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
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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

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

(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
#linux and #libera) which have asshole moderators in them.


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

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

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

                    ䷩ 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:


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


                                         #techrights_log_as_HTML5                                                                                  #boycottnovell_log_as_HTML5


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


                                    #boycottnovell-social_log_as_HTML5                                                                               #techbytes_log_as_HTML5


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


                                          #techrights_log_as_text                                                                                   #boycottnovell_log_as_text


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


                                     #boycottnovell-social_log_as_text                                                                                #techbytes_log_as_text


                          Enter_the_IRC_channels_now


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


CID                                              Description     Object type


                                                 IRC log for
 QmdL3o3joKbABMPixejdyJsh9qRfNHKxiEqoBvkadczGhT #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
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§ Bulletin for Yesterday⠀➾


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                    ䷩ 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)


⣿⣻⣿⣿⣿⡟⡿⠿⢿⢿⢿⡿⢿⢻⣿⠿⢻⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⡿⠿⠛⣿⡿⡿⢿⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⣟⢻⣿⣿⣿⣿⡾⢿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢿⡿⡿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⡿⡿⢿⢿⣿⣿⢿⣿⣿⡿⠿⠿⣿⣿⡿⣿⢿⣿⣿⣿
⣿⣿⣿⣿⡘⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡈⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣾⣷⣯⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣷⣷⣾⣾⣿⣿⣾⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣇⢸⣿⣿⣧⣾⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⣼⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣤⣦⣿⣿⣿⣿⣿⣿⣷⣷⣧⣼⣾⣽⣿⣾⣿⣿⣷⣦⣤⣿⣿⣶⣿⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣿⣿⣿⣿⣄⢹⣽⣭⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣻⣿⣿⣽⣛⢿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⣿⡿⠿⢿⣿⢿⣿⣧⠹⢻⢿⢿⢿⣿⣿⣿⣿⣿⡿⡟⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⢿⢿⣿⠿⠿⠿⣿⣿⠟⡿⢿⡿⠿⡿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡷⣾⣶⣾⣿⡿⡿⠄⣶⡶⣾⣿⢿⠿⠿⣿⣿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣶⣶⣿⣿⣶⣷⣾⣷⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⡦⠹⢷⣿⣷⣶⣶⣶⣾⣿⣷⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⣿⣽⣯⣧⣴⣤⣮⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣭⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣠⣾⣿⣿⣷⣍⠙⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠉⠈⠁⠘⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⢻⠿⠿⠿⣿⠿⠿⠿⣿⣿⡿⠟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣕⠀⢀⡀⠹⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠈⠉⠘⠁⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⣿⣿⣿⣿⣿⡻⣩⠛⠓⠄⣐⠀⠀⠀⠀⣀⣠⡄⠄⡠⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡯⠙⡽⢛⣯⣭⣦⠀
⠟⠻⠟⠿⡟⣧⡁⠀⠁⠀⠀⠁⠀⠀⠀⣉⠉⠿⠘⢇⠐⠖⠀⠁⠙⠁⠁⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣭⣦⣿⣮⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠔⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢨⡄⠀⠀⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣶⣿⣿⣿⣿⣿⣿⣿⠷
⢰⣄⣰⣷⣀⡀⢰⣧⣤⠶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⢀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⡉⢉⣽⣿⣿⣿⠋⠀
⣿⣷⣿⣿⣿⣿⣿⠙⠳⣮⠙⡨⢗⣀⢀⡠⠀⠰⣒⠤⠄⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠸⣷⡀⣼⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣾⣿⣿⠿⠃⠀⠀
⢈⣹⣿⣿⣿⣿⣿⣶⣤⣴⢀⠙⠾⠟⢻⣄⣀⡈⠉⢩⣉⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣦⣹⣷⣿⣿⣿⣿⣿⣿⣿⣋⣩⠅⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀
⠎⠛⣿⣿⣿⣿⣿⣿⠿⠛⡍⢙⠁⡀⠀⢭⢎⡁⠀⢀⡀⠀⠀⠀⠀⢸⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⣩⣿⠿⢶⠖⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢢⣾⣿⣿⣿⣿⣿⡿⠾⠀⣵⣅⡊⠄⣀⢺⣿⣿⣿⣿⣯⠀⠀⠀⠒⢴⣭⣧⡜⠛⠿⠿⠿⠿⠿⠿⠾⠟⠋⡙⢁⣀⣤⣿⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢯⣴⣿⣿⣿⣿⣿⣽⣾⣾⣿⣿⣷⣷⣯⣿⣿⣿⣿⣿⣿⣠⣲⣶⣌⣩⣽⣥⣿⣆⣀⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣼⣿⣿⡏⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣤⣷⣿⣿⣗⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢻⠀⣸⣿⣿⣧⡘⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⠗⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠉⠋⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀
⠀⣾⣾⣿⣿⣿⣿⣿⡦⠀⠀⠜⠻⣿⠿⠛⠉⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠘⠟⠐⠆⠀⠀⠈⠉⠙⠛⠋⠉⠉⠀⠂⠀⠀⠀⠙⠁⢀⡀⠉⠉⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⢰⣿⣿⣿⣿⣿⠹⢛⡁⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠚⠀⠀⠀⠀⠀⡉⢻⣿⣿⣿⣿⣿⠯⠙⡽⢛⣯⣭⣦⠀
⠈⣿⠃⠘⢿⣿⣧⠛⠈⠀⠀⠀⠀⠀⠀⠀⠺⠽⢣⠀⡬⠁⣤⡤⠂⠚⠁⠀⠀⠀⠀⠀⣠⡀⠀⠀⠐⠶⡯⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣯⣭⣦⣿⣤⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠈⠟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣄⡀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣀⣨⣻⣀⣀⢈⣷⣀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⢀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⡉⢉⣽⣿⣿⣿⠛⠀
⣸⣦⣿⣿⣿⣿⣿⠠⠻⢭⣄⠺⢑⣦⠀⠠⠠⠀⢠⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠘⣷⡄⣤⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣾⣿⣿⠟⠁⠀⠀
⣟⠋⣿⣿⣿⣿⣿⣄⣄⣀⣉⠀⠲⣼⡿⠶⠋⠀⠀⠓⠒⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣷⣿⣿⣖⣦⠆⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀
⠻⡖⣿⣿⣿⣿⣿⣜⣿⣿⠿⡒⠀⠀⠀⢈⡛⡝⠃⠀⠈⠀⠀⠀⠀⠰⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⣹⣿⠿⠶⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⢄⣿⣿⣿⣿⣿⡯⣿⣴⠀⣃⡀⢄⣁⢸⣿⣾⣶⣶⣾⠀⠀⠀⠀⣤⣿⡓⣌⠛⠿⠿⠿⠿⠿⠿⠶⠟⠋⠉⠁⠀⢀⣵⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣞⣿⣿⣿⣿⣿⣤⣶⣴⣴⣿⣿⣿⣯⣿⣿⣿⣿⢿⣻⠠⠀⢤⣤⠚⣟⣟⣹⣧⣀⣀⣠⣤⣤⣴⣶⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⣰⣿⣿⡏⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣀⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣠⣦⣿⣿⡇⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⡇⠀⣿⣿⣿⡆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⠆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠳⠀⠀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀
⠀⢰⣷⣾⣿⣿⣿⣿⣷⡌⠁⠈⠹⣿⣿⠿⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⢤⠀⠀⠀⠛⠛⠟⠟⠛⠛⠉⢡⠏⠉⠉⠙⠛⠉⡉⠉⠛⠋⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⡀⢸⡟⣿⣿⣿⡿⠿⢯⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⢸⠋⠁⡀⠀⠀⠉⢻⣿⣿⣿⣿⣿⡯⠙⡽⢛⣯⣭⣦⠀
⠁⠻⠀⠉⠿⣿⣿⡖⠋⠑⠌⠀⠠⠀⣀⠀⠠⣶⡶⡄⢠⡛⢀⣀⡠⠴⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢴⣼⣻⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣭⣦⣿⣬⡿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⠹⠿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠠⢦⢬⠥⠈⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⣀⠀⠩⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣀⣹⣏⣀⠀⣲⡆⢀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⢀⠀⠀⢰⣤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⣉⢩⣽⣿⣿⣿⠟⠁
⣀⢶⣿⣿⣿⣿⣿⠀⡺⢿⣍⠡⡅⢦⡄⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠘⣷⡄⣤⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣾⣿⣿⠟⠁⠀⠀
⣿⡿⣿⣿⣿⣿⣿⢄⣀⣀⣉⡓⠠⣤⣶⣦⠖⠃⠀⠱⠾⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⠄⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀
⠻⢷⣿⣿⣿⣿⣿⣐⢫⣿⣿⠇⠀⠀⠀⠀⠛⢂⠶⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⢉⣹⣿⠿⠷⣞⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠉⣿⣿⣿⣿⣿⣿⣿⣏⡄⠀⡀⠀⣀⢺⣿⣿⣶⣤⣶⠀⠄⠀⠀⢠⣾⡷⣬⠻⠿⠿⠿⠿⠿⠿⠷⠾⠋⠋⠁⠀⠀⣑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣈⣷⣿⣿⣿⣿⣿⣭⣴⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⢠⠀⢀⣀⣨⠿⢿⣿⣧⣀⣀⣀⣤⣤⣴⣶⣦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣍⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠁⠀⢰⣿⣿⡏⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣦⣿⣿⡇⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⢻⣿⠃⢹⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⡃⠀⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⠀⠄⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠀
⣇⠀⠀⣹⣠⣾⣿⣿⣿⣾⡿⠿⠛⢿⣿⣿⣿⣿⠿⣿⣿⣿⠿⠿⠋⠉⠉⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠿⠿⠟⡛⠛⠛⠛⠿⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⡿⠀⠀⠩⣿⣿⣿⣿⣿⣍⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡶⠆⠀⠀⠉⢻⣿⣿⣿⣿⣿⡯⠙⣽⢛⣯⣭⣦⠀
⠿⠷⠀⠀⠟⣿⣿⣿⡥⡼⠦⡛⠂⣀⠀⠀⠀⠀⣀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⣾⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⠀⠀⠂⠀⠂⠀⠀⣼⣿⣭⣧⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷
⢼⡃⠀⠀⠀⠀⢹⣿⣿⣤⣄⠀⠀⠨⠁⠡⠄⠀⣽⣯⣽⠙⢣⠐⠿⠋⠀⠀⠀⠀⠀⠀⠈⠍⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⢰⣅⡿⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢀⣀⣀⣸⣷⠂⠀⢭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⣉⢉⣽⣿⣿⣿⡟⠁
⠀⠀⣿⣿⣿⣿⣿⣄⠀⢸⣷⡶⢛⡫⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠀⢿⣆⢠⣽⣷⣄⠀⠀⠀⠁⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣤⣾⣿⣿⠟⠋⠀⠀
⠀⢰⣿⣿⣿⣿⣿⣉⡀⠐⠉⠻⠧⠹⡐⣿⣆⡦⠄⠀⢨⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣙⣿⣾⣿⣿⣿⣶⣤⣤⣤⣤⡄⠀⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀
⠐⢶⣿⣿⣿⣿⣿⡄⠉⢿⣷⣶⠀⠀⠈⠛⠋⢥⡤⣤⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⠿⠷⣟⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣿⣿⣿⣿⣿⣖⣾⢺⡟⡃⠀⠀⣀⢠⣶⣶⣜⣧⣀⠀⠀⡀⠀⢀⣠⣻⣌⠿⠿⠿⠿⣿⣿⣿⡿⡶⠛⠛⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⣴⣾⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⢠⣿⣿⣧⣅⣀⣀⣀⣀⣠⣤⣶⡆⠀⣄⣀⣀⣀⣠⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣟⣿⣦⣶⣮⣥⣬⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡟⠉⠉⢩⣿⣿⣿⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣴⣿⣿⣇⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠙⣿⡿⠁⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣼⣿⠃⠀⠀⠐⠖⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⢀⡀⠈⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀
⣿⡗⠀⠈⣧⣠⣿⣿⣿⣦⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠻⠃⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⢰⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⠿⡿⠀⠀⢉⣿⣿⣿⣿⣙⠏⠀⠀⠀⠈⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠋⠀⠠⠀⠠⠈⠈⠉⠉⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡤⠀⠀⠉⢻⣿⣿⣿⣿⣿⡯⠙⡽⢛⣯⣭⣦⠀
⠀⣷⠄⠀⠠⠿⣿⣿⣟⢋⣵⣄⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣦⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠈⠁⠠⠀⠀⣴⣿⣭⣦⣿⣮⣿⣿⣿⣿⣿⣿⣿⣷
⢧⣴⠀⠀⠀⠈⠙⣿⣿⣯⣥⡤⠁⠀⠽⡦⣤⡄⢸⣿⣷⡖⠰⠎⠰⡶⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠺⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠀⠀⠀⠀⣴⣿⡿⢿⡏⠈⠀⠀⠀⠀⠀⠁⠈⢻⠫⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠆⠀⢀⣀⣀⣀⣿⡧⠀⢘⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣍⣩⢉⣽⣿⣿⣿⡟⠃
⠁⠀⣿⣿⣿⣿⣿⣧⡐⢀⣿⣥⠾⠿⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣄⠀⢿⣦⢀⣼⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣾⣿⣿⠟⠁⠁⠀
⠀⠀⣿⣿⣿⣿⣿⠛⠃⠐⠊⠹⢶⠝⠢⠷⣆⠐⣀⠀⠠⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣘⣿⣿⣿⣿⣿⣧⣄⣠⣄⣠⡄⢀⣠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠠⣿⣿⣿⣿⣿⢁⠉⢲⢶⣦⢀⠀⠈⠿⠟⢛⣀⣀⡀⠀⠀⠀⠀⠀⢯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠷⣟⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣯⠵⣦⣿⠟⠃⠀⢀⢠⣠⣤⣭⢾⡉⠀⠀⠀⠀⠀⢀⣱⣌⠿⣿⣿⣿⣿⣿⣿⣿⡶⠚⠛⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣤⣴⣯⣿⣿⣿⣿⡿⠟⠀⠀⠈⠁⢰⣿⣿⣿⣅⠀⠀⠀⣀⣀⣤⣶⣄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢻⣿⣤⣤⣓⣄⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣟⠛⠙⢉⣽⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣠⣼⣿⣟⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠀⠈⠹⣿⣿⡇⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠂⣽⣿⠁⠀⠀⣀⡀⠀⠀⠀⠷⠀⠀⠀⠈⠹⠀⠙⠿⠇⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠐
⣿⣷⣦⡄⠘⢿⠁⣸⣿⣿⣇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣇⡀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠦⠒⠀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⠙⣿⣷⠀⠀⠀⢰⣿⣿⣿⡿⣖⠍⠉⠉⠉⠉⠉⠙⠋⠛⠋⠉⠉⠉⠉⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢶⠤⠀⠀⠀⠀⠛⢻⠿⠿⠛⠛⠉⢡⡏⠉⠉⠙⠛⠉⣩⣉⣹⢿⣿⣿⣿⣿⣿⡯⠟⣽⢛⣯⣭⣦⠀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⢿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠴⡩⠁⢀⡀⡀⠀⢹⡿⣿⣿⣾⣿⣭⣦⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷
⠠⠤⠀⠁⠀⠀⠉⣿⣿⣿⣷⣿⣿⣯⡥⣦⣬⣄⡀⢠⣦⣤⣀⣀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠘⡛⠀⠀⠀⠀⠀⣠⣼⣿⣿⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠘⠁⠁⠀⠀⠀⠉⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢦⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠛⠄⠀⠈⠙⠙⠻⠀⣿⠍⠘⠁⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣶⣿⣿⣿⣿⣿⣿⣿⡿
⢺⣧⣀⣀⣀⣀⣀⢸⣿⡛⠩⣿⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⣩⣭⣿⣿⣿⣿⡿⢁
⣮⠧⣿⣿⣿⣿⣿⢈⣿⢩⡀⢺⣖⣠⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣄⠀⢸⣷⡀⣈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣭⣿⣿⣿⠿⠛⠀⠀
⡀⠀⣿⣿⣿⣿⣿⣴⣿⡷⠀⡾⠿⣿⡰⠇⢦⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡤⢿⣿⣿⣿⣿⣷⣆⠀⠀⣀⣄⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀
⠁⠀⣿⣿⣿⣿⣿⣷⠖⠐⢄⣠⠀⠀⠀⠰⣤⣷⡦⠖⠀⠀⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡷⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⢄⣴⣂⣐⣗⡪⠄⠁⢠⠮⠀⠐⠛⣹⠂⠀⠀⠀⢠⡀⠓⢫⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⠛⠋⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣴⣦⣾⣴⣾⣿⣿⣿⣿⠤⠀⠄⠀⠤⣷⣶⣶⡆⠀⠁⠉⠉⠉⣉⣵⣅⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣤⣀⢀⣤⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣂⣦⣤⣤⣤⣶⣾⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⣻⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣠⣿⣿⢻⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⡇⠀⠹⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣩⣽⣿⠉⣙⣃⠀⠀⠀⠀⠀⠀⢻⡀⢨⠀⠀⠀⢽⢿⢿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣤⣄⠀⠉⢿⣿⠇⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣼⡟⠀⠀⠠⢤⠀⠀⠀⠙⠛⠀⠀⠀⠀⠘⠂⠙⠛⠃⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⢻⡜⢿⣿⡇⠀⠈⠁⢀⣽⣿⣿⣅⠀⢩⣽⠿⢿⣿⣛⣿⣿⣿⡿⠿⣹⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠉⠙⠛⠁⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠟⣿⢛⣯⣽⣶⡀
⠀⠁⠀⠛⠻⠀⠀⣴⣿⣿⣿⣿⣿⣿⠢⠀⠀⠀⠸⠋⠉⠉⠉⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠀⠈⡿⠖⠀⠀⠀⢨⢙⣿⡿⠿⠭⣃⣠⣿⠄⣂⣈⡌⢕⣴⣾⣿⣿⣭⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢀⡈⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣄⣠⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⡆⠀⠀⠀⠨⣶⡇⠘⠛⠿⣿⠉⣷⢾⡗⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⢲⡀⠀⣀⣠⡀⠟⢿⣿⣿⣿⣿⣿⣿⠿⠟⣿⣿⣯⡄⠀⣿⣶⣶⢶⠇⠀⠀⠀⠀⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⡿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠉⣻⣆⣈⣛⣂⠀⠀⣿⣿⣿⣿⣟⠉⠀⠀⠈⠙⠈⠁⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣍⣩⣭⣿⣿⣿⣿⡿⠣
⠁⣀⣿⣿⣿⣿⣿⠀⠀⢻⣯⢷⢝⣿⠠⠤⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⣄⠀⠠⣶⡄⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣭⣿⣿⣿⡿⠛⠁⠀
⣴⣟⣿⣿⣿⣿⣿⢸⣄⣼⣿⡐⠢⣿⣥⠶⠿⢶⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠋⠉⠀⠀⠀⠀
⣿⣷⣿⣿⣿⣿⣿⢿⣿⣞⡛⠃⠀⠀⠀⢶⠙⡈⢵⣂⢀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⣶⣷⣶⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣭⣀⣿⣿⣿⣿⣿⣉⡿⠟⢉⠁⠂⢀⣀⢰⢀⠙⡾⠟⢛⠀⠀⠀⠈⠐⣒⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⢙⡛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡟⠉⣿⣿⣿⣿⣿⣭⣽⣾⣯⣶⣾⣿⣿⣭⡎⣟⣕⡠⠀⡀⠌⠀⠀⢀⠹⢶⠎⠟⠛⠛⠛⠛⠛⠛⣉⣅⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠻⢽⣸⣿⣿⣿⣷⣤⣤⣴⣶⣶⣿⣿⣛⡂⢀⣀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠃⣢⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⣀
⣿⣿⣿⠟⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣇⣿⣿⣿⡥⣧⣿⣿⣿⣇⠀⠄⠀⠀⠀⠘⣿⠄⢰⠆⠀⠀⣿⣿⣿⣄⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⠀⠉⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⠁⢼⣶⠂⠀⠀⠀⠀⠀⠘⣷⡼⠀⠀⠀⣟⣸⡌⢿⣿⡇⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⣿⣧⣤⠀⠈⠚⠁⣹⣿⣍⡀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡸⠟⠋⠀⠀⠀⠛⠂⠀⡀⠀⠀⠈⠉⡁⠀⠒⠲⡦⠖⢠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢛⣯⣿⣶⡁
⠉⠉⠃⠘⣿⣷⠀⠀⣠⣾⣿⣿⣿⣷⣶⣞⠛⠋⠛⢛⣿⠿⠿⠿⠿⣻⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠡⣾⣤⠤⠀⠀⠘⢿⣿⣿⣿⣿⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⡀⣠⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⠀⠈⠍⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⢀⡀⠀⠉⠽⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣀⣀⣀⡀⣘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⠀⢀⣼⣏⣀⡀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⠇⠀⠀⠀⠸⠿⠿⠛⠉⠋⠟⠃⠟⠉⠉⠘⠻⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠄⣿⣿⣌⣻⣿⡃⠁⠙⣿⣿⣿⣿⣿⠻⠉⠁⠛⣿⡻⠂⠈⣿⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣭⣭⣭⣿⣿⣿⣿⡿⠛
⣿⡆⣿⣿⣿⣿⣿⠀⠀⠠⣿⣿⣟⣿⣿⣦⢠⣤⠁⠀⠁⠀⠀⠈⠁⠀⣠⣶⣶⣦⡀⠀⢠⣶⡀⠀⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⣿⣿⣿⠟⠁⠤
⡍⣀⣿⣿⣿⣿⣿⠀⢠⣶⣸⣿⢃⡱⣾⣟⣧⣶⡄⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣦⢀⣿⣿⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣼⣿⠀⠀⠈⢿⣉⢭⠰⣤⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣴⣤⣤⣤⣤⡽⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⠻⣿⣷⡆⠀⠀⣀⢈⣛⠀⢮⣽⣶⡔⠀⠀⠀⠤⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠽⡛⠛⠿⠝⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣤⣾⣿⣿⡿⡶⡶⠍⠀⠐⢂⠶⠀⠀⠓⢳⣆⡿⠿⠿⠿⠿⠿⠟⢫⡁⠀⠀⠀⠀⠀⠙⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⣮⣥⣴⣤⣤⣷⣮⣿⣤⣀⣠⣤⣤⣴⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⢿⣿⣯⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣦⣤⣴⣶⣶⣿⣿⣶⣶⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣾⣿⣴⣾⣷⣶⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣽⣯⣿⣿⣸⣿⣷⣏⣹⣠⣿⣿⣷⠀⣀⠀⠀⠀⠀⣿⡏⠁⡇⠀⠀⢸⣿⣿⣇⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣴⣿⡏⢉⣯⡥⠀⠀⠀⠀⠀⠈⣧⣄⡇⠀⠀⢸⠯⣏⢿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⣧⣄⡀⠈⠻⠋⠈⣿⣿⡋⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡇⠾⠛⠀⠀⠀⠰⠦⠀⠀⠘⠉⠀⠒⠂⠘⠩⠭⣤⡭⠭⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣿⣿⣷⡟
⠛⠛⠙⠈⢻⣿⣏⠀⠀⣠⣾⣿⣿⣿⣦⣤⠶⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⡄⠘⣤⣖⣤⡈⠀⠀⢿⣿⣿⣿⣿⣿⠟⢿⣿⣟⣿⣻⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠈⠋⠛⣀⣼⣿⣿⣿⣿⣿⣿⣿⡣⠀⠀⠀⢿⠃⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠆⠀⠀⠁⡄⠈⠉⠉⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⢀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣶⣦⣤⠀⠀⢠⣶⡐⠋⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⠀⠀⠀⠸⢿⣿⡿⠿⠟⢻⡿⢸⡿⠿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣈⣿⣯⣛⣦⡷⠚⠉⢻⣿⣿⣿⣿⡿⡟⠋⠹⢿⡿⠶⠀⢺⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⡿⠿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣭⣭⣭⣿⣿⣿⣿⡿⠓
⣿⣷⣿⣿⣿⣿⣿⠉⠁⢠⢸⣿⣿⣿⣿⡧⠠⢠⠀⠈⠑⠀⠀⠈⠻⠀⣠⣶⣶⣤⡀⠀⢠⣤⡀⠀⢺⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⣿⣿⡿⠟⠁⠀
⣿⠛⣿⣿⣿⣿⣿⠀⠀⣼⠄⣿⡟⠾⢽⡿⠗⣫⣅⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣦⣸⣿⣿⣴⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠁⠀⠀⠀⠀
⣡⣾⣿⣿⣿⣿⣿⢠⣤⣿⣏⣿⠁⠀⠈⢿⣛⢭⡃⣄⡀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⣔⣀⣀⣠⣤⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣙⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡅⠀⠀⣀⠀⠛⠇⣵⣈⣷⣀⠀⠀⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⠿⠛⠛⢩⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣬⣤⣼⣿⣿⡿⣧⣤⠝⠉⠀⠀⢠⡄⠀⠴⠾⣥⡿⠿⠿⠿⡿⠿⠟⢻⣭⠀⠈⠚⠛⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡽⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣟⣮⣴⣶⣦⣒⣁⣀⣠⣴⣬⣹⣇⣀⣀⣀⣤⣴⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⣛⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣶⣄⣤⣄⣀⣤⣤⣼⣷⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣶⣦⣤⣴⣿⣯⣭⣯⣤⣾⣷⣆⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡏⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⠏⠀⠇⠀⠀⠀⢻⣾⣧⡄⠀⠀⠀⣸⣿⣿⠿⣿⣿⠀⠀⠀⠀⣆⡀⠀⠀⠩⠻⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣥⠶⣾⡿⣿⡇⠠⠇⠀⠀⠀⠈⢿⠂⢰⡇⠀⠘⣿⢿⣿⣶⣯⣛⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣁⠀⠁⠉⢻⡿⡏⣿⣿⣿⠿⢿⣿⣿⣿⣩⣽⣿⣿⣿⣿⣿⣿⣴⣿⠛⠁⠀⠒⠂⠀⠀⠀⠀⠀⠘⢿⡮⠀⠀⠀⣿⣾⠌⠻⠿⠿⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⡏⢿⣷⣦⡄⠀⠃⢀⣿⣿⣮⡄⠀⠉⠉⣿⣿⢿⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⠁⠀⠀⠀⠀⠛⢁⣀⡸⠖⠒⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠀⠀⠀⢹⣿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⠭⠛⣿⡻⠿⠻⣿⠟⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠸⠁⠘⠾⣷⠆⠀⠀⢘⣻⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠿⠀⠀⠀⠀⠀⠉⢣⣼⣿⣿⣿⣿⣿⣿⣿⣯⢝⠀⠈⠀⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣀⣀⣀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⣀⣐⣶⣦⣤⣤⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣴⣂⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣾⣿⣿⠇⠀⠀⠀⠘⠋⠋⠉⠁⠀⠙⠁⠛⠋⠉⠛⠛⠏⢻⣿⣯⣭⣭⣿⣿⣿⣿⡿⠋
⣿⣯⣿⣿⣿⣿⣿⠝⠷⣿⠏⠩⣿⣿⣿⣿⣿⠿⠁⠀⠙⠉⠙⠃⠀⠆⣠⣶⣶⣤⡀⠀⢠⣤⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⣿⣿⡿⠋⠁⣠
⣿⣿⣿⣿⣿⣿⣿⠄⠀⠴⠀⠔⢿⣿⡿⠿⡿⣧⡀⠄⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣆⣼⣿⣧⣠⣶⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⢱⣼⣀⣀⣠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⢠⣧⠀⡀⠀⢨⣿⣥⣴⣶⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣀⣤⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠳⣿⣿⣿⣿⣿⠀⣠⣾⣿⡇⠀⠀⠀⠸⠛⢯⣜⠲⣛⠀⠀⠀⠀⠀⡨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⢿⣿⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⣿⣿⣿⣿⣿⣤⣿⣿⣽⣿⣿⣬⣷⣶⣦⣤⡍⠘⠷⡾⠶⠌⠀⠀⠛⠓⠻⠿⠿⠿⣿⠿⠿⠟⢯⣯⠀⠀⠀⠉⣉⡀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢃⠑⠀⠀⣀⢀⠠⠓⠀⠈⠉⡁⣀⣀⣀⣤⣴⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣧⣬⣻⣿⣾⣾⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⡶⣒⣀⠀⠀⣴⡶⠿⣷⠟⠻⣇⣀⠩⣽⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣺⣷⣶⣶⣷⣶⣿⣿⣿⣷⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠁⠃⠀⠀⢻⣇⢻⡌⠛⠁⠀⠉⢿⣾⣿⣿⣿⡇⠀⠀⠀⢈⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⡟⣿⣿⡿⠟⠗⢸⣿⣿⡁⠈⠃⠀⠀⠀⢿⣾⠓⢀⡀⠀⢰⣼⣿⣟⠸⡿⡇⠀⠀⠀⠈⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡋⠁⠈⠓⢽⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡍⠉⢹⣍⣽⣿⣿⣿⡿⠚⠋⠉⠉⠙⠃⠈⠁⡀⠀⠀⠀⢯⣠⠹⠁⠀⢨⡟⣟⢻⣿⣾⡇⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⢿⣶⣄⡀⠀⠹⡙⠈⣿⣿⠏⠉⠻⡿⡿⣿⣿⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡀⢠⡌⠝⠁⠠⠀⣸⠛⠛⣀⣉⣉⠁⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠛⠹⠛⠈⠃⠹⣿⣯⠀⠀⣤⣶⣿⣿⣿⣦⣤⣦⣼⣿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣶⠆⠀⠀⣀⠀⠀⠒⠀⠀⠀⣠⠀⠣⣰⣶⠈⠁⠀⢿⣿⣿⣿⣿⣿⣿⡛⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣀⠀⠀⠀⠀⠛⢿⠃⣸⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠰⠗⠛⠋⠁⠀⠀⠀⠀⠀⢄⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⣤⠀⠙⠛⠀⠀⠀⠦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⣉⣛⣀⣀⣀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣶⣶⠆⠀⠀⠀⠹⠿⠿⠙⠛⠙⠿⠃⠿⠛⠿⠿⢿⣿⣯⣭⣭⣿⣿⣿⣿⣿⠿
⣤⡷⣿⣿⣿⣿⣿⣿⡝⢿⣼⣯⣏⢿⣿⣿⣿⣿⣿⣿⠟⠈⠳⠿⣤⠀⣴⣶⣶⣤⡀⠀⠀⣤⡀⠀⠀⣾⣦⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠁⠀
⣶⣿⣿⣿⣿⣿⣿⢩⣟⠐⠋⠽⠦⠸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⢤⣿⣿⣄⣤⣽⣿⣽⠦⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⣀⣀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣼⡟⠀⠀⠀⠀⠀⠈⠟⠀⢽⡯⠖⣀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡓⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠉⠀⠂⢀⣄⡀⠀⣈⢣⠁⣿⣿⡛⣟⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡜⢿⣿⣿⣿⠿⠗⠋⠉⠉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣿⣿⣿⣿⣿⣥⣤⣼⣿⣿⣿⣿⣽⣥⣌⣁⠙⠻⠂⣀⢀⣄⡀⠤⠀⣈⡿⠿⠿⠿⠿⠿⠟⠛⣩⣵⡆⠀⠀⠉⠉⠉⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠀⠈⠋⠉⠁⠀⣤⡀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⣆⠀⠀⠀⠀⠐⠒⠀⠀⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡇⠀⠀⣤⣦⣔⣖⣞⣧⣂⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣽⣏⣡⣀⡀⠀⠀⠀⣀⣼⣿⣫⣿⡇⠉⠩⢼⣭⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣤⣄⣤⣤⣀⣀⣀⠀⣀⣀⣰⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣿⣷⣶⣶⣿⣿⣿⣭⣴⣿⣶⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠘⢿⣇⢻⡟⠿⠿⡛⠟⢯⣟⣿⣯⣿⡿⠁⠀⠀⠁⠂⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣧⢰⣾⣿⠏⠀⠄⠀⠀⠀⢻⣿⠧⠄⠀⠀⢠⣼⣿⣟⣻⣿⣷⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣧⠈⠉⠯⢹⡝⣿⣿⣿⣿⣿⣯⣼⣿⣿⠍⠍⠍⢶⣿⣷⣸⡿⠛⠋⠁⠈⠉⢻⡶⠀⠦⠀⠀⠀⠈⢟⠀⢰⠃⠀⠘⡿⠿⢿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⢻⡿⠘⣿⣿⡟⠛⢿⣿⣿⣷⣶⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⡘⡿⠆⣀⠀⠀⢧⠿⣾⠟⠿⠟⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡯⠽⢻⣿⡟⣏⢿⣿⣶⡤⠀⢣⣴⣿⣿⣶⣤⣬⣤⢉⣿⣿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠰⢿⠇⠀⠀⠀⠀⠙⠂⠠⠁⠀⠀⠀⠀⢟⢠⣤⠜⠓⠉⣽⣿⣿⣿⣿⣿⣿⠿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡙⠛⠁⠀⠀⢀⠀⠉⠀⢿⣿⡇⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⢛⣿⣿⠃⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠘⠀⠈⠳⠿⠂⠀⠀⢈⣩⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣴⣾⣻⣇⣀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢀⣤⣤⡄⠀⠀⠈⠻⣿⣿⡿⠿⠛⣿⡏⢸⡿⣿⣿⣿⣯⣯⣭⣿⣿⣿⣿⡿⠛
⠀⢀⣿⣿⣿⣿⣿⠺⣶⣶⣶⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⠷⠘⢦⣴⣮⣶⣿⣷⣦⡀⠀⠀⣶⣄⠀⠀⢰⣦⢄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⡿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠛⠁⠀
⣬⣉⣿⣿⣿⣿⣿⠀⢙⣿⠮⠿⠿⠗⠸⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⣿⣿⣦⣤⣼⣿⣿⣷⣆⠀⠀⠀⠀⠀⠈⢉⡩⠋⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠀
⣛⣿⣿⣿⣿⣿⣿⣄⣸⡿⠀⠀⠀⠀⠀⢿⡿⠛⣻⣯⠄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⣀⠀⠀⣀⣀⣿⣿⣿⣿⠥⡖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⡀⠀⡀⢸⣗⠂⣿⣷⡶⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⠉⠋⠙⠋⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣴⣾⣿⣿⣿⣿⣏⠑⠋⠛⠶⠈⠀⠐⡀⢀⣀⠙⠻⠿⠿⠿⠿⠿⠟⠛⣭⣭⡄⠈⠈⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣳⣷⣤⡄⠀⠙⠾⠛⠒⣁⣀⠀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⡉⠀⠀⣀⣄⣀⣨⣵⣯⢁⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣠⠄⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡇⠛⢛⣽⣚⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⠯⣿⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣆⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣻⣋⣩⣷⡤⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣷⣿⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⠻⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⠟⠿⠟⡿⠏⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⠟⡏⠁⠀⠀⠻⣇⣿⠌⠉⠹⠆⠀⢻⣷⠿⣻⣿⡇⠀⠀⠀⠀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣯⣽⣿⣿⢻⡉⠉⠀⠉⡍⢿⣿⣼⣭⣧⣈⡉⢻⣿⣿⠿⢿⣿⣿⣿⠟⠉⠉⠈⠀⠀⠘⣿⣿⡀⠈⡀⠀⠀⠀⢿⡏⠙⢀⠀⠀⢸⣿⣿⣧⣾⠿⠟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣮⡑⠀⠀⠃⢸⣞⡟⣿⣿⡿⣿⣿⣿⣿⣯⡀⢸⣿⣿⠏⠀⠀⠀⠀⢀⣀⠀⠀⠛⠃⠈⠁⡀⠀⠀⠈⢶⣤⡚⠀⠀⢸⣦⣏⣻⣿⣿⣦⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⣿⣿⡿⠿⣿⣿⣿⣿⣿⣶⣤⣀⡀⢹⣄⣼⣿⣦⡤⣬⠙⠛⢫⣷⣿⣿⡏⠀⠀⠀⠀⠀⠘⠿⠀⠰⣿⢰⢠⡄⠁⣄⠀⠰⠆⠀⠈⠃⠠⡬⠉⠈⣿⡤⠲⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⡹⣃⣀⠈⠉⠛⠟⠻⠇⠻⣿⣿⠃⣠⣿⣿⣿⣿⣿⣿⡀⣄⣸⣿⢿⡟⠀⠀⠀⠀⠀⠀⠹⠗⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣟⠀⠀⠀⠛⣻⣿⣿⣿⣿⣯⣬⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢠⣤⣀⣀⣀⣄⡄⠀⠀⠀⠛⠟⣨⣿⣿⣿⣿⣿⣿⣿⡷⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⠿
⣠⡾⣿⣿⣿⣿⣿⠃⠀⣠⡀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⢀⣠⣾⣿⣷⣦⡀⠀⢠⣶⣄⠀⠀⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣴⣷⣿⠃⠀⠀⠀⠈⠋⠉⠈⠁⠀⠀⠁⠘⠉⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠛⠛⣿⣿⣿⣿⣿⠄⠀⠼⣿⣽⠷⣿⣿⠏⢻⣿⣿⣿⣿⠉⠋⠁⠀⢻⣿⣿⣿⣿⣿⣧⣸⣿⣿⣦⣴⣼⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠀⠀
⠤⣤⣿⣿⣿⣿⣿⣶⡄⠀⣸⣏⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣀⣠⡀⠀⣅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣠⣿⣿⣿⣿⣿⣉⣑⣶⡿⠅⠀⠀⠀⢀⡈⣿⣃⢠⣾⠀⢀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣻⣿⣿⣿⣫⣿⣞⡙⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣴⣦⣿⣼⣿⠆⠘⠛⠀⠀⠄⠀⠀⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡭⠉⠉⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠦⡀⡀⡀⠀⠠⣄⣶⣤⡀⠀⢀⣀⣈⣉⣉⣉⣉⣝⣛⣙⠿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡾⠿⠛⠀⠀⠈⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⣿⣿⣿⣿⡿⠂⠛⠁⠀⠀⠀⢸⣿⣾⣿⣿⢻⠿⠿⣃⣖⢠⣯⣷⣿⣿⣿⣿⡿⠿⣯⣿⣿⣿⣿⢿⣿⣿⣿⣯⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣷⣿⣿⣷⠶⠴⠶⠶⣶⣶⣿⣷⠟⣷⡀⠀⣚⣷⣾⣾⣿⣿⣿⣿⢿⣿⣯⣶⣿⣿⣿⢹⣯⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⡀⣀⠀⠀⣠⡀⣠⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⡿⠃⠀⠙⢿⡆⢿⠛⠿⢋⡙⠛⢷⣽⣿⣿⣿⡻⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣭⣥⡙⠙⣿⣿⣟⠛⠉⠉⠉⡙⣿⣿⠹⠉⡉⠙⠻⢛⣯⣭⣿⣿⣿⡿⠟⠛⠋⠁⠈⠀⠀⠹⣿⣿⠁⠃⠀⠀⠀⠈⢿⡜⠡⠀⠀⠀⢠⣼⣿⣏⣠⣿⣿⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⣽⠛⣿⣿⣿⣷⣿⣦⣐⠃⠀⠀⠀⢳⣹⡟⣿⣿⣿⣿⣶⣾⣿⡿⠩⣿⡿⠃⠀⠀⠀⠀⢠⣤⡄⠀⠉⣹⡗⠀⠂⠀⠀⠀⠈⣅⣀⠰⠀⠀⢸⡋⡙⢻⣿⣧⣄⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⢿⠇⠉⣿⡿⣿⣿⣿⣿⣶⣤⣄⠀⠈⣷⡅⣿⣿⣥⡍⠛⠿⠟⠒⢾⣿⡏⠀⠀⠀⠀⠀⣈⣿⠃⠸⠂⣤⢀⢀⡀⠂⠀⠀⠀⠉⠛⠠⠄⢀⣐⠾⠛⢾⢋⣛⣋⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⠀⣀⣁⣀⣃⣿⡿⣿⡟⢿⣿⣿⠂⢈⣾⣿⣿⣿⣷⣀⠀⡀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠘⠟⠼⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢉⣠⡴⠈⠁⠀⠿⢻⣿⣿⣿⣿⣛⡛⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣃⣉⣙⣉⣀⠀⢀⠀⠁⠈⠿⡿⢰⣿⣿⣿⣿⣿⣿⢫⣤⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠂⠐⢟⢈⣯⣏⣯⣷⣿⡯⢻⣿⣯⣭⣭⣿⣿⣿⣿⣿⠋
⠉⠁⣿⣿⣿⣿⣿⠛⠏⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⠉⣫⡤⠀⣴⣿⣿⣷⣄⠀⠀⢴⣶⡄⠀⠀⢸⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣤⡄⠀⠀⠀⠀⠁⠁⠉⠓⠉⠉⠁⠈⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠶⢿⣿⣿⣿⣿⣿⣀⡀⠐⠦⣴⡶⡶⠸⣟⠟⢿⣿⣿⣿⡇⠙⠿⠓⣹⣿⣿⣿⣿⣿⣤⡌⣿⣿⣦⣦⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠉⠀⠀⠀⠀
⡀⠀⣿⣿⣿⣿⣿⣿⣥⡄⠀⢙⠁⠀⠀⠛⠀⢸⣿⣿⣿⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠈⣿⣿⣿⣿⣿⣿⠟⠡⣤⡖⠀⠀⠀⠀⠀⠸⣿⠟⢙⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣯⣥⣤⣤⣤⣤⣿⣼⣿⠐⠸⠄⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠯⡀⠀⠀⠀⠀⢀⠀⣦⣀⢀⣈⣉⠛⠻⢿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣁⡀⢀⣴⣶⠆⠀⣀⠙⠛⢉⣥⣿⣿⣿⣿⣿⣿⣹⣿⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣾⣿⣿⣿⠋⠿⠋⠀⠀⠐⢻⣯⣱⣤⡾⢿⣻⣿⠋⡄⢀⢷⣭⣶⣶⣶⠦⢙⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⡶⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣿⣿⣿⣿⣷⣴⣴⠶⠶⠖⣀⣸⣿⣿⣿⡇⠉⠩⢾⣌⣧⣼⣿⣿⣿⣿⣿⣤⣽⣿⣿⡏⣿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣯⣅⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⢿⣏⢻⣿⣯⣿⣿⣿⠿⠛⢿⣿⡿⠿⠛⠛⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣄
⣿⣿⡟⢻⠭⠌⠉⠉⣿⣿⣿⣿⠉⠉⠙⠉⢿⣿⡯⡙⠋⠀⢨⣿⠉⠹⣿⣿⣿⣿⠟⠉⠉⠀⠀⠁⠙⠛⢟⣿⡿⢿⠃⠀⠀⠈⢿⡈⡧⠈⠁⠐⠀⠀⢻⣟⠟⠻⣿⣆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣯⠽⣿⣻⣿⣿⣶⣶
⠝⠿⠉⠻⣿⣿⣦⣤⣼⡉⠋⠉⠀⠀⠀⢀⡸⣿⢩⣥⣤⣤⣀⡀⢬⣾⣿⣿⣿⠋⠀⠀⠀⠀⢠⣤⡄⠀⠘⢿⣇⡀⠀⠀⠀⠀⠈⢿⠈⠐⡀⠀⠀⢾⠟⣿⣶⣜⡋⠉⠀⠀⠀⠀⢴⣯⣭⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠠⣷⣽⢼⣿⣿⠛⢿⣿⣿⢹⣿⣿⠁⠀⠀⠀⠀⠀⢀⣹⠁⠘⠁⠀⠙⠁⠈⠀⠀⠀⠀⠘⣖⡆⠁⠀⠀⢐⣤⢄⣿⠿⠿⠇⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠃⠀⣀⣠⣛⣿⣿⣿⣿⡿⣿⣷⣦⣄⠘⢏⣼⣿⣿⣀⠀⠀⠉⠘⡿⠋⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⣘⡇⡆⢴⠈⠁⣀⠀⠠⠀⠀⠈⠀⠲⠎⠁⡀⠻⠉⢱⣶⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⢲⣤⣤⣈⣿⣿⡿⠟⠛⠁⠻⠈⢿⣿⡇⣴⣿⣿⣿⣿⡿⣷⠆⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⡍⠀⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠲⣻⠃⠀⠀⠀⠁⠀⠋⠛⠛⠁⠀⡀⣿⣯⣭⣭⣭⣿⣿⣿⣿⡿⢁
⣿⠿⣿⣿⣿⣿⣿⠀⣀⣠⡅⠀⠀⠈⠙⣵⣿⣿⣿⣿⣿⠗⠨⣵⠶⢺⣿⣿⣿⣄⠀⠀⢠⣶⣦⠀⠀⠀⢹⣿⣷⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀
⢺⣇⣿⣿⣿⣿⣿⠛⠋⠘⠃⢰⡦⠀⣀⠊⣿⣿⣿⣿⣿⣦⣠⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣇⣄⣠⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣆⣾⣿⡿⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠀⠀
⠉⠈⣿⣿⣿⣿⣿⣤⢦⣤⠄⠀⠀⠀⠈⠀⣸⡄⠀⣿⣿⢿⣟⠛⠉⠘⠻⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠀⣿⣿⣿⣿⣿⣾⣾⣿⡖⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⢹⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⠿⠿⠿⠿⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡛⠀⣿⣿⣿⣿⣿⣿⣿⣯⣥⣼⣶⣦⣤⣤⡄⣠⡀⢹⡋⠀⠙⣷⣄⣀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⡟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡧⠘⠁⠀⠀⠈⠙⣿⣷⣤⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⠏⠀⠀⢀⣀⣀⠀⠸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣿⣟⢃⣤⣶⣿⡿⢿⡟⠋⠁⠀⢠⡽⠏⠛⣓⣶⢧⣼⡿⠛⠋⣰⠫⠍⠀⢸⡏⠉⢩⣛⣛⡿⣿⣿⣿⣿⣷⣙⣄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⢿⣿⠿⣿⡿⠶⠾⠷⠖⠀⠀⠠⣯⡶⣿⡏⠹⠲⢛⡡⣬⢀⣭⣿⣿⣿⣿⡀⢤⣼⡇⢻⠃⠈⣿⣿⣿⣿⣿⣯⣴⣿⣥⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⣿⣿⣿⣿⡿⠛⠛⢻⣿⣿⣿⣈⠈⠻⡉⢻⣿⣿⠉⢤⠁⠀⠈⣹⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠛⠀⠀⢹⡆⢸⠚⠛⠃⠛⠋⠁⣬⣿⡿⣋⣁⡀⠂⠈⠻⣿⣿⣿⣿⣟⠯⠹⡿⢛⣯⣭⣶⣶
⣿⣿⠋⠹⢻⣥⣦⡀⠀⠘⠻⠿⠿⠇⠀⠀⠀⠀⢿⣿⠤⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣤⡄⠀⢹⣿⡍⠑⠀⠀⠀⠀⢹⡄⠁⢀⠀⠀⠀⣤⠹⣯⣄⢨⡝⠇⠀⠀⢴⣯⣭⣦⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿
⠉⣿⠀⠀⠀⠙⢿⣿⣿⣧⣤⣤⣤⣤⠀⢀⣤⣤⣼⣧⣿⣿⡿⢷⣦⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⡀⢈⠃⠐⠀⠛⠤⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⢀⠈⠶⣷⣦⣤⡀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠹⣿⢋⣿⡏⠀⠀⠙⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⣀⡀⠀⣀⠠⠄⠀⠀⠈⠘⠀⡤⠀⠀⠲⠛⠰⣯⠉⢉⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣀⣈⣉⣀⣹⣿⣿⣿⣿⡿⢻⡝⢿⣿⣿⠂⣨⣾⣿⣿⣦⡀⠀⠀⠍⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠲⢠⠄⠋⠀⠀⠒⠄⠀⠀⠀⠀⠀⠉⣀⣰⠀⠀⠀⠘⠛⠛⠛⠛⠋⠉⢻⣯⣭⣭⣭⣽⣿⣿⣿⡿⠁
⠀⣴⣿⣿⣿⣿⣿⠙⠛⠻⠉⠩⠀⠁⠈⢿⣿⣼⣿⣿⣿⠍⠉⠙⠉⢀⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⣿⣧⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣽⣿⣿⣿⡿⠋⠀⠀
⢸⡟⣿⣿⣿⣿⣿⣀⣀⣴⡤⢴⡆⠀⠀⣀⣺⣿⣿⣿⣿⠢⠀⠈⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠸⣿⣝⠀⠀⣠⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⡀⡀⠈⢁⡀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠀⠀
⢸⣇⣿⣿⣿⣿⣿⣭⣯⣤⣴⣶⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⣿⠿⣿⣿⣷⠀⡀⣠⣿⣿⣿⣷⣿⣿⣿⣿⠻⠻⠿⣿⡿⠿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣇⣿⣿⣿⣿⣿⠿⠿⣟⢛⡇⠀⠀⠀⠘⠛⠛⠟⠁⢸⠀⠀⠂⠀⠀⠁⠀⠈⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢣⣤⣄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣾⣧⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⠀⠀⠇⠀⠀⠀⠀⣛⠊⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡲⡇⠀⠀⠀⠀⠀⠀⠀⢈⣀⢘⣆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⣿⠛⢋⣻⣿⣿⣿⠷⠆⠀⠀⠻⣷⢶⣏⢉⡀⠀⣽⣿⡿⠆⣀⣙⠛⠛⡏⠉⠛⠛⠛⠿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠾⣿⣿⣿⣿⣿⣿⠿⡷⠀⠀⠀⠀⡀⢈⣠⣴⠿⣋⣻⡟⠉⠀⢺⣮⣡⣤⣆⡀⠀⠀⣰⠁⡖⠀⠉⣿⣿⣿⣿⣧⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀
⣿⣿⣤⣿⣽⣿⣿⢿⠿⠻⣿⣿⣿⣇⡉⠩⡏⠙⣿⡻⡏⠁⡄⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠇⠀⠉⣿⠈⣯⠽⠚⠹⠟⠛⢡⣝⣿⣿⢛⣂⠠⡍⠻⣿⣿⣿⣿⡟⠧⠙⣿⢛⣯⣭⣦⣤
⣿⣿⡟⠻⠿⣟⣉⡁⠀⠀⠿⣿⣿⣿⠃⠀⠀⠀⢺⣿⣇⡄⠁⠀⠀⣼⣿⣟⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣤⡄⠀⣿⣿⠉⠇⠀⠀⠀⠈⣇⠘⠀⡀⠀⠀⢀⣌⣿⣍⡈⢹⣿⠁⠀⢴⣯⣭⣦⣿⣤⡿⣿⣿⣿⣿⣿⣿⣿
⠿⢻⠀⠀⠀⠙⠻⣿⣷⣶⣤⣤⣤⣤⡤⠀⢤⣤⣤⣿⣵⣶⣶⣶⣤⣤⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠛⢻⠤⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠈⠉⠸⢽⣯⣭⣀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠸⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣯⣀⠈⠘⢿⣿⢻⣿⠋⠀⠘⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠼⠃⢼⣏⣛⣛⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣀⣀⣛⣋⣙⣷⣿⣿⣿⣿⡿⢿⢻⣿⣷⣦⠈⣣⣿⣿⣦⡀⠀⠐⣟⡻⢟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡇⣬⠸⠇⠀⠀⠠⠀⠀⠀⠀⠀⠐⠂⣀⣤⠈⠁⠀⠿⠛⠿⠿⠿⠛⢻⣯⣭⣭⣭⣽⣿⣿⣿⡿⠁
⠀⢀⣿⣿⣿⣿⣿⠘⠿⢿⠟⠛⠇⠘⠀⢹⣿⣇⣾⣿⣿⡿⠯⠉⠒⢲⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⡆⠀⠀⢘⣿⣇⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣽⣿⣿⣿⡿⠋⠀⠀
⠀⣼⣿⣿⣿⣿⣿⣤⣄⣐⣠⣤⣀⣐⣠⣤⣾⣿⣿⣿⣿⠋⠀⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⡅⠀⠀⣸⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣼⣄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠈⢻⣿⣿⣿⡿⠿⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⡀⢀⡀⣼⣿⣿⣿⣶⣿⣿⣿⣏⠛⣿⠟⠛⠋⠉⠉⠀⠀⠀⠀⢰⣿⣼⣿⣿⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢹⣿⣿⣿⣿⣿⠋⠽⢿⡧⠄⠀⠀⠀⢸⠀⠀⢈⠁⠀⠀⠀⠠⠀⠀⠛⠀⠀⠙⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠁⠀⢰⣆⡀⠀⠀⠀⠀⠀⠘⠟⠛⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣈⣿⣿⣿⣿⣿⣴⣶⣶⣷⣿⣧⣤⣤⣷⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⠀⠀⠀⠀⠶⠶⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠅⠀⣀⣀⠀⠀⠀⠐⡎⢁⠈⢂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⠟⠛⣿⣿⣿⣿⣤⠄⠀⠐⣾⡯⣼⡛⠁⠀⢙⣶⣶⣶⢀⡉⠷⠿⢻⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠶⣿⣿⣷⣶⣿⣿⡿⢿⡅⠀⠀⠀⠀⠀⠃⣉⣽⣿⣲⣾⠋⠉⠠⣿⣙⣁⣠⠀⠀⠀⠀⡖⢰⡆⠉⢉⣿⣿⣿⣿⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂
⣿⣿⡋⠉⢉⡙⣿⣿⣿⣏⣿⣿⣿⣍⣉⠉⠉⣉⠙⣛⢿⡏⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⠈⠛⣿⡟⢿⢛⣿⠛⣿⠿⠛⠹⣿⣿⡿⠯⠙⣻⣿⣿⣿⣿⡟⠧⠙⠹⢛⣯⣭⣦⠀
⣿⣿⡇⠀⣼⣿⣿⡿⠻⠋⠁⣹⣿⣿⠵⠆⠀⠈⠀⢹⣇⣇⠀⠂⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠠⣤⡄⠀⣿⣿⡿⠀⠀⠀⠈⣇⠸⠀⠀⠀⠀⠀⠀⣻⡷⠊⠳⢶⡖⣼⣯⣭⣤⣿⣤⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⠀⠀⠀⠻⣦⣶⣦⣤⣬⣽⣭⣼⣤⠤⣤⢤⣤⣿⢿⣅⣄⣀⣀⣻⣿⣿⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣈⠁⠀⠻⡀⠀⠀⠀⠀⠀⠸⠆⠀⠐⠀⠀⠰⠛⠋⣛⣿⠐⠃⠁⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⡉⠀⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⠻⣿⣿⢸⣧⠙⠉⢻⣿⣿⣿⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⣀⣶⠈⡿⠿⠿⠆⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠁⢀⣀⣠⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣦⣄⠙⢏⣸⣿⣀⠀⠀⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⡀⣦⠐⠀⠀⠀⠀⠀⠀⠃⠀⡤⢈⢀⠈⠛⠀⢸⡿⢿⣿⣿⣿⣿⣭⣭⣭⣿⣿⣿⣿⡿⠁
⠀⠀⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⡯⠸⠌⢿⣿⡏⣴⣿⣽⣿⠟⠷⢠⣿⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⡆⠀⠀⢸⣷⡚⠀⠀⠀⠀⠀⠁⠀⠀⣀⣠⣤⠀⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣽⣿⣿⣿⡿⠋⡀⠀
⠀⠀⣿⣿⣿⣿⣿⢛⣿⣿⣿⣥⣤⣴⣤⣶⣾⣿⣿⣿⣿⠙⠓⠀⠀⠸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣿⣯⡅⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠉⠀⠀⠁⠀
⠀⠈⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⠁⠀⠈⢻⣿⣿⡿⢿⣿⠀⠀⡀⠀⠀⣿⣿⣽⠍⠿⣿⡇⠀⡄⢠⣿⣿⣿⣷⣄⣼⣿⣿⠙⢙⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣰⣆⣴⣷⡷⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠲⠂⣿⣿⣿⣿⣿⠿⠀⠀⣀⠀⠀⠀⠀⠀⣏⠀⠀⠀⢛⠀⠀⠀⠀⢀⣿⣽⠋⠉⠛⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⢠⣄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣤⣤⣬⣭⣯⣤⣿⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆⣀⣀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠈⠀⠀⠀⣭⡄⠦⠀⢄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣶⣿⡋⠁⠀⠀⣼⡛⢋⡿⠟⠓⠢⣤⣀⣀⠁⠲⣦⣴⣖⠟⠛⠻⠿⠿⠿⢿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⣿⣿⠿⣴⣶⣾⡿⣿⡋⠉⠁⠀⠀⠙⠏⠛⡣⡶⣤⣼⠿⠟⢉⣴⢦⠌⢉⠀⠀⠀⠀⠰⠀⡦⠈⠛⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛
⣿⣿⣿⣿⣿⠛⠻⢻⣿⣿⣿⣿⣿⣿⡟⠩⠍⠉⡉⠭⣽⣿⣿⠯⠉⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠈⢻⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣽⣿⢿⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠯⠙⠹⠛⣋⣭⣤⠀
⣿⣿⣿⣿⡀⠀⢠⣀⣿⣿⣿⣴⡿⣿⣷⡄⠄⠀⠀⠄⠀⣈⢻⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠰⣶⠀⢸⣿⣿⡿⠃⠀⠈⢻⠀⢧⠘⠒⠈⠛⠉⠁⣌⣛⠻⣏⣽⣯⣭⣤⣿⣤⠿⢿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⠏⠀⠺⣿⣿⣿⣽⣥⣤⣬⣼⣷⣤⣤⡄⣤⣤⢸⣾⡄⠀⠀⡟⢹⣿⣿⡿⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣈⠀⠸⣿⠟⠁⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⣠⠼⠯⣄⠈⡛⠿⣿⣿⣿⣻⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣛⡀⡀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⣯⣻⡀⠄⣿⠲⢾⣿⣾⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⡀⠠⣶⣤⣄⡀⠹⣿⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣀⣀⣀⣻⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠁⠙⠣⠀⣿⡀⠈⡿⣿⣿⣿⣏⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⠛⠠⣬⠙⢋⣥⣤⣿⣿⣭⣭⣭⣿⣿⣿⣿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⠙⠟⠻⣯⣿⣿⣿⣿⡿⣟⣿⣿⣶⡆⠀⠐⣿⣧⣴⣦⡠⣿⣻⣿⣿⣿⣶⣤⠀⠀⠀⠀⣶⣦⠀⠀⠀⢴⣦⣤⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣆⣀⠀⠀⠘⠋⠉⠛⢻⣿⣭⣿⣿⣿⡿⠋⠀⠀
⠯⠅⣿⣿⣿⣿⣿⢀⣀⣴⡾⣿⣿⠿⣿⣶⣿⣾⣿⣿⣶⠀⠀⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣻⠀⠀⠀⢨⣿⣿⣶⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢈⣠⣤⣴⣦⣤⡄⠀⠀⠀⠙⢟⠛⠋⠁⠀⠀⠀⠀
⠿⣅⣿⣿⣿⣿⣿⢶⠿⢿⣛⣛⠁⡀⠈⢻⣿⣿⣿⣿⣿⠀⠱⠭⠄⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣄⣴⣷⣿⣿⡀⠀⠀⣿⠿⠿⢿⢿⠿⣿⣿⣿⣿⣿⣟⠿⢿⣋⣭⣙⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠲⣄⣿⣿⣿⣿⣿⠀⠀⠀⠰⠓⠂⠀⠀⠘⠛⠛⠛⠻⠛⠀⠀⠀⠀⠸⣿⣟⣿⣿⣶⡈⣻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⠢⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣾⣧⣿⣿⡏⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣿⣿⣿⣤⣧⣯⣤⣤⣤⣤⣤⣤⡄⠀⡄⠀⠀⠀⠀⠀⠀⠰⣿⣿⠷⠌⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠈⠻⠛⠿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠆⠀⠀⠀⠀⠀⠀⠀⠛⣙⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⣿⣿⣦⣄⡼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⣀⠀⣼⡯⠤⠶⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠘⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⠻⣽⠷⠖⠀⠀⡀⠀⢿⣗⣞⣛⠀⠀⠐⢶⣉⡀⠁⠈⠛⠛⠿⡿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠶⣶⠿⢷⣿⣿⡿⠿⠿⣯⣿⣿⣧⠄⠀⠀⠲⣮⢩⣼⠙⠀⠈⣳⣶⣶⠄⠀⣹⠂⠀⠀⠀⠀⠀⣤⠀⠓⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢀⠉⠉⠹⢛⢿⣿⣿⠿⠿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⡹⠛⣋⣭⣤⠀
⣿⣿⣿⣿⣿⠟⠁⠈⠘⢹⣿⡿⢉⣿⣿⣧⠉⠀⠀⠀⠉⠁⠻⢷⠀⠀⣻⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠠⣤⡄⢸⣿⣿⣿⣿⣿⡿⠈⠙⢻⡟⢛⠙⣛⡟⢋⡝⠃⠀⠿⠿⣿⣯⣭⣤⣿⣬⠿⢿⣿⣽⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣧⠀⣤⣶⣾⣿⣧⣿⣧⣽⣼⣧⣤⣤⣤⣤⠀⢲⣠⠀⠸⡟⢾⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⡍⠁⢨⣿⣿⣿⣿⡏⠀⠀⠀⠈⠅⠸⠀⠀⠀⠈⠀⠀⣸⣗⠂⠘⢿⣿⣿⣿⣻⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣀⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⡾⠀⠈⡏⡳⣠⣿⣦⣼⣻⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠋⣿⡆⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⢈⣉⠀⡈⢻⣿⣥⣶⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣛⣃⣇⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⠯⠀⠛⠀⢆⠀⣿⢸⣿⣿⣿⣿⡟⣁⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⢶⠀⠙⠻⠿⢒⣻⣯⣭⣯⣭⣿⣿⣿⣿⡿⠿
⣷⣿⣿⣿⣿⣿⣿⠡⢤⣼⣿⡿⣿⣿⣿⣿⣿⡿⣿⣶⣤⠀⠀⢀⣿⢷⣿⡋⠉⠋⢿⡿⣿⣷⣤⡀⠀⠀⣠⣤⠀⠀⠀⢰⣶⣴⡂⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⢀⡀⠀⠉⠁⠸⠿⠛⢿⣿⣭⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠀⠸⣿⣿⣿⣿⡇⠷⠘⣿⣿⠀⠀⠀⠁⢹⣿⣿⣦⡁⣾⣿⣿⣿⣿⣿⣦⡄⣿⡿⡇⠀⠀⠀⣿⣿⣶⣿⣥⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⢁⣠⣶⠂⠀⠀⠀⠙⢟⠛⠋⠁⠀⠀⠀⠀
⢩⣥⣿⣿⣿⣿⣿⢠⣀⣲⣶⠀⠀⠀⠀⠈⠁⠀⠀⠘⢻⠀⠀⠀⠠⢸⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⠀⠀⢰⣿⠿⠽⣿⣿⣟⣿⢿⣿⣿⣿⣿⣿⡶⠶⠒⠒⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⣄⣿⣿⣿⣿⣿⢉⡙⠁⠈⠀⡀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠙⠃⠁⠀⣐⡆⣠⣴⡶⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣤⣤⣤⣤⣬⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡟⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⢿⠿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣶⣀⡀⣸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢶⠄⠀⠀⠀⠀⠀⠀⣀⠀⣰⡶⢀⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠻⡿⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣾⣿⡿⣯⣿⣟⡁⠀⠀⠀⠀⣤⣇⡼⡿⠀⠙⠋⣁⠤⠔⠛⠛⠿⣿⣿⣿⣿⣿⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠖⠲⣶⠏⢶⠶⣿⣿⣿⣿⣿⡿⣶⣮⣟⠉⠀⠀⢄⣒⠄⣹⠿⠛⠒⢄⣀⣀⢠⠀⠀⠀⠀⠀⠀⢤⠀⠐⢶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀
⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣽⣉⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠛⢉⣥⠄⠀
⣿⣿⡟⣯⣥⣶⢾⠿⠏⠻⡿⣿⣿⠿⣿⢀⠀⠀⠀⠀⠀⠀⠘⠒⠂⢸⣿⡿⣿⣟⣠⣿⣿⠃⠀⠀⠀⠀⢀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣿⣿⣿⣏⣠⣽⣿⣿⣿⡏⠉⣿⣿⣽⣧⣿⣌⠿⢿⣿⣽⣿⡏⠀⠀
⣿⣿⣷⣿⣿⣿⠀⣤⣤⣤⣤⣿⣯⣤⣤⣤⣤⣤⣄⡠⢤⠀⠀⠀⠀⠀⡿⠉⠛⠈⣻⡟⠃⠀⠀⠀⠀⠀⠐⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⡛⣧⠉⡿⣿⣷⠖⢦⢠⣌⣿⣿⣿⣯⣙⠻⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣄⣼⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⣿⡟⠐⠚⠛⠁⠀⠀⠀⠀⠀⠀⠘⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⡃⠀⠀⢰⢹⣧⠁⠀⠀⠉⠁⠠⠿⣾⠿⡰⣿⣿⣥⣦⣴⣿⣿⣿⣿⣷⣶⡤
⣿⢿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣗⣻⣿⣿⣿⠓⣠⠀⠀⠀⠀⢸⣿⣾⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡿⠿⡷⠄⠠⣿⣷⡞⠀⠀⠀⢀⡟⢻⣄⣤⠀⠀⠀⠠⣦⣤⣰⢶⣾⣿⣫⣉⣉⢉⣽⣿⣿⣿⡟⢠
⠀⢻⣿⣿⣿⣿⣿⢁⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⠎⠁⠀⠀⠀⠀⢸⣿⣿⡿⣦⣶⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡂⠀⠀⠀⠀⠁⠀⠈⣼⣖⡈⠙⠛⣿⡿⠀⠀⠀⢐⠛⠛⠃⢤⠤⠩⣿⣿⣥⣿⣿⣿⠟⠋⠀⠈
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣙⣹⠿⠿⣿⣿⡿⡿⣷⣦⠀⠀⠀⠀⢸⣿⣷⣮⠽⠟⠛⢿⣿⣶⣀⠀⢿⣷⡀⠀⠘⣿⣿⣄⣬⣟⡗⡂⠀⠀⠿⡿⢿⣀⢀⢠⣄⡀⠀⢚⣂⣴⣄⠄⠀⠀⠀⠋⢝⣛⠛⠉⠁⠀⠀⠀⠀
⢭⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠁⠀⠀⠁⠻⠁⠸⠈⢻⠀⠀⠀⠀⢸⣿⣿⡇⠀⣄⠀⠀⠙⠻⠿⠷⠶⠾⠶⠶⠶⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠛⠛⠑⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢾⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠤⠄⣻⣿⣿⣿⣿⣤⣤⣶⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠈⣿⣿⣿⣿⣶⣤⣶⣶⣶⣾⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⣼⣿⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣯⣺⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣀⠀⢀⣀⣀⠀⠀⢀⣴⣤⠀⠀⣠⠄⠀⠀⠀⠿⣿⣿⣿⣿⡀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀
⠁⠀⠸⠿⠿⠿⢿⠿⢿⡿⠿⠿⠿⠿⢿⢿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛⠛⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠨⠿⠀⠈⣿⣿⣶⣆⣈⣿⡿⠶⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠶⠒⠒⠀⠀⠀⠀⠀⢤⠶⣖⣐⡧⠀⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠀⠀⠀⠀⠀⠈⠻⡿⠛⠛⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠰⠶⠶⢖⣀⣀⣘⡟⢋⣩⣿⠓⠀⠀⠀⠀⠀⠐⠀⢘⠇⠀⠀⠈⠀⠀⠀⠈⠉⠉⠹⣭⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠀⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣯⣭⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣯⣭⣮⣿⣿⠿⢿⣿⣿⣿⣿⠀⠀
⣿⣿⡄⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢘⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⢿⣿⡿⠀⢶⡿⠿⠿⠯⠈⠛⣿⣿⣿⣋⠻⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣃⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣭⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠹⠀⠀⠀⠀⠀⠁⠀⠀⠦⢹⣿⣥⣤⣤⣿⠿⠟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⣿⠻⣿⠿⠿⠿⠿⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⣁⡀⠀⠀⠀⠀⣀⠀⢀
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⣭⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣷⣶⣴⣶⣶⣶⣤⣀⠀⢀⡀⣀⠀⣠⣿⣶⣦⣸⠛⠛⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠻⣦⣤⣤⣴⣾⠟⠋⣠⣿
⠋⠀⣿⣿⣿⣿⣿⠛⠷⠀⠀⠀⠢⢽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠰⠎⠉⠀
⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠓⠀⠀⡀⠈⠛⢻⢻⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⢿⣯⣀⣂⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠒⠉⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠠
⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠳⡀⠃⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⠠⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣠⣤⣤⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⢭⣿⣿⣿⣿⠀⢀⣿⣿⣿⣋⣿⠋⠱⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⣠⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀
⠉⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⣿⡿⠀⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠿⠿⠿⠿⢿⡿⠿⠿⠿⢿⣿⡿⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⠒⠀⣤⣀⠀⠀⢀⣄⡀⠀⢀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢿⠁⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠛⠀⠀⠸⣿⣿⣤⣄⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠂⢶⠌⠹⠽⠶⠆⠀⠀⠀⠀⣴⣾⣯⣬⣀⠲⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠉⠛⢛⣫⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣥⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠉⠀⠀⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⠽⣿⣻⣯⣽⡶⠀
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣥⣦⣿⣿⡿⣿⣿⣿⣿⣿⡅⠀
⣿⣿⡀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠸⣿⣉⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠈⣿⣿⣿⡟⠁⣼⣿⣿⣿⡟⠛⣿⣿⣿⣿⠛⣿⣿⣿⣿⡟⠀⠀
⣿⣿⣁⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠈⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠙⠿⠃⠀⠉⠁⠀⠀⠀⠀⣹⣿⣭⣦⣔⣿⡿⠿⠁⠀⠀⠀
⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢿⣿⣿⣿⣷⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⣁⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣶⣾⣿⣿⣷⣶⣶⣤⣤⣄⣀⣤⣼⣿⣷⣬⣿⡶⠀⠀⠀⠈⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢽⣦⣤⣤⠄⠀⠀⠀⣠⣿
⠿⠋⣿⣿⣿⣿⣿⠟⠛⠧⠁⠀⠀⠌⣿⣿⣿⣿⣟⡙⢻⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢛⠛⠋⢁⡴⠟⠛⠛
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠃⠀⠀⠈⠹⠟⣿⣿⠿⠻⠀⠀⠀⠀⠀⢿⡿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢿⣿⣦⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠚⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢁⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣂⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⡀⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣄⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡀⠦⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣹⡿⠛⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⠃⠈⣿⣿⣿⣿⢀⣾⣿⣿⣿⣿⠇⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣦⣤⣴⡆⠀⠀⠀⠀⠂⠙⠀⠀⠀
⠀⠀⠸⠿⠿⠿⠿⠿⣿⡿⠿⠿⠿⣿⢿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣽⣶⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠉⠙⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠃⠀⠈⢻⠆⠀⠀⣿⣷⡆⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠹⠿⠿⠆⠀⠀⠀⠀⢀⣴⣶⣂⡁⠠⡤⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠙⠉⢉⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢿⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣥⡄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠁⠈⠉⠁⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣿⣿⣿⠇⠉⠉⢛⣯⣽⣶⡄
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣯⣩⣯⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣟⡈⠙⢿⣿⣿⣿⢿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠛⣿⣿⠀⠰⠿⠛⠛⠁⢹⣿⣥⣾⣿⣿⣿⣿⡿⠛⠁⠀
⡟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠈⠃⠀⠀⠀⠉⠀⠀⠀⢻⡉⣁⠀⠀⠠⠞⠀⠀⠀⠀
⠦⣸⣿⣿⣿⣿⣿⣿⣿⣟⠂⠙⠉⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣽⣿⣿⡗⠒⢴⣶⣴⣶⣶⣶⣶⣶⣦⣠⣤⣄⢀⣠⣶⣿⣿⠻⠟⠿⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣤⣤⣶⠆⠀⠀⠀⢀
⠀⠘⣿⣿⣿⣿⣿⢽⣿⣯⡙⠶⠀⠀⠀⠸⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⠾⠛⠓⠀⢸⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢀⠀⠤⠄⢈⣉
⠀⠰⢿⣿⣿⣿⣿⣿⣿⡗⠀⠠⠀⠀⠀⠦⡄⣄⡈⠉⠋⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠻⠶⣦⣄⡠⠤⣤⡤⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⢠⣤⠍⠀⠲⠶⠀⠀⠀⠀⢀⣄⣴⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢼⣿⣿⣿⣿⣿⣿⣤⣤⣀⣀⣠⣤⣌⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠂⠿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣏⣽⠿⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⣿⣿⣈⠛⢿⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⠀⠐⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠹⠿⠿⠿⠿⢿⡿⠿⣿⠿⠿⠿⠿⠿⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⢿⣿⠀⢀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⣾⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⢰⣄⠀⠀⢀⣤⡀⠀⠀⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⠶⠄⠠⠴⣶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠙⣿⣧⠀⠀⠀⠚⠀⠀⠘⢿⣿⣦⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠉⠁⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⠽⠽⠛⢋⣭⣶⡀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣯⣭⣦⣿⣯⠿⢿⣷⣼⣿⣿⣿⣷
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢛⣿⣿⣿⣿⣿⣿⣿⣟
⣿⣿⣧⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠈⢻⣽⣿⡍⠇⠈⢿⣿⣿⣿⣥⣤⣴⣿⣿⣿⡉⠉⠉⠉
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠄⠀⠘⢿⠃⠀⠘⠃⠀⠀⢹⠉⡁⠀⠉⠙⠛⠉⠀⠀⠀
⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣻⣿⣿⠀⠀⠀⠀⠀⡿⠯⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣤⣤⡤⠀⠀⠀⠀⠀
⠀⠈⢻⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣀⠘⠉⣯⠀⢀⡄⠁⠀⢠⣶⣿⣿⠛⡿⠿⢧⡄⠀⠀⠀⠀⢨⣉⠁⠈⠉⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⣀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⠌⢩⣾⣿⡿⠁⠀⠀⠀⠈⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠗⡎⠀⣴⣢⠀⣠⣿⣿⣿⣿⣇⣷⡄⠀⢘⣶⣆⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠛⠋⢿⣿⣿⣿⣿⣦⣾⣿⣿⠀⠀⠀⠀⠀⠀⠒⠸⠿⠿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣀⣀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣶⣾⣿⣿⠻⣿⣿⣿⣷⠀⠀⣸⣿⣿⡋⣹⣿⠷⠚⣿⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀
⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠻⢿⣿⣿⠃⠀⢽⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⠁⠋⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠽⠿⠿⠿⠿⠿⣿⠿⠿⢿⠿⠿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠿⠇⢀⣾⣿⣿⣿⣦⣿⣿⣿⣿⣿⣏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣤⣄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠁⠲⣇⠈⠀⠀⠀⢳⡄⠀⠀⣴⣄⠀⠀⢴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠂⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠻⣿⢛⣏⣭⣶⡀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢓⣯⣭⣦⣿⣮⣿⣿⣿⣿⣿⣛⣿⣷
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⡟⢻⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣇⣀⣀⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡀⠈⠛⣟⣿⣿⠻⡏⠻⣿⣿⣿⣥⣤⣄⣿⣿⣿⣿⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠻⢿⣿⣿⣿⣿⣿⣿⢿⡷⠀⠀⠙⢿⠿⠀⠀⠠⠜⠙⢻⠉⣁⠀⠈⠽⢿⡿⠀⠀⠀
⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⠀⠀⠀⠀⠀⣸⣻⡛⠉⠰⠟⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⣤⣤⡄⠀⠀⠀⠀⠀
⠀⠀⢽⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠏⠉⠄⢠⡀⠀⠀⠻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀
⠀⣤⣼⣿⣿⣿⣿⠋⡱⣶⣿⣿⠁⡀⠀⠀⠀⠙⢻⣿⣿⠀⠀⠀⠀⢀⡶⠀⠀⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠀⠀⠀
⠿⠿⣿⣿⣿⣿⣿⠀⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⢀⣄⠀⠀⣼⣿⣿⣷⣤⣀⣀⠀⠀⠀⣤⣶⣀⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣄⣸⠃⠀⡀⠈⠁⠀⠀⠀⠀⠈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣾⣿⣿⣥⣿⠛⢿⠆⢤⣴⣤⠀⠀⣤⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⢀⠀⠀⠀⠀
⢀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⢿⣿⣟⠋⢻⣿⣿⣆⢀⣸⣿⣿⣿⣿⡿⠀⠀⢀⡄⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠸⠿⠿⠿⠿⢿⣿⠿⢿⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣿⣷⣾⠀⠀⠀⠀⠀
⠀⠆⠲⣶⠀⢶⠄⠠⠰⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⢸⣆⠀⠐⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠤⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣷⣦⣤⣄⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠋⠠⠉⠙⠛⣋⣭⣤⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢏⣁⣤⣿⣤⠿⢿⣿⣿⣿⠃⠀⠀
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⡮⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣯⣲⣿⣿⣿⢛⠻⣿⣿⣿⣿⣶⣦⣦
⣿⣿⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠑⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣤⣤⡤⠸⢿⣿⣿⡿⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣆⠀⠀⠴⢾⣿⡉⠛⠈⠛⠻⠉⠁⠀⠀⠀⠛⠛⠋⠀⠀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⣤⣬⠀⠞⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠉⠁⠀⠀⠀⠈⢿⠃⠀⠈⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⢰⣿⣿⠟⠻⣿⣿⣿⣟⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠤⣿⣇⣿⣦⣴⠿⠿⢿⠁⡀⠈⢿⡟⠛⢿⣧⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣶⣆⠀⠀⣾⣿⣟⠀⠀⠀⠀⠙⠻⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣴⣶⣭⣿⠛⠁⠠⠯⡖⡊⠀⡁⠸⠃⠀⠀⠻⣿⠀⠀⠀⠀⠀⡾⣾⡇⠀⠀⢰⣗⠀⠀⠈⠋⠀⠙⠻⡦⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣿⣿⣿⠿⠉⠀⣀⣀⣠⣿⣿⣟⣁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⣷⣄⢀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⡀⢀⣤⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠈⣿⣿⣿⣿⣿⣿⡏⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢻⣿⣿⣿⣿⣿⡂⠀⠀⢀⣀⣠⣶⣿⡟⠀⠀⠀⠋⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⠀⠈⠀⠀⠂⠛⢛⠛⠛⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⢿⣿⣿⢀⢠⣽⣿⣿⣿⣿⢷⡀⠀⠀⠀⠘⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⡿⠿⠟⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣤⣄⡀⠀⠀⠀⠀
⡀⠆⠲⣶⠀⠰⠄⠠⠰⠖⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣤⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣽⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀
⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠉⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠣⠉⠹⢛⣫⣭⣦⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⢤⣷⣄⠴⢿⣿⣿⣿⣿⣿⠗
⣿⣿⡇⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠠⢤⠀⠀⠀⠀⠀⣦⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⣿⣆⠀
⣿⣿⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⢮⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣶⣴⠿⠿⢿⣿⣿⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠂⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡀⠈⠙⢛⣻⣿⡟⣿⡛⣿⣉⣁⠀⠀⠀⠈⠋⣻⠗⢀
⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣶⣶⣿⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠈⠹⡿⠆⠈⠁⠀⠑⣤⡀⠀⡀⠀⠀⠀⣠⠿
⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣽⢻⣿⣿⣷⣦⡀⣠⠶⢾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠛⠛⢿⣿⠀⣘⡟⣻⣿⠁⡀⠈⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰⠏⠀⠈⣽⣿⣿⣿⣿⣦⣤⣭⣿⣿⣿⡟⠀⠀⠀⠉⠙⠿⡿⠟⠿⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⢀⡈⣛⣿⣰⡿⠏⠈⡀⠀⠀⣁⢺⣿⡇⠈⠻⣿⠀⠀⠀⠀⠀⣨⡄⣤⠺⠉⣠⣤⡀⠈⠉⠙⠁⠙⠻⣿⠿⠿⣿⣿⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣸⣿⣿⣿⡁⠀⣀⣐⣋⣿⣿⣿⣯⡿⠁⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⠗⠂⠀⣩⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⡿⠻⠻⠏⠁⠐⢭⣿⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣤⣴⣿⣿⣿⣿⠀⠀⢀⣀⢁⣼⣾⣿⣿⠗⠠⠀⢰⣤⠀⠀⣤⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠻⠓⠀⠠⠠⠤⠤⠾⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⢿⣿⣿⣿⣇⣤⢼⣿⣿⣿⣿⣿⣟⡀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠆⠀⠸⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⢇⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢶⡶⣶⠀⠶⠄⠠⠠⠖⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠛⠉⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣸⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣧⣤⣿⡟⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣟⣿⣤⠘⢿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠉⢠⣿⣿⣿⢹⣿⣿⡀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣿⣿⣷⡿⠏⠹⠿⠷⢆⣙⢛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⢿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⡿⠿⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠈⠛⠻⣿⣦⣀⡀⠀⠀⠀⠶⠟⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠙⠛⠛⢿⡿⢿⡛⢿⣿⣯⡙⠦⠀⠀⢿⣿⣿⣿
⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠙⣿⣿⡄⣠⣤⣤⡁⣉⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣄⠀⠀⠘⢿⣯⡀⠁⠀⠉⠉⠁⠀⠀⠀⠐⠛⠛⢿
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⣀⠀⡐⠲⢶⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⢿⣟⣿⢿⣿⣿⣼⡍⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⠻⠟⠋⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠝⢫⣷⡗⣶⡶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⢾⣷⣦⣀⣬⣿⣿⣿⠃⠀⠀⠀⠀⠘⠛⠿⠟⣿⠿⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠂⠉⢩⣿⣿⣿⣿⡏⠁⠙⢶⣾⣿⣿⣻⠃⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠿⠿⠿⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣶⠆⠂⠉⠀⠀⠐⠸⣿⣿⡿⠹⠇⠀⠀⠈⠻⣿⣿⣻⣶⣶⣟⢾⠄⠀⠈⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣀⣀⣿⣿⠁⠀⠀⠀⡀⠀⠀⠓⠸⢱⠿⠐⠘⢷⣤⣠⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡏⠀⡀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢷⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠻⣿⣇⣀⡀⠀⠀⠀⢶⣿⣿⣿⣿⡃⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠤⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢸⣷⣄⡀⢀⣹⣿⣿⠟⠋⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⢶⣶⠁⠲⠄⠠⠠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⣶⣄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠠⠿⠋⠁⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢻⣿⣿⣿⣿⡯⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⠷⠆⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢀⡿⢿⣦⣀⡀⢨⡉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠋⠙⠋⠀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢿⣿⣿⣿⣿⣿⣿⢯⣿⣿⡿⠟⠋⠁⠙⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠙⠷⠆⠁⠀⠀⠙⢿
⠻⠛⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣾⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠛⢯⠉⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⡈⣘⡿⠿⣿⣿⣿⣿⠿⢿⡉⠡⣿⣿⣻⣟⠁⠀⠀⠀⢠⣤⡄⢠⣤⡄⣤⡄⣤⡄⣤⣭⢠⣭⢹⣶⢢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠋⠀⠀⣾⣿⣿⡿⣯⠀⠀⠙⢿⣿⣿⣍⡋⠁⣤⣆⡆⢸⣿⡇⢸⣿⡇⣿⣷⢸⡇⣿⣿⢸⣿⠸⣿⣾⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢼⣿⠁⠀⠀⠀⠀⠀⢙⣿⣿⡶⠾⠀⠀⠀⠈⠻⢿⢿⣿⠙⠻⣝⠛⢸⣿⣷⢸⣿⡇⣿⡹⣾⡇⣿⣿⢸⣿⢰⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⢄⢬⡿⠇⠀⠀⠀⠡⠄⠀⠐⠀⠀⠛⠀⠀⠙⢿⡸⠿⠿⠸⠿⠇⠿⠇⠿⠇⣝⠿⠾⡟⠸⠿⠸⠿⢤⡄⠀⠀⢤⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠂⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠾⣶⣄⠀⢀⣿⣿⡿⠟⠙⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠾⠿⣷⠀⠶⠟⠠⠴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣏⣽⣿⣿⣦⣶⡇⠀⢙⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⢏⣉⠏⠹⢿⣧⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠈⠉⠁⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⡖⠈⢻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠿⠛⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣄⡇⠀⠀⠀⠀⠿⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣶⣄⢠⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠉⠙⢛⣻⣷⠘⣒⠻⣿⣿⡀⠀⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠉⣿⣿⣿⣿⣿⠟⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣤⡀⠀⠀⠺⣿⡄⠈⠀⢀⡀⠀⠀⠀⠀⠀
⠋⠉⠛⠋⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⡉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣹⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣾⣦⣄⠀⣠⣤⡀⠀⠀⠉⠉⠉⠁⣠⣿⣿⡿⣿⣽⣿⢻⣿⣿⣿⡄⠉⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠤⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⠿⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⠇⣾⣿⠹⠏⠁⢠⣤⡄⢠⣤⡄⣤⡄⢩⡝⣧⣬⢩⣽⢱⣶⢢⣶⣶⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣁⣼⠿⠿⣿⣿⣿⡟⠉⣽⣿⣰⣜⣿⡿⢼⠶⠆⢸⣿⡇⢸⣿⡇⣿⣧⢸⡇⣿⣿⢸⣿⠘⣿⣾⡏⠙⠿⠿⠿⠟⠈⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⣾⣿⣿⠿⡆⠀⠈⠻⣿⣿⣿⢗⣾⡶⢶⢸⣿⡇⢸⣿⡇⣿⡹⣾⡇⣿⣿⢸⣿⢠⣿⢻⣧⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠙⣿⣷⡶⠶⠀⠀⠀⠘⠉⠁⢸⡿⠃⠀⠸⠿⠿⠸⠿⠇⠿⠇⠿⠇⣝⠿⠾⠟⠸⠿⠸⠿⠄⠀⣀⠀⠀⠀⣀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣀⡙⠋⠀⠀⠉⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠈⠁⠀⡤⠀⢴⣿⣿⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠶⠶⣴⡀⠰⠄⠠⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠉⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣳⣾⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢏⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⣿⣿⣿⣿⣿⣿⣿⡗⢸⣿⣿⣿⡿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣥⣈⢑⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠈⠛⠛⠛⢿⣧⠙⣂⠻⣿⣿⣇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⣶⡾⢿⡶⣾⣶⣿⣿⣿⣿⡿⠛⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⢹⣷⡄⠈⠀⠀⣀⠀⠀⠀
⣿⣿⣿⠏⢿⣿⠿⢿⡿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⣀⡀⠀⠀⠀⠀⠙⠿⣿⣼⣇⠀⠉⣻⣿⣿⡟⠀⠀⠀⠉⠙⠻⠿⠿⠛⠛⠉⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠀⠀⠁⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣾⡇⢠⣤⡄⢠⣤⡄⣤⡄⢬⡍⣤⣭⢩⣿⢡⣤⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠛⢛⠉⢠⣋⣹⠿⢿⣿⣿⣿⠛⢻⣉⠀⢾⣿⡟⣏⣀⢸⣿⡇⢸⣿⡇⣿⣷⢸⡇⣿⣿⢸⣿⠸⣿⣾⡏⠙⢿⣿⣿⣷⣒⠖⠐⠛⠉⠉⠉⠛⠛⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠞⠁⠀⢀⣾⣿⣿⣯⡀⠀⠘⢿⣿⣾⣥⣝⣻⢸⣿⡇⢸⣿⡇⣿⡹⣾⡇⣿⣿⢸⣿⢠⣿⢻⣧⢀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⠀⠈⢿⣿⣧⣬⡅⠀⠀⠀⠹⠛⢲⣿⠍⠸⢿⠿⠸⠿⠇⠿⠇⠿⠇⠙⠿⠾⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⡀⠈⠿⠟⠀⠀⠒⢀⠀⠐⠀⠘⠋⠀⠀⠉⠛⠀⠀⠀⠀⠀⠈⣣⣤⠟⠋⠓⠀⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣤⠤⢴⣄⠠⠰⠶⠆⠀⠀⠀⠀⠀⢈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠛⠿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⠛⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣭⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠏⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠈⠻⠻⣿⣿⡟⠻⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠙⢻⣿⣿⣿⣿⣿⣿⣿⡦⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⣄⣀⠀⠀⠀⠀⣠⣿⣦⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⠙⠿⠿⠿⣿⡏⠛⠓⢾⣿⣿⡟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣧⢼⡉⠉⠀⠀⣀⣸⣿⣿⠏⠉⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⠄⠀⠀⠀⠀⠉⠉⠀⠒⠈⠛⠛⠁⠀
⣿⣿⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⣀⠀⠀⠀⠈⠛⠛⠛⠿⣄⣠⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠂⠀⠀
⣿⣿⣟⠋⠀⠹⠏⠁⠁⠀⣿⣿⣿⣿⣿⣿⣯⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣷⢺⣥⡄⢠⣤⡄⣤⡄⢤⡄⣬⣭⢠⣬⢹⣿⢻⣿⣷⣿⣿⣿⣶⣶⣦⡄⣄⣠⣀⣤⣴⣾⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠟⠛⠟⣻⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⣿⣿⡿⢸⣿⡇⢸⣿⡇⣿⣷⢸⡇⣿⣿⢸⣿⠘⣿⣾⡏⠿⠿⢿⣿⣿⡿⠻⣿⠣⠿⠟⠛⠿⠿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠜⠊⠁⢀⣼⣿⣿⡟⠀⠈⠻⣷⣿⣿⡗⢷⢸⣿⡇⢸⣿⡇⣿⡹⣾⡇⣿⣿⢸⣿⢰⣿⢻⣧⠀⠀⠀⢿⣿⠿⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⣼⣿⣿⢇⢲⡄⠀⠀⠈⠻⠿⢟⣷⠸⠿⠿⠸⠿⠇⠿⠇⠿⠇⡙⠿⠾⣟⡸⠿⠸⠿⢄⠈⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠃⠹⣿⣿⡟⠓⣀⠀⠀⠀⠀⠸⠟⠁⠀⠙⠇⠀⠀⠀⠀⠀⢀⡿⠟⠁⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠰⢠⠀⠀⠀⠠⠠⠴⠆⠀⠀⠀⠀⠀⠀⠰⠤⠀⠉⠋⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⣠⣶⣿⣿⣤⡴⠆⢀⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣠⣾⣏⠀⣠⠉⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⠀⠀⠀⣨⣿⣿⣿⣿⠛⠛⠋⠉⠛⠃⢀⣀⣀⠀⢰⣿⣿⣿⣿⣷⣤⣾⡟⠁⠘⢯⣿⣧⠴⣆⠐⠛⠿⠿⠿⣿⣿⡙⢻⣿⣿⣿⣿⣆⣀⣀⢀⣿⣯⣿⣿⣿⣿⠀⠁⠀⠜⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠐⠋⣛⡲⠦⠉⠀⠀⠀⠀⠀⠀⠻⠇⢈⣿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣾⣤⣠⠄⠀
⠀⠀⠀⠀⠀⠀⠀⣈⣶⣷⣤⣤⠀⠸⣿⠿⡿⣿⣿⣿⣿⣟⣻⣿⣷⣶⣦⠀⠀⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣀⣀⣀⠀⠀⠀⠠⣶⣿⣧⣤⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣄⣃⣀⣘⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠆⠹⢿⣿⣿⣶⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⣿⣿⠟⠁⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣭⠉⠉⠉⠈⠙⠻⠟⠛⠛⠯⠙⠁⠀⣀⣴⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⠛⣛⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣻⣷⡀⠀⢀⣶⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⣿⣿⡿⠟⠋⠀⠻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣏⣀
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⡀⣙⣿⡉⠀⠀⣿⣿⣯⣭⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠁⠀⠀⠀⢀⣶⣿⣼⣿⣿⣄⡀⠀⢀⠛⠛⠋⠉⠉⠋⠉⠉⠁⠙⢿⣿⣿⣿⡿⣿⣿⣿⣯⣤
⢀⡀⢴⣦⣄⣤⣶⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢤⣄⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⡿⢤⣄⠀⠀⠀⠀⠀⢀⣀⣤⡴⢠⡞⣿⠀⣿⣿⣿⠇⣶
⠈⠀⠀⢠⣿⡿⠿⠀⠀⠀⠻⢿⣿⣿⣿⣧⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣙⠀⠀⠀⢀⣴⣾⣿⡿⠁⣿⣿⣯⣾⣿⣿⣠⠟⠉
⠀⠀⠈⢸⣏⡀⠀⠀⠀⠀⠀⠈⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣯⡄⣤⣤⣤⣤⢠⣤⢠⣤⢠⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠈⠛⣿⠛⢱⣶⣿⣿⣿⣿⡿⠋⠁⠀⠀
⠀⠀⡰⠇⠉⠁⠀⠀⠀⠀⠀⠀⣵⣿⠗⠀⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⡟⠘⠉⠀⠙⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⣤⣸⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣷⣾⣿⡿⠛⠛⠉⠀⠀⠀⠉⠁⢰⡟⠀⣾⣿⣿⣿⣿⢿⣿⣇⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣟⣻⣯⣿⣷⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣤⣼⣿⣿⣿⣿⠿⠿⠿⠇⠿⠧⠿⠿⠙⠿⠿⠟⠸⠿⠹⠿⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠓⠂⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣿⣿⡿⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⡅⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠
⠐⠖⠶⣶⠿⢶⠄⠰⠶⠶⠖⠀⣠⣿⣿⠿⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣶⣆⠀⠀⠀⠀⣀⣀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⣀⣴⡿⠋⠩⢛⣻⣏⡀⡀⠒⠤⣿⣿⣿⣿⠉⣭⣿⣿⣿⣿⠇⠀⠀⠀⣀⣀⣠⣾⡇⠀⠀⠀⣼⠏⠤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡀⠠⠻⠩⢤⠐⠂⠀⠀⠉⠙⠛⡀⠙⣻⣿⣿⣿⣤⣤⣄⣸⣿⣿⣻⣟⣳⠀⠀⠐⠋⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠴⠛⠉⠁⠙⠛⣧⣿⣿⣿⣿⣿⣿⣤⣧⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣄⠀⣶⡖⠀⠀⠁⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣷⣿⣦⡆⢠⠴⠄⠀⠀⢨⣿⣷⣴⡄⠀⠀⠀⣾⣟⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⠶⠶⠶⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠉⠉⠀⠀⠙⠛⠙⠃⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡿⢷⣶⣿⣥⣿⣿⣭⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣭⣥⣼⣇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠿⠿⣿⣿⣧⣼⣿⣏⣀⣤⣤⣿⣿⣿⣿⣿⣿⣭⣥⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⣿⠋⣡⣶⣤⣬⣿⣿⠿⣿⡿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣀⣯⠤⠤⠴⠦
⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣴⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣤⣦⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⠟⣿⣿⣿⠶⠀⢀⣀
⠀⠘⠛⢳⣾⣿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⡄⠀⠀⠀⣤⣶⡾⢰⣦⠎⢠⣿⠿⣏⣸⣿⣿⣿
⠀⠀⠀⡾⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⣷⣾⣥⡀⠀⢸⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⠟⠀⠈⠛⠒
⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣧⣀⡀⠹⣁⣀⣸⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡇⣿⣷⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⠻⢿⣾⣿⠿⣿⣿⣶⣿⡛⠛⣿⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣴⣾⣿⣿⠟⠋⠉⠉⠉⠁⠘⠛⢸⣿⡟⢹⣿⡇⣿⣿⣿⣇⣿⣿⢸⣿⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⣿⣿⣿⣦⣬⣥⣴⣿⣷⣀⠀⠀⠀⢀⡄
⠛⠛⠏⠉⣸⣿⣿⢿⣍⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠧⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠀⠈⠉⠁⠀⠸⢿⣯
⠀⠀⠀⠀⠉⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣠⣶⠿
⠀⠶⠶⣾⠿⢷⠿⠻⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⡶⣷⣾⣿⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣟⠻⣷⣶⣾⣿⣦⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠀⣾⣿⠿⢿⣿⡇⠘⢻⣿⣿⣿⣧⣤⣤⡀⣸⣿⣿⣿⣟⣿⡆⠀⠰⠋⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⣆⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠈⡟⠀⢨⡿⠟⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣥⡄⠀⠀⠀⣠⠤
⠀⠀⠀⠀⢀⣰⣤⣶⡆⡀⠈⠛⠛⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡄⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀
⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣦⣤⣤⡔⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⣁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⢿⣟⣛⣹⡆⠈⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢻⣿⡟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡆⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⢈⠛⠷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣯⣤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⢀⣿⣿⣿⠿⠋⠙⠿⠿⣿⣿⡿⣿⣿⣿⣿⡶⠀⣀⣀
⢦⣴⣾⡇⠀⠈⢻⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⠂⢼⡷⣼⣿⡟⠋⢀⣤⣤⣴⢀⡜⢻⠇⣿⣷⢿⣃⣾⣿⣿⣿
⣼⡿⠋⠃⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣦⣁⠀⠉⠁⣴⣾⣿⣿⠃⢸⣾⣿⣴⣿⣿⡧⠋⠀⠹⠿⠒
⡠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠈⢟⣋⡁⣷⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠻⠛⠋⣻⣿⣿⣿⣿⠛⠃⢠⣤⣴⢠⣤⡄⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⠿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣏⣉⠁⠀⣀⣀⣠⣴⣾⣿⣿⡿⠋⠀⠀⠀⢸⣿⡿⢸⣿⡇⣿⣷⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⣀⠉⠛⢻⡿⠛⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣭⣿⣷⣦⡀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣷⠀⠀⠉⢡⣄⣾⠇⢀⣾⣿⣿⣿⣟⡿⠿⢿⣿⣿⠟⠛⠙⠛⠿⠗⠀⠀⠻⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠸⢿⠀⢸⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠙⠛⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⢿⣿⣿⡿⠋⠛⢳⡄⠀⠀⢀⣠⣤⣤⣤⣿⣿⡋⠁
⠀⠷⠶⣶⠏⢷⠶⠱⠶⠶⠖⠀⠸⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣴⣾⣷⣶⣾⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣤⣶⣿⣿⣿⣿⡃⠙⠋⠉⠛⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⢠⣿⠟⠉⠉⠉⣧⠀⠸⣿⣿⣿⠿⣿⣿⣶⣾⣿⣿⣾⣿⣶⡆⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣷⣶⣶⠺⢿⡦⠀⠀⣠⣤⠀⠘⠋⠀⠀⠀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣴⣴⣾⣇⣀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠉⠉⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⣀⣠⣶⣐⣻⣿⣽⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⠶⠶⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⣿⣿⣿⠿⢿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⣿⣿⣷⣿⣇⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠱⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⡿⠿⠛⠉⠛⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡉⡉⢀⣀
⠀⠀⢀⡄⠀⣰⣶⣶⣾⣿⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⡀⣸⣿⣿⠇⠀⠀⠀⠀⡀⠀⡌⢙⠿⣿⢹⣿⣽⣿⢫⣵⣿⣿⣿
⠛⣿⣿⣧⠀⠙⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥⣈⠿⠃⠀⠀⢠⣤⣿⣿⣿⠁⣯⣶⡏⣸⣿⣿⢹⠟⠛⣿⣟⣛
⢸⠿⠋⠻⠃⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣷⠀⠀⠘⢿⣿⠟⢣⣤⣿⣿⣿⣿⣿⠛⠁⠀⠀⠈⠀⠀
⡼⢤⣆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣷⣦⣤⣈⣷⣶⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⢱⣿⣿⣿⢫⣤⡽⢫⣭⡅⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⠉⠙⠿⢿⣿⣅⡀⠀⠀⠀⠀⠀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⢿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⢸⣿⡇⢸⣿⡇⣿⣷⣹⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⣀⠀⠉⢹⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣦⠀⠀⠠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣄⣀⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⡿⠋⠁⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣧⠀⠀⠉⢀⣀⣿⠀⢠⣿⣿⣿⣿⣿⣭⡉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣀⣀⣠⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠸⠿⠿⠿⠿⠿⠛⠁⠈⠙⠇⢀⣀⣴⣿⣭⣿⣿⣿⣿⣆⣀
⠀⠖⠲⣶⠏⢶⠄⠰⢶⣿⣿⡟⠋⠁⠀⠀⠀⣼⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⣀⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣾⣿⣷⣦⣤⣤⣷⠀⠘⠋⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠐⠒⠀⠀⠘
⠀⠀⠀⢶⣄⣾⣿⣷⣶⠘⣁⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣯⣤⢤⠉⢿⣿⣿⣿⣄⣤⣶⣶⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⠿⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⠟⣿⣿⡿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠐⠀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠄⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⠻⠋⠀⠛⠏⠁⠇⠘⠿⣯⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡏⠉⠛⠋⠙⠛⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣛⣉⣀⣠⡙
⢀⣤⡄⠠⢿⣿⣿⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⢈⡍⣻⢿⣿⢹⣿⣻⣿⢻⣿⣿⣿⣿⣷
⣿⣿⡄⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢠⣤⣿⣿⣿⢱⣿⣾⣏⣼⣿⣿⣿⡟⢿⣿⠛⣿⠿
⠃⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⠀⠀⠘⢿⡿⠟⣧⣼⣿⣿⣿⣿⣿⠿⠋⠀⠈⠉⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⠛⢻⣿⣿⣿⠉⠋⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣤⣈⣷⣶⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡀⠀⢨⣿⡿⠃⠀⢀⠹⠟⠋⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣯⡉⠀⠀⠀⠀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠛⠉⠀⠁⠀⢺⣿⡅⢠⣤⡄⣤⡄⣤⣤⣭⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⡀⠐⢰⣿⣿⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⢸⣿⡇⣿⣿⣿⡿⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⣹⠏⠈⣿⣿⣿⣟⡛⠿⠿⠋⠁⠀⠀⠈⠉⠀⠀⣘⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢸⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⠀⣸⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣠⣤⣀⣸⣿⣿⡿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣤⣀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣾⣿⣿⣿⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠉⣿⡟⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣾⣿⣭⣿⣿⣿⣿⣷⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠉⠙⠛⠛⠛⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠖⠲⣶⠏⢶⠄⠰⠶⠶⠖⣨⣿⣶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣇⠀⠀
⠀⠀⠀⢀⠀⢠⣶⡃⡀⠀⠀⠈⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣄⡀⠀⠀⠀⣸⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇⠀⢰⣾⣿⣿⣿⣿⣋⣀⡀⠀⣿⣾⣤⣤⠀⠀⣠⣼⣾⣟⠛⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢻⠿⢿⣿⡷⠶⠶⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠉⢻⣿⣿⣷⣿⣿⣿⣿⣿⣇⣠⣼⣿⣿⣿⣿⠉⠉⠉⠉⠀⣸⣹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠿⠗⣴⣶⣤⣤⣿⣿⣯⣥⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣆⡀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣤⣿⣿⣿⣿⣿⠟⢻⣿⢃⣼⣿⡯⠀⣤⡀⣰⣿⣿⣿⣿⣿⣿⣫⣴⣶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢹⣿⡟⠁⠀⣼⣿⣿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⡟⠿⢧⣄⠘⠿⠛⠛⠋⠁⠀⠿⠛⣿⣿⣿⣿⣿⣿⣿⣁⣼⡧⠀⠄⠀⠀⠀⠀
⢀⣀⠀⠀⢴⣶⣶⣾⣿⣗⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠛⠛⠻⠿⣿⢛⣿⢻⣿⡷⢒⣶⣶⣶⣷⣄
⣿⡿⠀⠀⠈⢿⣿⣿⣿⣿⣦⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠆⡤⠀⠈⢘⡟⣟⢏⣀⣿⣿⣿⣿⣿⡉
⠁⠀⣠⣰⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡛⠃⠀⣿⣷⣆⣾⣷⣯⡘⠁⠀⠋⠀⠚⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠿⣿⣿⣿⣿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡙⣯⣀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠁⠁⣴⣿⠟⠛⠋⣀⣴⣾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠛⠻⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⣼⣿⡗⠀⠀⠼⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣶⣄⡀⠀⠀⠀⣀⣶⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⢠⣤⣿⢫⣤⡄⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠿⣿⣿⣻⠿⡋⠉⠉⠈⠉⠁⠀⠀⠀⠻⣿⣤⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣴⣶⡾⢿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⡴⠶⣶⣾⣿⣯⡀⢀⣄⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣀⡀⠀⠀⢀⣠⣾⣿⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠾⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠟⠻⠿⠿⠏⠀⠈⠉⠻⣿⣿⣿⣿⣿⡅⠞⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⠛⠛⠋⠁⣀⣠⣶⣿⠿⠿⠻⣷⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡃⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠁⠀⠀⠀⠈⠻⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡿⠃⠀⠀⠀
⠀⠸⣷⣼⣿⣷⣶⣀⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⡋⠉⠉⠉⠁⣈⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣟⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠻⣿⡿⠛⢹⣿⡿⠁⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣠⣤⣿⣿⣿⣿⡿⠻⢿⣿⣏⣽⣿⡏⠈⣤⣤⣿⣿⣿⣿⣿⣿⣿⣯⣅⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⠀⢀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣇⡈⢩⡿⠙⠛⠛⠁⠘⠿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣥⣤⡤⠄⢀⡀⠀
⠀⠀⠀⣀⣀⣀⣾⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠉⢉⡉⠙⢛⠉⠁⠁⠀⠀⢤⡄⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣤⣴⣗⠀
⡆⠀⠈⠻⣿⣿⣿⣿⣿⣅⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⣤⣴⣶⢷⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⠟
⡅⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⠟⢻⠿⠛⠛
⢁⣦⣤⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣯⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⠏⣼⣿⣿⣧⣶⣿⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠩⠿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠘⣾⣿⣿⣿⠿⠛⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣤⡀⠀⠀⠀⢴⣶⡆⠄⠀
⠀⠀⠈⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠹⢿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠟⠁⠃⢘⣿⣿⣀⡀⠀
⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢫⣤⡄⣤⡄⣤⡌⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⣿⣿⣿⣿⣿⣷⠠⠴⠀⠀⠀⠀⣶⣾⣿⣿⡿⠓
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣧⢸⣿⡇⣿⣿⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣿⢷⣦⣾⣿⣿⣩⣿⣧⣤
⢀⢀⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠉⠀⠀⣀⣤⣤⣤⣤⣀⣀⣀⣴⣾⣿⢻⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⡿⠛⠋⠙⢿⣿⣿⣿⣿⡿⠟⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣌⠉
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⣷⣿⢿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⢿⣿⣛⣰⣶⠀⠀⠀⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠈⠛⢻⣿⣿⡇⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢘⣿⣿⡿⠿⠛⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣁⣠⡴⢄⣀⠀⠀
⠀⠀⢠⣤⣤⣤⣾⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣀⠿⡾⠎⠁⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣴⣿⣀⡀
⠃⠀⠈⢻⣿⣿⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⡆⠀⠀⠀⠀⢀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⠭
⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⢿⡟⠛⠃⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⠻⠿⠛⠛⠲
⠀⠀⠀⠀⠀⣘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⠿⠟⢃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⡖
⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠁⣾⣿⣿⢿⣯⣥⣶⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⣠⣶⣴⣤⠿⠀
⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠁⠀⠀⢠⣾⣿⣿⣿⡿⢿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠟⣿⣿⣷⣿⣿⣿⣿⣿⣟⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣿⣿⢿⠟⠀⠲⣷⣶⣿⡏⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣶⣶⣶⣤⣤⣤⣴⣾⣿⢿⣿⡟⢩⣤⡄⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠘⣿⣿⣷⣤⡄⠀⣽⣿⣯⣿⣿⣿⣿⣿⣟⣺⣿
⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⢻⣿⣿⣿⣿⣿⡿⠟⢸⣿⡇⢸⣿⡇⣿⣷⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠋⠁⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿
⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣤⣤⣴
⠿⢪⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠿⣿⣷⣿⣧⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣶⣷⣿⣿⣿⣿⢿⠻⣿⣿⢣⣿⣿⣿⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠞⠋⠈⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡷⠶⠾⢛⣶⡦⠀⠀
⠄⠀⢿⣿⣿⣿⣿⣿⣏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⢀⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀
⠀⠀⠀⠻⢿⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠙⡿⠛⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠟⠋⠛⠉⠻⣿⣿
⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣽⣿⣿⣿⣯⣿⣿⣷⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀
⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠉⠀⣨⣾⣿⣿⣿⣿⣿⠿⠟⡛⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣾⣿⣿⣿⣟⡇⠀
⠀⠀⠀⠀⢤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⣀⣤⣶⣾⣿⣿⣿⡿⠁⠈⠉⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠛⢋⣻⠿⠿⠟⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣏⠙⠀⠀⠸⠏⢀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠛⠛⠻⠻⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠟⠛⠁⠀⢠⣤⡄⢠⣤⡄⣤⡄⣤⡄⣤⣤⢠⣤⢠⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠸⣿⣿⣦⣀⣀⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣷⣻⡇⣿⣿⢸⣿⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⣿⡇⣿⣿⢸⣿⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣻⡿⠛
⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠿⠇⠿⠇⠙⠿⠿⠟⠸⠿⠸⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣾
⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠍⠀⠀⢼⣗⡀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⡏⠰⠛⠀⠀⠠⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢙⣶⣮⡉⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣆⣿⡿⠁⢹⡆⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⣷⠀⠀⠀⠀⠀⢀⣼⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠙⡛⣿⣿⣿⣿⡿⠛⠛⠉⠀⠈⠉⢨⣽⣿⣛⣿⣟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣼⣧⣼⣭⣴⣾⣿
⠀⠀⠀⠀⠀⢹⣿⣽⡟⢳⣿⡆⡀⠀⢠⣾⡏⠿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⢠⣿⡏⣿⣿⣷⣭⣻⣿⣿⣿⣿⣿⣟⠋⠈⠛⠛⡷⠌⠛⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⢚⣻⣿⣿⣾⣿⣷⣿⡠⣶⣏⣉⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⣿⣷⣤⣴⣶⣶⠀⠀⢀⣾⣿⣧⣴⣿⣿⣿⠛⠛
⠀⠀⠈⠁⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⡻⢈⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⢀⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠙⠷⠃⣿⣿⣿⣿⣿⡉⣆⣿⣿⣿⡟⣿⣿⡿⢿⠷⣽⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⠛⠉⠉⠉⠉⠉⠁⠀⣴⣻⣿⣿⣟⢻⣦⡈⠀⣀⠈⠘⣧⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠸⢿⣿⣿⣿⣿⣿⠻⠛⢿⣧⣿⣿⢿⣿⣿⣿⣯⠙⢿⣿⣿⣿⣶⣆⡀⢀⣀⣤⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣽⠋⠸⣋⠀⣶⡿⠁⠠⠟⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⡟⠋⠹⠿⢿⣿⣿⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣴⣦⣤⣬⣨⣭⣯⠉⠈⠉⠈⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡀⠨⣿⣦⣻⣿⣿⣤⣵⣿⠒⣉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠻⠛⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠩⠀⢸⡿⣿⣿⣿⣿⠿⠿⠏⠁⢉⣦⣤⣤⣽⣷⣤⣀⡀⠀⣠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠠⣤⣿⣿⣽⡿⠑⠘⣺⣿⣿⣿⣿⠻⣉⠉⠙⠛⠻⠿⣿⡶⢿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠃⠙⠛⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠠⠀⠘⠈⠛⠀⠁⠀⠀⠈⠛⠛⠿⠟⠻⠐⠀⠀⠀⠘⠀⠆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⢷⠀⠐⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣤⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠍⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣽⣿⠟⠀⠀⠠⠟⠀⠀⢀⣈⡀⠀⢀⠀⠀
⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⣆⣀⣴⠋⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠂⠀⠀⠀⠁⠀⠀⠘⠋⢁⣾⣿⡿⢷
⠀⠖⠶⣶⠿⢿⣶⠴⠶⠶⠖⠀⠀⠐⠈⠉⠀⠏⠀⣴⣼⣙⡿⢟⣵⣿⣿⠟⠏⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⣉⡸⠿⠋⠫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣢⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣾⡇⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢚⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⠘⠋⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠶⠀⢸⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠁⣦⠀⠀⠀⠀⠀⢠⣼⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢛⡛⣿⡿⢿⣿⠟⠛⠛⠉⠀⠉⠉⢀⣽⣿⠉⣽⡟⢛⣿⣿⣿⣿⣿⡿⠉⠹⣿⣿⣞⢿⠐⠂⠀⠀⢠⣤⣶⣤⣤⣾⣿
⠀⠀⠀⠀⠀⢨⣿⣽⡿⢶⣿⣆⡀⠀⢀⣴⡎⠛⣿⣿⣸⣿⣿⣿⣿⡋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣷⣾⣿⣿⡂⢀⣿⠙⣿⠹⣤⡈⣺⡿⢿⣿⣿⣟⣀⡀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢻⠛⢿⣿⣿⣿⣋
⠀⠀⢀⡀⠀⠘⣻⣿⣿⣾⣿⣿⣿⣀⠘⣁⣀⣀⣻⣿⣿⣿⣿⣟⣛⣧⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣻⠒⣿⣦⣿⣿⣿⡿⠿⠟⠉⠙⠿⣿⣦⣤⣤⡄⠀⠀⠀⠀⢰⡀⣠⡈⠀⠈⠀⠉
⠀⠀⠈⠁⠀⣿⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠛⢿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠟⣿⣿⣿⣿⣿⣿⠗⠀⠉⠀⠻⣿⣿⣿⣾⣿⠿⠛⠻⠧⠀⠀⠀⠀⠀⠈⣿⣿⡟⠁⠀⠀⣴⣾⣿⣿⣿⣿⣶⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠓⠀⡿⠿⣿⣿⢏⠡⢼⣿⣿⣿⡏⣿⣿⡟⠁⠀⠈⣿⣿⠿⠟⠃⠘⠛⠉⠀⠀⠀⠛⠋⠉⠉⠉⠀⠀⠀⠀⡤⢻⣿⣿⡟⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠴⠀⠀⢠⣿⡇⢹⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠈⢙⣿⣿⣿⣿⣿⠿⠻⢿⣤⡿⠋⢾⡗⢲⣶⣄⠀⠀⣶⣶⣦⣄⢀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣤⠃⣬⠁⢙⠁⠙⣀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⣤⣤⣼⡏⠁⠘⠙⢲⣷⣄⣠⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣴⣦⣤⣄⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⣛⣹⣵⣿⣿⣿⣿⣿⣿⣷⣤⣀⣄⣤⣠⣿⣤⣙⠑⡿⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣤⣤⣤⣤⣘⣿⣟⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠐⠿⠁⠀⠀⣠⣤⣀⡀⠀⢀⣄⣀⢀⣠⣿⣿⣿⣵⣽⡧⠀⢨⣿⣿⣿⣿⣿⣷⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠛⢿⣿⣿⣿⣿⣿⡟⢣⣿⣷⣶⣾⣿⡭⠉⠻⢷⡾⠋⢿⣿⣿⣿⣿⣿⣿⡿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠙⠛⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠠⠄⠀⠈⠙⠛⠈⠀⠀⠈⠙⠉⠻⠿⠟⣿⠇⠀⠀⠈⠃⠶⣖⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣽⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠩⠁⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠋⠀⠀⠸⠟⠀⠘⢿⣿⡿⢿⣿⣿
⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⢆⣴⣟⣿⡛⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠻⠛⠀⠀⠀⠀⠀⠀⠀⠙⠃⣴⣿⣿⣿
⠀⠖⠶⣶⠿⢿⣷⡴⠶⠶⢖⠀⠀⠀⢂⡉⠉⠉⠔⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠠⠯⣉⡸⠿⠉⠿⠌⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣐⡀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⣼⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡰⠉⠞⠋⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠢⠀⢺⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡙⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶
⠀⠀⠀⠀⠀⢀⠄⣰⣮⢏⣠⠀⠀⠀⠀⠀⣠⣼⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣉⣿⣿⣿⣿⣿⣟⠛⠋⠁⠉⠉⠉⢈⣽⣿⣉⣼⣟⢻⣿⣿⣿⣿⣿⡿⠉⢿⣿⣷⣻⣿⠐⠂⠀⠀⢠⣤⣷⣤⣶⣾⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣤⠀⠀⢠⢾⡏⢙⣿⣿⣼⣿⣿⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⡆⢂⣿⠙⣿⠿⣦⣍⣻⡿⠟⣿⣿⣿⣿⣀⡀⠉⠛⠁⠀⠀⠀⠀⠀⠻⠛⠻⠽⣽⡿⣟
⠀⠀⢠⡀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡀⠌⣀⣀⣈⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⡿⣿⣿⣻⠒⢿⣶⣿⣿⣿⣿⡿⠿⠟⠉⠙⠻⣷⣤⣶⡆⠀⠀⠀⠀⢰⠀⣠⡀⠀⠈⠁⠉
⠀⠀⠈⠁⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠀⢻⣿⣿⣿⣾⣿⡿⠛⠻⡷⠀⠀⠀⠀⠀⠀⠈⣿⡟⠋⠀⠀⣤⣿⣿⣿⣿⣿⡖⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠷⠀⡿⠿⣿⣿⣿⠳⣽⣿⣿⣿⢻⣿⣿⠛⠁⠀⠸⣿⠿⠿⣿⣿⠛⠛⠋⠉⠉⣹⣿⣿⣿⣿⣿⣿⠀⠀⠀⡤⣻⣿⣿⣟⣡⣤⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠠⡯⠤⠀⠀⢰⣿⡇⢸⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠈⢙⣿⣿⣿⣿⣿⠛⠻⢿⣼⣿⣿⣾⡶⣶⣦⣄⠀⢰⣾⣿⣷⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣤⠃⣬⠁⣹⠉⢙⣁⠀⣰⠇⠀⠀⠀⠉⠀⠀⠀⠀⢁⣤⣤⣤⡾⠟⠁⠀⠀⠠⣤⡀⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣼⣦⣤⣄⣀⣽⣿⣧⠌⠁⠉⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣿⣤⣽⠑⣿⣤⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⣀⠐⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠚⠛⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⢀⣤⣾⣀⠀⠀⠀⠀⠀⠀⠹⠷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠑⠉⣿⣽⣿⣿⣿⣿⠇⣰⣶⣶⡤⠴⠒⠉⠀⠀⢶⡀⠁⠹⢿⣻⠟⠛⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠈⠛⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡄⠀⠀⠉⠛⠀⠀⠀⠀⠉⠛⠛⠻⢟⡀⣄⠄⠀⠀⠀⠣⢤⣆⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠐⢷⣶⣾⣷⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣬⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠝⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣭⣿⣿⣿⣿⠃⠀⠀⣼⠁⠀⠀⣸⣫⣯⢀⣀
⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢶⣄⢶⣴⣾⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠛⠋⠀⠂⠀⠈⠀⠀⠀⠛⠉⣵⣿⣿
⠀⠗⠶⣶⠟⢷⢾⣶⡶⠶⠖⠀⠀⠀⠒⠉⠛⠿⠋⢄⠉⣀⣿⣿⣿⣿⣿⣷⡾⠿⠋⠹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠠⠀⠼⢏⣉⡿⠟⢿⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣐⡀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣤⠷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣹⣿⡀⠀⠀⠀⠉⠘⠃⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠢⠀⢸⣿⣿⡛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡙⢛⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠄⣰⣎⢏⣠⠀⠀⠀⠀⠀⡀⣼⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣙⣿⣿⣿⣿⣿⣿⣿⠟⣋⣉⠉⠉⢈⢼⣿⣙⣽⣿⢛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣻⢿⠐⠀⠀⠀⢠⣤⣷⣤⣤⣾⣿
⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣄⠀⠀⣤⢺⠏⢙⣿⣿⣸⣿⣿⣿⣿⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⡿⣿⢻⣷⣍⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠻⠟⠛⠉⣯⡟⠉
⠀⠀⢀⣀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣆⠉⣀⣀⣈⣿⣿⣿⣿⣿⣟⣻⣦⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⣿⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠀⢀⠀⠀⠈⠀⠉
⠀⠀⠀⠁⠀⣿⣻⣿⣿⣿⣿⣿⣿⡟⡛⣻⣿⣿⣿⣿⣾⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠻⢿⢿⣿⣿⣿⣿⣿⣿⠟⠻⣷⣄⠀⠀⠀⠉⢹⣿⣿⣿⣿⠇⠀⣤⣷⣶⣶⣿⣷⡔⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠳⠀⡿⢿⣿⣿⣏⠣⣼⣿⣿⣿⠉⣿⣝⠋⠀⠀⠈⣿⣿⠿⣿⡟⠛⠛⠋⠉⠁⣿⣿⠛⠉⠉⠉⠉⠉⠁⠀⢴⣿⣿⣿⣿⢫⣼⡏⠀⣀⠀⠐⣶⣶⡀⠀⢸⣿⣿⣿⣿⠆⢸⣿⡇⢸⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠈⢹⣿⣿⣿⣿⡿⠛⠛⢿⣼⣿⣻⣾⡆⣶⣦⣄⠀⢰⣶⣾⣶⣄⣀⣰⣾⣿⣇⣀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⠿⠀⠀⠀⠹⣿⣿⣿⣧⣿⠟⠁⠀⠀⠀⣤⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣴⣦⣤⣄⡀⣸⣯⣅⠀⠁⠀⠀⠛⢛⠛⣋⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠏⠀⠀⠀⠀⠀⣿⡿⠟⠛⠁⠀⠀⠀⣀⠀⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣅⠀⣀⣀⣀⣼⣿⣥⣀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣤⣽⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⡛⠋⠙⠿⡟⠋⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠈⠛⠛⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⠀⠀⠀⠙⠃⠀⠀⠀⠈⠛⠛⠛⠿⣷⣠⡦⠀⠀⠀⠀⠠⠶⢻⣿⣏⡛⠛⠁⠀⠀⠀⠀⠀⠲⡶⣶⠳⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠩⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣿⣿⡟⠀⠀⢠⡆⠀⠀⠀⣈⣀⠀⢀
⠂⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠠⣤⣼⣿⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠛⠟⠁⠐⠀⠀⠁⠀⠀⠈⠋⢩⣾⣿
⠀⠗⠻⣿⠿⢷⠶⣶⡶⠶⠖⠀⠀⠀⠐⠈⠙⠛⠿⠋⡀⠁⣐⣿⣿⣿⣿⣿⣷⠿⠏⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠼⣍⣑⠿⠟⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣦⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡛⠻⠟⠛⠛⢿⣿⣿⣷⡜⠀⡀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡌⣽⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⣇⠀⠉⠙⣿⣶⣿⣿⣿⣿⣶⡶⣿⣿⣿⣿⣿⢷⡙⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠎⠀⠀⠀⠀⠀⠀⠀⣤⣽⣷⠨⣿⡄⢬⣾⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⣉⢻⣿⠟⠻⠈⠉⠋⠉⠀⠀⠀⠁⠀⢴⣯⠁⣸⡟⢉⣿⣿⣷⣿⣷⡯⠉⠺⣿⣷⡿⠿⠘⠀⠀⠀⢀⣤⣦⣤⣴⣾⣭
⠀⠀⠀⠀⠀⠀⣀⣈⢺⢲⣿⡀⢀⠀⢠⡺⠃⢘⣿⣏⣀⣿⣿⣿⣿⠉⣿⣿⣿⣿⢻⣿⣶⣿⣿⣿⣿⣷⣶⣶⣷⣾⣶⣶⣿⣶⠂⣠⣯⠘⡏⠘⢄⣠⣾⣿⣟⣥⡀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠻⠛⠋⠭⣯⡿⠛
⠀⠀⠀⠀⠀⠐⠛⢻⣷⣼⣿⣿⣿⣇⠈⣁⣀⣘⣿⣿⣿⣿⣿⣛⣻⣤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢫⣿⡿⣎⣿⣻⠀⢷⣶⣌⣿⣿⣿⡿⣿⣿⠿⠿⣿⣶⣴⣶⡄⠀⠀⠀⠀⠰⠆⣀⡀⠀⠈⠀⠙
⠀⠀⠀⠀⠀⣀⢹⣿⣿⣿⣿⣻⣿⠟⣿⣻⣿⣿⣷⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⣿⣿⣿⣿⣿⣿⠃⠀⠉⠀⢙⣿⣿⣿⣾⣿⡿⠛⠻⠷⠀⠈⠉⠀⠀⠀⠉⢻⡟⠃⠀⢠⣶⣶⣿⣾⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠒⠀⠿⢿⣿⣿⣉⠨⢼⣿⣿⣿⢹⣿⣿⡟⡏⠀⣸⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠛⠋⠉⠉⠁⠀⠀⠀⠀⡤⣹⣿⣿⡟⢡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠇⠀⢼⣿⡇⢼⣿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠁⣹⣿⣿⣿⣿⡟⠛⠻⣧⣼⣿⣹⣿⡏⣿⣦⣄⣀⣰⣿⣿⡷⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣴⠗⣤⢇⣸⠀⠈⣀⠀⣶⡗⠀⠀⠀⠉⠿⠀⠀⠀⠈⢠⣤⣀⣽⣿⠃⠀⠀⣴⣧⡀⢠⡄⠀
⠀⠀⠀⠀⠀⠄⠀⠂⠀⣿⣿⣿⣿⣿⣿⣾⣦⣤⣅⢀⣿⣿⣧⠈⠉⠛⠘⠛⠛⢋⣁⡀⣿⣧⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⣈⣤⡍⣻⣿⣦⣼⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⣄⡘⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣤⣤⠀⡿⣿⣿⣿⣶⣿⣿⣅⠀⢀⣤⣤⣶⣶⣦⣤⣀⡀⠀⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢹⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⠉⠉⣿⣿⣻⣁⣀⡀⠀⠀⠀⠀⣤⠀⠀⠀⣀⠒
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠩⠿⣌⣿⠛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠉⠛⠃⠉⠀⠀⠉⠙⠛⢿⣿⣿⣿⢿⠀⠀⠀⠙⠀⢰⡿⣿⣿⣿⣿⣷⠀⠀⢰⣾⠷⠒⠺⠃⠀⠀
⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠟⠁⢠⣿⣧⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⡜⣐⣿⣿⣿⣿⠋⠀⠀⢺⠁⠀⠀⣀⣀⡀⠀
⣿⢀⠀⣢⣤⡀⠀⠀⠙⢺⣱⣄⠠⠛⠷⣶⣾⣶⣾⣿⣿⣿⣿⠏⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠓⠟⠛⠀⠐⠀⠈⠀⠀⠈⠉⠉⢰⣿
⠀⠿⠾⣿⠯⢷⠶⢶⣿⡿⠾⢀⠀⠀⣩⢾⣟⣿⣿⣿⣿⠉⠁⣀⣿⣿⣿⣿⣿⡿⠿⠍⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⢠⠒⠀⠼⢏⣅⡿⠿⠷⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣆⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠠⠀⠀⠀⣶⠂⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⢤⣵⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢐⠃⠀⠀⠀⠚⠁⠘⠁⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡏⢻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼
⠀⠀⠀⠀⠁⠀⣠⣶⣾⡟⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣬⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣀⣙⣻⣻⣿⡿⢿⢯⠛⠛⠉⢀⠀⠈⠁⠀⣼⣿⣁⣼⡟⢋⣿⣿⣿⣿⣷⠍⠉⠘⣿⣷⣹⠿⢸⠀⠀⠀⢠⣴⣦⣴⣶⣾⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣴⢀⢀⣤⠐⠃⣚⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡖⢨⣿⠘⡟⠩⢦⣨⣿⣿⡟⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠟⠛⠽⣿⣿⣟
⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠷⠁⣀⣀⣹⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⡿⣯⣿⣿⡃⢿⣶⣦⣿⣿⣿⢻⣤⣤⣴⣿⣷⣤⣴⣶⡀⠀⠀⠀⣤⠰⠃⢠⣄⠀⠈⠁⠉
⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢫⣿⣿⣿⣿⣿⣿⣓⠀⠉⠀⢻⣿⣿⣷⣿⣿⣿⠛⠚⠷⠈⠻⡿⠀⠀⠉⠙⣿⡟⡃⠀⠀⣴⣾⣿⣷⣿⣿⡗⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠖⠸⠿⠿⣿⡿⠉⠀⢸⣿⣟⠉⢹⣿⡟⠃⠀⠀⠈⠛⠿⠿⡿⠟⠛⠋⠉⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠰⢹⣿⣿⡟⢡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠆⠀⢰⣿⣇⢼⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⣙⣿⣇⣿⣿⡟⠋⠻⠃⠈⠉⠱⣿⠶⠶⣦⡀⠀⢰⣶⣶⠀⠀⢀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣤⠟⣴⠋⢉⠁⢘⡀⠀⣺⠟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⣴⣦⣾⣿⡇⠀⠀⠀⣤⣀⣠⠴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠇⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⢀⣻⣧⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣍⢹⡿⣦⠼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣶⣶⣾⣿⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠬⣿⠿⠂⠀⡝⠃⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡒⠚⠀⠀⣼⣿⣿⣿⣿⠷⠂⣤⣴⣾⠿⢻⣁⠀⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣷⣴⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⢁⠛⠛⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢡⡆⠀⠀⠉⠃⠀⠀⠈⠁⠈⠛⠻⣿⣿⡿⣿⠟⠁⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠁⠀⢿⣿⡿⢿⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⣾⣦⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠉⠀⠀⣾⠁⠀⢀⣿⣿⡿
⣿⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢶⣶⣦⣶⣿⣿⣿⣿⣿⠟⢁⣾⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠟⠛⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⣥
⠀⠖⠿⣿⠟⢷⠶⠶⣾⡶⠖⠀⠀⠀⠀⠒⠉⠛⢿⣿⣿⡏⢉⠀⣰⣾⣿⣿⣿⣿⠿⠋⠙⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣐⠂⠠⠼⢏⣍⠿⠾⠯⢁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣦⠀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⢤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⣈⠁⠀⠀⠀⠚⠁⠘⠁⠀⠀⠀⠸⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡏⢻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼
⠀⠀⠀⠀⠀⠀⣠⣶⣾⡟⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣬⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠐⢉⣛⣿⣿⡿⢿⢛⠛⠛⠉⠀⠀⠈⠁⠀⣼⣿⣁⣸⡟⢛⣿⣿⣿⣿⣷⠉⠉⠘⣿⣷⣻⡇⠸⠀⠀⠀⢠⣴⣦⣴⣶⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣰⢠⢀⣤⠀⠃⣘⣿⣿⣿⣹⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣾⣿⣿⣷⡖⢠⣿⠘⡿⠩⢦⣀⣿⣿⡟⠉⠈⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠿⠛⢻⢿⣿⣿⣟
⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡷⢁⣀⣀⣹⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⡿⣯⣿⣿⡃⢿⣶⣬⣿⣿⣿⣃⣀⡀⣠⣭⣵⣄⣴⣶⠀⠀⠀⢠⡄⠞⠀⣠⣀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢻⣿⣿⣿⣿⣿⣿⣓⠀⠉⠀⢻⣿⣿⣷⣿⣿⣿⠛⠘⠷⠛⣿⡏⠉⠉⠉⠻⣿⠛⡁⠀⢠⣶⣿⣿⣿⣿⣿⡗⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠖⠘⢿⢿⣿⣿⡟⢤⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠿⠿⠿⡿⠟⠛⠋⠉⠀⠀⠀⠛⠉⠀⠈⠉⠀⠀⠀⠀⠠⢻⣿⣿⡟⢡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡶⠀⠀⣾⣿⡀⣿⣿⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⢈⣛⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⠱⣿⠶⢶⣦⡀⠀⢰⣶⣶⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣤⠟⣴⠃⣉⠁⠈⡀⠀⣲⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣤⣤⣿⡿⢀⠉⠁⢡⣤⣀⣠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣿⣿⣭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⢀⣻⣧⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⣈⣠⣍⠹⡿⣦⠼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⣿⣷⣿⣿⣯⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣽⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠛⠮⣿⠿⠂⠀⡟⠃⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣀⠀⠀⠉⢻⣿⣿⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠒⠂⠀⣼⣿⣿⣿⣿⠷⠀⣤⣴⣾⠿⢛⡁⠀⠀⠀⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⢃⠻⠛⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢡⡂⠀⠀⠉⠃⠀⠀⠈⠁⠈⠛⠛⣿⣷⡿⣿⠏⠁⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⡿⢿⣿⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢠⣼⣦⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠯⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡟⠉⠀⠀⢾⠁⠀⠀⣿⣿⣿
⣿⡇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣶⡦⣴⣿⣿⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⣡
⠀⠖⠾⣿⠿⢷⠶⠲⣾⣶⠖⠀⠀⠀⠀⠒⠉⠙⢿⣿⣿⣟⠉⠁⢠⣾⣿⣿⣿⣿⡿⠋⠉⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠒⠀⢤⢯⣩⡸⠿⠿⠅⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⢠⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣘⠁⠀⠀⠀⠚⠁⠛⠁⠀⠀⠀⡖⠚
⠀⠀⠀⠀⠀⠀⠀⢠⢂⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣯⢾⡋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣾
⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⠀⠆⠀⠀⠀⠀⡀⣾⣿⣿⣮⢅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⠛⠛⠉⠀⠀⠈⠁⠀⣼⣿⣉⣽⡟⢛⣿⣿⣿⣿⣯⠉⠉⠹⣿⣿⣿⡇⠖⠀⠀⠀⣀⣼⣄⣤⣼⣿⣯
⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣤⣢⣧⣀⣦⠠⢋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⠆⣸⣟⢸⡟⠩⣄⣩⣾⣿⡟⠁⠈⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠠⣿⠻⢿⣻⣿⠟⠛
⠀⠀⠀⣀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡿⠁⣀⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡿⣿⣿⣻⠘⣷⣶⣬⣿⣟⡿⠃⠀⠀⢀⣿⣆⣀⣴⣶⠀⠀⠀⢠⡄⠶⠀⣤⠁⠈⠉⠘⠒
⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠓⠂⢻⣿⣿⣵⣾⣿⡿⠛⠹⠦⢰⣷⣷⠛⠛⠿⠟⣿⡟⡃⠀⢠⣴⣷⣿⣾⣿⣿⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠖⠸⠿⢿⣿⣿⡃⢮⣿⣿⣿⡏⣿⣿⣿⠏⠉⢡⣿⣿⣿⣿⣿⡿⠿⠿⠛⢋⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠤⣻⣿⣿⡛⣡⣤⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠘⠿⠇⠀⣼⣿⡀⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⢈⣿⣿⣿⣿⣿⡟⢿⣿⣷⣿⡏⢿⣿⣷⣾⣧⣌⣠⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⠷⣼⠃⣹⠀⢉⡀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠟⠀⠀⠀⢠⣤⣀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⣿⣯⣥⡀⠀⠈⠁⠀⠉⠀⠋⠻⠿⠿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⢁⣠⣉⠿⠿⣤⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⡀⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣴⣦⣦⣤⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⡾⣿⣿⣆⣠⣷⠇⠀⠀⢀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠀⣿⣿⣿⣿⣿⡟⠃⢢⣾⡿⠿⠟⠛⠛⠋⠒⠺⠟⠛⢻⡿⠛⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⠃⠘⠛⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⡔⠀⠀⠉⠋⠀⠀⠀⠉⠀⠛⠛⢠⣦⣤⢰⡿⠋⠀⠀⠀⠀⢸⣿⣶⣦⣠⣤⣴⠀⠀⠘⢿⡧⠀⠛⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⣬⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡌⠙⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠝⠃⠀⠀⠆⠀⠀⢀⣠⡶
⣿⣿⢆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣶⣶⣴⣿⣿⣿⣿⣿⣿⡿⠛⣱⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⠀⢀⣄⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⠛⠃⠀⠀⠐⠂⠀⠀⠈⠉⢉
⠀⠖⠶⣿⠟⢿⠥⠶⢶⣷⡖⠀⠀⠀⠀⠐⠊⠙⠻⣿⣿⣟⣋⡙⠛⢁⣴⣿⣿⣿⣿⡿⠏⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠠⡽⣉⡙⠿⣿⠅⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⣶⡆⠀⢸⣖⢉⡠⠄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣢⣰⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠌⣿⣿⠙⠁⣾⣿⠷⠛⠁⠰⠃⣰⣾⡿
⠀⠀⠀⠀⡀⠀⠀⠠⢂⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡖⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣠⣮⣿⡟⠀⠀⡀⠀⠀⣭⣽⣿
⠀⠀⠀⠀⠀⢀⣶⣶⣿⡏⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣦⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⣉⣻⣿⣿⣿⢿⣯⠙⠛⠟⠉⠀⠀⠈⠁⠀⣼⣯⣉⣹⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⢀⣶⣿⣥⣶⣼⣿⣯
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣴⢰⢣⡀⡆⠀⢁⣨⣿⣿⣿⣿⣿⣿⣏⢰⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣿⣿⠗⣬⣿⢸⡿⢻⣧⣹⣾⣿⣿⣟⠛⣿⣿⠛⠋⢛⠟⠀⠸⡿⢀⣶⣾⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⣛⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣌⣽⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⢿⣿⢿⣿⠘⣿⣦⣽⣿⣿⣿⣿⣿⣦⣿⣿⣿⣷⣿⣶⣤⣄⣠⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣝⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⠃⠺⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⠿⠿⣿⢿⣿⣿⡟⣿⠿⠁⣽⣿⣿⣿⣿⣿⣿⡿⢿⠃⠉
⠀⠀⠀⠀⠀⠳⠖⠘⠿⢿⣿⢯⡁⢤⣿⣿⣿⢉⣿⣽⡿⠉⠁⢸⣿⣿⣿⠿⠟⠛⠛⠛⠋⠁⠀⠈⠛⠉⠉⠉⠉⠁⠀⠀⠀⣼⣿⣿⣿⣿⣡⣤⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣤⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠁⠀⢐⣻⣿⣿⣿⣿⠛⠙⠿⣬⣿⡏⣿⡿⢶⣿⣤⡀⢠⣶⣶⣶⣶⢀⡀⠶⢶⣤⣄⢀⠀⠀⠀⠀⠀⢠⣼⢶⣿⣿⣿⠿⣿⣅⠠⣿⡿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⢿⣿⣿⡿⠟⠊⣽⣿⣥⣴⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣦⣤⣄⠀⢀⠈⠀⠀⠀⠀⠀⠘⠻⢿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣼⣻⣿⣷⣤⣽⣿⢿⣉⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠉⠁⠀⠀⣐⡻⠛⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣅⣉⡼⣿⣣⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠛⢷⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⢘⣾⡿⣿⡿⢿⡛⠉⣉⣿⠿⠿⠛⠛⣛⠋⠙⠛⠋⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠘⠃⠘⠋⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠠⠀⠀⠀⠙⠁⠀⠁⠀⠁⠈⠙⠃⣴⣶⣄⢾⠟⠀⠀⠀⠀⠀⢾⠻⣿⣿⣧⣀⡂⠀⠀⠻⡤⠀⠉⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⡏⠛⠀⠀⠠⠀⠀⠀⢀⡀
⠠⣿⡿⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣶⣦⢤⣿⣿⣿⣿⣿⣿⣿⡿⠛⢡⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠛⠃⠀⠀⠀⠐⠀⠀⠀⠉⠀
⠀⠖⠲⣾⠟⢿⠏⠴⠶⢶⣶⠀⠀⠀⠀⠀⠊⠉⠻⣿⣿⣿⣋⠙⠛⠋⢁⣴⣿⣿⣿⡿⠟⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠠⡼⣏⡁⠿⢾⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀⠀⡠⠋⠉⠁⠂⠀⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠂⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⢠⣄⣀⣠⣦⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣦⡀⠀⠀⠀⣄⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣾⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣹⣿⣿⣿⣿⣯⣇⣤⣦⣀⠁⠀⠀⠀⠀⢀⡀⠀⣤⣴⣧⣤⣄⣀⡈⠀⢥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⣤⣴⣿⣿⣿⣿⣷⣾⣿⣿⣦⠀⣀⣴⣤⣄⣀⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠛⣻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⢰⣿⡿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⠟⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣶⣾⣿⣿⡟⠫⠀⠻⣿⣿⡿⠏⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣟⠻⠟⠛⢻⡿⣶⣄⣼⣿⠿⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⠽⣿⢿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⢷⠆⠐⢆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢛⣿⣿⣿⠿⠀⠀⠀⠸⢿⢿⡿⢿⣟⡃⢀⡀⢉⡉⡅⠀⠀⠈⠀⠀⠀⠀⠀⣧⡀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠻⡿⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⢠⣀⣰⣶⡿⠛⠂⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⠉⠙⡛⠉⠉⠃⠀⠀⠀⠀⣷⠀⠀⠀⣤⣤⣶⣿⠃⠀⠀⠈⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⢀⡀⠀⡠⠋⠉⠁⠂⠀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠊⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣯
⢤⣄⣀⣤⣄⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣷⣦⡀⠀⠀⠀⣄⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣹⣿⣿⣿⣿⣯⣆⣠⣤⣀⠁⠀⠀⠀⠀⢀⡀⢠⣶⣶⣿⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣴⣿⣿⣿⣿⣶⣾⣿⣿⣶⠀⢀⣴⣤⣄⣀⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠙⣻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⢰⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣧⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⡟⠻⠛⢿⣿⣿⣿⡿⠏⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣏⠻⠟⠛⢻⠿⣶⣄⣤⣾⠿⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⠽⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⢷⡶⠺⣿⣛⣿⠛⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢻⣿⣿⣿⠿⠀⠀⠀⠸⣿⢟⡿⢿⣟⡁⢃⡀⢉⡉⡅⠀⠀⠈⠀⠀⠀⠀⠀⣷⡀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠻⡿⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⣀⣸⣶⣿⣿⣯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣠⣿⣿⣿⠋⠀⠀⠀⠀⠈⠀⠘⠁⠙⡛⠛⠋⠃⠐⠀⠁⠀⣶⠀⠀⠀⣶⣴⣶⣿⠃⠀⠀⠈⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠞⠙⠿⠟⠁⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⣀⡄⠀⡤⠋⠉⠑⠂⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣯
⢠⡀⢀⣤⣄⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣷⣦⡄⠀⠀⠀⣄⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⢿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣹⣿⣿⣿⣿⣯⣇⣠⣤⣀⠀⠀⠀⠀⠀⢀⡀⠀⣔⣴⣾⣾⣿⣿⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⢠⣤⣾⣿⣿⣿⣶⣾⣿⣿⣶⠀⢀⣤⣤⣄⣀⣤⣤⣤⣬⣤⣤⣤⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣹⣷⡿⣿⣿⡄⠀⠈⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣶⣾⣿⣿⡟⠛⠉⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣍⠙⠿⠛⢛⡿⣶⣄⣤⣶⠿⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⠽⢿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠿⢷⠖⠻⣿⡉⣽⠿⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠲⢞⣿⣿⣿⠯⠀⠀⠀⠨⢿⢿⡿⢿⣟⡁⢀⡀⢉⡉⡅⠀⠀⠈⠀⠀⠀⠀⠀⣷⡀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠻⠿⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣸⣾⣿⣿⣯⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⠁⠙⡛⠛⠋⠀⠐⠀⠀⠀⠦⠀⠀⠀⣤⣤⣶⣿⠇⠀⠀⠈⢹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠛⠿⠟⠁⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡄⠀⡤⠋⠉⠑⠂⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣧
⠀⠀⠀⣠⣄⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿
⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⠁⠀⣀⣀⣤⠀⠀⢀⣤⣄⢀⣀⣰⣿⣿⣿⣷⣿⣷⣄⠀⠀⣰⣿⣿⣿⣹⣿⣿⣿⣿⣯⣆⣠⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⢄⣠⣶⣾⣆⣶⣾⣇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣿⣶⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠛⠙⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⡶⢠⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣄⠈⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣟⣱⡖⠈⠋⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣶⣶⣾⣿⣟⠛⠉⠉⢿⣿⣿⣿⡟⠃⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡄⠀⠝⠉⠙⠖⣦⣄⣠⣄⠉⠉⠉⢙⣿⡿⠿⠿⢿⡿⠷⠘⠟⠋⡍⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⠟⢳⠀⠘⣷⠉⠩⠁⠀⠀⠀⠀
⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢚⣿⣿⣿⠧⠀⠀⠀⠠⠐⢟⡿⢿⣛⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠐⢻⣿⣿⣿⣿⣿⠏⠹⠿⠉⠀⢹⣿⣿⣿⣿⣿⣿⣇⠀⢀⣰⣾⣿⢿⣧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⣀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⣾⠂⠀⠀⠈⠹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢹⣿⣿⣿⠞⠛⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠄⢸⣿⠆⠀⠰⢶⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⡄⠀⡤⠋⠉⠁⡂⠀⣼⣀⠄⠀⠈⠁⠀⠀⣄⣼⣿⣷⣤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⡟⠁⠀⠀⠀⠀⠀⠀⠊⠊⠘⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿
⠀⡀⢀⣠⣄⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣶⡀⠀⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣹⣿⣿⣿⣿⣯⣆⣠⣤⣀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⣴⣿⣿⣿⣿⣿⣶⣾⣿⣿⣦⠀⢀⣤⣤⣀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣶⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠛⠛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡖⢠⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣇⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⠟⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣹⣿⠿⠙⠁⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣵⣶⠹⡯⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠟⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣏⠉⠿⠋⢛⠗⣶⣄⣤⣾⠟⠉⠙⢻⣿⣿⡿⢿⣿⣿⣿⠿⠿⠿⡿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠛⠁⠀⠀⠀
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢚⣿⣿⣿⠿⠀⠀⠀⠠⠸⢟⡿⠻⣟⡁⢀⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠐⢿⣿⣿⣿⣿⣿⠏⠙⠟⠋⠀⠹⣿⣿⣿⣷⣄⠀⠀⠀⠀⣰⣾⣿⣿⣿⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣤⣀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠘⡛⠍⠉⠀⠐⠂⠀⠀⠦⠀⠀⠀⢶⣤⣶⣿⠃⠀⠀⠈⠹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⢹⣿⣿⣦⠀⠘⠿⠟⠁⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⡄⠀⡤⠋⠉⠑⠂⠀⢰⣄⠠⠀⠀⠀⠀⠀⠀⠈⠀⣠⣤⣼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠊⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣿⣿
⢤⣄⣀⣤⣤⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣦⡀⠀⠀⠀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣙⣿⣿⣿⣿⣯⣦⣤⣦⣌⠁⠀⠀⠀⠀⢀⡀⢀⡄⠀⠀⠀⢠⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣤⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣠⣴⣤⣄⣠⣤⣤⣤⣽⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣶⣿⣿⣿⣿⣴⣴⣀⡶⣘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⣿⣿⣿⣿⠛⠙⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠊⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡶⢰⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣧⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣿⡀⠀⠀⠘⢿⣿⣿⠿⠿⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⡻⣿⣿⡀⠀⠈⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣒⣂⠉⠀⠀⠀⠀⠈⠓⠿⠃⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣟⠻⠿⠛⢛⠟⣶⣄⣤⣿⠿⠛⢛⢻⣿⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣁⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠶⢾⣿⣿⣿⠿⠀⠀⠀⢠⢿⢿⡿⢿⣿⡁⢁⣀⠉⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⢿⣿⣿⣿⣿⣿⠏⠻⠿⠛⠀⢿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢴⠖⠒⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣀⣿⣿⡿⠋⠀⠀⠀⠀⠈⠁⠈⠁⠙⡻⠟⠉⠀⠐⠒⠁⠀⢶⠀⠀⠀⣶⣴⣶⣿⠇⠀⠀⠈⢹⠟⠋⠁⠈⠒⠀⠀⠀⠀⠀⠈⠛⠋⠹⣿⣿⣿⠞⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⡀⠀⡤⠋⠉⠁⠂⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⣯
⢠⡄⢀⣤⣄⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣦⡀⠀⠀⠀⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣽
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣙⣿⣿⣿⣿⣧⣆⣠⣦⣀⠁⠀⠀⠀⠀⢀⡀⢀⣤⣤⣾⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⢀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣦⠀⢀⣴⣦⣄⣀⣤⣤⣤⣭⣤⣤⣤⣤⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠙⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠘⠉⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⢴⣿⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣧⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣵⣶⡙⡿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⡛⠛⠉⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣏⠙⠿⠛⢛⠟⣶⣄⣤⣿⠿⠛⠛⢻⣿⣿⡿⢿⣿⣿⣿⠿⢿⡿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠀⠻⣿⡍⣉⠈⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠲⢚⣿⣿⣿⠿⠀⠀⠀⠠⡾⢟⡿⢻⣟⡁⢀⣀⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠐⢿⣿⣿⣿⣿⣿⠏⠛⠿⠛⠀⢻⣿⣿⣿⣿⣿⣿⣇⠀⣀⣸⣾⣿⣿⣧⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠟⠋⠀⠐⠂⠁⠀⠶⠀⠀⠀⢶⣤⣶⣾⠇⠀⠀⠈⢹⠟⠋⠁⠈⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠛⠿⠟⠁⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣀⡀⠀⡤⠋⠉⠁⠂⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣮⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⣾⣿⣯
⢠⡄⣀⣤⣄⡀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣷⣦⡄⠀⠀⠀⢤⡶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣿⣿⣿⣾
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣉⣿⣿⣿⣿⣿⣤⣠⣤⣀⠁⠀⠀⠀⠀⢀⡀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⣤⣾⣿⣿⣿⣷⣾⣿⣿⣦⠀⢀⣴⣤⣄⣀⣤⣤⣤⣭⣤⣤⣤⣤⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠛⣻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠛⠋⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⢠⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣧⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⡹⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⠟⠋⠉⣿⣿⣿⣿⡿⠛⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣏⠙⠿⠋⢛⠟⣶⣄⣬⣶⠿⠉⠛⢻⣿⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⠶⠀⠹⣿⡟⣿⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠲⢚⣿⣿⣿⠿⠀⠀⠀⠠⡾⢟⡿⢿⣿⡁⢀⣀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⢿⣿⣿⣿⣿⡿⠟⠛⠿⠟⠁⢻⣿⣿⣿⣿⣿⣿⣇⠀⣀⣸⣾⣿⣿⣿⡄⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠙⡻⠟⠉⠐⠐⠒⠀⠀⢦⠀⠀⠀⢶⣤⣶⣿⠃⠀⠀⠈⢹⠟⠋⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠛⠿⠟⠁⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣀⡄⠀⡤⠋⠉⠑⠂⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣬⡿⠃⠀⠀⠀⠀⠀⠀⠂⠎⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⣾⣿⣯
⢠⣄⢀⣤⣄⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣦⣄⠀⠀⠀⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣿⣿⣿⣾
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⡀⠀⢀⣀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣉⣿⣿⣿⣿⣿⣤⣠⣤⣀⠁⠀⠀⠀⠀⢀⡀⢠⣴⣬⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⠀⢀⣴⣤⣄⣀⣤⣤⣤⣭⣤⣤⣤⣤⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠛⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠛⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡖⢠⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣅⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣏⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢏⠀⠀⠀⠀⠀⠡⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⠛⠉⠈⣿⣿⣿⣿⡿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣧⡄⠀⠭⠉⢛⠗⣶⣄⣬⣶⠿⠉⢛⢻⣿⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⠶⠀⠻⣿⡏⣿⠿⠇⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⢺⣿⣿⣿⠧⠀⠀⠀⠠⡺⢟⡿⢿⣿⡁⢀⣀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠘⢻⣿⣿⣿⣿⡿⠏⠛⠿⠛⠁⢻⣿⣿⣿⣿⣿⣿⣇⠀⣀⣸⣾⣿⣿⣿⡀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠙⡻⠟⠋⠐⠐⠒⠀⠀⢦⠀⠀⠀⢶⣤⣶⣿⠃⠀⠀⠈⢹⠟⠋⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⣿⣿⣿⠟⠛⠿⠿⠁⠀⠉⠀⠀⠀⠀⠀
⣿⠀⣿⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⣿⣿⣞⣻⣿⣿⣿⣿⣿⣟⣗⠟⡻⣿⣿⠀⣀⡘⠋⢿⣿⡿⢿⣿⣯⣴⡶⣋⣀⡟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣠⡄⠠⠎⠉⠛⢿
⣷⣿⣿⣽⣿⣿⣿⣶⣄⣺⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⡿⠟⢻⣷⣆⡀⠀⠀⠀⣰⢶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⡟⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠘⣿⣿⡇⠀⠀⣐⣙⠋⠻⢿⠫⠿⠿⣿⠘⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣦⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣠⣿⡿⠿⠟⠁⠁⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢦⠄⢠⣿⣿⣷⣶⣶⣿⣿⣿⣇⢐⡿⠟⣴⠟⠀⠛⠁⠹⢿⣿⣅⣻⣿⣿⣿⣿⢏⣽⣾⣷⣤⣄⣀⣀⣀
⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⢀⡀⡀⠀⠛⣿⡇⠐⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢸⣿⠇⣠⠿⢿⣿⣛⣿⣿⣾⣷⣟⣫⣤⢰⣦⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⡟⠻⠛⠿⣿
⠀⠀⢀⣀⢉⣿⣿⣿⣿⣿⣿⠁⠀⢹⡇⠀⠀⠀⠰⣤⡀⠀⠀⢾⠽⡿⣗⠈⠛⠛⣿⣿⣿⣿⣯⣿⣗⠀⠀⠀⠀⠀⠬⠋⠀⠀⠀⠈⢹⣿⠛⠛⢛⣿⣿⣿⣿⣸⣿⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡷⠊
⠀⠀⠈⠉⠁⠉⠛⠛⠻⣿⣿⡄⠀⠘⢷⣤⠄⠀⠀⠀⠦⢀⣠⣭⡀⠀⠩⢠⡀⠀⣻⣿⣿⣿⣿⣟⣯⣾⣿⣿⠆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡀⠀⠙⢉⣤⣬⣏⣀⣿⣿⣹⣟⣛⠋⡙⡿⣇⠈⢉⣷⣦⣤⣤⣼⣿⢢
⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠉⢟⣟⣄⠄⣿⣿⡿⢻⣿⣿⣿⣿⣿⡛⠛⠀⢀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣶⣶⣼⡿⢿⣿⠈⠙⠙⠛⠿⢿⣿⣾⠁⢨⣴⣿⣟⣳⣶⣿⠾⠻⢿
⠀⠀⠀⠀⠀⠀⣀⠖⠀⠀⡸⠖⣂⣀⣠⣀⢀⡀⠀⠀⠀⠀⠸⠿⠛⠴⢾⣿⠋⠀⣿⣿⠟⠿⠟⢫⡇⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡌⢛⠉⠀⠘⠿⣿⡿⣭⣿⣿⣦⣤⣿
⠀⠀⠀⠀⣶⣾⣯⠀⠀⣀⣿⢟⣿⣿⡿⣇⣈⣁⢠⠁⠀⠀⠀⠀⠀⠀⠀⣞⠛⠒⠉⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⣉⢿⣽⣿⣿⣯⠀⢀⣠⣼⣷⣶⣾⣶⣆⣀⣤⣾⣷⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠈⠉⠉⠁⠀⠸⣿⣿⠘⠉⣿⣶⣿⣿⡿⠿⣵⡀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⢯⠋⠁⠀⠀⠈⣻⣿⣿⣿⣶⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣏⣻⣿⣿⣽⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣤⡾⠿⣿⣿⠛⠂⠛⠒⠦⠀⣄⣶⣄⠀⢈⡁⠘⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡆⠀⠀⣀⠀⢼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠊⠀⠚⠛⢿⣿⣿⣿⠛⣿⣶
⣶⡒⠂⣠⠀⠈⠀⠀⠛⢿⣿⣿⠃⠙⠛⠋⠁⠀⠀⠀⠀⠘⢷⣯⡙⠟⠛⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠘⠿⠄⠀⠀⠃⠲⡖⠉⠀⠈⠻⢿⣿⣿⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠉⠛⠫⢹⣿⡏
⠀⠀⠀⠉⠀⠀⠀⠀⠀⡄⠀⢀⣆⣰⣶⣶⣻⣇⡀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠐⣦⣄⣀⣀⣀⣀⣀⢀⣄⣬⡄⠘⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋
⠀⠀⣠⢂⠀⠀⢠⣼⣿⡇⠀⠀⠀⠹⠗⠱⠍⠉⠁⠀⠀⠀⠀⠀⠀⢐⣓⣷⣦⣤⣮⣻⣿⣄⢄⣄⠀⣤⣄⠸⣶⡀⠀⢠⣤⠃⠀⠀⠀⠀⢀⣘⣛⣿⣿⣻⣿⣿⣿⣿⣿⣾⣿⣦⣠⣴⣶⣶⣦⣤⣤⣄⣀⣀⣀⣤⣄⣀
⠐⠷⠿⣾⠟⢶⠾⠱⠿⠶⠶⠀⠀⠀⠀⠀⢚⣶⣶⣾⣶⣶⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠬⣼⣿⡇⢈⣿⣿⣿⡅⠀⠀⣿⡧⣴⣦⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣿⣿⣿⣿⣿⡛⠛⢁⣿⣿⣿⣿⣿⡇⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣭⣽⡛⣙⣁⠀⠀⠀⣀⢀⡀⣠⣤⣉⣀⣬⣤⡄⠲⠟⠛⠿⣧
⣿⣿⣿⣾⣿⣿⡿⣶⣮⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠐⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠿⣿⣿⣿⣿⢿⢿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣾⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⠿⠿⣿⣧⡾⠿⠛⠛⠂⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⡝⠉⠀⠀⠈⠉⠀⠸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⢿⣿⣇⣘⣿⣿⣿⣿⡿⢩⣽⣿⣷⣤⣀⣀⠀⠀
⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣷⠠⣄⡄⠀⠈⠻⠟⠀⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⢿⣿⣿
⠀⠐⢶⠤⣽⣿⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠳⠆⠀⠀⢘⡷⠿⢿⡀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣶⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣿⠉
⠀⠀⠀⠀⠀⠉⠉⠙⢿⠿⠀⠀⠀⠡⠤⠀⠀⠀⠀⠘⠂⢤⣶⣦⠀⠀⣠⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠙⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣛⠛⠛⢻⢯⡀⠈⢹⣷⣦⣼⣽⣿⣿⣿
⠀⠀⠈⠙⠗⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⣘⣽⡰⣶⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣷⡎⠀⣠⣾⣟⣩⣶⣿⣟⠿⢿⣿
⠀⠀⠀⠀⢀⣤⠏⠀⠀⡸⢏⣠⣤⣤⣄⣀⣀⠀⠰⠆⠀⠘⠛⠛⠿⢿⣿⣯⠀⢸⣿⣿⣿⠿⠿⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣀⠙⠋⢀⠀⠛⢿⣿⢷⣿⣿⣷⣾⣿⣿
⠀⠀⠀⣸⡿⠟⠀⢀⣠⣿⠏⣿⣿⠟⠂⣄⣐⢀⡅⠀⠀⠀⠀⠀⠀⠀⢸⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡯⣭⡿⣿⣿⣿⣿⣿⢏⣏⣥⣿⣶⣾⣷⣶⣤⣤⣴⣿⣷⣿⣿⣿⣿⣛⣙
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠈⢿⣦⣄⠛⠛⠻⢷⠄⠀⠂⠀⠀⠀⠀⣴⡶⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠏⠀⠀⠀⠀⣻⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⠋⡻⡿⢿⣿⣿⣯⢹⣿⣿⣭⣭⣯
⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣶⣶⡿⠻⠧⣤⠀⠀⠙⠓⠂⠄⢀⣶⣦⡘⠋⢀⠌⠓⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠀⠀⢠⠀⠀⢿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠈⠉⠻⣿⣿⣿⣛⣷⣾⣿
⠏⠁⢤⠀⠀⠀⠀⠈⠛⠿⠏⠃⠀⠚⠋⠁⠀⠀⠀⠀⠀⠻⢿⡁⠙⠃⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠈⠃⠀⠀⠀⠙⠳⣷⣿⣿⡿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠉⠉⠭⣿⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢤⣼⣶⣟⣥⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢘⡿⠉⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠹⠾⣀⣀⣀⣀⣀⣀⣤⣤⣤⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤
⢘⡄⡼⠀⠀⠠⣶⣿⡇⠀⠀⠀⠀⠛⠒⠃⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠘⣶⣤⡤⠈⠻⢽⡇⢀⣀⢠⣤⣄⢀⣤⠀⠀⢠⣦⠀⠀⠀⠀⢀⣀⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣶⣶⣶⣶⣤⣤⣤⣀⣀⣀⣤⣄⣀
⢸⣿⠶⣶⠏⢶⠄⠰⠶⠶⠆⠀⠀⠀⠀⢈⣷⣾⣿⣿⣗⡀⠀⠀⢀⣀⣭⣿⣿⣷⠀⢀⣸⠇⣀⣿⡁⠙⠛⢻⡇⠀⠀⠀⣿⠓⠲⠶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣟⣛⠋⢩⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠉⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣴⣿⣿⣯⣟⣉⣉⣀⡀⠀⢀⣀⣀⣀⣬⣭⣅⣠⣤⣴⠰⠾⠛⠻⢿⣭
⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⣿⣿⡟⠁⠉⠉⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠚⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⢿⣿⣿⡿⡿⡿⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠤
⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠿⣿⣿⣶⡿⠟⠉⠛⠁⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠿⠟⠛⠁⠀⠀⠀⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⢿⣿⣧⣿⣿⣿⣿⣿⡟⣩⣿⣿⣾⣤⣀⣀⡀⣀
⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡇⠠⣄⡄⠀⠉⠛⠋⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⡿⣿⣿
⠀⠰⠶⠴⣿⣿⣿⣿⣿⡟⠀⠀⣿⠁⠀⠀⠀⠈⠿⠆⠀⠀⢻⠾⠿⣧⠀⠉⠙⣇⣤⣤⣿⣿⣿⣿⣿⡆⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⣿⣿⣿⣷⣟⠀
⠀⠀⠀⠀⠀⠉⠉⠹⠿⠿⠀⠀⠈⠤⠂⠀⠀⠀⠀⠘⠠⠴⣶⣤⠀⢀⣴⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣛⡋⠛⣿⢿⠀⠉⣽⣶⠾⣿⢿⣿⣿⣿
⠀⠀⠉⠙⠓⠀⡀⠀⠐⢀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⣩⣿⢲⣯⣿⣿⠏⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⢿⣿⣷⠍⢀⣶⣿⣟⣵⣾⣿⡿⢿⣿⣿
⠀⠀⠀⠀⣠⡴⠃⠀⢀⣞⣋⣤⣤⣤⡄⢡⡀⠀⠰⠄⠀⠘⠛⠻⢿⣿⣿⣧⠀⢿⣿⣿⣿⡿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⡌⠛⠉⠀⠀⠿⣿⡿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⢀⣻⠿⠇⠀⣀⡴⠿⠍⣿⡿⠛⢢⣤⣆⣰⡀⠀⠀⠀⠀⠀⠀⠉⣼⠻⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠯⣽⢿⣿⣿⣿⣿⣿⣿⣻⣿⣶⣶⣾⣷⣦⣤⣤⣾⣿⣶⣿⣿⣿⣿⣛⣻
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠹⣿⣶⡌⠉⠙⠛⠃⡀⠀⠀⠀⠀⠀⢀⣴⡶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠇⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢛⣿⣿⣿⣿⣿⣍⣽⣿⣿⣭⣽⣯
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣿⡟⠋⢰⡖⠐⠂⠛⠓⠢⠀⣨⡿⢆⡚⠋⢀⠀⠒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡷⠀⠀⠠⠀⠸⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⡟⡋⠈⠀⠛⠛⢻⣿⣿⣿⣛⣾⣿⣍
⠍⠁⡔⠀⠀⠀⠀⠉⠛⠿⠍⠁⠀⠛⠉⠁⠀⠀⠀⠀⠀⠻⠧⠀⠉⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠙⠋⠀⠀⠈⠛⢻⣿⣿⣿⡿⣿⡷⡇⠀⠀⠀⠀⠀⠈⠉⠉⢽⣿⣭⠶
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠂⢤⣿⣶⣻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣙⣿⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠷⢗⣀⣀⣀⣀⣀⣠⣤⣤⣤⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠤
⢁⢠⠟⠀⠀⢠⡾⣿⠇⠀⠀⠀⠘⠉⠘⢁⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣶⡄⠙⠿⠽⠇⢀⣀⢠⣄⡀⢠⠤⠀⠀⢰⣎⠀⠀⠀⠀⢀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣷⣶⣶⣶⣤⣤⣤⣀⣀⣤⣤⣤⣀
⠃⡶⢶⣶⠯⢶⠄⠰⠴⠶⠆⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⡀⠀⠀⢀⣠⣽⣿⣿⡷⠀⠀⢴⢇⣝⣿⠋⠉⠉⢈⠀⠀⠀⠘⣿⠲⠶⢦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣿⣁⠈⢡⣿⣿⣿⣿⣿⣣⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣬⣤⣀⣀⣀⣬⣤⣤⣶⣿⣦⣶⣶⣿⠿⠟⠋⠙⢳⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⠋⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠙⠁⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⡿⡿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣀⠀⠘⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣯⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢧⣬⣷⡄⠒⠚⣛
⣿⣿⣟⣿⣿⣿⣿⣿⣿⡉⠉⠙⠛⠙⢿⣿⣟⠛⠉⠉⠁⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠛⠁⠀⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧⣤⣴⣿
⠉⠉⠿⣿⣿⣿⣿⣿⣻⠏⠘⢦⣆⠀⠀⠉⢋⡀⠀⠀⠀⣺⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠲⠔⠝⠿⢿⣿⣿⠉⠀⠀⢸⡇⠀⠀⠀⠀⠙⠓⠀⠀⠹⠛⠛⠿⣆⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣻⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠚⣻⣶⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⢠⣴⣷⣿⣿⣿⡿⠯⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⢀⣤⣶⠛⠀⠀⣠⣤⣶⣶⣾⡶⠰⠆⠀⠈⠁⠀⠀⠉⠉⠻⢿⢿⣿⡄⠙⠛⠻⠿⠛⠙⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡼⠟⠛⠀⢠⣖⡋⠸⣿⡟⠋⢑⣶⣶⣼⣢⠀⠀⠀⠀⠀⠀⠀⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣹⣿⣿⡏⠀⢈⠋⣡⡄⠀⠀⠀⠀⠀⠀⣰⡾⠋⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠂⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⡀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡿⠏⢁⣒⡓⠈⠉⠉⠉⢃⣀⣠⠿⣣⣌⠉⠐⠀⠈⠛⠆⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⡖⣀⣹⠿⠙⢻⣿⣿⣿⣿⣿⣿⣿⡟⡋⠀⠀⠉⠉⠙⢿⣿⣿⣭⣿⣿⡇⠀
⠀⠺⠁⠀⠀⠀⠀⠈⠙⡇⠀⠀⠉⠁⣀⡀⠀⠀⠀⠈⠛⠻⠉⠉⠀⠀⠀⢰⣄⣀⣤⣤⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡀⠀⠀⠈⠁⠀⠀⠀⠉⠹⠿⢿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠑⠺⢿⣴⠿⠂
⠀⡀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠲⣿⢿⡽⣦⠄⠀⠀⠀⠀⠀⠂⠀⠀⣠⠀⠀⠹⣝⣣⣿⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠯⣤⣤⣄⣀⣄⣤⣤⣀⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀
⢰⠃⠀⠀⠐⠟⠿⠃⠀⠀⠀⠈⠉⠘⠁⠄⢀⣤⢀⡀⠀⠀⠀⠀⠀⠀⣲⣿⠆⠈⠓⠀⠀⠸⠀⠀⠀⢀⠠⠿⠆⠀⠀⣦⡀⠀⠀⠀⢠⣤⣤⣭⣭⣽⣿⣿⣿⣯⣝⣳⣶⣦⣤⣤⣿⣷⣶⣶⣤⣤⣤⣤⣤⣦⣶⣦⣤⣤
⣧⢶⡶⣶⠋⢶⠄⠰⠶⠶⠆⢀⣀⣀⣥⣾⣿⢻⣿⣯⣄⢀⣀⣀⣤⣾⣿⣿⣿⡄⠀⠲⠀⠀⣰⠀⠀⠀⢠⠄⠀⠀⠀⢹⠇⠂⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛
⣛⣻⣿⣤⣄⠀⢾⣿⣿⣿⣿⢧⣴⣿⣟⠻⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣇⣄⠀⢻⣿⣿⣿⣿⡂⠈⠛⠛⣻⣿⣿⣿⣿⣿⣷⣿⣦⣶⣦⣄⣀⣀⣤⣤⣤⣶⣦⣤⣴⣶⣿⠛⠛⠃⠘⢻⣶⣶⣤
⣿⣿⣿⣯⣭⣿⣾⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣬⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣄⠁⠈⢺⣿⢻⣿⣿⣷⣾⣷⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠀⠀⠀⠀⠉⠀⣾⠛
⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⠟⢫⣿⣄⠈⣛⣿⣿⣿⠟⢿⡁⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⡿⠛⠉⠉⢿⣿⣿⣿⣿⣻⣿⣿⣿⡧⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⡯⡿⠿⠀⠀⠀⠀⠐⠒⠋⠀
⣇⠘⣿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠈⠹⣿⡏⠉⠀⠀⠀⣀⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢣⡀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⣿⣷⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣤⣤⣴⣖⣂
⠈⠰⣾⣿⣿⡿⠁⠓⠀⠘⢠⡆⠀⠀⠀⢀⡀⠀⠀⠀⣹⣍⣻⡾⠻⢷⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠉⠁⠀⠀⠉⠀⠀⢸⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣽⣛⣿⣿⠿⢿
⠃⠃⠙⠛⠻⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠙⠃⠀⠀⢸⠋⠉⠑⠀⠀⢸⣶⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣄⣈
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⡻⣗⢀⠠⣿⣶⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠒⠒⠂⠀⠀⠀⣨⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢠⣾⢿⣿⣿⣿⣟⠁⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣶⣶⡄⠀⠀⡶⠶⢾⣿⠏⠀⠘⠀⢀⠈⠀⠀⠀⠀⠀⠙⠻⣿⣿⠆⠈⠛⠉⠈⠉⠙⢿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠠⠖⠋⠀⠀⠀⣾⡄⠈⠻⣥⣄⡰⠿⣶⣿⡦⠀⠀⠀⠀⠀⠀⠀⠛⠁⣀⡀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠰⣿⣇⣀⣴⣿⡿⠃⠀⣈⢀⣴⣄⡀⠀⠀⢀⡀⠀⣠⠞⠫⣁⡀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠃⠀⠀⠀⣠⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣭⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀
⢀⠀⠀⠀⠀⠺⣿⣿⠿⠛⠃⣀⣿⠅⠀⠀⠀⠀⢠⣤⡴⠟⣷⣤⠀⠀⠀⠈⠙⠂⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣤⡽⠿⠉⠹⣿⣻⣿⣿⣿⣿⣿⠟⡁⠀⠀⠀⠈⠉⠛⠟⠏⢤⣿⠿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠠⣄⣈⣁⣀⣤⠀⠀⠀⠀⠀⠉⠻⠂⠀⠀⠀⠀⠹⣤⣤⣶⣶⣴⣾⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠘⠛⠳⣿⡟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠄⠉⠀⠀
⡄⠀⠀⢀⣠⣶⡄⠀⠀⠙⣿⣿⣿⠾⠶⠄⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⣀⠹⢯⣥⡿⠋⠉⢁⡀⠀⠀⠀⠀⣰⣀⠀⠀⠀⠀⠀⠀⠙⠣⢶⣶⣦⣤⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠋⠛⠀⠀⠀⠀⠉⠁⢈⣠⢆⣠⣦⣀⣀⠀⠀⠀⠀⢠⣤⣿⣿⣷⣌⠛⠀⠀⠀⢸⣇⣀⣀⣼⡟⠟⢳⣼⡒⣶⡀⠀⠀⢴⣶⣶⣾⣿⣿⣿⣿⣿⣷⣾⣽⣿⣷⣶⣶⣿⣿⣿⣷⣶⣶⣶⣦⣶⣶⣶⣤⣶⣶⣶
⢠⠖⠲⣶⠎⢶⠤⠰⠶⠶⣶⣤⣾⣾⣿⣿⣿⣿⣿⣦⣠⣶⣶⣾⣿⣿⣿⢿⣧⣪⢾⣧⣤⣸⣿⡿⣶⣽⣖⠀⣾⡯⠋⢸⠏⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭
⣻⣿⣯⣤⠀⠀⣼⣿⣿⣿⣿⢄⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣴⣶⣶⣶⣾⣿⣿⣿⣿⡿⢀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠉⠉⣵⣾⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣴⣦⣶⣶⣶⣤⣶⣾⡏⠈⠉⠀⢉⣽⠷⣶⡆
⣿⣿⣿⣯⣿⣷⣾⣿⡿⡿⣿⣌⣽⢿⣿⣦⣿⣿⣿⣇⣭⡿⣷⣤⣼⡿⡷⢾⣟⣿⣿⣿⣿⣿⣆⢈⠐⢀⣿⢂⣻⡄⠀⠀⠀⠀⣿⡹⣿⣿⣛⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⠁⠰⡟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠚⢛⣯⡀⠛⠿⢾⣿⠽⠻⣟⠀⣸⣼⣿⣿⡏⢹⢿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣿⣾⣿⣷⣀⣤⣶⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⢺⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀
⡏⢻⣿⣿⣿⣷⣶⡄⠈⠁⠀⠈⠙⣷⣾⠙⠉⠉⠉⠀⣠⣶⣿⣿⣿⣞⢛⣺⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠛⢿⣿⣿⣿⣿⣿⣿⣯⣥⣽⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣶⣶⣾⡥⠀
⠁⠈⣿⢿⣿⣿⠇⠉⠀⠠⢠⠀⠀⠀⠉⡀⠀⠀⠀⠀⣻⢛⣿⡽⢿⣧⡘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠀⠀⢨⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⠛⠉⠻
⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠉⠓⠀⠀⠀⡽⠛⠋⠀⠀⠀⣤⠄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠏⠀⠘⠓⠀⠀⢽⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⣿⣿⣷⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢉⠻⡆⠀⠀⡶⣶⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢟⣮⣾⣿⡃⢰⣿⡿⠋⣻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠛⠛⠻⠟⠃⢀⣴⣄⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⢀⣴⣦⠀⠀⠀⡆⡾⢿⡧⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠈⠈⣿⠇⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣝⠃⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠠⠞⠋⠁⠀⠀⣦⠀⠈⢿⣡⣄⡾⠷⣶⣿⠄⠀⠀⠀⠀⠀⠀⠀⠉⢀⣤⡀⠀⠀⠀⠀⠀⠛⠛⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠛⠟⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢤
⠀⠀⠀⠀⠀⢰⣿⣄⣠⣾⣿⠿⠀⠀⣡⡈⣦⣄⡀⠀⢀⣠⡀⢀⡴⠋⢡⣀⡀⠀⠀⠀⣠⣤⣄⣀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡭⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠲⣿⣿⠿⠿⢀⣩⡯⠁⠀⠀⠀⠀⢠⣤⡚⢻⣷⡤⠀⠁⠀⠈⠙⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⣬⠿⠏⠉⠻⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⢿⡄⠀⠀
⠂⠀⠀⠀⠀⠀⠁⢹⢀⠀⣈⣁⣀⣤⠠⠀⠀⠀⠀⠙⠓⠀⠀⠁⠀⠀⢣⣤⣶⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⠀⠙⠉⠛⠿⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣋⠀⠀⠀
⠀⠀⠀⢀⣠⣤⠀⠀⠀⠑⣿⡿⣷⠾⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠻⣿⡿⠿⢹⡏⢹⡁⠀⠀⠀⣠⣿⣿⣷⣤⡀⠀⠀⠀⠈⡹⠿⣶⣶⣶⣿⣿⣷⡾⣶⣦⣀⠀⠀⢠⣤⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠈⠀⠀⠀
⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠉⠁⢈⢰⣀⣰⣦⣀⣀⠀⠀⣀⣀⣠⣤⣿⣿⣷⡿⣟⣈⣍⣁⣺⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣨⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⠖⠶⣶⠯⢶⠶⠰⠶⢶⣶⣶⣶⣾⣿⡟⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣖⣄⡀⢿⣿⣿⣿⣿⣳⣿⣿⣯⣛⣿⣿⣿⡿⣿⣿⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⡆⡀⢹⣿⢸⡇⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣤⣶⣶⣾⣾⣿⣿⣶⣿⡿⡏⠉⠉⠁⢈⣿⣿⣶⣆⠀
⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⡾⠙⣿⣿⣿⣿⣿⣿⣿⠟⢻⠟⣿⣟⣭⢻⣿⣿⣿⣿⣿⣿⣿⣆⣄⣃⣼⣏⣽⣿⡟⠀⠀⢀⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⡀⣸⡟⠉⠀
⣿⣿⣿⣿⣟⢛⠛⠿⠟⠑⠺⢷⣦⣌⢭⡝⠿⠌⠈⠁⣄⣼⣿⣿⣿⣯⣼⣿⣿⣿⣽⣿⣿⣷⡿⠚⠿⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣟⣿⣿⣄⣀⡀⠀⠈⢡⣀⣠⣴
⠸⣿⣿⣿⣿⣿⣆⠀⡀⢀⠀⠀⠛⠿⠀⠀⠀⠀⠀⣴⡿⠿⣿⣿⡿⢏⣯⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⡸⣿⡋⡿⠿⠋⠈⠀⠁⡧⠀⠀⠀⠀⢦⣄⠀⠀⠀⢼⣧⣿⠋⠉⠛⠿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣿⡿⠟⠛⠋⣿⣿⡿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⠛⠛⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⢋⣀⠀⠀⠀⠀⠰⣟⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣀⣠⣴⣿⠟⠃⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⣙⣧⢠⢀⣖⣶⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠻⠃⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠄⠀⠀⠀⢀⣀⣀⠄⠀⣀⠀⠀⠤⠀⠀⠸⠿⠿⢾⣿⣿⡏⠀⢿⡿⠟⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣙
⠀⠂⠀⠀⠀⣰⠇⢛⣻⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⡿⠟⠀⠀⠀⠀⠀⠀⠘⢿⣿⡏⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀
⠀⠀⠀⠀⠸⣇⠀⠈⢻⣤⡀⠀⠹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣀
⠀⠀⠀⠀⢸⣿⣤⣄⡘⠻⢋⠀⠀⠷⠷⠶⣤⡀⠀⢀⣤⡄⠀⠜⠉⠑⠤⣄⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠀⠀
⠀⠀⠀⠈⠛⠿⡟⠂⠀⠐⠚⠉⠁⠀⠀⠀⠈⠷⣶⡊⡩⠿⠖⠀⠁⡀⠀⠀⠁⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡇⠆⠀⠀⠀⠀⠈⠻⠿⣿⣿⣟⣿⣆⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠙⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣋⠀⠀⠀⠀
⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣄⣤⡨⣿⣟⡿⠁⠀⠀⣶⡆⠀⠀⢀⠀⢀⡀⠋⠀⠀⠀⠀⠀⠀⠛⣿⣿⣾⣿⣿⣿⣿⣷⣷⣶⣄⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡼⢤⣤⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⡇⠉⣀⠀⠀⠀⡿⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠏⢶⠄⠰⠶⠶⠶⢀⣿⣿⣄⣌⢻⣶⣆⣄⣴⣤⣼⣿⣿⣿⣿⣷⠀⢩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣬⠀⡂⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⢒⣶⣬⣿⣿⣿⣿⣧⣛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣯⣄⣺⣿⣯⣿⡿⣿⣿⣿⣿⣿⡏⠘⢣⡀⣿⣦⣿⣿⣿⡷⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠁⠀⠀⣼⡿⢿⣿⣆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣗⠘⠿⣿⣿⣿⣿⣿⠟⠉⣿⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⡈⢀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠠⣤⣻⠃⠀⣢
⣿⣿⣿⣿⣭⣍⠉⠉⠉⠈⠙⢻⣷⡖⠻⠛⠛⠓⠉⢸⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠈⠿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣀⣀⣤⣤⡾⠟
⢹⣿⣿⣿⣿⠻⠃⠠⢀⡄⠀⠀⠙⠋⠀⠀⠀⠀⠰⣿⠛⣛⣿⣷⣄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡊⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠘⠿⠻⡿⠍⠀⠀⠀⢸⡇⠀⠀⠀⠈⠳⠦⠀⠀⠘⠿⠿⠛⠀⠈⠉⢋⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣰⣿⣿⡿⠛⠛⠉⣿⣿⡿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣄⠀⠀⣀⣀⣹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠉⠀⠀⢀⣴⣿⠗⠃⠈⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⣧⣽⣆⣦⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣶⠿⠿⠂⠀⠀⠀⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠀⢀⡀⣤⣤⡴⠄⠠⠤⠀⣶⠛⠀⠈⠛⠛⠻⣿⣿⣿⣏⠙⠿⠻⠗⠿⠿⣿⣿⣿⣿⣿⣿⡿⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠾
⠶⠀⠀⢀⣀⡾⠉⢉⣿⠁⠀⠀⠀⠸⠓⠀⠀⠀⠀⠀⠀⠈⠹⠟⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⠻⡿⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⢸⣿⡇⠀⠀⢘⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣾
⠀⠀⠀⣸⣿⣿⣶⠦⠚⠙⣡⡤⠄⠀⠉⠁⢲⠀⠀⣰⣶⡄⠐⠋⠀⠈⠲⠄⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠙⠇⠀⢼
⠀⠀⠀⠈⠉⠡⠍⠀⠀⠚⠉⠀⠀⠀⠀⠀⠈⢷⣆⠀⠒⠛⠁⠀⠀⠄⠀⣀⣀⣀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠦⣤⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢴⣴⣺⣁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣿⣻⡿⠙⠛⠁⠀⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣤⣀⣀⠈⡛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠽⠿⠥⠀⠀⠀⠀
⠀⣴⣾⡿⠀⠀⠀⠀⠀⠒⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⢀⡙⠟⠁⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⣙⣿⣿⣿⣿⣻⣿⣿⡿⣛⣴⣤⣴⣶⣶⣶⣦⣤⣤⣄⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡶⣿⣶⣶⠀⠀⠀⠀⠀⣴⣴⣶⡄⠚⠀⠀⠄⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠏⢶⠶⠰⠶⠶⢶⣜⠟⠃⣤⡙⢿⣿⣷⣶⣾⣿⠋⠛⠛⠛⠋⢁⣀⣤⣀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⣻⣷⣾⣿⣿⣿⣿⣮⣻⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢘⢷⠠⣶⠀⣿⣷⣿⢷⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠾⠛⣿⡿⠆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣀⠹⢿⣿⣿⣿⣿⡿⠇⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡈⠀⢀⣯⣴⣿⡿⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⠦⠟⠀⢀⣶
⣿⣿⣿⣷⣶⣆⠈⠉⠀⠈⠙⣿⣿⡟⠋⠉⠉⠉⢁⣵⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⡟⠙⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣶⣾⡟⠛
⣿⣿⣿⣿⣿⠍⠀⠐⣠⠂⠀⠀⠉⢁⠀⠀⠀⠀⢻⣟⣹⡿⠿⣧⣄⡿⠿⢹⣿⣿⣿⣿⣿⣿⣿⣦⣤⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠛⠛⠻⠛⡣⠀⠀⠀⢿⠁⠀⠀⠀⠈⠛⠂⠀⠀⢹⠟⠛⠃⠀⠀⠉⣁⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢨⣿⣿⡿⠟⠛⠉⢙⣿⣿⠿⠟⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠶⢹⡶⠀⠀⣠⣄⣀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠋⠀⠀⠀⢠⣾⡿⠟⠈⠁⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢠⣶⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⢠⣶⠶⠷⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⣤⣠⣶⣶⡒⠀⠐⠂⢨⠍⠁⠀⠈⠉⠉⠻⣿⣿⣿⡦⠙⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⡏⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠿
⠓⠀⠀⣤⣔⠛⠀⢼⡟⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠈⠛⠙⠅⠀⠀⠀⠀⠀⠀⠈⢿⠿⠉⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣀
⠀⠀⠀⣿⣿⡀⠀⠀⣽⣿⡆⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿
⠀⠀⠠⣿⣿⣿⡟⠒⠉⢉⣶⠒⠀⠀⠁⠉⠃⠀⣠⡾⠷⣀⠈⠀⠀⠐⠶⠄⠀⠀⢰⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠙⠙⠻⣿⣿⣿⣿⣿⣿⡇⠘⠃⠀⢿
⠀⠀⠀⠈⠑⠂⠁⠀⠘⠉⠁⣀⠀⠀⠀⠀⠈⠻⣧⠀⠉⠉⠀⠀⠀⢀⣀⣀⣠⣤⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠉⠻⠿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠟⢿⣿⣿⠿⠶⠾⠷⠈
⠀⠀⣀⡀⠀⠀⠀⠀⠶⢷⢯⢭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣧⣿⠟⠊⠙⠉⠀⣰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣠⣦⣤⣆⣀⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠟⠳⠆⠀⠀⠀⠀
⠰⠿⠿⠃⠀⠀⠀⠀⠘⠀⠐⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄⣠⠘⠋⠀⠀⠀⠀⣴⠏⠀⠀⠀⠐⠀⠀⠀⠀⠀⡄⠀⠀⢠⣭⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣷⣾⣿⣿⣿⣶⣶⣦⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠇⠿⣿⣇⣀⠀⠀⣀⣀⣕⣼⣶⣤⣏⡀⠐⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠶⣶⠮⢶⠶⠰⠶⠶⠶⠝⠛⠠⡄⠙⠿⠿⢿⣿⣿⣿⣦⣻⣏⢹⣿⣧⣤⣤⡀⠀⢀⣷⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣯⣟⣿⣶⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠜⡂⢻⠀⠸⠟⠁⠀⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢦⣨⣥⣤⣾⡏⠁⢒⣀
⣿⣿⣿⣟⣻⠻⠿⠿⠿⠾⣿⣦⣽⣿⡿⠿⠿⠿⠻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠸⢿⢿⣇⣀⣀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣺⣿⣿⣿⣿⣿⣿⢿⣯⣤⣶⣿⠟
⣿⣿⣿⣿⢿⡆⠀⡀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠠⣾⡿⣿⣿⣿⡛⢹⣿⠏⢛⣿⣿⣿⣿⣿⣧⠀⠀⣜⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⣿⣿⡟⠋⠀⠀⠀⠸⡧⠀⠀⠀⠐⢦⣄⠀⠀⠠⣿⣾⣿⡋⠙⠻⠚⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠈⠁⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⡀⠀⠉⠀⠀⠰⣃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣽⣝⢻⣿⣿⣿⠿⠋⠀⠀⢀⣼⣿⡏⠡⠄⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⣛⡍⣤⣲⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣶⡿⠛⠁⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠀⠀⠀⠑⢀⣀⣀⣄⡀⣀⠀⠀⡤⠄⠀⠻⠿⢿⣿⣿⣿⣿⡻⣿⠿⠏⢿⣿⣿⣿⣿⣿⣿⣿⡟⢻⢹⠟⣿⠛⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣽⣿
⣀⠀⠀⠀⢸⣿⢛⣿⡿⠀⠀⠀⢀⡮⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⡛⠻⣿⠷⢯⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀
⠀⠀⠀⣾⣯⠀⠈⠛⣶⣦⡄⠈⠙⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣾⠆⠀⠀⠀⠀⠀⠀⠈⢛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⣦⡀⢀⣤⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢷⣾⣿
⠀⠀⠀⣿⣿⣦⣤⣼⠟⠋⣅⣀⡲⠢⠶⢤⡀⠀⢠⣤⡀⠰⠛⠒⠒⢤⡄⠀⠀⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠁⠋⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣽⣿
⠀⠀⠀⠻⣋⡛⠛⠉⠶⠞⠋⠁⠀⠀⠀⠀⠰⢶⣟⠩⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣧⣀⣴⡏⠿
⠀⠀⠀⠀⠈⠁⢀⣀⣤⣤⣤⣖⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠠⡶⠾⢺⣿⠿⢿⣿⠗⠀⢀⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠉⠛⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⠁⠀⠀
⣀⣴⣾⡷⠀⠀⠀⠉⠻⠿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠛⢿⠏⠀⠀⠉⠀⢀⣾⠃⠀⠀⣀⠄⠃⠀⠀⢀⠀⠀⠀⡿⢿⣿⣿⣿⠿⣿⡿⠶⠟⠀⠀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣬⣁⣀⣀⣀⠀⠀
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⣧⣤⠀⠀⠀⠀⠀⠀⣄⣜⡛⣠⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠠⠤⠄⡿⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠄⠀⠀⠀⠀⠀⣤⣤⣄⣾⣿⣉⡙⣿⣿⣶⣶⣶⣶⡟⠛⠿⠷⠄⠀⠀⢀⣄⣀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠟⢷⠖⠰⠶⠶⠟⠁⠈⠉⠃⠈⠉⠈⠉⠁⠁⠀⣀⣀⣀⣀⣀⣀⣸⡏⠀⣀⣴⣿⠃⠀⠀⠀⣠⣤⣤⣤⣠⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠮⣹⣯⡄⠛⣿⣿⣿⠿⠿⣿⡃⢸⣿⣿⣿⣿⣻⢿⣿⣿⣻⡿⢿⣏⣁⠀⠀⢠⣧⣤⡋⠀⢀⣀⣰⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣤⠀⠀⠀⠀⠀⠀⠃⠀⠀⣤⠀
⣿⣿⣷⣶⣀⠈⠀⠀⠈⠹⣿⣿⠉⠉⠈⠀⠀⣀⣿⣿⣿⣿⡟⠛⣛⣋⠻⠿⣿⣿⣿⣿⣏⠀⠀⢸⣿⣿⣰⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠁⣹⣿⣿⣧⣽⣿⣿⣿⣿⣟⣴⣿⣷⣦⣤⣤⣄⣀⣠⡀⠀⠀⠁⠀
⠛⠟⠉⠀⠉⠀⠂⣤⠀⠀⠀⠉⣀⠀⠀⠀⠀⣹⠋⣼⡿⠿⣷⣄⠛⠋⢠⣾⣿⣿⣿⣿⣿⣧⣦⣾⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣙⠿⢿⠿⠷⢿⣧⡄⠀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠛⠀⠀⠀⠸⠛⠛⠀⠀⠀⠀⡀⠀⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⡿⠟⠛⠉⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⠀⠀⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠛⠸⢟⢀⠠⠤⣄⡀⣴⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠟⠙⠛⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣾⣴⣿⡟⠁⣾⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⠃⠉⣿⣿⣿⡟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣋
⠀⠈⠀⠀⣦⠘⣿⣯⡉⠀⠙⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⣿⣿⠀⠈⠉⠁⠈⠉⠙⢻⣿⣿⢻⣿⣿⣀⡠⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠚⠛⠛
⠀⠀⠀⡀⠀⠐⠿⣟⣁⠀⠠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠈⠻⠋⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀
⠀⠀⠀⣿⣂⡀⢠⣿⣿⠇⠀⠈⠀⣀⣀⡀⠀⠀⢀⡀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⢀⣺⡇⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣏⡉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠛⠻⢿⣦
⠀⠀⢰⡿⠿⡿⠿⠋⣐⣶⠖⠀⠀⠀⠀⢁⣀⠴⠿⣛⣄⠀⠀⠍⠑⠲⠄⠀⠀⣰⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠉⢻⣿⢿⣿⣿⣿⣿⣿⡿⡅⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⢿⡇⠀⠀⠀⢿⣿
⠀⠀⠀⠈⠓⠦⠀⠘⠉⠀⣠⠀⠀⠀⠀⠘⠿⣦⠈⠉⠁⠀⠀⠐⣆⣠⣤⣤⣤⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⡿⠓⠒⠒⠋⠈⠈
⣠⣤⣤⠀⠀⠂⠲⣶⣿⣿⢿⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⢽⣿⣿⣏⠉⠿⡏⠀⠰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠠
⠿⠿⠛⠀⠀⠀⠀⠉⠁⠈⡡⡆⢀⣤⠀⡀⠀⠀⠀⠀⢠⡠⣿⣾⣦⣠⠙⣯⡁⠁⠀⠰⣶⣄⣹⣿⣄⢀⣀⡁⣀⣀⣀⣴⠀⠀⢠⣼⣶⣿⣿⣿⣿⣿⣭⣥⣤⣴⣲⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⡤⠤
⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣷⣿⣿⣿⣿⣯⣤⣤⣤⣶⣿⣿⣿⣿⣿⣧⣴⣿⣿⣦⣤⣤⡀⠛⢻⣿⣿⢸⣿⠟⠿⣻⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀
⠀⠀⠠⠄⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣴⣿⣿⣿⣿⣤⣿⣿⣿⣿⡅⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠷⠶⣶⠿⢿⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠻⠿⠿⠿⠉⠰⢿⣶⢈⣭⣿⠿⠋⠛⠙⢠⣀⣿⣿⠿⣿⣅⡉⢿⣿⣯⣿⠛⣷⣤⠀⠀⢠⡆⠀⠀⠀⢠⣶⣴⣿⣿⣿⣿⣿⣿⣤⣽⣿⣹⣿⢸⣿⣿⣿⢻⣿⣿⣿⣿⣿⠏⢭⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀
⣿⠿⠯⢥⠀⠀⠀⠀⠀⠛⢻⠅⠀⠀⠀⠀⢠⣾⠿⣿⣿⡌⠀⢩⣤⠀⠛⣻⣿⣿⣿⣿⡀⠀⠀⢇⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⣹⣿⣿⣶⣿⣿⣿⣿⣿⣼⣿⣿⣿⣶⣶⣶⣶⣴⣆⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⣄⡀⠀⠀⠠⣇⣼⡟⠉⠛⠳⠊⠁⠀⢿⣿⣿⣿⣿⣿⣷⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠉⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣭⡝⠛⠋⠉⣿⠖⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣋⠀⠀⠀⠀⠀⠐⠀⣐⣿⣿⡿⠿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠀⠀⢰⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢷⣤⣤⣀⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⢈⣛⠁⠀⣘⣳⡖⢘⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠀⠀⠀⣀⣤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠛⠛⠳⠟⢉⣁⠀⠸⡿⠏⠉⣿⣿⡿⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⠛⠀⠀⠀⠀⢠⣤⠀⠀⢀⡀⣀⣤⡄⡗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣟⣉⣉⣁⣄
⠀⠀⠀⠸⠀⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠙⢻⣟⠉⣿⣿⡀⢈⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣯⣿⡿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠈⢡
⠀⠀⣤⡄⠀⠈⢷⣶⡄⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠘⠏⠀⠸⠟⠘⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣯⣐⣀⣀⣾⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣀⣀⠀⠁
⠀⠀⣹⣷⣤⣠⣿⠿⣇⣀⣀⠀⠒⠶⠄⠀⠀⣠⣤⠀⠰⠚⠋⢀⣀⠀⠀⠀⢀⣠⣶⣿⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⣻⣦⡀
⠀⠀⠛⢉⠻⠉⠁⣠⡿⠇⠀⠀⠀⠀⢠⣤⡚⠉⠭⠶⠆⠀⠀⠀⠈⠃⠀⠀⢼⣿⣿⠿⠦⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣷⡶⠆⠀⠈⠉⠛⠛⠿⣿⣿⣻⣧⣀⣀⡀⠙⠿⠃
⠀⠀⠀⠀⢈⣀⣀⣭⣄⣶⠆⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠈⢰⣶⣷⣾⣿⣿⣿⣿⠷⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡈⢙⢿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣏⡉⠉⠉⠁⠀⢀⣾
⣶⣷⡆⠀⠈⠉⢻⡿⢿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣘⠛⢿⣿⠧⠄⢿⣿⡆⠸⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣾⣿⣷⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⡀⠀⢀⣈⡉⢁⠀⠀⠀⠀⠘⠻
⠉⠉⠀⠀⠀⠀⠀⢀⠈⣧⣿⣴⣿⣤⣤⠀⠀⠀⠀⣐⣶⣽⣿⣿⡔⠀⣠⣤⣀⣰⣿⣿⣷⣾⣿⣿⣅⣰⣶⣶⣾⣿⣾⣿⡏⠁⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⢀⣤⣴⣾⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠁⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠷⠶⣶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡠⠀⠉⠉⠈⠀⠙⣿⣴⠛⠋⠉⠉⠁⢀⣼⣿⣿⣿⠿⠟⠿⢛⢉⣿⣿⣿⣤⣾⡿⠁⠀⠀⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠙⣿⣿⣿⣹⣿⣿⣿⣿⣿⢏⣽⣿⣥⣄⣀⣀⣀⠀⣀⠀⠀⠘⠀⠀⠀
⠉⠁⠉⠀⠐⢠⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⡟⢉⣽⠿⣿⣤⡘⠿⠃⣤⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠷⠒⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣶⣦⣀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠓⠂⠀⠀⢈⡜⠛⠁⠀⠀⠉⢁⣀⢠⣭⣿⣿⣿⣿⣿⣿⣿⢿⡆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠟⠃⠀⠀⠀⠀⠐⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠉⠉⠀⣿⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠶⡯⣶⡀⠀⢀⣀⣀⣸⣿⡿⢿⣿⣿⣭⣽⣿⣿⣿⣀⡀⢸⣿⣿⣿⣿⣿⣿⡟⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣿⣦⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣦⣄⣤⣶⣾⠟⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢽⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀
⠀⠀⣠⠠⣶⣶⠒⠀⠐⠂⠀⠀⠐⠀⠀⠉⠉⠙⠻⠿⣾⡄⠈⠿⠟⠛⠛⠻⣿⣿⣿⠿⣿⡿⠀⠀⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡥⠼⢷⣶⣶
⠀⠀⠈⠐⢿⣿⡃⢠⣤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠉⠁⠀⢹⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⠿⠻⠯⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⢨⠿⠛
⠀⠀⠀⠀⢀⣿⣿⡄⠀⠘⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠀⠀⠀⠀⠀⠀⣸⢟⠀⠀⠀⠀⠸⠿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣆⣤⣽⣏⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣶⣾⣷⠀⠀
⠀⠰⣷⡖⠹⠿⠃⣲⡶⠀⠀⠉⠉⠁⠀⢀⣼⡿⢦⡀⠀⠀⠈⠓⠦⠀⠀⢠⣾⣿⠿⣀⣀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⡆⢰
⠀⠀⠀⢄⠀⠀⠛⠋⢀⡀⠀⠀⠀⠘⠿⣧⡀⠛⠉⠁⠀⠀⢄⣀⣠⣀⣤⣼⣿⣧⡀⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠛⠋⢿⣿⣿⣿⣷⠶⠿⠈⠙⣿⣿
⣀⠀⠀⠀⠁⠢⣆⣶⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣿⣿⣿⡿⠛⢿⢿⠀⠀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣄⣛⣿⡛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⢿⣿⡶⠦⠄⠀⠀⢰⣿⣿
⠟⠀⠀⠀⠀⠀⠉⠀⠈⣉⠁⣀⡀⠀⠀⠀⠀⠀⠀⣀⣹⣶⣶⢉⡽⠟⠁⠀⠀⠀⢤⣀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣻⣿⣷⣾⣿⣷⣶⣶⣶⣴⣦⣤⣤⣤⣶⣶⣦⣤⣤⣤⣄⣀⣈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣆⡀⣀⣠⣴⣿⣿⡿⡿⠋⠀⣤⣦⣄⡀⠀⠈⠛⠁⢹⣿⡆⠀⠀⠀⠀⢀⣠⣼⣶⣤⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢲⠿⣿⣿⡿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣄⣬⣿⣿⣿⣿⣿⡃⠂⠀⢻⠀⠀⠀⠀⣀⣾⣿⣿⣿⣟⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠛⠋⠉⠙⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣴⣿⡇⠀⣽⣿⣿⣿⣿⣿⣿⣧⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠿⢷⣶⠴⠶⠶⠶⣨⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣆⡀⠀⠀⠀⠀⠈⢷⣿⠉⠁⠀⠀⠀⣠⣾⣿⣿⣿⣛⠛⣛⣷⣾⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣿⣿⣧⣽⣿⣿⣿⣿⣟⣴⣿⣿⣷⣦⣤⣤⣄⣠⣄⠀⠀⠈⠀⠀⠀
⠃⠀⠁⠀⠈⣴⠀⠀⠀⠁⣀⡀⠀⠀⠀⣹⢇⣴⡟⠻⠷⣦⡟⠻⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡿⣿⣿⡿⢿⣷⣤⠀⠀⠀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠙⡀⠀⢀⣜⠋⠉⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠄⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣤⣾⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠻⠻⢿⠄⠀⠠⣴⡄⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⢸⣿⣿⣿⣿⣿⣿⡿⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣳⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣶⣴⣾⣿⡟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀
⠀⠀⣦⢼⣿⣏⡉⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⠉⠛⢻⣿⡆⠘⠛⠛⠛⠉⠻⣿⣿⡟⠛⣿⡇⠀⣀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣟⣿
⠀⠀⠀⠙⢛⣿⠉⠀⠐⠀⣾⡤⠀⠀⠀⠀⠀⠀⠀⠛⠋⢀⣀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠘⠁⠀⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣤⣤⣤⣶⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣿⣟⣋
⠀⢀⡀⠀⣼⣿⠿⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⡀⠀⢀⡶⠯⣁⡀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣯⣯⠉⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣂⢀
⠀⠸⠿⠞⠉⣥⡶⠖⠂⠀⠀⠀⠀⠀⢀⡤⠿⢛⣀⡀⠀⠀⠀⠁⠀⠀⠀⣼⣿⠀⠀⣀⣀⡀⠀⠀⢠⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣸⣿⣿⣂⣾
⠀⠀⠐⢦⡀⠀⠀⠀⣠⠀⠀⠀⠀⠈⠿⠄⠀⠉⠉⠀⠀⠲⢠⣀⠀⢀⣤⣿⣧⠀⠀⠉⠁⠀⠠⣶⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠿⣿⣿⣿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠉⠹⠿⣿⣿⡿⠿⠿⠟⠈⢹⣿⣿
⣤⠀⠀⠀⠘⢻⡿⠿⢥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡼⠛⠙⠛⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣈⡉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠗⠒⠀⠀⠀⣾⣿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡠⢀⠀⠀⠀⠀⠀⠀⢀⢀⣶⡇⠀⠘⠁⠀⠀⠀⠀⣤⣀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣭⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣌⣉⡉
⠀⠀⠀⠀⠀⠀⣀⣀⢰⣿⣿⠿⣿⣯⣤⣠⣤⣦⣴⣾⣿⣟⣿⠀⡠⡀⠀⢀⣀⠀⠈⠁⠀⠀⣶⡄⠀⠀⠀⠀⢠⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠹⠭⠿⠛⠿⠶⠟⠿⢿⣿⡿⠿⠿⠻⢿⣿⣿⣿⣾⣤⣼⣿⣿⣿⣄⠀⠀⠀⣻⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⣿⡿⠃⠀⢰⣿⣿⣿⣿⣾⣿⠃⣠⣤⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⠶⣶⡷⠰⢶⠶⠶⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡺⠿⣿⣿⣿⣿⣿⣿⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠷⡄⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⢴⡿⢿⣿⣿⣿⡁⠠⠷⠀⢙⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣶⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣾⣧⣬⡁⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠲⣄⡀⠀⠀⠼⣳⣾⠏⠉⠛⠿⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠿⣿⣿⣿⠆⠀⠀⠀
⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠤⢀⣠⣼⣅⠀⠀⠀⠀⠀⢰⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⢛⡛⠓⠀⣀⣲⣶⠸⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢸⣿⣿⣿⢿⣿⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀
⠀⠀⠀⣀⣀⣀⡀⢀⡀⠀⠀⡀⠀⠘⠾⠿⣷⣿⣿⣿⡏⢰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣟⣛⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⡏⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣤⣤
⠀⠷⢾⣿⣯⡀⣀⡈⠀⢠⡀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠟⠀⠁⠀⠈⠀⠀⠙⠻⣿⠈⠹⡿⠀⢠⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⢹⣿⣿⠟
⠀⠀⠈⢿⣬⣤⡀⠁⠁⠻⠷⠂⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣿⠃⠀
⢀⣀⣠⣾⣿⡿⠇⠀⠀⠀⠠⠾⠤⠀⠀⠀⣠⡀⠾⠋⢀⣀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠋⠀⣾⣿⣿⣿⡏⢻⡆⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⣿⣿⣻⣷
⠘⠿⠋⠁⢀⣤⠖⠂⠀⠀⠀⠀⢠⣤⡴⠒⢋⡽⠆⠀⠀⠈⠉⠂⠀⠀⢀⣿⡇⠀⠰⠶⠄⠀⠀⠀⣴⣾⡿⠟⣿⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣤⠀⠀⢻⣿⣮⠙⠻⠿⢿⣿⣿⣿⣿⣦⣤⣴⡿⢿⣿⣿⣿
⠀⠐⠲⢄⣀⣀⣀⣠⠄⠀⠀⠀⠀⠙⠃⠀⠁⠀⠀⠀⠀⠁⠴⠤⠀⣾⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣟⢉⡁⠀⠈⣿⣿⣷⡀⠤⢤⣽⣿⣿⣋⠉⠉⠉⠉⢠⣿⣿⣿
⠀⠀⠀⠈⠛⠿⠟⠓⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠋⠀⠀⠉⠀⠀⠀⢀⣨⣁⡀⠐⠖⠳⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠼⣿⣦⣀⣠⣤⣤⣄⣿⣿⣿⣿⣄⢀⣈⣿⣯⣉⣀⣀⠀⠀⠘⠿⢿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣠⣀⣀⠀⠀⠀⠀⠀⠤⡄⣸⣿⡀⠀⠉⠀⠀⠀⠀⠀⣶⡄⠈⠛⠉⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤
⠀⠀⠀⠀⠀⣠⣤⣀⣿⣿⠿⢿⣿⣦⣤⣤⣴⣶⡾⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠖⠛⠋⠙⠻⠋⠙⠻⠿⠿⠟⠛⠁⠀⣀⠀⠀⢀⣀⣀⡀⠰⣿⣿⣿⣷⣤⣽⣿⡁⠀⢀⣀⡀⣀⣴⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣁⣠⣿⣿⣿⣿⣿⣿⠿⠛⣿⣭⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠶⠶⣶⣿⣿⠆⢰⢶⡶⠖⠀⢀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⠏⠀⠰⠿⢿⣿⣷⣤⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡄⠀⠀⠀⠁⣀⠀⠀⠀⠀⣸⢇⣲⡖⠙⠷⠦⠀⠁⠀⣴⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠐⣿⣿⣿⣿⢿⣅⣽⣿⣿⣿⣿⣶⣦⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣷⠟⠛⠻⣿⣿⣷⢶⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠇⠀⠀⠀⠀⠈⠑⠀⠀⠀⠰⠊⠉⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⠻⠆⠀⢸⣿⣿⣿⣿⣿⣯⣹⣏⠉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠿⢿⣿⣿⠇⣀⣀⠀⣸⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠳⠿⠂⠀⠀⢀⡄⢰⡆⢀⣾⣿⣯⢼⣿⣿⣛⣿⣀⠀⠀⠟⣿⣿⣿⣻⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⢒⣛⣻⣿⣿⣿⣿⣿⣿⣆⠰⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣷⣠⣶⠾⠉⠁⢸⣿⣿⠛⠛⠛⠻⢿⠿⢟⡿⣿⠃⠀⠀⡹⡿⠿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣾⣿⣿⣿⠗⠀⠀⠀⢠
⠄⠐⢿⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⣿⠇⠈⠋⠉⠀⠀⠀⠀⢻⡆⠈⠓⡾⠀⠀⢰⣿⣿⡧⣶⡆⣶⣿⣟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠶⠟⢿⣖⣿⣿⣿
⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡿⠿⠋⠀⢹⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⡛⠉⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠰⠟⠃⠀⠀
⠀⠀⢠⣼⣷⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⡼⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣽⣿⣿⣿⡙⠀⠀⠀⢸⣿⣿⠀⠀⠸⠃⠉⠉⠉⠁⠀⠀⠠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠹⠾⣿⣅⠀⠀⠀⠘
⠿⠖⠀⠀⠠⣴⣆⠀⠀⠀⠀⢀⣀⣠⡼⠿⣂⡀⠀⠀⠀⠙⠂⠀⠀⠀⠿⠁⠀⢀⣀⠀⠀⠀⢠⣤⡻⠟⢿⣿⡁⠀⠀⢠⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⢿⣿⠃⣺⣷⡄
⠀⠀⠀⠐⠚⠉⣀⠀⠀⠀⠀⠈⠻⠇⠀⠚⠉⠀⠀⠀⢀⣀⣀⣀⣤⣴⣿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠈⠉⠁⡀⠀⣸⣿⣿⠇⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠉⠀⠾⢿⡾⠛⠒⠒⠂⠀⠁⣽⣿⣿⣟
⠀⠀⠀⢨⣿⣶⣯⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣿⣿⡟⠉⠻⠿⠀⠀⢶⣶⢖⣰⠀⢰⣶⠆⠀⠀⠘⠃⢾⣿⠿⠟⠀⠀⠀⠴⠶⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠙⠁⣴⠟⠛⠂⠀⠀⠀⠀⢸⣿⣿⡛⠉
⠀⠀⠀⠀⠉⠙⢀⡀⠀⣠⠀⠀⠀⠀⣀⣀⠀⢀⢀⣶⣷⠀⢬⠏⠀⠀⠀⠀⢲⣄⡈⠿⣿⣿⡿⠛⠀⢀⣠⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⡄⠀⠠⡿⣶⣶⣿⣷⣶⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣽⣿⡿⣿⣿⣿⣶⣾⣿⣿⣷⣾⣿⣿⣿⣷⣴⣤⣤⣠⣀⣀⣀⣭⣷⣶⡾⡻⠿⣿⣿⣿⡋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀
⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣷⣿⣿⣿⣿⣽⣃⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡉⣹⣿⣿⣷⣶⣾⣿⣿⣿⣿⣆⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠨⠀⠀⠀⠀⠠⣄⠀⠀⠀⠠⢄⣼⡟⠁⠙⠛⠂⠀⠀⠸⢿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⢸⣿⣿⣿⡟⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⣉⣉⢻⠿⠿⠟⠿⣦⡄⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠿⠟⢛⣛⣿⠁⠁⠀⠀⣸⣿⣿⣿⣿⣷⣤⣹⡍⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠟⢛⣻⣿⣟⣁⣀⡀⣀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠉⡋⠁⠀⣀⣀⣴⠀⣻⣀⣼⣿⣿⣖⡶⣶⣯⣽⣦⣄⠀⠈⢹⣿⣿⣯⣯⣿⢿⣿⣷⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣙⣛⣿⣿⣿⡿⣿⣿⣷⡀⠂⠀⠀⠂⠀
⠀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠻⠣⣾⣓⠂⡀⠀⣻⣿⡏⠉⠉⠉⢻⡟⡋⣿⠻⡏⠀⠀⢀⣹⣛⠛⠛⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠛⣻⣿⣿⣾⡿⢿⡟⠁⠀⢀⣠⣇
⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠈⠀⠀⠀⠀⠀⠘⢿⠀⠉⠙⠁⠀⢀⣿⣿⣿⣚⣶⢰⣿⣛⠛⠙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠐⠛⠹⣿⣻⣿⢿⣁
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⠿⢿⣿⣿⣿⣿⠛⠉⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡀⠛⠉⠀⠀⣀
⣀⡀⠰⠞⠂⠀⠀⠀⠀⠤⠤⠀⠀⢀⣀⠀⠠⠶⠋⠁⠤⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⢴⣿⣿⣿⣧⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⢿⣿⣿⣿⠟⠙⠛⣿⣿⣿⣿⣿⣷⠆⠀⠛⢿⣦⡀⠀⠀⠈⠛
⠛⠁⠀⢀⣽⠿⠂⠀⠀⠀⠀⣤⣤⠞⢛⣥⡤⠀⠀⠀⠀⠈⠁⠀⠀⠐⡁⠀⠀⠤⡄⠀⠀⠀⣶⣮⠓⠙⣿⣧⡀⠀⠀⢀⠚⣛⣿⡋⠁⠘⠻⠂⠀⠀⠉⠀⠀⠙⠋⣀⣀⣙⣻⢿⢿⣿⠿⣛⡀⠀⠀⠹⣿⣇⣘⣿⡄⠀
⠀⠀⢀⣈⣀⣠⡄⠀⠀⠀⠀⠈⠙⠂⠈⠁⠀⠀⠀⠀⣤⣶⠤⣴⣶⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡀⡀⢀⣿⣿⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⠀⠀⠛⢿⡿⠛⠉⠙⠉⠀⠀⣠⣿⣿⣿⠀
⠀⠀⠰⣿⡿⠿⠾⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⢀⠘⠿⣷⡟⠀⠘⠛⠃⠀⠘⢿⣷⣤⣧⣀⡾⠛⠀⠀⠀⠈⠁⠁⠛⠛⠛⠁⠀⠀⠀⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡃⠀⠀⠋⠛⠃⠀⠀⠀⠀⠐⠿⠿⠍⠈⠁
⠀⠀⠀⠀⠀⢠⣴⣀⣠⣆⣀⣀⠀⣀⣤⣤⡀⣄⣬⣿⣇⠘⠏⠀⠀⠀⠀⠈⢷⣤⠘⠻⣿⡿⣿⣅⣠⣤⣤⡶⢿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⡀⠀⠘⠛⣿⣿⣿⣷⣾⣷⣶⣶⣦⣤⡀⠀⠀⠀⠀
⠀⠀⠀⣀⣠⣴⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣤⣤⣤⣤⣴⣾⣿⣿⣶⣁⣉⣽⣿⣿⡿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢑⣙⣿⣿⣿⣿⣿⢟⣄⡀⠀⠀⣠⣤⣶⣶⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⢙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣶⣾⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣤⣶⡆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠃⠀⠀⠀⠀⠈⠲⠀⠀⠀⢘⡴⠟⠁⠀⠀⠈⠀⠀⠀⣩⣿⣿⣷⣿⣿⣿⣿⠿⡆⠀⠀⣿⣿⣿⣿⣅⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣽⠛⠛⠉⢹⠗⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⣴⡄⠀⠀⠀⠀⢀⣤⠤⢿⣿⡏⢉⣻⣿⣿⣿⡀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣼⡄⢀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣤⡄⣠⡴⠶⠟⠈⣿⣶⡾⢿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⢡⠄⠀
⣴⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⣥⡄⠀⠿⠿⠃⠀⠀⠈⢹⣋⠻⠿⣿⠁⠀⢀⣽⣿⣭⣉⣉⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣧⣤⣤⣶⣿⠆⣀
⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣸⣿⡍⠉⠁⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⣿⠿⠛⠻⠗⠀
⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢻⣿⣿⣿⡿⡅⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢳⣤⣴⡏⠀⠀⠀⢰⡿⠏
⠀⠀⠀⠠⠤⠀⠀⠚⠓⠒⠀⠀⣰⣶⡀⠀⠉⠀⠀⠐⠦⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⢿⣿⠇⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⠉⣉⣭⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⣿⣿⡄⢤⣤⠀⠀⠀
⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠶⣾⡉⠴⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣬⣥⠀⠐⠒⠂⠀⠀⠀⠿⠃⠉⠈⠿⠦⠀⠀⠘⠀⠀⢠⣼⣿⡿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠟⢿⣭⣷⣦⣤⣦⠘⠛⢰⣾⣿⡧⠀⠀
⠀⣀⣠⣠⣘⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⣟⣻⣿⠿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠤⢶⡗⢁⠀⠀⠘⠿⠏⠀⠀⠀⠀⠻⠿⠿⢿⢿⠏⠉⠉⠙⠛⠁⠀⠀⠈⣿⡄⠀⠀⠀⠀⣠⣿⣿⠿⠷⠀⠀
⠀⠈⠙⠋⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣤⣤⡈⢛⡻⠃⠀⠈⠀⢀⡀⠀⢀⣠⡤⢤⣤⠛⠁⠀⠀⢀⣀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣠⣄⣀⣀⡀⠘⠛⠛⠃⠀⠀⠀
⠀⠀⠀⠀⠸⣦⣠⣼⣧⣶⣄⡀⠀⠀⣀⣳⣶⣿⣿⣧⣆⠀⠀⠀⠀⠀⠀⠛⠓⢀⣠⣤⣀⣀⡶⢶⣶⣦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠹⢿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⢿⡿⠟⢿⣿⣷⣦⣤⣄⣀⣀⣿⣿⣿⣿⣿⣾⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⢻⣿⣿⣿⣿⣿⣿⣿⣧⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⡿⣹⣿⣿⣴⣤⣄⣠⣶⣿⣿⣧⠀⠀⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⡆⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⢿⠿⢛⣛⣛⡟⠃⠀⠀⠈⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡰⢀⣀⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⢛⢻⣿⣿⣿⣷⣀⣀⡖⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⢛⣛⡻⡫⣿⣽⣿⣧⣴⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⡀⠀⠀⠀⠀⠀⣢⣤⣾⣿⣿⣾⡿⢿⣿⡿⠟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠂⠀⠀⠀⠀⠀⠀⠉⣍⡀⢀⣠⣤⣶⠀⣿⣷⣶⣿⣿⣿⣿⣷⣦⣧⣶⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡁⠀⠀⢷⡤⠀⢠⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠛⠛⠣⠿⣿⣳⣄⠀⢻⣿⡿⠋⠝⠩⡿⣿⠿⠿⠻⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣅⣀⣤⣼⣧⠄⠀⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠀⠀⠁⠀⠀⠀⠀⠀⢻⡇⠀⠀⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠙⣿⣿⠿⢿⣷⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡿⠿⣿⣿⣿⣿⣟⠉⠁⠀⠈⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣼⡟⠁⠀⢸⣿⣿⠆⠀⠀
⠀⣀⠀⠀⠐⠢⠄⠀⠀⣠⣄⣀⡀⠀⠀⠀⠡⢤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡰⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠙⣻⣷⣇⢀⣀⠘⠋⣿⠀⠀⠀
⠃⠀⠀⠀⠀⠀⠀⣤⠐⠛⠡⠼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠠⠄⢸⣿⠟⠃⠛⣿⡄⠀⠀⢠⣾⣿⡻⢿⣿⣿⣿⣿⠟⠏⣿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣄⣀⣤⠻⠿⣧⣼⣿⣷⡂⠁⠀⠀⠀
⠀⢠⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖⢰⣶⠾⠿⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣴⣤⡀⠀⠙⣉⠁⠀⢻⠿⠏⠁⠀⣴⣿⣿⣿⠅⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡋⠉⠉⠁⢀⣾⣿⣿⣿⠁⠀⢶⣤⣤
⠄⠐⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠏⠀⠀⠀⠀⠉⢰⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⠯⠔⠂⠃⡀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠀⠛⠿
⠀⠀⠀⢀⡀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠸⣻⣧⠀⠀⠀⠀⠀⠀⠀⠸⠦⠄⠉⣹⣁⠀⠀⢀⡀⠀⠀⢀⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠿⠛⠋⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣦⣤⣶⣲⣶⣦⡄⠀
⠠⢤⣴⣿⡟⠛⣿⣥⣄⠀⢀⣤⣤⠚⠷⣿⡯⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣤⡁⣼⣷⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤
⠀⠚⠋⠉⠛⠉⠉⠈⠉⠀⠈⠃⠁⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣷⣦⣀⣀⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⠀⠀⢀⣤⣶⣩⣿⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣀⣤⣤⣶⣶⣾⡿⠿⠋⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣿⣟⣟⠿⢿⣿⣿⣿⣅⠀⠠⠶⠶⠿⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣌⣉⡉⠙⠛⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠽⢿⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠀⠀⠀⠀⠉⢛⣉⠀⢀⣀⣰⡆⠸⣿⣭⣽⣿⣿⣿⣿⣿⣛⣹⣠⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⢿⣿⣿⡭⣿⠿⠿⠿⢬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠄⠀⢠⣆⡀⡀⢀⣿⣿⣏⠀
⠀⠀⠀⠀⠀⠘⠺⠿⢴⣿⣿⣏⡁⠘⣿⣿⣿⠉⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠈⠹⠏⠁⣿⠸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣹⣿⡀⠛⠛⠿⠿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠃⠀⠉⠋⠀⠀⠀⠈⠙⣿⡆⠀⠹⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⣰⡄⡀⣿⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠚⢻⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣿⣿⣼⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣼⣿⠿⠚⣿⣿⣦⡄⠀⠀⠐⣶
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⢨⣿⣿⣿⣿⠛⠀⠀⠀⠀⣿⣿⡏⠉⠉⢹⣿⣿⣿⣿⣿⠉⠉⠉⣿⣿⠉⠉⠉⢿⣿⠉⠉⠉⡿⠿⠉⠉⠀⠀⢠⠈⠉⠉⡅⢠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡿⠷⣒⣷⡄⠀⠀⠀⠈⠉⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⣻⣿⡿⠟⢿⣿⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠈⢿⠆⠀⠀⠃⡀⠀⠀⢰⣾⣿⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⠄⠈⠁⠁⠀⠀⠀⠀⢀⣤⡤⢤⣤⣾⣷⡀⠀⠀⠀⠀⠈⠵⠉⠉⠁⠀⠀⠉⣁⣀⠀⠀⢿⡿⠿⠃⠀⠀⢸⡿⠋⣻⣿⣿⠀⠀⠀⠛⠇⠀⠀⢠⡀⠈⡀⠠⣄⠿⠇⠀⠀⢸⣿⣿⠄⠀⠀⣤⣀⠀⠀⠀
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢿⡴⠾⠋⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠙⠛⢧⣤⣶⣾⣷⠆⠀⠀⠈⠁⠸⠿⢿⣿⠀⠀⠀⠀⢀⠀⠀⢸⣧⠀⡨⢊⠈⣶⣤⠀⠀⠈⠿⠟⠀⠀⠀⢻⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣾⣆⠀⠀⠀⠀⠀⠀⠀⢒⣀⡀⠐⠾⣿⠓⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⡟⠃⠀⠀⠀⠀⠀⢀⣀⣸⣿⡀⠀⠀⣿⣿⠀⠀⠸⠋⠉⠀⠀⣈⣿⣿⣧⣄⣀⠀⠀⣀⣠⣄⣀⠉⠀⠀⠀
⣴⡶⠾⣿⣓⣀⡀⠀⢀⣀⣠⣦⣾⣿⣇⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣾⣘⣿⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠉⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠴⢿⣿⣿⣿⡿⣿⠿⠿⠿⠿⠿⢿⣁⠀⠀⠀
⠿⢧⡤⠾⠟⠿⠿⣷⠿⠾⠟⠀⠉⠉⠉⠀⠀⠀⢀⣀⠠⠄⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣴⡿⠁⡴⠀⠢⠀⠀⠀⢠⣶⢸⢠⡄⠀⠀⠀⠈⢛⢘⠎⣿⡟⠠⢙⣷⣄⢀⣼⣿⣾⠃⢨⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣿⣿⣄⣀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⢉⣡⣤⣤⣶⡀⠰⠶⣶⡌⢤⡠⡼⠀⠀⠀⢸⡿⣸⣿⣿⡄⠀⠀⢠⣐⢐⡄⣿⢁⣠⣁⢻⣿⢸⣿⣿⣿⡐⠲⠀⠂
⠀⠀⠀⠀⠀⢦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢥⣤⣶⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣬⣥⡀⠀⠀⠀⠀⠀⢨⣷⣿⣿⡿⠀⠀⠀⣨⣿⣶⣾⣷⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡮⠬⠵
⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣌⣙⠻⢿⣿⣿⣿⣿⣿⣷⣾⣷⢦⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣤⣤⣀⣀⣀⣀⣠⣤⣀⣀⣀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤
⣿⣿⣿⣿⣿⡿⣼⣿⡁⣾⣿⣿⣶⠀⡸⣿⠿⣿⣶⣶⣦⡀⢸⣿⣿⣿⣿⣿⠟⠉⠛⠛⣿⣿⣿⣿⣿⣿⡿⠿⣿⠁⠛⠱⠸⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏⠀⢿⣿⣿⣿⣿⣿⣿⣻⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣅⠀⠺⡟⠛⢿⣿⠀⢹⣿⣿⠟⠁⠀⣠⣤⡀⠀⠩⣼⠟⠛⠃⡇⠀⢸⠀⣸⣤⣿⣿⠏⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⣹⠛⣺⠛⠃⠀⠀⠀⢙⡛⠳⠀⠀⡄⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠄⣾⡗⡰⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣄⣠⣀⠀⠀⠋⠀⣤⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⣀⠀⠀⠉⣠⠟⠁⠀⠀⠀⠀⠈⢹⠛⠀⠀⠁⣰⠿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢀⡀⠀⠀⠀⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⢞⡻⡿⠖⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⡉⣭⣿⠉⠉⠉⠉⢿⣛⠉⠉⠉⠿⢿⢩⡉⢡⣼⣏⠈⠁⠀⠀⠀⠀⠉⠉
⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⡞⠁⢸⣿⣿⣿⣿⣿⣿⡾⠛⠓⠀⠀⠀⠀⠈⢿⡇⠀⠀⣤⣄⠈⠁⢸⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣧⠚⢿⣿⣿⣿⡿⠙⠿⢹⣿⣿⣿⣿⣤⣿⣶⣦⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⠉⠀⠀⣠⣿⣿⣀⣠⣀⣸⡷⣠⣾⣿⣿⠁⠀⣼⣿⣿⡃⠀⠀⠀⠀⢀⡀⠀
⠹⠿⠛⢋⣉⣽⣿⣷⡆⠉⠻⣿⣷⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣾⣿⣿⡇⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠰⠿⠿⠛⠉⠉⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣩⠊⠈⣿⡿⠉⠉⠈⠛⠿⠣⠉⠀⣀⣐⠂⠀⠀
⠀⠀⠀⠾⠉⠙⠋⠋⣿⢡⡄⠀⠛⠛⠻⠟⠈⠉⠉⠉⢸⣿⣿⣿⣵⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠀⠀⠀⠀⠀⢀⣰⣾⣀⣀⣰⣿⣿⣿⣏⣹⣿⣿⣉⣀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠛⠿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠐⠛⢁⡿⢿⡿⢸⢷⡆⣦⣤⡤⣴⣶⣾⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⡿⣿⢿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠠⣶⠤⠙⠉⠩⡿⠻⣿⣿⣿⡿⣾⠋⠀⢿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⢸⡘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣦⣴⣿⣿⣿⣿⣴⣇⠀⠐⠀⠀⠀⠀⠀⡴⠠⠢⠀⠀⠀⢹⡿⢸⡓⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠑⣾⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⢿⡏⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠈⡀⠘⠸⠷⠆⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠀⣿⣿⣿⣿⣿⢟⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⠄⠀⢿⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠉⠁⠉⠀⠀⠈⠛⠛⠛⠛⢻⣿⠿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠶⣾⠏⢿⠍⠹⠿⠿⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠟⣿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠛⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣼⣿⣷⣿⣿⣿⣵⠁⡰⣿⠿⣿⣶⣶⣶⣅⣽⣿⣿⣿⣿⣿⠿⠋⠛⠻⣿⣿⢿⣿⣿⣿⣿⠻⣿⡅⠋⠰⠼⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠍⠀⠻⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣤⣤⠀⠼⡿⠛⣿⣿⡀⢸⣿⣿⠟⠁⠀⣠⣤⡀⠈⠋⣬⡟⠛⠃⡇⠀⣸⡀⣸⣧⣿⣿⠎⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠙⠛⠿⣿⠿⠿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠈⣹⡟⣿⣟⠋⠀⠀⠀⠙⡛⠣⠀⠀⡎⠀⠀⠰⢠⣾⣿⣿⣿⣿⣿⣿⠆⣾⡗⣰⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⠀⠀⠀⠀⠀⠴⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡄⣀⠀⠀⠈⣱⣟⠋⠀⠀⠀⠀⠈⢹⠓⠀⠀⠀⠰⠟⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠐⣶
⣿⣿⣿⣿⣿⣷⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡾⣾⢯⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⣉⣭⣿⡟⠁⠀⠀⠒⢟⠈⠁⠈⣇⠏⠉⢩⣹⣯⣽⠉⠉⠁⢄⡀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣶⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⠟⠈⠉⠋⠀⢀⣠⠀⠀⢾⣁⠀⠀⣷⣀⠀⠈⢋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠻⣿⣿⡋⡹⢹⣿⣿⣯⣿⣥⣿⣶⣦⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠃⠀⢼⣿⣿⣿⡿⠛⠀⠀⢀⣵⣿⣿⣷⣠⣰⣈⣿⣧⣼⣿⣿⣾⣁⣰⣿⣿⠀⠁⠀⠛⠀⠀⠀⠀
⠙⠿⠟⠛⢋⣭⣿⣿⣿⣦⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⡷⠀⠀⣀⣾⣿⣿⣿⣿⣿⣶⡇⠀⠀⠈⠛⠉⠁⠀⢀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⣿⣿⠸⠉⠙⠛⠛⠃⢤⢦⣿⠂⠐⠀⠀
⠀⠀⠀⠰⠏⢉⡁⡉⣹⢻⣿⣧⢀⣀⡘⢛⠃⠀⠈⠉⢸⣿⣿⡿⢁⣶⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣰⣿⣄⣀⣀⣿⣿⣿⣿⣻⣿⣿⣋⣁⣀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⠋⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠏⠁⡛⣻⡿⢸⢻⡇⣿⣷⣤⣴⣶⣾⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠠⠄⠀⠀⣶⠤⠙⠋⠹⡿⠿⣿⣿⣿⣿⣿⠟⠋⢸⠿⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⣿⣿⣽⣿⣿⣿⣿⣴⣦⠀⠐⠂⠀⠀⠀⠀⡴⠠⠢⠀⠀⠀⢹⣿⢸⣷⠉⠀⠀⠘⠈⠃⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿⡟⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠈⠁⠈⠹⠷⠌⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠛⠃⠀⠀⠀⠀⠀⢰⣿⣿⠛⢳⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⡷⠘⣿⣿⣿⣿⣿⡏⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠋⠀⠀⠙⠛⠈⠈⠀⠀⠈⠉⠉⠉⠛⢻⣿⡿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⠿⠶⣶⣏⣷⠄⠹⠿⠿⠟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢿⡟⢿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣟⣼⣿⣷⣿⣿⣿⣵⠁⢰⣿⡿⣿⣤⣴⣼⣜⣿⣿⣿⣿⣿⣿⠿⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠋⠰⠮⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠍⠀⠻⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣥⣨⢀⢼⡿⠟⣿⣿⡀⢹⣿⣿⠟⠁⠀⢀⣀⡀⠈⠃⣬⠟⠛⠋⡟⠀⢸⡀⣸⣧⣿⣿⠏⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠛⠻⢿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠙⢹⡟⣷⣿⠋⠀⠀⠀⠛⠛⠇⠀⠀⡌⠀⠀⠰⢠⣾⣿⣿⣿⣿⣿⣿⠆⣾⡗⡰⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⠀⠀⠀⠀⠀⠰⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⢀⡄⣀⠀⠀⠈⣡⢿⠋⠀⠀⠀⠀⠘⢳⠲⠀⠀⠀⢰⡟⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠈⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⠀⠀⠀⠐⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡾⣺⣿⡷⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠿⣿⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣏⠀⠀⠀⣬⣿⣿⠿⠟⠟⢿⠁⠀⠉⣇⠟⠉⢹⣽⣧⣽⠁⠉⠁⠄⡀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠿⣿⣿⣿⣿⣿⣾⣿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⣿⠟⢁⢀⣤⣿⣿⣿⣉⣴⠀⠀⣾⡂⠀⠀⣧⣀⠀⠀⢛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⢿⣿⣿⣿⣿⣥⣿⣶⣦⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢅⠀⢸⠿⠉⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⣦⣰⣈⣿⣷⣴⣿⣿⣾⣅⣰⣿⣿⡀⠈⠀⡋⠀⠀⠀⠀
⠹⠿⠟⠛⢋⣩⣿⣿⣿⣿⣿⣿⡷⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣭⣿⡇⠀⠀⠀⠐⠂⠀⠈⢹⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⣿⣿⠹⠋⠙⠻⠛⠃⢤⢶⣿⣀⠐⠀⠀
⠀⠀⠀⠰⠏⢉⡉⠉⢹⢻⣿⣿⢻⣷⣆⠀⠀⠉⠛⢿⣿⠋⢹⣿⠁⢰⣾⣿⣿⣿⣯⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣠⣾⣆⣀⣀⣿⣿⣿⣿⣻⣿⣿⣋⣁⣀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠻⠿⢿⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠏⠁⡛⣻⡿⢸⢻⡇⣿⣶⣄⣤⣾⣿⣶⣾⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠠⠄⠀⠀⢴⠤⠛⠋⢙⡿⡿⣿⣿⣿⣿⣿⠟⠋⢺⠿⡿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣌⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⠀⠐⠂⠀⠀⠀⠀⡴⠠⠢⠀⠀⠀⢹⣿⢸⣷⠉⠀⠀⠸⠈⠃⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⡆⢀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⣰⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⡟⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠈⠉⠈⠹⠷⠌⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠛⠃⠀⠀⠀⠀⠀⢸⣿⣿⠛⢳⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⡧⠸⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠋⠁⠀⠙⠛⠁⠉⠀⠀⠈⠉⠉⠉⠛⢻⣿⡿⣿⣿⣿⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⠿⠶⣶⣯⣷⠄⠸⠿⠿⠟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢿⡿⠿⠿⣿⡤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣇⣾⣿⡆⠀⣼⣯⣴⠀⠠⣾⢿⣶⣶⣤⣤⣀⠸⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⠟⠀⣾⣿⣿⠟⢿⡏⠘⠀⠄⢧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠘⢿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⡀⠀⠿⠟⢹⣿⠀⠈⣿⣿⠿⠃⠀⠀⠀⠀⠈⠋⠀⠚⠋⠉⠈⠀⠀⠃⢀⣃⣽⣿⠈⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⠀⠀⠈⠛⠿⠿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠂⣼⠛⠀⠀⠀⠸⣿⣧⠀⠀⢤⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠀⣾⡗⡈⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡀⡀⠀⠀⠀⠀⠂⠀⠀⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⢀⠀⠀⠀⣀⣴⠋⠀⠀⠀⠀⠀⠦⠄⠀⠀⠈⢀⡜⠷⢶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣧⡴⡱⣯⠶⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡏⠉⠫⢿⣿⣿⣿⣿⣿⣭⠉⣭⣿⣿⡿⠉⠙⢿⣋⠁⠈⠉⡇⠛⠉⠉⢠⣈⣽⠀⠉⠀⢀⡀⠀⠀⠈
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣫⡾⣴⠫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⠀⠀⠀⠀⢿⡆⠀⠀⡀⠀⠀⠀⠀⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠹⠁⣻⣿⣿⡷⢀⣯⣴⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢠⡀⢘⡣⠠⣴⣿⣿⠀⠀⢰⣿⣿⠀⠀⠀⠃⠀⠀⠀⠀
⠀⠋⠉⠉⣹⣬⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⠇⣻⡟⠁⠈⠹⣿⣿⣿⠀⠀⠀⢀⣤⡀⠀⣤⣀⣿⣿⡿⠁⠉⠹⠿⠇⠀⠀⠀⠛⠛⠛⠛⢻⠈⠙⢿⣿⣿⣿⣿⣾⣿⣢⣩⠊⠈⣿⣿⠀⠀⠈⠛⠛⠀⠀⢠⡷⠀⠐⠀⠀
⠀⠀⠀⠸⠗⠀⠁⠈⠙⣿⣿⣿⢹⣷⣌⡉⠘⠛⣛⠂⠀⠀⠻⠿⠛⠀⠀⣶⣼⣿⣄⣠⣿⣿⣿⣿⠛⠁⠀⠀⠐⠆⠀⠀⠀⠀⠀⢀⣠⣼⣀⣀⣀⣿⣿⣿⣉⣻⣿⣿⣁⣀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠺⠿⣟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⢻⡿⢸⢻⠃⢻⣿⡟⣿⣿⣦⣤⡀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠄⠀⠀⣴⠤⠛⠛⠙⡻⠛⢿⣿⣿⣿⣯⠍⠁⠾⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠁⠘⠈⢠⣟⣿⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⣿⡿⠋⠁⢀⣾⣿⣿⣤⣤⠀⠐⠆⠁⠀⠀⠀⡴⠠⠢⠀⠁⠀⢨⡿⢸⡷⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠺⣿⣇⠀⠀⠀⠀⠈⣸⣿⡿⢻⣋⣿⢼⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣤⣴⣿⣿⣿⡏⠁⢾⡷⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠚⠃⢨⠹⡧⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣿⡟⠁⠐⣿⣾⣾⣿⡟⠙⣻⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠅⠀⠀⣴⣿⠿⣿⠷⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣦⣀⣀⣠⣤⣄⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠡⠄⠁⠀⠀⠈⠉⠉⠉⠉⢻⣯⠉⠁⠀⢒⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡿⣷⣶⣿⣷⣶⡴⠶⠶⠆⠈⣧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣸⣿⡇⢠⣿⣿⣥⡂⠀⢿⣿⣿⣷⣦⣤⣄⠸⣿⣿⣿⣿⣿⠿⠙⠿⠻⣿⣿⠟⢠⣿⣿⣿⡟⢿⡿⠀⠁⠦⢹⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣤⡄⠸⣿⠛⢻⣿⡀⠈⣿⣿⠟⠁⠀⠀⠀⠀⠈⠛⢀⠟⠋⠛⠈⠃⠀⠛⠀⣳⣼⣿⠋⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠙⠿⠿⢿⡻⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠉⡛⢂⣽⠋⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠄⣾⡗⣸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣤⡤⠀⠀⠀⠀⠀⠴⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⣿⣿⣿⣿⣵⣀⠀⣀⠀⠀⠈⣡⣼⠋⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⡿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡟⢀⡀⠀⠀⠀⠰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣾⣿⣿⣿⣿⣿⣾⣷⡼⣻⢯⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣭⡉⣭⣿⡟⠉⠉⠈⠉⢏⠀⠈⠉⣿⠋⠉⢩⢹⣧⣼⠀⠉⠁⠂⠄⠀⠀⠈
⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣾⣿⣿⣿⣿⣿⣿⣿⣾⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡽⠃⠘⣿⣿⣿⣿⣿⣿⣾⣿⣿⠁⠀⠀⠀⠀⣾⡆⠀⠀⣧⣀⠀⠀⠙⣿⣻⠀⠀⠀⣀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⣿⣿⠏⢻⠏⣿⣿⣿⣽⣥⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿⡿⠟⠉⢁⣴⣤⣤⣠⣴⣌⣿⡧⣼⣿⣿⠢⡀⢰⣿⣿⡂⠈⠀⣏⠀⠀⠀⠀
⠈⠋⠛⠋⣙⣩⣿⣿⣿⢃⠀⠘⢻⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⢀⣼⣿⡇⠀⣀⣠⣿⣿⣿⣿⣿⣿⠿⡗⠂⠀⠠⡛⠛⠛⠻⠿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣮⠈⠿⠿⠀⠉⠉⠛⠛⠁⠠⢶⣿⡂⠐⠀⠀
⠀⠀⠀⠀⠿⠉⠉⠉⢻⢻⣇⣀⠀⠉⠉⠉⠁⠉⠉⠉⢡⣿⣿⣿⣷⣶⣶⣾⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⡿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣻⣿⣿⣋⣀⡀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠛⠛⠿⠊⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠈⠀⡛⢻⡿⢸⠻⢻⢰⣶⣦⣶⣶⣾⣿⣿⣿⣿⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠐⠇⠀⠀⠴⠦⠀⠀⠈⠽⠟⢿⣿⣿⣿⣿⠟⠉⠸⠿⠿⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣁⣾⣿⣿⣿⣿⣧⣶⡀⠀⠂⠀⠀⠀⠀⡴⠠⠢⠀⠀⠀⠈⣿⢸⣷⡙⠀⠀⠐⠀⠁⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⣾⡆⠀⠀⠀⠀⠀⠈⣱⣿⣿⠝⢻⣿⣽⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢾⡿⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠀⡁⠀⠘⠿⠌⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢠⣿⣿⠛⠓⣿⣿⣿⣿⡟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣿⠇⠀⢻⣿⣿⣿⠿⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⠉⠀⠀⠈⠉⠁⠉⠀⠀⠈⠉⠛⠛⠛⣿⣿⠿⣿⣿⣧⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠉⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⡿⠶⣶⠏⢷⠄⠹⠿⠿⠟⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠸⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣰⣿⣇⠀⣿⣿⣵⡎⠀⠻⡿⣿⣿⣶⣤⣄⠘⣿⣿⣿⣿⣿⡿⠹⠿⠿⢿⣿⠟⠠⣿⣿⣿⡟⠿⡿⠁⠁⠠⢸⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡄⠀⠿⠛⠹⣿⡄⠀⣿⣿⠟⠋⠀⠀⠀⠀⠈⠛⠀⠛⠋⠙⠀⠃⠀⠘⠈⢳⣾⣿⠋⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠀⠀⠀⠙⠿⠿⠿⠿⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠇⠀⠀⠀⠀⠀⡛⢢⣜⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⣠⣼⣿⣿⣿⣿⣿⠄⣾⡗⣸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⠀⠀⠀⠀⠀⠀⠠⠖
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣂⡀⢀⠀⠀⠈⣀⣴⡋⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡴⠿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⡿⠂⠀⠀⠀⠀⠀⣶
⣤⣌⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡤⣳⢮⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⣿⣭⣉⣭⣿⣿⣿⠿⠟⠿⡟⠉⠈⠉⣿⠚⠉⢉⣽⣧⣼⡅⠈⠁⠆⣀⠀⠀⠀
⢻⣝⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣷⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢼⠋⠘⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⢸⣆⡀⢀⣯⣤⠀⠈⢻⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣷⣌⠝⣿⣿⣿⣿⣿⣿⣿⠃⢹⠇⣟⣿⣯⣿⣣⣾⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⡿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠠⠀⠈⡁⠠⣤⣿⣿⠀⠀⢸⣿⣿⡆⠐⠀⡟⠀⠀⠀⠀
⠀⠋⠛⠋⣅⣀⠀⠉⣿⣿⣿⣿⣿⢄⣢⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣾⣿⡇⠀⢀⣀⣼⣿⣿⣿⣿⣿⡿⡇⠀⠀⠠⠾⠋⠛⣻⣿⠈⠙⠻⣿⡿⠀⠀⢠⣤⣤⣬⣮⠈⢿⣿⠀⠉⠘⠻⠛⠁⠀⢤⣿⠆⠀⠀⠀
⠀⠀⠀⠰⠟⠁⡈⠀⠀⠉⠛⠿⢿⣿⡟⠛⠛⠛⠛⠛⢩⣿⣿⡿⠀⠀⣠⣾⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⠔⠇⠀⠀⠀⠀⠀⠀⠹⠛⠀⠀⡀⣵⣶⣶⣾⣻⣿⣿⣋⣁⡀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠾⠿⢿⣔⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢢⡄⢠⠀⢠⣠⣄⣄⢀⣀⣸⣿⣿⣷⣾⡛⠿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠐⠇⠀⠀⢰⠤⠀⠀⠀⠺⡿⢿⣿⢿⣿⣿⡝⠋⠘⠿⠿⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠘⠄⠸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣯⣤⣾⣿⣿⣿⣿⣅⣴⠀⠀⠂⠀⠀⠀⠀⡴⠠⠢⠀⠀⠁⠈⣿⢸⣷⠝⠀⠀⠀⠀⠋⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠈⣴⣿⣿⠛⢩⣿⣾⣿⢿⣿⣿⣿⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠇⠉⢾⡿⠀⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠀⠉⢈⠙⠷⠌⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢠⣿⣿⠛⠓⣿⣿⣿⣿⡏⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⠃⠀⢻⣿⣟⡿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠘⠁⠀⠀⠈⠉⠀⠁⠀⠀⠈⠉⠙⠛⢛⣻⡿⣿⣿⣿⣧⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⠿⠶⣶⠏⣶⠄⠰⠶⠶⠟⢹⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠻⡿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠰⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣇⣾⣿⠀⣼⣿⣯⣔⠀⢸⣿⣿⣿⣤⣤⣤⢸⢿⣿⣿⣿⣿⡿⠽⠿⠿⢿⣿⠟⢱⣿⣿⣿⡟⢿⡿⠀⠁⠲⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠘⢻⣿⣿⣿⣿⣿⣟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⣅⠀⢿⡿⠻⣿⡇⠈⢻⣿⡿⠋⠀⠀⠀⠀⠈⠛⢁⠿⠛⠛⠀⠇⢀⣙⡀⣻⣾⣿⠉⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠘⠛⠛⠛⠛⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⡛⠓⣼⠛⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠇⣰⣿⣿⣿⣿⣿⣿⠆⣾⡗⣸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣄⣀⠀⠀⠀⠀⠀⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣆⡀⠀⡀⠀⠈⢁⣴⡟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠾⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠏⣀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣤⢟⣶⣿⣿⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⣿⡓⠟⠏⠉⠉⢹⣿⣿⣿⣿⣿⣭⣉⣭⣿⣿⣿⡿⠟⢿⣻⠋⠈⠉⣿⡏⠉⠉⣽⣿⣶⡈⠀⠉⠘⠢⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠘⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⢉⣠⡤⠈⢤⡆⢈⢀⣿⣆⠀⢀⢸⣟⣿⠋⠀⠀⠂⡀⠀⠀⠀
⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⢸⣿⣿⣿⣿⣽⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣯⡁⠀⠀⠘⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣵⣠⣮⣧⣿⣿⣿⣿⠾⣧⣸⣿⣿⡇⠀⠓⣿⡁⠀⠀⠀
⠉⠹⠻⠟⠛⣋⣽⣿⣿⣿⣿⣿⣿⣇⢨⣠⣼⣿⣿⡟⠉⠉⠉⢿⡇⠀⠀⠀⢴⣿⡯⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠈⠛⠙⠻⠿⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡿⠿⠀⠙⠉⠻⠛⠁⠀⢴⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠾⠏⠉⠉⠛⣿⣿⣿⣇⢿⣿⣽⣛⡸⣿⣳⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⣤⣿⣿⣿⣿⣿⡗⢈⠁⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣠⣀⣀⣿⣿⣿⣿⣿⣿⣿⣟⣉⣠⡆⠈⠃⠀⠀⠀⠀⠀⠀⠚⠻⠟⠲⠁⠀
⠀⠀⠀⠀⠀⠀⠁⠐⠀⢘⡛⢺⡗⢸⢻⣏⣿⣿⣿⣿⣇⠀⠀⢀⣀⡀⠒⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠃⠀⠀⠀⠶⠀⠀⠠⡦⠄⠛⠉⡹⡟⢿⣿⢿⣿⣿⡿⠛⠁⠿⠿⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠏⡁⢸⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢺⣿⣿⣿⣘⣿⣿⣿⣿⢣⣴⡀⠀⠆⠀⠀⠀⠀⡴⠠⠢⠀⠀⠁⠈⣹⢸⣷⡝⠇⠀⠀⠀⠋⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⢡⣿⣿⡟⢛⣻⣧⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠈⠰⣿⠃⠀⠀⠀⠀⠈⢤⡠⡼⠀⠀⠀⠀⠉⣈⠈⠿⠆⠃⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⠀⠘⠛⠀⠀⠀⠀⠀⠀⣼⣿⡟⠗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⡿⠀⠛⣿⣿⣿⡿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠻⠉⠀⠀⠉⠉⠈⠁⠀⠀⠉⠉⠉⠙⠿⢯⠭⠟⠁⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣙⠿⠷⣶⠏⢷⡤⠰⠿⠿⠟⠉⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⡀⠀⠀⢾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣛⣙⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣤⣶⣶⣶⣦⣤⣁⣀⣀⠀⠉⠉⠉⠉⠛⡛⠛⠛⠛⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠀⠀⠀⠘⠛⠛⠛⠿⠟⢿⣿⣿⣿⣿⣧⣀⣀⠀⠀⠉⠉⠁⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣟⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣤⣤⣤⣤⣤⣤⣀⣠⣄⣀⡀
⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠉⠛⠿⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣶⣶⣴⣷⣶⣾⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⣿⣿⣿⠋⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠡⠿⠿⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠏⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠉⠯⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠸⡿⡁⣀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⡀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣶⣄⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡘⡏⠾⠷⣿⣿⣿⣿⣏⢭⡶⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣠⣤⣤⣶⣶⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣽⣿⣿⣿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⢀⣀⣤⣠⣤⣀⠀⠀⠀⠀⠺⢿⣿⣿⣿⢅⠀⣤⣶⣻⣿⣿⣿⠿⠛⠋⢻⣿⣿⠿⡹⢛⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣴⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠘⠛⠛⠛⢿⣿⣷⣦⣤⣤⣤⡀⠀⠀⠀⠐⠉⠙⠻⠻⣿⣿⠇⠀⠀⠀⠋⠛⠛⠻⢾⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣿⣶⣶⣾⣿⣦⡈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠋⠉⠀⠉⡋⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⣤⣤⣤⣤⣀⠀⣀⣀⣀⣨⣭⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢺⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⠏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢾⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠈⠻⠿⠳⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣍⣀⣀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣆⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣤⣦⣌⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠐⠈⠈⠉⠍⠉⠛⢀⣁⣔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀
⣿⠿⠋⠁⠀⣴⣷⣶⣦⣤⣠⣤⣄⣤⣤⣾⣿⣿⣿⣶⣿⣧⡀⢀⣀⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠡⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⠿⣿⣿⣿⢿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⣦⣤⣤⣴⣤⣶⣟⡙⠉⢹⣿⣿⡿⠿⠻⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣆⡰⠀⠤⣼⣿⡟⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⣶⣦⣤⣶⣶⣶⣶
⠀⠀⠀⠀⠀⣠⣤⣯⣽⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣦⣾⣿⣿⡿⠿⠟⠉⠻⠈⠁⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢹⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠋⠁⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠉⢻⣿⣿⡿⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠁⠸⠿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣃⠈⠉⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣼⣿⣿⣿⢿⠿⠿⠿⠿⠻⠡⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⣿⣿⣿⣷⣴⣦⣤⣾⠇⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣤⣤⣴⣦⣴⣿⠿⠛⠇⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠰⠆⣀⠀⠀⠀⠀⣀⣀⣀⠀⢠⣄⢀⣼⣿⣿⡟⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣶⣶⣾⣿⣟⠀⠀⠀⠀⢴⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⢿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⡶⠄⠀⠀⠀⣠⣶⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣄⡀⠀⠀⢀⣀⣿⣿⡿⢿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢁⣤⣶⣶⡾⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣧⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢴⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠟⠉⠁⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⡿⣻⢛⣗⣞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠀⢠⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠛⠉⠁⠀⢠⣶⣿⢛⣯⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣢⣿⣿⣼⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣟⠻⢿⣿⣷⡰⣿⣿⣿⡗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣥⣤⣴⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠂⠀⢼⣿⣿⣿⠿⠟⣿⣷⠄⠀⠀⠀⠀⠀⢀⣠⡤⡀⠀⠀⠀⠀⢀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠸⢻⣿⡿⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣈⣿⣿⣿⣀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⣀⣴⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⢠⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣴⣶⣶⣾⣷⣶⣶⣿⣦⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠁⠀⠀⠠⣴⠾⠶⢇⣤⣶⣦⣠⣤⠤⠀⠀⠚⠷⣤⡔⠀⠀⠀⣤⣤⣤⣄⣀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠛⠋⠉⠀⠀⠀⠀⢶⠆⠀⠀⠺⠿⠿⢿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣄⣀⣀⣀⡀⠀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⡀⠄⣄⣶⣶⣂⡀⠾⠦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠹⢿⣿⣿⣿⣿⣿⠛⠉⠋⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⣭⣿⣿⠿⠿⠛⠋⠀⠈⠛⠁⠘⢷⣶⣶⣶⣶⣶⣦⣤⣤⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣴⣶⣶⡤⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣤⣤⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣈⣉⣡⣄⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠺⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠛⠉⠀⠀⠀⠘⠀⣴⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣾⠿⢿⣿⠿⣿⣿⣿⠤⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣶⣶⣦⣤⣤⣤⣶⣿⣿⣿⣷⣿⣥⣥⣥⣤⣨⣅⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣦⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⠁⠛⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣶⣼⣄⢀⣀⣠⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡈⠁⠀⣠⣠⣼⣿⣿⣿⣷⣆⣀⣀⣙⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⡀⣤⣤⣤⣄⣀⣀⡀⢀⣀⡀⣀⣀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⠀⠀⠈⠉⠉⠁⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠤⣶⣶⠂⠀⠀⠀⠠⡄⠀⢀⣀⣀⡀⠀⠀⠀⠈⠛⠻⡿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠁⢀⣀⣀⡀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣶⣤⣤⣤⣿⣧⣾⣿⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⢉⣹⣿⣤⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠈⠑⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠻⠿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⢟⣛⠛⡻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠈⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠋⠉⠀⠀⠀⢈⣾⠖⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠛⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⡇⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣀⣄⣰⣶⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠑⡙⠋⠚⠛⢃⢸⡟⠃⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⣶⣷⣿⣶⣾⣿⣿⣆⠀⢀⣿⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡀⠀⠀⠐⣀⣴⣷⣶⣶⣦⣀⡀⠈⠉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⠿⠿⣿⣻⣿⣿⣿⣿⣿⣷⣴⣴⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⢀⣀⡀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠉⠛⣷⣤⣠⣄⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣴⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⠛⠛⠛⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⢛⠟⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠘⢶⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⣤⣠⣭⣽⣧⣤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠄⠗⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣛⢻⣯⢽⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣠⣄⡀⣀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⢿⣿⣿⣿⣿⣿⣶⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣾⣿⣿⣶⣾⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⢿⣅⢖⡄⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠒⣛⣦⣤⣴⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢽⣦⣇⣦⣽⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⣠⣦⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠹⣿⡿⡭⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⠠⣶⠿⠟⠀⣠⣄⣀⣤⣄⠘⠐⠿⣧⣤⠖⢂⡀⢀⣠⣤⣤⣄⣹⡿⠿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⣼⠿⠉⠛⠛⠃⠀⠀⠀⠰⡿⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⣶⣿⣿⣶⣷⣤⣄⣀⣀⡀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠀⣐⣶⣶⣂⢐⠷⠄⠀⠀⣠⣤⠀⠈⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⠤⠀⠀⠀⣄⣨⣿⣿⡿⢿⠟⠟⠀⠘⠋⠀⠿⣿⣿⣶⣶⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣧⡁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣶⣶⣦⡤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠛⠙⠋⠁⠀⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣈⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠻⣛⡿⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⡟⠁⠹⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠋⠁⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡿⠿⠟⠙⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠟⠂⢲⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠿⡿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⢀⣄⣤⣶⣶⣶⣦⣤⠁⠀⠻⢉⣉⣉⣽⣷⣶⣾⣧⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣄⢀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠘⠛⣻⠿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠙⢟⠿⠟⡋⢙⣿⣿⣶⣶⣾⣷⣄⣀⣤⣠⣤⣤⣤⣤⣤⣤⣀⣄⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣧⠀⠀⠙⠀⣀⠀⠀⣰⠆⠀⠀⠀⠀⠈⠛⠉⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⠿⢷⣄⠀⠀⠘⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠆⠀⠀⠀⠐⠀⠴⠿⠛⠉⠉⠀⠀⠀⠀⠙⠁⠀⢲⣶⣷⣶⣶⣶⣤⣤⣤⣤⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⢠⣿⣷⣤⣤⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠿⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠁⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣴⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣏⣹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠙⠿⠁⠙⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⠀⠀⠀⢉⣉⣡⣼⠿⠿⠛⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠘⠛⠋⠻⠿⠿⣿⣿⣷⣾⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⡿⠿⠿⢿⡿⠿⣟⠁⠀⠘⡛⠛⢋⡉⠉⣽⣷⣶⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⢼⣿⡀⠻⣷⡀⠀⠘⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠾⠚⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⣶⣶⣶⣤⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⠟⠃⠀⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠙⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣴⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⢶⣾⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠟⠛⢿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠺⣿⠇⠹⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣶⣶⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣄⣀⣤⣹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣤⣤⣞⡋⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋⠉⠉⠉⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⢊⣧⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠀⠀⠀⡀⠂⠀⠀⣤⣤⣶⣷⣿⣶⣤⡀⠀⠀⢀⣠⣤⡴⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣧⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠙⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡿⠿⡿⠖⠒⣶⣶⣶⣶⣀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣥⠀⠀⠙⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠋⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠒⠂⠤⠀⠀⠀⣤⣈⣁⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠤⠿⠛⠉⠋⠀⠀⠀⠀⠋⠀⠀⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣄⣀⣠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣤⣶⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢭⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠻⣟⣿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⣿⡿⣿⠿⢿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⢾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣏⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣶⣶⣾⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⣀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⡀⠀⠀⠀⠉⣉⣀⡠⠖⠶⢶⣾⣿⣿⣿⣿⣿⣷⠅⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠛⠛⠋⠻⠿⠷⣾⣿⣿⣿⣿⣿⣷⣤⣤⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣟⣋⣀⣀⣠⣴⣿⣶⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠼⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣴⣦⣤⣄⣤⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⣾⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣴⣿⣿⣿⣿⠿⠛⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠶⠰⣆⠀⢼⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢙⣻⣿⣿⠏⠉⠉⠁⠀⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠟⠿⡿⠿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠸⢿⣄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣷⣶⣷⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣤⣶⣿⣿⣿⣷⣶⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣾⣾⣿⣯⣧⡄⢀⡬⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⠿⠗⠐⠛⢺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2876

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

(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

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

(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.


_____
* They love “Linux” so much that they promote Windows.


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Leverage_the_power_of_an_#Ubuntu_development_environment_on
#Windows_using_Windows_Subsystem_for_Linux_(#WSL)._Join_Kyle_Harper_(Dell)
Oliver_Smith_and_Jean-Baptiste_Lallement_(Canonical)_on_a_tour_of_Ubuntu_on
WSL.⦈_


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⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢉⣀⣤⣤⣤⣀⡉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣾⢿⡿⣿⡿⣿⡿⣿⣷⣄⠘⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡷⣿⣿⣿⠿⣇⣿⡾⢿⢸⣾⣿⡽⡇⣿⣾⣻⣿⣸⣿⣿⢿⣿⣽⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣽⣿⣿⡀⠻⣿⡿⣽⣻⣿⣯⡇⣿⣿⡿⠀⣿⣿⣿⣸⣿⣸⣾⣿⣿⣼⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠛⠿⠿⠿⠿⠿⠛⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣿⢻⣿⣿⣿⣿⡿⣿⢿⣧⠈⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡏⣿⣿⣿⢿⣟⣿⣶⣲⣤⣤⣤⣶⣶⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣼⣿⣿⣯⣿⣷⣿⣾⣿⣦⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣴⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠑⠠⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢷⣼⣿⣿⣿⣽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣵⢶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⠿⠟⢊⣈⣈⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⢨⣭⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⡟⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢂⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠕⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣴⣿⣿⣿⣷⣆⠀⠰⠻⠟⠜⠻⠿⠇⠿⠟⠘⠿⠠⠛⠣⠛⠛⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠺⠪⠀⠇⠅⠀⠀⠀
⣿⣿⣿⣿⣿⣿⠀⢠⢀⣄⣄⢤⣄⡤⣤⡠⣄⣤⠀⡤⣤⢠⡄⢠⢄⡤⣀⣄⣠⣄⠄⢠⠤⡆⢠⡄⣤⠀⢠⡄⡆⡆⢤⡀⣤⢤⡤⡄⡄⡠⣆⣤⠄⣄⣄⣆⢤⡤⣤⢤⡄⣤⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⢿⣿⣿⠿⠃⠀⠈⠉⠉⠈⢈⠁⠁⠉⠘⠋⠉⠀⠁⠉⠈⠁⠘⠉⠉⠈⠈⢈⢉⠀⠈⠁⠁⠈⠁⠉⠀⠀⠀⠉⠁⢉⠈⠉⠈⢉⢉⢁⡈⠁⠉⡈⠈⠉⠉⠉⠋⣉⠈⠁⡉⠀⠁⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠹⠱⠻⠸⠯⠿⠹⠏⠏⠸⠇⠿⠩⠀⠯⠸⠇⠐⠿⠙⠞⠇⠸⠁⠯⠸⠅⠞⠧⠧⠘⠼⠿⠸⠏⢾⡽⠈⠎⠎⠿⠹⠯⠿⠵⠿⠎⠿⠀⠷⠸⠇⠯⠺⢝⡎⠿⠯⠿⠾⠹⠇⠸⠫⠇⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⢰⠠⡄⢠⢄⠄⢰⢠⣤⢂⢆⠶⣂⡆⢰⠀⢠⢠⡄⣦⠄⢠⡴⣄⢴⣤⡄⢠⣰⣤⣠⢤⢄⣤⢠⠄⡄⡖⣄⣤⡆⣴⠀⡔⢢⣶⢄⣤⣤⡤⠠⣒⠠⡤⣰⡦⡦⡄⢠⣤⢤⡠⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠁⠉⠉⣁⡘⠈⠁⢈⢈⠈⢉⠉⠉⢀⠘⠈⡁⡉⠀⠈⠈⠊⠈⠉⡁⠀⡈⣉⠉⠘⠁⠉⠈⠀⡁⠉⠁⢉⡁⠙⠀⠉⠁⠉⠈⢈⠉⠁⠈⠉⠀⠁⢉⡉⡁⡁⡈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡸⠿⠾⠇⠏⠒⠯⠷⠿⡯⠿⠽⠿⠽⠽⠇⠸⠤⠿⠇⠿⠷⠏⠿⠺⠿⠹⠯⠀⡟⠤⠸⠇⠹⠪⠿⠹⠗⠭⠿⠾⡸⠀⠽⠏⠇⠸⠇⠸⠽⠕⠧⠿⠁⠯⠿⠁⠣⠇⠯⠰⠇⠿⠩⠣⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢤⠀⣦⣦⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠈⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⡆⣤⡠⡄⣤⣴⢤⣤⡤⢠⢤⡤⣤⣄⠤⠀⡦⢰⡦⢰⢀⡄⠖⢆⡆⢰⡆⣦⠆⡖⣴⢖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣈⣉⣘⣃⣈⣁⣉⣉⣁⣈⣈⣈⣁⣉⣈⣀⣉⣈⣉⣁⣘⣈⣈⣁⣉⣁⣈⣁⣀⣉⣊⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣤⣪⣭⣭⢪⣹⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠈⠛⠙⡒⠯⢟⢷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⡖⢦⣿⠊⡆⣶⢑⡴⢲⣼⡖⣿⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠃⠘⠙⢃⠙⠫⢀⣙⢫⣼⠵⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢂⡎⢱⢱⢣⢲⠑⡁⡏⣆⢮⡟⡾⣽⡯⣺⣿⡽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠉⠀⠀⠉⠀⠉⠉⠉⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⢛⣋⣛⣿⣿⣶⣄⠀⠀⠀⠀⠀⢠⢔⣼⣾⣛⢿⣿⣉⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⣰⣿⣿⡟⢫⣽⣿⣿⣾⡄⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣷⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⣿⣿⣧⠀⠀⢰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⢀⣤⡾⣠⣭⢿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣯⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⡏⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠛⠻⠟⠀⠀⠠⣶⣹⣿⣿⡿⠟⠋⢻⣭⣴⣾⣿⠃⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣦⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⢷⣿⣮⣿⡀⠀⠀⠀⢿⠿⠟⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⣉⢉⢉⢀⢀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣋⣋⢛⣻⣗⣙⣙⡀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠴⠏⠉⠉⠉⠁⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 3183

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.21.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


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.


===============================================================================
* Gemini_(Primer) links can be opened using Gemini_software. It’s like the
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.


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


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