𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Wednesday, September 21, 2022
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Generated Thu 22 Sep 02:42:28 BST 2022
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
Full hyperlinks for navigation omitted but are fully available in the originals
The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈
Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔
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Gemini index for the day: gemini://gemini.techrights.org/2022/09/21/
╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕
Previous bulletins in IPFS (past 21 days, in chronological order):
QmcZN6RDP7J7Dk8c2QYXeoVfYifxDsaK62EM44gSje2HDr
QmcvJBJvcdzE6YbN5kUFP3Cqgwc9K38gcNKU3B86eL6WLr
QmUZ8Zpgu5W6CLgXAAXnvYwpAw9fCGWhqWM6MWMHcNxEwP
QmUtqYa5g8brBCgtMeneus47sgXJXCdgZvkekvW8UuYchF
QmdXKq8frFc6SxT7BErqJC3fnDsbXQfhNmEGEc1BVWprrQ
QmWERMsn1DfZrtyJQLRpzrUSCM3So8WboRGV5qBDKU6pKo
QmeWggouo6JzSCSNPBkF9EbHtca8pg2uefQDca6Z63NbCy
QmPd8eLQ2K4AVwUwwDXWDzcs9Y6q6rEafAqGPGCsRaNu1n
QmfCsH16QBNTRxCFWkRbN8iKEXme1kZFksZvXhwcAkGbv1
QmbPTxQodgGofF9SkH91qnwS4xfGFrHEdPESATQe3KmLup
QmVuPxmX77pHLEiaxQUdUu9Hv2c5on5vmDiepeKvhokhrK
QmSSVivjsb74DwAwvNFUWiXAExS8esEHiJBzykMK9Da4BW
QmYr91F9jQ6C4UgdRQqHE5QbcXGHYUcZYCYnigDogJGkyy
QmVMkxTFB9LnSNGEQQ9wHzrmgcc9R1GBBrkXQwesnZn9sF
QmVp5xT7mzD29ygLxoepcfrYB5u4Vyc9cndBz66AV7cb69
QmYPR3iBujyTHUCpxPHwsMNXJiNSLgfQa4AuzchgiUJ3M8
QmWTRh2ZdgwUGq9b4v8Cnv5g51yvN18PNFNC89vkDa478d
QmQCpGVvMV5EduUzKqAToqKEmsDN4YWubH4KwPsA11BkFL
Qmac6ycg4HgCXK32zmYm12JDmDQfL8BtJPF89Q129UbkCn
QmTscUZbUfSgcCFNAKKV4rEvAsHABZ2Ct9K7RCSGGzRRDT
QmcB3PmzUDz4gMMbVfzAbgcnKwRGZjhaY7foe2B7ox9dZW
╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕
⦿ Pale Moon’s Greed and Corrosive People (Boosted by Microsoft) in “FOSS” “Communities” | Techrights
⦿ [Meme] EPO Abuse Continues, Managers Acting Deaf | Techrights
⦿ The Life of Linux Will Be Shortened by a Misguided Adoption of Rust | Techrights
⦿ IRC Proceedings: Tuesday, September 20, 2022 | Techrights
⦿ Linux Foundation ’Europe’ a Front Group for Patent Trolls and American Monopolies | Techrights
⦿ The EPO’s Local Staff Committee The Hague (LSCTH) is “Requesting Immediate Action” | Techrights
⦿ Official Ubuntu Blog Has Just Promoted Microsoft Windows+Systemd | Techrights
䷼ Bulletin articles (as HTML) to comment on (requires login):
http://techrights.org/2022/09/21/corrosive-trolls/#comments
http://techrights.org/2022/09/21/epo-managers-acting-deaf/#comments
http://techrights.org/2022/09/21/going-rusty-faster/#comments
http://techrights.org/2022/09/21/irc-log-200922/#comments
http://techrights.org/2022/09/21/lf-openwashing-front-group/#comments
http://techrights.org/2022/09/21/lscth-open-letter/#comments
http://techrights.org/2022/09/21/ubuntu-windows-systemd/#comments
䷞ Followed by Daily Links (assorted news picks curated and categorised):
http://techrights.org/2022/09/21/debuginfod-in-ubuntu/#comments
http://techrights.org/2022/09/21/i3-4-21-released/#comments
䷩ 𝚕𝚒𝚗𝚎 66
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/21/corrosive-trolls/#comments
Gemini version at gemini://gemini.techrights.org/2022/09/21/corrosive-trolls/
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Gemini_version_available_♊︎
✐ Pale_Moon’s_Greed_and_Corrosive_People_(Boosted_by_Microsoft)in“FOSS”
“Communities”⠀✐
Posted in Deception, Free/Libre_Software, Microsoft at 6:04 pm by Guest
Editorial Team
Reprinted with permission from Ryan
NoScript’s legacy XUL version supports Pale Moon.
It works fine, but by default, “MoonChild” has set it to disable NoScript and
warn the user that the extension may “cause issues”.
I went to install NoScript, the legacy XUL version, which works fine in
SeaMonkey.
Pale Moon immediately disabled it and told me it was dangerous to use that
extension because it might break Web sites.
Then when I clicked to know more about this issue, I_was_led_to_a_page_on_Pale
Moon_Forums where “MoonChild”, the main developer, explains that he doesn’t
want people coming to bitch to him if an extension that disables JavaShit
breaks a Web site.
So it just turns it off and makes it sound like the extension is sketchy, and
then you have to read that and say “Oh bullshit!” and turn the extension back
on.
The cynic in me would say that since it breaks Pale Moon’s default start.me
page full of ads and shit, he’s worried he may lose money if you don’t see that
every time you load the browser.
So he is scaring people away from NoScript to keep the spice flowing.
It’s understandable that people who spend significant time and effort to create
a program deserve to be compensated for it, but scaring the users of an
extension that enhances Web browser security by reducing the Active Content
attack surface (which is present in all Web browsers) is not the right way to
handle this.
“MoonChild” doesn’t need to deal with his revenue problem by implying that
NoScript is malicious software, which is dishonest to say the least. He should,
rather, put a one time notice in the browser explaining that he needs revenue
and that blocking the start.me page harms his ability to fund Pale Moon
development, and then asking the user or offering to the user to whitelist that
page, and ultimately respecting the user’s decision.
Free Software (as defined by the Free_Software_Definition in “The Freedom to
run the program as you wish.”) is about respecting user choices.
If your program doesn’t respect what the user wants, it may technically fall
under a Free Software license as source code, but it violates the spirit of the
Free Software Definition.
When I went to learn more about the issue that Pale Moon causes for NoScript, I
came to a different forum where I learned that after “MoonChild” made the
childish decision about overriding the user’s clearly expressed intention of
installing NoScript to protect them from Active Content, users flooded the Pale
Moon forums to complain, and the result of the complaining was that NoScript_is
declared_a_“banned_subject”_on_their_forums, and threats of being banned from
the Pale Moon forums by “MoonChild”.
I’m starting to seriously wonder about “MoonChild’s” version of the events that
led to former Pale Moon developer Matt Tobin being expelled from the project.
Tobin hangs out at the #SeaMonkey IRC room on Libera Chat, and he doesn’t seem
like a bad/mean person to me. The description of a developer as a Prima Donna
and a “Hitler”-like figure sounds more to me like “MoonChild” because of the
ongoing NoScript debacle.
I would generally like to have another browser to recommend to people.
I’m going to hold off on Pale Moon. It does seem to have fewer Web
compatibility issues than SeaMonkey, but there are still quite a few.
I noticed that the Palefills extension to fix some of these up also works in
SeaMonkey (it’s in the manifest and makes GitHub and Gitlab and dozens of other
sites work again in both browsers).
Typically, both browsers should generally appeal to people who don’t like the
“Modern Web” very much and who think Firefox has gone completely off the rails,
who are willing to deal with “Modern Web” breakage by deploying clever hacks
and workarounds where needed (or just opening some Modern browser to pay their
electric bill and close it again for a month), but the developers of Pale Moon
seem to be difficult people, to put it mildly.
I’ve noticed that “MoonChild” has made Matt Tobin another “graylisted” subject
on his forums. Either you say Tobin is Hitler or you disappear too.
“Communities” such as this are impossible and ultimately fail due to attrition.
They can be fun to make fun of, though, but you have to find your own platform
to do it on.
For example, when MinceR in #techrights IRC said, “Has he heard of the ability
to change home pages?”, I said, “ALERT: Changing your home page is dangerous
and may cause Pale Moon to become unstable, resulting in profile corruption. We
cannot support this if you proceed. -M.C. Hitler”.
Gone are the days where we can have mild disagreements, or disagreements that
aren’t even about Free Software, or even an off beat sense of humor, without
the Cancel Mob trying to hijack everything and kill us with fire.
Recently, Matthew J. Garrett, or Matt GULAG as I call him on #Techrights IRC
has been petitioning Roy to cancel me over some personal beliefs that I have
expressed that aren’t even that unusual. Roy hasn’t acted on that.
Matt GULAG’s career in software development is on a jack stand provided by
Microsoft and other companies that are hostile to software freedom.
Unfortunately, when Freenode turned into The Pretender’s “Freenode Autonomous
Zone”, people who are bad in other ways, like Matt GULAG and “MoonChild”
(cough M.C. Hitler) (which MinceR refers to as “ManChild”) forked it and
created Libera.Chat. Libera.Chat is awful because it’s been politicized by the
cancel mob.
Freenode, before The Pretender took it over, had almost 100,000 users and was
the place to discuss Free Software.
Libera.Chat only has about 49,000 users at peak hours, and it’s because they
cancel anyone who isn’t some total leftist freak-of-nature or a Microsoft toady
that supports their sabotage efforts of GNU/Linux.
Libera.Chat has banned me like 7 times (sort of like Matrix.org has), but K-
Lines don’t mean much of anything to me like they did in the days of dial-up or
direct connect over my real IP which only changed every several months or so.
I change IP addresses and VPN providers every so often so good luck making any
of that stick. I’m on Libera.Chat in several different ways all at once right
now.
Eventually the bans don’t happen as often because you know which rooms (such as
Microsoft has virtually succeeded in planting moles in every high profile place
where “Linux” is up for discussion, and they’ve made sure that people who don’t
like Microsoft and say why get banned. Even if it’s like, a one-liner and
you’re not up on a soap box. Or you make a joke about something that really
happened.
(Like the time Microsoft_did_the_BIG_BOOBIES_debacle with the Linux kernel in
their HyperV driver and then says all the perverts are in open source.)
The bans happened to me on Reddit and Libera, and whether the ban itself sticks
or not, they know that you know that if you come back and criticize them again,
the ban will just happen again.
This is part of their strategy to make it seem like everyone “loves” Microsoft
or are at least indifferent.
When communities fall apart, and the center cannot hold, due to people like
Matt GULAG re-defining “community” into something that creates proprietary
“standards” that people have no control over, which lock them out of their
computer (e.g., “secure boot community”), then projects like GNU/Linux become
little more than another crappy “vendor UNIX”, which everyone hated due to the
lock-in and incompatibilities.
Oh, you want to go make something else?
It won’t be compatible, it’ll probably have bugs if you try, but “you have
every right to do that”, says Matt GULAG on his Twitter blog.
(In reference to IBM’s systemd. The creator of systemd now works for Microsoft.
I’m assuming that Mr. GULAG was trying to bring his manure spreader of FUD to
bear on Devuan_GNU/Linux.)
Mr. GULAG has repeatedly defended Microsoft “Secure” Boot even though he
himself admits that their Platinum-level OEM partner, Lenovo, has now sabotaged
it to prevent Linux kernels from booting, either nearly entirely, on a laptop
that was hard coded to only boot if the OS entry was Windows Boot Manager, or
Red Hat Enterprise Linux, or on a very recent one that doesn’t enable the
third-party certificate that his Linux implementation of “Secure” Boot needs to
start up, and in which case Windows screws up your Bitlocker and potentially
causes data loss on your Windows partition if you try to re-configure this.
I had another system, the Yoga 900-ISK2 that was sabotaged so badly that I
filed a lawsuit against Lenovo in Illinois before they agreed to change it.
My reward? Mr. GULAG’s white glove character assassination, as usual. He only
ever attacks defenders of Free Software, and people who write Free Software. He
never attacks the rapists, stranglers, and pedophiles of Microsoft and their
affiliates.
Peter Bright of Ars Technica? Posted pro-Microsoft articles constantly.
Silence. (Tried to rape a 9 year old. Now in prison.)
Jeremy Soule of Microsoft Bethesda? Silence. (Raped a woman in the office, sent
her a video of himself masturbating. Tried to force himself on an immigrant and
threaten her immigration status if she refused. Quietly slinked away with no
punishment.)
Alex Gravely of Microsoft GitHub? Silence. (Strangled an immigrant Latina woman
and raped her. Court gave him a pre-trial diversion as pretend punishment.)
Rick Allen Jones? Silence. (Personal engineer of Bill Gates. Arrested in the
Gates mansion after police found a Child Pornography dungeon in his house.)
Silence from Mr. GULAG again.
I’ve never actually gotten him to offer me his opinion of those people or why
we’re letting them form “communities”. The only community most Microsoft
toadies should be in is that one under the bridge in Florida, obviously.
He only attacks defenders and writers of Free Software. He himself seems to be
currently employed writing some proprietary software for these self-driving
cars. Which don’t have a very good safety record. Many brands of these cars run
over people and the company goes “Welp, thought she was a shopping bag! How
little can we get the family to settle for?!”.
I’ve been driving for decades and haven’t managed to injure anyone. But money
talks, and pretty soon we’ll all be forced onto the road with buggy/dodgy
software and we all get to hope it doesn’t get in front of us and randomly slam
the brakes or mistake us for shopping bags, because it will be the law.
But back to Microsoft… Microsoft has regrouped and changed its strategy, but
the clear endgame is still against Free Software, and they have an army of
useful idiots to help them.
Using difficult people as pawns to manipulate and pull apart communities is one
of the center pieces of this strategy.
But as Robert Reich would say, “Don’t believe it!”.
If it seems like all you hear is good things about the corporate takeover of
FOSS, it’s because they’re taking out all of their critics by any means
necessary. █
䷩ 𝚕𝚒𝚗𝚎 361
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/21/epo-managers-acting-deaf/#comments
Gemini version at gemini://gemini.techrights.org/2022/09/21/epo-managers-acting-deaf/
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Gemini_version_available_♊︎
✐ [Meme]_EPO_Abuse_Continues,_Managers_Acting_Deaf⠀✐
Posted in Europe, Patents at 2:51 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇EPO staff and EPO managers⦈
Summary: EPO management continues to gaslight and abuse_staff, even in direct
violation of the EPO’s rules and legal contracts
⣶⣠⣬⣷⣊⣉⡩⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠿⠿⢿⢿⣿⡿⢿⣿⣮⣿⣽⣿⣿⣿⣷⣿⣟⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⢿⣻⣿⠇⣿⣯⡷⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣿⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡷⠾⠟⠉⠀⠐⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣮⣽⣿⢿⣿⣷⣾⣷⣿⣿⣿
⣿⣷⣶⣶⣶⣶⣾⣿⣿⣷⣿⣿⡇⣿⣿⣶⣿⣿⣿⡷⣶⣶⣾⣿⣷⣶⣶⣮⣭⣴⣬⣭⣭⣭⣽⣷⣦⣭⣽⣛⣿⣿⣆⣸⣿⣿⣿⣿⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠿⠿⠿⠿⠻⣾⣿⣿⣿⣿⣿⠟⣦
⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣭⣥⣽⣵⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⣭⣭⢭⣽⡙⣿⣿⣽⣿⡏⣿⡟⣶⣾⣾⣿⡿⣿⡟⣿⣟⣻⣿⣿⣷⣿⣏⣿⣷⣿⠚⠿⠿⠿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿
⣤⣿⣿⣼⣿⣧⣿⣽⣇⣿⣿⣿⣧⣿⣿⣷⣿⣷⣶⣆⣿⣟⣻⣿⣿⣷⣺⣿⣿⣾⣿⣦⣶⣶⣿⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡏⣿⡧⣿⡿⣿⢽⢿⠿⠇⢿⢿⣇⣿⣿⣿⣸⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠿⠿⠻⠟⠿⠿⠿⢿⣿⣛⣛⡿
⣿⣿⣷⣿⣿⣷⣶⣶⣼⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣻⣿⣍⣙⣿⣿⣿⣿⠿⠛⠉⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⢴⠶⢿⠿⣿⣿⣿⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣯⣥⣤⣽⣧⣤⣁⣡⣬⣥⣮⣿⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠛⠁⠀⠀⠀⣠⣿⣿⣷⡀⠀⠀⠀⠀⠀⡿⣿⠀⠼⣿⡿⢿⢿⣿⠿⠿⣿⣿⣯⣿⣝⣯⣿⣬⡽⢷
⣭⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣀⠀⠀⠀⣸⣷⣿⣶⡶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿
⣿⣿⣿⣿⣿⣽⣏⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣭⣿⣿⣿⣿⡿⠿⠿⢿⣟⣿⣿⣛⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣿⣶⣶⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣿⣇⣿⣿⠯⠏⠉⠨⠟⠿⠟⣛⣛⣩⣽⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⣸⣗⣯⣋⣿⣛⣛⣡⣼⣿⣭⣭⣵⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⣧⣤⣴⣶⣶⣾⣶⣿⡟⣿⣿⣿⣿⣿⠿⠛⣛⣿⣿⡿
⠶⠶⢾⣟⣟⣛⣻⣿⣿⣿⣿⣏⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣀⣈⠉⣉⣁⣀⣤⣤⢿⣿⣿⣿⠿⡏⢱⣶⣶⣶⣤⠈⣻⣧⣭⣽⣻⣿⣿⣿⣷⣿⣿⣿⣷⠒⢻⣭⣭⣿⡽⠢
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣻⢿⣿⣿⣷⣶⣶⣶⣶⣾⡿⢿⣿⣿⣭⣭⣉⣽⣿⣷⣾⡟⣿⠁⠀⠀⣿⣿⣀⠀⢸⣿⡇⣸⣿⢀⣿⣿⢺⣿⣷⣹⣿⣿⣿⣿⣿⣿⡿⠃⠈⣉⣠⣷⣗⣛
⠿⠿⠟⠛⠛⠉⠉⠉⠛⢉⣁⣠⣤⡤⠤⠤⣶⣾⣶⣿⣿⣿⣯⣽⣷⣶⣶⣾⣿⡶⠖⢸⡧⢯⣿⣿⣿⡿⠿⠿⠛⣛⣩⣧⠅⠀⠀⢠⣿⡿⠛⠀⣾⣿⠿⠿⠟⢸⣿⡟⢹⣿⡇⣿⣿⣿⢿⠿⣿⣿⣿⣿⡿⢿⣟⣉⣡⡭
⣀⣠⡤⠤⢖⣒⣒⣿⣭⣭⣭⣵⣶⣾⣿⣿⣿⣿⣿⢽⣿⣿⣿⡿⣿⡭⠙⢛⣉⣉⣡⣼⣥⣬⣤⣤⡤⣴⠚⢻⣩⣽⡶⠂⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⣧⡿⠿⠾⡋⣙⣛⣽⢿⣟⣿⣽⢹⣿⠿⣿
⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣟⣛⣻⣿⣮⣭⣭⣤⣤⣤⣾⣿⡿⡛⣻⣿⣿⣿⣿⣿⣿⣧⢸⠀⠀⠙⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⡵⠶⣾⣿⣿⣿⠗⠘⢻⣛⣿⣵⣶⣾⣿⠉
⠛⣿⣷⢀⣈⣉⣩⣤⣤⣴⢶⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢟⣛⣭⣤⣤⣤⠖⠀⠀⣠⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣩⣴⣶⠾⠯⡍⠀⠂⣘⣻⣥⠼
⣿⠿⠾⠿⢟⠛⠋⠉⠉⠙⠞⢿⣿⣿⣿⣿⣿⡿⡿⠿⠟⠉⢁⣰⣼⣧⣭⣽⡿⠷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢀⣿⣶⣶⡞⣿⣿⣿⡄⠰⢡⣴⣿⣷⣒⣾⠟⠛⣛⡻
⠀⠀⠘⠻⣭⡤⠀⠀⠀⠀⢁⣀⣩⣍⣹⣷⣤⣶⣄⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠛⠛⢛⣻⡟⣿⠁⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠀⣿⣿⢹⣷⡿⡿⠿⢛⣋⣤⠶⠚⠺⠉⢀
⠀⠀⠀⢐⣈⣠⣤⣤⣶⡶⡿⣿⣛⣿⣟⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣍⣩⣴⣶⡿⢟⡟⣿⡋⠄⠃⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢠⣿⣿⠿⠦⠶⠚⠩⡾⡛⣁⣠⡴⠟⠛⠹
⣶⢾⣿⣿⣿⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⡏⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠘⠻⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢸⣿⡟⠀⠀⣀⣀⣴⢗⣛⠫⡇⠂⠀⠀⠒
⣿⣿⣿⣿⢿⣿⡿⠿⠿⢛⣉⣋⣠⣬⣿⣿⣿⣾⣿⣿⣟⣫⠀⠀⢸⣿⣿⣿⣿⡟⠉⠉⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠘⣛⣃⠖⠛⠉⠛⠊⠛⠍⠀⠀⠀⠀⣀⡤
⠛⣁⣿⣿⣤⣴⣶⢶⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⠛⣫⠥⠈⠐⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡠⠔⠂⠉⠀⢀⣀⠀⢒⢨⢆⣀
⣿⣿⣿⣶⣶⣿⣿⣿⣿⠙⢻⠉⠛⠛⠛⣛⣿⢿⣿⣿⡿⢿⡏⠁⠠⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠎⠀⠀⠀⡀⠀⣨⡅⠀⣊⡥⠶⣿⣷
⣿⣿⠿⠿⠛⠛⢛⣙⣹⣾⣿⣷⠶⠿⠛⠋⠀⠘⣿⣿⡷⠊⠁⠀⣀⠀⣀⠤⠔⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠎⠂⢁⠤⣶⣿⣥⣴⣾⣿⣿
⣭⣥⣤⡶⣾⡿⠟⠛⠋⠀⠀⠼⠃⠀⠀⠀⠀⣠⡬⠛⠫⣠⣴⣶⣭⣤⡁⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣁⠄⠂⣙⣥⣾⣿⣿⣿⣿⣿⣿⣿
⠻⠿⣷⣷⠿⢷⠶⠰⠶⠶⠶⣀⣠⡤⠶⠒⠛⠉⠁⠄⠀⠹⣿⣿⣿⣿⣿⣶⣶⣚⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠖⠂⣁⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣶⣀⣬⣗⣊⣉⡹⠿⠿⠿⣿⣿⣿⢿⣯⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠏⠻⠛⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣗⣟⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⣷⣶⣦⣤⣤⣶⣤⣴⣬⣯⣬⣛⣿⣭⣟⣛⣛⣻⠿⠿⠿⠿⣿⣿⣿⣿⣤⣤⣤⣀⡀⠀⠀⠀⠁⠉⠛⠻⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣓⣾⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀⠈⠊⠹⢿⣯⣿⡿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿
⣿⣿⣿⣿⣿⣿⢿⣻⣿⡇⣿⣯⡷⣿⣿⣿⣿⣷⣿⡟⣿⣿⣿⣿⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠶⢿⠋⠁⠐⠂⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣮⣽⣿⢿⣿⣷⣾⣷⣿⣿⣿
⣿⣷⣶⣶⣷⣶⣾⣿⣿⣷⣿⣿⡗⣿⣿⣶⣿⣷⣿⣷⣶⣶⣾⣿⣷⣶⣶⣯⣥⣤⣬⣭⣭⣭⣽⣷⣦⣭⣿⣟⣿⣿⣣⣼⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⠿⣾⣿⣿⣿⣿⣿⠿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣭⣭⣥⣽⣽⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⣭⣭⢭⣽⡹⣿⣿⣽⣿⡟⣿⡟⣶⣿⣾⣷⡿⣿⡟⣿⣟⣻⣿⣻⣷⣿⣏⣿⣿⣿⠚⠿⠿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿
⣤⣿⣿⣼⣿⣧⣿⣽⣇⣿⣿⣿⣧⣿⣿⣷⣿⣷⣶⣆⣿⣟⣻⣿⣿⣷⣾⣿⣿⣾⣿⣦⣶⣶⣿⣷⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡏⣿⡧⣿⡿⣿⢽⢿⠿⠇⢿⢿⣇⣿⣿⣿⣸⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠿⠿⠛⠟⠛⠿⠿⢿⣿⣛⣻⡿
⣿⣿⣷⣿⣿⣷⣶⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⡿⣿⣿⣿⣍⣈⣝⡿⠿⠿⠛⠛⠋⠘⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠿⠿⣿⣿⣿⣷⣶⣿⣷⣮⣿⣿⣿⣿⣿⣽⣿⡟
⣿⣿⣿⣿⣿⣯⣥⣥⣽⣧⣬⣁⣩⣤⣥⣾⣶⣶⣶⣶⣶⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⠀⢸⢿⡿⢿⢿⣿⠻⠿⣿⣿⣯⣿⣍⣭⣿⣬⣽⢷
⣭⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⠀⠠⠀⠀⠀⣀⣿⣿⣿⣿⣶⣄⠀⠀⠀⢰⣿⣿⣶⣶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣟
⣿⣿⣿⣿⣿⣽⡏⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠿⢿⣟⣿⣿⣛⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣿⣶⣶⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣾⣿⢸⣿⡽⠏⠉⠘⠟⠻⠟⣛⣋⣩⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⣻⣗⣯⣛⣿⣛⣛⣡⣼⣿⣭⣭⣵⣶⣶⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣻⣤⣴⣶⣶⣾⣾⣿⡟⣿⣿⣿⣿⣿⠿⠛⣛⣽⣿⡿
⠶⠶⢿⣟⣛⣛⣛⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣀⣉⠉⣉⣉⣀⣤⣤⢽⣿⣿⣿⠿⡏⢱⣶⣶⣶⣤⠀⣻⣯⣭⣽⣻⣿⣿⣿⣷⣿⡿⣿⣷⠒⣛⣭⣭⣿⡮⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣟⣻⠿⣿⣿⣷⣶⣲⣶⣶⣾⡿⢿⣿⣿⣭⣭⣉⣽⣿⣷⣾⣟⣿⠇⠀⠁⣿⣿⣀⠀⢸⣿⡇⣸⣿⢀⣿⣿⣾⣿⣷⢹⣿⣿⣿⣿⣿⣿⡿⠃⠈⣉⣠⣷⣿⣿
⠿⠿⠿⠻⠛⠋⠉⠉⠋⢉⣉⣠⣤⣤⠤⠤⢶⣶⣶⣿⣿⣿⣯⣭⣿⣶⣶⣶⣿⡶⠖⢸⡧⠙⣿⣿⣿⠿⠿⠿⠛⣛⣩⣧⡄⠀⠀⢠⣿⡿⠛⠀⣼⣿⠿⠿⠟⢸⣿⡟⢻⣿⡇⣿⣿⣿⠿⠿⣿⣿⣿⣿⡿⢿⣟⣋⣥⡭
⣀⣠⣤⢤⡶⢒⣒⣿⣯⣭⣽⣵⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⡿⠛⠛⣋⣙⣵⣼⣅⣬⣤⣤⣦⣴⠚⠻⣭⣽⣶⠂⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⣧⣿⡿⠾⡞⣙⣻⣿⢿⣟⣿⣽⢹⣿⠿⣿
⣿⣿⡇⠨⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠟⣛⣛⣻⣿⣮⣭⣭⣥⣤⣤⣾⣿⡿⣛⣛⣿⣯⣿⣿⣿⣿⣧⢸⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⡵⢶⣾⣿⣿⣿⡿⠀⢻⣛⣻⣵⣶⣿⣻⣏
⠛⣿⣷⢀⣀⣉⣩⣤⣤⣴⣶⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢟⣛⣭⣤⣤⣤⡖⠀⠀⣠⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣉⣩⣴⣶⡾⠯⡍⠀⠶⣈⣩⣥⢵
⣿⠿⠾⠿⠟⠛⠋⠉⡋⠹⠞⢯⣿⣿⣿⣿⣿⡟⠿⠿⠛⠉⠁⣰⣼⣯⣭⣽⠿⠷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢀⣷⣶⣶⡞⣿⣿⣿⡄⠰⢫⣴⣿⣷⣖⣾⡟⠛⣛⣻
⠀⠀⠘⢻⣭⣀⠀⠀⠀⠀⢁⣀⢈⣉⣩⣭⣽⣶⡄⣤⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⡟⠛⠿⢛⣻⡟⣿⠇⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠀⣿⣿⢹⣷⡿⣿⠿⠻⣋⡤⠶⠚⠺⠉⢀
⠀⠀⠀⢀⣀⣨⣤⣴⣶⣶⣿⢟⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣏⣋⣩⣵⣶⡿⣿⣟⣿⡏⠤⠃⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢀⣿⣿⠿⠧⠶⠚⠩⣺⠟⣃⣠⡴⠟⠛⠹
⣶⢶⣿⣿⣿⣿⣿⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣤⣿⣉⣉⣭⣶⣾⣿⢟⣻⣭⣽⣶⣞⣿⣻⣿⠟⠁⠀⠀⠀⠀⠀⠘⠻⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢸⣿⡟⠁⠰⣀⣀⣴⢷⣻⠋⡏⠀⠀⠀⠒
⣿⣿⣿⣿⢿⣿⡿⠿⠿⢛⣙⣉⣩⣽⣿⣿⣷⡌⣽⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠘⣛⣣⠖⠛⠉⠓⠚⡙⠉⠀⠀⠀⠀⣀⡤
⠛⣉⣿⣿⣦⣴⣶⠶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢉⠉⠉⢻⣿⣿⣿⣿⡏⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡠⠔⠂⢉⠁⢀⡀⠀⢒⡨⠆⣀
⣿⣿⣿⣶⣶⣿⣿⣿⣷⠉⢻⡙⠛⠛⠛⣛⣻⢿⣿⣿⣿⣿⣿⣄⡴⠿⠋⠉⠉⠀⣀⣀⣀⣠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⡞⠁⠀⠀⡀⠀⣨⡅⠀⣘⡥⠶⣻⣷
⣿⣿⠿⠿⠛⠛⢋⣉⣹⣾⣿⣷⠶⠿⠛⠋⠀⠈⢻⣿⣿⣉⠹⠟⣁⠀⣀⠤⠔⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠎⠂⣀⠥⢶⣻⣵⣴⣾⣿⣿
⣭⣥⣤⡶⣾⡿⠿⠛⠋⠀⠀⠼⠃⠀⠀⠀⠀⢠⣬⡻⠿⠅⠀⣀⣉⣡⠁⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⢙⣥⣶⣿⣿⣿⣿⣿⣿⣿
⠻⠿⣷⣷⠿⢷⠶⠰⠶⠶⢶⣀⣠⡤⠶⠒⠛⠉⠁⠀⠀⠀⣿⣿⣿⣿⣷⣤⣶⠚⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠂⢁⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣶⣂⣀⣝⣛⣟⣻⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠟⠉⠻⣿⡿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣾⣿⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⣶⣦⣬⣭⣭⣦⣭⣬⣽⣭⣟⣻⣯⣻⣟⣛⣻⡿⡿⠿⠿⣿⣿⣿⣿⣅⣀⣠⣀⡀⠀⠀⠀⠁⠈⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⣻⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠄⠀⠀⠀⠈⠁⠙⠻⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⣿⣯⡷⣿⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⠃⠁⠀⠂⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣭⣿⡿⣿⣶⣶⣾⣿⣿⣿
⣿⣷⣶⣶⣶⣶⣶⣿⣿⣷⣿⣿⣗⣿⣿⣶⢿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣶⣮⣭⣭⣭⣭⣭⣭⣭⣿⣧⣬⣻⣛⣛⣿⣇⡈⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠻⠿⠿⠿⠟⢳⣿⣿⣿⣿⣿⡿⣳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣭⣵⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡏⣭⣭⣽⣽⡙⣿⣿⡽⣿⡟⣿⡟⣾⣷⡾⣿⡿⣿⡟⣿⣟⣻⣿⣻⣿⣿⣏⣿⣿⣿⠿⠿⠿⡿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣿⣿⣾⣿⣧⣿⣽⣇⣿⣿⣿⣧⣿⣿⣧⣿⣷⣶⣆⣿⣟⣻⣿⣿⣷⣾⣿⣿⣞⣿⣶⣴⣶⣶⣷⣶⣶⣶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡏⣿⡏⣿⡿⣿⢽⣿⠿⠇⣿⣿⣇⣿⢿⣿⣸⣛⣛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣟⣛⣿
⣿⣿⣷⣿⣿⣷⣶⣶⣶⣾⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⢟⣟⣿⣯⣁⠙⡻⠻⣿⠿⠿⠟⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⠿⣿⣿⣿⣷⣶⣾⣿⣶⣿⣿⣿⣿⣿⣏⣿⣿
⢿⣿⣿⣿⣿⣿⣋⣩⣸⣿⣌⣉⣉⣭⣭⣾⣿⣿⣷⣾⣾⣷⣶⣿⣿⣷⣿⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⡍⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⠿⠿⣿⡿⠿⣿⣿⣽⣽⣯⣩⣽⣧⣭⡷
⣭⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡆⠠⠤⠀⠀⠀⣠⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣷⣶⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛
⣿⣿⣟⣽⣿⣯⣿⢿⣿⣿⣿⣿⣿⡯⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣷⣦⣤⣤⣶⣿⣷⣶⣾⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣿⣧⣿⣿⠿⠍⠁⠙⠛⠿⢛⣛⣉⣽⣾⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡛⢋⣿⣺⣙⣻⣛⣙⣋⣤⣿⣯⣩⣥⣭⣶⣶⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣣⣤⣶⣶⣶⣶⣾⣿⢿⣿⣿⣿⣿⡿⠟⠛⣻⣿⣿
⠶⠶⠶⣿⣻⣛⣛⣻⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣀⣈⠉⠉⣉⣁⣠⣤⣤⡽⣿⣿⠿⡗⢻⣿⣶⣶⣤⠀⣨⣭⣭⣽⡻⣿⣿⣿⣿⣾⣿⣿⣿⡖⢚⣋⣭⣽⣯⠥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⣿⢿⣿⣿⣶⣖⣶⣶⣶⣿⠿⣿⣿⣯⣭⣍⣹⣿⣷⣶⣿⢿⣿⡇⠀⣿⣿⣀⠀⢸⣿⡇⣸⣿⢀⣿⣿⣾⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⠏⠀⢉⣁⣾⣿⢚
⠿⠿⠿⠟⠛⠋⠉⠉⠙⠉⣉⣡⣤⣤⡤⠤⠤⣶⣷⣾⣿⣿⣿⣿⣽⣿⣶⣶⣿⡷⠶⠸⣿⠘⢻⣿⣿⡿⠿⠿⠿⢛⣋⣿⣨⡤⠀⢠⣿⡟⠛⠀⣼⣿⠿⠿⠟⢸⣿⡟⢸⣿⡇⣸⣿⣿⡿⠿⢿⣿⣿⣿⣿⠿⢿⣛⣉⣬
⣀⣀⣤⡤⢴⠶⣒⣺⣿⣭⣭⣭⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠝⠛⣛⣉⣉⣤⣯⣈⣤⣤⣤⢠⡖⠛⣋⣭⣷⡶⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡧⣿⣿⡶⢞⢋⣙⣫⡷⣾⣻⣯⣏⣿⠿⠿
⣿⣿⣧⠀⢽⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⠿⢟⣻⣿⣷⣭⣭⣭⣤⣤⣴⣿⠿⢟⢛⣻⣿⣿⣿⣿⣿⣿⢸⠁⠀⠉⠋⠋⠁⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠀⠶⢶⣿⣿⣿⣿⠇⠘⣟⣛⣯⣶⣾⣞⡟
⠛⣻⣿⡆⣀⣉⣉⣬⣤⣤⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣛⣋⣈⣤⣤⣤⠖⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣈⣉⣭⣶⣶⠾⢭⠁⠴⠆⣛⣭⣭
⣾⡿⠾⠿⠿⠛⠛⠉⡛⠉⢷⠻⣿⣿⣿⣿⣿⣿⢿⠿⠻⠋⠉⣠⣤⣿⣬⣭⣿⠷⡶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢀⣷⣶⣶⡆⣾⣿⣿⡇⠠⠞⣅⣾⣿⣆⣒⣿⠿⢛⣛
⠀⠀⠴⠻⣯⠥⠀⠀⠀⠀⢘⡀⠉⣉⣉⣭⣭⣤⣤⣠⣴⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⠛⠿⠛⣛⣛⣿⣿⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠀⣿⣿⢭⣿⣿⢿⡿⠿⢟⣡⡴⠖⠓⠉⠁
⠀⠀⠀⠀⣂⣃⣤⣤⣴⡶⢾⡿⢟⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣟⣋⣉⣥⣶⣾⢿⣟⣿⣟⢉⠍⠃⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢀⣿⣿⠿⢯⠴⠒⠋⢡⠟⠋⣀⣤⠾⠓⠛
⡶⡶⣾⣿⣿⣿⣿⣿⣦⣶⣿⣾⣿⣿⣿⣿⣿⣿⠛⢿⣌⣈⣩⣴⣶⣿⣿⣻⣯⣭⣿⣞⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⠻⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢸⣿⡟⠇⠀⢀⣀⣠⡾⣞⡛⡿⠁⠈⠀⠐
⣿⣿⣿⣿⡿⣿⣿⠿⠿⠛⣋⣉⣉⣭⣽⣿⣿⣿⣷⣾⣿⣿⣿⣷⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠘⢛⣣⡴⠚⠋⠙⠒⠋⠋⠀⠀⠀⠀⢀⣠
⠛⢃⣻⣿⣧⣴⣶⡶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⣿⣟⣁⠀⠉⢻⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⡅⠀⣀⡀⠔⣂⡤⢀
⣿⣿⣿⣷⣶⣿⣿⣿⣿⠊⠻⡏⠛⠛⠛⢛⣻⣿⡻⣿⣿⣿⣿⣿⣤⡶⠟⠋⠀⠀⢀⣀⣀⣀⡤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⠋⠀⠀⢀⠀⢠⣍⠀⢀⣫⡴⠾⣭
⣿⣿⣿⠿⠟⠛⠋⣉⣉⣴⣿⣷⡶⠾⠟⠛⠁⠀⠀⢹⣿⣯⠄⠛⠛⡀⣀⡤⠤⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠔⢀⡫⠴⣾⣯⣦⣶⣿⣿
⣭⣭⣤⣖⣶⣿⠿⠻⠛⠁⠀⢰⠇⠀⠀⠀⠀⢀⣤⣤⡟⠃⠀⣠⣤⣤⣇⠀⠀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠒⢉⣫⣴⣿⣿⣿⣿⣿⣿⣿
⠻⠿⢿⣶⡿⢷⠶⠰⠶⠶⠖⣀⣀⣤⠴⠖⠛⠋⠉⠀⢀⠀⠸⣿⣿⣿⣿⣷⣴⣖⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠒⢈⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣖⣀⣘⣺⠚⠛⣛⡿⢿⡿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⠭⠙⠟⠛⣿⣿⣿⣻⣿⣽⣿⣿⣿⣿⣿⣷⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣭⣭⣽⣯⣭⣭⣭⣭⣟⣿⣏⣿⠛⠟⡻⠿⣿⡿⢿⣿⣿⣿⣿⣟⣉⣀⣀⣀⡀⠀⠀⠈⠉⠈⠛⠿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⢿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣷⣿⣿⣛⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣰⣠⠄⠀⠀⠀⠈⠉⠘⠻⣿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⡗⣿⣿⣿⣿⣷⣿⡟⣿⣿⣿⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⣿⠃⠁⠀⠂⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣦⣽⡿⢿⣷⣶⣶⣯⣽⣿⣿
⣿⣷⣶⣶⣶⣶⣾⣿⣿⣷⣿⣿⣗⣿⣿⣶⣿⣿⣿⣇⣽⣭⣿⣿⣿⣶⣶⣭⣭⣭⣭⣭⣭⣭⣽⣯⣤⣙⣛⣛⣻⣿⣯⣉⠙⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠿⠿⠿⠿⠿⢼⣿⣿⣿⣿⣿⡿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣽⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⡏⣭⣭⢭⣽⡙⣿⣿⡽⣿⡏⣿⡏⣾⣿⣾⣷⡿⣿⡟⣿⣟⣻⣿⣻⣷⣿⣏⣿⣿⣿⠘⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿
⣄⣿⣿⣼⣿⣇⣿⣽⣇⣿⣿⣿⣧⣿⣽⣷⣿⣷⣷⣆⣿⣟⣻⣿⣿⣷⣾⣿⣿⣾⣿⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡏⣿⡏⣿⡿⣿⢽⢿⠿⠇⢿⣿⣏⣿⣿⣿⣸⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣾⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⡿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿
⣿⣿⣷⣿⣿⣷⣶⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⢿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣝⣛⣛⡛⠹⢿⣿⣿⣿⠟⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⣿⣿⣿⣶⣖⣶⣶⣶⣿⣶⣾⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣋⣉⣹⣧⣉⣉⣉⣹⣷⣮⣿⣭⣽⣶⣶⣷⣾⣿⣿⣷⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡆⠀⠀⠀⠀⠀⣿⢸⢿⣿⢿⠿⣿⠿⠿⣿⣏⣿⣿⣝⣫⣿⣬⣽⠷
⣭⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠤⠤⠀⣀⠀⠀⢀⣸⣿⣿⣿⣧⣀⠀⠀⠀⢰⣿⣶⣾⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢛
⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⣿⣿⡿⣿⠿⠿⢿⣻⣿⣛⣻⣿⣿⣻⣿⣷⣤⣤⣤⣼⣿⣶⣶⣿⣿⣿⣇⢠⣿⣿⣿⣿⣿⣿⣿⣧⣆⣠⣿⣇⡟⠛⠉⠉⠟⠻⠟⢛⣛⣋⣯⣽⣿⣿⣿⣿⣿⣿
⢿⣫⣿⣿⠟⢻⣿⡬⣛⣿⣛⣛⣁⣴⣿⣍⣩⣥⣭⣶⣶⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣤⣶⣶⣶⣶⣶⡿⣿⣿⣿⣿⣿⠿⠿⢟⣛⣿⣿
⠶⠶⠾⠿⣿⣛⣛⣛⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣟⣀⠈⠉⠉⢉⣁⣡⣤⣤⡤⣿⣿⣿⡗⢷⣾⣿⣿⣤⠀⣠⣤⣽⣽⡻⣿⣿⣿⣷⣿⣿⣿⣧⠖⣛⣋⣭⣿⡯⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣛⣿⣿⣿⣷⣶⣒⣶⣶⣾⡿⠿⣿⣿⣻⣭⣩⣹⣿⣶⣶⣿⣿⣿⣿⠁⣿⣿⣀⠀⢸⣿⡇⢸⣿⢀⣿⣿⢸⣿⣷⢹⣿⣿⣿⣿⣿⣿⡿⠃⠉⣉⣁⣿⡷⣲
⠿⠿⠛⠻⠛⠋⠉⠉⠛⠋⣉⣀⣀⣀⣤⠤⠤⣶⣶⣾⣿⣿⣿⣽⣭⣿⣶⣶⣿⣶⠆⢸⡇⠘⢻⣿⣿⡿⠿⠿⠿⢛⣉⣯⣩⡭⠄⢠⣿⡟⠛⠀⣼⣿⠿⠿⠟⢸⣿⡟⢸⣿⡇⣹⣿⣿⣿⡿⡿⣟⣿⣿⣿⠿⣿⣋⣁⡭
⣀⣀⣠⡤⠤⠒⣒⣒⣟⣭⣭⣭⣴⣶⣿⣿⣿⣿⣿⠽⣿⣿⣿⣿⣿⡟⠛⠛⣻⣛⣁⣸⣇⣨⣤⣤⣤⣤⠖⠚⣋⣩⣷⣶⠄⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⠶⠇⢘⣛⣻⠿⣿⣿⡿⢹⡿⠿⠿
⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢛⣻⣿⣮⣭⣭⣤⣤⣤⣾⣿⢿⠛⣻⣛⣿⣿⣿⣿⣿⣿⢹⠀⠀⠙⠛⠋⠁⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠁⠰⣶⣿⣿⣿⣿⠀⢺⠛⣻⣭⣶⣷⣾⠋
⠛⣿⣷⡀⢉⣉⣉⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣛⣋⣨⣤⣤⣴⡶⠂⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⣴⣶⡶⠛⡍⠩⠾⠉⣫⣥⡥
⣾⠿⠿⠿⠿⠛⠛⠙⠋⠹⡜⢹⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠉⣤⣼⣯⣭⣭⡽⠿⢶⢶⣾⢿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢀⣿⣶⣶⡆⣾⣿⣿⡄⠠⢛⣰⣾⣷⣔⣺⡿⠿⢛⣛
⠀⠀⠐⢻⣩⣒⡄⠀⠀⠀⢉⡀⢉⣉⣹⣿⣿⣧⡄⣤⡶⣾⣿⣻⣿⣿⣿⣾⣿⣿⣿⡿⣿⠻⠿⢛⣛⣛⡿⣼⠃⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠀⣿⣿⢽⣷⣾⣿⠿⠿⣋⣡⠶⠖⠲⠉⠀
⠀⠀⠀⠀⣈⣀⣤⣤⣴⣶⣿⡿⣛⣛⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⡿⠿⠿⣟⣋⣉⣥⣶⡿⣿⣟⣿⡏⠹⠅⠃⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢀⣿⣿⠿⢧⠴⠓⠛⣺⠛⢋⣠⣤⠾⠚⢻
⣶⢶⣿⣿⡿⣿⣿⣵⣶⣶⣿⣿⣿⣿⣿⡿⢿⣿⣏⣽⣦⣭⣭⣵⣶⣿⣿⣻⣯⣭⣥⣾⣿⣿⣿⣿⣥⡄⠀⠀⠀⠀⠘⠻⠶⠿⠋⠀⠀⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢸⣿⡟⠁⠀⢀⣀⣤⡷⣚⠛⡏⠂⠀⠀⠐
⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⣉⣩⣭⣤⣶⣿⣿⣿⢿⣿⣾⣿⠟⠛⠻⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠘⢛⣣⠔⠛⠉⠁⠚⠛⠉⠀⠀⠀⠀⣀⣤
⠛⢃⣿⣿⣤⣴⣶⠶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣷⣟⠀⣀⣽⠿⠿⠟⠛⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠈⠃⠀⣀⠠⠒⣪⠄⢀
⣿⣿⣿⣷⣶⣿⣿⣿⡷⠛⢻⡙⠛⠿⠟⣛⣫⣷⡞⣿⣿⣟⡩⢿⠿⠋⠁⠀⠀⠀⣀⣀⣀⣀⠤⠴⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠉⠀⠀⠀⠀⢨⡉⠀⣘⣭⠴⢿⣽
⣿⣿⣿⠿⠛⠛⠋⣉⣙⣴⣿⣷⡶⠿⠿⠋⠈⠌⠀⠸⠿⠅⠀⣀⣀⠀⣀⣤⠴⠚⠿⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠐⢀⡭⢶⣿⣵⣴⣾⣿⣿
⣩⣭⣤⡶⣶⡿⠿⠟⠋⠁⠀⢸⠃⠀⠀⠀⠀⢠⣤⡀⠀⠀⣿⣿⣿⣿⣧⣄⠀⠀⠀⢀⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡅⠂⢉⣣⣴⣿⣿⣿⣿⣿⣿⣿
⠛⠿⣿⣷⠿⢷⠶⠰⠶⠶⠶⢀⣠⣤⠴⠖⠟⠉⠉⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⣶⣛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣆⣀⣘⡿⠿⠛⣻⡿⣿⢿⣿⣿⣿⣿⣺⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⣭⣿⣿⣿⣿⣾⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣶⣦⣬⣭⣍⣩⣭⣍⣭⣭⣍⣹⣻⣿⣙⡿⠻⠿⢿⣿⡿⣿⠿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠉⠐⣲⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣟⣿⣿⣛⣿⣿⣿⣶⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣟⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⣿⣯⡗⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⢻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣷⠎⢀⣀⣀⡀⣀⣀⠐⡀⠈⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⠿⣿⣿⣿⣿⣽⣿⣿⣿
⣿⣷⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⣓⣿⣿⣾⣿⣿⣿⣧⣯⣭⣿⣿⣧⣴⣮⣭⣭⣭⣭⣝⣭⣭⣽⣥⣌⣛⣻⣿⣿⣶⣿⣿⣿⣿⣽⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠋⠿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣽⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣾⣿⣿
⡏⣭⣭⢭⣽⡹⣿⣿⣽⣿⡟⣿⡟⣾⣷⣾⣷⡿⣿⡟⣿⣟⣻⣿⣻⣷⣿⣏⣿⣿⡗⠻⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣄⣀⣤⠴⢲⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿
⣤⣿⣿⣾⣿⣇⣿⣹⣇⣿⣿⣿⣧⣿⣿⣷⣿⣷⣿⣆⣿⣟⣻⣿⣿⣷⢾⣿⣿⣾⣷⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⢠⣨⢿⣿⣿⣿⣿⣿⣿⡇⢹⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡏⣿⡯⣿⡿⣿⢽⣿⠿⠇⢿⣿⣏⣿⣿⣿⣸⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⣤⣿⠏⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿
⣿⣿⣷⣿⣿⣷⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⣿⣯⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡉⠁⢀⣀⠀⠀⠀⠀⣸⣿⡿⢿⣿⣿⣷⣶⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⠿
⡿⣿⣿⣿⣿⣿⣿⣍⣿⣏⣙⣉⣉⣛⣻⣿⣿⣽⣿⣿⣿⣵⣶⣾⣿⣾⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣿⣿⣿⣿⣿⡿⠯⠽⣗⣺⣿⣿⣷⣤⣀⠀⣿⡇⡿⣿⡿⢿⢿⡿⠿⣿⣿⣻⣻⣟⣻⣿⣯⣭⣿⣴
⣽⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣟⣛⣻⣿⡟⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⢿⣷⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠺⣿
⣿⣯⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⠿⢿⣿⣟⣿⣻⣿⣿⣿⣿⣦⢭⣭⣬⣾⣷⣬⣅⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠋⠉⠹⠛⠿⠿⣛⣛⣻⣭⣽⣿⣿⣿⣷⣿⣿
⣛⣻⣿⡿⠛⢿⣇⡬⢻⣟⣛⣟⣁⣼⣿⣛⣻⣥⣭⣵⣾⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⡀⠀⠀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣶⣶⣶⣶⡿⣿⣿⣿⣿⣿⠿⠿⣛⣿⣿⣿
⠶⠶⠾⠿⣟⣛⣟⣿⣿⣿⣿⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣏⠀⠉⠉⠉⢉⣉⣁⣤⣤⡤⣿⣿⣿⡇⢷⣶⣿⣿⣥⠀⣠⣤⣬⣼⣿⣿⣿⣿⣾⣿⣿⣿⡤⢖⣛⣋⣽⣏⠟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣟⣻⣭⣭⣿⣿⣶⣼⣿⣿⣿⣿⡇⣿⣿⣀⠀⢸⣿⡇⢸⣿⠀⣿⣿⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⠟⠀⠉⣉⣸⣿⣶⣛
⡿⠿⠿⠟⠟⠛⠛⠛⠛⢋⣉⣈⣉⣁⣠⢤⣤⣶⣶⣿⣿⣿⣿⣭⣭⣿⣧⣤⣤⣿⣿⣿⣿⠿⠿⠿⣿⣿⠿⠿⠟⢛⣹⣁⣩⡭⠤⢴⣿⡿⠛⠀⣼⣿⠿⠿⠟⢸⣿⡟⢸⣿⡏⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⣟⣉⣩⣿
⣀⣀⣠⠤⠤⠶⣒⣲⣿⣭⣭⣭⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠙⠛⠉⡉⢉⣉⣀⣀⣀⠀⠀⠈⠙⢿⣿⣭⣭⣷⣶⡆⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡇⡗⠓⠷⠐⢉⣛⣿⢿⣿⣿⡏⣿⣿⠿⣿
⣹⣿⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⣿⣿⣜⣫⣭⣁⣡⣤⣴⡿⠿⠟⡛⠛⠛⠛⣿⣧⠀⠀⣀⡼⠟⠻⣿⣿⡿⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⢰⣿⣿⣿⠟⠸⡟⢛⣯⣥⡽⣶⡿⣩
⢹⣿⣇⠀⢉⣁⣁⣡⣭⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⣶⣼⠿⠀⠐⠈⠛⠛⣈⣙⡉⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣩⣴⣶⡞⢿⠉⠥⠞⢈⣩⣥⠤
⣿⡯⠿⠿⠿⠛⠛⠛⠋⢥⣟⣿⡿⢿⣿⣿⣿⡿⡿⠻⠋⠉⠭⣤⣹⣇⣀⣥⡤⠤⠶⢲⡖⢚⠩⠉⣍⠀⠀⠀⡠⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢀⣷⣶⣶⡆⣶⣾⣿⡌⠜⣃⣾⣿⣦⣶⣾⣿⠛⣛⣫
⠀⠀⠚⣿⣥⣤⠄⠀⠀⠘⣿⣿⣷⣦⣭⣭⣭⣤⢀⣤⡴⣾⣿⣟⣛⣋⠁⣶⠂⠀⠀⢸⡇⠀⠈⠀⣀⣀⢤⠸⠁⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⠀⢸⣿⣇⠀⠀⣿⣿⢽⣷⢿⡿⠿⢟⣉⣤⠶⠒⠎⠉⠀
⠀⠀⠀⠈⣁⣀⣤⣤⣤⣶⣿⣿⣷⡜⣿⣍⣿⠿⢺⣿⢾⣿⣿⣿⠟⠍⠋⣁⣈⣀⣤⣴⠶⠶⠞⠚⠋⠛⠉⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢀⣿⣿⡿⠧⠖⠛⢳⡿⠟⣁⣤⡴⠗⠚⡟
⣶⢶⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⢉⣇⣀⣈⣠⣴⣶⡿⠟⠛⢩⡉⠀⠐⠓⠻⠀⠁⣀⡆⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠀⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢸⣿⡟⠀⠤⣀⣠⣼⢶⡻⢻⠑⠊⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⣁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⠈⠉⢀⣠⣤⡴⠎⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠘⠛⡃⠖⠛⠉⠓⠚⡋⠁⠀⠀⠀⠀⣠⡤
⠛⢙⣿⣿⣤⣴⣶⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠛⠛⠋⢈⣤⠤⠶⠖⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⡙⠀⢀⣀⠄⢒⡧⠄⣠
⣿⣿⣿⣧⣾⣿⣿⣿⡆⠛⣿⠻⠿⠿⠿⣿⠿⠃⠉⠀⠶⠖⠚⠂⠈⠀⠀⠀⠀⠀⡀⠀⣀⣀⠤⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⢀⠀⠂⣎⠉⠐⣢⡥⠾⣻⣿
⣿⣿⡿⠿⠛⠛⠋⣙⣡⣾⣿⣶⡶⠾⠛⠃⠈⢠⣶⣾⣷⣤⣀⢀⡀⢀⣀⡤⠴⠺⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠕⠂⣨⠭⣾⣯⣥⣴⣿⣿⣿
⣩⣥⣤⢶⣶⡿⠿⠟⠋⠉⠁⡿⠀⠀⠀⠐⠀⠈⢻⣿⣿⣿⣿⣿⣿⣬⡀⠀⠀⠀⠀⡀⢀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠔⠈⣙⣥⣾⣿⣿⣿⣿⣿⣿⣿
⠿⠿⣿⣶⠿⢷⠶⠰⠶⠶⠶⣀⣠⡤⠴⠖⠗⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣾⣟⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣀⣸⣿⣻⣛⣻⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡷⠶⣿⣿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣯⣿⣿⣷⣿⣟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣶⣦⣤⣤⣭⣭⣵⣭⣭⣭⣯⣽⣛⣿⣏⣛⣛⣛⡻⠿⠿⠿⠿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣒⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⣶⣶⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣿⣟⣿⡿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣿⡧⣿⣯⡿⣿⣿⣿⣿⣷⣿⣟⣿⣿⣻⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣾⣽⣟⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣶⣶⣶⣾⣶⣿⣿⣿⣿⣷⣿⣿⣗⣿⡿⣶⣿⣿⣿⣧⣿⣿⣿⣷⣶⣶⣭⣥⣤⣬⣭⣭⣭⣭⣷⣤⣭⣟⣻⡛⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠻⠻⠿⠟⠻⢿⡿⣿⣿⣿⠿⢿⣿⣿
⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠏⣭⣭⢭⣽⡹⣿⣿⣽⣿⡟⣿⡟⣶⣾⡾⣿⡿⣿⡟⣿⣟⣻⣿⣻⣷⣿⣏⡿⡿⠘⠿⠿⠿⢿⢿⣿⠿⣿⣿⣧⣾⣿⣿⣿⣿⣷⣶⠒⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣿⣿⣟⣻
⣦⣿⣿⣾⣿⣇⣿⣽⣧⣿⣿⣽⣧⣿⣿⣷⣿⣷⣶⣆⣿⣟⣻⣿⣿⣷⣾⣿⣿⣷⣦⣶⣶⣿⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢹⡏⣿⡯⣿⡿⣿⢽⢿⠿⠇⢿⢿⡇⣿⣿⣿⣸⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⠿⠿⠻⠟⠿⠿⣿⣟⣛⣛⣛⣛
⣿⣿⣷⣿⣿⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣍⣻⣿⣿⣿⣿⡿⠿⠟⠳⣄⣀⣀⡀⠀⠀⠀⠀⠀⣴⢶⠷⠿⢿⣿⣿⣿⣷⣞⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡟⠿
⣿⣿⣿⣿⣿⣿⣥⣿⣧⣉⣉⣉⣩⣽⣯⣭⣭⣿⣶⣶⣶⣾⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⠛⠛⠋⠁⠀⠀⠀⣴⣿⣿⣿⢀⠀⠀⠀⢀⣿⣽⠀⠸⢿⡿⠻⢿⣿⠛⢿⣿⣿⣯⣿⣽⣯⣿⣾⣾⣷⣿
⣯⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣀⣄⣀⣼⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⣛⣛
⣿⣟⣿⣿⣽⡟⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⢟⣻⣿⣟⣻⣿⣿⣿⣿⣷⣤⣤⣤⣶⣿⣶⣶⣷⣶⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠓⠈⠃⠁⠡⠛⠛⢛⣛⣋⣩⣷⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠛⢿⣇⣍⣛⣛⣋⣟⣡⣼⣿⣍⣭⣴⣭⣶⣾⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡶⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⢹⣦⣶⣶⣶⣾⣿⣿⡿⢻⣿⣿⣿⡿⠿⣛⣻⣭⣿⣿⠿
⠶⠾⠿⣟⣛⣛⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣀⣈⡉⢉⣁⣠⣤⣤⣤⢾⡿⣿⣿⠿⡇⢰⣶⣶⣶⣤⠉⣻⣥⣭⣽⣻⣿⣿⣷⣿⣿⣿⣷⠚⣭⣭⣭⣿⡏⠹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⡿⣿⣿⣟⣭⣭⣭⣿⣿⣷⣶⣿⣿⣿⠀⠀⠀⣿⣿⣀⡀⢸⣿⡇⣸⣿⢀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⢁⣀⣁⣤⣷⡟⣿⣭
⠿⠿⠛⠛⠛⠛⠛⠛⠋⣉⣤⣠⣄⡤⠤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣽⣧⡿⠿⢿⣿⠿⠿⠿⠛⣛⣩⣧⡤⠄⠀⠀⢰⣿⡿⠛⠀⣼⣿⠿⠿⠟⢸⣿⡟⢻⣿⣿⣿⣿⢿⢿⣿⣿⣿⣷⣿⣿⣟⣫⣥⣽⣷
⣀⣠⠤⠤⠖⣒⣲⣿⣭⣭⣥⣴⣶⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⠟⠁⢩⣿⣿⣿⣧⣨⣤⣤⣤⣴⠚⢛⣉⣹⣶⠆⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡟⠷⠞⣃⣉⣩⡵⢾⣛⣯⡽⢹⣿⢿⣻⣿
⣿⡇⠠⣾⣾⣿⣿⣿⣿⣿⠿⡿⠿⠿⠛⣛⣻⣿⣎⣩⣭⣥⣤⣼⣿⣶⣶⣾⣿⣿⣿⡿⠿⢿⣿⣿⢹⠀⠀⠙⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠱⣿⣿⣿⡿⠿⠀⢛⣉⣭⣶⣶⣛⣿⠋⠴
⣿⣷⠀⢈⣉⣉⣈⣭⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⢿⣿⢀⣤⣤⠄⠀⠀⠀⠀⠀⠉⠿⣾⣤⡤⠴⠂⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣩⣶⣷⠾⠛⡭⠀⢟⣀⣩⣶⣖⢒
⡯⠿⠿⠿⠛⠛⠛⠋⠙⠼⢏⣝⢿⢿⣿⣿⣿⠿⠛⠉⠉⠀⣠⣰⣧⣤⣤⡶⠶⠶⢳⣶⠂⠀⠀⠀⣸⣿⡿⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⠀⣷⣶⣶⡏⣿⣿⣦⡄⢠⣼⣿⣷⣶⣿⠟⠛⣋⡥⠶
⠀⠒⠻⣥⠀⠀⠀⠀⠀⢁⡉⣿⣿⣧⣤⣤⣤⡄⣠⣴⢾⣿⣟⣩⣍⡥⡞⡛⠈⠐⠺⠿⠀⠀⢷⡾⠟⢱⠃⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⡀⠤⣿⣿⠹⠷⡿⢛⠛⣫⣴⠾⠛⢙⠀⣀⣀
⠀⠀⠀⢉⣀⣤⣤⣤⣶⡿⠿⢿⣿⣿⡙⣿⣿⣟⣿⡶⢿⣿⣿⡿⠿⠋⣋⣁⣀⣤⣶⠿⠟⢛⡋⠁⠀⠁⠀⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢠⣿⣿⠿⠖⠛⠩⣿⠋⣋⣤⡴⡛⠛⠹⢀
⢶⣾⣿⣟⣿⣿⣽⣷⣶⣾⣿⣿⣻⣿⣧⣿⣿⣿⣿⣈⣁⣠⣴⣶⣿⠟⠛⢭⣭⣤⡄⡊⠌⠐⠀⢀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠀⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢺⣿⡏⠀⣄⣀⡴⣟⣻⠋⡇⠀⠁⠀⠊⠁
⣿⣿⣿⢿⣿⣿⠿⠿⠛⠋⣉⣉⣭⣻⣿⣹⣿⣿⣿⣯⣿⣿⣶⣿⡇⠀⠀⠈⠉⠋⢀⣠⢤⡶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⣘⡛⠃⠋⠉⠓⠁⡉⠉⠀⠀⠀⠀⢠⡴⠞
⢛⣿⣿⣤⣤⣦⡶⠾⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⢀⣤⠤⠶⠖⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁⠇⣀⡤⠄⠚⠩⢖⣠⣴
⣿⣿⣵⣾⣾⣿⣿⡿⠙⢿⡙⠿⠿⠟⢛⣻⣿⣿⠤⠛⠖⠛⠓⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⢀⠀⠐⣠⠅⢀⣉⡵⠖⣻⣾⣿
⣿⣿⠿⠟⠛⠛⢙⣑⣴⣿⣷⡶⠾⠛⠋⠈⠛⠳⠀⣀⣤⣄⣀⣀⡀⣀⡤⠴⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢛⣩⠵⣲⣿⣷⣶⣿⣿⣿⣿
⣭⣤⡴⣶⣾⠿⠟⠋⠉⠀⢸⠃⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣥⡅⠀⠀⠀⠀⢀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡠⠄⠈⣁⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⡷⣿⠿⢷⠶⠰⠶⠶⢖⣀⣤⠴⠖⠞⠋⠀⠀⠉⠻⣿⣿⣿⣿⣿⣷⣶⣶⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣤⣭⣗⣛⣉⣿⠿⢿⠿⡿⣿⣿⣿⣿⣿⣿⢻⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⠟⠛⠋⠉⠈⠽⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣗⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣦⣴⣿⣤⣶⣮⣦⣼⣟⣿⣭⣏⣙⣛⣛⡛⣿⣟⣟⣿⣿⣿⣷⣤⣴⣤⣤⡄⠀⠀⠀⠀⠀⠉⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡠⠔⠀⠀⠀⠀⠀⠈⠻⣿⣟⣛⣛⣻⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿
⢿⣿⣿⢟⡿⣿⣿⣿⣿⡇⣿⣯⡗⣿⣿⣿⣿⣷⣿⡟⣿⣿⣽⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣾⣟⣻⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⣿⣯⣶⣿⣿⣿⣷⣶⣾⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣯⣾⣾⣶⣭⣽⣿⣽⣧⣄⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣏⣛⣛⣿⣟⡛⢿⣿⣿⣿⣿⡟⣻⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣭⣥⣽⣿⣿⣷⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠏⣭⣭⢭⣽⡹⣿⣿⣽⣿⡟⣿⡟⣾⣿⡾⣿⡿⣿⡟⣿⣟⣻⣿⢻⣿⣿⣏⡿⡟⠘⠻⠿⠛⠻⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣴⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⣿⣻⣿⣹
⣦⣿⣿⣾⣿⣇⣿⣽⣧⣿⣿⣿⣧⣿⣿⣷⣿⣷⣶⡆⣿⣿⣿⣿⣿⣷⣺⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢨⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢹⡏⣿⡯⣿⡿⣿⢼⢿⠿⠇⢿⢿⡇⣿⣿⣿⣸⣻⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⢿⣿⠿⠿⠟⠟⠛⣛⠻⢛⣛⣛⣙⣛⣛⣩
⣿⣿⣷⣿⣿⣷⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⣿⢿⣿⣿⠿⠿⠿⣿⣿⣟⣿⣟⣻⣿⣭⡾⠛⠛⠻⠿⠟⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢟⣛⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛
⣿⣿⣿⣿⣿⣿⣭⣿⣧⣤⣀⣤⣭⣵⣾⣶⣾⣿⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠺⢻⣿⠙⢿⣿⠉⣻⣻⣿⣿⣿⣯⣵⣿⣶⣾⣿⣿
⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⣿⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣋⣻⣿
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢸⣟⣿⣿⣿⣿⣿⣿⣿⡼⢿⣿⣻⣛⣿⣿⣿⣿⣽⣯⣭⣿⣷⣢⣶⣶⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⡼⣏⠾⠁⠉⠃⠃⠛⢛⣫⣭⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⠿⣿⠛⣹⣗⣋⣛⣛⣛⣟⣥⣼⣿⣭⣭⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⣶⣶⣾⣿⣿⣿⣿⣿⢻⣿⣿⡿⠿⣛⣛⣫⣭⣿⣿⡿
⠶⣿⣟⣟⣛⣻⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⠿⣟⣿⣿⣿⣿⣿⣀⣈⣀⡀⣀⣤⣤⣤⣾⣿⣿⣿⣿⠿⡏⢱⣶⣶⣶⣤⠘⣻⣭⣭⣽⣻⣿⣿⣿⣿⣿⣿⣷⡋⣭⣥⡶⣾⡞⢛⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢻⣛⡿⠿⣿⣿⣿⣶⣶⣾⣿⣿⡿⣟⣻⣯⣭⣷⣤⣶⣿⣿⣿⣿⣿⡟⠀⠉⠁⣿⣿⣀⠀⢸⣿⡇⣸⣿⢀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣤⣤⣿⣿⣿⣯
⠿⠟⠛⠛⠋⠉⠉⠛⣉⣁⣤⣤⡤⠤⢴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⡇⢸⡇⡜⠻⡿⠿⠿⠿⠟⣛⣋⣡⣧⠤⠇⠀⠀⢠⣿⡿⠛⠀⣼⣿⠿⠿⠟⢸⣿⡿⢹⣿⡿⣿⠿⢿⡟⣿⣿⣷⢷⣟⣛⣿⣭⣵⣶⣺
⣠⡤⠤⠒⣒⣒⣿⣯⣽⣿⣶⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⡟⣟⣛⣻⣙⣩⣬⣥⣬⣴⣶⡦⣴⠛⠋⣭⣵⣾⠖⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⣸⣿⣿⠿⢟⣛⣁⡤⠴⣛⣿⣽⡿⢸⡿⣛⣿⣿
⣿⡀⠰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣛⣛⣻⣿⣮⣭⣭⣤⣤⣶⣾⣿⣟⣛⣻⣫⣽⣿⣿⣿⣿⡇⢸⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠙⣿⣿⣿⣿⠿⠃⣩⣍⣽⠶⣷⣿⡽⠥⠖
⣿⣷⢀⣈⣉⣩⣤⣬⣶⢶⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢿⣿⣿⣿⣿⢿⠿⠟⣛⣩⣥⣤⣤⣴⠶⠂⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣉⣭⡬⠿⣿⠟⢙⡶⠘⠛⣀⣵⣶⣲⡈
⠷⠿⠿⠛⠛⠋⠙⠋⠹⡾⢿⣿⣿⡿⣿⠿⠿⠿⠙⠋⠉⢁⣰⣼⣧⣬⡽⠶⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢀⣷⣶⣶⡏⣷⣿⣧⣄⣠⣼⣿⣿⣿⣻⠏⠛⣩⠥⠶
⠀⠺⣫⣅⣤⡀⠀⠀⠀⣃⡀⣈⣉⣬⣤⣶⣶⣾⣷⣶⣿⣿⣯⣽⣿⣷⣿⣿⣿⣿⣿⣿⠙⢛⣛⣻⣯⣿⡞⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠤⣿⣿⠹⠷⢿⣛⠛⣭⣴⡾⠋⢙⡀⣀⡭
⠈⠀⢁⣈⣠⣤⣤⣶⡾⣿⣟⣛⣻⣛⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠿⣛⣻⣯⣭⣴⣶⣿⣟⣻⣿⡏⠈⠻⠁⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢠⣿⣿⠿⠞⠋⠹⢿⢛⣩⣤⡶⡛⠛⠙⣃
⢶⣿⣿⣿⣯⣿⣵⣶⣶⣾⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣾⣿⣶⣿⣿⣛⣫⣭⣥⡰⢾⣿⣿⣿⣿⣃⠈⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢹⣿⡏⢀⣀⣤⠴⣟⣯⠉⠇⠀⠀⠀⠈⠁
⣾⣿⣿⣿⣿⣿⠿⠿⢛⣉⣉⣭⣬⣴⣶⣿⣟⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⣘⠛⠃⠉⠁⠚⢃⡈⠀⠀⠀⠀⢀⠤⠶⠛
⢚⣿⣿⣤⣴⣶⠶⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠈⠀⡇⣀⠤⠔⣊⠱⣂⣠⣶
⣭⣯⣿⣿⣿⣿⣿⣿⠙⢿⠘⠻⠿⢛⣛⣿⣿⣛⠶⠾⣿⣿⡋⠹⡆⠀⠀⠀⠀⣀⣀⣀⡤⠤⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠙⠀⠀⠀⠠⡐⠥⠤⢀⡨⠶⠚⣫⣽⣿
⣿⡿⠿⠟⠛⢋⣉⣁⣾⣿⣷⡶⠿⠛⡋⠀⠀⠀⠀⠀⠿⠫⠁⠀⠀⠠⠤⠖⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡈⠙⣃⣩⠖⣺⣿⣾⣿⣿⣿⣿⣿
⣥⣤⣶⣶⣿⠟⠟⠋⠀⠀⢼⠃⠀⠀⠀⠀⢠⣤⣤⠄⠀⠀⣴⣿⣿⣷⣦⡀⠀⠀⣀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠠⠔⠉⣠⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠙⣿⠷⣿⠿⢷⠶⠰⠶⢶⣶⣠⡤⠶⠖⠛⠉⠁⠀⠀⠈⠀⠈⢻⣿⣿⣿⣿⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢈⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣉⡻⠹⠟⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠯⠟⠟⠛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣤⣭⣭⣭⣭⣥⣮⣭⣭⣟⣻⣯⣯⣛⣻⣛⠿⠿⠿⠿⣻⣿⣿⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠻⠿⢿⣿⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣗⣿⣿⡧⣿⣯⡿⣿⣿⣿⣿⣷⣿⣟⣿⣟⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠃⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣾⣽⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⣾⣶⣶⣷⣾⣿⣿⣷⣿⣿⣿⣿⣗⣿⣿⣶⣿⣿⣿⣧⣿⣿⣿⣶⣶⣾⣥⣤⣤⣬⣬⣭⣭⣿⣧⣭⣿⣻⣿⣿⣿⣿⣿⣇⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠿⠿⠿⢿⣿⣿⣿⣿⠿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣟⣿⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⡟⣭⣭⣭⣽⡹⣿⣿⣿⣿⡟⣿⡟⣾⣿⣾⣿⡿⣿⡟⣿⣟⣻⣿⣿⣷⣿⣏⣿⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡔⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣟⣛⣿⣿⣃⣏
⣆⣿⣿⣿⣿⣇⣿⣹⣧⣿⣿⣿⣧⣿⣿⣧⣿⣷⣿⣆⣿⣟⣿⣿⣿⣷⣾⣿⣿⣶⣴⣶⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡏⣿⡯⣿⡿⣿⢽⣿⠿⠇⢿⣿⣟⣿⣿⣿⣸⣻⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠿⠿⠿⠟⠛⠻⠿⣟⣿⣛⣛⣛⣋⣉
⣿⣿⣷⣿⣿⣷⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡯⣿⣿⣿⠿⢿⢿⣿⣿⡿⢿⣟⣿⣯⣛⣟⣛⣻⣿⠛⠋⠉⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡖⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠿⣿
⣿⣿⣿⣿⣻⣭⣹⣿⣉⣉⣉⣉⣿⣾⣽⣯⣿⣿⣶⣾⣶⣾⣿⣷⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠰⣶⡟⣿⠙⠿⣿⡏⠻⣿⣿⣿⣽⣿⣯⣿⣷⣿⣷⣿⣾
⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠿⠷⣤⡄⠀⢀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣘⣛⣛
⣿⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⡏⣿⣻⣿⣿⣿⣿⣿⣿⡷⠿⠿⠿⠿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣷⣶⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣦⣄⣀⣤⣾⡧⠿⠃⠙⠟⠛⠛⣻⣏⣩⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠻⣿⡨⣝⣻⣟⣻⣛⣠⣿⣏⣛⣽⣬⣽⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠾⠿⠟⢳⣶⣶⣾⣿⣿⣿⢻⣿⣿⣿⠿⠿⢛⣛⣭⣿⡿⣿⣷
⠶⠾⠿⣟⣛⣛⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣃⣀⡉⢉⣉⣁⣤⣤⣤⣴⣿⠿⣿⣿⠿⡆⢰⣶⣶⣶⣤⠀⣰⣯⣭⣽⣻⣿⣿⣿⣿⣿⣿⡖⢫⣭⣥⣾⢷⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣟⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣯⣭⣭⣭⣿⣿⣶⣿⣿⣿⠿⠃⠀⠀⣿⣿⣀⡀⢸⣿⡇⣸⣿⢀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢋⣀⣀⣤⣾⣿⢿⣿⣷
⠿⠿⠿⠛⠛⠛⠛⠛⣋⣁⣉⣁⣠⡤⠤⢴⣿⣾⣿⣿⣿⣿⣭⣿⣿⣷⣿⣿⣿⣾⣿⣬⣛⣿⣿⡿⠿⠿⠟⣛⣋⣽⣤⠍⠀⠀⠀⢰⣿⡿⠛⠀⣾⣿⠿⠿⠟⢸⣿⡟⢹⣿⣿⣿⡿⠿⣿⣿⣯⡿⣿⣿⣿⣻⣭⣶⣿⣿
⣀⡤⠤⠴⣒⣒⣚⣯⣽⣭⣵⣶⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⢟⣻⠿⣿⡿⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣿⣫⣍⠷⠖⠀⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡟⠟⣛⣃⣠⡭⢾⣟⣿⣿⢫⣿⢿⣿⣿⣿
⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⢟⣛⣿⣧⣩⣭⣥⣤⣤⣴⣿⢿⣷⣿⣿⡿⠿⠿⠛⠁⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠙⣿⣿⣷⡾⠗⢈⣋⣹⣷⡿⢿⣿⡏⠴⠉
⣿⡄⠀⢉⣋⣉⣩⣭⣵⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⡟⣿⡋⣽⣷⣤⡴⠶⠲⠄⠒⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣥⣵⢾⡶⠋⣹⠃⠚⣉⣨⣶⣶⡒⠙
⡽⠿⠽⠟⠛⠛⠛⠉⣧⡛⣿⣿⣿⣿⣿⣿⠿⡿⠿⠛⠉⢡⣤⣽⣬⣭⣤⠴⠶⡖⢲⡾⣻⣿⣿⠉⠀⠀⠀⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢀⣿⣶⣶⡎⣿⣷⣶⡏⣤⣿⣿⣶⡻⡿⠿⣛⣥⢴⢒
⢐⡲⠛⣂⠂⠀⡀⠀⢘⡀⠉⣉⣉⣭⣭⣤⣤⣠⣴⣶⣿⣿⣿⣿⣯⣷⣿⢿⠏⠓⠸⠀⠉⠀⢈⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠄⣿⣿⠹⢷⢟⡛⣫⣥⡶⠟⠉⡃⣀⣨⠽
⠐⠛⢛⣛⣉⣤⣤⣤⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣋⣁⣠⣴⡶⠶⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢠⣿⣿⠿⠟⠍⢹⠝⣋⣥⡴⢞⡻⠙⢇⣀
⣶⣿⣿⣻⣿⣯⣯⣷⣶⣾⣿⣿⣿⣯⠍⠋⢉⣸⣏⣁⣡⣭⣶⣾⡿⣿⣏⣩⢅⡄⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠐⢹⣿⡟⣀⣠⡤⢾⣻⡍⠿⠈⠁⠀⠀⠉⢀
⣿⣿⣿⣿⣿⣿⠿⠿⠃⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠑⠈⠀⠈⣀⣤⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⣀⡼⠛⠃⠉⠙⠋⣉⠌⠀⠀⠀⠀⢠⢴⣞⢋
⣻⣿⣧⣤⣤⡴⠶⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠿⠛⠛⠁⣨⣤⠴⠶⠚⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠁⠴⢀⣠⠤⢚⣭⣖⣉⣴⣶
⣿⣭⣿⣿⣿⣿⣿⡟⠻⡏⠻⣿⣿⣿⣿⣿⣿⣣⠴⠶⠚⠛⠂⡇⠀⠀⠀⠀⢀⣀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⢺⠋⠀⢀⡀⠄⣺⡤⢄⣠⣵⡶⣛⣽⣿⣿
⣿⡿⠿⠛⠛⠛⣋⣠⣶⣿⣶⢿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⢀⡀⢀⣀⡤⠖⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣀⠉⠛⣋⡭⣒⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣴⣶⡿⠿⠛⠉⠉⠠⡟⠀⢻⠟⠉⠀⠈⠀⣤⠤⠖⠚⠋⠉⡌⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡳⠈⣁⠥⠊⢉⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⡿⡾⣷⠿⢷⠶⠰⠶⠶⢖⣠⡄⠀⠠⣾⣿⣿⣷⣦⣄⡀⠀⢀⣥⣤⠤⠖⠚⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠒⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣛⠿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠶⠶⠯⣭⠿⣿⣿⣷⣿⣟⣷⣿⣿⣿⣿⣟⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣵⣭⣭⣭⣉⣉⣭⣉⣭⣹⣏⣻⢻⣿⣙⡿⠿⢿⠿⢿⣿⡿⡿⣿⣏⣁⣀⣀⠀⠀⠀⠈⠀⠉⠻⠿⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣟⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠊⠹⢿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣯⡿⣿⣿⣿⣿⣷⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⠿⠑⠄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿
⣭⣭⣿⣭⣿⣿⣿⣿⣿⣿⣿⣯⣅⣿⣏⣭⣿⣿⣿⣏⣽⣿⣧⣴⣬⣭⣭⣭⣭⣝⣽⣽⣯⣭⣌⣛⣿⣟⠙⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⢿⣿⡟⠿⠛⠿⠿⢿⣿⣿⣿⣿⣿⡿⢿⣾⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣭⣿⣿⣭⣭⣭⣿⣷⣿⣷⣿⣿⣿⣿⢿⡿⠿⠿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣾
⡟⣭⣭⢭⣽⡹⣿⣿⣽⣿⡟⣿⡏⣿⣿⣾⣿⡿⣿⡟⣿⣟⣻⣿⣻⣷⣿⣏⡿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⣙
⣁⣿⣻⣿⣿⡇⣿⣹⣇⣿⣿⣿⣇⣿⣿⣧⣿⣿⣿⡆⣿⣟⣻⣿⣿⣷⣾⣿⣿⣦⣴⣶⣶⣶⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⣿⡯⣿⡿⣿⢽⢿⠿⠏⢿⠿⣟⣿⣿⣿⣹⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣟⣛⣻⣛⣛⡛
⣿⣿⣷⣿⣿⣷⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠟⠿⣿⣿⣿⡿⡿⠟⠉⢀⣠⣄⣀⡀⠀⠀⠀⠀⣀⣾⡷⣶⣿⠿⠿⣿⣿⣿⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣽⣽⡿⣿⣿
⣿⣿⣿⣛⣛⣛⣿⣏⡛⢉⣛⣻⣻⣿⣯⣿⣽⣭⣯⣭⣿⣿⣿⣾⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄⠈⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⢁⠀⠀⠀⢀⣿⠩⢟⣿⠀⢿⢻⡿⠿⣿⣿⠛⢟⣿⣽⣯⣿⣽⣯⣷⣾⣿⢷⣿⡗
⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⣿⣿⣧⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣤⣶⣿⣶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣛⣛⣛
⣿⣿⣿⣻⡏⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣭⣭⣼⣿⣶⣶⣄⣼⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⢻⡷⣿⣿⡿⠟⠈⠁⠏⠛⠛⣛⣋⣹⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⢿⠟⢹⡧⠝⠻⣿⠟⣿⣃⣼⣿⣛⣛⣽⣭⣭⣽⣿⣷⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⢪⣤⣤⣤⣴⣶⣶⣾⣿⣿⡟⣿⣿⣿⣿⡿⠿⣛⣻⣽⣿⠿⠾⢚
⠶⠶⠶⠿⢿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣟⣀⠈⠉⠉⢉⣁⣸⣿⡿⠟⠋⠉⣿⣿⠿⡇⢰⣶⣶⣿⣽⢿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣷⡚⣩⣭⣭⡿⡟⢻⣗⣾
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣷⣶⣿⣷⣶⣾⡿⣿⣿⣿⣿⣭⣍⣽⣽⣷⣼⡟⠉⠁⠀⠀⠀⠀⣿⣿⣀⡀⢸⣿⡇⣼⣿⢲⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡟⠃⢉⣉⣰⣷⣟⣿⣿⣶
⠿⠿⠟⠛⠛⠛⠛⠛⠉⣉⣉⣉⣉⣤⡤⣴⣶⣶⣿⣿⣿⣯⣭⣽⣿⣿⠿⢿⣿⣿⡧⣾⣿⣿⣿⡿⠿⠿⠟⢛⡹⠃⠀⠀⠀⠀⠀⢰⣿⡿⠛⠁⣾⣿⡿⠿⡟⢼⣿⡟⢹⣿⣯⣿⢿⣿⣿⣿⣿⣾⡿⣿⣟⣩⣭⣿⣾⣟
⣀⣠⠤⠤⠴⣒⣒⣻⣍⣭⣭⣶⣶⣾⣿⣿⣿⢹⣿⣿⣿⡟⣛⣿⣿⣅⣠⣿⣿⣿⣷⣍⣩⣭⣤⣴⠒⠚⠉⠍⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⣸⣿⡇⠞⣗⣈⣩⡵⢿⣻⣯⣝⣽⠿⢿⣿⣿⣿
⡅⢠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⢻⣿⣌⣋⣩⣁⣠⣬⣿⢛⡛⠛⠛⠛⠿⠛⠻⢿⣿⣏⢹⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⢻⠿⠿⢟⣿⣿⣿⣷⡷⠒⢛⣛⣯⣷⡶⣿⣿⠩⠞⠁
⣧⠀⠙⠛⣛⣉⣉⣭⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣹⣿⣾⣧⣤⡄⠀⠀⠀⠘⢿⣾⡄⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠅⠀⣉⣡⣠⡶⣶⠾⠉⡍⠐⠻⣁⣽⣶⡶⠚⠛
⣿⡿⠿⠟⠛⠛⠛⢻⡼⢿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠉⢠⣨⣇⣉⣭⣥⠤⠶⠲⣶⠂⡀⠀⢀⠍⠀⠀⠀⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢰⣿⣷⣿⡟⣿⣶⣾⣥⣴⣿⣷⣶⣿⠟⠛⣋⡥⣶⣚
⠴⠶⣶⠄⠀⠀⠀⠀⠇⠘⠛⠛⣩⣭⢭⣥⡄⣠⣴⣶⣾⣿⣿⣯⣩⣶⣿⣿⡿⠧⡿⠈⠹⢾⡟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⠀⢸⣿⣇⣤⠄⣿⣿⠹⠭⢛⠛⣫⣴⠾⠋⢙⠀⣀⡩⠿
⠐⠃⠘⢁⣀⣤⣤⣤⣾⡿⡿⣛⣿⣿⣿⣻⣷⣿⣿⣿⣿⣿⣿⠿⠿⢛⣋⣁⣤⣴⡶⠶⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢠⣿⣿⠿⠟⠉⡿⢛⣋⣤⠶⠛⠛⠹⢀⣀
⣶⣾⣿⣿⣿⣭⣭⣾⣾⣾⣿⣿⢿⣿⣿⣿⣿⣟⣁⣉⣩⣤⣴⣾⢿⣛⡫⣭⣥⣤⡄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢹⣿⡇⣸⣿⡗⠚⢹⣿⡟⣀⣀⡴⢟⣯⠉⡇⠈⠀⠀⠊⠁⣸
⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⣉⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠑⠛⠉⢉⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⢁⣀⡼⠛⠃⠉⠃⠈⡉⠁⠀⠀⠀⠀⠠⠶⠚⠉
⣿⣿⣌⣡⣥⡤⠶⢾⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⣥⡤⠴⠶⠚⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠚⠉⠀⠀⣀⡤⠖⠊⠀⠇⣀⡤⠄⣪⠡⣂⣡⣴⣶
⣿⣭⣭⣿⣿⣷⣷⠚⢿⠙⠿⠿⠛⢛⣿⣿⣿⡿⢻⠶⠒⠳⠀⠁⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⠚⠁⠀⢀⠠⡀⣀⠡⢀⣨⡴⠚⣃⣿⣿⣿
⣿⠿⠿⠛⠛⠙⢉⣴⣾⣧⣤⠶⠿⠟⠹⣿⠟⠉⠀⠀⠀⠀⣀⠀⣀⣠⡤⠶⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠐⢛⣨⠴⢲⣯⣶⣿⣿⣿⣿⣿⣿
⣠⣤⣶⣶⡿⠿⠛⠉⠉⢹⠇⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⣞⠋⢁⡅⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠁⢀⣠⠄⠈⣁⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢉⠷⡿⣷⠿⢷⠖⠰⠶⠶⣶⣠⣤⠴⠶⠂⠀⠈⢿⣿⣿⣿⣿⣾⣄⣠⠴⠖⢻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠨⠐⠂⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
[30A⣛⡿⠿⠛⣻⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⠿⠛⠻⠗⡖⢲⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣦⣤⣬⣭⣭⣽⣭⣭⣭⣭⣽⣛⣿⣭⣟⣛⣛⣻⠿⠿⢿⣋⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣭⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡴⡦⢀⡀⠀⠀⠀⠀⠉⠻⣿⣯⣿⣿⣟⣟⣛⣛⣻⡿⢿⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣽⣿⣿⣿⡧⣿⣿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣻⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣽⣿⣿⣿⣿⣿⣿⣿⣽⡿⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿
⣿⣷⣾⣶⣿⣿⣿⣾⣾⣶⣿⣿⣗⣿⣯⣶⣿⣿⣿⣧⣿⣿⣷⣶⣶⣭⣥⣥⣬⣭⣽⣭⣽⣷⣦⣭⠛⢻⣿⣿⣿⣿⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣟⣻⣿⣿⣿⠛⢛⣻⣿⡿⢿⣿⣿⣿⣿⣿⣟⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⠿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⡏⣭⣭⢭⣽⡹⣿⣿⡽⣿⡟⣿⡏⣿⣿⣾⣿⡿⣿⡟⣿⣟⣻⣿⣿⣷⣿⣏⡿⠚⠿⢿⠿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟⢩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣻⣿⣿⣥⣇
⣄⣿⣿⣽⣿⣇⣿⣹⣇⣿⣿⣿⣇⣿⣿⣧⣿⣷⣿⡆⣿⣟⣿⣿⣿⣷⣾⣿⣿⣦⣶⣶⣿⣶⡾⢿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡏⣿⡯⣿⡿⣿⢽⢿⠿⠇⢿⣿⣟⣿⣿⣿⣸⣻⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⢿⣿⣿⣿⣿⣿⠿⠻⠿⠟⠟⣛⡻⢟⣛⣛⣋⣿⣟⣩⣭
⣿⣿⣷⣿⣿⣷⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢿⣿⣿⡿⢿⣿⠿⣿⣿⠿⣿⡟⠿⣿⣿⣿⣿⣿⠿⠛⠃⣤⣤⣤⡀⠀⠀⠀⠀⣰⣶⣿⣿⣿⡿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣟⣩⣍⣿⣇⣉⣉⣉⣹⣿⣿⣭⣭⣿⣿⣷⣴⣾⣿⣿⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠛⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⠀⠀⢀⣿⡏⣯⡿⣿⠅⠸⡿⣿⢻⢿⣿⡟⢛⣿⣧⣿⣿⣯⣿⣿⣶⡾⠿⣿⣾
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⢿⣧⣀⣀⣀⡀⠀⠀⣸⣿⣿⣿⣿⣷⣦⣀⣀⣼⣿⣶⣶⣶⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣇⣹⣯⣭
⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢟⣻⣿⣟⣻⣿⣿⣿⣿⣷⣦⣤⣴⣶⣿⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣾⡿⠾⠟⠀⠀⠛⠙⢛⣻⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠟⢹⣯⠿⢻⣿⣛⣟⣁⣼⣿⣙⣫⣥⣭⣼⣶⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠙⣤⣥⣴⣶⣴⣾⣾⣿⣿⣿⣿⢻⣿⣿⣿⠿⢟⣋⣻⣽⣿⠿⡟⢛
⠾⠾⡾⣟⣛⣻⣿⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣻⣿⣿⣟⣿⣀⣈⣁⣈⣉⣨⣿⡿⠟⠋⠉⠀⣿⣿⢿⡇⢰⣶⣶⣿⣽⢿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡯⣭⣵⡶⢾⢟⢛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣻⣿⣿⣿⣿⡶⣶⣷⣶⣾⣿⢿⣿⣟⣯⣽⣭⣾⣾⣿⣷⠏⠁⠀⠀⠀⠀⠀⣿⣿⣀⡀⢸⣿⣧⣼⣿⢛⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣠⣤⣿⣿⣿⣿⣿
⠿⠿⠟⠛⠛⠛⠛⠋⢉⣉⣉⣁⣠⠤⢤⢴⣶⣾⣿⣿⣿⣯⣭⣿⣿⠛⠁⣠⣾⣿⣧⢿⣿⣿⡿⠿⠿⠿⠟⣛⠉⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⠁⣾⣿⡿⠿⡟⢸⣿⡟⣹⣿⡿⠿⢿⢟⣿⣿⣽⣶⣿⣛⣿⣭⣴⣶⣾⣿
⣀⡤⠤⠴⠖⣒⣞⣯⣭⣭⣴⣶⣾⣿⣿⣿⣿⢻⣿⣿⣿⡟⢛⣿⠿⠿⠶⠿⠿⣿⣿⣿⣯⣭⣶⢰⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠘⠄⢸⣿⡇⣸⣿⡏⢛⣛⣁⣥⠤⢟⣻⣽⣷⠷⠿⢛⣻⣿⡿
⡇⠠⣾⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⠟⠛⢻⣿⣎⣩⣭⣭⣤⣤⣶⣶⢦⠖⢂⣀⠀⠀⠀⠈⠻⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⢈⣻⠿⠿⠟⣻⣿⣿⣿⠿⠂⢙⣭⣩⠷⡾⣿⣯⠏⠖⠃
⣧⠀⠈⢙⣋⣁⣉⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⢳⣾⣷⡿⠿⠥⠀⠀⠀⠀⠈⢻⠗⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠰⢿⣀⣈⣭⡤⠴⢿⡿⠋⣳⠒⠛⣋⣭⣷⣶⡊⠙
⠽⠿⠿⠟⠛⠛⠛⠙⣼⣻⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⢠⣤⣿⣤⣬⡥⠶⣶⡖⣶⠚⢆⣠⣴⠋⠀⠀⠀⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢶⣿⣿⣿⡏⣾⣷⣾⡇⣦⣿⣿⣿⠿⠿⡙⣩⠥⢶⣿
⠒⢾⣧⠤⠄⠀⠀⠀⢇⠈⠉⣉⣉⣤⣤⣤⡄⣠⣴⣶⣿⣿⣿⣭⣭⣶⣿⣾⣿⠶⢿⠀⠁⢉⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⠀⢸⣿⣇⣰⠄⣿⣿⠹⠧⢟⡙⣩⣴⠾⠋⢉⣃⣀⡬⠝
⠛⠙⠋⣁⣠⣤⣤⣴⣾⡿⣛⣿⣿⣿⣿⣿⠇⣿⢽⣿⣿⣿⣿⠿⠟⢛⣋⣉⣤⣶⡾⢿⡛⠙⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢹⣿⡟⠛⢠⣿⣿⠿⠋⠁⢼⢟⣋⣤⡶⠛⠋⠉⢃⡠
⣶⣿⣿⣿⣿⣭⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣠⣽⣉⣈⣥⣴⣶⣿⣿⣿⣯⣭⣵⣦⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⣸⣿⡷⠋⢹⣿⡟⣀⣤⠴⢞⣫⡍⠸⠀⠀⠀⠀⠁⣀
⣿⣿⣿⣿⣿⡿⠿⠟⠛⢉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⠈⠉⠛⠛⠛⢉⣩⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⣀⣠⠼⠛⠃⠁⠈⠁⣈⠉⠀⠀⠀⠀⠠⠴⠚⠉
⣿⣿⣤⣤⣤⡴⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠁⣡⡤⠶⠖⠚⠁⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠚⠉⠀⠀⣀⡤⠖⠊⠁⠸⢀⡤⠄⣊⠅⣖⣤⣴⣶
⣿⣽⣿⣿⣿⣿⣯⡘⢿⡟⠻⠿⠿⣿⣿⣿⡿⠧⠶⠶⠚⠛⠀⡅⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⢹⠁⠀⠀⡠⣀⣠⠤⢄⣨⢵⠞⣫⣾⣿⣿
⣿⡿⠟⠛⠛⠉⣁⣰⣿⣷⣶⠶⠿⠻⣿⠟⠃⠈⠀⠀⠀⠀⣀⡀⣀⡠⠤⠒⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⢈⠁⢉⣨⠵⣺⣿⣿⣿⣿⣿⣿⣿⣿
⣥⡤⣴⣶⡿⠿⠛⠉⠉⢸⠇⠀⠀⠀⠁⠀⣠⣶⣶⣦⣖⠚⠋⢉⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⡀⠁⢀⡠⠴⠈⣡⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢉⡷⡾⣷⠿⢷⠖⠰⠶⠶⣖⣠⡤⠴⠀⠀⠙⣿⣿⣿⣿⣿⣦⡀⣤⣤⠴⠖⠛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠕⠂⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
[30A⣬⣽⣉⣉⣩⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠙⠂⠚⠿⠻⢿⣿⣷⡶⣾⣾⣿⣿⣿⣿⣯⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣶⣶⣾⣶⣾⣹⣿⣬⣯⣉⣿⣛⣛⣛⣛⣉⣿⣤⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⠸⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠽⢿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠇⣤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣟⣿⣟⣻⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⢿⣿⠿⣿⢿⣿⣿⣿⣿⡧⣿⣯⡗⣿⣿⣿⣿⣷⣿⡿⣿⣿⣟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣶⣿⣿⣿⣧⣿⣿⣿⣶⣿⣶⣶⣶⣶⡶⣶⣶⣶⣷⣷⣶⣿⣭⣭⣽⣭⣸⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⣛⣹⣛⣛⣛⣿⣿⣿⣿⣿⣟⣻⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⣭⣭⢭⣽⡹⣿⣿⡽⣿⡟⣷⡟⣾⣿⡾⣿⡿⣿⡟⣿⣟⣻⣿⢻⣷⣿⣏⣿⡇⠚⠻⠿⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣵
⣦⣿⣿⣾⣿⣧⣿⣽⣧⣿⣿⣿⣧⣿⣿⣷⣿⣷⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡏⣿⡧⣿⣿⣿⢼⢿⠿⠇⢿⣿⣇⣿⣿⣿⣸⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠛⠛⣛⡛⣛⣙⣛⣛⣿⣯⣭⣭⣯⣭
⣿⣿⣷⣿⣿⣷⣶⣾⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⠿⣿⣿⣿⣟⣿⣟⣿⣷⣽⣿⣿⠿⡿⠿⠿⠙⠀⢤⣤⣶⣶⣄⠀⠀⠀⠀⠀⢠⣤⠚⣛⣛⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡟⣻
⣿⣿⣿⣿⣩⣼⣼⣿⣤⣤⣤⣬⣭⣿⣾⣿⣿⣿⣾⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠐⠻⢻⣟⣛⣻⢿⣙⣻⣿⣶⣷⣿⣶⣶⣿⣿⡿⣿⣿
⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⡿⢿⣧⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣦⢀⠀⠀⢀⣾⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣁⣭⣭
⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⡏⣿⣟⣿⣿⣿⣿⣿⣿⣿⠿⣿⣛⣛⣻⣿⣯⣿⣯⣯⣭⣽⣿⣷⣲⣶⣶⣾⣟⣿⣿⣿⣿⣆⢰⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⡟⠿⠿⠏⠀⠘⠛⣙⣙⣭⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢛⣿⣖⣛⣛⣫⣹⣯⣤⣿⣧⣭⣭⣶⣶⣶⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⣶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⡿⠟⣛⣩⣭⣾⣿⣟⣛
⢾⣛⣛⣛⣛⣯⣿⣿⣿⣿⣩⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠟⣿⣿⣿⣿⣿⣯⣀⣀⣀⡀⢠⣤⣴⣶⣾⣿⡿⣿⣿⠿⡇⢰⣶⣶⣶⣤⠺⣻⣭⣭⣽⣻⣿⣿⣿⣿⣿⣻⣿⠩⣵⣶⠶⡿⣏⣱⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣟⣻⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡟⣿⣿⣯⣽⣷⣶⣷⣿⣿⣿⡏⠿⠏⠈⠁⠀⣿⣿⣀⡀⢸⣿⡇⣸⣿⢀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⣤⣴⣿⣿⣿⡿
⠿⠛⠛⠋⠉⠉⠉⠉⣉⣠⣤⣤⠤⠤⢶⣶⣷⣾⣿⣿⣿⣽⣷⣶⣿⣿⣿⣿⡾⢖⢿⡷⣿⡿⢿⠿⠿⠛⢛⣛⣩⡽⠧⠔⠀⠀⠀⢠⣿⡿⠛⠀⣾⣿⠿⠿⠟⢸⣿⡟⢹⣿⡿⡿⢿⠿⣻⣿⣿⣷⣾⣟⣻⣯⣵⣶⣾⣿
⣠⡤⠴⠒⣒⣚⣿⣭⣭⣷⢦⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⠟⣉⣛⣏⣩⣥⣬⣤⣤⣴⣶⡆⡶⠋⠉⣤⣴⡿⠃⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡿⢛⣛⣇⣤⡴⠾⣻⣯⣿⣾⠾⢛⣛⣿⠿
⣿⠀⢾⣿⣿⣿⣿⣿⡿⠿⠹⠿⠿⢟⣛⣋⣿⣷⣬⣭⣭⣤⣴⣶⣿⣿⣛⣛⣟⣯⣿⣿⣿⣿⣿⡇⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⢟⠙⣿⣿⣿⡿⠟⢈⣹⣭⠵⢾⢿⣿⣿⠃⠊
⣿⡆⢀⣉⣩⣅⣥⣤⡶⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⢿⡟⣿⣿⣿⣿⣿⡿⠿⣟⣋⣭⣥⣤⣴⠶⠂⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣡⣤⠤⢿⣿⠟⣃⡖⠐⢋⣤⣴⣶⡿⠉
⠿⠿⠿⠛⠛⠋⠛⠉⢵⣋⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠈⣀⣶⣾⣧⣤⣷⢶⣞⣛⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⠀⣿⣶⣾⡏⣾⣿⣧⣅⣠⣾⣿⣿⡿⠿⢟⣉⡥⠔⣻
⠐⢿⣟⠁⠀⠀⠀⠀⠘⣁⡀⣉⣉⣥⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠛⢛⣛⣿⣿⠏⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⣠⠶⣿⣿⠹⠗⢼⣛⢉⣥⣶⠛⠉⣘⣀⣠⡤
⠁⠈⣀⣉⣬⣤⣴⣶⢾⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣟⣸⣿⡇⢸⣿⡟⠛⢠⣿⣿⠿⠛⠉⠐⡿⣛⣤⡴⢞⡋⠉⢙⡡
⣶⣿⣿⣻⣽⣿⣷⣶⣿⣿⣿⣿⣿⠿⠻⠟⢟⣽⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠟⢹⣿⡏⣀⣤⡤⢾⣻⣽⠃⠇⠀⠀⠀⠁⢀
⢽⣿⣿⣿⣿⡿⠿⠟⢛⣋⣉⣭⣤⣶⣾⣿⣿⣿⣽⣿⣿⣿⣿⡾⠟⠛⠙⠉⠀⠀⣠⢤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⣠⠼⠛⠃⠉⠀⠉⣀⡄⠂⠀⠀⢀⣀⠴⣞⠋
⣸⣿⣿⣤⣴⣶⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣤⠶⠖⠛⠋⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠊⠉⠀⢇⣤⠄⢀⡭⢴⣧⣤⣾
⣭⣽⣶⣾⣿⣿⣿⡏⠙⣿⠛⠿⠛⣛⣋⣽⣟⡻⠾⣿⡿⠏⠠⠮⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⡏⠀⠀⣀⢄⣈⡿⠼⣀⡥⢾⢋⣿⣿⣿
⣿⠿⠛⠛⠛⢉⣁⣣⣾⣿⣶⠾⠟⡛⠃⠀⠀⠀⠀⠁⠀⣀⣀⣀⢀⣠⠤⠒⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡁⢋⣉⣭⣒⣻⣿⣿⣿⣿⣿⣿⣿
⣤⣴⢶⣾⡿⠿⠛⠉⠀⠀⡟⠀⠀⠀⠀⠀⣤⣤⡤⠀⠸⣿⣿⣿⣿⣄⠀⠀⠀⢀⣀⣄⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠨⠀⡀⠤⠒⢉⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⣿⢶⣷⠿⢷⠶⠰⠶⢶⣖⣠⡤⠶⠚⠛⠉⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣶⡋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣙⡳⠻⠛⢛⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠟⠙⠿⠛⠿⣿⣿⣿⣿⣬⣼⣯⣿⣿⣿⣿⣿⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣭⣭⣩⣽⣭⣭⣭⣭⣭⣟⣿⣯⣫⣛⢛⣻⠿⢿⠿⠿⢽⣿⣿⡟⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣛⣿⣿⣿⣭
⣿⣿⣿⣿⣿⣿⣯⣿⣿⡟⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡄⠀⢀⡀⠀⠀⠀⠈⠙⢿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⢿⡏⣿⣿⡇⣿⣯⡷⣿⣿⣿⣿⣷⣿⡟⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⣾⣿⣾⣷⣾⣿⣿⣿⣷⣷⣿⣿⣗⣿⣏⣾⣿⣿⣿⣇⣽⣿⣿⣴⣶⣬⣥⣭⣭⣭⣭⣭⣭⣥⣤⣜⣟⣛⣻⣿⠛⠹⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⠛⠿⠿⠿⠿⢻⣿⣿⢿⣿⣿⠟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⡟⣭⣭⢭⣽⡹⣿⣿⣽⣿⡟⣿⡟⣾⣿⣾⣿⡿⣿⡟⣿⣟⣻⣿⣻⣷⣿⣏⣿⠂⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣟⣛⣿⣿⣃⣇
⣆⣿⣿⣿⣿⡇⣿⢹⣇⣿⣿⣿⣇⣿⣿⣧⣿⣷⣿⡆⣿⣟⣻⣿⣿⣷⣾⣿⣿⣦⣴⣶⣷⣶⣶⣶⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢑⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡏⣿⡏⣿⠿⣿⢽⢿⠿⠇⠿⣿⢟⣿⣿⣿⣸⣻⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠿⠿⠿⠛⠛⠿⠿⢟⣟⣛⣛⣛⣛⣛
⣿⣿⣷⣿⣿⣷⣺⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⣿⣿⣍⣻⠿⣿⣿⣿⣿⣿⣿⣿⠏⠡⣀⣤⣤⣄⠀⠀⠀⠀⠀⣤⠿⡿⢿⣿⣿⣷⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣋⣝⣹⣯⣈⣉⣉⣉⣻⣽⣿⣿⣿⣯⣿⣴⣿⣿⣿⣷⣿⡷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠙⠛⠛⠟⠛⠁⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⢰⡏⠸⠿⣾⠻⠿⣿⡟⠻⣻⣯⣿⣽⣧⣽⣿⣶⣶⣿⣾⣾
⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣀⡀⠀⣼⣷⢾⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣙⣏⣙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣿⣷⣶⣿⣿⣿⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠿⠷⠡⠀⠟⠛⠛⣛⣋⣩⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⢿⣿⡼⢝⣻⣛⣛⣋⣠⣿⣝⣛⣧⣬⣽⣶⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣴⣶⣶⣾⣿⣿⣿⢻⣿⣿⣿⠿⠿⢛⣛⣭⣽⣿⠷⡒
⠶⠾⠷⠿⣟⣻⣿⣿⣿⣿⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⣿⣿⣿⣿⣿⣃⣀⡉⠉⣉⣉⣠⣤⣤⣼⣿⣿⣿⣿⠿⡟⢻⣾⣿⣿⣭⠀⣻⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡶⢋⣭⣥⣼⢿⠗⣶⣷
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣶⣶⣿⠿⠷⢾⣿⣿⣿⣿⣿⣭⣯⣯⣷⣶⣿⣻⣿⡿⠉⠋⠁⣿⣿⣀⠀⢸⣿⡇⣸⣿⢀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢃⣀⣀⣠⣿⣿⢿⡿⣿
⠿⠿⠿⠛⠛⠛⠛⠋⠉⣉⣉⣉⣀⣤⠤⢴⣷⣶⣿⣿⣿⣿⣭⣽⣾⣷⣾⠗⠸⠀⣶⠀⠀⠀⠀⠉⠻⢿⣿⢛⣋⣿⣬⠥⠀⠀⠀⢠⣿⡿⠛⠀⣾⣿⠿⠿⠟⢸⣿⡟⢹⣿⣿⣿⠿⡿⣿⣿⣽⣷⣿⣿⣿⣫⣥⣴⣿⣿
⣀⡠⠤⠤⠖⣒⠒⣿⣭⣭⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⠛⠉⢁⣀⣁⣀⣋⣀⣠⣤⡤⠀⠀⠈⠿⣿⣿⠶⠀⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡷⠗⣛⣉⣨⡬⠿⣛⣿⣭⣿⡟⠛⣻⣿⣿
⡇⠀⢰⣾⣿⣿⣮⣯⡭⣎⠻⠿⠿⠿⠟⢛⣿⣯⣉⣭⣍⣡⣤⣤⣿⠿⡟⢛⠛⠛⠛⣿⣿⣿⣏⠀⣀⣀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠛⣿⣿⣷⡿⠂⢛⣟⣫⡷⠶⣞⣿⠏⠰⠁
⣿⡀⠀⠉⣈⣈⣁⣩⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⠋⠾⣿⣿⣿⣷⣿⠿⠏⢛⣋⣀⣿⠿⠟⠁⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣅⣵⢾⡶⠛⣻⠀⠘⣀⣢⣷⣶⡒⠉
⣽⠿⠿⠟⠛⠛⠛⠉⣤⠛⣹⣿⣿⣿⣿⣿⣿⠟⠟⠛⠁⢠⣤⣿⣀⣤⣤⠤⠶⠖⢶⡞⣿⣿⣽⡇⣝⠆⠀⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢠⣿⣶⣾⡏⣾⣷⣶⡅⣤⣿⣿⣶⣿⠿⠚⢉⣥⢴⡶
⠰⠶⠛⠂⠀⠀⠀⠀⠙⠀⣿⣇⣉⣥⣥⣥⣤⣠⣤⣶⣾⣿⣿⣯⣭⣴⣾⣺⣯⠀⢸⠂⠘⠛⢛⣉⠎⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⠀⢸⣿⣇⣠⠄⣿⣿⠹⢷⠿⡛⣫⣤⡶⠛⠉⡃⣀⣈⠭
⠆⠀⠀⣀⣀⣤⣤⣤⣾⣿⣿⣿⣿⣟⣿⣿⡿⣿⣧⣿⣿⣿⣿⠿⠟⢛⣋⣁⣠⣴⡶⠿⠟⡛⠛⠈⠀⠀⠀⠀⠀⠀⣰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢠⣿⣿⠿⠟⠉⢩⠟⣋⣡⡴⠞⠛⠋⠇⣀
⣶⣾⡿⢻⣿⣭⣭⣴⣴⣿⣿⢿⣿⣿⣿⣿⣇⣸⣉⣁⣩⣥⣶⣿⣿⢟⣿⣭⣁⣀⣀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠀⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⣷⠒⢹⣿⡟⢀⣤⡤⢾⣻⡍⠻⠁⠀⠀⠀⠁⢀
⣿⣿⣿⣾⣿⣿⠿⠟⠛⠙⣁⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠈⠓⠉⠉⣁⣤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⢁⣀⡸⠛⠃⠉⠉⠀⣉⠁⠀⠀⠀⠀⠠⠴⡖⠋
⢻⣿⣧⣥⣤⣤⠶⠿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⣠⣤⠴⠶⠚⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡤⠖⠂⠁⠸⢀⣠⠤⢂⡍⣖⣀⣴⣶
⣿⣭⣽⣿⣿⣿⣿⡚⠻⡇⢿⣿⠿⣿⣿⣿⣟⣫⠴⠶⠒⠛⠀⡇⠀⠀⠀⠀⢀⡀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⢺⠋⠀⠀⠀⠀⢢⠶⢄⣀⣥⡞⣻⣷⣿⣿
⣿⡿⠟⠹⠋⠁⢉⣠⣶⣷⣤⠶⠾⢻⠿⠋⠁⠀⠀⠀⠀⠀⢀⡀⢀⣀⡤⠖⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢚⣉⡥⢒⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣴⣶⡿⠿⠛⠉⠉⢰⡇⠀⠀⠀⠀⢀⣾⣿⣿⣶⣶⠚⠋⠉⡬⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⢉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⡿⡾⣿⠿⢷⠶⠰⠶⠶⢖⣀⣤⠴⠁⠀⠙⣿⣿⣿⣿⣿⣦⣄⣡⣤⠤⠖⠚⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠒⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⢛⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⢷⢾⣭⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿⣴⣭⣭⣉⣉⣩⣏⣩⣭⣽⣉⣿⢻⣿⣻⠛⠻⠿⠿⢿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣳⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣿⣿⣿⣿⡟⣿⣿⣟⣿⣿⣟⣯⣿⣯⣿⣿⣿⣯⣯⣿⣿⣿⣿⣛⣿⣻⣿⣿⣻⣿⣿⣷⣶⣿⣿⣶⣶⣾⣶⣆⡀⡀⡀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⢿⢿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣭⣶⣾⣿⣿
⣿⣿⣿⣿⣿⡷⣿⢿⣿⣧⣿⣯⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣾⣿⣽⣿⣿⣿⣿
⣭⣭⣿⣿⣭⣿⣿⣿⣿⣿⣿⣯⣇⣿⣏⣾⣿⣿⣿⣏⣭⣿⣿⣤⣶⣭⣭⣭⣭⣭⣭⣭⣽⣯⣥⣄⣛⣻⢿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠿⠿⣿⣿⠹⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣷⣿⣿⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡄⣀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶
⡏⣭⣭⢭⣽⡹⣿⣿⣽⣿⡟⣿⡟⣶⣿⣾⣿⡿⣿⡟⣿⣟⣻⣿⣻⣷⣿⣏⣿⡇⠿⣿⣿⢿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣶⡤⠴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣋⣻
⣄⣿⣻⣿⣿⡇⣿⢻⣇⣿⣿⣿⣇⣿⣿⣧⣿⣯⣿⡆⣿⣟⣻⣿⣿⣷⣾⣿⣿⣦⣤⣶⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡏⣿⡿⣿⡿⣿⢽⢿⠿⠏⢿⢿⢏⣿⣿⣿⣸⣻⣻⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣟⣛⣿⢛⣛
⣿⣿⣷⣿⣿⣷⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠅⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⣾⢾⠿⢿⣿⣿⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿
⣿⣿⣿⣿⣿⣿⣙⣿⣉⣋⡛⣋⣛⣫⣿⣿⣿⣿⣿⣯⣽⣿⣾⣷⣾⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠛⠛⠋⠁⠀⠀⠀⣼⣿⣷⠆⠀⠀⠀⠀⣾⣟⢿⡇⠓⣿⣾⠿⠿⣿⡿⠿⣿⣿⣹⣽⣯⣿⣿⣧⣭⣿⣾⣿
⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣄⡀⠀⠀⣿⣯⣾⣷⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢙⣛⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣻⣿⣛⣿⣿⣦⢤⣤⣤⣶⣶⣶⣤⣀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠙⢿⡿⠿⠃⠀⠹⠛⠟⢛⣛⣋⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠟⣿⣯⠟⠻⣿⢿⣟⣁⣽⣏⣛⣻⣬⣭⣭⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣤⣤⣶⣶⣶⣾⣾⣿⠿⣿⣿⣿⣿⠿⠟⣛⣫⣽⣿⡿⠶
⣴⢶⢶⠾⢿⣛⣿⣿⣿⣿⢟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣇⠀⠉⠉⠉⢉⣉⣡⣼⣿⣿⣿⣿⣿⠿⡏⢹⣶⣶⣶⣬⣿⣻⣭⣭⣽⣻⣿⣿⣿⣿⣿⣿⡖⠚⣩⣭⣽⣿⣷⢺⣞
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⣶⣿⣿⣷⣾⣿⡿⣿⣟⣯⣭⣭⣿⣿⣶⣾⣿⡟⠙⠛⠉⠁⣿⣿⣀⠀⢸⣿⡇⣸⣿⢀⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣈⣁⣸⣷⣿⣯⣿
⡿⠿⠿⠟⠛⠛⠛⠛⠛⢉⣉⣉⣉⣁⣤⢤⣶⣶⣾⣿⣿⣿⣯⣽⣿⣷⣶⣶⣤⠌⣿⣥⣿⣿⣿⣿⣿⠿⠿⠟⢛⣹⣥⠀⠀⠀⠀⢠⣿⡿⠛⠀⣼⣿⠿⠿⠟⢺⣿⡟⢸⣿⣿⣿⡿⠿⢿⣿⣿⣵⣿⠿⣿⣟⣡⣬⢿⣾
⣀⣀⡤⠤⠴⢖⣒⣚⣯⣭⣭⣵⣶⣶⣿⣿⣿⡯⣿⣿⣿⣿⣿⣛⠛⠛⠛⣛⣛⣓⣻⣈⣩⣭⣥⣄⡴⠒⠛⣉⣽⡗⠀⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢹⣿⡿⠷⢖⢊⣉⣉⡿⢿⣻⣯⣏⣿⠿⢿⣿⣿
⣿⠀⣴⣾⣿⣿⡿⣿⣿⣿⠛⠻⠿⠿⠿⠛⣿⣧⣙⣉⣉⣉⣤⣥⣶⣿⡿⠟⣻⣛⣿⣿⣿⣿⣿⡇⡇⠀⠈⠘⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠶⣿⣿⣿⣿⠖⠸⣟⣛⣭⡷⣶⢟⡟⠹⠛
⣿⡆⠀⠉⢉⣋⣁⣩⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢟⣛⣁⣡⣤⣤⠀⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣹⣷⣶⠾⢭⡅⠐⢄⣈⣽⣴⠶⠖
⣯⡿⠿⠿⠟⠛⠛⠋⢣⢟⣻⣿⣿⣿⣿⣿⣿⡟⣿⠋⠁⠩⣥⣿⣏⣽⣿⣭⠴⣶⢶⡶⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⠀⣷⣶⣾⡏⣿⣷⣦⡍⢡⣾⣽⣶⣶⣿⠿⢛⣛⠵⠶
⠀⢲⡞⠀⠐⠀⠀⠀⠘⠀⠉⠉⣉⣩⣭⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⢿⡟⠿⠿⢛⣛⣿⡏⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣏⣠⡤⣿⣿⠻⢿⡿⠟⢛⣩⡴⠖⠋⠏⠀⣈⡹
⠆⠈⠘⢀⣀⣠⣤⣤⣴⣿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢿⣛⣛⣩⣭⣶⢷⣾⣟⣻⣃⡟⠀⠀⠀⠀⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢠⣿⣿⠿⠖⠋⢙⡜⣏⣡⣤⠶⠛⠋⠏⢀
⣶⣶⣿⢟⣿⣿⣭⣶⣶⣶⣿⣿⣿⣿⡿⠿⠋⣛⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠀⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⣷⠖⢺⣿⡟⢈⣀⣠⡶⢟⡛⢹⠃⠉⠀⠀⠊⠁
⣾⣿⣿⣼⣿⣿⣿⠿⠛⠛⣋⣉⣤⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⢀⣘⠟⠃⠋⠙⠂⢉⠨⠁⠀⠀⠀⢀⣠⡶⠛
⢻⣿⣿⣤⣤⣤⡶⠾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠏⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⣀⡤⠒⠈⢸⠀⣀⠀⠐⡋⠁⢀⣡⣴
⣿⣯⣽⣿⣿⣿⣿⡿⠛⣿⠛⠿⠿⠟⣛⣫⡽⣿⡤⠾⣿⣿⣿⠋⠀⠀⠀⠀⠀⡀⢀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒⠏⠀⠀⢀⠀⠂⣈⠁⢀⣡⠴⢞⣹⣿⣿
⣿⣿⠿⠛⠛⠛⢁⣂⣶⣿⣶⡶⠾⡟⠋⠁⠉⠀⠀⠀⠛⠁⠀⠀⠀⢀⣤⠴⠚⠻⠉⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢛⡣⠔⣾⣿⣷⣶⣿⣿⣿⣿
⣡⣤⢤⣶⣾⠿⠟⠋⠉⠁⣿⠀⠀⠀⠀⠀⣠⣄⣀⡄⡀⠀⣾⣿⣿⣷⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⠈⠀⢀⡠⠄⠉⣉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⢾⣿⠿⢷⠶⠰⠶⠶⠖⣀⣤⠴⠶⠞⠉⠉⠁⠀⠠⠀⠙⣿⣿⣿⣿⣶⣒⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠖⠂⣀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣿⣿⣿⣥⣤⣬⣎⣮⣉⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡟⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠓⠒⠈⠙⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣶⣧⣴⣶⣿⣤⣿⣿⣯⣽⣉⣙⣛⡻⢿⣿⣿⣛⣿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣭⣽⣯⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢿⣿⣷
⣿⠿⣿⡿⠿⠿⠿⡿⢿⣧⣿⣯⡗⣿⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣯⣟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣲⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣿⣿⣻⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡯⣿⢿⣿⣿⣷⣷⣿⣶⣶⣶⣿⣿⣶⣿⣶⣶⣶⣶⣶⣷⣮⣾⣶⣶⣬⣭⣿⣿⡿⣽⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠙⠿⠻⠿⠿⠿⣿⢿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣽⣵⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣤⣭⢭⣽⡹⣿⣿⡽⣿⡟⣷⡟⣶⣾⡾⣷⡿⣿⡟⣿⣟⣻⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⠀⠻⠿⠿⢿⣿⣿⣿⣿⢿⣷⣬⣿⣿⣿⣧⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⣿⣿⣻
⣿⣿⣿⣿⣿⣧⣿⣿⣧⣿⣿⣿⡷⣿⣾⣷⣿⣷⣿⡦⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣷⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢹⡟⣿⡯⣿⣿⣿⢽⣿⡿⠇⢿⣿⣇⣿⣿⣿⣸⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣛
⣿⣿⣷⣿⣿⣷⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⣿⣿⡿⠿⢿⣿⣿⣿⣛⣿⣟⣿⣭⣭⡝⠛⣿⠻⠿⠛⢛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⡿⢿⣿⣿⣷⣖⣾⣿⣿⣿⣿⣿⣿⣿⣯
⢿⣿⣿⣿⣿⣿⣿⣿⣭⣦⣼⣷⣤⣤⣬⣭⣭⣷⣶⣿⣿⣷⣾⣷⣿⣿⣿⡷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡄⠀⠀⠀⠀⢸⣿⠸⠿⣿⠿⠿⣿⡟⠛⣻⣯⣿⣽⣯⣿⣽⣧
⣿⢵⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠿⣿⡀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠄⠰⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠇⣿⣽⣿⣿⣿⣿⣿⣿⡿⢿⣿⣛⣛⣿⣿⣽⣿⣽⣿⣭⣿⣷⣦⣴⣶⣶⣿⣷⣶⣶⣶⣤⡀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣶⣴⣿⣿⡽⠟⠏⠁⠟⠛⠛⣛⣛⣉⣽⣶⣶⣿⣿⣿
⠃⠐⠿⠿⢿⢛⣛⣙⣿⣟⣩⣭⣭⣽⣥⣴⣿⣯⣭⣷⣶⣶⣶⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣷⣾⣿⢻⣿⣿⣿⣿⠿⠿⠟⣻
⠿⠿⣛⣛⣛⣛⣛⣫⣭⣽⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢟⣻⣿⣿⣿⣿⣀⣈⣁⣈⣉⣠⣤⡤⣿⣿⢿⡇⣷⣶⣿⣿⣿⠉⣩⣭⣭⣤⣠⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⢚⣫⣭⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⢿⣟⣛⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣭⣭⣴⣶⣾⣿⣷⣿⣿⡇⣿⣿⣈⠉⢸⣿⡇⢸⣿⠀⣿⣿⢸⣿⣷⠋⣿⢹⣿⣿⣿⣿⣿⣿⡿⠇⠈⢉⣁⣿
⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⢉⣉⣀⣤⣤⠤⠤⣶⣶⣺⣿⣿⣿⣿⣯⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠟⠛⣛⣡⣧⣭⢽⣿⡟⠛⠀⣼⣿⠿⠿⠟⢸⣿⡏⢸⣿⡇⢷⡿⢻⣿⣿⣿⡿⣿⣿⣿⣽⣿⠿⢿⣟
⣀⣤⣤⣤⡤⠖⠒⢚⣫⣭⣭⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣽⣿⣿⣿⣟⡁⠀⠀⠹⣿⣿⡉⢽⣶⣶⡫⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡇⠘⡇⠀⠻⠶⠾⢋⣙⣻⡿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⡿⠿⠿⠟⠻⢛⣛⣋⣹⣿⣮⣭⣭⣥⣽⣿⣿⣧⣾⣿⣿⣋⣀⣡⣿⣷⠀⠀⠀⢉⣿⣿⣏⠉⠁⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⠀⠀⠖⣿⣿⣿⣿⠓⢿⠛⣻⣭⣬⣾
⠿⠿⢛⣿⣿⣀⣀⣤⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣯⣿⡿⠿⠿⠿⢟⣁⣤⣾⣿⠟⠙⣿⣥⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣉⣽⣷⣶⡾⣭⠉⠠⠀⢙
⣾⠿⠿⠿⠛⢛⡛⠋⠉⠉⠉⠘⡞⢽⣿⣿⣿⣿⣿⣿⡿⠻⠋⠉⢁⣰⣾⣧⣭⣵⠶⣶⣾⡿⣿⣻⣿⣷⣾⣯⣵⣄⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢀⣷⣶⣶⡆⣶⣶⣦⡯⠿⠇⠸⢋⣑⣾⣿⣤⣶⣿⠿
⠀⠀⠀⠀⠉⠋⠷⠓⠀⠀⠀⠀⣁⣀⣉⣉⣭⣿⣳⣶⣦⣶⣶⣿⣿⣯⣭⣽⣷⣾⣿⣿⡿⠻⠟⠘⠛⢋⣋⣍⣽⠃⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠀⣿⣿⠉⣡⣴⣿⣾⣿⡿⠿⣛⣫⣽⠶⠲
⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣛⣋⣍⣩⣤⣶⠿⠟⢛⣯⠍⠀⠃⠀⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣟⣸⣿⡇⢸⣿⡟⠛⠀⣿⡿⠿⠿⣛⣭⠴⠞⠛⣶⠿⠏⣀⣤⡼
⣶⣶⢟⣻⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⠿⠏⣿⣿⣿⣼⣿⣧⣶⣿⣿⢿⠋⢉⣥⣴⢶⠿⠮⠈⠃⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢸⣿⡇⠐⢒⠋⠒⣀⣀⣠⡿⣞⡛⡏⠑⠀
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⣋⣉⣩⣭⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠈⠁⢀⣤⣴⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠘⠛⠃⢀⣨⠔⠟⠋⠿⠒⠒⠙⠀⠁⠀⠀
⠿⢛⣋⣩⣿⣿⣶⣶⣶⣞⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢀⣦⠴⠖⠚⠋⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠤⠐⠂⡇⠀⢀⡀⠴⢒
⣻⣿⣽⣿⣶⣶⣿⣿⣿⣿⡿⠉⢻⡉⠿⠟⣛⣻⣽⣟⣿⣿⣿⡟⠋⠁⢠⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡖⠋⠀⠀⠀⠀⢐⣛⠁⢔⣫⡭
⣿⣿⣿⣿⠿⠛⠋⢋⣉⣩⣬⣾⣿⣷⠾⢛⠛⠅⠀⠀⠙⠋⠀⢀⠀⠀⣀⢀⣠⠤⠖⠚⠿⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠽⠿⢒⣩⢥⣾⣿⣿⣴
⣭⣭⣤⣶⣶⡾⣿⡿⠛⠋⠉⠀⠀⠾⠃⠀⠀⠀⠀⣀⢀⠀⢾⣿⣿⣿⣍⣼⠀⠀⠀⠀⠀⣀⣠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⢈⡅⠒⠋⣻⣵⣾⣿⣿⣿⣿
⠻⠿⠿⣿⣿⣿⠶⠰⠶⠶⠶⢀⣀⣀⣤⠴⠖⠚⠋⠁⠠⠀⠘⢿⣿⣿⣿⣷⣦⡴⠖⠚⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠉⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣿⣿⣶⣀⣬⣽⣛⣙⣻⠿⢿⡿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⣿⣿⣿⣿⡻⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣷⣷⣶⣦⣥⣤⣼⣬⣥⣮⣭⣬⣟⣿⣯⣛⣛⣛⣻⠿⠿⠿⠿⢻⣯⣿⣿⣿⣿⠿⠟⠛⠛⠋⠛⠛⠛⠛⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⢿⡿⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠻⢿⣿⣿⢿⣿⡿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⣿⣯⡗⣿⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣟⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣾⣷⣦⣀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⣽⣟⣿⣿⣿⣾⣿⣿
⣶⣶⣿⣿⣶⣾⣾⣷⣾⣿⣿⣿⣗⣿⣯⣶⣿⣿⣿⣷⣷⣶⣶⣶⣾⣿⣷⣶⣶⣿⣭⣤⣬⣭⣽⣭⣽⣷⣴⣭⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿
⣾⣴⣾⣿⣿⣿⣿⣿⣿⣿⣽⣭⣥⣭⣵⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣬⣭⢭⣽⡹⣿⣿⡽⣿⡏⣷⡟⣶⣾⡾⣷⡿⣿⡟⣿⣟⣻⣿⣻⣷⣿⣏⣿⣿⣿⣿⣿⠈⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⠁⡙⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⡟⢛
⣿⣿⣿⣿⣿⣇⣿⣽⣧⣿⣿⣿⡧⣿⣼⣧⣿⣿⣷⡦⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣦⣶⣶⣿⣶⣶⣶⣿⣿⡿⢻⣿⣧⣉⣵⣿⣿⣿⣿⣷⡀⣠⡤⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢹⣿⣿⡯⣿⣿⣿⢽⣿⡿⠇⣿⣿⣇⣿⣿⣿⣸⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠛
⣿⣿⣷⣿⣿⣷⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣼⣿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⠏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣾⣷⣾⣿⣷⣾⣿⣿⣏
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣧⣥⣉⣩⣽⣭⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣾⣿⣿⣿⣿⠿⠻⠟⠛⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⣿⣿⠻⢻⣻⣏⣿⣿⣟⣻⣿⣤
⣿⣯⣭⣿⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⡾⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⣀⣆⣦⡀⠀⠀⠀⢰⡿⢿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⢰⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢽⣿⣻⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣟⣿⣿⣛⣻⣿⣿⣿⣿⣷⣾⣿⣿⡇⢀⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⣀⠀⣸⣿⠸⠇⠟⠿⠛⢛⣛⣉⣯⣽⣿⣶⣾⣿
⠃⠠⠾⠿⡿⢿⠛⣹⣿⣟⣙⣋⣟⣛⣡⣴⣿⣭⣭⣷⣷⣶⣾⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⡆⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⢛⣛
⠿⠶⠶⠶⢟⣟⣛⣛⣻⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣤⣼⠉⣉⣁⣠⡤⣿⣿⢿⡇⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣷⣿⣿⣿⣧⠶⣚⣋⣩⣽
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣻⡿⣿⣿⣿⣶⣶⣶⣶⣾⡿⣿⣿⣿⣿⣿⠉⠁⣿⣰⣼⡏⣿⡇⣿⣿⣸⡛⢸⣿⡟⢻⣿⠉⣿⣿⢸⣿⡷⠀⠠⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⢉⣁⣿
⣿⠿⠿⠿⠿⠛⠛⠉⠉⠉⠉⢉⣁⣤⣤⣤⠤⠴⣶⢾⣷⣿⣿⣿⣭⣭⣿⣶⣶⣶⣶⡦⠆⢺⣯⡿⡿⣿⣿⡿⠀⠀⢻⣏⣩⣇⣠⢴⣿⡿⠛⠀⣼⣿⠿⠿⠟⢸⣿⡏⢸⣿⡇⠀⠀⣈⣿⣿⣿⡿⣿⣿⣿⣭⣿⣿⠿⠛
⣀⣀⣀⣠⡤⠴⡒⢒⣚⣭⣩⣽⣿⣶⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⡟⠛⠉⣛⣛⣁⣽⣅⣠⣤⣿⣿⡇⠀⠀⢸⣿⠗⠂⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠹⡧⠒⠗⠈⣛⣩⡽⢿⣟⣻⢽⣟
⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠻⣛⣛⣻⣿⣦⣭⣭⣤⣤⣤⣾⡿⣿⠛⣛⣛⣋⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⠀⠀⠒⣿⣿⣿⡿⠀⢿⠟⣻⣭⣭⠼
⣿⠿⠛⣿⣷⣀⣀⣁⣭⣤⣤⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⢷⣿⣿⣿⣿⠿⠿⠿⠟⣻⣿⣿⣷⣾⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢉⣭⣶⣴⡾⣯⠉⠥⠈⢛
⣶⣿⠿⠷⠿⠟⡛⠛⠋⡙⠋⠹⡾⡽⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⢀⣤⣼⣧⣭⣽⡷⢶⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢠⣿⣶⣶⡆⣶⣶⣦⡄⢹⠀⠨⢛⣱⣾⣧⣤⣶⣿⢿
⠀⠀⠀⢀⢘⠿⠿⡀⠀⠀⠀⠀⣁⣀⣁⣉⣭⣭⣿⣦⣔⣤⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠿⡇⠛⠛⢋⣀⣠⣤⢠⡿⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⡀⠀⣿⣿⠉⠁⢰⣶⣶⣾⡿⠿⢛⣉⣽⠴⠢
⠀⠀⠀⠀⠀⢀⣁⣤⣤⣶⣶⢶⣿⣟⣻⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡿⠿⠿⠋⣋⣏⣡⣤⣶⡿⢾⣛⣻⠋⠹⠷⠘⢰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢀⣿⡿⠿⠀⣈⣩⡴⠗⠚⣾⠿⠃⣀⣠⡶
⣶⣶⠾⢻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣷⣿⣿⣧⣶⣾⣿⣿⠛⣩⣭⣶⣞⣯⡿⠿⠋⣠⠃⠀⠀⠘⠿⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢸⣿⡇⠀⠀⠉⠀⢀⢁⣠⡷⡖⠻⡏⠑⠀
⣷⣿⣿⣿⣿⣿⠿⣿⣿⠿⠟⣛⣋⣉⣭⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⡧⣿⡇⠀⠁⠘⠛⠋⢉⣠⣤⣶⠞⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠘⠛⠃⠀⢠⠴⠞⠛⠟⠒⠊⠋⠀⠁⠀⠀
⠿⢟⣛⣉⣿⣿⣶⣶⣶⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢈⣦⠴⠶⠚⠛⠀⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⢊⠁⠀⠀⡀⠴⢒
⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠉⢿⠙⠿⠿⣛⣛⣭⣿⣿⡿⠿⠏⠈⠃⢨⠀⠀⠀⠀⠀⣀⣀⣀⣠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠨⠐⠊⠁⠐⣋⣭
⣿⣿⣿⣿⡿⠟⠛⠋⣉⣉⣥⣾⣿⣶⠶⠟⡛⠁⠀⠀⠉⠀⢀⣤⣤⣀⣀⢀⣀⡤⠖⠺⠿⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠶⢆⣉⢭⣶⣯⣭⣤
⣩⣭⣤⣴⣶⣲⣿⡿⠛⠋⠉⠀⠀⠿⠀⠀⠀⠀⠀⣀⠔⠀⢻⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡀⠐⠚⣫⣴⣾⣿⣿⣿⣿
⠛⠿⠿⣿⣿⢷⠷⠰⠶⠶⠶⠀⢀⣀⣤⠤⠶⠚⠛⠉⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣶⡚⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⣁⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣿⣖⣈⣉⣿⡛⣟⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⣿⣛⠿⣿⣿⣿⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣷⣷⣷⣦⣥⣭⣭⣭⣤⣭⣭⣭⣥⣟⣿⣯⣽⣛⣛⣛⡿⠿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣻⣿⣿⣿⠋⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣯⣽⣿⣿⣿⣿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣯⡗⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣦⡥⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣶⣿⣷⣶⣶⣶⣷⣾⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣶⣯⣭⣤⣤⣭⣽⣭⣿⣷⣶⣭⣿⣿⣿⣿⣿⣿⡟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⢿
⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣭⣵⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡍⣭⣭⢭⣿⡹⣿⣿⣽⣿⡟⣿⡟⣶⣿⡾⣿⡿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣿⠘⠿⢿⡿⣿⣿⣄⠠⣿⣿⣿⣿⣇⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣾⣿⣇⣿⣽⣇⣿⣿⣿⣧⣿⣽⣧⣿⣷⣶⣆⣿⣟⣻⣿⣿⣷⣾⣿⣿⣾⣿⣿⣶⣴⣶⣿⣶⣶⣾⣷⣾⣿⣿⣿⣿⣷⣤⣿⠁⢽⣧⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⣿⡯⣿⣿⣿⢽⣿⡿⢇⣿⣿⣏⣿⣿⣿⣾⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣿⡟⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠻⠿⠿⣻⣛⣛
⣿⣿⣷⣿⣿⣷⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣻⣯⣿⣿⣿⣿⣿⣿⡟⠉⠛⠛⠋⠀⠀⠀⠀⠀⢠⣾⣿⣿⢿⣶⣿⡿⢿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣍⣉⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠑⠈⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣼⡟⣻⣿⣻⡇⠩⠟⣿⠿⠿⣿⡟⠻⣛⣿⣽⣽⣯⣿⣿⣷⣷
⣫⣭⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⡀⠀⢀⣰⣿⣧⣧⣾⣿⣶⣶⣾⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿
⢠⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣻⣿⣛⣻⣿⣿⣿⣿⣷⣦⣤⣤⣤⣀⣀⣀⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣼⢿⠿⠙⠋⠉⠟⠻⠛⢛⣛⣉⣭⣷⣶⣿⣿⣿⣿
⠤⣽⣿⣿⣿⠟⢻⣿⣻⣙⣿⣿⣛⣋⣴⣿⣽⣯⣷⣯⣿⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣷⣴⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠻⣦⣥⣤⣤⣴⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⣻⣿
⠶⠶⠶⠿⢿⣿⣛⣛⣻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣀⣈⡉⢉⣉⣉⡼⠿⠛⣿⣿⢿⡆⢰⣶⣶⣶⣭⠻⣿⣭⣭⣽⡻⣿⣿⣿⣿⣿⣾⣿⣿⣿⡖⣺⣯⣭⣽⣧
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣭⣭⣽⣶⣶⡿⠀⠀⠀⣿⣿⣀⡀⢸⣿⡇⣸⣿⢠⣿⣿⢾⣿⣷⣻⣟⣿⣿⣿⣿⣿⣿⣿⠟⠀⣉⣉⣼⣿
⣿⡿⠿⠿⠿⠟⠋⠉⠉⠛⢋⣉⣀⣭⣥⡤⠤⢤⢶⣶⣿⣿⣿⣿⣯⣭⣿⣿⣶⣿⣿⡶⢸⣿⣿⣿⣿⣿⡿⠿⠿⠟⢛⠁⠀⠀⠀⢰⣿⡿⠛⠁⣾⣿⠿⠿⠟⢸⣿⡿⢻⣿⡇⣛⣸⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⢿⣛⣛
⣀⣀⣀⣠⠤⢴⠒⣒⣺⣻⣭⣭⣵⣶⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⠟⠛⣻⣛⣉⣨⣥⣈⣥⣤⣤⢰⠖⠚⠉⠉⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⣸⣿⣯⣿⣿⡿⠶⠛⢋⣉⣩⡶⣿⣻⣯⣯⣿⠿
⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢛⣛⣿⣧⣭⣭⣭⣤⣤⣴⣿⢿⡟⣛⣛⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⣽⣿⠶⣶⣿⣿⣿⣿⠆⠚⣿⢛⣭⣷⣷⣞
⣿⠟⣿⣿⡀⣈⣛⣫⣭⣬⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⣿⣿⣿⣿⡿⠿⠿⣛⡁⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡿⠀⠙⣙⣋⣭⣷⣶⢾⣭⠍⠲⠁⢛⣿
⣶⣾⠿⠿⠿⠟⠛⠛⠛⡛⠉⣾⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⣵⣼⣿⣭⣭⡿⠿⢶⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢠⣷⣶⣶⡶⣶⣿⣿⡯⠇⠨⠏⣁⣾⣿⣖⣶⣿⠿⠿
⠀⠀⠀⢒⡻⡿⣷⠧⠳⠂⠀⢛⣀⢁⣉⣩⢭⣯⣯⣄⣴⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⠛⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢹⣿⠀⢸⣿⣏⡀⠀⣿⣿⠩⢥⣾⣿⣿⣿⠿⢟⣩⣴⠷⠒⠎
⠀⠀⠀⠀⠈⣁⣁⣥⣤⣶⣶⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣛⣛⣛⣥⣶⡿⡿⠋⠀⠀⠀⠀⠀⠀⣶⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣟⣸⣿⡇⢸⣿⡟⠛⢢⣿⣿⠿⢋⣭⡵⠞⠛⢳⠿⠟⣀⣤⡴⠷
⣶⡶⠾⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⡿⠿⣭⣿⣉⣭⣭⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠿⠋⠀⠀⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⡇⢀⣸⣿⡟⠒⠋⠀⢄⣈⣠⡼⣶⡛⢿⠁⠁⠀
⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣛⣛⣫⣭⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠻⠿⠛⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠁⠘⠛⢃⣠⡔⠞⠛⠻⠗⠛⡙⠁⠀⠀⠀⢀
⠿⢟⣛⣿⣿⣦⣴⣶⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⡿⠛⠟⣥⡤⠶⢖⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠖⠋⠉⠀⠀⣀⠤⠔⠂⣹⠀⢀⣀⠤⣒⡨
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⢻⡏⠻⠿⢿⢋⡁⢀⣴⣶⣄⠀⠴⠿⢴⡅⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢲⠋⠁⠀⠀⠀⣄⣾⠉⠐⣋⣥⠾
⣿⣿⣿⣿⠿⠟⠛⢋⣉⣙⣵⣿⣷⡶⠾⠿⠋⠀⢸⣿⣿⣿⣶⠶⠶⣀⡀⣀⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠠⠐⠪⠷⠟⣫⠭⣶⣿⣵⣦⣿
⣻⣭⣥⣤⡖⣾⣿⠿⠿⠋⠁⠀⢸⠇⠈⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣏⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢐⠀⠀⢐⣩⠐⠊⣛⣷⣾⣿⣿⣿⣿⣿
⣻⢿⠿⣷⡿⣿⠷⠴⠶⠶⠶⠀⣀⣠⡤⠴⠖⠟⠋⠸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⡥⠄⠈⣁⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣶⣦⣤⣭⣟⣛⣛⣿⡿⢿⣻⣿⢿⣿⣿⣿⣿⣿⣻⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢿⡿⢿⣿⡷⢾⣶⣾⣿⣿⣿⣿⣝⣛⣻⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣶⣶⣶⣶⣾⣶⣾⣽⣿⣮⣮⣩⣩⣟⣛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣟⣥⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣏⣟⣛⣛⣿⣻⣟⣿⣿⣿⣿⣟⣿⣿⢿⣿
⣿⣿⢿⣿⡿⣿⡿⣿⣿⡇⣿⣯⡗⣿⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣶⣿⣿⣿⣷⣶⣾⣷⣿⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣯⣿⣿⣿⣿⣟⣿⣟⣛⣋⣛⣛⣛⣻⣿⣿⣿⣿⣿⣛
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣥⣭⣵⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⡏⢈⣿⣿⣿⣿⣿⣧⣤⠴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠍⣭⣭⢽⣽⡹⣿⣿⡽⣿⡟⣿⡟⣾⣿⡾⣿⡿⣿⡟⣿⣿⣻⣿⣻⣷⣿⣏⣿⣿⣿⡏⠘⠻⠟⢓⣨⣿⣿⣿⣿⣿⣿⣿⣚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣦⣿⣿⣿⣿⣧⣿⣿⣧⣿⣿⣿⣧⣿⣿⣷⣿⣿⣶⣦⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡏⣿⡧⣿⣿⣿⢽⣿⠿⠇⣿⣿⣇⣿⡿⣿⣸⣛⣛⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢀⣠⣤⡀⠀⠀⠀⢀⡀⣰⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⡿⠛⢛⡛⢛⣛⡛⣛⣛⣿⣭⣭
⣿⣿⣷⣿⣿⣷⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⢿⡿⠿⠿⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣷⣷⣿⣿⣿⣿⠿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣤⣬⣭⣥⣭⣵⣶⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣧⣀⢀⣼⣿⣿⣿⣿⣿⣽⣿⠁⠸⠿⣿⠛⠻⣿⠏⣙⣽⣧⣿⣿⣯⣵⣾⣷⣶
⣭⣽⣯⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣶⣶⣾⢿⣿⣿⡛⢿⡟⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣟⣏
⣼⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⢹⣟⣿⣿⣿⣿⣿⣷⣿⡾⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⣀⣀⣀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠟⠛⠿⠋⠀⠋⠛⢛⣩⣭⣥⣾⣿⣿⣿⣿⣿⣿
⠴⢽⣿⡿⡟⢛⣿⣗⣏⣛⣟⣛⣋⣥⣾⣯⣭⣭⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢹⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣧⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⠿⢟⣛⣉⣽⣽
⠶⠶⠾⣻⣛⣛⣛⣻⣽⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⠸⣿⢿⣿⡿⣿⣿⠿⡟⢻⣿⣿⣶⣽⢿⣻⣭⣭⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠩⣭⣶⣾⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⠀⠀⠈⠁⠀⣿⣿⣀⠀⢸⣿⡇⣸⣿⢈⣿⣿⣺⣿⣿⣭⢹⣿⣿⣿⣿⣿⣿⣿⣃⣀⣠⣤⣾⣿
⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⣉⣀⣤⣤⠤⠤⣶⣶⣶⣠⢰⡐⡌⢿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠛⠿⣿⢛⡋⠀⠀⠀⠀⢠⣿⡿⠛⠀⣾⣿⠿⠿⠟⢾⣿⡟⢸⣿⣇⣉⣼⣿⢿⢿⢟⣿⣿⣿⣾⣿⣻⣟⣫⣭
⣀⣀⣠⡤⠴⢒⣒⣛⣽⣭⣽⣥⣶⣶⣿⣿⣽⣿⣧⣇⠻⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣴⣶⡦⣴⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢹⣿⣏⣿⠿⠟⢛⣛⣀⣤⠴⢾⣻⣯⣿⣷⡿⠿
⣿⣿⣿⡀⠨⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢛⣛⣙⣿⣤⡀⣀⣀⠀⠀⠀⠀⣾⢟⣛⣛⣫⣿⣿⣿⣿⣿⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⢟⣵⡾⢚⣿⣿⣿⣷⡿⠀⢹⣏⣩⡶⠶⣟⣟
⡿⢛⣿⣇⣀⣁⣉⣭⣥⣤⣶⢶⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⢰⣟⣼⣿⣿⣿⠿⠿⠿⠛⣛⣩⣥⡄⠀⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⢇⠀⣉⣭⡅⢽⣿⡾⠋⣡⠀⠘⣀⣨⣿
⣿⠿⠷⠿⠟⠛⠛⠉⠉⠍⠱⡎⡱⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣧⣭⣽⠶⣶⣛⣻⣿⣿⣿⡟⠁⠀⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢠⣷⣶⣶⡖⣿⣿⣿⡯⠇⠐⡂⣤⣿⣿⡶⢿⠿⠙⢛
⠀⠀⠀⠛⠛⠱⠂⠀⠀⠀⠈⣃⡀⣀⣀⣤⣴⣶⣾⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢹⣿⡀⢸⣿⣏⡀⠀⣿⣿⠭⣵⣿⡿⢿⢿⡙⣫⣥⠶⠛⠉⠃
⠀⠀⠀⠀⣀⣀⣤⣤⣶⡶⠾⠿⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⢿⣛⣛⣭⣭⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣟⣸⣿⡇⢸⣿⡟⠛⢡⣿⣿⠿⢯⡴⠖⠛⠉⢣⠛⣉⣠⡴⠞⠛
⣶⠾⢿⣿⣿⣿⣿⣯⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡿⣻⡟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠀⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⣇⣀⢼⣿⡟⠉⠃⠀⣀⣀⡤⠾⣻⡋⠿⠀⠀⠀
⣿⣿⣿⣿⣿⢿⣿⡿⠿⠟⣛⣉⣉⣭⣤⣶⣾⣿⣿⣿⣿⡟⠀⠀⠀⠸⣧⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠉⠀⠘⢛⣃⡴⠖⠛⠉⠓⠊⣉⠁⠀⠀⠀⠀⢀
⠟⣛⣹⣿⣿⣤⣶⣶⣾⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠶⠚⠉⠀⠀⣀⣤⠖⠒⠁⡇⢀⣀⠤⠐⣫⡴
⣿⣯⣯⣿⣶⣶⣿⣿⣿⣿⠙⢿⠙⠿⢿⣿⣻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡤⠴⠒⠺⠁⠀⠀⣀⢀⢦⣭⠄⣈⣭⡶⢟
⣿⣿⣿⡿⠿⠛⠛⣉⣉⣥⣾⣿⣷⠶⠟⣻⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠓⢛⣛⡥⢖⣾⣷⣴⣶⣿
⣭⣭⣤⣶⣲⣿⣿⠟⠋⠉⠀⠀⡿⠀⠀⠀⠸⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠖⠀⠁⠀⣈⠥⠈⢉⣹⣾⣿⣿⣿⣿⣿⣿
⠻⠿⠿⣷⢿⢷⠶⠴⠶⠶⠶⢀⣀⣤⠴⠶⠚⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠨⠴⠂⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣿⣧⣶⣮⣭⣯⣭⣟⣛⣿⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⢻⠿⠿⠿⠿⠿⡿⣿⠿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⠛⠻⠿⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣷⣾⣿⣿⣶⣿⣤⣭⣭⣛⣽⣭⣭⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣒
⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣭⣿⣭⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣻⣿
⣿⣿⠿⠿⠿⣿⢿⣿⣿⣇⣿⣯⡟⣿⣿⣿⣿⣷⣿⡟⠿⣿⣿⣿⣿⡙⠛⠿⣿⠿⠿⠿⣿⣿⣿⣿⡿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣾⣿⢿⣿⣿⣿⣿⣿⢁⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣭⣭⣭⣽⣭⣽⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⣭⣭⢭⣿⡹⣿⣿⡽⣿⡟⣿⡟⣾⣿⡞⣿⡿⣿⡿⣿⡿⢻⣿⢿⣿⣿⣟⣿⣿⣿⣏⠉⢛⣛⣛⣛⣻⣛⣿⣿⡦⡻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣾⣿⣧⣿⣿⣧⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⡦⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡏⣿⣧⣿⣿⣿⢽⣿⠿⠇⣿⣿⣇⣿⡿⣿⣸⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠈⣿⣤⣶⡟⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣚⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣩⣍⣫⣭⣭⣭⣭
⣿⣿⣷⣿⣿⣷⣷⣶⣶⣾⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⣿⣿⣿⡿⣻⣟⣻⣿⣿⣿⣿⣭⣽⣿⣾⣿⣿⡿⠁⠀⠀⠛⠋⢹⣶⣾⡿⠁⠀⠀⠀⠀⠀⢠⣿⡟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣤⣤⣴⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣛⣛⣿⣛⣛⣿⣇⣙⣷⣿⣾⣿⣿⣶⣿⣿⣿
⢶⣾⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣟⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢺⣯⣿⣿⣿⣿⣿⢿⣿⣟⣛⣛⣛⣿⣿⣿⣽⣽⣾⣿⡿⠟⠉⠀⠀⢀⣿⣿⣷⣤⣤⣤⣤⠀⠀⢀⣴⣿⣿⣤⣤⣴⣾⣿⣿⣿⠻⠿⠟⠛⢀⣋⣉⣉⣭⣷⣶⣾⣿⣿⣿⣿⣿⣿
⠶⠾⢿⣿⣟⣋⣿⣿⣪⣽⣯⣭⣧⣴⣿⣿⣯⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠸⡟⠉⢿⣿⠿⠿⠿⠷⠾⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠿⣛⣯⣭⢵⣾
⣿⣿⣛⣛⣛⣯⣭⣭⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢟⣿⣿⣿⣿⣷⣦⣤⠀⠀⠀⠹⣦⣶⣶⠞⣿⣿⢿⡆⢰⣶⣶⣶⣤⠀⣠⣬⣭⣽⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠹⢶⠶⢾⡷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣛⣛⣯⣽⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠿⣿⣿⣷⣶⣾⣿⣷⣶⣎⢿⡿⠃⠀⣿⣿⣀⡀⢸⣿⡇⣸⣿⢀⣿⣿⣼⣿⣷⡽⣯⣿⣿⣿⣿⣿⣿⣿⣏⢀⣤⣤⣾⣿
⠿⠿⠛⠛⠛⠋⠉⠉⠉⣉⣉⣤⡤⠤⠴⣶⣒⣒⣿⣿⣿⣿⣿⣿⣶⣾⣿⣯⣿⣿⢟⡃⢸⡇⠸⠿⠿⠿⠟⠛⣛⣿⣿⠏⠙⠁⠀⢰⣿⡿⠛⠀⣾⣿⠿⠿⠟⢸⣿⡟⢹⣿⡏⡇⢼⣿⣿⣿⡟⢻⣿⡿⢿⣿⣛⣿⣯⣽
⣤⣄⣤⠴⢖⣒⣛⣯⣽⣿⣷⣦⣶⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⠿⠿⢏⣉⣉⣥⣤⣤⣼⣤⣤⣶⣶⡶⢶⠉⠉⡿⠋⠀⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡇⠠⠸⣟⣛⣻⣥⢤⡶⢟⣿⣽⣷⠯⠿⣿
⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⠿⠟⠛⣛⣛⣛⣛⣩⣿⣿⣦⣶⣶⣤⣶⣶⣿⣟⣟⣩⣭⣭⣽⣿⣿⣿⣿⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠀⠈⠛⣿⣿⣿⣿⣿⠋⣉⣯⣭⢶⣟⢿⣯
⠿⢻⣿⣇⣀⣩⣤⣬⣤⣶⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⣾⣿⣿⣿⠿⠿⠛⢋⣉⣭⣵⡴⠀⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣤⣤⢼⣿⡿⢛⣲⠆⠘⣫⣥⣿
⡿⠿⠷⠟⢛⡛⠋⡩⠉⠁⢸⡿⢽⣿⣿⣿⣿⠿⠟⠛⠛⠛⢛⣐⣶⣾⣷⣶⢷⣶⣛⣻⣻⣿⣽⣿⣿⣿⠀⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⠀⣷⣶⣶⡆⣶⣿⣿⡯⣟⣈⣉⣴⣿⣿⣿⠿⡿⢻⢫
⠀⠀⡰⡽⣿⡾⠶⠁⠠⠀⢈⣥⣀⣠⣥⣴⣶⣶⣶⣦⣶⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠿⣿⠋⣉⣉⠍⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠀⣿⣿⢽⣷⣿⠿⢿⣟⣙⣫⣴⠾⠛⠉⣃
⠀⠀⠀⢈⣈⣩⣤⣴⣶⡶⠿⣿⣿⣭⣿⣿⣿⣿⣿⠿⡿⣿⣿⡿⠿⠿⣛⣛⣯⣥⣤⣶⣿⣟⣻⣯⡍⠀⠀⠀⠀⠀⣶⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢀⣿⣿⠿⣯⠴⠞⠋⡉⢸⢝⣋⣤⡶⣞⡋
⣶⣟⣻⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡿⠟⠛⣻⣦⣧⣤⣤⣴⣶⣿⡿⣟⣽⣷⣶⡶⢾⡿⠿⠟⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡟⢻⣿⡇⢸⣿⡇⠀⢸⣿⡏⠉⠇⢀⣠⣤⡴⣞⣿⡭⠹⠀⠉⠀
⣿⣿⣿⣿⣿⢿⣿⠿⠿⢛⣋⣉⣭⣵⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠛⣛⠁⣠⡤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠘⣛⣃⠴⠞⠋⠉⠘⢉⣉⠵⠀⠀⠀⠀⢀
⢛⣛⣹⣿⣿⣶⣶⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⡉⢡⣶⠶⠚⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⣀⠤⠖⠊⠁⠸⢀⣤⠤⢒⡭⣶
⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠙⠿⢿⣛⣻⣽⣿⡿⠶⠞⠛⠉⠁⢸⠀⠀⠀⠀⢀⣄⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠂⠹⠁⠀⢀⣠⣄⣿⣷⠆⣘⣭⡶⢿
⣿⣿⣿⠿⠟⠛⣋⣉⣩⣭⣿⣿⣿⠿⠛⠿⠁⠁⠀⠀⠀⠀⠀⠀⣀⣤⣀⡤⠴⠒⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣐⣊⠙⢛⣋⣵⢖⣿⣿⣿⣿⣿
⣭⣥⣴⣶⡶⣿⣿⣿⣏⢁⣿⣿⡿⠁⠀⠀⠀⢀⣰⣦⡤⠶⠒⠋⠉⠉⢰⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣻⠗⢋⣩⠵⠊⢁⣾⣾⣿⣿⣿⣿⣿⣿
⡻⠿⠿⣶⢿⢷⠶⣿⣿⣾⣿⣿⣿⣤⣶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠖⠋⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠗⢚⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣿⣧⣴⣦⣥⣥⣬⣟⣛⣉⣹⣿⣿⣿⣿⣾⣿⣿⣿⣯⢙⠿⠿⠿⠿⠿⡿⠿⠿⢿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣻⣟⣻⣿⣟⣻⣿⣿⣿⣿⣿⣿⣦⣭⣿⣿⣿⣿⣾⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣿⣿⣷⣾⣼⣿⣶⣯⣤⣬⣭⣙⣍⣭⣥⣽⣧⣻⣿⠿⠋⠉⠁⠀⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣿⣿⣿⣿⣻⣿⣿⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣯⣽⣯⣭⣿⣭⣏⡿⣿⣿⣿⣛⣿⣿⠻⣿
⣿⡿⠿⠿⠿⠿⠟⣿⣿⡇⣿⣯⡇⣿⣿⣿⣿⣷⣿⡟⠿⣿⣿⢿⣽⡉⠛⠻⠿⠿⠿⠿⢿⠿⢿⣿⠿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣽⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡟⣿⡿⣿⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣾⣿⣿⣷⣶⣾⣿⣿⣿⠽⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣿⣿⣭⣭⣭⣭⣭⣹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⢻⣿⣿⣿⣿⣷⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⣭⣭⢭⣽⠙⣿⣿⡽⣿⡏⣷⡎⣶⣾⡾⣿⡟⣿⡟⣿⡟⢻⣿⢻⣷⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⢛⣛⣻⣻⣳⣄⢛⣿⣿⣿⣿⣿⣿⣼⡏⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣷⣿⣛⣿⣿⣿⣿⣽⣯
⣷⣿⣿⣾⣿⣧⣿⣿⣧⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⡆⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⡿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡏⣿⡧⣿⠿⣿⢽⢿⠿⠇⠿⣿⣇⣿⡿⣿⣸⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣟⣛⣉⣉⣛⣡⣍⣛⣭⣭⣭⣭
⣿⣿⣷⣿⣿⣷⣶⣶⡶⣾⡾⢿⣿⣿⣿⣿⣿⠿⣿⡿⠿⣿⣿⣿⢤⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣤⣤⣤⠄⠀⠀⠀⢺⠛⣍⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡗⠿
⣿⣿⣿⣿⣿⣯⣭⣴⣤⣿⣦⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢬⣭⠛⠿⢿⡿⠟⠁⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⡄⣋⣿⣙⣛⣿⣇⣈⣧⣿⡾⣾⣷⣶⣾⣿⣿
⠶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠊⠰⠿⠿⠗⣿⡀⠉⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⡏⣿⠻⠏⢿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣟⣻⣏
⢲⣯⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⢺⣯⣿⣿⠿⣿⠿⢿⣿⣿⣟⣛⣛⣫⣿⣿⣿⣿⣧⣼⣿⣿⣿⣒⣶⣶⣿⡿⢻⣧⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠀⠀⣈⣉⣉⣩⣤⣤⣾⣿⣛⣿⣿⣿⣿
⠲⠈⠺⢿⣟⣉⣹⣿⣪⣩⣿⣭⣥⣤⣾⣷⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠈⠀⠛⢿⡿⠿⠟⠿⠟⠃⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⠿⢛⣋⣭⢵⡶
⠟⣓⣛⣛⣛⣋⣭⣭⣽⣿⣿⣿⣏⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣄⠀⠀⠤⣤⣶⣶⡖⣿⣿⢿⡇⣷⣾⣿⣿⣿⠛⣫⣭⣭⣭⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠡⠶⠶⢾⡧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⠿⠿⠿⠿⢟⣛⣭⣭⣿⣿⣿⣿⠿⢽⣿⣿⣿⣿⣿⣿⠉⠰⢒⡤⣾⠉⠥⠔⡿⠙⠉⠀⣿⣿⣀⠈⢸⣿⡇⢸⣿⠀⣿⣿⢸⣿⣷⠀⣷⣿⣿⣿⣿⣿⣽⣿⣉⢀⣠⣤⣾⣿
⠿⠟⠛⠛⠛⠋⠉⠀⠀⣉⣀⣠⡤⠤⠤⣶⣒⣒⣿⣿⢿⣿⣯⣷⣶⣶⣿⣯⣿⡅⢹⣿⣿⣿⠉⣿⣆⠈⠀⠉⠁⣀⡀⠤⠇⠀⠀⢠⣿⡟⠛⠀⣼⣿⠿⠿⠟⢸⣿⡏⢸⣿⡇⠀⢸⣿⠿⣟⢛⣿⣿⠿⢾⣻⣛⣿⣯⡴
⣤⣀⣤⠴⠒⡒⣋⣭⣍⣩⣴⣦⣶⣞⣻⣿⣧⣿⣿⣿⢈⣿⡿⠿⠿⠭⠋⣁⣉⣠⣬⣿⣿⣿⡀⢹⣿⣆⢰⠈⠉⠀⠀⠀⣼⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠉⣛⣻⣠⡤⠤⢚⣯⣽⡷⠝⠿⣛
⣿⣿⣿⠀⠨⣿⠿⣿⣿⢿⠿⠟⠛⠛⣛⣛⣛⣉⣿⣿⣦⣤⣶⣤⣴⣶⣿⡟⣛⣉⣭⣿⣿⣿⡇⠸⢿⡿⠂⠀⠀⠀⠀⢠⢿⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠷⠿⠟⠀⠀⠀⠀⠹⢿⡿⠿⠃⣈⣯⡡⠶⠞⢻⣿
⠟⢹⣿⣇⣀⣀⣤⣤⣤⣶⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⢺⡏⢬⣿⡿⡿⢿⣿⣿⣷⡀⠀⣄⠀⠀⠀⠀⢀⣾⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⢻⠟⢋⣲⠀⠈⢃⣤⣾
⠿⠿⠷⠛⢛⠛⠉⠉⠉⠀⠰⡎⠙⢿⣿⣿⢻⠛⠛⠋⠋⠁⠀⣐⣶⣼⣷⣶⠶⣖⡛⠛⢛⣿⣿⣿⣿⣿⣧⡀⠀⣤⣼⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⠀⣷⣶⣶⡆⣶⣶⣦⡄⢀⣀⣃⣴⣿⣾⣯⠩⠛⠉⢩
⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⣡⣀⣀⣤⣴⣲⣶⣶⣦⣶⣾⣿⣯⣯⣿⣶⣾⣿⣿⡍⠙⠟⠛⢿⣿⠿⠿⠟⢋⣫⣽⣿⠿⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠀⣿⣿⠉⠁⠈⠿⠿⣟⡉⣡⣴⡞⠋⠉⣃
⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⠾⠟⣛⣉⣹⣻⣿⣿⣟⣿⣏⣿⣿⡿⠿⠿⣟⣛⣫⣥⣤⡶⢾⣟⡂⠀⠀⠀⠀⢸⠣⠃⢳⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢀⣿⣿⠿⠀⠰⠒⠋⠁⠨⠄⣁⣤⡴⠞⠋
⢶⡟⢻⣿⣿⣿⣭⣷⣶⣶⣿⣿⣿⡿⢻⣿⣿⢁⣿⣿⣿⣤⣤⣶⣾⣿⡿⠛⣽⣷⣶⠄⠐⠩⠣⠆⠀⣠⣴⠇⠀⠀⠘⠿⠶⠿⠋⠀⠀⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⠀⢸⣿⡇⠀⠀⠀⣠⣤⠴⡞⢫⡍⠹⠀⠀⠀
⣿⣿⢿⣿⣿⠛⠿⠿⠛⠛⣉⣁⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠇⠀⠀⠛⢉⠀⣠⡤⠶⠶⠿⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠘⠛⠃⠀⠀⠉⠉⠀⠁⣁⠐⠀⠀⠀⠀⠀
⢛⣉⣨⣿⣿⣶⣶⣶⣾⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⡉⢠⣶⠶⠚⠛⠉⠀⠁⠀⠀⠀⠀⠸⢧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠊⠁⠸⢀⡠⠤⢀⡉⠔
⣿⣽⣿⣶⣶⣿⣷⣾⢿⡗⠉⢻⠘⠛⠟⣻⣿⣿⣿⣿⣿⡿⠛⠉⠁⠸⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠈⡡⠤⣀⡥⠖⢛
⣿⣿⡿⠟⠋⠋⢈⣀⣠⣤⣾⡿⣷⠿⠛⠛⣿⣿⣿⣿⡿⠃⠀⠀⣀⣤⣀⡤⠴⠒⠛⠛⠃⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢙⣁⡤⠒⣿⣷⣶⣾⣿
⣥⣤⣶⣶⠶⡿⠿⠛⠋⠁⠀⠀⠾⠀⠀⠀⠸⣿⡿⠋⠁⠐⠚⠋⠉⠉⢰⠀⠀⠀⠀⣀⣠⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⢀⣨⣶⣿⣿⣿⣿⣿⣿
⠙⠿⠿⣶⠿⢷⠶⠰⠶⠶⠖⣀⣀⣤⠴⠖⠛⠋⠁⠀⣴⣶⣶⣦⣄⣀⣤⣤⠶⠒⠋⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣶⣠⣬⣗⣘⣉⣫⠿⠿⢿⣿⢿⣷⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠛⠛⠻⠿⣿⣿⣻⡿⣿⣶⣶⣷⣶⣶⣿⣽⣾⣭⣛⣿⣿⣿⣿⣿⣿⣿⣟⣿
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣾⣶⣶⣶⣷⣴⣏⣿⣷⣿⣍⣙⣿⣛⣟⣛⣛⡻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣋⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣹⣻⣛⣻⣛⡿⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣯⡗⣿⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣶⣿⣿⣿⣷⣶⣷⣿⣿⣿⣾⣿⣶⣶⣶⣶⣶⣶⣾⣶⣷⣶⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⣛⣻⣿⣛⣛⣙⣛⣛⣛⣿⣿⣿⣿⣿⣟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣭⣷⣿⣷⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⣭⣭⢭⣿⡹⣿⣿⣽⣿⡟⣿⡟⣾⣿⡾⣿⡿⣿⡟⣿⣟⣻⣿⣿⣷⣿⣏⣿⣿⣿⠀⠻⠿⡿⡿⠿⠿⠿⠇⠈⡻⣿⣿⣿⣷⡄⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣯⣿⣭
⣤⣿⣿⣼⣿⣧⣿⣿⣧⣿⣿⣿⣧⣿⣿⣷⣿⣷⣿⡦⣿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣡⣾⠁⢿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡏⣿⡯⣿⣿⣿⢽⣿⠿⠇⢿⣿⣇⣿⣿⣿⣸⣛⣛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣟⠛⠛⣛⡛⣋⣛⣛⣛⣻⣯⣭⣭
⣿⣿⣷⣿⣿⣷⣷⣶⣸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣻⣛⣛⣛⣿⣮⣭⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⢰⢟⡿⢻⣟⣻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿
⣿⣿⣿⣿⣿⣿⣯⣤⣼⣧⣤⣍⣭⣭⣽⣷⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡗⠁⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⣿⢸⡇⠛⠟⣿⣟⣿⣿⣿⣙⣿⣿⣼⣷⣿⣶⣾⣿⣾⡿
⣭⣯⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠿⠿⠿⣟⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⢰⣿⣿⣿⣿⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣁
⢟⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠯⣿⣻⣿⡿⣿⣿⣿⣿⡿⢿⡿⣿⣛⣿⣿⣯⣯⣭⣭⣭⣿⣿⣖⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣤⣤⣾⣿⣟⠿⠿⠛⠛⠋⠘⠙⢋⣩⣭⣥⣴⣾⣿⣿⣿⣿⣿⣿
⠬⣽⣿⣿⠟⢻⣿⣮⣛⣿⣟⣿⣡⣴⣿⣯⣭⣧⣶⣶⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣻⣿⣶⣶⡦⠄⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡏⣿⣿⣿⡿⠿⣛⣛⣭⣮⣿
⠶⠶⢞⣛⣻⣛⣛⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣤⣀⣀⣀⠀⣠⣤⣤⣶⠜⣿⣿⣿⣗⣿⣾⣿⣿⣿⠉⣩⣼⣭⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣭⣶⠶⡷⡖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⣻⡿⣿⣿⣿⣿⣷⣿⢿⣿⣿⢿⠿⣿⣭⣭⣤⣦⣔⣸⣷⣿⡻⠿⠁⠀⣿⣿⣉⠀⢸⣿⡇⢸⣿⢀⣿⣿⢼⣿⣷⡏⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣤⣴⣿⣿
⠿⠿⠿⠛⠛⠋⠉⠉⠉⢉⣁⣠⣤⡤⠤⠤⡶⣾⣶⣿⣿⣿⣯⣿⣷⣶⣾⣾⣿⡶⡆⢸⣿⠘⠟⠛⠿⠿⠛⠛⢛⣛⣩⣿⠅⠀⠀⢠⣿⡟⠛⠀⣼⣿⠿⠿⠟⢸⣿⡟⢸⣿⡇⣤⣿⡿⢿⠿⢛⣿⣿⢷⣿⣿⣿⣿⣭⣴
⣀⣀⣤⠤⠖⣒⣒⣯⣭⣭⣽⣷⣶⣾⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠿⡭⠉⣙⣉⣉⣭⣬⣥⣤⣤⣶⣶⢤⡞⠛⢉⣁⡾⠇⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡇⢿⠿⠛⣛⣃⣨⠤⠴⣛⣯⣿⡿⣼⠿⣟
⣿⣿⡇⠀⠺⣿⣿⣿⣿⡿⠿⠟⠛⠛⠟⣛⣛⣻⣿⣷⣥⣥⣤⣤⣴⣶⣿⢿⣟⣟⣿⣭⣭⣿⣿⣿⣿⠘⡇⠀⠈⠙⡱⠁⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⠵⠞⠛⣿⣿⣿⡿⠏⢀⣹⣉⡴⠶⠾⣛⣿
⠛⣿⣿⣀⣀⣀⣠⣤⣤⣴⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⣿⠁⣿⣿⣿⣿⡿⠿⠟⢛⣯⣭⣤⣤⣤⣶⡎⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣩⣤⠰⢾⣿⠛⣙⡆⠈⢃⣨⣵⣷
⣿⠿⠾⠿⠛⠛⠋⠉⠉⠉⣶⠻⠿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠀⣀⣦⣿⣤⣬⠶⢶⣞⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⢀⣿⣶⣶⡆⣿⣿⣿⡯⠀⢛⢡⣼⣿⣿⠞⢹⠏⢉⣩
⠀⠀⠘⠛⠃⠦⠄⠀⠀⠀⢈⣀⣀⣈⣩⣤⣾⣶⣶⣠⣶⣾⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⢿⠛⠛⣛⣻⣿⣽⣿⠈⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢸⣿⡀⢸⣿⣇⠀⠀⣿⣿⢹⣷⡟⠻⡟⣛⢛⣬⡶⠟⠋⢑⢀
⠀⠀⠀⠀⣀⣀⣤⣤⣶⡶⠾⢟⣛⠛⣟⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⢿⣛⣿⣿⣿⣶⣿⣿⣿⣿⣭⣝⣽⠋⠀⠀⣴⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣟⣸⣿⡇⢸⣿⡟⠛⢀⣿⣿⠿⠧⠶⠚⠉⠉⡞⢍⣩⣤⠶⣛⠉
⣶⠶⣿⣿⣿⣯⣿⣷⣶⣶⣾⣿⣿⣿⣿⠿⠗⠋⢠⣸⣌⣭⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⡟⠉⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⡇⠀⢸⣿⡏⠉⠀⢀⣠⡤⠶⣟⣯⢹⠇⠈⠁⠀
⣾⡿⣿⣿⡿⢿⣿⠿⠿⠛⣑⣁⣡⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⡟⠛⠛⠿⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠘⣛⡣⠶⠛⠉⠉⠂⢉⡡⠁⠀⠀⠀⠀⠤
⢛⣃⣻⣿⣧⣴⣶⡶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢑⣿⠇⠀⠀⠀⠈⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⠴⠒⠉⠠⢁⣀⡤⢔⣊⠡⣂
⣿⣿⣿⣷⣶⣿⣿⣿⣿⠉⠻⡏⠻⠿⢿⣟⣻⣽⣟⠶⠶⣿⣿⣿⣷⣿⡟⠀⠀⠀⢀⣀⣀⣠⠄⠀⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠊⠋⠀⠀⣀⠀⣐⡨⠠⢀⣩⠴⠚⣻
⣿⣿⡿⠿⠟⠋⠁⣀⣁⣴⣿⣷⡶⠿⠛⠛⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⢁⡤⠴⠒⠛⠋⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠘⣛⣣⠴⢾⣿⣶⣷⣿⣿
⣭⣥⣤⣖⣶⣿⠿⠛⠉⠁⠀⢰⠇⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⠋⡬⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡠⠔⠉⣁⣷⣾⣿⣿⣿⣿⣿⣿
⠛⠿⢷⣶⡿⢷⠶⠰⠶⠶⠶⣀⣠⣤⠴⠖⠚⠋⠉⠀⠸⠋⠉⠀⠀⢰⣤⡤⠶⠖⠋⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠒⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[30A⣅⠙⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣻⡿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⣭⣭⣋⣛⣛⣻⣙⣫⣙⣟⣛⡿⣿⣟⡻⠿⠿⠿⢿⣿⣿⡿⠿⠿⠛⠋⠋⠉⠛⠛⠛⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⢿⣟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣯⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣭⣿⣿⣷⣾⣿⣿⣿⣿⣿
⣿⣯⣿⣿⣭⣯⣽⣿⣿⣿⣿⣯⡇⣿⣯⣽⣿⣿⣿⣏⣭⣿⣿⣿⣷⣬⣭⣽⣛⣉⣉⣙⣋⣛⣻⣯⣬⣛⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣽⣿⣷⣿⣿⣾⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⡟⣭⣭⣭⣿⡹⣿⣿⣽⣿⡟⣿⡿⣶⣿⣾⣿⡿⣿⡿⣿⣟⣻⣿⣿⣷⣿⣏⣿⣿⣿⠸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣁⣿⣿⣿⣿⡇⣿⢻⣇⣿⣿⣿⣇⣿⣻⣷⣿⣿⣿⡆⣿⣟⣻⣿⣿⣷⢮⣿⣿⣿⣿⣤⣤⣴⣶⣶⣾⣦⠌⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⡏⣿⡿⣿⣿⣿⢽⣿⡿⠏⣿⣿⣏⣿⣿⣿⣸⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣇⠀⣀⡈⠛⣂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⠛⠿⠿⠿⢿⣟⣛⣻
⣿⣿⣷⣿⣿⣷⣷⣶⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⠛⠉⣿⣿⣿⢃⣤⡿⠀⠀⠀⠀⠀⠀⢀⣶⣷⣶⣶⢿⠿⢿⣿⣿⣷⣶⣶⣿⣶⣿⣿⣿⣿⣿⣯⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣛⣹⣿⣉⠛⢛⣛⣛⣻⣽⣫⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠉⠁⠘⠿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⡇⢾⢿⣿⠻⣿⣿⡟⠻⣿⣯⣹⣿⣯⣻⣽⣧⣽⣿
⣚⣿⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⢿⣝⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣾⣾⣷⡶⢶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠨
⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⣛⣿⣟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⣤⣤⣶⣿⣿⣿⢿⡿⠿⠿⠿⠙⠹⠛⠛⢛⣛⣋⣽⣿⣿⣿⣿⣿⣿⣿
⣋⣛⣿⣿⣿⠏⣿⢽⠻⢿⡿⠿⠟⣠⣿⣟⣛⣫⣿⣭⣭⣿⣷⣿⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣷⣶⣶⠆⣶⠄⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣤⣤⣶⣶⣶⣶⣶⣿⢿⣿⣿⣿⣿⡿⠿⠿⣫⣿⣿
⣤⣬⣼⣿⣶⠾⣿⣿⣿⣿⣿⣿⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡉⠛⠻⡟⠋⠈⢹⣀⣄⣿⣿⣿⠿⡏⢱⣶⣶⣶⣤⠀⣢⣽⣭⣽⡻⣿⣿⣿⣿⣾⣿⣿⣿⡶⢚⣛⣭⣽⣯⠇
⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣛⣿⣿⣾⣭⣯⣿⣶⣾⣿⣿⠷⣛⡛⣿⣯⣿⣶⣿⣄⣨⡿⠁⠀⣿⣿⣀⡀⢸⣿⡇⣸⣿⢀⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢉⣉⣼⣷⣟
⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠋⢉⣉⣉⣉⣿⣯⣭⣭⣶⣾⣿⣿⣷⣿⣭⣭⣿⣯⡍⠈⢹⣿⠈⠩⠿⢿⠿⣿⢿⠿⢿⣿⣿⡿⠁⠀⢰⣿⡿⠛⠀⣾⣿⠿⠿⠟⢸⣿⡟⢸⣿⡇⣸⣿⣿⣿⡿⠿⣿⣿⣿⣿⢿⢿⣿⣋⣭
⠀⠀⣀⣀⡠⠤⠤⣶⣒⣒⣛⣫⣭⣭⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠟⠛⠋⠀⠂⣐⣃⣀⣀⣠⣤⢠⡴⠶⠚⣻⣿⠃⠀⠀⠀⢸⣿⣧⣤⠀⣿⣿⠀⠀⠀⢸⣿⡇⢸⣿⡇⢿⣿⣶⠶⠂⣉⣉⡵⢾⣿⣿⣋⣿⡽⠿
⣿⣿⣟⠀⣴⣾⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⡟⣾⣿⣇⣙⣽⡿⢿⣬⣥⣶⡾⠿⠿⡟⠛⢻⣿⣿⣿⣷⢸⠁⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠀⠀⠀⠈⠻⠿⠿⠟⢡⠶⢶⣿⣿⣿⣿⡆⠚⣿⢛⣭⣴⡷⣿⣻
⠿⢿⣿⡄⠀⠉⢋⣉⣁⣡⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁⣼⡿⣿⢋⢶⣾⣿⣷⣷⠟⠿⠿⠛⣋⣈⣀⠀⠀⠀⠀⣤⣤⣤⣄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣉⣩⣶⣶⠞⢿⡍⠑⠂⢐⣩⣥
⣶⣿⣽⣿⠿⠿⠟⠛⠛⠛⣧⢟⣹⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢤⣄⣿⣀⣀⣥⡭⠵⠶⣶⠖⣾⣿⣯⡉⠁⠀⠀⠀⢸⣿⡇⠹⠿⠀⠛⣿⣿⠟⠃⢠⣿⣿⣿⠀⠀⣿⣶⣶⡖⣿⣿⣿⡏⠈⠜⣃⣶⣿⣶⡲⡾⠏⠛⣛
⠁⠀⠰⠶⠖⢄⡀⠀⠀⠀⠺⠀⢻⣿⣿⣿⣿⣿⠟⠁⣠⣶⣶⣿⣿⣿⣿⣵⣶⣶⣖⠗⣿⠈⠛⠛⣉⠁⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⣿⣿⠀⠀⣸⣿⢹⣿⠀⢸⣿⣇⡀⠀⣿⣿⢩⣷⡷⣿⡿⠿⢟⣋⣤⡶⠒⠎⠁
⠀⠀⠀⠀⠁⠀⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⠃⠀⢠⡯⣿⣿⣿⠿⡿⠿⠿⣛⣋⣡⣤⣾⡶⠶⡟⠃⠀⠀⠀⠀⠀⣰⣶⠈⣿⣿⠀⠀⣿⣿⠀⢀⣿⣏⣸⣿⡇⢸⣿⡟⠛⢠⣿⣿⠿⣯⡥⠶⠛⢙⡜⠛⢃⣤⡴⠿⠚
⣤⡶⣶⣶⣿⣟⣿⣯⣭⣥⣶⣾⣿⣿⣿⡿⠟⠀⠀⣸⡀⢈⣉⣥⣴⣶⡿⣿⣟⣋⣩⣭⣥⣾⡟⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠿⠋⠀⠠⣿⡏⠀⢸⣿⡏⢻⣿⡇⢸⣿⠇⢀⣼⣿⡟⡏⠀⠀⣀⣀⣴⢷⣛⢻⠇⠈⠁⠀
⣴⣶⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⡹⣎⢱⠀⢀⡀⣻⣿⣿⣿⣯⡝⣿⠈⠙⠹⠏⠙⠉⣋⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠘⠛⣃⡤⠖⠛⠉⠳⠚⡈⠁⠀⠀⠀⠀⣀
⠿⠋⢹⣿⣧⣠⣤⣤⡶⢾⣿⡆⡘⠗⠈⠀⣾⣿⣿⣿⣟⠿⠿⠛⠁⣡⣤⡤⠶⠶⠂⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠚⠉⠁⠀⢀⡤⠴⠂⢹⠀⢀⣀⠠⠒⣠⠤
⣾⣿⣿⣯⣭⣿⣿⣿⣿⠚⠻⡇⠙⠊⠀⠀⣿⣿⣿⣿⣿⣶⡖⠒⠀⡏⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠰⠏⠁⠀⠀⡀⠐⣊⣉⠁⣚⣭⠾⢿
⣿⣿⣿⡿⠟⠛⠉⠉⢉⣠⣶⣿⣤⡶⠾⠟⠙⢿⣿⣿⣿⣿⣿⣦⡀⠁⢀⣀⡤⠴⠾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠐⠬⠒⣙⡥⢶⣟⣭⣦⣾⣿
⣛⣉⣥⣤⣴⣶⡿⠿⠛⠋⠉⢩⡗⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣧⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠀⠀⠀⣀⠄⠂⢙⣫⣽⣿⣿⣿⣿⣿⣿
⠿⠿⠿⣿⡿⢿⠶⠰⠶⠶⠶⠀⢀⣠⣤⠴⠶⠞⠋⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣔⠚⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⠴⠈⢉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
䷩ 𝚕𝚒𝚗𝚎 1018
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/21/going-rusty-faster/#comments
Gemini version at gemini://gemini.techrights.org/2022/09/21/going-rusty-faster/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.21.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ The_Life_of_Linux_Will_Be_Shortened_by_a_Misguided_Adoption_of_Rust⠀✐
Posted in Free/Libre_Software, GNU/Linux, Kernel at 7:27 pm by Dr. Roy
Schestowitz
Video_download_link | md5sum 77e0c252bb9df82b7f88b6374b6a0a31
Linux Will Rust Along With Bloat
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/rust-in-linux-a-mistake.webm
Summary: There are currently loads of puff pieces (mindless corporate fluff, no
technical considerations) about Rust coming to Linux in the sense that Linux
will become dependent on a monstrous shebang controlled by Microsoft
proprietary software; a lot of developers very well understand the risk, but it
feels like nobody wants to face the mob (for saying out loud that the emperor
is naked)
MORE than two years ago we argued_that_Linus_Torvalds_was_pressured_to_make_a
mistake by adopting Rust as part of the kernel’s code. Since then Rust has had
countless security problems, some emergency-level patches, and many people
resigned from the Rust project in protest; some resigned en masse (whole
teams). Everything we’ve been saying about Rust, cautioning about adoption in
core projects such as Linux, turned out to be true. That’s putting side
censorship issue, training/skill issues, and long-term sustainability aspects.
“Every software project has a limited ‘shelf life’ and Torvalds — who in effect
betrayed or abandoned his mantra, for the kernel neglects its own principles —
went along with a mistake after years of lobbying (mostly by Google).”The above
video is long but unscriped; I’ve been sitting on it for two days already
(pondering whether to do a video or just a long article, textually). I’ve been
seeing lots of puff pieces (we’ll link to none), including one just a few hours
ago, so the propaganda clearly isn’t ending. Nobody expresses any ‘dissenting’
views about the decision — that of course would be deemed “hateful”!
The subject has been discussed here for years and there are many rebuttals in
IRC (the logs are public), especially the past week’s proceedings. But I’ve
attempted to summarise at least some of the issues in the video above.
The conclusion is, Linux shortened its lifetime and made a more compelling case
for developers to adopt (and develop around) other, simpler kernels. Every
software project has a limited ‘shelf life’ and Torvalds — who in effect
betrayed or abandoned his mantra, for the kernel neglects its own principles —
went along with a mistake after years of lobbying (mostly by Google).
My scepticism of Rust and criticism of legal and technical aspects have earned
me defamatory condemnation by serial_trolls_salaried_by_Google. No, they didn’t
respond to my legal and technical arguments; instead they threw baseless
innuendo, insinuating Rust critics are somehow transphobic. Welcome to the new
Maoism. █
䷩ 𝚕𝚒𝚗𝚎 1093
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/21/irc-log-200922/#comments
Gemini version at gemini://gemini.techrights.org/2022/09/21/irc-log-200922/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.21.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ IRC_Proceedings:_Tuesday,_September_20,_2022⠀✐
Posted in IRC_Logs at 2:03 am by Needs Sunlight
Also available via the Gemini protocol at:
* gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-200922.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-200922.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-social-200922.gmi
* gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-200922.gmi
Over HTTP:
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#techrights_log_as_HTML5 #boycottnovell_log_as_HTML5
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🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_
#techrights_log_as_text #boycottnovell_log_as_text
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#boycottnovell-social_log_as_text #techbytes_log_as_text
Enter_the_IRC_channels_now
=> =============================================================================
§ IPFS Mirrors⠀➾
CID Description Object type
IRC log for
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IRC log for
#boycottnovell
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IRC log for
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as HTML)
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as plain/ASCII
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IRC log for
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(full IRC log
as HTML)
IRC log for
#techrights
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as plain/ASCII
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🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈
§ Bulletin for Yesterday⠀➾
Local_copy | CID (IPFS): QmcB3PmzUDz4gMMbVfzAbgcnKwRGZjhaY7foe2B7ox9dZW
䷩ 𝚕𝚒𝚗𝚎 1220
╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕
(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/21/lf-openwashing-front-group/#comments
Gemini version at gemini://gemini.techrights.org/2022/09/21/lf-openwashing-front-group/
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.21.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Linux_Foundation_‘Europe’_a_Front_Group_for_Patent_Trolls_and_American
Monopolies⠀✐
Posted in Deception, Europe, Kernel at 7:53 pm by Dr. Roy Schestowitz
Ingore the paid-for puff_pieces
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LF_Europe⦈_
🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇LF_clap⦈_
Summary: About 90% of the Linux_Foundation‘s money is spent in the United
States (see IRS_filing); it’s not global but a front for American corporate
interests so adding ‘Europe’ to the name is misleading to say the least; it
enables hostile interference in Linux’s name (the lobbyists_like_to_claim_to_be
speaking_for_those_whom_they’re_against by hijacking_words/names)
⣿⣻⣿⣿⣿⡟⡿⠿⢿⢿⢿⡿⢿⢻⣿⠿⢻⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⡿⠿⠛⣿⡿⡿⢿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣟⢻⣿⣿⣿⣿⡾⢿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢿⡿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⡿⡿⢿⢿⣿⣿⢿⣿⣿⡿⠿⠿⣿⣿⡿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⡘⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡈⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣾⣷⣯⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣷⣷⣾⣾⣿⣿⣾⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣇⢸⣿⣿⣧⣾⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⣼⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣤⣦⣿⣿⣿⣿⣿⣿⣷⣷⣧⣼⣾⣽⣿⣾⣿⣿⣷⣦⣤⣿⣿⣶⣿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣿⣿⣿⣿⣄⢹⣽⣭⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⣿⣿⣽⣛⢿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡿⠿⢿⣿⢿⣿⣧⠹⢻⢿⢿⢿⣿⣿⣿⣿⣿⡿⡟⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⢿⢿⣿⠿⠿⠿⣿⣿⠟⡿⢿⡿⠿⡿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡷⣾⣶⣾⣿⡿⡿⠄⣶⡶⣾⣿⢿⠿⠿⣿⣿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣶⣶⣿⣿⣶⣷⣾⣷⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⡦⠹⢷⣿⣷⣶⣶⣶⣾⣿⣷⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⣿⣽⣯⣧⣴⣤⣮⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣭⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣠⣾⣿⣿⣷⣍⠙⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠉⠈⠁⠘⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⢻⠿⠿⠿⣿⠿⠿⠿⣿⣿⡿⠟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣕⠀⢀⡀⠹⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠈⠉⠘⠁⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⣿⣿⣿⣿⣿⡻⣩⠛⠓⠄⣐⠀⠀⠀⠀⣀⣠⡄⠄⡠⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡯⠙⡽⢛⣯⣭⣦⠀
⠟⠻⠟⠿⡟⣧⡁⠀⠁⠀⠀⠁⠀⠀⠀⣉⠉⠿⠘⢇⠐⠖⠀⠁⠙⠁⠁⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣭⣦⣿⣮⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠔⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢨⡄⠀⠀⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣶⣿⣿⣿⣿⣿⣿⣿⠷
⢰⣄⣰⣷⣀⡀⢰⣧⣤⠶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⢀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⡉⢉⣽⣿⣿⣿⠋⠀
⣿⣷⣿⣿⣿⣿⣿⠙⠳⣮⠙⡨⢗⣀⢀⡠⠀⠰⣒⠤⠄⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠸⣷⡀⣼⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣾⣿⣿⠿⠃⠀⠀
⢈⣹⣿⣿⣿⣿⣿⣶⣤⣴⢀⠙⠾⠟⢻⣄⣀⡈⠉⢩⣉⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣦⣹⣷⣿⣿⣿⣿⣿⣿⣿⣋⣩⠅⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀
⠎⠛⣿⣿⣿⣿⣿⣿⠿⠛⡍⢙⠁⡀⠀⢭⢎⡁⠀⢀⡀⠀⠀⠀⠀⢸⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⣩⣿⠿⢶⠖⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢢⣾⣿⣿⣿⣿⣿⡿⠾⠀⣵⣅⡊⠄⣀⢺⣿⣿⣿⣿⣯⠀⠀⠀⠒⢴⣭⣧⡜⠛⠿⠿⠿⠿⠿⠿⠾⠟⠋⡙⢁⣀⣤⣿⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢯⣴⣿⣿⣿⣿⣿⣽⣾⣾⣿⣿⣷⣷⣯⣿⣿⣿⣿⣿⣿⣠⣲⣶⣌⣩⣽⣥⣿⣆⣀⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣼⣿⣿⡏⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣤⣷⣿⣿⣗⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠈⢻⠀⣸⣿⣿⣧⡘⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⠗⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠉⠋⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀
⠀⣾⣾⣿⣿⣿⣿⣿⡦⠀⠀⠜⠻⣿⠿⠛⠉⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠘⠟⠐⠆⠀⠀⠈⠉⠙⠛⠋⠉⠉⠀⠂⠀⠀⠀⠙⠁⢀⡀⠉⠉⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⢰⣿⣿⣿⣿⣿⠹⢛⡁⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠚⠀⠀⠀⠀⠀⡉⢻⣿⣿⣿⣿⣿⠯⠙⡽⢛⣯⣭⣦⠀
⠈⣿⠃⠘⢿⣿⣧⠛⠈⠀⠀⠀⠀⠀⠀⠀⠺⠽⢣⠀⡬⠁⣤⡤⠂⠚⠁⠀⠀⠀⠀⠀⣠⡀⠀⠀⠐⠶⡯⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣯⣭⣦⣿⣤⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠈⠟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣄⡀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣀⣨⣻⣀⣀⢈⣷⣀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⢀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⡉⢉⣽⣿⣿⣿⠛⠀
⣸⣦⣿⣿⣿⣿⣿⠠⠻⢭⣄⠺⢑⣦⠀⠠⠠⠀⢠⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠘⣷⡄⣤⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣾⣿⣿⠟⠁⠀⠀
⣟⠋⣿⣿⣿⣿⣿⣄⣄⣀⣉⠀⠲⣼⡿⠶⠋⠀⠀⠓⠒⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣷⣿⣿⣖⣦⠆⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀
⠻⡖⣿⣿⣿⣿⣿⣜⣿⣿⠿⡒⠀⠀⠀⢈⡛⡝⠃⠀⠈⠀⠀⠀⠀⠰⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⣹⣿⠿⠶⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⢄⣿⣿⣿⣿⣿⡯⣿⣴⠀⣃⡀⢄⣁⢸⣿⣾⣶⣶⣾⠀⠀⠀⠀⣤⣿⡓⣌⠛⠿⠿⠿⠿⠿⠿⠶⠟⠋⠉⠁⠀⢀⣵⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣞⣿⣿⣿⣿⣿⣤⣶⣴⣴⣿⣿⣿⣯⣿⣿⣿⣿⢿⣻⠠⠀⢤⣤⠚⣟⣟⣹⣧⣀⣀⣠⣤⣤⣴⣶⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⣰⣿⣿⡏⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣠⣦⣿⣿⡇⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠻⡇⠀⣿⣿⣿⡆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⠆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠳⠀⠀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀
⠀⢰⣷⣾⣿⣿⣿⣿⣷⡌⠁⠈⠹⣿⣿⠿⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⢤⠀⠀⠀⠛⠛⠟⠟⠛⠛⠉⢡⠏⠉⠉⠙⠛⠉⡉⠉⠛⠋⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⡀⢸⡟⣿⣿⣿⡿⠿⢯⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⢸⠋⠁⡀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡯⠙⡽⢛⣯⣭⣦⠀
⠁⠻⠀⠉⠿⣿⣿⡖⠋⠑⠌⠀⠠⠀⣀⠀⠠⣶⡶⡄⢠⡛⢀⣀⡠⠴⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢴⣼⣻⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣭⣦⣿⣬⡿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⠹⠿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠠⢦⢬⠥⠈⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⣀⠀⠩⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⣹⣏⣀⠀⣲⡆⢀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⢀⠀⠀⢰⣤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⣉⢩⣽⣿⣿⣿⠟⠁
⣀⢶⣿⣿⣿⣿⣿⠀⡺⢿⣍⠡⡅⢦⡄⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠘⣷⡄⣤⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣾⣿⣿⠟⠁⠀⠀
⣿⡿⣿⣿⣿⣿⣿⢄⣀⣀⣉⡓⠠⣤⣶⣦⠖⠃⠀⠱⠾⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⠄⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀
⠻⢷⣿⣿⣿⣿⣿⣐⢫⣿⣿⠇⠀⠀⠀⠀⠛⢂⠶⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢉⣹⣿⠿⠷⣞⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠉⣿⣿⣿⣿⣿⣿⣿⣏⡄⠀⡀⠀⣀⢺⣿⣿⣶⣤⣶⠀⠄⠀⠀⢠⣾⡷⣬⠻⠿⠿⠿⠿⠿⠿⠷⠾⠋⠋⠁⠀⠀⣑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣈⣷⣿⣿⣿⣿⣿⣭⣴⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⢠⠀⢀⣀⣨⠿⢿⣿⣧⣀⣀⣀⣤⣤⣴⣶⣦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣍⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⢰⣿⣿⡏⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣦⣿⣿⡇⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⡀⠀⢻⣿⠃⢹⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⡃⠀⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⠀⠄⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠀
⣇⠀⠀⣹⣠⣾⣿⣿⣿⣾⡿⠿⠛⢿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠿⠋⠉⠉⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠿⠿⠟⡛⠛⠛⠛⠿⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⡿⠀⠀⠩⣿⣿⣿⣿⣿⣍⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡶⠆⠀⠀⠉⢻⣿⣿⣿⣿⣿⡯⠙⣽⢛⣯⣭⣦⠀
⠿⠷⠀⠀⠟⣿⣿⣿⡥⡼⠦⡛⠂⣀⠀⠀⠀⠀⣀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⣾⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⠀⠀⠂⠀⠂⠀⠀⣼⣿⣭⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷
⢼⡃⠀⠀⠀⠀⢹⣿⣿⣤⣄⠀⠀⠨⠁⠡⠄⠀⣽⣯⣽⠙⢣⠐⠿⠋⠀⠀⠀⠀⠀⠀⠈⠍⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⢰⣅⡿⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢀⣀⣀⣸⣷⠂⠀⢭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⣉⢉⣽⣿⣿⣿⡟⠁
⠀⠀⣿⣿⣿⣿⣿⣄⠀⢸⣷⡶⢛⡫⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠀⢿⣆⢠⣽⣷⣄⠀⠀⠀⠁⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣤⣾⣿⣿⠟⠋⠀⠀
⠀⢰⣿⣿⣿⣿⣿⣉⡀⠐⠉⠻⠧⠹⡐⣿⣆⡦⠄⠀⢨⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣙⣿⣾⣿⣿⣿⣶⣤⣤⣤⣤⡄⠀⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀
⠐⢶⣿⣿⣿⣿⣿⡄⠉⢿⣷⣶⠀⠀⠈⠛⠋⢥⡤⣤⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⠿⠷⣟⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣿⣿⣿⣿⣿⣖⣾⢺⡟⡃⠀⠀⣀⢠⣶⣶⣜⣧⣀⠀⠀⡀⠀⢀⣠⣻⣌⠿⠿⠿⠿⣿⣿⣿⡿⡶⠛⠛⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⣴⣾⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⢠⣿⣿⣧⣅⣀⣀⣀⣀⣠⣤⣶⡆⠀⣄⣀⣀⣀⣠⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣟⣿⣦⣶⣮⣥⣬⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡟⠉⠉⢩⣿⣿⣿⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣴⣿⣿⣇⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⡀⠀⠙⣿⡿⠁⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣼⣿⠃⠀⠀⠐⠖⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⢀⡀⠈⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀
⣿⡗⠀⠈⣧⣠⣿⣿⣿⣦⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠻⠃⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⢰⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⠿⡿⠀⠀⢉⣿⣿⣿⣿⣙⠏⠀⠀⠀⠈⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠋⠀⠠⠀⠠⠈⠈⠉⠉⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡤⠀⠀⠉⢻⣿⣿⣿⣿⣿⡯⠙⡽⢛⣯⣭⣦⠀
⠀⣷⠄⠀⠠⠿⣿⣿⣟⢋⣵⣄⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣦⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠈⠁⠠⠀⠀⣴⣿⣭⣦⣿⣮⣿⣿⣿⣿⣿⣿⣿⣷
⢧⣴⠀⠀⠀⠈⠙⣿⣿⣯⣥⡤⠁⠀⠽⡦⣤⡄⢸⣿⣷⡖⠰⠎⠰⡶⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠺⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠀⠀⠀⠀⣴⣿⡿⢿⡏⠈⠀⠀⠀⠀⠀⠁⠈⢻⠫⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠆⠀⢀⣀⣀⣀⣿⡧⠀⢘⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣍⣩⢉⣽⣿⣿⣿⡟⠃
⠁⠀⣿⣿⣿⣿⣿⣧⡐⢀⣿⣥⠾⠿⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣄⠀⢿⣦⢀⣼⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣾⣿⣿⠟⠁⠁⠀
⠀⠀⣿⣿⣿⣿⣿⠛⠃⠐⠊⠹⢶⠝⠢⠷⣆⠐⣀⠀⠠⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣘⣿⣿⣿⣿⣿⣧⣄⣠⣄⣠⡄⢀⣠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠠⣿⣿⣿⣿⣿⢁⠉⢲⢶⣦⢀⠀⠈⠿⠟⢛⣀⣀⡀⠀⠀⠀⠀⠀⢯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠷⣟⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣯⠵⣦⣿⠟⠃⠀⢀⢠⣠⣤⣭⢾⡉⠀⠀⠀⠀⠀⢀⣱⣌⠿⣿⣿⣿⣿⣿⣿⣿⡶⠚⠛⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣤⣴⣯⣿⣿⣿⣿⡿⠟⠀⠀⠈⠁⢰⣿⣿⣿⣅⠀⠀⠀⣀⣀⣤⣶⣄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢻⣿⣤⣤⣓⣄⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣟⠛⠙⢉⣽⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣠⣼⣿⣟⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣀⠀⠈⠹⣿⣿⡇⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠂⣽⣿⠁⠀⠀⣀⡀⠀⠀⠀⠷⠀⠀⠀⠈⠹⠀⠙⠿⠇⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠐
⣿⣷⣦⡄⠘⢿⠁⣸⣿⣿⣇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣇⡀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠦⠒⠀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⠙⣿⣷⠀⠀⠀⢰⣿⣿⣿⡿⣖⠍⠉⠉⠉⠉⠉⠙⠋⠛⠋⠉⠉⠉⠉⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢶⠤⠀⠀⠀⠀⠛⢻⠿⠿⠛⠛⠉⢡⡏⠉⠉⠙⠛⠉⣩⣉⣹⢿⣿⣿⣿⣿⣿⡯⠟⣽⢛⣯⣭⣦⠀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⢿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠴⡩⠁⢀⡀⡀⠀⢹⡿⣿⣿⣾⣿⣭⣦⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷
⠠⠤⠀⠁⠀⠀⠉⣿⣿⣿⣷⣿⣿⣯⡥⣦⣬⣄⡀⢠⣦⣤⣀⣀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠘⡛⠀⠀⠀⠀⠀⣠⣼⣿⣿⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠘⠁⠁⠀⠀⠀⠉⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢦⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠛⠄⠀⠈⠙⠙⠻⠀⣿⠍⠘⠁⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣶⣿⣿⣿⣿⣿⣿⣿⡿
⢺⣧⣀⣀⣀⣀⣀⢸⣿⡛⠩⣿⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⣩⣭⣿⣿⣿⣿⡿⢁
⣮⠧⣿⣿⣿⣿⣿⢈⣿⢩⡀⢺⣖⣠⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣄⠀⢸⣷⡀⣈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣭⣿⣿⣿⠿⠛⠀⠀
⡀⠀⣿⣿⣿⣿⣿⣴⣿⡷⠀⡾⠿⣿⡰⠇⢦⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡤⢿⣿⣿⣿⣿⣷⣆⠀⠀⣀⣄⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀
⠁⠀⣿⣿⣿⣿⣿⣷⠖⠐⢄⣠⠀⠀⠀⠰⣤⣷⡦⠖⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡷⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⢄⣴⣂⣐⣗⡪⠄⠁⢠⠮⠀⠐⠛⣹⠂⠀⠀⠀⢠⡀⠓⢫⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⠛⠋⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣴⣦⣾⣴⣾⣿⣿⣿⣿⠤⠀⠄⠀⠤⣷⣶⣶⡆⠀⠁⠉⠉⠉⣉⣵⣅⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣤⣀⢀⣤⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣂⣦⣤⣤⣤⣶⣾⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⣻⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣠⣿⣿⢻⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
[16A⣿⡇⠀⠹⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣩⣽⣿⠉⣙⣃⠀⠀⠀⠀⠀⠀⢻⡀⢨⠀⠀⠀⢽⢿⢿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣤⣄⠀⠉⢿⣿⠇⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣼⡟⠀⠀⠠⢤⠀⠀⠀⠙⠛⠀⠀⠀⠀⠘⠂⠙⠛⠃⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⢻⡜⢿⣿⡇⠀⠈⠁⢀⣽⣿⣿⣅⠀⢩⣽⠿⢿⣿⣛⣿⣿⣿⡿⠿⣹⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠉⠙⠛⠁⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠟⣿⢛⣯⣽⣶⡀
⠀⠁⠀⠛⠻⠀⠀⣴⣿⣿⣿⣿⣿⣿⠢⠀⠀⠀⠸⠋⠉⠉⠉⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠀⠈⡿⠖⠀⠀⠀⢨⢙⣿⡿⠿⠭⣃⣠⣿⠄⣂⣈⡌⢕⣴⣾⣿⣿⣭⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢀⡈⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣄⣠⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⡆⠀⠀⠀⠨⣶⡇⠘⠛⠿⣿⠉⣷⢾⡗⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⢲⡀⠀⣀⣠⡀⠟⢿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣯⡄⠀⣿⣶⣶⢶⠇⠀⠀⠀⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⡿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠉⣻⣆⣈⣛⣂⠀⠀⣿⣿⣿⣿⣟⠉⠀⠀⠈⠙⠈⠁⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣍⣩⣭⣿⣿⣿⣿⡿⠣
⠁⣀⣿⣿⣿⣿⣿⠀⠀⢻⣯⢷⢝⣿⠠⠤⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⣄⠀⠠⣶⡄⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣭⣿⣿⣿⡿⠛⠁⠀
⣴⣟⣿⣿⣿⣿⣿⢸⣄⣼⣿⡐⠢⣿⣥⠶⠿⢶⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠋⠉⠀⠀⠀⠀
⣿⣷⣿⣿⣿⣿⣿⢿⣿⣞⡛⠃⠀⠀⠀⢶⠙⡈⢵⣂⢀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⣶⣷⣶⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣀⣿⣿⣿⣿⣿⣉⡿⠟⢉⠁⠂⢀⣀⢰⢀⠙⡾⠟⢛⠀⠀⠀⠈⠐⣒⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⢙⡛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠉⣿⣿⣿⣿⣿⣭⣽⣾⣯⣶⣾⣿⣿⣭⡎⣟⣕⡠⠀⡀⠌⠀⠀⢀⠹⢶⠎⠟⠛⠛⠛⠛⠛⠛⣉⣅⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠻⢽⣸⣿⣿⣿⣷⣤⣤⣴⣶⣶⣿⣿⣛⡂⢀⣀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⣢⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⣀
[16A⣿⣿⣿⠟⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣇⣿⣿⣿⡥⣧⣿⣿⣿⣇⠀⠄⠀⠀⠀⠘⣿⠄⢰⠆⠀⠀⣿⣿⣿⣄⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⠀⠉⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⠁⢼⣶⠂⠀⠀⠀⠀⠀⠘⣷⡼⠀⠀⠀⣟⣸⡌⢿⣿⡇⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⣿⣧⣤⠀⠈⠚⠁⣹⣿⣍⡀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡸⠟⠋⠀⠀⠀⠛⠂⠀⡀⠀⠀⠈⠉⡁⠀⠒⠲⡦⠖⢠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢛⣯⣿⣶⡁
⠉⠉⠃⠘⣿⣷⠀⠀⣠⣾⣿⣿⣿⣷⣶⣞⠛⠋⠛⢛⣿⠿⠿⠿⠿⣻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠡⣾⣤⠤⠀⠀⠘⢿⣿⣿⣿⣿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⡀⣠⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⠀⠈⠍⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⢀⡀⠀⠉⠽⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣀⣀⣀⡀⣘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⠀⢀⣼⣏⣀⡀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⠇⠀⠀⠀⠸⠿⠿⠛⠉⠋⠟⠃⠟⠉⠉⠘⠻⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠄⣿⣿⣌⣻⣿⡃⠁⠙⣿⣿⣿⣿⣿⠻⠉⠁⠛⣿⡻⠂⠈⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣭⣭⣭⣿⣿⣿⣿⡿⠛
⣿⡆⣿⣿⣿⣿⣿⠀⠀⠠⣿⣿⣟⣿⣿⣦⢠⣤⠁⠀⠁⠀⠀⠈⠁⠀⣠⣶⣶⣦⡀⠀⢠⣶⡀⠀⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⣿⣿⣿⠟⠁⠤
⡍⣀⣿⣿⣿⣿⣿⠀⢠⣶⣸⣿⢃⡱⣾⣟⣧⣶⡄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣦⢀⣿⣿⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣼⣿⠀⠀⠈⢿⣉⢭⠰⣤⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣴⣤⣤⣤⣤⡽⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣷⡆⠀⠀⣀⢈⣛⠀⢮⣽⣶⡔⠀⠀⠀⠤⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠽⡛⠛⠿⠝⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣤⣾⣿⣿⡿⡶⡶⠍⠀⠐⢂⠶⠀⠀⠓⢳⣆⡿⠿⠿⠿⠿⠿⠟⢫⡁⠀⠀⠀⠀⠀⠙⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⣮⣥⣴⣤⣤⣷⣮⣿⣤⣀⣠⣤⣤⣴⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⢿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣦⣤⣴⣶⣶⣿⣿⣶⣶⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣾⣿⣴⣾⣷⣶⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀
[16A⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣽⣯⣿⣿⣸⣿⣷⣏⣹⣠⣿⣿⣷⠀⣀⠀⠀⠀⠀⣿⡏⠁⡇⠀⠀⢸⣿⣿⣇⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣴⣿⡏⢉⣯⡥⠀⠀⠀⠀⠀⠈⣧⣄⡇⠀⠀⢸⠯⣏⢿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣧⣄⡀⠈⠻⠋⠈⣿⣿⡋⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡇⠾⠛⠀⠀⠀⠰⠦⠀⠀⠘⠉⠀⠒⠂⠘⠩⠭⣤⡭⠭⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣿⣿⣷⡟
⠛⠛⠙⠈⢻⣿⣏⠀⠀⣠⣾⣿⣿⣿⣦⣤⠶⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⡄⠘⣤⣖⣤⡈⠀⠀⢿⣿⣿⣿⣿⣿⠟⢿⣿⣟⣿⣻⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠈⠋⠛⣀⣼⣿⣿⣿⣿⣿⣿⣿⡣⠀⠀⠀⢿⠃⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠆⠀⠀⠁⡄⠈⠉⠉⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⢀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣶⣦⣤⠀⠀⢠⣶⡐⠋⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⠀⠀⠀⠸⢿⣿⡿⠿⠟⢻⡿⢸⡿⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣈⣿⣯⣛⣦⡷⠚⠉⢻⣿⣿⣿⣿⡿⡟⠋⠹⢿⡿⠶⠀⢺⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⡿⠿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣭⣭⣭⣿⣿⣿⣿⡿⠓
⣿⣷⣿⣿⣿⣿⣿⠉⠁⢠⢸⣿⣿⣿⣿⡧⠠⢠⠀⠈⠑⠀⠀⠈⠻⠀⣠⣶⣶⣤⡀⠀⢠⣤⡀⠀⢺⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⣿⣿⡿⠟⠁⠀
⣿⠛⣿⣿⣿⣿⣿⠀⠀⣼⠄⣿⡟⠾⢽⡿⠗⣫⣅⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣦⣸⣿⣿⣴⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠁⠀⠀⠀⠀
⣡⣾⣿⣿⣿⣿⣿⢠⣤⣿⣏⣿⠁⠀⠈⢿⣛⢭⡃⣄⡀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⣔⣀⣀⣠⣤⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣙⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡅⠀⠀⣀⠀⠛⠇⣵⣈⣷⣀⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⠿⠛⠛⢩⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣬⣤⣼⣿⣿⡿⣧⣤⠝⠉⠀⠀⢠⡄⠀⠴⠾⣥⡿⠿⠿⠿⡿⠿⠟⢻⣭⠀⠈⠚⠛⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡽⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣟⣮⣴⣶⣦⣒⣁⣀⣠⣴⣬⣹⣇⣀⣀⣀⣤⣴⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣛⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣶⣄⣤⣄⣀⣤⣤⣼⣷⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⣦⣤⣴⣿⣯⣭⣯⣤⣾⣷⣆⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡏⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⠏⠀⠇⠀⠀⠀⢻⣾⣧⡄⠀⠀⠀⣸⣿⣿⠿⣿⣿⠀⠀⠀⠀⣆⡀⠀⠀⠩⠻⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣥⠶⣾⡿⣿⡇⠠⠇⠀⠀⠀⠈⢿⠂⢰⡇⠀⠘⣿⢿⣿⣶⣯⣛⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣁⠀⠁⠉⢻⡿⡏⣿⣿⣿⠿⢿⣿⣿⣿⣩⣽⣿⣿⣿⣿⣿⣿⣴⣿⠛⠁⠀⠒⠂⠀⠀⠀⠀⠀⠘⢿⡮⠀⠀⠀⣿⣾⠌⠻⠿⠿⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⡏⢿⣷⣦⡄⠀⠃⢀⣿⣿⣮⡄⠀⠉⠉⣿⣿⢿⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⠁⠀⠀⠀⠀⠛⢁⣀⡸⠖⠒⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠀⠀⠀⢹⣿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⠭⠛⣿⡻⠿⠻⣿⠟⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠸⠁⠘⠾⣷⠆⠀⠀⢘⣻⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠿⠀⠀⠀⠀⠀⠉⢣⣼⣿⣿⣿⣿⣿⣿⣿⣯⢝⠀⠈⠀⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣀⣀⣀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⣀⣐⣶⣦⣤⣤⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣴⣂⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣾⣿⣿⠇⠀⠀⠀⠘⠋⠋⠉⠁⠀⠙⠁⠛⠋⠉⠛⠛⠏⢻⣿⣯⣭⣭⣿⣿⣿⣿⡿⠋
⣿⣯⣿⣿⣿⣿⣿⠝⠷⣿⠏⠩⣿⣿⣿⣿⣿⠿⠁⠀⠙⠉⠙⠃⠀⠆⣠⣶⣶⣤⡀⠀⢠⣤⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⣿⣿⡿⠋⠁⣠
⣿⣿⣿⣿⣿⣿⣿⠄⠀⠴⠀⠔⢿⣿⡿⠿⡿⣧⡀⠄⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣆⣼⣿⣧⣠⣶⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⢱⣼⣀⣀⣠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⢠⣧⠀⡀⠀⢨⣿⣥⣴⣶⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣀⣤⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠳⣿⣿⣿⣿⣿⠀⣠⣾⣿⡇⠀⠀⠀⠸⠛⢯⣜⠲⣛⠀⠀⠀⠀⠀⡨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⢿⣿⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⣤⣿⣿⣽⣿⣿⣬⣷⣶⣦⣤⡍⠘⠷⡾⠶⠌⠀⠀⠛⠓⠻⠿⠿⠿⣿⠿⠿⠟⢯⣯⠀⠀⠀⠉⣉⡀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢃⠑⠀⠀⣀⢀⠠⠓⠀⠈⠉⡁⣀⣀⣀⣤⣴⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣧⣬⣻⣿⣾⣾⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡶⣒⣀⠀⠀⣴⡶⠿⣷⠟⠻⣇⣀⠩⣽⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣺⣷⣶⣶⣷⣶⣿⣿⣿⣷⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠁⠃⠀⠀⢻⣇⢻⡌⠛⠁⠀⠉⢿⣾⣿⣿⣿⡇⠀⠀⠀⢈⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⡟⣿⣿⡿⠟⠗⢸⣿⣿⡁⠈⠃⠀⠀⠀⢿⣾⠓⢀⡀⠀⢰⣼⣿⣟⠸⡿⡇⠀⠀⠀⠈⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡋⠁⠈⠓⢽⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡍⠉⢹⣍⣽⣿⣿⣿⡿⠚⠋⠉⠉⠙⠃⠈⠁⡀⠀⠀⠀⢯⣠⠹⠁⠀⢨⡟⣟⢻⣿⣾⡇⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⢿⣶⣄⡀⠀⠹⡙⠈⣿⣿⠏⠉⠻⡿⡿⣿⣿⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡀⢠⡌⠝⠁⠠⠀⣸⠛⠛⣀⣉⣉⠁⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠛⠹⠛⠈⠃⠹⣿⣯⠀⠀⣤⣶⣿⣿⣿⣦⣤⣦⣼⣿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣶⠆⠀⠀⣀⠀⠀⠒⠀⠀⠀⣠⠀⠣⣰⣶⠈⠁⠀⢿⣿⣿⣿⣿⣿⣿⡛⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣀⠀⠀⠀⠀⠛⢿⠃⣸⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠰⠗⠛⠋⠁⠀⠀⠀⠀⠀⢄⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⣤⠀⠙⠛⠀⠀⠀⠦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⣉⣛⣀⣀⣀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣶⣶⠆⠀⠀⠀⠹⠿⠿⠙⠛⠙⠿⠃⠿⠛⠿⠿⢿⣿⣯⣭⣭⣿⣿⣿⣿⣿⠿
⣤⡷⣿⣿⣿⣿⣿⣿⡝⢿⣼⣯⣏⢿⣿⣿⣿⣿⣿⣿⠟⠈⠳⠿⣤⠀⣴⣶⣶⣤⡀⠀⠀⣤⡀⠀⠀⣾⣦⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠁⠀
⣶⣿⣿⣿⣿⣿⣿⢩⣟⠐⠋⠽⠦⠸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⢤⣿⣿⣄⣤⣽⣿⣽⠦⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣀⣀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠈⠟⠀⢽⡯⠖⣀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡓⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠉⠀⠂⢀⣄⡀⠀⣈⢣⠁⣿⣿⡛⣟⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡜⢿⣿⣿⣿⠿⠗⠋⠉⠉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣿⣿⣿⣿⣿⣥⣤⣼⣿⣿⣿⣿⣽⣥⣌⣁⠙⠻⠂⣀⢀⣄⡀⠤⠀⣈⡿⠿⠿⠿⠿⠿⠟⠛⣩⣵⡆⠀⠀⠉⠉⠉⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠈⠋⠉⠁⠀⣤⡀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⣆⠀⠀⠀⠀⠐⠒⠀⠀⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡇⠀⠀⣤⣦⣔⣖⣞⣧⣂⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣏⣡⣀⡀⠀⠀⠀⣀⣼⣿⣫⣿⡇⠉⠩⢼⣭⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣤⣄⣤⣤⣀⣀⣀⠀⣀⣀⣰⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣿⣷⣶⣶⣿⣿⣿⣭⣴⣿⣶⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠘⢿⣇⢻⡟⠿⠿⡛⠟⢯⣟⣿⣯⣿⡿⠁⠀⠀⠁⠂⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣧⢰⣾⣿⠏⠀⠄⠀⠀⠀⢻⣿⠧⠄⠀⠀⢠⣼⣿⣟⣻⣿⣷⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣧⠈⠉⠯⢹⡝⣿⣿⣿⣿⣿⣯⣼⣿⣿⠍⠍⠍⢶⣿⣷⣸⡿⠛⠋⠁⠈⠉⢻⡶⠀⠦⠀⠀⠀⠈⢟⠀⢰⠃⠀⠘⡿⠿⢿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⢻⡿⠘⣿⣿⡟⠛⢿⣿⣿⣷⣶⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⡘⡿⠆⣀⠀⠀⢧⠿⣾⠟⠿⠟⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡯⠽⢻⣿⡟⣏⢿⣿⣶⡤⠀⢣⣴⣿⣿⣶⣤⣬⣤⢉⣿⣿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠰⢿⠇⠀⠀⠀⠀⠙⠂⠠⠁⠀⠀⠀⠀⢟⢠⣤⠜⠓⠉⣽⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡙⠛⠁⠀⠀⢀⠀⠉⠀⢿⣿⡇⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⢛⣿⣿⠃⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠘⠀⠈⠳⠿⠂⠀⠀⢈⣩⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣴⣾⣻⣇⣀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢀⣤⣤⡄⠀⠀⠈⠻⣿⣿⡿⠿⠛⣿⡏⢸⡿⣿⣿⣿⣯⣯⣭⣿⣿⣿⣿⡿⠛
⠀⢀⣿⣿⣿⣿⣿⠺⣶⣶⣶⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⠷⠘⢦⣴⣮⣶⣿⣷⣦⡀⠀⠀⣶⣄⠀⠀⢰⣦⢄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⡿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠛⠁⠀
⣬⣉⣿⣿⣿⣿⣿⠀⢙⣿⠮⠿⠿⠗⠸⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⣿⣿⣦⣤⣼⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⢉⡩⠋⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠀
⣛⣿⣿⣿⣿⣿⣿⣄⣸⡿⠀⠀⠀⠀⠀⢿⡿⠛⣻⣯⠄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⣀⠀⠀⣀⣀⣿⣿⣿⣿⠥⡖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⡀⠀⡀⢸⣗⠂⣿⣷⡶⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⠉⠋⠙⠋⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣴⣾⣿⣿⣿⣿⣏⠑⠋⠛⠶⠈⠀⠐⡀⢀⣀⠙⠻⠿⠿⠿⠿⠿⠟⠛⣭⣭⡄⠈⠈⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣳⣷⣤⡄⠀⠙⠾⠛⠒⣁⣀⠀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⡉⠀⠀⣀⣄⣀⣨⣵⣯⢁⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣠⠄⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡇⠛⢛⣽⣚⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⠯⣿⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣆⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣻⣋⣩⣷⡤⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣷⣿⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⠻⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⠟⠿⠟⡿⠏⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⠟⡏⠁⠀⠀⠻⣇⣿⠌⠉⠹⠆⠀⢻⣷⠿⣻⣿⡇⠀⠀⠀⠀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣽⣿⣿⢻⡉⠉⠀⠉⡍⢿⣿⣼⣭⣧⣈⡉⢻⣿⣿⠿⢿⣿⣿⣿⠟⠉⠉⠈⠀⠀⠘⣿⣿⡀⠈⡀⠀⠀⠀⢿⡏⠙⢀⠀⠀⢸⣿⣿⣧⣾⠿⠟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣮⡑⠀⠀⠃⢸⣞⡟⣿⣿⡿⣿⣿⣿⣿⣯⡀⢸⣿⣿⠏⠀⠀⠀⠀⢀⣀⠀⠀⠛⠃⠈⠁⡀⠀⠀⠈⢶⣤⡚⠀⠀⢸⣦⣏⣻⣿⣿⣦⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⡿⠿⣿⣿⣿⣿⣿⣶⣤⣀⡀⢹⣄⣼⣿⣦⡤⣬⠙⠛⢫⣷⣿⣿⡏⠀⠀⠀⠀⠀⠘⠿⠀⠰⣿⢰⢠⡄⠁⣄⠀⠰⠆⠀⠈⠃⠠⡬⠉⠈⣿⡤⠲⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⡹⣃⣀⠈⠉⠛⠟⠻⠇⠻⣿⣿⠃⣠⣿⣿⣿⣿⣿⣿⡀⣄⣸⣿⢿⡟⠀⠀⠀⠀⠀⠀⠹⠗⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣟⠀⠀⠀⠛⣻⣿⣿⣿⣿⣯⣬⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢠⣤⣀⣀⣀⣄⡄⠀⠀⠀⠛⠟⣨⣿⣿⣿⣿⣿⣿⣿⡷⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⠿
⣠⡾⣿⣿⣿⣿⣿⠃⠀⣠⡀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⢀⣠⣾⣿⣷⣦⡀⠀⢠⣶⣄⠀⠀⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣴⣷⣿⠃⠀⠀⠀⠈⠋⠉⠈⠁⠀⠀⠁⠘⠉⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠛⠛⣿⣿⣿⣿⣿⠄⠀⠼⣿⣽⠷⣿⣿⠏⢻⣿⣿⣿⣿⠉⠋⠁⠀⢻⣿⣿⣿⣿⣿⣧⣸⣿⣿⣦⣴⣼⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠀⠀
⠤⣤⣿⣿⣿⣿⣿⣶⡄⠀⣸⣏⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣀⣠⡀⠀⣅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣠⣿⣿⣿⣿⣿⣉⣑⣶⡿⠅⠀⠀⠀⢀⡈⣿⣃⢠⣾⠀⢀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣻⣿⣿⣿⣫⣿⣞⡙⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣴⣦⣿⣼⣿⠆⠘⠛⠀⠀⠄⠀⠀⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡭⠉⠉⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠦⡀⡀⡀⠀⠠⣄⣶⣤⡀⠀⢀⣀⣈⣉⣉⣉⣉⣝⣛⣙⠿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡾⠿⠛⠀⠀⠈⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⣿⣿⣿⣿⡿⠂⠛⠁⠀⠀⠀⢸⣿⣾⣿⣿⢻⠿⠿⣃⣖⢠⣯⣷⣿⣿⣿⣿⡿⠿⣯⣿⣿⣿⣿⢿⣿⣿⣿⣯⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣷⣿⣿⣷⠶⠴⠶⠶⣶⣶⣿⣷⠟⣷⡀⠀⣚⣷⣾⣾⣿⣿⣿⣿⢿⣿⣯⣶⣿⣿⣿⢹⣯⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⡀⣀⠀⠀⣠⡀⣠⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⡿⠃⠀⠙⢿⡆⢿⠛⠿⢋⡙⠛⢷⣽⣿⣿⣿⡻⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣭⣥⡙⠙⣿⣿⣟⠛⠉⠉⠉⡙⣿⣿⠹⠉⡉⠙⠻⢛⣯⣭⣿⣿⣿⡿⠟⠛⠋⠁⠈⠀⠀⠹⣿⣿⠁⠃⠀⠀⠀⠈⢿⡜⠡⠀⠀⠀⢠⣼⣿⣏⣠⣿⣿⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⣽⠛⣿⣿⣿⣷⣿⣦⣐⠃⠀⠀⠀⢳⣹⡟⣿⣿⣿⣿⣶⣾⣿⡿⠩⣿⡿⠃⠀⠀⠀⠀⢠⣤⡄⠀⠉⣹⡗⠀⠂⠀⠀⠀⠈⣅⣀⠰⠀⠀⢸⡋⡙⢻⣿⣧⣄⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⢿⠇⠉⣿⡿⣿⣿⣿⣿⣶⣤⣄⠀⠈⣷⡅⣿⣿⣥⡍⠛⠿⠟⠒⢾⣿⡏⠀⠀⠀⠀⠀⣈⣿⠃⠸⠂⣤⢀⢀⡀⠂⠀⠀⠀⠉⠛⠠⠄⢀⣐⠾⠛⢾⢋⣛⣋⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠀⣀⣁⣀⣃⣿⡿⣿⡟⢿⣿⣿⠂⢈⣾⣿⣿⣿⣷⣀⠀⡀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠘⠟⠼⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢉⣠⡴⠈⠁⠀⠿⢻⣿⣿⣿⣿⣛⡛⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣃⣉⣙⣉⣀⠀⢀⠀⠁⠈⠿⡿⢰⣿⣿⣿⣿⣿⣿⢫⣤⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠂⠐⢟⢈⣯⣏⣯⣷⣿⡯⢻⣿⣯⣭⣭⣿⣿⣿⣿⣿⠋
⠉⠁⣿⣿⣿⣿⣿⠛⠏⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⠉⣫⡤⠀⣴⣿⣿⣷⣄⠀⠀⢴⣶⡄⠀⠀⢸⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣤⡄⠀⠀⠀⠀⠁⠁⠉⠓⠉⠉⠁⠈⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠶⢿⣿⣿⣿⣿⣿⣀⡀⠐⠦⣴⡶⡶⠸⣟⠟⢿⣿⣿⣿⡇⠙⠿⠓⣹⣿⣿⣿⣿⣿⣤⡌⣿⣿⣦⣦⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠀
⡀⠀⣿⣿⣿⣿⣿⣿⣥⡄⠀⢙⠁⠀⠀⠛⠀⢸⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠈⣿⣿⣿⣿⣿⣿⠟⠡⣤⡖⠀⠀⠀⠀⠀⠸⣿⠟⢙⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣯⣥⣤⣤⣤⣤⣿⣼⣿⠐⠸⠄⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠯⡀⠀⠀⠀⠀⢀⠀⣦⣀⢀⣈⣉⠛⠻⢿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣁⡀⢀⣴⣶⠆⠀⣀⠙⠛⢉⣥⣿⣿⣿⣿⣿⣿⣹⣿⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣾⣿⣿⣿⠋⠿⠋⠀⠀⠐⢻⣯⣱⣤⡾⢿⣻⣿⠋⡄⢀⢷⣭⣶⣶⣶⠦⢙⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⡶⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣷⣴⣴⠶⠶⠖⣀⣸⣿⣿⣿⡇⠉⠩⢾⣌⣧⣼⣿⣿⣿⣿⣿⣤⣽⣿⣿⡏⣿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣯⣅⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣏⢻⣿⣯⣿⣿⣿⠿⠛⢿⣿⡿⠿⠛⠛⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣄
⣿⣿⡟⢻⠭⠌⠉⠉⣿⣿⣿⣿⠉⠉⠙⠉⢿⣿⡯⡙⠋⠀⢨⣿⠉⠹⣿⣿⣿⣿⠟⠉⠉⠀⠀⠁⠙⠛⢟⣿⡿⢿⠃⠀⠀⠈⢿⡈⡧⠈⠁⠐⠀⠀⢻⣟⠟⠻⣿⣆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⠽⣿⣻⣿⣿⣶⣶
⠝⠿⠉⠻⣿⣿⣦⣤⣼⡉⠋⠉⠀⠀⠀⢀⡸⣿⢩⣥⣤⣤⣀⡀⢬⣾⣿⣿⣿⠋⠀⠀⠀⠀⢠⣤⡄⠀⠘⢿⣇⡀⠀⠀⠀⠀⠈⢿⠈⠐⡀⠀⠀⢾⠟⣿⣶⣜⡋⠉⠀⠀⠀⠀⢴⣯⣭⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠠⣷⣽⢼⣿⣿⠛⢿⣿⣿⢹⣿⣿⠁⠀⠀⠀⠀⠀⢀⣹⠁⠘⠁⠀⠙⠁⠈⠀⠀⠀⠀⠘⣖⡆⠁⠀⠀⢐⣤⢄⣿⠿⠿⠇⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠃⠀⣀⣠⣛⣿⣿⣿⣿⡿⣿⣷⣦⣄⠘⢏⣼⣿⣿⣀⠀⠀⠉⠘⡿⠋⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⣘⡇⡆⢴⠈⠁⣀⠀⠠⠀⠀⠈⠀⠲⠎⠁⡀⠻⠉⢱⣶⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⢲⣤⣤⣈⣿⣿⡿⠟⠛⠁⠻⠈⢿⣿⡇⣴⣿⣿⣿⣿⡿⣷⠆⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⡍⠀⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠲⣻⠃⠀⠀⠀⠁⠀⠋⠛⠛⠁⠀⡀⣿⣯⣭⣭⣭⣿⣿⣿⣿⡿⢁
⣿⠿⣿⣿⣿⣿⣿⠀⣀⣠⡅⠀⠀⠈⠙⣵⣿⣿⣿⣿⣿⠗⠨⣵⠶⢺⣿⣿⣿⣄⠀⠀⢠⣶⣦⠀⠀⠀⢹⣿⣷⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀
⢺⣇⣿⣿⣿⣿⣿⠛⠋⠘⠃⢰⡦⠀⣀⠊⣿⣿⣿⣿⣿⣦⣠⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣇⣄⣠⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣆⣾⣿⡿⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠀⠀
⠉⠈⣿⣿⣿⣿⣿⣤⢦⣤⠄⠀⠀⠀⠈⠀⣸⡄⠀⣿⣿⢿⣟⠛⠉⠘⠻⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⣿⣿⣿⣿⣿⣾⣾⣿⡖⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⢹⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⠿⠿⠿⠿⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡛⠀⣿⣿⣿⣿⣿⣿⣿⣯⣥⣼⣶⣦⣤⣤⡄⣠⡀⢹⡋⠀⠙⣷⣄⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⡟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡧⠘⠁⠀⠀⠈⠙⣿⣷⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⠏⠀⠀⢀⣀⣀⠀⠸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣿⣟⢃⣤⣶⣿⡿⢿⡟⠋⠁⠀⢠⡽⠏⠛⣓⣶⢧⣼⡿⠛⠋⣰⠫⠍⠀⢸⡏⠉⢩⣛⣛⡿⣿⣿⣿⣿⣷⣙⣄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⢿⣿⠿⣿⡿⠶⠾⠷⠖⠀⠀⠠⣯⡶⣿⡏⠹⠲⢛⡡⣬⢀⣭⣿⣿⣿⣿⡀⢤⣼⡇⢻⠃⠈⣿⣿⣿⣿⣿⣯⣴⣿⣥⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⣿⣿⣿⣈⠈⠻⡉⢻⣿⣿⠉⢤⠁⠀⠈⣹⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠛⠀⠀⢹⡆⢸⠚⠛⠃⠛⠋⠁⣬⣿⡿⣋⣁⡀⠂⠈⠻⣿⣿⣿⣿⣟⠯⠹⡿⢛⣯⣭⣶⣶
⣿⣿⠋⠹⢻⣥⣦⡀⠀⠘⠻⠿⠿⠇⠀⠀⠀⠀⢿⣿⠤⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣤⡄⠀⢹⣿⡍⠑⠀⠀⠀⠀⢹⡄⠁⢀⠀⠀⠀⣤⠹⣯⣄⢨⡝⠇⠀⠀⢴⣯⣭⣦⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿
⠉⣿⠀⠀⠀⠙⢿⣿⣿⣧⣤⣤⣤⣤⠀⢀⣤⣤⣼⣧⣿⣿⡿⢷⣦⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⡀⢈⠃⠐⠀⠛⠤⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⢀⠈⠶⣷⣦⣤⡀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠹⣿⢋⣿⡏⠀⠀⠙⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⣀⡀⠀⣀⠠⠄⠀⠀⠈⠘⠀⡤⠀⠀⠲⠛⠰⣯⠉⢉⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣀⣈⣉⣀⣹⣿⣿⣿⣿⡿⢻⡝⢿⣿⣿⠂⣨⣾⣿⣿⣦⡀⠀⠀⠍⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠲⢠⠄⠋⠀⠀⠒⠄⠀⠀⠀⠀⠀⠉⣀⣰⠀⠀⠀⠘⠛⠛⠛⠛⠋⠉⢻⣯⣭⣭⣭⣽⣿⣿⣿⡿⠁
⠀⣴⣿⣿⣿⣿⣿⠙⠛⠻⠉⠩⠀⠁⠈⢿⣿⣼⣿⣿⣿⠍⠉⠙⠉⢀⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⣿⣧⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣽⣿⣿⣿⡿⠋⠀⠀
⢸⡟⣿⣿⣿⣿⣿⣀⣀⣴⡤⢴⡆⠀⠀⣀⣺⣿⣿⣿⣿⠢⠀⠈⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠸⣿⣝⠀⠀⣠⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⡀⡀⠈⢁⡀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠀⠀
⢸⣇⣿⣿⣿⣿⣿⣭⣯⣤⣴⣶⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⣿⠿⣿⣿⣷⠀⡀⣠⣿⣿⣿⣷⣿⣿⣿⣿⠻⠻⠿⣿⡿⠿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣇⣿⣿⣿⣿⣿⠿⠿⣟⢛⡇⠀⠀⠀⠘⠛⠛⠟⠁⢸⠀⠀⠂⠀⠀⠁⠀⠈⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢣⣤⣄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣾⣧⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⠀⠀⠇⠀⠀⠀⠀⣛⠊⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡲⡇⠀⠀⠀⠀⠀⠀⠀⢈⣀⢘⣆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⣿⠛⢋⣻⣿⣿⣿⠷⠆⠀⠀⠻⣷⢶⣏⢉⡀⠀⣽⣿⡿⠆⣀⣙⠛⠛⡏⠉⠛⠛⠛⠿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠾⣿⣿⣿⣿⣿⣿⠿⡷⠀⠀⠀⠀⡀⢈⣠⣴⠿⣋⣻⡟⠉⠀⢺⣮⣡⣤⣆⡀⠀⠀⣰⠁⡖⠀⠉⣿⣿⣿⣿⣧⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀
⣿⣿⣤⣿⣽⣿⣿⢿⠿⠻⣿⣿⣿⣇⡉⠩⡏⠙⣿⡻⡏⠁⡄⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠇⠀⠉⣿⠈⣯⠽⠚⠹⠟⠛⢡⣝⣿⣿⢛⣂⠠⡍⠻⣿⣿⣿⣿⡟⠧⠙⣿⢛⣯⣭⣦⣤
⣿⣿⡟⠻⠿⣟⣉⡁⠀⠀⠿⣿⣿⣿⠃⠀⠀⠀⢺⣿⣇⡄⠁⠀⠀⣼⣿⣟⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣤⡄⠀⣿⣿⠉⠇⠀⠀⠀⠈⣇⠘⠀⡀⠀⠀⢀⣌⣿⣍⡈⢹⣿⠁⠀⢴⣯⣭⣦⣿⣤⡿⣿⣿⣿⣿⣿⣿⣿
⠿⢻⠀⠀⠀⠙⠻⣿⣷⣶⣤⣤⣤⣤⡤⠀⢤⣤⣤⣿⣵⣶⣶⣶⣤⣤⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠛⢻⠤⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠈⠉⠸⢽⣯⣭⣀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠸⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣯⣀⠈⠘⢿⣿⢻⣿⠋⠀⠘⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠼⠃⢼⣏⣛⣛⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣀⣀⣛⣋⣙⣷⣿⣿⣿⣿⡿⢿⢻⣿⣷⣦⠈⣣⣿⣿⣦⡀⠀⠐⣟⡻⢟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡇⣬⠸⠇⠀⠀⠠⠀⠀⠀⠀⠀⠐⠂⣀⣤⠈⠁⠀⠿⠛⠿⠿⠿⠛⢻⣯⣭⣭⣭⣽⣿⣿⣿⡿⠁
⠀⢀⣿⣿⣿⣿⣿⠘⠿⢿⠟⠛⠇⠘⠀⢹⣿⣇⣾⣿⣿⡿⠯⠉⠒⢲⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⡆⠀⠀⢘⣿⣇⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣽⣿⣿⣿⡿⠋⠀⠀
⠀⣼⣿⣿⣿⣿⣿⣤⣄⣐⣠⣤⣀⣐⣠⣤⣾⣿⣿⣿⣿⠋⠀⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⡅⠀⠀⣸⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣼⣄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠈⢻⣿⣿⣿⡿⠿⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⡀⢀⡀⣼⣿⣿⣿⣶⣿⣿⣿⣏⠛⣿⠟⠛⠋⠉⠉⠀⠀⠀⠀⢰⣿⣼⣿⣿⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢹⣿⣿⣿⣿⣿⠋⠽⢿⡧⠄⠀⠀⠀⢸⠀⠀⢈⠁⠀⠀⠀⠠⠀⠀⠛⠀⠀⠙⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⠀⢰⣆⡀⠀⠀⠀⠀⠀⠘⠟⠛⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣈⣿⣿⣿⣿⣿⣴⣶⣶⣷⣿⣧⣤⣤⣷⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⠀⠀⠀⠀⠶⠶⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠅⠀⣀⣀⠀⠀⠀⠐⡎⢁⠈⢂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⠟⠛⣿⣿⣿⣿⣤⠄⠀⠐⣾⡯⣼⡛⠁⠀⢙⣶⣶⣶⢀⡉⠷⠿⢻⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣿⣿⣷⣶⣿⣿⡿⢿⡅⠀⠀⠀⠀⠀⠃⣉⣽⣿⣲⣾⠋⠉⠠⣿⣙⣁⣠⠀⠀⠀⠀⡖⢰⡆⠉⢉⣿⣿⣿⣿⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂
⣿⣿⡋⠉⢉⡙⣿⣿⣿⣏⣿⣿⣿⣍⣉⠉⠉⣉⠙⣛⢿⡏⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⠈⠛⣿⡟⢿⢛⣿⠛⣿⠿⠛⠹⣿⣿⡿⠯⠙⣻⣿⣿⣿⣿⡟⠧⠙⠹⢛⣯⣭⣦⠀
⣿⣿⡇⠀⣼⣿⣿⡿⠻⠋⠁⣹⣿⣿⠵⠆⠀⠈⠀⢹⣇⣇⠀⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠠⣤⡄⠀⣿⣿⡿⠀⠀⠀⠈⣇⠸⠀⠀⠀⠀⠀⠀⣻⡷⠊⠳⢶⡖⣼⣯⣭⣤⣿⣤⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⠀⠀⠀⠻⣦⣶⣦⣤⣬⣽⣭⣼⣤⠤⣤⢤⣤⣿⢿⣅⣄⣀⣀⣻⣿⣿⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣈⠁⠀⠻⡀⠀⠀⠀⠀⠀⠸⠆⠀⠐⠀⠀⠰⠛⠋⣛⣿⠐⠃⠁⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⡉⠀⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⠻⣿⣿⢸⣧⠙⠉⢻⣿⣿⣿⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⣀⣶⠈⡿⠿⠿⠆⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠁⢀⣀⣠⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⣄⠙⢏⣸⣿⣀⠀⠀⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⡀⣦⠐⠀⠀⠀⠀⠀⠀⠃⠀⡤⢈⢀⠈⠛⠀⢸⡿⢿⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⡿⠁
⠀⠀⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⡯⠸⠌⢿⣿⡏⣴⣿⣽⣿⠟⠷⢠⣿⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⡆⠀⠀⢸⣷⡚⠀⠀⠀⠀⠀⠁⠀⠀⣀⣠⣤⠀⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣽⣿⣿⣿⡿⠋⡀⠀
⠀⠀⣿⣿⣿⣿⣿⢛⣿⣿⣿⣥⣤⣴⣤⣶⣾⣿⣿⣿⣿⠙⠓⠀⠀⠸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣯⡅⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠁⠀
⠀⠈⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⠁⠀⠈⢻⣿⣿⡿⢿⣿⠀⠀⡀⠀⠀⣿⣿⣽⠍⠿⣿⡇⠀⡄⢠⣿⣿⣿⣷⣄⣼⣿⣿⠙⢙⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣰⣆⣴⣷⡷⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠲⠂⣿⣿⣿⣿⣿⠿⠀⠀⣀⠀⠀⠀⠀⠀⣏⠀⠀⠀⢛⠀⠀⠀⠀⢀⣿⣽⠋⠉⠛⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⢠⣄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣤⣤⣬⣭⣯⣤⣿⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆⣀⣀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠈⠀⠀⠀⣭⡄⠦⠀⢄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣶⣿⡋⠁⠀⠀⣼⡛⢋⡿⠟⠓⠢⣤⣀⣀⠁⠲⣦⣴⣖⠟⠛⠻⠿⠿⠿⢿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⣿⣿⠿⣴⣶⣾⡿⣿⡋⠉⠁⠀⠀⠙⠏⠛⡣⡶⣤⣼⠿⠟⢉⣴⢦⠌⢉⠀⠀⠀⠀⠰⠀⡦⠈⠛⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛
⣿⣿⣿⣿⣿⠛⠻⢻⣿⣿⣿⣿⣿⣿⡟⠩⠍⠉⡉⠭⣽⣿⣿⠯⠉⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠈⢻⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣽⣿⢿⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠯⠙⠹⠛⣋⣭⣤⠀
⣿⣿⣿⣿⡀⠀⢠⣀⣿⣿⣿⣴⡿⣿⣷⡄⠄⠀⠀⠄⠀⣈⢻⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠰⣶⠀⢸⣿⣿⡿⠃⠀⠈⢻⠀⢧⠘⠒⠈⠛⠉⠁⣌⣛⠻⣏⣽⣯⣭⣤⣿⣤⠿⢿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⠏⠀⠺⣿⣿⣿⣽⣥⣤⣬⣼⣷⣤⣤⡄⣤⣤⢸⣾⡄⠀⠀⡟⢹⣿⣿⡿⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣈⠀⠸⣿⠟⠁⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⣠⠼⠯⣄⠈⡛⠿⣿⣿⣿⣻⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣛⡀⡀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⣯⣻⡀⠄⣿⠲⢾⣿⣾⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⡀⠠⣶⣤⣄⡀⠹⣿⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣀⣀⣀⣻⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠁⠙⠣⠀⣿⡀⠈⡿⣿⣿⣿⣏⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⠛⠠⣬⠙⢋⣥⣤⣿⣿⣭⣭⣭⣿⣿⣿⣿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⠙⠟⠻⣯⣿⣿⣿⣿⡿⣟⣿⣿⣶⡆⠀⠐⣿⣧⣴⣦⡠⣿⣻⣿⣿⣿⣶⣤⠀⠀⠀⠀⣶⣦⠀⠀⠀⢴⣦⣤⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣆⣀⠀⠀⠘⠋⠉⠛⢻⣿⣭⣿⣿⣿⡿⠋⠀⠀
⠯⠅⣿⣿⣿⣿⣿⢀⣀⣴⡾⣿⣿⠿⣿⣶⣿⣾⣿⣿⣶⠀⠀⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣻⠀⠀⠀⢨⣿⣿⣶⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢈⣠⣤⣴⣦⣤⡄⠀⠀⠀⠙⢟⠛⠋⠁⠀⠀⠀⠀
⠿⣅⣿⣿⣿⣿⣿⢶⠿⢿⣛⣛⠁⡀⠈⢻⣿⣿⣿⣿⣿⠀⠱⠭⠄⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣄⣴⣷⣿⣿⡀⠀⠀⣿⠿⠿⢿⢿⠿⣿⣿⣿⣿⣿⣟⠿⢿⣋⣭⣙⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠲⣄⣿⣿⣿⣿⣿⠀⠀⠀⠰⠓⠂⠀⠀⠘⠛⠛⠛⠻⠛⠀⠀⠀⠀⠸⣿⣟⣿⣿⣶⡈⣻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⠢⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣾⣧⣿⣿⡏⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣿⣿⣿⣤⣧⣯⣤⣤⣤⣤⣤⣤⡄⠀⡄⠀⠀⠀⠀⠀⠀⠰⣿⣿⠷⠌⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠈⠻⠛⠿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠆⠀⠀⠀⠀⠀⠀⠀⠛⣙⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⣿⣿⣦⣄⡼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⣀⠀⣼⡯⠤⠶⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠘⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⠻⣽⠷⠖⠀⠀⡀⠀⢿⣗⣞⣛⠀⠀⠐⢶⣉⡀⠁⠈⠛⠛⠿⡿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠶⣶⠿⢷⣿⣿⡿⠿⠿⣯⣿⣿⣧⠄⠀⠀⠲⣮⢩⣼⠙⠀⠈⣳⣶⣶⠄⠀⣹⠂⠀⠀⠀⠀⠀⣤⠀⠓⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢀⠉⠉⠹⢛⢿⣿⣿⠿⠿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⡹⠛⣋⣭⣤⠀
⣿⣿⣿⣿⣿⠟⠁⠈⠘⢹⣿⡿⢉⣿⣿⣧⠉⠀⠀⠀⠉⠁⠻⢷⠀⠀⣻⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠠⣤⡄⢸⣿⣿⣿⣿⣿⡿⠈⠙⢻⡟⢛⠙⣛⡟⢋⡝⠃⠀⠿⠿⣿⣯⣭⣤⣿⣬⠿⢿⣿⣽⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣧⠀⣤⣶⣾⣿⣧⣿⣧⣽⣼⣧⣤⣤⣤⣤⠀⢲⣠⠀⠸⡟⢾⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⡍⠁⢨⣿⣿⣿⣿⡏⠀⠀⠀⠈⠅⠸⠀⠀⠀⠈⠀⠀⣸⣗⠂⠘⢿⣿⣿⣿⣻⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⡾⠀⠈⡏⡳⣠⣿⣦⣼⣻⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠋⣿⡆⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⢈⣉⠀⡈⢻⣿⣥⣶⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣛⣃⣇⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⠯⠀⠛⠀⢆⠀⣿⢸⣿⣿⣿⣿⡟⣁⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⢶⠀⠙⠻⠿⢒⣻⣯⣭⣯⣭⣿⣿⣿⣿⡿⠿
⣷⣿⣿⣿⣿⣿⣿⠡⢤⣼⣿⡿⣿⣿⣿⣿⣿⡿⣿⣶⣤⠀⠀⢀⣿⢷⣿⡋⠉⠋⢿⡿⣿⣷⣤⡀⠀⠀⣠⣤⠀⠀⠀⢰⣶⣴⡂⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⢀⡀⠀⠉⠁⠸⠿⠛⢿⣿⣭⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠸⣿⣿⣿⣿⡇⠷⠘⣿⣿⠀⠀⠀⠁⢹⣿⣿⣦⡁⣾⣿⣿⣿⣿⣿⣦⡄⣿⡿⡇⠀⠀⠀⣿⣿⣶⣿⣥⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⢁⣠⣶⠂⠀⠀⠀⠙⢟⠛⠋⠁⠀⠀⠀⠀
⢩⣥⣿⣿⣿⣿⣿⢠⣀⣲⣶⠀⠀⠀⠀⠈⠁⠀⠀⠘⢻⠀⠀⠀⠠⢸⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⠀⠀⢰⣿⠿⠽⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⡶⠶⠒⠒⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⣄⣿⣿⣿⣿⣿⢉⡙⠁⠈⠀⡀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠙⠃⠁⠀⣐⡆⣠⣴⡶⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣤⣤⣤⣤⣬⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡟⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⢿⠿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣶⣀⡀⣸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢶⠄⠀⠀⠀⠀⠀⠀⣀⠀⣰⡶⢀⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠻⡿⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣾⣿⡿⣯⣿⣟⡁⠀⠀⠀⠀⣤⣇⡼⡿⠀⠙⠋⣁⠤⠔⠛⠛⠿⣿⣿⣿⣿⣿⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠶⣿⣿⣿⣿⣿⡿⣶⣮⣟⠉⠀⠀⢄⣒⠄⣹⠿⠛⠒⢄⣀⣀⢠⠀⠀⠀⠀⠀⠀⢤⠀⠐⢶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣽⣉⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠛⢉⣥⠄⠀
⣿⣿⡟⣯⣥⣶⢾⠿⠏⠻⡿⣿⣿⠿⣿⢀⠀⠀⠀⠀⠀⠀⠘⠒⠂⢸⣿⡿⣿⣟⣠⣿⣿⠃⠀⠀⠀⠀⢀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣿⣿⣿⣏⣠⣽⣿⣿⣿⡏⠉⣿⣿⣽⣧⣿⣌⠿⢿⣿⣽⣿⡏⠀⠀
⣿⣿⣷⣿⣿⣿⠀⣤⣤⣤⣤⣿⣯⣤⣤⣤⣤⣤⣄⡠⢤⠀⠀⠀⠀⠀⡿⠉⠛⠈⣻⡟⠃⠀⠀⠀⠀⠀⠐⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⡛⣧⠉⡿⣿⣷⠖⢦⢠⣌⣿⣿⣿⣯⣙⠻⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣄⣼⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⣿⡟⠐⠚⠛⠁⠀⠀⠀⠀⠀⠀⠘⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⡃⠀⠀⢰⢹⣧⠁⠀⠀⠉⠁⠠⠿⣾⠿⡰⣿⣿⣥⣦⣴⣿⣿⣿⣿⣷⣶⡤
⣿⢿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣗⣻⣿⣿⣿⠓⣠⠀⠀⠀⠀⢸⣿⣾⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡿⠿⡷⠄⠠⣿⣷⡞⠀⠀⠀⢀⡟⢻⣄⣤⠀⠀⠀⠠⣦⣤⣰⢶⣾⣿⣫⣉⣉⢉⣽⣿⣿⣿⡟⢠
⠀⢻⣿⣿⣿⣿⣿⢁⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⠎⠁⠀⠀⠀⠀⢸⣿⣿⡿⣦⣶⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡂⠀⠀⠀⠀⠁⠀⠈⣼⣖⡈⠙⠛⣿⡿⠀⠀⠀⢐⠛⠛⠃⢤⠤⠩⣿⣿⣥⣿⣿⣿⠟⠋⠀⠈
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣙⣹⠿⠿⣿⣿⡿⡿⣷⣦⠀⠀⠀⠀⢸⣿⣷⣮⠽⠟⠛⢿⣿⣶⣀⠀⢿⣷⡀⠀⠘⣿⣿⣄⣬⣟⡗⡂⠀⠀⠿⡿⢿⣀⢀⢠⣄⡀⠀⢚⣂⣴⣄⠄⠀⠀⠀⠋⢝⣛⠛⠉⠁⠀⠀⠀⠀
⢭⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠁⠀⠀⠁⠻⠁⠸⠈⢻⠀⠀⠀⠀⢸⣿⣿⡇⠀⣄⠀⠀⠙⠻⠿⠷⠶⠾⠶⠶⠶⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠛⠛⠑⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢾⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠤⠄⣻⣿⣿⣿⣿⣤⣤⣶⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠈⣿⣿⣿⣿⣶⣤⣶⣶⣶⣾⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⣼⣿⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣯⣺⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣀⠀⢀⣀⣀⠀⠀⢀⣴⣤⠀⠀⣠⠄⠀⠀⠀⠿⣿⣿⣿⣿⡀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠁⠀⠸⠿⠿⠿⢿⠿⢿⡿⠿⠿⠿⠿⢿⢿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛⠛⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠨⠿⠀⠈⣿⣿⣶⣆⣈⣿⡿⠶⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠶⠒⠒⠀⠀⠀⠀⠀⢤⠶⣖⣐⡧⠀⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠀⠀⠀⠀⠀⠈⠻⡿⠛⠛⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⢖⣀⣀⣘⡟⢋⣩⣿⠓⠀⠀⠀⠀⠀⠐⠀⢘⠇⠀⠀⠈⠀⠀⠀⠈⠉⠉⠹⣭⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠀⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣯⣭⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣯⣭⣮⣿⣿⠿⢿⣿⣿⣿⣿⠀⠀
⣿⣿⡄⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢘⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⢿⣿⡿⠀⢶⡿⠿⠿⠯⠈⠛⣿⣿⣿⣋⠻⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣃⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣭⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠹⠀⠀⠀⠀⠀⠁⠀⠀⠦⢹⣿⣥⣤⣤⣿⠿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⣿⠻⣿⠿⠿⠿⠿⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⣁⡀⠀⠀⠀⠀⣀⠀⢀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⣭⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣷⣶⣴⣶⣶⣶⣤⣀⠀⢀⡀⣀⠀⣠⣿⣶⣦⣸⠛⠛⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠻⣦⣤⣤⣴⣾⠟⠋⣠⣿
⠋⠀⣿⣿⣿⣿⣿⠛⠷⠀⠀⠀⠢⢽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠰⠎⠉⠀
⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠓⠀⠀⡀⠈⠛⢻⢻⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⢿⣯⣀⣂⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠒⠉⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠠
⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠳⡀⠃⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠠⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣠⣤⣤⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⢭⣿⣿⣿⣿⠀⢀⣿⣿⣿⣋⣿⠋⠱⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⣠⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀
⠉⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⣿⡿⠀⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠿⠿⠿⢿⡿⠿⠿⠿⢿⣿⡿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⠒⠀⣤⣀⠀⠀⢀⣄⡀⠀⢀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢿⠁⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠛⠀⠀⠸⣿⣿⣤⣄⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠂⢶⠌⠹⠽⠶⠆⠀⠀⠀⠀⣴⣾⣯⣬⣀⠲⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠉⠛⢛⣫⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣥⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠉⠀⠀⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⠽⣿⣻⣯⣽⡶⠀
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣥⣦⣿⣿⡿⣿⣿⣿⣿⣿⡅⠀
⣿⣿⡀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠸⣿⣉⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠈⣿⣿⣿⡟⠁⣼⣿⣿⣿⡟⠛⣿⣿⣿⣿⠛⣿⣿⣿⣿⡟⠀⠀
⣿⣿⣁⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠈⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠙⠿⠃⠀⠉⠁⠀⠀⠀⠀⣹⣿⣭⣦⣔⣿⡿⠿⠁⠀⠀⠀
⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢿⣿⣿⣿⣷⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⣁⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣶⣾⣿⣿⣷⣶⣶⣤⣤⣄⣀⣤⣼⣿⣷⣬⣿⡶⠀⠀⠀⠈⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢽⣦⣤⣤⠄⠀⠀⠀⣠⣿
⠿⠋⣿⣿⣿⣿⣿⠟⠛⠧⠁⠀⠀⠌⣿⣿⣿⣿⣟⡙⢻⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢛⠛⠋⢁⡴⠟⠛⠛
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠃⠀⠀⠈⠹⠟⣿⣿⠿⠻⠀⠀⠀⠀⠀⢿⡿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣦⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠚⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢁⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣄⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡀⠦⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣹⡿⠛⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⠃⠈⣿⣿⣿⣿⢀⣾⣿⣿⣿⣿⠇⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣦⣤⣴⡆⠀⠀⠀⠀⠂⠙⠀⠀⠀
⠀⠀⠸⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⣿⢿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣽⣶⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠉⠙⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⠀⠈⢻⠆⠀⠀⣿⣷⡆⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠹⠿⠿⠆⠀⠀⠀⠀⢀⣴⣶⣂⡁⠠⡤⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠙⠉⢉⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢿⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣥⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠁⠈⠉⠁⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⠇⠉⠉⢛⣯⣽⣶⡄
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣯⣩⣯⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣟⡈⠙⢿⣿⣿⣿⢿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠛⣿⣿⠀⠰⠿⠛⠛⠁⢹⣿⣥⣾⣿⣿⣿⣿⡿⠛⠁⠀
⡟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠈⠃⠀⠀⠀⠉⠀⠀⠀⢻⡉⣁⠀⠀⠠⠞⠀⠀⠀⠀
⠦⣸⣿⣿⣿⣿⣿⣿⣿⣟⠂⠙⠉⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⣿⣿⡗⠒⢴⣶⣴⣶⣶⣶⣶⣶⣦⣠⣤⣄⢀⣠⣶⣿⣿⠻⠟⠿⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣤⣤⣶⠆⠀⠀⠀⢀
⠀⠘⣿⣿⣿⣿⣿⢽⣿⣯⡙⠶⠀⠀⠀⠸⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⠾⠛⠓⠀⢸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢀⠀⠤⠄⢈⣉
⠀⠰⢿⣿⣿⣿⣿⣿⣿⡗⠀⠠⠀⠀⠀⠦⡄⣄⡈⠉⠋⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠻⠶⣦⣄⡠⠤⣤⡤⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⢠⣤⠍⠀⠲⠶⠀⠀⠀⠀⢀⣄⣴⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢼⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⣠⣤⣌⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠂⠿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣏⣽⠿⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⣿⣿⣈⠛⢿⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⠀⠐⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠹⠿⠿⠿⠿⢿⡿⠿⣿⠿⠿⠿⠿⠿⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢿⣿⠀⢀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⣾⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⢰⣄⠀⠀⢀⣤⡀⠀⠀⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠴⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠙⣿⣧⠀⠀⠀⠚⠀⠀⠘⢿⣿⣦⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠉⠁⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⠽⠽⠛⢋⣭⣶⡀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣯⣭⣦⣿⣯⠿⢿⣷⣼⣿⣿⣿⣷
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢛⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣧⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠈⢻⣽⣿⡍⠇⠈⢿⣿⣿⣿⣥⣤⣴⣿⣿⣿⡉⠉⠉⠉
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠄⠀⠘⢿⠃⠀⠘⠃⠀⠀⢹⠉⡁⠀⠉⠙⠛⠉⠀⠀⠀
⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣻⣿⣿⠀⠀⠀⠀⠀⡿⠯⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣤⣤⡤⠀⠀⠀⠀⠀
⠀⠈⢻⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣀⠘⠉⣯⠀⢀⡄⠁⠀⢠⣶⣿⣿⠛⡿⠿⢧⡄⠀⠀⠀⠀⢨⣉⠁⠈⠉⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⣀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⠌⢩⣾⣿⡿⠁⠀⠀⠀⠈⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠗⡎⠀⣴⣢⠀⣠⣿⣿⣿⣿⣇⣷⡄⠀⢘⣶⣆⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠛⠋⢿⣿⣿⣿⣿⣦⣾⣿⣿⠀⠀⠀⠀⠀⠀⠒⠸⠿⠿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣀⣀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣶⣾⣿⣿⠻⣿⣿⣿⣷⠀⠀⣸⣿⣿⡋⣹⣿⠷⠚⣿⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠻⢿⣿⣿⠃⠀⢽⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⠁⠋⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠽⠿⠿⠿⠿⠿⣿⠿⠿⢿⠿⠿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠿⠇⢀⣾⣿⣿⣿⣦⣿⣿⣿⣿⣿⣏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣤⣄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠁⠲⣇⠈⠀⠀⠀⢳⡄⠀⠀⣴⣄⠀⠀⢴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠂⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠻⣿⢛⣏⣭⣶⡀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢓⣯⣭⣦⣿⣮⣿⣿⣿⣿⣿⣛⣿⣷
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⡟⢻⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣀⣀⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡀⠈⠛⣟⣿⣿⠻⡏⠻⣿⣿⣿⣥⣤⣄⣿⣿⣿⣿⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠻⢿⣿⣿⣿⣿⣿⣿⢿⡷⠀⠀⠙⢿⠿⠀⠀⠠⠜⠙⢻⠉⣁⠀⠈⠽⢿⡿⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⠀⠀⠀⠀⠀⣸⣻⡛⠉⠰⠟⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣤⣤⡄⠀⠀⠀⠀⠀
⠀⠀⢽⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠏⠉⠄⢠⡀⠀⠀⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀
⠀⣤⣼⣿⣿⣿⣿⠋⡱⣶⣿⣿⠁⡀⠀⠀⠀⠙⢻⣿⣿⠀⠀⠀⠀⢀⡶⠀⠀⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠀⠀⠀
⠿⠿⣿⣿⣿⣿⣿⠀⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⢀⣄⠀⠀⣼⣿⣿⣷⣤⣀⣀⠀⠀⠀⣤⣶⣀⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣄⣸⠃⠀⡀⠈⠁⠀⠀⠀⠀⠈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣾⣿⣿⣥⣿⠛⢿⠆⢤⣴⣤⠀⠀⣤⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⢀⠀⠀⠀⠀
⢀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⢿⣿⣟⠋⢻⣿⣿⣆⢀⣸⣿⣿⣿⣿⡿⠀⠀⢀⡄⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠸⠿⠿⠿⠿⢿⣿⠿⢿⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣿⣷⣾⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⢸⣆⠀⠐⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠤⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣷⣦⣤⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠋⠠⠉⠙⠛⣋⣭⣤⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢏⣁⣤⣿⣤⠿⢿⣿⣿⣿⠃⠀⠀
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⡮⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣯⣲⣿⣿⣿⢛⠻⣿⣿⣿⣿⣶⣦⣦
⣿⣿⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠑⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣤⣤⡤⠸⢿⣿⣿⡿⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣆⠀⠀⠴⢾⣿⡉⠛⠈⠛⠻⠉⠁⠀⠀⠀⠛⠛⠋⠀⠀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⣤⣬⠀⠞⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠉⠁⠀⠀⠀⠈⢿⠃⠀⠈⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⢰⣿⣿⠟⠻⣿⣿⣿⣟⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠤⣿⣇⣿⣦⣴⠿⠿⢿⠁⡀⠈⢿⡟⠛⢿⣧⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣶⣆⠀⠀⣾⣿⣟⠀⠀⠀⠀⠙⠻⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣴⣶⣭⣿⠛⠁⠠⠯⡖⡊⠀⡁⠸⠃⠀⠀⠻⣿⠀⠀⠀⠀⠀⡾⣾⡇⠀⠀⢰⣗⠀⠀⠈⠋⠀⠙⠻⡦⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣿⠿⠉⠀⣀⣀⣠⣿⣿⣟⣁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⣷⣄⢀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⡀⢀⣤⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠈⣿⣿⣿⣿⣿⣿⡏⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢻⣿⣿⣿⣿⣿⡂⠀⠀⢀⣀⣠⣶⣿⡟⠀⠀⠀⠋⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⠀⠈⠀⠀⠂⠛⢛⠛⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⢿⣿⣿⢀⢠⣽⣿⣿⣿⣿⢷⡀⠀⠀⠀⠘⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⡿⠿⠟⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣤⣄⡀⠀⠀⠀⠀
⡀⠆⠲⣶⠀⠰⠄⠠⠰⠖⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡁⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣤⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣽⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠉⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠣⠉⠹⢛⣫⣭⣦⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⢤⣷⣄⠴⢿⣿⣿⣿⣿⣿⠗
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠠⢤⠀⠀⠀⠀⠀⣦⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⣿⣆⠀
⣿⣿⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⢮⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣴⠿⠿⢿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠂⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡀⠈⠙⢛⣻⣿⡟⣿⡛⣿⣉⣁⠀⠀⠀⠈⠋⣻⠗⢀
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣶⣶⣿⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠈⠹⡿⠆⠈⠁⠀⠑⣤⡀⠀⡀⠀⠀⠀⣠⠿
⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣽⢻⣿⣿⣷⣦⡀⣠⠶⢾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠛⠛⢿⣿⠀⣘⡟⣻⣿⠁⡀⠈⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⠏⠀⠈⣽⣿⣿⣿⣿⣦⣤⣭⣿⣿⣿⡟⠀⠀⠀⠉⠙⠿⡿⠟⠿⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⢀⡈⣛⣿⣰⡿⠏⠈⡀⠀⠀⣁⢺⣿⡇⠈⠻⣿⠀⠀⠀⠀⠀⣨⡄⣤⠺⠉⣠⣤⡀⠈⠉⠙⠁⠙⠻⣿⠿⠿⣿⣿⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣸⣿⣿⣿⡁⠀⣀⣐⣋⣿⣿⣿⣯⡿⠁⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⠗⠂⠀⣩⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⡿⠻⠻⠏⠁⠐⢭⣿⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣤⣴⣿⣿⣿⣿⠀⠀⢀⣀⢁⣼⣾⣿⣿⠗⠠⠀⢰⣤⠀⠀⣤⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠓⠀⠠⠠⠤⠤⠾⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⢿⣿⣿⣿⣇⣤⢼⣿⣿⣿⣿⣿⣟⡀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠆⠀⠸⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⢇⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢶⡶⣶⠀⠶⠄⠠⠠⠖⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠛⠉⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡄⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣸⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣧⣤⣿⡟⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣟⣿⣤⠘⢿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠉⢠⣿⣿⣿⢹⣿⣿⡀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣿⣿⣷⡿⠏⠹⠿⠷⢆⣙⢛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⢿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠈⠛⠻⣿⣦⣀⡀⠀⠀⠀⠶⠟⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠙⠛⠛⢿⡿⢿⡛⢿⣿⣯⡙⠦⠀⠀⢿⣿⣿⣿
⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠙⣿⣿⡄⣠⣤⣤⡁⣉⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣄⠀⠀⠘⢿⣯⡀⠁⠀⠉⠉⠁⠀⠀⠀⠐⠛⠛⢿
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⣀⠀⡐⠲⢶⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⢿⣟⣿⢿⣿⣿⣼⡍⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⠻⠟⠋⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠝⢫⣷⡗⣶⡶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⢾⣷⣦⣀⣬⣿⣿⣿⠃⠀⠀⠀⠀⠘⠛⠿⠟⣿⠿⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠂⠉⢩⣿⣿⣿⣿⡏⠁⠙⢶⣾⣿⣿⣻⠃⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠿⠿⠿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣶⠆⠂⠉⠀⠀⠐⠸⣿⣿⡿⠹⠇⠀⠀⠈⠻⣿⣿⣻⣶⣶⣟⢾⠄⠀⠈⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣀⣀⣿⣿⠁⠀⠀⠀⡀⠀⠀⠓⠸⢱⠿⠐⠘⢷⣤⣠⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡏⠀⡀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢷⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠻⣿⣇⣀⡀⠀⠀⠀⢶⣿⣿⣿⣿⡃⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠤⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢸⣷⣄⡀⢀⣹⣿⣿⠟⠋⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⢶⣶⠁⠲⠄⠠⠠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⣶⣄⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠠⠿⠋⠁⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢻⣿⣿⣿⣿⡯⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⠷⠆⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢀⡿⢿⣦⣀⡀⢨⡉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠋⠙⠋⠀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢿⣿⣿⣿⣿⣿⣿⢯⣿⣿⡿⠟⠋⠁⠙⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠙⠷⠆⠁⠀⠀⠙⢿
⠻⠛⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣾⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠛⢯⠉⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⡈⣘⡿⠿⣿⣿⣿⣿⠿⢿⡉⠡⣿⣿⣻⣟⠁⠀⠀⠀⢠⣤⡄⢠⣤⡄⣤⡄⣤⡄⣤⣭⢠⣭⢹⣶⢢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠋⠀⠀⣾⣿⣿⡿⣯⠀⠀⠙⢿⣿⣿⣍⡋⠁⣤⣆⡆⢸⣿⡇⢸⣿⡇⣿⣷⢸⡇⣿⣿⢸⣿⠸⣿⣾⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢼⣿⠁⠀⠀⠀⠀⠀⢙⣿⣿⡶⠾⠀⠀⠀⠈⠻⢿⢿⣿⠙⠻⣝⠛⢸⣿⣷⢸⣿⡇⣿⡹⣾⡇⣿⣿⢸⣿⢰⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⢄⢬⡿⠇⠀⠀⠀⠡⠄⠀⠐⠀⠀⠛⠀⠀⠙⢿⡸⠿⠿⠸⠿⠇⠿⠇⠿⠇⣝⠿⠾⡟⠸⠿⠸⠿⢤⡄⠀⠀⢤⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠂⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠾⣶⣄⠀⢀⣿⣿⡿⠟⠙⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠾⠿⣷⠀⠶⠟⠠⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣏⣽⣿⣿⣦⣶⡇⠀⢙⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⢏⣉⠏⠹⢿⣧⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠈⠉⠁⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⡖⠈⢻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠿⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣄⡇⠀⠀⠀⠀⠿⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣶⣄⢠⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠉⠙⢛⣻⣷⠘⣒⠻⣿⣿⡀⠀⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠉⣿⣿⣿⣿⣿⠟⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣤⡀⠀⠀⠺⣿⡄⠈⠀⢀⡀⠀⠀⠀⠀⠀
⠋⠉⠛⠋⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⡉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣹⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣾⣦⣄⠀⣠⣤⡀⠀⠀⠉⠉⠉⠁⣠⣿⣿⡿⣿⣽⣿⢻⣿⣿⣿⡄⠉⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⠿⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⠇⣾⣿⠹⠏⠁⢠⣤⡄⢠⣤⡄⣤⡄⢩⡝⣧⣬⢩⣽⢱⣶⢢⣶⣶⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣁⣼⠿⠿⣿⣿⣿⡟⠉⣽⣿⣰⣜⣿⡿⢼⠶⠆⢸⣿⡇⢸⣿⡇⣿⣧⢸⡇⣿⣿⢸⣿⠘⣿⣾⡏⠙⠿⠿⠿⠟⠈⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⣾⣿⣿⠿⡆⠀⠈⠻⣿⣿⣿⢗⣾⡶⢶⢸⣿⡇⢸⣿⡇⣿⡹⣾⡇⣿⣿⢸⣿⢠⣿⢻⣧⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠙⣿⣷⡶⠶⠀⠀⠀⠘⠉⠁⢸⡿⠃⠀⠸⠿⠿⠸⠿⠇⠿⠇⠿⠇⣝⠿⠾⠟⠸⠿⠸⠿⠄⠀⣀⠀⠀⠀⣀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣀⡙⠋⠀⠀⠉⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠈⠁⠀⡤⠀⢴⣿⣿⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣴⡀⠰⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠉⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣳⣾⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢏⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⣿⣿⣿⣿⣿⣿⣿⡗⢸⣿⣿⣿⡿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣥⣈⢑⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠈⠛⠛⠛⢿⣧⠙⣂⠻⣿⣿⣇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⣶⡾⢿⡶⣾⣶⣿⣿⣿⣿⡿⠛⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⢹⣷⡄⠈⠀⠀⣀⠀⠀⠀
⣿⣿⣿⠏⢿⣿⠿⢿⡿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⡀⠀⠀⠀⠀⠙⠿⣿⣼⣇⠀⠉⣻⣿⣿⡟⠀⠀⠀⠉⠙⠻⠿⠿⠛⠛⠉⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠀⠀⠁⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣾⡇⢠⣤⡄⢠⣤⡄⣤⡄⢬⡍⣤⣭⢩⣿⢡⣤⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠛⢛⠉⢠⣋⣹⠿⢿⣿⣿⣿⠛⢻⣉⠀⢾⣿⡟⣏⣀⢸⣿⡇⢸⣿⡇⣿⣷⢸⡇⣿⣿⢸⣿⠸⣿⣾⡏⠙⢿⣿⣿⣷⣒⠖⠐⠛⠉⠉⠉⠛⠛⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠞⠁⠀⢀⣾⣿⣿⣯⡀⠀⠘⢿⣿⣾⣥⣝⣻⢸⣿⡇⢸⣿⡇⣿⡹⣾⡇⣿⣿⢸⣿⢠⣿⢻⣧⢀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠀⠈⢿⣿⣧⣬⡅⠀⠀⠀⠹⠛⢲⣿⠍⠸⢿⠿⠸⠿⠇⠿⠇⠿⠇⠙⠿⠾⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⡀⠈⠿⠟⠀⠀⠒⢀⠀⠐⠀⠘⠋⠀⠀⠉⠛⠀⠀⠀⠀⠀⠈⣣⣤⠟⠋⠓⠀⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣤⠤⢴⣄⠠⠰⠶⠆⠀⠀⠀⠀⠀⢈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⠛⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠏⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠈⠻⠻⣿⣿⡟⠻⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢻⣿⣿⣿⣿⣿⣿⣿⡦⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⣄⣀⠀⠀⠀⠀⣠⣿⣦⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠙⠿⠿⠿⣿⡏⠛⠓⢾⣿⣿⡟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣧⢼⡉⠉⠀⠀⣀⣸⣿⣿⠏⠉⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⠄⠀⠀⠀⠀⠉⠉⠀⠒⠈⠛⠛⠁⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⣀⠀⠀⠀⠈⠛⠛⠛⠿⣄⣠⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠂⠀⠀
⣿⣿⣟⠋⠀⠹⠏⠁⠁⠀⣿⣿⣿⣿⣿⣿⣯⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣷⢺⣥⡄⢠⣤⡄⣤⡄⢤⡄⣬⣭⢠⣬⢹⣿⢻⣿⣷⣿⣿⣿⣶⣶⣦⡄⣄⣠⣀⣤⣴⣾⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠟⠛⠟⣻⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⣿⣿⡿⢸⣿⡇⢸⣿⡇⣿⣷⢸⡇⣿⣿⢸⣿⠘⣿⣾⡏⠿⠿⢿⣿⣿⡿⠻⣿⠣⠿⠟⠛⠿⠿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠜⠊⠁⢀⣼⣿⣿⡟⠀⠈⠻⣷⣿⣿⡗⢷⢸⣿⡇⢸⣿⡇⣿⡹⣾⡇⣿⣿⢸⣿⢰⣿⢻⣧⠀⠀⠀⢿⣿⠿⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⣼⣿⣿⢇⢲⡄⠀⠀⠈⠻⠿⢟⣷⠸⠿⠿⠸⠿⠇⠿⠇⠿⠇⡙⠿⠾⣟⡸⠿⠸⠿⢄⠈⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠃⠹⣿⣿⡟⠓⣀⠀⠀⠀⠀⠸⠟⠁⠀⠙⠇⠀⠀⠀⠀⠀⢀⡿⠟⠁⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠰⢠⠀⠀⠀⠠⠠⠴⠆⠀⠀⠀⠀⠀⠀⠰⠤⠀⠉⠋⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⣠⣶⣿⣿⣤⡴⠆⢀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣠⣾⣏⠀⣠⠉⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⠀⠀⠀⣨⣿⣿⣿⣿⠛⠛⠋⠉⠛⠃⢀⣀⣀⠀⢰⣿⣿⣿⣿⣷⣤⣾⡟⠁⠘⢯⣿⣧⠴⣆⠐⠛⠿⠿⠿⣿⣿⡙⢻⣿⣿⣿⣿⣆⣀⣀⢀⣿⣯⣿⣿⣿⣿⠀⠁⠀⠜⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠐⠋⣛⡲⠦⠉⠀⠀⠀⠀⠀⠀⠻⠇⢈⣿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣾⣤⣠⠄⠀
⠀⠀⠀⠀⠀⠀⠀⣈⣶⣷⣤⣤⠀⠸⣿⠿⡿⣿⣿⣿⣿⣟⣻⣿⣷⣶⣦⠀⠀⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣀⣀⣀⠀⠀⠀⠠⣶⣿⣧⣤⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣄⣃⣀⣘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠆⠹⢿⣿⣿⣶⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⣿⣿⠟⠁⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣭⠉⠉⠉⠈⠙⠻⠟⠛⠛⠯⠙⠁⠀⣀⣴⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⠛⣛⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣻⣷⡀⠀⢀⣶⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⣿⣿⡿⠟⠋⠀⠻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣏⣀
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⡀⣙⣿⡉⠀⠀⣿⣿⣯⣭⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠁⠀⠀⠀⢀⣶⣿⣼⣿⣿⣄⡀⠀⢀⠛⠛⠋⠉⠉⠋⠉⠉⠁⠙⢿⣿⣿⣿⡿⣿⣿⣿⣯⣤
⢀⡀⢴⣦⣄⣤⣶⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢤⣄⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⡿⢤⣄⠀⠀⠀⠀⠀⢀⣀⣤⡴⢠⡞⣿⠀⣿⣿⣿⠇⣶
⠈⠀⠀⢠⣿⡿⠿⠀⠀⠀⠻⢿⣿⣿⣿⣧⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣙⠀⠀⠀⢀⣴⣾⣿⡿⠁⣿⣿⣯⣾⣿⣿⣠⠟⠉
⠀⠀⠈⢸⣏⡀⠀⠀⠀⠀⠀⠈⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣯⡄⣤⣤⣤⣤⢠⣤⢠⣤⢠⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠈⠛⣿⠛⢱⣶⣿⣿⣿⣿⡿⠋⠁⠀⠀
⠀⠀⡰⠇⠉⠁⠀⠀⠀⠀⠀⠀⣵⣿⠗⠀⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⡟⠘⠉⠀⠙⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⣤⣸⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣷⣾⣿⡿⠛⠛⠉⠀⠀⠀⠉⠁⢰⡟⠀⣾⣿⣿⣿⣿⢿⣿⣇⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣟⣻⣯⣿⣷⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣤⣼⣿⣿⣿⣿⠿⠿⠿⠇⠿⠧⠿⠿⠙⠿⠿⠟⠸⠿⠹⠿⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠓⠂⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣿⣿⡿⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⡅⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠
⠐⠖⠶⣶⠿⢶⠄⠰⠶⠶⠖⠀⣠⣿⣿⠿⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣶⣆⠀⠀⠀⠀⣀⣀⣀⣴⣿
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⣀⣴⡿⠋⠩⢛⣻⣏⡀⡀⠒⠤⣿⣿⣿⣿⠉⣭⣿⣿⣿⣿⠇⠀⠀⠀⣀⣀⣠⣾⡇⠀⠀⠀⣼⠏⠤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡀⠠⠻⠩⢤⠐⠂⠀⠀⠉⠙⠛⡀⠙⣻⣿⣿⣿⣤⣤⣄⣸⣿⣿⣻⣟⣳⠀⠀⠐⠋⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠴⠛⠉⠁⠙⠛⣧⣿⣿⣿⣿⣿⣿⣤⣧⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣄⠀⣶⡖⠀⠀⠁⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣷⣿⣦⡆⢠⠴⠄⠀⠀⢨⣿⣷⣴⡄⠀⠀⠀⣾⣟⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⠶⠶⠶⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠉⠉⠀⠀⠙⠛⠙⠃⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡿⢷⣶⣿⣥⣿⣿⣭⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣭⣥⣼⣇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠿⠿⣿⣿⣧⣼⣿⣏⣀⣤⣤⣿⣿⣿⣿⣿⣿⣭⣥⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⣿⠋⣡⣶⣤⣬⣿⣿⠿⣿⡿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣀⣯⠤⠤⠴⠦
⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣴⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣤⣦⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⠟⣿⣿⣿⠶⠀⢀⣀
⠀⠘⠛⢳⣾⣿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⡄⠀⠀⠀⣤⣶⡾⢰⣦⠎⢠⣿⠿⣏⣸⣿⣿⣿
⠀⠀⠀⡾⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⣷⣾⣥⡀⠀⢸⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⠟⠀⠈⠛⠒
⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣧⣀⡀⠹⣁⣀⣸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡇⣿⣷⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⠻⢿⣾⣿⠿⣿⣿⣶⣿⡛⠛⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣴⣾⣿⣿⠟⠋⠉⠉⠉⠁⠘⠛⢸⣿⡟⢹⣿⡇⣿⣿⣿⣇⣿⣿⢸⣿⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⣿⣿⣿⣦⣬⣥⣴⣿⣷⣀⠀⠀⠀⢀⡄
⠛⠛⠏⠉⣸⣿⣿⢿⣍⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠧⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠈⠉⠁⠀⠸⢿⣯
⠀⠀⠀⠀⠉⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣠⣶⠿
⠀⠶⠶⣾⠿⢷⠿⠻⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⡶⣷⣾⣿⣧⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣟⠻⣷⣶⣾⣿⣦⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠀⣾⣿⠿⢿⣿⡇⠘⢻⣿⣿⣿⣧⣤⣤⡀⣸⣿⣿⣿⣟⣿⡆⠀⠰⠋⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⣆⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠈⡟⠀⢨⡿⠟⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣥⡄⠀⠀⠀⣠⠤
⠀⠀⠀⠀⢀⣰⣤⣶⡆⡀⠈⠛⠛⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡄⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀
⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣦⣤⣤⡔⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⣁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⢿⣟⣛⣹⡆⠈⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢻⣿⡟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡆⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⢈⠛⠷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣯⣤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⢀⣿⣿⣿⠿⠋⠙⠿⠿⣿⣿⡿⣿⣿⣿⣿⡶⠀⣀⣀
⢦⣴⣾⡇⠀⠈⢻⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⠂⢼⡷⣼⣿⡟⠋⢀⣤⣤⣴⢀⡜⢻⠇⣿⣷⢿⣃⣾⣿⣿⣿
⣼⡿⠋⠃⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣦⣁⠀⠉⠁⣴⣾⣿⣿⠃⢸⣾⣿⣴⣿⣿⡧⠋⠀⠹⠿⠒
⡠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠈⢟⣋⡁⣷⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠛⠋⣻⣿⣿⣿⣿⠛⠃⢠⣤⣴⢠⣤⡄⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⠿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣏⣉⠁⠀⣀⣀⣠⣴⣾⣿⣿⡿⠋⠀⠀⠀⢸⣿⡿⢸⣿⡇⣿⣷⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⣀⠉⠛⢻⡿⠛⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣭⣿⣷⣦⡀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣷⠀⠀⠉⢡⣄⣾⠇⢀⣾⣿⣿⣿⣟⡿⠿⢿⣿⣿⠟⠛⠙⠛⠿⠗⠀⠀⠻⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠸⢿⠀⢸⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠙⠛⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⢿⣿⣿⡿⠋⠛⢳⡄⠀⠀⢀⣠⣤⣤⣤⣿⣿⡋⠁
⠀⠷⠶⣶⠏⢷⠶⠱⠶⠶⠖⠀⠸⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣴⣾⣷⣶⣾⣿⣿⣿⣿⣤
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣤⣶⣿⣿⣿⣿⡃⠙⠋⠉⠛⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⢠⣿⠟⠉⠉⠉⣧⠀⠸⣿⣿⣿⠿⣿⣿⣶⣾⣿⣿⣾⣿⣶⡆⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣷⣶⣶⠺⢿⡦⠀⠀⣠⣤⠀⠘⠋⠀⠀⠀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣴⣴⣾⣇⣀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠉⠉⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⣀⣠⣶⣐⣻⣿⣽⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⠶⠶⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⣿⣿⣿⠿⢿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⣿⣿⣷⣿⣇⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠱⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⡿⠿⠛⠉⠛⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡉⡉⢀⣀
⠀⠀⢀⡄⠀⣰⣶⣶⣾⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⡀⣸⣿⣿⠇⠀⠀⠀⠀⡀⠀⡌⢙⠿⣿⢹⣿⣽⣿⢫⣵⣿⣿⣿
⠛⣿⣿⣧⠀⠙⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥⣈⠿⠃⠀⠀⢠⣤⣿⣿⣿⠁⣯⣶⡏⣸⣿⣿⢹⠟⠛⣿⣟⣛
⢸⠿⠋⠻⠃⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣷⠀⠀⠘⢿⣿⠟⢣⣤⣿⣿⣿⣿⣿⠛⠁⠀⠀⠈⠀⠀
⡼⢤⣆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣷⣦⣤⣈⣷⣶⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⢱⣿⣿⣿⢫⣤⡽⢫⣭⡅⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⠉⠙⠿⢿⣿⣅⡀⠀⠀⠀⠀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⢿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⢸⣿⡇⢸⣿⡇⣿⣷⣹⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⣀⠀⠉⢹⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣦⠀⠀⠠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣄⣀⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⡿⠋⠁⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣧⠀⠀⠉⢀⣀⣿⠀⢠⣿⣿⣿⣿⣿⣭⡉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣀⣀⣠⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠸⠿⠿⠿⠿⠿⠛⠁⠈⠙⠇⢀⣀⣴⣿⣭⣿⣿⣿⣿⣆⣀
⠀⠖⠲⣶⠏⢶⠄⠰⢶⣿⣿⡟⠋⠁⠀⠀⠀⣼⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
[16A⠀⠀⠀⠀⠀⠀⣀⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣾⣿⣷⣦⣤⣤⣷⠀⠘⠋⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠐⠒⠀⠀⠘
⠀⠀⠀⢶⣄⣾⣿⣷⣶⠘⣁⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣯⣤⢤⠉⢿⣿⣿⣿⣄⣤⣶⣶⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠿⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⠟⣿⣿⡿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⠻⠋⠀⠛⠏⠁⠇⠘⠿⣯⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡏⠉⠛⠋⠙⠛⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣛⣉⣀⣠⡙
⢀⣤⡄⠠⢿⣿⣿⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⢈⡍⣻⢿⣿⢹⣿⣻⣿⢻⣿⣿⣿⣿⣷
⣿⣿⡄⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢠⣤⣿⣿⣿⢱⣿⣾⣏⣼⣿⣿⣿⡟⢿⣿⠛⣿⠿
⠃⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⠀⠀⠘⢿⡿⠟⣧⣼⣿⣿⣿⣿⣿⠿⠋⠀⠈⠉⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⠛⢻⣿⣿⣿⠉⠋⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣤⣈⣷⣶⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡀⠀⢨⣿⡿⠃⠀⢀⠹⠟⠋⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣯⡉⠀⠀⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠛⠉⠀⠁⠀⢺⣿⡅⢠⣤⡄⣤⡄⣤⣤⣭⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⡀⠐⢰⣿⣿⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⢸⣿⡇⣿⣿⣿⡿⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⣹⠏⠈⣿⣿⣿⣟⡛⠿⠿⠋⠁⠀⠀⠈⠉⠀⠀⣘⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⠀⣸⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣠⣤⣀⣸⣿⣿⡿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣤⣀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣾⣿⣿⣿⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠉⣿⡟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣾⣿⣭⣿⣿⣿⣿⣷⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠉⠙⠛⠛⠛⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⣨⣿⣶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣇⠀⠀
[16A⠀⠀⠀⢀⠀⢠⣶⡃⡀⠀⠀⠈⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣄⡀⠀⠀⠀⣸⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇⠀⢰⣾⣿⣿⣿⣿⣋⣀⡀⠀⣿⣾⣤⣤⠀⠀⣠⣼⣾⣟⠛⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢻⠿⢿⣿⡷⠶⠶⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠉⢻⣿⣿⣷⣿⣿⣿⣿⣿⣇⣠⣼⣿⣿⣿⣿⠉⠉⠉⠉⠀⣸⣹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠿⠗⣴⣶⣤⣤⣿⣿⣯⣥⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣆⡀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣤⣿⣿⣿⣿⣿⠟⢻⣿⢃⣼⣿⡯⠀⣤⡀⣰⣿⣿⣿⣿⣿⣿⣫⣴⣶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢹⣿⡟⠁⠀⣼⣿⣿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⡟⠿⢧⣄⠘⠿⠛⠛⠋⠁⠀⠿⠛⣿⣿⣿⣿⣿⣿⣿⣁⣼⡧⠀⠄⠀⠀⠀⠀
⢀⣀⠀⠀⢴⣶⣶⣾⣿⣗⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠛⠛⠻⠿⣿⢛⣿⢻⣿⡷⢒⣶⣶⣶⣷⣄
⣿⡿⠀⠀⠈⢿⣿⣿⣿⣿⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠆⡤⠀⠈⢘⡟⣟⢏⣀⣿⣿⣿⣿⣿⡉
⠁⠀⣠⣰⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡛⠃⠀⣿⣷⣆⣾⣷⣯⡘⠁⠀⠋⠀⠚⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠿⣿⣿⣿⣿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡙⣯⣀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠁⠁⣴⣿⠟⠛⠋⣀⣴⣾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠛⠻⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⣼⣿⡗⠀⠀⠼⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣶⣄⡀⠀⠀⠀⣀⣶⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⢠⣤⣿⢫⣤⡄⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠿⣿⣿⣻⠿⡋⠉⠉⠈⠉⠁⠀⠀⠀⠻⣿⣤⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣴⣶⡾⢿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⡴⠶⣶⣾⣿⣯⡀⢀⣄⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣀⡀⠀⠀⢀⣠⣾⣿⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠾⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠟⠻⠿⠿⠏⠀⠈⠉⠻⣿⣿⣿⣿⣿⡅⠞⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⠛⠛⠋⠁⣀⣠⣶⣿⠿⠿⠻⣷⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠁⠀⠀⠀⠈⠻⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡿⠃⠀⠀⠀
[16A⠀⠸⣷⣼⣿⣷⣶⣀⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⡋⠉⠉⠉⠁⣈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣟⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⣿⡿⠛⢹⣿⡿⠁⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣠⣤⣿⣿⣿⣿⡿⠻⢿⣿⣏⣽⣿⡏⠈⣤⣤⣿⣿⣿⣿⣿⣿⣿⣯⣅⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⠀⢀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣇⡈⢩⡿⠙⠛⠛⠁⠘⠿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣥⣤⡤⠄⢀⡀⠀
⠀⠀⠀⣀⣀⣀⣾⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠉⢉⡉⠙⢛⠉⠁⠁⠀⠀⢤⡄⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣤⣴⣗⠀
⡆⠀⠈⠻⣿⣿⣿⣿⣿⣅⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⣤⣴⣶⢷⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⠟
⡅⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⠟⢻⠿⠛⠛
⢁⣦⣤⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣯⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⠏⣼⣿⣿⣧⣶⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠩⠿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠘⣾⣿⣿⣿⠿⠛⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣤⡀⠀⠀⠀⢴⣶⡆⠄⠀
⠀⠀⠈⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠹⢿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠟⠁⠃⢘⣿⣿⣀⡀⠀
⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢫⣤⡄⣤⡄⣤⡌⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⣿⣿⣿⣿⣿⣷⠠⠴⠀⠀⠀⠀⣶⣾⣿⣿⡿⠓
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣧⢸⣿⡇⣿⣿⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣿⢷⣦⣾⣿⣿⣩⣿⣧⣤
⢀⢀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠉⠀⠀⣀⣤⣤⣤⣤⣀⣀⣀⣴⣾⣿⢻⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⡿⠛⠋⠙⢿⣿⣿⣿⣿⡿⠟⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣌⠉
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⣷⣿⢿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠉
[16A⠀⠀⠀⠀⢿⣿⣛⣰⣶⠀⠀⠀⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠈⠛⢻⣿⣿⡇⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢘⣿⣿⡿⠿⠛⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣁⣠⡴⢄⣀⠀⠀
⠀⠀⢠⣤⣤⣤⣾⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣀⠿⡾⠎⠁⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣴⣿⣀⡀
⠃⠀⠈⢻⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⡆⠀⠀⠀⠀⢀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⠭
⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⢿⡟⠛⠃⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⠻⠿⠛⠛⠲
⠀⠀⠀⠀⠀⣘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⠿⠟⢃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⡖
⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠁⣾⣿⣿⢿⣯⣥⣶⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⣠⣶⣴⣤⠿⠀
⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠁⠀⠀⢠⣾⣿⣿⣿⡿⢿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠟⣿⣿⣷⣿⣿⣿⣿⣿⣟⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣿⣿⢿⠟⠀⠲⣷⣶⣿⡏⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣶⣶⣶⣤⣤⣤⣴⣾⣿⢿⣿⡟⢩⣤⡄⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠘⣿⣿⣷⣤⡄⠀⣽⣿⣯⣿⣿⣿⣿⣿⣟⣺⣿
⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⢻⣿⣿⣿⣿⣿⡿⠟⢸⣿⡇⢸⣿⡇⣿⣷⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠋⠁⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣤⣤⣴
⠿⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠈⠿⣿⣷⣿⣧⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣶⣷⣿⣿⣿⣿⢿⠻⣿⣿⢣⣿⣿⣿⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠞⠋⠈⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡷⠶⠾⢛⣶⡦⠀⠀
⠄⠀⢿⣿⣿⣿⣿⣿⣏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⢀⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀
⠀⠀⠀⠻⢿⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⡿⠛⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠟⠋⠛⠉⠻⣿⣿
⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣽⣿⣿⣿⣯⣿⣿⣷⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀
⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠉⠀⣨⣾⣿⣿⣿⣿⣿⠿⠟⡛⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣾⣿⣿⣿⣟⡇⠀
⠀⠀⠀⠀⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⣀⣤⣶⣾⣿⣿⣿⡿⠁⠈⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠛⢋⣻⠿⠿⠟⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣏⠙⠀⠀⠸⠏⢀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠛⠛⠻⠻⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠟⠛⠁⠀⢠⣤⡄⢠⣤⡄⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠸⣿⣿⣦⣀⣀⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣷⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⡿⠛
⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣾
⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠍⠀⠀⢼⣗⡀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⡏⠰⠛⠀⠀⠠⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢙⣶⣮⡉⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣆⣿⡿⠁⢹⡆⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⣷⠀⠀⠀⠀⠀⢀⣼⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠙⡛⣿⣿⣿⣿⡿⠛⠛⠉⠀⠈⠉⢨⣽⣿⣛⣿⣟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣼⣧⣼⣭⣴⣾⣿
⠀⠀⠀⠀⠀⢹⣿⣽⡟⢳⣿⡆⡀⠀⢠⣾⡏⠿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⢠⣿⡏⣿⣿⣷⣭⣻⣿⣿⣿⣿⣿⣟⠋⠈⠛⠛⡷⠌⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⢚⣻⣿⣿⣾⣿⣷⣿⡠⣶⣏⣉⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⣿⣷⣤⣴⣶⣶⠀⠀⢀⣾⣿⣧⣴⣿⣿⣿⠛⠛
⠀⠀⠈⠁⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⡻⢈⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⢀⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠙⠷⠃⣿⣿⣿⣿⣿⡉⣆⣿⣿⣿⡟⣿⣿⡿⢿⠷⣽⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⠛⠉⠉⠉⠉⠉⠁⠀⣴⣻⣿⣿⣟⢻⣦⡈⠀⣀⠈⠘⣧⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠸⢿⣿⣿⣿⣿⣿⠻⠛⢿⣧⣿⣿⢿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣶⣆⡀⢀⣀⣤⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣽⠋⠸⣋⠀⣶⡿⠁⠠⠟⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⡟⠋⠹⠿⢿⣿⣿⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣴⣦⣤⣬⣨⣭⣯⠉⠈⠉⠈⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡀⠨⣿⣦⣻⣿⣿⣤⣵⣿⠒⣉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠻⠛⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠩⠀⢸⡿⣿⣿⣿⣿⠿⠿⠏⠁⢉⣦⣤⣤⣽⣷⣤⣀⡀⠀⣠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠠⣤⣿⣿⣽⡿⠑⠘⣺⣿⣿⣿⣿⠻⣉⠉⠙⠛⠻⠿⣿⡶⢿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠃⠙⠛⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠠⠀⠘⠈⠛⠀⠁⠀⠀⠈⠛⠛⠿⠟⠻⠐⠀⠀⠀⠘⠀⠆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⢷⠀⠐⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣤⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠍⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣽⣿⠟⠀⠀⠠⠟⠀⠀⢀⣈⡀⠀⢀⠀⠀
⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⣆⣀⣴⠋⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠂⠀⠀⠀⠁⠀⠀⠘⠋⢁⣾⣿⡿⢷
⠀⠖⠶⣶⠿⢿⣶⠴⠶⠶⠖⠀⠀⠐⠈⠉⠀⠏⠀⣴⣼⣙⡿⢟⣵⣿⣿⠟⠏⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⣉⡸⠿⠋⠫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣢⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣾⡇⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢚⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⠘⠋⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠶⠀⢸⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠁⣦⠀⠀⠀⠀⠀⢠⣼⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢛⡛⣿⡿⢿⣿⠟⠛⠛⠉⠀⠉⠉⢀⣽⣿⠉⣽⡟⢛⣿⣿⣿⣿⣿⡿⠉⠹⣿⣿⣞⢿⠐⠂⠀⠀⢠⣤⣶⣤⣤⣾⣿
⠀⠀⠀⠀⠀⢨⣿⣽⡿⢶⣿⣆⡀⠀⢀⣴⡎⠛⣿⣿⣸⣿⣿⣿⣿⡋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣷⣾⣿⣿⡂⢀⣿⠙⣿⠹⣤⡈⣺⡿⢿⣿⣿⣟⣀⡀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢻⠛⢿⣿⣿⣿⣋
⠀⠀⢀⡀⠀⠘⣻⣿⣿⣾⣿⣿⣿⣀⠘⣁⣀⣀⣻⣿⣿⣿⣿⣟⣛⣧⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣻⠒⣿⣦⣿⣿⣿⡿⠿⠟⠉⠙⠿⣿⣦⣤⣤⡄⠀⠀⠀⠀⢰⡀⣠⡈⠀⠈⠀⠉
⠀⠀⠈⠁⠀⣿⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠛⢿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠟⣿⣿⣿⣿⣿⣿⠗⠀⠉⠀⠻⣿⣿⣿⣾⣿⠿⠛⠻⠧⠀⠀⠀⠀⠀⠈⣿⣿⡟⠁⠀⠀⣴⣾⣿⣿⣿⣿⣶⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠓⠀⡿⠿⣿⣿⢏⠡⢼⣿⣿⣿⡏⣿⣿⡟⠁⠀⠈⣿⣿⠿⠟⠃⠘⠛⠉⠀⠀⠀⠛⠋⠉⠉⠉⠀⠀⠀⠀⡤⢻⣿⣿⡟⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠴⠀⠀⢠⣿⡇⢹⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠈⢙⣿⣿⣿⣿⣿⠿⠻⢿⣤⡿⠋⢾⡗⢲⣶⣄⠀⠀⣶⣶⣦⣄⢀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣤⠃⣬⠁⢙⠁⠙⣀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⣤⣤⣼⡏⠁⠘⠙⢲⣷⣄⣠⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣴⣦⣤⣄⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⣛⣹⣵⣿⣿⣿⣿⣿⣿⣷⣤⣀⣄⣤⣠⣿⣤⣙⠑⡿⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣤⣤⣤⣤⣘⣿⣟⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠐⠿⠁⠀⠀⣠⣤⣀⡀⠀⢀⣄⣀⢀⣠⣿⣿⣿⣵⣽⡧⠀⢨⣿⣿⣿⣿⣿⣷⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠛⢿⣿⣿⣿⣿⣿⡟⢣⣿⣷⣶⣾⣿⡭⠉⠻⢷⡾⠋⢿⣿⣿⣿⣿⣿⣿⡿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠙⠛⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠠⠄⠀⠈⠙⠛⠈⠀⠀⠈⠙⠉⠻⠿⠟⣿⠇⠀⠀⠈⠃⠶⣖⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣽⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠩⠁⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠋⠀⠀⠸⠟⠀⠘⢿⣿⡿⢿⣿⣿
⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⢆⣴⣟⣿⡛⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠻⠛⠀⠀⠀⠀⠀⠀⠀⠙⠃⣴⣿⣿⣿
⠀⠖⠶⣶⠿⢿⣷⡴⠶⠶⢖⠀⠀⠀⢂⡉⠉⠉⠔⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠠⠯⣉⡸⠿⠉⠿⠌⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣐⡀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⣼⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡰⠉⠞⠋⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠢⠀⢺⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡙⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶
⠀⠀⠀⠀⠀⢀⠄⣰⣮⢏⣠⠀⠀⠀⠀⠀⣠⣼⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⣿⣿⣿⣿⣿⣟⠛⠋⠁⠉⠉⠉⢈⣽⣿⣉⣼⣟⢻⣿⣿⣿⣿⣿⡿⠉⢿⣿⣷⣻⣿⠐⠂⠀⠀⢠⣤⣷⣤⣶⣾⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⠀⠀⢠⢾⡏⢙⣿⣿⣼⣿⣿⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡆⢂⣿⠙⣿⠿⣦⣍⣻⡿⠟⣿⣿⣿⣿⣀⡀⠉⠛⠁⠀⠀⠀⠀⠀⠻⠛⠻⠽⣽⡿⣟
⠀⠀⢠⡀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡀⠌⣀⣀⣈⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⡿⣿⣿⣻⠒⢿⣶⣿⣿⣿⣿⡿⠿⠟⠉⠙⠻⣷⣤⣶⡆⠀⠀⠀⠀⢰⠀⣠⡀⠀⠈⠁⠉
⠀⠀⠈⠁⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠀⢻⣿⣿⣿⣾⣿⡿⠛⠻⡷⠀⠀⠀⠀⠀⠀⠈⣿⡟⠋⠀⠀⣤⣿⣿⣿⣿⣿⡖⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠷⠀⡿⠿⣿⣿⣿⠳⣽⣿⣿⣿⢻⣿⣿⠛⠁⠀⠸⣿⠿⠿⣿⣿⠛⠛⠋⠉⠉⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡤⣻⣿⣿⣟⣡⣤⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠠⡯⠤⠀⠀⢰⣿⡇⢸⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠈⢙⣿⣿⣿⣿⣿⠛⠻⢿⣼⣿⣿⣾⡶⣶⣦⣄⠀⢰⣾⣿⣷⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣤⠃⣬⠁⣹⠉⢙⣁⠀⣰⠇⠀⠀⠀⠉⠀⠀⠀⠀⢁⣤⣤⣤⡾⠟⠁⠀⠀⠠⣤⡀⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣼⣦⣤⣄⣀⣽⣿⣧⠌⠁⠉⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣿⣤⣽⠑⣿⣤⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⣀⠐⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠚⠛⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⢀⣤⣾⣀⠀⠀⠀⠀⠀⠀⠹⠷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠑⠉⣿⣽⣿⣿⣿⣿⠇⣰⣶⣶⡤⠴⠒⠉⠀⠀⢶⡀⠁⠹⢿⣻⠟⠛⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠈⠛⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡄⠀⠀⠉⠛⠀⠀⠀⠀⠉⠛⠛⠻⢟⡀⣄⠄⠀⠀⠀⠣⢤⣆⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠐⢷⣶⣾⣷⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣬⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠝⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣭⣿⣿⣿⣿⠃⠀⠀⣼⠁⠀⠀⣸⣫⣯⢀⣀
⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢶⣄⢶⣴⣾⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠛⠋⠀⠂⠀⠈⠀⠀⠀⠛⠉⣵⣿⣿
⠀⠗⠶⣶⠟⢷⢾⣶⡶⠶⠖⠀⠀⠀⠒⠉⠛⠿⠋⢄⠉⣀⣿⣿⣿⣿⣿⣷⡾⠿⠋⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠠⠀⠼⢏⣉⡿⠟⢿⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣐⡀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣤⠷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣹⣿⡀⠀⠀⠀⠉⠘⠃⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠢⠀⢸⣿⣿⡛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡙⢛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠄⣰⣎⢏⣠⠀⠀⠀⠀⠀⡀⣼⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣙⣿⣿⣿⣿⣿⣿⣿⠟⣋⣉⠉⠉⢈⢼⣿⣙⣽⣿⢛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣻⢿⠐⠀⠀⠀⢠⣤⣷⣤⣤⣾⣿
⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣄⠀⠀⣤⢺⠏⢙⣿⣿⣸⣿⣿⣿⣿⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⡿⣿⢻⣷⣍⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠻⠟⠛⠉⣯⡟⠉
⠀⠀⢀⣀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣆⠉⣀⣀⣈⣿⣿⣿⣿⣿⣟⣻⣦⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⣿⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠀⢀⠀⠀⠈⠀⠉
⠀⠀⠀⠁⠀⣿⣻⣿⣿⣿⣿⣿⣿⡟⡛⣻⣿⣿⣿⣿⣾⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠻⢿⢿⣿⣿⣿⣿⣿⣿⠟⠻⣷⣄⠀⠀⠀⠉⢹⣿⣿⣿⣿⠇⠀⣤⣷⣶⣶⣿⣷⡔⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠳⠀⡿⢿⣿⣿⣏⠣⣼⣿⣿⣿⠉⣿⣝⠋⠀⠀⠈⣿⣿⠿⣿⡟⠛⠛⠋⠉⠁⣿⣿⠛⠉⠉⠉⠉⠉⠁⠀⢴⣿⣿⣿⣿⢫⣼⡏⠀⣀⠀⠐⣶⣶⡀⠀⢸⣿⣿⣿⣿⠆⢸⣿⡇⢸⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠈⢹⣿⣿⣿⣿⡿⠛⠛⢿⣼⣿⣻⣾⡆⣶⣦⣄⠀⢰⣶⣾⣶⣄⣀⣰⣾⣿⣇⣀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⠿⠀⠀⠀⠹⣿⣿⣿⣧⣿⠟⠁⠀⠀⠀⣤⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣴⣦⣤⣄⡀⣸⣯⣅⠀⠁⠀⠀⠛⢛⠛⣋⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⠀⠀⣿⡿⠟⠛⠁⠀⠀⠀⣀⠀⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣅⠀⣀⣀⣀⣼⣿⣥⣀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣤⣽⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⡛⠋⠙⠿⡟⠋⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠈⠛⠛⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⠀⠀⠀⠙⠃⠀⠀⠀⠈⠛⠛⠛⠿⣷⣠⡦⠀⠀⠀⠀⠠⠶⢻⣿⣏⡛⠛⠁⠀⠀⠀⠀⠀⠲⡶⣶⠳⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠩⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣿⣿⡟⠀⠀⢠⡆⠀⠀⠀⣈⣀⠀⢀
⠂⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠠⣤⣼⣿⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠛⠟⠁⠐⠀⠀⠁⠀⠀⠈⠋⢩⣾⣿
⠀⠗⠻⣿⠿⢷⠶⣶⡶⠶⠖⠀⠀⠀⠐⠈⠙⠛⠿⠋⡀⠁⣐⣿⣿⣿⣿⣿⣷⠿⠏⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠼⣍⣑⠿⠟⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣦⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡛⠻⠟⠛⠛⢿⣿⣿⣷⡜⠀⡀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡌⣽⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⣇⠀⠉⠙⣿⣶⣿⣿⣿⣿⣶⡶⣿⣿⣿⣿⣿⢷⡙⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠎⠀⠀⠀⠀⠀⠀⠀⣤⣽⣷⠨⣿⡄⢬⣾⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⣉⢻⣿⠟⠻⠈⠉⠋⠉⠀⠀⠀⠁⠀⢴⣯⠁⣸⡟⢉⣿⣿⣷⣿⣷⡯⠉⠺⣿⣷⡿⠿⠘⠀⠀⠀⢀⣤⣦⣤⣴⣾⣭
⠀⠀⠀⠀⠀⠀⣀⣈⢺⢲⣿⡀⢀⠀⢠⡺⠃⢘⣿⣏⣀⣿⣿⣿⣿⠉⣿⣿⣿⣿⢻⣿⣶⣿⣿⣿⣿⣷⣶⣶⣷⣾⣶⣶⣿⣶⠂⣠⣯⠘⡏⠘⢄⣠⣾⣿⣟⣥⡀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠻⠛⠋⠭⣯⡿⠛
⠀⠀⠀⠀⠀⠐⠛⢻⣷⣼⣿⣿⣿⣇⠈⣁⣀⣘⣿⣿⣿⣿⣿⣛⣻⣤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢫⣿⡿⣎⣿⣻⠀⢷⣶⣌⣿⣿⣿⡿⣿⣿⠿⠿⣿⣶⣴⣶⡄⠀⠀⠀⠀⠰⠆⣀⡀⠀⠈⠀⠙
⠀⠀⠀⠀⠀⣀⢹⣿⣿⣿⣿⣻⣿⠟⣿⣻⣿⣿⣷⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⣿⠃⠀⠉⠀⢙⣿⣿⣿⣾⣿⡿⠛⠻⠷⠀⠈⠉⠀⠀⠀⠉⢻⡟⠃⠀⢠⣶⣶⣿⣾⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠒⠀⠿⢿⣿⣿⣉⠨⢼⣿⣿⣿⢹⣿⣿⡟⡏⠀⣸⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠛⠋⠉⠉⠁⠀⠀⠀⠀⡤⣹⣿⣿⡟⢡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠇⠀⢼⣿⡇⢼⣿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠁⣹⣿⣿⣿⣿⡟⠛⠻⣧⣼⣿⣹⣿⡏⣿⣦⣄⣀⣰⣿⣿⡷⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣴⠗⣤⢇⣸⠀⠈⣀⠀⣶⡗⠀⠀⠀⠉⠿⠀⠀⠀⠈⢠⣤⣀⣽⣿⠃⠀⠀⣴⣧⡀⢠⡄⠀
⠀⠀⠀⠀⠀⠄⠀⠂⠀⣿⣿⣿⣿⣿⣿⣾⣦⣤⣅⢀⣿⣿⣧⠈⠉⠛⠘⠛⠛⢋⣁⡀⣿⣧⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⣈⣤⡍⣻⣿⣦⣼⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⣄⡘⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣤⣤⠀⡿⣿⣿⣿⣶⣿⣿⣅⠀⢀⣤⣤⣶⣶⣦⣤⣀⡀⠀⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢹⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⠉⠉⣿⣿⣻⣁⣀⡀⠀⠀⠀⠀⣤⠀⠀⠀⣀⠒
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠩⠿⣌⣿⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠉⠛⠃⠉⠀⠀⠉⠙⠛⢿⣿⣿⣿⢿⠀⠀⠀⠙⠀⢰⡿⣿⣿⣿⣿⣷⠀⠀⢰⣾⠷⠒⠺⠃⠀⠀
⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠟⠁⢠⣿⣧⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⡜⣐⣿⣿⣿⣿⠋⠀⠀⢺⠁⠀⠀⣀⣀⡀⠀
⣿⢀⠀⣢⣤⡀⠀⠀⠙⢺⣱⣄⠠⠛⠷⣶⣾⣶⣾⣿⣿⣿⣿⠏⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠓⠟⠛⠀⠐⠀⠈⠀⠀⠈⠉⠉⢰⣿
⠀⠿⠾⣿⠯⢷⠶⢶⣿⡿⠾⢀⠀⠀⣩⢾⣟⣿⣿⣿⣿⠉⠁⣀⣿⣿⣿⣿⣿⡿⠿⠍⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⢠⠒⠀⠼⢏⣅⡿⠿⠷⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣆⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠠⠀⠀⠀⣶⠂⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⢤⣵⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢐⠃⠀⠀⠀⠚⠁⠘⠁⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡏⢻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼
⠀⠀⠀⠀⠁⠀⣠⣶⣾⡟⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣬⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣀⣙⣻⣻⣿⡿⢿⢯⠛⠛⠉⢀⠀⠈⠁⠀⣼⣿⣁⣼⡟⢋⣿⣿⣿⣿⣷⠍⠉⠘⣿⣷⣹⠿⢸⠀⠀⠀⢠⣴⣦⣴⣶⣾⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣴⢀⢀⣤⠐⠃⣚⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡖⢨⣿⠘⡟⠩⢦⣨⣿⣿⡟⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠟⠛⠽⣿⣿⣟
⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠷⠁⣀⣀⣹⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⡿⣯⣿⣿⡃⢿⣶⣦⣿⣿⣿⢻⣤⣤⣴⣿⣷⣤⣴⣶⡀⠀⠀⠀⣤⠰⠃⢠⣄⠀⠈⠁⠉
⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢫⣿⣿⣿⣿⣿⣿⣓⠀⠉⠀⢻⣿⣿⣷⣿⣿⣿⠛⠚⠷⠈⠻⡿⠀⠀⠉⠙⣿⡟⡃⠀⠀⣴⣾⣿⣷⣿⣿⡗⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠖⠸⠿⠿⣿⡿⠉⠀⢸⣿⣟⠉⢹⣿⡟⠃⠀⠀⠈⠛⠿⠿⡿⠟⠛⠋⠉⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠰⢹⣿⣿⡟⢡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠆⠀⢰⣿⣇⢼⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⣙⣿⣇⣿⣿⡟⠋⠻⠃⠈⠉⠱⣿⠶⠶⣦⡀⠀⢰⣶⣶⠀⠀⢀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣤⠟⣴⠋⢉⠁⢘⡀⠀⣺⠟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⣴⣦⣾⣿⡇⠀⠀⠀⣤⣀⣠⠴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠇⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⢀⣻⣧⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣍⢹⡿⣦⠼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣶⣶⣾⣿⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠬⣿⠿⠂⠀⡝⠃⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡒⠚⠀⠀⣼⣿⣿⣿⣿⠷⠂⣤⣴⣾⠿⢻⣁⠀⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣷⣴⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⢁⠛⠛⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢡⡆⠀⠀⠉⠃⠀⠀⠈⠁⠈⠛⠻⣿⣿⡿⣿⠟⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠁⠀⢿⣿⡿⢿⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⣾⣦⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠉⠀⠀⣾⠁⠀⢀⣿⣿⡿
⣿⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢶⣶⣦⣶⣿⣿⣿⣿⣿⠟⢁⣾⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠟⠛⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⣥
⠀⠖⠿⣿⠟⢷⠶⠶⣾⡶⠖⠀⠀⠀⠀⠒⠉⠛⢿⣿⣿⡏⢉⠀⣰⣾⣿⣿⣿⣿⠿⠋⠙⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣐⠂⠠⠼⢏⣍⠿⠾⠯⢁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣦⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⢤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⣈⠁⠀⠀⠀⠚⠁⠘⠁⠀⠀⠀⠸⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡏⢻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼
⠀⠀⠀⠀⠀⠀⣠⣶⣾⡟⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣬⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠐⢉⣛⣿⣿⡿⢿⢛⠛⠛⠉⠀⠀⠈⠁⠀⣼⣿⣁⣸⡟⢛⣿⣿⣿⣿⣷⠉⠉⠘⣿⣷⣻⡇⠸⠀⠀⠀⢠⣴⣦⣴⣶⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣰⢠⢀⣤⠀⠃⣘⣿⣿⣿⣹⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣾⣿⣿⣷⡖⢠⣿⠘⡿⠩⢦⣀⣿⣿⡟⠉⠈⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠿⠛⢻⢿⣿⣿⣟
⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡷⢁⣀⣀⣹⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⡿⣯⣿⣿⡃⢿⣶⣬⣿⣿⣿⣃⣀⡀⣠⣭⣵⣄⣴⣶⠀⠀⠀⢠⡄⠞⠀⣠⣀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢻⣿⣿⣿⣿⣿⣿⣓⠀⠉⠀⢻⣿⣿⣷⣿⣿⣿⠛⠘⠷⠛⣿⡏⠉⠉⠉⠻⣿⠛⡁⠀⢠⣶⣿⣿⣿⣿⣿⡗⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠖⠘⢿⢿⣿⣿⡟⢤⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠿⠿⠿⡿⠟⠛⠋⠉⠀⠀⠀⠛⠉⠀⠈⠉⠀⠀⠀⠀⠠⢻⣿⣿⡟⢡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡶⠀⠀⣾⣿⡀⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⢈⣛⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠱⣿⠶⢶⣦⡀⠀⢰⣶⣶⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣤⠟⣴⠃⣉⠁⠈⡀⠀⣲⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣤⣤⣿⡿⢀⠉⠁⢡⣤⣀⣠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣿⣿⣭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⢀⣻⣧⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣈⣠⣍⠹⡿⣦⠼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⣿⣷⣿⣿⣯⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣽⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠛⠮⣿⠿⠂⠀⡟⠃⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣀⠀⠀⠉⢻⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠒⠂⠀⣼⣿⣿⣿⣿⠷⠀⣤⣴⣾⠿⢛⡁⠀⠀⠀⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⢃⠻⠛⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢡⡂⠀⠀⠉⠃⠀⠀⠈⠁⠈⠛⠛⣿⣷⡿⣿⠏⠁⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⡿⢿⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢠⣼⣦⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠯⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡟⠉⠀⠀⢾⠁⠀⠀⣿⣿⣿
⣿⡇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣶⡦⣴⣿⣿⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⣡
⠀⠖⠾⣿⠿⢷⠶⠲⣾⣶⠖⠀⠀⠀⠀⠒⠉⠙⢿⣿⣿⣟⠉⠁⢠⣾⣿⣿⣿⣿⡿⠋⠉⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠒⠀⢤⢯⣩⡸⠿⠿⠅⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⢠⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣘⠁⠀⠀⠀⠚⠁⠛⠁⠀⠀⠀⡖⠚
⠀⠀⠀⠀⠀⠀⠀⢠⢂⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣯⢾⡋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣾
⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⠀⠆⠀⠀⠀⠀⡀⣾⣿⣿⣮⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⠛⠛⠉⠀⠀⠈⠁⠀⣼⣿⣉⣽⡟⢛⣿⣿⣿⣿⣯⠉⠉⠹⣿⣿⣿⡇⠖⠀⠀⠀⣀⣼⣄⣤⣼⣿⣯
⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣤⣢⣧⣀⣦⠠⢋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⠆⣸⣟⢸⡟⠩⣄⣩⣾⣿⡟⠁⠈⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠠⣿⠻⢿⣻⣿⠟⠛
⠀⠀⠀⣀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡿⠁⣀⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡿⣿⣿⣻⠘⣷⣶⣬⣿⣟⡿⠃⠀⠀⢀⣿⣆⣀⣴⣶⠀⠀⠀⢠⡄⠶⠀⣤⠁⠈⠉⠘⠒
⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠓⠂⢻⣿⣿⣵⣾⣿⡿⠛⠹⠦⢰⣷⣷⠛⠛⠿⠟⣿⡟⡃⠀⢠⣴⣷⣿⣾⣿⣿⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠖⠸⠿⢿⣿⣿⡃⢮⣿⣿⣿⡏⣿⣿⣿⠏⠉⢡⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠤⣻⣿⣿⡛⣡⣤⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠘⠿⠇⠀⣼⣿⡀⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⢈⣿⣿⣿⣿⣿⡟⢿⣿⣷⣿⡏⢿⣿⣷⣾⣧⣌⣠⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⠷⣼⠃⣹⠀⢉⡀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠟⠀⠀⠀⢠⣤⣀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⣿⣯⣥⡀⠀⠈⠁⠀⠉⠀⠋⠻⠿⠿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⢁⣠⣉⠿⠿⣤⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⡀⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣦⣦⣤⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⡾⣿⣿⣆⣠⣷⠇⠀⠀⢀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⣿⣿⣿⣿⣿⡟⠃⢢⣾⡿⠿⠟⠛⠛⠋⠒⠺⠟⠛⢻⡿⠛⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⠃⠘⠛⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⡔⠀⠀⠉⠋⠀⠀⠀⠉⠀⠛⠛⢠⣦⣤⢰⡿⠋⠀⠀⠀⠀⢸⣿⣶⣦⣠⣤⣴⠀⠀⠘⢿⡧⠀⠛⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⣬⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡌⠙⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠝⠃⠀⠀⠆⠀⠀⢀⣠⡶
⣿⣿⢆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣶⣶⣴⣿⣿⣿⣿⣿⣿⡿⠛⣱⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⠀⢀⣄⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⠛⠃⠀⠀⠐⠂⠀⠀⠈⠉⢉
⠀⠖⠶⣿⠟⢿⠥⠶⢶⣷⡖⠀⠀⠀⠀⠐⠊⠙⠻⣿⣿⣟⣋⡙⠛⢁⣴⣿⣿⣿⣿⡿⠏⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠠⡽⣉⡙⠿⣿⠅⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⣶⡆⠀⢸⣖⢉⡠⠄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣢⣰⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⣿⣿⠙⠁⣾⣿⠷⠛⠁⠰⠃⣰⣾⡿
⠀⠀⠀⠀⡀⠀⠀⠠⢂⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡖⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣠⣮⣿⡟⠀⠀⡀⠀⠀⣭⣽⣿
⠀⠀⠀⠀⠀⢀⣶⣶⣿⡏⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣦⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⣉⣻⣿⣿⣿⢿⣯⠙⠛⠟⠉⠀⠀⠈⠁⠀⣼⣯⣉⣹⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⢀⣶⣿⣥⣶⣼⣿⣯
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣴⢰⢣⡀⡆⠀⢁⣨⣿⣿⣿⣿⣿⣿⣏⢰⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⠗⣬⣿⢸⡿⢻⣧⣹⣾⣿⣿⣟⠛⣿⣿⠛⠋⢛⠟⠀⠸⡿⢀⣶⣾⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⣛⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣌⣽⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⢿⣿⢿⣿⠘⣿⣦⣽⣿⣿⣿⣿⣿⣦⣿⣿⣿⣷⣿⣶⣤⣄⣠⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣝⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠃⠺⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⠿⠿⣿⢿⣿⣿⡟⣿⠿⠁⣽⣿⣿⣿⣿⣿⣿⡿⢿⠃⠉
⠀⠀⠀⠀⠀⠳⠖⠘⠿⢿⣿⢯⡁⢤⣿⣿⣿⢉⣿⣽⡿⠉⠁⢸⣿⣿⣿⠿⠟⠛⠛⠛⠋⠁⠀⠈⠛⠉⠉⠉⠉⠁⠀⠀⠀⣼⣿⣿⣿⣿⣡⣤⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣤⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠁⠀⢐⣻⣿⣿⣿⣿⠛⠙⠿⣬⣿⡏⣿⡿⢶⣿⣤⡀⢠⣶⣶⣶⣶⢀⡀⠶⢶⣤⣄⢀⠀⠀⠀⠀⠀⢠⣼⢶⣿⣿⣿⠿⣿⣅⠠⣿⡿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⢿⣿⣿⡿⠟⠊⣽⣿⣥⣴⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣦⣤⣄⠀⢀⠈⠀⠀⠀⠀⠀⠘⠻⢿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣼⣻⣿⣷⣤⣽⣿⢿⣉⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠉⠁⠀⠀⣐⡻⠛⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣅⣉⡼⣿⣣⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠛⢷⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⢘⣾⡿⣿⡿⢿⡛⠉⣉⣿⠿⠿⠛⠛⣛⠋⠙⠛⠋⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠘⠃⠘⠋⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠠⠀⠀⠀⠙⠁⠀⠁⠀⠁⠈⠙⠃⣴⣶⣄⢾⠟⠀⠀⠀⠀⠀⢾⠻⣿⣿⣧⣀⡂⠀⠀⠻⡤⠀⠉⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⡏⠛⠀⠀⠠⠀⠀⠀⢀⡀
⠠⣿⡿⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣶⣦⢤⣿⣿⣿⣿⣿⣿⣿⡿⠛⢡⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠛⠃⠀⠀⠀⠐⠀⠀⠀⠉⠀
⠀⠖⠲⣾⠟⢿⠏⠴⠶⢶⣶⠀⠀⠀⠀⠀⠊⠉⠻⣿⣿⣿⣋⠙⠛⠋⢁⣴⣿⣿⣿⡿⠟⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠠⡼⣏⡁⠿⢾⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀⠀⡠⠋⠉⠁⠂⠀⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠂⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⢠⣄⣀⣠⣦⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣦⡀⠀⠀⠀⣄⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣾⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣹⣿⣿⣿⣿⣯⣇⣤⣦⣀⠁⠀⠀⠀⠀⢀⡀⠀⣤⣴⣧⣤⣄⣀⡈⠀⢥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⣤⣴⣿⣿⣿⣿⣷⣾⣿⣿⣦⠀⣀⣴⣤⣄⣀⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠛⣻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⢰⣿⡿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⠟⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣶⣾⣿⣿⡟⠫⠀⠻⣿⣿⡿⠏⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣟⠻⠟⠛⢻⡿⣶⣄⣼⣿⠿⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⠽⣿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⢷⠆⠐⢆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢛⣿⣿⣿⠿⠀⠀⠀⠸⢿⢿⡿⢿⣟⡃⢀⡀⢉⡉⡅⠀⠀⠈⠀⠀⠀⠀⠀⣧⡀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠻⡿⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⢠⣀⣰⣶⡿⠛⠂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⠉⠙⡛⠉⠉⠃⠀⠀⠀⠀⣷⠀⠀⠀⣤⣤⣶⣿⠃⠀⠀⠈⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⢀⡀⠀⡠⠋⠉⠁⠂⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠊⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣯
⢤⣄⣀⣤⣄⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣷⣦⡀⠀⠀⠀⣄⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣹⣿⣿⣿⣿⣯⣆⣠⣤⣀⠁⠀⠀⠀⠀⢀⡀⢠⣶⣶⣿⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣴⣿⣿⣿⣿⣶⣾⣿⣿⣶⠀⢀⣴⣤⣄⣀⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠙⣻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⢰⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣧⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⡟⠻⠛⢿⣿⣿⣿⡿⠏⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣏⠻⠟⠛⢻⠿⣶⣄⣤⣾⠿⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⠽⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⢷⡶⠺⣿⣛⣿⠛⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢻⣿⣿⣿⠿⠀⠀⠀⠸⣿⢟⡿⢿⣟⡁⢃⡀⢉⡉⡅⠀⠀⠈⠀⠀⠀⠀⠀⣷⡀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠻⡿⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⣀⣸⣶⣿⣿⣯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣠⣿⣿⣿⠋⠀⠀⠀⠀⠈⠀⠘⠁⠙⡛⠛⠋⠃⠐⠀⠁⠀⣶⠀⠀⠀⣶⣴⣶⣿⠃⠀⠀⠈⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠞⠙⠿⠟⠁⠀⠁⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⣀⡄⠀⡤⠋⠉⠑⠂⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣯
⢠⡀⢀⣤⣄⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣷⣦⡄⠀⠀⠀⣄⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⢿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣹⣿⣿⣿⣿⣯⣇⣠⣤⣀⠀⠀⠀⠀⠀⢀⡀⠀⣔⣴⣾⣾⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⢠⣤⣾⣿⣿⣿⣶⣾⣿⣿⣶⠀⢀⣤⣤⣄⣀⣤⣤⣤⣬⣤⣤⣤⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣹⣷⡿⣿⣿⡄⠀⠈⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣶⣾⣿⣿⡟⠛⠉⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣍⠙⠿⠛⢛⡿⣶⣄⣤⣶⠿⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⠽⢿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠿⢷⠖⠻⣿⡉⣽⠿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠲⢞⣿⣿⣿⠯⠀⠀⠀⠨⢿⢿⡿⢿⣟⡁⢀⡀⢉⡉⡅⠀⠀⠈⠀⠀⠀⠀⠀⣷⡀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠻⠿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣸⣾⣿⣿⣯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⠁⠙⡛⠛⠋⠀⠐⠀⠀⠀⠦⠀⠀⠀⣤⣤⣶⣿⠇⠀⠀⠈⢹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠛⠿⠟⠁⠀⠁⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡄⠀⡤⠋⠉⠑⠂⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣧
⠀⠀⠀⣠⣄⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿
⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⠁⠀⣀⣀⣤⠀⠀⢀⣤⣄⢀⣀⣰⣿⣿⣿⣷⣿⣷⣄⠀⠀⣰⣿⣿⣿⣹⣿⣿⣿⣿⣯⣆⣠⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⢄⣠⣶⣾⣆⣶⣾⣇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣿⣶⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠛⠙⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡶⢠⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣄⠈⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣟⣱⡖⠈⠋⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣶⣾⣿⣟⠛⠉⠉⢿⣿⣿⣿⡟⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡄⠀⠝⠉⠙⠖⣦⣄⣠⣄⠉⠉⠉⢙⣿⡿⠿⠿⢿⡿⠷⠘⠟⠋⡍⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⠟⢳⠀⠘⣷⠉⠩⠁⠀⠀⠀⠀
⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢚⣿⣿⣿⠧⠀⠀⠀⠠⠐⢟⡿⢿⣛⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠐⢻⣿⣿⣿⣿⣿⠏⠹⠿⠉⠀⢹⣿⣿⣿⣿⣿⣿⣇⠀⢀⣰⣾⣿⢿⣧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⣀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⣾⠂⠀⠀⠈⠹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢹⣿⣿⣿⠞⠛⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠄⢸⣿⠆⠀⠰⢶⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⡄⠀⡤⠋⠉⠁⡂⠀⣼⣀⠄⠀⠈⠁⠀⠀⣄⣼⣿⣷⣤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⡟⠁⠀⠀⠀⠀⠀⠀⠊⠊⠘⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿
⠀⡀⢀⣠⣄⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣶⡀⠀⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣹⣿⣿⣿⣿⣯⣆⣠⣤⣀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⣴⣿⣿⣿⣿⣿⣶⣾⣿⣿⣦⠀⢀⣤⣤⣀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣶⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠛⠛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡖⢠⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣇⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⠟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣹⣿⠿⠙⠁⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣵⣶⠹⡯⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠟⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣏⠉⠿⠋⢛⠗⣶⣄⣤⣾⠟⠉⠙⢻⣿⣿⡿⢿⣿⣿⣿⠿⠿⠿⡿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠛⠁⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢚⣿⣿⣿⠿⠀⠀⠀⠠⠸⢟⡿⠻⣟⡁⢀⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⠏⠙⠟⠋⠀⠹⣿⣿⣿⣷⣄⠀⠀⠀⠀⣰⣾⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⣀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠘⡛⠍⠉⠀⠐⠂⠀⠀⠦⠀⠀⠀⢶⣤⣶⣿⠃⠀⠀⠈⠹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⢹⣿⣿⣦⠀⠘⠿⠟⠁⠀⠁⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⡄⠀⡤⠋⠉⠑⠂⠀⢰⣄⠠⠀⠀⠀⠀⠀⠀⠈⠀⣠⣤⣼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠊⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣿⣿
⢤⣄⣀⣤⣤⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣦⡀⠀⠀⠀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣙⣿⣿⣿⣿⣯⣦⣤⣦⣌⠁⠀⠀⠀⠀⢀⡀⢀⡄⠀⠀⠀⢠⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣤⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣠⣴⣤⣄⣠⣤⣤⣤⣽⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣶⣿⣿⣿⣿⣴⣴⣀⡶⣘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⣿⣿⣿⣿⠛⠙⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠊⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡶⢰⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣧⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⡀⠀⠀⠘⢿⣿⣿⠿⠿⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⡻⣿⣿⡀⠀⠈⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣒⣂⠉⠀⠀⠀⠀⠈⠓⠿⠃⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣟⠻⠿⠛⢛⠟⣶⣄⣤⣿⠿⠛⢛⢻⣿⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣁⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠶⢾⣿⣿⣿⠿⠀⠀⠀⢠⢿⢿⡿⢿⣿⡁⢁⣀⠉⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⢿⣿⣿⣿⣿⣿⠏⠻⠿⠛⠀⢿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢴⠖⠒⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣀⣿⣿⡿⠋⠀⠀⠀⠀⠈⠁⠈⠁⠙⡻⠟⠉⠀⠐⠒⠁⠀⢶⠀⠀⠀⣶⣴⣶⣿⠇⠀⠀⠈⢹⠟⠋⠁⠈⠒⠀⠀⠀⠀⠀⠈⠛⠋⠹⣿⣿⣿⠞⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⡀⠀⡤⠋⠉⠁⠂⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣯
⢠⡄⢀⣤⣄⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣦⡀⠀⠀⠀⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣽
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣙⣿⣿⣿⣿⣧⣆⣠⣦⣀⠁⠀⠀⠀⠀⢀⡀⢀⣤⣤⣾⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⢀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣦⠀⢀⣴⣦⣄⣀⣤⣤⣤⣭⣤⣤⣤⣤⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠙⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠘⠉⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⢴⣿⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣧⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣵⣶⡙⡿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⡛⠛⠉⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣏⠙⠿⠛⢛⠟⣶⣄⣤⣿⠿⠛⠛⢻⣿⣿⡿⢿⣿⣿⣿⠿⢿⡿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠀⠻⣿⡍⣉⠈⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠲⢚⣿⣿⣿⠿⠀⠀⠀⠠⡾⢟⡿⢻⣟⡁⢀⣀⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠐⢿⣿⣿⣿⣿⣿⠏⠛⠿⠛⠀⢻⣿⣿⣿⣿⣿⣿⣇⠀⣀⣸⣾⣿⣿⣧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠟⠋⠀⠐⠂⠁⠀⠶⠀⠀⠀⢶⣤⣶⣾⠇⠀⠀⠈⢹⠟⠋⠁⠈⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠛⠿⠟⠁⠀⠁⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣀⡀⠀⡤⠋⠉⠁⠂⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣮⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⣾⣿⣯
⢠⡄⣀⣤⣄⡀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣷⣦⡄⠀⠀⠀⢤⡶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣿⣿⣿⣾
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣉⣿⣿⣿⣿⣿⣤⣠⣤⣀⠁⠀⠀⠀⠀⢀⡀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⣤⣾⣿⣿⣿⣷⣾⣿⣿⣦⠀⢀⣴⣤⣄⣀⣤⣤⣤⣭⣤⣤⣤⣤⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠛⠋⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⢠⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣧⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⡹⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⠟⠋⠉⣿⣿⣿⣿⡿⠛⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣏⠙⠿⠋⢛⠟⣶⣄⣬⣶⠿⠉⠛⢻⣿⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⠶⠀⠹⣿⡟⣿⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠲⢚⣿⣿⣿⠿⠀⠀⠀⠠⡾⢟⡿⢿⣿⡁⢀⣀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⢿⣿⣿⣿⣿⡿⠟⠛⠿⠟⠁⢻⣿⣿⣿⣿⣿⣿⣇⠀⣀⣸⣾⣿⣿⣿⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠙⡻⠟⠉⠐⠐⠒⠀⠀⢦⠀⠀⠀⢶⣤⣶⣿⠃⠀⠀⠈⢹⠟⠋⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠛⠿⠟⠁⠀⠉⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣀⡄⠀⡤⠋⠉⠑⠂⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⣾⣿⣯
⢠⣄⢀⣤⣄⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣦⣄⠀⠀⠀⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣿⣿⣿⣾
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⡀⠀⢀⣀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣉⣿⣿⣿⣿⣿⣤⣠⣤⣀⠁⠀⠀⠀⠀⢀⡀⢠⣴⣬⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⠀⢀⣴⣤⣄⣀⣤⣤⣤⣭⣤⣤⣤⣤⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠛⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠛⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡖⢠⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣅⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣏⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢏⠀⠀⠀⠀⠀⠡⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⠛⠉⠈⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣧⡄⠀⠭⠉⢛⠗⣶⣄⣬⣶⠿⠉⢛⢻⣿⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⠶⠀⠻⣿⡏⣿⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢺⣿⣿⣿⠧⠀⠀⠀⠠⡺⢟⡿⢿⣿⡁⢀⣀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠘⢻⣿⣿⣿⣿⡿⠏⠛⠿⠛⠁⢻⣿⣿⣿⣿⣿⣿⣇⠀⣀⣸⣾⣿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠙⡻⠟⠋⠐⠐⠒⠀⠀⢦⠀⠀⠀⢶⣤⣶⣿⠃⠀⠀⠈⢹⠟⠋⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠛⠿⠿⠁⠀⠉⠀⠀⠀⠀⠀
[16A⣿⠀⣿⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⣿⣿⣞⣻⣿⣿⣿⣿⣿⣟⣗⠟⡻⣿⣿⠀⣀⡘⠋⢿⣿⡿⢿⣿⣯⣴⡶⣋⣀⡟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣠⡄⠠⠎⠉⠛⢿
⣷⣿⣿⣽⣿⣿⣿⣶⣄⣺⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⡿⠟⢻⣷⣆⡀⠀⠀⠀⣰⢶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠘⣿⣿⡇⠀⠀⣐⣙⠋⠻⢿⠫⠿⠿⣿⠘⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣦⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣠⣿⡿⠿⠟⠁⠁⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢦⠄⢠⣿⣿⣷⣶⣶⣿⣿⣿⣇⢐⡿⠟⣴⠟⠀⠛⠁⠹⢿⣿⣅⣻⣿⣿⣿⣿⢏⣽⣾⣷⣤⣄⣀⣀⣀
⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⢀⡀⡀⠀⠛⣿⡇⠐⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢸⣿⠇⣠⠿⢿⣿⣛⣿⣿⣾⣷⣟⣫⣤⢰⣦⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⡟⠻⠛⠿⣿
⠀⠀⢀⣀⢉⣿⣿⣿⣿⣿⣿⠁⠀⢹⡇⠀⠀⠀⠰⣤⡀⠀⠀⢾⠽⡿⣗⠈⠛⠛⣿⣿⣿⣿⣯⣿⣗⠀⠀⠀⠀⠀⠬⠋⠀⠀⠀⠈⢹⣿⠛⠛⢛⣿⣿⣿⣿⣸⣿⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡷⠊
⠀⠀⠈⠉⠁⠉⠛⠛⠻⣿⣿⡄⠀⠘⢷⣤⠄⠀⠀⠀⠦⢀⣠⣭⡀⠀⠩⢠⡀⠀⣻⣿⣿⣿⣿⣟⣯⣾⣿⣿⠆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡀⠀⠙⢉⣤⣬⣏⣀⣿⣿⣹⣟⣛⠋⡙⡿⣇⠈⢉⣷⣦⣤⣤⣼⣿⢢
⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠉⢟⣟⣄⠄⣿⣿⡿⢻⣿⣿⣿⣿⣿⡛⠛⠀⢀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣶⣶⣼⡿⢿⣿⠈⠙⠙⠛⠿⢿⣿⣾⠁⢨⣴⣿⣟⣳⣶⣿⠾⠻⢿
⠀⠀⠀⠀⠀⠀⣀⠖⠀⠀⡸⠖⣂⣀⣠⣀⢀⡀⠀⠀⠀⠀⠸⠿⠛⠴⢾⣿⠋⠀⣿⣿⠟⠿⠟⢫⡇⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡌⢛⠉⠀⠘⠿⣿⡿⣭⣿⣿⣦⣤⣿
⠀⠀⠀⠀⣶⣾⣯⠀⠀⣀⣿⢟⣿⣿⡿⣇⣈⣁⢠⠁⠀⠀⠀⠀⠀⠀⠀⣞⠛⠒⠉⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⣉⢿⣽⣿⣿⣯⠀⢀⣠⣼⣷⣶⣾⣶⣆⣀⣤⣾⣷⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠈⠉⠉⠁⠀⠸⣿⣿⠘⠉⣿⣶⣿⣿⡿⠿⣵⡀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⢯⠋⠁⠀⠀⠈⣻⣿⣿⣿⣶⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣏⣻⣿⣿⣽⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣤⡾⠿⣿⣿⠛⠂⠛⠒⠦⠀⣄⣶⣄⠀⢈⡁⠘⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡆⠀⠀⣀⠀⢼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠊⠀⠚⠛⢿⣿⣿⣿⠛⣿⣶
⣶⡒⠂⣠⠀⠈⠀⠀⠛⢿⣿⣿⠃⠙⠛⠋⠁⠀⠀⠀⠀⠘⢷⣯⡙⠟⠛⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠘⠿⠄⠀⠀⠃⠲⡖⠉⠀⠈⠻⢿⣿⣿⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠉⠛⠫⢹⣿⡏
⠀⠀⠀⠉⠀⠀⠀⠀⠀⡄⠀⢀⣆⣰⣶⣶⣻⣇⡀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠐⣦⣄⣀⣀⣀⣀⣀⢀⣄⣬⡄⠘⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋
⠀⠀⣠⢂⠀⠀⢠⣼⣿⡇⠀⠀⠀⠹⠗⠱⠍⠉⠁⠀⠀⠀⠀⠀⠀⢐⣓⣷⣦⣤⣮⣻⣿⣄⢄⣄⠀⣤⣄⠸⣶⡀⠀⢠⣤⠃⠀⠀⠀⠀⢀⣘⣛⣿⣿⣻⣿⣿⣿⣿⣿⣾⣿⣦⣠⣴⣶⣶⣦⣤⣤⣄⣀⣀⣀⣤⣄⣀
⠐⠷⠿⣾⠟⢶⠾⠱⠿⠶⠶⠀⠀⠀⠀⠀⢚⣶⣶⣾⣶⣶⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠬⣼⣿⡇⢈⣿⣿⣿⡅⠀⠀⣿⡧⣴⣦⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣠⣿⣿⣿⣿⣿⡛⠛⢁⣿⣿⣿⣿⣿⡇⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣭⣽⡛⣙⣁⠀⠀⠀⣀⢀⡀⣠⣤⣉⣀⣬⣤⡄⠲⠟⠛⠿⣧
⣿⣿⣿⣾⣿⣿⡿⣶⣮⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠐⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠿⣿⣿⣿⣿⢿⢿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣾⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⠿⣿⣧⡾⠿⠛⠛⠂⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⡝⠉⠀⠀⠈⠉⠀⠸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢿⣿⣇⣘⣿⣿⣿⣿⡿⢩⣽⣿⣷⣤⣀⣀⠀⠀
⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣷⠠⣄⡄⠀⠈⠻⠟⠀⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⢿⣿⣿
⠀⠐⢶⠤⣽⣿⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠳⠆⠀⠀⢘⡷⠿⢿⡀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣶⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣿⠉
⠀⠀⠀⠀⠀⠉⠉⠙⢿⠿⠀⠀⠀⠡⠤⠀⠀⠀⠀⠘⠂⢤⣶⣦⠀⠀⣠⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠙⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣛⠛⠛⢻⢯⡀⠈⢹⣷⣦⣼⣽⣿⣿⣿
⠀⠀⠈⠙⠗⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⣘⣽⡰⣶⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣷⡎⠀⣠⣾⣟⣩⣶⣿⣟⠿⢿⣿
⠀⠀⠀⠀⢀⣤⠏⠀⠀⡸⢏⣠⣤⣤⣄⣀⣀⠀⠰⠆⠀⠘⠛⠛⠿⢿⣿⣯⠀⢸⣿⣿⣿⠿⠿⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣀⠙⠋⢀⠀⠛⢿⣿⢷⣿⣿⣷⣾⣿⣿
⠀⠀⠀⣸⡿⠟⠀⢀⣠⣿⠏⣿⣿⠟⠂⣄⣐⢀⡅⠀⠀⠀⠀⠀⠀⠀⢸⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡯⣭⡿⣿⣿⣿⣿⣿⢏⣏⣥⣿⣶⣾⣷⣶⣤⣤⣴⣿⣷⣿⣿⣿⣿⣛⣙
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠈⢿⣦⣄⠛⠛⠻⢷⠄⠀⠂⠀⠀⠀⠀⣴⡶⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠏⠀⠀⠀⠀⣻⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⠋⡻⡿⢿⣿⣿⣯⢹⣿⣿⣭⣭⣯
⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣶⣶⡿⠻⠧⣤⠀⠀⠙⠓⠂⠄⢀⣶⣦⡘⠋⢀⠌⠓⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠀⠀⢠⠀⠀⢿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠈⠉⠻⣿⣿⣿⣛⣷⣾⣿
⠏⠁⢤⠀⠀⠀⠀⠈⠛⠿⠏⠃⠀⠚⠋⠁⠀⠀⠀⠀⠀⠻⢿⡁⠙⠃⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠈⠃⠀⠀⠀⠙⠳⣷⣿⣿⡿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠉⠉⠭⣿⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢤⣼⣶⣟⣥⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢘⡿⠉⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠹⠾⣀⣀⣀⣀⣀⣀⣤⣤⣤⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤
⢘⡄⡼⠀⠀⠠⣶⣿⡇⠀⠀⠀⠀⠛⠒⠃⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠘⣶⣤⡤⠈⠻⢽⡇⢀⣀⢠⣤⣄⢀⣤⠀⠀⢠⣦⠀⠀⠀⠀⢀⣀⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣶⣶⣤⣤⣤⣀⣀⣀⣤⣄⣀
⢸⣿⠶⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢈⣷⣾⣿⣿⣗⡀⠀⠀⢀⣀⣭⣿⣿⣷⠀⢀⣸⠇⣀⣿⡁⠙⠛⢻⡇⠀⠀⠀⣿⠓⠲⠶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣼⣿⣿⣿⣿⣟⣛⠋⢩⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠉⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣴⣿⣿⣯⣟⣉⣉⣀⡀⠀⢀⣀⣀⣀⣬⣭⣅⣠⣤⣴⠰⠾⠛⠻⢿⣭
⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⣿⣿⡟⠁⠉⠉⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠚⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⢿⣿⣿⡿⡿⡿⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠤
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠿⣿⣿⣶⡿⠟⠉⠛⠁⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠿⠟⠛⠁⠀⠀⠀⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⢿⣿⣧⣿⣿⣿⣿⣿⡟⣩⣿⣿⣾⣤⣀⣀⡀⣀
⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡇⠠⣄⡄⠀⠉⠛⠋⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⡿⣿⣿
⠀⠰⠶⠴⣿⣿⣿⣿⣿⡟⠀⠀⣿⠁⠀⠀⠀⠈⠿⠆⠀⠀⢻⠾⠿⣧⠀⠉⠙⣇⣤⣤⣿⣿⣿⣿⣿⡆⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⣿⣿⣿⣷⣟⠀
⠀⠀⠀⠀⠀⠉⠉⠹⠿⠿⠀⠀⠈⠤⠂⠀⠀⠀⠀⠘⠠⠴⣶⣤⠀⢀⣴⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣛⡋⠛⣿⢿⠀⠉⣽⣶⠾⣿⢿⣿⣿⣿
⠀⠀⠉⠙⠓⠀⡀⠀⠐⢀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⣩⣿⢲⣯⣿⣿⠏⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⢿⣿⣷⠍⢀⣶⣿⣟⣵⣾⣿⡿⢿⣿⣿
⠀⠀⠀⠀⣠⡴⠃⠀⢀⣞⣋⣤⣤⣤⡄⢡⡀⠀⠰⠄⠀⠘⠛⠻⢿⣿⣿⣧⠀⢿⣿⣿⣿⡿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⡌⠛⠉⠀⠀⠿⣿⡿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⢀⣻⠿⠇⠀⣀⡴⠿⠍⣿⡿⠛⢢⣤⣆⣰⡀⠀⠀⠀⠀⠀⠀⠉⣼⠻⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠯⣽⢿⣿⣿⣿⣿⣿⣿⣻⣿⣶⣶⣾⣷⣦⣤⣤⣾⣿⣶⣿⣿⣿⣿⣛⣻
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠹⣿⣶⡌⠉⠙⠛⠃⡀⠀⠀⠀⠀⠀⢀⣴⡶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠇⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣿⣿⣿⣿⣿⣍⣽⣿⣿⣭⣽⣯
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣿⡟⠋⢰⡖⠐⠂⠛⠓⠢⠀⣨⡿⢆⡚⠋⢀⠀⠒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡷⠀⠀⠠⠀⠸⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⡟⡋⠈⠀⠛⠛⢻⣿⣿⣿⣛⣾⣿⣍
⠍⠁⡔⠀⠀⠀⠀⠉⠛⠿⠍⠁⠀⠛⠉⠁⠀⠀⠀⠀⠀⠻⠧⠀⠉⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠙⠋⠀⠀⠈⠛⢻⣿⣿⣿⡿⣿⡷⡇⠀⠀⠀⠀⠀⠈⠉⠉⢽⣿⣭⠶
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠂⢤⣿⣶⣻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣙⣿⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠷⢗⣀⣀⣀⣀⣀⣠⣤⣤⣤⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠤
⢁⢠⠟⠀⠀⢠⡾⣿⠇⠀⠀⠀⠘⠉⠘⢁⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣶⡄⠙⠿⠽⠇⢀⣀⢠⣄⡀⢠⠤⠀⠀⢰⣎⠀⠀⠀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣷⣶⣶⣶⣤⣤⣤⣀⣀⣤⣤⣤⣀
⠃⡶⢶⣶⠯⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⡀⠀⠀⢀⣠⣽⣿⣿⡷⠀⠀⢴⢇⣝⣿⠋⠉⠉⢈⠀⠀⠀⠘⣿⠲⠶⢦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣿⡿⢿⣿⣿⣁⠈⢡⣿⣿⣿⣿⣿⣣⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣬⣤⣀⣀⣀⣬⣤⣤⣶⣿⣦⣶⣶⣿⠿⠟⠋⠙⢳⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠙⠁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⡿⡿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣀⠀⠘⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢧⣬⣷⡄⠒⠚⣛
⣿⣿⣟⣿⣿⣿⣿⣿⣿⡉⠉⠙⠛⠙⢿⣿⣟⠛⠉⠉⠁⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠛⠁⠀⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧⣤⣴⣿
⠉⠉⠿⣿⣿⣿⣿⣿⣻⠏⠘⢦⣆⠀⠀⠉⢋⡀⠀⠀⠀⣺⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠲⠔⠝⠿⢿⣿⣿⠉⠀⠀⢸⡇⠀⠀⠀⠀⠙⠓⠀⠀⠹⠛⠛⠿⣆⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣻⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠚⣻⣶⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⢠⣴⣷⣿⣿⣿⡿⠯⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⢀⣤⣶⠛⠀⠀⣠⣤⣶⣶⣾⡶⠰⠆⠀⠈⠁⠀⠀⠉⠉⠻⢿⢿⣿⡄⠙⠛⠻⠿⠛⠙⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡼⠟⠛⠀⢠⣖⡋⠸⣿⡟⠋⢑⣶⣶⣼⣢⠀⠀⠀⠀⠀⠀⠀⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣹⣿⣿⡏⠀⢈⠋⣡⡄⠀⠀⠀⠀⠀⠀⣰⡾⠋⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠂⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⡀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡿⠏⢁⣒⡓⠈⠉⠉⠉⢃⣀⣠⠿⣣⣌⠉⠐⠀⠈⠛⠆⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⡖⣀⣹⠿⠙⢻⣿⣿⣿⣿⣿⣿⣿⡟⡋⠀⠀⠉⠉⠙⢿⣿⣿⣭⣿⣿⡇⠀
⠀⠺⠁⠀⠀⠀⠀⠈⠙⡇⠀⠀⠉⠁⣀⡀⠀⠀⠀⠈⠛⠻⠉⠉⠀⠀⠀⢰⣄⣀⣤⣤⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡀⠀⠀⠈⠁⠀⠀⠀⠉⠹⠿⢿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠑⠺⢿⣴⠿⠂
⠀⡀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠲⣿⢿⡽⣦⠄⠀⠀⠀⠀⠀⠂⠀⠀⣠⠀⠀⠹⣝⣣⣿⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠯⣤⣤⣄⣀⣄⣤⣤⣀⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀
⢰⠃⠀⠀⠐⠟⠿⠃⠀⠀⠀⠈⠉⠘⠁⠄⢀⣤⢀⡀⠀⠀⠀⠀⠀⠀⣲⣿⠆⠈⠓⠀⠀⠸⠀⠀⠀⢀⠠⠿⠆⠀⠀⣦⡀⠀⠀⠀⢠⣤⣤⣭⣭⣽⣿⣿⣿⣯⣝⣳⣶⣦⣤⣤⣿⣷⣶⣶⣤⣤⣤⣤⣤⣦⣶⣦⣤⣤
⣧⢶⡶⣶⠋⢶⠄⠰⠶⠶⠆⢀⣀⣀⣥⣾⣿⢻⣿⣯⣄⢀⣀⣀⣤⣾⣿⣿⣿⡄⠀⠲⠀⠀⣰⠀⠀⠀⢠⠄⠀⠀⠀⢹⠇⠂⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛
[16A⣛⣻⣿⣤⣄⠀⢾⣿⣿⣿⣿⢧⣴⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣇⣄⠀⢻⣿⣿⣿⣿⡂⠈⠛⠛⣻⣿⣿⣿⣿⣿⣷⣿⣦⣶⣦⣄⣀⣀⣤⣤⣤⣶⣦⣤⣴⣶⣿⠛⠛⠃⠘⢻⣶⣶⣤
⣿⣿⣿⣯⣭⣿⣾⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣬⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣄⠁⠈⢺⣿⢻⣿⣿⣷⣾⣷⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠀⠀⠀⠀⠉⠀⣾⠛
⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⠟⢫⣿⣄⠈⣛⣿⣿⣿⠟⢿⡁⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⡿⠛⠉⠉⢿⣿⣿⣿⣿⣻⣿⣿⣿⡧⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⡯⡿⠿⠀⠀⠀⠀⠐⠒⠋⠀
⣇⠘⣿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠈⠹⣿⡏⠉⠀⠀⠀⣀⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢣⡀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⣿⣷⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣤⣤⣴⣖⣂
⠈⠰⣾⣿⣿⡿⠁⠓⠀⠘⢠⡆⠀⠀⠀⢀⡀⠀⠀⠀⣹⣍⣻⡾⠻⢷⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠉⠁⠀⠀⠉⠀⠀⢸⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣽⣛⣿⣿⠿⢿
⠃⠃⠙⠛⠻⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠙⠃⠀⠀⢸⠋⠉⠑⠀⠀⢸⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣄⣈
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⡻⣗⢀⠠⣿⣶⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠒⠒⠂⠀⠀⠀⣨⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢠⣾⢿⣿⣿⣿⣟⠁⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣶⣶⡄⠀⠀⡶⠶⢾⣿⠏⠀⠘⠀⢀⠈⠀⠀⠀⠀⠀⠙⠻⣿⣿⠆⠈⠛⠉⠈⠉⠙⢿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠠⠖⠋⠀⠀⠀⣾⡄⠈⠻⣥⣄⡰⠿⣶⣿⡦⠀⠀⠀⠀⠀⠀⠀⠛⠁⣀⡀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠰⣿⣇⣀⣴⣿⡿⠃⠀⣈⢀⣴⣄⡀⠀⠀⢀⡀⠀⣠⠞⠫⣁⡀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠃⠀⠀⠀⣠⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣭⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀
⢀⠀⠀⠀⠀⠺⣿⣿⠿⠛⠃⣀⣿⠅⠀⠀⠀⠀⢠⣤⡴⠟⣷⣤⠀⠀⠀⠈⠙⠂⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣤⡽⠿⠉⠹⣿⣻⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠈⠉⠛⠟⠏⢤⣿⠿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠠⣄⣈⣁⣀⣤⠀⠀⠀⠀⠀⠉⠻⠂⠀⠀⠀⠀⠹⣤⣤⣶⣶⣴⣾⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠘⠛⠳⣿⡟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠄⠉⠀⠀
⡄⠀⠀⢀⣠⣶⡄⠀⠀⠙⣿⣿⣿⠾⠶⠄⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⣀⠹⢯⣥⡿⠋⠉⢁⡀⠀⠀⠀⠀⣰⣀⠀⠀⠀⠀⠀⠀⠙⠣⢶⣶⣦⣤⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠋⠛⠀⠀⠀⠀⠉⠁⢈⣠⢆⣠⣦⣀⣀⠀⠀⠀⠀⢠⣤⣿⣿⣷⣌⠛⠀⠀⠀⢸⣇⣀⣀⣼⡟⠟⢳⣼⡒⣶⡀⠀⠀⢴⣶⣶⣾⣿⣿⣿⣿⣿⣷⣾⣽⣿⣷⣶⣶⣿⣿⣿⣷⣶⣶⣶⣦⣶⣶⣶⣤⣶⣶⣶
⢠⠖⠲⣶⠎⢶⠤⠰⠶⠶⣶⣤⣾⣾⣿⣿⣿⣿⣿⣦⣠⣶⣶⣾⣿⣿⣿⢿⣧⣪⢾⣧⣤⣸⣿⡿⣶⣽⣖⠀⣾⡯⠋⢸⠏⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭
[16A⣻⣿⣯⣤⠀⠀⣼⣿⣿⣿⣿⢄⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣴⣶⣶⣶⣾⣿⣿⣿⣿⡿⢀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠉⠉⣵⣾⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣴⣦⣶⣶⣶⣤⣶⣾⡏⠈⠉⠀⢉⣽⠷⣶⡆
⣿⣿⣿⣯⣿⣷⣾⣿⡿⡿⣿⣌⣽⢿⣿⣦⣿⣿⣿⣇⣭⡿⣷⣤⣼⡿⡷⢾⣟⣿⣿⣿⣿⣿⣆⢈⠐⢀⣿⢂⣻⡄⠀⠀⠀⠀⣿⡹⣿⣿⣛⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⠁⠰⡟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠚⢛⣯⡀⠛⠿⢾⣿⠽⠻⣟⠀⣸⣼⣿⣿⡏⢹⢿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⣾⣿⣷⣀⣤⣶⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⢺⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀
⡏⢻⣿⣿⣿⣷⣶⡄⠈⠁⠀⠈⠙⣷⣾⠙⠉⠉⠉⠀⣠⣶⣿⣿⣿⣞⢛⣺⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠛⢿⣿⣿⣿⣿⣿⣿⣯⣥⣽⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣶⣶⣾⡥⠀
⠁⠈⣿⢿⣿⣿⠇⠉⠀⠠⢠⠀⠀⠀⠉⡀⠀⠀⠀⠀⣻⢛⣿⡽⢿⣧⡘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⠀⢨⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⠛⠉⠻
⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠉⠓⠀⠀⠀⡽⠛⠋⠀⠀⠀⣤⠄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠏⠀⠘⠓⠀⠀⢽⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⣿⣿⣷⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢉⠻⡆⠀⠀⡶⣶⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢟⣮⣾⣿⡃⢰⣿⡿⠋⣻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠛⠛⠻⠟⠃⢀⣴⣄⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⢀⣴⣦⠀⠀⠀⡆⡾⢿⡧⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠈⠈⣿⠇⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣝⠃⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠠⠞⠋⠁⠀⠀⣦⠀⠈⢿⣡⣄⡾⠷⣶⣿⠄⠀⠀⠀⠀⠀⠀⠀⠉⢀⣤⡀⠀⠀⠀⠀⠀⠛⠛⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠛⠟⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢤
⠀⠀⠀⠀⠀⢰⣿⣄⣠⣾⣿⠿⠀⠀⣡⡈⣦⣄⡀⠀⢀⣠⡀⢀⡴⠋⢡⣀⡀⠀⠀⠀⣠⣤⣄⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡭⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠲⣿⣿⠿⠿⢀⣩⡯⠁⠀⠀⠀⠀⢠⣤⡚⢻⣷⡤⠀⠁⠀⠈⠙⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⣬⠿⠏⠉⠻⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⢿⡄⠀⠀
⠂⠀⠀⠀⠀⠀⠁⢹⢀⠀⣈⣁⣀⣤⠠⠀⠀⠀⠀⠙⠓⠀⠀⠁⠀⠀⢣⣤⣶⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⠀⠙⠉⠛⠿⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣋⠀⠀⠀
⠀⠀⠀⢀⣠⣤⠀⠀⠀⠑⣿⡿⣷⠾⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠻⣿⡿⠿⢹⡏⢹⡁⠀⠀⠀⣠⣿⣿⣷⣤⡀⠀⠀⠀⠈⡹⠿⣶⣶⣶⣿⣿⣷⡾⣶⣦⣀⠀⠀⢠⣤⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠈⠀⠀⠀
⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠉⠁⢈⢰⣀⣰⣦⣀⣀⠀⠀⣀⣀⣠⣤⣿⣿⣷⡿⣟⣈⣍⣁⣺⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣨⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠖⠶⣶⠯⢶⠶⠰⠶⢶⣶⣶⣶⣾⣿⡟⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣿⣷⣖⣄⡀⢿⣿⣿⣿⣿⣳⣿⣿⣯⣛⣿⣿⣿⡿⣿⣿⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⡆⡀⢹⣿⢸⡇⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣤⣶⣶⣾⣾⣿⣿⣶⣿⡿⡏⠉⠉⠁⢈⣿⣿⣶⣆⠀
⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⡾⠙⣿⣿⣿⣿⣿⣿⣿⠟⢻⠟⣿⣟⣭⢻⣿⣿⣿⣿⣿⣿⣿⣆⣄⣃⣼⣏⣽⣿⡟⠀⠀⢀⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⡀⣸⡟⠉⠀
⣿⣿⣿⣿⣟⢛⠛⠿⠟⠑⠺⢷⣦⣌⢭⡝⠿⠌⠈⠁⣄⣼⣿⣿⣿⣯⣼⣿⣿⣿⣽⣿⣿⣷⡿⠚⠿⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣟⣿⣿⣄⣀⡀⠀⠈⢡⣀⣠⣴
⠸⣿⣿⣿⣿⣿⣆⠀⡀⢀⠀⠀⠛⠿⠀⠀⠀⠀⠀⣴⡿⠿⣿⣿⡿⢏⣯⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⡸⣿⡋⡿⠿⠋⠈⠀⠁⡧⠀⠀⠀⠀⢦⣄⠀⠀⠀⢼⣧⣿⠋⠉⠛⠿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣿⡿⠟⠛⠋⣿⣿⡿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⠛⠛⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⢋⣀⠀⠀⠀⠀⠰⣟⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣀⣠⣴⣿⠟⠃⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⣙⣧⢠⢀⣖⣶⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠻⠃⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠄⠀⠀⠀⢀⣀⣀⠄⠀⣀⠀⠀⠤⠀⠀⠸⠿⠿⢾⣿⣿⡏⠀⢿⡿⠟⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣙
⠀⠂⠀⠀⠀⣰⠇⢛⣻⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⡿⠟⠀⠀⠀⠀⠀⠀⠘⢿⣿⡏⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀
⠀⠀⠀⠀⠸⣇⠀⠈⢻⣤⡀⠀⠹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣀
⠀⠀⠀⠀⢸⣿⣤⣄⡘⠻⢋⠀⠀⠷⠷⠶⣤⡀⠀⢀⣤⡄⠀⠜⠉⠑⠤⣄⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠀⠀
⠀⠀⠀⠈⠛⠿⡟⠂⠀⠐⠚⠉⠁⠀⠀⠀⠈⠷⣶⡊⡩⠿⠖⠀⠁⡀⠀⠀⠁⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡇⠆⠀⠀⠀⠀⠈⠻⠿⣿⣿⣟⣿⣆⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠙⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣋⠀⠀⠀⠀
⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⣤⡨⣿⣟⡿⠁⠀⠀⣶⡆⠀⠀⢀⠀⢀⡀⠋⠀⠀⠀⠀⠀⠀⠛⣿⣿⣾⣿⣿⣿⣿⣷⣷⣶⣄⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡼⢤⣤⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⡇⠉⣀⠀⠀⠀⡿⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⢀⣿⣿⣄⣌⢻⣶⣆⣄⣴⣤⣼⣿⣿⣿⣿⣷⠀⢩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣬⠀⡂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣿⣷⢒⣶⣬⣿⣿⣿⣿⣧⣛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣄⣺⣿⣯⣿⡿⣿⣿⣿⣿⣿⡏⠘⢣⡀⣿⣦⣿⣿⣿⡷⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠁⠀⠀⣼⡿⢿⣿⣆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣗⠘⠿⣿⣿⣿⣿⣿⠟⠉⣿⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⡈⢀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠠⣤⣻⠃⠀⣢
⣿⣿⣿⣿⣭⣍⠉⠉⠉⠈⠙⢻⣷⡖⠻⠛⠛⠓⠉⢸⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠈⠿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣀⣀⣤⣤⡾⠟
⢹⣿⣿⣿⣿⠻⠃⠠⢀⡄⠀⠀⠙⠋⠀⠀⠀⠀⠰⣿⠛⣛⣿⣷⣄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡊⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠘⠿⠻⡿⠍⠀⠀⠀⢸⡇⠀⠀⠀⠈⠳⠦⠀⠀⠘⠿⠿⠛⠀⠈⠉⢋⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⡿⠛⠛⠉⣿⣿⡿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣄⠀⠀⣀⣀⣹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠉⠀⠀⢀⣴⣿⠗⠃⠈⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⣧⣽⣆⣦⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣶⠿⠿⠂⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠀⢀⡀⣤⣤⡴⠄⠠⠤⠀⣶⠛⠀⠈⠛⠛⠻⣿⣿⣿⣏⠙⠿⠻⠗⠿⠿⣿⣿⣿⣿⣿⣿⡿⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠾
⠶⠀⠀⢀⣀⡾⠉⢉⣿⠁⠀⠀⠀⠸⠓⠀⠀⠀⠀⠀⠀⠈⠹⠟⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⠻⡿⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⢸⣿⡇⠀⠀⢘⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣾
⠀⠀⠀⣸⣿⣿⣶⠦⠚⠙⣡⡤⠄⠀⠉⠁⢲⠀⠀⣰⣶⡄⠐⠋⠀⠈⠲⠄⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠙⠇⠀⢼
⠀⠀⠀⠈⠉⠡⠍⠀⠀⠚⠉⠀⠀⠀⠀⠀⠈⢷⣆⠀⠒⠛⠁⠀⠀⠄⠀⣀⣀⣀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠦⣤⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢴⣴⣺⣁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣿⣻⡿⠙⠛⠁⠀⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣤⣀⣀⠈⡛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠽⠿⠥⠀⠀⠀⠀
⠀⣴⣾⡿⠀⠀⠀⠀⠀⠒⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⢀⡙⠟⠁⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⣙⣿⣿⣿⣿⣻⣿⣿⡿⣛⣴⣤⣴⣶⣶⣶⣦⣤⣤⣄⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡶⣿⣶⣶⠀⠀⠀⠀⠀⣴⣴⣶⡄⠚⠀⠀⠄⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠏⢶⠶⠰⠶⠶⢶⣜⠟⠃⣤⡙⢿⣿⣷⣶⣾⣿⠋⠛⠛⠛⠋⢁⣀⣤⣀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣿⣏⣻⣷⣾⣿⣿⣿⣿⣮⣻⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢘⢷⠠⣶⠀⣿⣷⣿⢷⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠾⠛⣿⡿⠆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣀⠹⢿⣿⣿⣿⣿⡿⠇⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡈⠀⢀⣯⣴⣿⡿⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⠦⠟⠀⢀⣶
⣿⣿⣿⣷⣶⣆⠈⠉⠀⠈⠙⣿⣿⡟⠋⠉⠉⠉⢁⣵⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⡟⠙⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣶⣾⡟⠛
⣿⣿⣿⣿⣿⠍⠀⠐⣠⠂⠀⠀⠉⢁⠀⠀⠀⠀⢻⣟⣹⡿⠿⣧⣄⡿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣦⣤⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠛⠛⠻⠛⡣⠀⠀⠀⢿⠁⠀⠀⠀⠈⠛⠂⠀⠀⢹⠟⠛⠃⠀⠀⠉⣁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢨⣿⣿⡿⠟⠛⠉⢙⣿⣿⠿⠟⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠶⢹⡶⠀⠀⣠⣄⣀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠋⠀⠀⠀⢠⣾⡿⠟⠈⠁⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢠⣶⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⢠⣶⠶⠷⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⣤⣠⣶⣶⡒⠀⠐⠂⢨⠍⠁⠀⠈⠉⠉⠻⣿⣿⣿⡦⠙⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⡏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠿
⠓⠀⠀⣤⣔⠛⠀⢼⡟⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠈⠛⠙⠅⠀⠀⠀⠀⠀⠀⠈⢿⠿⠉⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣀
⠀⠀⠀⣿⣿⡀⠀⠀⣽⣿⡆⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿
⠀⠀⠠⣿⣿⣿⡟⠒⠉⢉⣶⠒⠀⠀⠁⠉⠃⠀⣠⡾⠷⣀⠈⠀⠀⠐⠶⠄⠀⠀⢰⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠙⠙⠻⣿⣿⣿⣿⣿⣿⡇⠘⠃⠀⢿
⠀⠀⠀⠈⠑⠂⠁⠀⠘⠉⠁⣀⠀⠀⠀⠀⠈⠻⣧⠀⠉⠉⠀⠀⠀⢀⣀⣀⣠⣤⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠉⠻⠿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠟⢿⣿⣿⠿⠶⠾⠷⠈
⠀⠀⣀⡀⠀⠀⠀⠀⠶⢷⢯⢭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣧⣿⠟⠊⠙⠉⠀⣰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣠⣦⣤⣆⣀⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠟⠳⠆⠀⠀⠀⠀
⠰⠿⠿⠃⠀⠀⠀⠀⠘⠀⠐⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄⣠⠘⠋⠀⠀⠀⠀⣴⠏⠀⠀⠀⠐⠀⠀⠀⠀⠀⡄⠀⠀⢠⣭⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣷⣾⣿⣿⣿⣶⣶⣦⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠇⠿⣿⣇⣀⠀⠀⣀⣀⣕⣼⣶⣤⣏⡀⠐⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠮⢶⠶⠰⠶⠶⠶⠝⠛⠠⡄⠙⠿⠿⢿⣿⣿⣿⣦⣻⣏⢹⣿⣧⣤⣤⡀⠀⢀⣷⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣿⣶⣿⣿⣿⣿⣯⣟⣿⣶⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠜⡂⢻⠀⠸⠟⠁⠀⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢦⣨⣥⣤⣾⡏⠁⢒⣀
⣿⣿⣿⣟⣻⠻⠿⠿⠿⠾⣿⣦⣽⣿⡿⠿⠿⠿⠻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠸⢿⢿⣇⣀⣀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣺⣿⣿⣿⣿⣿⣿⢿⣯⣤⣶⣿⠟
⣿⣿⣿⣿⢿⡆⠀⡀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠠⣾⡿⣿⣿⣿⡛⢹⣿⠏⢛⣿⣿⣿⣿⣿⣧⠀⠀⣜⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⣿⣿⡟⠋⠀⠀⠀⠸⡧⠀⠀⠀⠐⢦⣄⠀⠀⠠⣿⣾⣿⡋⠙⠻⠚⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠈⠁⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⡀⠀⠉⠀⠀⠰⣃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣽⣝⢻⣿⣿⣿⠿⠋⠀⠀⢀⣼⣿⡏⠡⠄⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⣛⡍⣤⣲⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣶⡿⠛⠁⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⠀⠀⠑⢀⣀⣀⣄⡀⣀⠀⠀⡤⠄⠀⠻⠿⢿⣿⣿⣿⣿⡻⣿⠿⠏⢿⣿⣿⣿⣿⣿⣿⣿⡟⢻⢹⠟⣿⠛⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿
⣀⠀⠀⠀⢸⣿⢛⣿⡿⠀⠀⠀⢀⡮⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⡛⠻⣿⠷⢯⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⠀⠀⠀⣾⣯⠀⠈⠛⣶⣦⡄⠈⠙⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣾⠆⠀⠀⠀⠀⠀⠀⠈⢛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⣦⡀⢀⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢷⣾⣿
⠀⠀⠀⣿⣿⣦⣤⣼⠟⠋⣅⣀⡲⠢⠶⢤⡀⠀⢠⣤⡀⠰⠛⠒⠒⢤⡄⠀⠀⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠁⠋⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣽⣿
⠀⠀⠀⠻⣋⡛⠛⠉⠶⠞⠋⠁⠀⠀⠀⠀⠰⢶⣟⠩⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣧⣀⣴⡏⠿
⠀⠀⠀⠀⠈⠁⢀⣀⣤⣤⣤⣖⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠠⡶⠾⢺⣿⠿⢿⣿⠗⠀⢀⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠛⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⠁⠀⠀
⣀⣴⣾⡷⠀⠀⠀⠉⠻⠿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠛⢿⠏⠀⠀⠉⠀⢀⣾⠃⠀⠀⣀⠄⠃⠀⠀⢀⠀⠀⠀⡿⢿⣿⣿⣿⠿⣿⡿⠶⠟⠀⠀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣬⣁⣀⣀⣀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⣧⣤⠀⠀⠀⠀⠀⠀⣄⣜⡛⣠⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠠⠤⠄⡿⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠄⠀⠀⠀⠀⠀⣤⣤⣄⣾⣿⣉⡙⣿⣿⣶⣶⣶⣶⡟⠛⠿⠷⠄⠀⠀⢀⣄⣀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠟⢷⠖⠰⠶⠶⠟⠁⠈⠉⠃⠈⠉⠈⠉⠁⠁⠀⣀⣀⣀⣀⣀⣀⣸⡏⠀⣀⣴⣿⠃⠀⠀⠀⣠⣤⣤⣤⣠⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣿⣿⣿⣿⣿⣿⣷⠮⣹⣯⡄⠛⣿⣿⣿⠿⠿⣿⡃⢸⣿⣿⣿⣿⣻⢿⣿⣿⣻⡿⢿⣏⣁⠀⠀⢠⣧⣤⡋⠀⢀⣀⣰⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣤⠀⠀⠀⠀⠀⠀⠃⠀⠀⣤⠀
⣿⣿⣷⣶⣀⠈⠀⠀⠈⠹⣿⣿⠉⠉⠈⠀⠀⣀⣿⣿⣿⣿⡟⠛⣛⣋⠻⠿⣿⣿⣿⣿⣏⠀⠀⢸⣿⣿⣰⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠁⣹⣿⣿⣧⣽⣿⣿⣿⣿⣟⣴⣿⣷⣦⣤⣤⣄⣀⣠⡀⠀⠀⠁⠀
⠛⠟⠉⠀⠉⠀⠂⣤⠀⠀⠀⠉⣀⠀⠀⠀⠀⣹⠋⣼⡿⠿⣷⣄⠛⠋⢠⣾⣿⣿⣿⣿⣿⣧⣦⣾⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣙⠿⢿⠿⠷⢿⣧⡄⠀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠛⠀⠀⠀⠸⠛⠛⠀⠀⠀⠀⡀⠀⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⡿⠟⠛⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⠀⠀⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠛⠸⢟⢀⠠⠤⣄⡀⣴⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠟⠙⠛⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣾⣴⣿⡟⠁⣾⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⠃⠉⣿⣿⣿⡟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣋
⠀⠈⠀⠀⣦⠘⣿⣯⡉⠀⠙⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⣿⣿⠀⠈⠉⠁⠈⠉⠙⢻⣿⣿⢻⣿⣿⣀⡠⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠚⠛⠛
⠀⠀⠀⡀⠀⠐⠿⣟⣁⠀⠠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠈⠻⠋⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀
⠀⠀⠀⣿⣂⡀⢠⣿⣿⠇⠀⠈⠀⣀⣀⡀⠀⠀⢀⡀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⢀⣺⡇⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣏⡉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠛⠻⢿⣦
⠀⠀⢰⡿⠿⡿⠿⠋⣐⣶⠖⠀⠀⠀⠀⢁⣀⠴⠿⣛⣄⠀⠀⠍⠑⠲⠄⠀⠀⣰⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠉⢻⣿⢿⣿⣿⣿⣿⣿⡿⡅⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⢿⡇⠀⠀⠀⢿⣿
⠀⠀⠀⠈⠓⠦⠀⠘⠉⠀⣠⠀⠀⠀⠀⠘⠿⣦⠈⠉⠁⠀⠀⠐⣆⣠⣤⣤⣤⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⡿⠓⠒⠒⠋⠈⠈
⣠⣤⣤⠀⠀⠂⠲⣶⣿⣿⢿⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⢽⣿⣿⣏⠉⠿⡏⠀⠰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠠
⠿⠿⠛⠀⠀⠀⠀⠉⠁⠈⡡⡆⢀⣤⠀⡀⠀⠀⠀⠀⢠⡠⣿⣾⣦⣠⠙⣯⡁⠁⠀⠰⣶⣄⣹⣿⣄⢀⣀⡁⣀⣀⣀⣴⠀⠀⢠⣼⣶⣿⣿⣿⣿⣿⣭⣥⣤⣴⣲⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⡤⠤
⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣷⣿⣿⣿⣿⣯⣤⣤⣤⣶⣿⣿⣿⣿⣿⣧⣴⣿⣿⣦⣤⣤⡀⠛⢻⣿⣿⢸⣿⠟⠿⣻⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀
⠀⠀⠠⠄⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣴⣿⣿⣿⣿⣤⣿⣿⣿⣿⡅⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠷⠶⣶⠿⢿⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣿⣿⠻⠿⠿⠿⠉⠰⢿⣶⢈⣭⣿⠿⠋⠛⠙⢠⣀⣿⣿⠿⣿⣅⡉⢿⣿⣯⣿⠛⣷⣤⠀⠀⢠⡆⠀⠀⠀⢠⣶⣴⣿⣿⣿⣿⣿⣿⣤⣽⣿⣹⣿⢸⣿⣿⣿⢻⣿⣿⣿⣿⣿⠏⢭⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀
⣿⠿⠯⢥⠀⠀⠀⠀⠀⠛⢻⠅⠀⠀⠀⠀⢠⣾⠿⣿⣿⡌⠀⢩⣤⠀⠛⣻⣿⣿⣿⣿⡀⠀⠀⢇⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⣹⣿⣿⣶⣿⣿⣿⣿⣿⣼⣿⣿⣿⣶⣶⣶⣶⣴⣆⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⣄⡀⠀⠀⠠⣇⣼⡟⠉⠛⠳⠊⠁⠀⢿⣿⣿⣿⣿⣿⣷⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣭⡝⠛⠋⠉⣿⠖⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣋⠀⠀⠀⠀⠀⠐⠀⣐⣿⣿⡿⠿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠀⠀⢰⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢷⣤⣤⣀⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⢈⣛⠁⠀⣘⣳⡖⢘⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠀⠀⠀⣀⣤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠛⠛⠳⠟⢉⣁⠀⠸⡿⠏⠉⣿⣿⡿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⠛⠀⠀⠀⠀⢠⣤⠀⠀⢀⡀⣀⣤⡄⡗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣟⣉⣉⣁⣄
⠀⠀⠀⠸⠀⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠙⢻⣟⠉⣿⣿⡀⢈⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣯⣿⡿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠈⢡
⠀⠀⣤⡄⠀⠈⢷⣶⡄⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠘⠏⠀⠸⠟⠘⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣯⣐⣀⣀⣾⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣀⣀⠀⠁
⠀⠀⣹⣷⣤⣠⣿⠿⣇⣀⣀⠀⠒⠶⠄⠀⠀⣠⣤⠀⠰⠚⠋⢀⣀⠀⠀⠀⢀⣠⣶⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⣻⣦⡀
⠀⠀⠛⢉⠻⠉⠁⣠⡿⠇⠀⠀⠀⠀⢠⣤⡚⠉⠭⠶⠆⠀⠀⠀⠈⠃⠀⠀⢼⣿⣿⠿⠦⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣷⡶⠆⠀⠈⠉⠛⠛⠿⣿⣿⣻⣧⣀⣀⡀⠙⠿⠃
⠀⠀⠀⠀⢈⣀⣀⣭⣄⣶⠆⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠈⢰⣶⣷⣾⣿⣿⣿⣿⠷⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡈⢙⢿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣏⡉⠉⠉⠁⠀⢀⣾
⣶⣷⡆⠀⠈⠉⢻⡿⢿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣘⠛⢿⣿⠧⠄⢿⣿⡆⠸⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣾⣿⣷⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⡀⠀⢀⣈⡉⢁⠀⠀⠀⠀⠘⠻
⠉⠉⠀⠀⠀⠀⠀⢀⠈⣧⣿⣴⣿⣤⣤⠀⠀⠀⠀⣐⣶⣽⣿⣿⡔⠀⣠⣤⣀⣰⣿⣿⣷⣾⣿⣿⣅⣰⣶⣶⣾⣿⣾⣿⡏⠁⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⢀⣤⣴⣾⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠁⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠷⠶⣶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣷⡠⠀⠉⠉⠈⠀⠙⣿⣴⠛⠋⠉⠉⠁⢀⣼⣿⣿⣿⠿⠟⠿⢛⢉⣿⣿⣿⣤⣾⡿⠁⠀⠀⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠙⣿⣿⣿⣹⣿⣿⣿⣿⣿⢏⣽⣿⣥⣄⣀⣀⣀⠀⣀⠀⠀⠘⠀⠀⠀
⠉⠁⠉⠀⠐⢠⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⡟⢉⣽⠿⣿⣤⡘⠿⠃⣤⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠷⠒⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣶⣦⣀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠓⠂⠀⠀⢈⡜⠛⠁⠀⠀⠉⢁⣀⢠⣭⣿⣿⣿⣿⣿⣿⣿⢿⡆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠟⠃⠀⠀⠀⠀⠐⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠉⠉⠀⣿⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠶⡯⣶⡀⠀⢀⣀⣀⣸⣿⡿⢿⣿⣿⣭⣽⣿⣿⣿⣀⡀⢸⣿⣿⣿⣿⣿⣿⡟⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣿⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣦⣄⣤⣶⣾⠟⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢽⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀
⠀⠀⣠⠠⣶⣶⠒⠀⠐⠂⠀⠀⠐⠀⠀⠉⠉⠙⠻⠿⣾⡄⠈⠿⠟⠛⠛⠻⣿⣿⣿⠿⣿⡿⠀⠀⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡥⠼⢷⣶⣶
⠀⠀⠈⠐⢿⣿⡃⢠⣤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠉⠁⠀⢹⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⠿⠻⠯⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢨⠿⠛
⠀⠀⠀⠀⢀⣿⣿⡄⠀⠘⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠀⠀⠀⠀⠀⠀⣸⢟⠀⠀⠀⠀⠸⠿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣆⣤⣽⣏⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣶⣾⣷⠀⠀
⠀⠰⣷⡖⠹⠿⠃⣲⡶⠀⠀⠉⠉⠁⠀⢀⣼⡿⢦⡀⠀⠀⠈⠓⠦⠀⠀⢠⣾⣿⠿⣀⣀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⡆⢰
⠀⠀⠀⢄⠀⠀⠛⠋⢀⡀⠀⠀⠀⠘⠿⣧⡀⠛⠉⠁⠀⠀⢄⣀⣠⣀⣤⣼⣿⣧⡀⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠛⠋⢿⣿⣿⣿⣷⠶⠿⠈⠙⣿⣿
⣀⠀⠀⠀⠁⠢⣆⣶⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣿⣿⣿⡿⠛⢿⢿⠀⠀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣄⣛⣿⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⢿⣿⡶⠦⠄⠀⠀⢰⣿⣿
⠟⠀⠀⠀⠀⠀⠉⠀⠈⣉⠁⣀⡀⠀⠀⠀⠀⠀⠀⣀⣹⣶⣶⢉⡽⠟⠁⠀⠀⠀⢤⣀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣻⣿⣷⣾⣿⣷⣶⣶⣶⣴⣦⣤⣤⣤⣶⣶⣦⣤⣤⣤⣄⣀⣈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣆⡀⣀⣠⣴⣿⣿⡿⡿⠋⠀⣤⣦⣄⡀⠀⠈⠛⠁⢹⣿⡆⠀⠀⠀⠀⢀⣠⣼⣶⣤⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢲⠿⣿⣿⡿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣄⣬⣿⣿⣿⣿⣿⡃⠂⠀⢻⠀⠀⠀⠀⣀⣾⣿⣿⣿⣟⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠛⠋⠉⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣴⣿⡇⠀⣽⣿⣿⣿⣿⣿⣿⣧⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⣶⠴⠶⠶⠶⣨⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣷⣆⡀⠀⠀⠀⠀⠈⢷⣿⠉⠁⠀⠀⠀⣠⣾⣿⣿⣿⣛⠛⣛⣷⣾⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣿⣿⣧⣽⣿⣿⣿⣿⣟⣴⣿⣿⣷⣦⣤⣤⣄⣠⣄⠀⠀⠈⠀⠀⠀
⠃⠀⠁⠀⠈⣴⠀⠀⠀⠁⣀⡀⠀⠀⠀⣹⢇⣴⡟⠻⠷⣦⡟⠻⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡿⣿⣿⡿⢿⣷⣤⠀⠀⠀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠙⡀⠀⢀⣜⠋⠉⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣤⣾⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠻⠻⢿⠄⠀⠠⣴⡄⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⢸⣿⣿⣿⣿⣿⣿⡿⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣳⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣶⣴⣾⣿⡟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⣦⢼⣿⣏⡉⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⠉⠛⢻⣿⡆⠘⠛⠛⠛⠉⠻⣿⣿⡟⠛⣿⡇⠀⣀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣟⣿
⠀⠀⠀⠙⢛⣿⠉⠀⠐⠀⣾⡤⠀⠀⠀⠀⠀⠀⠀⠛⠋⢀⣀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠘⠁⠀⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣤⣤⣤⣶⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣿⣟⣋
⠀⢀⡀⠀⣼⣿⠿⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⡀⠀⢀⡶⠯⣁⡀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣯⣯⠉⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣂⢀
⠀⠸⠿⠞⠉⣥⡶⠖⠂⠀⠀⠀⠀⠀⢀⡤⠿⢛⣀⡀⠀⠀⠀⠁⠀⠀⠀⣼⣿⠀⠀⣀⣀⡀⠀⠀⢠⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣸⣿⣿⣂⣾
⠀⠀⠐⢦⡀⠀⠀⠀⣠⠀⠀⠀⠀⠈⠿⠄⠀⠉⠉⠀⠀⠲⢠⣀⠀⢀⣤⣿⣧⠀⠀⠉⠁⠀⠠⣶⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠿⣿⣿⣿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠉⠹⠿⣿⣿⡿⠿⠿⠟⠈⢹⣿⣿
⣤⠀⠀⠀⠘⢻⡿⠿⢥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡼⠛⠙⠛⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣈⡉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠗⠒⠀⠀⠀⣾⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡠⢀⠀⠀⠀⠀⠀⠀⢀⢀⣶⡇⠀⠘⠁⠀⠀⠀⠀⣤⣀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣭⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣌⣉⡉
⠀⠀⠀⠀⠀⠀⣀⣀⢰⣿⣿⠿⣿⣯⣤⣠⣤⣦⣴⣾⣿⣟⣿⠀⡠⡀⠀⢀⣀⠀⠈⠁⠀⠀⣶⡄⠀⠀⠀⠀⢠⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠹⠭⠿⠛⠿⠶⠟⠿⢿⣿⡿⠿⠿⠻⢿⣿⣿⣿⣾⣤⣼⣿⣿⣿⣄⠀⠀⠀⣻⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⣿⡿⠃⠀⢰⣿⣿⣿⣿⣾⣿⠃⣠⣤⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠶⣶⡷⠰⢶⠶⠶⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡺⠿⣿⣿⣿⣿⣿⣿⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠷⡄⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⢴⡿⢿⣿⣿⣿⡁⠠⠷⠀⢙⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣶⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣬⡁⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠲⣄⡀⠀⠀⠼⣳⣾⠏⠉⠛⠿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠿⣿⣿⣿⠆⠀⠀⠀
⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠤⢀⣠⣼⣅⠀⠀⠀⠀⠀⢰⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⢛⡛⠓⠀⣀⣲⣶⠸⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢸⣿⣿⣿⢿⣿⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀
⠀⠀⠀⣀⣀⣀⡀⢀⡀⠀⠀⡀⠀⠘⠾⠿⣷⣿⣿⣿⡏⢰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣟⣛⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⡏⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣤⣤
⠀⠷⢾⣿⣯⡀⣀⡈⠀⢠⡀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠟⠀⠁⠀⠈⠀⠀⠙⠻⣿⠈⠹⡿⠀⢠⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⢹⣿⣿⠟
⠀⠀⠈⢿⣬⣤⡀⠁⠁⠻⠷⠂⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣿⠃⠀
⢀⣀⣠⣾⣿⡿⠇⠀⠀⠀⠠⠾⠤⠀⠀⠀⣠⡀⠾⠋⢀⣀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠋⠀⣾⣿⣿⣿⡏⢻⡆⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⣿⣻⣷
⠘⠿⠋⠁⢀⣤⠖⠂⠀⠀⠀⠀⢠⣤⡴⠒⢋⡽⠆⠀⠀⠈⠉⠂⠀⠀⢀⣿⡇⠀⠰⠶⠄⠀⠀⠀⣴⣾⡿⠟⣿⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣤⠀⠀⢻⣿⣮⠙⠻⠿⢿⣿⣿⣿⣿⣦⣤⣴⡿⢿⣿⣿⣿
⠀⠐⠲⢄⣀⣀⣀⣠⠄⠀⠀⠀⠀⠙⠃⠀⠁⠀⠀⠀⠀⠁⠴⠤⠀⣾⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣟⢉⡁⠀⠈⣿⣿⣷⡀⠤⢤⣽⣿⣿⣋⠉⠉⠉⠉⢠⣿⣿⣿
⠀⠀⠀⠈⠛⠿⠟⠓⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠋⠀⠀⠉⠀⠀⠀⢀⣨⣁⡀⠐⠖⠳⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠼⣿⣦⣀⣠⣤⣤⣄⣿⣿⣿⣿⣄⢀⣈⣿⣯⣉⣀⣀⠀⠀⠘⠿⢿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣠⣀⣀⠀⠀⠀⠀⠀⠤⡄⣸⣿⡀⠀⠉⠀⠀⠀⠀⠀⣶⡄⠈⠛⠉⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤
⠀⠀⠀⠀⠀⣠⣤⣀⣿⣿⠿⢿⣿⣦⣤⣤⣴⣶⡾⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠖⠛⠋⠙⠻⠋⠙⠻⠿⠿⠟⠛⠁⠀⣀⠀⠀⢀⣀⣀⡀⠰⣿⣿⣿⣷⣤⣽⣿⡁⠀⢀⣀⡀⣀⣴⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣁⣠⣿⣿⣿⣿⣿⣿⠿⠛⣿⣭⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⣿⣿⠆⢰⢶⡶⠖⠀⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⠏⠀⠰⠿⢿⣿⣷⣤⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⡄⠀⠀⠀⠁⣀⠀⠀⠀⠀⣸⢇⣲⡖⠙⠷⠦⠀⠁⠀⣴⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠐⣿⣿⣿⣿⢿⣅⣽⣿⣿⣿⣿⣶⣦⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣷⠟⠛⠻⣿⣿⣷⢶⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠰⠊⠉⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⠻⠆⠀⢸⣿⣿⣿⣿⣿⣯⣹⣏⠉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠿⢿⣿⣿⠇⣀⣀⠀⣸⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠳⠿⠂⠀⠀⢀⡄⢰⡆⢀⣾⣿⣯⢼⣿⣿⣛⣿⣀⠀⠀⠟⣿⣿⣿⣻⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⢒⣛⣻⣿⣿⣿⣿⣿⣿⣆⠰⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣷⣠⣶⠾⠉⠁⢸⣿⣿⠛⠛⠛⠻⢿⠿⢟⡿⣿⠃⠀⠀⡹⡿⠿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣾⣿⣿⣿⠗⠀⠀⠀⢠
⠄⠐⢿⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⣿⠇⠈⠋⠉⠀⠀⠀⠀⢻⡆⠈⠓⡾⠀⠀⢰⣿⣿⡧⣶⡆⣶⣿⣟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠶⠟⢿⣖⣿⣿⣿
⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡿⠿⠋⠀⢹⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⡛⠉⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠰⠟⠃⠀⠀
⠀⠀⢠⣼⣷⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⡼⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣽⣿⣿⣿⡙⠀⠀⠀⢸⣿⣿⠀⠀⠸⠃⠉⠉⠉⠁⠀⠀⠠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠹⠾⣿⣅⠀⠀⠀⠘
⠿⠖⠀⠀⠠⣴⣆⠀⠀⠀⠀⢀⣀⣠⡼⠿⣂⡀⠀⠀⠀⠙⠂⠀⠀⠀⠿⠁⠀⢀⣀⠀⠀⠀⢠⣤⡻⠟⢿⣿⡁⠀⠀⢠⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⢿⣿⠃⣺⣷⡄
⠀⠀⠀⠐⠚⠉⣀⠀⠀⠀⠀⠈⠻⠇⠀⠚⠉⠀⠀⠀⢀⣀⣀⣀⣤⣴⣿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠈⠉⠁⡀⠀⣸⣿⣿⠇⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠉⠀⠾⢿⡾⠛⠒⠒⠂⠀⠁⣽⣿⣿⣟
⠀⠀⠀⢨⣿⣶⣯⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣿⣿⡟⠉⠻⠿⠀⠀⢶⣶⢖⣰⠀⢰⣶⠆⠀⠀⠘⠃⢾⣿⠿⠟⠀⠀⠀⠴⠶⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠙⠁⣴⠟⠛⠂⠀⠀⠀⠀⢸⣿⣿⡛⠉
⠀⠀⠀⠀⠉⠙⢀⡀⠀⣠⠀⠀⠀⠀⣀⣀⠀⢀⢀⣶⣷⠀⢬⠏⠀⠀⠀⠀⢲⣄⡈⠿⣿⣿⡿⠛⠀⢀⣠⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⡄⠀⠠⡿⣶⣶⣿⣷⣶⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣽⣿⡿⣿⣿⣿⣶⣾⣿⣿⣷⣾⣿⣿⣿⣷⣴⣤⣤⣠⣀⣀⣀⣭⣷⣶⡾⡻⠿⣿⣿⣿⡋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀
⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣷⣿⣿⣿⣿⣽⣃⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡉⣹⣿⣿⣷⣶⣾⣿⣿⣿⣿⣆⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠨⠀⠀⠀⠀⠠⣄⠀⠀⠀⠠⢄⣼⡟⠁⠙⠛⠂⠀⠀⠸⢿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⢸⣿⣿⣿⡟⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⣉⣉⢻⠿⠿⠟⠿⣦⡄⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠿⠟⢛⣛⣿⠁⠁⠀⠀⣸⣿⣿⣿⣿⣷⣤⣹⡍⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠟⢛⣻⣿⣟⣁⣀⡀⣀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠉⡋⠁⠀⣀⣀⣴⠀⣻⣀⣼⣿⣿⣖⡶⣶⣯⣽⣦⣄⠀⠈⢹⣿⣿⣯⣯⣿⢿⣿⣷⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣙⣛⣿⣿⣿⡿⣿⣿⣷⡀⠂⠀⠀⠂⠀
⠀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠻⠣⣾⣓⠂⡀⠀⣻⣿⡏⠉⠉⠉⢻⡟⡋⣿⠻⡏⠀⠀⢀⣹⣛⠛⠛⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠛⣻⣿⣿⣾⡿⢿⡟⠁⠀⢀⣠⣇
⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠈⠀⠀⠀⠀⠀⠘⢿⠀⠉⠙⠁⠀⢀⣿⣿⣿⣚⣶⢰⣿⣛⠛⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠐⠛⠹⣿⣻⣿⢿⣁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⠿⢿⣿⣿⣿⣿⠛⠉⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠛⠉⠀⠀⣀
⣀⡀⠰⠞⠂⠀⠀⠀⠀⠤⠤⠀⠀⢀⣀⠀⠠⠶⠋⠁⠤⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⢴⣿⣿⣿⣧⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⢿⣿⣿⣿⠟⠙⠛⣿⣿⣿⣿⣿⣷⠆⠀⠛⢿⣦⡀⠀⠀⠈⠛
⠛⠁⠀⢀⣽⠿⠂⠀⠀⠀⠀⣤⣤⠞⢛⣥⡤⠀⠀⠀⠀⠈⠁⠀⠀⠐⡁⠀⠀⠤⡄⠀⠀⠀⣶⣮⠓⠙⣿⣧⡀⠀⠀⢀⠚⣛⣿⡋⠁⠘⠻⠂⠀⠀⠉⠀⠀⠙⠋⣀⣀⣙⣻⢿⢿⣿⠿⣛⡀⠀⠀⠹⣿⣇⣘⣿⡄⠀
⠀⠀⢀⣈⣀⣠⡄⠀⠀⠀⠀⠈⠙⠂⠈⠁⠀⠀⠀⠀⣤⣶⠤⣴⣶⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡀⡀⢀⣿⣿⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⠀⠀⠛⢿⡿⠛⠉⠙⠉⠀⠀⣠⣿⣿⣿⠀
⠀⠀⠰⣿⡿⠿⠾⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⢀⠘⠿⣷⡟⠀⠘⠛⠃⠀⠘⢿⣷⣤⣧⣀⡾⠛⠀⠀⠀⠈⠁⠁⠛⠛⠛⠁⠀⠀⠀⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡃⠀⠀⠋⠛⠃⠀⠀⠀⠀⠐⠿⠿⠍⠈⠁
⠀⠀⠀⠀⠀⢠⣴⣀⣠⣆⣀⣀⠀⣀⣤⣤⡀⣄⣬⣿⣇⠘⠏⠀⠀⠀⠀⠈⢷⣤⠘⠻⣿⡿⣿⣅⣠⣤⣤⡶⢿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⡀⠀⠘⠛⣿⣿⣿⣷⣾⣷⣶⣶⣦⣤⡀⠀⠀⠀⠀
⠀⠀⠀⣀⣠⣴⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣤⣤⣤⣤⣴⣾⣿⣿⣶⣁⣉⣽⣿⣿⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢑⣙⣿⣿⣿⣿⣿⢟⣄⡀⠀⠀⣠⣤⣶⣶⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⢙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣶⣾⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣤⣶⡆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠃⠀⠀⠀⠀⠈⠲⠀⠀⠀⢘⡴⠟⠁⠀⠀⠈⠀⠀⠀⣩⣿⣿⣷⣿⣿⣿⣿⠿⡆⠀⠀⣿⣿⣿⣿⣅⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣽⠛⠛⠉⢹⠗⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⣴⡄⠀⠀⠀⠀⢀⣤⠤⢿⣿⡏⢉⣻⣿⣿⣿⡀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣼⡄⢀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣤⡄⣠⡴⠶⠟⠈⣿⣶⡾⢿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⢡⠄⠀
⣴⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⣥⡄⠀⠿⠿⠃⠀⠀⠈⢹⣋⠻⠿⣿⠁⠀⢀⣽⣿⣭⣉⣉⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣧⣤⣤⣶⣿⠆⣀
⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣸⣿⡍⠉⠁⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⠿⠛⠻⠗⠀
⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢻⣿⣿⣿⡿⡅⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢳⣤⣴⡏⠀⠀⠀⢰⡿⠏
⠀⠀⠀⠠⠤⠀⠀⠚⠓⠒⠀⠀⣰⣶⡀⠀⠉⠀⠀⠐⠦⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⢿⣿⠇⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⠉⣉⣭⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⣿⣿⡄⢤⣤⠀⠀⠀
⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠶⣾⡉⠴⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣬⣥⠀⠐⠒⠂⠀⠀⠀⠿⠃⠉⠈⠿⠦⠀⠀⠘⠀⠀⢠⣼⣿⡿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠟⢿⣭⣷⣦⣤⣦⠘⠛⢰⣾⣿⡧⠀⠀
⠀⣀⣠⣠⣘⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⣟⣻⣿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠤⢶⡗⢁⠀⠀⠘⠿⠏⠀⠀⠀⠀⠻⠿⠿⢿⢿⠏⠉⠉⠙⠛⠁⠀⠀⠈⣿⡄⠀⠀⠀⠀⣠⣿⣿⠿⠷⠀⠀
⠀⠈⠙⠋⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣤⣤⡈⢛⡻⠃⠀⠈⠀⢀⡀⠀⢀⣠⡤⢤⣤⠛⠁⠀⠀⢀⣀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣠⣄⣀⣀⡀⠘⠛⠛⠃⠀⠀⠀
⠀⠀⠀⠀⠸⣦⣠⣼⣧⣶⣄⡀⠀⠀⣀⣳⣶⣿⣿⣧⣆⠀⠀⠀⠀⠀⠀⠛⠓⢀⣠⣤⣀⣀⡶⢶⣶⣦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠹⢿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⢿⡿⠟⢿⣿⣷⣦⣤⣄⣀⣀⣿⣿⣿⣿⣿⣾⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⢻⣿⣿⣿⣿⣿⣿⣿⣧⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⡿⣹⣿⣿⣴⣤⣄⣠⣶⣿⣿⣧⠀⠀⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⡆⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⢿⠿⢛⣛⣛⡟⠃⠀⠀⠈⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡰⢀⣀⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⢛⢻⣿⣿⣿⣷⣀⣀⡖⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⢛⣛⡻⡫⣿⣽⣿⣧⣴⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⡀⠀⠀⠀⠀⠀⣢⣤⣾⣿⣿⣾⡿⢿⣿⡿⠟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠂⠀⠀⠀⠀⠀⠀⠉⣍⡀⢀⣠⣤⣶⠀⣿⣷⣶⣿⣿⣿⣿⣷⣦⣧⣶⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡁⠀⠀⢷⡤⠀⢠⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠛⠛⠣⠿⣿⣳⣄⠀⢻⣿⡿⠋⠝⠩⡿⣿⠿⠿⠻⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣅⣀⣤⣼⣧⠄⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠀⠀⠁⠀⠀⠀⠀⠀⢻⡇⠀⠀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠙⣿⣿⠿⢿⣷⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡿⠿⣿⣿⣿⣿⣟⠉⠁⠀⠈⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣼⡟⠁⠀⢸⣿⣿⠆⠀⠀
⠀⣀⠀⠀⠐⠢⠄⠀⠀⣠⣄⣀⡀⠀⠀⠀⠡⢤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡰⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠙⣻⣷⣇⢀⣀⠘⠋⣿⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⣤⠐⠛⠡⠼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠠⠄⢸⣿⠟⠃⠛⣿⡄⠀⠀⢠⣾⣿⡻⢿⣿⣿⣿⣿⠟⠏⣿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣄⣀⣤⠻⠿⣧⣼⣿⣷⡂⠁⠀⠀⠀
⠀⢠⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖⢰⣶⠾⠿⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣴⣤⡀⠀⠙⣉⠁⠀⢻⠿⠏⠁⠀⣴⣿⣿⣿⠅⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡋⠉⠉⠁⢀⣾⣿⣿⣿⠁⠀⢶⣤⣤
⠄⠐⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠏⠀⠀⠀⠀⠉⢰⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⠯⠔⠂⠃⡀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠀⠛⠿
⠀⠀⠀⢀⡀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠸⣻⣧⠀⠀⠀⠀⠀⠀⠀⠸⠦⠄⠉⣹⣁⠀⠀⢀⡀⠀⠀⢀⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠿⠛⠋⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣦⣤⣶⣲⣶⣦⡄⠀
⠠⢤⣴⣿⡟⠛⣿⣥⣄⠀⢀⣤⣤⠚⠷⣿⡯⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣤⡁⣼⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤
⠀⠚⠋⠉⠛⠉⠉⠈⠉⠀⠈⠃⠁⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣷⣦⣀⣀⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⠀⠀⢀⣤⣶⣩⣿⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣀⣤⣤⣶⣶⣾⡿⠿⠋⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣿⣟⣟⠿⢿⣿⣿⣿⣅⠀⠠⠶⠶⠿⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣌⣉⡉⠙⠛⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠽⢿⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
[16A⠀⠀⠀⠀⠀⠉⢛⣉⠀⢀⣀⣰⡆⠸⣿⣭⣽⣿⣿⣿⣿⣿⣛⣹⣠⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⢿⣿⣿⡭⣿⠿⠿⠿⢬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠄⠀⢠⣆⡀⡀⢀⣿⣿⣏⠀
⠀⠀⠀⠀⠀⠘⠺⠿⢴⣿⣿⣏⡁⠘⣿⣿⣿⠉⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠈⠹⠏⠁⣿⠸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣹⣿⡀⠛⠛⠿⠿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠃⠀⠉⠋⠀⠀⠀⠈⠙⣿⡆⠀⠹⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⣰⡄⡀⣿⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠚⢻⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣿⣿⣼⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣼⣿⠿⠚⣿⣿⣦⡄⠀⠀⠐⣶
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⢨⣿⣿⣿⣿⠛⠀⠀⠀⠀⣿⣿⡏⠉⠉⢹⣿⣿⣿⣿⣿⠉⠉⠉⣿⣿⠉⠉⠉⢿⣿⠉⠉⠉⡿⠿⠉⠉⠀⠀⢠⠈⠉⠉⡅⢠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡿⠷⣒⣷⡄⠀⠀⠀⠈⠉⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⣻⣿⡿⠟⢿⣿⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠈⢿⠆⠀⠀⠃⡀⠀⠀⢰⣾⣿⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⠄⠈⠁⠁⠀⠀⠀⠀⢀⣤⡤⢤⣤⣾⣷⡀⠀⠀⠀⠀⠈⠵⠉⠉⠁⠀⠀⠉⣁⣀⠀⠀⢿⡿⠿⠃⠀⠀⢸⡿⠋⣻⣿⣿⠀⠀⠀⠛⠇⠀⠀⢠⡀⠈⡀⠠⣄⠿⠇⠀⠀⢸⣿⣿⠄⠀⠀⣤⣀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢿⡴⠾⠋⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠙⠛⢧⣤⣶⣾⣷⠆⠀⠀⠈⠁⠸⠿⢿⣿⠀⠀⠀⠀⢀⠀⠀⢸⣧⠀⡨⢊⠈⣶⣤⠀⠀⠈⠿⠟⠀⠀⠀⢻⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣾⣆⠀⠀⠀⠀⠀⠀⠀⢒⣀⡀⠐⠾⣿⠓⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⡟⠃⠀⠀⠀⠀⠀⢀⣀⣸⣿⡀⠀⠀⣿⣿⠀⠀⠸⠋⠉⠀⠀⣈⣿⣿⣧⣄⣀⠀⠀⣀⣠⣄⣀⠉⠀⠀⠀
⣴⡶⠾⣿⣓⣀⡀⠀⢀⣀⣠⣦⣾⣿⣇⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣾⣘⣿⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠉⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠴⢿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⢿⣁⠀⠀⠀
⠿⢧⡤⠾⠟⠿⠿⣷⠿⠾⠟⠀⠉⠉⠉⠀⠀⠀⢀⣀⠠⠄⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣴⡿⠁⡴⠀⠢⠀⠀⠀⢠⣶⢸⢠⡄⠀⠀⠀⠈⢛⢘⠎⣿⡟⠠⢙⣷⣄⢀⣼⣿⣾⠃⢨⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣿⣿⣄⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⢉⣡⣤⣤⣶⡀⠰⠶⣶⡌⢤⡠⡼⠀⠀⠀⢸⡿⣸⣿⣿⡄⠀⠀⢠⣐⢐⡄⣿⢁⣠⣁⢻⣿⢸⣿⣿⣿⡐⠲⠀⠂
⠀⠀⠀⠀⠀⢦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢥⣤⣶⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣬⣥⡀⠀⠀⠀⠀⠀⢨⣷⣿⣿⡿⠀⠀⠀⣨⣿⣶⣾⣷⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡮⠬⠵
⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣌⣙⠻⢿⣿⣿⣿⣿⣿⣷⣾⣷⢦⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣤⣤⣀⣀⣀⣀⣠⣤⣀⣀⣀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤
[16A⣿⣿⣿⣿⣿⡿⣼⣿⡁⣾⣿⣿⣶⠀⡸⣿⠿⣿⣶⣶⣦⡀⢸⣿⣿⣿⣿⣿⠟⠉⠛⠛⣿⣿⣿⣿⣿⣿⡿⠿⣿⠁⠛⠱⠸⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⠀⢿⣿⣿⣿⣿⣿⣿⣻⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣅⠀⠺⡟⠛⢿⣿⠀⢹⣿⣿⠟⠁⠀⣠⣤⡀⠀⠩⣼⠟⠛⠃⡇⠀⢸⠀⣸⣤⣿⣿⠏⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⣹⠛⣺⠛⠃⠀⠀⠀⢙⡛⠳⠀⠀⡄⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠄⣾⡗⡰⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣠⣀⠀⠀⠋⠀⣤⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⣀⠀⠀⠉⣠⠟⠁⠀⠀⠀⠀⠈⢹⠛⠀⠀⠁⣰⠿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢀⡀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⢞⡻⡿⠖⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⡉⣭⣿⠉⠉⠉⠉⢿⣛⠉⠉⠉⠿⢿⢩⡉⢡⣼⣏⠈⠁⠀⠀⠀⠀⠉⠉
⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⡞⠁⢸⣿⣿⣿⣿⣿⣿⡾⠛⠓⠀⠀⠀⠀⠈⢿⡇⠀⠀⣤⣄⠈⠁⢸⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⠚⢿⣿⣿⣿⡿⠙⠿⢹⣿⣿⣿⣿⣤⣿⣶⣦⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⠉⠀⠀⣠⣿⣿⣀⣠⣀⣸⡷⣠⣾⣿⣿⠁⠀⣼⣿⣿⡃⠀⠀⠀⠀⢀⡀⠀
⠹⠿⠛⢋⣉⣽⣿⣷⡆⠉⠻⣿⣷⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣾⣿⣿⡇⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠰⠿⠿⠛⠉⠉⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣩⠊⠈⣿⡿⠉⠉⠈⠛⠿⠣⠉⠀⣀⣐⠂⠀⠀
⠀⠀⠀⠾⠉⠙⠋⠋⣿⢡⡄⠀⠛⠛⠻⠟⠈⠉⠉⠉⢸⣿⣿⣿⣵⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠀⠀⠀⠀⠀⢀⣰⣾⣀⣀⣰⣿⣿⣿⣏⣹⣿⣿⣉⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠛⠿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠐⠛⢁⡿⢿⡿⢸⢷⡆⣦⣤⡤⣴⣶⣾⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⡿⣿⢿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠠⣶⠤⠙⠉⠩⡿⠻⣿⣿⣿⡿⣾⠋⠀⢿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⢸⡘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣦⣴⣿⣿⣿⣿⣴⣇⠀⠐⠀⠀⠀⠀⠀⡴⠠⠢⠀⠀⠀⢹⡿⢸⡓⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠑⣾⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⢿⡏⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠈⡀⠘⠸⠷⠆⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠀⣿⣿⣿⣿⣿⢟⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⠄⠀⢿⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠉⠁⠉⠀⠀⠈⠛⠛⠛⠛⢻⣿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠶⣾⠏⢿⠍⠹⠿⠿⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠟⣿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠛⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣟⣼⣿⣷⣿⣿⣿⣵⠁⡰⣿⠿⣿⣶⣶⣶⣅⣽⣿⣿⣿⣿⣿⠿⠋⠛⠻⣿⣿⢿⣿⣿⣿⣿⠻⣿⡅⠋⠰⠼⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠍⠀⠻⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣤⣤⠀⠼⡿⠛⣿⣿⡀⢸⣿⣿⠟⠁⠀⣠⣤⡀⠈⠋⣬⡟⠛⠃⡇⠀⣸⡀⣸⣧⣿⣿⠎⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠙⠛⠿⣿⠿⠿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠈⣹⡟⣿⣟⠋⠀⠀⠀⠙⡛⠣⠀⠀⡎⠀⠀⠰⢠⣾⣿⣿⣿⣿⣿⣿⠆⣾⡗⣰⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⠀⠀⠀⠀⠀⠴⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡄⣀⠀⠀⠈⣱⣟⠋⠀⠀⠀⠀⠈⢹⠓⠀⠀⠀⠰⠟⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠐⣶
⣿⣿⣿⣿⣿⣷⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡾⣾⢯⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣉⣭⣿⡟⠁⠀⠀⠒⢟⠈⠁⠈⣇⠏⠉⢩⣹⣯⣽⠉⠉⠁⢄⡀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣶⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⠟⠈⠉⠋⠀⢀⣠⠀⠀⢾⣁⠀⠀⣷⣀⠀⠈⢋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠻⣿⣿⡋⡹⢹⣿⣿⣯⣿⣥⣿⣶⣦⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠃⠀⢼⣿⣿⣿⡿⠛⠀⠀⢀⣵⣿⣿⣷⣠⣰⣈⣿⣧⣼⣿⣿⣾⣁⣰⣿⣿⠀⠁⠀⠛⠀⠀⠀⠀
⠙⠿⠟⠛⢋⣭⣿⣿⣿⣦⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⡷⠀⠀⣀⣾⣿⣿⣿⣿⣿⣶⡇⠀⠀⠈⠛⠉⠁⠀⢀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⣿⣿⠸⠉⠙⠛⠛⠃⢤⢦⣿⠂⠐⠀⠀
⠀⠀⠀⠰⠏⢉⡁⡉⣹⢻⣿⣧⢀⣀⡘⢛⠃⠀⠈⠉⢸⣿⣿⡿⢁⣶⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣰⣿⣄⣀⣀⣿⣿⣿⣿⣻⣿⣿⣋⣁⣀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⠋⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠏⠁⡛⣻⡿⢸⢻⡇⣿⣷⣤⣴⣶⣾⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠠⠄⠀⠀⣶⠤⠙⠋⠹⡿⠿⣿⣿⣿⣿⣿⠟⠋⢸⠿⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⣿⣿⣽⣿⣿⣿⣿⣴⣦⠀⠐⠂⠀⠀⠀⠀⡴⠠⠢⠀⠀⠀⢹⣿⢸⣷⠉⠀⠀⠘⠈⠃⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿⡟⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠈⠁⠈⠹⠷⠌⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠛⠃⠀⠀⠀⠀⠀⢰⣿⣿⠛⢳⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⡷⠘⣿⣿⣿⣿⣿⡏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠋⠀⠀⠙⠛⠈⠈⠀⠀⠈⠉⠉⠉⠛⢻⣿⡿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⠿⠶⣶⣏⣷⠄⠹⠿⠿⠟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢿⡟⢿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣟⣼⣿⣷⣿⣿⣿⣵⠁⢰⣿⡿⣿⣤⣴⣼⣜⣿⣿⣿⣿⣿⣿⠿⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠋⠰⠮⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠍⠀⠻⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣥⣨⢀⢼⡿⠟⣿⣿⡀⢹⣿⣿⠟⠁⠀⢀⣀⡀⠈⠃⣬⠟⠛⠋⡟⠀⢸⡀⣸⣧⣿⣿⠏⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠛⠻⢿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠙⢹⡟⣷⣿⠋⠀⠀⠀⠛⠛⠇⠀⠀⡌⠀⠀⠰⢠⣾⣿⣿⣿⣿⣿⣿⠆⣾⡗⡰⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⠀⠀⠀⠀⠀⠰⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⢀⡄⣀⠀⠀⠈⣡⢿⠋⠀⠀⠀⠀⠘⢳⠲⠀⠀⠀⢰⡟⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠈⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⠀⠀⠀⠐⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡾⣺⣿⡷⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠿⣿⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣏⠀⠀⠀⣬⣿⣿⠿⠟⠟⢿⠁⠀⠉⣇⠟⠉⢹⣽⣧⣽⠁⠉⠁⠄⡀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠿⣿⣿⣿⣿⣿⣾⣿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⠟⢁⢀⣤⣿⣿⣿⣉⣴⠀⠀⣾⡂⠀⠀⣧⣀⠀⠀⢛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⢿⣿⣿⣿⣿⣥⣿⣶⣦⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢅⠀⢸⠿⠉⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⣦⣰⣈⣿⣷⣴⣿⣿⣾⣅⣰⣿⣿⡀⠈⠀⡋⠀⠀⠀⠀
⠹⠿⠟⠛⢋⣩⣿⣿⣿⣿⣿⣿⡷⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣭⣿⡇⠀⠀⠀⠐⠂⠀⠈⢹⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⣿⣿⠹⠋⠙⠻⠛⠃⢤⢶⣿⣀⠐⠀⠀
⠀⠀⠀⠰⠏⢉⡉⠉⢹⢻⣿⣿⢻⣷⣆⠀⠀⠉⠛⢿⣿⠋⢹⣿⠁⢰⣾⣿⣿⣿⣯⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣠⣾⣆⣀⣀⣿⣿⣿⣿⣻⣿⣿⣋⣁⣀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠻⠿⢿⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠏⠁⡛⣻⡿⢸⢻⡇⣿⣶⣄⣤⣾⣿⣶⣾⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠠⠄⠀⠀⢴⠤⠛⠋⢙⡿⡿⣿⣿⣿⣿⣿⠟⠋⢺⠿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣌⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⠀⠐⠂⠀⠀⠀⠀⡴⠠⠢⠀⠀⠀⢹⣿⢸⣷⠉⠀⠀⠸⠈⠃⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡆⢀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣰⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⡟⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠈⠉⠈⠹⠷⠌⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠛⠃⠀⠀⠀⠀⠀⢸⣿⣿⠛⢳⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⡧⠸⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠋⠁⠀⠙⠛⠁⠉⠀⠀⠈⠉⠉⠉⠛⢻⣿⡿⣿⣿⣿⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⠿⠶⣶⣯⣷⠄⠸⠿⠿⠟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢿⡿⠿⠿⣿⡤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣇⣾⣿⡆⠀⣼⣯⣴⠀⠠⣾⢿⣶⣶⣤⣤⣀⠸⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⠟⠀⣾⣿⣿⠟⢿⡏⠘⠀⠄⢧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠘⢿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⡀⠀⠿⠟⢹⣿⠀⠈⣿⣿⠿⠃⠀⠀⠀⠀⠈⠋⠀⠚⠋⠉⠈⠀⠀⠃⢀⣃⣽⣿⠈⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠈⠛⠿⠿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠂⣼⠛⠀⠀⠀⠸⣿⣧⠀⠀⢤⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠀⣾⡗⡈⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⡀⠀⠀⠀⠀⠂⠀⠀⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⢀⠀⠀⠀⣀⣴⠋⠀⠀⠀⠀⠀⠦⠄⠀⠀⠈⢀⡜⠷⢶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣧⡴⡱⣯⠶⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡏⠉⠫⢿⣿⣿⣿⣿⣿⣭⠉⣭⣿⣿⡿⠉⠙⢿⣋⠁⠈⠉⡇⠛⠉⠉⢠⣈⣽⠀⠉⠀⢀⡀⠀⠀⠈
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣫⡾⣴⠫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⠀⠀⠀⠀⢿⡆⠀⠀⡀⠀⠀⠀⠀⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⠁⣻⣿⣿⡷⢀⣯⣴⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢠⡀⢘⡣⠠⣴⣿⣿⠀⠀⢰⣿⣿⠀⠀⠀⠃⠀⠀⠀⠀
⠀⠋⠉⠉⣹⣬⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⠇⣻⡟⠁⠈⠹⣿⣿⣿⠀⠀⠀⢀⣤⡀⠀⣤⣀⣿⣿⡿⠁⠉⠹⠿⠇⠀⠀⠀⠛⠛⠛⠛⢻⠈⠙⢿⣿⣿⣿⣿⣾⣿⣢⣩⠊⠈⣿⣿⠀⠀⠈⠛⠛⠀⠀⢠⡷⠀⠐⠀⠀
⠀⠀⠀⠸⠗⠀⠁⠈⠙⣿⣿⣿⢹⣷⣌⡉⠘⠛⣛⠂⠀⠀⠻⠿⠛⠀⠀⣶⣼⣿⣄⣠⣿⣿⣿⣿⠛⠁⠀⠀⠐⠆⠀⠀⠀⠀⠀⢀⣠⣼⣀⣀⣀⣿⣿⣿⣉⣻⣿⣿⣁⣀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠺⠿⣟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⢻⡿⢸⢻⠃⢻⣿⡟⣿⣿⣦⣤⡀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠄⠀⠀⣴⠤⠛⠛⠙⡻⠛⢿⣿⣿⣿⣯⠍⠁⠾⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠁⠘⠈⢠⣟⣿⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣿⡿⠋⠁⢀⣾⣿⣿⣤⣤⠀⠐⠆⠁⠀⠀⠀⡴⠠⠢⠀⠁⠀⢨⡿⢸⡷⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠺⣿⣇⠀⠀⠀⠀⠈⣸⣿⡿⢻⣋⣿⢼⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣤⣴⣿⣿⣿⡏⠁⢾⡷⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠚⠃⢨⠹⡧⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣿⡟⠁⠐⣿⣾⣾⣿⡟⠙⣻⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠅⠀⠀⣴⣿⠿⣿⠷⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣦⣀⣀⣠⣤⣄⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠡⠄⠁⠀⠀⠈⠉⠉⠉⠉⢻⣯⠉⠁⠀⢒⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡿⣷⣶⣿⣷⣶⡴⠶⠶⠆⠈⣧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣸⣿⡇⢠⣿⣿⣥⡂⠀⢿⣿⣿⣷⣦⣤⣄⠸⣿⣿⣿⣿⣿⠿⠙⠿⠻⣿⣿⠟⢠⣿⣿⣿⡟⢿⡿⠀⠁⠦⢹⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣤⡄⠸⣿⠛⢻⣿⡀⠈⣿⣿⠟⠁⠀⠀⠀⠀⠈⠛⢀⠟⠋⠛⠈⠃⠀⠛⠀⣳⣼⣿⠋⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠙⠿⠿⢿⡻⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠉⡛⢂⣽⠋⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠄⣾⡗⣸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣤⡤⠀⠀⠀⠀⠀⠴⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⣿⣿⣿⣿⣵⣀⠀⣀⠀⠀⠈⣡⣼⠋⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⡿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡟⢀⡀⠀⠀⠀⠰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣾⣿⣿⣿⣿⣿⣾⣷⡼⣻⢯⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⡉⣭⣿⡟⠉⠉⠈⠉⢏⠀⠈⠉⣿⠋⠉⢩⢹⣧⣼⠀⠉⠁⠂⠄⠀⠀⠈
⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣾⣿⣿⣿⣿⣿⣿⣿⣾⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡽⠃⠘⣿⣿⣿⣿⣿⣿⣾⣿⣿⠁⠀⠀⠀⠀⣾⡆⠀⠀⣧⣀⠀⠀⠙⣿⣻⠀⠀⠀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⣿⣿⠏⢻⠏⣿⣿⣿⣽⣥⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿⡿⠟⠉⢁⣴⣤⣤⣠⣴⣌⣿⡧⣼⣿⣿⠢⡀⢰⣿⣿⡂⠈⠀⣏⠀⠀⠀⠀
⠈⠋⠛⠋⣙⣩⣿⣿⣿⢃⠀⠘⢻⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⢀⣼⣿⡇⠀⣀⣠⣿⣿⣿⣿⣿⣿⠿⡗⠂⠀⠠⡛⠛⠛⠻⠿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣮⠈⠿⠿⠀⠉⠉⠛⠛⠁⠠⢶⣿⡂⠐⠀⠀
⠀⠀⠀⠀⠿⠉⠉⠉⢻⢻⣇⣀⠀⠉⠉⠉⠁⠉⠉⠉⢡⣿⣿⣿⣷⣶⣶⣾⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⡿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣻⣿⣿⣋⣀⡀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠛⠛⠿⠊⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠈⠀⡛⢻⡿⢸⠻⢻⢰⣶⣦⣶⣶⣾⣿⣿⣿⣿⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠐⠇⠀⠀⠴⠦⠀⠀⠈⠽⠟⢿⣿⣿⣿⣿⠟⠉⠸⠿⠿⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣁⣾⣿⣿⣿⣿⣧⣶⡀⠀⠂⠀⠀⠀⠀⡴⠠⠢⠀⠀⠀⠈⣿⢸⣷⡙⠀⠀⠐⠀⠁⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⣾⡆⠀⠀⠀⠀⠀⠈⣱⣿⣿⠝⢻⣿⣽⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢾⡿⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠀⡁⠀⠘⠿⠌⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢠⣿⣿⠛⠓⣿⣿⣿⣿⡟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣿⠇⠀⢻⣿⣿⣿⠿⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⠉⠀⠀⠈⠉⠁⠉⠀⠀⠈⠉⠛⠛⠛⣿⣿⠿⣿⣿⣧⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠉⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⡿⠶⣶⠏⢷⠄⠹⠿⠿⠟⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠸⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣰⣿⣇⠀⣿⣿⣵⡎⠀⠻⡿⣿⣿⣶⣤⣄⠘⣿⣿⣿⣿⣿⡿⠹⠿⠿⢿⣿⠟⠠⣿⣿⣿⡟⠿⡿⠁⠁⠠⢸⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡄⠀⠿⠛⠹⣿⡄⠀⣿⣿⠟⠋⠀⠀⠀⠀⠈⠛⠀⠛⠋⠙⠀⠃⠀⠘⠈⢳⣾⣿⠋⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠀⠀⠀⠙⠿⠿⠿⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠇⠀⠀⠀⠀⠀⡛⢢⣜⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⣠⣼⣿⣿⣿⣿⣿⠄⣾⡗⣸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⠀⠀⠀⠀⠀⠀⠠⠖
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣂⡀⢀⠀⠀⠈⣀⣴⡋⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡴⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⡿⠂⠀⠀⠀⠀⠀⣶
⣤⣌⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡤⣳⢮⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣭⣉⣭⣿⣿⣿⠿⠟⠿⡟⠉⠈⠉⣿⠚⠉⢉⣽⣧⣼⡅⠈⠁⠆⣀⠀⠀⠀
⢻⣝⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣷⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢼⠋⠘⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⢸⣆⡀⢀⣯⣤⠀⠈⢻⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣷⣌⠝⣿⣿⣿⣿⣿⣿⣿⠃⢹⠇⣟⣿⣯⣿⣣⣾⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⡿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠠⠀⠈⡁⠠⣤⣿⣿⠀⠀⢸⣿⣿⡆⠐⠀⡟⠀⠀⠀⠀
⠀⠋⠛⠋⣅⣀⠀⠉⣿⣿⣿⣿⣿⢄⣢⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣾⣿⡇⠀⢀⣀⣼⣿⣿⣿⣿⣿⡿⡇⠀⠀⠠⠾⠋⠛⣻⣿⠈⠙⠻⣿⡿⠀⠀⢠⣤⣤⣬⣮⠈⢿⣿⠀⠉⠘⠻⠛⠁⠀⢤⣿⠆⠀⠀⠀
⠀⠀⠀⠰⠟⠁⡈⠀⠀⠉⠛⠿⢿⣿⡟⠛⠛⠛⠛⠛⢩⣿⣿⡿⠀⠀⣠⣾⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⠔⠇⠀⠀⠀⠀⠀⠀⠹⠛⠀⠀⡀⣵⣶⣶⣾⣻⣿⣿⣋⣁⡀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠾⠿⢿⣔⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢢⡄⢠⠀⢠⣠⣄⣄⢀⣀⣸⣿⣿⣷⣾⡛⠿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠐⠇⠀⠀⢰⠤⠀⠀⠀⠺⡿⢿⣿⢿⣿⣿⡝⠋⠘⠿⠿⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠘⠄⠸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣯⣤⣾⣿⣿⣿⣿⣅⣴⠀⠀⠂⠀⠀⠀⠀⡴⠠⠢⠀⠀⠁⠈⣿⢸⣷⠝⠀⠀⠀⠀⠋⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠈⣴⣿⣿⠛⢩⣿⣾⣿⢿⣿⣿⣿⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠇⠉⢾⡿⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠀⠉⢈⠙⠷⠌⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢠⣿⣿⠛⠓⣿⣿⣿⣿⡏⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⠃⠀⢻⣿⣟⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠘⠁⠀⠀⠈⠉⠀⠁⠀⠀⠈⠉⠙⠛⢛⣻⡿⣿⣿⣿⣧⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠿⠶⣶⠏⣶⠄⠰⠶⠶⠟⢹⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠻⡿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠰⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀
[16A⣿⣿⣿⣿⣿⣿⣇⣾⣿⠀⣼⣿⣯⣔⠀⢸⣿⣿⣿⣤⣤⣤⢸⢿⣿⣿⣿⣿⡿⠽⠿⠿⢿⣿⠟⢱⣿⣿⣿⡟⢿⡿⠀⠁⠲⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠘⢻⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⣅⠀⢿⡿⠻⣿⡇⠈⢻⣿⡿⠋⠀⠀⠀⠀⠈⠛⢁⠿⠛⠛⠀⠇⢀⣙⡀⣻⣾⣿⠉⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠘⠛⠛⠛⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⡛⠓⣼⠛⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠇⣰⣿⣿⣿⣿⣿⣿⠆⣾⡗⣸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣄⣀⠀⠀⠀⠀⠀⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣆⡀⠀⡀⠀⠈⢁⣴⡟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠾⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠏⣀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣤⢟⣶⣿⣿⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⣿⡓⠟⠏⠉⠉⢹⣿⣿⣿⣿⣿⣭⣉⣭⣿⣿⣿⡿⠟⢿⣻⠋⠈⠉⣿⡏⠉⠉⣽⣿⣶⡈⠀⠉⠘⠢⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠘⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⢉⣠⡤⠈⢤⡆⢈⢀⣿⣆⠀⢀⢸⣟⣿⠋⠀⠀⠂⡀⠀⠀⠀
⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⢸⣿⣿⣿⣿⣽⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣯⡁⠀⠀⠘⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣵⣠⣮⣧⣿⣿⣿⣿⠾⣧⣸⣿⣿⡇⠀⠓⣿⡁⠀⠀⠀
⠉⠹⠻⠟⠛⣋⣽⣿⣿⣿⣿⣿⣿⣇⢨⣠⣼⣿⣿⡟⠉⠉⠉⢿⡇⠀⠀⠀⢴⣿⡯⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠈⠛⠙⠻⠿⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡿⠿⠀⠙⠉⠻⠛⠁⠀⢴⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠾⠏⠉⠉⠛⣿⣿⣿⣇⢿⣿⣽⣛⡸⣿⣳⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⣤⣿⣿⣿⣿⣿⡗⢈⠁⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣠⣀⣀⣿⣿⣿⣿⣿⣿⣿⣟⣉⣠⡆⠈⠃⠀⠀⠀⠀⠀⠀⠚⠻⠟⠲⠁⠀
⠀⠀⠀⠀⠀⠀⠁⠐⠀⢘⡛⢺⡗⢸⢻⣏⣿⣿⣿⣿⣇⠀⠀⢀⣀⡀⠒⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠃⠀⠀⠀⠶⠀⠀⠠⡦⠄⠛⠉⡹⡟⢿⣿⢿⣿⣿⡿⠛⠁⠿⠿⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠏⡁⢸⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢺⣿⣿⣿⣘⣿⣿⣿⣿⢣⣴⡀⠀⠆⠀⠀⠀⠀⡴⠠⠢⠀⠀⠁⠈⣹⢸⣷⡝⠇⠀⠀⠀⠋⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⢡⣿⣿⡟⢛⣻⣧⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠈⠰⣿⠃⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠀⠉⣈⠈⠿⠆⠃⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⠀⠘⠛⠀⠀⠀⠀⠀⠀⣼⣿⡟⠗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⡿⠀⠛⣿⣿⣿⡿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠻⠉⠀⠀⠉⠉⠈⠁⠀⠀⠉⠉⠉⠙⠿⢯⠭⠟⠁⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣙⠿⠷⣶⠏⢷⡤⠰⠿⠿⠟⠉⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⡀⠀⠀⢾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣛⣙⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣤⣶⣶⣶⣦⣤⣁⣀⣀⠀⠉⠉⠉⠉⠛⡛⠛⠛⠛⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠀⠀⠀⠘⠛⠛⠛⠿⠟⢿⣿⣿⣿⣿⣧⣀⣀⠀⠀⠉⠉⠁⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣟⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣤⣤⣤⣤⣤⣤⣀⣠⣄⣀⡀
⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠉⠛⠿⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣶⣶⣴⣷⣶⣾⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⣿⣿⣿⠋⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠡⠿⠿⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠏⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠉⠯⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠸⡿⡁⣀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⡀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣶⣄⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡘⡏⠾⠷⣿⣿⣿⣿⣏⢭⡶⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣠⣤⣤⣶⣶⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣽⣿⣿⣿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⢀⣀⣤⣠⣤⣀⠀⠀⠀⠀⠺⢿⣿⣿⣿⢅⠀⣤⣶⣻⣿⣿⣿⠿⠛⠋⢻⣿⣿⠿⡹⢛⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣴⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠘⠛⠛⠛⢿⣿⣷⣦⣤⣤⣤⡀⠀⠀⠀⠐⠉⠙⠻⠻⣿⣿⠇⠀⠀⠀⠋⠛⠛⠻⢾⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣶⣶⣾⣿⣦⡈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠋⠉⠀⠉⡋⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⣤⣤⣤⣤⣀⠀⣀⣀⣀⣨⣭⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢺⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⠏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢾⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠈⠻⠿⠳⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣍⣀⣀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣆⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣤⣦⣌⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠐⠈⠈⠉⠍⠉⠛⢀⣁⣔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀
⣿⠿⠋⠁⠀⣴⣷⣶⣦⣤⣠⣤⣄⣤⣤⣾⣿⣿⣿⣶⣿⣧⡀⢀⣀⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠡⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⠿⣿⣿⣿⢿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⣦⣤⣤⣴⣤⣶⣟⡙⠉⢹⣿⣿⡿⠿⠻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣆⡰⠀⠤⣼⣿⡟⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⣶⣦⣤⣶⣶⣶⣶
⠀⠀⠀⠀⠀⣠⣤⣯⣽⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⣾⣿⣿⡿⠿⠟⠉⠻⠈⠁⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢹⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠋⠁⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠉⢻⣿⣿⡿⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠁⠸⠿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣃⠈⠉⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣼⣿⣿⣿⢿⠿⠿⠿⠿⠻⠡⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⣿⣿⣿⣷⣴⣦⣤⣾⠇⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣤⣤⣴⣦⣴⣿⠿⠛⠇⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠰⠆⣀⠀⠀⠀⠀⣀⣀⣀⠀⢠⣄⢀⣼⣿⣿⡟⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣶⣶⣾⣿⣟⠀⠀⠀⠀⢴⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⢿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⡶⠄⠀⠀⠀⣠⣶⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣄⡀⠀⠀⢀⣀⣿⣿⡿⢿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢁⣤⣶⣶⡾⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢴⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠟⠉⠁⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⡿⣻⢛⣗⣞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠀⢠⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠛⠉⠁⠀⢠⣶⣿⢛⣯⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣢⣿⣿⣼⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣟⠻⢿⣿⣷⡰⣿⣿⣿⡗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣥⣤⣴⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠂⠀⢼⣿⣿⣿⠿⠟⣿⣷⠄⠀⠀⠀⠀⠀⢀⣠⡤⡀⠀⠀⠀⠀⢀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠸⢻⣿⡿⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣈⣿⣿⣿⣀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⣀⣴⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⢠⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣶⣾⣷⣶⣶⣿⣦⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠁⠀⠀⠠⣴⠾⠶⢇⣤⣶⣦⣠⣤⠤⠀⠀⠚⠷⣤⡔⠀⠀⠀⣤⣤⣤⣄⣀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠛⠋⠉⠀⠀⠀⠀⢶⠆⠀⠀⠺⠿⠿⢿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣄⣀⣀⣀⡀⠀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⡀⠄⣄⣶⣶⣂⡀⠾⠦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠹⢿⣿⣿⣿⣿⣿⠛⠉⠋⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⣭⣿⣿⠿⠿⠛⠋⠀⠈⠛⠁⠘⢷⣶⣶⣶⣶⣶⣦⣤⣤⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣴⣶⣶⡤⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣤⣤⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣈⣉⣡⣄⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠺⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠛⠉⠀⠀⠀⠘⠀⣴⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣾⠿⢿⣿⠿⣿⣿⣿⠤⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣶⣶⣦⣤⣤⣤⣶⣿⣿⣿⣷⣿⣥⣥⣥⣤⣨⣅⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣦⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⠁⠛⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣶⣼⣄⢀⣀⣠⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡈⠁⠀⣠⣠⣼⣿⣿⣿⣷⣆⣀⣀⣙⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⡀⣤⣤⣤⣄⣀⣀⡀⢀⣀⡀⣀⣀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⠀⠀⠈⠉⠉⠁⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠤⣶⣶⠂⠀⠀⠀⠠⡄⠀⢀⣀⣀⡀⠀⠀⠀⠈⠛⠻⡿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠁⢀⣀⣀⡀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣶⣤⣤⣤⣿⣧⣾⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⢉⣹⣿⣤⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠈⠑⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠻⠿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⢟⣛⠛⡻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠈⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠋⠉⠀⠀⠀⢈⣾⠖⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠛⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⡇⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣀⣄⣰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠑⡙⠋⠚⠛⢃⢸⡟⠃⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⣶⣷⣿⣶⣾⣿⣿⣆⠀⢀⣿⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡀⠀⠀⠐⣀⣴⣷⣶⣶⣦⣀⡀⠈⠉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⠿⠿⣿⣻⣿⣿⣿⣿⣿⣷⣴⣴⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⢀⣀⡀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠉⠛⣷⣤⣠⣄⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣴⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⠛⠛⠛⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⢛⠟⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠘⢶⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⣤⣠⣭⣽⣧⣤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠄⠗⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣛⢻⣯⢽⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣠⣄⡀⣀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⢿⣿⣿⣿⣿⣿⣶⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣾⣿⣿⣶⣾⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⢿⣅⢖⡄⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠒⣛⣦⣤⣴⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢽⣦⣇⣦⣽⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣠⣦⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠹⣿⡿⡭⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⣤⠠⣶⠿⠟⠀⣠⣄⣀⣤⣄⠘⠐⠿⣧⣤⠖⢂⡀⢀⣠⣤⣤⣄⣹⡿⠿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⣼⠿⠉⠛⠛⠃⠀⠀⠀⠰⡿⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⣶⣿⣿⣶⣷⣤⣄⣀⣀⡀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠀⣐⣶⣶⣂⢐⠷⠄⠀⠀⣠⣤⠀⠈⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⠤⠀⠀⠀⣄⣨⣿⣿⡿⢿⠟⠟⠀⠘⠋⠀⠿⣿⣿⣶⣶⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣧⡁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣶⣶⣦⡤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠛⠙⠋⠁⠀⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣈⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠻⣛⡿⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⡟⠁⠹⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠋⠁⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡿⠿⠟⠙⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠟⠂⢲⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠿⡿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⢀⣄⣤⣶⣶⣶⣦⣤⠁⠀⠻⢉⣉⣉⣽⣷⣶⣾⣧⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣄⢀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠘⠛⣻⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠙⢟⠿⠟⡋⢙⣿⣿⣶⣶⣾⣷⣄⣀⣤⣠⣤⣤⣤⣤⣤⣤⣀⣄⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣧⠀⠀⠙⠀⣀⠀⠀⣰⠆⠀⠀⠀⠀⠈⠛⠉⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⢷⣄⠀⠀⠘⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠆⠀⠀⠀⠐⠀⠴⠿⠛⠉⠉⠀⠀⠀⠀⠙⠁⠀⢲⣶⣷⣶⣶⣶⣤⣤⣤⣤⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⢠⣿⣷⣤⣤⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠿⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠁⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣴⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣏⣹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠙⠿⠁⠙⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⠀⠀⠀⢉⣉⣡⣼⠿⠿⠛⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠘⠛⠋⠻⠿⠿⣿⣿⣷⣾⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⡿⠿⠿⢿⡿⠿⣟⠁⠀⠘⡛⠛⢋⡉⠉⣽⣷⣶⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⢼⣿⡀⠻⣷⡀⠀⠘⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠾⠚⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⣶⣶⣶⣤⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⠟⠃⠀⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠙⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣴⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⢶⣾⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠟⠛⢿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠺⣿⠇⠹⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣶⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣄⣀⣤⣹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣤⣤⣞⡋⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋⠉⠉⠉⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⢊⣧⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠀⠀⠀⡀⠂⠀⠀⣤⣤⣶⣷⣿⣶⣤⡀⠀⠀⢀⣠⣤⡴⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣧⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠙⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡿⠿⡿⠖⠒⣶⣶⣶⣶⣀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣥⠀⠀⠙⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠋⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠒⠂⠤⠀⠀⠀⣤⣈⣁⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠤⠿⠛⠉⠋⠀⠀⠀⠀⠋⠀⠀⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣄⣀⣠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣤⣶⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢭⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠻⣟⣿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⣿⡿⣿⠿⢿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⢾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣏⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣶⣶⣾⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⣀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⡀⠀⠀⠀⠉⣉⣀⡠⠖⠶⢶⣾⣿⣿⣿⣿⣿⣷⠅⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠛⠛⠋⠻⠿⠷⣾⣿⣿⣿⣿⣿⣷⣤⣤⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣟⣋⣀⣀⣠⣴⣿⣶⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠼⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣴⣦⣤⣄⣤⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⣾⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣴⣿⣿⣿⣿⠿⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠶⠰⣆⠀⢼⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢙⣻⣿⣿⠏⠉⠉⠁⠀⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠟⠿⡿⠿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠸⢿⣄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣷⣶⣷⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣤⣶⣿⣿⣿⣷⣶⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
[16A⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠂⠀⠀⠀⠑⠒⠀⠀⡤⣀⣶⣤⣤⣤⣀⠀⠀⠘⢏⣉⣉⣩⣵⣶⣶⣾⣿⣿⡟⠛⠛⠟⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣶⣿⣿⠿⠿⡿⠿⠿⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣠⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⠿⠗⠐⠛⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
䷩ 𝚕𝚒𝚗𝚎 2876
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/21/lscth-open-letter/#comments
Gemini version at gemini://gemini.techrights.org/2022/09/21/lscth-open-letter/
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Gemini_version_available_♊︎
✐ The_EPO’s_Local_Staff_Committee_The_Hague_(LSCTH)is“Requesting_Immediate
Action”⠀✐
Posted in Europe, Patents at 3:42 pm by Dr. Roy Schestowitz
Video_download_link | md5sum 7d12153c747f7ab91b69c309bcc83489
EPO Staff Still Resents the EPO
Creative Commons Attribution-No Derivative Works 4.0
http://techrights.org/videos/epo-stiffing.webm
Summary: Despite relatively quiet weeks there is no calm at the EPO; the
quality of patents continues to fall and staff isn’t being properly rewarded
for the work
THE national delegates will discuss the EPO next_month (warning: epo.org link)
in a meeting that involves some new representatives (Bulgaria and the UK for
instance). These are the people who enabled Benoît_Battistelli‘s countless
crimes and continue to support the same from António_Campinos, in_exchange_for
bribes_of_course!
The EPO has become so tragic on so many levels. As noted in the video above,
it’s staining_Germany’s_reputation (warning: epo.org link) and lobbying a
government that reciprocates kindly for corruption. It’s difficult not to feel
cynical about the EPO emulating_China_as_well (warning: epo.org link)… all this
while pretending_to_be_“green”_and_to_value_science (warning: epo.org link).
The PR strategy is shallow and superficial, complete with “Hey Hi” (AI) hype
instead of actual substance.
“The EPO has become so tragic on so many levels.”However, the video above
focuses on the following new letter. The Local Staff Committee The Hague
(LSCTH) further and more widely disseminated a message to staff earlier today,
stating:
§ Education Allowance Portal: legal drawbacks – Letter to VP4
requesting immediate action⠀➾
Please find in attachment an open letter to VP4 concerning severe
deficiencies of the Education Allowance Portal. Please_read_the
letter_carefully_as_it_contains_important_information_regarding_the
Portal_and_the_procedure_to_follow.
In the meantime to have legal certainty_we_would_advise_you_to_send
to_hrservices@epo.org_the_request_for_reimbursement_of_any
educational_costs_forcedly_deducted_when_requesting_the_advancement
and/or_the_reimbursement. Please make sure to have your ticket open
and a written trace of the HR reaction (e.g. rejection). Once your
claim has been officially rejected, we would like to remind you of
the possibility to launch a request for review within 3 months from
the official rejection.
From now on until the problems with the Education Allowance Portal
are solved, we advise you to send all the requests for full
reimbursement to hrservices@epo.org, and to use the portal only in
case you need an advancement urgently, mentioning a disclaimer in
your request if needed. In our previous publication you find more
details about the excluded education costs, guidance on how to have
them reimbursed, and the disclaimer to be used to safeguard your
rights.
Please do not hesitate to contact us for assistance.
With kind regards,
Your Local Staff Committee The Hague (LSCTH)
Shown above (in the video) but not discussed much is the corresponding open
letter:
European Patent Office | Postbus 5818 | 2280 HV RIJSWIJK |
NETHERLANDS
Ms. Nellie Simon
Vice-President Corporate Services, DG4
ISAR – Munich
Open Letter on issues with the Education Allowance Portal
Dear Ms. Simon, dear Nellie,
We are addressing you concerning an important IT issue regarding the
Education Allowance Portal. When sending the request for
reimbursement or advancement, it appears that the Education Allowance
Portal does not provide any feedback, and only in the cases where
there is a problem, it automatically sends an error message rejecting
the claim with no indication of what the problem is.
It appears that the reason for these problems is that there is
presently no possibility in the portal to have the request partially
approved where the submitted costs are considered only to be
partially reimbursable or advanceable. Therefore, colleagues are
expected and asked verbally to modify their request and resubmit it
in order to make their claims processed even if the amount applicable
is contested by the requester.
We believe that the Education Allowance Portal by not providing a
complete record of the facts and submissions is not fit for purpose.
This and many other important features are still missing in the
portal. This results in legal uncertainty for the users by depriving
the colleagues to exercise their legal rights according to Article
107 ServRegs. and moreover, it goes against the provisions of Article
106 (2) ServRegs., by which “any decision adversely affecting a staff
member shall state the grounds on which it is based”.
We therefore request that this issue be corrected as soon as
possible. We expect that the Education Allowance Portal leaves a
written permanent trace of any action, including request for
correction handled by phone, to both parties. In the meantime we urge
your services to provide alternative means to the colleagues affected
in order for them to be able to request the reimbursement of the
education expenses according to Article 71 ServRegs. without being
deprived of their legal rights according to Articles 106 and 107
ServRegs.
We feel it is our duty as staff representatives to warn the
colleagues about this fact and recommend them to send their requests
via email to hrservices@epo.org until the problem is solved.
We thank you for your attention to this matter,
Jorge Raposo
On behalf of the Local Staff Committee The Hague
SUEPO The Hague Committee is also involved. “To address the plethora of
different legal aspects related to the Education and Childcare Reform,” it
recently said, “we have prepared a table collating the legal cases already
initiated, their status and timeline.”
Action is underway, coordinated, to give staff what it is entitled to.
“The video does not say much about this topic as it concerns financial details
and staff salaries.”It’s not just staff in The Netherlands by the way. Munich
too is taking action. There is coordination across sites. “SUEPO Munich informs
you that the Local Staff Committee The Hague (LSCTH) organises a hybrid
information session on the topic of rewards / career advancement: promotions,
steps, bonuses on Tuesday September 13th, at 11:30,” a recent announcement
said. “Check which of the following dates is the earliest and note it down: 1)
having been informed verbally by the line manager of not having received a
reward; 2) reception of email with link to salary slip of July 2022…”
The video does not say much about this topic as it concerns financial details
and staff salaries. Those aspects don’t relate to the topics we typically
cover, including software_patents. Expect our EPO coverage to carry on for
years to come. █
䷩ 𝚕𝚒𝚗𝚎 3066
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(ℹ) Images, hyperlinks and comments at http://techrights.org/2022/09/21/ubuntu-windows-systemd/#comments
Gemini version at gemini://gemini.techrights.org/2022/09/21/ubuntu-windows-systemd/
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Gemini_version_available_♊︎
✐ Official_Ubuntu_Blog_Has_Just_Promoted_Microsoft_Windows+Systemd⠀✐
Posted in Microsoft, Windows at 12:38 pm by Dr. Roy Schestowitz
Ubuntu’s “Product Manager” (it’s not a community, it’s a product) Oliver Smith
is_at_it_again (he did it many times this year; it’s a marketing_campaign*)
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Systemd support lands in WSL – unleash the full power of
Ubuntu today⦈
Summary: When people try to install Ubuntu on their PC (if they can get past
the illegal_technical_obstacles) Canonical_recommends_Microsoft's_proprietary
software and it also keeps promoting Windows (WSL); what sort of deal/s has
Canonical signed with Microsoft [1, 2]? Ubuntu is fast becoming a ‘filthy’
distro [1, 2] like SUSE after Novell signed the deal with Microsoft.
🄸🄼🄰🄶🄴🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽⦇Leverage_the_power_of_an_#Ubuntu_development_environment_on
Oliver_Smith_and_Jean-Baptiste_Lallement_(Canonical)_on_a_tour_of_Ubuntu_on
WSL.⦈_
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢉⣀⣤⣤⣤⣀⡉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣾⢿⡿⣿⡿⣿⡿⣿⣷⣄⠘⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡷⣿⣿⣿⠿⣇⣿⡾⢿⢸⣾⣿⡽⡇⣿⣾⣻⣿⣸⣿⣿⢿⣿⣽⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣽⣿⣿⡀⠻⣿⡿⣽⣻⣿⣯⡇⣿⣿⡿⠀⣿⣿⣿⣸⣿⣸⣾⣿⣿⣼⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠛⠿⠿⠿⠿⠿⠛⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⡿⣿⢿⣧⠈⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⣿⣿⣿⢿⣟⣿⣶⣲⣤⣤⣤⣶⣶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⣿⣿⣯⣿⣷⣿⣾⣿⣦⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣴⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠑⠠⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢷⣼⣿⣿⣿⣽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣵⢶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⠿⠟⢊⣈⣈⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⢨⣭⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢂⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠕⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣷⣆⠀⠰⠻⠟⠜⠻⠿⠇⠿⠟⠘⠿⠠⠛⠣⠛⠛⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠺⠪⠀⠇⠅⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⢠⢀⣄⣄⢤⣄⡤⣤⡠⣄⣤⠀⡤⣤⢠⡄⢠⢄⡤⣀⣄⣠⣄⠄⢠⠤⡆⢠⡄⣤⠀⢠⡄⡆⡆⢤⡀⣤⢤⡤⡄⡄⡠⣆⣤⠄⣄⣄⣆⢤⡤⣤⢤⡄⣤⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⢿⣿⣿⠿⠃⠀⠈⠉⠉⠈⢈⠁⠁⠉⠘⠋⠉⠀⠁⠉⠈⠁⠘⠉⠉⠈⠈⢈⢉⠀⠈⠁⠁⠈⠁⠉⠀⠀⠀⠉⠁⢉⠈⠉⠈⢉⢉⢁⡈⠁⠉⡈⠈⠉⠉⠉⠋⣉⠈⠁⡉⠀⠁⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠹⠱⠻⠸⠯⠿⠹⠏⠏⠸⠇⠿⠩⠀⠯⠸⠇⠐⠿⠙⠞⠇⠸⠁⠯⠸⠅⠞⠧⠧⠘⠼⠿⠸⠏⢾⡽⠈⠎⠎⠿⠹⠯⠿⠵⠿⠎⠿⠀⠷⠸⠇⠯⠺⢝⡎⠿⠯⠿⠾⠹⠇⠸⠫⠇⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⢰⠠⡄⢠⢄⠄⢰⢠⣤⢂⢆⠶⣂⡆⢰⠀⢠⢠⡄⣦⠄⢠⡴⣄⢴⣤⡄⢠⣰⣤⣠⢤⢄⣤⢠⠄⡄⡖⣄⣤⡆⣴⠀⡔⢢⣶⢄⣤⣤⡤⠠⣒⠠⡤⣰⡦⡦⡄⢠⣤⢤⡠⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠁⠉⠉⣁⡘⠈⠁⢈⢈⠈⢉⠉⠉⢀⠘⠈⡁⡉⠀⠈⠈⠊⠈⠉⡁⠀⡈⣉⠉⠘⠁⠉⠈⠀⡁⠉⠁⢉⡁⠙⠀⠉⠁⠉⠈⢈⠉⠁⠈⠉⠀⠁⢉⡉⡁⡁⡈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡸⠿⠾⠇⠏⠒⠯⠷⠿⡯⠿⠽⠿⠽⠽⠇⠸⠤⠿⠇⠿⠷⠏⠿⠺⠿⠹⠯⠀⡟⠤⠸⠇⠹⠪⠿⠹⠗⠭⠿⠾⡸⠀⠽⠏⠇⠸⠇⠸⠽⠕⠧⠿⠁⠯⠿⠁⠣⠇⠯⠰⠇⠿⠩⠣⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢤⠀⣦⣦⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠈⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⡆⣤⡠⡄⣤⣴⢤⣤⡤⢠⢤⡤⣤⣄⠤⠀⡦⢰⡦⢰⢀⡄⠖⢆⡆⢰⡆⣦⠆⡖⣴⢖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣈⣉⣘⣃⣈⣁⣉⣉⣁⣈⣈⣈⣁⣉⣈⣀⣉⣈⣉⣁⣘⣈⣈⣁⣉⣁⣈⣁⣀⣉⣊⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣤⣪⣭⣭⢪⣹⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠈⠛⠙⡒⠯⢟⢷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⡖⢦⣿⠊⡆⣶⢑⡴⢲⣼⡖⣿⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠃⠘⠙⢃⠙⠫⢀⣙⢫⣼⠵⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢂⡎⢱⢱⢣⢲⠑⡁⡏⣆⢮⡟⡾⣽⡯⣺⣿⡽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠉⠀⠀⠉⠀⠉⠉⠉⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⢛⣋⣛⣿⣿⣶⣄⠀⠀⠀⠀⠀⢠⢔⣼⣾⣛⢿⣿⣉⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣰⣿⣿⡟⢫⣽⣿⣿⣾⡄⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣷⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⣿⣿⣧⠀⠀⢰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⢀⣤⡾⣠⣭⢿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣯⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⡏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠛⠻⠟⠀⠀⠠⣶⣹⣿⣿⡿⠟⠋⢻⣭⣴⣾⣿⠃⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣦⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⢷⣿⣮⣿⡀⠀⠀⠀⢿⠿⠟⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⣉⢉⢉⢀⢀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣋⣋⢛⣻⣗⣙⣙⡀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠴⠏⠉⠉⠉⠁⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀
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䷩ 𝚕𝚒𝚗𝚎 3183
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Gemini_version_available_♊︎
✐ Links_21/09/2022:_Debuginfod_in_Ubuntu⠀✐
Posted in News_Roundup at 7:17 am by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Desktop/Laptop
o Server
o Audiocasts/Shows
o Kernel_Space
o Instructionals/Technical
o Games
o Desktop_Environments/WMs
# K_Desktop_Environment/KDE_SC/Qt
# GNOME_Desktop/GTK
* Distributions_and_Operating_Systems
o BSD
o Fedora_Family_/_IBM
o Debian_Family
o Canonical/Ubuntu_Family
o Devices/Embedded
o Open_Hardware/Modding
o Mobile_Systems/Mobile_Applications
* Free,_Libre,_and_Open_Source_Software
o Events
o Web_Browsers
# Chromium
o SaaS/Back_End/Databases
o Programming/Development
# Python
o Standards/Consortia
* Leftovers
o Hardware
o Health/Nutrition/Agriculture
o Proprietary
o Security
# Privacy/Surveillance
o Defence/Aggression
o Environment
# Energy
o Finance
o AstroTurf/Lobbying/Politics
o Censorship/Free_Speech
o Freedom_of_Information_/_Freedom_of_the_Press
o Civil_Rights/Policing
o Monopolies
# Copyrights
* Gemini*_and_Gopher
o Personal
o Technical
# Science
# Internet/Gemini
* § GNU/Linux⠀➾
o § Desktop/Laptop⠀➾
# ⚓ GamingOnLinux ☛ System76_reveal_their_new_and_improved
Thelio_desktop_design⠀⇛
Linux hardware vendor and Pop!_OS distro maker
System76 have today revealed their brand new Thelio
desktop design, and I must admit I continue to be
jealous and feel like I just need to own this case.
o § Server⠀➾
# ⚓ Kubernetes Blog ☛ Kubernetes_1.25:_Use_Secrets_for_Node-
Driven_Expansion_of_CSI_Volumes⠀⇛
Kubernetes v1.25, released earlier this month,
introduced a new feature that lets your cluster
expand storage volumes, even when access to those
volumes requires a secret (for example: a
credential for accessing a SAN fabric) to perform
node expand operation. This new behavior is in
alpha and you must enable a feature gate
(CSINodeExpandSecret) to make use of it. You must
also be using CSI storage; this change isn’t
relevant to storage drivers that are built in to
Kubernetes.
To turn on this new, alpha feature, you enable the
CSINodeExpandSecret feature gate for the kube-
apiserver and kubelet, which turns on a mechanism
to send secretRef configuration as part of
NodeExpansion by the CSI drivers thus make use of
the same to perform node side expansion operation
with the underlying storage system.
o § Audiocasts/Shows⠀➾
# ⚓ Tux Digital ☛ Hands-On_With_System76’s_New_Redesigned
Thelio_Desktop_For_Linux!_–_DasGeek_–_TuxDigital⠀⇛
In this video, we take a look at the recently
released redesigned System76 Thelio. Check out the
new accent panels, redesigned slimmed down case,
and beautiful attention to detail that only
System76 delivers.
# ⚓ Video ☛ Why_Are_Linux_Login_Screens_Called_Display
Managers??_–_Invidious⠀⇛
LightDM, SDDM, GDM, all of those provide Linux
login screens but we call them Display Managers,
why though? They don’t manage our screen shouldn’t
they be called login or session managers instead.
Like everything involving X those is a 30 year old
reason.
o § Kernel Space⠀➾
# ⚓ uni Toronto ☛ I_believe_SELinux_needs_active_support_from
your_distribution⠀⇛
We have a single machine that uses SELinux, because
it has a need for an unusually thorough level of
security. This machine runs CentOS 7, because at
the time we built this machine (several years ago),
CentOS 7 was the obvious long term support Linux to
use to get a high security, SELinux based
environment. Since CentOS has effectively imploded,
we are going to need to replace that machine with
some other distribution before the middle of 2024,
and the default choice is Ubuntu.
# ⚓ Barry Kauler ☛ Kernel_5.15.69_compiled⠀⇛
Preparing for the next release of EasyOS, have
bumped the kernel to 5.15.69.
o § Instructionals/Technical⠀➾
# ⚓ Video ☛ How_to_install_PyCharm_Professional_on_Linux_Mint
21_–_Invidious⠀⇛
In this video, we are looking at how to install
PyCharm Professional on Linux Mint 21.
# ⚓ Linux Made Simple ☛ How_to_install_Ultimaker_Cura_on_a
Chromebook⠀⇛
Today we are looking at how to install Ultimaker
Cura 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.
# ⚓ Make Use Of ☛ How_to_Extend_Logical_Volumes_on_Ubuntu
Server⠀⇛
Running out of disk space and managing disk
partitions has long been a headache for IT
engineers. Luckily, Linux tries to solve this
problem by using logical volumes.
On Ubuntu Server, logical volumes are the default
method for managing your server disk space.
Unfortunately, when using these volumes, not all
disk space is used up and this might leave you
wondering where all your disk space went. Let’s
take a look at how to adjust or increase your LVM
hard disk space on Ubuntu.
# ⚓ Linux Hint ☛ How_To_Use_Zenmap_Nmap_GUI⠀⇛
This tutorial explains how to install and use the
Zenmap Graphical User Interface for Nmap (Network
Mapper) in Debian and Ubuntu Linux distributions.
While the installation process focuses on Debian-
based Linux distributions like Ubuntu (I also
included instructions for CentOS), the rest of the
tutorial on Zenmap usage is valid for all Linux
distributions with popular X Window Managers.
After reading this article, you can execute
different scan types for various purposes,
including vulnerability detection and exploitation.
All instructions are optimized for new and
experienced Nmap users.
All examples in this document contain screenshots,
making it easy for every reader.
# ⚓ Linux Hint ☛ Bash_“For”_Loop_To_Iterate_Through_an_Array⠀⇛
A “for” loop is a fundamental part of almost every
programming language. It helps write the code you
want to be repeated in the desired number of times.
For Linux-based systems, Bash also features
dedicated syntax that enables its users to leverage
loops for automating their day-to-day tasks through
scripts.
Though you can use the “for” loop in a virtually
infinite number of scenarios, this guide will look
at three basic scenarios that you can plug into
more extensive and complex scenarios to achieve
bigger goals. We will explore three basic scenarios
that employ the for loop for iterating through an
array.
To demonstrate the working of the “For” loop, I
will demonstrate the Bash scripts using Ubuntu
22.04.
# ⚓ Linux Hint ☛ How_to_Install_and_Use_the_Deepin_Screen
Recorder⠀⇛
Deepin is a reliable screen recorder. You can use
it to capture screenshots and even record your
screen. However, only the video gets recorded when
recording the screen and not the audio. Still, the
screen recorder is easy to use and offers some
basic yet helpful editing.
Using it to capture a screenshot has great features
that help modify how the captured image should
look. Before saving the screenshot, you can add
texts and other shapes to the image. If you are
looking for a good screen recorder, this guide
covers on how to install and use the Deepin screen
recorder.
# ⚓ Linux Hint ☛ Linux_Check_If_Port_Is_Blocked_by_Firewall⠀⇛
We all know that network communication occurs
because of the ports and sockets. A port allows you
to connect to the desired web server at any time
you want while using the Internet. However, there
are times that the firewall running on your system
blocks certain ports due to security concerns.
Therefore, if you ever wish to find out whether
your firewall blocks a certain port or not in
Linux, then you can follow this guide.
# ⚓ UNIX Cop ☛ How_to_Install_NextCloud_on_Ubuntu_22.04_with
Snap⠀⇛
We’ve talked a lot about Nextcloud because we love
it, but today we offer you another method to get
it. In this post, you will learn how to install
Nextcloud using Snap on Ubuntu 22.04.
Nextcloud is a self-hosted file share and
collaboration platform. It works much like cloud
applications like Dropbox and Google Drive. It
allows you to store and share your files in a
secure and convenient manner across both desktop
and hand-held devices such as smartphones.
# ⚓ Make Tech Easier ☛ Linux_Command_Line_Cheatsheet_–_Make
Tech_Easier⠀⇛
Despite the beautiful interfaces found on most
modern distros, knowledge of Linux command lines is
a useful tool to have. Knowing these basic
shortcuts can make you more efficient and
supercharge your productivity, not to mention make
coding at the terminal that much easier. Regardless
of your current background knowledge of Linux, you
can start using this list of useful Linux commands
right away.
# ⚓ Linux Journal ☛ FileRun_on_Docker_|_Linux_Journal⠀⇛
You may want to set up a file server like FileRun
for any number of reasons. The main reason, I would
think, would be so you can have your own Google
Drive alternative that is under your control
instead of Google’s.
FileRun claims to be “Probably the best File
Manager in the world with desktop Sync and File
Sharing,” but I think you’ll have to be the judge
of that for yourself.
Just to be completely transparent here, I like
FileRun, but there is a shortcoming that I hope
they will eventually fix. That shortcoming is that
there are some, in my opinion, very important
settings that are locked away behind an Enterprise
Licence requirement.
That aside, I really like the ease-of-use and
flexibility of FileRun. So let’s take a look at it.
# ⚓ ByteXD ☛ How_to_Chown_Recursively_in_Linux_–_ByteXD⠀⇛
A recursive action affects a file or directory with
its subdirectories. We mainly use the -R option to
denote a recursive action. chown is the primary
command to change ownership.
This tutorial simplifies changing a file’s
ownership recursively. It starts by taking you
through an overview of file permission and
ownership in Linux. It then walks you through
changing a file’s owner practically.
# ⚓ ID Root ☛ How_To_Install_Alacritty_on_Ubuntu_22.04_LTS_–
idroot⠀⇛
In this tutorial, we will show you how to install
Alacritty on Ubuntu 22.04 LTS. For those of you who
didn’t know, Alacritty is a free and open-source
GPU-accelerated terminal emulator focused on
performance and simplicity. By integrating with
other applications, rather than reimplementing
their functionality, it manages to provide a
flexible set of features with high performance. Its
supported platforms currently consist of BSD,
Linux, macOS and Windows.
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 Alacritty terminal emulator on
Ubuntu 22.04 (Jammy Jellyfish). You can follow the
same instructions for Ubuntu 22.04 and any other
Debian-based distribution like Linux Mint,
Elementary OS, Pop!_OS, and more as well.
# ⚓ Make Use Of ☛ How_to_Install_REMnux_on_VirtualBox⠀⇛
REMnux is a free and open-source reverse
engineering and malware analysis-oriented Linux
distribution based on Ubuntu 20.04. It’s a crowd
favorite among professional malware analysts due to
being modular and feature-rich.
If you’re looking to kickstart your journey as a
malware analyst, having REMnux in your arsenal is a
must. Let’s learn how you can install REMnux on
VirtualBox.
# ⚓ Create_and_Manage_VirtualBox_VM_Groups_–_kifarunix.com⠀⇛
In this tutorial, you will learn how to create and
manage VirtualBox vm groups. In VirtualBox, it is
possible to create virtual machines groups. You can
group together virtual machines that servers the
same purpose or just group them as you so wish.
# ⚓ XDA ☛ Can_the_HP_EliteBook_840_run_Linux?⠀⇛
Some of the best HP laptops are powered by just
Windows. That said, if you’re considering buying
the HP EliteBook 840 G9 for use in your operations,
you might be wondering if it runs Linux. Well, the
answer to that question is yes, but not officially,
at least.
We say that because while the HP EliteBook 840 G9
is not sold with a Linux configuration, Linux is an
open-source operating system that can still run on
almost any laptop (if you know the right tricks.)
Also, most devices in businesses these days will
run either macOS or Windows. Only specialty laptops
like the XPS 13 Developer edition are sold with a
Linux option. We’ll explain why that is in this
guide and what you can do if you want to try Linux
unofficially.
o § Games⠀➾
# ⚓ GamingOnLinux ☛ Steam_Bash_Bash_event_now_live_with_demos
and_discounts⠀⇛
The latest Steam event is now live with Steam Bash
Bash, a celebration of various types of fighting
games. Specifically, those that are all about melee
combat.
# ⚓ GamingOnLinux ☛ Girl_Genius:_Adventures_In_Castle
Heterodyne_has_a_new_trailer_up⠀⇛
Girl Genius: Adventures In Castle Heterodyne, the
upcoming action-adventure from Rain Games
(Teslagrad / World to the West) now has a new
trailer to finally show it off a bit more. This was
crowdfunded on Kickstarter back in 2020, so we’ve
been waiting a while to see how it’s been coming
along.
# ⚓ GamingOnLinux ☛ A_new_Proton_Experimental_release_hooks_up
NVAPI_for_lots_of_games_on_Linux⠀⇛
Proton Experimental has a new release out from
September 20th, that as usual fixes some bugs but
also does a rather big change in enabling the
NVIDIA NVAPI for a long list of games.
# ⚓ GamingOnLinux ☛ NVIDIA_Linux_driver_515.76_is_out,_as_is
Mesa_22.2_for_AMD_/_Intel⠀⇛
Two new driver releases are now available for
desktop Linux users with NVIDIA 515.76 and Mesa
22.2 for AMD / Intel.
# ⚓ GamingOnLinux ☛ Valve_finally_fixes_up_the_Steam_Deck_on-
screen_keyboard_some_more⠀⇛
There’s a new Steam Deck Client Beta update
available and with it comes some much needed
improvements to the on-screen keyboard. Want to try
it out? Head to the Settings >System and select
either Beta or Preview from the Steam Update
Channel dropdown box.
# ⚓ GamingOnLinux ☛ GE-Proton_7-35_out_now_with_more_fixes_for
Linux_/_Steam_Deck⠀⇛
GE-Proton (GloriousEggroll), the community
maintained version of the Windows compatibility
layer version 7-35 is out now and here’s what’s
new. Well, technically it’s two version as 7-34
went up first with the main additions and 7-35 was
a quick extra hot-fix.
o § Desktop Environments/WMs⠀➾
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ Kubuntu_Council_Elects_3_Councillors_|_Kubuntu⠀⇛
Members of the Kubuntu Council are
responsible for considering proposals made by
the wider Kubuntu community. The council
formalises and ratifies proposals, then votes
to obtain an outcome which directs the course
of progress for Kubuntu.
On 11 September I (Rick Timmis) will have
been a councilor for the Kubuntu Council for
5 years. Being a councilor is a lot of fun,
provides a wonderful sense of fulfillment and
also carries a lot of ‘Kudos’ in
conversations with those of a technical
persuasion.
If you have been using Kubuntu for a while,
and have explored some of our community, why
not consider getting involved a little deeper
? We are always looking for testers,
contributors, bug reporters, documentation,
and blog writers.
# § GNOME Desktop/GTK⠀➾
# ⚓ Felipe_Borges:_Google_Summer_of_Code_2022:_It’s_a
wrap!⠀⇛
Another program year is ending and we are
extremely happy with the resulting work of
our contributors!
This year GNOME had nine Google Summer of
Code projects covering various areas, from
improving apps in our ecosystem to
standardizing our web presence. We hope our
interns had a glimpse of our community that
motivated them to continue engaged with their
projects and involved with the broad GNOME
ecosystem.
* § Distributions and Operating Systems⠀➾
o ⚓ Talospace ☛ Void_PPC_Goes_Chimera_(and_Bust)⠀⇛
Void PPC maintainer Daniel Kolesa has announced that
instead of simply phasing out big-endian support in Void
in 2022, he will instead cease maintaining the PowerPC/
Power ISA fork of Void Linux entirely in favour of
Chimera Linux, a fusion of a Linux kernel, musl libc and
FreeBSD userland built with LLVM. There may even be a
return of support for big-endian, at least for 64-bit
Power (32-bit Power to be considered), as well as
Chimera’s core support for ppc64le, aarch64 and x86_64
(with 64-bit RISC-V coming).
o § BSD⠀➾
# ⚓ MWL ☛ “OpenBSD_Mastery:_Filesystems”_draft_done!⠀⇛
I’m asking tech reviewers to get any comments to me
by 15 October 2022. That’s four weeks. It might
seem tight, but experience shows that people either
get their comments to me immediately, or wait until
the last possible weekend. I’m not complaining–I do
exactly the same thing. Please return any comments
either a) in plain text, with enough context that I
can find them when page numbers change, or b) as
annotations directly on the PDF.
# ⚓ Ruben Schade ☛ aria2_can_download_torrent_files,_then_their
files⠀⇛
For example, I can download NetBSD 9.2 by giving it
the torrent file, instead of having to download it
first…
# ⚓ DragonFly BSD Digest ☛ In_Other_BSDs_for_2020/09/17⠀⇛
o § Fedora Family / IBM⠀➾
# ⚓ Linuxiac ☛ RHEL-Based_EuroLinux_Desktop_Debuts_on_the_Linux
Scene⠀⇛
EuroLinux Desktop is a modern operating system
based on RHEL 9 intended for usage in office work,
companies, and private users.
Regarding Red Hat Enterprise Linux-based systems,
the three most hyped names to date are AlmaLinux,
Rocky Linux, and Oracle Linux. But, of course, they
are far from exhausted the RHEL-based distributions
competing for their share of the enterprise Linux
segment.
We are glad to introduce you to one of the less
popular RHEL derivatives today, thanks to the
release of the EuroLinux Desktop edition. But,
before we go any further, let’s make a few
necessary clarifications.
o § Debian Family⠀➾
# ⚓ LWN ☛ Debian’s_firmware_vote_[LWN.net]⠀⇛
The Debian project has begun voting on changes to
its approach to firmware needed to install a
working distribution. The original ballot options
described in this article are still there, but this
is Debian so there are several others as well. Some
of the additions include changes to the Debian
Social Contract that explicitly allow the shipping
of firmware needed to use Debian on hardware
requiring that firmware.
o § Canonical/Ubuntu Family⠀➾
# ⚓ Ubuntu ☛ Debuginfod_is_now_available_in_Ubuntu⠀⇛
We are happy to announce that Ubuntu now has a
debuginfod service available for its users!
o § Devices/Embedded⠀➾
# ⚓ Stacey on IoT ☛ 5_ways_Matter_will_disappoint_users_at
launch⠀⇛
After participating in a panel on Matter at Silicon
Labs’ Works With event on Tuesday and conversing
with attendees throughout the event, I think the
initial response to Matter is going to be tepid at
best and downright aggravated at worst.
One person I spoke with, who declined to be named
for this article, said they had the feeling that,
given the delays and the constant influx of new
members to the Connectivity Standards Alliance
(CSA), which led to ballooning features requests,
the CSA decided to just push something — anything —
out. While I imagine the CSA’s thinking was
probably along the lines of “Don’t let perfection
be the enemy of the good,” based on my
conversations, it may be that the 1.0 version of
the standard may not be that good.
# ⚓ Pete Warden ☛ How_to_build_Raspberry_Pi_Pico_programs_with
no_software_installation⠀⇛
To solve this problem, I’ve actually turned to what
might seem an unlikely tool, Google’s Colab
service. If you have run across this, you probably
associate it with Python notebooks, because that’s
its primary use case. I’ve found it to be useful
for a lot more though, because it effectively gives
you a free, temporary Linux virtual machine that
you control through the browser. Instead of running
Python commands, you can run Linux shell commands
by putting an exclamation point at the start. There
are some restrictions, such as needing a Google
account to sign in, and the file system
disappearing after you leave the page or are idle
too long, but I’ve found it great for documenting
all sorts of installation and build processes in an
accessible way.
# ⚓ CNX Software ☛ $199+_NVIDIA_Jetson_Orin_Nano_system-on-
module_delivers_up_to_40_TOPS_–_CNX_Software⠀⇛
NVIDIA Jetson Orin Nano system-on-module (SoM) is
an update to the Jetson Nano entry-level Edge AI
and robotics module that delivers up to 40 TOPS of
AI performance, meaning it’s up to 80 times faster
than the original module.
The new SoM features an hexa-core Arm Cortex-A78AE
processor, an up to 1024-core NVIDIA Ampere
architecture GPU with 32 Tensor cores, up to 8GB
RAM, and the same 260-pin SO-DIMM connector found
in the Jetson Orin NX modules.
# ⚓ GamingOnLinux ☛ Intel_announce_their_NUC_12_Enthusiast_Mini
PC_and_Kit_with_Arc_graphics⠀⇛
Intel have revealed their new NUC 12 Enthusiast
Mini PC and Kit (code-named Serpent Canyon) and I
must admit, it looks and sounds pretty nice. Coming
with an Intel Arc A770M GPU with 16GB GDDR6 VRAM,
this new Mini PC has plenty going for it with a
12th Gen Intel Core™ i7-12700H mobile processor.
# ⚓ Linux Gizmos ☛ New_Khadas_Edge2_integrates_Rockchip_RK3588S
and_it_launches_at_$199⠀⇛
Khadas officially launched the Edge2 SBC featuring
the powerful octa-core Rockchip RK3588S SoC along
with a 6 TOPS performance NPU. The device is
available in two models which offer upgradable RAM
and storage capacity.
o § Open Hardware/Modding⠀➾
# ⚓ Tom’s Hardware ☛ Raspberry_Pi_Live_Streaming_Camera_Sports
Microphone_for_Audio_Support_|_Tom’s_Hardware⠀⇛
The Raspberry Pi’s camera support makes for an
excellent go-to board for a huge variety of video-
based projects. Such is the case today with this
impressive live streaming rig created by Mark
Lambiase. Lambiase has built an all-in-one device
that can aid in his streaming needs without the
need for any external components or accessories.
The system is fitted with a camera module and can
stream to platforms like YouTube in real time. The
housing is made by Lambiase, as well, and shields
it from excess light around the lens as well as any
passing debris if used outside. It’s not water-
tight, but it should protect the components inside
from excess wear.
In addition to the video streaming support, it has
a built-in microphone that can capture audio for
live streams. This is one of the best additions to
the rig as it makes for a more dynamic stream.
Whether you’re gaming or setting up a nature cam,
no one can deny the useful impact of having a
microphone thrown into the mix.
# ⚓ Tom’s Hardware ☛ LattePanda_3_Delta_Review:_The_Maker
Desktop_|_Tom’s_Hardware⠀⇛
If you need an all-in-one device that provides a
typical desktop experience and a GPIO, LattePanda 3
Delta is a contender for your dollars.
[...]
Another group of alternatives are boards that can
still be classified as SBCs but feature Intel CPUs
at their core. The latest to cross our bench is the
$279 LattePanda 3 Delta, a rather large and
powerful SBC powered by an 11th Gen Intel Jasper
Lake CPU. Because it is Intel based, we have an
expansive choice of potential operating systems.
LattePanda provides both Windows 10 and 11, but if
Linux is more your thing, you are well catered for.
[...]
Essentially the LattePanda 3 Delta is an Intel x86
Jasper Lake based PC in a large single board
computer form factor. This means that we are free
to use Windows (LattePanda offers Windows 10 and 11
downloads via its site) or many other Linux
distributions.
# ⚓ Tom’s Hardware ☛ Portable_Raspberry_Pi_Tricorder_Detects
Starlink_Satellites_|_Tom’s_Hardware⠀⇛
Just when you think the Raspberry Pi community has
done it all, one maker boldly goes where no maker
has gone before. Today we’ve got an exciting update
to share: Maker and developer Saveitforparts is
using his homemade Raspberry Pi Tricorder to detect
Starlink satellites. If you’re wondering what a
Tricorder is, these are handheld gadgets from the
Star Trek universe used to scan the environment
around them.
Saveitforparts does just that with his Tricorder,
using a variety of sensors to scan for things like
RF signals and thermal bodies. We first reported on
it last year, but today we’re excited to share the
project’s latest update. There’s something quite
appropriate in using a DIY Tricorder to scan for
low-orbit satellites. In this case, he’s looking
for Starlink satellites which are run by SpaceX and
used to provide internet access and intended to
reach global support within the coming years.
# ⚓ Bunnie Huang ☛ Book_Review:_Open_Circuits_–_bunnie’s_blog⠀⇛
There’s a profound beauty in well-crafted
electronics.
Somehow, the laws of physics conspired with the
evolution of human consciousness such that sound
engineering solutions are also aesthetically
appealing: from the ideal solder fillet, to the
neat geometric arrangements of components on a
circuit board, to the billowing clouds of standard
cells laid down by the latest IC place-and-route
tools, aesthetics both inspire and emerge from the
construction of practical, everyday electronics.
# ⚓ Roberto Frenna ☛ Over-engineering_my_TV_watching:_Part_1:
bypassing_geo-block_with_a_custom_reverse_proxy⠀⇛
This is the first part of a series of posts where I
will detail how I built a complex system to consume
Italian TV abroad entirely from a single web app
and a Chromecast.
# ⚓ Arduino ☛ Beating_unscrupulous_arcade_owners_at_their_own
games_|_Arduino_Blog⠀⇛
Mark Rober isn’t just a talented mechanical
engineer and entertaining personality, he is also
something of a champion of justice for the common
man. He’s already proved that several times with
his famous yearly porch pirate-targeted pranks, but
now he’s taking on the corrupt fat cats running
arcades for children. Those arcades are often full
of rigged games that are either more difficult than
they seem or downright unwinnable. In his most
recent video, Rober built machines that could beat
several of those games with ease.
We don’t have enough space here to provide detail
on every contraption that Rober created, but they
all accomplish a common goal of defeating rigged
arcade games. Some of those, like Skee-Ball, are
only nefarious in the sense that have misleading
difficulty and rely on misdirection to swindle
players. Others, like Quik Drop, are almost
impossible for humans to win. For good measure,
Rober even made a robot that can block every shot a
human opponent takes in air hockey.
o § Mobile Systems/Mobile Applications⠀➾
# ⚓ Computer World ☛ Android’s_underappreciated_design
revolution_|_Computerworld⠀⇛
# ⚓ Android Police ☛ The_best_education_apps_on_Android_in
2022⠀⇛
# ⚓ Android Police ☛ The_top_17_Android_music_players⠀⇛
# ⚓ Google_Pixel_6a_owners_just_got_a_major_free_Android
upgrade_|_T3⠀⇛
# ⚓ The Sun ☛ Every_Android_phone_owner_urged_to_turn_on_new
setting_–_ignoring_it_could_cost_you_|_The_Sun⠀⇛
# ⚓ PR Newswire ☛ How_to_Bypass_Google_Verification_on_Samsung
—_PassFab_Android_Unlocker⠀⇛
# ⚓ 9to5Google ☛ Carsifi_Review:_Wireless_Android_Auto_with_a
quick-switch_button⠀⇛
# ⚓ SDTimes ☛ Android_Studio_Dolphin_2021.3.1_release_focuses
on_3_key_areas_–_SD_Times⠀⇛
# ⚓ Notebook Check ☛ Chromecast_with_Google_TV_(HD)_almost
official_in_Android_TV_Guide_leak_as_European_pricing
surfaces_–_NotebookCheck.net_News⠀⇛
# ⚓ 9to5Google ☛ Galaxy_S21_gets_its_Android_13_beta_in_the_US
–_9to5Google⠀⇛
# ⚓ Android Police ☛ OnePlus_10_Pro_is_getting_stable_Android
13,_beating_Samsung_flagships_to_the_punch⠀⇛
# ⚓ Nokia_5.4_gets_new_Android_12_Build,_Android_12_for_Nokia
3.4_available_in_more_markets_–_Nokiapoweruser⠀⇛
# ⚓ LG_Android_12_update_roll_out_tracker_[Cont._updated]⠀⇛
# ⚓ GSM Arena ☛ Xiaomi_Pad_5_is_getting_the_Android_12_and_MIUI
13.1_update_globally_–_GSMArena.com_news⠀⇛
# ⚓ FOSSBytes ☛ How_To_Use_Clipboard_On_Android?⠀⇛
# ⚓ Android Headlines ☛ Top_Android_Devices_Designed_For_Mobile
Gaming⠀⇛
# ⚓ Android Police ☛ These_two_Android_phone_makers_are_asking
users_about_Dynamic_Island-like_features⠀⇛
* § Free, Libre, and Open Source Software⠀➾
o ⚓ OpenSource.com ☛ My_favorite_open_source_alternatives_to_Notion⠀⇛
If you have notes to yourself scattered throughout your
hard drive, you might need a notes application to collect
and organize your personal reminders. A notes system can
help you track ideas, important tasks, and works in
progress. A popular application that isn’t open source is
Notion, but here are two options that respect your
privacy and data.
o ⚓ Liam Proven ☛ EmuTOS_and_its_relatives:_a_free_ST-compatible_OS
based_on_DR’s_GPL_code⠀⇛
I have an ST, and an Amiga, but I didn’t use either back
in the day. But I think this is amazing work and really
impressive.
So I stuck in on HN and some pillock went “yah boo TOS
sucks Amiga is better” like it was 1986. I paraphrase. I
am unimpressed.
In fact, while I don’t want to be mean, you’re missing
two or possibly three different points… among which are
the reasons I posted this link.
o § Events⠀➾
# ⚓ FOSDEM ☛ FOSDEM_2023_dates:_4_&_5_February_2023⠀⇛
FOSDEM 2023 will take place on Saturday 4th and
Sunday 5th of February 2023. We are aiming for a
physical conference.
# ⚓ NetBSD ☛ EuroBSDCon_2022⠀⇛
No videos are available yet to provide much-needed
context to presentations, but we’ll keep you
posted.
o § Web Browsers⠀➾
# ⚓ Wasmtime_Reaches_1.0:_Fast,_Safe_and_Production_Ready!⠀⇛
As of today, the Wasmtime WebAssembly runtime is
now at 1.0! This means that all of us in the
Bytecode Alliance agree that it is fully ready to
use in production.
In truth, we could have called Wasmtime production-
ready more than a year ago. But we didn’t want to
release just any WebAssembly engine. We wanted to
have a super fast and super safe WebAssembly
engine. We wanted to feel really confident when we
recommend that people choose Wasmtime.
So to make sure it’s production ready for all of
you, a number of us in the Bytecode Alliance have
been running Wasmtime in production ourselves for
the past year. And Wasmtime has been doing great in
these production environments, providing a stable
platform while also giving us security and speed
wins.
# § Chromium⠀➾
# ⚓ [Old] IT World CA ☛ Google’s_manifest_V3_rules
restrict_AdGuard’s_new_ad_blocker⠀⇛
Another problem is the inability to load
rules into the filtering engine from the
extension’s server. With the new rules,
AdGuard is now expected to define a set of
declarative rules and let Chrome be in charge
of the network filtering process. Since the
new syntax for the rules is very limited, not
all existing rules can be converted,
including cookie rules that block certain
trackers.
# ⚓ [Old] The Register UK ☛ Ad_blockers_struggle_under
Chrome’s_new_rules⠀⇛
The future of content blocking in web
browsers looks a lot like the way it was
described by Alexei Miagkov and Bennet
Cyphers from the EFF last December. They
wrote, “Under Manifest V2, extensions are
treated like first-class applications with
their own persistent execution environment.
But under V3, they are treated like
accessories, given limited privileges and
only allowed to execute reactively.”
o § SaaS/Back End/Databases⠀➾
# ⚓ A_minimal_distributed_key-value_database_with_Hashicorp’s
Raft_library⠀⇛
So I built my own single-file example. It’s not
perfect but it helped me get started and may help
you too. We’ll walk through that code, ~260 lines
of Go, in this post.
The key-value database will only be able to set
keys, not delete them. But it will be able to
overwrite existing entries. And it will expose this
distributed key-value database over an HTTP API.
# ⚓ TecMint ☛ 20_mysqladmin_Commands_for_MYSQL/MariaDB_Database
Administration⠀⇛
mysqladmin is a command-line database
administration utility that comes with MySQL/
MariaDB server, which is used by Database
Administrators to perform some basic MySQL tasks
such as setting the root password, changing the
root password, monitoring mysql processes,
reloading privileges, creating/dropping databases,
checking server status, show usage statistic, kill
running queries, etc.
The command to use mysqladmin and the general
syntax is…
o § Programming/Development⠀➾
# ⚓ [Old] Learn_You_a_Haskell_for_Great_Good!⠀⇛
Welcome to Learn You a Haskell for Great Good! If
you’re reading this, chances are you want to learn
Haskell. Well, you’ve come to the right place, but
let’s talk about this tutorial a bit first.
I decided to write this because I wanted to
solidify my own knowledge of Haskell and because I
thought I could help people new to Haskell learn it
from my perspective. There are quite a few
tutorials on Haskell floating around on the
internet. When I was starting out in Haskell, I
didn’t learn from just one resource. The way I
learned it was by reading several different
tutorials and articles because each explained
something in a different way than the other did. By
going through several resources, I was able put
together the pieces and it all just came falling
into place. So this is an attempt at adding another
useful resource for learning Haskell so you have a
bigger chance of finding one you like. bird
This tutorial is aimed at people who have
experience in imperative programming languages (C,
C++, Java, Python …) but haven’t programmed in a
functional language before (Haskell, ML, OCaml …).
Although I bet that even if you don’t have any
significant programming experience, a smart person
such as yourself will be able to follow along and
learn Haskell.
# ⚓ Content_based_change_detection_with_Make⠀⇛
We can use Make and a couple of short shell scripts
to implement file content-based caching and read/
write that cache to remote storage, such as S3. The
demo repository contains a version using minio for
ease of demonstration.
# ⚓ Yoshua Wuyts ☛ Futures_Concurrency_IV:_Join_Ergonomics⠀⇛
On Thursday this week Rust 1.64 will be released,
and in it it will include a stabilized version of
IntoFuture. Much like IntoIterator is used in the
desugaring of for..in loops, IntoFuture will be
used in the desugaring of .await.
In this post I want to show some of the ergonomics
improvements IntoFuture might enable, inspired by
Swift’s recent improvements in async/await
ergonomics.
# ⚓ LWN ☛ The_perils_of_pinning⠀⇛
Instead, he has come up with a solution that uses
(or abuses) struct initialization and macros. Your
editor will not attempt a full description of how
it works; the whole thing can be seen in Lossin’s
slides. Among other things, it requires using some
complex macros that implement a not-Rust-like
syntax, making the code look foreign even to those
who are accustomed to Rust.
# ⚓ Rlang ☛ Enforcing_Style_in_an_R_Project⠀⇛
In the previous post we looked at how to apply a
linter and styler to a Python Project. Now we’re
going to do the same for an R project. We’ll use
the {precommit} R package to make the setup a
breeze.
# ⚓ Daniel Lemire ☛ Escaping_strings_faster_with_AVX-512⠀⇛
Such a character-by-character approach is unlikely
to provide the best possible performance on modern
hardware.
# ⚓ Alexandru Nedelcu ☛ Java’s_Cultural_Problem⠀⇛
Java is good by modern standards, from a technical
perspective, the platform having received a lot of
improvements from Java 8 to 17. Unfortunately, it
still stinks, and the problem is its “enterprise”
culture.
Let me illustrate the problem via examples …
# ⚓ Help Net Security ☛ The_25_most_popular_programming
languages_and_trends [Ed: It seems like a bunch of Microsoft
boosters though; mentions "list of fastest-growing languages
in GitHub’s 2018 and 2019 State of the Octoverse" (i.e.
Microsoft as the dataset)]⠀⇛
CircleCI released the 2022 State of Software
Delivery report, which examines two years of data
from more than a quarter billion workflows and
nearly 50,000 organizations around the world, and
provides insight for engineering teams to
understand how they can better succeed.
# § Python⠀➾
# ⚓ OpenSource.com ☛ 6_Python_interpreters_to_try_in
2022⠀⇛
Python, one of the most popular programming
languages, requires an interpreter to execute
the instructions defined by the Python code.
In contrast to other languages, which compile
directly into machine code, it’s up to the
interpreter to read Python code and translate
its instructions for the CPU performing the
related actions. There are several
interpreters out there, and in this article,
I’ll take a look at a few of them.
o § Standards/Consortia⠀➾
# ⚓ Matt Rickard ☛ Standards,_Protocols,_and_Platforms⠀⇛
I came across an interesting article on standards/
platforms by Michael Mignano, The Standards
Innovation Paradox (and a rebuttal The Standards
Innovation Paradox: is it real?). I don’t feel as
strongly as the authors do about RSS, although I’ve
collected my thoughts on RSS.
* § Leftovers⠀➾
o ⚓ TechXplore ☛ Send_in_the_drones:_Unmanned_aerial_program_offers
independent_testing_and_prototyping⠀⇛
Ever since the Wright brothers innovated in the back of
their bicycle shop in Dayton, Ohio, aviation has been—at
heart—a nuts-and-bolts endeavor. For all the
sophisticated equipment Idaho National Laboratory’s
Unmanned Aerial Systems team has at its disposal for
testing high-tech cameras, radios and sensors, there is
still a lot of gearhead ingenuity involved.
Here, a $500,000 high-tech surveillance camera is kept
aloft on an aircraft powered by a 1/2-horsepower gasoline
engine adapted from a Honda pressure washer. The
launching catapult for the plane is basically an
oversized potato gun.
o ⚓ Bryan Lunduke ☛ The_(very_real)_history_of_🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇:-
)⦈__–_by_Bryan_Lunduke⠀⇛
This is Scott Fahlman. Wearing a T-Shirt celebrating his
creation.
o § Hardware⠀➾
# ⚓ Old VCR ☛ Old_Vintage_Computing_Research:_Refurb_weekend:
New_batteries_for_the_Palm_Pilots⠀⇛
Everything portable has a battery, and every
portable thing’s battery dies. This is bad on
earlier PalmOS devices that lack a non-volatile
file system because they’ll lose their data and
you’ll lose your mind. Fortunately many of my
stable of Palm Pilots and other PalmOS devices use
regular old batteries (like my original USRobotics
Pilot 1000 and Handspring Visor Deluxe); of my
rechargeable units, the AlphaSmart dana has a
replaceable battery (I have multiple spares, or you
can use regular batteries), and so does the Palm
Centro, which has a non-volatile file system to
boot.
# ⚓ IT Wire ☛ iTWire_–_India_PC_shipments_fall_below_5m_for
first_time_in_four_quarters [Ed: Terrible news for Windows,
helps explains why many PCs there are converted to GNU/
Linux]⠀⇛
India’s PC shipments for the second quarter of 2022
dropped to 4.6 million units, a fall of 12%, the
technology analyst firm Canalys says.
The company, which includes desktops, notebooks and
tablets when counting PC shipments, said in a
statement this was the first time shipments had
fallen below five million units in the last four
quarters.
Notebooks were the biggest contributor with 2.6
million units, though this was only 2% year-on-year
growth. By contrast, desktops saw 70% year-on-year
growth, though this amounted to only 900,000 units
shipped.
o § Health/Nutrition/Agriculture⠀➾
# ⚓ Nanoplastics_can_move_up_the_food_chain_from_plants_to
insects_and_from_insects_to_fish⠀⇛
“Our results show that lettuce can take up
nanoplastics from the soil and transfer them into
the food chain. This indicates that the presence of
tiny plastic particles in soil could be associated
with a potential health risk to herbivores and
humans if these findings are found to be
generalizable to other plants and crops and to
field settings. However, further research into the
topic is still urgently needed,” lead author, Dr
Fazel Monikh of the University of Eastern Finland
concludes.
# ⚓ The Nation ☛ A_Higher_Court⠀⇛
In October 2019, a scant few months before the
coronavirus was first detected in Wuhan, the
Brooklyn Nets and the Los Angeles Lakers were
scheduled to play a low-stakes exhibition game in
Shanghai before the start of the upcoming season.
The game was part of the league’s ongoing courtship
of international markets, but it was suddenly
overshadowed by a tweet from then–Houston Rockets
executive Daryl Morey that seemed to express
support for the protests in Hong Kong. (The since-
deleted tweet was an image that read: “Fight for
Freedom Stand With Hong Kong.”) The protests had
been ongoing since March, but the backlash was
immediate: The Chinese Basketball Association
suspended its relationship with the Rockets, while
Chinese state television and the streaming giant
Tencent announced that they would stop broadcasting
NBA games. The Nets’ scheduled visit to a Chinese
school was canceled, but the exhibition game
eventually took place despite the tense atmosphere.
o § Proprietary⠀➾
# ⚓ Adobe_to_Acquire_Figma⠀⇛
Figma’s mission is to help teams collaborate
visually and make design accessible to all. Founded
by Dylan Field and Evan Wallace in 2012, the
company pioneered product design on the web. Today,
it is making it possible for everyone who designs
interactive mobile and web applications to
collaborate through multi-player workflows,
sophisticated design systems and a rich, extensible
developer ecosystem. Figma has attracted a new
generation of millions of designers and developers
and a loyal student following.
# ⚓ Reuters ☛ Adobe_to_buy_Figma_in_$20_billion_bid_on_future
of_work_that_spooks_investors⠀⇛
Adobe Inc agreed on Thursday to acquire cloud-based
designer platform Figma for $20 billion, sparking
investor concerns about the rich price tag that led
to a drop of more than $30 billion in the market
value of the Photoshop maker.
# ⚓ Bloomberg ☛ Adobe_Tumbles_After_Deal_to_Buy_Figma_for_About
$20_Billion⠀⇛
The deal announced by Adobe, which is a mix of half
cash and half stock, confirms an earlier Bloomberg
report and would mark the biggest ever takeover of
a private software company, according to data
compiled by Bloomberg. It’s also Adobe’s biggest
acquisition and the market found the deal
expensive, sending shares to their steepest single-
day decline since 2010.
# ⚓ CNBC ☛ Adobe_shares_plunge_on_deal_to_acquire_design
platform_Figma_for_$20_billion⠀⇛
Figma, whose backers include the likes of Index
Ventures, Greylock Partners and Kleiner Perkins, is
expected to generate more than $400 million in
annual recurring revenue this year, sources
familiar with the company’s financials previously
told CNBC. Adobe confirmed Figma’s ARR will surpass
$400 million exiting 2022.
That means Adobe is paying in the neighborhood of
50 times revenue at a time when sales multiples for
cloud software are contracting dramatically from
their record highs reached last year. For the top
cloud companies in the BVP Nasdaq Emerging Cloud
Index, forward multiples have fallen to just over 9
times revenue from about 25 in February 2021.
# ⚓ New York Times ☛ Adobe_Agrees_to_Buy_Figma,_a_Design
Platform,_for_$20_Billion⠀⇛
Figma, which was founded in 2012, has raised more
than $332 million in funding, according to
Crunchbase, and was valued at $10 billion in 2021.
The company allows multiple people to collaborate
on design projects in the same files at once.
# ⚓ Fortune ☛ Wall_Street_thinks_Adobe_overpaid_for_Figma._Why
company_officials_are_confident_in_their_$20_billion
purchase⠀⇛
Nearly a decade ago, Brown University student Dylan
Field made a big bet on himself. The college junior
dropped out of the Ivy League school after earning
a $100,000, Peter Thiel-sponsored fellowship to
chase his entrepreneurial dreams.
Field’s first product, drone-modifying software,
didn’t pan out. His next venture, the collaborative
software editing company Figma, very much did. It
sold Thursday for $20 billion (pending regulatory
approval).
# ⚓ ABC ☛ Adobe_buying_Figma_in_$20B_cash-and-stock_deal⠀⇛
The companies said that Figma’s web-based, multi-
player capabilities will accelerate the delivery of
Adobe’s creative cloud technologies on the web,
making the creative process more productive and
accessible to more people.
# ⚓ [Old] Sorbet_Leopard_–_Your_Power_Mac_Unleashed_(Revision
1.5_Released)⠀⇛
I would like to make absolutely clear that there
are NO “free” and “paid” versions of Sorbet
Leopard. Sorbet is, has always been, and always
will be a freely available passion project made in
earnest specifically for certain compatible models
of the PowerPC-based Power Macintosh, intended to
be used exclusively by the vintage Mac community.
It was created with the express purpose of simply
making life easier on these two-decade-old
machines, and absolutely no other reason besides
that.
That aside, due to running the risk of downloading
potentially tampered or outdated images, I strongly
advise against acquiring any builds of Sorbet
Leopard from any sources other than either
Macintosh Garden or the MediaFire backup mirror
(also available on Macintosh Garden), which are the
only locations at present where all hosted builds
are officially maintained and updated.
Moreover, Sorbet Leopard does not contain any code,
assets, or components from any builds of the
recently discovered Mac OS X Snow Leopard early
alpha whatsoever. The system components are
comprised primarily of highly matured binaries /
libraries found in the final releases of both Mac
OS X 10.5.8 and 10.6.8, with the remainder portion
being made up of newer community software.
# ⚓ Barrons ☛ Apple_to_Hike_App_Store_Prices_in_Europe_and
Asia⠀⇛
The tech giant said app prices and in-app purchases
will increase in all countries using the euro
currency as well as Chile, Egypt, Japan, Malaysia,
Pakistan, Poland, South Korea, Sweden, Vietnam.
# ⚓ Macworld ☛ Apple_prepares_large_App_Store_price_hike_in
Europe_and_elsewhere⠀⇛
The increase will take place on October 5 and will
apply to the existing pricing tiers: In the Euro
zone, for example, the lowest (non-free) tier will
increase from €0.99 to €1.19. Developers are free
to compensate for the higher tier prices by
dropping their apps to a lower tier, but may not be
able to keep the price exactly the same.
In full, there are updated tier price lists for the
Euro zone (plus a separate list for Montenegro),
Chile, Egypt, Japan, Malaysia, Pakistan, Poland,
South Korea, Sweden, and Vietnam. The Verge notes
that Japan is facing the highest increase, with
prices rising by more than 30 percent.
# ⚓ Reuters ☛ Apple_to_raise_App_Store_prices_in_some_countries
in_Europe,_Asia⠀⇛
Apart from euro zone countries, the price increases
will hit Sweden and Poland in Europe; Japan,
Malaysia, Pakistan, South Korea and Vietnam in
Asia; and Chile in South America.
# ⚓ MacRumors ☛ App_Store_Prices_to_Increase_in_Europe_Next
Month⠀⇛
For those unfamiliar with how App Store pricing
works, Apple provides developers with preset tiers
that they can price their app at, and these tiers
will be increasing for the euro next month. For
example, tier one will be rising from €0.99 to
€1.19, while the maximum tier is set to increase
from €999 to €1,199, according to Apple.
# ⚓ AppleInsider ☛ Apple_to_hike_App_Store_prices_in_Europe_and
other_countries_in_October⠀⇛
The changes are set to take place as early as
October 5, 2022, and will include the prices of
apps and in-app purchases but exclude auto-
renewable subscriptions.
# ⚓ 9to5Mac ☛ Apple_to_raise_App_Store_prices_in_multiple
countries_next_month⠀⇛
There are no details as to why Apple will increase
App Store prices in these countries, but this is
probably related to the exchange rate of local
currencies dropping against the dollar. For
instance, the euro has now reached parity with the
dollar, something that has never happened in the
last 20 years. Apple products have also become more
expensive in Europe for the same reason.
# ⚓ CNA ☛ Apple_to_raise_App_Store_prices_in_some_countries_in
Europe,_Asia⠀⇛
A rapid rise in inflation, interest rates and
energy prices this year has hammered the yen, the
euro and most emerging economy currencies. The euro
has dropped to two-decade lows this year and has
been languishing around parity against the dollar
for weeks.
# ⚓ Nasdaq ☛ Apple_to_raise_App_Store_prices_in_some_countries
in_Europe,_Asia⠀⇛
Apple Inc AAPL.O said on Tuesday it will raise
prices of apps and in-app purchases on its App
Store from next month in all of the euro zone and
some countries in Asia and South America.
# ⚓ CNBC ☛ Apple_hiked_the_price_of_the_iPhone_14_in_key
markets_despite_keeping_it_the_same_in_the_U.S.⠀⇛
The iPhone 14 base model will start at $799, the
same amount that it initially charged for last
year’s iPhone 13. The highest price iPhone 14 Pro
Max starts at $1,099, the same as the iPhone 13 Pro
Max.
# ⚓ MacRumors ☛ Apple_Executive_Responds_to_Annoying_iOS_16
Copy_and_Paste_Prompt:_‘Absolutely_Not_Expected_Behavior’⠀⇛
Apple has responded to user complaints regarding an
annoying pop-up in iOS 16 that asks for user
permission if an app wants to access the clipboard
to paste text, images, and more.
[...]
As user annoyance with the behavior boils high,
Apple has finally responded, saying the constant
pop-up is not how the feature is intended to work.
MacRumors reader Kieran sent an email to Craig
Federighi and Tim Cook, complaining about the
constant prompt and advocating for Apple to treat
access to the clipboard the same way iOS treats
third-party access to location, camera, microphone,
and more.
o § Security⠀➾
# ⚓ BBC ☛ How_is_a_thief_taking_thousands_from_London_gym-
goers?⠀⇛
A serial thief is targeting London gym-goers and
emptying their bank accounts, a BBC Radio 4
investigation has found.
Journalist Shari Vahl from the You and Yours
programme has spoken to a number of women with
near-identical experiences – all of which included
the loss of many thousands of pounds.
Vahl shared her findings with the Met Police, which
had previously closed a number of individual
investigations, to show the cases could be linked.
Now the force will reopen the inquiry.
# ⚓ Bruce Schneier ☛ Credit_Card_Fraud_That_Bypasses_2FA [Ed:
'Smart' things are not smart, they're fake security]⠀⇛
Someone in the UK is stealing smartphones and
credit cards from people who have stored them in
gym lockers, and is using the two items in
combination to commit fraud…
# ⚓ Trinity_Guard_Brings_Security_Suite_Up_to_Speed_with_IBM_i
7.5_–_IT_Jungle⠀⇛
IBM put a major focus on improving security with
the release of IBM i 7.5 earlier this year, with
stronger out-of-the-box default configurations, new
password controls, and improved monitoring. With
the launch of TG Suite 3.0, Trinity Guard is
helping its customers get the most out of those
security improvements.
# ⚓ LinuxInsider ☛ Google_Debugs,_JFrog_Jumps_Code,
Confidential_Kubernetes,_Meta-PyTorch [Ed: Google spun as a
security champion even though it works for NSA and has
already been caught putting back-doored ciphers inside
Linux]⠀⇛
As the open-source model continues to prove its
sustainability in the enterprise, the software
community is ramping up its security mindedness.
That concern was evident in recent weeks as leading
Linux groups led the way for better code security.
Google announced a new initiative to zero in on
software vulnerabilities. Already a generous
provider of patching incentives, the software
developer upped the ante to encourage more
researchers to submit troublesome codes for cash.
Edgeless Systems made a striking open-source
contribution, JFrog offered advancements in support
a more polished Rust Foundation, and Facebook, too,
pushed the limits for Meta AI.
# § Privacy/Surveillance⠀➾
# ⚓ Lawfare ☛ The_Data_Broker_Caught_Running_Anti-
Abortion_Ads—to_People_Sitting_in_Clinics⠀⇛
In 2015, Copley Advertising and its one owner
and employee John Flynn provided these
capabilities to Bethany Christian Services,
an anti-abortion, Michigan-based, evangelical
Christian organization that provides adoption
services—though until 2021, not to LGBTQ+
parents—and whose website features articles
about women deciding to not get an abortion.
According to the settlement with the
Massachusetts attorney general, Copley
Advertising geofenced medical facilities for
Bethany Christian Services, including
reproductive health clinics, in New York
City; Columbus, Ohio; Richmond, Virginia; St.
Louis, Missouri; and Pittsburgh,
Pennsylvania. It then enabled Bethany
Christian Services to run ads to devices
within a geofenced area—including abortion
clinic waiting rooms.
# ⚓ The Nation ☛ The_Prying_Eyes_of_Social_Media⠀⇛
When the Finnish prime minister, Sanna Marin,
was recently captured on video dancing at a
party with friends, a great deal of ink was
spilled evaluating her behavior. She was
criticized for conduct unbecoming a prime
minister and for an exuberance that some on
the far right gleefully—and falsely—claimed
must have been excited by illicit drug use.
This framing put the onus on Marin to closely
monitor herself even in closed rooms, and it
does the same for us all. It compels us to
perpetually distrust weddings, birthday
parties—anywhere there are others who have
cell phones. Ascribing the video’s
circulation to individual intentionality
restricts our imagination to carelessness and
“leaks.” One cybersecurity expert “raised the
possibility Russia had hacked the phone or
social accounts of someone who is part of the
close circle of the Finnish premier.”
o § Defence/Aggression⠀➾
# ⚓ FAIR ☛ Biden’s_Afghan_Shell_Game_Prompts_Media_Shrugs_and
Stenography⠀⇛
More than a year after it froze $7 billion of
Afghanistan’s central bank reserves in the wake of
the Taliban’s military victory, the US has
announced it will use half the money to establish a
fund at a Swiss bank to help stabilize the
cratering Afghan economy.
# ⚓ Meduza ☛ Putin_announces_Russia’s_partial_mobilization_as
occupied_regions_schedule_annexation_‘referendums’_—_Meduza⠀⇛
In a national address aired Wednesday morning,
President Vladimir Putin announced a partial
mobilization of Russia’s armed forces.
# ⚓ Counter Punch ☛ How_could_Chile_reject_a_perfectly
progressive_constitution?⠀⇛
The new constitution would replace one created by
the previous 17-year authoritarian military junta
headed by General Augusto Pinochet. The elected
President Salvador Allende was violently overthrown
by a military coup led by Pinochet in 1973, who
remained Chile’s dictator until 1990.
# ⚓ New York Times ☛ In_One_Corner_of_Kosovo,_Cheers_Still_Ring
Out_for_Putin⠀⇛
Many ethnic Serbs, nursing grievances against NATO
for a 1999 bombing campaign that broke Serbia’s
grip on the territory, see President Vladimir V.
Putin’s Russia as a potential savior.
# ⚓ New York Times ☛ Strike_Near_Another_Ukrainian_Nuclear
Plant_Escalates_Fears_of_Disaster_–_The_New_York_Times⠀⇛
A powerful Russian missile hit 300 yards from the
plant far from the front lines, Ukraine said, a
reminder that despite its recent retreat, Russia
can still threaten nuclear sites.
# ⚓ US News And World Report ☛ Russian_Pop_Star’s_War_Criticism
Stirs_Vigorous_Debate⠀⇛
A Russian mega-pop star’s criticism of President
Vladimir Putin’s war in Ukraine has set off intense
reactions on social media, posing a critical
question: Will the iconic singer’s disapproving
Instagram post mark a turning point in Russian
public opinion?
# ⚓ RFERL ☛ Ukraine_Pushes_‘Pace,’_Stabilization_In_Eastern
Offensive_To_Deny_Russia_‘Any_Foothold’⠀⇛
Ukrainian officials have announced efforts to
urgently stabilize recently retaken eastern
territory and stressed the need for rapid gains in
order to deny Russia “any foothold on Ukrainian
soil” with Russia’s invasion nearing the seven-
month mark.
# ⚓ New York Times ☛ Russian_Setbacks_Are_Hampering_Army
Recruitment,_Says_Pentagon_Official⠀⇛
A Ukrainian official said that of 146 bodies
exhumed so far in a northeastern city, most were
civilians and some had been tortured.
# ⚓ US News And World Report ☛ Hungary_Says_EU_Should_Not
Consider_New_Sanctions_Against_Russia⠀⇛
Hungary’s foreign minister said on Tuesday the
European Union should not consider new sanctions
against Russia
# ⚓ The Strategist ☛ What’s_behind_Poland’s_reparation
debate?⠀⇛
Ever since Russia invaded Ukraine on 24 February,
Poland has received daily threats from Russian
propagandists that it will be next.
# ⚓ US News And World Report ☛ Ukraine_Warns_of_‘Nuclear
Terrorism’_After_Strike_Near_Plant⠀⇛
A Russian missile has blasted a crater close to a
nuclear power plant in southern Ukraine, damaging
nearby industrial equipment but not hitting its
three reactors.
# ⚓ JURIST ☛ Russia_missile_nearly_strikes_nuclear_plant_in
Ukraine⠀⇛
The Ukraine Ministry for Defense Monday reported
that a Russian missile attempted to strike the
South Ukraine Nuclear Power Plant in the Mykolaiv
region. Authorities estimate that the missiles
landed just 300 metres away from the plant. Since
the Russian invasion of Ukraine in February,
concerns have been raised about a possible nuclear
disaster.
# ⚓ US News And World Report ☛ Russia’s_Wagner_Trying_to
Recruit_Over_1,500_Felons_for_Ukraine_War_-U.S._Official⠀⇛
The Wagner Group, a Russian private military
company, is trying to recruit over 1,500 convicted
felons to take part in Russia’s war in Ukraine, but
many are refusing to join, a senior U.S. defense
official said on Monday.
# ⚓ US News And World Report ☛ Russia_Moves_to_Formally_Annex
Swathes_of_Ukraine⠀⇛
Russia on Tuesday paved the way for the formal
annexation of swathes of Ukrainian territory,
backing referendum plans in areas of Ukraine its
soldiers control in a direct challenge to the West
that could sharply escalate the war.
# ⚓ US News And World Report ☛ 4_Ukrainian_Regions_Schedule
Votes_This_Week_to_Join_Russia⠀⇛
The separatist leaders of four Russian-controlled
areas of Ukraine say they are planning to hold
referendums this week for the territories to become
part of Russia as Moscow loses ground in the war it
launched.
# ⚓ JURIST ☛ EU_Council_Presidency_calls_for_war-crimes
tribunal_after_mass_graves_discovered_in_Ukraine_–_JURIST_–
News⠀⇛
The Czech Republic’s Minister of Foreign Affairs
called on Saturday for “the speedy establishment of
a special international tribunal that will
prosecute the crime of aggression” after the
discovery of mass graves left by Russian forces in
Izium, Ukraine. The Czech Republic currently holds
the EU’s rotating presidency as of July 2022
# ⚓ RFERL ☛ U.K._Says_Russia_Relocated_Black_Sea_Submarines_As
‘Threat_Level’_Rose_From_Ukrainian_Attacks⠀⇛
British defense intelligence has said in its latest
assessment that it believes Russia’s Black Sea
Fleet has moved submarines from their home port on
the annexed Crimean Peninsula to southern Russia in
a sign of the increased threat to Russian forces of
Ukraine’s “long-range strike capability.”
The British Defense Ministry said in its
intelligence update that the Black Sea Fleet’s
command “has almost certainly relocated its KILO-
class submarines” from the waters off Sevastopol to
Novorossiisk in the Krasnodar region.
# ⚓ Meduza ☛ Shoigu:_300_thousand_reservists_to_be_drafted_into
army_—_Meduza⠀⇛
Sergei Shoigu says 300 thousand reservists will be
called up in Russia as a result of the partial
mobilization announced by Vladimir Putin.
# ⚓ Meduza ☛ Shoigu_says_5,937_Russian_soldiers_have_died_in
Ukraine_—_Meduza⠀⇛
In the first announcement in months, Russian
Defense Minister Sergei Shoigu said in an interview
to the Rossiya-24 TV channel that 5,937 Russian
servicemen have died during the war in Ukraine.
# ⚓ Meduza ☛ Russia_sees_spike_in_Google_searches_for_‘How_to
leave_Russia’_—_Meduza⠀⇛
In the hours before Russian President Vladimir
Putin was expected to address the nation regarding
plans to conduct “referendums” in Ukraine’s
occupied territories Tuesday, searches for the
phrase “How to leave Russia” spiked on Google. The
surge was noted by the Telegram channel Mozhem
Obyasnit, though it’s available for all to see on
Google Trends. The phrase’s popularity appears to
have peaked at about 6:00 pm Moscow time.
o § Environment⠀➾
# ⚓ [Old] EPA ☛ Joint_Statement_by_Environment_and_Climate
Change_Canada_and_the_U.S._Environmental_Protection_Agency_on
the_50th_Anniversary_of_the_signing_of_the_United_States-
Canada_Great_Lakes_Water_Quality_Agreement⠀⇛
Fifty years ago on April 15, 1972, in response to
the significant deterioration of water quality, our
two countries affirmed our commitment to work
closely together to restore and protect the Great
Lakes through a new framework for binational
cooperation, the United States-Canada Great Lakes
Water Quality Agreement.
Under the Great Lakes Water Quality Agreement,
Canada and the United States have engaged state and
provincial governments, municipalities and local
authorities, First Nations, Métis and Tribal
governments, industry, nongovernment organizations
and the public in working together to achieve a
healthy and sustainable Great Lakes ecosystem for
the benefit of present and future generations.
# ⚓ Counter Punch ☛ Extreme_Heat⠀⇛
Mountains of carbon in the permafrost
# ⚓ France24 ☛ UN_chief_warns_that_world_is_in_‘great_peril’_as
leaders_arrive_for_General_Assembly⠀⇛
Warning that the world is in “great peril,” the
head of the United Nations says leaders meeting in
person for the first time in three years must
tackle conflicts and climate catastrophes,
increasing poverty and inequality — and address
divisions among major powers that have gotten worse
since Russia invaded Ukraine.
# § Energy⠀➾
# ⚓ Helsinki Times ☛ YLE:_LNG_from_Russia_used_to_fill_up
new_terminal_in_Hamina,_Finland⠀⇛
A LONG-AWAITED tanker filled with liquefied
natural gas (LNG) arrived in Hamina, a
coastal town in south-eastern Finland, on
Monday, reports YLE.
# ⚓ Xe’s Blog ☛ My_new,_weird_smartcard_and_how_I_learned
to_use_it⠀⇛
When you speak for professional conferences,
sometimes you get a goodie bag with random
stuff in it. Recently I spoke at RustConf
about authentication technologies. Among
other things (such as a very nice picnic bag
that I will be sure to make use of), I got a
Ledger Nano X hardware cryptocurrency wallet.
It is a custom engraved one too. It looks
really, really nice. Here’s a picture of it:
[...]
o § Finance⠀➾
# ⚓ CoryDoctorow ☛ The_Chokepoint_Capitalism_tour⠀⇛
I’m writing this from a hotel room in Ottawa, the
day before the first event in the tour Chokepoint
Capitalism, the book Rebecca Giblin and I are about
to publish with Beacon Press; this tour is a little
different from the usual so I thought I’d do a post
explaining how it’ll all work.
This is my first tour since the pandemic hit; I had
four (!) book releases during the first year of the
lockdown and did a slew of online events. In some
ways, these were amazing: I could do a UK event in
the morning and a US event in the evening. But I
don’t think anyone – not the booksellers, nor the
readers, nor the special guests who helped me out –
would say they were as good as an in-person event.
# ⚓ The Strategist ☛ A_shift_to_Asia_won’t_solve_Russia’s
economic_woes⠀⇛
Russian President Vladimir Putin sought this month
to contrast the vibrant economies of Asia with the
decadence of the West, signalling that Russia’s
future lay with the East.
The economic and political dominance of the United
States was waning, he told an economic forum in
Vladivostok, and the Western elites were blind to
the ‘irreversible, or should I say tectonic shifts’
in international relations as emerging nations, led
by the Asia–Pacific, played a much bigger role.
‘Asia–Pacific countries emerged as new centres of
economic and technological growth, attracting human
resources, capital and manufacturing.’
# ⚓ New York Times ☛ [Reposted]_‘Crippling’_Energy_Bills_Force
Europe’s_Factories_to_Go_Dark⠀⇛
The furnace, heated to 1,500 degrees Celsius, was
glowing red. Workers at the Arc International glass
factory loaded it with sand that slowly pooled into
a molten mass. Nearby on the factory floor,
machines transformed the shapeless liquid with a
blast of hot air into thousands of delicate wine
glasses, destined for sale to restaurants and homes
worldwide.
Nicholas Hodler, the chief executive, surveyed the
assembly line, shimmering blue with natural gas
flames. For years, Arc had been powered by cheap
energy that helped turn the company into the
world’s largest producer of glass tableware — and a
vital employer in this working-class region of
northern France.
# ⚓ Vox ☛ Student_loan_forgiveness_isn’t_the_midterms_savior
some_Democrats_wanted_–_Vox⠀⇛
But there’s one “win” some Democrats are concerned
may be more of a liability than an asset: the Biden
administration’s plan to cancel up to $20,000 in
student loans.
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ Idiomdrottning ☛ Balance_of_Power⠀⇛
The “false balance” media bias is one reason for
this.
False balance, also bothsidesism, is a media bias
in which journalists present an issue as being more
balanced between opposing viewpoints than the
evidence supports. […] producers and editors may
feel that a story portrayed as a contentious debate
will be more commercially successful than a more
accurate account of the issue. Unlike most other
media biases, false balance may stem from an
attempt to avoid bias; producers and editors may
confuse treating competing views fairly—i.e., in
proportion to their actual merits and
significance—with treating them equally, giving
them equal time to present their views even when
those views may be known beforehand to be based on
false information.
# ⚓ Variety ☛ LinkedIn_Hires_Ex-CNN_Digital_Exec_Courtney_Coupe
as_First_Head_of_Original_Programming⠀⇛
Coupe comes to LinkedIn with nearly 20 years of
media experience. At CNN, where she worked for more
than seven years, she had led content strategy and
programming for CNN+, before Warner Bros. Discovery
shut down the subscription-video service one month
after it launched earlier this year. In addition,
Coupe oversaw all development and production for
CNN Audio’s slate of podcasts, including Anderson
Cooper’s recently launched “All There Is With
Anderson Cooper.”
# ⚓ Gizmodo ☛ Apple’s_Quietly_Funding_an_‘Astroturf_Lobbying
Group’_Claiming_to_Represent_App_Developers⠀⇛
Washington D.C. tech industry group The App
Association boldly refers to itself as, “the
leading industry voice on the app economy,” and
says it represents more than 5,000 app makers and
connected device companies spread out around 27
countries worldwide.
# ⚓ Quartz ☛ Never_mind_Elon_Musk:_Twitter’s_bots_are_actually
good⠀⇛
With Elon Musk’s $44 billion acquisition of Twitter
hanging in the legal balance, bots—automated
twitter accounts that, in Musk’s words, inspired
him to purchase the platform and then, later, gave
him an excuse to back out of the deal—have been at
the center of attention.
The focus has mainly been on spam bots that harass
users or try to sucker them into scams, often
related to cryptocurrency. Still, legal experts are
skeptical that arguments over the precise ratio of
bots to active human users will scuttle the deal.
But in the controversy, something important got
lost: Bots are great! I like bots.
# ⚓ Gizmodo ☛ The_Pentagon_Is_Reportedly_Auditing_the_U.S.
Military’s_Own_Pro-America_Social_Media_Psyop⠀⇛
# ⚓ Michael West Media ☛ Murdoch_takes_a_pay_cut,_ABC_spends
big_on_Queen_–_Michael_West⠀⇛
As Queen Elizabeth is laid to rest, only one living
person remains who can match her for length of
service at the head of a family firm. And while
Rupert Murdoch’s publications have caused the royal
family plenty of grief, there are many similarities
between him and the late monarch.
# § Misinformation/Disinformation⠀➾
# ⚓ RTL ☛ Misinformation_shrouds_Philippine_martial_law
era_horrors⠀⇛
Amnesty estimates thousands of people were
killed and tens of thousands tortured and
imprisoned after Marcos imposed martial law
on September 21, 1972.
Under legislation signed in 2013 by former
president Benigno Aquino, 11,103 victims of
torture, killings, enforced disappearances
and other abuses have been officially
recognised and compensated.
In the run-up to Wednesday’s 50th anniversary
of the start of martial law, pro-Marcos posts
have flooded Facebook and TikTok with false
and misleading claims that cast doubt on
Amnesty’s findings and downplay the abuses.
o § Censorship/Free Speech⠀➾
# ⚓ [Old] Death_threats_against_bloggers_are_NOT_“protected
speech”_(why_I_cancelled_my_ETech_presentations)⠀⇛
Update: I could not bear to leave this post up on
the site, as one of the last things people will see
and remember about this blog — and especially with
that horrible photo. So, I have moved the post to a
separate web page here. The content is exactly as
it was posted, athough it lost some formatting.
Comments are closed (after 1100 of them), but you
can still read them here. I deleted only one
comment from this thread.
# ⚓ RTL ☛ Hong_Kong_arrests_harmonica_player_for_sedition_at
queen_vigil⠀⇛
A police source confirmed to AFP that the man
arrested was the harmonica player.
After 2019′s democracy protests, China has cracked
down on dissent in Hong Kong using national
security legislation and charges of sedition.
The latter is a colonial-era law that had fallen
into obscurity for decades until prosecutors dusted
it off in the aftermath of the protests.
The song “Glory to Hong Kong” contains the popular
protest chant “liberate Hong Kong, revolution of
our times” which has been declared by the courts to
be a threat to national security.
o § Freedom of Information / Freedom of the Press⠀➾
# ⚓ Jacobin Magazine ☛ Secret_Documents_Have_Exposed_the_CIA’s
Julian_Assange_Obsession⠀⇛
Stefania Maurizi was no stranger to the Ecuadorian
embassy in London. The Italian investigative
reporter had worked as a partner journalist with
WikiLeaks for all its major releases since 2009.
Maurizi had also pursued litigation in four
separate countries seeking to compel their
governments to release information about Julian
Assange and WikiLeaks. Assange, at that point, was
trapped in the embassy. In 2012, Ecuador’s
democratic socialist government granted him
political asylum, but the United Kingdom made clear
they would arrest the journalist should he ever set
foot outside the embassy. Maurizi had visited him a
number of times.
While Maurizi met with Assange on December 29,
2017, embassy security held on to her electronics
for the duration of the visit. As she talked to her
journalistic counterpart, employees of the Spanish
security firm UC Global accessed her devices,
photographed them, disassembled one of her phones,
and removed its SIM card. On at least one occasion,
the same security contractor took audio and video
recordings of her meeting with Assange.
o § Civil Rights/Policing⠀➾
# ⚓ NPR ☛ Why_your_bad_boss_will_probably_lose_the_remote-work
wars⠀⇛
Nicholas Bloom, one of the co-authors of this new
study, is an economist at Stanford University. Over
the last few years, Bloom has been a machine,
pumping out some of the best research we have on
remote work to date.
The biggest battle in the remote wars between
bosses and office workers, Bloom says, was fought
back in 2020. “Everyone wanted more days than their
employers were committing to after the pandemic,”
Bloom says. “That battle was just decisively won by
employees. The employees routed employers.
Employers basically had to shift.”
# ⚓ RTL ☛ New_Iran_protests_over_woman’s_death_after_‘morality
police’_arrest⠀⇛
Public anger has grown since authorities on Friday
announced the death of Mahsa Amini, 22, in a
hospital after three days in a coma, following her
arrest by Tehran’s morality police during a visit
to the capital on September 13. Demonstrations were
held in Tehran, including in several universities,
and the second city Mashhad, according to the Fars
and Tasnim news agencies.
# ⚓ NPR ☛ For_the_first_time_in_230_years,_Congress_has_full
U.S._Indigenous_representation⠀⇛
With her recent swearing-in, it became official for
the first time in more than 230 years: A Native
American, a Native Alaskan and a Native Hawaiian
are all members of the House — fully representing
the United States’ Indigenous people for the first
time, according to Rep. Kaiali’i Kahele of Hawaii.
Now, there are six Indigenous Americans who are
representatives in the House.
# ⚓ CSP:_Platteville_PD_vehicle_with_female_suspect_inside_hit
by_train⠀⇛
A 20-year-old female suspect was taken to the
hospital after the Platteville police vehicle she
was in was hit by a train Friday evening. The
officer was not in the vehicle when the train
struck the patrol car, according to the Colorado
Bureau of Investigations.
# ⚓ Kansas City ☛ Cops_put_woman_in_police_car_parked_on
tracks,_CO_officials_say._Then_a_train_came⠀⇛
Officers placed the woman in the back of the
Platteville officer’s patrol car and went to search
her vehicle, the release said.
A train traveling northbound then hit the police
car, the agency said.
# ⚓ Counter Punch ☛ Justice_for_Farmworkers⠀⇛
Currently farmworkers must vote at a site specified
by the state’s Agricultural Relations Board, and
supporters of the bill argue that mail-in ballots
would free the workers, many of whom are
undocumented, from intimidation and retaliation by
employers.
o § Monopolies⠀➾
# ⚓ RFI ☛ Google_loses_appeal_against_record_EU_antitrust
fine⠀⇛
The European Union’s second-highest court on
Wednesday overwhelmingly upheld the EU’s record
fine against Google over its Android operating
system for mobile phones, slightly reducing the fee
for technical reasons.
In a statement, the EU’s General court said it
“largely confirms the commission’s decision that
Google imposed unlawful restrictions on
manufacturers of Android mobile devices” in order
to benefit its search engine.
# ⚓ AccessNow ☛ Meta_and_Google_must_use_their_powers_to_stop
Myanmar’s_alternative_propaganda_machine⠀⇛
The Myanmar junta’s intensifying control of online
spaces must be stopped — Google and Meta must use
their powers to intervene. As part of its efforts
to dominate and weaponize the internet against
people, the military is planning to “ban” Facebook
(Meta) and YouTube (Google) across the country.
Access to both platforms has already been
curtailed, with some people using Virtual Private
Networks (VPNs) to connect — a workaround likely to
be penalized under the new censorship measures, and
cemented in the disastrous draft cybersecurity law.
As military-run government agencies in Myanmar use
Google products, and Meta has international sway,
these companies can use their leverage to challenge
the ban and the likelihood of the junta penalizing
people for accessing blocked sites through other
means.
“The Myanmar junta is determined to silence people
by stamping out all means of communication and
expression,” said Wai Phyo Myint, Asia Pacific
Policy Analyst at Access Now. “The military
aggressively propagates hate and stifles dissent,
while creating communication blackholes that hide
its own human rights violations.”
# § Copyrights⠀➾
# ⚓ Publishing Perspectives ☛ French_Publishers_Cheer_a
Court’s_Order_to_Block_a_Book_Piracy_Site⠀⇛
A judgment was handed down in Paris on August
25, according to SNE and that court ruling
has ordered Internet service providers to
block the site (and associated domain names)
of a piracy group called “Z-Library.” The
result, according to the syndicate, is that
209 domain names and their extensions on
mirror sites are being rendered inaccessible.
* § Gemini* and Gopher⠀➾
o § Personal⠀➾
# ⚓ Re:_The_Amazing_Hypothetical_Moon_of_Saturn⠀⇛
# ⚓ Two_cubes⠀⇛
Two six-sided dice, where one with three blank
sides and three two-pip sides, and the other has
three one-pip sides and three two-pip sides, have
an equal distribution of 1 through 4.
o § Technical⠀➾
# ⚓ Vim_Has_Spoiled_Me⠀⇛
I started using vim about two years ago. Powering
through the steep learning curve was something I
knew I had to persevere through as I started my
journey into the world of Linux and minimal
computing.
Over time I became much more comfortable using vim
and it’s now my go-to editor. I write all my
content for this capsule and my other blogs in vim
and I’ve only now started to realize the dramatic
increase in efficiency versus common word
processors.
Over the last few days I’ve had to spend a lot more
time in LibreOffice Writer and it felt so clunky
compared to vim. I’m not a programmer, so I’m
almost exclusively using vim to write prose. And
I’ll be honest, in the beginning I would give up
half way through typing something up because I was
spending most of my time looking up a command for
something I needed to do. However, over time,
muscle-memory kicked in and I started to remember
the commands and tricks I used most. The best part
is that I’m not even close to realizing the
benefits of all the tools available to me.
# ⚓ Using_Arion_to_use_NixOS_modules_in_containers⠀⇛
NixOS is cool, but it’s super cool because it has
modules for many services, so you don’t have to
learn how to manage them (except if you want them
in production), and you don’t need to update them
like a container image.
# ⚓ “I_Just_Play_Here”⠀⇛
As I mentioned in my last post I’ve been pretty
hooked on OpenTTD lately (that’s also why I haven’t
been as active posting).
I decided to try a multiplayer game and looked in
the listing for one that had active players and
wasn’t password protected. I picked one of them at
random and joined.
There was one other player there and we’ve chatted
a bit. Apparently it’s just been them for a very
long time, with others popping in and leaving
immediately from time to time. It’s been fun
sharing a world with someone.
# § Science⠀➾
# ⚓ New York Times ☛ One_Man’s_Dream_of_Fusing_A.I._With
Common_Sense_–_The_New_York_Times⠀⇛
Artificial intelligence systems can process
vast amounts of data in seconds, but they
can’t make sense of the world or explain
their decisions. David Ferrucci wants to
change that.
# § Internet/Gemini⠀➾
# ⚓ A_Gemtext_Mirror_of_The_Anarchist_Library⠀⇛
I have published a new capsule that serves as
a gemtext front-end for The Anarchist
Library. The Anarchist Library is an
invaluable repository of new and historical
leftist literature.
=> =============================================================================
World Wide Web but a lot lighter.
䷩ 𝚕𝚒𝚗𝚎 5867
╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕
⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.21.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧
Gemini_version_available_♊︎
✐ Links_21/09/2022:_GNOME_43_and_i3_4.21_Released⠀✐
Posted in News_Roundup at 1:41 pm by Dr. Roy Schestowitz
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈
§ Contents⠀➾
* GNU/Linux
o Kernel_Space
o Applications
o Instructionals/Technical
o Games
o Desktop_Environments/WMs
# K_Desktop_Environment/KDE_SC/Qt
# GNOME_Desktop/GTK
* Distributions_and_Operating_Systems
o SUSE/OpenSUSE
o Arch_Family
o Red_Hat_and_Derivatives
o Debian_Family
o Canonical/Ubuntu_Family
o Open_Hardware/Modding
o Mobile_Systems/Mobile_Applications
* Free,_Libre,_and_Open_Source_Software
o Web_Browsers
# Mozilla
o Productivity_Software/LibreOffice/Calligra
o Content_Management_Systems_(CMS)
o Funding
o Openness/Sharing/Collaboration
o Programming/Development
# Python
# Shell/Bash/Zsh/Ksh
# Java
* Leftovers
o Science
o Education
o Hardware
o Health/Nutrition/Agriculture
o Linux_Foundation
o Security
# Privacy/Surveillance
o Defence/Aggression
o Environment
# Energy
# Overpopulation
o Finance
o AstroTurf/Lobbying/Politics
o Censorship/Free_Speech
o Freedom_of_Information_/_Freedom_of_the_Press
o Civil_Rights/Policing
o Internet_Policy/Net_Neutrality
o Monopolies
# Copyrights
* Gemini*_and_Gopher
o Personal
o Politics
* § GNU/Linux⠀➾
o ⚓ Framework_|_Introducing_the_Framework_Laptop_Chromebook_Edition⠀⇛
Framework began with the goal to remake consumer
electronics to respect people and do less harm to the
planet. To enable this, we strive to expand our mission
into new categories. Today, we are excited to announce
that we have partnered with Google to create the
Framework Laptop Chromebook Edition. We’ve taken the best
parts of the Framework Laptop and merged those with the
powerful simplicity of ChromeOS to create a high-
performance, upgradeable, repairable, customizable
Chromebook.
The Chromebook Edition is available for pre-order in the
US and Canada today starting at $999 USD, with first
shipments starting in early December. We’re using a batch
pre-order system, with only a fully-refundable $100
deposit required at the time of pre-order. All of the
replacement parts and modules that make up the Chromebook
Edition are also available for waitlisting on the
Marketplace today.
o ⚓ Linux Links ☛ Linux_Around_The_World:_Switzerland_–_LinuxLinks⠀⇛
We cover events and user groups that are running in
Switzerland. This article forms part of our Linux Around
The World series.
o § Kernel Space⠀➾
# ⚓ Metro UK ☛ Nintendo_Switch_2_rumours_resurface_after_Linux
confirms_T239_chip_|_Metro_News⠀⇛
At the time, such a chip didn’t exist. Or at least
wasn’t public knowledge. Recently, however, a Linux
employee confirmed its existence via the company’s
mailing list.
# ⚓ LWN ☛ Overriding_kernel_version_in_built_docs_[LWN.net]⠀⇛
Hello:
Upon suggestion from Jakub Kicinski, we now build
linux-next documentation and
make it available at https://docs.kernel.org/next/.
However, I want to make
sure that we override the version string in the
built docs so it doesn’t say
“6.0.0-rc6″ but “next-20220919″.
What’s the proper way to do this, preferably via
passing something to the
“make htmldocs” command?
Regards,
Konstantin
# ⚓ LWN ☛ Rendered_linux-next_documentation_on_kernel.org_
[LWN.net]⠀⇛
Konstantin Ryabitsev has announced the availability
of rendered documentation from linux-next on
kernel.org. This will be useful for anybody wanting
to see what the documentation for the next kernel
release will look like.
# ⚓ TechRadar ☛ Torvalds_confirms_Rust_is_coming_to_the_new
version_of_Linux_|_TechRadar⠀⇛
Linux creator Linus Torvalds has reportedly
committed to bringing Rust to the operating system.
o § Applications⠀➾
# ⚓ 9to5Linux ☛ Ventoy_1.0.80_Adds_Secondary_Boot_Menu,_Now
Supports_More_Than_1000_ISOs⠀⇛
Ventoy 1.0.80 is here almost two months after
version 1.0.79 and it’s a big milestone for the
popular multiboot USB creator utility as the number
of supported ISO files reached and passed beyond
the 1000 mark. Yes, you’re reading that right,
Ventoy now supports more than 1000 ISOs and that’s
a huge thing!
On top of that, the Ventoy 1.0.80 release
introduces several new features like a secondary
boot menu that makes it easier for users to select
Ventoy’s special modes, such as WIMBOOT mode, GRUB2
mode, or MEMDISK mode. Previously, these modes were
only accessible via hotkeys, which are still in
effect.
# ⚓ Linux Links ☛ Streaming_with_Linux:_Deezer_–_LinuxLinks⠀⇛
This is a series that surveys popular streaming
services from a Linux perspective. We are not
reviewing any of the streaming services themselves
although we may make subjective comments along the
way.
Deezer is a French online music streaming service.
It allows users to listen to music content from
record labels, as well as podcasts on various
devices online or offline. The service offers 90
million tracks, 160,000 podcast titles, and in
excess of 32,000 radio stations. The breadth of its
content means it’s broadly comparable to the
material available with Spotify and Amazon Music
Unlimited. Like its rivals, there is a free plan
and various paid subscriptions. Deezer offers
lossless FLAC files at 16-bit/44.1 KHz, which is
significantly higher than the bitrate offered by
Spotify. Like Spotify, Deezer offers some exclusive
content.
There is a desktop app available for Linux. We
installed it from the Arch User Repository. This
isn’t a native application (it’s Electron-based).
# ⚓ Sam_Thursfield:_Status_update_21/09/22⠀⇛
Last week I attended OSSEU 2022 in Dublin, gave a
talk about BuildStream 2.0 and the REAPI, and saw
some new and old faces. Good times apart from the
common cold I picked up on the way — I was glad
that the event mandated face-masks for everyone so
I could cover my own face without being the “odd
one out”. (And so that we were safer from the 3+
COVID-19 cases reported at the event).
Being in the same room as Javier allowed some
progress on our slightly “skunkworks” project to
bring OpenQA testing to upstream GNOME. There was
enough time to fix the big regressions that had
halted testing completely since last year, one
being an expired API key and the other, removal of
virtio VGA support in upstream’s openqa_worker
container. We prefer using the upstream container
over maintaining our own fork, in the hope that our
limited available time can go on maintaining tests
instead, but the containers are provided on a “best
effort” basis and since our tests are different to
openqa.opensuse.org, regressions like this are to
be expected.
# ⚓ LinuxSecurity ☛ Linux_Log_Analysis_|_LinuxSecurity.com⠀⇛
Understanding how log files work is an essential
first step for any user interested in discovering
what happens behind their operating systems.
Additionally, learning more about log analysis and
tools will expand users’ knowledge and help them
for technology roles in administration and
development. Good log analysis means bug-free
development environments and faster deployments.
For cybersecurity and information technology
professionals, practical log analysis means
malicious activity not going unnoticed. The
importance of log analysis across technology
sectors speaks to the extent of learning log
analysis as an aspiring technology professional or
a professional looking to expand their knowledge;
users like you! We hope that this article brings
our readers further insight into log analysis.
# ⚓ Testing_syslog-ng_4.0_–_Blog_–_syslog-ng_Community_–
syslog-ng_Community⠀⇛
This week’s syslog-ng blog does not demonstrate any
new syslog-ng features or integrations. Instead of
those, it is a request for testing syslog-ng 4.0
and points you at a few related blogs and
resources.
o § Instructionals/Technical⠀➾
# ⚓ Its FOSS ☛ What_is_Fork_Bomb_in_Bash?_Understanding_:(){_:
|:-_};:⠀⇛
Nuking my system by installing Arch Linux was not
enough, so I used a Fork Bomb.
# ⚓ Linux Shell Tips ☛ How_to_Install_Latest_Python_on_Debian
Linux⠀⇛
Python is an on-demand programming language that
continues to grow in popularity under the Linux
operating system ecosystem. Aside from its strong
attributes like versatility and ease of use,
mastering Python can transform the life of a Linux
user for good reasons.
# ⚓ LinuxConfig ☛ How_to_install_and_setup_Ghost_CMS_on
Ubuntu⠀⇛
Ghost is a free and open source blogging platform
written in Javascript, which saw its first release
in 2013. It supports writing posts both using a
WYSIWYG (What You See Is What You Get) editor, and
the Markdown language. Unlike WordPress, it is
focused on simplicity and on being purely a
blogging platform, therefore it includes SEO and
and social sharing features out of the box. Ghost
offers a ready-to-go hosting service, Ghost(Pro),
but can be easily self-hosted.
In this tutorial we see how to install and setup
the Ghost blogging platform on Ubuntu, both in
development and production mode.
# ⚓ Trend Oceans ☛ How_to_Increase_Margin_on_Konsole_Terminal_–
TREND_OCEANS⠀⇛
One of the KDE-based users read the article where
we discussed how to increase the padding of the
gnome terminal, which he liked very much, and
because of that, he asked me “Can we do something
similar for Konsole?”
On that, I said, “Of course, we can do this by
doing a little bit of tweaking on Konsole, like
creating a profile if the default profile is not
available, then we will add the one line of a
statement which will increase the padding of the
Konsole.”
# ⚓ ID Root ☛ How_To_Install_ImageMagick_on_Rocky_Linux_9_–
idroot⠀⇛
In this tutorial, we will show you how to install
ImageMagick on Rocky Linux 9. For those of you who
didn’t know, ImageMagick is an open-source software
suite for creating, editing, converting, and
modifying various formats of images such as PNG,
GIF, JPEG, PDF, EXR, WebP, and TIFF. ImageMagick is
one of your choices if you need a program to
manipulate and display images.
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 ImageMagick on Rocky Linux. 9.
# ⚓ HowTo Forge ☛ How_to_Install_Prestashop_with_Apache_and
Let’s_Encrypt_SSL_on_Debian_11⠀⇛
PrestaShop is a free, open-source, efficient, and
innovative e-commerce solution that helps you to
sell your products online. It is a powerful and
adaptable e-commerce CMS that provides all features
needed to create an online store.
# ⚓ HowTo Forge ☛ How_to_Install_VNC_Server_on_Rocky_Linux⠀⇛
Virtual Network Computing (VNC) is a desktop
sharing protocol that allows you to control a
computer remotely using VNC client software. In
this tutorial, you will set up the VNC Server with
TigerVNC on a Rocky Linux server. You will also
learn how to connect securely to the VNC Server via
SSH tunneling.
# ⚓ Red Hat Official ☛ How_to_configure_your_CA_trust_list_in
Linux_|_Enable_Sysadmin⠀⇛
Trust is important. You can’t blindly trust
everybody and everything; instead, you should base
trust on experience and reputation. In the world of
networking, a certificate authority (CA) is an
organization that vouches for Secure Sockets Layer
(SSL) certificates, which indicate that a web
server can be trusted.
# ⚓ Citizix ☛ How_to_set_up_an_SFTP_server_on_Alma/Rocky_Linux
Server_9⠀⇛
In this guide we are going to set up an sftp server
on RHEL 9 server like Rocky Linux or Alma 9. We
will also set up a form of chroot where users can
only access sftp with the shared credentials.
The File Transfer Protocol is a standard
communication protocol used for the transfer of
computer files from a server to a client on a
computer network.
FTP isn’t popular today because it Lacks Security.
When a file is sent using this protocol, the data,
username, and password are all shared in plain
text, which means a hacker can access this
information with little to no effort. For data to
be secure, you need to use an upgraded version of
FTP like SFTP.
# ⚓ H2S Media ☛ How_to_uninstall_Spotify_from_Ubuntu_Linux?_–
Linux_Shout⠀⇛
Want to get rid completely of Spotify from Ubuntu
Linux then here are the commands to follow using
the command terminal.
Spotify client is a free application available for
Linux including Windows, macOS, and smartphones.
However, maybe after some usage, if you don’t like
the app anymore or just don’t want it on your
Ubuntu Linux; then, we can remove it easily.
However, removing Spotify from Linux completely
depends on what method you have used to install it.
For Example, APT, SNAP, GUI, or Flatpak. Here we
discuss all of these methods to let you know the
process of removing the Spotify client.
# ⚓ AddictiveTips ☛ How_to_play_GTFO_on_Linux⠀⇛
GTFO is a survival horror FPS video game that is
played cooperatively. It was developed and
published by developer 10 Chambers and released on
Microsoft Windows. Here’s how you can play GTFO on
Linux.
# ⚓ TechRepublic ☛ How_to_install_the_Containerd_runtime_engine
on_Ubuntu_Server_22.04_|_TechRepublic⠀⇛
Jack Wallen walks you through the process of
manually installing the Containerd container
runtime engine on Ubuntu Server 22.04.
Containerd is a container runtime engine created
for simplicity and portability. This runtime is
considered an industry standard and is available as
a daemon for Linux and Windows and can manage the
entire container lifecycle for image transfer and
storage, container deployment and supervision,
storage and network, and more.
# ⚓ TechRepublic ☛ How_to_deploy_SonarQube_with_Docker_|
TechRepublic⠀⇛
Jack Wallen shows you how to deploy the continuous
code inspection tool, SonarQube using Docker on
Ubuntu Server 22.04.
SonarQube is a continuous code inspection tool that
is used for the automatic inspection of code
quality. The tool runs these automated reviews to
detect bugs and code smells (deeper problems) in 29
different programming languages. SonarQube presents
itself with a user-friendly web-based GUI and can
be deployed as a docker container.
# ⚓ Make Tech Easier ☛ How_to_Install_and_Manage_Python
Versions_in_Linux_–_Make_Tech_Easier⠀⇛
The Python programming language was introduced in
1991. In all these years, it has gone through many
changes, with each version adding and removing
various features. Due to these changes, software
written in newer versions of Python may or may not
work with older versions.
This version mismatch costs developer experience
and productivity, so it’s important to learn how to
manage Python versions installed on your computer
to run them all efficiently. This tutorial shows
you how to do that.
# ⚓ H2S Media ☛ 3_Ways_to_Install_Spotify_App_on_Debian_11
Bullseye_–_Linux_Shout⠀⇛
Tutorial to install Spotify on Debian 11 Bullseye
using command terminal for streaming music online.
Spotify is one of many Music Streaming Services
over the Internet, you can listen to songs via
stream legally on your smartphone and PC.
Meanwhile, Spotify is also available as an app on
many TVs. Thanks to providers such as Spotify,
Deezer, Tidal, and Co., the download of music is no
longer necessary. The music is streamed over the
Internet, i.e. only temporarily cached. On request,
however, a download of individual songs is also
possible.
# ⚓ DebugPoint ☛ How_to_Access_Android_Devices_Internal_Storage
and_SD_Card_in_Ubuntu,_Linux_Mint_using_Media_Transfer
Protocol_(MTP)⠀⇛
This tutorial will show how to access android
devices using MTP in Ubuntu and how to access SD
card contents.
MTP, or media transfer protocol, is an extension of
the Picture transfer protocol and is implemented in
the Android marshmallow version. After the
marshmallow update, you can’t use the android
devices as typical mass storage devices you can
just plug in and see the internal storage contents
and the SD card contents in a file manager such as
in Thunar or GNOME Files. This is due to the OS
being unable to determine the MTP devices, and
also, a list of supported devices is not yet
implemented.
# ⚓ ID Root ☛ How_To_Install_Flameshot_on_Ubuntu_22.04_LTS_–
idroot⠀⇛
In this tutorial, we will show you how to install
Flameshot screenshot tool on Ubuntu 22.04 LTS. For
those of you who didn’t know, Flameshot is a free
and open-source, cross-platform tool to take
screenshots. The best thing about this screenshot
tool is that it operates with both the graphical
user interface as well as the command-line
interface. It is a very easy-to-use screenshot tool
that provides users with a high level of
flexibility and customization.
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 Flameshot screenshot software
on Ubuntu 22.04 (Jammy Jellyfish). You can follow
the same instructions for Ubuntu 22.04 and any
other Debian-based distribution like Linux Mint,
Elementary OS, Pop!_OS, and more as well.
# ⚓ FOSSLinux ☛ How_to_install_missing_Perl_modules_on_Debian_|
FOSS_Linux⠀⇛
Perl is a dynamic interpreted scripting language
famous for its powerful text processing abilities.
Syntactically it resembles C, but it’s far more
compressed, allowing developers to very tourist
code like one-liners that hack a solution much
faster than other scripting languages.
# ⚓ HowTo Geek ☛ How_to_Use_AppImages_on_Linux⠀⇛
AppImages let Linux developers wrap their
applications into a single file that installs on
any Linux distribution. That simplifies things
tremendously. Here’s how to use them, and integrate
them into your desktop.
# ⚓ TechRepublic ☛ How_to_use_the_Amazon_Linux_container_image
with_Docker_for_development_|_TechRepublic⠀⇛
Jack Wallen helps you take your first steps with
Amazon Linux as a deployable container image.
# ⚓ Trend Oceans ☛ How_to_Increase_Padding_in_GNOME_Terminal⠀⇛
Don’t you feel you should give some extra space
around the terminal border? If yes, check how it
looks after adding padding to the GNOME terminal.
o § Games⠀➾
# ⚓ Boiling Steam ☛ New_Steam_Games_with_Native_Linux_Clients_–
2022-09-21_Edition_–_Boiling_Steam⠀⇛
Between 2022-09-14 and 2022-09-21 there were 26 New
Steam games released with Native Linux clients. For
reference, during the same time, there were 246
games released for Windows on Steam, so the Linux
versions represent about 10.6 % of total released
titles.
# ⚓ Godot Engine ☛ Godot_Engine_–_Release_candidate:_Godot
3.5.1_RC_2⠀⇛
We released Godot 3.5 in early August, and like any
release, there are few rough edges to iron out
which warrant making maintenance “patch” releases
(3.5.x).
We’ve had successful testing of a first Release
Candidate for 3.5.1, and a few more fixes got
backported in the meantime so let’s have another
round of testing before publishing 3.5.1 stable.
Please give it a try if you can. It should be as
safe to use as 3.5-stable is, but we still need a
significant number of users to try it out and
report how it goes to make sure that the few
changes in this update are working as intended and
not introducing new regressions.
o § Desktop Environments/WMs⠀➾
# ⚓ DebugPoint ☛ GSoC_2022_Brings_New_Features_to_Thunar,
Screenshooter_in_Xfce_Desktop⠀⇛
Google summer of code (GSoC) 2022 is a yearly
competition which is about improving open-source
projects. Thousands of students develop
contributions while enhancing their skills and
eventually benefit from open-source projects.
This year’s GSoC final project submission will be
completed on September 12, 2022. And we have some
updates on the Xfce desktop’s native apps.
# § K Desktop Environment/KDE SC/Qt⠀➾
# ⚓ i3_v4.21_released⠀⇛
This is i3 v4.21. This version is considered
stable. All users of i3 are
strongly encouraged to upgrade.
# § GNOME Desktop/GTK⠀➾
# ⚓ Make Use Of ☛ GNOME_43_Lands_With_Major_Linux_Desktop
UI,_Device_Security_Enhancements⠀⇛
Version 43 of the GNOME desktop for Linux has
been released. The new version debuts with
changes to the system menu, file manager, and
new device security options.
Celebrating “Hard Work” of GNOME Developers
The GNOME project took to Twitter to announce
GNOME 43:
As a testament to the developers, GNOME 43 is
codenamed “Guadalajara,” as the GUADEC GNOME
developer’s conference was held in the
Mexican city in July 2022.
# ⚓ Video ☛ Video ☛ GNOME_43:_building_a_better_Linux
platform_takes_time_–_Invidious⠀⇛
⚓ 9to5Linux ☛ 9to5Linux ☛ GNOME_43_Released_with_Quick
Settings,_More_GTK_4_Ports,_and_New_Device_Security
Panel⠀⇛
After nearly six months of development, the
GNOME 43 “Guadalajara” desktop is finally
here and introduces a few interesting
changes, the most prominent one being the
Quick Settings menu that can be accessed from
the system top bar, very similar to those you
probably saw on Android devices or the latest
Windows 11 and macOS systems.
# ⚓ DebugPoint ☛ GNOME_43_Arrives_&_There’s_No_Place_Like
“GNOME”!⠀⇛
GNOME 43 shines further today, bringing GNOME
43 polished desktop for Ubuntu, Fedora, SUSE
and more distros.
GNOME 43 code named “Guadalajara” is a
milestone release because it seems almost a
closure of the modernization and improvement
efforts that started from GNOME 40 onwards.
The years of efforts includes GTK4 porting of
core shell and native apps, adoption of
libadwaita and many more performance
improvements.
Since it’s now officially out, let’s give you
a brief about what are the new features of
this desktop.
# ⚓ GNOME_Release_Notes⠀⇛
After 6 months of hard work, the GNOME
project is proud to present version 43. This
latest GNOME release comes with improvements
across the board, ranging from a new quick
settings menu, a redesigned Files app, and
hardware security integration. GNOME 43
continues the trend of GNOME apps migrating
from GTK 3 to GTK 4, and includes many other
smaller enhancements.
GNOME 43 is code-named “Guadalajara”, in
recognition of the work done by the
organizers of GUADEC 2022.
# ⚓ Its FOSS ☛ GNOME_43_Releases_With_Plenty_of_User
Experience_Enhancements⠀⇛
As one of the biggest open-source desktop
environment projects, GNOME has raised the
bar in simplicity for years. The last major
GNOME version, GNOME 42, brought many
improvements, particularly in simplifying and
improving the UI.
# ⚓ OMG Ubuntu ☛ GNOME_43_Released,_This_is_What’s_New_–
OMG!_Ubuntu!⠀⇛
Whether you’re an eager GNOME acolyte or just
a casual admirer, there is a lot to enjoy in
the latest version of the GNOME desktop
environment.
GNOME 43 arrives six months after the
(rather) substantial GNOME 42 release. In
many respects it’s a direction continuation
of the path set out there, and contains
confident collection of changes, some small,
some big, but all intended to make it easier
to use GNOME.
I whip through the core user-facing changes
in this post, share a few screenshots, and
give a few of my thoughts on some of the
chances based on first-hand experience of
using it. If you read my run-through of GNOME
43 new features — gold star for those who did
— most of the changes I mention below will be
familiar to you.
* § Distributions and Operating Systems⠀➾
o § SUSE/OpenSUSE⠀➾
# ⚓ SUSE’s Corporate Blog ☛ 3_Reasons_to_Migrate_to_SUSE
Manager_4.3_|_SUSE_Communities⠀⇛
SUSE Manager 4.1 will NO LONGER be supported after
October 31,2022.
# ⚓ Virtualbox,_grep,_gawk_update_in_Tumbleweed_–_openSUSE
News⠀⇛
The rhythm of openSUSE Tumbleweed snapshots being
released this week continues at a steady pace.
The rolling release appears to be producing
consistent snapshots since the 20220903 release.
Two packages were released in snapshot 20220919. An
update of libksba 1.6.1, which works with X.509
certificates, fixed rpmlint warnings and now
ensures an Online Certificate Status Protocol
server does not to return the sent nonce. The other
package to update was xfce4-pulseaudio-plugin
0.4.5, which fixed the accidental toggling of the
mute switch and compilation with GNU Compiler
Collection 10.
An update of virtualbox 6.1.38 arrived in snapshot
20220918. This version upgrade fixed a couple
Common Vulnerabilities and Exposures. Both CVE-
2022-21571 and CVE-2022-21554 could allow virtual
machine access and result in an unauthorized
ability to cause a hang or repeatable crash. An
update of the virtualbox-kmp package introduced
initial support for Linux Kernel 6.0. The package
also fixes the permission problem with /dev/
vboxuser. Other packages to update in the snapshot
were ibus-m17n 1.4.17, python-charset-normalizer
2.1.1 and python-idna 3.4, which updated to the
recently announced Unicode 15.0.0.
o § Arch Family⠀➾
# ⚓ DebugPoint ☛ Garuda_Linux:_All-Rounder_Distro_Based_on_Arch
Linux⠀⇛
A review of the Arch Linux based Garuda Linux,
which brings a collection of desktop environments,
window managers, and tools for general users and
gamers.
Over the years, we reviewed a couple of Arch-based
distros – spread across new ones, stables distros
and more. Each one of them is a little different
from the others. Finally, we review the Garuda
Linux in 2022 – it’s our first review of this
distro, and we will continue with all the major
releases.
o § Red Hat and Derivatives⠀➾
# ⚓ Red Hat Official ☛ Using_Red_Hat_Enterprise_Linux_to
overcome_the_challenges_of_managing_multiple_databases⠀⇛
PeerSpot members, like most IT professionals, find
themselves juggling more than one relational
database management system (RDBMS). This means
having to stay on top of multiple system
configurations, updating processes and patch
management. Without the right tools, it can be very
demanding work.
# ⚓ Red Hat Official ☛ Customer_success_stories:_How_Red_Hat_is
helping_organizations_save_money,_enhance_customer_experience
and_improve_uptime⠀⇛
In this month’s customer success highlights, learn
how three companies are making use of Red Hat
OpenShift, Red Hat Ansible Automation Platform and
Red Hat Satellite to save money, enhance customer
experience and improve both uptime and security
posture.
# ⚓ Red Hat ☛ Boost_OpenShift_Data_Science_with_the_Intel_AI
Analytics_Toolkit_|_Red_Hat_Developer⠀⇛
Intel has been partnering with Red Hat to offer a
solution for Red Hat OpenShift Data Science that
includes Intel AI tools. With the help of these
tools, OpenShift Data Science can perform faster
and more efficiently.
The partnership between Intel and Red Hat came in
response to the needs of their customers for an
enterprise-grade solution for data science. The
need for a more efficient and faster solution stems
from the rise in demand for data scientists, which
is happening at an exponential rate.
The new tools include support for popular
frameworks such as TensorFlow, PyTorch, and MXNet,
as well as optimized workflows for deploying AI
models on Kubernetes clusters. OpenShift Data
Science also provides tight integration with key
components of the Intel Xeon Scalable processors
family, including Intel Deep Learning Boost
(DLBoost), which delivers performance that’s up to
three times better than previous generations for
deep learning workloads.
# ⚓ Red Hat ☛ Bind_services_created_with_AWS_Controllers_for
Kubernetes_|_Red_Hat_Developer⠀⇛
Application developers can define Amazon Web
Services (AWS) resources directly from Kubernetes
using AWS Controllers for Kubernetes (ACK). You can
use the Service Binding Operator to easily connect
applications to any AWS service provisioned through
ACK.
This article explores the connection with an RDS
database and demonstrates configuring ACK to create
a service instance for the AWS Relational Database
Service (RDS). You can also learn how to use
Service Binding Operator annotations to bind a
PostgreSQL service created using RDS and a REST
API.
# ⚓ Enterprisers Project ☛ 6_tactics_to_boost_creativity_on
your_IT_team⠀⇛
For IT teams, creativity is not just about looking
toward the future; it also involves examining the
present. Creativity is necessary for productivity.
In IT, there are many Information Technology
Infrastructure Library- (ITIL) and Capability
Maturity Model (CMM)-based processes that provide a
framework for carrying out certain tasks. At times,
employees fall back on these processes to boost
productivity. But in the end, it’s the creative
companies – the ones that are developing leaner,
more efficient, and more flexible processes within
those frameworks – that come out on top.
# ⚓ Enterprisers Project ☛ Digital_transformation:_6_tips_to
stay_on_track⠀⇛
Digital transformations are constant and ongoing –
chances are, you’re undergoing some phase of one as
you read this. Pre-pandemic, many transformations
were progressing at a steady, maybe even relaxed,
pace. Then COVID put them on the fast track.
If your digital transformation progress feels
slower than anticipated, it could be because you’ve
lost sight of one of the most important components:
the human element. People need to adopt and use the
new systems. Digital transformation changes roles,
skills, capabilities, ways of working, and even the
culture across large swaths of the organization.
# ⚓ Unicorn Media ☛ Community_Owned_CentOS_Replacement,
AlmaLinux,_Elects_Board⠀⇛
Since the organization was formed last year, it’s
been operating with an appointed board of
directors, so this will be the first fully elected
board in the organization’s brief history. The
election returns four board members to their seats,
and elects three new members.
# ⚓ EuroLinux_Desktop_Is_Now_Available_For_Download_|
Itsubuntu.com⠀⇛
EuroLinux Desktop based on Red Hat® Enterprise
Linux® 9 is now available for download. EuroLinux
Desktop, a new player in the Linux universe is
developed by the Polish Open Source solutions
manufacturer company called EuroLinux.
o § Debian Family⠀➾
# ⚓ Make Use Of ☛ What_Is_SparkyLinux?_The_Midweight_Debian
Alternative_Explained⠀⇛
SparkyLinux is a Linux distro based on Debian that
aims to offer a lightweight yet functional desktop
with some useful apps included, such as Firefox and
LibreOffice. It also has multiple editions, which
will be mentioned in detail below.
SparkyLinux began life as an Ubuntu version based
on the Enlightenment desktop in 2011 called ue17r
for Ubuntu Enlightenment Remix but eventually
changed its name to SparkyLinux. The community also
changed from being based on Ubuntu to Debian.
# ⚓ ZDNet ☛ StarlingX,_the_cloud_for_edge_computing,_gets_a
major_upgrade_|_ZDNET⠀⇛
The biggest single change is that StarlingX no
longer uses CentOS for its base operating system.
Instead, it now uses Debian. Specifically, the
latest Debian Stable Release, Bullseye. The
developers moved to Debian because they didn’t want
to rely on a commercial Linux distro.
o § Canonical/Ubuntu Family⠀➾
# ⚓ 9to5Linux ☛ Ubuntu_Users_Get_New_Linux_Kernel_Security
Updates_That_Patch_15_Vulnerabilities⠀⇛
The new Linux kernel security updates are available
for Ubuntu 22.04 LTS, Ubuntu 20.04 LTS, Ubuntu
18.04 LTS, and Ubuntu 16.04 ESM releases. They
address 15 security vulnerabilities including two
that are common to all supported Ubuntu releases,
namely CVE-2021-33655, an out-of-bounds write flaw
discovered in the framebuffer driver that could
allow a local attacker to cause a denial of service
(system crash) or possibly execute arbitrary code,
as well as CVE-2022-36946, a security issue
discovered by Domingo Dirutigliano and Nicola
Guerrera in the netfilter subsystem that could
allow a remote attacker to crash the vulnerable
system.
# ⚓ 9to5Linux ☛ Ubuntu_Core_Will_Support_the_Matter_Standard
Out_of_the_Box_for_IoT_Devices⠀⇛
As of today, Canonical is a participant member of
the Connectivity Standards Alliance (CSA), which
the company behind the popular Ubuntu Linux
distribution will help develop and promote open
standards for IoT (Internet of Things) and its
Ubuntu Core operating system for embedded devices.
Canonical is also the first company to join the
Connectivity Standards Alliance which offers a
major independent GNU/Linux distribution and
promises to support the Matter standard out-of-the-
box in its Ubuntu Core operating system to increase
interoperability and accessibility.
# ⚓ Ubuntu ☛ Canonical_joins_the_Connectivity_Standards
Alliance_|_Ubuntu⠀⇛
Canonical, the publisher of Ubuntu, announces today
that it has joined the Connectivity Standards
Alliance as a participant member.
In this role, Canonical will help the alliance to
develop open standards for the Internet of Things
(IoT) and advocate for the role of open-source
software in this domain. Canonical is the first
company offering a major independent Linux
distribution to join the alliance.
o § Open Hardware/Modding⠀➾
# ⚓ CNX Software ☛ Makerfabs_3.5-inch_TFT_touchscreen_display
features_ESP32-S3_SoC_–_CNX_Software⠀⇛
This display offers a 320×480 resolution through
the ILI9488 LCD driver, uses a 16-bit parallel
interface for communication with ESP32-S3 clocked
at up to 20 Mhz making it suitable for smooth
graphics user interface, and the company also
claims it is smooth enough for video displays, but
more on that later.
# ⚓ Hackaday ☛ It’s_Pi_All_The_Way_Down_With_This_Pi-Powered
Pi-Picking_Robot⠀⇛
While most of us live in a world where the once
ubiquitous Raspberry Pi is now as rare as hens’
teeth, there’s a magical place where they’ve got so
many Pis that they needed to build a robotic
dispenser to pick Pi orders. And to add insult to
injury, they even built this magical machine using
a Raspberry Pi. The horror.
# ⚓ Hackaday ☛ Raspberry_Pi_Grants_Remote_Access_Via_PCIe_(Sort
Of)⠀⇛
[Jeff] found a Raspberry Pi — well, the compute
module version, anyway — in an odd place: on a PCI
Express card. Why would you plug a Raspberry Pi
into a PC? Well, you aren’t exactly. The card uses
the PCI Express connector as a way to mount in the
computer and connect to the PC’s ground. The Pi
exposes its own network cable and is powered by PoE
or a USB C cable. So what does it do? It offers
remote keyboard, video, and mouse (KVM) services.
The trick is you can then get to the PC remotely
even if you need to access, say, the BIOS setup
screen or troubleshoot an OS that won’t boot.
o § Mobile Systems/Mobile Applications⠀➾
# ⚓ Ubuntu Pit ☛ Top_10_Best_Apps_To_Learn_Code_for_Beginners
in_2022⠀⇛
# ⚓ Android Police ☛ Your_next_Samsung_phone_might_support
seamless_Android_system_updates⠀⇛
# ⚓ GSM Arena ☛ Samsung’s_Android_13_Beta_expands_to_the_Galaxy
S21_lineup_in_the_US_–_GSMArena.com_news⠀⇛
# ⚓ Notebook Check ☛ OnePlus_10_Pro_upgrades_to_OxygenOS_13
based_on_Android_13,_with_slight_caveats_–_NotebookCheck.net
News⠀⇛
# ⚓ Android Authority ☛ Wallpaper_Wednesday:_Android_wallpapers
2022-09-21_–_Android_Authority⠀⇛
# ⚓ OnePlus_takes_just_one_month_to_update_to_Android_13_|_Ars
Technica⠀⇛
# ⚓ Top_9_Ways_to_Fix_Android_Phone_Keeps_Restarting⠀⇛
# ⚓ Top_8_Ways_to_Fix_YouTube_Videos_Lagging_on_Android⠀⇛
# ⚓ Hulu_stuttering_or_freezing_on_Android_after_v4.49.2
update⠀⇛
# ⚓ The Sun ☛ Warning_for_MILLIONS_of_Android_users_–_battery
life_ruined_by_simple_mistake_|_The_US_Sun⠀⇛
# ⚓ 9to5Google ☛ Logitech’s_G_Cloud_runs_your_cloud_games_with
a_12-hour_battery⠀⇛
* § Free, Libre, and Open Source Software⠀➾
o § Web Browsers⠀➾
# § Mozilla⠀➾
# ⚓ 9to5Linux ☛ Firefox_106_Promises_PDF_Annotation
Features,_Wayland_Screen_Sharing_Improvements⠀⇛
Firefox 106 won’t be a massive update to the
open-source and cross-platform web browser,
but it will bring a few interesting changes
for those who deal a lot with PDF documents,
such as annotation capabilities in the built-
in PDF viewer to let you write text, draw, or
add signatures to PDF files.
This feature was implemented in previous
Firefox releases, but it wasn’t enabled by
default, which means that you had to manually
enable it from the about:config settings by
setting the pdfjs.annotationEditorMode
variable from -1 to 0. With the Firefox 106
release, the PDF annotation capabilities will
be enabled by default.
# ⚓ dwaves.de ☛ CyberSec_Update,_Update,_Update_–_Ladies
&_Gentlemen:_Update_Your_FeuerFuchse_(Firefox)_and
DonnerVögel_(Thunderbird)⠀⇛
Responses Victims to a pre-prepared HTML
email with a meta tag could potentially
exclude information about it. Due to the
error (CVE-2022-3033 “high”) you could run
JavaScript and read or even manipulate
messages about it. Users who have set the
display of message text to simple html or
plain text are not affected by the
vulnerability.
# ⚓ The Register UK ☛ Firefox_105_is_out:_Faster_and_more
memory-frugal_•_The_Register⠀⇛
The Mozilla Foundation has let Firefox 105
out of the gate, and if you use a Chrome-
based browser, it’s a good time to take
another look.
Firefox 105 appeared on Tuesday, and while
this isn’t a show-stopping release, there is
some new stuff that is well worth having.
It’s not quite five months since Firefox 100
came out, which is long enough for Mozilla’s
rapid development cycle to have made some
substantial changes in the browser.
Some of the new features are relatively
small, but will make some users’ lives
better. If you have to print a page, there’s
a new option to print just the current page –
handy for tickets and other documents with
loads of irrelevant small print tacked on the
end. Here at the Reg FOSS desk, we’re rather
traditionalist and favor a plain old three-
button mouse, but we hear that trackpad
handling on Windows and macOS has been
improved and there are some new multi-finger
gestures in this version. Apparently this
doesn’t work on Linux just yet, but we can’t
say that we’ve noticed.
o § Productivity Software/LibreOffice/Calligra⠀➾
# ⚓ Its FOSS ☛ LibreOffice_is_Available_for_$8.99_on_Mac_App
Store:_Here’s_Why!⠀⇛
LibreOffice is a free and open-source office suite
available across multiple platforms.
o § Content Management Systems (CMS)⠀➾
# ⚓ WordPress_6.1_Beta_1_Now_Available⠀⇛
WordPress 6.1 Beta 1 is now available for download
and testing.
This version of the WordPress software is under
development. Please do not install, run, or test
this version of WordPress on production or mission-
critical websites. Instead, it is recommended that
you test Beta 1 on a test server and site.
o § Funding⠀➾
# ⚓ Document Foundation ☛ LibreOffice_Conference_Sponsors’
Interviews⠀⇛
The two main sponsors of LibreOffice Conference
2022 are allotropia and Collabora, the two largest
ecosystem companies fully focused on the
development of LibreOffice. They both develop new
features and improve the existing ones, manage
interoperability issues with MS Office non standard
document format by tweaking LibreOffice behavior
and the import/export filters, and look at bugs and
regressions.
Employees of both companies have been with
LibreOffice since the beginning, and in some cases
have started their journey into free open source
software during the previous decade, with
OpenOffice and other FOSS projects. Allotropia and
Collabora have also hired several young developers
who have started contributing to LibreOffice as
volunteers.
# ⚓ OSI Blog ☛ Atlantic.Net:_Why_we_sponsor_OSI⠀⇛
# ⚓ Its FOSS ☛ Wow!_Rust-based_Redox_OS_Gets_an_Anonymous
Donation_of_$390,000_in_Cryptocurrency⠀⇛
Redox OS is a Unix-like operating system written in
Rust.
The project was launched in 2015 by Jeremy Soller,
popularly recognized as the Principal Engineer at
System76 and a maintainer for Pop!_OS.
o § Openness/Sharing/Collaboration⠀➾
# ⚓ FOSSLife ☛ New_Open_Source_Database_Tracks_Global_Fossil
Fuel_Emissions⠀⇛
The registry uses “fully open source data combined
with a new cutting-edge emissions conversion
model,” according to Carbon Tracker, to help
governments and policymakers answer the critical
question of how to transition away from fossil
fuels.
# ⚓ Hackaday ☛ Open_Source:_Free_As_The_Air_You_Breathe⠀⇛
[Carolyn Barber] recently interviewed a 15-year-old
who has been making Corsi-Rosenthal boxes for
people in his community that are at risk for COVID.
Not only is it great that a teenager has such
community spirit, but it is also encouraging that
[Richard Corsi] and [Jim Rosenthal] made an open-
source design that can help people at a greatly
reduced cost.
# ⚓ Hackaday ☛ Finding_Digital_Solace_In_An_Old_Nokia_Phone⠀⇛
We don’t have to tell you that the current mobile
phone market is a bit bleak for folks who value
things like privacy, security, and open source.
While there have been a few notable attempts to
change things up, from phone-optimized versions of
popular Linux distributions to the promise of
modular handsets — we still find ourselves left
with largely identical slabs released by a handful
of companies which often seem to treat the customer
as a product.
o § Programming/Development⠀➾
# ⚓ Barry Kauler ☛ PKGget_package_manager_freeze_fixed⠀⇛
Rick C sent me an email recently reporting this. I
know about this problem, it has been there since
the very early days of the Puppy Package Manager.
If you try to drag the divide between “Package” and
“Description”, as shown by the red arrows, another
windows appears, then the entire desktop becomes
unresponsive, requiring the power button to be held
down to power-off.
# ⚓ Ubuntu Pit ☛ Top_10_Best_Apps_To_Learn_Code_for_Beginners
in_2022⠀⇛
Even though there are plenty of books available,
the best way to learn code is to practice. Hence,
those pursuing a career in programming often prefer
self-studying rather than only going after academic
degrees. And as it’s the digital era, people love
learning with digital resources such as mobile apps
to learn code.
One can use these applications anywhere and
anytime, and they often focus on teaching from
level zero so that nobody’s left out. These apps
are usually highly interactive and well put
together. They have a great learning curve and a
few tactics to motivate users to work harder as
well.
# ⚓ Linux Links ☛ Excellent_Free_Tutorials_to_Learn_MoonScript
–_LinuxLinks⠀⇛
MoonScript is a fully-fledged dynamic scripting
programmer friendly language that compiles into
Lua, or it can be dynamically compiled and run
using the moonloader.
Write MoonScript code, then run a program called
the MoonScript compiler which reads a MoonScript
program and converts it into an equivalent Lua
program that would do the exact same thing when
run.
It’s designed to be a language that’s more elegant
and more readable than Lua. It offers the power of
one of the fastest scripting languages combined
with a rich set of features. It supports features
like functions as first class objects, closures,
tail-recursion and a high performance.
# ⚓ dwaves.de ☛ PHP_HowTo_–_search_elements_of_array_(of
strings)_for_string_pattern_(case_in_sensitive)_–_remove
element⠀⇛
# ⚓ General_Availability_of_the_SCM/CI_Integration_Feature_–
Open_Build_Service⠀⇛
In May of 2021 we took our first steps towards
putting OBS builds into the continuous integration
cycle with the SCM/CI feature. Thanks to the
valuable feedback we received from users who
started as early testers and became heavy users of
the feature, we are ready today to push it out of
the beta program, making it generally available in
OBS.
# § Python⠀➾
# ⚓ TecAdmin ☛ Python_–_How_to_create_a_nested_directory
structure_–_TecAdmin⠀⇛
The pathlib module offers classes
representing filesystem paths with semantics
appropriate for different operating systems.
We can create nested directory structure
suing pathlib.Path.mkdir function in Python.
# § Shell/Bash/Zsh/Ksh⠀➾
# ⚓ dwaves.de ☛ GNU_Linux_bash_–_global_search_replace
string_in_all_files_in_all_subdirectories_below_current
directory⠀⇛
# § Java⠀➾
# ⚓ Ubuntu Handbook ☛ Oracle_Java_JDK_19_Released_with
Linux/RISC-V_Port_[How_to_Install]_|_UbuntuHandbook⠀⇛
Oracle Java JDK 19 is out! Here are the new
features and how to install instructions for
Ubuntu users.
First, for Linux users the release now ported
to support the RV64GV configuration of RISC-
V, a general-purpose 64-bit ISA.
The release also introduced record patterns
to deconstruct record values. Record patterns
and type patterns can be nested to enable a
powerful, declarative, and composable form of
data navigation and processing. Though it’s a
preview feature so far.
There are also 2 other preview features: a
foreign function & memory API can
interoperate with code and data outside of
the Java runtime; a lightweight virtual
threads that dramatically reduce the effort
of writing, maintaining, and observing high-
throughput concurrent applications; pattern
matching for switch expressions and
statements.
JDK 19 also introduced an API to express
vector computations that reliably compile at
runtime to optimal vector instructions, and
an API for structured concurrency.
* § Leftovers⠀➾
o ⚓ The Nation ☛ Sinking_Before_Our_Eyes⠀⇛
o ⚓ The Nation ☛ Does_the_NBA_Deserve_Becky_Hammon?⠀⇛
Does the NBA deserve Becky Hammon? It’s a question worth
asking a year after hoops watchers openly wondered, “Does
Becky Hammon ‘deserve’ to coach in the NBA?” Hammon’s
career as a three-time college All-American at Colorado
State, the all-time leading scorer in the Western
Athletic Conference, an unlikely WNBA all-star (after her
athleticism was questioned coming out of college and she
wasn’t even drafted), and eight years on the San Antonio
Spurs staff was seen as not enough to earn a gig. Even
though she had already been the first woman to be a paid
NBA assistant, and even though she coached the Spurs
Summer League team with great success, she found herself
with her nose pressed against Adam Silver’s window.
Despite the fact that the Gregg Popovich coaching tree in
the past four years has produced head coaches in
Charlotte (the bafflingly fired James Borrego) and Boston
(Ime Udoka, who unexpectedly led the Boston Celtics to
the NBA Finals), Hammon was not chosen to fill any of the
vacancies. Teams like the hapless Portland Trailblazers
turned down the opportunity to become a part of
history—to live up to its moniker—and give Hammon her
well-earned shot.
o ⚓ Tedium ☛ USA_Today_Sports_Center:_The_National_Newspaper’s_First
Online_Foray⠀⇛
As I’ve made clear many times over the years, I am an
enthusiast for newspapers’ attempts at innovation in the
pre-internet age. They had a window and they made plenty
of attempts, but they let that window close just before
it led anywhere good. In recent years, the most
innovative newspaper, coverage left off to the side, has
probably been The New York Times, followed directly by
The Washington Post. Often, attempts to innovate in
newspapers end up like the Wikitorial—embarrassing for
all involved, but thankfully forgotten quickly. But in
1982, true innovation and success was to be found in the
form of USA Today. It was easily the most experimental
paper of its kind when it first came out, and that early
experimentation paid off as Gannett’s daily newspaper
became a mainstay of hotels and newspaper racks
throughout the United States. The paper recently
celebrated its 40th anniversary, a huge feat. I have
heard complaints from many editors over the years about
the paper’s writing style, but the fact of the matter is,
it was hugely popular in its early days. But did you know
it had its own CompuServe-like online service … just for
sports? I learned this by literally buying a software
package that appeared on my front door almost exactly on
the paper’s 40th anniversary. Today’s Tedium talks USA
Today Sports Center
o § Science⠀➾
# ⚓ Checkmate_–_by_Joe_Posnanski_–_JoeBlogs⠀⇛
There’s something wild happening in the chess world
right now, and I’m going to tell you right up front
that I don’t really understand it. But I want to
talk about it anyway because it speaks to something
larger happening in all sports, something confusing
and alluring and perilous.
First, for those of you who don’t follow chess —
you know, the 99.7% of you — let me explain
something that I didn’t know: There is not a player
on earth and there never again will be a player on
earth who can defeat the best chess engine. Some of
you old enough might remember that in 1996, the
chess world champion, Garry Kasparov, played an IBM
supercomputer called “Deep Blue” in what was being
overhyped as the “Chess Battle for Humanity.”
# ⚓ Omicron Limited ☛ African_ubuntu_can_deepen_how_research_is
done⠀⇛
Many academic studies have been centered on Western
theories and methodologies for a long time. This
approach to research is broadly defined as
“universalist.” It assumes that “one-size-fits-all”
and set norms can be applied across cultures. For
example, Western ideas about identity revolve
around the individual. That shapes how research is
conducted: it focuses mainly on the individual and
emphasizes analysis at the individual level. Using
Western approaches in non-Western contexts misses
out on contextual issues such as power relations
between an individual and their community.
o § Education⠀➾
# ⚓ Common Dreams ☛ ‘Great_News’:_After_Strike,_Seattle
Teachers_Approve_Three-Year_Contract⠀⇛
Well over two-thirds of the union’s 6,000 members
voted in favor of a new contract with Seattle
Public Schools (SPS), yielding three separate pacts
covering different categories of employees. Just
over 70% of classroom teachers and other certified
staff voted for their contract, while 66% of
paraprofessionals and 82% of educational office
professionals voted for their respective contracts.
o § Hardware⠀➾
# ⚓ Hackaday ☛ 3D_Printed_String_Vase_Shows_What’s_Possible⠀⇛
# ⚓ Hackaday ☛ Mechanical_Color_Picker_Types_Hex_Codes_For
You⠀⇛
Hex codes are a simple, unambiguous way to
designate colors in digital media. However, going
from a color in your head to a hex code can be
difficult for the unpracticed. [Guy Dupont] built a
little gadget by the name of the Dial Toner to do
it for him (Nitter).
# ⚓ Hackaday ☛ Ride-on_Star_Wars_Land_Speeder_Gets_A_Real_Jet
Engine⠀⇛
When it comes to children’s ride-on toys, the Star
Wars Land Speeder is one of the cooler examples out
there. However, with weedy 12-volt motors, they
certainly don’t move quickly. [Joel Creates]
decided to fix all that, hopping up his land
speeder with a real jet engine.
o § Health/Nutrition/Agriculture⠀➾
# ⚓ Pro Publica ☛ Judge_Lifts_U.S._Ban_on_Mexicans_Entering
Country_to_Sell_Blood_Plasma⠀⇛
A federal district judge in Washington, D.C., has
ordered immigration officials to allow Mexican
citizens with visas to sell their blood plasma in
the U.S.
# ⚓ Common Dreams ☛ GOP_Seizes_on_Biden’s_‘Pandemic_Is_Over’
Remark_to_Demand_Medicaid_Cuts⠀⇛
Sen. Richard Burr (R-N.C.), the top Republican on
the Senate Health, Education, Labor, and Pensions
Committee, wrote in a letter to Biden that he
“watched with great interest” the “60 Minutes”
interview in which the president said that while
the United States still has “a problem with Covid,”
the pandemic has come to an end.
# ⚓ Democracy Now ☛ Is_the_Pandemic_Over?_Public_Health
Advocates_Decry_Biden’s_Claim_as_Thousands_Still_Dying_from
COVID⠀⇛
President Biden declared that “the pandemic is
over” during an interview on “60 Minutes” Sunday,
despite data collected by Johns Hopkins showing
COVID-19 killed 13,000 people across the U.S. over
the past month as 2.2 million new infections were
reported. “I think it’s very premature to say that
we see the end is in sight with this pandemic,”
says Steven Thrasher, author of “The Viral
Underclass: The Human Toll When Inequality and
Disease Collide.” He adds that the sentiment from
the nation’s leader is dangerous because it
discourages people from wearing masks and seeking
booster vaccinations, which are still vital to
prevent the virus’s spread.
o § Linux Foundation⠀➾
# ⚓ LinkedIn_donates_Feathr,_their_feature_store,_to_the_Linux
Foundation_–_Dataconomy [Ed: More Microsoft openwashing.
LinkedIn is spying and it is proprietary.]⠀⇛
LinkedIn announced today that Feathr, its open
source feature store, has joined LF AI & Data, the
Linux Foundation’s umbrella foundation for big data
and AI initiatives.
o § Security⠀➾
# ⚓ Techdirt ☛ Security_Experts_Ask_UK_Government_To_Roll_Back
Old_Computer_Abuse_Law_That_Harms_Security_Research⠀⇛
The US government passed the Computer Fraud and
Abuse Act in 1986, years before computers became
something everyone had at home and carried around
in their pockets every day. The CFAA had a purpose,
but its value declined as computing advanced. The
abuse it was written to address tended to take a
backseat to abuses of the law by prosecutors and
private companies to punish people for discovering
security flaws or using technology in ways some
people never expected.
# ⚓ LWN ☛ Security_updates_for_Wednesday_[LWN.net]⠀⇛
Security updates have been issued by Fedora
(libconfuse, moodle, rizin, and thunderbird),
Oracle (ELS kernel, gnupg2, ruby, and webkit2gtk3),
Red Hat (booth, dbus-broker, gnupg2, kernel,
kernel-rt, kpatch-patch, mysql, nodejs, nodejs-
nodemon, ruby, and webkit2gtk3), Slackware (expat
and mozilla), SUSE (kubevirt, virt-api-container,
virt-controller-container, virt-handler-container,
virt-launcher-container, virt-libguestfs-tools-
container, virt-operator-container and vsftpd), and
Ubuntu (bind9, ghostscript, linux, linux-aws,
linux-aws-5.15, linux-azure, linux-azure-5.15,
linux-kvm, linux-lowlatency, linux, linux-aws,
linux-aws-5.4, linux-azure, linux-azure-5.4, linux-
bluefield, linux-gkeop, linux-hwe-5.4, linux-ibm,
linux-ibm-5.4, linux-kvm, linux-oracle, linux-
oracle-5.4, linux-raspi, linux, linux-aws, linux-
aws-hwe, linux-azure-4.15, linux-dell300x, linux-
gcp, linux-gcp-4.15, lnux-hwe, inux-kvm, linux-
oracle, linux-raspi2, linux-snapdragon, linux-hwe-
5.15, linux-lowlatency-hwe-5.15, and mako).
# ⚓ The Register UK ☛ ‘I_Don’t_Care_About_Cookies’_extension
sold_to_Avast⠀⇛
The lone developer of anti-cookie-warning browser
add-on “I Don’t Care About Cookies” has sold it to
Avast, resulting in both concern – and new forks.
Web users the world over have been suffering under
the well-intentioned but ill-advised EU cookie law
for a decade now. As a result, websites pester with
warnings to get us to consent to cookies, and if
you don’t consent, they have no way to record that
fact and so pester you every visit.
Enter I don’t care about cookies, a handy browser
extension by Croatian developer Daniel Kladnik.
IDCAC, available for pretty much every web browser
out there, automatically dismisses cookie warnings.
You can tweak its settings if you want, but it
automatically accepts the minimal cookies for the
site to work.
# ⚓ The New Stack ☛ Shikitega:_New_Malware_Program_Targeting
Linux_–_The_New_Stack⠀⇛
Of course, you may not even know there’s such a
minute file hiding inside a larger package. So,
just like with Windows, be sure you know what’s in
every package and where it came from before
installing it.
[...]
So, how do you keep from getting a base case of
Shikitega? Simple. Just to the basics, of
installing security patches, keeping backups, and
never installing unknown programs.
# § Privacy/Surveillance⠀➾
# ⚓ Project Censored ☛ Entering_the_Resistance_Phase_of
the_Surveillance_Education_Cycle:_Finding_Ways_to
Protect_Privacy_in_Schools_–_Censored_Notebook,
Dispatches_from_Project_Censored:_On_Media_and
Politics⠀⇛
In The Master Switch: The Rise and Fall of
Information Empires, technology scholar Tim
Wu argues that throughout U.S. history,
communication technologies progress in a
cycle from a universally accessible medium
that brings pandemonium and creativity, to an
homogenized, sanitized, and pasteurized
vehicle that serves industrial interests. At
the start of the cycle, the public has a
positive view of the medium, believing it
will deliver a utopian future, but by the end
of the cycle, the public is left with
skepticism and scorn toward the medium.
# ⚓ Internet Freedom Foundation ☛ Har_Ghar_Privacy
Violation?_#SaveOurPrivacy⠀⇛
As India celebrates Azadi ka Amrit Mahotsav,
Indians across the nation were encouraged to
geo-tag their own homes under the Har Ghar
Tiranga campaign. Back in August, we wrote to
the Ministry of Culture, highlighting the
specific deficiencies in the harghartiranga
[dot]com website and its privacy policy. Even
though the website states that the data
collected will be deleted at the end of the
campaign, i.e., after August 15, the data is
still up on the website. Concerned with the
consequent privacy implications, we once
again wrote to the Ministry today, urging
them to delete the data at the earliest.
o § Defence/Aggression⠀➾
# ⚓ Meduza ☛ Russian_pop_legend_Alla_Pugacheva_under
investigation_for_‘discrediting’_Russian_army_—_Meduza⠀⇛
Russian authorities are investigating pop superstar
Alla Pugacheva for “discrediting” the army,
according to Russian state media outlet RIA
Novosti. The investigation is in connection to a
social media post Pugacheva made on Sunday in which
she asked to be added to the Russian Justice
Ministry’s “foreign agents” registry and criticized
Russia’s war against Ukraine.
# ⚓ Meduza ☛ Russia_barrels_ahead_towards_annexation_A_summary
of_Russia’s_‘referendum’_plans_and_new_mobilization_laws_—
Meduza⠀⇛
After months of uncertainty surrounding the Russian
authorities’ plans to conduct “referendums” on
annexing Ukraine’s occupied territories, the
Kremlin postponed the project “indefinitely” in
early September due to Ukraine’s successful Kharkiv
offensive. On September 20, however, Russian-
installed officials in the occupied territories
announced that definitive dates for the
“referendums” have been chosen: September 23–27.
Meanwhile, deputies in Russia’s State Duma
unanimously passed a number of changes to the
Criminal Code introducing the concepts of
“mobilization” and “martial law,” as well as new
penalties for wartime crimes. Here are the key
points.
# ⚓ Meduza ☛ Ukraine_recaptures_first_village_in_Luhansk_region
—_Meduza⠀⇛
Ukrainian troops have liberated a village in the
Luhansk region after months of controlling no
territory in the region. Advance detachments of the
Ukrainian Armed Forces first entered Bilohorivka
several days ago, and on September 19, Luhansk
Regional Governor Serhiy Haidai announced that the
village was under total Ukrainian control. Haidai
warned, on the other hand, that the process of
liberating the Luhansk region “won’t be a fast
one,” and that “every centimeter of Luhansk land
will require a difficult fight.”
# ⚓ Meduza ☛ Russian_Duma_introduces_concepts_of_‘mobilization’
and_‘martial_law’_into_Criminal_Code,_as_well_as_articles_on
looting_and_surrender_—_Meduza⠀⇛
State Duma deputies have unanimously adopted
amendments to the Russian Criminal Code in the
second and third readings. The session was
broadcast on the Duma website. At the second
reading, 381 MPs voted for the amendments and one
abstained. At the third reading, 389 deputies voted
for it.
# ⚓ Meduza ☛ Russian_Public_Opinion_Research_Center:_77%_of
Russians_have_not_been_abroad_in_the_past_five_years_—
Meduza⠀⇛
According to the Russian Public Opinion Research
Center, most Russians (77%) have not traveled
outside their country in the past five years.
# ⚓ Meduza ☛ ‘At_the_moment,_such_prospects_are_not_being
looked_at.’_Dmitry_Peskov_on_the_possibility_of_ending_the
war_diplomatically._—_Meduza⠀⇛
Dmitry Peskov, press secretary for the Russian
President, said that the Kremlin does not currently
see a possibility of ending the war in Ukraine “in
a political or diplomatic way.”
# ⚓ The Nation ☛ What_Do_Americans_Care_About?_Not_a_Cold_War
With_Russia_and_China.⠀⇛
The Biden administration will soon release its
National Security Strategy, which is being revised
in the wake of Russia’s invasion of Ukraine. The
document will no doubt trigger a renewed debate
about how the United States should gear up for a
new Cold War, against both Russia and China. But
before we plunge into a global great-power
competition, it’s worth recalling President Biden’s
promise to create a “foreign policy for the middle
class” and take a look at what most concerns
Americans.
# ⚓ Meduza ☛ ‘LNR,’_‘DNR,’_and_Russian-occupied_Zaporizhzhia
and_Kherson_regions_set_‘referendum’_dates_on_joining_Russia
—_Meduza⠀⇛
RIA Novosti reports that the assembly of the
Russian-controlled Luhansk People’s Republic has
set a “referendum on joining Russia” that will run
from September 23 to September 27 this year.
# ⚓ Meduza ☛ ‘Almost_an_exact_copy_of_Stalin’s_amendments’_How
politicians,_journalists,_and_analysts_reacted_to_Russia’s
new_‘mobilization’_laws_—_Meduza⠀⇛
On September 20, the Russian State Duma unanimously
passed a set of amendments to the Criminal Code
that introduced the concepts of “mobilization,”
“martial law,” and “wartime.” New articles about
“voluntary surrender” (punishable by up to 10 years
in prison) and “looting” (punishable by up to 15
years in prison) were also added, while the penalty
for unauthorized abandonment of a unit during
mobilization or martial law was raised to 10 years.
Despite the Russian authorities’ repeated denials
that there will be a general mobilization, Russian
officials, lawmakers, and propagandists have
increasingly begun calling for one — and the new
legislation makes the prospect seem likelier than
ever. Meduza has compiled a brief list of some of
the initial reactions from Russian politicians,
political scientists, and journalists to the new
amendments.
# ⚓ Meduza ☛ ‘The_war_party_has_won’:_Kremlin_plans_‘immediate’
annexation_of_Ukrainian_territories_—_and_mobilization_at
home._Here’s_this_new_decision’s_background._—_Meduza⠀⇛
# ⚓ Common Dreams ☛ Opinion_|_Peace_Activists_Hit_the_Streets
From_DC_to_San_Francisco_Urging_Ceasefire_in_Ukraine⠀⇛
On Sunday President Biden warned Russian President
Valdamir Putin “Dont. Don’t. Don’t.” use nuclear
weapons in retaliation for severe battlefield
losses in Ukraine. While Putin dismissed Biden’s
worries as unfounded, the specter of nuclear
Armageddon drove US anti-war activists to the
streets days before in a September Week of Action
organized by the Peace in Ukraine Coalition.
# ⚓ Common Dreams ☛ Near_Miss_at_Second_Ukraine_Plant
Intensifies_Fears_of_Nuclear_Disaster⠀⇛
“There is no other way to characterize this except
for nuclear terrorism.”
# ⚓ Counter Punch ☛ BMW’s_Nazi_Billions⠀⇛
Much of the Quandt’s wealth is linked to a cold
February morning in 1933 when about two dozen of
Nazi Germany’s wealthiest and most influential
businessmen gathered to meet super-Nazi Hermann
Göring. Among them was Günther Quandt, a textile
producer turned arms and battery tycoon and grand-
daddy of Susanne Klatten.
# ⚓ TruthOut ☛ Jan._6_Panel_Members_Propose_Reforms_to
Electoral_College_Certification_Process⠀⇛
# ⚓ Counter Punch ☛ Nukes_Are_Our_Corporate_Death_Wish…the_Sun
is_the_People’s_Cure⠀⇛
The eruptions already stretch from Kyshtym, Iron
Mike, Castle Bravo, Windscale, SL-1, Chalk River,
Santa Susanna, Fermi I, Perry, Davis-Besse, North
Anna, Tokaimura, Three Mile Island, Church Rock,
Surry, Chernobyl, Vandellòs, Sosnovy Bor, WIPP,
Fukushima, Fort Calhoun to South Texas and too many
more.
# ⚓ Counter Punch ☛ Back_Door_Proliferation⠀⇛
When the AUKUS announcement was made in September
last year, its significance shook security
establishments in the Indo-Pacific. It was also no
less remarkable, and troubling, for signalling the
transfer of otherwise rationed nuclear technology
to a third country. As was rightly observed at the
time by Ian Stewart, executive director of the
James Martin Center in Washington, such
“cooperation may be used by non-nuclear states as
more ammunition in support of a narrative that the
weapons states lack good faith in their commitments
to disarmament.”
# ⚓ Counter Punch ☛ ‘Leading_from_Behind’:_Is_Washington_at_War
with_Moscow?⠀⇛
Devex’s Funding Platform states that “a relatively
small percentage of that funding is humanitarian-
focused”. The same source also indicates that the
total amount of mostly military aid provided by the
West to Ukraine between February 24 and August 16
has topped the $100 billion mark.
# ⚓ USCERT ☛ Iranian_State_Actors_Conduct_Cyber_Operations
Against_the_Government_of_Albania⠀⇛
CISA and the Federal Bureau of Investigation (FBI)
have released a joint Cybersecurity Advisory (CSA),
Iranian State Actors Conduct Cyber Operations
Against the Government of Albania, detailing
malicious cyber operations that included ransomware
and disk wiper, rendering websites and services
unavailable. The advisory indicates Iranian state
cyber actors acquired initial access to the
victim’s network approximately 14 months before
launching the destructive cyber attack,
periodically accessing and exfiltrating email
content.
o § Environment⠀➾
# ⚓ Democracy Now ☛ Juan_González:_Hurricane_Fiona_Damage_Shows
Puerto_Rico_Still_Hampered_by_U.S._Colonial_Control⠀⇛
Democracy Now! co-host Juan González says people
are showing resilience in the face of Hurricane
Fiona in his native Puerto Rico, where the power
grid crashed across the entire island due to the
storm. Many who learned from 2017’s Hurricane Maria
are dipping into their personal water reserves and
using power generators, he says. “Puerto Rican
people … have actually been able to recognize the
fact that the government, when it comes to these
crises, is inept, and many people have been able to
develop their own ability to survive,” says
González.
# ⚓ TruthOut ☛ Hurricane_Fiona_Damage_Shows_Puerto_Rico_Still
Hampered_by_US_Colonial_Control⠀⇛
# § Energy⠀➾
# ⚓ DeSmog ☛ A_Global_Database_on_Fossil_Fuel_Projects
Goes_Live⠀⇛
The Global Registry of Fossil Fuels, launched
by Carbon Tracker and Global Energy Monitor,
is the first public and free-to-use database
of fossil fuel production, reserves, and
emissions. The registry contains more than
50,000 fields across 89 countries, and it
covers 75 percent of global production. The
database is not only a high-level look at
figures for a whole country, but it also
includes data that drills down to the
individual project level.
# ⚓ DeSmog ☛ How_Canada’s_Oil_Sands_‘Bankrolled_the
Assault_on_Truth’⠀⇛
But the oil that comes from them is
distinctive in several ways. Oil sands’
unique texture means it takes more money and
energy to refine than traditional crude. In
addition, its oil is some of the most carbon-
heavy in the world, with up to 20 percent
higher emissions, and that has drawn the
attention of climate advocates. Because of
these factors, as Geoff Dembicki explains in
his new book The Petroleum Papers: Inside the
Far-Right Conspiracy to Cover Up Climate
Change (Greystone Books, September 20), oil
sands producers and refiners, like Imperial
Oil or Koch Industries, are particularly
vulnerable to any efforts to mitigate climate
change that would increase the already higher
costs of extracting and refining bitumen.
# ⚓ DeSmog ☛ Exxon_Could_Have_Helped_Stop_Climate_Change
30_Years_Ago,_‘Proprietary’_Docs_Show⠀⇛
That’s according to a newly reviewed 1993
document labeled “proprietary” that was
written by the company’s Canadian subsidiary
Imperial Oil, one of the top producers in a
heavily polluting oil deposit known as the
Alberta tar sands.
# ⚓ Common Dreams ☛ Manchin_‘Getting_Desperate’_as
Opposition_to_Dirty_Permitting_Deal_Grows_Louder⠀⇛
“Manchin is getting desperate, it’s the only
reason he’d host a press conference like
this,” argued Jamie Henn, the director of
Fossil Free Media. “But the more he defends
his dirty deal, the clearer it is this is
just a grab bag of handouts to his fossil
fuel industry donors. Today’s performance
only strengthens our opposition.”
# ⚓ TruthOut ☛ AOC:_Fossil_Fuel_Reliance_Aided
“Tragically_Predictable”_Puerto_Rico_Blackout⠀⇛
# ⚓ Common Dreams ☛ UN_Chief_Blasts_PR_Industry_for
Spearheading_Big_Oil’s_Propaganda_Machine⠀⇛
“Fossil fuel interests need to spend less
time averting a PR disaster—and more time
averting a planetary one.”
# § Overpopulation⠀➾
# ⚓ Common Dreams ☛ Number_of_Ultrarich_Hits_All-Time
High_as_Someone_Dies_From_Hunger_Every_4_Seconds⠀⇛
“This is about the injustice of the whole of
humanity.”
o § Finance⠀➾
# ⚓ Telex (Hungary) ☛ Unemployment_in_Hungary_expected_to_rise
sharply_in_season_ahead⠀⇛
# ⚓ TruthOut ☛ GOP:_Student_Loan_Forgiveness_Hurts_Ability_to
Lure_Poor_People_Into_Military⠀⇛
# ⚓ TruthOut ☛ Stock_Ban_May_Not_Come_to_Vote_This_Month_as
Pelosi_Claimed,_Lawmakers_Say⠀⇛
# ⚓ Common Dreams ☛ World-Renowned_Economists_Call_for
‘Emergency’_Corporate_Profit_Taxes_to_Avert_Global
Recession⠀⇛
Published Tuesday, the report notes that “the
battle against the global pandemic has left many
governments vulnerable, saddling them with massive
debts they took on as tax revenues fell, health
needs soared, and as they strived to soften the
economic blow.” According to data from the
Institute of International Finance, 32 emerging-
market governments have a combined $83 billion in
U.S.-dollar debt due in 2023.
# ⚓ Counter Punch ☛ Do_Workers_Have_to_Take_It_on_the_Chin_to
Fight_Inflation?⠀⇛
It seems more than a bit absurd, that when we have
all these various public and private initiatives
that are supposed to improve the lot of
disadvantaged groups, we can have an arm of the
government, the Federal Reserve Board, just swamp
these efforts by creating a tidal wave of
unemployment. I don’t want to disparage well-
meaning efforts to help the disadvantaged, but they
can’t come to close to offsetting the impact of a
three or four percentage point rise in the
unemployment rate for Blacks or Hispanics. And, the
hit could be much larger.
# ⚓ Robert Reich ☛ The_Truth_Behind_“Self-Made”_Billionaires⠀⇛
# ⚓ Counter Punch ☛ Wall-to-Wall_Mourning_in_Food_Bank
Britain⠀⇛
+ Medals and gold braid, medals and gold braid,
medals and gold braid, galore!
o § AstroTurf/Lobbying/Politics⠀➾
# ⚓ Common Dreams ☛ Noting_High_Stakes_of_Midterms,_Jayapal
Says,_‘Trump_Is_a_Fascist._Period.’⠀⇛
“Donald Trump is a fascist. Period,” the Washington
Democrat tweeted just seven weeks before this
year’s midterm elections. “We have to reject this
dangerous movement across the country in
November—our democracy depends on it.”
# ⚓ The Nation ☛ The_New_King⠀⇛
As prince, King Charles tried not to act Like some
aloof high-muck-a-muck. He spoke his mind, like
common folk. So please feel free to call him Chuck.
# ⚓ The Nation ☛ “To_Hell_With_Kings!”_What_Happened_to
American_Skepticism_About_Monarchy?⠀⇛
In the fall of 1919, as Americans were struggling
with the bitter legacy of World War I, King Albert
of Belgium announced that he would tour American
cities. A.T. Van Scoy, the president of the
Milwaukee Association of Commerce, wrote a letter
urging Milwaukee Mayor Dan Hoan to issue a formal
invitation to the monarch.
# ⚓ The Nation ☛ Democracy’s_Fair-Weather_Friends_in_the
Mainstream_Media⠀⇛
Joe Biden will never be celebrated for Lincolnian
eloquence, but on occasion he can rise to the
gravitas, if not the lapidary grace, of the Great
Emancipator. The speech Biden delivered in
Philadelphia on the cusp of Labor Day earnestly and
soberly warned of the danger of a radicalized
faction, whom the president described as “MAGA
Republicans,” who reject the fundamental democratic
principle of acknowledging election results.
“Democracy cannot survive when one side believes
there are only two outcomes to an election: Either
they win or they were cheated,” he said.
# ⚓ The Nation ☛ Reining_In_the_War_Economy⠀⇛
America has a national security problem. But it
goes well beyond the challenges posed by Russia or
China. The biggest threat is right here at home:
the Pentagon’s stranglehold on our national budget,
alongside the woefully inadequate investments in
addressing urgent, nonmilitary problems like
climate change, pandemics, and racial and economic
injustice.
# ⚓ The Nation ☛ The_Antidemocratic_Theory_Endorsed_by_the
Supreme_Court’s_Conservatives⠀⇛
Supreme Court Justices Clarence Thomas, Samuel J.
Alito, Neil M. Gorsuch, and Brett M. Kavanaugh seem
bent on having the court adopt the “independent
state legislature” (ISL) theory. The doctrine would
give state legislatures complete and almost
unchallengeable control over the appointment of
presidential electors, under Article II clause 2 of
the Constitution, and over the election of US
Representatives and Senators, under Article I
section 4, “The Election Clause.” Governors would
lose their authority to veto proposed state laws
governing federal elections, and state supreme
courts would be unable to invalidate laws that
violate state law or Constitutions. As Justice
Gorsuch put it, “The Constitution provides that
state legislatures—not federal judges, not state
judges, not state governors, no other state
officials—bear primary responsibility for setting
election rules.”
# ⚓ The Nation ☛ It_Isn’t_Populist_to_Defund_Rural_Schools⠀⇛
Rural Americans have been voting Republican for
more than half a century. And while Democrats have
periodically attempted to convince rural voters
that their economic interests are ill-served by the
GOP’s agenda, they have mostly failed. That’s
because Republicans have used a kind of fake
populism—populism expressed chiefly through culture
war, rather than through policy—to maintain their
white, working-class base.
# ⚓ Common Dreams ☛ Launching_Criminal_Probe,_Texas_Sheriff
Says_Migrants_Were_‘Preyed_Upon’_With_DeSantis_Flights⠀⇛
“I believe there is some criminal activity involved
here,” Bexar County Sheriff Javier Salazar said
Monday at a press conference, though he did not
mention DeSantis, who is suspected of using the
false promise of refugee resettlement benefits to
beguile 48 Venezuelan asylum-seekers onto flights
from the San Antonio Migrant Resource Center to
Martha’s Vineyard in Massachusetts.
# ⚓ Common Dreams ☛ Migrants_Flown_to_Martha’s_Vineyard_Sue
DeSantis_Over_‘Fraudulent’_Scheme⠀⇛
“Defendants manipulated them, stripped them of
their dignity, deprived them of their liberty,
bodily autonomy, due process, and equal protection
under law.”
# ⚓ Common Dreams ☛ Lula_Up_16_Points_Over_Bolsonaro_as_Lead
Grows_Ahead_of_Brazilian_Election⠀⇛
Brazilian pollster IPEC’s latest survey shows da
Silva leading Bolsonaro 47% to 31% in the first-
round contest, which will take place on October 2.
That’s a one-point boost from the previous week’s
polling.
# ⚓ Common Dreams ☛ Opinion_|_Candidates_Who_Deny_Election
Results_Should_Be_Barred_From_Public_Office⠀⇛
One of the most horrific legacies of Trump is the
unwillingness of Republican candidates to commit to
being bound by election results.
# ⚓ Common Dreams ☛ Opinion_|_First_a_Billionaire._Now_a_King⠀⇛
By November 1948, the postwar “Baby Boom” in the
United States had been roaring along for nearly
three years. But America’s media spotlight didn’t
go whole-hog on babies until that November, the
month that saw the young Queen Elizabeth give birth
to her first, the British empire’s future king.
# ⚓ Counter Punch ☛ The_Future_of_Autocracy⠀⇛
An even tighter alliance between Moscow and
Pyongyang, now just one goose step from reality,
suggests the possibility of a future Eurasian Union
of autocracies, including China and several Central
Asian states. Just a few years ago, an anti-Western
alliance making up nearly 20% of the world’s
landmass and roughly the same percentage of its
population would have seemed unlikely indeed. For
all its autocratic tendencies, Russia was still
pretending to be a democracy then and, together
with China, maintaining reasonable economic
relations with the West. North Korea, on the other
hand, was an isolated outsider, suffering under a
hereditary dictatorship and tight sanctions that
restricted its access to the global economy.
# ⚓ Pro Publica ☛ Congresswoman_Calls_for_Examination_of
Military_Pretrial_Confinement⠀⇛
Rep. Veronica Escobar, a Democrat who represents El
Paso and sits on the House Armed Services
Committee, said this month that an August
investigation by ProPublica and The Texas Tribune
raises serious questions about the use of pretrial
confinement in the military. The news
organizations’ first-of-its-kind analysis of nearly
8,400 Army courts-martial cases over the past
decade revealed that soldiers accused of sexual
assault are less than half as likely to be placed
in pretrial confinement than those accused of
offenses like drug use and distribution, disobeying
an officer or burglary.
# ⚓ Common Dreams ☛ Opinion_|_Donald_Trump_and_the_Presidential
Privatization_of_Secrecy⠀⇛
Thanks to Donald Trump, secrecy is big news these
days. However, as political pundits and legal
experts race to expose the layers of document-
related misdeeds previously buried at his Mar-a-
Lago estate, one overlooked reality looms large:
despite all the coverage of the thousands of
documents Trump took with him when he left the
White House, there’s been next to no acknowledgment
that such a refusal to share information has been
part and parcel of the Washington scene for far
longer than the current moment.
# ⚓ TruthOut ☛ Trump’s_Hiding_of_Information_Isn’t
“Unprecedented.”_It’s_a_Horrifying_Norm.⠀⇛
# ⚓ TruthOut ☛ Democrats’_Failure_to_Embrace_the_Progressive
Grassroots_Could_Spell_Their_Doom⠀⇛
# ⚓ TruthOut ☛ Trump’s_Lawyers_Are_Already_Bickering_With_the
Special_Master,_Whom_They_Picked⠀⇛
# ⚓ Common Dreams ☛ ‘You_Can’t_Have_Your_Cake_and_Eat_It,’
Special_Master_Tells_Trump_Lawyer_Stalling_on
Declassification_Claims⠀⇛
The exchange came during Judge Raymond Dearie’s
first meeting with Trump’s lawyers and U.S.
Department of Justice (DOJ) prosecutors at a
federal courthouse in Brooklyn.
o § Censorship/Free Speech⠀➾
# ⚓ Project Censored ☛ The_Past_and_Present_of_Mining_–_The
Project_Censored_Show⠀⇛
# ⚓ TruthOut ☛ Texas_Banned_More_Books_Than_Any_Other_State
Last_Year,_Analysis_Finds⠀⇛
# ⚓ AccessNow ☛ Tunisia:_President_must_scrap_decree-law
undermining_free_expression_and_the_press_–_Access_Now⠀⇛
Human rights organisations have condemned a new
communications and information law in Tunisia, and
urge the President of the Republic to withdraw it
with immediate effect in order to uphold freedom of
expression and press freedom in the country.
The undersigned human rights associations and
organisations express their deep alarm regarding
Decree-law No. 54 of 2022 issued on 13 September
2022, which seeks to combat crimes related to
information and communication systems. The
provisions of the law are in flagrant contravention
of articles 37, 38 and 55 of the Tunisian
Constitution and article 19 of the International
Covenant on Civil and Political Rights, which
Tunisia has ratified.
# ⚓ AccessNow ☛ Courts_must_#KeepItOn_to_protect_the_right_to
education_–_Access_Now⠀⇛
Civil society is making strides in the battle to
end internet shutdowns during exams, which
negatively impact the lives and rights of millions.
Last week, the Indian Supreme Court responded to
the Software Freedom Law Centre’s petition
challenging the use of internet shutdowns to
prevent exam cheating, issuing notice to the Union
government to explain the protocol for these
disruptions. As it stands, state governments in
India often cite the administration of education as
a rationale for exam shutdowns, as do authorities
across the MENA region. Courts must scrutinize and
reject these justifications. As we explain below,
regardless of the reasoning, shutdowns are not
compatible with the right to education.
o § Freedom of Information / Freedom of the Press⠀➾
# ⚓ Meduza ☛ Done_but_not_over:_Journalist_Peter_Leonard_says
long-term_demographics_and_economics_favor_Tajikistan_in_the
border_conflict_with_Kyrgyzstan_—_Meduza⠀⇛
o § Civil Rights/Policing⠀➾
# ⚓ Common Dreams ☛ Opinion_|_Nobody_Should_Be_Shocked_by_GOP
Cruelty—It’s_Their_Whole_Brand⠀⇛
Editorials in America’s major newspapers are
shocked—shocked, I tell you!—that DeSantis and
Abbott would exploit asylum-seekers to rack up
votes from their racist base.
# ⚓ Democracy Now ☛ Reverse_Freedom_Rides:_Flying_Migrants
North,_Florida_Gov._Steals_Page_from_Segregationists_60_Years
Ago⠀⇛
As human rights advocates denounce efforts by
Republicans to send dozens of buses full of asylum
seekers to sanctuary cities across the United
States, we look at the related history of the
Reverse Freedom Rides of 1962, when Southern
segregationists bused Black families to the North
to antagonize Northern liberals and civil rights
activists. Mwalim Peters, English and Black studies
professor at the University of Massachusetts
Dartmouth, recounts the little-known story of the
Reverse Freedom Rides and says the strategy to
humiliate liberals is “basically identical to
what’s happening now in Martha’s Vineyard” and
other sanctuary cities, where Florida Governor Ron
DeSantis and Texas Governor Greg Abbott are sending
asylum seekers under false pretenses of free
housing and jobs. Instead, they find themselves
being used as a media stunt and stranded. “We’re
looking at any number of, basically, potentially
criminal infractions, let alone just moral and
ethical,” he adds.
# ⚓ TruthOut ☛ Medication_Abortion_Is_Not_Enough_to_Solve_the
Abortion_Access_Crisis⠀⇛
# ⚓ Techdirt ☛ LA_County_Sheriff_Still_Targeting_Critics,
Searches_Home_Of_Civilian_Oversight_Board⠀⇛
Current Los Angeles County sheriff Alex Villanueva
campaigned with the promise he would clean up the
literally gang-infested Los Angeles Sheriff’s
Department (LASD). Once he took office, however, he
just became part of the problem. Rogue units of
deputies continued to freely operate, resulting in
federal lawsuits, a bunch of whistleblowing, and
[re-reads report] the attempted removal of an LASD
gang tattoo with a [re-re-reads report] handgun.
# ⚓ Techdirt ☛ Saudi_Prosecutors_Are_Targeting_A_US_Citizen_For
Tweets_Criticizing_The_Government⠀⇛
The Saudi government is decidedly unconcerned that
other nations may have concerns about its
censorship efforts. I mean, if need be, it will
murder and dismember critics who prove unwilling to
be silenced by less drastic efforts.
# ⚓ Common Dreams ☛ Opinion_|_Decolonizing_the_Mind:_A
Narrative_Spun_24_Hours_a_Day⠀⇛
It is vital to free ourselves from belief in the
systems of white supremacy and imperialism that are
inculcated in the educational system and are
affirmed and amplified by the media and
establishment opinion. The recent death of Queen
Elizabeth II puts the need for political and
psychological liberation in high relief. We are
encouraged to admire an anachronistic monarchy, and
are exhorted to join in mourning an individual and
a system that have caused great harm to Black and
other oppressed people around the world.
o § Internet Policy/Net Neutrality⠀➾
# ⚓ Techdirt ☛ Big_Telecom_Drops_Its_Legal_Assault_On_Maine
Over_Broadband_Privacy_Rules⠀⇛
When it comes to manhandling US regulators and
gutting telecom industry oversight, the nation’s
biggest telecom monopolies have had an impressive
five year run.
# ⚓ Techdirt ☛ The_Internet_Is_Not_Disneyland;_People_Should
Stop_Demanding_It_Become_Disneyland⠀⇛
Disneyland can be a fun experience for kids (and
potentially a frustrating one for parents), but
it’s a very controlled environment in which
everything is set up to bend over backwards to be
welcoming to children. And that’s great for what it
is, but the world would kinda suck if everything
was Disneyland. I mean, some countries have tried
that, and it’s… not great, especially if you
believe in basic freedoms.
o § Monopolies⠀➾
# ⚓ Common Dreams ☛ ‘We_Are_Coming_for_You!’:_Teamsters_Union
Rallies_Outside_Amazon_Headquarters⠀⇛
“Amazon will not bust unions and get away with it.
Amazon will not churn and burn American workers and
get away with it.”
# § Copyrights⠀➾
# ⚓ Torrent Freak ☛ New_Piracy_Lawsuit_Paves_the_Way_for
a_FIFA_World_Cup_Site_Blocking_Order⠀⇛
Bell Media and several other companies have
sued two “John Doe” operators of streaming
servers at Canada’s Federal Court. The
rightsholders want to take action to reduce
the availability of pirated sports streams
during the upcoming FIFA World Cup. The
targeted services were allegedly indexed by
popular streaming aggregators such as
soccerstreamlinks.com and Bingsport.
# ⚓ Torrent Freak ☛ French_Publishers_Win_Z-Library
Piracy_Blocking_Order⠀⇛
The National Publishing Union, an industry
group representing more than 700 members in
the publishing sector, says that legal action
launched in the summer to prevent piracy has
been successful. The expedited process at a
Paris court targeted more than 200 domains
related to Z-Library, all of which must now
be blocked by French ISPs.
# ⚓ Techdirt ☛ Study_Shows_That_Copyright_Filters_Harm
Creators_Rather_Than_Help_Them⠀⇛
The EU Copyright Directive contains one of
the worst ideas in modern copyright: what
amounts to a requirement to filter uploads on
major sites. Despite repeated explanations
of why this would cause huge harm to both
creators and members of the public, EU
politicians were taken in by the soothing
words of the legislation’s proponents, who
even went so far as to deny that upload
filters would be required at all.
# ⚓ Techdirt ☛ Rockstar_Tries_To_Bury_‘GTA6’_Leak_With
DMCAs,_Streisands_Them_Instead⠀⇛
At this point, we probably have enough
stories about companies trying to bury leaked
information or content that hasn’t been
publicly released via DMCA takedowns that it
warrants its own metatag. It’s both amazing
and frustrating that this is still a tactic
companies, particularly tech companies, think
somehow works. It doesn’t. Once a leak is out
on the internet, the game is already over.
That footage is out there, and trying to do
battle with internet to disappear it just
isn’t going to work.
* § Gemini* and Gopher⠀➾
o § Personal⠀➾
# ⚓ Fed_Up⠀⇛
I’m just so tired at the moment. Work is wearing me
down, I’m in pain all of the time, I’m so
desperately lonely, and there’s absolutely nothing
I can do about any of it. I’m trying to be positive
but it’s hard. There’s so many things that I
imagined I’d be doing at this point in my life. I
know that it’s not a race and that there are
genuine reasons for why I’m still living out of my
childhood bedroom. It doesn’t stop me feeling that
I’ve failed in some way.
# ⚓ introversion⠀⇛
It was a long day, you want to be alone for a
while, because the world just makes you tired, and
you need some rest and time by yourself.
Then right when you’re back home, the first thing
you heard are people caring about you, which sounds
good, but you were just too outwardly focused that
you desperately need some inward time of yours.
So you chose not to response, simply because it
would be way too tiring to bother in a place of
relaxation, and that you don’t really want to risk
any “bad answers”, because you’re that type of a
person to answer with cold answers without meaning
it.
# ⚓ Stream⠀⇛
Beat Roxanne with 0 losses, despite kayla wrongly
declaring a poll otherwise (because I lost a
pokemon before roxanne). To make things more
interesting and less grind-y, I’m allowed to use
rare candies to get my pokemon up to the right
level before each gym.
# ⚓ SpellBinding:_ACEOKLG_Wordo:_LOCKS⠀⇛
o § Politics⠀➾
# ⚓ Putin_vs_Progessives⠀⇛
Oh boy … deep breath … here goes …
I am fascinated by the idea of a live debate
between Putin and Feminists. Putin is called the
strongman. I have seen quite a few videos of Putin
and I can definitely say that he exudes a strong
masculine energy. Detractors may say that his
machismo is a product of deeper-seated
insecurities, but I would reject that claim. He
projects a lot of power that seems to be part of
his make-up.
His skill as a communicator is off the charts.
Whilst Trump has that arrogant air about him, Putin
always seems calm and analytical. Part of it may be
that Trump is an extrovert, whilst Putin is an
introvert. Trump is ESFP. Putin is an INTJ. Polar
opposites in terns of personality. Putin’s ability
to get to the heart of the matter is unparalleled.
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World Wide Web but a lot lighter.
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