered from applications that
                             people download onto their phones. Those app
                             developers then take the location data and
                             sell it to data brokers and companies like
                             Fog Data. The EFF says Fog Data lets law
                             enforcement subscribe to a service that lays
                             out the location of these devices on a map
                             that officers can use to see what devices are
                             in the vicinity of a crime or follow specific
                             devices as they roam about a city. Officers
                             don’t need a warrant for this, although some
                             do get one. This is terrifying and should be
                             clearly disclosed to users. It probably
                             should also be illegal or at least
                             inadmissible in court. (EFF) — Stacey
                             Higginbotham


          o § Defence/Aggression⠀➾


                # ⚓ Light Blue Touchpaper ☛ ExtremeBB:_Supporting_Large-Scale
                  Research_into_Misogyny_and_Online_Extremism_|_Light_Blue
                  Touchpaper⠀⇛


                       Online anonymous platforms such as forums enable
                       freedom of speech, but also facilitate misogyny,
                       extremism, and political polarisation.


                       [...]


                       Far-right extremism has been associated with a
                       growing number of mass killings, overtaking
                       Islamist terrorism in about 2018. Examples include
                       the Wisconsin Sikh temple shooting (2012), the
                       riots in Charlottesville (2017), the Pittsburgh
                       synagogue shooting (2018), the Christchurch mosque
                       shootings (2019), the US Capitol riots (January
                       2021), and recently the Buffalo shooting (May
                       2022). Misogyny has been explicitly linked with
                       terror attacks including the Isla Vista killings
                       (2014), the Toronto Van attack (2018), the Hanau
                       shootings (early 2020), and most recently, the
                       Plymouth shooting in the UK (August 2021).


          o § Environment⠀➾


                # § Energy⠀➾


                      # ⚓ Rlang ☛ Electricity_markets:_Can_the_EU_deal_with
                        forward_hedging_when_taxing_infra-marginal_profits?_|
                        R-bloggers⠀⇛


                             Sounds similar to my recent proposal. A
                             difference to my main proposal is that the EU
                             does not want to reduce the spot market
                             prices, but suggests that governments rather
                             collect the difference between a technology’s
                             price cap and the actual spot market as a tax
                             that can be used to finance other support
                             measures (e.g. lump-sum transfers to
                             consumers).


          o § Finance⠀➾


                # ⚓ Business Insider ☛ Amazon’s_Jeff_Bezos_on_Profits,_Failure,
                  Succession,_Big_Bets⠀⇛


                       What really matters is, companies that don’t
                       continue to experiment, companies that don’t
                       embrace failure, they eventually get in a desperate
                       position where the only thing they can do is a Hail
                       Mary bet at the very end of their corporate
                       existence.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Michael Geist ☛ Why_Have_So_Many_Cabinet_Members_Still_Not
                  Spoken_Out_on_Stopping_Government_Funding_for_an_Anti-Semite?
                  –_Michael_Geist⠀⇛


                       Earlier this week, Liberal MP Anthony Housefather
                       called on all 338 Members of Parliament to say
                       something about the need to combat anti-semitism
                       and to express concern about the government’s
                       funding of an anti-semite as part of its anti-hate
                       program. At that point, there were few MPs who had
                       spoken publicly, leaving the issue largely to
                       Jewish MPs to express concern. As I noted in a post
                       reflecting on the issue, the message in the silence
                       is that anti-semitism is a Jewish problem, not a
                       broader societal concern. While I realize there is
                       something performative about issuing a statement
                       via tweet, elected officials do this all the time
                       as a signal of their priorities or interests and to
                       amplify their message.


                       Yet days later, the message has not been amplified
                       and it would appear that the issue is not a
                       priority. As of last night, I could find that only
                       1/3 of the cabinet has said anything about this
                       issue in the weeks since it emerged: 11 cabinet
                       ministers by tweet or retweet, Prime Minister
                       Justin Trudeau in two press conferences, and
                       Heritage Minister Pablo Rodriguez in a statement
                       provided in response to a journalist query (but, to
                       date, no actual statement has been publicly
                       released).


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ I_should_have_culled_those_photos⠀⇛


                       I’m feeling a bit more at ease today with regards
                       to web browsers.


                       [...]


                       A small step, but probably cathartic and long
                       overdue. I have so many photos from the last…
                       almost 20 years? Crikey, how old am I now :X I
                       found pictures of people who are no longer in my
                       life, for sad reasons as well as reasons I’m very
                       thankful for. I found pictures of the person I used
                       to be, who I’m gladly not anymore. It’s really nice
                       to be 15kg heavier, stronger and more at ease with
                       life*.


                # ⚓ Diachronic_Operations⠀⇛


                       This series is thought provoking in a way that I
                       have only other encountered in one other novel:
                       Seveneves. Incidentally, that is also a Neal
                       Stephenson book. This guy is good. There are also
                       heavy elements of humor within; I laughed out loud
                       several times at the audacity of some of the
                       characters and their situations throughout time
                       (intentionally being vague here, avoiding
                       spoilers). If you want details with the spoilers,
                       see the bottom of this post.


                # ⚓ Drunking_Ramblings_–_Tech,_Social_and_Whatnot⠀⇛


                       Like, we’d expect people to have develop good
                       communication skills amid the boom of mobile
                       phones, email and later on social media and intant
                       messaging. But no. I’ve seen way too many people
                       who expect others to instantly understnat what they
                       are thinking.


          o § Technical⠀➾


                # ⚓ 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.


                       We are going to see how to deploy them on NixOS.


                # ⚓ A_little_bit_of_ricing⠀⇛


                       Yesterday I wrote on my blog about setting up
                       `powerline` in bash, vim, and tmux. This is the
                       only amount of “rice” I have in my computer, and it
                       was actually prompted (hehe) by adding `starship`
                       to the terminal of my work computer.


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



                    ䷩ 𝚕𝚒𝚗𝚎 3174

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_03/09/2022:_grep_3.8_and_Games,_General_News⠀✐


Posted in News_Roundup at 8:49 am by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o BSD
          o Arch_Family
    * Free,_Libre,_and_Open_Source_Software
          o GNU_Projects
    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary
          o Security
                # Integrity/Availability/Authenticity
                # Privacy/Surveillance
                # Confidentiality
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy
                # Overpopulation
    * Finance
    * AstroTurf/Lobbying/Politics
    * Censorship/Free_Speech
    * Freedom_of_Information_/_Freedom_of_the_Press
    * Civil_Rights/Policing
    * Internet_Policy/Net_Neutrality
    * Digital_Restrictions_(DRM)
    * Monopolies
          o Copyrights
    * § GNU/Linux⠀➾


          o § Instructionals/Technical⠀➾


                # ⚓ How_to_install_Monit_on_Arch_Linux_–_NextGenTips⠀⇛


                       In this tutorial, we will be learning how to
                       install Monit on Arch Linux.


                       Monit is a small open-source utility for managing
                       and monitoring Unix systems. Monit conducts
                       automatic maintenance and repair and can execute
                       meaningful causal actions in error situations.


                       With Monit, systems status can be viewed directly
                       from the command line, or via the native HTTP(s)
                       webserver. It is able to do automatic maintenance,
                       repair, and run meaningful causal actions in error
                       situations.


                # ⚓ Linux Capable ☛ How_to_Install_PyCharm_IDE_on_Fedora_36
                  Linux_–_LinuxCapable⠀⇛


                       PyCharm is a robust Python integrated development
                       environment (IDE) that is popular among Python
                       developers. It has many essential tools, such as
                       code analysis, debugging, and integration. It also
                       has a command line interface, which makes it easy
                       to use. PyCharm connects to databases, creates
                       virtual environments, and manages your version
                       control system (Git). It is an effective
                       development tool with many Python developers’
                       essential features. However, it is important to
                       note that PyCharm is not free software, and there
                       is a cost associated with using it, depending on
                       the version. Nevertheless, it is still worth
                       considering if you are looking for a powerful
                       Python IDE. Thanks to its wide range of features,
                       PyCharm can help you be more productive in your
                       Python development projects.


                       The following tutorial will teach you how to
                       install PyCharm on Fedora 36 Linux with options for
                       Community, Professional, or Educational using the
                       third-party repository by phracek/PyCharm or
                       alternative third-party installation managers
                       Flatpak and Snapcraft using the command line
                       terminal.


                # ⚓ ID Root ☛ How_To_Install_PyCharm_on_Fedora_36_–_idroot⠀⇛


                       In this tutorial, we will show you how to install
                       PyCharm on Fedora 36. For those of you who didn’t
                       know, PyCharm is an integrated development
                       environment (IDE) used in computer programming,
                       specifically for the Python programming language.
                       The Community Edition is released under the Apache
                       License, and there is also an educational version,
                       as well as a Professional Edition with extra
                       features (released under a subscription-funded
                       proprietary license).


                       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 PyCharm IDE on a Fedora 36.


                # ⚓ ELinux ☛ Install_CXS_on_clean_CentOS_|_Linux_Webhosting
                  blog⠀⇛


                       ConfigServer eXploit Scanner (cxs) is a tool which
                       performs an active scanning of files as they are
                       uploaded to the server. CXS Should only work on a
                       cPanel/WHM server per the product’s requirements.
                       However, you can still install it on a ‘clean’
                       CentOS machine as long as the required perl
                       libraries are provided.


                       We’ve created an easy list of “copy & paste”
                       actions for your convenience.


                # ⚓ ELinux ☛ Allow_a_cPanel_server_to_run_a_VHOST_from_multiple
                  IP_addresses_|_Linux_Webhosting_blog⠀⇛


                       Every once in a while a hosting provider has to
                       change an IP address for a single user or even an
                       entire server on the fly. If you’ll try do this the
                       usual way, by changing the IP address in WHM you
                       can expect downtime ranging from several minutes to
                       several hours until the DNS cache is cleared.


                       While cPanel does not officially allow accounts to
                       have more than one IP address, there is no such
                       restriction for Apache. So the solution is to
                       override the default cPanel configurations with
                       your own.


                # ⚓ Set_Static_Routes_via_an_Interface/IP_on_CentOS/Ubuntu_–
                  kifarunix.com⠀⇛


                       In this tutorial, you will learn how to set static
                       routes via an interface/IP on CentOS/Ubuntu
                       systems. In a network, a route is a path between
                       networks. Routes through which a packet, in a
                       packet-switching network, uses to travel from one
                       network to the other is decided by a router in a
                       specific network. So, how can one set static routes
                       via an interface/IP on CentOS/Ubuntu systems?


                # ⚓ ELinux ☛ cPanel_–_Preventing_users_from_downloading_/
                  restoring_accounts_|_Linux_Webhosting_blog⠀⇛


                       As hosting providers, you sometimes have to deal
                       with huge account backups (over 100GB per account
                       for example). JetBackup will make your life easier
                       backing up these huge accounts, however restoring
                       them is not always something we want to do.


                # ⚓ ELinux ☛ CL_PHPSelector_–_Allow_per_user_php.ini_changes_|
                  Linux_Webhosting_blog⠀⇛


                       PHP Selector is a CloudLinux component integrated
                       on top of CageFS.
                       It allows each user to select a unique PHP version
                       and modules based the user’s needs. PHP Selector
                       requires an active account and CageFS to be
                       enabled.


                       A cPanel user is allowed to change php.ini settings
                       from his cPanel GUI. However the changes are
                       limited to what CloudLinux permits by default.


                       You can easily edit Cloudlinux’s settings file and
                       add any needed settings.


                       Make sure that the user has a cagefs enabled cPanel
                       account.
                       Login to the server via SSH as root user and edit
                       the following file: “/etc/cl.selector/php.conf”


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ A_genre_is_born:_Horde_games⠀⇛


                       Vampire Survivors entered Steam Early Access in
                       December 2021, and was described by the developer
                       as “a gothic horror casual game with rogue-lite
                       elements.” The game skyrocketed to success almost
                       immediately, and at time of writing has over
                       100,000 Steam reviews and an Overwhelmingly
                       Positive rating.


                # ⚓ GamingOnLinux ☛ This_great_bundle_of_Native_Linux_games
                  will_tease_your_brain⠀⇛


                       Want some games that will test your brain and
                       perhaps help you learn a little in the process? The
                       Level Up and Learn: Programming Games bundle from
                       Humble Bundle will do just that.


                # ⚓ GamingOnLinux ☛ Move_over_Wordle,_I’m_all_about_Farmbound
                  now⠀⇛


                       Is the hype of Wordle over yet? Okay good. Need
                       something new to try each day? Why not take a
                       little look over at Farmbound.


                # ⚓ GamingOnLinux ☛ [I]_Doesn’t_Exist:_AI_Breathes_New_Life
                  Into_Text_Adventures⠀⇛


                       [I] Doesn’t Exist is an up-and coming text-based
                       game by LUAL Games that will combine old-school
                       adventuring with modern design, most notably a
                       narrative AI that promises to smooth out the player
                       experience. We caught up with the developers at
                       Gamescom 2022 in Cologne, Germany to see how this
                       ambitious project is progressing.


                # ⚓ GamingOnLinux ☛ Stellaris:_Toxoids_Species_Pack_coming_with
                  a_free_update_on_September_20⠀⇛


                       Paradox Interactive has announced some more goodies
                       coming for Stellaris with the Toxoids Species Pack
                       and a free update landing on September 20th.


                # ⚓ GamingOnLinux ☛ Splitgate_development_is_over,_as_the_devs
                  move_onto_their_next_game⠀⇛


                       Splitgate, the first-person shooter with portals,
                       is no longer getting actively developed as the
                       developer has seemingly given up with it to move
                       onto a new game.


                # ⚓ GamingOnLinux ☛ dbrand_reveal_the_full_details_of_Project
                  Killswitch_for_Steam_Deck⠀⇛


                       After waiting quite some time, Project Killswitch
                       from dbrand for the Steam Deck is finally coming
                       but there’s been a few changes and it seems not
                       everyone is happy with it.


                # ⚓ GamingOnLinux ☛ Steam_Deck_Client_Beta_updated_with_Mode
                  Shift_support_in_Steam_Input⠀⇛


                       Valve continues tweaking and improving the Steam
                       Deck software both the Steam Client and SteamOS. A
                       new Beta is available with more improvements to
                       Steam Input. This is available for anyone in the
                       Beta or Preview update channels. You can change it
                       in Settings >System >Steam Update Channel.


                # ⚓ GamingOnLinux ☛ Get_a_free_copy_of_Immortal_Redneck_during
                  The_GOG_Sale_Finale⠀⇛


                       The GOG Sale Finale is on and another game is being
                       given away. This time it’s Immortal Redneck, a
                       pretty good FPS set in Egypt with rogue-lite
                       elements. The giveaway will last until Monday,
                       September 5th, 1 PM UTC. To claim it, you need to
                       be logged in on GOG and scroll down the homepage to
                       find the banner.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ 9to5Linux ☛ digiKam_7.8_Open-Source_Digital_Photo
                        Manager_Released_with_New_Camera_Support,_More⠀⇛


                             digiKam 7.8 is here about two and a half
                             months after digiKam 7.7. It’s based on KDE
                             Frameworks 5.96 and features an updated
                             internal RAW processor based on libraw 2022-
                             07-14, which adds support for new cameras
                             like Canon EOS R3, Canon EOS R7, Canon EOS
                             R10, Fujifilm X-H2S, Fujifilm X-T30 II,
                             Olympus System OM-1, Leica M11, Sony A7-IV,
                             DJI Mavic 3, and Nikon Z9.


    * § Distributions and Operating Systems⠀➾


          o § BSD⠀➾


                # ⚓ Undeadly ☛ OpenBSD_may_soon_gain_further_memory
                  protections:_immutable_userland_mappings⠀⇛


                       My next attempt is to lock memory mappings. The
                       current working name is mimmutable(void *addr,
                       size_t len). This identifies all current mapped
                       memory in a region, and tags the mappings. Such
                       mappings can never be unmapped. No new mmap can be
                       done on top of the mappings. And the permissions
                       cannot be changed. Other than that, the underlying
                       storage memory works fine, it is just the mapping
                       that is locked.


                # ⚓ Undeadly ☛ ps(1)_gains_support_for_tree-like_display_of
                  processes⠀⇛


                       This (great, convenience) feature was previously
                       unavailable in the base system, but could be found
                       in ports such as pstree(1).


          o § Arch Family⠀➾


                # ⚓ 9to5Linux ☛ First_Arch_Linux_ISO_Powered_by_Linux_Kernel
                  5.19_Is_Now_Available_for_Download⠀⇛


                       Arch Linux’s September 2022 ISO release is out now
                       for those who want to deploy the lightweight and
                       powerful GNU/Linux distribution on new computers.
                       Arch Linux devs release a new ISO image every
                       month, but the September 2022 snapshot is special
                       because it ships with Linux kernel 5.19 by default.


                       Linux kernel 5.19 brings new features like support
                       for AMD’s Secure Nested Paging feature, support for
                       ZSTD-compressed firmware files, initial support for
                       Loongson’s “LoongArch” RISC ISA CPU architecture,
                       support for the ARM Scalable Matrix Extension
                       (SME), as well as new and improved security
                       features.


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


          o ⚓ Unicorn Media ☛ FOSS_Force_Open_Source_News_Quiz_(9/2/22)⠀⇛


          o § GNU Projects⠀➾


                # ⚓ GNU ☛ grep_3.8_released_[stable]⠀⇛


                       This is to announce grep-3.8, a stable release.
                       Special thanks to Carlo Arenas for adding PCRE2
                       support
                       and to Paul Eggert for his many fine changes.

                       There have been 104 commits by 6 people in the 55
                       weeks since 3.7.
                       See the NEWS below for a brief summary.

                       Thanks to everyone who has contributed!
                       The following people contributed changes to this
                       release:

                         Carlo Marcelo Arenas Belón (2)
                         Helge Kreutzmann (1)
                         Jim Meyering (27)
                         Ondřej Fiala (1)
                         Paul Eggert (71)
                         Ulrich Eckhardt (2)

                       Jim [on behalf of the grep maintainers]
                       ==================================================================

                       Here is the GNU grep home page:

                       http://gnu.org/s/grep/

                       For a summary of changes and contributors, see:

                       http://git.sv.gnu.org/gitweb/
                       ?p=grep.git;a=shortlog;h=v3.8

                       or run this command from a git-cloned grep
                       directory:
                         git shortlog v3.7..v3.8

                       To summarize the 432 gnulib-related changes, run
                       these commands
                       from a git-cloned grep directory:
                         git checkout v3.8
                         git submodule summary v3.7

                       ==================================================================
                       Here are the compressed sources:
                         https://ftp.gnu.org/gnu/grep/grep-3.8.tar.gz
                       (2.8MB)
                         https://ftp.gnu.org/gnu/grep/grep-3.8.tar.xz
                       (1.7MB)

                       Here are the GPG detached signatures:

                       https://ftp.gnu.org/gnu/grep/grep-3.8.tar.gz.sig


                       https://ftp.gnu.org/gnu/grep/grep-3.8.tar.xz.sig

                       Use a mirror for higher download bandwidth:

                       https://www.gnu.org/order/ftp.html

                       Here are the SHA1 and SHA256 checksums:
                       eb3bf741fefb2d64e67d9ea6d74c723ea0efddb6  grep-
                       3.8.tar.gz
                       jeYKUWnAwf3YFwvZO72ldbh7/Pp95jGbi9YNwgvi+5c  grep-
                       3.8.tar.gz
                       6d0d32cabaf44efac9e1d2c449eb041525c54b2e  grep-
                       3.8.tar.xz
                       SY18wbT7CBkE2HND/rtzR1z3ceQk+35hQa/2YBOrw4I  grep-
                       3.8.tar.xz

                       Each SHA256 checksum is base64 encoded, preferred
                       over the much
                       longer hexadecimal encoding that most checksum
                       tools default to.

                       Use a .sig file to verify that the corresponding
                       file (without the
                       .sig suffix) is intact.  First, be sure to download
                       both the .sig file
                       and the corresponding tarball.  Then, run a command
                       like this:

                         gpg --verify grep-3.8.tar.gz.sig

                       The signature should match the fingerprint of the
                       following key:

                         pub   rsa4096/0x7FD9FCCB000BEEEE 2010-06-14
                       [SCEA]
                               Key fingerprint = 155D 3FC5 00C8 3448 6D1E
                       EA67 7FD9 FCCB 000B EEEE
                         uid   Jim Meyering <jim@meyering.net>

                       If that command fails because you don't have the
                       required public key,
                       or that public key has expired, try the following
                       commands to retrieve
                       or refresh it, and then rerun the 'gpg --verify'
                       command.

                         gpg --locate-external-key jim@meyering.net
                         gpg --recv-keys 7FD9FCCB000BEEEE
                         wget -q -O- 'https://savannah.gnu.org/project/
                       release-gpgkeys.php?group=grep&download=1' | gpg --
                       import -

                       As a last resort to find the key, you can try the
                       official GNU
                       keyring:

                         wget -q https://ftp.gnu.org/gnu/gnu-keyring.gpg
                         gpg --keyring gnu-keyring.gpg --verify grep-
                       3.8.tar.gz.sig

                       This release was bootstrapped with the following
                       tools:
                         Autoconf 2.72a.55-bc66c
                         Automake 1.16i
                         Gnulib v0.1-5279-g19435dc207

                       ==================================================================
                       NEWS

                       * Noteworthy changes in release 3.8 (2022-09-02)
                       [stable]

                       ** Changes in behavior

                         The -P option is now based on PCRE2 instead of
                       the older PCRE,
                         thanks to code contributed by Carlo Arenas.

                         The egrep and fgrep commands, which have been
                       deprecated since
                         release 2.5.3 (2007), now warn that they are
                       obsolescent and should
                         be replaced by grep -E and grep -F.

                         The confusing GREP_COLOR environment variable is
                       now obsolescent.
                         Instead of GREP_COLOR='xxx', use
                       GREP_COLORS='mt=xxx'.  grep now
                         warns if GREP_COLOR is used and is not overridden
                       by GREP_COLORS.
                         Also, grep now treats GREP_COLOR like GREP_COLORS
                       by silently
                         ignoring it if it attempts to inject ANSI
                       terminal escapes.

                         Regular expressions with stray backslashes now
                       cause warnings, as
                         their unspecified behavior can lead to unexpected
                       results.
                         For example, '\a' and 'a' are not always
                       equivalent
                         <https://bugs.gnu.org/39678>.  Similarly, regular
                       expressions or
                         subexpressions that start with a repetition
                       operator now also cause
                         warnings due to their unspecified behavior; for
                       example, *a(+b|{1}c)
                         now has three reasons to warn.  The warnings are
                       intended as a
                         transition aid; they are likely to be errors in
                       future releases.

                         Regular expressions like [:space:] are now errors
                       even if
                         POSIXLY_CORRECT is set, since POSIX now allows
                       the GNU behavior.

                       ** Bug fixes

                         In locales using UTF-8 encoding, the regular
                       expression '.' no
                         longer sometimes fails to match Unicode
                       characters U+D400 through
                         U+D7FF (some Hangul Syllables, and Hangul Jamo
                       Extended-B) and
                         Unicode characters U+108000 through U+10FFFF
                       (half of Supplemental
                         Private Use Area plane B).
                         [bug introduced in grep 3.4]

                         The -s option no longer suppresses "binary file
                       matches" messages.
                         [Bug#51860 introduced in grep 3.5]

                       ** Documentation improvements

                         The manual now covers unspecified behavior in
                       patterns like \x, (+),
                         and range expressions outside the POSIX locale.
    * § Leftovers⠀➾


          o ⚓ Hackaday ☛ 3D_Printing_A_Prosthetic-Compatible_Golf_Club⠀⇛


                 Relearning an old sport, or starting a new one, can be
                 challenging for amputees. Besides the obvious physical
                 aspects, custom prosthetics or adaptors might need to be
                 made and fitted, which can be very expensive. With the
                 power of 3D printing and some machining, [Ian Davis] was
                 able to build a custom prosthetic golf club to get a
                 quadruple amputee back on the greens.


          o ⚓ Counter Punch ☛ Play_It_Again: _On_the_Riches_of_Repeating_Bass
            Lines⠀⇛


                 The reverie of Dexter Gordon’s “As Time Goes By” expands
                 soulfully: Augustine’s distension animi…


          o § Science⠀➾


                # ⚓ Hackaday ☛ Fixing_A_Hot_Shop,_With_Science⠀⇛


                       We know that pretty much everybody in the Northern
                       hemisphere has had a hellish summer, and there’s
                       little room for sympathy when someone busts out
                       with, “Oh yeah? You think THAT’s hot? Well, lemme
                       tell you…” But you’ve got to pity someone who lives
                       in north Texas and has a steel Quonset hut for a
                       shop. That’s got to be just stupidly hot.


                # ⚓ Hackaday ☛ Hackaday_Prize_2022:_A_Cooler_For_Your
                  Footwear⠀⇛


                       Sweaty feet can be uncomfortable, and the smell
                       generated in one’s shoes isn’t much to admire,
                       either. In an effort to help solve this issue,
                       [Revoxdyna] has created a cooler for one’s feet
                       that should help out in hot conditions.


          o § Hardware⠀➾


                # ⚓ Computer World ☛ Decline_in_PC_and_tablet_shipments_will
                  continue_through_2023,_says_IDC⠀⇛


                       Global shipments of PCs and tablets are in steep
                       decline, but will pick up again in 2024, according
                       to a new study by IDC.


                       Shipments of traditional PCs are forecast to
                       decline 12.8% to 305.3 million units in 2022, while
                       IDC expects tablet shipments will fall 6.8% to
                       156.8 million. The combined market for PCs and
                       tablets will decline by 2.6% in 2023 before
                       returning to growth in 2024, according to IDC.


                # ⚓ Hackaday ☛ Oops!_All_Analog_Sticks⠀⇛


                       Knowing his friend is a first-person shooter
                       enthusiast, [Solderking] came up with a unique
                       modified XBox controller as a gift. Tongue in
                       cheek, you could argue that this controller is
                       fully analog, as all of the buttons have been
                       removed and replaced with analog sticks — each
                       stick emulating four different buttons with its
                       four different directions.


                # ⚓ Hackaday ☛ Cutting_The_Grass_With_Frickin’_Lasers⠀⇛


                       We techie types are quite often much more
                       comfortable in front of a keyboard knocking out
                       code, than out in the yard splitting logs for
                       winter, and even the little jobs like cutting the
                       grass are sometimes just too much like hard manual
                       labour for our liking. The obvious solution is a
                       robot mower, but they’re kinda boring, with their
                       low-tech spinning metal blades. What we need is a
                       big frickin’ laser. YouTuber [rctestflight] has
                       been experimenting with using a 40W blue diode
                       laser module to cut the weeds, (Video, embedded
                       below) and it sort of works, albeit in a rather
                       dangerous fashion.


                # ⚓ Hackaday ☛ Magnetic_Gearbox_Can_Go_Fast_But_Not_Hard⠀⇛


                       3D printed gearboxes are great for experimental
                       designs, but due to roughness and inaccuracies in
                       the printed surfaces, they can wear quickly and be
                       rather noisy. As a possible alternative, [Resetman]
                       is experimenting with magnetic 3D printed gearboxes
                       that work without physical contact between the
                       rotating wheels, and can also be “geared” for
                       different ratios in some interesting ways.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Common Dreams ☛ Opinion_|_Jackson,_Mississippi_Has_Been
                  Paralyzed_by_Racism,_Classism,_and_the_Worsening_Climate
                  Crisis⠀⇛


                       Jackson, the state capital of Mississippi, has a
                       population of over 150,000 people, more than 80% of
                       whom are African American. Mississippi is the
                       poorest state in the country. Jackson residents,
                       already under a water boil notice for over a month,
                       have now had no running water for days, to drink,
                       to bathe in, or to flush toilets. The Pearl River
                       flooded following record rainfall, overwhelming the
                       city’s water treatment plant. On Sunday, Mayor
                       Chokwe Antar Lumumba urged city residents, “If you
                       are capable of getting out now, get out now.”
                       Jackson has been paralyzed by the confluence of
                       racism, classism, and the worsening climate crisis.


          o § Proprietary⠀➾


                # ⚓ The Verge ☛ Google_expands_Play_Store_billing_alternatives
                  to_many_countries⠀⇛


                       Google has quietly expanded its “User Choice
                       Billing” pilot to let more developers of non-gaming
                       Android apps offer third-party payment options as
                       alternatives to Google Play’s. Developers will see
                       their service fees of 15 to 30 percent reduced by 4
                       percent when users select a new third-party billing
                       option, which the developer — not Google — must
                       support in case of customer issues. The news was
                       first reported by 9to5Google.


                # ⚓ The Hill ☛ Michigan_police_investigating_voting_machine
                  sold_on_eBay⠀⇛


                       Michigan Secretary of State Jocelyn Benson
                       announced on Thursday that the state government is
                       working with police to investigate a possible
                       illegal selling of a voter assist terminal.


                # ⚓ The State of Michigan ☛ Statement_from_Secretary_Benson_on
                  alleged_illegal_attempt_to_sell_voter_assist_terminal⠀⇛


                       “We are actively working with law enforcement to
                       investigate allegations of an illegal attempt to
                       sell a voter assist terminal acquired in Michigan.
                       Voter assist terminals are not used to tabulate
                       ballots, but are typically used by voters with
                       disabilities who need assistance marking their
                       ballot privately at polling places.


                # ⚓ The Economist ☛ The_tech_winners_and_losers_of_the
                  pandemic⠀⇛


                       Look beyond the boom and bust of consumer tech,
                       though, and you see the real successes. The market
                       for the infrastructure technology that underpins
                       people’s daily lives, such as cloud computing,
                       cybersecurity and digital payments, is thriving.
                       The cloud-computing industry is expected to grow to
                       almost $500bn this year, up from $243bn in 2019.
                       Amazon’s cloud offering, the largest in the world,
                       is still growing at 33% each year. It accounted for
                       three-quarters of the firm’s operating income over
                       the past 12 months, and is propping up the tech
                       giant’s ailing e-commerce business. Its closest
                       rivals are the cloud services of Microsoft and
                       Google. Their annual sales are growing by 40% and
                       36%, respectively.


                # ⚓ TechRadar ☛ [Repeat]_Dodgy_Microsoft_Azure_update_knocks
                  Ubuntu_VMs_offline⠀⇛


                       According to a statement from Microsoft, the issues
                       began after Ubuntu 18.04 (bionic) VM users
                       installed an update called “systemd version 237-
                       3ubuntu10.54″.


                       After installing the update, the impacted users
                       began experiencing domain name system (DNS) errors.


                # ⚓ Hindustan Times ☛ Google_allows_this_app_in_Play_Store,
                  year_after_banning_it_over_Capitol_riots⠀⇛


                       Tech giant Google has allowed social media network
                       Park back into its Play Store, this a year after it
                       banned the platform in the wake of 2021 Capitol
                       violence.


                       The tech giant had pulled down the app popular with
                       American conservatives days after the violent
                       attack on the seat of US government on January 6
                       last year, alleging the platform allowed content
                       that could incite more violence, AFP reported.


                # ⚓ The Hill ☛ Parler_app_available_again_in_Google_Play
                  Store⠀⇛


                       The social media platform Parler is available again
                       for users to download from the Google Play Store a
                       year and a half after the app was removed, the
                       company said Friday.


                       Parler, which boasts its limited content moderation
                       measures, was banned from the app store since
                       January 2021 over a lack of moderation on posts
                       that were deemed to incite violence around the Jan.
                       6 riot at the Capitol.


          o § Security⠀➾


                # § Integrity/Availability/Authenticity⠀➾


                      # ⚓ Undeadly ☛ Portable_OpenSSH_commits_now_SSH-signed⠀⇛


                             Damien Miller (djm@) notes that all (new)
                             commits to the portable OpenSSH repository
                             are now signed using git’s SSH signature
                             support.


                # § Privacy/Surveillance⠀➾


                      # ⚓ [Old] Newsweek ☛ CIA_spying_on_Assange_“illegally”
                        swept_up_US_lawyers,_journalists:_Lawsuit⠀⇛


                             The suit – filed on behalf of four Americans
                             who visited Assange – seeks damages
                             personally from then-CIA Director Mike Pompeo
                             for violating the plaintiffs’ Fourth
                             Amendment rights against unreasonable search
                             and seizure. The suit also seeks damages
                             against a Spanish security firm contracted to
                             protect the embassy, and its CEO, alleging
                             that they abused their position to illegally
                             spy on visitors and passed on the
                             surveillance data they collected to the CIA,
                             which is also named a defendant in the suit.


                             Legal experts, including a former senior
                             intelligence official, told Newsweek that the
                             allegations in the lawsuit, if proven, show
                             the CIA crossed lines drawn to protect
                             American citizens from surveillance by
                             overzealous intelligence agencies.


                      # ⚓ [Old] EFF ☛ Geek_Squad’s_Relationship_with_FBI_Is
                        Cozier_Than_We_Thought⠀⇛


                             EFF filed a Freedom of Information Act (FOIA)
                             lawsuit last year to learn more about how the
                             FBI uses Geek Squad employees to flag illegal
                             material when people pay Best Buy to repair
                             their computers. The relationship potentially
                             circumvents computer owners’ Fourth Amendment
                             rights.


                             The documents released to EFF show that Best
                             Buy officials have enjoyed a particularly
                             close relationship with the agency for at
                             least 10 years. For example, an FBI memo from
                             September 2008 details how Best Buy hosted a
                             meeting of the agency’s “Cyber Working Group”
                             at the company’s Kentucky repair facility.


                      # ⚓ [Old] CNET ☛ FBI_paid_Geek_Squad_staff_to_be
                        informants,_documents_show⠀⇛


                             Agents paid managers in the retailer’s device
                             repair unit to pass along information about
                             illegal content discovered on customers’
                             devices, according to documents posted online
                             by the Electronic Frontier Foundation. The
                             digital rights group sued the FBI for the
                             documents last year after the bureau denied a
                             Freedom of Information Act request.


                             The EFF filed the lawsuit to learn the extent
                             to which the agency trains and directs Best
                             Buy Geek Squad employees to conduct
                             warrantless searches of customers’ devices
                             during maintenance. The EFF said it was
                             concerned that use of repair technicians to
                             root out evidence of criminal behavior
                             circumvents people’s constitutional rights.


                      # ⚓ Techdirt ☛ Encrypted_Phone_Provider_Calls_It_Quits
                        After_Failing_To_Persuade_Middlemen_To_Roll_Their_Own
                        Device_Management_Systems⠀⇛


                             Over the past few years, international law
                             enforcement has been cracking down on
                             encrypted device purveyors. We’re not just
                             talking about regular device encryption,
                             which has been mainstream for several years
                             now. These would be specialized manufacturers
                             that appear to cater to those seeking more
                             protection than the major providers offer —
                             services that ensure almost no
                             communications/data originating from these
                             phones can be obtained from third-party
                             services.


                      # ⚓ Techdirt ☛ Gun_Detection_AI_The_Latest_Tech_To_Make
                        Schools_Less_Safe⠀⇛


                             We’re just going to keep getting kids killed
                             in America. We’ll never stop throwing money
                             in the direction of the problem, but not
                             directly at the problem. Nothing gets safer.
                             It just gets more budget line items.


                # § Confidentiality⠀➾


                      # ⚓ [Old] A_New_Future_for_GnuPG⠀⇛


                             For many years our work was mainly financed
                             by donations and smaller projects. Now we
                             have reached a point where we can benefit
                             from a continuous revenue stream to maintain
                             and extend the software without asking for
                             donations or grants. This is quite a new
                             experience to us and I am actually a bit
                             proud to lead one of the few self-sustaining
                             free software projects who had not to
                             sacrifice the goals of the movement.


          o § Defence/Aggression⠀➾


                # ⚓ VOA News ☛ IAEA_Visit_to_Ukraine_Nuclear_Plant_Highlights
                  Risks⠀⇛


                       Inspectors from the International Atomic Energy
                       Agency are used to risky missions — from the
                       radioactive aftermath of the Fukushima disaster in
                       Japan to the politically charged Iranian nuclear
                       program. But their deployment amid the war in
                       Ukraine to Zaporizhzhia takes the threat to a new
                       level and underscores the lengths to which the
                       organization will go in attempts to avert a
                       potentially catastrophic nuclear disaster.


                # ⚓ BBC ☛ Cristina_Fernández_de_Kirchner:_Gun_jams_during_bid
                  to_kill_Argentina_vice-president⠀⇛


                       Video circulating on social media shows the gun
                       emerging from the crowd as Ms Fernández de Kirchner
                       approaches. She initially appears confused by what
                       is going on, ducking down to retrieve an object
                       dropped on the floor.


                       In another video, people in the crowd appear to try
                       to block Ms Fernández de Kirchner from the
                       suspected gunman, who came within inches of her.


                # ⚓ Scheerpost ☛ Chris_Hedges_&_Robert_Scheer_on_Gorbachev,
                  Russia_&_Ukraine⠀⇛


                       Journalists Chris Hedges and Robert Scheer discuss
                       Mikhail Gorbachev, his life, his role in the end of
                       the Cold War and his legacy today.


                # ⚓ Common Dreams ☛ Opinion_|_Gorbachev_Rode_the_Tiger_and
                  Ended_Up_Inside_It⠀⇛


                       So what are we to say about Mikhail Gorbachev, who
                       passed away on August 30?


                # ⚓ FAIR ☛ NPR_Devotes_Almost_Two_Hours_to_Afghanistan_Over_Two
                  Weeks—and_30_Seconds_to_US_Starving_Afghans⠀⇛


                       NPR ran several stories on Afghanistan to mark the
                       anniversary of the August 2021 US withdrawal, even
                       sending host Steve Inskeep to the country to
                       produce a series of pieces. His visit happened to
                       coincide with Biden’s claimed assassination of
                       Ayman al-Zawahiri; Inskeep says that he and his
                       team were staying in close proximity to the Al
                       Qaeda leader.


                # ⚓ TruthOut ☛ Trump_Claims_He’s_“Financially_Supporting”
                  Participants_in_Capitol_Attack⠀⇛


                # ⚓ Meduza ☛ The_fog_of_war_Military_analyst_Rob_Lee_on
                  Ukraine’s_push_to_liberate_Kherson_and_Russia’s_manpower
                  problem_—_Meduza⠀⇛


                       Ukraine’s long-awaited counteroffensive to recover
                       territories in the southern Kherson region is now
                       underway, but the situation at the front remains
                       under wraps. The Ukrainian Defense Ministry has
                       barred journalists from reporting in front-line
                       areas and has urged the press “not to question the
                       actions of the command and not to serve as
                       additional tools in the hands of Russian
                       propaganda.” (Russian state media claimed that the
                       counteroffensive had failed before it had even
                       begun.) In this context, one of the only ways to
                       assess the situation on the ground is to sift
                       through and verify bits and pieces of open-source
                       information. Military analyst Rob Lee, a senior
                       fellow at the Foreign Policy Research Institute
                       (FPRI), has been meticulously gathering operational
                       data ever since Russia began its full-scale
                       invasion in February. Meduza sat down with Rob Lee
                       to talk about Ukraine’s push to liberate the
                       Kherson region from Russian occupation.


                # ⚓ Meduza ☛ Levada_Center:_Almost_half_of_Russians_support
                  annexing_Ukraine’s_Kherson_and_Zaporizhzhia_regions_—
                  Meduza⠀⇛


                       45 percent of Russians believe Ukraine’s Kherson
                       and Zaporizhzhia regions should become part of
                       Russia, according to a new survey from the
                       independent Levada Center that was published by
                       Novaya Gazeta Europe. 21 percent of respondents
                       said they believe the regions should become
                       independent states, while 14 percent said they
                       should remain part of Ukraine.


                # ⚓ Meduza ☛ ‘Let’s_not_exaggerate_Russian_propaganda’s
                  influence’_Ukrainian_socialist_Taras_Bilous_serves_in_the
                  Territorial_Defense_Forces._He’s_also_fighting_the_Western
                  Left’s_stereotypes_about_Ukraine._—_Meduza⠀⇛


                # ⚓ Meduza ☛ ‘A_great_excuse_to_sleep_in’:_What_Russians_think
                  about_the_Kremlin’s_new_pro-war_lesson_series_—_Meduza⠀⇛


                       When Russian students returned to school this week,
                       many of them learned that Mondays are now going to
                       look a little different from what they’re used to.
                       First of all, each week will start with a flag-
                       raising ceremony and the Russian national anthem.
                       After that, the Education Ministry wants teachers
                       to give lessons from the new government-designed
                       curriculum package “Conversations About What’s
                       Important.” The class is intended to teach students
                       about topics “related to key aspects of life in
                       modern Russia” — including the war in Ukraine.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ NPR ☛ BYU_says_it_has_no_proof_that_the_fan_banned_over
                  racist_slurs_said_them⠀⇛


                       McBride said BYU Athletics staffers have been
                       combing through the school’s video recordings of
                       the match to find anyone responsible.


                       “However, we have been unable to find any evidence
                       of that person using slurs in the match,” he said.


                       Similarly, BYU Police Lt. George Besendorfer told
                       the Tribune that his agency did not find proof that
                       the man yelled slurs, after reviewing video
                       records.


          o § Environment⠀➾


                # ⚓ TruthOut ☛ We_Need_a_World_Without_Borders_on_Our
                  Increasingly_Warming_Planet⠀⇛


                # ⚓ The Nation ☛ Thinking_About_Climate_Action?⠀⇛


                # § Energy⠀➾


                      # ⚓ Common Dreams ☛ Green_Groups_Want_Ruling_on_Wyoming
                        Fossil_Fuel_Leases_to_Embolden_Biden⠀⇛


                             “We are pleased to see this well-reasoned
                             order in such an important case,” the
                             groups—which were represented by Earthjustice
                             and the Western Environmental Law Center
                             (WELC), and defended the administration’s
                             postponements and leasing pause—said in a
                             statement.


                      # ⚓ Meduza ☛ G7_countries_agree_to_impose_price_cap_on
                        Russian_oil_—_Meduza⠀⇛


                             G7 finance ministers announced that they have
                             agreed to implement a price cap on Russian
                             oil in an effort to inhibit Russia’s ability
                             to finance its war against Ukraine. The level
                             at which the prices will be capped has not
                             yet been determined; the bloc’s official
                             statement said the ceiling will be “set at a
                             level based on a range of technical inputs.”


                      # ⚓ Meduza ☛ Ukraine_accuses_Russia_of_‘distorting’_facts
                        as_IAEA_mission_wraps_up_first_day_of_nuclear_plant
                        inspections_—_Meduza⠀⇛


                             A mission from the International Atomic
                             Energy Agency (IAEA) examined the
                             Zaporizhzhia Nuclear Power Plant’s emergency
                             systems, its diesel generators, and the
                             shields around its power units, IAEA and
                             delegation leader Director General Rafael
                             Grossi reported on Friday. According to
                             Grossi, the “physical integrity” of the plant
                             has been violated multiple times, but it
                             wasn’t clear whether the damage was
                             intentional or accidental.


                # § Overpopulation⠀➾


                      # ⚓ [Old] Dawn Media ☛ Population_and_security⠀⇛


                             IT is a nightmare scenario that is fast
                             unfolding. Yet the threat that population
                             explosion presents to national security is
                             missing from our policy discourse. Aside from
                             a fleeting reference to population
                             management, there is not enough recognition
                             of the gravity of the problem in the recently
                             launched integrated National Security Policy
                             (NSP). There is no clear strategy on how to
                             deal with the exponential population growth
                             that continues to have a destabilising effect
                             on our society.


                      # ⚓ Population_growth_(annual_%)_–_Pakistan⠀⇛


    * § Finance⠀➾


          o ⚓ TruthOut ☛ LA_Ballot_Measure_Would_Let_Unhoused_People_Stay_in
            Hotels_Past_Pandemic⠀⇛


          o ⚓ Democracy Now ☛ L.A._Ballot_Measure_Would_Let_Unhoused_People
            Stay_in_Hotels_Past_Pandemic_Amid_Deepening_Homeless_Crisis⠀⇛


                 The housing crisis is worsening in Los Angeles, where an
                 estimated 60,000 people remain unhoused in Los Angeles
                 County and thousands more are on the cusp of evictions,
                 even as 20,000 hotel rooms remain vacant across the
                 region. This comes as a new ballot measure could require
                 hotels to house homeless people in vacant rooms. The
                 measure is backed by California’s largest hospitality
                 union, UNITE HERE Local 11, and attempts to revive a
                 statewide pandemic policy known as Project Roomkey,
                 which, now set to end, provided vouchers for people
                 experiencing homelessness to use at hotels and motels.
                 “Project Roomkey is one piece of the puzzle,” says Kurt
                 Petersen, co-president for UNITE HERE Local 11, who,
                 along with UCLA professor Ananya Roy, notes massive
                 investments are desperately needed to secure permanent
                 affordable housing. We also speak with former Echo Park
                 Lake encampment resident Will Sens Jr., who is in Project
                 Roomkey and says the program provided stability for him
                 and others.


          o ⚓ FAIR ☛ NYT_Etiquette_Column_Offers_Advice_for_the_Resentful
            Rich⠀⇛


                 As a teenager, I was an avid reader of Judith Martin, the
                 columnist more commonly known as Miss Manners. I was
                 particularly fascinated by esoteric topics that seemed to
                 belong to another era, such as how to address a formal
                 wedding invitation to a woman doctor and her non-
                 physician husband, or which fork is ideal for serving
                 wedges of lemon (a three-tined lemon fork, of course).
                 Martin taught me that etiquette is best viewed as a means
                 of conveying appreciation and respect for others: Lemon
                 forks may not always be necessary but thank-you notes
                 will never go out of style.


          o ⚓ TruthOut ☛ 2_Red_States_Are_Taxing_Student_Debt_Relief_—_But
            Didn’t_Tax_PPP_Forgiveness⠀⇛


          o ⚓ Common Dreams ☛ Warren_Grills_DOJ_on_Why_It’s_Still_Trying_to
            Crush_Student_Debtors_in_Bankruptcy_Court⠀⇛


                 “Those who continue to struggle with student debt are in
                 need of updated undue hardship guidance.”


          o ⚓ TruthOut ☛ Economy_Adds_315,000_Jobs_in_August,_But_Unemployment
            Ticks_Upward⠀⇛


          o ⚓ Common Dreams ☛ ‘Worst_Yet_to_Come’_as_Global_Civil_Unrest_Index
            Hits_All-Time_High⠀⇛


                 “With more than 80% of countries around the world seeing
                 inflation above 6%, socioeconomic risks are reaching
                 critical levels.”


          o ⚓ Common Dreams ☛ ‘The_Most_Inane_Idea’:_Outrage_Greets_This
            Proposal_to_Remedy_Housing_Crisis_for_Teachers⠀⇛


                 “That this retrograde solution would be considered in
                 this day and age is appalling.”


          o ⚓ Common Dreams ☛ Social_Security_Enemy_Ron_Johnson_Endorses_Plan
            to_‘Coax’_Retirees_Back_to_Work⠀⇛


                 “There are a number of innovative ideas I would support,”
                 Johnson (R-Wis.) said during a tele-town hall with
                 constituents on Wednesday as he’s locked in a close
                 reelection race with Democratic challenger Mandela Barnes
                 in the key battleground state of Wisconsin.


          o ⚓ Common Dreams ☛ Opinion_|_US_Working_Class_Must_Stand_Up_to_This
            Nation’s_Oligarchs⠀⇛


                 Let’s be clear. The most important economic and political
                 issues facing this country are the extraordinary levels
                 of income and wealth inequality, the rapidly growing
                 concentration of ownership, the long-term decline of the
                 American middle class, and the evolution of this country
                 into oligarchy.


    * § AstroTurf/Lobbying/Politics⠀➾


          o ⚓ [Old] Op_Ed:_MC5_and_the_Sound_of_Freedom⠀⇛


                 At the shows in the Grande Ballroom in Detroit, JC
                 Crawford, the official MC of the MC5, would introduce the
                 band. His words speak to us in our deeply troubled time:
                 “Brothers and sisters, I want to hear some revolution out
                 there, I want to hear some revolution. The time has come
                 for each and every one of you to decide whether you are
                 gonna be the problem, or whether you are gonna be the
                 solution. You must choose, brothers, you must choose. It
                 takes five seconds. Five seconds of decision. Five
                 seconds to realize your purpose here on the planet. It
                 takes five seconds to realize that it’s time to move.
                 It’s time to get down with it. Brothers and sisters, it’s
                 time to testify, and I want to know — are you ready to
                 testify? Are you ready? I give you a testimonial, THE
                 MC5!”


          o ⚓ RNZ ☛ New_Zealand_democracy_on_‘shaky_foundations’:_Electoral_law
            ripe_for_change⠀⇛


                 Regardless, overseas voting changes are temporary. Allan
                 is waiting for the findings of a panel of six experts
                 reviewing the entire electoral system – apart from online
                 voting and alternatives to MMP – before making such a
                 move permanent.


          o ⚓ Variety ☛ Analysis:_Why_Netflix_Initially_Struggled_in
            Indonesia⠀⇛


                 The state claimed the carrier’s decision was a commercial
                 one, rather than a political one. But that seemed
                 scarcely credible when the government was simultaneously
                 moving to appease more conservative elements in society
                 through content controls and to expand its taxation of
                 the growing digital economy. Ministers were also
                 explicitly calling for foreign digital companies to work
                 through local partner companies.


          o ⚓ Copenhagen Post ☛ EU_approves_visa_ban_on_Russian_citizens⠀⇛


                 During an official EU meeting in Prague it has been
                 decided that Russians will no longer be able to freely
                 visit Europe for holiday as long as the War in Ukraine
                 continues.


          o ⚓ RTL ☛ Climate_activists_target_UK_parliament⠀⇛


                 Members of climate activist group Extinction Rebellion on
                 Friday glued themselves to the Speaker’s chair in the UK
                 House of Commons, calling for a “Citizens’ Assembly” to
                 help shape environmental policy.


          o ⚓ RTL ☛ African_countries_to_stand_by_1.5C_target_at_climate_talks
            talks⠀⇛


                 The talks “reiterated the need to further accelerate
                 climate action on all fronts, namely in adaptation, loss
                 and damage, climate finance, and adopting more ambitious
                 mitigation measures to keep the 1.5-degree target within
                 reach,” Egyptian Foreign Minister Sameh Shoukry, who will
                 chair the COP27, said in a statement.


                 African countries are among the nations that are least to
                 blame for the fossil-fuel gases that stoke global
                 warming, accounting for less than four percent of global
                 emissions of carbon dioxide.


                 But they are also among the countries that are most
                 exposed to climate impacts, such as worsening drought,
                 floods and cyclones.


          o ⚓ NBC ☛ Anti-trans_stalkers_at_Kiwi_Farms_are_chasing_one_victim
            around_the_world._Their_list_of_targets_is_growing.⠀⇛


                 Clara Sorrenti and those supporting her are hoping to
                 open up Kiwi Farms to debilitating virtual attacks by
                 demanding Cloudflare, one of its internet security
                 service vendors, drop the site. Cloudflare has so far
                 refused to budge.


          o ⚓ The Nation ☛ Florida_Keys⠀⇛


          o ⚓ The Nation ☛ Biden’s_Return_to_Form⠀⇛


                 For much of the past year and a half, the folksy, feisty
                 Joe Biden from the campaign trail seemed to have been
                 replaced by a wooden stage prop. For months, as his
                 popularity plummeted, nothing seemed to go right for the
                 now-president. The man who told Trump to shut up during a
                 live debate, who cried with affecting sincerity when he
                 talked about his son Beau, looked worn, strained. When he
                 spoke, it was the gaffes rather than the substance that
                 made the headlines.


          o ⚓ Democracy Now ☛ Historian_of_Radical_Right:_Biden_Is_Correct,
            Trump_Poses_Existential_Threat_to_Future_of_Democracy⠀⇛


                 In a primetime address Thursday, President Biden warned
                 Donald Trump and his radical supporters are threatening
                 the foundations of the republic. Biden said, “Too much of
                 what’s happening in our country today is not normal,” and
                 that MAGA Republicans present a “clear and present danger
                 to our democracy,” referring to Trump’s campaign slogan
                 of “Make America Great Again.” We speak with Nancy
                 MacLean, author and Duke University historian, who says
                 Biden’s speech was a “wake-up call” for the nation and
                 mainstream media. “He was absolutely right, in my
                 opinion, that the Trump wing of the party and the MAGA
                 Republicans have jumped the rails of constitutional
                 democracy, of the factual universe and of representative
                 democracy.”


          o ⚓ Common Dreams ☛ Opinion_|_More_Money,_More_Problems_(for_Our
            Democracy_and_Our_Planet)⠀⇛


                 Young people—as revealed in poll after poll and
                 conversation after conversation—despair of our democracy.
                 Older people share some of that despair; until it
                 happened, it was impossible for many of us to imagine
                 American citizens trying to stage a coup. And yet,
                 despite months of inaction, legislative packages now
                 passing through Congress give those of us in college a
                 glimmer of hope for a Washington that works for change,
                 one that we’ve rarely seen in our lifetimes.


          o ⚓ TruthOut ☛ Trump_Falsely_Claims_Biden’s_Speech_Threatened_His
            Loyalists_With_Military_Force⠀⇛


          o ⚓ Scheerpost ☛ Medea_Benjamin_&_Jodie_Evans:_What_Killed_America’s
            Peace_Movement?⠀⇛


                 On this week’s “Scheer Intelligence, Robert Scheer is
                 joined by CODEPINK founders Medea Benjamin and Jodie
                 Evans, rare voices of conscience confronting the
                 bipartisan warmongers.


          o ⚓ TruthOut ☛ Ron_DeSantis_Exploited_Parkland_Grief_to_Take_Over_a
            School_Board,_Critics_Say⠀⇛


          o ⚓ TruthOut ☛ Trump_Brags_Mar-a-Lago_Search_Improved_His_Polling_—
            It_Didn’t⠀⇛


          o ⚓ Common Dreams ☛ Opinion_|_Lock_Him_Up—and_Let_Him_Run⠀⇛


                 An important debate has been playing out in recent days
                 on The Bulwark, a national website to which I have been
                 contributing since early June. It came down to this
                 question: Should Donald Trump be tried at the ballot box,
                 or in a court of law?


          o ⚓ Common Dreams ☛ Hillary_Clinton_Under_Fire_for_Supportive_Remarks
            of_Far-Right_PM_Contender_in_Italy⠀⇛


                 Italy is scheduled to hold its general election on
                 September 25, and “polls are led by Giorgia Meloni’s
                 Fratelli d’Italia, part of a right-wing coalition widely
                 expected to secure a majority of seats,” historian David
                 Broder, Jacobin’s Europe editor, explained Friday. “With
                 her own party backed by around one-quarter of voters,
                 Meloni looks likely to become prime minister.”


          o ⚓ Common Dreams ☛ House_Dems_Voice_‘Grave_and_Urgent_Concerns’_Over
            Chilean_Plebiscite_Misinformation⠀⇛


                 “Continued inaction could abet interference in this
                 historic referendum.”


          o ⚓ Common Dreams ☛ ‘Where_Did_the_Classified_Content_Go?’_Dozens_of
            Empty_Folders_Seized_From_Trump_Home⠀⇛


                 “Where did the classified content go?” asked Rep. Ilhan
                 Omar (D-Minn.), voicing a sentiment also expressed by
                 reporters and watchdogs in response to the inventory,
                 which indicates that the FBI retrieved from Mar-a-Lago 18
                 documents marked “top secret,” 54 marked “secret,” and 48
                 empty folders with “classified” banners.


          o ⚓ The Dissenter ☛ How_We_Talk_About_‘the_Left’—Plus,_Right-Wing
            Media_Response_To_Trump_Raid⠀⇛


          o ⚓ Meduza ☛ United_Russia_shrinks_its_supporter_database_by_15
            million_—_Meduza⠀⇛


                 United Russia has cleansed its supporter database in
                 preparation for the 2024 presidential election. The party
                 removed about 15 million people, says RBC, citing sources
                 within the party.


          o ⚓ Counter Punch ☛ Chile’s_Choice:_Approve_a_New_Constitution_or
            Stick_with_Pinochet’s_Legacy?⠀⇛


                 The composition of the 155 popularly elected delegates to
                 the convention — half of them women — further cemented
                 the sense that their efforts would be approved. As I was
                 told again and again on a recent visit to Chile, the
                 delegates “look like us, like the real country.”


          o ⚓ Telex (Hungary) ☛ New_US_Ambassador_to_Hungary_welcomed_only_by
            lower_ranking_official⠀⇛


    * § Censorship/Free Speech⠀➾


          o ⚓ Hollywood Reporter ☛ 100_Years_Ago:_How_Hollywood’s_Early_Self-
            Censorship_Battles_Shaped_the_MPA⠀⇛


                 Pressures from social reformers during an “era of
                 scandal” led the industry to self-regulate by creating
                 the organization in 1922 and paving the way for a
                 Production Code that impacted film content and satisfied
                 many anti-Hollywood activists for nearly two decades.


          o ⚓ Quillette ☛ Salman_Rushdie_and_the_Islamic_Punishment_for
            Blasphemy⠀⇛


                 This article attempts to summarize the development of the
                 Islamic punishment for blasphemy in Muslim thought and
                 life. Several essential primary sources of Islam are
                 examined in this regard, including the Qur’an; the sunna
                 (practice) of Muhammad, the messenger of Islam, as
                 presented in early Muslim narratives and the traditions
                 attributed to him; and Islamic Law. I also describe
                 writings by later Muslim authorities that both explained
                 the theological reasons for the prohibition against
                 blasphemy, and sharpened the application of the
                 punishment meted out to offenders. When these sources are
                 taken together, it may be said that all of them reflect
                 the extreme veneration that Muslims exhibit toward
                 Muhammad.


          o ⚓ Dawn Media ☛ Did_the_PTA_illegally_block_YouTube_during_Imran
            Khan’s_speech?⠀⇛


                 Apart from hundreds of social media users complaining
                 about being unable to access YouTube, independent
                 internet watchdog Netblocks ran network analysis tests in
                 Pakistan through users which showed that YouTube was
                 working for only 38 per cent of users who ran the test.
                 This means that YouTube was accessible on only a few
                 networks and not on others.


                 Because the Pakistan Telecommunication Authority (PTA)
                 has not made any public comments to the media or on its
                 website regarding the outage, we have to evaluate the
                 available evidence to determine how the censorship of
                 YouTube over a short span of time panned out.


          o ⚓ Techdirt ☛ The_Supreme_Court_Already_Explained_Why_California’s
            Age_Appropriate_Design_Code_Is_Unconstitutional⠀⇛


                 In July of 1995, Time Magazine published one of its most
                 regrettable stories ever. The cover just read “CYBERPORN”
                 with the subhead reading: “EXCLUSIVE A new study shows
                 how pervasive and wild it really is. Can we protect our
                 kids—and free speech?” The author of that piece, Philip
                 Elmer-Dewitt later admitted that it was his “worst” story
                 “by far.”


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


          o ⚓ Common Dreams ☛ Shireen_Abu_Akleh’s_Niece_Decries_Biden’s_Failure
            to_Hold_Israel_Accountable⠀⇛


                 “Most importantly, he isn’t upholding the values that he
                 continues to preach.”


          o ⚓ The Nation ☛ What_Happens_When_a_School_Tries_to_Silence_Queer
            Voices?⠀⇛


                 Republicans are attacking the right to be safely queer in
                 public at all levels of government. One of the key fronts
                 in this assault against LGBTQ rights is in the schools.
                 Conservatives are censoring teachers and students across
                 the country, making it difficult for schools to be safe
                 havens for queer youth. Florida recently passed a bill
                 dubbed “Don’t Say Gay,” which bans the discussion of
                 sexual orientation and gender identity in some elementary
                 school grades and constrains it through the 12th grade.
                 Other states are now pushing for similar legislation.


    * § Civil Rights/Policing⠀➾


          o ⚓ Common Dreams ☛ First_NYC_‘Just_Cause’_Lawsuit_Targets_Starbucks
            for_Union-Busting⠀⇛


                 “As we approach Labor Day, it’s important to remember
                 that workers are the backbone of our city and deserve the
                 right to organize.”


          o ⚓ Teen Vogue ☛ Starbucks_Fired_Workers_for_Unionizing,_But_Workers
            Are_Fighting_Back⠀⇛


                 Under the National Labor Relations Act (NLRA), it is
                 illegal to fire workers for organizing a union. In
                 response to losing our jobs, we filed unfair labor
                 practice charges with the NLRB, alleging that we were
                 fired in response to our union activity. To date, the
                 NLRB has issued an official complaint against Starbucks
                 on behalf of the seven of us who were fired in Memphis,
                 and a Federal District Court Judge recently ruled that
                 Starbucks must reinstate us.


                 We are fighting to get our jobs back and fighting for the
                 right to organize. We love our job at Starbucks and find
                 joy in making our customers’ days. Starbucks claims to be
                 a different kind of company – one that does everything
                 “through the lens of humanity.” Starbucks’s mission and
                 values include “challenging the status quo” and treating
                 each other with “dignity and respect.” We do not believe
                 that Starbucks has been living up to its mission and
                 values and we are working to change that. In fact, since
                 the return of interim CEO Howard Schultz, we’ve felt
                 Starbucks has doubled down on efforts to stamp out
                 unionization across the country.


          o ⚓ Mexico News Daily ☛ School_relents,_allows_indigenous_student_to
            attend_despite_his_long_hair⠀⇛


                 On Thursday, staff at the Secundaria Número 4 Ricardo
                 Flores Magón school in Tijuana said that Acoyani, a 12-
                 year-old student whose dark, braided hair reached all the
                 way down his back, wouldn’t be allowed to continue
                 attending classes. The reasons they gave were that he
                 could be confused for a girl or that his long hair might
                 encourage other male students to come to school with long
                 hair.


          o ⚓ The Nation ☛ Autocracy_and_Anti-Abortion_Go_Hand_in_Hand⠀⇛


                 One of the more disingenuous arguments for overturning
                 Roe v. Wade (1973) was the claim that it would take the
                 contested social issue of abortion out of the hands of
                 unelected courts and give it to the democratically
                 elected Congress and state legislatures. When Roe was
                 rescinded by the Dobbs decision in June, right-wing
                 columnist Katie Pavlich wrote in The Hill, “Abortion law
                 being returned to the states by the Supreme Court allows
                 Americans to have more of a say and additional
                 opportunities to engage in the democratic process. The
                 overturning of Roe is not only a win for life, but for
                 the restoration of the U.S. Constitution and democracy.”1


          o ⚓ Site36 ☛ Human_rights_violations_in_Malta:_Frontex_Fundamental
            Rights_Officer_criticises_own_air_surveillance⠀⇛


                 An emergency at sea in May this year shows how Maltese
                 authorities lets unseaworthy boats pass unrescued so that
                 refugees are taken on board much later by neighbouring
                 Italy or drown. Frontex’s acting Fundamental Rights
                 Officer has clearer words for this than his predecessor.


          o ⚓ FAIR ☛ Ivey_Camille_Manybeads_Tso_on_Indigenous_Resistance,_Alex
            Vitale_on_the_End_of_Policing⠀⇛


          o ⚓ Techdirt ☛ Appeals_Court:_No_Immunity_For_School_Cop_Who
            Assaulted_A_Student_Over_Perceived_Disrespect⠀⇛


                 Putting cops in schools is still a bad idea. It turns
                 regular disciplinary problems — ones handled for decades
                 by administrators, teachers, and parents — into police
                 matters, subjecting students to the whims of armed
                 officers who have been trained to react with violence to
                 nearly any misbehavior.


          o ⚓ Scheerpost ☛ U.S._Approval_of_Labor_Unions_at_Highest_Point_Since
            1965⠀⇛


                 71% of Americans now approve of labor unions and 40% of
                 union members say their membership is “extremely
                 important.”


          o ⚓ TruthOut ☛ Biden_Is_Still_Issuing_Calls_to_Increase_Police
            Funding⠀⇛


          o ⚓ TruthOut ☛ Amazon_Loses_Bid_to_Overturn_Union’s_Historic_Win_in
            New_York⠀⇛


          o ⚓ Common Dreams ☛ ‘Great_Day_for_Labor’:_NLRB_Rejects_Amazon
            Attempt_to_Overturn_Union_Win⠀⇛


                 In a new filing, the NLRB officer who presided over weeks
                 of virtual hearings on Amazon’s election objections
                 concluded that the corporation’s protests against the
                 union’s landmark victory “should be overruled in their
                 entirety.”


          o ⚓ Common Dreams ☛ Opinion_|_Behind_the_Rise_in_Union_Support—And
            the_Challenge_Ahead⠀⇛


                 Reports of the biggest rise in public support for unions
                 in a half century is an encouraging response to the
                 chokehold the policies of neoliberalism have held over
                 U.S. workers for decades that led to a staggering
                 inequality, the weakening of unions, and facilitated the
                 ascendancy of the right.


          o ⚓ Pro Publica ☛ Illinois_Choate_Mental_Health_Center_Abuse
            Allegations_Continue⠀⇛


                 A 24-year-old man with developmental disabilities,
                 Reichard was accustomed to workers at the state-run
                 residential facility telling him what to do. But this
                 time he didn’t obey.


          o ⚓ Pro Publica ☛ Choate_Mental_Health_Center’s_History_of_Abuse
            Allegations⠀⇛


                 “What I am presently seeing occur at Choate and hearing
                 occur at other facilities concerns me more than it has my
                 entire career,” Barry Smoot, a decades-long IDHS
                 employee, wrote to Illinois Department of Human Services
                 Secretary Grace Hou on May 26, 2021. Among the
                 recommendations he wanted to make: that cameras be
                 installed inside the facility.


          o ⚓ Common Dreams ☛ ‘Honor_Her_Memory…_by_Fighting_Like_Hell’:
            Barbara_Ehrenreich_Dies_at_81⠀⇛


                 Her death was announced on Twitter by her son, Ben
                 Ehrenreich, and daughter, Rosa Brooks.


    * § Internet Policy/Net Neutrality⠀➾


          o ⚓ Remembering_Barbara_Ehrenreich⠀⇛


                 For more than 40 years, Barbara kept our IPS family
                 learning and laughing. As a staff member in the 1980s,
                 she shared an office with longtime IPS Director John
                 Cavanagh and gave him an education in feminism. In
                 between writing books and essays, she pulled together
                 progressive women leaders in a working group that
                 published A National Agenda for Change: Toward Economic
                 Justice for Women in 1985. John still keeps a copy in his
                 office.


          o ⚓ Broadband Breakfast ☛ FCC_Commits_Additional_$800_Million_From
            Rural_Digital_Opportunity_Fund⠀⇛


                 The announcement means the FCC has committed over $6
                 billion from the $9.2-billion fund, which initially
                 announced winners under a different-look commission in
                 December 2020, but which was scrutinized over the past
                 year-and-a-half due to claims that the winning bids would
                 go to areas that don’t need the connectivity promised.
                 Under new Chairwoman Jessica Rosenworcel, the FCC has
                 been purging the fund of what it sees as potential
                 wasteful spending and provided those winning bidders with
                 opportunities to let go of those bids.


          o ⚓ Linux On Mobile ☛ LINMOB.net_–_Re-Evaluating_Priorities⠀⇛


                 That’s not the only thing. With increased stress levels,
                 I really need to reduce my social media use, as it simply
                 does not make me feel better overall and also likely eats
                 an uncomfortably large amount of time.


    * § Digital Restrictions (DRM)⠀➾


          o ⚓ Techdirt ☛ Ubisoft_Backtracks_After_Backlash_To_Make_DLC
            Permanently_Downloadable_Despite_Server_Shutdown⠀⇛


                 You may recall that a few weeks back we discussed
                 Ubisoft’s decision to shutdown game servers for several
                 titles, including major AAA titles like Assassin’s Creed
                 3 and Far Cry 3. While server shutdowns are the norm
                 after some period of time, as is the loss of certain
                 online gaming features, notable in Ubisoft’s announcement
                 was that anyone who bought the PC DLC for those games was
                 simply going to lose all that bought DLC. Making matters
                 worse, updated versions of the game on PC are available
                 for purchase and include all that DLC, making it so that
                 Ubisoft was tacitly telling gamers to just go buy the
                 content all over again.


          o ⚓ Techdirt ☛ Cloud-Based_Smart_Home_Gadgets_Keep_Getting_Bricked
            Because_You_No_Longer_Own_What_You_Buy⠀⇛


                 We’ve noted more times than I can count how you no longer
                 really own the things you buy. Whether it’s smart home
                 hardware, or routers that become useless paperweights
                 when the manufacturer implodes, or post-purchase firmware
                 updates that actively make your device less useful, you
                 simply never know if the product you bought yesterday
                 will be the same product you think you own tomorrow.


    * § Monopolies⠀➾


          o § Copyrights⠀➾


                # ⚓ The Verge ☛ PSA:_Bandcamp_Friday_is_back⠀⇛


                       Bandcamp is bringing back its Bandcamp Fridays
                       promotion where it waives its cut of any money you
                       spend buying music from artists or their labels on
                       its marketplace. Historically, the company ran the
                       promotion on the first Friday of every month, and
                       that appears to be the case this time around, too.
                       According to its update page, it has Bandcamp
                       Fridays scheduled for September 2nd, October 7th,
                       November 4th, and December 2nd.


                # ⚓ Torrent Freak ☛ Google_Removes_YouTube_Rippers_from_UK
                  Search_Results⠀⇛


                       Google has removed several popular YouTube rippers
                       from its UK search results. The company took this
                       action following a notice from local music group
                       BPI, which pointed out that local ISPs are required
                       to block the sites due to a High Court order. In
                       response, Google voluntarily took the same action.


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



                    ䷩ 𝚕𝚒𝚗𝚎 5131

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.03.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_03/09/2022:_Encrypted_Audio_and_Video_Calls_With_Kaidan⠀✐


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Instructionals/Technical
          o Desktop_Environments/WMs
                # K_Desktop_Environment/KDE_SC/Qt
    * Distributions_and_Operating_Systems
          o Fedora_Family_/_IBM
          o Canonical/Ubuntu_Family
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Programming/Development
                # Perl_/_Raku
          o Standards/Consortia
    * Leftovers
          o Security
          o AstroTurf/Lobbying/Politics
          o Civil_Rights/Policing
    * Gemini*_and_Gopher
          o Personal
          o Politics
          o Technical
                # Internet/Gemini
                # Programming
    * § GNU/Linux⠀➾


          o § Audiocasts/Shows⠀➾


                # ⚓ Video ☛ Does_GNOME_Really_Want_To_Destroy_Theming?_–
                  Invidious⠀⇛


                       Even today I still here people saying that GNOME
                       wants to destroy theming or you can’t theme
                       Libadwaita so let’s actually look at the facts and
                       see what it’s like


                # ⚓ Video ☛ Is_it_Time_to_Retire_the_OTB_[OldTechBloke]
                  Channel?_–_Invidious⠀⇛


                       This is my first video upload for three months and
                       during that time I’ve received many messages and
                       comments asking about my health, what’s happening
                       with the channel, and yes, implying that possibly I
                       may be thinking the channel has reached the end of
                       its natural life. Well in this video I will be
                       answering those questions as well as giving an
                       update on my biking experiences over the last few
                       months and, of course, touching on Linux in the
                       process.


          o § Instructionals/Technical⠀➾


                # ⚓ Make Use Of ☛ How_to_Install_and_Use_Homebrew_on_Linux⠀⇛


                       Homebrew is a free and open-source package manager
                       for Linux and macOS. Although different Linux
                       distros ship with their own package managers, such
                       as APT, DNF, Pacman, etc., to facilitate software
                       installation, you’ll want Homebrew on your system
                       if you wish to install programs that aren’t
                       available in the default Linux distro repositories.


                       Let’s check out Homebrew and the steps to install
                       and use it on Linux.


                # ⚓ OMG Ubuntu ☛ How_to_Make_Console_Your_Default_Terminal_App
                  on_Ubuntu_–_OMG!_Ubuntu!⠀⇛


                       Ubuntu developers have decided not to make GNOME’s
                       Console the default terminal emulator in the
                       upcoming Ubuntu 22.10 release, but that doesn’t
                       meant you can’t.


                       Console is billed as a “simple user-friendly
                       terminal emulator for the GNOME desktop” and, by
                       all accounts, that’s exactly what it is.
                       Functionally speaking, it’s not as avanced as GNOME
                       Terminal, which is the VTE Ubuntu and most Linux
                       distros that ship the GNOME desktop environment
                       use.


                       But honestly? Speaking as a Linux user who uses the
                       terminal daily for package management, system
                       monitoring, and playing around with awesome command
                       line tools like ncdu, mapscii, and musikcube, I’m
                       yet to encounter anything Console can’t do.


                # ⚓ ELinux ☛ Exclude_ai1wm-backup_folder_from_Softaculous
                  backups_|_Linux_Webhosting_blog⠀⇛


                       For WordPress websites that use both Softaculous
                       backups and AllInOne Migration plugin backups,
                       Softaculous backups include the .wpress files
                       created by the ai1wm plugin and therefore this will
                       significantly increase the size of Softaculous
                       backup files. To exclude ai1wm-backup folder from
                       Softaculous backups SSH into your server and
                       navigate to the following path:


                # ⚓ ELinux ☛ How_to_move_email_accounts_from_G-Suite_to_cPanel
                  |_Linux_Webhosting_blog_CPanel_/_WHM⠀⇛


                       In this guide I will be using IMAPSync tool to move
                       emails from G-Suite to cPanel.


                # ⚓ ELinux ☛ How_to_Create_Secure_Passwords_from_the_Terminal_|
                  Linux_Webhosting_blog⠀⇛


                       Studies on passwords show that people are still
                       using the same passwords even through several
                       years.The worst passwords are the same. This is a
                       danger in our security, sooner or later we could be
                       hacked. Take a look of the summary of the worst
                       passwords from Wikipedia.


                # ⚓ ELinux ☛ How_to_enable_comodo_WAF_modsecurity_in_cpanel_for
                  free⠀⇛


                       Login to WHM > ModSecurity™ Vendors and under
                       “OWASP ModSecurity Core Rule Set V3.0” click on the
                       “+ install” link and to add a third-party rule set
                       click on “Add Vendor” button.


                # ⚓ ELinux ☛ How_to_create_bulk_email_accounts_in_cpanel
                  server⠀⇛


                       Here is how to bulk create email accounts in cPanel
                       under a single domain name.


                # ⚓ MakeTech Easier ☛ How_to_Hide_the_Top_Bar_and_Side_Panel_in
                  Ubuntu_–_Make_Tech_Easier⠀⇛


                       You decided to try Ubuntu 22.04 and the Gnome
                       desktop environment that comes with it. You feel,
                       though, that Gnome’s top bar and side panel are
                       always in the way and would prefer your apps to
                       take up the whole screen. Learn how to hide the top
                       bar and side panel in Ubuntu 22.04.


                # ⚓ ELinux ☛ How_to_stop_xmlrpc_ddos_attack_on_wordpress_in
                  cpanel_and_whm⠀⇛


                       xmlrpc.com is a WordPress file that was intended to
                       be used for API’s but lately it’s more and more
                       used as a way for hackers to brute-force WordPress
                       installations.


          o § Desktop Environments/WMs⠀➾


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


                      # ⚓ Encrypted_Audio_and_Video_Calls_–_Kaidan⠀⇛


                             Kaidan will receive a grant by NLnet for
                             adding encrypted audio and video calls.


                             The calls will be end-to-end encrypted and
                             authenticated via OMEMO. Furthermore, Kaidan
                             will support small group calls. We strive for
                             interoperability between Kaidan and other
                             XMPP apps supporting calls. In order to
                             achieve that, we will implement a large
                             number of XEPs (XMPP Extension Protocols).
                             They make it possible to have a modern call
                             experience.


                             Calls have become more widespread over the
                             past few years in free XMPP chat apps.
                             Especially, grants by NLnet made that
                             possible. The development speed and
                             interoperability between different apps have
                             increased. Such an intense development often
                             results in improved specifications. But
                             sometimes the development overtakes the
                             standardization. In that case, the
                             standardization needs to catch up what has
                             already been implemented.


                             We have to handle that circumstance with
                             group calls and invitations to calls at the
                             moment. There are some adjustments that are
                             not yet official. To make calls from Kaidan
                             to other apps already supporting them, we
                             have to base our work on those changes. If
                             those unofficial adjustments are being
                             modified later to become official, we will
                             need to modify Kaidan as well. But we see the
                             evolution of calls in XMPP as a huge progress
                             and are ready for adaption!


                      # ⚓ GSOC_Update_3⠀⇛


                             These last few weeks have been a good
                             learning experience with Krita as I try to
                             implement a node visitor and save context
                             classes. First we want to create a
                             saveContext class for svg called
                             KisScalableVectorGraphicsSaveContext that
                             will be used to save to the file when
                             visiting all nodes. This class is fairly
                             cookie cutter and takes a KoStore to use to
                             write to a specified file. The real work will
                             happen in our node visitor class
                             KisScalableVectorGraphicsSaveVisitor. Most of
                             this right now includes some template visit
                             functions like visit(KisPaintLayer *layer)
                             that just calls saveLayer(KisLayer *layer) to
                             save the specific type of layer. One small
                             quirk here was when trying to find out where
                             vector layers are processed. After
                             experimenting with the ora plugin I found out
                             this would be visited under the group layer
                             function visit(KisGroupLayer *layer) so I
                             similar for the svg plugin.


    * § Distributions and Operating Systems⠀➾


          o ⚓ Beta News ☛ Chinese-made_deepin_20.7_Linux_distro_is_ready_to
            replace_Windows_11_on_your_PC⠀⇛


                 Once of the most beautiful and user-friendly operating
                 systems is a Linux distribution from China called deepin.
                 If you are dissatisfied with Windows 11 or macOS, and you
                 are intrigued by Linux, deepin can be a great choice if
                 you highly value beauty and well-designed user
                 interfaces.


                 The newest version of that operating system, deepin 20.7,
                 is now ready to be downloaded, and it is chock-full of
                 bug fixes and new features such as improved Grand Search
                 with Google integration and an enhanced Mail app with new
                 calendar functionality. Yes, this looks to be the best
                 version of deepin yet!


                 “In deepin 20.7, we have developed and integrated a great
                 number of practical functions based on the community
                 users’ feedback, synchronized with the upstream kernel
                 version, fixed underlying vulnerabilities, upgraded the
                 Stable kernel to V5.15.45, added the HWE 5.18 kernel to
                 be compatible with more devices, and further improved
                 system compatibility and security,” explains the
                 development team.


          o § Fedora Family / IBM⠀➾


                # ⚓ Slashdot ☛ What_Happened_with_CentOS_Will_Not_Happen_with
                  Rocky_Linux’⠀⇛


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ Linuxiac ☛ Ubuntu_Unity_Is_Likely_to_Become_the_Next
                  Official_Ubuntu_Flavor⠀⇛


                       Ubuntu Unity, the unofficial fork with a dash of
                       nostalgia from the Unity days, has applied to
                       become the official Ubuntu flavor.


                       Many Linux enthusiasts had used Ubuntu at some
                       point in their careers and will recall the not-so-
                       distant days when Canonical made a difference with
                       their Unity desktop.


                       We shall specify for novice Linux users that Unity
                       is a graphical shell for the GNOME desktop
                       environment designed and maintained by Canonical
                       for Ubuntu. It was beautiful and innovative, but
                       another controversial Canonical decision threw it
                       out in 2017.


                # ⚓ DebugPoint ☛ DebugPoint_Weekly_Roundup_#22.03:_Ubuntu_Unity
                  Becomes_Official_+_More⠀⇛


                       Here’s the weekly roundup #22.03 for you across the
                       GNU/Linux and tech world.


                       Welcome to the DebugPoint Weekly roundup #22.03,
                       where you can find all the happenings from this
                       week, mainly from the Linux and open-source space.
                       If you have missed some stories, no worries!


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Android Police ☛ What_is_Sony_doing_with_Android_phones?
                  The_Android_Police_podcast_is_at_IFA_2022_to_find_out⠀⇛


                # ⚓ Android Authority ☛ Why_don’t_the_best_premium_Android
                  phones_have_flat_displays?⠀⇛


                # ⚓ TechRadar ☛ Key_Pixel_Tablet_specs_may_have_been_revealed
                  through_hidden_Android_code_|_TechRadar⠀⇛


                # ⚓ Android Authority ☛ 5_Android_apps_you_shouldn’t_miss_this
                  week_–_Android_Apps_Weekly⠀⇛


                # ⚓ Make Use Of ☛ 4_Ways_to_Get_More_From_Google_Password
                  Manager_on_Android⠀⇛


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


          o § Programming/Development⠀➾


                # ⚓ Linux Links ☛ 8_Top_Free_and_Open_Source_Kotlin_Web
                  Frameworks_–_LinuxLinks⠀⇛


                       One of the types of software that’s important for a
                       web developer is the web framework. A framework “is
                       a code library that makes a developer’s life easier
                       when building reliable, scalable, and maintainable
                       web applications” by providing reusable code or
                       extensions for common operations. By saving
                       development time, developers can concentrate on
                       application logic rather than mundane elements.


                       A web framework offers the developer a choice about
                       how to solve a specific problem. By using a
                       framework, a developer lets the framework control
                       portions of their application. While it’s perfectly
                       possible to code a web application without using a
                       framework, it’s more practical to use one.


                       Kotlin is a cross-platform, statically typed,
                       general-purpose programming language with type
                       inference. Kotlin is a more modern version of Java.
                       It adopts functional ideas such as immutability and
                       first-class functions, out of the box, and it is
                       also object oriented.


                # ⚓ Barry Kauler ☛ BaCon_4.5.1pre_and_utilities_now_compile_in
                  OE⠀⇛


                # ⚓ Bozhidar Batsov ☛ Setting_up_Emacs_for_OCaml_Development_–_
                  (think)⠀⇛


                       I’ve promised you articles about OCaml and here
                       they come! The first order of business when
                       learning a new programming language is to setup
                       Emacs for effective programming in it.


                # ⚓ More_recursive_definitions⠀⇛


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ Death:_A_Terminal_Experience_|_Saif_
                        [blogs.perl.org]⠀⇛


                             A program being executed, self terminating on
                             encountering an non-viable condition is a
                             typical scenario in Perl programs. The death
                             sentence can deliver information about the
                             departed application to the user as
                             justification and demand appropriate
                             resolution for the subsequent reincarnation.


                             Now I know my code fails more often than it
                             succeeds, and it is for this reason I am
                             planning an alternative wake for the
                             programmed parting of my future terminal
                             applications. As a once-in-a-run-time event,
                             death might be more elaborately delivered,
                             something to be celebrated. The last words of
                             a dying application softens the developers
                             ensuing grief, while encouraging
                             resuscitation with an appropriately delivered
                             injection of code.


          o § Standards/Consortia⠀➾


                # ⚓ Jim Nielsen ☛ Validating_HTML_–_Jim_Nielsen’s_Blog⠀⇛


                       To bluntly answer the question: I validate, but
                       only when I encounter a perplexing cross-browser
                       issue I can’t seem to solve.


                       In those cases, I’ll copy the one-off HTML document
                       I’m dealing with and paste it into the W3C’s
                       browser-based markup validation service to check
                       for any errors I can’t seem to spot.


                       While that service is useful for manually
                       validating individual documents, it’s not
                       particularly practical for systematically
                       validating HTML as part of an automated software
                       development pipeline.


                       That said, a while back I discovered the W3C Nu
                       HTML Checker which also validates HTML. It has a
                       HTTP API which you can leverage to automate the
                       process of validating multiple HTML documents.


                       I wrote a little script to interface with the API
                       and check the HTML files output by my static site
                       generator, but it kept returning 503 errors on many
                       of the files.


    * § Leftovers⠀➾


          o § Security⠀➾


                # ⚓ Ruben Schade ☛ Rubenerd:_Hyundai’s_AES_key_was_lifted_from
                  an_example⠀⇛


                       The Register’s Thomas Claburn reported on a blog
                       post by greenluigi1 where they investigate the
                       feasibility of modifying the car’s In-Vehicle
                       Infotainment system. It’s well written with clear
                       steps and screenshots; I love reading through
                       someone’s thought process when it comes to this
                       stuff.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Michael West Media ☛ Who_gets_the_Google_dollars_at_ABC,
                  the_soy_latte_sippers_or_the_Bundy_–_Rum_brigade?⠀⇛


                       Murdoch would have us believe ABC is a hot-bed of
                       leftist activists but the reach of ABC Rural,
                       funded by Google, is conservative, broad and well
                       funded. Brian Burkett, Emma Mesikämmen and Lisa
                       Waller analysed the corporation’s Rural Reports to
                       test claims of bias.


          o § Civil Rights/Policing⠀➾


                # ⚓ Internet Freedom Foundation ☛ Comments_on_the_consultation
                  paper_on_the_need_for_a_new_framework_for_governing
                  telecommunications_in_India⠀⇛


                       On July 23, 2022, the Department of
                       Telecommunications (DoT) released a consultation
                       paper on the need for a new framework for governing
                       telecommunications in India. Read our response
                       engaging with specific issues such as internet
                       shutdowns, net neutrality, and an overhaul of the
                       surveillance framework contained in the Indian
                       Telegraph Act, 1885.


                       [...]


                       The paper has been divided into 10 sections related
                       to issues such as simplifying the regulatory
                       framework, spectrum management, right of way,
                       insolvency, and the Universal Service Obligation
                       Fund (USOF). The paper also indicates a need for a
                       new law and a simplified regulatory framework. A
                       bulleted summary of the paper highlighting its main
                       suggestions may be accessed here. While the paper
                       discusses certain essential issues which have to be
                       addressed in this overhaul, it conspicuously misses
                       certain important points.


    * § Gemini* and Gopher⠀➾


          o § Personal⠀➾


                # ⚓ Sirius_Cybernetics⠀⇛


                       Recently, I read about people who use the EV
                       charging stations, but not for charging the
                       batteries of their electric cars, just as a parking
                       spot.


                # ⚓ The_dog_and_the_typewriter.⠀⇛


                       In the days after the cannery shut down, I had
                       returned home. I found a typewriter. I made text
                       together with it every day, and I felt as one with
                       it.


                       One day it stopped stamping letters when I pressed
                       its keys. I had fear that it would never again be
                       as it was before. I wondered what to do, and
                       thought to ask someone for help. A dog of mine came
                       by, and spoke to me.


                # ⚓ ZEILRVC_Wordo:_TUNED⠀⇛


          o § Politics⠀➾


                # ⚓ Nosegay⠀⇛


                       Not a 1450s-ish English contraction of nose
                       (meaning nose) and gay (meaning bringing joy), to
                       make something which brings your nose joy which is
                       clearly preposterous; not a word commonly used in
                       bridal shops… but a sodding mountweazel if ever I
                       saw one.


          o § Technical⠀➾


                # ⚓ Late_Night_updates⠀⇛


                       I work as the QA lead for the Vivaldi web browser.
                       Being a small team I also have an additional role
                       where I am responsible for much of the release
                       process for our desktop browser, including version
                       daily versions to a small external (volunteer)
                       testing group, weekly public “snapshots” (sort of
                       like beta releases for the upcoming version), and
                       major and minor updates to our stable version.


                # ⚓ How_i_alias_git_to_manage_my_home_directory_(for
                  dotfiles)⠀⇛


                       I am writing this on the first Saturday of
                       September 2022 but the solution described is in use
                       since exactly two years ago already.


                # ⚓ Roll_and_move⠀⇛


                       Moving one marker along a track like Snakes and
                       Ladders is basically a way to keep track of the sum
                       of those moves. As a race game, that’s not fun,
                       becomes just luck. But if that is combined with
                       stuff you do outside of the track, like being far
                       ahead (or far behind) or having passed/not passed
                       certain thresholds, that might be interesting.
                       Pondering about an idea where the movement track is
                       central and looks like the main part of the game
                       (to get the classic nostalgic roll-and-move feel)
                       but there’s actually other things going on on the
                       side (on cards or on smaller player boards) which
                       is where the skill is actually hiding. Just green
                       hat brainstorming but something like “winner has
                       the most sets when anyone reaches the end” or
                       “winner has the most sets when last person reaches
                       the end”.


                       There’s also variants in this category where there
                       there is a random race but you don’t have your
                       permanently own central markers, instead you bet on
                       them or auction for them etc.


                # ⚓ Managing_a_fleet_of_NixOS_Part_2_–_A_KISS_design⠀⇛


                       Let’s continue my series trying to design a NixOS
                       fleet management.


                       [...]


                       The mechanism is so simple, it could be adapted to
                       many cases, like using GitHub or any data source
                       instead of a central server. I will personally use
                       this with my laptop as a central system to manage
                       remote servers, which is funny as my goal is to use
                       a server to manage workstations 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽
                       ⦇:-)⦈


                # ⚓ Sneakernet_in_a_Free,_Developed_Society⠀⇛


                       Regardless, the coolness of the very idea of
                       sneakernet is incredible. I just want to use one.
                       For something! I don’t even know what, just
                       something. When I talk about “sneakernet” in this
                       post I don’t mean the occasional file moved on a
                       USB thumb drive between friends once in a while
                       (even though that technically counts). I’m thinking
                       about organised sneakernets between several actors,
                       be they individuals or organisations.


                       But is there an actually useful purpose of
                       sneakernets in democratic countries in the
                       developed world?


                       Suppose that you aren’t persecuted or part of a
                       criminal network. Which actual use do you have for
                       a sneakernet then? It’s super simple to set up a
                       server with sftp or file upload and download
                       through https. That’s also a lot faster and less
                       costly than posting microSD cards to each other.


                # § Internet/Gemini⠀➾


                      # ⚓ More_Brainless_Content_Please⠀⇛


                             A good chunk of people complaining about the
                             world dumbing with YouTube click-bait no
                             doubt saw the kind of nonsense I watch and
                             thought ‘the BBC showed much more
                             enlightening and informative content than
                             this modern drivel’. This comparison doesn’t
                             work.


                             We shouldn’t compare these videos to
                             television, but to radio. Lots of us have
                             large sections of the day where we sit in our
                             little box-houses, clicking through
                             spreadsheets, doing the dishes, and broadly
                             doing jobs which machines can almost but not-
                             quite perform. It’d be nice to spend this
                             time learning a language, or how to perform
                             quadratic equations, but the tasks demand
                             just enough mental attention to prohibit any
                             serious thinking, so we don’t do serious
                             thinking. I like Space Feather, Shaun, and
                             anything related to Computerphile. Other
                             people like Joe Rogan, or rants about what
                             Jordan Peterson thinks about frogs, or why
                             Jordan Peterson’s opinions on frogs don’t
                             work.


                      # ⚓ Early_Internet⠀⇛


                             I mourn the escapism of early internet. True
                             and fun eureka moments in a environment which
                             had no motives to provide information, except
                             enthusiasm for sharing. A community waiting
                             to be found, an outlet for conversation more
                             specific than could have ever been had in
                             near geography. A place where we could all
                             grow together.


                      # ⚓ New_Year_2023:_Making_the_game_fun⠀⇛


                             I discovered a tiny gemini game full of nice
                             ideas I feel like stea… *cough*
                             reimplementing in 2023cards (yes, that’s the
                             short name of this project from now on). The
                             game in question is Astrobotany [1].


                # § Programming⠀➾


                      # ⚓ The_slacker’s_guide_to_managing_dotfiles⠀⇛


                             In the past I was using Git for managing
                             dotfiles, and it worked pretty well. Main
                             advantages of this solution were a
                             possibility of syncing settings between
                             devices and an ability to easily experiment
                             with different configurations in separate
                             branches (let’s say switch your code editor
                             to emacs and switch back by just changing a
                             branch if emacs didn’t appeal to you).


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


╘══════════════════════════════════════════════════════════════════════════════╛
                       ¶ Lines in total: 5920
    ➮ Generation completed at 02:43, i.e. 64 seconds to (re)generate ⟲