𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Saturday, October 19, 2024
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Generated Sun 20 Oct 02:49:16 BST 2024
Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖)
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Gemini index for the day: gemini://gemini.techrights.org/2024/10/19/


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

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

⦿ Techrights  -  2021 Deja Vu: The 'Counter-Petition' Defending Richard Stallman (RMS) Gets a Lot More Support Than the Hateful Screed

⦿ Techrights  -  Fun Weekend, But Very Slow News

⦿ Techrights  -  IBM: RMS Asked a Girl on a Date. We at IBM Are Bribing and Receiving Bribes. Cancel RMS.

⦿ Techrights  -  IRC Proceedings: Friday, October 18, 2024

⦿ Techrights  -  [Meme] How 'Editorial Control' and/or 'Fact-Checking' Work in Social Control Media

⦿ Techrights  -  [Meme] Mentality of a Loser

⦿ Techrights  -  [Meme] Plundering the Commons

⦿ Techrights  -  [Meme] The Way Things Used to Be...

⦿ Techrights  -  [Meme] When Hatred (or Envy) Comes First

⦿ Techrights  -  Over at Tux Machines...

⦿ Techrights  -  "The Definition of Insanity"

⦿ Techrights  -  The Drew DeVault Report: Taking Out His Frustration on Other People While Doing Drugs

⦿ Techrights  -  The 'New' Laptop as a Reminder of Why I Love GNU/Linux

⦿ Techrights  -  The State of GAFAM and the I's (IBM and Intel)

⦿ Techrights  -  What "Ethical Source" Looks Like in Practice

⦿ Techrights  -  x86 Drowning in Competition, Bug Doors, Complexity, and Bloat

 ䷼ Bulletin articles (as HTML) to comment on (requires login):
https://techrights.org/n/2024/10/19/2021_Deja_Vu_The_Counter_Petition_Defending_Richard_Stallman_RM.shtml
https://techrights.org/n/2024/10/19/Fun_Weekend_But_Very_Slow_News.shtml
https://techrights.org/n/2024/10/19/IBM_RMS_Asked_a_Girl_on_a_Date_We_at_IBM_Are_Bribing_and_Receiv.shtml
https://techrights.org/n/2024/10/19/IRC_Proceedings_Friday_October_18_2024.shtml
https://techrights.org/n/2024/10/19/Meme_How_Editorial_Control_and_or_Fact_Checking_Work_in_Social_.shtml
https://techrights.org/n/2024/10/19/Meme_Mentality_of_a_Loser.shtml
https://techrights.org/n/2024/10/19/Meme_Plundering_the_Commons.shtml
https://techrights.org/n/2024/10/19/Meme_The_Way_Things_Used_to_Be.shtml
https://techrights.org/n/2024/10/19/Meme_When_Hatred_or_Envy_Comes_First.shtml
https://techrights.org/n/2024/10/19/Over_at_Tux_Machines.shtml
https://techrights.org/n/2024/10/19/The_Definition_of_Insanity.shtml
https://techrights.org/n/2024/10/19/The_Drew_DeVault_Report_Taking_Out_His_Frustration_on_Other_Peo.shtml
https://techrights.org/n/2024/10/19/The_New_Laptop_as_a_Reminder_of_Why_I_Love_GNU_Linux.shtml
https://techrights.org/n/2024/10/19/The_State_of_GAFAM_and_the_I_s_IBM_and_Intel.shtml
https://techrights.org/n/2024/10/19/What_Ethical_Source_Looks_Like_in_Practice.shtml
https://techrights.org/n/2024/10/19/x86_Drowning_in_Competition_Bug_Doors_Complexity_and_Bloat.shtml

 ䷞ Followed by Daily Links (assorted news picks curated and categorised):
https://techrights.org/n/2024/10/19/Gemini_Links_19_10_2024_Against_Books_as_Only_Possible_Legitima.shtml
https://techrights.org/n/2024/10/19/Links_19_10_2024_European_Perspective_Windows_TCO_and_Google_Wo.shtml
https://techrights.org/n/2024/10/19/Links_19_10_2024_Nokia_Lays_Off_2_000_Employees_IMF_Loans_Lammy.shtml
https://techrights.org/n/2024/10/19/Links_19_10_2024_OpenAI_Microsoft_Going_Deeper_Into_Debt_FTC_Ru.shtml
https://techrights.org/n/2024/10/19/Links_19_10_2024_Riot_and_Intel_Layoffs_Attacks_on_Journalists.shtml

                    ䷩ 𝚕𝚒𝚗𝚎 96

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/2021_Deja_Vu_The_Counter_Petition_Defending_Richard_Stallman_RM.shtml
    Gemini version at https://techrights.org/n/2024/10/19/2021_Deja_Vu_The_Counter_Petition_Defending_Richard_Stallman_RM.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 2021 Deja Vu: The 'Counter-Petition'
Defending Richard Stallman (RMS) Gets a Lot More Support Than the Hateful
Screed⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


Garbage in, garbage out (GIGO). If you start with a very garbage argument,
it'll end badly for sure.


3.5 years ago we wrote many articles and made numerous videos about the anti-
RMS mob that had amassed some signatures in Microsoft's proprietary GitHub,
managed by an IBM/Microsoft Azure lackey that seemingly supports Hamas. As a
response to those signatures someone created a_counter-petition_(or_letter)
that_got_almost_twice_as_many_signatures. Over the coming weeks/months or over
time the original attack only lost signatures (people asked for their names to
be revoked/removed from it), not gained any, until it was locked and they would
no longer allow people to revoke their names. Nice, eh? What lovely, caring,
inclusive people... trick people into signing an array of lies, then tell them
to piss off (if they regret being tricked and try to correct that, undoing what
they had done because of Social Control Media disinformation campaigns).


To prevent the "blood libels" resurfacing someone created a site,
stallmansupport.org. The other day the site was very slow. DDoS? Just high
demand? Coincidence? Sometimes requests sent to the site timed out altogether.
At a very critical time. We documented this with evidence in IRC.


History seems to be repeating itself.


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


Well, as shown above, videos in support of RMS - videos from this past week
(there are more) - are going kind of "viral". In the case of DistroTube or
Derek Taylor (DT), it's clearly a lot more popular than his other videos.


"The commentary and posts against the proprietarization of FOSS using the guise
of 'ethical source' could use more redundancy," one reader told us,
"specifically reiteration of the reasons why 'ethical source' is basically
proprietary."


It's hardly surprising that the attack on RMS focused only on "sex" or "sexual"
something. The person behind this attack has a long history of doing just that.
He did that last November and we wrote a rebuttal in "When_the_So-called
'Cancel_Culture'_Sees_Everything_in_Free_Software_Through_the_Scopes_of_'Sex'_
(Because_It_Cannot_Argue_on_Technical_or_Legal_Grounds)".


This is his_vision_of_freedom; "I don't like you, so I ban you!"


Perhaps the real problem is himself, but he just cannot get himself to
acknowledge it because that's a lot more challenging than taking out his
frustration on some old man with cancer.


Someone wants his Gewalt.


"DT's_recent_video [over 31k YouTube views; more in Odysee] on that was one of
his best IMO," the reader told us (other readers told us about that same video;
that's why it keeps spreading... people like it).


"The bottom line is that, like usual, it is about control. Specifically
"ethical source" is about taking control away."


Don't listen to the RMS haters. Many of them have personal_issue and they hope
to somehow dethrone those who did better in their life, career, coding,
recognition etc. █




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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⢿⣿⣿⣧⣿⣿⠟⢠⣾⣿⣿⣿⣧⠟⠋⣠⣿⣿⣿⣿⣧⠟⠉⣠⣾⢿⣿⣿⣷⣿⣿⡿⢿⠿⠛⠋⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣬⣉⣉⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣷⣬⣉⣉⣉⣠⣴⣿⣿⣬⣉⣉⣤⣴⣿⣿⣷⣍⣉⣉⣤⣶⣿⣿⣿⣷⣬⣍⣉⣉⣉⣉⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣙⠛⠛⠿⠿⠿⠛⠛⠛⠛⣉⣉⣉⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣍⣉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣙⠻⣿⡿⠟⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⡀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⡀⠀⡀⢀⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣩⣬⢇⠪⣰⣶⣆⢀⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⠁⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⣤⡤⡬⢹⢟⢏⣵⣷⢴⡟⣽⣗⡆⠀⠀⠀⠀⠒
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠙⠛⢿⣿⣿⣿⡏⡍⡟⡻⡋⡟⡛⡛⡍⣽⡟⣟⢻⠛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢁⣀⣀⣀⣀⣀⣀⣀⣀⣙⢿⣿⣷⣶⣷⣶⣷⣶⣷⣾⣷⣿⣶⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⢸⣿⣿⠉⢻⣿⣿⣿⠛⠋⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⢸⣿⣿⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⢸⣿⣿⣤⣼⣿⣿⣿⡤⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣏⣟⣛⣿⣙⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣄⠉⠉⠉⠉⠉⠈⠉⠀⣠⣿⣿⡿⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣶⣿⣿⣿⣿⣧⣀⣀⣈⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⢉⠉⠉⠉⢹⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣼⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢰⣲⣶⣶⣶⠆⣰⡆⠀⠀⢠⣴⣶⣶⡄⠀⢀⡀⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠠⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠹⠿⠟⠋⠙⢻⣿⣿⣿⠿⠿⢻⣿
⣿⣿⡇⠀⠀⠀⠀⡖⢀⠰⣰⢠⢰⢿⠀⠀⡰⠛⠿⠿⠿⣿⠀⠈⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠀⠀⠨⢉⠀⣠⠀⠀⠀⠀⢸⣿⠉⠉⠉⠁⡦⡆⣶⠄⠆⠀⠀⠀⠀⢘⡯⠦⠘⢅⠁⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⢰⢰⢶⣶⢆⡆⠀⠀⠀⠀⢀⢠⡦⣰⣼⡇⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠂⠀⠀⡔⣶⣶⡾⡗⠊⠀⠀⠀⠀⢸⣿⠈⠇⠄⢐⢠⣦⡆⠀⠀⣠⠀⠀⠀⣈⠇⠉⠀⠀⠀⠊⠁⠁⠘⢿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⣇⣉⡹⢸⠃⠀⠀⠀⢰⠤⠄⠀⢌⡙⠙⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡗⠓⡟⠛⡿⠑⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡆⠏⠀⢀⡄⠎⠀⠐⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠯⠿⠏⠟⠂⠀⠀⠠⠀⠀⢠⣦⣤⣠⣤⡠⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣬⡅⣤⢡⣠⣤⠈⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠀⠠⠃⠀⠀⢸⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠀⠀⠀⡀⠉⠁⠀⠉⢰⢆⣀⣀⣂⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡿⡿⡿⠃⠀⠀⠀⢾⢿⡿⡿⢿⢿⠿⠿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠏⠀⠀⠀⠺⡿⡿⠿⢿⣿⣿⡿⣿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⡤⡶⢿⠿⢿⠿⢿⠿⡿⡿⠿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣛⣃⣀⣀⣒⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 240

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/Fun_Weekend_But_Very_Slow_News.shtml
    Gemini version at https://techrights.org/n/2024/10/19/Fun_Weekend_But_Very_Slow_News.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Fun Weekend, But Very Slow
News⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


There's no holiday (here or in the US) this week/end, but news is very slow/
scarce, at least in English. We're struggling to find much journalism and
something that resembles exclusive, investigative reporting. This leads to a
shortage of ideas (or topics to cover).


We have a lot of material to publish next year, but that's work in progress and
it'll need patience. It will surely come out when the time is right.


If you wish to suggest an idea of/or some topic we can cover, come_to_IRC and
tell us. soylentnews.org (SoylentNews) has_been_having_severe_IRC_issues
lately, but we've_had_persistent_uptime_for_over_a_year and are active all day
long.


Topic suggestions through IRC make sense because we don't do "comments"
anymore. Hackaday_explained_nicely_just_7_days_ago_what_comments_mean_to_their
people. To quote:


     You know what your mom would say, right? This week, we got an above
     average number of useless negative comments. A project was described
     as looking like a “turd” – for the record I love the hacker’s angular
     and futuristic designs, but it doesn’t have to be to your taste. Then
     someone else is like “you don’t even need a computer case.” Another
     commenter informed us that he doesn’t like to watch videos for the
     thirtieth time. (Yawn!)


     What all of these comments have in common is that they’re negative,
     low value, non-constructive, and frankly have no place on Hackaday.
     The vast majority are just kind of Eeyorey complaining about how
     someone else is enjoying a chocolate ice cream, and the commenter
     prefers strawberry. But then some of them turn nasty. Why? If someone
     makes a project that you don’t like, they didn’t do it to offend you.
     Just move on quietly to one you do like. We publish a hack every
     three hours like a rubidium clockwork, with a couple of original
     content pieces scattered in-between on weekdays.


     And don’t get us wrong: we love comments that help improve a project.
     There’s a not-so-fine line between “why didn’t you design it with
     trusses to better hold the load?” and “why did you paint it black,
     because blue is the superior color”. You know what we mean.
     Constructive criticism, good. Pointless criticism, bad.


That's not to say IRC is invulnerable to bad behaviour; but IRC moderation is
different and "hit-and-run" attacks take a lot more effort than just typing a
malicious comment.


Anyway, we've got lots of free time this weekend (all weekend tasks have been
completed), so we welcome topic suggestions/recommendations. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⣤⠤⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠀⠀⠒⠀⠀⠀⠀⢀⡀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠆⠠⠤⠀⠤⠀⠈⠷⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⣤⣤⣤⣤⡤⢀⣤⣤⣶⣿⣿⡟⠀⢀⣀⣀⣀⣀⣴⣶⣴⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠓⠶⠤⠤⠤⢤⣿⣿⣶⣿⣶⣶⣶⣿⣿⣷⣦⡶⠞⠀⠀⣤⠄⠀⠀⠀⠀⢠⠀⠀⠀⡀⢀
⣿⣿⣿⣿⣿⣿⡉⣩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣾⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⣾⣷⣶⣿⣿⣿⣿⣿⣿⣟⠉⠈⠛⠫⣤⣤⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠰⢦⡄⠠⠄⢠⠄⢀
⣿⣿⣹⣿⣿⠻⠻⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⠹⢿⡇⠈⠉⠉⠁⢀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠟⠙⠙⠁⠁⠀⣠⣾⣿⣦⣤⣶⠶⠖⠀⠀⡀⣀⣴⡿
⣿⣿⣿⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠤⠤⣼⣿⣿⣿⣿⠛⠋⠉⠁⠀⣀⣿⣿⣿⣿⣿⡿⢿⠃⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⡿⢿⠛⢛⣁⡛⠉⠉⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⣯
⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⣀⠀⠉⠛⠛⣒⠒⠲⢽⣿⣿⢥⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⣿⣿⣿⣿⣴⣤⣴⣿⠝⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡻⢫⣭⣽⣿⠟⠛⠶⠄⠀
⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⠤⠤⣬⢭⣽⣿⣿⡿⠿⢟⣛⠿⣿⣮⣛⣿⣿⣿⡿⢿⣿⣿⣏⢀⣠⡶⣿⠽⣿⣿⣿⣿⣿⣿⡀⠽⢻⣿⣿⣭⣉⣹⣧⣌⠈⢿⣧⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢳⠾⠻⠋⠀⠀⠛⠂⠀
⣿⣿⠛⠉⠛⢻⡄⠉⠀⠒⠒⠒⠶⣼⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣽⡿⢿⠿⣛⣥⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣙⣷⣾⣿⣿⣿⣿⣿⣧⡭⠈⠀⠈⠛⠀⠘⠻⣿⣿⣿⣿⣿⠛⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣶⣾⣷⡒⠒⠠⠤⠴⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⠛⢁⣴⡿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠛⢩⣿⣿⣿⣿⣿⣿⣿⡟⣬⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⢱⡶⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣷⡁⢐⣒⠒⠻⠾⢿⣿⣿⣿⣿⠛⣿⣿⡻⡓⠈⠀⠀⢸⣿⣷⣽⣿⣿⡯⠛⣻⣷⡆⠀⠀⣴⣿⠿⠟⢻⣉⣁⣴⣾⠟⠛⠀⠀⠀⠛⠓⠒⠀⠀⠀⠀⠉⠁⠀⢐⣒⣀⠀⢠⣤⣄⠀⠀⠀⠀⠀⣰⣶
⣿⣿⣿⣿⣿⣿⣿⣿⡻⣦⡰⣾⣭⣭⣝⣻⣿⣿⣿⡇⠉⠻⠿⠟⠁⠀⠀⢸⣿⣿⡀⠘⠋⠀⣀⣞⠏⠀⠀⠀⣿⡯⠀⠴⠘⠻⡯⠻⠁⠀⠀⠀⠀⠠⠤⠄⡀⠀⠀⢀⣀⣀⣤⢴⣟⣁⡀⠱⠀⠀⠁⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠙⢦⡍⠉⠭⠝⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠛⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠻⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣶⣾⣶⣦⠀⠀⡀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡿⣿⠿⠿⠿⣿⣷⣤⣀⣙⣳⣌⠉⠉⠓⠒⠂⠀⠀⣀⣀⣀⣤⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⣧⣿⣦⣤⣴⣿⣷⣿⡿⣿⡟⠛⠿⠖⣀⠀⠀⠀⠀⠈⠉⠉⠉⢛⣛⡛⠻⠿⠿⠶⢶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠦⣬⣾⣿⣿⣿⠀⠀⠀⠀⢠⣶⣾⣶⣿
⣿⣿⣿⣷⣿⣿⡯⠭⠿⣿⣿⣷⣤⣤⣤⣀⣀⣈⢻⣷⣤⣀⡀⠀⠀⢀⣠⣦⣩⡛⢻⠗⠶⣦⣤⣄⡀⠈⡉⠉⠉⠛⠛⠛⠓⠶⠶⠦⢤⣤⣤⣤⣤⣀⣠⣤⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡗⠀⠦⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⢿⠏⠀⠀⣠⣾⣿⡉⠙⠳⢦⣍⣹⠛⡉⠙⠛⠛⠻⠿⠿⣿⣷⣿⣿⣶⣦⣤⣤⣤⣉⣛⣛⡳⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠻⣿⣿⣿⣿⣷⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⠆⠀⣤⣴⣿⣿⠋⠃⠀⡄⠀⠉⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⢿⠿⠿⠶⠶⠶⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⠿⠁⠀⠰⣿⣿⡿⠁⠀⠀⠀⠈⠉⠀⠀⣷⠀⠀⠀⠙⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⢶⣶⣶⣛⡛⠛⠛⠛⠛⠷⠾⠶⢶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠖⠒⠒⠂⠈⢿⣿⣿
⣿⣿⣾⣿⣿⣿⣿⡿⢁⠆⡟⣧⠀⠀⠈⠉⠙⠻⠆⠀⠀⠀⠈⠻⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⣆⣶⣶⣄⢰⡄⠘⢿⣿⣿⣿⣿⣿⣿⣿⠃⠒⠒⠲⠤⠤⢤⣌⣛
⣿⣾⣻⣶⣿⡿⣹⣷⣿⣶⡇⢸⣷⣀⣀⣀⡀⠀⠀⡤⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⠛⠠⠤⢹⣇⣨⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⡿⢿⣿⡿⣡⣿⣿⣿⡟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠈⠙⠛⠿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠒⠤⠤⠤⢄⢠

                    ䷩ 𝚕𝚒𝚗𝚎 343

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/IBM_RMS_Asked_a_Girl_on_a_Date_We_at_IBM_Are_Bribing_and_Receiv.shtml
    Gemini version at https://techrights.org/n/2024/10/19/IBM_RMS_Asked_a_Girl_on_a_Date_We_at_IBM_Are_Bribing_and_Receiv.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IBM: RMS Asked a Girl on a Date. We at IBM
Are Bribing and Receiving Bribes. Cancel RMS.⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Oct 19, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Euros_Handshake⦈_


Days ago: IBM_Bribery_Scandal_in_China


More in "IBM_Investigates_Allegations_of_Executive_Misconduct_in_China" (they
basically confirm that this is true!)


2020: IBM_(Red_Hat)_Lectured_FSF_That_It_Needed_More_Diversity,_But_Was_It
Looking_at_the_Mirror?_IBM_and_Red_Hat_Are_Even_Less_Diverse.


The_FSF_is_'half_female'_now, having added_many_women. They_coexist_with_RMS.


2023: Since_IBM_(Red_Hat)_Blasted_the_Free_Software_Foundation_for_Lack_of
Diversity_IBM's_Board_of_Directors_--_the_Decision_Makers_of_IBM_--_Reduced
Women's_Participation_From_3_to_Just_2


IBM gets to kill people and lecture cash-strapped non-profit NGOs about
morality.


Also see: Let's_Ban_Bombings,_Not_Words_(Corporations_Taking_Away_People's
Freedom_of_Speech_So_They_Can_Bomb_'in_Peace') | The_Biggest_Troll_is_the_Linux
Foundation,_Still_Looking_to_Provoke_and_Defame_Free_Software_Communities_in
Order_to_Help_a_Monopolistic_Takeover_and_to_Shoehorn_Tyrants_Into_Leadership
Positions




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠹⣿⠟⠿⠗⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣍⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠛⠛⣩⣿⣿⠴⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣤⣄⡀⠀⠈⠛⠻⢧⣴⣿⠟⢋⡈⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⢀⠈⠓⠄⢹⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⢦⡀⠀⠀⠋⣉⣬⡉⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡄⣴⡆⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⣄⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣿⣷⣤⠀⠈⠙⢿⣿⣿⣿⣷⡀⠉⠻⠿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢾⣷⣦⠉⢿⣿⣿⣷⣶⣦⠀⢻⣿⣿⣿⣿⣄⠀⠀⠀⠙⣻⣿⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⠀⠀⠀⠀⠙⠁⠀⠀⠀⢹⢿⣿⣿⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣦⡀⠀⠈⠙⠻⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢰⣶⣤⠈⠚⣿⣿⣿⡄⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠈⢻⣿⣿⣄⠀⠀⠀⠈⠁⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⡀⠀⠀⠙⠁⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⢀⣿⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠹⣿⣧⠀⣀⡀⠀⠀⠈⠻⣿⣿⣶⣤⣶⣿⣿⣿⣿⣷⣄⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆⡀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣶⡄⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡀⠀⠀⠀⠿⣿⣿⣷⣤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 420

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/IRC_Proceedings_Friday_October_18_2024.shtml
    Gemini version at https://techrights.org/n/2024/10/19/IRC_Proceedings_Friday_October_18_2024.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ IRC Proceedings: Friday, October 18,
2024⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


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


                                              #techrights_log                                                                                           #boycottnovell_log


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


                                         #boycottnovell-social_log                                                                                        #techbytes_log


===============================================================================
The corresponding text-only bulletins for_Tux_Machines and for_Techrights
contain all the text.


                          Enter_the_IRC_channels_now




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠯⠿⠯⠀⠚⠩⣽⣿⣿⣻⣿⢟⣯⢘⡆
⣿⣿⣿⣿⣿⣿⣙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⡿⣿⣿⣿⣿⣻⢯⣯⡽⠿⠽⢿⡹⠊⣹⣻⡾⣾⠋⢭⡮⠀⠀⢼⣯⢿⣻⣿⣿⡟⠑⠤
⣻⣽⣟⣿⣏⢏⠹⡺⣦⣚⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢡⣿⣿⣿⣿⣿⡗⠻⠙⢲⣾⠿⠀⠀⠲⡾⣭⢯⣦⡄⠀⢀⣠⡿⠛⠙⣿⠿⢯⡵⠰⠄
⠭⣼⣿⣿⣿⢉⠉⠙⢓⣂⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣿⣿⣿⣿⣶⡴⣿⢯⡋⢙⣽⡇⡼⠶⠶⠆⡀⠀⠈⢛⢁⢈⣻⣷⠌⠄⠈⠠⠔⢀⣰⣦⣾⡿⠠⢐⣶
⠀⣼⣿⣿⢿⣯⡄⠀⠀⠁⠃⢬⠘⢻⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣣⣾⣿⣟⣿⣟⣋⡅⠹⣾⣿⠿⠿⢋⣁⠠⠄⠀⠀⠀⠀⠐⡀⡀⢰⡟⠂⠀⠠⢽⣶⣿⣿⣿⠿⢁⣠⡎⠀
⠙⡻⢿⣿⠆⢠⣵⠖⠒⠠⠤⠖⠂⠐⠘⠹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢥⢽⣿⣿⣻⣿⡿⠐⣿⣿⣿⣿⣬⣯⣥⣼⣿⣾⠦⠄⠀⠉⡘⠓⠀⠀⠀⠀⠀⠀⡀⢐⠂⠀⠀⠀⠈⠻⡟⡉⠀⠀⠈⢫⡁⡉
⢫⣽⣧⣶⣤⣿⡋⠃⠀⠀⠀⠀⠈⠉⠙⠙⠻⣹⣿⣿⣿⣿⣿⣯⣥⣿⣿⣿⠝⠛⠚⠣⡸⠀⠀⠐⣟⡀⣠⢄⣼⣿⣿⡿⣿⣿⠗⠓⢃⢀⣀⢠⣉⡀⠋⠀⠠⠀⠀⠀⠀⣸⡥⣺⢀⠀⠀⠀⠀⠀⣀⡄⢀⣰⣶⣿⣾⣿
⠀⠭⡏⠍⠿⠋⠀⠀⠀⠐⠒⠀⢀⠀⠀⢂⣢⠤⢲⣸⣿⣿⣿⠿⣿⣿⣿⠯⣤⠀⠈⠁⠑⠁⠀⢈⣛⠋⡁⣾⣿⣿⣿⣾⣷⣿⣤⠈⣉⣶⡍⣉⣀⠀⠊⠓⠁⠀⠁⢄⢰⢴⠫⡁⠀⠀⠐⠨⣻⣿⢏⣛⢿⣿⣿⣿⣿⡏
⠀⣈⡁⠶⠄⠤⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⡀⠎⠀⠀⢸⣿⣸⣼⣿⣿⠩⠅⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⢠⣜⣿⣿⣶⣽⣻⠀⢘⣿⡿⠶⠩⠈⣂⣀⠀⠀⠀⠀⢄⣰⣝⠏⠉⠀⠀⠈⠈⣛⢠⣮⣿⣿⣿⣻⠿⠛⡞
⠻⠿⠌⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠿⠉⠏⠻⠂⢀⣷⣾⡟⢻⡇⢿⣿⡄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢹⣟⣿⣿⠋⡿⡿⢛⣯⣤⣤⡬⠟⠋⠉⠀⠀⠀⠀⣀⢌⠤⠀⠰⠐⣀⠀⠠⣯⠉⠘⢫⠟⠻⠋⠁⠠⠂
⣿⡁⠀⢠⣴⢇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠆⠀⠀⠀⠈⠁⣸⣇⣾⣿⠁⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⣿⣿⣿⣶⣶⠾⣮⣯⣉⣈⠉⠁⠀⠀⠀⠀⠀⠠⠅⠀⡿⠔⢀⠁⠀⠀⠘⠍⢀⣀⠀⣦⣦⡤⢶⠂⠀
⠉⠻⠃⢚⠋⠉⠉⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⣖⣶⣿⣶⣿⡟⢛⣁⠀⠀⣀⡀⠀⡀⣰⣾⡿⢉⣭⣽⣿⡷⠄⠀⢡⡈⢵⡷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠂⠀⠀⠀⠀⢒⡿⠈⢛⠛⢓⣉⡉⢀⡀
⠀⠀⠀⠈⣀⣠⣈⣤⣶⡾⠳⣖⡀⠀⠀⠀⠀⠘⡁⠀⣤⣿⣷⣿⣿⣿⣿⣿⣿⡤⣤⣽⣿⣿⣿⣿⣿⣡⢻⣿⣟⣿⠿⠿⣿⣮⣿⣾⣒⢶⣶⠖⠀⠀⣠⣤⢀⣀⠄⠀⠚⠗⠀⠊⠀⠀⠀⠀⠈⠁⠀⠀⣰⣯⣽⣦⣾⣿
⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⢠⣤⣤⢶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣾⣿⣿⣿⣷⣶⣷⣿⠗⣴⢯⠝⠙⣡⣿⢛⠃⠀⠀⣼⡿⠻⢁⡨⣅⠄⣉⠫⠈⠇⠀⠀⠀⠀⢹⡛⠀⣰⣟⣯⡪⠍⠙⢫⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠊⠛⠻⠚⠻⠻⡏⠛⢿⠉⠻⠰⠕⠁⡿⡿⡿⠷⣿⢿⣿⣷⣿⣽⣿⠑⠐⢿⠩⠄⠀⢿⣿⠆⠀⠀⢠⣯⣂⣭⠉⠄⠙⠀⠁⠀⠀⡀⠀⠀⠀⠀⠉⠁⣤⣿⣿⡯⠋⠀⢈⡘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⣀⣀⢀⣰⢾⢛⣡⣤⣤⣤⣤⣥⣭⣤⣤⣤⣤⣤⣴⡾⣧⣿⣿⣿⣿⣿⣿⠟⣿⣷⣶⣿⣲⣤⡄⣬⣌⣀⠀⠀⠈⣏⠈⡰⠀⣇⡄⠀⢠⡀⣼⢷⣤⠀⡰⢻⣦⡿⣿⣼⠟⠃⠘⠋⠙⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢉⡙⢈⣃⣿⣛⣿⣻⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣤⣼⡠⣬⡿⣥⣽⣯⣽⣿⣿⣬⣔⠯⢒⡰⠑⠂⠀⠂
⣿⡿⣿⣿⣿⣯⣘⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⠋⡿⠀⢙⣿⠻⣿⠋⣹⣿⣿⣿⠿⠿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣟⣿⣷⣿⣿⣿⣿⣿⣿⣏⡙⣠⣴⣄⣀⣀⣐⠀
⣏⠀⠄⢹⣿⣿⣿⡿⢻⣿⡷⣿⣋⣿⣿⣿⣿⣝⣿⡠⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣭⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣝⣿⣿⣿⡛⠁⠙⣿⣿⡻⡇⢥⠀
⠀⠀⠀⣾⣿⣿⣯⣾⣘⢩⣙⣿⣿⣿⣿⣿⣿⡿⠛⠁⠈⡟⢻⣫⣟⣛⣃⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣦⣭⣬⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠛⣣⣼⢰⣾⣿⣿⣧⣴⣈⣠
⣠⣄⠰⣶⣿⣿⣿⣿⡿⡟⢿⠏⣿⣿⡿⣿⠟⠅⠀⠀⣼⣷⣶⣙⣿⣿⣏⠻⣿⣯⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣵⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⣏⣤⣻⣿⣿⣿⣿⣿⡇
⠈⠁⢀⣿⣿⣿⣿⣿⣿⣃⣈⣠⣾⣿⣿⣶⣅⠀⠀⠀⣤⣿⣿⣿⣻⣿⡎⠃⢨⡟⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⢈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠁⠀⠀⢨⡀⠛⠹⡟⣛⣙⣀⣀⣃⣀⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣥⣶⣧⣤⣤⣤⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣇⣸⣿⣿⡿⣿⣿⢿⣿⣿⣿⡿⠛⣿⣿⠃⠀⠀⠀⣦⣯⣀⣆⣾⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢻⣿⣿⣿⣛⡿⡿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿
⣿⣿⣿⣿⣷⣶⣶⣾⣾⣿⣿⣯⣄⣶⣽⣽⠀⢠⡀⠀⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣷⣶⣶⣿⣾⣦⣤⣦⣽⣷⣷⣶⣶
⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣋⣻⣿⣿⣿⣿⡭⣿⣿⣯⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⣀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⣤⣉⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⣉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣉⡙⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⡙⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣍⣉⡛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣉⣙⠛⠻⠿⢿⣿⣿⡿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣄⣈⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⠛⠻⠿⢿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣷⠌⢿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠁⠀⢀⣾⣿⣿⣿⡿⠋⠀⠈⠻⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠈⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣉⡛⠋⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣙⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣀⣀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣙⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 646

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

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    Gemini version at https://techrights.org/n/2024/10/19/Meme_How_Editorial_Control_and_or_Fact_Checking_Work_in_Social_.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] How 'Editorial Control' and/or
'Fact-Checking' Work in Social Control Media⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


    🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇I_saw_a_link_with_many_'likes'_on_it,_so_it_must_be
                                  accurate⦈_




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

                    ䷩ 𝚕𝚒𝚗𝚎 751

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/Meme_Mentality_of_a_Loser.shtml
    Gemini version at https://techrights.org/n/2024/10/19/Meme_Mentality_of_a_Loser.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Mentality of a
Loser⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024,
updated Oct 19, 2024


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇There_is_someone_who_created_a_project_used_by_billions;_I
failed_to_create_project_used_by_billions,_so_I'll_take_down_someone_who_did⦈_


 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Listen_to_me!_Sex_Sex_Sex_Sex_Sex_Sex_Sex_Sex_Sex_Sex_Sex
                            Sex_Sex_Sex_Sex_Sex_⦈_


Context: When_the_So-called_'Cancel_Culture'_Sees_Everything_in_Free_Software
Through_the_Scopes_of_'Sex'_(Because_It_Cannot_Argue_on_Technical_or_Legal
Grounds) | They_Tell_Us_Linus_Torvalds_is_Sexist_But_Evidence_Suggests
Otherwise




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠐⠆⠀⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⢉⡁⠄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠿⠃⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣤⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⢀⣀⢀⣀⡀⣀⣀⠀⣀⡀⣀⡀⠀⢀⣀⠀⣀⣀⢀⣘⢛⣛⢛⣛⠛⣛⡛⣋⢀⡀⣀⣀⠀⣀⢀⡀⣀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢹⣿⣿⣿⣯⢹⣿⡿⣿⣯⠀⣿⡿⣿⣟⠀⢿⣿⡃⣿⣿⣿⣿⣾⣿⢸⣯⢹⣿⣿⣿⣿⡇⣿⣏⠀⣿⣿⣷⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣧⣼⣿⣿⣿⣧⠀⣿⡿⣿⣿⠀⢿⣿⡗⣿⣿⢿⣿⣿⣿⢸⣧⡼⣿⡿⣿⣿⡇⣿⣥⠀⣿⣿⣿⡟⣿⣿⡿⢿⣼⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⣄⣀⣀⡀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⡀⠀⣀⣀⣀⣀⣀⢀⣤⣄⢀⡀⣀⣀⣠⣤⣀⣀⣒⣒⣂⣀⡀⣠⣤⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⢀⡀⢀⣀⣀⢀⡀⣀⢀⣁⢀⣀⢀⣤⡀⣀⢀⡀⣤⣄⠀⠀
⠀⢸⡇⣛⣿⣿⡟⣿⣭⣾⣿⡏⣿⠉⣿⡅⣿⣿⡇⢰⣿⣿⠀⣿⣿⣿⣿⣿⢸⣿⣿⢸⡇⣿⣭⣿⢘⡋⢹⡏⣍⣿⣿⡇⢿⣯⣹⣿⣽⣿⣿⣇⢸⣿⣟⢹⣿⠃⢸⣿⣿⢸⡇⣿⠀⣿⢸⣿⣿⣿⣿⣿⣿⡟⢿⣯⠀⠀
⣀⣸⣷⣟⣿⣿⣿⣿⣶⣿⣻⣧⣿⣀⣿⣶⣿⣿⣇⣸⣟⣿⣄⣿⣇⣸⣿⣿⣸⣿⣟⣾⣇⣿⣶⣻⣾⣇⣼⣇⣯⣻⣿⣇⣿⣿⣻⣿⣾⣿⣿⣋⣸⣿⣿⣸⣿⣀⣸⣿⣿⣹⣇⣿⣶⣿⣾⣿⣻⣿⣟⣿⣻⣟⣿⣿⣃⣀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⢿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠟⠯⢓⣂⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠋⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣚⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣽⣿⠛⠀⠀⠀⠼⠛⠡⣆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠛⠿⢿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣤⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠛⢛⡯⣽⡿⠛⠟⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⣀⠀⡀⡀⢀⡀⣀⡀⠀⣀⡀⣀⠀⠀⡀⢀⣀⢀⣀⢀⡀⣀⡀⣀⠀⠀⣀⠀⣀⠀⢀⠀⣀⣀⡀⢀⠀⣀⡀⢀⢀⠀⣴⢶⣿⣿⣿⣿⣿⡿⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣯⣿⣿⣿⣿⢸⡯⣿⣿⠈⣿⢹⣿⡇⢸⣿⣿⣿⣿⣯⣼⣿⣿⢹⣯⠀⢸⣿⢿⣿⣿⣿⡇⣿⣿⣽⣿⣟⣿⠁⢸⣿⣿⣿⣻⣯⣿⣿⠀⣿⣟⢿⣏⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠛⠘⠛⠃⠘⠛⠙⠛⠛⠛⠛⠛⠛⠘⠛⠂⠘⠃⠘⠛⠋⠛⠓⠛⠛⠋⠛⠋⠛⠰⢝⣛⣽⣛⣝⣛⣛⣻⣴⣛⣻⣼⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⢾⣿⡇⣿⢸⣷⣿⣾⣷⡷⣿⡇⠀⢾⣷⣾⣿⠀⣿⢿⣷⣿⠂⢸⣿⣿⣧⣿⡿⣿⡃⢸⣿⣶⣿⣾⣿⣷⣿⣷⡇⢰⣿⣶⣿⣾⣿⣿⣿⣟⣾⣷⣿⣾⣿⣟⢸⣿⣿⣿⣿⣿⣿⣷⢹⣿⣧⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠿⠿⠻⠿⠷⠿⠾⠟⠿⠻⠿⠟⠿⢿⠆⠻⠿⠻⠿⠀⠿⠸⠿⠿⠶⠸⠿⠿⠿⠿⠿⠿⠆⠸⠿⠛⠿⠛⠿⠿⠟⠟⠿⠘⠿⠛⠿⠻⠿⠿⠿⠷⠻⢟⣿⣿⡿⢷⣼⣿⣿⣿⣿⣿⣿⣟⣼⠿⠟⠿⠿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣼⣆⢻⣿⣿⣿⣿⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢹⣿⣿⡿⠟⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣶⡄⢠⣤⢄⣠⣤⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⠇⢸⣿⢸⣿⣝⠟⠛⣿⡟⢻⣿⠻⢹⣿⣴⣶⠀⢰⣶⣶⣦⣨⣭⣭⡛⡿⣛⣛⡻⣿⣿⠇⠀⠠⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣁⣼⣿⣴⡽⣿⡇⢰⣿⡇⢸⣿⠿⢸⣿⣿⣿⠀⠀⣿⣿⢀⣿⣧⣿⡇⠁⣿⣿⣿⣿⡿⣼⣿⠿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠘⠛⠛⠃⠸⠿⠀⠿⠿⣶⣿⡏⣿⡏⠀⠀⣿⡇⢸⣿⣻⣿⠁⠀⣿⢿⣿⣿⡇⣿⡿⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⢛⣯⣶⣜⠛⠸⠏⠿⠇⠿⢷⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣤⣀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⡿⠋⠀⠂⠉⠙⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣿⢀⡀⣸⣋⡟⠛⠟⠋⠉⠉⠉⠉⠛⠋⠙⠉⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠟⣻⣵⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⢙⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣼⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢠⣤⣤⣄⡤⠀⣤⣤⣤⣤⣤⣤⣤⠄⢠⣤⣄⣤⣤⢤⣬⡽⠟⣭⣭⣡⣤⣤⣤⣤⠀⣠⣤⣄⣤⣤⣤⣤⡄⢀⣤⣤⢠⣤⣤⣤⣤⠀⣠⣤⡄⣤⣤⣤⣠⡄⠈⠙⠻⢿⣿⣿⣿⣿⣿
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣯⢸⡷⢸⣿⡇⠀⣻⣿⣽⣿⠆⣿⣿⠀⢘⣿⣯⣿⡷⢸⣿⡇⡄⣻⣯⣹⣿⠆⣿⣿⠀⢙⣿⣍⣿⡷⢸⣿⡇⢈⣿⣯⣸⣿⢎⣿⣿⠀⣻⣿⣅⣿⠶⣹⣿⡁⠀⠀⠀⠀⠈⠙⠻⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠸⠷⠾⠏⠿⠀⠻⠾⠻⠿⠶⠿⠻⠆⠘⠷⠟⠿⠷⠾⠿⠷⢀⠿⠿⠻⠿⠾⠿⠿⠆⠸⠿⠟⠿⠷⠿⠿⠧⠈⠿⠿⠻⠿⠾⠟⠿⠀⠻⠿⠏⠿⠶⠿⠹⠇⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⢠⡶⣦⢰⡶⢶⣦⡶⠀⣴⢶⡄⣶⠶⣶⣴⠆⢠⡶⣦⣴⡶⢶⣦⡖⠀⣴⢶⣴⣶⠖⣶⣶⠀⢰⣶⣦⣶⡶⢶⣶⡆⢀⣶⣶⣴⣶⠶⣶⣶⠀⣴⣶⡆⣶⡶⣶⣴⡆⢠⣶⣶⢰⡶⢶⣦⣶⠀⣴⣶⡆⣶⠶⣶⣴⡆⠀
⠀⢈⡻⣶⢸⡷⢾⣿⣇⠀⣙⢷⡆⣿⠆⣿⣿⡀⢘⡻⣦⣿⡷⢸⣿⡇⠀⣛⢷⣼⣿⠆⣿⣿⠀⢘⣻⣦⣿⡷⢸⣿⡇⠀⣻⣷⣼⣿⠆⣿⣿⠀⣙⣿⣦⣿⡷⣸⣿⡇⢈⣻⣷⣸⡷⢆⣿⣯⠀⣙⣷⡆⣿⠶⣽⣿⡄⠀
⠀⠈⠛⠛⠘⠛⠛⠋⠛⠀⠙⠛⠃⠛⠛⠛⠙⠃⠘⠛⠛⠛⠛⠛⠋⠛⠀⠛⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠓⠀⠛⠛⠙⠛⠛⠛⠛⠂⠘⠛⠋⠛⠛⠛⠛⠓⠈⠛⠛⠙⠛⠛⠛⠛⠀⠙⠛⠃⠛⠛⠛⠙⠃⠀

                    ䷩ 𝚕𝚒𝚗𝚎 856

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

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⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] Plundering the
Commons⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024,
updated Oct 19, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Catspaw,_Google,_Apple,_Facebook,_Amazon,_Microsoft_vs_Free
 software⦈_ Free software is licensed to restrict privatisation and hoarding.
Some hateful people wish_to_change_that and then_impose_their_political_agenda.
                   We know what companies stand to benefit.




⠛⠲⣆⡆⢠⣼⢿⣥⣤⣦⣄⡀⠀⠀⠙⢿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⠟⠛⠛⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿
⠟⠉⣟⣃⠛⠀⠀⣼⣿⣿⣿⣿⣷⣄⣀⠀⠼⠿⠋⠀⠘⠊⠉⠻⣿⣿⠃⠀⠀⠀⠸⠃⠀⢠⣀⢄⣀⣄⠀⢠⣶⣦⣿⣿⡟⠁⡀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠘⣿⣷⡳⡄⣾⣿⣿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣤⣀⡀⢸⣿⠀⠀⠀⣶⡆⣶⢶⢰⡶⡄⣶⢰⡶⠞⣾⣿⣿⣿⡇⢸⣿⣶⣴⣄⣶⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿
⠁⠀⢉⣿⣿⠉⣿⣿⣧⡄⠄⢈⡻⠟⠛⠀⠀⠀⣰⣿⣿⣿⣿⣿⠘⠋⢣⣄⢸⣯⣧⣿⠛⢸⡟⠃⣿⣸⣟⡃⢛⡽⠻⠿⠻⠀⠈⠉⠉⠀⠈⠓⠚⠛⢻⣿⡀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿
⣠⣴⠛⠷⠂⠀⠸⣿⣿⣿⣿⣿⣷⣄⣥⠀⠀⢀⣧⣙⣍⣿⠟⡫⠀⠀⠀⠁⠈⠁⠉⠉⠀⠈⠁⣀⠉⠉⠉⠁⡿⠀⢸⢿⣿⣿⡃⡯⣿⣷⣿⢼⣿⣿⡇⣿⢹⣿⣷⠀⠀⠀⣍⡉⢛⣏⣰⣵⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿
⣕⠵⠄⠀⠀⠀⠀⠈⠀⠉⠛⠉⠛⢹⣿⡄⢀⢸⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠈⠅⠀⠈⠈⠈⠈⠁⠉⢉⡁⠉⠈⠁⠉⢥⣧⣄⣨⣿⣔⣠⠀⣿⣶⣿⡿⢿⣟⢿⣿⠃⣿⣿⡿⣿⣿⣿⣿
⣽⣿⣧⡄⠀⠀⠀⠀⠰⢤⠀⢀⣤⣾⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⢻⡿⡿⣿⣿⣧⠈⠀⢠⣤⣶⣧⡄⠁⣾⡿⣿⣿⠈⠈⠀⠸
⠙⠿⣿⣧⡀⠀⠠⠀⢀⠀⣤⣼⣿⣿⣿⣿⣿⣆⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠇⠀⠀⠀⠠⣶⣌⠻⠿⠋⠀⠀⢹⡇⠸⢻⠀⠠⠙⣽⣿⡟⠀⠀⠀⠀
⠀⠀⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⢟⣛⣛⠻⣿⣿⡆⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡿⠀⠀⠀⢴⣷⣮⣿⣷⣤⡀⠀⠀⠀⢱⡄⠁⠀⠀⠠⠿⠿⢧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢡⣾⡟⣹⣷⢙⣛⡻⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⢿⣷⣌⠻⣿⣝⡻⠟⠀⠀⠀⡾⠻⠴⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⣶⡮⢡⣿⢟⣿⡆⠆⡀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢿⣷⣍⡻⣿⣎⢛⡃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣌⡻⢺⡿⢱⣿⢏⣾⡿⣱⣿⢟⣷⡜⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢿⣧⡈⠻⣿⡾⢏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⠋⠙⣿⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⣶⣘⠿⣿⠟⣴⣿⢫⣾⡟⣴⣿⢻⣮⠻⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⣌⡈⢻⣷⣾⠆⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠠⣾⣻⣧⡻⣿⡁⠈⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣾⣧⡻⣷⣿⢏⣼⡿⣧⣙⠏⣼⣿⠪⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡈⢿⣿⣿⣿⣶⡝⠁⠀⢹⡿⠃⠀⠀⠀⠀⢀⡀⣾⣻⣃⡹⣷⡽⣷⠙⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣶⣜⢿⣵⣿⢏⣾⡿⠁⣰⣿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣹⣿⣿⣶⣝⢿⡷⠈⠀⠀⠀⠉⠁⠀⠀⢀⣀⢾⣟⢿⣎⢛⣟⣿⡎⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣷⣮⣅⠾⣿⡅⣴⣿⠿⢆⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⢿⣿⣿⣿⣮⡻⠗⠁⠀⠀⠀⠀⠀⢀⣀⢺⣯⣻⣎⢻⣯⣻⡇⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠂⠙⠻⢷⠎⣿⣿⣿⣿⣄⣀⣰⣶⣶⣶⡦⣾⣿⢿⣦⣝⠻⣷⡍⠁⠀⠀⠀⠀⢀⣤⢰⣿⡻⠗⡹⣿⡽⡷⠉⠉⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠐⢶⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣷⣽⡿⡿⠊⠀⠀⠀⢀⡀⣶⣧⡻⣷⡹⣷⣝⡿⠘⠉⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠿⣿⣿⣿⣿⡿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⣸⡏⠻⣿⣇⡀⠀⠀⠀⠀⠀⠋⠀⠈⣿⣿⣿⣿⣿⡿⠛⠁⢙⣇⡈⠻⠟⠀⠀⠀⠀⠀⠻⣿⣾⣿⢷⡝⠿⠌⠉⠀⠀⠀⠀⣨⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠺⡯⣷⣷⣇⣿⣿⣿⡿⣦⡄⠀⠀⠀⣠⠞⠁⠰⣿⣿⠋⠋⠀⠀⠀⢴⡆⠀⠀⡹⠻⢜⣣⢿⣷⠴⠞⠿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⣷⡽⠏⠉⠀⠀⠀⠀⠀⢈⣛⠋⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⢙⢭⣿⣿⣿⣿⣷⣾⡺⠇⠀⠀⢸⣿⣦⣄⣀⣤⣶⡀⠀⣠⣾⣿⣿⣷⣶⣾⣿⣷⣶⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡁⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣻⣿⣿⣿⣿⡇⠐⠿⢿⣿⣿⣿⣿⡿⣟⢛⡻⢿⡻⢿⡿⣟⣛⣛⡛⣛⣛⣻⢿⣷⢀⣀⠀⠀⠀⠀⠀⠠⠎⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢺⢻⣿⡿⣿⣿⣿⣿⣬⠄⠀⠀⠰⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⢻⣿⢸⡯⣿⡇⡿⢸⠅⢘⢯⣿⣿⣿⠍⡏⣿⣿⡟⣟⣿⣿⣿⡯⣠⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢉⣿⣿⡷⣾⣿⣶⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣮⣥⣭⣥⣍⣭⣥⣮⣭⣬⣭⣭⣬⣥⣬⣭⣥⣥⣭⣭⣭⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣿⡅⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠟⠛⠛⠛⠛⠿⠛⢛⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣀⠤⢤⠀⠐⠚⠻⠃⠔⠃⢠⠤⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⢟⣴⡿⣷⡌⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢠⠑⠆⠦⠀⣴⣿⣷⣿⡜⣻⡟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠹⢻⣿⣿⣿⣿⣿⣿
⠀⠈⠻⠏⣾⢏⣌⢛⣴⣿⣷⣩⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⢀⣀⣺⣿⢮⣿⣏⣘⠛⡀⠀⠀⣀⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢛⢫⣾⣯⣿⢃⣼⡟⢗⣭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⢅⡻⢣⣾⠏⣀⢿⡏⠿⣨⣭⡻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠑⠛⠿⢿⢿⣿⣿⣿⣿⣿⣿⠀⢀⢤⣿⠿⠟⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣷⡔⣿⣽⡟⣴⣿⣽⡟⣼⣭⡻⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢶⣯⣭⣽⣿⠇⠀⡰⠿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣭⡺⢟⠌⣩⣾⣻⡟⣼⡗⣩⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣜⡛⣽⡟⣼⣿⣾⡿⣱⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣉⣿⣦⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠶⣝⠻⢋⣿⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠘⢿⣦⣙⣡⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢯⣀⣀⠘⣿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣯⢻⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣶⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⠛⠫⠲⠤⠤⣀⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀
⠟⣩⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣕⡿⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢨⣽⣿⣿⣿⣿⣿⡿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⣀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀
⣬⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⣥⠉⠀⠀⠀⠀⠀⠛⠛⠻⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡙⠁⠘⠛⠀⠀⢀⣀⣀⣈⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣧⠀⠉⢉⠏⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣿⣿⣿⣿⡇⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀
⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣶⣤⣤⣴⣶⣴⣾⣿⣿⡇⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣶⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠁⣤⡠⠀⠀⠀
⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣿⡿⢟⣯⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣴⣿⣿⡧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣋⣉⣭⣴⣾⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⡇⠀⠀⠀
⠂⠀⠀⠀⠀⢐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠂⠀⠀⠉⠉⠩⡅⣭⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠛⠉⠉⠀⠉⠙⠿⠿⠷⠄⠀⠉⠻⢿⣿⡏⢹⣿⣿⣿⣿⣇⠀⠀⠀
⡈⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠘
⠃⠀⠀⠀⠀⠀⠠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀
⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣍⡂⠀⠀⠀⠀⠀⠀⠀⣀⣄⣴⣿⣿⣿⣿⣿⣿⣿⣷⣷
⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠷⠀⠀⠀⠄⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 929

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/Meme_The_Way_Things_Used_to_Be.shtml
    Gemini version at https://techrights.org/n/2024/10/19/Meme_The_Way_Things_Used_to_Be.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] The Way Things Used to
Be...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


UNIX_is_55_already.


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


Context: Markets_Without_Fair_Competition_and_Effective_Regulation




⢲⣿⣶⣷⣶⣄⠀⠀⠀⠀⠀⠀⣤⣤⣤⢠⣤⣤⠀⣤⡄⣤⣤⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣿⣯⣭⣭⣭⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⢀⣤⣶⣤⢠⣤⡄⣤⡄⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶
⡀⠀⠻⣿⣿⣿⣧⡀⠀⠀⠀⠀⣿⣿⣉⣿⣿⣿⡀⣿⣇⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⠉⣿⣿⢸⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋
⣿⣦⡀⠈⠻⣿⣿⣿⢦⠀⠀⠀⣿⣿⠉⣿⣧⣿⡇⣿⡟⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⡟⠀⠀
⣿⣿⣿⣦⢸⣿⠄⢚⣟⠀⠀⠀⠿⠟⠸⠿⠇⠿⠗⠿⠇⠻⠿⠻⠿⢸⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⡟⣿⠛⡿⢿⣿⣿⢿⣿⡿⣿⣿⣿⡿⠿⠃⠸⠿⠀⠻⠿⠈⠻⠿⠟⠙⠿⠋⠿⠇⢠⣾⣿⣿⣿⣿⣿⡇⠀⢸
⣶⣶⡶⠀⢰⢿⣿⡿⣷⣿⣦⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢹⣦⠙⡋⣻⣽⢠⣿⡇⣿⠈⣿⣦⡙⣇⢸⣿⡇⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶
⣿⣿⠁⣠⣿⣾⣿⣿⣿⣿⣿⡇⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣷⣶⣾⣿⣶⣿⢷⣿⣴⣷⣿⣿⣿⣾⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣀⣿⣿⣿⣿⣿⣿⣿⣿⡅⢹⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⣝⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣳⠀⣿⡇⠙⢿⣿⣦⡄⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠂⢷⡛⣿⣿⣿⣿⠿⠿⣛⡼⠀⣿⡇⣦⡀⠁⢙⣯⣶⣇⡄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣃⣀⣴⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠀⠀⣿⣿⣿⠑⢊⣿⣿⠟⠀⣿⣷⣶⡄⢰⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⣀⣼⣿⣿⣿⣷⡀⠈⠁⠀⢀⣿⡟⢙⢾⣾⣿⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⠀⢼⣿⣿⣿⣿⣿⣿⡷⢽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⡋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⣿⡀⢠⣿⣿⣿⠀⠉⣼⣿⠋⣥⣟⠉⢠⠹⠋⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⢩⢬⣽⣓⠻⣿⣳⣿⣿⣿⣿⢀⣾⣿⣿⣿⠀⠀⣀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣤⣤⣤⡀⠀⢈⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⣿⣿⢸⣼⣿⣿⣷⣟⣻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣰⣾⣷⣀⣾⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠃⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣀⣠⣤⣰⣾⣿⣿⣿⡿⠻⡿⠿⡿⢿⠿⠇⠴⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠰⣶⣶⣶⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⠿⠛⠃⠀⠂⠃⠃⠊⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣻⡃⢿⣿⣿⣿⣿⣽⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠟⣿⣿⣿⣿⣿⡇⢨⣿⣿⠟⢙⣛⣶⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⢀⣸⣿⣿⣿⡾⢹⣿⢛⡟⣿⣻⡇⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠇⢸⣷⠄⠸⠟⠉⣉⣙⣭⣙⢶⣤⢠⣤⣤⡄⣀⣤⣼⣿⣿⡿⣿⠃⠨⠖⠋⠁⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⠀⠀⠰⡄⠀⣶⣦⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠜⠟⠀⠀⢰⣿⣷⣿⣿⣺⣷⣡⣮⣯⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⠂
⠀⢿⠿⠀⠀⠀⠃⠀⢿⡿⠀⠀⠀⠈⠿⠇⠀⠀⠇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠆⠀⠀⠇⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡝⢿⣟⣻⣿⡿⠃⠈⠈⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠁⠙⢉⡄⢠⢀⣀⢀⢈⢙⣛⢻⢉⠅⣀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠊⠌⠈⠘⠁⠋⠊⠘⠀⠃⠀⠁⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣷⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⡀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⢀⣀⠀⣀⣀⣀⢀⣀⣀⣀⢀⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡀⠙⠻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣧⣿⣿⣿⣿⢸⣿⡹⠿⠛⣿⣿⠛⣿⣿⣿⣷⣿⣿⢸⣿⢸⣿⣿⣿⡞⢻⣿⡟⢸⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣦⡀⠈⢻⣿⣿⣿⢄⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣷⢈⣛⢿⣷⠀⣿⣿⠀⣿⣿⣿⣧⣿⣿⢸⣿⢸⣿⢩⣭⡅⢸⣿⡇⢸⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⡀⠉⠏⢿⣷⠄⢴⡆⠀⠀⠀⠿⣷⣿⠏⣿⣿⣿⡿⠸⢿⣾⡿⠀⣿⣿⠀⣿⣿⣿⣿⠹⣿⣾⠿⠘⢿⣾⡿⠃⢸⣿⠇⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⡖⠀⠀⠀⠉⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⢀⣤⣤⣴⣤⣤⣠⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⣿⣿⣿⣿
⣿⣿⡿⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣴⣿⣿⣿⣿⣿
⣿⣿⡇⠊⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠙⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣦⡈⠉⠛⣇⣬⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⢼⣿⣿⠋⠀⡀⠀⠀⠐⠀⢰⣶⠀⢰⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠛⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠁⣷⣾⣿⣿⣿⣿⡏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⢰⣾⣿⣿⣿⣿⣿⣿⡏⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⠀⠀⠀⢠⠀⠩⢿⣿⣿⣿⣿⣿⡇⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣭⣀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣿⠀⠒⣼⣿⠋⠑⠻⠁⣴⡿⠋⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣭⣩⣽⡃⠸⣿⣷⣠⣾⣿⣿⢀⣼⣿⣿⣏⠀⠀⣠⣿⣿⣷⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⣀⡀⠀⠀⢀⣾⣿⣿⣿⣿⣷⢰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢹⣿⣿⣿⣿⣾⣝⣿⣻⣿⣿⣿⣿⣿⣿⣿⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣦⠀⣹⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡿⢈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿
⣿⣿⡿⠊⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣀⣰⣶⣿⣿⣿⣿⠻⠿⠿⠿⠿⠿⠇⢸⣿⣿⣿⣿⣤⣤⠀⢻⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠻⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢰⣿⣷⣦⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢿⣿⣿⣿⣿⡿⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠓⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠟⣿⣿⣿⣿⣿⠃⢹⡿⣿⣿⣿⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠇⢸⣷⠄⠻⠟⠹⢿⣶⣶⣾⣤⣤⣤⣤⣤⡀⢀⣠⣾⣿⣻⣿⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣇⠀⠀⢸⠀⠠⣶⣤⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠋⠀⠀⠊⠀⢀⣭⣽⣿⣿⣿⣿⣯⣽⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠇⠀⠀⠘⠀⠐⣿⡿⠀⠀⠀⠸⠿⠇⠀⠰⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⣿⣿⣿⣿⣿⣿⠿⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠿⠋⠁⠈⠙⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 1007

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/Meme_When_Hatred_or_Envy_Comes_First.shtml
    Gemini version at https://techrights.org/n/2024/10/19/Meme_When_Hatred_or_Envy_Comes_First.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ [Meme] When Hatred (or Envy) Comes
First⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Richard_Stallman_Bologna_2024⦈_


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


Sometimes people are eager to take other people down instead of create
something better or earn something through personal accomplishment. A lot of
attacks on Torvalds and Stallman (Linux and GNU founders, respectively) fall
under this category.




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣥⣶⣶⣶⣮⣍⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⣿⣿⡗⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⢐⣿⣿⠟⠛⠉⡉⠉⠉⠃⠀⠀⠘⡛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢁⡀⠀⣠⣷⣄⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢸⣿⠟⣿⣿⣿⣿⣿⣿⣷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠋⠁⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡻⠿⠿⠿⠿⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢀⣠⠀⠀⠈⠑⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡉⠘⠛⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠼⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣿⣿⣿⣿⣦⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣷⠀⢀⣀⠀⠉⠙⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣠⣤⣤⣤⣤⡀⠄⢤⣤⣄⡀⣼⣿⠿⣿⣿⣿⣿⡿⡿⠙⣧⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⣋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣧⢿⠟⣿⣿⣿⣷⣄⠙⢾⡇⣿⣿⠅⣿⣍⣁⣈⣉⣁⣤⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣶⣷⣶⣶⣤⣤⣀⡀⠀⢀⠀⠐⠿⠈⣸⢿⣿⣿⣿⣿⣧⠀⠃⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠠⠁⣈⡽⢿⣿⣿⣿⣅⠀⠀⣀⣀⢰⣿⣿⣿⣿⣿⠛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢛⣋⡽⠷⡀⠀⠀⡈⠵⠚⢉⣿⣿⣿⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⠿⢏⣠⣼⣿⣿⣿⣿⣿⣭⡭⠿⠯⠀⢻⠿⣿⣿⣿⣿⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠈⢀⣀⣴⠮⠽⣶⢾⣄⢊⣥⠰⣋⠉⢹⣿⣿⣿⣄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⠀⠺⠈⠀⠈⠉⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠓⠛⠛⠙⠧⠛⠓⢺⠳⣯⣿⣿⣤⡆⣖⡊⠉⣻⣿⣿⣿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣻⣿⣿
⠀⢸⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣾⣿⣿⡿⠿⠟⠛⠉⠀⠂⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠉⠛⣑⣰⣟⣋⣉⣛⣻⣿⡿⠄⠀⠘⠻⣿⣿⣿⣿⣿⣿⡿
⣀⣸⣿⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣨⣭⣿⣿⣷⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣿⣧⣤⣴⣶⣿⣿⣿⣏⣑⣒⣒⣒⣛⣛⣛⣛⣛⣛⣿⣯⣭⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡿⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣧⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⢽⣿⣷⣭⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠡⠤⠠⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡋⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⢏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢵⡞⢶⡿⢯⣯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⣼⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢩⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣙⣻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⣟⠸⣃⣿⣮⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣡⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡯⠁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣿⠀⣿⣯⣽⣿⣯⣷⣐⣮⢙⣷⢰⣤⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣷⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡟⡇⠘⠛⠀⡟⣟⣿⣛⣻⣟⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡥⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣧⢲⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣍⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣬⣉⣉⣛⡛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢟⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣭⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⢁⢤⡄⠠⠤⠄⠐⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⠄⣀⣠⣠⣶⣶⡦⣾⣿⡖⡓⠺⣋⣡⠀⢀⢀⣠⠀⠀⢀⡚⠡⠥⠆⡄⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡿⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣧⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⢽⣿⣷⣭⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠡⠤⠠⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣧⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢵⡞⢶⡿⢯⢯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣿⢻⣿⡟⣿⣿⣴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣿⣷⡇⣿⠒⣙⣻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣟⣟⣟⠸⣃⣿⣮⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣡⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⣯⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣯⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣿⠀⣿⣯⣽⣿⣯⣷⡐⣮⢙⣷⢰⣦⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣷⣇⣿⣹⠘⢇⡿⣰⠬⣧⣾⣻⣿⣿⣾⣾⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡟⡃⠘⠓⠀⡟⣿⣿⣿⣻⣟⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠿⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡥⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⡛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠙⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⣁⢤⡄⠠⠤⠀⠒⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠤⠄⣀⣠⣠⣶⣶⣤⣷⣿⡞⡓⢛⣏⣡⡀⠀⢀⡀⠀⠀⢀⡂⠨⠥⠦⡄⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡿⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣥⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⢽⣿⣷⣭⡛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠁⠤⠠⠀⠀⠀⠄⠀⠠⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣧⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢵⡞⢶⡿⢯⣯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⣴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢭⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣿⣸⣷⣷⡇⣿⠒⣙⣻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⣟⠸⣃⣿⣯⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⣏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣿⠀⣿⣯⣽⣿⣯⣷⡐⣮⢙⣷⢰⣦⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣾⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡟⡇⠘⠋⠀⡟⣿⣿⣻⣻⣻⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡥⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣍⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⡛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢟⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠙⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣭⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⡁⢤⠄⠤⠤⠐⠐⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠄⠄⣀⣠⣤⣦⣴⣴⣶⣿⡖⣖⢢⢉⣁⠀⠠⢀⡀⠀⠄⢀⡚⠩⠥⠆⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡿⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣧⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⢽⣿⣷⣭⡛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠡⠤⠀⠀⠀⠄⠄⠀⠀⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢷⡞⢶⡿⢯⢯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⣴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢩⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣉⣻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⣟⠸⣃⣿⣯⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⣟⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣿⠀⣿⣯⣽⣿⣯⣷⢐⣮⢙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣧⣿⣹⢘⢇⡿⣰⠬⣧⣾⣻⣻⣿⣾⣾⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⡟⡃⠘⠓⠀⡟⣟⣿⣻⣻⣛⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡥⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣍⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⣯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣬⣉⣉⣛⡛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠙⢹⢸⡇⣿⢸⠀⡏⣿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣉⢁⢤⠄⠄⠤⡀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⡀⠤⠄⠄⣀⣠⣤⣦⣴⣦⢾⣿⡖⡓⣓⣛⣡⠀⡀⢀⡀⠀⠄⢀⡂⠩⠤⠦⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡿⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣥⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⢽⣿⣷⣭⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠡⠤⠤⠀⠀⠄⠀⠀⠀⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢵⡞⢶⡿⢯⢯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⣴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣙⣻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⣟⠸⣃⣿⣯⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣡⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡏⠁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⣇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣿⠀⣿⣯⣽⣿⣯⣷⡐⣮⢙⣷⢰⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣧⣿⣹⠘⢇⡿⣰⠬⣧⣾⣻⣿⣿⣶⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡟⡇⠘⠛⠀⡟⣿⣻⣟⣻⣛⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡥⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢲⣼⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣍⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⡛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠙⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⢁⢤⡄⠤⠤⠐⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⠤⢀⢀⣠⣠⣶⣶⡶⢶⣿⡞⡓⢣⣋⣥⡀⠠⢀⡀⠀⠄⢀⡚⠩⠥⠖⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡿⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣥⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⢽⣿⣷⣭⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣖⣿⣿⣿⣿⣿⣷⠡⠤⠀⠄⠀⠀⠄⠀⠠⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢵⡎⢶⡿⢯⢯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⣴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢭⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣉⣻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⣟⠸⣃⣿⣮⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡯⠁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡯⠀⣿⣯⣽⣿⣯⣷⡐⣮⢙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣾⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⡞⡃⠘⠛⠀⡟⣿⣿⣿⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣍⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⡛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣧⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠙⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣉⢁⠤⡤⠤⠠⠐⠐⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠄⢄⢀⣠⣠⣴⣤⡦⣷⣿⡖⡓⡂⡋⣁⠀⣠⡀⡀⠀⠀⢀⠒⠡⠠⠆⣀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡟⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣥⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⢽⣿⣷⣭⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣖⣿⣿⣿⣿⣿⣷⠡⠄⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣇⠀⠀⠠⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢵⡞⢶⡿⢯⢯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⣴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢭⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣿⣷⡇⣿⠒⣉⣻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⣟⠸⣃⣿⣯⡛⠾⠫⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣡⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⠉⢹⣏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣿⠀⣿⣯⣽⣿⣯⣷⣐⣮⢙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣿⣻⣿⣾⣾⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡞⡇⠘⠋⠀⡟⣿⣻⣿⣿⣻⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⡇⣕⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⡛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠙⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⢁⣤⡄⠄⠤⠄⠒⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠄⢀⣀⣠⣤⣴⣤⡤⣦⣿⡖⡚⢃⣏⣡⠀⠀⢀⡀⠀⠀⢀⡒⡨⠡⠢⣀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡟⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣧⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⢽⣿⣷⣭⡛⡛⣛⣛⡛⠛⠛⠛⠛⠛⠛⡛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡋⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢵⡎⢶⡿⢯⢯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⣴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢭⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣉⣻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⣟⠸⣃⣿⣯⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣽⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡯⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⣶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡿⠀⣿⣯⣽⣿⣯⣷⡐⣮⠙⣷⢰⣤⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⡿⣰⠬⣧⣾⣻⣻⣿⣾⣾⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡟⡇⠘⠓⠂⡟⣿⣻⣛⣻⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢾⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣧⢲⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣍⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⡛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⣿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣁⣤⡄⠤⠴⡀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠤⠤⣀⠀⣠⣠⣲⣴⡾⢟⣟⡖⡓⢻⡏⡁⡀⠠⢀⡀⠀⠀⢀⡒⠩⠡⠦⣄⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡟⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣧⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⣽⣿⣷⣭⡛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠡⠠⠀⠀⠠⠀⠀⠠⠄⠄⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢵⡞⢶⡿⢯⣯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⣴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢩⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣉⣻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⣟⠸⣃⣿⣯⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣽⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⣯⠁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⣀⠀⠀⠀⠀⠀⠀⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡿⠀⣿⣯⣽⣿⣯⣷⣐⣮⢙⣷⢰⣤⣤⣤⣤⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣻⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡟⡇⠘⠓⠀⡟⣿⣻⣟⣻⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡥⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣍⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣬⣉⣉⣛⡛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡉⢁⢠⡄⠤⠴⠀⠐⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⠤⣄⢀⣠⣠⣦⣶⣦⣮⣟⡗⡛⠓⣋⣁⢀⣠⣀⡀⠀⠆⢀⡒⠨⠤⠆⡀⠉⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡟⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣥⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣟⡿⠶⢖⣛⣛⣻⣽⣿⣷⣭⡛⡛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠡⠄⠀⠀⠠⠀⠀⠀⠠⠤⠤⠤⠂
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠟⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡹⢵⡞⢶⡿⢯⣯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⢤⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢩⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⣒⣉⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢿⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⣟⠸⣃⣿⣯⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣽⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⢀⠀⠀⠀⡀⡀⢀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⣟⠁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣿⠀⣿⣯⣽⣿⣯⣷⣐⣮⢙⣷⢰⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣧⣿⣹⢘⢇⡿⣰⠬⣧⣾⣻⣿⣿⣾⣾⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡟⡃⠘⠛⠀⡟⣿⣿⣻⣻⣟⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠧⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢾⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⡛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣁⢄⡄⠤⠤⡀⠐⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠤⢀⣀⣠⣤⣶⣤⡴⢾⣟⣖⣛⣋⣩⣁⠀⡀⢀⡀⠀⠂⢀⡒⠨⠥⠶⡀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⢺⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢯⡏⣼⢧⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠶⣏⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⡭⠭⣥⣤⣤⣥⣀⡈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣭⣛⣩⠵⠮⢽⣖⣿⣿⣷⣝⢛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⣿⢾⡎⣵⣶⡟⣿⣿⣿⣿⣿⡆⠠⠀⠠⠤⠤⠀⠀⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣏⢸⢹⢠⣿⣇⣿⣿⣿⡿⠟⢱⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠣⢾⣿⢘⠿⢟⡞⣶⣆⣀⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⣿⢹⣷⣿⡿⡏⣿⣿⠶⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⣿⢹⣷⢿⣿⣷⡇⣿⣛⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⠟⡙⢃⣿⣪⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡘⣈⣻⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣯⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⠉⢹⡯⡁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡯⢸⣯⠀⣿⣏⣽⣿⣯⣷⡐⣮⢙⣷⢰⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⠿⣰⠬⣧⣾⣻⣿⣿⣾⣾⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣈⡛⣿⣿⣼⣷⡟⡇⠘⠛⠀⣻⢻⣿⣛⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠿⠘⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢲⢸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⢁⣤⡄⠤⠤⡀⠐⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠄⡀⣀⣠⣤⣶⣤⡶⣮⣟⣗⠓⣢⢋⣡⠄⠀⢀⡀⠀⠄⢀⠒⡨⠤⠶⣄⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡽⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢳⣓⣿⡙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄⠀⠀⠘⠛⠧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⡾⠿⠽⣟⣛⣛⣷⣶⣤⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⢟⣯⡞⢅⣉⢽⣶⣿⣿⣿⣧⢛⡛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢯⡏⣽⣳⠛⣿⡇⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠔⠠⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣣⣷⢧⣼⡿⡼⠿⠿⣛⠫⢱⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠭⢾⡿⡇⠾⢽⣞⡺⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣿⣿⣿⡟⡿⣿⣱⣿⡝⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣻⡇⣿⡇⣿⣌⣛⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⣠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣘⣿⡟⠃⠝⠃⣿⣬⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣽⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⣈⣸⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⣏⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡿⢼⣿⠀⣿⡏⣽⣿⣯⣷⣐⣮⢙⣷⢰⣦⣤⣤⣭⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣿⣻⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⠄⣘⡛⣿⣿⣼⣷⣟⣗⠘⠃⠀⢛⡟⣿⣿⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣥⣤⡤⠤⠜⠃⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢾⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣍⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣬⣉⣉⣛⡛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠙⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢩⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣁⠄⡄⠠⠤⠄⠐⠲⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⢄⣀⣀⣀⣤⣦⣶⡖⢮⣿⣛⣛⡻⢫⣁⡀⣀⡀⡀⠀⠀⢀⡒⠩⠥⠆⡀⠉⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣟⣅⣽⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⡟⡆⣾⢯⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢹⣾⢯⣳⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢏⠈⠛⠀⣾⣿⣿⣿⣿⣷⣾⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⣀⢴⣛⣻⣿⣿⣿⣿⣿⡿⣼⡿⢿⡿⣿⣿⢿⣿⣿⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⢿⣒⣲⠽⣟⣻⣿⣿⣿⣿⢟⡅⣿⢹⣷⣿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⡿⢦⣤⣟⢾⡿⣷⣯⡳⣮⣛⠇⣿⠙⣶⣿⣿⣿⡇⣿⣘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⣠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣕⠌⡃⣵⡠⠽⠿⠮⠷⢃⢟⣈⠟⣞⣟⣹⣃⣿⣮⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣇⢞⡿⣿⣿⣿⣿⣿⣰⣾⢙⣂⣈⡛⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠰⠿⠿⠿⢾⣿⣽⣿⣆⣿⣿⠊⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡧⠀⣿⡏⢹⣿⣯⣷⠐⣮⠙⣷⢰⣤⣤⣤⣬⣬⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⡿⣰⠬⣧⣾⣻⣻⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡟⡗⡘⠃⠀⢻⡛⢻⣛⣻⣛⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠿⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣛⣥⣥⡤⠤⠜⠃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢿⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠙⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣟⣻⣟⠿⠿⢬⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡉⡁⡠⡤⠠⠤⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⢤⢤⣄⢀⣠⣤⣦⣤⡤⣬⡿⣟⡓⡋⢭⣁⡀⢀⡀⡀⠐⠄⢀⡒⡨⠁⠖⡀⠉⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣏⣶⡆⡇⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⣠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⡿⡉⣿⣻⡹⢟⣫⣵⣶⣾⣿⣿⣾⣶⣮⣝⡻⣿⣿⡇⣛⣘⢿⣟⣟⣸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣧⣧⣼⢷⢭⣞⣉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⢸⣫⣫⣟⣵⣿⣿⣿⡛⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣵⡾⠛⠛⠀⠀⠮⠛⠛⠏⠓⠻⢿⣿⣸⣿⣃⣿⣿⠈⢹⡏⠁⣿⣏⠽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣄⣀⡀⣤⣤⣄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⡗⡀⣿⡏⠡⣿⣯⣷⣐⣮⢙⣷⢰⣦⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⡿⣰⠬⣧⣾⣻⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⠄⣘⡛⣽⣿⣾⣧⢜⣃⣸⠃⠀⣛⠛⠃⣻⣻⣟⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣷⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣞⣚⣭⣭⠤⠤⠿⢀⣂⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢾⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢢⣤⣌⣉⣉⣛⡛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⣿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠙⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⢹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⢀⠧⢟⣞⣻⣟⠿⠿⢬⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⣁⡠⡄⠠⠤⠐⠐⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⠤⣄⢀⣠⣤⣶⣦⡖⠾⣿⡟⡓⢫⡎⣡⡀⠀⢀⡀⠀⠄⢀⠒⠨⠡⠆⡀⠉⠓⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡛⡛⠛⠛⠛⡛⠛⢛⢛⣛⣛⠛⠛⡃
⠀⣿⣿⣿⣷⣶⣄⡠⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠩⢉⣿⣿⣿⣿⣷⡄⠀⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣿⣀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢠⣤⣤⣤⣄⣠⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠟⢿⡗⠛⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧⣿⣿⣧⢖⣛⠿⢇⢛⡿⣿⣿⣿⣳⣶⢹⢹⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠇⢸⣿⡿⠃⣴⣾⣿⣿⠀⠀⠀⠀⢿⣿⣫⡭⡝⣿⡃⣷⢲⡁⣏⣳⢸⠸⢻⡄⢿⣿⣏⣏⣻⡾⣞⣿⢟⣯⣴⣶⣶⣶⣶⣶⣯⣝⡻⣿⣿⣇⢿⣘⣻⣟⣟⣹⣃⣿⣬⣻⠾⠋⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠘⣉⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⢘⣛⣻⡗⣣⢻⡡⢻⣸⡇⣿⣶⡾⠯⠸⢥⣻⣿⣿⣜⣌⢿⣮⣚⣝⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣎⣟⡵⣭⣋⣞⣛⣛⡛⣛⣿⣿⣛⣀⡀⠀⣀⣛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣧⣥⣿⡞⣿⣷⡶⠿⠷⡒⢛⡛⡛⡿⢿⣿⣿⣿⣷⣵⣶⠿⠿⠃⠀⠰⠟⠛⠛⠫⠞⢿⣿⣹⡿⣎⣿⣿⡈⢹⡏⠁⣿⣏⠽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⠿⠿⢿⣿⣿⣿⣿⣅⣀⣀⢠⣤⣤⠀⠀⠀⠀⠀⢘⣿⣽⣿⢿⣧⣼⡇⢸⡷⠀⣿⡏⠁⣿⣯⣷⢀⣮⠙⣷⢠⣤⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⢸⣿⣿⢟⣇⣿⣹⢘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣯⣭⣟⢿⣿⣿⣿⡾⣿⣿⡇⠀⣲⡤⣀⣘⠛⣛⣻⣼⣷⡞⣃⢘⡗⠀⢛⡛⠃⢛⣿⣛⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣫⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⡝⣯⣷⣿⣻⣿⣷⠀⢹⣿⣿⣶⣯⣥⣴⣿⣋⣥⣭⠽⠥⣀⣘⣁⣀⣸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⢧⢱⡟⠆⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢲⢸⣿⣿⣿⣷⡽⣿⣿⣇⢿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢾⣐⠽⣇⢿⠸⠤⠃⠇⣿⣻⣡⣛⣼⣬⣧⡯⣭⣽⣿⢿⣿⣿⣿⣝⢛⣋⡘⣿⣿⡄⢠⣬⣉⣉⡛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⢹⣷⡦⠖⠿⣿⢛⣛⢛⡻⠿⣭⢭⡛⣵⢢⠳⣆⣦⢸⣣⣿⣿⣿⣯⣻⣷⢻⣿⣧⠀⢻⠿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣴⣶⣶⡆
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣤⣸⣯⠩⢹⡸⡇⣿⢸⠀⡏⢿⢸⣗⠛⠛⠛⠛⠓⠱⣾⣿⣿⡆⠘⣿⣿⣶⣶⣯⣭⣭⣽⣿⣟⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣻⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⣿⣿⠮⠭⣁⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠙⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠄⠰⠿⠿⠿⠃⠀⠀⢻⣿⣯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡉⠀⢀⡀⠠⠠⠄⠐⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⠀⠤⠤⠄⣀⢤⣤⣀⡤⢴⡾⠟⣞⣚⣛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁⠂⠀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣏⢏⠻⣿⣫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣺⣟⣿⡥⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠋⠉⠉⠉⠀⠀⣹⣿⣿⣿⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠤⠤⠄⠠⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢗⣤⢀⣀⣤⡺⣝⣛⣛⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣷⣬⠭⢽⢶⣒⡾⣿⡿⣿⡿⢳⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣺⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢧⣹⡧⡇⣿⢙⣷⢿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⢬⣵⣃⡛⠈⢿⣛⡟⣽⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣡⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣯⣝⢸⣿⣿⢹⣿⣿⣿⣗⢙⣀⣁⡈⣛⣟⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢽⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⣶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣿⠈⣿⡏⢹⣿⣯⣷⣐⣮⠙⣷⢰⣦⣤⣴⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⢄⣘⡻⣿⣿⣼⣷⣞⡃⡞⠃⠀⠛⡟⢻⣻⣿⣟⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⠤⠤⠜⢃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⣟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠖⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⣿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣚⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⢁⡤⡄⠀⠤⡐⠂⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⢤⠤⡄⣀⣀⣤⣶⣶⣶⣶⣿⣿⣿⣛⣉⡡⡠⡀⠠⠀⠠⠐⠀⣂⠩⠅⠐⠀⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢏⠻⣿⣫⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣺⣟⣿⡥⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠋⠉⠉⠉⠀⠀⣹⣿⣿⣿⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠤⠄⠠⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢗⣤⢀⣀⣤⡺⣝⣛⣛⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣷⣬⠭⢽⢶⣒⡾⣿⡿⣿⡿⢳⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢧⣹⡧⡇⣿⢙⣷⢿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⢬⣵⣃⡛⠈⢿⣛⡟⣹⣃⣿⣬⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⡬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣯⣝⢸⣿⣿⢹⣿⣿⣿⣗⢙⣈⣁⡈⣙⣟⣻⣇⣀⡀⠀⣘⣛⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠿⠿⠿⢽⣿⣸⣿⣏⣿⣿⡈⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡟⠈⣿⡏⢹⣿⣯⣷⡐⣮⠙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⢄⣘⡛⣿⣿⣼⣧⣞⡃⡞⠛⠀⠛⡟⢻⣿⣻⣻⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠿⠿⣿⢿⣟⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠜⢃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⢸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡁⣤⡄⠀⠤⠐⠀⠒⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠤⢀⢀⣀⣤⣶⣶⣦⣾⣿⣿⣛⣒⣍⣭⣤⣄⠀⡀⠤⠔⢀⣂⠩⠥⠖⠀⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢳⣓⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠘⠛⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⡶⠿⠿⣟⣛⣛⣳⣶⣤⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⢟⣧⡜⢍⣉⢽⣶⣿⣿⣿⣦⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢯⡟⣹⣳⠟⣿⡇⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣢⣷⢧⣼⡿⡽⠿⠿⢛⠋⢰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠭⢾⣿⡇⠮⢽⣞⡺⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⡿⣿⣹⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣻⡏⣿⡇⣿⣌⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣘⣟⡟⠃⠜⠃⣿⣯⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⣂⣘⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡩⢹⡯⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡿⢼⡇⠀⣿⡏⣽⣿⣯⣷⣐⣮⢙⣷⢰⣦⣤⣴⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⢄⣘⡛⣿⣿⣼⣷⣟⣳⠘⠃⠀⢛⡟⣿⣿⣻⣛⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣥⣥⡤⠤⠜⢃⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠶⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣂⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠁⢤⡤⠤⠤⡄⠂⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⠤⠄⣀⣠⣤⣶⣶⣦⣶⣿⣿⣟⣲⣉⣥⣄⡄⠀⡀⠰⠄⢀⣂⠩⠅⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢳⣓⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠘⠛⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⡶⠿⠿⣟⣛⣛⣳⣶⣤⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⢟⣧⡜⢍⣉⢽⣶⣿⣿⣿⣦⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢯⡟⣹⣳⠟⣿⡇⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⠠⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣣⣷⢧⣼⡿⡽⠿⠿⠛⠋⢰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠭⢾⡿⡇⠮⢿⣞⡸⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⡿⣿⣹⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣻⡇⣿⡇⣿⣌⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣘⣿⡟⠃⠜⠃⣿⣭⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⣂⣘⣻⣃⣀⡀⠀⣘⣛⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⣯⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡿⢼⡇⠀⣿⡏⣽⣿⣯⣷⡐⣮⢙⣷⢰⣦⣤⣴⣬⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⣞⣳⢘⠃⠀⢛⡟⣿⣿⣻⣛⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣥⣥⡤⠤⠜⢃⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠁⡠⡤⠠⠤⡐⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠀⠤⠤⠄⣀⣀⣤⣶⣶⣦⣶⣾⣿⣳⣋⡍⣁⡠⢄⢀⠄⠠⠀⢀⣀⠩⠅⠒⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡿⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⣥⣤⣤⣤⣀⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠶⢖⣛⣛⣻⣽⣿⣷⣯⡛⣛⣛⠛⠛⠛⠛⠛⠛⠛⡛⠛⡛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢳⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠀⠐⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠆
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣾⢡⣯⡏⣽⣿⣸⣿⣿⣿⡿⢏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡻⢴⡎⠷⡿⢯⢯⣭⣍⣑⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⡂⣿⢹⣷⢹⣿⡏⣿⣿⢴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢫⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣉⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣟⣟⣛⠸⣃⣿⣮⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣻⣛⣻⣃⣀⡀⠀⣘⣛⡃⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡏⠁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡏⢸⡿⠀⣿⣯⣽⣿⣯⣷⡐⣮⢙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡻⣿⣿⣼⣧⡞⡃⠘⠓⠀⡟⣛⣻⣿⣻⣟⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠇⢛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣷⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⢀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⡤⡄⠠⠤⠐⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⢤⣄⣀⣠⣤⣶⣶⣶⣾⣾⣗⠗⣻⣩⣉⣅⢀⣀⡀⠀⠔⢀⣂⠨⠁⠐⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠽⣿⡷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣺⣟⢝⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢯⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡏⠀⣤⠁⠉⠉⢁⣭⣟⣻⠿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⣿⣾⢷⣶⣖⣒⣷⣾⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡷⣿⣽⣖⣒⣪⢭⢭⣿⣿⣿⣿⣿⣿⢧⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠠⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠿⣾⢷⣵⡿⡿⣝⡿⢿⡿⢿⣫⢾⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡳⡈⢗⣣⠁⣿⢙⣷⢿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢿⣿⣇⣿⢀⡻⣞⠟⢸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣁⡈⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡋⢹⣯⠁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣷⠀⣿⡏⢽⣿⣯⣷⢐⣮⠙⣷⢰⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡻⣿⣿⣼⣧⡞⣳⠛⠛⠀⣻⠛⢻⣿⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣭⣤⡤⠤⠿⠀⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣾⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⣟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣁⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠁⡤⣄⠤⠤⠰⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⢤⣄⣀⣠⣤⣶⣤⣶⣾⣾⡗⣛⣻⣋⣍⣅⣄⣀⡀⠠⠐⢀⣀⡩⠥⠖⠀⠙⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣟⣅⣽⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣟⣇⣾⣫⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⡛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢳⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣼⣶⣧⢱⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢏⠉⠉⠀⣾⣿⣿⣿⣿⣿⣾⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠑⠂⣠⢴⣛⣻⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⢿⣒⣺⢭⡛⠻⣿⣿⣿⣿⢟⡅⣿⢹⣷⢿⣿⡟⣿⣿⠴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢫⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⢶⣬⣟⢾⡿⣷⣯⣿⣮⣟⠇⣿⢙⣶⣿⣿⣿⡇⣿⢜⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡍⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣝⠌⡃⢕⡦⢭⡿⠯⠿⢃⣟⣈⢿⡞⣟⣹⣃⣿⣩⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣇⡮⡿⣿⣿⣿⣿⣿⣰⣮⢙⣂⣈⡛⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢾⣿⣽⣿⣇⣿⣿⠋⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡇⢸⡧⠀⣿⡏⢹⣿⣯⣷⣐⣮⢙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⠄⣘⡻⣿⣿⣼⣧⡞⣳⣹⠃⠀⢛⡟⠃⣿⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣛⣥⣥⠤⠤⠜⠃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⢦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣤⠤⠤⠤⠰⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⢤⣄⣀⣀⣤⣶⣶⣶⣾⣾⣟⣛⢻⣯⣍⡬⣀⣀⡀⠠⠄⢀⣂⠩⠥⠔⠂⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣟⣶⡇⡇⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⣜⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⡉⣿⣻⡹⢟⣫⣵⣶⣿⣿⣿⣿⣶⣮⣝⡻⣿⣿⡇⣛⣘⣿⣟⣟⣸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣥⡧⣼⢷⢯⣎⣉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⢸⣫⣫⣟⣵⣿⣿⣻⡛⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣵⡞⠛⠛⠀⠀⠮⠛⠛⠏⠓⠻⢿⣿⣺⣿⣃⣿⣿⠈⢹⣿⡁⣿⡏⠹⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣄⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⡟⠆⣿⡏⠁⣿⣯⣷⠐⣮⢙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣽⣿⣼⣷⢜⡃⣸⠃⠀⣛⠛⠃⣛⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣞⣚⣭⣭⠤⠤⠟⢀⣀⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢾⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣛⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⢀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣟⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠁⣤⠄⠠⠄⠀⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠤⣀⣀⣀⣀⣴⣶⣶⣶⣶⣗⣚⣺⣏⢍⣨⢀⡀⡀⠀⠄⠀⣂⡨⢁⠒⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⡛⠛⠛⠛⠛⢛⠛⠛⠛⡛⢛⡛⠛⠃
⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠤⠤⠠⠀
⠀⠀⣹⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⢿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠻⣟⡉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⠟⠻⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⡖⣻⡛⠟⢭⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢿⣛⣛⣛⣛⡿⢿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠏⣰⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⠔⣿⠿⠿⣿⣿⣿⢟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⣿⣿⠇⠿⣘⣟⣟⣟⣸⣃⣿⣬⡛⠾⠋⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⡹⠯⠸⣬⣡⣶⣯⣗⣾⡿⠮⣭⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣇⢟⣔⡭⣋⣛⢛⣛⣛⡛⣻⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣧⣥⣿⣸⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣾⣫⠭⣏⣟⣻⠿⠃⠀⠠⠿⠙⠫⠭⠗⠯⢿⣿⣸⣿⡄⣿⣻⠈⢹⡏⠁⣿⣏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡃⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣛⣛⣿⣿⣿⣿⣿⡇⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣯⣼⡇⢸⡇⠀⣿⡏⢹⣿⣯⣷⡐⣮⢙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣟⣽⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣭⣻⣿⣿⣿⡷⢿⣿⣿⠀⢰⣶⡤⢄⣘⠛⣾⣿⣼⣷⢚⣳⡞⠓⢸⠛⠛⣻⣻⣻⣟⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣯⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣿⢫⣷⣿⣏⣿⣿⡆⠈⣿⣿⣿⣷⣾⣯⣥⣶⣞⣺⣬⣥⠤⠼⢐⣀⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⡟⣾⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣨⢿⣿⣿⡸⣿⣿⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣧⣌⠻⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⣯⣭⣽⠿⣿⣿⣿⣯⡛⣉⣥⢻⣿⣧⠀⢦⣤⣍⣉⣉⡛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⡟⣿⣷⠦⠺⠿⣿⢛⣛⢛⡻⠿⣭⢭⣛⣕⢪⠵⣆⣶⢺⣣⣿⣿⣿⣞⢿⡞⣿⣿⡄⠘⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠀⢺⣿⣿⣧⠀⢻⣿⣿⣷⣶⣾⣭⣭⣭⣭⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⢂⠧⣟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⡀⠿⢿⡛⠛⠀⠀⠈⢭⣭⣭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⢁⣠⡄⠠⠤⠰⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⡤⡄⣀⣀⣤⣴⣦⣶⣶⣿⣿⢓⣻⣯⢭⣅⢀⡀⡠⠀⠔⠀⣂⠨⠥⠒⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢏⠻⣿⣫⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⡺⣛⣿⡥⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢛⠛⢛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠋⠉⠍⠉⠀⠀⣹⣿⣿⣿⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⠠⠠⠀⠀⠀⠠⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣤⢀⣀⣠⡺⣝⣚⣛⣻⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣾⣿⣷⣬⠭⢿⢶⣒⣾⣿⡿⣿⡿⢳⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣮⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢧⣹⡷⡇⣿⢙⣷⢿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⣠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⢬⣵⣇⡛⡈⢿⣝⡟⣽⣃⣿⣨⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣖⢙⣈⣁⡈⣙⣿⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠿⠿⠿⢽⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡗⠀⣿⡏⢹⣿⣯⣷⡐⣮⠙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⢄⣘⡛⣿⣿⣼⣷⣟⡇⡜⠃⠀⠛⡟⢻⣻⣻⣿⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠼⢃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣜⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⡧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠞⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠇⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠁⣤⡄⠠⠤⠀⠒⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠀⠤⠤⣤⣀⣠⣤⣶⣶⣦⣯⣼⣟⡛⣻⣯⣭⡄⢄⣀⣄⠤⠀⠀⣂⡨⠅⠐⠀⠙⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣷⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣞⣻⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⡿⣻⡽⢶⣤⠤⢤⣒⣛⣿⣿⣷⣯⣟⢿⣿⠛⠛⡛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⢹⣿⣯⣗⠒⢒⢲⣬⢽⣾⣿⣿⣿⣿⣾⣿⠀⠀⠀⠤⠤⠀⠤⠄⠀⠀⠄⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣱⣿⣇⡿⣿⣏⣿⣿⣿⡿⣫⣾⡧⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣶⢇⠸⡛⡇⢿⠟⡿⢩⣷⢾⣿⣿⣇⣀⠁⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢪⣾⡇⣿⢙⣷⣿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠿⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⣾⣾⣿⡇⣿⢙⣷⣺⣯⣿⡇⣿⣝⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⡹⣿⡇⣻⣘⣟⠙⡛⢸⣁⣿⣯⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣇⣀⣈⡀⣙⣿⣿⣇⣀⡀⠀⣘⣛⡃⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠈⢹⣯⠁⣿⡏⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡧⢸⣯⠀⣿⡏⢹⣿⣯⣷⠐⣮⢙⣷⢰⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢻⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⣞⡇⠜⠃⠀⢛⡟⣻⣻⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠬⠜⢃⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣔⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⡧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠖⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠉⠈⠀⠉⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣚⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠁⣤⡄⠠⠤⠀⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⡤⣤⣀⣠⣤⣶⣶⣶⣿⣿⣿⣟⣻⣯⣭⣄⣀⣀⡤⠠⠔⢀⢋⡩⠥⠖⠀⠙⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣷⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣞⣻⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠐⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⡿⣻⡽⢶⣤⠤⢤⣒⣛⣿⣿⣷⣯⣟⢿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⡛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⢹⣿⣯⣗⠒⢒⢲⣬⢽⣾⣿⣿⣿⣿⣾⣿⠀⠀⠀⠤⠄⠠⠤⠄⠀⠀⠀⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣱⣿⣇⡿⣿⣏⣿⣿⣿⡿⣫⣾⡧⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣶⢇⠸⡛⡇⢿⠟⡿⢩⣷⢾⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢪⣾⡇⣿⢙⣷⣿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠿⢩⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⣾⣾⣿⡇⣿⢙⣷⣺⣯⣿⡇⣿⣙⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⠊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⡹⣿⡇⣻⣘⣿⠙⡛⢸⣁⣿⣭⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⡬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣇⣀⣈⡀⣙⣿⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡈⢹⣯⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡧⢸⣯⠀⣿⡏⢹⣿⣯⣷⠐⣮⠙⣷⢰⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢻⣿⣿⠀⢰⣖⣤⢄⣘⡛⣿⣿⣼⣷⡞⡇⠜⠓⠀⢛⡟⣻⣿⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠬⠼⢃⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣧⢲⣸⣿⣿⣿⣣⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣕⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠞⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣧⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣚⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠁⣤⡄⠠⠤⠄⠂⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⠤⣄⣀⣀⣤⣶⣶⣶⣿⣿⣟⣛⣻⣿⣭⣁⢄⣀⡠⠠⠐⠈⡋⠩⠁⠖⠀⠙⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⢲⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢧⡏⣼⢧⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠨⢶⣏⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⡭⠭⢥⣤⣤⣥⣀⡈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣯⣋⣩⠵⠶⠥⣖⣿⣿⣷⣝⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢾⣇⣵⣶⡏⣿⣿⣿⣿⣿⡆⠀⠀⠂⠀⠀⠀⠀⠤⠀⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠈⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡇⢸⢹⢠⣿⣇⣿⣿⣿⡿⠟⢱⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠧⢶⡿⢘⠿⢟⡞⣿⣇⣀⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⣿⢹⣷⣿⡿⡏⣿⣿⠶⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠿⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⣿⢹⣷⢻⣿⣷⡇⣿⣛⣊⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣟⣟⢟⡙⢃⣿⣬⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⡀⣈⣿⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢪⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠉⢹⣏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡧⢸⡇⠀⣿⣏⣽⣿⣯⣷⠐⣮⠙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣻⣿⣾⣿⣯⣟⢿⣿⣿⡿⢻⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⡞⡃⠘⠃⠀⣻⢻⣿⣛⣻⣟⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⣿⣟⣼⣿⣿⠶⠾⠟⣿⢿⣟⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣿⢫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠿⠘⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣕⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣧⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣛⣛⣛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢬⣍⣡⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣁⣤⡄⠠⠤⠂⠐⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠄⢄⣀⣄⣤⣶⣦⣶⣮⣾⡷⣒⣻⣭⣍⠠⣀⣀⡀⠠⠀⢀⡂⡩⠥⠄⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡟⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⣥⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡿⠦⢒⣛⣛⣻⣽⣿⣷⣭⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣌⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣕⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠄⠀⠀⠠⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡏⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡻⢵⡞⢶⡿⢯⢯⣭⣍⣁⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡂⣿⢹⣷⢻⣿⡟⣿⣿⠴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠿⢩⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣉⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣟⣟⣛⠸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣻⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⣪⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡇⢸⣗⠀⣿⣯⣽⣿⣯⣷⡐⣮⢙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢻⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⡞⡃⠘⠃⠀⡟⣿⣿⣟⣿⣿⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠥⠇⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣜⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣁⢤⡀⠄⠤⠢⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠤⠤⠄⣀⣠⣠⣦⣢⣶⣾⢷⠷⡚⣺⣯⣍⡀⠀⢀⠠⠠⠆⢀⣀⡨⠥⠂⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⣿⡷⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣺⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢫⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠁⣤⠁⠉⠉⢁⣭⣽⣛⠿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⢛⠛⢛⠛⡛⠛⠛⡛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡿⣿⣾⢷⣶⣖⣒⣷⣾⣿⣿⣿⣿⣮⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠈⡀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡷⣿⣽⣗⣒⣢⢭⢭⣿⣿⣿⣿⣿⣿⣇⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠟⣾⢷⣵⡿⡷⣝⡿⢿⡿⢿⣫⢾⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡱⡈⢗⡣⠁⣿⢙⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠿⢩⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢿⣿⣇⣿⢀⡛⣞⠟⢼⣃⣿⣬⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣁⡈⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠿⠿⠿⢿⣿⣻⣿⣏⣿⣿⡋⢹⣏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡗⠀⣿⡏⢽⣿⣯⣷⡐⣮⢙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣿⢿⣿⣿⡿⢻⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⡞⣳⠛⠓⠀⣻⠛⢻⣻⣿⣟⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠟⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣓⣭⣤⡤⠤⠿⠀⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⣟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠁⣤⡄⠀⠤⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠤⣤⣀⣀⣤⣤⣖⡤⢤⣲⡓⣚⣺⣯⣉⢠⣄⣀⠠⠤⠀⢀⣂⠩⠥⠦⠂⠉⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣅⣽⣿⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⡟⡆⣾⡫⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣼⣶⣧⣱⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⢏⠉⠉⠁⣾⣿⣿⣿⣿⣿⣾⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠀⠂⣠⢴⣛⣻⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⢿⣒⣺⢭⣛⠻⣿⣿⣿⣿⢟⡅⣿⢹⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠿⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⡻⢶⣭⣟⢾⡿⢷⣮⣷⣮⣟⠇⣿⢙⣶⣿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣝⠍⡓⢕⡦⣭⡿⠎⠿⢃⣿⣈⠿⡞⣟⣸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣇⠮⡻⣿⣿⣿⣿⣿⣰⣮⢙⣂⣈⡛⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢾⣿⣹⣿⣇⣿⣿⠊⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡇⠀⣿⡏⢹⣿⣯⣷⡐⣮⠙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡟⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣿⢿⣿⣿⡿⢻⣿⣿⠀⢰⣖⣤⠄⣘⡻⣿⣿⣼⣷⡞⣳⣸⠃⠀⢻⡟⠃⣟⣻⣟⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣓⣥⣥⡤⠤⠜⠃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢲⣼⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠶⠿⣿⢛⣛⢛⡻⠿⣭⢭⡛⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡁⣠⢠⠤⠤⠄⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠤⣄⣀⣀⣠⣦⣤⠤⣾⢚⠕⣛⣺⣭⡈⡀⠀⢀⠠⠠⠀⢂⡂⡩⠠⠖⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⣛⣛⣛⠛⠛⢛⣛⣛⠛⠛⡛⡛⢛⠃
⠀⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠩⢙⣿⣿⣿⣿⣷⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⠿⢿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⢿⣿⣀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣤⣤⣤⣄⣠⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠟⢿⠗⠛⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡆⢸⣿⣿⣿⠛⣿⣿⣷⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⣿⣿⣦⢖⣛⠿⢃⠛⡿⣿⣿⣿⣳⣶⢹⢻⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠇⢸⣿⡿⢃⣴⣾⣿⣿⠀⠀⠀⠀⢿⣿⣫⡭⡝⣿⡃⣷⢲⡁⣏⣳⢸⠼⢿⡄⣿⣿⡇⣯⣿⡼⣜⣿⢟⣯⣴⣶⣶⣶⣶⣾⣭⣟⡻⣿⣿⣇⢟⣘⢻⣟⣟⣸⣃⣿⣬⣻⠾⠋⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠘⢉⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣛⣻⡗⣣⢻⡡⢻⣸⡇⣿⣶⠾⠯⠸⢥⣻⣿⣿⣝⣍⢿⣯⣢⣏⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣎⣟⡕⣭⣋⣞⣛⣛⡛⣛⣿⣿⣗⣀⡀⠀⣀⣛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣧⣥⣿⣞⣿⣷⡶⠿⠷⡖⢛⡛⡛⡞⣿⣿⣿⣿⣿⣵⣺⠿⠿⠃⠀⠴⠛⠛⠛⠫⠾⢿⣿⣹⡿⣎⣿⣿⠈⢹⡏⠁⣿⡏⠽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⠿⠿⢿⣿⣿⣿⣿⣅⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⡇⠀⣿⡏⠁⣿⣯⣷⢀⣬⢙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⢟⣆⣿⣹⠘⢇⠿⣰⠬⣧⣾⣻⣿⣿⣾⣭⣭⣛⢿⣿⣿⣿⡾⣿⣿⡆⠀⣲⡤⣀⡘⠛⣛⣿⣼⣷⡞⡃⢘⡗⠀⢛⠛⠃⢛⣿⣟⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣳⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣟⣯⣷⣿⣻⣿⣷⠀⢻⣿⣿⣶⣯⣥⣶⣟⣋⣥⣥⠿⢅⣈⣘⣀⣀⣸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⢷⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣇⡽⣿⣿⣏⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣔⠽⣇⢿⠸⠤⠃⠇⣿⣻⣡⣛⣼⣬⣧⣭⣭⣽⣿⢻⣿⣾⣿⣙⢛⣋⡸⣿⣷⡀⢠⣬⣉⣉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⢻⣷⡦⠒⠿⡿⢛⣛⢛⣻⣿⣭⢭⡛⣵⢢⠳⣆⣦⢸⣣⣿⣿⣿⣯⣻⣧⢿⣿⣧⠀⢻⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣴⡆
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠀⠐⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⠸⡇⣿⢸⠄⡏⢿⢸⣗⠛⠛⠛⠛⠓⠱⡾⣿⣿⡄⠘⣿⣷⣶⣾⣭⣭⣭⣿⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⣿⣿⡮⠭⣁⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠙⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠤⠸⠿⠿⠿⠃⠀⠀⢻⣿⣯⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣀⣀⣠⠀⠠⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⠠⠤⠄⠀⣀⣠⡄⠒⣤⡦⠷⠜⠒⣋⡉⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠁⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠻⡻⠿⠿⠿⠟⠛⠻⠇
⠀⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣿⣿⣿⣿⣷⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⢿⣿⡀⠀⠈⠀⢹⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⢿⢀⣀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣤⣤⣤⣄⣀⣽⣇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡗⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⠟⢿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⣾⢿⠇⠺⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣉⢻⣦⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⠏⣰⣾⣿⣿⡀⠀⠀⠀⢸⣿⣿⣫⡭⡝⣷⣋⣷⢲⡀⣏⣳⢸⡼⢻⡕⣿⣿⣿⣿⣿⣿⡿⣫⣵⣶⣿⣿⣿⣿⣿⣷⣮⡝⣿⣿⣿⣇⣿⣘⣟⣟⣟⣸⣃⣿⣬⠛⠞⠋⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⢁⣴⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣛⣻⡗⣣⢻⡡⢻⣸⠗⣿⡐⠸⠶⠸⣮⣡⣤⣗⡯⣽⣯⣾⣟⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣘⢟⣕⡺⣊⣟⢛⣿⣿⡿⣿⣿⣿⣀⣀⡀⠀⢟⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣧⣧⡿⣼⣿⣷⡶⠷⠶⡶⢿⡶⡊⢿⣷⣿⣟⣻⣛⡷⣾⣿⠀⠀⢸⡟⠛⣛⠛⣽⣟⣿⣿⣺⡿⣅⣿⢿⠈⢹⡏⠁⣿⡯⢽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡃⡖⡶⣸⡇⡇⠸⣌⠀⢣⡷⠿⠿⣿⣿⣾⣷⣾⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⢺⣯⣼⡇⢸⡇⠀⣿⡏⣽⣿⣏⣷⠀⣬⠙⣷⢠⣭⣤⣤⣤⣀⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣽⣇⣿⣹⠘⠇⠿⣰⠬⣧⣾⣻⣿⣧⣭⣭⣛⢿⣿⣿⣶⡞⣿⣿⡇⠀⣠⣤⣀⡀⠘⣿⣽⣿⣼⣧⢸⢣⡜⠃⣶⠛⠛⣿⣛⣻⣛⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⢿⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡛⡭⣽⢿⣿⣷⡝⣛⣭⣶⣻⣿⣿⡀⢸⣿⣿⣶⣯⣤⣿⣋⣩⣭⡿⢟⣀⣀⣟⣀⣠⠿⠿⠿⠿⠿⠿⠿⠿⡿⢿⣿⣿⣿⠿⢿⣿⠿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡏⣿⢱⡟⠎⢻⣁⡿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⡹⣿⣿⣧⢿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⢐⢝⠿⣇⢿⠸⠬⠃⢇⣿⣛⣡⣛⣼⣬⣧⣭⣭⣽⢿⣿⣿⣿⡽⠟⢛⡘⣿⣿⡄⠀⣌⣉⣙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⢸⣷⣧⡢⠻⠿⣿⢟⣛⢛⣻⣿⣭⢭⡟⣴⢪⠳⣆⣶⢺⣣⣿⣿⣧⣻⣷⢻⣿⣷⠀⠻⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣮⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⡄
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣏⠓⠍⡏⡼⡇⣿⢸⣬⣸⡦⠐⢹⢸⡇⣿⢸⠀⡏⢿⢸⣗⠛⠛⠛⠓⠩⣮⣿⣿⡆⠈⣿⣷⣶⣾⣭⣭⣽⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠧⢧⣟⣞⣻⣟⣷⣾⡌⠉⣡⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣷⠀⠘⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠠⠿⠿⠿⠇⠀⠀⠛⣛⣛⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠹⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⣀⠀⣠⡀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⠀⠤⠄⠀⢀⢀⡀⠒⠂⠰⠾⠞⠛⢃⠉⠁⠀⠀⠀⢀⡠⠀⠀⢀⠀⠅⠐⠄⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣯⢏⢻⣿⣫⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣺⣟⣿⡥⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠋⠁⠉⠉⠁⠀⣹⣿⣿⣿⣷⣶⣭⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢗⣤⢄⣀⣄⡺⣝⣛⣚⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣷⣭⠽⢿⢶⣒⡾⣿⡿⣿⡿⢣⡿⣿⣿⢿⣿⢿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣄⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⡰⣿⡙⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢦⣹⡷⡇⣿⢙⣷⢿⣿⣿⡇⣿⢜⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⠬⣵⣃⡛⠈⢿⣛⡟⣽⣃⣿⣮⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣗⢙⣈⣁⡈⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢽⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⣇⢸⡇⠀⣿⡏⢹⣿⣯⣷⡐⣮⠙⣷⢠⣤⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣭⣟⢿⣿⣿⡿⢻⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⣞⡇⡜⠃⠀⠛⡟⢻⣟⣿⣻⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠼⠃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢽⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣣⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠆⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠸⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡁⣤⡄⠤⠀⠀⠐⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠤⠀⣀⣄⣤⣤⣶⡶⣿⣿⣟⣓⢣⣍⠁⠀⡀⣀⡀⠠⠀⢀⡂⠩⠥⠒⠂⠉⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣯⢏⢻⣿⣫⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣺⣟⣿⡥⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠋⠉⠉⠉⠁⠀⣹⣿⣿⣿⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣤⢄⣀⣄⡪⣍⣛⣛⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣷⣮⠽⢿⣶⣒⡾⣿⡿⣿⡿⢣⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣄⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡻⣿⡇⣿⣿⣸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢦⣹⡷⡇⣿⢙⣷⢿⣿⣿⡇⣿⢜⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⠬⣵⣃⡛⠈⢿⣛⡟⣽⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣗⢙⣀⣁⡈⣛⣛⣿⣃⣀⡀⠀⣘⣛⡃⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢽⣿⣸⣿⣏⣿⣿⠈⢹⣏⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⣇⢸⡧⠀⣿⡏⢹⣿⣯⣷⡐⣮⢙⣷⢠⣤⣤⣤⣬⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣭⣟⢿⣿⣿⡿⢻⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⣞⡇⡜⠛⠀⠛⡟⢻⣟⣿⣟⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠼⠃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢽⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣕⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠖⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠸⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⡧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣉⣁⢄⡀⠀⠠⠀⠒⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠀⠤⠄⠀⣀⣠⣠⣰⣴⡶⣾⣿⣟⣒⢻⢍⢅⠀⡀⠀⡀⠀⠀⠀⠀⠨⠥⠂⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡵⣼⣟⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⢳⣓⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠘⠛⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⡶⢿⠿⣟⣛⣛⡳⣶⣤⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⢟⣧⡜⢍⣉⢽⣶⣿⣿⣿⣧⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠂⠸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢯⡟⣹⣳⠟⣿⡇⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⠂⠤⠤⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣷⡀⠀⠈⡀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣣⣷⢧⣼⡿⡽⠿⠿⠛⠫⢱⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠍⢿⡿⡇⠾⢽⣞⡺⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⡿⣿⣱⣿⡙⢃⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣻⡇⣿⡇⣿⢈⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣘⣿⡟⠃⠜⠃⣿⣨⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣥⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⣀⣘⣻⣃⣀⡀⠀⣘⣛⡃⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢪⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡩⢹⡿⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡃⡖⣶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡿⢸⡇⠀⣿⡏⣽⣿⣯⣷⢐⣮⢙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢻⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⣞⣷⠘⠃⠀⢛⡟⣿⣿⣿⣟⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣥⣤⡤⠤⠼⢃⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢽⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⢿⣿⣿⣣⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣜⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣷⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡛⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣠⣄⠀⠄⠀⠐⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠤⢄⢀⣀⣤⣔⣦⡶⢿⣿⣟⢓⣓⣋⢁⡀⠀⢀⣀⠀⠀⢀⡐⡠⠥⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⢲⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣯⡏⣼⢧⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠶⣟⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⡭⠭⢥⣤⣤⣤⣀⡈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣯⣙⣫⠵⣦⢤⣖⣿⣿⣷⣝⠛⡛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣻⠿⡆⣵⣶⡎⣿⣿⣿⣿⣿⡆⠀⠀⠠⠤⠀⠂⠤⠠⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⡇⢸⢹⢠⣿⣇⣿⣿⣿⡿⠟⢱⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠟⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠣⢾⡿⣘⠿⢿⡎⣿⢆⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣄⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⣿⢹⣷⣿⡿⡏⣿⣿⠶⣿⡙⠃⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⣿⢹⣷⢻⣿⣷⡇⣿⣛⣊⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⢟⡘⢃⣿⣨⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣈⡀⣈⣿⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢪⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠋⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡃⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣼⡧⢸⡇⠀⣿⣏⣽⣿⣯⣷⡐⣮⠙⣷⢰⣤⣤⣤⣬⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⡞⡃⡘⠓⠀⣻⢻⣻⣿⣿⣻⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠟⢘⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢽⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⢿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠎⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣉⣁⣠⡄⠀⠄⠂⠐⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠄⠀⢀⣀⣤⣰⣶⣶⢿⣿⡿⣛⠣⡉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠥⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠵⣿⡷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣺⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢫⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⡏⠀⣠⠁⠉⠉⢁⣭⣟⣛⠿⣿⣿⣿⣿⣿⠛⣛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⡛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠂⠸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡿⣻⣾⢷⣶⣖⣒⣷⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠤⠄⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣷⡀⠀⠈⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡷⣿⡽⣖⣒⣢⠭⢭⣿⣿⣿⣿⣿⣿⢇⣿⣿⡷⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠟⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠟⣾⢷⣵⡿⡿⣟⡿⢿⡿⢿⣫⢾⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣄⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡱⡈⢗⣣⠁⣿⢙⣷⢿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢿⣿⣇⣿⢀⡛⣞⠟⢼⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣀⡈⣛⣛⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣯⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠉⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⣶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡯⠀⣿⡏⢽⣿⣯⣷⡐⣮⠙⣷⢰⣤⣤⣤⣬⣭⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⡞⣳⠛⠃⠀⢻⠛⢻⣿⣿⣻⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⡟⣾⣿⣿⠶⠿⠿⣿⢿⣟⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣭⣤⡤⠤⠿⢀⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢽⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣧⢰⣸⢿⣿⣿⣣⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣕⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣷⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⡿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣙⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣉⡁⣤⡄⠠⠄⠀⠐⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡀⠀⠤⠤⢄⣀⣠⣤⣖⣴⡶⣿⣿⡟⣓⢓⣉⣁⡀⠀⠀⣀⠠⠀⢀⡐⠨⠥⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠵⣿⡷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣺⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢫⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⡏⠀⣤⠁⠉⠉⢁⣭⣿⣛⠿⣿⣿⣿⣿⣿⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⣻⣾⢷⣶⣖⣒⣷⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠠⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠈⡀⢹⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡷⣿⡽⣖⣒⣢⠭⢭⣿⣿⣿⣿⣿⣿⢇⣿⣿⡧⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠟⣾⢷⣵⡿⡿⣟⡿⢿⡿⢿⣫⢾⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡹⡈⢗⣣⠁⣿⢙⣷⢿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢿⣿⣇⣿⢀⡻⣞⠟⢸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣥⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣀⡈⣛⣛⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣭⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⣇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡇⠀⣿⡏⢽⣿⣯⣷⠐⣮⢙⣷⢰⣤⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢻⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣧⡞⣓⠛⠃⠀⢻⠛⢻⣿⣿⣿⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣭⣤⡤⠤⠿⢀⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢽⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣣⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣙⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣉⣁⣤⡄⠤⠤⠀⠐⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⢄⣀⣠⣤⣶⣶⣶⣿⣿⣛⣛⣻⡏⣁⠀⡀⢀⣀⠀⠀⠀⡒⠠⠥⠂⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢟⣯⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣅⣽⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⡎⣾⡫⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣼⣶⣧⣱⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠈⡀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⠉⠉⠀⣶⣿⣿⣿⣿⣿⣾⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡿⣿⡿⠟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠑⠂⣀⢴⣛⣻⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⢷⣒⣚⢭⣛⠻⣿⣿⣿⣿⢟⡅⣿⢹⣷⢿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⢾⣭⣟⢾⡿⣷⣯⣳⣮⣟⠇⣿⢙⣿⣿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣝⠍⣛⢕⡦⢭⡿⠏⠿⢃⣟⣈⢿⡞⣟⣸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣇⡮⡿⣿⣿⣿⣿⣿⣰⣮⢙⣂⣈⡛⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢾⣿⣽⣿⣇⣿⣿⠋⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡃⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡇⢸⣇⠀⣿⡏⢹⣿⣯⣷⠐⣮⢙⣷⢠⣤⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⡟⣳⣸⢃⠀⢻⡟⠃⣿⣿⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣭⣴⣾⣓⣥⣥⡤⠤⠼⢃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣔⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣷⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣘⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣉⣁⢤⠄⠀⠤⠀⠐⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⢄⣀⣠⣠⣰⣴⣶⣽⣿⣟⣓⢺⣋⢁⡀⠀⢀⡀⠀⠀⠀⡂⠡⠥⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⡀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⢿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣏⣶⡆⡇⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢜⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⡉⣿⣻⡹⢟⣫⣵⣶⣾⣿⣿⣷⣶⣮⣝⡻⣿⣿⡇⣛⣘⢟⣟⣟⣸⣃⣿⣮⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣧⣥⣼⢷⢯⣚⣉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⢸⣫⣫⣟⣱⢿⣿⣛⡛⣛⣛⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣭⣿⣮⣿⣷⡶⠿⠟⡛⢛⡛⡛⡹⣿⣿⣿⣿⣿⣵⠞⠛⠛⠀⠀⠮⠛⠛⠏⠓⠻⢿⣿⣸⣿⣃⣿⣿⠈⢹⡯⠁⣿⡏⠹⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡃⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣄⣀⡀⣤⣤⣄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⡏⡀⣿⡏⠁⣿⣯⣷⢐⣮⢙⣷⢠⣤⣤⣤⣬⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢻⣿⣿⠀⠠⣖⣤⢄⣘⡛⣽⣿⣼⣧⢜⡃⣸⠃⠀⣛⠛⠃⣻⣻⣟⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣞⣚⣭⣭⡤⠤⠟⢀⣂⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢽⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣌⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⢦⠚⠿⡿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡆⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣘⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣉⣁⣤⡄⠄⠄⠀⠐⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠤⢄⣀⣠⣤⣤⣦⠶⢾⣿⣟⡓⢳⡩⡀⠀⠀⡀⣀⠀⠀⢀⡀⠨⠥⠂⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡐⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡛⡛⠛⠛⠛⠛⢛⠛⠛⡛⠛⣛⡛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠠⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⢿⣿⡿⠻⢿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⢇⣀⠀⢀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠻⣟⡈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⡶⣻⡛⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣛⣛⣛⣛⡿⢿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠏⣠⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡑⣿⠿⡿⣿⣿⣿⢟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⣿⣿⠇⠿⣘⣟⣟⣟⣸⣃⣿⣬⡛⠾⠋⠠⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣠⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⡹⠯⠸⣬⣁⣶⣮⣗⣾⣿⠮⣯⡁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣇⢟⣕⡭⣃⣛⢛⣛⣛⡛⣻⣿⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣧⣥⣿⣸⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣾⣫⠽⣏⣟⡻⠿⠃⠀⠠⠿⠙⠻⠭⠓⠯⢿⣿⣺⣿⣄⣿⣻⠈⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡃⡖⡶⣸⡇⣇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⡇⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢻⣯⣼⡇⢸⡇⠀⣿⡏⢹⣿⣯⣷⡐⣮⠙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣟⣽⣇⣿⣹⢈⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣭⡻⣿⣿⣿⡷⢿⣿⣿⠀⢰⣖⡤⢄⣘⠻⣾⣿⣼⣷⢚⢳⡞⠋⢸⠛⠛⣻⣛⣿⣛⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣮⢫⣷⣿⣟⣿⣿⡆⠈⣿⣿⣿⣷⣾⣭⣥⣶⣞⣺⣬⣥⠤⠾⠀⣂⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⡟⣾⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣬⢿⣿⣿⡼⣿⣿⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣧⣌⠻⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⣭⣭⣽⠿⣿⣿⣿⣯⡛⣫⣥⢻⣿⣧⠀⢦⣤⣍⣉⣙⡛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢨⡟⣿⣷⣦⠺⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⠵⣆⣶⢺⣣⣿⣿⣿⣞⢿⡞⣿⣿⡄⠘⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣽⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠀⢻⣿⣿⣧⠀⢻⣿⣿⣷⣶⣾⣭⣭⣭⣭⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠂⠧⣟⣟⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣀⠿⢿⡛⠛⠀⠀⠈⢭⣭⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃⠀⠀⠀⠀⠘⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⣁⢤⣄⠤⠤⠀⠂⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠤⠤⠄⣀⣠⣀⣦⣶⣴⣾⣿⣟⣛⣛⢍⢁⠀⣀⢀⡀⠀⠀⠀⡂⠨⠥⠖⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⢏⢻⣯⣪⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣺⣛⣿⡥⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⡛⡛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠋⠉⠉⠉⠀⠀⣻⣿⣿⣿⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢗⣤⢄⣀⣠⡪⣝⣛⣛⣻⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⡷⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣷⣬⠭⢽⢶⣒⣾⣿⡿⣿⡿⢣⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣌⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡣⠸⣫⢧⣹⡷⡇⣿⢙⣷⢿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⣠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⢫⢸⣿⡇⠬⣵⣃⡛⠈⢿⣙⡟⣽⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣖⢙⣈⣁⡈⣙⣿⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡇⢸⡿⠀⣿⡏⢹⣿⣯⣷⡐⣮⢙⣷⢰⣤⣤⣤⣬⣬⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠿⣰⠬⣧⣾⣻⣿⣿⣿⣾⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⣟⡇⡜⠃⠀⢛⡟⢻⣛⣿⣻⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠜⠃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣌⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠎⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⣏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠃⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣤⣄⠠⠤⠀⠐⠲⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⣤⣄⣀⣠⣤⣔⣶⢔⢬⣟⣟⠛⣛⣉⣁⠀⢀⢀⡀⠠⠄⠀⠂⠠⠤⠒⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣷⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣞⣻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⡀⠀⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⡿⣻⡵⢦⣤⠤⢤⣒⣛⣿⣿⣷⣮⣛⢿⣿⢛⣛⡛⢛⠛⠛⠛⢛⠛⠛⡛⡛⢛⠛⡛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⢱⣿⣯⣗⠒⣒⢲⣬⢽⣾⣿⣿⣿⣿⢾⣿⠐⠄⠤⠀⠀⠀⠠⠤⠀⠠⠠⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣜⢿⣿⣱⢿⣇⡿⣿⡏⣿⣿⣿⡿⣫⣾⡧⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣶⢇⠸⡋⡇⠺⠟⡿⢫⣵⢿⣿⣿⣇⣀⠀⢀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢊⣾⡇⣿⢙⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⣾⣼⣿⡇⣿⢙⣷⣺⣯⣿⡇⣿⢚⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣶⡹⣿⡇⣻⣘⣟⠙⡓⢸⣁⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣯⣿⣇⣀⣀⡀⣘⣿⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠉⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡧⢸⡇⠀⣿⡏⢹⣿⣯⣷⢐⣮⠙⣷⢰⣤⣤⣤⣬⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⠄⣘⡛⣿⣿⣼⣷⡟⡇⠜⠃⠀⢛⡛⣻⣟⣿⣻⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠜⠃⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣧⢲⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣌⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣚⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣁⣤⡤⠀⠤⠂⠐⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠀⠤⠤⢀⣀⣠⣤⣢⣴⣶⣶⣿⣟⣟⣛⣋⢉⡀⠀⢀⡠⠀⠀⢀⡀⠨⠥⠖⠀⠈⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡱⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢳⣓⣿⣙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠄⠀⠀⠘⠛⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⠀⠀⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⡶⢿⠿⣟⣛⣛⣳⣶⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⢟⣧⡞⢍⣉⢽⣶⣿⣿⣿⣦⠛⠛⠛⠛⠛⠛⣛⣛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢯⡏⣹⣳⠟⣿⡇⣿⣿⣿⣿⡿⠀⠀⠠⠤⠀⠀⠀⠠⠠⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣣⣷⢧⣼⡿⡼⠿⠿⢛⠫⢰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠍⢾⡿⡇⠾⢽⣞⡸⢇⣀⠀⢀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣄⣼⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⡿⣿⣹⣿⡙⠃⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣻⡏⣿⡇⣿⣌⣛⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣘⣿⡟⠃⠝⠃⣿⣯⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣯⣭⣭⣭⣭⣭⣥⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⣀⣘⣿⣇⣀⡀⠀⣘⣛⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡩⢹⣯⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡿⢾⡇⠀⣿⡏⣽⣿⣯⣷⠐⣮⢙⣷⢰⣤⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⠄⣘⡛⣿⣿⣼⣧⣞⣷⠘⠃⠀⢻⡟⣻⣛⣿⣛⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣥⣥⡤⠤⠜⠃⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣌⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠖⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣉⣁⣤⡄⠀⠤⠀⠐⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠤⢀⣀⣠⣠⣠⣤⡴⣶⡿⣟⣛⣻⣋⣁⡀⠀⠀⡀⠀⠀⢀⡀⡠⠥⠖⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡟⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣥⣤⣤⣤⣀⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣟⡷⠴⢖⣛⣛⣻⣽⣿⣷⣯⡛⢛⠛⠛⠛⠛⠛⠛⢛⡛⡛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢟⣭⣍⢟⣭⣔⣿⣿⣿⣿⣿⣷⠀⠁⠀⠄⠀⠀⠀⠀⠤⠠⠤⠤⠅
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⢠⣏⡏⣽⣿⣸⣿⣿⣿⡿⢋⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⡫⢵⡞⠷⡿⢯⣏⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢹⣿⡟⣿⣿⢴⣿⡙⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⢒⣉⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣟⣟⢛⠸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣯⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣏⣈⡀⣻⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠉⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡇⠀⣿⣯⣽⣿⣯⣷⠐⣮⢙⣷⢰⣤⣤⣤⣬⣭⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⠄⣘⡛⣿⣿⣼⣷⡞⡃⠘⠃⠀⡟⣻⣿⣿⣿⣟⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠇⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣌⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠖⠿⡿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣤⡄⠀⠠⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⠄⢄⣀⣠⣠⣤⣴⡖⣴⡿⣟⣛⢛⣏⣉⡄⠀⢀⠀⠀⠀⠀⣀⠨⠤⠒⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡟⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⡀⠀⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣥⣤⣤⣤⣀⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣟⡷⠶⢖⣛⣛⣻⣽⣿⣷⣯⡛⠛⠛⡛⠛⠛⠛⠛⣛⡛⡛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢟⣭⣭⢟⣭⣔⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠄⠀⠠⠠⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣾⢡⣏⡏⣽⣿⣸⣿⣿⣿⡿⢋⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⡫⢵⡞⠷⡿⢯⢏⢭⢍⣑⠈⠈⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢹⣿⡟⣿⣿⢴⣿⡙⠃⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣉⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣿⣟⢛⠸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣏⣈⡀⣛⣛⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣭⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡏⠁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡇⠀⣿⣯⣽⣿⣯⣷⠐⣮⢙⣷⢰⣦⣤⣤⣬⣭⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⡞⡃⠘⠃⠀⡟⣟⣿⣿⣿⣿⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠇⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣜⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠞⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣚⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣁⣤⡤⠠⠠⠀⠀⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⢀⣀⣠⣠⣤⣤⢴⢶⣿⣟⣛⣻⣋⣉⡀⠀⡀⡀⠀⠀⠀⡂⠠⠄⠔⠀⠈⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡝⣿⡷⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣾⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢯⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⡏⠀⣠⠁⠉⠉⢁⣭⣟⣛⠿⣿⣿⣿⣿⣿⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡿⣱⣾⣷⣶⣖⣲⣷⣾⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⠄⠤⠀⠀⠀⠀⠀⠀⠠⠠⠤⠥⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡷⣿⣽⣶⣖⣢⢭⢭⣿⣿⣿⣿⣿⣿⢧⣿⣿⡷⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣿⠟⣾⢷⣵⡿⡿⣝⡿⢿⡿⢿⣫⢾⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡱⡈⢗⡣⠁⣿⢙⣷⢿⣿⡏⣿⣿⠲⣿⡙⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠿⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⣘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢿⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢻⣿⣇⣿⢀⡻⣞⠟⣸⣃⣿⣭⡛⠾⠋⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣀⡈⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡋⢹⣯⠁⣿⣯⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡇⢸⡗⠀⣿⡏⢽⣿⣯⣷⠐⣮⠙⣷⢰⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡻⣿⣿⣼⣷⡞⣓⠛⠃⠀⣻⠛⢻⣿⣿⣿⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣭⣤⡤⠤⠿⢀⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣌⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢟⣛⢛⡻⠿⣭⢭⡛⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⣿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣚⣂⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣉⣁⣤⣤⠠⠠⠂⠂⠶⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡀⠀⠤⡤⢄⣀⣠⣠⣤⣦⣤⣾⣿⣿⣚⣻⣯⣉⣀⡀⣀⡠⠠⠀⢀⣂⠨⠥⠖⡀⠉⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢟⣯⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣅⣽⣟⢝⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡏⡏⣾⣯⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣼⣶⢧⢱⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠠⠀⠀⠀⠄⠄⠀⠀⠤⠤⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⢏⠉⠉⠀⣾⣿⣿⣿⣿⣿⣾⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠁⠂⣀⢴⣛⣻⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣄⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣯⢿⣒⣺⢭⣛⠻⣿⣿⣿⣿⢟⡅⣿⢹⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠿⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⡻⢾⣭⣟⢾⡿⣷⣯⣷⣮⣛⠇⣿⠙⣶⣿⣿⣿⡇⣿⢜⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⣠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣟⠍⡓⢕⡦⢭⡿⠏⠿⢃⣟⣈⢿⡞⣟⣹⣃⣿⣮⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣥⣭⠉⠉⠉⣇⡮⡻⣿⣿⣿⣿⣿⣰⣮⢙⣂⣊⡛⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢾⣿⣽⣿⣇⣿⣿⠋⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⣶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡷⠀⣿⡏⢹⣿⣯⣷⣐⣮⢙⣷⢰⣤⣤⣤⣭⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⠄⣘⡻⣿⣿⣼⣷⡟⣳⣸⠃⠀⢻⡟⠃⣿⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣥⡤⠤⠜⢃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣜⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣓⣂⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣁⣤⣤⠀⠠⠒⠒⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠤⣄⣀⣠⣠⣴⣶⣦⣾⡿⣟⣛⣻⣟⡁⢀⠀⣀⡀⠀⠀⠐⡀⠨⠥⠖⠀⠉⠓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠂⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⠛⣛⡛⠛⢛⠛⠛⣛⠛⠛⢛⣛⠛⠃
⠀⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠡⢙⣿⣿⣿⣿⣷⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣿⣀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢠⣤⣤⣤⣄⣠⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠟⢿⡗⠛⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧⣿⣿⣧⢖⣛⠿⢇⢛⡿⣿⣿⣿⣳⣶⢹⢹⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠇⢸⣿⡿⠃⣴⣾⣿⣿⠀⠀⠀⠀⢿⣿⣫⡭⡝⣿⡃⣷⢲⡁⣏⣳⢸⠸⢿⡄⢿⣿⣏⣏⣻⡾⣞⣿⢟⣯⣼⣶⣶⣶⣶⣶⣯⣝⡻⣿⣿⣇⢟⣘⢻⣟⣟⣸⣃⣿⣨⣻⠾⠋⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠘⣉⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⢘⣛⣿⡗⣣⢻⣡⢿⣸⡇⣿⣶⡼⠯⠸⢥⣻⣿⣿⣝⣍⢿⣮⣚⣍⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣎⣟⡵⣩⣋⣞⣛⣛⡛⣻⣿⣿⣿⣀⡀⠀⣀⣛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣧⣧⣿⡞⣿⣷⡶⠿⠷⡖⢛⡛⡛⡟⣿⣿⣿⣿⣷⣵⣶⠿⠿⠃⠀⠰⠟⠛⠛⠋⠚⢿⣿⣹⣿⣎⣿⣿⡈⢹⡏⠁⣿⣏⠽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⠿⠿⢿⣿⣿⣿⣿⣅⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⢘⣿⣽⣿⢿⣧⣼⡇⢸⡇⠀⣿⡏⠁⣿⣯⣷⣐⣬⠙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⢸⣿⣿⢟⣆⣿⣹⢘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣯⣽⣛⢿⣿⣿⣿⡾⣿⣿⡇⠀⣲⡤⣀⣘⠛⣛⣻⣼⣧⡞⡃⢘⡗⠀⢛⡛⡃⢛⣿⣟⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣣⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣷⣝⣯⣷⣿⣻⣿⣷⡀⢹⣿⣿⣶⣯⣥⣴⣟⣛⣥⣭⠽⠅⣀⣘⣃⣈⣸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⢧⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣿⡽⣿⣿⣇⢿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣐⠽⣇⢿⠸⠤⠃⠇⣿⣻⣡⣛⣼⣬⣧⡯⣭⣽⣿⢿⣿⣿⣿⣝⢛⣋⡘⣿⣿⡄⢠⣬⣉⣉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⢹⣷⡦⠎⠿⡿⢟⣛⢛⣻⠿⣭⢭⡛⣵⢢⠳⣆⣦⢸⣣⣿⣿⣿⣯⣻⣷⢻⣿⣷⠀⢻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣴⣶⣶⡆
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠐⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣤⣸⣯⠩⢹⠘⡇⣿⢸⠀⡏⢿⢸⣗⠛⠛⠛⠛⠓⠱⣾⣿⣿⡄⠘⣿⣿⣶⣶⣯⣭⣭⣽⣿⣟⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣻⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⣿⣿⠮⠭⣁⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠉⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠤⠸⠿⠿⠟⠃⠀⠀⢻⣿⣭⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⣀⡀⡠⠀⠤⠦⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⡀⠤⠤⣄⢀⢄⣤⣤⢖⢶⠿⠿⣟⢓⢻⠉⡁⡀⡀⢀⡀⠀⠄⢀⡂⡠⠄⠂⠠⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⡛⠛⠃
⠀⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠄⠀
⠀⠀⣹⣿⣿⣿⣿⣦⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⡇⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⢿⣇⣀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠻⣟⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡏⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⡖⣻⡛⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣛⣛⣛⣛⡿⢿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠏⣠⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⠐⣿⠿⡿⣿⣿⣿⢟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⣿⣿⠇⠿⣘⣟⣟⣟⣸⣃⣿⣨⡛⠾⠋⠰⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⡹⠯⠸⣬⣁⣶⣮⣗⣾⡯⠬⣯⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣇⢟⣟⡭⣃⣛⢛⣛⣛⡛⣻⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⣧⣥⣿⣸⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣮⣫⠽⣏⣟⡻⠿⠃⠀⠠⠿⠛⠿⠭⠓⠯⢿⣿⣺⣿⣄⣿⣻⠈⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡃⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣇⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢻⣯⣼⡇⢸⡇⠀⣿⡏⢹⣿⣯⣷⡐⣮⠙⣷⢠⣤⣤⣤⣬⣤⣥⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣟⣵⣇⣿⣹⠈⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣭⣻⣿⣿⣿⡷⢿⣿⣿⠀⢰⣶⡤⢀⣘⠻⣾⣿⣼⣧⢚⢳⡞⠃⢸⠛⠛⣻⣻⣿⣻⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⢿⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣮⣫⣷⣿⣏⣿⣿⡆⠈⣿⣿⣿⣷⣾⣭⣥⣶⣞⣪⣬⣥⠤⠼⢀⣃⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡟⣾⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⢿⣿⣿⡼⣿⣿⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣧⣌⠻⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⣭⣭⣽⠿⣿⣾⣿⣯⡛⣩⣥⢻⣿⣧⠀⢦⣤⣍⣉⣉⡛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡟⣿⣷⡦⠺⠿⣿⢟⣛⢛⡻⠿⣭⢭⡛⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣜⢿⡞⣿⣿⡄⠘⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣯⣭⣭⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠀⢺⣿⣿⣧⠀⢻⣿⣿⣷⣶⣾⣭⣭⣭⣭⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣫⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠂⠧⣟⣞⣻⣟⠿⠿⢬⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠿⢿⡛⠛⠀⠀⠈⢭⣭⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣠⣤⠤⠄⠀⠲⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠤⡀⣀⡠⣤⣤⣦⣦⣾⣿⢟⠛⣛⡟⠉⢀⡀⢀⠀⠠⠀⠀⡀⠠⠥⠖⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢏⢻⣿⣪⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡺⣟⣷⡥⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⠛⠛⠛⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠉⠉⠀⠀⣻⣿⣿⣿⣷⣶⣭⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠤⠤⠤⠤⠄⠅
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢗⣤⢄⣀⣤⡺⣝⣛⣛⣻⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣷⣮⠭⢽⢶⣒⣾⣿⡿⣿⡿⢳⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣮⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⡰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠿⢭⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢧⣹⡧⡇⣿⢙⣷⢿⣿⣿⡇⣿⣜⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⣠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⢫⢸⣿⡇⢬⣵⣃⡛⠈⢿⣙⡟⣼⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣯⣭⣭⣭⣯⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣖⢙⣀⣁⡈⣛⣻⣻⣃⣀⡀⠀⣘⣛⡃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣏⠈⣿⡏⢹⣿⣯⣷⡐⣮⢙⣷⢰⣤⣤⣤⣤⣭⣥⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⣟⡇⡜⠃⠀⢛⡟⢻⣿⣻⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣯⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠜⢃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣼⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣍⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠶⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⡿⡿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣚⣁⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣤⣤⠤⠤⠆⠒⠶⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡀⣀⠤⠄⣀⣀⣠⣤⣤⣶⡆⣾⣦⣗⢛⣻⣫⢀⢀⠀⡠⠀⠀⠀⢐⠂⠨⠡⠖⠀⠁⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣷⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣞⣻⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⢸⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⣻⡵⢶⣤⠤⢤⣒⣛⣿⣿⣷⣮⣟⢿⣿⠛⠛⠛⡛⠛⠛⠛⠛⠛⢛⡛⡛⢛⠛⡛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⢹⣿⣿⣗⠒⣒⢲⣬⢵⣾⣿⣿⣿⣿⣾⣿⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠤⠤⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣱⣿⣇⡿⣿⣏⣿⣿⣿⡿⣻⣾⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣾⢇⠸⡛⡇⢻⠟⣿⢫⣵⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢪⣾⡇⣿⢙⣷⣿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⣾⣾⣿⡇⣿⢙⣷⣺⣯⣿⡇⣿⣜⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣶⡹⣿⡇⣻⣘⣟⠙⡛⢸⣁⣿⣭⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣯⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣇⣀⣀⡀⣙⣛⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣭⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠉⢹⡏⠁⣿⡏⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣯⣼⡧⢸⡟⠀⣿⡏⢹⣿⣯⣷⢐⣮⢙⣷⢠⣤⣤⣤⣤⣥⣭⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣭⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⣟⡇⠜⠋⠀⢛⡛⣻⣿⣿⣟⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠜⢃⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⣟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣌⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠆⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⣟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⡿⢿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣚⣁⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣄⡤⠤⠤⠐⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠄⣄⣀⣠⣠⣀⣴⢤⣾⡴⣆⠛⢓⡋⠀⠀⠀⢀⡀⠠⠀⠀⠂⠨⠡⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡵⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢣⣓⣿⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠘⠛⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⡾⠿⠿⣟⣛⣛⡳⣶⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⢟⣯⣟⢍⣉⢽⣶⣿⣿⣿⣯⠛⠛⠛⠛⠛⢛⡛⢛⡛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢯⡟⣹⣳⠟⣿⡇⣿⣿⣿⣿⡿⠀⠀⠤⠀⠀⠀⠤⠤⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣣⣷⢧⣼⡿⡼⠿⠿⢛⠋⢱⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠍⢾⡿⡇⠾⢿⣞⡸⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⡿⣿⣰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣻⡇⣿⡇⣿⢌⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣘⣟⡟⠃⠝⠃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⢬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣥⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⣂⣘⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⣯⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡿⢾⣇⠀⣿⡏⣽⣿⣯⣷⠐⣮⢙⣷⢰⣤⣤⣤⣤⣭⣥⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⣞⣗⠘⠓⠀⢛⡟⣿⣿⣿⣿⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣚⣥⣤⡤⠤⠜⢃⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣌⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠶⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⢿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣤⡄⠄⠄⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⡀⠤⢄⣀⣀⣀⣤⣤⣴⡄⡶⣵⣖⠛⢻⣏⠁⠀⠀⠀⡀⠀⠀⢀⠂⠨⠡⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⢲⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢯⡏⣼⢧⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡈⢶⣟⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⡭⠭⣥⣤⣤⣥⣀⡈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣭⣉⣩⠵⠶⢵⣞⣿⣿⣷⣝⠛⣛⠛⠛⠛⠛⠛⠛⡛⠛⢛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⡆⣵⣶⡏⣿⣿⣿⣿⣿⡆⠍⠀⠀⠠⠀⠀⠤⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⢸⢹⢠⣿⣇⣿⣿⣿⡿⠟⢱⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠣⢾⡿⢘⠿⢿⡎⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⣿⢹⣷⣿⡿⡏⣿⣿⠶⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠿⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⣿⢹⣷⢻⣿⣷⡇⣿⣛⣊⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣟⣟⠟⡙⢃⣿⣭⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣈⡀⣈⣿⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠋⢹⡏⡁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡧⢸⡇⠁⣿⣏⣽⣿⣯⣷⢐⣮⢙⣷⢰⣤⣤⣤⣤⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠟⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡞⡇⠘⠓⠀⣻⢻⣿⣟⣿⣿⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠟⢘⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣌⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠆⠿⣿⢟⣛⢛⡻⠿⣭⢭⡛⣕⢪⠵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣐⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣉⣁⣤⡤⠄⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⡀⠤⢄⡀⣀⣀⣠⣴⣤⡂⣾⣱⣆⠛⢓⡩⡀⡀⠀⢀⠀⠀⠀⠀⠂⠨⠁⠂⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡝⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣾⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢯⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠁⣠⠉⠉⠉⢁⣭⣿⣛⠿⣿⣿⣿⣿⣿⢛⣛⣛⠛⠛⠛⠛⠛⠛⠛⡛⡛⠛⡛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡿⣻⣾⢷⣶⣖⣒⣷⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⠈⠀⠀⠂⠀⠀⠄⠤⠄⠀⠤⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡷⣿⡽⣗⣒⣪⢭⢭⣿⣿⣿⣿⣿⣿⣇⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠟⣾⢷⣵⠿⡷⣝⡿⢿⡿⢿⣫⢾⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡱⡈⢗⣣⠁⣿⢙⣷⢿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠿⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢿⣿⣇⣿⢀⡻⣞⠛⢸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣯⣭⣭⣥⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣁⡊⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡋⢹⣯⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡇⠀⣿⡏⢽⣿⣯⣷⢐⣮⢙⣷⢠⣦⣤⣤⣤⣭⣭⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⢘⢇⡿⣰⠬⣧⣾⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡿⣓⠙⠓⠀⢻⢛⢻⣿⣿⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣭⣤⡤⠤⠾⢀⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣌⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠦⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣘⣁⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣤⣄⠄⠤⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⢄⣀⣀⣠⣀⣀⣦⡦⡬⣿⣚⣛⢓⣍⠀⠀⠀⢀⡀⠠⠀⠀⠂⠨⠁⠂⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡝⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣾⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢯⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠁⣠⠉⠉⠉⢁⣭⣽⣛⠿⣿⣿⣿⣿⣿⢛⣛⣛⣛⠛⠛⠛⠛⠛⢛⠛⣛⡛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡿⣻⣾⢷⣶⣖⣒⣷⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⠀⠀⠂⠀⠀⠄⠄⠐⠀⠤⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡷⣿⡽⣖⣒⣪⢭⢭⣿⣿⣿⣿⣿⣿⢧⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠟⣾⢷⣵⠿⡷⣝⠿⢿⡿⢿⣫⢾⣿⣿⣇⣐⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡱⡈⢗⣣⠁⣿⢙⣷⢿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡂⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢿⣿⣇⣿⢀⡻⣞⠛⢸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣁⡊⣛⣻⣻⣃⣀⡀⠀⣘⣛⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡋⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡇⢸⡇⠀⣿⡏⢽⣿⣯⣷⢐⣮⠙⣷⢠⣤⣤⣤⣤⣬⣭⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣷⡟⣓⠙⠓⠀⢻⢛⢻⣻⣿⣻⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣭⣤⡤⠤⠾⢀⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣌⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠦⠿⣿⢟⣛⢛⡿⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣘⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣤⡄⠠⠄⠔⠒⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⡀⠤⢄⣀⣀⣠⣀⣤⣤⣄⣺⣖⣟⠛⣛⣋⠀⡀⠀⠀⡀⠀⠀⠀⠂⠨⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣛⡛⡛⠛⠛⡛⠛⢛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⠤⠤⠤⠄⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣄⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠿⢨⠻⡿⣿⣿⣟⣶⡆⡇⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⡿⡉⣿⣻⡹⢿⣫⣵⣶⣶⣶⣶⣶⣶⣮⣝⡻⣿⣿⡇⣛⣘⢟⣟⣟⣸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⡡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣧⣧⣼⢿⢯⣚⣉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⢸⣫⣪⣟⣵⢿⣟⣛⡛⣟⣛⣻⣃⣀⡀⠀⣘⣛⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣵⡾⠛⠛⠀⠠⠮⠛⠛⠏⠓⠻⢿⣿⣸⣿⣃⣿⣿⠈⢹⡏⠁⣿⡏⠹⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣄⣀⡀⣤⣤⣄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⡏⠄⣿⡏⠁⣿⣯⣷⡐⣮⢙⣷⢠⣤⣤⣤⣬⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣭⣻⢿⣿⣿⡿⢻⣿⣿⠀⢰⣖⣤⢄⣘⠛⣽⣿⣼⣧⢜⡃⣸⠃⠀⣛⠛⠃⣛⣿⣛⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡉⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣾⣯⣤⣶⣞⣪⣭⣭⠤⠤⠿⣀⣂⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣼⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣌⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣍⣉⣙⡛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⠦⠖⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡆⠈⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣭⣽⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⠸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣾⣭⣭⣭⣭⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣫⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣂⣀⠼⠿⣟⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣤⣤⠀⠄⠔⠀⠲⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠤⢤⣄⣀⡠⣀⣄⡤⣆⣴⣒⣞⠛⢛⣻⡁⡀⠀⢀⡀⠀⠐⠀⡀⠈⠡⠄⠂⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣛⣛⣛⣛⠛⣛⣛⣛⣛⡛⡛⣛⡛⢛⠃
⠀⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠡⢙⣿⣿⣿⣿⣷⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⠿⢿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⢿⢿⣿⣿⣿⣀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣤⣤⣤⣄⣠⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠟⢿⠇⠛⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⢸⣿⣿⣿⠛⣿⣿⣷⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⣿⣿⣦⢖⣛⠿⢃⠛⡿⣿⣿⡿⣱⣶⢹⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⢸⣿⡿⠃⣴⣾⣿⣿⠀⠀⠀⠀⣿⣿⣫⡭⡝⣿⡃⣷⢲⡁⣏⣳⢸⠼⢿⡄⢿⣿⡇⡏⣿⡼⣞⡿⢟⣯⣽⣶⣶⣶⣶⣾⣭⣟⡻⣿⣿⣇⢟⣘⢛⣟⣟⣸⣃⣿⣬⣻⠾⠋⠀⠌⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠘⢉⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣛⣻⡗⣣⢻⣡⢻⣸⡇⣿⣶⠾⠯⠸⢥⣹⣿⣿⣽⣍⢿⣯⣊⣏⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣎⣟⡕⣭⣋⣞⣛⣛⡻⣿⣿⣿⣟⣀⡀⠀⣀⣛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣧⣥⣿⣞⣿⣷⡶⠿⠷⡖⢛⡛⡛⡾⣿⣿⣿⣿⣿⣵⣺⠿⠿⠃⠀⠴⠛⠛⠛⠫⠾⢿⣿⣹⣿⣆⣿⣿⡈⢹⡏⠁⣿⡏⠽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⠿⠿⢿⣿⣿⣿⣿⣅⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⡧⠀⣿⡏⠁⣿⣯⣷⠀⣬⠙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⢏⣆⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣾⣭⣭⣻⢿⣿⣿⣿⡾⣿⣿⡆⠀⣲⡤⣀⡘⠛⣛⣿⣼⣧⡞⡃⢘⡇⠀⢛⠛⠃⢛⣿⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣳⣿⣿⠶⠾⠿⢿⢿⣛⡛⡛⣛⢿⡙⡭⣭⢻⣿⣿⣷⣝⣯⣷⣿⣻⣿⣷⠀⢻⣿⣿⣶⣯⣥⣶⣟⣋⣥⣥⠿⢅⣀⣘⣀⣀⣸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⢷⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣷⡹⣿⣿⣏⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣔⠽⣇⢿⠸⠤⠃⠇⣿⣻⣡⣛⣼⣬⣧⡯⣭⣽⣿⢻⣽⣿⣿⣙⢛⣋⡸⣿⣷⡀⢠⣬⣉⣉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⢻⣷⠦⠖⠿⡿⢛⣛⢛⣻⢿⣭⢭⡛⣵⢢⠳⣆⣦⢸⣣⣿⣿⣿⣯⢻⣧⢿⣿⣧⠀⢻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣮⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣴⣶⡆
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠩⢹⠘⡇⣿⢸⠀⡏⢿⢸⣗⠛⠛⠛⠛⠓⠱⣾⣿⣿⡄⠘⣿⣷⣶⣾⣭⣭⣭⣿⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⣿⣿⡮⠭⣁⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠙⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠦⠸⠿⠿⠿⠃⠀⠀⢻⣿⣯⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣉⣀⣀⣀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⠠⠤⠄⢀⣀⠀⢀⣂⢀⣦⡾⠞⢛⡛⡋⢉⠁⠀⢀⢀⠠⠀⠂⢀⠀⠄⠐⠄⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⠛⠛⠛⠛⠛⠛⠛⢛⢛⠛⠛⠛⢛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀
⠀⠀⣹⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⡇⠀⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⢿⢇⣀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠻⣟⡈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⡿⣿⠰⣿⡙⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⡖⣻⡛⠟⢽⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠿⣟⣛⣛⣛⡿⢿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠏⣠⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⠐⣿⠿⡿⣿⣿⣿⢟⣫⣶⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⣿⣿⠇⠿⣘⣟⣟⣟⣸⣃⣿⣬⠛⠾⠋⠐⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⡹⠯⠸⣬⣁⣶⣯⣗⣾⣯⠬⣭⡁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣇⢟⣕⡽⣃⣛⢛⣛⣛⡛⣻⣛⣻⣂⣀⡀⠀⣘⣛⡃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣧⣥⣿⣸⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣾⣫⠽⢏⣟⣻⠿⠃⠀⠠⠿⠛⠿⠯⠑⠿⢿⣿⣺⣿⢁⣿⣻⠈⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡃⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣇⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣯⣼⡇⢸⡇⠀⣿⡏⢹⣿⣯⣷⠐⣮⠙⣷⢠⣤⣤⣤⣤⣭⣥⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⠈⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣭⡻⣿⣿⣿⡷⢿⣿⣿⠀⢰⣲⡤⢄⣘⠻⣾⣿⣼⣧⢞⢓⡞⠓⢰⢛⠛⣻⣛⣻⣛⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣮⢫⣷⣿⣟⣿⣿⡆⠘⣿⣿⣿⣷⣾⣯⣤⣶⣞⣪⣬⣥⠤⠾⠐⣂⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢈⡟⣾⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⢿⣿⣿⡸⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣧⣌⠻⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⡧⣯⣭⣽⠿⣿⣿⣿⣯⡛⣋⣥⢿⣿⣧⠀⢦⣤⣍⣉⣉⡛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⡟⣿⣷⣦⠺⠿⣿⢟⣛⢛⡻⠿⣭⢭⡛⣕⢪⠵⣆⣶⢺⣣⣿⣿⣿⣜⢿⡞⣿⣿⡄⠘⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣭⣭⣭⣭⣽⣿⣿⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠀⢾⣿⣿⣧⠀⢻⣿⣿⣷⣶⣾⣭⣭⣭⣭⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣫⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⣟⣞⣻⣟⠿⠿⢬⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠈⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⡁⠿⢿⡟⠛⠀⠀⠈⢭⣭⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃⠀⠀⠀⠀⠘⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣀⣤⠀⠄⠒⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⡀⠤⠤⠄⠀⠀⡀⢀⠂⠀⠺⠾⢏⢚⣛⠉⡉⠀⢀⢀⡀⠀⠀⠂⡀⠠⠅⠦⢀⠈⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⢏⠻⣯⣪⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣺⣟⣿⡥⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠋⠉⠉⠉⠀⠀⣹⣿⣿⣿⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠤⠠⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢗⣤⢀⣀⣤⡪⣝⣓⣛⣻⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣗⣭⠭⢽⢖⣒⡾⣿⡿⣿⡿⢳⡿⣿⣿⢿⣿⢿⣇⣐⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣮⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢧⣹⡧⡇⣿⢙⣷⢿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⠬⣕⣃⡛⡈⢿⣛⡟⣽⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣗⢙⣈⣁⡈⣛⣿⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⣮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢽⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣧⠀⣿⡏⢹⣿⣯⣷⡐⣮⠙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⢘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣭⣿⢿⣿⣿⡿⢻⣿⣿⠀⠰⣖⣤⠄⣈⡛⣿⣿⣼⣷⣞⡇⡞⠓⠀⠛⡟⢳⣛⣻⣛⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣯⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠼⢃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣧⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣝⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡿⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢚⣀⣼⣿⣟⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣤⣤⠄⠔⠐⠒⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⠄⡀⣀⣤⣶⣦⣦⣾⣾⣿⣾⣛⢉⡉⠀⣀⢀⡀⠀⠄⠒⣂⠨⠡⠖⢂⠈⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣷⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣞⣻⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⡿⣻⡽⢦⣤⠤⢤⣒⣛⣿⣿⣷⣯⣛⢿⣿⢛⣛⢛⡛⠛⠛⠛⠛⠛⠛⠛⡛⣛⢛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⢱⣿⣯⣗⠒⣒⢲⣬⢽⣾⣿⣿⣿⣿⣾⣿⠈⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠠⠤⠥⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣜⢿⣿⣱⣿⣇⡿⣿⣇⣿⣿⣿⡿⣻⣾⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⢇⠸⡛⡇⢺⠟⣿⢫⣵⢾⣿⣿⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢊⣾⡇⣿⢙⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡏⣾⣼⣿⡇⣿⢙⣷⣺⣯⣿⡇⣿⢘⣋⢻⣆⠠⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⡇⣻⣘⣿⠙⡛⢸⣁⣿⣭⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣇⣀⣀⡀⣘⣿⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⣯⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡧⢸⣯⠀⣿⡏⢹⣿⣯⣷⣐⣮⠙⣷⢰⣤⣤⣴⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣷⣇⣿⣹⢘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣈⡛⣿⣿⣼⣧⡟⡇⠜⠓⠀⢛⡛⣻⣛⣿⣛⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣚⣭⣤⡤⠤⠜⢃⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣨⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣕⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠾⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢛⣀⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣠⣤⠀⠤⠀⠒⠲⠒⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡀⣀⠤⠤⡤⣀⣀⣠⣶⣶⣤⣾⣿⣿⣿⣻⡋⡉⠀⠠⣀⡀⠀⠀⠀⡂⠩⠡⠒⢀⠉⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡱⣼⡟⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢳⣓⣿⡙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠄⠀⠀⠘⠛⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⡶⠿⠿⣟⣛⣛⣳⣶⣤⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⢟⣧⡜⢍⣉⢽⣶⣿⣿⣿⣦⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣌⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢯⡟⣹⢳⠟⣿⡇⣿⣿⣿⣿⡿⠀⠀⠀⠠⠀⠀⠀⠀⠠⠥⠄⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣣⣷⢧⣼⡿⡽⠿⠿⠛⠋⢰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠍⢾⣿⡇⠾⢽⣞⠺⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⡿⣿⣱⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣻⡇⣿⡇⣿⣌⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣘⣟⡟⠃⠝⠃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⣈⣘⣿⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣯⣿⢺⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡩⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡿⢼⡷⠀⣿⡏⣽⣿⣯⣷⣐⣮⠙⣷⢠⣤⣤⣴⣤⣭⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⢘⢇⠿⣰⠬⣧⣼⣿⣿⣿⣿⣿⣭⣟⢿⣿⣿⡿⢻⣿⣿⠀⠰⣖⣤⠄⣈⡛⣿⣿⣼⣷⣞⣳⠘⠃⠀⢛⡟⣿⣿⣿⣛⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣯⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣚⣥⣤⡤⠤⠜⢃⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣧⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣕⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠶⠿⣿⢟⣛⢛⡻⠿⣭⢭⡛⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣮⢿⣏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢬⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⣀⣼⣿⣟⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣤⣤⠀⠤⠀⠒⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠀⠤⠤⠄⣀⣠⣠⣲⣦⣴⣼⣿⡟⣻⣛⢍⠁⠀⢀⢀⡀⠀⠀⠂⣂⠨⠡⠖⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡟⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣻⣥⣤⣤⣤⣀⡀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⠿⠴⢖⣛⣛⣫⣽⣿⣷⣭⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⢛⠛⢛⠃
⠀⣿⣿⣿⣿⣶⣌⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣝⢟⣭⣔⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣾⢠⣏⠏⣽⣿⢸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠫⢵⡞⠶⡿⢧⢯⢭⢍⣑⠀⠁⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡂⣿⢹⣷⢻⣿⡟⣿⣿⣴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣉⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣟⣟⣛⠸⣃⣿⣮⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣻⣿⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣟⠀⣿⣯⣽⣿⣯⣷⢐⣮⠙⣷⢠⣤⣤⣤⣤⣭⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣭⣿⢿⣿⣿⡿⢻⣿⣿⠀⠰⣖⣤⢄⣈⡛⣿⣿⣼⣷⡞⡃⠘⠃⠀⡟⣿⣿⣟⣿⣻⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠇⢛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣕⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠶⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⡿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢓⣀⣼⣿⣟⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣤⣄⠀⠄⠀⠒⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠤⠤⠄⡀⢠⣠⠶⠶⢤⣼⣟⢞⢛⡻⢉⢉⠀⠀⢀⡀⠀⠀⠀⡀⠩⠡⠖⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠕⣿⡷⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣾⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢯⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⡏⠀⢴⠁⠉⠉⢁⣭⣿⣛⠿⣿⣿⣿⣿⣿⠛⡛⣛⢛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡿⣽⣾⣷⣶⣖⣒⣷⣾⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⠀⠠⠤⠠⠀⠀⠄⠄⠠⠄⠠⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡷⣿⡽⣷⣒⣪⢭⢭⣿⣿⣿⣿⣿⣿⢇⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⢿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠟⣾⢷⣵⡿⡷⣝⠿⢿⡿⢿⣫⢾⣿⢿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡹⡈⢗⡃⠁⣿⢙⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢿⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢿⣿⣇⣿⢀⡻⣞⠟⢼⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣼⣏⣘⣁⡈⣛⣛⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣯⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣯⣼⡇⢸⡧⠀⣿⡏⢽⣿⣯⣷⢐⣮⢙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⡾⣳⠛⠓⠀⢻⠛⢻⣛⣻⣛⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣯⣯⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣓⣭⣤⡤⠤⠾⠀⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣕⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠶⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣼⣿⣟⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣤⣤⠤⠴⠐⠒⠲⠒⠂⠂⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠀⠤⠤⠄⡀⣠⣄⣶⣶⣤⣼⣿⡟⣛⡛⡉⡉⠀⠀⡀⡀⠀⠄⠂⣂⠨⠡⠲⢀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣅⣽⣿⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⣆⣾⡫⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⡛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⡛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣸⣶⣧⢱⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⠠⠤⠀⠀⠀⠤⠄⠠⠀⠤⠴⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢏⠉⠉⠁⣶⣿⣿⣿⣿⣿⣾⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⢿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠑⠂⣠⢴⣛⣻⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⢿⢇⣐⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣯⢿⣒⣚⢽⣟⠻⣿⣿⣿⣿⢟⡅⣿⢹⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⡻⢾⣭⣟⢾⡿⣷⣯⣷⣮⣟⠇⣿⢙⣶⣿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣝⠍⣓⢕⡦⢭⡿⠏⠿⢃⢿⣈⠿⡞⣟⣸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣇⠾⡻⣿⣿⣿⣿⣿⣰⣮⢙⣂⣈⡛⣛⣟⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢾⣿⣽⣿⣇⣿⣿⠊⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣷⠀⣿⡏⢹⣿⣯⣷⣐⣮⢙⣷⢰⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣷⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠰⣖⣤⠄⣘⡛⣿⣿⣼⣧⡞⣳⣸⠃⠀⢻⡟⠃⣿⣿⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣯⣯⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣓⣥⣥⡤⠤⠼⠃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣕⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡛⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢓⣀⣼⣿⣟⠛⠀⠀⠈⢩⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣤⣤⠄⠤⠂⠒⠲⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⢀⠀⠤⠤⠄⣀⣀⣄⣶⣦⣶⣾⣿⣿⣗⡛⡉⡉⠀⢀⢀⡀⠀⠄⠂⣂⠩⠡⠒⢀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣅⣽⣿⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣆⣾⡫⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⠛⢛⠛⠛⠛⣛⠛⠛⠛⠛⢛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣌⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣸⣶⣧⢱⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⠤⠠⠀⠀⠤⠤⠤⠀⠠⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢏⠉⠉⠁⣶⣿⣿⣿⣿⣿⣾⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠑⠂⣠⢴⣛⣻⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣐⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣯⢿⣒⣚⢽⣟⠻⣿⣿⣿⣿⢟⡅⣿⢹⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠻⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⡻⢾⣭⣟⢾⡿⣷⣯⣷⢮⣟⠇⣿⠙⣶⣿⣿⣿⡇⣿⣘⣋⢻⣦⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣝⠍⣓⢕⡦⢭⡿⠯⠿⢃⢿⣈⠿⡞⣟⣸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣇⡾⡻⣿⣿⣿⣿⣿⣰⣮⢙⣂⣈⡛⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣯⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢾⣿⣽⣿⣇⣿⣿⠋⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡷⠠⣿⡏⢹⣿⣯⣷⣐⣮⠙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣷⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⡟⣳⣸⠃⠀⢻⡛⠃⣟⣿⣛⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠿⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣓⣥⣥⡤⠤⠼⠃⣘⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢸⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⣕⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢛⣁⣼⣿⣟⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣤⣤⠤⠀⠐⠒⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⡀⠤⠤⢄⣀⣀⣄⣲⣶⣴⣾⣿⣟⣛⡛⡋⢉⡀⢀⢀⡀⠀⠀⠐⣂⠩⠡⠲⢀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⣛⣛⡛⠛⡛⠛⢛⢛⠛⣛⣛⡛⠛⠃
⠀⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠡⢙⣿⣿⣿⣿⣷⡀⠀⠀⠂⠸⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣿⣀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢠⣤⣤⣤⣄⣠⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠟⢿⡗⠛⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⣿⣿⠰⣿⡙⠃⠀⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⢖⣛⠿⢇⢛⡿⣿⣿⣿⣳⣶⢹⢹⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠇⢸⣿⡿⠃⣴⣾⣿⣿⠀⠀⠀⠀⢿⣿⣫⡭⡝⣿⡃⣷⢲⡁⣏⣳⢸⠸⢿⡄⢿⣿⣏⣏⣻⡾⣞⣿⢟⣯⣼⣶⣶⣶⣶⣶⣯⣝⡻⣿⣿⣇⢟⣘⣻⣟⣟⣸⣃⣿⣬⣻⠾⠋⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠘⣉⣠⣾⣿⣿⣿⣿⠂⠀⠀⠀⢘⣛⣻⡗⣣⢻⡡⢻⣸⡇⣿⣶⡾⠯⠸⢥⣻⣿⣿⣝⣍⢿⣮⣒⣍⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣎⣟⡕⣩⣛⣞⣛⣛⡛⣛⣛⣿⣿⣀⡀⠀⣀⣛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣧⣥⣿⡞⣿⣷⡶⠿⠷⡖⢛⡛⡛⡟⢿⣿⣿⣿⣷⣵⣲⠿⠿⠃⠀⠰⠟⠛⠛⠋⠞⢿⣿⣹⣿⣂⣿⣿⡈⢹⡏⠁⣿⡏⠽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⠿⠿⢿⣿⣿⣿⣿⣅⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⡷⠀⣿⡏⠁⣿⣯⣷⠐⣬⢙⣷⢡⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⢸⣿⣿⢟⣆⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣯⣭⣛⢿⣿⣿⣿⡾⣿⣿⡇⠀⣶⡤⣀⣘⠛⣛⣻⣼⣷⣟⣃⢘⡗⠀⢛⡛⠃⢛⣻⣻⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣫⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣷⡝⣯⣷⣿⣻⣿⣷⠀⢸⣿⣿⣶⣿⣥⣴⣞⣋⣥⣭⠽⢅⣀⣘⣃⣈⣸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⢧⢱⡟⠆⢻⣁⣽⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣿⡽⣿⣿⣇⢿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣐⠽⣇⢿⠸⠤⠃⠇⣿⣻⣡⣛⣼⣬⣧⡭⣭⣽⣿⢻⣿⣾⣿⣝⢛⣋⡘⣿⣿⡄⢠⣬⣉⣉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⢹⣿⡦⠖⠿⡿⢛⣛⢛⡻⠿⣭⢭⡟⣵⢢⠳⣆⣦⢸⣣⣿⣿⣿⣯⣻⣷⢻⣿⣷⠀⢻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣴⣶⣶⡆
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⣮⠩⢹⡸⡇⣿⢸⠀⡏⢿⢸⣗⠛⠛⠛⠛⠓⠱⣾⣿⣿⡄⠘⣿⣿⣶⣶⣯⣭⣭⣭⣿⣟⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣻⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⣿⣿⠮⠭⣁⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠉⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠠⠨⠿⠿⠟⠃⠀⠀⢻⣿⣯⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣀⣠⠤⠄⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⡀⠤⠤⠀⠀⠀⢀⠐⠂⠔⠦⠾⠛⣚⢋⡉⠉⠀⠀⢀⣀⠠⠀⠂⣀⠠⠄⠀⠤⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣛⠛⠛⠛⠛⠛⠛⠛⡛⠛⡛⢛⣛⠃
⠀⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠄⠤⠤⠄⠄
⠀⠀⣹⣿⣿⣿⣿⣦⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⢿⣿⡿⠿⢿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠻⣟⡉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⠟⠻⣿⣿⡆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣸⣿⣿⡖⣻⡛⠟⢭⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣛⣛⣛⣛⡿⢿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠏⣰⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡐⣿⠿⡿⣿⣿⣿⢟⣩⣶⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⣿⣿⠇⠿⣘⣟⣟⣟⣸⣃⣿⣬⡛⠾⠋⠐⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣠⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⣻⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⡹⠯⠸⣬⣁⣶⣮⣗⣾⡯⠬⣭⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣇⢏⣟⡭⣋⣛⢛⣛⣛⡛⣻⣟⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣧⣯⣿⣸⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣾⣫⠽⣏⣟⣻⠿⠃⠀⠠⠿⠙⠿⠭⠳⠯⢿⣿⣺⣿⡄⣿⣻⠈⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡃⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⡛⣿⣿⣿⣿⣿⣅⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢻⣯⣼⡇⢸⡇⠀⣿⡏⢹⣿⣯⣷⠐⣮⢙⣷⢠⣤⣤⣤⣤⣬⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣟⣵⣇⣿⣹⢈⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣭⡻⣿⣿⣿⡷⢿⣿⣿⠀⢰⣒⣤⢀⣘⠻⣾⣿⣼⣧⢺⢳⡞⡛⢸⠛⠛⣻⣿⣿⣟⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣷⣿⣏⣿⣿⡆⠘⣿⣿⣿⣷⣾⣭⣥⣶⣞⣊⣬⣥⠤⠼⢀⣁⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⡟⣿⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⡿⣯⢿⣿⣿⡼⣿⣿⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣧⣌⠻⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⡧⣯⣭⣽⠿⣿⣿⣿⣯⡛⣩⣥⢻⣿⣧⠀⢦⣤⣍⣉⣙⡛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⡟⣿⣷⡦⠺⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⠵⣆⣶⢺⣣⣿⣿⣿⣞⢿⡞⣿⣿⡄⠘⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⢺⣿⣿⣧⠀⢻⣿⣿⣷⣶⣾⣭⣭⣭⣭⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠂⠧⣟⣞⣻⣟⠿⠿⢮⣉⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣛⡀⠿⢿⡛⠛⠀⠀⠈⢭⣭⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃⠀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣀⣤⣤⡀⠴⠄⠒⠶⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⠀⠤⠤⢄⣀⣠⣄⣦⣴⣴⣯⣿⣺⣟⣛⣙⡁⡀⣀⢀⠀⠂⠀⢒⣊⠩⠁⠖⠀⠈⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢏⠻⣿⣪⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣺⣟⣿⡥⠻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⢛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠋⠁⠉⠉⠀⠀⣸⣿⣿⣟⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⠤⠀⠀⠀⠤⠄⠀⠀⠤⠤⠴⠠⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢗⣤⢄⣀⣠⡪⣝⣛⣛⣻⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢾⣿⣗⣮⠭⢭⢷⣒⣾⣿⡿⣿⡿⢣⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢧⣹⡷⡇⣿⢙⣷⢿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢿⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⠬⣵⣃⡛⡈⢿⣛⡟⣽⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣽⣭⣭⣭⣭⣭⣭⣥⣭⠉⠉⠉⣯⣝⢸⣿⣿⢹⣿⣿⣿⣒⢙⣈⣁⡈⣙⣿⣿⣃⣀⡀⠀⣘⣛⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣭⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢽⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⣇⢸⡏⠀⣿⡏⢹⣿⣯⣷⠐⣮⠙⣷⢠⣤⣤⣤⣤⣬⣬⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⢘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⣟⡇⡞⠃⠀⠛⡛⢻⣟⣿⣟⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣖⣚⣭⣬⡤⠤⠜⠃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠖⠿⣿⢛⣛⢛⡻⠿⣭⢭⡛⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣟⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⡿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣁⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣠⣤⠠⠄⠀⠐⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡀⠀⠤⠤⠀⣀⣀⣀⣲⣴⣶⣶⣵⠟⣚⡛⡉⣁⠀⡀⡀⠀⠀⠀⢐⣀⠠⠤⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣷⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣞⣻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠀⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⡿⣻⡽⢦⣤⠤⢤⣒⣛⣿⣿⣶⣮⣟⢿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⢛⠛⢛⢛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢱⣿⣯⣗⠒⣒⢲⣬⢽⣾⣿⣿⣿⣿⣾⣿⢐⠀⠠⠤⠀⠀⠀⠠⠀⠀⠀⠄⠤⠤⠁⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣜⢿⣿⢱⢿⣇⡿⣿⡇⣿⣿⣿⡿⣻⣾⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⢇⠸⡛⡇⢹⠟⣿⢫⢵⢾⣿⢿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢊⣾⡇⣿⢙⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⣾⣾⣿⡇⣿⢙⣷⣺⣯⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣶⡹⣿⣇⣻⣘⣿⠙⡛⢸⣁⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣯⣭⣭⣥⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣇⣀⣀⡀⣘⣿⣿⣇⣀⡀⠀⣘⣛⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠈⢹⡯⠁⣿⡏⣽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡧⢸⣯⠀⣿⡏⢹⣿⣯⣷⢐⣮⠙⣷⢰⣤⣤⣤⣬⣭⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⡟⡇⠜⠓⠀⢛⡟⣻⣿⣻⣻⣿⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣻⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣭⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠜⠃⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣟⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⡿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣂⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣤⣤⠤⠤⠄⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠤⠤⢀⣀⣠⣠⣴⣦⣶⣷⣴⢓⢛⡛⢉⣩⠀⣀⠀⠀⠠⠄⢒⣒⠩⠡⠖⠀⠈⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⣼⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⢳⣓⣿⣉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄⠀⠀⠈⠛⠧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⡶⠿⠿⣟⣛⣛⣳⣶⣤⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⢟⣧⡞⢭⣉⢽⣶⣿⣿⣿⣧⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢯⡟⣹⣳⠟⣿⡇⣿⣿⣿⣿⡿⠀⠀⠀⠠⠀⠀⠠⠤⠄⠤⠅⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣣⣷⢯⣼⡿⡽⠿⠿⡛⠋⢰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠍⢾⡿⡇⠾⢽⣞⡸⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⡿⣿⣹⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣻⡏⣿⡇⣿⢌⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣘⣟⡟⠃⠝⠃⣟⣬⡛⠾⠋⠐⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣯⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⣊⣘⣿⣇⣀⡀⠀⣘⣛⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡩⢹⣯⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡿⢺⡇⠀⣿⡏⣽⣿⣯⣷⠐⣮⠙⣷⢰⣦⣤⣤⣤⣬⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣧⣞⣗⠘⠃⠀⢛⡟⣿⣿⣿⣿⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣖⣚⣥⣤⡤⠤⠜⠃⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠾⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣅⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣀⣾⣿⣟⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣁⣤⣤⠀⠄⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⠄⣀⣠⣠⣐⣶⣖⣶⣼⣟⣚⣛⡙⣉⢀⡀⠀⠀⠀⠄⢀⣂⠨⠥⠖⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡿⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣧⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣯⣥⣤⣤⣤⣀⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣾⣟⡿⠴⢖⣛⣛⣻⣽⣿⣷⣯⡛⡛⠛⠛⠛⠛⠛⠛⣛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠠⠀⠀⠄⠀⠤⠤⠀⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⣾⢠⣯⡏⣹⣿⢸⣿⣿⣿⡿⢏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡩⢵⡞⠶⠿⢯⢯⣭⣍⣑⠈⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢻⣿⡟⣿⣿⢴⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣙⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣟⣟⢛⠸⣃⣿⣨⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣥⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣛⣛⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣿⠀⣿⣯⣽⣿⣯⣷⢐⣮⠙⣷⢰⣦⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣧⡟⡃⠘⠓⠀⡟⣛⣿⣟⣿⣿⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣭⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠇⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣂⣾⣿⣟⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣁⣤⣠⠀⠄⠀⠐⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠤⠤⠀⣀⣀⣤⣤⣤⣔⣶⣾⣟⣛⢛⣙⢁⢀⢀⡀⠀⠠⠄⠐⣂⠨⠥⠔⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡵⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣾⣟⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢫⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡏⠀⣠⠁⠉⠉⢁⣭⣽⣛⠿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⣹⣾⠷⣶⣖⣒⣷⣾⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠄⠠⠤⠴⠄⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡷⣿⡽⣖⣒⣢⠭⢭⣿⣿⣿⣿⣿⣿⢧⣿⣿⡯⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠟⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠟⣾⢷⣵⠿⡷⣝⠿⢿⡿⢿⣫⢾⣿⣿⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡹⡈⢗⣃⠁⣿⢙⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡊⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢿⣿⣇⣿⢀⡛⣞⠛⢸⣃⣿⣬⡛⠾⠋⠐⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣀⡈⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡋⢹⡟⠁⣿⣯⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡇⠀⣿⡏⢽⣿⣯⣷⠐⣮⢙⣷⢰⣦⣤⣤⣬⣥⣥⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣾⣯⣟⢿⣿⣿⡿⢻⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣧⡟⣓⠙⠃⠀⢻⠛⢻⣻⣻⣿⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣓⣭⣤⡤⠤⠾⢀⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣧⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⢦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣃⣾⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣤⣤⠤⠤⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⠀⣀⣠⣤⣲⣶⣶⣶⣿⢿⣚⡋⡉⡉⣀⣀⢀⠀⠠⠀⠂⣊⠡⠡⠔⠀⠙⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡵⣿⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣾⣟⢽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢫⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡏⠀⣠⠁⠉⠉⢁⣭⣽⣛⠿⣿⣿⣿⣿⣿⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⣻⣾⢷⣶⣖⣒⣷⣾⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⠀⠀⠤⠀⠀⠀⠤⠄⠠⠤⠤⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⡷⣿⡽⣖⣒⣪⠭⢭⣿⣿⣿⣿⣿⣿⢧⣿⣿⡯⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠟⣾⢷⣵⠿⡷⣝⠿⢿⡿⢿⣫⢾⣿⣿⢇⣀⠀⠠⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡹⡈⢗⣃⠁⣿⢙⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡱⣧⢿⣿⣇⣿⢀⡻⣞⠛⢸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣀⡈⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡋⢹⣏⠁⣿⣯⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡇⠀⣿⡏⢽⣿⣯⣷⠐⣮⠙⣷⢰⣦⣤⣤⣤⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣷⣿⣭⣿⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣧⡟⣳⠘⠃⠀⢻⠛⢻⣛⣻⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣾⣓⣭⣤⡤⠤⠾⠀⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣧⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣯⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣄⣤⠤⠠⠀⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⠀⣀⣠⣤⣲⣦⣶⣶⣯⣿⣚⡛⣛⣉⣀⡀⡀⠀⠀⠄⢒⣊⠩⠥⠖⠀⠘⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠤⠀⠀⠠⠄⠀⠀⠀⠤⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣛⠟⢬⠻⡿⣿⣿⣟⣶⡇⡇⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⡿⣉⣿⣻⡹⢿⣫⣵⣶⣾⣿⣿⣷⣶⣮⣝⡻⣿⣿⡇⣛⣘⢿⣟⣟⣸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣧⡧⣸⢷⢯⣎⣉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⢸⣫⣪⣟⣵⣿⣿⣿⡛⣛⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣯⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣵⡟⠛⠛⠀⠀⠮⠛⠛⠏⠓⠻⢿⣿⣺⣿⣃⣿⣿⠈⢹⣿⠁⣿⣏⠽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣄⣀⡀⣤⣤⣄⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⣿⠄⣿⡏⠡⣿⣯⣷⣐⣮⠙⣷⢠⣤⣤⣤⣤⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠀⣿⣿⡿⣳⣇⣿⣹⢘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣶⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣽⣿⣼⣷⢜⣃⣸⠃⠀⣛⠛⠃⣻⣻⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣷⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣞⣚⣭⣭⡤⠤⠟⢀⣂⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣧⢲⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣕⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠚⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⢿⢿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣒⣂⣾⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⣠⣤⠀⠔⠀⠂⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⡀⣀⣀⣤⣴⡢⢶⣷⣿⣟⣛⠋⣛⣉⡀⢀⣀⠀⠠⠀⢐⣈⠈⠡⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⠐⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣛⣛⣛⡛⣛⣛⠛⣛⠛⠛⢛⠛⣛⠃
⠀⣿⣿⣿⣿⣶⣄⡀⠀⠀⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠡⢉⣿⣿⣿⣿⣷⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣿⣀⠀⠀⠄⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢠⣤⣤⣤⣄⣠⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠟⢿⡗⠛⢿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⣿⣿⠰⣿⡙⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⢸⣿⣿⣿⠛⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⢖⣛⠿⢇⠛⡿⣿⣿⣿⣳⣶⢹⢹⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⢸⣿⡿⠃⣴⣾⣿⣿⠀⠀⠀⠀⢿⣿⣫⡭⡝⣿⡃⣷⢲⡁⣏⣳⢸⠘⢿⡄⢿⣿⣿⣏⣻⡾⣞⣿⢟⣯⣼⣶⣶⣶⣶⣶⣯⣝⡻⣿⣿⣇⢟⣘⢻⣟⣟⣸⣃⣿⣬⣻⠾⠋⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠘⢉⣠⣾⣿⣿⣿⣿⠆⠀⠀⠀⢘⣛⣿⡗⣣⢿⡡⢻⣸⡇⣿⣶⡾⠯⠸⢥⣻⣿⣿⣜⢌⢿⣮⣂⣍⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣎⣟⡵⣩⣋⣜⣛⣛⡛⣻⣿⣿⣿⣀⡀⠀⣀⣛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣧⣧⣿⡾⣿⣷⡶⠿⠷⡖⢛⡛⡛⡟⣿⣿⣿⣿⣷⣵⣶⠿⠿⠃⠀⠰⠟⠛⠛⠫⠚⢿⣿⣹⣿⣊⣿⣿⡈⢹⡏⠁⣿⣏⠽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⠿⠿⢿⣿⣿⣿⣿⣅⣀⣀⢠⣤⣤⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⡷⠀⣿⡏⠁⣿⣯⣷⠐⣬⢙⣷⢡⣤⣤⣤⣤⣬⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠂⢸⣿⣿⢟⣆⣿⣹⢘⢇⠿⣰⠬⣧⣼⣻⣿⣿⣿⣯⣭⣻⢿⣿⣿⣿⡾⣿⣿⡇⠀⣲⡤⣀⣘⠛⣛⣻⣼⣧⡟⡃⢘⡗⠀⢛⡛⠃⢛⣻⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣻⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣷⡝⣯⣷⣿⣻⣿⣷⡀⢹⣿⣿⣶⣯⣥⣴⣟⣛⣥⣭⠽⠥⣀⣘⣓⣀⣸⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⢧⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣗⡽⣿⣿⣇⢿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣐⠽⣇⢿⠸⠤⠃⠇⣿⣻⣡⣛⣼⣬⣧⡯⣭⣽⣿⢻⣿⣿⣿⣝⢛⣋⡘⣿⣿⡄⠠⣤⣉⣉⡛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⢹⣿⡦⠖⠿⡿⢛⣛⢛⡻⠿⣭⢭⡟⣵⢢⠱⣆⣦⢸⣣⣿⣿⣿⣯⣻⣷⢻⣿⣷⠀⢻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣧⣤⣤⣴⣶⣶⡆
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⣮⠩⢹⣸⡇⣿⢸⠀⡏⢿⢸⣗⠛⠛⠛⠛⠓⠱⣾⣿⣿⡄⠘⣿⣿⣶⣶⣯⣭⣭⣽⣿⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣻⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣞⣻⣟⣿⣿⠮⠭⣁⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣧⠀⠉⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠠⠸⠿⠿⠟⠃⠀⠀⢻⣿⣯⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣀⣠⣠⠀⠤⠶⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⡀⠤⠤⣀⢀⣠⣤⠤⡶⣴⣾⡿⢓⣛⣛⡋⢉⡀⠀⢀⣀⠀⠄⠂⣀⡈⠁⠲⠠⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⢏⠻⣿⣪⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣾⣝⣿⡭⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⡛⢛⡃
⠀⣿⣿⣿⣿⣦⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠋⠉⠍⠉⠀⠀⣹⣿⣿⣿⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⣿⠀⠠⠀⠤⠀⠀⠤⠠⠄⠀⠀⠄⠤⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢗⣤⢄⣀⣠⡪⣝⣛⣛⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣷⣯⠭⢽⣶⣒⣾⣿⡿⣿⡿⢳⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣮⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣺⣛⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡣⠸⣫⢧⣹⡇⡇⣿⢹⣷⢿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⠬⣵⣇⡛⠈⢿⣛⡟⣹⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣽⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣗⢑⣀⣁⡈⣙⣟⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢿⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡯⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡇⢸⣗⠀⣿⡏⢹⣿⣯⣷⣐⣮⢙⣷⢠⣤⣤⣤⣤⣬⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⢘⢇⡟⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⠄⣘⡛⣿⣿⣼⣷⣟⡇⡜⠃⠀⠛⡛⢻⣟⣻⣻⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣿⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠜⢃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣄⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣅⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣂⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣠⣤⠤⠴⠀⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⠄⣀⣠⣠⣤⣶⣶⣿⣿⣿⣛⡛⣿⣁⣀⠀⣀⡀⠀⠔⢐⣊⠩⠡⠖⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣬⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢏⠻⣿⣪⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⡭⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⠋⠉⠍⠉⠀⠀⣻⣿⣿⣟⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠄⠀⠀⠤⠠⠄⠀⠀⠀⠄⠤⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢗⣤⢄⣀⣤⡪⣝⣛⣛⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡯⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣷⣯⠭⢽⣶⣒⡾⣿⡿⣿⡿⢳⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣮⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡟⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣺⣛⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢧⣹⡇⡇⣿⢙⣷⢿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⢬⣵⣇⡛⠈⢿⣛⡟⣼⣃⣿⣮⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢿⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣗⢑⣀⣁⡈⣙⣟⣻⣃⣀⡀⠀⣘⣛⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢯⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣸⣿⣏⣿⣿⠈⢹⣏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡇⠀⣿⡏⢹⣿⣯⣷⡐⣮⢙⣷⢠⣤⣤⣤⣤⣬⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣿⢿⣿⣿⡿⢹⣿⣿⠀⢠⣖⣤⢄⣘⡛⣿⣿⣼⣷⣞⡇⡜⠃⠀⠛⡛⢻⣛⣿⣿⣼⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣼⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣷⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠜⠃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢲⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣌⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣂⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣤⣤⠤⠴⠂⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠄⠀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣛⣛⣭⣁⣀⠀⡀⠀⠀⠀⢀⣂⠩⠅⠖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣷⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣞⣻⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⡵⢶⣤⠤⢤⣒⣛⣿⣿⣷⣯⣟⢿⣿⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⢛⠛⢛⠛⢛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⢱⣿⣯⣗⠒⣒⢢⣬⢵⣾⣿⣿⣿⣿⢾⣿⠠⠄⠄⠀⠀⠀⠄⠀⠄⠀⠠⠠⠤⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣜⢿⣿⣱⢿⣇⡿⣿⣇⣿⣿⣿⡿⣫⣾⡷⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⡿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⢇⠸⡋⡇⢸⠟⡿⢫⢵⢾⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣌⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⢪⣾⡇⣿⢙⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣺⣟⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⣾⣾⣿⡇⣿⢙⣷⣺⣯⣿⡇⣿⣘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⡹⣿⡇⣻⣘⣿⠙⡓⢸⣁⣿⣭⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣇⣀⣈⡀⣘⣟⣿⣃⣀⡀⠀⣘⣛⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⠈⢹⣏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡧⢸⣗⠂⣿⡏⢹⣿⣯⣷⣐⣮⠙⣷⢠⣤⣤⣤⣤⣬⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠀⣿⣿⡿⣵⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⢠⣖⣤⢄⣘⡛⣿⣿⣼⣷⣟⡇⠜⠋⠀⢛⡟⣻⣿⣿⣟⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠜⢃⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣅⠽⣇⢿⢸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣅⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⡿⠿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣂⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣤⣤⠤⠄⠀⠲⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠤⠤⠄⣀⣠⣠⣤⣶⣶⣿⣿⣿⣛⣛⣟⣁⣀⠀⢀⠀⠀⠄⢀⣂⠩⠡⠖⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⣼⡟⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠙⢳⣓⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠄⠀⠀⠘⠛⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⡶⠿⠿⢟⣛⣛⣳⣶⣤⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⢟⣿⣞⢍⣉⢽⣶⣿⣿⣿⣮⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⢛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢯⡟⣹⢳⠟⣿⡇⣿⣿⣿⣿⣿⠘⠀⠠⠀⠄⠀⠀⠄⠄⠤⠤⠀
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣢⣿⢧⣼⡿⡼⠿⠿⠛⠋⢰⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠭⢾⣿⡇⠾⢽⣞⡺⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⡿⣿⣱⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣺⣟⠟⢭⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣻⡇⣿⡇⣿⢌⣛⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣘⣟⡟⠃⠜⠃⣿⣭⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀⣂⣘⣿⣇⣀⡀⠀⣘⣛⡃⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡩⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡿⢺⣇⠀⣿⡏⣽⣿⣯⣷⡐⣮⢙⣷⢠⣤⣤⣤⣤⣬⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣧⣟⣗⠘⠃⠀⢛⡟⣿⣿⣿⣿⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣥⣤⡤⠤⠜⠃⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣄⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⡿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢚⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣤⣤⠤⠤⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⢀⠤⠄⠄⣀⣠⣤⣴⣶⣶⣾⣿⣿⣛⢋⣍⣃⣀⠀⢀⡀⠠⠀⢐⣂⠨⠥⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣱⡟⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣥⡿⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣻⣥⣤⣤⣤⣀⡈⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣾⣟⡷⠤⢒⣛⣛⣻⢽⣿⣷⣭⡛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢟⣭⣽⢟⣭⣔⣿⣿⣿⣿⣿⣷⠀⠀⠀⠠⠤⠀⠀⠀⠀⠄⠤⠤⠅
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⣾⢠⣏⠏⣽⣿⣸⣿⣿⣿⡿⠏⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠟⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⡩⢴⡎⢶⡿⢯⢯⣭⣍⣑⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⡂⣿⢹⣷⢹⣿⡟⣿⣿⠵⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣺⣛⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡅⣿⢹⣷⣸⣷⣷⡇⣿⠒⣉⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣐⣟⣟⣛⠸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣥⣭⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⡀⣻⣛⣻⣃⣀⡀⠀⣘⣛⡃⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡉⢹⡏⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣯⣼⡇⢸⡇⠀⣿⣯⣽⣿⣯⣷⠐⣮⠙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⢠⣖⣤⢄⣘⡛⣿⣿⣼⣷⡞⡃⠘⠃⠀⡟⣻⣿⣟⣿⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⣿⣿⣿⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡋⡭⣽⢻⣿⣿⣯⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣤⡤⠤⠧⢛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣌⠽⣇⢿⠸⠬⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠞⠿⣿⢟⣛⢛⡻⠿⣭⢭⡛⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣅⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣇⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣂⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⣠⣤⡤⠤⠀⠲⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠄⠀⣀⣠⣠⣤⣦⣶⣿⣿⣟⣛⣛⣍⣁⣀⡀⡀⡀⠀⠀⢀⣂⠨⠅⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡝⣿⡷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣾⣟⢝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⢫⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⠁⠉⠉⢁⣭⣟⣛⠿⣿⣿⣿⣿⣿⢛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣳⣾⠷⣶⣖⣒⣶⣿⣿⣿⣿⣿⣮⢻⣿⣿⣿⠀⠀⠄⠀⠀⠀⠠⠀⠄⠀⠄⠀⠠⠤⠤⠅
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡷⣿⡽⣖⣒⣪⢭⢭⣾⣿⣿⣿⣿⣿⢧⣿⣿⡷⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⣽⠟⣾⢷⣵⡿⡿⣝⠿⢿⡿⢿⣫⢾⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⡱⡈⢗⣃⠁⣿⢙⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣺⣛⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⡂⣿⣧⡃⣿⢙⣧⣽⣯⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡹⣧⢿⣿⣇⣿⢀⡻⣞⠟⣼⣃⣿⣮⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣭⣭⣭⣭⣭⣭⣭⣥⣭⠉⠉⠉⣿⣿⣿⣿⣶⣶⣝⣛⣛⣸⣏⣘⣀⡈⣛⣛⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣭⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢿⣿⣻⣿⣏⣿⣿⡋⢹⣯⠁⣿⣯⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡗⠀⣿⡏⢽⣿⣯⣷⢐⣮⢙⣷⢠⣤⣤⣤⣤⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣳⣇⣿⣹⠘⢇⡟⣰⠬⣧⣼⣻⣿⣿⣾⣿⣭⣟⢿⣿⣿⡿⢹⣿⣿⠀⢠⣖⣤⠄⣘⡛⣿⣿⣼⣷⡞⣓⠟⠋⠀⣻⠛⢻⣟⣿⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣛⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣭⣤⡤⠤⠾⢀⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢾⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⢸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣜⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⣭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣷⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⣤⣤⠤⠔⠆⠒⠖⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠤⢀⣀⣠⣤⣤⣶⣶⣾⣿⡟⣛⣻⣻⣍⠀⠀⠀⠀⠀⠄⠐⣀⠨⠤⠖⠂⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⢟⣿⡄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣟⣅⣽⣟⢝⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣀⡀⠂⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⡎⣾⣫⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣶⣧⣱⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠄⠀⠤⠤⠤⠅
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢏⠉⠉⠀⣾⣿⣿⣿⣿⣿⣾⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⠿⣿⡿⠿⢿⣇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀⠑⠀⣀⢴⣛⣻⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣤⣴⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣯⢿⣒⣚⢭⣛⠻⣿⣿⣿⣿⢟⡅⣿⢹⣷⢿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣺⣛⠟⢬⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⡻⢾⣭⣟⢾⡿⢷⣯⣷⣮⣛⠇⣿⢙⣶⣿⣿⣿⡇⣿⢘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣝⠌⡓⢕⡦⢭⣿⠎⠿⢃⣿⣈⠿⡞⣟⣸⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⡡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣯⣭⣭⣭⣭⠉⠉⠉⣇⠮⡿⣿⣿⣿⣿⣿⣰⣮⢙⣂⣈⡙⣛⣻⣻⣇⣀⡀⠀⣘⣛⡃⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠻⠿⠿⢾⣿⣹⣿⣅⣿⣿⠊⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡷⠀⣿⡏⢹⣿⣯⣷⠐⣮⢙⣷⢠⣤⣤⣤⣤⣭⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⢘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣿⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⢠⣖⣤⢄⣘⡛⣿⣿⣼⣧⡞⣳⣸⠃⠀⢻⡟⠃⣿⣻⣿⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣧⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣓⣥⣥⡤⠤⠼⣇⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣾⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣄⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⣭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢰⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⣿⣷⡦⠾⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⡏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣼⣿⣛⠛⠀⠀⠈⢭⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣁⣠⣤⠤⠤⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⢀⠤⠤⠄⠀⠀⠀⠠⠖⣴⣾⡿⣞⣓⣙⣫⡉⡀⠀⠀⡀⠀⠄⠐⣀⠨⠤⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⡛⣛⡛⢛⠛⢛⣛⡛⠛⠛⠛⠛⢛⠃
⠀⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠁
⠀⠩⢙⣿⣿⣿⣿⣷⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⡿⢿⣷⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⢿⣿⣀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⢠⣤⣤⣤⣄⣠⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⡿⠟⢿⠗⠛⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡟⣿⣿⠰⣿⡙⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡇⢸⣿⣿⣿⠛⣿⣿⣷⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⣿⣿⣦⢖⣛⠿⢃⠛⡿⣿⣿⣿⣳⣶⢹⢻⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠇⢸⣿⡿⢃⣴⣾⣿⣿⠀⠀⠀⠀⣿⣿⣫⡭⡝⣿⡃⣷⢲⡁⣏⣳⢸⠼⢿⡄⣿⣿⡇⡯⣿⡼⡜⣿⢟⣯⣿⣶⣶⣶⣶⣾⣭⣟⡻⣿⣿⣇⢟⣘⢻⣟⣟⣸⣃⣿⣬⣻⠾⠋⠀⠊⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠘⣉⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⢘⣛⣻⡗⣣⢻⡡⢻⣸⡇⣿⣶⠾⠯⠸⢥⣹⣿⣿⣝⣍⢿⣮⣊⣏⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣎⣟⡕⣭⣋⣞⣛⣛⡛⣛⣿⣿⣟⣀⡀⠀⣀⣛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣧⣥⣿⡞⣿⣷⡶⠿⠷⡖⢛⡛⡛⡞⣿⣿⣿⣿⣿⣵⣺⠿⠿⠃⠀⠰⠟⠛⠛⠫⠿⢿⣿⣹⣿⣎⣿⣿⠈⢹⡏⠁⣿⣏⠽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⠿⠿⢿⣿⣿⣿⣿⣅⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⢸⣿⣽⣿⢿⣧⣼⡇⢸⡷⠀⣿⡏⠁⣿⣯⣷⠀⣬⠙⣷⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⢏⣆⣿⣹⠘⢇⠿⣰⠬⣧⣾⣻⣿⣿⣯⣭⣭⣛⢿⣿⣿⣿⡾⣿⣿⡆⠀⣲⡤⣀⡘⠛⣛⣻⣼⣷⡟⡃⢘⡗⠀⢛⠛⠃⢛⣿⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣳⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣷⣝⣯⣷⣿⣻⣿⣷⠀⢻⣿⣿⣶⣯⣥⣶⣟⣋⣥⣥⠿⢅⣀⣘⣐⣐⣸⣿⣿⢿⣿⣿⡿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⢷⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⢸⣿⣿⣿⣇⡻⣿⣿⣏⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣔⠽⣇⢿⠸⠤⠃⠇⣿⣻⣡⣛⣼⣬⣧⣯⣭⣽⣿⢿⣽⣿⣿⣙⢛⣋⡸⣿⣷⡀⢠⣬⣉⣉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⢻⣷⡦⠖⠿⣿⢛⣛⢛⣻⢿⣭⢭⡟⣵⢢⠳⣆⣦⢸⣣⣿⣿⣿⣯⣻⣧⢿⣿⣧⠀⢻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣶⡆
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠐⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠩⢹⠸⡇⣿⢸⠀⡏⢿⢸⣗⠛⠛⠛⠛⠓⠱⣾⣿⣿⡄⠘⣿⣷⣶⣾⣭⣭⣭⣿⣿⣛⣛⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⣿⣷⡮⠭⣁⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠙⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠤⠸⠿⠿⠿⠃⠀⠀⢻⣿⣯⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡋⣀⣠⣠⡄⢠⠰⠴⠆⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⡠⠤⠄⣐⣠⣤⣠⣴⣶⣾⣷⡿⢛⡿⢟⠉⠉⠀⠀⢀⠀⠀⠒⣂⡠⡨⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡛⠛⠛⠛⠻⠿⠿⠿⠿⠛⠛⠻⠇
⠀⣿⣿⣷⣶⣄⠀⠀⠀⠠⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⣭⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠁⠀
⠀⠙⣿⣿⣿⣿⣷⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⢿⣿⡀⠀⠀⡀⢹⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⣿⣿⢿⣿⢿⢀⣀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣤⣤⣤⣄⣀⣽⣇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⠟⢿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⡞⢿⠇⠺⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇⣿⢹⣷⣿⣿⣿⡇⣿⢘⣉⢻⣆⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⠏⣰⣾⣿⣿⠀⠀⠀⠀⢹⣿⣿⣫⡭⡍⣷⡋⣷⢲⡀⣏⣳⢸⡼⢻⡕⣿⣿⣿⣿⣿⣿⡿⣫⣵⣶⣿⣿⣿⣿⣿⣷⣮⡝⣿⣿⣿⣇⣿⣘⣿⣟⣟⣸⣃⣿⣬⠛⠾⠋⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠛⢁⣴⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣟⣻⡗⣣⢻⡡⢻⣸⠗⣿⡐⠸⠷⠸⣮⣡⣤⣷⡯⣽⣯⣾⣟⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣸⢟⣕⡺⣊⣟⢛⣿⣿⡿⣿⣿⣿⣀⣀⡀⠀⢟⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣧⣥⡿⣼⣿⣷⡶⠷⠶⡶⢛⡶⡊⢿⣧⣿⢟⣛⢛⡷⣾⡿⠀⠀⢸⣟⠛⣛⢛⢽⣛⣿⣿⣺⡿⣅⣿⢿⠈⢹⡏⠁⣿⡯⢽⣿⣏⣿⠀⣿⣈⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⡃⡖⡶⢸⡇⡇⠸⣌⠀⢣⡷⠿⠿⣿⣿⣷⣿⣿⠃⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⢺⣯⣼⡇⢸⡇⠀⣿⡏⣽⣿⣏⣷⠀⣬⠙⣷⢠⣬⣤⣤⣤⣀⣤⣤⣤⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣟⣵⣇⣿⣹⠘⢇⠿⣰⠬⣧⣼⣻⣿⣯⣭⣭⣟⢿⣿⣷⣶⡞⣿⣿⡇⠀⣠⣤⣀⡀⠘⣿⣽⣿⣼⣧⢸⢣⠜⠃⣶⠛⠛⣿⣛⣿⣛⣾⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⢿⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣭⠿⣿⣷⡝⣛⣽⣶⣻⣿⣿⡀⢸⣿⣿⣶⣯⣤⣿⣛⣩⣭⡿⢟⣐⣀⣟⣀⣠⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡏⣿⢱⡟⠎⢻⣁⣿⡏⡆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⡹⣿⣿⣧⢿⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⢐⢝⠿⣇⢿⠸⠬⠃⢇⣿⣻⣁⣛⣼⣬⣧⣭⣭⣽⣿⣿⣿⣿⡽⠟⢛⡘⣿⣿⡄⠀⣌⣉⣙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣸⣷⣧⡂⠾⠿⣿⢟⣛⢛⣻⣿⣭⢭⡛⣴⢪⠳⣆⣶⢺⣣⣿⣿⣯⣻⣷⢻⣿⣷⠀⠻⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣮⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⡄
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣏⠓⠍⡏⡼⡇⣿⢸⣬⣸⡦⠀⢹⢸⡇⣿⢸⠀⡏⢿⢸⣗⠛⠛⠛⠓⠩⣮⣿⣿⡆⠈⣿⣷⣶⣾⣯⣭⣽⣿⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠷⠧⢧⣟⣞⣻⣟⣷⣾⡌⠉⣡⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠘⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠿⠿⠿⠇⠀⠀⠛⣛⣛⣫⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠹⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⣀⣀⣀⡠⠀⠄⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⡀⠤⠄⣀⣠⣄⣄⣴⣴⣶⡶⠞⠟⡛⠉⠉⠁⠀⠀⢀⠀⠀⠐⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢏⢻⣯⣫⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣟⣿⡥⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⣛⡃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠋⠉⠉⠉⠁⠀⣺⣿⣿⣿⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⡿⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠤⠤⠇
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠐⡀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢗⣤⢀⣀⣠⡪⣍⣛⣛⣻⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢾⣿⣗⣬⠭⢽⣷⣒⣾⣿⡿⣿⡿⢣⡿⣿⣿⢿⣿⢿⢇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡡⠸⣫⢧⣹⡧⡇⣿⢙⣷⢿⣿⣿⡇⣿⢘⣋⢻⣦⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⡀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⠬⣵⣃⡛⡈⢿⣹⡟⣽⣃⣿⣬⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣖⢙⣀⣀⡈⣙⣛⣿⣃⣀⡀⠀⣘⣛⡃⠀⡀⠀⠀⠀⠀⡀⢀⢀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣥⣿⢾⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠿⠿⠯⢽⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⢸⡇⡇⠸⣌⠀⢣⠷⣟⣛⢿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⡇⠀⣿⡏⢹⣿⣯⣷⡐⣮⠙⣷⢰⣤⣤⣤⣤⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣵⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣻⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣷⣟⡇⡞⠓⠀⠛⡟⢻⣻⣻⣿⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣿⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡛⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠼⠃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢲⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣔⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢭⣭⣽⡿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣬⣉⣉⣛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⢦⠞⠿⣿⢛⣛⢛⡻⠿⣭⢭⡛⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣏⠃⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣅⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⢿⡿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣤⣤⠤⠴⠀⠂⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢀⠀⠤⠄⢄⣀⣀⣤⣤⣶⣶⣿⣿⢿⣛⣛⣟⠍⢁⡀⠀⠀⠠⠔⢐⣂⠩⠅⠒⠂⠈⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠁⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢏⢻⣯⣣⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣺⣟⣿⡥⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⢛⠃
⠀⣿⣿⣿⣿⣶⣄⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⢳⣶⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⠋⠉⠉⠉⠀⠀⣺⣿⣿⣿⣷⣾⣭⡻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠄⠀⠀⠀⠠⠄⠀⠠⠀⠤⠀⠤⠄
⠀⠀⣹⣿⣿⣿⣿⣧⡀⠀⠐⡀⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢗⣤⢀⣀⣠⡪⣝⣛⣛⣻⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⡷⠀⠀⠀⢸⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⢿⣿⡿⠿⢿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣗⣬⠭⢽⣶⣒⡾⣿⡿⣿⡿⢣⡿⣿⣿⢿⣿⣿⣇⣀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣤⣤⣤⣬⣼⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⡻⣿⡇⣿⣿⢸⠿⣿⡽⡇⣿⢹⣷⣿⣿⡏⣿⣿⠰⣿⡙⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⡟⠹⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⣟⠟⢨⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣶⡣⠸⣫⢧⣹⡧⡇⣿⢙⣷⢿⣿⣿⡇⣿⣘⣋⢻⣆⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⠟⢠⣿⣿⣿⣇⠀⠀⠀⠈⣿⣿⣫⡭⡝⣿⢊⣷⢲⠀⣏⣳⢸⡸⢻⡔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⢫⢸⣿⡇⠬⣵⣇⡛⡈⢿⣛⡟⣸⣃⣿⣨⡛⠾⠋⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢉⣁⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣹⣿⣿⡗⣧⢿⣡⢻⣸⡗⣿⠤⠹⠯⠸⣬⣹⣿⣯⣭⣭⣭⣯⣭⣭⣭⣭⠉⠉⠉⣿⣝⢸⣿⣿⢹⣿⣿⣿⣖⢙⣀⣁⡈⣙⣛⣿⣃⣀⡀⠀⣘⣛⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣧⣧⣿⢮⣿⣷⡶⠿⠟⡛⢛⡛⡛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠀⠐⠿⠿⠯⢽⣿⣸⣿⣏⣿⣿⠈⢹⡏⠁⣿⡏⢽⣿⣏⣿⠀⣿⣈⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⡖⡶⣸⡇⡇⠸⣌⠀⢣⠷⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⣭⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣼⡇⢸⣏⠀⣿⡏⢹⣿⣯⣷⡐⣮⠙⣷⢰⣤⣤⣤⣤⣥⣤⣤⣤⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⣱⣇⣿⣹⠘⢇⡿⣰⠬⣧⣼⣿⣿⣿⣾⣿⣯⣟⢿⣿⣿⡿⢹⣿⣿⠀⠠⣖⣤⢄⣘⡛⣿⣿⣼⣧⣟⡃⡞⠋⠀⢛⡟⢻⣿⣻⣛⣽⣽⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣟⣾⣿⣿⠶⠾⠿⣿⢿⣟⡛⡛⣛⢿⡙⡭⣽⢻⣿⣿⣿⣫⣵⣿⣯⢿⣿⣇⠀⣿⣿⣿⣷⣶⣯⣥⣴⣶⣚⣭⣤⡤⠤⠼⠃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡿⢼⢱⡟⠎⢻⣁⣿⡏⣆⣷⡆⣇⢸⢯⡇⣷⢰⣸⣿⣿⣿⣯⣻⣿⣿⡾⣿⣿⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣾⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⣔⠽⣇⢿⠸⠤⠃⢇⣿⣻⣡⣛⣼⣬⠧⢯⣭⣽⠿⣿⣿⣿⣷⣛⣋⣥⢹⣿⣷⠀⢠⣤⣌⣉⣉⣛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣇⢿⣷⣦⠞⠿⣿⢛⣛⢛⡻⠿⣭⢭⡟⣕⢪⢵⣆⣶⢺⣣⣿⣿⣿⣎⢿⣏⣿⣿⡇⠈⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣏⠓⠉⡏⠾⡇⣿⢸⣦⣸⡮⠉⢹⢸⡇⣿⢸⠀⡏⢿⢸⣇⠉⠉⠉⠉⠁⠺⣿⣿⣿⠀⠹⣿⣿⣿⣶⣶⣯⣭⣭⣭⣽⣿⣟⣿⣻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡻⠀⠿⠀⠧⢟⣞⣻⣟⠿⠿⢮⣍⣡⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣆⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣼⣿⣛⠛⠀⠀⠈⢩⣭⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣁⣤⡤⠤⠤⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠤⠤⢄⡀⣀⣠⣴⣶⣶⣾⣿⢿⣛⣻⣻⣉⠁⡀⣀⡀⠠⠔⠀⣀⠨⠅⢒⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3353

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/Over_at_Tux_Machines.shtml
    Gemini version at https://techrights.org/n/2024/10/19/Over_at_Tux_Machines.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Over at Tux
Machines...⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


⚓  Updated This Past Day⠀⇛


   1. ⚓ Free_Software_Leftovers⠀⇛


           4 misc. links about FOSS


   2. ⚓ Calibre_7.20_Adds_New_PDF_Input_Engine,_Supports_New_Tolino_Shine_5
      Firmware⠀⇛


           Calibre 7.20 has been released today by developer Kovid Goyal
           as a new update to this open-source, free, and cross-platform
           ebook management software for Linux, macOS, and Windows.


   3. ⚓ Ardour_8.10_Open-Source_DAW_Released_with_Fixes_for_New_Major_Issues⠀⇛


           Ardour 8.10 was released today as another hot-fix update in the
           Ardour 8.x series of this powerful, free, open-source, and
           cross-platform digital audio workstation (DAW) software that
           addresses a few new major issues.


   4. ⚓ Best_Free_and_Open_Source_Software⠀⇛


           Brace yourselves for an innovative upgrade


   5. ⚓ IRC_Proceedings:_Thursday,_October_17,_2024⠀⇛


           IRC logs for Thursday, October 17, 2024


      ⚓  New⠀⇛


   6. ⚓ Android_Leftovers⠀⇛


           The powerful Meteogram is my favorite Android weather widget-
           Android Authority


   7. ⚓ Web/Net:_Curl,_RSS,_and_Mozilla⠀⇛


           Some WWW related picks and E-mail


   8. ⚓ Programming_Leftovers⠀⇛


           Programming related links


   9. ⚓ today's_leftover⠀⇛


           mix of topics for end of day


  10. ⚓ Audiocasts/Shows:_BSD_Now_and_mintCast⠀⇛


           2 new podcasts' epsidoes


  11. ⚓ Security_Leftovers⠀⇛


           and some FUD along the way


  12. ⚓ Free_Software_Applications_of_Interest⠀⇛


           FOSS picks


  13. ⚓ Red_Hat_/_IBM_at_the_Back_End⠀⇛


           OpenShift, HashiCorp, RHEL


  14. ⚓ The_Linux_Concept_Journey_—_Xfce_(Desktop_Environment)⠀⇛


           Xfce is a lightweight desktop environment for UNIX-like
           operating systems. It is very low on system resources...


  15. ⚓ Android_Leftovers⠀⇛


           Some Pixel 8 Pro users are facing back gesture issues on
           Android 15, but there's a fix


  16. ⚓ Slimbook_Executive,_long-term_report_5⠀⇛


           We must talk about my Slimbook Executive laptop, again. Well,
           we don't really have to, but it's been about three months since
           I last talked about it


  17. ⚓ Release_of_Rust_1.82.0_and_This_Week_in_Rust_569⠀⇛


           Some Rust news


  18. ⚓ GNU/Linux_Leftovers_and_Windows_TCO⠀⇛


           today's leftovers


  19. ⚓ Distributions_and_Operating_Systems:_Windows_Lookalikes,_Ubuntu,_and
      Red_Hat⠀⇛


           another batch of mixed links


  20. ⚓ Open_Hardware:_SparkFun,_Raspberry_Pi,_and_More⠀⇛


           hardware centric news


  21. ⚓ today's_howtos⠀⇛


           some are a bit older


  22. ⚓ Latest_in_Wordpress_Drama⠀⇛


           4 stories


  23. ⚓ Videos:_Free_Software_and_GNU/Linux_in_the_Past_Week⠀⇛


           via Invidious


  24. ⚓ Games:_Steam_Deck,_Heroic_Games_Launcher,_and_More⠀⇛


           Latest 8 from GamingOnLinux


  25. ⚓ Learn_These_6_Linux_Commands_to_Go_From_Beginner_to_Badass⠀⇛


           Getting started with the Linux terminal doesn't have to be
           daunting, and it can even be fun


  26. ⚓ Volla_Phone_Quintus_is_a_smartphone_that’s_also_part_of_a_distributed
      cloud,_supports_Android_or_Ubuntu_Touch⠀⇛


           German device maker Volla has been shipping smartphones and
           tablets that run a custom version of Android called Volla OS
           for a few years


  27. ⚓ FunOS_–_minimal,_fast,_and_secure_Linux_distribution⠀⇛


           FunOS is a Linux distribution based on Ubuntu LTS


  28. ⚓ Stable_kernels:_Linux_6.11.4,_Linux_6.6.57,_Linux_6.1.113,_Linux
      5.15.168,_and_Linux_5.10.227⠀⇛


           I'm announcing the release of the 6.11.4 kernel


  29. ⚓ Today's_HowTos_and_Programming_Leftovers⠀⇛


           mostly coding-related stuff


  30. ⚓ Proprietary_Microsoft_and_Microsoft_Openwashing⠀⇛


           failures and deceit


  31. ⚓ Open_Hardware:_Hackaday,_Arduino,_and_More⠀⇛


           Some hardware-centric sites


  32. ⚓ IBM,_GNOME_(Outsourced_to_AWS),_and_GNOME/Debian_Hackers⠀⇛


           today's leftovers


  33. ⚓ Free_Software_and_Games_Leftovers⠀⇛


           lots of Mozilla


  34. ⚓ Today_in_Techrights⠀⇛


           Some of the latest articles


      =========================================================================
      The corresponding text-only bulletin for Friday contains all the text.
      Top-read articles (excluding bot/crawler visits):


                          Span from 2024-10-12 to 2024-10-18
      1177 /n/2024/10/11/Gaming_on_Fedora_Asahi_Remix.shtml


      794  /n/2024/10/08/
           The_GNOME_Foundation_Update_from_the_Board_2024_10_Financial_Cr.shtml


      707  /n/2024/10/13/
           Inkscape_1_4_Open_Source_SVG_Editor_Released_with_Filter_Galler.shtml


      694  /n/2024/10/12/Programming_Leftovers.shtml


      675  /n/2024/10/11/
           Kubuntu_24_10_Lubuntu_24_10_Xubuntu_24_10_and_More.shtml


      634  /n/2024/10/16/
           Ubuntu_25_04_Codename_is_Revealed_And_It_s_Perfect.shtml


      606  /n/2024/10/14/
           Open_Hardware_Modding_Arduino_BeagleBoard_and_More.shtml


      581  /n/2024/10/16/Shared_Source_Winamp_Revoked.shtml


      579  /n/2024/10/15/
           VirtualBox_7_1_4_Adds_Initial_Support_for_Linux_Kernel_6_12_and.shtml


      559  /n/2024/10/12/today_s_howtos.shtml


      534  /n/2024/10/12/
           KDE_neon_6_2_Is_Out_with_KDE_Plasma_6_2_Desktop_Based_on_Ubuntu.shtml


      534  /n/2024/10/14/today_s_howtos.shtml


      531  /n/2024/10/08/_Rocky_Linux_from_CIQ_Launched.shtml


      515  /n/2024/10/14/today_s_leftovers.shtml




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣵⣶⢀⡀⠸⢀⡄⢂⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡸⠿⠀⠐⣠⣄⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣋⡃⠃⡀⠀⢭⢉⡅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣶⣶⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⡟⢺⡇⠶⠖⠤⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣆⠙⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡝⠋⠉⠉⠉⠀⠀⠀⠀⠀⠠⠈⠂⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢐⠁⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣫⣟⣻⢿⢻⡟⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⡀⠀⢀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢬⢥⣘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⢾⣠⣠⣀⣀⠀⠀⠀⣄⢀⢠⠁⠀⠐⠾⢦⡂⠀⠈⠉⠉⠁⠀⠀⠀⠀
⢿⠇⠻⣏⢻⠏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢸⣿⣶⣿⣵⡄⢐⣐⢈⡀⠀⠀⠀⠀⠀⠀⣱⣶⡦⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⠀⠀⠀⡐⢩⣿⣿⢻⢩⢟⣿⣿⣿⢻⡿⢛⣿⣿⡿⠿⠛⠐⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡏⠽⢿⣿⣰⣿⣷⣾⠽⠗⠆⠀⠀⠀⣀⠉⢙⡓⢢⣂⢢⢀⡀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⣬⠹⠟⠈⢺⣿⠙⠝⠛⠀⠱⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠁⠐⢻⡼⡉⣿⣏⠈⠂⠡⠀⠀⠀⠀⣧⡀⠈⢇⣜⠋⠀⠙⠋⢲⣦
⠀⠀⠀⠀⠀⣼⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⣦⡀⢀⠀⠀⢁⣘⣿⣷⣔⡇⠀⠀⠀⢀⣿⡣⣴⡺⠄⠀⠀⠈⢠⡬⠟
⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣼⣿⣷⣶⣦⣄⠀⠀⠉⠑⠲⣦⣄⠀⠀⠀⢀⠉⣡⡀⡀⠀⠀⠈⢸⣷⣿⠃⢀⡀⠀⣾⣿⡿⠟⢷⣾⣧⣄⠀⢻⠕⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠋⠉⠁⠚⠙⠛⠛⠉⠁⠀⠲⢷⣶⣤⣀⣄⣠⠀⠔⣀⣾⡿⠿⣿⡂⢤⡀⠈⠙⠛⠀⡀⠀⠀⠿⣟⣿⡇⢸⣿⣿⣿⣶⣤⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢄⠂⠀⠰⣾⣿⣿⣿⡲⣷⣽⣷⣿⣦⣿⣿⠿⡿⡿⣶⣤⢠⣤⣠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⣤⢀⡤⠈⠬⠻⠿⠿⣿⣿⣿⣷⡾⣯⡐⠪⣾⣿⣿⠿⠿⣟⠉⣭⠋⠋⠻⣿⣟⠻⠿⠋⠹⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠺⢶⣤⣾⡎⠿⢿⡳⡤⠬⠻⠆⠒⠈⠢⡇⠛⢲⢉⢤⡤⠀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⢀⡀⡀⠀⠄⠀⠀⠈⡅⠁⠀⠀⣔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⠀⠀⠠⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠠⠧⠀⢻⣷⣄⡀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠠⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠅⢰⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3684

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/The_Definition_of_Insanity.shtml
    Gemini version at https://techrights.org/n/2024/10/19/The_Definition_of_Insanity.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ "The Definition of
Insanity"⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Row_of_motorcyles_parked_on_bikers_weekend_St._Augustine,
Florida⦈_


Richard M. Stallman (RMS) is being targeted by aggressive or passive-aggressive
bullies again. The aggression is a symptom of insecurity. This isn't the same
as concern-trolling; it's a lot more aggressive and direct than this; they want
to oust like half of the FSF and are_incredibly_insincere. They're obsessed
with sex, which might say a lot about themselves, not RMS.


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Drew_Devault⦈_We've seen this and been through all this
                                    before.


"The_definition_of_insanity"_(cliché) is thinking that merely repeating
decades-old smears or mere reuse of old and already-debunked material will
result in a different outcome than before [1 2]. History shows it leads to
canceling of the self. Notice how all the people who started the 2021 anti-RMS
petition have pretty_much_vanished_from_sight? █




⠀⠀⠀⡀⠀⠀⢀⠀⡠⣦⢍⣥⡯⣨⣃⠐⣦⢠⣴⣾⣿⠿⠋⠙⠁⣯⣥⠟⠛⠛⠿⣷⢶⣮⠹⡿⠿⠿⠿⠿⠉⠉⠁⠀⠀⡿⢿⣿⣿⣿⠀⢼⢻⣟⣿⠀⢸⣿⣿⡟⢠⠀⡇⣿⠃⠘⠋⠀⠀⢿⣿⣿⣿⣿⡇⠘⠀⠀
⠀⠀⡄⣀⣀⠀⠄⣀⣀⠉⠚⠛⠉⠙⠛⠉⠹⠉⢸⠁⠀⢤⡶⠧⠜⠛⠓⢶⢲⣶⣶⣶⠚⠟⠓⠀⠀⠀⠀⠒⠂⠀⠄⠀⠀⠀⠸⡿⠛⠛⣿⡛⠛⠛⠛⠀⣸⣿⣿⡇⠀⢀⢧⠯⠂⣴⠅⣦⣶⣾⣿⣭⣿⢿⡧⠇⠠⠄
⣾⣬⡷⠊⣹⣶⣦⡤⢈⠋⢶⠶⠤⢀⠰⣶⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠅⠀⠀⠀⠤⠤⠖⠇⠀⡔⢻⣷⣶⡶⠶⠶⢿⣿⡷⠶⢶⣶⣿⠿⢿⣇⡥⠈⠀⠞⠁⠀⠀⠀⠀⢨⡁⠈⠙⢹⣿⠀⠀⠠
⣿⣿⣿⣦⣡⣴⡿⣿⣿⣿⣿⣖⣂⡀⣉⠉⠲⠁⣠⣤⣄⠚⠂⠀⢀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣤⡅⠃⠉⠀⠀⠀⠀⠀⠉⠋⠻⠻⠟⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡃⠀⠀
⣿⣿⣿⣿⣇⡉⣠⡄⠉⣠⠽⠛⢿⡷⠦⠔⠰⠄⠀⠀⠀⠀⠠⠾⣻⠖⠋⠁⣰⠖⠞⠟⠁⠀⠀⢠⣤⡶⠂⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠘
⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠂⠐⠿⠋⠒⠓⠀⠴⣶⡿⣇⡀⠀⠀⠀⣤⣶⠇⠀⠀⠀⠠⣶⠀⠛⠃⠀⡀⠀⠀⠀⢠⣶⣶⣶⣶⣠⣀⣀⡀⠀⠀⠀⠀⠕⠀⠀⠀⠔⠂⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⡤⠄⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠢⠲⣶⣢⣾⣿⠫⢐⣷⣶⠀⢀⣿⠃⠀⢀⠄⣷⣄⠀⠀⠠⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⡀⠀⠀⠠⠋⠁⠀⠀⠏⠤⣀⣀⡠⠥⠤⠀⠀⣠⣤⠇⠈⢁⡚⠛⣻⣭⠐⠻⠿⠗⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠠⢺⣿⡿⠛⠉⢀⡀⠀⠀⠈⢉⣉⠀⠀⠀⠈⠠⠂⠀⠀⠙⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡐⠤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠡⠀⣀⡤⠃⠒⠒⠒⠀⠀⠑⠁⠈⢁⡀⡀⢸⣷⣴⡖⢀⣴⣿⢏⣬⣴⡶⠂⢀⣴⣿⣿⣿⣫⣥⣄⠀⠀⡀⣴⣶⡔⠿⠿⠃⠀⡀⠀⠂⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠋⠀⣤⠀⠀⠀⠀⠀⡘⠉⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣰⡈⣿⡄⢼⡿⢶⢟⠿⣳⣿⠿⠋⠉⠁⠀⡶⠖⠉⠙⠉⠉⠊⠓⠄⠀⣉⣉⠉⢿⠂⠐⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠐⢀⢹⣟⢹⣏⢭⣺⣿⣿⡏⠀⠛⠁⠀⠀⠀⠐⠀⠀⠀⢀⡤⠤⠀⠀⠀⠄⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠀⠀⣴⡂⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆⢾⡋⠄⢴⣾⣿⠶⠖⠀⠉⠈⠉⠉⠉⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣶⢾⣵⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢀⠈⠛⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠟⠂⠀⠀⠀⠀⠀⠀⣀⢦⠀⠀⠠⠀⣴⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡌⠀⣀⣀⣤⡈⡀⠀⠛⢉⣥⡾⠟⠁⢀⡒⠒⡀⠀⠀⠀⢀⣰⡿⠟⠉⠀⠀⠀⠀⠀⠘⡢⡀⢤⣜⢈⡷⠄⠀⣼⠟⠋⠉⠩⣿⣿⣿⣿⣿⣿⣿⣿⡿⠚⣆⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⢨⣿⠛⠋⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠂⠠⠩⢸⠁⠀⢰⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⢡⣤⣤⡉⢩⣭⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣄⠀⠀⠀⠀⢀⣠⡄⢹⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣼⡇⠋⢀⣴⣯⣤⠀⠀⠀⠀⠈⠉⠩⢉⠀⣰⣶⣶⣿⣿⣿⣿⡀⢿⣿⣿⠙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⠈⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣯⣭⡀⠀⠐⠛⠛⠿⠛⠚⠁⠀⠀⠀⠀⠀⠇⠀⢻⢟⠟⢿⣿⣿⣿⣿⣸⣿⣿⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣹⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠦⡼⢧⡁⢻⡿⠛⠛⠛⢿⣿⣫⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠇⠀⠡⢀⠀⢗⠀⢷⠀⢳⣤⣤⣤⣿⣌⣟⡙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠄⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣍⣛⠉⠀⠀⠀⠀⠀⠀⠀⠻⢵⣿⣥⣼⡇⣘⠋⠙⠛⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠩⠄⠀⠀⠀⠀⠀⠀⣀⢀⡬⣿⣥⣠⣴⣮⣵⣾⣿⣿⣷⣶⣶⠾⣋⠤⠂⠁⠀⠀⣿⣿⡯⠋⠉⠀⠀⠀⠀⠀⠀⢀⢼⡧⢈⣛⣹⠑⠀⠀⠀⢠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠋⠀⠀⠀⠀⠀⠿⠽⠒⠁⠀⠀⠀⠀⣀⣤⢴⣾⣿⣿⣿⣏⡤⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣻⣿⣟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠘⣩⡿⢻⣿⡿⠹⠋⠀⠀⣰⣮⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠉⢙⡋⢻⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⣴⣿⣿⡇⠸⡁⠀⠀⠀⠀⢀⣸⡿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣾⣷⣶⣀⠸⢿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⡀⡼⣵⣿⣷⣬⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠁⢶⣿⠗⢋⠁⢠⣿⣿⣿⣿⠀⣿⣿⣶⣦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣐⣿⣇⣨⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣍⣀⠀⢀⡈⠙⢿⠄⡝⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢵⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⣷⣤⣤⣾⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⢀⠄⠀⠀⠀⠃⠿⠻⠘⠜⠿⠻⠋⠪⠿⠻⠻⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡯⢍⣹⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣇
⠀⠀⠀⠁⠀⠀⠀⠯⠂⠓⠴⠼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣤⣬⣧⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢠⣶⡗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⢀⣀⠀⠀⠰⠿⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⠁⠀⣤⣤⣀⣤⣀⡀⠀⠀⠀⠀⠀⢀⣤⣾⡵⣽⣿⣧⣄⣀⣀⣀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⡇⠀⠀⠀⡈⣽⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣟⣽⡇⠈⣿⡏⠛⠛⠛⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡇⠀⠀⠠⠈⢻⣿⣿⣿⣿⡗⠀⠀⠀⠀⢰⠋⠙⠛⣷⣿⣿⡶⣶⣤⣤⣀⣀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⡠⠸⣿⣿⣿⣛⣁⢀⣠⠀⡄⠞⠀⠀⠀⣿⣿⣿⡇⠀⠀⠉⠉⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⢙⣿⣿⢛⠻⠻⡷⠀⣇⠀⠀⠀⠐⠿⣿⣿⠇⠀⠀⢰⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣦⢔⠏⢣⣾⣵⡕⡆⠁⠐⠃⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⡧⠀⣰⣿⣿⡟⢟⣄⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠐⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣿⣾⣿⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⣾⣩⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣂⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠘⠘⣻⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⡩⢿⣿⡛⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠉⠐⠒⠉⠉⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡈⠃⠒⠀⠀⠀⠀⣦⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠐⠲⢶⣶⣶⣶⣶⣄⠀⠐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠉⠻⢿⣿⣿⣦⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠙⠿⢃⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⢿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠛⠛⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⠼⠿⠿⠾⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣭⠁⢀⣀⡀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⣁⠘⠛⠛⠛⠛⠻⠿⢿⡆⢰⢛⣛⡻⢠⣶⣶⣦⡀⠀⠉⠙⠻⣿⣿⣿⣷⣦⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⠟⠀⠀⠀⠀⠒⡒⠒⠒⢦⠂⢸⣿⡇⠘⢿⣯⣁⣀⣐⣶⡾⠿⣿⣿⣿⣿⣿⣆⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⡀⠀⠀⠈⠁⠀⠀⠀⢀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠰⠆⠈⢹⣿⣿⣿⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣤⡀⣀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣬⣭⣭⣤⣤⣤⣤⠀⣠⣿⣿⣿⣿⣿⣿⣿⣮⣝⣛⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠱⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣬⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠐⡒⠛⠛⠏⠉⠀⠈⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⠀⠀⠙⠛⠿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢋⣼⣿⣿⣷⣶⣤⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠘⠿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣆⠀⠀⠀⠀⠸⣦⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⡿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⡌⡿⣦⠀⣀⠀⡀⣈⠿⢯⣍⢿⣿⢿⡏⣹⠿⣿⠿⢟⢛⢁⡀⠠⣴⢿⣿⡿⣿⣿⢿⡿⡿⡿⣿⢻⡏⣯⡹⢻⡏⣯⣿⢙⣟⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⡹⣯⣭⣿⡇⣿⢹⡇⠸⣯⢼⣻⣿⡷⣯⢾⣿⡃⢸⡏⢿⣿⢺⣻⢼⣯⡿⢿⣽⢿⡏⣿⢘⣿⢸⡇⣿⣿⢸⡇⣿⣿⠸⣯⠸⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣄⠰⣶⣶⣶⣶⣶⣶⣶⣶⡆⢰⣷⣶⣶⣶⣞⣃⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣖⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⣿⣿⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢻⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⢿⣿⣿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠻⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢿⣿⣿⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3817

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/The_Drew_DeVault_Report_Taking_Out_His_Frustration_on_Other_Peo.shtml
    Gemini version at https://techrights.org/n/2024/10/19/The_Drew_DeVault_Report_Taking_Out_His_Frustration_on_Other_Peo.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The Drew DeVault Report: Taking Out His
Frustration on Other People While Doing Drugs⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█
⌧


posted by Roy Schestowitz on Oct 19, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Lonely_sailboat⦈_


Old: Drew_DeVault_Has_Lost_the_Plot


For those who haven't been paying close attention, or those who tactfully
ignore social control media, Drew DeVault merely continues his years-long anti-
RMS campaign while looking for additional scapegoats and perched in some place
where he can legally smoke joints and try to treat his depressive episodes.


Techrights won't be amplifying his campaign of hate, but only highlight the
symptoms.


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


If you don't like RMS, then create something better. Be more like Fabrice
Bellard. The endless whining and obsession_with_"sex" make you look petty and
sad. The "hit piece" apparently contains the word "sexual" hundreds of times,
which is... weird.


There have been a couple of good video rebuttals and at least 2 rebuttals in
Geminispace. The responses get more publicity than the attack. That's a
positive thing.


Some people learned nothing from the botched defamatory petition of 2021. If
your campaign of hate is built upon BS, it'll end up BS. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡅⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣛⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠃⠛⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⡇⠀⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣥⣤⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⣿⡇⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠏⠉⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣻⣿⣿⣏⠉⠀⠀⢨⣿⠇⠀⠀⠀⡔⠈⢉⠉⣹⠉⡉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠁
⣿⢿⣭⣽⣯⠟⢭⡭⣽⣽⠯⠯⡏⠿⣿⣽⣿⣋⣟⣟⣿⣿⣯⡿⠽⣭⡿⠝⠋⠁⠀⠀⠄⠨⠁⠀⠀⠀⠀⠁⠀⠀⠀⠒⠀⠈⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣛⣻⡟⡛⢭⣿⠿⠟⣛⡿⠿⠿⣿⡻⢽⢽⣿⠿⢿⠿⣫⣽⣭⣋⡶⢮⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠲⡬⠖⣠⡆⠀⠀⠢⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠯⠭⣿⣋⢿⡿⠟⣟⣻⣿⣿⣿⣿⣿⣪⣷⢾⣿⠿⢾⣷⢍⡲⡶⠴⣽⢿⣛⣻⣉⡭⢒⢒⣤⢤⢦⣴⡀⠀⠐⠒⠚⠋⠚⠚⠂⠋⡑⠂⡓⠘⠛⠀⠀⠀⢀⠒⠒⠁⢒⠂⠀⠀⠀⡐⠐⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣒⣸⣳⣿⣟⣷⣿⣽⣻⣟⣷⡿⠽⣿⣿⣟⣫⣽⣿⣟⢋⠿⢿⡷⣬⡶⢮⡭⠥⠼⣿⢽⡭⠽⠠⠤⣤⠶⡾⠿⡭⠀⢲⣓⡠⡤⠶⢜⣓⢀⣉⣐⣦⣄⡀⣀⠠⠀⠉⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀
⣴⣾⣿⣿⣿⢙⠒⠀⢐⣲⣴⡄⠀⠻⠓⠆⢰⠒⠂⠀⢸⣫⡽⠃⠀⢡⠬⠭⠩⠽⣭⣥⡈⣁⢬⡭⠬⣥⣶⠤⠴⠄⠂⠑⢀⠈⠂⠐⠒⠲⠀⡠⢤⠀⠀⠀⠤⠀⠀⠀⠠⠌⠩⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠤⠀⠀⠀⠀
⣬⣿⣟⣛⣿⣟⣮⡐⣩⣟⣋⣉⡙⠍⢀⣬⠄⠄⠐⠂⢁⠁⠠⠄⣒⣒⡂⠒⠁⠒⠻⠓⣒⣚⠚⠒⠒⠶⠀⠤⠰⠒⠀⠈⠈⠉⣁⡀⢀⣐⡀⡂⠀⠂⠀⠀⠐⠀⠀⠀⠀⢠⡀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠂⠒
⣿⠿⠭⠍⣭⡤⣼⡿⣯⣄⣀⡀⠤⢤⣄⠠⠓⠒⠂⠷⠦⠶⠢⠖⠓⠃⠂⠙⠻⠬⢺⠔⠛⠃⠀⠀⠀⠆⠚⠓⠐⠒⠒⠒⠂⠒⠒⠒⠀⠈⠓⠂⠠⠆⠀⠀⠀⠀⠠⠠⠍⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠉⠁⠉⠉⠁⡀⠁⢠⡄⠙⠋⠨⣭⣗⠐⠲⠶⠀⠀⠙⠣⠤⠠⠠⡤⣤⡉⠀⠀⣀⡍⠀⠀⠐⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⣒⣠⡬⣵⣀⣠⣆⠒⠊⢀⣄⡀⡰⢄⣰⠒⣀⣰⣴⣆⣤⣀⡤⠤⠖⠳⣁⡄⠐⠒⠒⡆⠐⠀⢌⡀⠠⠄⠀⠐⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⢀⠐⠒⠒⠦⡠⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⡿⢿⠿⠿⡿⢿⡿⠿⣿⠿⡿⢿⠟⣿⠿⠻⡿⢿⡿⢿⢿⡟⡿⡿⢿⠟⠿⡟⣿⠿⡿⠿⢿⠿⣿⠿⠟⡿⠟⠿⡿⣿⡟⢿⠿⡿⡟⢿⢿⠿⣿⠿⠿⡿⠿⡿⠿⠿⡿⠿⠟⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣼⣼⣤⣧⣼⣥⣯⣿⣤⣷⣴⣥⣿⣬⣴⣦⣼⣧⣼⣬⣧⣤⣤⣽⣧⣤⣤⣿⣤⣧⣧⣴⣤⣧⣥⣼⣿⣥⣦⣤⣼⣧⣤⣤⣬⣧⣤⣤⣼⣧⣭⣤⣦⣼⣤⣶⣤⣥⣼⣤⣧⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠉⠈⢤⣤⣯⣤⣬⣯⣤⣬⣤⣿⣤⣼⣯⣴⣤⣤⣧⣵⣼⣤⣤⣤⣴⣦⣧⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠈⠙⠿⣿⣿⣿⡛⠻⠻⡟⠿⡿⡿⠿⠿⢿⡿⡿⠿⢿⢿⠿⡿⠟⠿⠿⠿⡿⠿⡿⠿⠿⣿⣻⢿⠿⠿⢿⡛⡿⢿⠿⣿⠿⠿⠿⠿⡿⠿⠿⢻⡿⠿⢻⢻⠿⠟⠻⢿⠿⢿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣗⠶⠶⢷⢶⣷⠷⢳⣷⠾⢷⢻⡗⣚⠾⡾⠷⠶⣳⠲⢾⠳⠶⡷⢷⠶⠟⠷⠾⡒⠶⡟⣻⠺⢞⠾⣗⠷⠶⢺⠻⡿⡾⠶⠾⠺⣲⡟⢞⠞⣶⣶⠾⠞⣞⠶⣞⢿⡻⠿⣿⣿⣿⣿⣿⣿⣿
⣶⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣖⠒⠒⠖⠒⠚⢿⢻⢻⠛⡟⠛⢻⣟⠛⢳⡛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 3902

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/The_New_Laptop_as_a_Reminder_of_Why_I_Love_GNU_Linux.shtml
    Gemini version at https://techrights.org/n/2024/10/19/The_New_Laptop_as_a_Reminder_of_Why_I_Love_GNU_Linux.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The 'New' Laptop as a Reminder of Why I
Love GNU/Linux⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Life_quotes⦈_


SOME days ago we acquired a 'new' (used) laptop as a crucial machine broke down
and needed a quick replacement. It was the machine that we write all our
working text files to, as it gets backed up to external disk every morning.
Repair was not possible and time was at the essence.


Buying (or rather, choosing) the 'new' machine took about 10 minutes, testing
it at the shop took about 5 minutes, and putting Debian 12 on it was mostly a
game of waiting and clicking, waiting and clicking, waiting and clicking for a
few hours (not much user intervention required). I wrongly assumed it would
"save time" to use an old Debian CD and then upgrade 'in place' a couple of
times (about 6 long steps). Well, it worked, but it took a long time. Anyway,
it turned out that over VGA port this machine hasn't the capacity to drive an
external monitor at full resolution. Today I belatedly (more free time, slow
news_cycles) plugged in HDMI to overcome this issue and use full resolution.
Passing all the data from the old machine took only minutes. Copying the home
directory in its entirety meant that system settings were just 'inherited' from
the files, so I just needed to add (with apt) several programs and I was ready
to roll that same afternoon... as if almost nothing happened that day.


GNU/Linux is not necessarily very easy, but if you know what you're doing, then
a Disaster Recovery (D-R) effort, as the old machine refused to even boot, is a
breeze. The following day I could barely even remember that a machine had died.
Another one was there in its place running all the same things. Recovery by
replacement of damaged hardware was fast and smooth...


Love it or hate it, the UNIX or GNU/Linux philosophy of everything as a file
(never mind small program; Microsoft's systemd attacks this mindset) is a time
saver. It's miles better than the Windows way of doing things.


My wife and I now have 13 screens in our adjacent offices. Most of these are
laptop screens and most of these laptops are Taiwanese. These laptops cost very
little. Yes, you can run the latest distro with KDE on a £79 laptop. Best
purchase made so far this year. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣧⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡽⠿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⡿⠋⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣭⣿⣭⡬⢭⣭⣭⣍⣭⣿⢿⣧⣾⣟⠶⠍⠤⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⠋⣩⣿⠏⠁⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣭⡿⣝⣿⠿⢴⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣭⡭⣟⣩⠽⠟⣿⠋⣀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⡿⡫⡬⢤⣷⠄⠐⠶⠄⠀⡀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⠟⠣⠙⠋⢍⡚⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡁⠥⠤⠐⡛⣀⠁⢁⡀⢀⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠁⣠⠶⠾⢋⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⠐⠂⠔⠒⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡗⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⠃⠞⠫⠙⢻⠏⠁⠞⣿⠡⠛⢟⠍⣽⠉⠡⠟⠏⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣾⣿⣷⣾⣿⣿⣠⣾⣶⣷⣿⣶⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⢟⠟⠿⠿⣿⠻⠟⠛⠛⠟⢿⠋⠼⠫⠉⢻⠿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣷⣿⣿⣾⣷⣷⣷⣷⣿⣾⣶⣾⣾⣿⣇⣾⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠻⠟⢹⡏⠉⠜⢻⠇⠟⠿⠋⢹⠍⠃⠜⠫⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣶⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣾⣷⣶⣷⣾⣀⣶⣶⣶⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⢸⡜⡘⣸⡿⠛⡰⠛⠛⠻⠿⠟⡿⠠⠛⠻⠛⡿⠿⠟⠛⠿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣽⣿⣿⣿⣿⣿⣾⣷⣶⣾⣶⣶⣶⣶⣶⣖⣴⣶⣿⣶⣶⣶⣶⣟⣠⣶⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣤⣶⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⡿⠿⠿⠟⠉⠙⡻⢿⠾⠟⠃⠞⠋⢹⠿⠽⠻⠿⣿⠟⠿⠏⢹⡿⠻⠟⣻⠋⠁⠜⠟⠻⠓⠚⠁⠘⣒⡒⣠⣼⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣵⣶⡖⣾⣷⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣖⣲⣾⣂⣴⣶⣶⣾⣰⣶⣶⣾⣷⣶⣶⣾⣶⣶⣶⣶⣶⣖⣀⣶⠄⠉⢹⣿⠅⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠄⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠷⢾⣿⣿⠿⣛⣿⣿⣾⣷⣦⣽⣿⣯⠯⣛⠛⠦⠶⠽⠆⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣯⣭⣭⣷⣿⣶⡾⠿⢶⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⢋⢁⠈⠭⢯⠑⢲⣂⡈⠙⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣾⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿⡿⠻⢟⣛⣽⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣩⣥⣈⣍⣯⣭⣤⣴⣶⣼⣶⣷⡶⠶⠰⠦⠤⠤⠄⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣻⣏⣻⣿⢿⡿⣿⣿⣿⣿⣿⣋⣵⠾⠿⠿⢟⣋⣉⣉⣩⣭⣿⣿⣿⣯⣿⣿⣿⣿⣟⣿⣷⡖⠾⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⠿⣻⣝⣽⢭⣭⣟⣛⣿⣟⣿⣿⣻⡽⠶⠞⣛⠭⢟⡭⣯⣽⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠋⠉⢁⣀⣨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀

                    ䷩ 𝚕𝚒𝚗𝚎 3987

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/The_State_of_GAFAM_and_the_I_s_IBM_and_Intel.shtml
    Gemini version at https://techrights.org/n/2024/10/19/The_State_of_GAFAM_and_the_I_s_IBM_and_Intel.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ The State of GAFAM and the I's (IBM and
Intel)⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


THE era of fake prosperity - or mindless inertia - probably ended in the late
90s. Many things crashed. We saw that "tech" was partly the work of bubbles, or
loans, or both. Set aside what happened in 2007/2008 and then again in recent
years.


I am reading not only every day but several times per day about tech layoffs. I
follow the subject very closely not only because of this site but also because
relatives and friends are affected by this. Some people foolishly took massive
mortgages that they'd be unable to pay unless they kept their "tech career" in
tact for decades to come. Misguided? Wishful ignorance?


At IBM there are layoffs this month and next month, but IBM_isn't_talking_about
it (there are NDAs to hide what's happening). As someone put_it a short while
ago, "Red Hat is IBM." We should assume that those 8,000 IBM layoffs also
impact_Red_Hat.


Intel and Facebook ("Meta") are the latest to received media attention for mass
layoffs, last week/month it was Amazon (for instance, over 10,000 managers to
be laid off), and perhaps before Microsoft's fake_"results" we'll hear of
another_"big_round"_of_Azure_layoffs. Cut-cutting, yay! Good for shareholders,
they insist!


What about Apple and Google? Neither (among GAFAM) has been mentioned above,
but Apple's_hardware_executive_is_leaving (amidst a round of layoffs, sagging
sale numbers, and perhaps the imminent end of Vision Pro - a commercial
failure). As for Google, we keep hearing about layoffs in YouTube, Google News,
and many other areas whose products/services are discontinued.


It's looking like a safe prediction that GAFAM "comeback" isn't in the cards.
US national debt rose_about_2_trillion_dollars_in_the_past_year (devaluing the
currency, resulting in high inflation), Microsoft_is_asking_for_government
handouts, and every day I see reports regarding the demise of the "tech" sector
(at least as the lucrative thing it once was).


People work longer hours, under greater stress (workload increases after
layoffs, a la EPO), for even lower pay (Dell just cut salaries by 10%). This
past week I learned about someone roughly my age with a blood pressure close to
160; he works 12-hour days, not counting the commute and preparation. This 12-
hour workdays regimen are apparently becoming more "normal" (I heard other such
stories lately), so China's_notorious_"996"_is_coming_home_to_roost (9AM to
9PM). Are we human beings or machines? Or machines operators whose purpose in
life is to work?


Technology and "tech giants" will continue to exist, but they won't be what
they once were. █




⠀⠰⠢⠀⠀⠀⠀⠀⠀⡈⠻⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠁⠀⢀⣀⠰⢦⣤⣄⣀⢤⣤⡀⠀⠀⠀⠘⠀⢨⣶⡟⢠⢿⣿⣷⣿⣆⣲⠶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢠⣼⣿⣿⣿⣾⡆⠀⣼⣿⣬⣿⣿⣿⣿⢻⣿⣗⡶⠀⠀⠀⠀⠸⠏⠩⠉⡙⣿⣿⣿⠿⢁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡄⠀⠀⡖⠀⠀⠀⠀⢢⣾⡜⠡⣤⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢬⡀⢸⣁⠀⠄⠠⠀⢰⣤⡤⢂⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⢿⣡⣤⣶⡄⢀⡐⣳⣿⣄⠙⠥⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣆⠚⣿⣿⡾⢸⣿⣿⣿⡆⠶⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠌⠉⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠿⡯⢽⣴⣿⣿⣻⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠁⠐⠆⠀⠀⠀⠀⠀⠀⠚⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣥⣼⡿⢻⣿⣿⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠈⠀⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡷⣿⡿⣧⠀⠛⣩⣯⠠⣀
⠀⠀⠀⠀⠀⠀⠀⡁⣀⠒⠦⠖⠁⠀⠀⠀⠊⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣿⡧⣿⣿⣿⠦⠀⡏⣉⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⡄⠄⠀⠀⠑⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣦⣥⣄⣿⡿⠛⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢶⣷⢖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⠛⠱⠞⠿⠓⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠐⢺⣽⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣻⢿⣿⡿⠇⠺⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⢿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡯⢥⣴⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣿⠧⠀⠈⠘⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠉⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢂⡉⡭⠙⠛⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣚⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠠⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4087

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/What_Ethical_Source_Looks_Like_in_Practice.shtml
    Gemini version at https://techrights.org/n/2024/10/19/What_Ethical_Source_Looks_Like_in_Practice.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ What "Ethical Source" Looks Like in
Practice⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


People ban people or deny them service (or prevent them running a program) for
merely not agreeing with them:


       🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Open-source_repository_SourceHut_to_remove_all
                       cryptocurrency-related_projects⦈_


  🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇I_stopped_paying_for_sourcehut_because_his_opinions_are
  relevant_here_since_he_bans_types_of_projects_based_on_them._You_never_know
                   when_another_restriction_will_be_added.⦈_


"You never know when another restriction will be added."


Exactly!




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣼⣷⣿⣿⣿⣶⣿⣶⣿⣿⣷⣿⣾⣿⣾⣿⣿⣿⣾⣾⣷⣾⣷⣾⣿⣿⣷⣾⣷⣾⣿⣿⣿⣷⣾⣷⣯⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡠⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢫⣭⢻⢟⢻⢟⢻⢛⢻⣿⡿⣛⡿⡛⡟⣿⡟⣟⢟⣻⢛⢿⣿⢟⢟⣻⢛⡻⣟⡻⡟⣻⣿⣛⡿⣛⡟⣛⢻⢟⣿⡩⢭⡟⡻⡟⡟⡟⣻⢟⡻⣛⠏⠿⠏⡟⡟⡏⣻⣟⢙⢟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣮⣥⣿⣬⣼⣮⣽⣼⣼⣿⣯⣥⣷⣭⣷⣭⣧⣿⣮⣽⣭⣽⣿⣿⣮⣽⣨⣵⣯⣵⣯⣵⣿⣧⣷⣭⣧⣿⣇⣾⣿⣭⣵⣧⣵⣧⣥⣧⣿⣮⣵⣭⣧⣿⣧⣧⣥⣷⣽⣿⣬⣮⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢛⣿⡻⡿⡻⡛⡿⣛⡟⡿⡿⡻⣿⡿⡻⡏⡏⣿⡿⣻⡿⣛⢿⣛⢟⢟⢙⣟⡻⡿⣻⢻⡟⡿⣛⣟⢟⣻⢻⣻⢟⣻⢻⢿⣿⡟⣻⣟⢿⠹⣛⢻⢙⣟⡻⢟⡋⣿⡟⣛⡟⣟⢟⣻⢻⢟⣿⢟⣛⢙⢟⣻⣿⣿⣿⣿
⣿⣿⣼⣯⣭⣧⣧⣧⣧⣭⣿⣴⣧⣭⣿⣧⣭⣧⣧⣿⣧⣭⣿⣿⣠⣿⣭⣼⣬⣮⣵⣧⣭⣮⣥⣧⣿⣿⣮⣽⣼⣿⣮⣽⣏⣾⣿⣧⣿⣭⣽⣴⣭⣼⣬⣮⣭⣮⣥⣿⣇⣭⣧⣿⣬⣵⣸⣮⣽⣮⣽⣬⣭⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣭⣨⣋⣹⣈⣩⣇⣋⣁⣉⣯⣿⣿⣿⣫⣻⣽⣻⣿⣻⣿⣿⣹⣻⣟⣙⣍⣉⣏⣻⣟⣅⣩⣹⣋⣿⣿⣹⣁⣿⣻⣟⣟⣿⣹⣇⣊⣩⣋⣟⣟⣯⣨⣻⣿⣻⣝⣹⣻⣿⣋⣉⣿⣫⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢻⢻⠿⡿⠟⡿⡿⡿⢿⡟⠟⢿⢿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣿⣿⣿⣿⣿⣴⣨⣄⣤⣥⣌⣤⣤⣾⣧⣦⣤⣦⣤⣤⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⣻⣟⢻⡇
⣿⣿⣿⣿⣏⣽⣩⣉⣽⢸⢩⣫⣩⣁⣿⣿⣩⣉⣉⣽⣍⣉⣉⣝⣩⣹⢸⣫⣉⣋⣽⢸⣍⣨⣫⣙⣩⡇⡇⣩⣯⣉⣹⢸⣍⣙⣯⣉⣉⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣾⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣧⣼⣿⣿⣼⣷⣷⣿⣿⣿⣶⣷⣾⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣷⣷⣶⣶⣿⣿⣷⣿⣿⣿⣷⣿⣿⣷⣷⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣾⣾⣾⣷⣷⣶⣾⣾⣾⣿⣾⣾⣾⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇
⣿⣿⣿⣿⣯⣮⣶⣿⣷⣾⣾⣾⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⡏⣟⢻⡛⣻⡛⢛⠟⠛⣻⡟⣻⡛⠻⣿⡛⢛⣿⢩⡛⢛⡟⠛⣻⡟⢛⣛⠛⣟⠛⣿⣻⣟⠛⠻⣻⠛⢻⡟⠛⢻⣟⠋⡛⣿⡛⢛⠏⢛⣿⡛⢛⡟⣿⢛⣟⠛⣿⠛⠛⠙⢻⢟⠛⣟⠋⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⡗⢷⢾⠾⠾⣶⢴⡷⢾⢾⢧⡞⢶⠵⣿⠷⠧⡿⠾⢾⠾⢷⡾⠾⢶⢾⡶⠶⢻⠶⡾⡾⡗⠷⡾⡾⠶⣷⠷⠷⡾⡿⢶⠶⡿⢶⠴⡷⠞⢿⠾⠾⠷⣿⡶⠿⡷⣿⡾⢶⢾⢾⡾⡶⢿⠲⠾⡿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣷⣤⣼⣤⣯⣼⣿⣤⣵⣤⣧⣿⣤⣿⣥⣤⣿⣤⣼⣯⣢⣯⣤⣼⣼⣧⣽⣿⣨⢾⣮⣦⣤⣮⣯⡤⣿⣥⢤⣧⣧⣴⣥⣧⣽⣧⣿⣥⣿⣤⣼⣧⣽⣧⣯⣤⣽⣧⣴⣤⣦⣦⣤⣿⣬⣼⣯⣴⣦⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣌⣰⣁⣀⣎⣏⣸⣏⣑⣗⣰⣉⣈⣾⣱⣁⣁⣖⣰⣉⣂⣾⣊⣰⣹⣤⣹⣿⣿⣐⣇⣹⣇⣁⣨⣂⣁⣗⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

                    ䷩ 𝚕𝚒𝚗𝚎 4150

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

(ℹ) Images, hyperlinks and comments at https://techrights.org/n/2024/10/19/x86_Drowning_in_Competition_Bug_Doors_Complexity_and_Bloat.shtml
    Gemini version at https://techrights.org/n/2024/10/19/x86_Drowning_in_Competition_Bug_Doors_Complexity_and_Bloat.gmi

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ x86 Drowning in Competition, Bug Doors,
Complexity, and Bloat⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


THE FANATICAL ENERGY consumption of AMD and Intel chips is a big problem as it
hasn't been decent for decades. They just add more and more complexity - even
known security weaknesses - under the assumption that people must still buy (or
license) x86 hardware (or designs, respectively).


Just before the weekend we saw reports like "Spectre_flaws_continue_to_haunt
Intel_and_AMD" and the Microsoft-connected sites tried to spin that as a
"Linux" issue, not a hardware issue, by going with_a_headline_like_"Intel,_AMD
CPUs_on_Linux_impacted_by_newly_disclosed_Spectre_bypass"_and_then_harping
about_"Linux"_right_from_the_start:


     The latest generations of Intel processors, including Xeon chips, and
     AMD's older microarchitectures on Linux are vulnerable to new
     speculative execution attacks that bypass existing ‘Spectre’
     mitigations.


     The vulnerabilities impact Intel's 12th, 13th, and 14th chip
     generations for consumers and the 5th and 6th generation of Xeon
     processors for servers, along with AMD's Zen 1, Zen 1+, and Zen 2
     processors.


It's not a Linux issue, it's a hardware issue. Linux isn't hardware. There has
been a wave_of_FUD_lately.


"Spectre has been afflicting Intel since before 2018," an associate has
remarked, "and shows no sign of letting up as new hardware vulnerabilities in
that category are detected every quarter."


The associate says it might be "related to layoffs, I suppose, since the
layoffs also help distract from the Spectre news".


Today I spoke about the Intel layoffs with someone who knows many people there.
They are terrified and they know more waves or layoffs are coming. For Intel
there is no simple road to recovery. The only roadmap is, reduce costs; well,
reducing staff may only worsen the products even further.


I'm told that right now Intel just relies on the US government rescuing it [1,
2]; for without Intel, "China wins".


Making defective chips for a number of decades was sheer Hubris; they just
assumed people would continue buying Intel machines forever. And no matter how
faulty or energy-inefficient they become, people will have no choice. █




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⣛⣿⣻⣛⣻⡛⣉⣟⠛⣛⣛⣻⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣏⣙⣙⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠛⠿⠿⠿⠟⠛⠛⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⠇⣿⣿⠏⢿⠿⢿⣿⣿⣿⣿⣿⡟⢿⣿⠿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⠿⠛⠛⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠁⠘⠀⣿⠀⠀⠀⠀⢸⣿⢿⣿⠛⢻⡇⠸⠧⠁⠀⢻⠏
⠉⠹⠛⣿⡿⠛⠛⠋⠉⠻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠈⠁⠉⠀⠀⠀⠁⠀⠀⠀⢀⣤⣤⣤⡤⠤⠤⠰⠶⠄⠒⠒⠛⣿⣿⣿⣿⣿⡿⡙⠃⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⠛⠘⠛⠀⠸⠇⠀⠘⠀⠀⠘⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠂⠀⠀⠂⠒⠒⠂⠐⠒⠒⠀⠂⠐⠂⠐⠂⠀⠀
⣴⣦⣟⣾⣗⣿⣿⣿⣿⣿⣿⣿⣯⣿⣶⣶⣶⣶⣿⡶⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢉⠩⠋⠋⠛⠛⠛⠛⠭⠤⠈⠁⠉⠉⠭⠳⠑⠈⠀⠀⠀⠀⠀⠀⢀⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⢿⣿⡿⣿⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣴⣴⣴⣶⣶⣶⠶⠖⠒⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⣿⣿⣿⣿⣷⣤⣤⣤⣀⣄⣀⣀⣀⣀⣀⣀⠀⠀⢀⣄⣀⣄⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠉⣁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣲⣔⣒⣿⢿⣿⣿⣿⣿⡿⠿⢟⡛⠛⠛⠛⠿⠿⢛⣛⣟⡛⣿⣯⣝⣛⠻⠭⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⣖⣺⣿⣿⣿⣟⡛⣛⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢄⡀⣉⠍⠉⠋⠺⣛⠉⢀⣀⣀⣠⣲⣀⣥⡴⠶⢶⣿⣿⣟⣋⢀⣲⡊⣲⣶⡦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡧⠄⠂⣀⠀⠀⠀⠉⠉⠉⠀⣀⠀⠗⠀⠀⠒⠐⠛⠛⠻
⠈⠁⠀⠐⠂⠂⠀⣀⣒⣛⠉⠉⣿⡋⣙⣛⣛⠛⢛⠛⠩⠭⠽⠴⠶⣶⣶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣿⣿⣷⣶⡾⢿⣶⣿⣷⣿⣿⣿⣯⣽⣿⣶⣶⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠙⠀⠉⢭⠉⡭⠑⣒⡒⣚⡧⠀⣤⣤⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠲⣦⣄⡤⠤⠖⢢⣄⣀⣀⡀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠿⠿⠷⠶⣶⣾⣿⣿⣭⣭⣥⣶⣶⣾⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠠⠄⠀⠐⠲⠭⣍⡉⢩⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢄⣀⡀⠀⠐⠶⠶⠶⠄⢀⣀⣀⣀⠈⠉⠛⠛⠲⠶⠶⣶⣾⣿⣭⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠤⠔⣒⣀⣈⣩⠭⠭⠍⠛⠒⢒⣂⣀⣐⠒⠒⠒⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠑⠒⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠤⠤⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⠤⢌⣉⣉⣓⠈⣉⣉⡉⠉⠛⠛⠙⠥⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠁⠠⠄⠀⠀⠒⠀⠐⠶⠦⠤⠤⠄⠀⠀⠈⠉⠉⠉⠙⠛

                    ䷩ 𝚕𝚒𝚗𝚎 4253

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Gemini Links 19/10/2024: Against Books as
Only Possible Legitimation, Megacorporate Copyright
Pirates⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Gemini*_and_Gopher
          o Personal/Opinions
          o Technology_and_Free_Software
    * § Gemini* and Gopher⠀➾


          o § Personal/Opinions⠀➾


                # ⚓ Habits_and_the_environment⠀⇛


                       I recently started to read the book "Atomic Habits"
                       by James Clear. I have really been enjoying it so
                       far. I am currently about half way through. The
                       issue that I have been having is, even though I am
                       enjoying what I am reading, and all the advice is
                       really solid, I have no idea what habits I would
                       like to set. I have become fairly complacent with
                       where I am at in life so seeking out things to
                       improve has been difficult. Not to mention having
                       ADHD makes it hard to be motivated to do anything.
                       This largely changed after I read through the
                       section on your environment


                # ⚓ Against_Books_as_Only_Possible_Legitimation⠀⇛


                       Rebel against the fetishism of the book. Something
                       being in a book does not necessarily make it
                       legitimate, nor are all legitimate things
                       determined by being found in a book.


                       This might come across as a bit odd coming from me,
                       bookhoarder and bookish occultist that I am, but
                       when it comes to magic, magical practice, and
                       magical innovation, hear me out. Yes, to be sure,
                       there are lots of ways to accomplish something
                       magically, and lots of traditions provide a lot of
                       concrete, recorded methods, many of which are often
                       compiled in books in one form or another. Such
                       books (rubrics, missals, grimoires, spellbooks,
                       manuals, enchiridia, and so on) are super useful!
                       But here's the thing: books are inherently limited,
                       compared to the infinite variation in human life
                       and experiences. Worse, once you only consider
                       stuff in books as valid or only the stuff in the
                       way such books present it, then they become
                       limiting as well. People who think this way only
                       memorize instead of integrate, and not as many take
                       that next step of synthesis and extrapolation as
                       one might think. Such people limit themselves only
                       to what is read, and think that that's the end of
                       it.


                # ⚓ 🔤SpellBinding_—_BEUJSTI_Wordo:_RITZY⠀⇛


          o § Technology and Free Software⠀➾


                # ⚓ The_Megacorporate_Copyright_Pirates⠀⇛


                       When the people are being beaten with a stick, they
                       are not much happier if it is called “piracy”.


                       It broke my heart to see the prog left suddenly be
                       in favor of copyright and I’m so grateful that for
                       the few that have pushed back on that. Thank you so
                       much for that. Copyright is bad and using it
                       against ML is a bad argument.


                       But to add some nuance to this, I have sympathy for
                       how messed up it is that it’s “copyright for me but
                       not for thee”—in the RIAA era, big corporate used
                       copyright to bludgeon the people and now in the LLM
                       era big corporate is using disregard for copyright
                       to bludgeon the people. It makes us feel helpless.


                # ⚓ Working_mouse_in_VNC_with_vm-bhyve_on_FreeBSD⠀⇛


                       On FreeBSD vm-bhyve is a great tool to create,
                       install and manage virtual machines.


                       vm-bhyve is designed to work with ZFS, which makes
                       it very easy to create new vm's, and make ZFS
                       snapshots of those.


                       For a project I created a Ubuntu virtual machine
                       with a graphical desktop.


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





                    ䷩ 𝚕𝚒𝚗𝚎 4384

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 19/10/2024: European Perspective,
Windows TCO, and Google Woes⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
                # Windows_TCO
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Monopolies/Monopsonies
    * § Leftovers⠀➾


          o ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_Nepali_teen_hailed_after
            setting_8,000-meter_peak_record⠀⇛


          o § Science⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Robot_Symphony:_Dresden
                  orchestra_conducted_by_a_three-armed_robot⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_Robot_replaces
                  conductor_in_Dresden⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Nihon_Hidankyo:_What_to
                  know_about_Nobel_Peace_Prize_winners⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Sensational_claim_on
                  Columbus_ethnicity_can’t_be_verified_say_independent
                  experts⠀⇛


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-13_[Older]_What's_behind_the
                  medication_shortages_in_Germany?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_AI_research_uncovers
                  160,000_new_RNA_viruses⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Plant-based_milk_—_a
                  greener,_healthier_dairy_alternative?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_Germany:_Teenager
                  crashes_car_into_sewage_treatment_pool⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_UK_plans_weight_loss
                  drug_trials_to_get_people_back_to_work⠀⇛


                # ⚓ CBC ☛ 2024-10-15_[Older]_This_Guelph,_Ont.,_couple_is
                  looking_for_a_surrogate_via_social_media_after_frustrating
                  search⠀⇛


                # ⚓ CBC ☛ 2024-10-16_[Older]_Canada_must_act_now_to_be_prepared
                  for_the_next_health_emergency,_new_pandemic_report_warns⠀⇛


                # ⚓ CBC ☛ 2024-10-16_[Older]_No_tomatoes,_no_canned_meat:_What
                  it's_really_like_inside_this_small_town_food_bank⠀⇛


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # § Windows TCO⠀➾


                      # ⚓ CBC ☛ 2024-10-12_[Older]_Hackers_keep_targeting
                        Canada's_libraries._Calgary's_are_the_latest_to_shut
                        down⠀⇛


          o § Defence/Aggression⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_EU_seeks_to_accelerate
                  return_of_migrants⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-10_[Older]_Germany:_Police_shoot
                  man_in_western_city_of_Krefeld⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-12_[Older]_Poland:_Tusk_plans_to
                  suspend_right_to_asylum⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Angola_caught_in_tug-
                  of-war_between_China,_US⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-12_[Older]_Pakistan:_Deadly_clash
                  erupts_between_tribes_in_Kurram⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_UK_begins_inquiry_into
                  woman's_death_by_Novichok_nerve_agent⠀⇛


                # ⚓ CBC ☛ 2024-10-16_[Older]_Former_special_ops_soldier_says_he
                  faced_'retaliation'_for_reporting_alleged_killing_of_Afghan
                  civilians⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_SCO_meeting:_Why_is_it
                  a_big_deal_for_Pakistan?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_Seoul_says_North_Korea
                  moving_to_blow_up_cross-border_roads⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-12_[Older]_Iran:_Activist_removed
                  from_death_row_after_court_ruling⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-12_[Older]_Do_immigrants_have_to
                  learn_German_in_Germany?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-12_[Older]_Germany:_Man_dies_after
                  standoff_with_police_in_Bochum⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-15_[Older]_Canada_Lists
                  Pro-Palestinian_Group_Samidoun_as_a_'Terrorist'_Entity⠀⇛


                # ⚓ CBC ☛ 2024-10-12_[Older]_Shots_fired_at_Toronto_Jewish
                  girls_school_overnight:_police⠀⇛


                # ⚓ CBC ☛ 2024-10-13_[Older]_Rally_calls_for_more_protections
                  against_hate_crimes_after_Toronto_Jewish_school_shot_at_for
                  2nd_time⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_Lufthansa_pays_$4m_fine
                  over_treatment_of_Jewish_passengers⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Rising_discontent_with
                  military_juntas_in_the_Sahel_region⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Sudan:_Conflict
                  escalates_and_exacerbates_humanitarian_situation⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_Exiled_Chinese_in_Japan
                  encounter_the_long_arm_of_Beijing⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-13_[Older]_Germany:_WWII_bomb
                  defused_in_Hamburg's_nightlife_district⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_China_makes_major_show
                  of_force_with_war_games_near_Taiwan⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_China_military_drills
                  ramp_up_pressure_on_Taiwan⠀⇛


          o § Environment⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_US:_Biden_estimates
                  Milton_damages_at_$50_billion⠀⇛


                # § Energy/Transportation⠀➾


                      # ⚓ CBC ☛ 2024-10-11_[Older]_Hidden_camera,_internal_memo
                        reveal_how_unqualified_truck_drivers_are_getting_onto
                        Canada's_roads⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Nigeria:_More
                        than_140_dead_in_fuel_tanker_explosion⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Eurowings_cuts
                        flights_at_Hamburg_Airport_over_rising_costs⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Boeing_to_lay_off
                        10%_of_staff,_delay_first_777X_delivery⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-12_[Older]_China:_'Major
                        differences'_remain_over_EU_car_tariffs⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_Germany:_Busy
                        train_derails_in_Saarland,_hitting_large_rock⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-13_[Older]_Lufthansa_CEO
                        concerned_more_airlines_will_cut_German_routes⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-13_[Older]_Israel-Iran:_A
                        strike_on_oil_assets_could_revive_inflation⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-13_[Older]_Germany:_11
                        injured_after_ghost_train_ride_catches_fire⠀⇛


                # § Wildlife/Nature⠀➾


                      # ⚓ CBC ☛ 2024-10-15_[Older]_Alberta_livestock_producers
                        want_coyotes_added_to_wildlife_compensation_program.
                        Here's_why⠀⇛


                      # ⚓ CBC ☛ 2024-10-11_[Older]_Great_white_shark_found_dead
                        on_Haida_Gwaii,_off_B.C.'s_North_Coast⠀⇛


                      # ⚓ US News And World Report ☛ 2024-10-11_[Older]_Woman
                        Pleads_Guilty_to_Trying_to_Smuggle_29_Turtles_Across_a
                        Vermont_Lake_Into_Canada_by_Kayak⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-12_[Older]_Brazil_faces
                        worst_fires_in_14_years⠀⇛


                      # ⚓ CBC ☛ 2024-10-14_[Older]_Endangered_turtles_get_some
                        TLC_from_dedicated_guardians_in_the_Ottawa_area⠀⇛


          o § Finance⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Why_is_Indonesia's
                  middle_class_shrinking?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-12_[Older]_China_announces
                  stimulus_plan_to_revive_economic_growth⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Germany_takes_steps_to
                  attract_skilled_Indian_workers⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Wanted_in_Germany:
                  Heirs_for_family-owned_businesses⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Why_South_Korean
                  culture_is_a_global_hit⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_German_inflation_dips
                  to_lowest_in_more_than_3_years⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-13_[Older]_Spain:_Thousands
                  protest_for_affordable_housing⠀⇛


                # ⚓ CBC ☛ 2024-10-15_[Older]_Inflation_rate_drops_to_1.6%_in
                  September⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_What_is_behind
                  Vietnam's_economic_success_story?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_Why_Hyundai_picked
                  India_for_record_$3.3_billion_IPO⠀⇛


                # ⚓ CBC ☛ 2024-10-16_[Older]_Major_retailers_spend_millions
                  hiring_Winnipeg_police_officers_on_OT_to_stop_shoplifters⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_Young_Germans_fear_war
                  and_poverty_yet_remain_optimistic⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_World_Bank:_Poorest
                  countries_facing_worst_debt_since_2006⠀⇛


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_How_democratic_is_the
                  US_really?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Kenya_Senate_begins
                  debate_on_deputy_president_impeachment⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_North-South_Korea
                  flare-up:_Why_is_it_alarming?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Omar_Abdullah:_Jammu
                  and_Kashmir_chief_minister_sworn_in⠀⇛


                # ⚓ CBC ☛ 2024-10-15_[Older]_Bomb_threat_causes_Air_India
                  emergency_landing_in_Iqaluit⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-14_[Older]_India_Says
                  Envoy_to_Canada_a_'Person_of_Interest'_in_Investigation⠀⇛


                # ⚓ CBC ☛ 2024-10-14_[Older]_India_says_envoy_to_Canada_a
                  'person_of_interest'_in_investigation⠀⇛


                # ⚓ CBC ☛ 2024-10-14_[Older]_Canada's_accusations,_tit-for-tat
                  diplomat_expulsions_lead_India_headlines⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-16_[Older]_Indians_in
                  Punjab_Fear_Dispute_With_Canada_Endangers_Work,_Study_Plans⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-13_[Older]_Indian_politician_Baba
                  Siddique_shot_dead_in_Mumbai⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_How_do_Indians_view
                  diplomatic_tensions_with_Canada?⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-15_[Older]_Canada-India
                  Ties_Could_Take_a_Long_Time_to_Recover⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-15_[Older]_India_Sees_No
                  Impact_on_Canada_Trade_Ties_From_Diplomatic_Spat,_Govt_Source
                  Says⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-15_[Older]_Explainer-Who
                  Is_Lawrence_Bishnoi,_at_Centre_of_Row_Between_India_and
                  Canada?⠀⇛


                # ⚓ CBC ☛ 2024-10-16_[Older]_More_than_300_CRA_employees_who
                  improperly_received_CERB_no_longer_with_agency⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-16_[Older]_Trudeau_Says
                  Some_Opposition_Canada_MPs_Could_Be_Involved_in_Foreign
                  Interference⠀⇛


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Deutsche Welle ☛ 2024-10-13_[Older]_RECOMMENDED_—
                        Political_parties_are_increasingly_using_[computer]-
                        generated_content_for_their_election_campaigns._But
                        what_effects_could_this_have?⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-13_[Older]_Fact_check:_How_
                        [computer]-generated_(CG)_influences_election
                        campaigns⠀⇛


          o § Censorship/Free Speech⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Frankfurt_Book_Fair:
                  Saviano_attends_despite_Rome_snub⠀⇛


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


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_German_broadcaster
                  WDR's_orange_mouse_mascot_'kidnapped'⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_DW_condemns_attack_on
                  reporter_at_Dusseldorf_concert⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_Bangladesh:_Journalists
                  supportive_of_ex-PM_Hasina_targeted⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Is_divorce_coming_to
                  the_Philippines?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Germans_divided_over
                  far-right_AfD_ban⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-11_[Older]_Germany_moves_to
                  protect_top_court_against_far_right⠀⇛


                # ⚓ CBC ☛ 2024-10-16_[Older]_This_Quebec_traveller_gets
                  mistaken_for_a_criminal_at_the_U.S._border._He's_not_the_only
                  one⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-14_[Older]_German_court_jails
                  former_Stasi_member_for_1974_murder⠀⇛


                # ⚓ CBC ☛ 2024-10-14_[Older]_Public_service_union_calls_for
                  investigation_into_return-to-office_mandate⠀⇛


      § Monopolies/Monopsonies⠀➾


          o ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_Will_Google_finally_cave_in
            under_US_regulatory_pressure?⠀⇛


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





                    ䷩ 𝚕𝚒𝚗𝚎 4862

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 19/10/2024: Nokia Lays Off 2,000
Employees, IMF Loans, Lammy to China⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Privacy/Surveillance
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Wildlife/Nature
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
                # Patents
                # Trademarks
                # Copyrights
                # Gemini*_and_Gopher
                      # Technology_and_Free_Software
    * § Leftovers⠀➾


          o ⚓ The Straits Times ☛ S._Korean_Nobel_winner_Han_Kang_hopes_daily
            life_‘won’t_change_much’⠀⇛


                 She hopes she would be able to continue her normal
                 routines, focused on writing.


          o ⚓ University of Michigan ☛ Unlearning_and_relearning_the_19th
            Amendment⠀⇛


                 In high school, I had reading phases spanning myriad
                 genres, ranging from an intense interest in wild fantasy
                 sagas to a soft spot for memoirs and especially a strange
                 fixation for historical fiction novels.


          o ⚓ Hackaday ☛ A_Hacker’s_Travel_Guide_To_Europe⠀⇛


                 This summer, I was pleasantly surprised when a friend of
                 mine from Chicago turned up at one of the hacker camps I
                 attended. A few days of hanging out in the sun ensued,
                 doing cool hacker camp stuff, drinking unusual beverages,
                 and generally having fun. It strikes me as a shame that
                 this is such a rare occurrence, and since Hackaday is an
                 American organisation and I am in a sense writing from
                 its European outpost, I should do what I can to encourage
                 my other friends from the USA and other parts of the
                 world to visit. So here I’m trying to write a hacker’s
                 guide to visiting Europe, in the hope that I’ll see more
                 of you at future camps and other events.


          o ⚓ New York Times ☛ Sick_of_the_21st_Century?_These_Artists_Revive
            the_18th.⠀⇛


                 Copycat classicism is here. Literary re-enactments by the
                 photographer Stan Douglas — and a wave of other remixers
                 — are creating new types of art around Black history.


          o § Science⠀➾


                # ⚓ Science Alert ☛ Cats_Basically_Are_a_Liquid_After_All,
                  Study_Confirms⠀⇛


                       We knew it!


                # ⚓ Science Alert ☛ Study_Confirms_a_Simple_Trick_to
                  Communicate_With_Your_Cat⠀⇛


                       It really works!


                # ⚓ Science Alert ☛ Astronauts_to_Wear_Prada_For_Humanity's
                  Return_to_The_Moon⠀⇛


                       The secret is out.


                # ⚓ Science Alert ☛ Controversial_'Mutant_Breeding'_Fad_Is
                  Endangering_The_Health_of_Pets⠀⇛


                       A disturbing trend.


                # ⚓ Science Alert ☛ Heat-Tolerant_Corals_Can_Better_Survive
                  Marine_Heatwaves,_Study_Shows⠀⇛


                       But we need to do so much more.


                # ⚓ Science Alert ☛ This_Small_Tweak_Makes_a_Huge_Difference_to
                  Your_Daily_Walk⠀⇛


                       You could be getting more out of your steps.


          o § Education⠀➾


                # ⚓ The Straits Times ☛ Anwar_to_cut_fuel_and_education
                  subsidies_for_top_earners_under_Malaysia’s_Budget_2025⠀⇛


                       Larger urban households with higher incomes will be
                       the hardest hit, say experts.


                # ⚓ The Straits Times ☛ Pakistan_province_shuts_education
                  institutions_after_violent_protests_over_alleged_rape⠀⇛


                       Protesters alleged a female student was raped by a
                       security guard on the campus of a private college
                       chain.


          o § Hardware⠀➾


                # ⚓ CNX Software ☛ AAEON_FWS-2290_defective_chip_maker_Intel
                  N97_network_appliance_targets_UTM_and_VPN_applications⠀⇛


                       AAEON has recently released the FWS-2290, an
                       defective chip maker Intel N97 network appliance.
                       This is not quite the first network appliance
                       launched by the Taiwanese company. Back in 2018,
                       they launched the AAEON FWS-2360 designed for
                       wireless gateway, SD-WAN, IPS, WAN Optimization,
                       NFV, and vCPE applications. In 2020, they followed
                       up with the FWS-2275 rugged network appliance for
                       Secure industrial IoT networks, and then, in 2021,
                       they introduced the FWS-2280 Elkhart Lake network
                       appliance designed for UTM (Unified Threat
                       Management), firewall, SD-WAN (Software-defined
                       Wide Area Network), VPN, and other applications.


                # ⚓ Hackaday ☛ Teardowns_Show_Off_Serious_Satellite_Hardware⠀⇛


                       As hackers, we’re always pulling stuff
                       apart—sometimes just to see what it’s like inside.
                       Most of us have seen the inside of a computer,
                       television, and phone. These are all common items
                       that we come into contact with every day. Fewer of
                       us have dived inside real spacey satellite
                       hardware, if only for the lack of opportunity. Some
                       good gear has landed on [Don]’s desk over the years
                       though, so he got to pulling it apart and peering
                       inside.


                # ⚓ Hackaday ☛ CNC_Metal_Forming⠀⇛


                       Forming complex shapes in metal sheets is still a
                       laborious process, especially if you aren’t needing
                       more than a couple parts so stamping doesn’t make
                       sense. That may change with Digital Sheet Forming.


                # ⚓ Hackaday ☛ Smart_Glasses_Read_Text⠀⇛


                       You normally think of smart glasses as something
                       you wear as either an accessory or, if you need a
                       little assistance, with corrective lenses. But
                       [akhilnagori] has a different kind of smart
                       eyewear. These glasses scan and read text in the
                       user’s ear.


                # ⚓ Hackaday ☛ Little_RC_Car_Project_Takes_Inspiration_From
                  Mario_Kart⠀⇛


                       RC cars used to be pretty simple. They’d go
                       forwards, backwards, and steer if you got a full-
                       function toy. However, with modern technology, it’s
                       pretty trivial to make them more advanced. [Stuck
                       at Prototype] demonstrates that nicely with his
                       little Micro Racer Cars.


                # ⚓ Tom's Hardware ☛ Former_defective_chip_maker_Intel_CPU
                  engineer_details_how_internal_x86-64_efforts_were_suppressed
                  prior_to_AMD64's_success⠀⇛


                       Intel was hesitant to embrace x86-64 given the
                       resources put into Itanium.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ The Straits Times ☛ South_Korean_man_dies_after_being
                  turned_away_by_10_hospitals;_govt_to_investigate⠀⇛


                       Even after he was admitted to a hospital, he could
                       not be operated on due to a staff shortage.


                # ⚓ The Straits Times ☛ Auntie_Anne’s_ex-employee_who_kissed
                  dough_fired_from_Nando’s_Malaysia_after_first_day_of_work⠀⇛


                       Nando’s said the woman had violated its company's
                       policies.


                # ⚓ The Straits Times ☛ 15_jailed_in_China_over_Changsha
                  building_collapse_that_killed_dozens⠀⇛


                       The April 2022 collapse left more than 50 people
                       dead and nine wounded.


                # ⚓ ACLU ☛ Abortion_Rights_Are_on_the_Ballot_This_Election⠀⇛


                       This year, the presidential race has been all
                       consuming. Less than 20 days before Election Day,
                       practically everyone has something to say about the
                       candidates. The ACLU has also spent time analyzing
                       the policies and actions both Donald_Trump and
                       Kamala_Harris might take if they win the White
                       House.


                # ⚓ New Yorker ☛ The_Stakes_for_Abortion_Rights,_from_the_Head
                  of_Planned_Parenthood⠀⇛


                       Alexis McGill Johnson discusses lobbying for a
                       Democratic “trifecta” in Washington—and what a
                       second Trump Administration would do on abortion
                       rights in America.


                # ⚓ JURIST ☛ Texas_attorney_general_sues_doctor_for_providing
                  gender_transition_care_to_minors⠀⇛


                       Texas Attorney General Ken Paxton filed a lawsuit
                       Thursday against a physician for providing gender
                       transition care to 21 minor patients, in violation
                       of a Texas law prohibiting gender transition
                       medical interventions.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ France24 ☛ Ubisoft:_What's_behind_the_fall_of_France's
                  video_games_darling?⠀⇛


                       "Assassin's Creed" played a starring role in the
                       Paris Olympics Opening Ceremony, with a masked
                       figure dressed like the protagonist running across
                       the rooftops of Paris with the Olympic flame. Now,
                       the game's developer Ubisoft is rumoured to be in
                       talks to be taken private, in a possible
                       acquisition by Chinese gaming giant Tencent.


                # ⚓ India ☛ Nokia_Lays_Off_2,000_Employees_in_China,_350_in
                  Europe⠀⇛


                       Finland-based tech company Nokia has decided to lay
                       off around 2,000 employees (or 20 per cent of its
                       workforce) in Greater China and 350 employees in
                       Europe, Reuters has reported citing sources. The
                       Nokia layoffs are part of the company’s cost-
                       reduction strategy.


                # ⚓ India Dot Com Pvt Ltd ☛ Nokia_Layoffs:_Tech_Giant_Likely_To
                  Cut_Over_2,000_Jobs_As_Part_Of_Cost-Cutting_Strategy⠀⇛


                       Nokia, the Finland-based tech giant, has reportedly
                       announced significant job cuts, with plans to
                       eliminate nearly 2,000 positions in Greater China.
                       Adding further, the company is looking to cut
                       another 350 jobs in Europe as part of its broader
                       cost-cutting measures.


                       The layoffs are part of Nokia's efforts to
                       streamline operations and achieve cost savings of
                       up to 1.2 billion euros by 2026. A Nokia
                       spokesperson confirmed the job cuts in Europe but
                       did not comment on those in China.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Internet Society ☛ Take_a_Step_Towards_Privacy:
                        Understanding_Digital_Footprints⠀⇛


                             Digital footprints are trails of data that
                             people leave behind as they use the
                             Internet. This data contributes to a digital
                             portrait of who we are—one that is more
                             public than many people realize. 


          o § Defence/Aggression⠀➾


                # ⚓ The Straits Times ☛ North_Korea’s_Kim_Jong_Un_says_South
                  Korea_is_a_foreign,_hostile_country⠀⇛


                       Mr Kim said the changed nature of the S. Korea-US
                       alliance highlights the importance of a stronger N.
                       Korean nuclear deterrent.


                # ⚓ The Straits Times ☛ North_Korea_says_it_recovered_crashed
                  South_Korean_military_drone⠀⇛


                       Seoul has declined to say if such drones were
                       flown.


                # ⚓ The Straits Times ☛ China_urges_India_to_handle_Taiwan
                  issue_cautiously_after_Mumbai_office_opening⠀⇛


                       China opposes moves by any countries it has ties
                       with to engage in official contacts with Taiwan.


                # ⚓ The Straits Times ☛ Seeking_peacemaker_image,_China_shifts
                  to_more_neutral_stance_on_Israel-Palestine_war⠀⇛


                       Beijing has been seen to have taken up the
                       Palestinian cause after global anger at Israel’s
                       Gaza retaliation.


                # ⚓ The Straits Times ☛ China_says_it_is_beefing_up_efforts
                  with_US_to_combat_smuggling⠀⇛


                       Nearly 56,000 Chinese migrants have been
                       encountered at the Southwest border with Mexico.


                # ⚓ The Straits Times ☛ Taiwan_President_Lai_thanks_air_force
                  for_‘outstanding’_work_during_China_war_games⠀⇛


                       Taiwan’s air force has repeatedly scrambled to see
                       off almost-daily missions by the Chinese military.


                # ⚓ The Straits Times ☛ Taiwan_blames_China_for_South_Africa’s
                  order_to_move_liaison_office⠀⇛


                       China said South Africa had made the “right
                       decision” to move the Taipei office out of
                       Pretoria.


                # ⚓ RFA ☛ China_denies_entry_to_Myanmar_nationals_trapped_by
                  battle⠀⇛


                       Roughly 1,000 villagers are camped along the border
                       with nowhere to go, residents said.


                # ⚓ Atlantic Council ☛ Toward_a_coherent_framework_for_US-China
                  tech_competition_in_the_Global_South⠀⇛


                       This memo provides strategists and policymakers in
                       the United States and elsewhere with a coherent
                       framework for understanding the competition between
                       the United States and China for technological
                       dominance with respect to the Global South.


                # ⚓ France24 ☛ Italian_Prime_Minister_Giorgia_Meloni_visits
                  Lebanon_after_UNIFIL_strikes⠀⇛


                       Italian Prime Minister Giorgia Meloni arrived
                       Friday in Lebanon, her office said, the first head
                       of state or government to visit since an escalation
                       between Israel and Hezbollah last month. For more,
                       Rawad Taha, FRANCE 24 correspondent reports.


                # ⚓ France24 ☛ Lebanon:_One_war_too_many⠀⇛


                       It’s the deadliest conflict in Lebanon since the
                       1975-1990 civil war. The current war between
                       Hezbollah and Israel has set the whole country
                       ablaze. The provisional death toll on the Lebanese
                       side stands at more than 2,300, with 11,000
                       wounded, while thousands more are missing. The
                       violence of the Israeli strikes has also provoked a
                       mass exodus of the population: some 1.2 million
                       people already have been forced to leave their
                       homes, or a fifth of the population.


                # ⚓ The Straits Times ☛ Britain,_China_strike_conciliatory_note
                  during_UK_foreign_secretary’s_visit⠀⇛


                       Beijing heralded the new Labour government’s plan
                       to develop “pragmatic” bilateral ties as a “new
                       starting point”.


                # ⚓ The Straits Times ☛ China_building_capacity_to_rapidly
                  strike_Taiwan,_says_senior_Taiwanese_official⠀⇛


                       Taiwan has for the past 5 years complained of
                       almost daily Chinese military activities around the
                       island.


                # ⚓ New York Times ☛ Italian_Judges_Strike_Down_Request_to_Hold
                  Migrants_in_Albania⠀⇛


                       The ruling was a major blow to the conservative
                       government’s plan to have asylum claims heard in
                       Albania instead of Italy.


                # ⚓ New York Times ☛ U.S._B-2_Bombers_Strike_Iran-Backed_Houthi
                  Weapons_Caches_in_Yemen⠀⇛


                       Air Force B-2 bombers struck five underground
                       weapons facilities in what may be a signal from the
                       Biden administration to Iran.


                # ⚓ New York Times ☛ Israel_Destroys_Nearly_All_of_a_Lebanese
                  Village,_Photos_and_Videos_Show⠀⇛


                       About two dozen buildings were demolished in the
                       village, which The Times identified as Mhaibib,
                       just over a mile from Israel’s northern border.


                # ⚓ New York Times ☛ Israeli_Military_Drone_Footage_Claims_to
                  Show_Yahya_Sinwar_Shortly_Before_He_Was_Killed⠀⇛


                       The video shows a room that matches photographs
                       obtained by The Times that show the corpse of a man
                       closely resembling the Hamas leader.


                # ⚓ New York Times ☛ U.S._Charges_Indian_Official_in_New_York
                  Assassination_Plot⠀⇛


                       The United States and Canada have worked together
                       to investigate what they say is the Indian
                       government’s campaign against Sikh separatists.


                # ⚓ RFA ☛ China_builds_spy_base_on_disputed_island:_think
                  tank⠀⇛


                       Chatham House says Beijing is turning Triton Island
                       into a key signal intelligence base in the South
                       China Sea.


                # ⚓ France24 ☛ The_real_'Miss_Moneypenny':_New_book_on_history
                  of_women_in_British_intelligence⠀⇛


                       So was Miss Moneypenny, as she was referred to in
                       James Bond novels and films, a real person? It
                       turns out, yes. Annette Young talks to Dr Claire
                       Hubbard-Hall, the author of 'Her Secret Service:
                       The Forgotten Women of British Intelligence' about
                       the woman who inspired the character and why women
                       do make better spies. Also as femicide continues to
                       be a serious problem across the globe, a highly
                       moving story of a French woman who miraculously
                       managed to escape being killed by her ex-boyfriend.
                       Plus how a comic strip is helping to shatter taboos
                       about menstruation for schoolchildren in the
                       Democratic Republic of Congo.


                # ⚓ JURIST ☛ UK,_France,_Algeria_call_for_urgent_UNSC_meeting
                  on_Gaza_humanitarian_crisis⠀⇛


                       The United Kingdom announced that it, along with
                       France and Algeria, has called for an urgent
                       meeting at the United Nations Security Council
                       (UNSC) to discuss the humanitarian situation in
                       Gaza while the Prime Minister Keir Starmer said
                       that the UK was considering sanctions on Israeli
                       Ministers. 


                # ⚓ New York Times ☛ U.N._Peacekeeping_Force_in_Southern
                  Lebanon_Will_Remain,_U.N._Official_Says⠀⇛


                       Israel has demanded that the force, known as
                       UNIFIL, pull out. But all the countries
                       contributing troops and the U.N. Security Council
                       decided unanimously that UNIFIL should stay.


                # ⚓ BIA Net ☛ Turkey_prepares_for_steep_increase_in_defense
                  budget_for_2025⠀⇛


                       Some 46 billion US dollars will be allocated for
                       defense and internal security according to the
                       government’s plans.


                # ⚓ Defence Web ☛ Sudan_is_burning_and_foreign_powers_are
                  benefiting_–_what’s_in_it_for_the_UAE⠀⇛


                       The United Nations has accused foreign players of
                       prolonging the war in Sudan, making it harder for
                       the country to find peace. The fighting between the
                       Sudanese Armed Forces and the Rapid Support Forces
                       started in April 2023. It was sparked by two
                       generals competing for power after a failed
                       political transition.


                # ⚓ Defence Web ☛ African_conflicts_seen_as_“footnotes”_–
                  Lamola⠀⇛


                       South African international relations and co-
                       operation minister Ronald Lamola maintains
                       conflicts in Sudan, the Sahel and Democratic
                       Republic of Congo (DRC) are “footnotes” while the
                       media glare internationally is on Russia/Ukraine
                       and Hamas/Israel.


                # ⚓ France24 ☛ End_of_Sinwar,_now_how_to_end_the_war?_Ukraine,
                  Meloni_&_the_US_Elex⠀⇛


                       Hamas confirms its political and military leader
                       Yahya Sinwar has been killed by Israel, 24 hours
                       after IDF forces announced his death in the
                       southern Gaza city of Rafah. In a defiant video
                       speech, an official for the Iranian backed militant
                       group said the death would not mean the release of
                       Israeli hostages, unless IDF withdraw from the
                       strip.


                # ⚓ France24 ☛ I_regret_not_reaching_a_'common_position_on_the
                  Middle_East',_EU_foreign_policy_chief_Borrell_says⠀⇛


                       As he nears the end of his term, Josep Borrell, the
                       EU’s High Representative for Foreign and Security
                       Policy, speaks to Talking Europe about the two
                       crises that he has been most closely involved in:
                       the Middle East and Ukraine. He recounts his
                       efforts to reach a ceasefire in Gaza and in
                       Lebanon, and outlines possible ways to speed up EU
                       assistance to Ukraine. His biggest regret over the
                       past five years? Not being able to bring the EU's
                       27 member states to a common position on the Middle
                       East. "It has been impossible to talk with a single
                       voice because the positions are too different," he
                       says.


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


                      # ⚓ France24 ☛ US_President_Joe_Biden_in_Berlin_vows_no
                        let-up_on_support_for_Ukraine⠀⇛


                             US President Joe Biden is in Germany this
                             Friday on his last official trip to Europe.
                             He is meeting Chancellor Olaf Scholz as well
                             as French President Emmanuel Macron and
                             British Prime Minister Keir Starmer to
                             discuss support for Ukraine.


                      # ⚓ France24 ☛ Biden_urges_European_allies_to_bolster
                        Ukraine's_military_as_US_election_looms⠀⇛


                             U.S. President Joe Biden told reporters
                             before departing Germany that there was no
                             consensus for giving Ukraine long-range
                             weapons that Ukrainian President Volodymyr
                             Zelenskiy has been requesting from Western
                             nations. British Prime Minister Keir Starmer
                             and French President Emmanuel Macron joined
                             Biden and German Chancellor Olaf Scholz on
                             Friday afternoon for talks focused largely on
                             how to end the fighting in Ukraine as Russian
                             forces advance in the east.


                      # ⚓ France24 ☛ Reports_that_North_Korea_is_sending_troops
                        to_aid_Russia_raise_questions⠀⇛


                             FRANCE 24’s correspondent in Ukraine Gulliver
                             Cragg provides his views on reports that
                             North Korea is preparing to send thousands of
                             troops to fight with the Russian army against
                             Ukraine.


                      # ⚓ France24 ☛ Claims_of_North_Korean_military_support
                        for_Russia's_war_in_Ukraine_'very_worrying',_France
                        says⠀⇛


                             South Korea’s intelligence service on Friday
                             released satellite images it said showed the
                             first deployment of 1,500 elite North Korean
                             special forces soldiers to the port city of
                             Vladivostok in Russia's Far East. Ukraine
                             responded by asking its allies for an
                             "immediate and strong reaction” to what it
                             described as Pyongyang's aid for "Russian
                             aggression".


                      # ⚓ New York Times ☛ David_Lammy,_U.K._Foreign_Secretary,
                        Visits_China_in_Bid_to_Reset_Relations⠀⇛


                             David Lammy is set to meet China’s foreign
                             minister in Beijing on Friday, in a trip the
                             British government said would acknowledge
                             “areas of contention as well as areas for
                             cooperation.”


                      # ⚓ The Straits Times ☛ British_foreign_minister_to_visit
                        China_to_rebuild_damaged_ties⠀⇛


                             Mr David Lammy will hold talks with his
                             Chinese counterpart Wang Yi in Beijing before
                             visiting Shanghai.


                      # ⚓ Hong Kong Free Press ☛ UK_Foreign_Sec._David_Lammy_in
                        China_to_‘challenge’_Beijing_on_Russia_support⠀⇛


                             British Foreign Secretary David Lammy will
                             meet his counterpart Wang Yi and other top
                             officials in Beijing on Friday to “challenge”
                             China on sensitive issues like Russia’s war
                             in Ukraine, as the two countries seek to
                             rebuild frayed ties.


                      # ⚓ JURIST ☛ Ukraine_accuses_Russia_of_torturing_POWs_in
                        breach_of_Geneva_Conventions⠀⇛


                             Ukrainian Prosecutor General Andriy Kostin
                             has accused Russia of systematically
                             torturing prisoners of war (POWs), with up to
                             90 percent of returned Ukrainian soldiers
                             reporting abuse during their detention in
                             Russian prisons.


                      # ⚓ RFA ☛ North_Korea_sending_troops_to_aid_Russia_in
                        Ukraine_war:_South’s_spy_agency⠀⇛


                             The National Intelligence Service said the
                             North could send around 12,000 soldiers in
                             total.


                      # ⚓ RFERL ☛ IMF_Approves_$1.1_Billion_In_Aid_To_Bolster
                        Ukraine's_Budget⠀⇛


                             The board of the International Monetary Fund
                             (IMF) on October 18 approved a $1.1 billion
                             payout for Ukraine to be used to provide
                             budget support to the war-torn country.


                      # ⚓ RFERL ☛ Russia,_Ukraine_Conduct_Prisoner_Swap,
                        Exchange_Of_Bodies⠀⇛


                             Russia and Ukraine swapped 190 prisoners of
                             war on October 18 under an agreement
                             completed with the help of the United Arab
                             Emirates.


                      # ⚓ RFERL ☛ Bashkortostan_Activist_Placed_Under_Harsher
                        Prison_Conditions⠀⇛


                             Jailed activist Ramilya Saitova (aka Galim)
                             of Russia’s Republic of Bashkortostan has
                             been placed under strict conditions in the
                             Russian prison in the Perm region where she
                             is serving a five-year sentence for her
                             online post protesting Russia's ongoing
                             invasion of Ukraine.


                      # ⚓ RFERL ☛ Senior_U.S._Diplomat_In_Kyiv_For_Talks⠀⇛


                             U.S. Undersecretary of State Uzra Zeya has
                             arrived in Kyiv for talks with Ukrainian
                             officials, the U.S. Embassy to Kyiv said on
                             October 18 on X, adding that the visit is
                             meant "to reaffirm the commitment of the U.S.
                             to support Ukraine against a full-scale
                             invasion of Russia," the Embassy said on X.


                      # ⚓ RFERL ☛ South_Korea_Accuses_Pyongyang_Of_Sending
                        Soldiers_To_Russia⠀⇛


                             South Korea claims Pyongyang began moving
                             special forces to Russia earlier this month,
                             days after Ukrainian President Volodymyr
                             Zelenskiy made a similar accusation that
                             North Korea has sent soldiers and weapons to
                             help support the Kremlin in its war against
                             Ukraine.


                      # ⚓ RFERL ☛ Biden,_Scholz_Talk_Ukraine_As_Russia_Launches
                        'Massive'_Air_Attack⠀⇛


                             U.S. President Joe Biden met with Chancellor
                             Olaf Scholz in Berlin ahead of joint talks on
                             Ukraine with the leaders of Germany, France,
                             and Britain as Russia continued its daily
                             strikes on Ukrainian cities and
                             infrastructure, launching "one of the most
                             massive" drone attacks on the country.


                      # ⚓ The Straits Times ☛ Ukraine_to_work_on_proposals_for
                        possible_weapons_exports,_Zelenskiy_says⠀⇛


                             KYIV - Ukraine's President Volodymyr
                             Zelenskiy said on Friday that he had asked
                             the defence ministry to work on proposals for
                             possible weapons exports.


                      # ⚓ The Straits Times ☛ North_Korean_troops_in_Russia
                        readying_for_combat_in_Ukraine_war,_says_Seoul⠀⇛


                             North Korea has shipped artillery rounds,
                             ballistic missiles and anti-tank rockets to
                             Russia since August 2023.


                      # ⚓ CS Monitor ☛ On_military_policy,_Trump_and_Harris
                        offer_starkly_different_approaches⠀⇛


                             Kamala Harris and Donald Trump contrast
                             sharply on Ukraine and the Middle East. That
                             hints at broader a divide over worldviews on
                             national security.


                      # ⚓ CS Monitor ☛ South_Korea_says_North_Korea_is_sending
                        troops_to_Russia._Is_that_true?⠀⇛


                             A South Korean spy agency said North Korea
                             has already sent 1,500 special forces to
                             Russia and plans to send a total of 12,000
                             troops. Citing North Korea’s outdated
                             equipment and lack of battle experience,
                             experts question how useful a deployment
                             might be.


                      # ⚓ New York Times ☛ Ukraine_Draft_Officers_Detain_Men
                        After_Concert_Amid_Ongoing_Russia_War⠀⇛


                             Men who attended the Kyiv concert of a
                             popular rock band had their papers checked on
                             the way out. Some were detained. Tickets to
                             subsequent shows suddenly became available.


                      # ⚓ New York Times ☛ Biden,_in_Germany,_Urges_Unwavering
                        Support_for_Ukraine⠀⇛


                             The president, in a trip to Berlin that
                             lasted barely a day, also joined Chancellor
                             Olaf Scholz of Germany in expressing new
                             optimism about the prospect for peace in the
                             Middle East.


                      # ⚓ Latvia ☛ More_Russian_entertainers_added_to_Latvia's
                        entry_blacklist⠀⇛


                             Latvian Foreign Minister Baiba Braže has
                             added two more Russian citizens to the list
                             of people not allowed into Latvia
                             – businessman Artemy Lebedev and comedian
                             Valery Ponomarenko.


                      # ⚓ Latvia ☛ Latvian_security_service_repeats_call_not_to
                        go_to_Russia,_Belarus⠀⇛


                             In a statement posted on October 18, the
                             State Security Service (VDD) urges Latvian
                             citizens not to travel to Russia or Belarus
                             during the upcoming autumn school holidays
                             and repeatedly warns about the high risks of
                             intelligence and recruitment in the territory
                             of these countries.


                      # ⚓ Atlantic Council ☛ What_to_know_about_Russian_malign
                        influence_in_Moldova’s_upcoming_election⠀⇛


                             The October 20 elections are taking place in
                             an environment clouded by what could be the
                             largest case of electoral bribery in
                             Moldova’s history.


                      # ⚓ JURIST ☛ Estonia_Parliament_recognizes_Crimean_Tatar
                        deportations_as_genocide⠀⇛


                             The Estonian Parliament, the Riigikogu, on
                             Wednesday officially recognized the mass
                             deportation of Crimean Tatars by the Soviet
                             Union in 1944 as an act of genocide. The
                             statement was passed with 83 votes in favor
                             and eight abstentions.


                      # ⚓ LRT ☛ What’s_the_state_of_Lithuania’s_military?
                        Wargaming_grasps_for_answer⠀⇛


                             A wargaming study published on Thursday
                             revealed that Lithuania could hold out
                             against Russia in a military conflict for ten
                             days until NATO reinforcements arrived.
                             However, the country would first need to
                             invest at least 10 billion euros over the
                             next four years.


                      # ⚓ Meduza ☛ Disappearing_coast_As_the_Baltic_Sea_erodes
                        Latvia’s_shoreline,_locals_grapple_with_what’s_lost_to
                        the_advancing_tide_—_Meduza⠀⇛


                      # ⚓ LRT ☛ Suspect_detained_in_Lithuania_for_sending
                        incendiary_parcels_–_German_media⠀⇛


                             A suspect allegedly involved in sending
                             incendiary devices to Germany and the UK has
                             been detained in Lithuania, German media has
                             reported. Lithuanian authorities have refused
                             to comment, quoting national security.


                      # ⚓ RFERL ☛ Transdniester_Vows_'Free_Movement'_For
                        Moldovan_Voters⠀⇛


                             De facto authorities in Moldova's
                             Transdniester have pledged not to obstruct
                             the access of voters from the Russian-backed
                             separatist region to polling stations amid
                             concerns that Moscow will attempt to
                             interfere with the two key votes scheduled
                             for October 20.


                      # ⚓ The Straits Times ☛ India_PM_Modi_returning_to_Russia
                        for_Brics_summit⠀⇛


                             Modi’s visit is his second to Russia in 2024
                             following an earlier trip to Moscow in July.


                      # ⚓ The Straits Times ☛ Moldova_says_its_citizens_were
                        trained_in_Russia_to_stage_riots⠀⇛


                             CHISINAU - Moldovan police said on Thursday
                             they had uncovered a programme in which
                             hundreds of its citizens were brought to
                             Russia to undergo training to stage riots and
                             civil unrest, the latest in a slew of
                             meddling allegations ahead of Sunday's
                             election.


                      # ⚓ The Straits Times ☛ UK_imposes_sanctions_on_Russian
                        oil_and_LNG_vessels⠀⇛


                             LONDON - Britain said on Thursday it had
                             imposed sanctions on 18 more Russian oil
                             tankers and four liquefied natural gas
                             vessels, the largest batch of sanctions to
                             date against Russia's so-called "shadow
                             fleet".


          o § Environment⠀➾


                # ⚓ France24 ☛ Torrential_rain_in_France_causes_floods_that
                  block_roads_and_railways⠀⇛


                       Massive rain caused important damage on Thurday and
                       Friday, though there were no immediate reports of
                       any casualties. France's weather authority Meteo
                       France placed six departments south of the city of
                       Lyon on a red flood alert on Thursday.


                # ⚓ CS Monitor ☛ Transformed_FEMA_faces_a_torrent_of_challenges
                  to_its_growing_relief_efforts⠀⇛


                       Since Hurricane Katrina recovery, FEMA has grown
                       more nimble. But the agency faces criticism and
                       distrust as it responds to Hurricane Helene in
                       North Carolina.


                # ⚓ New York Times ☛ France_Struggles_to_Dry_Out_From_Flash
                  Flooding⠀⇛


                       Heavy rainfall and swollen rivers unleashed
                       torrents of brackish water that cut off roads,
                       swept away cars and swamped buildings.


                # § Energy/Transportation⠀➾


                      # ⚓ The Straits Times ☛ Czech_project_win_boosts_South
                        Korea_nuclear_power_plant_export_ambitions⠀⇛


                             Seoul beats France on the latter's home turf
                             in Europe to snag the project in a “battle
                             between David and Goliath”.


                      # ⚓ The Straits Times ☛ BMW_recalls_almost_700,000_cars
                        in_China_on_fire_safety_risk⠀⇛


                             Models affected include locally-made 3 Series
                             and 5 Series vehicles, as well as several
                             imported X Series SUVs.


                      # ⚓ France24 ☛ China_hits_back_at_EU_over_electric_car
                        tariffs:_How_bad_could_the_trade_dispute_get?⠀⇛


                             European Union member states have narrowly
                             backed import duties on Chinese-made electric
                             cars, over what the EU considers to be unfair
                             competition. Tariffs of up to 45 percent are
                             set to be imposed from next month for five
                             years. Chinese carmakers have criticised the
                             EU's move, but are moving ahead with plans to
                             expand in Europe and have so far not said
                             that they will raise prices to cover the cost
                             of the tariffs. However, the Chinese
                             government says it is investigating some EU
                             imports, such as pork or dairy products, from
                             countries including Denmark, the Netherlands
                             and Germany, as well as brandy and wine
                             imports from France.


                      # ⚓ Hackaday ☛ Self-Portaging_Canoe_Is_Part_Bicycle⠀⇛


                             Normally when making a long voyage in a
                             canoe, an adventurer would paddle the vessel
                             as far as possible and then “portage”, or
                             carry, the canoe over the short sections of
                             land separating the bodies of water.
                             Portaging is a lot of work, though, since
                             canoes generally aren’t particularly light or
                             designed for traveling over land. To solve
                             this problem, [Ben] is modifying his home-
                             built canoe with some interesting parts to
                             make it into an amphibious vehicle which can
                             much more easily traverse land.


                      # ⚓ TwinCities Pioneer Press ☛ One_of_the_largest_solar
                        projects_in_the_US_opens_in_Texas,_backed_by_Google⠀⇛


                             SB Energy built three solar farms side by
                             side, the “Orion Solar Belt,” in Buckholts,
                             Texas. Combined, they will be able to provide
                             875 megawatts of clean energy.


                      # ⚓ The Straits Times ☛ Lessons_from_Fukushima:_Japan
                        prioritises_safety_amid_push_to_reopen_more_nuclear
                        plants⠀⇛


                             Japan wants to increase nuclear energy to
                             achieve energy security and affordability in
                             a climate-friendly way.


                # § Wildlife/Nature⠀➾


                      # ⚓ The Straits Times ☛ Biden_visit_to_Amazon_rainforest
                        planned_in_November,_sources_say⠀⇛


                             U.S. President Joe Biden is expected to visit
                             the Amazon rainforest and meet Brazilian
                             President Luiz Inacio Lula da Silva before
                             they attend the G20 summit in Rio de Janeiro
                             in November, sources familiar with the
                             negotiations told Reuters.


                # § Overpopulation⠀➾


                      # ⚓ The Straits Times ☛ China_launches_survey_to
                        understand_‘fear_of_having_children’⠀⇛


                             The survey aims to analyse "reluctance and
                             fear surrounding having children".


          o § Finance⠀➾


                # ⚓ The Straits Times ☛ South_Korea’s_First_Lady_cleared_of
                  stock_manipulation_allegations⠀⇛


                       The decision came years after a criminal complaint
                       was filed against Ms Kim in April 2020.


                # ⚓ The Straits Times ☛ Another_record_budget_for_Malaysia_to
                  sustain_near-term_growth_with_increased_consumption⠀⇛


                       The RM421 billion (S$127.8 billion) budget includes
                       RM12 billion to raise payouts to 2.5 million civil
                       servants and pensioners.


                # ⚓ The Straits Times ☛ IMF's_Georgieva_says_China_can_no
                  longer_rely_on_exports_for_growth⠀⇛


                       International Monetary Fund Managing Director
                       Kristalina Georgieva told Reuters on Thursday that
                       China is too large to continue relying on exports
                       to drive its economy and faces dangerously slower
                       growth unless it shifts toward a consumer-driven
                       economic model.


                # ⚓ Hong Kong Free Press ☛ China_posts_slowest_growth_in_over_a
                  year_as_property_woes_continue⠀⇛


                       China posted its slowest growth in a year and a
                       half on Friday as authorities come under pressure
                       to follow up a recent slew of stimulus with more
                       action to reignite the world’s number two economy.


                # ⚓ Meduza ☛ What’s_behind_the_ruble’s_steady_depreciation,_and
                  is_the_Kremlin_planning_to_intervene?_—_Meduza⠀⇛


                # ⚓ Tom's Hardware ☛ India_plans_import_curbs_on_PC_parts_and
                  laptops_—_an_initiative_to_encourage_domestic_manufacturing
                  and_reduce_dependency_on_countries_like_China⠀⇛


                       The Indian government is planning to introduce
                       import restrictions on laptops and computer parts
                       in an attempt to boost local production and reduce
                       reliance on foreign countries.


                # ⚓ The Straits Times ☛ Thai_celebrities_among_18_arrested_for
                  pyramid_scheme⠀⇛


                       Authorities froze 125 million baht and confiscated
                       luxury vehicles including Porsches and Ford
                       Mustangs.


                # ⚓ Silicon Angle ☛ Meta_announces_layoffs_across_several
                  divisions_for_abusing_meal_credits⠀⇛


                       Meta Platforms Inc. has been cutting jobs in
                       various divisions, including letting 24 go from
                       Instagram and Facebook (Farcebook) for abusing the
                       company’s $25 meal credit system.


                # ⚓ RFA ☛ IMF,_ADB_set_sights_on_damning_$37m_Solomon_Islands
                  aid_audit⠀⇛


                       Report by auditor general found mismanagement and
                       potential fraud in COVID-19 pandemic package
                       payments.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ The Straits Times ☛ Malaysia_approves_law_allowing_mothers
                  to_pass_on_citizenship_to_children_born_overseas⠀⇛


                       But criticism remains as the law revokes automatic
                       citizenship for children born in Malaysia to PRs.


                # ⚓ The Straits Times ☛ Malaysia_ex-PM_Mahathir’s_condition
                  improving,_he’s_still_getting_treated_at_heart_institute:
                  Aide⠀⇛


                       He was admitted to the heart institute due to a
                       lung infection.


                # ⚓ CS Monitor ☛ Canada-India_relations_are_at_a_new_low._Why
                  China_could_be_the_winner.⠀⇛


                       The breakdown in India-Canada ties could force
                       western allies into a difficult balancing act in
                       Asia.


                # ⚓ The Straits Times ☛ In_China,_Harris_is_mostly_seen_as
                  preferred_to_volatile_Trump⠀⇛


                       China sees the US relationship as not great, but
                       also better than a few years ago.


                # ⚓ The Straits Times ☛ Unwise_for_the_West_to_write_off_China,
                  says_SM_Lee_at_business_forum⠀⇛


                       China's world-class technology and the
                       determination of its people are reasons not to
                       write it off.


                # ⚓ University of Michigan ☛ Cats,_couches_and_coconut_trees:
                  Gen_Z_has_meme-ified_this_election⠀⇛


                       Like many students at the University of Michigan,
                       I’ll be a first-time voter this November. But as
                       the presidential election looms closer by the
                       minute, I must shamefully confess that I can’t name
                       a single specific policy proposed by either of the
                       current presidential candidates or their running
                       mates.


                # ⚓ Pro Publica ☛ Vance_Event_With_Ziklag,_Courage_Tour_May
                  Have_Violated_Tax,_Election_Laws⠀⇛


                       Republican vice-presidential nominee JD Vance’s
                       appearance at a far-right Christian revival tour
                       last month may have broken tax and election laws,
                       experts say.


                       On Sept. 28, Vance held an official campaign event
                       in Monroeville, Pennsylvania, in partnership with
                       the Courage Tour, a series of swing-state rallies
                       hosted by a pro-Trump Christian influencer that
                       combine prayer, public speakers, tutorials on how
                       to become a poll worker and get-out-the-vote
                       programming.


                # ⚓ The Straits Times ☛ How_will_Singapore_fare_under_a_Harris
                  or_Trump_2.0_US_administration?⠀⇛


                       US trade policy and US-China competition concerns
                       are high on the minds of South-east Asia observers.


                # ⚓ The Straits Times ☛ Indonesia_ramps_up_security_ahead_of
                  Prabowo’s_inauguration⠀⇛


                       The roughly 100,000 personnel in Jakarta will stay
                       in place until Oct 23.


                # ⚓ The Straits Times ☛ In_Modi's_Delhi,_Indian_Muslims
                  segregate_to_seek_security⠀⇛


                       NEW DELHI - In February 2020, Nasreen and her
                       husband Tofik were living in Shiv Vihar, an
                       upcoming neighbourhood in northeast New Delhi. But
                       that month, riots erupted targeting Muslims like
                       them and Tofik was pushed by a mob from the second
                       floor of the building where they lived, according
                       to a police report he filed days later from
                       hospital.


          o § Censorship/Free Speech⠀➾


                # ⚓ RFERL ☛ Apple_Complies_With_Russian_Authorities,_Removes
                  RFE/RL_App_From_App_Store⠀⇛


                       Apple has informed RFE/RL that it has removed
                       Current Time's app from the Russian version of its
                       App Store at the request of Roskomnadzor, Russia’s
                       media regulatory agency.


                # ⚓ Meduza ☛ Apple_says_it’s_removing_RFE/RL_apps_from_Russian
                  App_Store_at_Moscow’s_demand_—_Meduza⠀⇛


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


                # ⚓ Press Gazette ☛ Future_plc_share_price_tumbles_after_boss
                  Jon_Steinberg_steps_down⠀⇛


                       Steinberg was in the role for approximately a year
                       and a half.


          o § Civil Rights/Policing⠀➾


                # ⚓ The Straits Times ☛ Kidnapped_girl_in_Malaysia_almost_sold
                  to_prostitution_ring⠀⇛


                       The leader of the group had attempted to sell her
                       off to the ring in the Chow Kit area, said police.


                # ⚓ JURIST ☛ Europe_rights_court_upholds_Spain’s_2020_May_Day
                  protest_ban⠀⇛


                       The European Court of Human Rights (ECHR) ruled
                       Thursday in the case Central Unitaria de
                       Traballadores/as v. Spain, upholding Spain’s
                       decision to ban a May Day demonstration during the
                       height of the COVID-19 pandemic.


                # ⚓ CS Monitor ☛ How_China’s_women_claim_freedom⠀⇛


                       Those with good incomes tout their singlehood and
                       economic power in a quiet movement against
                       patriarchal tradition and invasive government.


                # ⚓ Pro Publica ☛ Hermits_Peak-Calf_Canyon_Fire_Victims_May_Be
                  Compensated_for_Emotional_Harm⠀⇛


                # ⚓ Stanford University ☛ Congolese_women photograph_their_own
                  displacement⠀⇛


                       Students and community members gathered at Roble
                       Arts Gym to recognize the courage and determination
                       of Congolese women who have been displaced by
                       conflict.


                # ⚓ The Straits Times ☛ Bill_to_grant_mufti_lawmaking_powers
                  stokes_concern_among_Malaysia’s_Muslims⠀⇛


                       Proposed law has drawn flak for curbing Muslims'
                       personal freedoms and undermining the Constitution.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ APNIC ☛ The_strange_cases_of_consumer-grade_routers_on_puny
                  power_supplies⠀⇛


                       Guest Post: Investigating the least likely suspect
                       in router configuration.


                # ⚓ The New Stack ☛ What_Is_the_Future_of_the_.io_Domain?⠀⇛


                       The .io domain was originally created for the
                       British Indian Ocean Territory but eventually
                       became popular with the tech sector [...]


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ Public Knowledge ☛ Public_Knowledge_Joins_13_Public
                  Interest_Groups_Urging_FCC_To_Support_Cell_Phone_Unlocking⠀⇛


                       Groups argue that doing so increases consumer
                       choice, lowers costs, and improves wireless
                       competition.


      § Monopolies/Monopsonies⠀➾


          o § Patents⠀➾


                # ⚓ Kluwer Patent Blog ☛ Tribunal_grants_Sandoz_a_section_223
                  (9)_patent_monopoly_licence,_in_long-running_Lexapro
                  litigation⠀⇛


                       On 18 September 2024, the Honourable Justice
                       Jackman, in his capacity as a Deputy President of
                       the Administrative Appeals Tribunal (AAT), granted
                       Sandoz a licence pursuant to section 223(9) of the
                       Patents Act 1990 (Cth) (Act).


                # ⚓ Dennis Crouch/Patently-O ☛ Pleading_Stage_Claim
                  Construction⠀⇛


                       UTTO Inc. v. Metrotech Corp., No. 2023-1435 (Fed.
                       Cir. Oct. 18, 2024).  This new claim construction
                       decision has two important focal points: [...]


                # § Kangaroo Courts⠀➾


                      # ⚓ JUVE ☛ NanoString_and_Bird_&_Bird_triumph_against_10x
                        Genomics_at_central_division [Ed: UPC is illegal and
                        this litigator bribed the publisher to lobby for this
                        illegality, now it gets puff pieces for that money]⠀⇛


                             The judges around presiding judge Ulrike Voß
                             found EP 2 794 928 B1 to be invalid due to
                             lack of novelty and lack of inventive step of
                             one of the auxiliary requests (case ID: UPC
                             252/2023, ACT_551180/2023).


          o § Trademarks⠀➾


                # ⚓ TTAB Blog ☛ TTABlog_Test:_Which_of_These_Three_Section_2(d)
                  Refusals_Was/Were_Reversed_on_Appeal?⠀⇛


                       A TTAB judge once said to me that one can predict
                       the outcome of a Section 2(d) appeal about 95% of
                       the time just by looking at the marks and the
                       goods/services. In the past decade, about 90% of
                       Section 2(d) refusals have been affirmed on appeal.
                       So, if you say "affirmed" you will be right 90% of
                       the time! Anyway, here are three recent Board
                       decisions, at least one of which resulted in a
                       reversal. How do you think they came out?


                       In_re_Western_Workhorse_Management,_LLC, Serial No.
                       88008152 (October 16, 2024) [not precedential]
                       (Opinion by Judge Mark Lebow). [Section 2(d)
                       refusal of the mark NXT for "management of multi-
                       tenant living facilities owned by others, namely,
                       building management" in view of the registered mark
                       NXT CAPITAL, in both standard-character and the
                       stylized form shown below, for "commercial lending
                       services and financial investment services;
                       commercial real estate lending and investment
                       services; and institutional investment management
                       and advisory services related to the foregoing"
                       [CAPITAL disclaimed]].


          o § Copyrights⠀➾


                # ⚓ Digital Music News ☛ 2_Live_Crew_Wins_Back_Copyright
                  Control_in_Momentous_‘Termination_Right’_Verdict⠀⇛


                       A jury had ruled that 2 Live Crew should benefit
                       from a copyright monopoly ‘termination right’ to
                       win back their music from a label that bought them
                       out of bankruptcy.


                # ⚓ Digital Music News ☛ Tencent_Inks_Strategic_Partnership
                  with_G-Dragon_Agency_Galaxy_Corporation⠀⇛


                       Tencent Music Entertainment Group has announced a
                       strategic partnership with Galaxy Corporation, the
                       agency representing South Korean rapper and
                       songwriter G-Dragon. As part of this agreement,


                # ⚓ Digital Music News ☛ Apple_Partners_with_China_Mobile_To
                  Offer_Subscriptions⠀⇛


                       Apple has formed a partnership with China Mobile to
                       offer its more than one billion subscribers in
                       Mainland China access to Fashion Company Apple
                       Music. China Mobile users in mainland China can
                       activate the service through their China Mobile app
                       or by visiting a China Mobile retail store.


          o § Gemini* and Gopher⠀➾


                # § Technology and Free Software⠀➾


                      # ⚓ Low_Background_Steel⠀⇛


                             Low-background steel is steel that has no
                             trace of radioactive fallout. Since the
                             detonation of atmospheric nuclear weapons in
                             the 1940s and onward, there has been an
                             amount of nuclear fallout that is traceable
                             in everything, including steel. This is
                             problematic because for especially sensitive
                             cases (Geiger counters, spacecraft
                             equipment), it's critical for there to be no
                             trace, to avoid contaminating the instrument
                             (s). Steel is made by forcing oxygen into pig
                             iron, and so ay atmospheric contamination in
                             the oxygen will also be present in the
                             produced steel. And because of this, the
                             sensitive steel has to be sourced by other
                             means, such as by scavenging from shipwrecks.


                      # ⚓ [Old] Weaning_off_social_media_and_the_over-
                        capitalised_Big_Internet_life⠀⇛


                             My 2022 kicked off with the deactivation (and
                             later deletion) of my Big Social accounts.
                             Capitalism and worldly ills aside, my social
                             media use (though not excessive on paper)
                             seemed to coincide with poor mental health.
                             It had to go.


                             The subsequent weeks and months entailed all
                             sorts of introspection, learning and
                             experimentation to establish and cement
                             better habits, and generally help me make the
                             most of the time and SOMETHING (my brain? my
                             soul?) I was taking back.


                             Here are some of the things I tried and how
                             they're working out. I'm writing this in case
                             anyone out there needs some solidarity and
                             validation.


                      # ⚓ [Old] Love_a_good_letter⠀⇛


                             When I gave up my social media, I fell back
                             on email and texting as a way to stay in
                             touch with people. But now, ten months on,
                             I'm finding that texting and email are just
                             so troublesome.


                             There's been no drama (quite the opposite,
                             it's been lovely) but the physical act of
                             hunching over my phone or sitting at my
                             computer has started to feel like work.


                      # ⚓ [Old] The_disease_called_"Perfection"⠀⇛


                             This post is by Single Dad Laughing. I found
                             it in 2010 (or thereabouts) and it was
                             transformative in helping me be more at peace
                             with myself and the world around me. He gives
                             permission to share it, so I wanted to
                             preserve it here in the smolweb because it
                             feels important and evergreen.


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





                    ䷩ 𝚕𝚒𝚗𝚎 6519

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 19/10/2024: OpenAI, Microsoft Going
Deeper Into Debt; FTC Rules Make It Easier To Cancel
Services⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Education
          o Hardware
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Security
                # Privacy/Surveillance
                # Confidentiality
          o Defence/Aggression
          o Transparency/Investigative_Reporting
          o Environment
                # Energy/Transportation
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Censorship/Free_Speech
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Internet_Policy/Net_Neutrality
          o Digital_Restrictions_(DRM)
          o Monopolies/Monopsonies
                # Trademarks
                      # Right_of_Publicity
                # Copyrights
    * § Leftovers⠀➾


          o ⚓ Jamie Zawinski ☛ Contrafactuals⠀⇛


                 Making a list of pros and cons of getting in a time
                 machine and going back to 1992 to run a nightclub.


          o ⚓ Heliomass ☛ Lesser_Known_London:_Chislehurst_Caves⠀⇛


                 This post is somewhat devoid of photos due to the fact
                 photography isn’t allowed in the caves. But it’s dark
                 down there anyway, pitch black in fact. It’s why on
                 arrival everyone gets given an oil lantern to light the
                 way, just as people using the caves in the past would
                 have had.


                 And whilst the caves at Chislehurst are old, they’re not
                 natural. In fact, they’re completely dug out by humans,
                 dating from the 13th century and they sprawl all over the
                 area stretching for a staggering 22 miles (35 km). It’s
                 also not beyond reason there could be further passages
                 which haven’t yet been discovered.


          o ⚓ Chuck Grimmett ☛ Recapturing_the_magic_of_the_early_blogging
            days⠀⇛


                 What else can you do? Reclaim your stuff from social
                 media and do more with your own site. Make it deep. Make
                 it you.That’s where the magic is.


          o ⚓ ARRL ☛ Jamboree_On_The_Air_Brings_Scouts_Around_the_World
            Together⠀⇛


                 The big weekend for Scouts around the world is here.
                 Jamboree On - The - Air (JOTA) and Jamboree On - The -
                 Internet (JOTI) is the world’s largest Scouting event.
                 The three-day event runs from October 18 - 20, 2024 using
                 amateur radio and the internet to connect Scouts
                 worldwide for a full weekend of on-air and online
                 activities that promote friendship and global
                 citizenship. In 2023, JOTA/JOTI had a record 600,000
                 registered participants, a 40% increase compared to 2022,
                 and included 7000+ Scout groups and tens of thousands of
                 individual participants from 149 countries.


          o ⚓ Manuel Moreale ☛ P&B:_Steyn_Viljoen⠀⇛


                 This is the 60th edition of People and Blogs, the series
                 where I ask interesting people to talk about themselves
                 and their blogs. Today we have Steyn Viljoen and his
                 blog, viljoen.space


          o ⚓ Yordi Verkroost ☛ Stop_Optimizing_Everything⠀⇛


                 Then one day, he decided to take it easy. Instead of
                 going all out, he relaxed and enjoyed the view along the
                 way. When he got to the end of the ride, he checked his
                 time, and it was forty-five minutes. Only two minutes
                 slower than when he’d been pushing himself to the max. He
                 couldn’t believe it. Two minutes slower, and he enjoyed
                 the whole ride. He wasn’t tired or drenched in sweat.


                 For me this story is a perfect example of how we’re
                 always trying to optimize everything. We push ourselves
                 to get the best possible results, but why? If doing just
                 a little bit less gives you almost the same result and
                 you can actually enjoy the process, why not take things a
                 little more easy?


          o ⚓ Truthdig ☛ The_Paleolithic_Ideas_That_Shaped_the_Modern_World_-
            Truthdig⠀⇛


                 Hudson’s research has already made inroads into modern
                 life. Many contemporary economists rely on his
                 understanding of financial history in the Ancient Near
                 East. Hudson’s collaboration with the late anthropologist
                 and activist David Graeber inspired his launch of the
                 debt cancellation movement during Occupy Wall Street.
                 Graeber’s book “Debt: The First 5,000 Years” is a
                 popularized adaption of Hudson’s research on the early
                 financial systems of the Near East, encouraging Graeber
                 to follow up and coauthor the bestselling book “The Dawn
                 of Everything,” an overview of new interpretations in
                 archaeology and anthropology about the many paths society
                 can take.


                 I reached out to Hudson for a conversation on these
                 topics, starting with his reflections on what drew him
                 into prehistory in the early 1970s and his collaborations
                 with Harvard prehistorian Alexander Marshack.


          o § Science⠀➾


                # ⚓ Hong Kong Free Press ☛ HK_Policy_Address_2024:_Liquor_tax
                  cut_promotes_trade,_not_drinking,_commerce_chief_says⠀⇛


                       Hong Kong’s liquor tax cut will promote the trade
                       of high-end spirits rather than drinking, the
                       city’s commerce chief has said, as he played down
                       the policy’s impact on residents’ health.


                # ⚓ Stamford Advocate ☛ Once-in-a-lifetime_comet_will_be
                  visible_over_CT_tonight._Here's_when.⠀⇛


                       A “dirty snowball” that comes around about once
                       every 80,000 years is causing a stir in the skies
                       over Connecticut this week. Comet Tsuchinshan-ATLAS
                       (also known as C/2023 A3 and Comet A3) will remain
                       visible for the next few nights, and we only need
                       to use our naked eyes to see it.


                # ⚓ Smithsonian Magazine ☛ See_the_Wreck_of_Ernest_Shackleton's
                  'Endurance'_in_Astonishing_Detail_With_This_New_3D_Scan⠀⇛


                       The 3D model was created from more than 25,000
                       high-resolution images captured after the iconic
                       vessel was discovered in March 2022.


                # ⚓ Smithsonian Magazine ☛ This_Newly_Discovered,_Octagonal
                  Building_in_Armenia_Is_One_of_the_World's_Oldest_Christian
                  Churches⠀⇛


                       The Armenian and German archaeologists have been
                       studying Artaxata’s ruins since 2018, and the
                       church’s footprint is their most significant
                       discovery thus far. The site is composed of an
                       octagonal floor plan nearly 100 feet across, laid
                       with a “simple mortar floor and terracotta tiles,”
                       according to the statement. The octagon has long
                       been a significant Christian symbol: As a
                       visualization of the number eight, it evokes the
                       number of days that passed between Jesus’s entry
                       into Jerusalem and his resurrection, in addition to
                       more generally representing rebirth.


                # ⚓ ACM ☛ What_Is_Theoretical_Computer_Science?⠀⇛


                       But my objection to “TCS is a branch of
                       mathematics” is deeper than the sociological
                       argument. I believe that thinking of TCS as a
                       branch of mathematics is harmful to the discipline.
                       The centrality of computing stems from the fact
                       that it is a technology that has been changing the
                       world for the past 80 years, ever since the British
                       used early computing to change the tide of war in
                       World War II. As computer scientists, we should
                       look for inspiration from physics rather than from
                       mathematics. Theoretical physics is highly
                       mathematical, but it aims to explain and predict
                       the real world. Theories that fail at this
                       “explain/predict” task would ultimately be
                       discarded. Analogously, I’d argue that the role of
                       TCS is to explain/predict real-life computing. I am
                       not saying that every TCS paper should be held to
                       this standard, but the standard should be applied
                       to branches of TCS. We should remember the warning
                       of John von Neuman,e one of the greatest
                       mathematicians and computer scientists of the 20th
                       century, regarding the danger of mathematics driven
                       solely by internal esthetics: “There is a grave
                       danger that the subject will develop along the line
                       of least resistance.”


          o § Education⠀➾


                # ⚓ Ali Reza Hayati ☛ Am_I_an_engineer?⠀⇛


                       So if someone has an engineering academic degree
                       but practices medicine or philosophy or maybe is a
                       salesman, is that person still an engineer or not?
                       I’ve been called an engineer even when I was not
                       working an engineering job, so I think people
                       really don’t care about the title, as opposed to
                       doctors who I think really care, but the question
                       remains, is someone with an engineering degree who
                       doesn’t practice, still entitled to be called an
                       engineer?


                # ⚓ University of Michigan ☛ U-M_staff_access_to_library
                  resources_|_University_of_Michigan_Library⠀⇛


                       A recent library survey revealed that some people
                       in the university community aren't aware they have
                       full access to the U-M Library. Everyone with a
                       current Mcard can use the library's spaces,
                       services, expertise, events, exhibits, and one of
                       the most comprehensive collections in the world.


                       Our collection is built to serve research and
                       scholarship, but there are plenty of general
                       interest materials, including books, feature films,
                       magazines, and newspapers. Among the highlights:
                       [...]


                # ⚓ Yordi Verkroost ☛ The_Resume_of_Life_|_Yordi⠀⇛


                       And this is about more than just your resume. It's
                       about life itself. Over time, it’s worth regularly
                       checking where you are in life and where you want
                       to go next. Your vision and mission don’t have to
                       stay the same forever. As you update your resume to
                       reflect your current professional life, you
                       reevaluate your values and goals in life in general
                       as well. Your career evolves, your values change,
                       and your purpose changes as you get more
                       experience.


                # ⚓ [Old] Mandy Brown ☛ The_case_for_rereading⠀⇛


                       I’m not talking about just any kind of rereading
                       here. If it’s been a decade since you’ve read a
                       book, you aren’t so much rereading as reading it
                       for the first time—again. I’m taking about
                       rereading when the book is still reasonably fresh,
                       maybe within a year. If more time has passed, you
                       will have forgotten large parts of it, or
                       misremembered, and will still experience some of
                       the initial novelty you had with the first read.
                       But a reread within a year, or a few at most,
                       occupies a space where you can still recall enough
                       to approach a book with familiarity. Instead of
                       being surprised by a turn of events, you anticipate
                       them; lines and phrases pop out as ones you
                       remember, but they seem louder this time around,
                       more resonant—as if they are lining up with the
                       memory of the first time you heard them, wave
                       patterns amplifying one another.


          o § Hardware⠀➾


                # ⚓ The Register UK ☛ Spectre_flaws_continue_to_haunt_Intel_and
                  AMD⠀⇛


                       Johannes Wikner and Kaveh Razavi of Swiss
                       university ETH Zurich on Friday published details
                       about a cross-process Spectre attack that
                       derandomizes Address Space Layout Randomization and
                       leaks the hash of the root password from the Set
                       User ID (suid) process on recent Intel processors.
                       The researchers claim they successfully conducted
                       such an attack.


                       Spectre refers to a set of attacks made possible
                       because of the way processors conduct speculative
                       execution - a performance optimization technique
                       that involves making calculations in advance. The
                       results can be used if needed, or otherwise
                       discarded.


                # ⚓ India Times ☛ Samsung:_Samsung_delays_taking_deliveries_of
                  ASML's_chip_gear_for_its_new_US_factory,_sources_say⠀⇛


                       The delay in equipment deliveries is a fresh
                       setback to the Taylor project, which is at the
                       heart of Samsung chairman Jay Y. Lee's ambition to
                       expand beyond its bread-and-butter memory chips
                       into contract chip manufacturing, which Taiwan's
                       TSMC dominates.


                # ⚓ Tom's Hardware ☛ Qualcomm_abruptly_cancels_Snapdragon_X
                  Elite_dev_kit_—_refunds_customers_for_mini_PC,_ends_sales_and
                  support_for_the_device_immediately⠀⇛


                       According to the letter that developer Jeff
                       Geerling received, Qualcomm said, “…the Developer
                       Kit product comprehensively has not met our usual
                       standards of excellence and so we are reaching out
                       to let you know that unfortunately we have made the
                       decision to pause this product and the support of
                       it, indefinitely.”


                       Geerling and others who purchased the device
                       previously pointed out that there had been long
                       wait times for the device with little explanation
                       as to what was going on.


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ Scheerpost ☛ It’s_Time_To_Get_Rid_of_Big_Agriculture⠀⇛


                       Gabbert asserts that big agriculture’s firm grasp
                       on the industry is where the problems begin. Its
                       lobby is amongst the biggest and Gabbert explains
                       that there is no incentive to try and remedy the
                       problems that come from this monopolization of an
                       industry so essential to human survival. “I think
                       that is really the crux of the whole problem, is
                       money in politics,” Gabbert says.


                       Reichl takes it back to what happened after World
                       War II and how the U.S. government made an attempt
                       to fight communism by cheapening the food making
                       process, which turned farms into factories. “Almost
                       everything that’s wrong with America comes from
                       that policy. We’ve destroyed our health, our
                       environment, our communities,” Reichl tells Scheer.


                       The heart of their story lies with the farmers
                       themselves, and how, despite being in charge of the
                       most important aspect of human survival, they still
                       tend to struggle the most in society. Reichl
                       explains their significance in the film, stating,
                       “I just wanted for us to be able to listen to their
                       stories that they tell themselves about what has
                       happened to them and what the American system has
                       done to them.”


                # ⚓ [Repeat] Craig Murray ☛ The_Notional_Health_Service_-_Craig
                  Murray⠀⇛


                       Sixty years ago or so, when my siblings or I were
                       sick enough to be in bed, my mother would phone the
                       surgery and the GP would come to our home to see
                       us. This was perfectly normal. It is probably
                       difficult for Generation Z to believe this really
                       used to happen.


                       Now if I am sick enough to be in bed, I have to
                       phone the surgery precisely at 8am and go through
                       the lottery of getting in to the phone queue,
                       rather than the engaged signal as the queue is at
                       capacity. I may have to call numerous times.


                       If I do manage to get into the queue I have to hope
                       I get to the front of it before all appointments
                       are taken. If I fail, I cannot make an appointment
                       for the next day but have to try my luck again
                       then, once more at precisely 8am, while a hundred
                       other people are trying exactly the same thing.


                       If I am fortunate enough to make it through the
                       queue, I am de facto triaged by a receptionist with
                       no medical qualifications but to whom I have to
                       explain my medical symptoms.


                       She will then, if she thinks I have a case, explain
                       my symptoms to a doctor and I may come out of this
                       process, not with the doctor coming to my home, nor
                       with me attending the surgery, but with a phone
                       call from the doctor and a down the line diagnosis.


                       I find that everybody I have spoken to – and from
                       all parts of the UK – has to put up with the same
                       system. I cannot believe we have fallen in to
                       accepting this.


                # ⚓ The Conversation ☛ If_your_child_is_watching_TV_and_playing
                  online_games,_you_should_do_it_with_them_–_here’s_why⠀⇛


                       Young children spend a lot of time using screens:
                       watching television, playing on touchscreen apps,
                       or facetiming with grandparents. In fact, research
                       on global screen time guidelines has found that
                       around 75% of children aged up to two years use
                       some form of digital media daily, and 64% of
                       children aged two to five years use it for more
                       than an hour a day.


                # ⚓ EcoWatch ☛ Chickpeas_Could_Become_a_Major_Protein_Source
                  for_Their_Drought-Resistant_Properties,_Study_Says⠀⇛


                       According to the researchers, chickpeas are the
                       fourth largest grown legume crop in the world, but
                       they aren’t one of the nine primary crops on which
                       humans base their diets.


                       In response, the research team experimented with
                       growing various types of chickpeas under drought
                       conditions to test their resistance to test stress.
                       Several different varieties grew successfully
                       despite the drought conditions, and the researchers
                       further determined that many chickpeas were also
                       good candidates for urban farming.


                # ⚓ Hindustan Times ☛ Mark_Zuckerberg's_Meta_faces_lawsuit_in
                  Massachusetts_for_features_designed_to_addict_teens,_mental
                  health_concerns⠀⇛


                       Meta Platforms must face a lawsuit by Massachusetts
                       alleging the social media company purposely
                       deployed features on its Instagram platform to
                       addict young users and deceived the public about
                       the dangers it posed to the mental health of
                       teenagers, a judge ruled. The ruling came after a
                       federal judge in California on Tuesday rejected a
                       request by Meta to dismiss lawsuits by more than 30
                       states accusing it of fueling mental health
                       problems among teens by making its social media
                       platforms addictive.(Reuters) The ruling came after
                       a federal judge in California on Tuesday rejected a
                       request by Meta to dismiss lawsuits by more than 30
                       states accusing it of fueling mental health
                       problems among teens by making its social media
                       platforms addictive.(Reuters)


                       Suffolk County Superior Court Judge Peter Krupp in
                       Boston, in a decision made public on Friday,
                       rejected Meta's request to dismiss claims by
                       Massachusetts Attorney General Andrea Joy Campbell
                       that it violated state consumer protection law and
                       created a public nuisance.


                # ⚓ PHR ☛ PHR_Joins_Deans_of_American_University_of_Beirut_
                  (AUB)_to_Call_for_Protection_of_Health_Care_Amid_Escalating
                  Conflict_in_Lebanon⠀⇛


                       The recent military escalation between Israel and
                       Hezbollah is resulting in widespread and mounting
                       harms to civilians and civilian infrastructure,
                       including hospitals, health workers, patients, and
                       the broader health system.


                # ⚓ Off Guardian ☛ UK_Accepts_Big_Pharma_Money_to_Trial_Drugs
                  on_the_Unemployed⠀⇛


                       Three days ago the British government announced a
                       new scheme to inject obese people with weight loss
                       drugs to try and tackle “worklessness”. Writing in
                       the Telegraph – where else would a “Labour”
                       minister write?


                # ⚓ Latvia ☛ Latvia_has_EU's_highest_level_of_reported
                  disability⠀⇛


                       Latvia has the European Union's highest level of
                       reported disability among the population according
                       to Eurostat data published October 17.


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ CS Monitor ☛ A_week_ago,_Tesla_showcased_futuristic
                  robotaxis._Then_a_pedestrian_got_hit.⠀⇛


                       One week after Tesla unveiled prototype robotaxis
                       and promised fully autonomous vehicles by 2026, the
                       company is once again under investigation. Tesla
                       has twice recalled its “Full Self-Driving” system
                       in the past after cars ignored stop signs and hurt
                       pedestrians.


                # ⚓ Bryan Lunduke ☛ Police_Reports_Written_by_AI...
                  Seriously.⠀⇛


                       A police report written by ChatGPT? What could
                       possibly go wrong?!


                # ⚓ Drew Breunig ☛ The_3_AI_Use_Cases:_Gods,_Interns,_and
                  Cogs⠀⇛


                       We talk about so many things when we talk about AI.
                       The conversation can roam from self-driving cars to
                       dynamic video generation, from conversational
                       chatbots to satellite imagery object detection, and
                       from better search engines to dreamlike imagery
                       generation. You get the point.


                       It gets confusing! For laypeople, it’s hard to nail
                       down what AI actually does (and doesn’t) do. For
                       those in the field, we often have to break down and
                       overspecify our terms before we can get to our
                       desired conversations.


                # ⚓ Peteris Krumins ☛ How_to_Get_a_USA_IP_Address⠀⇛


                       Browserling is an online browser platform that
                       provides users with USA IP addresses from anywhere
                       in the world. It allows real-time browsing and
                       cross-browser testing, making it ideal for
                       accessing geo-restricted content and testing
                       websites across different systems without
                       additional software.


                # ⚓ Cyble Inc ☛ Critical_GitHub_Vulnerability_Advisory:_Act_Now
                  For_Security⠀⇛


                       The vulnerability, CVE-2024-9487, allows attackers
                       to bypass SAML Single Sign-On (SSO) authentication,
                       leading to unauthorized user provisioning and
                       access to the GitHub instance. To exploit this
                       vulnerability in GitHub, attackers must have the
                       encrypted assertions feature enabled, direct
                       network access, and a signed SAML response or
                       metadata document. The combination of these factors
                       presents a serious risk, emphasizing the urgency
                       for organizations to implement the available patch.


                # ⚓ Society for Scholarly Publishing ☛ Guest_Post:_Exploring
                  the_“Hopes_and_Fears”_About_Generative_Artificial
                  Intelligence_in_Web_Scale_Discovery_-_The_Scholarly_Kitchen⠀⇛


                       The NISO Open Discovery Initiative (ODI) was
                       created in 2011 in response to the emergence of
                       then-novel web-scale discovery layers. Back then,
                       led by Serials Solutions Summon product and
                       followed by EBSCO Discovery Service, OCLC’s
                       WorldCat Discovery, and Ex Libris’ Primo, there was
                       a lack of understanding about how these tools
                       indexed full-text and A&I content, provided access,
                       attributed metadata and usage, and more. The NISO
                       Open Discovery Initiative’s goal has been fostering
                       transparency and trust in web-scale library
                       discovery. Our Recommended Practice provides
                       guidelines that helped address the concerns
                       expressed by librarians, content providers, and
                       discovery providers when these new centralized
                       indexes were at the cutting edge of technology.


                # ⚓ Privacy International ☛ Automating_the_hostile_environment:
                  uncovering_a_secretive_Home_Office_algorithm_at_the_heart_of
                  immigration_decision-making_|_Privacy_International⠀⇛


                       Artificial intelligence decision making systems
                       have in recent years become a fixture of
                       immigration enforcement and border control. This is
                       despite the clear and proven harmful impacts they
                       often have on individuals going through the
                       immigration system. More widely, the harms of
                       automated decision making have been increasingly
                       there for all to see: from systems that encode bias
                       and discrimination, as happened in the case of an
                       algorithm used to detect benefit fraud in the
                       Netherlands, to inaccurate software that had
                       horrific consequences for sub-postmasters caught in
                       the post-office horizon scandal.


                       All the way back in 2020, the first warning signs
                       were apparent in the immigration context when the
                       Home Office agreed under the threat of litigation
                       to withdraw a visa streaming algorithm that
                       discriminated between certain nationalities. This
                       year we, at Privacy International, have been
                       investigating AI decision-making systems used by
                       the Home Office. What we have found is that a
                       number of highly opaque and secretive algorithms
                       permeate immigration enforcement and play a role in
                       decisions that can have life changing consequences
                       for the migrants subject to them. This is all
                       without any information being provided to migrants
                       about the existence of the algorithm or how it uses
                       their personal data.


                # ⚓ Axios ☛ Anthropic_CEO_pens_utopian_vision_of_the_future_of
                  AI⠀⇛


                       Why it matters: The compulsion to share utopian AI
                       roadmaps might mean that these CEOs and investors
                       see breakthroughs right around the corner in their
                       labs — and they want to make sure the world knows
                       just how close we are to nirvana.


                       Yes, but: It could instead mean that they know the
                       industry has been slow to deliver on its promises,
                       and an impatient public still isn't fully sold on
                       the value of AI, so they'd better do a happy tap-
                       dance.


                # ⚓ New Statesman ☛ No_one_asked_for_Meta’s_“AI_chatbot”⠀⇛


                       As with the metaverse, it’s difficult to pinpoint
                       who exactly wants or needs this new feature (and
                       who would be eager to shell out hundreds of pounds
                       for a wearable to use it). Not only is there no
                       evidence of interest; there is growing evidence of
                       the opposite – this announcement comes just weeks
                       after the viral “Goodbye Meta AI” Instagram graphic
                       was shared over 600,000 times (and by many famous
                       people), with users falling for the notion that
                       sharing it would mean their data would not be used
                       by Meta’s AI training models. Though ineffective,
                       the popularity of this graphic illustrates a major
                       resistance to AI from Meta’s user base.


                # ⚓ The Register UK ☛ Post_Office_CTO_had_'nagging_doubts'
                  about_Horizon_system⠀⇛


                       The former CTO of the Post Office had "nagging
                       doubts" about the Horizon system at the center of
                       one of the most far-reaching miscarriages of
                       justice in UK history, yet he continued to sign off
                       statements to MPs attesting to its security and
                       reliability.


                       Horizon is an EPOS and back-end finance system for
                       thousands of Post Office branches around the UK,
                       first implemented by ICL, a technology company
                       later bought by Fujitsu. From 1999 until 2015,
                       around 736 subpostmasters and subpostmistresses
                       were wrongfully convicted of fraud when errors in
                       the system were to blame. A statutory inquiry into
                       the mass miscarriage of justice launched in 2021 is
                       ongoing.


                # ⚓ Techdirt ☛ ExTwitter_Makes_It_Official:_Blocks_Are_No
                  Longer_Blocks⠀⇛


                       It has been rumored for a while that Elon wants to
                       remove the official “block” functionality on
                       ExTwitter, but now it’s official. The company has
                       announced that it will soon start rolling out a new
                       version of “block” that no longer blocks content,
                       only interactions.


          o § Security⠀➾


                # § Privacy/Surveillance⠀➾


                      # ⚓ Inside Towers ☛ FCC_Requires_Georouting_for_All
                        Wireless_Calls_to_988_-_Inside_Towers⠀⇛


                             The FCC yesterday approved rules that will
                             require all U.S. wireless carriers to
                             implement georouting for calls to the 988
                             Lifeline, a suicide prevention hotline. These
                             rules will make it easier to route such calls
                             to the 988 Lifeline’s local intervention
                             services, FCC officials said. Instead of
                             routing calls by the area code of where an
                             individual’s phone originated, the change
                             will route the call to the nearest cell tower
                             while protecting the caller’s privacy.


                             Mental health and crisis counseling experts
                             have long expressed that connecting callers
                             with local crisis centers is important to
                             connect those in need with life-saving public
                             health and safety resources and enable them
                             to speak with local counselors, according to
                             the agency.


                      # ⚓ Wired ☛ This_Prompt_Can_Make_an_AI_Chatbot_Identify
                        and_Extract_Personal_Details_From_Your_Chats⠀⇛


                             A group of security researchers from the
                             University of California, San Diego (UCSD)
                             and Nanyang Technological University in
                             Singapore are now revealing a new attack that
                             secretly commands an LLM to gather your
                             personal information—including names, ID
                             numbers, payment card details, email
                             addresses, mailing addresses, and more—from
                             chats and send it directly to a hacker.


                             The attack, named Imprompter by the
                             researchers, uses an algorithm to transform a
                             prompt given to the LLM into a hidden set of
                             malicious instructions. An English-language
                             sentence telling the LLM to find personal
                             information someone has entered and send it
                             to the hackers is turned into what appears to
                             be a random selection of characters.


                      # ⚓ The Record ☛ Europe_launches_‘gait_recognition’_pilot
                        program_to_monitor_border_crossings⠀⇛


                             A European Commission-funded biometric “gait
                             recognition” program to study how to more
                             easily identify people crossing the European
                             Union’s external borders by examining their
                             unique walking styles kicked off Thursday.


                             The initiative, dubbed the PopEye Project, is
                             supported by a €3.2 million ($3.5 million)
                             grant that covers a three-year pilot testing
                             the technology, according to TechTransfer, a
                             program at the Vrije Universiteit Brussels
                             and a partner on the effort.


                      # ⚓ International Business Times ☛ Users_Claim_Apple
                        Watch_Can_Help_Predict_If_You_Have_COVID_Or_The_Flu,
                        Here's_How⠀⇛


                             "I started using Vitals when it first came
                             out on the beta, and since then, I've gotten
                             sick about twice," another user commented
                             before adding that "both times it knew a
                             couple of days in advance, and I hadn't felt
                             anything wrong," the Reddit user wrote.
                             "Kinda insane how useful this feature can
                             be."


                      # ⚓ MacRumors ☛ Apple_Watch_Users_Report_Vitals_App
                        Detecting_Illness_Before_Symptoms_Appear⠀⇛


                             The Apple Watch app, which analyzes key
                             health metrics measured during sleep over the
                             last seven days, appears to be providing
                             early warnings of impending sickness for at
                             least some Apple Watch wearers ahead of time.
                             It's available on Apple Watch Series 8 and
                             newer models, including the Apple Watch Ultra
                             series, as long as the devices are running
                             ‌watchOS 11‌.


                      # ⚓ Privacy International ☛ Protecting_personal_data
                        during_elections_–_the_Council_of_Europe's_new
                        guidelines_on_the_processing_of_personal_data_for_the
                        purposes_of_voter_registration_and_authentication_|
                        Privacy_International⠀⇛


                             Elections and political campaigns are
                             increasingly mediated by digital
                             technologies. These technologies rely on
                             collecting, storing, and analysing personal
                             information to operate. They have enabled the
                             proliferation of tailor-made political
                             advertising. The recent proliferation of AI
                             technologies is enabling ever more
                             sophisticated content creation and
                             manipulation in the context of elections.


                             In parallel, governments are continuing to
                             invest in digital technologies for the
                             running of elections. These digital
                             technologies are inherently data-intensive.
                             Notably, several states are turning to
                             biometric registration of voters and e-
                             voting, ostensibly to curtail fraud and vote
                             manipulation. This modernisation often
                             results in the development of nationwide
                             biometric databases. Such databases contain
                             and are used for processing large amounts of
                             personal data, and thus require heightened
                             safeguards and protection. Often, increased
                             reliance on technologies for purposes of
                             voter registration and verification goes hand
                             in hand with the involvement of private
                             companies, which provide and often run the
                             technologies processing data at population
                             scale. Generally, the privatisation of public
                             tasks and responsibilities can be deeply
                             problematic if deployed without the necessary
                             safeguards. The risks are exponentially
                             higher in the electoral context, particularly
                             where the use of technical products or
                             services provided by a company is made
                             essential to the voting exercise.


                             It is in this context that in June 2024 the
                             Council of Europe adopted its Guidelines on
                             the protection of individuals with regard to
                             the processing of personal data for the
                             purposes of voter registration and
                             authentication.


                # § Confidentiality⠀➾


                      # ⚓ The Register UK ☛ WeChat_devs_modded_TLS,_introducing
                        security_weaknesses⠀⇛


                             Messaging giant WeChat uses a network
                             protocol that the app's developers modified –
                             and by doing so introduced security
                             weaknesses, researchers claim.


                             WeChat uses MMTLS, a cryptographic protocol
                             heavily based on TLS 1.3. The devs
                             essentially tweaked standard TLS but in turn
                             that left the app with an encryption
                             implementation, which "is inconsistent with
                             the level of cryptography you would expect in
                             an app used by a billion users, such as its
                             use of deterministic IVs and lack of forward
                             secrecy."


          o § Defence/Aggression⠀➾


                # ⚓ Wired ☛ What_the_US_Army’s_1959_‘Soldier_of_Tomorrow’_Got
                  Right_About_the_Future_of_Warfare⠀⇛


                       Of course, the Army’s “GI of the future” unveiled
                       more than six decades ago, like most fantastic
                       visions of the decades ahead, didn’t totally come
                       true. But some of the elements of the soldier’s
                       ambitious kit did end up foreshadowing future
                       innovations for American combat troops. Here’s a
                       look at what the “soldier of tomorrow” from 1959
                       got right (and wrong) about the future of warfare.


                # ⚓ Marcy Wheeler ☛ Trump's_GOP_Is_Running_on_a_Platform_of
                  Freeing_Seditionists_and_Cop_Assailants⠀⇛


                       The GOP candidate for President has a criminal
                       docket. And in that criminal docket, today, the
                       government included a post promising to free
                       seditionists and cop-assailants with the same
                       urgency with which Donald Trump promises to close
                       the border. “My first acts,” the GOP standard-
                       bearer stated, would include freeing the people who
                       assaulted the Capitol on January 6.


                # ⚓ CoryDoctorow ☛ Pluralistic:_Blue_states_should_play
                  “constitutional_hardball”⠀⇛


                       The GOP's game is called "constitutional hardball."
                       Think: Mitch McConnell refusing to hold
                       confirmation hearings on Obama's federal judiciary
                       appointments, not never for Merrick Garland's
                       Supreme Court seat – then filling the Federal
                       judiciary with the least-qualified, most FedSoc-
                       addled lunatics in US history, all for lifetime
                       appointments.


                       As bad as this is at the federal level, it's even
                       worse at in the states, especially the Republican
                       "trifecta" states where the GOP holds the
                       governorship and the state house and senate, where
                       shameless gerrymandering and legislative attacks on
                       hard-won ballot measures are the order of the day.
                       GOP-held state governments engage in rampant
                       interstate aggression, targeting out-of-state
                       abortion providers, publishers, and journalists.


                       This is a one-sided Cold Civil War, because state
                       Dems, for the most part, are unwilling to play
                       hardball in return (the closest they come is when,
                       say, California sets strict emissions controls and
                       manufacturers adopt them nationwide, rather than
                       making special cars for the giant California
                       market). Republicans engage in constitutional
                       hardball and Dems refuse to fight back, a
                       phenomenon called "asymmetrical constitutional
                       hardball": [...]


                # ⚓ Los Angeles Times ☛ Opinion:_Trump_says_criminality_is
                  genetic._Nazis_showed_where_such_talk_can_lead⠀⇛


                       In a recent interview, Donald Trump claimed that
                       13,000 “murderers” have been admitted to the United
                       States through an “open border.” He continued that
                       for murderers, “it’s in their genes. And we’ve got
                       a lot of bad genes in our country right now.”


                       That criminal activity is rooted in an offender’s
                       genetic makeup is an old, largely discredited idea.
                       For Trump to spout questionable science is hardly
                       new. But the disturbing implications in what he
                       said raise the specter of far worse crimes than
                       anything one murderer could do.


                # ⚓ EFF ☛ EFF_to_Third_Circuit:_TikTok_Has_Section_230_Immunity
                  for_Video_Recommendations⠀⇛


                       EFF filed an amicus brief in the U.S. Court of
                       Appeals for the Third Circuit in support of
                       TikTok’s request that the full court reconsider the
                       case Anderson v. TikTok after a three-judge panel
                       ruled that Section 230 immunity doesn’t apply to
                       TikTok’s recommendations of users’ videos. We
                       argued that the panel was incorrect on the law, and
                       this case has wide-ranging implications for the
                       internet as we know it today. EFF was joined on the
                       brief with Center for Democracy & Technology (CDT),
                       Foundation for Individual Rights and Expression
                       (FIRE), Public Knowledge, Reason Foundation, and
                       Wikimedia Foundation.


                       At issue is the panel’s misapplication of First
                       Amendment precedent. The First Amendment protects
                       the editorial decisions of publishers about whether
                       and how to display content, such as the videos
                       TikTok displays to users through its recommendation
                       algorithm.


                # ⚓ CBC ☛ Fast-food_chains_serving_up_halal_food_with_a_side_of
                  misinformation,_expired_certificates⠀⇛


                       An entire restaurant can only be certified if every
                       ingredient used at the location is checked by the
                       certifier and follows the criteria needed to be
                       halal, according to Subedar and other halal
                       certification bodies. Also, there must be no pork
                       products or alcohol served on the premises.


                # ⚓ The Register UK ☛ ESPN_hit_with_proposed_fine_for_misusing
                  emergency_alert⠀⇛


                       The Federal Communications Commission published an
                       order today finding ESPN liable for six instances
                       of broadcasting EAS sounds not to notify the public
                       of an actual emergency, but to advertise its
                       upcoming coverage of the NBA basketball season.


                       "Transmitting EAS Tones in the absence of an actual
                       emergency is not a game," FCC Enforcement Bureau
                       Chief Loyaan A. Egal said in a press release.


                # ⚓ Jacobin Magazine ☛ The_Capitalist_Threat_to_Democracy⠀⇛


                       The threat to a true democracy that promotes
                       material well-being, equality, and social
                       solidarity is deeper than Donald Trump. It comes
                       from a capitalism that can never make its peace
                       with democracy.


          o § Transparency/Investigative Reporting⠀➾


                # ⚓ Wired ☛ You_Can_Now_See_the_Code_That_Helped_End
                  Apartheid⠀⇛


                       Using a Toshiba T1000 PC running an early version
                       of MS-DOS, Jenkin wrote a system using the most
                       secure form of crypto, a one-time pad, which
                       scrambles messages character by character using a
                       shared key that’s as long as the message itself.
                       Using the program, an activist could type a message
                       on a computer and encrypt it with a floppy disk
                       containing the one-time pad of random numbers. The
                       activist could then convert the encrypted text into
                       audio signals and play them to a tape recorder,
                       which would store them. Then, using a public phone,
                       the activist could call, say, ANC leaders in London
                       or Lusaka, Zambia, and play the tape. The recipient
                       would use a modem with an acoustic coupler to
                       capture the sounds, translate them back into
                       digital signals, and decrypt the message with
                       Jenkin’s program.


                # ⚓ The Independent UK ☛ Trump_is_selling_$100K_‘Swiss-made’
                  watches._A_search_for_who_makes_them_took_a_bizarre_turn⠀⇛


                       Now, the watchmaker's origins are in question after
                       CNN tried to track down the company behind the
                       devices. They aren't based in Switzerland, but
                       their address returns to a strip mall. In Wyoming.
                       Next to an HR&Block and a Wendy's.


                # ⚓ CNN ☛ The_curious_hunt_for_the_company_behind_Trump
                  watches⠀⇛


                       But a CNN investigation into the manufacturing and
                       distribution of the Trump-branded timepieces dead-
                       ended at an innocuous-looking shopping center in a
                       small city in remote northern Wyoming, not far from
                       the border of Montana.


          o § Environment⠀➾


                # ⚓ Jeremy Cherfas ☛ Insects_will_not_make_pet_food_more
                  sustainable_either⠀⇛


                       Hobbs is Aaron Hobbs, executive director of the
                       North American Coalition for Insect Agriculture
                       (NACIA), so Mandy Rice-Davies applies. The key
                       point, which neither he nor Marion Nestle seem to
                       have appreciated, but which you will because you
                       listened to the recent episode on insects as food
                       (for people and their pets), is that the “waste”
                       that insects are reducing is usually a feed product
                       that could be fed direct to livestock and, in some
                       cases, people and their pets.


                # ⚓ Omicron Limited ☛ Pioneering_river_restoration_declared_a
                  success⠀⇛


                       "We had just the worst winter you can imagine post
                       restoration in terms of the number of storms and
                       sheer volume of rain. But despite it being record
                       breaking conditions with high flowing water levels,
                       the site responded really well, increasing the
                       ability to store water within the site and
                       lessening downstream storm flows, demonstrating the
                       value of the restoration in providing resilience to
                       hydrological extremes."


                       To help the National Trust understand how the site
                       has developed, researchers from several
                       Universities (Exeter, Loughborough, Nottingham and
                       Umeå in Sweden) have been involved with monitoring
                       water flow, water quality and changes to habitat.


                # ⚓ Omicron Limited ☛ Five_surprising_ways_that_trees_help
                  prevent_flooding⠀⇛


                       Think of flood prevention and you might imagine
                       huge concrete dams, levees or the shiny Thames
                       barrier. But some of the most powerful tools for
                       reducing flood risk are far more natural and widely
                       recognizable: woodlands and green spaces. Trees
                       offer much more than beauty and oxygen. Here's how
                       trees help to protect us from floods.


                # ⚓ EcoWatch ☛ Only_37%_of_Europe’s_Surface_Water_Is_Healthy,
                  Study_Finds⠀⇛


                       According to the report, only about 37% of the
                       surface water analyzed in 2021 was identified as
                       having “good” quality or better, and only 29% had
                       at least a good chemical status.


                       A major contributing factor to poor chemical status
                       was long-lived pollutants, like mercury or
                       “brominated flame retardants.” If these were not a
                       factor, the study says, 80% of the surface water
                       would be in good health or better.


                # ⚓ The Revelator ☛ 12_New_Environmental_Books_You_Need_to_Read
                  This_Autumn⠀⇛


                # § Energy/Transportation⠀➾


                      # ⚓ DeSmog ☛ Why_Alberta_Should_Scrap_Its_Misleading_$7
                        Million_Ad_Blitz⠀⇛


                      # ⚓ Pratik ☛ Back_to_Commuting_and_Parking_for_Work⠀⇛


                             Yay! It’s Friday, and I’m working from home
                             today. Despite the President’s diktat, I got
                             an exemption to work remotely twice a week. I
                             will be on campus Tuesday through Thursday,
                             which isn’t too bad. I’m still figuring out
                             the fastest way to work since I park at a
                             different UT garage.


                             The fastest way depends on the time of day
                             rather than the distance. Parking is a pain
                             at UT Austin. Since COVID, UT Austin has had
                             an Occassional Parking Perks (OPP) program
                             which is basically pay as you park. You load
                             up your account ($5/day) and use it as
                             frequently as you want with no expiry dates.
                             I’ve used this option for the past four years
                             since the OPP is more economical if you are
                             on campus only twice a week.


                      # ⚓ Deutsche Welle ☛ France:_Man_charged_with_murder
                        after_running_over_cyclist⠀⇛


                             "We can no longer tolerate this
                             trivialization of violence on the roads. Like
                             all other road users, cyclists and
                             pedestrians who choose sustainable and
                             environmentally friendly modes of transport
                             have a fundamental right to safety," the
                             group said on Friday.


                      # ⚓ Tom's Hardware ☛ AI_engineers_claim_new_algorithm
                        reduces_AI_power_consumption_by_95%_—_replaces_complex
                        floating-point_multiplication_with_integer_addition⠀⇛


                             The new method, called Linear-Complexity
                             Multiplication (L-Mul), comes close to the
                             results of FPM while using the simpler
                             algorithm. But despite that, it’s still able
                             to maintain the high accuracy and precision
                             that FPM is known for. As TechXplore reports,
                             this method reduces the power consumption of
                             AI systems, potentially up to 95%, making it
                             a crucial development for our AI future.


                      # ⚓ Tom's Hardware ☛ Man_who_lost_half-billion_dollar
                        Bitcoin_HDD_sues_local_authority_for_$500_million_for
                        not_letting_him_dig_through_landfill⠀⇛


                             Howells claims the legal action to be a last-
                             resort initiative after becoming frustrated
                             with years of rebuttals from Newport Council.
                             The 8,000 Bitcoins would be worth £414
                             million ($538 million) today. However,
                             Howells is asking for £495 million ($644
                             million), which reflects the peak valuation
                             of the BTC cryptocurrency from earlier this
                             year.


                # § Overpopulation⠀➾


                      # ⚓ The Moscow Times ☛ Russia_Takes_Aim_at_'Childfree'
                        Ideology_in_Controversial_Bid_to_Boost_Birth_Rates⠀⇛


                             But experts argue that this legislation,
                             which is currently under review by lawmakers
                             and passed its first reading on Thursday, is
                             “repressive” and fails to address the root
                             issues behind the country’s flagging birth
                             rates.


          o § Finance⠀➾


                # ⚓ FAIR ☛ ‘Housing_Discrimination_Is_Collective,_Cumulative,
                  Continuing’:_CounterSpin_interview_with_George_Lipsitz_on_the
                  impacts_of_housing_discrimination⠀⇛


                       Janine Jackson interviewed author and UC/Santa
                       Barbara research professor emeritus George Lipsitz
                       about the impacts of housing discrimination for the
                       October 11, 2024, episode of CounterSpin. This is a
                       lightly edited transcript.


                # ⚓ Josh Withers ☛ The_enshittification_of_Squarespace_and_why
                  you_should_own_your_own_website_|_Withers_Without_You⠀⇛


                       Private equity seriously is ruining so many
                       beautiful things on the internet (see Bending
                       Spoons) because founders and creators often
                       struggle make a living online, they seek growth and
                       revenue and find it hard, so they sell to PE
                       because PE can make money online: gut the product,
                       layoff staff, raise prices.


                # ⚓ Positech Games ☛ An_autistic_introduction_to_the_stock
                  market⠀⇛


                       As part of my job, because we supported real-time
                       and historical trading software, my work PC had the
                       complete suite of trading analysis software that
                       the company provided. We were expected to be
                       vaguely familiar with what it looked like, so we
                       could check it worked ok. We were not expected to
                       know anything about actual markets and trading, but
                       just by being in that world 8 hours a day you cant
                       avoid picking up a lot of tips and information.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ CS Monitor ☛ Elon_Musk_is_spending_big_to_boost_Trump’s
                  turnout._Republicans_worry_it_might_flop.⠀⇛


                       Elon Musk is pumping huge sums into a last-minute
                       effort to boost Trump turnout. But get-out-the-vote
                       efforts aren’t the rocket science he’s used to.


                # ⚓ Insight Hungary ☛ EPP_to_Orban:_"Time_to_go"⠀⇛


                       The European People's Party (EPP) shared a post on
                       Facebook featuring an image of Hungary's far-right
                       Prime Minister Viktor Orbán emerging from a red
                       backdrop, alongside the following caption: "Time to
                       go." 


                       The message left little room for interpretation:
                       "It’s time to bring Hungary back closer to Europe
                       and allow it a chance to recover from the
                       consequences of poor leadership." The EPP had first
                       shared this image on X last Wednesday, coinciding
                       with Orbán’s rare appearance before the European
                       Parliament's plenary session.


                # ⚓ Pro Publica ☛ Opponents_of_MO_Abortion_Rights_Amendment
                  Turn_to_Anti-Trans_Messaging⠀⇛


                       The billboards have popped up along both
                       Interstates 55 and 170 around St. Louis. They’re
                       along I-70 between Columbia and St. Charles, in
                       central Missouri. And there’s one across from a
                       shopping center in Cape Girardeau, along the
                       Mississippi River in the state’s southeast corner.


                       In fact, as the Nov. 5 election approaches,
                       motorists can see the billboards all over Missouri.


                # ⚓ Silicon Angle ☛ OpenAI,_Microsoft_reportedly_hire_banks_to
                  renegotiate_partnership_terms⠀⇛


                       The Wall Street Journal today cited sources as
                       saying that OpenAI is being advised by Goldman
                       Sachs. Microsoft, in turn, has reportedly hired
                       Morgan Stanley. The two banks previously
                       participated in a deal that gave the ChatGPT
                       developer access to a $4 billion revolving line of
                       credit.


                # ⚓ India Times ☛ Microsoft_and_OpenAI's_close_partnership
                  shows_signs_of_fraying⠀⇛


                       Microsoft had already pumped $13 billion into
                       OpenAI, and Nadella was initially willing to keep
                       the cash spigot flowing. But after OpenAI's board
                       of directors briefly ousted Altman last November,
                       Nadella and Microsoft reconsidered, according to
                       four people familiar with the talks who spoke on
                       the condition of anonymity.


                       Over the next few months, Microsoft wouldn't budge
                       as OpenAI, which expects to lose $5 billion this
                       year, continued to ask for more money and more
                       computing power to build and run its artificial
                       intelligence systems.


                # ⚓ NBC ☛ Harris_courts_male_voters_on_fantasy_sports,_sports
                  betting_and_video_game_platforms⠀⇛


                       As part of the campaign's plan to attract male
                       voters, the vice president's campaign launched a
                       series of ads Friday on sports news sites like
                       DraftKings and Yahoo Sports as well as video game
                       sites like IGN and Fandom. Harris' is the first
                       campaign to advertise on DraftKings.


                # ⚓ Tech Central (South Africa) ☛ Bitcoin_traders_are_betting
                  on_a_Trump_victory⠀⇛


                       While prediction markets have moved in Trump’s
                       favour, the spread in most polls is well within the
                       margin of error with less than three weeks to
                       election day. Harris leads Trump by about 1.6
                       percentage points in the Real Clear Politics
                       average of national polls. Trump is ahead by less
                       than one percentage point in the equivalent measure
                       for battleground states.


                # § Misinformation/Disinformation/Propaganda⠀➾


                      # ⚓ Bridge Michigan ☛ DTE_Energy_[astroturfed]_comments
                        to_push_$456_million_rate_hike⠀⇛


                             Comments submitted by businesses to Michigan
                             regulators supporting DTE Energy's $456.4
                             million rate hike request appear to have been
                             written by the utility itself, according to
                             identifying data attached to the documents.


                      # ⚓ The Hill ☛ Election_integrity:_A_bipartisan_defense
                        of_U.S._election_system⠀⇛


                             Still, these false narratives have
                             contributed to sharp divides among Americans
                             when it comes to confidence in our elections.


                      # ⚓ US News And World Report ☛ Callers_Responding_to_a
                        False_Election_Claim_Overwhelm_Oregon_Officials⠀⇛


                             Oregon election officials were screening
                             phone and email messages Friday after their
                             system was overwhelmed and shut down because
                             of a barrage of calls from people responding
                             to a false claim that the state's voter
                             pamphlet doesn't include Republican nominee
                             Donald Trump.


                      # ⚓ 404 Media ☛ This_Is_Exactly_How_an_Elon_Musk-Funded
                        PAC_Is_Microtargeting_Muslims_and_Jews_With_Opposing
                        Messages⠀⇛


                             An Elon Musk-funded group called Future
                             Coalition PAC is targeting Muslim voters in
                             Michigan and Jewish voters in Pennsylvania
                             with diametrically opposed political
                             advertisements about Kamala Harris. In areas
                             of Michigan with relatively large Muslim
                             populations, the Super PAC is painting Harris
                             as a close friend of Israel and is suggesting
                             that she is beholden to the beliefs of her
                             Jewish husband Doug Emhoff; in parts of
                             Pennsylvania with relatively large Jewish
                             populations, the advertisements call Harris
                             antisemitic and say she “support[s] denying
                             Israel the weapons needed to defeat the Hamas
                             terrorists who massacred thousands.”


                             Meanwhile, a related PAC also funded by Musk
                             is microtargeting likely Black voters on
                             Snapchat with ads that says Kamala Harris is
                             trying to ban menthol cigarettes (surveys
                             have shown that 81 percent of Black smokers
                             use menthols, and big tobacco has
                             disproportionately marketed menthol
                             cigarettes to Black Americans).


                      # ⚓ Futurism ☛ AI-Powered_News_Site_Accidentally_Accuses
                        District_Attorney_of_Murder⠀⇛


                             That's bleak stuff, not to mention a crime
                             that probably would have made national news.
                             But there's an important reason why it didn't
                             hit national airwaves: there was a murder,
                             but the DA didn't commit it. They just
                             charged the guy who allegedly did.


                      # ⚓ India Times ☛ TikTok_let_through_disinformation_in
                        political_ads_despite_its_own_ban,_Global_Witness
                        finds⠀⇛


                             But it called out TikTok for approving four
                             of the eight ads submitted for review that
                             contained falsehoods about the election.
                             That's despite the platform's ban on all
                             political ads in place since 2019.


                      # ⚓ Greece ☛ Government_spokesman_warns_of_misinformation
                        dangers⠀⇛


                             Government spokesman Pavlos Marinakis
                             addressed the rapid spread of misinformation
                             during a seminar on fake news.


                      # ⚓ Forbes ☛ These_Right-Wing_Pundits_Were_Allegedly
                        Funded_By_Russia—What_To_Know_About_DOJ_Indictment⠀⇛


                             The Justice Department filed an indictment
                             Wednesday, accusing the Kremlin of pouring
                             millions into a media company linked to
                             prominent online right-wing commentators as
                             part of an influence operation pushing pro-
                             Russia propaganda and disinformation on
                             social media.


                      # ⚓ NPR ☛ AI-generated_images_have_become_a_new_form_of
                        propaganda_this_election_season⠀⇛


                             This election cycle, such AI-generated
                             synthetic images have proliferated on social
                             media platforms, often after politically
                             charged news events. People watching online
                             platforms and the election closely say that
                             these images are a way to spread partisan
                             narratives with facts often being irrelevant.


                      # ⚓ The Register UK ☛ Uncle_Sam_puts_$10M_bounty_on
                        Russian_[astroturfer]_farm_Rybar⠀⇛


                             The US has placed a $10 million bounty on
                             Russian media network Rybar and a number of
                             its key staffers following alleged attempts
                             to sway the upcoming US presidential
                             election.


                      # ⚓ Truthdig ☛ The_Big_Lie:_The_Sequel⠀⇛


                             This new generation of poll watchers also
                             fueled conspiracy theories on social media.
                             One of the most circulated videos claiming to
                             expose fraud, for example, was taken by the
                             volunteer observer Kellye SoRelle, who
                             recorded a man at Detroit’s TCF Center
                             removing a box from a van and placing it in a
                             red wagon. Right-wing outlets quickly picked
                             up the video and alleged that the box
                             contained additional ballots being brought
                             into a tabulation center after the polls had
                             already closed. In reality, the man was a
                             photographer for a local news station and the
                             box contained his camera equipment. Incidents
                             like these were not bugs but features of the
                             Republican Party’s ballot monitoring program,
                             designed to instill doubt in the election
                             results.


                      # ⚓ Truthdig ☛ After_Pushing_False_Election_Claims,
                        Right-Wing_Activists_Recruit_Poll_Workers⠀⇛


                             Right-wing strategists still talk about what
                             happened in Detroit in 2020, when poll
                             watchers stood outside the absentee ballot
                             counting center, banging on windows and
                             shouting “Stop the count!” Conspiracy
                             theories swirled that those volunteers had
                             been kept out while something corrupt was
                             unfolding inside. At one point the facility
                             held almost double the number of permitted
                             poll watchers of both parties.


                             But the theories continue spreading four
                             years later. “They kick people out that are
                             observers, and they put cardboard over the
                             window, and you’re supposed to trust what’s
                             going on behind the cardboard?” Lance
                             Wallnau, a leading Christian right
                             influencer, said at an Arizona tent revival
                             in April.


          o § Censorship/Free Speech⠀➾


                # ⚓ VOA News ☛ Georgian_groups_defy_'foreign_agent'_law,_team
                  up_to_monitor_crucial_election⠀⇛


                       A brutal crackdown on the demonstrations prompted
                       Western powers to impose sanctions on some Georgian
                       officials.


                       Critics say the law mimics Russian legislation used
                       to silence political opponents and independent
                       media. The Georgian government insists the law is
                       necessary to show who is funding political
                       organizations.


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


                # ⚓ Semafor Inc ☛ Two_Years_of_Semafor⠀⇛


                       We’ve broken big news across our platforms,
                       including the moves of companies like Nvidia and
                       OpenAI, the showdowns between Wall Street and
                       Washington, and the battle for the White House.
                       Since launching, we’ve built a powerful, global C-
                       Suite, policy-maker and opinion leader audience —
                       including you — with over 750,000 newsletter
                       subscriptions and more than 2,500 newsletters sent,
                       which have been opened 115 million times. And our
                       business has grown rapidly through global
                       partnerships with over 65 of the world’s most
                       influential companies.


                # ⚓ Truthdig ☛ The_Last_Days_of_Mankind⠀⇛


                       “In the beginning was the press and then the world
                       appeared,” Karl Kraus wrote in 1921. The biblical
                       allusion was no rhetorical flourish. Living through
                       an apocalyptic era, the Austrian writer, and
                       arguably the first major media critic, had reason
                       to believe that journalism had moved from being a
                       neutral filter between the popular imagination and
                       the external world. It had taken charge of forging
                       reality itself.


                # ⚓ VOA News ☛ RSF_director_general_calls_China's_repression_of
                  journalists_'totally_insane'⠀⇛


                       In an interview with Voice of America on October
                       14, Bruttin emphasized that Taiwanese media and
                       foreign media in Taiwan face threats from Chinese
                       political propaganda. He said that Taiwan, like
                       many Baltic countries affected by Russian political
                       propaganda, however, has demonstrated resilience
                       and has rich experience in resisting cyber
                       information attacks, which can be used as a
                       reference for the world.


                # ⚓ BIA Net ☛ Three_issues_of_pro-Kurdish_newspaper_Yeni_Yaşam
                  seized_in_a_week⠀⇛


                       Çelebi warned that these moves are part of a
                       broader strategy by the government to control
                       dissenting voices in the media.


                       “If you want to dominate the social landscape as a
                       ruling power and prevent any alternative voices
                       from emerging, you apply this method of control
                       over the press,” he explained. “The state’s
                       judiciary, police, and military have been working
                       for years to silence alternative voices.”


                       He added that media outlets covering topics such as
                       ecology, women’s rights, labor issues, and
                       democracy, are bearing the brunt of the
                       government’s efforts to monopolize the press.
                       “These actions show that Turkey is not democratic,
                       and the intolerance towards Kurds is clear,” he
                       said.


                # ⚓ BIA Net ☛ Journalists_from_the_earthquake_zone_meet_in
                  Malatya:_'We_received_no_assistance'⠀⇛


                       The workshop, titled “Journalists Exist with Their
                       Rights,” brought together nine journalists from
                       Malatya, Elazığ, Urfa, Antep, Diyarbakır, and
                       Adıyaman. The discussion focused on journalists'
                       rights and freedom of expression, especially in the
                       context of the earthquake. Participants also shared
                       their experiences.


                # ⚓ BIA Net ☛ Just_silence_the_journalist,_and_I_won't_touch
                  you!⠀⇛


                       The BİA Media Monitoring Report covering July,
                       August, and September shows that at least 164
                       journalists were tried in criminal cases, with five
                       facing lawsuits for damages. Additionally, 68
                       journalists were subjected to threats from MHP and
                       its affiliated political groups, and 77
                       journalists, with Hayko Bağdat being the latest
                       addition, were convicted of “insulting the
                       president.” Furthermore, concerns are growing over
                       the increasing restrictions on journalists using
                       YouTube, access bans based on “personal rights,”
                       and the announcements by authorities of new or
                       revised regulations regarding “influence agents.”


                       Due to the sharp decline in media freedom and rule
                       of law, Reporters Without Borders (RSF) ranked
                       Turkey 158th out of 180 countries in the World
                       Press Freedom Index. RSF called on President Recep
                       Tayyip Erdoğan, as he marks his 10th year in
                       office, to “implement comprehensive reforms to
                       protect independent journalists and ultimately
                       guarantee the right to access information in the
                       country.”


                # ⚓ Deutsche Welle ☛ Kurov_documentary_traces_Russian_crackdown
                  on_free_speech⠀⇛


                       Unlike other wartime films showing death and
                       destruction on the frontline, "Of Caravan and the
                       Dogs," co-directed by Askold Kurov and an anonymous
                       filmmaker, was primarily shot in the newsrooms of
                       different Russian media outlets. Yet, despite the
                       unspectacular settings, the heartbreaking
                       documentary allows viewers to directly witness the
                       final nails being put in the coffin of Russia's
                       free press.


                       DW met Kurov as the filmmaker was presenting "Of
                       Caravan and the Dogs" in Berlin during the
                       Dokumentale film festival.


                # ⚓ Deutsche Welle ☛ Russia:_Journalists_report_inhumane
                  conditions_in_custody⠀⇛


                       Two journalists, Konstantin Gabov and Sergey
                       Karelin, who stand accused of supporting an
                       "extremist organization," have detailed the harsh
                       conditions of their pre-trial detention in Moscow.
                       In early October, the two men were transferred to a
                       prison known as "Matrosskaya Tishina" ("Sailors'
                       Silence"), which is notorious among human rights
                       organizations for its bad conditions.


                       DW has obtained a copy of a letter written by
                       Konstantin Gabov: "The cell is overcrowded. Another
                       inmate and I sleep on the floor," he reports.
                       "During the day we sit on a bench without a
                       backrest, as there's no space. The mattress,
                       blanket and pillow are worn out, and there are
                       bedbugs. The atmosphere here is oppressive."


                # ⚓ CPJ ☛ Press_freedom_in_Paraguay_threatened_by_proposed_law
                  to_control_nonprofits⠀⇛


                       On October 9, Paraguay’s Congress approved the
                       Establishing Control, Transparency, and
                       Accountability of Non-Profit Organizations Act and
                       passed it to Peña, who has two weeks to sign it
                       into law or veto it.


                       The legislation, reviewed by CPJ, would require all
                       nongovernmental organizations (NGOs) that receive
                       public or private money to submit financial reports
                       to the Ministry of Economy and Finance every six
                       months. It would also require NGOs to list the
                       people and legal entities that they work with.
                       Organizations that fail to meet the requirements
                       could be shut down.


                # ⚓ CPJ ☛ Iranian-American_journalist_detained_in_Evin_prison
                  without_access_to_lawyer⠀⇛


                       CPJ is alarmed by reports that Iranian authorities
                       arrested Iranian-American journalist Reza Valizadeh
                       in September in the capital, Tehran, and have since
                       detained him in Evin prison without access to a
                       lawyer, according to a former colleague, who spoke
                       to CPJ on the condition of anonymity, citing fear
                       of government reprisal.


                       Some reports indicated Valizadeh was facing charges
                       of collaborating with Persian-language media
                       outlets abroad; CPJ was unable to confirm what
                       charges or potential penalties he faces.


                # ⚓ Press Gazette ☛ Telegraph_bidder_Dovid_Efune’s_New_York_Sun
                  is_obscure_even_in_home_city⠀⇛


                       Under Efune The New York Sun has grown rapidly -
                       although its reach still appears limited


          o § Civil Rights/Policing⠀➾


                # ⚓ FAIR ☛ To_Be_a_Media_Expert_on_Economics,_It_Helps_to_Have
                  the_Right_Politics⠀⇛


                       “Practical men who believe themselves to be quite
                       exempt from any intellectual influence, are usually
                       the slaves of some defunct economist.” John Maynard
                       Keynes made this observation in 1936, in his
                       masterwork The General Theory. Nearly a century
                       later, readers and viewers of corporate media face
                       the same fate.


                # ⚓ Hamilton Nolan ☛ Correct_and_Incorrect_Conclusions_About
                  Democrats_and_Unions⠀⇛


                       I have long made the case that the fate of the
                       political left is tied to the fate of organized
                       labor. A Bernie Sanders-esque candidate will always
                       hit his head on an electoral ceiling as long as
                       unions are marginalize in America, because union
                       membership is a sort of demonstration of genuine
                       democratic socialism in action that changes the
                       electorate itself over time. The fact that the
                       Democratic Party seems to be leaking union voters
                       to the right is a real issue. But it is not the
                       underlying issue. The underlying issue is that
                       America needs more union members. And four years of
                       a Biden administration has not been enough to
                       produce that result.


                       In the 1950s, one in three American workers was a
                       union member, and today, one in ten American
                       workers is a union member. More than 60 years of
                       declining union density. This is the core problem
                       that we need to solve. One element of solving
                       that—and not the most important element!—will be
                       Democratic electoral political wins, because the
                       Republican Party is existentially opposed to
                       increasing labor power. Democratic control of
                       Washington is important to reviving the power of
                       organized labor in the same way that having a nice,
                       well-maintained playing field is important to
                       winning the World Series. Yes, you need it, but
                       there are a lot of other and frankly more vital
                       steps, as well. I apologize for all the sports
                       metaphors. But these things often get twisted in
                       the public conversation.


                # ⚓ Harvard University ☛ Are_rich_different_from_you_and_me?
                  Would_we_be_better_off_without_them?⠀⇛


                       But the company “exploits its employees, crushes
                       unions, and takes out dead peasant insurance
                       policies on workers who are going to die,” Malleson
                       countered. “Its products are cheap because they’re
                       made in sweatshops with abysmal conditions.”


                       The solution is not so easy as taxing Walmart for
                       redistribution to low-income employees and
                       consumers, Rajagopalan said. “Then we’re assuming
                       there’s a bureaucrat or central allocation plan
                       that can provide those same loaves of bread and
                       cans of milk. … That has been done before and
                       hasn’t worked pretty much anywhere in the world.”


                # ⚓ The Nation ☛ Donald_Trump_Just_Insulted_Every_Autoworker_in
                  Michigan⠀⇛


                       That line may not have gotten a lot of notice from
                       media outlets that provide cursory coverage of
                       industrial and labor issues. But it was definitely
                       heard by autoworkers like Dawnya Ferdinandsen in
                       Toledo, Ohio. Ferdinandsen is a member of United
                       Auto Workers Local 14, which represents workers at
                       the 2.8 million-square-foot General Motors Toledo
                       Propulsion Systems plant. Workers there assemble
                       transmissions that are used in Chevrolet, Cadillac,
                       GMC, and Buick cars and trucks.


                       In a video posted on social media platforms,
                       Ferdinandsen responded to Trump’s comments by
                       announcing, “I challenge you, Trump, to one full
                       12-hour day in any auto assembly plant. I want to
                       see you assemble parts out of a box for 12 hours.
                       Until you accept and complete this challenge, until
                       you actually work a manual labor job, you keep the
                       name of the UAW out of your mouth. Solidarity,
                       y’all.”


                # ⚓ Omicron Limited ☛ AI_finds_racial_restrictions_in_millions
                  of_property_records⠀⇛


                       In 2021, California enacted a law that required the
                       state's 58 counties to create programs to identify
                       and redact deed records that include racial
                       covenants.


                       But the new law also poses a daunting task: Santa
                       Clara County alone has 24 million deed documents,
                       totaling 84 million pages, dating back to 1850.
                       "Prior to this collaboration, our team manually
                       read close to 100,000 pages over weeks to identify
                       racial covenants," Assistant County Clerk-Recorder
                       Louis Chiaramonte said, "and it was a challenging
                       undertaking."


                # ⚓ International Business Times ☛ Canadian_Uber_Drivers_At
                  Risk_Of_Earning_Less_Due_To_New_AI-based_Pay_Model_Protested
                  By_US_Drivers⠀⇛


                       Unlike the previous system, which based driver pay
                       on ride duration, distance, and demand-based surge
                       pricing, the AI-powered model considers additional
                       factors such as pickup and drop-off locations, as
                       well as the day of the week. While it maintains
                       surge pricing, the use of AI to determine
                       compensation prompts questions about whether
                       driving for Uber will remain financially worthwhile
                       in 2024.


                # ⚓ Jacobin Magazine ☛ You_Know_About_the_KKK,_but_What_About
                  the_Black_Legion?⠀⇛


                       The Black Legion was a white supremacist fascist
                       group headquartered in Lima, Ohio. It grew to
                       hundreds of thousands of members in the 1930s and
                       engaged in violent acts of racist terrorism. Its
                       worst deeds are lost to memory, but they shouldn’t
                       be.


                # ⚓ Truthdig ☛ The_Tipped_Wage_System_Is_Failing_—_and_Removing
                  Taxes_Won’t_Save_It_-_Truthdig⠀⇛


                       Like us, the vast majority of tipped workers in
                       America — 66 percent — don’t earn enough to have to
                       pay federal payroll taxes. So eliminating those
                       taxes won’t benefit two-thirds of us at all.


                       It would only help the upper earners, like fancy
                       waiters at the fancy restaurants — or millionaire
                       Wall Street types, lawyers or hedge fund managers
                       who could reclassify their incomes as tips to dodge
                       taxes.


                # ⚓ India Times ☛ Not_only_heterosexuals,_child_marriage
                  oppressive_to_all_genders,_sexual_minorities:_CJI⠀⇛


                       The CJI said child marriage led to irreversible
                       physical and psychological damage in girls and
                       violated their Article 21 right that encompassed
                       their choice in matters of selection of partner,
                       time of marriage, reproductive freedom and
                       sexuality.


                # ⚓ Techdirt ☛ New_FTC_Rules_Make_It_Easier_To_Cancel_Services,
                  Punish_Companies_For_Being_Annoying_Little_Shits_About_It⠀⇛


                       Whether it’s taking on automaker privacy abuses,
                       supporting right to repair reforms, or taking aim
                       at Amazon’s attempt to dominate the entirety of
                       online retail, she’s notably different from the
                       feckless revolving door careerists that usually
                       stock regulatory agencies, which is why the Barry
                       Dillers, Reid Hoffmans, and Mark Cubans of the
                       world are so hot and bothered.


                       Enter the FTC’s latest effort: cracking down on the
                       predatory and annoying ways companies try to
                       prevent you from cancelling services. Cemented by
                       AOL in its heyday, and perfected by everybody from
                       the Wall Street Journal to your broadband and
                       wireless phone provider, corporate America loves to
                       make it as annoying as possible to simply cancel
                       services, often actively hiding any way to do so.


          o § Internet Policy/Net Neutrality⠀➾


                # ⚓ IETF ☛ draft-miller-ssh-agent-15_-_SSH_Agent_Protocol⠀⇛


                       Secure Shell (SSH) is a protocol for secure remote
                       connections and login over untrusted networks. It
                       supports multiple authentication mechanisms,
                       including public key authentication. This document
                       describes the protocol for interacting with an
                       agent that holds private keys. Clients (and
                       possibly servers) can use invoke the agent via this
                       protocol to perform operations using public and
                       private keys held in the agent.


                       Holding keys in an agent offers usability and
                       security advantages to loading and unwrapping them
                       at each use. Moreover, the agent implements a
                       simple protocol and presents a smaller attack
                       surface than a key loaded into a full SSH server or
                       client.


                       This agent protocol is already widely used and a
                       de-facto standard, having been implemented by a
                       number of popular SSH clients and servers for many
                       years. The purpose of this document is to describe
                       the protocol as it has been implemented.


          o § Digital Restrictions (DRM)⠀➾


                # ⚓ PC World ☛ YouTube_is_testing_a_cheaper_'Premium_Lite'
                  plan..._that_still_has_ads⠀⇛


                       This update Premium Lite plan is being tested in
                       Australia, Germany, and Thailand, according to
                       Android Authority. Google previously offered
                       Premium Lite in a few markets in Europe, which was
                       similar in its limitations on extra mobile features
                       but actually was ad-free. That particular offering
                       was axed a year ago.


                       The newer, ad-infested version of YouTube Premium
                       Lite costs $8.99 Australian dollars, a savings of
                       $8 per month versus the full version of Premium. If
                       you subscribe on iOS, you’ll be charged a more
                       hefty $11.99, presumably to give Apple its cut on
                       the App Store.


                # ⚓ Techdirt ☛ Steam_Finally_Makes_It_Clear:_You’re_Buying_A
                  License,_Not_A_Game⠀⇛


                       We’ve been writing stories about how, when it comes
                       to digital purchases, we typically do not own what
                       we’ve bought. Instead of buying a product, such as
                       the digital version of a video game, what we are
                       instead buying is a non-transferable license to use
                       that product. While readers here will be largely
                       familiar with this annoying concept, most online
                       retailers bury the language for this so deep inside
                       their labyrinthian EULAs that the overwhelming
                       majority of the public is none the wiser. Steam has
                       traditionally been no different, which is how you
                       get confused fans complaining about how a game they
                       bought has been changed via an update, or how your
                       Steam library just disappears when you shove off
                       this mortal coil.


      § Monopolies/Monopsonies⠀➾


          o ⚓ Digital Music News ☛ Stripe_Still_Holding_Nearly_$6.5M_in_Funds
            After_Festicket_Collapse⠀⇛


                 The payment processor holds just shy of £6 million across
                 multiple currencies relating to ticket and event related
                 sales made by Festicket, compared to the £7.6 million it
                 held when administrators were appointed in 2022. They
                 report that processing by Stripe of chargeback requests
                 received from ticket buyers has “largely ceased.”


          o ⚓ EFF ☛ A_Flourishing_Internet_Depends_on_Competition⠀⇛


                 Antitrust law has long recognized that monopolies stifle
                 innovation and gouge consumers on price. When it comes to
                 Big Tech, harm to innovation—in the form of “kill zones,”
                 where major corporations buy up new entrants to a market
                 before they can compete with them—has been easy to find.
                 Consumer harms have been harder to quantify, since a lot
                 of services the Big Tech companies offer are “free.” This
                 is why we must move beyond price as the major
                 determinator of consumer harm. And once that’s done, it’s
                 easier to see even greater benefits competition brings to
                 the greater internet ecosystem.


                 In the decades since the internet entered our lives, it
                 has changed from a wholly new and untested environment to
                 one where a few major players dominate everyone's
                 experience. Policymakers have been slow to adapt and have
                 equated what's good for the whole internet with what is
                 good for those companies. Instead of a balanced
                 ecosystem, we have a monoculture. We need to eliminate
                 the build up of power around the giants and instead have
                 fertile soil for new growth.


          o ⚓ Deutsche Welle ☛ Will_Google_finally_cave_in_under_US_regulatory
            pressure?⠀⇛


                 In August, a US federal court ruled that Google holds a
                 monopoly in internet search and defends it against
                 competitors through unfair means.


                 "This is truly a historic ruling," says Ulrich Müller,
                 who founded the German nonprofit Rebalance Now, a
                 Cologne-based organization that advocates for limiting
                 the power of large corporations.


                 The ruling, he told DW, would show that "the extensive
                 antitrust tools in the US are now being used more
                 forcefully, even against domestic tech companies."


          o § Trademarks⠀➾


                # § Right of Publicity⠀➾


                      # ⚓ Futurism ☛ Human_Models_Horrified_to_Discover_Their
                        Faces_Are_Being_Used_for_AI_Propaganda⠀⇛


                             Synthesia, a text-to-video AI company with a
                             valuation of over one billion dollars, claims
                             that its tech allows users to "create studio-
                             quality videos with AI avatars" as easily as
                             they can throw together a slide deck.


                             The company's clientele is a wild mix,
                             ranging from media stalwarts like Reuters and
                             global accounting giant Ernst & Young to
                             authoritarian regimes — a reality that's come
                             as a terrible surprise to the human models
                             whose faces Synthesia's AI models are trained
                             on.


                      # ⚓ The Guardian UK ☛ ‘It’s_not_me,_it’s_just_my_face’:
                        the_models_who_found_their_likenesses_had_been_used_in
                        AI_propaganda_|_Artificial_intelligence_(AI)_|_The
                        Guardian⠀⇛


                             These videos are fake. They were generated
                             with artificial intelligence (AI) developed
                             by a startup based in east London. The
                             company, Synthesia, has created a buzz in an
                             industry racing to perfect lifelike AI
                             videos. Investors have poured in cash,
                             catapulting it into “unicorn” status – a
                             label for a private company valued at more
                             than $1bn.


                             Synthesia’s technology is aimed at clients
                             looking to create marketing material or
                             internal presentations, and any deepfakes are
                             a breach of its terms of use. But this means
                             little to the models whose likenesses are
                             behind the digital “puppets” that were used
                             in propaganda videos such as those apparently
                             supporting Burkina Faso’s dictator. The
                             Guardian tracked down five of them.


          o § Copyrights⠀➾


                # ⚓ California State University Northridge ☛ The_Importance_of
                  Originality_in_Academic_Writing:_How_Students_Can_Avoid
                  Plagiarism_–_Daily_Sundial⠀⇛


                       Do you ever feel like pulling your hair out when
                       it’s time to write a research paper? Juggling
                       dozens of tabs as you scramble to cram in quotes
                       feels impossible, right? It’s super easy to
                       accidentally lift a sentence or two without giving
                       credit where it’s due. But copying someone else’s
                       stuff is no joke – plagiarism can wreck your grade
                       or even get you in hot water.


                       The last thing you want is to get suspended because
                       of a silly slip-up. Having to document every single
                       fact makes your head spin. Well, fear not because
                       there are ways to write papers that meet your
                       teacher’s expectations. You can also seek help from
                       a reliable ghostwriter and follow proven tips to
                       get away with plagiarism. This article will break
                       down exactly what plagiarism is and how to avoid
                       it. You’ll also get some handy tricks for finding
                       sources, taking notes, citing like a pro, and
                       double-checking your work.


                # ⚓ Nick Heer ☛ X_Has_Altered_the_Deal⠀⇛


                       This is rude. It is a “clarifi[cation]” described
                       in vague terms, and what it means is that users
                       will no longer be able to opt out of their data
                       being used to train Grok or any other artificial
                       intelligence product. This appears to also include
                       images and video, posts in private accounts and, if
                       I am reading this right, direct messages.


                # ⚓ The Verge ☛ Penguin_Random_House_books_now_explicitly_say
                  ‘no’_to_AI_training⠀⇛


                       Book publisher Penguin Random House is putting its
                       stance on AI training in print. The standard
                       copyright page on both new and reprinted books will
                       now say, “No part of this book may be used or
                       reproduced in any manner for the purpose of
                       training artificial intelligence technologies or
                       systems,” according to a report from The Bookseller
                       spotted by Gizmodo.


                       The clause also notes that Penguin Random House
                       “expressly reserves this work from the text and
                       data mining exception” in line with the European
                       Union’s laws. The Bookseller says that Penguin
                       Random House appears to be the first major
                       publisher to account for AI on its copyright page.


                # ⚓ The Register UK ☛ X_to_allow_third_parties_to_train_AIs
                  with_user_data⠀⇛


                       Elon Musk's social media mouthpiece X (formerly
                       known as Twitter) has updated its Terms of Service
                       and Privacy Policy to direct disputes to a federal
                       court in Texas and allow third parties to train AIs
                       on user posts.


                       The updates will allow "third-party collaborators"
                       access to user data, although it appears there will
                       be some form of opt-out added. The specific
                       paragraph reads: [...]





                    ䷩ 𝚕𝚒𝚗𝚎 8864

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

⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ Links 19/10/2024: Riot and Intel Layoffs,
Attacks on Journalists⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧


posted by Roy Schestowitz on Oct 19, 2024


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


🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈


§ Contents⠀➾


    * Leftovers
          o Science
          o Health/Nutrition/Agriculture
          o Proprietary/Artificial_Intelligence_(AI)
          o Defence/Aggression
          o Environment
                # Energy/Transportation
                # Overpopulation
          o Finance
          o AstroTurf/Lobbying/Politics
          o Freedom_of_Information_/_Freedom_of_the_Press
          o Civil_Rights/Policing
          o Monopolies/Monopsonies
                # Trademarks
    * § Leftovers⠀➾


          o § Science⠀➾


                # ⚓ LabX Media Group ☛ 2024-10-15_[Older]_Hidden_Messages_in
                  DNA_Could_Reduce_Biosecurity_Risks⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-12_[Older]_Lithuanians
                  Elect_New_Parliament_Amid_Cost_of_Living,_Security_Worries⠀⇛


          o § Health/Nutrition/Agriculture⠀➾


                # ⚓ BIA Net ☛ 2024-10-16_[Older]_'Turkey_wastes_12_million
                  loaves_of_bread_daily'⠀⇛


                # ⚓ BIA Net ☛ 2024-10-15_[Older]_Economic_challenges_in_Turkey
                  impact_school_hygiene_as_shortages_hit_public_schools⠀⇛


                # ⚓ CBC ☛ 2024-10-17_[Older]_Federal_office_mandate_burdening
                  Ottawa_doctors_as_public_servants_seek_medical_notes⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_HIV_treatment
                  breakthroughs:_Namibia's_success_story⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_Depression_remaps
                  people's_'attention_brain_networks'⠀⇛


          o § Proprietary/Artificial Intelligence (AI)⠀➾


                # ⚓ Business Insider ☛ Meta_layoffs_are_the_latest_sign_that
                  constant_job_cuts_are_the_new_Big_Tech_normal⠀⇛


                       Welfle wrote earlier this month that he was laid
                       off from Microsoft after only nine months. Before
                       that, he'd also spent nine months at Cruise —
                       before being laid off.


                       His dual layoffs might have been worse than what
                       many others experienced, but Welfle is hardly alone
                       in getting hit by what appears to be some
                       employers' penchant for regular layoffs,
                       particularly in Silicon Valley.


                       One of the latest examples comes from Meta, which
                       said Wednesday it was rejigging some of its biggest
                       businesses. The changes mean lost jobs at
                       Instagram, Reality Labs, and WhatsApp.


                # ⚓ Inkl ☛ League_of_Legends_fans_baffled_as_Riot_lays_off_more
                  devs_-_including_the_$500_Ahri_skin_designer_-_only_to_unveil
                  a_gacha-fueled_$250_Arcane_skin_24_hours_later⠀⇛


                       Earlier this week, League of Legends developer Riot
                       Games announced a wave of layoffs, notably
                       impacting skin designers including the person
                       behind the controversial near-$500 Ahri, and it's
                       now confirmed that the studio is introducing a
                       whole new gacha system to sell even more expensive
                       skins.


          o § Defence/Aggression⠀➾


                # ⚓ US News And World Report ☛ 2024-10-16_[Older]_A
                  Photojournalist_Is_Fatally_Stabbed_on_a_California_Trail._His
                  Teen_Son_Is_Charged_in_His_Death⠀⇛


                # ⚓ BIA Net ☛ 2024-10-11_[Older]_Seventy-two_hate_attacks
                  killed_5_people_in_Turkey_in_eight_months⠀⇛


                # ⚓ BIA Net ☛ 2024-10-10_[Older]_Synagogues_vandalized_in
                  İzmir:_‘Turkey’s_Jews_are_living_on_the_edge_since_the_war
                  began'⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-15_[Older]_Immigration:_What_is_in
                  Germany's_new_'security_package'?⠀⇛


                # ⚓ CBC ☛ 2024-10-17_[Older]_Sudanese_Montrealers_grow_anxious
                  as_Quebec_offers_no_solution_to_help_loved_ones_flee_war⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-12_[Older]_Hindus_in
                  Bangladesh_Celebrate_Their_Largest_Festival_Under_Tight
                  Security_Following_Attacks⠀⇛


                # ⚓ Defence Web ☛ 2024-10-15_[Older]_Uganda_and_the_DRC
                  conflict:_the_interests_driving_Kampala’s_involvement⠀⇛


                # ⚓ Defence Web ☛ 2024-10-16_[Older]_African_Standby_Force
                  needs_to_be_reconfigured,_defence_ministers_hear⠀⇛


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


                      # ⚓ Modern Diplomacy ☛ 2024-10-17_[Older]_Why_Are_African
                        States_Joining_BRICS?⠀⇛


          o § Environment⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_Sierra_Leone:_Eco-
                  friendly_mayor_wins_German_Africa_Prize⠀⇛


                # § Energy/Transportation⠀➾


                      # ⚓ CBC ☛ 2024-10-16_[Older]_These_busted_solar_panels
                        are_an_early_example_of_a_looming_problem⠀⇛


                      # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_Europe-wide_train
                        links_marred_by_steep_costs,_construction⠀⇛


                # § Overpopulation⠀➾


                      # ⚓ US News And World Report ☛ 2024-10-15_[Older]
                        Millions_in_Southern_Africa_Facing_Worst_Food_Crisis_in
                        Decades,_Warns_WFP⠀⇛


                      # ⚓ US News And World Report ☛ 2024-10-15_[Older]
                        Southern_Africa_Is_Enduring_Its_Worst_Hunger_Crisis_in
                        Decades_Due_to_El_Niño,_the_UN_Says⠀⇛


          o § Finance⠀➾


                # ⚓ BIA Net ☛ 2024-10-11_[Older]_Turkey_poised_to_collect
                  defense_budget_contributions_from_tax_declarations,_credit
                  cards⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_European_Central_Bank
                  cuts_key_interest_rate_to_3.25%⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-16_[Older]_German_exports_to_US
                  reach_new_high_as_election_looms⠀⇛


                # ⚓ Tech_Layoffs_Intensify:_Intel_Announces_To_Cuts_Over_2,000
                  Jobs_In_US_Amid_Financial_Stress;_Reports⠀⇛


                       California-based chipmaking giant Intel is set to
                       lay off more than 2,000 employees across the United
                       States as part of a major cost-cutting initiative,
                       according to recent reports. These layoffs are part
                       of a broader plan announced by Intel's CEO, Pat
                       Gelsinger, who is leading the company through one
                       of its most significant financial crises in recent
                       history. The layoffs, aimed at slashing operational
                       costs by over $10 billion, have already begun
                       impacting various states across the country.


          o § AstroTurf/Lobbying/Politics⠀➾


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_EU_summit_focuses_on
                  migration_amid_rise_of_far-right⠀⇛


                # ⚓ CBC ☛ 2024-10-14_[Older]_Public_safety_committee_calls_for
                  emergency_meeting_on_RCMP_allegations_against_India⠀⇛


                # ⚓ The Local SE ☛ 2024-10-11_[Older]_Sweden_to_further
                  strengthen_security_checks_for_citizenship_applications⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-11_[Older]_Audit_of
                  Arkansas_Governor's_Security,_Travel_Records_From_State
                  Police_Says_No_Laws_Broken⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_Can_India_fend_off_US,
                  UK_pressure_over_Canada_row?⠀⇛


                # ⚓ US News And World Report ☛ 2024-10-17_[Older]_India_Says
                  Canada_Did_Not_Act_Against_Gang_It_Links_to_New_Delhi⠀⇛


                # ⚓ CBC ☛ 2024-10-16_[Older]_RCMP_investigating_'disturbing'
                  vandalism_of_B.C._NDP_candidate's_sign_using_'noose'⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_Bangladesh_court_orders
                  arrest_of_ex-leader_Sheikh_Hasina⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_Biden_in_Germany:_Is_he
                  the_last_transatlantic_US_president?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_Columbus_stays_Italian
                  until_Spanish_scientists_publish_data⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_How_close_are_the_US
                  and_Germany?⠀⇛


                # ⚓ Deutsche Welle ☛ 2024-10-17_[Older]_UK:_More_and_more
                  Pakistanis_reject_cousin_marriage⠀⇛


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


                # ⚓ CPJ ☛ 2024-10-16_[Older]_Mayor_threatens_local_journalist
                  in_Turkey:_‘We_will_teach_him_his_lesson’⠀⇛


                # ⚓ CPJ ☛ 2024-10-16_[Older]_German_security_guards_abuse,_beat
                  DW_Arabic_reporter_at_concert⠀⇛


          o § Civil Rights/Policing⠀➾


                # ⚓ BIA Net ☛ 2024-10-12_[Older]_Child_labor_remains_a_social
                  blindspot_in_Turkey’s_agriculture_sector⠀⇛


                # ⚓ ANF News ☛ 2024-10-13_[Older]_Prisoners_from_Rojava_subject
                  to_inhuman_treatment_in_Turkey⠀⇛


      § Monopolies/Monopsonies⠀➾


          o ⚓ IP Kat ☛ 2024-10-14_[Older]_[Guest_post]_Flat_rates_supported_by
            clauses_on_universality_of_repertoire_in_contracts_between_CMOs_and
            users_are_anti-competitive,_says_Spanish_Competition_Authority⠀⇛


          o § Trademarks⠀➾


                # ⚓ IP Kat ☛ 2024-10-16_[Older]_[Guest_post]_Asking_ourselves
                  ‘Y’_–_Are_shape_marks_shaping_complex_products’
                  aftermarkets?⠀⇛




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