𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, September 03, 2022
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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
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Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
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Gemini index for the day: gemini://gemini.techrights.org/2022/09/03/
╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
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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⦈_
⣿⠶⠀⠐⠂⠂⠒⠆⠲⠀⠀⠒⠒⠲⠒⠂⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⣿⣿⣿
⣿⣯⣼⣿⣯⣭⣥⣭⣥⣭⣭⣽⣭⣭⣯⣬⣥⣯⣯⣭⣭⣯⣦⣭⣽⣮⣭⣭⣥⣽⣯⣿⣭⣭⣭⣽⣭⣯⣽⣤⣭⣬⣘⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿
⣿⣯⣼⣿⡐⠒⡔⠒⠖⡴⠖⠗⠄⠐⡦⢼⠰⡧⠆⡶⠦⠒⢦⠖⢦⡗⠂⠖⠖⢤⠳⠴⡶⠻⡌⠃⠧⠔⠻⠬⢳⠳⠣⠠⠒⢠⠐⠠⢵⢦⠞⡇⠖⢳⡇⠘⢷⣯⣤⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣏⣏⣹⣉⣉⣉⣉⣿⣶⣯⣏⣉⣉⣯⣹⣉⣍⣉⣉⣿⣤⣟⣏⣩⣯⣉⣩⣉⣹⣇⣾⣩⣉⣉⣿⣉⣉⣉⣹⣹⣹⣩⣉⣍⣹⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣾⣿⠵⠶⡒⠒⡼⠒⢶⣶⠒⠆⢲⠓⠳⡖⣶⠒⠚⠓⠒⠓⢷⢪⡗⠖⠺⢶⠘⡖⡐⡗⠔⠶⢲⠳⠲⠒⡶⠒⡧⠶⡾⠚⣷⣴⣶⣴⣶⣶⣶⣾⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣹⣿⣉⣋⣻⣉⣻⣛⣛⣛⣟⣛⣙⣛⣛⣟⣋⣟⣛⣛⣙⣛⣻⣛⣛⣙⣻⣋⣍⣻⣛⣻⣛⣻⣋⣛⣟⣛⣛⣛⣛⣛⣉⣻⣛⣟⣛⣛⣋⣛⣻⣻⣛⣋⣻⣛⣋⣟⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣿⣶⣿⣶⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠬⠧⡯⠭⢼⠼⡴⠧⡵⢼⢽⢤⡿⢿⡿⡿⢿⡿⡿⣿⠿⢿⠿⣿⢿⢿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠭⠭⠭⠬⠭⠭⠭⠭⠭⠥⠬⠬⠭⠬⠭⠭⠭⠤⠭⠬⠥⠭⠭⠭⠬⠥⠭⠬⠭⠭⠭⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠍⠉⠉⠍⠉⠍⠉⠍⠩⠿⠿⠿⠿
⡇⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠩⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢩⣭⣭⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⣭⣭⣭⣭⣭⣭⣭⡭⠭⢭⣭⣭⣭⢩⣭⣭⣭⠩⣩⣭⣭⣭⣽
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣋⣛⣚⣁⣏⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⣛⣒⣚⣉⣿⣿⣿⣿⣹⣋⣛⣛⣻⣋⣲⣋⣹⣉⣛⣟⣿⣿⣿⣏⣛⣃⣀⣉⣉⣿⣿⣿⣏⣛⣑⣣⣘⣛⣻⣿⢸⣿⣹⣋⣂⣊⣛⣹⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠧⠤⠤⡇⠦⢾⣿⣿⡦⠤⡼⠤⡤⢤⠦⠘⡤⢤⠯⠠⡴⢤⣿⣧⣴⠠⠤⢤⠣⢼⣤⣿⣷⡧⠤⢤⠤⠠⠤⢤⣿⢸⣿⣤⡤⠤⠤⣧⣼⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢹⣉⣯⣉⣩⣹⣿⣿⣷⣉⣋⣻⣋⣉⣋⣉⣩⣉⣉⣉⣹⣿⣿⣿⣉⣉⣋⣋⣉⣉⣽⣿⣿⢉⣉⣏⣉⣉⣙⣉⣿⢸⣉⡋⣉⣉⣙⣉⣋⣽⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢄⠚⠲⠒⠢⠸⠟⣷⣰⠀⣶⡖⢲⣶⠀⡆⢀⡆⢰⠂⣶⠀⣾⣿⣶⡞⠘⠛⠑⣧⣾⣿⣿⣤⣶⠃⠂⢳⢴⣶⣿⢸⡟⠗⡦⠲⠓⠣⠟⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⠏⣉⡉⣹⡿⣿⣿⢸⠀⣿⡇⢸⣿⠀⡇⢹⡇⢨⠀⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣁⣹⣉⡉⣉⣹⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣶⣶⣷⣶⣦⣿⣿⢨⣀⣿⡇⢸⣿⣿⡇⢘⡇⣸⠂⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣦⣶⣶⣶⣶⣶⣾⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡧⢼⣿⣿⡇⢸⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⡇⢸⣿⣿⡇⣿⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⡇⣿⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⡏⠉⣍⢍⣩⠭⣉⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡏⠉⠉⠉⠉⣉⣽⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⢨⣭⣭⣭⣽⣭⣭⣯⣿⣿⣾⣿⣿⣿⣿⣧⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼
⡇⣇⣀⣆⣠⣀⣆⣤⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣶⣶⣶⢶⣶⣶⣶⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢰⣶⣶⣶⣶⣶⣶⣶⣶⢾
⡇⡇⠀⠀⠠⠀⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠰⠶⠶⠶⠾⠶⠶⠶⠿⠿⠾⠿⠿⠿⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⢾
⡇⡧⠤⠧⠤⠦⠶⠤⠤⠼⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠸⠿⠿⠿⠿⠧⠼⠿⣿⣿⢻⣿⣿⣿⣿⡟⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻
⡇⡇⠀⡀⠘⠛⠛⡛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻
⡇⡗⢒⠛⢒⢒⠒⣒⣒⣒⣚⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⢘⣛⣛⣛⣻⣓⣚⣛⣿⣿⣹⣿⣿⣿⣿⣏⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣹
⡇⡏⠀⡄⠀⠀⠀⡉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡏⠍⠭⣍⡉⣭⣭⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⢨⣭⣭⣭⣽⣭⣭⣭⣿⣿⣼⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼
⡇⣇⣀⣖⣂⣀⣆⣀⣄⣀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢰⣶⣶⣶⣶⣶⣶⣶⣶⢾
⡇⡗⠒⠒⠖⠖⠶⠾⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠰⠶⠶⠶⠾⠶⠶⠷⠿⠿⠾⠿⠿⠿⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⢾
⡇⣯⣄⣯⣥⣬⣧⣭⣬⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⣼⣿⣾⣿⢿⣷⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿
⡇⡏⠍⣩⠩⡉⡿⡿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⡿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⡧⡦⡷⡶⣶⢾⢶⢶⢶⡶⣶⡿⡿⡿⢿⢿⢿⢿⢿⠿⡿⡿⡿⡿⣿⢸⢿⢿⣿⢿⡷⡾⡿⣿⣿⣻⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻
⡇⡇⠀⡐⢐⠀⠛⠛⠛⠛⠛⡛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻
⡇⡗⠓⠛⠛⠛⣛⣛⣛⣛⣛⣛⣚⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⢘⣛⣛⣛⣻⣛⣛⣛⣿⣿⣹⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣹
⡇⡇⠀⢠⡈⠄⠈⠍⠉⡍⠉⠉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡏⠉⠉⢉⠉⢭⣭⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⢨⣭⣭⣭⣭⣭⣭⣭⣿⣿⣼⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼
⡇⣇⣀⣰⣄⣀⣠⣂⣆⣀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣶⣶⣶⢶⣶⣶⣶⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢰⣶⣶⣶⣶⣶⣶⣶⣶⢾
⡇⡇⠀⠐⠠⠀⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠰⠶⠶⠶⠶⠶⠶⠶⠿⠿⠾⠿⠿⠿⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⢾
⡇⡧⠤⠼⠦⠤⠤⠼⠤⠼⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠸⠿⠿⠿⢿⠧⠼⠿⣿⣿⢻⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻
⡇⡇⠁⢉⣒⠀⢛⠛⢛⡛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⠛⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻
⡇⣗⣒⣞⣒⣒⣚⣲⣚⣒⣛⣛⣟⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⢸⣛⣛⣛⣲⣓⣚⣟⣿⣿⣻⣿⣿⣿⣿⣏⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣙⣋⣋⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣏⣹⣛⣹
⡇⡇⠠⢨⠀⠀⠨⠀⠀⠁⢀⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡯⠯⠿⡯⡿⣿⣽⣽⣽⣿⣿⣯⣯⣿⣿⣿⣽⣽⣿⣯⣯⣿⣿⣯⣿⢸⣽⣽⣿⣽⣯⣯⣯⣿⣿⣽⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽
⡇⣧⣥⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣬⣭⣭⣥⣭⣭⣭⣭⣥⣭⣥⣭⣭⣭⣭⣥⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣌⠉⠉⡍⠉⠉⢩⠉⡍⢹
⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⡇⡗⠀⠂⠃⠂⠘⣀⡃⣘⡀⢛⣛⡛⣛⠛⠛⣛⣛⣛⡛⠛⣛⣛⣛⣛⣛⠛⣛⡛⣛⣛⣛⠛⣛⣛⢛⣛⣛⣛⣛⣛⣛⣛⣛⢛⡛⡛⣛⣛⣛⢛⣛⣛⣛⣛⣛⢛⡛⡛⣛⣛⢛⣛⣛⣛⡛⣛⣛⣛⣛⣛⢛⣃⣃⣈⣃⣸
⡇⣇⣀⣀⣀⣀⣀⣿⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣾⣶⣦⣶⣶⣶⣶⣶⣾⣶⣴⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⠿⣿⣿⣿⡟⣿⣿⣿⡿⠿⣿⣿⣿⣿⣻⣿⣿⣿⠿⢿⣿⣿⣿⣻
⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢻⠒⠝⣛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢣⠒⠘⢻⣿⣿⣿⡟⡛⢻⠻⠛⣟⠑⡜⠛⡟⠻⠛⢻⣿⢸⣿⠻⠛⠴⡂⠟⠛⣿⡇⣿⡟⠟⠃⠊⠛⠛⣿⣿⣿⣿⠻⠛⠑⠙⠻⢻⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣍⢍⢏⠩⣿⣿⣏⣍⠭⢯⣩⡩⡏⣍⢏⣭⣙⡽⠩⣉⣹⢸⣏⣉⢍⣭⡉⢩⣉⣩⡇⣯⠍⠭⢉⣽⣉⣉⢩⣿⣏⢩⡽⣩⠹⣡⡩⣉⢩⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢒⣲⢚⠒⠒⣿⣿⣿⡗⡒⢲⢲⠓⡓⠒⠒⠒⡚⠒⠒⣶⣿⢸⣿⢛⠒⠓⠓⡒⠛⢻⡇⣿⢚⠒⠛⠒⠓⠒⠚⣿⣿⣶⣖⡒⠒⡒⠒⣶⣾⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠭⢯⠥⠭⠭⠿⢿⡆⢲⢰⣶⡶⣶⡖⢴⠀⢰⠀⠢⢰⢰⢒⢸⣇⣥⡽⣌⠬⡤⣥⣽⡇⣿⣦⡼⠼⢮⢬⣤⣽⣿⣿⣯⠍⢭⠭⠭⠽⢭⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢒⡒⣒⣶⣶⣾⡇⢹⢰⣿⡇⣿⡇⢸⠐⢺⠀⠐⢸⢸⢸⢸⣿⣿⣿⣿⣶⣷⣿⣿⡇⣿⣿⣷⣶⣾⣾⣿⣿⣿⣿⣛⢲⢚⡓⢒⡒⣚⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣬⣥⣬⣤⣾⣿⡇⢸⠰⣿⡇⣿⣿⣿⠀⢸⠀⠀⢸⢸⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢹⣿⡧⢿⣿⣿⠀⢸⢸⡇⢸⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣾⣿⣿⢰⣾⢸⡇⢸⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⢸⣿⢸⡇⢸⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⡯⠍⢩⠉⠉⢭⠉⠍⠍⠉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣭⣭⣭⡭⠭⢭⣭⣩⣭⣭⣍⣭⣭⣩⣭⢨⣭⢨⣥⣬⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡷⠿⠾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⡇⡇⣁⢨⣀⣠⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⣭⣭⣭⣭⣉⣩⣭⣬⣭⣭⣭⣭⣭⣬⣭⢨⣭⢨⣭⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣽
⡇⡏⠉⢋⠉⠉⣭⣽⣽⣭⣭⣭⣯⣭⣯⣭⣽⣭⣽⣭⣭⣯⣭⣯⣭⡿⣭⣽⣭⣭⣭⣭⣯⣽⢿⣷⣿⣿⣿⣿⢿⣿⢸⣿⢸⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣼
⡇⣇⣀⣰⣤⣴⣆⣠⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣤⣴⣶⣶⡶⣶⣶⣶⣶⣶⣶⢰⣶⢰⣶⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⠆⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢾
⡇⡇⠀⠀⠠⠀⠲⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠾⠿⠷⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠆⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⢾
⡇⡧⠤⠼⠦⠤⠤⠬⠤⠤⠦⠤⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠷⠦⠴⠾⢿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⢸⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⠛⠻⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⠻⠛⢻
⡇⡇⠀⢀⠂⠀⠀⢀⠀⠘⠀⠀⠀⢀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻
⡇⡗⢒⢚⠚⠒⠒⠚⠓⡚⠒⠒⡒⠚⢟⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣛⣛⣛⣛⣒⣒⣚⣻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣹⢸⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣉⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣏⣹⣉⣹
⡇⣧⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⣭⣬⣭⣭⣬⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽
⢸⣭⠉⠩⠉⠉⠍⡍⠩⡍⠩⠉⠩⠉⠭⠩⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⣭⣭⣥⣭⣭⣭⣭⣽⡇
⢸⣖⣰⣶⣲⣒⣶⣒⣖⣒⣒⣒⣖⣲⣲⣒⣲⣲⣲⣒⣒⢲⣒⣒⣒⣆⣒⣒⣖⣖⣲⣒⣖⣒⣲⣒⣲⣒⣖⣲⣒⣒⣒⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⡿⢿⣿⢿⠿⢿⠿⡿⣿⢿⣿⣿⢿⢿⠿⡿⢿⢿⢿⡿⠿⠿⣿⢿⣿⡿⣿⠿⣿⣿⢿⠿⢿⣿⢿⡿⡿⠿⣿⢿⠿⡿⠷⢷⢿⣿⡿⠿⢿⢿⠿⣿⠿⡿⠿⠿⢿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣷⣾⣿⢺⣖⣖⣚⣓⣛⣚⣚⣺⣒⣚⣒⣗⣚⣒⣲⣚⡒⣒⣗⣛⣳⣓⣒⣲⣛⣺⣚⣚⣖⣛⣖⣓⣓⣒⣓⣚⣺⣓⣓⣒⣚⣒⣖⣖⣚⣚⣖⣻⣒⣒⣟⡒⡛⣾⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣙⣛⣛⣛⣙⣏⣻⣿⣿⣿⣙⣛⣛⣛⣝⣟⣛⣛⣛⣻⣿⣛⣟⣟⣛⣟⣛⣛⣛⣻⣿⣹⣿⣉⣙⣻⣛⣿⣋⣻⣛⣻⣙⣟⣛⣙⣛⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣧⣼⣿⠤⠭⠽⢧⡭⠭⠧⢽⡭⠥⠭⠭⠼⢥⢭⡤⠽⠧⠭⠥⠵⢭⠽⢬⠭⠼⢬⠽⡽⠬⡭⡭⠯⢭⠯⠯⠥⡽⠬⡯⠭⡭⠭⠽⣽⣭⣭⣭⣭⣭⣯⣯⣭⣧⣭⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⡟⢻⣿⠻⠶⡷⡟⠷⡿⠷⡾⣷⠟⢿⠿⠾⠿⠿⢷⠳⠻⠟⠿⡿⡾⠾⠾⠷⢾⢞⠒⢿⠷⢷⠶⢿⠾⠶⡿⠷⡷⠿⢷⠾⡷⡿⡾⠿⠿⠿⡿⠿⡿⡿⡿⠿⢻⢿⠿⢿⠿⠿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⠿⠿⠭⠽⠯⠭⠽⠭⠭⠽⠭⠭⠽⠽⠯⠯⠯⠽⠯⠯⠭⠽⠽⠯⠭⠭⠽⠽⠯⠿⠽⠽⠽⠯⠽⠿⠭⠯⠯⠭⠽⠭⠯⠭⠯⠝⠿⠭⠯⠽⠽⠯⠿⠭⠯⠟⠭⠯⠹⠝⠯⠭⠯⠽⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠐⠒⠂⠀⠃⠀⠃⠘⠛⠃
⢸⠖⠒⠒⡖⢒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣀⣀⣰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀
⢸⠉⠉⠩⠉⠍⡍⠉⠉⣉⠙⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣶⣶⣶⣶⣶⣶⣾⣿⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣧⣬⣤⡄⠀
⢸⠭⠭⠭⠭⡭⠭⠭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡉⣉⣩⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⡅⠀
⢸⢟⠟⠻⠻⠟⠿⠻⠻⢟⠿⠻⠛⢟⣿⣻⣛⣟⣿⣻⣟⣟⣿⣻⣟⣿⣋⣭⣭⣭⣭⣭⣭⣽⣿⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣋⣍⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣏⣝⣉⡁⠀
⢸⠷⠷⢾⠷⠷⠶⢾⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡿⠟⠿⢿⣿⢸⣿⣿⣽⣿⣿⣿⣿⣹⣿⢸⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣒⡒⠚⣒⢒⢒⣚⢛⡛⢻⡛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣟⣉⣋⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣟⣙⣉⡁⠀
⢸⣚⣒⣒⣒⣒⣒⣒⣒⣒⣒⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⢛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀
⢸⠤⠤⠤⠤⠷⠶⠤⠬⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣛⣛⣛⣛⣒⣒⣺⣿⢸⣿⣿⣿⣿⣿⣿⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⡟⠻⠛⠃⠀
⢸⣦⣦⣴⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀
⢸⣿⣟⠛⠛⠛⡟⡛⠛⢿⢛⠛⡛⡟⠻⢻⣻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⢛⠛⠛⡛⠛⢛⠻⡟⠛⠛⠛⠛⠛⡛⠟⣛⠛⠛⠛⠛⠻⡟⠛⡛⡟⠛⠛⠛⠛⢛⠛⠛⢿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣕⣉⣉⣉⣉⣉⣉⣉⣉⣹⣅⣉⣉⣭⣉⣍⣍⣉⣻⣉⣉⣸⣈⣉⣍⣉⣉⣍⣈⣉⣍⣕⣉⢉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⡠⠅⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠤⠼⠿⢿⣿⢸⡿⡿⠿⠿⠿⡿⠧⡸⠿⡿⠿⠿⢿⣿⣿⡿⡿⠇⠤⠼⠿⢿⣿⣿⡿⠿⠇⠴⠿⡿⣿⡇⣿⡿⣿⠗⠄⠿⠿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣷⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣚⣓⣳⣒⣺⣿⢸⣷⣗⣒⣒⣗⣓⣒⣛⣒⣇⣒⣲⣾⣿⣟⣓⣓⣒⣒⣒⣘⣚⣿⣟⣛⣚⣒⣒⣒⣑⣛⡇⣿⣗⣟⣒⣒⣱⣂⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠤⠧⡤⢼⣿⢸⣥⣤⣭⡼⠠⠤⢥⠼⠬⡤⣤⣼⣴⣿⣿⠿⠦⠤⠼⠤⠼⠿⣿⡿⠴⠤⠾⠤⠥⠤⠼⡇⡿⠿⠿⠤⠦⡼⠿⠿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣉⣉⣉⣋⣿⢸⣿⣿⣋⣉⣻⣚⣏⣚⣛⣉⣩⣿⣿⣿⣿⣍⣱⣋⣁⣉⣡⣙⣿⣿⣍⣼⣹⣜⣹⣉⣿⡇⣷⣿⣑⣋⣋⣙⣻⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡔⠴⠤⢴⣴⣼⢀⣰⢠⣶⡖⣶⡆⢰⠆⣴⠀⡆⢰⡆⣰⣿⣿⣧⣦⣤⣼⣿⣿⣿⣿⣿⣷⣤⣴⣽⣿⣿⡇⣿⠴⠤⡶⠄⠄⠶⣾⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣙⣹⣉⣹⣿⠀⢸⠰⣿⠀⣿⡇⢸⡆⣿⠀⡅⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣏⣉⣉⣍⣉⣉⣉⣙⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣘⣿⠢⣿⣿⣿⡄⣻⢀⡗⢺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢰⣿⡤⣿⣿⣿⡆⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣰⣿⡀⣿⣿⣿⣿⣿⢸⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣭⣿⣿⣿⣿⣿⢸⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⢸⠉⢉⠍⠉⡍⠩⠍⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⣩⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⡅⠀
⢸⠿⢿⠿⠿⢿⠿⢿⠿⡿⠿⡿⠿⠿⢿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣏⣭⣭⣯⣭⣭⣭⣽⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣯⣅⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣝⣭⡅⠀
⢸⠭⠭⢬⠭⡭⠥⠭⠬⢥⣭⣭⣥⣤⣬⣭⣬⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠉⠩⢩⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⡅⠀
⢸⠒⠒⢒⠒⡓⡒⠒⠒⠚⠻⣛⠛⠛⢛⡛⡛⠛⢛⡛⠛⠛⠛⣛⣛⣛⣛⣭⣭⣯⣽⣭⣭⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣋⣙⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣏⣛⣉⡁⠀
⢸⣒⣒⣓⣒⣒⣓⣒⣒⣛⣒⣓⣒⣒⣒⣚⣓⣒⣚⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⢛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⡃⠀
⢸⠾⡷⢦⠷⠤⡦⢶⠶⡾⢿⢿⠿⡿⠿⠿⠿⡿⠿⢿⠿⡿⢿⠿⠿⠿⠿⣛⣛⣛⣛⣒⣒⣺⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⡟⡿⠛⡃⠀
⢸⠤⠤⠤⠥⠥⠤⠤⠤⠤⠧⠬⠤⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠻⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀
⢸⠤⡤⢤⠤⠤⡥⢤⠬⡿⢿⢿⠿⡿⠿⠿⠿⡿⠿⢿⠿⡿⢿⠿⠿⠿⠿⣿⣿⡿⣷⢶⡶⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠟⡟⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⠛⣿⠛⠇⠀
⢸⠭⠽⠭⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀
⢸⣉⣉⣉⣏⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠤⠤⢼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⡿⢿⠿⠇⠀
⢸⣀⣀⣐⣀⣂⣆⣀⣀⣤⣈⣂⣐⣐⣐⣀⣀⣀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣷⣶⣶⡆⠀
⢸⣒⣒⣶⣒⣲⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⣤⣴⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀
⢸⡉⠋⠙⠝⢏⠛⢙⠉⠋⣟⢝⡉⡋⢙⡙⣩⣯⣽⣽⣯⣯⣽⣽⣯⣯⣥⣶⣶⣶⣶⣶⣶⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣵⣦⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣧⣯⣤⡄⠀
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀
⠸⠿⠙⠛⠉⠛⠻⠩⠟⠉⠛⠟⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿
⢸⣽⣼⣿⣯⣽⣭⣽⣬⣭⣭⣯⣭⣽⣭⣭⣯⣯⣭⣭⣹⣥⣯⣭⣧⣭⣭⣧⣭⣭⣽⣭⣭⣽⣭⣯⣽⣭⣯⣭⣭⣽⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢻⢻⣿⠛⡛⡛⣻⠛⡟⢻⡛⠛⣛⠛⡟⣻⢛⠛⡛⠛⠛⢛⡟⢻⡛⢛⢻⡛⣟⣛⣛⡟⣛⠛⡟⢛⡟⠻⣛⣟⢟⠛⡛⠛⠛⡿⡟⢛⣻⢛⡛⣛⠛⣿⡟⢛⡛⠛⠻⠛⢻⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⠭⢭⣬⣭⣥⣭⣯⣥⣭⣽⠭⢭⣭⣬⣭⣧⣭⣬⣥⣽⣬⣭⡯⠭⣭⣭⣥⣽⣬⣭⣽⣭⣭⠭⢭⣽⣤⣭⣥⣯⣼⣼⣥⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⢿⢿⣿⢮⣽⠧⢥⡾⢤⠤⢤⡼⡿⢬⢽⠥⠦⠴⠤⡦⠧⢤⡤⠦⣿⠧⢤⢧⠤⢤⠧⠤⢬⠤⠼⠿⡭⠼⠴⣬⢴⢤⢤⠬⢥⠿⡼⢤⠬⠥⠥⠼⣤⡿⠿⡿⢿⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣾⣾⣿⣒⣑⣶⣖⣓⣙⣒⣒⣲⣂⣞⣚⣚⣒⣚⣐⣗⣒⣚⣚⣲⣚⣗⣓⣞⣂⣚⣾⣐⣒⣒⣖⣚⣟⣒⣖⣓⣲⣶⣶⣶⣷⣷⣷⣶⣶⣷⣾⣶⣾⣶⣿⣶⣶⣾⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣬⣼⣿⠬⠭⠽⠭⢽⠭⢭⠭⠯⠭⢭⢭⠽⣭⠥⠯⠭⠭⡭⠭⠭⢭⠭⠭⠽⡥⠭⠭⠭⣭⠭⠽⡭⠭⡯⢭⠭⡭⢭⡽⡭⠽⢽⠩⡭⠭⠭⢭⡯⢯⠭⣭⠯⠭⠼⣭⣭⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠨⠭⠭⠭⠭⠬⠬⠭⠥⠤⠬⠬⠤⠤⠭⠬⠤⠭⠥⠥⠥⠭⠥⠥⠤⠬⠬⠤⠥⠥⠭⠥⠭⠭⠬⠥⠭⠭⠤⠬⠬⠤⠭⠬⠥⠭⠤⠭⠬⠬⠥⠭⠤⠬⠥⠬⠭⠥⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠉⠉⠩⠉⠉⠭⠩⠉⠉⠿
⠐⡒⠒⠲⠒⡒⢒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣀⣀⢰⣶⣶⣶⣶⣶⡆⣶⡆⣶⡆⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠈⠉⠉⠍⠩⢩⠉⠉⢉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣼⣿⣿⣿⡇⣧⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣧⣤⣥⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿
⠈⠭⠍⢩⠉⠉⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢉⢨⣭⣭⣭⣭⣭⡅⣭⡅⣭⡅⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⠨⠯⠽⡽⡽⣿⣯⣿⣽⣽⣭⣯⣯⣿⣽⣽⣭⣯⣯⣽⣽⣽⣯⣯⣯⣽⣿⣽⣭⣭⣭⣭⣭⢸⣿⣽⣿⣿⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠠⠭⠭⠬⠬⠭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⢨⣭⣭⣭⣭⣭⡅⣭⡅⣭⡅⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽
⠐⠒⠒⠚⠒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣹⣿⣿⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⢐⣒⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢘⣛⣛⣛⣛⣛⡃⣛⡃⣛⡃⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻
⢰⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣒⢸⣿⣻⣿⣿⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⢀⣀⣀⣐⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢘⣛⣛⣛⣛⣛⡃⣛⡃⣛⡃⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⠠⠤⠤⠬⠤⠤⠼⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣻⣻⣛⣟⣛⣒⢸⣿⢻⣿⣿⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠠⠥⠤⠦⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⢸⣏⢌⣩⣉⣇⣅⣉⡻⣌⢩⢹⣩⣁⣯⣇⣉⣉⣉⣉⣉⡉⣁⡉⣹⣉⣬⡨⣁⣉⡉⣉⣇⢁⣉⣉⣉⣩⣙⣨⣍⣉⣉⣉⣙⣏⣉⣩⡇⣉⣉⣈⣍⣉⣉⣻⣉⣈⢉⣉⣉⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⢸⣷⣥⣶⣤⣤⣤⣤⣤⠴⠼⠤⡀⢀⠦⠴⠤⣤⣵⣤⣤⣧⣤⣤⣤⣤⣤⡴⣄⡀⡠⢦⣴⢰⠴⢤⠤⣤⢿⠿⡉⠉⡿⠿⠿⡿⠿⠿⡇⣿⡿⠿⠏⡩⠹⠿⣿⣿⢸⣿⠿⠿⢉⠹⠿⢿⣿⡇⣿⣿⠿⢏⢩⣹⡿⣿⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢓⡒⡒⠒⢚⣿⢸⣶⣖⠒⢒⡖⡒⡗⣒⢲⠒⢒⠓⢲⣶⡇⣿⠓⡒⠒⡒⠒⢒⣛⣿⢸⡟⢒⡒⢒⠒⠒⣚⣻⡇⡟⣛⠒⡒⡒⣲⠒⡛⣻⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⠸⠤⠤⣿⢸⣿⠤⠤⡤⡏⠼⠤⠤⠇⠼⠤⠤⠤⣿⡇⣿⠿⠦⠤⠼⠤⠼⢿⣿⢸⡿⠤⠤⠧⠤⠤⠤⢿⡇⣿⣤⠴⠤⢤⠤⢬⣤⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⣍⣉⣁⣁⣿⢨⠍⡍⣡⣥⠥⡍⡍⠍⠈⡍⠩⠉⡅⡭⡅⣿⣉⣱⡎⠁⠈⣉⣿⣿⢸⣿⣅⣿⠙⠉⢉⣹⣿⡇⣉⣉⣩⡉⡉⣉⣹⣉⣹⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠐⠒⡖⠒⠒⠒⢸⠃⡇⣽⣿⢸⡇⡇⡆⠤⡇⠀⠄⡇⠀⡇⣿⣿⣿⣶⣶⣧⣿⣿⣿⢸⣿⣿⣷⣶⣾⣼⣿⣿⡇⣿⠛⠓⠒⠒⠒⠛⠛⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣺⣿⣿⢸⠄⡇⣽⣿⢸⡇⣷⡇⠀⡇⢐⠦⡇⣤⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣥⡇⣼⣿⣸⡇⣿⡇⠠⡇⣾⠁⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣽⣿⢰⡇⣿⡇⣦⡇⣿⠆⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⣿⣿⢰⡇⣿⡇⣿⡇⣿⠀⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠥⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸
⢨⣭⣭⣭⣽⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠶⠤⢸⣿⣿⣿⣿⣿⡇⡿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿
⠀⠵⠈⠯⠈⠭⠕⠹⠾⠾⠾⠷⠷⠿⠾⠾⠷⠷⠷⠿⠿⠾⠷⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠶⠾⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⠆⠿⠿⠿⠿⠿⠿⠾⠶⠶⢿
⢈⣉⣉⣉⣉⣭⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⡯⠬⠤⢸⣿⣿⣿⣿⣿⡇⡿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿
⢀⣀⣀⣄⣀⣄⣂⣰⣀⣀⣀⣐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣷⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿
⢐⣒⣒⡒⢲⠒⡒⡒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣠⣀⢰⣶⣶⣶⣶⣶⡆⣶⡆⣶⡆⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠈⢫⠉⡍⠉⠉⡉⠉⢩⡉⠉⠉⡉⠋⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⡇⣿⡇⣷⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣧⣤⣭⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿
⠘⠛⠛⠛⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣙⢸⣿⣿⣿⣼⣿⡇⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠨⢭⠩⡍⠍⠭⠉⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⡇⣯⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣧⣤⣧⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣴⣧⣤⣿
⠨⠭⠭⠭⠭⠭⠭⠭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠉⠉⢨⣭⣭⣭⣭⣭⡅⣭⡅⣭⡅⣭⣭⡅⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽
⠐⠚⠒⠚⣒⣒⣒⣚⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⡇⣿⡇⣏⡇⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣏⣉⣛⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣏⣋⣉⣋⣉⣿
⠐⡒⠒⢒⠛⣛⣛⠛⡛⡛⢛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⢘⣛⣛⣛⣛⣛⡃⣛⡃⣛⡃⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⢐⣖⣲⣲⣒⣓⣖⣖⣒⣲⣒⣒⣟⣟⣛⣻⣛⣟⣟⣻⣻⣛⣛⣟⣟⣻⣿⣻⣻⣛⣟⣟⣛⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⣻⡇⣿⡇⣿⣿⣿⣿⣿⣟⣙⣏⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣙⢏⣛⣿
⢐⣒⣒⣓⣐⣒⣒⣒⣂⣚⣑⣂⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⢘⣛⣛⣛⣛⣛⡃⣛⡃⣛⡃⣛⣛⡃⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻
⠠⠤⠤⠬⠤⠤⠤⠴⠦⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣛⣛⣛⣓⣒⣒⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⢻⡇⣿⡇⣿⣿⣿⣿⣿⡟⠛⠟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⠟⠛⣿
⠠⠼⠤⠧⠤⠤⠥⠤⠼⠤⠬⠴⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⢨⣭⣤⣭⣭⣭⣵⣭⣭⣭⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠶⠤⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⢿⡇⣿⡇⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿
⠨⠉⠉⠭⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠇⠿⠇⠿⠇⠿⠿⠇⠿⠇⠿⠿⠿⠿⠿⠿⠷⠾⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠾⠿⢿
⢈⣋⣉⣹⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⠯⠭⠤⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⢿⡇⣿⡇⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿
⢀⣀⣀⣂⣐⣰⣀⣀⣠⣀⣰⣀⣂⣂⣆⣀⣀⣀⣠⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⣾⡇⣿⡇⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿
⢐⣒⣒⢖⢲⣒⠖⣒⢒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⣀⢰⣶⣶⣶⣶⣶⡆⣶⡆⣶⡆⣶⣶⡆⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⠈⠉⠉⠍⠉⢩⠉⠉⢉⠉⢩⠉⡉⠋⠉⡩⠉⡉⣭⣭⣭⣭⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⡇⣿⡇⣿⡇⣿⣾⡇⣿⡇⣿⣿⣿⣿⣿⣧⣤⣵⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠾⠿⠷⠿⠷⠿⠷⠿⠿⠷⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠸⠿⠙⠛⠉⠛⠻⠹⠏⠉⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⡇
⢸⣼⣼⣿⣯⣽⣭⣽⣬⣭⣭⣯⣭⣿⣭⣭⣭⣭⣭⣭⣽⣵⣭⣭⣧⣭⣭⣯⣤⣯⣭⣭⣭⣭⣭⣭⣧⣭⣬⣭⣭⣿⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⢛⣻⣿⣛⣛⣛⣻⣛⣛⣛⣛⢻⣛⣛⣟⣻⣛⢛⣛⢛⣛⣛⣟⣻⣛⣛⣻⣛⣟⣛⣛⣿⣻⣟⣟⣻⣛⡛⣻⣻⡛⣛⣛⣛⣛⢻⣛⣻⢿⣛⣻⣛⣛⣟⣿⣻⣛⡻⢻⣟⣟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⢬⢬⣥⣭⣧⣤⣧⣥⣬⣭⢦⢬⣥⣥⣼⣧⣦⣥⣤⣼⣦⣭⡯⡬⣷⣦⣬⣧⣬⣭⣽⣭⡬⣤⣥⣿⣤⣭⣭⣯⣼⣬⣤⣭⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠿⢿⣿⡮⠼⠶⠶⡶⢶⠶⠶⠼⠿⠬⢼⠶⠶⠶⠴⣷⠶⢦⢶⠦⣿⠧⠴⠧⠴⠶⠷⠤⠶⠶⠿⠷⠭⠷⠶⡶⢾⠥⠦⠦⠶⠷⡷⠶⡦⠴⠶⢷⡾⠿⠿⠿⡿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣉⣉⣙⣏⣙⣉⣉⣩⣉⣉⣉⣉⣉⣍⣏⣙⣹⣍⣉⣉⣹⣈⣏⣋⣏⣋⣙⣇⣋⣍⣋⣩⣻⣉⣹⣛⣋⣽⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣤⣼⣿⠤⠀⠘⠬⠘⢠⢰⢨⠇⠄⣭⢩⡝⣀⡁⠂⠀⠠⡅⢢⡷⢩⠠⢅⡚⡕⢴⡘⢨⡭⠍⢸⠁⠍⠩⡀⠠⣄⡭⡅⡌⢧⡭⠉⠮⠉⣥⠈⢸⣄⣭⠡⠉⠤⢳⣤⣬⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠛⠛⠏⠋⠹⠉⠙⠋⠹⠇
⢨⠭⠭⡭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⠉⣭⣭⣭⡅⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⠀
⢸⠓⠒⢓⠓⠒⠒⠛⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢸⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⡇⣿⣿⢸⣹⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣋⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⠀
⢸⠾⠶⢾⠶⠶⡶⢶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⢻⠟⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⢖⠒⠚⠒⠲⢒⠚⡛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢸⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⡇⣿⣿⢸⣹⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣏⣉⣋⣉⣿⠀
⢸⣒⣒⣒⣓⣒⣒⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⣶⣶⣶⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣛⣛⣛⣛⣚⣳⣿⣿⣿⡇⣿⣿⢸⣻⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣛⢟⣛⣿⠀
⢸⠚⠒⢒⠚⢒⠒⡒⣒⣒⣚⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⢛⣛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⠒⠒⠚⢒⡒⠒⡒⠒⡛⠛⠛⢛⠛⠛⢛⠛⢛⣛⣛⣛⣛⣛⣛⣛⢸⣿⣿⣟⣿⣗⣾⣶⣿⣿⣿⡇⣿⣿⢸⣿⢸⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⠟⠛⣿⠀
⠸⠀⠂⠀⠀⠑⠄⠐⠲⠷⠾⠷⠶⠶⠶⠾⠶⠶⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀
⢸⣋⣉⣹⣍⣭⣍⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠿⠿⠧⠼⢤⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⡿⠿⡿⠿⣿⠀
⢸⣄⣒⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⠀
⢸⣉⣉⣹⣉⣉⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⡿⡿⡧⢼⢥⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿⠀
⢸⣂⣆⣀⣀⣀⣀⣄⣀⣰⣀⣂⣀⣀⣀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⠀
⢸⣒⣒⣲⣒⣒⣒⣒⣒⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣦⣰⣤⣶⣶⣶⡆⣶⣶⢰⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀
⢸⣛⣛⣛⣟⣛⣛⣛⣻⣛⡻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣵⣶⣿⠀
⠸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠀
⢰⡒⢒⠒⡖⡂⠒⠖⡒⢒⢒⠒⠖⣒⡢⠒⠒⢒⠒⠒⠒⠒⠒⡖⠂⡂⡒⠒⠒⠒⢲⠒⢒⢒⠒⠒⡒⠖⠒⠒⠒⠒⠒⡖⠒⠒⡖⠒⠒⠒⠒⠒⠒⢲⠒⠒⠒⠒⠒⡆⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⠒⠒⠒⢶⣶⠀
⢸⣉⣍⣇⣍⣩⣉⣍⣍⣩⣩⣭⣕⣩⣥⣩⣉⣬⣭⣹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡬⠤⢛⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠷⠤⠿⢿⣿⡟⠿⠟⠿⢿⠟⢧⠤⢸⠿⠿⢻⠿⠿⢿⣿⣿⠻⠿⠦⠼⠟⢿⣿⢸⣿⡟⠿⠤⠠⠻⠿⣿⡇⣿⣿⠻⠣⠴⠼⠟⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣍⡩⣹⢈⢹⣿⣿⡿⣏⢍⣽⡩⡭⠩⢍⠏⡍⠍⢩⣿⣿⣿⣭⡩⠉⢉⠉⣍⣉⣿⢸⣏⢩⡁⣍⠍⠉⠉⣽⡇⣏⠭⠉⢍⣏⠽⢉⣍⣽⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣒⢲⣚⣓⣺⣿⣿⣷⣒⣲⣲⣒⣓⣒⡛⣒⣓⣚⣒⣺⣿⣿⣟⣓⣓⣒⣒⣒⣻⣿⢸⣟⣒⢒⣒⣒⣒⣒⣻⡇⣿⣶⣒⣒⣲⣒⣲⣶⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠧⠤⠧⠤⠠⠤⢿⣶⣰⠀⡆⡖⣲⢰⠐⠀⢴⠀⠆⢰⡦⢰⣿⣧⣤⠛⠐⢀⣴⣼⣿⢸⣿⣦⡞⠀⠚⣠⣴⣿⡇⣥⣦⡴⠄⠄⠤⣬⣤⣼⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣉⣈⢉⣏⢉⣉⣹⣿⢸⠀⡇⡏⣹⢸⢸⠐⢺⠀⡄⢸⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣾⣿⣿⡇⣿⣉⣉⣉⣉⣉⣩⣩⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⣶⣾⣿⣿⣿⢸⣀⡇⡇⣾⢸⣿⠀⢸⢀⡗⢺⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⡧⢽⢸⣿⠈⢺⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡇⡇⣿⢸⣿⢸⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⣿⢸⣿⢸⣿⢸⡗⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢨⠭⠭⢭⠭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⡍⢩⠉⣭⣭⣭⡅⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⠀
⢸⠟⡛⠒⠒⢲⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⢸⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⡇⣿⣿⢸⣿⢸⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣉⣛⣉⣿⠀
⢸⠶⠷⣶⢿⢾⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⢻⠛⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⠒⡒⠒⡒⠒⠒⡒⢛⠛⢛⠛⠛⠛⠛⠛⠛⣛⡛⣛⣛⣛⣛⣛⣛⢸⣿⣭⣯⣯⣭⣭⣽⣿⣿⣿⡇⣿⣿⢸⣿⢸⣹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⠀
⢸⣒⣓⣒⣒⣒⣒⣓⣚⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⣷⣶⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣛⣛⣛⣛⣚⣳⣿⣿⣿⡇⣿⣿⢸⣿⢸⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣛⢟⣛⣿⠀
⢘⣒⣒⣒⣚⣓⣒⣒⣒⣊⣒⣒⣒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⠤⠤⠤⠧⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣛⣛⣛⣓⣚⣲⣿⣿⣿⡇⣿⣿⢸⣿⢸⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⠿⠛⣿⠀
⢸⣤⣤⣤⣶⣤⣤⣤⣤⣦⣬⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⡤⠤⠤⠧⢤⠤⠬⠿⡿⡿⠿⠿⢿⠿⠿⠿⡿⡿⠿⠿⢿⠿⠿⠿⢸⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⡟⠛⣿⠀
⠸⠤⠬⠥⠬⠧⠤⠭⠤⠼⠭⠤⠤⠥⠤⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀
⢸⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠿⠿⠧⠼⢤⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿⠀
⢸⠩⠯⠝⠩⠝⠽⠍⠉⠩⠭⠍⠽⠨⠬⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠾⠾⠿⣿⠀
⢸⣉⣉⣉⣩⣏⣉⣉⣽⣏⣉⣍⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠿⠿⠧⠼⢤⣿⣿⣿⡇⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠿⡿⠿⣿⠀
⢸⣄⣒⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⠀
⢸⣆⣂⣒⣂⣀⣐⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣦⣴⣤⣶⣶⣶⡆⣶⣶⢰⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⠆⣶⣶⣶⣶⣶⣶⠶⡶⠶⣿⠀
⢸⣃⣦⣔⣒⣊⣒⣒⣔⣓⣱⣶⣶⣾⣶⣶⣶⣷⣷⣶⣶⣾⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣶⣷⣶⣿⠀
⢸⡒⠒⡒⢲⡒⣒⣒⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣀⣶⣶⣶⡆⣶⣶⢰⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀
⢸⢋⠋⢉⣙⡙⠉⠉⡉⡋⠫⡉⠍⠝⡉⢉⠉⠋⣋⣯⣭⣽⣽⣽⣭⢸⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣥⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿⠀
⢸⣲⠲⢒⠒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣆⣰⣂⣶⣶⣶⡆⣶⣶⢰⣶⢰⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀
⢸⠍⡍⠉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢸⣿⣶⣷⣷⣶⣶⣾⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣥⣬⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣤⣥⣤⣿⠀
⠸⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠭⠭⠬⠭⠬⠭⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠬⠭⠭⠭⠭⠭⠭⠭⠭⠥⠭⠭⠭⠭⠭⠭⠭⠭⠭⠿⠀
⢰⠒⢖⠒⡖⠒⠒⠖⠒⢖⢒⠒⠒⣶⠒⠲⠒⠲⠒⠒⠒⠲⠒⡖⠒⡖⠒⠒⠒⠒⢶⠒⢒⠲⠒⠒⡒⠖⠒⠒⠒⠒⠒⡖⠒⠒⡖⠒⠒⠒⠲⠒⠒⢶⠒⠒⠒⠲⠒⡖⠒⠒⠒⠒⠒⠒⠒⠖⡖⠒⠒⠒⠶⠲⠒⢶⣶⠀
⢸⣉⣉⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣈⣩⣹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡬⠄⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠗⠔⠿⢿⣿⡿⠿⠿⠿⢿⠿⢧⠤⢸⠿⠿⢿⠿⠿⢿⣿⣿⠿⠿⠦⠺⠿⢿⣿⢸⣿⡿⠿⠥⠄⠿⠿⣿⡇⣿⣿⠿⠇⠴⠽⠿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣷⣾⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣀⣐⣱⢈⣹⣿⣿⣾⣇⣋⣽⣁⣚⣑⣚⣎⣂⠛⣛⣶⣾⣿⣛⡨⣂⣈⡐⣘⣈⣿⢸⣏⢙⣀⣃⣅⣀⣊⣹⡇⣏⣉⣐⣈⣇⣸⣀⣉⣹⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠒⢲⡚⠓⢺⣿⣿⣧⢒⢲⢲⠂⡓⠐⠚⡒⠓⠒⠒⢺⣿⣿⡟⠓⠒⠒⠒⠒⢻⣿⢸⡟⠒⠒⡒⠒⠒⠐⢻⡇⣿⣤⡒⠐⢲⠒⢲⣶⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠧⠭⠯⠭⠭⠥⢿⣿⢹⠛⡏⡿⢿⢹⠝⠹⢹⠉⠯⢹⡟⢻⣿⣇⣬⠽⠤⢤⣬⣬⣿⢸⣿⣢⡼⠬⠾⢤⣬⣿⡇⣭⣍⡭⠭⠭⠭⣭⣭⣽⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣘⣀⣒⣆⣀⣚⣸⣿⢸⠀⡇⡇⢿⢸⢰⠐⢺⠀⠑⢸⡇⣹⣿⣿⣿⣾⣶⣶⣿⣿⣿⢸⣿⣿⣿⣶⣶⣾⣿⣿⡇⣿⣉⣑⣂⣒⣂⣉⣛⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⣶⣼⣿⣿⣿⢺⠀⡇⡇⣿⢸⣿⠀⢸⠀⣇⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⠠⡇⡧⢿⢸⣿⠈⢺⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡇⡇⢿⢸⣿⢸⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⣿⢸⣿⢸⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⠿⠿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⢻⠿⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢸⣒⣒⠒⠓⣒⠒⢒⠛⢛⣛⠛⡛⠛⡛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢸⣿⣯⣯⣯⣯⣽⣽⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣏⣟⣋⣉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⣿⣿⣿⣿⣿⣉⣏⣉⣿⠀
⢘⣒⣒⣒⣒⣚⣓⣒⣒⣒⣚⣒⣒⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⣶⣶⣾⣷⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣛⣛⣛⣛⣚⣳⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣛⢟⣛⣿⠀
⢸⣑⣂⣛⣃⣒⣒⣒⣒⣐⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⡛⢛⠛⣛⣛⣛⡃⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⠀
⢸⠤⠴⠧⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣛⣛⣛⣓⣚⣲⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠛⠟⠛⣿⠀
⢸⣤⣤⣤⣶⣤⣤⣤⣤⣦⣬⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣸⣿⣸⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⢰⠶⠀⠀⠀⠀⠐⠀⠲⠠⠀⠀⠀⠐⠠⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾
⢸⣮⣼⣿⣬⣽⣤⣽⣬⣭⣭⣽⣭⣬⣯⣬⣤⣧⣧⣬⣿⣭⣧⣮⣥⣮⣧⣵⣦⣼⣽⣭⣭⣭⣭⣤⣽⣬⣥⣬⣥⣼⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣹⣿⣙⣻⣛⣻⣛⣏⣻⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣛⣟⣻⣝⣛⣻⣋⣹⣹⣛⣟⣋⣙⣟⣛⣝⣓⣂⣒⣒⣲⣶⣀⣒⣖⣒⣰⣀⣰⣤⣢⣂⣀⣂⣀⣔⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⢸⣿⣿⣿⣴⣦⡽⣴⣶⣦⣴⣴⣶⣧⣶⣴⣼⣶⣦⣤⣴⣶⣿⣶⣴⣶⣶⡷⢴⣶⣶⣽⣶⣤⣼⣴⣴⢶⣶⡦⣦⣴⣼⣯⣶⣶⣾⣼⣷⣦⣼⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⢻⣿⠻⠿⡿⠶⢾⢶⠶⠶⠶⠿⢿⠿⠷⠶⠶⠶⡶⠷⠶⡶⡶⢾⠿⠶⣾⠧⢶⠾⠶⠶⡶⢾⠿⠾⠿⠾⢶⠶⡯⠶⠴⡶⠾⢶⠷⠷⠶⠶⠶⢶⠾⠿⠻⣿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣩⣭⣍⣏⣭⣹⣭⣩⣍⣏⣏⣉⣉⣭⣩⣍⣏⣽⣭⣉⣍⣯⣭⣭⣍⣍⣉⣽⣨⣩⣍⣩⣭⣭⣩⣏⣭⣩⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣥⣼⣿⠠⢀⠘⠰⠼⠌⢱⠧⠃⢥⢰⣤⢬⠃⠂⠃⠀⠀⠌⠁⠸⡂⡔⠌⡐⢡⠣⣂⠃⣤⠨⠁⡇⠨⠈⢀⠀⢄⣨⢍⢠⠹⣭⠀⣴⠀⢠⠩⣬⠣⣍⠀⠜⢄⠁⣤⣭⣵⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠛⠛⠏⠙⠹⠏⠹⠋⠻
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠠⡦⠀⠀⠀⣶⢠⢀⡄⣤⡤⢤⣤⠀⣤⢀⡄⢠⠀⣤⠀⢰⣶⣂⡴⠂⠖⢀⣠⣶⡆⣶⣶⣤⠖⠰⠆⣀⣴⣶⢠⣠⣀⠄⠀⠀⢠⣆⣄⣶⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣐⣒⣖⣒⣒⣲⢸⢉⡇⣿⡇⢸⣿⠀⣯⢸⡏⢰⢨⣿⢸⢸⣿⣿⣷⣶⣶⣿⣿⣿⡇⣿⣿⣿⣶⣶⣶⣿⣿⣿⢸⣟⡛⢒⣒⣒⣚⣛⣻⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⢸⡀⠀⣿⡧⢸⣿⣶⣟⠸⡟⢺⢬⣿⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⠍⣿⣇⣸⣿⣿⣯⢸⣿⡿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⡇⢸⣿⣿⣿⣾⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⢨⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢛⠛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⢸⠦⠤⠼⠦⠬⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣛⣛⣛⣛⣚⣒⢸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇
⠸⠤⠤⠤⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢰⢦⠤⠬⠥⠤⠧⠤⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣾⣶⢸⣿⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇
⠸⠮⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣉⣽⣉⣍⣩⣩⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠼⠤⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇
⢸⣀⣀⣀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣾⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⢸⣛⣉⣹⣉⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣼⣤⢸⣿⣿⣷⣿⣿⣷⠿⣷⣿⣷⣿⣿⣾⣿⢸⣿⣿⣿⣿⣿⢿⣿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⠿⢿⠿⢿⡇
⢸⣐⣠⣢⣐⣰⣀⣀⣢⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣾⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣶⣾⣶⣾⡇
⢰⠒⠒⡖⢒⠒⢒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣰⣀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⢉⠉⡉⠉⠉⡉⠉⠉⣉⠉⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣤⣬⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⣬⣤⣼⡇
⢰⠒⠒⢒⢲⠒⠲⠖⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣰⣀⢰⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⠩⠉⠉⠉⠭⠉⢩⠉⠩⠩⠉⠉⠉⠍⠍⠉⠉⠉⢭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣤⣬⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⣬⣤⣼⡇
⢨⢭⠭⠭⢭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠳⠒⠞⠞⠟⠛⠳⠚⠛⠛⢟⣛⣛⣛⣛⣛⣛⣟⣛⣛⣻⣛⣛⣟⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣉⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣯⣝⣩⣹⡇
⢨⠥⠭⠤⠬⠭⠬⠥⢬⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠒⣒⠚⣒⣒⣒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣭⣭⣽⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣉⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣉⣙⣉⣹⡇
⢘⠒⠒⠒⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢛⠛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⢸⠒⠓⠓⣒⠒⠚⠚⠚⢛⠛⠛⠛⠛⠛⠛⡛⠛⢛⣛⣛⣛⣛⣛⣛⣻⣿⣛⣛⣛⣓⣚⣒⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠛⠻⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⡟⠻⠛⢻⡇
⠸⠀⠀⠀⠀⠀⠄⠀⠰⠶⠶⠾⠶⠶⠶⠶⠷⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣯⣭⣽⣭⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠼⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⢿⠿⢿⡇
⠸⠭⠩⠍⠍⠉⠉⠯⠌⠌⠅⠉⠋⠍⠬⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠶⠷⠾⠇⠿⠿⠿⠿⠿⠿⠿⠿⠷⠸⠿⠿⠿⠿⠿⠷⠶⠷⢿⡇
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⢈⣍⡩⣉⣏⣉⣙⣏⣍⣩⣩⣉⣉⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣏⣉⣉⣉⣉⣙⣏⣉⣉⣉⣉⣍⣋⣭⣉⣉⣉⣉⣻⣉⣉⣍⣉⣉⣉⣉⣉⣉⣙⣏⣉⣉⣉⣉⣩⣉⣉⣉⣉⣉⣉⣉⣉⣹⣉⣉⣉⣉⣉⣉⣉⣿⡇
⢠⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣼⢤⠤⣤⣤⣤⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠿⠿⣿⣿⣿⡟⣿⣿⣿⡿⠿⢿⣿⣿⣿⢻⣿⣿⣿⠿⠿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡛⡖⣂⢹⡝⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⡒⠚⢻⣿⢸⡛⢛⠛⣻⠛⢻⣐⣹⢛⣛⡛⣛⣛⣛⢸⣿⣏⠛⣒⡂⡛⣛⣿⡇⣿⣿⡛⢓⣒⢚⡛⣻⣿⢸⣿⡏⠛⣒⡓⡛⢻⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⢬⡨⠴⣿⢸⡿⠧⠤⠼⡤⡄⠧⠠⠽⢥⠄⠤⠿⣿⢸⣧⣤⠠⠤⡤⠤⢤⣼⡇⣿⡄⠤⢬⠤⠠⠤⢤⣿⢸⡤⠤⠤⠬⠤⠧⠤⢤⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣉⣹⣉⣈⣍⣿⢸⣷⣉⣉⣋⣉⣉⣉⣉⣉⣍⣉⣉⣹⣿⢸⣿⠉⢉⢉⢉⠉⢉⣿⡇⣿⡉⠉⡉⣉⡉⠉⣉⣿⢸⣿⣯⣁⣉⢏⣉⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠒⠓⠒⠒⠒⢛⢸⢈⠏⣷⡟⢻⣿⠀⡿⢰⡯⠸⢠⣾⢩⢸⣿⣵⡖⠂⠛⢶⣶⣿⡇⣿⣿⣶⡓⠚⠒⣶⣾⣿⢰⣶⣴⠒⠒⠒⢲⣷⣶⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣭⡭⠧⢤⣤⣼⢸⢰⠇⣿⡇⢸⣿⢀⣿⢹⣗⢸⢰⣿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣯⣍⣭⣬⣭⣬⣭⣽⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⢸⢡⣀⣿⡇⢸⣿⣿⣷⢘⣟⣸⢰⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠅⣿⣗⢺⣿⣿⣷⢸⣿⣟⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣂⣿⡇⣸⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠰⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢨⠭⠭⢭⠍⠭⠭⠭⡭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠿⢿⡿⠿⢿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣭⣝⣭⡅⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⣯⣙⣭⣽⡇
⢨⠬⠤⠬⡭⠬⠤⣥⣭⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠒⠒⡒⠓⢒⠒⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣉⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣏⣙⣉⣹⡇
⢘⣒⣒⣚⣒⣚⣒⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢛⠛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⢸⣶⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣛⡻⣛⡃⣿⣿⣿⣿⣿⣿⣿⣿⣟⢸⣿⣿⣿⣿⣿⣟⡻⣛⣻⡇
⢘⣒⣒⣒⣚⣒⣒⣒⣒⣚⣒⣒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⢛⠛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⣛⣛⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⢸⠤⠴⠤⠬⠤⠬⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣛⣛⣛⣓⣚⣒⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠛⠻⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⡟⠻⠛⢻⡇
⠸⠴⠤⠦⠶⠤⠤⠤⠼⠤⠤⠤⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣾⣥⣼⡤⣤⣤⣭⢥⢿⡿⣿⣿⢿⢿⢿⣿⣿⡿⣿⣿⢿⣿⣿⡿⣿⣿⠿⠿⢿⠷⠾⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠛⢻⠛⠃⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⡟⢿⠛⢻⡇
⠸⠭⠭⠭⠽⠭⠭⠭⠭⠽⠭⠭⠭⠭⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠷⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣩⣍⣉⣏⣝⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠧⠼⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⢿⠿⢿⡇
⢸⣀⣀⣢⣀⣰⣀⣀⣠⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣷⣶⣶⣾⡇
⢸⣉⣉⣋⣙⣟⣉⣛⣛⣋⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣼⣤⢸⣿⣿⣷⣿⣿⣷⣿⣷⣿⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⢿⠿⢿⡇
⢸⣚⣒⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣾⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣷⣾⣶⣾⡇
⢰⢒⠖⠒⠒⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⣰⣀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⣉⠉⡉⠉⠉⠉⢉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣴⣬⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⣬⣤⣼⡇
⢸⠟⠛⠛⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣉⢸⣿⣿⣧⣿⣿⣿⣿⣷⣿⣿⣿⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠩⢉⢍⠩⢩⠉⠉⢍⡩⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⣤⣼⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⣼⣤⣼⡇
⢨⠭⠭⠭⠭⢭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⢩⠉⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⣭⣭⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇
⢸⠲⢒⠛⠚⠒⡒⠓⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣟⣛⣛⣻⣛⣛⣛⣻⣿⣭⣭⣭⣭⣭⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣍⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⣿⣿⣏⣙⣉⣹⡇
⢸⣾⣶⣶⣶⣶⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣯⣿⣿⣯⣿⣯⣿⣯⣿⣿⣽⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠠⠤⠤⠤⡤⠤⢤⡤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⣤⡄
⠐⠓⠊⡆⠓⠒⠒⡓⠓⠚⠚⢲⠢⠛⠒⠒⠒⠒⢒⢲⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣷⣶⣿⣶⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⣻⣿⣿⢸⣿⣿⣿⣿⣿⣿⢉⢽⣿⣿⣿⣿⣿⣿⢸⣿⡿⣿⣉⡉⣿⣿⣿⡇⣿⣿⢿⣏⣉⣹⣿⣿⣿⢸⣿⡿⣿⣉⣍⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣦⣧⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠒⠂⠀⢘⣿⢸⣶⡔⠂⢺⠀⠘⡖⠚⢴⠒⠒⠒⣶⣶⢸⡟⠓⠀⠒⠒⠒⠒⢻⡇⣿⠛⠂⠐⠒⠒⠒⠚⣿⢸⠛⠃⠐⠒⠒⡖⠘⠛⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⢭⠽⠪⠭⣿⢸⣏⠭⠭⡭⠯⠧⠭⠬⠭⠽⠥⠭⢭⣿⢸⣿⠿⠬⠭⠯⠭⠽⣿⡇⣿⠧⠭⠽⠭⠬⠭⠽⣿⢸⣯⡭⠍⠭⡭⠭⣭⣽⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣒⣞⣂⣒⣃⣿⢸⠻⡶⣶⣶⣶⣶⠒⣶⢒⡷⢲⠒⣾⠿⢸⣿⢄⣰⣐⣴⣀⣐⣿⡇⣿⣦⣠⣆⣢⣂⣀⣲⣿⢘⣛⢛⣒⣒⣑⣒⣟⣛⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠤⡄⠀⠀⢰⢸⢘⡅⣿⡗⢸⣿⠀⣯⢼⣏⢨⢘⣿⢸⢸⣿⣿⣧⣤⣤⣽⣿⣿⡇⣿⣿⣿⣦⣤⣥⣿⣿⣿⢸⡿⠿⠤⡠⠠⠘⠿⢿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣹⣿⣿⢸⠜⠁⣿⡇⢸⣿⣶⣟⢸⣷⢸⢘⣿⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣼⠆⣿⣇⣸⣿⣿⣟⢰⣷⣾⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡁⣿⡗⢸⣿⣿⣿⣼⣿⣷⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣶⣿⣇⣺⣿⣿⣿⣿⣿⣿⢘⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠬⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⢸⣭⣽⣼⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠷⠼⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⢿⠿⢿⡇
⠸⠭⠭⠭⠫⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠷⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠿⠿⠿⠿⠷⠿⢿⡇
⢸⣉⣩⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠧⠼⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢸⣿⣿⣿⣿⣿⠿⢿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⡿⢿⠿⢿⡇
⢸⣀⣀⣢⣀⣰⣀⣀⣠⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣷⣶⣶⣾⡇
⢰⣒⣒⣒⣒⣲⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣤⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⢸⣟⣚⣛⣓⣛⣻⣞⣚⣚⣓⣻⣓⣾⣾⣾⣷⣷⣷⣿⣿⣾⣿⣷⣷⣿⣿⣶⣶⣾⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣮⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣮⣶⣾⡇
⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃
⡿⠿⠙⠋⠙⠋⠏⠻⠉⠙⠙⠋⠋⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿
⣿⣤⣿⣿⣭⣼⣬⣯⣭⣭⣯⣤⣯⣬⣵⣯⣭⣭⣭⣬⣦⣥⣭⣽⣦⣤⣬⣭⣭⣬⣥⣬⣯⣥⣬⣥⣽⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣉⣿⣿⣙⣛⣛⣋⣟⣛⣛⣛⣛⣻⣛⣟⡛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣏⣛⣻⣉⣛⡋⣻⣙⣛⣛⣛⣟⣛⣙⣋⣙⣻⣁⣰⣒⣒⣀⣒⣴⢐⣀⢐⣂⣒⣒⡒⣒⣒⣐⣂⣂⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⣿⣿⣿⣿⡶⢶⡾⣶⣴⣶⣶⣾⣶⡶⢶⡾⣶⣾⣴⣾⣶⢶⣶⣶⣶⠷⡶⢶⣶⣾⣷⣶⣶⣶⠷⢶⢷⢶⣴⣿⣿⣿⣿⣿⢿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⣿⣿⠳⠾⠖⠶⢲⡖⠶⠶⠟⢷⢺⠗⠖⠶⠶⠾⢶⢲⠶⡾⠿⢲⠳⠶⠶⠷⠲⠖⢾⡿⠶⠺⠲⡶⠾⠶⠖⠶⠶⠾⠶⠶⠶⠶⠶⠞⠟⠟⠻⠿⠿⢿⠿⠻⢿⠿⢿⠻⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣿⢭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣯⣭⣩⣭⣭⣭⣭⣍⣭⣽⣭⣏⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣒⢒⢒⣒⣓⣒⢲⣓⣒⠖⣶⣓⢲⣓⣒⣐⣒⣖⣲⣒⡒⣞⡚⣒⣦⣖⣒⣲⣒⣒⣐⣖⡲⣒⡶⣒⣚⣒⣐⢒⣒⡖⡒⠓⣶⣒⣓⣒⣳⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣦⣤⣤⣴⣤⣿
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⡖⠒⣶⣶⡆⣶⣶⣶⣶⣶⣶⡖⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⠒⢲⣶⣶⣶⣶⣶⣶⣶⣶⠒⢲⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⣭⣥⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠧⠭⢭⠩⢿⡇⡿⠤⠭⠬⢽⠤⢭⠭⠯⠭⠥⠯⠭⡽⢿⡿⠿⠧⠭⠭⠭⠤⡽⠿⢿⡿⠿⠧⠭⠭⠯⠤⠽⠿⣿⣿⣬⣬⡭⡬⠬⢭⣭⣭⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣉⢉⣹⣈⢹⡇⣿⣿⣿⣉⢹⣉⢏⡉⣉⢏⡈⣏⣿⣿⣿⣿⠏⠁⡉⠉⢉⠉⠉⠹⣿⣿⣿⣷⡯⣉⢉⣹⡿⢿⣿⣏⡉⣉⣉⣉⡉⣩⢍⣉⣹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣖⣒⣒⣚⣶⡇⠛⡛⢛⣛⣒⣒⠒⢒⠒⢒⠒⡛⢛⡛⢛⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣰⣓⣒⣒⣂⡳⣶⣿⣿⣷⣖⣒⣔⣒⣒⣲⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⠤⡄⠄⠀⡄⠒⡇⣸⣿⡇⢾⠀⢸⢀⣸⠀⠇⢸⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣦⣤⣤⣦⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣯⣭⣿⣿⡇⠀⡇⢸⣿⡇⣺⢠⣼⠀⢸⠀⣇⣸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣤⡗⢺⣿⡇⢿⢸⣿⠀⢸⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⡇⢸⣿⡏⣼⢸⣿⢠⣼⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣧⣾⣿⡇⣿⢸⣿⢸⣿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⡧⠤⠤⠤⠬⠧⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣉⡁⣿⡟⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⡇⠀⠀⠀⠀⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠓⠒⠓⣒⣒⣒⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠿⠤⠄⣿⣯⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣇⡀⣀⣁⣀⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡿⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠷⠿⠿⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣿
⡧⠤⠤⠴⠬⠧⠬⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣉⡁⣿⡟⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⡇⠀⠀⠀⠀⠛⢛⠛⢛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠓⠒⠚⣒⣚⣓⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠿⠤⠄⣿⣯⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣧⡀⣀⣁⣀⣉⣉⣉⣉⣉⣉⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡿⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠷⠿⠿⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣿
⡧⠥⠤⠤⠤⠯⠤⠤⠤⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣉⡁⣿⡟⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⡇⠀⠀⠀⠀⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠒⠒⠚⣒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠿⠤⠄⣿⣯⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿
⣧⡀⣄⣡⣄⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⣭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡿⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠷⠿⠿⠿⠿⠸⠿⠸⠿⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣿
⡧⠦⠭⠤⠤⠧⠬⠤⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⢻⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⣿
⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠒⠒⢚⣓⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣹⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣏⣋⣩⣿
⣧⡀⣀⣀⣈⣉⣉⣉⣍⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⡭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡟⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠾⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⣿
⡧⠤⠭⠤⠶⠤⠤⠤⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣿
⡇⠀⠀⠀⠘⡁⠈⠁⣀⣁⣀⣂⣀⣀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠒⠒⠚⠒⠒⠒⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣿⢸⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣏⣋⣉⣿
⣧⡀⣀⣠⣉⣀⣈⣀⣬⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⡭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡟⠻⠛⠟⠛⠛⠻⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠾⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠷⠷⠶⣿
⡧⠤⠭⠤⠤⠭⠤⠤⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⣿⢸⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⣿
⡇⠀⠀⠀⠘⠁⡈⠁⠀⢁⣀⣈⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⢓⠒⡒⠚⠒⠓⠒⡒⠚⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣿⢸⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣟⣋⣉⣿
⣧⡉⣈⣅⣁⣅⣀⣀⣉⣁⣤⣥⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⡭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡟⠛⠛⠛⠻⠛⠛⠛⠛⠿⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠾⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⣿
⡧⠤⠭⠤⠬⠤⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿
⡇⠀⡀⠃⠀⢀⠐⠈⠈⢀⣀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⠓⠒⠒⠒⠚⠒⠓⠒⠚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣯⣏⣉⣿
⣧⡀⣀⣀⣉⣀⣈⣄⣈⣈⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣭⣭⣭⣭⡭⠭⠅⣭⣭⣭⣭⣭⣭⢨⣭⢨⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⡟⠛⠛⠛⠛⠛⠛⠛⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠇⠿⠿⠿⠿⠿⠿⠸⠿⠸⠿⠸⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⣿
⡧⠤⠤⠬⠤⠥⠭⠤⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇⣿⣿⣿⣿⣏⣉⡁⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿
⡇⠁⠉⠁⠀⠀⠁⠈⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⣓⣒⣒⣒⣒⣒⡂⣛⣛⣛⣛⣛⣛⢘⣛⢘⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿
⡗⢒⠓⠚⠒⠒⢒⠒⠒⠚⠛⢛⠛⠛⢛⣛⣛⣛⣛⣛⣻⣿⣿⣿⡇⡿⠿⠿⠿⠧⠤⠄⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⣿
⣧⠉⡄⠁⢀⠀⠈⣥⣤⣤⣬⣤⣬⡤⣬⡭⣭⡭⣭⣭⣭⣭⣭⣭⣥⢭⣭⢭⣭⢭⣭⢥⣭⣭⣭⣭⣭⣭⣬⣭⣬⣭⡌⡉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿
⣿⣏⣏⣋⣋⣙⣛⣛⣛⣋⣛⣛⣙⣛⣋⣛⣛⣏⣻⣉⣉⣉⣹⣙⣛⣙⣻⣹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡅⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿
⣟⣃⣃⣀⣀⣀⣈⣀⣈⣁⣀⣁⣈⣀⣁⣛⣛⣛⣛⣛⣛⣋⣛⣋⣛⣋⣛⣋⣛⣛⣛⣛⣛⣙⣛⣙⣛⣛⣛⣛⣛⣛⣃⣃⣛⣛⣛⣛⣛⣛⣛⣐⣀⣓⣂⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣛⣛⣛⣛⣛⣛⣛⣈⣐⣃⣀⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⣿⡸⣷⣉⣿⣿⡿⢿⣿⣿⣿⡇⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⡟⢿⡿⡿⣿⣿⣿⡶⠶⣾⣿⣿⡄⣾⣿⣿⣿⡢⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⠀⠠⠀⢀⣀⣠⣤⣀⣘⣿⠀⡇⣿⠻⣿⣿⣿⣼⣿⢻⡿⣷⢸⣿⡿⣿⢧⣀⣿⣿⣿⣿⠇⠀⠈⠁⠀⣿⣿⣿⣷⠀⢸⣿⣿⡇⣿⣿⣿⣿⡋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠩⣌⡀⣼⣿⣿⣿⣿⣿⣿⣤⣷⢿⡿⣿⣿⣿⣿⣿⣾⣟⣿⠸⣿⣿⣿⣿⡇⠠⠟⠁⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣧⠀⠀⠀⠀⠈⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠋⠉⢉⣉⠉⢩⣤⣤⣤⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡄⣿⣿⣿⣟⠛⡖⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠻⢿⣿⣿⣿⣿⡇⠀⣹⣟⡃⠄⠀⣨⣀⠀⢰⣿⣿⣿⣿⡿⡿⣿⢿⣿⡿⢿⠿⣀⠀⢰⠿⢿⣟⣿⣿⣿
⣤⣤⣬⣽⠿⠀⣸⣿⣿⣿⡸⣿⣿⡆⠀⠸⢿⣿⣿⣿⣿⣿⣾⡇⠉⠉⢉⣿⠿⠛⣶⡀⢀⣠⣤⣄⣀⡄⠀⠀⠤⠼⠿⢿⣿⣿⡇⢸⠇⠀⠀⠀⠀⣿⣿⣿⢩⣵⣷⣦⣿⣅⠀⠀⢠⢸⣿⣎⣸⣁⣀⣧⣶⣾⣿⣿⣿⡿
⢳⣾⣿⣿⣾⣿⣯⣿⠿⣿⡛⢿⣿⣇⢤⣼⣯⣭⣽⣿⣶⣶⣿⣇⢸⠟⠋⠀⠀⠀⣿⣿⣿⣿⣉⣙⡛⠁⠀⠀⠀⠀⢶⡾⠿⣛⣧⣼⣥⣆⡀⠀⠀⢿⡟⠋⡜⣿⣿⣿⣀⣻⣿⣷⣙⣿⣿⣿⡿⠛⣿⡏⣿⣿⣿⢻⠃⠁
⠛⠋⠉⠉⢍⣀⣰⣿⣿⣿⣿⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⡿⠆⠀⠀⠀⠈⠃⠰⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⡠⡗⢻⡇⣿⠿⠿⡻⣻⣿⣿⣿⡿⠁⠁⣿⣿⣟⡃⣀⣙⣿⣏⡸⠟
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣯⢴⣿⢿⣿⣿⣿⣿⣿⡶⣶⣷⣿⣿⣿⣿⣿⣾⣿⣞⣛⣻⣿⣿⣿⣿⠟⠛⠉⠀
⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⢏⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⣿⣿⢸⣟⠩⢠⣿⣿⣿⣿⣿⡇⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀
⣛⡻⠭⣽⣉⣀⣤⣤⠤⠒⠒⠩⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⢛⠛⠓⠀⢀⣴⣿⣿⠂⠀⠀⠀⣰⣿⣿⣿⣿⣌⣹⠟⠙⣿⣿⣿⣥⣶⣿⣶⣼⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠚⣒⣿⡇⣡⣤⡴⣏⡭⠥⠀⠀⠀⠈⠈⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠀⣴⣿⣿⣿⣿⣤⢀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⣿⡼⣷⣚⣻⣭⣽⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣁⣀⣼⣿⣿⣿⣿⣿⣿⠛⠀⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⠟⠭⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⡞⠬⠙⠤⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⠀⠀⠀⠀⠈⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡯⢁⡁⠀⠀⠠⠀⠀⢸⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠻⢿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣏⣗⣌⣤⡡⢦⡈⠀⠀⣸⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⣷⠈⠁⠀⠐⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠿⠟⢸⡥⠀⠀⠁⠀⣿⣿⡿⠛⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⣄⣀⣀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⡁⢁⡉⠁⠈⠀⠀⠀⠿⠋⠀⠀⠀⠀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡹⣟⣻⡖⢦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
[22A⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⣿⡸⣷⣉⣿⣿⡿⢿⣿⣿⣿⡇⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠟⢿⡿⡿⣿⣿⣿⡶⠶⣾⣿⣿⡄⣾⣿⣿⣿⡧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⠀⠠⠀⢀⣀⣠⣤⣀⣘⣿⠁⡇⣿⡻⣿⣿⣿⣼⣿⢻⣿⣷⢸⣿⡿⣿⢧⣀⣿⣿⣿⣿⠇⠀⠈⠁⠀⣿⣿⣿⣷⠀⢸⣿⣿⡇⣿⣿⣿⣿⠿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠩⣌⡀⣼⣿⣿⣿⣿⣿⣿⣤⣷⢿⡿⣿⣿⣿⣿⣿⣼⣟⣿⠸⣿⣿⣿⣿⡇⠠⠟⠁⠀⠀⠀⠀⠠⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⡇⠀⠀⠀⠀⠈⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⠉⣉⣉⠉⢩⣤⣤⣤⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⡄⣿⣿⣿⣟⠻⡆⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠻⢿⣿⣿⣿⣿⡇⠀⣹⣟⡃⠅⠀⣰⣀⠀⢰⣿⣻⣿⣿⡿⡿⠿⢿⣿⡿⢿⠿⣀⠀⢰⠿⢿⣟⣿⣿⣿
⣤⣤⣬⡽⠿⠃⢸⣿⣿⣿⡾⣿⣿⡆⠀⠸⢿⣿⣿⣿⣿⣿⣾⡇⠉⠉⢉⣿⠿⠛⣶⡀⢀⣰⣤⣄⣀⡄⠀⠀⠤⠼⠿⣿⣿⣿⡇⢸⠇⠀⠀⠀⠀⣿⣿⣿⢩⣵⣷⣦⣿⣅⠒⠀⢠⢸⣿⣎⣸⣁⣀⣧⣶⣾⣿⣿⣿⡿
⢳⣾⣿⣿⣾⣿⣯⣿⠿⣿⡛⢿⣿⣇⢤⣼⣯⣭⣽⣿⣶⣶⣾⣧⠸⠟⠋⠀⠀⠀⣿⣿⣿⣯⣉⣙⡛⠁⠀⠀⡀⠀⢶⡾⠿⣛⣧⣼⣤⣆⡀⠀⠀⢿⡟⠋⡘⣿⣿⣿⣀⣿⣿⣷⣙⣿⣿⣿⡿⠻⣿⡏⣿⣿⣿⢻⠃⠁
⠛⢋⠉⠉⢍⣀⢰⣿⣿⣿⣿⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⡿⠆⠀⠀⠀⠈⠃⢴⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⡠⡗⢻⡇⣿⠿⠿⡻⣻⣿⣿⣿⡿⠁⠁⣿⣿⣟⡇⣈⣙⣿⣏⣸⠟
⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⡟⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣯⢴⣿⢿⣿⣿⣿⣿⣿⡶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣞⣛⣻⣿⣿⣿⣿⠟⠛⠉⠀
⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⢟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⣿⣿⢸⣟⠩⢠⣿⣿⣿⣿⣿⡇⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀
⣛⡻⠭⣽⣉⣀⣤⣤⠤⠒⠒⠩⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⢛⠛⠓⠀⢀⣴⣿⣿⠂⠀⠀⠀⣰⣿⣿⣿⣿⣌⣹⠟⠙⣿⣿⣿⣥⣶⣿⣶⣼⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠒⢒⣿⡇⣡⣤⡴⣏⣭⠥⠀⠀⠀⠈⠈⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠈⠀⣴⣿⣿⣿⣿⣤⢀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⢿⡼⣷⣚⣻⣭⣽⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣁⣀⣼⣿⣿⣿⣿⣿⣿⠓⠀⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⡄⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⢟⣉⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣛⡟⠖⠹⠁⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⠀⠀⠀⠀⠈⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡩⠇⠨⠀⠀⠀⠀⠀⢸⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠻⢿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣏⢽⣚⢏⡢⠠⠀⠀⠀⣸⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠤⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠂⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠅⠈⠀⣿⣿⡿⠟⠀⠀⠀⢀⣀⣤⣤⣶⣦⣦⣄⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣛⠉⠂⠍⠃⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠑⠞⠗⢙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠆⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
[22A⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣇⣿⣜⣿⣿⣿⣿⣿⢹⡏⣿⢸⣿⡿⣿⣿⠀⣿⣿⣿⣿⣿⢸⢿⣿⢿⣿⣿⣿⣯⡽⢶⣿⣿⡇⢰⣾⣿⣿⡿⡂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠄⠀⠄⠀⢀⠀⣀⣀⣀⣿⡇⢹⢹⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣽⣧⠀⣿⣿⣿⣿⣿⠀⠀⠋⠀⢻⣿⣿⣿⡀⠸⣿⣿⣧⢸⣿⣿⣿⡿⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠉⠁⣁⢨⣷⣿⣿⣿⣿⣿⣇⣾⣼⣷⣿⣿⣿⣛⣿⣿⣿⣽⡇⣿⣿⣼⣷⣯⢁⡸⠋⠁⠀⠀⠀⠀⣠⣼⣿⣿⣿⣷⣾⣿⣿⣿⠘⢻⣿⣿⣿⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠒⠛⠛⢋⡉⠉⣩⣡⣤⠈⣿⢿⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢛⡒⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠿⣿⣿⣿⣿⣿⠀⠘⣿⣛⢐⠀⠀⣀⠀⠀⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⡟⠛⠛⣿⣿⣿⣿⣿⣿
⢀⣤⣄⣡⡽⠧⠀⣿⣿⣿⡇⣿⣿⣧⠀⠈⣬⣿⣿⣿⣿⣼⣿⣿⠘⠛⠋⢻⣿⠿⣤⡀⠀⠀⣄⣀⢀⡀⠀⠀⠀⠠⠿⢿⣿⣿⣿⠀⡏⠉⠀⠀⠀⢸⣿⣷⠚⣭⣭⣷⣿⡟⠀⠀⠀⡋⣶⣾⡁⡏⠁⣰⣤⣴⣿⣾⣿⣿
⡿⣾⣿⣿⣷⣶⣿⣿⣿⡿⠿⢿⣿⣿⢠⣤⣛⣿⣭⣭⣽⣿⣶⣿⠐⣿⠏⠉⠀⠀⢹⣷⣾⣿⡛⠛⠿⠃⠀⠀⠀⠀⢠⣼⢿⡿⣿⣠⣧⣤⠀⠀⠀⢸⣿⠟⠄⣿⣿⣿⡇⢸⣿⣷⢘⣿⣿⣿⣿⡿⣿⣟⢹⣿⣿⡿⡿⠑
⠛⠛⠛⠋⠉⢉⠁⣼⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠁⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠣⢨⣶⣾⣿⣿⣿⣿⣿⣿⣄⣀⡤⣽⢴⡷⢹⣿⣿⠿⢿⣿⣿⣿⣿⡯⠙⢻⣿⣿⣻⠈⠉⣿⣿⠃⣶
⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣩⣾⣿⣿⣿⣾⣾⣿⣾⣤⣶⣿⣿⣿⣿⣽⣷⣶⣶⣖⣻⣶⣾⣿⣿⡿⠟⠛⠃
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢺⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡝⡿⢛⡁⣿⣿⣿⣿⣿⣯⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠋⠀⠀⠀⠀⠀
⣟⣛⠛⢯⡏⣉⣀⣤⡤⠤⠒⠒⠏⣿⣿⡜⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⡛⠛⠗⡀⠀⣠⣾⣿⡆⠀⠀⠀⢠⣿⣿⣶⣿⡗⢲⡿⠛⢿⣿⣿⣧⣤⣶⣦⣬⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠤⢗⢺⣿⢉⣥⣤⢶⢈⣉⠀⠀⠈⠉⠁⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣴⣿⣿⣿⣥⣀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠯⣭⣿⣼⣟⣻⣭⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⣀⣠⣿⣿⣿⣿⣿⣿⡟⠁⠀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⡄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣇⠈⢼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣶⠆⠀⠀⠀⠀⠉⠀⠉⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣻⠩⠁⠪⠈⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡽⣫⠿⣪⡂⠀⠀⢸⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⡀⣂⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⠠⠊⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠇⠆⢁⠁⢸⣿⣿⠿⠃⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⣿⣿⣿⣿⣟⡮⠞⡐⠁⠄⠀⢸⠟⠋⠀⠀⠀⢀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢟⠯⣺⠴⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⣫⡫⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
[22A⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸⣿⣿⡸⣷⣹⣿⣿⣿⣿⣇⢿⣿⡇⢻⣿⢿⣿⡇⢸⣿⣿⣿⣿⡇⡿⣿⡿⡿⣿⣿⣿⣬⢭⣼⣿⣿⡇⣼⣾⣿⣯⡣⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⠀⠠⠄⠀⠀⢀⣀⣀⣈⣿⠀⡇⣿⠹⣿⣿⣿⣿⣿⣿⣯⣷⢸⣿⣧⣽⡄⢀⣿⣿⣿⣿⡇⠀⠘⠃⠀⣿⣿⣿⣷⠀⢻⣿⣿⡇⣿⣿⣿⣧⠭⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠜⠊⠉⢜⡀⢸⣿⣿⣿⣿⣿⣿⣄⣷⢿⡿⣿⣿⣟⣻⣿⣿⣿⣿⢸⣿⣧⣿⣾⡏⣁⠛⠉⠁⠁⠀⠀⣀⣀⣿⣿⣿⣿⣶⣿⣿⣿⡇⠻⣿⣿⣿⡇⠀⠀⠀⠀⠘⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠒⠛⠛⠋⣉⠉⢉⣭⣤⣄⢸⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⠓⠂⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⢻⡿⡏⠀⠀⢀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⢩⣿⣿⣿⣿⣿
⠀⣠⣤⣄⣬⠿⠃⢸⣿⣿⣿⣼⣿⣿⡆⠀⢠⡼⣿⣿⣿⣧⣿⣿⡇⠛⠛⠙⣿⡿⢧⡄⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⣸⠿⣿⣿⣿⡇⢸⠉⠉⠁⠀⠀⣿⣿⣖⢚⣩⣭⣝⣿⠃⠁⠈⢈⢹⣷⡜⢰⠏⠀⣎⣡⣼⣿⣿⣿
⣾⢳⣾⣿⣿⣶⣾⣯⣿⡿⠿⡟⣿⣿⡇⣤⣜⣛⣿⣭⣽⣿⣶⣾⡇⢺⡿⠉⠁⠀⢸⣿⣶⣶⡟⠛⠿⠟⠀⠀⠀⠀⠠⣤⣾⣿⠿⣇⣸⣠⡄⠀⠀⠀⣿⡿⠇⢸⣿⣿⣿⠈⣿⣶⣦⠺⣾⣿⣿⣿⠿⣿⡟⣿⣿⣿⢿⡟
⠛⠛⠛⠋⠉⠉⡁⢠⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠱⠀⢩⣶⣶⣿⣿⣿⣿⣿⣧⢀⣀⣌⡧⣶⠜⣿⣿⣿⠿⣿⣿⣿⣿⣿⡋⠋⣿⣶⡿⠇⠙⠛⣟⡾⠠
⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⣿⣋⣽⣿⣿⣿⣶⣷⣿⣧⣭⣠⣶⣷⣿⣿⣯⣿⣴⣦⡴⠽⢿⣿⣷⣾⣿⣿⠿⠳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣏⢿⠾⣛⢸⣿⣿⣿⣿⣿⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠀⠀⠀
⣟⣛⡛⠯⣽⢉⣁⣤⣤⠤⠐⠒⢺⢻⣿⣷⢹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣟⠛⠻⢀⠀⢀⣰⣷⣶⠀⠀⠀⠀⣾⣿⣷⣾⣗⠐⣾⠟⠿⣿⣿⣿⣀⣴⣦⣭⣹⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀
⣤⠤⠔⡒⣿⡏⣡⣤⡴⡇⣉⡅⠀⠀⠉⠉⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⣾⣿⣿⣏⣄⠀⠀⢰⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⣯⠽⣷⣟⣻⣯⣽⣶⣶⡆⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣂⣀⣼⣿⣿⣿⣿⣿⣿⠏⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠏⠀⠍⠌⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣟⣃⠀⠀⠀⠀⠈⠁⠈⠻⣿⣿⣿⣿⣿⡿⣛⢟⡛⠅⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣝⠉⠐⠀⠔⠂⠀⠀⠀⠀⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣷⣶⣶⡶⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⣻⠡⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡯⠛⠂⡒⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⢿⡽⡭⢎⠆⠀⠄⠀⠀⠀⠀⢨⣿⠟⠁⠀⠀⠀⢀⣴⣾⣾⣿⣿⣿⣿⣷⣶⡶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠞⡒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣠⡤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
[22A⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢿⣿⣧⢸⡏⣽⣿⣿⡿⣿⣿⣿⣿⡀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠸⢿⣿⠿⢸⣿⣿⣷⡶⠶⣾⣿⣿⠀⣷⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡠⣤⠀⢰⠀⡀⣀⣤⣤⣄⣸⣏⠼⣼⣿⢿⣿⣿⣧⣿⡏⣿⢿⡇⣿⣿⢾⣿⢆⣸⣿⣿⣿⣿⡄⠀⠘⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⣧⢅⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡊⠉⠩⣉⣀⣿⣿⣿⣿⣿⡟⣿⣐⡇⡿⠸⣿⣿⣿⣿⣿⣹⣿⡇⢹⣿⣾⣿⡿⠀⠜⠋⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⣿⣿⡀⠀⠀⠀⠀⢘⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⣉⣍⠁⣤⣤⣤⡄⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣾⣿⣷⢸⣿⣿⣿⠛⡗⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡟⠿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠃⠋⠀⣘⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠋⠛⢹⣿⣿⣿⣿
⠀⢠⣴⣶⣄⡿⠟⢀⢹⣿⣿⣷⣻⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⠈⠉⠉⣹⡿⠟⣤⠀⠀⢠⣀⡀⠀⣀⠀⡀⠀⠠⠿⠿⣿⣿⣿⠀⠟⠉⠀⠀⠀⢸⣿⣗⡖⣭⣭⣥⣹⣟⠁⠀⠃⠈⣽⣷⡏⢸⠉⢰⣊⣤⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⣿⣿⡄⣤⣽⣭⣭⣿⣷⣶⣿⣿⡄⠿⠋⠁⠀⠀⣿⣷⣾⣿⠛⠻⠿⠃⠀⠀⠀⠀⢤⣴⣿⡿⣿⣠⣥⣤⠀⠀⠀⢸⣿⠟⠂⣿⣿⣿⡇⠈⣿⣶⡄⢿⣿⣿⣿⣿⡿⣿⢛⣿⣿⣿⣿
⠛⠋⣉⢉⡍⣁⣀⡀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⠿⠇⠀⠀⠀⠈⠇⣨⣶⣾⣿⣿⣿⣿⣿⣿⡄⣀⣠⣹⠴⡶⢸⣿⣿⡿⡿⣿⣿⣿⣿⣟⡙⠸⣷⣷⠿⠊⠙⢻⣷⡞
⣤⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣟⣩⣿⣿⣿⣷⣾⣾⣿⣬⣅⣶⣼⣾⣿⣿⣿⣯⣶⣦⠦⠽⣿⣿⣷⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⣹⣿⣿⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠝⡿⢛⡁⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀
⣛⡻⠯⠭⢹⣧⣠⣤⡴⠶⠒⡒⠉⠇⣿⣿⡇⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢻⡛⡛⠄⡀⠀⣠⣿⣿⡆⠀⠀⠀⣸⣿⣿⣶⣿⡒⢺⡿⠻⢿⣿⣿⣇⣠⣶⣬⣍⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀
⣤⣔⡒⢺⣩⣿⠠⣴⣶⢺⡩⠤⠀⠀⠀⠉⠁⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣠⣾⣿⣿⣿⣤⣄⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠟⢳⣦⣿⣷⣿⣭⣿⣷⣾⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣋⣄⣴⣿⣿⣿⣿⣿⣿⡟⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⢸⣽⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣻⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠉⠉⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⠟⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠁⠍⢮⠉⣺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠉⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣽⠽⡍⢋⠘⠂⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠿⢿⣿⡿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⡪⣫⣂⡘⠖⠠⠀⢸⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣶⣿⣿⣇⠀⡁⠀⢀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⡷⠠⠑⠀⠀⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢁⡀⠂⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⠿⠛⠙⡑⠨⠁⠀⠀⣿⠿⠋⠀⠀⠀⢀⣀⣴⣷⣿⣿⣿⣿⣷⣶⡤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠁⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣗⠝⠣⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⠂⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
[22A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣇⣿⣰⣿⣿⣿⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣧⠘⠻⣿⢳⣿⣿⣿⣿⠛⢻⣿⣿⡇⢸⣿⣿⣿⣯⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⢿⣿⣿⣿⣿⣿⣿⣿
⢠⢴⣴⣧⡀⡇⢠⣤⣴⣶⣶⣤⣿⡖⢹⢻⡏⣿⣿⣿⣷⣿⡿⣿⣿⠘⣿⣿⣿⣟⡤⠿⣿⣿⠿⠿⠀⠀⠁⠀⣿⣿⣿⣿⣀⣸⣿⣿⡇⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣀⣀⣢⣤⣼⣿⠿⠿⠿⠿⢹⣷⣾⡸⠓⣻⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣇⠠⠉⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⣿⠀⠀⠀⠀⠀⢉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠠⢄⣤⡄⢰⣶⣶⣶⡸⣿⣿⡇⠀⢺⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣉⡏⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠙⠻⣿⣿⣿⣿⣿⠀⣘⣿⠯⠨⠂⢠⣄⡀⢀⣿⣿⣿⣿⣿⢿⢻⠿⣿⣿⠿⡟⢿⡀⠀⣼⠿⣿⣛
⣠⣀⣴⣿⣷⣾⣋⣁⣌⣿⣿⣿⣧⣿⣿⣇⠀⠈⣿⣿⣿⣿⠿⢿⣿⣇⢀⣁⣠⠟⠛⢱⣦⡀⣀⣰⣤⣀⣀⡄⠀⠀⠀⠒⠛⢻⣿⣿⣿⠀⠃⠀⠀⠀⠀⣿⣿⣿⢩⣵⣷⣶⣿⣏⡰⠀⢀⣄⣿⣿⣁⣟⣀⣸⣤⣶⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠷⣿⣿⣿⣭⣹⣿⣿⢰⣶⣶⣶⣾⣿⣿⣿⣿⣿⠘⠋⠁⠀⠀⠀⣿⣿⣿⣏⣉⣙⠋⠀⠀⠀⡀⠰⣾⠾⢿⣛⣿⣤⣶⣆⡀⠀⠀⢿⡟⠉⡼⣿⣿⣿⣄⣸⣿⣷⣘⣿⣿⣿⣿⢛⢻⣿⢹⣿⣿⡿
⠉⢉⣠⣤⣤⢀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⠟⠿⠀⠀⠀⠀⠙⠀⢼⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⠰⡟⢻⡇⣿⠿⠿⡻⣻⣿⣿⣿⣿⠭⠁⢹⣿⣿⣛⠀⣉⣻⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣟⣥⢶⣿⢿⣿⣿⣿⣿⣷⡶⣴⣷⣿⣿⣿⣿⣿⣷⣾⣖⣒⣻⣶⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⢛⣫⢻⣿⣧⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⡇⢻⡛⠭⣸⣿⣿⣿⣿⣿⠑⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠀
⠭⠭⠙⠒⣂⣿⡦⠶⠶⠚⣋⡩⠁⠰⠸⢿⣿⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⣟⠛⠐⠠⠀⣠⣾⣿⡯⠀⠀⠀⢠⣿⣿⣿⣿⡏⠀⣿⠏⢟⣿⣿⣿⣤⣶⣶⣶⣼⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀
⣶⣶⣭⣍⡥⢾⣇⢲⣾⣿⣷⠒⣀⠀⠀⠀⠀⠘⠻⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢠⣾⣿⣿⣿⣷⣖⡄⠀⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠛⠛⠉⢹⣾⣿⣿⣷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⠰⣫⣴⣴⣿⣿⣿⣿⣿⣿⣿⠁⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠎⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡠⠑⡰⢠⠎⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣯⡯⠚⠂⠁⠁⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢖⠵⢻⠑⠀⠀⠀⠀⢀⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⡀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢿⠌⠁⠨⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⡙⠀⠁⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⢿⡿⠩⠫⠒⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣷⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡳⡽⠯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠚⠈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
[22A⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡞⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠃⠻⠏⢻⣿⣿⣿⣟⠉⢿⣿⣿⡇⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢻⣿⣿⣿⣿⣿⣿
⣐⣶⡳⠿⠧⠸⠀⢲⣶⣿⣿⣿⣿⣿⢠⣇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣯⣿⣵⠚⠛⡿⠟⠛⠃⠀⠀⠀⠀⣿⣿⣿⣿⣤⣼⣿⣿⡇⢽⣿⣿⣿⡭⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠿⠷⠶⠤⠤⠷⠶⠿⠛⠛⠛⠛⠉⢿⣿⣿⠉⠉⣽⣿⣿⣿⣿⣿⣟⣿⢸⣿⣿⣿⣿⣆⡂⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⡿⠧⠀⠀⠄⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿
⠀⠀⠀⢀⣀⡒⡲⣾⠀⢼⣿⣿⣷⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡈⠿⠿⢿⣧⣤⢄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⢹⣿⣿⣿⣿⡇⢠⠼⠯⠃⠀⠀⣼⣤⢀⣸⢿⠿⢿⣿⡿⠟⠻⠻⡿⠿⢛⠛⣳⠄⢀⠾⠛⣿
⣶⣦⣴⣿⣿⣿⣿⣭⣴⣾⣿⣿⣿⣾⣿⣿⡇⠀⠨⠿⠿⣿⣟⣛⣿⣿⡇⢤⡤⠚⠉⠀⢸⣧⣠⣤⣿⣶⣦⡶⠀⠀⠐⠀⠉⠉⣿⣿⣿⡇⢸⠀⠀⠀⠀⢸⣿⣿⡇⢶⣾⣿⣿⠻⣄⣉⡀⢠⣸⣯⣿⣤⣧⣄⣾⣶⣾⣿
⣿⣿⡿⠾⠿⠿⠟⠛⠛⢻⣿⣿⣶⣦⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣤⡌⠀⠀⠀⢠⡄⠻⢟⣛⣫⣽⣷⣾⣿⣤⠀⠀⠘⢻⣏⣱⢸⣿⣿⣿⣤⣿⣿⣟⣬⣿⣿⡿⣯⣩⣽⣏⢾⣿⣿
⠀⠀⢰⣶⣶⣾⣰⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠁⠰⢿⣿⣿⣿⣿⣿⡿⢿⣧⣴⣆⣲⢉⣿⠸⠿⢟⢛⣛⣿⣿⣿⣿⠿⠒⠀⢿⣿⡿⣏⣀⣁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⢵⣾⣿⡿⣿⣿⣿⣿⣿⣿⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⠿⠿
⣿⣿⣿⠿⠿⣿⣿⠛⠛⢉⣉⣉⣉⠥⠆⣿⣿⡇⣿⣿⣿⣿⣿⣿⢧⣐⣤⡀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠃⠀⠀⠀⣤⣄⡀⠀⠀⠀⢸⣿⣿⣊⣯⡡⢆⣿⣿⣿⣿⣿⡟⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⠀⠀⠀
⣒⠒⢊⣉⡹⠴⣿⡚⢛⣉⣩⡴⠂⠀⠋⠻⠿⠧⣿⣿⣿⣿⣿⡟⣼⣿⣿⣷⡀⠛⠛⠛⠛⠛⢻⠟⠂⠁⠂⣠⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣉⠹⡟⢙⣿⣿⣿⣷⣴⣾⣷⣷⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣶⣛⣻⡇⣿⠿⣷⣏⣥⡄⠀⠀⠀⠀⠉⠙⠛⠿⠟⠁⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⡤⠀⢀⣾⣿⣿⣿⣿⣿⣵⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⢉⣀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⠿⠿⠀⠀⠀⠀⠀⠀⣨⣶⣿⣿⣿⣿⣿⣿⣿⣿⡧⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⠿⠿⠊⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡻⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣠⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣃⠚⠿⢍⢾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⠀⠀⠆⠀⢸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣝⣿⣽⣯⡲⡡⠀⠀⣸⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣰⣤⠠⡄⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡭⡌⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠼⡫⢍⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣤⣀⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠛⣛⡉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⡿⣟⣻⡿⠴⠀⠀⠀⠀⡿⠛⠁⠀⠀⠀⣂⣶⣾⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡿⣯⢿⠿⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡿⣛⡿⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
[22A⠀⠀⢀⣀⣀⠀⣠⠀⠀⠀⣀⣀⠀⢻⡟⣹⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⡄⣿⣿⢹⣿⡀⢸⣿⣿⣿⣿⠈⠈⠻⠀⢹⣿⣿⣿⡏⠈⣿⣿⣿⠀⣿⣿⣿⣿⣟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⣿⣿⣿⣿⣿⣿
⣤⣼⣯⠟⠛⢓⠚⢀⣿⣿⣿⣿⣿⣿⣗⣺⣿⣿⣾⣿⣿⣿⣿⣿⣿⢺⡇⣿⣿⣼⣿⣶⠛⠿⠋⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣿⣿⣿⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⠓⠒⠒⠛⠛⡛⠛⣉⣉⣉⡉⣿⣿⡇⠉⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠿⠬⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠟⠷⡀⢀⡀⠀⢀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠀⢀⣠⣰⣙⣻⡷⠐⣿⣿⣿⡧⣿⣿⣧⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⠟⣿⡾⠧⣄⠀⠀⢀⡀⠀⠀⠀⠈⠉⠁⠉⣿⣿⣿⣿⣿⠀⡴⠛⠓⠂⠁⢠⣾⣆⣠⠼⠿⢟⣿⣿⠟⠏⠛⠻⢿⣟⣫⢍⡧⠄⡀⠟⠛
⣿⣿⣷⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿⠿⢿⣿⣿⢀⣀⣶⣛⣛⣿⣯⣽⣿⣿⠠⠶⠂⠀⠀⠐⣿⣷⣶⡾⠿⠿⡿⠃⠐⠀⠉⠉⠉⣩⣿⣿⣿⠀⠂⠀⠀⠀⠀⣸⣿⣿⠀⣿⣿⣿⡏⠻⣤⣆⠀⣼⣼⣿⣯⣬⣧⣤⣷⣾⣿
⠿⠿⠿⠟⠛⠛⠛⠋⣉⠉⣿⣿⣿⣿⣾⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣾⠀⠀⠀⠀⢤⠈⢛⣯⣥⣼⣿⣷⣿⣧⣄⠀⠀⠙⢿⣁⡇⣿⣿⣿⣧⣮⣿⣿⣧⣽⣿⣿⣿⣿⣩⣿⡇⣿⣿
⣀⣀⣈⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣶⣶⣶⣶⣾⣿⣿⢛⡀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⣿⣿⣿⡿⢟⣿⣴⣾⣜⣏⣹⣇⠹⠟⣛⣯⣻⣿⣿⣿⣿⠓⡂⠈⠿⣿⢿⣇⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡷⣞⣿⡿⢻⣿⣿⣿⣿⣿⡟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⡿⠿
⣿⠿⠿⢿⣟⣛⣿⡏⣉⣁⣠⡤⠤⠄⠚⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢈⠀⠀⢀⣰⣤⡄⠀⠀⠀⢸⣿⣿⣇⣺⣅⣒⣼⣿⣿⣿⣿⣿⠇⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠈⠀⠀
⣮⣍⣉⡤⠥⢔⢻⣯⢉⣩⣤⢶⢒⠀⠈⠉⠛⠛⢶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠛⠛⠛⠛⠛⡟⠀⠀⠈⣠⣾⣿⣿⢇⡀⠀⠀⣼⣿⣿⣿⣿⣦⣀⣟⣃⣻⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⢯⣭⣿⣼⣿⣻⣿⣤⣦⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢀⣼⣿⣿⣿⣿⣿⣿⡂⠀⢻⣿⡿⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣉⢉⣀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⠟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠿⠟⠛⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⠭⡹⠶⡝⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠇⠠⠅⢛⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡣⡡⢂⣬⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢝⣽⢰⢽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣞⢮⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡬⡾⠣⠐⣹⣿⣿⡿⠋⠀⠀⠀⠀⢀⡀⢀⣄⣠⢀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⣉⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣿⡾⡜⠌⠱⠀⠺⠟⠋⠀⠀⠀⠄⣠⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣈⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡿⠡⠊⠂⠀⠂⠀⠀⠀⠀⣐⣦⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣿⢿⢿⡞⠛⠙⡁⠁⠀⠀⠀⠀⠀⣂⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
[22A⠀⠀⣀⣀⣠⡄⠀⡄⠀⢀⢀⣀⣀⣀⣿⠡⣧⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠈⠏⠈⣿⣿⣿⣿⠀⢸⣿⣿⣧⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢉⣿⣿⣿⣿⣿
⣷⣤⣿⣿⠋⠉⢥⣁⢸⣿⣿⣿⣿⣿⣿⣇⣾⢹⣇⣿⣿⣿⣟⣿⣿⣿⣿⠈⣿⣿⣿⣷⡏⡉⠋⠁⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣶⣾⣿⣿⣿⠸⢿⣿⣿⣯⠁⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠓⠛⠛⣋⣉⡉⢉⣭⣤⣤⢸⣿⣿⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡿⢶⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠛⡖⠀⡜⠀⠀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣻
⣀⣄⠀⠀⣠⣤⣥⣭⠿⠇⠸⣿⣿⣿⣾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣻⡇⠛⠛⠛⠿⠾⣰⣄⠀⠀⣤⣄⡀⣀⠀⠈⠉⠀⢈⣿⣿⣿⣿⣿⠀⠒⠛⠚⠈⠁⣼⣷⣤⠤⠿⣟⡛⣿⡿⠛⠙⠛⠿⣟⣛⡭⢩⠥⠀⡠⠛
⣿⣿⣿⣿⣿⣾⣿⣿⣶⣾⣯⣿⡿⢿⡟⣿⣿⣇⣠⣜⣛⣿⣯⣭⣽⣿⣿⡇⠰⠂⠀⠀⠀⢸⣿⣾⣿⡛⠛⠻⠛⠀⠀⠈⠉⢁⣀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡆⢸⣿⣿⣿⠛⢣⣤⡀⢠⣦⣿⣾⣧⣼⣤⣴⣷⣿
⠟⠛⠛⠛⠛⠛⢉⠉⠩⣍⣠⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⡇⠀⠀⠀⠲⡄⠙⣫⣭⣵⣾⣿⣾⣿⣤⡀⠀⠀⠹⣏⣹⢸⣿⣿⣿⣶⣼⣿⣿⣴⣿⣿⣿⢿⣏⣽⣿⡤⢿
⣀⣠⣤⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣶⣶⣶⣶⣶⣿⣞⠋⣀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣽⣿⡿⠿⣻⣷⣶⣧⣹⣉⣿⡌⠟⢛⡛⣝⣽⣿⣿⣿⡟⣓⠀⠸⠿⡿⢯⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⡟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠊⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢾⣻⣿⠟⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⠿
⡿⠿⣟⣛⣻⠿⠭⣽⣉⣠⣤⣤⠤⠒⠒⣣⣿⣿⣧⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡁⠀⠄⠀⠀⣰⣶⣤⠀⠀⠀⠀⣿⣿⣿⣰⣯⣐⣢⣿⣿⣿⣿⣿⡟⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠁⠀
⣿⣭⣥⣤⡜⡒⢟⣿⡇⣤⣤⡴⣏⡁⠀⠁⠈⠛⠻⣾⣿⣿⣿⣿⣿⡧⣰⣦⣿⣿⣟⠛⠛⠛⠛⢻⠁⠀⠀⣠⣶⣿⣿⣏⣀⠀⠀⣼⣿⣿⣿⣿⣧⣄⣹⣋⣘⣿⣿⣿⣷⣾⣿⣷⣷⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠿⠿⣷⢼⣷⣛⣿⣭⣷⣶⡆⠀⠀⠀⠀⠀⠈⠉⠛⠻⠟⠁⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⠆⢀⣠⣿⣿⣿⣿⣿⣷⠓⠀⠘⣿⡿⠿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢭⣄⣠⣤⣴⡆⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠛⠛⠛⠉⠁⠹⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡷⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡽⡪⣿⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⢏⡩⡏⡘⠀⣸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠂⠀⠀⣾⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡴⣠⡌⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢟⡥⢅⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡱⠂⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⢀⣠⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠉⢭⢥⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣏⡛⠤⠠⠀⢺⡿⠛⠁⠀⠀⡠⣢⣶⣶⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⡿⠹⠀⠈⠀⠀⠀⠀⠀⠐⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡻⣽⣿⣿⠁⠋⣀⡀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
[22A⠀⠀⠀⣀⣄⣤⡄⢠⠄⠀⣀⣠⣤⣀⣸⣿⢼⡿⣿⠿⢿⣿⣿⣿⣿⣾⣾⡇⢿⣿⣿⣿⡄⢸⣿⣿⣿⣿⡇⠁⠙⠃⠹⣿⣿⣿⣿⠀⢹⣿⣿⡇⢸⣿⣿⣿⣷⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢁⣿⣿⣿⣿
⣿⣷⣶⣿⣞⠉⠩⣍⡀⣽⣿⣿⣿⣿⣟⣿⣨⡇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣷⣿⣿⢉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣶⣾⣿⣿⡇⠺⣿⣿⣿⣄⠁⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠋⠉⣉⣉⠉⣭⣤⣤⡄⣿⣿⣷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⡟⠃⠆⠀⡂⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡋
⣤⣤⡄⡀⠀⣤⣤⣭⡮⠻⢀⢹⣿⣿⣷⣻⣿⣿⠀⠀⢭⣿⣿⣿⣿⣇⣻⣿⠘⠛⠛⠻⠿⢃⣦⡀⠀⣠⣤⣀⣀⡀⠀⠉⠁⠀⣸⣿⣿⣿⣿⡇⠐⠒⠓⠁⠀⢠⣶⣦⠤⠴⢿⣛⣻⣿⡿⠛⠙⠋⡿⣛⣫⡍⣩⠅⢀⠈
⣻⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⢿⣿⠻⣿⣿⡆⣤⣿⣿⣯⣭⣽⣿⣿⣿⡄⠚⠁⠀⠀⠸⣿⣿⣿⣟⠛⣛⠟⠁⠀⠈⠈⢀⣀⣤⣿⣿⣿⡇⠀⡀⠀⠀⠀⢸⣿⣷⠀⣿⣿⣿⡟⠙⣦⣤⡀⢠⣽⣷⣿⣤⣿⣤⣼⣶
⠛⠛⠛⠛⠛⠋⣉⡉⠉⢥⡀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⠀⠀⠀⠐⢦⠈⢻⣭⣭⣶⣿⣿⣿⣧⣆⠀⠀⠈⢿⣉⡅⣿⣿⣿⣷⣦⣿⣿⣿⣼⣿⡿⡟⣿⣟⣹⣿⠰
⣇⣠⣤⣤⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⠏⠀⠀⣶⣶⣶⣶⣶⣾⣷⠙⢡⡀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⠿⢛⣿⣶⣾⣌⣏⣹⣧⠸⠛⣛⢩⣩⣿⣿⣿⣿⢟⡒⢀⠽⢿⡿⣭⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⡷⣟⣿⡿⢿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿
⣿⡿⣛⣛⡛⠿⠭⢽⣧⣠⣤⡤⠤⠒⠒⣊⡝⣿⣿⡎⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠠⠀⠀⣠⣶⣦⠀⠀⠀⠀⢸⣿⣿⣇⣾⣅⣂⣼⣿⣿⣿⣿⣿⠂⢛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀
⣿⣷⣶⣤⣔⣒⢺⣩⣿⢠⣤⣴⢺⡁⠀⠀⠀⠙⠛⢷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⠛⠛⠛⠛⠛⢻⡿⠀⠀⢀⣴⣿⣿⣿⣀⠀⠀⢠⣿⣿⣿⣿⣿⣄⣈⣛⣁⣻⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀
⣿⣿⣿⡿⠿⠟⢓⣦⣿⣿⣿⣭⣽⣶⣦⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⣠⣾⣿⣿⣿⣿⣿⠞⠀⠈⢿⣿⠿⠿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠥⣶⣄⣤⣴⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠿⠛⠋⠉⠉⠀⠿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠻⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣉⠝⠥⣿⠇⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⠻⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣫⣟⢌⠢⠅⢀⢰⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣽⣿⣿⣷⢯⣗⢬⣒⠁⢸⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣽⡽⢧⢀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡏⠟⣜⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢲⠀⡀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠩⣀⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣝⣿⣿⣽⡟⠎⠠⠀⠀⣿⠟⠋⠀⠀⠀⠠⣦⣵⣿⣾⣷⣿⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡯⣯⣿⣽⠯⡹⠐⠁⠈⠀⠀⠀⠀⠀⠀⢀⣔⣲⣾⣿⣿⣿⣿⣿⣿⣿⡗
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣻⡿⠇⠁⠂⠁⠀⠀⠀⠀⠀⠀⢄⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
[22A⠀⠀⠀⢀⣠⣄⣤⠀⢤⠀⢀⣀⣄⣄⣀⣿⡧⢻⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⠀⠈⠙⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⣿⡋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿
⣿⣿⣦⣾⣿⡟⠉⠩⣉⠠⣿⣿⣿⣿⣿⣻⣇⣾⢸⣧⣿⣿⣿⣟⣿⣿⣿⣿⡄⣿⣿⣾⣷⡏⠉⠉⠁⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣷⣶⣿⣿⣿⠀⠿⣿⣿⣷⡂⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠋⠉⣉⡉⠉⣭⣤⣤⢸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠛⠕⠅⠀⠀⠀⢠⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛
⢀⣤⣤⡀⠀⢀⣤⣤⣥⡼⠇⠀⣿⣿⣿⡎⣿⣿⡇⠀⠨⣭⣿⣿⣿⣿⣝⣻⡇⠙⠛⠛⡿⠶⣰⡄⠀⠀⣤⣀⡀⢀⠀⠈⠉⠁⢀⣿⣿⣿⣿⣿⠀⠒⠚⠒⠀⠀⣼⣶⡄⠤⠾⠟⣛⣿⣿⠟⠋⡟⠹⢟⣟⣩⠍⡭⠀⢀
⣿⣿⣿⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⡿⢿⣟⢿⣿⣷⢠⣬⣿⣿⣭⣭⣽⣷⣿⣷⠐⠞⠀⠀⠀⣿⣿⣾⣿⡛⠛⠿⠇⠀⠀⠈⠀⣀⣀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡖⢸⣿⣿⣿⡏⢻⣤⢄⠀⣼⣼⣷⣿⣤⣧⣤⣾
⡿⠛⠛⠛⠛⠛⠉⣉⠉⠉⣄⢀⣿⣿⣿⣿⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿⡇⠀⠀⠀⢲⡄⠙⣯⣭⣵⣾⣿⣾⣿⣤⡀⠀⠀⠙⡏⣩⠸⣿⣿⣿⣶⣼⣿⣿⣧⣿⣿⢿⢿⣿⣉⣿⡇
⣿⣀⣤⣤⣤⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡿⠃⠀⣶⣶⣶⣶⣶⣶⣷⡌⠋⡀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣯⣿⣿⡿⠟⣻⣷⣶⣧⣹⣉⣿⡄⠿⠛⡛⣝⣽⣿⣿⢿⡿⠓⡂⠀⠿⡿⠏⣅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠿⢟⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⢘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⢾⣻⣿⠿⣿⣿⣿⣿⣿⡿⢳⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿
⣿⣿⠿⣛⣛⠻⠯⠭⣿⣅⣤⣤⠤⠔⠒⢒⣩⢹⣿⣿⢸⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⡇⢳⡁⠀⠄⠀⢀⣴⣶⡄⠀⠀⠀⠀⣿⣿⣿⣸⣭⢐⣠⣿⣿⣿⣿⣿⡇⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈
⣿⣿⣷⣦⣤⣖⠒⣋⣹⣇⢤⣤⡖⣏⠀⠀⠈⠈⠛⢻⣾⣿⣿⣿⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢸⡧⠀⠀⣠⣾⣿⣿⣃⡀⠀⠀⣼⣿⣿⣿⣿⣧⣀⣹⣃⣘⣿⣿⣿⣷⣾⣿⣷⣷⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀
⣿⣿⣿⣿⠿⠿⠛⣲⣼⣿⣾⣯⣭⣿⣶⡄⠀⠀⠀⠀⠁⠈⠉⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢂⣀⣴⣿⣿⣿⣿⣿⡷⡃⠀⠹⣿⡿⠿⢿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢤⣦⣤⣤⣶⡆⣽⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡗⠦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠚⠿⠙⠛⠉⠉⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣝⣽⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣍⡀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣽⣕⢫⡪⢅⠁⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠹⢿⣿⣿⣿⣻⣿⣿⣿⡿⢛⠛⠃⠀⠈⠀⠀⣻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣯⡶⠢⢀⠀⠀⠀⣿⣿⣿⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡅⠡⣐⠀⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⢼⡎⠄⢤⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⢿⣿⡀⢀⠄⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣻⣽⠏⢜⠂⠃⠀⠀⠀⢸⡿⠟⠁⠀⠀⠀⠀⢀⣤⣤⣶⣦⢠⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡏⠿⣿⡟⢇⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣾⣿⣿⣿⣿⣿⣿⡆
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⢵⣓⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
[22A⡀⠀⠀⠀⠀⣀⣀⡄⠠⡄⠀⠀⢀⣀⣀⣸⣿⠻⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠃⠙⠇⠀⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣾⣿⣿
⣿⣿⣧⣤⣿⠿⠛⠛⠑⡁⢸⣿⣿⣿⣿⣿⣿⣠⣧⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢸⣿⣷⣿⣾⠉⠉⠋⠉⠉⠁⠀⠀⢀⣀⣿⣿⣿⣿⣤⣾⣿⣿⡇⠸⢿⣿⣿⣧⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠒⠛⠛⠛⣉⠉⢉⣍⣁⡀⢿⣿⣿⠀⠀⣹⣿⣿⣿⣿⣯⣿⣿⢸⣿⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⠻⠂⠀⢀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛
⡆⣠⣤⣤⠄⠀⣠⣤⣭⣠⠿⠂⢸⣿⣿⣿⢸⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠛⢻⣷⢂⡄⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⠈⢸⣿⣿⣿⣿⡇⠐⠒⠓⠒⠈⢀⣶⣦⢠⠤⠿⢟⣻⣿⡿⠛⠹⠛⠿⣿⣛⡭⢉⡭⠀
⣿⡾⣿⣿⣿⣿⣻⣾⣿⣿⣶⣿⣿⣿⡿⢿⠿⣿⣿⡇⣠⣘⣛⣿⣯⣭⣿⣿⣿⡇⠲⠒⠀⠀⢸⣿⣦⣶⡾⠿⠿⡿⠂⠂⠀⠈⠉⣁⣀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡂⣿⣿⣿⣿⠙⣧⣄⡀⢠⣧⣿⣾⣧⢼⣤⣤
⣿⡿⠿⠟⠛⠛⠛⢛⠉⠉⢉⣁⣸⣿⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣶⠀⠀⠀⠰⣄⠘⢛⣭⣭⣾⣿⣷⣿⣧⡄⠀⠀⠈⢿⢍⡁⢿⣿⣿⣿⣤⣿⣿⣿⣬⣿⣿⣿⣿⣯⣩⣿
⣿⣷⣀⣤⣤⡸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡟⠀⣶⣶⣶⣶⣶⣶⣷⡝⠛⡉⠁⠈⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⡿⢟⣿⣴⣾⣘⣎⣹⣧⠸⠟⢛⢫⣋⣿⣿⣿⣿⠿⠒⠀⠸⣿⡿⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣾⡿⠿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡟⣧⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡷⣞⣿⡿⢿⣿⣿⣿⣿⣿⠟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣿⣿
⣿⣿⡿⠿⣛⣛⣻⠯⠭⣿⣁⣤⣤⡤⠔⠒⣒⡏⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⡀⠁⡀⠀⠀⣠⣶⣤⠀⠀⠀⠀⣽⣿⣿⣇⢯⡅⢂⣾⣿⣿⣿⣿⣿⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉
⢿⣿⣿⣵⣤⣤⡚⠒⣟⣿⡄⣤⣤⢾⡀⠀⠁⠀⠛⠛⣷⣿⣿⣿⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⣷⠀⠀⢀⣤⣿⣿⡟⣀⠀⠀⢠⣿⣿⣿⣿⣿⣀⠸⣝⢉⣻⣿⣿⣿⣴⣾⣿⣶⣼⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀
⣾⣿⣿⣿⣿⠿⠿⠟⣦⢿⣗⣻⣯⣽⣷⣆⠀⠀⠀⠀⠉⠈⠉⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⣠⣾⣿⣿⣿⣿⣷⢗⠀⠘⣿⣿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠩⣤⣄⣤⣤⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣷⡿⠿⠛⠛⠋⠉⠀⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣝⣷⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⡇⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣿⣿⣯⣍⡉⠉⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⠻⠟⢙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⡙⠛⠃⠐⠀⢰⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣺⣮⠦⠀⠂⠂⠀⢸⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢐⢀⠂⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠕⠂⠔⠀⠂⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡋⠼⠅⠁⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠭⢥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡻⠿⣓⠉⠁⠠⠐⠀⠀⣿⡿⠛⠁⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣟⢿⡿⠗⠈⠁⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⡾⠄
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣿⡳⠭⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
[22A⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⡀⠀⠀⢀⣀⠀⢸⣿⠉⡟⣿⢿⣿⣿⣿⣶⣾⣸⣹⡇⢻⣿⡆⣿⡆⢸⣿⣿⣿⣿⡇⠁⠙⠇⠁⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⣷⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿
⣿⣷⣶⣶⣀⣿⣿⠟⠛⡂⠃⢰⣾⣾⣿⣿⡿⣿⠠⡇⣿⣴⣾⣿⣿⣿⣿⣿⣿⣧⢸⣿⣇⣿⣴⠈⠙⠛⠛⠛⠇⠀⠀⠀⢀⣿⣿⣿⣿⣤⣼⣿⣿⡇⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠦⠖⠚⠓⠚⠛⢛⣉⣉⡉⣿⣿⣷⠉⠙⣿⣿⣿⣻⣿⣯⣯⣿⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⠛⠀⠀⡀⠀⠀⣐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣇⣀⣀⣀⠀⠀⢀⣀⣀⣀⣹⠀⢸⣿⣿⣷⢹⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠘⠿⠟⢻⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢹⣿⣿⣿⣿⡇⠀⠐⠛⠒⠀⢀⣶⣧⣀⠤⠿⠿⢻⣿⡿⠛⠹⠛⠿⣿⣛⡭⢉⡭
⣿⣿⡾⣿⣿⣾⣶⣾⣽⣿⣿⣶⣶⣾⣿⣿⡿⠾⣿⣿⡆⣀⣰⣞⣛⣛⣿⣭⣭⣿⡄⠖⠀⠀⢰⣿⣄⣠⣤⣶⣦⣤⠆⠀⠐⠀⠀⠉⠈⢉⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⣾⣿⣿⡿⠻⣦⣐⡀⢠⣆⣿⣿⣧⢼⣥
⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⢹⣷⣿⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣬⠉⠀⠀⠠⢤⡄⠻⣛⣙⣮⣽⣿⣷⣿⣦⡀⠀⠀⠘⢿⢁⡆⣿⣿⣿⣷⣤⣿⣿⣿⣬⣽⣿⣿⢿⡉⡉
⣿⣿⣷⢀⣀⣀⣰⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⠋⠀⣶⣶⣶⣶⣶⣶⣿⡛⢿⠛⠋⠛⠀⠀⠀⠀⠈⠁⠰⣿⣿⣿⣻⣿⣿⡿⢿⣿⣤⣶⡐⡎⣹⠇⠻⠿⢛⢛⣋⣿⣿⡿⣿⠿⠶⠀⠸⣿⡿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⢸⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡟⡇⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⢵⣖⣿⡿⣿⣿⣿⣿⣿⣿⢷⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣛⣛⣿
⣄⣿⣿⣿⠿⠿⢿⣛⡛⠿⣿⢉⣉⣠⣤⠤⠤⠒⡏⣿⣿⡎⣿⣿⣿⡿⠃⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸⠀⠂⠁⠀⠀⠀⣦⣤⡄⠀⠀⠀⠀⣿⣿⣿⣬⣯⡡⢆⣿⣿⣿⣿⣿⣿⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠉⢻⣿⣿⣭⣭⣥⠤⠔⣒⣿⡉⣩⣤⢴⠀⠀⠉⠑⠻⠟⣷⣿⣿⣿⠇⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢸⡇⠀⠁⠂⣀⣼⣿⣿⠃⠀⠀⠀⣴⣿⣿⣿⣿⣯⣍⡹⠟⠙⣻⣿⣿⣧⣤⣾⣷⣦⣼⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀
⣶⣼⣿⣿⣿⣿⡿⠿⠿⣭⢿⣗⣟⣻⣭⣧⡄⠀⠀⠀⠀⠋⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣴⣿⣿⣿⣿⣿⣧⡀⠀⢿⣿⡿⠿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⡟⢉⢭⣅⣀⣤⣴⣘⣻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣶⣤⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡧⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⡇⣶⠎⠝⠛⠛⠋⠁⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠛⢰⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀
⢹⡇⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⠻⠿⣿⣿⠿⠿⠟⠙⠛⠋⠉⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⠫⠁⠉⠀⠄⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣻⣽⠞⢔⢈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣻⣿⣖⠈⠁⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠠⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⣟⡄⠅⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣷⠲⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠉⠩⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠛⡗⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⡻⠱⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠦⡬⣿⡜⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠠⢓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣽⣿⣿⣿⠄⠀⠀
[22A⣇⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⡀⡀⠀⣿⣏⢹⢻⡿⣿⣿⣿⣧⣾⡇⡇⣿⢸⣿⣷⢹⣧⠀⣿⣿⣿⣿⣿⠀⠈⠟⠈⢸⣿⣿⣿⡇⠈⣿⣿⣿⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿
⣿⣿⣶⣶⣆⣐⣿⡿⠛⢓⠘⠀⣶⣷⣿⣿⣿⢿⡇⣼⢸⣇⣶⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣸⣷⡖⠋⠉⠙⠛⠿⠀⠀⠀⠀⣸⣿⣿⣿⣧⣤⣿⣿⣿⠀⣿⣿⣿⣯⡅⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⠿⠷⠴⠖⠛⠒⠛⠛⣋⣉⣉⢹⣿⣿⡎⠁⢻⣿⣿⣟⣿⣿⣽⣽⡆⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠟⠇⠀⠀⠀⠀⢀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣀⣀⣀⡀⠀⠀⣀⣀⡀⣘⡇⠀⣿⣿⣿⡜⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠿⠿⠛⢇⡀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠈⠉⠉⠉⣿⣿⣿⣿⣿⠀⠐⠚⠒⠂⠀⣴⣶⡄⡤⠼⠿⠛⣿⣿⠟⠋⠟⠻⢟⣟⣫⠍⣩
⣿⣿⣷⢿⣿⣷⣶⣶⣯⣿⣿⣷⣶⣶⣿⣿⣿⠷⣿⣿⣧⢀⣐⣶⣛⣛⣿⣭⣭⣽⡇⠀⠀⠀⣸⣿⣄⣤⣼⣶⣦⣤⠂⠀⠐⠀⠀⠉⠉⠉⣹⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⡇⢸⣿⣿⣿⠏⢳⣤⣀⠀⣼⣼⣷⣿⡤⣭
⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⢋⠉⠉⣿⣿⣿⣿⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢹⣿⣿⣿⣧⣤⣬⠁⠀⠀⠠⠤⣤⠘⢟⣋⣧⣽⣿⣿⣾⣧⣄⠀⠀⠘⠻⡏⣰⢸⣟⣿⣿⣤⣼⣿⣿⣣⣬⣿⣿⡿⣿⣉
⠸⣿⣿⡆⣀⣀⣀⣶⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⡿⠁⠀⣶⣶⣶⣶⣶⣶⣿⡛⠻⠉⠈⠛⠀⠀⠀⠀⠀⠉⠀⢿⣿⣿⣻⣿⣿⡿⠿⣿⣤⣶⣖⢲⣉⣿⠸⠿⠟⡛⣛⣹⣿⣿⢿⡿⠗⠆⠀⢿⡿
⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⡇⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⡿⡇⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⣶⣿⣿⢿⣿⣿⣿⣿⣿⡟⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻
⣷⣸⣿⣿⡿⠿⠿⣛⣛⠻⢿⡏⣉⣀⣤⡤⠤⠒⢺⢻⣿⣷⢹⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢠⠂⠀⠃⠀⠀⢀⣷⣶⡄⠀⠀⠀⢀⣿⣿⣿⣧⣽⡍⠰⣸⣿⣿⣿⣿⣿⠇⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠉⠉⣿⣿⣯⣭⣭⡤⠄⠒⣻⣏⣩⣥⡤⡆⠀⠉⠉⠺⠟⢿⣾⣿⡟⠀⠀⢰⣷⣿⡛⠛⠛⠛⠛⠃⠈⠂⠀⠁⠂⣠⣿⣿⣿⢁⡀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡽⠟⠉⣻⣿⣿⣿⣤⣶⣿⣶⣤⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀
⣶⣶⣿⣿⣿⣿⣿⠿⠿⢿⡭⣿⣺⣛⣯⣽⣄⠀⠀⠀⠀⠘⠉⠙⠁⠀⢠⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⡆⠀⠀⣸⣿⣿⣿⣿⣿⡷⡆⠀⠻⠿⠟⢙⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⠋⢩⣭⣀⣠⣤⣆⣹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⡥⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣡⣤⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⡶⡮⠽⠛⠛⠋⠉⠸⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠙⠆⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀
⡃⣿⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠛⠍⠌⠊⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢿⣻⣽⣏⢜⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠠⣢⢁⡀⡀⠀⠀⠀⠀⠀⣿⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⡯⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣻⣽⣿⣻⢝⣃⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣟⣭⢷⠯⡾⠄⠂⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢉⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣓⣿⡷⠹⠰⡍⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢏⠯⢁⢎⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣐⣶⣔⡖⠀⠀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠃⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣴⣿⣿⣾⡍⠀⠀
[22A⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢸⣿⠹⡾⣿⣿⣿⣿⣿⣶⣿⣸⢸⡇⣿⣿⡘⣿⡀⢸⣿⣿⣿⣿⡇⠀⢹⠃⢹⣿⣿⣿⡏⠀⣻⣿⣿⡇⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸
⣿⣿⣷⣶⣶⣀⣺⣿⠿⠛⡢⠃⢰⣾⣾⣿⣿⡿⣿⢰⡇⣿⣰⣾⣿⣿⣿⣿⣿⣿⡇⢻⣿⣟⣯⠖⠈⠉⠙⠻⢿⡇⠀⠀⠀⢈⣿⣿⣿⣿⣤⣾⣿⣿⡇⢼⣿⣿⣿⣥⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⠿⠿⠿⠤⠶⠾⠓⠚⠛⢛⣋⣉⡉⣿⣿⣧⠉⠙⣿⣿⣿⣻⣿⣿⣿⣷⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⠛⠀⡀⡠⠀⠀⣐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣀⣀⣀⡀⠀⢀⣀⣐⢈⣻⠀⢸⣿⣿⣧⢻⣿⣿⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠸⠿⠟⣀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠄⠀⠉⠁⠉⢹⣿⣿⣿⣿⡇⠠⠘⠓⠂⠀⢠⣶⣦⣀⠤⠿⠟⢻⣿⡿⠛⠹⠛⠿⣿⣛⡭⢉
⢻⣿⣿⡾⣿⣿⣶⣶⣿⣽⣿⣷⣶⣶⣾⣿⣿⡿⢾⣿⣿⡀⣀⣶⣾⣛⣻⣿⣭⣭⠟⠀⠀⠀⣿⣧⣠⣤⣾⣶⣤⡖⠀⠀⠀⠀⠂⠀⠉⠉⢉⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣷⢰⣿⣿⣿⡞⠻⣦⣀⡀⢠⣦⣿⣿⣧⢬
⣸⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⡛⠋⠉⢹⣿⣾⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⢿⣿⣿⣿⣦⣤⡎⠀⠀⠈⠡⠤⣤⠀⠻⣛⣛⣯⣿⣿⣷⣿⣤⠀⠀⠀⠛⢿⣁⡎⣿⣿⣿⣧⣤⣿⣿⣟⣬⣽⣿⣿⢿⡏
⡀⢿⣿⣷⢀⣀⣀⣰⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⠟⠀⠀⣶⣶⣶⣶⣶⣾⣿⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⣼⣿⣟⣻⣿⣿⣿⡿⢿⣧⣴⣆⠲⡋⡹⡇⠿⠿⢛⣛⣋⣿⣿⡿⣿⠿⠶⠀⠘⣿
⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠴⢿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⢦⣶⣿⣿⣿⣿⣿⣷⣷⣿⣿⣟⣛⣛
⣿⣆⣿⣿⣿⠿⠿⢿⣛⡛⢿⣯⢉⣉⣠⣤⠤⠄⠚⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⡇⢃⠊⠀⡀⠀⠀⣸⣿⣶⠀⠀⠀⠀⣸⣿⣿⣿⣿⣼⣏⠥⢰⣿⣿⣿⣿⣿⡧⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⢹⣿⣿⣭⣫⣥⠤⠜⣚⣿⢉⣭⣤⢴⠀⠈⠉⠃⢿⢻⣿⣿⣿⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠃⢘⠀⠀⠀⢁⣴⣿⣿⣿⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⠿⠋⢛⣿⣿⣿⣧⣴⣿⣶⣦⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀
⣶⣶⣾⣿⣿⣿⣿⡿⠿⠿⣯⢿⣷⣟⣿⣽⣧⠀⠀⠀⠀⠈⠋⠙⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⣸⣿⣿⣿⣿⣿⡿⠁⡄⠙⣿⣿⡿⢿⣿⣿⣷⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀
⣿⣿⡏⠉⣭⣅⣀⣤⣴⣘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⣾⣴⣈⠉⣿⣟⣳⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣾⠿⠟⠛⠛⠉⠉⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⠷⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣸⡇⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠙⠹⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢭⠟⣬⣅⠡⠉⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣠⣴⡡⠂⠐⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣇⢺⣛⣟⣇⣀⡐⣠⠀⠀⣿⣿⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡳⣉⡔⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠗⣡⡆⠔⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣿⣿⡟⡨⣊⡀⠈⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⡭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⡿⣻⣝⡻⡥⠔⠐⡢⠀⠀⢲⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⡿⡷⣽⠐⠹⣽⠀⠊⠀⠁⠁⠀⠈⠋⠀⠀⠀⠀⠀⢠⣠⣤⠠⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢿⣂⠫⠅⠈⠐⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣬⣿⣷⢭⠀⠀⠀
[22A⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠟⣇⣿⣼⣿⣿⣿⣿⣿⣷⣿⣷⢸⣿⣿⣿⡆⠀⣿⣿⣿⣿⡇⠀⠘⠏⠀⣿⣿⣿⣿⠉⢹⣿⣿⣿⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣿⣿⣿⣶⣶⣄⣰⣶⡿⠿⠦⠜⠀⣦⣶⣿⣿⣿⣿⡆⢼⢸⡇⣾⣿⣿⠿⣿⣿⣿⣿⢸⣿⣯⠟⠁⠀⠉⠙⠻⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣤⣼⣿⣿⡿⢸⣿⣿⣿⣭⡍⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾
⣿⣿⣿⣿⣿⣿⠿⠷⠦⠤⠬⠾⠒⠛⠛⣛⣋⡉⢹⣿⣿⠈⠁⠻⣿⣿⣿⣿⣿⣿⣿⠈⣿⡟⠀⠀⠀⠀⠀⠀⠘⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣿⣿⠿⠰⠀⠐⠀⠀⢀⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⡀⢀⣀⣀⠀⠀⣀⣀⠀⡚⡆⠈⣿⣿⣿⣼⣿⣿⡆⠀⢹⣽⣿⣿⣿⣿⡹⣿⡄⠿⢇⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠙⠛⠈⢹⣿⣿⣿⣿⣿⠀⠤⠝⠙⠀⠀⣴⣤⣀⣀⢼⠿⠿⣿⣿⡿⠛⠟⢻⠿⠿⢛⡋
⠘⣿⣿⣧⢿⣿⣧⣶⡾⣭⣿⣿⣦⣶⣖⣿⣿⣿⡷⣿⣿⡇⣀⡸⠿⣿⣛⣛⣿⡯⠉⠁⠀⢸⣿⣤⣶⡾⠿⠶⡾⠁⠁⠀⠠⠀⠒⠀⠀⠉⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⣶⣾⣿⣷⠻⢧⣈⡀⠀⣀⣸⣿⣿⣀
⣅⣿⣿⣿⣾⠿⠿⠿⠿⠿⠛⠛⢛⠋⠉⣿⣷⣾⣷⣿⣿⣷⢹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⢿⣿⣿⣷⢶⣶⠀⠀⠀⠀⠣⠤⢤⡀⠺⢟⣛⣫⣽⣿⣿⣾⣦⡀⠀⠀⠘⢿⡟⡂⣿⣿⣿⣿⣠⣸⣿⣾⣢⣽⣿⣿⣿⡿
⣉⠸⣿⣿⡄⢀⣀⡀⣶⣿⣿⣤⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠏⠀⠀⣶⣶⣶⣶⣶⣶⣿⠉⠁⡀⠈⠀⠀⠀⠀⠀⠈⠙⢳⣿⣟⣻⣿⣿⣿⣿⣿⢿⣷⣤⣶⠐⡞⢻⣇⢸⠿⠿⢛⣚⣻⣿⣿⣿⡿⠧⠌⠀⣻
⣿⡄⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠘⢧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢽⢶⣿⡿⣿⣿⣿⣿⣿⣿⢶⣴⣾⣿⣿⣿⣻⣿⣾⣷⣾⣶⣒⣒
⣿⣧⣹⣿⣿⡿⠿⠿⣿⣛⡛⣿⡉⣉⣁⣠⡤⠤⢽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣇⠀⢈⠀⠀⠀⣼⣶⡦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⣟⡫⠄⣿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠙⣿⣿⣯⣍⣩⡤⠤⠒⣻⡏⣉⣥⡴⡂⠀⠉⠙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢹⠀⠀⠀⢀⣼⣿⣿⣇⡤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢻⠛⠹⣻⣿⣿⣧⣴⣶⣦⣤⣼⣿⣿⣿⣿⣿⡿⠟⠋⠉
⣴⣶⣦⣿⣿⣿⣿⣿⠿⠿⣭⡽⣷⣿⣛⣿⣧⡄⠀⠀⠀⠉⠛⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⢀⣼⣿⣿⣿⣿⣿⡻⠀⠎⣹⣿⣿⣿⢿⣿⣿⣧⡜⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀
⣿⣿⣿⠉⣩⣭⣀⣀⣤⡔⣹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠢⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⢲⣿⣿⣿⣿⣿⣿⣿⡟⣺⣾⡟⠛⠿⢿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⡾⠯⠛⠛⠋⠁⠹⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠯⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣋⣿⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠉⠡⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⢿⣟⣿⡏⠋⠂⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣏⠩⢁⠁⠠⠂⠀⠀⠀⠀⠀⢸⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⢫⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡧⢑⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⠉⠩⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⡨⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⡏⡒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠨⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢔⣭⣓⡉⠀⠀⠀
[22A⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢻⢸⣧⣿⣿⣿⡿⠿⣿⣿⣿⠈⣿⣿⣻⣿⠀⢿⣿⣿⣿⣿⠀⠀⢻⠀⢸⣿⣿⣿⡏⠉⣿⣿⣿⠀⣿⣿⣿⡇⡠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣷⣶⣴⣆⣀⣶⣿⠿⠧⠬⠁⣰⣶⣿⣿⣷⢾⡇⠸⡸⣧⣿⣿⣿⣿⣿⣿⢹⢿⡄⣿⡿⠈⠉⠀⠉⠙⢿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣇⣠⣿⣿⣿⠀⣿⣿⣿⣇⡉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤
⢻⣿⣿⣿⣿⣿⣿⡿⠷⠤⠤⠵⠶⠟⠛⠛⠛⠋⠙⣿⣯⡇⠉⠉⣿⣿⣿⣿⣿⣺⣻⡇⣿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡿⠃⠄⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⡆⠀⣀⣀⡀⠀⢀⣀⠀⠀⠣⠀⢿⣿⣿⡇⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣽⡇⠹⢀⠀⠀⠀⣀⠀⠀⢀⣿⣿⣿⢃⠈⠙⠛⠋⠋⣿⣿⣿⣿⣿⠀⠠⠭⠍⠀⠀⣠⣤⡀⣀⣠⡿⠿⣿⣿⡿⠟⠻⠟⡿⠿⢟⡛
⠀⢿⣿⣷⣽⣿⣷⣶⣶⢯⣽⣿⣧⣤⣶⣸⣿⣿⣷⢿⣿⣿⠀⡀⠿⠿⢿⣛⣛⡛⠋⠁⠀⣿⣷⣴⣶⠟⠛⠾⠏⠁⠉⠉⠄⠠⠀⠀⠀⠀⠉⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡅⣰⣶⣶⣷⡝⠿⣀⠀⠀⢀⢲⣿⣽⣇
⣭⣸⣿⣿⣷⡿⠿⠿⠿⠾⠟⠛⠛⠛⠉⣹⣿⣶⣶⣼⣿⣿⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣶⢾⡇⠀⠀⠀⠀⠶⣄⣀⡀⠰⠶⣛⣋⣭⣿⣿⣶⣆⡀⠀⠀⠨⢿⡏⢡⢸⡿⣿⣿⣄⣠⣿⣿⣆⣉⣿⣿⡿⣷
⣉⡀⣿⣿⣇⠀⢀⡀⢰⣶⣶⣦⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⠏⠀⠀⣶⣶⣶⣶⣶⣶⣷⠉⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣀⣤⡠⢄⠓⣿⢸⣿⠿⠿⡻⢻⣿⣿⣿⢿⡯⡍⠁⢻
⣿⣇⢹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠻⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⣿⣯⣿⣿⣿⣯⡵⣾⣿⣿⣿⣿⣿⣿⣾⡶⣠⣤⣷⣿⣿⣿⣿⣾⣵⣶⣶⡶⠖
⣿⣿⣘⣿⣿⣿⠿⠿⠿⣟⣛⢻⡏⢉⣉⣀⣨⠤⠤⢘⢻⣿⣷⢹⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⢈⠀⠀⢀⣷⣶⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⣟⡋⡅⣼⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⠉⢿⣿⣧⣭⣉⡥⠤⢔⢺⣯⢉⣉⣥⡆⠀⠈⠉⠸⣿⣿⣾⣿⣿⣷⣤⡀⠛⠛⠛⠛⠛⠛⠋⠇⠀⠀⠈⢠⣾⣿⣿⣣⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢰⡿⠛⢛⣿⣿⣿⣀⣤⣶⣬⣈⣿⣿⣿⣿⣿⣿⠿⠛⠋
⣤⣶⣶⣼⣿⣿⣿⣿⡿⠷⢯⡭⣿⢸⣟⣓⣿⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢰⡀⠀⢀⣿⣿⣿⣿⣿⣿⠃⢀⠊⣹⣿⣿⣿⠿⣿⣿⣧⡴⢲⣶⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀
⣿⣿⣿⡋⠉⣭⢁⣀⣤⣤⢘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢘⡤⣴⣿⣿⣿⣿⣿⣿⣿⡗⣪⣾⡿⠛⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣧⡴⠏⠟⠛⠉⠉⠸⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠉⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣇⣿⠀⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠡⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢍⠀⠓⠨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⠋⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⡂⡉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢆⠀⡗⡐⠀⡡⠂⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠁⠀⠀⠀
[22A⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⡆⣿⣼⣾⣿⣿⠉⢻⠹⢸⡇⣿⣿⠉⢿⠅⢸⣿⣿⣿⣿⡇⠀⠿⠇⠁⣿⣿⣿⣿⠛⢻⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⢹⣿⣿⣶⣦⣶⣀⣰⣾⡿⠿⠤⠏⠠⣶⣾⣿⣷⡶⣿⠀⡇⣿⠨⣿⣿⣿⣿⣿⡆⣾⡇⢸⣿⠇⠉⠁⠈⠛⢿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣀⣸⣿⣿⡇⢸⣿⣿⣿⣘⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀
⡘⣿⣿⣿⣿⣿⣿⣿⠿⠦⠤⠬⠶⠼⠛⠛⠛⠛⠋⣿⣿⣧⠉⠉⣭⣿⣿⣿⣿⣟⣟⣇⢸⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⠟⠀⠀⠀⠀⠀⠨⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣷⠀⠀⣀⡀⠀⠀⣀⡀⠀⠠⠄⢸⣿⣿⣧⢹⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⠀⣀⠀⠀⠀⣀⡀⠀⣠⣿⣿⣿⡏⡈⠉⠛⠋⠛⢻⣿⣿⣿⣿⡇⢀⡘⠿⠍⠀⢀⣤⡀⠀⢀⣿⣿⣿⣿⣿⢿⢻⡿⣿⣿⡿⠟
⠤⢸⣿⣿⣮⣿⣿⣶⣶⣾⣽⣿⣾⣤⣴⣞⣿⣿⣿⣾⣿⣿⡀⠀⠼⠿⠿⠿⣚⣛⡓⠋⠀⣿⣦⣴⣶⠟⠛⠾⠟⠛⠉⠉⠁⠀⠀⠀⠀⠒⠚⠛⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⡏⢩⣥⣶⣶⡼⢿⡉⠀⠈⠀⠄⣶⣲⡏
⣿⣅⣿⣿⣿⣿⠿⠿⠿⠷⠿⠛⠛⠛⠋⢩⣿⣷⣶⣦⣿⣿⡇⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢹⣿⣿⣿⣷⣶⡇⠀⠀⠀⠠⣴⣤⣄⡀⠰⣶⠖⠶⣛⣿⣿⣧⣦⡀⠀⠀⠀⢿⣿⠧⢸⣿⣿⣿⡇⡀⣿⣯⡧⢘⣻⣿⣿⣿
⣉⡁⢹⣿⣿⠀⢀⣀⢰⣶⣶⣶⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⠏⠀⣶⣶⣶⣶⣶⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⡄⢤⠿⣿⠀⣿⣿⡿⠯⠿⣿⣿⣿⣿⣿⣋⠉⠸
⣿⣿⠘⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢻⣿⣿⢸⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠸⡆⠀⠀⠀⡀⠀⠀⠀⠀⠁⢢⣽⣏⣿⣿⣿⣟⣭⣴⣿⣿⣿⣷⣾⣶⣿⣧⣅⣀⣴⣿⣾⠿⢿⣯⣯⣤⣤⡤⠤
⣿⣿⣇⣿⣿⣿⡿⠿⠿⣿⣛⣛⣿⠉⣉⣁⣀⠥⠤⠔⣸⣿⣿⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢈⠀⠀⢀⣷⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣿⠟⣋⢰⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠉⠉⢹⣿⣿⣬⣉⣡⠤⠔⠚⣿⢉⣉⣡⠄⠀⠀⠉⠋⣿⢿⣶⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠋⣿⠐⠀⠀⢀⣼⣿⣿⣃⣄⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡇⢰⡿⠛⢟⣿⣿⣿⣁⣤⣭⣉⡉⣿⣿⣿⣿⣿⣿⣿⠿⠟
⣤⣶⣶⣼⣿⣿⣿⣿⣿⠿⠯⣍⣿⣦⣿⣛⣾⣄⠀⠀⠀⠀⠘⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢠⣿⣿⣿⣿⣿⣿⠇⠀⠈⣹⣿⣿⣿⣿⣿⣿⣶⣴⢲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀
⣿⣿⣿⡟⠉⠩⡅⢀⣠⣤⢈⣻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣤⣴⣿⣿⣿⣿⣿⣿⣿⡷⢎⣴⡿⠿⢿⣿⠯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣧⡶⠂⠙⠛⠊⠉⠈⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣿⣟⢸⡇⠀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠀⠀⠀⠈⠉⢍⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠈⢻⣿⡏⠩⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠟⠁⠀⠀⠀⠀⠀⠸⣿⠐⠐⢀⠂⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⡆⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢔⡐⠄⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠑⠁⠠⠂⢅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠌⠡⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⡇⣿⢰⣿⣿⣿⣏⣿⡆⣾⡇⢸⣿⡟⢿⠃⠸⣿⣿⣿⣿⡇⠃⠻⡏⠁⣿⣿⣿⣿⠛⢻⣿⣿⡇⢸⣿⣿⣿⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣶⣦⣶⣄⣰⣶⡷⠿⠤⠝⠀⣦⣾⣿⣷⣶⣿⠀⢃⢿⡌⣽⣿⣿⣿⣿⣇⡟⣧⢸⣿⡇⠛⠃⠀⠛⢿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣀⣸⣿⣿⡇⢸⣿⣿⣿⠨⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀
⣀⣿⣿⣿⣿⣿⣿⣿⠿⠧⠤⠬⠶⠼⠟⠛⠛⠛⠛⢻⣷⣼⠘⠁⣭⣿⣿⣿⣿⣿⣗⣿⢸⡏⠀⠀⠀⠀⠀⠀⠹⣿⣧⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⠿⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢹⣿⣿⠀⠀⣀⣀⠀⠀⣀⡀⠀⢂⡄⠸⣿⣿⣿⢸⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠈⠉⠛⠏⠛⢻⣿⣿⣿⣿⡇⢀⣘⡿⠋⠀⠀⣄⡀⠀⠀⣼⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⠿
⠠⠸⣿⣿⣦⣿⣿⣷⣶⡾⣭⣿⣿⣤⣴⡆⣿⣿⣿⣾⣿⣿⡆⠀⠨⠿⠿⠿⣞⣛⣛⠟⠀⢸⣦⣀⣴⡾⠿⠿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠚⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣟⢩⣭⣭⣶⣼⢿⡋⠀⠀⠀⠉⣶⣖⡟
⣿⣅⣿⣿⣿⣾⠿⠿⠿⠷⠿⠛⠛⠛⠛⢉⣿⣷⣶⣦⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠸⣿⣿⣿⣷⣶⣶⠀⠀⠀⢠⣴⣦⣀⡀⠠⣶⠶⠶⣟⣻⣿⣧⣤⠀⠀⠀⠀⣿⣿⠷⠸⣿⣿⣿⡇⠀⣾⣧⣦⠘⢳⣿⣿⣿
⣉⣁⢸⣿⣿⡀⢀⣀⠀⣶⣶⣷⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⡿⠁⣶⣶⣶⣶⣶⣿⣿⠙⠋⠁⠈⠀⠀⠀⠀⠈⠛⢷⡟⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡄⢀⠽⢶⠆⣿⣿⣿⡯⡿⣿⣿⣿⣿⣿⣛⠋⠸
⣿⣿⡀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢾⣿⣿⢸⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣽⣏⣿⣿⣿⣟⣫⣵⣿⣿⣿⣷⣾⣶⣾⡧⣉⣀⣴⣶⣶⣿⣿⣯⣗⣭⣤⣤⣤
⣿⣿⣇⣻⣿⣿⡿⠿⠿⣿⣛⣛⣿⠉⣉⣁⣀⡡⠤⠄⡺⣿⣿⡘⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⡿⣇⠀⠈⠀⠀⠀⣥⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣳⠟⣛⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠛⠉⠉⢹⣿⣿⣬⣍⣡⠤⠤⠒⣿⠉⣉⣩⢄⠀⠀⠉⠁⣿⢿⣧⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢹⡆⠀⠁⢂⣰⣿⣿⣇⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠰⣾⠻⣿⣿⣿⣿⠁⣈⣭⣉⡉⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣤⣶⣶⣶⣿⣿⣿⣿⡿⠿⠿⣭⢿⡧⣿⣛⣺⣄⠀⠀⠀⠀⠘⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⣿⣿⣿⣿⣷⠦⠀⠈⣻⣿⣿⣿⣿⣿⣿⣷⣬⢷⣴⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀
⣿⣿⣿⣟⠉⢩⣅⣀⣠⣤⢈⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣥⣴⣿⣿⣿⣿⣿⣿⣿⡷⢔⣴⣿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⡿⢶⠮⠝⠛⠛⠉⠁⠿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣸⡇⠀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⣉⡉⠉⠉⠀⠀⠈⠙⢋⣉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠦⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠿⠿⠋⠑⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠈⢻⣿⣋⡛⡀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⠗⠈⣐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⡀⡈⠀⠄⡀⠠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡊⡀⠊⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠨⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠇⣿⣠⣷⣿⣿⣿⣿⡇⡗⡇⢸⣿⡟⣿⠇⠀⣿⣿⣿⣿⡇⠀⠸⡟⠁⣿⣿⣿⣿⠛⢻⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠘⣿⣿⣶⣦⣴⣄⣀⣶⡿⠿⠦⠸⠀⣤⣦⣿⣷⣶⣿⡄⢸⢹⡏⣭⣿⣿⣿⣿⣿⣇⣿⢸⣿⣟⠛⠃⠀⠛⢿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡀⣸⣿⣿⡇⢸⣿⣿⣿⠐⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀
⣄⣿⣿⣿⣿⣿⣿⣿⡿⠧⠤⠬⠶⠴⠿⠛⠛⠛⠛⢹⣷⣼⠘⠃⣿⣿⣿⣿⣿⣿⣿⣿⠘⡿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢻⣿⣿⡿⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡀⠀⠀⢀⠀⠀⢀⣀⠀⠀⡄⠠⣿⣿⣿⢸⣿⣿⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠉⠉⠻⠿⠙⢻⣿⣿⣿⣿⡇⠀⢈⣻⡛⠀⠀⣀⡀⠀⠀⢰⣾⣿⣿⣿⣿⠿⣿⢿⣿⣿⡿
⣠⠈⣿⣿⣧⢿⣿⣧⣦⡾⣭⣿⣿⣤⣤⡆⣿⣿⣿⣾⣿⣿⡇⠀⢠⠭⠿⠿⢿⣚⣛⡻⠂⢀⣷⡄⣠⣴⡷⢶⢶⠿⠉⠋⢁⠁⠀⠀⠀⠀⠘⠛⢻⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣟⢈⣭⣭⣥⣸⣿⡏⠀⠀⠀⠈⢽⣦⣴
⣿⣥⣻⣿⣿⣾⡿⠿⠿⠿⠿⠟⠛⠛⠛⢋⣽⣿⣶⣦⣿⣿⡇⢿⣷⣿⣿⣿⣿⡟⠉⠀⠀⠀⣿⣿⣿⣷⣤⣴⡄⠀⠀⢠⣤⣄⣀⠀⠠⣶⡴⠶⢞⣻⣿⣧⣤⠀⠀⠀⠀⣾⣿⠛⠘⣿⣿⣿⡏⠈⣸⣶⣆⠐⢷⣿⣿⣿
⣉⣁⠸⣿⣿⡄⠀⣀⡀⣶⣶⣶⣤⣶⣷⣾⣿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⡿⠋⣶⣶⣶⣶⣶⣷⣿⠙⠛⠋⠉⠁⠀⠀⠀⠈⠳⢾⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⡀⢀⠹⢴⠇⣿⣾⣿⡿⡿⣿⣿⣿⣿⣿⣛⠛⠹
⣿⣿⡄⣿⣿⣯⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⢸⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣸⣏⣿⣿⣿⡿⣋⣭⣾⣿⣿⣷⣾⣶⣮⣧⡉⣉⣤⣴⣶⣿⣿⣏⣯⣋⣭⣀⣄
⣿⣿⣧⣹⣿⣿⡿⠿⠿⢿⣛⣛⣿⠉⢉⣉⣀⡩⠥⠤⡎⣿⣿⡆⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⣇⠄⠈⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣿⠾⢛⢸⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣶
⠛⠉⠉⠹⣿⣿⣮⣍⣩⠤⠤⠒⢻⡉⣉⣉⡔⠀⠐⠈⠁⣿⢿⣧⣿⣿⠃⠀⠀⠛⠛⠛⠛⠛⠛⠃⢸⡆⠄⠁⠀⣠⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡷⠨⣾⠿⡿⣿⣿⣿⠃⢈⣍⣙⠋⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣤⣶⣶⣶⣿⣿⣿⣿⣿⠿⠾⣭⣽⡇⣿⣛⣺⣆⠀⠀⠀⠈⠘⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⣿⣿⣿⣿⣿⣵⠀⢈⣿⣿⣿⣿⣿⣿⣿⣷⣌⢭⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀
⣿⣿⣿⣟⠉⢩⠅⢀⣀⣤⡄⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⣤⣾⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⠿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⢿⣿⠶⠄⠘⠉⠚⠋⠁⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣸⡇⠀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣛⣛⠛⠛⠛⠉⠉⠉⠉⠛⢛⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣠⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢅⠀⠈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⡁⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢧⢿⣦⣿⣿⣿⣿⣿⣷⣇⣷⢸⣿⣿⣿⡟⠀⣿⣿⣿⣿⡇⠈⠹⡿⠻⣿⣿⣿⣷⠖⢻⣿⣿⣿⠀⣿⣿⣿⡇⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠈⣿⣿⣷⣦⣤⣄⠀⣶⣾⠾⠧⠨⠁⣤⣦⣶⣶⣶⣿⡇⢸⢸⡏⣭⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡻⠓⠀⠿⢿⣿⣿⣿⠀⠀⠁⠀⣿⣿⣿⣿⡀⢐⣿⣿⣿⢀⣿⣿⣿⡇⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀
⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⠬⠷⠤⠿⠿⠟⠛⠛⢺⣷⣾⠘⠃⢿⣿⣿⣿⣿⣿⣻⣿⠀⣿⠏⠀⠀⠀⠀⠀⠙⢿⣿⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⣿⣿⠅⠀⠀⠀⠀⠘⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⡂⠀⣿⣿⣿⣸⣿⣿⡇⠀⠘⣻⣿⣿⣿⣿⢹⣻⡀⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠛⠻⠿⠻⠿⣿⣿⣿⣿⡿⠀⠀⣿⣛⠀⠀⣄⡠⠀⠀⢰⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿
⠐⡀⣿⣿⣧⣼⣿⣷⣦⣤⣯⣿⣷⣧⣥⣤⣿⣿⣿⣧⣿⣿⡇⠀⢨⣬⡽⠿⠿⢿⣖⡻⠃⠀⣶⣄⢀⣤⣶⣶⣶⡾⠛⠛⠋⡉⠀⠀⠀⠀⠐⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⠐⣊⣩⣭⣽⣿⡟⠈⠀⠁⠈⢩⡭⣴
⣷⣧⣹⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠛⣿⣿⣿⣦⣿⣿⣧⢹⣿⣾⣿⣿⣿⡿⠋⠀⠀⠀⣿⣿⣿⣿⣦⣤⡄⠀⠀⠠⣤⣀⠀⠀⠀⣤⡴⠤⠚⣿⣿⣧⣤⠀⠀⠀⠀⢸⣿⠿⡀⣿⣿⣿⡟⠈⣹⣶⣢⠀⢦⣾⣿⣿
⣉⣉⠙⣿⣿⡆⠀⢀⠀⣶⣶⣶⣄⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠋⣶⣶⣶⣶⣶⣿⣿⠟⡻⠛⠉⠃⠀⠀⠀⠈⠳⢿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⢀⡹⢰⡇⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⠛⠹
⣿⣿⡆⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠘⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⣟⣿⣿⣿⡿⣛⣩⣿⣿⣿⣷⣤⣦⣮⣧⡉⢉⣡⣰⣴⣿⣿⣟⣯⣋⣁⣀⣀
⣿⣿⣷⢸⣿⣿⣿⡿⠿⠿⣿⣛⣻⠛⠉⣉⣉⣉⠩⠤⠆⣿⣿⡇⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡏⢇⠀⠈⠆⠀⠀⠀⣄⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇⣿⠾⢟⢹⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶
⠛⠛⠉⠉⣿⣿⣧⣍⣉⠡⠤⠴⢻⡏⣉⣉⡽⠀⠐⠒⠡⣿⣿⣧⣿⡟⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⢸⡆⠄⠂⠄⢀⣼⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠩⣼⠿⡿⣿⣿⣿⠃⢈⣉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣤⣴⣶⣦⣿⣿⣿⣿⣿⡿⠶⣭⣹⡇⠿⣟⣛⣆⠀⠀⠀⠈⠙⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⣿⣿⣿⣿⣿⣧⡆⠀⠻⢿⣿⠟⢻⣿⣿⣿⣄⡥⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀
⣿⣿⣿⣿⠋⠉⡍⢁⣀⣠⡄⣺⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⣀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠄⢀⣀⣤⣴⢿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⠜⠝⠛⠛⠋⠁⠿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣴⣶⣶⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣉⣏⠀⢀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⣜⠛⠛⠛⠛⠛⠋⠉⠉⠛⢿⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠿⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⡿⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠱⢄⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣁⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢷⢸⣇⣾⣿⣿⡿⢿⣿⣇⣿⢸⣿⣿⢿⣿⠀⣿⣿⣿⣿⣿⠈⠹⣿⠛⢸⣿⣿⣷⡶⠶⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀
⠀⣿⣿⣷⣦⣤⣄⠀⢤⣶⡶⡧⢀⠀⢤⣠⣶⣶⣶⣾⡇⢸⢸⡇⣿⣿⣿⣗⣶⣿⢻⣿⠈⣿⣿⠺⠟⠀⠻⢿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⣿⣿⣿⠀⣿⣿⣿⡇⠿⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀
⣆⢹⣿⣿⣿⣿⣿⣿⣿⣭⣀⣤⡵⠦⠿⠿⠿⠟⠛⢻⣷⣞⡜⠛⠛⣿⣿⣿⣿⣿⢸⣿⡀⣿⡟⠀⠀⠀⠀⠀⠈⢿⣿⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⣿⣿⠆⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⡘⣿⣽⡇⠀⢰⣿⣿⣿⣿⣿⣺⢹⡇⣿⠁⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠋⠛⠻⠿⠻⠿⣿⣿⣿⣿⣿⠀⠀⣻⣟⠁⠀⢀⡀⠀⠀⢰⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠄⡀⢿⣿⣧⣸⣿⣷⣤⣤⣞⣿⣶⣦⣤⣤⢿⣿⣿⣧⣿⣿⡇⠀⢘⣿⣿⠭⠿⠿⢷⡺⠃⠀⢰⣤⠀⣤⣴⣶⣴⣲⠟⠛⠛⠈⠀⠀⠀⠠⠴⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⠒⣂⣩⣭⣝⣿⡟⠊⠀⠃⢈⢩⡭⣴
⣯⣖⢸⣿⣿⣷⣿⣿⣿⡿⠼⠿⠿⠿⠛⠛⣻⣯⣿⣧⣹⣿⣿⢸⣷⣶⣾⣿⣿⡿⠋⠀⠀⠀⢾⣿⣿⣿⣦⣤⣬⠀⠀⠀⣀⣄⠀⠀⠀⣤⣤⢤⠺⣿⣿⣿⣤⠀⠀⠀⠀⢸⣿⡿⡀⣿⣿⣿⣿⠈⢹⣶⣢⡀⢶⣾⣿⣿
⢉⣉⠉⣿⣿⡇⠀⠀⠀⣰⣦⣶⣆⣶⣶⣶⣿⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿⡟⠋⣶⣶⣶⣶⣶⣾⣿⠛⠛⠛⠉⠛⠀⠀⠀⠈⠛⢿⣿⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⠀⡹⢴⡇⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⡿⠛⠙
⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡆⣿⣿⡟⠁⠀⣿⣿⣿⣿⣿⣿⡿⣇⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⣟⣩⣽⣿⣿⣿⣤⣧⣮⣧⡉⢉⣁⣰⣴⣿⣿⣿⣯⣋⣉⣁⣀
⣿⣿⣿⢸⣿⣿⣿⣿⡿⠿⢿⣟⣻⡛⠛⢉⣉⣉⣉⠡⠇⣿⣿⡇⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠸⠠⠈⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣯⢻⠾⠟⢛⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶
⠛⠛⠋⠉⣿⣿⣗⣀⣉⡉⠥⠤⢿⡟⢋⣉⣩⠀⠀⠒⠺⢻⣿⣧⣿⠏⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⡇⠀⠐⠠⠀⣰⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡭⣼⡿⡿⢿⣿⣿⠇⢈⣉⡛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣤⣤⣴⣦⣽⣿⣿⣾⣿⣷⡶⣾⣩⣧⠽⢿⣗⣧⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⣾⣿⣿⣿⣿⣯⡆⠀⠙⠿⣿⡿⠿⢿⣿⣿⣅⡭⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀
⣿⣿⣿⣿⠛⢋⣉⢉⣀⣠⡄⡹⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡆⠀⠀⠀⠀⠀⠀⢟⣡⣤⣾⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣰⡊⠺⠈⠛⠛⠃⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀
⣿⣿⡃⣿⠀⠀⣀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠉⠉⠛⠻⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⡋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⠃⢁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠐⠐⠀⢀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣄⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⢀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⢸⣇⣾⣿⣿⡿⢿⣿⣿⣿⠸⣿⣿⢿⣿⠀⣿⣿⣿⣿⣿⠈⠻⢿⠛⢸⣿⣿⣷⡶⠶⣿⣿⣿⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⢿⣿⣷⣶⣤⣤⠀⢤⡴⣶⣇⣀⠇⢠⣠⣶⣶⣶⣼⡇⠸⢸⣧⣿⣿⣿⣟⣶⣿⢸⣿⠀⣿⣿⢰⠟⠀⠙⠻⢿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⡇⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⣦⢸⣿⣿⣿⣿⣿⣿⣿⣭⣀⣀⣦⡦⠿⠿⠿⠿⠛⠻⣷⣆⡏⠛⠙⣿⣿⣿⣿⣿⢸⢺⡆⣿⣿⠆⠀⠀⠀⠀⠀⠘⢿⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⣿⣿⡿⠆⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣾⣷⣶⡆⣿⣽⡇⠀⢰⣾⣿⣿⣿⣿⣟⢹⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠛⠻⠿⠻⠿⣿⣿⣿⣿⣿⠀⠀⣻⣟⠃⠀⢀⡀⠀⠀⢰⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠄⡂⢻⣿⣿⣵⣿⣿⣥⣤⣞⣻⣷⣮⣤⣤⢸⣿⣿⣧⣿⣿⣧⠀⠈⣿⣿⡽⠿⠿⠿⡾⠃⠀⠀⣿⣆⣠⣴⠿⢷⣶⠟⠛⠛⠈⠀⠀⠀⠄⠤⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⠒⣂⣩⣭⣝⣿⡟⠀⠀⠁⠈⢩⡭⣴
⣷⣶⡸⣿⣿⣷⣿⣿⣿⣿⠾⠿⠿⠿⠛⠛⣻⣯⣽⣷⣸⣿⣿⢸⣷⣶⣶⣿⣿⠿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣤⣴⡆⠀⠀⠠⣄⠀⠀⠀⣤⣤⢤⠺⢿⣿⣿⣤⠀⠀⠀⠀⢸⣿⣿⡀⣿⣿⣿⣿⠈⢹⣶⣲⡀⢶⣾⣿⣿
⠛⢉⡉⣿⣿⣇⠀⠀⠀⢀⣤⣴⣆⣴⣶⣶⣿⣿⣿⣿⡿⣿⣿⣸⣿⣿⣿⡿⠁⣶⣶⣶⣶⣶⣶⡾⣟⠉⠟⠉⠉⠁⠀⠀⠀⠈⠻⢿⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⢀⡸⢷⡆⢿⣿⣿⣿⣻⣿⣯⣿⣾⣿⡟⡛⠋
⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡇⢹⡅⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣿⣿⣿⣟⣩⣽⣿⣿⣿⣤⣧⣮⣥⡈⢉⣁⣴⣶⣿⣿⣿⣹⣏⣉⣅⣀
⣿⣿⣿⠘⣿⣿⣿⣿⡿⠿⠿⢿⣛⡛⠛⠉⣉⣉⣉⡩⠽⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⡇⠈⡇⠐⠈⠆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠹⣿⡿⠿⡟⠻⠾⠛⠛⠿⢿⣿⠿⠻⠏⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣶
⠟⠛⠛⠉⣿⣿⣗⣒⣈⣉⠥⠤⢾⡗⢛⣉⣉⠀⠀⠒⠺⢹⡿⣿⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⢛⠀⠈⠀⠀⢀⣾⣿⣿⠀⠀⠀⢸⣿⠀⣿⣿⣿⣷⣸⡇⣿⡇⣿⣷⣿⣻⣷⠈⣉⡛⠋⢿⣿⣿⣿⣿⣿⣿⣿⡿
⣤⣤⣴⣦⣼⣿⣿⣿⣿⣿⣶⣾⣉⣷⠼⠿⣗⣣⠀⠀⠀⠀⢃⣠⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣴⣿⣿⣿⣿⣿⣵⠀⢸⣿⠀⣿⣿⣿⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢺⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀
⣿⣿⣿⣿⠛⠋⣉⠉⣀⣠⣄⢺⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣤⣤⣾⣿⣿⣿⣿⣿⣿⣧⡀⠸⠿⠶⠿⠿⠿⠏⠿⠇⠿⣷⡿⠛⢿⣾⠿⣰⣿⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣵⣔⠛⠿⠟⠛⠋⠹⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣛⣛⡛⢉⣐⡲⢶⣿⣓⠚⣙⡛⣗⣛⢓⣒⡾⢿⣳⠖⣚⣛⡛⠛⢛⣉⡛⢿⡟⠀⠀⠀⠀⠀
⣿⣿⣇⣿⠀⠀⢀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠘⣿⣿⢣⣿⣿⣿⣸⣿⣻⣷⢿⣷⣿⡏⣿⣿⣇⢸⣿⠀⣿⡟⣿⡧⣿⣿⠿⠀⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⢿⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠀⠇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠻⠿⠹⠿⠾⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠠⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣆⣤⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠼⠔⠠⠈⠠⠀⡁⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠄⠒⠄⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢉⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[22A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⢸⡙⠀⢻⡇⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠤⠼⣿⣿⣿⣿⣿⡿⠟⠒⣺⠒⢐⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⡇⠀⠀⡇⠀⢸⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⣶⣾⡟⢻⣿⣿⣿⠋⠉⣉⣩⡉⠉⢩⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣹⠟⠋⠁⠀⠀⠠⠤⠤⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠭⠭⠤⠤⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠾⣿⣯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠄⠐⢠⣤⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡿⠋⠁⠉⠛⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣿⣿⣶⡆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣧⣤⣤⣤⣤⣼⣿⣶⣌⣻
⣩⣭⠛⠛⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠄⠀⠀⢸⡿⠛⠿⠟⠋⠛⠛⠉⠉⠉⠀
⠿⠿⠂⠀⠀⢻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣶⠶⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⡄⣴⣿⢷⠀⠀⠸⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣄⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⡀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⣦⣤⣤⡀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣄⠀⠈⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⢀⢀⡀⡀⣰⣾⠀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⢿⣾⠿⠀⠀⣀⣿⣇⡀⠀⠀⠀⠀⠀⠀⢸
⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠶⣴⣾⣿⣿⣿⣿⣿⣿⠿⠀⠀⢀⣀⣠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡛⢃⣀⡀⢀⣀⣀⠀⣀⡀⣀⣀⢀⣀⡚⢛⣒⠶⣚⣛⡛⠛⢛⣛⡙⢿⣀⣤⣦⣤⣤⣀
⠀⠀⠙⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠋⠁⠀⠔⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣾⣧⣿⣟⠀⠀⠀⠀⠁⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠀⢀⠀⣿⣿⠸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⢀⣿⣿⣿⣿⣛⣻
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠈⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⣃⡻⠿⠟⣸⡿⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⢷⣶⣤⣀⣤⣠⠼⣤⠙⡻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢲⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣤⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣺⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡤⠉⠀⢹⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣷⣶⣶⣶⣬⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⡄⠀⠈⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⠟⠛⣭⣬⣭⣿⣿⠛⣻⠿⢿⣿⣿⣿⣿⡿⡿⣭⣷⣿⣿⡟⢛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⠦⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣦⣷⣒⠈⠉⣭⣿⣿⣿⣯⣹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[22A⣿⣿⣿⣟⣛⣉⣉⣙⣿⣿⣿⣏⣉⠉⠍⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⣭⡉⠁⢸⠟⠁⣿⢻⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣭⣭⡤⠿⠥⠤⣿⣿⠿⠤⡶⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⡇⠀⢸⡆⠀⢿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣷⣶⡖⢺⣿⡒⠚⢛⣟⣛⣋⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡂⠀⠹⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣍⣉⣉⡥⠤⠤⠬⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣋⣉⣉⡩⠭⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣴⣶⣶⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠄⢀⣀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠛⠉⠛⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⣾⣸⣿⣤⡄⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣅⣀⣀⣀⣀⣴⣶⣭⡛
⢟⣛⣛⠿⠿⠟⠛⠙⠛⠀⠀⠐⢾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⠿⣿⡿⠻⠿⠟⠛⠛⠋
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡂⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣤⡄⠀⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠀⠀⢻⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣴⣤⣄⣀⡀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀
⣿⣭⣥⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣠⣴⣶⡀⠀⠀⡀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠏⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⠄⠀⠀⠀⣤⡆⠀⠀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⢿⣾⠿⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣴⣷⣾⣿⣿⣧⡬⣴⣾⣿⣿⣿⣿⣿⣿⡏⠁⠁⠉⣀⡘⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡛⢋⣁⡀⢀⣀⣀⠀⣀⡀⣀⣀⢀⣀⡺⢟⣓⠶⣆⣒⡲⠶⢛⣛⡛⠲⡖⠀⣀⣀⣀⡀
⠈⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⡿⠛⠁⢀⠴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠀⣿⣿⠸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠀⣽⣿⣿⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⢿⣃⡻⠿⠟⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢳⣦⣤⣀⣀⡀⢭⣯⣉⠻⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠄⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣄⣀⡘⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣠⣤⣤⣶⣿⣿⠿⣿⣿⣿⣾⢷⣾⣧⡍⠋⠙⣿⣿⣿⣿⣷⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣯⣤⣤⣤⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⡉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠛⣛⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣷⣾⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⡀⣼⣿⣿⣿⣿⣷⣾⣥⣬⠭⠍⠛⠛⢿⣶⣿⣿⡿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
[22A⢺⣿⡿⣶⢖⡚⠛⠛⠛⢿⣿⣿⣟⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⣛⣋⡉⠁⢸⡿⠃⣿⡿⣤⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣙⣿⣟⣉⣉⣉⣛⣋⣀⣿⣿⡯⠤⣤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡇⠀⢸⡦⠀⣿⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⣤⢤⣤⣴⠤⠤⠤⢼⣿⠶⠖⠒⠟⠒⠒⢒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠄⠀⢼⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣴⣾⣿⣿⠒⠒⠒⣺⣿⣏⣉⣉⣉⣉⣉⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⣛⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣚⣛⣻⣿⣿⣯⣭⣭⣿⣿⣭⣤⣤⣤⣤⣤⣖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡉⠁⢀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⠿⠛⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡀⣶⢸⣿⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡋⠀⠀⠀⠀⢩⣭⣝
⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡿⠿⣿⡿⠿⠿
⣿⣿⣿⣧⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀
⠉⣉⣁⣤⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠁⠸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⣾⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣀⣠⣄⡀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀
⣔⣒⣒⣠⣤⣴⣿⣿⣿⣽⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⠖⠀⠀⠀⠀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⢿⣾⠿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣯⣿⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠏⠁⠀⠃⢀⣸⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡛⢋⣀⡀⢀⣀⣀⠀⣀⡀⣀⣀⢀⣀⡸⢟⣳⠶⣒⣃⡀⠤⢄⣈⡙⢷⣤⡄⠀⠀⠀⠀
⠛⠻⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠟⠋⢀⢤⣶⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⣟⣗⣶⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣬⡿⣿⣿⣿⡿⠋⠀⠀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣿⣿⠸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢙⣻⣿⣿⣿⣿
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢰⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⣃⠻⠿⠟⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⣦⣤⣀⠉⠉⢉⣛⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⣀⣀⣠⣀⣠⣤⣤⣀⣀⣀⣀⣀⠀⠀⠻⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣶⣿⣧⣶⣛⠻⠛⢿⣿⣿⣿⣿⣆⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⡗⢿⣿⣃⣀⣀⣸⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣭⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢈⠉⠙⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠉⠁⣰⣶⣿⣿⣿⣯⣝⣉⡛⣛⡿⠿⢿⣿⣭⣾⣿⣿⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠋⠀⣀⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣤⣶⣿⣿⣿⣶⣿⣿⣿
[22A⠾⢾⣿⣿⣶⡶⠶⠚⠓⠺⢿⣿⣿⡿⠛⠛⠛⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠛⠛⠛⠋⠸⣿⠛⢿⡿⣯⣽⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠒⠚⢿⣟⣛⣛⣋⣻⣏⣉⣽⣿⣿⣉⣩⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⡇⠀⢸⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣉⣉⣉⣩⣭⣭⡧⠤⠤⢤⣿⡥⠤⠶⠾⠶⠶⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠛⠇⠀⠀⡇⠀⢸⡅⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠤⠤⢤⣴⣿⣿⡗⠒⠒⢺⣿⡗⠒⠒⣋⣉⣉⣙⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠿⠿⠟⠛⠛⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠶⣿⣿⣿⣿⣟⣋⣉⣿⣿⣋⣉⣉⣩⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡂⠀⠉⠉⠉⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⣬⣴⣿⡂⡀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡟⠁⠀⠀⠈⢙⣛
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣟⠛⣿⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣶⣶⣶⣶⣾⣿
⣶⣶⣶⣿⣇⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠙⠉⠈⠉⠁⠀
⠉⠉⠉⢉⣁⡀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠛⠛⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡏⠀⠀⠀⢀⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⢀⡀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢐⣒⣂⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⡀⠐⠀⠀⣀⠄⠁⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⢿⣾⠿⣰⣿⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣛⡋⢉⢉⣭⣿⣷⣞⠛⣛⣿⣿⡿⠀⠀⠀⠀⠘⠀⠀⠂⠀⢸⣿⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡻⢛⣉⡀⢀⣀⣀⠀⣀⡀⣀⣀⢀⣀⡀⢘⣳⠶⣞⣛⡛⠀⢀⣀⡀⢻⣧⣀⣀⠀⠀⠀
⠿⠿⠿⠿⠟⠛⠛⠃⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠈⣿⡽⣯⢤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣰⣛⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢹⣿⢿⣿⣿⣿
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢠⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⣠⣾⣷⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣤⣀⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⢿⣿⣛⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣻⣿⣿⣾⣷⣾⣭⣿⣶⡭⠿⠿⠿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠭⣿⡿⠏⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣯⣭⣿⣿⣿⣟⣛⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠋⣭⣤⣶⣿⣿⡟⠻⠻⠿⢿⣿⣿⣿⣿⣟⣭⣴⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⠗⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣂⡀⢉⣽⣿⣿⣿⣭⣿⣿
[22A⣉⣉⣉⣿⣿⣿⣿⣭⣥⣤⠿⠧⢼⣿⣿⣿⣷⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣤⣬⢿⠿⠿⠿⠟⢻⣿⡿⣿⣿⠗⣿⣻⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⠤⠤⠤⠤⠾⣿⣿⠿⠷⠗⢶⡖⠒⣺⣿⡿⠓⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡆⠀⢸⡍⠀⣿⠏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⠒⠒⠒⠒⠒⠛⣛⣛⣻⣋⣉⣉⣩⣿⣛⣉⣍⣯⣁⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⡇⠀⢈⣷⠀⢿⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⣉⣉⣉⣉⣉⣉⣹⣿⣿⡭⠥⠤⣽⣿⡧⠤⠤⠧⠄⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠘⠀⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⣩⣭⣥⣤⣴⣿⣾⣿⣿⠶⠶⠶⣾⣿⠗⠒⠒⠒⢒⣋⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿
⣶⢶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⠀⢐⢠⣤⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠋⠉⠉
⣗⣒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⣿⣿⠿⣶⡆⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣧⣀⣀⣀
⣿⣿⣭⣭⣭⣵⣶⡎⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⠿⠟⠿
⣿⠙⠛⠛⠛⠛⠛⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣤⠤⠶⠶⠶⠿⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠁⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⡷⠀⠀⠀⢀⡠⠤⠀⢀⣘⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣶⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢹⣿⣿⣿⣿⠀⠀⠀⠀⣤⣄⠀⠀
⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⣸⣿⣿⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⣟⣿⣿⣟⠁⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⡄⠐⣀⠀⢀⣶⡏⢀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣛⣛⡿⢟⣛⡻⢗⣀⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣘⣛⡻⠿⢛⣛⡀⠀⠀⢰⣿⠃⠀⠀
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠇⣼⣿⣿⣿⣴⣄⠀⠀⢀⣼⣿⣿⣿⣿⠇⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢰⣶⣿⣿⡷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠟⠋⠁⠠⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣰⣿⢿⣿⣿⣿
⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⠛⣛⣿⡿⠁⠀⠀⠀⠈⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠾⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⢸⡇⣰⣿⣁⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⡃⠀⠹⠿⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣷⣾⢃⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣤⣤⣔⡲⣯⠌⣛⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣤⣤⣶⣦⣴⣶⣶⣤⣤⣤⣤⣤⣀⣀⣘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⣤⣶⣶⣶⣾⣿⣟⡻⢿⣿⣿⢿⣿⣿⣴⠈⠀⢻⣿⣿⣿⣿⣧⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣥⣤⣤⣼⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣴⣉⣩⠝⡛⠻⠿⣿⣯⣽⣿⡿
[22A⣉⣉⣉⣉⣹⣿⣿⣿⣏⣭⣍⣽⣿⣬⣿⣿⣿⣿⡤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣃⣘⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⡿⢾⡿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣭⣤⡤⠤⠤⠬⣿⣿⡿⠿⠾⢦⣤⠤⢨⣿⣿⠿⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣶⡦⠀⠀⡿⠁⢸⡏⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⠤⠶⠶⠶⠖⠒⠚⠛⡓⠒⡖⠒⠒⢒⣿⣟⣛⣋⣹⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⠀⠀⣏⠀⢸⡇⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⡒⠒⠚⢛⠛⠋⣉⣉⣿⣿⣏⣉⣉⣩⣿⣯⠭⠭⠭⠤⠤⢤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠋⠀⠘⠇⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣉⣉⣉⣩⣭⣿⣿⣿⣿⡧⠤⠤⢼⣿⡿⠶⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠩⠭⠭⠤⠤⠄⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿
⣿⣥⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡄⠰⠀⣤⡄⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡟⠛
⣶⣞⡒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⢹⣿⣿⣧⣄⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣏⣀⣀
⣿⣿⣿⣿⣭⣭⣭⣭⣿⡿⡿⠛⠻⠿⡟⠛⠛⠛⠋⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠿⠿
⣿⣿⠿⠿⠿⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣤⡤⠤⠤⠶⠶⠿⠆⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⠀⠀⠀⢀⣀⣀⠀⠀⠀⣿⡶⠶⠶⣶⣶⣶⣦⣤⣶⣶⣴⣾⣷⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀⠀
⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⡿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣛⣻⣿⣻⣿⢿⣿⣿⣿⣿⣿⣿⡀⡀⡠⢀⠀⠀⣴⡞⠁⣀⣀⣤⣤⣶⣶⣶⣿⣿⣛⣛⡿⢟⣛⡻⢿⣛⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣘⡻⠿⢟⣛⡛⠇⠀⠀⠀⣿⡇⠀
⣿⣿⣿⣿⠿⠿⠶⠶⠷⢿⣿⡇⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢠⣴⣶⣾⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠈⣭⣥⣿⣿⣿⣟
⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⠛⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⠀⡾⢻⡟⢀⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠀⠹⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣶⣿⠗⠀⣀⣠⣤⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣤⣤⣀⠼⣥⡬⣻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠠⢄⣠⣤⣤⣤⣴⣶⣤⣤⣀⣀⣀⣀⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡛⠀⠀⠀⠀⢠⣤⣴⣶⣾⣿⣿⠿⣿⣿⣿⠿⣿⣿⣥⡉⠉⢻⣿⣿⣿⣿⣧⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣭⣤⣤⣘⣻⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣷⣶⣾⣿⣿⣯⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠉⠁⣰⣶⣿⣿⣿⣯⣹⣙⢛⣛⠿⠿⣿⣿⣟⣝⣶
[22A⢈⣉⣉⣉⣉⣹⣿⣿⣿⣿⣭⣭⣹⣿⣧⣿⣿⣿⣿⣤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⣨⣸⣿⣿⣿⣿⠛⣿⣿⢿⣿⣿⢾⡿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿
⢠⣬⣭⡤⠤⠤⠬⣿⣿⣿⣿⣷⣧⣤⠤⢬⣿⣿⡿⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣦⠀⠀⡟⠃⢸⡏⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿
⠰⡦⠴⠶⠶⠶⠒⠺⣿⣿⣿⣿⣿⡒⠒⣺⣟⣛⣋⣹⣏⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⠀⠀⣿⠀⢸⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿
⠐⣗⠒⠚⠛⡛⠋⣛⣛⣿⣿⣿⠟⣽⢉⣿⣿⠭⠭⠭⠤⠤⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠈⠇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿
⠈⣿⣏⣉⣉⣉⣭⣽⣷⣿⠟⠋⠀⠘⠀⠉⠀⠐⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠩⠭⠥⠤⠤⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿
⠀⣿⣯⣤⣶⣶⣶⣶⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡄⠠⠀⣤⡄⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⡿
⣤⣶⣶⡒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⢸⣷⣿⣧⣤⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⣏⣀
⠻⣿⣿⣿⣿⣭⣭⣭⣬⣭⠛⠛⢻⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠘⠛⣢⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡿
⠀⣿⣿⠿⠿⠿⠿⠿⠟⠛⠀⠀⣉⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⡆⠀⠀⠀⠀⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⣿⣿⣦⡤⠤⠤⠶⠶⠿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⢿⣿⠀⠀⠀⠀⣀⡀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⠈⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣀
⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⢿⣛⣻⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣤⡀⡀⣀⠀⢀⣶⡏⢀⣀⣤⣤⣶⣾⣿⣿⢿⣛⣛⡿⢟⣛⡻⢿⣛⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡻⢿⡇⠀⠀⠀⣿⡇
⣿⡿⠿⠿⠯⠽⠷⠶⠶⣾⣿⣿⡧⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⣸⣧⣤⣤⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⣿⣭⣽⣿⣿⣶
⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⠟⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⣀⣽⡿⢿⡏⠨⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⡒⠀⠹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢶⣾⣶⣿⠖⠂⢉⣀⣤⣴⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣤⣤⣠⠿⣧⣌⡻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣠⣤⣤⣤⣤⣶⣤⣤⣀⣀⣀⣀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠋⠀⠀⠀⠀⣤⣤⣴⣶⣾⣿⣿⢿⣿⣿⣿⠿⣿⣿⣥⠉⠁⢻⣿⣿⣿⣿⣇⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣭⣤⣤⣘⣻⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣶⣾⣿⣿⣭⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢰⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠉⠉⠉⣰⣶⣾⣿⣿⣏⣩⡛⠛⡻⠿⢿⣿⣿⢛⣙
[22A⠀⢈⣉⣉⣉⣉⣹⣿⣿⣯⣿⣿⣿⡿⢻⡦⣿⣿⣿⣿⡤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⣼⣿⣿⣿⣿⢻⣿⣿⢿⣿⡿⢺⡿⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠠⠦⠤⠤⠤⠤⠬⢿⣿⣿⡿⠿⠧⠿⠀⠈⣿⣿⠟⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣶⡆⠈⠈⡟⠁⢸⡏⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠰⡶⠶⠖⠒⠒⠒⠚⠛⣿⣛⠀⠀⠀⠀⠀⠈⠉⢉⣹⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⡇⠀⠀⣟⠀⢸⡇⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸
⠀⠐⣟⡛⣛⣛⣉⣉⣉⣉⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠘⠇⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢿
⠀⢈⣿⣍⣍⣭⣭⣤⣾⣷⣿⣿⡷⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠩⠭⠤⠤⠤⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣻
⠀⠠⣿⢯⡴⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⡄⠠⠀⣤⡄⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⣤⣤⣶⣾⣒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⢻⣷⣿⣧⡆⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣃
⡏⢻⣿⣿⢿⣯⣭⣭⣭⣶⡞⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠘⠛⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠿
⡇⠀⣿⣿⠙⠛⠛⠛⠛⠛⠋⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⡇⠀⣿⣿⣤⠤⠤⠶⠶⠾⠿⠃⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⡇⠀⢿⡿⠀⠀⠀⠀⡠⠤⠄⢀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀
⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣟⣛⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣧⠀⠂⡄⠀⢰⣾⢀⣠⣤⣶⣶⣿⣿⣿⢟⣛⣛⡿⢟⣛⡻⢿⣛⣂⠒⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠘⢟⣛⡻⣿⣿⡇⠀⠀⢰⣿
⠿⠛⠛⠛⠉⠛⠒⠒⠲⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⣸⣿⣧⣤⣶⣾⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠠⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠈⣿⣯⣭⣷⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠛⢛⣿⡿⠋⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⢃⠻⠿⠟⢀⣯⣿⡯⢿⠅⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢐⡃⠈⠛⠿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠐⣶⣿⣶⡷⠚⢉⣁⣢⣤⣾⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣶⣦⣖⣿⡧⢌⣻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠤⣠⣤⣤⣤⣤⣶⣦⣤⣤⣀⣀⣀⣀⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠉⠀⠀⠀⠀⣤⣶⣶⣶⣿⣿⣟⠿⣿⣿⡿⣿⣿⣿⡶⠉⠈⣿⣿⣿⣿⣿⣄⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣭⣤⣤⣤⣝⣛⣛⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣶⣾⣿⣿⣭⣭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠉⢠⣶⣶⣿⣿⣿⣍⡍⠛⣛⡿⠿⣿⣿⡿⣉
[22A⠀⠀⣉⣁⣀⣀⣤⣽⣿⣿⣯⣿⣬⣯⠝⠛⠁⠀⠀⢻⣷⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⣷⠿⠿⠿⠿⠟⢻⣿⡿⣿⣿⡗⣿⢿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠴⠧⠴⠦⠦⠤⠾⢿⣿⣿⠛⠒⠂⠀⠀⠀⠀⠈⠑⠒⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⣶⣶⡆⠀⢸⡙⠀⢿⠋⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⢲⠒⠒⠒⠒⠒⠒⢛⣻⣟⣉⣟⣉⣁⡀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⢸⡀⠀⢹⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⢸⣏⣉⣉⣉⣉⣉⣉⣩⣿⣿⡯⠤⠤⢴⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠘⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⢸⣿⣥⣤⣤⣤⣴⠿⢿⣿⣿⡷⠒⠒⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠸⠿⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣦⠀⠀⢠⣤⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣶⣶⣾⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⣿⣾⣿⣶⡆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⠉⢻⣿⣟⣿⣭⣭⣽⣶⣶⡎⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠛⢃⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⠀⢸⣿⡟⠛⠛⠛⠛⠛⠛⠁⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⣿⠀⢸⣿⡷⠶⠶⠒⠒⠛⠛⠛⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⡿⠀⠘⠿⠇⠀⠀⠀⠠⠤⠄⢀⣀⣐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⡀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀
⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⣛⣻⣟⣿⣯⠿⠿⢿⣿⣿⣿⣿⣿⡿⠄⠄⠤⠠⠠⣿⣇⣠⣴⣶⣾⣿⣿⣿⢟⣛⣛⡻⢟⣛⡻⢷⣚⣒⠐⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢙⣛⡻⣿⣿⣿⡇⠀⠀⣾
⠛⠋⠉⠉⠉⠀⠀⠚⠻⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣀⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⣿⣷⣶⣾⣿
⠀⣀⣀⣀⣀⣀⣤⣤⣤⣽⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠈⣿⣿⣧⣶⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣛⣛⣻⣿⠏⠀⠀⠀⠀⠀⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢀⣿⣽⡿⢹⣇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣇⡀⠙⠛⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⢲⣾⣷⣶⠒⢉⣀⣤⣤⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣶⣶⣚⣿⣦⣝⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢥⣴⣦⣤⣤⣶⣶⣶⣤⣤⣤⣄⣀⣀⣀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡍⠁⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣻⢿⣿⣿⣟⣿⣿⣶⠂⠀⢹⣿⣿⣿⣿⣧⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣶⣤⣦⣬⣽⣛⣛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⣼⣿⣿⣿⣿⣯⣜⣋⠙⣛⡻⠿⢿⣿⣋
[22A⠀⠀⠀⠠⠤⠤⠤⠴⠾⠿⣿⣿⣾⣿⡾⠷⠛⠛⠋⠁⠈⢿⠓⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠾⠟⠛⠛⠛⠛⢸⣿⠿⢿⡿⣏⣹⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⢘⠓⠒⠒⠓⠒⠚⢻⣿⣿⣛⣉⣉⣁⠀⠀⠀⠀⠀⢩⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠿⣿⣿⣿⡇⠀⠸⡏⠀⢸⠇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⢘⣋⣉⣉⣉⣉⣉⣉⣉⣿⣧⣬⠤⠤⠤⠀⠀⠀⠀⠀⠠⠴⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⡧⠀⢸⡅⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⢠⣯⣤⣤⠤⠤⠤⢤⣤⣾⣿⣿⠒⠒⢲⡆⠀⠀⠀⠀⠀⠈⠙⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠿⠿⠿⠿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠠⣿⠶⢶⣶⣶⣶⣟⣛⣿⣿⣿⣋⣩⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠉⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠘⣛⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⠂⣠⣰⣾⡆⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀
⣿⣿⣿⣿⣿⣿⣭⣼⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢹⣟⠿⣿⡇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⡇⠸⣿⣿⣽⣷⣶⣾⣿⣿⣇⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢰⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠁⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠹⣿⡇⠀⣿⣿⠉⠉⠉⠉⢉⣉⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⢠⣿⡇⠀⣿⣿⠛⠛⠋⠉⠉⠉⠉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣹⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⢸⣿⠀⣿⣿⢻⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠸⠿⠃⠀⠛⠛⠀⠀⠀⢀⣒⣒⣀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀
⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣟⣛⣛⣛⣩⡉⣩⣽⣿⣶⣾⣛⣛⣻⣿⣿⣿⣿⣿⡏⠃⠀⠚⠀⡐⣿⣤⣶⣾⣿⣿⣿⣿⣟⣛⣛⡻⢟⣛⡻⢗⣚⣒⠂⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣘⡻⣿⣿⣿⣿⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡿⠿⣿
⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠀⣿⣿⢿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⡿⠁⠀⠀⠀⠀⠀⡌⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢀⣿⠷⠚⠛⠸⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣧⣄⣈⠉⠙⠛⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⣁⣤⣤⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣷⣯⣿⣴⣮⡟⠿⠿⣿⣿⣿⣿⣷⡀⠀⠀⢰⣾⣿⣿⣷⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⣿⢿⣿⠿⠁⠀⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣟⣿⣿⡿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠿⠿⢛⣉⣙⣛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣧⠀⠀⢠⣾⣿⣿⣿⣿⣷⣮⣥⣜⠭⠭⠛⠻⠟
[22A⠄⠀⠀⠀⠤⠤⠤⠤⠤⠿⢿⣿⣿⣾⢷⣿⣿⣿⣿⣿⣿⣿⡿⠓⠓⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠒⠟⠛⠛⣛⠛⠃⢿⡿⠟⣿⣿⣍⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠂⠀⠀⠀⠒⠒⠒⠒⠒⠒⠛⣻⣿⣿⣛⣉⣿⣿⣿⠿⢿⣿⣉⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⠁⠀⢸⠁⠀⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀
⠂⠀⠀⠀⣹⣋⣉⣉⣉⣉⣉⣉⣩⣿⣥⣬⠍⠉⠀⠀⠀⠠⠴⠿⠦⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⢸⠀⠀⣿⠈⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣁⠀⠀⠀⢸⣥⣤⣤⠤⠤⠤⣤⣤⣿⣾⣿⠂⠀⠀⠀⠀⠀⠈⠋⢉⣁⣙⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠸⠿⠿⠿⠿⠛⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⡤⠀⠀⠀⢸⣿⠶⢶⣶⣶⣾⣿⣻⣿⣿⣿⣋⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣒⠒⠂⠀⠉⠉⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀
⣶⠀⠀⠀⠘⣛⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣗⠀⣥⢸⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⣿⣿⢻⣿⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⠀⢹⣿⣏⣿⣶⣶⣾⣿⣿⡀⠀⠨⢿⣿⣿⣿⣿⣄⡀⠀⢀⣀⣤⣤⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⢹⣿⠀⢸⣿⡏⠉⠉⠉⠉⣉⣁⣀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠙⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⢸⣿⠀⢸⣿⡟⠛⠛⠉⠉⠉⠉⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀
⠿⠸⠟⠀⠈⠛⠃⠀⠀⠀⣐⣒⣂⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠈⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣛⣛⣛⣛⣉⢉⣽⣿⣷⣶⣿⣛⣛⣿⣿⣿⣿⣿⣿⠛⠀⠀⠃⢀⢸⣿⣴⣶⣿⣿⣿⣿⢟⣛⣛⡛⢟⣛⡻⢷⣛⣓⠒⣐⡂⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣀⡹⣿⣿⣿⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣤⣴⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⡿⠿⠟
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠈⣿⣿⡿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⡟⠁⠀⠀⠀⠀⢠⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⣠⣿⠿⠿⠛⠋⢉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣦⣄⡈⠉⠙⢛⣿⢛⢿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣤⣴⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣿⣿⣿⣾⣽⣯⣴⣿⠛⠿⢻⣿⣿⣿⣿⣇⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣥⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⠽⣿⡿⠏⠀⠸⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⣛⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠿⠟⣋⣉⣽⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⡆⠠⠠⣴⣿⣿⣿⣿⣿⣷⣷⣦⣶⠯⠍⠛⠛
[22A⠤⠀⠀⠀⠠⠤⠤⠤⠤⠴⠿⣿⣿⣿⣿⣿⣿⣿⠓⠺⢿⣿⣿⠟⠚⢛⠉⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠛⠓⢛⡛⠛⠘⣿⠟⢹⡿⣯⣽⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀
⠒⠀⠀⠀⠐⡚⠒⠒⠒⠒⠒⢻⣿⣿⣿⣿⣿⣿⣏⣉⣿⣿⣏⣩⡅⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⡟⠀⠀⣧⠀⢸⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀
⠒⠀⠀⠀⠈⣟⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿⣿⠤⢼⣿⠵⠴⠾⠷⠖⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠀⠀⡇⠀⢼⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀
⣉⡁⠀⠀⠀⣽⣤⣤⣤⠤⠤⠤⣤⣾⣿⣿⣿⣿⣷⣿⣿⡒⠀⣛⣉⣉⣉⣋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠽⠿⠿⠟⠛⠛⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀
⣥⠄⠀⠀⠀⣿⣷⠶⢶⣶⣶⣿⣛⣿⣿⣿⣿⣿⣿⠟⣋⣉⣉⣩⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣒⡒⠀⠈⠉⠉⠉⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⣶⡆⠀⠀⠀⠛⣛⣟⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠙⣻⣿⣿⣿⣿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡃⢨⡄⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀
⢿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⡿⠿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠉⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⢸⣷⡛⣻⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀
⢰⡿⣿⡇⠈⣿⣿⣿⣷⣶⣾⣿⣿⣷⠀⠠⠤⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀
⢘⡇⢿⡇⠀⣿⣿⡏⠉⠉⠉⢉⣉⣀⡀⠀⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡏⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⢸⡇⣼⡇⠀⢹⣿⡟⠛⠋⠉⠉⠉⠉⠁⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣰⡀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢻⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⠸⠇⠟⠇⠀⠘⠛⠁⠀⠀⢀⣒⣒⣀⣤⣤⣬⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠄⠀⠀⣀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀
⠿⠿⠿⠻⠻⠿⠿⠿⠿⢿⣿⣿⣛⣛⣛⣭⡉⢩⣽⣷⣶⣾⣟⣛⣻⣿⣿⣿⣿⣿⡟⠃⠂⠚⠀⡀⣿⣤⣶⣾⣿⣿⣿⢿⣛⣛⡛⢛⣛⡻⢷⣚⣛⠒⣂⡒⣂⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣀⡀⢿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⠉⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⢠⣤⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⣿⣿⣿⠟⠛
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠘⣿⣿⣿⢿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⣭⣵⣿⠋⠀⠀⠀⠀⠀⡼⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣄⡻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢰⣿⠿⠟⠛⠉⢁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢷⣤⣀⡉⡉⢙⣻⣟⠻⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣴⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣀⣀⣘⣿⣿⣿⣿⣿⣮⣿⣥⣶⣟⠻⠟⣿⣿⣿⣿⣿⡀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡭⢿⡿⠏⠁⠀⠿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣛⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡛⠛⠿⠛⢫⣥⣭⣭⣿⡿⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⠷⠀⠄⢠⣾⣿⣿⣿⣿⣿⣷⣶⣦⣒⠊⠉⠙
[22A⠤⠄⠀⠀⠀⠤⠤⠤⠤⠤⠿⢿⣿⣿⣿⡿⡿⠳⠒⠚⢿⣿⣿⡟⠒⠚⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠚⠛⠛⡛⠛⠀⣿⡟⠹⡿⢿⣭⣯⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠒⠂⠀⠀⠀⡚⠒⠒⠒⠒⠒⠛⣿⣿⣿⣋⣉⣉⣉⣉⣽⣿⣏⢉⡥⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⣃⡀⠀⡏⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠒⠂⠀⠀⠀⣛⣉⣉⣉⣉⣉⣉⣉⣩⣽⣷⣤⠤⠤⢴⣿⠥⠤⠶⠷⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⠀⠀⠰⠀⠀⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⣉⡁⠀⠀⠀⣸⣥⣤⣤⠤⠤⠤⣤⠤⣿⣶⣿⠒⠒⢺⣿⣓⠂⢚⣉⣉⣉⣋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠸⠿⠟⠛⠛⢛⢃⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⣭⡤⠀⠀⠀⢼⣿⠶⢶⡶⢶⣾⣛⣻⣿⣿⣿⣍⣉⣿⣿⣉⣉⣨⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣒⡂⠀⠈⠉⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡇
⣶⣶⠀⠀⠀⠘⣛⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣃⢠⣥⣿⡇⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠄
⠿⣿⣿⣿⣿⣿⣿⣯⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠘⣿⠛⢻⣿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⢠⣿⣿⣿⠀⢻⣿⣏⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⠈⣿⢻⣿⠀⢸⣿⡏⠉⠉⠉⠉⣉⣭⣿⣿⣿⣿⣿⣿⠛⠿⠿⠿⣿⣿⣿⠋⠁⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⠀⡗⢸⣿⠀⢸⣿⡟⠛⠋⠉⠉⠉⠉⠉⠚⡿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀
⠀⡇⠻⠛⠀⠘⠛⠃⠀⠀⢀⣐⣒⣂⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀
⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢀⡀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀
⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣛⣛⣛⣭⡍⢩⣽⣶⣶⣶⣆⣒⣃⣴⣤⣴⣤⣴⡟⠃⠀⠐⠀⢀⢿⣧⣶⣾⣿⣿⣿⢿⣛⣛⡛⢛⣛⡻⢗⣚⣛⠒⣂⡐⣂⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣀⡀⢿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⢀⣀⣀⣀⣈⡉⢩⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢨⣿⡿⣿⣿⣟⣛
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠅⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⣿⣿⣿⢻⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣭⣥⣾⠋⠀⠀⠀⠀⠀⢰⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣄⡻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢠⡿⠟⠛⠛⠉⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣦⣄⡀⣉⠉⣛⣿⠻⢿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣀⣀⣈⣿⣿⣿⣿⣿⣶⣿⣯⣶⣞⡛⠟⣿⣿⣿⣿⣿⡄⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⡿⢿⣿⠟⠁⠀⠸⢿⣿⣿⣿⡿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣯⣽⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡉⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡟⠛⠛⠛⢫⣥⣤⣭⣿⣿⢛⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⠷⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣦⣶⣒⠒⠈⠉
[22A⣉⣁⠀⠀⠀⢉⣉⣉⣭⣉⣽⣿⣿⣿⣿⣿⣿⠿⠤⠤⣿⣿⣿⡷⠦⠶⠖⠲⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠧⠼⠼⠧⠿⠿⠛⠹⣿⠟⢻⣿⣟⣻⣋⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠤⠤⠀⠀⠀⠠⠦⠤⠦⠤⠤⠾⢿⣿⡿⡿⠒⠒⠒⠒⣺⣿⣟⢓⣃⣈⣁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣶⣶⣶⣾⡇⠀⠀⡇⠀⢸⠆⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀
⠶⠦⠀⠀⠀⠐⠖⠒⠒⠒⠒⠚⢛⣛⣙⣿⣯⣍⣉⣉⣿⣯⣥⣤⡧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⢿⣿⡧⠀⠀⡃⠀⢸⡁⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⠒⡒⠀⠀⠀⢈⣏⣉⣉⣉⣉⣉⣩⣭⣼⣯⣿⡧⠤⢴⣿⡗⠀⠒⠓⠒⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⠁⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣉⣭⡀⠀⠀⠀⣿⣤⠤⢤⠤⠶⠿⢿⣾⣿⣿⣗⣒⣺⣿⣛⣉⣉⣉⣉⡉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠉⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⣷⣶⡄⠀⠀⠀⠿⢶⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠂⣈⣀⣶⡆⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⣿⣶⣶⣶⣿⣯⣍⣹⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⢹⡟⠟⣿⡇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀
⡗⣸⣿⣿⡇⠙⣿⣿⣻⣷⣶⣶⣶⣿⡇⠈⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠁⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀
⡇⢸⡟⣿⡇⠀⣿⣿⠈⠉⠉⠉⠉⣉⣁⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⡄⢸⡇⣿⡇⠀⣿⣿⠖⠚⠛⠛⠛⠋⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⡇⢸⠛⠿⠇⠀⠛⠛⠀⠀⠀⢀⣒⣒⣀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀
⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀
⠛⠙⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣛⣛⣛⣻⣭⠉⡩⣽⣷⣾⣿⡛⡆⠀⠀⠀⠀⠀⠀⠒⠐⠐⠂⢀⢿⣧⣶⣾⣿⣿⣿⢟⣛⣛⡛⢛⣛⡻⢗⣚⣓⠒⣀⡂⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢀⣀⡸⣿⣿⣿⣿⣿⣇⣠
⠀⢀⣀⣀⣀⣀⣀⣀⣬⣏⣉⣽⣿⣿⣿⣿⣿⡇⣯⣿⣿⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣽⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⡿⣿⣿⣟⢛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣿⣿⣛⣿⢟⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣿⣄⡻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠟⠛⠉⢀⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢱⣦⣤⣀⣈⡉⣹⣏⡙⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠄⢀⣀⣀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣷⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣀⣀⣠⣬⣿⣿⣿⣿⣿⣷⣿⣶⣶⣋⡛⠛⣿⣿⣿⣿⣷⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣯⣿⣿⡖⢻⣿⣓⣀⡀⠻⠿⠿⡿⠿⠿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣯⣭⣭⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⡉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠉⠛⠋⠉⣤⣴⣶⣾⣿⣙⠿⠻⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠿⠁⠀⣀⡾⠿⣿⣿⣿⣿⣿⣿⣶⣬⣉⡀⠈⠉
[22A⣋⣙⣛⠀⠀⠀⢈⣹⣿⣿⣝⣙⣿⣿⣿⣿⣿⣿⣿⣍⣉⣿⣿⡯⠭⠅⠅⠀⠀⠀⠀⠿⠿⠿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣯⣭⣿⣿⣷⡶⢶⣷⣿⢆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠃⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀
⣉⣉⣭⠀⠀⠀⠨⢭⣥⡤⠤⠼⢿⣿⣿⣿⣿⡿⠿⠶⠾⣿⣿⣿⠖⠒⠒⠒⠂⠀⠀⠀⠀⠀⠈⠻⣿⠿⠴⠷⠟⠺⠛⠛⠉⣿⡿⢹⣿⣋⣹⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠶⠶⠦⠄⠀⠀⠀⠛⠒⠒⠒⠒⠚⣻⣿⣟⣿⣛⣉⣉⣉⣿⣿⣋⣩⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣾⣿⣿⣿⣿⠀⠀⠇⠀⢸⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠
⣛⣛⣛⡃⠀⠀⠀⣏⣉⣉⣩⣉⣉⣭⣭⣭⣿⣿⣧⠤⢴⣿⠷⠶⠾⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠛⠻⣿⣿⠀⠀⠂⠀⠸⡆⣹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⣭⣭⣭⡅⠀⠀⠀⣽⡤⠤⠤⠦⠶⣶⣖⢲⣿⣾⣟⢒⣿⣿⣉⣉⣉⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠁⠛⠛⠛⢛⣛⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⣿⣶⡶⠆⠀⠀⠀⣾⣟⣒⣺⣻⣛⣛⣿⣿⣿⣿⣯⣭⣿⣯⣥⣤⣤⣴⣖⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣍⠉⢉⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸
⣿⣿⣿⣿⣀⣀⣀⣩⣯⣯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡅⣶⣼⣿⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⣿⣿⡛⣿⣿⣿⠿⣿⣿⣷⣖⣛⣛⣋⣭⠻⠿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠸⠏⣉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸
⡟⢻⠀⣿⣿⣿⠀⣿⣿⠾⠿⠿⠿⠿⠿⠂⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠈⠀⡟⢸⣿⠀⣿⣿⣤⣤⠤⠤⠴⠶⠖⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⣿⠃⡇⣾⣿⠀⢸⣿⠀⠀⠀⢀⡀⠤⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢠⣤
⣿⣏⣠⣥⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣼⡏
⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⠿⠿⠿⢟⡛⢛⣛⣿⣯⣿⣿⣄⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠀⣶⣇⣠⣤⣶⣶⣿⢟⣛⣛⡻⢟⣛⡻⢿⣛⣛⠀⣒⡒⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠀⢙⣛⡻⣿⣿⣿⠀⣀⣿⠃
⠀⠀⣀⣀⣀⣀⣄⣤⣴⣶⣛⢛⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢀⡾⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⠿⠿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⠁⠀⠔⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢿⡷⣿⡟⠛⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣇⣄⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⣃⠻⠿⠟⠀⠋⠁⣀⣬⣴⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⢷⣦⣄⣀⣈⢹⣿⣉⠻⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⣿⣿⣿⡿⡿⠇⠀⠀⢀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣷⣿⣟⡙⠋⢿⣿⣿⣿⣷⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣷⣶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⠻⣿⣛⣀⣀⡸⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣯⣭⣽⣿⣿⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠿⠟⠛⠀⠀⠀⠀⡉⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠉⠉⠉⠉⣶⣶⣶⣾⣿⣩⠟⠛⠿⠿⣿⣿⡿⣋⣵
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠃⠀⣀⣒⣻⡿⢿⣿⣿⣿⣿⣷⣬⣅⣀⣀⣮⣯⣭
[22A⠤⠤⠤⠤⠀⠀⠀⠠⣼⣿⡿⠦⢿⣿⣿⣷⣶⣶⣶⡤⠝⢿⣿⣷⠴⠒⠒⠒⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣾⣇⣀⣀⣤⣤⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⡿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠶⠶⠖⠒⠀⠀⠀⠸⠛⠛⠛⠓⣾⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣍⣉⣉⣀⡀⠀⠀⠀⠀⠉⠙⢻⣿⣯⣉⣏⣿⣿⣿⣿⠻⣿⣿⣿⣿⡧⣿⢿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⣧
⣋⣉⣉⣉⡀⠀⠀⢈⣿⣭⣭⣭⣭⣽⣿⣿⣿⣿⠭⠥⠤⢽⣿⠿⠧⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣭⣤⣤⣤⣤⣤⠀⠀⡏⠁⢸⡀⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿
⣯⡭⠤⠤⠄⠀⠀⠰⡦⠶⠶⠖⠒⠒⠛⠛⢺⣷⣖⣒⣀⣿⣛⣋⣹⣏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⢿⣿⣿⠀⠀⡇⠀⢸⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿
⣿⠖⡒⠒⠂⠀⠀⠈⣛⣉⣛⣉⣉⣉⣉⣭⣽⣯⣿⡯⢼⣿⡧⠄⠼⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠻⠀⠀⠀⠀⠘⠀⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿
⣿⣿⣽⣯⡁⠀⠀⠠⣽⡯⠥⡤⣴⠶⠿⣶⣿⣿⣿⣗⣺⣿⣛⣋⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠐⠒⠒⠒⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡃⠀⠀⢸⣿
⣽⣿⣿⣶⡆⠀⠀⠀⣻⣲⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⣥⢰⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠅⠀⠀⠈⠀
⣿⣿⣿⠿⣿⣿⡿⣿⣿⣿⣭⡽⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⣿⡜⢻⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣶
⣳⡿⡿⢰⡿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⡾⠀⠱⢈⡇⣿⡇⠀⣿⣿⣀⣀⣀⣠⣤⣤⠄⣴⣾⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⡇⢠⣾⢸⡇⣿⡇⠀⣿⣏⠉⠀⠀⢀⣀⡀⠀⠘⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⠀
⣿⣞⣋⣈⣃⣉⣁⣀⣨⣥⣤⣤⣤⣶⣶⣶⣿⣿⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⡟⠀
⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠆⠀⠀⠀⠀⠀⠠⢤⣶⣿⣿⣿⡇⠀⠀⢀⠠⢠⣴⢀⣀⣤⣴⣶⣾⢟⣛⣛⡿⢟⣛⡻⢿⣛⣃⠐⣒⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠘⢟⣛⡻⣿⣿⠀⠀⣿⡇⠀
⠀⠀⢀⣀⣀⣀⣀⣠⣈⣭⠿⠿⠶⣷⣶⣿⣿⣿⡆⣿⣤⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⠁⠀⠈⣀⣼⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣿⠾⢿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠰⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢲⣾⡿⠿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣯⣉⣉⣿⠏⠀⠀⠀⠈⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⠀⠈⢘⣃⣸⣿⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢶⣤⣄⢉⡉⣛⣿⡛⢿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣀⣀⣀⣼⣿⣿⣿⣿⣷⣾⣷⣶⣋⡛⠛⣿⣿⣿⣿⣧⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⡌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⢻⣿⣛⣀⣀⠿⠿⢿⣿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣯⣭⣿⣿⣿⣛⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠛⠛⠛⠀⠀⠀⠀⡉⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡮⠉⠉⠉⣰⣶⣶⣾⣿⣉⠝⠛⠻⠿⢿⣿⡿⣋⣱⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠀⢠⣔⣻⣿⡿⢿⣿⣿⣿⣾⣶⣬⣀⣠⣾⣿⣭⣭
[22A⠛⠛⡛⣛⠓⠀⠀⠀⣛⣿⣾⣷⣛⣿⣿⣿⣟⣻⣭⣉⣛⣿⣿⣯⣉⣉⣉⡁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀
⣭⣩⣭⣭⣍⠀⠀⠀⣭⡿⠿⠯⢭⣿⣿⣿⣿⣿⣿⣿⡧⢤⣿⣿⡗⠃⠐⠂⠀⠀⠀⠈⠉⠉⠛⢿⣿⣿⠛⡿⣿⢿⣿⣿⣷⣾⣿⣿⣷⣖⣿⣿⣟⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⠁⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⡟
⠶⠶⠶⠶⠒⠀⠀⠀⢲⡶⢲⠒⠒⠛⣿⣿⣿⣿⣟⣛⣛⣛⣿⣿⣟⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⣟⣓⣛⣛⣛⣉⠉⠀⡿⠛⢻⡛⣥⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿
⣿⣟⣟⣛⣛⠀⠀⠀⢨⣉⣩⣍⣩⡭⠽⠿⠯⢽⣯⡤⠤⢴⡿⡿⠐⡖⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⠀⠀⡇⠀⢸⠃⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿
⣿⣿⣭⡥⠥⠄⠀⠀⠸⠶⠶⠶⠒⠒⠒⠒⢒⣾⣟⣿⣛⣿⣟⣉⣉⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠇⠀⠸⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿
⢿⣿⣾⣷⣖⠂⠀⠀⢘⣿⣛⣛⣩⣭⣿⣿⣭⣿⣿⣿⢤⣿⡿⠶⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠭⠭⠭⠭⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿
⣙⣻⣿⣿⣯⡅⠀⠀⢸⠿⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡦⠀⡂⣤⡄⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠁
⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣚⣿⣿⠟⠿⠿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⣿⠿⢷⣦⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⣤
⠹⢻⡿⡟⢰⣿⣿⡇⢹⣿⣿⣿⣶⣶⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠉⠐⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉
⠀⡿⠀⠃⢸⡟⣿⡇⢸⣿⡏⠉⠉⢉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣠⡇⢠⣶⢸⣇⣿⡇⢸⣿⡟⠉⠉⠉⠉⠉⠁⠀⢀⣴⣶⣶⣶⣶⣤⣤⣶⣿⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⣿⣷⣼⠏⠘⠉⣋⣁⣀⣉⣁⣠⣤⣬⣭⣥⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⠀⣿⣿⣿⣿⣿⡇⠀⢠⣿⠀⠀
⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣟⣛⣿⣿⣿⣿⣿⣇⠀⠀⢀⠀⠀⢠⣴⢀⣀⣤⣤⣶⣾⢟⣛⣛⡿⢟⣛⡻⢷⣛⣃⠐⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡀⠻⢟⣛⡻⢿⡇⠀⢸⡟⠀⠀
⠀⢀⣀⣀⣀⣀⣠⣤⣬⣭⣭⡽⠿⠿⣶⣶⣶⣾⣷⢸⣷⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⠉⠈⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢸⣷⣾⣿⡷⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣴⣿⠿⣿⡿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣛⣛⣿⠟⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠈⣿⢀⣷⣥⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣤⣈⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⣨⣿⣿⣿⣿⣷⣽⣧⣿⣟⠿⢿⣿⣿⣿⣿⡄⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣺⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⡷⢻⣿⣛⣀⣀⠿⣿⣿⡿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣭⣽⣿⣿⣟⣛⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠿⠛⠛⠛⠂⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣌⠉⠉⠁⣶⣶⣾⣿⣏⣉⡛⢛⡿⠿⢿⣿⣋⣱⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠁⠀⣤⣾⣟⣿⡿⢿⣿⣿⣿⣷⣦⣤⣀⣶⣿⣿⣿⣧
[22A⠤⣤⣤⣤⣤⡤⠀⠀⠀⠯⣭⣭⡭⢿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⡴⠦⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀
⠒⠶⠒⠖⠒⠒⠀⠀⠀⣲⣿⣿⣛⣺⣿⣿⣿⣻⣿⣿⣿⣋⣹⣿⣿⣸⡉⡉⠉⠁⠀⠀⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⣴⣶⡦⣰⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠻⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿
⣉⣭⣭⣍⣉⣉⠀⠀⠀⢭⣭⣭⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⢿⣿⣿⡶⠔⠒⠂⠀⠀⠀⠀⠀⠀⠈⢻⡿⠧⠼⠾⠿⠿⠟⠋⣿⡿⢿⠿⣓⣿⣻⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⣶⣶⡶⠶⠤⠦⠀⠀⠀⢒⠒⠺⣿⣿⣿⣿⣿⣟⣿⣛⣋⣁⣸⣿⣏⣩⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣶⣶⣾⣿⣿⠀⠀⡇⠀⢸⠃⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⣿⣿⣿⣛⣛⣛⠀⠀⠀⢹⣍⣭⣽⣿⣿⣿⢿⣷⣽⢿⣶⢤⣿⡷⠶⢾⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠇⠀⢸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⣽⣿⣿⣽⣭⣥⠄⠀⠀⠸⡶⠶⠶⠒⡻⠁⠈⠃⠀⠘⠟⢹⣿⣯⡉⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⣛⣛⣛⣋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿
⠒⠺⣿⣿⣿⣟⡂⠀⠀⢸⣟⣫⣿⣯⣭⣤⣄⠀⠀⠀⠀⠈⠀⠐⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣭⣄⠀⠄⣀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠘⠛⠛
⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣷⣓⢺⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⣷⣿⣧⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀
⡟⠻⢿⣿⡿⢹⣿⣿⠋⢿⣿⣿⣯⣭⣭⣷⣶⠉⠙⣻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠛⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠚⠛⠋
⡇⠀⣼⠁⠇⢸⡿⣿⠀⢸⣿⡟⠛⠛⠉⢉⣉⡀⠀⣼⣿⣿⣿⣶⣶⣶⣶⣆⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣧⢀⡇⢠⣴⢸⣇⣿⠀⢸⣿⡟⠛⠋⠉⠉⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣧⡸⠏⠸⠘⠛⠀⢈⣛⣁⣀⣀⣀⣬⣥⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⡀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⣿⠀⠀⣾⡇⠀⠀
⠛⠟⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢀⠀⠀⠀⣤⠂⣀⣀⣤⣴⣶⢟⣛⣛⡿⢟⣛⡻⢷⣛⣃⠒⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡻⢿⠀⠀⣿⠁⠀⠀
⠀⠀⣀⣀⣀⣀⣀⣠⣤⣝⣛⢻⢯⡽⢿⣿⣷⣶⣶⡆⣿⣾⣿⣿⣧⣴⣾⣿⣿⣿⣿⠘⠈⠈⢀⣨⣿⣿⣿⣿⣿⣿⣿⡚⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢰⣶⣾⣿⢤⡤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣶⣿⣿⣟⣟⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣟⣛⣻⠟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⢸⣂⣼⣽⣀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣤⣀⠉⠙⢻⡿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣤⣴⣶⣾⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⣀⣿⡿⣿⣿⣷⣼⣧⣿⣟⠿⢿⣿⣿⣿⣿⡄⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⡄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣞⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⡷⠻⣿⣛⣀⣀⠿⣿⣿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣯⣭⣿⣿⣿⣛⣛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⠿⠛⠛⠙⠂⠀⠀⠀⢠⠈⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⡄⠉⠁⢰⣶⣿⣿⣿⣭⣋⣛⢛⡿⠿⣿⣟⣽⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢠⣬⣿⣿⣿⣿⡿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣷⣾
[22A⠒⡒⢒⠒⠒⠒⠒⠀⠀⠀⡷⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣒⡒⡒⠒⠒⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀
⣉⣉⣉⣉⣉⣉⣉⠀⠀⠀⣍⣿⣿⣯⣹⣿⣿⣿⣿⣿⣯⣭⠿⣿⣿⡤⠤⠤⠤⠤⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣉⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⣷
⡤⠴⠶⠶⠶⠶⠦⠀⠀⠀⠾⠟⠛⠓⢺⣿⣿⡿⢿⣿⣿⣿⣒⣿⣿⣯⣁⣀⣁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣹⣹⣿⣿⣿⡿⣿⣿⣿⣿⡯⣿⢿⣏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣟⣻⣿⣛⣛⣛⣋⠀⠀⠀⢩⣭⣭⣭⠭⢽⣿⣷⡿⠋⠩⠭⠭⣽⣿⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣭⣬⣬⣥⣤⡄⠀⠟⠉⢸⡅⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⠽⠶⠤⠀⠀⠀⢲⠶⠖⠒⠒⠒⠚⠉⠀⠀⠀⠀⢠⣿⣻⣩⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡇⠀⠁⠀⢸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣿⣻⣿⣿⣻⣛⣛⡀⠀⠀⢨⣭⣩⣭⠭⢭⣭⠤⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠀⠀⠀⠈⠀⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿
⣿⣭⣭⣿⣿⣯⡿⠄⠀⠀⢸⡷⠖⣶⣲⣞⣛⣻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⡒⠀⡀⠉⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠸⡿⠿⣿
⠿⢶⣶⣾⣿⣿⣿⣆⣀⣀⣨⣭⡯⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠀⣦⣿⣇⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⠿⡿⣿⣿⢛⣿⣿⠟⣿⣿⣿⣖⣛⣛⣯⣝⠛⠻⢿⣿⣷⣤⣤⣤⣀⡀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠟⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠸⠿⠿⠿
⣿⣧⠀⣲⠋⠇⢸⡿⣿⠀⢸⣿⠟⠻⠛⠛⠛⠛⠀⢈⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠰⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣇⠀⡏⢀⣠⢸⡇⣿⠀⢸⣿⠶⠖⠒⠒⠛⠛⠁⠸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣶⣧⣸⡟⠸⠛⠟⠀⠘⠛⠀⠀⣀⣐⣒⣂⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⣿⣿⣿⣿⣿⡇⠀⢰⣶⠀⠀⠀
⠿⠟⠻⠿⠷⠶⠶⠒⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣀⠄⠀⢀⣀⣤⣴⢒⣛⣛⡿⢟⣛⡻⢷⣚⣁⠲⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡸⠿⢟⣛⡛⠇⠀⢸⡏⠀⠀⠀
⠀⠀⠀⢀⢀⣀⣀⣀⣀⣈⣛⣛⣛⣻⣯⣭⣭⣭⣷⣶⠀⣶⣾⣿⣿⣭⣭⣿⣿⣿⣿⡗⠀⠐⠂⢀⣿⣷⣿⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢠⣴⣿⣧⣤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⢿⣿⣷⢿⢆⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣿⣿⣿⣿⠛⢛⡻⠁⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⢨⢀⣏⣁⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣤⣀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠀⠀⣿⣿⣾⣠⣤⣴⣶⣾⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⣀⣀⣻⣿⣿⣿⣷⣭⣯⣬⣟⠿⢿⣿⣿⣿⣿⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣿⣿⠚⣿⣟⣀⣀⡿⣿⢿⡿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣽⣿⣿⣟⣛⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⠟⠛⠉⠁⠀⠀⠀⠀⡀⠉⠉⠉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠁⣴⣶⣿⣿⣯⣝⣙⠛⡻⠿⢿⣿⣯⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢠⣼⣿⣛⣻⣿⠿⣿⣿⣿⣦⣤⣤⣶⣿⣿⣷⣶⣿
[22A⣉⣛⣛⣛⣛⣛⣓⣒⡂⠀⠀⢘⣛⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀
⠤⠤⠤⠤⠦⠤⠤⠤⠄⠀⠀⠠⢭⣭⣭⠽⣿⣿⣿⣿⣿⣿⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡟⡿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣮⣦
⣗⡒⠒⣒⣛⣛⣓⣒⡂⠀⠀⢐⣺⣿⣿⣛⣻⣿⣿⣿⣿⣻⣿⣏⣹⣿⡯⠍⠉⠉⠉⠀⠀⠈⠙⠻⢿⣿⣿⡿⠿⢿⣿⣷⣿⣿⣿⣿⣧⡤⢴⣶⣶⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⠘⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣿
⣽⣿⡧⠭⠭⡭⠭⠤⠤⠀⠀⠨⢥⠤⠤⠤⠿⣿⣿⣿⡿⠟⠙⠓⢿⣿⣷⣒⡒⠂⠀⠀⠀⠀⠀⠀⠈⣿⡿⠇⠒⠛⠚⠛⠛⢹⡿⠛⡿⣏⣹⣽⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣓⣿⣷⣾⣿⣗⣓⣒⣂⠀⠀⠀⣉⣉⣉⣉⣉⣹⣿⠁⠀⠀⠀⠀⣾⡿⠭⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⠀⠸⠀⠀⡇⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣭⠤⠤⠀⠀⠀⠷⠖⠲⠒⠒⠒⠒⠒⠀⠀⠀⠀⠈⠛⢋⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠀⠀⠀⠀⠇⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣿⣿⣷⢚⣻⣿⣿⣛⣓⠀⠀⠀⣻⣭⣭⣭⣭⡿⣯⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠭⠭⠭⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⣭⣭⣽⣿⣿⣧⠀⠀⠀⠿⣶⢾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠄⣐⢰⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠻
⣿⣿⣦⣾⣿⣿⣿⡿⢿⣿⣿⢿⣿⣿⡭⠿⠿⢟⣻⠿⢿⣿⣿⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠙⠚⠛⠓⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣤⣤⣴⣤
⣿⣿⣿⣇⠘⣹⠛⡇⢾⢻⡇⠀⣿⡗⠿⠿⠿⠿⠿⠀⠀⢺⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁
⣿⣿⣿⠋⠀⠏⠀⡁⣼⢸⡇⠀⣿⣧⡤⠤⠤⠴⠶⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣦⡸⣄⢸⠇⢿⠸⠇⠀⠿⠇⠀⠀⠠⠤⠄⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⣿⣿⣿⣿⣿⡇⠀⣠⡄⠀⠀⠀
⠿⠿⠿⠻⠟⠯⠤⠤⠴⠶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⡀⠀⠀⢀⣀⣤⢄⣒⣛⡿⢟⣛⡻⢷⣛⣀⠖⣂⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡻⠿⢟⣛⡛⠁⠀⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⠿⠿⣿⣛⣛⣛⣿⣯⣭⣭⠅⣥⣶⣶⣾⣍⣩⣿⣿⣿⣿⠁⠀⠀⢀⣸⣷⣶⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣤⣿⣀⡀⠀⠀
⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣤⣼⣿⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢿⣿⡿⡧⣤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⢛⠋⠀⠀⠀⠀⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⢹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⣈⡙⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢨⣄⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⣾⣷⣗⣀⣤⣤⣶⣾⣿⣿⣿⣿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠏⠀⠀⠀⠀⣀⣀⣈⣿⣿⣿⣿⣮⣽⣦⣽⡻⠿⣿⣿⣿⣿⡆⠀⠀⢲⣿⣿⣿⣾⣿⣷⣶⣶⣶⣶⣤⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣯⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣾⣿⣿⡿⢻⣿⣋⣀⣸⠿⢿⡿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣛⣛⣻⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣧⠈⠉⢁⣶⣶⣿⣿⣯⣉⠛⢛⡿⠿⣿⣏⣽⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⠉⠉⠀⢠⣬⣽⣟⣻⣿⡿⣿⣿⣷⣦⣤⣴⣾⣿⣿⣶⣿⣿
[22A⢒⣒⣒⣚⣛⣒⠒⠒⠒⠀⠀⠀⣗⣲⣺⣗⣒⣺⣿⣷⣿⣿⣿⣿⣿⣿⡟⢛⡛⡛⠻⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠤⠤⢤⣬⣭⡥⠬⠤⠤⠀⠀⠀⠭⣭⣭⡭⢿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠤⠤⠤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⣿⠿⠿⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⡦
⣶⡒⠒⠒⢒⣒⣒⠒⡒⠀⠀⠀⣒⣟⣿⣓⣺⣿⣿⣿⣿⣿⣿⣗⣹⣿⣿⢘⠉⠉⠉⠀⠀⠈⠛⠛⢿⣿⣿⡿⢿⣿⣿⣿⣿⣛⣛⣿⣿⣤⢤⣴⣶⢀⡆⠀⠀⠀⠀⠀⠀⠀⠸⡈⠟⢻⣿⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣷
⣯⣿⣿⠭⣭⣭⣭⡭⠭⠀⠀⠀⠭⠥⠤⠤⠽⢿⣿⣿⣿⣿⠿⠟⠾⣿⣿⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⢹⣿⠧⠼⠼⠿⠟⠛⠙⣿⠟⣟⢿⣺⣋⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⠿⢺⣿⣶⣿⣷⣒⡒⣒⠂⠀⠀⣘⣓⣛⣃⣈⣙⣿⣿⣿⡿⠉⠩⢹⣿⠯⢭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⠀⠀⡀⠀⡟⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣹⣿⣿⣿⣿⣿⣭⣭⠭⠄⠀⠀⢨⠤⠴⠦⠔⠒⠚⠛⠋⠁⠀⠒⣿⣟⣒⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠂⠀⠏⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⠖⢟⣿⣾⣗⣒⡂⠀⠀⢘⣟⣉⣉⣭⣽⣯⡄⠀⠀⠀⠀⠙⠷⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠉⠩⠭⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⣯⣭⣭⣿⣿⣭⡄⠀⠀⠸⠷⡶⣶⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠄⢐⣠⣤⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠻
⣼⣿⣧⣴⣿⣿⣿⣿⠿⣿⣷⠶⣾⣿⣯⠽⠿⠿⢿⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠘⠛⠛⠒⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⢠⣤⣤⣤
⣿⣿⣿⣿⠀⢏⡟⠏⢸⣿⣿⠀⢹⣿⠺⣿⡿⠿⠿⠇⠀⠐⣿⣦⡀⠀⠀⢀⣀⡀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠀⠉
⣿⣿⣿⡟⠀⡾⠀⢘⢰⡇⣿⠀⢸⣿⣤⠤⠤⠤⠶⠶⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣧⣀⢇⠀⡿⢸⠳⠿⠀⠸⠿⠀⠀⠀⠤⠤⢀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⣿⣿⣿⣿⣿⡇⠀⢠⡄⠀⠀⠀
⠻⠿⠟⠛⠟⠾⠥⠤⠤⠶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⢄⣐⣒⡿⢟⣛⡻⢷⣛⣁⠒⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡹⠿⢟⣛⡛⠃⠀⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⠿⠿⢿⣟⣛⣛⣛⣏⣭⣭⡍⢭⣥⣶⣶⣏⣩⣽⣿⣿⣿⠁⠀⠀⠀⣸⣧⣶⣾⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣤⣿⣀⡀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣤⣤⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠰⢶⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢿⣿⡽⡧⢤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⢐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⢈⠁⠹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣄⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⣾⣷⣞⣀⣠⣤⣴⣾⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⣈⣿⣿⣷⣿⣾⣽⣧⣭⠟⠿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣾⣿⣷⣶⣶⣶⣶⣤⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⡿⢿⣿⣛⣀⣸⠿⠿⡿⠿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣟⣛⣛⣻⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠸⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣧⠈⠉⠁⣶⣶⣿⣿⣯⣍⠛⢛⡻⠿⣿⣟⣽⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠉⠉⠉⠀⢠⣬⣽⣟⣿⣿⡿⢿⣿⣷⣦⣤⣤⣶⣿⣿⣶⣿⣿
[22A⠒⠒⢒⣒⣒⡒⢒⠒⠒⠂⠀⠀⢲⣶⣶⣿⣖⣶⣿⣷⣾⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣭⣭⣭⣭⣭⣭⣬⣥⣤⠄⠀⠀⠹⣭⣭⡭⢿⣿⣿⣿⢽⡿⠿⠿⣿⣿⡭⠭⠭⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢈⣦
⣶⡖⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢒⣿⣻⣛⣚⣿⣿⣿⣛⣾⣿⣷⣚⣿⣷⣀⡉⢉⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣛⣿⣿⣤⣤⣤⣴⠄⣶⠀⠀⠀⠀⠀⠀⠀⠸⡆⠻⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣴⣿⣿
⣛⣻⣿⣍⣭⣭⣭⣭⠭⠅⠀⠀⠨⠭⠭⠭⠭⢿⣿⣿⢽⣿⡿⠿⠶⣿⣿⡖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠤⠼⠿⠿⠟⠋⣿⠿⣿⣟⣒⣟⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠿⠷⣿⣷⣶⣷⣖⡒⠒⠂⠀⠀⢐⣓⣚⣒⣖⣛⣿⣿⣙⣹⡏⢉⢩⣿⡯⠭⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢶⣶⣿⣿⠂⠀⠃⠀⢸⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣯⠀⠀⠀⣿⣿⣿
⣩⣿⣿⣿⣿⣿⣯⣯⠭⠅⠀⠀⠸⠥⠤⠾⣿⣿⣾⣿⡗⣾⣻⣷⣾⣗⣒⣚⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡀⠀⠀⠀⠸⢨⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡗⠀⠀⢸⣿⣿⣿
⢾⣿⣿⡶⠾⢿⣷⣶⣒⡂⠀⠀⢘⣟⣋⣙⣿⣿⣿⣿⣿⣿⣿⣧⣿⠷⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡀⠈⠉⠩⠭⠭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⣯⣩⣭⣿⣿⣯⡥⠀⠀⠸⠿⡶⢶⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡤⢀⡀⣤⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠻
⣴⣿⣧⣵⣿⣿⣿⣿⡿⣿⣿⡶⣾⣿⣯⡭⠿⠿⠛⠀⠀⠀⠀⠀⠙⠿⢯⡝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠘⠃⠛⠒⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢠⣤⣤⣤
⣿⣿⣿⣿⡀⠈⡼⢻⠁⡟⣿⡇⢸⣿⡿⢿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠀⠉
⣿⣿⣿⣿⠃⢸⠃⠈⠀⡇⣻⡇⢸⣿⣧⡤⠤⠤⠶⠶⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⣼⡀⣿⠁⡇⡿⠇⠘⠿⠀⠀⠀⠠⠤⠀⣀⣈⣻⣿⣷⣄⣀⡀⣠⣤⣦⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢿⣿⣿⣿⣿⡇⠀⢠⡄⠀⠀⠀
⠻⠿⠿⠿⠿⠮⠥⠤⠤⠴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⢀⣀⣒⡻⢟⣛⡻⢷⣛⣃⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠇⠀⣼⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣘⠿⠿⢿⣿⣛⣻⣿⣿⣭⣭⣍⢩⣵⣶⣾⣏⣉⣽⣿⣿⣿⠉⠀⠀⢀⢸⣧⣶⣾⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣠⣿⣀⡀⠀⠀
⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣴⣿⣿⣿⣿⣇⢸⣹⣿⣿⣿⣿⣿⡿⠛⠁⠰⢲⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢿⣿⡽⠧⢄⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣿⡿⠛⠋⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⢈⡋⠁⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢢⣄⡉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣶⣿⣾⣀⣠⣤⣴⣶⣷⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⣀⣿⣿⣷⣷⣾⣽⣮⣽⠟⠿⣿⣿⣿⣿⡇⠀⠀⢰⣾⣿⣿⣾⣿⣷⣶⣶⣶⣶⣤⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⠽⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⡿⠛⣿⣛⣀⡸⠿⠿⣿⠿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣟⣛⣛⣿⡿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣷⡀⠉⠁⣰⣶⣿⣿⣯⣍⡛⢛⡻⠿⢿⣟⣝⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠉⠉⠉⠀⢠⣬⣽⣟⣛⣿⡿⢿⣿⣷⣦⣤⣴⣶⣿⣿⣶⣾⣿
[22A⠒⠒⠒⠒⢒⡒⠒⠒⠒⠂⠀⠀⢸⣲⣶⣿⣒⣲⣿⣿⢺⣿⣿⣿⣿⣿⡟⠛⠛⠛⠻⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⢬⣭⣭⣭⣭⣭⡭⠥⠭⠄⠀⠀⠸⢭⣭⡭⢽⣿⣿⣿⢽⡿⠿⠿⣿⣿⡥⠭⠥⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣻⣿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⡄
⣶⣖⠒⠒⠒⠓⠒⠒⠒⠂⠀⠀⢐⣺⣻⣛⣒⣿⣿⣿⣛⣾⣿⣷⣚⣿⣿⣀⡉⢈⠁⠀⠀⠀⠛⠻⢿⣿⣿⣿⢿⣿⣿⣿⣿⣟⣛⣿⣿⣤⡤⣤⣴⡆⣴⠀⠀⠀⠀⠀⠀⠀⠀⡆⠻⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣄⣶⣿
⣛⣻⣿⣏⣩⣭⣭⣭⡭⠅⠀⠀⠨⠭⠭⠭⠭⢿⣿⣿⢽⣿⡿⠿⠶⣿⣿⡖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠹⣿⠷⠤⠾⠧⠿⠛⠋⢻⠿⢻⡟⣓⣟⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠿⣷⣿⣷⣶⣶⡖⡒⠒⠂⠀⠀⢐⣒⣒⣓⣀⣈⣻⣿⣛⣹⣏⠉⢭⣿⡯⠭⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣶⣾⣿⣿⡇⠀⠁⠀⢸⠡⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣉⣿⣿⣿⣿⣿⣯⣭⠭⠅⠀⠀⠨⠥⠤⠤⠤⠀⠐⠒⠒⢺⣟⣷⣺⣗⣒⣚⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⠀⠸⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⢾⣿⣿⡖⠾⣻⣷⣗⣒⡒⠀⠀⢀⣻⣋⣉⣩⣭⣿⣭⣭⣿⣿⣿⣿⠷⠄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡀⠀⠉⠩⠭⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⢿⣿⣿⣯⣩⣭⣿⢿⣯⣥⠀⠀⠐⠿⣶⢶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡤⢀⡀⣤⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠛
⣤⣿⣿⣥⣿⣿⣿⣿⡿⢿⣿⡶⣾⣿⣯⡭⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣯⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠘⠃⠛⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⢠⣤⣤⣤
⣿⣿⣿⣿⠃⠨⣼⢻⠁⣿⣿⡇⢸⣿⡿⢿⣿⡿⠿⠷⠀⠀⢺⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠈
⣿⣿⣿⣿⠁⢰⠃⠀⡀⡇⢹⡇⠈⣿⣧⡤⠤⠤⠴⠶⠢⢿⣿⣿⣿⣿⣿⠿⠿⠁⠀⠀⠀⣼⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡀⡸⡀⣾⠃⡇⡿⠇⠀⠿⠃⠀⠀⠠⠤⠄⠀⠘⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⡇⠀⢠⣄⠀⠀⠀
⠛⠿⠿⠿⠿⠣⠥⠤⠤⠴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⢀⣀⢀⣀⣒⡻⢟⣛⡻⢷⣚⣋⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠇⠀⣸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣘⠿⠿⢿⣿⣛⣛⣟⣯⣩⣭⣤⠀⠀⠀⠀⡀⣀⣀⣤⣤⣶⠈⠀⠈⣀⣸⣧⣶⣾⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣠⣿⣁⡀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⠰⢮⣟⣯⣿⣿⣿⡿⠋⠁⠐⠺⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢿⣿⡽⠯⢤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣥⣾⣿⣿⠛⠋⠀⠀⠀⠀⢈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠀⢈⠁⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢠⣄⡉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣾⣁⣠⣤⣴⣶⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⣀⣿⣿⣷⣿⣾⣽⣦⣽⠟⠿⣿⣿⣿⣿⡇⠀⠀⠐⣾⣿⣿⣶⣿⣿⣶⣶⣶⣶⣤⣤⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣷⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⡿⠛⣿⣋⣀⡸⠿⠿⡿⠿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣽⣿⣿⣟⣛⣛⣿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣷⠀⠉⠁⣰⣶⣿⣿⣯⣍⡙⠛⡛⠿⢿⣟⣽⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠉⠉⠉⠀⢰⣬⣽⣿⣛⣻⣿⠿⣿⣷⣶⣤⣤⣶⣿⣿⣶⣾⣿
[22A⣒⣒⣚⣛⣛⣟⣒⡒⢒⡂⠀⠀⢸⣒⣾⣿⣒⣲⣿⣿⣺⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⡃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠤⠤⠤⣤⣤⡤⠤⠤⠤⠄⠀⠀⠸⢭⣭⣭⠽⣿⣿⣿⢽⡿⠿⠿⢿⣿⡦⠄⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⡿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡤
⣿⣖⠒⠒⢒⣛⣒⣒⣒⡂⠀⠀⢐⣺⣻⣿⣚⣿⣿⣿⣟⣿⣿⣿⡋⣿⣿⠍⠉⠉⠉⠁⠀⠀⠛⠿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣛⣿⣿⣥⠤⣴⣶⡆⣴⠀⠀⠀⠀⠀⠀⠀⠀⡃⠻⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣷⣿
⣿⣿⣿⡯⢭⢭⡭⠭⠭⠅⠀⠀⠨⠭⠤⠤⠬⠿⣿⣿⣾⣿⡿⠟⠓⢿⣿⡗⡒⢒⠒⠀⠀⠀⠀⠀⠈⢻⣿⠷⠔⠛⠓⠛⠛⠋⢿⡟⢻⡿⣋⣟⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠟⢿⣿⣷⣾⣿⣖⣒⣒⡂⠀⠀⢀⣉⣉⣉⣉⣉⣻⣿⡯⢭⡯⠭⢤⣿⠯⠥⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⡇⠀⠀⠄⢸⠁⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣉⣿⣿⣿⣿⣿⣿⡭⠤⠤⠀⠀⠀⠧⠒⠒⠒⠒⠒⠒⠒⣲⣟⣿⣺⣟⣛⢙⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠾⣿⣿⣗⢺⣻⣿⣷⣚⣓⠀⠀⠀⣻⣍⣭⣭⣭⠿⢦⣤⣿⣿⣿⣿⠷⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠩⠭⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠿⢿⣿⣿⣭⣭⡽⣿⣯⣧⠀⠀⠀⠿⣶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡦⢀⡂⣴⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠉⠈⠛
⣴⣿⣿⣦⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⣿⡬⠿⠿⢛⣛⠿⢿⣿⣿⣿⣿⣯⣭⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠈⠗⠛⠛⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⣴⣦
⣿⣿⣿⣿⡇⠸⣸⠻⠁⣿⣿⡇⠘⣿⡟⠿⠿⠿⠿⠿⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠁⢰⠇⠀⡁⡿⢸⡇⠀⣿⣧⠤⠤⠤⠶⠶⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣀⡸⡄⢸⠇⡇⠿⠇⠀⠿⠃⠀⠀⠠⠄⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⡿⠀⢠⣤⠀⠀⠀
⠛⠿⠿⠛⠛⠃⠤⠤⠶⠶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⢀⣀⣒⡺⢟⣛⡻⢷⣛⣛⠁⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠇⠀⣸⡇⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣝⠻⢿⣿⣛⣛⣻⣿⣭⣭⣭⣭⢠⣴⣶⣶⣮⡉⠀⠀⠀⠀⠈⠀⢈⣀⣜⣷⣶⣾⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢀⣤⣿⣁⣀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⢸⣾⣿⣿⣿⣿⣤⠀⠀⠀⠐⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠈⢽⣿⡟⡿⢤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⡏⠀⠀⠀⠀⢠⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⠄⢀⣝⣀⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣤⣈⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣞⣀⣤⣴⣶⣶⣿⣿⣿⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⠇⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣶⣭⣧⣭⣟⠿⢿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣿⣿⣷⠺⣿⣋⣀⣸⣿⠿⣿⣿⣻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣭⣿⣿⣿⣛⣛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⡄⠀⠀⣸⣿⣿⣿⣯⣼⡉⠙⢛⠻⠿⢟⣥⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠉⠁⠀⢰⣾⣭⣽⣿⣛⣿⡿⢿⣿⣶⣤⣤⣿⣿⣶⣶⣾⣿
[22A⠭⠭⢭⣭⣭⣭⠍⡍⠉⠁⠀⠀⢸⣭⣽⣿⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⡯⠉⠭⠭⠉⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⡒⠒⠲⠶⠶⡶⠖⠖⠒⠂⠀⠀⠐⢲⣶⣶⠚⣿⣿⣿⣾⣟⣛⣛⢻⣿⣗⡒⣒⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣹⡟⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠐⣄
⣿⣯⣉⣉⣉⣩⣍⣭⣉⡉⠀⠀⢨⣽⠽⠯⠭⣽⣿⣿⣯⣿⣿⣿⡧⣿⣿⡄⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⠛⡟⣿⣿⣿⣯⣭⣿⣿⣷⡒⣾⣿⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⠙⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣿⣿
⣬⣽⣿⡷⠰⣶⠶⠖⠒⠂⠀⠀⠐⣒⣒⣒⣒⣛⣿⣿⣟⣿⣟⣛⣉⣻⣿⣏⡉⠉⠉⠁⠀⠀⠀⠀⠈⢻⣿⣛⣒⣛⣛⣉⡉⠁⢹⡟⢹⡟⣥⣯⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣟⣙⣛⣿⣿⣿⣯⣭⣭⡍⠀⠀⠀⡭⠭⠭⠤⠤⠽⠿⠧⠤⣷⡀⢲⡿⡓⣒⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⡇⠀⠰⠀⢸⠃⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠤⢶⣿⠿⢿⣿⣿⠶⠒⠒⠀⠀⠀⣗⣒⣚⣋⣉⣉⣉⣉⣹⣯⣿⣽⡯⠭⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡇⠀⠘⠀⠘⠀⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣛⣿⣿⣏⣙⣹⣿⣿⣭⡭⠀⠀⠀⣽⠤⢤⢶⣶⣿⣷⣶⣿⣿⣿⣿⣟⣋⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠐⠒⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠛⣻⣿⠿⣶⣶⣿⣻⣷⣶⣀⣀⢀⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⠀⣅⣶⡆⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉
⢶⣿⣿⣶⡿⢿⣿⣿⡟⣻⣿⡟⢻⣿⡿⣖⣛⣛⣫⣿⠛⠿⢿⣿⣿⣿⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠿⠉⠙⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠶⠶⠶
⣿⣿⣿⣿⣧⠀⣸⠙⡇⢿⢻⡇⠀⣿⡏⠛⠛⠛⠛⠛⠀⠀⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠁⢀⠃⢀⡅⣼⢸⡇⠀⣿⡷⠖⠒⠒⠛⠛⠃⠸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣄⡜⠦⠸⠃⠛⠚⠃⠀⠛⢃⣀⣀⣐⣒⣀⣤⣤⣽⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⣿⠀⢰⣶⠀⠀⠀
⠛⠛⠛⠛⠉⠁⠐⠒⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣤⠀⠀⣀⣀⣤⢄⣐⣒⡿⢟⣛⡻⢷⣛⣛⠛⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡈⠿⢟⣛⡻⠏⠀⢸⡇⠀⠀⠀
⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣝⡛⣛⣿⣯⣭⠽⢿⣷⣶⣶⣿⣲⡔⠋⠁⠀⠀⠀⢀⣾⣿⡇⠀⢀⣀⣤⣿⣾⣿⣿⣿⣿⡘⣿⣿⢃⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢠⣴⣿⣧⣤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠸⣿⢀⠀⠀⠀⣰⡿⠛⠁⢀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠺⠿⣿⠛⡲⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣾⣿⣿⣿⣉⠉⠀⠀⠀⠀⠀⠝⢿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣟⠀⠻⠿⠟⠸⠿⠸⠿⠈⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⠀⣀⣠⣥⣄⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣶⣤⣈⣉⢙⣛⡿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⢟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠃⠀⠀⠀⢠⣤⣤⣽⣿⢿⣿⣿⣶⣷⣶⣋⠛⢻⣿⣿⣿⣧⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣟⣉⣿⣥⣤⣼⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠁⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠟⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣿⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⠿⢿⣿⣿⠆⠀⢀⣼⣿⣿⣿⣷⣾⣥⣉⠭⠛⠛⣫⣶⢿⠿⢿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⢐⣿⣶⣾⣯⣽⣿⡛⠿⠿⢿⣶⣶⣿⣿⣿⣿⣿⣿
[22A⠤⠤⠤⠤⠭⠯⠥⠥⠤⠄⠀⠀⢸⣭⠿⢿⣭⣽⣿⣿⢽⣿⣿⣿⣿⣿⠯⠤⠥⠤⠭⠅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀
⣒⣒⣒⣛⣒⣗⣒⣒⣒⡂⠀⠀⢘⣲⣶⣶⣚⣿⣿⣿⣻⣛⣋⣛⣻⣿⣇⣁⣁⣀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟⠛⠛⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣔⣀
⣿⣿⣭⠭⠭⡭⠭⠭⠭⠅⠀⠀⠸⠼⠿⠿⠤⣽⣿⣿⢧⣿⣿⣿⡃⣿⣿⡒⠒⠒⠀⠀⠀⠀⠛⠛⢿⣿⣿⣟⠛⡟⣿⣿⣿⡿⣶⣿⣿⣷⣖⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿
⣶⣿⣿⡗⢒⣒⣒⣒⣒⡂⠀⠀⢀⣒⣒⣒⣈⣙⣿⣿⣿⣿⣟⠋⠉⣿⣿⠯⠭⠭⠉⠀⠀⠀⠀⠀⠀⠙⣿⣏⣉⣉⣉⣩⡍⠁⠛⠏⢸⡝⣧⣷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣽⣍⣿⣿⣿⣿⣯⡭⠭⠅⠀⠀⠠⡤⠤⠤⠤⠀⠚⠛⠓⢲⣗⣒⣺⣟⣓⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⡇⠀⠐⠀⢸⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⡶⢶⣿⠛⢿⣿⣿⣓⣒⣒⠀⠀⢀⣏⣉⣉⣉⣉⡭⠭⠭⣽⣿⣿⣿⡷⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠐⠀⠈⠀⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣛⣻⣿⣯⢭⢽⣿⣯⡭⠦⠀⠀⠀⣿⠶⣲⣶⣒⣛⣻⣾⣿⣿⣿⣿⣏⣉⣩⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠒⠒⠀⠀⠀⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⡿⠿⣿
⠛⣛⣿⠿⣖⣶⣿⣿⣿⣿⣀⣀⣀⣯⡭⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠠⡤⣿⣆⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⡿⢻⢿⣿⡏⣿⣿⡟⢻⣿⡿⣿⣛⣿⣭⣍⠛⠛⣿⣿⣿⣿⣿⡷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠟⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠿⠿⠟
⣿⣿⣿⣿⡧⠘⡾⠙⡁⣿⢿⡇⠀⣿⡏⠛⠛⠛⠛⠛⣤⡀⠉⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠁⢨⠃⢠⡆⣿⣸⡇⠀⣿⡗⠒⠚⠛⠁⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⡞⠦⠸⠁⠃⠛⠃⣀⣛⣁⣀⣀⣠⣬⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⡿⠀⢰⡶⠀⠀⠀
⠙⠛⠙⠉⠉⠑⠒⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⢤⢴⣶⣿⣿⣿⣿⣿⣧⢀⠀⢀⡀⠀⣤⠀⣀⣠⣤⣴⢟⣛⣛⡿⢟⣛⡻⢷⣚⣛⠒⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡈⠿⢟⣛⡻⠇⠀⣼⡇⠀⠀⠀
⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣝⣛⣿⣯⣭⡽⠿⢿⣷⣶⣿⣶⢀⣾⣿⣿⣷⣶⣾⣿⣿⣿⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⢠⣶⣿⣦⣤⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⠛⠁⠠⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠿⠿⣿⠛⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣭⡍⠀⠀⠀⠀⠀⡎⠿⣿⣿⣿⣿⣿⣿⣿⣧⡿⢟⡀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⠟⢀⣤⣤⣧⣤⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣶⣤⣄⣉⠹⣟⡿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⢀⣀⣀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⢱⣿⣶⣴⣶⣶⣿⣿⣿⡿⢿⣿⣛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⣿⣿⣿⣿⠃⠀⠀⠀⣤⣤⣶⣿⣟⡿⣿⣿⡾⣷⣿⡭⠛⢿⣿⣿⣿⣧⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣟⣙⣿⣷⣦⣼⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣶⣶⣿⣿⣿⣭⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠿⠿⢛⣋⣛⣻⣿⢿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣯⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠿⠿⠿⠆⠀⠀⣼⣿⣿⣿⣿⣶⣦⣌⡉⠉⠛⣻⣶⣿⣟⢿⣿
⣿⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣯⣽⠟⠛⠻⡿⣿⣾⣿⣿⣿⣿⣿⣿
[22A⠲⠶⠶⠶⠶⠶⠰⠤⠤⠀⠀⠀⢸⡶⠿⠿⣶⣿⣿⣿⢾⣿⣿⣿⣿⣿⠃⠐⠒⠐⠘⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀
⣛⣛⣛⣛⣛⣟⣛⣛⣛⡁⠀⠀⢈⣹⣿⣿⣉⣿⣿⣿⣽⣩⣭⣝⢿⣿⡍⠩⠭⠭⠤⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣼⠋⠉⢉⣉⡁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣾⣧
⣿⣷⣤⡤⠤⠤⠤⠦⠤⠄⠀⠀⠰⠾⠞⠓⠲⣿⣿⣿⢶⣿⣿⣿⣒⣿⣿⣒⣒⣐⣀⠀⠀⠀⠈⠉⠻⢿⣿⣟⢙⣻⣟⣿⣿⡿⣷⣿⣿⣿⣍⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣾⣿⣿⣗⣺⣿⣿⣛⣋⡁⠀⠀⢨⣝⣩⣭⠉⠹⣿⣿⣽⢿⡯⠭⢭⣿⡿⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣭⣭⣭⣭⣥⡄⠀⡟⠉⢸⠃⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠽⠭⣿⣿⣿⣿⡷⠦⠤⠄⠀⠀⢰⣶⣶⣶⠒⠒⣚⣛⣒⣺⣧⣀⣽⣿⣩⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠛⠻⢿⣿⡇⠀⠁⠀⢸⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣒⣲⣿⣛⣿⣿⣟⣟⣋⣃⠀⠀⠸⣿⣿⣿⣭⣭⣤⠤⢤⣿⣾⡟⣿⣗⠒⢚⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠈⠐⠿⠿⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡯⠥⢿⣷⣿⢷⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠉⡉⢉⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠿⠿⣿
⠙⣿⡿⢿⣿⣿⣿⣿⣿⣿⣤⣀⣠⣭⡿⠽⡿⠃⠉⠃⠉⠛⠿⠟⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢰⡆⣿⣤⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⡀
⣿⣿⣿⣿⠟⠻⢻⣿⠏⣿⣿⡏⢻⣿⣿⣯⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠛⠁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠀⠀⠘⠛⠛⠟
⣿⣿⣿⣿⡆⢘⡟⠘⠀⡏⢿⡇⢸⣿⡟⠛⠛⠉⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣏⣿⠀⢸⠀⣤⡆⡇⣼⡇⠈⣿⡟⠋⠉⠉⠉⠉⠀⢸⣿⣿⣶⣶⣤⣶⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣦⠊⠆⠻⠀⣃⣋⣁⣀⣉⣀⣠⣤⣬⣭⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢸⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀
⠋⠙⠉⠉⠉⠉⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣟⣛⣿⠿⢿⣿⡇⠀⠠⠀⠠⠀⢠⣦⣀⣤⣴⣶⣿⢟⣛⣛⡛⢛⣛⡻⢷⣒⣒⠒⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠇⠀⣿⠇⠀⠀⠀
⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣍⣉⣭⣿⣿⡿⢛⣻⣿⣿⣿⣷⢸⣿⣿⣿⣿⣶⣿⣿⣿⣷⠄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠰⢿⣿⣶⣖⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡿⠋⠁⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠻⠻⣯⡯⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣭⠄⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⠀⣬⣴⣿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣷⣦⣤⣈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⢻⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⠃⠀⠀⠀⣴⣶⣶⣿⣟⣿⣿⣿⢿⣾⣯⡝⢿⣿⣿⣿⣿⣷⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⡿⠿⠿⣿⠀⠀⠀⠀⠛⠛⠿⠿⠿⣿⣿⣯⣋⣛⣿⣶⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠻⠛⢋⣭⣽⣿⡿⢿⠿⣿⣿⣿⣿⣿⢟⣛⣯⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⠂⢀⡠⠿⣿⣿⣿⣿⣷⣶⣤⣒⠉⢉⣵⣿⣿⣛⣻⣿
⠿⢿⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣤⣄⡀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⠭⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿
[22A⠒⠒⣒⣒⣺⣒⢒⠒⠒⠀⠀⠀⣻⠟⢛⡛⣿⣿⣿⣗⣿⣿⣿⣿⣿⣟⣒⣒⣒⡂⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀
⣭⣭⠭⢭⣭⣭⣭⠭⠭⠀⠀⠀⠭⣽⣿⣿⣽⣿⣿⣿⢯⣥⣦⡭⢿⣿⡤⠠⠀⠂⠐⠆⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣉⣀⣠⣠⡀⡄⠀⠀⠀⠀⠀⠀⠀⢰⠌⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣿⣆
⢿⣷⣖⠒⠒⣒⢒⡒⠒⠀⠀⠀⢒⣛⣻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣹⣿⣯⣉⠈⠍⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣸⣹⣿⣿⡿⠿⣿⡿⣿⣿⢼⡿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠐⢣⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠰⣿⣿⣿
⣿⣿⣿⣍⣭⣭⣽⡭⠭⠀⠀⠀⠤⠯⢿⣿⣿⣿⣿⣿⠾⢿⠖⠒⢺⣿⡛⢒⡒⠂⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣦⣶⣶⣶⠀⠀⡟⠀⣿⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⠞⠒⣿⣿⣿⣿⣖⣒⣒⠂⠀⠀⢸⣒⣛⣿⣿⣿⣿⡏⠉⣿⣯⡭⣿⡯⠤⢼⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⠀⠀⡇⠀⢹⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣏⣽⣯⣽⣿⣿⣿⣭⣭⡅⠀⠀⢸⡦⠴⠶⠚⠛⠛⠁⠀⠙⢿⣿⣿⣏⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠛⠛⣛⣛⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣿⣿⣿⡖⠒⢿⣿⣟⣿⡃⠀⠀⢸⣟⣭⣽⣭⣤⣄⠀⠀⠀⠀⠈⠙⢶⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣩⣭⡀⠠⢀⣀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇⠀⠀⠘⠛⠻⢿
⣩⣿⣟⣻⣿⣿⣿⣿⣿⣷⣤⣤⣴⣶⣓⣻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⢸⡿⣿⣤⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⣀
⣿⣿⣿⣿⠉⠿⣿⣿⢠⣿⣿⠋⢻⣿⣻⣿⣷⣶⣶⡎⠉⠁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠈⠁⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠘⠋⠉⠛
⣿⣿⣿⣿⠆⢰⠇⠸⠈⡇⣿⡆⢸⣿⡉⢉⣉⣉⣩⣤⠀⣰⣿⣿⣷⣶⣶⣶⣆⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣟⡏⠀⣼⠀⣶⠰⡇⣿⠇⢸⣿⠉⠉⠉⠉⣁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⣿⣿⣿⣿⣿⡇⠀⢀⡀⠀⠀⠀
⣿⣿⣿⣿⣶⠙⣂⣛⣀⣁⣉⣠⣤⣥⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢹⣿⣿⣿⣿⡇⠀⣾⡇⠀⠀⠀
⠉⠉⠉⠉⠀⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣟⡛⢛⣻⣿⣿⡿⠿⢿⣷⣤⣀⠀⠀⠐⠀⣰⣦⣴⣶⣿⣿⣿⢟⣛⣛⡛⢛⣛⡛⢓⣀⣒⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡘⠿⢟⣛⡛⠁⣀⣿⠀⠀⠀⠀
⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣍⣹⣿⣶⣶⣛⣛⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠘⣿⣿⣿⣇⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠛⢻⠷⢳⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⡘⠙⠻⣿⣿⣿⣿⣿⣿⣿⣧⡿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⢟⣠⣶⣾⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣷⣦⣄⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢤⣴⣦⣦⣴⣶⣦⣤⣤⣤⣄⣀⣀⠻⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠁⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⠻⣿⣿⣿⣿⣧⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠿⠿⠿⢿⠀⠀⠀⠀⡍⠛⠛⠻⠿⠿⠿⢍⣋⣩⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠛⠋⣥⣤⣿⣿⣟⠟⠿⠿⣿⣿⣿⡟⣻⣭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠃⢀⣐⣿⣿⣿⣿⣿⣿⣿⣮⣅⣀⣩⣭⣿⣿⣭⣿⣿
⠿⡿⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡋⠉⢹⣿⣟⣿⣿⣿⣿⣿⣿⣿
[22A⣉⣉⣉⣉⣭⣉⣉⣉⣉⠀⠀⠈⣟⣋⣉⣛⣿⣿⣿⣯⣿⣿⣿⣿⣿⡏⠍⠭⠍⠍⠩⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⡄
⣶⠤⠤⠶⠶⠶⠶⠶⠶⠀⠀⠀⡖⣿⣿⣷⣿⣿⣿⣿⣷⣶⣶⡞⣻⣿⣖⣖⣂⣂⣘⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣤⣤⣤⣤⢠⡆⠀⠀⠀⠀⠀⠀⠀⠸⠘⠟⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣼⣿⣧
⣿⣿⣦⣉⣛⣛⣛⣉⣉⠀⠀⠀⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⡿⠧⢿⣿⣧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠈⣿⡿⠦⠼⠿⠿⠿⢿⢹⣿⠿⣿⣟⣺⣛⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⢿⣿⣿⣤⣶⣶⠴⠦⠶⠀⠀⠀⡚⠒⠒⠒⠚⣻⣷⣾⠟⠳⣂⣀⣼⣿⡉⣩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⣶⣿⣿⣿⠀⠐⣍⠀⡯⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣒⣛⣿⣿⣿⣿⣛⣋⣉⡀⠀⠀⣭⡭⠭⠭⠥⠭⠉⠁⠀⠀⠀⢶⣿⠒⢒⣛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣭⣿⣿⢿⢿⣿⢾⣶⡶⠀⠀⠀⢺⣖⣒⣒⣒⣲⣤⣀⠀⠀⠀⠀⠉⠡⠤⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣘⠉⠉⠭⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣾⣟⣿⣚⣛⣿⣿⣿⣿⡁⠀⠀⠽⡯⡽⣿⣿⣶⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠄⢰⢠⣄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠙⠿
⣴⣿⣯⣻⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣍⣻⣿⡿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢹⡼⢿⣶⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢠⣤⣤⣤
⣿⣿⣿⣿⠉⣋⡿⡟⢰⣿⣿⠀⢿⣿⢿⣶⣶⣿⣿⠇⠀⠸⣿⣿⣶⣤⣤⣤⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠈⠁⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠈⠁
⣿⣿⣿⡟⠀⡾⠁⠁⢸⠏⣿⠀⢸⣿⣀⣀⣀⣤⣤⡤⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⢸⣿⠀⣿⣿⢸⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⣇⠰⡿⢸⢰⣿⠀⢸⡿⠁⠀⠀⣀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⢿⣦⠀⣿⣿⣿⣿⣿⡇⠀⣤⡀⠀⠀⠀
⣿⣿⣿⣿⣎⣈⣀⣥⣬⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⣾⣿⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⢿⣿⣿⣿⣿⠁⠀⣿⠁⠀⠀⠀
⠉⠉⠀⠀⠀⠈⠀⠀⠉⢿⣿⣿⣿⡿⠿⢿⣿⣟⣻⣿⣿⡋⢭⣭⣿⣿⣛⣛⣿⣿⣿⡖⠂⠀⣢⣴⣿⣾⣿⣿⣿⣿⣿⢟⣛⣛⡛⢛⣛⡛⢂⣀⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡸⠿⢟⣛⡛⣀⣼⣟⣀⠀⠀⠀
⣤⣤⣤⣶⣶⣶⣶⣶⣶⣷⣤⣾⣿⣿⣿⣍⣭⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠈⣿⣿⣿⡧⣠⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠃⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⠉⣹⡗⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⡙⠻⣿⣿⣿⣿⣿⣿⣶⣤⣄⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠟⠿⠿⠿⠃⠻⠿⢟⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣶⣌⠻⠿⣿⣿⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣷⣶⣶⣶⣤⣤⣤⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣭⢿⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢺⣿⣿⣿⡿⠀⠀⠀⠐⣿⣿⣿⣿⣿⡿⣷⣦⣄⣀⠉⢻⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣟⣛⣟⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠛⠛⠻⠇⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠋⠁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣧⠉⠉⠁⣶⣶⣾⣿⣏⣙⡛⣻⠿⠿⣿⣫⣝⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⣤⣽⣿⣛⣿⣿⣿⣿⣿⣶⣦⣤⣴⣿⣿⣿⣶⣿⣿
⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⣿⣿⣶⣦⣤⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣁⣀⣽⣯⣽⣿⣿⣿⣿⢿⣿⣿
[22A⠤⠤⠤⠴⠶⠴⠤⠤⠄⠀⠀⠸⠭⣤⣤⡼⢿⣿⣿⣿⣿⠿⠿⣿⣿⡘⠒⠒⢒⠀⡂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣿⣭
⣗⡒⢛⣛⣛⣛⣛⣛⡃⠀⠀⢸⣹⣿⣿⣉⣹⣿⣿⣿⣿⣿⣯⢭⣿⣿⠼⠥⠬⠄⠅⠀⠀⠙⠛⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣭⣿⣿⣷⡖⣾⣿⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠉⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿
⣿⣿⡧⠭⠭⠭⠥⠤⠄⠀⠀⠨⡤⠤⠦⠐⢻⣿⣿⣟⣿⣿⣛⡚⣿⣿⣖⣒⡘⠀⠀⠀⠀⠀⠀⠀⢻⣿⣛⡒⣛⣛⣛⡛⠇⢻⡟⢹⡟⣭⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣷⣾⣿⣟⣛⣛⡃⠀⠀⢨⣉⣉⣉⣉⠩⠽⢿⡿⠛⠀⠠⢴⡿⠏⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⣿⣿⡇⠀⢸⠄⢸⠃⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⣭⣽⣿⣿⣿⣿⡧⠤⠤⠀⠀⠀⡷⠒⠒⠒⠒⣒⣂⠀⠀⠀⠀⠙⠯⠉⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠘⠀⠘⠂⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⣾⣿⡞⣟⣿⣟⣿⣿⣃⠀⠀⠈⣿⣭⣭⣭⡭⡷⢶⣶⡄⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿
⠿⣿⣿⣭⣽⣿⣿⣿⣷⠀⠀⠀⣟⣶⣻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⠀⣅⣶⡆⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⢛
⣿⣿⣮⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⣷⡮⠿⢿⣛⣛⠿⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠿⢙⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⡶⠶⢿⠿
⣿⣿⣿⡇⠸⣽⠻⠇⣿⣿⡇⠈⣿⡗⠿⠿⠿⠿⠟⠀⠀⣻⣿⣿⣶⣶⣶⡄⠀⠀⠀⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠃⢐⠇⢀⡃⣿⢸⡇⠀⣿⣧⠤⠤⠴⠶⠾⠂⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡀⡸⣄⢸⠇⠿⠾⠇⠀⠿⠃⠀⠀⠠⣄⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⠘⣿⣿⣿⣿⣿⠀⢠⣶⠀⠀⠀⠀
⣿⣿⣿⣿⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⠀⣿⣿⣿⣿⡟⠀⢸⡏⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣛⣛⣿⣿⣭⣭⣭⣿⢠⣶⣶⣿⣿⣭⣽⣿⣿⣿⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡻⢟⣛⡛⢂⣚⣒⠂⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣀⡻⠿⢟⣛⡣⢴⣾⣧⣤⠀⠀⠀
⣤⣤⣶⣶⣶⣶⣾⣿⣿⣷⣬⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡺⣿⣿⣿⣿⣿⣿⣿⡿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⢿⣿⣻⡲⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣛⣛⠋⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠿⠿⠿⠃⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣿⣷⠀⢰⣿⣮⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠇⠀⠀⠀⢳⣦⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⢟⣴⣿⣿⣿⢟⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡟⠀⠀⠀⢀⣈⣻⣯⣹⢿⣿⠛⢿⣿⣿⣿⣿⡃⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣶⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣭⣄⠀⢀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠟⠛⠛⠛⠀⠀⠀⠀⢰⠀⠀⠀⠈⠙⠋⠁⠐⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣻⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣧⠀⢀⣸⣿⣿⣿⣿⣶⣭⣍⠭⠟⠛⢿⣶⣿⡿⢿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣶⣷⣿⣯⣿⣿⣻⡿⠿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿
⠿⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⢿⣿⠛⠿
[22A⠲⠶⠶⠶⠶⠶⠲⠖⠀⠀⠀⡟⢲⣶⣶⠚⣿⣿⣷⣟⣛⣛⣻⣿⣷⣃⣀⣀⣀⣠⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⢠⡐⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣷
⣍⣉⣉⣉⣩⣩⣉⣉⠀⠀⠀⣭⡿⠿⠯⢭⣿⣿⣿⣿⣿⣿⡤⢼⣿⡗⠂⠀⠂⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⢻⢻⣿⣿⣿⣿⣶⣿⣿⣿⣻⣿⣿⣳⡇⠀⠀⠀⠀⠀⠀⠀⠨⢇⠉⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿
⣿⣿⠤⣶⣶⠶⠶⠒⠀⠀⠀⢒⣖⣒⣒⣚⣿⣿⣿⣿⣿⣛⣉⢙⣿⣿⠩⠉⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣉⣉⣉⣩⣭⠉⠀⡿⠉⣿⢻⣾⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿
⣛⣿⣿⣿⣿⣽⣭⣭⠁⠀⠀⢬⡭⠭⠥⠤⠽⣿⣿⣿⡗⠒⠒⣾⣿⣒⣲⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⠀⠀⡇⠀⢿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿
⢤⡿⢿⣿⣿⣾⠶⠶⠂⠀⠀⢸⣒⣒⣛⣉⣉⣹⣿⠟⠉⠹⢩⣿⡯⠭⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠄⠀⠁⠀⠘⢸⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣛⣻⣿⣿⣿⣭⡅⠀⠀⢨⣿⢤⢴⣶⠾⣿⠀⠀⠀⠀⠘⢛⣛⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠒⠂⠀⠈⠉⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇⠀⠀⠸⠿⠿⣿⣿
⣿⣿⣦⣴⣿⣿⣿⣿⣇⡀⠀⢘⣛⣟⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢨⣶⣿⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣩
⣿⣷⣾⠿⣿⣿⣿⠛⣿⣿⠿⣿⣿⣷⣞⣛⣛⣻⡟⠻⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠸⠏⣝⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠸⠟⠛⠿⠟
⣿⣿⣿⡄⢁⡟⢻⠸⡟⣿⡀⢸⣿⠾⠿⠿⠟⠛⠃⠀⢈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠁⢸⠁⣈⠀⡇⣿⡇⢸⣿⠶⠖⠒⠒⠛⠛⠀⢺⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⢇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣁⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣧⣀⠾⡀⣿⠀⠇⠟⠃⠘⠛⠀⢀⣀⣐⣒⣠⣤⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢸⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀
⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠈⠀⣀⠀⠀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡸⠿⠶⠿⠿⠼⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⢸⣿⣿⣿⣿⡇⠀⣿⠇⠀⠀⠀⠀
⠁⠁⠀⠀⠀⠀⠀⠀⠙⢿⣟⣛⣻⣿⢭⠭⢭⣿⣷⣶⣶⢸⣿⣿⣿⣷⣶⣾⣿⣿⡏⠁⢀⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡻⢟⣛⡛⢒⣒⣂⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠀⣀⣘⡻⠿⢟⣛⡲⢾⣿⣶⡦⠀⢀⣀
⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣮⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣧⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⠻⣯⡯⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣉⡝⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠃⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣸⣷⣤⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠿⠟⠀⠻⠿⠟⠸⠿⠸⠿⠘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⠃⠻⠿⠟⢴⡿⢿⣿⣋⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠃⠀⠀⠀⣀⣭⣿⣧⣽⣻⣿⠟⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⡀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⡷⢀⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠃⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠁⠀⠘⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢟⣋⣛⣻⣿⠿⣿⣿⣿⣿⣿⣿⠿⣛⣻⣿⣾⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⡿⠧⠀⠠⣾⣿⣿⣿⣿⣷⣶⣖⣋⠉⢛⣛⣿⣿⣟⣻⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣶⣤⣀⣸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⢯⡟⠛⠛
[22A⠒⠒⠚⣓⣚⣓⣒⠂⠀⠀⣚⣳⣶⣶⣞⣿⣿⣿⣛⣛⣛⣛⣿⣿⣍⢉⠭⠩⠤⡧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣉⣁⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⣗
⣉⠩⣭⢭⠭⠭⠭⠅⠀⠀⠼⠾⠿⠷⠦⣼⣿⣿⣿⣿⣿⡖⣲⣿⣿⡚⣒⣒⠀⠂⠀⠀⠈⠙⠻⣿⣿⣿⢙⣟⣿⣿⣿⡿⣿⣿⢿⣿⡯⣿⢿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⡖⣒⣒⣒⣒⣒⡂⠀⠀⢐⣖⣚⣛⣛⣿⣿⣿⣿⣿⠯⠭⠭⣿⡿⠯⠥⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣭⣭⣭⣵⡄⠀⢹⡏⢸⡏⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣭⠭⠅⠀⠀⢰⠤⠤⣾⣿⣿⣿⣿⣟⣗⣒⣒⣺⣟⣋⣉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⡇⠀⢸⠀⢸⠁⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣖⣒⡂⠀⠀⢘⣏⣉⣹⣿⣿⣿⣿⣿⣯⣿⡧⣿⡷⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠀⠈⠁⠿⠿⠿⠟⠛⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣍⣿⣿⣿⣿⣭⡥⠀⠀⠠⣿⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣀⣈⠉⡉⢉⡁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⢟⠛⠿⣿⣿
⣿⣷⣶⣾⣿⣿⣿⣷⣀⣀⣈⣽⡿⢽⣿⣿⣿⣿⠿⠋⠛⠿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⣶⣿⣧⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⣨⣭
⣿⣿⡿⢿⣿⣿⡟⣻⣿⡟⢻⣿⡿⣗⣛⣻⣯⡅⠀⠀⠀⠀⠈⠛⠻⠗⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠛⢲⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠛⠋⠛⠛⠋
⣿⣿⡇⠘⡾⠙⡇⣿⢿⡇⠀⣿⡏⠛⠛⠛⠛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠃⢸⠃⢀⡅⣿⢸⡇⠀⣿⡷⠒⠒⠚⠛⠛⠁⠐⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣬⣤⢸⣿⠀⣿⣿⢺⣷⢸⡇⣿⡇⣿⣧⣿⣻⣷⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣄⠜⠦⠸⠃⠻⠛⠃⠀⢛⣃⣀⣀⣐⣦⣤⣤⣴⣿⣿⣿⣶⣤⣀⣴⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⢸⣿⠀⣿⣿⢸⣿⣿⡇⣿⡇⣿⣏⣻⣿⣦⢹⣿⣿⣿⣿⠀⢠⣿⠀⠀⠀⠀⠀
⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠀⢠⡄⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠸⠿⠶⠿⠿⠾⠏⠿⠇⠻⣷⡿⠛⠿⣾⠿⣸⣿⣿⣿⡿⠀⢸⡟⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠈⢛⣿⣻⣿⣿⣿⠿⢿⣷⣶⣶⣿⡆⣿⣿⣿⣿⣶⣶⣿⣿⣶⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⣛⡛⢛⣛⡓⢒⣂⣀⠀⣀⡀⣀⣀⢀⣀⡀⢀⣀⠤⣀⣛⡻⠿⢛⣛⡛⢿⣿⣶⡂⢀⣤⣀
⣤⣶⣶⣶⣶⣶⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⢣⣿⣿⣿⢸⣿⣻⣷⢿⣷⣿⡏⣿⣿⡇⢸⣿⠀⣿⡟⣿⡇⣿⣿⠿⠀⢿⠻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣯⡭⠉⠀⠀⢀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠀⣿⣿⢸⣿⣿⣿⢸⣿⢻⣷⢸⣿⣿⣇⣿⣿⣿⢸⣿⠀⣿⡇⣿⡇⣽⣻⣷⠀⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠿⠟⠀⠻⠿⠟⠸⠿⠸⢿⡘⠿⠿⠹⠿⠹⠿⠼⠿⠿⠿⠿⠿⢃⠻⠿⠟⣐⣿⣿⣯⣽⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⡟⠀⠀⠀⢠⣤⣽⣿⣷⣿⣽⣟⣋⠻⣿⣿⣿⣿⣿⣂⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠁⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⠿⠛⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⢉⠉⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⠛⣭⣭⣭⣿⡟⡿⠿⣿⣿⣿⣿⡿⢻⣭⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠟⠂⣀⣴⣿⣿⣿⣿⣿⣷⣯⣭⣆⣉⣩⣿⣿⣿⣭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠉⠝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⠉⠉⠉
䷩ 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⦈
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# ⚓ 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.
=> =============================================================================
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.
=> =============================================================================
World Wide Web but a lot lighter.
䷩ 𝚕𝚒𝚗𝚎 5131
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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 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).
=> =============================================================================
World Wide Web but a lot lighter.
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