𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Monday, September 18, 2023
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Gemini index for the day: gemini://gemini.techrights.org/2023/09/18/


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

⦿ Rianne Schestowitz: Dissecting the Minds of the Mobsters | Techrights

⦿ IBM’s LVFS (Linux Vendor Firmware Service) is a Malicious Remote Backdoor and You Should Turn It Off Now | Techrights

⦿ GNU/Linux Versus Windows Around the World (Sept. 2023) | Techrights

⦿ 10 Years Ago, When GNU Had Almost Turned 30, Richard Stallman Gave This Internet Hall of Fame Induction Speech | Techrights

⦿ IRC Proceedings: Sunday, September 17, 2023 | Techrights

⦿ [Meme] Hatchet Job Gone Wrong | Techrights

⦿ Ring Doorbells Don’t Solve Crime. They Are a Felony to Use. | Techrights

⦿ Turning WebP Off in SeaMonkey and LibreWolf | Techrights

⦿ You Know the World Wide Web is Tied to a Particular Web Browser When... | Techrights

⦿ XWayland Rootfull: For When the Mountain Won’t Come to Muhammad | Techrights

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
		http://techrights.org/2023/09/18/dissecting-the-minds-of-the-mobsters/#comments
		http://techrights.org/2023/09/18/downsides-of-lvfs/#comments
		http://techrights.org/2023/09/18/gnu-linux-sept-2023/#comments
		http://techrights.org/2023/09/18/internet-hall-of-fame-rms-speech/#comments
		http://techrights.org/2023/09/18/irc-log-170923/#comments
		http://techrights.org/2023/09/18/meme-hatchet-job-gone-wrong/#comments
		http://techrights.org/2023/09/18/ring-doorbells-felony-to-use/#comments
		http://techrights.org/2023/09/18/turning-webp-off/#comments
		http://techrights.org/2023/09/18/world-wide-web-is-tied-to-chrome/#comments
		http://techrights.org/2023/09/18/xwayland-rootfull/#comments

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
		http://techrights.org/2023/09/18/7-new-distro-releases/#comments
		http://techrights.org/2023/09/18/climate-focus/#comments
		http://techrights.org/2023/09/18/flatpak-integration-in-qubes-os/#comments
		http://techrights.org/2023/09/18/gnuhealth-hospital-management-4-2-2/#comments

                    ䷩ 𝚕𝚒𝚗𝚎 77

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/dissecting-the-minds-of-the-mobsters/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/dissecting-the-minds-of-the-mobsters/

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Gemini_version_available_♊︎


✐ Rianne_Schestowitz:_Dissecting_the_Minds_of_the_Mobsters⠀✐


Posted in Free/Libre_Software, FUD, Microsoft at 4:36 am by Guest Editorial
Team


My original plan for this article was to dissect each paragraph which I wrote
in my_last_blog_post (A Poem For The Social Justice Warrior Wannabes). I have
now got a somewhat changed version of this original plan, so instead I’m going
to summarise the poem and retrofit it into four sentences in the best way that
I can do that. The people who are covered here and have been covered since the
beginning (all blogs previously posted can be found in [1, 2, 3, 4, 5]) are:


   1. Claiming to be Social Justice Warriors.
   2. Serial liars, defamers, and hypocrites.
   3. Bad people. They are basically mobsters – militants, rioters, trolls, and
      criminals.
   4. The great projectors – unemployed, suffering burn-out, epic pretenders,
      and yet constantly maligning and/or poor-shaming productive people
Again I want to use the same analogy which I mentioned here once before:


“I’m married to a trans person so I think I have this magic card I can play
where I accuse anyone who notices my horrendously shitty and documented
damaging actions a transphobe”


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Just like the puppetmaster, “gas the jews” DrAxe Garrett. Gulagboy (DrKnife
Garrett) together with his attack dog Brandon Lobsta (the loser) Lozza are
working in coordination; the pathetic losers and jobless individuals are
working like a mob. Desperate to sue Roy Schestowitz (Techrights) to garnish
some money. Do you really believe you can just drag your Ontario law any way
you want? If so, you are a completely deranged freak.


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


I need to have a good cover and a great escape to evade the authority.
Transformation is the key. Lovely idea you got there. That’s why you use TOR –
so you can completely troll Techrights 24/7:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


While shaming Richard Stallman at the same time.


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


You are even boasting that you trolled RMS. Well, not anymore. Richard Stallman
is already aware of your activities together with your puppetmaster (“kill the
jews” DrKnife Garrett).


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Another transphobic example from Brandon Lobsta (the loser) Lozza. One thing is
for sure – and I know you are unemployed, so is this just some of your ego-
feeding ways of showing you are practising as a paralegal?


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


How could it possibly be, you don’t even have the credibility. You are a
running, runaway criminal. A Social Justice Warrior wannabe, a parasite hiding
and using the community you are claiming to be part of. Police don’t put
handcuffs on random people, officers put cuffs on you, so it’s rather
revealing; you have done illegal stuff or committed a crime.


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


These people will keep doing this and they’re repeating the same tactics and
style, demoralising or supposedly ‘destroying’ people for merely thinking
differently. The saddest fact is that you have no clue or awareness that the
less tolerant side/person is the one who is more likely to hurt people. Those
are actual people, just like you, who just cannot stand the idea that other
people could think differently. You could just stop projecting your own biased
feelings onto other people. Instead you’d rather pound your chest and hate on
others, damaging their careers because like a 5-year-old you just didn’t get
your way. And as your fake SJW wannabe fellows show in public, they like to say
to anyone who disagrees with them, “F**k **f.”


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


As the_Abuse_Online_DB_(TAODB)_explains_regarding_the_3_classes_of_actors_in_a
smear_campaign below, there are some_pertaining_to_Garrett_himself:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


     This also has the strategic disposition of involving 3rd parties who
     will have both motivation for and experience campaigning against what
     is described by the false aspects of his claims, them not necessarily
     being aware they are false, and exemplifies why this serial defamer
     is such a dangerous element left unchecked in the communities he
     participates in. Additionally, this type of behaviour, when serial,
     unfortunately detracts from the credibility of legitimate claims to
     that cause.


     At the time of this writing, almost every instance of defamation in
     TAODB by Matthew Garrett and those linked with him involves this very
     theme.


     As previously written about in other publications around the nature
     of smear campaigns, some types of serial defamers tend to gravitate
     to socially empowered platforms in order to both encite mobs and to
     avoid accountability for their behaviour.


     Perhaps it’s the best he can do.


Playing victim and looking for sympathy is the game, followed by trolling and
flooding as part of all sorts of attacks, implemented in every possible way. In
reality they are not the victim. I am the victim, whereas they are just
attacking a woman who never even had an interaction with this mobster.
Misogynist and lunatic an individual, he seeks to enforce his twisted
worldviews by harassment and humiliation (sexual harassment), hate crimes, and
all sorts of abuse you can only ever imagine – as only an insane person is
capable of doing this with a straight face.


Let’s examine some instances.


Humiliating Rianne:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Channels in IRC (public) were crude sexual descriptions of me and there was
also one user called riannes_vibrator:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


There were many other offensive, obscene usernames. I was subjected to
harassment despite not being active in this network. It was being vandalised,
usually by sexual intimidation.


Here’s the thing: since you have a fetish for vibrators, it clearly shows your
sexual life boils down to zero because you only have vibrators, the only tool
you can use. I have a proposal: how about sticking a “riannes vibrator” in your
puppetmaster gulagboy “gas the jews” DrAxe Garrett’s stinky ass, then pull it
out and stick it in the mouth of the other attack dogs. Brandon Lobsta (the
loser) Lozza and Immibis, a.k.a. imbillsbitch, SolidGoldMagikarp, and
TwistedPersonality—isn’t it sweet? Let’s make it sweeter the second time
around. I’ll stick the “riannes vibrator” in each of Brandon Lobsta (the loser)
Lozza’ and Immibis’s asses, pull it out and stick it back into your
puppetmaster, “kill the jews,” DrKnife Garrett’s mouth. That is a brilliant
idea! Savouring each other’s dirty and stinky asses. How do you feel now? You
all started this crazy game; you think I am incapable of playing or defending
against your lunatic mind?


Another example of puppetmaster “kill the jews” DrKnife Garrett’s militant ape:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


These mobsters are racist as well:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Hate crime/racism:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


The militants and rioters hailing are Unabomber, a notorious domestic
terrorist:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Stabbing Sprees e.g. knife. See the mobsters’ aggressiveness:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Shaming RMS:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


The real freedom fighters are their targetted enemies. Inciting the group
(LGBTQ) to attack the freedom fighters while they are talking about sex in the
channel. These Social Justice Warrior wannabes are attacking gays as well:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


There are still many more examples like these (many hundreds of examples in my
files), but I just wanted to show enough. That’s only few of them in the
meantime. This might be too much for the the puppetmaster gulagboy (“gas the
jews” DrAxe Garrett) and the apes to handle, it’s either they are constipating
or having diarrhea. To be honest I don’t really care and don’t give a s**t,
they deserve whatever suffering they have now. You reap what you sow.


Gulagboy Garrett is not mad, but very very mad 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:-)⦈  He
worries that his family, friends and relatives in England will find out what he
is doing in his spare time and working hours. Do not worry, your name appears
in Gulag search already, along with your ape Brandon Lobsta (the loser) Lozza.
🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:-)⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


You are harassing me using your sockpuppets together with your savage dogs. You
expect me to throw bread at you while you are throwing stones at me? No, dude,
I’ll say this to you: If you throw stones at me I’m gonna throw rocks at you.
So F**k Y**.


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


By the way, for your peace of mind: I also reported you to the police for hate
crimes and many more things. I have the police reference number and the case is
still open, it is being actively investigated. 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:-)⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Burn-out “gas the jews” DrKnife Matt Gulag. He doesn’t know what to do with his
life.


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


“kill the jews” DrKnife Garrett talking about his death and even holding a gun,
that’s kind of… weird.


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


See the effect/s of burn-out? This person loses his mind. The apes trolling the
Techrights IRC channels with the puppetmaster’s approval. Savage attitude
deserves savage treatment.


Burn-out can cause doxing as well, Matt Gulag is everywhere in the channels,
plus he’s joined by his attack dogs. Spying and watching Techrights IRC
channels closely. Very productive life indeed. I’m going to make a separate bit
of coverage or blog post regarding the doxing. Doxing is considered a serious
crime here in the UK.


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


No, he doesn’t work for free. Microsoft is paying him to sabotage GNU/Linux.


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


More Microsoft works and inviting Microsoft employees to his cabin:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Too much drugs or high on cocaine… the crackhead’s hallucination?


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Poor-shaming people. The cheapskate can’t fix a thing. It needs a professional
plumber, but the great pretender Jack-of-all-trades (but master of none!) with
a Ph.D. in Axe and Knife refuses not to:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


The serial liar and defamer, defaming people as always and forever. This video
of_“gas_the_jews”_DrAxe_Garrett shows him heavily sniffing. Time stop at 3:47-
49, 7:28, 7:36, 8:41, 9:21, 18:32, 19:57, 22:00, 23:22, 24:45, 25:08, 25:44,
28:09 to witness the endless sniffing.


You sniff like a hundred times in your talk, so are you on drugs or you just
having a cold (or both)? The shirt says: “I would never do cybercrime”. Oh,
really? Spending 3 to 4 years in the IRC networks and channels spying on Roy
Schestowitz to look for ‘dirt’ so that you can take him down somehow… that’s
your hobby in collaboration with your boring, loser and criminal attack dogs?
In the video, go to 26:47, right after he talks about monitoring the scooters
being shipped around the world. He points out some of the people he was
watching and how one of them had the pattern of a drug dealer riding around on
a scooter. Excellent job! The “personal project” of burn-out “kill the jews”
DrKnife Garrett.


Oh, by the way, they also love to hijack names of existing and long-time
members:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


The very lowest of the lows. Inside the mind of the lunatics when all of them
(or their sockpuppets) got banned from the IRC channels.


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Impersonation is just one of the many resorts:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


Alex Oliva’s latest_article appears to have struck the nerves of Matt Gulag:


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from anti-Free software militants⦈


The tuberculosis guy, “gas the jews” DrKnife Garrett, can’t prevent himself
from opening his smelly big mouth. They are going to cancel Stallman until his
death. When someone holding opinions you don’t like is not “abuse” (they just
merely have different opinion from) you and your ilk just need to respect it,
as it’s called free speech. Do not condemn people if you think they refuse to
use the correct pronouns that you want to convey them to use. You are becoming
militant, enforcing rules that do even exist. Crazy people like you and your
collaborators are doing crazy things at the same time. Gulagboy (“kill the
jews” DrKnife Garrett) tries to defame people who actually do productive work
on the kernel while he fills it with Microsoft garbage. Matt Gulag’s lasting
legacy will be to be remembered as a universally shitty person. Stay tuned for
the next blog post. █


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣟⣿⣟⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⢿⣟⣿⣿⣩⣻⣟⣿⣟⣿⣿⣟⣿⣻⣿⣟⣻⡛⣻⣛⣿⣻⣿⣟⣛⣏⣟⣻⣻⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣻⣿⣿⣛⣿⣋⣟⣻⣙⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣧⣽⡯⡷⣭⣽⣿⣭⣭⣿⣭⣿⣽⣭⣿⣭⣿⣽⣧⣿⣿⣯⣿⣯⣧⣭⣽⣯⣽⣿⣯⣭⣯⣽⣯⣬⣿⣯⣿⣝⣿⣶⡿⣭⣿⣽⣭⣼⣽⣾⣯⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⠾⡿⡼⠗⣳⣿⠚⣿⣾⠾⢶⣾⢿⣶⠿⡶⢿⣶⣷⡿⣾⣿⢿⡳⠿⢾⡿⣿⡿⢴⣷⣷⡾⠿⣿⣿⣾⡶⣷⢿⣿⣶⣗⣿⣾⢷⣿⣷⣶⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣿⣙⣿⡿⣟⣻⣻⣿⣹⣻⣻⣿⣿⣿⣿⣿⣿⣏⣟⣻⣻⣿⣟⣹⣛⣿⣟⣿⣟⣿⣿⣟⣛⡿⣻⣛⣿⣻⣏⣻⣻⣿⣛⣻⣿⣻⣿⣻⣻⣿
⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠄⠀⠤⠀⠀⠀⠀⢰⣀⣲⣄⡔⣀⣔⣲⣒⣑⣄⣖⣢⣂⣢⣒⣄⣒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣽⣿⣿⣿⣭⣻⣝⣿⣯⣟⣏⣹⣿⣻⣽⣝⣹⣽⣛⣝⣿⣽⣟⣏⣽⣟⣝⣟⣽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠀⠀⠀⠀⠠⠤⠤⠄⠀⣿⣻⣋⣛⣛⣛⣿⣙⣻⣹⣟⢻⣟⣻⣉⣛⣿⣻⣟⣻⣻⣉⣛⣟⣛⣟⣙⣛⣿⣻⣹⣹⣻⣿⣟⣉⣏⣻⣻⣿⡟⣛⣛⣏⣻⣙⣟⣻⣟⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠀⠀⣤⠀⠀⠀⠀⢹⠛⠛⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⢺⠟⠿⢿⠿⠿⢿⢿⢿⡿⠿⠟⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⡿⡿⡿⢿⢿⠿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠀⠀⠀⠀⠈⠉⠈⠁⠀⢿⣾⢶⣶⣾⣷⣿⣼⣶⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⢸⣴⣤⣦⣦⣧⣤⣴⣼⣤⣤⣤⣧⣤⣤⣧⣾⣤⣥⣤⣷⣦⣤⣧⣤⣥⣧⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠐⠀⠒⠀⠀⠀⠀⣸⣧⣭⣧⣯⣥⣽⣹⣯⣭⣿⣭⣯⣬⣽⣭⣭⣯⣭⣭⣷⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⠀⠀⠶⠀⠀⠀⠀⢸⣉⣋⣻⣉⣋⣉⣉⣹⣉⣉⣙⣋⢹⣉⣙⣛⣝⣍⣙⡉⣏⣙⣉⣫⣏⣙⣹⣹⣙⣉⣻⣉⣋⢙⣋⣏⣙⣉⢉⣉⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⢸⠻⠛⣟⠙⢛⣻⡛⡟⠛⡟⠛⣛⠋⢟⠻⡏⠏⡫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣾⢛⢻⡻⠟⣟⡛⢟⠻⡟⢛⡟⠻⣻⡻⢟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⢻⠿⠿⢿⠿⠿⠿⢿⠿⠿⡾⢿⠿⡿⢿⠿⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣷⣾⣶⣾⣶⣾⢾⢶⣷⣾⣶⣷⣶⣶⣶⣷⣶⣶⣶⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⣸⣾⣶⣷⣶⣷⡾⣶⣷⣶⣾⢾⣶⣶⣾⡶⣶⣶⡿⣶⣷⡾⣶⣶⡾⣶⣾⣶⣷⣶⣷⣶⣷⣾⡶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠐⠶⠀⠆⠀⣿⠖⢾⡷⣶⠷⣷⣼⣾⣷⣾⣶⣷⣴⣷⣾⣷⣾⣶⣶⣶⣷⣾⣿⣶⣶⣶⣿⣷⣶⣷⣿⣷⣾⣷⣶⣾⣾⣿⣼⣶⣾⣶⣾⣾⣶⣷⣷⣾⣾⣶⣶⣾⣶⣾⣿⣷⣿⣶⣶⣷⣷⣾⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠟⠛⠟⣿⣟⢛⠻⠟⢻⠛⡿⠛⣛⠟⢻⠛⡟⠟⠛⡛⠟⠻⢿⠟⠛⠛⡟⠛⢻⠻⠛⡟⠻⠛⢻⡻⢻⠛⠻⠛⡟⠻⠛⢻⠛⠛⡟⠛⠟⠟⠿⠿⠻⢻⠛⢿⠛⡿⠛⠛⣿⣿⣿⣿⣿
⠀⠈⠀⠀⠀⠀⠈⠉⠉⠁⠀⣿⣭⣩⣏⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⢸⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠠⠀⠤⠀⠀⠀⠀⢸⣻⣛⣏⣛⣟⣋⣹⣍⣙⣋⣻⢛⣛⣹⢛⣛⣿⣛⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⣾⢻⠛⡟⢻⠟⠻⠛⡟⢻⠛⠛⡿⠛⠿⠛⠟⣿⠛⡟⡟⠛⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⠀⢻⢿⠟⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣶⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠀⠀⠀⠀⠈⠉⠉⠁⠀⢿⣶⣿⣶⣾⣷⣷⣾⣶⣿⣾⣶⣶⣼⣶⣷⣶⣷⣷⣾⣶⣿⣶⣶⣶⣷⣾⣾⣶⣧⣶⣶⣷⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠀⠀⠛⠀⠀⠀⠀⣸⣤⣬⡼⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠐⠀⠀⠀⠀⠐⠒⠒⠂⠀⣿⣵⡅⠠⣆⡦⡄⡖⠀⡆⠠⡖⠂⡆⡄⡆⣄⡶⡒⡶⣲⡆⠀⡖⠒⡶⢢⣶⠖⣶⡆⢰⣆⣰⣶⢔⣶⠀⣶⡐⣰⣶⡆⣲⣶⠀⢴⢶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⠄⢰⡀⢰⢖⢲⡶⣶⣶
⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢸⣻⣍⣟⣉⣻⣝⣛⣯⣛⣻⣏⣛⣫⣹⣹⣏⣏⣯⣟⣻⣉⡟⣛⡽⣛⣹⣙⣛⡟⢻⣯⣻⣟⣽⣛⣿⣏⣛⣿⣏⣹⣉⣟⣹⣭⣛⢫⣛⣟⣛⣻⣝⣉⣙⡿⣏⣙⣛⣿⣭⣙⣫⣛⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣔⣤⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠐⠒⠂⠀⠂⠀⠀⠀⠀⢸⣬⣭⣯⣴⣬⣯⣥⣯⣯⣽⣽⣿⣬⣭⣼⣽⣾⣭⣼⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⠒⠄⠀⠀⠀⠀⠀⢸⣹⣉⣉⣏⣏⣋⣹⣉⣋⣉⣏⣍⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠠⠤⠄⠀⠀⠀⠀⠀⠀⢸⣋⣛⣛⣛⣟⣙⣛⡛⣻⣛⣛⣟⣻⣛⣛⣿⣟⣻⡛⣻⣟⣟⣻⣿⣛⣟⣟⢻⣛⣽⣻⣛⣻⣏⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⢸⣻⠛⡟⡿⠟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢸⠞⢿⡿⢿⠿⢿⠿⡿⢿⠻⡿⢻⡿⠻⡿⠿⢿⠿⠿⢿⠿⠿⠿⣿⣟⠿⠿⢿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣷⣶⣶⣾⣶⣷⣶⣾⣾⣶⠷⣶⣾⣶⣾⣾⢶⣾⣷⣾⣶⣿⡷⣶⣿⣾⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣶⣶⣼⣾⣾⣶⣮⣾⣷⣾⣷⣿⣶⣾⣷⣷⣾⣶⣷⣧⣶⣶⣷⣾⣶⣵⣾⣶⣾⣶⣶⣾⣾⣶⣷⣷⣶⣦⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠈⠂⠀⠀⠀⠀⠀⢸⣬⣤⣼⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢸⣩⣹⣯⣭⣿⣿⣭⣏⣽⣭⣯⣯⣭⣩⣏⣯⣥⣿⣹⣭⣹⣩⣽⣍⣭⣭⣻⣭⣿⣽⣭⣏⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠄⠀⠀⠠⠀⠀⠀⢸⣙⡭⣝⣭⢩⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠤⠄⠠⠀⠀⠀⠀⠀⢸⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠻⣿⡿⢿⠿⠿⠿⢿⡟⠿⢿⠿⣿⢿⠟⠿⠟⡿⢿⠟⠿⡿⠟⠿⢿⣿⠿⠿⢿⠿⢿⠿⡿⠿⠿⣿⡿⠿⠿⡿⢿⠟⢿⡿⣿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⢄⠠⠄⠤⠠⠤⠠⠄⠤⡤⣼⠒⡶⠶⠲⠖⠶⠖⠶⠶⠶⠶⡶⠲⠶⡶⠶⡶⠶⣶⢖⠶⠶⠲⣶⠶⠲⠶⣒⡶⣶⠶⣶⠶⠶⢶⠶⣶⢶⣶⠶⠶⠶⠶⢶⠒⣶⡶⡿⠿⡿⣿⢻⡛⡿⠿⡟⣿⠛⠿⡿⢿⢿⢛⡿⠻⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣯⣽⣛⣟⣫⣒⣹⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⣟⣍⣿⣉⣽⣭⣽⣉⣏⣏⣹⣭⣹⣉⣏⢛⣋⣉⣩⣋⣋⣍⣹⣙⣿⣿⣍⣙⣏⡉⣋⣋⣿⡟⣉⣙⣛⣯⣽⣍⣍⣿⣽⣿⣉⣏⣝⣉⣹⣉⣋⣹⣉⣍⣹⣽⣉⣹⣹⣉⣍⣙⣉⣛⣹
⠀⠠⠠⠤⠄⠀⠀⠀⠀⠀⠀⢸⠠⡕⠸⠤⢥⣼⡽⡧⢼⠖⡽⢦⠴⡦⠶⠶⣤⣴⠦⡗⢤⠧⢼⠴⡝⣧⠜⠤⢿⠤⢧⢿⠜⡤⢤⠷⡤⢧⠄⣽⠤⡼⢦⡧⢼⡤⢾⢾⠧⡼⠤⣧⢴⠦⣼⠶⠧⣼⣼⠄⢼⠾⡿⢿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⣖⣖⣒⣶⣺⣊⣳⣺⣒⣳⣚⣗⡖⣛⣳⣾⣒⣷⣲⣒⣖⣛⣖⣓⣗⣷⣒⣺⣓⣞⣟⣲⣾⣃⣖⣻⣺⣓⣗⣲⣎⣓⣝⣾⣺⣗⣷⣗⣾⣂⣓⣞⣒⣗⣲⣗⣺⣊⣷⣿⣶⣾⣾⣿⣿
⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣛⣛⣉⣻⣿⣻⣟⣙⣻⢛⣿⢛⣻⣟⣟⣻⣛⣫⣛⣻⢛⣟⣟⣻⣟⣛⣏⣻⣟⣟⣻⣟⣛⣟⣿⣙⣋⣛⣻⣋⡻⣏⣻⣙⣛⣟⣛⣿⣛⣛⣻⣛⣛⣟⣻⣿⣛⣟⣟⣹⣛⣻⣋⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣥⣬⣵⣶⣧⣼⣤⣤⣴⣤⣼⣧⣼⣤⣤⣤⣬⣤⣧⣥⣤⣧⣧⣥⣤⣥⣤⣼⣤⣿⣧⣵⣤⣦⣼⣤⣤⣤⣧⣼⣼⣧⣼⣤⣥⣼⣤⣵⣤⣧⣤⣼⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠊⠂⠀⠀⠀⠀⠀⢸⣬⣭⣿⣞⣭⣥⣥⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢸⣭⣩⣿⣉⣩⣙⣏⣟⣙⣹⣻⣉⣁⣋⣏⣃⣋⣹⣍⣫⣝⣽⣍⣍⣫⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠠⠤⠄⠀⠀⠀⠀⠀⠀⢸⣻⣉⣙⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⢸⠛⠛⢛⢻⠛⠛⢻⠛⠛⠛⡟⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⢀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⣿⢿⣿⣿⠿⢿⠿⣿⢿⢿⢿⢿⠿⡿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠈⠀⠁⠁⠀⠀⠉⠀⠀⠀⠀⣷⣿⣿⣵⣷⣶⣿⣾⣿⣷⣿⣶⣶⣾⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠂⠖⠤⠀⠀⠶⠀⠀⠀⠀⣿⡟⣉⣍⣟⣯⣯⣫⣟⣍⣙⣏⣙⣉⣯⣟⣽⣿⣽⣿⣯⣿⣯⣽⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⢀⢀⡀⠀⢀⡀⠀⢀⠀⠀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠈⠁⠀⠀⠀⠁⠉⠀⠈⠁⠀⢀⣿⣿⣿⣿⣷⣿⣿⣿⣧⣿⣿⣿⣶⣷⣶⣶⣿⣷⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣶⣿⣷⣶⣾⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⣿⣿⣿⣛⣻⣻⣟⣿⣻⣿⣿⣟⣛⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢀⣿⣼⣷⣽⣿⣵⣥⣶⣤⣼⣯⣧⣿⣷⣵⣾⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠄⠀⡠⠀⠀⠀⠀⠀⣿⢟⢛⠿⠛⠛⡟⣿⠏⠛⣛⣿⡟⣻⢛⢻⠋⢙⣻⢙⠻⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⡀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠐⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠀⠃⠈⠀⠀⠛⠀⠀⠀⢀⣿⣿⣯⣦⣤⣤⣧⣭⣯⣽⣽⣽⣿⣽⣶⣤⣤⣧⣽⣴⣯⣤⣧⣬⣷⣭⣮⣽⣦⣤⣤⣧⣤⣼⣧⣽⣤⣤⣤⣧⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⢀⡀⠀⢀⢀⠀⢀⠀⢀⡀⠀⢹⣶⢶⣶⣶⠶⡖⣶⠶⠶⢶⡶⠶⢶⣶⣶⣶⣶⣶⢶⡶⢶⣶⡶⣶⣶⣶⢶⡶⠶⢶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⢶⣶⢶⣶⣶⣶⡶⣶⠖⡶⠶⠖⣶⣶⣶⣶⣶⣶⣶⣶⣶
⡀⠀⠀⠀⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣾⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠃⠀⠘⠑⠀⠘⠁⠐⠂⠀⢸⣿⣿⣭⣿⣽⣯⣭⣽⣼⣭⣭⣩⣽⣿⣿⣯⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣷⣦⣾⣿⢿⣿⣿⣿⣾⣶⣾⣿⣿⣿⣶⣷⣦⣿⣿⣧⢷⣼⣶⣾⣧⣤⣼⣿⣶⣷⣿⢧⣾⣷⣿⡿⣿⣿⣿⣿⣿⣽⣷⣾⣷⣾⣿⣾⣾⣼⣿⣿⣿⣿⢿⡯⣶⣼⣿⣿⣿⣿
⠀⠀⠀⠈⠈⠀⠈⠉⠀⠀⠁⠁⠀⠀⢸⣿⣷⠿⣿⢿⣶⣷⣴⡾⣶⣾⣿⣶⢿⣿⡷⣿⣾⣶⣶⣾⡾⣷⢿⣷⣿⣿⣿⠷⣿⠶⣿⡾⣿⣿⣿⣶⣷⣿⣿⣿⣷⣿⣿⣷⣿⣿⣷⣶⣦⣿⣿⣿⣾⣷⣶⣶⣶⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣾⣾⣿⣿⣿⣷⣾⣿⣿⣿⣶⣿⣯⣾⣮⣾⣿⣿⣷⣶⣶⣷⣾⣿⣾⣶⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠐⠀⠐⠒⠀⠀⠃⠂⠀⠀⢸⣿⣼⣿⣿⣭⣽⣭⣭⣽⣯⣯⣭⣭⣿⣯⣭⣥⣯⣩⣽⣽⣼⣽⣯⣿⣭⣿⣽⣯⣷⣽⣿⣯⣿⣿⣿⣯⣭⣭⣹⣭⣭⣽⣭⣼⣽⣭⣯⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠄⡀⠀⠀⡀⠀⠀⠀⠈⡿⡟⢿⢿⢻⢿⢿⣿⣿⢿⣟⠻⠿⢿⢿⢿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⡿⠿⣿⡿⠿⠿⣿⣻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠃⠀⠀⠀⠂⠘⠀⠐⠂⠀⢸⣿⣭⣿⣿⣭⣭⣽⣷⣧⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⣻⢿⡿⣿⣛⣻⠿⠟⡿⣟⠿⣿⢿⢛⠻⣿⢿⢽⢻⣿⣿⠿⢟⡛⡟⡻⣹⣿⣛⣟⡿⡻⠿⢟⠿⢟⡛⣿⢛⡛⣿⣟⢟⣻⢻⣿⢻⣿⡿⡟⣿⠿⡛⡟⣙⢛⢽⡟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠂⠄⠀⠂⠄⠀⠀⠀⠀⣿⣯⣏⣿⣿⣿⣟⣿⣹⣟⣫⣽⣟⣿⣟⢛⣻⣹⣻⣹⣿⣛⣹⣛⣛⣩⣿⣿⣙⣛⣿⣿⣫⣿⣽⣿⣿⣿⣛⣩⣻⣙⣯⣿⣝⢻⣟⣿⣯⣿⣽⣻⣿⣉⣫⣻⣭⣿⣏⣯⣻⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⣉⣉⣫⣭⣽⣯⣯⣉⣭⣯⣩⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⢠⡄⠀⠀⠀⡀⣠⠀⢀⡄⠀⢸⡿⣿⣿⣿⣿⣿⣿⡟⡿⣿⢿⣟⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⠠⠀⠠⠦⠀⠀⠆⠄⠀⠀⢸⣿⡷⡾⡾⣶⣶⡾⠿⢿⡿⣿⢾⡷⢾⣤⣴⣾⣴⣦⣿⣾⣶⣦⣤⣦⣧⣿⣾⣾⣬⣷⣦⣼⣿⣿⣿⣿⣾⣾⣾⣿⣷⣾⣿⣿⣿⣿⣷⣾⣾⣧⣷⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣮⣾⣾⣿⣾⣶⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠐⠀⠐⠓⠀⠀⠃⠂⠀⠀⢸⣿⣿⣮⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⢠⢀⠀⢀⣄⠀⠀⡄⡀⠀⠀⢸⣿⣟⡻⣿⣿⣿⣿⣿⠿⡟⢿⠿⣟⡿⣿⠿⣿⢿⣿⣿⣿⠿⡟⠿⠿⡿⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡤⣤⣤⣤⣤⠤⡤⣤⡤⣤⣤⣤⣤⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠷⠿⠿⠿⠿⠶⠧⠿⠾⠿⠿⠿⠿⢷⣽⣿⣿⣿⣯⣿⣿⣿⣷⣿⣷⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⠆⠀⠀⠔⠀⠴⠀⠐⠆⠀⢸⣿⣿⣿⣯⣉⣿⣉⣹⣻⣉⣩⣽⣿⣿⣿⣿⣿⣿⣏⣿⣙⣏⣉⣍⣝⣉⣉⣏⣉⣏⣉⣉⣋⣩⣿⣿⣿⣿⣿⣿⣿⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⢀⠀⢀⡀⠀⠀⠀⠀⢸⡿⡿⣿⠟⠿⡿⡿⡿⣿⣿⠟⠿⠿⠿⠿⠟⢿⡿⡿⣿⣿⡿⣿⢟⢿⠿⠿⠿⡿⣿⡿⣿⢿⠿⠿⠿⡿⠿⢿⡿⣟⢿⠿⠿⠿⠟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠁⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣷⣶⣷⣾⣶⣶⣴⣶⣶⣶⣶⣿⣿⣿⣶⣿⣿⣷⣿⣶⣶⣶⣾⣿⣾⣿⣿⣶⣶⣾⣶⣶⣿⣷⣿⣿⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠖⠔⠀⠰⠢⠀⠀⠀⠀⢸⣟⣛⣟⣿⣛⣛⣟⣝⣿⣻⣿⣹⣻⣻⣛⣻⣛⣗⣟⣗⣽⣛⣫⣩⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⡀⡀⠀⡀⠀⣀⠀⠀⢸⣿⠿⣿⢿⠿⠿⠿⢿⣿⣿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⢼⣷⣶⣶⣾⣶⣶⣶⣾⣿⣾⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠔⠀⠰⠂⠀⠀⠀⠀⢸⣟⣿⣏⣉⣉⣇⣯⣽⣩⣋⣩⣱⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⡀⡀⠀⡀⠀⣀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⢿⣿⡿⠿⠿⡿⢿⣿⡿⡿⠻⠿⠿⡿⠿⠿⡟⡿⠿⣿⣿⠿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢜⣛⣛⣚⣛⣛⣛⣛⣛⣛⣛⣚⣛⣚⣓⣚⣚⣛⣛⣒⣛⣛⣓⣓⣒⣒⣚⣛⣛⣓⣒⣓⣒⣓⣒⣛⣓⣒⣚⣛⣛⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠶⠀⠀⠦⠂⠠⠆⠀⠒⠀⠀⢸⣿⣿⣯⣿⣧⣼⣿⣿⣽⣿⣭⣯⣬⣯⣿⣉⣽⣯⣯⣭⣽⣭⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣿⣿⡿⠟⠿⠟⣿⣿⣿⡟⢛⣿⣿⡿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣷⣷⣿⣿⣾⣶⣷⣷⣷⣾⣿⣾⣾⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⢸⣟⣍⣭⣇⣩⣽⣃⣫⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢸⣿⢿⣿⡟⡟⣿⣿⣿⢿⣿⠿⡿⣿⠿⡿⢿⢻⣿⢿⢿⣿⠿⡿⠿⠻⠿⡟⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣷⣷⣷⣶⣶⣷⣿⣿⣷⣷⣿⣶⣾⣾⣿⣿⣾⣷⣶⣷⣿⣿⣶⣿⣷⣾⣷⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠒⠀⠀⠂⠐⠐⠂⠀⠂⠀⠀⢸⣿⣬⣽⣯⣭⣿⣿⣿⣿⣭⣭⣿⣯⣯⣭⣯⣿⣿⣿⣽⣿⣿⣭⣏⣭⣿⣽⣽⣿⣿⣿⣿⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠛⠀⠀⠋⠐⠐⠃⠀⠊⠀⠀⢸⣿⣿⣯⣯⣭⣼⣿⣿⣽⣿⣭⣽⣯⣥⣭⣭⣯⣿⣿⣽⣿⣿⣯⣬⣭⣜⣧⣿⣯⣿⣯⣿⣿⣿⣿⣽⣯⣿⣯⣽⣭⣥⣯⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⢸⣟⣟⣿⡛⠟⢟⡿⣟⣿⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠛⠀⠀⠃⠑⠐⠃⠀⠊⠀⠀⢸⣿⣿⣭⣯⣮⣯⣯⣿⣼⣿⣵⣯⣯⣵⣯⣭⣬⣧⣥⣽⣷⣭⣏⣭⣿⣍⣥⣽⣯⣭⣿⣽⣥⣭⣽⣿⣿⣿⣿⣽⣬⣿⣿⣿⣿⣿⣿⣧⣿⣽⣯⣽⣧⣭⣭⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⡠⣀⠀⢠⢀⠀⠀⠀⠀⢸⡿⢟⣻⡿⡛⠟⢛⢻⢟⣟⣻⡛⡿⣟⣿⣟⡿⡛⠿⠟⠟⢛⢿⡟⡟⠻⠛⡛⣿⣟⣿⣻⣟⣿⠻⡛⡻⣟⣟⡟⠟⢟⣿⣻⣻⣿⡻⣟⣟⣟⢟⠻⢻⢻⢟⠟⠛⠛⢻⡛⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠋⠒⠀⠘⠐⠀⠀⠀⠀⢸⣷⣷⣿⣦⣼⣵⣷⣷⣭⣿⣭⣼⣷⣿⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡠⠀⠀⡀⠀⢀⡀⠀⡀⠀⠀⢹⡿⣿⡿⠿⣿⡿⡿⢿⢛⣿⠟⣿⣿⠿⡿⣿⡿⣿⢿⢿⣿⡿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⡿⠿⡟⢿⠿⣿⡿⢿⠻⠟⠻⠿⢿⣿⠻⠿⢿⢿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠐⠀⠐⠂⠀⠀⠀⠀⢸⣟⣝⣝⣯⣫⣉⣱⣸⣅⣹⣹⣻⣟⣟⣟⣿⣯⣟⣝⣿⣛⣹⣿⣽⣏⣙⣭⣏⣇⣉⣬⣻⣏⣯⣍⣍⣯⣭⣹⣟⣟⣏⣬⣩⣹⣛⣻⣏⣉⣭⣼⣻⣙⣿⣻⣻⣛⣿⣋⣯⣿⣿⣿
⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡟⡿⡿⣿⣿⣿⣿⠿⢿⠿⡻⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣿⣾⣶⣶⣷⣾⣶⣷⣾⣾⣾⣷⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠂⠀⠀⠂⠂⠐⠂⠀⠂⠀⠀⢸⣿⣽⣿⣿⣏⣻⣽⣽⣯⣿⣿⣿⣽⣿⣿⣯⣿⣯⣿⣬⣽⣿⣿⣿⣿⣿⣧⣭⣍⣿⣯⣽⣿⣭⣽⣿⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢸⣿⠿⢿⡿⢿⣿⣿⠛⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣷⣿⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠐⠀⠐⠂⠀⠀⠀⠀⢸⣿⣏⣿⣿⣯⣩⣽⣉⣹⣜⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⡀⢀⢀⡀⠀⡀⠀⠀⢸⣿⠻⠿⣿⣿⡿⣿⠿⠟⣿⡿⠿⠿⠻⢻⢻⠿⡿⠿⡿⠿⠟⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣶⣿⣷⣾⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣾⣿⣷⣶⣿⣷⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠂⠀⠀⠂⠀⠐⠂⠀⠂⠀⠀⢸⣿⣿⣿⣿⣿⣧⣭⣭⣿⣿⣿⣽⣯⣽⣿⣿⣯⣽⣿⣿⣯⣽⣼⣯⣿⣽⣬⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⢀⠀⢀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⡿⢿⠿⢿⣿⣿⣿⡿⠻⠿⢻⡿⠿⠿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣷⣿⣷⣷⣶⣶⣿⣿⣷⣷⣷⣷⣶⣷⣿⣿⣿⣾⣶⣶⣿⣾⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠐⠀⠐⠀⠀⠀⠀⠀⢸⣯⣯⣧⣭⣭⣉⣯⣭⣿⣧⣭⣽⣽⣽⣯⣯⣿⣧⣽⣤⣭⣭⣯⣿⣿⣯⣿⣯⣿⣿⣿⣿⣯⣯⣥⣯⣭⣿⣿⣿⣿⣽⣬⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⡄⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⢸⡿⡿⡟⠟⢿⢻⢿⢿⡿⣿⢿⢿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⢿⣿⡿⣿⠻⠿⠿⡿⠿⢿⣿⣿⠿⡿⡿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣾⣾⣿⣾⣾⣿⣿⣿⣿⣾⣿⣿⣷⣾⣾⣷⣿⣷⣿⣿⣿⣿⣾⣷⣾⣷⣿⣷⣶⣿⣶⣷⣶⣿⣿⣾⣿⣿⣿⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠐⠀⠐⠀⠀⠀⠀⠀⢸⣿⣬⣭⣭⣵⣽⣿⣿⣽⣬⣭⣭⣹⣥⣬⣍⣩⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⡄⡀⠀⣀⡀⡀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⡿⣿⡿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠃⠂⠀⠒⠂⠂⠀⠀⠀⠀⠀⢸⣷⣭⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡄⠀⠀⡀⢀⢀⡀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠃⠂⠀⠒⠂⠂⠀⠀⠀⠀⠀⢸⣯⣽⣿⣯⣿⣿⣯⣯⣭⣧⣭⣯⣿⣯⣿⣿⣯⣿⣭⣬⣭⣽⣽⣿⣧⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⢀⠀⢀⢀⠀⠀⠀⠀⢸⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠐⠀⠐⠐⠀⠀⠀⠀⢸⣏⣽⣽⣯⣯⣭⣵⣼⣥⣽⣽⣿⣯⣿⣿⣿⣬⣭⣿⣯⣬⣥⣭⣮⣿⣯⣯⣽⣽⣭⣥⣽⣯⣭⣭⣥⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡿⡿⠿⠿⣿⠿⠿⡿⣿⢿⢿⢿⡿⡿⡿⡿⡿⢿⠿⢿⢿⣿⠿⡿⢿⣿⢿⠿⣿⢿⢿⢿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣶⣶⣷⣷⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠆⠒⠴⠐⠀⠰⠢⠰⠰⠀⠀⠀⣿⣛⣉⣉⣙⣉⣉⣋⣻⣉⣩⣩⣉⣙⣽⣽⣭⣿⣽⣽⣽⣿⣯⣽⣽⣽⣽⣯⣭⣭⣹⣽⣯⣯⣿⣯⣿⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⢀⠀⠀⣀⠀⠀⠀⡀⢀⣀⠀⠀⠀⣿⡿⢿⠿⢿⡿⠿⢿⡿⣿⡿⠿⢿⣿⣿⣿⡿⣿⣿⡿⡿⡿⣿⡿⠻⣿⢿⢿⢿⣿⣿⣿⡿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⣶⣶⣶⣶⣷⣾⣾⣷⣷⣶⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣷⣷⣾⣿⣿⣿⣾⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠇⠂⠴⠀⠀⠐⠀⠰⠰⠀⠀⠀⣿⣙⣉⣉⣿⣿⣿⣻⣿⣻⣯⣍⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⣀⢀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⡿⠿⠿⡿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⢿⣿⣿⣿⣿⣻⡿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⣾⣿⣿⣿⣷⣿⣾⣾⣿⣷⣶⣶⣷⣿⣷⣷⣾⣾⣷⣷⣿⣾⣷⣷⣿⣶⣶⣿⣾⣿⣷⣿⣾⣾⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⡆⠄⣠⠀⠀⠠⠀⢰⠢⠀⠀⠀⣿⣾⣿⣿⣿⣥⣤⣧⣧⣥⣧⣶⣤⣯⣽⣭⣯⣍⣧⣬⣿⣿⣿⣤⣿⣿⣿⣯⣿⣿⣿⣽⣝⣷⣽⣿⣿⣿⣧⣧⣤⣤⣿⣿⣤⣥⣯⣤⣤⣼⣤⣥⣼⣿⣯⣤⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠆⠀⠀⠰⠆⠀⠀⠀⠀⠀⣿⣑⣯⣟⣟⣛⣏⣙⣛⣟⣏⣨⣉⣉⣿⣿⣻⣻⣻⣻⣁⣉⣝⣟⣛⣹⣍⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⡀⢀⠀⢀⡀⠀⠀⠀⠀⠀⣿⢿⣿⠿⠿⣿⣿⣿⣿⡿⡿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠠⣿⣶⣾⣶⣶⣿⣶⣿⣷⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠠⠀⠀⡤⠀⠀⠀⠄⢠⣤⠀⠀⠀⣿⣿⣽⣿⡷⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣯⣥⡤⣽⢴⢿⣭⣤⣯⣦⣵⣿⣬⣿⣿⣿⣿⣯⣥⣤⣼⣭⣥⣧⣷⣭⣼⣷⣮⣤⣿⣿⣷⣽⣿⣷⣶⣤⣼⣤⣬⣦⣾⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣼⣷⣦⣼⣿⣶⣼⣽⣿⣶⣧⣾⣿⣿⣧⣤⣥⣤⣴⣾⣶⣾⣤⣶⣶⣴⣿⣾⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠆⠀⠀⠰⠆⠀⠀⠀⠀⠀⣿⣁⡯⣍⣿⣿⣯⣹⣹⣩⣍⣯⣽⣏⣿⣭⣎⣋⣈⣭⣍⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠿⢿⢿⠿⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣶⣾⣶⣶⣶⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠂⠐⠀⠰⠂⠀⠀⠀⠀⠀⣿⣛⣻⣻⣻⣛⣉⣙⣩⣛⣫⣛⣏⣛⣗⣋⣭⣍⣿⣹⣻⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⡀⢀⠀⢀⡀⠀⠀⠀⠀⠀⣿⣿⡿⢿⢿⢻⣿⢿⣿⡿⣿⣿⣿⢿⣿⢿⣿⣿⡿⠿⠿⠿⢿⣿⡿⣿⠻⠿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣾⣾⣿⣿⣶⣾⣷⣿⣾⣷⣿⣷⣾⣷⣿⣷⣶⣷⣷⣿⣷⣾⣷⣶⣿⣷⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠂⠐⠀⠐⠂⠂⠀⠀⠀⠀⣿⣹⣟⣛⣟⣻⣛⣿⣟⣏⣿⣫⣛⣉⣙⣏⣉⣽⣟⣙⣽⣫⣙⣟⣝⣯⣉⣣⣿⣻⣿⣏⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠻⢿⣿⣿⣿⣿⣿⢿⢿⡿⠿⢻⣿⣿⡿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⢿⢿⢿⡿⢿⠿⢿⢻⠛⠿⢿⠻⢻⣻⡿⠟⠿⡿⠟⢿⢻⣿⣿⣿⡿⢿⡿⡿⠿⠿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠃⠚⠀⠚⠂⠀⠘⠈⠀⠀⠀⢸⣿⣿⣟⣟⢿⣻⣟⢻⣻⣟⣟⣟⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⣸⣿⣯⣾⣿⣿⣿⣶⣾⣷⣯⣾⣿⣿⣯⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⢸⣿⢛⢻⣟⢿⣿⡿⢻⢻⡛⣛⢛⢻⣟⠛⢛⢻⠹⡿⣻⣿⡿⣿⡿⠛⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⣸⣯⣯⣿⣥⣷⣦⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⡄⠀⠀⢀⢀⡄⠀⢤⠀⠀⢸⣿⣿⣿⡟⡛⠛⠛⠛⠛⢻⡟⠛⣻⢛⡻⣿⢛⢻⠛⠛⡟⢛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠃⠀⠀⠐⠐⠃⠀⠚⠀⠀⢸⣷⣾⣷⣷⣷⣧⣵⣿⣾⣷⣶⣷⣷⣿⣷⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⡟⣿⣿⣿⣟⣿⣛⣻⣙⣟⣻⣻⣿⣻⣛⣛⣋⣟⣿⣿⣿⡟⣟⣿⣿⣟⣟⣿⣟⣿⣛⣙⣿⣿⣿⣿⣏⣛⣻⣹⣿⣻⡟⣿⣿⣿⣿⣿⣟⣿⣹⣿⣟⣛⣛⣿⣿
⠀⠀⠀⠁⠉⠀⠉⠁⠀⠈⠈⠀⠀⠀⢸⣿⣽⣽⣿⣿⣿⣿⣍⣛⣏⣹⣿⣿⣏⣟⣍⣻⣯⣛⣛⣻⣟⣻⣿⣯⣿⣟⣿⣉⣙⣙⣿⣏⣿⣽⣏⣟⣻⣙⣟⣙⣏⣯⣿⣿⣽⣟⣟⣛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠿⢿⣿⡿⣿⢿⣿⣿⡿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢼⣷⣷⣷⣷⣶⣿⣾⣿⣷⣿⣧⣷⣿⣿⣷⣿⣾⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠔⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣯⣉⣉⣙⣽⣯⣿⣿⣹⣉⣹⣹⣽⣿⣟⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢸⣿⣿⡿⠿⠿⢿⡿⡿⢿⣿⣿⣿⠿⠿⠿⡿⠿⢿⣿⡿⡿⡿⡿⠿⠿⠿⠿⡿⣿⣿⢿⢿⣿⣿⣿⣿⢿⣿⡿⣿⣿⡿⠿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠁⠀⠀⠈⠈⠁⠀⠉⠀⠀⢸⣿⣿⣶⣶⣶⣾⣾⣿⣾⣿⣿⣷⣶⣶⣿⣷⣶⣿⣿⣿⣷⣶⣷⣶⣶⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠔⠰⠀⠀⠠⠀⠀⠀⠀⢸⣯⣯⣫⣿⣽⣏⣿⣻⣝⣿⣙⣙⣍⣏⣯⣿⣹⣉⣯⣿⣙⣏⣝⣫⣩⣿⣹⣯⣯⣋⣹⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡿⣿⡿⡿⣿⢿⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣿⣿⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⡀⣀⠀⢀⡀⢀⢠⢀⠀⠀⠀⢸⣿⣛⣿⣿⣿⣋⣛⣏⣻⣟⣿⣿⣿⣿⣙⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣯⣿⣿⣿⣟⣉⣛⣽⣉⣉⣉⣉⣭⣩⣛⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣏⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠀⠈⠀⠀⠉⠀⠀⠀⠀⢸⣿⣝⣻⣿⣇⣍⣿⣻⣟⣿⣿⣿⣿⣿⣟⣫⣟⣿⣿⣿⣹⣟⣩⣏⣉⣋⣘⣫⣟⣈⣩⣇⣋⣩⣿⣝⣿⣿⣿⣿⣏⣨⣍⣿⣞⣽⣯⣿⣿⣿⣿⣿⣻⣟⣩⣉⣁⣏⣍⣻⣿⣿⣿
⠀⠀⠀⠀⠀⡠⣠⠀⠀⢀⠀⠀⠀⠀⢸⣟⢛⡻⡛⢛⣟⣟⣟⡿⣿⠛⠛⢛⣿⣟⣟⢛⢛⣻⣻⣿⡛⣟⢟⠛⠟⠛⢻⣛⠻⠛⡟⠛⢛⣛⣿⣻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠃⠀⠀⠐⠀⠃⠀⠚⠀⠀⢸⣿⣯⣯⣿⣼⣥⣭⣧⣭⣯⣬⣯⣿⣯⣤⣬⣶⣭⣼⣿⣿⣥⣽⣼⣬⣯⣨⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠟⢿⠻⠿⠿⡟⠟⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠃⠀⠂⠂⠀⠋⠀⠒⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⢿⠟⢿⠻⠿⠿⡟⠟⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣓⣚⣓⣓⣒⣒⣒⣓⣒⣒⣚⣒⣚⣚⣓⣛⣓⣛⣓⣒⣒⣓⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻
⠀⠀⠂⠂⠀⠀⠂⠀⠐⠀⠀⠂⠀⠀⢸⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⡀⠀⣀⢀⠀⠀⠀⠀⢸⡿⢿⣿⢿⠻⡿⢿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣶⣷⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠂⠂⠀⠀⠂⠐⠐⠀⠀⠂⠀⠀⢸⣿⣿⣽⣽⣽⣯⣿⣭⣭⣽⣼⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⡤⡀⠀⣤⢀⠀⠀⠀⠀⢸⣟⠻⠿⠻⢛⠿⣿⡟⠟⢛⢻⢟⣿⠻⡟⣻⣛⣛⡻⠛⣻⣻⣛⡟⣟⡟⣿⣻⠛⣿⡛⢟⡟⡟⡟⠻⡿⠻⡟⠟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿
⠀⠀⠄⠄⠀⠀⠆⠠⠠⠀⠀⠔⠀⠀⢸⣿⣿⢾⣿⣷⣿⢷⣶⢶⢷⣶⣾⡿⣷⠷⣿⣾⠿⡿⡿⣶⢶⡾⠶⣾⣶⡶⢼⣶⣶⢶⣶⣶⣿⢮⣿⣶⣷⣶⣶⣿⣿⣶⣶⣾⣴⣶⣷⣷⣾⣿⣷⣷⣶⣶⣶⣶⣶⣷⣷⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣶⣾⣿⣷⣾⣶⣾⣾⣶⣶⣶⣷⣷⣶⣶⣶⣿⣷⣶⣿⣿⣿⣷⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠊⠂⠀⠛⠐⠀⠀⠀⠀⢸⣿⣥⣵⣭⣤⣯⣭⣧⣿⣿⣩⣾⣿⣽⣵⣷⣷⣭⣯⣩⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⡤⡀⠀⣤⢀⠀⠀⠀⠀⢸⣿⢻⡛⠛⠟⠟⣿⣛⡟⣿⡻⠛⠛⣛⣛⢟⡿⡛⡛⣟⣟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠋⠂⠀⠛⠑⠀⠀⠀⠀⢸⣷⣷⣷⣿⣭⣦⣼⣴⣾⣗⣷⣷⣷⣷⣿⣮⣾⣧⣶⣵⣦⣤⣼⣬⣾⣷⣬⣾⣗⣵⣷⣔⣽⣦⣬⣤⣬⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣩⣛⣻⢹⣫⣉⣏⣿⣯⣛⣿⣟⣻⣿⣿⣿⣯⣏⣿⣿⣿⣿⣿⣟⣻⣻⣿⣿⣽⣿⣝⣛⣏⣍⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⡉⡉⠉⠉⡉⠉⢉⠉⠉⡉⠉⠉⢹⣿⢿⣿⣿⣿⢿⢿⠿⠿⢿⣿⣿⣿⣿⣿⡿⡿⠿⡿⡿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠂⠀⠒⠐⠀⠀⠀⠀⢸⣟⣈⣭⣟⣩⣉⣿⣭⣿⣝⣿⣯⣉⣉⣹⣿⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠻⣿⣿⣛⠿⣿⣟⣩⡏⣿⣿⣿⣿⡏⣯⣻⢝⢿⢹⣿⢻⡿⢛⣯⣯⣿⢛⣿⠻⡻⡿⢻⢿⣟⣹⣟⣿⣽⣿⠿⡏⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⡉⡉⠉⠉⡉⡉⢉⠉⠉⡉⠉⠉⢹⣿⠻⠿⡿⠿⢿⣿⠿⠻⠿⡿⣿⣿⢿⣿⠿⠿⠿⠿⠟⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⢜⣓⣒⣚⣓⣒⣒⣛⣓⣒⣒⣓⣓⣓⣒⣚⣒⣚⣒⣒⣒⣓⣓⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻
⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣭⣭⣽⣯⣿⣿⣿⣯⣿⣿⣼⣬⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⣿⢿⡿⠿⣿⠿⠿⡿⢿⠿⣿⣿⡿⠿⠿⡿⠿⢿⠿⠿⠟⢿⢿⡿⠛⠿⡿⠿⠿⢻⠻⡿⣿⡿⣿⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⣾⣾⣾⣾⣶⣷⣿⣾⣾⣾⣷⣷⣿⣷⣶⣾⣾⣶⣶⣾⣾⣷⣶⣷⣷⣷⣷⣾⣾⣶⣿⣾⣶⣾⣷⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⢸⣯⣽⣯⣿⣿⣭⣵⣼⣥⣭⣭⣍⣹⣭⣭⣭⣧⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠄⠀⠀⣤⠀⠀⠀⠀⠀⢸⡟⢙⢛⣛⡟⢛⣟⠛⠛⢻⠛⡏⠛⠛⠛⠋⢻⠛⢻⠙⣛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠃⠀⠘⠃⠓⠀⠈⠀⠛⠀⠂⠀⢸⣧⣴⣭⣼⣽⣶⣦⣍⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣭⣱⣿⣯⣮⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⢠⡀⣄⠀⠠⠀⣄⠠⡀⠀⢸⡟⢿⢿⠻⠿⠿⣿⣿⡿⣿⠿⠟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠟⡿⣿⣿⣿⣿⣿⡿⠿⡻⠟⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠀⠂⠀⠛⠀⠀⠀⠀⠀⢸⣷⣭⣽⣿⣯⣿⣾⣯⣭⣥⣭⣭⣭⣥⣿⣭⣤⣿⣿⣯⣭⣿⣭⣽⣼⣿⣯⣯⣭⣽⣽⣿⣭⣭⣿⣯⣯⣯⣿⣽⣭⣭⣵⣿⣯⣽⣤⣤⣿⣽⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⡀⠀⣀⢀⠀⠀⠀⠀⢸⡿⠻⠿⠿⣿⣿⠿⣿⠿⠿⣿⣿⣿⣿⡟⠿⣟⠿⡟⠟⠿⣿⢿⣿⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠂⠀⠐⠂⠂⠐⠐⠀⠒⠀⠀⠀⢸⣏⣉⣹⣉⣭⣼⣼⣾⣭⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⡀⠀⣀⠀⠀⠀⠀⠀⢹⡶⠶⢶⣶⣶⣶⣶⡶⣶⣶⣶⡲⢶⠶⢶⣲⣶⡶⡶⣶⢶⡶⠶⠖⡶⡶⢶⠒⠒⡶⠶⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣷⣶⣷⣿⣿⣾⣷⣷⣷⣷⣿⣷⣷⣶⣾⣿⣾⣾⣾⣾⣾⣶⣶⣷⣷⣷⣷⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⠀⠂⠀⠦⠀⠀⠀⠀⠀⢸⡏⣉⣝⣟⣛⣻⣟⣏⣉⣛⣻⣹⣟⣟⣝⢟⣫⣻⣓⣏⣉⣉⣿⡍⣝⣉⣁⣉⣟⣋⣋⣹⣈⣉⣝⣋⣋⣉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⢀⡀⡀⠀⢀⠀⣀⠀⠀⠀⢸⡿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣁⣀⣈⣁⣁⣀⣀⣀⣉⣀⣁⣀⣸⣷⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠷⠼⠿⠿⠦⠿⠿⠾⠾⠿⠗⠵⠿⠿⢽⣿⣿⣿⣷⣽⣿⣾⣾⣕⣷⣿⣽⣿⣿⣯⣿⣮⣷⣏⣽⣯⣿⣾⣯⣿⣿⣿⣿⣷⣤⣤⣤⣷⣶⣿⣿⣾⣿⣽⣫⣷⣶⣽⣵⣿⣼⣮⣿⣷⣷⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠄⠄⠀⠤⠀⠀⠀⠀⠀⢸⣟⡟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠀⠁⠀⠋⠀⠀⠀⠀⠀⣸⠷⠾⠬⠼⠽⠼⠼⠷⠯⠽⠴⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠄⠀⢠⠄⡄⠀⠠⠀⣤⠀⡀⠀⢸⡟⠛⡿⡿⢙⠹⣿⡻⣿⠛⢻⢿⡟⣿⣟⠛⡿⣿⣿⡏⢻⡿⣟⠟⡛⡿⢛⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠁⠀⠀⠛⠀⠀⠀⠀⠀⢸⣇⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡀⡀⠀⢀⠀⣀⠀⠀⠀⢸⣯⣹⣟⣿⣻⣟⣿⣿⣻⣻⣿⣻⣿⣻⣿⣿⣿⣿⣉⡛⢛⣿⣛⣻⣿⣿⣿⣿⣿⣟⣿⣯⣙⣽⣟⣿⣻⣟⣿⣯⣿⣿⣟⠻⣟⣋⣫⣏⣛⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠀⠈⠁⠉⠀⠀⠀⠉⠀⠁⠀⢸⣏⣉⣉⣽⣽⢭⣽⣿⣋⣯⣽⢍⣙⣹⣉⣉⣋⣫⣩⣿⣉⣩⣿⣯⣿⣍⣿⣿⣿⣯⣻⣻⣿⣏⣽⣽⣹⣿⣫⣿⣿⣹⣿⣍⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡀⡀⠀⣀⢀⠀⠀⠀⠀⢸⡟⠿⠟⣿⡿⡿⣿⣿⢻⡿⣿⣿⣿⢿⡿⠿⠿⡟⡿⠿⡿⢿⡿⠿⣿⠿⠿⢟⢿⢿⣿⡿⠿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣷⣿⣾⣿⣿⣷⣷⣾⣿⣷⣶⣶⣷⣿⣿⣿⣾⣾⣾⣿⣾⣶⣾⣷⣷⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠂⠂⠀⠒⠀⠀⠀⠀⠀⢸⣇⣈⣍⣹⣹⣹⣋⣏⣀⣑⣌⣻⣩⣟⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡠⣀⠀⢠⢀⠀⠀⠀⠀⢸⣟⠻⠿⠻⢻⢿⠻⣟⠻⠛⠿⢛⢻⣻⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠐⠀⠐⠐⠀⠀⠀⠀⢸⣷⣬⣦⣤⣿⣮⣦⣶⣕⣷⣶⣵⣵⣤⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⡠⣀⠀⢠⢀⠀⠀⠀⠀⢸⡟⣿⣟⣿⡿⢻⣿⣟⣿⢿⣿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠛⠀⠀⠃⠐⠐⠃⠀⠊⠀⠀⢸⣿⣵⣿⣿⣾⣿⣿⣯⣾⣭⣯⣼⣿⣽⣽⣯⣿⣼⣽⣷⣷⣽⣧⣧⣭⣭⣭⣯⣼⣿⣷⣷⣿⣿⣭⣽⣬⣯⣷⣿⣷⣿⣮⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⢀⠀⢀⢀⠀⠀⠀⠀⢸⡿⢟⡟⡟⠟⠛⡿⡻⡻⣻⢿⠟⡟⡛⣛⢟⡿⠻⠟⣟⡻⠿⢿⠛⣛⣟⣻⡟⠟⢛⢟⣟⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠛⠀⠀⠋⠐⠐⠃⠀⠊⠁⠀⢸⣿⣯⣿⣿⣽⣯⣭⣯⣿⣯⣭⣥⣿⣭⣼⣿⣭⣯⣿⣭⣭⣍⣧⣿⣭⣿⣭⣭⣯⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⡀⢀⢀⡀⠀⡀⠀⠀⢸⣟⠻⢿⡿⡿⣿⢿⣿⡿⣿⣿⡿⠿⣻⣿⢿⣿⢻⠿⡿⡿⣿⣿⠿⢛⣿⠻⣿⢿⢿⢿⢿⢿⣿⣿⢿⣿⣟⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠐⠀⠐⠐⠀⠀⠀⠀⢸⣿⣿⣭⣯⣯⣼⣿⣿⣭⣬⣥⣭⣼⣯⣭⣭⣧⣿⣯⣭⣽⣽⣽⣯⣿⣿⣽⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⡀⠀⢀⡀⠀⡀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠐⠐⠀⠀⠀⠀⢸⣟⣈⣭⣉⣇⣩⣭⣽⣟⣟⣍⣏⣏⣼⣟⣝⣍⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⡀⡀⢀⡄⠀⡀⠀⠀⢸⣿⢿⣿⡿⠿⡿⠿⡟⠻⠿⢿⣿⡿⠿⠿⣿⠻⢿⢿⠿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠿⠿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠒⠀⠀⠂⠀⠐⠂⠀⠂⠀⠀⢸⣟⣿⣩⣍⣿⣯⣫⣽⣩⣹⣫⣿⣽⣟⣿⣇⣩⣉⣿⣽⣽⣿⣿⣹⣟⣭⣏⣉⣉⣘⣹⣏⣿⣿⣭⣏⣫⣿⣻⣩⣻⣏⣿⣻⣻⣿⣿⣃⣯⣏⣈⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢸⡿⢿⣿⡿⡿⠿⢿⢿⢿⢿⣿⠻⠿⢿⠿⠻⠿⠿⢻⠿⠿⠿⢿⢿⡿⠿⠟⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣷⣿⣾⣶⣾⣿⣶⣾⣷⣶⣶⣾⣶⣾⣿⣷⣿⣷⣿⣿⣾⣿⣿⣿⣷⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠒⠀⠀⠂⠂⠐⠂⠀⠂⠀⠀⢸⣯⣯⣯⣽⣤⣯⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢱⣶⠲⠶⠶⡖⠶⠶⢶⣶⣶⠶⠶⡖⣶⡶⣶⡶⡶⢶⢶⡶⡶⠶⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣶⣾⣶⣷⣶⣿⣿⣷⣷⣷⣷⣿⣶⣷⣷⣷⣿⣿⣿⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠒⠀⠀⠂⠂⠐⠂⠀⠂⠀⠀⢸⣿⣈⣉⣉⣿⣉⣿⣟⣿⣿⣽⣋⣹⣿⣟⣽⣿⣟⣫⣯⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣷⣩⣿⣿⣾⣿⣯⣿⣿⣯⣯⣉⣩⣽⣿⣿⣿⣷⣏⣉⣿⣫⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⡿⠿⢿⠿⠿⠻⢿⢿⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⢿⣿⣿⡿⢿⣿⢿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠀⠀⠉⠈⠀⠀⠀⠀⢸⣷⣶⣶⣷⣿⣶⣶⣾⣶⣶⣮⣿⣾⣾⣾⣾⣷⣾⣿⣾⣷⣾⣾⣷⣷⣷⣿⣿⣾⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠆⠆⠀⠆⠦⠂⠰⠀⠰⠆⠀⠀⢸⣏⣟⣯⣿⣉⣉⣍⣹⣉⣉⣹⣯⣯⣝⣽⣍⣫⣙⣙⣏⣯⣯⣽⣽⣽⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡿⣿⢿⣿⡿⢿⠿⣿⡿⡿⢿⠿⠿⡿⠿⡿⣿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠁⠀⠉⠈⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣷⣾⣿⣷⣷⣾⣶⣾⣿⣾⣿⣿⣶⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠆⠆⠐⠆⠦⠀⠰⠀⠰⠖⠀⠀⢸⣯⣿⣙⣽⣿⣽⣹⣩⣻⣹⣿⣽⣿⣛⣏⣛⣹⣻⣹⣯⣝⣭⣝⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠀⠁⠀⠉⠈⠀⠀⠀⠀⢸⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⠄⠀⠄⠄⠠⠠⠀⠀⠔⠀⠀⢸⡟⠛⣟⢻⣿⢟⣿⠏⢛⣻⣹⣿⣟⣿⣛⣛⡛⣟⡛⠋⣻⡿⣿⣿⣟⢻⢛⢻⢙⢛⡛⠛⣛⡟⢿⢙⡟⣿⢹⢟⣟⣝⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠁⠀⠀⠉⠀⠀⠀⠀⠀⢸⣧⣧⣬⣧⣦⣦⣾⣧⣿⣴⣤⣧⣿⣽⣽⣥⣤⣵⣽⣼⣴⣾⣼⣯⣯⣯⣯⣧⣭⣮⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠄⠀⠀⣤⠄⠀⠀⠀⠀⢸⡟⠛⡏⠛⣿⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠃⠃⠀⠃⠓⠁⠈⠀⠘⠃⠀⠀⢸⣧⣤⣤⣼⣽⣿⣽⣬⣬⣯⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⡄⠀⠀⣤⢄⠀⠀⠀⠀⢸⡟⣟⣟⣿⠿⣛⢻⢟⠛⢟⡿⢻⢛⣻⣙⣟⠛⠛⠛⢻⣟⡟⢟⣿⣟⡟⣝⠟⢻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠃⠃⠀⠃⠓⠀⠘⠀⠘⠋⠀⠀⢸⣷⣷⣵⣗⣦⣤⣼⣤⣷⣴⣿⣯⣿⣦⣥⣶⣮⣦⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⡤⡀⠀⣤⢄⠀⠀⠀⠀⢸⡟⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠋⠂⠀⠛⠑⠀⠀⠀⠀⢸⣧⣭⣥⣧⣦⣬⣇⣦⣶⣷⣔⣾⣼⣿⣮⣽⣬⣬⣥⣧⣮⣦⣥⣽⣤⣥⣵⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠀⡀⠀⣠⢀⠀⠀⠀⠀⢸⣟⢛⠟⢿⣻⠻⠻⠻⠛⣻⠟⢿⠻⢛⣟⡟⣟⣿⡟⡻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠂⠀⠒⠐⠀⠀⠀⠀⢸⣯⣽⣹⣻⣉⣬⣩⣽⣯⣉⣨⣟⣝⣋⣽⣭⣧⣙⣭⣉⣿⣩⣉⣯⣏⣿⣹⣟⣫⣏⣿⣻⣻⣿⣿⣟⣯⣯⣽⣁⣈⣏⣫⣍⣿⣿⣏⣭⣩⣏⣿⣏⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⢉⢉⡉⡉⣉⢉⣉⣉⣉⢉⡉⡉⡉⠉⠉⠉⠉⢹⡿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠂⠀⠐⠋⠈⠂⠃⠛⠘⠀⠁⠃⠀⠀⠀⠀⢸⣿⣥⣽⣿⣼⣿⣷⣾⣿⣷⣿⣿⣧⣽⣾⣷⣿⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⡀⡀⢀⢀⠀⡀⠀⣀⡀⢀⠀⢀⢀⢀⠀⠀⠀⢸⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠊⠁⠃⠉⠘⠑⠊⠀⠃⠋⠚⠐⠋⠚⠑⠀⠀⠀⢸⣿⣾⣿⣷⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢭⡭⣯⣽⣿⣭⣿⣿⣯⣭⣿⡽⡯⠭⡽⢿⣭⡿⣽⣿⣯⣿⣧⣹⣭⣯⣏⣧⣧⣭⣽⣬⣬⣭⣭⣭⣭⣿⣮⣧⣷⣿⣭⣽⣿⣿⣭⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢽⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡯⠭⠯⠭⠿⡯⣿⣿⣿⣿⣭⣿⣭⣽⣭⣭⣯⣯⣯⣿⣽⣽⣹⣭⣽⣭⣭⣽⣯⣭⣭⣭⣹⣯⣭⣽⣍⣯⣽⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⢹⡫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡯⣭⢭⠭⢿⣯⢿⡉⢯⡿⢙⠹⣉⡩⠿⠩⡏⠩⣿⢉⡽⠍⢻⠩⣙⠏⢹⠩⡹⠉⡉⠉⠍⢉⠏⠹⡉⢩⠯⠉⢹⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢸⣂⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣚⣝⣊⣗⣿⣺⡧⣾⣷⣒⣢⣋⣿⣆⣔⣶⣨⣁⣈⣂⣰⣆⣆⢌⣒⣈⢮⣅⣷⣷⣶⣶⣾⣶⣶⣷⣿⣾⣶⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣷⣿⣚⣓⣻⣟⣲⣺⣲⣟⣗⣓⣛⣺⣲⣔⣶⣲⣳⣲⣒⣒⣓⡶⣷⣶⣾⣾⣾⣶⣾⢶⣶⣾⣶⣶⣷⣶⣷⣿⣿⣶⣿⣷⣶⣿⣶⣾⣿⣷⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣗⣒⣗⣺⣿⣿⣿⣗⣿⣿⣗⣺⣺⣺⣗⣓⣿⣺⣒⣗⣗⣒⣟⣾⣒⣚⣶⣳⢛⣺⣒⣛⣺⣚⣓⣲⣗⣶⣟⣻⣔⣸⣿⣛⣿⣻⣟⣟⣿⣟⣻⣟⣛⣟⣻⣿⣛⣿⣛⣻⣻⡛⣿⣿⣿
⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣛⣛⣛⣷⣶⣗⣿⣶⣞⣓⣓⣲⣖⣒⣷⣒⣒⣛⣟⣛⣟⢛⣟⣛⣻⣛⣟⣛⣻⣛⣛⣛⣛⣛⣟⣛⣟⣛⣟⣛⣿⣻⣛⣿⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⢸⠕⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣗⠶⣲⢒⣋⣿⣿⡗⣿⣿⠁⠒⣢⡿⢣⢲⡟⢒⡀⠀⢡⠐⠋⢠⡜⣻⠟⢻⠛⣻⠛⢻⠛⡛⠛⡟⡟⢻⢛⣻⠛⢻⣿⡛⣻⠛⣟⠿⣿⢻⡿⡛⢛⡻⠛⡟⠛⢻⡛⢻⠛⣻⠻⢻⣿
⡟⢻⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⠿⡿⣿⢭⡝⣬⣭⠽⢭⠧⢭⡧⡥⣽⠆⡴⡿⡿⠿⢿⢿⠿⡻⡟⠿⠿⠿⠿⠿⠻⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⢽⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⠭⡯⢽⣿⣿⣿⣧⣿⣿⡯⢽⢽⢽⡯⡯⣿⠥⡯⡯⣿⢽⢽⢸⡭⣽⠭⠝⣬⣧⣭⢽⠭⣭⢬⢧⣭⡽⢹⣭⣯⣯⣭⣯⣽⣽⣿⣯⣭⣽⣯⣽⣿⣽⣯⣭⣯⣯⣭⣿⣿⣿⣿⣿⣿
⣿⢽⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡯⠭⠯⠽⣿⣿⣿⡯⣿⣿⡯⠽⠽⢽⡯⠭⣿⠭⠭⠅⢽⢽⢽⢭⠽⢿⠿⡿⠷⠿⠿⢾⠾⠿⠿⢿⠿⡿⢿⣿⠿⢿⠿⠿⣿⠿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢽⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡯⡭⢭⠭⣽⣿⣿⡯⣿⣿⡯⠭⠭⣽⡯⠭⣿⠭⠭⠥⡫⠩⡯⢭⠭⠭⠩⡹⠭⠯⢩⣭⡯⡩⣮⣭⣽⣽⣭⣽⣭⣭⣽⣯⣭⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡧⣸⢊⣿⢿⡿⣿⣿⣿⡿⣿⣿⣿⣯⣛⣽⣩⣥⣿⣿⣏⣿⣿⢖⢫⡁⢿⣇⣝⡿⡩⣀⣀⣂⣸⣧⣈⠀⣢⢄⣑⣃⣈⣀⡀⣑⣀⣙⠋⢉⣋⡏⣹⣉⣙⣹⣟⣍⣋⣿⣟⣉⣉⣹⣩⣝⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⣰⣂⣷⣾⣿⣶⣶⣷⣷⣾⣿⣶⣖⣚⣖⣚⣶⣶⣲⡯⣾⣷⣒⣲⣒⣲⣖⣗⣷⡃⣖⣞⣖⣒⣺⣂⣒⣲⣚⣲⣒⢲⣶⣶⣶⠾⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣷⣒⣗⣺⣿⣿⣿⣿⣿⣿⣗⣺⣺⣺⣗⣗⣿⣒⣗⡗⣿⣺⣺⣒⣗⣘⢲⣶⣾⣾⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣺⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣗⣒⣓⣚⣻⣿⣿⣗⣿⣿⣗⣚⣚⣺⣗⣒⣿⣒⣒⣂⣞⣚⣞⣚⣻⢒⣺⣗⣒⣺⣚⣰⣚⣓⣚⢶⣚⣛⢒⡖⣓⣞⣗⣒⣛⣷⣿⣿⣷⣾⣿⣿⣿⣶⣿⣿⣾⣿⣾⣾⣾⣿⣿⣿⣿
⡯⢺⠗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣗⣖⣲⡒⡾⣿⣿⣗⣿⣿⠕⢒⠂⣾⡗⡒⣿⡒⡀⡀⡡⡴⣣⠀⣤⣧⣴⣼⣤⣧⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣼⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣮⣴⣾⣿⣿⠧⡿⠿⢯⠵⡤⠿⠧⢮⡿⠴⢤⡤⠥⠼⠧⡞⢤⠼⠤⢼⠦⡽⡤⡤⠵⠠⡄⠠⣤⢧⡤⠧⢤⠾⡽⠤⡽⣭⣽⠿⣦⣿⣼⣶⣽⣮⣯⣿⣭⣬⣧⣬⣼⣿⣿⣿⣿
⡀⠨⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠭⠭⠀⡯⢸⡧⠭⠥⡿⢿⣤⠶⠤⢦⢼⡽⡴⡵⠥⡦⢤⣧⣼⣤⣤⣼⣬⣤⣤⣴⣬⣽⣮⣥⣽⣯⣿⣭⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡢⠬⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠬⠭⠭⠬⡯⠭⡯⢽⠭⠭⢽⡿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡯⠭⠭⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠭⠭⠭⡯⢭⠯⠭⠯⡭⠽⣿⠯⠭⡿⡿⠿⠿⡿⠿⡿⠿⢿⠿⡿⠿⡿⢿⠿⠿⢿⠿⢿⠿⠿⡿⠿⠿⣿⢿⣿⢿⢿⠿⡿⠿⡿⠿⠿⢿⠿⡿⠿⢿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿
⡊⢉⠭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⣯⢉⠉⠩⠏⡍⢽⣿⡉⠹⢩⠹⠏⣉⠏⠈⣹⣉⣏⣹⣉⣩⣉⣍⣉⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⢐⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣒⣒⠀⣟⢸⣇⣒⣂⣿⣺⣟⣗⣖⣚⣒⣇⣳⣒⣗⣍⣹⣉⣉⣉⣏⣋⣏⣍⣟⣍⣛⣽⣋⣻⣝⣽⣟⣿⣽⣿⣛⣛⣻⣩⣫⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢅⣐⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣒⣒⣐⣗⣚⣗⣲⣒⣓⣲⣶⣟⣚⣗⡶⣖⢒⣷⣷⣷⣶⣿⡿⡿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣗⣒⣒⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣒⣒⣒⣗⣒⣓⣚⣲⣖⣺⣿⣗⣒⣲⣖⣺⣶⣒⣞⣗⣓⣻⣓⣳⣒⣲⣛⡒⣞⣲⣒⣗⣛⣲⣟⣛⣚⣳⣖⣒⣲⣛⣾⣳⣚⣂⣻⣟⣛⣛⣟⣛⣛⣻⣛⣛⣿⣻⣻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠒⠒⡞⣛⣒⣿⠒⠓⢘⢓⡖⠒⣳⣶⣿⣷⣾⣶⣶⣶⣶⣷⣾⣶⣷⣷⣷⣶⣿⣶⣶⣷⣶⣾⣿⣷⣶⣷⣶⣷⣷⣶⣶⣷⣶⣶⣶⣼⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿
⣥⣬⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⡿⠤⠄⢮⣼⢯⣾⠿⠧⢤⡼⠄⠠⡧⡂⣧⠅⢠⠘⠁⢘⠀⡌⢠⠀⡗⣜⡄⠧⣴⡘⠧⣥⠠⣽⣧⡤⠾⡄⠿⢜⡔⡐⡘⡇⠀⠂⠃⢤⠀⡜⠀⠀⢻⣼⣼⣿⣿⣿⣿
⡛⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⠻⡿⠨⠭⠯⠬⡭⢿⡭⣭⠭⠽⠯⢭⣽⢯⣯⢿⡭⢭⠫⢤⠿⢭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣮⣭⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⡯⢭⡯⢽⡭⡭⢽⣯⣥⣽⣽⣿⣭⣷⣭⣿⣯⣽⣯⣭⣽⣭⣯⣭⣽⣽⣭⣍⣭⣭⣭⣭⣽⣿⣿⣿⣿⣭⣯⣭⣯⣯⣾⣯⣥⣽⣬⣭⣥⣍⣿⣯⣯⣯⣍⣿⣬⣽⣿⣿
⡫⠭⠭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠭⠭⠭⡯⠯⠯⠭⡭⠽⢽⡭⠿⠽⠭⠍⣽⡭⠭⠿⢿⠿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⢐⠅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⠀⣿⠀⡂⢈⣃⡱⣝⣉⢶⢶⢌⢰⡉⡁⠎⡴⢉⠐⣶⠶⡷⢾⠶⡿⢿⢿⣿⡿⣿⡿⣿⣿⣿⡿⣿⣿⡿⣿⢿⢿⣿⡿⣿⠿⢿⠿⡿⡿⠿⠿⣿⠿⢿⡿⣿⣿⢿⣿⣿⣿
⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣗⢒⣂⣲⣞⣳⣶⣖⣒⣇⣚⣲⣒⣓⣓⣗⣖⣗⢑⣒⣃⣳⣖⣒⣚⣪⢲⡎⣶⢛⣛⣚⣛⣻⣟⣒⣂⣗⣻⣒⣖⣗⣖⣚⣞⣲⣃⣳⣓⣆⣞⠖⣘⣓⣶⡒⣟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣸⣿⣿⣓⣻⣶⣿⣓⣛⣗⣺⣶⣖⣟⣺⣚⣖⣒⣲⣳⣒⣒⣗⣗⣺⣆⣳⣙⣲⣾⣿⣷⣶⣿⣷⣾⣿⣾⣿⣿⣶⣷⣶⣿⣶⣾⣶⣶⣿⣾⣶⣾⣶⣷⣾⣿⣿⣿⣿
⢗⣒⣒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣒⣒⣒⣗⣗⣗⣒⣒⣺⣻⣒⣒⣿⣒⣻⣛⣲⣗⣛⣚⣒⣒⣳⣒⣖⣚⣒⡟⣛⣟⣿⣛⣛⣛⣟⣿⣻⣛⣻⣟⣛⣛⣛⣟⣻⣛⣛⣛⣻⣛⣛⣟⣛⣻⣛⣟⣟⡛⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣤⣥⣿⣤⣿⣤⣤⣷⣤⣼⣴⣴⣧⣤⣷⣴⣤⣽⣴⣤⣧⣼⣤⣧⣷⣴⣼⣿⣦⣴⣾⣧⣤⣬⣿⣵⣼⣤⣼⣤⣥⣼⣤⣼⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡢⠬⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡬⠭⠭⠬⣿⠮⣦⣷⣿⡯⠧⢾⠭⣿⠭⢿⡽⠭⢽⡽⠥⠽⠼⢭⣯⡝⠯⡭⠻⠿⣯⡿⡿⢿⡦⡽⡧⣶⡯⢽⠟⡭⡭⡭⢭⠯⠯⠼⣽⡇⠽⡯⣯⢯⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿
⡫⠭⠭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠭⠭⠭⣿⠍⡿⡿⢿⡯⡯⢽⠭⣿⠽⠭⠭⠭⠭⢭⠭⠭⠯⢭⣿⣭⣯⣭⣽⣭⣽⣯⣿⣭⣭⣽⣭⣯⣭⣯⣽⣭⣽⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⢐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⢩⣿⢕⠅⡪⢸⣟⡏⢹⣀⣿⡁⣢⣀⢀⣐⣙⣆⣈⣄⣀⣏⣍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣕⣒⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣒⣒⣒⣿⣓⣷⣾⣾⣗⣒⣺⣒⣿⣢⣒⣒⣲⣂⣎⣖⣒⣏⣛⣛⣛⣟⣛⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠗⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⣒⣒⣒⣿⡒⡿⢿⢻⣗⣗⣺⠒⣿⡲⠚⠓⢂⢚⡓⡒⢚⡶⠚⣷⣶⣿⣿⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡁⠨⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠤⠤⢐⣿⡪⡆⢕⢸⡯⡧⢸⠤⣿⠄⠮⠴⢤⢟⡆⡧⠤⡜⠤⠦⣼⢤⡤⢬⠸⠷⡤⠿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡢⠬⠤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡬⠭⠭⠭⣿⠭⣾⣷⣿⡯⡯⣽⠭⣿⢥⠽⠯⠬⠭⠭⠯⠽⡼⠍⠿⠭⡯⠭⢽⢿⠽⢿⣯⠥⡭⠿⡯⡽⠿⠭⡽⠭⢽⢯⣤⣧⣯⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡫⠭⠭⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠭⠭⠭⣿⢍⡿⡻⢿⣯⣯⣿⠭⣿⠽⢭⠭⠭⢭⢭⠭⠭⠿⠯⣭⠯⠯⣭⠍⣿⢿⣿⢿⡿⠿⡿⡿⢿⡿⣿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢐⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣂⣒⢨⣿⣕⢅⡪⣸⣗⣗⣺⣒⣿⡃⣣⣜⣀⡉⣲⣃⣀⣶⠶⣿⣶⣶⣿⣷⣿⣾⣷⣾⣿⣾⣾⣶⣾⣾⣶⣾⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣕⣒⣒⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣒⣒⣒⣿⣓⣷⣿⣿⣗⣗⣻⣒⣿⣺⣒⣒⣚⣚⣃⣓⣒⣿⣲⣻⣛⣛⣿⣻⣟⣻⣿⣿⣿⣛⣟⣛⣿⣿⣟⣹⣻⣛⣛⣟⣛⣟⣛⡙⡛⢛⣻⣛⣛⣛⣿⣿⣛⣻⣿⣛⣿⣿⣿
⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢛⣷⡲⡖⢗⢻⣶⡿⣺⠒⣶⡺⠓⠓⢒⢓⡒⡘⢒⡶⠘⠒⡖⠓⢒⢶⡖⢻⡖⡚⠳⠚⣖⠚⠒⣲⠒⡖⢺⢒⢓⡖⠚⠛⠛⠛⣿⢛⠛⡛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠨⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠥⠥⠰⣿⡪⡂⢕⢸⡯⡯⢼⠤⣿⠤⡮⢴⠬⢽⠰⠤⡧⡇⠄⢴⠴⠼⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⠶⠀⠿⠶⠒⠦⠀⠩⠖⠖⠶⠂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⢛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠇⠶⠦⠷⠆⢠⠾⠾⠰⠀⡴⠴⡒⠰⠶⠦⠃⠰⠰⠴⠴⠶⠠⠶⠾⠘⠀⠶⠾⠀⠆⠠⠠⠶⠀⠆⠰⠆⠴⠶⠀⠖⠰⠰⠴⠾⠷⠆⢢⠀⠰⠶⠆⠆⠖⠀⠸⠴⠆⠠⠐⠀⠴⠰⠶⠄⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣤⢀⠀⢀⠀⢀⣀⢠⠀⠀⠀⣀⠀⣄⣀⡀⢀⠀⣀⢀⡀⣠⠀⣀⢀⢀⠀⢄⣀⢀⢀⠀⠀⢀⣠⣀⢀⠀⠀⠀⣀⣀⣤⠀⠀⡀⡀⠀⠀⣀⠀⣤⠀⣀⡄⢀⡀⣀⠀⢀⣄⡀⠀⡀⡠⠀⢀⣀⢀⣤⣀⠀⠀⠀⠀
⠀⠀⠁⠉⠈⠈⠀⠁⠉⠉⠈⠁⠀⠈⠉⠁⠉⠈⠈⠈⠈⠉⠉⠁⠉⠀⠉⠈⠈⠀⠈⠉⠉⠁⠁⠁⠈⠉⠉⠀⠃⠀⠁⠁⠈⠉⠀⠘⠁⠉⠈⠈⠉⠁⠉⠀⠉⠁⠉⠁⠁⠀⠈⠁⠁⠀⠉⠁⠀⠁⠈⠉⠉⠂⠀⠀⠀⠀
⠀⠀⠼⠶⠼⠾⠴⠶⠏⠀⠴⠀⠶⠶⠲⠀⠀⠶⠸⠶⠦⠆⢀⠆⠰⠠⠷⠆⠀⠸⠶⠦⠀⠀⠶⠞⠀⠔⡆⠈⡴⠆⠔⠴⡦⠦⠀⠀⠶⠾⠀⠆⠰⠆⠶⠆⠰⠂⠆⠰⠠⠦⠶⠀⠆⠀⠄⠠⠀⠦⠇⠢⠶⠾⠁⠀⠀⠀
⠀⠀⢀⣀⢀⡀⣀⢀⡀⣠⠀⠀⣀⡀⢀⠀⣀⠀⡀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠈⠁⠈⠈⠁⠉⠀⠀⠉⠁⠈⠀⠉⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⣛⣟⣹⣿⣛⣟⣻⣿⣿⣛⣿⣽⡿⠉⠛⠛⠭⠻⠛⠛⠛⠟⠛⠛⠟⠻⠛⠻⠛⠿⠛⠙⠙⠿⠛⠛⠋⠙⠿⠟⠿⡯⠻⠉⠛⠙⠿⠟⠛⠻⠍⠙⠩⠝⠭⠽⠉⠫⣉⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣍⣻⣙⣛⣟⣛⣛⣙⣻⣛⢟⣛⣛⣏⣻⡽⣙⣟⣛⣛⣛⣻⣏⣻⣻⣛⣟⣩⣟⣟⣛⣛⣿⣭⣙⣿⣽⣹
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢸⣿⣻⢻⢻⡛⠻⢛⣿⡟⣟⠛⡟⡟⣟⠛⡛⢛⡟⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢸⢿⡿⡿⡿⢿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠿⣷⡿⢿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⠿⠿⣿⡿⠿⢿⣿⡿⡿⠿⠿⢿⣿⣿⣿⠿⠿⣿⣿⢿⣿⣿⢿⣿⢿⡿⡿⠿⣿⢿⣿⠿⢿⣿⣿⠿⢿⡿⣿⢿⡿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠁⠀⠀⢸⣶⣷⣷⣿⣶⣷⢷⣾⣶⣾⣿⣿⣶⣷⣶⣾⣷⣶⣿⣾⣿⣿⣾⣶⣿⣷⣿⣶⣷⣾⣾⣿⣶⣾⣶⣾⣶⣾⣷⣾⣷⣶⣷⣾⣾⣾⣿⣿⣷⣾⣿⣿⣿⣿⣶⣿⣷⣾⣿⣾⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣶⣷⣶⣦⣷⣷⣴⣿⣶⣾⣾⣷⣴⣶⣿⣷⣼⣾⣴⣷⣼⣷⣧⣷⣴⣦⣾⣴⣷⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⣽⣯⣿⣯⣿⣭⣿⣭⣿⣬⣿⣯⣭⣯⣽⣧⣭⣽⣿⣭⣿⣯⣽⣬⣯⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⢸⣹⣙⣉⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢸⣛⢻⡟⣟⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢸⠿⠿⡿⠿⣿⠿⣿⠿⠿⡿⢿⠿⢿⢿⠿⢿⡿⣿⠻⠿⡿⢿⠿⡿⠻⠿⡿⡿⠿⠿⡿⣿⢿⠿⡿⠿⡿⢿⣿⡿⢿⢿⠿⡿⣿⢿⠿⣿⠿⡻⠿⡿⢿⣿⢿⢿⠿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⢿⡿⠿⠿⠿⣿⠟⠿⣿⠿⢿⡿⢿⡿⢿⢿⡿⢿⣿⣿⣿⠿⡿⡿⠿⢿⣿⡾⣿⡿⡿⣿⣿⣿⡿⡿⢿⣿⡿⣟⢿⡿⡿⢻⣿⠿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠃⠘⠀⠘⠀⠀⠂⠀⠀⠂⠀⢸⣛⣟⣛⣻⣟⣻⣟⣹⣿⣟⣻⣽⣿⣚⣿⣛⣟⣟⣻⣹⣟⣿⣛⣿⣟⣛⣛⣿⣏⣟⢻⣿⣿⡟⣿⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⣋⣛⣟⣛⣟⣛⣟⣟⢻⣛⣛⣿⣿⣝⣻⣻⣻⣟⣟⣹⣛⣟⣻⣟⣟⣻⣛⣟⣻⣛⣛⣋⣟⣛⣿⣛⣽⣛⣿⣻⣟⣿⣻⣛⣟⣛⣟⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣛⡻⣿⢟⡻⡟⣻⢟⡛⡛⣟⠻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⢿⠿⠿⡿⠿⣿⠿⢿⠿⡿⢿⠿⡿⡿⢿⠿⡿⡿⢿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣾⡷⣷⡷⣾⣶⣿⣶⣷⢾⡶⣿⣶⣾⣶⣷⣷⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣾⣾⣷⣷⣾⣿⣷⣾⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠒⠀⠐⠀⠀⠀⠀⠂⠀⠀⢸⣬⣿⣼⣽⣬⣽⣭⣭⣿⣿⣽⣭⣿⣭⣽⣼⣯⣬⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠯⣿⢽⠥⢿⡭⣿⣿⢯⢟⡽⢯⢽⡿⣿⡽⣿⡽⡬⠿⡽⠭⠯⢭⣿⣼⢯⣿⡯⢽⣿⣭⢯⣿⢮⢽⣽⢿⣽⢻⣿⣿⡯⣿⠽⢷⡭⣿⣽⠯⡿⡽⢿⢧⡿⣭⠯⣿⢿⣿⣿⣿⣿
⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⢲⣷⡞⢷⢻⡷⡞⡗⣿⠲⡷⢿⠛⢿⢾⠛⠷⢷⡖⡿⠷⡷⣾⣷⣶⣿⣾⣶⣷⣶⣷⣾⣷⣾⣶⣿⣶⣿⣾⣿⣿⣶⣿⣶⣷⣿⣶⣷⣿⣾⣷⣾⣷⣿⣶⣿⣶⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣟⣿⣿⣟⣿⣟⣿⣟⣾⣿⣞⣟⣿⣻⣿⣿⣟⣿⣻⣛⣿⡿⣛⣿⣿⣏⣿⣿⣙⣟⣏⣿⣛⣿⣿⣟⣿⣻⣿⣋⣿⣟⣻⣛⣿⣿⣿⣻⣙⣟⣯⣿⣿⣟⣻⣟⣻⡟⣻⣟⣻⣿⣿
⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠁⠁⠀⢸⣥⣭⣽⣯⣽⣯⣷⣯⣯⣯⣯⣭⣯⣿⣭⣿⣽⣭⣵⣯⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢸⣽⣘⣿⣏⣏⣽⣍⣏⣭⣿⣉⣯⣟⣭⣿⣩⣟⣭⣿⣩⣽⣭⣭⣹⣝⣟⣍⣿⣯⣭⣭⣯⣏⣽⣿⣏⣯⣽⣯⣽⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠤⠀⠠⠀⠀⠀⠀⠄⠀⠀⢸⣉⣿⣻⣟⣛⣿⣿⣉⣟⣟⣛⣿⣫⣿⣏⣻⢿⡿⣿⣻⣻⣟⣻⣟⣻⣛⣟⣿⣛⣛⣻⣛⣟⣻⣹⣻⣿⣟⣻⣿⣛⣏⣻⣿⣟⣻⣛⣏⣟⣿⣻⣛⣛⣿⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠄⠀⠀⠤⠠⠄⠄⠀⢸⣿⣟⣻⣻⣛⣟⣻⣿⣛⣟⣛⣻⣛⣟⣹⣟⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣟⣛⣟⣛⣛⣟⣿⣛⣿⣛⣿⣿⣋⣿⣟⣿⣛⣿⣿⣛⣟⣻⣟⣻⣻⣟⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣟⡻⣿⡟⣟⣿⣻⣟⣿⡛⣟⣛⣟⣿⣛⣿⢻⣿⡟⣿⣻⢿⣿⣛⣿⣛⢻⣻⣿⣿⣻⡟⣿⣻⣟⣻⣛⡿⣿⣛⣿⣿⢻⡟⣻⣻⣛⣿⣿⣻⡟⣿⣻⢻⣟⣻⣛⣛⣿⣿⣻⣿
⠀⠀⠀⠀⠐⠂⠀⠀⠒⠐⠂⠂⠀⢸⣯⣯⣯⣽⣭⣿⣽⣿⣽⣽⣭⣯⣭⣿⣽⣿⣿⣯⣽⣯⣿⣿⣯⣯⣭⣯⣏⣽⣽⣯⣿⣽⣭⣿⣭⣹⣽⣏⣽⣿⣽⣽⣽⣿⣭⣯⣽⣿⣭⣿⣯⣻⣭⣯⣿⣭⣽⣽⣿⣿⣯⣭⣽⣿
⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣼⡿⣾⣷⡿⣷⣿⣿⣷⣾⣶⣷⣾⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠘⠛⢻⣿⣿⣿⡿⢿⢿⠿⣷⢷⣿⣿⢿⣿⢿⢿⣿⠿⡿⡿⢿⢿⢿⣿⣿⣿⡿⡿⣿⡿⢿⠿⡿⢿⡿⢿⢿⣿⡿⡿⣿⣿⣿⢿⣿⡿⢿⢿⠿⢿⣿⡿⢿⠿⡿⢿⠿⣿⣿⠿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠠⠄⠀⠀⠤⠠⠄⠄⠀⢸⣿⠻⡛⢳⡚⣾⠒⡗⢲⠷⢿⢻⣺⢺⠖⡞⣒⣟⣒⢚⣖⣾⣾⠓⡞⢳⣻⣻⡓⣒⡚⡿⣟⡷⡚⢺⠛⠲⢗⢳⠻⡞⢺⣗⣗⢾⣾⡖⡞⢳⣲⣞⠒⡗⠺⣛⣓⡞⢲⠓⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣍⣏⣯⣭⣽⣽⣿⣹⣿⣽⣍⣿⣽⣯⣿⣯⣯⣯⣹⣍⣿⣽⣩⣯⣿⣉⣯⣽⣙⣽⣩⣯⣹⣯⣹⣍⣿⣉⣿⣿⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⢼⣿⣯⣯⣿⣽⣯⣿⢷⣽⣽⣽⣿⡭⣿⣭⣿⣿⣯⣿⢯⢽⣽⣿⣯⣿⣮⣧⣿⡯⣿⣿⣭⣯⣿⣷⣿⣭⣿⣿⣟⣽⣯⣿⡼⣿⣽⣯⣿⣯⣿⣽⣯⣿⣿⣿⣷⣿⣭⣯⣿⣿
⠀⠀⠀⠀⢀⡀⠀⠀⣀⢀⡀⡀⠀⢸⣿⣶⡺⢿⠶⡿⡿⡿⢦⠻⢷⢾⠶⢿⢿⠶⢿⢿⣾⢷⡾⢿⠾⣷⠷⠷⣿⡦⣷⡾⡷⠾⣷⣺⠶⢷⡿⡷⢿⠶⣾⡿⢷⢶⡾⢿⣶⣿⡿⣶⠿⣿⠷⡿⢷⣾⠾⣷⡿⣦⠷⣾⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣛⣿⣘⣟⣛⣿⣛⣍⣛⣞⣝⣽⣻⣻⣛⣏⣻⣛⣿⣿⣻⣛⣟⣿⢻⣿⣻⣿⣻⣛⣟⣻⣿⣿⣿⣿⣟⣿⣻⣛⣿⣷⣿⣻⣿⣿⣯⣿⣿⣟⣻⢻⣿⣙⣟⣝⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣯⣯⣯⣯⣯⣽⣯⣿⣿⣭⣭⣿⣿⣯⣽⣯⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠄⠀⠄⠤⠠⠄⠄⠀⢸⣿⢿⣯⢧⢯⡧⢿⢿⡬⢧⢯⠧⣿⠿⣽⡮⠯⡾⢧⡤⡿⣬⢥⢽⣤⡿⡥⠭⡿⠿⣵⠯⢼⢧⣽⢬⣧⠼⡧⠼⡼⣭⠧⣽⠤⣧⠧⡼⢥⠧⣤⢧⡯⢾⠾⡦⣧⣽⣤⣷⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⢾⣶⢿⡾⣾⣷⣿⣟⢷⣿⢶⡿⣷⢿⣿⣞⢷⡶⣿⢿⡿⣿⣿⢿⣶⢷⢶⣿⣾⣾⣶⢿⡿⣿⢿⢿⣶⡷⢿⢿⣿⠿⣿⣾⣷⣿⣷⡟⢾⢷⣾⠶⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⢀⡀⠀⠀⣀⢀⡀⡀⠀⢸⣟⣛⣿⣿⣛⣻⣟⣻⣙⣿⣟⣻⣿⣟⣻⣻⣿⣻⣟⣿⣻⡛⣟⢻⣛⣿⣻⣻⣛⣿⡛⣿⣛⣿⣟⣟⣛⣿⣿⣻⣿⣏⣻⣻⣟⣙⣟⣻⣛⣟⣛⣻⣟⣏⣻⣙⣟⣻⣻⣿⣿⣿⣿⣿
⠀⠀⠁⠀⠈⠀⠀⠁⠀⠈⠁⠀⠀⢸⣯⣿⡭⣽⣭⣼⣯⣭⣽⣽⣿⣽⣭⣽⣯⣽⣭⣏⣯⣿⣼⣿⣽⣯⣽⣿⣯⣽⣯⣿⣭⣭⣯⣽⣭⣯⣿⣿⣽⣯⣽⣯⣿⣯⣽⣯⣯⣿⣯⣽⣼⣿⣿⣯⣽⣿⣽⣭⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢾⠷⡷⢧⠿⣷⢷⢾⡿⢿⣿⠿⠿⣿⢿⡿⢿⠿⡿⢿⢿⠿⡿⡿⢿⠿⣿⢿⢿⣿⣿⢿⠿⠿⢿⢿⠿⠿⢿⣿⢿⣿⠿⢿⢿⠿⢿⢿⠿⠿⡿⡿⣿⠿⣿⣿⠿⣿⠿⡿⢿⣿⣿
⠀⠀⠀⠀⠐⠒⠂⠁⠀⠀⠀⠀⠀⢸⣿⡟⡖⣓⡖⡗⠳⡾⣛⢲⣞⢿⣖⡖⢚⣻⡚⡟⡒⠛⢒⣚⣲⣳⠗⢺⡒⠓⣾⣾⡛⡟⣲⡒⠳⡟⢲⢒⣲⠒⡟⣒⠛⠒⢚⡖⡖⢺⡒⠒⣶⣷⣷⣶⣶⣶⣷⣶⣾⣶⣶⣾⣿⣿
⠀⠀⡀⠀⢀⠀⠀⡀⡀⢀⡀⡀⠀⢸⣿⣿⣿⣿⣟⣻⣋⣿⣿⣙⣟⣿⣛⣿⣟⣿⣿⣻⣿⣋⣻⢛⣟⣛⣙⣟⣟⣟⣛⣿⣟⣿⣿⣿⣟⣿⣿⣛⡛⣟⣻⣿⣟⣿⣋⣟⣻⡝⡟⣻⣻⣛⣿⣻⣟⣻⣿⣛⣿⣟⣻⣿⣛⣿
⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣭⣯⣽⣭⣭⣽⣹⣯⣵⣭⣽⣭⣽⣯⣿⣭⣿⣽⣯⣭⣿⣽⣿⣯⣭⣤⣿⣼⣭⣿⣍⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠄⠀⠀⠤⠠⠄⠄⠀⢸⣯⢽⠽⡿⡯⢽⢤⡯⡯⣼⠥⣿⠯⡼⠿⣭⣼⣧⣽⣿⣿⣽⣽⣯⣯⣿⣼⣵⣿⣯⣽⣿⣽⣯⣿⣿⣯⣽⣿⣬⣿⣭⣿⣽⣬⣭⣽⣿⣥⣿⣽⣿⣽⣷⣽⣾⣿⣷⣿⣿⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣶⣷⣷⢺⡾⡶⣷⠾⡶⣾⡶⠷⣾⡿⣿⢿⡟⢿⣿⣿⢿⢿⢿⡿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⢿⡿⠿⣿⢿⣿⡿⠿⣿⠿⡿⣿⡿⣿⢿⣿⠿⣿⢿⡿⢿⠿⢿⢿⣿⣿⣿
⠀⠀⠀⠀⠒⠂⠀⠀⠐⠚⠃⠀⠀⢸⣯⣿⣛⣿⣻⣛⣛⣛⣫⣿⣛⣻⣛⣟⣿⣿⣿⣛⢻⣛⣟⣿⣟⣻⣻⣛⣿⣙⣟⣻⣟⣛⣿⣻⣿⣛⣻⣛⣻⣛⣟⣹⣟⣛⢛⣿⣛⣟⣛⣟⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⡿⠟⣿⣿⢿⣿⡿⠻⣿⣿⣿⡛⢻⡟⠟⢿⣿⢻⠻⢿⣿⣿⢛⣿⡻⠟⣿⠿⢿⣟⡟⠻⣿⢻⣿⡟⣟⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣟⣻⣿⣿⣛⣟⣿⣙⣿⣻⣿⣛⣿⣿⣟⣻⣿⣿⣟⣻⣟⣟⣻⣿⣻⣿⡛⣿⣟⣟⣻⣛⣛⣿⣿⣛⣿⣿⣟⣻⣟⣿⣟⣟⣋⣿⣟⣻⣟⣟⣫⣟⣻⣿⣿⣏⣛⣿⣿
⠀⠀⠰⠀⠀⠀⠐⠀⠀⠂⠀⠀⠰⠀⠀⢸⣯⣉⣹⣍⣿⣝⣫⣽⣍⣉⣯⣿⣉⣿⣏⣿⣉⣋⣽⣭⣏⣽⣟⣽⣉⣙⣽⣭⣿⣍⣽⣽⣏⣹⣹⣽⣯⣏⣯⣩⣏⣹⣹⣍⣉⣟⣉⣿⣯⣯⣍⣉⣏⣹⣍⣯⣍⣉⣩⣯⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣯⣽⣿⣿⣿⣿⣽⣽⣯⣽⣯⣭⣿⣿⣯⣿⣿⣽⣿⣽⣿⣭⣽⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣿⣿⣯⣿⣿⣯⣽⣼⣿⣿⣿⣴⣿⣿⣿⣯⣯⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣬⣽⣷⣬⣿⣿⣤⣽⣿⣶⣾⣦⣤⣽⣷⣧⣿⣴⣾⣿⣿⣯⣼⣿⣾⣧⣴⣯⣴⣿⣽⣼⣿⣿⣬⣧⣾⣧⣿⣿⣯⣵⣿⣿⣼⣿⣽⣦⣧⣥⣾⣷⣤⣼⣿⣿⣴⣤⣭⣿⣿
⠀⠀⢠⠀⠀⠀⠠⠀⠀⠄⠀⠀⢠⠀⠀⢸⣯⣼⣽⣿⣿⣿⣽⣿⣯⣿⣯⣿⣿⣯⣿⢿⣿⣯⣼⣿⣥⡿⡿⣿⣿⣿⣿⣥⣯⣿⣽⣿⣿⣯⣿⣿⣿⣧⣿⣿⡽⣿⣭⣿⣿⢿⣥⣧⣿⣿⣷⣿⣯⣯⣽⣼⣿⣿⣽⣯⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣾⣷⣶⣶⣿⣿⣿⣦⣾⣷⣶⣾⣷⣿⣾⣿⣷⣶⣿⣷⣿⣿⣿⣾⣧⣾⣿⣿⣿⣷⣶⣿⣶⣿⣶⣷⣿⣿⣿⣷⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣷⡿⣿⣿⣷⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡷⣾⡿⣦⣿⣿⡿⣿⣷⡾⣷⣾⣿⣾⣿⣿⣾⣿⡿⢿⣿⢿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢿⡿⢿⣾⣿⣿⣿⠷⣾⢿⣿⡶⠿⣷⡷⠻⣿⡿⡷⣿⣷⡿⠿⡷⢾⢷⣶⣾⣿⡿⢶⡿⢶⣶⡿⢿⠿⣷⡾⠷⣿⣶⣿⣾⣿⡿⠻⠾⣿⣿⠿⢾⣿⡷⣾⡷⠿⢿⣿⢿⣿
⠀⠀⠐⠀⠀⠀⠐⠀⠀⠐⠀⠀⠐⠀⠀⢸⣿⣿⣿⡟⠻⡿⣿⢿⢿⠿⣿⡿⡟⣿⣷⢿⣿⣿⣿⣿⢿⢻⣿⡿⢻⣿⠿⢿⡿⣿⡿⣿⡿⣿⣿⡿⢟⣿⣿⣿⡿⠿⣿⡿⣿⡿⢿⣿⡿⣾⡛⣿⡿⣿⣿⠿⢷⣿⡿⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣛⣿⣟⣻⣟⣿⣿⣛⣛⣿⣛⣻⣿⣿⣋⣛⣻⣿⣟⣻⣿⣿⣿⣿⣿⢿⣟⣻⣿⣏⣛⣿⣟⣻⣿⣟⣻⣿⣏⣻⣿⣟⣟⣻⣟⣹⣿⣿⣟⣻⣛⣟⣿⣿⣏⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣻⣿⣛⣿⣟⣿⣟⣻⣿⣹⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⠀⠀⠀⠠⠀⠀⠄⠀⠀⢠⠀⠀⢸⣿⠻⣿⣿⡿⠻⡻⣿⠟⡟⣿⠿⠛⠻⣿⣿⣿⢿⡿⠟⣿⢿⣿⣿⣿⠿⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⢿⠿⢿⣿⣿⠿⢿⣿⢿⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⠿⡿⠿⢿⣿⡿⣿⣿⡿⣿⣿⠿⣿⣿⣿⠿⣿⠿⡿⠿⣿⡿⣿⣿⣿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠀⠀⠀⠐⠀⠀⠐⠀⠀⠐⠀⠀⢸⡿⠻⢿⡟⣿⣿⣿⡟⣿⣿⢿⣿⣿⣷⠟⣟⠻⣿⢿⣷⠾⠿⣿⠟⡿⠿⡛⢿⣿⣿⢿⢿⣿⠿⡿⢿⣿⠛⠿⣿⣿⣾⡿⣟⢻⢿⣿⢿⣟⣛⣿⣷⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⢿⠿⣿⡿⠿⣿⣿⣿⢿⢿⡿⠿⣿⣿⠿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⣿⢿⢿⢿⣿⣿⢟⡿⢿⣿⣿⠿⡿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡿⠻⣿⡿⠿⣿⣿⣿⠻⢿⡟⣿⠻⣿⢿⣿⣿⣿⢿⡿⢻⣿⡟⠿⣿⣿⢻⢿⣿⣿⠟⣿⣿⣿⢿⣿⣿⣿⣿⣿⠻⢿⠿⣿⠿⢿⡿⣿⣿⡿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⠈⠀⠀⠉⠀⠀⠈⠀⠀⢸⣿⣹⣿⣼⣿⣿⣿⣿⣿⣛⣟⣙⣿⣿⣾⣽⣛⣿⣿⣛⣻⣿⣟⣟⣿⣏⣛⣿⣛⣿⣟⣿⣿⣿⣛⣿⣿⣻⣿⣛⣿⣟⣟⣙⣿⣿⣿⣹⣿⣿⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⣿⣻⣿⣟⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠀⠀⠀⠠⠀⠀⠤⠀⠀⠠⠀⠀⢸⣿⣿⣛⣿⣟⣟⢛⣿⣛⣟⣿⣿⣛⣟⣿⣻⣿⣿⣻⣿⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠿⠿⣿⣿⣿⡟⣻⣿⢿⣿⣿⡿⣿⠻⣿⣿⢿⣿⣿⣿⢿⡿⣿⣿⢿⠿⣻⣿⣿⣿⣿⠿⣿⣿⠟⣿⣿⡿⢿⣿⡿⢿⣿⡿⢿⣿⣿⣿⢿⢿⢿⣿⡿⣿⣿⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⡿⠿⣿⡿⢿⡿⠟⣿⡟⠿⢻⢿⠻⢿⡿⢿⣿⠟⣿⣿⣿⣿⣷⠿⢿⣿⠿⣿⡿⣿⣿⣿⣿⠿⡿⣿⣿⢻⣿⡿⣿⡞⠿⣿⣿⣻⠻⢿⣿⡿⡛⠿⣿⣿⣿⣿⡿⣿
⠀⠀⠘⠀⠀⠀⠈⠀⠀⠁⠀⠀⠘⠀⠀⢸⣟⣛⣿⣿⣿⣿⣻⣻⣻⣟⣛⣿⣿⣛⣟⣿⣟⣻⣿⣟⣛⣿⣛⣻⣹⣿⣛⣙⣿⣿⣛⣿⣟⣹⣿⣛⣻⣿⣋⣻⣿⣻⣛⣏⣿⣿⣻⣛⣛⣛⣿⣿⣟⣻⣻⣛⣿⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣻⣟⣿⣿⣛⣹⣯⣻⣿⣻⣟⣿⣿⣿⣫⣻⣟⣻⣋⣻⣿⣹⣯⣿⣿⣏⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⡀⠀⡀⠀⡀⠀⡀⣀⡀⠀⠀⠀⣟⣏⣿⣛⣿⣻⣋⣻⣿⣿⣻⣿⣿⣿⣋⣛⣿⣿⣿⣛⣿⣿⣿⣙⣿⣏⣛⣿⣿⣟⣻⣿⣿⣿⣙⣻⣟⣏⣿⣙⣻⣿⣛⣹⣿⣟⣙⣿⣹⢛⣛⣿⣿⣛⣙⣙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣯⣼⣽⣿⣿⣯⣭⣼⣯⣯⣟⣭⣿⣿⣭⣽⣿⣿⣯⣯⣿⣿⣿⣿⣿⣭⣽⣿⣽⣯⣼⣭⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣟⣽⣿⣥⣭⣿⣿⣯⣥⣽⣿⣼⣽⣧⣽⣽⣬⣽⣿⣯⣿⣯⣯⣿⣭⣽⣿⣟⣽⣽⣭⣿⣿⣿⣿⣿⣽⣿⣿⣿⣭⣽⣿⣿⣿⣯⣼⣿⣿⣯⣿⣿⣿⣭⣽⣿⣿⣿⣿
⠀⠀⠈⠀⠁⠀⠁⠀⠉⠀⠁⠉⠁⠀⠀⠀⣷⢶⣾⣷⣾⣿⣿⡿⡶⣶⣿⣿⣷⣾⣿⣶⣷⣿⣿⣷⣶⣷⣶⣾⣿⣽⣶⣾⣦⣿⣷⣿⣶⣾⣿⣿⣧⣼⣿⣶⣾⣶⣾⣿⣿⣶⣷⣾⣧⣿⣿⣿⣿⣿⣾⣶⣿⣿⣦⣿⣿⣿
⣤⢤⣤⢤⣤⣤⡤⣤⣤⠤⣤⣤⣤⣤⣤⡤⡷⡶⢿⣿⣷⠾⣷⣶⣶⣿⡿⢿⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠒⠒⠚⠛⠛⠒⠚⠚⠚⠚⠛⠛⠚⠛⠓⣿⡷⣶⢾⢿⣾⡿⣿⡾⡾⣷⣾⠿⠷⣶⣷⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⢿⣿⣿⠿⣿⢿⡿⠿⠿⡿⠿⢿⠿⣿⣿⣿⣿⡿⢿⣿⣿⡿⣿⡿⣿⣿⠿⣿⡿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠲⣿⣾⣶⣿⣷⣿⣷⢷⡿⡿⢶⢶⣿⡿⢷⡿⣿⣿⣿⢿⡶⣶⡾⠿⢾⣿⣿⠷⢶⡟⢿⣶⠾⣾⣷⠶⣾⣿⣷⣾⠖⡗⢿⣿⡿⡗⡞⠺⢾⣷⣿⣶⣿⣿⣶⡟⡟⠷⣿⣿
⠀⠀⠘⠀⠀⠀⠈⠀⠛⠐⠑⠛⠃⠂⠀⠀⣟⣿⣿⣛⢿⣋⣻⣿⣿⡟⣻⣷⣿⣟⣿⣿⣟⣿⣿⣿⣿⣟⣛⣿⣿⣹⣟⣙⣛⣿⣿⣏⣛⣟⣋⣿⣯⣿⣛⣻⣟⣋⣛⣿⣻⣿⣿⣏⣟⣛⣿⣛⣻⣋⣻⣿⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣩⣽⣟⣯⣽⣿⣯⣻⣏⣽⣿⣿⣿⣽⣿⣻⣿⣿⣹⣹⣿⣉⣉⣛⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⡿⠿⢿⠿⡿⢿⣿⠿⢻⢿⡿⢿⠿⣿⠿⣿⡟⢿⠿⢿⠿⣿⡿⢿⢻⣿⢿⡿⣿⡿⡿⢿⣿⠿⡿⠿⣿⠿⢿⡿⡿⠿⡿⢿⡿⣿⡿⢿⣯⠿⡿⢿⠿⡏⢿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣅⣦⣓⣇⣿⣸⣂⣇⣟⣿⣘⣠⣇⣟⣺⣏⣿⣑⣻⣇⣟⣻⣸⣛⣿⣜⣸⣻⣧⣿⣼⣸⣟⣟⣻⣯⣓⣟⣟⣿⣸⣟⣱⣸⣇⣇⣟⣼⣺⣷⣹⣟⣇⣟⣻⣛⣇⣇⣻⣽⣿⣿⣿⣿⣿
⣟⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⣿⢻⢻⣛⣛⡟⢿⣟⣻⣿⢻⠸⣟⡟⡿⢻⣿⡟⠿⣿⣾⢻⢻⢻⣛⣿⣟⡿⣷⣿⢻⡻⡟⡇⢿⢿⢻⡿⣟⡏⡎⣾⡟⣻⣟⠿⡟⣻⣟⣻⢻⢿⡟⣿⣿⣿⢻⢹⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣼⣮⣾⣭⣭⣧⣭⣭⣭⣿⣮⣼⣭⣷⣽⣯⣾⣧⣥⣿⣭⣼⣼⣼⣭⣿⣯⣽⣭⣿⣮⣷⣵⣧⣬⣮⣿⣷⣭⣧⣥⣿⣧⣯⣵⣥⣧⣭⣭⣭⣮⣿⣯⣽⣿⣽⣼⣼⣭⣿⣿⣿⣿
⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⣮⣮⣲⣱⣇⣺⣰⣿⣗⣺⣒⣇⣼⣜⣿⣂⣿⣻⣸⣆⣇⣸⣯⣮⣸⣿⣶⣵⣝⣕⣥⣽⣗⣺⣲⣾⣧⣪⣾⣰⣩⣬⣣⣇⣗⣺⣰⣳⣸⣾⣔⣾⣼⣿⣱⣷⣩⣆⣿⣰⣫⣞⣿⣿⣿
⠸⠹⠽⠿⠉⠹⠻⢁⡐⠠⠀⠂⠰⠐⠐⠄⢸⣿⣜⣫⣽⣏⣩⣻⣻⣈⣻⣿⣿⣿⣿⣻⣋⣙⣿⣿⣿⣿⣿⣻⣭⣅⣨⣿⣟⣝⣝⣟⣉⣉⣋⣽⣙⣈⣍⣿⣟⣿⣿⣿⣿⣻⣏⣝⣿⣻⣿⣿⣟⣸⣉⣿⣿⣽⣻⣿⣿⣿
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⡿⡿⡿⡿⢿⢿⢿⣿⡿⢿⡿⣿⠿⣿⢿⣿⠿⣿⣿⡿⡿⡿⣿⢿⣿⡿⢿⠻⣿⡿⣿⠿⡟⡿⡿⢿⣿⡿⡿⠿⢿⡿⠿⢿⡿⣿⠿⣿⠿⣿⠿⡟⡿⢿⡿⢿⢻⠻⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣥⣽⣜⣜⣛⣛⣋⣂⣓⣟⣿⣜⣛⣜⣼⣛⣗⣻⣿⣑⣸⣟⣛⣛⣛⣣⣳⣿⣜⣻⣸⣿⣜⣧⣛⣇⣞⣟⣻⣿⣜⣜⣛⣻⣿⣺⣛⣕⣸⣸⣸⣸⣻⣛⣿⣟⣽⣿⣻⣸⣸⣚⣿⣿
⡇⠀⡶⢲⣲⠒⣖⢲⢒⢲⠂⠀⠄⡄⠄⠄⠄⠀⠄⠀⠀⢸⣿⢹⢟⣿⣛⣿⣿⡟⢿⢛⣿⡿⣿⣟⣿⠻⣿⣻⣿⡟⢻⡟⠫⡿⣿⡟⣻⣿⢹⡟⠛⢿⡟⡿⣻⣿⡿⡟⣿⣿⡟⢿⣿⡏⢻⠟⢿⡿⣛⢿⣟⣿⣿⣿⣿⣿
⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⠗⠽⠸⠇⢯⠻⠹⢘⢌⡟⠂⣀⠱⠱⠐⠁⠂⠃⠇⠈⠄⠑⠄⠀⣿⣿⣸⣼⣞⡧⣿⣿⣣⣝⣞⣃⣟⣽⣟⣇⣟⣏⣿⣯⣏⣞⣇⣧⣻⣿⣞⣇⣟⣿⣜⣕⣇⣟⢞⣞⣫⣋⣓⣸⣣⣿⣜⣧⣫⣻⣸⣻⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⡿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⣟⣘⣁⣈⣨⣈⡇⣄⡀⠎⠄⠃⠃⠁⠇⠰⠈⠂⠀⢸⣿⣼⣦⣽⣼⣷⣽⣧⣯⣼⣥⣮⣿⣿⣤⣷⣿⣷⣽⣧⣿⣯⣧⣿⣼⣧⣷⣾⣼⣧⣦⣷⣴⣼⣮⣿⣦⣽⣦⣧⣼⣷⣷⣼⣧⣯⣥⣧⣶⣼⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⡶⡶⣶⣶⢶⣶⣶⣶⣲⡶⣾⣿⢿⣿⢿⣿⡿⣿⣿⣿⣿⣿⡟⣿⡿⡿⣟⡿⡿⣿⡿⡿⠛⣻⢿⢿⣿⣿⡿⣿⢿⣿⣿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣼⣧⣿⣦⣿⣼⣧⣿⣼⣿⣿⣾⣿⣦⣿⣧⣿⣿⣧⣿⣽⣿⣿⣽⣿⣼⣮⣼⣿⣿⣼⣧⣿⣼⣽⣧⣾⣼⣧⣿⣽⣿⣮⣿⣦⣷⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣆⣴⣶⣶⣶⣶⣶⣶⡶⢶⢶⠶⠒⠒⢲⣶⣾⢿⢟⠿⡏⢟⠿⢻⠿⣿⢉⢿⢻⣿⠛⠛⡿⠻⣿⢿⡿⠙⠛⠛⢿⠛⡯⣿⣿⢿⡟⠋⣿⢟⢿⣻⢿⡿⡋⢹⡿⣯⡏⣹⢿⢿⡿⣿⠟⠛⣿⣟⢿⡿⣟⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣒⣒⣒⣒⣒⣒⣒⣒⡲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⡇⠀⠀⠀⡏⠉⠛⠋⣿⡇⣿⢉⠛⠛⠋⠛⠛⢻⡇⣿⠋⠙⠋⠉⣿⣿⡟⠍⠛⠛⠙⡛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣶⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣴⣤⣤⣿⣥⣾⣿⣤⣤⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⣤⣅⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣤⢤⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⢠⠀⠀⠠⠀⠀⠠⠄⢠⣤⣤⠀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣤⡄⡤⠀⠀⠄⠠⠀⠄⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠤⠤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⡁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⡯⡭⠭⠭⡭⠭⠭⠭⠭⠭⠭⠭⢭⠭⠭⠭⠭⠭⠭⠭⠭
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣹⣩⣭⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣩⣭⣍⣿⣿⣩⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣏⣯⣭⣍⣭⣽⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣟⣒⣒⣒⣒⣒⣚⣒⣒⣒⣒⣒⣓⣒⣒⣒⣒⣒⣒⣒⣻⣿⣤⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣗⣗⣒⣒⣓⣚⣒⣗⣒⣒⣒⣒⣺⣒⣒⣒⣓⣒⣒⣒⣚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣷⣾⣶⣶⣾⣶⣾⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⣶⣷⣷⣶⣷⣷⣾⣶⣶⣶⣶⣶⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠟⠿⠟⠿⠻⠿⢿⡿⠿⠿⢿⡟⠿⠿⠿⠿⢿⠻⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣷⣷⣤⣾⣾⣮⣵⣷⣶⣮⣥⣶⣶⣷⣷⣶⣶⣶
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⢸⠛⠻⠿⠿⣿⣿⡏⠀⠀⠈⡟⡛⠿⠿⠿⣿⣿⢸⣿⠀⠀⠀⡟⢻⠿⠿⢿⣿⣿⠃⠀⠀⢹⠛⡿⠿⠿⡟⠻⢿⣿⣿⣿⡇⠀⠈⣿⢛⠻⠿⠿⢿⣿⣿⣿⡇⠀⠀⢹⢻⠻⠿⠻⡿⣿⣿⡇⠀⠀⢸⠛⢿⢿⠻⢿
⣀⣀⣸⣾⣶⣶⣶⣿⣿⣧⣀⣀⣠⣷⣶⣴⣶⣶⣿⣿⣸⣿⣀⣀⣀⣷⣶⣾⣶⣾⣿⣿⣄⣀⣀⣼⣶⣶⣶⣶⣷⣶⣾⣿⣿⣿⣇⣀⣐⣽⣶⣶⣶⣶⣾⣿⣿⣿⣇⣀⣀⣼⣶⣶⣶⣶⣾⣿⣿⣇⣀⣀⣼⣶⣶⣶⣶⣾
⠉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⠠⠿⢿⢻⣿⡿⠿⢿⢻⢻⠻⠿⣿⢿⢻⠿⢿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠿⢿⢻⡿⠶⢶⣼⢚⢶⢺⣶⢻⡾⠶⣶⢺⠓⣶⡒⠛⣿⡛⡛⡿⡛⠛⣿⡛⠟⡛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⣷⣷⣶⣴⣿⣶⣶⣿⣶⣶⣿⣶⣾⣷⣶⣶⣿⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⡟⢻⣿⡿⢻⠿⢿⣿⣿⢻⢻⣿⠻⡿⠿⠿⢿⢻⣿⡛⠛⡛⡛⡟⣿⣿⡛⠛⡿⡟⡛⡿⡟⠟⢿⡟⠛⣛⣻⣿⡿⠟⢻⡿⠿⠿⠿⠿⣿⡿⢿⣿⢿⢿⢿⢻⠿⢿⠿⢿⣿⠻⠿⡿⡿⣿⠻⠿⡿⡿⣿⠻⢿⡿⡿⣿⣿
⢰⣵⣿⣿⣶⣶⣾⣼⣼⣿⣶⣶⣷⣷⣾⣤⣶⣶⣶⣿⣶⣶⣶⣶⣥⣿⣯⣶⣶⣷⣷⣷⣷⣷⣶⣿⣷⣶⣾⣯⣿⣿⣶⣾⣶⣶⣶⣶⣶⣮⣽⣾⣶⣾⣿⣶⣾⣶⣶⣾⣿⣿⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣖⣶⣶⣶⣶⣶⣶⡖⣶⣶⣒⣶⠶⠲⣶⣶⢲⣶⣾⣟⡿⠟⢻⣿⣿⣿⣿⠿⠿⣿⡿⠟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡿⢿⣿⣿⣻⣿⢿⣿⠛⢿⣟⡟⠿⣿⣟⣿⣿⣿⣿⣻⠻⣿⣻⣿⣿⣿⠿⡛⣿⣿⣿⣿⡟⠟⢿⣿⣿⣿⣿⠟⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢸⣝⣛⣻⣹⣿⣟⢿⣝⣿⣳⣏⣻⣿⡛⣛⣛⣿⣿⣭⣻⣏⣛⣛⢋⣻⣻⡋⣻⠹⠿⠛⠯⠽⠛⠏⠿⠹⠻⠿⠻⠛⠟⠫⠹⠭⠩⠉⠝⠹⠍⠝⠙⠿⠟⠋⢻⣿⣿⣿
⠀⠀⠈⠀⠁⠉⠀⠈⠀⠀⠁⠁⠈⠀⠀⠀⠀⠀⢸⣍⣉⣙⣋⣉⣏⣉⣫⣏⣻⣹⣿⣿⣟⣽⣉⣉⣿⣏⣉⣉⣍⣯⣝⣿⣙⣉⣽⣯⣝⣉⣉⣽⣍⣉⣻⣿⣝⣍⣯⡉⣩⣿⣝⣙⣍⣩⣻⣿⣙⣩⣫⣹⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣷⣶⣵⣿⣿⣭⣼⣭⣭⣭⣽⣿⣭⣭⣿⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣭⣽⣿⣿⣿⣭⣽⣴⣿⣿⣿⣽⣬⣯⣽⣿⣷⣿⣯⣿⣿⣽⣯⣩⣽⣡⣽⣽⣭⣽⣹⣸⣹⣿⣽⣥⣬⣩⣭⣿⣽⣻⣭⣽⣯⣿⣭⣭⣿⣿⣫⣽⣿⣿⣽⣻⣿⣿⣴⣿⣿⣷⣤⣿⣿⣯⣿⣏⣹⣩⣉⣽⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣮⣵⣿⣷⣽⣯⣥⣽⣯⣥⣧⣬⣯⣯⣽⣾⣷⣷⣬⣵⣷⣿⣽⣿⣯⣿⣥⣇⣧⣽⣿⣿⣾⣿⣥⣯
⠀⠆⠀⠀⠶⠖⠀⠀⠀⠀⠂⠐⠀⠀⠀⠂⠀⠂⢸⣿⣽⣽⣽⣽⣉⣿⣯⣿⣏⣯⣿⣿⣏⣉⣻⣿⣿⣿⣿⣿⣿⣏⣉⣯⣽⣿⣙⣍⣿⣍⣉⣯⣭⣙⣽⣍⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠃⠁⠀⠀⠀⠀⠀⠀⣸⣯⣤⣤⣧⣤⣧⣤⣧⣥⣥⣧⣤⣧⣾⣤⣤⣿⣤⣮⣧⣤⣧⣧⣧⣴⣧⣤⣼⣧⣾⣴⣼⣧⣤⣯⣧⣤⣿⣥⣼⣼⣧⣤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠂⠄⠀⠦⠴⠀⠠⠀⠀⠖⠠⠀⠀⠄⠄⠄⠀⢸⣿⣛⣻⣟⣿⣟⣟⢻⣿⣿⣿⣻⣿⣿⢛⣹⣿⣿⣿⣿⣟⣋⡟⣻⣟⣻⣻⣿⣛⣟⣻⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⣀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⠀⡀⢸⡿⢿⣿⠿⢿⣿⠿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣶⣿⣾⣿⣷⣶⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⣯⣭⣽⣿⣿⣯⣭⣿⣽⣯⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣟⣿⣿⣿⣝⣻⣿⣟⣛⣿⣿⣹⣻⣿⣿⣟⣝⣿⣻⣏⣿⣻⣿⣿⡏⣻⣿⢛⣿⣿⣿⣿⣿⣻⣿⣿⣟⣹⣿⣿⣏⣏⣙⣿⣿⣿⡻⡋⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣯⣭⣿⣭⣿⣿⣿⣿⣿⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠐⠀⠰⠂⠆⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⢹⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠟⣟⣿⣿⣿⢿⡿⣿⣿⣿⣿⠟⣿⣿⢿⡿⢿⢿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣧⣾⣿⣿⣾⣿⣧⣦⣼⣿⣿⣶⣾⣿⣿⣾⣿⣶⣾⣿⣷⣶⣾⣿⣿⣾⣦⣾⣿⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠄⠆⠀⠠⠆⠀⠤⠀⠢⠂⠀⠀⠀⢸⣿⣝⣫⣹⣏⣿⣛⣿⡿⣯⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡠⠠⣠⠀⢀⣄⠀⠀⠀⠀⠀⢸⣿⣿⠿⡟⠿⣿⢿⣿⣿⡿⣿⣿⢻⢿⡿⢿⡿⣿⢿⣿⡿⠿⣿⡿⢿⠿⣿⣿⣿⢿⢿⡿⢿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠃⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⣿⣾⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠄⠂⠀⠢⠆⠀⠤⠀⠢⠂⠀⠀⠀⢸⣿⣿⣻⣿⣏⣏⣛⣯⣟⣛⣻⣿⣝⣿⣟⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⣿⡟⣿⡿⣿⢿⢿⣻⡟⠿⡟⣿⣿⣻⣿⣿⢿⣿⣿⣻⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⡟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣿⣯⣬⣽⣭⣽⣿⣿⣯⣭⣿⣿⣿⣯⣩⣿⣿⣯⣽⣯⣯⣯⣽⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣾⣤⣾⣤⣽⣿⣿⣦⣼⣽⣧⣿⣧⣿⣤⣭⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠼⢮⣭⣾⣿⣿⣭⣼⣮⣿⣾⣮⣿⣭⣿⣯⣽⣾⣿⣯⣯⣽⣽⣿⣯⣽⣽⣿⣾⣷⣿⣯⣿⣿⣿⣿⣿⣭⣿⣷⣭⣽⣿⣭⣯⣿⣿⣿⣿⣷⣿⣿⣿⣭⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠆⠀⠢⠆⠀⠤⠀⠠⠂⠀⠀⠀⢸⣿⣿⣿⣉⣛⣯⣭⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⢀⣄⠀⠀⠀⠀⠀⢹⣿⡿⢿⣿⣿⣿⣿⡿⢛⣿⠿⠿⣿⣿⠻⠿⢿⣿⣿⡿⠿⡿⣿⣿⢿⣿⣿⣿⠻⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠁⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣾⣷⣷⣿⣿⣷⣶⣷⣷⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣆⣂⣀⣶⣖⣀⣀⣆⣀⣂⣐⣀⣀⣀⣂⣀⣀⣸⣿⣝⣻⣭⣟⣿⣿⣿⣿⣿⣟⣿⣟⣿⣟⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣏⣭⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⠀⠀⢠⠀⠄⡀⣤⠀⠠⠀⠀⢀⣤⠀⠀⠀⠀⣿⣿⠿⢿⡿⠻⣿⣿⣿⣿⣿⢿⣿⢿⢿⣿⢿⣿⡿⣿⣿⡿⢿⣿⣿⠻⣿⣿⣿⠿⣿⡿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⣿⣿⣶⣾⣷⣾⣶⣷⣾⣾⣶⣧⣾⣿⣯⣿⣶⣶⣷⣶⣷⣿⣷⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⠀⠂⠄⠶⠀⠐⠀⠀⠠⠶⠔⠀⠀⠀⣿⣽⣛⣛⣽⣿⣏⣿⣝⣛⣻⣙⣻⣿⣿⣹⣭⣿⣿⣙⣋⣿⣯⣯⣻⣹⣿⣿⣏⣛⣙⣙⣿⣟⣻⣙⣻⣯⣿⣻⣽⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⣀⡀⠀⠀⠀⠀⠈⣿⡛⠿⣿⣿⣿⢿⢻⣻⣿⠿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣁⣀⣘⣀⣁⣀⣙⣀⣈⣐⣐⣀⣛⣂⣀⣀⣀⣿⣼⣭⣭⣧⣼⣼⣿⣷⣼⣧⣿⣷⣶⣷⣽⣤⣤⣿⣾⣦⣧⣧⣭⣵⣿⣤⣽⣿⣮⣧⣿⣿⣼⣧⣤⣼⣿⣤⣼⣼⣾⣤⣤⣼⣧⣼⣿⣿⣦⣬⣿⣦⣿⣤⣿⣧⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠀⠤⠄⠄⠤⠄⠀⠀⠀⠀⠀⣿⣿⣿⣻⣻⣻⣛⣻⣿⣻⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣀⡀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⠿⣿⢻⢿⡿⢿⣿⢿⡿⠿⡿⢿⣿⠿⢿⣿⠿⠿⣿⡿⠿⣿⡟⠿⣿⠻⠿⣿⣿⠿⣿⠿⠿⢿⠿⢿⡿⢿⣿⣿⣻⠿⣿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⣿⢾⣾⣷⡶⣶⣾⣾⡾⣿⣿⣾⣿⣷⣶⣷⣾⣿⣶⡶⣿⣶⣷⣿⣷⣾⣿⣶⣾⣷⣶⣾⣾⣿⣿⣿⣶⣷⡾⣶⣿⣶⣶⣾⣿⣿⣿⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣼⢦⢿⠧⠷⠾⣿⢯⡷⡾⢽⣷⣷⠯⢴⠿⣾⣾⠦⢽⢿⣿⢷⣦⡿⢿⡦⡷⢾⣶⡶⣷⣤⣿⣿⣾⣷⣤⣼⣷⣶⣿⣿⣶⣿⣾⣷⣾⣿⣿⣿⣿⣷⣿⣷⣿⣴⣿⣿
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠈⠀⠀⣿⣿⡿⢶⣶⣷⣾⣿⣾⣿⣾⣶⡿⣿⣶⠾⣷⡿⣿⡶⣟⣿⣿⣶⡿⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⡿⣿⠛⡿⣿⡿⢿⢿⣿⢿⢻⡟⠿⣻⣿⠿⠿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⠿⣿⠿⡿⡿⠿⣿⢿⣟⣿⣿⣿⠿⡿⡿⠻⢿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⢿⣿⡷⢿⢿⠿⣿⠿⡿⡿⠾⠿⢿⠿⡿⠿⡿⡿⢿⠷⢾⢿⢿⡷⢿⣿⢿⢿⢾⡾⡿⢿⢿⠿⡿⢿⣾⠿⠾⠿⡾⣿⣿⢾⣾⡾⠿⡿⢿⢿⣷⣿⡿⠿⣿⣿⣿⣿
⠀⠀⠂⠐⠀⠀⠀⠀⠀⠒⠀⠀⠂⠂⠀⠂⠀⠀⣿⣾⣿⣷⣿⣿⡷⣷⣷⢶⣾⣿⢶⣶⣾⣗⡿⡖⣿⣷⣺⡿⣿⣿⣿⢶⢲⣿⣿⣿⣾⣷⢷⣶⢿⣷⣗⢾⢿⣶⣶⣾⢿⡿⡟⣿⣿⣷⣶⣷⡿⣷⣿⣿⣿⣷⢾⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣒⡶⡖⣿⠿⢟⣿⠿⠻⠿⠿⢿⡛⣿⢿⡟⠿⡿⠟⢿⢿⣿⡿⣟⣿⢿⣿⣿⣿⡿⡿⢿⣿⣛⡿⢿⣿⢿⣿⣟⡟⠿⣿⠿⡿⡻⡿⣿⢿⡟⣿⣿⣿⠿⡿⡟⠻⢿⣿⣿⣿⡿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡿⣿⣿⣿⣿⡿⢿⣿⡿⡿⢿⡿⣿⣾⡿⡿⣿⣿⢿⠿⣿⠿⣿⡿⣿⣿⡿⡿⣿⡿⢿⢿⣿⡿⢾⢿⣿⣿⡿⠿⣿⡿⣿⣿⣿⣿⡿⠿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣿
⠀⠒⠀⠐⠀⠂⠀⠒⠀⠊⠈⠀⠀⠒⠀⠀⠀⠀⣿⡿⣶⢿⡟⠿⣷⣷⡶⠺⣶⣿⣿⣷⠿⢷⣶⣷⠿⣿⣾⣶⢿⣾⣷⣶⣾⣿⣿⣿⣿⣷⣶⣾⣿⣷⣾⣶⣾⣿⣷⣶⣿⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠉⠁⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠀⠐⠀⠂⠀⠒⠀⠊⠈⠀⠀⠒⠀⠀⠀⠀⣿⣽⣭⣿⣿⣼⣿⣥⣽⣿⣽⣿⣽⣥⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡛⢿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⣟⣟⠻⣿⣟⢛⣿⣿⡿⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠉⠉⠉⠉⣉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣿⣾⣿⣷⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣶⣿⣶⣶⣾⣶⣾⣿⣶⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⠀⠂⠉⠘⠁⠓⠘⠒⠀⠘⠙⠀⠉⠂⠚⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠒⠐⠂⠂⠒⠈⠃⠒⠒⠀⠒⠀⠐⠀⠂⠀⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠉⠿⢟⡋⠻⠿⠛⠟⠏⠋⠿⠿⢻⢟⠭⠙⠻⢿⠋⢿⠝⠏⡿⠛⠻⠿⠿⠻⠿⠟⠛⠛⠟⠿⠟⠿⣟⠿⠟⠟⠿⠿⠛⠹⠻⠋⠙⠛⠿⠻⠛⠋⢿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣉⣙⣋⣙⣛⣉⣈⣉⣉⣛⣋⣙⣻⣋⣉⣛⣛⣛⣙⣉⣉⣈⣟⣉⣒⣉⣙⣃⣙⣋⣉⣉⣘⣙⣛⣙⣛⣛⣛⣛⣋⣉⣛⣉⣛⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢨⡽⠟⢫⠏⠭⠏⠯⡋⡋⣿⢙⢹⡟⢹⢝⣙⢻⡏⠻⠟⡯⣋⡛⡟⢻⡏⢛⢹⡏⢩⠟⠯⡋⠿⠙⠻⢝⢩⢝⠽⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⡀⢀⢀⢀⠀⣀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⢿⣿⢿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠀⠉⠀⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣷⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⣀⣀⢀⢀⠀⠀⠀⠀⢸⡿⠿⠿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡿⢻⡟⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠈⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣾⣿⣶⣷⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠐⠀⠀⠀⠀⢸⣿⣽⣿⣯⣿⣿⣷⣯⣯⣿⣼⣿⣵⣬⣯⣷⣭⣽⣿⣿⣽⣭⣿⣿⣿⣿⣽⣭⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡀⠀⡀⢀⣀⠀⡀⠀⠀⠀⢸⣿⢿⠿⡟⢿⣿⣿⡿⠿⠿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠂⠀⠋⠘⠘⠀⠂⠀⠀⠀⢸⣿⣶⣶⣾⣴⣷⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢩⡫⣍⣋⣍⣉⣸⣿⣿⣉⣙⣏⣯⣻⣟⣏⡻⣏⣭⣝⣑⣙⣯⣽⣫⣈⣛⣯⣽⣯⣻⣿⣽⣉⣿⣟⣻⣿⣩⣉⣉⣯⣯⡋⣯⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠄⠀⠤⠠⠤⠀⠄⠀⠀⠀⢸⡿⡛⣛⠛⣟⡋⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⢀⢀⠀⠀⣀⡀⠀⠀⠀⠀⢸⡿⣿⠿⠿⣿⡿⠿⣿⠿⢿⠿⠿⡿⡿⠿⡿⡿⠿⠿⠿⡿⢿⡿⠿⠿⢿⢿⠿⠿⡿⢿⢿⠿⠿⢿⠿⣿⠿⠿⡿⢿⠿⢿⢿⡿⠿⠿⡿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣁⢉⣀⣀⢈⣈⣁⣁⣀⣀⣀⣸⣿⣿⡦⣾⣷⣾⢾⣶⣷⣾⣶⣶⣾⣾⣷⣿⣶⣶⣶⣶⣾⣶⣿⣶⣶⣿⣶⣶⣶⣮⣾⣿⣶⣶⣷⣶⣾⣶⣾⣽⣶⣷⣿⣿⣶⡶⣶⣶⣿⣿⣶⣿⣿⣿⣿⣿⠿⣿⡿⣿⣿⣿
⣿⣿⣯⣷⣥⣤⣤⣁⣤⣤⣴⣴⣤⣧⣤⣧⣦⣴⣮⣤⣾⣨⣤⣤⣧⣭⣤⣴⣯⣼⣷⣁⣧⣭⣬⣤⣬⣤⣼⣭⣥⣤⣤⣤⣶⣧⣥⣤⣤⣤⣶⣿⣧⣶⣦⣴⣤⣤⣤⣦⠤⣴⣿⣯⣤⣤⡦⢷⣥⠤⣾⣤⣼⣦⣤⣬⣤⣼
⡿⣿⣿⣿⣿⣿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣷⣾⣿⣿⣶⣿⣯⣷⣶⣷⣷⣶⣾
⠿⠵⠼⠮⠭⠷⠴⠼⠵⠾⠽⠯⠿⠿⠽⢯⣷⣾⣶⣾⣯⣮⣭⣿⣿⣿⣶⣶⣷⣿⣿⣽⣿⣿⣴⣿⣯⣭⣴⣮⣽⣶⣶⣶⣿⣿⣬⣯⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠒⠂⠀⠀⠀⢸⣿⣯⣯⣯⣯⣩⣭⣿⣭⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⢠⠀⡀⠀⠠⠀⠀⠀⠀⢸⣟⣿⣛⣻⣿⣟⣻⣿⣿⣿⣟⣻⢿⡟⣿⡏⠛⣟⣿⣿⣿⡟⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠈⠀⠀⠀⠀⢸⣷⣷⣿⣷⣽⣶⣾⣿⣿⣿⣿⣾⣾⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⠀⠠⠠⠀⠀⠀⠀⠀⠀⢸⣏⣿⡛⢻⢻⣹⡿⡿⡟⡟⡿⣛⡟⡛⢻⢻⢙⡛⢻⡛⡛⠛⠙⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⢀⢀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣶⣿⣾⣶⣷⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠰⠀⠄⠀⠠⠂⠀⠀⠀⢸⣏⣿⣻⣿⣿⣹⣿⣿⣟⣿⣿⣻⣟⣿⣻⣿⣛⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⢸⣷⣿⣾⣿⣷⣷⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⠖⠤⠰⠀⠀⠀⠀⠀⠀⢸⣏⣯⣉⣉⣩⣟⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⡀⠀⠀⠀⠀⢸⣿⠿⣿⣿⡿⠻⢿⣿⡿⣿⡿⠻⡿⣿⣿⠿⢿⡿⠿⠿⠿⢿⢿⠿⡿⡿⣿⠿⡿⠿⢿⠟⠿⢿⣿⢿⠿⢿⢿⡿⣿⠿⠿⢿⣿⣿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠀⠀⠀⢸⣷⣶⣿⣷⣿⣶⣾⣿⣿⣾⣿⣶⣷⣾⣷⣶⣿⣿⣷⣴⣴⣾⣿⣶⣾⣷⣾⣿⣿⣷⣶⣶⣦⣿⣿⣿⣶⣶⣶⣿⣷⣶⣶⣾⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠰⠀⠄⠀⠰⠀⠀⠀⠀⢸⣏⣉⣹⣿⣿⣿⣟⣹⣹⣩⣉⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡿⢿⠿⢿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⢸⣿⣾⣶⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠰⠀⠄⠀⠰⠀⠀⠀⠀⢸⣯⣍⣿⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠢⠠⠀⠠⠠⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣙⣻⢛⣻⣛⣛⣻⣛⣛⣛⣻⣿⣿⣿⣋⣿⣻⣿⣿⣿⣛⣛⣛⣟⣙⣛⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣖⣶⣶⡖⠶⠶⣶⣶⣶⡶⢶⣶⣶⣶⣶⡶⣿⡿⣿⢻⡿⠿⣿⣿⣿⣿⢿⣿⡛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠟⠛⠛⠓⠚⠚⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣾⣿⣶⣾⣿⡿⣿⣿⣾⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⢀⣷⣷⣶⣿⣾⣦⣤⣥⣯⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠠⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⣿⣿⣹⣻⣙⣿⣿⣟⣛⣿⣿⣙⣻⣿⣻⣉⣏⣛⣻⣟⣟⣻⢛⣛⣫⣛⣻⣛⣻⣛⣻⣙⣿⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠈⠀⠀⠁⠈⠀⠀⠈⠀⠀⠀⠀⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⠂⠀⠆⠠⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⢉⣉⣿⣻⣉⣏⣉⣹⣍⣍⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⢿⣿⠿⡿⣿⣿⡟⠿⠿⢿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣷⣾⣶⣿⣷⣷⣶⣶⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠐⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⣯⣍⣻⣹⣩⣨⣝⣭⣯⣅⣏⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡖⠲⠒⠲⠒⠒⠂⠀⠀⢸⣟⣻⢟⠏⠛⠛⡿⢿⠛⠉⠟⢟⣿⣛⠙⢻⡿⣿⢛⠻⡿⡿⡻⡛⡿⢻⠛⢛⠟⡙⠻⠿⡛⠛⠛⢹⠛⠛⠛⡿⠙⠛⢙⠻⡟⠛⢻⡿⡟⠟⢻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⡄⠤⢤⣤⣤⣤⠠⣤⣤⣤⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠚⠒⠒⠓⠛⠚⠛⠒⠒⠓⠓⢻⡾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠃⠁⠃⠈⠋⠘⠀⠂⢸⣧⣔⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡖⠒⠒⠲⠒⠒⠂⠀⠀⢸⣟⣿⢛⠏⠛⡛⣿⢿⣛⠉⠟⣟⣿⡿⡟⣹⡿⢻⢻⠟⣻⡿⣿⣿⡟⣿⡏⡽⡛⡏⢛⡛⡛⢻⡻⡿⣿⡟⠻⠛⣛⠋⡏⡛⣿⠟⣿⢛⠟⡟⢛⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⡟⠿⠿⣿⣿⢿⠛⣿⡿⣿⢿⡿⢻⠛⡿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⢿⢻⣿⠟⣿⣟⡿⠿⢿⢿⢿⢿⣿⢿⠿⢻⠛⢿⣿⣿⣿⣿⢿⡻⠟⡿⡟⡟⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣛⡻⠲⡖⢛⢻⠿⢻⢒⣲⡛⠿⠶⢺⣞⣒⣳⣻⣺⢺⠿⢺⠳⢳⣳⣺⢳⠿⡞⢿⠻⣺⠛⢟⡻⡳⡛⡖⢿⢺⡺⣲⣳⣒⢖⠞⠻⢟⡗⠛⠺⠚⠓⡿⠶⡗⠒⠲⠚⢿⣿⣿⣿⣿
⠀⠀⠀⡖⠲⠒⢲⠒⠒⠂⠀⠀⢸⡏⠛⠛⠋⠛⡟⠛⡟⠛⡿⡟⠛⡿⣻⣛⢿⣿⣻⣿⣽⡛⠛⣫⡛⠛⠛⠛⠿⣟⢟⢟⣿⣏⡏⡟⠉⡻⠛⠛⠛⠛⠛⡟⠛⣻⠛⠛⡏⠋⠉⠛⢳⣾⢻⣟⠛⠛⢻⣟⠛⠚⡟⠛⠛⣿
⠀⠀⠀⠉⠉⠉⠈⠁⠉⠁⠀⠀⢸⣟⢻⢳⠟⡿⢛⠿⡷⠿⣹⡟⠛⢻⢿⡿⣿⡿⠟⣿⡿⠙⢛⡿⡻⣿⡻⣛⡏⣛⠹⢹⢻⢿⢿⢿⣟⣛⡷⠑⢿⢿⣿⢿⣿⣿⢟⢛⢻⣛⡿⣿⣏⣿⣾⢛⣛⣻⢻⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣟⣭⣉⣋⣏⣟⣍⣫⣽⣭⣯⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⡶⣶⣶⣶⢶⣶⢶⣶⢶⢶⢶⢶⠀⢀⡀⡀⢀⢀⠀⡀⣀⠀⡀⢀⠀⠀⠀⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⡿⣿⣿⣿⢻⢿⣿⡿⣿⣿⣿⣿⣿⡿⡿⣿⣿⢿⢻⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠸⠃⠚⠃⠛⠘⠼⠉⠙⠸⠢⠞⠐⠀⠀⠋⠉⠘⠐⠁⠈⠘⠈⠑⠀⠑⠀⠀⣿⣿⣼⣼⣽⣭⣭⣿⣷⣥⣯⣾⣼⣽⣧⣧⣯⣼⣿⣼⣼⣽⣿⣽⣮⣿⣿⣥⣧⣧⣯⣯⣿⣼⣼⣿⣽⣽⣵⣽⣧⣮⣯⣾⣿⣿⣿⣿⣿
⠹⠛⠟⠛⠟⠻⠋⠉⠩⠉⠩⠉⠉⠉⣿⣻⣟⣻⣛⣿⣛⢋⣛⣟⣛⣿⣛⣛⣻⣻⣛⣛⣿⣟⣛⣿⣛⣻⣿⣻⣿⣛⣏⣛⣻⣛⣛⣛⣻⣻⣛⣻⣻⣛⣛⣻⣿⣟⣿⣛⣛⣛⣻⣿⣟⣟⣛⡛⣟⣟⣛⣛⣻⣿⣿⣿⣿⣿
⠀⠖⠶⠲⠶⠖⠆⠰⠆⠀⠰⠠⠢⠀⣿⣉⣻⣫⣿⣋⣙⣋⣿⣟⣛⣟⣿⣟⣻⣛⣻⣟⣿⣟⣋⣹⣿⣿⣟⣛⣿⣻⣙⣻⣝⣿⣝⣯⣛⣿⣿⣉⣿⣋⣏⣛⣻⣿⣹⣛⣻⣟⣟⣛⣿⣟⣹⣽⣙⣿⣿⣋⣻⣟⣻⣟⣙⣿
⠀⠰⡒⡒⢶⠶⠆⠀⠠⠤⠄⡠⠀⢸⣟⢍⣛⡛⡿⣹⢿⡟⣟⢝⡻⣿⣻⢟⢿⢻⢛⡻⡛⣿⢻⡉⠟⣹⢹⢻⢛⠛⣿⠟⡟⠛⢿⠛⠿⡏⢻⣿⠟⡟⢻⠟⡛⢛⡛⣿⣻⣿⠟⡟⣛⢻⠹⣿⣿⢛⣏⠟⢿⢿⣿⡛⠏⢻
⠀⠋⠙⠙⠙⠏⠃⠐⠂⠐⠂⠐⠀⠀⣿⣭⣽⣿⣯⣭⣽⣽⣿⣿⣽⣿⣿⣭⣯⣯⣯⣭⣭⣯⣿⣿⣬⣭⣿⣍⣿⣯⣽⣽⣽⣯⣿⣽⣿⣿⣽⣯⣭⣭⣿⣭⣿⣿⣯⣽⣭⣿⣧⣭⣿⣿⣿⣽⣧⣯⣽⣿⣯⣯⣿⣽⣿⣿
⠘⠋⠟⡻⢿⠻⢃⠂⠠⠔⠀⠂⠀⢸⣏⣝⣉⣝⣹⣹⣭⣭⣭⣝⣹⣽⣭⣿⣍⣛⣯⣉⣩⣿⣋⣙⣽⣯⣯⣹⣽⣭⣯⣏⣍⣙⣉⣍⣫⣽⣭⣭⣯⣽⣯⣍⣉⣹⣙⣋⣻⣿⣝⣹⣉⣽⣍⣽⣯⣹⣉⣹⣍⣹⣽⣭⣽⣿
⠉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⠉⡉⠉⠉⢉⢉⠉⢉⠉⠉⠉⢹⣿⢿⢿⣿⢿⢿⣿⡿⣿⢿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⡿⣿⢿⡿⣿⢿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠱⠸⠗⠬⠺⠸⠽⠰⠤⠁⠂⠂⠀⠘⠀⠒⠑⠀⠀⢸⣯⣯⣼⣿⣼⣼⣮⣤⣿⣽⣧⣤⣿⣬⣧⣿⣥⣽⣥⣬⣿⣬⣿⣦⣧⣿⣴⣥⣷⣿⣧⣯⣤⣽⣧⣮⣤⣾⣧⣕⣦⣿⣾⣬⣽⣷⣯⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠖⠒⠲⠖⠆⠀⠠⠀⠀⠄⠀⠀⣿⢙⢛⠛⢛⠛⢏⡫⣿⢛⢻⢟⠛⡟⡛⡿⡛⠛⡛⢻⢛⠛⠛⠛⡛⡟⡟⠛⡋⢻⢝⢛⠛⣿⢻⠹⡛⠻⡏⠙⢟⠛⠛⡟⠙⡿⡛⠛⠋⡟⠛⠛⢛⢹⢻⡛⠛⡛⢻⣻⣿⣿⣿⣿
⠀⠀⢀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠉⡁⣀⢀⠈⠀⠀⠀⠀⣿⣬⣭⣭⣬⣽⣧⣬⣽⣭⣭⣌⣩⣭⣭⣧⣭⣿⣤⣥⣥⣽⣵⣽⣼⣯⣽⣽⣭⣍⣩⣧⣽⣏⣭⣷⣿⣽⣿⣭⣯⣯⣭⣽⣽⣭⣽⣦⣾⣮⣤⣧⣭⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢿⠿⠿⠟⣿⡟⠿⣿⢿⣿⢿⣿⠿⣿⣿⡟⢿⣿⢿⡿⠟⣿⠿⢿⡿⠿⡿⠿⣿⡿⢿⠿⢿⡻⢿⢛⠿⡿⠿⣿⢿⡿⢿⢿⠿⢿⢿⡿⢿⣿⠛
⣻⢿⠿⡿⢿⣿⢿⣿⡿⣿⣿⣿⡿⠿⣿⡿⣿⣿⡿⣿⢿⠿⣿⢿⢿⡷⣿⠾⡶⣶⣾⢿⣶⡷⣿⡖⡾⢾⢶⡞⣿⢿⣶⠷⣾⣾⣿⣿⣷⣶⣿⣷⣾⣿⣶⣾⣶⣿⣶⣷⣷⣿⣾⣾⣶⣾⣿⣾⣶⣷⣾⣾⣷⣾⣶⣷⣿⣶
⠉⠩⡭⠭⢭⣭⡍⠉⠉⢉⠉⣉⠉⠉⣿⠿⡾⢿⢿⢿⡿⠷⡿⢿⠿⢿⠿⢿⡿⠿⠿⢿⡿⣿⡿⠿⡿⢿⠿⠿⡿⠿⠿⠿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠀⠈⠀⠁⠈⠉⠀⠀⠀⠁⠀⣿⣾⣶⣾⣶⣶⣷⣶⣿⣶⣷⣾⣶⣶⣷⣾⣦⣾⣶⣾⣷⣦⣿⣾⣶⣾⣧⣾⣷⣿⣿⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠂⠀⠒⠀⠀⠀⠀⠀⣿⣬⣥⣤⣷⣼⣄⣿⣯⣤⣾⣤⣼⣷⣤⣵⣥⣤⣯⣤⣵⣗⣶⣤⣷⣦⣵⣿⣥⣼⣦⣼⣯⣦⣤⣥⣬⣤⣽⣧⣼⣦⣿⣯⣾⣬⣾⣤⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠖⠐⠲⡒⠄⠠⠠⠀⠀⠀⠄⠀⣿⣻⣏⣿⣏⣋⣏⣯⣫⡉⣭⣟⣋⣟⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⢉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⢹⡿⣻⣿⡛⢿⡛⠛⠙⡿⢿⣟⡛⣿⠻⢿⢛⣽⠟⣿⣟⠛⠛⡿⡟⠛⠛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⢛⣿⣿⣿⣟⣿⣿⣿⣿⡛⣿⡟⣿⣟⡿⡿⣿⣿⣿
⠀⠈⠀⠁⠈⠁⠈⠀⠀⠈⠁⠀⠀⠁⠀⢸⣿⣹⣯⣿⣿⣿⣏⣽⣭⣯⣿⣙⣿⣿⣉⣿⣏⣿⣯⣯⣉⣽⣿⣿⣩⣽⣿⣹⣏⣹⣿⣿⣹⣫⣿⣩⣭⣻⣿⣿⣉⣿⣫⣝⣹⣿⣿⣏⣻⣻⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠋⠉⠋⠩⠁⠀⠔⠀⠰⠠⠢⠀⢸⣏⣯⣹⣫⣁⣁⣟⣍⣉⣹⣟⣿⣻⣉⣉⣛⣻⣋⣉⣈⣻⣿⣻⣁⣉⣯⣏⣹⣈⣩⣟⣋⣍⣉⣟⣟⣟⣟⣁⣙⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠈⠘⠀⠀⠀⠛⠀⠋⠀⠁⠁⠀⢸⣧⣷⣶⣿⣧⣷⣶⣼⣤⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣤⣤⣤⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠶⡶⢶⣶⡶⠲⡶⠀⣀⢀⠀⡀⠀⠀⠀⢸⣿⣿⢿⡻⠟⣿⣿⠿⢿⠿⠟⠿⣿⠟⣿⣿⢿⠿⠿⠿⢿⣿⢿⡿⠿⡿⢿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣾⣶⣶⣾⣷⣷⣷⣧⣶⣶⣾⣷⣿⣷⣿⣴⣶⣷⣴⣿⣾⣷⣷⣷⣷⣵⣷⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠙⠹⠹⡋⠋⢝⠉⠀⠖⠰⠀⠂⠐⠐⠄⢸⣿⣿⣩⣍⣩⣁⣯⣭⣻⣝⣽⣽⣯⣻⣍⣈⣩⣏⣃⣹⣙⣽⣏⣭⣍⢉⣏⣯⣫⣋⣯⣁⣩⣭⣇⣉⣉⣿⣉⣟⣩⣯⣿⣽⣉⣫⣿⣿⣹⣿⣿⣽⣉⣙⣽⣟⣻⣭⢻⣿⣿
⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⡿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠠⠸⠨⠅⠅⠦⠠⠀⠋⠘⠀⠁⠈⠈⠂⢸⣿⣿⣼⣭⣤⣭⣽⣿⣭⣧⣤⣤⣿⣿⣿⣥⣤⣤⣤⣤⣽⣿⣥⣼⣧⣤⣤⣷⣿⣿⣬⣤⣤⣧⣿⣿⣿⣯⣤⣥⣥⣤⣈⣿⣿⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⠶⢶⢶⠶⠶⠶⠶⠀⣀⢀⠀⡀⠀⠀⠀⢸⣿⠟⠻⠟⣿⡿⠿⡟⡟⣿⡿⢿⠿⢻⡿⣟⠿⢻⣿⠿⣿⣿⢻⣿⢿⣿⢿⠿⠛⡟⣿⠿⢿⣿⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣶⣶⣾⣾⣾⣶⣷⣾⣷⣷⣶⣾⣷⣷⣶⣶⣶⣷⣷⣾⣶⣿⣾⣿⣾⣶⣶⣷⣶⣿⣾⣷⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠙⠻⠹⠻⠋⠛⠛⠀⠖⠠⠀⠆⠐⠐⠄⢸⣿⣿⣝⣍⣁⣽⣭⣯⣯⡋⣁⣉⣏⣿⣫⣙⣉⣉⣽⣏⣯⣉⣫⣮⣯⣫⣯⣸⣫⣿⣽⣹⣿⣉⣉⣹⣉⣙⣭⣽⣽⣍⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⡿⡿⠿⢿⠿⢿⠿⢿⡿⠿⡿⡿⡿⠿⠿⡿⡿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠠⠸⠨⠅⠅⠦⠠⠀⠋⠘⠀⠁⠈⠈⠂⢸⣿⣦⣿⣿⣥⣿⣿⣿⣿⣾⣶⣿⣿⣴⣦⣦⣵⣧⣿⣿⣴⣤⣾⣧⣦⣷⣼⣧⣽⣶⣿⣧⣿⣥⣿⣧⣤⣤⣦⣼⣿⣿⣤⣼⣤⣾⣿⣤⣴⣇⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⢰⠶⢶⢶⠶⠶⠶⠶⠀⣀⢀⠀⡀⠀⠀⠀⢸⣿⣿⠿⢿⡟⠿⢿⣿⠿⠿⠟⣿⣿⡿⣿⡟⢿⣿⠟⡿⣿⢿⢻⣿⢿⣿⠿⠿⢿⠿⠟⠿⢿⣿⣿⡿⢿⠿⠿⢻⢿⣿⠻⠿⢿⠿⣿⢻⢿⣿⣿⣿⢻⢿⠿⢿⠿⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣶⣾⣶⣾⣾⣷⣾⣶⣶⣯⣷⣷⣷⣷⣷⣿⣾⣷⣷⣿⣶⣿⣾⣧⣷⣮⣿⣿⣷⣾⣶⣿⣿⣶⣿⣴⣷⣾⣾⣷⣶⣶⣾⣾⣿⣾⣷⣷⣿⣾⣾⣷⣶⣾⣾⣿⣿⣿⣿
⢸⠙⠻⠹⠻⠋⠛⠛⠀⠖⠠⠀⠆⠐⠐⠄⢸⣿⣿⣝⣍⣁⣽⣫⣯⡟⣭⣋⣉⣈⣽⣉⣩⣝⣝⣳⣽⣽⣍⣽⢸⣏⣈⢿⣩⣯⡇⣏⣯⣯⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⡿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠠⠸⠨⠅⠅⠦⠠⠀⠋⠘⠀⠁⠈⠈⠂⢸⣿⣿⣮⣧⣤⣾⣿⣿⣿⣧⣴⣿⣿⣶⣽⣤⣤⣤⣵⣿⣿⣧⣤⣾⣶⣤⣤⣼⣠⣴⣴⣴⣦⣼⣧⣾⣿⣿⣴⣿⣷⣼⣬⣿⣷⣮⣧⣴⣤⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢩⣭⣭⣭⣭⣭⣭⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠸⠀⠯⠽⠕⠸⠡⡸⠁⠘⠠⠀⠇⠊⠀⠄⠢⠀⣿⣟⣇⣚⣿⣠⣻⣟⢠⣻⣓⣆⣻⣟⣹⣃⣻⣻⣸⣟⣰⣷⣹⣛⣁⣻⣫⣀⣻⣻⣻⣝⣝⣗⣀⣝⣿⣣⣐⣿⣟⣖⣜⣻⣋⣾⣜⣿⣛⣿⣛⣑⣄⣟⣿⣀⣻⣻⣿⣿
⠀⠀⠐⠤⠀⠀⠄⠠⠀⠠⠄⠀⠀⢸⣟⡹⡛⣻⢛⣙⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⣩⣟⣯⣻⣟⣟⣟⣏⣟⣻⣿⣿⣻⣿⣿⣿⣟⣻⣻⣟⣿⣿⣟⣿⣻⣟⣙⣽⣻⣿⣛⢛⣻⣿⣿⣙⣟⣻⢟⣛⣻⣿⣻⡟⣿⣿⣟⢿⣏⢿⣯⣟⣿⣟⣛⣻⣿⣻⣛⣽⣿⣿
⠐⠀⠀⠀⠐⠂⠒⠂⠂⠀⠂⠀⠀⢸⡋⣋⣉⣉⣃⡙⣉⢈⣋⣛⣈⣙⢉⣋⣋⣙⣋⣉⣋⣙⣋⣙⣉⣛⣙⣉⣛⣉⣁⣀⣙⣙⣉⣁⣙⣉⣉⣉⣉⣋⣈⣉⣃⣈⣉⣉⣉⣙⣋⣙⣉⣉⣈⣋⣙⣉⣁⣥⣇⣿⣿⣿⣿⣿
⣤⣤⡤⠤⠤⠤⠄⠤⠤⡤⢤⡤⠤⡼⠿⠖⠷⠶⢺⠿⣾⠾⠶⡿⠷⡶⠾⡿⢟⡿⠿⠿⠿⡿⢻⡿⠟⢿⣿⡿⠿⠿⣿⣿⡿⠿⡿⠿⠿⠿⣿⠿⠻⢟⡿⠿⡿⠻⣿⠿⢿⢿⠿⠿⢿⠿⢿⠿⠿⠿⡿⠿⠿⢿⠿⡿⠿⢿
⣿⣿⣷⣾⣶⣶⣾⣶⣷⣷⣾⣾⣷⣷⣶⣿⣶⣶⣷⣾⣾⣷⣾⣿⣷⣾⣶⣷⣿⣷⣶⣶⣾⣷⣾⣾⣶⣷⣷⣾⣾⣶⣿⣾⣶⣾⣶⣾⣶⣾⣶⣾⣶⣾⣶⡮⣒⢲⣿⢛⡛⢚⢰⢐⠏⠰⢲⣲⠓⡖⢓⣒⢚⠟⣿⣓⠞⣚
⠀⠀⠀⠠⠀⠀⠄⠀⠄⠀⠀⠀⠀⢸⣿⣛⣏⣿⣛⣿⣻⣻⣛⣟⣿⣛⣏⣟⣛⣏⣿⣛⣿⣻⣻⣹⣟⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⣀⠀⠀⡀⢀⠀⠀⡀⠀⠀⢸⡿⣿⠻⣿⠿⣿⠿⠿⠛⡿⢿⠻⢿⠻⠿⢿⠿⠻⣿⠻⢿⡿⢿⣿⠟⣿⠿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⡀⠀⠀⣀⠀⡀⢀⠀⣀⡀⢸⡿⢿⢿⠿⠿⠾⢿⠿⠿⠿⡿⠿⡿⠿⠿⢿⠿⠿⠿⡿⠾⢿⠿⠿⠿⠿⠾⠿⡿⠿⠿⠿⣿⠿⢿⡿⠿⠿⡿⢿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠁⠀⠀⠀⠀⠉⠈⠀⠉⠁⢸⣷⣶⣾⣶⣿⣶⣾⣶⢾⣶⢷⣶⣷⣿⣶⣶⣶⣶⣶⣷⣶⣾⣶⣶⣶⣶⣶⣶⣷⣾⣶⣶⣾⣶⣶⣷⣶⣶⣶⣾⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠀⠀⠀⢸⣷⣿⣾⣶⣿⣶⣿⣾⣶⣾⣶⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠂⠀⠀⠀⠐⠀⠀⠂⠀⠀⢸⣦⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠀⠂⠀⠂⠀⠀⠀⠀⢸⣯⣫⣹⣝⣯⣉⣉⣉⣈⣩⣹⣉⣽⣉⣍⣁⣹⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⢀⡀⣀⡀⡀⠀⡀⠀⠀⢸⣟⣘⣹⣉⣙⣉⣭⣉⣯⢽⡉⣙⣉⣩⣉⡯⣽⡍⣉⡍⣹⣯⣯⣝⣭⣍⣏⣙⣏⣝⣹⢉⣝⣻⣛⣙⢻⣏⢻⣯⣋⣹⣏⣏⣏⣹⣫⣹⣈⣏⣉⣽⣹⣛⣍⣉⣏⣹⣛⣿⣙⣫⣿⣿
⣀⣀⣀⣀⣀⠀⢀⠀⠀⡀⢀⠀⠀⠜⡁⢁⠀⠉⡁⠀⢁⠈⡀⢈⠉⡀⣁⠉⠈⠁⠈⡀⢉⠀⢀⠈⢁⣉⠀⠉⠈⠁⣐⡘⡚⣀⢊⠐⡊⢘⡐⡊⠀⢁⠐⣛⠛⡛⠛⠛⠛⠛⡛⢛⡛⡛⠛⠛⠛⣛⡛⢛⣛⡛⢛⠛⡛⣛
⣿⣿⣿⣿⣿⣿⣶⣿⣾⣴⣷⣶⣷⣶⣶⣷⣶⣶⣾⣷⣧⣶⣷⣾⣷⣶⣶⣶⣾⣿⣷⣶⣶⣾⣶⣿⣾⣷⣶⣿⣷⣶⣷⣾⣶⣶⣾⣶⣷⣶⣷⣶⣧⣾⣶⣾⣷⣷⣷⣾⣷⣾⣶⣾⣾⣿⣶⣶⣷⣾⣷⣶⣾⡖⠲⠚⡲⡻
⠉⠉⠩⣉⠉⠉⠉⢉⠉⠉⡉⠉⠉⢹⣿⠛⡛⢟⡟⠿⢟⢻⠛⢟⡟⡛⠻⡛⡿⢟⡻⡟⠛⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⢸⠿⠿⠿⡿⢿⡿⠻⢿⠿⠿⢻⠿⡿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡤⡤⢤⡤⣤⠤⢤⠤⣤⢤⣤⡤⡼⡷⡶⣿⡷⡶⡷⠶⣾⣶⣷⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⡗⡿⣾⡷⠶⢶⢿⣿⠷⡞⡿⡾⢷⣿⡻⠿⠿⣟⡶⣷⠻⣿⠿⢿⣿⠿⡿⢿⣿⡿⢿⣿⢿⣿⡿⢿⣿⠿⡿⣿⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢟⢻⣛⣿⣿⣿⡿⠟⠿⡟⠛⡟⠟⢿⡿⢿⣛⡟⡿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣟⡿⣟⠛⠛⢿⣿⡟⣿⡿⣿⣿⣿⣿⣿⠻⣿⣻⣿⢿⡛⠿⢻⣿⣿⠟⣻⣿⣿⠟⠿
⠀⢠⢠⢀⠠⢠⠄⡄⠀⢀⠄⠠⡄⠄⠄⠀⢸⣿⠙⣛⣿⣿⣿⣿⣙⣻⣻⣿⣻⣹⣻⣛⣻⣿⣝⣻⣿⡿⣻⣛⣟⣟⣟⢿⣛⢻⣩⣛⣛⢻⣿⣛⣿⣟⣻⣿⣿⣛⣟⣹⡿⡟⣛⣿⣿⣟⣻⣻⣿⣿⣛⣟⣿⣿⣿⣿⠙⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣙⣻⣻⣿⣻⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⢀⠀⡀⡀⠀⣀⢀⢀⠀⠀⠀⠀⢸⡿⢿⠻⠿⢿⣿⡿⠟⢻⣿⣛⠛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣶⣿⣾⣷⣿⣷⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⠐⠀⠂⠂⠀⠒⠐⠐⠀⠀⠀⠀⢸⣇⣅⣉⣃⣯⣺⣣⣘⣩⣝⣽⣫⣭⣏⣏⣈⣿⣉⣋⣭⣇⣉⣽⣿⣭⣉⣿⣝⣟⣯⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⢀⠀⡀⡀⠀⣀⢠⢀⠀⠀⠀⠀⢸⡟⡻⣿⡿⢿⢻⡟⠻⣿⠿⣿⡿⣿⡿⡟⠿⣿⢿⢿⠿⢻⣿⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣷⣿⣶⣿⣶⣷⣷⣶⣾⣶⣷⣿⣿⣷⣶⣾⣾⣷⣶⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠀⠀⠀⠂⠒⠀⠐⠀⠆⠂⠀⠀⠀⠇⢸⣏⣯⣽⣛⣧⣽⣀⣏⣿⣽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⠀⠀⠀⡀⣀⠀⢀⠀⡀⡀⠀⠀⠀⡄⢸⡿⣿⠿⡿⢿⣿⣿⣿⡿⡿⠿⠿⢿⣿⣿⡛⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠰⠠⠀⠄⠄⠀⠤⠰⠠⠀⠀⠀⠀⢸⣧⠧⢤⣮⣧⢬⣽⡿⣼⢿⣽⢾⢯⡿⣿⢼⡤⡼⡶⡿⡭⣽⢴⡥⠤⡴⢥⣤⡬⣭⣯⡿⡧⠤⡤⢧⢿⢯⢿⢽⢭⣤⣵⣾⢤⣤⣴⣽⣽⣽⣽⣽⣭⣥⣾⣯⣽⣷⣤⣼⣿
⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⣷⣿⢾⣾⣶⣾⣶⣷⣶⣾⣶⣾⣶⣷⣶⣾⣿⣿⣶⣷⣶⣶⣾⣾⣶⣷⣾⣿⢾⣶⣶⣷⣶⣶⣷⣾⣶⣿⣾⣷⣾⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠄⠀⠀⠠⠤⠤⠀⠠⠀⠄⠄⠀⠀⢸⡿⢿⣭⢶⣯⣿⣿⣿⣽⣵⡷⣿⣧⣯⣷⢿⣬⣿⣭⣽⣿⣽⣭⣾⣼⣭⣿⣧⣥⣦⣤⣿⣿⣯⣯⣮⣼⣿⢿⢿⡯⠮⣶⢿⢿⣿⣯⣦⣤⣧⣶⣯⣿⣿⣿⣧⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⢸⣧⣷⣿⣾⣿⣿⣿⣿⣾⡿⣧⣿⣾⣿⣿⣿⣷⣿⣭⣭⣮⣼⣿⣯⣯⣽⣿⣧⣼⡭⣭⣭⣯⣥⣯⣿⣽⣭⣽⣽⣮⣮⣶⣭⠾⣤⡤⣽⣽⣽⣵⣭⣤⣿⢿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣽⣾⢿⣿⣿⣿⣷⣿⣾⣿⣷⣷⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣿⣶⣿⡿⣷⣶⣶⣿⢾⣿⣶⣾⡿⡿⣿⣾⣿⡿
⣿⣿⣽⣽⣯⣬⣿⣿⣿⣯⣭⣯⣽⣿⣾⣯⣯⣴⣽⣿⣷⣴⣾⣥⣿⣽⣯⣯⣥⣤⣮⣯⣭⣥⣮⣼⣽⣿⣽⣿⣿⣴⣵⣴⣽⣿⣯⣧⣧⣤⣦⣮⣿⣼⣴⣦⣿⣿⣯⣿⣿⣷⢶⣿⣭⣥⢤⢾⣬⣥⣵⣵⣥⣧⣦⣮⣿⣤
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣶⣾⣿⣶⣶⣾⣾⣼⣶⣶⣿⣿⣿⣾⣷⣶⣶⣦
⠀⠀⠀⠀⠀⠄⠶⠂⠨⠘⠂⠀⠀⠀⠀⠀⢸⣿⣯⣥⣼⣭⣯⣿⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⠤⡤⠤⠤⠤⠄⠀⢀⠀⢀⠀⡀⠀⠀⣿⢛⠿⢿⣿⠿⠿⠛⣛⢿⠛⡛⣿⡟⢿⡿⡿⠿⣿⣿⠿⢿⡿⠟⢿⠿⢿⠻⠿⢿⢿⢿⢿⣿⡟⠻⠿⢿⡿⡟⡿⢿⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⠉⠈⠀⠀⠁⠈⠈⠈⠈⠀⠠⣿⣾⣶⣾⣿⣿⣶⣾⣾⣾⣿⣿⣷⣷⣾⣷⣷⣶⣿⣿⣶⣿⣿⣷⣶⣷⣿⣶⣷⣾⣿⣾⣶⣷⣿⣶⣶⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢈⣉⣋⣉⣉⣩⣁⠀⠴⠄⠰⠠⠢⠀⠀⣿⣰⣫⣹⣉⣻⣋⣉⣇⣉⣍⣻⣻⣏⣸⣉⣉⣟⣹⣊⣉⣀⣉⡟⣙⣏⣹⣝⣹⣯⣉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⢩⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠴⠠⠦⠄⠰⠰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣹⣿⣟⣛⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⢀⠀⢠⡀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⣿⡛⡛⠿⠿⡿⢿⠿⠿⡿⠿⣿⡿⠿⠿⠿⡿⢿⢿⣿⠿⠿⢻⡿⣿⠿⠻⢿⣿⡿⠿⠟⠿⡿⣿⣿⠻⠿⢿⣿⢿⡿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣟⣓⣓⣒⢒⣓⣛⣒⣓⡓⣓⣛⣛⣓⣓⣓⣛⣚⣓⣓⣓⣓⣚⣛⣚⣒⣚⣚⣛⣒⣒⣒⣓⣛⣚⣚⣒⣓⣓⣛⣚⣒⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣶⣵⣶⣤⣶⣤⣵⣮⣵⣷⣴⣷⣵⣤⣧⣿⣮⣾⣾⣧⣴⣾⣷⣿⣾⣾⣾⣷⣮⣤⣵⣏⣰⣾⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣎⣛⣏⣉⣉⣃⣙⣟⣻⣟⣋⣇⣙⣉⣻⣏⣻⣻⣙⣻⣃⣗⣊⣹⣐⣻⣟⣊⣹⣳⣋⣻⣿⣻⣋⣟⣙⣝⣺⣟⣫⢻⣋⣈⣻⣽⣒⣿⣺⣊⣁⣳⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡄⡄⠀⡀⢀⢀⡀⡀⡀⠀⢀⠀⠀⠀⠀⠀⢸⡟⢟⢿⣿⣿⠻⣿⣿⠿⣿⢿⠿⢿⣿⠿⡿⠟⡿⠿⣿⢿⢻⠿⠿⡿⣿⡿⡿⠿⣿⡟⡿⠿⢿⡟⢿⡿⠿⡿⣿⢿⣿⣿⠻⢻⢿⡟⣿⢻⢻⣿⡟⣿⣻⢻⢻⣿
⣀⣀⣀⣀⣁⣀⣀⣁⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣷⣷⣶⣷⣿⣶⣷⣷⣶⣾⣾⣷⣾⣷⣶⣷⣶⣶⣶⣿⣾⣾⣷⣶⣷⣾⣾⣷⣶⣿⣷⣷⣶⣿⣷⣾⣿⣶⣿⣾⣶⣷⣿⣿⣶⣾⣶⣾⣾⣾⣶⣷⣷⣷⣾⣶⣿
⣼⣏⣿⣟⣿⣏⣍⣽⣇⣽⣿⣝⣟⣿⣏⣿⣿⣿⡿⣩⣿⣏⣿⣟⣟⣿⣍⣽⣯⣝⣿⣏⣻⣯⣻⣿⣿⣭⣏⣻⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⢩⣭⣭⣭⣭⣭⣭⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠐⠘⠘⠅⠀⠄⠜⠀⠀⠚⠘⠐⠐⠁⠐⠀⠀⠀⢸⣧⣼⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣤⣤⣤⣤⣤⣤⣤⡄⠀⢀⠀⠀⡀⡀⠀⠀⠀⠀⢹⡿⡿⡿⣿⢿⣿⢿⢿⣿⢿⣿⢻⢿⡿⡿⣿⠿⢿⢿⢻⡿⣿⠿⣿⡿⡿⡿⡿⠿⣿⠻⡿⡿⠿⣿⡿⢿⡿⣿⢿⢟⡿⣿⢿⢿⢿⣿⢿⣿⠿⣿⣿⠿⣿⢿⣿⣿
⠀⠸⠴⠼⠬⠬⠴⠶⠼⠤⠄⠊⠈⠈⠀⠀⠐⠈⠂⠀⢸⣧⣧⣦⣾⣶⣼⣬⣬⣧⣬⣥⣴⣼⣧⣮⣾⣬⣯⣤⣤⣧⣼⣨⣦⣯⣤⣧⣦⣼⣿⣬⣧⣥⣧⣿⣬⣯⣥⣿⣥⣼⣧⣮⣴⣭⣥⣿⣬⣤⣼⣥⣤⣽⣥⣿⣿⣿
⠀⠀⡟⡛⣿⠛⢟⡟⣟⢻⠃⠀⡠⢠⢠⠠⢠⢠⠠⡀⠀⠀⣿⣟⢹⡹⣽⣩⣿⡛⢻⣟⢛⣿⡛⣿⡏⣿⡿⢻⡻⣿⡿⢹⡏⡏⠻⣿⡿⣿⠟⣿⠛⢿⡟⣻⣟⢛⣿⢻⡟⣻⠛⣿⣟⢻⡻⣿⣿⢹⡟⢻⢛⣿⣿⣿⣿⣿
⠀⠀⠛⠛⠓⠓⠓⠓⠓⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣷⣾⣾⣶⣿⣾⣷⣷⣶⣷⣷⣿⣷⣾⣶⣾⣿⣿⣶⣿⣿⣷⣾⣾⣿⣶⣷⣿⣶⣷⣯⣼⣾⣿⣿⣭⣷⣷⣿⣾⣾⣾⣽⣿⣾⣾⣾⣾⣷⣿⣾⣿⣿⣿
⠀⠀⡶⡶⡶⣶⡶⡶⣶⡶⠆⠀⢀⢀⢀⢀⢀⢀⢀⠀⠀⠀⣿⣿⣯⣿⢿⣿⠿⣿⡟⡟⠿⣿⡿⡿⣿⣿⢿⡿⢿⣿⠿⣿⣿⠿⣿⡿⣿⣿⢿⢿⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠇⠧⠹⠮⠄⠧⠇⠠⠄⠁⠈⠈⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣶⣿⣷⣿⣾⣿⣷⣷⣿⣷⣾⣷⣾⣿⣾⣾⣿⣦⣿⣷⣿⣿⣾⣿⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠙⠟⠏⠟⠛⠏⡟⡻⠃⠀⠖⠄⠂⠔⠄⠀⠆⠢⠂⢸⣿⣿⣫⣟⣟⣝⣿⣿⣟⣿⣿⣋⣟⣿⣹⣿⣻⣟⣹⢻⣿⣟⣻⣏⣯⣻⣏⣽⣿⣿⣟⣿⣟⣿⣹⣽⣝⣹⣿⣿⣟⣻⣏⣽⣟⣿⣛⣿⣹⣿⣻⣿⣻⣿⣿⣿⣿
⠀⠒⠲⠲⠲⠒⡒⠀⠤⠀⠄⠠⠀⠄⠀⣿⣻⣛⣛⣛⣻⣻⣟⣿⣟⣿⣻⣟⣿⣟⣟⣻⢛⣻⣿⣿⣿⣻⣻⣟⣛⣿⣻⣿⣻⣙⣛⣻⣟⣟⣛⣛⣟⣟⣿⣟⣛⣻⣙⣛⣛⣻⣿⣻⣿⡿⣻⣛⣟⣙⣛⣻⣿⣿⣿⣿⣿⣿
⣤⣀⣶⣰⣖⣆⣔⣆⡂⣂⣶⡲⣆⣆⣶⡲⣖⣒⣶⣲⣦⣶⣒⡲⣒⣒⣒⣶⣀⣒⣶⣶⢲⣆⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣋⣛⣛⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣀⣦⣰⢀⣒⣒⣦⣲⣰⣂⣐⣲⣒⣴⣒⣲⣢⣀⣲⣰⣄⣰⣀⣒⣒⣖⣀⣒⣢⡆⣲⣂⣀⣲⣂⣐⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣛⣛⢛⢛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣖⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⢲⠒⠒⠒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⠟⡟⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⢀⠀⠀⢀⠀⠀⠀⡥⠭⠭⠭⠭⡭⢭⠭⠭⠭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢶⣾⣷⣶⡷⡾⣶⡶⠶⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣈⢀⣀⣀⣀⣀⣀⡀⢀⣀⣓⣒⢚⢒⣒⢒⣓⣚⣒⣒⣒⣘⣐⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⠿⠶⠿⠾⣶⠷⢷⢶⠷⠶⡶⠷⢽⠾⢿⢾⠾⠾⠶⠻⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡛⠟⠚⠟⠓⠻⠚⢺⠓⠷⠗⠗⠛⠟⡾⢟⠓⡖⠚⠚⢿⢚⢻⠛⢛⠛⠛⢻⠛⢟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡶⢶⢶⢶⡶⣶⢶⢶⡶⠆⢀⢀⠀⢀⢀⢀⠀⡀⡀⠀⠀⣿⡟⡿⣿⡿⣿⠿⣿⢿⡿⢿⠿⣟⣟⣿⡿⣿⡿⣿⢿⡿⣿⢿⡿⣿⡿⣿⣿⡟⢿⢿⡿⣿⣟⢟⣿⣿⣿⢿⡿⣿⣿⢿⣿⢿⡿⣿⣿⡿⣿⢻⣿⢿⣿⣿⣿
⠀⠃⠘⠘⠘⠎⠛⠨⠢⠃⠀⠀⠊⠈⠐⠀⠁⠀⠁⠈⠂⠀⣿⣧⣵⣮⣵⣽⣥⣭⣯⣯⣼⣽⣿⣽⣽⣿⣿⣵⣯⣼⣯⣯⣽⣇⣯⣭⣼⣽⣧⣵⣮⣧⣽⣿⣵⣽⣥⣽⣨⣧⣽⣮⣾⣭⣼⣥⣯⣿⣥⣿⣼⣥⣪⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣹⣹⣉⣏⣿⣩⣟⣻⣻⣉⣹⣹⣉⣋⣏⣉⣏⣻⣉⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⡄⢤⠄⠀⠀⠀⠀⠀⠀⣷⣾⣭⣯⣼⢯⣻⣭⣽⢯⣿⣼⣼⣯⣭⣿⣿⣯⠽⣍⣼⣿⣿⣯⣭⣭⡯⣟⣭⣭⣭⣿⢤⡽⣿⣿⣬⣭⢼⣯⣭⣽⣬⣹⣼⣿⣯⣯⣽⣿⣯⣽⣯⣿⣿⣿⣶⣯⣭⣯⣭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⣶⣶⣿⣶⣶⣾⣿⣾⣦⣷⣿⣷⣷⣶⣷⣿⣶⣶⣶⣷⣾⣿⣾⣶⣷⣷⣿⣿⣷⣶⣾⣷⣷⣿⣷⣾⣶⣾⣷⣿⣶⣿⣶⣧⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠈⠀⠀⠀⣷⣶⣾⣷⣾⣶⣾⣾⣴⣷⣮⣷⣷⣿⣶⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠛⠑⠀⠀⠁⠀⠀⠀⠀⣧⣤⣤⣼⣤⣤⣼⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠒⠐⠂⠀⠀⠀⠀⠀⣧⣽⣯⣯⣭⣿⣮⣭⣿⣿⣭⣽⣾⣽⣭⣯⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡀⠠⡀⠀⠀⠀⠀⠀⠀⣯⣽⣭⣿⣯⣽⣯⣽⣍⣯⡭⣯⣭⣭⣭⣭⣿⣿⣽⣯⣯⣿⣯⣽⣭⣧⣽⡭⣯⣿⣯⣯⣯⣽⣭⣻⣿⣽⣯⢩⣽⣬⣍⣽⣯⣼⣿⣯⣽⣽⣭⣯⣭⣼⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡿⣶⡶⣶⣷⣾⣶⣿⢶⣷⣷⣶⣿⣾⣾⣷⣷⣾⣾⣶⣷⣾⣾⣶⣷⣷⣾⣿⣶⣷⣾⣷⣷⣼⣾⣶⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠈⠈⠁⠀⠀⠀⠀⠀⣷⣾⣷⣷⣾⣾⣷⣷⣼⣾⣷⣶⣷⣷⣶⣶⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠓⠐⠂⠀⠁⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⣏⣍⣍⣉⣭⣉⣍⣿⣅⣹⣭⣉⣫⣝⣽⣹⣋⣹⣹⣊⣹⣩⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠀⠄⠀⠀⠀⠠⠠⠀⠀⠀⣟⣟⣻⣹⢛⣻⣛⣟⣻⣟⣹⣏⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠀⡤⠀⠤⠄⢀⡀⠠⠀⠠⠀⣿⢟⢻⠛⠻⡟⠛⢻⣿⠛⡛⠛⡻⠛⠟⠛⠛⠟⠛⡛⠛⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠤⡤⠤⠤⡄⠀⠀⢀⠀⠀⠀⣿⠿⢿⢿⢻⠿⠿⠿⠿⠿⠿⠿⢿⢿⠿⠿⠿⢿⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠾⡶⡾⢶⠶⡿⡿⢷⠶⡾⡾⠾⡶⣶⠶⠶⡶⠿⠿⡿⣿⠿⠿⢿⢿⠿⠿⡿⠿⠿⠿⡿⡿⠿⠿⢿⡿⡿⢿⢿⡿⡿⡿⡿⢿⠿⡿⢿⡿⠿⣿⠿⢿⠿⢿⠿⡿⢿⡿⠿⢿⣿⠿⣿
⠀⠀⠀⠐⠂⠐⠒⠀⠂⠀⠀⠀⣿⠟⠓⣳⠓⠒⡖⠲⢳⡶⠒⠳⠓⡲⡗⡞⠐⡖⢑⡲⠒⡿⠒⡶⠛⠚⡔⠒⠒⣟⣖⣒⠖⢲⠓⡾⢶⣶⣦⣷⣾⣶⣶⣦⣷⣶⣶⣶⣾⣾⣾⣦⣶⣶⣷⣾⣶⣶⣷⣶⣷⣴⣾⣷⣶⣷
⠀⠀⠀⢀⡀⣀⣀⠀⡄⠀⠀⠀⣿⡿⠿⡿⠾⠻⠿⡿⡿⢿⡟⢾⠟⢛⡿⣿⡟⡟⠺⠟⡻⣿⠿⠿⢿⠿⠿⡿⢿⡿⡿⢿⠿⣿⠿⢟⠛⡿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣷⡿⢿⡿⢿⡿⠷⠿⡿⠿⠿⡿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠁⠀⠀⠀⠈⠉⠁⠀⠁⠀⣿⣷⣾⣶⣾⣷⣶⣶⣿⣶⣶⣷⣶⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠃⠙⠀⠁⠃⠀⠀⠀⣿⣤⣤⣤⣬⣤⣥⣤⣽⣤⣧⣬⣤⣼⣤⣧⣦⣰⣲⣤⣼⣤⣥⣧⣥⣧⣼⣤⣤⣤⣥⣠⣧⣬⣤⣬⣧⣤⣧⣥⣼⣶⣮⣥⣤⣬⣬⣧⣼⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠉⠋⠉⠉⠇⠀⠀⠐⠀⠄⠀⣿⣯⣭⣉⣇⣩⣽⣉⣍⣽⣹⣉⣭⣉⣟⣁⣙⣏⣩⣉⣏⣩⣧⣉⣈⣇⣩⣉⣹⣉⣅⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣻⣟⣟⣻⣿⣹⣿⣟⢿⣏⣿⣿⣿⢿⣽⣹⣿⣿⣫⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠒⠖⠒⠒⠆⠠⠤⠄⠀⠄⠀⣿⣝⣟⣛⣹⣿⣉⣻⣋⣟⣟⣛⣫⣻⣋⣿⣻⣛⣛⣏⣛⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡄⢠⣀⠀⡄⠀⠀⠀⣿⡟⣛⣻⠻⠛⡛⢟⡟⠟⢛⢿⡟⡛⡛⣟⠿⣻⠛⢻⠟⡻⠛⡿⠛⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡀⣀⠀⠀⡀⠀⠀⠀⣿⡿⢿⠿⠿⢿⠿⡷⠿⠿⡿⣿⢿⠿⠿⠿⠿⡿⢿⢿⠿⠿⢿⠿⠿⢿⠿⢿⠿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⢿⠿⢿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⡿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣈⣁⡈⠈⠀⠁⠀⠀⠀⣿⣷⣶⣷⣶⣾⣶⣷⣶⣶⣿⣾⣶⣶⣶⣶⣿⣷⣶⣾⣶⣷⣾⣶⣷⣶⣶⣾⣶⣶⣿⣶⣶⣾⣿⣿⣿⣿⣿⣾⣶⣶⣶⣾⣶⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣷⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿
⠈⠀⠁⠀⠀⠁⠀⠈⠉⠀⠀⠀⣿⣧⣤⣿⣤⣦⣤⣤⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠉⠋⠉⠉⠃⠐⠐⠂⠀⠀⠀⣿⣅⣩⣍⣏⣭⣻⣭⣭⣿⣍⣨⣭⣽⣩⣍⣿⣏⣑⣽⣭⣽⣯⣽⣩⣭⣏⣉⣺⣭⣋⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠒⠖⠖⠒⠆⠠⠤⠄⠀⠀⠀⣿⣏⣛⣛⣛⣿⣛⣛⣹⣟⣻⣛⣛⣿⣻⣫⣿⢛⣻⣛⣻⣻⣛⣻⢛⣻⣝⣛⣟⣛⣻⣛⣏⢻⣻⣋⣻⣉⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢩⢭⡭⠭⡭⢭⠍⠉⠉⡉⠉⡉⠉⢹⣟⠻⡟⢛⠻⠟⡿⠛⠟⣿⣿⠿⣿⡿⠿⡿⠿⠿⡿⠿⡿⠿⢿⠻⢿⢿⡿⠟⠻⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⡿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣘⣘⣁⣀⣋⣘⣀⣀⣈⣁⣀⣁⣀⣸⣧⣤⣤⣼⣤⣤⣧⣤⣼⣮⣤⣼⣬⣾⣤⣠⣰⣧⣼⣤⣬⣧⣼⣤⣤⣼⣤⣼⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣮⣽⣿⣧⣯⣿⣿⣯⣽⣍⣭⣿⣗⣖⣯⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣮⣽⣻⣇⣯⣿⣿⣽⣽⣿⣭⣛⣿⣷⣏⣥⣙⣻⣫⣸⣻⣺⣰⣎⣃⣿⣿⣻⣿⣫⣋⣏⣿⣿⣯⣟⣯⣭⣭⣿⣟⣿⣻⣣⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠲⠖⠲⠖⠲⠂⠀⠀⠄⠀⠀⠄⢸⣏⢹⣏⣩⣙⣋⣟⣙⣛⣟⣟⣿⣙⣛⣻⣽⣛⣋⣹⣙⣛⣋⣛⣻⣙⣉⣟⢛⡛⣟⢛⣋⣛⣽⣛⣛⣟⣛⣻⣋⣝⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⢀⣀⣀⡀⡀⢀⡀⠀⠀⢸⣿⣿⡟⠻⢻⢿⡿⠿⠿⡿⢿⡿⠿⣿⠿⣿⢿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⠿⢿⣿⢿
⠀⠀⠁⠀⠈⠉⣉⡀⡁⠈⠀⠀⠀⢸⣿⣿⣷⣾⣾⣾⣷⠀⠀⣷⣶⣶⠀⢰⣶⡎⢰⡎⠀⠀⣶⠀⣧⣬⠁⢠⣭⡄⠉⢩⡍⠉⣭⣥⣄⡀⠀⡄⣤⠀⣍⣭⣍⣤⣤⣄⡄⣬⣅⡬⢁⣄⠠⣤⠀⠠⢤⠀⡬⠝⢺⡇⢻⡖
⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡷⢶⣶⡶⡶⣶⡶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠈⠈⠁⠀⠁⠈⠀⠀⠀⠁⠀⠁⠁⢸⣯⣥⣽⣯⣧⣤⣤⣵⣶⣴⣽⣦⣤⣽⣼⣴⣵⣤⣧⣤⣽⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠹⠏⠩⠟⠻⠁⠂⠠⠔⠀⠂⠀⢸⣏⣙⣏⣉⣉⣟⣉⣉⣯⣉⣉⣹⣙⣙⣉⣉⣏⣈⣹⡋⣉⢩⣍⣍⣩⣈⣉⣍⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⢤⡤⢤⡤⢤⠄⠀⠀⡀⠀⠀⡀⢸⡟⣻⠿⢿⡿⣿⢿⡿⠿⢿⠿⠟⡟⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⣤⢤⣤⣤⣤⢤⣤⣤⠤⣤⣤⡤⢼⢿⢿⢿⠿⡿⡿⠿⢿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⣛⣓⣛⣛⣛⡓⠚⠓⠐⠛⠛⠓⢻⣿⣽⡾⢷⣿⣿⣷⣾⣷⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠘⠁⠁⠋⠘⠀⠀⠈⠁⠀⠁⠀⢸⣯⣤⣧⣴⣤⣼⣤⣤⣤⣥⣇⣤⣧⣧⣬⣥⣼⣤⣴⣤⣬⣮⣯⣤⣤⣾⣭⣧⣬⣴⣵⣶⣯⣼⣤⣯⣅⣤⣤⣤⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠲⠆⠲⠖⠲⠂⠀⠀⠄⠀⠀⠀⢸⣏⣉⣉⣿⣿⣿⣉⣹⣉⣏⣉⣩⣭⣹⣝⣉⣹⣉⣉⣿⣿⣿⣏⣉⣫⣽⣭⡟⢉⣉⣏⣽⣭⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠉⠉⠟⠉⠀⠤⠀⠲⠠⠂⢸⣿⣉⣭⣍⣙⣛⣩⣏⣉⣉⣛⣉⣏⣹⣙⡏⣹⣹⢩⡉⣏⣉⣭⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠒⠒⠶⠒⠀⠀⠤⠠⠀⠄⢸⣿⡟⠛⠻⢿⡛⢛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⢀⠀⡀⢀⠀⠀⠀⠀⢸⡿⠟⠿⣿⠟⣿⢿⡿⢿⡿⠻⡿⡿⡻⠿⠿⡿⣿⠿⣻⢻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡿⢿⡿⣿⠿⡿⢿⣿⠿⡿⣿⣿⠿⣿⣷⣿⡿⣿⠿⡿⢿⡿⢿⡿⣿⡿⠿⣿⣿⡿⠿⡿⠿⣿⡿⣿⠿⣿⢿⣿⡿⢿⠿⠿⡿⠿⣿⠿⢿⡿⢿⡿⢿⣿⠿⢿⠿⢿⠿⢿⢿
⠀⠀⠂⠐⠐⠀⠀⠀⠀⠀⠀⠀⢸⡟⠚⢻⢲⢳⠚⢛⢛⠒⡗⢲⠿⢶⠓⡖⠚⣲⢛⡓⡛⢓⠛⢿⢒⠚⠒⠚⢳⠓⢳⢒⡓⣖⠓⠚⠓⡶⡛⠛⡞⠒⡛⢒⠛⣿⠚⠶⡶⠟⢷⡛⢷⡞⢳⡖⠓⣾⠻⠒⠺⡖⡟⡖⢺⠖
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢸⣏⣭⣍⣉⣻⣋⣹⣉⣙⣉⣹⣏⣹⣉⣉⣭⣍⣿⣉⣉⣍⣉⣏⣹⣻⣉⣙⣉⣭⣉⣉⣉⣏⣙⣛⣏⣉⣉⣉⣏⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠰⠆⠠⠀⠄⠀⠀⠀⠀⠀⢸⣏⣙⣩⣭⣍⣏⣏⣛⢽⣩⡋⣏⣛⣉⣛⣫⣙⣿⣙⣿⣍⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⡄⣠⠀⡄⠀⠀⠀⠀⠀⢸⡿⠿⠛⠛⡟⠛⡟⠟⢻⡻⢻⡻⡟⡟⡟⢻⠟⠛⢻⠻⠛⢻⠟⠟⡟⠻⠛⢛⢻⠟⠛⠻⢛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⢀⠀⡀⠀⠀⠀⠀⠀⢸⡿⠿⢿⠿⢿⣿⠿⡿⡿⡿⢿⠿⡿⡿⡿⠿⣿⠿⡿⢿⠿⡿⠿⡿⠿⡿⠿⡾⢿⠿⡿⣿⡿⡿⠿⢿⢿⠿⡿⠿⡿⠿⠿⢿⣿⣿⡿⠿⠿⡿⣿⣿⡿⢿⠿⢿⢿⠿⢿⡿⡿⣿⣿⣿⣿
⠀⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⢸⡷⣶⣾⣶⣿⣾⣶⣷⣿⣶⣾⣷⣷⣷⣷⣾⣾⣶⣷⣶⣶⣷⣶⣶⣶⣷⣶⣷⣾⣶⣶⣷⣷⣶⣶⣾⣶⣶⣷⣶⣷⣾⣶⣶⣿⣿⣾⣿⣶⣷⣶⣿⣿⣶⣶⣾⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠈⠁⠈⠀⠁⠈⠀⠀⠀⠀⢸⣿⣵⣿⣶⣴⣦⣧⣥⣼⣶⣴⣦⣧⣦⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠂⠐⠀⠂⠐⠀⠀⠀⠀⢸⣿⣯⣿⣥⣿⣯⣬⣯⣥⣭⣯⣭⣥⣭⣽⣭⣽⣯⣽⣽⣯⣽⣭⣯⣭⣧⣿⣽⣭⣭⣽⣯⣯⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠒⠲⢶⠒⠀⠀⠠⠠⠀⠀⢸⣟⣋⣛⣻⣻⣉⣛⣟⣛⣟⣿⣻⣟⣻⣛⣛⣋⢻⣛⣛⣻⡟⣛⣟⣛⢛⣏⣛⣻⣻⡟⢛⢻⣿⣛⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⠤⢤⣤⠤⠀⠀⣀⢀⢀⠀⢸⣟⠛⣛⢻⢻⡛⠛⠻⣟⢻⠿⢿⢛⠿⣛⠿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢤⠤⢤⣬⡤⠀⠀⠀⣀⠀⠀⢸⣿⡿⢿⡿⢿⢿⠿⡿⡿⡿⢿⠿⡿⢿⡿⢿⣿⠿⠿⢿⠿⠿⠿⡿⢿⢿⠿⠿⡿⠿⡿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣀⣈⣁⣀⠀⠁⠉⠈⠈⠀⢸⣷⣶⣶⣷⣾⡾⣶⣾⣧⣶⣼⣶⣶⣶⣧⣶⣾⣶⣶⣾⣶⣶⣾⣷⣶⣿⣦⣶⣿⣷⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠋⠀⠀⠀⠁⠈⠀⠁⢸⣷⣤⣧⣤⣤⣤⣴⣤⣷⣥⣼⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠉⠉⠛⠉⠀⠀⠒⠐⠀⠂⢸⣗⣹⣋⣭⣩⣽⣹⣋⣀⣙⣏⣉⣫⣽⣉⣽⣭⣩⣝⣏⣩⣉⣯⣟⣉⣙⣏⣛⣅⣏⣏⣭⣾⣙⣭⣏⣯⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠒⠒⠶⠒⠀⠀⠠⠤⠀⠀⢸⣟⣋⢛⣛⡟⣛⣿⢛⣯⣹⣟⣛⡟⣛⣟⣟⣛⣛⣻⣯⣿⣛⣻⣻⣽⣻⠛⣻⣉⣿⣛⣛⣻⣛⣻⣯⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠤⠤⢤⣤⠤⠀⠀⢀⢀⠀⠀⢸⡟⡿⣿⠿⡿⠿⣿⠛⡿⠟⢿⢿⣿⠿⡟⠻⢿⢿⠿⢿⠿⡿⢿⠿⡟⠿⢻⣿⡿⡟⣿⢻⡟⡟⠻⡿⠿⣿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⢿⣿⢿⣿⡿⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣀⣈⣙⣀⠀⠀⠉⠈⠈⠀⢸⣿⣾⣶⣯⣶⣼⣾⣶⣾⣾⣶⣷⣾⣾⣷⣶⣾⣷⣿⣶⣾⣷⣦⣷⣿⣿⣶⣶⣼⣷⣿⣶⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡛⡟⡟⣿⡛⡟⣟⢻⡃⠀⡤⡀⡄⡄⡄⡄⠄⢠⠀⠀⣿⡏⡏⢿⡟⢻⡟⣿⣟⣿⢻⣛⢻⣿⣻⡏⡏⢻⡟⢻⢿⣿⢹⣝⢿⡟⣽⢿⡟⣿⠻⣟⠘⣿⢹⡟⡻⣿⡿⢻⣿⠻⡟⢻⣿⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠨⠤⠡⠥⠭⠬⠥⠧⠮⠤⠤⠁⠁⠁⠁⠀⠁⠈⠀⠁⠀⣿⣷⣿⣾⣷⣾⣷⣿⣶⣿⣾⣿⣿⣾⣾⣷⣿⣾⣷⣾⣿⣿⣾⣷⣿⣷⣿⣿⣷⣿⣾⣿⣶⣿⣶⣶⣿⣷⣿⣾⣿⣼⣿⣾⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣤⣤⣤⣤⣤⣤⣤⣤⠀⡀⢀⣀⢀⢀⢀⢀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⡟⣿⣿⣿⢻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⢸⢁⠃⡃⣈⢂⢘⣠⢀⣀⠁⠂⠀⠈⠘⠈⠀⠂⠀⣿⣿⣭⣿⣷⣼⣿⣧⣼⣧⣶⣿⣿⣷⣦⣧⣾⣹⣧⣼⣿⣼⢏⣿⣤⣿⣿⡅⣼⣧⣿⣿⣧⣿⣹⣧⣼⣷⣿⣷⣧⣿⣼⣮⣿⣿⣼⣽⣧⣼⣿⣤⣽⣿⣯⣿⣿⣿⣿
⠀⠒⠲⠲⠲⠒⡒⠀⠤⠀⠄⠠⠀⠄⠀⣿⣻⣛⣛⣛⣻⣻⣟⣿⣟⣿⣻⣟⣿⣟⣟⣻⢛⣻⣿⣿⣿⣻⣻⣟⣛⣿⣻⣿⣻⣙⣛⣻⣟⣟⣛⣛⣟⣟⣿⣟⣛⣻⣙⣛⣛⣻⣿⣻⣿⡿⣻⣛⣟⣙⣛⣻⣿⣿⣿⣿⣿⣿
⠐⡶⠒⠲⠶⡖⠠⠄⠀⢠⢀⢄⠀⣟⣛⢻⡛⣛⢟⣟⠿⣟⡻⠛⢻⢻⡛⠛⢛⠟⠻⡻⡟⠛⠻⣻⠛⢛⡟⠛⢻⡟⠻⢻⠛⢻⡻⠛⣻⡛⠟⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⢿⡿⡿⡿⣿⢿⠿⣿⣿⣿⡿⣿⢿⡿⠿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠁⠀⠁⠀⠀⠈⠉⠀⠀⠀⣿⣿⣷⣶⣷⣿⣷⣾⣿⣶⣾⣶⣾⣿⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠋⠉⠉⠉⠋⠀⠀⠐⠒⠀⠀⠀⣧⣤⣘⣻⣁⣛⣇⣈⣩⣍⣉⣹⣉⣉⣉⣏⣏⣽⣀⣩⣝⣛⣺⣋⣉⣟⣘⣹⣹⣩⣝⣉⣻⣋⣉⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⡖⠒⠒⠒⡖⠠⠄⠠⠄⠀⠄⠀⡏⣛⢻⠛⡛⡟⠙⡿⠛⡟⠙⢿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⡤⠤⢤⡤⡤⢀⡀⠀⣀⠀⡀⠀⡿⢿⢿⠿⠿⠿⡿⡿⢿⠛⠿⠿⠿⠿⢿⢿⠿⠿⠿⠿⢿⠿⡿⡿⠿⠿⠿⡿⡿⠿⡟⡿⣿⠿⠟⢿⠿⠿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠈⠈⠈⠠⣷⣶⣷⣶⣶⣶⣷⣷⣶⣾⣶⣷⣶⣶⣾⣾⣶⣶⣷⣾⣾⣶⣧⣶⣼⣶⣶⣶⣷⣶⣶⣷⣾⣷⣶⣷⣴⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠋⠈⠈⠉⠋⠀⠀⠐⠐⠐⠀⠀⣷⣶⣼⣤⣼⣩⣤⣽⣦⣤⣼⣦⣤⣇⣥⣤⣾⣴⣥⣬⣾⣶⣮⣦⣧⣷⣶⣷⣁⣬⣦⣯⣤⣥⣬⣦⣭⣼⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠖⠒⠖⠒⠖⠀⠀⠠⠤⠀⠀⠀⣟⣻⣟⣛⣻⣻⣛⣻⣟⣛⣿⣻⣛⣿⣙⣻⣿⣛⣟⣛⣛⣝⣿⣿⣹⣛⣿⣛⣹⣙⣿⣏⣛⣉⣿⣹⣉⣛⣛⣻⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠠⡤⠤⢤⠤⡤⢀⠀⢀⣀⠀⠀⠀⡿⡻⠿⢿⡿⠿⡟⠿⣿⠿⣿⠿⡿⠻⣿⠿⡟⡿⠿⢿⠿⠿⢻⠿⣿⢿⣿⣟⠟⡿⢿⡿⠟⠿⢿⡻⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣿⣾⣶⣷⣷⣾⣶⣿⣶⣷⣶⣾⣾⣶⣷⣾⣾⣶⣶⣾⣶⣶⣾⣿⣷⣷⣷⣷⣷⣶⣶⣿⣷⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠃⠀⠈⠀⠃⠈⠁⠈⠉⠐⠁⣀⣧⣬⣤⣮⣴⣮⣿⣿⣦⣴⣯⣴⣿⣥⣬⣭⣬⣽⣤⣬⣯⣮⣧⣤⣼⣥⣿⣧⣮⣤⣾⣥⣤⣥⣤⣬⣽⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀
⠀⢀⣴⣿⠛⠛⣿⣿⣿⠛⠛⢿⣦⠀⠀
⢀⣼⣿⣿⣶⠾⣿⣿⣿⠷⣶⣿⣿⣇⠀
⢸⣿⣿⣿⣧⣀⣿⣿⣿⣀⣼⣿⣿⣿⡇
⢸⣿⡟⠛⠿⠿⠿⠿⠿⠿⠿⠋⢻⣿⡇
⠈⢻⣷⣄⠀⣤⣤⣤⣤⣤⠀⢠⣼⡟⠁
⠀⠘⢻⣿⣷⣀⣀⣀⣀⣀⣼⣿⠟⠁⠀
⠀⠀⠀⠉⠉⠿⠿⠿⠿⠟⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠺⠋⠝⠗⠏⠓⠘⠜⠻⠇⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠛⠐⠂⠀⠈⠛⠀⠀⠀⠛⠀⠀⠠⠃⠀⠘⠀⠀⠀⠙⠘⠀⠀⠒⠃⠸⠂⠁⠀⠀⠐⠃⠚⠓⠀⠀⠸⠛⠂⠀⠀⠃⠛⠀⠀⠀⠐⠓⠉⠓⠗⠒⠀⠀⠁⠘⠀⠀⠛⠘⠘⠆⠀⠀⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡤⠤⠤⠤⠤⡤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢠⠤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⠤⣤⣤⠤⣤⣤⣤⠤⡄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀
⠀⢸⡇⣰⢆⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣧⣬⣤⣤⣿⣷⣶⣆⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣵⣶⣾⣰⣾⣿⣿⣯⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⡿⣿⣻⡿⣿⡿⣿⣿⢿⡿⣿⢿⢿⣿⣿⢿⣿⢿⣿⣿⢿⢿⣿⣿⣻⣿⢿⢛⢻⣻⣿⡿⡛⣿⡿⣿⣿⢿⠟⢻⢟⢿⡿⣿⣻⣿⡻⣿⣻⠿⡻⢟⣿⡛⣿⡿⡿⣻⡿⡿⣿⣿⣽⡻⣿⣛⣻⣿⠀⠀⠀
⠀⢸⣿⣿⣿⢿⣿⣿⢿⣿⣿⡿⡿⣿⣿⣿⣿⣿⢿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⢿⡿⣿⢿⡿⡿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⢿⡿⡿⡿⣿⡿⣿⡿⣿⣿⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣫⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣃⣏⣛⣽⣹⣯⣿⣳⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⡿⠿⣿⢿⣿⣿⣿⣿⢿⢿⣟⡿⣿⠿⣿⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣦⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣼⣿⣮⣦⣿⣦⣾⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣷⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣾⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣽⣿⣽⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣛⣛⣛⢿⡟⣛⣛⣿⢟⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣷⣿⣷⣿⣿⣿⣽⣿⣿⣿⣿⣽⣮⣽⣥⣭⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣿⣴⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣯⣿⣿⣿⣯⣿⣻⣿⣿⣿⢻⣿⣿⣟⣙⣿⣿⣯⣯⣿⣿⣽⣿⣿⣿⣽⣿⣽⣽⣿⣯⣯⣿⣿⣿⣭⣻⣿⣿⣿⣿⣽⣯⣿⣿⣯⣿⣿⣻⣿⣿⡿⣿⣟⣿⣯⣿⣫⣝⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⢿⡿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⢿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⣾⣶⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⢟⣿⣟⣿⣿⣿⣿⡿⣿⡟⣿⣻⣿⣻⣛⢛⣟⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣛⣛⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠸⠚⠰⠾⠧⠐⠖⠶⠀⠽⠴⠆⠰⠞⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠋⡭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⣀⠀⠀⡀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠙⠋⠛⠃⠀⠀⠘⠋⠙⠛⠋⠀⠀⠙⠘⠃⠋⠃⠃⠀⠉⠙⠁⠛⠋⠑⠃⠀⠈⠀⠈⠃⠁⠛⠫⠐⠀⠀⠙⠨⠋⠂⠀⠘⠋⠋⠘⠀⠀⠚⠘⠁⠀⠈⠛⠁⠃⠈⠢⠈⠓⠃⠀⠂⠛⠙⠛⠁⠒⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⡤⢠⣤⢄⠀⢀⡀⠀⢤⢀⠤⢤⣤⣦⠄⠀⠀⠠⣤⣴⠀⠠⡄⣤⢤⢄⠀⠀⠠⡄⠒⡤⡤⣦⡄⠀⡤⣴⣤⢠⠄⠀⠀⢤⡤⠀⣤⣴⡤⠀⠀⠤⣤⡤⣤⡄⢀⠲⢰⡄⠀⠀⡀⢤⣦⢤⣤⣤⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠙⠀⠘⠃⠀⠓⠋⠐⠁⠀⠘⠀⠃⠛⠃⠀⠀⠛⠛⠁⠃⠿⠃⠀⠀⠐⠙⠘⠃⠂⠀⠀⠃⠈⠙⠛⠋⠃⠀⠀⠙⠘⠃⠐⠀⠓⠋⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⢀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠈⠚⠚⠀⠛⠛⠊⠛⠈⠒⠚⠃⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠱⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⠀⡀⢀⠀⠄⢀⣀⢀⠀⡀⢀⢀⢠⣀⣄⢀⢀⣀⡀⡀⢀⢀⡀⣠⡀⡀⡀⣀⢠⣄⡀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠈⠁⠀⠀⠁⠁⠀⠋⠀⠈⠀⠈⠉⠁⠁⠀⠉⠉⠀⠀⠁⠁⠉⠀⠀⠀⠉⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⠶⠂⠾⠶⠒⠦⠐⠡⠶⠆⠲⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠡⠄⠁⠕⠀⠱⠶⠸⠀⠅⠕⠿⠃⠈⠠⠾⠶⠇⠏⠸⠈⠷⠶⠾⠿⠑⠅⠨⠺⠶⠼⠅⠺⠀⠇⠈⠨⠸⠆⠿⠑⠇⠱⠀⠇⠿⠪⠗⠸⠁⠈⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀
⠀⢀⣴⣿⠛⠛⣿⣿⣿⠛⠛⢿⣦⠀⠀
⢀⣼⣿⣿⣶⠾⣿⣿⣿⠷⣶⣿⣿⣇⠀
⢸⣿⣿⣿⣧⣀⣿⣿⣿⣀⣼⣿⣿⣿⡇
⢸⣿⡟⠛⠿⠿⠿⠿⠿⠿⠿⠋⢻⣿⡇
⠈⢻⣷⣄⠀⣤⣤⣤⣤⣤⠀⢠⣼⡟⠁
⠀⠘⢻⣿⣷⣀⣀⣀⣀⣀⣼⣿⠟⠁⠀
⠀⠀⠀⠉⠉⠿⠿⠿⠿⠟⠉⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⠉⣙⣟⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠀⠿⢻⣿⡻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣶⣖⣂⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⣍⣉⡍⢭⠍⢩⢭⡭⣭⡍⢭⣭⣭⣭⡭⣭⣭⠭⣭⣭⡍⡍⢩⠉⡭⣭⢭⣭⡍⢩⡭⣭⡍⣭⡭⡍⢭⡍⢩⣭⡭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿
⣿⡇⠤⢾⡷⠶⠦⠰⠴⠠⠶⠆⠴⠤⠰⠤⠄⠠⠤⠄⠦⢰⠖⢖⠠⠀⠠⠂⠄⠤⠤⠠⠤⠰⠠⠤⠤⠄⡤⠤⢤⠶⠤⠠⠶⠤⠠⠤⠄⡄⢠⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠶⠶⠆⠶⠂⠰⠲⠖⠶⠆⠲⠶⠶⠶⠖⠶⠶⠂⠶⠾⠆⠆⠐⠀⠶⠶⠀⠶⠶⠖⠶⠰⠶⠖⠖⠴⠀⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡷⠚⠲⠆⠛⠓⠘⠚⠐⠛⠃⠚⠒⠘⠒⠂⠑⠒⠃⠓⢸⠋⢫⠐⠀⠓⠚⠀⠛⠒⠂⠓⠚⠘⠒⠀⠓⠒⠃⠓⠒⠒⠐⢚⠒⠒⠂⠂⠒⠂⢒⠚⠒⠂⠛⠒⠒⠀⠒⠲⠒⠂⠐⠘⠚⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠛⠛⠃⠙⠁⠘⠙⠋⠛⠃⠑⠛⠛⠛⠋⠛⠛⠉⠛⠛⠃⠃⠈⠀⠛⠃⠛⠛⠛⠛⠀⠛⠛⠀⠃⠘⠛⠛⠙⠛⠛⠘⠙⠀⠛⠙⠛⠋⠃⠉⠛⠁⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡟⣀⣀⡀⣀⡀⢀⢀⡀⣀⡀⡀⣀⣀⣀⣀⣀⣀⡀⣀⣠⡀⡠⢀⠀⣀⣀⣀⢀⣀⠀⣀⣀⣀⣀⣀⡀⣀⣀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⣭⣉⡅⣬⣄⢨⢩⣁⣅⡅⣨⣍⢩⣉⡅⣍⣉⡄⣭⢩⡥⡥⢠⠀⣍⣉⠈⣄⡉⣀⣉⣉⣉⣀⢩⣡⣉⢩⣅⣩⢩⣉⣩⠀⢠⣄⣀⡤⢀⠀⣀⣄⢀⢀⣀⣀⣀⡀⢠⣀⢠⢤⣀⢀⣄⣀⣀⢀⣤⣀⣄⣀⣀⠀⣿⣿
⣿⡇⣤⣬⡅⢤⠄⢠⣠⡄⡤⡄⠄⡤⣤⣤⡤⣤⣤⠄⣤⣼⠖⡞⠠⠀⣤⡄⣦⡦⡄⢥⣤⡤⣤⠀⣤⡤⣤⡄⢰⢤⠠⣤⠤⡥⢠⣤⡤⣧⣤⣤⡦⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠶⢤⡆⠶⠦⠰⠰⠤⠦⠆⠴⠦⠴⠤⠆⠶⠤⠆⠶⢰⠖⢖⠰⠀⠶⠂⠤⠆⠶⠄⠦⠦⠴⠤⠆⠠⡤⠐⠲⠴⠰⠦⠴⠆⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠶⠶⠆⠲⠂⠰⠴⠆⠖⠆⠂⠶⠖⠶⠖⠶⠶⠂⠶⠾⠋⠯⠐⠀⠶⠶⠀⠷⠶⠒⠖⠶⠶⠶⠆⠰⠖⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠛⠲⠇⠛⠃⠘⠙⠓⠛⠃⠚⠓⠚⠒⠃⠛⠒⠃⠛⠸⠋⠣⠘⠀⠓⠚⠒⠐⠛⠓⠒⠃⠘⠒⠳⠚⠒⠐⠒⠖⠒⠁⠐⠑⠛⠚⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⣀⠀⡀⣀⡀⢀⣀⡀⣀⡀⢀⡀⣀⢀⣀⣀⡀⡀⣀⣀⠀⢀⣀⠀⠀⣀⣀⣀⣀⢀⡀⢀⢀⠀⡀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⣉⣙⡃⣉⡍⢈⣩⡁⣍⡁⡈⣉⣉⣉⣁⣉⣉⡁⣉⣈⠀⢈⣈⠉⡬⡉⣈⣍⣉⡉⣁⣬⠉⣉⣉⡁⣁⣉⣍⣀⣀⣀⡀⣀⣀⣠⣀⣀⡀⣄⣄⡀⣀⣀⣀⡀⣀⣀⡀⣀⣀⣀⠀⣤⣀⡀⣀⣀⣀⣄⡀⠀⠀⠀⣿⣿
⣿⡇⣭⣉⡅⣬⣅⢨⣬⡄⣭⡄⢠⣅⣥⣨⡥⣭⣌⡄⣭⢥⠀⢨⣭⣀⡅⢡⢬⣄⡍⣠⣅⡥⢡⣈⢀⢥⣬⣅⢭⠈⡅⣭⣠⣍⣉⢉⡉⠡⣥⡉⣭⡅⣨⣅⡍⣤⣬⠀⠁⠉⠉⠉⠀⠁⠉⠀⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿
⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣷⠶⠤⡆⠶⠦⠰⠶⠆⠶⠂⠰⠦⠶⠴⠖⠶⠶⠆⠶⠶⠀⠰⠶⡶⠦⠆⠶⠆⠲⠰⠀⡶⠴⠀⠖⠶⠄⠶⠦⠶⠶⠶⠴⠦⢶⠆⠢⠦⠶⠴⠶⠰⠶⠀⠶⠴⠀⠶⠲⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡟⠒⠶⠆⠚⠓⠘⠚⠂⠏⠁⠂⠖⠚⠒⠆⠖⠒⠃⠶⠐⠀⠐⠐⠒⠰⠒⠒⠛⠗⠒⠀⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡇⠛⠒⠇⢛⡓⢘⢛⠃⣛⡁⠘⠓⢛⠚⠛⠛⠛⡃⠛⠛⠀⠘⠛⠀⠃⠘⣛⡈⠛⠚⠈⠛⠃⠀⠀⡀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣟⣛⠛⡃⣙⡋⢘⣙⡀⣋⡀⢁⡋⣊⢙⣃⣛⣙⡁⣛⣈⠀⢈⣊⣉⡘⢙⢙⣉⣚⣁⣉⣉⡉⡉⡀⢙⣀⣋⣁⢙⡋⢋⣘⡁⢀⣀⣀⡀⢀⠀⣀⣀⠀⡀⣀⢀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣯⠉⠉⠃⠉⠉⠈⠉⠁⠉⠁⠈⠉⠉⠉⠁⠉⠉⠁⠉⠉⠀⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠁⠈⠁⠈⠉⠉⠉⠁⠉⠈⠉⠉⠘⠉⠉⠁⠉⠀⠉⠉⠁⠉⠉⠉⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⡏⣤⣠⡄⣤⣄⢠⣤⡄⣤⡄⢤⣤⣤⣤⡤⣤⣤⡄⣤⣤⠀⣤⣠⣤⡄⢠⣤⣤⣤⣤⣤⢠⣤⣄⣤⣤⠀⣤⣤⣤⣤⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⡄⠀⠀⠀⢀⢀⢀⣀⣀⡀⣀⡀⢀⢀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣴⣦⡀⠀⠀⠈⠛⠛⠁⠚⠋⠋⠙⠈⠊⠛⠃⠈⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢁⠰⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⢄⠀⡀⢀⠀⡀⡀⡠⠀⣀⢀⣀⢀⠀⢀⢀⢀⠀⢀⣀⢀⠀⢀⡀⣄⠀⠀⠀⣀⢀⢀⠀⣀⣀⣠⠀⠀⢀⣀⠀⡀⡀⠀⣀⡀⢀⢀⠀⣀⠀⣀⣀⡄⢀⣠⣀⢀⣀⠀⠀⠀⡀⢀⣀⡄⣀⠀⣀⢠⣀⡀⠀⠀⠀⠀
⠀⠀⠘⠉⠁⠈⠀⠈⠀⠁⠁⠁⠉⠐⠈⠁⠁⠈⠈⠁⠁⠈⠛⠈⠀⠉⠁⠉⠁⠈⠈⠉⠉⠉⠀⠉⠉⠉⠀⠁⠈⠉⠀⠁⠁⠈⠉⠁⠉⠀⠁⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠁⠈⠈⠈⠉⠉⠁⠉⠀⠁⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠔⠰⠾⠁⠔⠶⠀⠆⠝⠀⠰⠂⠶⠆⠰⠐⠖⠆⠰⠄⠶⠖⠆⠀⠶⠀⠀⠦⠆⠶⠆⠠⠀⠽⠄⠂⠰⠦⠀⠆⠀⠼⠸⠱⠰⠂⠴⠖⠆⠆⠖⠰⠗⠖⠄⠰⠲⠀⠼⠶⠶⠢⠲⠀⠔⠇⠃⠀⠰⠀⠷⠄⠀⠀⠀⠀
⠀⠀⢄⠠⣠⠀⡄⠄⢤⢀⢤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⢀⠀⡀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠛⠚⠃⠚⠛⠋⠙⠈⠒⠚⠃⠘⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢉⠱⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢤⢀⡀⠀⠀⣀⣀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⣀⡀⡀⠀⢀⣀⡀⡀⠀⣀⣀⡀⢀⣀⣠⣀⣀⠀⢀⡀⡤⠄⣤⣠⢤⠄⣀⣀⡀⢀⣀⡀⢠⢀⣠⣀⣄⡀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠈⠀⠀⠈⠀⠉⠉⠀⠀⠀⠋⠈⠀⠘⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠉⠀⠁⠀⠈⠈⠀⠀⠀⠉⠉⠁⠀⠀⠁⠁⠈⠀⠁⠈⠀⠈⠉⠐⠈⠉⠀⠈⠀⠉⠈⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⢲⠶⠀⠸⠆⠀⠀⠰⠶⠀⠀⠰⠸⠇⠀⠀⠸⠗⠀⠰⠶⠷⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠏⠀⠀⠀⠠⣰⣤⡤⢤⣄⠤⣄⢠⢢⣤⡤⢤⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡴⠾⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡢⡂⢄⠠⢀⠄⡄⣢⢔⠄⣤⢴⢔⠀⣤⡄⡆⢐⢤⣤⣤⠂⠂⢠⣰⣦⡔⢔⠀⢢⣤⡀⣶⠄⡐⠠⣰⠂⡆⢠⣤⢤⡆⡆⡢⠀⡔⢢⡠⣤⠂⢢⡄⢠⣤⡤⡀⢐⣄⡤⡐⠀⢠⣠⢠⢰⢀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣀⢀⢀⠀⣀⣀⢀⠀⡀⡀⣀⠀⣀⢀⢀⠀⢀⢀⢀⠀⡀⡀⡀⣀⢀⠀⢄⢈⠀⡀⢀⢀⣀⢀⠀⡀⣀⢀⠀⢄⡀⢀⣀⣀⢀⢀⣀⢀⢀⢀⡀⡀⡀⣀⡀⢀⠀⢀⢀⢀⡀⣀⡀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠐⠘⠀⠛⠃⠑⠀⠘⠊⠉⠁⠃⠙⠘⠁⠑⠑⠀⠘⠀⠘⠂⠙⠑⠈⠘⠛⠈⠀⠘⠘⠀⠙⠁⠛⠃⠑⠀⠘⠃⠀⠊⠛⠘⠘⠀⠘⠘⠋⠃⠃⠁⠋⠀⠘⠀⠃⠐⠙⠙⠋⠀⠐⠁⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠺⠶⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢆⣦⣤⠠⣦⡤⠤⡄⡔⣠⣤⡤⡤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠶⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⠢⡆⢰⢰⢔⠐⣴⡦⡂⠂⣲⡀⣶⢆⠢⢰⠂⡆⡆⠐⣴⣴⡆⢰⢔⠐⢢⣤⢔⡖⢰⠀⣲⢔⠀⢠⠂⡂⠐⣴⡆⢰⡦⢀⠂⣄⡶⢰⠐⠐⣴⢴⢰⢔⠐⢰⡖⢴⠀⡂⡆⡆⡆⠴⣦⣴⣆⢰⡆⡆⡆⠀⠀⠀
⠀⠀⢀⣀⡀⡀⡀⣀⢀⢀⣀⡀⣀⢀⡀⣀⡀⡀⠀⢀⡀⡀⡀⣀⠀⡀⣀⡀⡀⠀⡀⡀⣀⢀⡀⡀⡀⢀⢀⠀⣀⢀⡀⡀⣀⢀⢀⢀⡀⡀⡀⠀⢀⢀⣀⢀⢀⡀⢀⡀⡀⡀⣀⡀⡀⢀⠀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠛⠈⠊⠊⠘⠙⠑⠐⠘⠘⠘⠈⠊⠈⠂⠐⠐⠋⠋⠂⠃⠀⠃⠃⠀⠃⠀⠃⠈⠚⠘⠉⠃⠃⠀⠐⠙⠁⠐⠋⠋⠚⠑⠙⠐⠁⠋⠂⠒⠈⠙⠓⠑⠁⠁⠀⠂⠋⠂⠀⠀⠋⠐⠉⠊⠉⠊⠃⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢐⠂⠀⠀⠀⣄⡀⣀⣄⢀⣀⣀⣀⢀⠄⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⣤⣤⡀⠀⠀⠉⠀⠈⠉⠀⠉⠈⠈⠈⠈⠉⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢊⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⢀⢤⡀⣤⣠⣠⠠⠀⣄⡄⡠⢀⠀⢄⣠⡄⢄⣄⣠⢀⠄⠀⡄⡄⢄⠄⠀⣤⡄⠀⠄⢄⣠⢠⠠⡄⢠⣄⠄⣀⢀⠀⣄⡤⡠⠀⠠⢠⠀⢄⣠⡠⠀⠤⡀⡄⣄⣄⡄⠀⡠⣄⢠⠠⡠⢠⡀⡠⠠⡄⢄⡄⠀⠀⠀⠀
⠀⠈⠈⠈⠀⠉⠈⠈⠀⠀⠉⠁⠁⠈⠀⠁⠉⠁⠈⠁⠉⠀⠁⠁⠁⠁⠁⠈⠈⠉⠉⠈⠁⠀⠈⠈⠀⠁⠈⠁⠁⠉⠈⠈⠀⠁⠈⠀⠈⠈⠀⠁⠉⠈⠀⠉⠁⠁⠁⠁⠁⠀⠈⠁⠈⠀⠁⠈⠈⠁⠈⠁⠉⠁⠀⠀⠀⠀
⠀⠸⠪⠪⠒⠄⠱⠿⠈⠨⠺⠑⠆⠇⠹⠇⠃⠕⠰⠋⠵⠏⠂⠈⠮⠇⠪⠈⠀⠵⠽⠉⠮⠺⠉⠕⠛⠂⠇⠸⠺⠸⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠅⠀⠀⠀⣦⠄⣤⣤⠠⣤⢤⣤⢠⢂⣤⡤⢤⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠶⢶⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⡠⢄⡀⣰⣄⡄⡀⡄⠀⢠⣄⢠⠀⢠⠀⡠⣤⣤⢰⢤⢠⢠⠀⢀⢄⣴⢠⡠⡀⢠⡤⡄⢠⠀⡄⣢⣤⠀⡀⡤⣄⢀⣦⡀⠀⡆⢠⢠⢤⣤⡄⠀⣀⡄⡆⢠⢀⢤⠀⡠⣄⣰⣠⣤⡀⢄⢀⡄⣄⡄⠀⡀⣤⡄⠀⠀
⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠂⠛⠘⠓⠃⠋⠀⠍⠛⠃⠁⠐⠑⠋⠘⠁⠛⠓⠃⠀⠃⠀⠘⠛⠍⠀⠛⠈⠂⠋⠃⠘⠚⠚⠑⠘⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣘⡃⠀⠀⠀⠷⠆⡦⠶⠐⠴⠲⠶⠰⡡⢶⠖⠲⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠟⣛⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠔⠢⠰⠴⠆⠶⠀⠀⠷⠶⠦⠀⡒⠸⠀⠶⠰⠀⠐⠔⠂⢁⠁⠀⠶⣦⠀⠠⠂⠠⠆⠰⠦⠾⠆⠶⠄⠀⠰⠶⠸⠔⠀⠀⠀⠧⠶⠶⠄⠀⠺⠰⠔⠀⠰⢶⠔⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡶⠒⢒⢂⢤⠀⠀⠀⠀⠀⠀⣿⣿⣛⡟⠛⣛⠻⢻⡟⠙⢻⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠉⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⢿⢿⢿⣿⣿⢿⢿⣿⢿⣿⠿⡿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⢿⠿⢿⡿⣿⡿⣿⣿⡿⣿⣿⡿⢿⡿⣿⠿⣿⢿⠿⣿⢿⣿⣿⣿⣿⡿⡿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⣛⠉⣻⠠⠲⠀⠀⠀⠀⠀⠀⣿⣶⢶⢶⢿⠾⠾⣿⣿⢾⠷⢶⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣵⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣷⣿⣿⣿⣯⣷⣿⣾⣷⣿
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠭⠈⠝⠐⠙⠀⠀⠀⠀⠀⠀⣿⣾⣷⣿⣯⣤⣽⣿⣭⣥⣭⣽⣿⣿⣭⣽⣼⣬⣽⣭⣽⣿⣿⣿⣯⣭⣮⣯⣿⣿⣿⣯⣿⣿⣼⣿⣿⣏⣯⣽⣿⣿⣿⣥⣏⣽⣭⣩⣿⣼⣽⣽⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠃⢬⠈⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣧⣿⣿⣷⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⠀⠠⣠⡀⠀⠀⠀⠀⠀⢸⡟⡻⠿⣿⣿⣿⠿⠿⠟⠻⢿⠿⢿⢿⣿⣿⡿⠿⢿⠟⠿⠿⡟⡿⠿⢿⣿⣿⣿⢿⣿⣿⠿⣿⠿⡿⣿⡿⡿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣶⣷⣿⣿⣾⣶⣾⣿⣿⣶⣾⣾⣿⣷⣷⣾⣿⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣶⣾⣿⣿⣶⣷⣶⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠃⠀⠂⠊⠃⠀⠀⠀⠀⠀⢸⣯⣤⣬⣼⣤⣷⣿⣦⣼⣴⣽⣤⣿⣼⣤⣌⣀⣬⣿⣧⣷⣭⣬⣧⣬⣅⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡏⠛⣻⢟⠟⣛⡛⣿⣟⣻⣛⢛⢿⠟⠛⡛⣿⣟⠛⠛⣛⢻⢛⡿⠙⣿⢿⣛⣭⢙⠏⡿⣟⣿⢟⠛⠋⣹⡛⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠠⠤⣤⡄⠾⠻⠿⡟⣻⢿⡿⢿⡛⡟⠿⠿⣻⡟⠿⠻⠻⢿⠟⠟⠿⢿⣿⡿⡿⠿⡿⣿⣿⡿⠿⣿⣛⣿⣿⡿⡿⠻⣿⠿⢿⣟⣿⠿⡿⣿⡟⠿⠿⡿⡛⡟⣟⣿⡟⠿⣿⣿⢻⡻⡻⠻
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⡿⢾⠾⡿⢷⡶⢿⣶⠷⣷⠷⢷⢶⡿⡷⢶⠾⡿⣷⣶⣷⠶⡿⢷⣿⢷⢾⠷⣾⡶⣶⣿⣿⠿⣶⣾⣷⡾⣿⣿⣷⢾⣾⣿⢾⣷⡾⣿⢾⡶⣿⠿⣿⣿⣷⣷⣷⡷⣿⣶⣾⢾⣿⢿⡿⠿⡾
⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠋⠛⠛⠚⢻⣿⣿⣷⣾⣾⣷⣿⣿⣿⣦⣾⣿⣿⣿⣿⣶⣶⣾⣾⣾⣷⣿⣾⣧⣾⣿⣿⣷⣶⣷⣿⣿⣷⣿⣿⣷⣿⣧⣿⣾⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⠘⠃⠀⠂⠊⠃⠀⠀⠀⠀⠀⢸⣧⣽⣷⣵⣇⣥⣬⣮⣾⣭⣤⣼⣤⣽⣤⣬⣿⣬⣥⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠷⠇⠆⠽⠇⠲⠰⠆⠨⠇⠆⠰⠲⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠋⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠘⠋⠋⠀⠀⠛⠂⠀⠀⠀⠙⠛⠃⠀⠀⠙⠀⠈⠛⠋⠛⠁⠃⠐⠈⠛⠋⠃⠛⠀⠀⠀⠀⠂⠛⠀⠉⠚⠁⠀⠙⠘⠐⠀⠀⠙⠓⠈⠂⠀⠀⠋⠛⠏⠘⠙⠙⠐⠀⠘⠓⠁⠀⠉⠛⠸⠑⠀⠐⠛⠛⠁⠀⠀⠀
⠀⠀⢠⣤⢠⠀⢠⡆⣴⡤⣤⣤⠀⠀⢤⡤⢠⣴⠀⠀⠠⣤⡄⠀⢠⡆⡄⢠⡠⠠⣦⢤⡄⠠⡄⠠⣴⡤⣤⠄⠀⠀⢰⣤⢠⢄⠀⡀⣴⡄⠀⠀⢤⢠⣤⠄⠀⠀⣦⣤⠀⠠⡀⣤⣤⠀⢠⣤⡤⠀⠠⣤⠄⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⠙⠃⠀⠃⠚⠃⠀⠀⠀⠚⠛⠃⠀⠀⠀⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡒⠀⠀⠀⠀⡄⡄⡀⢠⣄⠀⡀⡀⠠⠄⢀⣀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣤⣤⣤⠀⠀⠀⠈⠉⠁⠈⠁⠀⠈⠁⠈⠁⠈⠉⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢀⣀⢠⣀⠀⠀⣄⣀⡀⠀⣀⠀⣀⠀⠀⠠⡀⠀⠀⣀⡀⢀⢄⠀⡀⣄⡀⠀⣠⢀⠀⢀⢀⢀⡀⡀⡀⠀⣄⣀⡄⡀⢀⣀⢠⠀⣀⡀⣀⢀⠀⢀⣀⢀⠀⡄⡀⡀⡀⡄⣀⡀⡀⠀⣀⣀⢠⠀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠁⠈⠉⠈⠁⠁⠈⠉⠉⠘⠀⠉⠘⠉⠁⠀⠈⠉⠀⠀⠉⠁⠉⠈⠈⠀⠉⠉⠈⠈⠘⠁⠈⠁⠁⠁⠁⠁⠀⠉⠁⠁⠁⠈⠉⠈⠀⠉⠁⠉⠉⠀⠈⠉⠀⠁⠁⠛⠈⠈⠁⠂⠉⠈⠀⠉⠉⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀
⠀⡦⠀⠖⠤⠶⠰⠄⠀⠦⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠣⠈⠂⠋⠊⠈⠚⠸⠁⠙⠑⠑⠅⠇⠑⠁⠉⠛⠋⠀⠆⠑⠛⠘⠨⠈⠘⠰⠉⠛⠀⠁⠙⠋⠊⠈⠃⠫⠀⠛⠋⠀⠑⠹⠈⠘⠑⠁⠑⠰⠉⠛⠀⠉⠁⠋⠃⠃⠁⠉⠈⠛⠈⠘⠫⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢤⣠⠤⢄⣤⡄⠆⡄⢄⡄⢠⣠⠠⠠⢠⣄⡤⠠⣠⣤⢠⠤⣠⠀⡤⡄⡦⣠⢀⠠⣠⣄⠄⠠⠠⣠⢤⡤⠀⢄⢤⢠⣄⢤⠀⠄⢤⡠⠀⡄⠠⢤⣤⠄⠠⢤⣤⣄⣠⠀⢀⠠⣠⡄⡠⠠⠠⣠⣄⠤⠄⡠⣤⡄⠀⠀⠀
⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠁⠈⠈⠈⠀⠀⠀⠀⠀⠈⠈⠈⠀⠈⠀⠁⠀⠉⠈⠈⠈⠀⠁⠁⠈⠀⠁⠈⠀⠀⠀⠉⠀⠀⠁⠁⠀⠈⠈⠈⠀⠈⠈⠉⠀⠀⠈⠈⠀⠈⠀⠈⠈⠈⠁⠈⠈⠀⠁⠁⠁⠁⠈⠁⠀⠀⠀⠀
⠀⠏⠱⠿⠸⠏⠀⠇⠰⠎⠷⠊⠸⠏⠸⠸⠸⠉⠸⠾⠁⠗⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⢀⡀⡀⢀⣀⢀⣀⠀⣀⡀⡀⡀⢀⡀⣀⢀⢀⣀⡀⣀⠀⣀⣀⠀⠀
⠀⠃⠘⠋⠘⠙⠀⠀⠁⠋⠻⠅⠀⠙⠋⠘⠅⠘⠙⠀⠛⠐⠀⠈⠃⠋⠀⠘⠙⠁⠈⠛⠛⠃⠀⠘⠛⠙⠂⠀⠈⠛⠙⠘⠀⠛⠙⠁⠘⠘⠋⠀⠓⠐⠀⠃⠘⠙⠘⠂⠈⠚⠋⠛⠐⠘⠈⠐⠂⠀⠛⠁⠐⠈⠘⠋⠀⠀
⠀⢢⠒⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠉⠉⠉⠉⠉⠉⢉⢉⠉⠉⠉⠉⠉⠉⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⠿⢛⢻⣿⠯⢿⣿⣿⡛⢻⣿⢻⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣟⣿⡿⢿⡿⣿⣿⣿⢻⣟⡿⣛⠿⣟⡛⣿⣿⣿⣿⣿⣟⣿⣿
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣟⣟⢛⣛⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⣿⣛⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣻⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣻⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠈⠀⠀⠀⠀⠀⢸⢿⣙⢙⢙⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⡉⢉⡉⠩⠩⡉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡿⣿⣿⣿⡿⣿⡿⣿⠿⢿⡿⣿⡿⢿⡿⢿⢿⣿⡿⣿⢿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣷⣷⣿⣿⣾⣶⣾⣶⣾⣾⣿⣾⣷⣿⣾⣾⣾⣿⣿⣾⣷⣷⣷⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⣏⡉⢏⣙⢩⠭⣍⣏⡏⣹⡙⣟⡭⣍⣩⣏⣉⣏⣉⣉⣭⣫⣭⣋⣯⢍⣹⡉⢏⣉⣏⣭⣙⣿⡋⢩⣋⣩⣏⣹⣍⣍⣹⣉⣝⣋⣽⣉⣽⣭⣩⣽⣍⣍⣹⣹⣭⣉⣽⣏⣭⣹⣭⣙⣿⣿
⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⣷⠶⠾⢶⠾⢶⠵⠶⢷⠶⠶⡧⠶⠷⠶⠾⠶⠦⠧⢶⠾⡶⠾⣶⢶⠾⣶⣶⣶⣾⣷⣷⣶⣾⣶⣶⣶⣾⣷⣾⣷⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠐⡿⠿⢾⠿⠿⠿⠿⠿⡿⢿⠾⠿⠿⡿⡿⠿⣿⡿⠿⠿⠿⡿⢿⠿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⡀⠀⠀⡀⡀⠐⡿⡿⠿⣿⠿⠿⢿⢿⠿⠿⠿⡿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⡀⠀⠀⡀⡀⠀⡟⠷⠿⣿⠿⠿⠿⢿⢿⢿⢿⠿⠿⠿⡿⠿⠿⢿⢿⠿⠿⣿⠻⠿⡿⠿⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⠀⠀⠀⠀⠀⡄⠀⠀⡿⠻⠿⠟⠿⠻⡻⠿⠻⠿⡿⠻⡿⠿⡿⠟⠿⠿⢿⠿⠿⠟⠿⠿⠿⠟⠻⡟⠻⠛⠛⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣛⣟⣛⢟⣟⣟⣟⣿⣟⣛⣛⣻⡟⣛⣟⣟⣻⣛⡻⣛⣻⣛⢛⢻⣟⣿⣟⣟⣻⣛⡛⣻⣻⣛⣟⣛⣛⣻⣛⣛⣿⣛⣟⣛⣛⣛⣛⣿⣛⣛⣛⣟⣿⣻⣛⣛⣻⣛⣻⣟⣛⣿
⠀⠐⠖⠒⠲⠆⠀⠀⠀⠀⠀⠈⣿⣉⣛⣏⣛⣻⣙⣛⣟⣛⣋⣏⣉⣹⣋⣏⣉⣛⣏⣻⣙⣹⣉⣛⣻⣋⣻⣙⣫⣟⣋⣟⣟⣻⣛⣛⣛⣛⣋⣟⣋⣏⣝⣹⣉⣛⣋⣻⣛⣟⣋⣙⣹⣛⣙⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠖⠒⠲⠖⠂⠀⠀⠠⠄⠠⠀⢸⣿⣩⣽⣹⡏⣛⣟⣛⣻⣟⣻⣻⣯⣍⣿⣛⣛⣙⣟⣻⣋⣟⣿⣛⣿⣿⣛⣻⣹⡛⣛⣛⣿⣛⣿⣻⣻⣟⣙⣿⣻⣛⣛⡛⣻⡛⣻⣛⣿⣛⣟⣙⣻⣝⣹⣟⣛⣟⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠀⣀⡀⠀⠀⠀⢀⡀⢀⠀⢸⣿⢛⣻⢻⡟⠿⡿⢿⢿⣿⢿⢻⣟⡛⠻⠿⡟⢿⡿⠿⢿⠛⡿⣿⠿⡿⠿⠿⠿⣿⠿⠻⡿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⢿⡷⣿⣿⣿⡿⣿⣿⢿⡿⡿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢾⣿⣿⡷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠐⠉⠓⠀⠀⠀⠈⠁⠀⠀⢸⣿⣾⣿⣾⣷⣶⣷⣾⣾⣿⣾⣶⣿⣷⣾⣿⣿⣶⣾⣶⣶⣶⣯⣶⣾⣶⣶⣶⣿⣷⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠋⠨⠛⠮⠀⠀⠀⠀⠂⠀⠀⢸⣯⣴⣬⣾⣦⣿⣮⣦⣽⣬⣾⣴⣯⣿⣤⣼⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠆⠀⠴⠆⠀⠀⠀⠀⠆⠀⠀⢸⣿⣹⣽⣻⣏⣉⣏⣹⣉⣭⣩⣉⣿⣏⣉⣽⣙⣉⣉⣍⣟⣏⣉⣹⣩⣉⣯⣉⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⡖⠒⢲⡖⠂⠀⠀⠀⡄⠀⠀⢸⣟⡛⠛⠛⣛⠟⢻⠛⠛⢛⡛⣿⠛⢛⡟⡛⡟⢛⢛⢛⡛⠻⠛⢻⠟⡟⡿⡿⡛⢻⠻⣟⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⡤⠤⢤⡤⠄⠀⠀⢀⡀⠀⠀⢸⡿⠿⠿⢿⣿⠿⠿⣿⣛⢻⣿⠿⡿⢿⠟⠿⡟⠿⠿⢿⠟⢿⠿⢿⠿⢿⣿⡿⠿⣿⠿⠿⣿⡿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣾⣿⣷⣿⣿⣾⠿⢶⣿⣷⣿⣿⣷⡶⣷⡷⣶⣿⣷⣿⣶⣿⣷⣿⣿⣾⣿⣾⣿⣿⣿⣷⣿⣷⢿⣷⡿⡿⡿⡿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠁⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⢸⣷⣶⣶⣾⣿⣶⣶⣿⣿⣾⣷⣴⣶⣶⣷⣾⣿⣶⣾⣶⣾⣷⣼⣷⣶⣷⣶⣶⣶⣷⣾⣶⣾⣾⣶⣶⣷⣷⣿⣷⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠋⠉⠛⠋⠁⠀⠀⠀⠂⠐⠀⢸⣯⣥⣭⣯⣿⣭⣥⣽⣶⣼⣿⣭⣿⣭⣽⣬⣽⣯⣭⣯⣭⣯⣽⣿⣬⣭⣽⣽⣿⣧⣭⣯⣯⣭⣭⣬⣽⣯⣭⣮⣯⣧⣶⣷⣥⣧⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠖⠒⠶⢖⠂⠀⠀⠠⠄⠠⠀⢸⣟⣛⣛⣟⣿⣛⣉⣻⣭⣩⣽⣛⣛⣻⣟⣻⣻⣻⣟⣋⣻⣻⣟⣹⣏⣻⣛⣻⣛⣙⣛⣛⣝⣿⣏⣭⣯⣉⣏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡤⠠⣤⡤⠀⠀⠀⢀⡀⠀⠀⢸⡿⠿⠿⡿⣿⠻⠛⢻⣿⠛⣟⠿⣻⢿⡟⣿⣟⣿⡟⡿⣿⠻⣻⠿⡿⡟⡟⡟⣟⡟⡿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡀⠈⣀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⠿⣿⡿⢿⠿⢿⣿⠿⢿⡿⡿⠿⡿⢷⠿⠿⠿⣿⡿⢿⢿⠿⡿⢿⣿⠿⡿⢿⠿⢿⠿⡿⠿⣿⠿⠿⢿⢿⣿⠿⡿⡿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣁⣀⣉⣁⡀⠀⠀⠈⠁⠀⠀⢸⣷⣶⣶⣷⣿⣷⣶⣾⣿⣶⣷⣶⣿⣶⣷⣾⣶⣷⣶⣶⣷⣾⣾⣶⣷⣷⣾⣶⣷⣾⣷⣾⣶⣷⣾⣶⣷⣷⣾⣶⣾⣶⣶⣶⣶⣿⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠃⠀⠚⠃⠀⠀⠀⠀⠃⠀⠀⢸⣧⣬⣤⣥⣥⣦⣤⣼⣿⣤⣤⣥⣼⣤⣧⣬⣼⣤⣬⣬⣤⣼⣽⣽⣴⣬⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠏⠉⠹⠏⠁⠀⠀⠀⠂⠀⠀⢸⣏⣙⣉⣍⣋⣍⣉⣹⣿⣉⣉⣹⣉⣹⣋⣉⣍⣉⣭⣏⣏⣏⣹⣹⣹⣉⣏⣫⣭⣉⣹⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠖⠒⠒⠒⠆⠀⠀⠀⠀⠀⠀⣿⠛⢛⡛⠛⡛⠛⢻⠛⠛⡛⠛⢛⠛⣟⠛⠛⠛⡟⢛⣻⠛⡟⣛⢻⠛⡛⢻⡟⠛⠛⠛⠛⡟⢻⢛⣛⢛⣛⠛⠛⡛⡟⢛⠛⢻⠻⠛⡟⡛⢛⢻⠛⢛⡛⢛⢻⠛⠛⣛⡻⡛⢻⡟⡟⡛
⠀⡄⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⣿⠛⠻⠛⠛⠻⠛⢻⠛⠛⠛⣛⡟⠛⠛⠟⢻⠛⠟⢿⠛⢻⠻⠛⠛⠟⠻⠛⠛⠛⡟⠟⡿⠻⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡤⠤⠤⠤⡄⢀⠀⢀⠀⠀⠀⣿⢿⠻⠿⢿⠿⠻⠟⠛⠻⠿⢻⠟⠿⡿⠿⠿⠿⠟⡿⡿⢿⠿⠿⢻⠿⡿⢿⠿⡿⠿⣿⢿⠿⢿⠿⢿⠿⠟⠻⢿⢿⡿⢿⢿⠿⡻⣿⣿⢻⠻⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⣿⢿⠿⠿⢿⠿⠿⠿⠛⢿⠿⠿⢿⠿⢷⠿⠿⠿⢿⠿⠿⠿⠿⡿⠿⠿⠿⢿⠿⠿⠾⡿⢿⣾⢿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⠿⢿⠿⠿⢿⠿⢿⠿⠿⠿⠿⡿⣿⠿⢿⡿⠿⠿⢿⠿⢿⢿⢿⠿⢿⢿⠿⡿⢿⠿⠿⠿⡿⠿⠿⠿⠿⡿⡿⠿⢿⡿⢿⠿⡿⠿⡿⠿⣿⠿⠿⡿⢿⢿⡿⢿⡿⠿⠿⢿⢿⣿⡿⡿⢿
⠀⣁⣀⣀⣀⡁⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⡶⣶⡶⣾⣶⣶⣶⣶⣶⢷⣶⣶⣷⢶⣶⣶⣶⣶⣶⣶⡶⣶⠾⡶⢶⢾⣶⣾⢷⣷⣷⣶⣷⣶⣷⣶⣶⣾⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣷⣾⣶⣾⣶⣶⣶⣶⣾⣶⣾⣷⣶⣶
⣀⣁⣀⣀⣀⣁⣈⣀⣈⣀⣀⣀⣟⡓⢒⡛⡚⣓⡓⡚⢒⢓⣛⠚⢓⣛⣛⢒⣛⢚⣛⣒⢚⣛⣓⢒⣒⣓⣒⡛⢚⣚⡓⣛⣒⣛⡛⢛⣛⣛⡛⡛⢛⢛⣛⣛⢛⢛⣛⡛⠛⠛⣛⣛⣛⣛⣛⡛⢛⣛⣛⢛⣛⣛⣛⣛⣛⣛
⠛⡛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⣿⠷⠶⣿⡶⠶⠾⡶⡶⠾⢿⢷⠶⢾⠶⣾⠶⢷⠷⠿⢾⠷⣶⡾⡿⠶⠾⠷⣿⢿⠷⣷⠾⣾⣷⣶⣶⣶⣶⣷⣿⣷⣶⣾⣷⣶⣿⣶⣾⣷⣶⣿⣶⣾⣾⣷⣾⣶⣷⣷⣾⣶⣶⣶⣶⣾
⣤⣥⣤⣤⣤⣥⣤⣤⣤⣤⣬⣤⡿⢶⠶⠶⠾⣶⠶⡾⣶⠶⠶⠶⣷⠷⠷⢶⣶⢶⠿⠶⢶⡷⠷⡶⢷⠶⡶⡷⣾⡶⡶⠾⠾⠿⠿⣿⡿⠿⣿⢿⡿⠿⡿⡿⠿⣿⠿⢿⡿⠿⠿⢿⡿⢿⡿⠿⠿⠿⠿⠿⢿⢿⡿⣿⠿⡿
⣻⡿⡿⣿⣿⣿⡟⡿⡿⢿⣿⣟⣷⢲⣷⡖⣶⣶⣶⣶⣷⢶⡞⡶⢶⡾⣶⠾⣾⢶⢷⣷⣶⣷⢶⢶⣶⣷⣿⣷⣶⣷⣶⣶⣾⣶⣾⣾⣷⣾⣶⣿⣿⣶⣿⣷⣷⣾⣶⣶⣷⣶⣶⣶⣿⣾⣿⣿⣶⣶⣶⣷⣶⣶⣶⣾⣶⣿
⠉⠉⠉⠉⠉⠉⡉⢉⠉⠉⠉⠉⣿⣟⠛⣿⠿⠿⡿⠟⠿⢿⢿⣛⠿⠿⠻⣿⡟⠿⠿⠿⡿⠛⣿⠛⡟⣿⢻⢻⢿⠿⠿⠻⠿⠟⡟⢿⡿⣿⠻⢿⡿⢿⠻⡿⡿⣿⠿⡟⢿⢛⠛⠟⡟⣿⣿⡿⠿⣿⣿⡟⡟⡿⣿⢿⡟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣏⣉⣉⣿⣩⣉⣉⣉⣛⣹⣉⣉⣉⣏⣉⣉⣍⣉⣉⣋⣉⣹⣙⣋⣈⣫⣩⣙⣋⣍⣏⣉⣏⣍⣩⣙⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣽⣩⣉⣩⣩⣯⣭⣽⣭⣭⣯⣫⣍⣹⣭⣩⣩⣍⣽⣽⣭⣍⣿⣉⣙⣏⣭⣩⣭⣍⣯⣍⣹⣏⣭⣍⣹⣉⣟⣉⣏⣋⣽⣹⣿⣫⣟⣯⣿⣿
⠀⠋⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⣿⣍⣩⣍⣉⣭⣉⣩⣉⣹⣉⣩⣯⣋⣩⣉⣍⣏⣹⣹⣭⣉⣹⣍⣭⣏⣉⣩⣍⣭⣭⣭⣭⣋⣩⣭⣫⣽⣿⣹⣹⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠸⠘⠀⠯⠀⠏⠃⠀⠒⠁⠈⠃⠃⠀⠀⢸⣧⣤⣄⣿⣥⣥⣾⣿⣤⣤⣄⣼⣿⣿⣿⣧⣸⣥⣤⣵⣿⣿⣤⣿⣧⣥⣴⣿⣧⣥⣬⣤⣼⣿⣿⣿⣥⣤⣿⣿⣿⣤⣼⣤⣼⣿⣯⣤⣼⣤⣼⣤⣤⣼⣤⣿⣧⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠃⠀⠾⠇⠰⠢⠖⠸⠁⠠⠲⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⣭⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠘⠃⠂⠀⠐⠀⠀⠐⠀⠁⠙⠛⠙⠋⠈⠓⠃⠀⠉⠋⠘⠙⠀⠘⠛⠑⠀⠙⠋⠘⠛⠁⠀⠚⠁⠂⠚⠟⠐⠀⠐⠙⠘⠁⠘⠋⠃⠐⠈⠋⠃⠀⠈⠛⠙⠀⠈⠆⠀⠛⠀⠀⠛⠛⠂⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣤⣄⡆⠀⣄⣴⣄⠀⢀⠀⣰⣄⡀⠀⡆⠀⢀⣴⣠⣄⠀⡀⠀⣠⣄⣆⠠⢤⡴⠀⡄⣦⡀⠀⣦⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⢀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⣄⣀⠀⠀⠘⠚⠘⠐⠛⠈⠋⠛⠀⠚⠘⠀⠋⠃⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡄⣀⠀⠀⠀⠀⢀⠀⠀⢀⠀⡄⣀⣀⠀⣀⣠⠀⠀⢀⡀⡀⡀⠀⢀⣀⡀⠀⠀⡀⡀⢀⡀⢀⠀⠀⠀⠀⡀⢀⡀⡀⠀⢀⡄⠀⣀⡀⢀⠀⣀⡀⣀⠀⢀⣀⣀⣀⢠⡀⠀⣄⢀⠀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠉⠀⠁⠀⠁⠀⠀⠁⠉⠈⠉⠑⠈⠁⠀⠉⠀⠀⠈⠁⠉⠉⠀⠈⠉⠉⠀⠈⠁⠉⠈⠉⠈⠁⠀⠀⠈⠁⠉⠁⠀⠀⠉⠁⠈⠉⠉⠈⠀⠉⠁⠉⠀⠈⠉⠉⠂⠈⠀⠀⠉⠁⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠗⠖⠄⠀⠰⠴⠗⠔⡄⠄⠠⠷⠴⠀⠀⠢⠀⡴⠷⠶⠿⡰⠀⠠⠦⠼⠄⠒⠲⠿⠀⠀⠶⠆⠀⠖⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠒⠀⠀⠀⢠⢠⣀⣀⣠⡀⣀⠀⠀⠤⢀⢀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⣤⣴⡄⠀⠀⠈⠉⠁⠀⠉⠈⠀⠉⠀⠈⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢀⠄⠠⢀⠠⣠⡄⢦⡐⠤⢠⣤⠤⣀⠄⠠⡠⣤⠤⠀⢄⣤⡤⡠⠠⢤⠠⣴⡤⠠⠠⠠⡆⡦⢄⢠⣤⢠⠤⣄⠄⡄⢄⡤⠀⣴⣄⠤⠄⣤⣶⡤⢤⡀⢄⡠⠀⡄⣤⠄⠐⣠⠤⣴⠄⡤⠠⣀⠤⣠⠤⣤⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⡀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠋⠋⠙⠉⠀⠈⠛⠙⠛⠃⠀⠀⠘⠃⠀⠛⠁⠀⠁⠙⠻⠝⠀⠀⠛⠘⠈⠀⠉⠛⠃⠙⠛⠑⠀⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⠀⠀⠀⠀⠷⠇⠆⠿⠇⠲⠲⠒⠸⠆⠶⠶⠰⠾⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠋⡭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⡀⡀⠀⠀⢀⡀⠀⠀⠀⠀
⠀⠐⠂⠀⠀⠂⠀⠐⠂⠁⠀⠀⠘⠀⠘⠀⠀⠀⠀⠐⠈⠀⠀⠐⠀⠈⠊⠀⠃⠘⠀⠀⠀⠛⠂⠃⠈⠘⠛⠏⠘⠛⠃⠈⠘⠙⠂⠀⠘⠿⠀⠐⠀⠘⠘⠙⠀⠀⠛⠃⠉⠛⠛⠀⠀⠛⠁⠁⠃⠛⠃⠀⠛⠛⠃⠀⠀⠀
⠀⠀⣦⣠⠀⣄⠀⠀⣠⣄⣤⡄⠀⢠⣤⢀⡄⢠⠄⠀⢠⣤⣄⡀⣠⣴⣴⢤⢠⡄⠀⠀⣤⡄⡦⠄⢀⣤⠄⠀⢀⣴⠀⢀⣤⡀⠠⣶⣄⠀⢀⣦⣤⡀⡄⠀⢴⢠⣰⠀⠀⢠⠀⣦⠄⢀⣤⡄⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠙⠛⠑⠀⠛⠛⠃⠀⠘⠛⠈⠙⠛⠃⠀⠐⠑⠛⠀⠀⠛⠃⠉⠓⠛⠀⠋⠐⠛⠂⠘⠃⠚⠓⠑⠙⠛⠂⠃⠚⠛⠃⠃⠀⠛⠋⠙⠛⠀⠃⠓⠘⠛⠛⠃⠃⠛⠃⠚⠓⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⡄⡤⣄⣤⡄⠀⣤⣆⡦⠄⣆⢤⢄⢠⣤⡄⡤⡄⢐⣦⣠⢀⢠⠀⡄⢠⠐⣤⡆⢄⢤⣤⡆⢄⠐⢠⣄⣤⣤⠀⠀⣤⡄⢢⠔⣤⡤⡀⡠⡤⢤⡀⣤⣤⡄⢠⣴⡆⣤⠀⡤⣰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣄⠠⣀⣀⣴⢄⢀⠀⡰⣆⡦⡆⣆⢄⢀⢀⣆⣴⡀⡦⠂⡀⠀⡄⡀⡠⣤⣦⡄⠀⣤⣤⡆⡆⠖⡤⡄⡀⢀⢤⢠⢠⢄⢀⡄⡴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠤⠀⠀⠀⢀⢀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⣄⣀⠀⠀⠘⠋⠘⠚⠛⠈⠋⠛⠀⠛⠘⠛⠃⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠰⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠀⠀⣀⢀⣀⢠⠄⠀⣠⡄⡀⢀⣀⡀⣀⡀⣄⣀⢀⠀⣀⣀⣀⠀⢀⣠⡀⣄⡀⠀⣀⣀⢀⣀⣀⡀⠀⣀⣀⢀⢀⢀⣀⢀⢀⢀⣀⢀⢄⡀⣀⣀⠀⣀⣀⡀⠀⢀⣀⡀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠁⠈⠀⠈⠀⠈⠙⠀⠉⠀⠀⠈⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠋⠁⠉⠀⠀⠈⠁⠀⠉⠈⠀⠀⠈⠉⠈⠀⠀⠉⠀⠀⠁⠈⠁⠀⠁⠉⠁⠀⠈⠉⠀⠀⠀⠉⠃⠁⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠷⠖⠖⠄⠀⠖⠶⠂⠷⠱⠇⠈⠲⠲⠂⠲⠂⠔⠐⠷⠔⠀⠴⠲⠲⠖⡀⠲⠶⠖⠀⡄⠠⠰⠰⠧⠂⠐⠖⠲⠲⠂⠀⠲⠰⡦⠂⠀⠺⠖⠲⠴⠀⠀⠄⠁⠎⠠⠂⠒⢲⠦⠀⠂⠐⠾⠲⡖⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣄⠀⠀⣀⣀⡀⢠⣀⣤⣀⡄⡀⠀⢄⣀⡀⠀⣀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠀⠈⠉⠈⠀⠈⠈⠉⠃⠃⠁⠀⠈⠉⠀⠀⠈⠁⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠜⠀⠸⠿⠂⠒⠴⠂⠏⠀⠴⠆⠒⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢛⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠡⠄⠇⠗⠆⠷⠸⠏⠇⠰⠼⠾⠃⠨⠺⠁⠠⠪⠧⠰⠾⠕⠕⠼⠇⠏⠸⠀⠇⠾⠎⠀⠱⠕⠣⠎⠨⠲⠾⠨⠊⠺⠈⠖⠅⠄⠨⠷⠞⠈⠭⠂⠱⠪⠢⠿⠏⠀⠇⠷⠷⠪⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠿⠀⠀⠀⢰⣠⢠⢠⣤⢄⡄⣠⠄⣔⢠⣠⡤⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⠾⡿⠤⠀⠀⠈⠁⠈⠈⠀⠀⠁⠁⠀⠈⠈⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠂⠀⠠⡀⢠⢠⣤⠀⡄⠀⢠⣤⠀⠀⢀⠀⣤⡔⢠⠀⣤⠀⢰⠀⠀⣤⣠⠀⢀⡀⠀⠀⣄⡤⢤⠄⣀⠀⢰⡲⠠⠰⡂⣄⣠⡆⠀⢠⢠⢤⢰⡆⠀⠄⣠⢄⣤⡀⠀⢀⠀⣤⢄⡀⢀⡤⠄⡤⢴⣤⡄⡆⠀⠀⠀
⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⠂⠟⠃⠀⠚⠙⠘⠀⠒⠛⠚⠀⠀⠘⠛⠐⠛⠀⠘⠚⠓⠀⠚⠘⠃⠀⠈⠘⠋⠣⠀⠀⠃⠀⠚⠃⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠃⠠⠿⠇⠠⠢⠖⠸⠅⠠⠲⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠛⡫⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⠀⠈⠊⠐⠙⠂⠁⠪⠈⠋⠛⠀⠃⠱⠘⠊⠉⠀⠋⠃⠋⠛⠊⠐⠢⠘⠃⠙⠘⠃⠪⠈⠋⠛⠃⠈⠈⠛⠁⠊⠋⠈⠃⠎⠑⠛⠐⠕⠍⠁⠓⠁⠈⠈⠚⠓⠅⠊⠀⠛⠘⠋⠐⠁⠈⠋⠋⠁⠁⠃⠀⠀⠀⠀⠀⠀
⠀⢠⣄⠤⡤⠀⢤⡄⡤⠀⠄⡠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⡀⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⠀⠀⠀⠓⠁⠐⠛⠃⠐⠑⠋⠘⠂⠐⠙⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠕⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠄⢀⢀⠀⣀⠀⣄⡀⣀⠀⡀⡀⡀⡀⡀⡀⠀⣀⣀⢀⢀⠀⢀⢀⣀⢀⡄⢀⢀⠀⡀⢀⣀⣄⣀⢀⣀⢀⢀⣀⡀⡀⡀⣀⢀⢀⠀⡀⣀⡀⡀⠀⡀⣀⣀⢀⣀⢀⡀⡀⡀⡀⣠⠀⡀⡀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀
⠀⠘⠀⠀⠁⠈⠈⠁⠉⠁⠉⠀⠈⠀⠁⠋⠂⠈⠈⠉⠉⠁⠀⠁⠘⠀⠀⠀⠁⠁⠁⠀⠂⠀⠉⠁⠁⠈⠀⠐⠉⠉⠉⠂⠂⠊⠈⠑⠀⠂⠈⠀⠂⠀⠀⠈⠁⠀⠀⠉⠀⠉⠂⠋⠈⠈⠈⠊⠉⠀⠁⠉⠁⠀⠀⠀⠀⠀
⠀⠸⠶⠔⠐⠀⠐⠐⠴⠶⠂⠂⠐⠶⠖⢆⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⡄⡄⠀⣤⡄⠀⡀⣀⢠⠄⠀⣀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⡤⢤⡀⠀⠀⠉⠀⠈⠉⠁⠈⠈⠁⠈⠁⠈⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠂⠠⣠⢀⢤⡀⡤⡄⠤⢀⡤⠄⠠⡤⢰⢄⠄⠄⢤⣤⣤⠄⡄⠠⡀⢤⡤⠤⡄⢄⡀⠄⠄⡠⠄⣤⡤⠠⠠⡀⡤⣤⣤⣤⣄⠤⢤⠀⣤⠄⠄⠠⣠⢠⠴⢤⡤⠤⣠⣤⢄⠄⠄⢀⡀⠄⣄⣤⢄⠄⠄⠀⠀⠀⠀⠀
⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠈⠛⠁⠊⠈⠈⠂⠛⠙⠈⠒⠁⠀⠐⠈⠊⠋⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠲⠖⡒⠒⠖⠠⠤⠄⠀⠄⠀⢸⣉⣻⣿⣛⣿⣻⣋⣻⣛⣛⣿⣻⣛⣛⣟⣻⣛⣿⣏⣏⣟⣻⣛⣟⣹⣛⢿⣹⣻⣻⣿⣟⡟⣿⣋⣙⣿⣟⣻⣏⣹⣻⣛⣏⣙⣻⣟⣻⣻⣟⣛⣻⣉⣙⣿⣉⣟⡻⣏⣟⣻⣛⣟⣻⣻
⠀⠖⠶⠲⠒⢖⠒⠂⠠⠄⠠⠀⠄⠄⠀⠀⣿⣿⣯⣝⣟⣋⣛⣏⣻⣙⣙⣛⣋⣯⣋⣛⣋⣏⣻⣉⣙⣙⣋⣙⡍⣟⣏⣫⣯⣟⣯⣯⣿⣽⣹⣽⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡤⣤⢤⡤⣤⣤⠄⢀⡀⢀⠀⡀⢀⠀⠀⣿⣿⡿⠿⡿⠿⡿⡿⣿⢿⠻⠿⠿⡿⠿⣿⠿⠿⡿⡟⠿⠿⠿⡿⡿⠿⠿⠿⢿⡿⡿⡿⡿⠿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠓⠛⠚⠒⠓⠚⠂⠈⠀⠈⠀⠁⠁⠁⠀⣿⣿⣾⣿⣾⣶⣿⣿⣷⣾⣶⣶⣶⣿⣾⣿⣾⣾⣾⣷⣶⣾⣾⣿⣶⣦⣴⣷⣶⣷⣷⣶⣶⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠒⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⣿⣺⣿⣍⣏⣹⣻⣿⣟⣿⣻⣿⣫⣹⣈⣭⣈⣸⣉⣉⣏⣍⣍⣝⣍⣛⣿⣟⣎⣿⣿⣈⣍⣏⣿⣿⣹⣿⣻⣿⣿⣏⣿⣯⣿⣟⣅⣏⣙⣿⣻⣏⣟⣏⣿⣫⣹⣧⣿⣿⣿⣿
⠀⠲⠖⠶⢖⠂⠀⠀⠀⠄⠀⣿⣝⣛⣟⣟⣟⡛⣟⣿⣛⣟⣏⣻⣛⣛⢛⣟⣏⣟⣛⣙⢛⣛⣋⣻⣏⣻⣛⣻⣋⣻⣻⣛⣛⣏⣻⣛⣻⣛⣻⣟⣛⣹⣏⣹⣻⣻⣛⣿⣻⣿⣻⣻⣛⣟⣻⣛⣛⣿⣟⣟⣟⣿⣛⣻⣿⣿
⣯⣏⣽⣫⣟⣭⣭⣭⣿⣿⣉⣿⣿⣿⣩⣏⣹⣉⣭⣭⣟⣽⣹⣽⣯⣫⣍⣽⡍⣹⡉⣿⢍⡏⣹⣯⣽⣏⣯⣻⢟⣿⣝⣯⣏⣉⣻⣍⣫⡩⣯⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠤⠤⠀⠀⠀⠶⠰⠀⠀⠀⠀⠀⣏⡏⣻⣉⣏⣹⣉⣋⣯⣋⣉⣯⣛⣯⣉⣉⣏⢍⣯⣉⢉⣙⢽⣛⣍⣏⣙⣉⣹⣉⣉⣛⣝⣹⣍⣏⣙⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣖⣦⣒⣖⣶⣖⣶⣶⣖⣲⣶⣶⣲⣶⣶⣶⣴⣴⣲⣖⣲⣲⣿⣻⣿⣿⣿⣹⢽⣽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣏⣙⣉⣏⣉⣭⣭⣋⣏⣙⣹⣋⣹⣉⣏⣏⣏⣽⣉⣍⣙⣏⣉⣟⣯⣏⣏⣉⣯⣹⣩⣉⣏⣙⣝⣙⣉⣹⣉⣏⣽⣉⣽⣙⣋⣉⣿⣯⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣯⣻⣯⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⣿⣿⣏⣿⣯⣯⣹⣿⣿⣻⣟⣟⣟⣿⣿⣟⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠛⠃⠛⠘⠁⠃⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡿⢿⣿⣿⣿⣿⣿⣭⣷⢿⣿⣿⣿⣽⣿⢿⣧⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣽⣿⣿⣷⣿⣧⣿⣿⣿⣯⡿⣿⣾⣿⣿⣿⡿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⢾⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠦⠄⠶⠰⠀⠄⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣻⣿⣟⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⢷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⣹⣯⣿⣿⣿⣿⣯⣭⣯⣻⣿⣿⣩⣿⣯⣟⣿⣻⣿⣿⣏⣽⣯⣿⣽⣿⣻⣿⣿⣹⣿⣹⣽⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣽⢿⣭⣿⣽⣿⣿⣽⣽⣿⣯⣯⣿⣽⣾⡫⣿⣽⣽⢿⣯⣧⣿⢧⣼⣿⣯⣿⣽⣭⣿⣯⡭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣷⣽⣯⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢿⣶⣾⣷⣯⣾⣷⣿⣴⣿⣿⣧⣶⣶⣾⣿⡷⣿⣧⣷⣦⣿⣯⣶⣾⣿⣴⣶⣿⣾⣷⣶⣷⣾⣷⣷⣴⣿⣾⣿⣿⣾⣷⣷⣷⣾⣿⣶⣿⣷⣶⣶⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡷⣿⢿⣾⠿⡿⢿⣾⠷⡾⢷⢶⡿⣿⠾⣞⡾⣾⠝⣿⢿⣷⠖⢿⢿⡿⡷⢗⣾⡿⢷⡾⠷⠿⣽⣿⡾⢲⢿⣶⠶⣻⣿⠿⢾⡟⢷⢿⠿⢿⠶⢿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢛⣟⣿⣛⣛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⣿⣿⣻⡿⣻⣻⣿⣻⣿⣟⣏⣻⣟⣟⣻⣿⣟⣿⣛⣟⣏⣯⣿⣿⣿⣟⢻⣟⣿⣿⣟⣿⣿⣛⣿⣿⣿⣿⣿⣿⣟⣻⣿⣻⣟⣻⣿⣿⣻⣟⣹⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⡧⣷⣯⣭⣿⣾⣥⣬⣽⣥⣿⣽⣿⣭⣿⣿⣽⣿⣯⣬⣿⣿⣿⣽⣭⣿⣿⣽⣯⣽⣽⣷⣿⣼⣼⣿⣧⣭⣹⣿⣿⣽⣭⣯⣿⣯⣭⣧⣽⣯⣼⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣶⣷⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡾⣿⣾⢾⡷⣾⣾⠾⣿⢺⢾⠷⢿⠾⣿⢶⢿⡶⢿⠾⡿⣾⣿⢿⢷⡶⣷⡶⢶⠿⢻⣾⠶⣿⡿⡿⢷⡿⢿⡎⢿⣷⢿⣷⠿⠷⠾⡣⢿⡷⢾⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⣻⣻⣿⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣻⣿⣿⣿⣯⣛⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣛⣿⣿⣿⣟⣿⣻⣯⣿⣿⣿⣿⣿⣟⣿⣿⣋⣿⣽⣿⣿⣿⣹⣿⣹⣿⣻⣍⣟⣽⣿⣻⣿⣟⣹⣏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣯⣿⣽⣿⣽⣿⣽⣿⣿⣹⣿⣯⣟⣿⣿⣿⣿⣭⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣽⣯⣿⣯⣿⣿⣽⣭⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠰⠀⠐⠀⠆⠢⠀⠀⠖⠄⠶⠀⠲⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣶⣶⣶⣶⣖⣲⣾⣻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣟⣻⡟⣻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⡀⡀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠙⠓⠃⠘⠛⠛⠙⠃⠑⠓⠛⠀⠛⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠁⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⡤⢀⡀⡄⠀⠀⣀⣀⡀⣄⠀⠠⣀⡀⣀⠀⠀⢀⢀⡀⠀⠀⡀⠀⣄⢀⠀⠀⠀⣀⡄⢀⠀⢀⢀⢀⢠⡄⠀⡀⢀⢀⣄⣀⠀⠀⢀⣀⡀⣀⣤⠀⠀⢀⢀⢀⡀⡀⡀⠀⠀⠀⠀⡀⣠⠀⠀⡀⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠐⠁⠈⠀⠁⠀⠈⠙⠑⠀⠁⠀⠀⠉⠁⠉⠀⠁⠀⠉⠉⠀⠈⠁⠀⠉⠘⠁⠀⠀⠉⠉⠈⠀⠊⠈⠈⠈⠁⠀⠀⠉⠉⠉⠉⠀⠀⠈⠃⠉⠉⠉⠀⠀⠁⠉⠉⠉⠁⠀⠀⠀⠉⠀⠁⠉⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠰⠦⠾⠶⠘⠠⠂⠷⠦⠸⠇⠰⠠⠰⠶⠠⠶⠀⠰⠂⠶⠲⠀⡴⠶⠖⠢⡰⠠⠆⠀⠼⠰⠒⠦⠆⠢⠀⢦⠆⠇⠀⠰⠔⠄⡄⠰⠰⠇⠶⠀⠰⠀⠠⠲⠒⠲⠼⠀⠶⠦⠦⠰⠴⠗⠄⠆⠷⠦⠆⠀⠰⠀⠀⠀⠀
⠀⠀⠠⣀⣠⣀⡄⢀⡄⣤⢄⡄⢄⡀⠠⣀⣠⠠⠠⣀⣀⣠⠀⡄⢀⡀⡠⡠⡀⠄⡠⡀⡀⠠⢀⡀⡄⡄⢄⠄⣀⡀⢀⣀⣤⣠⠀⣀⢠⢀⢀⣀⠄⢠⠠⣀⠀⡄⣄⣀⣠⠀⠄⣀⡀⡠⣠⣠⡠⡄⢀⣀⠠⠠⡀⠀⠀⠀
⠀⠀⠀⠉⠉⠉⠁⠉⠁⠉⠀⠁⠈⠀⠈⠈⠁⠀⠁⠉⠉⠈⠀⠁⠀⠁⠁⠈⠀⠁⠁⠈⠈⠀⠈⠉⠁⠁⠀⠁⠉⠉⠀⠀⠉⠈⠀⠁⠈⠈⠉⠉⠀⠈⠀⠉⠀⠁⠉⠉⠈⠀⠀⠉⠁⠁⠈⠈⠈⠁⠈⠉⠀⠈⠀⠀⠀⠀
⠀⠀⠈⠋⠯⠃⠑⠅⠇⠸⠚⠃⠪⠋⠉⠋⠪⠈⠓⠛⠑⠅⠕⠚⠃⠛⠃⠋⠁⠎⠸⠊⠘⠃⠨⠀⠈⠊⠛⠉⠨⠀⠸⠨⠂⠛⠁⠸⠀⠪⠊⠂⠛⠋⠒⠁⠑⠪⠸⠀⠁⠗⠛⠊⠘⠁⠽⠨⠛⠓⠁⠇⠪⠈⠀⠀⠀⠀
⠀⠀⠠⣤⡤⠠⠠⢀⠄⢤⠄⡠⡠⠠⣠⡄⠄⠤⢤⢤⠠⠀⠠⡤⣤⡠⠠⠠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⢿⣿⠻⡿⠿⡿⡿⢿⢻⠿⡿⢿⢿⠿⣿⢻⢿⡿⢿⡿⡿⣿⢿⣿⠿⢿⡿⡿⣿⠿⢿⣿⢿⡿⣿⠿⣿⢿⠿⢿⠿⡟⡿⣿⢿⠿⡿⡿⠻⢟⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣽⣼⣧⣯⣶⣧⣿⣴⣧⣾⣴⣶⣽⣿⣬⣾⣯⣯⣾⣶⣮⣿⣷⣭⣧⣾⣾⣮⣧⣿⣿⣦⣵⣿⣽⣥⣾⣽⣿⣨⣧⣶⣦⣿⣤⣿⣬⣧⣼⣧⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⡟⡟⣿⠻⣿⡟⡟⢿⠿⡟⣿⠿⠿⢿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠁⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣧⣧⣧⣿⣬⣼⣷⣥⣯⣤⣧⣿⣼⣤⣭⣬⣧⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢲⠶⣶⢶⡶⣶⡶⣶⡶⣶⣶⢶⣶⢶⡶⣶⡶⡶⢶⡶⣶⣶⣶⢿⡿⢿⡿⣿⡿⡿⢿⡿⣿⡿⣿⢿⣿⢿⣿⣿⡿⣿⡿⣿⢻⢿⡿⢿⡿⣿⢿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣾⣷⣾⣿⣿⣷⣿⣿⣿⣧⣿⣽⣿⣽⣧⣿⣿⣿⣼⣷⣿⣾⣿⣬⣿⣼⣷⣿⣾⣿⣼⣯⣾⣿⣿⣽⣿⣧⣿⣾⣿⣿⣼⣷⣿⣞⣷⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⢀⢀⢀⢀⠀⠀⢀⠀⡀⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀⣿⡿⣿⠿⣿⣿⣿⢿⠻⡿⢿⠿⣿⡿⡟⢿⢿⣿⠻⡿⢿⣿⢿⡿⢿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠈⠈⠈⠈⠈⠀⠀⠀⠁⠁⠁⠉⠈⠀⠀⠈⠀⠀⠀⠀⣿⣷⣿⣾⣿⣾⣿⣾⣶⣷⣼⣶⣿⣷⣷⣾⣷⣿⣶⣿⣾⣿⣾⣷⣾⣴⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠂⠃⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣧⣼⣧⣿⣼⣾⣼⣿⣼⣼⣧⣾⣾⣼⣤⣷⣿⣧⣿⣼⣧⣿⣧⣼⣯⣿⣼⣤⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢶⢶⣶⢶⣶⠶⡶⣶⢶⢶⠶⡶⢶⢶⢶⣶⣶⡶⢶⣶⣶⢶⣶⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⠿⢿⡿⡿⣿⢿⣿⣿
⣾⣶⣽⣼⣧⣿⣴⣧⣿⣼⣇⣾⣰⣦⣿⣿⣿⣿⣿⣴⣿⣷⣽⣧⣿⣼⣿⣿⣧⣽⣿⣼⣿⣼⣧⣿⣴⣿⣼⣷⣧⣿⣮⣿⣴⣶⣼⣿⣿⣼⣯⣿⣵⣿⣽⣯⣷⣾⣿⣯⣿⣿⣾⣿⣧⣿⣿⣦⣿⣮⣿⣿⣷⣿⣭⣿⣿⣿
⡖⣲⡒⠲⢶⣶⠖⣶⡲⢶⠒⣲⡶⣶⠲⣶⠒⣲⡶⣶⠶⡖⡶⠶⠶⠶⡶⢶⠒⠶⠖⠶⢶⠲⣶⡖⡖⡶⠶⢶⠲⣖⣶⡶⣶⣶⡖⣶⠶⠶⠲⣶⣶⠖⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⡿⣷⢶⢶⡶⣶⡶⣾⣿⣿⣶⣾⣶⣶⢶⣷⣦⣾⣾⣾⣶⣷⣷⣶⢾⣷⣶⣿⡾⣿⣷⣶⣶⣶⣷⣷⣷⣶⣶⣾⣴⣶⣶⣶⣷⣾⣶⣷⣶⣶⣶⣾⣦⣴⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠷⠮⠧⠤⠼⠿⠤⠽⠷⠿⠾⠦⠤⠾⠤⠤⠤⠦⠤⠾⠵⠧⠷⠦⠴⠾⠤⠤⠤⠀⠐⠶⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣦⣂⣂⣒⣐⣰⣲⣐⣀⣲⣂⣂⣚⣰⣐⣖⣆⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⣷⡧⣿⣿⣩⣯⣽⣯⣭⣿⣿⣯⣏⣭⣯⣿⣭⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠓⠓⠒⠒⠛⠛⠚⠒⠓⠓⠓⠒⣷⣷⣷⢾⣾⣶⢿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣷⣶⡿⣶⢾⡾⣶⢶⣶⣷⣾⣶⣶⡶⢾⣾⣶⣷⣶⣶⣾⣶⣶⣷⠶⣷⣶⣶⡶⠽⡾⡶⣷⣶⣿⣿⣿⢿⣿⣿⢿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⡷⠖⠳⠴⡶⢾⣾⠷⠞⡖⢳⠓⣒⡒⠓⠶⠺⠶⠴⠶⠶⠳⠶⠞⠷⡾⢖⠷⠾⡶⠗⢶⠗⠷⠳⠺⠾⢾⠞⠶⠶⡽⠾⢒⢶⠪⣷⣶⣾⣶⣶⣶⣶⣧⣤⣤⣤⣥⣤⣤⣤⣤⣬⣿⣿
⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠐⠉⠉⠍⠉⢩⠉⠍⠍⠉⠉⡍⠉⠉⠉⢉⠩⠉⠉⡍⡍⠉⠉⠩⢉⢩⡩⠈⢉⣉⣍⠉⠉⢉⡍⠉⠩⠩⠉⠉⠉⡍⡉⠩⡍⠉⠉⡍⠩⠉⡍⠉⠍⡭⠍⣩⠉⠉⢩⠩⠉⠭⠍⠉⠉⠩
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣉⣯⣭⣭⣹⣭⣏⣍⣻⣍⣉⣍⣩⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠭⠯⠬⠿⠭⠭⠭⠭⠥⠯⠯⠽⠭⠯⠭⠬⠭⠿⠭⠯⠭⠭⠯⠭⠯⠭⠷⠽⠤⠭⠭⠽⠩⠽⠽⠭⠿⠭⠍⠭⠽⠯⠽⠥⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠷⠤⠷⠽⠤⠿⠭⠽⠤⠯⠯⠮⠯⣽⣭⣥⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⡶⠶⡖⡶⢶⠒⣖⣲⣶⣶⢲⢶⡶⠶⡶⡶⡶⢶⡖⠶⠶⣶⢶⢶⡶⠾⣿⡿⢿⢿⣟⠿⡿⢿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣼⣁⣯⣸⣭⣧⣼⣿⣿⣤⣾⣿⣧⣾⣼⣵⣾⣧⣾⣼⣧⣷⣶⣼⣼⣽⣧⣼⣮⣿⣭⣧⣴⣅⣧⣽⣵⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣐⡂⣄⣖⣦⣒⣰⣤⣐⣶⣶⣒⣼⣂⣒⣐⣀⣖⣲⣀⣒⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⣯⣩⣙⣏⣍⣿⣫⣍⣉⣹⣨⣍⣫⣻⣙⣨⣋⣩⣃⣪⣹⣍⣏⣩⣿⣊⣩⣯⣽⣋⣩⣸⣽⣋⣽⣍⣉⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠷⠬⠅⠦⠮⠻⠥⠷⠭⠥⠯⠬⠶⠵⣼⣤⣧⣜⣥⣾⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠐⠒⠒⠀⠀⠀⠀⠀⠧⠥⠤⠤⠧⠤⠦⠧⠤⠧⠥⠬⠦⠤⠬⠥⠬⠬⠼⠤⠥⠬⠥⠬⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⣏⣉⣉⣁⣍⣙⣩⣭⣩⣉⣉⣏⣉⣏⣩⣉⣘⣯⣯⣭⣋⣉⣉⣉⣻⣋⣍⣉⣭⣅⣉⣍⣉⣙⣉⣹⣉⣉⣅⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠠⠀⠠⠀⠄⠀⠀⠀⠀⠀⣟⣋⢛⣿⣛⣫⣹⢛⣛⡟⣛⣟⣛⣻⠛⣋⣟⣟⣛⣋⡏⣏⣛⣻⡟⣛⣻⣛⣛⣋⣛⣛⣝⣛⣏⣟⣛⣛⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠛⡟⠛⢛⣿⠛⡛⣛⠛⠛⢻⠻⢛⡛⠛⠛⣛⠛⠟⡟⢻⠛⡛⡟⣛⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⢛⡛⣟⢻⠛⠛⢛⢻⢛⢛⣛⠛⢻⠛⢻⠟⣟⡟⠟⠛⡟⣛⣿⣛⡛⢻⣟⢻⠻⠛⣛⠟⢛⣟⣛⠟⡟⡟⢛⡛⢿⠛⡻⣟⣿⣛⠻⢛⢟⣛⣻⠛⣿⣛⠻⣛⡛⡿⢿⠛⣛⣻⡛⣿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢸⣤⣭⣽⣯⣼⣥⣼⣭⣭⣭⣯⣭⣬⣽⣽⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⢸⣼⣤⣭⣭⣭⣥⣵⣬⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠿⠩⠥⠭⠯⠭⠽⠽⠯⠭⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠐⠆⠀⠒⠀⠀⠀⠀⢸⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣙⣙⣏⣉⣛⣉⣙⣹⣹⣋⣟⣻⣉⣏⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠄⠠⠠⠀⠀⠀⠀⢸⣭⣟⣋⣛⣏⣛⣏⣛⣛⣿⣙⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣛⡛⢻⣛⣟⣛⣛⡛⣟⣷⣛⣟⣿⣻⣟⣛⣿⣛⣛⣷⣟⣻⡟⣛⣿⣛⣛⣛⣿⣻⢛⣛⣟⣛⣿⣻⣟⣛⣟⣛⣟⣿⣻⣟⣛⣛⣿⣟⣟⣟⣛⣟⣛⣻⣟⣟⡛⣟⣛⣟⣿⣟⣛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣭⣽⣽⣍⣯⣭⣯⣭⣯⣼⣭⣽⣯⣽⣥⣯⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣧⣤⣽⣤⣤⣧⣼⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⣧⣭⣥⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠒⠀⠐⠐⠀⠀⠀⠀⠀⠧⠭⠽⠭⠭⠯⠥⠼⠭⠭⠭⠭⠭⠼⠭⠩⠿⠼⠽⠭⠭⠽⠵⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⣏⣩⣍⣭⣍⣭⣍⣩⣽⣩⣭⣉⣭⣍⣭⣍⣉⣍⣏⣭⣉⣩⣍⣭⣽⣍⣉⣩⣭⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⠒⢲⡲⡦⡦⣶⣶⡖⣖⡖⠒⣖⢶⢴⢴⣶⡶⠵⣒⠂⠖⠖⠖⠰⡶⡦⡶⠶⡴⡖⡖⡶⣶⢲⢴⠴⡖⠲⡆⠒⠐⢖⢖⢴⣖⣶⡶⡶⣶⣶⠐⠢⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠉⠉⠁⠉⠉⠉⣁⣀⢉⠉⢉⠉⠉⠉⠉⠉⠀⠈⢹⡿⠿⢿⠿⡿⠿⠾⠿⢿⠿⠿⢿⢿⠿⢿⠿⠿⠿⠿⡿⠿⠿⠟⡿⠻⠻⠿⡿⠟⠿⠿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣁⣉⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣸⣷⣶⣷⣽⣷⣶⣶⣶⣷⣿⣷⣿⣷⣿⣾⣴⣶⣶⣿⣶⣶⣿⣶⣷⣶⣶⣶⣾⣶⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠷⠤⠖⠕⠷⠿⠿⠿⠧⠷⠮⠶⠯⠧⠴⠮⠶⠯⢶⣿⣾⣼⣤⣖⣕⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⡛⢛⠛⢹⢿⣿⠛⡟⠛⠛⢿⠛⠻⢛⢟⠛⡟⠟⡟⢻⡛⢿⠙⠻⢛⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⢉⠉⡉⡈⠉⠉⠉⠉⡉⠉⠉⠉⠉⢹⠛⠿⢿⠟⠟⠷⢿⠿⢾⡿⢿⠿⠿⠟⠿⡿⢿⠿⠟⠿⣿⡻⢟⡿⠛⡻⡻⠻⡛⣿⢛⢻⢻⢻⠛⡟⠿⠿⡿⠿⠿⣿⣟⣿⠿⠿⠿⣿⠿⢿⢿⠻⠿⡟⠿⢿⡿⡿⢛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠖⠒⠒⣲⡲⢺⠚⢲⠖⢺⢲⣲⡒⡒⢳⡳⢒⢒⢲⠚⣓⡒⠒⡖⠺⢺⡒⠓⠛⠚⢲⡓⡚⡲⠳⢒⠚⣲⣖⠒⠓⠺⢲⡲⠒⠒⡚⣖⡓⣲⠒⢶⣳⠒⢲⣲⠖⣟⢖⠚
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⢿⢿⠿⠿⠿⠿⢿⠿⢿⠿⠿⠿⠿⠶⡿⠿⠿⢿⢿⠿⠿⠿⡿⠿⢿⠿⠿⢿⣿⡿⠿⢿⢿⠿⢿⢿⠿⠿⠿⠿⡿⣿⠿⠿⠿⡿⠿⡿⡿⢿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣴⣶⣶⣶⣶⣾⣶⡾⠾⣶⢷⠶⡶⢴⠶⢶⡾⢷⠶⠶⠾⢿⢷⡶⡶⢶⡿⠿⢾⠶⢷⣾⡶⡾⢶⢶⢶⠶⢾⡶⡵⢶⡶⣶⢶⢶⢷⣾⣷⡶
⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣴⣿⣷⣶⣶⣶⣶⣽⣶⣶⣶⣷⣾⣯⣷⣾⣶⣶⣶⣿⣶⣶⣶⣿⣷⣶⣶⣧⣷⣶⣶⣾⣶⣾⣶⣶⣾⣿
⡿⣷⣧⣿⣿⣿⣶⣥⣼⣾⣤⣼⣼⣦⣮⢿⢯⠿⣶⣿⣿⢴⢯⣼⣾⠷⢧⢷⢴⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠗⠓⠁⠊⠛⠙⠐⠘⠃⠃⠃⠒⠋⠛⠂⠑⢴⣤⣧⣥⣤⣽⣽⣤⣧⣴⣴⣼⣵⣭⣤⣾⣼⣬⣼⣼⣯⣯⣷⣮⣼⣶⣶⣦⣿⣽⣭⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠀⠂⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⢛⣟⡛⣻⠛⢟⡛⠛⠛⢻⠛⠛⠛⡟⠟⠛⢛⢛⢛⡛⢻⠛⢻⠻⠟⠛⠛⢟⣿⠻⢻⠛⡟⠛⠛⠛⢻⣻⢛⣛⢛⠟⡛⡛⠻⠟⠛⢛⢿⡛⠛⢛⡛⣻⢛⡛⠛⠛⡟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⣎⣝⣈⣉⣉⣈⣈⣇⣜⣽⣝⣭⣅⣿⣩⣣⣩⣈⣡⣁⣩⣍⣍⣵⣫⣉⣩⣛⣯⣏⣭⣿⣸⣈⣞⣭⣽⣈⣽⣏⣍⣩⣸
⣯⣿⣉⣍⠿⣹⣩⣹⣋⣍⣇⣹⣋⣉⣙⣗⣉⣉⣟⣏⣹⣙⣹⣉⣻⣹⣈⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣝⣺⣋⣋⣹⣹⣝⣉⣹⣹⣛⣽⣿⣼⣉⣉⣏⣉⣙⣹⣉⣉⣻⣋⣉⣇⣟⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡝⣻⣟⣿⣟⣻⣿⣟⣛⣿⣿⣿⣿⢯⢙⣋⣟⡏⠻⠹⠟⠻⣭⠿⠿⠛⠛⠛⢙⠙⡻⠿⡻⠟⣏⣹⣻⣭⣿⣻⣿⣟⣟⣻⣽⣻⣙⣋⣋⣻⣟⣛⡛⣟⣫⣟⣛⣛⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣄⣲⣶⣶⣶⣖⣲⣶⣲⣲⡶⣶⣶⡦⡤⣖⣀⣶⠐⠰⠶⠖⠢⠴⠶⠒⠒⠲⠂⠂⠲⠶⠒⠖⢲⣀⣖⣦⣄⣒⣶⣶⣶⣒⣂⣒⣶⣖⣰⡐⣶⣆⣶⢖⣒⣶⣒⣲⣲⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣍⣻⣿⣿⣿⣟⣻⢝⣛⢟⣛⣛⣟⣛⡏⢹⣫⣋⣙⣟⣻⣿⣋⣻⣿⣿⣛⣏⣻⡯⣏⣛⣛⡿⣛⣙⣟⣻⣿⣹⣟⣻⣿⣿⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣍⣻⣿⣿⣿⣟⣻⢝⣛⢟⣛⣛⣟⣛⡏⢹⣹⣋⣩⣟⣙⣍⣹⣹⣻⣋⣻⣻⣽⣏⣟⣿⣟⣛⣿⣿⣿⣛⣋⣟⣹⣟⣻⣹⣿⠛⣙⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣄⣲⣶⣶⣶⣖⣲⣖⣖⣲⣒⣲⣔⣒⣖⣒⣖⣖⣖⡶⣆⣒⣲⣖⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⡝⣻⣟⣿⣟⣻⣿⣙⣿⣟⣟⣻⣟⣿⣻⣛⣿⣿⣛⣿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣆⣆⠔⣒⣒⠖⣒⣲⣦⣶⢶⡰⢒⢒⣲⡒⠒⠦⡐⠏⣏⢛⠉⢟⡻⡛⢛⡛⣍⡝⣛⣛⡻⢿⣻⡛⣻⢻⢙⣟⡟⣿⠙⢛⣟⣟⡛⣹⡟⢻⠻⣻⣻⡛⢛⠙⣻⡻⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠐⠐⠂⠄⠀⠀⠂⠀⠀⠀⣿⣡⣃⣵⣰⣈⣇⣸⡝⢉⣁⣃⣘⣋⠉⣟⣉⣉⣉⣋⣉⣉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⠈⠘⠁⠂⠀⠀⠁⠀⠀⠀⣿⣤⣼⣤⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣖⣶⠶⢒⣒⠖⢒⣲⣖⠲⢒⡒⢶⠒⣴⣶⡒⠒⠖⣞⣶⡔⢖⡲⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⡿⣷⣿⣶⣶⣾⣷⣿⣷⣾⢾⣶⣿⣶⣶⣿⣾⡿⣷⣷⣿⣾⣷⣷⡿⠿⠿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣷⣤⣤⣼⣽⣤⣶⣿⣯⣼⣦⣤⣯⣿⣧⣤⣼⣾⣧⣼⣾⣷⣦⣶⣤⣴⣷⣮⣤⣴⣟⣨⣶⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⡟⡿⡯⠛⠛⢫⠿⣋⣛⢭⠯⢿⠹⡟⠟⣿⠩⢙⠿⠻⢛⠏⣿⠋⠛⠿⡿⠛⠹⣿⠍⡽⠋⠿⣿⠉⡍⡟⡻⡏⠫⡍⡻⡯⠋⠟⣿⠭⢻⢛⠛⢿⢻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⡉⢉⢉⢉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡿⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣭⣭⣿⣽⣼⣿⣿⣿⣭⣿⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣟⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⢿⣿⣿⣿⣿⣻⣽⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣟⠛⢿⣟⣿⣻⣿⣻⣟⣟⣛⣻⣟⣿⣛⣿⣿⠿⠛⣿⣿⣿⣻⡟⠛⢻⣻⣿⢿⠛⠻⣿⣿⡛⠛⣿⢟⢻⠻⣻⣿⠛⢻⡿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣷⣵⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠆⠰⠆⠆⠀⠒⠴⠐⠀⠀⠀⠀⠀⠀⢸⣋⣹⣍⣉⣝⣩⣭⣏⣹⣙⣉⣉⣹⣉⣹⣉⣉⣉⣉⣭⣯⣋⣉⣍⣉⣹⣽⣹⣙⣉⣋⣹⣙⣝⣟⣫⣟⣻⣙⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⡍⢩⣍⢉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡿⢻⡿⠟⡿⡿⠿⢿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣼⣤⣾⣽⣽⣤⣯⣧⣥⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠖⠠⠄⠀⠀⠄⠰⠰⠀⠀⠀⠀⠀⠀⢸⣟⣽⣝⣯⣽⣭⣫⣯⣹⣹⣿⣯⣙⣋⣿⣿⣝⣟⣫⣟⣿⣍⣯⣉⣟⣹⣙⣹⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣛⡿⣿⠿⢻⢻⠛⣿⡿⠟⢿⣿⠻⠻⡛⢿⣿⡿⡻⣿⡟⠿⢻⠿⠻⣿⠿⠻⣻⣿⡿⡟⢿⣿⣿⡟⠛⠻⣿⠿⡟⠻⣻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣋⣙⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⣿⣿⣟⣻⣿⣟⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⢿⣟⣿⣿⣿⢻⢿⣛⣿⣿⣿⢿⣿⡟⠻⣿⣿⡿⣻⢿⡻⢿⣿⣿⣿⣿⣿⢿⣿⣛⣿⣿⡟⣿⣻⣿⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⡍⢉⡉⠉⠉⣉⢩⢉⠉⠉⠉⠉⠉⠉⢹⡿⢻⠿⢿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣾⣿⣯⣯⣬⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠆⠠⠄⠀⠀⠄⠰⠠⠀⠀⠀⠀⠀⠀⢸⣍⣿⢿⣛⣟⣿⣟⡟⣋⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣖⣶⣶⢶⣶⣶⡶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠈⠉⠉⠉⠉⠉⠉⡁⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⢿⡿⠿⣿⡿⡿⢿⣿⡿⡿⣿⣿⣿⡿⣿⡿⣿⡿⡿⡿⡿⣿⡿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣷⣶⣾⣿⣶⣾⣿⣶⣷⣾⣿⣿⣿⣷⣶⣶⣷⣾⣷⣶⣿⣷⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠋⠐⠂⠀⠀⠂⠘⠐⠀⠀⠀⠀⠀⠀⢸⣇⣯⣫⣏⣿⣁⣸⣻⣾⣿⣍⣇⣉⣬⣉⣸⣙⣁⣸⣉⣫⣫⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⢖⢲⡶⠂⢶⣖⡲⢴⡆⣶⢶⣖⡖⣶⢶⢒⡶⣶⠰⣿⠟⣿⢛⠻⠻⣻⣻⣿⢛⣿⡿⠟⠛⡿⣿⣿⡟⣿⠹⠿⢛⢿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⠉⢉⢉⠉⠉⠉⠉⠉⣿⢛⡿⠿⠻⣿⡿⡿⠿⠛⠿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣈⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣿⣴⣤⣤⣤⣴⣬⣴⣽⣿⣯⣧⣴⣬⣤⣼⣾⣽⣤⣤⣷⣥⣤⣼⣼⣵⣼⣴⣼⣼⣤⣤⣤⣤⣬⣴⣼⣴⣤⣤⣥⣦⣴⣬⣥⣮⣵⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣭⣿⣯⣿⣿⣯⣿⣯⣿⣭⣿⣽⣿⣽⣿⣭⣿⣷⣶⣿⣿⣿⣿⣴⣿⣾⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠭⠿⠯⠿⠿⠯⠿⠯⠿⠯⠯⠧⠿⠿⠯⠿⠿⠿⠧⣾⣿⣿⣿⣿⣿⣯⣽⣯⣽⣿⣿⣿⣿⣯⣗⣴⣿⣿⣿⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣖⠤⡶⠐⢶⠆⢶⣖⡦⢴⠆⠲⣶⠴⠆⡶⡆⠖⢒⠶⡛⢛⢿⣛⣿⢻⠫⣿⣿⢻⣿⣻⠻⣿⡛⢟⣿⡋⡟⣻⡟⢻⣻⣻⢿⣻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣉⡻⡟⠿⡯⣯⢛⠛⠛⡿⡟⠟⠛⡿⠟⠛⠙⢹⢿⡛⢹⠛⢿⠛⠛⠛⡟⠛⡟⡻⣟⠿⡿⣛⢻⡛⡿⣟⠛⢻⢹⢟⠛⠛⣯⡿⣟⢿⢛⠛⡻⡟⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡉⣉⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣍⣉⣫⣻⣿⣍⡿⣽⣻⣭⣛⣙⣝⣽⢭⣋⣻⣙⣛⣯⣿⣙⣫⣯⣋⣿⣯⣙⣫⣙⣛⣿⣿⣽⣭⣯⣩⣙⣟⣟⣙⡿⣯⣯⣽⣯⣻⣻⣻⣋⣽⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠙⠉⠈⠋⠛⠙⠉⠁⠝⠃⠛⠙⠘⠛⠛⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣕⣞⣍⣬⣅⣉⣼⣏⣁⣩⣩⣉⣱⣸⣋⣝⣈⣍⣉⣬⣊⣯⣭⣛⣉⣃⣩⣇⣋⣍⣿⣁⣩⣭⣏⣉⣡⣟⣩⣭⣿⣏⣨⣉⣝⣹⣆⣹⣩⣞⣍⣹⣛⣭⣅⣩⣻⣨⣹⣮⣅⣠⣧⣌⣩⣏⣋⣏⣩⣟⣟⣍⣈⣭⣗⣾
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣾⣫⣿⣷⣵⣾⣾⣤⣴⣤⣥⣥⣤⣼⣯⣤⣤⣴⣯⣦⣶⣤⣧⣭⣵⣧⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣉⣻⣛⣏⣉⣇⣇⣉⣝⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣮⣻⣏⣛⣟⣙⣛⣻⣻⣿⣛⣻⣻⣽⣻⣿⣿⣛⣯⣿⣽⣿⣽⣻⣿⣿⢟⣽⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣻⣏⣛⣟⣙⣛⣿⣻⣿⣿⣛⣿⣻⣻⣻⣛⣹⣍⣛⣿⣛⣟⣿⣿⣿⣟⣟⣻⣟⣻⣿⣿⣿⣿⣟⡯⣩⣛⣿⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⢉⡉⡉⢉⡉⠉⡉⠉⠉⠉⠉⠉⠉⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⠛⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⢿⢿⠟⠿⣿⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⢿⠿⣿⡿⡿⣿⣿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠐⠃⠁⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣿⣼⣥⣬⣧⣤⣮⣥⣬⣼⣶⣧⣴⣷⣿⣵⣬⣮⣭⣧⣿⣤⣽⣧⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠶⠠⠆⠂⠀⠀⠰⠰⠀⠀⠀⠀⠀⠀⣿⣹⣿⣟⣙⣫⣹⣏⣙⣋⣻⣏⣟⣋⣿⣯⣙⣿⣻⣿⣟⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⢀⡀⠀⠀⢀⢠⢠⠀⠀⠀⠀⠀⠀⣿⣛⠻⣿⡟⢻⠻⣿⡿⡿⢿⡿⢿⠿⣿⣿⣟⡛⢿⡿⠿⢿⣿⠻⢿⣿⣿⣿⠿⡟⡛⠟⢛⡿⢿⠛⡿⢿⡿⠿⣿⠿⣟⠿⠿⠿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠑⠈⠃⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣴⣿⣿⣦⣯⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⢀⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣧⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⣯⣿⣭⣿⣿⣿⣯⣼⣿⣿⣽⣿⣯⣿⣿⣿⣿⣽⣾⣷⣧⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣧⣾⣤⣼⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣽⣿⣿⣿⣿⣿⣯⣭⣽⣿⣟⣻⣽⣝⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢄⢠⡄⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣻⣿⢿⡟⣿⢿⠻⣿⣟⢻⡻⣿⣿⣟⡛⣻⣻⠿⣛⡻⡟⣻⣿⣿⣟⣿⣟⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣷⣷⣽⣾⣿⣿⣿⣾⣿⣷⣷⣶⣯⣿⣿⣷⣷⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣾⣶⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠒⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣟⣟⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣟⣻⡿⣟⣿⣿⣋⣟⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠍⠉⢉⢍⠉⠉⠉⡍⢉⡍⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠤⠆⠀⠀⠤⠔⠀⠤⠂⠄⠀⠐⠄⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣷⣿⣷⣾⣾⣿⣾⣿⣿⣿⣶⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⣀⢠⢀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⢿⡿⡿⠿⡿⠿⡿⢿⣿⣿⣿⣿⠿⠿⢿⡿⢿⡿⠿⡟⠿⢿⢿⠟⢻⣿⡟⣟⢿⡿⡿⢿⡿⠿⢿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣷⣷⢶⣷⣶⣿⣾⣿⣾⢶⣶⣾⣷⣿⣾⣶⣷⡶⣷⣿⣷⣷⣷⣾⣷⣿⢷⣷⣶⣷⢶⣾⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⢿⣿⡖⡶⠿⠿⣶⠟⠿⢶⡿⢿⠳⠶⠾⢾⡿⡿⠷⠾⠾⢶⢿⠿⢿⢦⢾⣿⠿⣷⡶⠿⠿⠶⢾⡿⣿⣿⢻⠻⠿⢿⣿⢿⡿⠿⣿⣿⠿⢿⣿⡿⢿⡿⣿
⠀⠀⠀⡄⠀⠀⡄⠀⢠⡄⠀⠀⣤⠄⠄⠀⠀⠀⡀⠀⢸⣳⠛⠛⠿⡗⠟⡗⡒⠛⠒⠲⢾⣷⠻⠒⠲⣗⠺⠓⠛⣗⢓⡗⡟⠚⢺⢓⡛⣿⠛⠒⠳⢓⢾⠚⠒⠚⠛⡚⡚⢺⢿⡟⠺⡗⡛⠗⢶⡿⡟⡖⠲⣿⢛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣋⣛⣻⣛⢿⣿⣿⡿⣛⣙⣿⣿⣟⢛⣟⣻⣿⣿⣛⢛⣿⣿⣉⣛⣯⣿⣏⣛⣛⣋⣫⣿⣛⣛⢛⢛⣹⣿⣻⣙⣛⣍⣿⣿⣟⡛⣛⣙⣙⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣼⣿⣯⣭⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠂⠀⠠⠢⠀⠀⠀⠆⠠⠆⠀⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠒⠂⠀⠀⠒⠂⠀⠐⠀⠂⠀⠀⠂⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠄⠀⢀⡄⠀⠄⠀⡆⢀⡄⠀⠠⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠴⠄⠂⠀⠦⠔⠄⠤⠀⠆⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣖⣶⣶⡶⣶⣲⢶⢶⣶⣲⣶⣖⣶⣶⠶⣲⣶⣖⣖⣶⡻⣿⣿⣟⡟⣿⡟⣿⣻⣿⣿⠛⣿⣿⣿⡿⣿⣟⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣻⡿⢛⣿⣻⣛⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⢻⢿⣿⡟⢻⠻⣿⢿⣛⣿⣿⡟⠻⣿⣿⣿⡛⢿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣻⣿⣿⠻⡟⢛⣻⣿⣟⡟⢻⣿⣿⡟⣿⢿⣿⡟⢿⣿⡛⣻⣿⣿⣿⢻⣿⣿⢿⣿⡿⣿⣿⣿
⣲⡶⣶⣲⣶⣶⣶⣶⠶⣶⣶⣶⣶⡶⢶⣶⣶⢖⣖⠲⢿⡿⣿⣿⣿⢻⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⡿⢻⢟⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⡉⠉⢉⡉⢉⣉⠉⠉⠉⣉⣉⢉⠉⠉⠉⠉⠉⣿⢿⢿⣿⣿⠿⣿⢿⣿⣿⢿⣿⣿⢿⣿⣿⡿⢿⠿⣿⣿⠿⣿⣿⠿⠿⡿⡿⡿⣿⣿⡿⡿⢿⣿⡿⢿⣿⣿⡿⣿⢿⣿⣿⡿⢿⣿⡿⣿⣿⠿⣿⣿⢿⡿⢿⣿⣿
⠀⠀⠀⠈⠀⠈⠁⡈⢉⢀⠈⡀⣈⠉⢈⠀⠁⠀⠀⠀⣿⣷⡷⡾⢾⣷⣾⡷⢿⣿⡿⣿⣿⣿⣿⣿⣶⣿⣶⣾⣿⣦⣾⣿⣶⣾⣿⣿⣷⣶⣾⣿⣿⣶⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣷⣽⣷⣷⣿⣿⣷⣾⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠁⠀⠘⠃⠘⠛⠀⠐⠀⠙⠙⠘⠀⠃⠀⠀⠀⣿⣛⣿⣿⣻⣿⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠁⠉⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠰⠖⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣛⣃⣹⣹⣲⣯⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣻⣿⣟⣿⣟⣟⣟⣿⣿⣿⣻⣿⣟⣿⣿⣽⣿⣿⣿⣟⣿⣻⣟⡛⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⣿⣿⣿⣿⢟⢻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⣉⡉⢉⢉⠉⠉⠉⠉⠉⣿⡻⣿⣿⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠛⠃⠀⠀⠀⠀⠀⢀⣿⣾⣿⣿⣿⣿⣤⣼⣽⣧⣤⣯⣿⣿⣾⣮⣼⣯⣧⣧⣼⣮⣷⣧⣤⣼⣿⣿⣷⣬⣼⣧⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠠⠂⠦⠆⠆⠶⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⡻⣟⣿⣿⣻⣟⣛⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⢀⠀⠀⠀⠀⠀⣿⠿⢿⡿⢿⢿⣿⣿⢿⡿⣿⡿⠿⢿⠿⣿⡿⠿⡿⢿⠿⣿⢿⠿⢿⡿⢿⢿⢿⣿⣿⠿⣿⡿⠿⡿⣿⣿⡿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣶⣶⣿⣾⣿⣷⣿⣷⣾⣾⣶⣾⣶⣷⣿⣾⣶⣿⣾⣶⣾⣾⣾⣶⣿⣿⣾⣶⣶⣷⣷⣷⣿⣷⣷⣶⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠂⠘⠀⠀⠀⠀⠀⠀⣿⣦⣽⣽⣧⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣲⣶⡒⣶⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⡶⣶⣿⣿⡿⢿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣻⣿⣻⠿⣻⣿⣿⣿⣿⣿⣟⢿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⢛⠻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⢛⡛⡛⠓⢓⡛⢛⣛⠛⠛⠛⠛⠛⡛⠓⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⢈⡁⠉⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣍⣏⣿⣿⣯⣽⣫⣽⣯⣽⣯⣏⣙⣹⣿⣿⣿⣿⣍⣹⣿⣿⣙⣿⣉⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠃⠀⠘⠃⠚⠙⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣿⣿⠛⣿⣿⣿⣿⣿⠛⣛⣿⣿⡟⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⣤⡄⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣯⣭⣽⣽⣽⣯⣿⣿⣿⣼⣽⣿⣥⣯⣽⣽⣿⣧⣽⣽⣿⣿⣯⣿⣯⣭⣿⣭⣿⣿⣟⣭⣥⣽⣽⣿⣿⣯⣯⣯⣿⣿⣯⣭⣭⣧⣭⣽⣽⣭⣯⣽⣽⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣶⣾⣿⣧⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⠥⠿⠧⠼⠿⠶⠿⠧⠧⠿⠾⠽⠿⠤⠼⠼⠿⠿⠷⣶⣯⣼⣿⣧⣦⣼⣿⣾⣦⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⠂⠆⠀⠰⠂⠴⠒⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣉⣯⣯⣽⣯⣭⣽⣯⣏⣋⣏⣟⣿⣍⣩⣿⣯⣭⣯⣿⣽⣉⣋⣯⣯⣹⣽⣿⣽⣿⣽⣿⣯⣿⣉⣯⣏⣩⣭⣙⣏⣭⣯⣹⣽⣽⣽⣭⣏⣿⣛⣽⣽⣋⣹⣽⣽⣍⣫⣏⣯⣏⣏⣋⣫⣯⣉⣹⣽⣹⣿⣿⣿⣿⣿⣿⣿
⣶⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣶⣶⣿⣿⣟⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⢉⡉⠉⡉⠉⡉⢉⢉⠉⡉⠉⠉⠉⠉⡉⠉⠉⣿⣻⣻⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣟⣟⣟⣿⣿⣻⣿⣛⣟⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠁⠁⠁⠁⠁⢈⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣹⣻⣏⣭⣹⣿⣩⣽⣯⣿⣽⣯⣽⣯⣿⣿⣏⣹⣽⣿⣯⣿⣿⣿⣿⣿⣿⣽⣹⣻⣿⣍⣹⣿⣯⣹⣽⣙⣿⣿⣻⣿⣍⣋⣿⣙⣹⣿⣿⣿⣽⣿⣭⣿⣿⣍⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠒⠒⠀⠒⠀⠂⠐⠐⠀⠂⠀⠀⠀⠀⠂⠀⠀⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠄⠠⠄⠤⠄⠠⠠⠠⠄⠀⠀⠠⠀⠄⠀⠀⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣷⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠍⢉⡭⢭⠩⠍⠍⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠆⠠⠤⠤⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⡿⠿⠿⠿⡿⡿⣿⠛⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠛⠚⠑⠊⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠄⠰⠶⠴⠲⠔⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⢠⠀⣠⢀⣄⡠⢠⠠⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣟⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠚⠋⠊⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠴⠀⠶⠖⠴⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣟⣽⣝⣉⣿⣿⣛⣿⣹⣉⣿⣿⣹⣏⣏⣿⣏⣝⣹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠋⠀⠘⠁⠀⠀⠈⠉⠁⡘⡋⠀⠈⠘⠑⠁⠀⠀⠀⢸⣿⣯⢾⣿⣿⣿⢼⣿⣿⣿⢾⣿⣿⣿⣧⣿⣿⣿⣧⣿⣧⣿⣷⣿⡧⣿⣿⣽⡧⢿⣿⣾⣿⢾⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⡵⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣾⡷⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣷⣿⣿⢿⣿⣿⣷⢾⣿⣾⡗⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣔⣶⣖⢖⠒⣖⣖⢲⣖⡖⢖⡖⣖⣲⣖⣶⣖⠲⣲⡲⡚⣛⣟⡛⡟⣿⡛⣟⠞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⡟⠿⠻⣟⣟⢻⣟⡟⡿⣿⠛⠿⠻⣟⣟⣿⣿⢿⠻⠿⡻⠿⣟⠛⠛⠿⡿⣟⢟⣿⡛⢟⢻⢻⢻⢿⣟⣛⠿⢟⣿⢻⡛⢟⠻⠟⠟⢻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠉⠉⠉⠉⡉⢉⠉⠉⠉⢉⢉⢉⠉⠉⠉⠉⠉⠁⢹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⢘⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠀⠀⠀⠈⠘⠃⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⢸⣷⣭⣭⣭⣽⣭⣤⣤⣽⣤⣬⣬⣽⣿⣭⣽⣯⣭⣿⣭⣍⣷⣿⣬⣽⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣮⣿⣏⣛⣙⣯⣯⣹⣯⣏⣋⣏⣯⢿⣯⣿⣯⣛⣿⣝⣛⣯⣫⣝⣟⣿⣝⣏⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠠⢠⡄⠠⠠⠀⢠⣠⡀⠀⠀⠀⠀⠀⢸⣻⣛⡟⣻⠛⠛⠟⣟⡛⠛⠛⠛⣛⡟⠟⢛⠻⠛⠻⣟⣛⡟⠛⢟⠛⠛⢟⣿⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣄⢤⠤⠤⣤⡤⠀⡀⡤⣤⣄⢤⡤⠤⣤⡤⡀⡀⠄⡬⡍⣭⠭⢭⠭⡍⢭⡭⣉⢭⣭⡩⠭⢭⢩⣭⢭⣭⡭⠭⢬⣭⢩⣭⢭⠩⠭⠭⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭
⠛⠓⠓⠓⠒⠒⡓⠚⠒⠓⠛⠓⢓⢓⠒⠒⠛⠚⠒⠓⢻⢶⢷⣷⣷⣶⣶⣶⣷⣿⣾⣾⣶⣷⣾⣶⣶⣾⣷⣷⣶⣷⣿⣾⣶⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⣀⣀⣀⣀⣁⣈⣀⣀⣀⣁⣈⣈⣀⣀⣀⣀⣀⣀⣸⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣿⣭⣭⣭⣿⣿⣼⣶⣧⣭⣯⣿⣿⣿⣿⣿⣭⣿⣯⣭⣿⣽⣯⣿⣿⣯⣯⣥⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⣯⣿⣯⣭⣿⣯⣽⣿⣽⣻⣯⣭⣽⣽⣿⣽⣭⣭⣿⣭⣩⣽⣯⣿⣿⣿⣥⣽⣿⣯⣧⣭⣿⣿⣭⣽⣯⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣧⣖⣍⣇⣋⣛⣿⣧⣕⣯⣯⣗⣌⣇⣟⣩⣽⣇⣗⣇⣸⣸⣬⣽⣟⣇⣟⣿⣍⣧⣯⣙⣟⣟⣿⣟⣍⣹⣯⣝⣫⣩⣸⣥⣬⣝⣟⣻⣟⣊⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠆⠠⠰⠠⠤⠄⠰⠠⠀⠀⠀⠀⠀⠀⢸⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣔⣶⣖⡖⡒⣖⣖⣶⢲⣶⠒⣖⡖⠲⣶⣶⣖⠖⢲⣲⡺⠛⣟⣟⡿⢻⡻⢛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⠟⢟⡻⣟⣟⣿⢻⡿⡿⣿⠛⢞⣟⠻⢟⣿⣻⡿⢿⢛⠛⢟⣻⣿⣻⣛⡛⡿⡛⢿⣿⣛⣿⣟⢿⢻⡻⢿⡻⡻⢻⠛⠻⢟⣟⣛⣟⣟⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠉⠉⠉⠉⠉⡉⢉⠉⠉⡉⣉⢉⢉⠉⠉⠉⠉⠉⠁⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⣀⣀⣀⣀⣁⡈⡀⡀⣉⣁⣉⣀⣀⣀⣀⣀⣀⣀⣘⣓⣚⣛⣛⣛⣛⣛⡛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⣷⡯⡦⣧⣤⣥⣧⣷⡮⡯⣤⣥⡧⡬⣭⣼⣧⣤⣬⡼⢤⣤⢥⣧⢧⣬⣤⡤⣧⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠷⠯⠮⠤⠥⠤⠤⠧⠵⠮⠿⠿⠯⠤⠭⠤⠧⠼⠤⠥⢯⣭⣼⣽⣵⣶⣦⣤⣧⣼⣥⣭⣯⣤⣭⣤⣿⣧⣥⣼⣧⣤⣬⣴⣼⣦⣾⣤⣤⣵⣥⣧⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⣤⢀⡄⠄⠀⢀⣤⠠⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡤⣤⡤⠤⠤⡤⠤⡤⣤⣤⢤⢤⢤⠤⡤⢤⢤⠤⡤⡤⠾⢿⢿⠿⢿⢿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣶⡷⣶⠾⡷⠶⢶⢷⡾⣾⣾⢾⡾⠶⡾⡾⣶⣷⣷⣶⠾⠾⣶⢾⣾⢷⠾⠶⣶⠿⣿⣿⠿⣿⡿⣿⢿⣿⣿⢿⢿⢿⠿⢿⠿⡿⡿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠓⠒⠛⠛⠓⠚⠚⠓⠛⠛⠛⠛⠓⠛⠛⠛⠛⠓⢺⢾⣶⣾⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣶⣿⣵⣾⣿⣷⣾⣶⣷⣷⣿⣿⣯⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠘⠃⠀⠀⠈⠘⠈⠀⠀⠀⠀⠀⠀⡸⠤⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣧⣒⣏⣭⣻⣟⣋⣐⣕⣇⣉⣏⣟⣟⣻⣿⣟⣭⣛⣻⣩⣟⣛⣟⣯⣿⣫⣏⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⣿⣛⣟⣿⣹⣛⣛⣟⡋⣿⣙⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣖⠒⠲⣲⣒⢲⡖⢖⡖⣶⠖⡒⣒⡶⣖⡖⢲⣲⡲⡒⣞⣟⢿⠻⠟⠿⣻⣻⣟⣛⣿⢿⣛⣟⣛⡿⠟⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⡿⠿⢿⢾⣾⡟⡿⣾⡷⣿⣿⠿⣿⡟⢿⠿⠿⣿⢿⠻⣿⠿⠿⣻⣿⡿⣿⣿⣿⣿⠿⢿⡿⢿⣿⠿⢻⠟⢻⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⣛⠛⠛⠛⠓⠚⠛⠛⠛⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣆⠀⢒⢲⡶⣲⡖⡲⡖⣶⣲⢲⡖⡆⡒⠶⣖⡲⣶⡆⣷⡶⢲⠖⢒⣲⣶⠀⣶⡶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣟⠉⢛⢿⡻⢻⡟⡻⡟⣿⠝⠻⢿⠹⠿⠝⢛⢿⣟⠿⠟⠛⢻⣿⣿⣟⢿⡛⣿⣻⡿⢻⠻⡛⢻⢻⠿⡟⠛⠟⠻⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠀⠀⢠⡀⣤⣤⡠⣀⢠⡤⣠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⡲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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                    ䷩ 𝚕𝚒𝚗𝚎 2336

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/downsides-of-lvfs/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/downsides-of-lvfs/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IBM’s_LVFS_(Linux_Vendor_Firmware_Service)_is_a_Malicious_Remote_Backdoor_and
You_Should_Turn_It_Off_Now⠀✐


Posted in Free/Libre_Software, GNOME, GNU/Linux, IBM, Red_Hat at 5:19 pm by
Guest Editorial Team


Reprinted with permission from Ryan_Farmer.


The Linux Vendor Firmware Service is a Malicious Remote Backdoor, and You
Should Turn it Off Now.


For context, see: You_May_Get_“Failed_to_load_signature:_Need_more_input”_Error
on_Debian_12_and_Other_Distributions_With_LVFS._What_is_LVFS?


As that article is now incorporated by reference, let us continue the series.


I even ran into this with KDE the other day. The Linux Vendor Firmware Service
screwed up, but the error message was vague and Plasma Discover (the software
center) merely passed it along to me, the user, verbatim.


It turns out it’s not even KDE’s fault. If something happens lower down in the
stack it just opens a dialog box and pastes “What LVFS said.” So the solution
was kill LVFS by removing it from the list of “software repositories”.


The only thing it includes for my Lenovo computers are Microsoft blacklists of
things they don’t want your computer to boot, when you have “Security Theater
Boot” turned on, which I do not. So disabling it closes a serious hole in my
actual security.


In my case, once I finally tracked down the root cause for the error message,
it turned out that IBM is misconfiguring their “Content Delivery Network” for
LVFS and causing a four byte signature mismatch.


So LVFS runs into that problem, it too was “designed” by IBM, and the error
message is bogus and jargon (of course), and never hints that LVFS is the
problem, so KDE passed the message to me and it was unclear what even happened.


If it takes me half an hour to figure out what’s happening, you’ve messed up
and most people wouldn’t even stand a chance.


Since LVFS is a remote backdoor, not even controlled by Debian, and a repo for
blobs thrown in directly by hardware vendors, one has to wonder how this made
it past not only the Debian Social Contract, but how it is Debian Free Software
Guidelines compatible, or acked by Debian Security.


Hmm.


If they’re worried about Free Software Guidelines enough to not include CPU
microcode updates, why are they including a repo they don’t even control for
Microsoft Security Theater Boot revocation lists? Thrown in directly by
Microsoft!


If CPU and sound firmware is defined as “Non-Free software“, then why aren’t
firmware blobs thrown in by Microsoft and hardware vendors into IBM’s remote
backdoor, LVFS?


This violates the Debian Free Software Guidelines:


     Free redistribution.


     Inclusion of source code.


     Allowing for modifications and derived works.


     Integrity of the author’s source code (as a compromise).


     No discrimination against persons or groups.


     No discrimination against fields of endeavor, like commercial use.


     The license needs to apply to all to whom the program is
     redistributed.


     License must not be specific to a product. License must not restrict
     other software.


     –Debian_Free_Software_Guidelines


When I highlight “License must not restrict other software.”, LVFS bringing in
Microsoft “dbx” updates restricts other software. It stops bootloaders that
were previously allowed using Microsoft’s third-party certificate from booting
at all, at Microsoft’s sole discretion.


So LVFS puts Microsoft in control of your computer long after you’ve even
removed Windows, and gives them a backdoor, a remote hole, to decide what you
can boot in the future.


Nobody can even argue that these are Free Software, or that the user could load
modified copies into the UEFI and run them. The only thing you CAN do is turn
off LVFS so it doesn’t flash anymore “updates” into your UEFI firmware which
can’t be backed out.


This probably violates the Debian Social Contract too:


     Debian will remain 100% free.


     We will give back to the free software community.


     We will not hide problems.


     Our priorities are our users and free software.


     Works that do not meet our free software standards [go into ‘contrib’
     or ‘non-Free’].


     -Debian_Social_Contract


Again, firmwares are (usually) not Free, the dbx firmware’s sole purpose is to
prevent the user from booting things. And firmware updates mostly happen to
silently hide problems with hardware so that vendors don’t have to recall it
and provide a corrected version or a refund.


The way LVFS itself is designed, hides problems. (Like the cryptic error
messages IBM put inside it to make it not obvious where its own errors come
from!)


That last one is extraneous, as no Free operating system has ever tried to stop
the user from adding non-Free bits.


Technically, you could take the FSF-approved Triquel_GNU/Linux_distribution,
and add the regular Linux kernel, with blobs, and run Google Chrome. You’d be
missing the whole reason that Trisquel even exists, and basically turn it back
into Ubuntu….but it wouldn’t stop you.


Technically, disabling proprietary software and Snap making sure it doesn’t end
up in the distribution is better than running Ubuntu even if the user does end
up running a normal, blobbed, Linux kernel. But the reason the FSF endorses
Trisquel is that it does not promote ANY ethical harms against the user. The
FSF does not endorse Debian, because there has been far too much compromise,
including LVFS.


Finally, Debian Security.


This thing is not hosted by Debian, and it’s a source of blobs that nobody is
allowed to decompile and study. Nobody can audit them. Some make permanent,
non-reversible changes to your computer, at the whim of a manufacturer, for
malign purposes in the case of Microsoft “dbx” updates.


How did this all get past Debian Security?


To turn off LVFS:


Open Plasma Discover, go to Settings, and uncheck everything that says “LVFS”
under “Firmware Updates”.


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


It should look like this after it asks for your administrative password.


GNOME Software also has an option to disable LVFS repositories, but I don’t
have GNOME on any of my computers now. It shouldn’t be that difficult to find.


Unfortunately, if Microsoft or other “vendors” have damaged your computer
already through IBM’s remote backdoor, then there’s not much you can do to
revert it, but you can make them stop throwing in more things. In the future,
perhaps you should even install Debian or your chosen Linux distribution
offline and make sure LVFS is turned off before you even allow the computer
onto the Internet.


Alternatively, you could get rid of the fwupd junk to make sure LVFS doesn’t
come back:


WARNING! This is definitely a more radical step than turning off the LVFS
repos, but since there’s nothing in those repos for my laptop except Microsoft
“dbx” updates, I decided I didn’t want fwupd at all.


If you have a computer from a vendor that actually updates your UEFI or if
System76 is updating Coreboot for you this way (I don’t know if this is how
they service it or not. ASK THEM.), you may want to skip this.


NOTE: I did this on Debian 12 KDE and it worked for me without proposing
anything stupid or unrelated to fwupd.


I don’t know what happens to GNOME or other Linux distributions if you try to
remove fwupd, and frankly I don’t care since I no longer use GNOME.


If you attempt to remove it from GNOME, be careful that it does not propose
removing other important packages!


Also note, there may be other fwupd packages to tie it into GNOME that I didn’t
include here.


If you totally destroy your OS somehow, you get to keep both pieces. 🙂


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


I opened Synaptic Package manager, and typed fwupd, and arranged the packages
so it shows the installed ones.


Then right-clicked and selected “mark for complete removal” fwupd, fwupd-amd64-
signed, libfwupd2, and plasma-discover-backend-fwupd.


Alternatively,


sudo apt purge fwupd fwupd-amd64-signed libfwupd2 plasma-discover-backend-fwupd


I then verified that LVFS is gone from Plasma Discover:


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


Will this screw up direct loading sound, graphics, WiFi, and CPU firmware?


No, the kernel direct-loads these on boot, so my system did not have any
trouble when I restarted it. I verified that the processors still have the
latest firmware from Intel and the firmware for my devices is still loading
normally.


fwupd appears to only manage updates to system firmwares.


On some computers, this can include entire UEFI upgrades, but on mine it
doesn’t. I don’t want UEFI upgrades in the background even if it did. They can
screw up and brick your entire PC. The firmware that’s in there now works. The
one they offer you has Never Worked. █


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⢿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣯⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣽⣭⣽⣭⣽⣽⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣯⣽⣿⣽⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣒⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣿⣻⣿⣻⣿⣟⣿⣿⣿⡇⠀⠀
⠀⠀⢸⠛⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⡿⢿⠻⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⠴⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣯⣭⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⢿⠿⢿⣿⢿⣿⡿⣿⣿⢿⣿⢿⡿⣿⣿⢿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢘⣾⣻⣳⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣂⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣿⣛⣿⣛⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⢿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣽⣽⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣿⣛⣻⣛⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣒⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⠛⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣛⣻⣿⣟⣻⣿⣿⣟⣿⣻⣿⣟⣟⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⠴⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣯⣭⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢘⣾⣻⣳⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 2699

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(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/gnu-linux-sept-2023/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/gnu-linux-sept-2023/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ GNU/Linux_Versus_Windows_Around_the_World_(Sept._2023)⠀✐


Posted in GNU/Linux, Microsoft, Windows at 12:00 am by Dr. Roy Schestowitz


On desktops/laptops (not counting Android, which is bigger than Windows):


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


Summary: This month’s statCounter_statistics (underlying_data_as_OpenDocument
Format) show that on desktops/laptops GNU/Linux exceeds 10% in several
countries


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠇⢿⣿⢻⣿⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢻⣿⣿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣿⣿⣿⡿⢿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠁⣿⡿⡇⠀⠈⠁⢸⠉⢸⠛⢸⣟⢻⠿⠇⡿⠆⣿⡿⡇⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⠿⢸⣿⣿⣿⣿⣿⡇⣿⣿⡿⠇⣿⡿⣿⣿⢸⣿⢸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣿⣿⡇⠀⡟⠃⡇⠀⠀⠀⢸⠀⢸⠀⢸⠉⠈⠀⠀⡇⠀⡟⠁⡇⠀⢸⣿⣿⠀⢸⣿⢿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠚⠀⣿⡇⡇⠀⣿⡇⡏⠉⢸⠛⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⢸⣿⣿⠀⢸⠛⠸⣿⡝⡇⠀⣿⡍⣿⣿⣿⣿⣿⠀⢸⣿⣿⣯⢹⠀⠀⡇⠀⡇⠀⡇⠁⠀⠀⢸⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⢸⣿⣿⠀⢸⠀⢸⠁⠀⡇⠀⡏⠁⣿⡛⣿⣟⢿⠀⢸⣿⣿⠉⠈⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⢸⡷⢹⠀⢸⠀⢘⠀⠀⡃⠀⡇⠀⡟⠃⠻⠛⢸⠀⢸⣿⣿⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⣿⣿⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢨⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⣿⢹⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠉⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢰⠀⠀⡆⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢰⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⠸⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⠸⣿⣿⣿⣿⣧⣿⣽⣿⣿⣽⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⣿⣿⣷⣿⣷⣾⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣥⣤⣥⣤⣥⣤⣤⣤⣬⣤⣬⣤⣬⣤⣤⣤⣤⣥⣤⣥⣤⣥⣤⣤⣤⣬⣤⣬⣤⣬⣤⣤⣥⣤⣥⣤⣥⣤⣤⣤⣬⣤⣬⣤⣬⣤⣤⣤⣤⣥⣤⣥⣤⣥⣤⣤⣤⣬⣤⣬⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⡿⣽⣿⣿⡿⣫⣿⣿⣿⣿⣿⠿⣿⣟⣿⡿⣽⡿⣿⣿⣻⣿⣻⣿⣿⣿⢿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣻⡿⣯⣿⣿⣿⣟⣿⢿⣿⣿⣿⡿⣿⡿⣿⡿⣯⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⣟⣯⣿⣿⣟⣿⣿⣿⡿⣿⣿⢿⣿⣿⣷⣿⣷⣾⣷⣿⣿⣿⣷⣿⣯⣿⣿⣷⣿⣽⣿⣿⢟⣿⢿⣷⣿⣿⣿⣻⣾⣿⣿⣿⣶⣯⣿⣟⣵⣿⣿⣟⣯⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 2754

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/internet-hall-of-fame-rms-speech/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/internet-hall-of-fame-rms-speech/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ 10_Years_Ago,_When_GNU_Had_Almost_Turned_30,_Richard_Stallman_Gave_This
Internet_Hall_of_Fame_Induction_Speech⠀✐


Posted in Free/Libre_Software, GNU/Linux, Videos at 7:43 pm by Dr. Roy
Schestowitz


Video_download_link


http://techrights.org/wp-content/uploads/2023/09/rms-hall-of-fame.webm


Summary: A decade ago, the founder of the GNU/Linux operating system (which
many, according to him, erroneously call just “Linux”) gave a speech in which
he explained the connection between software freedom and the Internet (his
predictions aged well)



                    ䷩ 𝚕𝚒𝚗𝚎 2788

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/irc-log-170923/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/irc-log-170923/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ IRC_Proceedings:_Sunday,_September_17,_2023⠀✐


Posted in IRC_Logs at 2:54 am by Needs Sunlight


Also available via the Gemini protocol at:


    * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-170923.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-170923.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-social-170923.gmi
    * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-170923.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
 QmS4x2EbCiYjtW4zdQiFsgb3KSB4JMSR6x85pPaZtGJjg6 #boycottnovell  🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


                                                 IRC log for
                                                 #boycottnovell
 QmT8dmn7pociokz5FDGfGr6T8X9rvwsb39nk6LfBhtad38 (full IRC log   🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈
                                                 as plain/ASCII
                                                 text)


                                                 IRC log for
                                                 #boycottnovell-
 QmR54kPr9VpkrkzBk3thVgkBuXC1NVZsfNx1R7HUZnbTb1 social          🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈
                                                 (full IRC log
                                                 as HTML)


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                    ䷩ 𝚕𝚒𝚗𝚎 2915

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/meme-hatchet-job-gone-wrong/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/meme-hatchet-job-gone-wrong/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ [Meme]_Hatchet_Job_Gone_Wrong⠀✐


Posted in Deception, Free/Libre_Software, GNU/Linux, Microsoft at 5:17 am by
Dr. Roy Schestowitz


His old homepage:


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Matthew_Garrett_is_22_years_old_and_an_agriculture_student
   in_Devon._He_is_in_no_way_related_to_Matthew_Garrett_(formerly)_of_Jesus
 College,_Cambridge,_who_is_frankly_terrified_at_the_idea_of_anyone_wanting_to
 know_anything_about_him_and_wishes_you'd_all_go_away_and_stop_bothering_him.
He's_sorely_tempted_to_write_a_book_entitled_'Axe-murdering_for_fun_and_profit'
in_order_to_ensure_that_this_happens_if_you_carry_on._Note:_Any_'Chris_Buckley'
 mentioned_within_this_site_is_a_fictional_character._Resemblance_to_any_other
'Chris_Buckley',_living_or_dead,_is_entirely_coincidental._Note,_too,_that_this
site_is_now_newly_updated_and_full_of_exciting_stuff_that_wasn't_there_before.⦈


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


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


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Tried_to_cancel_everyone;_Ended_up_homeless,_seeking
                                   revenge⦈_


Summary: Matthew_J._Garrett and other_militants did not envision their evil
plot backfiring this badly


        🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Offensive messages from Matthew J. Garrett⦈


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

                    ䷩ 𝚕𝚒𝚗𝚎 3158

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/ring-doorbells-felony-to-use/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/ring-doorbells-felony-to-use/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Ring_Doorbells_Don’t_Solve_Crime._They_Are_a_Felony_to_Use.⠀✐


Posted in America, Deception at 12:02 am by Guest Editorial Team


Reprinted with permission from Ryan_Farmer.
Also available in Gemini.


Yesterday, my spouse told me we were going to his friend’s house.


When we got there, it was yet another friend with one of these damned Ring
Doorbells.


I don’t recall the part of the Illinois_Felony_Eavesdropping_Law or the
Biometric_Information_Privacy_Act, where I gave Amazon or random homeloaners
(they usually don’t own their house, they owe debt to banks) permission to
record me, my face, my voice, or my conversations.


Yet it seems the government is promoting these. Chicago even has a program that
pays people to put them in.


Something that causes the homeloaner and Amazon to commit felonies every day
and open themselves up to civil lawsuits for stolen biometrics at $5,000 per
incident be damned, the police have people to spy on!


The people who install these things have been hoisted on their own petard
before, like that dude in Michigan who got convicted after he filmed himself
shooting at the black kid who “missed the school bus” and ended up with video
footage from his own doorbell, which they pulled from Amazon’s server, which he
could not delete, center stage at his own trial.


Typically, they tell people who don’t like Ring that we are paranoid nutcases.


No, the paranoid nutcases are the people who install the Ring. They are
committing serious crimes, at least in Illinois, just by having it there and
doing what it does, and they are all freaked out that someone will break into
their house and steal from them and rape them by a hyper-sensationalized news
media, which is working with the government to make Americans suspicious of
each other.


Where making them fear a crime wave that isn’t actually going on hasn’t worked,
the media has started blasting more garbage about COVID.


The situation in America benefits when people don’t want to know or care about
anyone else, and adopt a bunker mentality where it’s all about them and the
things they need….to protect their television set, or something, I don’t know.
It’s fucking stupid, isn’t it?


I have never installed a Ring and I never will.


This is Surveillance Capitalism and police state horseshit.


The_police_don’t_even_solve_very_many_crimes_when_you_do_have_a_video_camera.
(NBC News. They admit it to your face and people still buy these things.)


Anecdotally, my ex was mugged in Chicago and the mugger actually grinned real
big at the camera. The Chicago police gave us a report number and nothing ever
happened after that.


The Ring doesn’t solve crime.


The Ring turns you into a criminal for recording me. █


     (720 ILCS 5/14-4)(from Ch. 38, par. 14-4)
     Sec. 14-4.Sentence.
     (a) Eavesdropping, for a first offense, is a Class 4 felony and, for
     a second or subsequent offense, is a Class 3 felony.
     (b) The eavesdropping of an oral conversation or an electronic
     communication of any law enforcement officer, State's Attorney,
     Assistant State's Attorney, the Attorney General, Assistant Attorney
     General, or a judge, while in the performance of his or her official
     duties, if not authorized by this Article or proper court order, is a
     Class 3 felony, and for a second or subsequent offense, is a Class 2
     felony.
     (Source: P.A. 98-1142, eff. 12-30-14.)


     –Illinois_Felony_Eavesdropping_Law_720_ILCS_5/14



                    ䷩ 𝚕𝚒𝚗𝚎 3270

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/turning-webp-off/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/turning-webp-off/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Turning_WebP_Off_in_SeaMonkey_and_LibreWolf⠀✐


Posted in Free/Libre_Software, Google, Patents at 5:28 am by Guest Editorial
Team


Reprinted with permission from Ryan_Farmer.


SeaMonkey is still not patched for the recent_WebP_security_disaster.


Fortunately, until it is patched, I can just turn it off in about:config with
image.webp.enabled to false.


It’s a bad vulnerability and I spent a few days sort of ignoring SeaMonkey
except to deal with my E-Mail, since that doesn’t open remote content by
default anyway, then I found this.


To test it, I took a WebP file and dropped it on SeaMonkey before and after.
After turning WebP off, it offered to “download” the file somewhere instead of
opening the image with its native WebP support.


This is a really terrible image format.


I decided to turn it off in LibreWolf (Firefox fork) too and see if it breaks
anything I use terribly. Already, I see an improvement. With WebP and AVIF
turned off in LibreWolf, Reddit has gone back to sending me real JPEG files!


In Firefox/LibreWolf you can also turn off AVIF (which SeaMonkey doesn’t
support yet) with image.avif.enabled to false.


The way Google writes bad code, if it doesn’t end up breaking the Web for me
it’ll just be more Web browser junk I turn off now.


Jamie Zawinski called WebP “another_turd_in_the_punchbowl” 12 years ago. █



                    ䷩ 𝚕𝚒𝚗𝚎 3330

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/world-wide-web-is-tied-to-chrome/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/world-wide-web-is-tied-to-chrome/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ You_Know_the_World_Wide_Web_is_Tied_to_a_Particular_Web_Browser_When…⠀✐


Posted in Google at 7:13 pm by Dr. Roy Schestowitz


          🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Browser_Market_Share_Worldwide_in_2023⦈_


Summary: This month’s figures_from_statCounter show that only a handful of
nations aren’t overwhelmed by Chrome (many of the “other” browsers are also
based on Chromium and thus represent a similar codebase); a userbase
distribution such as this cannot be reconciled with an “Open Web”


⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⢿⣿⢿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⠉⡉⣩⣭⣧⣬⣤⠶⢿⣧⣿⠥⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠛⠛⠿⠿⠏⠀⠀⠀⠁⠀⠀⠀⠙⢻⣷⠀⠀⠀⠀⠀⣴⡿⠿⠉⠉⠓⠛⠻⢿⢿⠏⡰⠞⠉⠉⠁⠀⠀⠀⠀⠉⠉⠋⠀⠒⠛⠻⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⣾⣄⠀⣠⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⣿⢱⡖⠒⡶⠶⠶⡶⠶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡎⣿⣿
⣿⣿⣟⣥⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠂⢀⠟⠉⠋⢋⣿⣿⢸⡧⠤⣷⣥⣼⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣥⣾⣿⣿⣿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣢⣴⣬⣥⣬⣤⣼⣿⣿⢸⡇⠀⣧⣦⣦⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣀⣀⠠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣡⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣀⣇⣄⣷⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠈⠙⢿⣿⣿⣷⣶⣄⣠⣄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣤⣿⣟⠀⠰⠛⠠⠼⢩⣯⣭⣉⣽⣿⡬⣿⣿⣿⣿⢸⡇⠀⡏⠙⣿⣿⢛⠟⠛⢻⢹⡿⢛⣿⠛⡿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠛⢃⣺⣿⣿⣿⣿⣿⣧⣠⣄⣐⠂⠰⡄⢌⣨⣙⢻⣿⡾⡰⡟⢻⢸⡏⠉⡟⠟⡟⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣠⣀⣴⣵⣽⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠈⢻⣿⣠⣳⣴⣃⣿⣿⣘⣓⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣦⡀⢀⣼⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3388

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

(ℹ) Images, hyperlinks and comments at http://techrights.org/2023/09/18/xwayland-rootfull/#comments
    Gemini version at gemini://gemini.techrights.org/2023/09/18/xwayland-rootfull/

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ XWayland_Rootfull:_For_When_the_Mountain_Won’t_Come_to_Muhammad⠀✐


Posted in Free/Libre_Software, GNU/Linux, IBM, Red_Hat, Site_News at 5:34 am by
Guest Editorial Team


Reprinted with permission from Ryan_Farmer.


I was actually looking into the problem of IBM Red Hat/Fedora trying to kill
the X.org Server with fire, and came across something funny that I didn’t know
about.


XWayland_“Rootfull”,_or_Rootful.


They’ve spelled it both ways in patches, and as everyone who has dealt with IBM
Red Hat knows, quite often the patches are the documentation.


Anyway, the idea with “Rootfull” is that desktop environments that
don’t“support”Wayland (because their developers don’t like going down rabbit
holes) will run under Wayland whether they like it or not.


Since IBM has done about umpteen million patches to try to beat XWayland into
some sort of shape so the user can run something besides the three applications
with native Wayland support that are not from their desktop environment, and it
STILL does not work properly in common cases under a native Wayland window
manager, they are apparently going to have a session for these desktops that’s
technically Wayland.


As long as you define Wayland as, “About the only thing it does is open
XWayland, then run the X11 window managers and give them the entire screen.”


Well, that’s one way to handle this, I guess.


     “We have to kill X11!”


     Why?


     “So you can run X11!”


     -IBM Red Hat


Since KWin_Wayland is nowhere near ready, it would be really nice if Fedora
would at least let KDE users run the working KWin_X11 under XWayland Rootfull
as an X11 window manager.


In fact, KDE should have only “supported” Wayland like this if a distribution
insisted on dropping the X Server.


They should not have written one line of code for “native” Wayland support,
because it duplicates everything that already works fine, and does it poorly,
and now IBM is pissed that almost nobody wants Wayland and is going to open up
a really big fake-o X Server that’s really doing and drawing everything the
user is interacting with the desktop for.


Nothing running directly under Wayland is very stable or dependable.


I’m going to laugh hard when they do this “Rootfull” thing and Cinnamon, MATE,
Xfce, and the dozens of X11 window managers which will never be ported to
Wayland work better than the ones where they rewrote everything, despite the
fact that the Wayland specification is woefully incomplete, inadequate, buggy,
requires custom protocols to handle totally foreseeable use cases, and largely
has to be re-written in different code for each window manager leading to
different bugs depending on what implementation you’re using.


The most reliable way to support Wayland appears to be to not lift a finger,
keep using X11, and let IBM continue to pay salaries claiming that we’ve moved
beyond the X Server.


And sure everyone involved in this Wayland quagmire has done more work trying
to get rid of X11 only to fail and keep the bulk of it around forever anyway.


Just don’t say “wasted efforts” or “angry users” or “confused developers”. Just
don’t tell them they’re_on_meth.


IBM Red Hat has invested a lot of money in this thing, and now like George W.
Bush having failed to find the WMDs, has to explain why it really is all a
success and you’re just not smart enough to see it for what an incredible
success it really is.


About the only thing I’ve heard anyone say Wayland does better than X11 that
might be true is “crash the entire desktop if the screen locker dies instead of
just unlocking the screen”, however Jamie Zawinski did a really good job at not
allowing unauthorized screen unlocks with XScreenSaver.


It was when other people came in, started screwing around, and tying_it_into
complex_GUI_toolkits,_code_libraries,_and_stuff, that you could just “mash_the
keyboard_and_crash_the_screen_locker”.


No matter how good the code you write is, nothing is going to stop people from
[1] screwing it up with their own incompetence, or [2] (IBM_Red_Hat)_swiping
code_they’re_too_dumb_to_understand_and_plagiarizing_it, and then going on to
write Wayland.


For what it’s worth, I think XScreenSaver is a good program.


I use it on KDE on Debian on X11 now that this Wayland nightmare on GNOME has
(for me) been put to bed, and for live wallpaper of flying_toasters on my
Android phone.


When I was a child in 1994 and woke up in the recovery room after a fairly
awful surgery, I probably sat and stared at Flying Toasters for an hour because
I was in a lot of pain and I couldn’t really move and it was the After Dark
module on one of the monitors in the hospital.


I ended up buying a port of After Dark to Windows, published by Sierra On-Line
(one of the better software publishers for games in the 90s for the PCs of the
era).


One thing Wayland definitely does do is take my Flying Toasters from me again.
It has no concept of screensavers, just like GNOME 3 didn’t.


I want to know, where on the doll, screensavers touched Red Hat. █



                    ䷩ 𝚕𝚒𝚗𝚎 3546

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_18/09/2023:_Linux_6.6_RC2_and_7_New_Distro_Releases⠀✐


Posted in News_Roundup at 12:11 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Audiocasts/Shows
          o Kernel_Space
          o Graphics_Stack
          o Applications
          o Instructionals/Technical
          o Games
          o Desktop_Environments/WMs
    * Distributions_and_Operating_Systems
          o Reviews
          o New_Releases
          o BSD
          o Fedora_Family_/_IBM
          o Debian_Family
          o Devices/Embedded
          o Open_Hardware/Modding
          o Mobile_Systems/Mobile_Applications
    * Free,_Libre,_and_Open_Source_Software
          o Education
          o FSF
          o Programming/Development
                # Perl_/_Raku
                # Shell/Bash/Zsh/Ksh
    * § GNU/Linux⠀➾


          o ⚓ 9to5Linux ☛ 9to5Linux_Weekly_Roundup:_September_17th,_2023⠀⇛


                 This week we got quite some cool news for everyone,
                 starting with the beta version of Linux Mint Debian
                 Edition (LMDE) 6, the end of life of Linux kernel 6.4,
                 Fedora Project’s plans to remove the X11 session from its
                 KDE SPin, and the return of ZFS installation on Ubuntu
                 Linux.


                 On top of that, this week brought us new updates for our
                 LibreOffice and KDE Gear software, as well as new Linux
                 devices from TUXEDO Computers and Purism. Below, you can
                 read this week’s hottest news and access all the distro
                 and package downloads in 9to5Linux’s Linux weekly roundup
                 for September 17th, 2023.


          o ⚓ Linux Made Simple ☛ 2023-09-11_[Older]_Linux_Weekly_Roundup
            #252⠀⇛


          o § Audiocasts/Shows⠀➾


                # ⚓ 2023-09-16_[Older]_Zorin_OS_16.3_Core_Quick_Overview
                  #shorts⠀⇛


                # ⚓ 2023-09-15_[Older]_An_Emacs_“Killer_Feature”_Is_Bulk
                  Renaming⠀⇛


                # ⚓ 2023-09-15_[Older]_How_to_install_Nitrux_3.0.0⠀⇛


                # ⚓ 2023-09-15_[Older]_A_new_Steam_console_is_on_the_way.
                  Here’s_what_we_know.⠀⇛


                # ⚓ 2023-09-15_[Older]_Linux_on_a_MacBook_Pro_(M1_Pro):_How
                  good_is_Asahi_now?⠀⇛


                # ⚓ 2023-09-14_[Older]_Nitrux_3.0.0_overview_|_Be_Bold._Be
                  Different.⠀⇛


                # ⚓ 2023-09-14_[Older]_How_To_Make_Your_Own_AI_Images_In
                  Swiftkey!⠀⇛


                # ⚓ 2023-09-14_[Older]_How_to_install_Intellij_Idea_Community
                  on_Debian_12⠀⇛


                # ⚓ 2023-09-14_[Older]_Debian_Linux_0.01_Released_30_Years
                  Ago!!⠀⇛


                # ⚓ 2023-09-13_[Older]_Windows_is_an_imposter_😜⠀⇛


                # ⚓ 2023-09-13_[Older]_How_to_install_Intellij_Idea_Ultimate_on
                  Debian_12⠀⇛


                # ⚓ 2023-09-13_[Older]_How_to_install_Linux_Lite_6.6⠀⇛


                # ⚓ 2023-09-13_[Older]_KDE_Compositor_Handoff_Revolutionizes
                  Wayland⠀⇛


                # ⚓ 2023-09-13_[Older]_Automate_Your_Tasks_with_systemd_Timers:
                  A_Step-by-Step_Guide⠀⇛


                # ⚓ 2023-09-13_[Older]_Is_The_Government_Secretly_Microchipping
                  People?⠀⇛


                # ⚓ 2023-09-12_[Older]_The_Best_Rust_LS_Clone_Is_Dead…_For
                  Now⠀⇛


                # ⚓ 2023-09-12_[Older]_UBUNTU_without_the_CONTROVERSIAL
                  choices:_try_these_5_Linux_distros!⠀⇛


                # ⚓ 2023-09-12_[Older]_Bodhi_Linux_7.0_RELEASED!_THIS_is_The
                  Fastest_Linux_Distro_of_2023🚀!_DistroFocus_Ep:1_(NEW)⠀⇛


                # ⚓ 2023-09-12_[Older]_Linux_Lite_6.6_overview_|_Simple_Fast
                  Free.⠀⇛


                # ⚓ 2023-09-12_[Older]_How_to_install_Viber_on_Debian_12⠀⇛


                # ⚓ 2023-09-11_[Older]_A_Quick_Look_at_AntiX_23⠀⇛


                # ⚓ 2023-09-11_[Older]_Web_Based_Desktop_Environments_Are
                  Really_Weird⠀⇛


                # ⚓ 2023-09-11_[Older]_Linux_Mint_21.2_Mate_Overview_#shorts⠀⇛


                # ⚓ 2023-09-11_[Older]_How_to_install_Telegram_on_Debian_12⠀⇛


                # ⚓ 2023-09-10_[Older]_How_to_install_the_Shotcut_video_editor
                  on_Debian_12⠀⇛


                # ⚓ 2023-09-10_[Older]_Why_Aren’t_Linux_Distros_Setting_A_Root
                  Password?⠀⇛


                # ⚓ 2023-09-09_[Older]_Plasma_6_release_date,_new_Ubuntu_App
                  Store,_GNOME_breaks_extensions:_Linux_&_Open_Source_News⠀⇛


                # ⚓ 2023-09-09_[Older]_You_Are_Wrong_About_Github’s_2FA
                  Initiative⠀⇛


                # ⚓ 2023-09-09_[Older]_Lite-XL…A_Simple_Yet_Powerful_Text
                  Editor⠀⇛


                # ⚓ 2023-09-09_[Older]_Peppermint_OS_2023-07-01_Overview
                  #shorts⠀⇛


                # ⚓ 2023-09-14_[Older]_Enterprise_Linux_Security_Episode_74_–
                  Unlucky_in_Vegas⠀⇛


                # ⚓ Going Linux ☛ 2023-09-12_[Older]_Going_Linux_#445_·
                  Listener_Feedback⠀⇛


                # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_1018⠀⇛


                # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_1017⠀⇛


                # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_1016⠀⇛


                # ⚓ The TLLTS Podcast ☛ The_Linux_Link_Tech_Show_Episode_1015⠀⇛


                # ⚓ Gradually,_Then_Suddenly⠀⇛


                       The Justice Department is taking Google to court
                       over whether Google has illegally maintained a
                       monopoly in online search. Apple announced new
                       iPhones this past week: should you upgrade to the
                       iPhone 15 / 15 Pro? Plus, Rod Pyle stops by the
                       show to talk about NASA’s UFO report that came out.


                # ⚓ [Old]_Too_Many_Distros⠀⇛


                       The Untitled Linux Show covers the week’s hottest
                       Linux news for desktop, gaming, and even
                       enterprise. ULS is the weekly update you don’t want
                       to miss, from the latest kernel development to the
                       updates on your favorite apps! Each episode
                       finishes with a killer command line tip from each
                       host.


                # ⚓ That’s_In_Chapter_Three⠀⇛


                       Writing a tech book is easy if you start with the
                       proper guidance.


                # ⚓ [Repeat] Show_Me_The_ProofMode⠀⇛


                       Doc Searls and Simon Phipps talk with Nathan
                       Freitas, founder of the Guardian Project about
                       ProofMode.


          o § Kernel Space⠀➾


                # ⚓ Hot Hardware ☛ Linux_Mesa_Drivers_Tip_Intel’s_Arc
                  Battlemage_GPU_Draws_Near⠀⇛


                       Work continues apace on Intel’s Arc graphics
                       drivers, but things have gotten to a pretty good
                       state already. The heavily AMD-optimized Starfield
                       notwithstanding, recent games like Armored Core VI:
                       Fires of Rubicon and Baldur’s Gate 3 both worked
                       just fine on launch day, and most other
                       applications we have tested on an Arc Alchemist GPU
                       have been both fully functional and pretty
                       performant, too.


                       It would seem work is also progressing on Intel’s
                       next-generation GPUs, as well. We haven’t heard an
                       official peep from Intel about its “Battlemage” GPU
                       yet, but we know the “Xe2″ architecture upon which
                       it will be based is also slated to show up in the
                       company’s Lunar Lake processors that are expected
                       to come after Arrow Lake, likely in 2025.


                # ⚓ LWN ☛ Linux_6.6-rc2⠀⇛


                       Another week, another -rc.

                       I think the most notable thing about 6.6-rc2 is
                       simply that it's
                       exactly 32 years to the day since the 0.01 release.
                       And that's a round
                       number if you are a computer person.

                       Because other than the random date, I don't see
                       anything that really
                       stands out here. We've got random fixes all over,
                       and none of it looks
                       particularly strange. The genpd -> pmdomain rename
                       shows up in the
                       diffstat, but there's no actual code changes
                       involved (make sure to
                       use "git diff -M" to see them as zero-line
                       renames).

                       And other than that, things look very normal. Sure,
                       the architecture
                       fixes happen to be mostly parisc this week, which
                       isn't exactly the
                       usual pattern, but it's also not exactly a huge
                       amount of changes.

                       Most of the (small) changes here are in drivers,
                       with some tracing
                       fixes and just random things. The shortlog below is
                       short enough to
                       scroll through and get a taste of what's been going
                       on.

                       Please go test,

                                   Linus
                # ⚓ LWN ☛ Kernel_prepatch_6.6-rc2⠀⇛


                       The 6.6-rc2 kernel prepatch is out for testing.


                # ⚓ Slashdot ☛ 2023-09-16_[Older]_KSMBD_Finally_Reaches
                  ‘Stable’_State_in_Release_Candidate_for_Linux_Kernel_6.6⠀⇛


          o § Graphics Stack⠀➾


                # ⚓ Nate Graham ☛ So_let’s_talk_about_this_Wayland_thing⠀⇛


                       Wayland. It comes up a lot: “Bug X fixed in the
                       Plasma Wayland session.” “The Plasma Wayland
                       session has now gained support for feature Y.” And
                       it’s in the news quite a bit lately with the
                       announcement that Fedora KDE is proposing to drop
                       the Plasma X11 session for version 40 and only ship
                       the Plasma Wayland session. I’ve read a lot of
                       nervousness and fear about it lately.


                       So today, let’s talk about it!


                       Wayland is a set of protocols that govern how a
                       compositor draws stuff on the screen, and how apps
                       interact with the compositor’s drawing-stuff-on-
                       the-screen infrastructure. It’s similar to the HTTP
                       and SMTP protocols that govern how web browsers and
                       email clients send and receive web pages and data.


                       Wayland also includes an implementation of those
                       protocols in a set of extremely lightweight
                       libraries called libwayland-client and libwayland-
                       server that offer stable and versioned APIs. Apps
                       and compositors such as KDE’s KWin and GNOME’s
                       Mutter use those APIs to do stuff.


          o § Applications⠀➾


                # ⚓ Linux Links ☛ 12_Excellent_Free_and_Open_Source
                  Scorewriters_–_Compose,_arrange,_print,_and_publish_music⠀⇛


                       Fortunately, there is a wide range of open source
                       scorewriters which are supported in Linux. This
                       article recommends cost-effective alternatives to
                       Sibelius and Finale. The software featured here is
                       released under open source licenses, all are
                       available to download at no charge, and generate
                       music scores which are engraved with traditional
                       layout rules.


                       This article does not limit itself to software with
                       a graphical user interface. One of the benefits of
                       using software which doesn’t depend on a graphical
                       interface is that you can create and edit music on
                       any type of device, even small handheld devices.


                       To provide an insight into the quality of software
                       that is available, we have compiled a list of 12
                       high quality free Linux scorewriters. Whatever your
                       requirements, one or more of these applications
                       will meet your composition needs.


                # ⚓ Make Use Of ☛ The_7_Best_PDF-to-Word_Converters_for_Linux
                  [Ed: Well, better yet, convert to ODF, which is a Free and
                  Open standard]⠀⇛


                       Have you ever felt the need to edit or customize
                       your PDFs with the ease and familiarity of a Word
                       document? If so, you can use PDF-to-Word converters
                       that are designed to transform static PDF documents
                       into editable Word files, suitable for Linux users
                       of all levels of expertise.


                       Whether your goal is streamlined document
                       collaboration, preservation of complex formatting,
                       or user-friendly conversion, here are the best
                       Linux-based PDF-to-Word converters.


                # ⚓ It’s FOSS ☛ Beaver_Notes:_A_Private_Open-Source_Note-Taking
                  App⠀⇛


                       Are you looking for a privacy-focused, note-taking
                       app?


                       Well, then, we stumbled upon just the right thing
                       for you!


                       Beaver Notes is an open-source, cross-platform
                       note-taking app that stores notes locally,
                       foregoing any risk of data breaches and allowing
                       for offline access to the stored notes.


                       I think it can make its way to our list of best
                       note-taking apps for Linux soon.


                       Allow me to take you through this app; I also share
                       my initial impressions below.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Handbook ☛ 2023-09-15_[Older]_Jenkins_on_EC2:
                  Automating_Deployment_with_Terraform⠀⇛


                # ⚓ 2023-09-15_[Older]_Video:_Welcome_to_Unix_Tutorial_YouTube
                  channel⠀⇛


                # ⚓ Linux Handbook ☛ Start_Learning_Linux⠀⇛


                # ⚓ Make Use Of ☛ 2023-09-14_[Older]_How_to_Tether_Any
                  Smartphone_to_Linux_for_Mobile_Internet⠀⇛


                # ⚓ Make Use Of ☛ 2023-09-13_[Older]_How_to_Disable_the
                  Touchscreen_on_a_Chromebook⠀⇛


                # ⚓ Make Use Of ☛ 2023-09-09_[Older]_How_to_Change_Your
                  Password_on_a_Chromebook⠀⇛


                # ⚓ Make Use Of ☛ How_to_Update_and_Upgrade_Linux_on_Your
                  Chromebook⠀⇛


                       Once you’ve set up a Linux environment on your
                       Chromebook, it’s recommended that you update and
                       upgrade the installed Linux packages.


                # ⚓ Linux Made Simple ☛ 2023-09-15_[Older]_How_to_install_Miku
                  Miku_Dance_on_a_Chromebook_in_2023⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-14_[Older]_How_to_install
                  Intellij_Idea_Community_on_Debian_12⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-14_[Older]_How_to_install
                  Pokemon_Infinite_Fusion_on_a_Chromebook⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-13_[Older]_How_to_install
                  Intellij_Idea_Ultimate_on_a_Chromebook_in_2023⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-13_[Older]_How_to_install
                  Intellij_Idea_Ultimate_on_Debian_12⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-12_[Older]_How_to_install_Viber
                  on_Debian_12⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-12_[Older]_How_to_restore
                  applications_at_startup_on_a_Chromebook⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-11_[Older]_How_to_install
                  Telegram_on_Debian_12⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-11_[Older]_How_to_install_WPS
                  Office_on_a_Chromebook_in_2023⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-10_[Older]_How_to_install
                  Natron_on_a_Chromebook_in_2023⠀⇛


                # ⚓ Linux Made Simple ☛ 2023-09-10_[Older]_How_to_install_the
                  Shotcut_video_editor_on_Debian_12⠀⇛


          o § Games⠀➾


                # ⚓ GamingOnLinux ☛ GE-Proton_8-15_release_fixes_Mafia
                  Definitive_Edition⠀⇛


                       Not one to be left out of the updating festivities
                       it seems, Glorious Eggroll has dropped GE-Proton 8-
                       15. This version makes a few changes but honestly
                       it’s a smaller update than 8-14 was. The biggest
                       news here is for fans of Mafia Definitive Edition
                       but here’s the full rundown:


                # ⚓ GamingOnLinux ☛ Heroes_of_Might_and_Magic_II_game_engine
                  fheroes2_v1.0.8_out_now⠀⇛


                       A fresh 1.0.8 version of the Heroes of Might and
                       Magic 2 game engine has been released recently and
                       here’re some tips about what’s new in the fheroes2
                       project.


                # ⚓ [Repeat] GeekWire ☛ Here’s_why_so_many_video_game
                  developers_are_suddenly_abandoning_the_Unity_engine⠀⇛


                       This would’ve been controversial enough by itself.
                       Unity usually makes money off of its engine by
                       sharing revenue with companies who make successful
                       products, but this changes the deal dramatically in
                       Unity’s favor, using shaky metrics that aren’t
                       readily accessible to companies outside of Unity
                       itself.


                       Then developers subsequently noticed that Unity had
                       quietly revised its terms of service to suggest
                       that these changes could be applied retroactively.


                # ⚓ Positech Games ☛ A_longer_perspective_on_the_unity_pricing
                  fiasco⠀⇛


                       There is a lot of online outrage, and justifiably
                       so, and to be honest, there is not nearly enough
                       outrage enough. My perspective on this is
                       different, because I’ve never used unity (I tried
                       once and despised it), and have nothing at stake
                       here. Every game I have made has had its engine
                       coded by me, and I pay nobody anything for the
                       privilege. I thought it might be worth blogging my
                       view, because I think its a different one to
                       everybody else. I’ve been thinking it over, and
                       reckon the best way to articulate my thoughts is a
                       series of separate points


          o § Desktop Environments/WMs⠀➾


                # ⚓ Linuxiac ☛ Xfce’s_Path_to_Wayland_Compatibility:_A_Slow_but
                  Steady_March⠀⇛


                       The transition to the Wayland display protocol has
                       been a hot topic of discussion in the past years
                       among leading desktop environments. Touted as the
                       future of Linux graphics, Wayland promises smoother
                       and more secure graphical experiences.


                       At the same time, its widespread adoption across
                       various desktop environments has been slow, and in
                       many ways, it is still being prepared for prime
                       time.


                       However, GNOME already provides excellent
                       compatibility with Wayland, and the upcoming KDE
                       Plasma 6 intends to make it the default choice.
                       Unfortunately, Xfce, a beloved lightweight desktop
                       environment, lags far behind this trend.


                # ⚓ Make Use Of ☛ 2023-09-14_[Older]_10_Lightweight_Linux
                  Distributions_to_Give_Your_Old_PC_New_Life⠀⇛


                       Need a lightweight operating system? These special
                       Linux distros can run on older PCs, some with as
                       little as 100MB of RAM.


    * § Distributions and Operating Systems⠀➾


          o § Reviews⠀➾


                # ⚓ Distro Watch ☛ Review:_Bodhi_Linux_7.0.0⠀⇛


                       Bodhi Linux 7.0.0 is a nice, light Linux
                       distribution. By design, there is not a lot of
                       preinstalled software, but the Bodhi AppCenter does
                       provide a nice curated selection of recommended
                       software. While my own personal preference for a
                       desktop Linux ISO is for it to come bundled with a
                       complete selection of preinstalled applications,
                       and there is a forthcoming version of Bodhi Linux
                       7.0.0 that will do just that (the AppPack image), I
                       can appreciate the minimalist approach taken by the
                       currently available Bodhi images. Lightness and
                       minimalism are Bodhi’s defining features and it
                       does what it sets out to do and does it well.
                       Having to install all the applications post-install
                       is not for everyone, but for those who wish to go
                       that route, Bodhi Linux 7.0.0 is a solid choice for
                       a starting point from which to customize the
                       application selection.


          o § New Releases⠀➾


                # ⚓ Hyperbola ☛ [Hyperbola_GNU/Linux-libre]_Milky_Way_v0.4.3
                  install_medium_release⠀⇛


                       We hereby announce a new revision of Hyperbola live
                       image for Hyperbola GNU/Linux-libre.


                       Much has changed now for the new release v0.4.3 as
                       we have fixed and updated many packages within our
                       repositories [core] and [extra] and added more
                       options for running Hyperbola GNU/Linux-libre on
                       the desktop: We have therefore added fluxbox-extra
                       and slim-theme-hyperbola as packages. With this
                       version we end also our cycle for GNU/Linux-libre
                       and focus on HyperbolaBSD. We have removed support
                       for zstd, protobuf and redis, more information
                       about that here. Also we do not support PHP any
                       longer (more information to read here). This makes
                       Hyperbola GNU/Linux-libre acting on purpose for
                       freedom, stability and security. So we are happy to
                       hand over the system towards the community and
                       invite everybody interested to enhance it.


                # ⚓ 4MLinux Blog ☛ 4MLinux_44.0_BETA_released.⠀⇛


                       4MLinux 44.0 BETA is ready for testing. Basically,
                       at this stage of development, 4MLinux BETA has the
                       same features as 4MLinux STABLE, but it provides a
                       huge number of updated packages.


                # ⚓ HardenedBSD ☛ HardenedBSD_14-STABLE_Now_Available⠀⇛


                       HardenedBSD 14-STABLE is now officially a thing!
                       Our mirrors are catching up with our inaugural
                       build, and with our build infrastructure limited at
                       200Mbps, please be considerate with bandwidth use.


                # ⚓ Peropesis_2.2:_bison,_gettext,_gperf_and_texinfo⠀⇛


                       Peropesis 2.2 Linux OS is released. In the new
                       edition part of the old software was updated and a
                       few new packages was installed. The newly installed
                       tools are mainly intended for software development
                       purposes.


                # ⚓ Univention_Corporate_Server_5.0-5⠀⇛


                       Univention Corporate Server 5.0-5 is the fifth
                       point release for Univention Corporate Server (UCS)
                       5.0. It contains all erratas released since version
                       5.0-4 for bug fixes, performance improvements and
                       security updates for Samba, Linux, OpenSSH, Bind
                       and Python, among others.


                # ⚓ SysLinuxOS_12.1_released⠀⇛


                       SysLinuxOS 12.1 brings some improvements and bug
                       fixes. By default, it includes the latest kernel
                       6.4 directly from the backports repository,
                       replacing the removed 6.3.8 version. Additionally,
                       VMware Player 17 has been added. Other changes
                       relate to some system icons, and further
                       adjustments have been made in preparation for the
                       upcoming integration of new custom repositories for
                       SysLinuxOS. The changes apply to both versions,
                       Gnome and Mate.


                # ⚓ Fatdog64-900_Final_Release_Notes⠀⇛


                       Fatdog64-900 Final was released 12 September 2023.


                       The Fatdog64 team is pleased to announce the first
                       release of Fatdog64 GNU/Linux 900 series. Release
                       900 is based on LFS (Linux From Scratch) 11.3,
                       replacing the LFS 8.2 used in the 800 series, with
                       packages updated to BLFS (Beyond LFS) of the same
                       version (11.3) or newer.


                       At the time of release there are more than 2400
                       packages and more will be added as time permits.


          o § BSD⠀➾


                # ⚓ Frederic Cambus ☛ On_the_importance_of_distfiles⠀⇛


                       I’ve been involved with the OpenBSD ports
                       collection since 2015, and have accumulated some
                       notes on the topic over the years. This is an
                       attempt at doing a redacted version, mostly for my
                       personal use.


                       It will come at no surprise that distfiles are at
                       the core of the problem domain. The ports system
                       fetches distribution files, most often tarballs,
                       verifies their checksum and starts building
                       programs. In order to be able to reliably build
                       packages from the source tarballs, we need both
                       availability and integrity.


          o § Fedora Family / IBM⠀➾


                # ⚓ LinuxTechi ☛ How_to_Install_Kubernetes_on_Rocky_Linux_9_|
                  AlmaLinux_9⠀⇛


                # ⚓ Red Hat Official ☛ 2023-09-13_[Older]_diary_of_a_Binutils
                  Release⠀⇛


                # ⚓ Red Hat Official ☛ 2023-09-11_[Older]_Red_Hat_is_joining
                  customers_and_partners_for_exciting_Catalyst_projects_at_TM
                  Forum_Digital_Transformation_World_Copenhagen⠀⇛


                # ⚓ Red Hat Official ☛ 2023-09-08_[Older]_Performance_tuning_at
                  the_edge_using_Cache_Allocation_Technology⠀⇛


                # ⚓ Red Hat Official ☛ 2023-09-08_[Older]_You_Asked._We_Acted:
                  Acting_on_your_feedback_from_Red_Hat_Summit_2023⠀⇛


          o § Debian Family⠀➾


                # ⚓ 2023-09-12_[Older]_Freexian_Collaborators:_Monthly_report
                  about_Debian_Long_Term_Support,_August_2023_(by_Roberto_C.
                  Sánchez)⠀⇛


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Realtek_RTL8852BE_based_WiFi_6_and_Bluetooth
                  5.2_module_targets_Smart_Home,_industrial_and_healthcare
                  applications⠀⇛


                       The module only works with Linux as the company
                       only provides drivers for Linux for x86, ARM32, and
                       ARM64 targets. The module targets home automation
                       and security products such as Smart Home appliances
                       and IP cameras, healthcare and medical equipment
                       such as medical wearables and wellness devices,
                       industrial and building automation, robotics, smart
                       cities/parking, pet and animal trackers, and so on.


                       The Realtek RTL8852BE wireless chip does not have a
                       product page on the Realtek website, but it’s
                       already widely used, as we reviewed the GL.iNet
                       Beryl AX router earlier this year, tested an
                       RTL8852BE WiFi 6 M.2 module with the Rock 5B SBC,
                       and also noted its presence in another Rockchip SBC
                       and an Android mini PC.


          o § Open Hardware/Modding⠀➾


                # ⚓ Linux On Mobile ☛ 2023-09-10_[Older]_Weekly_GNU-like_Mobile
                  Linux_Update_(36/2023):_Phosh_0.31.0_and_a_postmarketOS
                  Service_Pack⠀⇛


                # ⚓ SparkFun Electronics ☛ 2023-09-15_[Older]_A_New_DataLogger
                  and_Useful_Sensor⠀⇛


                # ⚓ FSFE ☛ 2023-09-15_[Older]_Router_Freedom:_German_telcos
                  want_to_exclude_fiber⠀⇛


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ Android_users_have_a_new_Nintendo_Switch_emulator_to_play
                  with_–_Phandroid⠀⇛


                # ⚓ Hacker News ☛ Hook:_New_Android_Banking_Trojan_That_Expands
                  on_ERMAC’s_Legacy⠀⇛


                # ⚓ Android Central ☛ OnePlus’_upcoming_budget_Android_tablet
                  appears_in_marketing_renders_|_Android_Central⠀⇛


                # ⚓ CNX Software ☛ Amlogic_S905X5_Armv9_TV_Box_SoC_supports
                  AV1,_H.266,_Ai-SR_–_CNX_Software⠀⇛


                # ⚓ Phone Arena ☛ Google_makes_a_small_change_to_the_Android
                  version_of_the_YouTube_app_–_PhoneArena⠀⇛


                # ⚓ Make Tech Easier ☛ Protecting_Your_Privacy_and_Security_on
                  Android_–_Make_Tech_Easier⠀⇛


                # ⚓ Notebook Check ☛ OPPO_A2_Pro_launches_with_a_premium_gloss
                  over_mid-range_Android_specs_–_NotebookCheck.net_News⠀⇛


                # ⚓ SlashGear ☛ Boosting_Audio_Quality_In_Android_Auto:_Tips
                  And_Tricks⠀⇛


                # ⚓ SlashGear ☛ Every_Android_Foldable_Phone_Released_In_2023,
                  Ranked⠀⇛


                # ⚓ Forbes ☛ Google’s_Latest_Move_To_Improve_Android_Tablets⠀⇛


                # ⚓ Make Use Of ☛ How_to_Set_an_Alarm_on_Your_Android_Phone⠀⇛


                # ⚓ Giz China ☛ How_to_Fix_Android_Smart_TV_App_Problems_–
                  Gizchina.com⠀⇛


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


          o ⚓ [Old] COSS ry ☛ Open_online_meeting:_Project_report_2021 [PDF]⠀⇛


                 The purpose in the first phase of the project was to
                 conduct a preliminary study on how single open source
                 based solutions and tools could be combined to a
                 comprehensive joint solution and research the technical
                 compatibility between the different OS solutions.


                 The project aims to create a comprehensive example
                 solution that is based on open source components. The
                 created example solution aims to offer new business
                 opportunities for COSS member organizations as well as
                 provide new open source solutions especially for smaller
                 businesses and municipalities.


          o ⚓ Hackaday ☛ PyOBD_Gets_Python3_Upgrades⠀⇛


                 One of the best things about open source software is
                 that, instead of being lost to the ravages of time like
                 older proprietary software, anyone can dust off an old
                 open source program and bring it up to the modern era.
                 PyOBD, a python tool for interfacing with the OBD system
                 in modern vehicles, was in just such a state with its
                 latest version still being written in Python 2 which
                 hasn’t had support in over three years. [barracuda-fsh]
                 rewrote the entire program for Python 3 and included a
                 few other upgrades to it as well.


          o § Education⠀➾


                # ⚓ Aigars Mahinovs ☛ Debconf_23_photos⠀⇛


                       And it has been my pleasure to again be here and
                       take lots of pictures of the event and of the
                       surroundings. In total I took 1852 photos and
                       walked just over 50 km between the two venue
                       buildings and all the rooms where action happened.


          o § FSF⠀➾


                # ⚓ [Repeat] FSF ☛ 2023-09-11_[Older]_Call_for_Volunteers:
                  Flyering_for_the_fortieth_anniversary_of_GNU⠀⇛


                # ⚓ [Repeat] FSF ☛ 2023-09-11_[Older]_FSF_Blogs:_The_GNU_System
                  is_turning_forty:_Come_and_celebrate_with_us⠀⇛


          o § Programming/Development⠀➾


                # ⚓ Hackaday ☛ The_End_Of_Basic?⠀⇛


                       Many people, one way or another, got started
                       programming computers using some kind of Basic. The
                       language was developed at Dartmouth specifically so
                       people could write simple programs without much
                       training. However, Basic found roots in small
                       computers and grew to where it is today, virtually
                       unrecognizable. Writing things in something like
                       Visual Basic may be easier than some programming
                       tasks, but it requires a lot of tools and some
                       reading or training. We aren’t sure where the name
                       EndBasic came from, but this program — written in
                       Rust — aims to bring Basic back to a simpler time.
                       Sort of.


                # § Perl / Raku⠀➾


                      # ⚓ Perl ☛ 2023-09-16_[Older]_Of_Go,_C,_Perl_and_fastq
                        file_conversion_Vol_IV_:_gone_in_60_seconds_(or_less)⠀⇛


                      # ⚓ Perl ☛ 2023-09-15_[Older]_CGI::Tiny_&_Dispatch::Fu_–
                        nearly_a_perfect_match⠀⇛


                      # ⚓ Perl ☛ 2023-09-14_[Older]_Perl_Weekly_Challenge_#234
                        –_Sharing_is_Caring⠀⇛


                      # ⚓ Perl ☛ 2023-09-13_[Older]_Get_more_from_you_constants
                        with_constant::more⠀⇛


                      # ⚓ Perl ☛ 2023-09-11_[Older]_Perl_Weekly_Challenge_233:
                        Frequency_Sort⠀⇛


                      # ⚓ Perl ☛ 2023-09-11_[Older]_Perl_Weekly_Challenge_234:
                        Common_Characters⠀⇛


                      # ⚓ Perl ☛ 2023-09-10_[Older]_Announcing_Dancer_Core_Team
                        Changes⠀⇛


                # § Shell/Bash/Zsh/Ksh⠀➾


                      # ⚓ Oil Shell ☛ Oils_0.18.0_–_Progress_on_All_Fronts⠀⇛


                             We’re moving toward the fast C++
                             implementation, so there are two tarballs:
                             [...]



                    ䷩ 𝚕𝚒𝚗𝚎 4553

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Leftover_Links_18/09/2023:_A_Week’s_Catchup,_Climate_Focus⠀✐


Posted in News_Roundup at 12:08 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
    * Defence/Aggression
    * Transparency/Investigative_Reporting
    * Environment
          o Energy/Transportation
          o Wildlife/Nature
          o Overpopulation
    * Finance
    * AstroTurf/Lobbying/Politics
    * Censorship/Free_Speech
    * Freedom_of_Information_/_Freedom_of_the_Press
    * Civil_Rights/Policing
    * Twitter
    * Digital_Restrictions_(DRM)
    * Monopolies
          o Patents
          o Software_Patents
          o Trademarks
          o Copyrights
    * § Leftovers⠀➾


          o ⚓ Drew DeVault ☛ Hyprland_is_a_toxic_community⠀⇛


                 Hyprland is an open source Wayland compositor based on
                 wlroots, a project I started back in 2017 to make it
                 easier to build good Wayland compositors. It’s a project
                 which is loved by its users for its emphasis on
                 customization and “eye candy” – beautiful graphics and
                 animations, each configuration tailored to the unique
                 look and feel imagined by the user who creates it. It’s a
                 very exciting project!


          o ⚓ India Times ☛ Tinder_partners_with_Centre_for_Social_Research_for
            user_safety⠀⇛


                 Online dating platform Tinder on Sunday said it has
                 partnered with the not-for-profit organisation Centre for
                 Social Research to offer safety guidance to its users.
                 The additional safety guide, along with the existing 15
                 safety features on the app, is part of Tinder’s efforts
                 to ensure the safety of its users, utilising NGO CSR
                 India’s insights amid the intersection of technology and
                 violence against women, Tinder told PTI.


          o ⚓ APNIC ☛ Re:_Appointment_of_an_Official_Receiver_for_AFRINIC⠀⇛


                 We see the appointment of a receiver as a positive
                 development, as it will help to ensure that AFRINIC’s
                 members keep receiving registry services and benefit from
                 related activities in the coming months. The
                 establishment of an election timeline puts the
                 organization on a path towards resolving its previous
                 governance issues, which is to the benefit of both the
                 staff and the AFRINIC community. These measures also
                 allow AFRINIC to honour its commitments as set out in
                 Internet Coordination Policy 2 (ICP-2), in the NRO MOU
                 with the other RIRs, and the ASO MOU between the RIRs and
                 ICANN to ensure the operation of the Joint Internet
                 Numbers Registry.


          o § Science⠀➾


                # ⚓ The Conversation ☛ 2023-09-13_[Older]_Flowering_plants
                  survived_the_dinosaur-killing_asteroid_–_and_may_outlive_us⠀⇛


                # ⚓ The Conversation ☛ 2023-09-13_[Older]_Possible_hints_of
                  life_found_on_distant_planet_–_how_excited_should_we_be?⠀⇛


          o § Education⠀➾


                # ⚓ The Economist ☛ The_resumption_of_student-loan_payments
                  will_hit_American_growth⠀⇛


                       By next year, student-loan payments will drop out
                       of growth calculations, because monthly bills will
                       be part of the baseline. Yet for folk struggling to
                       make payments, the holiday will be difficult to
                       forget. According to Dan Collier of the University
                       of Memphis, who studies the impact of student debt,
                       many borrowers saved money to buy a first home or
                       decided that they could afford to have more
                       children.


                # ⚓ Teen Vogue ☛ University_Boards_Are_Swayed_by_Corporate
                  Interests,_but_Students_Can_Take_Power_Back⠀⇛


                       Most Americans believe universities should serve
                       the public good. They’re meant to cultivate
                       critical-thinking skills and equip young people
                       with the knowledge, experience, and values to keep
                       society moving along paths of progress. Today,
                       though, other interests capture universities,
                       steering them away from their promised broad social
                       benefit. Allegations of improper influence due to
                       the presence of corporations, donors, and
                       politicians in higher education abound; we’ve seen
                       claims of energy-sector donors biasing climate
                       research and dogmatic politicians undermining anti-
                       racism initiatives and academic freedoms.
                       Meanwhile, the issues that students, faculty, and
                       staff care about most — quality, affordable
                       education, safe and equitable campuses,
                       institutional sustainability — receive what we
                       believe is lackluster attention from university
                       governing boards.


                # ⚓ Chris Coyier ☛ Live_Coding_Interviews⠀⇛


                       The good news is that companies can get all this
                       information in a better way: the take-home coding
                       exercise. Give people a setup repo with a starter
                       dev environment and problem setup. Then ask them to
                       spend one hour on it and commit their code. The
                       actual interview can then be them talking through
                       how they approached the problem and their code.
                       This is a much closer proxy to day-to-day work, and
                       you’ll learn more about them.


                # ⚓ The Drone Girl ☛ American_drone_maker_Skydio_to_host_first-
                  ever_keynote_(and_there’s_a_virtual_version_too)⠀⇛


                       Skydio has long piqued the interest of the drone
                       industry as an American drone maker that could
                       disrupt a market that’s otherwise largely dominated
                       by DJI. And for folks looking to see behind the
                       Skydio current, here’s a golden opportunity: a
                       free-to-attend keynote hosted by Skydio itself.


          o § Hardware⠀➾


                # ⚓ Deutsche Welle ☛ 2023-09-13_[Older]_China_denies_reports_of
                  ban_on_iPhones⠀⇛


                # ⚓ Hackaday ☛ 3D_Printing_At_100C⠀⇛


                       Normally, 3D printing with filament takes
                       temperatures of around 200 °C. However, there are
                       some crafting plastics that melts in hot water at
                       60 °C. You can get spools of similar plastic that
                       prints at very low temperatures, and some 3D
                       printing pens use it. [Lost in Tech] picked up a
                       spool of the stuff meant for medical printing and
                       found that printing with it was a challenge. You
                       can watch a video of the results below.


                # ⚓ Hackaday ☛ Buck_Converter_Takes_8V_To_100V⠀⇛


                       For those living before the invention of the
                       transistor, the modern world must appear almost
                       magical. Computers are everywhere now and are much
                       more reliable, but there are other less obvious
                       changes as well. Someone from that time would have
                       needed a huge clunky machine like a motor-generator
                       set to convert DC voltages, but we can do it with
                       ease using a few integrated circuits. This one can
                       take a huge range of input voltages to output a
                       constant 5V.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ US News And World Report ☛ 2023-09-13_[Older]_Explainer-Why
                  Has_France_Banned_Sales_of_Apple’s_IPhone_12?⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-13_[Older]_France’s
                  Apple_IPhone_12_Move_Has_Implications_for_Europe:_German
                  Watchdog⠀⇛


                # ⚓ CBC ☛ 2023-09-13_[Older]_Apple_disputes_French_claim_that
                  iPhone_12_above_EU_electromagnetic_radiation_limits⠀⇛


                # ⚓ Engadget ☛ 2023-09-15_[Older]_Apple_will_release_software
                  update_to_address_iPhone_12_radiation_concerns⠀⇛


                # ⚓ CBC ☛ 2023-09-15_[Older]_Apple_will_update_iPhone_12_after
                  France_said_devices_put_out_too_much_radiation [Ed: So Apple
                  lied about radiation levels. It accepts there's a problem
                  now.]⠀⇛


                # ⚓ CNET ☛ 2023-09-15_[Older]_Apple_Has_Fix_for_iPhone_12_in
                  France_Over_Radio_Frequency_Concerns_–_CNET⠀⇛


                # ⚓ Gizmodo ☛ 2023-09-15_[Older]_Apple_Says_It’s_Going_to_Fix
                  Those_Alleged_High-Radiation_iPhone_12s [Ed: The issue which
                  it previous denied existed (it lied)]⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-11_[Older]_Is_COVID_back_in
                  Germany? [Ed: What does "back" mean? It never went away. The
                  response to it was an epic failure.]⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-15_[Older]_Glyphosate:_Will_EU_end
                  use_of_harmful_herbicide?⠀⇛


                # ⚓ CBC ☛ 2023-09-16_[Older]_Additional_Calgary-area_daycares
                  ordered_to_close_after_more_children_test_positive_for_E.
                  coli⠀⇛


                # ⚓ CBC ☛ 2023-09-12_[Older]_Drug_overdoses,_COVID-19_drive
                  Sask._life_expectancy_to_lowest_level_in_22_years⠀⇛


                # ⚓ CBC ☛ 2023-09-13_[Older]_My_COVID-19_rapid_tests_expired.
                  Can_I_still_use_them?⠀⇛


                # ⚓ CBC ☛ 2023-09-13_[Older]_Staggering_mental_health,
                  addiction_stats_push_northern_First_Nations_to_call_for
                  emergency_declaration⠀⇛


                # ⚓ BBC ☛ How_the_fentanyl_crisis’_fourth_wave_has_hit_every
                  corner_of_the_US⠀⇛


                       That year, the US witnessed a grim milestone: for
                       the first time ever, drug overdoses killed more
                       than 100,000 people across the country in one
                       single year.


                       Of those deaths, more than 66% were tied to
                       fentanyl, a synthetic opioid 50 times more powerful
                       than heroin.


                # ⚓ RFA ☛ Cambodian_farmer_says_raising_rats_for_food_has
                  boosted_his_family’s_income⠀⇛


                       Once the rats have matured and fattened up to
                       around 1 kilogram (2.2 pounds) or more, they can be
                       taken to market and sold for 20,000 to 25,000 riel
                       (about $5-6) per head.


                # ⚓ New Yorker ☛ The_Covid_Bump⠀⇛


                       The coronavirus has long since lapsed as a primary
                       concern for most Americans. Can we make progress on
                       a problem when so few seem to care?


                # ⚓ Dr._Vinay_Prasad_embraces_antivax_“do_not_comply”
                  messaging⠀⇛


                       The last three and a half years, during which
                       the COVID-19 pandemic arrived, have been highly
                       educational to me. As much as I thought I knew in
                       early 2020, as news stories about an outbreak of a
                       mysterious infectious pneumonia in China that was
                       found to be due to a novel coronavirus, watching in
                       real time what happened. Although by 2020 I had
                       given up my rather naïve belief from many years ago
                       that mass death from a pandemic of a deadly virus
                       for which a vaccine was developed would fatally
                       erode antivax beliefs among most people and thereby
                       weaken the antivaccine movement, even I never
                       anticipated how massively the pandemic and public
                       health responses to it did exactly the opposite:
                       Strengthen the antivaccine movement beyond anything
                       it had ever achieved before and normalize
                       antivaccine beliefs in our political discourse. By
                       2020, I had also come to understand how a
                       combination of antivaccine messaging equating
                       “resistance” to vaccine mandates (e.g., “do not
                       comply,” which I will get to in a moment)
                       had shifted the political center of gravity of the
                       antivaccine movement sharply right over
                       the preceding decade, but the pandemic taught me
                       that the situation could get so much worse, with an
                       increasing affinity between antivax beliefs and
                       outright fascism. Perhaps most disturbing, I
                       discovered that the pathway from having contrarian
                       beliefs about public health to becoming a full-on
                       pandemic conspiracy theorist antivaxxer was much
                       shorter and easier than I had ever suspected, as I
                       observed in my year-end post for 2020,
                       later speculating why so many physicians
                       are attracted to “contrarian” beliefs and then so
                       easily slide from these beliefs deeper and deeper
                       into conspiracy theory and science denial prodded
                       by audience capture.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Hackaday ☛ Hackaday_Links:_September_17,_2023⠀⇛


                       OK, it’s official — everyone hates San Francisco’s
                       self-driving taxi fleet. Or at least so it seems,
                       if this video of someone vandalizing a Cruise
                       robotaxi is an accurate reflection of the public’s
                       sentiment. We’ve been covering the increasingly
                       fraught relationship between Cruise and San
                       Franciscans for a while now — between their cabs
                       crashing into semis and being used for — ahem —
                       non-transportation purposes, then crashing into
                       fire trucks and eventually having their test fleet
                       cut in half by regulators, Cruise really seems to
                       be taking it on the chin.


                # ⚓ Hackaday ☛ Chromebooks_Now_Get_Ten_Years_Of_Software
                  Updates⠀⇛


                       It’s an acknowledged problem with the mobile phone
                       industry and particularly within the Android
                       ecosystem, that the operating system support on a
                       typical device can persist for far too short a
                       time, leaving the user without critical security
                       updates. With the rise of the Chromebook, this has
                       moved into larger devices, with schools and other
                       institutions left with piles of what’s essentially
                       e-waste.


                # ⚓ Hackaday ☛ Helping_Robots_Learn_By_Letting_Them_Fail⠀⇛


                       The [MIT Technology Review] has just released its
                       annual list of the top innovators under the age of
                       35, and there are some interesting people on this
                       list of the annoyingly accomplished at a young age.
                       Like [Lerrel Pinto], an associate professor of
                       computer science at NY University. His work focuses
                       on teaching robots how to do things in the home by
                       failing.


                # ⚓ India Times ☛ Low-code_software_platform_Airtable_to_lay
                  off_27%_of_workforce⠀⇛


                       Airtable, a low-code platform for building
                       collaborative apps, has announced to lay off about
                       27% of the workforce, or 237 employees, in the
                       second round of job cuts.


                # ⚓ MSN_Is_Getting_Blasted_After_Outrageous_AI-Generated
                  Headline_About_The_Death_Of_Former_NBA_Player⠀⇛


                       Earlier this week, MSN faced backlash for
                       publishing an obituary for former NBA player
                       Brandon Hunter, which was later taken down due to
                       its offensive content. The obituary, believed to be
                       possibly generated by AI, not only carried a
                       derogatory headline but was also fraught with
                       nonsensical and grammatical errors.


                       The obituary for former NBA player Brandon Hunter,
                       which appeared on MSN, created a stir as it
                       referred to the basketball forward as “useless” in
                       its headline. Although Microsoft, the owner of the
                       news aggregation site, has not officially confirmed
                       the use of AI in generating the content, reports
                       strongly suggest this possibility.


                # ⚓ Daniel Aleksandersen ☛ 2023-09-10_[Older]_Microsoft_has_not
                  stopped_forcing_Edge_on_Windows_11_users⠀⇛


          o § Linux Foundation⠀➾


                # ⚓ Datanami ☛ Linux_Foundation_and_Fujitsu_Release_New_AI
                  Technologies_as_Open_Source_Ahead_of_Europe_Summit⠀⇛


                       The Linux Foundation approved the incubation of two
                       new projects, “SapientML” and “Intersectional
                       Fairness” on August 24 to encourage developers
                       worldwide to further experiment and innovate with
                       AI and machine learning technologies, with plans to
                       host future activities like hackathons to engage
                       and build a community to promote open source AI.


                       With these projects, Fujitsu and the Linux
                       Foundation aim to further democratize AI to realize
                       a world in which developers everywhere can easily
                       and securely use the latest technologies on open
                       platforms to create new applications and find
                       innovative solutions to challenges facing business
                       and society.


          o § Security⠀➾


                # ⚓ CyberRisk Alliance LLC ☛ Linux,_macOS_systems_could_be
                  compromised_with_ncurses_library_bugs⠀⇛


                       Malicious actors could exploit various memory
                       corruption vulnerabilities impacting the ncurses
                       programming library to facilitate code execution
                       attacks against systems running on Linux and macOS,
                       reports The Hacker News.


                       Patches have already been issued for the identified
                       flaws, collectively tracked as CVE-2023-29491,
                       which include a denial-of-service with canceled
                       strings bug, an off-by-one error, a stack
                       information leak vulnerability, a heap out-of-
                       bounds during terminfo database file parsing bug,
                       and a stack information leak flaw, according to a
                       Microsoft Threat Intelligence report.


                # ⚓ Gizmo China ☛ Linux_was_Being_Infiltrated_by_Malware_for_3
                  Years_Without_Raising_any_Alarms [Ed: False headline; this is
                  not an original or official source for software]⠀⇛


                       A hidden malware operation has infiltrated the
                       Linux community for a solid three years without
                       raising alarms, says Kaspersky, a Russian
                       cybersecurity firm. Despite Linux being hailed as a
                       secure alternative to mainstream operating systems
                       like Windows and macOS, it appears even the
                       cybersecurity experts missed this one.


                       This quiet attack particularly exploited a so-
                       called free download manager designed for Debian
                       users. What’s unusual? This software was laced with
                       malicious code way back since January 2020. It
                       contained a hidden post-installation script that
                       set off the malware, complete with comments in both
                       Russian and Ukrainian.


                # ⚓ South Africa ☛ Website_served_password-stealing_Linux
                  malware_for_3_years [Ed: So do not download software from
                  unofficial Web sites.]⠀⇛


                       Security researchers at Kaspersky have discovered a
                       seemingly benign website has been serving Linux
                       users with malware for over three years.


                       The official Free Download Manager website
                       (freedownloadmanager[.]org) initially only offered
                       a non-harmful version of the Linux Free Download
                       Manager on a Debian repository for several years.


                # ⚓ Data Breaches ☛ “I’m_Not_Pro-Russia_and_I’m_Not_a
                  Terrorist!”_—-_InfraGard_and_Airbus_Hacker_“USDoD”_Unveils
                  His_New_Campaigns⠀⇛


                       The first time DataBreaches remembers hearing about
                       the man who calls himself “USDoD” was when he
                       posted a sales listing for member data from
                       InfraGard. He had not only managed to acquire data
                       on 80,000 members of an organization dedicated to
                       protecting critical infrastructure, but his
                       revelation of his method exposed some
                       embarrassingly inept security on InfraGard’s part.
                       But that incident and his newest leak involving
                       3,200 vendors of Airbus aren’t the only reasons to
                       pay attention to him. In a somewhat rambling
                       interview with DataBreaches, conducted over several
                       days online, USDoD reveals some of his current
                       operations and future plans with respect to US
                       defense agencies and firms.


                # ⚓ Data Breaches ☛ Sweden’s_Privacy_Protection_Agency_fines
                  insurer_Trygg-Hansa_for_exposing_sensitive_customer_data⠀⇛


                       Trygg-Hansa’s security flaws have meant that
                       information on 650,000 customers has been
                       accessible via the internet. The Privacy Protection
                       Agency (IMY) is now issuing an administrative
                       sanction fee of SEK 35 million against the company.


                # ⚓ Personal_Data_Protection_Commissioner_of_Singapore
                  announces_two_decisions⠀⇛


                       A financial penalty of $3,000 was imposed on
                       Autobahn Rent A Car for failing to put in place
                       reasonable security arrangements to protect the
                       personal data in its possession or under its
                       control. Directions were also issued to strengthen
                       access control measures to administrator accounts
                       and to conduct reasonable security review of
                       technical and administrative arrangements for the
                       protection of personal data.


                       Separately, a financial penalty of $9,000 was also
                       imposed on Century Evergreen for failing to put in
                       place reasonable security arrangements to protect
                       the personal data of jobseekers in its possession
                       or under its control.


                # ⚓ Bleeping Computer ☛ BlackCat_ransomware_hits_Azure_Storage
                  with_Sphynx_encryptor [Ed: Microsoft TCO]⠀⇛


                       The BlackCat (ALPHV) ransomware gang now uses
                       stolen Microsoft accounts and the recently spotted
                       Sphynx encryptor to encrypt targets’ Azure cloud
                       storage.


                       While investigating a recent breach, Sophos X-Ops
                       incident responders discovered that the attackers
                       used a new Sphynx variant with added support for
                       using custom credentials.


                # ⚓ FTX_restores_claims_portal_after_security_breach_incident⠀⇛


                       In a recent turn of events, the claims portal for
                       the globally renowned cryptocurrency exchange FTX
                       has resumed its full-fledged operation. The
                       operations were suspended following a security
                       incident that took place with Kroll, the third-
                       party agent responsible for handling the creditor
                       claims amidst the ongoing FTX bankruptcy.


                       The cybersecurity incident is just one of the
                       myriad challenges FTX has had to navigate as it
                       deals with its bankruptcy case.


                # ⚓ Hearst Communications ☛ As_AI_boosts_Texas_cybercrime,
                  challenges_in_bringing_international_criminals_to_justice
                  remain⠀⇛


                       It used to be easier.


                       Christopher Delzotto remembers the days not so long
                       ago when many online financial scams could be
                       spotted just by reading them. They were full of
                       misspellings, poor grammar and awkward phrasing —
                       all signs that they were created in other countries
                       where a hacker’s first language isn’t English.


                       The rise of artificial intelligence has changed
                       that, offering tools that help cybercriminals clean
                       up their language and opening new doors for hackers
                       to break into computer networks through emails that
                       trick recipients into sharing personal information
                       or by fabricating images or videos used to extort
                       victims.


                # ⚓ Iranian_state-backed_hackers_target_global_satellite,
                  defense,_and_pharma_companies [Ed: Classic Microsoft pulling
                  political cards to distract from its own neglect,
                  incompetence, and very comprehensive damage. Microsoft is the
                  culprit, not the expert.]⠀⇛


                       Microsoft analysts have revealed that Iranian
                       state-backed hackers have been actively targeting
                       satellite, defense, and pharmaceutical companies
                       worldwide.


                # ⚓ The Guardian UK ☛ Federal_government_could_pay_millions_in
                  compensation_over_asylum_seeker_data_breach⠀⇛


                       The Australian government may be liable for tens of
                       millions of dollars in compensation to asylum
                       seekers after it posted their personal details
                       online while they were in immigration detention.


                       The mass data breach, discovered by Guardian
                       Australia in 2014, resulted in information being
                       used, in some cases, to allegedly threaten asylum
                       seekers, or persecute and even jail their family
                       members.


                       Of the nearly 10,000 asylum seekers whose privacy
                       was breached nearly a decade ago, those who
                       suffered “extreme loss and damage” will each be
                       eligible for more than $20,000 in compensation
                       after a decision from the Administrative Appeals
                       Tribunal.


          o ⚓ Open Source Security (Audio Show) ☛ Episode_393_–_Can_you_secure
            something_you_don’t own?⠀⇛


                 Josh and Kurt talk about the weird world we live in how
                 where we can’t control a lot of our hardware. We don’t
                 really have control over most devices we interact with on
                 a daily basis. The conversation shifts into a question of
                 how can we decide what to trust and where. It’s a very
                 strange problem we experience now.


          o ⚓ US News And World Report ☛ 2023-09-16_[Older]_Two_Vegas_Casinos
            Fell_Victim_to_Cyberattacks,_Shattering_the_Image_of_Impenetrable
            Casino_Security [Ed: Windows TCO]⠀⇛


          o ⚓ Vox ☛ 2023-09-15_[Older]_The_chaotic_and_cinematic_MGM_casino
            hack,_explained [Ed: Windows TCO]⠀⇛


          o ⚓ Engadget ☛ 2023-09-11_[Older]_MGM_Resorts_hit_by_‘cybersecurity
            issue,’_leading_to_massive_outage⠀⇛


          o ⚓ LWN ☛ Security_updates_for_Monday⠀⇛


                 Security updates have been issued by Debian (firefox-esr,
                 libwebp, and thunderbird), Fedora (chromium, curl, flac,
                 libtommath, libwebp, matrix-synapse, python-matrix-
                 common, redis, and rust-pythonize), Gentoo (binwalk,
                 ghostscript, python-requests, rar, samba, and wireshark),
                 Oracle (.NET 6.0, kernel, and kernel-container),
                 Slackware (python3), and SUSE (firefox).


          o ⚓ 2023-09-14_[Older]_Password-Stealing_Linux_Malware_Served_For_3
            Years_and_No_One_Noticed [Ed: Nobody "noticed" because it's not an
            official source and you ought not use unofficial sites]⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-10_[Older]_Football_Leaks:_Hacker_Rui
            Pinto’s_trial_set_to_end⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-10_[Older]_Football_Leaks:_Hacker_Rui
            Pinto_gets_suspended_prison_sentence⠀⇛


          o ⚓ CISA ☛ 2023-09-15_[Older]_Fortinet_Releases_Security_Updates_for
            Multiple_Products⠀⇛


          o ⚓ CISA ☛ 2023-09-13_[Older]_Mozilla_Releases_Security_Updates_for
            Multiple_Products⠀⇛


          o ⚓ CISA ☛ 2023-09-12_[Older]_Adobe_Releases_Security_Updates_for
            Multiple_Products⠀⇛


          o ⚓ CISA ☛ 2023-09-12_[Older]_Apple_Releases_Security_Updates_for_iOS
            and_macOS⠀⇛


          o ⚓ CISA ☛ 2023-09-12_[Older]_CISA_Releases_its_Open_Source_Software
            Security_Roadmap⠀⇛


          o ⚓ CISA ☛ 2023-09-12_[Older]_NSA,_FBI,_and_CISA_Release
            Cybersecurity_Information_Sheet_on_Deepfake_Threats⠀⇛


          o ⚓ CISA ☛ 2023-09-15_[Older]_CISA_Releases_Continuous_Diagnostics
            and_Mitigation_Program:_Identity,_Credential,_and_Access_Management
            (ICAM)_Reference_Architecture⠀⇛


          o ⚓ CISA ☛ 2023-09-14_[Older]_CISA_Adds_One_Known_Vulnerability_to
            Catalog⠀⇛


          o ⚓ CISA ☛ 2023-09-14_[Older]_CISA_Releases_Seven_Industrial_Control
            Systems_Advisories⠀⇛


          o ⚓ CISA ☛ 2023-09-14_[Older]_Siemens_SIMATIC,_SIPLUS_Products⠀⇛


          o ⚓ CISA ☛ 2023-09-14_[Older]_Siemens_Parasolid⠀⇛


          o ⚓ CISA ☛ 2023-09-14_[Older]_Siemans_QMS_Automotive⠀⇛


          o ⚓ CISA ☛ 2023-09-14_[Older]_Siemens_RUGGEDCOM_APE1808_Product
            Family⠀⇛


          o ⚓ CISA ☛ 2023-09-14_[Older]_Siemens_SIMATIC_IPCs⠀⇛


          o ⚓ CISA ☛ 2023-09-14_[Older]_Siemans_WIBU_Systems_CodeMeter⠀⇛


          o ⚓ CISA ☛ 2023-09-14_[Older]_Rockwell_Automation_Pavilion8⠀⇛


          o ⚓ CISA ☛ 2023-09-13_[Older]_CISA_Adds_Three_Known_Vulnerabilities
            to_Catalog⠀⇛


          o ⚓ CISA ☛ 2023-09-12_[Older]_CISA_Adds_Two_Known_Vulnerabilities_to
            Catalog⠀⇛


          o ⚓ CISA ☛ 2023-09-12_[Older]_CISA_Releases_Three_Industrial_Control
            Systems_Advisories⠀⇛


          o ⚓ CISA ☛ 2023-09-12_[Older]_Microsoft_Releases_September_2023
            Updates⠀⇛


          o ⚓ CISA ☛ 2023-09-12_[Older]_Hitachi_Energy_Lumada_APM_Edge⠀⇛


          o ⚓ CISA ☛ 2023-09-12_[Older]_Fujitsu_Software_Infrastructure
            Manager⠀⇛


          o ⚓ CISA ☛ 2023-09-11_[Older]_CISA_Adds_Two_Known_Vulnerabilities_to
            Catalog⠀⇛


          o ⚓ Counter Punch ☛ 2023-09-13_[Older]_The_Security_Dilemma⠀⇛


                # § Privacy/Surveillance⠀➾


                      # ⚓ US News And World Report ☛ 2023-09-13_[Older]_Dutch
                        Group_Summons_X_to_Appear_in_Court_Over_Alleged_Data
                        Misuse⠀⇛


                      # ⚓ New Statesman ☛ Now_mine_has_been_stolen,_I_realise
                        how_personal_a_phone_is⠀⇛


                             Home, I google “what to do when your phone is
                             stolen”. I wipe my phone remotely. I cancel
                             my SIM and order a new one. I borrow my
                             flatmate’s phone to call my banks (why do I
                             have four?!): because I use Apple Pay, they
                             cancel my cards as a precaution. I file a
                             police report, though I know nothing will
                             come of it, and an insurance claim; they tell
                             me they will phone the next working day, and
                             I hope they are cleverer than that. I change
                             the passwords on my emails and social media –
                             though I know my phone’s new “owners” likely
                             aren’t interested in my data, just what
                             little money they can get for the handset
                             (and the joke’s on them, really, because the
                             battery life is dire). At this point, I’d buy
                             it from them myself, just to save the hassle.


                      # ⚓ Hollywood Reporter ☛ TikTok_Hit_With_$368M_Fine_Under
                        Europe’s_Strict_Data_Privacy_Rules⠀⇛


                             The investigation found that the sign-up
                             process for teen users resulted in settings
                             that made their accounts public by default,
                             allowing anyone to view and comment on their
                             videos. Those default settings also posed a
                             risk to children under 13 who gained access
                             to the platform even though they’re not
                             allowed.


                      # ⚓ Computer World ☛ UK_rolls_back_controversial
                        encryption_rules_of_Online_Safety_Bill⠀⇛


                             Companies will not be required to scan
                             encrypted messages until it is “technically
                             feasible and where technology has been
                             accredited as meeting minimum standards of
                             accuracy in detecting only child sexual abuse
                             and exploitation content,” said Stephen
                             Parkinson, the Parliamentary Under-Secretary
                             of State for Arts and Heritage, in a planned
                             statement during the bill’s third reading in
                             the House of Lords on Wednesday afternoon.


                      # ⚓ Site36 ☛ Asylum_seekers:_EU_fingerprint_database_to
                        be_expanded_as_it_reaches_capacity_limit⠀⇛


                      # ⚓ NL Times ☛ 2023-09-15_[Older]_TikTok_fined_€345
                        million_in_data_privacy_case_partially_launched_by
                        Dutch_regulator⠀⇛


                      # ⚓ Engadget ☛ 2023-09-15_[Older]_European_regulators
                        fine_TikTok_$368_million_over_failing_to_protect_the
                        data_of_young_users⠀⇛


                      # ⚓ JURIST ☛ Ireland_regulator_fines_TikTok_record_€345
                        million_for_child_data_privacy_violations⠀⇛


                             The Irish Data Protection Commission (DPC)
                             announced on Friday a €345m million fine
                             against social media giant TikTok for severe
                             breaches of data protection regulations. The
                             DPC’s investigation into TikTok’s practices
                             was prompted by escalating concerns over the
                             platform’s handling of personal data,
                             particularly that of minors.


                # § Confidentiality⠀➾


                      # ⚓ Unmitigated Risk ☛ Words_matter_in_cryptography_or_at
                        least_they_used_to⠀⇛


                             With this background in mind, let’s explore
                             three different “Hybrid” approaches to PQC
                             and classical cryptography. By giving each a
                             unique name and using simple examples, to see
                             if we we can show how they differ: Nested
                             Hybrid Signatures, Side-by-Side Hybrid
                             Protocols, and the proposed Merged Hybrid
                             Signatures.


    * § Defence/Aggression⠀➾


          o ⚓ Deutsche Welle ☛ 2023-09-11_[Older]_China:_How_is_Beijing
            whitewashing_its_Xinjiang_policy?⠀⇛


          o ⚓ Spiegel ☛ 2023-09-08_[Older]_Gangs,_Corruption_and_Collapse:_The
            Slow_and_Steady_Demise_of_South_Africa⠀⇛


          o ⚓ Jacobin Magazine ☛ 2023-09-10_[Older]_Unmasking_Canada’s_Role_in
            the_Chilean_Coup⠀⇛


          o ⚓ Axios ☛ IAEA:_Iran_expels_several_inspectors_in_“unprecedented”
            move⠀⇛


                 Iran has informed the International Atomic Energy Agency
                 that it is withdrawing the designation of several senior
                 UN inspectors who were working in the country, IAEA chief
                 Rafael Grossi said on Saturday.


                 Why it matters: The decision is a significant escalation
                 by Iran that could hamper the UN nuclear watchdog’s
                 ability to monitor Tehran’s nuclear program.


          o ⚓ US News And World Report ☛ EU_Urges_Iran_to_Reconsider_Barring_of
            IAEA_Inspectors⠀⇛


                 “The European Union is highly concerned by the … decision
                 by Iran to withdraw the official designation of several
                 experienced IAEA inspectors to monitor and verify its
                 nuclear programme,” the spokesman for EU foreign affairs
                 Peter Stano said in a statement.


          o ⚓ BBC ☛ Lampedusa:_Ursula_von_der_Leyen_and_Giorgia_Meloni_visit
            island_after_migrant_boat_fears⠀⇛


                 More than 8,000 migrants have arrived on the island over
                 the past three days.


                 PM Giorgia Meloni says Italy is being placed under
                 “unsustainable pressure”.


                 Ms von der Leyen acknowledged on Sunday that the issue
                 was “a European challenge and needs a European answer”.


          o ⚓ France24 ☛ EU’s_von_der_Leyen_announces_plan_to_address_migrant
            crisis_during_Lampedusa_visit⠀⇛


                 EU Commission President Ursula von der Leyen pledged the
                 swift return of irregular migrants and a crackdown on the
                 “brutal business” of migrant smuggling Sunday during a
                 visit with Italy’s premier to a tiny fishing island
                 overwhelmed with nearly 7,000 arrivals in a single day
                 this week.


          o ⚓ Deutsche Welle ☛ EU_and_Italian_leaders_visit_Lampedusa_amid
            migrant_spike⠀⇛


                 Around 8,500 migrants landed on the island in 199 boats
                 between Monday and Wednesday this week, according to the
                 UN migration agency.


                 Meloni called for action at the EU level to prevent
                 migrant departures from North Africa to Europe, including
                 the possibility of a naval blockade of North Africa to
                 keep smugglers’ boats from reaching Europe.


          o ⚓ The Strategist ☛ Can_TikTok_alone_tackle_CCP-linked_information
            ops?⠀⇛


                 In a welcome development last year, TikTok announced that
                 it would start publishing insights about the covert
                 influence operations it identifies and removes from its
                 platform globally in its quarterly community guidelines
                 enforcement reports.


                 [...]


                 Since then, the platform has published three quarterly
                 reports that identified 22 separate covert influence
                 operations originating in countries as various as Russia,
                 Azerbaijan, Ireland, Georgia, Kenya, and Taiwan. But
                 there has been one glaring exception: China.


          o § Russia, Belarus, and War in Ukraine⠀➾


                # ⚓ Federal News Network ☛ The_spotlight_is_on_Ukraine_at_UN
                  leaders’_gathering,_but_is_there_room_for_other_global
                  priorities?⠀⇛


                       The war in Ukraine and its visiting president take
                       center stage at the United Nations this week. But
                       developing countries will be vying for the
                       spotlight as well as they push for faster action on
                       poverty and inequality at the first full-on meeting
                       of world leaders since the COVID-19 pandemic
                       disrupted travel. The annual meeting at the U.N.
                       General Assembly takes place at a polarizing and
                       divisive juncture in history.


                # ⚓ Meduza ☛ Ukrainian_General_Staff_says_fighting_near
                  Klishchiivka_still_ongoing_after_earlier_reports_of_its
                  liberation_—_Meduza⠀⇛


                # ⚓ Meduza ☛ Russia_convicts_pregnant_woman_of_failing_to_show
                  up_for_military_service_—_Meduza⠀⇛


                # ⚓ Meduza ☛ Red_Cross_confirms_mayor_of_Kherson_in_Russian
                  captivity_—_Meduza⠀⇛


                # ⚓ Meduza ☛ Ramzan_Kadyrov_appears_in_video_on_his_Telegram
                  channel_as_rumors_spread_of_him_being_in_‘critical_condition’
                  —_Meduza⠀⇛


                # ⚓ Meduza ☛ Drone_crashes_into_oil_depot_in_Russia’s_Oryol
                  region_—_Meduza⠀⇛


                # ⚓ Meduza ☛ First_two_cargo_ships_to_use_temporary_Black_Sea
                  corridor_to_load_grain_arrive_at_port_in_Odesa_region_—
                  Meduza⠀⇛


                # ⚓ Meduza ☛ Ukraine_shoots_down_six_missiles_and_six_drones
                  launched_by_Russia_in_overnight_attack_—_Meduza⠀⇛


                # ⚓ Modern Diplomacy ☛ 2023-09-16_[Older]_Russia’s_Far_East
                  Witnessing_Series_of_Record-Breaking_Agreements_for_the_8th
                  Consecutive_Year⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-16_[Older]_North_Korea’s_Kim_meets
                  Russia’s_Shoigu_in_Vladivostok⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-16_[Older]_Russian_Soyuz_docks_at
                  ISS,_cosmonauts_and_astronaut_aboard⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-16_[Older]_Russia_will_stay
                  ‘infected_with_apathy’_until_Putin_is_gone⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-16_[Older]_Ukraine_updates:_Russia
                  may_attack_power_grids_in_winter⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_North_Korea’s
                  Kim_Inspects_Russian_Nuclear-Capable_Bombers,_Hypersonic
                  Missiles⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_‘Bring_Them
                  Back’:_Ukrainian_Orphans_Demand_Return_of_Children_in
                  Russia⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_North_Korean
                  Arms_for_Russia_Probably_Wouldn’t_Make_a_Big_Difference_in
                  the_Ukraine_War,_Milley_Says⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_Russia_Denies
                  Ukraine_Has_Retaken_Andriivka,_Ukraine_Posts_Video_of
                  Fighting⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_Russian
                  Forces_Near_Norway_at_’20%_or_Less’_Than_Before_Ukraine_War_–
                  Norway’s_Armed_Forces_Chief⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_Russian-
                  Installed_Crimea_Authorities_to_Sell_Ukrainian_Properties⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_Russia_Says
                  It_Downed_Ukrainian_Drones_Over_Three_Regions⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_Russia_Says
                  U.S._Conviction_of_Kremlin-Linked_Businessman_‘Politically
                  Motivated’_–_RIA⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_Ukrainian
                  Minister_Vows_More_Drones_for_Strikes_on_Russian_Warships⠀⇛


                # ⚓ Gizmodo ☛ 2023-09-15_[Older]_Russia’s_Soyuz_Rocket
                  Successfully_Launches_New_ISS_Crew⠀⇛


                # ⚓ Modern Diplomacy ☛ 2023-09-15_[Older]_China,_Russia_and
                  North_Korea:_Kim_Jong-un’s_meeting_with_Putin⠀⇛


                # ⚓ International Business Times ☛ 2023-09-15_[Older]_US_warns
                  Russia_of_consequences_after_it_expels_two_of_its_diplomats⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-15_[Older]_U.S.
                  Ambassador_to_Russia_Visits_Jailed_WSJ_Reporter_Evan
                  Gershkovich⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-15_[Older]_Russian
                  General_in_Algeria_in_Apparent_Return_to_Work_After_Wagner
                  Mutiny_–_Paper⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-15_[Older]_U.S.
                  Ambassador_to_Russia_Visits_Jailed_Reporter_Gershkovich⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-15_[Older]_Soyuz
                  Spacecraft_With_US_Astronaut,_Two_Russian_Cosmonauts_Docks_at
                  ISS⠀⇛


                # ⚓ Modern Diplomacy ☛ 2023-09-14_[Older]_Developing_Far
                  Eastern_Region_Russia’s_Priority⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-14_[Older]_Can_India_mediate_the
                  conflict_between_Russia_and_the_West?⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-14_[Older]_The_Black_Sea_plays_a
                  key_role_in_Russia’s_war_on_Ukraine⠀⇛


                # ⚓ Truthdig ☛ 2023-09-14_[Older]_Can_the_US_Work_With_Russia
                  in_Nagorno-Karabakh?⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_New_US
                  Sanctions_Target_Workarounds_That_Let_Russia_Get_Western_Tech
                  for_War⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_US_Sanctions
                  Five_Turkey-Based_Firms_in_Broad_Russia_Action_on_Over_100
                  Targets⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_U.S._Imposes
                  Fresh_Russia-Related_Sanctions_on_Dozens_of_Entities⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Russia_Expels
                  2_US_Diplomats,_Accusing_Them_of_‘Illegal_Activity’⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_EU_Removes
                  Three_Russian_Business_Leaders_From_Sanctions_List⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Kremlin_Calls
                  Businessmen_Who_Criticise_Russia_to_Get_Sanctions_Relief
                  ‘Traitors’⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Russia_Expels
                  Two_US_Embassy_Staff_for_‘Illegal_Activity’⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Satellite
                  Images_Show_Damage_to_Russian_Naval_Vessels_Struck_in_Ukraine
                  Attack⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Slovakia
                  Expels_Russian_Diplomat_-Foreign_Ministry⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_South_Korea
                  Warns_North_Korea,_Russia_Against_Breaching_UN_Resolutions⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_The_BBC_Says
                  a_Russian_Pilot_Tried_to_Shoot_Down_a_British_Plane_Over_the
                  Black_Sea_Last_Year⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Ukraine
                  Attacks_Russian_Air_Defences_in_Western_Crimea_–_Military⠀⇛


                # ⚓ Latvia ☛ 2023-09-13_[Older]_Saeima_committee_discusses
                  dropping_treaty_agreement_with_‘immoral’_Russia⠀⇛


                # ⚓ Scheerpost ☛ 2023-09-13_[Older]_Blinken:_US_Does_Not_Oppose
                  Ukraine_Targeting_Russian_Territory_With_US-Provided
                  Missiles⠀⇛


                # ⚓ CBC ☛ 2023-09-13_[Older]_Putin_and_Kim_put_on_a_show_as
                  worries_mount_over_what_Russia_might_promise_North_Korea⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-13_[Older]_Baltic_states_shut
                  borders_to_Russia-registered_cars⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-13_[Older]_Putin_and_Kim_Jong_Un
                  meet_in_Russian_Far_East⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-13_[Older]_Russian
                  Spaceport_Visited_by_North_Korea’s_Kim_Has_a_History_of
                  Corruption_and_Construction_Delays⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-13_[Older]_India,_Russia
                  to_Widen_Maritime_Cooperation_-Statement⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-13_[Older]_Kim_Jong_Un’s
                  Trip_to_Russia_Provides_Window_Into_Unique_North_Korean_and
                  Russian_Media_Coverage⠀⇛


                # ⚓ CPJ ☛ 2023-09-12_[Older]_Russian_journalist_Abdulmumin
                  Gadzhiev_sentenced_to_17_years_on_terrorism_charges⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-12_[Older]_How_Russia_drafts
                  migrants_to_fight_in_Ukraine⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-12_[Older]_Ukraine_updates:_Putin
                  says_1,000_Russian_soldiers_sign_up_each_day⠀⇛


                # ⚓ International Business Times ☛ 2023-09-12_[Older]_US_warns
                  North_Korea_not_to_sell_arms_to_Russia_ahead_of_Putin,_Kim
                  meeting⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-12_[Older]_EU_to_Cease
                  Sanctions_Against_Three_Russian_Businessmen_This_Week_-
                  Sources⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-12_[Older]_G7_Condemns
                  ‘Sham_Elections’_Held_by_Russia_on_Ukrainian_Territory⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-12_[Older]_Investigation
                  Into_Russian_Nationalist_Girkin_Extended_Till_Dec_18_–
                  Supporters⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-12_[Older]_Russia’s_Rift
                  With_Old_Ally_Armenia_Deepens_Doubts_About_Its_Clout_in_Ex-
                  USSR⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-12_[Older]_Ukraine
                  Conducted_Drone_Attack_Near_Nuclear_Plant_–_Russia’s
                  Rosatom⠀⇛


                # ⚓ CBC ☛ 2023-09-11_[Older]_Russia_confirms_North_Korean
                  leader_Kim_Jong-un_will_soon_visit⠀⇛


                # ⚓ Counter Punch ☛ 2023-09-11_[Older]_Rightwing_Russians_Want
                  to_Push_Cuba_Toward_a_Neoliberal_Economy⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-11_[Older]_Kim_Jong_Un_to_visit
                  Russia,_governments_confirm⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-11_[Older]_Russia’s_regional_vote:
                  What’s_left_of_democracy?⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Russian
                  Regional_Vote_Delivers_Strong_Result_for_Putin_Amid_Claims_of
                  Rigging⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_In_Russia’s
                  Pacific_Port,_Residents_Await_North_Korea’s_Kim_Jong_Un⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Kremlin:
                  North_Korea’s_Kim_to_Visit_Russia_at_Putin’s_Invitation⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_North_Korea’s
                  Kim_En_Route_to_Russia_for_Talks_With_Putin⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Russia_Says
                  Ban_on_Russians_Bringing_Cars,_Some_Goods_Into_EU_Is_Racist⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Russia_Says
                  Ruling_Party_Wins_Most_Votes_in_Ukrainian_Regions_It
                  Occupies._West_Calls_Elections_Sham⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_North_Korean
                  Leader_Kim_Jong_Un_Will_Visit_Russia,_Setting_the_Stage_for_a
                  Meeting_With_Putin⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Ukraine
                  Collects_Russian_Bodies_on_‘Road_of_Death’_in_Retaken
                  Southeast⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Ukraine_Says
                  Russia_May_Soon_Launch_Big_Mobilisation_Drive⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_UN_Rights
                  Chief_Criticizes_Russia_for_Quitting_Black_Sea_Grain_Deal⠀⇛


                # ⚓ CBC ☛ 2023-09-10_[Older]_Canadian_aid_volunteer_in_Ukraine
                  reportedly_killed_after_Russian_attack⠀⇛


                # ⚓ CBC ☛ 2023-09-10_[Older]_Trudeau_and_Canadian_delegation
                  still_in_New_Delhi_after_plane_grounded⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-10_[Older]_G20:_Russia,_Brazil
                  praise_outcome_of_Delhi_summit⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-10_[Older]_Ukraine_updates:_Kyiv
                  pushes_for_tribunal_for_Russians⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-10_[Older]_Excluding
                  Russia_From_Grain_Deal_Talks_Will_Not_Be_Sustainable,_Erdogan
                  Says⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-10_[Older]_Macron_Says
                  G20_Declaration_Not_a_Victory_for_Russia⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-10_[Older]_Russia_to
                  Return_to_Grain_Deal_Once_All_Moscow’s_Conditions_Met,_Lavrov
                  Says⠀⇛


                # ⚓ Scheerpost ☛ 2023-09-09_[Older]_EU_and_The_Washington_Post
                  Escalate_Their_Censorship_Campaign_with_a_New_Fraudulent
                  “Disinformation_Study”_About_Twitter_and_Russia⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-09_[Older]_Russian-occupied
                  Ukraine:_Organizers_of_sham_elections_face_10_years_in_jail⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-09_[Older]_Ukraine_updates:_Kyiv
                  slams_Russia_language_in_G20_statement⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_Russia_Sticks
                  to_Demands_on_Black_Sea_Grain_Deal,_Rejects_UN_Bank
                  Proposal⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_Rakuten_CEO
                  Touts_Viber’s_Ability_to_Counter_Russian_‘Fake_News’_During
                  Kyiv_Visit⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_Romania_Finds
                  New_Suspected_Russian_Drone_Fragments_on_Its_Territory_-
                  Defence_Ministry⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_Russia_Shoots
                  Down_Three_Drones_in_Crimea,_Says_Russia-Installed_Official⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_EU_Takes_Aim
                  at_Russian_‘Cynicism’_on_Black_Sea_Grain_Deal_at_G20⠀⇛


                # ⚓ Scheerpost ☛ 2023-09-16_[Older]_Ukraine’s_Reconstruction_in
                  BlackRock’s_Hands_&_Gabor_Maté_on_Explosion_of
                  Antidepressants⠀⇛


                # ⚓ Scheerpost ☛ 2023-09-16_[Older]_Zelensky_Implies_Ukrainian
                  Refugees_in_Europe_Will_Resort_to_Terrorism_If_West_Curtails
                  Aid⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_White_House:
                  Biden_to_Meet_With_Zelenskiy,_More_Aid_Coming_for_Ukraine⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_Lithuania
                  Calls_for_More_Money_for_Ukraine_in_EU_Budget_Review⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_Romanian
                  Farmers_Ask_Government_to_Ban_Ukrainian_Grain⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-16_[Older]_Two_Ships
                  Headed_to_Ukraine’s_Black_Sea_Ports_to_Load_Grain_-Official⠀⇛


                # ⚓ Gizmodo ☛ 2023-09-15_[Older]_Senate_Probe_Wants_to_Know
                  Exactly_What_Elon_Musk_Did_in_Ukraine⠀⇛


                # ⚓ Counter Punch ☛ 2023-09-15_[Older]_Bidenomics:_Millions_to
                  Rebuild_Maui,_Billions_for_Ukraine⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-15_[Older]_Germany’s_Baerbock
                  talks_Ukraine_with_US_counterpart⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-15_[Older]_Ukraine_updates:_EU
                  halts_eastern_grain_export_restrictions⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-15_[Older]_Ukraine_war:_Why
                  controlling_Crimea_could_be_key_to_victory⠀⇛


                # ⚓ Engadget ☛ 2023-09-15_[Older]_The_US_Senate_wants_answers
                  over_Starlink’s_Ukrainian_satellite_internet_denial⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-15_[Older]_Biden_Set_for
                  Busy_Week_of_Foreign_Policy,_Including_Talks_With_Brazil,
                  Israel_and_Ukraine_Leaders⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-15_[Older]_Poland,
                  Hungary,_Slovakia_to_Introduce_Own_Bans_on_Ukraine_Grains⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-15_[Older]_Ukraine’s
                  Zelenskiy_Welcomes_EU_Lifting_Grain_Export_Ban,_Warns
                  Neighbours⠀⇛


                # ⚓ Counter Punch ☛ 2023-09-14_[Older]_Depleted_Uranium_Won’t
                  Bring_Peace_to_Ukraine⠀⇛


                # ⚓ Counter Punch ☛ 2023-09-14_[Older]_Ukraine’s_Bandera_Itch⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-14_[Older]_Ukraine:_Kim_talks_show
                  Putin’s_isolation,_Klimkin_says⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-14_[Older]_Ukraine_updates:_Kyiv,
                  Moscow_exchange_volley_of_drones⠀⇛


                # ⚓ The Local SE ☛ 2023-09-14_[Older]_Ukrainian_pilots_complete
                  first_test_of_Swedish_Gripen_jets⠀⇛


                # ⚓ The Local SE ☛ 2023-09-14_[Older]_‘We_just_want_equality’:
                  Ukrainians_in_Sweden_submit_personal_number_petition⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Biden_Names
                  Penny_Pritzker_as_Representative_for_Ukraine’s_Economic
                  Recovery⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Danger_Lurks
                  Behind_‘Every_Bush’_for_Brigade_in_Ukrainian
                  Counteroffensive⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Ukraine
                  Thanks_Bulgaria_for_Not_Extending_Food_Export_Restrictions⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Ukrainian
                  Government_Seeks_to_Use_Tax_Paid_by_Service_Personnel_to_Fund
                  Arms_Production⠀⇛


                # ⚓ Modern Diplomacy ☛ 2023-09-13_[Older]_“To_The_Last
                  Ukrainian”⠀⇛


                # ⚓ Scheerpost ☛ 2023-09-13_[Older]_Does_Elon_Musk’s_Refusal_to
                  Comply_with_All_of_Ukraine’s_Demands_Constitute_Treason?⠀⇛


                # ⚓ 2023-09-13_[Older]_Denmark_to_give_Ukraine_5.8_billion
                  kroner_for_military_equipment⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-13_[Older]_Analysis-Von
                  Der_Leyen_Talks_up_Ukraine’s_EU_Prospects_but_Hungary_Seen_as
                  Stumbling_Block⠀⇛


                # ⚓ Modern Diplomacy ☛ 2023-09-12_[Older]_Are_the_strategic
                  objectives_of_the_West_and_Ukraine_still_aligned?⠀⇛


                # ⚓ Counter Punch ☛ 2023-09-12_[Older]_“A_Good_Investment”:_The
                  Ukraine_War_and_the_US_Arms_Racket⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-12_[Older]_Ukraine:_Which_weapons
                  is_Germany_supplying?⠀⇛


                # ⚓ International Business Times ☛ 2023-09-12_[Older]_G20
                  Summit_adopts_New_Delhi_Declaration_amid_Ukraine_text
                  controversy⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-12_[Older]_Denmark_to
                  Donate_Military_Aid_Package_to_Ukraine,_Worth_$833_Million⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-12_[Older]_Sweden_to
                  Consider_Sending_Fighter_Jets_to_Ukraine,_SR_Radio_Reports⠀⇛


                # ⚓ Counter Punch ☛ 2023-09-11_[Older]_Evaluating_Three_Peace
                  Plans_for_the_Ukraine_War⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-11_[Older]_Ukraine_updates:
                  Germany’s_Baerbock_makes_surprise_visit_to_Kyiv⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-11_[Older]_Ukraine_updates:
                  Putin’s_party_wins_vote_in_annexed_regions⠀⇛


                # ⚓ International Business Times ☛ 2023-09-11_[Older]_Former
                  British_soldier_fighting_in_Ukraine_found_dead_in_water⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Germany_to
                  Provide_Ukraine_Additional_20_Million_Eur_in_Aid_-Baerbock_in
                  Kyiv⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Ukraine_Says
                  It_Has_Retaken_Offshore_Drilling_Platforms_Near_Crimea⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Ukraine_Says
                  It_Regains_More_Territory_in_Counteroffensive⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-11_[Older]_Ukraine’s
                  Place_Is_in_the_EU,_Says_German_Foreign_Minister_in_Kyiv⠀⇛


                # ⚓ Scheerpost ☛ 2023-09-10_[Older]_Ukrainian_Dissident_Resists
                  NATO’s_Proxy_War⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-10_[Older]_Ukraine’s
                  Zelenskiy_Notes_Advances_in_South,_Movement_in_East⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-09_[Older]_How_war_in_Ukraine
                  impacted_Germany’s_budget⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_Ukraine_Says
                  G20_Summit_Declaration_‘Nothing_to_Be_Proud_Of’⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_Ukraine’s
                  Counteroffensive_to_Continue_After_Onset_of_Bad_Weather_Spy
                  Chief⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_Ukrainian
                  Shelling_Kills_One_in_Donetsk_City_–_Mayor⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_UN_Atomic
                  Watchdog_Warns_of_Threat_to_Nuclear_Safety_as_Fighting_Spikes
                  Near_a_Plant_in_Ukraine⠀⇛


                # ⚓ Scheerpost ☛ 2023-09-08_[Older]_US_Intelligence_Official:
                  Media_Misleading_Americans_About_Ukraine’s_Battlefield
                  Success⠀⇛


    * § Transparency/Investigative Reporting⠀➾


          o ⚓ India Times ☛ Letter_found_in_Vatican_reveals_Church_was_told
            about_Holocaust_as_it_happened⠀⇛


                 The document, which was made public this weekend by Milan
                 newspaper Corriere della Sera, adds to the evidence that
                 some scholars say shows Pius knew about the Holocaust as
                 it happened. Some scholars say Pius didn’t want to
                 confront or offend Hitler because he feared communism,
                 believed that the Axis powers would win the war and
                 wanted to avoid alienating millions of German and Nazi-
                 sympathizing Catholics.


          o ⚓ The Dissenter ☛ Arkansas_Governor_Sarah_Huckabee_Sanders_And_The
            Lies_She_Spread_About_People_‘Weaponizing_FOIA’⠀⇛


    * § Environment⠀➾


          o ⚓ NPR ☛ Thousands_expected_to_march_in_New_York_to_demand_that
            Biden_‘end_fossil_fuels’⠀⇛


                 Protesters are calling on Biden to stop federal approvals
                 of new fossil fuel projects, phase out oil and gas
                 drilling on public lands, and declare climate change a
                 national emergency. They want the U.S. to halt oil and
                 gas exports, and transition to a reliance on renewable
                 energy.


                 Burning fossil fuels like coal, oil and gas remains the
                 primary driver of global warming.


          o ⚓ NPR ☛ California_sues_oil_giants,_saying_they_downplayed_climate
            change._Here’s_what_to_know⠀⇛


                 The state of California has filed a sweeping climate
                 lawsuit against Exxon Mobil, Shell, BP, ConocoPhillips,
                 and Chevron, as well as the domestic oil industry’s
                 biggest lobby, the American Petroleum Institute.


                 The suit, filed on Friday in San Francisco Superior
                 Court, claims that the companies misled the public for
                 decades about climate change and the dangers of fossil
                 fuels. It demands the companies help fund recovery
                 efforts related to California’s extreme weather events,
                 from rising sea levels to drought and wildfires, that
                 have been supercharged by human-caused climate change.


          o ⚓ Omicron Limited ☛ Humanity_deep_in_the_danger_zone_of_planetary
            boundaries:_Study⠀⇛


                 “And there’s no indications that any of the
                 boundaries”—except the ozone layer, slowly on the mend
                 since the chemicals destroying it were banned—”have
                 started to bend in the right direction”, he told
                 journalists in a briefing.


                 “This means we are losing resilience, that we are putting
                 the stability of the Earth system at risk.”


                 The study quantifies boundaries for all nine interlocking
                 facets of the Earth system.


          o ⚓ Jacobin Magazine ☛ A_Montana_Judge_Just_Ruled_the_State’s
            Constitution_Bans_New_Fossil_Fuel_Plants⠀⇛


                 In Montana, young residents just won a lawsuit charging
                 that construction of a new gas power plant was barred by
                 the state constitution. But “pro-climate” President Joe
                 Biden is arguing fiercely against letting the US Supreme
                 Court hear a similar case.


          o ⚓ CBC ☛ 2023-09-16_[Older]_Cement_is_everywhere._The_industry_is
            turning_to_carbon_capture_to_curb_emissions,_and_it’s_not_alone⠀⇛


          o ⚓ CBC ☛ 2023-09-11_[Older]_B.C._drought_brings_increased_flood
            risks,_far-reaching_damage,_experts_warn⠀⇛


          o ⚓ Green Party UK ☛ 2023-09-15_[Older]_Green_Party_calls_for_green
            jobs_revolution_in_Wales_following_Port_Talbot_deal⠀⇛


          o ⚓ Green Party UK ☛ 2023-09-14_[Older]_Green-led_Lord_rebellion
            halts_watering_down_of_pollution_rules⠀⇛


          o ⚓ Green Party UK ☛ 2023-09-12_[Older]_Greens_call_for_water_action
            now,_not_more_legal_squabbling⠀⇛


          o ⚓ Modern Diplomacy ☛ 2023-09-16_[Older]_Dire_Consequences_in
            Failing_the_Climate_Change_Goals⠀⇛


          o ⚓ NL Times ☛ 2023-09-16_[Older]_Climate_activists_block_A12_in_The
            Hague_for_eighth_day_in_a_row;_removed_by_police⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-16_[Older]_California_accuses_oil_giants
            downplaying_climate_risks⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-16_[Older]_Climate_Change
            Could_Bring_More_Monster_Storms_Like_Hurricane_Lee_to_New_England⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-16_[Older]_UAW_Strike_Exposes
            Tensions_Between_Biden’s_Goals_of_Tackling_Climate_Change_and
            Supporting_Unions⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-16_[Older]_Dutch_Police_Use
            Water_Cannon_to_Clear_Climate_Protesters_From_Highway⠀⇛


          o ⚓ Gizmodo ☛ 2023-09-15_[Older]_Excessive_Heat_and_Rainfall_Combos
            Will_Be_Practically_Everywhere_If_Emissions_Keep_Rising,_Study
            Says⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-15_[Older]_Fridays_for_Future_climate
            protests_held_worldwide⠀⇛


          o ⚓ International Business Times ☛ 2023-09-15_[Older]_Climate
            Protesters_Arrested_Outside_Citigroup_Headquarters_in_Tribeca⠀⇛


          o ⚓ The Local SE ☛ 2023-09-15_[Older]_Swedish_climate_campaigner
            Greta_Thunberg_to_face_trial_again⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-15_[Older]_Climate_Change
            Could_Bring_More_Storms_Like_Hurricane_Lee_to_New_England⠀⇛


          o ⚓ The Age AU ☛ 2023-09-14_[Older]_Bowen_announces_end_to_‘remnants
            of_climate_wars’⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-14_[Older]_As_Climate_Risks
            Increase,_New_York_Could_Require_Flood_Disclosures_in_Home_Sales⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-14_[Older]_In_Climate_Fight,
            Europe’s_Olive,_Wine_Farmers_Turn_to_Tech_and_Tradition⠀⇛


          o ⚓ University of Michigan ☛ 2023-09-13_[Older]_Climate_action
            opportunities_will_abound_at_Earthfest⠀⇛


          o ⚓ Bridge Michigan ☛ 2023-09-13_[Older]_Opinion_|_Transition_to_EVs
            should_be_good_for_climate_AND_unions⠀⇛


          o ⚓ CBC ☛ 2023-09-13_[Older]_A_grim_report_about_climate_change_in
            Ontario_was_kept_quiet_for_8_months⠀⇛


          o ⚓ Vox ☛ 2023-09-13_[Older]_Climate_disasters_will_happen
            everywhere,_anytime⠀⇛


            UAW Strike Exposes Tensions Between Biden’s Goals of Tackling
            Climate Change and Supporting Unions www.usnews.com/news/business/
            articles/2023-09-16/auto-worker-strike-creates-test-of-bidens-
            goals-on-labor-and-climate”


          o ⚓ NL Times ☛ 2023-09-12_[Older]_Police_defend_referring_child
            climate_protestors’_families_to_social_services⠀⇛


          o ⚓ Bridge Michigan ☛ 2023-09-12_[Older]_Climate_change,_bad
            infrastructure_drives_away_Michigan_residents,_report_says⠀⇛


          o ⚓ Counter Punch ☛ 2023-09-12_[Older]_Second_and_Third-Stage
            Consequences_of_Fossil-Fueled_Climate_Disruptions_Emerging_Fast⠀⇛


          o ⚓ The Age AU ☛ 2023-09-12_[Older]_Government_keeping_climate_report
            hidden_blasted_as_‘fatal_mistake’⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-12_[Older]_As_US_Hits_Record
            of_Costly_Climate_Disasters,_Red_Cross_Plans_$1bn_Effort⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-12_[Older]_US_SEC_Chief:
            Climate_Rule_Won’t_Require_Private_Farmers’_Emissions_Data⠀⇛


          o ⚓ NL Times ☛ 2023-09-11_[Older]_Over_1,000_climate_activists_block
            A12_again,_police_use_water_cannon_and_arrests_made⠀⇛


          o ⚓ NL Times ☛ 2023-09-11_[Older]_All_climate_activists_removed_from
            A12,_more_than_500_people_arrested⠀⇛


          o ⚓ NL Times ☛ 2023-09-11_[Older]_D66_wants_climate_bonus_of_250
            euros_for_all_Dutch_people⠀⇛


          o ⚓ NL Times ☛ 2023-09-11_[Older]_Climate_protestors_block_Hague
            highway_for_third_day;_3,000_arrests_so_far⠀⇛


          o ⚓ NL Times ☛ 2023-09-11_[Older]_Maas_river_deteriorating_due_to
            harmful_substances,_climate_change:_water_companies⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-11_[Older]_Island_States_Seek
            Climate_Protection_From_Law_of_the_Sea⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-11_[Older]_Dutch_Police_Use
            Water_Cannon_to_Clear_Climate_Activists_From_Highway⠀⇛


          o ⚓ Modern Diplomacy ☛ 2023-09-10_[Older]_Nairobi’s_Climate_Summit
            Seeks_External_Funding_Amid_Geopolitical_Challenges⠀⇛


          o ⚓ NL Times ☛ 2023-09-10_[Older]_Police_start_removing_climate
            activists_from_A12_in_The_Hague,_over_10,000_protesters⠀⇛


          o ⚓ NL Times ☛ 2023-09-10_[Older]_XR_climate_activists_block_the_A12
            in_The_Hague,_stopped_by_police⠀⇛


          o ⚓ Counter Punch ☛ 2023-09-10_[Older]_Halmahera:_EVs_For_Uncontacted
            People⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-10_[Older]_Netherlands_police_detain
            thousands_of_climate_protesters⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-10_[Older]_Dutch_Police_Detain
            500_Activists_on_Second_Day_of_Climate_Protests⠀⇛


          o ⚓ Modern Diplomacy ☛ 2023-09-09_[Older]_Climate_and_Urban
            Development:_Uncovering_Societal_Injustice_in_Indonesia’s_New
            Capital⠀⇛


          o ⚓ Scheerpost ☛ 2023-09-09_[Older]_UN_Puts_Out_‘Truly_Damning_Report
            Card’_for_Climate_Action_Before_Global_Summits⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-09_[Older]_Dutch_Police
            Cleared_Out_Climate_Protesters_Blocking_a_Highway_Over_Fossil_Fuel
            Subsidies⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-09_[Older]_Netherlands_Police
            Use_Water_Cannon,_Detain_2,400_Climate_Activists⠀⇛


          o ⚓ Vox ☛ 2023-09-09_[Older]_The_Southern_Hemisphere,_where_it’s
            winter,_has_been_really_hot_too⠀⇛


          o ⚓ Truthdig ☛ 2023-09-08_[Older]_Mobile_Homes_Are_a_Climate_Solution
            and_Deserve_More_Respect⠀⇛


          o § Energy/Transportation⠀➾


                # ⚓ Deutsche Welle ☛ 2023-09-14_[Older]_China_denounces_Europe
                  investigation_of_EVs⠀⇛


                # ⚓ Scheerpost ☛ 2023-09-09_[Older]_Ecuador_Faces_Economic
                  Dilemma_After_Vote_to_Ban_Oil_Drilling_In_the_Amazon⠀⇛


                # ⚓ Deutsche Welle ☛ 2023-09-15_[Older]_Lithium:_The_Czech
                  Republic’s_‘white_gold’_rush⠀⇛


                # ⚓ CBC ☛ 2023-09-12_[Older]_Federal_government_will_break_even
                  in_20_years_on_its_$28.2B_EV_plant_subsidies:_report⠀⇛


                # ⚓ CBC ☛ 2023-09-13_[Older]_‘They’re_ramming_it_down_our
                  throats,’_Alberta_First_Nation_Chief_says_of_oilsands_carbon
                  capture_project⠀⇛


                # ⚓ CBC ☛ 2023-09-15_[Older]_Why_producing_a_barrel_of_oil
                  causes_higher_emissions_in_Saskatchewan_compared_to_Alberta⠀⇛


                # ⚓ Vox ☛ 2023-09-13_[Older]_Is_the_future_of_energy_…_pouring
                  water_on_hot_rocks_in_the_ground?⠀⇛


                # ⚓ Modern Diplomacy ☛ 2023-09-10_[Older]_5_ways_to_power_the
                  energy_transition⠀⇛


                # ⚓ Modern Diplomacy ☛ 2023-09-09_[Older]_Guterres_leads_call
                  to_make_Africa_‘renewable_energy_superpower’⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-09_[Older]_Group_of_20
                  Countries_Agree_to_Increase_Clean_Energy_but_Reach_No_Deal_on
                  Phasing_Out_Fossil_Fuels⠀⇛


                # ⚓ Vox ☛ 2023-09-09_[Older]_We_know_where_the_next_big
                  earthquakes_will_happen_—_but_not_when⠀⇛


                # ⚓ Tom MacWright ☛ Playing_with_bikeshare_data,_part_one⠀⇛


                       Since July, I’ve been archiving data from the Citi
                       Bike GBFS feed. Every five minutes, I have a
                       datapoint for each of the roughly 2,090 stations
                       with numbers for how many bikes are available or
                       broken, and how many bikes are electric. It’s a
                       long-term project that combines my interests in
                       bikes, large datasets, and visualiation. It’s far
                       from finished, though: these are just casual, early
                       “lab notes”.


                # ⚓ H2 View ☛ Tata_Steel_and_UK_Government_approve_electric_arc
                  furnace_deal_for_Port_Talbot⠀⇛


                       Tata Steel and the UK Government have signed a
                       joint agreement on a proposal to invest in electric
                       arc furnace steelmaking at the Port Talbot site in
                       South Wales.


                # ⚓ India Times ☛ Billionaire_investor_Mark_Cuban_loses_$870K
                  in_[cryptocurrency]_scam⠀⇛


                       This is not the first time Cuban has experienced
                       cryptocurrency losses. He lost an unspecified
                       amount of assets when Iron Finance’s TITAN
                       stablecoin collapsed in a rumoured rug pull in
                       2021, the report said.


                # ⚓ Bridge Michigan ☛ 2023-09-14_[Older]_Michigan_Democrats
                  push_carbon-neutral_energy_goal_back_5_years_to_2040⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Offshore_Wind
                  Energy_Plans_Advance_in_New_Jersey_Amid_Opposition⠀⇛


                # ⚓ US News And World Report ☛ 2023-09-14_[Older]_Wholesale
                  Inflation_Spikes_in_August_on_Energy_Prices⠀⇛


                # ⚓ Bridge Michigan ☛ 2023-09-13_[Older]_Opinion_|_It’s_time_to
                  strengthen_renewable_energy_and_efficiency_requirements⠀⇛


          o § Wildlife/Nature⠀➾


                # ⚓ Deutsche Welle ☛ 2023-09-08_[Older]_Wolves_rebalance
                  ecosystems_but_pose_danger_to_livestock⠀⇛


                # ⚓ Omicron Limited ☛ Flowering_plants_survived_the_dinosaur-
                  killing_asteroid—and_may_outlive_us⠀⇛


                       Following this event, known as the Cretaceous-
                       Paleogene mass extinction (K-Pg), a new dawn
                       emerged for Earth. Ecosystems bounced back, but the
                       life inhabiting them was different.


          o § Overpopulation⠀➾


                # ⚓ Kansas Reflector ☛ ‘It’s_an_emergency.’_Midwest_towns
                  scramble_as_drought_threatens_drinking_water.⠀⇛


                       Coltrane said the city’s crisis would likely help
                       it compete for state and federal funding. That’s
                       because the city would tackle dual problems: the
                       ongoing drought and the replacement of lead in its
                       pipes, a major priority of the federal government.


                # ⚓ US News And World Report ☛ 2023-09-15_[Older]_Kansas
                  Cancels_Its_Fall_Turkey_Hunting_Season_Amid_Declining
                  Populations_in_Pockets_of_the_US⠀⇛


                # ⚓ 2023-09-14_[Older]_Recession_continues_in_Turkey’s_largest
                  lake⠀⇛


    * § Finance⠀➾


          o ⚓ International Business Times ☛ 2023-09-12_[Older]_Renters_face
            25%_increase_over_next_3_years_as_landlords_also_grapple_with
            increased_costs⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-14_[Older]_ECB_raises_interest_rates_by
            0.25%⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-14_[Older]_Exclusive-U.S.
            Treasury_Official_Says_Iraq_Must_Act_to_Avoid_Further_Action_on
            Banks⠀⇛


          o ⚓ 2023-09-12_[Older]_Danish_banks_in_dilemma_over_closure_of_ATMs
            in_capital’s_Christianshavn⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-11_[Older]_India_Cenbank,
            Banks_Plan_New_Features_to_Boost_Digital_Currency_Transactions_–
            Sources⠀⇛


          o ⚓ DaemonFC (Ryan Farmer) ☛ Racist_New_York_Times_Calls_South_Korea
            “World’s_Largest_Baby_Exporter”;_Says_Country_With_Terrible
            Unemployment_“Burdened”_By_Low_Birth_Rates.⠀⇛


                 The South Koreans are so ashamed over a situation of high
                 unemployment, that it has become a euphemism to describe
                 over half a million unemployed youth (just the youth) as
                 “taking a break”.


                 But the New York Times says they suffer from “low birth
                 rates”.


                 Apparently more than half a million unemployed young
                 people are suffering…from not having half a million more
                 young people competing with them for jobs,


                 In America now, we have millions of layoffs, hiring
                 freezes, reduced hours (involuntary), but they also tell
                 Americans we “suffer” from less people to contend with
                 for jobs and housing and everything else.


          o ⚓ The Straits Times ☛ Good_times_are_over_for_gig_economy_drivers
            and_riders_in_post-pandemic_Malaysia⠀⇛


                 Higher competition, fee structure changes mean they earn
                 less than what they made during Covid-19.


    * § AstroTurf/Lobbying/Politics⠀➾


          o ⚓ Deutsche Welle ☛ 2023-09-13_[Older]_Japan_PM_Kishida_reshuffles
            Cabinet_as_popularity_wanes⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-13_[Older]_Far-right_AfD’s_Björn_Höcke
            faces_trial_over_Nazi_slogan⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-10_[Older]_Germany:_AfD_candidate_leads
            mayoral_race,_but_runoff_needed⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-14_[Older]_Argentina_shuts_down_Nazi_and
            antisemitic_publisher⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-15_[Older]_Polish_government_under_fire
            over_cash-for-visas_scandal⠀⇛


          o ⚓ Spiegel ☛ 2023-09-09_[Older]_Assad’s_Criminal_Conglomerate:
            Syrian_Economy_Continues_to_Spiral_Toward_Collapse⠀⇛


          o ⚓ Mint Press News ☛ 2023-09-14_[Older]_Seymour_Hersh_Publishes
            Leaked_Memo_Undermining_US_Narrative_on_2013_Syria_Sarin_Attack⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-16_[Older]_Erdogan:_Turkey_can_part_ways
            with_European_Union⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-16_[Older]_Erdogan_Says_Turkey
            May_Part_Ways_With_the_EU._He_Implied_the_Country_Could_End_Its
            Membership_Bid⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-16_[Older]_Erdogan_Says_Turkey
            Could_‘Part_Ways’_With_EU_if_Necessary⠀⇛


          o ⚓ 2023-09-15_[Older]_Analysis:_Cracks_in_Turkey’s_opposition_could
            secure_local_election_revenge_for_Erdoğan⠀⇛


          o ⚓ US News And World Report ☛ 2023-09-09_[Older]_Biden_Gives_Saudi
            Crown_Prince_Mohammed_a_Hearty_Handshake_a_Year_After_an_Awkward
            Fist_Bump_Moment⠀⇛


          o ⚓ HRW ☛ 2023-09-13_[Older]_Saudi_Arabia:_Investment_Fund_Linked_to
            Abuses⠀⇛


          o ⚓ France24 ☛ What_to_expect_as_world_leaders_gather_for_the_UN
            General_Assembly⠀⇛


                 For two years, it was the coronavirus pandemic. Then, it
                 became Russia’s war in Ukraine. Throughout both
                 developments, the perils of climate change, poverty and
                 inequality have steadily, increasingly thrummed through
                 each convening of world leaders at the UN General
                 Assembly in New York.


    * § Censorship/Free Speech⠀➾


          o ⚓ The Nation ☛ The_FOSTA-SESTA_Fallout_Is_About_to_Get_Worse⠀⇛


                 From the outset, there was ample warning about FOSTA-
                 SESTA, even if the law had noble intentions. The Justice
                 Department raised objections before it even passed,
                 concerned that its language extended beyond trafficking
                 to cover “commercial sex transactions involving
                 consenting adults,” which was of “minimal federal
                 interest.” Freedom Network USA, the largest national
                 organization of anti-trafficking social service providers
                 and advocates, also opposed this aspect of the
                 legislation, stating that “further criminalizing
                 consensual commercial sex work, where there is no force,
                 fraud or coercion, is no way to protect victims.” (Sex
                 trafficking survivors typically favor prevention
                 strategies that are structural in nature, like affordable
                 housing, universal basic income, a living wage, and the
                 expunging of criminal records.) Concerned with the threat
                 of censorship, the ACLU warned that the law posed a “real
                 and significant” risk to the “vibrancy of the Internet as
                 a driver of political, artistic, and commercial
                 communication.” But all of these considerations went
                 unheeded, and FOSTA-SESTA sailed through Congress.


          o ⚓ NPR ☛ Hollywood_relies_on_China_to_stay_afloat._What_does_that
            mean_for_movies?⠀⇛


                 This is FRESH AIR. I’m Tonya Mosley. There’s a practice
                 in Hollywood of film studios relying on the Chinese
                 market to break even. But in order for movies to be shown
                 in China, filmmakers often have to self-censor. That’s
                 according to a book by author Erich Schwartzel. For
                 example, when China started allowing U.S. films to be
                 shown there, Hollywood filmmakers had to ensure the
                 movies wouldn’t offend the Chinese government. Schwartzel
                 explores how this relationship has reshaped big-budget
                 movies and the film industry as a whole in the book “Red
                 Carpet: Hollywood, China, And The Global Battle For
                 Cultural Supremacy.” Erich Schwartzel reports on the film
                 industry for The Wall Street Journal. Terry spoke with
                 him last year.


          o ⚓ Quillette ☛ The_Cancellation_of_Bertrand_Russell⠀⇛


                 In February 1940, Russell was appointed Professor of
                 Philosophy at the College of the City of New York by
                 unanimous vote of the Board of Higher Education of New
                 York City. (He was assigned to teach three courses with
                 unwieldy names: logic and its relation to science,
                 mathematics, and philosophy; problems in the foundations
                 of mathematics; and relations of the pure to applied
                 sciences and the reciprocal influence of metaphysics and
                 scientific theories.) But within scarcely a month,
                 Justice John E. McGeehan of the New York Supreme Court
                 (in New York State, this is the designation of the trial
                 court) ordered the Board to revoke Russell’s appointment,
                 ruling that the appointment “adversely affects public
                 health, safety, and morals” and would “aid, abet, or
                 encourage … conduct tending to a violation of penal law.”
                 A year later, in 1941, philosopher and educational
                 reformer John Dewey noted that, although the Russell case
                 was closed, “the issue underlying it is no more settled
                 than the Dred Scott case [which ruled that no African
                 American could ever become a US citizen] settled the
                 slavery issue.” Eight decades later, the issues raised by
                 the Russell case—the rights to free speech and academic
                 freedom—have still not been settled.


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


          o ⚓ CPJ ☛ 2023-09-12_[Older]_Hold_The_Line_Coalition_Welcomes
            Acquittal_of_Maria_Ressa_and_Rappler,_Calls_for_All_Remaining_Cases
            to_Be_Dropped⠀⇛


          o ⚓ CPJ ☛ 2023-09-11_[Older]_Brazilian_police_threaten_Dutch_and
            Colombian_journalists_in_the_Amazon⠀⇛


          o ⚓ 2023-09-13_[Older]_Journalist_from_Cyprus_sentenced_in_Turkey_for
            insulting_the_President⠀⇛


    * § Civil Rights/Policing⠀➾


          o ⚓ Counter Punch ☛ 2023-09-13_[Older]_Indigenous_Voices_Bring_a
            Reality_Check_at_the_Assembly_of_the_Peoples_of_the_Earth_for_the
            Amazon⠀⇛


          o ⚓ Bloomberg ☛ How_Auto_Executives_Misread_the_UAW_Ahead_of_Historic
            Strike⠀⇛


                 Detroit automakers survived a pandemic and semiconductor
                 shortage. They were embracing a historic transition to
                 the electric-vehicle era, underwritten by billions in
                 subsidies from the Biden administration. Profits were
                 rolling in.


          o ⚓ BNN ☛ How_Auto_Executives_Misread_the_UAW_and_Ignited_a_Historic
            Strike⠀⇛


                 The walkout led by United Auto Workers President Shawn
                 Fain at three General Motors Co., Ford Motor Co. and
                 Stellantis NV factories is no ordinary labor-versus-
                 industry clash. The 54-year-old former Chrysler
                 electrician is pushing for a dramatic reset of the wage
                 scales and working conditions that would meaningfully
                 change the economics of car manufacturing. He’s taken
                 aback executives with eye-watering demands for 40% pay
                 increases over the next four years and a 32-hour work
                 week — unheard of in American manufacturing.


                 Just as jarring has been Fain’s unconventional
                 negotiating style. Instead of following decades of
                 precedent and targeting one company at a time, Fain has
                 taken on all three companies employing 146,000 union
                 members at once. He’s inflicting significant damage by
                 disrupting truck and sport utility vehicle output, while
                 taking pains not to burn through too much of the UAW’s
                 strike fund. He’s left himself the option to bring down
                 even more lucrative pickup plants, if need be.


          o ⚓ US News And World Report ☛ 2023-09-14_[Older]_Auto_Union_Chief
            Shawn_Fain_Quotes_Malcolm_X,_Shines_on_Facebook_as_Takes_on_Detroit
            Three⠀⇛


          o ⚓ CBC ☛ 2023-09-09_[Older]_Canadian_actors’_union_blames_‘corporate
            greed’_for_long-running_labour_disputes⠀⇛


          o ⚓ CBC ☛ 2023-09-08_[Older]_Loopholes_keeping_TIFF_star-studded
            during_the_strikes_|_About_That⠀⇛


          o ⚓ Jacobin Magazine ☛ 2023-09-16_[Older]_UAW_President_Shawn_Fain:
            “It_Is_Long_Past_Time_to_Stand_Up_for_the_Working_Class”⠀⇛


          o ⚓ ABC ☛ Iranian_authorities_detain_Mahsa_Amini’s_father_on_1-year
            anniversary_of_her_death⠀⇛


                 Iranian authorities detained the father of Mahsa Amini,
                 the 22-year-old woman who died in police custody last
                 year, as he left his home to visit his daughter’s grave
                 on the first anniversary of her death, human rights
                 observers said.


                 A few hours later, Amjad Amini was taken home by security
                 guards and has been under house arrest, the Hengaw
                 Organization for Human Rights said Saturday.


          o ⚓ NBC ☛ Iran’s_protests_have_been_crushed,_but_Mahsa_Amini’s_death
            is_still_felt_a_year_later_around_the_world⠀⇛


                 Though the underlying human rights issues and economic
                 troubles that drove much of the protests persist, the
                 government’s intense crackdown has largely quashed public
                 unrest — and the authorities want to keep it that way.


          o ⚓ New York Times ☛ ‘An_Innocent_and_Ordinary_Young_Woman’⠀⇛


                 On Saturday, security agents swarmed the neighborhood of
                 Ms. Amini’s family home and prevented her parents from
                 attending a commemoration they had planned at her
                 gravesite. Her father was briefly detained for
                 interrogation and released on Friday, according to Saleh
                 Nikbakht, the family’s lawyer. To further prevent
                 visitors from visiting Ms. Amini’s grave in Saghez, the
                 authorities imposed checkpoints along the road leading to
                 the cemetery and intentionally opened a nearby dam to
                 flood it, residents said on social media.


          o ⚓ Jacobin Magazine ☛ Donald_Trump_Is_Siding_With_Auto_Bosses
            Against_Workers⠀⇛


                 Instead, Trump framed workers’ economic fight against
                 corporate giants Ford, General Motors, and Stellantis as
                 a partisan skirmish, lumping the UAW in with Joe Biden.
                 In a statement delivered late last month, Trump railed
                 against UAW leadership, claiming, “Autoworkers are
                 getting totally ripped off by crooked Joe Biden and also
                 their horrendous leadership. Because these people are
                 allowing our country to do these electric vehicles that
                 very few people want.”


    * § Twitter⠀➾


          o ⚓ Gizmodo ☛ 2023-09-15_[Older]_Did_Elon_Musk_Regret_Buying_Twitter?
            |_Walter_Isaacson_Interview⠀⇛


          o ⚓ International Business Times ☛ 2023-09-14_[Older]_Elon_Musk’s
            biography_reveals_why_the_billionaire_decided_to_buy_Twitter⠀⇛


          o ⚓ Gizmodo ☛ 2023-09-13_[Older]_DoJ_Says_Elon_Musk_May_Have_Violated
            Twitter’s_Privacy_Agreement⠀⇛


          o ⚓ Engadget ☛ 2023-09-13_[Older]_Twitter_spinoff_Bluesky_hits_1
            million_users⠀⇛


          o ⚓ Gizmodo ☛ 2023-09-12_[Older]_Ethereum_Founder_Vitalik_Buterin
            Says_a_SIM_Swap_Was_Behind_His_Twitter_Hack⠀⇛


          o ⚓ Gizmodo ☛ 2023-09-11_[Older]_Ethereum_Founder’s_Twitter_Account
            Hacked_to_Shakedown_Crypto_Bros⠀⇛


          o ⚓ International Business Times ☛ 2023-09-11_[Older]_Twitter_faces
            drop_in_downloads_since_its_rebranding_as_X_by_Elon_Musk⠀⇛


    * § Digital Restrictions (DRM)⠀➾


          o ⚓ Vox ☛ 2023-09-16_[Older]_Apple_has_an_AirPod_repair_problem⠀⇛


    * § Monopolies⠀➾


          o ⚓ IP Kat ☛ 2023-09-14_[Older]_[Guest_post]BREAKING:_BGH_asks_CJEU
            for_clarification_of_‘pastiche’⠀⇛


          o ⚓ Gizmodo ☛ 2023-09-13_[Older]_10_Wacky_Moments_From_Day_One_of
            Google’s_Antitrust_Trial⠀⇛


          o ⚓ The Age AU ☛ 2023-09-11_[Older]_China_just_took_a_$300bn_bite_out
            of_Apple._It_could_be_a_sign_of_things_to_come [Ed: Fictional
            "value" for a fictional "company" that most makes ads,
            commercials]⠀⇛


          o ⚓ International Business Times ☛ 2023-09-11_[Older]_Apple_to_update
            its_accessories_with_USB-C_ports_by_2024⠀⇛


          o ⚓ Florian Müller ☛ 2023-09-14_[Older]_French_publishers’_U.S.
            antitrust_class_action_against_Apple_is_largely_dismissed,_making
            it_economically_irrelevant_short_of_successful_appeal:_Northern
            District_of_California⠀⇛


          o ⚓ CCIA ☛ 2023-09-11_[Older]_The_FTC’s_Amazon_Complaint_–_Market
            Definition_Pulled_Out_of_a_Hat⠀⇛


          o ⚓ Deutsche Welle ☛ 2023-09-12_[Older]_US_and_Google_face_off_in
            landmark_antitrust_trial⠀⇛


          o § Patents⠀➾


                # ⚓ Florian Müller ☛ 2023-09-16_[Older]_Four_of_numerous_flaws
                  of_proposed_EU_SEP_Regulation_are_illustrated_by_OPPO’s
                  Swedish_victory_over_Nokia:_binary_register_won’t_reflect
                  non-binary_world,_and_jurisdictional_differences_matter⠀⇛


                # ⚓ Florian Müller ☛ 2023-09-16_[Older]_New_FTC_initiative_and
                  very_recent_D.C._Circuit_dismissal_of_FTC_antitrust_case
                  relate_to_use_of_patents_in_connection_with_Abbreviated_New
                  Drug_Applications⠀⇛


                # ⚓ Florian Müller ☛ 2023-09-14_[Older]_Huawei_and_Xiaomi_sign
                  patent_cross-license_agreement [Ed: They are owned by the
                  same "company" (regime)]⠀⇛


                # ⚓ Florian Müller ☛ 2023-09-14_[Older]_OPPO_wins_in_Swedish
                  court_as_two_of_Nokia’s_standard-essential_patents_(on_which
                  it_prevailed_in_Mannheim)_are_declared_invalid;_also,_Nokia’s
                  UK_SEP_injunction_can’t_be_enforced_pending_appeal⠀⇛


                # ⚓ Florian Müller ☛ 2023-09-14_[Older]_UPC’s_Vienna_Local
                  Division_demonstrates_its_potential_to_become_attractive,
                  efficient,_inexpensive_patent_litigation_forum [Ed: This is
                  totally illegal (UPC) and Microsoft Florian is OK with it]⠀⇛


                # ⚓ IP Kat ☛ 2023-09-13_[Older]_US_CAFC_finds_obviousness-type
                  double-patenting_based_on_PTA_(In_re_Cellect_LLC)⠀⇛


                # ⚓ Florian Müller ☛ 2023-09-09_[Older]_Standard-essential
                  utility_models_are_major_loophole_in_proposed_EU_SEP
                  Regulation,_presumably_because_of_fundamental_rights_issues:
                  structural_problems⠀⇛


                # ⚓ Tom’s Hardware ☛ Asus_Sues_Samsung_Over_Alleged_Smartphone
                  Patent_Infringement⠀⇛


                       Asus sues Samsung over 4G and 5G patents
                       infringement after the two companies failed to come
                       to a licensing agreement.


                # ⚓ IP Kat ☛ 2023-09-10_[Older]_Interpretation_of_G_2/21:
                  Inventive_step_may_be_supported_solely_by_post-published_data
                  (T_0116/18) [Ed: The kangaroo court of the EPO issues another
                  "decision" (like the dictator asked)]⠀⇛


          o § Software Patents⠀➾


                # ⚓ International Business Times ☛ 2023-09-12_[Older]
                  Microsoft’s_patent_for_‘game_changer’_AI-powered_smart
                  backpack_gets_approved⠀⇛


          o § Trademarks⠀➾


                # ⚓ IP Kat ☛ 2023-09-14_[Older]_Pelham_II:_‘Parody’_as_an_all-
                  encompassing_term_for_‘pastiche’_and_‘caricature’_too?⠀⇛


                # ⚓ IP Kat ☛ 2023-09-13_[Older]_European_Parliament_approves
                  Regulation_for_Non-Agri_Geographical_Indications⠀⇛


                # ⚓ IP Kat ☛ 2023-09-12_[Older]_ALDI_SÜD_may_not_sell_JOOP!_and
                  Calvin_Klein_perfumes⠀⇛


                # ⚓ IP Kat ☛ 2023-09-11_[Older]_Italy_strengthens_protection_of
                  PDOs_and_PGIs⠀⇛


          o § Copyrights⠀➾


                # ⚓ Gizmodo ☛ 2023-09-12_[Older]_Pulitzer_Winner_Michael_Chabon
                  Sues_Meta_for_Allegedly_Using_His_Copyrighted_Material_to
                  Train_AI⠀⇛


                # ⚓ Idiomdrottning ☛ Sympathy_for_the_Copyright_Devil⠀⇛


                       Markets use prices to distribute resources, and
                       prices are set by supply and demand, and that
                       started breaking down in the cassette and floppy
                       disk age where making the initial recording was
                       very expensive but making copiesnof that was cheap.
                       Big capital has tried to patch the hole to their
                       advantage at the expense of the public by
                       introducing artificial scarcity in the form of an
                       exclusive right to make copies, “copyright”.


                       And now it’s getting twisted one more turn, since
                       now the initial work itself is easy to make, but
                       the models, the makers themselves, are wholly owned
                       by big corporations like Microsoft and Google.
                       Capitalism was bad before. It’s going to get
                       cataclysmic now that the workers are wholly owned
                       machines.


                # ⚓ DaemonFC (Ryan Farmer) ☛ Copyright_Plagiarism_of
                  XScreenSaver_by_IBM_Red_Hat_Employee._A_Code_Thief_Assigns
                  IBM_Software_Patents.⠀⇛


                       IBM has managed to violate the freaking BSD license
                       by doing basically the only thing it does not
                       allow. Falsely attributing the work to someone else
                       and then the others have followed along and not
                       done anything to bring themselves out of violation.


                # ⚓ Torrent Freak ☛ Copyright_Trolls_Invade_Canada_Again,
                  Pirates_Surprised_Despite_6,000_Days’_Notice⠀⇛


                       Reports indicate that thousands of Canadian
                       BitTorrent users are receiving new waves of letters
                       demanding cash settlements for movie piracy. Why
                       this controversial business model has been allowed
                       to continue for more than two decades is no longer
                       the big question. Eclipsing that by far is the
                       inexplicable lack of awareness among otherwise
                       savvy internet users who just keep feeding the
                       trolls.



                    ䷩ 𝚕𝚒𝚗𝚎 7187

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Gemini_Links_18/09/2023:_Systemd_Rants_and_Flatpak_integration_in_Qubes_OS⠀✐


Posted in News_Roundup at 7:59 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal/Opinions
          o Technology_and_Free_Software
                # Internet/Gemini
    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ 🔤SpellBinding:_GHWORTN_Wordo:_VINES⠀⇛


                # ⚓ More_Fall_Scenery_(publ._2023-09-18)⠀⇛


                       These photos are from last Wednesday (Sept 13).
                       Here are some interesting catkins I observed


                # ⚓ Annoyed⠀⇛


                       I would never say this to my IRL friends, as it
                       would precipitate a crisis. But we’re all just here
                       drinking and what is griped about shall never pass
                       beyond the wooden door. So…


                       DEAR FRIENDS, STOP TALKING ABOUT BLOODY STARFIELD


                # ⚓ Coffee_3⠀⇛


                       I am 3 months without coffee. I don’t have lust or
                       cravings. But I have gained some weight as I
                       replaced this addiction with adding more sugary
                       food.


          o § Technology and Free Software⠀➾


                # ⚓ Two:_Curation_or_Isolation⠀⇛


                       At any given moment, I’m juggling conflicting ideas
                       on the concept of technological detachment. I have
                       a visceral distaste for talking to Siri, having
                       Google map a route to my destination, or purchasing
                       digital streaming video or audio or games. My
                       partner ribs me about my insistence on keeping a
                       physical media collection and a backup hard drive
                       of all the music I’ve ever bought. Yeah, I
                       subscribe to Spotify, but how much longer is that
                       service model tenable? Further, I think about a
                       world where a connection to the power grid is not
                       assured, let alone stable access to the Internet.


                # ⚓ My_stance_on_systemd⠀⇛


                       I was thinking if I should write this post for a
                       long time. I feel bad when critiquing others (but I
                       still often do it). But this is my own little space
                       and I want to share opinion on systemd, for
                       journaling purposes.


                # ⚓ Hi!_I_wrote_new_post_on_my_capsule⠀⇛


                       I’m not a big fan of systemd due to it taking over
                       so many parts of the system. If it were just an
                       init system I’d be more open to it.


                # ⚓ Flatpak_integration_in_Qubes_OS_templates⠀⇛


                       I recently wanted to improve Qubes OS accessibility
                       to new users a bit, yesterday I found why GNOME
                       Software wasn’t working in the offline templates.


                       Today, I’ll explain how to install programs from
                       Flatpak in a template to provide to other qubes. I
                       really like flatpak as it provides extra security
                       features and a lot of software choice, and all the
                       data created by Flatpak packaged software are
                       compartmentalized into their own tree in `~/.var/
                       app/program.some.fqdn/`.


                # ⚓ Using_multiple_different_terminal_emulators⠀⇛


                       I primarily use the bundled Terminal.app on macOS.
                       It’s pretty good as long as you don’t need or want
                       24-bit color (which you really do if you use
                       Kakoune or Helix or Micro).


                # § Internet/Gemini⠀➾


                      # ⚓ Introducing_AuraGem_Music’s_Public_Radio_(Updated)⠀⇛


                             I am now introducing AuraGem Music’s new
                             Public Radio! It livestreams public domain
                             and royalty free mp3 music over Gemini.


                      # ⚓ AuraGem_Public_Radio_Bugfix⠀⇛


                             Songs should be properly randomized now 🄸🄼🄰🄶🄴
                             🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇:D⦈


                             I have also made an announcement post for the
                             AuraGem Public Radio that has more
                             information on Supported Clients as well as a
                             new project that I intend to work on very
                             soon…


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



                    ䷩ 𝚕𝚒𝚗𝚎 7345

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 09.18.23⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


Gemini_version_available_♊︎


✐ Links_18/09/2023:_GNUHealth_Hospital_Management_4.2.2_and_Celluloid_Video
Player_0.26_Released⠀✐


Posted in News_Roundup at 8:05 pm by Dr. Roy Schestowitz


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * GNU/Linux
          o Desktop/Laptop
          o Audiocasts/Shows
          o Applications
          o Instructionals/Technical
          o Games
    * Distributions_and_Operating_Systems
          o Arch_Family
          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 SaaS/Back_End/Databases
    * Leftovers
          o Science
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Monopolies
                # Patents
                # Software_Patents
    * § GNU/Linux⠀➾


          o § Desktop/Laptop⠀➾


                # ⚓ Neowin ☛ A_quick_look_back_at_when_Lenovo_revealed_a
                  Windows-Linux-Android_tablet-laptop_hybrid⠀⇛


                       Lenovo first revealed the IdeaPad U1 PC at CES
                       2010. It ran Windows 7 in laptop mode but switched
                       to a Linux (later Android) OS tablet when the
                       display detached. The product ultimately didn’t
                       launch.


          o § Audiocasts/Shows⠀➾


                # ⚓ GNU World Order (Audio Show) ☛ GNU_World_Order_530⠀⇛


                       Listener feedback. The year of the Linux desktop.
                       Flatpaks and the future.


                       shasum -
                       a256=73ad32712ee8779d5e3b3d646fe376d2d8f3a35e945280ef901c4f44a72bdfbc


                # ⚓ Jupiter Broadcasting ☛ Where’s_Your_Data?_|_LINUX_Unplugged
                  528⠀⇛


                       Today’s theme is data sovereignty, and we’ll check
                       in with two crucial projects that are giving you
                       more options. Special Guest: Noah Chelliah.


          o § Applications⠀➾


                # ⚓ 9to5Linux ☛ HP_Linux_Imaging_and_Printing_Drivers_Now
                  Support_Fedora_38_and_Ubuntu_23.04⠀⇛


                       HPLIP (HP Linux Imaging and Printing) 3.23.8 is
                       here about three and a half months after the
                       previous release, HPLIP 3.23.5, which only added
                       support for 45 HP Color LaserJet Enterprise
                       printers, to add support for some of the latest
                       releases of popular GNU/Linux distributions,
                       including Fedora Linux 38, Ubuntu 23.04, and
                       openSUSE Leap 15.5.


                       HPLIP 3.23.8 also brings support for new printers
                       from the HP Color LaserJet Pro series, including
                       MFP 4301dwe, MFP 4301fdne, MFP 4301fdwe, MFP
                       4301cdwe, and many others.


                # ⚓ Linux Links ☛ Alternatives_to_popular_CLI_tools:_vi⠀⇛


                       This article spotlights alternative tools to vi, a
                       screen-oriented text editor originally created for
                       the Unix operating system.


                # ⚓ Linux Links ☛ 15_Best_Free_and_Open_Source_Linux_Computer
                  Algebra_Systems⠀⇛


                       A computer algebra system (CAS) is mathematical
                       software that can manipulate mathematical formulae
                       in a way similar to the traditional manual
                       computations of mathematicians and scientists.


                # ⚓ GNU ☛ health_@_Savannah:_GNUHealth_Hospital_Management
                  4.2.2_patchset_released⠀⇛


                       Dear community
                       GNU Health 4.2.2 patchset has been released !


                # ⚓ Linux Links ☛ Stonks_–_terminal_based_stock_visualizer_and
                  tracker⠀⇛


                       Stonks is a terminal based stock visualizer and
                       tracker that displays realtime stocks in graph
                       format. It’s written in Go.


                # ⚓ Ubuntu Handbook ☛ Celluloid_Video_Player_Released_0.26_with
                  more_ported_to_GNOME_Style⠀⇛


                       Celluloid, formerly GNOME MPV, released version
                       0.26 yesterday. Celluloid is a free open-source
                       video player uses mpv as backend, and is default in
                       Linux Mint 21 Cinnamon.


          o § Instructionals/Technical⠀➾


                # ⚓ Linux Buzz ☛ How_to_Install_Terraform_on_Ubuntu_22.04_Step-
                  by-Step⠀⇛


                       In this guide, we will cover how to install
                       Terraform on Ubuntu 22.04 and provide you with some
                       useful Terraform examples to kickstart your journey
                       into the world of infrastructure automation.


                # ⚓ TecAdmin ☛ Setting_Up_Laravel_with_Docker_and_Docker-
                  compose⠀⇛


                       Laravel, a popular PHP framework, provides a great
                       ecosystem for web application development. Docker,
                       on the other hand, is a tool designed to make it
                       easier to create, deploy, and run applications
                       using containers.


                # ⚓ TecAdmin ☛ Using_Composer_with_Different_PHP_Versions_in
                  Linux⠀⇛


                       Composer is a dependency manager for PHP, allowing
                       developers to declare the libraries their projects
                       depend on. However, when working on multiple
                       projects, developers can often find themselves in a
                       position where they need to juggle different PHP
                       versions. Fortunately, Linux, with its versatile
                       environment, provides the flexibility to
                       accommodate this scenario.


                # ⚓ TecAdmin ☛ Setting_Up_Development_Environments_with_PHP_and
                  Docker⠀⇛


                       A local development environment is crucial for PHP
                       developers to test and debug their applications.
                       Traditionally, developers would rely on tools like
                       XAMPP, MAMP, or WAMP, which provide a full-fledged
                       LAMP stack (Linux, Apache, MySQL, PHP) for local
                       development.


                # ⚓ How_to_Use_AppImage_in_Linux_(A_Complete_Beginner’s
                  Guide)⠀⇛


                       This article focuses on explaining different
                       software packaging concepts, highlighting what
                       AppImage is, its installation, and its removal from
                       your Linux system.


                # ⚓ TecMint ☛ 16_Apache_Web_Server_Security_and_Hardening
                  Tips⠀⇛


                       Apache web server is one of the most popular and
                       widely used web servers for hosting files and
                       websites.


                # ⚓ Ubuntu Pit ☛ How_to_Free_Up_Space_in_/boot_Partition_on
                  Ubuntu_Linux?⠀⇛


                       If you use a separate /boot partition on Ubuntu,
                       you might face the problem where your /boot
                       partition becomes almost full or runs out of space.
                       This can happen for various reasons, including old
                       kernel files getting piled. To resolve this
                       problem, you can free up some space from that
                       partition.


                # ⚓ Ubuntu_22.04_LTS:_What’s_New_and_How_to_Customize_It⠀⇛


                       Ubuntu is arguably one of the most widely used
                       operating systems thanks to its simple and neat UI,
                       which makes for a smooth user experience.


                # ⚓ ID Root ☛ How_to_Get_Current_Date_and_Time_on_Linux⠀⇛


                       In the ever-evolving landscape of computing,
                       precision and accuracy remain paramount. For Linux
                       system administrators and enthusiasts, accurate
                       time management is not just essential; it’s a
                       fundamental requirement.


                # ⚓ Own HowTo ☛ How_to_fix_“Failed_to_execute_the_default_web
                  browser”_error_on_Linux⠀⇛


                       Web browser is a button on XFCE desktop, that will
                       open the default web browser when you click it.
                       This button will only launch the default web
                       browser of your system, no matter the web browser.


                # ⚓ It’s FOSS ☛ Install_VirtualBox_on_Windows_[So_that_You_Can
                  Run_Linux_VM]⠀⇛


                       Easy-to-follow guide to help you install Oracle
                       VirtualBox on Windows so that you can install Linux
                       in virtual machines.


                # § idroot⠀➾


                      # ⚓ ID Root ☛ How_To_Install_WebERP_on_Ubuntu_22.04_LTS⠀⇛


                             In this tutorial, we will show you how to
                             install WebERP on Ubuntu 22.04 LTS. WebERP is
                             a powerful open-source web-based accounting
                             and business management system that can
                             streamline financial and operational
                             processes for businesses of all sizes.


                      # ⚓ ID Root ☛ How_To_Install_Observium_on_AlmaLinux_9⠀⇛


                             In this tutorial, we will show you how to
                             install Observium on AlmaLinux 9. For those
                             of you who didn’t know, Observium, a renowned
                             network monitoring and management tool, is
                             essential for maintaining the health and
                             performance of your network infrastructure.


                      # ⚓ ID Root ☛ How_To_Install_Apache_Hadoop_on_Debian_12⠀⇛


                             In this tutorial, we will show you how to
                             install Apache Hadoop on Debian 12. Big Data
                             is the backbone of modern data-driven
                             businesses, and Hadoop has emerged as the go-
                             to solution for processing and analyzing
                             massive datasets.


          o § Games⠀➾


                # ⚓ Tom’s Hardware ☛ Valve’s_SteamOS_3.5_Previews_VRR_and_HDR
                  for_Steam_Deck⠀⇛


                       SteamOS improves performance in Starfield, adds
                       preview of VRR and HDR for Steam Deck.


    * § Distributions and Operating Systems⠀➾


          o § Arch Family⠀➾


                # ⚓ ZDNet ☛ Want_an_elegant,_user-friendly_Windows_alternative?
                  Try_Manjaro_23.0_with_KDE_Plasma⠀⇛


                       Manjaro is an enigma to some. It’s based on Arch
                       Linux, which is generally considered one of the
                       more challenging Linux distributions on the market.
                       And yet, Manjaro has been making Arch Linux easy
                       for some time. With the release of version 23.0
                       (aka Uranos), Manjaro once again proves it’s the
                       best of all the Arch clones and the KDE Plasma
                       version of the operating system could easily serve
                       as a Windows alternative for the masses.


                       The 23.0 KDE Plasma release includes a few
                       important changes, including a window tiling
                       system, a new app theme, a number of improved tools
                       and widgets, a cleaner System Settings app, better
                       Wayland support, and plenty of bug fixes and
                       reliability improvements.


          o § Fedora Family / IBM⠀➾


                # ⚓ Linux Magazine ☛ Fedora_Linux_40_to_Drop_X11_for_KDE
                  Plasma⠀⇛


                       With 2024 on the horizon, it’s time to consider
                       what’s in store for the likes of Fedora 40, and
                       there is plenty.


                       First off, Fedora 40 will ship with KDE Plasma 6,
                       filled with Qt 6 and KDE Frameworks 6 goodness.
                       This update alone will be considerable, especially
                       when you know that it will finally drop X11 and
                       default to Wayland.


                       Although you can already opt for Plasma Wayland
                       with KDE Plasma 5.27, it’s buggy. By the time
                       version 40 arrives, the plan is to have all those
                       bugs fixed so Plasma 6 runs like a champ.


                # ⚓ Data Swamp ☛ Flatpak_integration_in_Qubes_OS_templates⠀⇛


                       I recently wanted to improve Qubes OS accessibility
                       to new users a bit, yesterday I found why GNOME
                       Software wasn’t working in the offline templates.


                       Today, I’ll explain how to install programs from
                       Flatpak in a template to provide to other qubes. I
                       really like flatpak as it provides extra security
                       features and a lot of software choice, and all the
                       data created by Flatpak packaged software are
                       compartmentalized into their own tree in `~/.var/
                       app/program.some.fqdn/`.


                # ⚓ Red Hat ☛ A_statistics_update_in_Open_vSwitch_user_space
                  datapath⠀⇛


                       With the demands for higher bandwidth, came the
                       need for scaling and processing packets on more CPU
                       resources. In Open vSwitch (OVS) using DPDK for
                       faster IO, this translated to using more receive
                       and transmit queues to allow more PMD threads to
                       process the packets. This adds some complexity to a
                       system not easy to understand in the first place.
                       Support or operation people still want to know how
                       much traffic is received and how it is distributed
                       across the CPU resources. To offer help, this
                       article describes new statistics added for the user
                       space datapath in OVS 2.17 and later.


                       § Per queue statistics for DPDK ports


                       A first evolution in OVS 2.17 consisted of exposing
                       receive_and_transmit_queues_statistics per DPDK
                       physical ports in ovsdb.


                # ⚓ Anaconda_F40′s_Advanced_Partitioner_(Blivet-GUI)_on_Fedora
                  Rawhide⠀⇛


                # ⚓ Red Hat ☛ Comparing_OpenShift_Service_Mesh_and_Service
                  Interconnect⠀⇛


                       In today’s digital landscape, where organizations
                       increasingly rely on interconnected applications
                       and services to execute business operations, the
                       ability to connect software and data across
                       different environments is becoming increasingly
                       vital. However, achieving seamless connectivity is
                       no easy feat, as varying application architectures
                       and on-premises and cloud infrastructures often
                       present disparities that require careful management
                       of interconnections for optimal operation, risk
                       management, managing skill sets across the
                       technical team, ensuring enough observability, and
                       how security is being handled.


                       This article discusses two Red Hat technologies,
                       Red_Hat_OpenShift_Service_Mesh and Red_Hat_Service
                       Interconnect, that offer different approaches to
                       address these requirements and provides guidance to
                       help you make informed decisions on which to use
                       when.


                       § What is OpenShift Service Mesh?


                # ⚓ Talospace ☛ The_Talospace_Project:_Partial_ppc64le_JIT
                  available_again_for_Firefox_115ESR⠀⇛


                       I’ve been rehabilitating the old ppc64le JIT
                       against more current Firefoxes and there is now
                       available a set of patches you can apply to the
                       current 115ESR. This does not yet include support
                       for Ion or Wasm; the first still has some
                       regressions, and the second has multiple outright
                       crashes. Still, even with just the Baseline
                       Interpreter and Baseline Compiler it is several
                       times faster on benchmarks than the interpreter-
                       only 115. I’ve included also the relevant LTO-PGO
                       and WebRTC patches so you can just apply the
                       changesets numerically and build.


          o § Debian Family⠀➾


                # ⚓ Valhalla’s_Things:_Non-e_(Note)Book⠀⇛


                       Some time ago our LUG bought some things from
                       soldered.com and while browsing around the website
                       my SO and I decided to add a junk box to the order
                       and see what we would get.


                       Other than a few useful things, there were two
                       mostly unpopulated boards for the inkplate 10 which
                       would have been pretty hard to reuse as
                       electronics.


                # ⚓ Sergio_Talens-Oliag:_GitLab_CI/CD_Tips:_Using_a_Common_CI
                  Repository_with_Assets⠀⇛


                       This post describes how to handle files that are
                       used as assets by jobs and pipelines defined on a
                       common gitlab-ci repository when we include those
                       definitions from a different project.


          o § Canonical/Ubuntu Family⠀➾


                # ⚓ DebugPoint ☛ 10_Best_Linux_Mint_Themes_for_Everyone⠀⇛


                       Linux Mint, known for its user-friendly interface
                       and reliability, offers very few Cinnamon themes
                       that can give your desktop a fresh, stylish look.
                       We prepared a list of unique themes which will best
                       fit most of the use cases. Let’s have a look.


          o § Devices/Embedded⠀➾


                # ⚓ CNX Software ☛ Amlogic_S905X5_Armv9_TV_Box_SoC_supports
                  AV1,_H.266,_Ai-SR⠀⇛


                       The Amlogic S905X5 may be first the Armv9 processor
                       designed for set-top boxes (STB) and TV boxes,
                       supports the latest AV1 and H.266 video codecs, and
                       also comes with a 4 TOPS AI accelerator. We don’t
                       have the full details yet, and the news comes from
                       a tease from SEI Robotics which is about to unveil
                       an Amlogic S905X5 AI-SR (AI Super Resolution)
                       Android TV box at IBC 2023.


          o § Open Hardware/Modding⠀➾


                # ⚓ Linux Gizmos ☛ Romeo_ESP32-S3_Dev_kit_targets_robotic
                  applications⠀⇛


                       DFRobot recently launched a small development board
                       designed for robotics and FPV applications. The
                       ESP32-based device supports both 2WD and 4WD robots
                       and offers multiple peripherals to add sensors and
                       other actuators.


                # ⚓ Tom’s Hardware ☛ Modder_Turns_Framework_Laptop_PCB_Into_a
                  Handheld_Gaming_PC⠀⇛


                       Framework motherboards in handhelds: another great
                       modding idea for these replaceable, upgradable, and
                       recyclable system components.


                # ⚓ Andrew Hutchings ☛ Amiga_CD32_Restoration:_Part_1⠀⇛


                       I recently acquired a CD32 which is pretty much in
                       a destroyed state. This is going to be a lot of
                       work to restore, so, let’s make a start.


          o § Mobile Systems/Mobile Applications⠀➾


                # ⚓ The Sun ☛ Millions_of_Android_users_urged_to_delete_list_of
                  17_‘common’_apps_to_avoid_‘killer_bloat’_that_takes_up_your
                  storage_|_The_US_Sun⠀⇛


                # ⚓ Android Central ☛ New_Pixel_update_rolls_out_ahead_of
                  Android_14_|_Android_Central⠀⇛


                # ⚓ Android Authority ☛ Android_TV_14:_Release_date,_features,
                  and_compatibility⠀⇛


                # ⚓ Android Police ☛ Google_Pixels_are_getting_the_September
                  security_update,_but_Android_14_remains_missing⠀⇛


                # ⚓ 9to5Google ☛ Android_13_September_update_rolling_out:
                  What’s_fixed_on_Pixel⠀⇛


                # ⚓ 9to5Google ☛ Android_can_automatically_archive_apps_you
                  don’t_use_–_here’s_how⠀⇛


                # ⚓ Phone Arena ☛ Two_fake_Android_apps_need_to_be_uninstalled
                  now_to_ensure_your_Android_phone_is_protected_–_PhoneArena⠀⇛


                # ⚓ Medevel ☛ 20_Open-source_Free_Android_Apps,_File_and_Photo
                  Backup_Solutions⠀⇛


                       Android Backup Solutions refer to the various
                       methods and tools available to backup data on an
                       Android device. It is important to backup your
                       Android device to ensure that your valuable data is
                       protected and can be restored in case of device
                       loss, damage, or data corruption.


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


          o § SaaS/Back End/Databases⠀➾


                # ⚓ PostgreSQL ☛ Apache_Arrow_Flight_SQL_adapter_for_PostgreSQL
                  0.1.0⠀⇛


                       The Apache Arrow team is pleased to announce the
                       0.1.0 release of
                       the Apache Arrow Flight SQL adapter for PostgreSQL.


                       Read the_blog_post_of_this_release about what’s new
                       in the release.


                       § What is Apache Arrow Flight SQL adapter for
                       PostgreSQL?


                       Apache Arrow Flight SQL adapter for PostgreSQL is a
                       PostgreSQL extension that adds an Apache_Arrow
                       Flight_SQL endpoint to PostgreSQL.


                # ⚓ PostgreSQL ☛ dbMigration_.NET_v16.4_released⠀⇛


                       dbMigration_.NET_v16.4 is a simple, easy and
                       intuitive multiple database migration and sync
                       tool,
                       With it you can easily migrate and synchronize data
                       to PostgreSQL and vice versa without complicated
                       procedures. (Free for non-commercial and a single
                       executable file without installation)


                # ⚓ PostgreSQL ☛ Credcheck_version_2.2_released⠀⇛


                       Antananarivo, Madagascar – September 16, 2023


                       § PostgreSQL credcheck extension


                       The credcheck PostgreSQL extension provides few
                       general credential checks, which will be evaluated
                       during the user creation, during the password
                       change and user renaming. By using this extension,
                       we can define a set of rules: [...]


    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ LRT ☛ What_to_do_with_space_trash?_Lithuanian_startup_is
                  working_on_a_solution⠀⇛


                       The first satellite was launched into the Earth’s
                       orbit in 1957. Today, there are around 8,500 active
                       satellites orbiting our planet, according to
                       Orbiting Now, and an unknown number of disused
                       ones, making up the bulk of the space debris. A
                       Lithuanian startup is working to offer solutions.


          o § Hardware⠀➾


                # ⚓ Ruben Schade ☛ My_“Aldi”_Commodore_64_case⠀⇛


                       I previewed this machine in my latest Commodore 64
                       post, but I forgot that I only mentioned receiving
                       it on Mastodon, and didn’t blog about it.


                       What_colour_was_the_Commodore_64?


                       Below is my new (to me), genuine, bonafide “Aldi”
                       Commodore 64 that arrived in the post a couple of
                       weeks ago under several layers of foam, wrapping
                       paper, and tape. I’ve had new computers shipped
                       with less care than this treasure, which is saying
                       something.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ NYPost ☛ Bob_Odenkirk_admits_he_dismissed_‘cranky
                  conservative’_doctor’s_medical_advice⠀⇛


                       Actor Bob Odenkirk said he regretted dismissing a
                       “cranky” conservative doctor’s medical advice
                       during a podcast.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ TechXplore ☛ Cisco,_other_tech_companies_chop_Bay_Area_jobs
                  in_fresh_layoffs⠀⇛


                       Cisco Systems has revealed plans to chop hundreds
                       more Bay Area jobs in a disquieting suggestion that
                       the region’s tech layoffs have yet to run their
                       course.


                       The tech titan reported that it plans to jettison
                       350 jobs on or around Oct. 16, affecting workers in
                       San Jose and Milpitas, according to official
                       filings with the state Employment Development
                       Department.


                       Cisco has decided to lay off 227 workers in San
                       Jose and another 123 employees in Milpitas, the EDD
                       filings show.


                # ⚓ GO Media ☛ It’s_Time_To_Start_Killing_Your_Subscriptions⠀⇛


                       There’s a problem at the heart of subscription
                       entertainment and it’s that very few people
                       actually have the time or money to truly justify
                       them. I can’t keep up with every new Star Wars
                       spin-off and extended Marvel Cinematic Universe
                       show, let alone the critically-acclaimed hits that
                       debut every other month on competing platforms.
                       It’s even worse in video games. The Xbox Game Pass
                       library grows every week, while PlayStation Plus
                       and Switch Online regularly bring classic games
                       from decades ago back into circulation. And while a
                       single season of TV lasts 10 hours at most, games
                       frequently extend beyond that.


                       Meanwhile, each of these subscription services has
                       decided to hike the price while simultaneously
                       getting worse. Disney Plus jumped from $11 a month
                       to $14. Max increased by only a dollar while nuking
                       tons of old shows like the cult hit Westworld. Game
                       Pass Ultimate increased by $2 a month, followed by
                       the most basic tier of PS Plus going from $60 a
                       year up to $80. After 12 years at just $10 a month,
                       even Spotify raised its price to $11.


                # ⚓ Engadget ☛ Panos_Panay_is_reportedly_heading_to_Amazon
                  after_leaving_Microsoft⠀⇛


                       It didn’t take long to learn Panos Panay’s new
                       home. The industry veteran, instrumental in
                       developing Windows 11 and the Microsoft Surface
                       line of 2-in-1s and laptops, has reportedly been
                       hired by Amazon, according to Bloomberg.
                       Microsoft’s former chief product officer will lead
                       Amazon’s division responsible for Alexa and Echo
                       smart devices.


                # ⚓ TechCrunch ☛ Chief_Product_Officer_Panos_Panay_is_out_at
                  Microsoft,_reportedly_heading_to_Amazon⠀⇛


                       Speaking of Dave Limp, Panay is reportedly heading
                       over to Amazon next, where he will resume the same
                       role. We have reached out to Amazon for comment.
                       Both companies holding devices events this week, so
                       things are about to get interesting. Microsoft’s
                       event will likely be focused on Surface products,
                       Panay’s long time focus, while Amazon will almost
                       certainly be announcing a number of Echo/Alexa
                       products. Bringing on someone with PC experience
                       could mark a shift in focus for the division, which
                       was impacted by last year’s Amazon layoffs.


                # ⚓ Bloomberg ☛ Amazon_Is_Poised_to_Hire_Departing_Microsoft
                  Product_Chief⠀⇛


                # ⚓ MSN ☛ Microsoft_Product_Chief_Is_Exiting,_in_Blow_to
                  Hardware_Unit [Ed: Microsoft site, Microsoft writer (Dina
                  Bass) disguised as "journalist" (she has a long history with
                  the company)]⠀⇛


                       Microsoft Corp. said its chief product officer is
                       leaving, a significant departure for the company’s
                       hardware and Windows divisions.


                # ⚓ TechXplore ☛ Microsoft’s_chief_product_exec_to_step_down.
                  Panos_Panay_was_behind_Surface_devices_and_Windows_11⠀⇛


          o § Security⠀➾


                # ⚓ The Register UK ☛ Microsoft_worker_accidentally_exposes
                  38TB_of_sensitive_data_in_GitHub_blunder [Ed: But the
                  mainstream media will still have the audacity to present
                  Microsoft as security authority and champion]⠀⇛


                       A Microsoft employee accidentally exposed 38
                       terabytes of private data while publishing a bucket
                       of open-source AI training data on GitHub,
                       according to Wiz security researchers who spotted
                       the leaky account and reported it to the Windows
                       giant.


                # ⚓ Make Tech Easier ☛ Protecting_Your_Privacy_and_Security_on
                  Android⠀⇛


                       With Android being one of the top mobile operating
                       systems, it’s often targeted by cybercriminals. You
                       can fight back against vulnerabilities and exploits
                       by focusing on Android security and digital
                       privacy.


                # ⚓ AccessNow ☛ Fundamental_rights_impact_assessments_are_key
                  for_effective_DSA_enforcement⠀⇛


                       Under the EU DSA, companies designated as VLOPs or
                       VLOSEs must assess fundamental rights risks
                       stemming from their services. Access Now and ECNL
                       have published a new policy paper to support
                       enforcement of this requirement.


                # ⚓ Mitigations_for_Critical_c-ares_DoS,_Code_Execution_Bug
                  Released⠀⇛


                       A critical buffer overflow vulnerability has been
                       found in c-ares before 1_16_1 thru 1_17_0 via the
                       function ares_parse_soa_reply in
                       ares_parse_soa_reply.c ( CVE-2020-22217 ). Due to
                       how simple this bug is to exploit and its
                       significant threat to the confidentiality,
                       integrity, and availability of impacted systems, it
                       has received a National Vulnerability Database base
                       score of 9.8 out of 10 (”Critical” severity).


                # ⚓ Security Week ☛ Imagine_Making_Shadowy_Data_Brokers_Erase
                  Your_Personal_Info._Californians_May_Soon_Live_the_Dream⠀⇛


                       California state Legislature has passed the Delete
                       Act to allow individuals to order data brokers to
                       delete their personal data — and to cease acquiring
                       and selling it in the future.


                # § Privacy/Surveillance⠀➾


                      # ⚓ Ruben Schade ☛ Data_privacy_in_Musk’s_data_centre
                        move⠀⇛


                             This story of Space Karen’s physical data
                             centre move has been drawing the ire and glee
                             of many a sysadmin and project manager today.
                             They did everything predictably wrong, and
                             faced the consequences.


                             CNBC:_Elon_Musk_moving_servers_himself_shows
                             his_‘maniacal_sense_of_urgency’_at_X,
                             formerly_Twitter


                             But this was the section that raised my
                             eyebrows, emphasis added: [...]


                      # ⚓ Federal News Network ☛ Indiana_attorney_general_sues
                        hospital_system_over_privacy_of_Ohio_girl_who_traveled
                        for_abortion⠀⇛


                             Indiana’s attorney general has sued the
                             state’s largest hospital system, claiming it
                             violated patient privacy laws when a doctor
                             publicly shared the story of an Ohio girl who
                             traveled to Indiana for an abortion. Friday’s
                             lawsuit marks Attorney General Todd Rokita’s
                             latest attempt to seek disciplinary legal
                             action against Dr. Caitlin Bernard. The
                             doctor’s account of a 10-year-old girl
                             traveling to Indiana to receive abortion
                             drugs became a flashpoint in the national
                             abortion debate days after the U.S. Supreme
                             Court overturned Roe v. Wade last summer.


                      # ⚓ New York Times ☛ In_Risky_Hunt_for_Secrets,_U.S._and
                        China_Expand_Global_Spy_Operations⠀⇛


                             The nations are taking bold steps in the
                             espionage shadow war to try to collect
                             intelligence on leadership thinking and
                             military capabilities.


          o § Defence/Aggression⠀➾


                # ⚓ JURIST ☛ Ghana_dispatch:_defence_chief_assures_country_that
                  armed_forces_are_‘not_interested’_in_military_coups⠀⇛


                       Lana Osei is a JURIST staff correspondent in Ghana
                       and a recent graduate of the GIMPA (Ghana Institute
                       of Management and Public Administration) Faculty of
                       Law. She files this dispatch from Accra. 


                # ⚓ The Strategist ☛ The_untapped_potential_of_Australia–India
                  defence_space_cooperation⠀⇛


                       Our security depends more and more on space.
                       Today’s militaries depend on space systems for
                       operations on land or sea, in the air, or in many
                       cases, in cyberspace. Space technologies are
                       integral to our …


                # ⚓ France24 ☛ Mali,_Niger_and_Burkina_Faso_military_leaders
                  establish_security_alliance⠀⇛


                       The military leaders of Mali, Burkina Faso and
                       Niger on Saturday signed a mutual defence pact,
                       ministerial delegations from the three Sahel
                       countries announced in Mali’s capital Bamako.


                # ⚓ AntiWar ☛ Why_the_Media_Aren’t_Telling_the_Whole_Story_of
                  Libya’s_Floods⠀⇛


                       The reality of the West’s trademark current foreign
                       policy – marketed for the past two decades under
                       the principle of a “Responsibility to Protect” – is
                       all too visible amid Libya’s flood wreckage.


                # ⚓ The Straits Times ☛ South_Korea_working_to_unfreeze
                  Teheran’s_funds_in_US-Iran_detainee_deal⠀⇛


                       The precise timing of the fund transfer has yet to
                       be publicly announced.


                # § Russia, Belarus, and War in Ukraine⠀➾


                      # ⚓ Latvia ☛ Turkish_builders_see_Rail_Baltica_bid
                        excluded_over_security_concerns:_LTV’s_De_Facto⠀⇛


                             The Turkish association of companies which
                             offered to build the Rail Baltica track route
                             for a cheaper price than its competitors in a
                             tender, has been excluded from the
                             procurement on the recommendation of the
                             State Security Service (VDD), Latvian
                             Television’s De Facto broadcast of September
                             17 reported.


                      # ⚓ RFERL ☛ Video_Appears_To_Show_Smiling_Chechen
                        Strongman_Kadyrov_Amid_Rumors_Of_Failing_Health⠀⇛


                             Ramzan Kadyrov’s Telegram channel on
                             September 17 released a video showing the
                             Chechen strongman smiling and talking to the
                             camera in an apparent attempt to counter
                             speculation about his health following rumors
                             on social media that suggested he was in a
                             coma and near death.


                      # ⚓ Latvia ☛ LTV’s_De_Facto_looks_at_border_fence-
                        building_acceleration_plans⠀⇛


                             One point of the new government declaration
                             is a commitment to complete the construction
                             of the fence on the border with Belarus by
                             the end of this year. If this step were not
                             taken, the process would extend into 2025,
                             reports Latvian Television’s De Facto
                             broadcast on September 17.


                      # ⚓ The Straits Times ☛ North_Korea’s_leader_wraps_up
                        Russia_trip_with_drones_gift⠀⇛


                             Government officials from the two countries
                             agreed to meet in Pyongyang in November.


                      # ⚓ The Straits Times ☛ North_Korea’s_Kim_heads_home
                        after_final_stop_in_Russia’s_Vladivostok_-KCNA⠀⇛


                             North Korean leader Kim Jong Un was headed
                             home after making a final stop in Russia’s
                             far eastern city of Vladivostok, where he
                             visited a university, an aquarium and a
                             fodder plant, state media KCNA reported on
                             Monday.


                      # ⚓ The Straits Times ☛ Kim_Jong_Un’s_sister_seen_holding
                        $9,500_Dior_bag_during_Russia_trip⠀⇛


                             It’s not the first time Kim family members
                             have appeared in public brandishing foreign
                             luxury goods.


                      # ⚓ The Straits Times ☛ Rifle,_fur_hat,_drones:_North
                        Korea’s_Kim_returns_with_gifts_from_Russia⠀⇛


                             Some of the items will be displayed at the
                             “friendship” museum, where gifts received by
                             the North’s leaders are kept.


                      # ⚓ RFERL ☛ Karabakh_Leaders_Say_Agreement_Made_On
                        Simultaneous_Aid_Shipments_Through_Agdam,_Lachin⠀⇛


                             Ethnic-Armenian authorities of Azerbaijan’s
                             breakaway region of Nagorno-Karabakh have
                             agreed on procedures for two simultaneous
                             routes of delivery of Russian-provided
                             humanitarian aid, the International Committee
                             of the Red Cross and separatist leaders said
                             on September 17.


                      # ⚓ LRT ☛ Lithuania’s_Landsbergis:_‘Russia_threat_has
                        shaped_our_identity’⠀⇛


                             Elected in 2020, Lithuania’s government
                             declared the ambitious goal of pursuing a
                             values-based foreign policy. But was there
                             more behind the rhetoric? In an interview
                             with LRT, Foreign Minister Gabrielius
                             Landsbergis talks about Taiwan, values in
                             politics, and Lithuania’s identity.


                      # ⚓ NYPost ☛ North_Korea’s_Kim_Jong_Un_heads_home_after
                        Russian_journey_that_raised_concern_about_weapons
                        deals⠀⇛


                             North Korean leader Kim Jong Un is on his way
                             home Sunday from Russia, ending a six-day
                             trip that triggered global concerns about
                             weapons transfer deals between the two
                             countries locked in separate standoffs with
                             the West.


                      # ⚓ New York Times ☛ U.S._and_Chinese_Officials_Meet_in
                        Malta_to_Discuss_Ukraine_and_Other_Flashpoints⠀⇛


                             The talks between Jake Sullivan, the White
                             House national security adviser, and Wang Yi,
                             China’s top diplomat, took place as the two
                             governments are trying to set up a Biden-Xi
                             meeting.


                      # ⚓ AntiWar ☛ Washington_Is_the_Matchmaker_for_the
                        Russia-North_Korea_Romance⠀⇛


                             The summit meeting between Russian president
                             Vladimir Putin and North Korean leader Kim
                             Jong-un has led to a surge of pearl clutching
                             among the U.S. foreign policy establishment
                             and its allies in the corporate news media. 


                      # ⚓ France24 ☛ 🔴_Live:_Chinese_foreign_minister_to_visit
                        Russia_for_security_talks⠀⇛


                             China’s top diplomat Wang Yi will begin a
                             four-day visit to Russia for security talks
                             on Monday, his foreign ministry said, the
                             latest in a series of high-level visits and
                             phone calls between the two countries.


                      # ⚓ France24 ☛ First_two_cargo_ships_arrive_in_Ukrainian
                        port_since_Moscow’s_exit_from_grain_deal⠀⇛


                             Two cargo ships arrived on Saturday at one
                             of Ukraine’s ports in the southern Odesa
                             region, the Ukrainian Sea Ports authority
                             said in a statement. The Palau-flagged
                             carriers are the first civilian cargo ships
                             to reach an Odesa port since Russia withdrew
                             from a wartime deal designed to ensure safe
                             Ukrainian grain exports via the Black Sea.


                      # ⚓ LRT ☛ Poland_joins_Baltics_with_ban_on_Russian-
                        registered_cars⠀⇛


                             The move is part of the EU’s sweeping
                             sanctions against Russia over its invasion of
                             Ukraine, with Poland joining its Baltic
                             allies. Poland’s interior minister said cars
                             registered in Russia have “no right” to
                             enter.


                      # ⚓ RFERL ☛ Heavy_Fighting_Reported_Around_Key_Eastern
                        Village_That_Ukraine_Says_It_Has_Liberated⠀⇛


                             Heavy fighting between Ukrainian soldiers and
                             invading Russian forces was reported early on
                             September 18 in and around Klishchiyivka, a
                             key village in the Donetsk region in eastern
                             Ukraine, the Ukrainian military said.


                      # ⚓ RFERL ☛ Canada_Pledges_Millions_To_Help_Buy_Air
                        Defenses_For_Ukraine⠀⇛


                             Canada will contribute C$33 million ($24.5
                             million) to a British-led partnership that is
                             buying air-defense equipment for Ukraine to
                             help it fend off Russian missile and drone
                             attacks, Defense Minister Bill Blair said on
                             September 17.


                      # ⚓ RFERL ☛ NATO_Chief_Predicts_Russia’s_War_Against
                        Ukraine_Won’t_End_Soon⠀⇛


                             Russia’s war against Ukraine will not end
                             anytime soon, NATO Secretary_General Jens
                             Stoltenberg stated in an interview published
                             on September 17 with the German publication
                             Die Welt.


                      # ⚓ RFERL ☛ Ukrainian_Forces_Reportedly_Retake_New
                        Village_In_Effort_To_Liberate_Bakhmut⠀⇛


                             Ukrainian forces appear to have recaptured
                             the key village of Klishchiyivka as part of
                             their drive to liberate the symbolic eastern
                             town of Bakhmut in a day marked by
                             intensified drone and missile attacks by both
                             sides.


                      # ⚓ The Straits Times ☛ Ukraine_says_it_downed_18_drones,
                        17_missiles_in_overnight_attack⠀⇛


                             Ukraine said on Monday it downed 18 Russian
                             drones and 17 cruise missiles attacking its
                             territory overnight.


                      # ⚓ YLE ☛ Finland_needs_to_improve_Finnish_language
                        instruction_for_Ukrainian_kids,_teachers’_union_says⠀⇛


                             Some Ukrainian children are ill-equipped to
                             join regular classrooms after a year in
                             preparatory education.


                      # ⚓ New York Times ☛ Ukraine_Says_It_Has_Retaken
                        Strategic_Village_Near_Bakhmut⠀⇛


                             The small village of Klishchiivka is the
                             second settlement in eastern Ukraine that
                             Kyiv’s forces say they have retaken in three
                             days.


                      # ⚓ New York Times ☛ Finland’s_President_Warns_Europe
                        About_Russia⠀⇛


                             President Biden has consulted Sauli Niinisto
                             throughout Russia’s war against Ukraine.
                             Europeans should not dismiss the risks of a
                             wider war, he says.


                      # ⚓ New York Times ☛ Zelensky_to_Make_a_Case_for_More_Aid
                        in_U.S._Visit⠀⇛


                             The Ukrainian leader’s second trip to America
                             comes at a more delicate diplomatic moment,
                             as he tries to navigate political currents
                             while expressing gratitude for Western
                             support.


          o § Environment⠀➾


                # ⚓ Ruben Schade ☛ A_hot_spring_weekend_☀️⠀⇛


                       It was more than 30 degrees in Sydney this weekend.
                       The cool sea breezes stopped it feeling hotter, but
                       it was still a bit disconcerting.


                       It’s been spring down here for two weeks, and it
                       already feels like summer. It’s not supposed to be
                       like this. What are we doing?


                # § Wildlife/Nature⠀➾


                      # ⚓ The Straits Times ☛ Snake_no_mistake:_Australian
                        fined_for_surfing_with_python⠀⇛


                             The man did not have a permit to remove the
                             reptile from its registered address.


          o § Finance⠀➾


                # ⚓ Hong Kong Free Press ☛ Foreign_capital_showing_confidence
                  in_Hong_Kong,_commerce_chief_says,_as_272_companies_set_up_in
                  city⠀⇛


                       The Hong Kong government has attracted 272
                       companies to develop business in Hong Kong this
                       year, the city’s commerce secretary has said.
                       Speaking on a Commercial Radio show on Saturday,


                # ⚓ BMO_shuttering_retail_auto_finance_business,_laying_off
                  employees⠀⇛


                       Bank of Montreal is closing its indirect retail
                       auto finance business and laying off an unknown
                       number of jobs as the bank shifts focus to other
                       areas.


                       Canada’s third-largest bank announced the
                       unexpected move on Saturday. BMO’s decision follows
                       news that its bad debt provisions rose to $492
                       million, versus $136 million a year previous for
                       the quarter ended July 31. Bad loans have been
                       rising as a result of a sharp rise in interest
                       rates and a slowing Canadian economy.


                       BMO has offered indirect retail auto financing in
                       both Canada and the United States. Auto dealerships
                       would arrange financing for car buyers through the
                       bank. BMO ended this agreement with dealerships as
                       of Sept. 15, however they will still fund all
                       contracts given the green-light before the
                       termination date.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Federal News Network ☛ Dominican_Republic’s_president
                  stands_resolute_on_his_closing_of_all_borders_with_Haiti⠀⇛


                       The president of the Dominican Republic is
                       defending his decision to close air, sea and land
                       traffic with neighboring Haiti in a dispute over
                       construction of a canal targeting a river that runs
                       through both countries. President Luis Abinader
                       said in a televised speech Sunday that the border
                       closures will remain in place until construction is
                       halted on the canal, which seeks to use water from
                       the Massacre River to alleviate a drought in
                       Haiti’s Maribaroux plain. He says the canal will
                       affect Dominican farmers and the environment.
                       Abinader’s administration also has stopped issuing
                       visas to Haitians.


                # ⚓ JURIST ☛ Federal_prosecutors_in_DC_2020_election
                  interference_case_request_order_to_prohibit_Trump_making
                  ‘inflammatory’_and_‘misleading’_statements⠀⇛


                       Federal prosecutors in former US President Donald
                       Trump’s 2020 election interference case requested a
                       court order on Friday to prevent Trump from making
                       certain prejudicial and extrajudicial statements in
                       an effort to limit jury interference. The case is
                       in the US District Court for the District of
                       Columbia.


                # ⚓ Atlantic Council ☛ On_China,_grant_the_US_the_wisdom_to
                  distinguish_between_what_it_can_and_cannot_change⠀⇛


                       In crafting its strategy on managing its relations
                       with China, the United States should begin with a
                       geopolitical serenity prayer.


                # ⚓ New York Times ☛ Monday_Briefing:_China_and_the_U.S._Vie
                  for_Secrets⠀⇛


                       Plus, confronting the world’s largest “baby
                       exporter.”


                # ⚓ The Straits Times ☛ China’s_Wang_Yi_visits_Russia_ahead_of
                  possible_Xi-Putin_meeting⠀⇛


                       Mr Wang is expected to lay the groundwork for Mr
                       Putin’s visit to Beijing for the third Belt and
                       Road Forum.


                # ⚓ France24 ☛ More_than_100_Chinese_warplanes_and_nine_navy
                  ships_spotted_around_Taiwan⠀⇛


                       Taiwan told China on Monday to stop its
                       “destructive unilateral actions” after more than
                       100 Chinese warplanes and nine navy ships were
                       detected in areas around the self-ruled island.


                # ⚓ Hong Kong Free Press ☛ Taipei_demands_Beijing_stop
                  ‘destructive_unilateral_actions’_after_103_Chinese_warplanes
                  detected_around_island⠀⇛


                       Taiwan told China on Monday to stop its
                       “destructive unilateral actions” after more than
                       100 Chinese warplanes and nine navy ships were
                       detected in areas around the self-ruled island.


                # ⚓ New York Times ☛ China_Flies_Record_Number_of_Military
                  Planes_Near_Taiwan⠀⇛


                       Taiwan’s defense ministry criticized the uptick in
                       Chinese military activity, saying Beijing should
                       “stop such destructive unilateral actions.”


                # ⚓ RFA ☛ China_says_its_camps_are_closed,_but_Uyghurs_remain
                  under_threat⠀⇛


                       Reports from Xinjiang suggest persecution against
                       members of the mostly Muslim community continues.


                # ⚓ The Straits Times ☛ China_complains_to_Germany_after
                  foreign_minister_calls_Xi_a_‘dictator’⠀⇛


                       China has complained to Germany after its foreign
                       minister labelled President Xi Jinping a
                       “dictator”, the Chinese foreign ministry said on
                       Monday, calling the title “absurd” and an “open
                       political provocation”.


                # ⚓ The Straits Times ☛ Thailand_eyes_India_to_boost_tourism
                  recovery_after_waiving_visa_for_Chinese_visitors⠀⇛


                       Thailand has been boosting measures to boost its
                       travel industry, a key growth driver of its
                       economy.


                # ⚓ The Straits Times ☛ Taiwan_urges_China_to_stop
                  ‘destructive’_military_activities⠀⇛


                       Taiwan has reported a sharp rise in Chinese
                       military activities near the island.


                # ⚓ The Straits Times ☛ China,_EU_should_maintain_open
                  attitude,_reject_protectionism_-Chinese_state_media⠀⇛


                       China and the European Union (EU) should continue
                       to maintain an “open attitude” and “reject
                       protectionism”, Chinese state media said on Monday,
                       citing Chinese Foreign Minister Wang Yi.


                # ⚓ The Straits Times ☛ China’s_anti-espionage_drive_turns
                  ordinary_citizens_into_spy_hunters⠀⇛


                       The result is a growing level of mistrust among
                       citizens.


                # ⚓ New York Times ☛ China’s_Import_Curbs_on_Cosmetics_Face
                  Pushback_in_Europe⠀⇛


                       Cosmetics sales in China are soaring, but a group
                       of exporting nations led by France are pushing
                       Beijing to lift restrictions they say are blocking
                       them unfairly.


                # ⚓ RFA ☛ China_restricts_Tibetans_from_attending_Buddhist
                  Kalachakra_sermon⠀⇛


                       More than 100,000 devotees have gathered for the
                       teaching by a prominent lama, sources on the ground
                       say.


                # ⚓ The Straits Times ☛ China_has_paused_its_spy_balloon
                  operations,_say_US_officials⠀⇛


                       A Chinese spy balloon was shot down off the coast
                       of South Carolina in February, setting off a
                       diplomatic crisis.


                # ⚓ The Straits Times ☛ Changsha’s_low_property_prices_and
                  vibrancy_draw_Chinese_in_search_of_work-life_balance⠀⇛


                       Hunan’s provincial capital was voted as China’s
                       most liveable city, and also ranked among top 10
                       most blissful cities.


                # ⚓ New York Times ☛ China_Is_Investigating_Its_Defense
                  Minister,_U.S._Officials_Say⠀⇛


                       General Li Shangfu’s recent absence from the public
                       eye, which follows the removal of two top
                       commanders, has raised questions about Xi Jinping’s
                       confidence in his military.


          o § Civil Rights/Policing⠀➾


                # ⚓ France24 ☛ US_auto_workers_threaten_to_‘amp_up’_historic
                  strike_if_wage_offers_do_not_improve⠀⇛


                       The United Auto Workers chief warned Sunday that a
                       historic strike at the top three car manufacturers
                       will expand if the companies do not raise their
                       wage offers in ongoing negotiations.


                # ⚓ New York Times ☛ South_Korean_Prosecutors_Want_to_Arrest
                  Hunger-Striking_Opposition_Leader⠀⇛


                       Lee Jae-myung has been the subject of a series of
                       investigations since losing the 2022 presidential
                       election. He says his rival now runs “a
                       dictatorship by prosecutors.​”


                # ⚓ JURIST ☛ Iran_cracks_down_protests_on_anniversary_of_Mahsa
                  Amini’s_death_which_sparked_‘Woman,_Life,_Freedom’
                  Movement’⠀⇛


                       Iranian security forces cracked down on protests in
                       Kurdish areas on Saturday. Local human rights
                       organisation Kurdistan Human Rights Network also
                       observed several arrests which targeted the
                       families of the victims of the Woman, Life, Freedom
                       protests.


                # ⚓ The Straits Times ☛ Iranian-U.S._detainees_involved_in
                  swap,_fund_release⠀⇛


                       The United States and Iran will each free five
                       people they each hold under an exchange agreement
                       that also involves the transfer of $6 billion
                       unfrozen Iranian assets from South Korea.


                # ⚓ New York Times ☛ How_a_Yale_Student’s_Rape_Accusation
                  Exposed_Her_to_a_Defamation_Lawsuit⠀⇛


                       The woman’s allegation led to the expulsion of
                       Saifullah Khan, who was acquitted in a criminal
                       trial. His lawsuit is now challenging these
                       disciplinary hearings.


                # ⚓ The Straits Times ☛ South_Korea_opposition_leader
                  hospitalised_after_hunger_strike;_prosecutors_seek_arrest⠀⇛


                       He is being investigated for bribery allegations
                       and his role in a development project.


                # ⚓ Federal News Network ☛ After_castigating_video_games_during
                  riots,_France’s_Macron_backpedals_and_showers_them_with
                  praise⠀⇛


                       French President Emmanuel Macron is extending an
                       olive branch to video gamers after previously
                       linking computer games to rioting that rocked
                       France earlier this year. Posting on the social
                       media platform X, previously known as Twitter,
                       Macron backpedaled on remarks in June where he
                       blamed video games for having “intoxicated” some
                       young rioters. Those comments dismayed some in the
                       gaming community, even beyond France. Japanese game
                       director Kastuhiro Harada was among Macron’s
                       critics at the time. But the French leader’s latest
                       comments struck an entirely different tone. In an
                       unusually lengthy post this weekend on X, Macron
                       issued a mea culpa to gamers and showered video
                       games and the industry with praise.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ Measuring_the_use_of_DNSSEC⠀⇛


                       How much of the DNS namespace has been signed with
                       DNSSEC?


          o § Monopolies⠀➾


                # § Patents⠀➾


                      # ⚓ Dennis Crouch/Patently-O ☛ Logos_Remain_Relevant:
                        Source_Confusion_and_Design_Patent_Infringement⠀⇛


                             In a previous post, I examined the important
                             issue of comparison prior art that emerged
                             from the dispute between Columbia Sportswear
                             and Seirus. This post will focus on another
                             key issue from the case – the relevance of
                             logos in design patent infringement analysis.


                             The Federal Circuit’s pair of decisions
                             provide guidance on how logos factor into the
                             design patent infringement inquiry, and begin
                             to tease-out differences in policy concerns
                             underlying design patent law versus trademark
                             law. As the court made clear, while logos are
                             often key for avoiding consumer confusion
                             about product source in the trademark sense,
                             the absence of source confusion does not
                             necessarily preclude a finding of design
                             patent infringement. Still, ornamental logos
                             found on the accused product can still be
                             relevant as visual distractors in the process
                             of evaluating similarities and differences
                             between the claimed design and accused
                             design.


                # § Software Patents⠀➾


                      # ⚓ The Register UK ☛ Sonos_secures_a_victory_in_audio
                        patent_fight_against_Google⠀⇛


                             The years-long legal drama resulting from a
                             brief fling between Google and smart speaker
                             maker Sonos has resulted in another loss for
                             the Chocolate Factory, which had its claims
                             of copyright infringement tossed out by a US
                             International Trade Commission (ITC) judge
                             Friday.


                             Google’s ITC complaint [PDF] alleging four
                             violated patents was filed in August last
                             year, just one day after it made allegations
                             of the same patent infringements against
                             Sonos in California. The ITC administrative
                             law judge Cameron Elliot said [PDF] Google
                             wasn’t able to get around counter-arguments
                             from Sonos’ legal team, despite Alphabet’s
                             gobs of money buying the finest commercially
                             available jurists.


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